LMFDB - Embedded newform 5.7.c.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,7,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$1.15027041810$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{201})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 101x^{2} + 2500 $ x^4 + 101*x^2 + 2500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.1
Root			$-6.58872i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.7.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.58872 - 9.58872i) q^{2} +(14.5887 - 14.5887i) q^{3} +119.887i q^{4} +(88.8309 - 87.9436i) q^{5} -279.774 q^{6} +(59.5240 + 59.5240i) q^{7} +(535.887 - 535.887i) q^{8} +303.338i q^{9} +O(q^{10})$	\(q+(-9.58872 - 9.58872i) q^{2} +(14.5887 - 14.5887i) q^{3} +119.887i q^{4} +(88.8309 - 87.9436i) q^{5} -279.774 q^{6} +(59.5240 + 59.5240i) q^{7} +(535.887 - 535.887i) q^{8} +303.338i q^{9} +(-1695.04 - 8.50745i) q^{10} +800.309 q^{11} +(1749.00 + 1749.00i) q^{12} +(-459.889 + 459.889i) q^{13} -1141.52i q^{14} +(12.9436 - 2578.91i) q^{15} -2604.17 q^{16} +(-2989.15 - 2989.15i) q^{17} +(2908.63 - 2908.63i) q^{18} +6971.14i q^{19} +(10543.3 + 10649.7i) q^{20} +1736.76 q^{21} +(-7673.94 - 7673.94i) q^{22} +(-12013.8 + 12013.8i) q^{23} -15635.8i q^{24} +(156.840 - 15624.2i) q^{25} +8819.50 q^{26} +(15060.5 + 15060.5i) q^{27} +(-7136.17 + 7136.17i) q^{28} -26318.7i q^{29} +(-24852.6 + 24604.4i) q^{30} +16163.1 q^{31} +(-9326.16 - 9326.16i) q^{32} +(11675.5 - 11675.5i) q^{33} +57324.3i q^{34} +(10522.3 + 52.8118i) q^{35} -36366.4 q^{36} +(16894.9 + 16894.9i) q^{37} +(66844.4 - 66844.4i) q^{38} +13418.4i q^{39} +(475.458 - 94731.2i) q^{40} -124725. q^{41} +(-16653.3 - 16653.3i) q^{42} +(-29630.9 + 29630.9i) q^{43} +95946.8i q^{44} +(26676.7 + 26945.8i) q^{45} +230394. q^{46} +(35714.9 + 35714.9i) q^{47} +(-37991.5 + 37991.5i) q^{48} -110563. i q^{49} +(-151320. + 148312. i) q^{50} -87215.7 q^{51} +(-55134.8 - 55134.8i) q^{52} +(45590.3 - 45590.3i) q^{53} -288822. i q^{54} +(71092.1 - 70382.0i) q^{55} +63796.3 q^{56} +(101700. + 101700. i) q^{57} +(-252363. + 252363. i) q^{58} +5231.18i q^{59} +(309179. + 1551.77i) q^{60} +20085.9 q^{61} +(-154983. - 154983. i) q^{62} +(-18055.9 + 18055.9i) q^{63} +345518. i q^{64} +(-408.029 + 81296.6i) q^{65} -223906. q^{66} +(-228348. - 228348. i) q^{67} +(358361. - 358361. i) q^{68} +350532. i q^{69} +(-100389. - 101402. i) q^{70} +471094. q^{71} +(162555. + 162555. i) q^{72} +(-24258.7 + 24258.7i) q^{73} -324002. i q^{74} +(-225649. - 230225. i) q^{75} -835751. q^{76} +(47637.6 + 47637.6i) q^{77} +(128665. - 128665. i) q^{78} -476823. i q^{79} +(-231330. + 229020. i) q^{80} +218293. q^{81} +(1.19595e6 + 1.19595e6i) q^{82} +(-296628. + 296628. i) q^{83} +208215. i q^{84} +(-528405. - 2652.08i) q^{85} +568245. q^{86} +(-383957. - 383957. i) q^{87} +(428875. - 428875. i) q^{88} +834303. i q^{89} +(2580.63 - 514171. i) q^{90} -54748.9 q^{91} +(-1.44030e6 - 1.44030e6i) q^{92} +(235799. - 235799. i) q^{93} -684921. i q^{94} +(613068. + 619253. i) q^{95} -272113. q^{96} +(-60336.2 - 60336.2i) q^{97} +(-1.06016e6 + 1.06016e6i) q^{98} +242764. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8}+O(q^{10}) $ 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8	\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8} - 4370 q^{10} - 1052 q^{11} + 3480 q^{12} + 1960 q^{13} - 90 q^{15} - 776 q^{16} - 3280 q^{17} - 870 q^{18} + 20340 q^{20} + 3828 q^{21} - 27520 q^{22} - 39010 q^{23} + 30400 q^{25} + 44068 q^{26} + 31320 q^{27} - 4840 q^{28} - 50640 q^{30} - 33172 q^{31} - 48760 q^{32} + 22260 q^{33} - 24970 q^{35} - 40836 q^{36} + 146860 q^{37} + 218040 q^{38} - 110100 q^{40} - 213932 q^{41} - 31680 q^{42} - 72050 q^{43} + 78210 q^{45} + 323288 q^{46} + 830 q^{47} - 74160 q^{48} - 203350 q^{50} - 172212 q^{51} - 173300 q^{52} - 29620 q^{53} + 470660 q^{55} + 467280 q^{56} + 195840 q^{57} - 554640 q^{58} + 620280 q^{60} - 111052 q^{61} - 610520 q^{62} - 350130 q^{63} - 406540 q^{65} - 457824 q^{66} - 146930 q^{67} + 775780 q^{68} - 133320 q^{70} + 1310188 q^{71} + 899460 q^{72} + 553540 q^{73} - 435450 q^{75} - 2073840 q^{76} - 476300 q^{77} + 268200 q^{78} - 1011520 q^{80} - 624816 q^{81} + 2554880 q^{82} + 536870 q^{83} - 1344920 q^{85} + 1019128 q^{86} - 763440 q^{87} - 187680 q^{88} + 947310 q^{90} + 1131548 q^{91} - 2552680 q^{92} + 444660 q^{93} + 912600 q^{95} - 568992 q^{96} - 59420 q^{97} - 1892810 q^{98}+O(q^{100}) \) 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8 - 4370 * q^10 - 1052 * q^11 + 3480 * q^12 + 1960 * q^13 - 90 * q^15 - 776 * q^16 - 3280 * q^17 - 870 * q^18 + 20340 * q^20 + 3828 * q^21 - 27520 * q^22 - 39010 * q^23 + 30400 * q^25 + 44068 * q^26 + 31320 * q^27 - 4840 * q^28 - 50640 * q^30 - 33172 * q^31 - 48760 * q^32 + 22260 * q^33 - 24970 * q^35 - 40836 * q^36 + 146860 * q^37 + 218040 * q^38 - 110100 * q^40 - 213932 * q^41 - 31680 * q^42 - 72050 * q^43 + 78210 * q^45 + 323288 * q^46 + 830 * q^47 - 74160 * q^48 - 203350 * q^50 - 172212 * q^51 - 173300 * q^52 - 29620 * q^53 + 470660 * q^55 + 467280 * q^56 + 195840 * q^57 - 554640 * q^58 + 620280 * q^60 - 111052 * q^61 - 610520 * q^62 - 350130 * q^63 - 406540 * q^65 - 457824 * q^66 - 146930 * q^67 + 775780 * q^68 - 133320 * q^70 + 1310188 * q^71 + 899460 * q^72 + 553540 * q^73 - 435450 * q^75 - 2073840 * q^76 - 476300 * q^77 + 268200 * q^78 - 1011520 * q^80 - 624816 * q^81 + 2554880 * q^82 + 536870 * q^83 - 1344920 * q^85 + 1019128 * q^86 - 763440 * q^87 - 187680 * q^88 + 947310 * q^90 + 1131548 * q^91 - 2552680 * q^92 + 444660 * q^93 + 912600 * q^95 - 568992 * q^96 - 59420 * q^97 - 1892810 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−9.58872	−	9.58872i	−1.19859	−	1.19859i	−0.974589	−	0.224002i	$-0.928088\pi$
$2$	−9.58872	−	9.58872i	−1.19859	−	1.19859i	−0.224002	−	0.974589i	$-0.571912\pi$
$3$	14.5887	−	14.5887i	0.540323	−	0.540323i	−0.383301	−	0.923624i	$-0.625213\pi$
$3$	14.5887	−	14.5887i	0.540323	−	0.540323i	0.923624	+	0.383301i	$0.125213\pi$
$4$			119.887i			1.87324i
$5$	88.8309	−	87.9436i	0.710647	−	0.703549i
$5$	88.8309	−	87.9436i	0.710647	−	0.703549i
$6$	−279.774			−1.29525
$7$	59.5240	+	59.5240i	0.173539	+	0.173539i	0.788533	−	0.614993i	$-0.210841\pi$
$7$	59.5240	+	59.5240i	0.173539	+	0.173539i	−0.614993	+	0.788533i	$0.710841\pi$
$8$	535.887	−	535.887i	1.04665	−	1.04665i
$9$			303.338i			0.416102i
$10$	−1695.04	−	8.50745i	−1.69504	−	0.00850745i
$11$	800.309			0.601284			0.300642	−	0.953737i	$-0.402799\pi$
$11$	800.309			0.601284			0.300642	+	0.953737i	$0.402799\pi$
$12$	1749.00	+	1749.00i	1.01215	+	1.01215i
$13$	−459.889	+	459.889i	−0.209326	+	0.209326i	−0.803981	−	0.594655i	$-0.797289\pi$
$13$	−459.889	+	459.889i	−0.209326	+	0.209326i	0.594655	+	0.803981i	$0.297289\pi$
$14$		−	1141.52i		−	0.416006i
$15$	12.9436	−	2578.91i	0.00383515	−	0.764123i
$16$	−2604.17			−0.635783
$17$	−2989.15	−	2989.15i	−0.608416	−	0.608416i	0.334116	−	0.942532i	$-0.391562\pi$
$17$	−2989.15	−	2989.15i	−0.608416	−	0.608416i	−0.942532	+	0.334116i	$0.891562\pi$
$18$	2908.63	−	2908.63i	0.498736	−	0.498736i
$19$			6971.14i			1.01635i	0.861254	+	0.508175i	$0.169680\pi$
$19$			6971.14i			1.01635i	−0.861254	+	0.508175i	$0.830320\pi$
$20$	10543.3	+	10649.7i	1.31791	+	1.33121i
$21$	1736.76			0.187535
$22$	−7673.94	−	7673.94i	−0.720693	−	0.720693i
$23$	−12013.8	+	12013.8i	−0.987409	+	0.987409i	−0.999922	−	0.0125129i	$-0.996017\pi$
$23$	−12013.8	+	12013.8i	−0.987409	+	0.987409i	0.0125129	+	0.999922i	$0.496017\pi$
$24$		−	15635.8i		−	1.13106i
$25$	156.840	−	15624.2i	0.0100378	−	0.999950i
$26$	8819.50			0.501792
$27$	15060.5	+	15060.5i	0.765153	+	0.765153i
$28$	−7136.17	+	7136.17i	−0.325081	+	0.325081i
$29$		−	26318.7i		−	1.07912i	−0.841946	−	0.539562i	$-0.818590\pi$
$29$		−	26318.7i		−	1.07912i	0.841946	−	0.539562i	$-0.181410\pi$
$30$	−24852.6	+	24604.4i	−0.920467	+	0.911273i
$31$	16163.1			0.542550			0.271275	−	0.962502i	$-0.412555\pi$
$31$	16163.1			0.542550			0.271275	+	0.962502i	$0.412555\pi$
$32$	−9326.16	−	9326.16i	−0.284612	−	0.284612i
$33$	11675.5	−	11675.5i	0.324887	−	0.324887i
$34$			57324.3i			1.45848i
$35$	10522.3	+	52.8118i	0.245419	+	0.00123176i
$36$	−36366.4			−0.779458
$37$	16894.9	+	16894.9i	0.333543	+	0.333543i	0.853930	−	0.520388i	$-0.174213\pi$
$37$	16894.9	+	16894.9i	0.333543	+	0.333543i	−0.520388	+	0.853930i	$0.674213\pi$
$38$	66844.4	−	66844.4i	1.21819	−	1.21819i
$39$			13418.4i			0.226207i
$40$	475.458	−	94731.2i	0.00742902	−	1.48017i
$41$	−124725.			−1.80968			−0.904838	−	0.425756i	$-0.860008\pi$
$41$	−124725.			−1.80968			−0.904838	+	0.425756i	$0.860008\pi$
$42$	−16653.3	−	16653.3i	−0.224777	−	0.224777i
$43$	−29630.9	+	29630.9i	−0.372683	+	0.372683i	−0.868454	−	0.495770i	$-0.834886\pi$
$43$	−29630.9	+	29630.9i	−0.372683	+	0.372683i	0.495770	+	0.868454i	$0.334886\pi$
$44$			95946.8i			1.12635i
$45$	26676.7	+	26945.8i	0.292748	+	0.295702i
$46$	230394.			2.36700
$47$	35714.9	+	35714.9i	0.343998	+	0.343998i	0.857868	−	0.513870i	$-0.171789\pi$
$47$	35714.9	+	35714.9i	0.343998	+	0.343998i	−0.513870	+	0.857868i	$0.671789\pi$
$48$	−37991.5	+	37991.5i	−0.343528	+	0.343528i
$49$		−	110563.i		−	0.939768i
