LMFDB - Embedded newform 680.2.bz.a.563.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [680,2,Mod(83,680)]

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, 3]))

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

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

chi := DirichletCharacter("680.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bz (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			563.49
Character	$\chi$	$=$	680.563
Dual form			680.2.bz.a.587.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.112635 - 1.40972i) q^{2} +(-2.79820 - 1.15905i) q^{3} +(-1.97463 + 0.317569i) q^{4} +(-0.756545 + 2.10420i) q^{5} +(-1.31877 + 4.07524i) q^{6} +(-3.46829 + 1.43661i) q^{7} +(0.670096 + 2.74790i) q^{8} +(4.36522 + 4.36522i) q^{9} +O(q^{10})$	\(q+(-0.112635 - 1.40972i) q^{2} +(-2.79820 - 1.15905i) q^{3} +(-1.97463 + 0.317569i) q^{4} +(-0.756545 + 2.10420i) q^{5} +(-1.31877 + 4.07524i) q^{6} +(-3.46829 + 1.43661i) q^{7} +(0.670096 + 2.74790i) q^{8} +(4.36522 + 4.36522i) q^{9} +(3.05154 + 0.829510i) q^{10} +(-4.85998 - 2.01307i) q^{11} +(5.89349 + 1.40008i) q^{12} +(-1.26662 - 1.26662i) q^{13} +(2.41587 + 4.72751i) q^{14} +(4.55584 - 5.01109i) q^{15} +(3.79830 - 1.25416i) q^{16} +(-2.93778 + 2.89300i) q^{17} +(5.66207 - 6.64543i) q^{18} +(4.99413 - 4.99413i) q^{19} +(0.825667 - 4.39526i) q^{20} +11.3701 q^{21} +(-2.29046 + 7.07795i) q^{22} +(0.957344 - 0.396545i) q^{23} +(1.30990 - 8.46587i) q^{24} +(-3.85528 - 3.18384i) q^{25} +(-1.64292 + 1.92825i) q^{26} +(-3.67810 - 8.87971i) q^{27} +(6.39235 - 3.93819i) q^{28} +(0.398139 + 0.961193i) q^{29} +(-7.57739 - 5.85804i) q^{30} +(2.45520 + 5.92738i) q^{31} +(-2.19584 - 5.21328i) q^{32} +(11.2660 + 11.2660i) q^{33} +(4.40922 + 3.81560i) q^{34} +(-0.398998 - 8.38482i) q^{35} +(-10.0059 - 7.23343i) q^{36} +(-3.88993 - 1.61126i) q^{37} +(-7.60285 - 6.47782i) q^{38} +(2.07619 + 5.01236i) q^{39} +(-6.28908 - 0.668898i) q^{40} +(0.670346 - 1.61836i) q^{41} +(-1.28067 - 16.0287i) q^{42} -7.00207 q^{43} +(10.2359 + 2.43168i) q^{44} +(-12.4878 + 5.88280i) q^{45} +(-0.666848 - 1.30492i) q^{46} +(0.832549 - 0.832549i) q^{47} +(-12.0821 - 0.893042i) 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} +11.8658 q^{53} +(-12.1036 + 6.18526i) q^{54} +(7.91268 - 8.70337i) q^{55} +(-6.27176 - 8.56785i) q^{56} +(-19.7631 + 8.18614i) q^{57} +(1.31017 - 0.669529i) q^{58} +(-1.39307 - 1.39307i) q^{59} +(-7.40473 + 11.3418i) q^{60} +(1.56801 + 0.649493i) q^{61} +(8.07941 - 4.12878i) q^{62} +(-21.4110 - 8.86872i) q^{63} +(-7.10194 + 3.68272i) q^{64} +(3.62348 - 1.70697i) q^{65} +(14.6129 - 17.1508i) q^{66} +(-5.98943 + 5.98943i) q^{67} +(4.88230 - 6.64554i) q^{68} -3.13846 q^{69} +(-11.7753 + 1.50690i) q^{70} +(2.89257 + 6.98328i) q^{71} +(-9.07009 + 14.9203i) q^{72} +(5.21241 - 12.5839i) q^{73} +(-1.83329 + 5.66520i) q^{74} +(7.09762 + 13.3775i) q^{75} +(-8.27557 + 11.4475i) q^{76} +19.7478 q^{77} +(6.83218 - 3.49142i) q^{78} +(9.53535 + 3.94967i) q^{79} +(-0.234587 + 8.94120i) q^{80} +10.5903i q^{81} +(-2.35694 - 0.762716i) q^{82} +5.42947i q^{83} +(-22.4517 + 3.61079i) q^{84} +(-3.86487 - 8.37035i) q^{85} +(0.788680 + 9.87096i) q^{86} -3.15108i q^{87} +(2.27507 - 14.7037i) q^{88} -3.29031 q^{89} +(9.69967 + 16.9417i) q^{90} +(6.21267 + 2.57337i) q^{91} +(-1.76447 + 1.08705i) q^{92} -19.4317i q^{93} +(-1.26744 - 1.07989i) q^{94} +(6.73035 + 14.2869i) q^{95} +(0.101927 + 17.1329i) q^{96} +(5.13078 + 2.12524i) 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^{2} - 8 q^{3} - 8 q^{8}+O(q^{10}) $ 416 * q - 8 * q^2 - 8 * q^3 - 8 * q^8	$ 416 q - 8 q^{2} - 8 q^{3} - 8 q^{8} + 4 q^{10} - 16 q^{11} - 16 q^{12} + 16 q^{14} - 16 q^{16} - 16 q^{17} - 8 q^{18} + 32 q^{19} + 12 q^{20} - 12 q^{22} - 24 q^{24} - 16 q^{25} + 8 q^{26} - 32 q^{27} + 44 q^{28} + 16 q^{30} - 8 q^{32} - 16 q^{33} - 16 q^{35} - 72 q^{36} - 16 q^{38} + 16 q^{40} - 16 q^{41} - 16 q^{43} + 32 q^{46} - 36 q^{48} - 48 q^{50} - 16 q^{51} + 24 q^{52} - 16 q^{54} - 8 q^{56} + 16 q^{57} + 8 q^{58} + 64 q^{60} - 56 q^{62} - 48 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 88 q^{70} - 24 q^{72} + 32 q^{73} + 16 q^{74} - 32 q^{75} - 40 q^{76} - 84 q^{78} + 16 q^{80} + 28 q^{82} - 48 q^{86} + 8 q^{88} - 32 q^{90} - 16 q^{91} + 48 q^{92} + 24 q^{94} - 8 q^{96} - 16 q^{97} + 40 q^{98}+O(q^{100}) $ 416 * q - 8 * q^2 - 8 * q^3 - 8 * q^8 + 4 * q^10 - 16 * q^11 - 16 * q^12 + 16 * q^14 - 16 * q^16 - 16 * q^17 - 8 * q^18 + 32 * q^19 + 12 * q^20 - 12 * q^22 - 24 * q^24 - 16 * q^25 + 8 * q^26 - 32 * q^27 + 44 * q^28 + 16 * q^30 - 8 * q^32 - 16 * q^33 - 16 * q^35 - 72 * q^36 - 16 * q^38 + 16 * q^40 - 16 * q^41 - 16 * q^43 + 32 * q^46 - 36 * q^48 - 48 * q^50 - 16 * q^51 + 24 * q^52 - 16 * q^54 - 8 * q^56 + 16 * q^57 + 8 * q^58 + 64 * q^60 - 56 * q^62 - 48 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 88 * q^70 - 24 * q^72 + 32 * q^73 + 16 * q^74 - 32 * q^75 - 40 * q^76 - 84 * q^78 + 16 * q^80 + 28 * q^82 - 48 * q^86 + 8 * q^88 - 32 * q^90 - 16 * q^91 + 48 * q^92 + 24 * q^94 - 8 * q^96 - 16 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.112635	−	1.40972i	−0.0796452	−	0.996823i
$2$	−0.112635	−	1.40972i	−0.0796452	−	0.996823i
$3$	−2.79820	−	1.15905i	−1.61554	−	0.669180i	−0.622041	−	0.782985i	$-0.713696\pi$
$3$	−2.79820	−	1.15905i	−1.61554	−	0.669180i	−0.993503	+	0.113804i	$0.963696\pi$
$4$	−1.97463	+	0.317569i	−0.987313	+	0.158784i
$5$	−0.756545	+	2.10420i	−0.338337	+	0.941025i
$5$	−0.756545	+	2.10420i	−0.338337	+	0.941025i
$6$	−1.31877	+	4.07524i	−0.538384	+	1.66371i
$7$	−3.46829	+	1.43661i	−1.31089	+	0.542988i	−0.925144	−	0.379617i	$-0.876056\pi$
$7$	−3.46829	+	1.43661i	−1.31089	+	0.542988i	−0.385746	+	0.922605i	$0.626056\pi$
$8$	0.670096	+	2.74790i	0.236915	+	0.971530i
$9$	4.36522	+	4.36522i	1.45507	+	1.45507i
$10$	3.05154	+	0.829510i	0.964983	+	0.262314i
$11$	−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	$0.916500\pi$
$12$	5.89349	+	1.40008i	1.70130	+	0.404168i
$13$	−1.26662	−	1.26662i	−0.351298	−	0.351298i	0.509294	−	0.860593i	$-0.329907\pi$
$13$	−1.26662	−	1.26662i	−0.351298	−	0.351298i	−0.860593	+	0.509294i	$0.829907\pi$
$14$	2.41587	+	4.72751i	0.645670	+	1.26348i
$15$	4.55584	−	5.01109i	1.17631	−	1.29386i
$16$	3.79830	−	1.25416i	0.949575	−	0.313540i
$17$	−2.93778	+	2.89300i	−0.712517	+	0.701655i
$17$	−2.93778	+	2.89300i	−0.712517	+	0.701655i
$18$	5.66207	−	6.64543i	1.33456	−	1.56634i
$19$	4.99413	−	4.99413i	1.14573	−	1.14573i	0.158350	−	0.987383i	$-0.449383\pi$
$19$	4.99413	−	4.99413i	1.14573	−	1.14573i	0.987383	−	0.158350i	$-0.0506175\pi$
$20$	0.825667	−	4.39526i	0.184625	−	0.982809i
$21$	11.3701			2.48116
$22$	−2.29046	+	7.07795i	−0.488328	+	1.50902i
$23$	0.957344	−	0.396545i	0.199620	−	0.0826853i	−0.280634	−	0.959815i	$-0.590545\pi$
$23$	0.957344	−	0.396545i	0.199620	−	0.0826853i	0.480254	+	0.877130i	$0.340545\pi$
$24$	1.30990	−	8.46587i	0.267383	−	1.72809i
$25$	−3.85528	−	3.18384i	−0.771056	−	0.636767i
$26$	−1.64292	+	1.92825i	−0.322203	+	0.378162i
$27$	−3.67810	−	8.87971i	−0.707850	−	1.70890i
$28$	6.39235	−	3.93819i	1.20804	−	0.744249i
$29$	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	$0.0704462\pi$
$31$	2.45520	+	5.92738i	0.440967	+	1.06459i	−0.534643	+	0.845078i	$0.679554\pi$
$32$	−2.19584	−	5.21328i	−0.388173	−	0.921587i
$33$	11.2660	+	11.2660i	1.96115	+	1.96115i
$34$	4.40922	+	3.81560i	0.756174	+	0.654370i
$35$	−0.398998	−	8.38482i	−0.0674430	−	1.41729i
$36$	−10.0059	−	7.23343i	−1.66766	−	1.20557i
$37$	−3.88993	−	1.61126i	−0.639501	−	0.264890i	0.0392830	−	0.999228i	$-0.487493\pi$
$37$	−3.88993	−	1.61126i	−0.639501	−	0.264890i	−0.678784	+	0.734338i	$0.737493\pi$
$38$	−7.60285	−	6.47782i	−1.23335	−	1.05084i
$39$	2.07619	+	5.01236i	0.332456	+	0.802620i
$40$	−6.28908	−	0.668898i	−0.994391	−	0.105762i
$41$	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	$0.0813232\pi$
$42$	−1.28067	−	16.0287i	−0.197612	−	2.47328i
$43$	−7.00207			−1.06781			−0.533903	−	0.845546i	$-0.679275\pi$
$43$	−7.00207			−1.06781			−0.533903	+	0.845546i	$0.679275\pi$
$44$	10.2359	+	2.43168i	1.54312	+	0.366590i
$45$	−12.4878	+	5.88280i	−1.86157	+	0.876956i
$46$	−0.666848	−	1.30492i	−0.0983214	−	0.192400i
$47$	0.832549	−	0.832549i	0.121440	−	0.121440i	−0.643775	−	0.765215i	$-0.722633\pi$
$47$	0.832549	−	0.832549i	0.121440	−	0.121440i	0.765215	+	0.643775i	$0.222633\pi$
$48$	−12.0821	−	0.893042i	−1.74390	−	0.128899i
$49$	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
$53$	11.8658			1.62989			0.814947	−	0.579536i	$-0.196766\pi$
