LMFDB - Embedded newform 820.2.bw.a.11.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(11,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bw (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [672,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$42$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.a.671.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.784452 - 1.17670i) q^{2} +(-1.17659 + 2.84053i) q^{3} +(-0.769269 + 1.84614i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(4.26544 - 0.843765i) q^{6} +(0.0665249 + 0.277096i) q^{7} +(2.77581 - 0.543004i) q^{8} +(-4.56293 - 4.56293i) q^{9} +(1.40459 - 0.164739i) q^{10} +(2.73125 - 3.19788i) q^{11} +(-4.33890 - 4.35727i) q^{12} +(-2.05901 - 3.36000i) q^{13} +(0.273875 - 0.295649i) q^{14} +(-1.99677 - 2.33792i) q^{15} +(-2.81645 - 2.84035i) q^{16} +(-0.281087 - 3.57155i) q^{17} +(-1.78982 + 8.94863i) q^{18} +(-1.97203 - 1.20846i) q^{19} +(-1.29568 - 1.52355i) q^{20} +(-0.865372 - 0.137061i) q^{21} +(-5.90550 - 0.705289i) q^{22} +(6.89158 + 5.00703i) q^{23} +(-1.72357 + 8.52367i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-2.33853 + 5.05860i) q^{26} +(9.80823 - 4.06270i) q^{27} +(-0.562733 - 0.0903474i) q^{28} +(0.343512 - 4.36473i) q^{29} +(-1.18467 + 4.18360i) q^{30} +(1.94443 - 5.98433i) q^{31} +(-1.13289 + 5.54225i) q^{32} +(5.87013 + 11.5208i) q^{33} +(-3.98216 + 3.13246i) q^{34} +(-0.277096 - 0.0665249i) q^{35} +(11.9339 - 4.91368i) q^{36} +(1.20825 + 3.71862i) q^{37} +(0.124961 + 3.26847i) q^{38} +(11.9668 - 1.89535i) q^{39} +(-0.776373 + 2.71979i) q^{40} +(-6.33812 + 0.910071i) q^{41} +(0.517562 + 1.12581i) q^{42} +(0.661732 + 4.17801i) q^{43} +(3.80267 + 7.50230i) q^{44} +(6.13713 - 1.99407i) q^{45} +(0.485677 - 12.0371i) q^{46} +(0.360148 - 1.50012i) q^{47} +(11.3819 - 4.65829i) q^{48} +(6.16469 - 3.14107i) q^{49} +(-0.490885 + 1.32629i) q^{50} +(10.4758 + 3.40379i) q^{51} +(7.78695 - 1.21647i) q^{52} +(-9.44518 - 0.743352i) q^{53} +(-12.4747 - 8.35440i) q^{54} +(1.60937 + 3.88537i) q^{55} +(0.335125 + 0.733044i) q^{56} +(5.75293 - 4.17975i) q^{57} +(-5.40547 + 3.01971i) q^{58} +(2.88318 - 3.96836i) q^{59} +(5.85217 - 1.88783i) q^{60} +(0.174231 - 1.10005i) q^{61} +(-8.56710 + 2.40640i) q^{62} +(0.960822 - 1.56792i) q^{63} +(7.41029 - 3.01456i) q^{64} +(3.92855 - 0.309184i) q^{65} +(8.95172 - 15.9449i) q^{66} +(4.20718 - 3.59327i) q^{67} +(6.80980 + 2.22856i) q^{68} +(-22.3311 + 13.6845i) q^{69} +(0.139089 + 0.378246i) q^{70} +(-0.838398 - 0.716060i) q^{71} +(-15.1435 - 10.1882i) q^{72} +(6.86411 - 6.86411i) q^{73} +(3.42790 - 4.33884i) q^{74} +(2.98962 - 0.717743i) q^{75} +(3.74800 - 2.71100i) q^{76} +(1.06782 + 0.544080i) q^{77} +(-11.6176 - 12.5945i) q^{78} +(-1.64895 - 0.683016i) q^{79} +(3.80942 - 1.21998i) q^{80} +13.2818i q^{81} +(6.04284 + 6.74419i) q^{82} +13.5713i q^{83} +(0.918738 - 1.49216i) q^{84} +(3.30988 + 1.37100i) q^{85} +(4.39719 - 4.05611i) q^{86} +(11.9940 + 6.11124i) q^{87} +(5.84498 - 10.3598i) q^{88} +(-6.38399 + 1.53266i) q^{89} +(-7.16072 - 5.65733i) q^{90} +(0.794067 - 0.794067i) q^{91} +(-14.5451 + 8.87105i) q^{92} +(14.7109 + 12.5643i) q^{93} +(-2.04772 + 0.752987i) q^{94} +(1.97203 - 1.20846i) q^{95} +(-14.4100 - 9.73894i) q^{96} +(12.3178 - 10.5204i) q^{97} +(-8.53201 - 4.79000i) q^{98} +(-27.0542 + 2.12921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 100 q^{12} + 24 q^{14} + 32 q^{16} - 8 q^{17} - 40 q^{21} + 52 q^{22} - 24 q^{24} + 28 q^{28} + 12 q^{30} - 20 q^{32} + 40 q^{33} + 44 q^{34} + 36 q^{36} - 80 q^{37} + 52 q^{38} - 160 q^{42}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 100 * q^12 + 24 * q^14 + 32 * q^16 - 8 * q^17 - 40 * q^21 + 52 * q^22 - 24 * q^24 + 28 * q^28 + 12 * q^30 - 20 * q^32 + 40 * q^33 + 44 * q^34 + 36 * q^36 - 80 * q^37 + 52 * q^38 - 160 * q^42 + 24 * q^44 + 16 * q^46 + 40 * q^48 - 16 * q^49 - 64 * q^52 - 64 * q^54 + 68 * q^56 + 56 * q^58 + 36 * q^62 + 120 * q^64 + 8 * q^65 - 304 * q^68 + 104 * q^69 + 24 * q^70 - 40 * q^72 - 28 * q^74 - 24 * q^76 - 160 * q^77 - 128 * q^78 - 192 * q^82 - 204 * q^84 + 32 * q^85 - 168 * q^88 + 8 * q^89 + 48 * q^90 - 56 * q^92 - 356 * q^94 - 136 * q^96 - 116 * q^98

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$	$1$

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 $

$2$	−0.784452	−	1.17670i	−0.554692	−	0.832056i
$2$	−0.784452	−	1.17670i	−0.554692	−	0.832056i
$3$	−1.17659	+	2.84053i	−0.679302	+	1.63998i	0.0859892	+	0.996296i	$0.472595\pi$
$3$	−1.17659	+	2.84053i	−0.679302	+	1.63998i	−0.765291	+	0.643684i	$0.777405\pi$
$4$	−0.769269	+	1.84614i	−0.384635	+	0.923069i
$5$	−0.453990	+	0.891007i	−0.203031	+	0.398470i
$5$	−0.453990	+	0.891007i	−0.203031	+	0.398470i
$6$	4.26544	−	0.843765i	1.74136	−	0.344466i
$7$	0.0665249	+	0.277096i	0.0251441	+	0.104733i	0.983531	−	0.180740i	$-0.0578494\pi$
$7$	0.0665249	+	0.277096i	0.0251441	+	0.104733i	−0.958387	+	0.285473i	$0.907849\pi$
$8$	2.77581	−	0.543004i	0.981399	−	0.191981i
$9$	−4.56293	−	4.56293i	−1.52098	−	1.52098i
$10$	1.40459	−	0.164739i	0.444169	−	0.0520951i
$11$	2.73125	−	3.19788i	0.823503	−	0.964198i	−0.176294	−	0.984338i	$-0.556411\pi$
$11$	2.73125	−	3.19788i	0.823503	−	0.964198i	0.999797	+	0.0201394i	$0.00641099\pi$
$12$	−4.33890	−	4.35727i	−1.25253	−	1.25784i
$13$	−2.05901	−	3.36000i	−0.571066	−	0.931896i	−0.999598	−	0.0283685i	$-0.990969\pi$
$13$	−2.05901	−	3.36000i	−0.571066	−	0.931896i	0.428531	−	0.903527i	$-0.359031\pi$
$14$	0.273875	−	0.295649i	0.0731961	−	0.0790155i
$15$	−1.99677	−	2.33792i	−0.515564	−	0.603648i
$16$	−2.81645	−	2.84035i	−0.704112	−	0.710089i
$17$	−0.281087	−	3.57155i	−0.0681735	−	0.866227i	−0.932005	−	0.362446i	$-0.881942\pi$
$17$	−0.281087	−	3.57155i	−0.0681735	−	0.866227i	0.863831	−	0.503781i	$-0.168058\pi$
$18$	−1.78982	+	8.94863i	−0.421865	+	2.10921i
$19$	−1.97203	−	1.20846i	−0.452414	−	0.277240i	0.277568	−	0.960706i	$-0.410472\pi$
$19$	−1.97203	−	1.20846i	−0.452414	−	0.277240i	−0.729982	+	0.683466i	$0.760472\pi$
$20$	−1.29568	−	1.52355i	−0.289723	−	0.340677i
$21$	−0.865372	−	0.137061i	−0.188840	−	0.0299093i
$22$	−5.90550	−	0.705289i	−1.25906	−	0.150368i
$23$	6.89158	+	5.00703i	1.43699	+	1.04404i	0.988660	+	0.150171i	$0.0479823\pi$
$23$	6.89158	+	5.00703i	1.43699	+	1.04404i	0.448333	+	0.893866i	$0.352018\pi$
$24$	−1.72357	+	8.52367i	−0.351821	+	1.73989i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	−2.33853	+	5.05860i	−0.458624	+	0.992074i
$27$	9.80823	−	4.06270i	1.88760	−	0.781868i
$28$	−0.562733	−	0.0903474i	−0.106347	−	0.0170741i
$29$	0.343512	−	4.36473i	0.0637886	−	0.810511i	−0.878936	−	0.476939i	$-0.841746\pi$
$29$	0.343512	−	4.36473i	0.0637886	−	0.810511i	0.942725	−	0.333571i	$-0.108254\pi$
$30$	−1.18467	+	4.18360i	−0.216290	+	0.763817i
$31$	1.94443	−	5.98433i	0.349229	−	1.07482i	−0.610051	−	0.792362i	$-0.708851\pi$
$31$	1.94443	−	5.98433i	0.349229	−	1.07482i	0.959281	−	0.282455i	$-0.0911488\pi$
$32$	−1.13289	+	5.54225i	−0.200268	+	0.979741i
$33$	5.87013	+	11.5208i	1.02186	+	2.00551i
$34$	−3.98216	+	3.13246i	−0.682934	+	0.537213i
$35$	−0.277096	−	0.0665249i	−0.0468378	−	0.0112448i
$36$	11.9339	−	4.91368i	1.98899	−	0.818946i
$37$	1.20825	+	3.71862i	0.198636	+	0.611337i	0.999915	+	0.0130470i	$0.00415310\pi$
$37$	1.20825	+	3.71862i	0.198636	+	0.611337i	−0.801279	+	0.598290i	$0.795847\pi$
$38$	0.124961	+	3.26847i	0.0202713	+	0.530217i
$39$	11.9668	−	1.89535i	1.91622	−	0.303499i
$40$	−0.776373	+	2.71979i	−0.122755	+	0.430036i
$41$	−6.33812	+	0.910071i	−0.989848	+	0.142129i
$41$	−6.33812	+	0.910071i	−0.989848	+	0.142129i
$42$	0.517562	+	1.12581i	0.0798616	+	0.173716i
$43$	0.661732	+	4.17801i	0.100913	+	0.637140i	0.985358	+	0.170496i	$0.0545371\pi$
$43$	0.661732	+	4.17801i	0.100913	+	0.637140i	−0.884445	+	0.466644i	$0.845463\pi$
$44$	3.80267	+	7.50230i	0.573274	+	1.13101i
$45$	6.13713	−	1.99407i	0.914869	−	0.297259i
$46$	0.485677	−	12.0371i	0.0716091	−	1.77478i
$47$	0.360148	−	1.50012i	0.0525329	−	0.218815i	−0.939929	−	0.341371i	$-0.889109\pi$
$47$	0.360148	−	1.50012i	0.0525329	−	0.218815i	0.992462	+	0.122555i	$0.0391089\pi$
$48$	11.3819	−	4.65829i	1.64284	−	0.672366i
$49$	6.16469	−	3.14107i	0.880670	−	0.448724i
$50$	−0.490885	+	1.32629i	−0.0694216	+	0.187565i
$51$	10.4758	+	3.40379i	1.46691	+	0.476626i
$52$	7.78695	−	1.21647i	1.07986	−	0.168694i
$53$	−9.44518	−	0.743352i	−1.29740	−	0.102107i	−0.589121	−	0.808045i	$-0.700526\pi$
$53$	−9.44518	−	0.743352i	−1.29740	−	0.102107i	−0.708274	+	0.705937i	$0.750526\pi$
$54$	−12.4747	−	8.35440i	−1.69759	−	1.13689i
$55$	1.60937	+	3.88537i	0.217008	+	0.523903i
$56$	0.335125	+	0.733044i	0.0447830	+	0.0979572i
$57$	5.75293	−	4.17975i	0.761994	−	0.553621i
$58$	−5.40547	+	3.01971i	−0.709773	+	0.396508i
$59$	2.88318	−	3.96836i	0.375358	−	0.516637i	−0.578989	−	0.815335i	$-0.696553\pi$
$59$	2.88318	−	3.96836i	0.375358	−	0.516637i	0.954347	+	0.298699i	$0.0965526\pi$
$60$	5.85217	−	1.88783i	0.755513	−	0.243717i
$61$	0.174231	−	1.10005i	0.0223080	−	0.140847i	−0.974020	−	0.226460i	$-0.927285\pi$
$61$	0.174231	−	1.10005i	0.0223080	−	0.140847i	0.996328	+	0.0856127i	$0.0272848\pi$
$62$	−8.56710	+	2.40640i	−1.08802	+	0.305614i
$63$	0.960822	−	1.56792i	0.121052	−	0.197539i
$64$	7.41029	−	3.01456i	0.926287	−	0.376820i
$65$	3.92855	−	0.309184i	0.487277	−	0.0383495i
$66$	8.95172	−	15.9449i	1.10188	−	1.96268i
$67$	4.20718	−	3.59327i	0.513988	−	0.438988i	−0.354238	−	0.935155i	$-0.615260\pi$
$67$	4.20718	−	3.59327i	0.513988	−	0.438988i	0.868227	+	0.496168i	$0.165260\pi$
