LMFDB - Embedded newform 680.2.bw.a.427.4

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			427.4
Character	$\chi$	$=$	680.427
Dual form			680.2.bw.a.43.4

$q$-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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$

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	0.113804	+	0.993503i	$0.463696\pi$
$3$	−1.15905	+	2.79820i	−0.669180	+	1.61554i	−0.782985	+	0.622041i	$0.786304\pi$
$4$	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	0.922605	+	0.385746i	$0.126056\pi$
$7$	1.43661	+	3.46829i	0.542988	+	1.31089i	−0.379617	+	0.925144i	$0.623944\pi$
$8$	−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	−0.499547	−	0.866287i	$-0.666500\pi$
$11$	−4.85998	−	2.01307i	−1.46534	−	0.606963i	−0.965790	+	0.259324i	$0.916500\pi$
$12$	−3.17732	+	5.15733i	−0.917214	+	1.48879i
$13$	1.26662	−	1.26662i	0.351298	−	0.351298i	−0.509294	−	0.860593i	$-0.670093\pi$
$13$	1.26662	−	1.26662i	0.351298	−	0.351298i	0.860593	+	0.509294i	$0.170093\pi$
$14$	−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	−0.158350	+	0.987383i	$0.550617\pi$
$19$	−4.99413	+	4.99413i	−1.14573	+	1.14573i	−0.987383	+	0.158350i	$0.949383\pi$
$20$	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	0.959815	−	0.280634i	$-0.0905446\pi$
$23$	0.396545	+	0.957344i	0.0826853	+	0.199620i	−0.877130	+	0.480254i	$0.840545\pi$
$24$	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	0.956525	−	0.291649i	$-0.0942040\pi$
$29$	0.398139	+	0.961193i	0.0739326	+	0.178489i	−0.882593	+	0.470138i	$0.844204\pi$
$30$	7.57739	−	5.85804i	1.38344	−	1.06953i
$31$	−2.45520	−	5.92738i	−0.440967	−	1.06459i	−0.975610	−	0.219511i	$-0.929554\pi$
$31$	−2.45520	−	5.92738i	−0.440967	−	1.06459i	0.534643	−	0.845078i	$-0.320446\pi$
$32$	−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	−0.999228	−	0.0392830i	$-0.987493\pi$
$37$	−1.61126	+	3.88993i	−0.264890	+	0.639501i	0.734338	+	0.678784i	$0.237493\pi$
$38$	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	−0.862851	−	0.505459i	$-0.831323\pi$
$41$	0.670346	−	1.61836i	0.104690	−	0.252745i	0.967541	+	0.252714i	$0.0813232\pi$
$42$	16.0287	+	1.28067i	2.47328	+	0.197612i
$43$			7.00207i			1.06781i	0.845546	+	0.533903i	$0.179275\pi$
$43$			7.00207i			1.06781i	−0.845546	+	0.533903i	$0.820725\pi$
$44$	−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	0.643775	−	0.765215i	$-0.277367\pi$
$47$	−0.832549	−	0.832549i	−0.121440	−	0.121440i	−0.765215	+	0.643775i	$0.777367\pi$
$48$	−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	$0.303234\pi$
$53$			11.8658i			1.62989i	−0.579536	+	0.814947i	$0.696766\pi$
$54$	−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	0.791949	−	0.610587i	$-0.209066\pi$
$59$	1.39307	+	1.39307i	0.181363	+	0.181363i	−0.610587	+	0.791949i	$0.709066\pi$
$60$	−11.3418	+	7.40473i	−1.46422	+	0.955946i
$61$	−1.56801	−	0.649493i	−0.200764	−	0.0831590i	0.280036	−	0.959989i	$-0.409654\pi$
$61$	−1.56801	−	0.649493i	−0.200764	−	0.0831590i	−0.480800	+	0.876830i	$0.659654\pi$
$62$	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	0.239236	−	0.970961i	$-0.423103\pi$
$67$	−5.98943	−	5.98943i	−0.731725	−	0.731725i	−0.970961	+	0.239236i	$0.923103\pi$
$68$	−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	−0.997379	−	0.0723502i	$-0.976950\pi$
$71$	−2.89257	−	6.98328i	−0.343285	−	0.828763i	0.654094	−	0.756413i	$-0.273050\pi$
$72$	9.07009	+	14.9203i	1.06892	+	1.75838i
