LMFDB - Embedded newform 43.7.d.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95704i q^{2} +(10.4424 + 6.02890i) q^{3} +60.1700 q^{4} +(-193.167 - 111.525i) q^{5} +(11.7988 - 20.4361i) q^{6} +(-30.2778 + 17.4809i) q^{7} -243.006i q^{8} +(-291.805 - 505.421i) q^{9} +O(q^{10})$	\(q-1.95704i q^{2} +(10.4424 + 6.02890i) q^{3} +60.1700 q^{4} +(-193.167 - 111.525i) q^{5} +(11.7988 - 20.4361i) q^{6} +(-30.2778 + 17.4809i) q^{7} -243.006i q^{8} +(-291.805 - 505.421i) q^{9} +(-218.259 + 378.036i) q^{10} +688.201 q^{11} +(628.316 + 362.759i) q^{12} +(-591.384 - 1024.31i) q^{13} +(34.2108 + 59.2549i) q^{14} +(-1344.75 - 2329.17i) q^{15} +3375.31 q^{16} +(-2373.46 - 4110.95i) q^{17} +(-989.130 + 571.075i) q^{18} +(-8832.15 - 5099.24i) q^{19} +(-11622.8 - 6710.45i) q^{20} -421.562 q^{21} -1346.84i q^{22} +(1298.84 - 2249.66i) q^{23} +(1465.06 - 2537.56i) q^{24} +(17063.1 + 29554.2i) q^{25} +(-2004.61 + 1157.36i) q^{26} -15827.2i q^{27} +(-1821.81 + 1051.82i) q^{28} +(34988.7 - 20200.7i) q^{29} +(-4558.28 + 2631.72i) q^{30} +(-27966.9 + 48440.1i) q^{31} -22158.0i q^{32} +(7186.44 + 4149.09i) q^{33} +(-8045.30 + 4644.96i) q^{34} +7798.21 q^{35} +(-17557.9 - 30411.2i) q^{36} +(40553.8 + 23413.8i) q^{37} +(-9979.44 + 17284.9i) q^{38} -14261.6i q^{39} +(-27101.2 + 46940.7i) q^{40} +46510.8 q^{41} +825.014i q^{42} +(71663.4 + 34434.3i) q^{43} +41409.1 q^{44} +130174. i q^{45} +(-4402.68 - 2541.89i) q^{46} -54839.3 q^{47} +(35246.1 + 20349.4i) q^{48} +(-58213.3 + 100828. i) q^{49} +(57838.9 - 33393.3i) q^{50} -57237.3i q^{51} +(-35583.6 - 61632.6i) q^{52} +(31883.7 - 55224.1i) q^{53} -30974.5 q^{54} +(-132938. - 76751.6i) q^{55} +(4247.96 + 7357.68i) q^{56} +(-61485.6 - 106496. i) q^{57} +(-39533.7 - 68474.4i) q^{58} -215519. q^{59} +(-80913.3 - 140146. i) q^{60} +(213769. - 123420. i) q^{61} +(94799.4 + 54732.5i) q^{62} +(17670.4 + 10202.0i) q^{63} +172655. q^{64} +263816. i q^{65} +(8119.96 - 14064.2i) q^{66} +(-49805.9 + 86266.3i) q^{67} +(-142811. - 247356. i) q^{68} +(27125.9 - 15661.2i) q^{69} -15261.4i q^{70} +(112708. - 65072.1i) q^{71} +(-122820. + 70910.3i) q^{72} +(445933. - 257459. i) q^{73} +(45821.8 - 79365.6i) q^{74} +411487. i q^{75} +(-531430. - 306821. i) q^{76} +(-20837.2 + 12030.4i) q^{77} -27910.5 q^{78} +(-275903. - 477878. i) q^{79} +(-651997. - 376431. i) q^{80} +(-117305. + 203179. i) q^{81} -91023.7i q^{82} +(106284. - 184089. i) q^{83} -25365.4 q^{84} +1.05880e6i q^{85} +(67389.4 - 140248. i) q^{86} +487153. q^{87} -167237. i q^{88} +(322273. + 186064. i) q^{89} +254756. q^{90} +(35811.6 + 20675.8i) q^{91} +(78151.3 - 135362. i) q^{92} +(-584081. + 337219. i) q^{93} +107323. i q^{94} +(1.13739e6 + 1.97001e6i) q^{95} +(133588. - 231382. i) q^{96} +757181. q^{97} +(197326. + 113926. i) q^{98} +(-200820. - 347831. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.95704i		−	0.244630i	−0.992491	−	0.122315i	$-0.960968\pi$
$2$		−	1.95704i		−	0.244630i	0.992491	−	0.122315i	$-0.0390319\pi$
$3$	10.4424	+	6.02890i	0.386754	+	0.223293i	0.680753	−	0.732513i	$-0.261653\pi$
$3$	10.4424	+	6.02890i	0.386754	+	0.223293i	−0.293999	+	0.955806i	$0.594986\pi$
$4$	60.1700			0.940156
$5$	−193.167	−	111.525i	−1.54534	−	0.892200i	−0.998488	−	0.0549670i	$-0.982495\pi$
$5$	−193.167	−	111.525i	−1.54534	−	0.892200i	−0.546847	−	0.837233i	$-0.684172\pi$
$6$	11.7988	−	20.4361i	0.0546241	−	0.0946118i
$7$	−30.2778	+	17.4809i	−0.0882733	+	0.0509646i	−0.543487	−	0.839418i	$-0.682896\pi$
$7$	−30.2778	+	17.4809i	−0.0882733	+	0.0509646i	0.455214	+	0.890382i	$0.349563\pi$
$8$		−	243.006i		−	0.474621i
$9$	−291.805	−	505.421i	−0.400281	−	0.693307i
$10$	−218.259	+	378.036i	−0.218259	+	0.378036i
$11$	688.201			0.517056			0.258528	−	0.966004i	$-0.416763\pi$
$11$	688.201			0.517056			0.258528	+	0.966004i	$0.416763\pi$
$12$	628.316	+	362.759i	0.363609	+	0.209930i
$13$	−591.384	−	1024.31i	−0.269178	−	0.466230i	0.699472	−	0.714660i	$-0.253419\pi$
$13$	−591.384	−	1024.31i	−0.269178	−	0.466230i	−0.968650	+	0.248430i	$0.920085\pi$
$14$	34.2108	+	59.2549i	0.0124675	+	0.0215943i
$15$	−1344.75	−	2329.17i	−0.398443	−	0.690123i
$16$	3375.31			0.824049
$17$	−2373.46	−	4110.95i	−0.483097	−	0.836749i	0.516714	−	0.856158i	$-0.327155\pi$
$17$	−2373.46	−	4110.95i	−0.483097	−	0.836749i	−0.999812	+	0.0194089i	$0.993822\pi$
$18$	−989.130	+	571.075i	−0.169604	+	0.0979209i
$19$	−8832.15	−	5099.24i	−1.28767	−	0.743438i	−0.309434	−	0.950921i	$-0.600140\pi$
$19$	−8832.15	−	5099.24i	−1.28767	−	0.743438i	−0.978239	+	0.207483i	$0.933473\pi$
$20$	−11622.8	−	6710.45i	−1.45286	−	0.838807i
$21$	−421.562			−0.0455201
$22$		−	1346.84i		−	0.126488i
$23$	1298.84	−	2249.66i	0.106751	−	0.184899i	−0.807701	−	0.589592i	$-0.799288\pi$
$23$	1298.84	−	2249.66i	0.106751	−	0.184899i	0.914452	+	0.404694i	$0.132622\pi$
$24$	1465.06	−	2537.56i	0.105979	−	0.183562i
$25$	17063.1	+	29554.2i	1.09204	+	1.89147i
$26$	−2004.61	+	1157.36i	−0.114054	+	0.0658492i
$27$		−	15827.2i		−	0.804104i
$28$	−1821.81	+	1051.82i	−0.0829907	+	0.0479147i
$29$	34988.7	−	20200.7i	1.43461	−	0.828273i	0.437143	−	0.899392i	$-0.355991\pi$
$29$	34988.7	−	20200.7i	1.43461	−	0.828273i	0.997468	+	0.0711195i	$0.0226572\pi$
$30$	−4558.28	+	2631.72i	−0.168825	+	0.0974713i
$31$	−27966.9	+	48440.1i	−0.938771	+	1.62600i	−0.171003	+	0.985271i	$0.554701\pi$
$31$	−27966.9	+	48440.1i	−0.938771	+	1.62600i	−0.767768	+	0.640728i	$0.778633\pi$
$32$		−	22158.0i		−	0.676209i
$33$	7186.44	+	4149.09i	0.199973	+	0.115455i
$34$	−8045.30	+	4644.96i	−0.204694	+	0.118180i
$35$	7798.21			0.181883
$36$	−17557.9	−	30411.2i	−0.376326	−	0.651817i
$37$	40553.8	+	23413.8i	0.800620	+	0.462238i	0.843688	−	0.536834i	$-0.180380\pi$
$37$	40553.8	+	23413.8i	0.800620	+	0.462238i	−0.0430676	+	0.999072i	$0.513713\pi$
$38$	−9979.44	+	17284.9i	−0.181868	+	0.315004i
$39$		−	14261.6i		−	0.240422i
$40$	−27101.2	+	46940.7i	−0.423457	+	0.733449i
$41$	46510.8			0.674843			0.337421	−	0.941354i	$-0.390445\pi$
$41$	46510.8			0.674843			0.337421	+	0.941354i	$0.390445\pi$
$42$			825.014i			0.0111356i
$43$	71663.4	+	34434.3i	0.901347	+	0.433098i
$43$	71663.4	+	34434.3i	0.901347	+	0.433098i
$44$	41409.1			0.486113
$45$			130174.i			1.42852i
$46$	−4402.68	−	2541.89i	−0.0452318	−	0.0261146i
$47$	−54839.3			−0.528200			−0.264100	−	0.964495i	$-0.585075\pi$
$47$	−54839.3			−0.528200			−0.264100	+	0.964495i	$0.585075\pi$
$48$	35246.1	+	20349.4i	0.318704	+	0.184004i
$49$	−58213.3	+	100828.i	−0.494805	+	0.857028i
$50$	57838.9	−	33393.3i	0.462711	−	0.267146i
$51$		−	57237.3i		−	0.431488i
$52$	−35583.6	−	61632.6i	−0.253069	−	0.438329i
$53$	31883.7	−	55224.1i	0.214161	−	0.370938i	−0.738852	−	0.673868i	$-0.764632\pi$
$53$	31883.7	−	55224.1i	0.214161	−	0.370938i	0.953013	+	0.302930i	$0.0979649\pi$
$54$	−30974.5			−0.196708
$55$	−132938.	−	76751.6i	−0.799024	−	0.461317i
$56$	4247.96	+	7357.68i	0.0241889	+	0.0418964i
$57$	−61485.6	−	106496.i	−0.332008	−	0.575055i
$58$	−39533.7	−	68474.4i	−0.202621	−	0.350949i
$59$	−215519.			−1.04937			−0.524685	−	0.851297i	$-0.675817\pi$
$59$	−215519.			−1.04937			−0.524685	+	0.851297i	$0.675817\pi$
$60$	−80913.3	−	140146.i	−0.374599	−	0.648824i
$61$	213769.	−	123420.i	0.941793	−	0.543744i	0.0512708	−	0.998685i	$-0.483673\pi$
$61$	213769.	−	123420.i	0.941793	−	0.543744i	0.890522	+	0.454941i	$0.150339\pi$
$62$	94799.4	+	54732.5i	0.397769	+	0.229652i
$63$	17670.4	+	10202.0i	0.0706683	+	0.0408003i
$64$	172655.			0.658628
$65$			263816.i			0.960643i
$66$	8119.96	−	14064.2i	0.0282437	−	0.0489196i
$67$	−49805.9	+	86266.3i	−0.165598	+	0.286825i	−0.936868	−	0.349684i	$-0.886289\pi$
$67$	−49805.9	+	86266.3i	−0.165598	+	0.286825i	0.771269	+	0.636509i	$0.219622\pi$
$68$	−142811.	−	247356.i	−0.454187	−	0.786674i
$69$	27125.9	−	15661.2i	0.0825729	−	0.0476735i
$70$		−	15261.4i		−	0.0444940i
$71$	112708.	−	65072.1i	0.314905	−	0.181811i	−0.334214	−	0.942497i	$-0.608471\pi$
$71$	112708.	−	65072.1i	0.314905	−	0.181811i	0.649119	+	0.760686i	$0.275138\pi$
$72$	−122820.	+	70910.3i	−0.329058	+	0.189982i
$73$	445933.	−	257459.i	1.14631	−	0.661821i	0.198322	−	0.980137i	$-0.436451\pi$
$73$	445933.	−	257459.i	1.14631	−	0.661821i	0.947985	+	0.318316i	$0.103117\pi$
$74$	45821.8	−	79365.6i	0.113078	−	0.195856i
$75$			411487.i			0.975378i
$76$	−531430.	−	306821.i	−1.21061	−	0.698948i
$77$	−20837.2	+	12030.4i	−0.0456422	+	0.0263516i
$78$	−27910.5			−0.0588145
$79$	−275903.	−	477878.i	−0.559596	−	0.969249i	−0.997530	−	0.0702419i	$-0.977623\pi$
$79$	−275903.	−	477878.i	−0.559596	−	0.969249i	0.437934	−	0.899007i	$-0.355710\pi$
$80$	−651997.	−	376431.i	−1.27343	−	0.735216i
$81$	−117305.	+	203179.i	−0.220731	+	0.382317i
$82$		−	91023.7i		−	0.165087i
$83$	106284.	−	184089.i	0.185880	−	0.321953i	−0.757993	−	0.652263i	$-0.773820\pi$
