LMFDB - Embedded newform 69.7.f.a.10.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			10.9
Character	$\chi$	$=$	69.10
Dual form			69.7.f.a.7.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.87564 - 4.47273i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.12344 - 28.6791i) q^{4} +(175.461 + 80.1304i) q^{5} +(-13.1295 - 91.3177i) q^{6} +(148.103 - 504.394i) q^{7} +(-462.896 + 297.485i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})$	\(q+(-3.87564 - 4.47273i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.12344 - 28.6791i) q^{4} +(175.461 + 80.1304i) q^{5} +(-13.1295 - 91.3177i) q^{6} +(148.103 - 504.394i) q^{7} +(-462.896 + 297.485i) q^{8} +(100.946 + 221.041i) q^{9} +(-321.623 - 1095.35i) q^{10} +(1720.84 + 1491.12i) q^{11} +(295.775 - 341.342i) q^{12} +(-1323.31 + 388.558i) q^{13} +(-2830.01 + 1292.42i) q^{14} +(1625.65 + 2529.56i) q^{15} +(1345.37 + 395.036i) q^{16} +(3046.11 - 437.965i) q^{17} +(597.425 - 1308.18i) q^{18} +(3561.54 + 512.072i) q^{19} +(3021.57 - 4701.66i) q^{20} +(6193.11 - 5366.36i) q^{21} -13475.9i q^{22} +(-8620.55 - 8586.15i) q^{23} -8577.48 q^{24} +(14133.5 + 16311.0i) q^{25} +(6866.58 + 4412.88i) q^{26} +(-539.088 + 3749.44i) q^{27} +(-13854.9 - 6327.31i) q^{28} +(-4457.77 - 31004.5i) q^{29} +(5013.61 - 17074.8i) q^{30} +(33572.4 - 21575.7i) q^{31} +(11181.9 + 24484.9i) q^{32} +(10000.1 + 34057.2i) q^{33} +(-13764.6 - 11927.1i) q^{34} +(66403.7 - 76633.9i) q^{35} +(6755.50 - 1983.59i) q^{36} +(-4706.27 + 2149.28i) q^{37} +(-11512.9 - 17914.4i) q^{38} +(-20628.3 - 6057.01i) q^{39} +(-105058. + 15105.0i) q^{40} +(38027.8 - 83269.4i) q^{41} +(-48004.6 - 6902.02i) q^{42} +(-14317.0 + 22277.7i) q^{43} +(49859.8 - 43203.8i) q^{44} +46872.9i q^{45} +(-4993.37 + 71834.3i) q^{46} +99594.3 q^{47} +(14313.7 + 16518.9i) q^{48} +(-133506. - 85798.9i) q^{49} +(18178.0 - 126431. i) q^{50} +(43637.3 + 19928.5i) q^{51} +(5686.93 + 39553.5i) q^{52} +(-80329.6 + 273578. i) q^{53} +(18859.5 - 12120.3i) q^{54} +(182457. + 399526. i) q^{55} +(81493.2 + 277540. i) q^{56} +(42389.8 + 36731.0i) q^{57} +(-121398. + 140101. i) q^{58} +(-272418. + 79989.0i) q^{59} +(79248.9 - 36191.8i) q^{60} +(-41689.2 - 64869.6i) q^{61} +(-226617. - 66540.8i) q^{62} +(126442. - 18179.6i) q^{63} +(103456. - 226537. i) q^{64} +(-263324. - 37860.3i) q^{65} +(113572. - 176721. i) q^{66} +(-262868. + 227776. i) q^{67} -89165.8i q^{68} +(-40686.6 - 185249. i) q^{69} -600120. q^{70} +(119063. + 137407. i) q^{71} +(-112484. - 72288.9i) q^{72} +(44537.4 - 309765. i) q^{73} +(27853.0 + 12720.0i) q^{74} +(47880.1 + 333013. i) q^{75} +(29371.6 - 100030. i) q^{76} +(1.00697e6 - 647143. i) q^{77} +(52856.5 + 115740. i) q^{78} +(28686.8 + 97698.3i) q^{79} +(204405. + 177118. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(-519824. + 152634. i) q^{82} +(-351722. + 160626. i) q^{83} +(-128366. - 199741. i) q^{84} +(569569. + 167241. i) q^{85} +(155130. - 22304.3i) q^{86} +(202840. - 444157. i) q^{87} +(-1.24016e6 - 178308. i) q^{88} +(196418. - 305633. i) q^{89} +(209650. - 181663. i) q^{90} +725014. i q^{91} +(-281790. + 211825. i) q^{92} +622098. q^{93} +(-385992. - 445458. i) q^{94} +(583879. + 375236. i) q^{95} +(-59715.3 + 415329. i) q^{96} +(-1.19971e6 - 547891. i) q^{97} +(133665. + 929661. i) q^{98} +(-155886. + 530899. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.87564	−	4.47273i	−0.484456	−	0.559091i	0.459920	−	0.887960i	$-0.347878\pi$
$2$	−3.87564	−	4.47273i	−0.484456	−	0.559091i	−0.944376	+	0.328869i	$0.893333\pi$
$3$	13.1138	+	8.42776i	0.485698	+	0.312139i
$3$	13.1138	+	8.42776i	0.485698	+	0.312139i
$4$	4.12344	−	28.6791i	0.0644287	−	0.448112i
$5$	175.461	+	80.1304i	1.40369	+	0.641043i	0.966109	−	0.258136i	$-0.0831082\pi$
$5$	175.461	+	80.1304i	1.40369	+	0.641043i	0.437581	+	0.899179i	$0.355835\pi$
$6$	−13.1295	−	91.3177i	−0.0607847	−	0.422767i
$7$	148.103	−	504.394i	0.431788	−	1.47054i	−0.400554	−	0.916273i	$-0.631182\pi$
$7$	148.103	−	504.394i	0.431788	−	1.47054i	0.832342	−	0.554262i	$-0.186999\pi$
$8$	−462.896	+	297.485i	−0.904094	+	0.581026i
$9$	100.946	+	221.041i	0.138472	+	0.303211i
$10$	−321.623	−	1095.35i	−0.321623	−	1.09535i
$11$	1720.84	+	1491.12i	1.29290	+	1.12030i	0.985674	+	0.168663i	$0.0539449\pi$
$11$	1720.84	+	1491.12i	1.29290	+	1.12030i	0.307222	+	0.951638i	$0.400601\pi$
$12$	295.775	−	341.342i	0.171166	−	0.197536i
$13$	−1323.31	+	388.558i	−0.602324	+	0.176858i	−0.568657	−	0.822575i	$-0.692537\pi$
$13$	−1323.31	+	388.558i	−0.602324	+	0.176858i	−0.0336670	+	0.999433i	$0.510719\pi$
$14$	−2830.01	+	1292.42i	−1.03135	+	0.471000i
$15$	1625.65	+	2529.56i	0.481674	+	0.749500i
$16$	1345.37	+	395.036i	0.328459	+	0.0964442i
$17$	3046.11	−	437.965i	0.620011	−	0.0891441i	0.174851	−	0.984595i	$-0.444056\pi$
$17$	3046.11	−	437.965i	0.620011	−	0.0891441i	0.445160	+	0.895451i	$0.353147\pi$
$18$	597.425	−	1308.18i	0.102439	−	0.224310i
$19$	3561.54	+	512.072i	0.519250	+	0.0746569i	0.396957	−	0.917837i	$-0.370066\pi$
$19$	3561.54	+	512.072i	0.519250	+	0.0746569i	0.122293	+	0.992494i	$0.460975\pi$
$20$	3021.57	−	4701.66i	0.377697	−	0.587708i
$21$	6193.11	−	5366.36i	0.668730	−	0.579458i
$22$		−	13475.9i		−	1.26558i
$23$	−8620.55	−	8586.15i	−0.708519	−	0.705692i
$23$	−8620.55	−	8586.15i	−0.708519	−	0.705692i
$24$	−8577.48			−0.620478
$25$	14133.5	+	16311.0i	0.904546	+	1.04390i
$26$	6866.58	+	4412.88i	0.390679	+	0.251074i
$27$	−539.088	+	3749.44i	−0.0273885	+	0.190491i
$28$	−13854.9	−	6327.31i	−0.631144	−	0.288234i
$29$	−4457.77	−	31004.5i	−0.182778	−	1.27125i	−0.850156	−	0.526530i	$-0.823493\pi$
$29$	−4457.77	−	31004.5i	−0.182778	−	1.27125i	0.667378	−	0.744719i	$-0.267416\pi$
$30$	5013.61	−	17074.8i	0.185689	−	0.632399i
$31$	33572.4	−	21575.7i	1.12693	−	0.724235i	0.162014	−	0.986788i	$-0.448201\pi$
$31$	33572.4	−	21575.7i	1.12693	−	0.724235i	0.964917	+	0.262553i	$0.0845646\pi$
$32$	11181.9	+	24484.9i	0.341243	+	0.747219i
$33$	10000.1	+	34057.2i	0.278267	+	0.947691i
$34$	−13764.6	−	11927.1i	−0.350207	−	0.303456i
$35$	66403.7	−	76633.9i	1.54877	−	1.78738i
$36$	6755.50	−	1983.59i	0.144794	−	0.0425153i
$37$	−4706.27	+	2149.28i	−0.0929119	+	0.0424314i	−0.461329	−	0.887229i	$-0.652627\pi$
$37$	−4706.27	+	2149.28i	−0.0929119	+	0.0424314i	0.368417	+	0.929661i	$0.379900\pi$
$38$	−11512.9	−	17914.4i	−0.209814	−	0.326476i
$39$	−20628.3	−	6057.01i	−0.347752	−	0.102109i
$40$	−105058.	+	15105.0i	−1.64153	+	0.236016i
$41$	38027.8	−	83269.4i	0.551760	−	1.20819i	−0.404195	−	0.914673i	$-0.632448\pi$
$41$	38027.8	−	83269.4i	0.551760	−	1.20819i	0.955955	−	0.293513i	$-0.0948244\pi$
$42$	−48004.6	−	6902.02i	−0.647940	−	0.0931597i
$43$	−14317.0	+	22277.7i	−0.180072	+	0.280198i	−0.919542	−	0.392992i	$-0.871440\pi$
$43$	−14317.0	+	22277.7i	−0.180072	+	0.280198i	0.739470	+	0.673190i	$0.235076\pi$
$44$	49859.8	−	43203.8i	0.585319	−	0.507182i
$45$			46872.9i			0.514380i
$46$	−4993.37	+	71834.3i	−0.0513004	+	0.738003i
$47$	99594.3			0.959270			0.479635	−	0.877468i	$-0.340769\pi$
$47$	99594.3			0.959270			0.479635	+	0.877468i	$0.340769\pi$
$48$	14313.7	+	16518.9i	0.129428	+	0.149368i
$49$	−133506.	−	85798.9i	−1.13478	−	0.729278i
$50$	18178.0	−	126431.i	0.145424	−	1.01145i
$51$	43637.3	+	19928.5i	0.328963	+	0.150233i
$52$	5686.93	+	39553.5i	0.0404453	+	0.281303i
$53$	−80329.6	+	273578.i	−0.539570	+	1.83761i	0.00666665	+	0.999978i	$0.497878\pi$
$53$	−80329.6	+	273578.i	−0.539570	+	1.83761i	−0.546237	+	0.837631i	$0.683940\pi$
$54$	18859.5	−	12120.3i	0.119771	−	0.0769718i
$55$	182457.	+	399526.i	1.09666	+	2.40136i
$56$	81493.2	+	277540.i	0.464042	+	1.58038i
$57$	42389.8	+	36731.0i	0.228895	+	0.198339i
$58$	−121398.	+	140101.i	−0.622197	+	0.718053i
$59$	−272418.	+	79989.0i	−1.32641	+	0.389470i	−0.866803	−	0.498650i	$-0.833829\pi$
$59$	−272418.	+	79989.0i	−1.32641	+	0.389470i	−0.459610	+	0.888121i	$0.652011\pi$
$60$	79248.9	−	36191.8i	0.366893	−	0.167554i
$61$	−41689.2	−	64869.6i	−0.183668	−	0.285793i	0.737194	−	0.675681i	$-0.236150\pi$
$61$	−41689.2	−	64869.6i	−0.183668	−	0.285793i	−0.920862	+	0.389888i	$0.872514\pi$
$62$	−226617.	−	66540.8i	−0.950862	−	0.279198i
$63$	126442.	−	18179.6i	0.505672	−	0.0727047i
$64$	103456.	−	226537.i	0.394654	−	0.864171i
$65$	−263324.	−	37860.3i	−0.958849	−	0.137862i
$66$	113572.	−	176721.i	0.395038	−	0.614691i
$67$	−262868.	+	227776.i	−0.874004	+	0.757329i	−0.971283	−	0.237929i	$-0.923532\pi$
$67$	−262868.	+	227776.i	−0.874004	+	0.757329i	0.0972788	+	0.995257i	$0.468986\pi$
$68$		−	89165.8i		−	0.283577i
$69$	−40686.6	−	185249.i	−0.123852	−	0.563910i
$70$	−600120.			−1.74962
$71$	119063.	+	137407.i	0.332662	+	0.383913i	0.897296	−	0.441429i	$-0.145528\pi$
$71$	119063.	+	137407.i	0.332662	+	0.383913i	−0.564634	+	0.825341i	$0.690983\pi$
$72$	−112484.	−	72288.9i	−0.301365	−	0.193675i
$73$	44537.4	−	309765.i	0.114487	−	0.796275i	−0.848976	−	0.528432i	$-0.822780\pi$
$73$	44537.4	−	309765.i	0.114487	−	0.796275i	0.963463	−	0.267843i	$-0.0863108\pi$
$74$	27853.0	+	12720.0i	0.0687347	+	0.0313901i
$75$	47880.1	+	333013.i	0.113494	+	0.789365i
$76$	29371.6	−	100030.i	0.0669092	−	0.227872i
$77$	1.00697e6	−	647143.i	2.20570	−	1.41752i
$78$	52856.5	+	115740.i	0.111382	+	0.243892i
$79$	28686.8	+	97698.3i	0.0581837	+	0.198155i	0.983456	−	0.181149i	$-0.0579816\pi$
$79$	28686.8	+	97698.3i	0.0581837	+	0.198155i	−0.925272	+	0.379304i	$0.876163\pi$
$80$	204405.	+	177118.i	0.399229	+	0.345934i
$81$	−38668.9	+	44626.3i	−0.0727623	+	0.0839722i
$82$	−519824.	+	152634.i	−0.942789	+	0.276828i
$83$	−351722.	+	160626.i	−0.615129	+	0.280920i	−0.698513	−	0.715598i	$-0.746154\pi$
