LMFDB - Embedded newform 117.3.bb.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(7,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 11]))

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

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

chi := DirichletCharacter("117.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.bb (of order $12$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	117.7
Dual form			117.3.bb.a.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.825818 + 3.08200i) q^{2} +(1.49477 + 2.60109i) q^{3} +(-5.35262 - 3.09034i) q^{4} +(-1.67984 + 6.26926i) q^{5} +(-9.25095 + 2.45885i) q^{6} +(5.59737 - 5.59737i) q^{7} +(4.91998 - 4.91998i) q^{8} +(-4.53132 + 7.77606i) q^{9} +(-17.9346 - 10.3545i) q^{10} +(-5.31002 - 1.42282i) q^{11} +(0.0372964 - 18.5420i) q^{12} +(12.9981 - 0.224655i) q^{13} +(12.6287 + 21.8735i) q^{14} +(-18.8179 + 5.00169i) q^{15} +(-1.26099 - 2.18411i) q^{16} +(14.1750 - 8.18397i) q^{17} +(-20.2237 - 20.3871i) q^{18} +(-1.38325 + 5.16237i) q^{19} +(28.3657 - 28.3657i) q^{20} +(22.9260 + 6.19247i) q^{21} +(8.77022 - 15.1905i) q^{22} +6.74000i q^{23} +(20.1515 + 5.44306i) q^{24} +(-14.8311 - 8.56275i) q^{25} +(-10.0416 + 40.2455i) q^{26} +(-26.9995 - 0.162927i) q^{27} +(-47.2583 + 12.6628i) q^{28} +(-17.6172 - 30.5138i) q^{29} +(0.124966 - 62.1271i) q^{30} +(-12.1589 + 45.3776i) q^{31} +(34.6560 - 9.28606i) q^{32} +(-4.23639 - 15.9386i) q^{33} +(13.5169 + 50.4459i) q^{34} +(25.6887 + 44.4941i) q^{35} +(48.2851 - 27.6190i) q^{36} +(10.2351 + 38.1979i) q^{37} +(-14.7681 - 8.52636i) q^{38} +(20.0135 + 33.4733i) q^{39} +(22.5798 + 39.1094i) q^{40} +(57.1181 + 57.1181i) q^{41} +(-38.0179 + 65.5441i) q^{42} -27.0023i q^{43} +(24.0255 + 24.0255i) q^{44} +(-41.1383 - 41.4706i) q^{45} +(-20.7727 - 5.56602i) q^{46} +(6.18939 + 23.0991i) q^{47} +(3.79615 - 6.54469i) q^{48} -13.6611i q^{49} +(38.6381 - 38.6381i) q^{50} +(42.4757 + 24.6374i) q^{51} +(-70.2679 - 38.9659i) q^{52} -56.5837 q^{53} +(22.7988 - 83.0778i) q^{54} +(17.8400 - 30.8998i) q^{55} -55.0779i q^{56} +(-15.4954 + 4.11860i) q^{57} +(108.592 - 29.0972i) q^{58} +(-27.3411 - 102.038i) q^{59} +(116.182 + 31.3814i) q^{60} +37.2534 q^{61} +(-129.813 - 74.9473i) q^{62} +(18.1620 + 68.8890i) q^{63} +104.390i q^{64} +(-20.4263 + 81.8656i) q^{65} +(52.6212 + 0.105845i) q^{66} +(-9.98624 - 9.98624i) q^{67} -101.165 q^{68} +(-17.5313 + 10.0748i) q^{69} +(-158.345 + 42.4283i) q^{70} +(17.3252 - 64.6586i) q^{71} +(15.9641 + 60.5521i) q^{72} +(84.7455 - 84.7455i) q^{73} -126.178 q^{74} +(0.103341 - 51.3764i) q^{75} +(23.3575 - 23.3575i) q^{76} +(-37.6862 + 21.7581i) q^{77} +(-119.692 + 34.0386i) q^{78} +(70.8339 - 122.688i) q^{79} +(15.8110 - 4.23654i) q^{80} +(-39.9343 - 70.4716i) q^{81} +(-223.207 + 128.869i) q^{82} +(9.77407 - 2.61895i) q^{83} +(-103.578 - 103.995i) q^{84} +(27.4956 + 102.615i) q^{85} +(83.2209 + 22.2990i) q^{86} +(53.0355 - 91.4350i) q^{87} +(-33.1254 + 19.1250i) q^{88} +(18.1333 + 67.6746i) q^{89} +(161.785 - 92.5407i) q^{90} +(71.4975 - 74.0124i) q^{91} +(20.8289 - 36.0767i) q^{92} +(-136.206 + 36.2028i) q^{93} -76.3027 q^{94} +(-30.0406 - 17.3439i) q^{95} +(75.9567 + 76.2629i) q^{96} +(90.1302 + 90.1302i) q^{97} +(42.1035 + 11.2816i) q^{98} +(35.1253 - 34.8438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 2 q^{5} + 10 q^{6} - 6 q^{7} + 18 q^{8} - 2 q^{9} - 12 q^{10} - 14 q^{11} - 54 q^{12} - 2 q^{13} - 4 q^{14} - 44 q^{15} + 162 q^{16} - 12 q^{17} + 34 q^{18} - 36 q^{19}+ \cdots - 524 q^{99}+O(q^{100}) $ 104 * q - 2 * q^2 - 2 * q^3 - 6 * q^4 - 2 * q^5 + 10 * q^6 - 6 * q^7 + 18 * q^8 - 2 * q^9 - 12 * q^10 - 14 * q^11 - 54 * q^12 - 2 * q^13 - 4 * q^14 - 44 * q^15 + 162 * q^16 - 12 * q^17 + 34 * q^18 - 36 * q^19 - 82 * q^20 + 106 * q^21 + 2 * q^22 - 66 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 + 74 * q^29 - 438 * q^30 - 34 * q^31 + 22 * q^32 - 68 * q^33 + 6 * q^34 - 106 * q^35 - 6 * q^36 + 14 * q^37 - 216 * q^38 - 176 * q^39 - 36 * q^40 - 26 * q^41 - 220 * q^42 + 496 * q^44 - 50 * q^45 + 118 * q^47 + 130 * q^48 + 92 * q^50 + 76 * q^52 - 208 * q^53 + 904 * q^54 - 4 * q^55 - 86 * q^57 - 76 * q^58 + 430 * q^59 - 358 * q^60 - 4 * q^61 - 282 * q^62 - 326 * q^63 + 406 * q^65 - 412 * q^66 - 72 * q^67 - 1068 * q^68 + 204 * q^69 - 106 * q^70 - 8 * q^71 - 642 * q^72 + 90 * q^73 + 356 * q^74 + 204 * q^75 - 194 * q^76 + 432 * q^77 + 646 * q^78 - 16 * q^79 - 278 * q^80 - 182 * q^81 - 12 * q^82 - 536 * q^83 + 310 * q^84 - 234 * q^85 + 414 * q^86 + 434 * q^87 - 6 * q^88 + 400 * q^89 + 798 * q^90 + 120 * q^91 + 48 * q^92 - 116 * q^93 - 244 * q^94 + 858 * q^95 + 1528 * q^96 + 344 * q^97 + 280 * q^98 - 524 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.825818	+	3.08200i	−0.412909	+	1.54100i	0.376078	+	0.926588i	$0.377272\pi$
$2$	−0.825818	+	3.08200i	−0.412909	+	1.54100i	−0.788987	+	0.614410i	$0.789394\pi$
$3$	1.49477	+	2.60109i	0.498257	+	0.867029i
$3$	1.49477	+	2.60109i	0.498257	+	0.867029i
$4$	−5.35262	−	3.09034i	−1.33815	−	0.772584i
$5$	−1.67984	+	6.26926i	−0.335969	+	1.25385i	0.566847	+	0.823823i	$0.308163\pi$
$5$	−1.67984	+	6.26926i	−0.335969	+	1.25385i	−0.902815	+	0.430029i	$0.858503\pi$
$6$	−9.25095	+	2.45885i	−1.54183	+	0.409809i
$7$	5.59737	−	5.59737i	0.799624	−	0.799624i	−0.183412	−	0.983036i	$-0.558714\pi$
$7$	5.59737	−	5.59737i	0.799624	−	0.799624i	0.983036	+	0.183412i	$0.0587142\pi$
$8$	4.91998	−	4.91998i	0.614998	−	0.614998i
$9$	−4.53132	+	7.77606i	−0.503480	+	0.864007i
$10$	−17.9346	−	10.3545i	−1.79346	−	1.03545i
$11$	−5.31002	−	1.42282i	−0.482729	−	0.129347i	0.00924404	−	0.999957i	$-0.497057\pi$
$11$	−5.31002	−	1.42282i	−0.482729	−	0.129347i	−0.491973	+	0.870610i	$0.663724\pi$