$53$	11.8658			1.62989			0.814947	+	0.579536i	$0.196766\pi$
$54$	−12.1036	+	6.18526i	−1.64709	+	0.841707i
$55$	7.91268	−	8.70337i	1.06695	−	1.17356i
$56$	−6.27176	−	8.56785i	−0.838099	−	1.14493i
$57$	−19.7631	+	8.18614i	−2.61768	+	1.08428i
$58$	1.31017	−	0.669529i	0.172034	−	0.0879135i
$59$	−1.39307	−	1.39307i	−0.181363	−	0.181363i	0.610587	−	0.791949i	$-0.290934\pi$
$59$	−1.39307	−	1.39307i	−0.181363	−	0.181363i	−0.791949	+	0.610587i	$0.790934\pi$
$60$	−7.40473	+	11.3418i	−0.955946	+	1.46422i
$61$	1.56801	+	0.649493i	0.200764	+	0.0831590i	0.480800	−	0.876830i	$-0.340346\pi$
$61$	1.56801	+	0.649493i	0.200764	+	0.0831590i	−0.280036	+	0.959989i	$0.590346\pi$
$62$	8.07941	−	4.12878i	1.02609	−	0.524356i
$63$	−21.4110	−	8.86872i	−2.69753	−	1.11735i
$64$	−7.10194	+	3.68272i	−0.887743	+	0.460340i
$65$	3.62348	−	1.70697i	0.449438	−	0.211723i
$66$	14.6129	−	17.1508i	1.79872	−	2.11112i
$67$	−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	$0.423103\pi$
$68$	4.88230	−	6.64554i	0.592066	−	0.805889i
$69$	−3.13846			−0.377826
$70$	−11.7753	+	1.50690i	−1.40742	+	0.180109i
$71$	2.89257	+	6.98328i	0.343285	+	0.828763i	0.997379	+	0.0723502i	$0.0230499\pi$
$71$	2.89257	+	6.98328i	0.343285	+	0.828763i	−0.654094	+	0.756413i	$0.726950\pi$
$72$	−9.07009	+	14.9203i	−1.06892	+	1.75838i
$73$	5.21241	−	12.5839i	0.610067	−	1.47283i	−0.252861	−	0.967503i	$-0.581371\pi$
$73$	5.21241	−	12.5839i	0.610067	−	1.47283i	0.862927	−	0.505328i	$-0.168629\pi$
$74$	−1.83329	+	5.66520i	−0.213115	+	0.658566i
$75$	7.09762	+	13.3775i	0.819563	+	1.54470i
$76$	−8.27557	+	11.4475i	−0.949273	+	1.31312i
$77$	19.7478			2.25047
$78$	6.83218	−	3.49142i	0.773592	−	0.395325i
$79$	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	$0.427818\pi$
$80$	−0.234587	+	8.94120i	−0.0262276	+	0.999656i
$81$			10.5903i			1.17670i
$82$	−2.35694	−	0.762716i	−0.260280	−	0.0842279i
$83$			5.42947i			0.595962i	0.954572	+	0.297981i	$0.0963132\pi$
$83$			5.42947i			0.595962i	−0.954572	+	0.297981i	$0.903687\pi$
$84$	−22.4517	+	3.61079i	−2.44968	+	0.393969i
$85$	−3.86487	−	8.37035i	−0.419203	−	0.907892i
$86$	0.788680	+	9.87096i	0.0850456	+	1.06441i
$87$		−	3.15108i		−	0.337831i
$88$	2.27507	−	14.7037i	0.242523	−	1.56742i
$89$	−3.29031			−0.348772			−0.174386	−	0.984677i	$-0.555794\pi$
$89$	−3.29031			−0.348772			−0.174386	+	0.984677i	$0.555794\pi$
$90$	9.69967	+	16.9417i	1.02243	+	1.78581i
$91$	6.21267	+	2.57337i	0.651265	+	0.269763i
$92$	−1.76447	+	1.08705i	−0.183958	+	0.113333i
$93$		−	19.4317i		−	2.01498i
$94$	−1.26744	−	1.07989i	−0.130726	−	0.111382i
$95$	6.73035	+	14.2869i	0.690519	+	1.46581i
$96$	0.101927	+	17.1329i	0.0104029	+	1.74862i
$97$	5.13078	+	2.12524i	0.520951	+	0.215785i	0.627635	−	0.778508i	$-0.284023\pi$
$97$	5.13078	+	2.12524i	0.520951	+	0.215785i	−0.106683	+	0.994293i	$0.534023\pi$
$98$	−7.63527	−	6.50544i	−0.771278	−	0.657148i
$99$	−12.4274	−	30.0024i	−1.24900	−	3.01535i
$100$	8.62383	+	5.06257i	0.862383	+	0.506257i
$101$		−	3.48631i		−	0.346900i	−0.984843	−	0.173450i	$-0.944508\pi$
$101$		−	3.48631i		−	0.346900i	0.984843	−	0.173450i	$-0.0554916\pi$
$102$	−7.91540	−	15.7874i	−0.783741	−	1.56318i
$103$	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	$-0.207413\pi$
$104$	2.63180	−	4.32932i	0.258069	−	0.424525i
$105$	−8.60199	+	23.9249i	−0.839468	+	2.33483i
$106$	−1.33651	−	16.7275i	−0.129813	−	1.62472i
$107$	5.16973	+	2.14137i	0.499777	+	0.207014i	0.618308	−	0.785936i	$-0.287818\pi$
$107$	5.16973	+	2.14137i	0.499777	+	0.207014i	−0.118531	+	0.992950i	$0.537818\pi$
$108$	10.0828	+	16.3661i	0.970216	+	1.57482i
$109$	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	$0.0400192\pi$
$110$	−13.1606	−	10.1744i	−1.25481	−	0.970087i
$111$	9.01728	+	9.01728i	0.855883	+	0.855883i
$112$	−11.3719	+	9.80647i	−1.07454	+	0.926625i
$113$	3.31469	+	8.00236i	0.311819	+	0.752799i	0.999638	+	0.0269157i	$0.00856856\pi$
$113$	3.31469	+	8.00236i	0.311819	+	0.752799i	−0.687818	+	0.725883i	$0.741431\pi$
$114$	13.7662	+	26.9384i	1.28932	+	2.52301i
$115$	0.110134	+	2.31444i	0.0102701	+	0.215823i
$116$	−1.09142	−	1.77156i	−0.101336	−	0.164485i
$117$		−	11.0582i		−	1.02233i
$118$	−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
$122$	0.738990	−	2.28362i	0.0669050	−	0.206749i
$123$	−3.75153	+	3.75153i	−0.338264	+	0.338264i
$124$	−6.73046	−	10.9247i	−0.604413	−	0.981064i
$125$	9.61611	−	5.70355i	0.860091	−	0.510141i
$126$	−10.0908	+	31.1825i	−0.898959	+	2.77795i
$127$	−7.87009			−0.698358			−0.349179	−	0.937056i	$-0.613539\pi$
$127$	−7.87009			−0.698358			−0.349179	+	0.937056i	$0.613539\pi$
$128$	5.99153	+	9.59695i	0.529582	+	0.848259i
$129$	19.5932	+	8.11578i	1.72509	+	0.714554i
$130$	−2.81448	−	4.91584i	−0.246846	−	0.431147i
$131$	−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
$133$	−10.1465	+	24.4957i	−0.879810	+	2.12405i
$134$	9.11804	+	7.76880i	0.787679	+	0.671122i
$135$	21.4673	−	1.02154i	1.84761	−	0.0879199i
$136$	−9.91827	−	6.13416i	−0.850485	−	0.526000i
$137$	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	$0.212516\pi$
$138$	0.353502	+	4.42436i	0.0300921	+	0.376626i
$139$	−3.78070	−	9.12743i	−0.320675	−	0.774178i	−0.999215	−	0.0396148i	$-0.987387\pi$
$139$	−3.78070	−	9.12743i	−0.320675	−	0.774178i	0.678540	−	0.734564i	$-0.262613\pi$
$140$	3.45063	+	16.4302i	0.291631	+	1.38860i
$141$	−3.29461	+	1.36467i	−0.277456	+	0.114926i
$142$	9.51867	−	4.86428i	0.798789	−	0.408201i
$143$	3.60596	+	8.70557i	0.301546	+	0.727996i
$144$	22.0551	+	11.1057i	1.83793	+	0.925479i
$145$	−2.32375	+	0.110577i	−0.192977	+	0.00918294i
$146$	−18.3269	−	5.93066i	−1.51674	−	0.490825i
$147$	−19.8473	+	8.22104i	−1.63698	+	0.678060i
$148$	8.19285	+	1.94632i	0.673448	+	0.159987i
$149$			13.8470i			1.13439i	0.823583	+	0.567195i	$0.191972\pi$
$149$			13.8470i			1.13439i	−0.823583	+	0.567195i	$0.808028\pi$
$150$	18.0591	−	11.5124i	1.47452	−	0.939988i
$151$	−11.6231	+	11.6231i	−0.945876	+	0.945876i	−0.998609	−	0.0527323i	$-0.983207\pi$
$151$	−11.6231	+	11.6231i	−0.945876	+	0.945876i	0.0527323	+	0.998609i	$0.483207\pi$
$152$	17.0699	+	10.3768i	1.38456	+	0.841674i
$153$	−25.4527	−	0.195509i	−2.05773	−	0.0158060i
$154$	−2.22430	−	27.8389i	−0.179239	−	2.24332i
$155$	−14.3298	+	0.681896i	−1.15100	+	0.0547712i
$156$	−5.69147	−	9.23821i	−0.455682	−	0.739649i
$157$	−6.34984	+	6.34984i	−0.506773	+	0.506773i	−0.913534	−	0.406762i	$-0.866658\pi$
$157$	−6.34984	+	6.34984i	−0.506773	+	0.506773i	0.406762	+	0.913534i	$0.366658\pi$
$158$	4.49392	−	13.8870i	0.357517	−	1.10479i
$159$	−33.2029	−	13.7531i	−2.63316	−	1.09069i
$160$	12.6310	−	0.676392i	0.998569	−	0.0534735i
$161$	−2.75066	+	2.75066i	−0.216783	+	0.216783i
$162$	14.9293	−	1.19284i	1.17296	−	0.0937183i
$163$	8.38321	−	3.47244i	0.656624	−	0.271983i	−0.0293932	−	0.999568i	$-0.509357\pi$
$163$	8.38321	−	3.47244i	0.656624	−	0.271983i	0.686017	+	0.727585i	$0.259357\pi$
$164$	−0.809743	+	3.40853i	−0.0632303	+	0.266162i
$165$	−32.2290	+	15.1826i	−2.50902	+	1.18196i
$166$	7.65404	−	0.611550i	0.594069	−	0.0474655i
$167$	−8.37250	−	3.46800i	−0.647884	−	0.268362i	0.0344462	−	0.999407i	$-0.489033\pi$
$167$	−8.37250	−	3.46800i	−0.647884	−	0.268362i	−0.682330	+	0.731044i	$0.739033\pi$
$168$	7.61906	+	31.2439i	0.587823	+	2.41052i
$169$		−	9.79132i		−	0.753179i
$170$	−11.3645	+	6.39118i	−0.871621	+	0.490181i
$171$	43.6010			3.33425
$172$	13.8265	−	2.22364i	1.05426	−	0.169551i
$173$	−1.23322	+	2.97725i	−0.0937597	+	0.226356i	−0.963801	−	0.266623i	$-0.914092\pi$
$173$	−1.23322	+	2.97725i	−0.0937597	+	0.226356i	0.870041	+	0.492979i	$0.164092\pi$
$174$	−4.44214	+	0.354923i	−0.336758	+	0.0269066i
$175$	17.9452	+	5.50392i	1.35653	+	0.416057i
$176$	−20.9844	−	1.55105i	−1.58176	−	0.116915i
$177$	2.28345	+	5.51275i	0.171635	+	0.414363i
$178$	0.370605	+	4.63842i	0.0277780	+	0.347664i
$179$	11.1838	+	11.1838i	0.835917	+	0.835917i	0.988319	−	0.152402i	$-0.0487007\pi$
$179$	11.1838	+	11.1838i	0.835917	+	0.835917i	−0.152402	+	0.988319i	$0.548701\pi$
$180$	22.7905	−	15.5821i	1.69870	−	1.16142i
$181$	2.03452	−	4.91177i	0.151225	−	0.365089i	−0.830054	−	0.557684i	$-0.811690\pi$
$181$	2.03452	−	4.91177i	0.151225	−	0.365089i	0.981278	+	0.192595i	$0.0616902\pi$
$182$	2.92797	−	9.04798i	0.217036	−	0.670681i
$183$	−3.63483	−	3.63483i	−0.268694	−	0.268694i
$184$	1.73118	+	2.36497i	0.127624	+	0.174348i
$185$	6.33332	−	6.96618i	0.465635	−	0.512164i
$186$	−27.3933	+	2.18870i	−2.00858	+	0.160483i
$187$	20.1014	−	8.14593i	1.46996	−	0.595690i
$188$	−1.37958	+	1.90836i	−0.100616	+	0.139182i