$83$	−351722.	+	160626.i	−0.615129	+	0.280920i	0.0833841	+	0.996517i	$0.473427\pi$
$84$	−128366.	−	199741.i	−0.216576	−	0.336999i
$85$	569569.	+	167241.i	0.927448	+	0.272323i
$86$	155130.	−	22304.3i	0.243893	−	0.0350666i
$87$	202840.	−	444157.i	0.308032	−	0.674495i
$88$	−1.24016e6	−	178308.i	−1.81982	−	0.261651i
$89$	196418.	−	305633.i	0.278620	−	0.433541i	−0.673536	−	0.739155i	$-0.735225\pi$
$89$	196418.	−	305633.i	0.278620	−	0.433541i	0.952156	+	0.305614i	$0.0988616\pi$
$90$	209650.	−	181663.i	0.287585	−	0.249194i
$91$			725014.i			0.962104i
$92$	−281790.	+	211825.i	−0.361878	+	0.272029i
$93$	622098.			0.773411
$94$	−385992.	−	445458.i	−0.464724	−	0.536320i
$95$	583879.	+	375236.i	0.681008	+	0.437657i
$96$	−59715.3	+	415329.i	−0.0674950	+	0.469438i
$97$	−1.19971e6	−	547891.i	−1.31451	−	0.600315i	−0.370068	−	0.929005i	$-0.620666\pi$
$97$	−1.19971e6	−	547891.i	−1.31451	−	0.600315i	−0.944438	+	0.328690i	$0.893393\pi$
$98$	133665.	+	929661.i	0.142017	+	0.987749i
$99$	−155886.	+	530899.i	−0.160658	+	0.547150i
$100$	526063.	−	338080.i	0.526063	−	0.338080i
$101$	71343.6	+	156221.i	0.0692454	+	0.151626i	0.941090	−	0.338157i	$-0.109803\pi$
$101$	71343.6	+	156221.i	0.0692454	+	0.151626i	−0.871844	+	0.489783i	$0.837076\pi$
$102$	−79987.9	−	272414.i	−0.0753744	−	0.256702i
$103$	640799.	+	555256.i	0.586422	+	0.508138i	0.896777	−	0.442483i	$-0.145902\pi$
$103$	640799.	+	555256.i	0.586422	+	0.508138i	−0.310355	+	0.950621i	$0.600448\pi$
$104$	496963.	−	573526.i	0.441798	−	0.509862i
$105$	1.51666e6	−	445331.i	1.31015	−	0.384694i
$106$	1.53497e6	−	700997.i	1.28879	−	0.588570i
$107$	161918.	+	251950.i	0.132174	+	0.205666i	0.901032	−	0.433753i	$-0.142811\pi$
$107$	161918.	+	251950.i	0.132174	+	0.205666i	−0.768858	+	0.639420i	$0.779175\pi$
$108$	105308.	+	30921.2i	0.0835967	+	0.0245462i
$109$	−1.02734e6	+	147709.i	−0.793292	+	0.114058i	−0.527035	−	0.849844i	$-0.676696\pi$
$109$	−1.02734e6	+	147709.i	−0.793292	+	0.114058i	−0.266258	+	0.963902i	$0.585787\pi$
$110$	1.07983e6	−	2.36450e6i	0.811294	−	1.77649i
$111$	−79830.8	−	11477.9i	−0.0583716	−	0.00839257i
$112$	398507.	−	620089.i	0.283649	−	0.441367i
$113$	−644755.	+	558683.i	−0.446848	+	0.387196i	−0.849013	−	0.528371i	$-0.822803\pi$
$113$	−644755.	+	558683.i	−0.446848	+	0.387196i	0.402166	+	0.915567i	$0.368258\pi$
$114$		−	331955.i		−	0.224060i
$115$	−824560.	−	2.19730e6i	−0.542161	−	1.44476i
$116$	−907564.			−0.581438
$117$	−219469.	−	253281.i	−0.137030	−	0.158141i
$118$	1.41356e6	+	908442.i	0.860338	+	0.552906i
$119$	230233.	−	1.60130e6i	0.136624	−	0.950239i
$120$	−1.50501e6	−	687317.i	−0.870958	−	0.397753i
$121$	485747.	+	3.37844e6i	0.274191	+	1.90704i
$122$	−128572.	+	437876.i	−0.0708055	+	0.241141i
$123$	1.20047e6	−	771492.i	0.645111	−	0.414587i
$124$	−480338.	−	1.05179e6i	−0.251931	−	0.551653i
$125$	323755.	+	1.10261e6i	0.165762	+	0.564535i
$126$	−571356.	−	495083.i	−0.285624	−	0.247495i
$127$	−2.29064e6	+	2.64354e6i	−1.11827	+	1.29055i	−0.165714	+	0.986174i	$0.552993\pi$
$127$	−2.29064e6	+	2.64354e6i	−1.11827	+	1.29055i	−0.952552	+	0.304375i	$0.901553\pi$
$128$	238728.	−	70097.0i	0.113835	−	0.0334249i
$129$	−375502.	+	171486.i	−0.174921	+	0.0798840i
$130$	851211.	+	1.32451e6i	0.387443	+	0.602872i
$131$	−1.96300e6	−	576390.i	−0.873187	−	0.256391i	−0.185717	−	0.982603i	$-0.559461\pi$
$131$	−1.96300e6	−	576390.i	−0.873187	−	0.256391i	−0.687470	+	0.726212i	$0.741279\pi$
$132$	1.01797e6	−	146361.i	0.442600	−	0.0636362i
$133$	785761.	−	1.72058e6i	0.333992	−	0.731340i
$134$	2.03757e6	+	292958.i	0.846832	+	0.121756i
$135$	−395033.	+	614683.i	−0.160558	+	0.249833i
$136$	−1.27975e6	+	1.10891e6i	−0.508753	+	0.440837i
$137$			3.02589e6i			1.17677i	0.808582	+	0.588384i	$0.200236\pi$
$137$			3.02589e6i			1.17677i	−0.808582	+	0.588384i	$0.799764\pi$
$138$	−670884.	+	899941.i	−0.255276	+	0.342434i
$139$	4.26159e6			1.58682			0.793409	−	0.608689i	$-0.208304\pi$
$139$	4.26159e6			1.58682			0.793409	+	0.608689i	$0.208304\pi$
$140$	−1.92398e6	−	2.22039e6i	−0.701160	−	0.809182i
$141$	1.30606e6	+	839356.i	0.465915	+	0.299426i
$142$	153135.	−	1.06508e6i	0.0534822	−	0.371977i
$143$	−2.85659e6	−	1.30456e6i	−0.976876	−	0.446125i
$144$	48490.4	+	337258.i	0.0162393	+	0.112947i
$145$	1.70224e6	−	5.79729e6i	0.558362	−	1.90161i
$146$	−1.55810e6	+	1.00133e6i	−0.500655	+	0.321751i
$147$	−1.02768e6	−	2.25031e6i	−0.323524	−	0.708418i
$148$	42233.5	+	143834.i	0.0130278	+	0.0443687i
$149$	2.97275e6	+	2.57590e6i	0.898667	+	0.778700i	0.975878	−	0.218315i	$-0.0700561\pi$
$149$	2.97275e6	+	2.57590e6i	0.898667	+	0.778700i	−0.0772112	+	0.997015i	$0.524602\pi$
$150$	1.30391e6	−	1.50480e6i	0.386345	−	0.445866i
$151$	−5.19405e6	+	1.52511e6i	−1.50860	+	0.442966i	−0.928424	−	0.371522i	$-0.878836\pi$
$151$	−5.19405e6	+	1.52511e6i	−1.50860	+	0.442966i	−0.580180	+	0.814488i	$0.697018\pi$
$152$	−1.80096e6	+	822469.i	−0.512829	+	0.234201i
$153$	404301.	+	629104.i	0.112883	+	0.175650i
$154$	−6.79717e6	−	1.99583e6i	−1.86108	−	0.546464i
$155$	7.61953e6	−	1.09552e6i	2.04613	−	0.294189i
$156$	−258769.	+	566626.i	−0.0681615	+	0.149253i
$157$	1.51067e6	+	217201.i	0.390364	+	0.0561259i	0.334703	−	0.942324i	$-0.391364\pi$
$157$	1.51067e6	+	217201.i	0.390364	+	0.0561259i	0.0556617	+	0.998450i	$0.482273\pi$
$158$	325799.	−	506952.i	0.0825996	−	0.128527i
$159$	−3.35908e6	+	2.91066e6i	−0.835658	+	0.724102i
$160$			5.19215e6i			1.26761i
$161$	−5.60753e6	+	3.07651e6i	−1.34367	+	0.737193i
$162$	349468.			0.0821982
$163$	−663265.	−	765449.i	−0.153153	−	0.176748i	0.673988	−	0.738742i	$-0.264580\pi$
$163$	−663265.	−	765449.i	−0.153153	−	0.176748i	−0.827141	+	0.561994i	$0.810034\pi$
$164$	−2.23129e6	−	1.43396e6i	−0.505853	−	0.325092i
$165$	−974389.	+	6.77702e6i	−0.216910	+	1.50865i
$166$	2.08159e6	+	950630.i	0.455062	+	0.207820i
$167$	−341732.	−	2.37680e6i	−0.0733730	−	0.510320i	−0.993055	−	0.117655i	$-0.962462\pi$
$167$	−341732.	−	2.37680e6i	−0.0733730	−	0.510320i	0.919682	−	0.392665i	$-0.128447\pi$
$168$	−1.27035e6	+	4.32643e6i	−0.267915	+	0.912434i
$169$	−2.46041e6	+	1.58121e6i	−0.509738	+	0.327589i
$170$	−1.45942e6	−	3.19569e6i	−0.297054	−	0.650457i
$171$	246334.	+	838936.i	0.0492647	+	0.167780i
$172$	579870.	+	502460.i	0.113958	+	0.0987452i
$173$	1.12145e6	−	1.29422e6i	0.216591	−	0.249960i	−0.637048	−	0.770824i	$-0.719845\pi$
$173$	1.12145e6	−	1.29422e6i	0.216591	−	0.249960i	0.853640	+	0.520864i	$0.174390\pi$
$174$	−2.77273e6	+	814147.i	−0.526332	+	0.154545i
$175$	1.03204e7	−	4.71315e6i	1.92567	−	0.879422i
$176$	1.72612e6	+	2.68590e6i	0.316617	+	0.492665i
$177$	−4.24657e6	−	1.24691e6i	−0.765805	−	0.224861i
$178$	−2.12826e6	+	305998.i	−0.377368	+	0.0542573i
$179$	−2.08196e6	+	4.55886e6i	−0.363006	+	0.794872i	0.636712	+	0.771102i	$0.280294\pi$
$179$	−2.08196e6	+	4.55886e6i	−0.363006	+	0.794872i	−0.999717	+	0.0237699i	$0.992433\pi$
$180$	1.34427e6	+	193277.i	0.230500	+	0.0331408i
$181$	−2.41198e6	+	3.75311e6i	−0.406759	+	0.632930i	−0.982839	−	0.184464i	$-0.940945\pi$
$181$	−2.41198e6	+	3.75311e6i	−0.406759	+	0.632930i	0.576080	+	0.817393i	$0.304582\pi$
$182$	3.24279e6	−	2.80989e6i	0.537904	−	0.466097i
$183$		−	1.20204e6i		−	0.196139i
$184$	6.54467e6	+	1.41001e6i	1.05059	+	0.226344i
$185$	−997989.			−0.157620
$186$	−2.41103e6	−	2.78248e6i	−0.374683	−	0.432407i
$187$	5.89495e6	+	3.78845e6i	0.901478	+	0.579345i
$188$	410671.	−	2.85628e6i	0.0618045	−	0.429860i
$189$	1.81135e6	+	827217.i	0.268298	+	0.122528i
$190$	−584576.	−	4.06582e6i	−0.0852276	−	0.592771i
$191$	1.73654e6	−	5.91412e6i	0.249221	−	0.848770i	−0.735926	−	0.677062i	$-0.763253\pi$
$191$	1.73654e6	−	5.91412e6i	0.249221	−	0.848770i	0.985148	−	0.171709i	$-0.0549288\pi$
$192$	3.26591e6	−	2.09887e6i	0.461424	−	0.296539i
$193$	3.92678e6	+	8.59844e6i	0.546216	+	1.19605i	0.958527	+	0.285003i	$0.0919945\pi$
$193$	3.92678e6	+	8.59844e6i	0.546216	+	1.19605i	−0.412311	+	0.911043i	$0.635278\pi$
$194$	2.19910e6	+	7.48943e6i	0.301189	+	1.02576i
$195$	−3.13411e6	−	2.71572e6i	−0.422679	−	0.366254i
$196$	−3.01114e6	+	3.47504e6i	−0.399910	+	0.461521i
$197$	5.83423e6	−	1.71308e6i	0.763106	−	0.224068i	0.123054	−	0.992400i	$-0.460731\pi$
$197$	5.83423e6	−	1.71308e6i	0.763106	−	0.224068i	0.640052	+	0.768332i	$0.278913\pi$
$198$	2.97873e6	−	1.36034e6i	0.383738	−	0.175247i
$199$	2.19831e6	+	3.42063e6i	0.278952	+	0.434057i	0.952253	−	0.305311i	$-0.0987605\pi$
$199$	2.19831e6	+	3.42063e6i	0.278952	+	0.434057i	−0.673301	+	0.739369i	$0.735124\pi$
$200$	−1.13946e7	−	3.34577e6i	−1.42433	−	0.418221i
$201$	−5.36685e6	+	771637.i	−0.660894	+	0.0950222i
$202$	422231.	−	924557.i	0.0512267	−	0.112171i
$203$	−1.62987e7	−	2.34340e6i	−1.94834	−	0.280129i
$204$	751468.	−	1.16931e6i	0.0885156	−	0.137733i
$205$	1.33448e7	−	1.15634e7i	1.54900	−	1.34222i
$206$		−	5.01810e6i		−	0.574034i
$207$	1.02768e6	−	2.77223e6i	0.115863	−	0.312549i
$208$	−1.93383e6			−0.214896
$209$	5.36529e6	+	6.19188e6i	0.587698	+	0.678240i
$210$	−7.86988e6	−	5.05766e6i	−0.849787	−	0.546125i
$211$	2.25704e6	−	1.56981e7i	0.240266	−	1.67108i	−0.410542	−	0.911842i	$-0.634660\pi$
$211$	2.25704e6	−	1.56981e7i	0.240266	−	1.67108i	0.650808	−	0.759243i	$-0.274430\pi$
$212$	7.51474e6	+	3.43186e6i	0.788690	+	0.360182i
$213$	403351.	+	2.80537e6i	0.0417392	+	0.290302i
$214$	499367.	−	1.70069e6i	0.0509540	−	0.173533i
$215$	−4.29720e6	+	2.76164e6i	−0.432384	+	0.277877i
$216$	−865861.	−	1.89597e6i	−0.0859186	−	0.188135i
$217$	−5.91045e6	−	2.01291e7i	−0.578417	−	1.96991i
$218$	4.64225e6	+	4.02253e6i	0.448084	+	0.388267i
$219$	3.19468e6	−	3.68685e6i	0.304155	−	0.351013i