$68$	6.80980	+	2.22856i	0.825809	+	0.270252i
$69$	−22.3311	+	13.6845i	−2.68835	+	1.64742i
$70$	0.139089	+	0.378246i	0.0166243	+	0.0452091i
$71$	−0.838398	−	0.716060i	−0.0994996	−	0.0849807i	0.598307	−	0.801267i	$-0.295840\pi$
$71$	−0.838398	−	0.716060i	−0.0994996	−	0.0849807i	−0.697806	+	0.716286i	$0.745840\pi$
$72$	−15.1435	−	10.1882i	−1.78468	−	1.20069i
$73$	6.86411	−	6.86411i	0.803383	−	0.803383i	−0.180240	−	0.983623i	$-0.557687\pi$
$73$	6.86411	−	6.86411i	0.803383	−	0.803383i	0.983623	+	0.180240i	$0.0576874\pi$
$74$	3.42790	−	4.33884i	0.398486	−	0.504380i
$75$	2.98962	−	0.717743i	0.345211	−	0.0828779i
$76$	3.74800	−	2.71100i	0.429926	−	0.310973i
$77$	1.06782	+	0.544080i	0.121689	+	0.0620037i
$78$	−11.6176	−	12.5945i	−1.31544	−	1.42605i
$79$	−1.64895	−	0.683016i	−0.185521	−	0.0768453i	0.287989	−	0.957634i	$-0.407013\pi$
$79$	−1.64895	−	0.683016i	−0.185521	−	0.0768453i	−0.473510	+	0.880788i	$0.657013\pi$
$80$	3.80942	−	1.21998i	0.425906	−	0.136398i
$81$			13.2818i			1.47576i
$82$	6.04284	+	6.74419i	0.667320	+	0.744771i
$83$			13.5713i			1.48965i	0.667262	+	0.744823i	$0.267466\pi$
$83$			13.5713i			1.48965i	−0.667262	+	0.744823i	$0.732534\pi$
$84$	0.918738	−	1.49216i	0.100243	−	0.162808i
$85$	3.30988	+	1.37100i	0.359007	+	0.148706i
$86$	4.39719	−	4.05611i	0.474161	−	0.437382i
$87$	11.9940	+	6.11124i	1.28589	+	0.655194i
$88$	5.84498	−	10.3598i	0.623077	−	1.10436i
$89$	−6.38399	+	1.53266i	−0.676702	+	0.162462i	−0.557208	−	0.830373i	$-0.688127\pi$
$89$	−6.38399	+	1.53266i	−0.676702	+	0.162462i	−0.119494	+	0.992835i	$0.538127\pi$
$90$	−7.16072	−	5.65733i	−0.754806	−	0.596335i
$91$	0.794067	−	0.794067i	0.0832408	−	0.0832408i
$92$	−14.5451	+	8.87105i	−1.51644	+	0.924871i
$93$	14.7109	+	12.5643i	1.52545	+	1.30285i
$94$	−2.04772	+	0.752987i	−0.211206	+	0.0776647i
$95$	1.97203	−	1.20846i	0.202326	−	0.123985i
$96$	−14.4100	−	9.73894i	−1.47071	−	0.993976i
$97$	12.3178	−	10.5204i	1.25068	−	1.06818i	0.255843	−	0.966718i	$-0.417647\pi$
$97$	12.3178	−	10.5204i	1.25068	−	1.06818i	0.994839	−	0.101465i	$-0.0323530\pi$
$98$	−8.53201	−	4.79000i	−0.861863	−	0.483863i
$99$	−27.0542	+	2.12921i	−2.71905	+	0.213994i
$100$	1.94572	−	0.462781i	0.194572	−	0.0462781i
$101$	6.92379	−	11.2986i	0.688943	−	1.12425i	−0.296629	−	0.954993i	$-0.595862\pi$
$101$	6.92379	−	11.2986i	0.688943	−	1.12425i	0.985571	−	0.169260i	$-0.0541377\pi$
$102$	−4.21250	−	14.9970i	−0.417100	−	1.48493i
$103$	2.01600	−	12.7285i	0.198642	−	1.25418i	−0.663756	−	0.747949i	$-0.731039\pi$
$103$	2.01600	−	12.7285i	0.198642	−	1.25418i	0.862398	−	0.506230i	$-0.168961\pi$
$104$	−7.53992	−	8.20868i	−0.739350	−	0.804927i
$105$	0.514993	−	0.708828i	0.0502582	−	0.0691745i
$106$	6.53459	+	11.6973i	0.634695	+	1.13614i
$107$	−15.0634	+	10.9442i	−1.45623	+	1.05801i	−0.471906	+	0.881649i	$0.656434\pi$
$107$	−15.0634	+	10.9442i	−1.45623	+	1.05801i	−0.984325	+	0.176365i	$0.943566\pi$
$108$	−0.0448625	+	21.2327i	−0.00431690	+	2.04311i
$109$	1.22469	+	2.95666i	0.117304	+	0.283197i	0.971616	−	0.236564i	$-0.0760211\pi$
$109$	1.22469	+	2.95666i	0.117304	+	0.283197i	−0.854312	+	0.519761i	$0.826021\pi$
$110$	3.30946	−	4.94165i	0.315545	−	0.471167i
$111$	−11.9845	−	0.943198i	−1.13751	−	0.0895244i
$112$	0.599687	−	0.969382i	0.0566651	−	0.0915980i
$113$	−5.13044	−	1.66698i	−0.482631	−	0.156816i	0.0575885	−	0.998340i	$-0.481659\pi$
$113$	−5.13044	−	1.66698i	−0.482631	−	0.156816i	−0.540220	+	0.841524i	$0.681659\pi$
$114$	−9.43122	−	3.49069i	−0.883315	−	0.326933i
$115$	−7.59000	+	3.86730i	−0.707771	+	0.360628i
$116$	7.79365	+	3.99183i	0.723622	+	0.370632i
$117$	−5.93632	+	24.7266i	−0.548813	+	2.28597i
$118$	−6.93131	−	0.279666i	−0.638079	−	0.0257454i
$119$	0.970962	−	0.315485i	0.0890080	−	0.0289204i
$120$	−6.81217	−	5.40537i	−0.621863	−	0.493441i
$121$	−1.04595	−	6.60387i	−0.0950864	−	0.600352i
$122$	−1.43111	+	0.657919i	−0.129567	+	0.0595652i
$123$	4.87226	−	19.0744i	0.439317	−	1.71988i
$124$	9.55211	+	8.19324i	0.857804	+	0.735774i
$125$	0.987688	−	0.156434i	0.0883415	−	0.0139919i
$126$	−2.59870	+	0.0993536i	−0.231510	+	0.00885112i
$127$	3.46866	+	10.6754i	0.307794	+	0.947292i	0.978620	+	0.205677i	$0.0659397\pi$
$127$	3.46866	+	10.6754i	0.307794	+	0.947292i	−0.670826	+	0.741615i	$0.734060\pi$
$128$	−9.36027	−	6.35495i	−0.827338	−	0.561704i
$129$	−12.6463	−	3.03612i	−1.11345	−	0.267315i
$130$	−3.44558	−	4.38020i	−0.302197	−	0.384169i
$131$	0.733247	+	1.43908i	0.0640641	+	0.125733i	0.920818	−	0.389993i	$-0.127522\pi$
$131$	0.733247	+	1.43908i	0.0640641	+	0.125733i	−0.856754	+	0.515725i	$0.827522\pi$
$132$	−25.7847	+	1.97449i	−2.24427	+	0.171857i
$133$	0.203671	−	0.626834i	0.0176605	−	0.0543534i
$134$	−7.52854	−	2.13186i	−0.650367	−	0.184164i
$135$	−0.832950	+	10.5836i	−0.0716889	+	0.910894i
$136$	−2.71961	−	9.76132i	−0.233204	−	0.837026i
$137$	18.9222	−	7.83783i	1.61663	−	0.669631i	0.622992	−	0.782228i	$-0.285917\pi$
$137$	18.9222	−	7.83783i	1.61663	−	0.669631i	0.993641	+	0.112597i	$0.0359169\pi$
$138$	33.6204	+	15.5423i	2.86196	+	1.32305i
$139$	−10.9708	−	15.1000i	−0.930532	−	1.28077i	−0.959652	−	0.281192i	$-0.909270\pi$
$139$	−10.9708	−	15.1000i	−0.930532	−	1.28077i	0.0291193	−	0.999576i	$-0.490730\pi$
$140$	0.335976	−	0.460382i	0.0283951	−	0.0389094i
$141$	3.83740	+	2.78803i	0.323167	+	0.234795i
$142$	−0.184908	+	1.54826i	−0.0155171	+	0.129927i
$143$	−16.3685	−	2.59252i	−1.36881	−	0.216798i
$144$	−0.109075	+	25.8116i	−0.00908960	+	2.15097i
$145$	3.73305	+	2.28762i	0.310013	+	0.189976i
$146$	−13.4616	−	2.69246i	−1.11409	−	0.222830i
$147$	1.66900	+	21.2067i	0.137657	+	1.74910i
$148$	−7.79456	−	0.630019i	−0.640709	−	0.0517872i
$149$	−5.58514	−	6.53936i	−0.457553	−	0.535725i	0.482888	−	0.875682i	$-0.339588\pi$
$149$	−5.58514	−	6.53936i	−0.457553	−	0.535725i	−0.940441	+	0.339956i	$0.889588\pi$
$150$	−3.18978	−	2.95486i	−0.260445	−	0.241263i
$151$	−2.56945	−	4.19296i	−0.209099	−	0.341218i	0.730847	−	0.682541i	$-0.239125\pi$
$151$	−2.56945	−	4.19296i	−0.209099	−	0.341218i	−0.939946	+	0.341323i	$0.889125\pi$
$152$	−6.13018	−	2.28364i	−0.497223	−	0.185228i
$153$	−15.0141	+	17.5793i	−1.21382	+	1.42120i
$154$	−0.197430	−	1.68331i	−0.0159094	−	0.135645i
$155$	4.44932	+	4.44932i	0.357378	+	0.357378i
$156$	−5.70659	+	23.5503i	−0.456893	+	1.88554i
$157$	1.07344	+	4.47121i	0.0856701	+	0.356842i	0.998696	−	0.0510610i	$-0.0162603\pi$
$157$	1.07344	+	4.47121i	0.0856701	+	0.356842i	−0.913025	+	0.407903i	$0.866260\pi$
$158$	0.489812	+	2.47612i	0.0389673	+	0.196989i
$159$	13.2246	−	25.9547i	1.04878	−	2.05834i
$160$	−4.42386	−	3.52554i	−0.349737	−	0.278719i
$161$	−0.928966	+	2.24272i	−0.0732128	+	0.176751i
$162$	15.6288	−	10.4189i	1.22791	−	0.818590i
$163$	−13.7087			−1.07375			−0.536875	−	0.843662i	$-0.680395\pi$
$163$	−13.7087			−1.07375			−0.536875	+	0.843662i	$0.680395\pi$
$164$	3.19560	−	12.4011i	0.249535	−	0.968366i
$165$	−12.9301			−1.00660
$166$	15.9694	−	10.6461i	1.23947	−	0.826294i
$167$	3.89431	−	9.40171i	0.301351	−	0.727526i	−0.698577	−	0.715535i	$-0.746183\pi$
$167$	3.89431	−	9.40171i	0.301351	−	0.727526i	0.999928	−	0.0119910i	$-0.00381694\pi$
$168$	−2.47654	+	0.0894432i	−0.191069	+	0.00690070i
$169$	−1.14819	+	2.25344i	−0.0883220	+	0.173342i
$170$	−0.983184	−	4.97024i	−0.0754068	−	0.381200i
$171$	3.48411	+	14.5123i	0.266436	+	1.10979i
$172$	−8.22223	−	1.99237i	−0.626939	−	0.151916i
$173$	15.5061	+	15.5061i	1.17890	+	1.17890i	0.980024	+	0.198881i	$0.0637306\pi$
$173$	15.5061	+	15.5061i	1.17890	+	1.17890i	0.198881	+	0.980024i	$0.436269\pi$
$174$	−2.21758	−	18.9074i	−0.168114	−	1.43336i
$175$	0.185073	−	0.216693i	0.0139902	−	0.0163804i
$176$	−16.7756	+	1.24896i	−1.26450	+	0.0941438i
$177$	7.87993	+	12.8589i	0.592292	+	0.966533i
$178$	6.81143	+	6.30978i	0.510538	+	0.472938i
$179$	12.8010	+	14.9880i	0.956791	+	1.12026i	0.992664	+	0.120902i	$0.0385788\pi$
$179$	12.8010	+	14.9880i	0.956791	+	1.12026i	−0.0358730	+	0.999356i	$0.511421\pi$
$180$	−1.03977	+	12.8640i	−0.0774998	+	0.958823i
$181$	−1.85124	−	23.5222i	−0.137601	−	1.74839i	−0.547996	−	0.836481i	$-0.684609\pi$
$181$	−1.85124	−	23.5222i	−0.137601	−	1.74839i	0.410394	−	0.911908i	$-0.365391\pi$
$182$	−1.55729	−	0.311475i	−0.115434	−	0.0230881i
$183$	2.91973	+	1.78921i	0.215833	+	0.132262i
$184$	21.8486	+	10.1564i	1.61070	+	0.748741i
$185$	−3.86185	−	0.611657i	−0.283929	−	0.0449699i
$186$	3.24446	−	27.1664i	0.237896	−	1.99194i
$187$	−12.1891	−	8.85590i	−0.891356	−	0.647608i
$188$	2.49238	+	1.81888i	0.181776	+	0.132655i
$189$	1.77825	+	2.44755i	0.129349	+	0.178033i
$190$	−2.96896	−	1.37252i	−0.215391	−	0.0995727i
$191$	−3.52365	+	1.45954i	−0.254962	+	0.105609i	−0.506504	−	0.862238i	$-0.669062\pi$
$191$	−3.52365	+	1.45954i	−0.254962	+	0.105609i	0.251542	+	0.967846i	$0.419062\pi$
$192$	−0.155909	+	24.5960i	−0.0112517	+	1.77507i
$193$	0.635589	−	8.07593i	0.0457507	−	0.581318i	−0.930729	−	0.365709i	$-0.880826\pi$
$193$	0.635589	−	8.07593i	0.0457507	−	0.581318i	0.976480	−	0.215609i	$-0.0691736\pi$
$194$	−22.0421	−	6.24166i	−1.58253	−	0.448125i
$195$	−3.74403	+	11.5229i	−0.268116	+	0.825175i
$196$	1.05653	+	13.7972i	0.0754668	+	0.985514i
$197$	4.40241	+	8.64022i	0.313659	+	0.615590i	0.992984	−	0.118247i	$-0.0377275\pi$
$197$	4.40241	+	8.64022i	0.313659	+	0.615590i	−0.679325	+	0.733837i	$0.737728\pi$
$198$	23.7282	+	30.1646i	1.68629	+	2.14370i
$199$	22.3822	+	5.37350i	1.58664	+	0.380917i	0.928307	−	0.371814i	$-0.121264\pi$
$199$	22.3822	+	5.37350i	1.58664	+	0.380917i	0.658328	+	0.752731i	$0.271264\pi$
$200$	−2.07088	−	1.92651i	−0.146433	−	0.136225i