$189$	25.5134	+	25.5134i	1.85583	+	1.85583i
$190$	19.3825	−	11.0971i	1.40615	−	0.805070i
$191$	3.60150			0.260595			0.130298	−	0.991475i	$-0.458407\pi$
$191$	3.60150			0.260595			0.130298	+	0.991475i	$0.458407\pi$
$192$	24.1412	−	2.07346i	1.74224	−	0.149639i
$193$	−0.301848	−	0.728724i	−0.0217275	−	0.0524547i	0.912643	−	0.408757i	$-0.134037\pi$
$193$	−0.301848	−	0.728724i	−0.0217275	−	0.0524547i	−0.934371	+	0.356302i	$0.884037\pi$
$194$	2.41808	−	7.47234i	0.173608	−	0.536483i
$195$	−12.1177	+	0.576631i	−0.867768	+	0.0412934i
$196$	−8.31085	+	11.4963i	−0.593632	+	0.821167i
$197$	−8.11756	+	3.36240i	−0.578352	+	0.239561i	−0.652631	−	0.757676i	$-0.726335\pi$
$197$	−8.11756	+	3.36240i	−0.578352	+	0.239561i	0.0742786	+	0.997238i	$0.476335\pi$
$198$	−40.8952	+	20.8985i	−2.90630	+	1.48519i
$199$	−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
$202$	−4.91472	+	0.392681i	−0.345798	+	0.0276290i
$203$	−2.76172	−	2.76172i	−0.193835	−	0.193835i
$204$	−21.3642	+	12.9367i	−1.49579	+	0.905751i
$205$	2.89820	+	2.63490i	0.202419	+	0.184029i
$206$	−21.6547	−	18.4503i	−1.50875	−	1.28549i
$207$	5.91003	+	2.44801i	0.410775	+	0.170149i
$208$	−6.39957	−	3.22247i	−0.443730	−	0.223438i
$209$	−34.3249	+	14.2178i	−2.37430	+	0.983469i
$210$	34.6963	+	9.43161i	2.39427	+	0.650843i
$211$	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	$0.0465327\pi$
$212$	−23.4305	+	3.76821i	−1.60922	+	0.258802i
$213$		−	22.8933i		−	1.56862i
$214$	2.43645	−	7.52908i	0.166552	−	0.514677i
$215$	5.29738	−	14.7337i	0.361278	−	1.00483i
$216$	21.9359	−	16.0573i	1.49255	−	1.09256i
$217$	−17.0307	−	17.0307i	−1.15612	−	1.15612i
$218$	−7.41193	−	2.39854i	−0.501999	−	0.162449i
$219$	−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
$223$	20.2865			1.35848			0.679242	−	0.733915i	$-0.262309\pi$
$223$	20.2865			1.35848			0.679242	+	0.733915i	$0.262309\pi$
$224$	15.1053	+	14.9266i	1.00926	+	0.997325i
$225$	−2.93100	−	30.7273i	−0.195400	−	2.04849i
$226$	10.9077	−	5.57413i	0.725572	−	0.370786i
$227$	−7.22164	+	2.99130i	−0.479317	+	0.198540i	−0.609242	−	0.792984i	$-0.708526\pi$
$227$	−7.22164	+	2.99130i	−0.479317	+	0.198540i	0.129925	+	0.991524i	$0.458526\pi$
$228$	36.4251	−	22.4407i	2.41231	−	1.48617i
$229$	−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	$0.386143\pi$
$230$	3.25031	−	0.415947i	0.214319	−	0.0274267i
$231$	−55.2584	−	22.8888i	−3.63574	−	1.50597i
$232$	−2.37447	+	1.73814i	−0.155892	+	0.114114i
$233$	7.98047	−	19.2666i	0.522818	−	1.26219i	−0.413328	−	0.910582i	$-0.635634\pi$
$233$	7.98047	−	19.2666i	0.522818	−	1.26219i	0.936146	−	0.351612i	$-0.114366\pi$
$234$	−15.5890	+	1.24554i	−1.01908	+	0.0814237i
$235$	1.12199	+	2.38171i	0.0731902	+	0.155365i
$236$	3.19319	+	2.30840i	0.207859	+	0.150264i
$237$	−22.1040	−	22.1040i	−1.43581	−	1.43581i
$238$	−20.7740	−	6.89928i	−1.34658	−	0.447214i
$239$	−12.6224			−0.816478			−0.408239	−	0.912875i	$-0.633857\pi$
$239$	−12.6224			−0.816478			−0.408239	+	0.912875i	$0.633857\pi$
$240$	11.0198	−	24.7474i	0.711322	−	1.59744i
$241$	−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
$243$	1.24042	−	2.99465i	0.0795732	−	0.192107i
$244$	−3.30250	−	0.784553i	−0.211421	−	0.0502259i
$245$	6.75905	+	14.3478i	0.431820	+	0.916649i
$246$	5.71117	+	4.86606i	0.364131	+	0.310248i
$247$	−12.6514			−0.804989
$248$	−14.6426	+	10.7186i	−0.929809	+	0.680630i
$249$	6.29305	−	15.1928i	0.398806	−	0.962803i
$250$	−9.12353	−	12.9136i	−0.577023	−	0.816728i
$251$			21.9157i			1.38331i	0.722229	+	0.691654i	$0.243118\pi$
$251$			21.9157i			1.38331i	−0.722229	+	0.691654i	$0.756882\pi$
$252$	45.0951	+	10.7130i	2.84073	+	0.674853i
$253$	−5.45094			−0.342698
$254$	0.886450	+	11.0946i	0.0556208	+	0.696139i
$255$	1.11299	+	27.9016i	0.0696981	+	1.74726i
$256$	12.8542	−	9.52735i	0.803386	−	0.595459i
$257$	13.5043			0.842375			0.421188	−	0.906974i	$-0.361613\pi$
$257$	13.5043			0.842375			0.421188	+	0.906974i	$0.361613\pi$
$258$	9.23409	−	28.5351i	0.574890	−	1.77652i
$259$	15.8062			0.982147
$260$	−6.61295	+	4.52133i	−0.410118	+	0.280401i
$261$	−2.45786	+	5.93379i	−0.152137	+	0.367292i
$262$	−9.06983	+	4.63491i	−0.560336	+	0.286346i
$263$			29.2007i			1.80059i	0.435278	+	0.900296i	$0.356650\pi$
$263$			29.2007i			1.80059i	−0.435278	+	0.900296i	$0.643350\pi$
$264$	−23.4085	+	38.5070i	−1.44069	+	2.36994i
$265$	−8.97701	+	24.9680i	−0.551453	+	1.53377i
$266$	35.6750	+	11.5446i	2.18738	+	0.707845i
$267$	9.20697	+	3.81365i	0.563457	+	0.233392i
$268$	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	$0.347884\pi$
$270$	−3.85806	−	30.1478i	−0.234794	−	1.83474i
$271$		−	8.19258i		−	0.497664i	−0.968547	−	0.248832i	$-0.919953\pi$
$271$		−	8.19258i		−	0.497664i	0.968547	−	0.248832i	$-0.0800467\pi$
$272$	−7.53031	+	14.6729i	−0.456592	+	0.889676i
$273$	−14.4016	−	14.4016i	−0.871627	−	0.871627i
$274$	−2.96063	−	2.52253i	−0.178858	−	0.152391i
$275$	12.3273	+	23.2343i	0.743364	+	1.40108i
$276$	6.19729	−	0.996677i	0.373033	−	0.0599929i
$277$	4.41038	−	10.6476i	0.264994	−	0.639752i	−0.734240	−	0.678890i	$-0.762461\pi$
$277$	4.41038	−	10.6476i	0.264994	−	0.639752i	0.999234	+	0.0391383i	$0.0124613\pi$
$278$	−12.4413	+	6.35781i	−0.746179	+	0.381316i
$279$	−15.1568	+	36.5918i	−0.907416	+	2.19070i
$280$	22.7733	−	6.71504i	1.36097	−	0.401301i
$281$	−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	$0.342841\pi$
$282$	2.29490	+	4.49077i	0.136659	+	0.267422i
$283$	−2.23460	−	5.39479i	−0.132833	−	0.320687i	0.843443	−	0.537219i	$-0.180525\pi$
$283$	−2.23460	−	5.39479i	−0.132833	−	0.320687i	−0.976275	+	0.216532i	$0.930525\pi$
$284$	−7.92942	−	12.8708i	−0.470524	−	0.763741i
$285$	−2.27358	−	47.7786i	−0.134675	−	2.83016i
$286$	11.8663	−	6.06396i	0.701667	−	0.358569i
$287$			6.57596i			0.388167i
$288$	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
$292$	−6.29632	+	26.5038i	−0.368464	+	1.55101i
$293$	0.436090	+	0.436090i	0.0254766	+	0.0254766i	0.719730	−	0.694254i	$-0.244265\pi$
$293$	0.436090	+	0.436090i	0.0254766	+	0.0254766i	−0.694254	+	0.719730i	$0.744265\pi$
$294$	13.8249	+	27.0532i	0.806284	+	1.57778i
$295$	3.98522	−	1.87738i	0.232028	−	0.109305i
$296$	1.82096	−	11.7689i	0.105841	−	0.684051i
$297$			50.5594i			2.93376i
$298$	19.5204	−	1.55966i	1.13079	−	0.0903487i
$299$	−1.71487	−	0.710322i	−0.0991734	−	0.0410790i
$300$	−18.2634	−	24.1616i	−1.05444	−	1.39497i
$301$	24.2852	−	10.0593i	1.39978	−	0.579806i
$302$	17.6945	+	15.0762i	1.01821	+	0.867537i
$303$	−4.04082	+	9.75540i	−0.232139	+	0.560433i
$304$	12.7058	−	25.2327i	0.728727	−	1.44719i
$305$	−2.55293	+	2.80804i	−0.146180	+	0.160788i
$306$	2.59125	+	35.9032i	0.148132	+	2.05245i
$307$	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	$0.103369\pi$
$308$	−38.9945	+	6.27128i	−2.22192	+	0.357340i
$309$	−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	$-0.900376\pi$
$311$	−24.8032	+	10.2738i	−1.40646	+	0.582576i	−0.455041	+	0.890470i	$0.650376\pi$
$312$	−12.3822	+	9.06393i	−0.701006	+	0.513144i
$313$	−16.7379	+	6.93305i	−0.946080	+	0.391879i	−0.801756	−	0.597651i	$-0.796101\pi$
$313$	−16.7379	+	6.93305i	−0.946080	+	0.391879i	−0.144324	+	0.989530i	$0.546101\pi$
$314$	9.66672	+	8.23629i	0.545525	+	0.464801i
$315$	34.8599	−	38.3433i	1.96413	−	2.16040i
$316$	−20.0830	−	4.77099i	−1.12976	−	0.268389i
$317$	12.6297	+	30.4908i	0.709355	+	1.71253i	0.701607	+	0.712565i	$0.252466\pi$
$317$	12.6297	+	30.4908i	0.709355	+	1.71253i	0.00774841	+	0.999970i	$0.497534\pi$
$318$	−15.6482	+	48.3560i	−0.877509	+	2.71167i
$319$		−	5.47286i		−	0.306421i
$320$	−2.37622	−	17.7300i	−0.132835	−	0.991138i
$321$	−11.9840	−	11.9840i	−0.668882	−	0.668882i
$322$	4.18749	+	3.56785i	0.233360	+	0.198828i
$323$	−0.223677	+	29.1197i	−0.0124457	+	1.62026i
$324$	−3.36314	−	20.9118i	−0.186841	−	1.16177i
$325$	0.850467	+	8.91592i	0.0471754	+	0.494566i
$326$	−5.83942	−	11.4269i	−0.323416	−	0.632876i
$327$	−11.7975	+	11.7975i	−0.652406	+	0.652406i
$328$	4.89629	+	0.757590i	0.270352	+	0.0418309i
$329$	−1.69147	+	4.08357i	−0.0932537	+	0.225134i
$330$	25.0333	+	43.7238i	1.37804	+	2.40691i
$331$	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	$0.232914\pi$
$332$	−1.72423	−	10.7212i	−0.0946294	−	0.588401i
$333$	−9.94690	−	24.0139i	−0.545087	−	1.31596i
$334$	−3.94588	+	12.1935i	−0.215909	+	0.667199i
$335$	−8.07166	−	17.1342i	−0.441002	−	0.936141i
$336$	43.1870	−	14.2599i	2.35605	−	0.777942i
$337$	11.6935	−	28.2306i	0.636986	−	1.53782i	−0.193688	−	0.981063i	$-0.562045\pi$
$337$	11.6935	−	28.2306i	0.636986	−	1.53782i	0.830675	−	0.556758i	$-0.187955\pi$