$220$	1.22104e7	−	3.58530e6i	1.14673	−	0.336711i
$221$	−3.86076e6	+	1.76315e6i	−0.357681	+	0.163348i
$222$	258058.	+	401546.i	0.0235862	+	0.0367009i
$223$	−8.42299e6	−	2.47321e6i	−0.759542	−	0.223022i	−0.121046	−	0.992647i	$-0.538625\pi$
$223$	−8.42299e6	−	2.47321e6i	−0.759542	−	0.223022i	−0.638496	+	0.769625i	$0.720443\pi$
$224$	1.40061e7	−	2.01377e6i	1.24616	−	0.179170i
$225$	−2.17866e6	+	4.77061e6i	−0.191268	+	0.418819i
$226$	4.99768e6	+	718558.i	0.432956	+	0.0622496i
$227$	−1.12345e7	+	1.74812e7i	−0.960452	+	1.49449i	−0.0937926	+	0.995592i	$0.529899\pi$
$227$	−1.12345e7	+	1.74812e7i	−0.960452	+	1.49449i	−0.866659	+	0.498900i	$0.833737\pi$
$228$	1.22821e6	−	1.06425e6i	0.103625	−	0.0897920i
$229$		−	1.02135e7i		−	0.850489i	−0.905079	−	0.425244i	$-0.860188\pi$
$229$		−	1.02135e7i		−	0.850489i	0.905079	−	0.425244i	$-0.139812\pi$
$230$	−6.63225e6	+	1.22040e7i	−0.545102	+	1.00304i
$231$	1.86593e7			1.51377
$232$	1.12869e7	+	1.30257e7i	0.903877	+	1.04313i
$233$	−5.83808e6	−	3.75191e6i	−0.461533	−	0.296609i	0.289136	−	0.957288i	$-0.406632\pi$
$233$	−5.83808e6	−	3.75191e6i	−0.461533	−	0.296609i	−0.750669	+	0.660679i	$0.770268\pi$
$234$	−282273.	+	1.96325e6i	−0.0220304	+	0.153225i
$235$	1.74749e7	+	7.98053e6i	1.34652	+	0.614934i
$236$	1.17072e6	+	8.14253e6i	0.0890670	+	0.619474i
$237$	−447183.	+	1.52297e6i	−0.0335924	+	0.114405i
$238$	−8.05450e6	+	5.17632e6i	−0.597459	+	0.383963i
$239$	−8.86148e6	−	1.94039e7i	−0.649101	−	1.42133i	−0.892339	−	0.451367i	$-0.850937\pi$
$239$	−8.86148e6	−	1.94039e7i	−0.649101	−	1.42133i	0.243237	−	0.969967i	$-0.421791\pi$
$240$	1.18783e6	+	4.04538e6i	0.0859253	+	0.292635i
$241$	−4.30247e6	−	3.72811e6i	−0.307374	−	0.266341i	0.487490	−	0.873128i	$-0.337912\pi$
$241$	−4.30247e6	−	3.72811e6i	−0.307374	−	0.266341i	−0.794864	+	0.606788i	$0.792458\pi$
$242$	1.32283e7	−	1.52663e7i	0.933378	−	1.07718i
$243$	−883197.	+	259330.i	−0.0615515	+	0.0180732i
$244$	−2.03231e6	+	928124.i	−0.139901	+	0.0638905i
$245$	−1.65500e7	−	2.57522e7i	−1.12538	−	1.75112i
$246$	−8.10325e6	−	2.37933e6i	−0.544320	−	0.159827i
$247$	−4.91197e6	+	706235.i	−0.325961	+	0.0468661i
$248$	−9.12210e6	+	1.99746e7i	−0.598053	+	1.30955i
$249$	−5.96615e6	−	857803.i	−0.386453	−	0.0555635i
$250$	3.67691e6	−	5.72138e6i	0.235322	−	0.366169i
$251$	1.44891e6	−	1.25548e6i	0.0916261	−	0.0793945i	−0.607843	−	0.794057i	$-0.707965\pi$
$251$	1.44891e6	−	1.25548e6i	0.0916261	−	0.0793945i	0.699469	+	0.714662i	$0.253420\pi$
$252$		−	3.70121e6i		−	0.231282i
$253$	−2.03164e6	−	2.76297e7i	−0.125454	−	1.70614i
$254$	2.07015e7			1.26329
$255$	6.05978e6	+	6.99335e6i	0.365457	+	0.421760i
$256$	−1.46473e7	−	9.41323e6i	−0.873045	−	0.561072i
$257$	3.63881e6	−	2.53085e7i	0.214368	−	1.49096i	−0.543971	−	0.839104i	$-0.683080\pi$
$257$	3.63881e6	−	2.53085e7i	0.214368	−	1.49096i	0.758340	−	0.651860i	$-0.226011\pi$
$258$	2.22232e6	+	1.01490e6i	0.129404	+	0.0590969i
$259$	387069.	+	2.69213e6i	0.0222787	+	0.154952i
$260$	−2.17160e6	+	7.39579e6i	−0.123555	+	0.420789i
$261$	6.40326e6	−	4.11512e6i	0.360147	−	0.231452i
$262$	5.02987e6	+	1.10139e7i	0.279674	+	0.612402i
$263$	4.93461e6	+	1.68057e7i	0.271260	+	0.923826i	0.976619	+	0.214976i	$0.0689674\pi$
$263$	4.93461e6	+	1.68057e7i	0.271260	+	0.923826i	−0.705359	+	0.708850i	$0.749214\pi$
$264$	−1.47605e7	−	1.27901e7i	−0.802213	−	0.695121i
$265$	−3.60166e7	+	4.15654e7i	−1.93538	+	2.23354i
$266$	−1.07410e7	+	3.15385e6i	−0.570690	+	0.167570i
$267$	5.15160e6	−	2.35266e6i	0.270650	−	0.123602i
$268$	5.44851e6	+	8.47805e6i	0.283057	+	0.440445i
$269$	3.66753e7	+	1.07689e7i	1.88416	+	0.553239i	0.995511	+	0.0946478i	$0.0301725\pi$
$269$	3.66753e7	+	1.07689e7i	1.88416	+	0.553239i	0.888647	+	0.458591i	$0.151646\pi$
$270$	4.28032e6	−	615417.i	0.217463	−	0.0312664i
$271$	3.62722e6	−	7.94251e6i	0.182249	−	0.399071i	−0.796353	−	0.604833i	$-0.793240\pi$
$271$	3.62722e6	−	7.94251e6i	0.182249	−	0.399071i	0.978602	+	0.205762i	$0.0659673\pi$
$272$	4.27115e6	+	614099.i	0.212246	+	0.0305163i
$273$	−6.11024e6	+	9.50771e6i	−0.300310	+	0.467292i
$274$	1.35340e7	−	1.17273e7i	0.657921	−	0.570092i
$275$			4.91434e7i			2.36302i
$276$	−5.48056e6	+	402991.i	−0.260674	+	0.0191676i
$277$	5.07338e6			0.238703			0.119352	−	0.992852i	$-0.461918\pi$
$277$	5.07338e6			0.238703			0.119352	+	0.992852i	$0.461918\pi$
$278$	−1.65164e7	−	1.90609e7i	−0.768742	−	0.887176i
$279$	8.15810e6	+	5.24289e6i	0.375644	+	0.241412i
$280$	−7.94054e6	+	5.52277e7i	−0.361723	+	2.51584i
$281$	2.97446e7	+	1.35839e7i	1.34057	+	0.612216i	0.951117	−	0.308831i	$-0.0999378\pi$
$281$	2.97446e7	+	1.35839e7i	1.34057	+	0.612216i	0.389450	+	0.921048i	$0.372665\pi$
$282$	−1.30762e6	−	9.09472e6i	−0.0583090	−	0.405548i
$283$	−4.06843e6	+	1.38558e7i	−0.179501	+	0.611326i	0.819753	+	0.572717i	$0.194111\pi$
$283$	−4.06843e6	+	1.38558e7i	−0.179501	+	0.611326i	−0.999254	+	0.0386084i	$0.987708\pi$
$284$	4.43165e6	−	2.84805e6i	0.193469	−	0.124335i
$285$	4.49450e6	+	9.84158e6i	0.194154	+	0.425138i
$286$	5.23617e6	+	1.78328e7i	0.223829	+	0.762291i
$287$	−3.63685e7	−	3.15135e7i	−1.53844	−	1.33306i
$288$	−4.28339e6	+	4.94329e6i	−0.179312	+	0.206937i
$289$	−1.40728e7	+	4.13216e6i	−0.583026	+	0.171192i
$290$	−3.25270e7	+	1.48546e7i	−1.33367	+	0.609069i
$291$	−1.11154e7	−	1.72959e7i	−0.451071	−	0.701881i
$292$	−8.70013e6	−	2.55459e6i	−0.349444	−	0.102606i
$293$	9.30705e6	−	1.33815e6i	0.370006	−	0.0531989i	0.0451962	−	0.998978i	$-0.485609\pi$
$293$	9.30705e6	−	1.33815e6i	0.370006	−	0.0531989i	0.324810	+	0.945779i	$0.394700\pi$
$294$	−6.08209e6	+	1.33179e7i	−0.239338	+	0.524076i
$295$	−5.42082e7	−	7.79397e6i	−2.11154	−	0.303594i
$296$	1.53913e6	−	2.39494e6i	0.0593473	−	0.0923462i
$297$	−6.51855e6	+	5.64836e6i	−0.248818	+	0.215602i
$298$		−	2.32796e7i		−	0.879682i
$299$	1.47438e7	+	8.01252e6i	0.551565	+	0.299748i
$300$	9.74797e6			0.361036
$301$	9.11633e6	+	1.05208e7i	0.334288	+	0.385789i
$302$	2.69517e7	+	1.73208e7i	0.978511	+	0.628851i
$303$	−381001.	+	2.64992e6i	−0.0136961	+	0.0952588i
$304$	4.58929e6	+	2.09586e6i	0.163352	+	0.0746004i
$305$	−2.11680e6	−	1.47227e7i	−0.0746071	−	0.518904i
$306$	1.24689e6	−	4.24651e6i	0.0435174	−	0.148207i
$307$	−3.01011e7	+	1.93448e7i	−1.04032	+	0.668574i	−0.945066	−	0.326879i	$-0.894003\pi$
$307$	−3.01011e7	+	1.93448e7i	−1.04032	+	0.668574i	−0.0952547	+	0.995453i	$0.530367\pi$
$308$	−1.44073e7	−	3.15476e7i	−0.493095	−	1.07973i
$309$	3.72378e6	+	1.26820e7i	0.126214	+	0.429847i
$310$	−3.44305e7	−	2.98342e7i	−1.15574	−	1.00145i
$311$	−2.86126e7	+	3.30208e7i	−0.951211	+	1.09776i	0.0439041	+	0.999036i	$0.486020\pi$
$311$	−2.86126e7	+	3.30208e7i	−0.951211	+	1.09776i	−0.995115	+	0.0987204i	$0.968525\pi$
$312$	1.13506e7	−	3.33285e6i	0.373728	−	0.109737i
$313$	−9.72172e6	+	4.43976e6i	−0.317037	+	0.144786i	−0.567577	−	0.823320i	$-0.692119\pi$
$313$	−9.72172e6	+	4.43976e6i	−0.317037	+	0.144786i	0.250540	+	0.968106i	$0.419392\pi$
$314$	−4.88333e6	−	7.59861e6i	−0.157735	−	0.245440i
$315$	2.36424e7	+	6.94203e6i	0.756414	+	0.222103i
$316$	2.92019e6	−	419860.i	0.0925444	−	0.0133059i
$317$	1.18487e7	−	2.59449e7i	0.371956	−	0.814470i	−0.627404	−	0.778694i	$-0.715883\pi$
$317$	1.18487e7	−	2.59449e7i	0.371956	−	0.814470i	0.999360	−	0.0357758i	$-0.0113902\pi$
$318$	2.60372e7	+	3.74358e6i	0.809678	+	0.116414i
$319$	3.85603e7	−	6.00010e7i	1.18787	−	1.84836i
$320$	3.63050e7	−	3.14585e7i	1.10794	−	0.960037i
$321$			4.66864e6i			0.141148i
$322$	3.54932e7	+	1.31575e7i	1.06311	+	0.394100i
$323$	1.10731e7			0.328596
$324$	1.12039e6	+	1.29300e6i	0.0329409	+	0.0380158i
$325$	−2.50407e7	−	1.60927e7i	−0.729452	−	0.468791i
$326$	−853067.	+	5.93321e6i	−0.0246224	+	0.171253i
$327$	−1.47172e7	−	6.72111e6i	−0.420902	−	0.192220i
$328$	7.16847e6	+	4.98578e7i	0.203144	+	1.41290i
$329$	1.47502e7	−	5.02347e7i	0.414201	−	1.41064i
$330$	3.40882e7	−	2.19071e7i	0.948554	−	0.609599i
$331$	−7.16794e6	−	1.56956e7i	−0.197656	−	0.432806i	0.784688	−	0.619891i	$-0.212823\pi$
$331$	−7.16794e6	−	1.56956e7i	−0.197656	−	0.432806i	−0.982344	+	0.187085i	$0.940096\pi$
$332$	3.15632e6	+	1.07494e7i	0.0862515	+	0.293745i
$333$	−950156.	−	823315.i	−0.0257313	−	0.0222963i
$334$	−9.30635e6	+	1.07401e7i	−0.249770	+	0.288250i
$335$	−6.43749e7	+	1.89022e7i	−1.71231	+	0.502780i
$336$	1.04519e7	−	4.77323e6i	0.275536	−	0.125833i
$337$	−5.60737e6	−	8.72524e6i	−0.146511	−	0.227975i	0.760240	−	0.649643i	$-0.225081\pi$
$337$	−5.60737e6	−	8.72524e6i	−0.146511	−	0.227975i	−0.906751	+	0.421667i	$0.861445\pi$
$338$	1.66080e7	+	4.87655e6i	0.430098	+	0.126288i
$339$	−1.31637e7	+	1.89265e6i	−0.337892	+	0.0485815i
$340$	7.14489e6	−	1.56451e7i	0.181785	−	0.398055i
$341$	8.99449e7	+	1.29321e7i	2.26837	+	0.326142i
$342$	2.79763e6	−	4.35320e6i	0.0699379	−	0.108825i
$343$	−1.63085e7	+	1.41314e7i	−0.404139	+	0.350189i
$344$		−	1.45714e7i		−	0.357952i
$345$	7.70520e6	−	3.57643e7i	0.187641	−	0.870948i
$346$	−1.01350e7			−0.244679
$347$	−9.90170e6	−	1.14272e7i	−0.236985	−	0.273495i	0.624782	−	0.780799i	$-0.285188\pi$
$347$	−9.90170e6	−	1.14272e7i	−0.236985	−	0.273495i	−0.861767	+	0.507304i	$0.830642\pi$
$348$	−1.19016e7	−	7.64873e6i	−0.282403	−	0.181489i
$349$	8.68808e6	−	6.04269e7i	0.204384	−	1.42152i	−0.586694	−	0.809809i	$-0.699571\pi$
$349$	8.68808e6	−	6.04269e7i	0.204384	−	1.42152i	0.791078	−	0.611715i	$-0.209520\pi$
$350$	−6.10788e7	−	2.78937e7i	−1.42458	−	0.650583i
$351$	−743495.	−	5.17112e6i	−0.0171932	−	0.119581i
$352$	−1.72676e7	+	5.88081e7i	−0.395918	+	1.34837i
$353$	−3.00573e6	+	1.93166e6i	−0.0683322	+	0.0439145i	−0.574361	−	0.818602i	$-0.694749\pi$
$353$	−3.00573e6	+	1.93166e6i	−0.0683322	+	0.0439145i	0.506029	+	0.862517i	$0.331113\pi$