$50$	−151320.	+	148312.i	−1.21056	+	1.18650i
$51$	−87215.7			−0.657483
$52$	−55134.8	−	55134.8i	−0.392117	−	0.392117i
$53$	45590.3	−	45590.3i	0.306228	−	0.306228i	−0.537216	−	0.843444i	$-0.680524\pi$
$53$	45590.3	−	45590.3i	0.306228	−	0.306228i	0.843444	+	0.537216i	$0.180524\pi$
$54$		−	288822.i		−	1.83421i
$55$	71092.1	−	70382.0i	0.427300	−	0.423032i
$56$	63796.3			0.363272
$57$	101700.	+	101700.i	0.549157	+	0.549157i
$58$	−252363.	+	252363.i	−1.29343	+	1.29343i
$59$			5231.18i			0.0254709i	0.999919	+	0.0127354i	$0.00405392\pi$
$59$			5231.18i			0.0254709i	−0.999919	+	0.0127354i	$0.995946\pi$
$60$	309179.	+	1551.77i	1.43138	+	0.00718414i
$61$	20085.9			0.0884915			0.0442457	−	0.999021i	$-0.485912\pi$
$61$	20085.9			0.0884915			0.0442457	+	0.999021i	$0.485912\pi$
$62$	−154983.	−	154983.i	−0.650295	−	0.650295i
$63$	−18055.9	+	18055.9i	−0.0722101	+	0.0722101i
$64$			345518.i			1.31805i
$65$	−408.029	+	81296.6i	−0.00148577	+	0.296028i
$66$	−223906.			−0.778814
$67$	−228348.	−	228348.i	−0.759228	−	0.759228i	0.216954	−	0.976182i	$-0.430388\pi$
$67$	−228348.	−	228348.i	−0.759228	−	0.759228i	−0.976182	+	0.216954i	$0.930388\pi$
$68$	358361.	−	358361.i	1.13971	−	1.13971i
$69$			350532.i			1.06704i
$70$	−100389.	−	101402.i	−0.292680	−	0.295633i
$71$	471094.			1.31623			0.658116	−	0.752917i	$-0.271354\pi$
$71$	471094.			1.31623			0.658116	+	0.752917i	$0.271354\pi$
$72$	162555.	+	162555.i	0.435515	+	0.435515i
$73$	−24258.7	+	24258.7i	−0.0623589	+	0.0623589i	−0.737598	−	0.675240i	$-0.764040\pi$
$73$	−24258.7	+	24258.7i	−0.0623589	+	0.0623589i	0.675240	+	0.737598i	$0.264040\pi$
$74$		−	324002.i		−	0.799562i
$75$	−225649.	−	230225.i	−0.534872	−	0.545720i
$76$	−835751.			−1.90387
$77$	47637.6	+	47637.6i	0.104346	+	0.104346i
$78$	128665.	−	128665.i	0.271130	−	0.271130i
$79$		−	476823.i		−	0.967109i	−0.875314	−	0.483555i	$-0.839345\pi$
$79$		−	476823.i		−	0.967109i	0.875314	−	0.483555i	$-0.160655\pi$
$80$	−231330.	+	229020.i	−0.451817	+	0.447304i
$81$	218293.			0.410757
$82$	1.19595e6	+	1.19595e6i	2.16906	+	2.16906i
$83$	−296628.	+	296628.i	−0.518774	+	0.518774i	−0.917200	−	0.398427i	$-0.869556\pi$
$83$	−296628.	+	296628.i	−0.518774	+	0.518774i	0.398427	+	0.917200i	$0.369556\pi$
$84$			208215.i			0.351297i
$85$	−528405.	−	2652.08i	−0.860420	−	0.00431846i
$86$	568245.			0.893389
$87$	−383957.	−	383957.i	−0.583075	−	0.583075i
$88$	428875.	−	428875.i	0.629336	−	0.629336i
$89$			834303.i			1.18346i	0.806136	+	0.591730i	$0.201555\pi$
$89$			834303.i			1.18346i	−0.806136	+	0.591730i	$0.798445\pi$
$90$	2580.63	−	514171.i	0.00353996	−	0.705310i
$91$	−54748.9			−0.0726526
$92$	−1.44030e6	−	1.44030e6i	−1.84965	−	1.84965i
$93$	235799.	−	235799.i	0.293152	−	0.293152i
$94$		−	684921.i		−	0.824626i
$95$	613068.	+	619253.i	0.715052	+	0.722266i
$96$	−272113.			−0.307565
$97$	−60336.2	−	60336.2i	−0.0661094	−	0.0661094i	0.673279	−	0.739388i	$-0.264885\pi$
$97$	−60336.2	−	60336.2i	−0.0661094	−	0.0661094i	−0.739388	+	0.673279i	$0.764885\pi$
$98$	−1.06016e6	+	1.06016e6i	−1.12640	+	1.12640i
$99$			242764.i			0.250195i
$100$	1.87314e6	+	18803.2i	1.87314	+	0.0188032i
$101$	−91011.0			−0.0883343			−0.0441672	−	0.999024i	$-0.514063\pi$
$101$	−91011.0			−0.0883343			−0.0441672	+	0.999024i	$0.514063\pi$
$102$	836288.	+	836288.i	0.788053	+	0.788053i
$103$	635957.	−	635957.i	0.581991	−	0.581991i	−0.353459	−	0.935450i	$-0.614995\pi$
$103$	635957.	−	635957.i	0.581991	−	0.581991i	0.935450	+	0.353459i	$0.114995\pi$
$104$			492897.i			0.438184i
$105$	154278.	−	152737.i	0.133271	−	0.131940i
$106$	−874305.			−0.734084
$107$	−277680.	−	277680.i	−0.226670	−	0.226670i	0.584630	−	0.811300i	$-0.301240\pi$
$107$	−277680.	−	277680.i	−0.226670	−	0.226670i	−0.811300	+	0.584630i	$0.801240\pi$
$108$	−1.80556e6	+	1.80556e6i	−1.43331	+	1.43331i
$109$		−	981017.i		−	0.757525i	−0.925494	−	0.378763i	$-0.876350\pi$
$109$		−	981017.i		−	0.757525i	0.925494	−	0.378763i	$-0.123650\pi$
$110$	−1.35656e6	−	6808.58i	−1.01920	−	0.00511539i
$111$	492951.			0.360441
$112$	−155010.	−	155010.i	−0.110333	−	0.110333i
$113$	1.44645e6	−	1.44645e6i	1.00246	−	1.00246i	0.00246631	−	0.999997i	$-0.499215\pi$
$113$	1.44645e6	−	1.44645e6i	1.00246	−	1.00246i	0.999997	−	0.00246631i	$-0.000785051\pi$
$114$		−	1.95035e6i		−	1.31643i
$115$	−10659.1	+	2.12373e6i	−0.00700850	+	1.39639i
$116$	3.15528e6			2.02145
$117$	−139502.	−	139502.i	−0.0871009	−	0.0871009i
$118$	50160.3	−	50160.3i	0.0305291	−	0.0305291i
$119$		−	355853.i		−	0.211169i
$120$	−1.37507e6	−	1.38894e6i	−0.795758	−	0.803787i
$121$	−1.13107e6			−0.638458
$122$	−192598.	−	192598.i	−0.106065	−	0.106065i
$123$	−1.81957e6	+	1.81957e6i	−0.977810	+	0.977810i
$124$			1.93775e6i			1.01632i
$125$	−1.36012e6	−	1.40171e6i	−0.696380	−	0.717673i
$126$	346266.			0.173101
$127$	1.78869e6	+	1.78869e6i	0.873220	+	0.873220i	0.992822	−	0.119602i	$-0.0381617\pi$
$127$	1.78869e6	+	1.78869e6i	0.873220	+	0.873220i	−0.119602	+	0.992822i	$0.538162\pi$
$128$	2.71621e6	−	2.71621e6i	1.29519	−	1.29519i
$129$			864555.i			0.402739i
$130$	783443.	−	775618.i	0.356597	−	0.353035i
$131$	−3.08768e6			−1.37347			−0.686735	−	0.726908i	$-0.740957\pi$
$131$	−3.08768e6			−1.37347			−0.686735	+	0.726908i	$0.740957\pi$
$132$	1.39974e6	+	1.39974e6i	0.608591	+	0.608591i
$133$	−414951.	+	414951.i	−0.176377	+	0.176377i
$134$			4.37913e6i			1.82001i
$135$	2.66231e6	+	13362.2i	1.08208	+	0.00543096i
$136$	−3.20369e6			−1.27360
$137$	−118847.	−	118847.i	−0.0462197	−	0.0462197i	0.683619	−	0.729839i	$-0.260405\pi$
$137$	−118847.	−	118847.i	−0.0462197	−	0.0462197i	−0.729839	+	0.683619i	$0.760405\pi$
$138$	3.36116e6	−	3.36116e6i	1.27894	−	1.27894i
$139$		−	2.22764e6i		−	0.829468i	−0.909943	−	0.414734i	$-0.863875\pi$
$139$		−	2.22764e6i		−	0.829468i	0.909943	−	0.414734i	$-0.136125\pi$
$140$	−6331.46	+	1.26149e6i	−0.00230738	+	0.459728i
$141$	1.04207e6			0.371740
$142$	−4.51719e6	−	4.51719e6i	−1.57762	−	1.57762i
$143$	−368053.	+	368053.i	−0.125864	+	0.125864i
$144$		−	789943.i		−	0.264550i
$145$	−2.31457e6	−	2.33792e6i	−0.759216	−	0.766876i
$146$	465219.			0.149486
$147$	−1.61297e6	−	1.61297e6i	−0.507778	−	0.507778i
$148$	−2.02549e6	+	2.02549e6i	−0.624805	+	0.624805i
$149$			1.55027e6i			0.468649i	0.972158	+	0.234325i	$0.0752879\pi$
$149$			1.55027e6i			0.468649i	−0.972158	+	0.234325i	$0.924712\pi$
$150$	−43879.9	+	4.37126e6i	−0.0130015	+	1.29519i
$151$	6.27210e6			1.82172			0.910860	−	0.412715i	$-0.135419\pi$
$151$	6.27210e6			1.82172			0.910860	+	0.412715i	$0.135419\pi$
$152$	3.73575e6	+	3.73575e6i	1.06377	+	1.06377i
$153$	906723.	−	906723.i	0.253163	−	0.253163i
$154$		−	913568.i		−	0.250137i
$155$	1.43578e6	−	1.42144e6i	0.385561	−	0.381710i
$156$	−1.60869e6			−0.423740
$157$	4.24526e6	+	4.24526e6i	1.09700	+	1.09700i	0.994760	+	0.102235i	$0.0325994\pi$
$157$	4.24526e6	+	4.24526e6i	1.09700	+	1.09700i	0.102235	+	0.994760i	$0.467401\pi$
$158$	−4.57212e6	+	4.57212e6i	−1.15917	+	1.15917i
$159$		−	1.33021e6i		−	0.330924i
$160$	−1.64863e6	−	8274.49i	−0.402497	−	0.00202014i
$161$	−1.43022e6			−0.342709
$162$	−2.09315e6	−	2.09315e6i	−0.492330	−	0.492330i
$163$	−4.99321e6	+	4.99321e6i	−1.15297	+	1.15297i	−0.167013	+	0.985955i	$0.553412\pi$
$163$	−4.99321e6	+	4.99321e6i	−1.15297	+	1.15297i	−0.985955	+	0.167013i	$0.946588\pi$
$164$		−	1.49529e7i		−	3.38995i
$165$	10358.9	−	2.06393e6i	0.00230601	−	0.459454i
$166$	5.68857e6			1.24359
$167$	−2.10663e6	−	2.10663e6i	−0.452314	−	0.452314i	0.443808	−	0.896122i	$-0.353627\pi$
$167$	−2.10663e6	−	2.10663e6i	−0.452314	−	0.452314i	−0.896122	+	0.443808i	$0.853627\pi$
$168$	930707.	−	930707.i	0.196284	−	0.196284i
$169$			4.40381e6i			0.912365i
$170$	5.04130e6	+	5.09216e6i	1.02611	+	1.03647i
$171$	−2.11462e6			−0.422905
$172$	−3.55237e6	−	3.55237e6i	−0.698124	−	0.698124i
$173$	1.97319e6	−	1.97319e6i	0.381093	−	0.381093i	−0.490403	−	0.871496i	$-0.663150\pi$
$173$	1.97319e6	−	1.97319e6i	0.381093	−	0.381093i	0.871496	+	0.490403i	$0.163150\pi$
$174$			7.36331e6i			1.39774i
$175$	939352.	−	920681.i	0.175273	−	0.171789i
$176$	−2.08414e6			−0.382286
$177$	76316.2	+	76316.2i	0.0137625	+	0.0137625i
$178$	7.99990e6	−	7.99990e6i	1.41848	−	1.41848i
$179$		−	1.84747e6i		−	0.322121i	−0.986945	−	0.161061i	$-0.948509\pi$
$179$		−	1.84747e6i		−	0.322121i	0.986945	−	0.161061i	$-0.0514915\pi$
$180$	−3.23046e6	+	3.19819e6i	−0.553919	+	0.548387i
$181$	−2.94668e6			−0.496932			−0.248466	−	0.968641i	$-0.579926\pi$
$181$	−2.94668e6			−0.496932			−0.248466	+	0.968641i	$0.579926\pi$
$182$	524972.	+	524972.i	0.0870807	+	0.0870807i
$183$	293027.	−	293027.i	0.0478140	−	0.0478140i
$184$			1.28761e7i			2.06695i
$185$	2.98659e6	+	14989.8i	0.471694	+	0.00236744i
$186$	−4.52202e6			−0.702739
$187$	−2.39224e6	−	2.39224e6i	−0.365831	−	0.365831i
$188$	−4.28176e6	+	4.28176e6i	−0.644390	+	0.644390i
$189$			1.79292e6i			0.265568i
$190$	59306.6	−	1.18164e7i	0.00864654	−	1.72276i
$191$	−2.03592e6			−0.292187			−0.146094	−	0.989271i	$-0.546670\pi$
$191$	−2.03592e6			−0.292187			−0.146094	+	0.989271i	$0.546670\pi$
$192$	5.04067e6	+	5.04067e6i	0.712172	+	0.712172i
$193$	321544.	−	321544.i	0.0447269	−	0.0447269i	−0.684390	−	0.729116i	$-0.739931\pi$