$83$	106284.	−	184089.i	0.185880	−	0.321953i	0.943873	+	0.330310i	$0.107153\pi$
$84$	−25365.4			−0.0427960
$85$			1.05880e6i			1.72408i
$86$	67389.4	−	140248.i	0.105949	−	0.220497i
$87$	487153.			0.739788
$88$		−	167237.i		−	0.245406i
$89$	322273.	+	186064.i	0.457145	+	0.263933i	0.710843	−	0.703351i	$-0.248314\pi$
$89$	322273.	+	186064.i	0.457145	+	0.263933i	−0.253698	+	0.967283i	$0.581647\pi$
$90$	254756.			0.349460
$91$	35811.6	+	20675.8i	0.0475225	+	0.0274371i
$92$	78151.3	−	135362.i	0.100363	−	0.173833i
$93$	−584081.	+	337219.i	−0.726147	+	0.419241i
$94$			107323.i			0.129214i
$95$	1.13739e6	+	1.97001e6i	1.32659	+	2.29772i
$96$	133588.	−	231382.i	0.150992	−	0.261526i
$97$	757181.			0.829630			0.414815	−	0.909906i	$-0.363846\pi$
$97$	757181.			0.829630			0.414815	+	0.909906i	$0.363846\pi$
$98$	197326.	+	113926.i	0.209655	+	0.121044i
$99$	−200820.	−	347831.i	−0.206968	−	0.358478i
$100$	1.02669e6	+	1.77828e6i	1.02669	+	1.77828i
$101$	60940.3	+	105552.i	0.0591480	+	0.102447i	0.894083	−	0.447901i	$-0.147828\pi$
$101$	60940.3	+	105552.i	0.0591480	+	0.102447i	−0.834935	+	0.550348i	$0.814495\pi$
$102$	−112016.			−0.105555
$103$	−509074.	−	881742.i	−0.465875	−	0.806919i	0.533366	−	0.845885i	$-0.320927\pi$
$103$	−509074.	−	881742.i	−0.465875	−	0.806919i	−0.999241	+	0.0389658i	$0.987594\pi$
$104$	−248913.	+	143710.i	−0.221283	+	0.127758i
$105$	81431.7	+	47014.6i	0.0703438	+	0.0406130i
$106$	−108076.	−	62397.7i	−0.0907427	−	0.0523903i
$107$	−1.30349e6			−1.06404			−0.532019	−	0.846732i	$-0.678567\pi$
$107$	−1.30349e6			−1.06404			−0.532019	+	0.846732i	$0.678567\pi$
$108$		−	952321.i		−	0.755983i
$109$	−245095.	+	424517.i	−0.189258	+	0.327805i	−0.945003	−	0.327061i	$-0.893942\pi$
$109$	−245095.	+	424517.i	−0.189258	+	0.327805i	0.755745	+	0.654866i	$0.227275\pi$
$110$	−150206.	+	260165.i	−0.112852	+	0.195466i
$111$	282318.	+	488990.i	0.206429	+	0.357545i
$112$	−102197.	+	59003.3i	−0.0727416	+	0.0419974i
$113$		−	2.62581e6i		−	1.81981i	−0.414812	−	0.909907i	$-0.636153\pi$
$113$		−	2.62581e6i		−	1.81981i	0.414812	−	0.909907i	$-0.363847\pi$
$114$	−208418.	+	120330.i	−0.140676	+	0.0812194i
$115$	−501787.	+	289707.i	−0.329933	+	0.190487i
$116$	2.10527e6	−	1.21548e6i	1.34876	−	0.778705i
$117$	−345138.	+	597796.i	−0.215494	+	0.373246i
$118$			421779.i			0.256708i
$119$	143726.	+	82980.2i	0.0852892	+	0.0492418i
$120$	−566002.	+	326781.i	−0.327547	+	0.189109i
$121$	−1.29794e6			−0.732653
$122$	−241538.	−	418355.i	−0.133016	−	0.230391i
$123$	485683.	+	280409.i	0.260998	+	0.150687i
$124$	−1.68277e6	+	2.91464e6i	−0.882591	+	1.52869i
$125$		−	4.12670e6i		−	2.11287i
$126$	19965.8	−	34581.7i	0.00998101	−	0.0172876i
$127$	2.55293e6			1.24632			0.623158	−	0.782096i	$-0.285849\pi$
$127$	2.55293e6			1.24632			0.623158	+	0.782096i	$0.285849\pi$
$128$		−	1.75601e6i		−	0.837329i
$129$	540734.	+	791626.i	0.251892	+	0.368766i
$130$	516300.			0.235002
$131$		−	503583.i		−	0.224005i	−0.993708	−	0.112002i	$-0.964274\pi$
$131$		−	503583.i		−	0.224005i	0.993708	−	0.112002i	$-0.0357264\pi$
$132$	432408.	+	249651.i	0.188006	+	0.108545i
$133$	356557.			0.151556
$134$	168827.	+	97472.3i	0.0701661	+	0.0405104i
$135$	−1.76513e6	+	3.05729e6i	−0.717421	+	1.24261i
$136$	−998985.	+	576764.i	−0.397139	+	0.229288i
$137$		−	2.58667e6i		−	1.00596i	−0.864299	−	0.502978i	$-0.832238\pi$
$137$		−	2.58667e6i		−	1.00596i	0.864299	−	0.502978i	$-0.167762\pi$
$138$	−30649.6	−	53086.7i	−0.0116624	−	0.0201999i
$139$	1.01220e6	−	1.75318e6i	0.376897	−	0.652805i	−0.613712	−	0.789530i	$-0.710324\pi$
$139$	1.01220e6	−	1.75318e6i	0.376897	−	0.652805i	0.990609	+	0.136725i	$0.0436577\pi$
$140$	469218.			0.170998
$141$	−572651.	−	330620.i	−0.204283	−	0.117943i
$142$	−127349.	−	220575.i	−0.0444764	−	0.0770355i
$143$	−406991.	−	704930.i	−0.139180	−	0.241067i
$144$	−984930.	−	1.70595e6i	−0.329851	−	0.571319i
$145$	−9.01155e6			−2.95594
$146$	−503859.	−	872710.i	−0.161901	−	0.280422i
$147$	−1.21577e6	+	701925.i	−0.382736	+	0.220973i
$148$	2.44012e6	+	1.40881e6i	0.752708	+	0.434576i
$149$	−771060.	−	445172.i	−0.233093	−	0.134576i	0.378905	−	0.925436i	$-0.376301\pi$
$149$	−771060.	−	445172.i	−0.233093	−	0.134576i	−0.611998	+	0.790859i	$0.709634\pi$
$150$	805299.			0.238607
$151$		−	1.39736e6i		−	0.405861i	−0.979193	−	0.202931i	$-0.934953\pi$
$151$		−	1.39736e6i		−	0.405861i	0.979193	−	0.202931i	$-0.0650466\pi$
$152$	−1.23915e6	+	2.14627e6i	−0.352852	+	0.611157i
$153$	−1.38517e6	+	2.39919e6i	−0.386749	+	0.669869i
$154$	23543.9	+	40779.3i	0.00644639	+	0.0111655i
$155$	1.08046e7	−	6.23802e6i	2.90143	−	1.67514i
$156$		−	858119.i		−	0.226034i
$157$	3.71057e6	−	2.14230e6i	0.958829	−	0.553580i	0.0630169	−	0.998012i	$-0.479928\pi$
$157$	3.71057e6	−	2.14230e6i	0.958829	−	0.553580i	0.895813	+	0.444432i	$0.146594\pi$
$158$	−935227.	+	539954.i	−0.237108	+	0.136894i
$159$	665881.	−	384447.i	0.165655	−	0.0956412i
$160$	−2.47117e6	+	4.28019e6i	−0.603313	+	1.04497i
$161$			90819.6i			0.0217622i
$162$	397630.	+	229572.i	0.0935263	+	0.0539974i
$163$	−3.44244e6	+	1.98749e6i	−0.794884	+	0.458926i	−0.841679	−	0.539978i	$-0.818432\pi$
$163$	−3.44244e6	+	1.98749e6i	−0.794884	+	0.458926i	0.0467953	+	0.998904i	$0.485099\pi$
$164$	2.79856e6			0.634457
$165$	−925455.	−	1.60294e6i	−0.206017	−	0.356832i
$166$	−360269.	−	208002.i	−0.0787595	−	0.0454718i
$167$	−3.55742e6	+	6.16163e6i	−0.763810	+	1.32296i	0.177063	+	0.984199i	$0.443340\pi$
$167$	−3.55742e6	+	6.16163e6i	−0.763810	+	1.32296i	−0.940873	+	0.338759i	$0.889993\pi$
$168$			102442.i			0.0216048i
$169$	1.71393e6	−	2.96862e6i	0.355086	−	0.615027i
$170$	2.07211e6			0.421762
$171$			5.95193e6i			1.19034i
$172$	4.31199e6	+	2.07191e6i	0.847407	+	0.407179i
$173$	4.89260e6			0.944934			0.472467	−	0.881348i	$-0.343363\pi$
$173$	4.89260e6			0.944934			0.472467	+	0.881348i	$0.343363\pi$
$174$		−	953379.i		−	0.180975i
$175$	−1.03327e6	−	596557.i	−0.192796	−	0.111311i
$176$	2.32289e6			0.426079
$177$	−2.25052e6	−	1.29934e6i	−0.405848	−	0.234316i
$178$	364136.	−	630703.i	0.0645660	−	0.111832i
$179$	−4.38158e6	+	2.52971e6i	−0.763962	+	0.441074i	−0.830717	−	0.556696i	$-0.812069\pi$
$179$	−4.38158e6	+	2.52971e6i	−0.763962	+	0.441074i	0.0667543	+	0.997769i	$0.478736\pi$
$180$			7.83257e6i			1.34303i
$181$	2.96459e6	+	5.13482e6i	0.499953	+	0.865944i	1.00000		5.43436e-5i	$-1.72981e-5\pi$
$181$	2.96459e6	+	5.13482e6i	0.499953	+	0.865944i	−0.500047	+	0.865998i	$0.666684\pi$
$182$	40463.5	−	70084.8i	0.00671196	−	0.0116255i
$183$	2.97634e6			0.485656
$184$	−546681.	−	315627.i	−0.0877568	−	0.0506664i
$185$	−5.22244e6	−	9.04553e6i	−0.824818	−	1.42863i
$186$	659953.	+	1.14307e6i	0.102559	+	0.177638i
$187$	−1.63342e6	−	2.82916e6i	−0.249788	−	0.432646i
$188$	−3.29968e6			−0.496590
$189$	276673.	+	479211.i	0.0409809	+	0.0709809i
$190$	3.85540e6	−	2.22591e6i	0.562093	−	0.324525i
$191$	8.34022e6	+	4.81523e6i	1.19695	+	0.691062i	0.959875	−	0.280429i	$-0.0904766\pi$
$191$	8.34022e6	+	4.81523e6i	1.19695	+	0.691062i	0.237079	+	0.971490i	$0.423810\pi$
$192$	1.80293e6	+	1.04092e6i	0.254727	+	0.147067i
$193$	−1.61610e6			−0.224801			−0.112400	−	0.993663i	$-0.535854\pi$
$193$	−1.61610e6			−0.224801			−0.112400	+	0.993663i	$0.535854\pi$
$194$		−	1.48184e6i		−	0.202953i
$195$	−1.59052e6	+	2.75487e6i	−0.214504	+	0.371532i
$196$	−3.50270e6	+	6.06685e6i	−0.465194	+	0.805740i
$197$	4.82878e6	+	8.36370e6i	0.631595	+	1.09396i	0.987226	+	0.159329i	$0.0509329\pi$
$197$	4.82878e6	+	8.36370e6i	0.631595	+	1.09396i	−0.355630	+	0.934627i	$0.615734\pi$
$198$	−680721.	+	393014.i	−0.0876947	+	0.0506306i
$199$		−	6.43626e6i		−	0.816722i	−0.912821	−	0.408361i	$-0.866100\pi$
$199$		−	6.43626e6i		−	0.816722i	0.912821	−	0.408361i	$-0.133900\pi$
$200$	7.18185e6	−	4.14644e6i	0.897732	−	0.518306i
$201$	−1.04018e6	+	600549.i	−0.128092	+	0.0739538i
$202$	206569.	−	119263.i	0.0250617	−	0.0144694i
$203$	−706253.	+	1.22327e6i	−0.0844252	+	0.146229i
$204$		−	3.44397e6i		−	0.405666i
$205$	−8.98435e6	−	5.18712e6i	−1.04286	−	0.602094i
$206$	−1.72561e6	+	996280.i	−0.197397	+	0.113967i
$207$	−1.51603e6			−0.170922
$208$	−1.99610e6	−	3.45735e6i	−0.221816	−	0.384197i
$209$	−6.07830e6	−	3.50931e6i	−0.665799	−	0.384399i
$210$	92009.7	−	159365.i	0.00993518	−	0.0172082i
$211$			3.99297e6i			0.425058i	0.977155	+	0.212529i	$0.0681701\pi$
$211$			3.99297e6i			0.425058i	−0.977155	+	0.212529i	$0.931830\pi$
$212$	1.91844e6	−	3.32284e6i	0.201345	−	0.348740i
$213$	1.56925e6			0.162388
$214$			2.55099e6i			0.260296i
$215$	−1.00027e7	−	1.46438e7i	−1.00647	−	1.47346i
$216$	−3.84610e6			−0.381645
$217$		−	1.95554e6i		−	0.191376i
$218$	830797.	+	479661.i	0.0801910	+	0.0462983i
$219$	6.20879e6			0.591118
$220$	−7.99886e6	−	4.61814e6i	−0.751208	−	0.433710i
$221$	−2.80725e6	+	4.86230e6i	−0.260078	+	0.450469i
