LMFDB - Embedded newform 96.3.m.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,3,Mod(19,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("96.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	96.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.61581053786$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	96.43
Dual form			96.3.m.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99038 - 0.195968i) q^{2} +(-0.662827 - 1.60021i) q^{3} +(3.92319 + 0.780100i) q^{4} +(-0.862642 + 2.08260i) q^{5} +(1.00569 + 3.31491i) q^{6} +(6.00123 - 6.00123i) q^{7} +(-7.65575 - 2.32151i) q^{8} +(-2.12132 + 2.12132i) q^{9} +O(q^{10})$	\(q+(-1.99038 - 0.195968i) q^{2} +(-0.662827 - 1.60021i) q^{3} +(3.92319 + 0.780100i) q^{4} +(-0.862642 + 2.08260i) q^{5} +(1.00569 + 3.31491i) q^{6} +(6.00123 - 6.00123i) q^{7} +(-7.65575 - 2.32151i) q^{8} +(-2.12132 + 2.12132i) q^{9} +(2.12510 - 3.97611i) q^{10} +(3.06868 - 7.40844i) q^{11} +(-1.35208 - 6.79499i) q^{12} +(-8.09339 - 19.5392i) q^{13} +(-13.1208 + 10.7687i) q^{14} +3.90437 q^{15} +(14.7829 + 6.12097i) q^{16} -20.9616i q^{17} +(4.63794 - 3.80651i) q^{18} +(9.19719 - 3.80960i) q^{19} +(-5.00895 + 7.49750i) q^{20} +(-13.5810 - 5.62543i) q^{21} +(-7.55964 + 14.1442i) q^{22} +(10.1250 + 10.1250i) q^{23} +(1.35954 + 13.7895i) q^{24} +(14.0846 + 14.0846i) q^{25} +(12.2798 + 40.4763i) q^{26} +(4.80062 + 1.98848i) q^{27} +(28.2255 - 18.8624i) q^{28} +(-30.1690 + 12.4964i) q^{29} +(-7.77117 - 0.765133i) q^{30} +7.63528i q^{31} +(-28.2240 - 15.0800i) q^{32} -13.8890 q^{33} +(-4.10780 + 41.7214i) q^{34} +(7.32126 + 17.6751i) q^{35} +(-9.97719 + 6.66751i) q^{36} +(-18.5090 + 44.6846i) q^{37} +(-19.0524 + 5.78018i) q^{38} +(-25.9022 + 25.9022i) q^{39} +(11.4390 - 13.9413i) q^{40} +(34.1279 - 34.1279i) q^{41} +(25.9289 + 13.8582i) q^{42} +(6.26795 - 15.1322i) q^{43} +(17.8183 - 26.6709i) q^{44} +(-2.58793 - 6.24780i) q^{45} +(-18.1683 - 22.1367i) q^{46} +81.9685 q^{47} +(-0.00368694 - 27.7128i) q^{48} -23.0295i q^{49} +(-25.2735 - 30.7938i) q^{50} +(-33.5429 + 13.8939i) q^{51} +(-16.5094 - 82.9696i) q^{52} +(16.9046 + 7.00211i) q^{53} +(-9.16536 - 4.89859i) q^{54} +(12.7817 + 12.7817i) q^{55} +(-59.8759 + 32.0120i) q^{56} +(-12.1923 - 12.1923i) q^{57} +(62.4967 - 18.9604i) q^{58} +(10.1659 + 4.21086i) q^{59} +(15.3176 + 3.04580i) q^{60} +(-70.3036 + 29.1207i) q^{61} +(1.49627 - 15.1971i) q^{62} +25.4611i q^{63} +(53.2211 + 35.5459i) q^{64} +47.6740 q^{65} +(27.6444 + 2.72181i) q^{66} +(-31.8993 - 77.0117i) q^{67} +(16.3521 - 82.2364i) q^{68} +(9.49095 - 22.9132i) q^{69} +(-11.1083 - 36.6148i) q^{70} +(-68.9646 + 68.9646i) q^{71} +(21.1650 - 11.3156i) q^{72} +(-94.0286 + 94.0286i) q^{73} +(45.5966 - 85.3120i) q^{74} +(13.2026 - 31.8739i) q^{75} +(39.0542 - 7.77107i) q^{76} +(-26.0439 - 62.8756i) q^{77} +(56.6311 - 46.4791i) q^{78} +40.4879 q^{79} +(-25.4999 + 25.5067i) q^{80} -9.00000i q^{81} +(-74.6154 + 61.2394i) q^{82} +(49.7241 - 20.5964i) q^{83} +(-48.8924 - 32.6642i) q^{84} +(43.6546 + 18.0823i) q^{85} +(-15.4410 + 28.8904i) q^{86} +(39.9937 + 39.9937i) q^{87} +(-40.6919 + 49.5933i) q^{88} +(34.7683 + 34.7683i) q^{89} +(3.92657 + 12.9426i) q^{90} +(-165.829 - 68.6888i) q^{91} +(31.8238 + 47.6208i) q^{92} +(12.2180 - 5.06087i) q^{93} +(-163.148 - 16.0632i) q^{94} +22.4404i q^{95} +(-5.42349 + 55.1596i) q^{96} +152.854 q^{97} +(-4.51305 + 45.8374i) q^{98} +(9.20603 + 22.2253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 40 q^{10} + 48 q^{12} + 32 q^{14} - 8 q^{16} - 24 q^{18} - 160 q^{20} - 184 q^{22} + 128 q^{23} - 72 q^{24} - 200 q^{26} - 120 q^{28} + 40 q^{32} + 120 q^{34} - 192 q^{35} + 280 q^{38} + 584 q^{40} - 192 q^{43} + 104 q^{44} + 32 q^{46} - 312 q^{50} - 192 q^{51} - 424 q^{52} + 320 q^{53} - 72 q^{54} - 256 q^{55} - 392 q^{56} - 352 q^{58} - 256 q^{59} - 144 q^{60} + 64 q^{61} - 48 q^{62} + 408 q^{64} + 144 q^{66} + 64 q^{67} + 856 q^{68} - 192 q^{69} + 984 q^{70} + 512 q^{71} + 1056 q^{74} + 384 q^{75} + 296 q^{76} - 448 q^{77} + 360 q^{78} + 512 q^{79} + 328 q^{80} - 760 q^{82} - 448 q^{86} - 1072 q^{88} + 192 q^{91} - 784 q^{92} - 480 q^{94} + 600 q^{96} + 272 q^{98}+O(q^{100}) $ 64 * q + 40 * q^10 + 48 * q^12 + 32 * q^14 - 8 * q^16 - 24 * q^18 - 160 * q^20 - 184 * q^22 + 128 * q^23 - 72 * q^24 - 200 * q^26 - 120 * q^28 + 40 * q^32 + 120 * q^34 - 192 * q^35 + 280 * q^38 + 584 * q^40 - 192 * q^43 + 104 * q^44 + 32 * q^46 - 312 * q^50 - 192 * q^51 - 424 * q^52 + 320 * q^53 - 72 * q^54 - 256 * q^55 - 392 * q^56 - 352 * q^58 - 256 * q^59 - 144 * q^60 + 64 * q^61 - 48 * q^62 + 408 * q^64 + 144 * q^66 + 64 * q^67 + 856 * q^68 - 192 * q^69 + 984 * q^70 + 512 * q^71 + 1056 * q^74 + 384 * q^75 + 296 * q^76 - 448 * q^77 + 360 * q^78 + 512 * q^79 + 328 * q^80 - 760 * q^82 - 448 * q^86 - 1072 * q^88 + 192 * q^91 - 784 * q^92 - 480 * q^94 + 600 * q^96 + 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	−1.99038	−	0.195968i	−0.995188	−	0.0979840i
$2$	−1.99038	−	0.195968i	−0.995188	−	0.0979840i
$3$	−0.662827	−	1.60021i	−0.220942	−	0.533402i
$3$	−0.662827	−	1.60021i	−0.220942	−	0.533402i
$4$	3.92319	+	0.780100i	0.980798	+	0.195025i
$5$	−0.862642	+	2.08260i	−0.172528	+	0.416520i	−0.986365	−	0.164574i	$-0.947375\pi$
$5$	−0.862642	+	2.08260i	−0.172528	+	0.416520i	0.813836	+	0.581094i	$0.197375\pi$
$6$	1.00569	+	3.31491i	0.167614	+	0.552484i
$7$	6.00123	−	6.00123i	0.857319	−	0.857319i	−0.133703	−	0.991021i	$-0.542687\pi$
$7$	6.00123	−	6.00123i	0.857319	−	0.857319i	0.991021	+	0.133703i	$0.0426868\pi$
$8$	−7.65575	−	2.32151i	−0.956969	−	0.290189i
$9$	−2.12132	+	2.12132i	−0.235702	+	0.235702i
$10$	2.12510	−	3.97611i	0.212510	−	0.397611i
$11$	3.06868	−	7.40844i	0.278971	−	0.673495i	−0.720837	−	0.693105i	$-0.756242\pi$
$11$	3.06868	−	7.40844i	0.278971	−	0.673495i	0.999808	+	0.0196097i	$0.00624236\pi$
$12$	−1.35208	−	6.79499i	−0.112673	−	0.566249i
$13$	−8.09339	−	19.5392i	−0.622568	−	1.50301i	−0.848677	−	0.528911i	$-0.822601\pi$
$13$	−8.09339	−	19.5392i	−0.622568	−	1.50301i	0.226109	−	0.974102i	$-0.427399\pi$
$14$	−13.1208	+	10.7687i	−0.937197	+	0.769190i
$15$	3.90437			0.260292
$16$	14.7829	+	6.12097i	0.923930	+	0.382561i
$17$		−	20.9616i		−	1.23303i	−0.787341	−	0.616517i	$-0.788543\pi$
$17$		−	20.9616i		−	1.23303i	0.787341	−	0.616517i	$-0.211457\pi$
$18$	4.63794	−	3.80651i	0.257663	−	0.211473i
$19$	9.19719	−	3.80960i	0.484063	−	0.200505i	−0.127287	−	0.991866i	$-0.540627\pi$
$19$	9.19719	−	3.80960i	0.484063	−	0.200505i	0.611350	+	0.791361i	$0.290627\pi$
$20$	−5.00895	+	7.49750i	−0.250447	+	0.374875i
$21$	−13.5810	−	5.62543i	−0.646714	−	0.267878i
$22$	−7.55964	+	14.1442i	−0.343620	+	0.642919i
$23$	10.1250	+	10.1250i	0.440217	+	0.440217i	0.892085	−	0.451868i	$-0.149242\pi$
$23$	10.1250	+	10.1250i	0.440217	+	0.440217i	−0.451868	+	0.892085i	$0.649242\pi$
$24$	1.35954	+	13.7895i	0.0566476	+	0.574565i
$25$	14.0846	+	14.0846i	0.563384	+	0.563384i
$26$	12.2798	+	40.4763i	0.472301	+	1.55678i
$27$	4.80062	+	1.98848i	0.177801	+	0.0736475i
$28$	28.2255	−	18.8624i	1.00806	−	0.673658i
$29$	−30.1690	+	12.4964i	−1.04031	+	0.430911i	−0.836424	−	0.548083i	$-0.815358\pi$
$29$	−30.1690	+	12.4964i	−1.04031	+	0.430911i	−0.203888	+	0.978994i	$0.565358\pi$
$30$	−7.77117	−	0.765133i	−0.259039	−	0.0255044i
$31$			7.63528i			0.246299i	0.992388	+	0.123150i	$0.0392995\pi$
$31$			7.63528i			0.246299i	−0.992388	+	0.123150i	$0.960700\pi$
$32$	−28.2240	−	15.0800i	−0.882000	−	0.471250i
$33$	−13.8890			−0.420880
$34$	−4.10780	+	41.7214i	−0.120818	+	1.22710i
$35$	7.32126	+	17.6751i	0.209179	+	0.505002i
$36$	−9.97719	+	6.66751i	−0.277144	+	0.185209i
$37$	−18.5090	+	44.6846i	−0.500242	+	1.20769i	0.449109	+	0.893477i	$0.351741\pi$
$37$	−18.5090	+	44.6846i	−0.500242	+	1.20769i	−0.949352	+	0.314215i	$0.898259\pi$
$38$	−19.0524	+	5.78018i	−0.501380	+	0.152110i
$39$	−25.9022	+	25.9022i	−0.664158	+	0.664158i
$40$	11.4390	−	13.9413i	0.285974	−	0.348531i
$41$	34.1279	−	34.1279i	0.832389	−	0.832389i	−0.155455	−	0.987843i	$-0.549684\pi$
$41$	34.1279	−	34.1279i	0.832389	−	0.832389i	0.987843	+	0.155455i	$0.0496842\pi$
$42$	25.9289	+	13.8582i	0.617354	+	0.329956i
$43$	6.26795	−	15.1322i	0.145766	−	0.351911i	−0.834086	−	0.551634i	$-0.814004\pi$
$43$	6.26795	−	15.1322i	0.145766	−	0.351911i	0.979852	+	0.199723i	$0.0640044\pi$
$44$	17.8183	−	26.6709i	0.404962	−	0.606156i
$45$	−2.58793	−	6.24780i	−0.0575095	−	0.138840i
$46$	−18.1683	−	22.1367i	−0.394964	−	0.481232i
$47$	81.9685			1.74401			0.872006	−	0.489496i	$-0.162819\pi$
$47$	81.9685			1.74401			0.872006	+	0.489496i	$0.162819\pi$
$48$	−0.00368694	−	27.7128i	−7.68113e−5	−	0.577350i
$49$		−	23.0295i		−	0.469991i
$50$	−25.2735	−	30.7938i	−0.505470	−	0.615875i
$51$	−33.5429	+	13.8939i	−0.657703	+	0.272430i
$52$	−16.5094	−	82.9696i	−0.317489	−	1.59557i
$53$	16.9046	+	7.00211i	0.318954	+	0.132115i	0.536416	−	0.843954i	$-0.319778\pi$
$53$	16.9046	+	7.00211i	0.318954	+	0.132115i	−0.217462	+	0.976069i	$0.569778\pi$
$54$	−9.16536	−	4.89859i	−0.169729	−	0.0907147i
$55$	12.7817	+	12.7817i	0.232394	+	0.232394i
$56$	−59.8759	+	32.0120i	−1.06921	+	0.571643i
$57$	−12.1923	−	12.1923i	−0.213900	−	0.213900i
$58$	62.4967	−	18.9604i	1.07753	−	0.326904i
$59$	10.1659	+	4.21086i	0.172304	+	0.0713705i	0.467168	−	0.884169i	$-0.345274\pi$
$59$	10.1659	+	4.21086i	0.172304	+	0.0713705i	−0.294864	+	0.955539i	$0.595274\pi$
