LMFDB - Embedded newform 680.2.bw.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [680,2,Mod(43,680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(680, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 4, 6, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("680.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bw (of order $8$, degree $4$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$104$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	680.43
Dual form			680.2.bw.a.427.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40972 + 0.112635i) q^{2} +(-1.15905 - 2.79820i) q^{3} +(1.97463 - 0.317569i) q^{4} +(2.02285 - 0.952933i) q^{5} +(1.94912 + 3.81414i) q^{6} +(1.43661 - 3.46829i) q^{7} +(-2.74790 + 0.670096i) q^{8} +(-4.36522 + 4.36522i) q^{9} +O(q^{10})$	\(q+(-1.40972 + 0.112635i) q^{2} +(-1.15905 - 2.79820i) q^{3} +(1.97463 - 0.317569i) q^{4} +(2.02285 - 0.952933i) q^{5} +(1.94912 + 3.81414i) q^{6} +(1.43661 - 3.46829i) q^{7} +(-2.74790 + 0.670096i) q^{8} +(-4.36522 + 4.36522i) q^{9} +(-2.74432 + 1.57121i) q^{10} +(-4.85998 + 2.01307i) q^{11} +(-3.17732 - 5.15733i) q^{12} +(1.26662 + 1.26662i) q^{13} +(-1.63457 + 5.05113i) q^{14} +(-5.01109 - 4.55584i) q^{15} +(3.79830 - 1.25416i) q^{16} +(-2.89300 + 2.93778i) q^{17} +(5.66207 - 6.64543i) q^{18} +(-4.99413 - 4.99413i) q^{19} +(3.69175 - 2.52408i) q^{20} -11.3701 q^{21} +(6.62447 - 3.38527i) q^{22} +(0.396545 - 0.957344i) q^{23} +(5.06004 + 6.91252i) q^{24} +(3.18384 - 3.85528i) q^{25} +(-1.92825 - 1.64292i) q^{26} +(8.87971 + 3.67810i) q^{27} +(1.73535 - 7.30480i) q^{28} +(0.398139 - 0.961193i) q^{29} +(7.57739 + 5.85804i) q^{30} +(-2.45520 + 5.92738i) q^{31} +(-5.21328 + 2.19584i) q^{32} +(11.2660 + 11.2660i) q^{33} +(3.74742 - 4.46731i) q^{34} +(-0.398998 - 8.38482i) q^{35} +(-7.23343 + 10.0059i) q^{36} +(-1.61126 - 3.88993i) q^{37} +(7.60285 + 6.47782i) q^{38} +(2.07619 - 5.01236i) q^{39} +(-4.92004 + 3.97407i) q^{40} +(0.670346 + 1.61836i) q^{41} +(16.0287 - 1.28067i) q^{42} -7.00207i q^{43} +(-8.95735 + 5.51843i) q^{44} +(-4.67042 + 12.9900i) q^{45} +(-0.451187 + 1.39425i) q^{46} +(-0.832549 + 0.832549i) q^{47} +(-7.91183 - 9.17478i) q^{48} +(-5.01543 - 5.01543i) q^{49} +(-4.05408 + 5.79348i) q^{50} +(11.5737 + 4.69014i) q^{51} +(2.90335 + 2.09887i) q^{52} -11.8658i q^{53} +(-12.9322 - 4.18492i) q^{54} +(-7.91268 + 8.70337i) q^{55} +(-1.62358 + 10.4932i) q^{56} +(-8.18614 + 19.7631i) q^{57} +(-0.453001 + 1.39986i) q^{58} +(1.39307 - 1.39307i) q^{59} +(-11.3418 - 7.40473i) q^{60} +(-1.56801 + 0.649493i) q^{61} +(2.79352 - 8.63250i) q^{62} +(8.86872 + 21.4110i) q^{63} +(7.10194 - 3.68272i) q^{64} +(3.76920 + 1.35518i) q^{65} +(-17.1508 - 14.6129i) q^{66} +(-5.98943 + 5.98943i) q^{67} +(-4.77964 + 6.71975i) q^{68} -3.13846 q^{69} +(1.50690 + 11.7753i) q^{70} +(-2.89257 + 6.98328i) q^{71} +(9.07009 - 14.9203i) q^{72} +(-12.5839 + 5.21241i) q^{73} +(2.70957 + 5.30223i) q^{74} +(-14.4781 - 4.44055i) q^{75} +(-11.4475 - 8.27557i) q^{76} +19.7478i q^{77} +(-2.36228 + 7.29988i) q^{78} +(9.53535 - 3.94967i) q^{79} +(6.48826 - 6.15650i) q^{80} -10.5903i q^{81} +(-1.12728 - 2.20593i) q^{82} +5.42947 q^{83} +(-22.4517 + 3.61079i) q^{84} +(-3.05258 + 8.69953i) q^{85} +(0.788680 + 9.87096i) q^{86} -3.15108 q^{87} +(12.0058 - 8.78837i) q^{88} +3.29031 q^{89} +(5.12086 - 18.8383i) q^{90} +(6.21267 - 2.57337i) q^{91} +(0.479005 - 2.01633i) q^{92} +19.4317 q^{93} +(1.07989 - 1.26744i) q^{94} +(-14.8615 - 5.34330i) q^{95} +(12.1869 + 12.0427i) q^{96} +(-2.12524 - 5.13078i) q^{97} +(7.63527 + 6.50544i) q^{98} +(12.4274 - 30.0024i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 8 q^{3}+O(q^{10}) $ 416 * q - 8 * q^3	$ 416 q - 8 q^{3} - 12 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{14} - 16 q^{16} - 8 q^{18} - 32 q^{19} + 12 q^{20} + 4 q^{22} + 24 q^{24} - 16 q^{25} + 8 q^{26} + 16 q^{27} - 20 q^{28} - 16 q^{30} - 16 q^{33} - 16 q^{35} - 72 q^{36} + 16 q^{38} - 24 q^{40} - 16 q^{41} - 24 q^{42} + 32 q^{46} - 100 q^{48} - 48 q^{50} - 16 q^{51} + 24 q^{52} + 16 q^{54} - 8 q^{56} - 32 q^{57} - 72 q^{58} - 40 q^{60} + 48 q^{62} + 48 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{67} - 116 q^{68} + 80 q^{70} + 24 q^{72} + 32 q^{73} - 16 q^{74} + 16 q^{75} - 40 q^{76} - 76 q^{78} + 16 q^{80} - 36 q^{82} - 16 q^{83} - 48 q^{86} + 72 q^{88} + 56 q^{90} - 16 q^{91} - 104 q^{92} - 24 q^{94} - 8 q^{96} - 40 q^{98}+O(q^{100}) $ 416 * q - 8 * q^3 - 12 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^16 - 8 * q^18 - 32 * q^19 + 12 * q^20 + 4 * q^22 + 24 * q^24 - 16 * q^25 + 8 * q^26 + 16 * q^27 - 20 * q^28 - 16 * q^30 - 16 * q^33 - 16 * q^35 - 72 * q^36 + 16 * q^38 - 24 * q^40 - 16 * q^41 - 24 * q^42 + 32 * q^46 - 100 * q^48 - 48 * q^50 - 16 * q^51 + 24 * q^52 + 16 * q^54 - 8 * q^56 - 32 * q^57 - 72 * q^58 - 40 * q^60 + 48 * q^62 + 48 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^67 - 116 * q^68 + 80 * q^70 + 24 * q^72 + 32 * q^73 - 16 * q^74 + 16 * q^75 - 40 * q^76 - 76 * q^78 + 16 * q^80 - 36 * q^82 - 16 * q^83 - 48 * q^86 + 72 * q^88 + 56 * q^90 - 16 * q^91 - 104 * q^92 - 24 * q^94 - 8 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40972	+	0.112635i	−0.996823	+	0.0796452i
$2$	−1.40972	+	0.112635i	−0.996823	+	0.0796452i
$3$	−1.15905	−	2.79820i	−0.669180	−	1.61554i	−0.782985	−	0.622041i	$-0.786304\pi$
$3$	−1.15905	−	2.79820i	−0.669180	−	1.61554i	0.113804	−	0.993503i	$-0.463696\pi$
$4$	1.97463	−	0.317569i	0.987313	−	0.158784i
$5$	2.02285	−	0.952933i	0.904646	−	0.426165i
$5$	2.02285	−	0.952933i	0.904646	−	0.426165i
$6$	1.94912	+	3.81414i	0.795725	+	1.55712i
$7$	1.43661	−	3.46829i	0.542988	−	1.31089i	−0.379617	−	0.925144i	$-0.623944\pi$
$7$	1.43661	−	3.46829i	0.542988	−	1.31089i	0.922605	−	0.385746i	$-0.126056\pi$
$8$	−2.74790	+	0.670096i	−0.971530	+	0.236915i
$9$	−4.36522	+	4.36522i	−1.45507	+	1.45507i
$10$	−2.74432	+	1.57121i	−0.867830	+	0.496862i
$11$	−4.85998	+	2.01307i	−1.46534	+	0.606963i	−0.965790	−	0.259324i	$-0.916500\pi$
$11$	−4.85998	+	2.01307i	−1.46534	+	0.606963i	−0.499547	+	0.866287i	$0.666500\pi$
$12$	−3.17732	−	5.15733i	−0.917214	−	1.48879i
$13$	1.26662	+	1.26662i	0.351298	+	0.351298i	0.860593	−	0.509294i	$-0.170093\pi$
$13$	1.26662	+	1.26662i	0.351298	+	0.351298i	−0.509294	+	0.860593i	$0.670093\pi$
$14$	−1.63457	+	5.05113i	−0.436857	+	1.34997i
$15$	−5.01109	−	4.55584i	−1.29386	−	1.17631i
$16$	3.79830	−	1.25416i	0.949575	−	0.313540i
$17$	−2.89300	+	2.93778i	−0.701655	+	0.712517i
$17$	−2.89300	+	2.93778i	−0.701655	+	0.712517i
$18$	5.66207	−	6.64543i	1.33456	−	1.56634i
$19$	−4.99413	−	4.99413i	−1.14573	−	1.14573i	−0.987383	−	0.158350i	$-0.949383\pi$
$19$	−4.99413	−	4.99413i	−1.14573	−	1.14573i	−0.158350	−	0.987383i	$-0.550617\pi$
$20$	3.69175	−	2.52408i	0.825500	−	0.564402i
$21$	−11.3701			−2.48116
$22$	6.62447	−	3.38527i	1.41234	−	0.721742i
$23$	0.396545	−	0.957344i	0.0826853	−	0.199620i	−0.877130	−	0.480254i	$-0.840545\pi$
$23$	0.396545	−	0.957344i	0.0826853	−	0.199620i	0.959815	+	0.280634i	$0.0905446\pi$
$24$	5.06004	+	6.91252i	1.03288	+	1.41101i
$25$	3.18384	−	3.85528i	0.636767	−	0.771056i
$26$	−1.92825	−	1.64292i	−0.378162	−	0.322203i
$27$	8.87971	+	3.67810i	1.70890	+	0.707850i
$28$	1.73535	−	7.30480i	0.327951	−	1.38048i
$29$	0.398139	−	0.961193i	0.0739326	−	0.178489i	−0.882593	−	0.470138i	$-0.844204\pi$
$29$	0.398139	−	0.961193i	0.0739326	−	0.178489i	0.956525	+	0.291649i	$0.0942040\pi$
$30$	7.57739	+	5.85804i	1.38344	+	1.06953i
$31$	−2.45520	+	5.92738i	−0.440967	+	1.06459i	0.534643	+	0.845078i	$0.320446\pi$
$31$	−2.45520	+	5.92738i	−0.440967	+	1.06459i	−0.975610	+	0.219511i	$0.929554\pi$
$32$	−5.21328	+	2.19584i	−0.921587	+	0.388173i
$33$	11.2660	+	11.2660i	1.96115	+	1.96115i
$34$	3.74742	−	4.46731i	0.642677	−	0.766137i
$35$	−0.398998	−	8.38482i	−0.0674430	−	1.41729i
$36$	−7.23343	+	10.0059i	−1.20557	+	1.66766i
$37$	−1.61126	−	3.88993i	−0.264890	−	0.639501i	0.734338	−	0.678784i	$-0.237493\pi$
$37$	−1.61126	−	3.88993i	−0.264890	−	0.639501i	−0.999228	+	0.0392830i	$0.987493\pi$
$38$	7.60285	+	6.47782i	1.23335	+	1.05084i
$39$	2.07619	−	5.01236i	0.332456	−	0.802620i
$40$	−4.92004	+	3.97407i	−0.777926	+	0.628356i
$41$	0.670346	+	1.61836i	0.104690	+	0.252745i	0.967541	−	0.252714i	$-0.0813232\pi$
$41$	0.670346	+	1.61836i	0.104690	+	0.252745i	−0.862851	+	0.505459i	$0.831323\pi$
$42$	16.0287	−	1.28067i	2.47328	−	0.197612i
$43$		−	7.00207i		−	1.06781i	−0.845546	−	0.533903i	$-0.820725\pi$
$43$		−	7.00207i		−	1.06781i	0.845546	−	0.533903i	$-0.179275\pi$
$44$	−8.95735	+	5.51843i	−1.35037	+	0.831935i
$45$	−4.67042	+	12.9900i	−0.696225	+	1.93643i
$46$	−0.451187	+	1.39425i	−0.0665239	+	0.205571i
$47$	−0.832549	+	0.832549i	−0.121440	+	0.121440i	−0.765215	−	0.643775i	$-0.777367\pi$
$47$	−0.832549	+	0.832549i	−0.121440	+	0.121440i	0.643775	+	0.765215i	$0.277367\pi$
$48$	−7.91183	−	9.17478i	−1.14197	−	1.32427i
$49$	−5.01543	−	5.01543i	−0.716490	−	0.716490i
$50$	−4.05408	+	5.79348i	−0.573334	+	0.819322i
$51$	11.5737	+	4.69014i	1.62064	+	0.656752i
$52$	2.90335	+	2.09887i	0.402622	+	0.291061i
$53$		−	11.8658i		−	1.62989i	−0.579536	−	0.814947i	$-0.696766\pi$
$53$		−	11.8658i		−	1.62989i	0.579536	−	0.814947i	$-0.303234\pi$
$54$	−12.9322	−	4.18492i	−1.75985	−	0.569495i
$55$	−7.91268	+	8.70337i	−1.06695	+	1.17356i
$56$	−1.62358	+	10.4932i	−0.216961	+	1.40221i
$57$	−8.18614	+	19.7631i	−1.08428	+	2.61768i
$58$	−0.453001	+	1.39986i	−0.0594819	+	0.183810i