$354$	1.08811e7	+	2.38263e7i	0.245281	+	0.537090i
$355$	9.88057e6	+	3.36501e7i	0.220850	+	0.752145i
$356$	−7.95537e6	−	6.89337e6i	−0.176324	−	0.152785i
$357$	1.65146e7	−	1.90589e7i	0.362965	−	0.418884i
$358$	2.84595e7	−	8.35646e6i	0.620266	−	0.182127i
$359$	−5.61746e7	+	2.56541e7i	−1.21411	+	0.554463i	−0.916427	−	0.400203i	$-0.868940\pi$
$359$	−5.61746e7	+	2.56541e7i	−1.21411	+	0.554463i	−0.297679	+	0.954666i	$0.596212\pi$
$360$	−1.39440e7	−	2.16973e7i	−0.298868	−	0.465048i
$361$	−3.27179e7	−	9.60683e6i	−0.695446	−	0.204201i
$362$	2.61346e7	−	3.75759e6i	0.550922	−	0.0792107i
$363$	−2.21027e7	+	4.83981e7i	−0.462088	+	1.01183i
$364$	2.07928e7	+	2.98955e6i	0.431130	+	0.0619871i
$365$	3.26362e7	−	5.07828e7i	0.671151	−	1.04433i
$366$	−5.37639e6	+	4.65867e6i	−0.109660	+	0.0950207i
$367$			4.55423e7i			0.921334i	0.887573	+	0.460667i	$0.152390\pi$
$367$			4.55423e7i			0.921334i	−0.887573	+	0.460667i	$0.847610\pi$
$368$	−8.20597e6	−	1.49570e7i	−0.164659	−	0.300123i
$369$	2.22447e7			0.442738
$370$	3.86785e6	+	4.46374e6i	0.0763598	+	0.0881239i
$371$	1.26094e8	+	8.10355e7i	2.46929	+	1.58691i
$372$	2.56518e6	−	1.78412e7i	0.0498298	−	0.346574i
$373$	1.12011e7	+	5.11539e6i	0.215842	+	0.0985717i	0.520402	−	0.853921i	$-0.325782\pi$
$373$	1.12011e7	+	5.11539e6i	0.215842	+	0.0985717i	−0.304560	+	0.952493i	$0.598509\pi$
$374$	−5.90198e6	−	4.10492e7i	−0.112819	−	0.784675i
$375$	−5.04684e6	+	1.71880e7i	−0.0957030	+	0.325935i
$376$	−4.61018e7	+	2.96278e7i	−0.867270	+	0.557361i
$377$	1.79460e7	+	3.92963e7i	0.334923	+	0.733378i
$378$	−3.32024e6	−	1.13077e7i	−0.0614743	−	0.209362i
$379$	−6.32826e7	−	5.48347e7i	−1.16243	−	1.00725i	−0.999789	−	0.0205652i	$-0.993453\pi$
$379$	−6.32826e7	−	5.48347e7i	−1.16243	−	1.00725i	−0.162641	−	0.986685i	$-0.552001\pi$
$380$	1.31690e7	−	1.51979e7i	0.239996	−	0.276970i
$381$	−5.23182e7	+	1.53620e7i	−0.945970	+	0.277762i
$382$	−3.31825e7	+	1.51539e7i	−0.595277	+	0.271854i
$383$	−2.41720e7	−	3.76123e7i	−0.430245	−	0.669475i	0.556667	−	0.830736i	$-0.312080\pi$
$383$	−2.41720e7	−	3.76123e7i	−0.430245	−	0.669475i	−0.986912	+	0.161261i	$0.948444\pi$
$384$	3.72141e6	+	1.09270e6i	0.0657224	+	0.0192978i
$385$	2.28541e8	−	3.28592e7i	4.00480	−	0.575804i
$386$	2.32397e7	−	5.08879e7i	0.404082	−	0.884816i
$387$	−6.36952e6	−	915798.i	−0.109894	−	0.0158004i
$388$	−2.06600e7	+	3.21476e7i	−0.353700	+	0.550368i
$389$	−1.30001e6	+	1.12647e6i	−0.0220850	+	0.0191368i	−0.665833	−	0.746101i	$-0.731924\pi$
$389$	−1.30001e6	+	1.12647e6i	−0.0220850	+	0.0191368i	0.643748	+	0.765237i	$0.277378\pi$
$390$			2.45432e7i			0.413750i
$391$	−3.00196e7	−	2.23789e7i	−0.502198	−	0.374376i
$392$	8.73232e7			1.44968
$393$	−2.08849e7	−	2.41024e7i	−0.344076	−	0.397085i
$394$	−3.02736e7	−	1.94556e7i	−0.494965	−	0.318095i
$395$	−2.79519e6	+	1.94409e7i	−0.0453544	+	0.315447i
$396$	1.45829e7	+	6.65980e6i	0.234833	+	0.107245i
$397$	−4.73579e6	−	3.29382e7i	−0.0756870	−	0.526414i	−0.992028	−	0.126016i	$-0.959781\pi$
$397$	−4.73579e6	−	3.29382e7i	−0.0756870	−	0.526414i	0.916341	−	0.400398i	$-0.131128\pi$
$398$	6.77971e6	−	2.30896e7i	0.107538	−	0.366241i
$399$	2.48050e7	−	1.59412e7i	0.390499	−	0.250958i
$400$	1.25714e7	+	2.75275e7i	0.196428	+	0.430117i
$401$	2.02504e6	+	6.89666e6i	0.0314052	+	0.106956i	0.973704	−	0.227817i	$-0.0731586\pi$
$401$	2.02504e6	+	6.89666e6i	0.0314052	+	0.106956i	−0.942299	+	0.334773i	$0.891340\pi$
$402$	2.42513e7	+	2.10139e7i	0.373300	+	0.323466i
$403$	−3.60432e7	+	4.15960e7i	−0.550691	+	0.635531i
$404$	4.77446e6	−	1.40191e6i	0.0724069	−	0.0212606i
$405$	−1.03608e7	+	4.73162e6i	−0.155965	+	0.0712270i
$406$	5.26865e7	+	8.19818e7i	0.787266	+	1.22501i
$407$	−1.13036e7	−	3.31903e6i	−0.167661	−	0.0492298i
$408$	−2.61280e7	+	3.75664e6i	−0.384703	+	0.0553119i
$409$	4.72083e7	−	1.03372e8i	0.689999	−	1.51089i	−0.161692	−	0.986841i	$-0.551695\pi$
$409$	4.72083e7	−	1.03372e8i	0.689999	−	1.51089i	0.851690	−	0.524045i	$-0.175578\pi$
$410$	−1.03440e8	−	1.48724e7i	−1.50084	−	0.215789i
$411$	−2.55014e7	+	3.96810e7i	−0.367315	+	0.571554i
$412$	1.85666e7	−	1.60880e7i	0.265485	−	0.230044i
$413$			1.49252e8i			2.11871i
$414$	−1.63824e7	+	6.14763e6i	−0.230874	+	0.0866377i
$415$	−7.45847e7			−1.04353
$416$	−2.43108e7	−	2.80562e7i	−0.337691	−	0.389716i
$417$	5.58858e7	+	3.59156e7i	0.770714	+	0.495308i
$418$	6.90064e6	−	4.79950e7i	0.0944845	−	0.657154i
$419$	−1.36561e7	−	6.23651e6i	−0.185645	−	0.0847813i	0.320424	−	0.947274i	$-0.396175\pi$
$419$	−1.36561e7	−	6.23651e6i	−0.185645	−	0.0847813i	−0.506069	+	0.862493i	$0.668902\pi$
$420$	−6.51787e6	−	4.53328e7i	−0.0879747	−	0.611877i
$421$	−1.77706e7	+	6.05210e7i	−0.238153	+	0.811073i	0.750502	+	0.660868i	$0.229812\pi$
$421$	−1.77706e7	+	6.05210e7i	−0.238153	+	0.811073i	−0.988655	+	0.150205i	$0.952007\pi$
$422$	−7.89607e7	+	5.07449e7i	−1.05069	+	0.675236i
$423$	1.00536e7	+	2.20144e7i	0.132832	+	0.290861i
$424$	−4.42010e7	−	1.50535e8i	−0.579876	−	1.97488i
$425$	5.01960e7	+	4.34951e7i	0.653886	+	0.566595i
$426$	1.09844e7	−	1.26767e7i	0.142085	−	0.163975i
$427$	−3.88941e7	+	1.14203e7i	−0.499575	+	0.146688i
$428$	7.89337e6	−	3.60478e6i	0.100677	−	0.0459777i
$429$	−2.64663e7	−	4.11824e7i	−0.335214	−	0.521603i
$430$	2.90065e7	+	8.51708e6i	0.364830	+	0.107124i
$431$	1.43259e7	−	2.05975e6i	0.178933	−	0.0257267i	−0.0522659	−	0.998633i	$-0.516644\pi$
$431$	1.43259e7	−	2.05975e6i	0.178933	−	0.0257267i	0.231199	+	0.972907i	$0.425735\pi$
$432$	−2.20643e6	+	4.83141e6i	−0.0273678	+	0.0599271i
$433$	−2.99536e7	−	4.30668e6i	−0.368965	−	0.0530492i	−0.0446615	−	0.999002i	$-0.514221\pi$
$433$	−2.99536e7	−	4.30668e6i	−0.368965	−	0.0530492i	−0.324304	+	0.945953i	$0.605130\pi$
$434$	−6.71255e7	+	1.04449e8i	−0.821142	+	1.27772i
$435$	7.11810e7	−	6.16787e7i	0.864762	−	0.749320i
$436$			3.00722e7i			0.362832i
$437$	−2.63057e7	−	3.49942e7i	−0.315214	−	0.419327i
$438$	−2.88717e7			−0.343598
$439$	2.61333e7	+	3.01594e7i	0.308887	+	0.356475i	0.888875	−	0.458151i	$-0.151488\pi$
$439$	2.61333e7	+	3.01594e7i	0.308887	+	0.356475i	−0.579987	+	0.814626i	$0.696942\pi$
$440$	−2.03312e8	−	1.30661e8i	−2.38674	−	1.53386i
$441$	5.48819e6	−	3.81712e7i	0.0639902	−	0.445062i
$442$	2.28491e7	+	1.04348e7i	0.264607	+	0.120842i
$443$	9.74484e6	+	6.77769e7i	0.112089	+	0.779597i	0.965882	+	0.258984i	$0.0833876\pi$
$443$	9.74484e6	+	6.77769e7i	0.112089	+	0.779597i	−0.853793	+	0.520613i	$0.825703\pi$
$444$	−658355.	+	2.24215e6i	−0.00752162	+	0.0256163i
$445$	5.89543e7	−	3.78876e7i	0.669014	−	0.429949i
$446$	2.15825e7	+	4.72591e7i	0.243275	+	0.532697i
$447$	1.72751e7	+	5.88335e7i	0.193418	+	0.658722i
$448$	−9.89417e7	−	8.57335e7i	−1.10039	−	0.953491i
$449$	−4.04733e7	+	4.67087e7i	−0.447126	+	0.516010i	−0.933908	−	0.357513i	$-0.883625\pi$
$449$	−4.04733e7	+	4.67087e7i	−0.447126	+	0.516010i	0.486783	+	0.873523i	$0.338170\pi$
$450$	2.97814e7	−	8.74460e6i	0.326819	−	0.0959627i
$451$	1.89605e8	−	8.65895e7i	2.06690	−	0.943921i
$452$	1.33640e7	+	2.07947e7i	0.144717	+	0.225184i
$453$	−8.09673e7	−	2.37741e7i	−0.870993	−	0.255747i
$454$	1.21730e8	−	1.75021e7i	1.30085	−	0.187035i
$455$	−5.80956e7	+	1.27212e8i	−0.616750	+	1.35049i
$456$	−3.05490e7	−	4.39229e6i	−0.322183	−	0.0463229i
$457$	−1.22173e7	+	1.90104e7i	−0.128004	+	0.199179i	−0.899340	−	0.437250i	$-0.855953\pi$
$457$	−1.22173e7	+	1.90104e7i	−0.128004	+	0.199179i	0.771336	+	0.636429i	$0.219589\pi$
$458$	−4.56823e7	+	3.95839e7i	−0.475501	+	0.412024i
$459$			1.16573e7i			0.120548i
$460$	−6.64168e7	+	1.45872e7i	−0.682346	+	0.149864i
$461$	3.89875e7			0.397945			0.198972	−	0.980005i	$-0.436240\pi$
$461$	3.89875e7			0.397945			0.198972	+	0.980005i	$0.436240\pi$
$462$	−7.23167e7	−	8.34579e7i	−0.733352	−	0.846333i
$463$	−5.89624e7	−	3.78928e7i	−0.594063	−	0.381781i	0.208788	−	0.977961i	$-0.433048\pi$
$463$	−5.89624e7	−	3.78928e7i	−0.594063	−	0.381781i	−0.802851	+	0.596180i	$0.796684\pi$
$464$	6.25054e6	−	4.34734e7i	0.0625696	−	0.435181i
$465$	1.09154e8	+	4.98490e7i	1.08563	+	0.495790i
$466$	5.84506e6	+	4.06533e7i	0.0577605	+	0.401733i
$467$	−4.86149e7	+	1.65567e8i	−0.477330	+	1.62564i	0.271190	+	0.962526i	$0.412583\pi$
$467$	−4.86149e7	+	1.65567e8i	−0.477330	+	1.62564i	−0.748521	+	0.663112i	$0.769235\pi$
$468$	−8.16885e6	+	5.24980e6i	−0.0796936	+	0.0512159i
$469$	7.59573e7	+	1.66323e8i	0.736294	+	1.61226i
$470$	−3.20318e7	−	1.09090e8i	−0.308523	−	1.05073i
$471$	1.79802e7	+	1.55799e7i	0.172080	+	0.149108i
$472$	1.02305e8	−	1.18067e8i	0.972910	−	1.12280i
$473$	−5.78561e7	+	1.69881e7i	−0.546721	+	0.160532i
$474$	8.54494e6	−	3.90234e6i	0.0802369	−	0.0366430i
$475$	4.19847e7	+	6.53295e7i	0.391751	+	0.609577i
$476$	−4.49747e7	−	1.32058e7i	−0.417011	−	0.122445i
$477$	−6.85807e7	+	9.86042e6i	−0.631898	+	0.0908532i
$478$	−5.24446e7	+	1.14838e8i	−0.480195	+	1.05148i
$479$	1.58508e8	+	2.27899e7i	1.44226	+	0.207366i	0.818615	−	0.574342i	$-0.194742\pi$
$479$	1.58508e8	+	2.27899e7i	1.44226	+	0.207366i	0.623645	+	0.781708i	$0.285651\pi$
$480$	−4.37582e7	+	6.80891e7i	−0.395672	+	0.615678i
$481$	5.39271e6	−	4.67281e6i	0.0484587	−	0.0419897i
$482$			3.36926e7i			0.300880i
$483$	−9.94644e7	−	6.91401e6i	−0.882727	−	0.0613605i
$484$	9.88938e7			0.872234
$485$	−1.66601e8	−	1.92267e8i	−1.46033	−	1.68531i
$486$	4.58287e6	+	2.94523e6i	0.0399235	+	0.0256573i
$487$	1.22779e7	−	8.53947e7i	0.106301	−	0.739340i	−0.865049	−	0.501687i	$-0.832713\pi$
$487$	1.22779e7	−	8.53947e7i	0.106301	−	0.739340i	0.971350	−	0.237653i	$-0.0763780\pi$
$488$	3.85955e7	+	1.76260e7i	0.332107	+	0.151668i
$489$	−2.24694e6	−	1.56278e7i	−0.0192161	−	0.133651i