$222$	956974.	−	552509.i	0.0874664	−	0.0504988i
$223$			3.55058e6i			0.320173i	0.987103	+	0.160087i	$0.0511774\pi$
$223$			3.55058e6i			0.320173i	−0.987103	+	0.160087i	$0.948823\pi$
$224$	387341.	+	670895.i	0.0344627	+	0.0596912i
$225$	9.95821e6	−	1.72481e7i	0.874246	−	1.51424i
$226$	−5.13881e6			−0.445182
$227$	853015.	+	492488.i	0.0729254	+	0.0421035i	0.536019	−	0.844206i	$-0.319927\pi$
$227$	853015.	+	492488.i	0.0729254	+	0.0421035i	−0.463094	+	0.886309i	$0.653261\pi$
$228$	−3.69959e6	−	6.40788e6i	−0.312140	−	0.540642i
$229$	1.00432e7	+	1.73953e7i	0.836307	+	1.44853i	0.892962	+	0.450133i	$0.148623\pi$
$229$	1.00432e7	+	1.73953e7i	0.836307	+	1.44853i	−0.0566542	+	0.998394i	$0.518043\pi$
$230$	566969.	+	982018.i	0.0465989	+	0.0807116i
$231$	−290119.			−0.0235364
$232$	−4.90890e6	−	8.50247e6i	−0.393116	−	0.680897i
$233$	−8.19208e6	+	4.72970e6i	−0.647629	+	0.373909i	−0.787547	−	0.616254i	$-0.788649\pi$
$233$	−8.19208e6	+	4.72970e6i	−0.647629	+	0.373909i	0.139918	+	0.990163i	$0.455316\pi$
$234$	1.16991e6	+	675449.i	0.0913074	+	0.0527163i
$235$	1.05931e7	+	6.11595e6i	0.816245	+	0.471259i
$236$	−1.29677e7			−0.986571
$237$		−	6.65356e6i		−	0.499815i
$238$	162396.	−	281278.i	0.0120460	−	0.0208643i
$239$	3.16690e6	−	5.48523e6i	0.231975	−	0.401792i	−0.726414	−	0.687257i	$-0.758815\pi$
$239$	3.16690e6	−	5.48523e6i	0.231975	−	0.401792i	0.958389	+	0.285465i	$0.0921480\pi$
$240$	−4.53893e6	−	7.86165e6i	−0.328337	−	0.568696i
$241$	417468.	−	241025.i	0.0298244	−	0.0172191i	−0.485014	−	0.874507i	$-0.661185\pi$
$241$	417468.	−	241025.i	0.0298244	−	0.0172191i	0.514838	+	0.857287i	$0.327852\pi$
$242$			2.54013e6i			0.179229i
$243$	−1.24421e7	+	7.18345e6i	−0.867111	+	0.500627i
$244$	1.28625e7	−	7.42616e6i	0.885432	−	0.511204i
$245$	2.24898e7	−	1.29845e7i	1.52928	−	0.882930i
$246$	548773.	−	950502.i	0.0368627	−	0.0638481i
$247$			1.20625e7i			0.800469i
$248$	1.17712e7	+	6.79613e6i	0.771733	+	0.445560i
$249$	2.21970e6	−	1.28155e6i	0.143779	−	0.0830111i
$250$	−8.07614e6			−0.516873
$251$	934315.	+	1.61828e6i	0.0590843	+	0.102337i	0.894055	−	0.447958i	$-0.147849\pi$
$251$	934315.	+	1.61828e6i	0.0590843	+	0.102337i	−0.834970	+	0.550295i	$0.814515\pi$
$252$	1.06323e6	+	613854.i	0.0664392	+	0.0383587i
$253$	893865.	−	1.54822e6i	0.0551963	−	0.0956029i
$254$		−	4.99620e6i		−	0.304887i
$255$	−6.38339e6	+	1.10564e7i	−0.384973	+	0.666793i
$256$	7.61336e6			0.453792
$257$		−	1.40240e7i		−	0.826177i	−0.910691	−	0.413088i	$-0.864450\pi$
$257$		−	1.40240e7i		−	0.826177i	0.910691	−	0.413088i	$-0.135550\pi$
$258$	1.54925e6	−	1.05824e6i	0.0902115	−	0.0616205i
$259$	−1.63717e6			−0.0942313
$260$			1.58738e7i			0.903154i
$261$	−2.04197e7	−	1.17893e7i	−1.14849	−	0.663084i
$262$	−985535.			−0.0547984
$263$	−6.26494e6	−	3.61707e6i	−0.344389	−	0.198833i	0.317822	−	0.948150i	$-0.397049\pi$
$263$	−6.26494e6	−	3.61707e6i	−0.344389	−	0.198833i	−0.662211	+	0.749317i	$0.730382\pi$
$264$	1.00826e6	−	1.74635e6i	0.0547972	−	0.0949116i
$265$	−1.23177e7	+	7.11165e6i	−0.661902	+	0.382149i
$266$		−	697797.i		−	0.0370753i
$267$	2.24353e6	+	3.88590e6i	0.117868	+	0.204154i
$268$	−2.99682e6	+	5.19064e6i	−0.155688	+	0.269660i
$269$	−2.01129e7			−1.03328			−0.516640	−	0.856202i	$-0.672818\pi$
$269$	−2.01129e7			−1.03328			−0.516640	+	0.856202i	$0.672818\pi$
$270$	5.98324e6	+	3.45443e6i	0.303980	+	0.175503i
$271$	1.94097e7	+	3.36186e7i	0.975239	+	1.68916i	0.679143	+	0.734006i	$0.262352\pi$
$271$	1.94097e7	+	3.36186e7i	0.975239	+	1.68916i	0.296096	+	0.955158i	$0.404315\pi$
$272$	−8.01114e6	−	1.38757e7i	−0.398096	−	0.689522i
$273$	249305.	+	431809.i	0.0122530	+	0.0212228i
$274$	−5.06222e6			−0.246087
$275$	1.17429e7	+	2.03392e7i	0.564646	+	0.977995i
$276$	1.63217e6	−	942332.i	0.0776314	−	0.0448205i
$277$	−5.98733e6	−	3.45678e6i	−0.281704	−	0.162642i	0.352490	−	0.935815i	$-0.385335\pi$
$277$	−5.98733e6	−	3.45678e6i	−0.281704	−	0.162642i	−0.634195	+	0.773173i	$0.718668\pi$
$278$	−3.43106e6	−	1.98092e6i	−0.159696	−	0.0922005i
$279$	3.26435e7			1.50309
$280$		−	1.89501e6i		−	0.0863253i
$281$	−4.68689e6	+	8.11794e6i	−0.211235	+	0.365870i	−0.952101	−	0.305783i	$-0.901082\pi$
$281$	−4.68689e6	+	8.11794e6i	−0.211235	+	0.365870i	0.740866	+	0.671653i	$0.234415\pi$
$282$	−647038.	+	1.12070e6i	−0.0288524	+	0.0499739i
$283$	−1.10408e6	−	1.91231e6i	−0.0487124	−	0.0843723i	0.840641	−	0.541593i	$-0.182178\pi$
$283$	−1.10408e6	−	1.91231e6i	−0.0487124	−	0.0843723i	−0.889353	+	0.457220i	$0.848845\pi$
$284$	6.78164e6	−	3.91538e6i	0.296060	−	0.170930i
$285$			2.74287e7i			1.18487i
$286$	−1.37958e6	+	796500.i	−0.0589723	+	0.0340477i
$287$	−1.40824e6	+	813050.i	−0.0595706	+	0.0343931i
$288$	−1.11991e7	+	6.46581e6i	−0.468820	+	0.270673i
$289$	802192.	−	1.38944e6i	0.0332342	−	0.0575632i
$290$			1.76360e7i			0.723113i
$291$	7.90676e6	+	4.56497e6i	0.320863	+	0.185250i
$292$	2.68318e7	−	1.54913e7i	1.07771	−	0.622215i
$293$	4.03133e7			1.60268			0.801338	−	0.598212i	$-0.204122\pi$
$293$	4.03133e7			1.60268			0.801338	+	0.598212i	$0.204122\pi$
$294$	1.37370e6	+	2.37931e6i	0.0540566	+	0.0936288i
$295$	4.16310e7	+	2.40357e7i	1.62163	+	0.936247i
$296$	5.68969e6	−	9.85483e6i	0.219388	−	0.379991i
$297$		−	1.08923e7i		−	0.415767i
$298$	−871221.	+	1.50900e6i	−0.0329215	+	0.0570217i
$299$	−3.07246e6			−0.114940
$300$			2.47592e7i			0.917007i
$301$	−2.77175e6	+	210146.i	−0.101638	+	0.00770585i
$302$	−2.73470e6			−0.0992860
$303$			1.46961e6i			0.0528292i
$304$	−2.98112e7	−	1.72115e7i	−1.06111	−	0.612630i
$305$	−5.50575e7			−1.94051
$306$	4.69532e6	+	2.71084e6i	0.163870	+	0.0946106i
$307$	2.54915e7	−	4.41526e7i	0.881010	−	1.52595i	0.0307904	−	0.999526i	$-0.490198\pi$
$307$	2.54915e7	−	4.41526e7i	0.881010	−	1.52595i	0.850220	−	0.526428i	$-0.176469\pi$
$308$	−1.25377e6	+	723866.i	−0.0429108	+	0.0247746i
$309$		−	1.22766e7i		−	0.416105i
$310$	−1.22081e7	−	2.11450e7i	−0.409791	−	0.709778i
$311$	−2.73823e7	+	4.74275e7i	−0.910308	+	1.57670i	−0.0966783	+	0.995316i	$0.530822\pi$
$311$	−2.73823e7	+	4.74275e7i	−0.910308	+	1.57670i	−0.813630	+	0.581384i	$0.802512\pi$
$312$	−3.46565e6			−0.114109
$313$	−4.17501e7	−	2.41044e7i	−1.36152	−	0.786075i	−0.371695	−	0.928355i	$-0.621223\pi$
$313$	−4.17501e7	−	2.41044e7i	−1.36152	−	0.786075i	−0.989826	+	0.142280i	$0.954557\pi$
$314$	−4.19257e6	−	7.26174e6i	−0.135423	−	0.234559i
$315$	−2.27556e6	−	3.94138e6i	−0.0728041	−	0.126100i
$316$	−1.66011e7	−	2.87539e7i	−0.526108	−	0.911245i
$317$	5.92019e7			1.85848			0.929240	−	0.369476i	$-0.120463\pi$
$317$	5.92019e7			1.85848			0.929240	+	0.369476i	$0.120463\pi$
$318$	−752379.	−	1.30316e6i	−0.0233967	−	0.0405243i
$319$	2.40793e7	−	1.39022e7i	0.741774	−	0.428263i
$320$	−3.33513e7	−	1.92554e7i	−1.01780	−	0.587628i
$321$	−1.36115e7	−	7.85863e6i	−0.411521	−	0.237592i
$322$	177738.			0.00532369
$323$			4.84113e7i			1.43661i
$324$	−7.05826e6	+	1.22253e7i	−0.207521	+	0.359437i
$325$	2.01817e7	−	3.49558e7i	0.587907	−	1.01828i
$326$	3.88961e6	+	6.73701e6i	0.112267	+	0.194453i
$327$	−5.11873e6	+	2.95530e6i	−0.146393	+	0.0845198i
$328$		−	1.13024e7i		−	0.320295i
$329$	1.66041e6	−	958638.i	0.0466259	−	0.0269195i
$330$	−3.13701e6	+	1.81116e6i	−0.0872920	+	0.0503981i
$331$	−2.84765e7	+	1.64409e7i	−0.785239	+	0.453358i	−0.838284	−	0.545234i	$-0.816441\pi$
$331$	−2.84765e7	+	1.64409e7i	−0.785239	+	0.453358i	0.0530445	+	0.998592i	$0.483107\pi$
$332$	6.39508e6	−	1.10766e7i	0.174756	−	0.302686i
$333$		−	2.73290e7i		−	0.740101i
$334$	1.20586e7	+	6.96202e6i	0.323636	+	0.186851i
$335$	1.92417e7	−	1.11092e7i	0.511810	−	0.295494i
$336$	−1.42290e6			−0.0375108
$337$	−6.32610e6	−	1.09571e7i	−0.165290	−	0.286291i	0.771468	−	0.636268i	$-0.219523\pi$
$337$	−6.32610e6	−	1.09571e7i	−0.165290	−	0.286291i	−0.936758	+	0.349977i	$0.886189\pi$
$338$	−5.80972e6	−	3.35424e6i	−0.150454	−	0.0868649i
$339$	1.58307e7	−	2.74196e7i	0.406351	−	0.703820i
$340$			6.37079e7i			1.62090i
$341$	−1.92469e7	+	3.33365e7i	−0.485397	+	0.840732i
$342$	1.16482e7			0.291193
$343$		−	8.18369e6i		−	0.202800i
$344$	8.36774e6	−	1.74146e7i	0.205557	−	0.427798i
$345$	−6.98645e6			−0.170137
$346$		−	9.57504e6i		−	0.231160i
$347$	−1.78574e7	−	1.03100e7i	−0.427395	−	0.246756i	0.270841	−	0.962624i	$-0.412698\pi$
$347$	−1.78574e7	−	1.03100e7i	−0.427395	−	0.246756i	−0.698236	+	0.715868i	$0.746031\pi$
$348$	2.93120e7			0.695516
$349$	−1.36505e7	−	7.88109e6i	−0.321123	−	0.185400i	0.330770	−	0.943711i	$-0.392691\pi$
$349$	−1.36505e7	−	7.88109e6i	−0.321123	−	0.185400i	−0.651893	+	0.758311i	$0.726025\pi$
$350$	−1.16749e6	+	2.02215e6i	−0.0272300	+	0.0471638i
$351$	−1.62119e7	+	9.35995e6i	−0.374898	+	0.216447i
$352$		−	1.52492e7i		−	0.349638i
$353$	−3.79415e7	−	6.57167e7i	−0.862563	−	1.49400i	−0.869447	−	0.494027i	$-0.835525\pi$