$73$	−12.5839	−	5.21241i	−1.47283	−	0.610067i	−0.505328	−	0.862927i	$-0.668629\pi$
$73$	−12.5839	−	5.21241i	−1.47283	−	0.610067i	−0.967503	+	0.252861i	$0.918629\pi$
$74$	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	0.847982	−	0.530026i	$-0.177818\pi$
$79$	9.53535	+	3.94967i	1.07281	+	0.444373i	0.224829	+	0.974398i	$0.427818\pi$
$80$	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	−0.994293	−	0.106683i	$-0.965977\pi$
$97$	−2.12524	+	5.13078i	−0.215785	+	0.520951i	0.778508	+	0.627635i	$0.215977\pi$
$98$	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	$0.0554916\pi$
$101$			3.48631i			0.346900i	−0.984843	+	0.173450i	$0.944508\pi$
$102$	−16.8439	+	5.30819i	−1.66780	+	0.525589i
$103$	14.2244	+	14.2244i	1.40158	+	1.40158i	0.795109	+	0.606466i	$0.207413\pi$
$103$	14.2244	+	14.2244i	1.40158	+	1.40158i	0.606466	+	0.795109i	$0.292587\pi$
$104$	−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	−0.992950	−	0.118531i	$-0.962182\pi$
$107$	−2.14137	+	5.16973i	−0.207014	+	0.499777i	0.785936	+	0.618308i	$0.212182\pi$
$108$	18.7022	−	4.44295i	1.79962	−	0.427523i
$109$	2.10806	−	5.08930i	0.201915	−	0.487466i	−0.790192	−	0.612859i	$-0.790019\pi$
$109$	2.10806	−	5.08930i	0.201915	−	0.487466i	0.992107	+	0.125393i	$0.0400192\pi$
$110$	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	0.0269157	−	0.999638i	$-0.491431\pi$
$113$	8.00236	−	3.31469i	0.752799	−	0.311819i	0.725883	+	0.687818i	$0.241431\pi$
$114$	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	$0.113539\pi$
$127$			7.87009i			0.698358i	−0.937056	+	0.349179i	$0.886461\pi$
$128$	−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	0.756556	−	0.653929i	$-0.226881\pi$
$131$	−2.75617	−	6.65399i	−0.240808	−	0.581362i	−0.997363	+	0.0725676i	$0.976881\pi$
$132$	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	0.785286	−	0.619133i	$-0.212516\pi$
$137$	1.94477	+	1.94477i	0.166153	+	0.166153i	−0.619133	+	0.785286i	$0.712516\pi$
$138$	4.42436	+	0.353502i	0.376626	+	0.0300921i
$139$	3.78070	+	9.12743i	0.320675	+	0.774178i	0.999215	+	0.0396148i	$0.0126131\pi$
$139$	3.78070	+	9.12743i	0.320675	+	0.774178i	−0.678540	+	0.734564i	$0.737387\pi$
$140$	−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	$0.191972\pi$
$149$			13.8470i			1.13439i	−0.823583	+	0.567195i	$0.808028\pi$
$150$	20.9102	−	4.62919i	1.70731	−	0.377972i
$151$	11.6231	−	11.6231i	0.945876	−	0.945876i	−0.0527323	−	0.998609i	$-0.516793\pi$
$151$	11.6231	−	11.6231i	0.945876	−	0.945876i	0.998609	+	0.0527323i	$0.0167930\pi$
$152$	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	0.913534	−	0.406762i	$-0.133342\pi$
$157$	6.34984	+	6.34984i	0.506773	+	0.506773i	−0.406762	+	0.913534i	$0.633342\pi$
$158$	−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	0.727585	−	0.686017i	$-0.240643\pi$
$163$	−3.47244	−	8.38321i	−0.271983	−	0.656624i	−0.999568	+	0.0293932i	$0.990643\pi$
$164$	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	−0.999407	−	0.0344462i	$-0.989033\pi$
$167$	−3.46800	+	8.37250i	−0.268362	+	0.647884i	0.731044	+	0.682330i	$0.239033\pi$
$168$	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	0.266623	−	0.963801i	$-0.414092\pi$
$173$	−2.97725	−	1.23322i	−0.226356	−	0.0937597i	−0.492979	+	0.870041i	$0.664092\pi$
$174$	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	0.152402	−	0.988319i	$-0.451299\pi$
$179$	−11.1838	−	11.1838i	−0.835917	−	0.835917i	−0.988319	+	0.152402i	$0.951299\pi$
$180$	−5.09714	−	27.1335i	−0.379918	−	2.02241i