$201$	5.25668	+	16.1784i	0.370778	+	1.14114i
$202$	−18.7265	+	0.715953i	−1.31759	+	0.0503743i
$203$	1.23230	−	0.195178i	0.0864907	−	0.0136988i
$204$	−14.3426	+	16.7213i	−1.00418	+	1.17073i
$205$	2.06657	−	6.06047i	0.144335	−	0.423282i
$206$	−16.5592	+	7.61269i	−1.15373	+	0.530401i
$207$	−8.59909	−	54.2925i	−0.597678	−	3.77359i
$208$	−3.74449	+	15.3116i	−0.259633	+	1.06167i
$209$	−9.25062	+	3.00571i	−0.639879	+	0.207909i
$210$	−1.23807	−	0.0499539i	−0.0854349	−	0.00344715i
$211$	−3.39985	+	14.1614i	−0.234056	+	0.974911i	0.724334	+	0.689449i	$0.242147\pi$
$211$	−3.39985	+	14.1614i	−0.234056	+	0.974911i	−0.958390	+	0.285463i	$0.907853\pi$
$212$	8.63822	−	16.8653i	0.593275	−	1.15831i
$213$	3.02044	−	1.53899i	0.206957	−	0.105450i
$214$	24.6946	+	9.13996i	1.68809	+	0.624795i
$215$	−4.02305	−	1.30717i	−0.274370	−	0.0891482i
$216$	25.0198	−	16.6032i	1.70238	−	1.12971i
$217$	1.78759	+	0.140686i	0.121349	+	0.00955040i
$218$	2.51841	−	3.76046i	0.170568	−	0.254691i
$219$	11.4215	+	27.5739i	0.771792	+	1.86327i
$220$	−8.41097	−	0.0177715i	−0.567068	−	0.00119816i
$221$	−11.4216	+	8.29829i	−0.768301	+	0.558204i
$222$	8.29137	+	14.8421i	0.556481	+	0.996135i
$223$	12.0184	−	16.5418i	0.804808	−	1.10772i	−0.187295	−	0.982304i	$-0.559972\pi$
$223$	12.0184	−	16.5418i	0.804808	−	1.10772i	0.992104	−	0.125420i	$-0.0400278\pi$
$224$	−1.61110	+	0.0547787i	−0.107646	+	0.00366006i
$225$	−1.00947	+	6.37351i	−0.0672977	+	0.424901i
$226$	2.06304	+	7.34468i	0.137231	+	0.488561i
$227$	8.32889	−	13.5915i	0.552808	−	0.902101i	−0.447163	−	0.894453i	$-0.647566\pi$
$227$	8.32889	−	13.5915i	0.552808	−	0.902101i	0.999971	−	0.00764797i	$-0.00243445\pi$
$228$	3.29084	+	13.8360i	0.217941	+	0.916314i
$229$	26.8323	−	2.11175i	1.77313	−	0.139548i	0.850685	−	0.525675i	$-0.176187\pi$
$229$	26.8323	−	2.11175i	1.77313	−	0.139548i	0.922446	+	0.386127i	$0.126187\pi$
$230$	10.5047	+	5.89748i	0.692657	+	0.388868i
$231$	−2.80185	+	2.39301i	−0.184348	+	0.157448i
$232$	−1.41654	−	12.3022i	−0.0930005	−	0.807680i
$233$	−2.54283	+	1.55825i	−0.166587	+	0.102084i	−0.603293	−	0.797520i	$-0.706145\pi$
$233$	−2.54283	+	1.55825i	−0.166587	+	0.102084i	0.436706	+	0.899604i	$0.356145\pi$
$234$	33.7526	−	12.4115i	2.20648	−	0.811365i
$235$	1.17312	+	1.00194i	0.0765256	+	0.0653591i
$236$	5.10820	+	8.37549i	0.332515	+	0.545198i
$237$	3.88025	−	3.88025i	0.252050	−	0.252050i
$238$	−1.13291	−	0.895053i	−0.0734354	−	0.0580177i
$239$	16.0193	−	3.84590i	1.03621	−	0.248771i	0.320555	−	0.947230i	$-0.396131\pi$
$239$	16.0193	−	3.84590i	1.03621	−	0.248771i	0.715650	+	0.698459i	$0.246131\pi$
$240$	−1.01671	+	12.2562i	−0.0656285	+	0.791132i
$241$	−23.7530	−	12.1027i	−1.53006	−	0.779606i	−0.532306	−	0.846552i	$-0.678675\pi$
$241$	−23.7530	−	12.1027i	−1.53006	−	0.779606i	−0.997757	+	0.0669457i	$0.978675\pi$
$242$	−6.95031	+	6.41120i	−0.446783	+	0.412127i
$243$	−8.30267	−	3.43908i	−0.532616	−	0.220617i
$244$	1.89682	+	1.16789i	0.121431	+	0.0747665i
$245$			6.91879i			0.442025i
$246$	−26.2670	+	9.22974i	−1.67472	+	0.588467i
$247$			9.11424i			0.579925i
$248$	2.14785	−	17.6672i	0.136389	−	1.12187i
$249$	−38.5497	−	15.9678i	−2.44299	−	1.01192i
$250$	−0.958872	−	1.03950i	−0.0606444	−	0.0657439i
$251$	−14.6925	−	7.48619i	−0.927381	−	0.472524i	−0.0760208	−	0.997106i	$-0.524222\pi$
$251$	−14.6925	−	7.48619i	−0.927381	−	0.472524i	−0.851360	+	0.524582i	$0.824222\pi$
$252$	2.15546	+	2.97996i	0.135781	+	0.187720i
$253$	34.8345	−	8.36303i	2.19003	−	0.525779i
$254$	9.84084	−	12.4560i	0.617469	−	0.781556i
$255$	−7.78872	+	7.78872i	−0.487748	+	0.487748i
$256$	−0.135224	+	15.9994i	−0.00845149	+	0.999964i
$257$	−4.55900	−	3.89375i	−0.284383	−	0.242886i	0.495801	−	0.868436i	$-0.334874\pi$
$257$	−4.55900	−	3.89375i	−0.284383	−	0.242886i	−0.780184	+	0.625550i	$0.784874\pi$
$258$	6.34784	+	17.2627i	0.395199	+	1.07473i
$259$	−0.950037	+	0.582183i	−0.0590324	+	0.0361751i
$260$	−2.45132	+	7.49049i	−0.152024	+	0.464540i
$261$	−21.4834	+	18.3486i	−1.32979	+	1.13575i
$262$	1.11817	−	1.99170i	0.0690810	−	0.123048i
$263$	−16.5572	+	1.30308i	−1.02096	+	0.0803512i	−0.577872	−	0.816128i	$-0.696117\pi$
$263$	−16.5572	+	1.30308i	−1.02096	+	0.0803512i	−0.443087	+	0.896479i	$0.646117\pi$
$264$	22.5502	+	28.7920i	1.38787	+	1.77203i
$265$	4.95035	−	8.07824i	0.304098	−	0.496243i
$266$	−0.897369	+	0.252061i	−0.0550212	+	0.0154549i
$267$	3.15775	−	19.9372i	0.193251	−	1.22014i
$268$	3.39722	+	10.5312i	0.207518	+	0.643296i
$269$	−3.23415	+	4.45143i	−0.197190	+	0.271408i	−0.896149	−	0.443753i	$-0.853647\pi$
$269$	−3.23415	+	4.45143i	−0.197190	+	0.271408i	0.698959	+	0.715161i	$0.253647\pi$
$270$	13.1072	−	7.32221i	0.797680	−	0.445616i
$271$	1.92501	−	1.39860i	0.116936	−	0.0849591i	−0.527780	−	0.849381i	$-0.676976\pi$
$271$	1.92501	−	1.39860i	0.116936	−	0.0849591i	0.644716	+	0.764422i	$0.276976\pi$
$272$	−9.35279	+	10.8575i	−0.567096	+	0.658330i
$273$	1.32128	+	3.18986i	0.0799677	+	0.193059i
$274$	−24.0664	−	16.1174i	−1.45390	−	0.973690i
$275$	−4.19253	−	0.329959i	−0.252819	−	0.0198973i
$276$	−8.08488	−	51.7534i	−0.486653	−	3.11519i
$277$	−5.23494	−	1.70093i	−0.314537	−	0.102199i	0.147494	−	0.989063i	$-0.452879\pi$
$277$	−5.23494	−	1.70093i	−0.314537	−	0.102199i	−0.462031	+	0.886864i	$0.652879\pi$
$278$	−9.16220	+	24.7547i	−0.549512	+	1.48469i
$279$	−36.1784	+	18.4338i	−2.16594	+	1.10360i
$280$	−0.805291	−	0.0341965i	−0.0481253	−	0.00204363i
$281$	−4.73118	+	19.7068i	−0.282239	+	1.17561i	0.633470	+	0.773767i	$0.281630\pi$
$281$	−4.73118	+	19.7068i	−0.282239	+	1.17561i	−0.915709	+	0.401842i	$0.868370\pi$
$282$	0.270437	−	6.70256i	0.0161043	−	0.399132i
$283$	−23.2550	+	7.55602i	−1.38237	+	0.449159i	−0.903447	−	0.428699i	$-0.858972\pi$
$283$	−23.2550	+	7.55602i	−1.38237	+	0.449159i	−0.478921	+	0.877858i	$0.658972\pi$
$284$	1.96690	−	0.996956i	0.116714	−	0.0591584i
$285$	1.11241	+	7.02346i	0.0658933	+	0.416034i
$286$	9.78971	+	21.2947i	0.578878	+	1.25918i
$287$	−0.673820	−	1.69573i	−0.0397743	−	0.100096i
$288$	30.4582	−	20.1196i	1.79477	−	1.18556i
$289$	4.11378	−	0.651558i	0.241987	−	0.0383270i
$290$	−0.236551	−	6.18723i	−0.0138907	−	0.363327i
$291$	15.3905	+	47.3672i	0.902209	+	2.77671i
$292$	7.39174	+	17.9524i	0.432569	+	1.05059i
$293$	−19.5398	−	4.69110i	−1.14153	−	0.274057i	−0.381768	−	0.924258i	$-0.624685\pi$
$293$	−19.5398	−	4.69110i	−1.14153	−	0.274057i	−0.759762	+	0.650201i	$0.774685\pi$
$294$	23.6448	−	18.5996i	1.37899	−	1.08475i
$295$	2.22690	+	4.37053i	0.129655	+	0.254462i
$296$	5.37311	+	9.66611i	0.312306	+	0.561832i
$297$	13.7967	−	42.4618i	0.800565	−	2.46389i
$298$	−3.31362	+	11.7019i	−0.191953	+	0.677872i
$299$	2.63377	−	33.4652i	0.152315	−	1.93534i
$300$	−0.974767	+	6.07138i	−0.0562782	+	0.350531i
$301$	−1.11369	+	0.461305i	−0.0641919	+	0.0265892i
$302$	−2.91827	+	6.31266i	−0.167927	+	0.363253i
$303$	23.9476	+	32.9610i	1.37575	+	1.89356i
$304$	2.12166	+	9.00482i	0.121686	+	0.516462i
$305$	0.901054	+	0.654654i	0.0515942	+	0.0374854i
$306$	32.4635	+	3.87709i	1.85582	+	0.221639i
$307$	−11.6821	−	1.85026i	−0.666730	−	0.105600i	−0.186110	−	0.982529i	$-0.559588\pi$
$307$	−11.6821	−	1.85026i	−0.666730	−	0.105600i	−0.480620	+	0.876929i	$0.659588\pi$
$308$	−1.82589	+	1.55279i	−0.104040	+	0.0884787i
$309$	33.7838	+	20.7027i	1.92189	+	1.17774i
$310$	1.74526	−	8.72582i	0.0991241	−	0.495594i
$311$	0.449760	+	5.71475i	0.0255036	+	0.324054i	0.996414	+	0.0846109i	$0.0269647\pi$
$311$	0.449760	+	5.71475i	0.0255036	+	0.324054i	−0.970910	+	0.239443i	$0.923035\pi$
$312$	32.1884	−	11.7591i	1.82231	−	0.665730i
$313$	−20.0793	−	23.5098i	−1.13495	−	1.32885i	−0.937277	−	0.348585i	$-0.886662\pi$
$313$	−20.0793	−	23.5098i	−1.13495	−	1.32885i	−0.197671	−	0.980269i	$-0.563338\pi$
$314$	4.41923	−	4.77058i	0.249392	−	0.269219i
$315$	0.960822	+	1.56792i	0.0541362	+	0.0883423i
$316$	2.52943	−	2.51876i	0.142291	−	0.141691i
$317$	−7.47331	+	8.75012i	−0.419743	+	0.491456i	−0.929479	−	0.368875i	$-0.879743\pi$
$317$	−7.47331	+	8.75012i	−0.419743	+	0.491456i	0.509736	+	0.860331i	$0.329743\pi$
$318$	−40.9151	+	4.79879i	−2.29440	+	0.269103i
$319$	−13.0197	−	13.0197i	−0.728963	−	0.728963i
$320$	−0.678213	+	7.97120i	−0.0379133	+	0.445604i
$321$	−13.3639	−	55.6647i	−0.745901	−	3.10690i
$322$	3.36775	−	0.666190i	0.187677	−	0.0371253i
$323$	−3.76176	+	7.38287i	−0.209310	+	0.410794i
$324$	−24.5200	−	10.2173i	−1.36222	−	0.567627i
$325$	−1.50804	+	3.64073i	−0.0836510	+	0.201951i
$326$	10.7538	+	16.1311i	0.595600	+	0.893420i
$327$	−9.83944			−0.544122
$328$	−17.0993	+	5.96781i	−0.944150	+	0.329517i
$329$	0.439637			0.0242380
$330$	10.1430	+	15.2149i	0.558355	+	0.837552i
$331$	0.132856	−	0.320744i	0.00730245	−	0.0176297i	−0.920186	−	0.391481i	$-0.871963\pi$
$331$	0.132856	−	0.320744i	0.00730245	−	0.0176297i	0.927489	+	0.373851i	$0.121963\pi$
$332$	−25.0545	−	10.4400i	−1.37505	−	0.572970i
$333$	11.4546	−	22.4810i	0.627710	−	1.23195i
$334$	−14.1179	+	2.79273i	−0.772499	+	0.152811i
$335$	1.29161	+	5.37993i	0.0705680	+	0.293937i
$336$	2.04797	+	2.84399i	0.111726	+	0.155152i
$337$	−20.4806	−	20.4806i	−1.11565	−	1.11565i	−0.992372	−	0.123278i	$-0.960659\pi$
$337$	−20.4806	−	20.4806i	−1.11565	−	1.11565i	−0.123278	−	0.992372i	$-0.539341\pi$
$338$	3.55233	−	0.416641i	0.193222	−	0.0226623i
$339$	10.7715	−	12.6118i	0.585028	−	0.684980i
$340$	−5.07724	+	5.05583i	−0.275352	+	0.274191i
$341$	−13.8265	−	22.5627i	−0.748745	−	1.22184i
$342$	14.3436	−	15.4840i	0.775615	−	0.837279i
$343$	2.57599	+	3.01610i	0.139091	+	0.162854i
$344$	4.10552	+	11.2381i	0.221355	+	0.605915i