$60$	15.3176	+	3.04580i	0.255294	+	0.0507634i
$61$	−70.3036	+	29.1207i	−1.15252	+	0.477389i	−0.875377	−	0.483440i	$-0.839387\pi$
$61$	−70.3036	+	29.1207i	−1.15252	+	0.477389i	−0.277141	+	0.960829i	$0.589387\pi$
$62$	1.49627	−	15.1971i	0.0241334	−	0.245114i
$63$			25.4611i			0.404144i
$64$	53.2211	+	35.5459i	0.831580	+	0.555404i
$65$	47.6740			0.733446
$66$	27.6444	+	2.72181i	0.418855	+	0.0412395i
$67$	−31.8993	−	77.0117i	−0.476109	−	1.14943i	−0.961420	−	0.275086i	$-0.911294\pi$
$67$	−31.8993	−	77.0117i	−0.476109	−	1.14943i	0.485311	−	0.874342i	$-0.338706\pi$
$68$	16.3521	−	82.2364i	0.240473	−	1.20936i
$69$	9.49095	−	22.9132i	0.137550	−	0.332075i
$70$	−11.1083	−	36.6148i	−0.158690	−	0.523069i
$71$	−68.9646	+	68.9646i	−0.971333	+	0.971333i	−0.999600	−	0.0282675i	$-0.991001\pi$
$71$	−68.9646	+	68.9646i	−0.971333	+	0.971333i	0.0282675	+	0.999600i	$0.491001\pi$
$72$	21.1650	−	11.3156i	0.293958	−	0.157162i
$73$	−94.0286	+	94.0286i	−1.28806	+	1.28806i	−0.352101	+	0.935962i	$0.614533\pi$
$73$	−94.0286	+	94.0286i	−1.28806	+	1.28806i	−0.935962	+	0.352101i	$0.885467\pi$
$74$	45.5966	−	85.3120i	0.616170	−	1.15286i
$75$	13.2026	−	31.8739i	0.176035	−	0.424985i
$76$	39.0542	−	7.77107i	0.513871	−	0.102251i
$77$	−26.0439	−	62.8756i	−0.338233	−	0.816567i
$78$	56.6311	−	46.4791i	0.726039	−	0.595886i
$79$	40.4879			0.512505			0.256252	−	0.966610i	$-0.417512\pi$
$79$	40.4879			0.512505			0.256252	+	0.966610i	$0.417512\pi$
$80$	−25.4999	+	25.5067i	−0.318748	+	0.318833i
$81$		−	9.00000i		−	0.111111i
$82$	−74.6154	+	61.2394i	−0.909944	+	0.746822i
$83$	49.7241	−	20.5964i	0.599086	−	0.248149i	−0.0624684	−	0.998047i	$-0.519897\pi$
$83$	49.7241	−	20.5964i	0.599086	−	0.248149i	0.661554	+	0.749898i	$0.269897\pi$
$84$	−48.8924	−	32.6642i	−0.582053	−	0.388859i
$85$	43.6546	+	18.0823i	0.513584	+	0.212733i
$86$	−15.4410	+	28.8904i	−0.179546	+	0.335935i
$87$	39.9937	+	39.9937i	0.459698	+	0.459698i
$88$	−40.6919	+	49.5933i	−0.462407	+	0.563560i
$89$	34.7683	+	34.7683i	0.390655	+	0.390655i	0.874921	−	0.484266i	$-0.160913\pi$
$89$	34.7683	+	34.7683i	0.390655	+	0.390655i	−0.484266	+	0.874921i	$0.660913\pi$
$90$	3.92657	+	12.9426i	0.0436286	+	0.143807i
$91$	−165.829	−	68.6888i	−1.82230	−	0.754822i
$92$	31.8238	+	47.6208i	0.345910	+	0.517617i
$93$	12.2180	−	5.06087i	0.131377	−	0.0544180i
$94$	−163.148	−	16.0632i	−1.73562	−	0.170885i
$95$			22.4404i			0.236215i
$96$	−5.42349	+	55.1596i	−0.0564947	+	0.574580i
$97$	152.854			1.57582			0.787909	−	0.615792i	$-0.211164\pi$
$97$	152.854			1.57582			0.787909	+	0.615792i	$0.211164\pi$
$98$	−4.51305	+	45.8374i	−0.0460516	+	0.467729i
$99$	9.20603	+	22.2253i	0.0929902	+	0.224498i
$100$	44.2692	+	66.2440i	0.442692	+	0.662440i
$101$	−33.1069	+	79.9270i	−0.327791	+	0.791357i	0.670965	+	0.741489i	$0.265880\pi$
$101$	−33.1069	+	79.9270i	−0.327791	+	0.791357i	−0.998756	+	0.0498678i	$0.984120\pi$
$102$	69.4857	−	21.0808i	0.681232	−	0.206674i
$103$	−57.4305	+	57.4305i	−0.557578	+	0.557578i	−0.928617	−	0.371039i	$-0.879001\pi$
$103$	−57.4305	+	57.4305i	−0.557578	+	0.557578i	0.371039	+	0.928617i	$0.379001\pi$
$104$	16.6005	+	168.376i	0.159621	+	1.61900i
$105$	23.4311	−	23.4311i	0.223153	−	0.223153i
$106$	−32.2743	−	17.2496i	−0.304474	−	0.162732i
$107$	30.4687	−	73.5580i	0.284754	−	0.687458i	−0.715180	−	0.698941i	$-0.753655\pi$
$107$	30.4687	−	73.5580i	0.284754	−	0.687458i	0.999934	+	0.0114826i	$0.00365510\pi$
$108$	17.2825	+	11.5462i	0.160024	+	0.106909i
$109$	36.5137	+	88.1519i	0.334988	+	0.808733i	0.998181	+	0.0602845i	$0.0192008\pi$
$109$	36.5137	+	88.1519i	0.334988	+	0.808733i	−0.663193	+	0.748448i	$0.730799\pi$
$110$	−22.9355	−	27.9451i	−0.208505	−	0.254047i
$111$	83.7728			0.754710
$112$	125.449	−	51.9822i	1.12008	−	0.464127i
$113$		−	106.775i		−	0.944908i	−0.881355	−	0.472454i	$-0.843368\pi$
$113$		−	106.775i		−	0.944908i	0.881355	−	0.472454i	$-0.156632\pi$
$114$	21.8779	+	26.6565i	0.191912	+	0.233829i
$115$	−29.8205	+	12.3521i	−0.259309	+	0.107409i
$116$	−128.107	+	25.4910i	−1.10437	+	0.219750i
$117$	58.6175	+	24.2802i	0.501004	+	0.207523i
$118$	−19.4088	−	10.3734i	−0.164481	−	0.0879101i
$119$	−125.795	−	125.795i	−1.05710	−	1.05710i
$120$	−29.8909	−	9.06406i	−0.249091	−	0.0755338i
$121$	40.0917	+	40.0917i	0.331336	+	0.331336i
$122$	145.637	−	44.1839i	1.19375	−	0.362163i
$123$	−77.2326	−	31.9908i	−0.627908	−	0.260088i
$124$	−5.95629	+	29.9547i	−0.0480346	+	0.241570i
$125$	−93.5476	+	38.7487i	−0.748381	+	0.309989i
$126$	4.98956	−	50.6771i	0.0395997	−	0.402199i
$127$		−	50.4772i		−	0.397458i	−0.980054	−	0.198729i	$-0.936319\pi$
$127$		−	50.4772i		−	0.397458i	0.980054	−	0.198729i	$-0.0636814\pi$
$128$	−98.9642	−	81.1793i	−0.773158	−	0.634213i
$129$	−28.3692			−0.219916
$130$	−94.8892	−	9.34258i	−0.729917	−	0.0718660i
$131$	80.5874	+	194.555i	0.615171	+	1.48515i	0.857252	+	0.514898i	$0.172170\pi$
$131$	80.5874	+	194.555i	0.615171	+	1.48515i	−0.242081	+	0.970256i	$0.577830\pi$
$132$	−54.4894	−	10.8348i	−0.412798	−	0.0820822i
$133$	32.3322	−	78.0567i	0.243099	−	0.586893i
$134$	48.3997	+	159.533i	0.361192	+	1.19055i
$135$	−8.28243	+	8.28243i	−0.0613513	+	0.0613513i
$136$	−48.6626	+	160.477i	−0.357813	+	1.17998i
$137$	95.5892	−	95.5892i	0.697732	−	0.697732i	−0.266189	−	0.963921i	$-0.585765\pi$
$137$	95.5892	−	95.5892i	0.697732	−	0.697732i	0.963921	+	0.266189i	$0.0857646\pi$
$138$	−23.3808	+	43.7459i	−0.169426	+	0.316999i
$139$	95.9396	−	231.619i	0.690213	−	1.66632i	−0.0541394	−	0.998533i	$-0.517242\pi$
$139$	95.9396	−	231.619i	0.690213	−	1.66632i	0.744352	−	0.667787i	$-0.232758\pi$
$140$	14.9344	+	75.0541i	0.106674	+	0.536101i
$141$	−54.3310	−	131.167i	−0.385326	−	0.930259i
$142$	150.780	−	123.751i	1.06183	−	0.871484i
$143$	−169.591			−1.18595
$144$	−44.3438	+	18.3747i	−0.307943	+	0.127602i
$145$		−	73.6101i		−	0.507656i
$146$	205.579	−	168.726i	1.40807	−	1.15566i
$147$	−36.8520	+	15.2646i	−0.250694	+	0.103841i
$148$	−107.473	+	160.867i	−0.726167	+	1.08694i
$149$	88.6028	+	36.7005i	0.594650	+	0.246312i	0.659650	−	0.751573i	$-0.270705\pi$
$149$	88.6028	+	36.7005i	0.594650	+	0.246312i	−0.0649997	+	0.997885i	$0.520705\pi$
$150$	−32.5244	+	60.8538i	−0.216829	+	0.405692i
$151$	−105.081	−	105.081i	−0.695902	−	0.695902i	0.267622	−	0.963524i	$-0.413762\pi$
$151$	−105.081	−	105.081i	−0.695902	−	0.695902i	−0.963524	+	0.267622i	$0.913762\pi$
$152$	−79.2555	+	7.81397i	−0.521417	+	0.0514077i
$153$	44.4662	+	44.4662i	0.290629	+	0.290629i
$154$	39.5156	+	130.250i	0.256595	+	0.845779i
$155$	−15.9012	−	6.58651i	−0.102589	−	0.0424936i
$156$	−121.826	+	81.4130i	−0.780933	+	0.521878i
$157$	136.553	−	56.5620i	0.869762	−	0.360267i	0.0972444	−	0.995261i	$-0.468997\pi$
$157$	136.553	−	56.5620i	0.869762	−	0.360267i	0.772518	+	0.634993i	$0.218997\pi$
$158$	−80.5861	−	7.93433i	−0.510038	−	0.0502173i
$159$		−	31.6920i		−	0.199321i
$160$	55.7528	−	45.7707i	0.348455	−	0.286067i
$161$	121.525			0.754812
$162$	−1.76371	+	17.9134i	−0.0108871	+	0.110576i
$163$	72.6138	+	175.305i	0.445484	+	1.07549i	0.973996	+	0.226567i	$0.0727502\pi$
$163$	72.6138	+	175.305i	0.445484	+	1.07549i	−0.528512	+	0.848926i	$0.677250\pi$
$164$	160.514	−	107.267i	0.978742	−	0.654069i
$165$	11.9813	−	28.9253i	0.0726138	−	0.175305i
$166$	−103.006	+	31.2502i	−0.620517	+	0.188254i
$167$	−3.00010	+	3.00010i	−0.0179647	+	0.0179647i	−0.716032	−	0.698067i	$-0.754044\pi$
$167$	−3.00010	+	3.00010i	−0.0179647	+	0.0179647i	0.698067	+	0.716032i	$0.254044\pi$
$168$	90.9132	+	74.5953i	0.541150	+	0.444020i
$169$	−196.775	+	196.775i	−1.16435	+	1.16435i
$170$	−83.3456	−	44.5456i	−0.490268	−	0.262033i
$171$	−11.4288	+	27.5916i	−0.0668351	+	0.161354i
$172$	36.3950	−	54.4768i	0.211599	−	0.316726i
$173$	−53.3928	−	128.902i	−0.308629	−	0.745096i	−0.999750	−	0.0223571i	$-0.992883\pi$
$173$	−53.3928	−	128.902i	−0.308629	−	0.745096i	0.691121	−	0.722739i	$-0.257117\pi$
$174$	−71.7651	−	87.4401i	−0.412443	−	0.502529i
$175$	169.050			0.965999
$176$	90.7108	−	90.7349i	0.515402	−	0.515539i
$177$		−	19.0586i		−	0.107676i
$178$	−62.3885	−	76.0154i	−0.350497	−	0.427053i
$179$	−216.813	+	89.8070i	−1.21125	+	0.501715i	−0.894617	−	0.446834i	$-0.852552\pi$
$179$	−216.813	+	89.8070i	−1.21125	+	0.501715i	−0.316631	+	0.948549i	$0.602552\pi$
$180$	−5.27902	−	26.5302i	−0.0293279	−	0.147390i
$181$	75.1706	+	31.1367i	0.415307	+	0.172026i	0.580546	−	0.814228i	$-0.302839\pi$
$181$	75.1706	+	31.1367i	0.415307	+	0.172026i	−0.165238	+	0.986254i	$0.552839\pi$
$182$	316.602	+	169.214i	1.73957	+	0.929746i
$183$	93.1983	+	93.1983i	0.509280	+	0.509280i
$184$	−54.0091	−	101.020i	−0.293528	−	0.549020i
$185$	−77.0936	−	77.0936i	−0.416722	−	0.416722i
$186$	−25.3102	+	7.67870i	−0.136077	+	0.0412833i
$187$	−155.293	−	64.3244i	−0.830443	−	0.343981i
$188$	321.578	+	63.9437i	1.71052	+	0.340126i
$189$	40.7430	−	16.8763i	0.215571	−	0.0892925i
$190$	4.39760	−	44.6648i	0.0231453	−	0.235078i
$191$		−	282.292i		−	1.47797i	−0.673722	−	0.738985i	$-0.735305\pi$
$191$		−	282.292i		−	1.47797i	0.673722	−	0.738985i	$-0.264695\pi$
$192$	21.6043	−	108.726i	0.112522	−	0.566279i
$193$	−68.7828			−0.356387			−0.178194	−	0.983995i	$-0.557025\pi$
$193$	−68.7828			−0.356387			−0.178194	+	0.983995i	$0.557025\pi$
$194$	−304.238	−	29.9546i	−1.56823	−	0.154405i
$195$	−31.5996	−	76.2882i	−0.162049	−	0.391222i
$196$	17.9654	−	90.3493i	0.0916600	−	0.460966i