$59$	1.39307	−	1.39307i	0.181363	−	0.181363i	−0.610587	−	0.791949i	$-0.709066\pi$
$59$	1.39307	−	1.39307i	0.181363	−	0.181363i	0.791949	+	0.610587i	$0.209066\pi$
$60$	−11.3418	−	7.40473i	−1.46422	−	0.955946i
$61$	−1.56801	+	0.649493i	−0.200764	+	0.0831590i	−0.480800	−	0.876830i	$-0.659654\pi$
$61$	−1.56801	+	0.649493i	−0.200764	+	0.0831590i	0.280036	+	0.959989i	$0.409654\pi$
$62$	2.79352	−	8.63250i	0.354777	−	1.09633i
$63$	8.86872	+	21.4110i	1.11735	+	2.69753i
$64$	7.10194	−	3.68272i	0.887743	−	0.460340i
$65$	3.76920	+	1.35518i	0.467512	+	0.168090i
$66$	−17.1508	−	14.6129i	−2.11112	−	1.79872i
$67$	−5.98943	+	5.98943i	−0.731725	+	0.731725i	−0.970961	−	0.239236i	$-0.923103\pi$
$67$	−5.98943	+	5.98943i	−0.731725	+	0.731725i	0.239236	+	0.970961i	$0.423103\pi$
$68$	−4.77964	+	6.71975i	−0.579616	+	0.814890i
$69$	−3.13846			−0.377826
$70$	1.50690	+	11.7753i	0.180109	+	1.40742i
$71$	−2.89257	+	6.98328i	−0.343285	+	0.828763i	0.654094	+	0.756413i	$0.273050\pi$
$71$	−2.89257	+	6.98328i	−0.343285	+	0.828763i	−0.997379	+	0.0723502i	$0.976950\pi$
$72$	9.07009	−	14.9203i	1.06892	−	1.75838i
$73$	−12.5839	+	5.21241i	−1.47283	+	0.610067i	−0.967503	−	0.252861i	$-0.918629\pi$
$73$	−12.5839	+	5.21241i	−1.47283	+	0.610067i	−0.505328	+	0.862927i	$0.668629\pi$
$74$	2.70957	+	5.30223i	0.314982	+	0.616372i
$75$	−14.4781	−	4.44055i	−1.67179	−	0.512750i
$76$	−11.4475	−	8.27557i	−1.31312	−	0.949273i
$77$			19.7478i			2.25047i
$78$	−2.36228	+	7.29988i	−0.267475	+	0.826549i
$79$	9.53535	−	3.94967i	1.07281	−	0.444373i	0.224829	−	0.974398i	$-0.427818\pi$
$79$	9.53535	−	3.94967i	1.07281	−	0.444373i	0.847982	+	0.530026i	$0.177818\pi$
$80$	6.48826	−	6.15650i	0.725409	−	0.688318i
$81$		−	10.5903i		−	1.17670i
$82$	−1.12728	−	2.20593i	−0.124488	−	0.243604i
$83$	5.42947			0.595962			0.297981	−	0.954572i	$-0.403687\pi$
$83$	5.42947			0.595962			0.297981	+	0.954572i	$0.403687\pi$
$84$	−22.4517	+	3.61079i	−2.44968	+	0.393969i
$85$	−3.05258	+	8.69953i	−0.331099	+	0.943596i
$86$	0.788680	+	9.87096i	0.0850456	+	1.06441i
$87$	−3.15108			−0.337831
$88$	12.0058	−	8.78837i	1.27982	−	0.936843i
$89$	3.29031			0.348772			0.174386	−	0.984677i	$-0.444206\pi$
$89$	3.29031			0.348772			0.174386	+	0.984677i	$0.444206\pi$
$90$	5.12086	−	18.8383i	0.539786	−	1.98573i
$91$	6.21267	−	2.57337i	0.651265	−	0.269763i
$92$	0.479005	−	2.01633i	0.0499398	−	0.210217i
$93$	19.4317			2.01498
$94$	1.07989	−	1.26744i	0.111382	−	0.130726i
$95$	−14.8615	−	5.34330i	−1.52475	−	0.548211i
$96$	12.1869	+	12.0427i	1.24382	+	1.22911i
$97$	−2.12524	−	5.13078i	−0.215785	−	0.520951i	0.778508	−	0.627635i	$-0.215977\pi$
$97$	−2.12524	−	5.13078i	−0.215785	−	0.520951i	−0.994293	+	0.106683i	$0.965977\pi$
$98$	7.63527	+	6.50544i	0.771278	+	0.657148i
$99$	12.4274	−	30.0024i	1.24900	−	3.01535i
$100$	5.06257	−	8.62383i	0.506257	−	0.862383i
$101$		−	3.48631i		−	0.346900i	−0.984843	−	0.173450i	$-0.944508\pi$
$101$		−	3.48631i		−	0.346900i	0.984843	−	0.173450i	$-0.0554916\pi$
$102$	−16.8439	−	5.30819i	−1.66780	−	0.525589i
$103$	14.2244	−	14.2244i	1.40158	−	1.40158i	0.606466	−	0.795109i	$-0.292587\pi$
$103$	14.2244	−	14.2244i	1.40158	−	1.40158i	0.795109	−	0.606466i	$-0.207413\pi$
$104$	−4.32932	−	2.63180i	−0.424525	−	0.258069i
$105$	−23.0000	+	10.8349i	−2.24457	+	1.05738i
$106$	1.33651	+	16.7275i	0.129813	+	1.62472i
$107$	−2.14137	−	5.16973i	−0.207014	−	0.499777i	0.785936	−	0.618308i	$-0.212182\pi$
$107$	−2.14137	−	5.16973i	−0.207014	−	0.499777i	−0.992950	+	0.118531i	$0.962182\pi$
$108$	18.7022	+	4.44295i	1.79962	+	0.427523i
$109$	2.10806	+	5.08930i	0.201915	+	0.487466i	0.992107	−	0.125393i	$-0.0400192\pi$
$109$	2.10806	+	5.08930i	0.201915	+	0.487466i	−0.790192	+	0.612859i	$0.790019\pi$
$110$	10.1744	−	13.1606i	0.970087	−	1.25481i
$111$	−9.01728	+	9.01728i	−0.855883	+	0.855883i
$112$	1.10690	−	14.9753i	0.104592	−	1.41504i
$113$	8.00236	+	3.31469i	0.752799	+	0.311819i	0.725883	−	0.687818i	$-0.241431\pi$
$113$	8.00236	+	3.31469i	0.752799	+	0.311819i	0.0269157	+	0.999638i	$0.491431\pi$
$114$	9.31415	−	28.7825i	0.872350	−	2.69573i
$115$	−0.110134	−	2.31444i	−0.0102701	−	0.215823i
$116$	0.480931	−	2.02443i	0.0446533	−	0.187964i
$117$	−11.0582			−1.02233
$118$	−1.80693	+	2.12075i	−0.166342	+	0.195231i
$119$	6.03297	+	14.2542i	0.553041	+	1.30668i
$120$	16.8229	+	9.16111i	1.53571	+	0.836291i
$121$	11.7888	−	11.7888i	1.07170	−	1.07170i
$122$	2.13731	−	1.09222i	0.193503	−	0.0988847i
$123$	3.75153	−	3.75153i	0.338264	−	0.338264i
$124$	−2.96576	+	12.4841i	−0.266333	+	1.12110i
$125$	2.76660	−	10.8326i	0.247452	−	0.968900i
$126$	−14.9141	−	29.1846i	−1.32865	−	2.59997i
$127$		−	7.87009i		−	0.698358i	−0.937056	−	0.349179i	$-0.886461\pi$
$127$		−	7.87009i		−	0.698358i	0.937056	−	0.349179i	$-0.113539\pi$
$128$	−9.59695	+	5.99153i	−0.848259	+	0.529582i
$129$	−19.5932	+	8.11578i	−1.72509	+	0.714554i
$130$	−5.46616	−	1.48588i	−0.479414	−	0.130321i
$131$	−2.75617	+	6.65399i	−0.240808	+	0.581362i	−0.997363	−	0.0725676i	$-0.976881\pi$
$131$	−2.75617	+	6.65399i	−0.240808	+	0.581362i	0.756556	+	0.653929i	$0.226881\pi$
$132$	25.8238	+	18.6683i	2.24767	+	1.62487i
$133$	−24.4957	+	10.1465i	−2.12405	+	0.879810i
$134$	7.76880	−	9.11804i	0.671122	−	0.787679i
$135$	21.4673	−	1.02154i	1.84761	−	0.0879199i
$136$	5.98108	−	10.0113i	0.512873	−	0.858465i
$137$	1.94477	−	1.94477i	0.166153	−	0.166153i	−0.619133	−	0.785286i	$-0.712516\pi$
$137$	1.94477	−	1.94477i	0.166153	−	0.166153i	0.785286	+	0.619133i	$0.212516\pi$
$138$	4.42436	−	0.353502i	0.376626	−	0.0300921i
$139$	3.78070	−	9.12743i	0.320675	−	0.774178i	−0.678540	−	0.734564i	$-0.737387\pi$
$139$	3.78070	−	9.12743i	0.320675	−	0.774178i	0.999215	−	0.0396148i	$-0.0126131\pi$
$140$	−3.45063	−	16.4302i	−0.291631	−	1.38860i
$141$	3.29461	+	1.36467i	0.277456	+	0.114926i
$142$	3.29115	−	10.1703i	0.276187	−	0.853471i
$143$	−8.70557	−	3.60596i	−0.727996	−	0.301546i
$144$	−11.1057	+	22.0551i	−0.925479	+	1.83793i
$145$	−0.110577	−	2.32375i	−0.00918294	−	0.192977i
$146$	17.1526	−	8.76543i	1.41956	−	0.725432i
$147$	−8.22104	+	19.8473i	−0.678060	+	1.63698i
$148$	−4.41696	−	7.16947i	−0.363072	−	0.589327i
$149$		−	13.8470i		−	1.13439i	−0.823583	−	0.567195i	$-0.808028\pi$
$149$		−	13.8470i		−	1.13439i	0.823583	−	0.567195i	$-0.191972\pi$
$150$	20.9102	+	4.62919i	1.70731	+	0.377972i
$151$	11.6231	+	11.6231i	0.945876	+	0.945876i	0.998609	−	0.0527323i	$-0.0167930\pi$
$151$	11.6231	+	11.6231i	0.945876	+	0.945876i	−0.0527323	+	0.998609i	$0.516793\pi$
$152$	17.0699	+	10.3768i	1.38456	+	0.841674i
$153$	−0.195509	−	25.4527i	−0.0158060	−	2.05773i
$154$	−2.22430	−	27.8389i	−0.179239	−	2.24332i
$155$	0.681896	+	14.3298i	0.0547712	+	1.15100i
$156$	2.50793	−	10.5569i	0.200795	−	0.845226i
$157$	6.34984	−	6.34984i	0.506773	−	0.506773i	−0.406762	−	0.913534i	$-0.633342\pi$
$157$	6.34984	−	6.34984i	0.506773	−	0.506773i	0.913534	+	0.406762i	$0.133342\pi$
$158$	−12.9973	+	6.64195i	−1.03401	+	0.528405i
$159$	−33.2029	+	13.7531i	−2.63316	+	1.09069i
$160$	−8.45319	+	9.40976i	−0.668284	+	0.743907i
$161$	−2.75066	−	2.75066i	−0.216783	−	0.216783i
$162$	1.19284	+	14.9293i	0.0937183	+	1.17296i
$163$	−3.47244	+	8.38321i	−0.271983	+	0.656624i	−0.999568	−	0.0293932i	$-0.990643\pi$
$163$	−3.47244	+	8.38321i	−0.271983	+	0.656624i	0.727585	+	0.686017i	$0.240643\pi$
$164$	1.83762	+	2.98277i	0.143494	+	0.232915i
$165$	33.5250	+	12.0536i	2.60992	+	0.938373i
$166$	−7.65404	+	0.611550i	−0.594069	+	0.0474655i
$167$	−3.46800	−	8.37250i	−0.268362	−	0.647884i	0.731044	−	0.682330i	$-0.239033\pi$
$167$	−3.46800	−	8.37250i	−0.268362	−	0.647884i	−0.999407	+	0.0344462i	$0.989033\pi$
$168$	31.2439	−	7.61906i	2.41052	−	0.587823i
$169$		−	9.79132i		−	0.753179i
$170$	3.32342	−	12.6077i	0.254894	−	0.966969i
$171$	43.6010			3.33425
$172$	−2.22364	−	13.8265i	−0.169551	−	1.05426i
$173$	−2.97725	+	1.23322i	−0.226356	+	0.0937597i	−0.492979	−	0.870041i	$-0.664092\pi$
$173$	−2.97725	+	1.23322i	−0.226356	+	0.0937597i	0.266623	+	0.963801i	$0.414092\pi$
$174$	4.44214	−	0.354923i	0.336758	−	0.0269066i
$175$	−8.79729	−	16.5810i	−0.665012	−	1.25341i
$176$	−15.9349	+	13.7414i	−1.20114	+	1.03580i
$177$	−5.51275	−	2.28345i	−0.414363	−	0.171635i
$178$	−4.63842	+	0.370605i	−0.347664	+	0.0277780i
$179$	−11.1838	+	11.1838i	−0.835917	+	0.835917i	−0.988319	−	0.152402i	$-0.951299\pi$
$179$	−11.1838	+	11.1838i	−0.835917	+	0.835917i	0.152402	+	0.988319i	$0.451299\pi$
$180$	−5.09714	+	27.1335i	−0.379918	+	2.02241i
$181$	−2.03452	−	4.91177i	−0.151225	−	0.365089i	0.830054	−	0.557684i	$-0.188310\pi$
$181$	−2.03452	−	4.91177i	−0.151225	−	0.365089i	−0.981278	+	0.192595i	$0.938310\pi$
$182$	−8.46828	+	4.32750i	−0.627710	+	0.320776i
$183$	3.63483	+	3.63483i	0.268694	+	0.268694i
$184$	−0.448154	+	2.89641i	−0.0330384	+	0.213526i
$185$	−6.96618	−	6.33332i	−0.512164	−	0.465635i
$186$	−27.3933	+	2.18870i	−2.00858	+	0.160483i
$187$	8.14593	−	20.1014i	0.595690	−	1.46996i
$188$	−1.37958	+	1.90836i	−0.100616	+	0.139182i
$189$	25.5134	−	25.5134i	1.85583	−	1.85583i
$190$	21.5524	+	5.85864i	1.56357	+	0.425031i
$191$	−3.60150			−0.260595			−0.130298	−	0.991475i	$-0.541593\pi$
$191$	−3.60150			−0.260595			−0.130298	+	0.991475i	$0.541593\pi$
$192$	−18.5365	−	15.6042i	−1.33776	−	1.12614i
$193$	−0.728724	−	0.301848i	−0.0524547	−	0.0217275i	0.356302	−	0.934371i	$-0.384037\pi$
$193$	−0.728724	−	0.301848i	−0.0524547	−	0.0217275i	−0.408757	+	0.912643i	$0.634037\pi$
$194$	3.57390	+	6.99359i	0.256591	+	0.502110i
$195$	−0.576631	−	12.1177i	−0.0412934	−	0.867768i