$181$	−2.03452	+	4.91177i	−0.151225	+	0.365089i	−0.981278	−	0.192595i	$-0.938310\pi$
$181$	−2.03452	+	4.91177i	−0.151225	+	0.365089i	0.830054	+	0.557684i	$0.188310\pi$
$182$	−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	−0.408757	−	0.912643i	$-0.634037\pi$
$193$	−0.728724	+	0.301848i	−0.0524547	+	0.0217275i	0.356302	+	0.934371i	$0.384037\pi$
$194$	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	0.997238	−	0.0742786i	$-0.0236654\pi$
$197$	3.36240	+	8.11756i	0.239561	+	0.578352i	−0.757676	+	0.652631i	$0.773665\pi$
$198$	−14.1398	−	43.6947i	−1.00487	−	3.10525i
$199$	−5.75966	−	13.9050i	−0.408291	−	0.985703i	−0.985587	−	0.169168i	$-0.945892\pi$
$199$	−5.75966	−	13.9050i	−0.408291	−	0.985703i	0.577296	−	0.816535i	$-0.304108\pi$
$200$	−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	−0.802567	−	0.596563i	$-0.796533\pi$
$211$	2.71295	−	6.54964i	0.186767	−	0.450896i	0.989334	+	0.145667i	$0.0465327\pi$
$212$	−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	$0.237691\pi$
$223$			20.2865i			1.35848i	−0.733915	+	0.679242i	$0.762309\pi$
$224$	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	0.792984	−	0.609242i	$-0.208526\pi$
$227$	−2.99130	−	7.22164i	−0.198540	−	0.479317i	−0.991524	+	0.129925i	$0.958526\pi$
$228$	−9.88843	−	41.6244i	−0.654877	−	2.75664i
$229$	−8.87676	+	8.87676i	−0.586593	+	0.586593i	−0.936707	−	0.350114i	$-0.886143\pi$
$229$	−8.87676	+	8.87676i	−0.586593	+	0.586593i	0.350114	+	0.936707i	$0.386143\pi$
$230$	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	−0.351612	−	0.936146i	$-0.614366\pi$
$233$	−19.2666	−	7.98047i	−1.26219	−	0.522818i	−0.910582	+	0.413328i	$0.864366\pi$
$234$	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	−0.491256	−	0.871015i	$-0.663462\pi$
$241$	−3.45764	+	1.43220i	−0.222726	+	0.0922561i	0.268530	+	0.963271i	$0.413462\pi$
$242$	−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	$0.243118\pi$
$251$			21.9157i			1.38331i	−0.722229	+	0.691654i	$0.756882\pi$
$252$	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	$0.138387\pi$
$257$			13.5043i			0.842375i	−0.906974	+	0.421188i	$0.861613\pi$
$258$	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	−0.302689	−	0.953089i	$-0.597884\pi$
$269$	2.57850	−	1.06805i	0.157214	−	0.0651203i	0.459903	+	0.887969i	$0.347884\pi$
$270$	−30.1478	−	3.85806i	−1.83474	−	0.234794i
$271$			8.19258i			0.497664i	0.968547	+	0.248832i	$0.0800467\pi$
$271$			8.19258i			0.497664i	−0.968547	+	0.248832i	$0.919953\pi$
$272$	−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	0.0391383	−	0.999234i	$-0.487539\pi$
$277$	−10.6476	−	4.41038i	−0.639752	−	0.264994i	−0.678890	+	0.734240i	$0.737539\pi$
$278$	−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	−0.880571	−	0.473915i	$-0.842841\pi$
$281$	−6.81680	+	6.81680i	−0.406656	+	0.406656i	0.473915	+	0.880571i	$0.342841\pi$
$282$	−4.79819	+	1.55272i	−0.285728	+	0.0924630i
$283$	−5.39479	+	2.23460i	−0.320687	+	0.132833i	−0.537219	−	0.843443i	$-0.680525\pi$
$283$	−5.39479	+	2.23460i	−0.320687	+	0.132833i	0.216532	+	0.976275i	$0.430525\pi$
$284$	−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	−0.719730	−	0.694254i	$-0.755735\pi$
$293$	−0.436090	+	0.436090i	−0.0254766	+	0.0254766i	0.694254	+	0.719730i	$0.255735\pi$
$294$	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	0.947733	−	0.319065i	$-0.103369\pi$
$307$	11.0152	+	11.0152i	0.628668	+	0.628668i	−0.319065	+	0.947733i	$0.603369\pi$
