LMFDB - Embedded newform 820.2.j.c.483.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.1
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41355 + 0.0431962i) q^{2} -1.95083i q^{3} +(1.99627 - 0.122120i) q^{4} +(0.661743 + 2.13591i) q^{5} +(0.0842684 + 2.75760i) q^{6} +3.68722 q^{7} +(-2.81656 + 0.258855i) q^{8} -0.805738 q^{9} +(-1.02767 - 2.99063i) q^{10} +(-0.288900 - 0.288900i) q^{11} +(-0.238236 - 3.89438i) q^{12} -0.323541 q^{13} +(-5.21209 + 0.159274i) q^{14} +(4.16679 - 1.29095i) q^{15} +(3.97017 - 0.487570i) q^{16} -0.730984 q^{17} +(1.13895 - 0.0348048i) q^{18} +(5.58536 + 5.58536i) q^{19} +(1.58185 + 4.18303i) q^{20} -7.19315i q^{21} +(0.420855 + 0.395897i) q^{22} +(0.658884 - 0.658884i) q^{23} +(0.504982 + 5.49462i) q^{24} +(-4.12419 + 2.82684i) q^{25} +(0.457342 - 0.0139757i) q^{26} -4.28063i q^{27} +(7.36069 - 0.450285i) q^{28} +(0.746773 + 0.746773i) q^{29} +(-5.83422 + 2.00481i) q^{30} +7.13529i q^{31} +(-5.59099 + 0.860702i) q^{32} +(-0.563595 + 0.563595i) q^{33} +(1.03328 - 0.0315757i) q^{34} +(2.44000 + 7.87557i) q^{35} +(-1.60847 + 0.0983970i) q^{36} +(-1.81268 + 1.81268i) q^{37} +(-8.13647 - 7.65393i) q^{38} +0.631173i q^{39} +(-2.41673 - 5.84461i) q^{40} +(-6.09068 + 1.97574i) q^{41} +(0.310717 + 10.1679i) q^{42} +(9.11240 + 9.11240i) q^{43} +(-0.612003 - 0.541442i) q^{44} +(-0.533192 - 1.72098i) q^{45} +(-0.902907 + 0.959829i) q^{46} -9.21021i q^{47} +(-0.951166 - 7.74513i) q^{48} +6.59563 q^{49} +(5.70766 - 4.17404i) q^{50} +1.42603i q^{51} +(-0.645874 + 0.0395109i) q^{52} -1.48020 q^{53} +(0.184907 + 6.05090i) q^{54} +(0.425886 - 0.808242i) q^{55} +(-10.3853 + 0.954456i) q^{56} +(10.8961 - 10.8961i) q^{57} +(-1.08786 - 1.02335i) q^{58} +2.81774 q^{59} +(8.16038 - 3.08593i) q^{60} -4.64411i q^{61} +(-0.308217 - 10.0861i) q^{62} -2.97094 q^{63} +(7.86599 - 1.45816i) q^{64} +(-0.214101 - 0.691053i) q^{65} +(0.772327 - 0.821017i) q^{66} -7.99283i q^{67} +(-1.45924 + 0.0892680i) q^{68} +(-1.28537 - 1.28537i) q^{69} +(-3.78926 - 11.0271i) q^{70} +(-4.34688 - 4.34688i) q^{71} +(2.26941 - 0.208569i) q^{72} +(9.05769 - 9.05769i) q^{73} +(2.48402 - 2.64062i) q^{74} +(5.51469 + 8.04560i) q^{75} +(11.8320 + 10.4678i) q^{76} +(-1.06524 - 1.06524i) q^{77} +(-0.0272643 - 0.892197i) q^{78} +(5.54896 - 5.54896i) q^{79} +(3.66864 + 8.15727i) q^{80} -10.7680 q^{81} +(8.52417 - 3.05591i) q^{82} +(7.83917 - 7.83917i) q^{83} +(-0.878429 - 14.3595i) q^{84} +(-0.483724 - 1.56131i) q^{85} +(-13.2745 - 12.4872i) q^{86} +(1.45683 - 1.45683i) q^{87} +(0.888487 + 0.738921i) q^{88} +(7.38530 + 7.38530i) q^{89} +(0.828035 + 2.40967i) q^{90} -1.19297 q^{91} +(1.23485 - 1.39577i) q^{92} +13.9197 q^{93} +(0.397846 + 13.0191i) q^{94} +(-8.23373 + 15.6259i) q^{95} +(1.67908 + 10.9071i) q^{96} -5.02356 q^{97} +(-9.32327 + 0.284906i) q^{98} +(0.232778 + 0.232778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.41355	+	0.0431962i	−0.999533	+	0.0305443i
$2$	−1.41355	+	0.0431962i	−0.999533	+	0.0305443i
$3$		−	1.95083i		−	1.12631i	−0.826351	−	0.563156i	$-0.809587\pi$
$3$		−	1.95083i		−	1.12631i	0.826351	−	0.563156i	$-0.190413\pi$
$4$	1.99627	−	0.122120i	0.998134	−	0.0610601i
$5$	0.661743	+	2.13591i	0.295941	+	0.955206i
$5$	0.661743	+	2.13591i	0.295941	+	0.955206i
$6$	0.0842684	+	2.75760i	0.0344024	+	1.12579i
$7$	3.68722			1.39364			0.696820	−	0.717246i	$-0.254598\pi$
$7$	3.68722			1.39364			0.696820	+	0.717246i	$0.254598\pi$
$8$	−2.81656	+	0.258855i	−0.995803	+	0.0915190i
$9$	−0.805738			−0.268579
$10$	−1.02767	−	2.99063i	−0.324979	−	0.945721i
$11$	−0.288900	−	0.288900i	−0.0871067	−	0.0871067i	0.662211	−	0.749318i	$-0.269618\pi$
$11$	−0.288900	−	0.288900i	−0.0871067	−	0.0871067i	−0.749318	+	0.662211i	$0.769618\pi$
$12$	−0.238236	−	3.89438i	−0.0687728	−	1.12421i
$13$	−0.323541			−0.0897341			−0.0448670	−	0.998993i	$-0.514286\pi$
$13$	−0.323541			−0.0897341			−0.0448670	+	0.998993i	$0.514286\pi$
$14$	−5.21209	+	0.159274i	−1.39299	+	0.0425678i
$15$	4.16679	−	1.29095i	1.07586	−	0.333321i
$16$	3.97017	−	0.487570i	0.992543	−	0.121892i
$17$	−0.730984			−0.177290			−0.0886448	−	0.996063i	$-0.528254\pi$
$17$	−0.730984			−0.177290			−0.0886448	+	0.996063i	$0.528254\pi$
$18$	1.13895	−	0.0348048i	0.268454	−	0.00820357i
$19$	5.58536	+	5.58536i	1.28137	+	1.28137i	0.939889	+	0.341479i	$0.110928\pi$
$19$	5.58536	+	5.58536i	1.28137	+	1.28137i	0.341479	+	0.939889i	$0.389072\pi$
$20$	1.58185	+	4.18303i	0.353713	+	0.935354i
$21$		−	7.19315i		−	1.56967i
$22$	0.420855	+	0.395897i	0.0897267	+	0.0844055i
$23$	0.658884	−	0.658884i	0.137387	−	0.137387i	−0.635069	−	0.772456i	$-0.719028\pi$
$23$	0.658884	−	0.658884i	0.137387	−	0.137387i	0.772456	+	0.635069i	$0.219028\pi$
$24$	0.504982	+	5.49462i	0.103079	+	1.12159i
$25$	−4.12419	+	2.82684i	−0.824838	+	0.565369i
$26$	0.457342	−	0.0139757i	0.0896922	−	0.00274087i
$27$		−	4.28063i		−	0.823808i
$28$	7.36069	−	0.450285i	1.39104	−	0.0850959i
$29$	0.746773	+	0.746773i	0.138672	+	0.138672i	0.773035	−	0.634363i	$-0.218738\pi$
$29$	0.746773	+	0.746773i	0.138672	+	0.138672i	−0.634363	+	0.773035i	$0.718738\pi$
$30$	−5.83422	+	2.00481i	−1.06518	+	0.366027i
$31$			7.13529i			1.28154i	0.767735	+	0.640768i	$0.221384\pi$
$31$			7.13529i			1.28154i	−0.767735	+	0.640768i	$0.778616\pi$
$32$	−5.59099	+	0.860702i	−0.988357	+	0.152152i
$33$	−0.563595	+	0.563595i	−0.0981094	+	0.0981094i
$34$	1.03328	−	0.0315757i	0.177207	−	0.00541519i
$35$	2.44000	+	7.87557i	0.412435	+	1.33121i
$36$	−1.60847	+	0.0983970i	−0.268078	+	0.0163995i
$37$	−1.81268	+	1.81268i	−0.298002	+	0.298002i	−0.840231	−	0.542229i	$-0.817581\pi$
$37$	−1.81268	+	1.81268i	−0.298002	+	0.298002i	0.542229	+	0.840231i	$0.317581\pi$
$38$	−8.13647	−	7.65393i	−1.31991	−	1.24163i
$39$			0.631173i			0.101069i
$40$	−2.41673	−	5.84461i	−0.382118	−	0.924114i
$41$	−6.09068	+	1.97574i	−0.951205	+	0.308559i
$41$	−6.09068	+	1.97574i	−0.951205	+	0.308559i
$42$	0.310717	+	10.1679i	0.0479446	+	1.56894i
$43$	9.11240	+	9.11240i	1.38963	+	1.38963i	0.826092	+	0.563535i	$0.190559\pi$
$43$	9.11240	+	9.11240i	1.38963	+	1.38963i	0.563535	+	0.826092i	$0.309441\pi$
$44$	−0.612003	−	0.541442i	−0.0922629	−	0.0816254i
$45$	−0.533192	−	1.72098i	−0.0794835	−	0.256549i
$46$	−0.902907	+	0.959829i	−0.133126	+	0.141519i
$47$		−	9.21021i		−	1.34345i	−0.740802	−	0.671724i	$-0.765554\pi$
$47$		−	9.21021i		−	1.34345i	0.740802	−	0.671724i	$-0.234446\pi$
$48$	−0.951166	−	7.74513i	−0.137289	−	1.11791i
$49$	6.59563			0.942232
$50$	5.70766	−	4.17404i	0.807185	−	0.590299i
$51$			1.42603i			0.199683i
$52$	−0.645874	+	0.0395109i	−0.0895666	+	0.00547917i
$53$	−1.48020			−0.203322			−0.101661	−	0.994819i	$-0.532416\pi$
$53$	−1.48020			−0.203322			−0.101661	+	0.994819i	$0.532416\pi$
$54$	0.184907	+	6.05090i	0.0251627	+	0.823424i
$55$	0.425886	−	0.808242i	0.0574265	−	0.108983i
$56$	−10.3853	+	0.954456i	−1.38779	+	0.127545i
$57$	10.8961	−	10.8961i	1.44322	−	1.44322i
$58$	−1.08786	−	1.02335i	−0.142843	−	0.134372i
$59$	2.81774			0.366838			0.183419	−	0.983035i	$-0.441283\pi$
$59$	2.81774			0.366838			0.183419	+	0.983035i	$0.441283\pi$
$60$	8.16038	−	3.08593i	1.05350	−	0.398392i
$61$		−	4.64411i		−	0.594617i	−0.954781	−	0.297309i	$-0.903911\pi$
$61$		−	4.64411i		−	0.594617i	0.954781	−	0.297309i	$-0.0960890\pi$
$62$	−0.308217	−	10.0861i	−0.0391436	−	1.28094i
$63$	−2.97094			−0.374303
$64$	7.86599	−	1.45816i	0.983249	−	0.182270i
$65$	−0.214101	−	0.691053i	−0.0265559	−	0.0857145i
$66$	0.772327	−	0.821017i	0.0950669	−	0.101060i
$67$		−	7.99283i		−	0.976479i	−0.872710	−	0.488240i	$-0.837639\pi$
$67$		−	7.99283i		−	0.976479i	0.872710	−	0.488240i	$-0.162361\pi$
$68$	−1.45924	+	0.0892680i	−0.176959	+	0.0108253i
$69$	−1.28537	−	1.28537i	−0.154740	−	0.154740i
$70$	−3.78926	−	11.0271i	−0.452903	−	1.31800i
$71$	−4.34688	−	4.34688i	−0.515880	−	0.515880i	0.400442	−	0.916322i	$-0.368857\pi$
$71$	−4.34688	−	4.34688i	−0.515880	−	0.515880i	−0.916322	+	0.400442i	$0.868857\pi$
$72$	2.26941	−	0.208569i	0.267452	−	0.0245801i
$73$	9.05769	−	9.05769i	1.06012	−	1.06012i	0.0620491	−	0.998073i	$-0.480236\pi$
$73$	9.05769	−	9.05769i	1.06012	−	1.06012i	0.998073	−	0.0620491i	$-0.0197635\pi$
$74$	2.48402	−	2.64062i	0.288761	−	0.306966i
$75$	5.51469	+	8.04560i	0.636782	+	0.929026i
$76$	11.8320	+	10.4678i	1.35722	+	1.20074i
$77$	−1.06524	−	1.06524i	−0.121395	−	0.121395i
$78$	−0.0272643	−	0.892197i	−0.00308707	−	0.101021i
$79$	5.54896	−	5.54896i	0.624307	−	0.624307i	−0.322323	−	0.946630i	$-0.604464\pi$
$79$	5.54896	−	5.54896i	0.624307	−	0.624307i	0.946630	+	0.322323i	$0.104464\pi$
$80$	3.66864	+	8.15727i	0.410166	+	0.912011i
$81$	−10.7680			−1.19644
$82$	8.52417	−	3.05591i	0.941337	−	0.337469i