$353$	−3.79415e7	−	6.57167e7i	−0.862563	−	1.49400i	0.00688380	−	0.999976i	$-0.497809\pi$
$354$	−2.54286e6	+	4.40437e6i	−0.0573209	+	0.0992828i
$355$	−2.90286e7			−0.648846
$356$	1.93912e7	+	1.11955e7i	0.429788	+	0.248138i
$357$	1.00056e6	+	1.73302e6i	0.0219906	+	0.0380889i
$358$	4.95075e6	+	8.57495e6i	0.107900	+	0.186888i
$359$	1.59571e7	+	2.76386e7i	0.344883	+	0.597355i	0.985333	−	0.170645i	$-0.0545853\pi$
$359$	1.59571e7	+	2.76386e7i	0.344883	+	0.597355i	−0.640450	+	0.768000i	$0.721252\pi$
$360$	3.16331e7			0.678007
$361$	2.84816e7	+	4.93316e7i	0.605401	+	1.04859i
$362$	1.00491e7	−	5.80183e6i	0.211836	−	0.122304i
$363$	−1.35536e7	−	7.82515e6i	−0.283357	−	0.163596i
$364$	2.15478e6	+	1.24406e6i	0.0446786	+	0.0257952i
$365$	−1.14853e8			−2.36190
$366$		−	5.82482e6i		−	0.118806i
$367$	3.40534e7	−	5.89823e7i	0.688911	−	1.19323i	−0.283280	−	0.959037i	$-0.591423\pi$
$367$	3.40534e7	−	5.89823e7i	0.688911	−	1.19323i	0.972191	−	0.234191i	$-0.0752441\pi$
$368$	4.38399e6	−	7.59329e6i	0.0879683	−	0.152365i
$369$	−1.35721e7	−	2.35075e7i	−0.270127	−	0.467873i
$370$	−1.77025e7	+	1.02205e7i	−0.349486	+	0.201776i
$371$			2.22942e6i			0.0436586i
$372$	−3.51441e7	+	2.02905e7i	−0.682691	+	0.394152i
$373$	5.89924e7	−	3.40593e7i	1.13676	−	0.656310i	0.191136	−	0.981564i	$-0.438783\pi$
$373$	5.89924e7	−	3.40593e7i	1.13676	−	0.656310i	0.945627	+	0.325254i	$0.105450\pi$
$374$	−5.53679e6	+	3.19667e6i	−0.105838	+	0.0611058i
$375$	2.48795e7	−	4.30925e7i	0.471789	−	0.817162i
$376$			1.33263e7i			0.250695i
$377$	−4.13836e7	−	2.38928e7i	−0.772331	−	0.445906i
$378$	937838.	−	541461.i	0.0173641	−	0.0100252i
$379$	−7.34243e7			−1.34872			−0.674361	−	0.738402i	$-0.735581\pi$
$379$	−7.34243e7			−1.34872			−0.674361	+	0.738402i	$0.735581\pi$
$380$	6.84365e7	+	1.18535e8i	1.24720	+	2.16022i
$381$	2.66586e7	+	1.53914e7i	0.482018	+	0.278293i
$382$	9.42361e6	−	1.63222e7i	0.169055	−	0.292811i
$383$			3.36582e7i			0.599093i	0.954082	+	0.299547i	$0.0968354\pi$
$383$			3.36582e7i			0.599093i	−0.954082	+	0.299547i	$0.903165\pi$
$384$	1.05868e7	−	1.83368e7i	0.186969	−	0.323840i
$385$	5.36674e6			0.0940434
$386$			3.16279e6i			0.0549931i
$387$	−3.50792e6	−	4.62683e7i	−0.0605225	−	0.798271i
$388$	4.55596e7			0.779982
$389$			6.56082e7i			1.11457i	0.830320	+	0.557287i	$0.188158\pi$
$389$			6.56082e7i			1.11457i	−0.830320	+	0.557287i	$0.811842\pi$
$390$	5.39139e6	+	3.11272e6i	0.0908881	+	0.0524743i
$391$	−1.23310e7			−0.206285
$392$	2.45019e7	+	1.41462e7i	0.406764	+	0.234845i
$393$	3.03605e6	−	5.25860e6i	0.0500186	−	0.0866348i
$394$	1.63681e7	−	9.45014e6i	0.267615	−	0.154507i
$395$			1.23080e8i			1.99709i
$396$	−1.20834e7	−	2.09290e7i	−0.194582	−	0.337026i
$397$	7.78074e6	−	1.34766e7i	0.124351	−	0.215382i	−0.797128	−	0.603810i	$-0.793648\pi$
$397$	7.78074e6	−	1.34766e7i	0.124351	−	0.215382i	0.921479	+	0.388428i	$0.126982\pi$
$398$	−1.25960e7			−0.199795
$399$	3.72329e6	+	2.14965e6i	0.0586150	+	0.0338414i
$400$	5.75933e7	+	9.97545e7i	0.899895	+	1.55866i
$401$	1.77334e6	+	3.07152e6i	0.0275017	+	0.0476343i	0.879449	−	0.475994i	$-0.157912\pi$
$401$	1.77334e6	+	3.07152e6i	0.0275017	+	0.0476343i	−0.851947	+	0.523628i	$0.824578\pi$
$402$	1.17530e6	+	2.03568e6i	0.0180913	+	0.0313351i
$403$	6.61568e7			1.01079
$404$	3.66677e6	+	6.35104e6i	0.0556084	+	0.0963165i
$405$	4.53190e7	−	2.61649e7i	0.682205	−	0.393871i
$406$	2.39399e6	+	1.38217e6i	0.0357720	+	0.0206530i
$407$	2.79092e7	+	1.61134e7i	0.413965	+	0.239003i
$408$	−1.39090e7			−0.204793
$409$			7.63411e7i			1.11581i	0.829906	+	0.557903i	$0.188394\pi$
$409$			7.63411e7i			1.11581i	−0.829906	+	0.557903i	$0.811606\pi$
$410$	−1.01514e7	+	1.75828e7i	−0.147291	+	0.255115i
$411$	1.55948e7	−	2.70109e7i	0.224622	−	0.389057i
$412$	−3.06310e7	−	5.30544e7i	−0.437995	−	0.758630i
$413$	6.52542e6	−	3.76745e6i	0.0926314	−	0.0534808i
$414$			2.96694e6i			0.0418127i
$415$	−4.10609e7	+	2.37065e7i	−0.574493	+	0.331684i
$416$	−2.26966e7	+	1.31039e7i	−0.315269	+	0.182021i
$417$	2.11395e7	−	1.22049e7i	0.291533	−	0.168317i
$418$	−6.86786e6	+	1.18955e7i	−0.0940357	+	0.162875i
$419$		−	4.94620e7i		−	0.672403i	−0.941790	−	0.336202i	$-0.890858\pi$
$419$		−	4.94620e7i		−	0.672403i	0.941790	−	0.336202i	$-0.109142\pi$
$420$	4.89975e6	+	2.82887e6i	0.0661341	+	0.0381826i
$421$	−1.95818e7	+	1.13055e7i	−0.262425	+	0.151511i	−0.625440	−	0.780272i	$-0.715081\pi$
$421$	−1.95818e7	+	1.13055e7i	−0.262425	+	0.151511i	0.363015	+	0.931783i	$0.381747\pi$
$422$	7.81442e6			0.103982
$423$	1.60024e7	+	2.77169e7i	0.211428	+	0.366204i
$424$	−1.34198e7	−	7.74793e6i	−0.176055	−	0.101645i
$425$	8.09972e7	−	1.40291e8i	1.05512	−	1.82753i
$426$		−	3.07109e6i		−	0.0397250i
$427$	−4.31496e6	+	7.47374e6i	−0.0554235	+	0.0959962i
$428$	−7.84312e7			−1.00036
$429$		−	9.81484e6i		−	0.124311i
$430$	−2.86586e7	+	1.95757e7i	−0.360454	+	0.246214i
$431$	−1.58064e8			−1.97425			−0.987125	−	0.159948i	$-0.948867\pi$
$431$	−1.58064e8			−1.97425			−0.987125	+	0.159948i	$0.948867\pi$
$432$		−	5.34216e7i		−	0.662621i
$433$	1.01929e8	+	5.88488e7i	1.25555	+	0.724893i	0.972207	−	0.234125i	$-0.0752225\pi$
$433$	1.01929e8	+	5.88488e7i	1.25555	+	0.724893i	0.283345	+	0.959018i	$0.408556\pi$
$434$	−3.82709e6			−0.0468165
$435$	−9.41018e7	−	5.43297e7i	−1.14322	−	0.660039i
$436$	−1.47473e7	+	2.55432e7i	−0.177932	+	0.308187i
$437$	−2.29431e7	+	1.32462e7i	−0.274921	+	0.158726i
$438$		−	1.21509e7i		−	0.144606i
$439$	−2.39904e7	−	4.15525e7i	−0.283559	−	0.491138i	0.688700	−	0.725047i	$-0.258182\pi$
$439$	−2.39904e7	−	4.15525e7i	−0.283559	−	0.491138i	−0.972259	+	0.233908i	$0.924848\pi$
$440$	−1.86511e7	+	3.23047e7i	−0.218951	+	0.379234i
$441$	6.79477e7			0.792244
$442$	9.51573e6	+	5.49391e6i	0.110198	+	0.0636231i
$443$	1.74298e7	+	3.01893e7i	0.200484	+	0.347249i	0.948685	−	0.316224i	$-0.102415\pi$
$443$	1.74298e7	+	3.01893e7i	0.200484	+	0.347249i	−0.748200	+	0.663473i	$0.769082\pi$
$444$	1.69871e7	+	2.94225e7i	0.194075	+	0.336148i
$445$	−4.15017e7	−	7.18830e7i	−0.470962	−	0.815729i
$446$	6.94865e6			0.0783242
$447$	−5.36779e6	−	9.29729e6i	−0.0600998	−	0.104096i
$448$	−5.22762e6	+	3.01817e6i	−0.0581393	+	0.0335667i
$449$	8.26213e7	+	4.77014e7i	0.912752	+	0.526978i	0.881316	−	0.472528i	$-0.156658\pi$
$449$	8.26213e7	+	4.77014e7i	0.912752	+	0.526978i	0.0314367	+	0.999506i	$0.489992\pi$
$450$	−3.37553e7	−	1.94886e7i	−0.370429	−	0.213867i
$451$	3.20088e7			0.348931
$452$		−	1.57995e8i		−	1.71091i
$453$	8.42454e6	−	1.45917e7i	0.0906258	−	0.156968i
$454$	963821.	−	1.66939e6i	0.0102998	−	0.0178398i
$455$	−4.61174e6	−	7.98777e6i	−0.0489588	−	0.0847991i
$456$	−2.58792e7	+	1.49414e7i	−0.272934	+	0.157578i
$457$			8.50365e7i			0.890957i	0.895293	+	0.445479i	$0.146966\pi$
$457$			8.50365e7i			0.890957i	−0.895293	+	0.445479i	$0.853034\pi$
$458$	3.40434e7	−	1.96550e7i	0.354354	−	0.204586i
$459$	−6.50647e7	+	3.75651e7i	−0.672833	+	0.388460i
$460$	−3.01925e7	+	1.74316e7i	−0.310188	+	0.179087i
$461$	−7.93376e7	+	1.37417e8i	−0.809798	+	1.40261i	0.103206	+	0.994660i	$0.467090\pi$
$461$	−7.93376e7	+	1.37417e8i	−0.809798	+	1.40261i	−0.913004	+	0.407951i	$0.866244\pi$
$462$			567776.i			0.00575773i
$463$	−8.51141e7	−	4.91407e7i	−0.857549	−	0.495106i	0.00564201	−	0.999984i	$-0.498204\pi$
$463$	−8.51141e7	−	4.91407e7i	−0.857549	−	0.495106i	−0.863191	+	0.504878i	$0.831537\pi$
$464$	1.18098e8	−	6.81837e7i	1.18219	−	0.682537i
$465$	1.50433e8			1.49619
$466$	9.25623e6	+	1.60323e7i	0.0914695	+	0.158430i
$467$	9.87858e7	+	5.70340e7i	0.969938	+	0.559994i	0.899217	−	0.437502i	$-0.144137\pi$
$467$	9.87858e7	+	5.70340e7i	0.969938	+	0.559994i	0.0707208	+	0.997496i	$0.477470\pi$
$468$	−2.07669e7	+	3.59694e7i	−0.202598	+	0.350910i
$469$		−	3.48260e6i		−	0.0337587i
$470$	1.19692e7	−	2.07312e7i	0.115284	−	0.199678i
$471$	5.16628e7			0.494441
$472$			5.23723e7i			0.498053i
$473$	4.93188e7	+	2.36977e7i	0.466047	+	0.223936i
$474$	−1.30213e7			−0.122270
$475$		−	3.48036e8i		−	3.24746i
$476$	8.64798e6	+	4.99292e6i	0.0801852	+	0.0462949i
$477$	−3.72152e7			−0.342899
$478$	−1.07348e7	−	6.19776e6i	−0.0982906	−	0.0567481i
$479$	−3.44914e7	+	5.97409e7i	−0.313837	+	0.543582i	−0.979190	−	0.202947i	$-0.934948\pi$
$479$	−3.44914e7	+	5.97409e7i	−0.313837	+	0.543582i	0.665352	+	0.746530i	$0.268281\pi$
$480$	−5.16097e7	+	2.97969e7i	−0.466668	+	0.269431i
$481$		−	5.53861e7i		−	0.497698i
$482$	−471697.	−	817002.i	−0.00421232	−	0.00729596i
$483$	−547542.	+	948370.i	−0.00485933	+	0.00841660i
$484$	−7.80970e7			−0.688808
$485$	−1.46262e8	−	8.44446e7i	−1.28206	−	0.740196i
$486$	1.40583e7	+	2.43497e7i	0.122469	+	0.212122i
$487$	−5.39696e7	−	9.34781e7i	−0.467264	−	0.809325i	0.532037	−	0.846721i	$-0.321427\pi$
$487$	−5.39696e7	−	9.34781e7i	−0.467264	−	0.809325i	−0.999301	+	0.0373964i	$0.988094\pi$
$488$	−2.99917e7	−	5.19472e7i	−0.258073	−	0.446995i