$193$	321544.	−	321544.i	0.0447269	−	0.0447269i	0.729116	+	0.684390i	$0.239931\pi$
$194$			1.15710e6i			0.158476i
$195$	1.18006e6	+	1.19197e6i	0.159148	+	0.160753i
$196$	1.32551e7			1.76041
$197$	5.21092e6	+	5.21092e6i	0.681578	+	0.681578i	0.960356	−	0.278778i	$-0.0899293\pi$
$197$	5.21092e6	+	5.21092e6i	0.681578	+	0.681578i	−0.278778	+	0.960356i	$0.589929\pi$
$198$	2.32780e6	−	2.32780e6i	0.299882	−	0.299882i
$199$		−	9.26912e6i		−	1.17620i	−0.808790	−	0.588098i	$-0.799877\pi$
$199$		−	9.26912e6i		−	1.17620i	0.808790	−	0.588098i	$-0.200123\pi$
$200$	−8.28877e6	−	8.45686e6i	−1.03610	−	1.05711i
$201$	−6.66261e6			−0.820457
$202$	872679.	+	872679.i	0.105877	+	0.105877i
$203$	1.56660e6	−	1.56660e6i	0.187271	−	0.187271i
$204$		−	1.04561e7i		−	1.23162i
$205$	−1.10794e7	+	1.09687e7i	−1.28604	+	1.27320i
$206$	−1.21960e7			−1.39514
$207$	−3.64425e6	−	3.64425e6i	−0.410863	−	0.410863i
$208$	1.19763e6	−	1.19763e6i	0.133086	−	0.133086i
$209$			5.57907e6i			0.611115i
$210$	−2.94388e6	−	14775.4i	−0.317879	−	0.00159544i
$211$	1.13498e7			1.20820			0.604101	−	0.796907i	$-0.293532\pi$
$211$	1.13498e7			1.20820			0.604101	+	0.796907i	$0.293532\pi$
$212$	5.46569e6	+	5.46569e6i	0.573638	+	0.573638i
$213$	6.87265e6	−	6.87265e6i	0.711190	−	0.711190i
$214$			5.32520e6i			0.543369i
$215$	−26289.6	+	5.23799e6i	−0.00264526	+	0.527047i
$216$	1.61415e7			1.60170
$217$	962093.	+	962093.i	0.0941538	+	0.0941538i
$218$	−9.40671e6	+	9.40671e6i	−0.907963	+	0.907963i
$219$			707806.i			0.0673879i
$220$	8.43791e6	+	8.52303e6i	0.792440	+	0.800435i
$221$	2.74935e6			0.254715
$222$	−4.72677e6	−	4.72677e6i	−0.432022	−	0.432022i
$223$	−2.22688e6	+	2.22688e6i	−0.200809	+	0.200809i	−0.800346	−	0.599538i	$-0.795351\pi$
$223$	−2.22688e6	+	2.22688e6i	−0.200809	+	0.200809i	0.599538	+	0.800346i	$0.295351\pi$
$224$		−	1.11026e6i		−	0.0987827i
$225$	4.73942e6	+	47575.7i	0.416081	+	0.00417674i
$226$	−2.77392e7			−2.40309
$227$	−134399.	−	134399.i	−0.0114899	−	0.0114899i	0.701338	−	0.712828i	$-0.252586\pi$
$227$	−134399.	−	134399.i	−0.0114899	−	0.0114899i	−0.712828	+	0.701338i	$0.752586\pi$
$228$	−1.21925e7	+	1.21925e7i	−1.02870	+	1.02870i
$229$		−	1.63704e7i		−	1.36318i	−0.731735	−	0.681589i	$-0.761289\pi$
$229$		−	1.63704e7i		−	1.36318i	0.731735	−	0.681589i	$-0.238711\pi$
$230$	2.04661e7	−	2.02617e7i	1.68210	−	1.66530i
$231$	1.38994e6			0.112762
$232$	−1.41039e7	−	1.41039e7i	−1.12947	−	1.12947i
$233$	1.12976e7	−	1.12976e7i	0.893137	−	0.893137i	−0.101680	−	0.994817i	$-0.532422\pi$
$233$	1.12976e7	−	1.12976e7i	0.893137	−	0.893137i	0.994817	+	0.101680i	$0.0324219\pi$
$234$			2.67529e6i			0.208797i
$235$	6.31349e6	+	31687.5i	0.486481	+	0.00244166i
$236$	−627152.			−0.0477130
$237$	−6.95623e6	−	6.95623e6i	−0.522551	−	0.522551i
$238$	−3.41217e6	+	3.41217e6i	−0.253105	+	0.253105i
$239$			1.90970e7i			1.39885i	0.714705	+	0.699426i	$0.246561\pi$
$239$			1.90970e7i			1.39885i	−0.714705	+	0.699426i	$0.753439\pi$
$240$	−33707.3	+	6.71592e6i	−0.00243832	+	0.485816i
$241$	−1.68760e6			−0.120564			−0.0602821	−	0.998181i	$-0.519200\pi$
$241$	−1.68760e6			−0.120564			−0.0602821	+	0.998181i	$0.519200\pi$
$242$	1.08455e7	+	1.08455e7i	0.765250	+	0.765250i
$243$	−7.79448e6	+	7.79448e6i	−0.543211	+	0.543211i
$244$			2.40804e6i			0.165766i
$245$	−9.72329e6	−	9.82139e6i	−0.661173	−	0.667843i
$246$	3.48948e7			2.34399
$247$	−3.20595e6	−	3.20595e6i	−0.212748	−	0.212748i
$248$	8.66160e6	−	8.66160e6i	0.567862	−	0.567862i
$249$			8.65485e6i			0.560611i
$250$	−398773.	+	2.64824e7i	−0.0255215	+	1.69487i
$251$	886478.			0.0560592			0.0280296	−	0.999607i	$-0.491077\pi$
$251$	886478.			0.0560592			0.0280296	+	0.999607i	$0.491077\pi$
$252$	−2.16467e6	−	2.16467e6i	−0.135267	−	0.135267i
$253$	−9.61475e6	+	9.61475e6i	−0.593713	+	0.593713i
$254$		−	3.43025e7i		−	2.09327i
$255$	−7.74745e6	+	7.67007e6i	−0.467238	+	0.462571i
$256$	−2.99767e7			−1.78675
$257$	−8.52467e6	−	8.52467e6i	−0.502202	−	0.502202i	0.409920	−	0.912122i	$-0.365557\pi$
$257$	−8.52467e6	−	8.52467e6i	−0.502202	−	0.502202i	−0.912122	+	0.409920i	$0.865557\pi$
$258$	8.28997e6	−	8.28997e6i	0.482719	−	0.482719i
$259$			2.01131e6i			0.115766i
$260$	−9.74643e6	−	48917.5i	−0.554530	−	0.00278320i
$261$	7.98348e6			0.449025
$262$	2.96069e7	+	2.96069e7i	1.64623	+	1.64623i
$263$	−9.22908e6	+	9.22908e6i	−0.507331	+	0.507331i	−0.913706	−	0.406376i	$-0.866792\pi$
$263$	−9.22908e6	+	9.22908e6i	−0.507331	+	0.507331i	0.406376	+	0.913706i	$0.366792\pi$
$264$		−	1.25135e7i		−	0.680090i
$265$	40449.3	−	8.05920e6i	0.00217357	−	0.433066i
$266$	7.95770e6			0.422807
$267$	1.21714e7	+	1.21714e7i	0.639451	+	0.639451i
$268$	2.73760e7	−	2.73760e7i	1.42222	−	1.42222i
$269$			4.44151e6i			0.228178i	0.993471	+	0.114089i	$0.0363949\pi$
$269$			4.44151e6i			0.228178i	−0.993471	+	0.114089i	$0.963605\pi$
$270$	−2.54000e7	−	2.56563e7i	−1.29046	−	1.30347i
$271$	5.48744e6			0.275716			0.137858	−	0.990452i	$-0.455978\pi$
$271$	5.48744e6			0.275716			0.137858	+	0.990452i	$0.455978\pi$
$272$	7.78424e6	+	7.78424e6i	0.386821	+	0.386821i
$273$	−798717.	+	798717.i	−0.0392559	+	0.0392559i
$274$			2.27918e6i			0.110797i
$275$	125521.	−	1.25042e7i	0.00603556	−	0.601253i
$276$	−4.20243e7			−1.99882
$277$	−1.03455e7	−	1.03455e7i	−0.486756	−	0.486756i	0.420525	−	0.907281i	$-0.361846\pi$
$277$	−1.03455e7	−	1.03455e7i	−0.486756	−	0.486756i	−0.907281	+	0.420525i	$0.861846\pi$
$278$	−2.13602e7	+	2.13602e7i	−0.994192	+	0.994192i
$279$			4.90289e6i			0.225756i
$280$	5.66708e6	−	5.61048e6i	0.258158	−	0.255580i
$281$	1.06286e7			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$281$	1.06286e7			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$282$	−9.99212e6	−	9.99212e6i	−0.445564	−	0.445564i
$283$	2.67853e7	−	2.67853e7i	1.18178	−	1.18178i	0.202501	−	0.979282i	$-0.435093\pi$
$283$	2.67853e7	−	2.67853e7i	1.18178	−	1.18178i	0.979282	−	0.202501i	$-0.0649069\pi$
$284$			5.64781e7i			2.46561i
$285$	1.79780e7	+	90231.8i	0.776616	+	0.00389785i
$286$	7.05832e6			0.301719
$287$	−7.42412e6	−	7.42412e6i	−0.314050	−	0.314050i
$288$	2.82898e6	−	2.82898e6i	0.118427	−	0.118427i
$289$		−	6.26754e6i		−	0.259659i
$290$	−223905.	+	4.46114e7i	−0.00918058	+	1.82916i
$291$	−1.76046e6			−0.0714409
$292$	−2.90830e6	−	2.90830e6i	−0.116813	−	0.116813i
$293$	−8.76469e6	+	8.76469e6i	−0.348445	+	0.348445i	−0.859530	−	0.511085i	$-0.829244\pi$
$293$	−8.76469e6	+	8.76469e6i	−0.348445	+	0.348445i	0.511085	+	0.859530i	$0.329244\pi$
$294$			3.09326e7i			1.21724i
$295$	460049.	+	464690.i	0.0179200	+	0.0181008i
$296$	1.81076e7			0.698208
$297$	1.20530e7	+	1.20530e7i	0.460074	+	0.460074i
$298$	1.48651e7	−	1.48651e7i	0.561719	−	0.561719i
$299$		−	1.10500e7i		−	0.413380i
$300$	2.76011e7	−	2.70525e7i	1.02226	−	1.00194i
$301$	−3.52750e6			−0.129350
$302$	−6.01414e7	−	6.01414e7i	−2.18350	−	2.18350i
$303$	−1.32773e6	+	1.32773e6i	−0.0477291	+	0.0477291i
$304$		−	1.81540e7i		−	0.646178i
$305$	1.78425e6	−	1.76643e6i	0.0628862	−	0.0622581i
$306$	−1.73886e7			−0.606878
$307$	2.94600e7	+	2.94600e7i	1.01816	+	1.01816i	0.999832	+	0.0183331i	$0.00583592\pi$
$307$	2.94600e7	+	2.94600e7i	1.01816	+	1.01816i	0.0183331	+	0.999832i	$0.494164\pi$
$308$	−5.71114e6	+	5.71114e6i	−0.195466	+	0.195466i
$309$		−	1.85556e7i		−	0.628926i
$310$	−2.73971e7	−	137507.i	−0.919644	−	0.00461571i
$311$	−5.27556e7			−1.75383			−0.876915	−	0.480645i	$-0.840403\pi$
$311$	−5.27556e7			−1.75383			−0.876915	+	0.480645i	$0.840403\pi$
$312$	7.19074e6	+	7.19074e6i	0.236761	+	0.236761i
$313$	−3.45882e7	+	3.45882e7i	−1.12796	+	1.12796i	−0.137457	+	0.990508i	$0.543893\pi$
$313$	−3.45882e7	+	3.45882e7i	−1.12796	+	1.12796i	−0.990508	+	0.137457i	$0.956107\pi$
$314$		−	8.14132e7i		−	2.62970i
$315$	−16019.8	+	3.19183e6i	−0.000512538	+	0.102119i
$316$	5.71649e7			1.81163
$317$	3.73217e7	+	3.73217e7i	1.17161	+	1.17161i	0.981826	+	0.189786i	$0.0607793\pi$
$317$	3.73217e7	+	3.73217e7i	1.17161	+	1.17161i	0.189786	+	0.981826i	$0.439221\pi$
$318$	−1.27550e7	+	1.27550e7i	−0.396642	+	0.396642i
$319$		−	2.10631e7i		−	0.648859i
$320$	3.03861e7	+	3.06927e7i	0.927312	+	0.936667i
$321$	−8.10201e6			−0.244950
$322$	1.37140e7	+	1.37140e7i	0.410768	+	0.410768i
$323$	2.08378e7	−	2.08378e7i	0.618364	−	0.618364i
$324$			2.61706e7i			0.769446i
$325$	7.11327e6	+	7.25753e6i	0.207214	+	0.211416i
$326$	9.57571e7			2.76387
$327$	−1.43118e7	−	1.43118e7i	−0.409309	−	0.409309i
$328$	−6.68384e7	+	6.68384e7i	−1.89411	+	1.89411i
$329$			4.25179e6i			0.119395i
$330$	−1.98898e7	+	1.96911e7i	−0.553462	+	0.547934i
$331$	−1.72069e7			−0.474481			−0.237241	−	0.971451i	$-0.576243\pi$
$331$	−1.72069e7			−0.474481			−0.237241	+	0.971451i	$0.576243\pi$
$332$	−3.55619e7	−	3.55619e7i	−0.971787	−	0.971787i
$333$	−5.12488e6	+	5.12488e6i	−0.138788	+	0.138788i
$334$			4.03999e7i			1.08428i
$335$	−4.03661e7	−	202598.i	−1.07370	−	0.00538891i
$336$	−4.52281e6			−0.119231
$337$	−3.84422e7	−	3.84422e7i	−1.00443	−	1.00443i	−0.999990	−	0.00443712i	$-0.998588\pi$
$337$	−3.84422e7	−	3.84422e7i	−1.00443	−	1.00443i	−0.00443712	−	0.999990i	$-0.501412\pi$
$338$	4.22269e7	−	4.22269e7i	1.09355	−	1.09355i
$339$		−	4.22038e7i		−	1.08331i
$340$	317950.	−	6.33490e7i	0.00808951	−	1.61177i
$341$	1.29355e7			0.326226
$342$	2.02765e7	+	2.02765e7i	0.506890	+	0.506890i