$197$	−31.2073	+	75.3412i	−0.158413	+	0.382443i	−0.983080	−	0.183175i	$-0.941362\pi$
$197$	−31.2073	+	75.3412i	−0.158413	+	0.382443i	0.824667	+	0.565618i	$0.191362\pi$
$198$	−13.9680	−	46.0409i	−0.0705455	−	0.232530i
$199$	178.182	−	178.182i	0.895386	−	0.895386i	−0.0996380	−	0.995024i	$-0.531768\pi$
$199$	178.182	−	178.182i	0.895386	−	0.895386i	0.995024	+	0.0996380i	$0.0317685\pi$
$200$	−75.1306	−	140.526i	−0.375653	−	0.702629i
$201$	−102.091	+	102.091i	−0.507915	+	0.507915i
$202$	81.5582	−	152.597i	0.403754	−	0.755430i
$203$	−106.057	+	256.045i	−0.522451	+	1.26131i
$204$	−142.434	+	28.3417i	−0.698205	+	0.138930i
$205$	41.6347	+	100.515i	0.203096	+	0.490317i
$206$	125.563	−	103.054i	0.609528	−	0.500261i
$207$	−42.9567			−0.207520
$208$	−0.0450191	−	338.385i	−0.000216438	−	1.62685i
$209$		−	79.8273i		−	0.381949i
$210$	−51.2283	+	42.0449i	−0.243944	+	0.200214i
$211$	320.807	−	132.882i	1.52041	−	0.629774i	0.542736	−	0.839903i	$-0.317388\pi$
$211$	320.807	−	132.882i	1.52041	−	0.629774i	0.977674	+	0.210129i	$0.0673883\pi$
$212$	60.8576	+	40.6579i	0.287064	+	0.191782i
$213$	156.069	+	64.6460i	0.732720	+	0.303502i
$214$	−75.0593	+	140.437i	−0.350744	+	0.656249i
$215$	26.1073	+	26.1073i	0.121429	+	0.121429i
$216$	−32.1361	−	26.3680i	−0.148778	−	0.122074i
$217$	45.8211	+	45.8211i	0.211157	+	0.211157i
$218$	−55.4010	−	182.611i	−0.254133	−	0.837665i
$219$	212.790	+	88.1404i	0.971643	+	0.402468i
$220$	40.1740	+	60.1159i	0.182609	+	0.273254i
$221$	−409.572	+	169.650i	−1.85327	+	0.767648i
$222$	−166.739	−	16.4168i	−0.751078	−	0.0739495i
$223$			356.738i			1.59972i	0.600186	+	0.799860i	$0.295093\pi$
$223$			356.738i			1.59972i	−0.600186	+	0.799860i	$0.704907\pi$
$224$	−259.877	+	78.8801i	−1.16017	+	0.352143i
$225$	−59.7559			−0.265582
$226$	−20.9244	+	212.522i	−0.0925859	+	0.940361i
$227$	64.2938	+	155.219i	0.283232	+	0.683784i	0.999907	−	0.0136239i	$-0.00433675\pi$
$227$	64.2938	+	155.219i	0.283232	+	0.683784i	−0.716675	+	0.697408i	$0.754337\pi$
$228$	−38.3215	−	57.3439i	−0.168077	−	0.251508i
$229$	91.8282	−	221.693i	0.400997	−	0.968091i	−0.586428	−	0.810001i	$-0.699466\pi$
$229$	91.8282	−	221.693i	0.400997	−	0.968091i	0.987425	−	0.158090i	$-0.0505336\pi$
$230$	61.7747	−	18.7414i	0.268586	−	0.0814843i
$231$	−83.3514	+	83.3514i	−0.360828	+	0.360828i
$232$	259.977	−	25.6317i	1.12059	−	0.110482i
$233$	−298.640	+	298.640i	−1.28172	+	1.28172i	−0.342026	+	0.939690i	$0.611113\pi$
$233$	−298.640	+	298.640i	−1.28172	+	1.28172i	−0.939690	+	0.342026i	$0.888887\pi$
$234$	−111.913	−	59.8138i	−0.478259	−	0.255615i
$235$	−70.7095	+	170.708i	−0.300891	+	0.726416i
$236$	36.5980	+	24.4505i	0.155076	+	0.103604i
$237$	−26.8365	−	64.7889i	−0.113234	−	0.273371i
$238$	225.728	+	275.032i	0.948438	+	1.15560i
$239$	−14.1094			−0.0590351			−0.0295175	−	0.999564i	$-0.509397\pi$
$239$	−14.1094			−0.0590351			−0.0295175	+	0.999564i	$0.509397\pi$
$240$	57.7179	+	23.8986i	0.240491	+	0.0995773i
$241$			54.7660i			0.227245i	0.993524	+	0.113622i	$0.0362454\pi$
$241$			54.7660i			0.227245i	−0.993524	+	0.113622i	$0.963755\pi$
$242$	−71.9408	−	87.6542i	−0.297276	−	0.362207i
$243$	−14.4019	+	5.96544i	−0.0592669	+	0.0245492i
$244$	−298.532	+	59.4023i	−1.22349	+	0.243452i
$245$	47.9614	+	19.8662i	0.195761	+	0.0810867i
$246$	147.453	+	78.8089i	0.599402	+	0.320361i
$247$	−148.873	−	148.873i	−0.602724	−	0.602724i
$248$	17.7254	−	58.4538i	0.0714734	−	0.235701i
$249$	−65.9170	−	65.9170i	−0.264727	−	0.264727i
$250$	193.788	−	58.7921i	0.775154	−	0.235168i
$251$	404.448	+	167.528i	1.61135	+	0.667441i	0.992962	−	0.118435i	$-0.0377876\pi$
$251$	404.448	+	167.528i	1.61135	+	0.667441i	0.618384	+	0.785876i	$0.287788\pi$
$252$	−19.8622	+	99.8887i	−0.0788182	+	0.396384i
$253$	106.081	−	43.9401i	0.419291	−	0.173676i
$254$	−9.89192	+	100.469i	−0.0389446	+	0.395546i
$255$		−	81.8419i		−	0.320949i
$256$	181.067	+	180.971i	0.707295	+	0.706919i
$257$	−165.338			−0.643339			−0.321670	−	0.946852i	$-0.604244\pi$
$257$	−165.338			−0.643339			−0.321670	+	0.946852i	$0.604244\pi$
$258$	56.4653	+	5.55945i	0.218858	+	0.0215483i
$259$	157.086	+	379.239i	0.606510	+	1.46424i
$260$	187.034	+	37.1905i	0.719363	+	0.143040i
$261$	37.4893	−	90.5071i	0.143637	−	0.346771i
$262$	−122.273	−	403.030i	−0.466689	−	1.53828i
$263$	−149.043	+	149.043i	−0.566702	+	0.566702i	−0.931203	−	0.364501i	$-0.881240\pi$
$263$	−149.043	+	149.043i	−0.566702	+	0.566702i	0.364501	+	0.931203i	$0.381240\pi$
$264$	106.331	+	32.2436i	0.402769	+	0.122135i
$265$	−29.1652	+	29.1652i	−0.110057	+	0.110057i
$266$	−79.6498	+	149.026i	−0.299435	+	0.560249i
$267$	32.5911	−	78.6818i	0.122064	−	0.294688i
$268$	−65.0702	−	327.016i	−0.242799	−	1.22021i
$269$	80.7409	+	194.926i	0.300152	+	0.724631i	0.999947	+	0.0102875i	$0.00327466\pi$
$269$	80.7409	+	194.926i	0.300152	+	0.724631i	−0.699795	+	0.714344i	$0.746725\pi$
$270$	18.1082	−	14.8621i	0.0670676	−	0.0550447i
$271$	152.720			0.563542			0.281771	−	0.959482i	$-0.409078\pi$
$271$	152.720			0.563542			0.281771	+	0.959482i	$0.409078\pi$
$272$	128.305	−	309.873i	0.471710	−	1.13924i
$273$			310.890i			1.13879i
$274$	−208.991	+	171.526i	−0.762741	+	0.626007i
$275$	147.566	−	61.1238i	0.536604	−	0.222268i
$276$	55.1094	−	82.4889i	0.199672	−	0.298873i
$277$	−285.657	−	118.323i	−1.03125	−	0.427159i	−0.198088	−	0.980184i	$-0.563473\pi$
$277$	−285.657	−	118.323i	−1.03125	−	0.427159i	−0.833164	+	0.553026i	$0.813473\pi$
$278$	−236.346	+	442.207i	−0.850164	+	1.59067i
$279$	−16.1969	−	16.1969i	−0.0580533	−	0.0580533i
$280$	−15.0168	−	152.313i	−0.0536315	−	0.543973i
$281$	−83.5699	−	83.5699i	−0.297402	−	0.297402i	0.542594	−	0.839995i	$-0.317442\pi$
$281$	−83.5699	−	83.5699i	−0.297402	−	0.297402i	−0.839995	+	0.542594i	$0.817442\pi$
$282$	82.4346	+	271.718i	0.292321	+	0.963539i
$283$	−63.7437	−	26.4035i	−0.225243	−	0.0932986i	0.267208	−	0.963639i	$-0.413899\pi$
$283$	−63.7437	−	26.4035i	−0.225243	−	0.0932986i	−0.492451	+	0.870340i	$0.663899\pi$
$284$	−324.361	+	216.762i	−1.14212	+	0.763247i
$285$	35.9093	−	14.8741i	0.125997	−	0.0521898i
$286$	337.550	+	33.2344i	1.18024	+	0.116204i
$287$		−	409.619i		−	1.42724i
$288$	91.8616	−	27.8826i	0.318964	−	0.0968146i
$289$	−150.388			−0.520374
$290$	−14.4252	+	146.512i	−0.0497421	+	0.505213i
$291$	−101.316	−	244.598i	−0.348165	−	0.840544i
$292$	−442.244	+	295.541i	−1.51453	+	1.01213i
$293$	−93.9708	+	226.866i	−0.320719	+	0.774285i	0.678493	+	0.734607i	$0.262633\pi$
$293$	−93.9708	+	226.866i	−0.320719	+	0.774285i	−0.999213	+	0.0396783i	$0.987367\pi$
$294$	76.3407	−	23.1605i	0.259662	−	0.0787772i
$295$	−17.5391	+	17.5391i	−0.0594546	+	0.0594546i
$296$	245.436	−	299.126i	0.829176	−	1.01056i
$297$	29.4631	−	29.4631i	0.0992024	−	0.0992024i
$298$	−169.161	−	90.4111i	−0.567654	−	0.303393i
$299$	115.888	−	279.779i	0.387586	−	0.935716i
$300$	76.6612	−	114.748i	0.255537	−	0.382494i
$301$	−53.1962	−	128.427i	−0.176732	−	0.426668i
$302$	188.559	+	229.744i	0.624366	+	0.760741i
$303$	149.844			0.494534
$304$	159.279	−	0.0211907i	0.523946	−	6.97063e-5i
$305$		−	171.535i		−	0.562410i
$306$	−79.7906	−	97.2185i	−0.260754	−	0.317708i
$307$	−134.864	+	55.8627i	−0.439298	+	0.181963i	−0.591360	−	0.806408i	$-0.701409\pi$
$307$	−134.864	+	55.8627i	−0.439298	+	0.181963i	0.152062	+	0.988371i	$0.451409\pi$
$308$	−53.1261	−	266.990i	−0.172487	−	0.866851i
$309$	129.967	+	53.8342i	0.420606	+	0.174221i
$310$	30.3587	+	16.2258i	0.0979314	+	0.0523412i
$311$	−158.125	−	158.125i	−0.508439	−	0.508439i	0.405608	−	0.914047i	$-0.367060\pi$
$311$	−158.125	−	158.125i	−0.508439	−	0.508439i	−0.914047	+	0.405608i	$0.867060\pi$
$312$	258.433	−	138.168i	0.828311	−	0.442848i
$313$	−364.612	−	364.612i	−1.16489	−	1.16489i	−0.983390	−	0.181503i	$-0.941904\pi$
$313$	−364.612	−	364.612i	−1.16489	−	1.16489i	−0.181503	−	0.983390i	$-0.558096\pi$
$314$	−282.875	+	85.8196i	−0.900877	+	0.273311i
$315$	−53.0253	−	21.9638i	−0.168334	−	0.0697263i
$316$	158.842	+	31.5846i	0.502664	+	0.0999513i
$317$	516.851	−	214.087i	1.63044	−	0.675352i	0.635162	−	0.772379i	$-0.280933\pi$
$317$	516.851	−	214.087i	1.63044	−	0.675352i	0.995282	+	0.0970272i	$0.0309334\pi$
$318$	−6.21062	+	63.0790i	−0.0195303	+	0.198362i
$319$			261.853i			0.820857i
$320$	−119.939	+	80.1751i	−0.374808	+	0.250547i
$321$	−137.904			−0.429606
$322$	−241.880	−	23.8150i	−0.751180	−	0.0739595i
$323$	−79.8553	−	192.788i	−0.247230	−	0.596866i
$324$	7.02090	−	35.3087i	0.0216695	−	0.108978i
$325$	161.209	−	389.193i	0.496028	−	1.19752i
$326$	−110.175	−	363.153i	−0.337959	−	1.11397i
$327$	116.859	−	116.859i	0.357367	−	0.357367i
$328$	−340.503	+	182.047i	−1.03812	+	0.555020i
$329$	491.912	−	491.912i	1.49517	−	1.49517i
$330$	−29.5157	+	55.2244i	−0.0894414	+	0.167347i
$331$	−105.672	+	255.116i	−0.319252	+	0.770742i	0.680042	+	0.733173i	$0.261961\pi$
$331$	−105.672	+	255.116i	−0.319252	+	0.770742i	−0.999294	+	0.0375691i	$0.988039\pi$
$332$	211.144	−	42.0139i	0.635977	−	0.126548i
$333$	−55.5269	−	134.054i	−0.166747	−	0.402564i
$334$	6.55925	−	5.38340i	0.0196385	−	0.0161180i
$335$	187.902			0.560902
$336$	−166.333	−	166.289i	−0.495039	−	0.494907i
$337$		−	175.777i		−	0.521594i	−0.965394	−	0.260797i	$-0.916015\pi$
$337$		−	175.777i		−	0.521594i	0.965394	−	0.260797i	$-0.0839854\pi$
$338$	430.218	−	353.095i	1.27283	−	1.04466i
$339$	−170.861	+	70.7731i	−0.504016	+	0.208770i
$340$	157.160	+	104.996i	0.462234	+	0.308810i