$345$	−2.05489	−	26.1098i	−0.110631	−	1.40571i
$346$	6.08230	−	30.4098i	0.326986	−	1.63484i
$347$	−17.3833	−	10.6525i	−0.933182	−	0.571855i	−0.0292694	−	0.999572i	$-0.509318\pi$
$347$	−17.3833	−	10.6525i	−0.933182	−	0.571855i	−0.903913	+	0.427717i	$0.859318\pi$
$348$	−20.5088	+	17.4414i	−1.09939	+	0.934955i
$349$	21.8426	+	3.45953i	1.16921	+	0.185184i	0.710693	−	0.703503i	$-0.248382\pi$
$349$	21.8426	+	3.45953i	1.16921	+	0.185184i	0.458515	+	0.888687i	$0.348382\pi$
$350$	−0.400165	−	0.0477913i	−0.0213897	−	0.00255455i
$351$	−33.8459	−	24.5905i	−1.80656	−	1.31254i
$352$	14.6293	+	18.7601i	0.779743	+	0.999918i
$353$	−6.99138	−	9.62281i	−0.372114	−	0.512171i	0.581360	−	0.813646i	$-0.302521\pi$
$353$	−6.99138	−	9.62281i	−0.372114	−	0.512171i	−0.953474	+	0.301476i	$0.902521\pi$
$354$	8.94968	−	19.3595i	0.475670	−	1.02895i
$355$	1.01864	−	0.421934i	0.0540637	−	0.0223939i
$356$	2.08151	−	12.9648i	0.110320	−	0.687131i
$357$	−0.246277	+	3.12924i	−0.0130343	+	0.165617i
$358$	7.59473	−	26.8204i	0.401394	−	1.41750i
$359$	9.44801	−	29.0780i	0.498647	−	1.53468i	−0.312548	−	0.949902i	$-0.601182\pi$
$359$	9.44801	−	29.0780i	0.498647	−	1.53468i	0.811195	−	0.584776i	$-0.198818\pi$
$360$	15.9527	−	8.86767i	0.840783	−	0.467367i
$361$	−6.19730	−	12.1629i	−0.326174	−	0.640152i
$362$	−26.2265	+	20.6304i	−1.37843	+	1.08431i
$363$	19.9891	+	4.79897i	1.04916	+	0.251880i
$364$	0.855106	+	2.07681i	0.0448197	+	0.108854i
$365$	2.99972	+	9.23220i	0.157013	+	0.483236i
$366$	−0.185013	−	4.83921i	−0.00967079	−	0.252950i
$367$	32.3614	−	5.12555i	1.68925	−	0.267551i	0.763535	−	0.645767i	$-0.223462\pi$
$367$	32.3614	−	5.12555i	1.68925	−	0.267551i	0.925718	+	0.378215i	$0.123462\pi$
$368$	−5.18806	−	33.6766i	−0.270446	−	1.75551i
$369$	33.0730	+	24.7678i	1.72171	+	1.28936i
$370$	2.30970	+	5.02407i	0.120075	+	0.261189i
$371$	−0.422360	−	2.66668i	−0.0219278	−	0.138447i
$372$	−34.5120	+	17.4930i	−1.78936	+	0.906969i
$373$	9.43644	−	3.06609i	0.488600	−	0.158756i	−0.0543479	−	0.998522i	$-0.517308\pi$
$373$	9.43644	−	3.06609i	0.488600	−	0.158756i	0.542948	+	0.839766i	$0.317308\pi$
$374$	−0.859014	+	21.2900i	−0.0444186	+	1.10088i
$375$	−0.717743	+	2.98962i	−0.0370641	+	0.154383i
$376$	0.185130	−	4.35962i	0.00954737	−	0.224830i
$377$	−15.3728	+	7.83283i	−0.791739	+	0.403411i
$378$	1.48509	−	4.01247i	0.0763850	−	0.206379i
$379$	6.94939	+	2.25799i	0.356966	+	0.115985i	0.482010	−	0.876166i	$-0.339907\pi$
$379$	6.94939	+	2.25799i	0.356966	+	0.115985i	−0.125043	+	0.992151i	$0.539907\pi$
$380$	0.713964	+	4.57027i	0.0366256	+	0.234450i
$381$	−34.4051	−	2.70774i	−1.76262	−	0.138722i
$382$	4.48159	+	3.00136i	0.229298	+	0.153563i
$383$	2.02637	+	4.89209i	0.103543	+	0.249974i	0.967157	−	0.254178i	$-0.0818050\pi$
$383$	2.02637	+	4.89209i	0.103543	+	0.249974i	−0.863615	+	0.504152i	$0.831805\pi$
$384$	29.0646	−	19.1110i	1.48320	−	0.975252i
$385$	−0.969558	+	0.704425i	−0.0494133	+	0.0359008i
$386$	−10.0016	+	5.58728i	−0.509067	+	0.284385i
$387$	16.0445	−	22.0834i	0.815589	−	1.12256i
$388$	9.94638	+	30.8333i	0.504951	+	1.56533i
$389$	2.53592	−	16.0112i	0.128576	−	0.811799i	−0.836142	−	0.548514i	$-0.815194\pi$
$389$	2.53592	−	16.0112i	0.128576	−	0.811799i	0.964718	−	0.263285i	$-0.0848061\pi$
$390$	16.4961	−	4.63358i	0.835313	−	0.234630i
$391$	15.9457	−	26.0210i	0.806408	−	1.31594i
$392$	15.4064	−	12.0665i	0.778142	−	0.609449i
$393$	−4.95047	+	0.389611i	−0.249718	+	0.0196532i
$394$	6.71351	−	11.9582i	0.338222	−	0.602444i
$395$	1.35718	−	1.15914i	0.0682870	−	0.0583226i
$396$	16.8812	−	51.5838i	0.848311	−	2.59218i
$397$	3.69693	−	2.26548i	0.185544	−	0.113701i	−0.426625	−	0.904429i	$-0.640297\pi$
$397$	3.69693	−	2.26548i	0.185544	−	0.113701i	0.612168	+	0.790727i	$0.290297\pi$
$398$	−11.2348	−	30.5526i	−0.563148	−	1.53146i
$399$	1.54090	+	1.31606i	0.0771417	+	0.0658852i
$400$	−0.642427	+	3.94807i	−0.0321214	+	0.197404i
$401$	7.08297	−	7.08297i	0.353707	−	0.353707i	−0.507780	−	0.861487i	$-0.669534\pi$
$401$	7.08297	−	7.08297i	0.353707	−	0.353707i	0.861487	+	0.507780i	$0.169534\pi$
$402$	14.9136	−	18.8767i	0.743822	−	0.941486i
$403$	−24.1109	+	5.78852i	−1.20105	+	0.288347i
$404$	15.5325	+	21.4739i	0.772771	+	1.06837i
$405$	−11.8342	−	6.02981i	−0.588045	−	0.299624i
$406$	−1.19635	−	1.29695i	−0.0593738	−	0.0643665i
$407$	15.1918	+	6.29263i	0.753027	+	0.311914i
$408$	30.9272	+	3.75990i	1.53112	+	0.186143i
$409$			3.47477i			0.171816i	0.996303	+	0.0859081i	$0.0273791\pi$
$409$			3.47477i			0.171816i	−0.996303	+	0.0859081i	$0.972621\pi$
$410$	−8.75251	+	2.32241i	−0.432256	+	0.114696i
$411$			62.9709i			3.10613i
$412$	21.9478	+	13.5135i	1.08129	+	0.665762i
$413$	1.29142	+	0.534924i	0.0635467	+	0.0263219i
$414$	−57.1407	+	52.7085i	−2.80831	+	2.59048i
$415$	−12.0921	−	6.16125i	−0.593580	−	0.302444i
$416$	20.9546	−	7.60504i	1.02738	−	0.372868i
$417$	55.8002	−	13.3964i	2.73255	−	0.656026i
$418$	10.7935	+	8.52741i	0.527927	+	0.417089i
$419$	−11.3357	+	11.3357i	−0.553787	+	0.553787i	−0.927532	−	0.373745i	$-0.878074\pi$
$419$	−11.3357	+	11.3357i	−0.553787	+	0.553787i	0.373745	+	0.927532i	$0.378074\pi$
$420$	0.912425	+	1.49603i	0.0445218	+	0.0729987i
$421$	15.7876	+	13.4839i	0.769440	+	0.657163i	0.944913	−	0.327321i	$-0.106146\pi$
$421$	15.7876	+	13.4839i	0.769440	+	0.657163i	−0.175474	+	0.984484i	$0.556146\pi$
$422$	19.3308	−	7.10832i	0.941010	−	0.346028i
$423$	−8.48829	+	5.20163i	−0.412715	+	0.252912i
$424$	−26.6217	+	3.06536i	−1.29286	+	0.148867i
$425$	−2.72422	+	2.32671i	−0.132144	+	0.112862i
$426$	−4.18032	−	2.34690i	−0.202537	−	0.113708i
$427$	0.316411	−	0.0249021i	0.0153122	−	0.00120510i
$428$	−8.61667	−	36.2281i	−0.416503	−	1.75115i
$429$	26.6231	−	43.4450i	1.28538	−	2.09754i
$430$	1.61774	+	5.75936i	0.0780144	+	0.277741i
$431$	1.10191	−	6.95716i	0.0530770	−	0.335115i	−0.946833	−	0.321724i	$-0.895738\pi$
$431$	1.10191	−	6.95716i	0.0530770	−	0.335115i	0.999910	−	0.0133904i	$-0.00426242\pi$
$432$	−39.1639	−	16.4165i	−1.88427	−	0.789837i
$433$	−15.8171	+	21.7703i	−0.760119	+	1.04621i	0.237085	+	0.971489i	$0.423808\pi$
$433$	−15.8171	+	21.7703i	−0.760119	+	1.04621i	−0.997204	+	0.0747257i	$0.976192\pi$
$434$	−1.23673	−	2.21382i	−0.0593650	−	0.106267i
$435$	−10.8903	+	7.91227i	−0.522150	+	0.379364i
$436$	−6.40053	−	0.0135237i	−0.306530	−	0.000647667i
$437$	−7.53959	−	18.2022i	−0.360668	−	0.870729i
$438$	23.4867	−	35.0701i	1.12224	−	1.67572i
$439$	−27.5537	−	2.16852i	−1.31506	−	0.103498i	−0.598559	−	0.801079i	$-0.704260\pi$
$439$	−27.5537	−	2.16852i	−1.31506	−	0.103498i	−0.716506	+	0.697581i	$0.754260\pi$
$440$	6.57709	+	9.91117i	0.313551	+	0.472497i
$441$	−42.4615	−	13.7966i	−2.02198	−	0.656980i
$442$	18.7244	+	6.93026i	0.890627	+	0.329639i
$443$	−8.05343	+	4.10343i	−0.382630	+	0.194960i	−0.634717	−	0.772745i	$-0.718883\pi$
$443$	−8.05343	+	4.10343i	−0.382630	+	0.194960i	0.252087	+	0.967705i	$0.418883\pi$
$444$	10.9606	−	21.3994i	0.520165	−	1.01557i
$445$	1.53266	−	6.38399i	0.0726551	−	0.302630i
$446$	−28.8927	−	1.16577i	−1.36811	−	0.0552008i
$447$	25.1466	−	8.17064i	1.18940	−	0.386458i
$448$	1.32829	+	1.85282i	0.0627559	+	0.0875376i
$449$	2.80029	+	17.6804i	0.132154	+	0.834388i	0.961330	+	0.275400i	$0.0888103\pi$
$449$	2.80029	+	17.6804i	0.132154	+	0.834388i	−0.829176	+	0.558988i	$0.811190\pi$
$450$	8.29162	−	3.81187i	0.390871	−	0.179693i
$451$	−14.4007	+	22.7542i	−0.678102	+	1.07145i
$452$	7.02417	−	8.18914i	0.330389	−	0.385185i
$453$	14.9334	−	2.36522i	0.701633	−	0.111128i
$454$	−22.5268	+	0.861247i	−1.05724	+	0.0404203i
$455$	0.347020	+	1.06802i	0.0162685	+	0.0500694i
$456$	13.6994	−	14.7261i	0.641535	−	0.689611i
$457$	4.07063	+	0.977273i	0.190416	+	0.0457149i	0.327532	−	0.944840i	$-0.393783\pi$
$457$	4.07063	+	0.977273i	0.190416	+	0.0457149i	−0.137116	+	0.990555i	$0.543783\pi$
$458$	−23.5336	−	29.9172i	−1.09965	−	1.39794i
$459$	−17.2671	−	33.8886i	−0.805959	−	1.58178i
$460$	−1.30081	−	16.9872i	−0.0606507	−	0.792032i
$461$	−5.90706	+	18.1801i	−0.275119	+	0.846730i	0.714068	+	0.700076i	$0.246851\pi$
$461$	−5.90706	+	18.1801i	−0.275119	+	0.846730i	−0.989188	+	0.146654i	$0.953149\pi$
$462$	5.01379	+	1.41975i	0.233263	+	0.0660529i
$463$	−0.963028	+	12.2364i	−0.0447557	+	0.568675i	0.933131	+	0.359538i	$0.117066\pi$
$463$	−0.963028	+	12.2364i	−0.0447557	+	0.568675i	−0.977886	+	0.209138i	$0.932934\pi$
$464$	−13.3649	+	11.3174i	−0.620449	+	0.525395i
$465$	−17.8734	+	7.40342i	−0.828861	+	0.343326i
$466$	3.82833	+	1.76979i	0.177344	+	0.0819840i
$467$	0.682974	+	0.940033i	0.0316043	+	0.0434995i	0.824527	−	0.565823i	$-0.191441\pi$
$467$	0.682974	+	0.940033i	0.0316043	+	0.0434995i	−0.792922	+	0.609323i	$0.791441\pi$
$468$	−41.0820	−	29.9806i	−1.89902	−	1.38586i
$469$	1.27556	+	0.926751i	0.0589000	+	0.0427934i
$470$	0.258729	−	2.16638i	0.0119343	−	0.0999277i
$471$	−13.9636	−	2.21162i	−0.643409	−	0.101906i
$472$	5.84835	−	12.5810i	0.269192	−	0.579088i
$473$	15.1681	+	9.29505i	0.697432	+	0.427387i
$474$	−7.60979	−	1.52204i	−0.349529	−	0.0699096i
$475$	0.181464	+	2.30572i	0.00832614	+	0.105794i
$476$	−0.164503	+	2.03522i	−0.00753999	+	0.0932843i
$477$	39.7059	+	46.4896i	1.81801	+	2.12861i
$478$	−17.0919	−	15.8331i	−0.781766	−	0.724190i
$479$	18.8521	+	30.7638i	0.861374	+	1.40563i	0.913433	+	0.406990i	$0.133422\pi$
$479$	18.8521	+	30.7638i	0.861374	+	1.40563i	−0.0520591	+	0.998644i	$0.516578\pi$
$480$	15.2195	−	8.41801i	0.694670	−	0.384228i
$481$	10.0068	−	11.7164i	0.456269	−	0.534222i
$482$	4.39171	+	37.4443i	0.200037	+	1.70554i
$483$	−5.27751	−	5.27751i	−0.240135	−	0.240135i
$484$	12.9963	+	3.14919i	0.590740	+	0.143145i