$489$	−4.79296e7			−0.409899
$490$	−2.54112e7	−	4.40135e7i	−0.215992	−	0.374108i
$491$	−1.04842e8	+	6.05305e7i	−0.885708	+	0.511364i	−0.872536	−	0.488550i	$-0.837526\pi$
$491$	−1.04842e8	+	6.05305e7i	−0.885708	+	0.511364i	−0.0131718	+	0.999913i	$0.504193\pi$
$492$	2.92235e7	+	1.68722e7i	0.245379	+	0.141670i
$493$	−1.66088e8	−	9.58912e7i	−1.38611	−	0.800272i
$494$	2.36067e7			0.195819
$495$			8.95859e7i			0.738625i
$496$	−9.43969e7	+	1.63500e8i	−0.773593	+	1.33990i
$497$	−2.27503e6	+	3.94047e6i	−0.0185318	+	0.0320981i
$498$	−2.50804e6	−	4.34405e6i	−0.0203070	−	0.0351728i
$499$	1.80985e8	−	1.04492e8i	1.45660	−	0.840970i	0.457760	−	0.889076i	$-0.348652\pi$
$499$	1.80985e8	−	1.04492e8i	1.45660	−	0.840970i	0.998842	+	0.0481061i	$0.0153186\pi$
$500$		−	2.48304e8i		−	1.98643i
$501$	−7.42957e7	+	4.28946e7i	−0.590813	+	0.341106i
$502$	3.16705e6	−	1.82850e6i	0.0250348	−	0.0144538i
$503$	1.34082e8	−	7.74123e7i	1.05358	−	0.608284i	0.129929	−	0.991523i	$-0.458525\pi$
$503$	1.34082e8	−	7.74123e7i	1.05358	−	0.608284i	0.923649	+	0.383240i	$0.125192\pi$
$504$	2.47915e6	−	4.29401e6i	0.0193647	−	0.0335407i
$505$		−	2.71854e7i		−	0.211087i
$506$	−3.02993e6	−	1.74933e6i	−0.0233874	−	0.0135027i
$507$	3.57950e7	−	2.06663e7i	0.274662	−	0.158576i
$508$	1.53610e8			1.17173
$509$	−7.70709e6	−	1.33491e7i	−0.0584436	−	0.101227i	0.835323	−	0.549759i	$-0.185280\pi$
$509$	−7.70709e6	−	1.33491e7i	−0.0584436	−	0.101227i	−0.893767	+	0.448532i	$0.851947\pi$
$510$	2.16378e7	+	1.24926e7i	0.163118	+	0.0941762i
$511$	−9.00123e6	+	1.55906e7i	−0.0674589	+	0.116842i
$512$		−	1.27284e8i		−	0.948340i
$513$	−8.07066e7	+	1.39788e8i	−0.597802	+	1.03542i
$514$	−2.74456e7			−0.202108
$515$			2.27098e8i			1.66261i
$516$	3.25360e7	+	4.76321e7i	0.236818	+	0.346698i
$517$	−3.77404e7			−0.273109
$518$			3.20402e6i			0.0230518i
$519$	5.10903e7	+	2.94970e7i	0.365457	+	0.210997i
$520$	6.41090e7			0.455941
$521$	4.59888e7	+	2.65516e7i	0.325191	+	0.187749i	0.653704	−	0.756750i	$-0.273214\pi$
$521$	4.59888e7	+	2.65516e7i	0.325191	+	0.187749i	−0.328513	+	0.944499i	$0.606547\pi$
$522$	−2.30723e7	+	3.99623e7i	−0.162210	+	0.280957i
$523$	−1.52865e6	+	882564.i	−0.0106857	+	0.00616938i	−0.505333	−	0.862924i	$-0.668630\pi$
$523$	−1.52865e6	+	882564.i	−0.0106857	+	0.00616938i	0.494648	+	0.869094i	$0.335297\pi$
$524$		−	3.03006e7i		−	0.210600i
$525$	−7.19316e6	−	1.24589e7i	−0.0497098	−	0.0860999i
$526$	−7.07876e6	+	1.22608e7i	−0.0486407	+	0.0842481i
$527$	2.65513e8			1.81407
$528$	2.42564e7	+	1.40045e7i	0.164788	+	0.0951403i
$529$	7.06440e7	+	1.22359e8i	0.477208	+	0.826549i
$530$	1.39178e7	+	2.41064e7i	0.0934853	+	0.161921i
$531$	6.28893e7	+	1.08928e8i	0.420043	+	0.727535i
$532$	2.14540e7			0.142487
$533$	−2.75058e7	−	4.76414e7i	−0.181653	−	0.314632i
$534$	7.60488e6	−	4.39068e6i	0.0499423	−	0.0288342i
$535$	2.51792e8	+	1.45372e8i	1.64430	+	0.949335i
$536$	2.09632e7	+	1.21031e7i	0.136133	+	0.0785965i
$537$	−6.10054e7			−0.393954
$538$			3.93619e7i			0.252772i
$539$	−4.00625e7	+	6.93903e7i	−0.255842	+	0.443131i
$540$	−1.06208e8	+	1.83957e8i	−0.674488	+	1.16825i
$541$	7.96691e7	+	1.37991e8i	0.503150	+	0.871482i	0.999993	+	0.00364171i	$0.00115919\pi$
$541$	7.96691e7	+	1.37991e8i	0.503150	+	0.871482i	−0.496843	+	0.867841i	$0.665507\pi$
$542$	6.57931e7	−	3.79857e7i	0.413221	−	0.238573i
$543$			7.14929e7i			0.446543i
$544$	−9.10904e7	+	5.25911e7i	−0.565817	+	0.326675i
$545$	9.46884e7	−	5.46684e7i	0.584934	−	0.337712i
$546$	845069.	−	487901.i	0.00519175	−	0.00299746i
$547$	−9.96347e7	+	1.72572e8i	−0.608763	+	1.05441i	0.382681	+	0.923881i	$0.375001\pi$
$547$	−9.96347e7	+	1.72572e8i	−0.608763	+	1.05441i	−0.991445	+	0.130529i	$0.958333\pi$
$548$		−	1.55640e8i		−	0.945755i
$549$	−1.24758e8	−	7.20289e7i	−0.753963	−	0.435301i
$550$	3.98048e7	−	2.29813e7i	0.239247	−	0.138130i
$551$	−4.12034e8			−2.46308
$552$	−3.80576e6	−	6.59177e6i	−0.0226269	−	0.0391909i
$553$	1.67074e7	+	9.64604e6i	0.0987949	+	0.0570393i
$554$	−6.76508e6	+	1.17175e7i	−0.0397872	+	0.0689135i
$555$		−	1.25942e8i		−	0.736703i
$556$	6.09042e7	−	1.05489e8i	0.354342	−	0.613738i
$557$	2.13546e8			1.23573			0.617867	−	0.786283i	$-0.287997\pi$
$557$	2.13546e8			1.23573			0.617867	+	0.786283i	$0.287997\pi$
$558$		−	6.38848e7i		−	0.367701i
$559$	−7.10930e6	−	9.37693e7i	−0.0406997	−	0.536816i
$560$	2.63214e7			0.149880
$561$		−	3.93908e7i		−	0.223103i
$562$	1.58872e7	+	9.17245e6i	0.0895029	+	0.0516745i
$563$	1.75125e8			0.981350			0.490675	−	0.871343i	$-0.336750\pi$
$563$	1.75125e8			0.981350			0.490675	+	0.871343i	$0.336750\pi$
$564$	−3.44564e7	−	1.98934e7i	−0.192058	−	0.110885i
$565$	−2.92843e8	+	5.07219e8i	−1.62364	+	2.81222i
$566$	−3.74248e6	+	2.16072e6i	−0.0206400	+	0.0119165i
$567$		−	8.20239e6i		−	0.0449978i
$568$	−1.58129e7	−	2.73888e7i	−0.0862912	−	0.149461i
$569$	6.32172e7	−	1.09495e8i	0.343161	−	0.594373i	−0.641857	−	0.766825i	$-0.721836\pi$
$569$	6.32172e7	−	1.09495e8i	0.343161	−	0.594373i	0.985018	+	0.172452i	$0.0551689\pi$
$570$	5.36792e7			0.289856
$571$	−1.18626e8	−	6.84885e7i	−0.637191	−	0.367882i	0.146341	−	0.989234i	$-0.453250\pi$
$571$	−1.18626e8	−	6.84885e7i	−0.637191	−	0.367882i	−0.783532	+	0.621352i	$0.786584\pi$
$572$	−2.44887e7	−	4.24156e7i	−0.130851	−	0.226641i
$573$	5.80610e7	+	1.00565e8i	0.308618	+	0.534542i
$574$	1.59117e6	+	2.75599e6i	0.00841360	+	0.0145728i
$575$	8.86493e7			0.466307
$576$	−5.03817e7	−	8.72636e7i	−0.263636	−	0.456631i
$577$	1.14132e8	−	6.58943e7i	0.594130	−	0.343021i	−0.172599	−	0.984992i	$-0.555217\pi$
$577$	1.14132e8	−	6.58943e7i	0.594130	−	0.343021i	0.766729	+	0.641971i	$0.221883\pi$
$578$	−2.71919e6	−	1.56992e6i	−0.0140817	−	0.00813009i
$579$	−1.68759e7	−	9.74333e6i	−0.0869425	−	0.0501963i
$580$	−5.42225e8			−2.77904
$581$			7.43172e6i			0.0378932i
$582$	8.93384e6	−	1.54739e7i	0.0453179	−	0.0784928i
$583$	2.19424e7	−	3.80053e7i	0.110733	−	0.191796i
$584$	−6.25642e7	−	1.08364e8i	−0.314114	−	0.544062i
$585$	1.33338e8	−	7.69829e7i	0.666020	−	0.384527i
$586$		−	7.88949e7i		−	0.392063i
$587$	−1.77267e8	+	1.02345e8i	−0.876423	+	0.506003i	−0.869477	−	0.493973i	$-0.835544\pi$
$587$	−1.77267e8	+	1.02345e8i	−0.876423	+	0.506003i	−0.00694580	+	0.999976i	$0.502211\pi$
$588$	−7.31528e7	+	4.22348e7i	−0.359831	+	0.207749i
$589$	4.94016e8	−	2.85220e8i	2.41766	−	1.39584i
$590$	4.70389e7	−	8.14738e7i	0.229035	−	0.396700i
$591$			1.16449e8i			0.564122i
$592$	1.36882e8	+	7.90286e7i	0.659751	+	0.380907i
$593$	−2.36883e8	+	1.36764e8i	−1.13598	+	0.655856i	−0.945431	−	0.325823i	$-0.894359\pi$
$593$	−2.36883e8	+	1.36764e8i	−1.13598	+	0.655856i	−0.190545	+	0.981678i	$0.561025\pi$
$594$	−2.13167e7			−0.101709
$595$	−1.85087e7	−	3.20580e7i	−0.0878669	−	0.152190i
$596$	−4.63947e7	−	2.67860e7i	−0.219144	−	0.126523i
$597$	3.88035e7	−	6.72097e7i	0.182368	−	0.315870i
$598$			6.01294e6i			0.0281179i
$599$	1.33167e8	−	2.30651e8i	0.619605	−	1.07319i	−0.369953	−	0.929050i	$-0.620626\pi$
$599$	1.33167e8	−	2.30651e8i	0.619605	−	1.07319i	0.989558	−	0.144136i	$-0.0460404\pi$
$600$	9.99940e7			0.462935
$601$			3.23099e8i			1.48837i	0.667972	+	0.744187i	$0.267163\pi$
$601$			3.23099e8i			1.48837i	−0.667972	+	0.744187i	$0.732837\pi$
$602$	411264.	+	5.42443e6i	0.00188509	+	0.0248636i
$603$	5.81344e7			0.265144
$604$		−	8.40792e7i		−	0.381573i
$605$	2.50719e8	+	1.44753e8i	1.13219	+	0.653673i
$606$	2.87609e6			0.0129236
$607$	4.25740e7	+	2.45801e7i	0.190361	+	0.109905i	0.592152	−	0.805826i	$-0.298279\pi$
$607$	4.25740e7	+	2.45801e7i	0.190361	+	0.109905i	−0.401790	+	0.915732i	$0.631612\pi$
$608$	−1.12989e8	+	1.95703e8i	−0.502719	+	0.870736i
$609$	−1.47499e7	+	8.51586e6i	−0.0653036	+	0.0377030i
$610$			1.07750e8i			0.474709i
$611$	3.24311e7	+	5.61723e7i	0.142180	+	0.246263i
$612$	−8.33458e7	+	1.44359e8i	−0.363605	+	0.629782i
$613$	−1.51047e8			−0.655740			−0.327870	−	0.944723i	$-0.606331\pi$
$613$	−1.51047e8			−0.655740			−0.327870	+	0.944723i	$0.606331\pi$
$614$	−8.64086e7	−	4.98880e7i	−0.373295	−	0.215522i
$615$	−6.25452e7	−	1.08331e8i	−0.268886	−	0.465725i
$616$	2.92345e6	+	5.06356e6i	0.0125070	+	0.0216628i
$617$	−1.91344e8	−	3.31418e8i	−0.814629	−	1.41098i	−0.909594	−	0.415499i	$-0.863607\pi$
$617$	−1.91344e8	−	3.31418e8i	−0.814629	−	1.41098i	0.0949642	−	0.995481i	$-0.469726\pi$
$618$	−2.40259e7			−0.101792
$619$	−1.04919e8	−	1.81725e8i	−0.442366	−	0.766200i	0.555499	−	0.831517i	$-0.312527\pi$
$619$	−1.04919e8	−	1.81725e8i	−0.442366	−	0.766200i	−0.997865	+	0.0653174i	$0.979194\pi$
$620$	6.50110e8	−	3.75341e8i	2.72780	−	1.57489i
$621$	−3.56058e7	−	2.05570e7i	−0.148678	−	0.0858391i
$622$	9.28176e7	+	5.35883e7i	0.385709	+	0.222689i
$623$	−1.30103e7			−0.0538050
$624$		−	4.81372e7i		−	0.198119i
$625$	−1.93619e8	+	3.35358e8i	−0.793064	+	1.37363i
$626$	−4.71734e7	+	8.17068e7i	−0.192298	+	0.333070i