$196$	−11.4963	−	8.31085i	−0.821167	−	0.593632i
$197$	3.36240	−	8.11756i	0.239561	−	0.578352i	−0.757676	−	0.652631i	$-0.773665\pi$
$197$	3.36240	−	8.11756i	0.239561	−	0.578352i	0.997238	+	0.0742786i	$0.0236654\pi$
$198$	−14.1398	+	43.6947i	−1.00487	+	3.10525i
$199$	−5.75966	+	13.9050i	−0.408291	+	0.985703i	0.577296	+	0.816535i	$0.304108\pi$
$199$	−5.75966	+	13.9050i	−0.408291	+	0.985703i	−0.985587	+	0.169168i	$0.945892\pi$
$200$	−6.16547	+	12.7274i	−0.435964	+	0.899964i
$201$	23.7017	+	9.81757i	1.67179	+	0.692478i
$202$	0.392681	+	4.91472i	0.0276290	+	0.345798i
$203$	−2.76172	−	2.76172i	−0.193835	−	0.193835i
$204$	24.3431	+	5.58585i	1.70436	+	0.391088i
$205$	2.89820	+	2.63490i	0.202419	+	0.184029i
$206$	−18.4503	+	21.6547i	−1.28549	+	1.50875i
$207$	2.44801	+	5.91003i	0.170149	+	0.410775i
$208$	6.39957	+	3.22247i	0.443730	+	0.223438i
$209$	34.3249	+	14.2178i	2.37430	+	0.983469i
$210$	31.2032	−	17.8649i	2.15322	−	1.23279i
$211$	2.71295	+	6.54964i	0.186767	+	0.450896i	0.989334	−	0.145667i	$-0.0465327\pi$
$211$	2.71295	+	6.54964i	0.186767	+	0.450896i	−0.802567	+	0.596563i	$0.796533\pi$
$212$	−3.76821	−	23.4305i	−0.258802	−	1.60922i
$213$	22.8933			1.56862
$214$	3.60104	+	7.04669i	0.246162	+	0.481702i
$215$	−6.67250	−	14.1641i	−0.455061	−	0.965985i
$216$	−26.8653	−	4.15679i	−1.82795	−	0.282834i
$217$	17.0307	+	17.0307i	1.15612	+	1.15612i
$218$	−3.54501	−	6.93705i	−0.240098	−	0.469836i
$219$	29.1708	+	29.1708i	1.97118	+	1.97118i
$220$	−12.8607	+	19.6987i	−0.867066	+	1.32809i
$221$	−7.38541	+	0.0567295i	−0.496796	+	0.00381604i
$222$	11.6962	−	13.7275i	0.784997	−	0.921331i
$223$		−	20.2865i		−	1.35848i	−0.733915	−	0.679242i	$-0.762309\pi$
$223$		−	20.2865i		−	1.35848i	0.733915	−	0.679242i	$-0.237691\pi$
$224$	0.126335	+	21.2357i	0.00844114	+	1.41887i
$225$	2.93100	+	30.7273i	0.195400	+	2.04849i
$226$	−11.6544	−	3.77143i	−0.775242	−	0.250872i
$227$	−2.99130	+	7.22164i	−0.198540	+	0.479317i	−0.991524	−	0.129925i	$-0.958526\pi$
$227$	−2.99130	+	7.22164i	−0.198540	+	0.479317i	0.792984	+	0.609242i	$0.208526\pi$
$228$	−9.88843	+	41.6244i	−0.654877	+	2.75664i
$229$	−8.87676	−	8.87676i	−0.586593	−	0.586593i	0.350114	−	0.936707i	$-0.386143\pi$
$229$	−8.87676	−	8.87676i	−0.586593	−	0.586593i	−0.936707	+	0.350114i	$0.886143\pi$
$230$	0.415947	+	3.25031i	0.0274267	+	0.214319i
$231$	55.2584	−	22.8888i	3.63574	−	1.50597i
$232$	−0.449956	+	2.90806i	−0.0295411	+	0.190923i
$233$	−19.2666	+	7.98047i	−1.26219	+	0.522818i	−0.910582	−	0.413328i	$-0.864366\pi$
$233$	−19.2666	+	7.98047i	−1.26219	+	0.522818i	−0.351612	+	0.936146i	$0.614366\pi$
$234$	15.5890	−	1.24554i	1.01908	−	0.0814237i
$235$	−0.890757	+	2.47748i	−0.0581066	+	0.161613i
$236$	2.30840	−	3.19319i	0.150264	−	0.207859i
$237$	−22.1040	−	22.1040i	−1.43581	−	1.43581i
$238$	−10.1103	−	19.4149i	−0.655355	−	1.25848i
$239$	−12.6224			−0.816478			−0.408239	−	0.912875i	$-0.633857\pi$
$239$	−12.6224			−0.816478			−0.408239	+	0.912875i	$0.633857\pi$
$240$	−24.7474	−	11.0198i	−1.59744	−	0.711322i
$241$	−3.45764	−	1.43220i	−0.222726	−	0.0922561i	0.268530	−	0.963271i	$-0.413462\pi$
$241$	−3.45764	−	1.43220i	−0.222726	−	0.0922561i	−0.491256	+	0.871015i	$0.663462\pi$
$242$	−15.2910	+	17.9467i	−0.982944	+	1.15366i
$243$	−2.99465	+	1.24042i	−0.192107	+	0.0795732i
$244$	−2.88998	+	1.78046i	−0.185012	+	0.113982i
$245$	−14.9248	−	5.36608i	−0.953512	−	0.342827i
$246$	−4.86606	+	5.71117i	−0.310248	+	0.364131i
$247$		−	12.6514i		−	0.804989i
$248$	2.77474	−	17.9331i	0.176196	−	1.13875i
$249$	−6.29305	−	15.1928i	−0.398806	−	0.962803i
$250$	−2.67999	+	15.5826i	−0.169498	+	0.985531i
$251$		−	21.9157i		−	1.38331i	−0.722229	−	0.691654i	$-0.756882\pi$
$251$		−	21.9157i		−	1.38331i	0.722229	−	0.691654i	$-0.243118\pi$
$252$	24.3119	+	39.4623i	1.53150	+	2.48589i
$253$			5.45094i			0.342698i
$254$	0.886450	+	11.0946i	0.0556208	+	0.696139i
$255$	27.8812	−	1.54147i	1.74599	−	0.0965308i
$256$	12.8542	−	9.52735i	0.803386	−	0.595459i
$257$		−	13.5043i		−	0.842375i	−0.906974	−	0.421188i	$-0.861613\pi$
$257$		−	13.5043i		−	0.842375i	0.906974	−	0.421188i	$-0.138387\pi$
$258$	26.7069	−	13.6479i	1.66270	−	0.849679i
$259$	−15.8062			−0.982147
$260$	7.87312	+	1.47900i	0.488270	+	0.0917236i
$261$	2.45786	+	5.93379i	0.152137	+	0.367292i
$262$	3.13596	−	9.69071i	0.193740	−	0.598694i
$263$	−29.2007			−1.80059			−0.900296	−	0.435278i	$-0.856650\pi$
$263$	−29.2007			−1.80059			−0.900296	+	0.435278i	$0.856650\pi$
$264$	−38.5070	−	23.4085i	−2.36994	−	1.44069i
$265$	−11.3073	−	24.0027i	−0.694603	−	1.47448i
$266$	33.3893	−	17.0628i	2.04723	−	1.04619i
$267$	−3.81365	−	9.20697i	−0.233392	−	0.563457i
$268$	−9.92483	+	13.7289i	−0.606255	+	0.838628i
$269$	2.57850	+	1.06805i	0.157214	+	0.0651203i	0.459903	−	0.887969i	$-0.347884\pi$
$269$	2.57850	+	1.06805i	0.157214	+	0.0651203i	−0.302689	+	0.953089i	$0.597884\pi$
$270$	−30.1478	+	3.85806i	−1.83474	+	0.234794i
$271$		−	8.19258i		−	0.497664i	−0.968547	−	0.248832i	$-0.919953\pi$
$271$		−	8.19258i		−	0.497664i	0.968547	−	0.248832i	$-0.0800467\pi$
$272$	−7.30402	+	14.7869i	−0.442871	+	0.896585i
$273$	−14.4016	−	14.4016i	−0.871627	−	0.871627i
$274$	−2.52253	+	2.96063i	−0.152391	+	0.178858i
$275$	−7.71243	+	25.1458i	−0.465077	+	1.51635i
$276$	−6.19729	+	0.996677i	−0.373033	+	0.0599929i
$277$	−10.6476	+	4.41038i	−0.639752	+	0.264994i	−0.678890	−	0.734240i	$-0.737539\pi$
$277$	−10.6476	+	4.41038i	−0.639752	+	0.264994i	0.0391383	+	0.999234i	$0.487539\pi$
$278$	−4.30167	+	13.2930i	−0.257997	+	0.797259i
$279$	−15.1568	−	36.5918i	−0.907416	−	2.19070i
$280$	6.71504	+	22.7733i	0.401301	+	1.36097i
$281$	−6.81680	−	6.81680i	−0.406656	−	0.406656i	0.473915	−	0.880571i	$-0.342841\pi$
$281$	−6.81680	−	6.81680i	−0.406656	−	0.406656i	−0.880571	+	0.473915i	$0.842841\pi$
$282$	−4.79819	−	1.55272i	−0.285728	−	0.0924630i
$283$	−5.39479	−	2.23460i	−0.320687	−	0.132833i	0.216532	−	0.976275i	$-0.430525\pi$
$283$	−5.39479	−	2.23460i	−0.320687	−	0.132833i	−0.537219	+	0.843443i	$0.680525\pi$
$284$	−3.49407	+	14.7080i	−0.207335	+	0.872757i
$285$	2.27358	+	47.7786i	0.134675	+	2.83016i
$286$	12.6786	+	4.10285i	0.749700	+	0.242607i
$287$	6.57596			0.388167
$288$	13.1718	−	32.3425i	0.776157	−	1.90580i
$289$	−0.261149	−	16.9980i	−0.0153617	−	0.999882i
$290$	0.417619	+	3.26338i	0.0245234	+	0.191632i
$291$	−11.8937	+	11.8937i	−0.697221	+	0.697221i
$292$	−23.1932	+	14.2888i	−1.35728	+	0.836189i
$293$	−0.436090	−	0.436090i	−0.0254766	−	0.0254766i	0.694254	−	0.719730i	$-0.255735\pi$
$293$	−0.436090	−	0.436090i	−0.0254766	−	0.0254766i	−0.719730	+	0.694254i	$0.755735\pi$
$294$	9.35386	−	28.9052i	0.545528	−	1.68579i
$295$	1.49047	−	4.14548i	0.0867785	−	0.241359i
$296$	7.03422	+	9.60945i	0.408856	+	0.558538i
$297$	−50.5594			−2.93376
$298$	1.55966	+	19.5204i	0.0903487	+	1.13079i
$299$	1.71487	−	0.710322i	0.0991734	−	0.0410790i
$300$	−29.9990	−	4.17063i	−1.73199	−	0.240791i
$301$	−24.2852	−	10.0593i	−1.39978	−	0.579806i
$302$	−17.6945	−	15.0762i	−1.01821	−	0.867537i
$303$	−9.75540	+	4.04082i	−0.560433	+	0.232139i
$304$	−25.2327	−	12.7058i	−1.44719	−	0.728727i
$305$	−2.55293	+	2.80804i	−0.146180	+	0.160788i
$306$	3.14248	+	35.8591i	0.179644	+	2.04993i
$307$	11.0152	−	11.0152i	0.628668	−	0.628668i	−0.319065	−	0.947733i	$-0.603369\pi$
$307$	11.0152	−	11.0152i	0.628668	−	0.628668i	0.947733	+	0.319065i	$0.103369\pi$
$308$	6.27128	+	38.9945i	0.357340	+	2.22192i
$309$	−56.2898	−	23.3160i	−3.20221	−	1.32640i
$310$	−2.57533	−	20.1243i	−0.146269	−	1.14298i
$311$	24.8032	+	10.2738i	1.40646	+	0.582576i	0.951420	−	0.307895i	$-0.0996244\pi$
$311$	24.8032	+	10.2738i	1.40646	+	0.582576i	0.455041	+	0.890470i	$0.349624\pi$
$312$	−2.34640	+	15.1647i	−0.132839	+	0.858534i
$313$	6.93305	−	16.7379i	0.391879	−	0.946080i	−0.597651	−	0.801756i	$-0.703899\pi$
$313$	6.93305	−	16.7379i	0.391879	−	0.946080i	0.989530	−	0.144324i	$-0.0461007\pi$
$314$	−8.23629	+	9.66672i	−0.464801	+	0.545525i
$315$	38.3433	+	34.8599i	2.16040	+	1.96413i
$316$	17.5745	−	10.8273i	0.988640	−	0.609080i
$317$	30.4908	+	12.6297i	1.71253	+	0.709355i	0.999970	+	0.00774841i	$0.00246642\pi$
$317$	30.4908	+	12.6297i	1.71253	+	0.709355i	0.712565	+	0.701607i	$0.247534\pi$
$318$	45.2578	−	23.1279i	2.53793	−	1.29695i
$319$			5.47286i			0.306421i
$320$	10.8568	−	14.2173i	0.606912	−	0.794769i
$321$	−11.9840	+	11.9840i	−0.668882	+	0.668882i
$322$	4.18749	+	3.56785i	0.233360	+	0.198828i
$323$	29.1197	−	0.223677i	1.62026	−	0.0124457i
$324$	−3.36314	−	20.9118i	−0.186841	−	1.16177i
$325$	8.91592	−	0.850467i	0.494566	−	0.0471754i
$326$	3.95093	−	12.2091i	0.218822	−	0.676200i
$327$	11.7975	−	11.7975i	0.652406	−	0.652406i
$328$	−2.92650	−	3.99789i	−0.161589	−	0.220747i
$329$	1.69147	+	4.08357i	0.0932537	+	0.225134i
$330$	−48.6186	−	13.2161i	−2.67637	−	0.727525i
$331$	1.38044	+	1.38044i	0.0758757	+	0.0758757i	0.744026	−	0.668150i	$-0.232914\pi$
$331$	1.38044	+	1.38044i	0.0758757	+	0.0758757i	−0.668150	+	0.744026i	$0.732914\pi$
$332$	10.7212	−	1.72423i	0.588401	−	0.0946294i
$333$	24.0139	+	9.94690i	1.31596	+	0.545087i
$334$	5.83196	+	11.4123i	0.319111	+	0.624452i
$335$	−6.40818	+	17.8232i	−0.350116	+	0.973787i
$336$	−43.1870	+	14.2599i	−2.35605	+	0.777942i
$337$	28.2306	−	11.6935i	1.53782	−	0.636986i	0.556758	−	0.830675i	$-0.312045\pi$
$337$	28.2306	−	11.6935i	1.53782	−	0.636986i	0.981063	+	0.193688i	$0.0620450\pi$
$338$	1.10285	+	13.8030i	0.0599871	+	0.750786i
$339$		−	26.2341i		−	1.42484i
$340$	−3.26501	+	18.1477i	−0.177070	+	0.984198i
$341$		−	33.7494i		−	1.82763i