$490$	−5.10411e7	+	1.73830e8i	−0.433842	+	1.47753i
$491$	1.63286e8	−	1.04937e8i	1.37944	−	0.886513i	0.380179	−	0.924913i	$-0.375862\pi$
$491$	1.63286e8	−	1.04937e8i	1.37944	−	0.886513i	0.999262	+	0.0384000i	$0.0122261\pi$
$492$	−1.71757e7	−	3.76095e7i	−0.144218	−	0.315793i
$493$	−2.71578e7	−	9.24909e7i	−0.226649	−	0.771895i
$494$	2.21959e7	+	1.92328e7i	0.184116	+	0.159537i
$495$	−6.98931e7	+	8.06609e7i	−0.576260	+	0.665040i
$496$	5.36904e7	−	1.57649e7i	0.439999	−	0.129195i
$497$	8.69407e7	−	3.97045e7i	0.708197	−	0.323423i
$498$	1.92860e7	+	3.00095e7i	0.156154	+	0.242980i
$499$	4.27486e7	+	1.25521e7i	0.344049	+	0.101022i	0.449192	−	0.893435i	$-0.351712\pi$
$499$	4.27486e7	+	1.25521e7i	0.344049	+	0.101022i	−0.105143	+	0.994457i	$0.533530\pi$
$500$	3.29568e7	−	4.73848e6i	0.263655	−	0.0379078i
$501$	1.55497e7	−	3.40490e7i	0.123654	−	0.270764i
$502$	−1.12309e7	−	1.61476e6i	−0.0887776	−	0.0127643i
$503$	5.18201e7	−	8.06337e7i	0.407188	−	0.633596i	−0.575730	−	0.817640i	$-0.695282\pi$
$503$	5.18201e7	−	8.06337e7i	0.407188	−	0.633596i	0.982918	+	0.184043i	$0.0589186\pi$
$504$	−5.31213e7	+	4.60299e7i	−0.414932	+	0.359541i
$505$			3.31275e7i			0.257226i
$506$	−1.15706e8	+	1.16170e8i	−0.893112	+	0.896689i
$507$	−4.55915e7			−0.349832
$508$	6.63691e7	+	7.65940e7i	0.506261	+	0.584256i
$509$	−2.90621e7	−	1.86770e7i	−0.220380	−	0.141630i	0.425793	−	0.904821i	$-0.359995\pi$
$509$	−2.90621e7	−	1.86770e7i	−0.220380	−	0.141630i	−0.646173	+	0.763191i	$0.723632\pi$
$510$	7.79386e6	−	5.42075e7i	0.0587546	−	0.408648i
$511$	−1.49647e8	−	6.83415e7i	−1.12152	−	0.512179i
$512$	1.23986e7	+	8.62341e7i	0.0923767	+	0.642494i
$513$	−3.83996e6	+	1.30777e7i	−0.0284430	+	0.0968679i
$514$	−1.27301e8	+	8.18113e7i	−0.937437	+	0.602454i
$515$	6.79425e7	+	1.48773e8i	0.497416	+	1.08919i
$516$	3.36971e6	+	1.14762e7i	0.0245270	+	0.0835311i
$517$	1.71386e8	+	1.48507e8i	1.24024	+	1.07467i
$518$	1.05410e7	−	1.21650e7i	0.0758391	−	0.0875230i
$519$	2.56139e7	−	7.52092e6i	0.183220	−	0.0537983i
$520$	1.33155e8	−	6.08096e7i	0.946991	−	0.432476i
$521$	−1.25916e8	−	1.95929e8i	−0.890364	−	1.38543i	−0.922519	−	0.385951i	$-0.873873\pi$
$521$	−1.25916e8	−	1.95929e8i	−0.890364	−	1.38543i	0.0321550	−	0.999483i	$-0.489763\pi$
$522$	−4.32226e7	−	1.26913e7i	−0.303878	−	0.0892267i
$523$	−1.25859e8	+	1.80958e7i	−0.879792	+	0.126495i	−0.567384	−	0.823453i	$-0.692045\pi$
$523$	−1.25859e8	+	1.80958e7i	−0.879792	+	0.126495i	−0.312408	+	0.949948i	$0.601135\pi$
$524$	−2.46247e7	+	5.39206e7i	−0.171150	+	0.374766i
$525$	1.75061e8	+	2.51700e7i	1.20979	+	0.173942i
$526$	5.60428e7	−	8.72042e7i	0.385090	−	0.599212i
$527$	9.28160e7	−	8.04255e7i	0.634149	−	0.549493i
$528$			4.97698e7i			0.338115i
$529$	591863.	+	1.48035e8i	0.00399811	+	0.999992i
$530$	3.25498e8			2.18636
$531$	−4.51802e7	−	5.21408e7i	−0.301762	−	0.348252i
$532$	−4.61046e7	−	2.96296e7i	−0.306203	−	0.196785i
$533$	−1.79675e7	+	1.24967e8i	−0.118661	+	0.825302i
$534$	−3.04886e7	−	1.39237e7i	−0.200223	−	0.0914387i
$535$	8.22153e6	+	5.71820e7i	0.0536898	+	0.373421i
$536$	5.39205e7	−	1.83636e8i	0.350154	−	1.19252i
$537$	−6.57235e7	+	4.22379e7i	−0.424422	+	0.272759i
$538$	−9.39744e7	−	2.05775e8i	−0.603480	−	1.32144i
$539$	−1.01806e8	−	3.46720e8i	−0.650141	−	2.21418i
$540$	1.59997e7	+	1.38638e7i	0.101609	+	0.0880444i
$541$	1.10410e8	−	1.27419e8i	0.697292	−	0.804718i	−0.291092	−	0.956695i	$-0.594019\pi$
$541$	1.10410e8	−	1.27419e8i	0.697292	−	0.804718i	0.988384	+	0.151977i	$0.0485640\pi$
$542$	−4.95825e7	+	1.45587e7i	−0.311409	+	0.0914378i
$543$	−6.32606e7	+	2.88901e7i	−0.395124	+	0.180447i
$544$	4.47847e7	+	6.96864e7i	0.278185	+	0.432864i
$545$	−1.92094e8	−	5.64038e7i	−1.18665	−	0.348432i
$546$	6.62066e7	−	9.51907e6i	0.406746	−	0.0584812i
$547$	9.18966e7	−	2.01226e8i	0.561484	−	1.22948i	−0.389725	−	0.920931i	$-0.627430\pi$
$547$	9.18966e7	−	2.01226e8i	0.561484	−	1.22948i	0.951209	−	0.308548i	$-0.0998430\pi$
$548$	8.67798e7	+	1.24771e7i	0.527323	+	0.0758177i
$549$	1.01305e7	−	1.57633e7i	0.0612227	−	0.0952644i
$550$	2.19805e8	−	1.90462e8i	1.32114	−	1.14478i
$551$		−	1.12706e8i		−	0.673742i
$552$	7.39426e7	+	7.36476e7i	0.439620	+	0.437866i
$553$	5.35270e7			0.316517
$554$	−1.96626e7	−	2.26919e7i	−0.115641	−	0.133457i
$555$	−1.30875e7	−	8.41081e6i	−0.0765556	−	0.0491993i
$556$	1.75724e7	−	1.22219e8i	0.102237	−	0.711071i
$557$	8.38022e7	+	3.82712e7i	0.484942	+	0.221466i	0.642856	−	0.765987i	$-0.277749\pi$
$557$	8.38022e7	+	3.82712e7i	0.484942	+	0.221466i	−0.157914	+	0.987453i	$0.550477\pi$
$558$	−8.16784e6	−	5.68086e7i	−0.0470116	−	0.326973i
$559$	1.02896e7	−	3.50432e7i	0.0589065	−	0.200617i
$560$	1.19610e8	−	7.68690e7i	0.681091	−	0.437710i
$561$	4.53773e7	+	9.93623e7i	0.257010	+	0.562773i
$562$	−5.45222e7	−	1.85686e8i	−0.307160	−	1.04609i
$563$	−1.73079e8	−	1.49974e8i	−0.969882	−	0.840407i	0.0173256	−	0.999850i	$-0.494485\pi$
$563$	−1.73079e8	−	1.49974e8i	−0.969882	−	0.840407i	−0.987207	+	0.159443i	$0.949030\pi$
$564$	2.94575e7	−	3.39958e7i	0.164194	−	0.189490i
$565$	−1.57897e8	+	4.63627e7i	−0.875444	+	0.257054i
$566$	7.77411e7	−	3.55032e7i	0.428747	−	0.195802i
$567$	1.67822e7	+	2.61136e7i	0.0920661	+	0.143258i
$568$	−9.59905e7	−	2.81853e7i	−0.523821	−	0.153808i
$569$	−7.27767e7	+	1.04637e7i	−0.395053	+	0.0568001i	−0.336979	−	0.941512i	$-0.609405\pi$
$569$	−7.27767e7	+	1.04637e7i	−0.395053	+	0.0568001i	−0.0580743	+	0.998312i	$0.518496\pi$
$570$	2.65997e7	−	5.82451e7i	0.143632	−	0.314511i
$571$	3.17894e7	+	4.57062e6i	0.170755	+	0.0245509i	0.227162	−	0.973857i	$-0.427055\pi$
$571$	3.17894e7	+	4.57062e6i	0.170755	+	0.0245509i	−0.0564069	+	0.998408i	$0.517964\pi$
$572$	−4.91926e7	+	7.65452e7i	−0.262852	+	0.409006i
$573$	7.26155e7	−	6.29217e7i	0.385981	−	0.334454i
$574$			2.84801e8i			1.50594i
$575$	1.82096e7	−	2.61962e8i	0.0957850	−	1.37795i
$576$	6.05174e7			0.316674
$577$	−1.18346e8	−	1.36579e8i	−0.616065	−	0.710977i	0.358890	−	0.933380i	$-0.383155\pi$
$577$	−1.18346e8	−	1.36579e8i	−0.616065	−	0.710977i	−0.974955	+	0.222403i	$0.928610\pi$
$578$	7.30233e7	+	4.69292e7i	0.378162	+	0.243030i
$579$	−2.09704e7	+	1.45853e8i	−0.108037	+	0.751413i
$580$	−1.59242e8	−	7.27235e7i	−0.816158	−	0.372727i
$581$	2.89276e7	+	2.01196e8i	0.147497	+	1.02587i
$582$	−3.42805e7	+	1.16749e8i	−0.173891	+	0.592220i
$583$	−5.46172e8	+	3.51003e8i	−2.75628	+	1.77136i
$584$	7.15342e7	+	1.56638e8i	0.359149	+	0.786428i
$585$	−1.82128e7	−	6.20271e7i	−0.0909723	−	0.309823i
$586$	−4.20560e7	−	3.64417e7i	−0.208995	−	0.181095i
$587$	−5.82349e7	+	6.72067e7i	−0.287918	+	0.332275i	−0.881221	−	0.472704i	$-0.843278\pi$
$587$	−5.82349e7	+	6.72067e7i	−0.287918	+	0.332275i	0.593303	+	0.804979i	$0.297824\pi$
$588$	−6.87744e7	+	2.01940e7i	−0.338295	+	0.0993322i
$589$	1.30618e8	−	5.96511e7i	0.639229	−	0.291926i
$590$	1.75232e8	+	2.72666e8i	0.853211	+	1.32762i
$591$	9.09466e7	+	2.67043e7i	0.440579	+	0.129366i
$592$	−7.18070e6	+	1.03243e6i	−0.0346100	+	0.00497617i
$593$	8.75181e7	−	1.91638e8i	0.419695	−	0.919004i	−0.575193	−	0.818018i	$-0.695073\pi$
$593$	8.75181e7	−	1.91638e8i	0.419695	−	0.919004i	0.994888	−	0.100986i	$-0.0321998\pi$
$594$	5.05272e7	+	7.26471e6i	0.241082	+	0.0346624i
$595$	1.68710e8	−	2.62518e8i	0.800922	−	1.24626i
$596$	8.61325e7	−	7.46342e7i	0.406844	−	0.352532i
$597$			6.33844e7i			0.297892i
$598$	−2.13040e7	−	9.69989e7i	−0.0996225	−	0.453590i
$599$	1.66945e8			0.776773			0.388386	−	0.921497i	$-0.373033\pi$
$599$	1.66945e8			0.776773			0.388386	+	0.921497i	$0.373033\pi$
$600$	−1.21230e8	−	1.39907e8i	−0.561251	−	0.647718i
$601$	2.10485e8	+	1.35270e8i	0.969610	+	0.623131i	0.926642	−	0.375946i	$-0.122682\pi$
$601$	2.10485e8	+	1.35270e8i	0.969610	+	0.623131i	0.0429687	+	0.999076i	$0.486318\pi$
$602$	1.17251e7	−	8.15498e7i	0.0537436	−	0.373795i
$603$	−7.68833e7	−	3.51114e7i	−0.350655	−	0.160139i
$604$	2.23215e7	+	1.55250e8i	0.101301	+	0.704563i
$605$	−1.85486e8	+	6.31708e8i	−0.837618	+	2.85266i
$606$	1.33290e7	−	8.56604e6i	0.0598936	−	0.0384913i
$607$	7.96232e7	+	1.74350e8i	0.356019	+	0.779574i	0.999896	+	0.0144440i	$0.00459783\pi$
$607$	7.96232e7	+	1.74350e8i	0.356019	+	0.779574i	−0.643876	+	0.765130i	$0.722675\pi$
$608$	2.72866e7	+	9.29297e7i	0.121406	+	0.413470i
$609$	−1.93989e8	−	1.68092e8i	−0.858865	−	0.744211i
$610$	−5.76466e7	+	6.65277e7i	−0.253971	+	0.293098i
$611$	−1.31794e8	+	3.86981e7i	−0.577791	+	0.169655i
$612$	1.97093e7	−	9.00092e6i	0.0859837	−	0.0392674i
$613$	−1.16827e8	−	1.81786e8i	−0.507179	−	0.789186i	0.489380	−	0.872070i	$-0.337223\pi$
$613$	−1.16827e8	−	1.81786e8i	−0.507179	−	0.789186i	−0.996559	+	0.0828849i	$0.973587\pi$
$614$	2.03185e8	+	5.96606e7i	0.877783	+	0.257740i
$615$	2.72455e8	−	3.91731e7i	1.17130	−	0.168408i
$616$	−2.73609e8	+	5.99120e8i	−1.17055	+	2.56314i
$617$	−1.19856e8	−	1.72327e7i	−0.510276	−	0.0733667i	−0.117632	−	0.993057i	$-0.537530\pi$
$617$	−1.19856e8	−	1.72327e7i	−0.510276	−	0.0733667i	−0.392644	+	0.919691i	$0.628440\pi$
$618$	4.22913e7	−	6.58066e7i	0.179178	−	0.278807i
$619$	−9.18141e7	+	7.95574e7i	−0.387113	+	0.335435i	−0.826576	−	0.562826i	$-0.809714\pi$
$619$	−9.18141e7	+	7.95574e7i	−0.387113	+	0.335435i	0.439463	+	0.898261i	$0.355169\pi$
$620$		−	2.23039e8i		−	0.935848i
$621$	3.68405e7	−	2.76935e7i	0.153833	−	0.115639i
$622$	2.58585e8			1.07457
$623$	−1.25069e8	−	1.44337e8i	−0.517233	−	0.596918i
$624$	−2.53599e7	−	1.62978e7i	−0.104374	−	0.0670773i
$625$	1.64463e7	−	1.14387e8i	0.0673641	−	0.468528i
$626$	5.75358e7	+	2.62757e7i	0.234539	+	0.107110i
$627$	1.81760e7	+	1.26417e8i	0.0737386	+	0.512863i
$628$	1.24583e7	−	4.24291e7i	0.0503014	−	0.171311i
$629$	−1.33945e7	+	8.60813e6i	−0.0538239	+	0.0345905i