$343$	1.35841e7	−	1.35841e7i	0.336626	−	0.336626i
$344$			3.17577e7i			0.780141i
$345$	3.08271e7	+	3.11381e7i	0.750715	+	0.758288i
$346$	−3.78408e7			−0.913549
$347$	2.41898e7	+	2.41898e7i	0.578955	+	0.578955i	0.934615	−	0.355661i	$-0.115744\pi$
$347$	2.41898e7	+	2.41898e7i	0.578955	+	0.578955i	−0.355661	+	0.934615i	$0.615744\pi$
$348$	4.60315e7	−	4.60315e7i	1.09224	−	1.09224i
$349$			3.28046e7i			0.771718i	0.922558	+	0.385859i	$0.126095\pi$
$349$			3.28046e7i			0.771718i	−0.922558	+	0.385859i	$0.873905\pi$
$350$	−1.78353e7	−	179036.i	−0.415985	−	0.00417577i
$351$	−1.38523e7			−0.320332
$352$	−7.46380e6	−	7.46380e6i	−0.171132	−	0.171132i
$353$	2.11688e7	−	2.11688e7i	0.481252	−	0.481252i	−0.424279	−	0.905531i	$-0.639473\pi$
$353$	2.11688e7	−	2.11688e7i	0.481252	−	0.481252i	0.905531	+	0.424279i	$0.139473\pi$
$354$		−	1.46355e6i		−	0.0329912i
$355$	4.18477e7	−	4.14297e7i	0.935376	−	0.926033i
$356$	−1.00022e8			−2.21690
$357$	−5.19143e6	−	5.19143e6i	−0.114099	−	0.114099i
$358$	−1.77149e7	+	1.77149e7i	−0.386091	+	0.386091i
$359$			5.98132e7i			1.29275i	0.763021	+	0.646374i	$0.223715\pi$
$359$			5.98132e7i			1.29275i	−0.763021	+	0.646374i	$0.776285\pi$
$360$	2.87356e7	+	144224.i	0.615904	+	0.00309123i
$361$	−1.55098e6			−0.0329673
$362$	2.82549e7	+	2.82549e7i	0.595618	+	0.595618i
$363$	−1.65008e7	+	1.65008e7i	−0.344974	+	0.344974i
$364$		−	6.56369e6i		−	0.136096i
$365$	−21523.1	+	4.28831e6i	−0.000442616	+	0.0881877i
$366$	−5.61952e6			−0.114619
$367$	−1.10433e7	−	1.10433e7i	−0.223410	−	0.223410i	0.586523	−	0.809933i	$-0.300496\pi$
$367$	−1.10433e7	−	1.10433e7i	−0.223410	−	0.223410i	−0.809933	+	0.586523i	$0.800496\pi$
$368$	3.12859e7	−	3.12859e7i	0.627777	−	0.627777i
$369$		−	3.78338e7i		−	0.753010i
$370$	−2.84939e7	−	2.87813e7i	−0.562531	−	0.568206i
$371$	5.42744e6			0.106285
$372$	2.82693e7	+	2.82693e7i	0.549144	+	0.549144i
$373$	−3.15257e7	+	3.15257e7i	−0.607489	+	0.607489i	−0.942289	−	0.334800i	$-0.891331\pi$
$373$	−3.15257e7	+	3.15257e7i	−0.607489	+	0.607489i	0.334800	+	0.942289i	$0.391331\pi$
$374$			4.58771e7i			0.876963i
$375$	−4.02915e7	−	606712.i	−0.764046	−	0.0115051i
$376$	3.82783e7			0.720095
$377$	1.21037e7	+	1.21037e7i	0.225888	+	0.225888i
$378$	1.71918e7	−	1.71918e7i	0.318308	−	0.318308i
$379$			7.24769e7i			1.33132i	0.746256	+	0.665659i	$0.231850\pi$
$379$			7.24769e7i			1.33132i	−0.746256	+	0.665659i	$0.768150\pi$
$380$	−7.42405e7	+	7.34990e7i	−1.35298	+	1.33946i
$381$	5.21894e7			0.943642
$382$	1.95219e7	+	1.95219e7i	0.350213	+	0.350213i
$383$	5.97718e7	−	5.97718e7i	1.06390	−	1.06390i	0.0660833	−	0.997814i	$-0.478950\pi$
$383$	5.97718e7	−	5.97718e7i	1.06390	−	1.06390i	0.997814	−	0.0660833i	$-0.0210503\pi$
$384$		−	7.92520e7i		−	1.39964i
$385$	8.42111e6	+	42265.7i	0.147566	+	0.000740638i
$386$	−6.16640e6			−0.107218
$387$	−8.98819e6	−	8.98819e6i	−0.155074	−	0.155074i
$388$	7.23355e6	−	7.23355e6i	0.123839	−	0.123839i
$389$		−	5.28956e7i		−	0.898608i	−0.893379	−	0.449304i	$-0.851672\pi$
$389$		−	5.28956e7i		−	0.898608i	0.893379	−	0.449304i	$-0.148328\pi$
$390$	114156.	−	2.27447e7i	0.00192445	−	0.383431i
$391$	7.18221e7			1.20151
$392$	−5.92492e7	−	5.92492e7i	−0.983613	−	0.983613i
$393$	−4.50454e7	+	4.50454e7i	−0.742117	+	0.742117i
$394$		−	9.99321e7i		−	1.63387i
$395$	−4.19335e7	−	4.23566e7i	−0.680409	−	0.687273i
$396$	−2.91043e7			−0.468675
$397$	−4.84200e7	−	4.84200e7i	−0.773844	−	0.773844i	0.204933	−	0.978776i	$-0.434303\pi$
$397$	−4.84200e7	−	4.84200e7i	−0.773844	−	0.773844i	−0.978776	+	0.204933i	$0.934303\pi$
$398$	−8.88791e7	+	8.88791e7i	−1.40978	+	1.40978i
$399$			1.21072e7i			0.190601i
$400$	−408438.	+	4.06880e7i	−0.00638185	+	0.635751i
$401$	2.84505e7			0.441222			0.220611	−	0.975362i	$-0.429195\pi$
$401$	2.84505e7			0.441222			0.220611	+	0.975362i	$0.429195\pi$
$402$	6.38859e7	+	6.38859e7i	0.983392	+	0.983392i
$403$	−7.43323e6	+	7.43323e6i	−0.113570	+	0.113570i
$404$		−	1.09111e7i		−	0.165471i
$405$	1.93912e7	−	1.91975e7i	0.291903	−	0.288988i
$406$	−3.00433e7			−0.448921
$407$	1.35212e7	+	1.35212e7i	0.200554	+	0.200554i
$408$	−4.67378e7	+	4.67378e7i	−0.688157	+	0.688157i
$409$		−	1.04600e7i		−	0.152883i	−0.997074	−	0.0764416i	$-0.975644\pi$
$409$		−	1.04600e7i		−	0.152883i	0.997074	−	0.0764416i	$-0.0243559\pi$
$410$	2.11413e8	+	1.06109e6i	3.06748	+	0.0153957i
$411$	−3.46765e6			−0.0499471
$412$	7.62431e7	+	7.62431e7i	1.09021	+	1.09021i
$413$	−311381.	+	311381.i	−0.00442020	+	0.00442020i
$414$			6.98873e7i			0.984912i
$415$	−263179.	+	5.24363e7i	−0.00368219	+	0.733647i
$416$	8.57799e6			0.119153
$417$	−3.24984e7	−	3.24984e7i	−0.448181	−	0.448181i
$418$	5.34961e7	−	5.34961e7i	0.732476	−	0.732476i
$419$			4.91256e7i			0.667829i	0.942603	+	0.333915i	$0.108370\pi$
$419$			4.91256e7i			0.667829i	−0.942603	+	0.333915i	$0.891630\pi$
$420$	1.83112e7	+	1.84959e7i	0.247155	+	0.249648i
$421$	−6.96342e7			−0.933203			−0.466601	−	0.884468i	$-0.654522\pi$
$421$	−6.96342e7			−0.933203			−0.466601	+	0.884468i	$0.654522\pi$
$422$	−1.08830e8	−	1.08830e8i	−1.44814	−	1.44814i
$423$	−1.08337e7	+	1.08337e7i	−0.143138	+	0.143138i
$424$		−	4.88625e7i		−	0.641030i
$425$	−4.71719e7	+	4.62343e7i	−0.614493	+	0.602279i
$426$	−1.31800e8			−1.70485
$427$	1.19559e6	+	1.19559e6i	0.0153568	+	0.0153568i
$428$	3.32903e7	−	3.32903e7i	0.424607	−	0.424607i
$429$			1.07388e7i			0.136015i
$430$	5.04777e7	−	4.99736e7i	0.634884	−	0.628543i
$431$	6.41393e7			0.801110			0.400555	−	0.916273i	$-0.368817\pi$
$431$	6.41393e7			0.801110			0.400555	+	0.916273i	$0.368817\pi$
$432$	−3.92200e7	−	3.92200e7i	−0.486471	−	0.486471i
$433$	4.66215e7	−	4.66215e7i	0.574278	−	0.574278i	−0.359043	−	0.933321i	$-0.616897\pi$
$433$	4.66215e7	−	4.66215e7i	0.574278	−	0.574278i	0.933321	+	0.359043i	$0.116897\pi$
$434$		−	1.84505e7i		−	0.225704i
$435$	−6.78738e7	−	340660.i	−0.824583	−	0.00413860i
$436$	1.17611e8			1.41903
$437$	−8.37500e7	−	8.37500e7i	−1.00355	−	1.00355i
$438$	6.78696e6	−	6.78696e6i	0.0807705	−	0.0807705i
$439$			1.03597e8i			1.22448i	0.790670	+	0.612242i	$0.209732\pi$
$439$			1.03597e8i			1.22448i	−0.790670	+	0.612242i	$0.790268\pi$
$440$	380513.	−	7.58142e7i	0.00446695	−	0.890005i
$441$	3.35379e7			0.391039
$442$	−2.63628e7	−	2.63628e7i	−0.305298	−	0.305298i
$443$	−6.41399e7	+	6.41399e7i	−0.737764	+	0.737764i	−0.972145	−	0.234381i	$-0.924694\pi$
$443$	−6.41399e7	+	6.41399e7i	−0.737764	+	0.737764i	0.234381	+	0.972145i	$0.424694\pi$
$444$			5.90985e7i			0.675193i
$445$	7.33716e7	+	7.41118e7i	0.832622	+	0.841022i
$446$	4.27059e7			0.481375
$447$	2.26164e7	+	2.26164e7i	0.253222	+	0.253222i
$448$	−2.05667e7	+	2.05667e7i	−0.228733	+	0.228733i
$449$		−	1.35473e8i		−	1.49663i	−0.663343	−	0.748315i	$-0.730863\pi$
$449$		−	1.35473e8i		−	1.49663i	0.663343	−	0.748315i	$-0.269137\pi$
$450$	−4.49888e7	−	4.59012e7i	−0.493704	−	0.503717i
$451$	−9.98182e7			−1.08813
$452$	1.73411e8	+	1.73411e8i	1.87785	+	1.87785i
$453$	9.15019e7	−	9.15019e7i	0.984318	−	0.984318i
$454$			2.57742e6i			0.0275434i
$455$	−4.86339e6	+	4.81482e6i	−0.0516303	+	0.0511147i
$456$	1.09000e8			1.14956
$457$	1.08878e8	+	1.08878e8i	1.14075	+	1.14075i	0.988313	+	0.152440i	$0.0487132\pi$
$457$	1.08878e8	+	1.08878e8i	1.14075	+	1.14075i	0.152440	+	0.988313i	$0.451287\pi$
$458$	−1.56971e8	+	1.56971e8i	−1.63389	+	1.63389i
$459$		−	9.00362e7i		−	0.931063i
$460$	−2.54609e8	−	1.27789e6i	−2.61577	−	0.0131286i
$461$	−5.72952e7			−0.584811			−0.292405	−	0.956294i	$-0.594456\pi$
$461$	−5.72952e7			−0.584811			−0.292405	+	0.956294i	$0.594456\pi$
$462$	−1.33278e7	−	1.33278e7i	−0.135155	−	0.135155i
$463$	8.86294e7	−	8.86294e7i	0.892965	−	0.892965i	−0.101836	−	0.994801i	$-0.532472\pi$
$463$	8.86294e7	−	8.86294e7i	0.892965	−	0.892965i	0.994801	+	0.101836i	$0.0324717\pi$
$464$			6.85384e7i			0.686088i
$465$	209209.	−	4.16832e7i	0.00208076	−	0.414574i
$466$	−2.16659e8			−2.14101
$467$	6.73039e7	+	6.73039e7i	0.660830	+	0.660830i	0.955576	−	0.294746i	$-0.0952350\pi$
$467$	6.73039e7	+	6.73039e7i	0.660830	+	0.660830i	−0.294746	+	0.955576i	$0.595235\pi$
$468$	1.67245e7	−	1.67245e7i	0.163161	−	0.163161i
$469$		−	2.71844e7i		−	0.263512i
$470$	−6.02344e7	−	6.08421e7i	−0.580165	−	0.586018i
$471$	1.23866e8			1.18546
$472$	2.80332e6	+	2.80332e6i	0.0266592	+	0.0266592i
$473$	−2.37139e7	+	2.37139e7i	−0.224088	+	0.224088i
$474$			1.33403e8i			1.25265i
$475$	1.08919e8	+	1.09336e6i	1.01630	+	0.0102019i
$476$	4.26622e7			0.395569
$477$	1.38293e7	+	1.38293e7i	0.127422	+	0.127422i
$478$	1.83116e8	−	1.83116e8i	1.67665	−	1.67665i
$479$		−	6.12787e7i		−	0.557575i	−0.960353	−	0.278787i	$-0.910068\pi$
$479$		−	6.12787e7i		−	0.557575i	0.960353	−	0.278787i	$-0.0899324\pi$
$480$	−2.41721e7	+	2.39306e7i	−0.218570	+	0.216387i
$481$	−1.55396e7			−0.139638
$482$	1.61819e7	+	1.61819e7i	0.144507	+	0.144507i
$483$	−2.08651e7	+	2.08651e7i	−0.185173	+	0.185173i
$484$		−	1.35601e8i		−	1.19598i
$485$	−1.06659e7	−	53532.4i	−0.0934916	−	0.000469236i
$486$	1.49478e8			1.30217
$487$	−1.31243e8	−	1.31243e8i	−1.13629	−	1.13629i	−0.989109	−	0.147184i	$-0.952979\pi$
$487$	−1.31243e8	−	1.31243e8i	−1.13629	−	1.13629i	−0.147184	−	0.989109i	$-0.547021\pi$
$488$	1.07638e7	−	1.07638e7i	0.0926200	−	0.0926200i