$338$	−13.8030	+	1.10285i	−0.750786	+	0.0599871i
$339$		−	26.2341i		−	1.42484i
$340$	10.2898	+	15.3010i	0.558044	+	0.829811i
$341$		−	33.7494i		−	1.82763i
$342$	−4.91102	−	61.4653i	−0.265557	−	3.32366i
$343$	−0.133439	+	0.322149i	−0.00720501	+	0.0173944i
$344$	−4.69206	−	19.2410i	−0.252979	−	1.03741i
$345$	2.37439	−	6.60394i	0.127833	−	0.355544i
$346$	4.33599	+	1.40315i	0.233104	+	0.0754337i
$347$	6.39247	+	15.4328i	0.343166	+	0.828476i	0.997392	+	0.0721765i	$0.0229945\pi$
$347$	6.39247	+	15.4328i	0.343166	+	0.828476i	−0.654226	+	0.756299i	$0.727005\pi$
$348$	1.00068	+	6.22221i	0.0536423	+	0.333545i
$349$	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	$0.0962306\pi$
$350$	5.73774	−	25.9176i	0.306695	−	1.38535i
$351$	−6.58849	+	15.9060i	−0.351668	+	0.849001i
$352$	0.177029	+	29.7568i	0.00943566	+	1.58604i
$353$	11.9693	−	11.9693i	0.637061	−	0.637061i	−0.312769	−	0.949829i	$-0.601256\pi$
$353$	11.9693	−	11.9693i	0.637061	−	0.637061i	0.949829	+	0.312769i	$0.101256\pi$
$354$	7.51424	−	3.83996i	0.399377	−	0.204092i
$355$	−16.8826	+	0.803369i	−0.896033	+	0.0426384i
$356$	6.49714	−	1.04490i	0.344348	−	0.0553796i
$357$	−33.4029	+	32.8936i	−1.76787	+	1.74092i
$358$	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	$0.596963\pi$
$360$	−24.5334	−	30.3731i	−1.29302	−	1.60081i
$361$		−	30.8828i		−	1.62541i
$362$	−7.15339	−	2.31487i	−0.375974	−	0.121667i
$363$	−19.3235	−	46.6511i	−1.01422	−	2.44855i
$364$	−13.0849	−	3.10850i	−0.685836	−	0.162930i
$365$	22.5355	+	20.4882i	1.17956	+	1.07240i
$366$	−4.71468	+	5.53350i	−0.246440	+	0.289241i
$367$	18.8104	−	7.79153i	0.981896	−	0.406715i	0.166769	−	0.985996i	$-0.446667\pi$
$367$	18.8104	−	7.79153i	0.981896	−	0.406715i	0.815128	+	0.579281i	$0.196667\pi$
$368$	3.13895	−	2.70686i	0.163629	−	0.141105i
$369$	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
$372$	6.17091	+	38.3704i	0.319947	+	1.98941i
$373$	−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	$0.362265\pi$
$374$	−13.7476	−	27.4198i	−0.710872	−	1.41784i
$375$	−33.5186	+	4.81411i	−1.73089	+	0.248600i
$376$	2.84565	+	1.72988i	0.146753	+	0.0892115i
$377$	0.713178	−	1.72176i	0.0367305	−	0.0886753i
$378$	33.0931	−	38.8405i	1.70212	−	1.99774i
$379$	16.6634	−	6.90220i	0.855940	−	0.354542i	0.0888218	−	0.996048i	$-0.471690\pi$
$379$	16.6634	−	6.90220i	0.855940	−	0.354542i	0.767118	+	0.641505i	$0.221690\pi$
$380$	−17.8270	−	26.0740i	−0.914506	−	1.33757i
$381$	22.0221	+	9.12187i	1.12823	+	0.467327i
$382$	−0.405656	−	5.07710i	−0.0207551	−	0.259767i
$383$		−	22.7411i		−	1.16201i	−0.813898	−	0.581007i	$-0.802659\pi$
$383$		−	22.7411i		−	1.16201i	0.813898	−	0.581007i	$-0.197341\pi$
$384$	−5.64215	−	33.7988i	−0.287925	−	1.72479i
$385$	−14.9401	+	41.5532i	−0.761418	+	2.11775i
$386$	−0.993299	+	0.507601i	−0.0505576	+	0.0258362i
$387$	−30.5656	−	30.5656i	−1.55374	−	1.55374i
$388$	−10.8063	−	2.56718i	−0.548606	−	0.130329i
$389$	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
$393$			21.8138i			1.10036i
$394$	5.65437	+	11.0648i	0.284863	+	0.557435i
$395$	−15.5248	+	17.0761i	−0.781137	+	0.859194i
$396$	34.0673	+	55.2969i	1.71194	+	2.77878i
$397$	−2.58906	−	6.25056i	−0.129941	−	0.313706i	0.845496	−	0.533981i	$-0.179305\pi$
$397$	−2.58906	−	6.25056i	−0.129941	−	0.313706i	−0.975438	+	0.220275i	$0.929305\pi$
$398$	−18.9535	+	9.68571i	−0.950053	+	0.485501i
$399$	56.7838	−	56.7838i	2.84275	−	2.84275i
$400$	−18.6365	−	7.25803i	−0.931827	−	0.362902i
$401$	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	$-0.0374614\pi$
$402$	−16.5097	−	32.3070i	−0.823428	−	1.61133i
$403$	4.39795	−	10.6176i	0.219077	−	0.528900i
$404$	1.10714	+	6.88415i	0.0550824	+	0.342499i
$405$	−22.2840	−	8.01202i	−1.10730	−	0.398120i
$406$	−3.58219	+	4.20433i	−0.177781	+	0.208657i
$407$	15.6614	+	15.6614i	0.776306	+	0.776306i
$408$	20.6435	+	28.6605i	1.02201	+	1.41890i
$409$		−	14.3152i		−	0.707843i	−0.935275	−	0.353922i	$-0.884848\pi$
$409$		−	14.3152i		−	0.707843i	0.935275	−	0.353922i	$-0.115152\pi$
$410$	3.38803	−	4.38243i	0.167323	−	0.216433i
$411$	−7.69594	+	3.18776i	−0.379613	+	0.157241i
$412$	−23.5707	+	32.6052i	−1.16125	+	1.60634i
$413$	6.83288	+	2.83027i	0.336224	+	0.139269i
$414$	2.78534	−	8.60722i	0.136892	−	0.423022i
$415$	−11.4247	−	4.10764i	−0.560815	−	0.201636i
$416$	−3.82197	+	9.38457i	−0.187387	+	0.460116i
$417$			29.9225i			1.46531i
$418$	23.9094	+	46.7871i	1.16945	+	2.28843i
$419$	12.9848	−	31.3482i	0.634351	−	1.53146i	−0.199750	−	0.979847i	$-0.564013\pi$
$419$	12.9848	−	31.3482i	0.634351	−	1.53146i	0.834101	−	0.551612i	$-0.185987\pi$
$420$	9.38791	−	49.9745i	0.458083	−	2.43850i
$421$	−40.5529			−1.97642			−0.988212	−	0.153088i	$-0.951078\pi$
$421$	−40.5529			−1.97642			−0.988212	+	0.153088i	$0.951078\pi$
$422$	−9.53874	−	3.08678i	−0.464339	−	0.150262i
$423$	7.26852			0.353408
$424$	7.95123	+	32.6061i	0.386146	+	1.58349i
$425$	20.5368	−	1.79989i	0.996181	−	0.0873073i
$426$	−32.2732	+	2.57859i	−1.56364	+	0.124933i
$427$	−6.37140			−0.308333
$428$	−10.8883	−	2.58667i	−0.526307	−	0.125031i
$429$		−	28.5395i		−	1.37790i
$430$	−21.3671	−	5.80829i	−1.03041	−	0.280100i
$431$	7.30907	−	17.6457i	0.352066	−	0.849962i	−0.644299	−	0.764773i	$-0.722851\pi$
$431$	7.30907	−	17.6457i	0.352066	−	0.849962i	0.996365	−	0.0851882i	$-0.0271491\pi$
$432$	−25.1071	−	29.1149i	−1.20796	−	1.40079i
$433$	32.6666			1.56986			0.784929	−	0.619586i	$-0.212699\pi$
$433$	32.6666			1.56986			0.784929	+	0.619586i	$0.212699\pi$
$434$	−22.0903	+	25.9268i	−1.06037	+	1.24453i
$435$	6.63049	+	2.38393i	0.317908	+	0.114301i
$436$	−2.54642	+	10.7189i	−0.121952	+	0.513343i
$437$	2.80071	−	6.76150i	0.133976	−	0.323447i
$438$	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	$0.542268\pi$
$440$	29.2183	+	15.9112i	1.39293	+	0.758536i
$441$	43.7869			2.08509
$442$	−0.751885	−	10.4178i	−0.0357635	−	0.495522i
$443$	−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	$0.812397\pi$
$444$	−20.6694	−	14.9422i	−0.980925	−	0.709123i
$445$	2.48927	−	6.92346i	0.118003	−	0.328204i
$446$	−2.28497	−	28.5983i	−0.108197	−	1.35417i
$447$	16.0494	−	38.7467i	0.759112	−	1.83266i
$448$	19.3410	−	22.9755i	0.913774	−	1.08549i
$449$	−20.7974	−	8.61456i	−0.981490	−	0.406546i	−0.166513	−	0.986039i	$-0.553251\pi$
$449$	−20.7974	−	8.61456i	−0.981490	−	0.406546i	−0.814977	+	0.579493i	$0.803251\pi$
$450$	−42.9868	+	7.59288i	−2.02642	+	0.357932i
$451$	−6.51573	+	6.51573i	−0.306814	+	0.306814i
$452$	−9.08656	−	14.7490i	−0.427396	−	0.693736i
$453$	45.9957	−	19.0520i	2.16107	−	0.895143i
$454$	5.03031	+	9.84357i	0.236084	+	0.461982i
$455$	−10.1150	+	11.1258i	−0.474200	+	0.521586i
$456$	−35.7379	−	48.8216i	−1.67358	−	2.28628i
$457$	20.5201			0.959888			0.479944	−	0.877299i	$-0.340657\pi$
$457$	20.5201			0.959888			0.479944	+	0.877299i	$0.340657\pi$
$458$	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	$-0.411988\pi$
$461$	26.5167	−	26.5167i	1.23500	−	1.23500i	0.962018	−	0.272987i	$-0.0880116\pi$
$462$	−26.0427	+	80.4770i	−1.21162	+	3.74413i
$463$	−6.03987	−	6.03987i	−0.280697	−	0.280697i	0.552690	−	0.833387i	$-0.313601\pi$
$463$	−6.03987	−	6.03987i	−0.280697	−	0.280697i	−0.833387	+	0.552690i	$0.813601\pi$
$464$	2.71774	+	3.15157i	0.126168	+	0.146308i
$465$	40.8882	+	14.7010i	1.89614	+	0.681742i
$466$	−28.0594	−	9.08014i	−1.29982	−	0.420629i
$467$			0.0694021i			0.00321155i	0.999999	+	0.00160577i	$0.000511134\pi$
$467$			0.0694021i			0.00321155i	−0.999999	+	0.00160577i	$0.999489\pi$
$468$	3.51174	+	21.8358i	0.162330	+	1.00936i
$469$	12.1686	−	29.3776i	0.561893	−	1.35653i
$470$	3.23117	−	1.84995i	0.149043	−	0.0853318i
$471$	25.1280	−	10.4083i	1.15784	−	0.479591i
$472$	2.89454	−	4.76152i	0.133232	−	0.219167i
$473$	34.0299	+	14.0956i	1.56470	+	0.648118i
$474$	−28.6707	+	33.6501i	−1.31689	+	1.54560i
$475$	−35.1543	+	3.35328i	−1.61299	+	0.153859i
$476$	−7.38617	+	30.0626i	−0.338545	+	1.37792i
$477$	51.7969	+	51.7969i	2.37162	+	2.37162i
$478$	1.42173	+	17.7941i	0.0650285	+	0.813884i
$479$	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
$482$	2.40845	+	4.71299i	0.109702	+	0.214671i
$483$	10.8851	−	4.50875i	0.495289	−	0.205155i
$484$	−27.0221	−	19.5346i	−1.22828	−	0.887938i
$485$	−8.35358	+	9.18832i	−0.379316	+	0.417220i
$486$	−4.36133	−	1.41135i	−0.197834	−	0.0640201i
$487$	−0.0459446	−	0.110920i	−0.00208195	−	0.00502627i	0.922835	−	0.385195i	$-0.125866\pi$
$487$	−0.0459446	−	0.110920i	−0.00208195	−	0.00502627i	−0.924917	+	0.380169i	$0.875866\pi$
$488$	−0.734023	+	4.74397i	−0.0332277	+	0.214750i
$489$	−27.4827			−1.24281