$341$	56.5656	+	23.4302i	0.165881	+	0.0687103i
$342$	28.1547	−	52.6779i	0.0823236	−	0.154029i
$343$	155.855	+	155.855i	0.454387	+	0.454387i
$344$	−83.1154	+	101.297i	−0.241615	+	0.294468i
$345$	39.5317	+	39.5317i	0.114585	+	0.114585i
$346$	81.0111	+	267.026i	0.234136	+	0.771751i
$347$	368.516	+	152.644i	1.06201	+	0.439897i	0.844163	−	0.536086i	$-0.180098\pi$
$347$	368.516	+	152.644i	1.06201	+	0.439897i	0.217843	+	0.975984i	$0.430098\pi$
$348$	125.704	+	188.102i	0.361218	+	0.540524i
$349$	251.549	−	104.195i	0.720771	−	0.298553i	0.00801769	−	0.999968i	$-0.497448\pi$
$349$	251.549	−	104.195i	0.720771	−	0.298553i	0.712753	+	0.701415i	$0.247448\pi$
$350$	−336.473	−	33.1284i	−0.961350	−	0.0946525i
$351$		−	109.894i		−	0.313087i
$352$	−198.330	+	162.820i	−0.563437	+	0.462557i
$353$	−246.999			−0.699713			−0.349857	−	0.936803i	$-0.613770\pi$
$353$	−246.999			−0.699713			−0.349857	+	0.936803i	$0.613770\pi$
$354$	−3.73489	+	37.9339i	−0.0105505	+	0.107158i
$355$	−84.1341	−	203.118i	−0.236997	−	0.572162i
$356$	109.280	+	163.525i	0.306966	+	0.459341i
$357$	−117.918	+	284.679i	−0.330302	+	0.797420i
$358$	449.139	−	136.261i	1.25458	−	0.380618i
$359$	54.1504	−	54.1504i	0.150837	−	0.150837i	−0.627655	−	0.778492i	$-0.715985\pi$
$359$	54.1504	−	54.1504i	0.150837	−	0.150837i	0.778492	+	0.627655i	$0.215985\pi$
$360$	5.30816	+	53.8396i	0.0147449	+	0.149554i
$361$	−185.190	+	185.190i	−0.512993	+	0.512993i
$362$	−143.516	−	76.7047i	−0.396453	−	0.211892i
$363$	37.5811	−	90.7288i	0.103529	−	0.249941i
$364$	−596.996	−	398.843i	−1.64010	−	1.09572i
$365$	−114.711	−	276.937i	−0.314277	−	0.758732i
$366$	−167.236	−	203.764i	−0.456928	−	0.556731i
$367$	−532.186			−1.45010			−0.725048	−	0.688698i	$-0.758183\pi$
$367$	−532.186			−1.45010			−0.725048	+	0.688698i	$0.758183\pi$
$368$	87.7018	+	211.651i	0.238320	+	0.575139i
$369$			144.793i			0.392392i
$370$	138.337	+	168.553i	0.373885	+	0.455549i
$371$	143.470	−	59.4270i	0.386710	−	0.160181i
$372$	51.8817	−	10.3235i	0.139467	−	0.0277513i
$373$	−340.239	−	140.932i	−0.912169	−	0.377833i	−0.123282	−	0.992372i	$-0.539342\pi$
$373$	−340.239	−	140.932i	−0.912169	−	0.377833i	−0.788887	+	0.614539i	$0.789342\pi$
$374$	296.485	+	158.462i	0.792742	+	0.423695i
$375$	124.012	+	124.012i	0.330698	+	0.330698i
$376$	−627.531	−	190.291i	−1.66897	−	0.506093i
$377$	488.340	+	488.340i	1.29533	+	1.29533i
$378$	−84.4010	+	25.6058i	−0.223283	+	0.0677403i
$379$	−237.695	−	98.4567i	−0.627165	−	0.259780i	0.0463832	−	0.998924i	$-0.485230\pi$
$379$	−237.695	−	98.4567i	−0.627165	−	0.259780i	−0.673548	+	0.739144i	$0.735230\pi$
$380$	−17.5058	+	88.0380i	−0.0460678	+	0.231679i
$381$	−80.7740	+	33.4577i	−0.212005	+	0.0878154i
$382$	−55.3203	+	561.868i	−0.144817	+	1.47086i
$383$		−	154.251i		−	0.402745i	−0.979515	−	0.201372i	$-0.935460\pi$
$383$		−	154.251i		−	0.402745i	0.979515	−	0.201372i	$-0.0645401\pi$
$384$	−64.3074	+	212.171i	−0.167467	+	0.552529i
$385$	153.411			0.398471
$386$	136.904	+	13.4792i	0.354672	+	0.0349203i
$387$	18.8038	+	45.3965i	0.0485888	+	0.117304i
$388$	599.677	+	119.242i	1.54556	+	0.307324i
$389$	53.2864	−	128.645i	0.136983	−	0.330706i	−0.840470	−	0.541857i	$-0.817721\pi$
$389$	53.2864	−	128.645i	0.136983	−	0.330706i	0.977453	+	0.211151i	$0.0677213\pi$
$390$	47.9451	+	158.035i	0.122936	+	0.405217i
$391$	212.236	−	212.236i	0.542802	−	0.542802i
$392$	−53.4634	+	176.309i	−0.136386	+	0.449767i
$393$	257.913	−	257.913i	0.656267	−	0.656267i
$394$	76.8788	−	143.842i	0.195124	−	0.365080i
$395$	−34.9265	+	84.3201i	−0.0884216	+	0.213469i
$396$	18.7791	+	94.3759i	0.0474219	+	0.238323i
$397$	118.215	+	285.397i	0.297772	+	0.718885i	0.999976	+	0.00690947i	$0.00219937\pi$
$397$	118.215	+	285.397i	0.297772	+	0.718885i	−0.702204	+	0.711976i	$0.747801\pi$
$398$	−389.567	+	319.731i	−0.978811	+	0.803344i
$399$	−146.338			−0.366761
$400$	122.000	+	294.422i	0.304999	+	0.736056i
$401$			660.631i			1.64746i	0.566984	+	0.823729i	$0.308110\pi$
$401$			660.631i			1.64746i	−0.566984	+	0.823729i	$0.691890\pi$
$402$	223.206	−	183.193i	0.555238	−	0.455703i
$403$	149.187	−	61.7953i	0.370191	−	0.153338i
$404$	−192.236	+	287.742i	−0.475831	+	0.712234i
$405$	18.7434	+	7.76378i	0.0462800	+	0.0191698i
$406$	261.271	−	488.843i	0.643525	−	1.20405i
$407$	274.245	+	274.245i	0.673821	+	0.673821i
$408$	289.051	−	28.4981i	0.708458	−	0.0698484i
$409$	155.756	+	155.756i	0.380823	+	0.380823i	0.871399	−	0.490576i	$-0.163214\pi$
$409$	155.756	+	155.756i	0.380823	+	0.380823i	−0.490576	+	0.871399i	$0.663214\pi$
$410$	−63.1710	−	208.222i	−0.154076	−	0.507858i
$411$	−216.322	−	89.6033i	−0.526330	−	0.218013i
$412$	−270.112	+	180.509i	−0.655613	+	0.438130i
$413$	86.2784	−	35.7377i	0.208907	−	0.0865319i
$414$	85.4999	+	8.41813i	0.206522	+	0.0203337i
$415$			121.323i			0.292344i
$416$	−66.2230	+	673.522i	−0.159190	+	1.61904i
$417$	−434.229			−1.04132
$418$	−15.6436	+	158.886i	−0.0374249	+	0.380111i
$419$	−136.248	−	328.931i	−0.325174	−	0.785038i	−0.998937	−	0.0460915i	$-0.985323\pi$
$419$	−136.248	−	328.931i	−0.325174	−	0.785038i	0.673764	−	0.738947i	$-0.264677\pi$
$420$	110.203	−	73.6460i	0.262388	−	0.175348i
$421$	−211.904	+	511.582i	−0.503335	+	1.21516i	0.444322	+	0.895867i	$0.353445\pi$
$421$	−211.904	+	511.582i	−0.503335	+	1.21516i	−0.947657	+	0.319291i	$0.896555\pi$
$422$	−664.566	+	201.618i	−1.57480	+	0.477768i
$423$	−173.882	+	173.882i	−0.411067	+	0.411067i
$424$	−113.162	−	92.8506i	−0.266891	−	0.218987i
$425$	295.235	−	295.235i	0.694672	−	0.694672i
$426$	−297.968	−	159.254i	−0.699455	−	0.373837i
$427$	−247.148	+	596.668i	−0.578801	+	1.39735i
$428$	176.917	−	264.814i	0.413358	−	0.618723i
$429$	112.409	+	271.380i	0.262027	+	0.632588i
$430$	−46.8471	−	57.0795i	−0.108947	−	0.132743i
$431$	−611.918			−1.41976			−0.709882	−	0.704321i	$-0.751252\pi$
$431$	−611.918			−1.41976			−0.709882	+	0.704321i	$0.751252\pi$
$432$	58.7956	+	58.7799i	0.136101	+	0.136065i
$433$		−	367.392i		−	0.848480i	−0.905550	−	0.424240i	$-0.860541\pi$
$433$		−	367.392i		−	0.848480i	0.905550	−	0.424240i	$-0.139459\pi$
$434$	−82.2217	−	100.181i	−0.189451	−	0.230831i
$435$	−117.791	+	48.7907i	−0.270785	+	0.112163i
$436$	74.4830	+	374.321i	0.170833	+	0.858535i
$437$	131.693	+	54.5492i	0.301358	+	0.124827i
$438$	−406.259	−	217.133i	−0.927532	−	0.495737i
$439$	2.21281	+	2.21281i	0.00504058	+	0.00504058i	0.709623	−	0.704582i	$-0.248865\pi$
$439$	2.21281	+	2.21281i	0.00504058	+	0.00504058i	−0.704582	+	0.709623i	$0.748865\pi$
$440$	−68.1805	−	127.526i	−0.154956	−	0.289832i
$441$	48.8530	+	48.8530i	0.110778	+	0.110778i
$442$	848.448	−	257.405i	1.91957	−	0.582364i
$443$	−218.661	−	90.5722i	−0.493591	−	0.204452i	0.121982	−	0.992532i	$-0.461075\pi$
$443$	−218.661	−	90.5722i	−0.493591	−	0.204452i	−0.615572	+	0.788080i	$0.711075\pi$
$444$	328.657	+	65.3512i	0.740218	+	0.147187i
$445$	−102.401	+	42.4159i	−0.230115	+	0.0953166i
$446$	69.9092	−	710.042i	0.156747	−	1.59202i
$447$		−	166.109i		−	0.371608i
$448$	532.711	−	106.073i	1.18909	−	0.236771i
$449$	292.977			0.652510			0.326255	−	0.945282i	$-0.394213\pi$
$449$	292.977			0.652510			0.326255	+	0.945282i	$0.394213\pi$
$450$	118.937	+	11.7102i	0.264304	+	0.0260228i
$451$	−148.107	−	357.563i	−0.328397	−	0.792822i
$452$	83.2949	−	418.897i	0.184281	−	0.926764i
$453$	−98.5010	+	237.802i	−0.217441	+	0.524950i
$454$	−97.5508	−	321.544i	−0.214870	−	0.708246i
$455$	286.103	−	286.103i	0.628797	−	0.628797i
$456$	65.0366	+	121.646i	0.142624	+	0.266767i
$457$	3.65622	−	3.65622i	0.00800049	−	0.00800049i	−0.703095	−	0.711096i	$-0.748199\pi$
$457$	3.65622	−	3.65622i	0.00800049	−	0.00800049i	0.711096	+	0.703095i	$0.248199\pi$
$458$	−226.217	+	423.257i	−0.493924	+	0.924142i
$459$	41.6817	−	100.629i	0.0908099	−	0.219234i
$460$	−126.628	+	25.1965i	−0.275277	+	0.0547751i
$461$	174.687	+	421.732i	0.378931	+	0.914821i	0.992167	+	0.124921i	$0.0398676\pi$
$461$	174.687	+	421.732i	0.378931	+	0.914821i	−0.613236	+	0.789900i	$0.710132\pi$
$462$	182.235	−	149.566i	0.394447	−	0.323737i
$463$	−124.458			−0.268808			−0.134404	−	0.990927i	$-0.542912\pi$
$463$	−124.458			−0.268808			−0.134404	+	0.990927i	$0.542912\pi$
$464$	−522.476	+	0.0695108i	−1.12603	+	0.000149808i
$465$			29.8110i			0.0641097i
$466$	652.930	−	535.882i	1.40114	−	1.14996i
$467$	−581.791	+	240.986i	−1.24581	+	0.516029i	−0.905524	−	0.424294i	$-0.860522\pi$
$467$	−581.791	+	240.986i	−1.24581	+	0.516029i	−0.340281	+	0.940324i	$0.610522\pi$
$468$	211.027	+	140.983i	0.450912	+	0.301246i
$469$	−653.600	−	270.730i	−1.39360	−	0.577249i
$470$	174.192	−	325.916i	0.370621	−	0.693438i
$471$	−181.022	−	181.022i	−0.384335	−	0.384335i
$472$	−68.0522	−	55.8376i	−0.144178	−	0.118300i
$473$	−92.8715	−	92.8715i	−0.196346	−	0.196346i
$474$	40.7181	+	134.213i	0.0859031	+	0.283151i
$475$	183.195	+	75.8820i	0.385674	+	0.159752i
$476$	−395.386	−	591.652i	−0.830644	−	1.24297i
$477$	−50.7137	+	21.0063i	−0.106318	+	0.0440384i
$478$	28.0830	+	2.76499i	0.0587510	+	0.00578449i
$479$			421.598i			0.880163i	0.897958	+	0.440082i	$0.145050\pi$
$479$			421.598i			0.880163i	−0.897958	+	0.440082i	$0.854950\pi$
$480$	−110.197	−	58.8780i	−0.229577	−	0.122662i
$481$	1022.90			2.12661
$482$	10.7324	−	109.005i	0.0222664	−	0.226151i
$483$	−80.5499	−	194.465i	−0.166770	−	0.402618i
$484$	126.012	+	188.563i	0.260355	+	0.389593i
$485$	−131.859	+	318.335i	−0.271873	+	0.656360i
$486$	29.8341	−	9.05117i	0.0613871	−	0.0186238i