$627$	−4.23145e7	−	7.32908e7i	−0.171667	−	0.297336i
$628$	2.23265e8	−	1.28902e8i	0.901449	−	0.520452i
$629$		−	2.22286e8i		−	0.893224i
$630$	−7.71345e6	+	4.45336e6i	−0.0308480	+	0.0178101i
$631$	1.93688e6	−	1.11826e6i	0.00770928	−	0.00445096i	−0.496140	−	0.868242i	$-0.665250\pi$
$631$	1.93688e6	−	1.11826e6i	0.00770928	−	0.00445096i	0.503850	+	0.863791i	$0.331917\pi$
$632$	−1.16127e8	+	6.70461e7i	−0.460026	+	0.265596i
$633$	−2.40732e7	+	4.16960e7i	−0.0949124	+	0.164393i
$634$		−	1.15861e8i		−	0.454641i
$635$	−4.93142e8	−	2.84716e8i	−1.92598	−	1.11196i
$636$	4.00661e7	−	2.31322e7i	0.155742	−	0.0899176i
$637$	1.37706e8			0.532763
$638$	−2.72072e7	−	4.71242e7i	−0.104766	−	0.181460i
$639$	−6.57775e7	−	3.79767e7i	−0.252101	−	0.145551i
$640$	−1.95839e8	+	3.39202e8i	−0.747065	+	1.29395i
$641$		−	1.87082e8i		−	0.710328i	−0.934804	−	0.355164i	$-0.884425\pi$
$641$		−	1.87082e8i		−	0.710328i	0.934804	−	0.355164i	$-0.115575\pi$
$642$	−1.53797e7	+	2.66384e7i	−0.0581222	+	0.100671i
$643$	−9.03837e7			−0.339983			−0.169992	−	0.985446i	$-0.554374\pi$
$643$	−9.03837e7			−0.339983			−0.169992	+	0.985446i	$0.554374\pi$
$644$			5.46461e6i			0.0204598i
$645$	−1.61658e7	−	2.13221e8i	−0.0602446	−	0.794605i
$646$	9.47431e7			0.351439
$647$		−	4.34673e8i		−	1.60491i	−0.596714	−	0.802454i	$-0.703527\pi$
$647$		−	4.34673e8i		−	1.60491i	0.596714	−	0.802454i	$-0.296473\pi$
$648$	4.93737e7	+	2.85059e7i	0.181456	+	0.104763i
$649$	−1.48320e8			−0.542583
$650$	−6.84100e7	−	3.94965e7i	−0.249103	−	0.143820i
$651$	1.17898e7	−	2.04205e7i	0.0427329	−	0.0740156i
$652$	−2.07132e8	+	1.19587e8i	−0.747315	+	0.431462i
$653$			3.49922e8i			1.25670i	0.777931	+	0.628350i	$0.216269\pi$
$653$			3.49922e8i			1.25670i	−0.777931	+	0.628350i	$0.783731\pi$
$654$	5.78366e6	+	1.00176e7i	0.0206761	+	0.0358121i
$655$	−5.61621e7	+	9.72756e7i	−0.199857	+	0.346163i
$656$	1.56988e8			0.556103
$657$	−2.60251e8	−	1.50256e8i	−0.917690	−	0.529828i
$658$	−1.87610e6	−	3.24949e6i	−0.00658533	−	0.0114061i
$659$	1.57401e8	+	2.72626e8i	0.549984	+	0.952601i	0.998275	+	0.0587130i	$0.0186997\pi$
$659$	1.57401e8	+	2.72626e8i	0.549984	+	0.952601i	−0.448290	+	0.893888i	$0.647967\pi$
$660$	−5.56846e7	−	9.64486e7i	−0.193688	−	0.335478i
$661$	1.50637e8			0.521588			0.260794	−	0.965395i	$-0.416016\pi$
$661$	1.50637e8			0.521588			0.260794	+	0.965395i	$0.416016\pi$
$662$	3.21755e7	+	5.57297e7i	0.110905	+	0.192093i
$663$	−5.86286e7	+	3.38492e7i	−0.201173	+	0.116147i
$664$	−4.47346e7	−	2.58276e7i	−0.152806	−	0.0882224i
$665$	−6.88750e7	−	3.97650e7i	−0.234205	−	0.135218i
$666$	−5.34840e7			−0.181051
$667$		−	1.04950e8i		−	0.353677i
$668$	−2.14050e8	+	3.70745e8i	−0.718101	+	1.24379i
$669$	−2.14061e7	+	3.70765e7i	−0.0714923	+	0.123828i
$670$	−2.17412e7	−	3.76568e7i	−0.0722868	−	0.125204i
$671$	1.47116e8	−	8.49375e7i	0.486959	−	0.281146i
$672$			9.34096e6i			0.0307811i
$673$	4.95395e8	−	2.86016e8i	1.62520	−	0.938308i	0.639699	−	0.768626i	$-0.279059\pi$
$673$	4.95395e8	−	2.86016e8i	1.62520	−	0.938308i	0.985499	−	0.169683i	$-0.0542743\pi$
$674$	−2.14436e7	+	1.23805e7i	−0.0700354	+	0.0404349i
$675$	4.67760e8	−	2.70061e8i	1.52094	−	0.878114i
$676$	1.03127e8	−	1.78622e8i	0.333836	−	0.578222i
$677$			4.29516e8i			1.38425i	0.721780	+	0.692123i	$0.243324\pi$
$677$			4.29516e8i			1.38425i	−0.721780	+	0.692123i	$0.756676\pi$
$678$	−5.36613e7	−	3.09814e7i	−0.172176	−	0.0994058i
$679$	−2.29258e7	+	1.32362e7i	−0.0732343	+	0.0422818i
$680$	2.57294e8			0.818283
$681$	5.93832e6	+	1.02855e7i	0.0188028	+	0.0325674i
$682$	6.52411e7	+	3.76670e7i	0.205669	+	0.118743i
$683$	1.38069e8	−	2.39142e8i	0.433344	−	0.750574i	−0.563815	−	0.825901i	$-0.690667\pi$
$683$	1.38069e8	−	2.39142e8i	0.433344	−	0.750574i	0.997159	+	0.0753273i	$0.0240002\pi$
$684$			3.58128e8i			1.11910i
$685$	−2.88478e8	+	4.99659e8i	−0.897513	+	1.55454i
$686$	−1.60158e7			−0.0496109
$687$			2.42198e8i			0.746965i
$688$	2.41886e8	+	1.16226e8i	0.742754	+	0.356894i
$689$	−7.54220e7			−0.230590
$690$			1.36728e7i			0.0416207i
$691$	−1.42399e8	−	8.22139e7i	−0.431591	−	0.249179i	0.268433	−	0.963298i	$-0.413494\pi$
$691$	−1.42399e8	−	8.22139e7i	−0.431591	−	0.249179i	−0.700024	+	0.714119i	$0.746827\pi$
$692$	2.94388e8			0.888386
$693$	1.21608e7	+	7.02103e6i	0.0365394	+	0.0210961i
$694$	−2.01770e7	+	3.49477e7i	−0.0603641	+	0.104554i
$695$	−3.91048e8	+	2.25771e8i	−1.16486	+	0.672535i
$696$		−	1.18381e8i		−	0.351119i
$697$	−1.10391e8	−	1.91204e8i	−0.326015	−	0.564674i
$698$	−1.54236e7	+	2.67145e7i	−0.0453545	+	0.0785564i
$699$	−1.14060e8			−0.333964
$700$	−6.21716e7	−	3.58948e7i	−0.181258	−	0.104650i
$701$	8.70026e7	+	1.50693e8i	0.252568	+	0.437460i	0.964232	−	0.265059i	$-0.0853916\pi$
$701$	8.70026e7	+	1.50693e8i	0.252568	+	0.437460i	−0.711664	+	0.702520i	$0.752058\pi$
$702$	1.83178e7	+	3.17274e7i	0.0529496	+	0.0917114i
$703$	−2.38785e8	−	4.13588e8i	−0.687292	−	1.19042i
$704$	1.18822e8			0.340547
$705$	7.37448e7	+	1.27730e8i	0.210457	+	0.364523i
$706$	−1.28610e8	+	7.42532e7i	−0.365479	+	0.211009i
$707$	−3.69027e6	−	2.13058e6i	−0.0104424	−	0.00602892i
$708$	−1.35414e8	−	7.81812e7i	−0.381560	−	0.220294i
$709$	3.35885e8			0.942437			0.471218	−	0.882017i	$-0.343814\pi$
$709$	3.35885e8			0.942437			0.471218	+	0.882017i	$0.343814\pi$
$710$			5.68103e7i			0.158727i
$711$	−1.61020e8	+	2.78894e8i	−0.447991	+	0.775944i
$712$	4.52148e7	−	7.83143e7i	0.125268	−	0.216971i
$713$	7.26492e7	+	1.25832e8i	0.200430	+	0.347155i
$714$	3.39159e6	−	1.95814e6i	0.00931770	−	0.00537958i
$715$			1.81559e8i			0.496706i
$716$	−2.63640e8	+	1.52212e8i	−0.718244	+	0.414678i
$717$	6.61398e7	−	3.81858e7i	0.179434	−	0.103596i
$718$	5.40899e7	−	3.12288e7i	0.146131	−	0.0843689i
$719$	2.85826e7	−	4.95064e7i	0.0768979	−	0.133191i	−0.825012	−	0.565115i	$-0.808832\pi$
$719$	2.85826e7	−	4.95064e7i	0.0768979	−	0.133191i	0.901910	+	0.431924i	$0.142165\pi$
$720$			4.39377e8i			1.17717i
$721$	3.08272e7	+	1.77981e7i	0.0822487	+	0.0474863i
$722$	9.65441e7	−	5.57398e7i	0.256516	−	0.148100i
$723$	5.81246e6			0.0153796
$724$	1.78379e8	+	3.08962e8i	0.470034	+	0.814122i
$725$	1.19403e9	+	6.89376e8i	3.13330	+	1.80901i
$726$	−1.53142e7	+	2.65249e7i	−0.0400206	+	0.0693176i
$727$		−	6.56586e8i		−	1.70879i	−0.519626	−	0.854394i	$-0.673929\pi$
$727$		−	6.56586e8i		−	1.70879i	0.519626	−	0.854394i	$-0.326071\pi$
$728$	5.02435e6	−	8.70243e6i	0.0130222	−	0.0225552i
$729$	−2.20204e6			−0.00568385
$730$			2.24772e8i			0.577794i
$731$	−2.85324e7	−	3.76333e8i	−0.0730443	−	0.963429i
$732$	1.79086e8			0.456592
$733$			4.27478e7i			0.108543i	0.998526	+	0.0542716i	$0.0172837\pi$
$733$			4.27478e7i			0.108543i	−0.998526	+	0.0542716i	$0.982716\pi$
$734$	−1.15431e8	−	6.66441e7i	−0.291900	−	0.168529i
$735$	3.13128e8			0.788607
$736$	−4.98480e7	−	2.87798e7i	−0.125030	−	0.0721861i
$737$	−3.42765e7	+	5.93686e7i	−0.0856236	+	0.148304i
$738$	−4.60053e7	+	2.65612e7i	−0.114456	+	0.0660812i
$739$		−	1.13630e8i		−	0.281554i	−0.990041	−	0.140777i	$-0.955040\pi$
$739$		−	1.13630e8i		−	0.281554i	0.990041	−	0.140777i	$-0.0449600\pi$
$740$	−3.14234e8	−	5.44269e8i	−0.775457	−	1.34313i
$741$	−7.27233e7	+	1.25960e8i	−0.178739	+	0.309585i
$742$	4.36307e6			0.0106802
$743$	−6.59741e8	−	3.80902e8i	−1.60845	−	0.928638i	−0.989718	−	0.143036i	$-0.954314\pi$
$743$	−6.59741e8	−	3.80902e8i	−1.60845	−	0.928638i	−0.618731	−	0.785603i	$-0.712353\pi$
$744$	8.19464e7	+	1.41935e8i	0.198981	+	0.344645i
$745$	9.92956e7	+	1.71985e8i	0.240138	+	0.415931i
$746$	−6.66555e7	−	1.15451e8i	−0.160553	−	0.278087i
$747$	−1.24056e8			−0.297616
$748$	−9.82826e7	−	1.70230e8i	−0.234840	−	0.406755i
$749$	3.94669e7	−	2.27862e7i	0.0939263	−	0.0542284i
$750$	−8.43339e7	−	4.86902e7i	−0.199903	−	0.115414i
$751$	3.52805e8	+	2.03692e8i	0.832943	+	0.480900i	0.854859	−	0.518860i	$-0.173643\pi$
$751$	3.52805e8	+	2.03692e8i	0.832943	+	0.480900i	−0.0219163	+	0.999760i	$0.506977\pi$
$752$	−1.85099e8			−0.435262
$753$			2.25316e7i			0.0527723i
$754$	−4.67593e7	+	8.09894e7i	−0.109082	+	0.188936i
$755$	−1.55841e8	+	2.69924e8i	−0.362109	+	0.627192i
$756$	1.66474e7	+	2.88341e7i	0.0385284	+	0.0667332i
$757$	−1.24829e8	+	7.20703e7i	−0.287759	+	0.166138i	−0.636931	−	0.770921i	$-0.719796\pi$
$757$	−1.24829e8	+	7.20703e7i	−0.287759	+	0.166138i	0.349172	+	0.937059i	$0.386463\pi$
$758$			1.43695e8i			0.329938i
$759$	1.86681e7	−	1.07780e7i	0.0426948	−	0.0246499i
$760$	4.78724e8	−	2.76392e8i	1.09055	−	0.629628i
$761$	8.24324e7	−	4.75924e7i	0.187044	−	0.107990i	−0.403554	−	0.914956i	$-0.632225\pi$
$761$	8.24324e7	−	4.75924e7i	0.187044	−	0.107990i	0.590598	+	0.806966i	$0.298892\pi$
$762$	3.01216e7	−	5.21721e7i	0.0680790	−	0.117916i
$763$		−	1.71379e7i		−	0.0385819i
$764$	5.01831e8	+	2.89732e8i	1.12532	+	0.649706i
$765$	5.35139e8	−	3.08962e8i	1.19531	−	0.690115i