$308$	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	0.455041	−	0.890470i	$-0.349624\pi$
$311$	24.8032	−	10.2738i	1.40646	−	0.582576i	0.951420	+	0.307895i	$0.0996244\pi$
$312$	−2.34640	−	15.1647i	−0.132839	−	0.858534i
$313$	6.93305	+	16.7379i	0.391879	+	0.946080i	0.989530	+	0.144324i	$0.0461007\pi$
$313$	6.93305	+	16.7379i	0.391879	+	0.946080i	−0.597651	+	0.801756i	$0.703899\pi$
$314$	−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	0.712565	−	0.701607i	$-0.247534\pi$
$317$	30.4908	−	12.6297i	1.71253	−	0.709355i	0.999970	−	0.00774841i	$-0.00246642\pi$
$318$	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	−0.668150	−	0.744026i	$-0.732914\pi$
$331$	1.38044	−	1.38044i	0.0758757	−	0.0758757i	0.744026	+	0.668150i	$0.232914\pi$
$332$	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	0.981063	−	0.193688i	$-0.0620450\pi$
$337$	28.2306	+	11.6935i	1.53782	+	0.636986i	0.556758	+	0.830675i	$0.312045\pi$
$338$	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	−0.756299	−	0.654226i	$-0.772995\pi$
$347$	−15.4328	+	6.39247i	−0.828476	+	0.343166i	−0.0721765	+	0.997392i	$0.522995\pi$
$348$	−6.22221	−	1.00068i	−0.333545	−	0.0536423i
$349$	12.2722	−	12.2722i	0.656916	−	0.656916i	−0.297733	−	0.954649i	$-0.596231\pi$
$349$	12.2722	−	12.2722i	0.656916	−	0.656916i	0.954649	+	0.297733i	$0.0962306\pi$
$350$	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	0.312769	−	0.949829i	$-0.398744\pi$
$353$	−11.9693	−	11.9693i	−0.637061	−	0.637061i	−0.949829	+	0.312769i	$0.898744\pi$
$354$	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	0.953961	−	0.299930i	$-0.0969633\pi$
$359$	12.3921	+	12.3921i	0.654031	+	0.654031i	−0.299930	+	0.953961i	$0.596963\pi$
$360$	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	−0.985996	−	0.166769i	$-0.946667\pi$
$367$	−7.79153	−	18.8104i	−0.406715	−	0.981896i	0.579281	−	0.815128i	$-0.303333\pi$
$368$	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	0.419329	−	0.907834i	$-0.362265\pi$
$373$	−9.43459	−	9.43459i	−0.488505	−	0.488505i	−0.907834	+	0.419329i	$0.862265\pi$
$374$	−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	−0.767118	−	0.641505i	$-0.778310\pi$
$379$	−16.6634	+	6.90220i	−0.855940	+	0.354542i	−0.0888218	+	0.996048i	$0.528310\pi$
$380$	−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	0.949470	−	0.313857i	$-0.101621\pi$
$389$	12.5362	+	12.5362i	0.635613	+	0.635613i	−0.313857	+	0.949470i	$0.601621\pi$
$390$	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	−0.533981	−	0.845496i	$-0.679305\pi$
$397$	−6.25056	+	2.58906i	−0.313706	+	0.129941i	0.220275	+	0.975438i	$0.429305\pi$
$398$	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	−0.619189	−	0.785242i	$-0.712539\pi$
$401$	7.48721	−	18.0757i	0.373893	−	0.902659i	0.993083	−	0.117417i	$-0.0374614\pi$
$402$	−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	$0.115152\pi$
$409$			14.3152i			0.707843i	−0.935275	+	0.353922i	$0.884848\pi$
$410$	−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	0.199750	+	0.979847i	$0.435987\pi$
$419$	−12.9848	+	31.3482i	−0.634351	+	1.53146i	−0.834101	+	0.551612i	$0.814013\pi$
$420$	−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	0.644299	+	0.764773i	$0.277149\pi$
$431$	−7.30907	+	17.6457i	−0.352066	+	0.849962i	−0.996365	+	0.0851882i	$0.972851\pi$
$432$	38.3407	−	2.83394i	1.84467	−	0.136348i
$433$		−	32.6666i		−	1.56986i	−0.619586	−	0.784929i	$-0.712699\pi$
$433$		−	32.6666i		−	1.56986i	0.619586	−	0.784929i	$-0.287301\pi$