$12$	0.0372964	−	18.5420i	0.00310803	−	1.54516i
$13$	12.9981	−	0.224655i	0.999851	−	0.0172812i
$13$	12.9981	−	0.224655i	0.999851	−	0.0172812i
$14$	12.6287	+	21.8735i	0.902047	+	1.56239i
$15$	−18.8179	+	5.00169i	−1.25453	+	0.333446i
$16$	−1.26099	−	2.18411i	−0.0788121	−	0.136507i
$17$	14.1750	−	8.18397i	0.833826	−	0.481410i	−0.0213346	−	0.999772i	$-0.506792\pi$
$17$	14.1750	−	8.18397i	0.833826	−	0.481410i	0.855161	+	0.518363i	$0.173458\pi$
$18$	−20.2237	−	20.3871i	−1.12354	−	1.13262i
$19$	−1.38325	+	5.16237i	−0.0728028	+	0.271704i	−0.992726	−	0.120395i	$-0.961584\pi$
$19$	−1.38325	+	5.16237i	−0.0728028	+	0.271704i	0.919923	+	0.392098i	$0.128251\pi$
$20$	28.3657	−	28.3657i	1.41828	−	1.41828i
$21$	22.9260	+	6.19247i	1.09172	+	0.294879i
$22$	8.77022	−	15.1905i	0.398646	−	0.690476i
$23$			6.74000i			0.293044i	0.989207	+	0.146522i	$0.0468078\pi$
$23$			6.74000i			0.293044i	−0.989207	+	0.146522i	$0.953192\pi$
$24$	20.1515	+	5.44306i	0.839648	+	0.226794i
$25$	−14.8311	−	8.56275i	−0.593244	−	0.342510i
$26$	−10.0416	+	40.2455i	−0.386217	+	1.54790i
$27$	−26.9995	−	0.162927i	−0.999982	−	0.00603433i
$28$	−47.2583	+	12.6628i	−1.68780	+	0.452244i
$29$	−17.6172	−	30.5138i	−0.607489	−	1.05220i	−0.991653	−	0.128937i	$-0.958844\pi$
$29$	−17.6172	−	30.5138i	−0.607489	−	1.05220i	0.384164	−	0.923265i	$-0.374490\pi$
$30$	0.124966	−	62.1271i	0.00416554	−	2.07090i
$31$	−12.1589	+	45.3776i	−0.392222	+	1.46379i	0.434238	+	0.900798i	$0.357018\pi$
$31$	−12.1589	+	45.3776i	−0.392222	+	1.46379i	−0.826460	+	0.562996i	$0.809649\pi$
$32$	34.6560	−	9.28606i	1.08300	−	0.290189i
$33$	−4.23639	−	15.9386i	−0.128376	−	0.482988i
$34$	13.5169	+	50.4459i	0.397557	+	1.48370i
$35$	25.6887	+	44.4941i	0.733962	+	1.27126i
$36$	48.2851	−	27.6190i	1.34125	−	0.767194i
$37$	10.2351	+	38.1979i	0.276624	+	1.03238i	0.954745	+	0.297426i	$0.0961281\pi$
$37$	10.2351	+	38.1979i	0.276624	+	1.03238i	−0.678120	+	0.734951i	$0.737205\pi$
$38$	−14.7681	−	8.52636i	−0.388634	−	0.224378i
$39$	20.0135	+	33.4733i	0.513166	+	0.858289i
$40$	22.5798	+	39.1094i	0.564496	+	0.977736i
$41$	57.1181	+	57.1181i	1.39313	+	1.39313i	0.818220	+	0.574906i	$0.194961\pi$
$41$	57.1181	+	57.1181i	1.39313	+	1.39313i	0.574906	+	0.818220i	$0.305039\pi$
$42$	−38.0179	+	65.5441i	−0.905188	+	1.56057i
$43$		−	27.0023i		−	0.627960i	−0.949430	−	0.313980i	$-0.898338\pi$
$43$		−	27.0023i		−	0.627960i	0.949430	−	0.313980i	$-0.101662\pi$
$44$	24.0255	+	24.0255i	0.546035	+	0.546035i
$45$	−41.1383	−	41.4706i	−0.914183	−	0.921568i
$46$	−20.7727	−	5.56602i	−0.451579	−	0.121000i
$47$	6.18939	+	23.0991i	0.131689	+	0.491471i	0.999990	−	0.00456799i	$-0.00145404\pi$
$47$	6.18939	+	23.0991i	0.131689	+	0.491471i	−0.868300	+	0.496039i	$0.834787\pi$
$48$	3.79615	−	6.54469i	0.0790865	−	0.136348i
$49$		−	13.6611i		−	0.278798i