$342$	−61.4653	+	4.91102i	−3.32366	+	0.265557i
$343$	−0.322149	+	0.133439i	−0.0173944	+	0.00720501i
$344$	4.69206	+	19.2410i	0.252979	+	1.03741i
$345$	−6.34863	+	2.99074i	−0.341799	+	0.161016i
$346$	4.05818	−	2.07383i	0.218169	−	0.111490i
$347$	−15.4328	−	6.39247i	−0.828476	−	0.343166i	−0.0721765	−	0.997392i	$-0.522995\pi$
$347$	−15.4328	−	6.39247i	−0.828476	−	0.343166i	−0.756299	+	0.654226i	$0.772995\pi$
$348$	−6.22221	+	1.00068i	−0.333545	+	0.0536423i
$349$	12.2722	+	12.2722i	0.656916	+	0.656916i	0.954649	−	0.297733i	$-0.0962306\pi$
$349$	12.2722	+	12.2722i	0.656916	+	0.656916i	−0.297733	+	0.954649i	$0.596231\pi$
$350$	14.2693	+	22.3837i	0.762728	+	1.19646i
$351$	6.58849	+	15.9060i	0.351668	+	0.849001i
$352$	20.9161	−	21.1664i	1.11483	−	1.12817i
$353$	−11.9693	+	11.9693i	−0.637061	+	0.637061i	−0.949829	−	0.312769i	$-0.898744\pi$
$353$	−11.9693	+	11.9693i	−0.637061	+	0.637061i	0.312769	+	0.949829i	$0.398744\pi$
$354$	8.02863	+	2.59810i	0.426717	+	0.138088i
$355$	0.803369	+	16.8826i	0.0426384	+	0.896033i
$356$	6.49714	−	1.04490i	0.344348	−	0.0553796i
$357$	32.8936	−	33.4029i	1.74092	−	1.76787i
$358$	14.5064	−	17.0257i	0.766685	−	0.899838i
$359$	12.3921	−	12.3921i	0.654031	−	0.654031i	−0.299930	−	0.953961i	$-0.596963\pi$
$359$	12.3921	−	12.3921i	0.654031	−	0.654031i	0.953961	+	0.299930i	$0.0969633\pi$
$360$	4.12935	−	38.8248i	0.217636	−	2.04624i
$361$			30.8828i			1.62541i
$362$	3.42135	+	6.69507i	0.179822	+	0.351885i
$363$	−46.6511	−	19.3235i	−2.44855	−	1.01422i
$364$	11.4505	−	7.05440i	0.600168	−	0.369751i
$365$	−20.4882	+	22.5355i	−1.07240	+	1.17956i
$366$	−5.53350	−	4.71468i	−0.289241	−	0.246440i
$367$	−7.79153	+	18.8104i	−0.406715	+	0.981896i	0.579281	+	0.815128i	$0.303333\pi$
$367$	−7.79153	+	18.8104i	−0.406715	+	0.981896i	−0.985996	+	0.166769i	$0.946667\pi$
$368$	0.305535	−	4.13361i	0.0159271	−	0.215479i
$369$	−9.99070	−	4.13829i	−0.520095	−	0.215431i
$370$	10.5337	+	8.14357i	0.547623	+	0.423364i
$371$	−41.1540	−	17.0466i	−2.13661	−	0.885013i
$372$	38.3704	−	6.17091i	1.98941	−	0.319947i
$373$	−9.43459	+	9.43459i	−0.488505	+	0.488505i	−0.907834	−	0.419329i	$-0.862265\pi$
$373$	−9.43459	+	9.43459i	−0.488505	+	0.488505i	0.419329	+	0.907834i	$0.362265\pi$
$374$	−9.21937	+	29.2548i	−0.476722	+	1.51273i
$375$	−33.5186	+	4.81411i	−1.73089	+	0.248600i
$376$	1.72988	−	2.84565i	0.0892115	−	0.146753i
$377$	1.72176	−	0.713178i	0.0886753	−	0.0367305i
$378$	−33.0931	+	38.8405i	−1.70212	+	1.99774i
$379$	−16.6634	−	6.90220i	−0.855940	−	0.354542i	−0.0888218	−	0.996048i	$-0.528310\pi$
$379$	−16.6634	−	6.90220i	−0.855940	−	0.354542i	−0.767118	+	0.641505i	$0.778310\pi$
$380$	−31.0427	−	5.83150i	−1.59246	−	0.299149i
$381$	−22.0221	+	9.12187i	−1.12823	+	0.467327i
$382$	5.07710	−	0.405656i	0.259767	−	0.0207551i
$383$	22.7411			1.16201			0.581007	−	0.813898i	$-0.302659\pi$
$383$	22.7411			1.16201			0.581007	+	0.813898i	$0.302659\pi$
$384$	27.8889	+	19.9097i	1.42320	+	1.01601i
$385$	18.8183	+	39.9468i	0.959071	+	2.03588i
$386$	1.06130	+	0.343441i	0.0540186	+	0.0174807i
$387$	30.5656	+	30.5656i	1.55374	+	1.55374i
$388$	−5.82592	−	9.45646i	−0.295766	−	0.480079i
$389$	12.5362	−	12.5362i	0.635613	−	0.635613i	−0.313857	−	0.949470i	$-0.601621\pi$
$389$	12.5362	−	12.5362i	0.635613	−	0.635613i	0.949470	+	0.313857i	$0.101621\pi$
$390$	2.17777	+	17.0177i	0.110276	+	0.861722i
$391$	1.66527	+	3.93456i	0.0842162	+	0.198979i
$392$	17.1427	+	10.4211i	0.865838	+	0.526344i
$393$	21.8138			1.10036
$394$	−3.82572	+	11.8222i	−0.192737	+	0.595595i
$395$	15.5248	−	17.0761i	0.781137	−	0.859194i
$396$	15.0116	−	63.1900i	0.754363	−	3.17542i
$397$	−6.25056	−	2.58906i	−0.313706	−	0.129941i	0.220275	−	0.975438i	$-0.429305\pi$
$397$	−6.25056	−	2.58906i	−0.313706	−	0.129941i	−0.533981	+	0.845496i	$0.679305\pi$
$398$	6.55331	−	20.2510i	0.328488	−	1.01509i
$399$	56.7838	+	56.7838i	2.84275	+	2.84275i
$400$	7.25803	−	18.6365i	0.362902	−	0.931827i
$401$	7.48721	+	18.0757i	0.373893	+	0.902659i	0.993083	+	0.117417i	$0.0374614\pi$
$401$	7.48721	+	18.0757i	0.373893	+	0.902659i	−0.619189	+	0.785242i	$0.712539\pi$
$402$	−34.5186	−	11.1704i	−1.72163	−	0.557128i
$403$	−10.6176	+	4.39795i	−0.528900	+	0.219077i
$404$	−1.10714	−	6.88415i	−0.0550824	−	0.342499i
$405$	−10.0918	−	21.4225i	−0.501467	−	1.06449i
$406$	4.20433	+	3.58219i	0.208657	+	0.177781i
$407$	15.6614	+	15.6614i	0.776306	+	0.776306i
$408$	−34.9461	−	5.13260i	−1.73009	−	0.254101i
$409$		−	14.3152i		−	0.707843i	−0.935275	−	0.353922i	$-0.884848\pi$
$409$		−	14.3152i		−	0.707843i	0.935275	−	0.353922i	$-0.115152\pi$
$410$	−4.38243	−	3.38803i	−0.216433	−	0.167323i
$411$	−7.69594	−	3.18776i	−0.379613	−	0.157241i
$412$	23.5707	−	32.6052i	1.16125	−	1.60634i
$413$	−2.83027	−	6.83288i	−0.139269	−	0.336224i
$414$	−4.11669	−	8.05576i	−0.202324	−	0.395919i
$415$	10.9830	−	5.17392i	0.539134	−	0.253978i
$416$	−9.38457	−	3.82197i	−0.460116	−	0.187387i
$417$	−29.9225			−1.46531
$418$	−49.9900	−	16.1770i	−2.44509	−	0.791243i
$419$	−12.9848	−	31.3482i	−0.634351	−	1.53146i	−0.834101	−	0.551612i	$-0.814013\pi$
$419$	−12.9848	−	31.3482i	−0.634351	−	1.53146i	0.199750	−	0.979847i	$-0.435987\pi$
$420$	−41.9755	+	28.6990i	−2.04820	+	1.40037i
$421$	40.5529			1.97642			0.988212	−	0.153088i	$-0.0489219\pi$
$421$	40.5529			1.97642			0.988212	+	0.153088i	$0.0489219\pi$
$422$	−4.56222	−	8.92759i	−0.222086	−	0.434588i
$423$		−	7.26852i		−	0.353408i
$424$	7.95123	+	32.6061i	0.386146	+	1.58349i
$425$	2.11515	+	20.5067i	0.102600	+	0.994723i
$426$	−32.2732	+	2.57859i	−1.56364	+	0.124933i
$427$			6.37140i			0.308333i
$428$	−5.87016	−	9.52826i	−0.283745	−	0.460566i
$429$			28.5395i			1.37790i
$430$	11.0017	+	19.2159i	0.530551	+	0.926673i
$431$	−7.30907	−	17.6457i	−0.352066	−	0.849962i	−0.996365	−	0.0851882i	$-0.972851\pi$
$431$	−7.30907	−	17.6457i	−0.352066	−	0.849962i	0.644299	−	0.764773i	$-0.277149\pi$
$432$	38.3407	+	2.83394i	1.84467	+	0.136348i
$433$			32.6666i			1.56986i	0.619586	+	0.784929i	$0.287301\pi$
$433$			32.6666i			1.56986i	−0.619586	+	0.784929i	$0.712699\pi$
$434$	−25.9268	−	22.0903i	−1.24453	−	1.06037i
$435$	−6.37416	+	3.00277i	−0.305617	+	0.143972i
$436$	5.77883	+	9.38001i	0.276756	+	0.449221i
$437$	−6.76150	+	2.80071i	−0.323447	+	0.133976i
$438$	−44.4083	−	37.8370i	−2.12191	−	1.80792i
$439$	−19.4207	−	8.04432i	−0.926900	−	0.383935i	−0.132399	−	0.991197i	$-0.542268\pi$
$439$	−19.4207	−	8.04432i	−0.926900	−	0.383935i	−0.794502	+	0.607262i	$0.792268\pi$
$440$	15.9112	−	29.2183i	0.758536	−	1.39293i
$441$	43.7869			2.08509
$442$	10.4050	−	0.911831i	0.494914	−	0.0433714i
$443$	−5.79756	−	5.79756i	−0.275450	−	0.275450i	0.555839	−	0.831290i	$-0.312397\pi$
$443$	−5.79756	−	5.79756i	−0.275450	−	0.275450i	−0.831290	+	0.555839i	$0.812397\pi$
$444$	−14.9422	+	20.6694i	−0.709123	+	0.980925i
$445$	6.65581	−	3.13545i	0.315515	−	0.148634i
$446$	2.28497	+	28.5983i	0.108197	+	1.35417i
$447$	−38.7467	+	16.0494i	−1.83266	+	0.759112i
$448$	−2.56999	−	29.9222i	−0.121421	−	1.41369i
$449$	20.7974	−	8.61456i	0.981490	−	0.406546i	0.166513	−	0.986039i	$-0.446749\pi$
$449$	20.7974	−	8.61456i	0.981490	−	0.406546i	0.814977	+	0.579493i	$0.196749\pi$
$450$	−7.59288	−	42.9868i	−0.357932	−	2.02642i
$451$	−6.51573	−	6.51573i	−0.306814	−	0.306814i
$452$	16.8543	+	4.00397i	0.792760	+	0.188331i
$453$	19.0520	−	45.9957i	0.895143	−	2.16107i
$454$	3.40349	−	10.5174i	0.159734	−	0.493607i
$455$	10.1150	−	11.1258i	0.474200	−	0.521586i
$456$	9.25155	−	59.7925i	0.433244	−	2.80004i
$457$		−	20.5201i		−	0.959888i	−0.877299	−	0.479944i	$-0.840657\pi$
$457$		−	20.5201i		−	0.959888i	0.877299	−	0.479944i	$-0.159343\pi$
$458$	13.5136	+	11.5139i	0.631449	+	0.538010i
$459$	−36.4944	+	15.4459i	−1.70341	+	0.720955i
$460$	−0.952469	−	4.53519i	−0.0444091	−	0.211454i
$461$	−26.5167	−	26.5167i	−1.23500	−	1.23500i	−0.962018	−	0.272987i	$-0.911988\pi$
$461$	−26.5167	−	26.5167i	−1.23500	−	1.23500i	−0.272987	−	0.962018i	$-0.588012\pi$
$462$	−75.3208	+	38.4908i	−3.50424	+	1.79076i
$463$	6.03987	+	6.03987i	0.280697	+	0.280697i	0.833387	−	0.552690i	$-0.186399\pi$
$463$	6.03987	+	6.03987i	0.280697	+	0.280697i	−0.552690	+	0.833387i	$0.686399\pi$
$464$	0.306763	−	4.15023i	0.0142411	−	0.192670i
$465$	39.3075	−	18.5172i	1.82284	−	0.858712i
$466$	26.2616	−	13.4203i	1.21654	−	0.621685i
$467$	−0.0694021			−0.00321155			−0.00160577	−	0.999999i	$-0.500511\pi$
$467$	−0.0694021			−0.00321155			−0.00160577	+	0.999999i	$0.500511\pi$
$468$	−21.8358	+	3.51174i	−1.00936	+	0.162330i
$469$	12.1686	+	29.3776i	0.561893	+	1.35653i
$470$	0.976667	−	3.59289i	0.0450503	−	0.165728i
$471$	−25.1280	−	10.4083i	−1.15784	−	0.479591i
$472$	−2.89454	+	4.76152i	−0.133232	+	0.219167i
$473$	14.0956	+	34.0299i	0.648118	+	1.56470i
$474$	33.6501	+	28.6707i	1.54560	+	1.31689i
$475$	−35.1543	+	3.35328i	−1.61299	+	0.153859i
$476$	16.4396	+	26.2308i	0.753506	+	1.20229i
$477$	51.7969	+	51.7969i	2.37162	+	2.37162i
$478$	17.7941	−	1.42173i	0.813884	−	0.0650285i
$479$	29.3093	+	12.1403i	1.33917	+	0.554704i	0.933258	−	0.359206i	$-0.116953\pi$
$479$	29.3093	+	12.1403i	1.33917	+	0.554704i	0.405916	+	0.913910i	$0.366953\pi$
$480$	36.1281	+	12.7473i	1.64902	+	0.581834i
$481$	2.88622	−	6.96795i	0.131600	−	0.317711i
$482$	5.03562	+	1.62955i	0.229366	+	0.0742240i
$483$	−4.50875	+	10.8851i	−0.205155	+	0.495289i
$484$	19.5346	−	27.0221i	0.887938	−	1.22828i
$485$	−9.18832	−	8.35358i	−0.417220	−	0.379316i
$486$	4.08190	−	2.08595i	0.185159	−	0.0946208i