$489$			1.45689e8i			1.24595i
$490$	−940607.	+	1.87408e8i	−0.00799503	+	1.59295i
$491$	−2.31192e8			−1.95312			−0.976561	−	0.215243i	$-0.930946\pi$
$491$	−2.31192e8			−1.95312			−0.976561	+	0.215243i	$0.930946\pi$
$492$	−2.18144e8	−	2.18144e8i	−1.83167	−	1.83167i
$493$	−7.86706e7	+	7.86706e7i	−0.656556	+	0.656556i
$494$			6.14820e7i			0.509996i
$495$	2.13496e7	+	2.15650e7i	0.176025	+	0.177800i
$496$	−4.20914e7			−0.344944
$497$	2.80414e7	+	2.80414e7i	0.228418	+	0.228418i
$498$	8.29889e7	−	8.29889e7i	0.671943	−	0.671943i
$499$		−	5.98790e7i		−	0.481918i	−0.970535	−	0.240959i	$-0.922538\pi$
$499$		−	5.98790e7i		−	0.481918i	0.970535	−	0.240959i	$-0.0774619\pi$
$500$	1.68047e8	−	1.63061e8i	1.34437	−	1.30449i
$501$	−6.14662e7			−0.488791
$502$	−8.50019e6	−	8.50019e6i	−0.0671920	−	0.0671920i
$503$	1.01711e8	−	1.01711e8i	0.799215	−	0.799215i	−0.183757	−	0.982972i	$-0.558826\pi$
$503$	1.01711e8	−	1.01711e8i	0.799215	−	0.799215i	0.982972	+	0.183757i	$0.0588259\pi$
$504$			1.93519e7i			0.151158i
$505$	−8.08458e6	+	8.00383e6i	−0.0627745	+	0.0621475i
$506$	1.84386e8			1.42324
$507$	6.42460e7	+	6.42460e7i	0.492972	+	0.492972i
$508$	−2.14441e8	+	2.14441e8i	−1.63575	+	1.63575i
$509$			2.18642e8i			1.65798i	0.559261	+	0.828992i	$0.311085\pi$
$509$			2.18642e8i			1.65798i	−0.559261	+	0.828992i	$0.688915\pi$
$510$	1.47834e8	+	741983.i	1.11446	+	0.00559350i
$511$	−2.88795e6			−0.0216435
$512$	1.13601e8	+	1.13601e8i	0.846396	+	0.846396i
$513$	−1.04989e8	+	1.04989e8i	−0.777663	+	0.777663i
$514$			1.63481e8i			1.20387i
$515$	564243.	−	1.12421e8i	0.00413090	−	0.823049i
$516$	−1.03649e8			−0.754425
$517$	2.85830e7	+	2.85830e7i	0.206840	+	0.206840i
$518$	1.92859e7	−	1.92859e7i	0.138756	−	0.138756i
$519$		−	5.75727e7i		−	0.411827i
$520$	4.33472e7	+	4.37845e7i	0.308284	+	0.311394i
$521$	7.37986e7			0.521837			0.260919	−	0.965361i	$-0.415975\pi$
$521$	7.37986e7			0.521837			0.260919	+	0.965361i	$0.415975\pi$
$522$	−7.65514e7	−	7.65514e7i	−0.538197	−	0.538197i
$523$	−1.14081e8	+	1.14081e8i	−0.797461	+	0.797461i	−0.982695	−	0.185233i	$-0.940696\pi$
$523$	−1.14081e8	+	1.14081e8i	−0.797461	+	0.797461i	0.185233	+	0.982695i	$0.440696\pi$
$524$		−	3.70174e8i		−	2.57283i
$525$	272394.	−	2.71355e7i	0.00188243	−	0.187525i
$526$	1.76990e8			1.21616
$527$	−4.83139e7	−	4.83139e7i	−0.330096	−	0.330096i
$528$	−3.04049e7	+	3.04049e7i	−0.206558	+	0.206558i
$529$		−	1.40627e8i		−	0.949952i
$530$	−7.76653e7	+	7.68896e7i	−0.521674	+	0.516464i
$531$	−1.58682e6			−0.0105985
$532$	−4.97473e7	−	4.97473e7i	−0.330396	−	0.330396i
$533$	5.73595e7	−	5.73595e7i	0.378812	−	0.378812i
$534$		−	2.33417e8i		−	1.53288i
$535$	−4.90868e7	−	246368.i	−0.320556	−	0.00160887i
$536$	−2.44737e8			−1.58930
$537$	−2.69523e7	−	2.69523e7i	−0.174050	−	0.174050i
$538$	4.25884e7	−	4.25884e7i	0.273492	−	0.273492i
$539$		−	8.84843e7i		−	0.565067i
$540$	−1.60196e6	+	3.19177e8i	−0.0101735	+	2.02698i
$541$	1.79424e8			1.13315			0.566575	−	0.824010i	$-0.308268\pi$
$541$	1.79424e8			1.13315			0.566575	+	0.824010i	$0.308268\pi$
$542$	−5.26176e7	−	5.26176e7i	−0.330471	−	0.330471i
$543$	−4.29883e7	+	4.29883e7i	−0.268504	+	0.268504i
$544$			5.57545e7i			0.346325i
$545$	−8.62742e7	−	8.71446e7i	−0.532956	−	0.538333i
$546$	1.53173e7			0.0941034
$547$	−1.02489e7	−	1.02489e7i	−0.0626205	−	0.0626205i	0.675103	−	0.737723i	$-0.264099\pi$
$547$	−1.02489e7	−	1.02489e7i	−0.0626205	−	0.0626205i	−0.737723	+	0.675103i	$0.764099\pi$
$548$	1.42482e7	−	1.42482e7i	0.0865805	−	0.0865805i
$549$			6.09282e6i			0.0368215i
$550$	−1.21103e8	+	1.18696e8i	−0.727891	+	0.713422i
$551$	1.83472e8			1.09677
$552$	1.87846e8	+	1.87846e8i	1.11682	+	1.11682i
$553$	2.83824e7	−	2.83824e7i	0.167832	−	0.167832i
$554$			1.98400e8i			1.16684i
$555$	4.37892e7	−	4.33519e7i	0.256147	−	0.253588i
$556$	2.67065e8			1.55379
$557$	2.01202e8	+	2.01202e8i	1.16430	+	1.16430i	0.983523	+	0.180781i	$0.0578626\pi$
$557$	2.01202e8	+	2.01202e8i	1.16430	+	1.16430i	0.180781	+	0.983523i	$0.442137\pi$
$558$	4.70124e7	−	4.70124e7i	0.270589	−	0.270589i
$559$		−	2.72539e7i		−	0.156024i
$560$	−2.74019e7	−	137531.i	−0.156033	−	0.000783133i
$561$	−6.97995e7			−0.395334
$562$	−1.01914e8	−	1.01914e8i	−0.574151	−	0.574151i
$563$	−1.36525e8	+	1.36525e8i	−0.765045	+	0.765045i	−0.977230	−	0.212185i	$-0.931942\pi$
$563$	−1.36525e8	+	1.36525e8i	−0.765045	+	0.765045i	0.212185	+	0.977230i	$0.431942\pi$
$564$			1.24931e8i			0.696358i
$565$	1.28334e6	−	2.55696e8i	0.00711536	−	1.41768i
$566$	−5.13674e8			−2.83295
$567$	1.29937e7	+	1.29937e7i	0.0712826	+	0.0712826i
$568$	2.52453e8	−	2.52453e8i	1.37764	−	1.37764i
$569$			1.51174e8i			0.820616i	0.911947	+	0.410308i	$0.134579\pi$
$569$			1.51174e8i			0.820616i	−0.911947	+	0.410308i	$0.865421\pi$
$570$	−1.71521e8	−	1.73251e8i	−0.926173	−	0.935516i
$571$	−1.50325e8			−0.807462			−0.403731	−	0.914878i	$-0.632287\pi$
$571$	−1.50325e8			−0.807462			−0.403731	+	0.914878i	$0.632287\pi$
$572$	−4.41249e7	−	4.41249e7i	−0.235774	−	0.235774i
$573$	−2.97015e7	+	2.97015e7i	−0.157876	+	0.157876i
$574$			1.42376e8i			0.752835i
$575$	1.85822e8	+	1.89590e8i	0.977448	+	0.997270i
$576$	−1.04809e8			−0.548442
$577$	−2.48351e7	−	2.48351e7i	−0.129282	−	0.129282i	0.639505	−	0.768787i	$-0.279139\pi$
$577$	−2.48351e7	−	2.48351e7i	−0.129282	−	0.129282i	−0.768787	+	0.639505i	$0.779139\pi$
$578$	−6.00977e7	+	6.00977e7i	−0.311225	+	0.311225i
$579$		−	9.38184e6i		−	0.0483339i
$580$	2.80286e8	−	2.77487e8i	1.43654	−	1.42219i
$581$	−3.53130e7			−0.180055
$582$	1.68805e7	+	1.68805e7i	0.0856283	+	0.0856283i
$583$	3.64863e7	−	3.64863e7i	0.184130	−	0.184130i
$584$			2.59998e7i			0.130536i
$585$	−2.46604e7	−	123771.i	−0.123178	−	0.000618231i
$586$	1.68084e8			0.835285
$587$	1.89183e7	+	1.89183e7i	0.0935337	+	0.0935337i	0.752325	−	0.658792i	$-0.228932\pi$
$587$	1.89183e7	+	1.89183e7i	0.0935337	+	0.0935337i	−0.658792	+	0.752325i	$0.728932\pi$
$588$	1.93374e8	−	1.93374e8i	0.951190	−	0.951190i
$589$			1.12675e8i			0.551420i
$590$	44504.0	−	8.86707e6i	0.000216692	−	0.0431742i
$591$	1.52041e8			0.736544
$592$	−4.39972e7	−	4.39972e7i	−0.212061	−	0.212061i
$593$	6.70320e7	−	6.70320e7i	0.321453	−	0.321453i	−0.527871	−	0.849324i	$-0.677010\pi$
$593$	6.70320e7	−	6.70320e7i	0.321453	−	0.321453i	0.849324	+	0.527871i	$0.177010\pi$
$594$		−	2.31147e8i		−	1.10288i
$595$	−3.12950e7	−	3.16107e7i	−0.148567	−	0.150066i
$596$	−1.85857e8			−0.877892
$597$	−1.35225e8	−	1.35225e8i	−0.635525	−	0.635525i
$598$	−1.05956e8	+	1.05956e8i	−0.495474	+	0.495474i
$599$			2.44898e7i			0.113947i	0.998376	+	0.0569737i	$0.0181451\pi$
$599$			2.44898e7i			0.113947i	−0.998376	+	0.0569737i	$0.981855\pi$
$600$	−2.44297e8	−	2.45233e6i	−1.13101	−	0.0113534i
$601$	4.81673e7			0.221886			0.110943	−	0.993827i	$-0.464613\pi$
$601$	4.81673e7			0.221886			0.110943	+	0.993827i	$0.464613\pi$
$602$	3.38243e7	+	3.38243e7i	0.155038	+	0.155038i
$603$	6.92666e7	−	6.92666e7i	0.315916	−	0.315916i
$604$			7.51944e8i			3.41252i
$605$	−1.00474e8	+	9.94701e7i	−0.453718	+	0.449186i
$606$	2.54625e7			0.114415
$607$	−1.57626e8	−	1.57626e8i	−0.704792	−	0.704792i	0.260643	−	0.965435i	$-0.416065\pi$
$607$	−1.57626e8	−	1.57626e8i	−0.704792	−	0.704792i	−0.965435	+	0.260643i	$0.916065\pi$
$608$	6.50140e7	−	6.50140e7i	0.289265	−	0.289265i
$609$		−	4.57093e7i		−	0.202373i
$610$	−3.40464e7	−	170880.i	−0.149997	−	0.000752836i
$611$	−3.28498e7			−0.144015
$612$	1.08705e8	+	1.08705e8i	0.474235	+	0.474235i
$613$	1.99141e8	−	1.99141e8i	0.864528	−	0.864528i	−0.127332	−	0.991860i	$-0.540641\pi$
$613$	1.99141e8	−	1.99141e8i	0.864528	−	0.864528i	0.991860	+	0.127332i	$0.0406413\pi$
$614$		−	5.64968e8i		−	2.44073i
$615$	−1.61439e6	+	3.21654e8i	−0.00694037	+	1.38281i
$616$	5.10568e7			0.218429
$617$	−2.14639e7	−	2.14639e7i	−0.0913805	−	0.0913805i	0.659939	−	0.751319i	$-0.270582\pi$
$617$	−2.14639e7	−	2.14639e7i	−0.0913805	−	0.0913805i	−0.751319	+	0.659939i	$0.770582\pi$
$618$	−1.77925e8	+	1.77925e8i	−0.753825	+	0.753825i
$619$		−	1.51441e8i		−	0.638514i	−0.947668	−	0.319257i	$-0.896567\pi$
$619$		−	1.51441e8i		−	0.638514i	0.947668	−	0.319257i	$-0.103433\pi$
$620$	1.70413e8	+	1.72132e8i	0.715034	+	0.722248i
$621$	−3.61868e8			−1.51104
$622$	5.05859e8	+	5.05859e8i	2.10212	+	2.10212i
$623$	−4.96611e7	+	4.96611e7i	−0.205377	+	0.205377i
$624$		−	3.49437e7i		−	0.143819i
$625$	−2.44091e8	−	4.90102e6i	−0.999798	−	0.0200746i
$626$	6.63314e8			2.70394
$627$	8.13915e7	+	8.13915e7i	0.330199	+	0.330199i
$628$	−5.08952e8	+	5.08952e8i	−2.05493	+	2.05493i
$629$		−	1.01003e8i		−	0.405865i
$630$	3.07591e7	−	3.04519e7i	0.123013	−	0.121785i
$631$	5.35161e7			0.213008			0.106504	−	0.994312i	$-0.466034\pi$
$631$	5.35161e7			0.213008			0.106504	+	0.994312i	$0.466034\pi$
$632$	−2.55523e8	−	2.55523e8i	−1.01223	−	1.01223i
$633$	1.65579e8	−	1.65579e8i	0.652820	−	0.652820i
$634$		−	7.15735e8i		−	2.80856i
$635$	3.16195e8	+	1.58699e6i	1.23490	+	0.00619801i
$636$	1.59475e8			0.619900
$637$	5.08466e7	+	5.08466e7i	0.196718	+	0.196718i
$638$	−2.01968e8	+	2.01968e8i	−0.777716	+	0.777716i
$639$			1.42901e8i			0.547686i
$640$	2.40991e6	−	4.80156e8i	0.00919309	−	1.83165i
$641$	−7.32342e7			−0.278061			−0.139030	−	0.990288i	$-0.544399\pi$