$485$	3.78157	+	15.7514i	0.171712	+	0.715234i
$486$	2.46627	+	12.4676i	0.111872	+	0.565541i
$487$	−13.9190	+	27.3176i	−0.630730	+	1.23788i	0.325578	+	0.945515i	$0.394441\pi$
$487$	−13.9190	+	27.3176i	−0.630730	+	1.23788i	−0.956308	+	0.292362i	$0.905559\pi$
$488$	−0.113699	−	3.14815i	−0.00514692	−	0.142510i
$489$	16.1295	−	38.9400i	0.729401	−	1.76093i
$490$	8.14138	−	5.42746i	0.367790	−	0.245188i
$491$	20.3256			0.917280			0.458640	−	0.888622i	$-0.348337\pi$
$491$	20.3256			0.917280			0.458640	+	0.888622i	$0.348337\pi$
$492$	31.4659	+	23.6682i	1.41859	+	1.06705i
$493$	−15.6854			−0.706435
$494$	10.7248	−	7.14968i	0.482530	−	0.321680i
$495$	10.3852	−	25.0721i	0.466781	−	1.12691i
$496$	−22.4740	+	11.3317i	−1.00911	+	0.508808i
$497$	0.142643	−	0.279953i	0.00639842	−	0.0125576i
$498$	11.4510	+	57.8877i	0.513132	+	2.59401i
$499$	2.08963	+	8.70394i	0.0935447	+	0.389642i	0.999426	−	0.0338910i	$-0.0107899\pi$
$499$	2.08963	+	8.70394i	0.0935447	+	0.389642i	−0.905881	+	0.423533i	$0.860790\pi$
$500$	−0.470999	+	1.94375i	−0.0210637	+	0.0869271i
$501$	22.1238	+	22.1238i	0.988420	+	0.988420i
$502$	2.71651	+	23.1613i	0.121244	+	1.03374i
$503$	−1.48226	+	1.73551i	−0.0660908	+	0.0773824i	−0.792466	−	0.609916i	$-0.791203\pi$
$503$	−1.48226	+	1.73551i	−0.0660908	+	0.0773824i	0.726376	+	0.687298i	$0.241203\pi$
$504$	1.81568	−	4.87398i	0.0808767	−	0.217105i
$505$	6.92379	+	11.2986i	0.308105	+	0.502781i
$506$	−37.1668	−	34.4295i	−1.65227	−	1.53058i
$507$	−5.05003	−	5.91282i	−0.224280	−	0.262598i
$508$	−22.3767	−	1.80866i	−0.992804	−	0.0802464i
$509$	−2.07029	−	26.3055i	−0.0917638	−	1.16597i	−0.854568	−	0.519340i	$-0.826178\pi$
$509$	−2.07029	−	26.3055i	−0.0917638	−	1.16597i	0.762804	−	0.646630i	$-0.223822\pi$
$510$	15.2749	+	3.05515i	0.676384	+	0.135284i
$511$	2.35865	+	1.44538i	0.104341	+	0.0639400i
$512$	18.9327	−	12.3917i	0.836714	−	0.547640i
$513$	−24.2517	−	3.84110i	−1.07074	−	0.169588i
$514$	−1.00548	+	8.41906i	−0.0443499	+	0.371349i
$515$	10.4260	+	7.57490i	0.459423	+	0.333790i
$516$	15.3335	−	21.0113i	0.675021	−	0.924971i
$517$	−3.81356	−	5.24892i	−0.167720	−	0.230847i
$518$	1.43032	+	0.661218i	0.0628445	+	0.0290522i
$519$	−62.2896	+	25.8012i	−2.73421	+	1.13255i
$520$	10.7370	−	2.99145i	0.470850	−	0.131184i
$521$	−0.969314	+	12.3163i	−0.0424664	+	0.539587i	0.938483	+	0.345325i	$0.112231\pi$
$521$	−0.969314	+	12.3163i	−0.0424664	+	0.539587i	−0.980950	+	0.194262i	$0.937769\pi$
$522$	38.4435	+	10.8861i	1.68263	+	0.476470i
$523$	9.67751	−	29.7843i	0.423168	−	1.30238i	−0.481569	−	0.876408i	$-0.659933\pi$
$523$	9.67751	−	29.7843i	0.423168	−	1.30238i	0.904737	−	0.425970i	$-0.140067\pi$
$524$	−3.22080	+	0.246636i	−0.140701	+	0.0107744i
$525$	0.397768	+	0.780663i	0.0173600	+	0.0340709i
$526$	14.5216	+	18.4607i	0.633174	+	0.804925i
$527$	−21.9198	−	5.26249i	−0.954844	−	0.229238i
$528$	16.1902	−	49.1209i	0.704587	−	2.13771i
$529$	15.3162	+	47.1383i	0.665920	+	2.04949i
$530$	−13.3890	+	0.511890i	−0.581582	+	0.0222351i
$531$	−31.2631	+	4.95159i	−1.35670	+	0.214881i
$532$	1.00054	+	0.858208i	0.0433791	+	0.0372081i
$533$	16.1081	+	19.4222i	0.697719	+	0.841270i
$534$	−25.9373	+	11.9241i	−1.12242	+	0.516005i
$535$	−2.91271	−	18.3901i	−0.125927	−	0.795074i
$536$	9.72718	−	12.2588i	0.420150	−	0.529498i
$537$	−57.6354	+	18.7269i	−2.48715	+	0.808125i
$538$	7.77505	+	0.313710i	0.335206	+	0.0135250i
$539$	6.79255	−	28.2930i	0.292576	−	1.21867i
$540$	−18.8981	−	9.67940i	−0.813244	−	0.416535i
$541$	−26.0793	+	13.2881i	−1.12124	+	0.571298i	−0.913480	−	0.406883i	$-0.866616\pi$
$541$	−26.0793	+	13.2881i	−1.12124	+	0.571298i	−0.207755	+	0.978181i	$0.566616\pi$
$542$	−3.15582	−	1.16803i	−0.135554	−	0.0501713i
$543$	68.9936	+	22.4174i	2.96080	+	0.962021i
$544$	20.1128	+	2.48831i	0.862331	+	0.106685i
$545$	−3.19040	−	0.251090i	−0.136662	−	0.0107555i
$546$	2.71704	−	4.05705i	0.116279	−	0.173626i
$547$	−15.2844	−	36.8998i	−0.653514	−	1.57772i	−0.807644	−	0.589671i	$-0.799257\pi$
$547$	−15.2844	−	36.8998i	−0.653514	−	1.57772i	0.154130	−	0.988051i	$-0.450743\pi$
$548$	−0.0865495	+	40.9624i	−0.00369721	+	1.74983i
$549$	−5.81446	+	4.22446i	−0.248155	+	0.180295i
$550$	2.90058	+	5.19221i	0.123681	+	0.221397i
$551$	−5.95202	+	8.19225i	−0.253565	+	0.349002i
$552$	−54.5563	+	50.1116i	−2.32207	+	2.13289i
$553$	0.0795651	−	0.502354i	0.00338345	−	0.0213623i
$554$	2.10506	+	7.49428i	0.0894354	+	0.318401i
$555$	6.28123	−	10.2500i	0.266623	−	0.435090i
$556$	36.3162	−	8.63764i	1.54015	−	0.366318i
$557$	10.5147	−	0.827525i	0.445522	−	0.0350634i	0.146286	−	0.989242i	$-0.453268\pi$
$557$	10.5147	−	0.827525i	0.445522	−	0.0350634i	0.299236	+	0.954179i	$0.403268\pi$
$558$	50.0713	+	28.1108i	2.11969	+	1.19003i
$559$	12.6756	−	10.8260i	0.536120	−	0.457890i
$560$	0.591473	+	0.974415i	0.0249943	+	0.0411766i
$561$	39.4970	−	24.2038i	1.66756	−	1.02188i
$562$	26.9005	−	9.89184i	1.13473	−	0.417262i
$563$	15.5986	+	13.3225i	0.657403	+	0.561475i	0.914337	−	0.404954i	$-0.132712\pi$
$563$	15.5986	+	13.3225i	0.657403	+	0.561475i	−0.256934	+	0.966429i	$0.582712\pi$
$564$	−8.09909	+	4.93962i	−0.341033	+	0.207995i
$565$	3.81446	−	3.81446i	0.160476	−	0.160476i
$566$	27.1337	+	21.4370i	1.14051	+	0.901064i
$567$	−3.68034	+	0.883571i	−0.154560	+	0.0371065i
$568$	−2.71606	−	1.53240i	−0.113963	−	0.0642979i
$569$	27.1771	+	13.8474i	1.13932	+	0.580514i	0.918744	−	0.394855i	$-0.129205\pi$
$569$	27.1771	+	13.8474i	1.13932	+	0.580514i	0.220580	+	0.975369i	$0.429205\pi$
$570$	7.39191	−	6.81854i	0.309613	−	0.285597i
$571$	27.8494	+	11.5356i	1.16546	+	0.482750i	0.879690	−	0.475548i	$-0.157750\pi$
$571$	27.8494	+	11.5356i	1.16546	+	0.482750i	0.285771	+	0.958298i	$0.407750\pi$
$572$	17.3780	−	28.2242i	0.726610	−	1.18012i
$573$		−	11.7263i		−	0.489874i
$574$	−1.46679	+	2.12310i	−0.0612226	+	0.0886167i
$575$		−	8.51846i		−	0.355244i
$576$	−47.5679	−	20.0574i	−1.98199	−	0.835727i
$577$	−6.53631	−	2.70743i	−0.272110	−	0.112712i	0.242456	−	0.970162i	$-0.422047\pi$
$577$	−6.53631	−	2.70743i	−0.272110	−	0.112712i	−0.514566	+	0.857451i	$0.672047\pi$
$578$	−3.99375	−	4.32958i	−0.166118	−	0.180087i
$579$	22.1921	+	11.3074i	0.922272	+	0.469921i
$580$	−7.09498	+	5.13194i	−0.294603	+	0.213092i
$581$	−3.76056	+	0.902831i	−0.156014	+	0.0374557i
$582$	43.6641	−	55.2674i	1.80993	−	2.29091i
$583$	−28.1743	+	28.1743i	−1.16686	+	1.16686i
$584$	15.3262	−	22.7807i	0.634205	−	0.942673i
$585$	−19.3365	−	16.5149i	−0.799465	−	0.682808i
$586$	9.80803	+	26.6726i	0.405166	+	1.10183i
$587$	−32.0475	+	19.6387i	−1.32274	+	0.810578i	−0.991137	−	0.132841i	$-0.957590\pi$
$587$	−32.0475	+	19.6387i	−1.32274	+	0.810578i	−0.331605	+	0.943418i	$0.607590\pi$
$588$	−40.4344	−	13.2325i	−1.66749	−	0.545697i
$589$	−11.0663	+	9.45150i	−0.455978	+	0.389442i
$590$	3.39593	−	6.04888i	0.139808	−	0.249028i
$591$	−29.7226	+	2.33922i	−1.22262	+	0.0962226i
$592$	7.15922	−	13.9052i	0.294242	−	0.571499i
$593$	−5.68534	+	9.27763i	−0.233469	+	0.380987i	−0.947823	−	0.318798i	$-0.896721\pi$
$593$	−5.68534	+	9.27763i	−0.233469	+	0.380987i	0.714354	+	0.699785i	$0.246721\pi$
$594$	−60.7879	+	17.0747i	−2.49416	+	0.700582i
$595$	−0.159709	+	1.00836i	−0.00654742	+	0.0413388i
$596$	16.3690	−	5.28041i	0.670502	−	0.216294i
$597$	−41.5982	+	57.2550i	−1.70250	+	2.34329i
$598$	−41.4447	+	23.1527i	−1.69480	+	0.946783i
$599$	17.2536	−	12.5355i	0.704963	−	0.512186i	−0.176582	−	0.984286i	$-0.556504\pi$
$599$	17.2536	−	12.5355i	0.704963	−	0.512186i	0.881545	+	0.472100i	$0.156504\pi$
$600$	7.90888	−	3.61570i	0.322879	−	0.147610i
$601$	−2.34773	−	5.66793i	−0.0957661	−	0.231200i	0.868736	−	0.495276i	$-0.164933\pi$
$601$	−2.34773	−	5.66793i	−0.0957661	−	0.231200i	−0.964502	+	0.264076i	$0.914933\pi$
$602$	1.41646	+	0.948611i	0.0577304	+	0.0386625i
$603$	−35.5929	−	2.80122i	−1.44945	−	0.114075i
$604$	9.71738	−	1.51804i	0.395395	−	0.0617683i
$605$	6.35894	+	2.06615i	0.258528	+	0.0840008i
$606$	19.9996	−	54.0356i	0.812430	−	2.19504i
$607$	37.7318	−	19.2253i	1.53149	−	0.780332i	0.533628	−	0.845719i	$-0.320828\pi$
$607$	37.7318	−	19.2253i	1.53149	−	0.780332i	0.997860	+	0.0653872i	$0.0208283\pi$
$608$	8.93168	−	9.56042i	0.362227	−	0.387726i
$609$	−0.895502	+	3.73004i	−0.0362876	+	0.151149i
$610$	0.0635008	−	1.57382i	0.00257107	−	0.0637221i
$611$	−5.78196	+	1.87867i	−0.233913	+	0.0760029i
$612$	−20.9039	−	41.2414i	−0.844990	−	1.66708i
$613$	5.73328	+	36.1985i	0.231565	+	1.46204i	0.779963	+	0.625826i	$0.215238\pi$
$613$	5.73328	+	36.1985i	0.231565	+	1.46204i	−0.548398	+	0.836218i	$0.684762\pi$
$614$	6.98681	+	15.1978i	0.281965	+	0.613332i
$615$	14.7834	+	13.0008i	0.596126	+	0.524243i
$616$	3.25950	+	0.930437i	0.131329	+	0.0374884i
$617$	−17.0542	+	2.70112i	−0.686575	+	0.108743i	−0.489969	−	0.871740i	$-0.662992\pi$
$617$	−17.0542	+	2.70112i	−0.686575	+	0.108743i	−0.196606	+	0.980483i	$0.562992\pi$
$618$	−2.14076	−	55.9938i	−0.0861140	−	2.25240i
$619$	6.25263	+	19.2436i	0.251314	+	0.773466i	0.994534	+	0.104418i	$0.0332979\pi$
$619$	6.25263	+	19.2436i	0.251314	+	0.773466i	−0.743219	+	0.669048i	$0.766702\pi$
$620$	−11.6368	+	4.79134i	−0.467345	+	0.192425i
$621$	87.9363	+	21.1116i	3.52876	+	0.847180i
$622$	6.37176	−	5.01218i	0.255484	−	0.200970i
$623$	−0.849389	−	1.66702i	−0.0340301	−	0.0667877i
$624$	−39.0873	−	28.6517i	−1.56474	−	1.14699i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	−11.9129	+	42.0697i	−0.476134	+	1.68144i
$627$	2.34634	−	29.8131i	0.0937039	−	1.19062i
$628$	−9.08024	−	1.45784i	−0.362341	−	0.0581743i
$629$	12.9416	−	5.36059i	0.516015	−	0.213741i