$83$	7.83917	−	7.83917i	0.860461	−	0.860461i	−0.130930	−	0.991392i	$-0.541796\pi$
$83$	7.83917	−	7.83917i	0.860461	−	0.860461i	0.991392	+	0.130930i	$0.0417964\pi$
$84$	−0.878429	−	14.3595i	−0.0958445	−	1.56674i
$85$	−0.483724	−	1.56131i	−0.0524672	−	0.169348i
$86$	−13.2745	−	12.4872i	−1.43142	−	1.34653i
$87$	1.45683	−	1.45683i	0.156188	−	0.156188i
$88$	0.888487	+	0.738921i	0.0947131	+	0.0787692i
$89$	7.38530	+	7.38530i	0.782840	+	0.782840i	0.980309	−	0.197469i	$-0.0632723\pi$
$89$	7.38530	+	7.38530i	0.782840	+	0.782840i	−0.197469	+	0.980309i	$0.563272\pi$
$90$	0.828035	+	2.40967i	0.0872825	+	0.254001i
$91$	−1.19297			−0.125057
$92$	1.23485	−	1.39577i	0.128742	−	0.145519i
$93$	13.9197			1.44341
$94$	0.397846	+	13.0191i	0.0410347	+	1.34282i
$95$	−8.23373	+	15.6259i	−0.844763	+	1.60318i
$96$	1.67908	+	10.9071i	0.171371	+	1.11320i
$97$	−5.02356			−0.510065			−0.255032	−	0.966932i	$-0.582086\pi$
$97$	−5.02356			−0.510065			−0.255032	+	0.966932i	$0.582086\pi$
$98$	−9.32327	+	0.284906i	−0.941793	+	0.0287798i
$99$	0.232778	+	0.232778i	0.0233951	+	0.0233951i
$100$	−7.88778	+	6.14678i	−0.788778	+	0.614678i
$101$	4.98228	+	4.98228i	0.495756	+	0.495756i	0.910114	−	0.414358i	$-0.135994\pi$
$101$	4.98228	+	4.98228i	0.495756	+	0.495756i	−0.414358	+	0.910114i	$0.635994\pi$
$102$	−0.0615989	−	2.01576i	−0.00609920	−	0.199590i
$103$	−10.5343	−	10.5343i	−1.03797	−	1.03797i	−0.999250	−	0.0387231i	$-0.987671\pi$
$103$	−10.5343	−	10.5343i	−1.03797	−	1.03797i	−0.0387231	−	0.999250i	$-0.512329\pi$
$104$	0.911271	−	0.0837501i	0.0893575	−	0.00821237i
$105$	15.3639	−	4.76002i	1.49936	−	0.464530i
$106$	2.09235	−	0.0639392i	0.203227	−	0.00621033i
$107$	2.86689	+	2.86689i	0.277152	+	0.277152i	0.831971	−	0.554819i	$-0.187212\pi$
$107$	2.86689	+	2.86689i	0.277152	+	0.277152i	−0.554819	+	0.831971i	$0.687212\pi$
$108$	−0.522752	−	8.54529i	−0.0503018	−	0.822271i
$109$	−10.6725	+	10.6725i	−1.02224	+	1.02224i	−0.0224917	+	0.999747i	$0.507160\pi$
$109$	−10.6725	+	10.6725i	−1.02224	+	1.02224i	−0.999747	+	0.0224917i	$0.992840\pi$
$110$	−0.567100	+	1.16089i	−0.0540709	+	0.110686i
$111$	3.53623	+	3.53623i	0.335644	+	0.335644i
$112$	14.6389	−	1.79778i	1.38325	−	0.169874i
$113$	0.210878	+	0.210878i	0.0198378	+	0.0198378i	0.716956	−	0.697118i	$-0.245535\pi$
$113$	0.210878	+	0.210878i	0.0198378	+	0.0198378i	−0.697118	+	0.716956i	$0.745535\pi$
$114$	−14.9315	+	15.8729i	−1.39847	+	1.48663i
$115$	1.84333	+	0.971303i	0.171891	+	0.0905744i
$116$	1.58196	+	1.39956i	0.146881	+	0.129946i
$117$	0.260689			0.0241007
$118$	−3.98302	+	0.121716i	−0.366667	+	0.0112048i
$119$	−2.69530			−0.247078
$120$	−11.4018	+	4.71462i	−1.04084	+	0.430384i
$121$		−	10.8331i		−	0.984825i
$122$	0.200608	+	6.56470i	0.0181622	+	0.594340i
$123$	3.85434	+	11.8819i	0.347534	+	1.07135i
$124$	0.871364	+	14.2440i	0.0782508	+	1.27914i
$125$	−8.76703	−	6.93824i	−0.784147	−	0.620575i
$126$	4.19958	−	0.128333i	0.374128	−	0.0114328i
$127$	−9.88222	−	9.88222i	−0.876905	−	0.876905i	0.116308	−	0.993213i	$-0.462894\pi$
$127$	−9.88222	−	9.88222i	−0.876905	−	0.876905i	−0.993213	+	0.116308i	$0.962894\pi$
$128$	−11.0560	+	2.40097i	−0.977222	+	0.212217i
$129$	17.7767	−	17.7767i	1.56515	−	1.56515i
$130$	0.332494	+	0.967592i	0.0291616	+	0.0848634i
$131$	−6.13854			−0.536327			−0.268163	−	0.963373i	$-0.586417\pi$
$131$	−6.13854			−0.536327			−0.268163	+	0.963373i	$0.586417\pi$
$132$	−1.05626	+	1.19391i	−0.0919357	+	0.103917i
$133$	20.5945	+	20.5945i	1.78577	+	1.78577i
$134$	0.345260	+	11.2983i	0.0298259	+	0.976024i
$135$	9.14303	−	2.83268i	0.786907	−	0.243798i
$136$	2.05886	−	0.189219i	0.176546	−	0.0162254i
$137$	14.7908			1.26366			0.631830	−	0.775107i	$-0.282304\pi$
$137$	14.7908			1.26366			0.631830	+	0.775107i	$0.282304\pi$
$138$	1.87246	+	1.76142i	0.159395	+	0.149942i
$139$	−9.30203			−0.788988			−0.394494	−	0.918899i	$-0.629080\pi$
$139$	−9.30203			−0.788988			−0.394494	+	0.918899i	$0.629080\pi$
$140$	5.83265	+	15.4238i	0.492949	+	1.30355i
$141$	−17.9676			−1.51314
$142$	6.33232	+	5.95679i	0.531397	+	0.499882i
$143$	0.0934710	+	0.0934710i	0.00781644	+	0.00781644i
$144$	−3.19892	+	0.392853i	−0.266577	+	0.0327378i
$145$	−1.10087	+	2.08921i	−0.0914219	+	0.173499i
$146$	−12.4123	+	13.1948i	−1.02725	+	1.09201i
$147$		−	12.8669i		−	1.06125i
$148$	−3.39723	+	3.83996i	−0.279250	+	0.315642i
$149$	9.20177	−	9.20177i	0.753838	−	0.753838i	−0.221355	−	0.975193i	$-0.571048\pi$
$149$	9.20177	−	9.20177i	0.753838	−	0.753838i	0.975193	+	0.221355i	$0.0710480\pi$
$150$	−8.14285	−	11.1347i	−0.664861	−	0.909142i
$151$	−3.29763	−	3.29763i	−0.268358	−	0.268358i	0.560080	−	0.828438i	$-0.310770\pi$
$151$	−3.29763	−	3.29763i	−0.268358	−	0.268358i	−0.828438	+	0.560080i	$0.810770\pi$
$152$	−17.1773	−	14.2857i	−1.39326	−	1.15872i
$153$	0.588982			0.0476163
$154$	1.55179	+	1.45976i	0.125047	+	0.117631i
$155$	−15.2403	+	4.72173i	−1.22413	+	0.379258i
$156$	0.0770790	+	1.25999i	0.00617126	+	0.100880i
$157$			11.4036i			0.910108i	0.890464	+	0.455054i	$0.150380\pi$
$157$			11.4036i			0.910108i	−0.890464	+	0.455054i	$0.849620\pi$
$158$	−7.60406	+	8.08345i	−0.604946	+	0.643085i
$159$			2.88763i			0.229004i
$160$	−5.53818	−	11.3723i	−0.437832	−	0.899057i
$161$	2.42945	−	2.42945i	0.191468	−	0.191468i
$162$	15.2211	−	0.465137i	1.19589	−	0.0365446i
$163$	10.4503	−	10.4503i	0.818534	−	0.818534i	−0.167362	−	0.985896i	$-0.553525\pi$
$163$	10.4503	−	10.4503i	0.818534	−	0.818534i	0.985896	+	0.167362i	$0.0535247\pi$
$164$	−11.9174	+	4.68791i	−0.930590	+	0.366064i
$165$	−1.57674	−	0.830832i	−0.122749	−	0.0646801i
$166$	−10.7425	+	11.4197i	−0.833778	+	0.886342i
$167$	1.11039			0.0859243			0.0429621	−	0.999077i	$-0.486321\pi$
$167$	1.11039			0.0859243			0.0429621	+	0.999077i	$0.486321\pi$
$168$	1.86198	+	20.2599i	0.143655	+	1.56309i
$169$	−12.8953			−0.991948
$170$	0.751212	+	2.18610i	0.0576153	+	0.167667i
$171$	−4.50033	−	4.50033i	−0.344149	−	0.344149i
$172$	19.3036	+	17.0780i	1.47189	+	1.30218i
$173$	−16.9599	+	16.9599i	−1.28944	+	1.28944i	−0.354305	+	0.935130i	$0.615283\pi$
$173$	−16.9599	+	16.9599i	−1.28944	+	1.28944i	−0.935130	+	0.354305i	$0.884717\pi$
$174$	−1.99638	+	2.12223i	−0.151345	+	0.160886i
$175$	−15.2068	+	10.4232i	−1.14953	+	0.787920i
$176$	−1.28784	−	1.00613i	−0.0970748	−	0.0758395i
$177$		−	5.49693i		−	0.413174i
$178$	−10.7585	−	10.1205i	−0.806386	−	0.758563i
$179$	16.3698	+	16.3698i	1.22354	+	1.22354i	0.966365	+	0.257173i	$0.0827911\pi$
$179$	16.3698	+	16.3698i	1.22354	+	1.22354i	0.257173	+	0.966365i	$0.417209\pi$
$180$	−1.27456	−	3.37043i	−0.0950001	−	0.251217i
$181$	0.345340	+	0.345340i	0.0256689	+	0.0256689i	0.719825	−	0.694156i	$-0.244222\pi$
$181$	0.345340	+	0.345340i	0.0256689	+	0.0256689i	−0.694156	+	0.719825i	$0.744222\pi$
$182$	1.68632	−	0.0515317i	0.124999	−	0.00381978i
$183$	−9.05986			−0.669724
$184$	−1.68523	+	2.02634i	−0.124237	+	0.149384i
$185$	−5.07124	−	2.67218i	−0.372845	−	0.196463i
$186$	−19.6763	+	0.601280i	−1.44274	+	0.0440880i
$187$	0.211181	+	0.211181i	0.0154431	+	0.0154431i
$188$	−1.12475	−	18.3860i	−0.0820311	−	1.34094i
$189$		−	15.7837i		−	1.14809i
$190$	10.9638	−	22.4437i	0.795400	−	1.62824i
$191$	−1.96988	+	1.96988i	−0.142535	+	0.142535i	−0.774774	−	0.632238i	$-0.782136\pi$
$191$	−1.96988	+	1.96988i	−0.142535	+	0.142535i	0.632238	+	0.774774i	$0.282136\pi$
$192$	−2.84462	−	15.3452i	−0.205293	−	1.10744i
$193$	−17.4367			−1.25512			−0.627561	−	0.778568i	$-0.715947\pi$
$193$	−17.4367			−1.25512			−0.627561	+	0.778568i	$0.715947\pi$
$194$	7.10107	−	0.216999i	0.509827	−	0.0155796i
$195$	−1.34813	+	0.417674i	−0.0965413	+	0.0299103i
$196$	13.1666	−	0.805460i	0.940474	−	0.0575328i
$197$	−11.2076	−	11.2076i	−0.798510	−	0.798510i	0.184350	−	0.982861i	$-0.440982\pi$
$197$	−11.2076	−	11.2076i	−0.798510	−	0.798510i	−0.982861	+	0.184350i	$0.940982\pi$
$198$	−0.339099	−	0.318989i	−0.0240987	−	0.0226696i
$199$	4.92977	+	4.92977i	0.349462	+	0.349462i	0.859909	−	0.510447i	$-0.170520\pi$
$199$	4.92977	+	4.92977i	0.349462	+	0.349462i	−0.510447	+	0.859909i	$0.670520\pi$
$200$	10.8843	−	9.02953i	0.769635	−	0.638484i
$201$	−15.5926			−1.09982
$202$	−7.25794	−	6.82751i	−0.510667	−	0.480382i
$203$	2.75352	+	2.75352i	0.193259	+	0.193259i
$204$	0.174147	+	2.84673i	0.0121927	+	0.199311i
$205$	−8.25047	−	11.7017i	−0.576238	−	0.817282i
$206$	15.3458	+	14.4357i	1.06919	+	1.00578i
$207$	−0.530888	+	0.530888i	−0.0368993	+	0.0368993i
$208$	−1.28451	+	0.157749i	−0.0890649	+	0.0109379i
$209$		−	3.22722i		−	0.223232i
$210$	−21.5121	+	7.39220i	−1.48447	+	0.510110i
$211$	12.6211	−	12.6211i	0.868873	−	0.868873i	−0.123474	−	0.992348i	$-0.539404\pi$
$211$	12.6211	−	12.6211i	0.868873	−	0.868873i	0.992348	+	0.123474i	$0.0394037\pi$