$490$	19.4651	−	11.1444i	0.879345	−	0.503455i
$491$	−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
$493$	−3.95037	−	1.67196i	−0.177916	−	0.0753014i
$494$	1.42499	+	17.8349i	0.0641135	+	0.802431i
$495$	72.5327	−	3.45152i	3.26010	−	0.155135i
$496$	16.7595	+	19.4348i	0.752523	+	0.872646i
$497$	−20.0645	−	20.0645i	−0.900018	−	0.900018i
$498$	−22.1264	−	7.16021i	−0.991507	−	0.320857i
$499$	−13.9575	+	33.6965i	−0.624826	+	1.50846i	0.221149	+	0.975240i	$0.429019\pi$
$499$	−13.9575	+	33.6965i	−0.624826	+	1.50846i	−0.845975	+	0.533223i	$0.820981\pi$
$500$	−17.1770	+	14.3162i	−0.768177	+	0.640238i
$501$	19.4084	+	19.4084i	0.867102	+	0.867102i
$502$	30.8950	−	2.46848i	1.37891	−	0.110174i
$503$	9.04727	+	21.8420i	0.403398	+	0.973888i	0.986835	+	0.161730i	$0.0517073\pi$
$503$	9.04727	+	21.8420i	0.403398	+	0.973888i	−0.583437	+	0.812158i	$0.698293\pi$
$504$	10.0230	−	64.7782i	0.446459	−	2.88545i
$505$	7.33587	+	2.63755i	0.326442	+	0.117369i
$506$	0.613968	+	7.68431i	0.0272942	+	0.341609i
$507$	−11.3487	+	27.3981i	−0.504013	+	1.21679i
$508$	15.5405	−	2.49930i	0.689498	−	0.110888i
$509$	−6.98751			−0.309716			−0.154858	−	0.987937i	$-0.549492\pi$
$509$	−6.98751			−0.309716			−0.154858	+	0.987937i	$0.549492\pi$
$510$	39.2080	−	4.71170i	1.73616	−	0.208638i
$511$			51.1327i			2.26198i
$512$	−14.8787	−	17.0477i	−0.657553	−	0.753408i
$513$	−62.7154	−	25.9776i	−2.76895	−	1.14694i
$514$	−1.52106	−	19.0373i	−0.0670911	−	0.839699i
$515$	19.1696	+	40.6924i	0.844713	+	1.79312i
$516$	−41.2666	−	9.80344i	−1.81666	−	0.431572i
$517$	−5.72214	+	2.37019i	−0.251660	+	0.104241i
$518$	−1.78033	−	22.2823i	−0.0782233	−	0.979027i
$519$	6.90158	−	6.90158i	0.302946	−	0.302946i
$520$	7.11866	+	8.81315i	0.312174	+	0.386482i
$521$	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	$0.452887\pi$
$522$	8.64183	+	2.79654i	0.378242	+	0.122401i
$523$	24.5138	−	24.5138i	1.07191	−	1.07191i	0.0747091	−	0.997205i	$-0.476197\pi$
$523$	24.5138	−	24.5138i	1.07191	−	1.07191i	0.997205	−	0.0747091i	$-0.0238028\pi$
$524$	7.55551	+	12.2639i	0.330064	+	0.535750i
$525$	−43.8349	−	36.2005i	−1.91311	−	1.57992i
$526$	41.1648	−	3.28903i	1.79487	−	0.143409i
$527$	−24.3607	−	10.3105i	−1.06117	−	0.449131i
$528$	56.9208	+	28.6622i	2.47716	+	1.24736i
$529$	−15.5042	+	15.5042i	−0.674095	+	0.674095i
$530$	36.2090	+	9.84280i	1.57282	+	0.427544i
$531$		−	12.1621i		−	0.527792i
$532$	12.2564	−	51.5921i	0.531382	−	2.23680i
$533$	−2.89893	+	1.20078i	−0.125567	+	0.0520114i
$534$	4.33915	−	13.4088i	0.187774	−	0.580256i
$535$	−8.41701	+	9.25809i	−0.363899	+	0.400262i
$536$	−20.4719	−	12.4449i	−0.884250	−	0.537537i
$537$	−18.3319	−	44.2572i	−0.791082	−	1.90984i
$538$	−1.79609	−	3.51467i	−0.0774347	−	0.151528i
$539$	−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	$0.0517731\pi$
$541$	9.38592	+	22.6596i	0.403532	+	0.974212i	−0.583270	+	0.812279i	$0.698227\pi$
$542$	−11.5493	+	0.922774i	−0.496083	+	0.0396365i
$543$	−11.3860	+	11.3860i	−0.488621	+	0.488621i
$544$	21.5329	+	8.96294i	0.923215	+	0.384283i
$545$	9.11404	+	8.28605i	0.390403	+	0.354935i
$546$	−18.6802	+	21.9244i	−0.799437	+	0.938279i
$547$	−0.909187	+	2.19497i	−0.0388740	+	0.0938502i	−0.942124	−	0.335264i	$-0.891174\pi$
$547$	−0.909187	+	2.19497i	−0.0388740	+	0.0938502i	0.903250	+	0.429115i	$0.141174\pi$
$548$	−3.22259	+	4.45778i	−0.137662	+	0.190427i
$549$	4.00955	+	9.67991i	0.171123	+	0.413129i
$550$	31.3654	−	19.9950i	1.33743	−	0.852592i
$551$	6.78869	+	2.81197i	0.289208	+	0.119794i
$552$	−2.10307	−	8.62419i	−0.0895126	−	0.367070i
$553$	−38.7455			−1.64763
$554$	−15.5069	−	5.01811i	−0.658825	−	0.213199i
$555$	−25.7961	+	12.1522i	−1.09498	+	0.515830i
$556$	10.3641	+	16.8226i	0.439534	+	0.713438i
$557$	4.04204	−	4.04204i	0.171267	−	0.171267i	−0.616269	−	0.787536i	$-0.711357\pi$
$557$	4.04204	−	4.04204i	0.171267	−	0.171267i	0.787536	+	0.616269i	$0.211357\pi$
$558$	53.2915	+	17.2454i	2.25601	+	0.730055i
$559$	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
$563$		−	10.6657i		−	0.449505i	−0.974416	−	0.224753i	$-0.927843\pi$
$563$		−	10.6657i		−	0.449505i	0.974416	−	0.224753i	$-0.0721574\pi$
$564$	6.07225	−	3.74098i	0.255688	−	0.157524i
$565$	−19.3462	+	0.920605i	−0.813902	+	0.0387301i
$566$	−7.35345	+	3.75780i	−0.309089	+	0.157952i
$567$	−15.2141	−	36.7301i	−0.638933	−	1.54252i
$568$	−17.2511	+	12.6280i	−0.723839	+	0.529858i
$569$	0.420694	+	0.420694i	0.0176364	+	0.0176364i	0.715870	−	0.698234i	$-0.246030\pi$
$569$	0.420694	+	0.420694i	0.0176364	+	0.0176364i	−0.698234	+	0.715870i	$0.746030\pi$
$570$	−67.0984	+	8.58667i	−2.81044	+	0.359656i
$571$	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	$-0.00995544\pi$
$572$	−9.88505	−	16.0451i	−0.413315	−	0.670879i
$573$	−10.0777	−	4.17433i	−0.421003	−	0.174385i
$574$	9.27027	−	0.740685i	0.386934	−	0.0309156i
$575$	−4.95336	−	1.51924i	−0.206570	−	0.0633565i
$576$	−47.0775	−	14.9257i	−1.96156	−	0.621903i
$577$	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	$0.249938\pi$
$578$	−23.9918	+	1.54643i	−0.997929	+	0.0643229i
$579$			2.38898i			0.0992825i
$580$	4.55342	−	0.956299i	0.189070	−	0.0397081i
$581$	−7.80005	−	18.8310i	−0.323600	−	0.781241i
$582$	−15.4271	+	18.1064i	−0.639476	+	0.750536i
$583$	−57.6675	−	23.8867i	−2.38834	−	0.989285i
$584$	38.0721	+	5.89080i	1.57543	+	0.243763i
$585$	23.2686	+	8.36602i	0.962039	+	0.345892i
$586$	0.565646	−	0.663884i	0.0233666	−	0.0274248i
$587$			13.9917i			0.577497i	0.957405	+	0.288749i	$0.0932392\pi$
$587$			13.9917i			0.577497i	−0.957405	+	0.288749i	$0.906761\pi$
$588$	36.5803	−	22.5364i	1.50855	−	0.929385i
$589$	41.8638	+	17.3405i	1.72497	+	0.714504i
$590$	−3.09545	−	5.40659i	−0.127438	−	0.222586i
$591$	26.6118			1.09466
$592$	−16.7959	−	1.24146i	−0.690307	−	0.0510239i
$593$		−	20.0242i		−	0.822296i	−0.911569	−	0.411148i	$-0.865128\pi$
$593$		−	20.0242i		−	0.822296i	0.911569	−	0.411148i	$-0.134872\pi$
$594$	71.2747	−	5.69478i	2.92444	−	0.233660i
$595$	25.4294	+	23.4785i	1.04250	+	0.962524i
$596$	−4.39737	−	27.3427i	−0.180123	−	1.12000i
$597$			45.5849i			1.86567i
$598$	−0.808201	+	2.49749i	−0.0330498	+	0.102130i
$599$			13.2866i			0.542876i	0.962456	+	0.271438i	$0.0874992\pi$
$599$			13.2866i			0.542876i	−0.962456	+	0.271438i	$0.912501\pi$
$600$	−32.0040	+	28.4678i	−1.30656	+	1.16219i
$601$	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	$0.449270\pi$
$602$	−16.9161	−	33.1023i	−0.689450	−	1.34915i
$603$	−52.2904			−2.12943
$604$	19.2602	−	26.6425i	0.783686	−	1.08407i
$605$	−33.7246	+	15.8871i	−1.37110	+	0.645903i
$606$	14.2075	+	4.59762i	0.577141	+	0.186766i
$607$	9.00960	−	21.7511i	0.365688	−	0.882850i	−0.628757	−	0.777601i	$-0.716436\pi$
$607$	9.00960	−	21.7511i	0.365688	−	0.882850i	0.994446	−	0.105249i	$-0.0335638\pi$
$608$	−37.0021	−	15.0695i	−1.50063	−	0.611150i
$609$	4.52688	+	10.9289i	0.183438	+	0.442860i
$610$	4.24610	+	3.28264i	0.171920	+	0.132910i
$611$	−2.10905			−0.0853232
$612$	50.3216	−	7.69691i	2.03413	−	0.311129i
$613$	−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	$0.339639\pi$
$614$	−16.7690	−	14.2876i	−0.676741	−	0.576601i
$615$	−5.05575	−	10.7322i	−0.203868	−	0.432762i
$616$	13.2329	+	54.2650i	0.533170	+	2.18640i
$617$	5.52489	+	2.28848i	0.222424	+	0.0921309i	0.491113	−	0.871096i	$-0.336590\pi$
$617$	5.52489	+	2.28848i	0.222424	+	0.0921309i	−0.268689	+	0.963227i	$0.586590\pi$
$618$	39.2093	+	76.7267i	1.57723	+	3.08640i
$619$	−10.2812	−	4.25862i	−0.413237	−	0.171168i	0.166372	−	0.986063i	$-0.446795\pi$
$619$	−10.2812	−	4.25862i	−0.413237	−	0.171168i	−0.579609	+	0.814895i	$0.696795\pi$
$620$	28.0795	−	5.89720i	1.12770	−	0.236837i
$621$	−7.04240	−	7.04240i	−0.282602	−	0.282602i
$622$	17.2770	+	33.8084i	0.692743	+	1.35559i
$623$	11.4118	−	4.72690i	0.457202	−	0.189379i
$624$	14.1723	+	16.4346i	0.567346	+	0.657910i
$625$	4.72637	+	24.5492i	0.189055	+	0.981967i
$626$	11.6589	+	22.8148i	0.465985	+	0.911863i
$627$	112.527			4.49391
$628$	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	$-0.884106\pi$
$631$	−14.5279	+	14.5279i	−0.578348	+	0.578348i	0.356100	+	0.934448i	$0.384106\pi$
$632$	−4.46371	+	28.8489i	−0.177557	+	1.14755i
$633$	−15.1828	+	15.1828i	−0.603461	+	0.603461i
$634$	41.5610	−	21.2387i	1.65060	−	0.843497i
$635$	5.95408	−	16.5602i	0.236280	−	0.657172i
$636$	69.9310	+	16.6130i	2.77294	+	0.658750i
$637$	−12.7053			−0.503403
$638$	−7.71520	+	0.616437i	−0.305448	+	0.0244050i
$639$	−17.8569	+	43.1103i	−0.706407	+	1.70542i
$640$	−24.7267	+	5.34684i	−0.977410	+	0.211352i