$630$	1.09126	−	2.36056i	0.0434768	−	0.0940471i
$631$	15.4709	+	21.2938i	0.615885	+	0.847693i	0.997045	−	0.0768157i	$-0.0244753\pi$
$631$	15.4709	+	21.2938i	0.615885	+	0.847693i	−0.381160	+	0.924509i	$0.624475\pi$
$632$	−4.94805	−	1.00054i	−0.196823	−	0.0397994i
$633$	−36.2257	−	26.3195i	−1.43984	−	1.04611i
$634$	16.1588	+	1.92983i	0.641747	+	0.0766433i
$635$	−11.0866	−	1.75595i	−0.439959	−	0.0696827i
$636$	37.7427	+	44.3805i	1.49659	+	1.75980i
$637$	−23.2471	−	14.2459i	−0.921084	−	0.564441i
$638$	−5.10701	+	25.5337i	−0.202188	+	1.01089i
$639$	0.558222	+	7.09288i	0.0220829	+	0.280590i
$640$	9.91178	−	5.45497i	0.391797	−	0.215627i
$641$	17.9271	+	20.9899i	0.708077	+	0.829051i	0.991522	−	0.129937i	$-0.0414776\pi$
$641$	17.9271	+	20.9899i	0.708077	+	0.829051i	−0.283446	+	0.958988i	$0.591478\pi$
$642$	−55.0176	+	59.3917i	−2.17137	+	2.34400i
$643$	−3.46583	−	5.65572i	−0.136679	−	0.223040i	0.776976	−	0.629530i	$-0.216753\pi$
$643$	−3.46583	−	5.65572i	−0.136679	−	0.223040i	−0.913655	+	0.406490i	$0.866753\pi$
$644$	−3.42575	−	3.44026i	−0.134993	−	0.135565i
$645$	8.44652	−	9.88960i	0.332581	−	0.389403i
$646$	11.6384	−	1.36503i	0.457906	−	0.0537063i
$647$	12.6527	+	12.6527i	0.497428	+	0.497428i	0.910636	−	0.413209i	$-0.135592\pi$
$647$	12.6527	+	12.6527i	0.497428	+	0.497428i	−0.413209	+	0.910636i	$0.635592\pi$
$648$	7.21207	+	36.8678i	0.283317	+	1.44831i
$649$	−4.81566	−	20.0587i	−0.189031	−	0.787372i
$650$	5.46705	−	1.08146i	0.214435	−	0.0424184i
$651$	−2.50287	+	4.91216i	−0.0980953	+	0.192523i
$652$	10.5457	−	25.3082i	0.413001	−	0.991145i
$653$	9.02449	−	21.7870i	0.353156	−	0.852593i	−0.643071	−	0.765806i	$-0.722340\pi$
$653$	9.02449	−	21.7870i	0.353156	−	0.852593i	0.996227	−	0.0867867i	$-0.0276599\pi$
$654$	7.71857	+	11.5781i	0.301820	+	0.452740i
$655$	−1.61512			−0.0631078
$656$	20.4359	+	15.4393i	0.797889	+	0.602805i
$657$	−62.6409			−2.44385
$658$	−0.344874	−	0.517323i	−0.0134446	−	0.0201674i
$659$	9.43787	−	22.7850i	0.367647	−	0.887579i	−0.626487	−	0.779432i	$-0.715508\pi$
$659$	9.43787	−	22.7850i	0.367647	−	0.887579i	0.994135	−	0.108148i	$-0.0344920\pi$
$660$	9.94671	−	23.8707i	0.387175	−	0.929166i
$661$	20.4194	−	40.0753i	0.794223	−	1.55875i	−0.0347069	−	0.999398i	$-0.511050\pi$
$661$	20.4194	−	40.0753i	0.794223	−	1.55875i	0.828930	−	0.559353i	$-0.188950\pi$
$662$	−0.481641	+	0.0952754i	−0.0187195	+	0.00370298i
$663$	−10.1330	−	42.2071i	−0.393534	−	1.63919i
$664$	7.36928	+	37.6715i	0.285984	+	1.46194i
$665$	0.466049	+	0.466049i	0.0180726	+	0.0180726i
$666$	−35.4391	+	4.15653i	−1.37324	+	0.161062i
$667$	24.2217	−	28.3599i	0.937867	−	1.09810i
$668$	14.3611	+	14.4219i	0.555646	+	0.557999i
$669$	32.8470	+	53.6014i	1.26994	+	2.07235i
$670$	5.31739	−	5.74014i	0.205429	−	0.221761i
$671$	−3.04197	−	3.56169i	−0.117434	−	0.137497i
$672$	1.74000	−	4.64084i	0.0671219	−	0.179024i
$673$	1.63066	+	20.7196i	0.0628575	+	0.798680i	0.944868	+	0.327451i	$0.106190\pi$
$673$	1.63066	+	20.7196i	0.0628575	+	0.798680i	−0.882011	+	0.471229i	$0.843810\pi$
$674$	−8.03358	+	40.1657i	−0.309442	+	1.54713i
$675$	−9.05193	−	5.54703i	−0.348409	−	0.213505i
$676$	−3.27690	−	3.85321i	−0.126035	−	0.148201i
$677$	−37.8468	−	5.99435i	−1.45457	−	0.230382i	−0.621443	−	0.783460i	$-0.713453\pi$
$677$	−37.8468	−	5.99435i	−1.45457	−	0.230382i	−0.833130	+	0.553078i	$0.813453\pi$
$678$	−23.2901	−	2.78152i	−0.894452	−	0.106824i
$679$	3.73460	+	2.71334i	0.143321	+	0.104129i
$680$	9.93207	+	2.00836i	0.380878	+	0.0770170i
$681$	28.8074	+	39.6500i	1.10390	+	1.51939i
$682$	−15.7035	+	33.9691i	−0.601318	+	1.30074i
$683$	16.4549	−	6.81583i	0.629628	−	0.260800i	−0.0449671	−	0.998988i	$-0.514318\pi$
$683$	16.4549	−	6.81583i	0.629628	−	0.260800i	0.674595	+	0.738188i	$0.264318\pi$
$684$	−29.4720	−	4.73176i	−1.12689	−	0.180923i
$685$	−1.60694	+	20.4181i	−0.0613980	+	0.780136i
$686$	1.52832	−	5.39717i	0.0583514	−	0.206065i
$687$	−25.5721	+	78.7027i	−0.975635	+	3.00270i
$688$	10.0033	−	13.6467i	0.381372	−	0.520276i
$689$	16.9501	+	33.2664i	0.645746	+	1.26735i
$690$	−29.1116	+	22.8999i	−1.10826	+	0.871785i
$691$	12.1305	+	2.91227i	0.461465	+	0.110788i	0.457510	−	0.889204i	$-0.348741\pi$
$691$	12.1305	+	2.91227i	0.461465	+	0.110788i	0.00395452	+	0.999992i	$0.498741\pi$
$692$	−40.5547	+	16.6980i	−1.54166	+	0.634762i
$693$	−2.38978	−	7.35498i	−0.0907801	−	0.279393i
$694$	1.10152	+	28.8113i	0.0418130	+	1.09366i
$695$	18.4349	−	2.91980i	0.699274	−	0.110754i
$696$	36.6115	+	10.4509i	1.38776	+	0.396140i
$697$	5.03192	+	22.3811i	0.190598	+	0.847744i
$698$	−13.0636	−	28.4161i	−0.494466	−	1.07557i
$699$	−1.43439	−	9.05641i	−0.0542538	−	0.342545i
$700$	0.257674	+	0.508366i	0.00973915	+	0.0192144i
$701$	20.3269	−	6.60461i	0.767737	−	0.249453i	0.101141	−	0.994872i	$-0.467751\pi$
$701$	20.3269	−	6.60461i	0.767737	−	0.249453i	0.666596	+	0.745419i	$0.267751\pi$
$702$	−2.38525	+	59.1167i	−0.0900256	+	2.23122i
$703$	2.11110	−	8.79335i	0.0796215	−	0.331647i
$704$	10.5992	−	31.9308i	0.399471	−	1.20344i
$705$	−4.22630	+	2.15341i	−0.159172	+	0.0811020i
$706$	−5.83881	+	15.7754i	−0.219746	+	0.593716i
$707$	3.59140	+	1.16692i	0.135069	+	0.0438865i
$708$	−29.8011	+	4.65550i	−1.11999	+	0.174964i
$709$	−12.1145	−	0.953433i	−0.454970	−	0.0358069i	−0.151096	−	0.988519i	$-0.548280\pi$
$709$	−12.1145	−	0.953433i	−0.454970	−	0.0358069i	−0.303874	+	0.952712i	$0.598280\pi$
$710$	−1.29557	−	0.867650i	−0.0486217	−	0.0325623i
$711$	4.40748	+	10.6406i	0.165293	+	0.399053i
$712$	−16.8885	+	7.72092i	−0.632925	+	0.289354i
$713$	43.3638	−	31.5057i	1.62399	−	1.17990i
$714$	3.87539	−	2.16495i	0.145033	−	0.0810211i
$715$	9.74112	−	13.4075i	0.364297	−	0.501412i
$716$	−37.5174	+	12.1026i	−1.40209	+	0.452294i
$717$	−7.92373	+	50.0285i	−0.295917	+	1.86835i
$718$	−41.6277	+	11.6928i	−1.55353	+	0.436371i
$719$	−6.76872	+	11.0456i	−0.252431	+	0.411930i	−0.953605	−	0.301060i	$-0.902659\pi$
$719$	−6.76872	+	11.0456i	−0.252431	+	0.411930i	0.701174	+	0.712990i	$0.252659\pi$
$720$	−22.9488	−	11.8154i	−0.855251	−	0.440334i
$721$	3.66114	−	0.288138i	0.136348	−	0.0107308i
$722$	−9.45065	+	16.8336i	−0.351717	+	0.626482i
$723$	62.3256	−	53.2311i	2.31791	−	1.97969i
$724$	44.8493	+	14.6773i	1.66681	+	0.545476i
$725$	−3.73305	+	2.28762i	−0.138642	+	0.0849600i
$726$	−10.0336	−	27.2859i	−0.372380	−	1.01267i
$727$	18.5780	+	15.8671i	0.689018	+	0.588477i	0.923479	−	0.383648i	$-0.125333\pi$
$727$	18.5780	+	15.8671i	0.689018	+	0.588477i	−0.234461	+	0.972126i	$0.575333\pi$
$728$	1.77300	−	2.63536i	0.0657118	−	0.0976731i
$729$	−8.63737	+	8.63737i	−0.319903	+	0.319903i
$730$	8.51044	−	10.7720i	0.314985	−	0.398690i
$731$	14.7359	−	3.53779i	0.545029	−	0.130850i
$732$	−5.54919	+	4.01384i	−0.205104	+	0.148356i
$733$	−16.8115	−	8.56587i	−0.620946	−	0.316388i	0.115065	−	0.993358i	$-0.463293\pi$
$733$	−16.8115	−	8.56587i	−0.620946	−	0.316388i	−0.736010	+	0.676970i	$0.763293\pi$
$734$	−31.4172	−	34.0591i	−1.15963	−	1.25714i
$735$	−19.6530	−	8.14055i	−0.724913	−	0.300269i
$736$	−35.5576	+	32.5225i	−1.31067	+	1.19879i
$737$		−	23.2682i		−	0.857094i
$738$	3.20022	−	58.3463i	0.117802	−	2.14776i
$739$			17.5510i			0.645625i	0.946463	+	0.322812i	$0.104628\pi$
$739$			17.5510i			0.645625i	−0.946463	+	0.322812i	$0.895372\pi$
$740$	4.10001	−	6.65898i	0.150719	−	0.244789i
$741$	−25.8893	−	10.7237i	−0.951066	−	0.393944i
$742$	−2.80657	+	2.58887i	−0.103032	+	0.0950405i
$743$	12.2358	+	6.23445i	0.448888	+	0.228720i	0.663795	−	0.747915i	$-0.268945\pi$
$743$	12.2358	+	6.23445i	0.448888	+	0.228720i	−0.214907	+	0.976635i	$0.568945\pi$
$744$	47.6571	+	26.8880i	1.74719	+	0.985763i
$745$	8.36222	−	2.00759i	0.306368	−	0.0735524i
$746$	−11.0103	−	8.69871i	−0.403116	−	0.318482i
$747$	61.9250	−	61.9250i	2.26572	−	2.26572i
$748$	25.7259	−	15.6902i	0.940633	−	0.573690i
$749$	−4.03468	−	3.44594i	−0.147424	−	0.125912i
$750$	4.08093	−	1.50064i	0.149015	−	0.0547956i
$751$	−6.95133	+	4.25978i	−0.253658	+	0.155442i	−0.643515	−	0.765434i	$-0.722524\pi$
$751$	−6.95133	+	4.25978i	−0.253658	+	0.155442i	0.389857	+	0.920875i	$0.372524\pi$
$752$	−5.27522	+	3.20207i	−0.192367	+	0.116768i
$753$	38.5517	−	32.9263i	1.40490	−	1.19990i
$754$	21.2761	+	11.9448i	0.774831	+	0.435002i
$755$	4.90246	−	0.385832i	0.178419	−	0.0140419i
$756$	−5.88647	+	1.40007i	−0.214089	+	0.0509200i
$757$	−0.628953	+	1.02636i	−0.0228597	+	0.0373036i	−0.863866	−	0.503722i	$-0.831964\pi$
$757$	−0.628953	+	1.02636i	−0.0228597	+	0.0373036i	0.841006	+	0.541025i	$0.181964\pi$
$758$	−2.79447	−	9.94867i	−0.101500	−	0.361352i
$759$	−17.2304	+	108.788i	−0.625423	+	3.94876i
$760$	4.81778	−	4.42528i	0.174759	−	0.160522i
$761$	−19.5974	+	26.9735i	−0.710404	+	0.977788i	0.289384	+	0.957213i	$0.406550\pi$
$761$	−19.5974	+	26.9735i	−0.710404	+	0.977788i	−0.999788	+	0.0205746i	$0.993450\pi$
$762$	23.8029	+	42.6087i	0.862289	+	1.54355i
$763$	−0.737808	+	0.536049i	−0.0267104	+	0.0194063i
$764$	0.0161171	−	7.62793i	0.000583095	−	0.275969i
$765$	−8.84699	−	21.3585i	−0.319864	−	0.772219i
$766$	4.16696	−	6.22205i	0.150558	−	0.224812i
$767$	−19.2702	−	1.51660i	−0.695806	−	0.0547611i
$768$	−45.2877	−	19.2088i	−1.63418	−	0.693138i
$769$	−36.5990	−	11.8918i	−1.31980	−	0.428828i	−0.437371	−	0.899281i	$-0.644090\pi$
$769$	−36.5990	−	11.8918i	−1.31980	−	0.428828i	−0.882425	+	0.470454i	$0.844090\pi$
$770$	1.58947	+	0.588296i	0.0572806	+	0.0212007i
$771$	16.4244	−	8.36864i	0.591509	−	0.301389i
$772$	14.4203	+	7.38595i	0.518999	+	0.265826i
$773$	−1.27103	+	5.29421i	−0.0457157	+	0.190419i	−0.990555	−	0.137114i	$-0.956217\pi$