$212$	−2.95489	+	0.180763i	−0.202942	+	0.0124149i
$213$	−8.48003	+	8.48003i	−0.581042	+	0.581042i
$214$	−4.17634	−	3.92866i	−0.285489	−	0.268558i
$215$	−13.4332	+	25.4933i	−0.916134	+	1.73863i
$216$	1.10806	+	12.0566i	0.0753941	+	0.820351i
$217$			26.3094i			1.78600i
$218$	14.6251	−	15.5471i	0.990538	−	1.05299i
$219$	−17.6700	−	17.6700i	−1.19403	−	1.19403i
$220$	0.751480	−	1.66548i	0.0506648	−	0.112286i
$221$	0.236503			0.0159089
$222$	−5.15140	−	4.84589i	−0.345739	−	0.325235i
$223$	−11.8759	+	11.8759i	−0.795268	+	0.795268i	−0.982345	−	0.187077i	$-0.940099\pi$
$223$	−11.8759	+	11.8759i	−0.795268	+	0.795268i	0.187077	+	0.982345i	$0.440099\pi$
$224$	−20.6152	+	3.17360i	−1.37741	+	0.212045i
$225$	3.32302	−	2.27769i	0.221535	−	0.151846i
$226$	−0.307197	−	0.288979i	−0.0204344	−	0.0192226i
$227$			9.13680i			0.606431i	0.952922	+	0.303215i	$0.0980601\pi$
$227$			9.13680i			0.606431i	−0.952922	+	0.303215i	$0.901940\pi$
$228$	20.4209	−	23.0821i	1.35240	−	1.52865i
$229$	11.0808	−	11.0808i	0.732237	−	0.732237i	−0.238825	−	0.971063i	$-0.576762\pi$
$229$	11.0808	−	11.0808i	0.732237	−	0.732237i	0.971063	+	0.238825i	$0.0767623\pi$
$230$	−2.64760	−	1.29336i	−0.174577	−	0.0852819i
$231$	−2.07810	+	2.07810i	−0.136729	+	0.136729i
$232$	−2.29664	−	1.91002i	−0.150782	−	0.125399i
$233$	−5.91331			−0.387394			−0.193697	−	0.981061i	$-0.562048\pi$
$233$	−5.91331			−0.387394			−0.193697	+	0.981061i	$0.562048\pi$
$234$	−0.368498	+	0.0112608i	−0.0240895	+	0.000736140i
$235$	19.6721	−	6.09479i	1.28327	−	0.397580i
$236$	5.62496	−	0.344103i	0.366154	−	0.0223992i
$237$	−10.8251	−	10.8251i	−0.703164	−	0.703164i
$238$	3.80995	−	0.116427i	0.246963	−	0.00754683i
$239$	3.20465	−	3.20465i	0.207292	−	0.207292i	−0.595824	−	0.803115i	$-0.703174\pi$
$239$	3.20465	−	3.20465i	0.207292	−	0.207292i	0.803115	+	0.595824i	$0.203174\pi$
$240$	15.9135	−	7.15689i	1.02721	−	0.461975i
$241$		−	11.4965i		−	0.740552i	−0.928922	−	0.370276i	$-0.879263\pi$
$241$		−	11.4965i		−	0.740552i	0.928922	−	0.370276i	$-0.120737\pi$
$242$	0.467948	+	15.3131i	0.0300808	+	0.984365i
$243$			8.16464i			0.523762i
$244$	−0.567140	−	9.27088i	−0.0363074	−	0.593508i
$245$	4.36461	+	14.0876i	0.278845	+	0.900026i
$246$	−5.96157	−	16.6292i	−0.380096	−	1.06024i
$247$	−1.80709	−	1.80709i	−0.114982	−	0.114982i
$248$	−1.84700	−	20.0970i	−0.117285	−	1.27616i
$249$	−15.2929	−	15.2929i	−0.969148	−	0.969148i
$250$	12.6924	+	9.42888i	0.802736	+	0.596335i
$251$	−13.6715			−0.862938			−0.431469	−	0.902128i	$-0.642005\pi$
$251$	−13.6715			−0.862938			−0.431469	+	0.902128i	$0.642005\pi$
$252$	−5.93079	+	0.362812i	−0.373604	+	0.0228550i
$253$	−0.380704			−0.0239346
$254$	14.3959	+	13.5422i	0.903280	+	0.849711i
$255$	−3.04586	+	0.943662i	−0.190739	+	0.0590944i
$256$	15.5246	−	3.87147i	0.970284	−	0.241967i
$257$			19.3012i			1.20397i	0.798506	+	0.601987i	$0.205624\pi$
$257$			19.3012i			1.20397i	−0.798506	+	0.601987i	$0.794376\pi$
$258$	−24.3605	+	25.8963i	−1.51662	+	1.61223i
$259$	−6.68375	+	6.68375i	−0.415308	+	0.415308i
$260$	−0.511794	−	1.35338i	−0.0317401	−	0.0839331i
$261$	−0.601704	−	0.601704i	−0.0372445	−	0.0372445i
$262$	8.67715	−	0.265161i	0.536076	−	0.0163817i
$263$	−22.6595			−1.39724			−0.698622	−	0.715491i	$-0.746203\pi$
$263$	−22.6595			−1.39724			−0.698622	+	0.715491i	$0.746203\pi$
$264$	1.44151	−	1.73329i	0.0887188	−	0.106676i
$265$	−0.979515	−	3.16158i	−0.0601712	−	0.194214i
$266$	−30.0010	−	28.2218i	−1.83948	−	1.73039i
$267$	14.4075	−	14.4075i	0.881722	−	0.881722i
$268$	−0.976086	−	15.9558i	−0.0596240	−	0.974657i
$269$			5.58140i			0.340304i	0.985418	+	0.170152i	$0.0544259\pi$
$269$			5.58140i			0.340304i	−0.985418	+	0.170152i	$0.945574\pi$
$270$	−12.8018	+	4.39909i	−0.779093	+	0.267720i
$271$		−	14.5456i		−	0.883584i	−0.897118	−	0.441792i	$-0.854343\pi$
$271$		−	14.5456i		−	0.883584i	0.897118	−	0.441792i	$-0.145657\pi$
$272$	−2.90213	+	0.356406i	−0.175968	+	0.0216103i
$273$			2.32728i			0.140853i
$274$	−20.9075	+	0.638905i	−1.26307	+	0.0385976i
$275$	2.00816	+	0.374805i	0.121096	+	0.0226016i
$276$	−2.72291	−	2.40898i	−0.163900	−	0.145003i
$277$	−13.1156	+	13.1156i	−0.788042	+	0.788042i	−0.981173	−	0.193131i	$-0.938136\pi$
$277$	−13.1156	+	13.1156i	−0.788042	+	0.788042i	0.193131	+	0.981173i	$0.438136\pi$
$278$	13.1489	−	0.401812i	0.788619	−	0.0240991i
$279$		−	5.74917i		−	0.344194i
$280$	−8.91102	−	21.5504i	−0.532535	−	1.28788i
$281$	4.00802	+	4.00802i	0.239099	+	0.239099i	0.816477	−	0.577378i	$-0.195924\pi$
$281$	4.00802	+	4.00802i	0.239099	+	0.239099i	−0.577378	+	0.816477i	$0.695924\pi$
$282$	25.3981	−	0.776130i	1.51243	−	0.0462179i
$283$	2.42191	−	2.42191i	0.143968	−	0.143968i	−0.631449	−	0.775417i	$-0.717540\pi$
$283$	2.42191	−	2.42191i	0.143968	−	0.143968i	0.775417	+	0.631449i	$0.217540\pi$
$284$	−9.20839	−	8.14671i	−0.546417	−	0.483418i
$285$	30.4834	+	16.0626i	1.80568	+	0.951466i
$286$	−0.136164	−	0.128089i	−0.00805154	−	0.00757404i
$287$	−22.4577	+	7.28501i	−1.32564	+	0.430020i
$288$	4.50488	−	0.693501i	0.265452	−	0.0408649i
$289$	−16.4657			−0.968568
$290$	1.46589	−	3.00076i	0.0860799	−	0.176211i
$291$			9.80011i			0.574492i
$292$	16.9754	−	19.1877i	0.993413	−	1.12288i
$293$		−	17.5741i		−	1.02669i	−0.858182	−	0.513345i	$-0.828406\pi$
$293$		−	17.5741i		−	1.02669i	0.858182	−	0.513345i	$-0.171594\pi$
$294$	0.555803	+	18.1881i	0.0324151	+	1.06075i
$295$	1.86462	+	6.01843i	0.108562	+	0.350406i
$296$	4.63629	−	5.57473i	0.269479	−	0.324025i
$297$	−1.23668	+	1.23668i	−0.0717592	+	0.0717592i
$298$	−12.6097	+	13.4047i	−0.730461	+	0.776512i
$299$	−0.213176	+	0.213176i	−0.0123283	+	0.0123283i
$300$	11.9913	+	15.3877i	0.692320	+	0.888410i
$301$	33.5994	+	33.5994i	1.93664	+	1.93664i
$302$	4.80383	+	4.51894i	0.276429	+	0.260036i
$303$	9.71958	−	9.71958i	0.558376	−	0.558376i
$304$	24.8981	+	19.4516i	1.42800	+	1.11562i
$305$	9.91938	−	3.07321i	0.567982	−	0.175971i
$306$	−0.832557	+	0.0254418i	−0.0475941	+	0.00145441i
$307$	9.18520	−	9.18520i	0.524227	−	0.524227i	−0.394618	−	0.918845i	$-0.629123\pi$
$307$	9.18520	−	9.18520i	0.524227	−	0.524227i	0.918845	+	0.394618i	$0.129123\pi$
$308$	−2.25659	−	1.99642i	−0.128581	−	0.113756i
$309$	−20.5506	+	20.5506i	−1.16908	+	1.16908i
$310$	21.3390	−	7.33274i	1.21198	−	0.416472i
$311$	−6.48430	+	6.48430i	−0.367691	+	0.367691i	−0.866634	−	0.498944i	$-0.833721\pi$
$311$	−6.48430	+	6.48430i	−0.367691	+	0.367691i	0.498944	+	0.866634i	$0.333721\pi$
$312$	−0.163382	−	1.77773i	−0.00924969	−	0.100644i
$313$			18.6043i			1.05158i	0.850615	+	0.525790i	$0.176230\pi$
$313$			18.6043i			1.05158i	−0.850615	+	0.525790i	$0.823770\pi$
$314$	−0.492593	−	16.1196i	−0.0277986	−	0.909683i
$315$	−1.96600	−	6.34564i	−0.110771	−	0.357537i
$316$	10.3996	−	11.7549i	0.585022	−	0.661262i
$317$			26.1953i			1.47127i	0.677376	+	0.735637i	$0.263117\pi$
$317$			26.1953i			1.47127i	−0.677376	+	0.735637i	$0.736883\pi$
$318$	−0.124735	−	4.08182i	−0.00699477	−	0.228897i
$319$		−	0.431486i		−	0.0241586i
$320$	8.31975	+	15.8361i	0.465088	+	0.885264i
$321$	5.59281	−	5.59281i	0.312160	−	0.312160i
$322$	−3.32922	+	3.53911i	−0.185530	+	0.197227i
$323$	−4.08281	−	4.08281i	−0.227173	−	0.227173i
$324$	−21.4958	+	1.31499i	−1.19421	+	0.0730551i
$325$	1.33434	−	0.914599i	0.0740161	−	0.0507328i
$326$	−14.3207	+	15.2235i	−0.793151	+	0.843154i
$327$	20.8202	+	20.8202i	1.15136	+	1.15136i
$328$	16.6433	−	7.14140i	0.918974	−	0.394318i
$329$		−	33.9601i		−	1.87228i
$330$	2.26470	+	1.10632i	0.124668	+	0.0609007i
$331$	−9.70469	−	9.70469i	−0.533418	−	0.533418i	0.388170	−	0.921588i	$-0.373107\pi$
$331$	−9.70469	−	9.70469i	−0.533418	−	0.533418i	−0.921588	+	0.388170i	$0.873107\pi$
$332$	14.6918	−	16.6064i	0.806316	−	0.911396i
$333$	1.46054	−	1.46054i	0.0800373	−	0.0800373i
$334$	−1.56959	+	0.0479645i	−0.0858842	+	0.00262450i
$335$	17.0719	−	5.28920i	0.932739	−	0.288980i
$336$	−3.50716	−	28.5580i	−0.191331	−	1.55797i
$337$	−3.56381	−	3.56381i	−0.194133	−	0.194133i	0.603346	−	0.797479i	$-0.293834\pi$
$337$	−3.56381	−	3.56381i	−0.194133	−	0.194133i	−0.797479	+	0.603346i	$0.793834\pi$
$338$	18.2282	−	0.557029i	0.991485	−	0.0302984i
$339$	0.411388	−	0.411388i	0.0223435	−	0.0223435i
$340$	−1.15631	−	3.05773i	−0.0627097	−	0.165829i
$341$	2.06139	−	2.06139i	0.111630	−	0.111630i
$342$	6.55586	+	6.16707i	0.354500	+	0.333477i
$343$	−1.49102			−0.0805076
$344$	−28.0244	−	23.3068i	−1.51097	−	1.25662i
$345$	1.89485	−	3.59602i	0.102015	−	0.193603i
$346$	23.2411	−	24.7063i	1.24945	−	1.32822i
$347$		−	3.97052i		−	0.213148i	−0.994305	−	0.106574i	$-0.966012\pi$
$347$		−	3.97052i		−	0.213148i	0.994305	−	0.106574i	$-0.0339882\pi$
$348$	2.73031	−	3.08613i	0.146360	−	0.165434i