$641$	−7.32342e7			−0.278061			−0.139030	+	0.990288i	$0.544399\pi$
$642$	7.76879e7	+	7.76879e7i	0.293595	+	0.293595i
$643$	−2.96289e8	+	2.96289e8i	−1.11450	+	1.11450i	−0.121971	+	0.992534i	$0.538922\pi$
$643$	−2.96289e8	+	2.96289e8i	−1.11450	+	1.11450i	−0.992534	+	0.121971i	$0.961078\pi$
$644$		−	1.71465e8i		−	0.641975i
$645$	7.60321e7	+	7.67991e7i	0.283346	+	0.286205i
$646$	−3.99616e8			−1.48233
$647$	−1.72144e8	−	1.72144e8i	−0.635592	−	0.635592i	0.313873	−	0.949465i	$-0.398373\pi$
$647$	−1.72144e8	−	1.72144e8i	−0.635592	−	0.635592i	−0.949465	+	0.313873i	$0.898373\pi$
$648$	1.16981e8	−	1.16981e8i	0.429921	−	0.429921i
$649$			4.18656e6i			0.0153152i
$650$	1.38325e6	−	1.37798e8i	0.00503688	−	0.501767i
$651$	2.80714e7			0.101747
$652$	−5.98622e8	−	5.98622e8i	−2.15978	−	2.15978i
$653$	8.72104e7	−	8.72104e7i	0.313205	−	0.313205i	−0.532945	−	0.846150i	$-0.678915\pi$
$653$	8.72104e7	−	8.72104e7i	0.313205	−	0.313205i	0.846150	+	0.532945i	$0.178915\pi$
$654$			2.74464e8i			0.981187i
$655$	−2.74282e8	+	2.71542e8i	−0.976052	+	0.966303i
$656$	3.24804e8			1.15056
$657$	−7.35858e6	−	7.35858e6i	−0.0259477	−	0.0259477i
$658$	4.07693e7	−	4.07693e7i	0.143105	−	0.143105i
$659$			7.70809e7i			0.269334i	0.990891	+	0.134667i	$0.0429964\pi$
$659$			7.70809e7i			0.269334i	−0.990891	+	0.134667i	$0.957004\pi$
$660$	2.47438e8	+	1.24190e6i	0.860668	+	0.00431971i
$661$	8.33416e7			0.288574			0.144287	−	0.989536i	$-0.453911\pi$
$661$	8.33416e7			0.288574			0.144287	+	0.989536i	$0.453911\pi$
$662$	1.64992e8	+	1.64992e8i	0.568709	+	0.568709i
$663$	4.01096e7	−	4.01096e7i	0.137628	−	0.137628i
$664$			3.17918e8i			1.08595i
$665$	−368159.	+	7.33527e7i	−0.00125190	+	0.249431i
$666$	9.82821e7			0.332699
$667$	3.16188e8	+	3.16188e8i	1.06554	+	1.06554i
$668$	2.52559e8	−	2.52559e8i	0.847291	−	0.847291i
$669$			6.49747e7i			0.217003i
$670$	3.85116e8	+	3.89002e8i	1.28046	+	1.29338i
$671$	1.60749e7			0.0532085
$672$	−1.61973e7	−	1.61973e7i	−0.0533746	−	0.0533746i
$673$	2.38317e8	−	2.38317e8i	0.781827	−	0.781827i	−0.198312	−	0.980139i	$-0.563546\pi$
$673$	2.38317e8	−	2.38317e8i	0.781827	−	0.781827i	0.980139	+	0.198312i	$0.0635459\pi$
$674$			7.37223e8i			2.40779i
$675$	2.37671e8	−	2.32946e8i	0.772794	−	0.757434i
$676$	−5.27961e8			−1.70908
$677$	−3.21631e8	−	3.21631e8i	−1.03655	−	1.03655i	−0.999306	−	0.0372467i	$-0.988141\pi$
$677$	−3.21631e8	−	3.21631e8i	−1.03655	−	1.03655i	−0.0372467	−	0.999306i	$-0.511859\pi$
$678$	−4.04680e8	+	4.04680e8i	−1.29844	+	1.29844i
$679$		−	7.18291e6i		−	0.0229452i
$680$	−2.84587e8	+	2.81744e8i	−0.905082	+	0.896043i
$681$	−3.92141e6			−0.0124165
$682$	−1.24035e8	−	1.24035e8i	−0.391012	−	0.391012i
$683$	9.24444e7	−	9.24444e7i	0.290147	−	0.290147i	−0.546991	−	0.837138i	$-0.684227\pi$
$683$	9.24444e7	−	9.24444e7i	0.290147	−	0.290147i	0.837138	+	0.546991i	$0.184227\pi$
$684$		−	2.53515e8i		−	0.792202i
$685$	−2.10091e7	−	105445.i	−0.0653637	−	0.000328061i
$686$	−2.60508e8			−0.806954
$687$	−2.38823e8	−	2.38823e8i	−0.736556	−	0.736556i
$688$	7.71638e7	−	7.71638e7i	0.236945	−	0.236945i
$689$			4.19329e7i			0.128203i
$690$	2.98213e6	−	5.94166e8i	0.00907778	−	1.80868i
$691$	3.46205e8			1.04930			0.524649	−	0.851319i	$-0.324197\pi$
$691$	3.46205e8			1.04930			0.524649	+	0.851319i	$0.324197\pi$
$692$	2.36561e8	+	2.36561e8i	0.713878	+	0.713878i
$693$	−1.44503e7	+	1.44503e7i	−0.0434188	+	0.0434188i
$694$		−	4.63899e8i		−	1.38786i
$695$	−1.95906e8	−	1.97883e8i	−0.583571	−	0.589459i
$696$	−4.11515e8			−1.22056
$697$	3.72821e8	+	3.72821e8i	1.10104	+	1.10104i
$698$	3.14554e8	−	3.14554e8i	0.924974	−	0.924974i
$699$		−	3.29635e8i		−	0.965165i
$700$	1.10378e8	+	1.12616e8i	0.321801	+	0.328327i
$701$	1.14851e8			0.333413			0.166706	−	0.986007i	$-0.446687\pi$
$701$	1.14851e8			0.333413			0.166706	+	0.986007i	$0.446687\pi$
$702$	1.32826e8	+	1.32826e8i	0.383947	+	0.383947i
$703$	−1.17777e8	+	1.17777e8i	−0.338996	+	0.338996i
$704$			2.76521e8i			0.792521i
$705$	9.25680e7	−	9.16434e7i	0.264176	−	0.261537i
$706$	−4.05964e8			−1.15365
$707$	−5.41734e6	−	5.41734e6i	−0.0153295	−	0.0153295i
$708$	−9.14934e6	+	9.14934e6i	−0.0257804	+	0.0257804i
$709$		−	1.57973e8i		−	0.443245i	−0.975133	−	0.221623i	$-0.928865\pi$
$709$		−	1.57973e8i		−	0.443245i	0.975133	−	0.221623i	$-0.0711353\pi$
$710$	−7.98523e8	−	4.00780e6i	−2.23107	−	0.0111978i
$711$	1.44639e8			0.402416
$712$	4.47092e8	+	4.47092e8i	1.23867	+	1.23867i
$713$	−1.94180e8	+	1.94180e8i	−0.535718	+	0.535718i
$714$			9.95584e7i			0.273516i
$715$	−326549.	+	6.50624e7i	−0.000893369	+	0.177997i
$716$	2.21489e8			0.603410
$717$	2.78601e8	+	2.78601e8i	0.755832	+	0.755832i
$718$	5.73532e8	−	5.73532e8i	1.54947	−	1.54947i
$719$			2.04633e8i			0.550540i	0.961367	+	0.275270i	$0.0887672\pi$
$719$			2.04633e8i			0.550540i	−0.961367	+	0.275270i	$0.911233\pi$
$720$	−6.94705e7	−	7.01713e7i	−0.186124	−	0.188002i
$721$	7.57095e7			0.201997
$722$	1.48719e7	+	1.48719e7i	0.0395143	+	0.0395143i
$723$	−2.46199e7	+	2.46199e7i	−0.0651437	+	0.0651437i
$724$		−	3.53269e8i		−	0.930872i
$725$	−4.11210e8	−	4.12784e6i	−1.07907	−	0.0108320i
$726$	3.16444e8			0.826964
$727$	−4.71448e8	−	4.71448e8i	−1.22696	−	1.22696i	−0.965108	−	0.261854i	$-0.915666\pi$
$727$	−4.71448e8	−	4.71448e8i	−1.22696	−	1.22696i	−0.261854	−	0.965108i	$-0.584334\pi$
$728$	−2.93392e7	+	2.93392e7i	−0.0760422	+	0.0760422i
$729$			3.86559e8i			0.997776i
$730$	4.13258e7	−	4.09131e7i	0.106231	−	0.105170i
$731$	1.77142e8			0.453493
$732$	3.51302e7	+	3.51302e7i	0.0895670	+	0.0895670i
$733$	−2.39548e8	+	2.39548e8i	−0.608247	+	0.608247i	−0.942488	−	0.334241i	$-0.891520\pi$
$733$	−2.39548e8	+	2.39548e8i	−0.608247	+	0.608247i	0.334241	+	0.942488i	$0.391520\pi$
$734$			2.11783e8i			0.535553i
$735$	−2.85132e8	−	1.43108e6i	−0.718098	−	0.00360415i
$736$	2.24085e8			0.562056
$737$	−1.82749e8	−	1.82749e8i	−0.456512	−	0.456512i
$738$	−3.62778e8	+	3.62778e8i	−0.902550	+	0.902550i
$739$			9.40080e7i			0.232933i	0.993195	+	0.116467i	$0.0371568\pi$
$739$			9.40080e7i			0.232933i	−0.993195	+	0.116467i	$0.962843\pi$
$740$	−1.79708e6	+	3.58054e8i	−0.00443478	+	0.883596i
$741$	−9.35415e7			−0.229906
$742$	−5.20422e7	−	5.20422e7i	−0.127393	−	0.127393i
$743$	−2.43455e8	+	2.43455e8i	−0.593542	+	0.593542i	−0.938586	−	0.345044i	$-0.887864\pi$
$743$	−2.43455e8	+	2.43455e8i	−0.593542	+	0.593542i	0.345044	+	0.938586i	$0.387864\pi$
$744$		−	2.52723e8i		−	0.613658i
$745$	1.36336e8	+	1.37712e8i	0.329718	+	0.333044i
$746$	6.04583e8			1.45626
$747$	−8.99786e7	−	8.99786e7i	−0.215863	−	0.215863i
$748$	2.86799e8	−	2.86799e8i	0.685288	−	0.685288i
$749$		−	3.30573e7i		−	0.0786724i
$750$	3.80526e8	+	3.92161e8i	0.901988	+	0.929568i
$751$	−2.93143e8			−0.692085			−0.346042	−	0.938219i	$-0.612475\pi$
$751$	−2.93143e8			−0.692085			−0.346042	+	0.938219i	$0.612475\pi$
$752$	−9.30076e7	−	9.30076e7i	−0.218708	−	0.218708i
$753$	1.29326e7	−	1.29326e7i	0.0302901	−	0.0302901i
$754$		−	2.32118e8i		−	0.541495i
$755$	5.57156e8	−	5.51591e8i	1.29460	−	1.28167i
$756$	−2.14949e8			−0.497473
$757$	3.79029e8	+	3.79029e8i	0.873746	+	0.873746i	0.992878	−	0.119132i	$-0.0380113\pi$
$757$	3.79029e8	+	3.79029e8i	0.873746	+	0.873746i	−0.119132	+	0.992878i	$0.538011\pi$
$758$	6.94961e8	−	6.94961e8i	1.59571	−	1.59571i
$759$			2.80534e8i			0.641593i
$760$	6.60385e8	+	3.31448e6i	1.50438	+	0.00755049i
$761$	−4.65585e8			−1.05644			−0.528221	−	0.849107i	$-0.677141\pi$
$761$	−4.65585e8			−1.05644			−0.528221	+	0.849107i	$0.677141\pi$
$762$	−5.00430e8	−	5.00430e8i	−1.13104	−	1.13104i
$763$	5.83941e7	−	5.83941e7i	0.131461	−	0.131461i
$764$		−	2.44081e8i		−	0.547336i
$765$	804476.	−	1.60286e8i	0.00179692	−	0.358022i
$766$	−1.14627e9			−2.55035
$767$	−2.40576e6	−	2.40576e6i	−0.00533171	−	0.00533171i
$768$	−4.37322e8	+	4.37322e8i	−0.965424	+	0.965424i
$769$			9.01841e7i			0.198313i	0.995072	+	0.0991565i	$0.0316144\pi$
$769$			9.01841e7i			0.198313i	−0.995072	+	0.0991565i	$0.968386\pi$
$770$	−8.03424e7	−	8.11530e7i	−0.175984	−	0.177759i
$771$	−2.48728e8			−0.542702
$772$	3.85490e7	+	3.85490e7i	0.0837841	+	0.0837841i
$773$	−9.17018e7	+	9.17018e7i	−0.198536	+	0.198536i	−0.799372	−	0.600836i	$-0.794834\pi$
$773$	−9.17018e7	+	9.17018e7i	−0.198536	+	0.198536i	0.600836	+	0.799372i	$0.294834\pi$
$774$			1.72371e8i			0.371741i
$775$	2.53503e6	−	2.52536e8i	0.00544600	−	0.542522i
$776$	−6.46669e7			−0.138387
$777$	2.93424e7	+	2.93424e7i	0.0625508	+	0.0625508i
$778$	−5.07201e8	+	5.07201e8i	−1.07706	+	1.07706i
$779$		−	8.69474e8i		−	1.83926i
$780$	−1.42902e8	+	1.41474e8i	−0.301129	+	0.298122i
$781$	3.77020e8			0.791428
$782$	−6.88682e8	−	6.88682e8i	−1.44012	−	1.44012i
$783$	3.96373e8	−	3.96373e8i	0.825694	−	0.825694i
$784$			2.87924e8i			0.597488i
$785$	7.50453e8	+	3.76654e6i	1.55137	+	0.00778634i
$786$	8.63855e8			1.77899
$787$	5.51822e8	+	5.51822e8i	1.13207	+	1.13207i	0.989832	+	0.142243i	$0.0454314\pi$
$787$	5.51822e8	+	5.51822e8i	1.13207	+	1.13207i	0.142243	+	0.989832i	$0.454569\pi$
$788$	−6.24722e8	+	6.24722e8i	−1.27676	+	1.27676i
$789$			2.69281e8i			0.548245i
$790$	−4.05654e6	+	8.08234e8i	−0.00822763	+	1.63929i
$791$	1.72197e8			0.347934
$792$	1.30094e8	+	1.30094e8i	0.261868	+	0.261868i
$793$	−9.23728e6	+	9.23728e6i	−0.0185236	+	0.0185236i