$641$	−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
$643$	13.4618	+	5.57608i	0.530883	+	0.219899i	0.631990	−	0.774976i	$-0.282238\pi$
$643$	13.4618	+	5.57608i	0.530883	+	0.219899i	−0.101107	+	0.994876i	$0.532238\pi$
$644$	4.55801	−	6.30506i	0.179611	−	0.248454i
$645$	−31.9003	+	35.0880i	−1.25607	+	1.38159i
$646$	41.0758	−	2.96458i	1.61611	−	0.116640i
$647$	−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	$0.955382\pi$
$648$	−29.1011	+	7.09650i	−1.14320	+	0.278777i
$649$	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
$652$	−15.4510	+	9.51902i	−0.605107	+	0.372794i
$653$	−1.78998	−	4.32140i	−0.0700474	−	0.169109i	0.884978	−	0.465632i	$-0.154173\pi$
$653$	−1.78998	−	4.32140i	−0.0700474	−	0.169109i	−0.955026	+	0.296523i	$0.904173\pi$
$654$	17.9601	+	15.3024i	0.702294	+	0.598372i
$655$	16.0865	−	0.765487i	0.628550	−	0.0299100i
$656$	0.516496	−	6.98773i	0.0201658	−	0.272825i
$657$	77.6848	−	32.1781i	3.03077	−	1.25539i
$658$	5.94721	+	1.92455i	0.231846	+	0.0750266i
$659$	23.2842			0.907024			0.453512	−	0.891250i	$-0.350171\pi$
$659$	23.2842			0.907024			0.453512	+	0.891250i	$0.350171\pi$
$660$	58.8187	−	40.2148i	2.28951	−	1.56536i
$661$	−1.86790	+	1.86790i	−0.0726528	+	0.0726528i	−0.742499	−	0.669847i	$-0.766360\pi$
$661$	−1.86790	+	1.86790i	−0.0726528	+	0.0726528i	0.669847	+	0.742499i	$0.266360\pi$
$662$	−2.10152	−	1.79055i	−0.0816778	−	0.0695916i
$663$	−20.6001	−	8.71883i	−0.800043	−	0.338611i
$664$	−14.9197	+	3.63827i	−0.578995	+	0.141192i
$665$	−43.8676	−	39.8823i	−1.70111	−	1.54657i
$666$	−32.7326	+	16.7272i	−1.26836	+	0.648165i
$667$	0.762312	+	0.762312i	0.0295168	+	0.0295168i
$668$	17.6339	+	4.18917i	0.682276	+	0.162084i
$669$	−56.7657	−	23.5131i	−2.19469	−	0.909071i
$670$	−23.2453	+	13.3087i	−0.898044	+	0.514160i
$671$	−6.31304	−	6.31304i	−0.243712	−	0.243712i
$672$	−24.9669	−	59.2755i	−0.963118	−	2.28660i
$673$	−37.5247	+	15.5432i	−1.44647	+	0.599148i	−0.961357	−	0.275304i	$-0.911222\pi$
$673$	−37.5247	+	15.5432i	−1.44647	+	0.599148i	−0.485113	+	0.874451i	$0.661222\pi$
$674$	−41.1144	−	13.3048i	−1.58367	−	0.512483i
$675$	−14.0914	+	45.9442i	−0.542380	+	1.76839i
$676$	3.10942	+	19.3342i	0.119593	+	0.743623i
$677$	−24.3641	−	10.0919i	−0.936388	−	0.387865i	−0.138290	−	0.990392i	$-0.544160\pi$
$677$	−24.3641	−	10.0919i	−0.936388	−	0.387865i	−0.798098	+	0.602527i	$0.794160\pi$
$678$	−36.9828	+	2.95489i	−1.42032	+	0.113482i
$679$	−20.8482			−0.800079
$680$	20.4111	−	16.2292i	0.782730	−	0.622362i
$681$	23.6747			0.907217
$682$	−47.5773	+	3.80138i	−1.82183	+	0.145562i
$683$	40.2494	+	16.6719i	1.54010	+	0.637931i	0.981493	−	0.191500i	$-0.0613351\pi$
$683$	40.2494	+	16.6719i	1.54010	+	0.637931i	0.558609	+	0.829431i	$0.311335\pi$
$684$	−86.0958	+	13.8463i	−3.29195	+	0.529427i
$685$	2.62087	+	5.56347i	0.100138	+	0.212569i
$686$	0.469171	+	0.151826i	0.0179130	+	0.00579674i
$687$	35.1277	−	14.5503i	1.34020	−	0.555130i
$688$	−26.5960	+	8.78171i	−1.01396	+	0.334800i
$689$	−15.0295	−	15.0295i	−0.572579	−	0.572579i
$690$	−9.57715	−	2.60339i	−0.364596	−	0.0991092i
$691$	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	$0.527354\pi$
$692$	1.48966	−	6.27058i	0.0566284	−	0.238372i
$693$	86.2036	+	86.2036i	3.27460	+	3.27460i
$694$	21.0359	−	10.7499i	0.798512	−	0.408060i
$695$	22.0662	−	1.05004i	0.837018	−	0.0398301i
$696$	8.65886	−	2.11153i	0.328213	−	0.0800372i
$697$	2.71257	+	6.69369i	0.102746	+	0.253542i
$698$	−18.6827	−	15.9181i	−0.707149	−	0.602509i
$699$	−44.6620	+	44.6620i	−1.68927	+	1.68927i
$700$	−37.1829	−	5.16937i	−1.40538	−	0.195384i
$701$	−21.1933			−0.800459			−0.400230	−	0.916415i	$-0.631070\pi$
$701$	−21.1933			−0.800459			−0.400230	+	0.916415i	$0.631070\pi$
$702$	23.1651	+	7.49635i	0.874312	+	0.282932i
$703$	−27.4737	+	11.3800i	−1.03619	+	0.429204i
$704$	41.9288	−	3.60123i	1.58025	−	0.135726i
$705$	−0.379018	−	7.96494i	−0.0142746	−	0.299977i
$706$	−18.2215	−	15.5252i	−0.685776	−	0.584298i
$707$	5.00847	+	12.0915i	0.188363	+	0.454748i
$708$	−6.25965	−	10.1605i	−0.235252	−	0.381854i
$709$	−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
$712$	−2.20483	−	9.04146i	−0.0826293	−	0.338843i
$713$	4.70095	+	4.70095i	0.176052	+	0.176052i
$714$	50.1332	+	43.3838i	1.87619	+	1.62360i
$715$	−21.0463	+	1.00150i	−0.787087	+	0.0374541i
$716$	−25.6355	−	18.5322i	−0.958043	−	0.692581i
$717$	35.3202	+	14.6301i	1.31906	+	0.546371i
$718$	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	$0.606628\pi$
$720$	−40.0543	+	38.0063i	−1.49274	+	1.41641i
$721$	−28.8995	+	69.7695i	−1.07627	+	2.59835i
$722$	−43.5361	+	3.47849i	−1.62025	+	0.129456i
$723$	11.3352			0.421560
$724$	−2.45760	+	10.3450i	−0.0913359	+	0.384469i
$725$	1.52534	−	4.97328i	0.0566498	−	0.184703i
$726$	−63.5886	+	32.4954i	−2.35999	+	1.20602i
$727$	0.889602	−	0.889602i	0.0329935	−	0.0329935i	−0.690418	−	0.723411i	$-0.742573\pi$
$727$	0.889602	−	0.889602i	0.0329935	−	0.0329935i	0.723411	+	0.690418i	$0.242573\pi$
$728$	−2.90829	+	18.7962i	−0.107788	+	0.696634i
$729$	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
$733$	21.5937			0.797580			0.398790	−	0.917042i	$-0.369430\pi$
$733$	21.5937			0.797580			0.398790	+	0.917042i	$0.369430\pi$
$734$	−13.1026	−	25.6399i	−0.483626	−	0.946384i
$735$	−2.28327	−	47.9823i	−0.0842198	−	1.76985i
$736$	−4.16947	−	4.12015i	−0.153689	−	0.151871i
$737$	41.1656	−	17.0514i	1.51635	−	0.628095i
$738$	−6.95913	−	13.6180i	−0.256169	−	0.501285i
$739$	29.1372	+	29.1372i	1.07183	+	1.07183i	0.997212	+	0.0746157i	$0.0237730\pi$
$739$	29.1372	+	29.1372i	1.07183	+	1.07183i	0.0746157	+	0.997212i	$0.476227\pi$
$740$	−10.2937	+	15.7669i	−0.378404	+	0.579602i
$741$	35.4012	+	14.6636i	1.30049	+	0.538683i
$742$	28.6663	+	56.0957i	1.05237	+	2.05934i
$743$	12.3325	+	5.10828i	0.452435	+	0.187405i	0.597252	−	0.802054i	$-0.296259\pi$
$743$	12.3325	+	5.10828i	0.452435	+	0.187405i	−0.144817	+	0.989458i	$0.546259\pi$
$744$	53.3965	−	13.0211i	1.95761	−	0.477378i
$745$	−29.1368	−	10.4759i	−1.06749	−	0.383806i
$746$	14.3628	+	12.2375i	0.525860	+	0.448046i
$747$	−23.7009	+	23.7009i	−0.867169	+	0.867169i
$748$	−37.1058	+	22.4687i	−1.35672	+	0.821538i
$749$	−21.0065			−0.767559
$750$	10.5619	+	46.7096i	0.385667	+	1.70559i
$751$	−7.98817	−	19.2851i	−0.291492	−	0.703725i	0.708506	−	0.705705i	$-0.249370\pi$
$751$	−7.98817	−	19.2851i	−0.291492	−	0.703725i	−0.999998	+	0.00198023i	$0.999370\pi$
$752$	2.11812	−	4.20642i	0.0772399	−	0.153392i
$753$	25.4015	−	61.3247i	0.925682	−	2.23479i
$754$	−2.50753	−	0.811450i	−0.0913190	−	0.0295513i
$755$	−15.6639	−	33.2507i	−0.570068	−	1.21012i
$756$	−58.4817	−	42.2772i	−2.12696	−	1.53761i
$757$	28.0814			1.02064			0.510318	−	0.859986i	$-0.329528\pi$
$757$	28.0814			1.02064			0.510318	+	0.859986i	$0.329528\pi$
$758$	−11.6071	−	22.7133i	−0.421587	−	0.824984i
$759$	15.2528	+	6.31794i	0.553643	+	0.229327i
$760$	−34.7491	+	28.0680i	−1.26048	+	1.01813i
$761$		−	14.3263i		−	0.519329i	−0.965699	−	0.259664i	$-0.916388\pi$
$761$		−	14.3263i		−	0.519329i	0.965699	−	0.259664i	$-0.0836119\pi$
$762$	10.3788	−	32.0725i	0.375985	−	1.16186i
$763$			20.6796i			0.748653i
$764$	−7.11161	+	1.14372i	−0.257289	+	0.0413784i
$765$	19.6675	−	53.4095i	0.711079	−	1.93102i
$766$	−32.0586	+	2.56145i	−1.15832	+	0.0925489i
$767$			3.52900i			0.127425i
$768$	−47.0113	+	11.7608i	−1.69637	+	0.424381i
$769$	41.2329			1.48690			0.743448	−	0.668794i	$-0.233189\pi$
$769$	41.2329			1.48690			0.743448	+	0.668794i	$0.233189\pi$
$770$	60.2613	+	16.3810i	2.17166	+	0.590330i
$771$	−37.7878	−	15.6522i	−1.36089	−	0.563701i
$772$	0.827456	+	1.34310i	0.0297808	+	0.0483393i
$773$			7.28782i			0.262125i	0.991374	+	0.131062i	$0.0418388\pi$
$773$			7.28782i			0.262125i	−0.991374	+	0.131062i	$0.958161\pi$
$774$	−39.6462	+	46.5317i	−1.42505	+	1.67255i
$775$	9.40632	−	30.6687i	0.337885	−	1.10165i
$776$	−2.40183	+	15.5230i	−0.0862208	+	0.557243i
$777$	−44.2289	−	18.3202i	−1.58670	−	0.657234i
$778$	16.2606	−	19.0846i	0.582970	−	0.684217i
$779$	−4.73450	−	11.4301i	−0.169631	−	0.409526i
$780$	23.7449	−	4.98684i	0.850202	−	0.178557i
$781$		−	39.7615i		−	1.42278i
$782$	5.73419	+	1.90439i	0.205054	+	0.0681009i
$783$	7.07072	−	7.07072i	0.252687	−	0.252687i
$784$	12.7600	−	25.3402i	0.455713	−	0.905009i
$785$	−8.55737	−	18.1652i	−0.305426	−	0.648346i
$786$	30.7514	−	2.45700i	1.09686	−	0.0876384i
$787$	−43.4239	−	17.9868i	−1.54789	−	0.641159i	−0.564960	−	0.825118i	$-0.691109\pi$
$787$	−43.4239	−	17.9868i	−1.54789	−	0.641159i	−0.982934	+	0.183959i	$0.941109\pi$
$788$	14.9613	−	9.21737i	0.532976	−	0.328355i