$349$	6.15012			0.329209			0.164604	−	0.986360i	$-0.447365\pi$
$349$	6.15012			0.329209			0.164604	+	0.986360i	$0.447365\pi$
$350$	21.0454	−	15.3906i	1.12492	−	0.822664i
$351$			1.38496i			0.0739236i
$352$	1.86390	+	1.36658i	0.0993460	+	0.0728391i
$353$	−2.24682	−	2.24682i	−0.119586	−	0.119586i	0.644781	−	0.764367i	$-0.276949\pi$
$353$	−2.24682	−	2.24682i	−0.119586	−	0.119586i	−0.764367	+	0.644781i	$0.776949\pi$
$354$	0.237446	+	7.77020i	0.0126201	+	0.412982i
$355$	6.40802	−	12.1611i	0.340102	−	0.645442i
$356$	15.6449	+	13.8411i	0.829179	+	0.733579i
$357$			5.25808i			0.278287i
$358$	−23.8467	−	22.4325i	−1.26034	−	1.18560i
$359$	29.8764			1.57681			0.788407	−	0.615154i	$-0.210906\pi$
$359$	29.8764			1.57681			0.788407	+	0.615154i	$0.210906\pi$
$360$	1.94725	+	4.70922i	0.102629	+	0.248198i
$361$			43.3924i			2.28381i
$362$	−0.503073	−	0.473239i	−0.0264409	−	0.0248729i
$363$	−21.1335			−1.10922
$364$	−2.38148	+	0.145686i	−0.124824	+	0.00763600i
$365$	25.3402	+	13.3525i	1.32637	+	0.698902i
$366$	12.8066	−	0.391352i	0.669412	−	0.0204563i
$367$	2.12338	−	2.12338i	0.110839	−	0.110839i	−0.649512	−	0.760351i	$-0.725027\pi$
$367$	2.12338	−	2.12338i	0.110839	−	0.110839i	0.760351	+	0.649512i	$0.225027\pi$
$368$	2.29463	−	2.93714i	0.119616	−	0.153109i
$369$	4.90750	−	1.59193i	0.255474	−	0.0828726i
$370$	7.28389	+	3.55822i	0.378672	+	0.184983i
$371$	−5.45785			−0.283357
$372$	27.7875	−	1.69988i	1.44072	−	0.0881348i
$373$	21.6019	+	21.6019i	1.11850	+	1.11850i	0.991961	+	0.126543i	$0.0403881\pi$
$373$	21.6019	+	21.6019i	1.11850	+	1.11850i	0.126543	+	0.991961i	$0.459612\pi$
$374$	−0.307639	−	0.289394i	−0.0159076	−	0.0149642i
$375$	−13.5353	+	17.1030i	−0.698962	+	0.883194i
$376$	2.38411	+	25.9411i	0.122951	+	1.33781i
$377$	−0.241612	−	0.241612i	−0.0124436	−	0.0124436i
$378$	0.681794	+	22.3110i	0.0350677	+	1.14756i
$379$	5.13353			0.263692			0.131846	−	0.991270i	$-0.457910\pi$
$379$	5.13353			0.263692			0.131846	+	0.991270i	$0.457910\pi$
$380$	−14.5285	+	32.1989i	−0.745296	+	1.65177i
$381$	−19.2785	+	19.2785i	−0.987669	+	0.987669i
$382$	2.69944	−	2.86962i	0.138115	−	0.146823i
$383$	−1.04487			−0.0533906			−0.0266953	−	0.999644i	$-0.508498\pi$
$383$	−1.04487			−0.0533906			−0.0266953	+	0.999644i	$0.508498\pi$
$384$	4.68388	+	21.5684i	0.239023	+	1.10066i
$385$	1.57034	−	2.98017i	0.0800318	−	0.151883i
$386$	24.6477	−	0.753199i	1.25454	−	0.0383368i
$387$	−7.34220	−	7.34220i	−0.373225	−	0.373225i
$388$	−10.0284	+	0.613478i	−0.509113	+	0.0311446i
$389$	23.6849			1.20087			0.600436	−	0.799673i	$-0.294994\pi$
$389$	23.6849			1.20087			0.600436	+	0.799673i	$0.294994\pi$
$390$	1.88761	−	0.648639i	0.0955827	−	0.0328451i
$391$	−0.481634	+	0.481634i	−0.0243573	+	0.0243573i
$392$	−18.5770	+	1.70731i	−0.938278	+	0.0862321i
$393$			11.9752i			0.604071i
$394$	16.3267	+	15.3585i	0.822528	+	0.773748i
$395$	15.5240	+	8.18007i	0.781100	+	0.411584i
$396$	0.493114	+	0.436260i	0.0247799	+	0.0219229i
$397$		−	1.91151i		−	0.0959359i	−0.998849	−	0.0479679i	$-0.984725\pi$
$397$		−	1.91151i		−	0.0959359i	0.998849	−	0.0479679i	$-0.0152745\pi$
$398$	−7.18144	−	6.75555i	−0.359973	−	0.338625i
$399$	40.1763	−	40.1763i	2.01133	−	2.01133i
$400$	−14.9955	+	13.2339i	−0.749774	+	0.661694i
$401$		−	17.9949i		−	0.898622i	−0.893375	−	0.449311i	$-0.851670\pi$
$401$		−	17.9949i		−	0.898622i	0.893375	−	0.449311i	$-0.148330\pi$
$402$	22.0410	−	0.673543i	1.09931	−	0.0335933i
$403$		−	2.30856i		−	0.114997i
$404$	10.5544	+	9.33753i	0.525101	+	0.464560i
$405$	−7.12565	−	22.9994i	−0.354076	−	1.14285i
$406$	−4.01119	−	3.77331i	−0.199072	−	0.187266i
$407$	1.04737			0.0519160
$408$	−0.369133	−	4.01648i	−0.0182748	−	0.198845i
$409$		−	10.1896i		−	0.503841i	−0.967748	−	0.251921i	$-0.918938\pi$
$409$		−	10.1896i		−	0.503841i	0.967748	−	0.251921i	$-0.0810622\pi$
$410$	12.1680	+	16.1846i	0.600932	+	0.799300i
$411$		−	28.8543i		−	1.42328i
$412$	−22.3157	−	19.7428i	−1.09942	−	0.972658i
$413$	10.3896			0.511240
$414$	0.727506	−	0.773371i	0.0357550	−	0.0380091i
$415$	21.9313	+	11.5562i	1.07656	+	0.567273i
$416$	1.80891	−	0.278472i	0.0886893	−	0.0136532i
$417$			18.1467i			0.888646i
$418$	0.139404	+	4.56185i	0.00681846	+	0.223127i
$419$			17.9836i			0.878559i	0.898351	+	0.439279i	$0.144766\pi$
$419$			17.9836i			0.878559i	−0.898351	+	0.439279i	$0.855234\pi$
$420$	30.0892	−	11.3785i	1.46820	−	0.555215i
$421$	−10.0387	+	10.0387i	−0.489254	+	0.489254i	−0.908071	−	0.418817i	$-0.862445\pi$
$421$	−10.0387	+	10.0387i	−0.489254	+	0.489254i	0.418817	+	0.908071i	$0.362445\pi$
$422$	−17.2954	+	18.3858i	−0.841929	+	0.895007i
$423$			7.42102i			0.360822i
$424$	4.16908	−	0.383158i	0.202469	−	0.0186078i
$425$	3.01472	−	2.06638i	0.146235	−	0.100234i
$426$	11.6207	−	12.3533i	0.563024	−	0.598519i
$427$		−	17.1239i		−	0.828682i
$428$	6.07318	+	5.37297i	0.293558	+	0.259712i
$429$	0.182346	−	0.182346i	0.00880375	−	0.00880375i
$430$	17.8873	−	36.6164i	0.862601	−	1.76580i
$431$	−36.6221			−1.76403			−0.882013	−	0.471225i	$-0.843812\pi$
$431$	−36.6221			−1.76403			−0.882013	+	0.471225i	$0.843812\pi$
$432$	−2.08711	−	16.9949i	−0.100416	−	0.817665i
$433$	−27.3498	−	27.3498i	−1.31435	−	1.31435i	−0.918178	−	0.396168i	$-0.870340\pi$
$433$	−27.3498	−	27.3498i	−1.31435	−	1.31435i	−0.396168	−	0.918178i	$-0.629660\pi$
$434$	−1.13647	−	37.1898i	−0.0545521	−	1.78517i
$435$	4.07569	+	2.14760i	0.195415	+	0.102970i
$436$	−20.0018	+	22.6085i	−0.957913	+	1.08275i
$437$	7.36020			0.352086
$438$	25.7408	+	24.2142i	1.22994	+	1.15700i
$439$	4.89423	−	4.89423i	0.233589	−	0.233589i	−0.580600	−	0.814189i	$-0.697182\pi$
$439$	4.89423	−	4.89423i	0.233589	−	0.233589i	0.814189	+	0.580600i	$0.197182\pi$
$440$	−0.990315	+	2.38670i	−0.0472114	+	0.113782i
$441$	−5.31435			−0.253064
$442$	−0.334310	+	0.0102160i	−0.0159015	+	0.000485927i
$443$	−21.8033	−	21.8033i	−1.03590	−	1.03590i	−0.999331	−	0.0365732i	$-0.988356\pi$
$443$	−21.8033	−	21.8033i	−1.03590	−	1.03590i	−0.0365732	−	0.999331i	$-0.511644\pi$
$444$	7.49110	+	6.62741i	0.355512	+	0.314523i
$445$	−10.8871	+	20.6615i	−0.516100	+	0.979448i
$446$	16.2742	−	17.3002i	0.770606	−	0.819188i
$447$	−17.9511	−	17.9511i	−0.849057	−	0.849057i
$448$	29.0037	−	5.37656i	1.37029	−	0.254018i
$449$	−34.2316			−1.61549			−0.807745	−	0.589532i	$-0.799312\pi$
$449$	−34.2316			−1.61549			−0.807745	+	0.589532i	$0.799312\pi$
$450$	−4.59888	+	3.36319i	−0.216793	+	0.158542i
$451$	2.33039	+	1.18881i	0.109734	+	0.0559788i
$452$	0.446722	+	0.395217i	0.0210120	+	0.0185894i
$453$	−6.43313	+	6.43313i	−0.302255	+	0.302255i
$454$	−0.394675	−	12.9154i	−0.0185230	−	0.606148i
$455$	−0.789438	−	2.54807i	−0.0370094	−	0.119455i
$456$	−27.8689	+	33.5099i	−1.30508	+	1.56925i
$457$	−22.4681			−1.05101			−0.525507	−	0.850789i	$-0.676124\pi$
$457$	−22.4681			−1.05101			−0.525507	+	0.850789i	$0.676124\pi$
$458$	−15.1846	+	16.1419i	−0.709530	+	0.754261i
$459$			3.12907i			0.146053i
$460$	3.79839	+	1.71387i	0.177101	+	0.0799097i
$461$	−13.2056			−0.615047			−0.307523	−	0.951541i	$-0.599500\pi$
$461$	−13.2056			−0.615047			−0.307523	+	0.951541i	$0.599500\pi$
$462$	2.84774	−	3.02728i	0.132489	−	0.140842i
$463$		−	34.0884i		−	1.58422i	−0.610376	−	0.792112i	$-0.708982\pi$
$463$		−	34.0884i		−	1.58422i	0.610376	−	0.792112i	$-0.291018\pi$
$464$	3.32892	+	2.60072i	0.154541	+	0.120735i
$465$	9.21129	+	29.7313i	0.427163	+	1.37875i
$466$	8.35878	−	0.255433i	0.387213	−	0.0118327i
$467$	10.6408	+	10.6408i	0.492398	+	0.492398i	0.909061	−	0.416663i	$-0.136800\pi$
$467$	10.6408	+	10.6408i	0.492398	+	0.492398i	−0.416663	+	0.909061i	$0.636800\pi$
$468$	0.520405	−	0.0318354i	0.0240557	−	0.00147159i
$469$		−	29.4713i		−	1.36086i
$470$	−27.5444	+	9.46508i	−1.27053	+	0.436591i
$471$	22.2465			1.02507
$472$	−7.93632	+	0.729385i	−0.365299	+	0.0335727i
$473$		−	5.26515i		−	0.242092i
$474$	15.7694	+	14.8342i	0.724314	+	0.681359i
$475$	−38.8240	−	7.24616i	−1.78137	−	0.332477i
$476$	−5.38055	+	0.329151i	−0.246617	+	0.0150866i
$477$	1.19266			0.0546080
$478$	−4.39151	+	4.66837i	−0.200863	+	0.213526i
$479$	23.5477	−	23.5477i	1.07592	−	1.07592i	0.0790492	−	0.996871i	$-0.474812\pi$
$479$	23.5477	−	23.5477i	1.07592	−	1.07592i	0.996871	−	0.0790492i	$-0.0251884\pi$
$480$	−22.1854	+	10.8040i	−1.01262	+	0.493135i
$481$	0.586475	−	0.586475i	0.0267410	−	0.0267410i
$482$	0.496603	+	16.2509i	0.0226196	+	0.740206i
$483$	−4.73945	−	4.73945i	−0.215653	−	0.215653i
$484$	−1.32294	−	21.6257i	−0.0601335	−	0.982987i
$485$	−3.32430	−	10.7298i	−0.150949	−	0.487217i
$486$	−0.352682	−	11.5412i	−0.0159980	−	0.523518i
$487$	−27.7461	+	27.7461i	−1.25730	+	1.25730i	−0.304920	+	0.952378i	$0.598630\pi$
$487$	−27.7461	+	27.7461i	−1.25730	+	1.25730i	−0.952378	+	0.304920i	$0.901370\pi$