$773$	−1.27103	+	5.29421i	−0.0457157	+	0.190419i	0.944840	+	0.327533i	$0.106217\pi$
$774$	−38.5718	−	1.55630i	−1.38644	−	0.0559402i
$775$	−5.98433	+	1.94443i	−0.214963	+	0.0698458i
$776$	28.4793	−	35.8912i	1.02235	−	1.28842i
$777$	−0.535909	−	3.38360i	−0.0192256	−	0.121386i
$778$	−20.8297	+	9.57597i	−0.746782	+	0.343315i
$779$	13.5987	+	5.86468i	0.487225	+	0.210124i
$780$	−18.3928	−	15.7762i	−0.658567	−	0.564880i
$781$	−4.57975	+	0.725361i	−0.163876	+	0.0259555i
$782$	−43.1277	+	1.64886i	−1.54224	+	0.0589631i
$783$	−14.3634	−	44.2059i	−0.513305	−	1.57979i
$784$	−26.2843	−	8.66325i	−0.938724	−	0.309402i
$785$	−4.47121	−	1.07344i	−0.159584	−	0.0383128i
$786$	4.34186	+	5.51961i	0.154869	+	0.196878i
$787$	−2.17432	−	4.26734i	−0.0775060	−	0.152114i	0.849001	−	0.528391i	$-0.177204\pi$
$787$	−2.17432	−	4.26734i	−0.0775060	−	0.152114i	−0.926507	+	0.376276i	$0.877204\pi$
$788$	−19.3377	+	1.48080i	−0.688876	+	0.0527514i
$789$	15.7795	−	48.5643i	0.561765	−	1.72893i
$790$	−2.42861	−	0.687708i	−0.0864059	−	0.0244676i
$791$	0.120612	−	1.53252i	0.00428847	−	0.0544902i
$792$	−73.9414	+	20.6009i	−2.62739	+	0.732020i
$793$	−4.05491	+	1.67960i	−0.143994	+	0.0596443i
$794$	−5.56587	−	2.57304i	−0.197525	−	0.0913136i
$795$	17.1220	+	23.5664i	0.607254	+	0.835813i
$796$	−27.1382	+	37.1870i	−0.961888	+	1.31806i
$797$	−43.0399	−	31.2703i	−1.52455	−	1.10765i	−0.959172	−	0.282822i	$-0.908729\pi$
$797$	−43.0399	−	31.2703i	−1.52455	−	1.10765i	−0.565380	−	0.824830i	$-0.691271\pi$
$798$	0.339845	−	2.84557i	0.0120304	−	0.100732i
$799$	−5.45899	−	0.864619i	−0.193125	−	0.0305880i
$800$	5.14967	−	2.34113i	0.182068	−	0.0827714i
$801$	36.1232	+	22.1363i	1.27635	+	0.782148i
$802$	−13.8908	−	2.77831i	−0.490502	−	0.0981057i
$803$	−3.20302	−	40.6982i	−0.113032	−	1.43621i
$804$	−33.9113	−	2.74099i	−1.19596	−	0.0966672i
$805$	−1.57654	−	1.84589i	−0.0555657	−	0.0650590i
$806$	25.7252	+	23.8306i	0.906133	+	0.839398i
$807$	−8.83915	−	14.4242i	−0.311153	−	0.507755i
$808$	13.0840	−	35.1225i	0.460293	−	1.23560i
$809$	−0.387154	+	0.453299i	−0.0136116	+	0.0159371i	−0.767170	−	0.641444i	$-0.778336\pi$
$809$	−0.387154	+	0.453299i	−0.0136116	+	0.0159371i	0.753558	+	0.657381i	$0.228336\pi$
$810$	2.18803	+	18.6554i	0.0768797	+	0.655485i
$811$	−39.0048	−	39.0048i	−1.36964	−	1.36964i	−0.860946	−	0.508696i	$-0.830128\pi$
$811$	−39.0048	−	39.0048i	−1.36964	−	1.36964i	−0.508696	−	0.860946i	$-0.669872\pi$
$812$	−0.587648	+	2.42515i	−0.0206224	+	0.0851059i
$813$	1.70783	+	7.11363i	0.0598962	+	0.249486i
$814$	−4.51264	−	22.8125i	−0.158168	−	0.799577i
$815$	6.22363	−	12.2146i	0.218004	−	0.427857i
$816$	−19.8366	−	39.3416i	−0.694419	−	1.37723i
$817$	3.74400	−	9.03883i	0.130986	−	0.316228i
$818$	4.08878	−	2.72579i	0.142961	−	0.0953050i
$819$	−7.24655			−0.253215
$820$	9.59872	+	8.47730i	0.335202	+	0.296040i
$821$	−52.8283			−1.84372			−0.921861	−	0.387521i	$-0.873331\pi$
$821$	−52.8283			−1.84372			−0.921861	+	0.387521i	$0.873331\pi$
$822$	74.0982	−	49.3977i	2.58447	−	1.72294i
$823$	−1.97897	+	4.77765i	−0.0689824	+	0.166538i	−0.954611	−	0.297857i	$-0.903728\pi$
$823$	−1.97897	+	4.77765i	−0.0689824	+	0.166538i	0.885628	+	0.464395i	$0.153728\pi$
$824$	−1.31560	−	36.4267i	−0.0458310	−	1.26899i
$825$	5.87013	−	11.5208i	0.204372	−	0.401102i
$826$	−0.383610	−	1.93924i	−0.0133475	−	0.0674749i
$827$	0.0201728	+	0.0840259i	0.000701478	+	0.00292187i	0.972720	−	0.231984i	$-0.0745218\pi$
$827$	0.0201728	+	0.0840259i	0.000701478	+	0.00292187i	−0.972018	+	0.234906i	$0.924522\pi$
$828$	106.846	+	25.8905i	3.71317	+	0.899756i
$829$	27.9152	+	27.9152i	0.969534	+	0.969534i	0.999549	−	0.0300154i	$-0.00955562\pi$
$829$	27.9152	+	27.9152i	0.969534	+	0.969534i	−0.0300154	+	0.999549i	$0.509556\pi$
$830$	2.23573	+	19.0621i	0.0776033	+	0.661655i
$831$	10.9909	−	12.8687i	0.381270	−	0.446410i
$832$	−25.3868	−	18.6916i	−0.880128	−	0.648013i
$833$	−12.9513	−	21.1346i	−0.448735	−	0.732269i
$834$	−59.5362	−	55.1515i	−2.06157	−	1.90974i
$835$	6.60900	+	7.73814i	0.228714	+	0.267790i
$836$	1.56726	−	19.3901i	0.0542050	−	0.670621i
$837$	−5.24116	−	66.5953i	−0.181161	−	2.30187i
$838$	22.2312	+	4.44648i	0.767963	+	0.153601i
$839$	43.9148	+	26.9110i	1.51611	+	0.929071i	0.997242	+	0.0742138i	$0.0236447\pi$
$839$	43.9148	+	26.9110i	1.51611	+	0.929071i	0.518864	+	0.854857i	$0.326355\pi$
$840$	1.04463	−	2.24722i	0.0360432	−	0.0775364i
$841$	9.71007	+	1.53792i	0.334830	+	0.0530318i
$842$	3.48193	−	29.1548i	0.119995	−	1.00474i
$843$	−50.4111	−	36.6258i	−1.73625	−	1.26146i
$844$	−23.5285	−	17.1705i	−0.809885	−	0.591034i
$845$	−1.48657	−	2.04608i	−0.0511394	−	0.0703874i
$846$	12.7794	+	5.90778i	0.439366	+	0.203114i
$847$	1.76033	−	0.729151i	0.0604855	−	0.0250539i
$848$	24.4905	+	28.9213i	0.841007	+	0.993161i
$849$	5.89845	−	74.9469i	0.202434	−	2.57217i
$850$	4.87487	+	1.38042i	0.167207	+	0.0473479i
$851$	−10.2925	+	31.6769i	−0.352821	+	1.08587i
$852$	0.517657	+	6.76004i	0.0177346	+	0.231595i
$853$	13.4901	+	26.4758i	0.461891	+	0.906513i	0.998051	+	0.0623964i	$0.0198743\pi$
$853$	13.4901	+	26.4758i	0.461891	+	0.906513i	−0.536160	+	0.844116i	$0.680126\pi$
$854$	−0.277512	−	0.352788i	−0.00949625	−	0.0120721i
$855$	−14.5123	−	3.48411i	−0.496312	−	0.119154i
$856$	−35.8704	+	38.5585i	−1.22602	+	1.31790i
$857$	−6.90186	−	21.2417i	−0.235763	−	0.725604i	−0.997019	−	0.0771528i	$-0.975417\pi$
$857$	−6.90186	−	21.2417i	−0.235763	−	0.725604i	0.761256	−	0.648451i	$-0.224583\pi$
$858$	−72.0065	+	2.75296i	−2.45826	+	0.0939845i
$859$	−14.8060	+	2.34504i	−0.505173	+	0.0800116i	−0.403819	−	0.914839i	$-0.632317\pi$
$859$	−14.8060	+	2.34504i	−0.505173	+	0.0800116i	−0.101354	+	0.994850i	$0.532317\pi$
$860$	5.50803	−	6.42155i	0.187822	−	0.218973i
$861$	5.60957	+	0.0811619i	0.191174	+	0.00276599i
$862$	−9.05092	+	4.16094i	−0.308276	+	0.141722i
$863$	4.59656	+	29.0215i	0.156469	+	0.987904i	0.933535	+	0.358486i	$0.116707\pi$
$863$	4.59656	+	29.0215i	0.156469	+	0.987904i	−0.777067	+	0.629418i	$0.783293\pi$
$864$	11.4049	+	58.9623i	0.388002	+	2.00594i
$865$	−20.8556	+	6.77640i	−0.709112	+	0.230404i
$866$	38.0250	+	1.53424i	1.29214	+	0.0521356i
$867$	−2.98944	+	12.4519i	−0.101527	+	0.422889i
$868$	−1.63486	+	3.19191i	−0.0554908	+	0.108340i
$869$	−6.68789	+	3.40765i	−0.226871	+	0.115597i
$870$	17.8533	+	6.60788i	0.605285	+	0.224028i
$871$	−20.7360	−	6.73753i	−0.702612	−	0.228292i
$872$	5.00499	+	7.54214i	0.169490	+	0.255409i
$873$	−104.209	−	8.20143i	−3.52694	−	0.277576i
$874$	−15.5042	+	23.1506i	−0.524436	+	0.783082i
$875$	0.109053	+	0.263278i	0.00368667	+	0.00890042i
$876$	−59.6914	−	0.126122i	−2.01679	−	0.00426127i
$877$	−10.0411	+	7.29528i	−0.339063	+	0.246344i	−0.744267	−	0.667883i	$-0.767201\pi$
$877$	−10.0411	+	7.29528i	−0.339063	+	0.246344i	0.405203	+	0.914227i	$0.367201\pi$
$878$	19.0628	+	34.1236i	0.643339	+	1.15162i
$879$	36.3155	−	49.9840i	1.22489	−	1.68592i
$880$	6.50311	−	15.5141i	0.219220	−	0.522982i
$881$	4.06384	−	25.6580i	0.136914	−	0.864442i	−0.819638	−	0.572881i	$-0.805826\pi$
$881$	4.06384	−	25.6580i	0.136914	−	0.864442i	0.956552	−	0.291560i	$-0.0941744\pi$
$882$	17.0745	+	60.7874i	0.574929	+	2.04682i
$883$	−22.1220	+	36.0998i	−0.744464	+	1.21486i	0.226122	+	0.974099i	$0.427395\pi$
$883$	−22.1220	+	36.0998i	−0.744464	+	1.21486i	−0.970586	+	0.240756i	$0.922605\pi$
$884$	−6.53349	−	27.4695i	−0.219745	−	0.923900i
$885$	−15.0348	+	1.18326i	−0.505388	+	0.0397749i
$886$	11.1461	+	6.25757i	0.374459	+	0.210227i
$887$	−16.3873	+	13.9961i	−0.550232	+	0.469942i	−0.880567	−	0.473921i	$-0.842838\pi$
$887$	−16.3873	+	13.9961i	−0.550232	+	0.469942i	0.330335	+	0.943864i	$0.392838\pi$
$888$	−33.7788	+	3.88947i	−1.13354	+	0.130522i
$889$	−2.72737	+	1.67133i	−0.0914731	+	0.0560548i
$890$	−8.71438	+	3.20445i	−0.292107	+	0.107413i
$891$	42.4737	+	36.2759i	1.42292	+	1.21529i
$892$	21.2932	+	34.9127i	0.712948	+	1.16896i
$893$	−2.52306	+	2.52306i	−0.0844310	+	0.0844310i
$894$	−29.3408	−	23.1807i	−0.981302	−	0.775279i
$895$	−19.1660	+	4.60134i	−0.640648	+	0.153806i
$896$	1.13824	−	3.01646i	0.0380260	−	0.100773i
$897$	91.9600	+	46.8560i	3.07046	+	1.56448i
$898$	18.6079	−	17.1645i	0.620953	−	0.572788i
$899$	−25.4521	−	10.5426i	−0.848874	−	0.351615i
$900$	−10.9898	−	6.76656i	−0.366328	−	0.225552i
$901$			33.9428i			1.13080i
$902$	38.0716	−	0.904219i	1.26765	−	0.0301072i
$903$		−	3.70623i		−	0.123336i
$904$	−15.1463	−	1.84138i	−0.503759	−	0.0612434i
$905$	21.7989	+	9.02938i	0.724618	+	0.300147i
$906$	−14.4977	−	15.7168i	−0.481654	−	0.522156i
$907$	−16.4322	−	8.37261i	−0.545621	−	0.278008i	0.159376	−	0.987218i	$-0.449052\pi$
$907$	−16.4322	−	8.37261i	−0.545621	−	0.278008i	−0.704997	+	0.709210i	$0.749052\pi$
$908$	18.6846	+	25.8318i	0.620072	+	0.857259i
$909$	−83.1475	+	19.9620i	−2.75783	+	0.662096i
$910$	0.984521	−	1.24615i	0.0326366	−	0.0413094i
$911$	−1.69067	+	1.69067i	−0.0560143	+	0.0560143i	−0.734559	−	0.678545i	$-0.762611\pi$
$911$	−1.69067	+	1.69067i	−0.0560143	+	0.0560143i	0.678545	+	0.734559i	$0.262611\pi$
$912$	−28.0748	−	4.56831i	−0.929649	−	0.151272i
$913$	43.3995	+	37.0667i	1.43631	+	1.22673i
$914$	−2.04326	−	5.55656i	−0.0675849	−	0.183795i
$915$	−2.91973	+	1.78921i	−0.0965233	+	0.0591496i
$916$	−16.7427	+	51.1607i	−0.553195	+	1.69040i
$917$	−0.349984	+	0.298914i	−0.0115575	+	0.00987102i
$918$	−26.3316	+	46.9022i	−0.869074	+	1.54800i
$919$	−33.0510	+	2.60117i	−1.09025	+	0.0858046i	−0.610816	−	0.791773i	$-0.709158\pi$
$919$	−33.0510	+	2.60117i	−1.09025	+	0.0858046i	−0.479435	+	0.877577i	$0.659158\pi$
$920$	−18.9685	+	14.8563i	−0.625372	+	0.489798i