$789$	33.8452	−	81.7095i	1.20492	−	2.90894i
$790$	25.8212	+	19.9623i	0.918678	+	0.710225i
$791$	−22.9926	−	22.9926i	−0.817522	−	0.817522i
$792$	74.1161	−	54.2537i	2.63360	−	1.92782i
$793$	−1.16342	−	2.80875i	−0.0413143	−	0.0997416i
$794$	−8.51992	+	4.35389i	−0.302361	+	0.154514i
$795$	54.0588	−	59.4607i	1.91727	−	2.10885i
$796$	15.7890	+	25.6282i	0.559626	+	0.908367i
$797$			17.8210i			0.631251i	0.948884	+	0.315626i	$0.102214\pi$
$797$			17.8210i			0.631251i	−0.948884	+	0.315626i	$0.897786\pi$
$798$	−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
$802$	−26.3251	−	8.51891i	−0.929570	−	0.300813i
$803$	−50.6644	+	50.6644i	−1.78791	+	1.78791i
$804$	−43.6843	+	26.9130i	−1.54063	+	0.949147i
$805$	−3.70694	−	7.86894i	−0.130652	−	0.277344i
$806$	−15.4632	−	5.00396i	−0.544668	−	0.176257i
$807$	−8.45311			−0.297564
$808$	9.58003	−	2.33616i	0.337024	−	0.0821858i
$809$	−21.4485	−	8.88425i	−0.754088	−	0.312354i	−0.0276799	−	0.999617i	$-0.508812\pi$
$809$	−21.4485	−	8.88425i	−0.754088	−	0.312354i	−0.726408	+	0.687263i	$0.758812\pi$
$810$	−8.78474	+	32.3167i	−0.308664	+	1.13549i
$811$	−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
$813$	−9.49565	+	22.9245i	−0.333027	+	0.803998i
$814$	20.3142	−	23.8422i	0.712011	−	0.835669i
$815$	0.964419	+	20.2670i	0.0337821	+	0.709921i
$816$	38.0781	−	32.3298i	1.33300	−	1.13177i
$817$	−34.9693	+	34.9693i	−1.22342	+	1.22342i
$818$	−20.1805	+	1.61240i	−0.705595	+	0.0563763i
$819$	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	$-0.794693\pi$
$821$	−26.9068	+	11.1452i	−0.939054	+	0.388969i	−0.139948	+	0.990159i	$0.544693\pi$
$822$	5.36069	+	10.4901i	0.186976	+	0.365883i
$823$	21.5625	+	52.0564i	0.751620	+	1.81457i	0.550128	+	0.835080i	$0.314579\pi$
$823$	21.5625	+	52.0564i	0.751620	+	1.81457i	0.201492	+	0.979490i	$0.435421\pi$
$824$	48.6191	+	29.5556i	1.69373	+	1.02962i
$825$	−7.56445	−	79.3024i	−0.263360	−	2.76095i
$826$	3.22027	−	9.95125i	0.112048	−	0.346248i
$827$	0.526605	−	0.218127i	0.0183119	−	0.00758502i	−0.373509	−	0.927627i	$-0.621845\pi$
$827$	0.526605	−	0.218127i	0.0183119	−	0.00758502i	0.391821	+	0.920042i	$0.371845\pi$
$828$	−12.4475	−	2.95707i	−0.432581	−	0.102765i
$829$		−	25.0999i		−	0.871755i	−0.900006	−	0.435877i	$-0.856438\pi$
$829$		−	25.0999i		−	0.871755i	0.900006	−	0.435877i	$-0.143562\pi$
$830$	−4.50380	+	16.5683i	−0.156329	+	0.575093i
$831$	−24.6823	+	24.6823i	−0.856219	+	0.856219i
$832$	13.6601	+	4.33087i	0.473579	+	0.150146i
$833$	−0.224631	+	29.2438i	−0.00778299	+	1.01324i
$834$	42.1823	−	3.37033i	1.46065	−	0.116705i
$835$	13.6315	−	14.9937i	0.471739	−	0.518878i
$836$	63.2637	−	38.9755i	2.18802	−	1.34799i
$837$	43.6029	−	43.6029i	1.50714	−	1.50714i
$838$	−45.6547	−	14.7741i	−1.57712	−	0.510362i
$839$	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	$0.463934\pi$
$840$	−71.5075	−	7.60544i	−2.46724	−	0.262413i
$841$	19.7407	−	19.7407i	0.680714	−	0.680714i
$842$	4.56768	+	57.1682i	0.157413	+	1.97015i
$843$	26.9759	−	11.1738i	0.929098	−	0.384845i
$844$	−3.27710	+	13.7946i	−0.112803	+	0.474831i
$845$	20.6029	+	7.40757i	0.708760	+	0.254828i
$846$	−0.818692	−	10.2466i	−0.0281472	−	0.352285i
$847$	−57.8227	−	23.9509i	−1.98681	−	0.822964i
$848$	45.0699	−	14.8816i	1.54771	−	0.511036i
$849$			17.6857i			0.606973i
$850$	−4.85051	−	28.7484i	−0.166371	−	0.986063i
$851$	−4.36294			−0.149560
$852$	7.27020	+	45.2057i	0.249073	+	1.54872i
$853$	10.5234	−	25.4058i	0.360315	−	0.869877i	−0.634939	−	0.772562i	$-0.718975\pi$
$853$	10.5234	−	25.4058i	0.360315	−	0.869877i	0.995254	−	0.0973147i	$-0.0310253\pi$
$854$	0.717644	+	8.98189i	0.0245573	+	0.307354i
$855$	−32.9861	+	91.7451i	−1.12810	+	3.13762i
$856$	−2.42007	+	15.6409i	−0.0827163	+	0.534593i
$857$	10.8692	+	26.2406i	0.371285	+	0.896360i	0.993533	+	0.113541i	$0.0362193\pi$
$857$	10.8692	+	26.2406i	0.371285	+	0.896360i	−0.622249	+	0.782820i	$0.713781\pi$
$858$	−40.2327	+	3.21455i	−1.37352	+	0.109743i
$859$	−10.3431	−	10.3431i	−0.352902	−	0.352902i	0.508286	−	0.861188i	$-0.330279\pi$
$859$	−10.3431	−	10.3431i	−0.352902	−	0.352902i	−0.861188	+	0.508286i	$0.830279\pi$
$860$	−5.78137	+	30.7759i	−0.197143	+	1.04945i
$861$	7.62190	−	18.4009i	0.259754	−	0.627101i
$862$	−25.6987	−	8.31623i	−0.875302	−	0.283252i
$863$	−31.5330	−	31.5330i	−1.07339	−	1.07339i	−0.997084	−	0.0763109i	$-0.975686\pi$
$863$	−31.5330	−	31.5330i	−1.07339	−	1.07339i	−0.0763109	−	0.997084i	$-0.524314\pi$
$864$	−38.2159	+	38.6733i	−1.30013	+	1.31569i
$865$	−5.33173	−	4.84735i	−0.181284	−	0.164815i
$866$	−3.67941	−	46.0508i	−0.125032	−	1.56487i
$867$	−20.4323	+	47.2612i	−0.693919	+	1.60507i
$868$	39.0377	+	28.2209i	1.32503	+	0.957878i
$869$	−38.3906	−	38.3906i	−1.30231	−	1.30231i
$870$	2.61385	−	9.61565i	0.0886179	−	0.326001i
$871$	15.1727			0.514108
$872$	15.3975	+	2.38242i	0.521425	+	0.0806788i
$873$	13.1199	+	31.6741i	0.444040	+	1.07201i
$874$	−9.84729	−	3.18663i	−0.333090	−	0.107789i
$875$	−25.1577	+	33.5962i	−0.850484	+	1.13576i
$876$	48.3377	−	66.8651i	1.63318	−	2.25916i
$877$	7.56748	−	3.13455i	0.255536	−	0.105846i	−0.251238	−	0.967925i	$-0.580838\pi$
$877$	7.56748	−	3.13455i	0.255536	−	0.105846i	0.506774	+	0.862079i	$0.330838\pi$
$878$	13.5277	+	26.4717i	0.456538	+	0.893377i
$879$	−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	$0.215779\pi$
$882$	−4.93195	−	61.7273i	−0.166067	−	2.07847i
$883$	−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	$0.836598\pi$
$884$	−14.6014	+	2.23336i	−0.491100	+	0.0751159i
$885$	−13.3274	+	0.634196i	−0.447997	+	0.0213183i
$886$	−7.51993	+	8.82595i	−0.252637	+	0.296514i
$887$	1.17313	+	0.485926i	0.0393898	+	0.0163158i	0.402291	−	0.915512i	$-0.368214\pi$
$887$	1.17313	+	0.485926i	0.0393898	+	0.0163158i	−0.362902	+	0.931827i	$0.618214\pi$
$888$	−18.7362	+	30.8211i	−0.628745	+	1.03429i
$889$	27.2958	−	11.3063i	0.915470	−	0.379200i
$890$	−10.0405	−	2.72935i	−0.336559	−	0.0914879i
$891$	21.3190	−	51.4685i	0.714212	−	1.72426i
$892$	−40.0582	+	6.44235i	−1.34125	+	0.215706i
$893$		−	8.31572i		−	0.278275i
$894$	−56.4298	−	18.2610i	−1.88730	−	0.610738i
$895$	−31.9940	+	15.0719i	−1.06944	+	0.503797i
$896$	−34.5675	−	24.6775i	−1.15482	−	0.824417i
$897$	3.97525	+	3.97525i	0.132730	+	0.132730i
$898$	−9.80161	+	30.2888i	−0.327084	+	1.01075i
$899$	−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
$903$	−79.6142			−2.64939
$904$	−19.7685	+	14.4708i	−0.657492	+	0.481291i
$905$	8.79612	+	7.99701i	0.292393	+	0.265830i
$906$	−32.0388	−	62.6952i	−1.06442	−	2.08291i
$907$	32.7807	−	13.5782i	1.08846	−	0.450856i	0.234993	−	0.971997i	$-0.424493\pi$
$907$	32.7807	−	13.5782i	1.08846	−	0.450856i	0.853471	+	0.521141i	$0.174493\pi$
$908$	13.3101	−	8.20007i	0.441711	−	0.272129i
$909$	15.2185	−	15.2185i	0.504766	−	0.504766i
$910$	16.8236	+	13.0062i	0.557696	+	0.431152i
$911$	19.0909	+	7.90772i	0.632511	+	0.261994i	0.675819	−	0.737067i	$-0.263790\pi$
$911$	19.0909	+	7.90772i	0.632511	+	0.261994i	−0.0433088	+	0.999062i	$0.513790\pi$
$912$	−64.7994	+	55.8795i	−2.14572	+	1.85035i
$913$	10.9299	−	26.3871i	0.361727	−	0.873286i
$914$	−2.31128	−	28.9276i	−0.0764505	−	0.956839i
$915$	10.3983	−	4.89848i	0.343757	−	0.161939i
$916$	14.7093	−	20.3473i	0.486009	−	0.672293i
$917$	19.1184	+	19.1184i	0.631346	+	0.631346i
$918$	17.6639	−	53.1867i	0.582996	−	1.75542i
$919$	36.8715			1.21628			0.608139	−	0.793830i	$-0.291916\pi$
$919$	36.8715			1.21628			0.608139	+	0.793830i	$0.291916\pi$
$920$	−6.28606	+	1.85354i	−0.207245	+	0.0611093i
$921$	−43.5898	+	18.0555i	−1.43633	+	0.594949i
$922$	−40.3678	−	34.3944i	−1.32944	−	1.13272i
$923$	5.18140	−	12.5090i	0.170548	−	0.411739i
$924$	116.383	+	27.6484i	3.82873	+	0.909567i
$925$	9.86678	+	18.5968i	0.324418	+	0.611458i
$926$	−7.83423	+	9.19484i	−0.257449	+	0.302161i
$927$	124.186			4.07879
$928$	4.13672	−	4.18623i	0.135794	−	0.137420i
$929$	8.29999	−	20.0379i	0.272314	−	0.657424i	−0.727268	−	0.686354i	$-0.759210\pi$
$929$	8.29999	−	20.0379i	0.272314	−	0.657424i	0.999581	+	0.0289302i	$0.00921007\pi$
$930$	16.1188	−	59.2968i	0.528557	−	1.94442i
$931$		−	50.0954i		−	1.64181i
$932$	−9.63999	+	40.5786i	−0.315768	+	1.32920i
$933$	81.3124			2.66205
$934$	0.0978376	−	0.00781713i	0.00320134	−	0.000255784i
$935$	1.93306	+	48.4600i	0.0632179	+	1.58481i
$936$	30.3869	−	7.41005i	0.993226	−	0.242205i
$937$	−45.4590			−1.48508			−0.742540	−	0.669801i	$-0.766379\pi$
$937$	−45.4590			−1.48508			−0.742540	+	0.669801i	$0.766379\pi$
$938$	−42.7848	−	13.8454i	−1.39697	−	0.452067i
$939$	54.8718			1.79067
$940$	−2.97186	−	4.34667i	−0.0969313	−	0.141773i