$766$	6.58705e7			0.146556
$767$	1.27454e8	+	2.20757e8i	0.282467	+	0.489248i
$768$	7.95014e7	+	4.59002e7i	0.175506	+	0.101328i
$769$	1.48012e8	−	2.56364e8i	0.325475	−	0.563739i	−0.656134	−	0.754645i	$-0.727809\pi$
$769$	1.48012e8	−	2.56364e8i	0.325475	−	0.563739i	0.981608	+	0.190906i	$0.0611425\pi$
$770$		−	1.05029e7i		−	0.0230059i
$771$	8.45494e7	−	1.46444e8i	0.184479	−	0.319527i
$772$	−9.72410e7			−0.211348
$773$		−	4.60390e8i		−	0.996752i	−0.866961	−	0.498376i	$-0.833930\pi$
$773$		−	4.60390e8i		−	0.996752i	0.866961	−	0.498376i	$-0.166070\pi$
$774$	−9.05490e7	+	6.86515e6i	−0.195281	+	0.0148056i
$775$	−1.90881e9			−4.10070
$776$		−	1.84000e8i		−	0.393760i
$777$	−1.70959e7	−	9.87034e6i	−0.0364443	−	0.0210411i
$778$	1.28398e8			0.272659
$779$	−4.10791e8	−	2.37170e8i	−0.868977	−	0.501704i
$780$	−9.57017e7	+	1.65760e8i	−0.201667	+	0.349298i
$781$	7.75659e7	−	4.47827e7i	0.162824	−	0.0940063i
$782$			2.41323e7i			0.0504636i
$783$	−3.19721e8	−	5.53773e8i	−0.666017	−	1.15358i
$784$	−1.96488e8	+	3.40327e8i	−0.407744	+	0.706233i
$785$	−9.55678e8			−1.97562
$786$	−1.02913e7	−	5.94169e6i	−0.0211935	−	0.0122361i
$787$	5.75589e7	+	9.96950e7i	0.118083	+	0.204526i	0.919008	−	0.394239i	$-0.128992\pi$
$787$	5.75589e7	+	9.96950e7i	0.118083	+	0.204526i	−0.800925	+	0.598765i	$0.795658\pi$
$788$	2.90548e8	+	5.03243e8i	0.593798	+	1.02849i
$789$	−4.36138e7	−	7.55414e7i	−0.0887960	−	0.153799i
$790$	2.40873e8			0.488548
$791$	4.59014e7	+	7.95035e7i	0.0927462	+	0.160641i
$792$	−8.45251e7	+	4.88006e7i	−0.170141	+	0.0982312i
$793$	−2.52839e8	−	1.45977e8i	−0.507020	−	0.292728i
$794$	−2.63744e7	−	1.52273e7i	−0.0526891	−	0.0304201i
$795$	−1.71502e8			−0.341324
$796$		−	3.87270e8i		−	0.767846i
$797$	8.88419e7	−	1.53879e8i	0.175486	−	0.303951i	−0.764843	−	0.644216i	$-0.777184\pi$
$797$	8.88419e7	−	1.53879e8i	0.175486	−	0.303951i	0.940329	+	0.340265i	$0.110517\pi$
$798$	4.20695e6	−	7.28665e6i	0.00827863	−	0.0143390i
$799$	1.30159e8	+	2.25441e8i	0.255172	+	0.441970i
$800$	6.54862e8	−	3.78085e8i	1.27903	−	0.738447i
$801$		−	2.17178e8i		−	0.422589i
$802$	6.01110e6	−	3.47051e6i	0.0116528	−	0.00672775i
$803$	3.06892e8	−	1.77184e8i	0.592705	−	0.342198i
$804$	−6.25877e7	+	3.61350e7i	−0.120426	+	0.0695281i
$805$	1.01286e7	−	1.75433e7i	0.0194162	−	0.0336298i
$806$		−	1.29472e8i		−	0.247269i
$807$	−2.10026e8	−	1.21259e8i	−0.399625	−	0.230724i
$808$	2.56497e7	−	1.48089e7i	0.0486237	−	0.0280729i
$809$	−7.98672e8			−1.50842			−0.754212	−	0.656632i	$-0.771981\pi$
$809$	−7.98672e8			−1.50842			−0.754212	+	0.656632i	$0.771981\pi$
$810$	−5.12059e7	−	8.86912e7i	−0.0963529	−	0.166888i
$811$	5.59703e8	+	3.23145e8i	1.04929	+	0.605807i	0.922450	−	0.386116i	$-0.126184\pi$
$811$	5.59703e8	+	3.23145e8i	1.04929	+	0.605807i	0.126839	+	0.991923i	$0.459517\pi$
$812$	−4.24952e7	+	7.36039e7i	−0.0793729	+	0.137478i
$813$			4.68077e8i			0.871055i
$814$	3.15346e7	−	5.46195e7i	0.0584674	−	0.101269i
$815$	8.86621e8			1.63782
$816$		−	1.93193e8i		−	0.355567i
$817$	−4.57353e8	−	6.69558e8i	−0.838659	−	1.22778i
$818$	1.49403e8			0.272960
$819$		−	2.41332e7i		−	0.0439302i
$820$	−5.40588e8	−	3.12109e8i	−0.980449	−	0.566063i
$821$	−1.02929e8			−0.185998			−0.0929991	−	0.995666i	$-0.529645\pi$
$821$	−1.02929e8			−0.185998			−0.0929991	+	0.995666i	$0.529645\pi$
$822$	−5.28615e7	−	3.05196e7i	−0.0951753	−	0.0549495i
$823$	−1.73865e8	+	3.01143e8i	−0.311898	+	0.540222i	−0.978773	−	0.204947i	$-0.934298\pi$
$823$	−1.73865e8	+	3.01143e8i	−0.311898	+	0.540222i	0.666876	+	0.745169i	$0.267631\pi$
$824$	−2.14269e8	+	1.23708e8i	−0.382981	+	0.221114i
$825$			2.83186e8i			0.504325i
$826$	−7.37307e6	−	1.27705e7i	−0.0130830	−	0.0226605i
$827$	−3.33777e8	+	5.78118e8i	−0.590119	+	1.02212i	0.404097	+	0.914716i	$0.367586\pi$
$827$	−3.33777e8	+	5.78118e8i	−0.590119	+	1.02212i	−0.994216	+	0.107400i	$0.965748\pi$
$828$	−9.12197e7			−0.160693
$829$	−2.81496e7	−	1.62522e7i	−0.0494094	−	0.0285265i	0.475092	−	0.879936i	$-0.342415\pi$
$829$	−2.81496e7	−	1.62522e7i	−0.0494094	−	0.0285265i	−0.524501	+	0.851410i	$0.675748\pi$
$830$	4.63947e7	+	8.03580e7i	0.0811399	+	0.140538i
$831$	−4.16812e7	−	7.21939e7i	−0.0726335	−	0.125805i
$832$	−1.02106e8	−	1.76852e8i	−0.177288	−	0.307072i
$833$	5.52667e8			0.956156
$834$	−2.38856e7	−	4.13710e7i	−0.0411753	−	0.0713178i
$835$	1.37435e9	−	7.93482e8i	2.36069	−	1.36294i
$836$	−3.65731e8	−	2.11155e8i	−0.625955	−	0.361395i
$837$	7.66670e8	+	4.42637e8i	1.30747	+	0.754869i
$838$	−9.67994e7			−0.164490
$839$			4.52584e8i			0.766326i	0.923681	+	0.383163i	$0.125165\pi$
$839$			4.52584e8i			0.766326i	−0.923681	+	0.383163i	$0.874835\pi$
$840$	1.14248e7	−	1.97884e7i	0.0192758	−	0.0333867i
$841$	5.18728e8	−	8.98464e8i	0.872071	−	1.51047i
$842$	2.21254e7	+	3.83224e7i	0.0370643	+	0.0641972i
$843$	−9.78844e7	+	5.65136e7i	−0.163392	+	0.0943344i
$844$			2.40257e8i			0.399621i
$845$	−6.62150e8	+	3.82293e8i	−1.09745	+	0.633616i
$846$	5.42432e7	−	3.13173e7i	0.0895847	−	0.0517218i
$847$	3.92987e7	−	2.26891e7i	0.0646738	−	0.0373394i
$848$	1.07617e8	−	1.86398e8i	0.176479	−	0.305671i
$849$		−	2.66254e7i		−	0.0435084i
$850$	−2.74556e8	−	1.58515e8i	−0.447069	−	0.258115i
$851$	1.05346e8	−	6.08216e7i	0.170934	−	0.0986890i
$852$	9.44218e7			0.152670
$853$	3.54126e8	+	6.13365e8i	0.570573	+	0.988261i	0.996507	+	0.0835071i	$0.0266121\pi$
$853$	3.54126e8	+	6.13365e8i	0.570573	+	0.988261i	−0.425934	+	0.904754i	$0.640055\pi$
$854$	1.46264e7	+	8.44457e6i	0.0234836	+	0.0135583i
$855$	6.63789e8	−	1.14972e9i	1.06202	−	1.83947i
$856$			3.16757e8i			0.505015i
$857$	−3.47087e8	+	6.01172e8i	−0.551437	+	0.955117i	0.446734	+	0.894667i	$0.352587\pi$
$857$	−3.47087e8	+	6.01172e8i	−0.551437	+	0.955117i	−0.998171	+	0.0604502i	$0.980746\pi$
$858$	−1.92081e7			−0.0304104
$859$			1.03223e9i			1.62854i	0.580488	+	0.814269i	$0.302862\pi$
$859$			1.03223e9i			1.62854i	−0.580488	+	0.814269i	$0.697138\pi$
$860$	−6.01863e8	−	8.81118e8i	−0.946242	−	1.38528i
$861$	−1.96072e7			−0.0307189
$862$			3.09339e8i			0.482962i
$863$	−8.67705e7	−	5.00970e7i	−0.135002	−	0.0779433i	0.430978	−	0.902362i	$-0.358169\pi$
$863$	−8.67705e7	−	5.00970e7i	−0.135002	−	0.0779433i	−0.565980	+	0.824419i	$0.691502\pi$
$864$	−3.50699e8			−0.543742
$865$	−9.45089e8	−	5.45647e8i	−1.46024	−	0.843070i
$866$	1.15170e8	−	1.99480e8i	0.177331	−	0.307146i
$867$	1.67535e7	−	9.67266e6i	0.0257069	−	0.0148419i
$868$		−	1.17665e8i		−	0.179924i
$869$	−1.89877e8	−	3.28876e8i	−0.289342	−	0.501156i
$870$	−1.06326e8	+	1.84161e8i	−0.161466	+	0.279667i
$871$	1.17818e8			0.178302
$872$	1.03160e8	+	5.95595e7i	0.155583	+	0.0898259i
$873$	−2.20949e8	−	3.82695e8i	−0.332085	−	0.575189i
$874$	2.59234e7	+	4.49007e7i	0.0388292	+	0.0672541i
$875$	7.21384e7	+	1.24947e8i	0.107682	+	0.186510i
$876$	3.73583e8			0.555743
$877$	3.38442e8	+	5.86199e8i	0.501748	+	0.869053i	0.999998	+	0.00201937i	$0.000642786\pi$
$877$	3.38442e8	+	5.86199e8i	0.501748	+	0.869053i	−0.498250	+	0.867033i	$0.666024\pi$
$878$	−8.13201e7	+	4.69502e7i	−0.120147	+	0.0693671i
$879$	4.20966e8	+	2.43045e8i	0.619841	+	0.357866i
$880$	−4.48705e8	−	2.59060e8i	−0.658435	−	0.380148i
$881$	−1.63728e8			−0.239439			−0.119720	−	0.992808i	$-0.538200\pi$
$881$	−1.63728e8			−0.239439			−0.119720	+	0.992808i	$0.538200\pi$
$882$		−	1.32977e8i		−	0.193807i
$883$	−1.25251e8	+	2.16942e8i	−0.181928	+	0.315109i	−0.942537	−	0.334101i	$-0.891567\pi$
$883$	−1.25251e8	+	2.16942e8i	−0.181928	+	0.315109i	0.760609	+	0.649210i	$0.224901\pi$
$884$	−1.68912e8	+	2.92565e8i	−0.244514	+	0.423511i
$885$	2.89817e8	+	5.01979e8i	0.418114	+	0.724195i
$886$	5.90817e7	−	3.41108e7i	0.0849477	−	0.0490446i
$887$			1.02506e9i			1.46885i	0.678691	+	0.734424i	$0.262548\pi$
$887$			1.02506e9i			1.46885i	−0.678691	+	0.734424i	$0.737452\pi$
$888$	1.18827e8	−	6.86051e7i	0.169698	−	0.0979755i
$889$	−7.72971e7	+	4.46275e7i	−0.110017	+	0.0635181i
$890$	−1.40678e8	+	8.12206e7i	−0.199552	+	0.115212i
$891$	−8.07296e7	+	1.39828e8i	−0.114130	+	0.197679i
$892$			2.13639e8i			0.301013i
$893$	4.84349e8	+	2.79639e8i	0.680148	+	0.392684i
$894$	−1.81952e7	+	1.05050e7i	−0.0254650	+	0.0147022i
$895$	1.12850e9			1.57410
$896$	3.06965e7	+	5.31679e7i	0.0426742	+	0.0739139i
$897$	−3.20837e7	−	1.85235e7i	−0.0444536	−	0.0256653i
$898$	9.33538e7	−	1.61693e8i	0.128915	−	0.223287i
$899$			2.25981e9i			3.11023i
$900$	5.99185e8	−	1.03782e9i	0.821927	−	1.42362i
$901$	−3.02698e8			−0.413843
$902$		−	6.26426e7i		−	0.0853592i
$903$	−3.02105e7	−	1.45162e7i	−0.0410294	−	0.0197146i
$904$	−6.38087e8			−0.863723
$905$		−	1.32250e9i		−	1.78423i
$906$	−2.85567e7	−	1.64872e7i	−0.0383993	−	0.0221698i
$907$	2.64567e8			0.354579			0.177290	−	0.984159i	$-0.443267\pi$
$907$	2.64567e8			0.354579			0.177290	+	0.984159i	$0.443267\pi$