$434$	−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	−0.794502	−	0.607262i	$-0.792268\pi$
$439$	−19.4207	+	8.04432i	−0.926900	+	0.383935i	−0.132399	+	0.991197i	$0.542268\pi$
$440$	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	−0.831290	−	0.555839i	$-0.812397\pi$
$443$	−5.79756	+	5.79756i	−0.275450	+	0.275450i	0.555839	+	0.831290i	$0.312397\pi$
$444$	−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	0.814977	−	0.579493i	$-0.196749\pi$
$449$	20.7974	+	8.61456i	0.981490	+	0.406546i	0.166513	+	0.986039i	$0.446749\pi$
$450$	−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	$0.159343\pi$
$457$			20.5201i			0.959888i	−0.877299	+	0.479944i	$0.840657\pi$
$458$	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	−0.272987	+	0.962018i	$0.588012\pi$
$461$	−26.5167	+	26.5167i	−1.23500	+	1.23500i	−0.962018	+	0.272987i	$0.911988\pi$
$462$	−75.3208	−	38.4908i	−3.50424	−	1.79076i
$463$	6.03987	−	6.03987i	0.280697	−	0.280697i	−0.552690	−	0.833387i	$-0.686399\pi$
$463$	6.03987	−	6.03987i	0.280697	−	0.280697i	0.833387	+	0.552690i	$0.186399\pi$
$464$	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	0.405916	−	0.913910i	$-0.366953\pi$
$479$	29.3093	−	12.1403i	1.33917	−	0.554704i	0.933258	+	0.359206i	$0.116953\pi$
$480$	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	−0.385195	−	0.922835i	$-0.625866\pi$
$487$	−0.110920	+	0.0459446i	−0.00502627	+	0.00208195i	0.380169	+	0.924917i	$0.375866\pi$
$488$	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	0.640915	−	0.767612i	$-0.278555\pi$
$491$	−2.80742	−	2.80742i	−0.126697	−	0.126697i	−0.767612	+	0.640915i	$0.778555\pi$
$492$	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	−0.221149	−	0.975240i	$-0.570981\pi$
$499$	13.9575	−	33.6965i	0.624826	−	1.50846i	0.845975	−	0.533223i	$-0.179019\pi$
$500$	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	−0.812158	−	0.583437i	$-0.801707\pi$
$503$	−21.8420	+	9.04727i	−0.973888	+	0.403398i	−0.161730	+	0.986835i	$0.551707\pi$
$504$	−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	0.803652	−	0.595099i	$-0.202887\pi$
$521$	21.7098	+	8.99248i	0.951122	+	0.393968i	0.147470	+	0.989067i	$0.452887\pi$
$522$	−4.13324	+	8.08814i	−0.180907	+	0.354008i
$523$	−24.5138	−	24.5138i	−1.07191	−	1.07191i	−0.997205	−	0.0747091i	$-0.976197\pi$
$523$	−24.5138	−	24.5138i	−1.07191	−	1.07191i	−0.0747091	−	0.997205i	$-0.523803\pi$
$524$	−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	−0.986802	−	0.161934i	$-0.948227\pi$
$541$	−9.38592	−	22.6596i	−0.403532	−	0.974212i	0.583270	−	0.812279i	$-0.301773\pi$
$542$	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	0.335264	−	0.942124i	$-0.391174\pi$
$547$	−2.19497	−	0.909187i	−0.0938502	−	0.0388740i	−0.429115	+	0.903250i	$0.641174\pi$
$548$	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	0.616269	−	0.787536i	$-0.288643\pi$
$557$	−4.04204	−	4.04204i	−0.171267	−	0.171267i	−0.787536	+	0.616269i	$0.788643\pi$
$558$	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	0.698234	−	0.715870i	$-0.253970\pi$
$569$	−0.420694	−	0.420694i	−0.0176364	−	0.0176364i	−0.715870	+	0.698234i	$0.753970\pi$
$570$	−8.58667	+	67.0984i	−0.359656	+	2.81044i
$571$	7.52381	−	18.1641i	0.314862	−	0.760144i	−0.684649	−	0.728873i	$-0.740045\pi$
$571$	7.52381	−	18.1641i	0.314862	−	0.760144i	0.999511	−	0.0312708i	$-0.00995544\pi$
$572$	−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	0.707244	−	0.706970i	$-0.249938\pi$