$630$	−6.05796e7	−	1.32651e8i	−0.242273	−	0.530504i
$631$	1.34656e8	+	4.58595e8i	0.535965	+	1.82533i	0.564074	+	0.825724i	$0.309233\pi$
$631$	1.34656e8	+	4.58595e8i	0.535965	+	1.82533i	−0.0281087	+	0.999605i	$0.508948\pi$
$632$	−4.23428e7	−	3.66903e7i	−0.167737	−	0.145345i
$633$	1.61898e8	−	1.86840e8i	0.638307	−	0.736646i
$634$	−1.61966e8	+	4.75575e7i	−0.635559	+	0.186617i
$635$	−6.13746e8	+	2.80288e8i	−2.39700	+	1.09467i
$636$	6.96242e7	+	1.08337e8i	0.270638	+	0.421121i
$637$	2.10007e8	+	6.16635e7i	0.812484	+	0.238567i
$638$	−4.17814e8	+	6.00726e7i	−1.60887	+	0.231321i
$639$	−1.83535e7	+	4.01885e7i	−0.0703421	+	0.154028i
$640$	4.75045e7	+	6.83011e6i	0.181215	+	0.0260548i
$641$	2.52755e8	−	3.93295e8i	0.959679	−	1.49329i	0.0922456	−	0.995736i	$-0.470596\pi$
$641$	2.52755e8	−	3.93295e8i	0.959679	−	1.49329i	0.867433	−	0.497553i	$-0.165768\pi$
$642$	2.08816e7	−	1.80940e7i	0.0789148	−	0.0683800i
$643$		−	1.21487e8i		−	0.456981i	−0.973546	−	0.228491i	$-0.926621\pi$
$643$		−	1.21487e8i		−	0.456981i	0.973546	−	0.228491i	$-0.0733790\pi$
$644$	6.51094e7	+	1.73505e8i	0.243773	+	0.649612i
$645$	−7.96273e7			−0.296744
$646$	−4.29155e7	−	4.95271e7i	−0.159190	−	0.183715i
$647$	−2.99561e8	−	1.92516e8i	−1.10604	−	0.710812i	−0.145617	−	0.989341i	$-0.546517\pi$
$647$	−2.99561e8	−	1.92516e8i	−1.10604	−	0.710812i	−0.960428	+	0.278529i	$0.910153\pi$
$648$	4.62402e6	−	3.21607e7i	0.0169940	−	0.118196i
$649$	−5.88061e8	−	2.68559e8i	−2.15124	−	0.982438i
$650$	2.50706e7	+	1.74370e8i	0.0912904	+	0.634939i
$651$	9.21348e7	−	3.13782e8i	0.333949	−	1.13733i
$652$	−2.46873e7	+	1.58656e7i	−0.0890700	+	0.0572418i
$653$	1.00245e8	+	2.19507e8i	0.360018	+	0.788330i	0.999804	+	0.0197771i	$0.00629567\pi$
$653$	1.00245e8	+	2.19507e8i	0.360018	+	0.788330i	−0.639786	+	0.768553i	$0.720977\pi$
$654$	2.69768e7	+	9.18747e7i	0.0964401	+	0.328445i
$655$	−2.98245e8	−	2.58430e8i	−1.06133	−	0.919644i
$656$	8.40558e7	−	9.70056e7i	0.297753	−	0.343625i
$657$	7.29664e7	−	2.14249e7i	0.257292	−	0.0755478i
$658$	−2.81853e8	+	1.28718e8i	−0.989339	+	0.451816i
$659$	1.80581e8	+	2.80989e8i	0.630980	+	0.981824i	0.998654	+	0.0518690i	$0.0165178\pi$
$659$	1.80581e8	+	2.80989e8i	0.630980	+	0.981824i	−0.367674	+	0.929955i	$0.619846\pi$
$660$	1.90341e8	+	5.58893e7i	0.662066	+	0.194400i
$661$	4.68610e8	−	6.73759e7i	1.62258	−	0.233292i	0.729761	−	0.683702i	$-0.239631\pi$
$661$	4.68610e8	−	6.73759e7i	1.62258	−	0.233292i	0.892822	+	0.450410i	$0.148722\pi$
$662$	−4.24218e7	+	9.28908e7i	−0.146223	+	0.320183i
$663$	−6.54889e7	−	9.41588e6i	−0.224712	−	0.0323088i
$664$	1.15027e8	−	1.78986e8i	0.392912	−	0.611384i
$665$	2.75741e8	−	2.38931e8i	0.937641	−	0.812471i
$666$			7.44067e6i			0.0251877i
$667$	−2.27781e8	+	3.05551e8i	−0.767609	+	1.02969i
$668$	−6.95736e7			−0.233408
$669$	−8.96141e7	−	1.03420e8i	−0.299294	−	0.345404i
$670$	3.34039e8	+	2.14674e8i	1.11064	+	0.713764i
$671$	2.49878e7	−	1.73794e8i	0.0827105	−	0.575264i
$672$	2.00645e8	+	9.16316e7i	0.661182	+	0.301952i
$673$	−5.27187e6	−	3.66667e7i	−0.0172950	−	0.120289i	0.979345	−	0.202196i	$-0.0648079\pi$
$673$	−5.27187e6	−	3.66667e7i	−0.0172950	−	0.120289i	−0.996640	+	0.0819073i	$0.973899\pi$
$674$	−1.72935e7	+	5.88962e7i	−0.0564811	+	0.192357i
$675$	−6.87762e7	+	4.41998e7i	−0.223628	+	0.143717i
$676$	3.52024e7	+	7.70824e7i	0.113955	+	0.249526i
$677$	3.98908e7	+	1.35856e8i	0.128560	+	0.437836i	0.998465	−	0.0553833i	$-0.0176381\pi$
$677$	3.98908e7	+	1.35856e8i	0.128560	+	0.437836i	−0.869905	+	0.493220i	$0.835820\pi$
$678$	5.94830e7	+	5.15423e7i	0.190855	+	0.165377i
$679$	−4.54034e8	+	5.23984e8i	−1.45037	+	1.67382i
$680$	−3.13403e8	+	9.20234e7i	−0.996727	+	0.292665i
$681$	−2.94655e8	+	1.34564e8i	−0.932979	+	0.426077i
$682$	−2.90752e8	−	4.52420e8i	−0.916580	−	1.42623i
$683$	4.93303e8	+	1.44847e8i	1.54829	+	0.454618i	0.940588	−	0.339550i	$-0.110275\pi$
$683$	4.93303e8	+	1.44847e8i	1.54829	+	0.454618i	0.607698	+	0.794168i	$0.292093\pi$
$684$	2.50757e7	−	3.60534e6i	0.0783582	−	0.0112662i
$685$	−2.42466e8	+	5.30926e8i	−0.754360	+	1.65182i
$686$	1.26412e8	+	1.81753e7i	0.391575	+	0.0563000i
$687$	8.60770e7	−	1.33938e8i	0.265471	−	0.413081i
$688$	−2.80621e7	+	2.43160e7i	−0.0861698	+	0.0746666i
$689$		−	3.93239e8i		−	1.20226i
$690$	−1.89827e8	+	1.04146e8i	−0.577843	+	0.317028i
$691$	−7.17522e7			−0.217471			−0.108735	−	0.994071i	$-0.534680\pi$
$691$	−7.17522e7			−0.217471			−0.108735	+	0.994071i	$0.534680\pi$
$692$	−3.24929e7	−	3.74988e7i	−0.0980552	−	0.113162i
$693$	2.44695e8	+	1.57256e8i	0.735233	+	0.472505i
$694$	−1.27352e7	+	8.85753e7i	−0.0381002	+	0.264993i
$695$	7.47743e8	+	3.41483e8i	2.22740	+	1.01722i
$696$	3.82365e7	+	2.65941e8i	0.113410	+	0.788782i
$697$	7.93681e7	−	2.70303e8i	0.234395	−	0.798274i
$698$	−3.03945e8	+	1.95334e8i	−0.893777	+	0.574395i
$699$	−4.49396e7	−	9.84039e7i	−0.131582	−	0.288125i
$700$	−9.26138e7	−	3.15414e8i	−0.270011	−	0.919573i
$701$	−7.16232e7	−	6.20619e7i	−0.207922	−	0.180165i	0.544674	−	0.838648i	$-0.316653\pi$
$701$	−7.16232e7	−	6.20619e7i	−0.207922	−	0.180165i	−0.752596	+	0.658482i	$0.771199\pi$
$702$	−2.02475e7	+	2.33669e7i	−0.0585275	+	0.0675444i
$703$	−1.78621e7	+	5.24479e6i	−0.0514123	+	0.0150960i
$704$	5.15826e8	−	2.35570e8i	1.47838	−	0.675152i
$705$	1.61905e8	+	2.51930e8i	0.462056	+	0.718973i
$706$	2.02890e7	+	5.95737e6i	0.0576561	+	0.0169294i
$707$	8.93630e7	−	1.28485e7i	0.252871	−	0.0363574i
$708$	−5.32706e7	+	1.16646e8i	−0.150103	+	0.328679i
$709$	−2.22452e8	−	3.19838e7i	−0.624163	−	0.0897410i	−0.177025	−	0.984206i	$-0.556647\pi$
$709$	−2.22452e8	−	3.19838e7i	−0.624163	−	0.0897410i	−0.447137	+	0.894465i	$0.647557\pi$
$710$	1.12214e8	−	1.74609e8i	0.313526	−	0.487856i
$711$	−1.86995e7	+	1.62032e7i	−0.0520260	+	0.0450808i
$712$			1.99908e8i			0.553847i
$713$	−4.74665e8	−	1.02264e8i	−1.30954	−	0.282132i
$714$	−1.49250e8			−0.410035
$715$	−3.96685e8	−	4.57799e8i	−1.08525	−	1.25244i
$716$	1.22159e8	+	7.85070e7i	0.332803	+	0.213880i
$717$	4.73235e7	−	3.29142e8i	0.128387	−	0.892949i
$718$	3.32456e8	+	1.51828e8i	0.898176	+	0.410183i
$719$	2.16159e7	+	1.50342e8i	0.0581551	+	0.404477i	0.998018	+	0.0629260i	$0.0200432\pi$
$719$	2.16159e7	+	1.50342e8i	0.0581551	+	0.404477i	−0.939863	+	0.341551i	$0.889048\pi$
$720$	−1.85165e7	+	6.30612e7i	−0.0496090	+	0.168953i
$721$	3.74972e8	−	2.40980e8i	1.00044	−	0.642947i
$722$	8.38340e7	+	1.83571e8i	0.222745	+	0.487744i
$723$	−2.50023e7	−	8.51500e7i	−0.0661554	−	0.225304i
$724$	9.76903e7	+	8.46491e7i	0.257416	+	0.223052i
$725$	4.42709e8	−	5.10914e8i	1.16173	−	1.34071i
$726$	3.02134e8	−	8.87145e7i	0.789568	−	0.231838i
$727$	−1.06911e8	+	4.88248e7i	−0.278241	+	0.127068i	−0.549648	−	0.835396i	$-0.685238\pi$
$727$	−1.06911e8	+	4.88248e7i	−0.278241	+	0.127068i	0.271407	+	0.962465i	$0.412511\pi$
$728$	−2.15681e8	−	3.35606e8i	−0.559007	−	0.869832i
$729$	−1.37677e7	−	4.04255e6i	−0.0355368	−	0.0104345i
$730$	−3.53624e8	+	5.08435e7i	−0.909020	+	0.130697i
$731$	−3.38544e7	+	7.41307e7i	−0.0866688	+	0.189778i
$732$	−3.44734e7	−	4.95652e6i	−0.0878922	−	0.0126370i
$733$	3.33644e8	−	5.19160e8i	0.847171	−	1.31822i	−0.0991756	−	0.995070i	$-0.531621\pi$
$733$	3.33644e8	−	5.19160e8i	0.847171	−	1.31822i	0.946347	−	0.323154i	$-0.104743\pi$
$734$	2.03699e8	−	1.76506e8i	0.515110	−	0.446345i
$735$		−	4.77190e8i		−	1.20179i
$736$	1.13837e8	−	3.07082e8i	0.285529	−	0.770231i
$737$	−7.91997e8			−1.97843
$738$	−8.62124e7	−	9.94944e7i	−0.214487	−	0.247531i
$739$	6.42417e7	+	4.12857e7i	0.159178	+	0.102298i	0.617805	−	0.786331i	$-0.288022\pi$
$739$	6.42417e7	+	4.12857e7i	0.159178	+	0.102298i	−0.458627	+	0.888629i	$0.651658\pi$
$740$	−4.11515e6	+	2.86215e7i	−0.0101552	+	0.0706312i
$741$	−7.03668e7	−	3.21354e7i	−0.172947	−	0.0789823i
$742$	−1.26244e8	−	8.78048e8i	−0.309030	−	2.14935i
$743$	−6.07276e7	+	2.06819e8i	−0.148054	+	0.504225i	−0.999806	−	0.0197204i	$-0.993722\pi$
$743$	−6.07276e7	+	2.06819e8i	−0.148054	+	0.504225i	0.851752	+	0.523946i	$0.175541\pi$
$744$	−2.87967e8	+	1.85065e8i	−0.699236	+	0.449372i
$745$	3.15193e8	+	6.90177e8i	0.762269	+	1.66914i
$746$	−2.05319e7	−	6.99251e7i	−0.0494552	−	0.168429i
$747$	−7.10099e7	−	6.15304e7i	−0.170356	−	0.147614i
$748$	1.32957e8	−	1.53440e8i	0.317692	−	0.366636i
$749$	1.51063e8	−	4.43560e7i	0.359510	−	0.105562i
$750$	9.64369e7	−	4.40412e7i	0.228591	−	0.104394i
$751$	−8.91869e7	−	1.38777e8i	−0.210563	−	0.327642i	0.719867	−	0.694112i	$-0.244203\pi$
$751$	−8.91869e7	−	1.38777e8i	−0.210563	−	0.327642i	−0.930430	+	0.366470i	$0.880566\pi$
$752$	1.33991e8	+	3.93433e7i	0.315081	+	0.0925160i
$753$	2.95817e7	−	4.25320e6i	0.0692847	−	0.00996164i
$754$	1.06209e8	−	2.32566e8i	0.247770	−	0.542541i
$755$	−1.03356e9	−	1.48604e8i	−2.40157	−	0.345294i
$756$	3.11929e7	−	4.85370e7i	0.0721921	−	0.112333i
$757$	6.18116e8	−	5.35601e8i	1.42489	−	1.23468i	0.493962	−	0.869483i	$-0.335548\pi$
$757$	6.18116e8	−	5.35601e8i	1.42489	−	1.23468i	0.930932	−	0.365194i	$-0.118997\pi$
$758$			4.95566e8i			1.13787i
$759$	2.06214e8	−	3.79454e8i	0.471620	−	0.867828i
$760$	−3.81903e8			−0.869985
$761$	3.53859e8	+	4.08376e8i	0.802928	+	0.926629i	0.998538	−	0.0540531i	$-0.0172140\pi$
$761$	3.53859e8	+	4.08376e8i	0.802928	+	0.926629i	−0.195610	+	0.980682i	$0.562669\pi$
$762$	2.71477e8	+	1.74467e8i	0.613575	+	0.394321i
$763$	−7.76486e7	+	5.40058e8i	−0.174808	+	1.21581i
$764$	−1.62451e8	−	7.41891e7i	−0.364287	−	0.166364i
$765$	2.05287e7	+	1.42780e8i	0.0458539	+	0.318921i
$766$	−7.45479e7	+	2.53887e8i	−0.165863	+	0.564877i
$767$	3.29411e8	−	2.11700e8i	0.730050	−	0.469174i
$768$	−1.12750e8	−	2.46887e8i	−0.248904	−	0.545023i