$921$	19.0006	−	31.0062i	0.626092	−	1.02169i
$922$	26.0264	−	7.31053i	0.857133	−	0.240759i
$923$	−0.679689	+	4.29139i	−0.0223722	+	0.141253i
$924$	−2.26245	−	7.01348i	−0.0744290	−	0.230727i
$925$	2.29823	−	3.16325i	0.0755655	−	0.104007i
$926$	15.1541	−	8.46570i	0.497995	−	0.278200i
$927$	−67.2783	+	48.8805i	−2.20971	+	1.60545i
$928$	23.8013	+	6.84859i	0.781316	+	0.224816i
$929$	6.24317	+	15.0723i	0.204832	+	0.494508i	0.992595	−	0.121470i	$-0.0387610\pi$
$929$	6.24317	+	15.0723i	0.204832	+	0.494508i	−0.787763	+	0.615978i	$0.788761\pi$
$930$	22.7325	+	15.2241i	0.745428	+	0.499219i
$931$	−15.9528	−	1.25551i	−0.522832	−	0.0411477i
$932$	−0.920621	−	5.89314i	−0.0301560	−	0.193036i
$933$	−16.7621	−	5.44633i	−0.548766	−	0.178305i
$934$	0.570381	−	1.54107i	0.0186634	−	0.0504253i
$935$	13.4244	−	6.84008i	0.439025	−	0.223694i
$936$	−3.05151	+	71.8598i	−0.0997416	+	2.34881i
$937$	12.1254	−	50.5060i	0.396120	−	1.64996i	−0.316637	−	0.948547i	$-0.602554\pi$
$937$	12.1254	−	50.5060i	0.396120	−	1.64996i	0.712757	−	0.701411i	$-0.247446\pi$
$938$	0.0898940	−	2.22795i	0.00293514	−	0.0727452i
$939$	90.4053	−	29.3745i	2.95027	−	0.958599i
$940$	−2.75215	+	1.39497i	−0.0897653	+	0.0454991i
$941$	0.878122	+	5.54425i	0.0286260	+	0.180737i	0.997858	−	0.0654097i	$-0.0208354\pi$
$941$	0.878122	+	5.54425i	0.0286260	+	0.180737i	−0.969233	+	0.246147i	$0.920835\pi$
$942$	8.35136	+	18.1660i	0.272102	+	0.591879i
$943$	−48.2364	−	25.4633i	−1.57079	−	0.829199i
$944$	−19.3919	+	2.98743i	−0.631152	+	0.0972325i
$945$	−2.98809	+	0.473268i	−0.0972027	+	0.0153954i
$946$	−0.961152	−	25.1399i	−0.0312498	−	0.817370i
$947$	12.6849	+	39.0400i	0.412203	+	1.26863i	0.914729	+	0.404069i	$0.132404\pi$
$947$	12.6849	+	39.0400i	0.412203	+	1.26863i	−0.502526	+	0.864562i	$0.667596\pi$
$948$	4.17852	+	10.1484i	0.135712	+	0.329606i
$949$	−37.1966	−	8.93012i	−1.20745	−	0.289884i
$950$	2.57080	−	2.02226i	0.0834078	−	0.0656107i
$951$	−16.0620	−	31.5234i	−0.520846	−	1.02222i
$952$	2.52390	−	1.40296i	0.0818001	−	0.0454703i
$953$	−9.10151	+	28.0116i	−0.294827	+	0.907383i	0.688453	+	0.725281i	$0.258290\pi$
$953$	−9.10151	+	28.0116i	−0.294827	+	0.907383i	−0.983280	+	0.182102i	$0.941710\pi$
$954$	23.5572	−	83.1909i	0.762692	−	2.69341i
$955$	0.299241	−	3.80222i	0.00968321	−	0.123037i
$956$	−5.22312	+	32.5325i	−0.168928	+	1.05217i
$957$	52.3016	−	21.6640i	1.69067	−	0.700299i
$958$	21.4114	−	46.3161i	0.691770	−	1.49640i
$959$	3.43063	+	4.72186i	0.110781	+	0.152477i
$960$	−21.8444	−	11.3053i	−0.705027	−	0.364876i
$961$	−6.95186	−	5.05082i	−0.224254	−	0.162930i
$962$	−21.6366	−	2.58404i	−0.697591	−	0.0833127i
$963$	118.671	+	18.7956i	3.82411	+	0.605679i
$964$	40.6158	−	34.5410i	1.30815	−	1.11249i
$965$	6.90715	+	4.23271i	0.222349	+	0.136256i
$966$	−2.07012	+	10.3500i	−0.0666049	+	0.333007i
$967$	−0.800651	−	10.1732i	−0.0257472	−	0.327149i	−0.996280	−	0.0861788i	$-0.972534\pi$
$967$	−0.800651	−	10.1732i	−0.0257472	−	0.327149i	0.970533	−	0.240970i	$-0.0774656\pi$
$968$	−6.48929	−	17.7632i	−0.208574	−	0.570930i
$969$	−16.5452	−	19.3720i	−0.531509	−	0.622317i
$970$	15.5683	−	16.8060i	0.499867	−	0.539608i
$971$	5.04523	+	8.23306i	0.161909	+	0.264212i	0.923298	−	0.384083i	$-0.125482\pi$
$971$	5.04523	+	8.23306i	0.161909	+	0.264212i	−0.761389	+	0.648295i	$0.775482\pi$
$972$	12.7360	−	12.6823i	0.408507	−	0.406785i
$973$	3.45433	−	4.04450i	0.110741	−	0.129661i
$974$	43.0635	−	5.05078i	1.37984	−	0.161837i
$975$	−8.56726	−	8.56726i	−0.274372	−	0.274372i
$976$	−3.61525	+	2.60336i	−0.115721	+	0.0833316i
$977$	2.53369	+	10.5536i	0.0810599	+	0.337639i	0.998133	−	0.0610807i	$-0.0194547\pi$
$977$	2.53369	+	10.5536i	0.0810599	+	0.337639i	−0.917073	+	0.398720i	$0.869455\pi$
$978$	−58.4737	+	11.5669i	−1.86978	+	0.369870i
$979$	−12.5350	+	24.6013i	−0.400621	+	0.786263i
$980$	−12.7730	−	5.32241i	−0.408020	−	0.170018i
$981$	7.90288	−	19.0792i	0.252319	−	0.609153i
$982$	−15.9444	−	23.9172i	−0.508808	−	0.763229i
$983$	−3.54546			−0.113083			−0.0565413	−	0.998400i	$-0.518007\pi$
$983$	−3.54546			−0.113083			−0.0565413	+	0.998400i	$0.518007\pi$
$984$	3.16701	−	55.5926i	0.100961	−	1.77223i
$985$	−9.69714			−0.308977
$986$	12.3044	+	18.4571i	0.391853	+	0.587793i
$987$	−0.517271	+	1.24880i	−0.0164649	+	0.0397498i
$988$	−16.8261	−	7.01130i	−0.535311	−	0.223059i
$989$	−16.3590	+	32.1064i	−0.520187	+	1.02092i
$990$	−37.6492	+	7.44756i	−1.19657	+	0.236699i
$991$	−6.74719	−	28.1041i	−0.214331	−	0.892755i	−0.971024	−	0.238983i	$-0.923186\pi$
$991$	−6.74719	−	28.1041i	−0.214331	−	0.892755i	0.756692	−	0.653771i	$-0.226814\pi$
$992$	30.9638	+	17.5561i	0.983103	+	0.557406i
$993$	0.754765	+	0.754765i	0.0239518	+	0.0239518i
$994$	−0.441318	+	0.0517608i	−0.0139978	+	0.00164175i
$995$	−14.9492	+	17.5032i	−0.473920	+	0.554889i
$996$	59.1339	−	58.8846i	1.87373	−	1.86583i
$997$	6.18049	+	10.0857i	0.195738	+	0.319416i	0.935418	−	0.353543i	$-0.115023\pi$
$997$	6.18049	+	10.0857i	0.195738	+	0.319416i	−0.739680	+	0.672959i	$0.765023\pi$
$998$	8.60275	−	9.28670i	0.272315	−	0.293965i
$999$	26.9585	+	31.5643i	0.852928	+	0.998651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.a.11.13	✓	672
4.3	odd	2	inner	820.2.bw.a.11.18	yes	672
41.15	odd	40	inner	820.2.bw.a.671.18	yes	672
164.15	even	40	inner	820.2.bw.a.671.13	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.a.11.13	✓	672	1.1	even	1	trivial
820.2.bw.a.11.18	yes	672	4.3	odd	2	inner
820.2.bw.a.671.13	yes	672	164.15	even	40	inner
820.2.bw.a.671.18	yes	672	41.15	odd	40	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bw (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.784452 - 1.17670i) q^{2} +(-1.17659 + 2.84053i) q^{3} +(-0.769269 + 1.84614i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(4.26544 - 0.843765i) q^{6} +(0.0665249 + 0.277096i) q^{7} +(2.77581 - 0.543004i) q^{8} +(-4.56293 - 4.56293i) q^{9} +(1.40459 - 0.164739i) q^{10} +(2.73125 - 3.19788i) q^{11} +(-4.33890 - 4.35727i) q^{12} +(-2.05901 - 3.36000i) q^{13} +(0.273875 - 0.295649i) q^{14} +(-1.99677 - 2.33792i) q^{15} +(-2.81645 - 2.84035i) q^{16} +(-0.281087 - 3.57155i) q^{17} +(-1.78982 + 8.94863i) q^{18} +(-1.97203 - 1.20846i) q^{19} +(-1.29568 - 1.52355i) q^{20} +(-0.865372 - 0.137061i) q^{21} +(-5.90550 - 0.705289i) q^{22} +(6.89158 + 5.00703i) q^{23} +(-1.72357 + 8.52367i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-2.33853 + 5.05860i) q^{26} +(9.80823 - 4.06270i) q^{27} +(-0.562733 - 0.0903474i) q^{28} +(0.343512 - 4.36473i) q^{29} +(-1.18467 + 4.18360i) q^{30} +(1.94443 - 5.98433i) q^{31} +(-1.13289 + 5.54225i) q^{32} +(5.87013 + 11.5208i) q^{33} +(-3.98216 + 3.13246i) q^{34} +(-0.277096 - 0.0665249i) q^{35} +(11.9339 - 4.91368i) q^{36} +(1.20825 + 3.71862i) q^{37} +(0.124961 + 3.26847i) q^{38} +(11.9668 - 1.89535i) q^{39} +(-0.776373 + 2.71979i) q^{40} +(-6.33812 + 0.910071i) q^{41} +(0.517562 + 1.12581i) q^{42} +(0.661732 + 4.17801i) q^{43} +(3.80267 + 7.50230i) q^{44} +(6.13713 - 1.99407i) q^{45} +(0.485677 - 12.0371i) q^{46} +(0.360148 - 1.50012i) q^{47} +(11.3819 - 4.65829i) q^{48} +(6.16469 - 3.14107i) q^{49} +(-0.490885 + 1.32629i) q^{50} +(10.4758 + 3.40379i) q^{51} +(7.78695 - 1.21647i) q^{52} +(-9.44518 - 0.743352i) q^{53} +(-12.4747 - 8.35440i) q^{54} +(1.60937 + 3.88537i) q^{55} +(0.335125 + 0.733044i) q^{56} +(5.75293 - 4.17975i) q^{57} +(-5.40547 + 3.01971i) q^{58} +(2.88318 - 3.96836i) q^{59} +(5.85217 - 1.88783i) q^{60} +(0.174231 - 1.10005i) q^{61} +(-8.56710 + 2.40640i) q^{62} +(0.960822 - 1.56792i) q^{63} +(7.41029 - 3.01456i) q^{64} +(3.92855 - 0.309184i) q^{65} +(8.95172 - 15.9449i) q^{66} +(4.20718 - 3.59327i) q^{67} +(6.80980 + 2.22856i) q^{68} +(-22.3311 + 13.6845i) q^{69} +(0.139089 + 0.378246i) q^{70} +(-0.838398 - 0.716060i) q^{71} +(-15.1435 - 10.1882i) q^{72} +(6.86411 - 6.86411i) q^{73} +(3.42790 - 4.33884i) q^{74} +(2.98962 - 0.717743i) q^{75} +(3.74800 - 2.71100i) q^{76} +(1.06782 + 0.544080i) q^{77} +(-11.6176 - 12.5945i) q^{78} +(-1.64895 - 0.683016i) q^{79} +(3.80942 - 1.21998i) q^{80} +13.2818i q^{81} +(6.04284 + 6.74419i) q^{82} +13.5713i q^{83} +(0.918738 - 1.49216i) q^{84} +(3.30988 + 1.37100i) q^{85} +(4.39719 - 4.05611i) q^{86} +(11.9940 + 6.11124i) q^{87} +(5.84498 - 10.3598i) q^{88} +(-6.38399 + 1.53266i) q^{89} +(-7.16072 - 5.65733i) q^{90} +(0.794067 - 0.794067i) q^{91} +(-14.5451 + 8.87105i) q^{92} +(14.7109 + 12.5643i) q^{93} +(-2.04772 + 0.752987i) q^{94} +(1.97203 - 1.20846i) q^{95} +(-14.4100 - 9.73894i) q^{96} +(12.3178 - 10.5204i) q^{97} +(-8.53201 - 4.79000i) q^{98} +(-27.0542 + 2.12921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 100 q^{12} + 24 q^{14} + 32 q^{16} - 8 q^{17} - 40 q^{21} + 52 q^{22} - 24 q^{24} + 28 q^{28} + 12 q^{30} - 20 q^{32} + 40 q^{33} + 44 q^{34} + 36 q^{36} - 80 q^{37} + 52 q^{38} - 160 q^{42}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 100 * q^12 + 24 * q^14 + 32 * q^16 - 8 * q^17 - 40 * q^21 + 52 * q^22 - 24 * q^24 + 28 * q^28 + 12 * q^30 - 20 * q^32 + 40 * q^33 + 44 * q^34 + 36 * q^36 - 80 * q^37 + 52 * q^38 - 160 * q^42 + 24 * q^44 + 16 * q^46 + 40 * q^48 - 16 * q^49 - 64 * q^52 - 64 * q^54 + 68 * q^56 + 56 * q^58 + 36 * q^62 + 120 * q^64 + 8 * q^65 - 304 * q^68 + 104 * q^69 + 24 * q^70 - 40 * q^72 - 28 * q^74 - 24 * q^76 - 160 * q^77 - 128 * q^78 - 192 * q^82 - 204 * q^84 + 32 * q^85 - 168 * q^88 + 8 * q^89 + 48 * q^90 - 56 * q^92 - 356 * q^94 - 136 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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