$794$			9.28572e8i			1.85504i
$795$	−1.16983e8	−	1.18164e8i	−0.232821	−	0.235170i
$796$	1.11125e9			2.20329
$797$	−1.79500e8	−	1.79500e8i	−0.354559	−	0.354559i	0.507244	−	0.861803i	$-0.330664\pi$
$797$	−1.79500e8	−	1.79500e8i	−0.354559	−	0.354559i	−0.861803	+	0.507244i	$0.830664\pi$
$798$	1.16093e8	−	1.16093e8i	0.228453	−	0.228453i
$799$		−	2.13514e8i		−	0.418588i
$800$	−1.47177e8	+	1.44251e8i	−0.287454	+	0.281740i
$801$	−2.53076e8			−0.492440
$802$	−2.72804e8	−	2.72804e8i	−0.528844	−	0.528844i
$803$	−1.94144e7	+	1.94144e7i	−0.0374954	+	0.0374954i
$804$		−	7.98761e8i		−	1.53691i
$805$	−1.27048e8	+	1.25779e8i	−0.243545	+	0.241112i
$806$	1.42550e8			0.272247
$807$	6.47959e7	+	6.47959e7i	0.123290	+	0.123290i
$808$	−4.87716e7	+	4.87716e7i	−0.0924556	+	0.0924556i
$809$		−	6.73245e7i		−	0.127153i	−0.997977	−	0.0635766i	$-0.979749\pi$
$809$		−	6.73245e7i		−	0.127153i	0.997977	−	0.0635766i	$-0.0202507\pi$
$810$	−3.70016e8	−	1.85712e6i	−0.696251	−	0.00349450i
$811$	−6.32767e8			−1.18626			−0.593132	−	0.805105i	$-0.702109\pi$
$811$	−6.32767e8			−1.18626			−0.593132	+	0.805105i	$0.702109\pi$
$812$	1.87815e8	+	1.87815e8i	0.350802	+	0.350802i
$813$	8.00548e7	−	8.00548e7i	0.148976	−	0.148976i
$814$		−	2.59301e8i		−	0.480763i
$815$	−4.43015e6	+	8.82672e8i	−0.00818362	+	1.63052i
$816$	2.27124e8			0.418016
$817$	−2.06561e8	−	2.06561e8i	−0.378777	−	0.378777i
$818$	−1.00298e8	+	1.00298e8i	−0.183244	+	0.183244i
$819$		−	1.66074e7i		−	0.0302309i
$820$	−1.31501e9	−	1.32828e9i	−2.38500	−	2.40906i
$821$	4.28302e8			0.773964			0.386982	−	0.922087i	$-0.373518\pi$
$821$	4.28302e8			0.773964			0.386982	+	0.922087i	$0.373518\pi$
$822$	3.32504e7	+	3.32504e7i	0.0598661	+	0.0598661i
$823$	7.00816e7	−	7.00816e7i	0.125720	−	0.125720i	−0.641447	−	0.767167i	$-0.721666\pi$
$823$	7.00816e7	−	7.00816e7i	0.125720	−	0.125720i	0.767167	+	0.641447i	$0.221666\pi$
$824$		−	6.81602e8i		−	1.21829i
$825$	−1.80589e8	−	1.84251e8i	−0.321610	−	0.328132i
$826$	5.97149e6			0.0105960
$827$	6.05979e8	+	6.05979e8i	1.07137	+	1.07137i	0.997249	+	0.0741255i	$0.0236165\pi$
$827$	6.05979e8	+	6.05979e8i	1.07137	+	1.07137i	0.0741255	+	0.997249i	$0.476383\pi$
$828$	4.36899e8	−	4.36899e8i	0.769644	−	0.769644i
$829$		−	6.84492e8i		−	1.20145i	−0.799456	−	0.600724i	$-0.794879\pi$
$829$		−	6.84492e8i		−	1.20145i	0.799456	−	0.600724i	$-0.205121\pi$
$830$	5.05320e8	−	5.00273e8i	0.883756	−	0.874929i
$831$	−3.01854e8			−0.526011
$832$	−1.58900e8	−	1.58900e8i	−0.275902	−	0.275902i
$833$	−3.30489e8	+	3.30489e8i	−0.571770	+	0.571770i
$834$			6.23235e8i			1.07437i
$835$	−3.72399e8	−	1.86908e6i	−0.639660	−	0.00321047i
$836$	−6.68859e8			−1.14476
$837$	2.43424e8	+	2.43424e8i	0.415133	+	0.415133i
$838$	4.71051e8	−	4.71051e8i	0.800454	−	0.800454i
$839$			4.58117e8i			0.775695i	0.921724	+	0.387847i	$0.126781\pi$
$839$			4.58117e8i			0.775695i	−0.921724	+	0.387847i	$0.873219\pi$
$840$	825756.	−	1.64525e8i	0.00139320	−	0.277584i
$841$	−9.78528e7			−0.164507
$842$	6.67703e8	+	6.67703e8i	1.11853	+	1.11853i
$843$	1.55057e8	−	1.55057e8i	0.258827	−	0.258827i
$844$			1.36069e9i			2.26325i
$845$	3.87287e8	+	3.91194e8i	0.641894	+	0.648370i
$846$	2.07763e8			0.343128
$847$	−6.73257e7	−	6.73257e7i	−0.110798	−	0.110798i
$848$	−1.18725e8	+	1.18725e8i	−0.194694	+	0.194694i
$849$		−	7.81528e8i		−	1.27709i
$850$	8.95646e8	+	8.99076e6i	1.45841	+	0.0146399i
$851$	−4.05945e8			−0.658686
$852$	8.23944e8	+	8.23944e8i	1.33223	+	1.33223i
$853$	1.74568e7	−	1.74568e7i	0.0281267	−	0.0281267i	−0.692904	−	0.721030i	$-0.743669\pi$
$853$	1.74568e7	−	1.74568e7i	0.0281267	−	0.0281267i	0.721030	+	0.692904i	$0.243669\pi$
$854$		−	2.29284e7i		−	0.0368129i
$855$	−1.87843e8	+	1.85967e8i	−0.300536	+	0.297534i
$856$	−2.97611e8			−0.474490
$857$	−5.06507e8	−	5.06507e8i	−0.804717	−	0.804717i	0.179112	−	0.983829i	$-0.442678\pi$
$857$	−5.06507e8	−	5.06507e8i	−0.804717	−	0.804717i	−0.983829	+	0.179112i	$0.942678\pi$
$858$	1.02972e8	−	1.02972e8i	0.163026	−	0.163026i
$859$			1.02651e9i			1.61952i	0.586764	+	0.809758i	$0.300402\pi$
$859$			1.02651e9i			1.61952i	−0.586764	+	0.809758i	$0.699598\pi$
$860$	−6.27968e8	−	3.15178e6i	−0.987284	−	0.00495520i
$861$	−2.16617e8			−0.339377
$862$	−6.15014e8	−	6.15014e8i	−0.960203	−	0.960203i
$863$	3.37658e8	−	3.37658e8i	0.525345	−	0.525345i	−0.393836	−	0.919181i	$-0.628852\pi$
$863$	3.37658e8	−	3.37658e8i	0.525345	−	0.525345i	0.919181	+	0.393836i	$0.128852\pi$
$864$		−	2.80913e8i		−	0.435543i
$865$	1.75068e6	−	3.48810e8i	0.00270495	−	0.538940i
$866$	−8.94081e8			−1.37665
$867$	−9.14354e7	−	9.14354e7i	−0.140300	−	0.140300i
$868$	−1.15343e8	+	1.15343e8i	−0.176372	+	0.176372i
$869$		−	3.81605e8i		−	0.581507i
$870$	6.47556e8	+	6.54089e8i	0.983376	+	0.993297i
$871$	2.10029e8			0.317852
$872$	−5.25715e8	−	5.25715e8i	−0.792868	−	0.792868i
$873$	1.83023e7	−	1.83023e7i	0.0275082	−	0.0275082i
$874$			1.60611e9i			2.40570i
$875$	2.47547e6	−	1.64395e8i	0.00369516	−	0.245394i
$876$	−8.48569e7			−0.126234
$877$	−4.08316e8	−	4.08316e8i	−0.605338	−	0.605338i	0.336386	−	0.941724i	$-0.390795\pi$
$877$	−4.08316e8	−	4.08316e8i	−0.605338	−	0.605338i	−0.941724	+	0.336386i	$0.890795\pi$
$878$	9.93362e8	−	9.93362e8i	1.46765	−	1.46765i
$879$			2.55731e8i			0.376545i
$880$	−1.85136e8	+	1.83286e8i	−0.271670	+	0.268957i
$881$	6.30879e8			0.922610			0.461305	−	0.887242i	$-0.347381\pi$
$881$	6.30879e8			0.922610			0.461305	+	0.887242i	$0.347381\pi$
$882$	−3.21586e8	−	3.21586e8i	−0.468696	−	0.468696i
$883$	−1.37438e7	+	1.37438e7i	−0.0199630	+	0.0199630i	−0.717018	−	0.697055i	$-0.754493\pi$
$883$	−1.37438e7	+	1.37438e7i	−0.0199630	+	0.0199630i	0.697055	+	0.717018i	$0.254493\pi$
$884$			3.29612e8i			0.477141i
$885$	1.34908e7	+	67710.4i	0.0194629	+	9.76844e-5i
$886$	1.23004e9			1.76855
$887$	3.78526e8	+	3.78526e8i	0.542406	+	0.542406i	0.924234	−	0.381827i	$-0.124705\pi$
$887$	3.78526e8	+	3.78526e8i	0.542406	+	0.542406i	−0.381827	+	0.924234i	$0.624705\pi$
$888$	2.64166e8	−	2.64166e8i	0.377258	−	0.377258i
$889$			2.12940e8i			0.303076i
$890$	7.09778e6	−	1.41418e9i	0.0100682	−	2.00601i
$891$	1.74702e8			0.246982
$892$	−2.66975e8	−	2.66975e8i	−0.376163	−	0.376163i
$893$	−2.48974e8	+	2.48974e8i	−0.349622	+	0.349622i
$894$		−	4.33726e8i		−	0.607019i
$895$	−1.62474e8	−	1.64113e8i	−0.226628	−	0.228914i
$896$	3.23359e8			0.449533
$897$	−1.61206e8	−	1.61206e8i	−0.223359	−	0.223359i
$898$	−1.29902e9	+	1.29902e9i	−1.79385	+	1.79385i
$899$		−	4.25392e8i		−	0.585478i
$900$	−5.70372e6	+	5.68196e8i	−0.00782403	+	0.779419i
$901$	−2.72552e8			−0.372628
$902$	9.57129e8	+	9.57129e8i	1.30422	+	1.30422i
$903$	−5.14618e7	+	5.14618e7i	−0.0698910	+	0.0698910i
$904$		−	1.55027e9i		−	2.09847i
$905$	−2.61756e8	+	2.59142e8i	−0.353143	+	0.349616i
$906$	−1.75477e9			−2.35959
$907$	8.38586e7	+	8.38586e7i	0.112390	+	0.112390i	0.761065	−	0.648676i	$-0.224677\pi$
$907$	8.38586e7	+	8.38586e7i	0.112390	+	0.112390i	−0.648676	+	0.761065i	$0.724677\pi$
$908$	1.61127e7	−	1.61127e7i	0.0215234	−	0.0215234i
$909$		−	2.76071e7i		−	0.0367561i
$910$	9.28017e7	+	465773.i	0.123149	+	0.000618088i
$911$	−2.63279e8			−0.348226			−0.174113	−	0.984726i	$-0.555706\pi$
$911$	−2.63279e8			−0.348226			−0.174113	+	0.984726i	$0.555706\pi$
$912$	−2.64844e8	−	2.64844e8i	−0.349145	−	0.349145i
$913$	−2.37394e8	+	2.37394e8i	−0.311930	+	0.311930i
$914$		−	2.08800e9i		−	2.73459i
$915$	259984.	−	5.17998e7i	0.000339378	−	0.0676183i
$916$	1.96260e9			2.55356
$917$	−1.83791e8	−	1.83791e8i	−0.238351	−	0.238351i
$918$	−8.63332e8	+	8.63332e8i	−1.11596	+	1.11596i
$919$		−	8.86087e7i		−	0.114164i	−0.998369	−	0.0570821i	$-0.981820\pi$
$919$		−	8.86087e7i		−	0.114164i	0.998369	−	0.0570821i	$-0.0181797\pi$
$920$	1.13237e9	+	1.14379e9i	1.45420	+	1.46887i
$921$	8.59569e8			1.10028
$922$	5.49388e8	+	5.49388e8i	0.700948	+	0.700948i
$923$	−2.16651e8	+	2.16651e8i	−0.275521	+	0.275521i
$924$			1.66636e8i			0.211229i
$925$	2.66620e8	−	2.61320e8i	0.336874	−	0.330178i
$926$	−1.69968e9			−2.14060
$927$	1.92910e8	+	1.92910e8i	0.242167	+	0.242167i
$928$	−2.45453e8	+	2.45453e8i	−0.307131	+	0.307131i
$929$			9.93524e8i			1.23917i	0.784929	+	0.619586i	$0.212699\pi$
$929$			9.93524e8i			1.23917i	−0.784929	+	0.619586i	$0.787301\pi$
$930$	−4.01695e8	+	3.97683e8i	−0.499399	+	0.494411i
$931$	7.70749e8			0.955133
$932$	1.35444e9	+	1.35444e9i	1.67306	+	1.67306i
$933$	−7.69637e8	+	7.69637e8i	−0.947635	+	0.947635i
$934$		−	1.29072e9i		−	1.58413i
$935$	−4.22887e8	−	2.12248e6i	−0.517356	−	0.00259662i
$936$	−1.49515e8			−0.182329
$937$	−4.21096e8	−	4.21096e8i	−0.511873	−	0.511873i	0.403227	−	0.915100i	$-0.367889\pi$
$937$	−4.21096e8	−	4.21096e8i	−0.511873	−	0.511873i	−0.915100	+	0.403227i	$0.867889\pi$
$938$	−2.60663e8	+	2.60663e8i	−0.315843	+	0.315843i
$939$			1.00920e9i			1.21893i
$940$	−3.79893e6	+	7.56906e8i	−0.00457380	+	0.911294i
$941$	1.18128e9			1.41770			0.708851	−	0.705359i	$-0.249214\pi$
$941$	1.18128e9			1.41770			0.708851	+	0.705359i	$0.249214\pi$
$942$	−1.18771e9	−	1.18771e9i	−1.42089	−	1.42089i
$943$	1.49842e9	−	1.49842e9i	1.78689	−	1.78689i
$944$		−	1.36229e7i		−	0.0161939i
$945$	1.57676e8	+	1.59267e8i	0.186840	+	0.188725i
$946$	4.54772e8			0.537180