$487$	177.946	−	177.946i	0.365392	−	0.365392i	−0.500402	−	0.865793i	$-0.666814\pi$
$487$	177.946	−	177.946i	0.365392	−	0.365392i	0.865793	+	0.500402i	$0.166814\pi$
$488$	605.831	−	59.7302i	1.24146	−	0.122398i
$489$	232.394	−	232.394i	0.475244	−	0.475244i
$490$	−91.5680	−	48.9402i	−0.186873	−	0.0998779i
$491$	86.5038	−	208.839i	0.176179	−	0.425333i	−0.810980	−	0.585073i	$-0.801066\pi$
$491$	86.5038	−	208.839i	0.176179	−	0.425333i	0.987159	+	0.159740i	$0.0510657\pi$
$492$	−278.043	−	185.755i	−0.565127	−	0.377551i
$493$	261.945	+	632.391i	0.531329	+	1.28274i
$494$	267.139	+	325.487i	0.540766	+	0.658881i
$495$	−54.2280			−0.109552
$496$	−46.7353	+	112.872i	−0.0942244	+	0.227564i
$497$			827.745i			1.66548i
$498$	118.282	+	144.117i	0.237514	+	0.289392i
$499$	405.750	−	168.067i	0.813126	−	0.336808i	0.0629254	−	0.998018i	$-0.479957\pi$
$499$	405.750	−	168.067i	0.813126	−	0.336808i	0.750200	+	0.661210i	$0.229957\pi$
$500$	−397.233	+	79.0420i	−0.794466	+	0.158084i
$501$	6.78932	+	2.81223i	0.0135515	+	0.00561323i
$502$	−772.173	−	412.702i	−1.53819	−	0.822116i
$503$	52.8541	+	52.8541i	0.105078	+	0.105078i	0.757691	−	0.652613i	$-0.226327\pi$
$503$	52.8541	+	52.8541i	0.105078	+	0.105078i	−0.652613	+	0.757691i	$0.726327\pi$
$504$	59.1082	−	194.924i	0.117278	−	0.386753i
$505$	−137.897	−	137.897i	−0.273063	−	0.273063i
$506$	−219.751	+	66.6688i	−0.434291	+	0.131757i
$507$	445.308	+	184.453i	0.878321	+	0.363812i
$508$	39.3773	−	198.032i	0.0775143	−	0.389826i
$509$	−218.700	+	90.5887i	−0.429667	+	0.177974i	−0.587027	−	0.809567i	$-0.699702\pi$
$509$	−218.700	+	90.5887i	−0.429667	+	0.177974i	0.157360	+	0.987541i	$0.449702\pi$
$510$	−16.0384	+	162.896i	−0.0314478	+	0.319404i
$511$			1128.57i			2.20856i
$512$	−324.928	−	395.684i	−0.634625	−	0.772821i
$513$	51.7275			0.100833
$514$	329.085	+	32.4010i	0.640243	+	0.0630370i
$515$	−70.0629	−	169.147i	−0.136044	−	0.328440i
$516$	−111.298	−	22.1308i	−0.215693	−	0.0428891i
$517$	251.535	−	607.259i	0.486528	−	1.17458i
$518$	−238.341	−	785.612i	−0.460119	−	1.51663i
$519$	−170.879	+	170.879i	−0.329247	+	0.329247i
$520$	−364.980	−	110.676i	−0.701885	−	0.212838i
$521$	481.972	−	481.972i	0.925091	−	0.925091i	−0.0722929	−	0.997383i	$-0.523032\pi$
$521$	481.972	−	481.972i	0.925091	−	0.925091i	0.997383	+	0.0722929i	$0.0230316\pi$
$522$	−92.3543	+	172.797i	−0.176924	+	0.331028i
$523$	−80.2099	+	193.644i	−0.153365	+	0.370256i	−0.981824	−	0.189794i	$-0.939218\pi$
$523$	−80.2099	+	193.644i	−0.153365	+	0.370256i	0.828459	+	0.560050i	$0.189218\pi$
$524$	164.387	+	826.144i	0.313716	+	1.57661i
$525$	−112.051	−	270.514i	−0.213430	−	0.515266i
$526$	325.858	−	267.443i	0.619503	−	0.508447i
$527$	160.048			0.303696
$528$	−205.320	−	85.0144i	−0.388864	−	0.161012i
$529$		−	323.969i		−	0.612419i
$530$	63.7651	−	52.3342i	0.120312	−	0.0987439i
$531$	−30.4978	+	12.6326i	−0.0574346	+	0.0237902i
$532$	187.737	−	281.009i	0.352890	−	0.528213i
$533$	−943.042	−	390.621i	−1.76931	−	0.732872i
$534$	−80.2876	+	150.220i	−0.150351	+	0.281310i
$535$	126.908	+	126.908i	0.237212	+	0.237212i
$536$	65.4294	+	663.637i	0.122070	+	1.23813i
$537$	287.420	+	287.420i	0.535232	+	0.535232i
$538$	−122.506	−	403.798i	−0.227705	−	0.750554i
$539$	−170.613	−	70.6703i	−0.316536	−	0.131114i
$540$	−38.9547	+	26.0324i	−0.0721383	+	0.0482082i
$541$	189.261	−	78.3945i	0.349836	−	0.144907i	−0.200844	−	0.979623i	$-0.564369\pi$
$541$	189.261	−	78.3945i	0.349836	−	0.144907i	0.550680	+	0.834717i	$0.314369\pi$
$542$	−303.970	−	29.9282i	−0.560831	−	0.0552182i
$543$		−	140.927i		−	0.259534i
$544$	−316.101	+	591.620i	−0.581068	+	1.08754i
$545$	−215.083			−0.394649
$546$	60.9245	−	618.788i	0.111583	−	1.13331i
$547$	−140.157	−	338.369i	−0.256229	−	0.618591i	0.742454	−	0.669897i	$-0.233662\pi$
$547$	−140.157	−	338.369i	−0.256229	−	0.618591i	−0.998683	+	0.0513058i	$0.983662\pi$
$548$	449.584	−	300.446i	0.820409	−	0.548259i
$549$	87.3621	−	210.911i	0.159130	−	0.384173i
$550$	−305.690	+	92.7412i	−0.555800	+	0.168620i
$551$	−229.864	+	229.864i	−0.417176	+	0.417176i
$552$	−125.854	+	153.384i	−0.227996	+	0.277870i
$553$	242.977	−	242.977i	0.439380	−	0.439380i
$554$	545.377	+	291.487i	0.984435	+	0.526150i
$555$	−72.2659	+	174.465i	−0.130209	+	0.314352i
$556$	557.075	−	833.842i	1.00193	−	1.49972i
$557$	79.3256	+	191.509i	0.142416	+	0.343822i	0.978952	−	0.204089i	$-0.0654232\pi$
$557$	79.3256	+	191.509i	0.142416	+	0.343822i	−0.836537	+	0.547911i	$0.815423\pi$
$558$	29.0638	+	35.4119i	0.0520857	+	0.0634623i
$559$	−346.399			−0.619676
$560$	0.0407242	+	306.102i	7.27217e−5	+	0.546611i
$561$			291.136i			0.518960i
$562$	149.958	+	182.713i	0.266830	+	0.325111i
$563$	−97.8337	+	40.5241i	−0.173772	+	0.0719788i	−0.467873	−	0.883795i	$-0.654980\pi$
$563$	−97.8337	+	40.5241i	−0.173772	+	0.0719788i	0.294101	+	0.955774i	$0.404980\pi$
$564$	−110.828	−	556.975i	−0.196503	−	0.987545i
$565$	222.369	+	92.1082i	0.393573	+	0.163023i
$566$	121.700	+	65.0446i	0.215017	+	0.114920i
$567$	−54.0111	−	54.0111i	−0.0952576	−	0.0952576i
$568$	688.079	−	367.874i	1.21141	−	0.647665i
$569$	−586.037	−	586.037i	−1.02994	−	1.02994i	−0.999538	−	0.0304047i	$-0.990320\pi$
$569$	−586.037	−	586.037i	−1.02994	−	1.02994i	−0.0304047	−	0.999538i	$-0.509680\pi$
$570$	−74.3878	+	22.5680i	−0.130505	+	0.0395930i
$571$	−267.656	−	110.867i	−0.468749	−	0.194162i	0.135790	−	0.990738i	$-0.456643\pi$
$571$	−267.656	−	110.867i	−0.468749	−	0.194162i	−0.604539	+	0.796576i	$0.706643\pi$
$572$	−665.338	−	132.298i	−1.16318	−	0.231290i
$573$	−451.726	+	187.111i	−0.788352	+	0.326546i
$574$	−80.2723	+	815.296i	−0.139847	+	1.42038i
$575$			285.212i			0.496022i
$576$	−188.303	+	37.4949i	−0.326915	+	0.0650953i
$577$	202.396			0.350774			0.175387	−	0.984500i	$-0.443882\pi$
$577$	202.396			0.350774			0.175387	+	0.984500i	$0.443882\pi$
$578$	299.329	+	29.4713i	0.517870	+	0.0509884i
$579$	45.5911	+	110.067i	0.0787411	+	0.190098i
$580$	57.4232	−	288.786i	0.0990056	−	0.497908i
$581$	174.802	−	422.010i	0.300864	−	0.726350i
$582$	153.723	+	506.698i	0.264130	+	0.870614i
$583$	103.749	−	103.749i	0.177958	−	0.177958i
$584$	938.149	−	501.571i	1.60642	−	0.858855i
$585$	−101.132	+	101.132i	−0.172875	+	0.172875i
$586$	231.496	−	433.132i	0.395044	−	0.739134i
$587$	−57.4757	+	138.759i	−0.0979143	+	0.236386i	−0.965245	−	0.261346i	$-0.915834\pi$
$587$	−57.4757	+	138.759i	−0.0979143	+	0.236386i	0.867331	+	0.497732i	$0.165834\pi$
$588$	−156.485	+	31.1377i	−0.266132	+	0.0529553i
$589$	29.0874	+	70.2231i	0.0493843	+	0.119224i
$590$	38.3465	−	31.4723i	0.0649941	−	0.0533429i
$591$	141.247			0.238996
$592$	−547.129	+	547.275i	−0.924204	+	0.924450i
$593$		−	232.488i		−	0.392054i	−0.980599	−	0.196027i	$-0.937196\pi$
$593$		−	232.488i		−	0.392054i	0.980599	−	0.196027i	$-0.0628040\pi$
$594$	−64.4165	+	52.8688i	−0.108445	+	0.0890048i
$595$	370.498	−	153.465i	0.622685	−	0.257925i
$596$	318.976	+	213.102i	0.535195	+	0.357554i
$597$	−403.231	−	167.024i	−0.675429	−	0.279772i
$598$	−285.489	+	534.155i	−0.477406	+	0.893236i
$599$	624.784	+	624.784i	1.04305	+	1.04305i	0.999031	+	0.0440142i	$0.0140147\pi$
$599$	624.784	+	624.784i	1.04305	+	1.04305i	0.0440142	+	0.999031i	$0.485985\pi$
$600$	−175.072	+	213.369i	−0.291786	+	0.355615i
$601$	296.941	+	296.941i	0.494079	+	0.494079i	0.909589	−	0.415510i	$-0.136397\pi$
$601$	296.941	+	296.941i	0.494079	+	0.494079i	−0.415510	+	0.909589i	$0.636397\pi$
$602$	80.7129	+	266.043i	0.134075	+	0.441932i
$603$	231.035	+	95.6979i	0.383143	+	0.158703i
$604$	−330.280	−	494.228i	−0.546821	−	0.818258i
$605$	−118.080	+	48.9102i	−0.195173	+	0.0808433i
$606$	−298.246	−	29.3646i	−0.492154	−	0.0484565i
$607$		−	434.943i		−	0.716546i	−0.933617	−	0.358273i	$-0.883366\pi$
$607$		−	434.943i		−	0.716546i	0.933617	−	0.358273i	$-0.116634\pi$
$608$	−317.030	−	31.1715i	−0.521431	−	0.0512689i
$609$	480.023			0.788215
$610$	−33.6154	+	341.420i	−0.0551072	+	0.559704i
$611$	−663.403	−	1601.60i	−1.08577	−	2.62127i
$612$	139.762	+	209.138i	0.228369	+	0.341728i
$613$	−8.70239	+	21.0094i	−0.0141964	+	0.0342731i	−0.930819	−	0.365481i	$-0.880905\pi$
$613$	−8.70239	+	21.0094i	−0.0141964	+	0.0342731i	0.916622	+	0.399754i	$0.130905\pi$
$614$	279.378	−	84.7586i	0.455013	−	0.138043i
$615$	133.248	−	133.248i	0.216664	−	0.216664i
$616$	53.4194	+	541.822i	0.0867198	+	0.879581i
$617$	−532.067	+	532.067i	−0.862345	+	0.862345i	−0.991610	−	0.129265i	$-0.958738\pi$
$617$	−532.067	+	532.067i	−0.862345	+	0.862345i	0.129265	+	0.991610i	$0.458738\pi$
$618$	−248.134	−	132.620i	−0.401511	−	0.214595i
$619$	249.114	−	601.415i	0.402446	−	0.971591i	−0.584624	−	0.811304i	$-0.698758\pi$
$619$	249.114	−	601.415i	0.402446	−	0.971591i	0.987070	−	0.160287i	$-0.0512419\pi$
$620$	−57.2455	−	38.2447i	−0.0923315	−	0.0616851i
$621$	28.4728	+	68.7395i	0.0458500	+	0.110692i
$622$	283.740	+	345.715i	0.456174	+	0.555811i
$623$	417.305			0.669831
$624$	−541.455	+	224.363i	−0.867717	+	0.359555i
$625$			269.717i			0.431547i
$626$	654.262	+	797.167i	1.04515	+	1.27343i
$627$	−127.740	+	52.9117i	−0.203732	+	0.0843887i
$628$	579.846	−	115.379i	0.923322	−	0.183724i
$629$	936.660	+	387.977i	1.48913	+	0.616816i
$630$	101.236	+	54.1074i	0.160692	+	0.0858848i
$631$	66.5767	+	66.5767i	0.105510	+	0.105510i	0.757891	−	0.652381i	$-0.226230\pi$
$631$	66.5767	+	66.5767i	0.105510	+	0.105510i	−0.652381	+	0.757891i	$0.726230\pi$