$488$	1.20215	+	13.0804i	0.0544187	+	0.592122i
$489$	−20.3868	−	20.3868i	−0.921925	−	0.921925i
$490$	−6.77814	−	19.7251i	−0.306205	−	0.891089i
$491$		−	25.8318i		−	1.16577i	−0.812554	−	0.582886i	$-0.801923\pi$
$491$		−	25.8318i		−	1.16577i	0.812554	−	0.582886i	$-0.198077\pi$
$492$	9.14531	+	23.2487i	0.412303	+	1.04813i
$493$	−0.545879	−	0.545879i	−0.0245852	−	0.0245852i
$494$	2.63248	+	2.47636i	0.118441	+	0.111417i
$495$	−0.343153	+	0.651231i	−0.0154236	+	0.0292707i
$496$	3.47895	+	28.3283i	0.156210	+	1.27198i
$497$	−16.0279	−	16.0279i	−0.718951	−	0.718951i
$498$	22.2779	+	20.9567i	0.998298	+	0.939094i
$499$	−22.3902	+	22.3902i	−1.00232	+	1.00232i	−0.00232702	+	0.999997i	$0.500741\pi$
$499$	−22.3902	+	22.3902i	−1.00232	+	1.00232i	−0.999997	+	0.00232702i	$0.999259\pi$
$500$	−18.3486	−	12.7800i	−0.820576	−	0.571537i
$501$		−	2.16618i		−	0.0967776i
$502$	19.3254	−	0.590557i	0.862535	−	0.0263579i
$503$			14.4478i			0.644197i	0.946706	+	0.322099i	$0.104388\pi$
$503$			14.4478i			0.644197i	−0.946706	+	0.322099i	$0.895612\pi$
$504$	8.36781	−	0.769041i	0.372732	−	0.0342558i
$505$	−7.34470	+	13.9387i	−0.326835	+	0.620263i
$506$	0.538145	−	0.0164449i	0.0239235	−	0.000731067i
$507$			25.1566i			1.11724i
$508$	−20.9344	−	18.5207i	−0.928813	−	0.821725i
$509$	−2.50378	+	2.50378i	−0.110978	+	0.110978i	−0.760415	−	0.649437i	$-0.775005\pi$
$509$	−2.50378	+	2.50378i	−0.110978	+	0.110978i	0.649437	+	0.760415i	$0.275005\pi$
$510$	4.26472	−	1.46549i	0.188845	−	0.0648929i
$511$	33.3977	−	33.3977i	1.47743	−	1.47743i
$512$	−21.7776	+	6.14314i	−0.962441	+	0.271491i
$513$	23.9089	−	23.9089i	1.05560	−	1.05560i
$514$	−0.833737	−	27.2832i	−0.0367746	−	1.20341i
$515$	15.5292	−	29.4712i	0.684300	−	1.29866i
$516$	33.3162	−	37.6580i	1.46667	−	1.65780i
$517$	−2.66083	+	2.66083i	−0.117023	+	0.117023i
$518$	9.15913	−	9.73655i	0.402429	−	0.427800i
$519$	33.0858	+	33.0858i	1.45231	+	1.45231i
$520$	0.781910	+	1.89097i	0.0342890	+	0.0829244i
$521$	5.19814	−	5.19814i	0.227735	−	0.227735i	−0.584011	−	0.811746i	$-0.698518\pi$
$521$	5.19814	−	5.19814i	0.227735	−	0.227735i	0.811746	+	0.584011i	$0.198518\pi$
$522$	0.876532	+	0.824549i	0.0383648	+	0.0360895i
$523$	−17.5010	+	17.5010i	−0.765267	+	0.765267i	−0.977269	−	0.212002i	$-0.932002\pi$
$523$	−17.5010	+	17.5010i	−0.765267	+	0.765267i	0.212002	+	0.977269i	$0.432002\pi$
$524$	−12.2542	+	0.749640i	−0.535326	+	0.0327482i
$525$	20.3339	+	29.6659i	0.887444	+	1.29473i
$526$	32.0304	−	0.978804i	1.39659	−	0.0426779i
$527$		−	5.21578i		−	0.227203i
$528$	−1.96278	+	2.51236i	−0.0854190	+	0.109337i
$529$			22.1317i			0.962250i
$530$	1.52117	+	4.42675i	0.0660752	+	0.192286i
$531$	−2.27036			−0.0985252
$532$	43.6271	+	38.5971i	1.89147	+	1.67340i
$533$	1.97058	−	0.639233i	0.0853555	−	0.0276883i
$534$	−19.7434	+	20.9881i	−0.854379	+	0.908242i
$535$	−4.22626	+	8.02055i	−0.182717	+	0.346758i
$536$	2.06898	+	22.5123i	0.0893664	+	0.972381i
$537$	31.9348	−	31.9348i	1.37809	−	1.37809i
$538$	−0.241095	−	7.88961i	−0.0103944	−	0.340145i
$539$	−1.90548	−	1.90548i	−0.0820747	−	0.0820747i
$540$	17.9060	−	6.77134i	0.770552	−	0.291392i
$541$		−	3.66778i		−	0.157690i	−0.996887	−	0.0788450i	$-0.974877\pi$
$541$		−	3.66778i		−	0.157690i	0.996887	−	0.0788450i	$-0.0251232\pi$
$542$	0.628316	+	20.5610i	0.0269885	+	0.883172i
$543$	0.673699	−	0.673699i	0.0289112	−	0.0289112i
$544$	4.08692	−	0.629160i	0.175225	−	0.0269750i
$545$	−29.8579	−	15.7330i	−1.27897	−	0.673927i
$546$	−0.100529	−	3.28973i	−0.00430227	−	0.140787i
$547$		−	12.2044i		−	0.521824i	−0.965363	−	0.260912i	$-0.915977\pi$
$547$		−	12.2044i		−	0.521824i	0.965363	−	0.260912i	$-0.0840233\pi$
$548$	29.5263	−	1.80625i	1.26130	−	0.0771593i
$549$			3.74193i			0.159702i
$550$	−2.85483	−	0.443062i	−0.121730	−	0.0188922i
$551$			8.34199i			0.355381i
$552$	3.95305	+	3.28760i	0.168253	+	0.139929i
$553$	20.4603	−	20.4603i	0.870059	−	0.870059i
$554$	17.9731	−	19.1062i	0.763604	−	0.811745i
$555$	−5.21298	+	9.89312i	−0.221278	+	0.419940i
$556$	−18.5693	+	1.13597i	−0.787515	+	0.0481757i
$557$	−36.0863			−1.52903			−0.764513	−	0.644608i	$-0.777021\pi$
$557$	−36.0863			−1.52903			−0.764513	+	0.644608i	$0.777021\pi$
$558$	0.248342	+	8.12677i	0.0105132	+	0.344033i
$559$	−2.94823	−	2.94823i	−0.124697	−	0.124697i
$560$	13.5271	+	30.0777i	0.571624	+	1.27101i
$561$	0.411979	−	0.411979i	0.0173938	−	0.0173938i
$562$	−5.83869	−	5.49243i	−0.246290	−	0.231684i
$563$			5.99745i			0.252763i	0.991982	+	0.126381i	$0.0403363\pi$
$563$			5.99745i			0.252763i	−0.991982	+	0.126381i	$0.959664\pi$
$564$	−35.8681	+	2.19420i	−1.51032	+	0.0923926i
$565$	−0.310869	+	0.589964i	−0.0130784	+	0.0248200i
$566$	−3.31889	+	3.52812i	−0.139503	+	0.148298i
$567$	−39.7040			−1.66741
$568$	13.3685	+	11.1180i	0.560928	+	0.466502i
$569$	33.7602			1.41530			0.707650	−	0.706563i	$-0.249755\pi$
$569$	33.7602			1.41530			0.707650	+	0.706563i	$0.249755\pi$
$570$	−43.7838	−	21.3886i	−1.83390	−	0.895869i
$571$	−4.72778	−	4.72778i	−0.197851	−	0.197851i	0.601227	−	0.799078i	$-0.294679\pi$
$571$	−4.72778	−	4.72778i	−0.197851	−	0.197851i	−0.799078	+	0.601227i	$0.794679\pi$
$572$	0.198008	+	0.175178i	0.00827913	+	0.00732458i
$573$	3.84290	+	3.84290i	0.160539	+	0.160539i
$574$	31.4305	−	11.2678i	1.31188	−	0.470310i
$575$	−0.854803	+	4.57993i	−0.0356477	+	0.190996i
$576$	−6.33793	+	1.17489i	−0.264080	+	0.0489539i
$577$		−	20.0079i		−	0.832940i	−0.909150	−	0.416470i	$-0.863267\pi$
$577$		−	20.0079i		−	0.832940i	0.909150	−	0.416470i	$-0.136733\pi$
$578$	23.2751	−	0.711254i	0.968116	−	0.0295843i
$579$			34.0160i			1.41366i
$580$	−1.94249	+	4.30506i	−0.0806574	+	0.178758i
$581$	28.9048	−	28.9048i	1.19917	−	1.19917i
$582$	−0.423327	−	13.8530i	−0.0175475	−	0.574224i
$583$	0.427632	+	0.427632i	0.0177107	+	0.0177107i
$584$	−23.1669	+	27.8561i	−0.958652	+	1.15269i
$585$	0.172509	+	0.556807i	0.00713238	+	0.0230212i
$586$	0.759135	+	24.8419i	0.0313596	+	1.02621i
$587$	28.5526			1.17849			0.589245	−	0.807954i	$-0.299425\pi$
$587$	28.5526			1.17849			0.589245	+	0.807954i	$0.299425\pi$
$588$	−1.57131	−	25.6859i	−0.0647999	−	1.05927i
$589$	−39.8531	+	39.8531i	−1.64212	+	1.64212i
$590$	−2.89571	−	8.42682i	−0.119215	−	0.346927i
$591$	−21.8642	+	21.8642i	−0.899372	+	0.899372i
$592$	−6.31284	+	8.08045i	−0.259456	+	0.332105i
$593$		−	36.1021i		−	1.48254i	−0.671209	−	0.741268i	$-0.734225\pi$
$593$		−	36.1021i		−	1.48254i	0.671209	−	0.741268i	$-0.265775\pi$
$594$	1.69469	−	1.80153i	0.0695339	−	0.0739176i
$595$	−1.78360	−	5.75691i	−0.0731204	−	0.236010i
$596$	17.2455	−	19.4929i	0.706402	−	0.798461i
$597$	9.61714	−	9.61714i	0.393603	−	0.393603i
$598$	0.292127	−	0.310544i	0.0119460	−	0.0126991i
$599$	−31.3272			−1.28000			−0.639998	−	0.768377i	$-0.721065\pi$
$599$	−31.3272			−1.28000			−0.639998	+	0.768377i	$0.721065\pi$
$600$	−17.6151	−	21.2334i	−0.719133	−	0.866849i
$601$	8.12796	+	8.12796i	0.331546	+	0.331546i	0.853174	−	0.521627i	$-0.174675\pi$
$601$	8.12796	+	8.12796i	0.331546	+	0.331546i	−0.521627	+	0.853174i	$0.674675\pi$
$602$	−48.9460	−	46.0433i	−1.99489	−	1.87658i
$603$			6.44012i			0.262262i
$604$	−6.98567	−	6.18026i	−0.284243	−	0.251471i
$605$	23.1384	−	7.16871i	0.940711	−	0.291450i
$606$	−13.3193	+	14.1590i	−0.541060	+	0.575170i
$607$	14.3700	−	14.3700i	0.583259	−	0.583259i	−0.352539	−	0.935797i	$-0.614681\pi$
$607$	14.3700	−	14.3700i	0.583259	−	0.583259i	0.935797	+	0.352539i	$0.114681\pi$
$608$	−36.0350	−	26.4204i	−1.46141	−	1.07149i
$609$	5.37165	−	5.37165i	0.217670	−	0.217670i
$610$	−13.8888	+	4.77262i	−0.562342	+	0.193238i
$611$			2.97988i			0.120553i
$612$	1.17577	−	0.0719266i	0.0475275	−	0.00290746i
$613$	28.4521	−	28.4521i	1.14917	−	1.14917i	0.162456	−	0.986716i	$-0.448059\pi$
$613$	28.4521	−	28.4521i	1.14917	−	1.14917i	0.986716	−	0.162456i	$-0.0519414\pi$
$614$	−12.5870	+	13.3805i	−0.507970	+	0.539995i
$615$	−22.8280	+	16.0953i	−0.920515	+	0.649024i
$616$	3.27605	+	2.72457i	0.131996	+	0.109776i
$617$	−2.12176	−	2.12176i	−0.0854190	−	0.0854190i	0.663106	−	0.748525i	$-0.269238\pi$
$617$	−2.12176	−	2.12176i	−0.0854190	−	0.0854190i	−0.748525	+	0.663106i	$0.769238\pi$
$618$	28.1616	−	29.9371i	1.13283	−	1.20425i
$619$	8.59784			0.345576			0.172788	−	0.984959i	$-0.444722\pi$
$619$	8.59784			0.345576			0.172788	+	0.984959i	$0.444722\pi$
$620$	−29.8471	+	11.2870i	−1.19869	+	0.453296i
$621$	−2.82044	−	2.82044i	−0.113180	−	0.113180i
$622$	8.88580	−	9.44600i	0.356288	−	0.378750i
$623$	27.2312	+	27.2312i	1.09100	+	1.09100i
$624$	0.307741	+	2.50587i	0.0123195	+	0.100315i
$625$	9.01792	−	23.3169i	0.360717	−	0.932675i
$626$	−0.803636	−	26.2982i	−0.0321198	−	1.05109i
$627$	−6.29576			−0.251429