$769$	8.00905e7	+	2.72763e8i	0.176117	+	0.599800i	0.999479	+	0.0322832i	$0.0102778\pi$
$769$	8.00905e7	+	2.72763e8i	0.176117	+	0.599800i	−0.823361	+	0.567517i	$0.807904\pi$
$770$	−1.03271e9	−	8.94851e8i	−2.26208	−	1.96010i
$771$	2.61013e8	−	3.01225e8i	0.569506	−	0.657245i
$772$	2.62788e8	−	7.71614e7i	0.571154	−	0.167706i
$773$	1.05686e8	−	4.82653e7i	0.228813	−	0.104495i	−0.297710	−	0.954656i	$-0.596223\pi$
$773$	1.05686e8	−	4.82653e7i	0.228813	−	0.104495i	0.526523	+	0.850161i	$0.323496\pi$
$774$	2.05899e7	+	3.20384e7i	0.0444049	+	0.0690953i
$775$	8.26417e8	+	2.42658e8i	1.77539	+	0.521302i
$776$	7.18333e8	−	1.03281e8i	1.53724	−	0.221021i
$777$	−1.76126e7	+	3.85662e7i	−0.0375457	+	0.0822137i
$778$	1.00768e7	+	1.44882e6i	0.0213984	+	0.00307663i
$779$	1.78078e8	−	2.77094e8i	0.376701	−	0.586158i
$780$	−9.08079e7	+	7.86855e7i	−0.191355	+	0.165810i
$781$			4.13993e8i			0.869041i
$782$	1.62505e7	+	2.21002e8i	0.0339818	+	0.462143i
$783$	1.18653e8			0.247168
$784$	−1.45721e8	−	1.68171e8i	−0.302394	−	0.348981i
$785$	2.47659e8	+	1.59161e8i	0.511971	+	0.329024i
$786$	−2.68614e7	+	1.86825e8i	−0.0553172	+	0.384740i
$787$	6.35928e8	+	2.90419e8i	1.30462	+	0.595800i	0.941836	−	0.336074i	$-0.109099\pi$
$787$	6.35928e8	+	2.90419e8i	1.30462	+	0.595800i	0.362784	+	0.931873i	$0.381826\pi$
$788$	−2.50727e7	−	1.74384e8i	−0.0512416	−	0.356393i
$789$	−7.69229e7	+	2.61975e8i	−0.156612	+	0.533371i
$790$	9.77873e7	−	6.28441e7i	0.198336	−	0.127463i
$791$	1.86306e8	+	4.07953e8i	0.376441	+	0.824292i
$792$	−8.57756e7	−	2.92125e8i	−0.172659	−	0.588021i
$793$	8.03731e7	+	6.96437e7i	0.161173	+	0.139657i
$794$	−1.28969e8	+	1.48838e8i	−0.257647	+	0.297340i
$795$	−8.22619e8	+	2.41543e8i	−1.63718	+	0.480721i
$796$	1.07165e8	−	4.89408e7i	0.212479	−	0.0970357i
$797$	8.90951e7	+	1.38635e8i	0.175986	+	0.273840i	0.918030	−	0.396512i	$-0.129779\pi$
$797$	8.90951e7	+	1.38635e8i	0.175986	+	0.273840i	−0.742043	+	0.670352i	$0.766143\pi$
$798$	−1.67436e8	−	4.91636e7i	−0.329488	−	0.0967464i
$799$	3.03375e8	−	4.36188e7i	0.594758	−	0.0855133i
$800$	−2.41333e8	+	5.28445e8i	−0.471353	+	1.03212i
$801$	8.73849e7	+	1.25641e7i	0.170035	+	0.0244474i
$802$	2.29986e7	−	3.57865e7i	0.0445839	−	0.0693739i
$803$	5.38538e8	−	4.66646e8i	1.04009	−	0.901241i
$804$			1.57099e8i			0.302276i
$805$	−1.23043e9	+	9.04745e7i	−2.35867	+	0.173436i
$806$	3.25739e8			0.622105
$807$	3.90198e8	+	4.50312e8i	0.742444	+	0.856826i
$808$	−7.94981e7	−	5.10903e7i	−0.150703	−	0.0968511i
$809$	2.81000e7	−	1.95440e8i	0.0530714	−	0.369120i	−0.945927	−	0.324379i	$-0.894845\pi$
$809$	2.81000e7	−	1.95440e8i	0.0530714	−	0.369120i	0.998999	−	0.0447407i	$-0.0142462\pi$
$810$	6.13181e7	+	2.80030e7i	0.115381	+	0.0526926i
$811$	−4.33757e7	−	3.01685e8i	−0.0813175	−	0.565576i	−0.989225	−	0.146405i	$-0.953230\pi$
$811$	−4.33757e7	−	3.01685e8i	−0.0813175	−	0.565576i	0.907907	−	0.419171i	$-0.137679\pi$
$812$	−1.34413e8	+	4.57769e8i	−0.251058	+	0.855024i
$813$	1.14504e8	−	7.35875e7i	0.213084	−	0.136941i
$814$	2.89635e7	+	6.34213e7i	0.0537005	+	0.117588i
$815$	−5.50415e7	−	1.87454e8i	−0.101676	−	0.346276i
$816$	5.08358e7	+	4.40494e7i	0.0935619	+	0.0810718i
$817$	−6.23983e7	+	7.20115e7i	−0.114421	+	0.132049i
$818$	−6.45317e8	+	1.89482e8i	−1.17900	+	0.346185i
$819$	−1.60257e8	+	7.31871e7i	−0.291720	+	0.133224i
$820$	−2.76600e8	−	4.30399e8i	−0.501662	−	0.780601i
$821$	−3.27100e8	−	9.60454e7i	−0.591087	−	0.173559i	−0.0275090	−	0.999622i	$-0.508758\pi$
$821$	−3.27100e8	−	9.60454e7i	−0.591087	−	0.173559i	−0.563578	+	0.826063i	$0.690576\pi$
$822$	2.76317e8	−	3.97284e7i	0.497499	−	0.0715295i
$823$	−4.06641e8	+	8.90419e8i	−0.729476	+	1.59733i	0.0706516	+	0.997501i	$0.477492\pi$
$823$	−4.06641e8	+	8.90419e8i	−0.729476	+	1.59733i	−0.800128	+	0.599829i	$0.795235\pi$
$824$	−4.61804e8	−	6.63974e7i	−0.825422	−	0.118678i
$825$	−4.14169e8	+	6.44459e8i	−0.737591	+	1.14771i
$826$	6.67565e8	−	5.78449e8i	1.18455	−	1.02642i
$827$		−	9.33672e8i		−	1.65074i	−0.564595	−	0.825368i	$-0.690968\pi$
$827$		−	9.33672e8i		−	1.65074i	0.564595	−	0.825368i	$-0.309032\pi$
$828$	−7.52675e7	−	4.09041e7i	−0.132592	−	0.0720569i
$829$	4.65973e8			0.817894			0.408947	−	0.912558i	$-0.365896\pi$
$829$	4.65973e8			0.817894			0.408947	+	0.912558i	$0.365896\pi$
$830$	2.89064e8	+	3.33597e8i	0.505544	+	0.583429i
$831$	6.65315e7	+	4.27572e7i	0.115938	+	0.0745086i
$832$	−4.88813e7	+	3.39977e8i	−0.0848735	+	0.590308i
$833$	−4.44250e8	−	2.02882e8i	−0.768586	−	0.351002i
$834$	−5.59525e7	−	3.89158e8i	−0.0964543	−	0.670854i
$835$	1.30493e8	−	4.44419e8i	0.224145	−	0.763366i
$836$	1.99701e8	−	1.28340e8i	0.341792	−	0.219656i
$837$	6.27982e7	+	1.37509e8i	0.107095	+	0.234506i
$838$	2.50318e7	+	8.52504e7i	0.0425363	+	0.144865i
$839$	−2.47424e6	−	2.14394e6i	−0.00418943	−	0.00363017i	0.652764	−	0.757562i	$-0.273610\pi$
$839$	−2.47424e6	−	2.14394e6i	−0.00418943	−	0.00363017i	−0.656953	+	0.753932i	$0.728155\pi$
$840$	−5.69576e8	+	6.57326e8i	−0.960979	+	1.10903i
$841$	−3.70678e8	+	1.08841e8i	−0.623174	+	0.182980i
$842$	3.39567e8	−	1.55075e8i	0.568838	−	0.259780i
$843$	2.75584e8	+	4.28817e8i	0.460014	+	0.715796i
$844$	−4.40900e8	−	1.29460e8i	−0.733352	−	0.215332i
$845$	−5.58409e8	+	8.02871e7i	−0.925513	+	0.133069i
$846$	5.95001e7	−	1.30287e8i	0.0982668	−	0.215174i
$847$	1.77601e9	+	2.55351e8i	2.92277	+	0.420230i
$848$	−2.16146e8	+	3.36329e8i	−0.354453	+	0.551540i
$849$	−1.70126e8	+	1.47415e8i	−0.278002	+	0.240890i
$850$		−	3.93084e8i		−	0.640072i
$851$	5.90246e7	+	2.18807e7i	0.0957733	+	0.0355037i
$852$	8.21187e7			0.132777
$853$	−1.62257e8	−	1.87255e8i	−0.261431	−	0.301707i	0.609825	−	0.792536i	$-0.291240\pi$
$853$	−1.62257e8	−	1.87255e8i	−0.261431	−	0.301707i	−0.871256	+	0.490829i	$0.836694\pi$
$854$	2.01820e8	+	1.29702e8i	0.324034	+	0.208244i
$855$	−2.40023e7	+	1.66939e8i	−0.0384020	+	0.267092i
$856$	−1.49903e8	−	6.84583e7i	−0.238995	−	0.109145i
$857$	4.47043e7	+	3.10926e8i	0.0710243	+	0.493985i	0.994022	+	0.109180i	$0.0348224\pi$
$857$	4.47043e7	+	3.10926e8i	0.0710243	+	0.493985i	−0.922998	+	0.384806i	$0.874269\pi$
$858$	−8.16239e7	+	2.77985e8i	−0.129228	+	0.440109i
$859$	−3.87499e8	+	2.49030e8i	−0.611351	+	0.392892i	−0.809364	−	0.587308i	$-0.800188\pi$
$859$	−3.87499e8	+	2.49030e8i	−0.611351	+	0.392892i	0.198012	+	0.980200i	$0.436551\pi$
$860$	6.14823e7	+	1.34627e8i	0.0966617	+	0.211660i
$861$	−2.11343e8	−	7.19768e8i	−0.331114	−	1.12767i
$862$	−6.47348e7	−	5.60930e7i	−0.101069	−	0.0875764i
$863$	−2.54492e8	+	2.93700e8i	−0.395952	+	0.456953i	−0.918362	−	0.395741i	$-0.870488\pi$
$863$	−2.54492e8	+	2.93700e8i	−0.395952	+	0.456953i	0.522410	+	0.852694i	$0.325033\pi$
$864$	−9.78325e7	+	2.87262e7i	−0.151685	+	0.0445387i
$865$	3.00477e8	−	1.37223e8i	0.464262	−	0.212021i
$866$	9.68269e7	+	1.50666e8i	0.149088	+	0.231985i
$867$	−2.19374e8	−	6.44140e7i	−0.336610	−	0.0988377i
$868$	−6.01658e8	+	8.65054e7i	−0.920006	+	0.132277i
$869$	−9.63144e7	+	2.10899e8i	−0.146768	+	0.321377i
$870$	−5.51745e8	−	7.93289e7i	−0.837877	−	0.120469i
$871$	2.59350e8	−	4.03557e8i	0.392494	−	0.610732i
$872$	4.31609e8	−	3.73991e8i	0.650940	−	0.564043i
$873$		−	3.20493e8i		−	0.481699i
$874$	−5.45684e7	+	2.53284e8i	−0.0817348	+	0.379378i
$875$	6.04097e8			0.901743
$876$	−9.25627e7	−	1.06823e8i	−0.137697	−	0.158911i
$877$	−6.52525e8	−	4.19352e8i	−0.967383	−	0.621699i	−0.0413511	−	0.999145i	$-0.513166\pi$
$877$	−6.52525e8	−	4.19352e8i	−0.967383	−	0.621699i	−0.926032	+	0.377445i	$0.876803\pi$
$878$	3.36117e7	−	2.33774e8i	0.0496600	−	0.345393i
$879$	1.33329e8	+	6.08892e7i	0.196317	+	0.0896549i
$880$	8.76452e7	+	6.09586e8i	0.128612	+	0.894514i
$881$	2.24207e7	−	7.63578e7i	0.0327884	−	0.111667i	−0.941473	−	0.337089i	$-0.890558\pi$
$881$	2.24207e7	−	7.63578e7i	0.0327884	−	0.111667i	0.974261	+	0.225422i	$0.0723759\pi$
$882$	−1.92000e8	+	1.23391e8i	−0.279831	+	0.179836i
$883$	−4.20950e6	−	9.21752e6i	−0.00611432	−	0.0133885i	0.906550	−	0.422098i	$-0.138706\pi$
$883$	−4.20950e6	−	9.21752e6i	−0.00611432	−	0.0133885i	−0.912665	+	0.408710i	$0.865979\pi$
$884$	3.46461e7	+	1.17994e8i	0.0501530	+	0.170805i
$885$	−6.45193e8	−	5.59063e8i	−0.930807	−	0.806549i
$886$	2.65380e8	−	3.06265e8i	0.381564	−	0.440348i
$887$	3.18297e8	−	9.34604e7i	0.456101	−	0.133923i	−0.0456085	−	0.998959i	$-0.514523\pi$
$887$	3.18297e8	−	9.34604e7i	0.456101	−	0.133923i	0.501710	+	0.865036i	$0.332705\pi$
$888$	4.03679e7	−	1.84354e7i	0.0576497	−	0.0263278i
$889$	9.94132e8	+	1.54690e9i	1.41494	+	2.20169i
$890$	−3.97947e8	−	1.16848e8i	−0.564489	−	0.165749i
$891$	−1.33086e8	+	1.91349e7i	−0.188148	+	0.0270516i
$892$	−1.05661e8	+	2.31366e8i	−0.148875	+	0.325990i
$893$	3.54709e8	+	5.09994e7i	0.498101	+	0.0716161i
$894$	1.96194e8	−	3.05284e8i	0.274583	−	0.427260i
$895$	−7.30607e8	+	6.33074e8i	−1.01909	+	0.883051i
$896$		−	1.30795e8i		−	0.181830i
$897$	1.25821e8	+	2.29332e8i	0.174331	+	0.317752i
$898$	3.65775e8			0.505110
$899$	−8.18602e8	−	9.44717e8i	−1.12666	−	1.30024i
$900$	1.27833e8	+	8.21535e7i	0.175354	+	0.112693i
$901$	−1.24876e8	+	8.68530e8i	−0.170728	+	1.18744i
$902$	−1.12213e9	−	5.12460e8i	−1.52906	−	0.698298i
$903$	3.08834e7	+	2.14798e8i	0.0419432	+	0.291721i
$904$	1.32255e8	−	4.50418e8i	0.179022	−	0.609691i
$905$	−7.23946e8	+	4.65252e8i	−0.976699	+	0.627686i
$906$	2.07465e8	+	4.54285e8i	0.278972	+	0.610863i
$907$	−7.44147e7	−	2.53433e8i	−0.0997326	−	0.339658i	0.894477	−	0.447113i	$-0.147548\pi$
$907$	−7.44147e7	−	2.53433e8i	−0.0997326	−	0.339658i	−0.994210	+	0.107455i	$0.965730\pi$
$908$	4.55021e8	+	3.94278e8i	0.607818	+	0.526678i
$909$	−2.73293e7	+	3.15397e7i	−0.0363862	+	0.0419919i