$941$	−19.0036	+	45.8788i	−0.619501	+	1.49561i	0.232784	+	0.972528i	$0.425216\pi$
$941$	−19.0036	+	45.8788i	−0.619501	+	1.49561i	−0.852285	+	0.523078i	$0.824784\pi$
$942$	−17.5032	−	34.2511i	−0.570284	−	1.11596i
$943$		−	1.81515i		−	0.0591093i
$944$	−7.03844	−	3.54417i	−0.229082	−	0.115353i
$945$	−72.9872	+	34.3832i	−2.37427	+	1.11848i
$946$	16.0380	−	49.5603i	0.521439	−	1.61134i
$947$	−48.0897	−	19.9194i	−1.56270	−	0.647293i	−0.577147	−	0.816640i	$-0.695834\pi$
$947$	−48.0897	−	19.9194i	−1.56270	−	0.647293i	−0.985556	+	0.169347i	$0.945834\pi$
$948$	50.6666	+	36.6276i	1.64558	+	1.18961i
$949$	−22.5412	+	9.33688i	−0.731719	+	0.303088i
$950$	8.68681	+	49.1801i	0.281837	+	1.59561i
$951$		−	99.9581i		−	3.24136i
$952$	43.2118	+	7.02633i	1.40050	+	0.227725i
$953$	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	$0.747918\pi$
$954$	67.1850	−	78.8533i	2.17519	−	2.55297i
$955$	−2.72469	+	7.57825i	−0.0881690	+	0.245226i
$956$	24.9246	−	4.00849i	0.806120	−	0.129644i
$957$	−6.34334	+	15.3142i	−0.205051	+	0.495037i
$958$	−20.4157	−	39.9504i	−0.659601	−	1.29074i
$959$	−3.95113	+	9.53888i	−0.127589	+	0.308027i
$960$	−13.9009	+	52.3664i	−0.448650	+	1.69012i
$961$	−7.18552	+	7.18552i	−0.231791	+	0.231791i
$962$	9.49777	−	4.85360i	0.306220	−	0.156486i
$963$	13.2195	+	31.9146i	0.425992	+	1.02843i
$964$	6.37272	−	3.92610i	0.205251	−	0.126451i
$965$	1.76174	−	0.0838337i	0.0567124	−	0.00269870i
$966$	−7.58213	−	14.8371i	−0.243951	−	0.477376i
$967$		−	15.4148i		−	0.495707i	−0.968798	−	0.247853i	$-0.920275\pi$
$967$		−	15.4148i		−	0.495707i	0.968798	−	0.247853i	$-0.0797251\pi$
$968$	−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	$0.662144\pi$
$972$	−1.49837	+	6.30723i	−0.0480601	+	0.202305i
$973$	26.2252	+	26.2252i	0.840740	+	0.840740i
$974$	−0.151191	+	0.0772626i	−0.00484448	+	0.00247565i
$975$	7.95425	−	25.9343i	0.254740	−	0.830562i
$976$	6.77036	+	0.500429i	0.216714	+	0.0160183i
$977$		−	49.8024i		−	1.59332i	−0.604428	−	0.796660i	$-0.706598\pi$
$977$		−	49.8024i		−	1.59332i	0.604428	−	0.796660i	$-0.293402\pi$
$978$	3.09552	+	38.7429i	0.0989839	+	1.23886i
$979$	15.9908	+	6.62362i	0.511069	+	0.211692i
$980$	−17.9030	−	26.1852i	−0.571891	−	0.836454i
$981$	31.4181	−	13.0138i	1.00310	−	0.415498i
$982$	−3.64147	+	4.27390i	−0.116204	+	0.136386i
$983$	19.2062	−	46.3678i	0.612581	−	1.47890i	−0.247573	−	0.968869i	$-0.579633\pi$
$983$	19.2062	−	46.3678i	0.612581	−	1.47890i	0.860155	−	0.510033i	$-0.170367\pi$
$984$	−12.8227	−	7.79496i	−0.408774	−	0.248494i
$985$	−0.933858	−	19.6247i	−0.0297552	−	0.625296i
$986$	−1.91205	+	5.75725i	−0.0608920	+	0.183348i
$987$	9.46616	−	9.46616i	0.301311	−	0.301311i
$988$	24.9818	−	4.01769i	0.794776	−	0.127820i
$989$	−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	$-0.518130\pi$
$991$	19.1645	−	7.93820i	0.608780	−	0.252165i	0.665707	+	0.746213i	$0.268130\pi$
$992$	25.5099	−	25.8152i	0.809940	−	0.819634i
$993$	−5.46275	+	2.26275i	−0.173355	+	0.0718061i
$994$	−26.0254	+	30.5454i	−0.825476	+	0.968841i
$995$	33.6164	−	1.59966i	1.06571	−	0.0507126i
$996$	−7.60168	+	31.9985i	−0.240868	+	1.01391i
$997$	6.32261	+	15.2641i	0.200239	+	0.483420i	0.991820	−	0.127644i	$-0.0407416\pi$
$997$	6.32261	+	15.2641i	0.200239	+	0.483420i	−0.791581	+	0.611065i	$0.790742\pi$
$998$	49.0748	+	15.8808i	1.55343	+	0.502699i
$999$			40.4678i			1.28035i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bw.a.43.4	✓	416	17.9	even	8
680.2.bw.a.43.101	yes	416	136.43	odd	8
680.2.bw.a.427.4	yes	416	40.27	even	4
680.2.bw.a.427.101	yes	416	5.2	odd	4
680.2.bz.a.563.49	yes	416	1.1	even	1	trivial
680.2.bz.a.563.50	yes	416	8.3	odd	2	inner
680.2.bz.a.587.49	yes	416	85.77	odd	8	inner
680.2.bz.a.587.50	yes	416	680.587	even	8	inner

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.bz (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.112635 - 1.40972i) q^{2} +(-2.79820 - 1.15905i) q^{3} +(-1.97463 + 0.317569i) q^{4} +(-0.756545 + 2.10420i) q^{5} +(-1.31877 + 4.07524i) q^{6} +(-3.46829 + 1.43661i) q^{7} +(0.670096 + 2.74790i) q^{8} +(4.36522 + 4.36522i) q^{9} +O(q^{10})\)	\(q+(-0.112635 - 1.40972i) q^{2} +(-2.79820 - 1.15905i) q^{3} +(-1.97463 + 0.317569i) q^{4} +(-0.756545 + 2.10420i) q^{5} +(-1.31877 + 4.07524i) q^{6} +(-3.46829 + 1.43661i) q^{7} +(0.670096 + 2.74790i) q^{8} +(4.36522 + 4.36522i) q^{9} +(3.05154 + 0.829510i) q^{10} +(-4.85998 - 2.01307i) q^{11} +(5.89349 + 1.40008i) q^{12} +(-1.26662 - 1.26662i) q^{13} +(2.41587 + 4.72751i) q^{14} +(4.55584 - 5.01109i) q^{15} +(3.79830 - 1.25416i) q^{16} +(-2.93778 + 2.89300i) q^{17} +(5.66207 - 6.64543i) q^{18} +(4.99413 - 4.99413i) q^{19} +(0.825667 - 4.39526i) q^{20} +11.3701 q^{21} +(-2.29046 + 7.07795i) q^{22} +(0.957344 - 0.396545i) q^{23} +(1.30990 - 8.46587i) q^{24} +(-3.85528 - 3.18384i) q^{25} +(-1.64292 + 1.92825i) q^{26} +(-3.67810 - 8.87971i) q^{27} +(6.39235 - 3.93819i) q^{28} +(0.398139 + 0.961193i) q^{29} +(-7.57739 - 5.85804i) q^{30} +(2.45520 + 5.92738i) q^{31} +(-2.19584 - 5.21328i) q^{32} +(11.2660 + 11.2660i) q^{33} +(4.40922 + 3.81560i) q^{34} +(-0.398998 - 8.38482i) q^{35} +(-10.0059 - 7.23343i) q^{36} +(-3.88993 - 1.61126i) q^{37} +(-7.60285 - 6.47782i) q^{38} +(2.07619 + 5.01236i) q^{39} +(-6.28908 - 0.668898i) q^{40} +(0.670346 - 1.61836i) q^{41} +(-1.28067 - 16.0287i) q^{42} -7.00207 q^{43} +(10.2359 + 2.43168i) q^{44} +(-12.4878 + 5.88280i) q^{45} +(-0.666848 - 1.30492i) q^{46} +(0.832549 - 0.832549i) q^{47} +(-12.0821 - 0.893042i) 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} +11.8658 q^{53} +(-12.1036 + 6.18526i) q^{54} +(7.91268 - 8.70337i) q^{55} +(-6.27176 - 8.56785i) q^{56} +(-19.7631 + 8.18614i) q^{57} +(1.31017 - 0.669529i) q^{58} +(-1.39307 - 1.39307i) q^{59} +(-7.40473 + 11.3418i) q^{60} +(1.56801 + 0.649493i) q^{61} +(8.07941 - 4.12878i) q^{62} +(-21.4110 - 8.86872i) q^{63} +(-7.10194 + 3.68272i) q^{64} +(3.62348 - 1.70697i) q^{65} +(14.6129 - 17.1508i) q^{66} +(-5.98943 + 5.98943i) q^{67} +(4.88230 - 6.64554i) q^{68} -3.13846 q^{69} +(-11.7753 + 1.50690i) q^{70} +(2.89257 + 6.98328i) q^{71} +(-9.07009 + 14.9203i) q^{72} +(5.21241 - 12.5839i) q^{73} +(-1.83329 + 5.66520i) q^{74} +(7.09762 + 13.3775i) q^{75} +(-8.27557 + 11.4475i) q^{76} +19.7478 q^{77} +(6.83218 - 3.49142i) q^{78} +(9.53535 + 3.94967i) q^{79} +(-0.234587 + 8.94120i) q^{80} +10.5903i q^{81} +(-2.35694 - 0.762716i) q^{82} +5.42947i q^{83} +(-22.4517 + 3.61079i) q^{84} +(-3.86487 - 8.37035i) q^{85} +(0.788680 + 9.87096i) q^{86} -3.15108i q^{87} +(2.27507 - 14.7037i) q^{88} -3.29031 q^{89} +(9.69967 + 16.9417i) q^{90} +(6.21267 + 2.57337i) q^{91} +(-1.76447 + 1.08705i) q^{92} -19.4317i q^{93} +(-1.26744 - 1.07989i) q^{94} +(6.73035 + 14.2869i) q^{95} +(0.101927 + 17.1329i) q^{96} +(5.13078 + 2.12524i) q^{97} +(-7.63527 - 6.50544i) q^{98} +(-12.4274 - 30.0024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 8 q^{2} - 8 q^{3} - 8 q^{8}+O(q^{10}) \) 416 * q - 8 * q^2 - 8 * q^3 - 8 * q^8	\( 416 q - 8 q^{2} - 8 q^{3} - 8 q^{8} + 4 q^{10} - 16 q^{11} - 16 q^{12} + 16 q^{14} - 16 q^{16} - 16 q^{17} - 8 q^{18} + 32 q^{19} + 12 q^{20} - 12 q^{22} - 24 q^{24} - 16 q^{25} + 8 q^{26} - 32 q^{27} + 44 q^{28} + 16 q^{30} - 8 q^{32} - 16 q^{33} - 16 q^{35} - 72 q^{36} - 16 q^{38} + 16 q^{40} - 16 q^{41} - 16 q^{43} + 32 q^{46} - 36 q^{48} - 48 q^{50} - 16 q^{51} + 24 q^{52} - 16 q^{54} - 8 q^{56} + 16 q^{57} + 8 q^{58} + 64 q^{60} - 56 q^{62} - 48 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 88 q^{70} - 24 q^{72} + 32 q^{73} + 16 q^{74} - 32 q^{75} - 40 q^{76} - 84 q^{78} + 16 q^{80} + 28 q^{82} - 48 q^{86} + 8 q^{88} - 32 q^{90} - 16 q^{91} + 48 q^{92} + 24 q^{94} - 8 q^{96} - 16 q^{97} + 40 q^{98}+O(q^{100}) \) 416 * q - 8 * q^2 - 8 * q^3 - 8 * q^8 + 4 * q^10 - 16 * q^11 - 16 * q^12 + 16 * q^14 - 16 * q^16 - 16 * q^17 - 8 * q^18 + 32 * q^19 + 12 * q^20 - 12 * q^22 - 24 * q^24 - 16 * q^25 + 8 * q^26 - 32 * q^27 + 44 * q^28 + 16 * q^30 - 8 * q^32 - 16 * q^33 - 16 * q^35 - 72 * q^36 - 16 * q^38 + 16 * q^40 - 16 * q^41 - 16 * q^43 + 32 * q^46 - 36 * q^48 - 48 * q^50 - 16 * q^51 + 24 * q^52 - 16 * q^54 - 8 * q^56 + 16 * q^57 + 8 * q^58 + 64 * q^60 - 56 * q^62 - 48 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 88 * q^70 - 24 * q^72 + 32 * q^73 + 16 * q^74 - 32 * q^75 - 40 * q^76 - 84 * q^78 + 16 * q^80 + 28 * q^82 - 48 * q^86 + 8 * q^88 - 32 * q^90 - 16 * q^91 + 48 * q^92 + 24 * q^94 - 8 * q^96 - 16 * q^97 + 40 * q^98

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