$628$	1.39261	+	22.7647i	0.0555713	+	0.908410i
$629$	1.32504	−	1.32504i	0.0528327	−	0.0528327i
$630$	3.05315	+	8.88498i	0.121640	+	0.353986i
$631$		−	37.5180i		−	1.49357i	−0.665066	−	0.746784i	$-0.731597\pi$
$631$		−	37.5180i		−	1.49357i	0.665066	−	0.746784i	$-0.268403\pi$
$632$	−14.1926	+	17.0653i	−0.564551	+	0.678823i
$633$	−24.6216	−	24.6216i	−0.978623	−	0.978623i
$634$	−1.13154	−	37.0285i	−0.0449391	−	1.47059i
$635$	14.5680	−	27.6470i	0.578113	−	1.09714i
$636$	0.352638	+	5.76448i	0.0139830	+	0.228577i
$637$	−2.13395			−0.0845503
$638$	0.0186386	+	0.609929i	0.000737908	+	0.0241473i
$639$	3.50245	+	3.50245i	0.138555	+	0.138555i
$640$	−12.4445	−	22.0258i	−0.491911	−	0.870645i
$641$	−1.33833	−	1.33833i	−0.0528607	−	0.0528607i	0.680182	−	0.733043i	$-0.261901\pi$
$641$	−1.33833	−	1.33833i	−0.0528607	−	0.0528607i	−0.733043	+	0.680182i	$0.761901\pi$
$642$	−7.66415	+	8.14733i	−0.302480	+	0.321549i
$643$			24.1966i			0.954219i	0.878844	+	0.477110i	$0.158315\pi$
$643$			24.1966i			0.954219i	−0.878844	+	0.477110i	$0.841685\pi$
$644$	4.55316	−	5.14653i	0.179419	−	0.202802i
$645$	49.7331	+	26.2058i	1.95824	+	1.03185i
$646$	5.94763	+	5.59490i	0.234006	+	0.220129i
$647$	−34.0833	+	34.0833i	−1.33995	+	1.33995i	−0.443850	+	0.896101i	$0.646388\pi$
$647$	−34.0833	+	34.0833i	−1.33995	+	1.33995i	−0.896101	+	0.443850i	$0.853612\pi$
$648$	30.3287	−	2.78735i	1.19142	−	0.109497i
$649$	−0.814045	−	0.814045i	−0.0319541	−	0.0319541i
$650$	−1.84666	+	1.35047i	−0.0724320	+	0.0529699i
$651$	51.3252			2.01159
$652$	19.5855	−	22.1379i	0.767027	−	0.866987i
$653$	−47.0718			−1.84206			−0.921030	−	0.389491i	$-0.872651\pi$
$653$	−47.0718			−1.84206			−0.921030	+	0.389491i	$0.872651\pi$
$654$	−30.3298	−	28.5311i	−1.18599	−	1.11566i
$655$	−4.06214	−	13.1113i	−0.158721	−	0.512303i
$656$	−23.2178	+	10.8137i	−0.906501	+	0.422203i
$657$	−7.29812	+	7.29812i	−0.284727	+	0.284727i
$658$	1.46695	+	48.0044i	0.0571876	+	1.87141i
$659$	15.2063	−	15.2063i	0.592353	−	0.592353i	−0.345914	−	0.938266i	$-0.612431\pi$
$659$	15.2063	−	15.2063i	0.592353	−	0.592353i	0.938266	+	0.345914i	$0.112431\pi$
$660$	−3.24906	−	1.46601i	−0.126470	−	0.0570644i
$661$		−	18.7956i		−	0.731065i	−0.930799	−	0.365532i	$-0.880887\pi$
$661$		−	18.7956i		−	0.731065i	0.930799	−	0.365532i	$-0.119113\pi$
$662$	14.1373	+	13.2989i	0.549462	+	0.516876i
$663$		−	0.461377i		−	0.0179184i
$664$	−20.0503	+	24.1087i	−0.778102	+	0.935599i
$665$	−30.3596	+	57.6161i	−1.17729	+	2.23426i
$666$	−2.00147	+	2.12765i	−0.0775553	+	0.0824446i
$667$	0.984074			0.0381035
$668$	2.21663	−	0.135601i	0.0857640	−	0.00524655i
$669$	23.1678	+	23.1678i	0.895721	+	0.895721i
$670$	−23.9036	+	8.21401i	−0.923477	+	0.317335i
$671$	−1.34168	+	1.34168i	−0.0517951	+	0.0517951i
$672$	6.19116	+	40.2168i	0.238829	+	1.55140i
$673$			3.46731i			0.133655i	0.997765	+	0.0668274i	$0.0212877\pi$
$673$			3.46731i			0.133655i	−0.997765	+	0.0668274i	$0.978712\pi$
$674$	5.19158	+	4.88369i	0.199972	+	0.188113i
$675$	12.1007	+	17.6541i	0.465755	+	0.679509i
$676$	−25.7425	+	1.57478i	−0.990097	+	0.0605685i
$677$	−17.7461	−	17.7461i	−0.682038	−	0.682038i	0.278421	−	0.960459i	$-0.410189\pi$
$677$	−17.7461	−	17.7461i	−0.682038	−	0.682038i	−0.960459	+	0.278421i	$0.910189\pi$
$678$	−0.563748	+	0.599289i	−0.0216506	+	0.0230156i
$679$	−18.5230			−0.710847
$680$	1.76659	+	4.27231i	0.0677456	+	0.163836i
$681$	17.8243			0.683030
$682$	−2.82484	+	3.00293i	−0.108169	+	0.114988i
$683$	10.2623			0.392674			0.196337	−	0.980536i	$-0.437095\pi$
$683$	10.2623			0.392674			0.196337	+	0.980536i	$0.437095\pi$
$684$	−9.53346	−	8.43429i	−0.364521	−	0.322493i
$685$	9.78769	+	31.5917i	0.373968	+	1.20706i
$686$	2.10764	−	0.0644064i	0.0804700	−	0.00245905i
$687$	−21.6167	−	21.6167i	−0.824728	−	0.824728i
$688$	40.6207	+	31.7349i	1.54865	+	1.20988i
$689$	0.478907			0.0182449
$690$	−2.52313	+	5.16501i	−0.0960540	+	0.196629i
$691$	−29.1990	+	29.1990i	−1.11078	+	1.11078i	−0.117738	+	0.993045i	$0.537564\pi$
$691$	−29.1990	+	29.1990i	−1.11078	+	1.11078i	−0.993045	+	0.117738i	$0.962436\pi$
$692$	−31.7853	+	35.9276i	−1.20830	+	1.36576i
$693$	0.858305	+	0.858305i	0.0326043	+	0.0326043i
$694$	0.171511	+	5.61254i	0.00651048	+	0.213049i
$695$	−6.15555	−	19.8683i	−0.233493	−	0.753646i
$696$	−3.72613	+	4.48035i	−0.141239	+	0.169827i
$697$	4.45219	−	1.44424i	0.168639	−	0.0547043i
$698$	−8.69353	+	0.265662i	−0.329055	+	0.0100555i
$699$			11.5359i			0.436326i
$700$	−29.0840	+	22.6646i	−1.09927	+	0.856640i
$701$	−19.1713			−0.724091			−0.362046	−	0.932160i	$-0.617922\pi$
$701$	−19.1713			−0.724091			−0.362046	+	0.932160i	$0.617922\pi$
$702$	−0.0598250	−	1.95771i	−0.00225795	−	0.0738891i
$703$	−20.2489			−0.763702
$704$	−2.69375	−	1.85122i	−0.101524	−	0.0697706i
$705$	−11.8899	−	38.3770i	−0.447800	−	1.44536i
$706$	3.27305	+	3.07895i	0.123183	+	0.115878i
$707$	18.3708	+	18.3708i	0.690905	+	0.690905i
$708$	−0.671287	−	10.9733i	−0.0252285	−	0.412404i
$709$	−0.968455	−	0.968455i	−0.0363711	−	0.0363711i	0.688687	−	0.725058i	$-0.258187\pi$
$709$	−0.968455	−	0.968455i	−0.0363711	−	0.0363711i	−0.725058	+	0.688687i	$0.758187\pi$
$710$	−8.53277	+	17.4671i	−0.320229	+	0.655529i
$711$	−4.47101	+	4.47101i	−0.167676	+	0.167676i
$712$	−22.7128	−	18.8894i	−0.851199	−	0.707910i
$713$	4.70133	+	4.70133i	0.176066	+	0.176066i
$714$	−0.227129	−	7.43257i	−0.00850008	−	0.278157i
$715$	−0.137792	+	0.261499i	−0.00515311	+	0.00977951i
$716$	34.6777	+	30.6795i	1.29596	+	1.14655i
$717$	−6.25173	−	6.25173i	−0.233475	−	0.233475i
$718$	−42.2318	+	1.29055i	−1.57608	+	0.0481627i
$719$	−19.8032	−	19.8032i	−0.738536	−	0.738536i	0.233759	−	0.972295i	$-0.424897\pi$
$719$	−19.8032	−	19.8032i	−0.738536	−	0.738536i	−0.972295	+	0.233759i	$0.924897\pi$
$720$	−2.95596	−	6.57263i	−0.110162	−	0.244947i
$721$	−38.8422	−	38.8422i	−1.44656	−	1.44656i
$722$	−1.87439	−	61.3375i	−0.0697575	−	2.28275i
$723$	−22.4276			−0.834092
$724$	0.731563	+	0.647217i	0.0271883	+	0.0240536i
$725$	−5.19085	−	0.968826i	−0.192783	−	0.0359813i
$726$	29.8733	−	0.912886i	1.10870	−	0.0338804i
$727$	27.8879			1.03431			0.517153	−	0.855893i	$-0.326992\pi$
$727$	27.8879			1.03431			0.517153	+	0.855893i	$0.326992\pi$
$728$	3.36006	−	0.308805i	0.124532	−	0.0114451i
$729$	−16.3762			−0.606525
$730$	−36.3966	−	17.7799i	−1.34710	−	0.658063i
$731$	−6.66101	−	6.66101i	−0.246367	−	0.246367i
$732$	−18.0859	+	1.10639i	−0.668475	+	0.0408935i
$733$	20.1553	−	20.1553i	0.744453	−	0.744453i	−0.228979	−	0.973431i	$-0.573539\pi$
$733$	20.1553	−	20.1553i	0.744453	−	0.744453i	0.973431	+	0.228979i	$0.0735387\pi$
$734$	−2.90979	+	3.09323i	−0.107402	+	0.114173i
$735$	27.4826	−	8.51461i	1.01371	−	0.314066i
$736$	−3.11671	+	4.25092i	−0.114884	+	0.156691i
$737$	−2.30913	+	2.30913i	−0.0850579	+	0.0850579i
$738$	−6.86824	+	2.46227i	−0.252824	+	0.0906373i
$739$	26.7923			0.985572			0.492786	−	0.870151i	$-0.335979\pi$
$739$	26.7923			0.985572			0.492786	+	0.870151i	$0.335979\pi$
$740$	−10.4499	−	4.71509i	−0.384145	−	0.173330i
$741$	−3.52533	+	3.52533i	−0.129506	+	0.129506i
$742$	7.71496	−	0.235758i	0.283225	−	0.00865496i
$743$	38.1092	+	38.1092i	1.39809	+	1.39809i	0.805511	+	0.592581i	$0.201891\pi$
$743$	38.1092	+	38.1092i	1.39809	+	1.39809i	0.592581	+	0.805511i	$0.298109\pi$
$744$	−39.2057	+	3.60319i	−1.43735	+	0.132099i
$745$	25.7433	+	13.5649i	0.943162	+	0.496980i
$746$	−31.4686	−	29.6023i	−1.15215	−	1.08382i
$747$	−6.31632	+	6.31632i	−0.231102	+	0.231102i
$748$	0.447364	+	0.395785i	0.0163573	+	0.0144713i
$749$	10.5709	+	10.5709i	0.386251	+	0.386251i
$750$	18.3941	−	24.7607i	0.671659	−	0.904131i
$751$	17.5322	+	17.5322i	0.639759	+	0.639759i	0.950496	−	0.310737i	$-0.100576\pi$
$751$	17.5322	+	17.5322i	0.639759	+	0.639759i	−0.310737	+	0.950496i	$0.600576\pi$
$752$	−4.49062	−	36.5661i	−0.163756	−	1.33343i
$753$			26.6708i			0.971938i
$754$	0.351968	+	0.331094i	0.0128179	+	0.0120577i
$755$	4.86125	−	9.22563i	0.176919	−	0.335755i
$756$	−1.92750	−	31.5084i	−0.0701026	−	1.14595i
$757$	14.0193			0.509540			0.254770	−	0.967002i	$-0.418000\pi$
$757$	14.0193			0.509540			0.254770	+	0.967002i	$0.418000\pi$
$758$	−7.25652	+	0.221749i	−0.263569	+	0.00805429i
$759$			0.742688i			0.0269579i
$760$	19.1459	−	46.1425i	0.694496	−	1.67376i
$761$	32.8630			1.19128			0.595641	−	0.803251i	$-0.296898\pi$
$761$	32.8630			1.19128			0.595641	+	0.803251i	$0.296898\pi$
$762$	26.4185	−	28.0840i	0.957040	−	1.01738i
$763$	−39.3519	+	39.3519i	−1.42463	+	1.42463i
$764$	−3.69185	+	4.17297i	−0.133566	+	0.150973i
$765$	0.389754	+	1.25801i	0.0140916	+	0.0454834i
$766$	1.47699	−	0.0451346i	0.0533657	−	0.00163078i
$767$	−0.911653			−0.0329179
$768$	−7.55258	−	30.2858i	−0.272530	−	1.09284i