$577$	0.00657344	+	0.00657344i	0.000273656	+	0.000273656i	−0.706970	+	0.707244i	$0.749938\pi$
$578$	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	$0.0874992\pi$
$599$			13.2866i			0.542876i	−0.962456	+	0.271438i	$0.912501\pi$
$600$	42.7600	−	2.50047i	1.74567	−	0.102081i
$601$	23.7568	+	9.84041i	0.969062	+	0.401399i	0.810363	−	0.585928i	$-0.199270\pi$
$601$	23.7568	+	9.84041i	0.969062	+	0.401399i	0.158699	+	0.987327i	$0.449270\pi$
$602$	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	−0.105249	−	0.994446i	$-0.533564\pi$
$607$	−21.7511	−	9.00960i	−0.882850	−	0.365688i	−0.777601	+	0.628757i	$0.783564\pi$
$608$	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	0.482747	−	0.875760i	$-0.339639\pi$
$613$	−9.73054	−	9.73054i	−0.393013	−	0.393013i	−0.875760	+	0.482747i	$0.839639\pi$
$614$	−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	−0.963227	−	0.268689i	$-0.913410\pi$
$617$	−2.28848	+	5.52489i	−0.0921309	+	0.222424i	0.871096	+	0.491113i	$0.163410\pi$
$618$	81.9791	−	26.5288i	3.29768	−	1.06715i
$619$	10.2812	+	4.25862i	0.413237	+	0.171168i	0.579609	−	0.814895i	$-0.303205\pi$
$619$	10.2812	+	4.25862i	0.413237	+	0.171168i	−0.166372	+	0.986063i	$0.553205\pi$
$620$	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	−0.356100	−	0.934448i	$-0.615894\pi$
$631$	14.5279	−	14.5279i	0.578348	−	0.578348i	0.934448	+	0.356100i	$0.115894\pi$
$632$	−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	0.816381	−	0.577514i	$-0.195977\pi$
$641$	−4.28512	−	10.3452i	−0.169252	−	0.408610i	−0.985633	+	0.168904i	$0.945977\pi$
$642$	15.5443	+	18.2439i	0.613484	+	0.720031i
$643$	5.57608	−	13.4618i	0.219899	−	0.530883i	−0.774976	−	0.631990i	$-0.782238\pi$
$643$	5.57608	−	13.4618i	0.219899	−	0.530883i	0.994876	+	0.101107i	$0.0322383\pi$
$644$	−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	−0.990192	−	0.139713i	$-0.955382\pi$
$647$	−21.6330	+	21.6330i	−0.850479	+	0.850479i	0.139713	+	0.990192i	$0.455382\pi$
$648$	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	−0.296523	−	0.955026i	$-0.595827\pi$
$653$	4.32140	−	1.78998i	0.169109	−	0.0700474i	0.465632	+	0.884978i	$0.345827\pi$
$654$	−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	−0.669847	−	0.742499i	$-0.733640\pi$
$661$	1.86790	−	1.86790i	0.0726528	−	0.0726528i	0.742499	+	0.669847i	$0.233640\pi$
$662$	−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	0.874451	+	0.485113i	$0.161222\pi$
$673$	15.5432	+	37.5247i	0.599148	+	1.44647i	−0.275304	+	0.961357i	$0.588778\pi$
$674$	−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	0.602527	+	0.798098i	$0.294160\pi$
$677$	−10.0919	+	24.3641i	−0.387865	+	0.936388i	−0.990392	+	0.138290i	$0.955840\pi$
$678$	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	−0.191500	−	0.981493i	$-0.561335\pi$
$683$	16.6719	−	40.2494i	0.637931	−	1.54010i	0.829431	−	0.558609i	$-0.188665\pi$
$684$	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	0.643808	−	0.765187i	$-0.277354\pi$
$691$	14.6675	+	6.07549i	0.557979	+	0.231123i	−0.0858284	+	0.996310i	$0.527354\pi$
$692$	−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	−0.921404	−	0.388607i	$-0.872957\pi$
$709$	−14.5027	−	35.0125i	−0.544659	−	1.31492i	0.376745	−	0.926317i	$-0.377043\pi$
$710$	−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	0.900266	+	0.435339i	$0.143372\pi$
$719$	15.3247	+	36.9970i	0.571513	+	1.37976i	−0.328753	+	0.944416i	$0.606628\pi$
$720$	−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	0.690418	−	0.723411i	$-0.257427\pi$