$632$	−309.965	−	93.9931i	−0.490451	−	0.148723i
$633$	−425.279	−	425.279i	−0.671846	−	0.671846i
$634$	−1070.68	+	324.826i	−1.68877	+	0.512345i
$635$	105.124	+	43.5438i	0.165549	+	0.0685728i
$636$	24.7229	−	124.334i	0.0388725	−	0.195493i
$637$	−449.978	+	186.387i	−0.706402	+	0.292601i
$638$	51.3149	−	521.186i	0.0804308	−	0.816907i
$639$		−	292.592i		−	0.457891i
$640$	254.435	−	136.074i	0.397554	−	0.212616i
$641$	−590.378			−0.921027			−0.460513	−	0.887653i	$-0.652335\pi$
$641$	−590.378			−0.921027			−0.460513	+	0.887653i	$0.652335\pi$
$642$	274.480	+	27.0247i	0.427539	+	0.0420945i
$643$	169.422	+	409.021i	0.263487	+	0.636114i	0.999149	−	0.0412346i	$-0.0131291\pi$
$643$	169.422	+	409.021i	0.263487	+	0.636114i	−0.735663	+	0.677348i	$0.763129\pi$
$644$	476.765	+	94.8015i	0.740318	+	0.147207i
$645$	24.4724	−	59.0817i	0.0379417	−	0.0915995i
$646$	121.162	+	399.369i	0.187557	+	0.618218i
$647$	366.031	−	366.031i	0.565735	−	0.565735i	−0.365196	−	0.930931i	$-0.618998\pi$
$647$	366.031	−	366.031i	0.565735	−	0.565735i	0.930931	+	0.365196i	$0.118998\pi$
$648$	−20.8936	+	68.9018i	−0.0322432	+	0.106330i
$649$	62.3919	−	62.3919i	0.0961354	−	0.0961354i
$650$	−397.136	+	743.049i	−0.610979	+	1.14315i
$651$	42.9517	−	103.695i	0.0659781	−	0.159285i
$652$	148.122	+	744.403i	0.227182	+	1.14172i
$653$	−244.879	−	591.190i	−0.375006	−	0.905344i	−0.992886	−	0.119071i	$-0.962008\pi$
$653$	−244.879	−	591.190i	−0.375006	−	0.905344i	0.617880	−	0.786272i	$-0.287992\pi$
$654$	−255.494	+	209.693i	−0.390663	+	0.320631i
$655$	−474.699			−0.724731
$656$	713.405	−	295.613i	1.08751	−	0.450630i
$657$		−	398.930i		−	0.607199i
$658$	−1075.49	+	882.691i	−1.63448	+	1.34148i
$659$	13.3524	−	5.53077i	0.0202617	−	0.00839266i	−0.372530	−	0.928020i	$-0.621509\pi$
$659$	13.3524	−	5.53077i	0.0202617	−	0.00839266i	0.392791	+	0.919628i	$0.371509\pi$
$660$	69.5695	−	104.133i	0.105408	−	0.157777i
$661$	−648.694	−	268.698i	−0.981383	−	0.406502i	−0.166446	−	0.986051i	$-0.553229\pi$
$661$	−648.694	−	268.698i	−0.981383	−	0.406502i	−0.814938	+	0.579548i	$0.803229\pi$
$662$	260.322	−	487.068i	0.393236	−	0.735752i
$663$	542.951	+	542.951i	0.818930	+	0.818930i
$664$	−428.490	+	42.2458i	−0.645317	+	0.0636232i
$665$	134.670	+	134.670i	0.202511	+	0.202511i
$666$	84.2491	+	277.699i	0.126500	+	0.416965i
$667$	−431.987	−	178.935i	−0.647657	−	0.268268i
$668$	−14.1103	+	9.42958i	−0.0211233	+	0.0141161i
$669$	570.854	−	236.455i	0.853294	−	0.353446i
$670$	−373.996	−	36.8229i	−0.558203	−	0.0549595i
$671$			610.203i			0.909393i
$672$	298.478	+	363.573i	0.444164	+	0.541032i
$673$	−854.964			−1.27038			−0.635189	−	0.772357i	$-0.719078\pi$
$673$	−854.964			−1.27038			−0.635189	+	0.772357i	$0.719078\pi$
$674$	−34.4467	+	349.863i	−0.0511079	+	0.519084i
$675$	39.6078	+	95.6217i	0.0586782	+	0.141662i
$676$	−925.491	+	618.482i	−1.36907	+	0.914914i
$677$	−71.1884	+	171.864i	−0.105153	+	0.253861i	−0.967695	−	0.252124i	$-0.918871\pi$
$677$	−71.1884	+	171.864i	−0.105153	+	0.253861i	0.862542	+	0.505985i	$0.168871\pi$
$678$	353.948	−	107.382i	0.522047	−	0.158380i
$679$	917.314	−	917.314i	1.35098	−	1.35098i
$680$	−292.231	−	239.779i	−0.429751	−	0.352616i
$681$	205.767	−	205.767i	0.302154	−	0.302154i
$682$	−107.995	−	57.7200i	−0.158351	−	0.0846334i
$683$	−179.259	+	432.769i	−0.262458	+	0.633629i	−0.999089	−	0.0426650i	$-0.986415\pi$
$683$	−179.259	+	432.769i	−0.262458	+	0.633629i	0.736632	+	0.676294i	$0.236415\pi$
$684$	−66.3616	+	99.3314i	−0.0970199	+	0.145221i
$685$	116.615	+	281.534i	0.170241	+	0.410998i
$686$	−279.667	−	340.752i	−0.407678	−	0.496723i
$687$	−415.621			−0.604979
$688$	185.282	−	185.331i	0.269305	−	0.269377i
$689$		−	386.972i		−	0.561643i
$690$	−70.9360	−	86.4299i	−0.102806	−	0.125261i
$691$	539.782	−	223.585i	0.781160	−	0.323567i	0.0437767	−	0.999041i	$-0.486061\pi$
$691$	539.782	−	223.585i	0.781160	−	0.323567i	0.737384	+	0.675474i	$0.236061\pi$
$692$	−108.914	−	547.358i	−0.157390	−	0.790979i
$693$	188.627	+	78.1318i	0.272189	+	0.112744i
$694$	−703.572	−	376.037i	−1.01379	−	0.541840i
$695$	399.608	+	399.608i	0.574975	+	0.574975i
$696$	−213.336	−	399.028i	−0.306518	−	0.573316i
$697$	−715.376	−	715.376i	−1.02636	−	1.02636i
$698$	−521.096	+	158.092i	−0.746556	+	0.226492i
$699$	675.832	+	279.939i	0.966856	+	0.400485i
$700$	663.215	+	131.876i	0.947450	+	0.188394i
$701$	316.245	−	130.993i	0.451134	−	0.186866i	−0.145535	−	0.989353i	$-0.546490\pi$
$701$	316.245	−	130.993i	0.451134	−	0.186866i	0.596669	+	0.802487i	$0.296490\pi$
$702$	−21.5356	+	218.730i	−0.0306776	+	0.311581i
$703$			481.484i			0.684900i
$704$	426.658	−	285.207i	0.606049	−	0.405124i
$705$	320.036			0.453952
$706$	491.620	+	48.4039i	0.696346	+	0.0685607i
$707$	280.979	+	678.342i	0.397424	+	0.959466i
$708$	14.8677	−	74.7707i	0.0209995	−	0.105608i
$709$	−328.428	+	792.895i	−0.463227	+	1.11833i	0.503837	+	0.863798i	$0.331921\pi$
$709$	−328.428	+	792.895i	−0.463227	+	1.11833i	−0.967065	+	0.254531i	$0.918079\pi$
$710$	127.654	+	420.768i	0.179794	+	0.592631i
$711$	−85.8877	+	85.8877i	−0.120799	+	0.120799i
$712$	−185.462	−	346.892i	−0.260481	−	0.487209i
$713$	−77.3071	+	77.3071i	−0.108425	+	0.108425i
$714$	290.489	−	543.510i	0.406847	−	0.761219i
$715$	146.296	−	353.190i	0.204610	−	0.493972i
$716$	−920.659	+	183.194i	−1.28584	+	0.255858i
$717$	9.35208	+	22.5779i	0.0130433	+	0.0314894i
$718$	−118.391	+	97.1679i	−0.164890	+	0.135331i
$719$	277.339			0.385729			0.192865	−	0.981225i	$-0.438222\pi$
$719$	277.339			0.385729			0.192865	+	0.981225i	$0.438222\pi$
$720$	−0.0143952	−	108.201i	−1.99934e−5	−	0.150279i
$721$			689.307i			0.956043i
$722$	404.890	−	332.307i	0.560789	−	0.460259i
$723$	87.6369	−	36.3004i	0.121213	−	0.0502080i
$724$	270.619	+	180.796i	0.373783	+	0.249718i
$725$	−600.926	−	248.912i	−0.828863	−	0.343326i
$726$	−92.5804	+	173.220i	−0.127521	+	0.238595i
$727$	−689.977	−	689.977i	−0.949075	−	0.949075i	0.0496900	−	0.998765i	$-0.484177\pi$
$727$	−689.977	−	689.977i	−0.949075	−	0.949075i	−0.998765	+	0.0496900i	$0.984177\pi$
$728$	1110.09	+	910.839i	1.52484	+	1.25115i
$729$	19.0919	+	19.0919i	0.0261891	+	0.0261891i
$730$	174.047	+	573.689i	0.238421	+	0.785875i
$731$	−317.194	−	131.386i	−0.433918	−	0.179735i
$732$	292.931	+	438.339i	0.400179	+	0.598824i
$733$	141.414	−	58.5756i	0.192925	−	0.0799122i	−0.284129	−	0.958786i	$-0.591704\pi$
$733$	141.414	−	58.5756i	0.192925	−	0.0799122i	0.477054	+	0.878874i	$0.341704\pi$
$734$	1059.25	+	104.291i	1.44312	+	0.142086i
$735$		−	89.9160i		−	0.122335i
$736$	−133.083	−	438.452i	−0.180819	−	0.595723i
$737$	−668.425			−0.906954
$738$	28.3747	−	288.192i	0.0384481	−	0.390504i
$739$	393.705	+	950.489i	0.532754	+	1.28618i	0.929692	+	0.368337i	$0.120073\pi$
$739$	393.705	+	950.489i	0.532754	+	1.28618i	−0.396938	+	0.917845i	$0.629927\pi$
$740$	−242.312	−	362.594i	−0.327449	−	0.489992i
$741$	−139.550	+	336.904i	−0.188327	+	0.454661i
$742$	−297.204	+	90.1667i	−0.400545	+	0.121518i
$743$	−459.991	+	459.991i	−0.619099	+	0.619099i	−0.945300	−	0.326201i	$-0.894231\pi$
$743$	−459.991	+	459.991i	−0.619099	+	0.619099i	0.326201	+	0.945300i	$0.394231\pi$
$744$	−105.287	+	10.3805i	−0.141515	+	0.0139523i
$745$	−152.865	+	152.865i	−0.205188	+	0.205188i
$746$	649.585	+	347.183i	0.870758	+	0.465393i
$747$	−61.7892	+	149.172i	−0.0827164	+	0.199695i
$748$	−559.064	−	373.501i	−0.747412	−	0.499333i
$749$	−258.589	−	624.289i	−0.345245	−	0.833496i
$750$	−222.528	−	271.132i	−0.296704	−	0.361510i
$751$	633.524			0.843574			0.421787	−	0.906695i	$-0.361403\pi$
$751$	633.524			0.843574			0.421787	+	0.906695i	$0.361403\pi$
$752$	1211.73	+	501.727i	1.61135	+	0.667190i
$753$		−	758.242i		−	1.00696i
$754$	−876.280	−	1067.68i	−1.16218	−	1.41602i
$755$	309.490	−	128.195i	0.409920	−	0.169795i
$756$	173.008	−	34.4253i	0.228846	−	0.0455362i
$757$	−471.649	−	195.363i	−0.623050	−	0.258076i	0.0487469	−	0.998811i	$-0.484477\pi$
$757$	−471.649	−	195.363i	−0.623050	−	0.258076i	−0.671797	+	0.740735i	$0.734477\pi$
$758$	453.809	+	242.547i	0.598692	+	0.319982i
$759$	−140.626	−	140.626i	−0.185278	−	0.185278i
$760$	52.0957	−	171.798i	0.0685470	−	0.226050i
$761$	−285.040	−	285.040i	−0.374560	−	0.374560i	0.494575	−	0.869135i	$-0.335324\pi$
$761$	−285.040	−	285.040i	−0.374560	−	0.374560i	−0.869135	+	0.494575i	$0.835324\pi$
$762$	167.327	−	50.7642i	0.219589	−	0.0666197i
$763$	748.147	+	309.893i	0.980533	+	0.406150i
$764$	220.216	−	1107.49i	0.288241	−	1.44959i
$765$	−130.964	+	54.2470i	−0.171195	+	0.0709111i
$766$	−30.2283	+	307.018i	−0.0394625	+	0.400807i
$767$		−	232.714i		−	0.303408i
$768$	169.575	−	409.698i	0.220800	−	0.533461i
$769$	102.033			0.132683			0.0663417	−	0.997797i	$-0.478867\pi$
$769$	102.033			0.132683			0.0663417	+	0.997797i	$0.478867\pi$
$770$	−305.347	−	30.0638i	−0.396554	−	0.0390438i
$771$	109.591	+	264.575i	0.142141	+	0.343158i
$772$	−269.848	−	53.6574i	−0.349544	−	0.0695045i
$773$	406.459	−	981.280i	0.525821	−	1.26944i	−0.408418	−	0.912795i	$-0.633919\pi$
$773$	406.459	−	981.280i	0.525821	−	1.26944i	0.934239	−	0.356648i	$-0.116081\pi$
$774$	−28.5305	−	94.0411i	−0.0368611	−	0.121500i
$775$	−107.540	+	107.540i	−0.138761	+	0.138761i
$776$	−1170.21	−	354.853i	−1.50801	−	0.457285i
$777$	502.740	−	502.740i	0.647027	−	0.647027i
$778$	−131.270	+	245.609i	−0.168728	+	0.315693i
$779$	183.867	−	443.895i	0.236030	−	0.569826i
$780$	−64.4589	−	323.944i	−0.0826397	−	0.415313i