$487$	−0.110920	−	0.0459446i	−0.00502627	−	0.00208195i	0.380169	−	0.924917i	$-0.375866\pi$
$487$	−0.110920	−	0.0459446i	−0.00502627	−	0.00208195i	−0.385195	+	0.922835i	$0.625866\pi$
$488$	3.87353	−	2.83546i	0.175346	−	0.128355i
$489$	27.4827			1.24281
$490$	21.6442	+	5.88362i	0.977787	+	0.265795i
$491$	−2.80742	+	2.80742i	−0.126697	+	0.126697i	−0.767612	−	0.640915i	$-0.778555\pi$
$491$	−2.80742	+	2.80742i	−0.126697	+	0.126697i	0.640915	+	0.767612i	$0.278555\pi$
$492$	6.21650	−	8.59924i	0.280262	−	0.387684i
$493$	1.67196	+	3.95037i	0.0753014	+	0.177916i
$494$	1.42499	+	17.8349i	0.0641135	+	0.802431i
$495$	−3.45152	−	72.5327i	−0.155135	−	3.26010i
$496$	−1.89171	+	25.5932i	−0.0849404	+	1.14917i
$497$	20.0645	+	20.0645i	0.900018	+	0.900018i
$498$	10.5827	+	20.7088i	0.474222	+	0.927982i
$499$	13.9575	+	33.6965i	0.624826	+	1.50846i	0.845975	+	0.533223i	$0.179019\pi$
$499$	13.9575	+	33.6965i	0.624826	+	1.50846i	−0.221149	+	0.975240i	$0.570981\pi$
$500$	2.02289	−	22.2690i	0.0904663	−	0.995900i
$501$	−19.4084	+	19.4084i	−0.867102	+	0.867102i
$502$	2.46848	+	30.8950i	0.110174	+	1.37891i
$503$	−21.8420	−	9.04727i	−0.973888	−	0.403398i	−0.161730	−	0.986835i	$-0.551707\pi$
$503$	−21.8420	−	9.04727i	−0.973888	−	0.403398i	−0.812158	+	0.583437i	$0.801707\pi$
$504$	−38.7178	−	52.8924i	−1.72463	−	2.35602i
$505$	−3.32222	−	7.05227i	−0.147837	−	0.313822i
$506$	−0.613968	−	7.68431i	−0.0272942	−	0.341609i
$507$	−27.3981	+	11.3487i	−1.21679	+	0.504013i
$508$	−2.49930	−	15.5405i	−0.110888	−	0.689498i
$509$	−6.98751			−0.309716			−0.154858	−	0.987937i	$-0.549492\pi$
$509$	−6.98751			−0.309716			−0.154858	+	0.987937i	$0.549492\pi$
$510$	−39.1310	+	5.31345i	−1.73275	+	0.235284i
$511$			51.1327i			2.26198i
$512$	−17.0477	+	14.8787i	−0.753408	+	0.657553i
$513$	−25.9776	−	62.7154i	−1.14694	−	2.76895i
$514$	1.52106	+	19.0373i	0.0670911	+	0.839699i
$515$	15.2189	−	42.3288i	0.670627	−	1.86523i
$516$	−36.1120	+	22.2478i	−1.58974	+	0.979406i
$517$	2.37019	−	5.72214i	0.104241	−	0.251660i
$518$	22.2823	−	1.78033i	0.979027	−	0.0782233i
$519$	6.90158	+	6.90158i	0.302946	+	0.302946i
$520$	−11.2655	−	1.19818i	−0.494025	−	0.0525438i
$521$	21.7098	−	8.99248i	0.951122	−	0.393968i	0.147470	−	0.989067i	$-0.452887\pi$
$521$	21.7098	−	8.99248i	0.951122	−	0.393968i	0.803652	+	0.595099i	$0.202887\pi$
$522$	−4.13324	−	8.08814i	−0.180907	−	0.354008i
$523$	−24.5138	+	24.5138i	−1.07191	+	1.07191i	−0.0747091	+	0.997205i	$0.523803\pi$
$523$	−24.5138	+	24.5138i	−1.07191	+	1.07191i	−0.997205	+	0.0747091i	$0.976197\pi$
$524$	−3.32931	+	14.0144i	−0.145442	+	0.612223i
$525$	−36.2005	+	43.8349i	−1.57992	+	1.91311i
$526$	41.1648	−	3.28903i	1.79487	−	0.143409i
$527$	−10.3105	−	24.3607i	−0.449131	−	1.06117i
$528$	56.9208	+	28.6622i	2.47716	+	1.24736i
$529$	15.5042	+	15.5042i	0.674095	+	0.674095i
$530$	18.6437	+	32.5635i	0.809831	+	1.41447i
$531$			12.1621i			0.527792i
$532$	−45.1477	+	27.8146i	−1.95740	+	1.20591i
$533$	−1.20078	+	2.89893i	−0.0520114	+	0.125567i
$534$	6.41321	+	12.5497i	0.277527	+	0.543079i
$535$	−9.25809	−	8.41701i	−0.400262	−	0.363899i
$536$	12.4449	−	20.4719i	0.537537	−	0.884250i
$537$	44.2572	+	18.3319i	1.90984	+	0.791082i
$538$	−3.75527	−	1.21522i	−0.161901	−	0.0523920i
$539$	34.4712	+	14.2785i	1.48478	+	0.615017i
$540$	42.0655	−	8.83449i	1.81021	−	0.380176i
$541$	−9.38592	+	22.6596i	−0.403532	+	0.974212i	0.583270	+	0.812279i	$0.301773\pi$
$541$	−9.38592	+	22.6596i	−0.403532	+	0.974212i	−0.986802	+	0.161934i	$0.948227\pi$
$542$	0.922774	+	11.5493i	0.0396365	+	0.496083i
$543$	−11.3860	+	11.3860i	−0.488621	+	0.488621i
$544$	8.63110	−	21.6680i	0.370056	−	0.929010i
$545$	9.11404	+	8.28605i	0.390403	+	0.354935i
$546$	21.9244	+	18.6802i	0.938279	+	0.799437i
$547$	−2.19497	+	0.909187i	−0.0938502	+	0.0388740i	−0.429115	−	0.903250i	$-0.641174\pi$
$547$	−2.19497	+	0.909187i	−0.0938502	+	0.0388740i	0.335264	+	0.942124i	$0.391174\pi$
$548$	3.22259	−	4.45778i	0.137662	−	0.190427i
$549$	4.00955	−	9.67991i	0.171123	−	0.413129i
$550$	8.04006	−	36.3173i	0.342829	−	1.54858i
$551$	−6.78869	+	2.81197i	−0.289208	+	0.119794i
$552$	8.62419	−	2.10307i	0.367070	−	0.0895126i
$553$		−	38.7455i		−	1.64763i
$554$	14.5134	−	7.41670i	0.616614	−	0.315105i
$555$	−9.64773	+	26.8335i	−0.409523	+	1.13902i
$556$	4.56689	−	19.2239i	0.193679	−	0.815275i
$557$	−4.04204	+	4.04204i	−0.171267	+	0.171267i	−0.787536	−	0.616269i	$-0.788643\pi$
$557$	−4.04204	+	4.04204i	−0.171267	+	0.171267i	0.616269	+	0.787536i	$0.288643\pi$
$558$	25.4885	+	49.8771i	1.07901	+	2.11147i
$559$	8.86899	−	8.86899i	0.375118	−	0.375118i
$560$	−12.0314	−	31.3477i	−0.508420	−	1.32468i
$561$	−65.6893	+	0.504579i	−2.77340	+	0.0213033i
$562$	10.3776	+	8.84198i	0.437753	+	0.372976i
$563$	−10.6657			−0.449505			−0.224753	−	0.974416i	$-0.572157\pi$
$563$	−10.6657			−0.449505			−0.224753	+	0.974416i	$0.572157\pi$
$564$	6.93900	+	1.64845i	0.292185	+	0.0694124i
$565$	19.3462	−	0.920605i	0.813902	−	0.0387301i
$566$	7.85684	+	2.54251i	0.330248	+	0.106870i
$567$	−36.7301	−	15.2141i	−1.54252	−	0.638933i
$568$	3.26903	−	21.1277i	0.137166	−	0.886498i
$569$	−0.420694	+	0.420694i	−0.0176364	+	0.0176364i	−0.715870	−	0.698234i	$-0.753970\pi$
$569$	−0.420694	+	0.420694i	−0.0176364	+	0.0176364i	0.698234	+	0.715870i	$0.253970\pi$
$570$	−8.58667	−	67.0984i	−0.359656	−	2.81044i
$571$	7.52381	+	18.1641i	0.314862	+	0.760144i	0.999511	+	0.0312708i	$0.00995544\pi$
$571$	7.52381	+	18.1641i	0.314862	+	0.760144i	−0.684649	+	0.728873i	$0.740045\pi$
$572$	−18.3354	−	4.35582i	−0.766641	−	0.182126i
$573$	4.17433	+	10.0777i	0.174385	+	0.421003i
$574$	−9.27027	+	0.740685i	−0.386934	+	0.0309156i
$575$	−2.42830	−	4.57682i	−0.101267	−	0.190867i
$576$	−14.9257	+	47.0775i	−0.621903	+	1.96156i
$577$	0.00657344	−	0.00657344i	0.000273656	−	0.000273656i	−0.706970	−	0.707244i	$-0.749938\pi$
$577$	0.00657344	−	0.00657344i	0.000273656	−	0.000273656i	0.707244	+	0.706970i	$0.249938\pi$
$578$	2.28272	+	23.9330i	0.0949487	+	0.995482i
$579$			2.38898i			0.0992825i
$580$	−0.956299	−	4.55342i	−0.0397081	−	0.189070i
$581$	7.80005	−	18.8310i	0.323600	−	0.781241i
$582$	15.4271	−	18.1064i	0.639476	−	0.750536i
$583$	23.8867	+	57.6675i	0.989285	+	2.38834i
$584$	31.0865	−	22.7556i	1.28637	−	0.941634i
$585$	−22.3691	+	10.5377i	−0.924847	+	0.435681i
$586$	0.663884	+	0.565646i	0.0274248	+	0.0233666i
$587$	−13.9917			−0.577497			−0.288749	−	0.957405i	$-0.593239\pi$
$587$	−13.9917			−0.577497			−0.288749	+	0.957405i	$0.593239\pi$
$588$	−9.93059	+	41.8018i	−0.409530	+	1.72388i
$589$	41.8638	−	17.3405i	1.72497	−	0.714504i
$590$	−1.63422	+	6.01185i	−0.0672797	+	0.247504i
$591$	−26.6118			−1.09466
$592$	−10.9986	−	12.7543i	−0.452042	−	0.524200i
$593$	−20.0242			−0.822296			−0.411148	−	0.911569i	$-0.634872\pi$
$593$	−20.0242			−0.822296			−0.411148	+	0.911569i	$0.634872\pi$
$594$	71.2747	−	5.69478i	2.92444	−	0.233660i
$595$	25.7871	+	23.0851i	1.05717	+	0.946396i
$596$	−4.39737	−	27.3427i	−0.180123	−	1.12000i
$597$	45.5849			1.86567
$598$	−2.33748	+	1.19451i	−0.0955866	+	0.0488472i
$599$		−	13.2866i		−	0.542876i	−0.962456	−	0.271438i	$-0.912501\pi$
$599$		−	13.2866i		−	0.542876i	0.962456	−	0.271438i	$-0.0874992\pi$
$600$	42.7600	+	2.50047i	1.74567	+	0.102081i
$601$	23.7568	−	9.84041i	0.969062	−	0.401399i	0.158699	−	0.987327i	$-0.449270\pi$
$601$	23.7568	−	9.84041i	0.969062	−	0.401399i	0.810363	+	0.585928i	$0.199270\pi$
$602$	35.3684	+	11.4454i	1.44151	+	0.466479i
$603$		−	52.2904i		−	2.12943i
$604$	26.6425	+	19.2602i	1.08407	+	0.783686i
$605$	12.6130	−	35.0808i	0.512790	−	1.42624i
$606$	13.2973	−	6.79523i	0.540164	−	0.276037i
$607$	−21.7511	+	9.00960i	−0.882850	+	0.365688i	−0.777601	−	0.628757i	$-0.783564\pi$
$607$	−21.7511	+	9.00960i	−0.882850	+	0.365688i	−0.105249	+	0.994446i	$0.533564\pi$
$608$	37.0021	+	15.0695i	1.50063	+	0.611150i
$609$	−4.52688	+	10.9289i	−0.183438	+	0.442860i
$610$	3.28264	−	4.24610i	0.132910	−	0.171920i
$611$	−2.10905			−0.0853232
$612$	−8.46903	−	50.1974i	−0.342340	−	2.02911i
$613$	−9.73054	+	9.73054i	−0.393013	+	0.393013i	−0.875760	−	0.482747i	$-0.839639\pi$
$613$	−9.73054	+	9.73054i	−0.393013	+	0.393013i	0.482747	+	0.875760i	$0.339639\pi$
$614$	−14.2876	+	16.7690i	−0.576601	+	0.676741i
$615$	4.01382	−	11.1637i	0.161853	−	0.450165i
$616$	−13.2329	−	54.2650i	−0.533170	−	2.18640i
$617$	−2.28848	−	5.52489i	−0.0921309	−	0.222424i	0.871096	−	0.491113i	$-0.163410\pi$
$617$	−2.28848	−	5.52489i	−0.0921309	−	0.222424i	−0.963227	+	0.268689i	$0.913410\pi$
$618$	81.9791	+	26.5288i	3.29768	+	1.06715i
$619$	10.2812	−	4.25862i	0.413237	−	0.171168i	−0.166372	−	0.986063i	$-0.553205\pi$
$619$	10.2812	−	4.25862i	0.413237	−	0.171168i	0.579609	+	0.814895i	$0.303205\pi$
$620$	5.89720	+	28.0795i	0.236837	+	1.12770i
$621$	7.04240	−	7.04240i	0.282602	−	0.282602i
$622$	−36.1228	−	11.6895i	−1.44839	−	0.468707i
$623$	4.72690	−	11.4118i	0.189379	−	0.457202i
$624$	1.59969	−	21.6423i	0.0640387	−	0.866386i
$625$	−4.72637	−	24.5492i	−0.189055	−	0.981967i
$626$	−7.88839	+	24.3766i	−0.315284	+	0.974286i
$627$		−	112.527i		−	4.49391i
$628$	10.5221	−	14.5551i	0.419876	−	0.580811i
$629$	16.0892	+	6.52001i	0.641516	+	0.259970i
$630$	−57.9799	−	44.8239i	−2.30997	−	1.78583i
$631$	14.5279	+	14.5279i	0.578348	+	0.578348i	0.934448	−	0.356100i	$-0.115894\pi$
$631$	14.5279	+	14.5279i	0.578348	+	0.578348i	−0.356100	+	0.934448i	$0.615894\pi$
$632$	−23.5555	+	17.2429i	−0.936989	+	0.685886i
$633$	15.1828	−	15.1828i	0.603461	−	0.603461i
$634$	−44.4061	−	14.3700i	−1.76359	−	0.570706i