$908$	5.13259e7	+	2.96330e7i	0.0685613	+	0.0395839i
$909$	3.55653e7	−	6.16009e7i	0.0473516	−	0.0820155i
$910$	−1.56324e7	+	9.02538e6i	−0.0207445	+	0.0119768i
$911$			4.44174e8i			0.587487i	0.955884	+	0.293744i	$0.0949012\pi$
$911$			4.44174e8i			0.587487i	−0.955884	+	0.293744i	$0.905099\pi$
$912$	−2.07533e8	−	3.59457e8i	−0.273591	−	0.473874i
$913$	7.31445e7	−	1.26690e8i	0.0961101	−	0.166468i
$914$	1.66420e8			0.217955
$915$	−5.74930e8	−	3.31936e8i	−0.750501	−	0.433302i
$916$	6.04300e8	+	1.04668e9i	0.786259	+	1.36184i
$917$	8.80308e6	+	1.52474e7i	0.0114163	+	0.0197737i
$918$	7.35166e7	+	1.27334e8i	0.0950292	+	0.164595i
$919$	1.26252e9			1.62664			0.813321	−	0.581816i	$-0.197658\pi$
$919$	1.26252e9			1.62664			0.813321	+	0.581816i	$0.197658\pi$
$920$	7.04005e7	+	1.21937e8i	0.0904091	+	0.156593i
$921$	5.32383e8	−	3.07372e8i	0.681468	−	0.393446i
$922$	2.68931e8	+	1.55267e8i	0.343121	+	0.198101i
$923$	−1.33308e8	−	7.69652e7i	−0.169531	−	0.0978789i
$924$	−1.74565e7			−0.0221279
$925$			1.59805e9i			2.01913i
$926$	−9.61704e7	+	1.66572e8i	−0.121118	+	0.209783i
$927$	−2.97100e8	+	5.14593e8i	−0.372962	+	0.645988i
$928$	−4.47608e8	−	7.75280e8i	−0.560085	−	0.970096i
$929$	4.79197e6	−	2.76664e6i	0.00597677	−	0.00345069i	−0.497009	−	0.867746i	$-0.665568\pi$
$929$	4.79197e6	−	2.76664e6i	0.00597677	−	0.00345069i	0.502985	+	0.864295i	$0.332235\pi$
$930$		−	2.94405e8i		−	0.366013i
$931$	1.02830e9	−	5.93688e8i	1.27429	−	0.735714i
$932$	−4.92917e8	+	2.84586e8i	−0.608873	+	0.351533i
$933$	−5.71871e8	+	3.30170e8i	−0.704130	+	0.406530i
$934$	1.11618e8	−	1.93328e8i	0.136992	−	0.237276i
$935$			7.28666e8i			0.891444i
$936$	1.45268e8	+	8.38705e7i	0.177151	+	0.102278i
$937$	2.96924e8	−	1.71429e8i	0.360933	−	0.208384i	−0.308557	−	0.951206i	$-0.599846\pi$
$937$	2.96924e8	−	1.71429e8i	0.360933	−	0.208384i	0.669490	+	0.742821i	$0.266513\pi$
$938$	−6.81560e6			−0.00825839
$939$	−2.90646e8	−	5.03414e8i	−0.351049	−	0.608035i
$940$	6.37388e8	+	3.67996e8i	0.767398	+	0.443057i
$941$	−1.06530e8	+	1.84515e8i	−0.127850	+	0.221443i	−0.922844	−	0.385175i	$-0.874141\pi$
$941$	−1.06530e8	+	1.84515e8i	−0.127850	+	0.221443i	0.794993	+	0.606618i	$0.207474\pi$
$942$		−	1.01106e8i		−	0.120955i
$943$	6.04102e7	−	1.04634e8i	0.0720403	−	0.124777i
$944$	−7.27441e8			−0.864732
$945$		−	1.23424e8i		−	0.146252i
$946$	4.63775e7	−	9.65191e7i	0.0547815	−	0.114009i
$947$	3.18533e8			0.375063			0.187532	−	0.982259i	$-0.439951\pi$
$947$	3.18533e8			0.375063			0.187532	+	0.982259i	$0.439951\pi$
$948$		−	4.00345e8i		−	0.469904i
$949$	−5.27435e8	−	3.04515e8i	−0.617122	−	0.356295i
$950$	−6.81122e8			−0.794427
$951$	6.18208e8	+	3.56922e8i	0.718775	+	0.414985i
$952$	2.01647e7	−	3.49263e7i	0.0233712	−	0.0404801i
$953$	−8.23481e8	+	4.75437e8i	−0.951426	+	0.549306i	−0.893524	−	0.449016i	$-0.851775\pi$
$953$	−8.23481e8	+	4.75437e8i	−0.951426	+	0.549306i	−0.0579023	+	0.998322i	$0.518441\pi$
$954$			7.28318e7i			0.0838834i
$955$	−1.07404e9	−	1.86029e9i	−1.23313	−	2.13584i
$956$	1.90552e8	−	3.30046e8i	0.218092	−	0.377747i
$957$	3.35259e8			0.382512
$958$	1.16916e8	+	6.75012e7i	0.132977	+	0.0767742i
$959$	4.52172e7	+	7.83185e7i	0.0512682	+	0.0887991i
$960$	−2.32177e8	−	4.02143e8i	−0.262426	−	0.454535i
$961$	−1.12055e9	−	1.94084e9i	−1.26258	−	2.18685i
$962$	−1.08393e8			−0.121752
$963$	3.80366e8	+	6.58812e8i	0.425914	+	0.737705i
$964$	2.51190e7	−	1.45025e7i	0.0280396	−	0.0161887i
$965$	3.12178e8	+	1.80236e8i	0.347392	+	0.200567i
$966$	1.85600e6	+	1.07156e6i	0.00205896	+	0.00118874i
$967$	−1.30171e9			−1.43957			−0.719787	−	0.694195i	$-0.755761\pi$
$967$	−1.30171e9			−1.43957			−0.719787	+	0.694195i	$0.755761\pi$
$968$			3.15407e8i			0.347733i
$969$	−2.91867e8	+	5.05528e8i	−0.320785	+	0.555615i
$970$	−1.65262e8	+	2.86242e8i	−0.181074	+	0.313630i
$971$	−2.89913e8	−	5.02144e8i	−0.316672	−	0.548492i	0.663120	−	0.748514i	$-0.269232\pi$
$971$	−2.89913e8	−	5.02144e8i	−0.316672	−	0.548492i	−0.979791	+	0.200022i	$0.935899\pi$
$972$	−7.48641e8	+	4.32228e8i	−0.815220	+	0.470667i
$973$			7.07767e7i			0.0768337i
$974$	−1.82941e8	+	1.05621e8i	−0.197986	+	0.114307i
$975$	4.21490e8	−	2.43347e8i	0.454751	−	0.262550i
$976$	7.21536e8	−	4.16579e8i	0.776083	−	0.448072i
$977$	−1.05202e8	+	1.82215e8i	−0.112808	+	0.195389i	−0.916901	−	0.399114i	$-0.869318\pi$
$977$	−1.05202e8	+	1.82215e8i	−0.112808	+	0.195389i	0.804093	+	0.594503i	$0.202651\pi$
$978$			9.38003e7i			0.100274i
$979$	2.21789e8	+	1.28050e8i	0.236369	+	0.136468i
$980$	1.35321e9	−	7.81276e8i	1.43776	−	0.830092i
$981$	2.86079e8			0.303026
$982$	1.18461e8	+	2.05180e8i	0.125095	+	0.216671i
$983$	−2.25072e8	−	1.29945e8i	−0.236952	−	0.136804i	0.376823	−	0.926285i	$-0.377017\pi$
$983$	−2.25072e8	−	1.29945e8i	−0.236952	−	0.136804i	−0.613775	+	0.789481i	$0.710350\pi$
$984$	6.81411e7	−	1.18024e8i	0.0715194	−	0.123875i
$985$		−	2.15412e9i		−	2.25404i
$986$	−1.87663e8	+	3.25042e8i	−0.195771	+	0.339085i
$987$	2.31181e7			0.0240437
$988$			7.25797e8i			0.752566i
$989$	1.70545e8	−	1.16494e8i	0.176299	−	0.120424i
$990$	1.75324e8			0.180690
$991$			3.25746e8i			0.334702i	0.985897	+	0.167351i	$0.0535213\pi$
$991$			3.25746e8i			0.334702i	−0.985897	+	0.167351i	$0.946479\pi$
$992$	1.07334e9	+	6.19691e8i	1.09951	+	0.634805i
$993$	−3.96482e8			−0.404926
$994$	7.71168e6	+	4.45234e6i	0.00785217	+	0.00453345i
$995$	−7.17803e8	+	1.24327e9i	−0.728679	+	1.26211i
$996$	1.33559e8	−	7.71106e7i	0.135175	−	0.0780434i
$997$		−	1.31924e9i		−	1.33119i	−0.746314	−	0.665594i	$-0.768178\pi$
$997$		−	1.31924e9i		−	1.33119i	0.746314	−	0.665594i	$-0.231822\pi$
$998$	−2.04495e8	−	3.54196e8i	−0.205727	−	0.356329i
$999$	3.70574e8	−	6.41853e8i	0.371688	−	0.643782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.10	yes	42
43.7	odd	6	inner	43.7.d.a.7.12	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.12	✓	42	43.7	odd	6	inner
43.7.d.a.37.10	yes	42	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.95704i q^{2} +(10.4424 + 6.02890i) q^{3} +60.1700 q^{4} +(-193.167 - 111.525i) q^{5} +(11.7988 - 20.4361i) q^{6} +(-30.2778 + 17.4809i) q^{7} -243.006i q^{8} +(-291.805 - 505.421i) q^{9} +O(q^{10})\)	\(q-1.95704i q^{2} +(10.4424 + 6.02890i) q^{3} +60.1700 q^{4} +(-193.167 - 111.525i) q^{5} +(11.7988 - 20.4361i) q^{6} +(-30.2778 + 17.4809i) q^{7} -243.006i q^{8} +(-291.805 - 505.421i) q^{9} +(-218.259 + 378.036i) q^{10} +688.201 q^{11} +(628.316 + 362.759i) q^{12} +(-591.384 - 1024.31i) q^{13} +(34.2108 + 59.2549i) q^{14} +(-1344.75 - 2329.17i) q^{15} +3375.31 q^{16} +(-2373.46 - 4110.95i) q^{17} +(-989.130 + 571.075i) q^{18} +(-8832.15 - 5099.24i) q^{19} +(-11622.8 - 6710.45i) q^{20} -421.562 q^{21} -1346.84i q^{22} +(1298.84 - 2249.66i) q^{23} +(1465.06 - 2537.56i) q^{24} +(17063.1 + 29554.2i) q^{25} +(-2004.61 + 1157.36i) q^{26} -15827.2i q^{27} +(-1821.81 + 1051.82i) q^{28} +(34988.7 - 20200.7i) q^{29} +(-4558.28 + 2631.72i) q^{30} +(-27966.9 + 48440.1i) q^{31} -22158.0i q^{32} +(7186.44 + 4149.09i) q^{33} +(-8045.30 + 4644.96i) q^{34} +7798.21 q^{35} +(-17557.9 - 30411.2i) q^{36} +(40553.8 + 23413.8i) q^{37} +(-9979.44 + 17284.9i) q^{38} -14261.6i q^{39} +(-27101.2 + 46940.7i) q^{40} +46510.8 q^{41} +825.014i q^{42} +(71663.4 + 34434.3i) q^{43} +41409.1 q^{44} +130174. i q^{45} +(-4402.68 - 2541.89i) q^{46} -54839.3 q^{47} +(35246.1 + 20349.4i) q^{48} +(-58213.3 + 100828. i) q^{49} +(57838.9 - 33393.3i) q^{50} -57237.3i q^{51} +(-35583.6 - 61632.6i) q^{52} +(31883.7 - 55224.1i) q^{53} -30974.5 q^{54} +(-132938. - 76751.6i) q^{55} +(4247.96 + 7357.68i) q^{56} +(-61485.6 - 106496. i) q^{57} +(-39533.7 - 68474.4i) q^{58} -215519. q^{59} +(-80913.3 - 140146. i) q^{60} +(213769. - 123420. i) q^{61} +(94799.4 + 54732.5i) q^{62} +(17670.4 + 10202.0i) q^{63} +172655. q^{64} +263816. i q^{65} +(8119.96 - 14064.2i) q^{66} +(-49805.9 + 86266.3i) q^{67} +(-142811. - 247356. i) q^{68} +(27125.9 - 15661.2i) q^{69} -15261.4i q^{70} +(112708. - 65072.1i) q^{71} +(-122820. + 70910.3i) q^{72} +(445933. - 257459. i) q^{73} +(45821.8 - 79365.6i) q^{74} +411487. i q^{75} +(-531430. - 306821. i) q^{76} +(-20837.2 + 12030.4i) q^{77} -27910.5 q^{78} +(-275903. - 477878. i) q^{79} +(-651997. - 376431. i) q^{80} +(-117305. + 203179. i) q^{81} -91023.7i q^{82} +(106284. - 184089. i) q^{83} -25365.4 q^{84} +1.05880e6i q^{85} +(67389.4 - 140248. i) q^{86} +487153. q^{87} -167237. i q^{88} +(322273. + 186064. i) q^{89} +254756. q^{90} +(35811.6 + 20675.8i) q^{91} +(78151.3 - 135362. i) q^{92} +(-584081. + 337219. i) q^{93} +107323. i q^{94} +(1.13739e6 + 1.97001e6i) q^{95} +(133588. - 231382. i) q^{96} +757181. q^{97} +(197326. + 113926. i) q^{98} +(-200820. - 347831. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

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