$781$	299.290	+	722.551i	0.383214	+	0.925161i
$782$	−464.020	+	380.837i	−0.593376	+	0.487004i
$783$	−169.679			−0.216704
$784$	140.963	−	340.443i	0.179800	−	0.434239i
$785$			333.177i			0.424430i
$786$	−563.886	+	462.801i	−0.717413	+	0.588805i
$787$	−230.489	+	95.4716i	−0.292870	+	0.121311i	−0.524281	−	0.851545i	$-0.675666\pi$
$787$	−230.489	+	95.4716i	−0.292870	+	0.121311i	0.231411	+	0.972856i	$0.425666\pi$
$788$	−181.206	+	271.233i	−0.229957	+	0.344205i
$789$	337.288	+	139.709i	0.427489	+	0.177072i
$790$	86.0410	−	160.984i	0.108913	−	0.203777i
$791$	−640.779	−	640.779i	−0.810087	−	0.810087i
$792$	−18.8827	−	191.524i	−0.0238418	−	0.241823i
$793$	1137.99	+	1137.99i	1.43504	+	1.43504i
$794$	−179.364	−	591.215i	−0.225900	−	0.744603i
$795$	66.0018	+	27.3388i	0.0830211	+	0.0343885i
$796$	838.041	−	560.042i	1.05282	−	0.703570i
$797$	307.352	−	127.309i	0.385636	−	0.159736i	−0.181438	−	0.983402i	$-0.558075\pi$
$797$	307.352	−	127.309i	0.385636	−	0.159736i	0.567074	+	0.823667i	$0.308075\pi$
$798$	291.267	+	28.6775i	0.364996	+	0.0359367i
$799$		−	1718.19i		−	2.15043i
$800$	−185.128	−	609.919i	−0.231410	−	0.762399i
$801$	−147.509			−0.184156
$802$	129.463	−	1314.90i	0.161425	−	1.63953i
$803$	408.062	+	985.149i	0.508172	+	1.22684i
$804$	−480.163	+	320.881i	−0.597218	+	0.399106i
$805$	−104.832	+	253.088i	−0.130226	+	0.314394i
$806$	−309.048	+	93.7600i	−0.383434	+	0.116328i
$807$	258.404	−	258.404i	0.320203	−	0.320203i
$808$	439.010	−	535.044i	0.543329	−	0.662183i
$809$	−791.792	+	791.792i	−0.978729	+	0.978729i	−0.999778	−	0.0210495i	$-0.993299\pi$
$809$	−791.792	+	791.792i	−0.978729	+	0.978729i	0.0210495	+	0.999778i	$0.493299\pi$
$810$	−35.7850	−	19.1259i	−0.0441790	−	0.0236123i
$811$	162.698	−	392.787i	0.200614	−	0.484324i	−0.791271	−	0.611466i	$-0.790580\pi$
$811$	162.698	−	392.787i	0.200614	−	0.484324i	0.991885	+	0.127141i	$0.0405802\pi$
$812$	−615.825	+	921.780i	−0.758405	+	1.13520i
$813$	−101.227	−	244.384i	−0.124510	−	0.300595i
$814$	−492.108	−	599.595i	−0.604555	−	0.736603i
$815$	−427.731			−0.524823
$816$	−580.905	+	0.0772842i	−0.711893	+	9.47111e-5i
$817$		−	163.052i		−	0.199574i
$818$	−279.491	−	340.537i	−0.341676	−	0.416305i
$819$	497.488	−	206.066i	0.607433	−	0.251607i
$820$	84.9291	+	426.819i	0.103572	+	0.520511i
$821$	419.205	+	173.640i	0.510602	+	0.211498i	0.623083	−	0.782155i	$-0.285880\pi$
$821$	419.205	+	173.640i	0.510602	+	0.211498i	−0.112481	+	0.993654i	$0.535880\pi$
$822$	413.002	+	220.736i	0.502435	+	0.268536i
$823$	−797.183	−	797.183i	−0.968631	−	0.968631i	0.0308918	−	0.999523i	$-0.490165\pi$
$823$	−797.183	−	797.183i	−0.968631	−	0.968631i	−0.999523	+	0.0308918i	$0.990165\pi$
$824$	572.999	−	306.348i	0.695388	−	0.371782i
$825$	−195.621	−	195.621i	−0.237117	−	0.237117i
$826$	−178.730	+	54.2236i	−0.216380	+	0.0656460i
$827$	−1283.37	−	531.590i	−1.55184	−	0.642794i	−0.568193	−	0.822895i	$-0.692357\pi$
$827$	−1283.37	−	531.590i	−1.55184	−	0.642794i	−0.983648	+	0.180102i	$0.942357\pi$
$828$	−168.527	−	33.5105i	−0.203535	−	0.0404716i
$829$	425.602	−	176.290i	0.513392	−	0.212654i	−0.110920	−	0.993829i	$-0.535380\pi$
$829$	425.602	−	176.290i	0.513392	−	0.212654i	0.624312	+	0.781175i	$0.285380\pi$
$830$	23.7754	−	241.478i	0.0286451	−	0.290937i
$831$			535.538i			0.644450i
$832$	263.797	−	1327.58i	0.317064	−	1.59565i
$833$	−482.736			−0.579515
$834$	864.279	+	85.0950i	1.03631	+	0.102032i
$835$	−3.66000	−	8.83602i	−0.00438323	−	0.0105821i
$836$	62.2733	−	313.178i	0.0744896	−	0.374615i
$837$	−15.1826	+	36.6541i	−0.0181393	+	0.0437922i
$838$	206.724	+	681.397i	0.246688	+	0.813123i
$839$	−458.488	+	458.488i	−0.546470	+	0.546470i	−0.925418	−	0.378948i	$-0.876286\pi$
$839$	−458.488	+	458.488i	−0.546470	+	0.546470i	0.378948	+	0.925418i	$0.376286\pi$
$840$	−233.778	+	124.987i	−0.278307	+	0.148794i
$841$	159.334	−	159.334i	0.189458	−	0.189458i
$842$	522.022	−	976.714i	0.619979	−	1.15999i
$843$	−78.3367	+	189.121i	−0.0929261	+	0.224343i
$844$	1362.25	−	271.062i	1.61404	−	0.321164i
$845$	−240.058	−	579.550i	−0.284092	−	0.685858i
$846$	380.165	−	312.014i	0.449367	−	0.368811i
$847$	481.199			0.568121
$848$	207.039	+	206.984i	0.244150	+	0.244085i
$849$			119.504i			0.140759i
$850$	−645.486	+	529.773i	−0.759396	+	0.623262i
$851$	−639.834	+	265.028i	−0.751861	+	0.311431i
$852$	561.860	+	375.368i	0.659460	+	0.440573i
$853$	−4.83739	−	2.00371i	−0.00567104	−	0.00234902i	0.379846	−	0.925050i	$-0.375977\pi$
$853$	−4.83739	−	2.00371i	−0.00567104	−	0.00234902i	−0.385517	+	0.922701i	$0.625977\pi$
$854$	608.846	−	1139.16i	0.712934	−	1.33391i
$855$	−47.6033	−	47.6033i	−0.0556763	−	0.0556763i
$856$	−404.027	+	492.409i	−0.471994	+	0.575244i
$857$	839.262	+	839.262i	0.979302	+	0.979302i	0.999790	−	0.0204883i	$-0.00652207\pi$
$857$	839.262	+	839.262i	0.979302	+	0.979302i	−0.0204883	+	0.999790i	$0.506522\pi$
$858$	−170.555	−	562.178i	−0.198782	−	0.655219i
$859$	−217.173	−	89.9559i	−0.252820	−	0.104722i	0.252674	−	0.967551i	$-0.418690\pi$
$859$	−217.173	−	89.9559i	−0.252820	−	0.104722i	−0.505495	+	0.862830i	$0.668690\pi$
$860$	82.0576	+	122.790i	0.0954158	+	0.142779i
$861$	−655.475	+	271.507i	−0.761295	+	0.315339i
$862$	1217.95	+	119.916i	1.41293	+	0.139114i
$863$			176.374i			0.204373i	0.994765	+	0.102186i	$0.0325838\pi$
$863$			176.374i			0.204373i	−0.994765	+	0.102186i	$0.967416\pi$
$864$	−105.506	−	128.516i	−0.122114	−	0.148746i
$865$	314.510			0.363595
$866$	−71.9971	+	731.248i	−0.0831375	+	0.844397i
$867$	99.6814	+	240.652i	0.114973	+	0.277569i
$868$	144.020	+	215.510i	0.165922	+	0.248283i
$869$	124.244	−	299.952i	0.142974	−	0.345169i
$870$	244.010	−	74.0286i	0.280472	−	0.0850903i
$871$	−1246.57	+	1246.57i	−1.43119	+	1.43119i
$872$	−74.8942	−	759.636i	−0.0858878	−	0.871142i
$873$	−324.253	+	324.253i	−0.371424	+	0.371424i
$874$	−251.430	−	134.381i	−0.287677	−	0.153754i
$875$	−328.861	+	793.940i	−0.375841	+	0.907360i
$876$	766.057	+	511.789i	0.874495	+	0.584235i
$877$	339.843	+	820.453i	0.387506	+	0.935522i	0.990467	+	0.137752i	$0.0439876\pi$
$877$	339.843	+	820.453i	0.387506	+	0.935522i	−0.602961	+	0.797771i	$0.706012\pi$
$878$	−3.97069	−	4.83797i	−0.00452243	−	0.00551022i
$879$	425.318			0.483866
$880$	110.714	+	267.186i	0.125811	+	0.303621i
$881$			1114.22i			1.26472i	0.774673	+	0.632362i	$0.217915\pi$
$881$			1114.22i			1.26472i	−0.774673	+	0.632362i	$0.782085\pi$
$882$	−87.6623	−	106.810i	−0.0993903	−	0.121099i
$883$	−1492.25	+	618.111i	−1.68998	+	0.700013i	−0.999723	−	0.0235510i	$-0.992503\pi$
$883$	−1492.25	+	618.111i	−1.68998	+	0.700013i	−0.690258	+	0.723564i	$0.742503\pi$
$884$	−1739.17	+	346.064i	−1.96739	+	0.391475i
$885$	39.6916	+	16.4408i	0.0448492	+	0.0185772i
$886$	417.468	+	223.123i	0.471183	+	0.251832i
$887$	1167.45	+	1167.45i	1.31618	+	1.31618i	0.916778	+	0.399397i	$0.130780\pi$
$887$	1167.45	+	1167.45i	1.31618	+	1.31618i	0.399397	+	0.916778i	$0.369220\pi$
$888$	−641.344	−	194.480i	−0.722234	−	0.219009i
$889$	−302.925	−	302.925i	−0.340748	−	0.340748i
$890$	212.129	−	64.3563i	0.238347	−	0.0723104i
$891$	−66.6760	−	27.6181i	−0.0748328	−	0.0309967i
$892$	−278.291	+	1399.55i	−0.311986	+	1.56900i
$893$	753.880	−	312.267i	0.844211	−	0.349683i
$894$	−32.5520	+	330.619i	−0.0364117	+	0.369820i
$895$		−	529.007i		−	0.591069i
$896$	−1081.08	+	106.732i	−1.20657	+	0.119120i
$897$	−524.518			−0.584747
$898$	−583.135	−	57.4142i	−0.649370	−	0.0639356i
$899$	−95.4138	−	230.349i	−0.106133	−	0.256228i
$900$	−234.434	−	46.6156i	−0.260482	−	0.0517951i
$901$	146.775	−	354.347i	0.162903	−	0.393282i
$902$	224.718	+	740.708i	0.249133	+	0.821184i
$903$	−170.250	+	170.250i	−0.188538	+	0.188538i
$904$	−247.879	+	817.440i	−0.274202	+	0.904248i
$905$	−129.691	+	129.691i	−0.143305	+	0.143305i
$906$	242.656	−	454.013i	0.267832	−	0.501118i
$907$	−433.512	+	1046.59i	−0.477962	+	1.15390i	0.482601	+	0.875840i	$0.339692\pi$
$907$	−433.512	+	1046.59i	−0.477962	+	1.15390i	−0.960563	+	0.278062i	$0.910308\pi$
$908$	131.151	+	659.109i	0.144439	+	0.725891i
$909$	−99.3206	−	239.781i	−0.109264	−	0.263786i
$910$	−625.519	+	513.385i	−0.687383	+	0.564159i
$911$	309.152			0.339354			0.169677	−	0.985500i	$-0.445727\pi$
$911$	309.152			0.339354			0.169677	+	0.985500i	$0.445727\pi$
$912$	−105.609	−	254.866i	−0.115799	−	0.279458i
$913$		−	431.582i		−	0.472707i
$914$	−7.99376	+	6.56076i	−0.00874591	+	0.00717807i
$915$	−274.492	+	113.698i	−0.299991	+	0.124260i
$916$	533.203	−	798.109i	0.582099	−	0.871298i
$917$	1651.19	+	683.947i	1.80065	+	0.745853i
$918$	−102.682	+	192.120i	−0.111854	+	0.209282i
$919$	−132.070	−	132.070i	−0.143710	−	0.143710i	0.631591	−	0.775302i	$-0.282402\pi$
$919$	−132.070	−	132.070i	−0.143710	−	0.143710i	−0.775302	+	0.631591i	$0.782402\pi$
$920$	256.974	−	25.3356i	0.279320	−	0.0275387i
$921$	178.784	+	178.784i	0.194119	+	0.194119i
$922$	−265.047	−	873.639i	−0.287470	−	0.947548i
$923$	1905.67	+	789.354i	2.06465	+	0.855205i
$924$	−392.026	+	261.981i	−0.424270	+	0.283529i
$925$	−890.056	+	368.673i	−0.962222	+	0.398565i
$926$	247.719	+	24.3898i	0.267515	+	0.0263389i
$927$		−	243.657i		−	0.262845i
$928$	1039.94	+	102.250i	1.12062	+	0.110183i
$929$	635.560			0.684133			0.342067	−	0.939676i	$-0.388873\pi$
$929$	635.560			0.684133			0.342067	+	0.939676i	$0.388873\pi$
$930$	5.84200	−	59.3351i	0.00628173	−	0.0638012i
$931$	−87.7333	−	211.807i	−0.0942356	−	0.227505i