$635$	−7.49967	−	15.9200i	−0.297615	−	0.631766i
$636$	−61.1959	+	37.7015i	−2.42657	+	1.49496i
$637$		−	12.7053i		−	0.503403i
$638$	−0.616437	−	7.71520i	−0.0244050	−	0.305448i
$639$	−17.8569	−	43.1103i	−0.706407	−	1.70542i
$640$	−13.7037	+	21.2652i	−0.541685	+	0.840582i
$641$	−4.28512	+	10.3452i	−0.169252	+	0.408610i	−0.985633	−	0.168904i	$-0.945977\pi$
$641$	−4.28512	+	10.3452i	−0.169252	+	0.408610i	0.816381	+	0.577514i	$0.195977\pi$
$642$	15.5443	−	18.2439i	0.613484	−	0.720031i
$643$	5.57608	+	13.4618i	0.219899	+	0.530883i	0.994876	−	0.101107i	$-0.0322383\pi$
$643$	5.57608	+	13.4618i	0.219899	+	0.530883i	−0.774976	+	0.631990i	$0.782238\pi$
$644$	−6.30506	−	4.55801i	−0.248454	−	0.179611i
$645$	−31.9003	+	35.0880i	−1.25607	+	1.38159i
$646$	−41.0255	+	3.59523i	−1.61413	+	0.141452i
$647$	−21.6330	−	21.6330i	−0.850479	−	0.850479i	0.139713	−	0.990192i	$-0.455382\pi$
$647$	−21.6330	−	21.6330i	−0.850479	−	0.850479i	−0.990192	+	0.139713i	$0.955382\pi$
$648$	7.09650	+	29.1011i	0.278777	+	1.14320i
$649$	−3.96595	+	9.57465i	−0.155677	+	0.375838i
$650$	−12.4732	+	2.20317i	−0.489238	+	0.0864154i
$651$	27.9159	−	67.3949i	1.09411	−	2.64141i
$652$	−4.19453	+	17.6565i	−0.164270	+	0.691480i
$653$	4.32140	+	1.78998i	0.169109	+	0.0700474i	0.465632	−	0.884978i	$-0.345827\pi$
$653$	4.32140	+	1.78998i	0.169109	+	0.0700474i	−0.296523	+	0.955026i	$0.595827\pi$
$654$	−15.3024	+	17.9601i	−0.598372	+	0.702294i
$655$	0.765487	+	16.0865i	0.0299100	+	0.628550i
$656$	4.57585	+	5.30629i	0.178657	+	0.207176i
$657$	32.1781	−	77.6848i	1.25539	−	3.03077i
$658$	−2.84445	−	5.56617i	−0.110888	−	0.216992i
$659$	−23.2842			−0.907024			−0.453512	−	0.891250i	$-0.649829\pi$
$659$	−23.2842			−0.907024			−0.453512	+	0.891250i	$0.649829\pi$
$660$	70.0273	+	13.1549i	2.72581	+	0.512054i
$661$	1.86790	+	1.86790i	0.0726528	+	0.0726528i	0.742499	−	0.669847i	$-0.233640\pi$
$661$	1.86790	+	1.86790i	0.0726528	+	0.0726528i	−0.669847	+	0.742499i	$0.733640\pi$
$662$	−2.10152	−	1.79055i	−0.0816778	−	0.0695916i
$663$	8.71883	+	20.6001i	0.338611	+	0.800043i
$664$	−14.9197	+	3.63827i	−0.578995	+	0.141192i
$665$	−39.8823	+	43.8676i	−1.54657	+	1.70111i
$666$	−34.9733	−	11.3175i	−1.35519	−	0.438546i
$667$	−0.762312	−	0.762312i	−0.0295168	−	0.0295168i
$668$	−9.50686	−	15.4312i	−0.367831	−	0.597053i
$669$	−56.7657	+	23.5131i	−2.19469	+	0.909071i
$670$	7.02623	−	25.8476i	0.271447	−	0.998579i
$671$	6.31304	−	6.31304i	0.243712	−	0.243712i
$672$	59.2755	−	24.9669i	2.28660	−	0.963118i
$673$	15.5432	−	37.5247i	0.599148	−	1.44647i	−0.275304	−	0.961357i	$-0.588778\pi$
$673$	15.5432	−	37.5247i	0.599148	−	1.44647i	0.874451	−	0.485113i	$-0.161222\pi$
$674$	−38.4802	+	19.6644i	−1.48220	+	0.757443i
$675$	42.4516	−	22.5233i	1.63396	−	0.866922i
$676$	−3.10942	−	19.3342i	−0.119593	−	0.743623i
$677$	−10.0919	−	24.3641i	−0.387865	−	0.936388i	−0.990392	−	0.138290i	$-0.955840\pi$
$677$	−10.0919	−	24.3641i	−0.387865	−	0.936388i	0.602527	−	0.798098i	$-0.294160\pi$
$678$	2.95489	+	36.9828i	0.113482	+	1.42032i
$679$	−20.8482			−0.800079
$680$	2.55868	−	25.9510i	0.0981210	−	0.995174i
$681$	23.6747			0.907217
$682$	3.80138	+	47.5773i	0.145562	+	1.82183i
$683$	16.6719	+	40.2494i	0.637931	+	1.54010i	0.829431	+	0.558609i	$0.188665\pi$
$683$	16.6719	+	40.2494i	0.637931	+	1.54010i	−0.191500	+	0.981493i	$0.561335\pi$
$684$	86.0958	−	13.8463i	3.29195	−	0.529427i
$685$	2.08074	−	5.78720i	0.0795008	−	0.221117i
$686$	0.439111	−	0.224397i	0.0167653	−	0.00856750i
$687$	−14.5503	+	35.1277i	−0.555130	+	1.34020i
$688$	−8.78171	−	26.5960i	−0.334800	−	1.01396i
$689$	15.0295	−	15.0295i	0.572579	−	0.572579i
$690$	8.61294	−	4.93120i	0.327889	−	0.187727i
$691$	14.6675	−	6.07549i	0.557979	−	0.231123i	−0.0858284	−	0.996310i	$-0.527354\pi$
$691$	14.6675	−	6.07549i	0.557979	−	0.231123i	0.643808	+	0.765187i	$0.277354\pi$
$692$	−5.48732	+	3.38062i	−0.208597	+	0.128512i
$693$	−86.2036	−	86.2036i	−3.27460	−	3.27460i
$694$	22.4759	+	7.27332i	0.853175	+	0.276092i
$695$	−1.05004	−	22.0662i	−0.0398301	−	0.837018i
$696$	8.65886	−	2.11153i	0.328213	−	0.0800372i
$697$	−6.69369	−	2.71257i	−0.253542	−	0.102746i
$698$	−18.6827	−	15.9181i	−0.707149	−	0.602509i
$699$	44.6620	+	44.6620i	1.68927	+	1.68927i
$700$	−22.6370	−	29.9476i	−0.855597	−	1.13191i
$701$	21.1933			0.800459			0.400230	−	0.916415i	$-0.368930\pi$
$701$	21.1933			0.800459			0.400230	+	0.916415i	$0.368930\pi$
$702$	−11.0795	−	21.6810i	−0.418169	−	0.818295i
$703$	−11.3800	+	27.4737i	−0.429204	+	1.03619i
$704$	−27.1017	+	32.1946i	−1.02143	+	1.21338i
$705$	7.96494	−	0.379018i	0.299977	−	0.0142746i
$706$	15.5252	−	18.2215i	0.584298	−	0.685776i
$707$	−12.0915	−	5.00847i	−0.454748	−	0.188363i
$708$	−11.6108	−	2.75829i	−0.436360	−	0.103663i
$709$	−14.5027	+	35.0125i	−0.544659	+	1.31492i	0.376745	+	0.926317i	$0.377043\pi$
$709$	−14.5027	+	35.0125i	−0.544659	+	1.31492i	−0.921404	+	0.388607i	$0.872957\pi$
$710$	−3.03410	−	23.7092i	−0.113868	−	0.889790i
$711$	−24.3827	+	58.8651i	−0.914424	+	2.20761i
$712$	−9.04146	+	2.20483i	−0.338843	+	0.0826293i
$713$	4.70095	+	4.70095i	0.176052	+	0.176052i
$714$	−42.6085	+	50.7937i	−1.59458	+	1.90091i
$715$	−21.0463	+	1.00150i	−0.787087	+	0.0374541i
$716$	−18.5322	+	25.6355i	−0.692581	+	0.958043i
$717$	14.6301	+	35.3202i	0.546371	+	1.31906i
$718$	−16.0736	+	18.8652i	−0.599863	+	0.704044i
$719$	15.3247	−	36.9970i	0.571513	−	1.37976i	−0.328753	−	0.944416i	$-0.606628\pi$
$719$	15.3247	−	36.9970i	0.571513	−	1.37976i	0.900266	−	0.435339i	$-0.143372\pi$
$720$	−1.44819	+	55.1972i	−0.0539709	+	2.05708i
$721$	−28.8995	−	69.7695i	−1.07627	−	2.59835i
$722$	−3.47849	−	43.5361i	−0.129456	−	1.62025i
$723$			11.3352i			0.421560i
$724$	−5.57725	−	9.05281i	−0.207277	−	0.336445i
$725$	−2.43806	−	4.59522i	−0.0905472	−	0.170662i
$726$	67.9416	+	21.9862i	2.52155	+	0.815986i
$727$	−0.889602	+	0.889602i	−0.0329935	+	0.0329935i	−0.723411	−	0.690418i	$-0.757427\pi$
$727$	−0.889602	+	0.889602i	−0.0329935	+	0.0329935i	0.690418	+	0.723411i	$0.257427\pi$
$728$	−15.3474	+	11.2345i	−0.568813	+	0.416377i
$729$	−15.5235	−	15.5235i	−0.574943	−	0.574943i
$730$	26.3443	−	34.0765i	0.975048	−	1.26123i
$731$	20.5706	+	20.2570i	0.760830	+	0.749231i
$732$	8.33173	+	6.02312i	0.307950	+	0.222621i
$733$		−	21.5937i		−	0.797580i	−0.917042	−	0.398790i	$-0.869430\pi$
$733$		−	21.5937i		−	0.797580i	0.917042	−	0.398790i	$-0.130570\pi$
$734$	8.86517	−	27.3951i	0.327219	−	1.01117i
$735$	2.28327	+	47.9823i	0.0842198	+	1.76985i
$736$	0.0348721	+	5.86165i	0.00128540	+	0.216063i
$737$	17.0514	−	41.1656i	0.628095	−	1.51635i
$738$	14.5502	+	4.70852i	0.535601	+	0.173323i
$739$	−29.1372	+	29.1372i	−1.07183	+	1.07183i	−0.0746157	+	0.997212i	$0.523773\pi$
$739$	−29.1372	+	29.1372i	−1.07183	+	1.07183i	−0.997212	+	0.0746157i	$0.976227\pi$
$740$	−15.7669	−	10.2937i	−0.579602	−	0.378404i
$741$	−35.4012	+	14.6636i	−1.30049	+	0.538683i
$742$	59.9357	+	19.3955i	2.20031	+	0.712031i
$743$	−5.10828	−	12.3325i	−0.187405	−	0.452435i	0.802054	−	0.597252i	$-0.203741\pi$
$743$	−5.10828	−	12.3325i	−0.187405	−	0.452435i	−0.989458	+	0.144817i	$0.953741\pi$
$744$	−53.3965	+	13.0211i	−1.95761	+	0.477378i
$745$	−13.1953	−	28.0104i	−0.483437	−	1.02622i
$746$	12.2375	−	14.3628i	0.448046	−	0.525860i
$747$	−23.7009	+	23.7009i	−0.867169	+	0.867169i
$748$	9.70161	−	42.2796i	0.354726	−	1.54589i
$749$	−21.0065			−0.767559
$750$	46.7096	−	10.5619i	1.70559	−	0.385667i
$751$	7.98817	−	19.2851i	0.291492	−	0.703725i	−0.708506	−	0.705705i	$-0.750630\pi$
$751$	7.98817	−	19.2851i	0.291492	−	0.703725i	0.999998	+	0.00198023i	$0.000630326\pi$
$752$	−2.11812	+	4.20642i	−0.0772399	+	0.153392i
$753$	−61.3247	+	25.4015i	−2.23479	+	0.925682i
$754$	−2.34688	+	1.19931i	−0.0854682	+	0.0436764i
$755$	34.5879	+	12.4358i	1.25878	+	0.452584i
$756$	42.2772	−	58.4817i	1.53761	−	2.12696i
$757$			28.0814i			1.02064i	0.859986	+	0.510318i	$0.170472\pi$
$757$			28.0814i			1.02064i	−0.859986	+	0.510318i	$0.829528\pi$
$758$	24.2681	+	7.85329i	0.881459	+	0.285244i
$759$	15.2528	−	6.31794i	0.553643	−	0.229327i
$760$	44.4184	+	4.72428i	1.61122	+	0.171368i
$761$			14.3263i			0.519329i	0.965699	+	0.259664i	$0.0836119\pi$
$761$			14.3263i			0.519329i	−0.965699	+	0.259664i	$0.916388\pi$
$762$	30.0176	−	15.3398i	1.08742	−	0.555701i
$763$	20.6796			0.748653
$764$	−7.11161	+	1.14372i	−0.257289	+	0.0413784i
$765$	−24.6502	−	51.3006i	−0.891229	−	1.85478i
$766$	−32.0586	+	2.56145i	−1.15832	+	0.0925489i
$767$	3.52900			0.127425
$768$	−41.5582	−	24.9259i	−1.49960	−	0.899435i
$769$	−41.2329			−1.48690			−0.743448	−	0.668794i	$-0.766811\pi$
$769$	−41.2329			−1.48690			−0.743448	+	0.668794i	$0.766811\pi$
$770$	−31.0280	−	54.1943i	−1.11817	−	1.95303i
$771$	−37.7878	+	15.6522i	−1.36089	+	0.563701i
$772$	−1.53482	−	0.364616i	−0.0552392	−	0.0131228i
$773$	−7.28782			−0.262125			−0.131062	−	0.991374i	$-0.541839\pi$
$773$	−7.28782			−0.262125			−0.131062	+	0.991374i	$0.541839\pi$
$774$	−46.5317	−	39.6462i	−1.67255	−	1.42505i
$775$	15.0348	+	28.3373i	0.540064	+	1.01791i
$776$	9.27806	+	12.6748i	0.333063	+	0.454997i
$777$	18.3202	+	44.2289i	0.657234	+	1.58670i
$778$	−16.2606	+	19.0846i	−0.582970	+	0.684217i
$779$	4.73450	−	11.4301i	0.169631	−	0.409526i
$780$	−4.98684	−	23.7449i	−0.178557	−	0.850202i
$781$		−	39.7615i		−	1.42278i
$782$	−2.79073	−	5.35906i	−0.0997964	−	0.191640i
$783$	7.07072	−	7.07072i	0.252687	−	0.252687i
$784$	−25.3402	−	12.7600i	−0.905009	−	0.455713i
$785$	6.79380	−	18.8957i	0.242481	−	0.674418i
$786$	−30.7514	+	2.45700i	−1.09686	+	0.0876384i