$769$		−	21.3601i		−	0.770264i	−0.922862	−	0.385132i	$-0.874156\pi$
$769$		−	21.3601i		−	0.770264i	0.922862	−	0.385132i	$-0.125844\pi$
$770$	−2.09103	+	4.28046i	−0.0753553	+	0.154257i
$771$	37.6533			1.35605
$772$	−34.8083	+	2.12937i	−1.25278	+	0.0766379i
$773$			34.0142i			1.22340i	0.791088	+	0.611702i	$0.209515\pi$
$773$			34.0142i			1.22340i	−0.791088	+	0.611702i	$0.790485\pi$
$774$	10.6958	+	10.0614i	0.384451	+	0.361651i
$775$	−20.1703	−	29.4273i	−0.724540	−	1.05706i
$776$	14.1491	−	1.30037i	0.507924	−	0.0466806i
$777$	13.0389	+	13.0389i	0.467767	+	0.467767i
$778$	−33.4798	+	1.02310i	−1.20031	+	0.0366798i
$779$	−45.0539	−	22.9834i	−1.61422	−	0.823466i
$780$	−2.64022	+	0.998424i	−0.0945349	+	0.0357493i
$781$			2.51163i			0.0898733i
$782$	0.660010	−	0.701620i	0.0236019	−	0.0250899i
$783$	3.19666	−	3.19666i	0.114239	−	0.114239i
$784$	26.1858	−	3.21583i	0.935206	−	0.114851i
$785$	−24.3571	+	7.54627i	−0.869341	+	0.269338i
$786$	−0.517285	−	16.9277i	−0.0184509	−	0.603789i
$787$	−15.7082	+	15.7082i	−0.559938	+	0.559938i	−0.929290	−	0.369352i	$-0.879580\pi$
$787$	−15.7082	+	15.7082i	−0.559938	+	0.559938i	0.369352	+	0.929290i	$0.379580\pi$
$788$	−23.7421	−	21.0048i	−0.845778	−	0.748263i
$789$			44.2048i			1.57373i
$790$	−22.2974	−	10.8924i	−0.793307	−	0.387534i
$791$	0.777556	+	0.777556i	0.0276467	+	0.0276467i
$792$	−0.715888	−	0.595377i	−0.0254380	−	0.0211558i
$793$			1.50256i			0.0533574i
$794$	0.0825699	+	2.70202i	0.00293030	+	0.0958911i
$795$	−6.16770	+	1.91087i	−0.218746	+	0.0677715i
$796$	10.4432	+	9.23912i	0.370148	+	0.327472i
$797$	5.89506	−	5.89506i	0.208814	−	0.208814i	−0.594949	−	0.803763i	$-0.702828\pi$
$797$	5.89506	−	5.89506i	0.208814	−	0.208814i	0.803763	+	0.594949i	$0.202828\pi$
$798$	−55.0559	+	58.5268i	−1.94896	+	2.07183i
$799$			6.73251i			0.238179i
$800$	20.6253	−	19.3546i	0.729213	−	0.684287i
$801$	−5.95061	−	5.95061i	−0.210255	−	0.210255i
$802$	0.777311	+	25.4367i	0.0274478	+	0.898202i
$803$	−5.23354			−0.184688
$804$	−31.1271	+	1.90418i	−1.09777	+	0.0671552i
$805$	6.79676	+	3.58141i	0.239554	+	0.126228i
$806$	0.0997209	+	3.26327i	0.00351252	+	0.114944i
$807$	10.8884			0.383289
$808$	−15.3226	−	12.7432i	−0.539046	−	0.448304i
$809$	19.3373	+	19.3373i	0.679863	+	0.679863i	0.959969	−	0.280106i	$-0.0903695\pi$
$809$	19.3373	+	19.3373i	0.679863	+	0.679863i	−0.280106	+	0.959969i	$0.590370\pi$
$810$	11.0660	+	32.2031i	0.388819	+	1.13150i
$811$	25.1970			0.884785			0.442392	−	0.896822i	$-0.354130\pi$
$811$	25.1970			0.884785			0.442392	+	0.896822i	$0.354130\pi$
$812$	5.83303	+	5.16051i	0.204699	+	0.181098i
$813$	−28.3761			−0.995192
$814$	−1.48051	+	0.0452422i	−0.0518918	+	0.00158574i
$815$	29.2364	+	15.4055i	1.02411	+	0.539632i
$816$	0.695287	+	5.66157i	0.0243399	+	0.198195i
$817$			101.792i			3.56125i
$818$	0.440150	+	14.4035i	0.0153895	+	0.503606i
$819$	0.961219			0.0335877
$820$	−17.8992	−	22.3522i	−0.625066	−	0.780572i
$821$	3.80782			0.132894			0.0664469	−	0.997790i	$-0.478834\pi$
$821$	3.80782			0.132894			0.0664469	+	0.997790i	$0.478834\pi$
$822$	1.24639	+	40.7871i	0.0434730	+	1.42261i
$823$			12.6631i			0.441408i	0.975341	+	0.220704i	$0.0708355\pi$
$823$			12.6631i			0.441408i	−0.975341	+	0.220704i	$0.929164\pi$
$824$	32.3972	+	26.9435i	1.12861	+	0.938623i
$825$	0.731180	−	3.91757i	0.0254564	−	0.136392i
$826$	−14.6863	+	0.448793i	−0.511002	+	0.0156155i
$827$	3.32821			0.115733			0.0578667	−	0.998324i	$-0.481570\pi$
$827$	3.32821			0.115733			0.0578667	+	0.998324i	$0.481570\pi$
$828$	−0.994963	+	1.12463i	−0.0345773	+	0.0390835i
$829$	49.2037			1.70892			0.854458	−	0.519521i	$-0.173890\pi$
$829$	49.2037			1.70892			0.854458	+	0.519521i	$0.173890\pi$
$830$	−31.5002	−	15.3880i	−1.09339	−	0.534125i
$831$	25.5864	+	25.5864i	0.887582	+	0.887582i
$832$	−2.54497	+	0.471774i	−0.0882309	+	0.0163558i
$833$	−4.82130			−0.167048
$834$	−0.783867	−	25.6513i	−0.0271431	−	0.888232i
$835$	0.734791	+	2.37168i	0.0254285	+	0.0820754i
$836$	−0.394109	−	6.44240i	−0.0136306	−	0.222815i
$837$	30.5436			1.05574
$838$	−0.776825	−	25.4209i	−0.0268350	−	0.878149i
$839$	−3.96526	−	3.96526i	−0.136896	−	0.136896i	0.635338	−	0.772234i	$-0.280861\pi$
$839$	−3.96526	−	3.96526i	−0.136896	−	0.136896i	−0.772234	+	0.635338i	$0.780861\pi$
$840$	−42.0411	+	17.3839i	−1.45056	+	0.599801i
$841$		−	27.8847i		−	0.961540i
$842$	13.7566	−	14.6238i	0.474082	−	0.503970i
$843$	7.81897	−	7.81897i	0.269300	−	0.269300i
$844$	23.6538	−	26.7364i	0.814198	−	0.920306i
$845$	−8.53339	−	27.5432i	−0.293558	−	0.947515i
$846$	−0.320560	−	10.4900i	−0.0110211	−	0.360654i
$847$		−	39.9440i		−	1.37249i
$848$	−5.87667	+	0.721703i	−0.201806	+	0.0247834i
$849$	−4.72474	−	4.72474i	−0.162153	−	0.162153i
$850$	−4.17221	+	3.05116i	−0.143105	+	0.104654i
$851$			2.38869i			0.0818832i
$852$	−15.8928	+	17.9640i	−0.544480	+	0.615437i
$853$	−18.6408	+	18.6408i	−0.638250	+	0.638250i	−0.950123	−	0.311874i	$-0.899043\pi$
$853$	−18.6408	+	18.6408i	−0.638250	+	0.638250i	0.311874	+	0.950123i	$0.399043\pi$
$854$	0.739686	+	24.2055i	0.0253115	+	0.828295i
$855$	6.63423	−	12.5904i	0.226886	−	0.430581i
$856$	−8.81686	−	7.33264i	−0.301354	−	0.250625i
$857$	30.6547	−	30.6547i	1.04714	−	1.04714i	0.0483118	−	0.998832i	$-0.484616\pi$
$857$	30.6547	−	30.6547i	1.04714	−	1.04714i	0.998832	−	0.0483118i	$-0.0153841\pi$
$858$	−0.249879	+	0.265633i	−0.00853074	+	0.00906855i
$859$		−	1.48910i		−	0.0508073i	−0.999677	−	0.0254037i	$-0.991913\pi$
$859$		−	1.48910i		−	0.0508073i	0.999677	−	0.0254037i	$-0.00808710\pi$
$860$	−23.7029	+	52.5319i	−0.808264	+	1.79132i
$861$	14.2118	+	43.8112i	0.484337	+	1.49308i
$862$	51.7674	−	1.58194i	1.76320	−	0.0538810i
$863$	33.1234	+	33.1234i	1.12753	+	1.12753i	0.990577	+	0.136958i	$0.0437324\pi$
$863$	33.1234	+	33.1234i	1.12753	+	1.12753i	0.136958	+	0.990577i	$0.456268\pi$
$864$	3.68435	+	23.9330i	0.125344	+	0.814217i
$865$	−47.4478	−	25.0016i	−1.61327	−	0.850081i
$866$	39.8418	+	37.4790i	1.35388	+	1.27359i
$867$			32.1217i			1.09091i
$868$	3.21291	+	52.5206i	0.109053	+	1.78267i
$869$	−3.20619			−0.108763
$870$	−5.85398	−	2.85970i	−0.198469	−	0.0969528i
$871$			2.58600i			0.0876234i
$872$	27.2970	−	32.8223i	0.924394	−	1.11150i
$873$	4.04767			0.136993
$874$	−10.4040	+	0.317933i	−0.351922	+	0.0107542i
$875$	−32.3260	−	25.5829i	−1.09282	−	0.864859i
$876$	−37.4319	−	33.1162i	−1.26471	−	1.11889i
$877$	−3.28367	+	3.28367i	−0.110882	+	0.110882i	−0.760371	−	0.649489i	$-0.774983\pi$
$877$	−3.28367	+	3.28367i	−0.110882	+	0.110882i	0.649489	+	0.760371i	$0.274983\pi$
$878$	−6.70684	+	7.12967i	−0.226345	+	0.240615i
$879$	−34.2841			−1.15637
$880$	1.29677	−	3.41651i	0.0437140	−	0.115170i
$881$			37.8065i			1.27373i	0.770975	+	0.636866i	$0.219770\pi$
$881$			37.8065i			1.27373i	−0.770975	+	0.636866i	$0.780230\pi$
$882$	7.51211	−	0.229560i	0.252946	−	0.00772967i
$883$	−52.3578			−1.76198			−0.880990	−	0.473135i	$-0.843122\pi$
$883$	−52.3578			−1.76198			−0.880990	+	0.473135i	$0.843122\pi$
$884$	0.472124	−	0.0288818i	0.0158792	−	0.000971401i
$885$	11.7409	−	3.63756i	0.394667	−	0.122275i
$886$	31.7619	+	29.8783i	1.06706	+	1.00378i
$887$		−	41.4039i		−	1.39021i	−0.718910	−	0.695103i	$-0.755359\pi$
$887$		−	41.4039i		−	1.39021i	0.718910	−	0.695103i	$-0.244641\pi$
$888$	−10.8754	−	9.04462i	−0.364953	−	0.303517i
$889$	−36.4380	−	36.4380i	−1.22209	−	1.22209i
$890$	14.4970	−	29.6764i	0.485942	−	0.994754i
$891$	3.11088	+	3.11088i	0.104218	+	0.104218i
$892$	−22.2572	+	25.1577i	−0.745225	+	0.842344i
$893$	51.4423	−	51.4423i	1.72145	−	1.72145i
$894$	26.1502	+	24.5994i	0.874595	+	0.822727i
$895$	−24.1318	+	45.7970i	−0.806637	+	1.53083i
$896$	−40.7660	+	8.85290i	−1.36190	+	0.295755i
$897$	0.415870	+	0.415870i	0.0138855	+	0.0138855i
$898$	48.3882	−	1.47868i	1.61474	−	0.0493440i
$899$	−5.32844	+	5.32844i	−0.177714	+	0.177714i
$900$	6.35548	−	4.95270i	0.211849	−	0.165090i
$901$	1.08201			0.0360468
$902$	−3.34549	−	1.57978i	−0.111393	−	0.0526009i
$903$	65.5468	−	65.5468i	2.18126	−	2.18126i
$904$	−0.648538	−	0.539364i	−0.0215700	−	0.0179390i
$905$	−0.509087	+	0.966139i	−0.0169226	+	0.0321155i
$906$	8.81568	−	9.37145i	0.292881	−	0.311346i
$907$	−22.8724	+	22.8724i	−0.759467	+	0.759467i	−0.976225	−	0.216759i	$-0.930452\pi$
$907$	−22.8724	+	22.8724i	−0.759467	+	0.759467i	0.216759	+	0.976225i	$0.430452\pi$
$908$	1.11579	+	18.2395i	0.0370287	+	0.605299i
$909$	−4.01441	−	4.01441i	−0.133150	−	0.133150i
$910$	1.22598	+	3.56773i	0.0406408	+	0.118269i
$911$	31.9063			1.05710			0.528551	−	0.848901i	$-0.322735\pi$
$911$	31.9063			1.05710			0.528551	+	0.848901i	$0.322735\pi$
$912$	37.9467	−	48.5719i	1.25654	−	1.60838i
$913$	−4.52948			−0.149904
$914$	31.7599	−	0.970537i	1.05052	−	0.0321025i