$910$	7.94142e8	−	2.33181e8i	1.05384	−	0.309435i
$911$	−5.88634e8	+	2.68820e8i	−0.778556	+	0.355555i	−0.764731	−	0.644350i	$-0.777128\pi$
$911$	−5.88634e8	+	2.68820e8i	−0.778556	+	0.355555i	−0.0138252	+	0.999904i	$0.504401\pi$
$912$	4.25199e7	+	6.61622e7i	0.0560541	+	0.0872219i
$913$	−8.44773e8	−	2.48048e8i	−1.11001	−	0.325929i
$914$	1.32378e8	−	1.90331e7i	0.173372	−	0.0249271i
$915$	9.63197e7	−	2.10911e8i	0.125734	−	0.275318i
$916$	−2.92915e8	−	4.21148e7i	−0.381114	−	0.0547959i
$917$	−5.81455e8	+	9.04762e8i	−0.754064	+	1.17335i
$918$	5.21401e7	−	4.51796e7i	0.0673974	−	0.0584002i
$919$			6.27077e7i			0.0807931i	0.999184	+	0.0403965i	$0.0128621\pi$
$919$			6.27077e7i			0.0807931i	−0.999184	+	0.0403965i	$0.987138\pi$
$920$	1.03535e9	+	7.71830e8i	1.32961	+	0.991192i
$921$	−5.57774e8			−0.713970
$922$	−1.51102e8	−	1.74381e8i	−0.192787	−	0.222487i
$923$	−2.10948e8	−	1.35568e8i	−0.268268	−	0.172406i
$924$	7.69403e7	−	5.35132e8i	0.0975300	−	0.678336i
$925$	−1.01573e8	−	4.63868e7i	−0.128337	−	0.0586097i
$926$	5.90328e7	+	4.10582e8i	0.0743465	+	0.517091i
$927$	−5.80480e7	+	1.97693e8i	−0.0728699	+	0.248172i
$928$	7.09295e8	−	4.55836e8i	0.887530	−	0.570381i
$929$	−2.87227e8	−	6.28939e8i	−0.358243	−	0.784444i	−0.999848	−	0.0174084i	$-0.994458\pi$
$929$	−2.87227e8	−	6.28939e8i	−0.358243	−	0.784444i	0.641605	−	0.767035i	$-0.278269\pi$
$930$	−2.00081e8	−	6.81414e8i	−0.248747	−	0.847153i
$931$	−4.31550e8	−	3.73940e8i	−0.534789	−	0.463397i
$932$	−1.31674e8	+	1.51960e8i	−0.162650	+	0.187708i
$933$	−6.53513e8	+	1.91889e8i	−0.804654	+	0.236268i
$934$	9.28952e8	−	4.24238e8i	1.14013	−	0.520678i
$935$	7.30764e8	+	1.13709e9i	0.894009	+	1.39111i
$936$	1.76939e8	+	5.19539e7i	0.215772	+	0.0633564i
$937$	4.82519e8	−	6.93758e7i	0.586538	−	0.0843314i	0.157344	−	0.987544i	$-0.449707\pi$
$937$	4.82519e8	−	6.93758e7i	0.586538	−	0.0843314i	0.429194	+	0.903212i	$0.358798\pi$
$938$	4.49536e8	−	9.84347e8i	0.544699	−	1.19272i
$939$	−1.64906e8	−	2.37100e7i	−0.199178	−	0.0286374i
$940$	3.00932e8	−	4.68259e8i	0.362313	−	0.563770i
$941$	−4.83137e8	+	4.18640e8i	−0.579831	+	0.502426i	−0.894675	−	0.446717i	$-0.852593\pi$
$941$	−4.83137e8	+	4.18640e8i	−0.579831	+	0.502426i	0.314845	+	0.949143i	$0.398048\pi$
$942$		−	1.40803e8i		−	0.168445i
$943$	−1.04278e9	+	3.91315e8i	−1.24354	+	0.466650i
$944$	−3.98100e8			−0.473235
$945$	2.51537e8	+	2.90289e8i	0.298062	+	0.343981i
$946$	3.00213e8	+	1.92935e8i	0.354614	+	0.227896i
$947$	6.37101e7	−	4.43114e8i	0.0750168	−	0.521753i	−0.917316	−	0.398160i	$-0.869649\pi$
$947$	6.37101e7	−	4.43114e8i	0.0750168	−	0.521753i	0.992333	−	0.123594i	$-0.0394420\pi$
$948$	4.18334e7	+	1.91047e7i	0.0491019	+	0.0224241i
$949$	6.14247e7	+	4.27219e8i	0.0718695	+	0.499863i
$950$	1.29483e8	−	4.40980e8i	0.151023	−	0.514338i
$951$	3.74039e8	−	2.40380e8i	0.434886	−	0.279484i
$952$	3.69791e8	+	8.09728e8i	0.428593	+	0.938488i
$953$	−4.58300e8	−	1.56083e9i	−0.529506	−	1.80333i	−0.592815	−	0.805338i	$-0.701984\pi$
$953$	−4.58300e8	−	1.56083e9i	−0.529506	−	1.80333i	0.0633093	−	0.997994i	$-0.479835\pi$
$954$	3.09897e8	+	2.68528e8i	0.356922	+	0.309274i
$955$	7.78597e8	−	8.98549e8i	0.893928	−	1.03165i
$956$	−5.93028e8	+	1.74129e8i	−0.678737	+	0.199295i
$957$	1.01135e9	−	4.61867e8i	1.15389	−	0.526964i
$958$	−5.12386e8	−	7.97288e8i	−0.582774	−	0.906815i
$959$	1.52624e9	+	4.48144e8i	1.73048	+	0.508115i
$960$	7.41223e8	−	1.06572e8i	0.837790	−	0.120456i
$961$	2.92915e8	−	6.41395e8i	0.330044	−	0.722695i
$962$	−4.18004e7	−	6.01000e6i	−0.0469522	−	0.00675070i
$963$	−3.93462e7	+	6.12238e7i	−0.0440579	+	0.0685554i
$964$	−1.24660e8	+	1.08018e8i	−0.139154	+	0.120578i
$965$			1.82335e9i			2.02903i
$966$	3.54564e8	+	4.71674e8i	0.393336	+	0.523251i
$967$	1.26861e9			1.40297			0.701484	−	0.712685i	$-0.252521\pi$
$967$	1.26861e9			1.40297			0.701484	+	0.712685i	$0.252521\pi$
$968$	−1.22989e9	−	1.41937e9i	−1.35594	−	1.56483i
$969$	1.45211e8	+	9.33215e7i	0.159598	+	0.102568i
$970$	−2.14276e8	+	1.49032e9i	−0.234778	+	1.63292i
$971$	−3.67009e8	−	1.67607e8i	−0.400884	−	0.183078i	0.204762	−	0.978812i	$-0.434358\pi$
$971$	−3.67009e8	−	1.67607e8i	−0.400884	−	0.183078i	−0.605646	+	0.795734i	$0.707085\pi$
$972$	3.79555e6	+	2.63987e7i	0.00413310	+	0.0287464i
$973$	6.31155e8	−	2.14952e9i	0.685169	−	2.33347i
$974$	−4.29533e8	+	2.76044e8i	−0.464857	+	0.298745i
$975$	−1.92755e8	−	4.22074e8i	−0.207966	−	0.455381i
$976$	−3.04615e7	−	1.03742e8i	−0.0327643	−	0.111585i
$977$	8.23751e8	+	7.13785e8i	0.883309	+	0.765391i	0.973055	−	0.230573i	$-0.0740602\pi$
$977$	8.23751e8	+	7.13785e8i	0.883309	+	0.765391i	−0.0897464	+	0.995965i	$0.528606\pi$
$978$	−6.11907e7	+	7.06178e7i	−0.0654137	+	0.0754914i
$979$	7.93741e8	−	2.33063e8i	0.845923	−	0.248385i
$980$	−8.06795e8	+	3.68451e8i	−0.857205	+	0.391472i
$981$	−1.36355e8	−	2.12172e8i	−0.144432	−	0.224741i
$982$	−1.10219e9	−	3.23633e8i	−1.16392	−	0.341758i
$983$	3.44538e8	−	4.95370e7i	0.362724	−	0.0521518i	0.0414564	−	0.999140i	$-0.486800\pi$
$983$	3.44538e8	−	4.95370e7i	0.362724	−	0.0521518i	0.321267	+	0.946989i	$0.395891\pi$
$984$	−3.26183e8	+	7.14242e8i	−0.342355	+	0.749652i
$985$	1.16095e9	+	1.66920e8i	1.21480	+	0.174662i
$986$	−3.08433e8	+	4.79931e8i	−0.321759	+	0.500666i
$987$	6.16798e8	−	5.34459e8i	0.641493	−	0.555857i
$988$			1.43783e8i			0.149086i
$989$	3.14700e8	−	6.91180e7i	0.325318	−	0.0714500i
$990$	6.31655e8			0.650990
$991$	−9.46772e7	−	1.09263e8i	−0.0972801	−	0.112267i	0.705022	−	0.709185i	$-0.250937\pi$
$991$	−9.46772e7	−	1.09263e8i	−0.0972801	−	0.112267i	−0.802302	+	0.596918i	$0.796392\pi$
$992$	9.03680e8	+	5.80760e8i	0.925720	+	0.594924i
$993$	3.82794e7	−	2.66239e8i	0.0390947	−	0.271909i
$994$	−5.14539e8	−	2.34982e8i	−0.523913	−	0.239263i
$995$	1.11621e8	+	7.76339e8i	0.113312	+	0.788101i
$996$	−4.92021e7	+	1.67567e8i	−0.0497973	+	0.169594i
$997$	7.56038e8	−	4.85876e8i	0.762884	−	0.490276i	−0.100429	−	0.994944i	$-0.532022\pi$
$997$	7.56038e8	−	4.85876e8i	0.762884	−	0.490276i	0.863313	+	0.504669i	$0.168385\pi$
$998$	−1.09536e8	−	2.39851e8i	−0.110196	−	0.241296i
$999$	−5.52150e6	−	1.88045e7i	−0.00553810	−	0.0188610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.10.9	yes	240
23.7	odd	22	inner	69.7.f.a.7.9	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.9	✓	240	23.7	odd	22	inner
69.7.f.a.10.9	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.87564 - 4.47273i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.12344 - 28.6791i) q^{4} +(175.461 + 80.1304i) q^{5} +(-13.1295 - 91.3177i) q^{6} +(148.103 - 504.394i) q^{7} +(-462.896 + 297.485i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})\)	\(q+(-3.87564 - 4.47273i) q^{2} +(13.1138 + 8.42776i) q^{3} +(4.12344 - 28.6791i) q^{4} +(175.461 + 80.1304i) q^{5} +(-13.1295 - 91.3177i) q^{6} +(148.103 - 504.394i) q^{7} +(-462.896 + 297.485i) q^{8} +(100.946 + 221.041i) q^{9} +(-321.623 - 1095.35i) q^{10} +(1720.84 + 1491.12i) q^{11} +(295.775 - 341.342i) q^{12} +(-1323.31 + 388.558i) q^{13} +(-2830.01 + 1292.42i) q^{14} +(1625.65 + 2529.56i) q^{15} +(1345.37 + 395.036i) q^{16} +(3046.11 - 437.965i) q^{17} +(597.425 - 1308.18i) q^{18} +(3561.54 + 512.072i) q^{19} +(3021.57 - 4701.66i) q^{20} +(6193.11 - 5366.36i) q^{21} -13475.9i q^{22} +(-8620.55 - 8586.15i) q^{23} -8577.48 q^{24} +(14133.5 + 16311.0i) q^{25} +(6866.58 + 4412.88i) q^{26} +(-539.088 + 3749.44i) q^{27} +(-13854.9 - 6327.31i) q^{28} +(-4457.77 - 31004.5i) q^{29} +(5013.61 - 17074.8i) q^{30} +(33572.4 - 21575.7i) q^{31} +(11181.9 + 24484.9i) q^{32} +(10000.1 + 34057.2i) q^{33} +(-13764.6 - 11927.1i) q^{34} +(66403.7 - 76633.9i) q^{35} +(6755.50 - 1983.59i) q^{36} +(-4706.27 + 2149.28i) q^{37} +(-11512.9 - 17914.4i) q^{38} +(-20628.3 - 6057.01i) q^{39} +(-105058. + 15105.0i) q^{40} +(38027.8 - 83269.4i) q^{41} +(-48004.6 - 6902.02i) q^{42} +(-14317.0 + 22277.7i) q^{43} +(49859.8 - 43203.8i) q^{44} +46872.9i q^{45} +(-4993.37 + 71834.3i) q^{46} +99594.3 q^{47} +(14313.7 + 16518.9i) q^{48} +(-133506. - 85798.9i) q^{49} +(18178.0 - 126431. i) q^{50} +(43637.3 + 19928.5i) q^{51} +(5686.93 + 39553.5i) q^{52} +(-80329.6 + 273578. i) q^{53} +(18859.5 - 12120.3i) q^{54} +(182457. + 399526. i) q^{55} +(81493.2 + 277540. i) q^{56} +(42389.8 + 36731.0i) q^{57} +(-121398. + 140101. i) q^{58} +(-272418. + 79989.0i) q^{59} +(79248.9 - 36191.8i) q^{60} +(-41689.2 - 64869.6i) q^{61} +(-226617. - 66540.8i) q^{62} +(126442. - 18179.6i) q^{63} +(103456. - 226537. i) q^{64} +(-263324. - 37860.3i) q^{65} +(113572. - 176721. i) q^{66} +(-262868. + 227776. i) q^{67} -89165.8i q^{68} +(-40686.6 - 185249. i) q^{69} -600120. q^{70} +(119063. + 137407. i) q^{71} +(-112484. - 72288.9i) q^{72} +(44537.4 - 309765. i) q^{73} +(27853.0 + 12720.0i) q^{74} +(47880.1 + 333013. i) q^{75} +(29371.6 - 100030. i) q^{76} +(1.00697e6 - 647143. i) q^{77} +(52856.5 + 115740. i) q^{78} +(28686.8 + 97698.3i) q^{79} +(204405. + 177118. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(-519824. + 152634. i) q^{82} +(-351722. + 160626. i) q^{83} +(-128366. - 199741. i) q^{84} +(569569. + 167241. i) q^{85} +(155130. - 22304.3i) q^{86} +(202840. - 444157. i) q^{87} +(-1.24016e6 - 178308. i) q^{88} +(196418. - 305633. i) q^{89} +(209650. - 181663. i) q^{90} +725014. i q^{91} +(-281790. + 211825. i) q^{92} +622098. q^{93} +(-385992. - 445458. i) q^{94} +(583879. + 375236. i) q^{95} +(-59715.3 + 415329. i) q^{96} +(-1.19971e6 - 547891. i) q^{97} +(133665. + 929661. i) q^{98} +(-155886. + 530899. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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