$787$	17.9868	+	43.4239i	0.641159	+	1.54789i	0.825118	+	0.564960i	$0.191109\pi$
$787$	17.9868	+	43.4239i	0.641159	+	1.54789i	−0.183959	+	0.982934i	$0.558891\pi$
$788$	4.06161	−	17.0969i	0.144689	−	0.609053i
$789$	33.8452	+	81.7095i	1.20492	+	2.90894i
$790$	−19.9623	+	25.8212i	−0.710225	+	0.918678i
$791$	22.9926	−	22.9926i	0.817522	−	0.817522i
$792$	−14.0448	+	90.7712i	−0.499060	+	3.22541i
$793$	−2.80875	−	1.16342i	−0.0997416	−	0.0413143i
$794$	9.10316	+	2.94583i	0.323059	+	0.104543i
$795$	−54.0588	+	59.4607i	−1.91727	+	2.10885i
$796$	−6.95737	+	29.2864i	−0.246597	+	1.03803i
$797$	17.8210			0.631251			0.315626	−	0.948884i	$-0.397786\pi$
$797$	17.8210			0.631251			0.315626	+	0.948884i	$0.397786\pi$
$798$	−86.4452	−	73.6534i	−3.06013	−	2.60730i
$799$	−0.0372881	−	4.85441i	−0.00131916	−	0.171737i
$800$	−8.13267	+	27.0898i	−0.287533	+	0.957771i
$801$	−14.3629	+	14.3629i	−0.507490	+	0.507490i
$802$	−12.5908	−	24.6384i	−0.444598	−	0.870012i
$803$	50.6644	−	50.6644i	1.78791	−	1.78791i
$804$	49.9198	+	11.8591i	1.76054	+	0.418239i
$805$	−8.18538	−	2.94298i	−0.288497	−	0.103726i
$806$	14.4725	−	7.39579i	0.509771	−	0.260506i
$807$		−	8.45311i		−	0.297564i
$808$	2.33616	+	9.58003i	0.0821858	+	0.337024i
$809$	21.4485	−	8.88425i	0.754088	−	0.312354i	0.0276799	−	0.999617i	$-0.491188\pi$
$809$	21.4485	−	8.88425i	0.754088	−	0.312354i	0.726408	+	0.687263i	$0.241188\pi$
$810$	16.6396	+	29.0631i	0.584656	+	1.02117i
$811$	−6.79702	+	16.4095i	−0.238676	+	0.576214i	−0.997146	−	0.0754930i	$-0.975947\pi$
$811$	−6.79702	+	16.4095i	−0.238676	+	0.576214i	0.758471	+	0.651707i	$0.225947\pi$
$812$	−6.33041	−	4.57633i	−0.222154	−	0.160598i
$813$	−22.9245	+	9.49565i	−0.803998	+	0.333027i
$814$	−23.8422	−	20.3142i	−0.835669	−	0.712011i
$815$	0.964419	+	20.2670i	0.0337821	+	0.709921i
$816$	49.8424	+	3.29936i	1.74483	+	0.115501i
$817$	−34.9693	+	34.9693i	−1.22342	+	1.22342i
$818$	1.61240	+	20.1805i	0.0563763	+	0.705595i
$819$	−15.8863	+	38.3530i	−0.555114	+	1.34016i
$820$	6.55962	+	4.28257i	0.229072	+	0.149554i
$821$	26.9068	+	11.1452i	0.939054	+	0.388969i	0.799106	−	0.601190i	$-0.205307\pi$
$821$	26.9068	+	11.1452i	0.939054	+	0.388969i	0.139948	+	0.990159i	$0.455307\pi$
$822$	11.2082	+	3.62702i	0.390930	+	0.126507i
$823$	−52.0564	−	21.5625i	−1.81457	−	0.751620i	−0.979490	−	0.201492i	$-0.935421\pi$
$823$	−52.0564	−	21.5625i	−1.81457	−	0.751620i	−0.835080	−	0.550128i	$-0.814579\pi$
$824$	−29.5556	+	48.6191i	−1.02962	+	1.69373i
$825$	79.3024	−	7.56445i	2.76095	−	0.263360i
$826$	4.75952	+	9.31367i	0.165605	+	0.324064i
$827$	0.218127	−	0.526605i	0.00758502	−	0.0183119i	−0.920042	−	0.391821i	$-0.871845\pi$
$827$	0.218127	−	0.526605i	0.00758502	−	0.0183119i	0.927627	+	0.373509i	$0.121845\pi$
$828$	6.71075	+	10.8927i	0.233215	+	0.378547i
$829$			25.0999i			0.871755i	0.900006	+	0.435877i	$0.143562\pi$
$829$			25.0999i			0.871755i	−0.900006	+	0.435877i	$0.856438\pi$
$830$	−14.9002	+	8.53086i	−0.517194	+	0.296111i
$831$	24.6823	+	24.6823i	0.856219	+	0.856219i
$832$	13.6601	+	4.33087i	0.473579	+	0.150146i
$833$	29.2438	−	0.224631i	1.01324	−	0.00778299i
$834$	42.1823	−	3.37033i	1.46065	−	0.116705i
$835$	−14.9937	−	13.6315i	−0.518878	−	0.471739i
$836$	72.2940	+	17.1744i	2.50034	+	0.593989i
$837$	−43.6029	+	43.6029i	−1.50714	+	1.50714i
$838$	21.8359	+	42.7296i	0.754309	+	1.47607i
$839$	25.9409	−	10.7451i	0.895580	−	0.370961i	0.113061	−	0.993588i	$-0.463934\pi$
$839$	25.9409	−	10.7451i	0.895580	−	0.370961i	0.782519	+	0.622627i	$0.213934\pi$
$840$	55.9413	−	45.1856i	1.93016	−	1.55905i
$841$	19.7407	+	19.7407i	0.680714	+	0.680714i
$842$	−57.1682	+	4.56768i	−1.97015	+	0.157413i
$843$	−11.1738	+	26.9759i	−0.384845	+	0.929098i
$844$	7.43703	+	12.0715i	0.255993	+	0.415520i
$845$	−9.33048	−	19.8064i	−0.320978	−	0.681360i
$846$	0.818692	+	10.2466i	0.0281472	+	0.352285i
$847$	−23.9509	−	57.8227i	−0.822964	−	1.98681i
$848$	−14.8816	−	45.0699i	−0.511036	−	1.54771i
$849$			17.6857i			0.606973i
$850$	−5.29156	−	28.6705i	−0.181499	−	0.983391i
$851$	−4.36294			−0.149560
$852$	45.2057	−	7.27020i	1.54872	−	0.249073i
$853$	25.4058	−	10.5234i	0.869877	−	0.360315i	0.0973147	−	0.995254i	$-0.468975\pi$
$853$	25.4058	−	10.5234i	0.869877	−	0.360315i	0.772562	+	0.634939i	$0.218975\pi$
$854$	−0.717644	−	8.98189i	−0.0245573	−	0.307354i
$855$	88.1983	−	41.5489i	3.01632	−	1.42094i
$856$	9.34851	+	12.7710i	0.319525	+	0.436504i
$857$	−26.2406	−	10.8692i	−0.896360	−	0.371285i	−0.113541	−	0.993533i	$-0.536219\pi$
$857$	−26.2406	−	10.8692i	−0.896360	−	0.371285i	−0.782820	+	0.622249i	$0.786219\pi$
$858$	−3.21455	−	40.2327i	−0.109743	−	1.37352i
$859$	10.3431	−	10.3431i	0.352902	−	0.352902i	−0.508286	−	0.861188i	$-0.669721\pi$
$859$	10.3431	−	10.3431i	0.352902	−	0.352902i	0.861188	+	0.508286i	$0.169721\pi$
$860$	−17.6738	−	25.8499i	−0.602671	−	0.881474i
$861$	−7.62190	−	18.4009i	−0.259754	−	0.627101i
$862$	12.2913	+	24.0522i	0.418643	+	0.819221i
$863$	31.5330	+	31.5330i	1.07339	+	1.07339i	0.997084	+	0.0763109i	$0.0243142\pi$
$863$	31.5330	+	31.5330i	1.07339	+	1.07339i	0.0763109	+	0.997084i	$0.475686\pi$
$864$	−54.3689	+	0.323451i	−1.84967	+	0.0110040i
$865$	−4.84735	+	5.33173i	−0.164815	+	0.181284i
$866$	−3.67941	−	46.0508i	−0.125032	−	1.56487i
$867$	−47.2612	+	20.4323i	−1.60507	+	0.693919i
$868$	39.0377	+	28.2209i	1.32503	+	0.957878i
$869$	−38.3906	+	38.3906i	−1.30231	+	1.30231i
$870$	8.64757	−	4.95102i	0.293180	−	0.167855i
$871$	−15.1727			−0.514108
$872$	−9.20305	−	12.5723i	−0.311655	−	0.425752i
$873$	31.6741	+	13.1199i	1.07201	+	0.444040i
$874$	9.21638	−	4.70980i	0.311749	−	0.159311i
$875$	−33.5962	−	25.1577i	−1.13576	−	0.850484i
$876$	66.8651	+	48.3377i	2.25916	+	1.63318i
$877$	−3.13455	+	7.56748i	−0.105846	+	0.255536i	−0.967925	−	0.251238i	$-0.919162\pi$
$877$	−3.13455	+	7.56748i	−0.105846	+	0.255536i	0.862079	+	0.506774i	$0.169162\pi$
$878$	28.2839	+	9.15279i	0.954534	+	0.308892i
$879$	−0.714817	+	1.72572i	−0.0241102	+	0.0582071i
$880$	−19.1393	+	42.9818i	−0.645186	+	1.44891i
$881$	26.3038	+	10.8954i	0.886197	+	0.367075i	0.778897	−	0.627152i	$-0.215779\pi$
$881$	26.3038	+	10.8954i	0.886197	+	0.367075i	0.107300	+	0.994227i	$0.465779\pi$
$882$	−61.7273	+	4.93195i	−2.07847	+	0.166067i
$883$	−11.2923	−	11.2923i	−0.380017	−	0.380017i	0.491091	−	0.871108i	$-0.336598\pi$
$883$	−11.2923	−	11.2923i	−0.380017	−	0.380017i	−0.871108	+	0.491091i	$0.836598\pi$
$884$	−14.5654	+	2.45739i	−0.489888	+	0.0826511i
$885$	−13.3274	+	0.634196i	−0.447997	+	0.0213183i
$886$	8.82595	+	7.51993i	0.296514	+	0.252637i
$887$	0.485926	+	1.17313i	0.0163158	+	0.0393898i	0.931827	−	0.362902i	$-0.118214\pi$
$887$	0.485926	+	1.17313i	0.0163158	+	0.0393898i	−0.915512	+	0.402291i	$0.868214\pi$
$888$	18.7362	−	30.8211i	0.628745	−	1.03429i
$889$	−27.2958	−	11.3063i	−0.915470	−	0.379200i
$890$	−9.02967	+	5.16979i	−0.302675	+	0.173292i
$891$	21.3190	+	51.4685i	0.714212	+	1.72426i
$892$	−6.44235	−	40.0582i	−0.215706	−	1.34125i
$893$	8.31572			0.278275
$894$	52.8144	−	26.9895i	1.76638	−	0.902663i
$895$	−11.9657	+	33.2806i	−0.399970	+	1.11245i
$896$	6.99327	+	41.8925i	0.233629	+	1.39953i
$897$	−3.97525	−	3.97525i	−0.132730	−	0.132730i
$898$	−28.3482	+	14.4867i	−0.945993	+	0.483426i
$899$	4.71984	+	4.71984i	0.157416	+	0.157416i
$900$	15.5457	+	59.7442i	0.518189	+	1.99147i
$901$	34.8592	+	34.3277i	1.16133	+	1.14362i
$902$	9.91926	+	8.45146i	0.330275	+	0.281403i
$903$			79.6142i			2.64939i
$904$	−24.2109	−	3.74609i	−0.805241	−	0.124593i
$905$	−8.79612	−	7.99701i	−0.292393	−	0.265830i
$906$	−21.6773	+	66.9871i	−0.720181	+	2.22550i
$907$	13.5782	−	32.7807i	0.450856	−	1.08846i	−0.521141	−	0.853471i	$-0.674493\pi$
$907$	13.5782	−	32.7807i	0.450856	−	1.08846i	0.971997	−	0.234993i	$-0.0755067\pi$
$908$	−3.61334	+	15.2100i	−0.119913	+	0.504761i
$909$	15.2185	+	15.2185i	0.504766	+	0.504766i
$910$	−13.0062	+	16.8236i	−0.431152	+	0.557696i
$911$	−19.0909	+	7.90772i	−0.632511	+	0.261994i	−0.675819	−	0.737067i	$-0.736210\pi$
$911$	−19.0909	+	7.90772i	−0.632511	+	0.261994i	0.0433088	+	0.999062i	$0.486210\pi$
$912$	−6.30735	+	85.3329i	−0.208857	+	2.82565i
$913$	−26.3871	+	10.9299i	−0.873286	+	0.361727i
$914$	2.31128	+	28.9276i	0.0764505	+	0.956839i
$915$	10.8165	+	3.88896i	0.357581	+	0.128565i
$916$	−20.3473	−	14.7093i	−0.672293	−	0.486009i
$917$	19.1184	+	19.1184i	0.631346	+	0.631346i
$918$	49.7072	−	25.8850i	1.64058	−	0.854333i
$919$	36.8715			1.21628			0.608139	−	0.793830i	$-0.291916\pi$
$919$	36.8715			1.21628			0.608139	+	0.793830i	$0.291916\pi$
$920$	1.85354	+	6.28606i	0.0611093	+	0.207245i
$921$	−43.5898	−	18.0555i	−1.43633	−	0.594949i
$922$	40.3678	+	34.3944i	1.32944	+	1.13272i
$923$	−12.5090	+	5.18140i	−0.411739	+	0.170548i
$924$	101.846	−	62.7451i	3.35049	−	2.06416i
$925$	−20.1268	−	6.17304i	−0.661764	−	0.202968i
$926$	−9.19484	−	7.83423i	−0.302161	−	0.257449i
$927$			124.186i			4.07879i
$928$	0.0350123	+	5.88522i	0.00114933	+	0.193192i
$929$	−8.29999	−	20.0379i	−0.272314	−	0.657424i	0.727268	−	0.686354i	$-0.240790\pi$
$929$	−8.29999	−	20.0379i	−0.272314	−	0.657424i	−0.999581	+	0.0289302i	$0.990790\pi$
$930$	−53.3269	+	30.5314i	−1.74866	+	1.00116i
$931$			50.0954i			1.64181i
$932$	−35.5099	+	21.8769i	−1.16317	+	0.716602i
$933$		−	81.3124i		−	2.66205i
$934$	0.0978376	−	0.00781713i	0.00320134	−	0.000255784i
$935$	−2.67726	−	48.4245i	−0.0875558	−	1.58365i
$936$	30.3869	−	7.41005i	0.993226	−	0.242205i
$937$			45.4590i			1.48508i	0.669801	+	0.742540i	$0.266379\pi$