$915$	−5.99530	−	19.3510i	−0.198199	−	0.639725i
$916$	20.7670	−	23.4734i	0.686161	−	0.775582i
$917$	−22.6342			−0.747446
$918$	−0.135164	−	4.42311i	−0.00446108	−	0.145984i
$919$	2.87849	+	2.87849i	0.0949528	+	0.0949528i	0.752988	−	0.658035i	$-0.228612\pi$
$919$	2.87849	+	2.87849i	0.0949528	+	0.0949528i	−0.658035	+	0.752988i	$0.728612\pi$
$920$	−5.44326	−	2.25858i	−0.179459	−	0.0744630i
$921$	−17.9188	−	17.9188i	−0.590443	−	0.590443i
$922$	18.6668	−	0.570432i	0.614760	−	0.0187862i
$923$	1.40639	+	1.40639i	0.0462920	+	0.0462920i
$924$	−3.89467	+	4.40223i	−0.128125	+	0.144823i
$925$	2.35168	−	12.6000i	0.0773226	−	0.414285i
$926$	1.47249	+	48.1858i	0.0483890	+	1.58348i
$927$	8.48787	+	8.48787i	0.278778	+	0.278778i
$928$	−4.81795	−	3.53245i	−0.158157	−	0.115958i
$929$	35.3097	−	35.3097i	1.15847	−	1.15847i	0.173670	−	0.984804i	$-0.444437\pi$
$929$	35.3097	−	35.3097i	1.15847	−	1.15847i	0.984804	−	0.173670i	$-0.0555627\pi$
$930$	−14.3049	−	41.6288i	−0.469077	−	1.36506i
$931$	36.8389	+	36.8389i	1.20735	+	1.20735i
$932$	−11.8046	+	0.722135i	−0.386671	+	0.0236543i
$933$	12.6498	+	12.6498i	0.414135	+	0.414135i
$934$	−15.5010	−	14.5817i	−0.507209	−	0.477129i
$935$	−0.311316	+	0.590812i	−0.0101811	+	0.0193216i
$936$	−0.734246	+	0.0674806i	−0.0239996	+	0.00220567i
$937$	−25.3935			−0.829568			−0.414784	−	0.909920i	$-0.636143\pi$
$937$	−25.3935			−0.829568			−0.414784	+	0.909920i	$0.636143\pi$
$938$	1.27305	+	41.6593i	0.0415666	+	1.36023i
$939$	36.2939			1.18441
$940$	38.5266	−	14.5692i	1.25660	−	0.475195i
$941$		−	40.4170i		−	1.31756i	−0.752337	−	0.658779i	$-0.771073\pi$
$941$		−	40.4170i		−	1.31756i	0.752337	−	0.658779i	$-0.228927\pi$
$942$	−31.4467	+	0.960965i	−1.02459	+	0.0313099i
$943$	−2.71127	+	5.31484i	−0.0882911	+	0.173075i
$944$	11.1869	−	1.37384i	0.364103	−	0.0447148i
$945$	33.7124	−	10.4447i	1.09666	−	0.339767i
$946$	0.227434	+	7.44257i	0.00739453	+	0.241979i
$947$	21.9379	+	21.9379i	0.712886	+	0.712886i	0.967138	−	0.254252i	$-0.0818291\pi$
$947$	21.9379	+	21.9379i	0.712886	+	0.712886i	−0.254252	+	0.967138i	$0.581829\pi$
$948$	−22.9317	−	20.2878i	−0.744788	−	0.658917i
$949$	−2.93053	+	2.93053i	−0.0951291	+	0.0951291i
$950$	55.1928	+	8.56578i	1.79069	+	0.277911i
$951$	51.1026			1.65711
$952$	7.59147	−	0.697692i	0.246041	−	0.0226123i
$953$	22.0816	+	22.0816i	0.715295	+	0.715295i	0.967638	−	0.252343i	$-0.0812012\pi$
$953$	22.0816	+	22.0816i	0.715295	+	0.715295i	−0.252343	+	0.967638i	$0.581201\pi$
$954$	−1.68589	+	0.0515183i	−0.0545826	+	0.00166797i
$955$	−5.51103	−	2.90392i	−0.178333	−	0.0939688i
$956$	6.00599	−	6.78869i	0.194247	−	0.219562i
$957$	−0.841756			−0.0272101
$958$	−32.2687	+	34.3030i	−1.04255	+	1.10828i
$959$	54.5369			1.76109
$960$	30.8935	−	16.2304i	0.997084	−	0.523835i
$961$	−19.9124			−0.642334
$962$	−0.803681	+	0.854348i	−0.0259117	+	0.0275453i
$963$	−2.30996	−	2.30996i	−0.0744374	−	0.0744374i
$964$	−1.40395	−	22.9500i	−0.0452182	−	0.739170i
$965$	−11.5386	−	37.2432i	−0.371441	−	1.19890i
$966$	6.90420	+	6.49474i	0.222139	+	0.208965i
$967$			42.4462i			1.36498i	0.730896	+	0.682489i	$0.239102\pi$
$967$			42.4462i			1.36498i	−0.730896	+	0.682489i	$0.760898\pi$
$968$	2.80419	+	30.5120i	0.0901302	+	0.980692i
$969$	−7.96486	+	7.96486i	−0.255868	+	0.255868i
$970$	5.16257	+	15.0236i	0.165760	+	0.482379i
$971$	−26.2522	−	26.2522i	−0.842473	−	0.842473i	0.146707	−	0.989180i	$-0.453133\pi$
$971$	−26.2522	−	26.2522i	−0.842473	−	0.842473i	−0.989180	+	0.146707i	$0.953133\pi$
$972$	0.997069	+	16.2988i	0.0319810	+	0.522785i
$973$	−34.2987			−1.09956
$974$	38.0221	−	40.4192i	1.21831	−	1.29511i
$975$	−1.78423	−	2.60308i	−0.0571410	−	0.0833652i
$976$	−2.26433	−	18.4379i	−0.0724793	−	0.590183i
$977$		−	32.1149i		−	1.02745i	−0.857956	−	0.513724i	$-0.828266\pi$
$977$		−	32.1149i		−	1.02745i	0.857956	−	0.513724i	$-0.171734\pi$
$978$	29.6985	+	27.9373i	0.949654	+	0.893335i
$979$		−	4.26723i		−	0.136381i
$980$	10.4333	+	27.5897i	0.333280	+	0.881320i
$981$	8.59923	−	8.59923i	0.274552	−	0.274552i
$982$	1.11584	+	36.5146i	0.0356077	+	1.16523i
$983$	18.2885	−	18.2885i	0.583314	−	0.583314i	−0.352499	−	0.935812i	$-0.614668\pi$
$983$	18.2885	−	18.2885i	0.583314	−	0.583314i	0.935812	+	0.352499i	$0.114668\pi$
$984$	−13.9316	−	32.4683i	−0.444125	−	1.03505i
$985$	16.5219	−	31.3550i	0.526431	−	0.999054i
$986$	0.795210	+	0.748050i	0.0253246	+	0.0238228i
$987$	−66.2504			−2.10877
$988$	−3.82812	−	3.38675i	−0.121789	−	0.107747i
$989$	12.0080			0.381833
$990$	0.456934	−	0.935373i	0.0145223	−	0.0297281i
$991$	−11.9252	−	11.9252i	−0.378817	−	0.378817i	0.491858	−	0.870675i	$-0.336318\pi$
$991$	−11.9252	−	11.9252i	−0.378817	−	0.378817i	−0.870675	+	0.491858i	$0.836318\pi$
$992$	−6.14136	−	39.8933i	−0.194988	−	1.26662i
$993$	−18.9322	+	18.9322i	−0.600795	+	0.600795i
$994$	23.3487	+	21.9640i	0.740576	+	0.696656i
$995$	−7.26728	+	13.7918i	−0.230388	+	0.437228i
$996$	−32.3963	−	28.6612i	−1.02652	−	0.908163i
$997$		−	6.56334i		−	0.207863i	−0.994584	−	0.103932i	$-0.966858\pi$
$997$		−	6.56334i		−	0.207863i	0.994584	−	0.103932i	$-0.0331423\pi$
$998$	30.6826	−	32.6170i	0.971241	−	1.03247i
$999$	7.75941	+	7.75941i	0.245497	+	0.245497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.1	✓	240
4.3	odd	2	inner	820.2.j.c.483.64	yes	240
5.2	odd	4		820.2.s.c.647.57	yes	240
20.7	even	4		820.2.s.c.647.120	yes	240
41.9	even	4		820.2.s.c.583.120	yes	240
164.91	odd	4		820.2.s.c.583.57	yes	240
205.132	odd	4	inner	820.2.j.c.747.64	yes	240
820.747	even	4	inner	820.2.j.c.747.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.1	✓	240	1.1	even	1	trivial
820.2.j.c.483.64	yes	240	4.3	odd	2	inner
820.2.j.c.747.1	yes	240	820.747	even	4	inner
820.2.j.c.747.64	yes	240	205.132	odd	4	inner
820.2.s.c.583.57	yes	240	164.91	odd	4
820.2.s.c.583.120	yes	240	41.9	even	4
820.2.s.c.647.57	yes	240	5.2	odd	4
820.2.s.c.647.120	yes	240	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41355 + 0.0431962i) q^{2} -1.95083i q^{3} +(1.99627 - 0.122120i) q^{4} +(0.661743 + 2.13591i) q^{5} +(0.0842684 + 2.75760i) q^{6} +3.68722 q^{7} +(-2.81656 + 0.258855i) q^{8} -0.805738 q^{9} +(-1.02767 - 2.99063i) q^{10} +(-0.288900 - 0.288900i) q^{11} +(-0.238236 - 3.89438i) q^{12} -0.323541 q^{13} +(-5.21209 + 0.159274i) q^{14} +(4.16679 - 1.29095i) q^{15} +(3.97017 - 0.487570i) q^{16} -0.730984 q^{17} +(1.13895 - 0.0348048i) q^{18} +(5.58536 + 5.58536i) q^{19} +(1.58185 + 4.18303i) q^{20} -7.19315i q^{21} +(0.420855 + 0.395897i) q^{22} +(0.658884 - 0.658884i) q^{23} +(0.504982 + 5.49462i) q^{24} +(-4.12419 + 2.82684i) q^{25} +(0.457342 - 0.0139757i) q^{26} -4.28063i q^{27} +(7.36069 - 0.450285i) q^{28} +(0.746773 + 0.746773i) q^{29} +(-5.83422 + 2.00481i) q^{30} +7.13529i q^{31} +(-5.59099 + 0.860702i) q^{32} +(-0.563595 + 0.563595i) q^{33} +(1.03328 - 0.0315757i) q^{34} +(2.44000 + 7.87557i) q^{35} +(-1.60847 + 0.0983970i) q^{36} +(-1.81268 + 1.81268i) q^{37} +(-8.13647 - 7.65393i) q^{38} +0.631173i q^{39} +(-2.41673 - 5.84461i) q^{40} +(-6.09068 + 1.97574i) q^{41} +(0.310717 + 10.1679i) q^{42} +(9.11240 + 9.11240i) q^{43} +(-0.612003 - 0.541442i) q^{44} +(-0.533192 - 1.72098i) q^{45} +(-0.902907 + 0.959829i) q^{46} -9.21021i q^{47} +(-0.951166 - 7.74513i) q^{48} +6.59563 q^{49} +(5.70766 - 4.17404i) q^{50} +1.42603i q^{51} +(-0.645874 + 0.0395109i) q^{52} -1.48020 q^{53} +(0.184907 + 6.05090i) q^{54} +(0.425886 - 0.808242i) q^{55} +(-10.3853 + 0.954456i) q^{56} +(10.8961 - 10.8961i) q^{57} +(-1.08786 - 1.02335i) q^{58} +2.81774 q^{59} +(8.16038 - 3.08593i) q^{60} -4.64411i q^{61} +(-0.308217 - 10.0861i) q^{62} -2.97094 q^{63} +(7.86599 - 1.45816i) q^{64} +(-0.214101 - 0.691053i) q^{65} +(0.772327 - 0.821017i) q^{66} -7.99283i q^{67} +(-1.45924 + 0.0892680i) q^{68} +(-1.28537 - 1.28537i) q^{69} +(-3.78926 - 11.0271i) q^{70} +(-4.34688 - 4.34688i) q^{71} +(2.26941 - 0.208569i) q^{72} +(9.05769 - 9.05769i) q^{73} +(2.48402 - 2.64062i) q^{74} +(5.51469 + 8.04560i) q^{75} +(11.8320 + 10.4678i) q^{76} +(-1.06524 - 1.06524i) q^{77} +(-0.0272643 - 0.892197i) q^{78} +(5.54896 - 5.54896i) q^{79} +(3.66864 + 8.15727i) q^{80} -10.7680 q^{81} +(8.52417 - 3.05591i) q^{82} +(7.83917 - 7.83917i) q^{83} +(-0.878429 - 14.3595i) q^{84} +(-0.483724 - 1.56131i) q^{85} +(-13.2745 - 12.4872i) q^{86} +(1.45683 - 1.45683i) q^{87} +(0.888487 + 0.738921i) q^{88} +(7.38530 + 7.38530i) q^{89} +(0.828035 + 2.40967i) q^{90} -1.19297 q^{91} +(1.23485 - 1.39577i) q^{92} +13.9197 q^{93} +(0.397846 + 13.0191i) q^{94} +(-8.23373 + 15.6259i) q^{95} +(1.67908 + 10.9071i) q^{96} -5.02356 q^{97} +(-9.32327 + 0.284906i) q^{98} +(0.232778 + 0.232778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more