$932$	−1404.59	+	938.653i	−1.50707	+	1.00714i
$933$	−148.223	+	357.841i	−0.158867	+	0.383538i
$934$	1205.21	−	365.640i	1.29037	−	0.391477i
$935$	267.924	−	267.924i	0.286550	−	0.286550i
$936$	−392.394	−	321.964i	−0.419225	−	0.343979i
$937$	−1046.11	+	1046.11i	−1.11645	+	1.11645i	−0.124193	+	0.992258i	$0.539634\pi$
$937$	−1046.11	+	1046.11i	−1.11645	+	1.11645i	−0.992258	+	0.124193i	$0.960366\pi$
$938$	1247.86	+	666.939i	1.33034	+	0.711022i
$939$	−341.779	+	825.128i	−0.363982	+	0.878731i
$940$	−410.576	+	614.559i	−0.436783	+	0.653786i
$941$	−291.022	−	702.589i	−0.309269	−	0.746641i	−0.999729	−	0.0232706i	$-0.992592\pi$
$941$	−291.022	−	702.589i	−0.309269	−	0.746641i	0.690460	−	0.723370i	$-0.257408\pi$
$942$	324.827	+	395.775i	0.344827	+	0.420144i
$943$	691.089			0.732862
$944$	124.507	+	124.474i	0.131893	+	0.131858i
$945$			99.4095i			0.105195i
$946$	166.649	+	203.049i	0.176162	+	0.214640i
$947$	157.175	−	65.1039i	0.165971	−	0.0687475i	−0.298151	−	0.954519i	$-0.596370\pi$
$947$	157.175	−	65.1039i	0.165971	−	0.0687475i	0.464122	+	0.885771i	$0.346370\pi$
$948$	−54.7427	−	275.115i	−0.0577455	−	0.290205i
$949$	2598.25	+	1076.23i	2.73788	+	1.13407i
$950$	−349.757	−	186.934i	−0.368165	−	0.196773i
$951$	−685.165	−	685.165i	−0.720468	−	0.720468i
$952$	671.023	+	1255.09i	0.704856	+	1.31838i
$953$	−269.699	−	269.699i	−0.283000	−	0.283000i	0.551305	−	0.834304i	$-0.314130\pi$
$953$	−269.699	−	269.699i	−0.283000	−	0.283000i	−0.834304	+	0.551305i	$0.814130\pi$
$954$	105.056	−	31.8722i	0.110122	−	0.0334090i
$955$	587.902	+	243.517i	0.615604	+	0.254992i
$956$	−55.3538	−	11.0067i	−0.0579015	−	0.0115133i
$957$	419.019	−	173.563i	0.437847	−	0.181362i
$958$	82.6198	−	839.139i	0.0862419	−	0.875928i
$959$		−	1147.31i		−	1.19636i
$960$	207.795	+	138.784i	0.216453	+	0.144567i
$961$	902.702			0.939337
$962$	−2035.96	−	200.456i	−2.11638	−	0.208374i
$963$	91.4062	+	220.674i	0.0949182	+	0.229153i
$964$	−42.7230	+	214.857i	−0.0443184	+	0.222881i
$965$	59.3349	−	143.247i	0.0614869	−	0.148443i
$966$	122.216	+	402.843i	0.126517	+	0.417022i
$967$	−255.007	+	255.007i	−0.263710	+	0.263710i	−0.826559	−	0.562850i	$-0.809705\pi$
$967$	−255.007	+	255.007i	−0.263710	+	0.263710i	0.562850	+	0.826559i	$0.309705\pi$
$968$	−213.859	−	400.005i	−0.220928	−	0.413229i
$969$	−255.570	+	255.570i	−0.263746	+	0.263746i
$970$	324.831	−	607.765i	0.334878	−	0.626562i
$971$	389.643	−	940.681i	0.401280	−	0.968776i	−0.586076	−	0.810256i	$-0.699328\pi$
$971$	389.643	−	940.681i	0.401280	−	0.968776i	0.987356	−	0.158520i	$-0.0506721\pi$
$972$	−61.1549	+	12.1687i	−0.0629166	+	0.0125192i
$973$	−814.241	−	1965.75i	−0.836836	−	2.02030i
$974$	−389.051	+	319.307i	−0.399436	+	0.327831i
$975$	−729.643			−0.748352
$976$	−1217.54	+	0.161983i	−1.24748	+	0.000165966i
$977$		−	1260.09i		−	1.28975i	−0.764286	−	0.644877i	$-0.776909\pi$
$977$		−	1260.09i		−	1.28975i	0.764286	−	0.644877i	$-0.223091\pi$
$978$	−508.094	+	417.010i	−0.519523	+	0.426391i
$979$	364.272	−	150.886i	0.372085	−	0.154123i
$980$	172.664	+	115.354i	0.176188	+	0.117708i
$981$	−264.456	−	109.541i	−0.269578	−	0.111663i
$982$	−213.101	+	398.715i	−0.217007	+	0.406024i
$983$	−1366.26	−	1366.26i	−1.38989	−	1.38989i	−0.825534	−	0.564352i	$-0.809126\pi$
$983$	−1366.26	−	1366.26i	−1.38989	−	1.38989i	−0.564352	−	0.825534i	$-0.690874\pi$
$984$	517.007	+	424.210i	0.525414	+	0.431108i
$985$	−129.985	−	129.985i	−0.131964	−	0.131964i
$986$	−397.441	−	1310.03i	−0.403084	−	1.32863i
$987$	−1113.21	−	461.108i	−1.12788	−	0.467181i
$988$	−467.921	−	700.193i	−0.473604	−	0.708697i
$989$	216.676	−	89.7501i	0.219086	−	0.0907483i
$990$	107.934	+	10.6270i	0.109024	+	0.0107343i
$991$		−	855.343i		−	0.863111i	−0.902086	−	0.431555i	$-0.857965\pi$
$991$		−	855.343i		−	0.863111i	0.902086	−	0.431555i	$-0.142035\pi$
$992$	115.140	−	215.498i	0.116069	−	0.217236i
$993$	478.280			0.481652
$994$	162.212	−	1647.52i	0.163191	−	1.65747i
$995$	217.375	+	524.789i	0.218467	+	0.527426i
$996$	−207.183	−	310.027i	−0.208015	−	0.311272i
$997$	−149.876	+	361.834i	−0.150327	+	0.362922i	−0.981047	−	0.193768i	$-0.937929\pi$
$997$	−149.876	+	361.834i	−0.150327	+	0.362922i	0.830720	+	0.556690i	$0.187929\pi$
$998$	−840.530	+	255.003i	−0.842215	+	0.255514i
$999$	−177.709	+	177.709i	−0.177887	+	0.177887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.3.m.a.43.2	✓	64
3.2	odd	2		288.3.u.b.235.15		64
4.3	odd	2		384.3.m.a.79.12		64
32.3	odd	8	inner	96.3.m.a.67.2	yes	64
32.29	even	8		384.3.m.a.175.12		64
96.35	even	8		288.3.u.b.163.15		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.43.2	✓	64	1.1	even	1	trivial
96.3.m.a.67.2	yes	64	32.3	odd	8	inner
288.3.u.b.163.15		64	96.35	even	8
288.3.u.b.235.15		64	3.2	odd	2
384.3.m.a.79.12		64	4.3	odd	2
384.3.m.a.175.12		64	32.29	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99038 - 0.195968i) q^{2} +(-0.662827 - 1.60021i) q^{3} +(3.92319 + 0.780100i) q^{4} +(-0.862642 + 2.08260i) q^{5} +(1.00569 + 3.31491i) q^{6} +(6.00123 - 6.00123i) q^{7} +(-7.65575 - 2.32151i) q^{8} +(-2.12132 + 2.12132i) q^{9} +O(q^{10})\)	\(q+(-1.99038 - 0.195968i) q^{2} +(-0.662827 - 1.60021i) q^{3} +(3.92319 + 0.780100i) q^{4} +(-0.862642 + 2.08260i) q^{5} +(1.00569 + 3.31491i) q^{6} +(6.00123 - 6.00123i) q^{7} +(-7.65575 - 2.32151i) q^{8} +(-2.12132 + 2.12132i) q^{9} +(2.12510 - 3.97611i) q^{10} +(3.06868 - 7.40844i) q^{11} +(-1.35208 - 6.79499i) q^{12} +(-8.09339 - 19.5392i) q^{13} +(-13.1208 + 10.7687i) q^{14} +3.90437 q^{15} +(14.7829 + 6.12097i) q^{16} -20.9616i q^{17} +(4.63794 - 3.80651i) q^{18} +(9.19719 - 3.80960i) q^{19} +(-5.00895 + 7.49750i) q^{20} +(-13.5810 - 5.62543i) q^{21} +(-7.55964 + 14.1442i) q^{22} +(10.1250 + 10.1250i) q^{23} +(1.35954 + 13.7895i) q^{24} +(14.0846 + 14.0846i) q^{25} +(12.2798 + 40.4763i) q^{26} +(4.80062 + 1.98848i) q^{27} +(28.2255 - 18.8624i) q^{28} +(-30.1690 + 12.4964i) q^{29} +(-7.77117 - 0.765133i) q^{30} +7.63528i q^{31} +(-28.2240 - 15.0800i) q^{32} -13.8890 q^{33} +(-4.10780 + 41.7214i) q^{34} +(7.32126 + 17.6751i) q^{35} +(-9.97719 + 6.66751i) q^{36} +(-18.5090 + 44.6846i) q^{37} +(-19.0524 + 5.78018i) q^{38} +(-25.9022 + 25.9022i) q^{39} +(11.4390 - 13.9413i) q^{40} +(34.1279 - 34.1279i) q^{41} +(25.9289 + 13.8582i) q^{42} +(6.26795 - 15.1322i) q^{43} +(17.8183 - 26.6709i) q^{44} +(-2.58793 - 6.24780i) q^{45} +(-18.1683 - 22.1367i) q^{46} +81.9685 q^{47} +(-0.00368694 - 27.7128i) q^{48} -23.0295i q^{49} +(-25.2735 - 30.7938i) q^{50} +(-33.5429 + 13.8939i) q^{51} +(-16.5094 - 82.9696i) q^{52} +(16.9046 + 7.00211i) q^{53} +(-9.16536 - 4.89859i) q^{54} +(12.7817 + 12.7817i) q^{55} +(-59.8759 + 32.0120i) q^{56} +(-12.1923 - 12.1923i) q^{57} +(62.4967 - 18.9604i) q^{58} +(10.1659 + 4.21086i) q^{59} +(15.3176 + 3.04580i) q^{60} +(-70.3036 + 29.1207i) q^{61} +(1.49627 - 15.1971i) q^{62} +25.4611i q^{63} +(53.2211 + 35.5459i) q^{64} +47.6740 q^{65} +(27.6444 + 2.72181i) q^{66} +(-31.8993 - 77.0117i) q^{67} +(16.3521 - 82.2364i) q^{68} +(9.49095 - 22.9132i) q^{69} +(-11.1083 - 36.6148i) q^{70} +(-68.9646 + 68.9646i) q^{71} +(21.1650 - 11.3156i) q^{72} +(-94.0286 + 94.0286i) q^{73} +(45.5966 - 85.3120i) q^{74} +(13.2026 - 31.8739i) q^{75} +(39.0542 - 7.77107i) q^{76} +(-26.0439 - 62.8756i) q^{77} +(56.6311 - 46.4791i) q^{78} +40.4879 q^{79} +(-25.4999 + 25.5067i) q^{80} -9.00000i q^{81} +(-74.6154 + 61.2394i) q^{82} +(49.7241 - 20.5964i) q^{83} +(-48.8924 - 32.6642i) q^{84} +(43.6546 + 18.0823i) q^{85} +(-15.4410 + 28.8904i) q^{86} +(39.9937 + 39.9937i) q^{87} +(-40.6919 + 49.5933i) q^{88} +(34.7683 + 34.7683i) q^{89} +(3.92657 + 12.9426i) q^{90} +(-165.829 - 68.6888i) q^{91} +(31.8238 + 47.6208i) q^{92} +(12.2180 - 5.06087i) q^{93} +(-163.148 - 16.0632i) q^{94} +22.4404i q^{95} +(-5.42349 + 55.1596i) q^{96} +152.854 q^{97} +(-4.51305 + 45.8374i) q^{98} +(9.20603 + 22.2253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 40 q^{10} + 48 q^{12} + 32 q^{14} - 8 q^{16} - 24 q^{18} - 160 q^{20} - 184 q^{22} + 128 q^{23} - 72 q^{24} - 200 q^{26} - 120 q^{28} + 40 q^{32} + 120 q^{34} - 192 q^{35} + 280 q^{38} + 584 q^{40} - 192 q^{43} + 104 q^{44} + 32 q^{46} - 312 q^{50} - 192 q^{51} - 424 q^{52} + 320 q^{53} - 72 q^{54} - 256 q^{55} - 392 q^{56} - 352 q^{58} - 256 q^{59} - 144 q^{60} + 64 q^{61} - 48 q^{62} + 408 q^{64} + 144 q^{66} + 64 q^{67} + 856 q^{68} - 192 q^{69} + 984 q^{70} + 512 q^{71} + 1056 q^{74} + 384 q^{75} + 296 q^{76} - 448 q^{77} + 360 q^{78} + 512 q^{79} + 328 q^{80} - 760 q^{82} - 448 q^{86} - 1072 q^{88} + 192 q^{91} - 784 q^{92} - 480 q^{94} + 600 q^{96} + 272 q^{98}+O(q^{100}) \) 64 * q + 40 * q^10 + 48 * q^12 + 32 * q^14 - 8 * q^16 - 24 * q^18 - 160 * q^20 - 184 * q^22 + 128 * q^23 - 72 * q^24 - 200 * q^26 - 120 * q^28 + 40 * q^32 + 120 * q^34 - 192 * q^35 + 280 * q^38 + 584 * q^40 - 192 * q^43 + 104 * q^44 + 32 * q^46 - 312 * q^50 - 192 * q^51 - 424 * q^52 + 320 * q^53 - 72 * q^54 - 256 * q^55 - 392 * q^56 - 352 * q^58 - 256 * q^59 - 144 * q^60 + 64 * q^61 - 48 * q^62 + 408 * q^64 + 144 * q^66 + 64 * q^67 + 856 * q^68 - 192 * q^69 + 984 * q^70 + 512 * q^71 + 1056 * q^74 + 384 * q^75 + 296 * q^76 - 448 * q^77 + 360 * q^78 + 512 * q^79 + 328 * q^80 - 760 * q^82 - 448 * q^86 - 1072 * q^88 + 192 * q^91 - 784 * q^92 - 480 * q^94 + 600 * q^96 + 272 * q^98

Introduction

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