$937$			45.4590i			1.48508i	−0.669801	+	0.742540i	$0.733621\pi$
$938$	−20.4633	−	40.0435i	−0.668149	−	1.30747i
$939$	−54.8718			−1.79067
$940$	−0.972141	+	5.17498i	−0.0317077	+	0.168789i
$941$	19.0036	+	45.8788i	0.619501	+	1.49561i	0.852285	+	0.523078i	$0.175216\pi$
$941$	19.0036	+	45.8788i	0.619501	+	1.49561i	−0.232784	+	0.972528i	$0.574784\pi$
$942$	36.5958	+	11.8426i	1.19235	+	0.385852i
$943$	1.81515			0.0591093
$944$	3.54417	−	7.03844i	0.115353	−	0.229082i
$945$	27.2972	−	75.9223i	0.887977	−	2.46975i
$946$	−23.7039	−	46.3850i	−0.770680	−	1.50811i
$947$	19.9194	+	48.0897i	0.647293	+	1.56270i	0.816640	+	0.577147i	$0.195834\pi$
$947$	19.9194	+	48.0897i	0.647293	+	1.56270i	−0.169347	+	0.985556i	$0.554166\pi$
$948$	−50.6666	−	36.6276i	−1.64558	−	1.18961i
$949$	−22.5412	−	9.33688i	−0.731719	−	0.303088i
$950$	49.1801	−	8.68681i	1.59561	−	0.281837i
$951$		−	99.9581i		−	3.24136i
$952$	−26.1297	−	35.1265i	−0.846868	−	1.13846i
$953$	0.285501	+	0.285501i	0.00924829	+	0.00924829i	0.711716	−	0.702468i	$-0.247918\pi$
$953$	0.285501	+	0.285501i	0.00924829	+	0.00924829i	−0.702468	+	0.711716i	$0.747918\pi$
$954$	−78.8533	−	67.1850i	−2.55297	−	2.17519i
$955$	−7.28528	+	3.43199i	−0.235746	+	0.111056i
$956$	−24.9246	+	4.00849i	−0.806120	+	0.129644i
$957$	15.3142	−	6.34334i	0.495037	−	0.205051i
$958$	−42.6853	−	13.8132i	−1.37910	−	0.446283i
$959$	−3.95113	−	9.53888i	−0.127589	−	0.308027i
$960$	−52.3664	−	13.9009i	−1.69012	−	0.448650i
$961$	−7.18552	−	7.18552i	−0.231791	−	0.231791i
$962$	−3.28392	+	10.1479i	−0.105878	+	0.327183i
$963$	31.9146	+	13.2195i	1.02843	+	0.425992i
$964$	−7.28236	−	1.73002i	−0.234549	−	0.0557203i
$965$	−1.76174	+	0.0838337i	−0.0567124	+	0.00269870i
$966$	5.13004	−	15.8528i	0.165056	−	0.510055i
$967$	−15.4148			−0.495707			−0.247853	−	0.968798i	$-0.579725\pi$
$967$	−15.4148			−0.495707			−0.247853	+	0.968798i	$0.579725\pi$
$968$	−24.4948	+	40.2939i	−0.787291	+	1.29510i
$969$	−34.3772	−	81.2236i	−1.10436	−	2.60928i
$970$	13.8939	+	10.7413i	0.446106	+	0.344882i
$971$	12.0093	−	12.0093i	0.385398	−	0.385398i	−0.487645	−	0.873042i	$-0.662144\pi$
$971$	12.0093	−	12.0093i	0.385398	−	0.385398i	0.873042	+	0.487645i	$0.162144\pi$
$972$	−5.51939	+	3.40038i	−0.177035	+	0.109067i
$973$	−26.2252	−	26.2252i	−0.840740	−	0.840740i
$974$	0.161541	+	0.0522756i	0.00517612	+	0.00167502i
$975$	−12.7138	−	23.9628i	−0.407168	−	0.767425i
$976$	−5.14122	+	4.43351i	−0.164566	+	0.141913i
$977$	49.8024			1.59332			0.796660	−	0.604428i	$-0.206598\pi$
$977$	49.8024			1.59332			0.796660	+	0.604428i	$0.206598\pi$
$978$	−38.7429	+	3.09552i	−1.23886	+	0.0989839i
$979$	−15.9908	+	6.62362i	−0.511069	+	0.211692i
$980$	−31.1750	−	5.85636i	−0.995850	−	0.187074i
$981$	−31.4181	−	13.0138i	−1.00310	−	0.415498i
$982$	3.64147	−	4.27390i	0.116204	−	0.136386i
$983$	46.3678	−	19.2062i	1.47890	−	0.612581i	0.510033	−	0.860155i	$-0.329633\pi$
$983$	46.3678	−	19.2062i	1.47890	−	0.612581i	0.968869	+	0.247573i	$0.0796332\pi$
$984$	−7.79496	+	12.8227i	−0.248494	+	0.408774i
$985$	−0.933858	−	19.6247i	−0.0297552	−	0.625296i
$986$	−2.80195	−	5.38060i	−0.0892323	−	0.171353i
$987$	9.46616	−	9.46616i	0.301311	−	0.301311i
$988$	−4.01769	−	24.9818i	−0.127820	−	0.794776i
$989$	−6.70339	−	2.77663i	−0.213155	−	0.0882918i
$990$	13.0354	+	101.862i	0.414293	+	3.23739i
$991$	−19.1645	−	7.93820i	−0.608780	−	0.252165i	0.0569265	−	0.998378i	$-0.481870\pi$
$991$	−19.1645	−	7.93820i	−0.608780	−	0.252165i	−0.665707	+	0.746213i	$0.731870\pi$
$992$	−0.215910	−	36.2923i	−0.00685515	−	1.15228i
$993$	2.26275	−	5.46275i	0.0718061	−	0.173355i
$994$	−30.5454	−	26.0254i	−0.968841	−	0.825476i
$995$	1.59966	+	33.6164i	0.0507126	+	1.06571i
$996$	−17.2512	−	28.0016i	−0.546625	−	0.887264i
$997$	15.2641	+	6.32261i	0.483420	+	0.200239i	0.611065	−	0.791581i	$-0.290742\pi$
$997$	15.2641	+	6.32261i	0.483420	+	0.200239i	−0.127644	+	0.991820i	$0.540742\pi$
$998$	−23.4717	−	45.9306i	−0.742983	−	1.45391i
$999$		−	40.4678i		−	1.28035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bw.a.43.4	✓	416
5.2	odd	4		680.2.bz.a.587.49	yes	416
8.3	odd	2	inner	680.2.bw.a.43.101	yes	416
17.2	even	8		680.2.bz.a.563.49	yes	416
40.27	even	4		680.2.bz.a.587.50	yes	416
85.2	odd	8	inner	680.2.bw.a.427.101	yes	416
136.19	odd	8		680.2.bz.a.563.50	yes	416
680.427	even	8	inner	680.2.bw.a.427.4	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bw.a.43.4	✓	416	1.1	even	1	trivial
680.2.bw.a.43.101	yes	416	8.3	odd	2	inner
680.2.bw.a.427.4	yes	416	680.427	even	8	inner
680.2.bw.a.427.101	yes	416	85.2	odd	8	inner
680.2.bz.a.563.49	yes	416	17.2	even	8
680.2.bz.a.563.50	yes	416	136.19	odd	8
680.2.bz.a.587.49	yes	416	5.2	odd	4
680.2.bz.a.587.50	yes	416	40.27	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bw (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40972 + 0.112635i) q^{2} +(-1.15905 - 2.79820i) q^{3} +(1.97463 - 0.317569i) q^{4} +(2.02285 - 0.952933i) q^{5} +(1.94912 + 3.81414i) q^{6} +(1.43661 - 3.46829i) q^{7} +(-2.74790 + 0.670096i) q^{8} +(-4.36522 + 4.36522i) q^{9} +O(q^{10})\)	\(q+(-1.40972 + 0.112635i) q^{2} +(-1.15905 - 2.79820i) q^{3} +(1.97463 - 0.317569i) q^{4} +(2.02285 - 0.952933i) q^{5} +(1.94912 + 3.81414i) q^{6} +(1.43661 - 3.46829i) q^{7} +(-2.74790 + 0.670096i) q^{8} +(-4.36522 + 4.36522i) q^{9} +(-2.74432 + 1.57121i) q^{10} +(-4.85998 + 2.01307i) q^{11} +(-3.17732 - 5.15733i) q^{12} +(1.26662 + 1.26662i) q^{13} +(-1.63457 + 5.05113i) q^{14} +(-5.01109 - 4.55584i) q^{15} +(3.79830 - 1.25416i) q^{16} +(-2.89300 + 2.93778i) q^{17} +(5.66207 - 6.64543i) q^{18} +(-4.99413 - 4.99413i) q^{19} +(3.69175 - 2.52408i) q^{20} -11.3701 q^{21} +(6.62447 - 3.38527i) q^{22} +(0.396545 - 0.957344i) q^{23} +(5.06004 + 6.91252i) q^{24} +(3.18384 - 3.85528i) q^{25} +(-1.92825 - 1.64292i) q^{26} +(8.87971 + 3.67810i) q^{27} +(1.73535 - 7.30480i) q^{28} +(0.398139 - 0.961193i) q^{29} +(7.57739 + 5.85804i) q^{30} +(-2.45520 + 5.92738i) q^{31} +(-5.21328 + 2.19584i) q^{32} +(11.2660 + 11.2660i) q^{33} +(3.74742 - 4.46731i) q^{34} +(-0.398998 - 8.38482i) q^{35} +(-7.23343 + 10.0059i) q^{36} +(-1.61126 - 3.88993i) q^{37} +(7.60285 + 6.47782i) q^{38} +(2.07619 - 5.01236i) q^{39} +(-4.92004 + 3.97407i) q^{40} +(0.670346 + 1.61836i) q^{41} +(16.0287 - 1.28067i) q^{42} -7.00207i q^{43} +(-8.95735 + 5.51843i) q^{44} +(-4.67042 + 12.9900i) q^{45} +(-0.451187 + 1.39425i) q^{46} +(-0.832549 + 0.832549i) q^{47} +(-7.91183 - 9.17478i) q^{48} +(-5.01543 - 5.01543i) q^{49} +(-4.05408 + 5.79348i) q^{50} +(11.5737 + 4.69014i) q^{51} +(2.90335 + 2.09887i) q^{52} -11.8658i q^{53} +(-12.9322 - 4.18492i) q^{54} +(-7.91268 + 8.70337i) q^{55} +(-1.62358 + 10.4932i) q^{56} +(-8.18614 + 19.7631i) q^{57} +(-0.453001 + 1.39986i) q^{58} +(1.39307 - 1.39307i) q^{59} +(-11.3418 - 7.40473i) q^{60} +(-1.56801 + 0.649493i) q^{61} +(2.79352 - 8.63250i) q^{62} +(8.86872 + 21.4110i) q^{63} +(7.10194 - 3.68272i) q^{64} +(3.76920 + 1.35518i) q^{65} +(-17.1508 - 14.6129i) q^{66} +(-5.98943 + 5.98943i) q^{67} +(-4.77964 + 6.71975i) q^{68} -3.13846 q^{69} +(1.50690 + 11.7753i) q^{70} +(-2.89257 + 6.98328i) q^{71} +(9.07009 - 14.9203i) q^{72} +(-12.5839 + 5.21241i) q^{73} +(2.70957 + 5.30223i) q^{74} +(-14.4781 - 4.44055i) q^{75} +(-11.4475 - 8.27557i) q^{76} +19.7478i q^{77} +(-2.36228 + 7.29988i) q^{78} +(9.53535 - 3.94967i) q^{79} +(6.48826 - 6.15650i) q^{80} -10.5903i q^{81} +(-1.12728 - 2.20593i) q^{82} +5.42947 q^{83} +(-22.4517 + 3.61079i) q^{84} +(-3.05258 + 8.69953i) q^{85} +(0.788680 + 9.87096i) q^{86} -3.15108 q^{87} +(12.0058 - 8.78837i) q^{88} +3.29031 q^{89} +(5.12086 - 18.8383i) q^{90} +(6.21267 - 2.57337i) q^{91} +(0.479005 - 2.01633i) q^{92} +19.4317 q^{93} +(1.07989 - 1.26744i) q^{94} +(-14.8615 - 5.34330i) q^{95} +(12.1869 + 12.0427i) q^{96} +(-2.12524 - 5.13078i) q^{97} +(7.63527 + 6.50544i) q^{98} +(12.4274 - 30.0024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 8 q^{3}+O(q^{10}) \) 416 * q - 8 * q^3	\( 416 q - 8 q^{3} - 12 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{14} - 16 q^{16} - 8 q^{18} - 32 q^{19} + 12 q^{20} + 4 q^{22} + 24 q^{24} - 16 q^{25} + 8 q^{26} + 16 q^{27} - 20 q^{28} - 16 q^{30} - 16 q^{33} - 16 q^{35} - 72 q^{36} + 16 q^{38} - 24 q^{40} - 16 q^{41} - 24 q^{42} + 32 q^{46} - 100 q^{48} - 48 q^{50} - 16 q^{51} + 24 q^{52} + 16 q^{54} - 8 q^{56} - 32 q^{57} - 72 q^{58} - 40 q^{60} + 48 q^{62} + 48 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{67} - 116 q^{68} + 80 q^{70} + 24 q^{72} + 32 q^{73} - 16 q^{74} + 16 q^{75} - 40 q^{76} - 76 q^{78} + 16 q^{80} - 36 q^{82} - 16 q^{83} - 48 q^{86} + 72 q^{88} + 56 q^{90} - 16 q^{91} - 104 q^{92} - 24 q^{94} - 8 q^{96} - 40 q^{98}+O(q^{100}) \) 416 * q - 8 * q^3 - 12 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^16 - 8 * q^18 - 32 * q^19 + 12 * q^20 + 4 * q^22 + 24 * q^24 - 16 * q^25 + 8 * q^26 + 16 * q^27 - 20 * q^28 - 16 * q^30 - 16 * q^33 - 16 * q^35 - 72 * q^36 + 16 * q^38 - 24 * q^40 - 16 * q^41 - 24 * q^42 + 32 * q^46 - 100 * q^48 - 48 * q^50 - 16 * q^51 + 24 * q^52 + 16 * q^54 - 8 * q^56 - 32 * q^57 - 72 * q^58 - 40 * q^60 + 48 * q^62 + 48 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^67 - 116 * q^68 + 80 * q^70 + 24 * q^72 + 32 * q^73 - 16 * q^74 + 16 * q^75 - 40 * q^76 - 76 * q^78 + 16 * q^80 - 36 * q^82 - 16 * q^83 - 48 * q^86 + 72 * q^88 + 56 * q^90 - 16 * q^91 - 104 * q^92 - 24 * q^94 - 8 * q^96 - 40 * q^98

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