$727$	−0.889602	−	0.889602i	−0.0329935	−	0.0329935i	−0.723411	+	0.690418i	$0.757427\pi$
$728$	−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	$0.130570\pi$
$733$			21.5937i			0.797580i	−0.917042	+	0.398790i	$0.869430\pi$
$734$	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	−0.997212	−	0.0746157i	$-0.976227\pi$
$739$	−29.1372	−	29.1372i	−1.07183	−	1.07183i	−0.0746157	−	0.997212i	$-0.523773\pi$
$740$	−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	−0.989458	−	0.144817i	$-0.953741\pi$
$743$	−5.10828	+	12.3325i	−0.187405	+	0.452435i	0.802054	+	0.597252i	$0.203741\pi$
$744$	−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	0.999998	−	0.00198023i	$-0.000630326\pi$
$751$	7.98817	+	19.2851i	0.291492	+	0.703725i	−0.708506	+	0.705705i	$0.750630\pi$
$752$	−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	$-0.829528\pi$
$757$		−	28.0814i		−	1.02064i	0.859986	−	0.510318i	$-0.170472\pi$
$758$	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	$-0.916388\pi$
$761$		−	14.3263i		−	0.519329i	0.965699	−	0.259664i	$-0.0836119\pi$
$762$	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	−0.183959	−	0.982934i	$-0.558891\pi$
$787$	17.9868	−	43.4239i	0.641159	−	1.54789i	0.825118	−	0.564960i	$-0.191109\pi$
$788$	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	0.726408	−	0.687263i	$-0.241188\pi$
$809$	21.4485	+	8.88425i	0.754088	+	0.312354i	0.0276799	+	0.999617i	$0.491188\pi$
$810$	16.6396	−	29.0631i	0.584656	−	1.02117i
$811$	−6.79702	−	16.4095i	−0.238676	−	0.576214i	0.758471	−	0.651707i	$-0.225947\pi$
$811$	−6.79702	−	16.4095i	−0.238676	−	0.576214i	−0.997146	+	0.0754930i	$0.975947\pi$
$812$	−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	0.139948	−	0.990159i	$-0.455307\pi$
$821$	26.9068	−	11.1452i	0.939054	−	0.388969i	0.799106	+	0.601190i	$0.205307\pi$
$822$	11.2082	−	3.62702i	0.390930	−	0.126507i
$823$	−52.0564	+	21.5625i	−1.81457	+	0.751620i	−0.835080	+	0.550128i	$0.814579\pi$
$823$	−52.0564	+	21.5625i	−1.81457	+	0.751620i	−0.979490	+	0.201492i	$0.935421\pi$
$824$	−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	0.927627	−	0.373509i	$-0.121845\pi$
$827$	0.218127	+	0.526605i	0.00758502	+	0.0183119i	−0.920042	+	0.391821i	$0.871845\pi$
$828$	6.71075	−	10.8927i	0.233215	−	0.378547i
$829$		−	25.0999i		−	0.871755i	−0.900006	−	0.435877i	$-0.856438\pi$
$829$		−	25.0999i		−	0.871755i	0.900006	−	0.435877i	$-0.143562\pi$
$830$	−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	0.782519	−	0.622627i	$-0.213934\pi$
$839$	25.9409	+	10.7451i	0.895580	+	0.370961i	0.113061	+	0.993588i	$0.463934\pi$
$840$	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	0.772562	−	0.634939i	$-0.218975\pi$
$853$	25.4058	+	10.5234i	0.869877	+	0.360315i	0.0973147	+	0.995254i	$0.468975\pi$
$854$	−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	−0.782820	−	0.622249i	$-0.786219\pi$
$857$	−26.2406	+	10.8692i	−0.896360	+	0.371285i	−0.113541	+	0.993533i	$0.536219\pi$
$858$	−3.21455	+	40.2327i	−0.109743	+	1.37352i
$859$	10.3431	+	10.3431i	0.352902	+	0.352902i	0.861188	−	0.508286i	$-0.169721\pi$
$859$	10.3431	+	10.3431i	0.352902	+	0.352902i	−0.508286	+	0.861188i	$0.669721\pi$
$860$	−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	0.0763109	−	0.997084i	$-0.475686\pi$
$863$	31.5330	−	31.5330i	1.07339	−	1.07339i	0.997084	−	0.0763109i	$-0.0243142\pi$
$864$	−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	0.862079	−	0.506774i	$-0.169162\pi$