$947$	−3.67092e8	−	3.67092e8i	−0.432240	−	0.432240i	0.457149	−	0.889390i	$-0.348870\pi$
$947$	−3.67092e8	−	3.67092e8i	−0.432240	−	0.432240i	−0.889390	+	0.457149i	$0.848870\pi$
$948$	8.33963e8	−	8.33963e8i	0.978863	−	0.978863i
$949$		−	2.23126e7i		−	0.0261067i
$950$	−1.03391e9	−	1.05487e9i	−1.20590	−	1.23035i
$951$	1.08895e9			1.26610
$952$	−1.90697e8	−	1.90697e8i	−0.221021	−	0.221021i
$953$	5.44279e8	−	5.44279e8i	0.628844	−	0.628844i	−0.318933	−	0.947777i	$-0.603324\pi$
$953$	5.44279e8	−	5.44279e8i	0.628844	−	0.628844i	0.947777	+	0.318933i	$0.103324\pi$
$954$		−	2.65210e8i		−	0.305454i
$955$	−1.80853e8	+	1.79047e8i	−0.207642	+	0.205568i
$956$	−2.28949e9			−2.62038
$957$	−3.07284e8	−	3.07284e8i	−0.350594	−	0.350594i
$958$	−5.87584e8	+	5.87584e8i	−0.668304	+	0.668304i
$959$		−	1.41485e7i		−	0.0160419i
$960$	8.91062e8	+	4.47226e6i	1.00715	+	0.00505491i
$961$	−6.26258e8			−0.705640
$962$	1.49005e8	+	1.49005e8i	0.167369	+	0.167369i
$963$	8.42311e7	−	8.42311e7i	0.0943178	−	0.0943178i
$964$		−	2.02322e8i		−	0.225846i
$965$	285285.	−	5.68408e7i	0.000317466	−	0.0632526i
$966$	4.00139e8			0.443894
$967$	−1.01015e9	−	1.01015e9i	−1.11714	−	1.11714i	−0.992160	−	0.124976i	$-0.960115\pi$
$967$	−1.01015e9	−	1.01015e9i	−1.11714	−	1.11714i	−0.124976	−	0.992160i	$-0.539885\pi$
$968$	−6.06125e8	+	6.06125e8i	−0.668245	+	0.668245i
$969$		−	6.07994e8i		−	0.668233i
$970$	1.01759e8	+	1.02786e8i	0.111496	+	0.112621i
$971$	−1.69787e9			−1.85459			−0.927295	−	0.374332i	$-0.877872\pi$
$971$	−1.69787e9			−1.85459			−0.927295	+	0.374332i	$0.877872\pi$
$972$	−9.34459e8	−	9.34459e8i	−1.01756	−	1.01756i
$973$	1.32598e8	−	1.32598e8i	0.143945	−	0.143945i
$974$			2.51691e9i			2.72390i
$975$	2.09652e8	+	2.10454e6i	0.226196	+	0.00227062i
$976$	−5.23070e7			−0.0562613
$977$	2.14608e8	+	2.14608e8i	0.230124	+	0.230124i	0.812744	−	0.582620i	$-0.197973\pi$
$977$	2.14608e8	+	2.14608e8i	0.230124	+	0.230124i	−0.582620	+	0.812744i	$0.697973\pi$
$978$	1.39697e9	−	1.39697e9i	1.49338	−	1.49338i
$979$			6.67699e8i			0.711595i
$980$	1.17746e9	−	1.16570e9i	1.25103	−	1.23853i
$981$	2.97580e8			0.315208
$982$	2.21684e9	+	2.21684e9i	2.34099	+	2.34099i
$983$	−7.60474e8	+	7.60474e8i	−0.800615	+	0.800615i	−0.983192	−	0.182576i	$-0.941556\pi$
$983$	−7.60474e8	+	7.60474e8i	−0.800615	+	0.800615i	0.182576	+	0.983192i	$0.441556\pi$
$984$			1.95017e9i			2.04686i
$985$	9.21157e8	+	4.62330e6i	0.963884	+	0.00483775i
$986$	1.50870e9			1.57388
$987$	6.20282e7	+	6.20282e7i	0.0645116	+	0.0645116i
$988$	3.84353e8	−	3.84353e8i	0.398528	−	0.398528i
$989$		−	7.11960e8i		−	0.735981i
$990$	2.06530e6	−	4.11495e8i	0.00212852	−	0.424091i
$991$	5.74834e8			0.590638			0.295319	−	0.955399i	$-0.404574\pi$
$991$	5.74834e8			0.590638			0.295319	+	0.955399i	$0.404574\pi$
$992$	−1.50740e8	−	1.50740e8i	−0.154416	−	0.154416i
$993$	−2.51027e8	+	2.51027e8i	−0.256373	+	0.256373i
$994$		−	5.37762e8i		−	0.547559i
$995$	−8.15160e8	−	8.23384e8i	−0.827511	−	0.835859i
$996$	−1.03761e9			−1.05016
$997$	4.89316e8	+	4.89316e8i	0.493746	+	0.493746i	0.909484	−	0.415738i	$-0.136477\pi$
$997$	4.89316e8	+	4.89316e8i	0.493746	+	0.493746i	−0.415738	+	0.909484i	$0.636477\pi$
$998$	−5.74163e8	+	5.74163e8i	−0.577622	+	0.577622i
$999$			5.08892e8i			0.510422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.7.c.a.2.1	✓	4
3.2	odd	2		45.7.g.a.37.2		4
4.3	odd	2		80.7.p.b.17.1		4
5.2	odd	4		25.7.c.c.18.2		4
5.3	odd	4	inner	5.7.c.a.3.1	yes	4
5.4	even	2		25.7.c.c.7.2		4
15.2	even	4		225.7.g.c.118.1		4
15.8	even	4		45.7.g.a.28.2		4
15.14	odd	2		225.7.g.c.82.1		4
20.3	even	4		80.7.p.b.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.7.c.a.2.1	✓	4	1.1	even	1	trivial
5.7.c.a.3.1	yes	4	5.3	odd	4	inner
25.7.c.c.7.2		4	5.4	even	2
25.7.c.c.18.2		4	5.2	odd	4
45.7.g.a.28.2		4	15.8	even	4
45.7.g.a.37.2		4	3.2	odd	2
80.7.p.b.17.1		4	4.3	odd	2
80.7.p.b.33.1		4	20.3	even	4
225.7.g.c.82.1		4	15.14	odd	2
225.7.g.c.118.1		4	15.2	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.58872 - 9.58872i) q^{2} +(14.5887 - 14.5887i) q^{3} +119.887i q^{4} +(88.8309 - 87.9436i) q^{5} -279.774 q^{6} +(59.5240 + 59.5240i) q^{7} +(535.887 - 535.887i) q^{8} +303.338i q^{9} +O(q^{10})\)	\(q+(-9.58872 - 9.58872i) q^{2} +(14.5887 - 14.5887i) q^{3} +119.887i q^{4} +(88.8309 - 87.9436i) q^{5} -279.774 q^{6} +(59.5240 + 59.5240i) q^{7} +(535.887 - 535.887i) q^{8} +303.338i q^{9} +(-1695.04 - 8.50745i) q^{10} +800.309 q^{11} +(1749.00 + 1749.00i) q^{12} +(-459.889 + 459.889i) q^{13} -1141.52i q^{14} +(12.9436 - 2578.91i) q^{15} -2604.17 q^{16} +(-2989.15 - 2989.15i) q^{17} +(2908.63 - 2908.63i) q^{18} +6971.14i q^{19} +(10543.3 + 10649.7i) q^{20} +1736.76 q^{21} +(-7673.94 - 7673.94i) q^{22} +(-12013.8 + 12013.8i) q^{23} -15635.8i q^{24} +(156.840 - 15624.2i) q^{25} +8819.50 q^{26} +(15060.5 + 15060.5i) q^{27} +(-7136.17 + 7136.17i) q^{28} -26318.7i q^{29} +(-24852.6 + 24604.4i) q^{30} +16163.1 q^{31} +(-9326.16 - 9326.16i) q^{32} +(11675.5 - 11675.5i) q^{33} +57324.3i q^{34} +(10522.3 + 52.8118i) q^{35} -36366.4 q^{36} +(16894.9 + 16894.9i) q^{37} +(66844.4 - 66844.4i) q^{38} +13418.4i q^{39} +(475.458 - 94731.2i) q^{40} -124725. q^{41} +(-16653.3 - 16653.3i) q^{42} +(-29630.9 + 29630.9i) q^{43} +95946.8i q^{44} +(26676.7 + 26945.8i) q^{45} +230394. q^{46} +(35714.9 + 35714.9i) q^{47} +(-37991.5 + 37991.5i) q^{48} -110563. i q^{49} +(-151320. + 148312. i) q^{50} -87215.7 q^{51} +(-55134.8 - 55134.8i) q^{52} +(45590.3 - 45590.3i) q^{53} -288822. i q^{54} +(71092.1 - 70382.0i) q^{55} +63796.3 q^{56} +(101700. + 101700. i) q^{57} +(-252363. + 252363. i) q^{58} +5231.18i q^{59} +(309179. + 1551.77i) q^{60} +20085.9 q^{61} +(-154983. - 154983. i) q^{62} +(-18055.9 + 18055.9i) q^{63} +345518. i q^{64} +(-408.029 + 81296.6i) q^{65} -223906. q^{66} +(-228348. - 228348. i) q^{67} +(358361. - 358361. i) q^{68} +350532. i q^{69} +(-100389. - 101402. i) q^{70} +471094. q^{71} +(162555. + 162555. i) q^{72} +(-24258.7 + 24258.7i) q^{73} -324002. i q^{74} +(-225649. - 230225. i) q^{75} -835751. q^{76} +(47637.6 + 47637.6i) q^{77} +(128665. - 128665. i) q^{78} -476823. i q^{79} +(-231330. + 229020. i) q^{80} +218293. q^{81} +(1.19595e6 + 1.19595e6i) q^{82} +(-296628. + 296628. i) q^{83} +208215. i q^{84} +(-528405. - 2652.08i) q^{85} +568245. q^{86} +(-383957. - 383957. i) q^{87} +(428875. - 428875. i) q^{88} +834303. i q^{89} +(2580.63 - 514171. i) q^{90} -54748.9 q^{91} +(-1.44030e6 - 1.44030e6i) q^{92} +(235799. - 235799. i) q^{93} -684921. i q^{94} +(613068. + 619253. i) q^{95} -272113. q^{96} +(-60336.2 - 60336.2i) q^{97} +(-1.06016e6 + 1.06016e6i) q^{98} +242764. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8}+O(q^{10}) \) 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8	\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8} - 4370 q^{10} - 1052 q^{11} + 3480 q^{12} + 1960 q^{13} - 90 q^{15} - 776 q^{16} - 3280 q^{17} - 870 q^{18} + 20340 q^{20} + 3828 q^{21} - 27520 q^{22} - 39010 q^{23} + 30400 q^{25} + 44068 q^{26} + 31320 q^{27} - 4840 q^{28} - 50640 q^{30} - 33172 q^{31} - 48760 q^{32} + 22260 q^{33} - 24970 q^{35} - 40836 q^{36} + 146860 q^{37} + 218040 q^{38} - 110100 q^{40} - 213932 q^{41} - 31680 q^{42} - 72050 q^{43} + 78210 q^{45} + 323288 q^{46} + 830 q^{47} - 74160 q^{48} - 203350 q^{50} - 172212 q^{51} - 173300 q^{52} - 29620 q^{53} + 470660 q^{55} + 467280 q^{56} + 195840 q^{57} - 554640 q^{58} + 620280 q^{60} - 111052 q^{61} - 610520 q^{62} - 350130 q^{63} - 406540 q^{65} - 457824 q^{66} - 146930 q^{67} + 775780 q^{68} - 133320 q^{70} + 1310188 q^{71} + 899460 q^{72} + 553540 q^{73} - 435450 q^{75} - 2073840 q^{76} - 476300 q^{77} + 268200 q^{78} - 1011520 q^{80} - 624816 q^{81} + 2554880 q^{82} + 536870 q^{83} - 1344920 q^{85} + 1019128 q^{86} - 763440 q^{87} - 187680 q^{88} + 947310 q^{90} + 1131548 q^{91} - 2552680 q^{92} + 444660 q^{93} + 912600 q^{95} - 568992 q^{96} - 59420 q^{97} - 1892810 q^{98}+O(q^{100}) \) 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8 - 4370 * q^10 - 1052 * q^11 + 3480 * q^12 + 1960 * q^13 - 90 * q^15 - 776 * q^16 - 3280 * q^17 - 870 * q^18 + 20340 * q^20 + 3828 * q^21 - 27520 * q^22 - 39010 * q^23 + 30400 * q^25 + 44068 * q^26 + 31320 * q^27 - 4840 * q^28 - 50640 * q^30 - 33172 * q^31 - 48760 * q^32 + 22260 * q^33 - 24970 * q^35 - 40836 * q^36 + 146860 * q^37 + 218040 * q^38 - 110100 * q^40 - 213932 * q^41 - 31680 * q^42 - 72050 * q^43 + 78210 * q^45 + 323288 * q^46 + 830 * q^47 - 74160 * q^48 - 203350 * q^50 - 172212 * q^51 - 173300 * q^52 - 29620 * q^53 + 470660 * q^55 + 467280 * q^56 + 195840 * q^57 - 554640 * q^58 + 620280 * q^60 - 111052 * q^61 - 610520 * q^62 - 350130 * q^63 - 406540 * q^65 - 457824 * q^66 - 146930 * q^67 + 775780 * q^68 - 133320 * q^70 + 1310188 * q^71 + 899460 * q^72 + 553540 * q^73 - 435450 * q^75 - 2073840 * q^76 - 476300 * q^77 + 268200 * q^78 - 1011520 * q^80 - 624816 * q^81 + 2554880 * q^82 + 536870 * q^83 - 1344920 * q^85 + 1019128 * q^86 - 763440 * q^87 - 187680 * q^88 + 947310 * q^90 + 1131548 * q^91 - 2552680 * q^92 + 444660 * q^93 + 912600 * q^95 - 568992 * q^96 - 59420 * q^97 - 1892810 * q^98

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