$877$	−3.13455	−	7.56748i	−0.105846	−	0.255536i	−0.967925	+	0.251238i	$0.919162\pi$
$878$	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	0.107300	−	0.994227i	$-0.465779\pi$
$881$	26.3038	−	10.8954i	0.886197	−	0.367075i	0.778897	+	0.627152i	$0.215779\pi$
$882$	−61.7273	−	4.93195i	−2.07847	−	0.166067i
$883$	−11.2923	+	11.2923i	−0.380017	+	0.380017i	−0.871108	−	0.491091i	$-0.836598\pi$
$883$	−11.2923	+	11.2923i	−0.380017	+	0.380017i	0.491091	+	0.871108i	$0.336598\pi$
$884$	−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	−0.915512	−	0.402291i	$-0.868214\pi$
$887$	0.485926	−	1.17313i	0.0163158	−	0.0393898i	0.931827	+	0.362902i	$0.118214\pi$
$888$	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	0.971997	+	0.234993i	$0.0755067\pi$
$907$	13.5782	+	32.7807i	0.450856	+	1.08846i	−0.521141	+	0.853471i	$0.674493\pi$
$908$	−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	0.0433088	−	0.999062i	$-0.486210\pi$
$911$	−19.0909	−	7.90772i	−0.632511	−	0.261994i	−0.675819	+	0.737067i	$0.736210\pi$
$912$	−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	−0.999581	−	0.0289302i	$-0.990790\pi$
$929$	−8.29999	+	20.0379i	−0.272314	+	0.657424i	0.727268	+	0.686354i	$0.240790\pi$
$930$	−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	$-0.733621\pi$
$937$		−	45.4590i		−	1.48508i	0.669801	−	0.742540i	$-0.266379\pi$
$938$	−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	−0.232784	−	0.972528i	$-0.574784\pi$
$941$	19.0036	−	45.8788i	0.619501	−	1.49561i	0.852285	−	0.523078i	$-0.175216\pi$
$942$	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	−0.169347	−	0.985556i	$-0.554166\pi$
$947$	19.9194	−	48.0897i	0.647293	−	1.56270i	0.816640	−	0.577147i	$-0.195834\pi$
$948$	−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	−0.702468	−	0.711716i	$-0.747918\pi$
$953$	0.285501	−	0.285501i	0.00924829	−	0.00924829i	0.711716	+	0.702468i	$0.247918\pi$
$954$	−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	0.873042	−	0.487645i	$-0.162144\pi$
$971$	12.0093	+	12.0093i	0.385398	+	0.385398i	−0.487645	+	0.873042i	$0.662144\pi$
$972$	−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	0.968869	−	0.247573i	$-0.0796332\pi$
$983$	46.3678	+	19.2062i	1.47890	+	0.612581i	0.510033	+	0.860155i	$0.329633\pi$
$984$	−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	−0.665707	−	0.746213i	$-0.731870\pi$
$991$	−19.1645	+	7.93820i	−0.608780	+	0.252165i	0.0569265	+	0.998378i	$0.481870\pi$
$992$	−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	−0.127644	−	0.991820i	$-0.540742\pi$
$997$	15.2641	−	6.32261i	0.483420	−	0.200239i	0.611065	+	0.791581i	$0.290742\pi$
$998$	−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.427.4	yes	416
5.3	odd	4		680.2.bz.a.563.50	yes	416
8.3	odd	2	inner	680.2.bw.a.427.101	yes	416
17.9	even	8		680.2.bz.a.587.50	yes	416
40.3	even	4		680.2.bz.a.563.49	yes	416
85.43	odd	8	inner	680.2.bw.a.43.101	yes	416
136.43	odd	8		680.2.bz.a.587.49	yes	416
680.43	even	8	inner	680.2.bw.a.43.4	✓	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bw.a.43.4	✓	416	680.43	even	8	inner
680.2.bw.a.43.101	yes	416	85.43	odd	8	inner
680.2.bw.a.427.4	yes	416	1.1	even	1	trivial
680.2.bw.a.427.101	yes	416	8.3	odd	2	inner
680.2.bz.a.563.49	yes	416	40.3	even	4
680.2.bz.a.563.50	yes	416	5.3	odd	4
680.2.bz.a.587.49	yes	416	136.43	odd	8
680.2.bz.a.587.50	yes	416	17.9	even	8

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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