$50$	38.6381	−	38.6381i	0.772763	−	0.772763i
$51$	42.4757	+	24.6374i	0.832856	+	0.483086i
$52$	−70.2679	−	38.9659i	−1.35131	−	0.749344i
$53$	−56.5837			−1.06762			−0.533809	−	0.845605i	$-0.679240\pi$
$53$	−56.5837			−1.06762			−0.533809	+	0.845605i	$0.679240\pi$
$54$	22.7988	−	83.0778i	0.422200	−	1.53848i
$55$	17.8400	−	30.8998i	0.324364	−	0.561814i
$56$		−	55.0779i		−	0.983534i
$57$	−15.4954	+	4.11860i	−0.271850	+	0.0722561i
$58$	108.592	−	29.0972i	1.87228	−	0.501675i
$59$	−27.3411	−	102.038i	−0.463408	−	1.72946i	−0.662113	−	0.749404i	$-0.730340\pi$
$59$	−27.3411	−	102.038i	−0.463408	−	1.72946i	0.198705	−	0.980059i	$-0.436326\pi$
$60$	116.182	+	31.3814i	1.93636	+	0.523024i
$61$	37.2534			0.610711			0.305355	−	0.952238i	$-0.401225\pi$
$61$	37.2534			0.610711			0.305355	+	0.952238i	$0.401225\pi$
$62$	−129.813	−	74.9473i	−2.09375	−	1.20883i
$63$	18.1620	+	68.8890i	0.288286	+	1.09348i
$64$			104.390i			1.63110i
$65$	−20.4263	+	81.8656i	−0.314250	+	1.25947i
$66$	52.6212	+	0.105845i	0.797291	+	0.00160372i
$67$	−9.98624	−	9.98624i	−0.149048	−	0.149048i	0.628644	−	0.777693i	$-0.283610\pi$
$67$	−9.98624	−	9.98624i	−0.149048	−	0.149048i	−0.777693	+	0.628644i	$0.783610\pi$
$68$	−101.165			−1.48772
$69$	−17.5313	+	10.0748i	−0.254077	+	0.146011i
$70$	−158.345	+	42.4283i	−2.26207	+	0.606119i
$71$	17.3252	−	64.6586i	0.244017	−	0.910684i	−0.729858	−	0.683599i	$-0.760414\pi$
$71$	17.3252	−	64.6586i	0.244017	−	0.910684i	0.973875	−	0.227085i	$-0.0729195\pi$
$72$	15.9641	+	60.5521i	0.221723	+	0.841001i
$73$	84.7455	−	84.7455i	1.16090	−	1.16090i	0.176618	−	0.984279i	$-0.443484\pi$
$73$	84.7455	−	84.7455i	1.16090	−	1.16090i	0.984279	−	0.176618i	$-0.0565159\pi$
$74$	−126.178			−1.70511
$75$	0.103341	−	51.3764i	0.00137789	−	0.685018i
$76$	23.3575	−	23.3575i	0.307335	−	0.307335i
$77$	−37.6862	+	21.7581i	−0.489431	+	0.282573i
$78$	−119.692	+	34.0386i	−1.53451	+	0.436392i
$79$	70.8339	−	122.688i	0.896632	−	1.55301i	0.0648593	−	0.997894i	$-0.479340\pi$
$79$	70.8339	−	122.688i	0.896632	−	1.55301i	0.831772	−	0.555117i	$-0.187327\pi$
$80$	15.8110	−	4.23654i	0.197637	−	0.0529568i
$81$	−39.9343	−	70.4716i	−0.493016	−	0.870020i
$82$	−223.207	+	128.869i	−2.72204	+	1.57157i
$83$	9.77407	−	2.61895i	0.117760	−	0.0315537i	−0.199458	−	0.979906i	$-0.563918\pi$
$83$	9.77407	−	2.61895i	0.117760	−	0.0315537i	0.317218	+	0.948353i	$0.397251\pi$
$84$	−103.578	−	103.995i	−1.23307	−	1.23804i
$85$	27.4956	+	102.615i	0.323477	+	1.20723i
$86$	83.2209	+	22.2990i	0.967685	+	0.259290i
$87$	53.0355	−	91.4350i	0.609604	−	1.05098i
$88$	−33.1254	+	19.1250i	−0.376425	+	0.217329i
$89$	18.1333	+	67.6746i	0.203745	+	0.760388i	0.989828	+	0.142267i	$0.0454392\pi$
$89$	18.1333	+	67.6746i	0.203745	+	0.760388i	−0.786083	+	0.618121i	$0.787894\pi$
$90$	161.785	−	92.5407i	1.79761	−	1.02823i
$91$	71.4975	−	74.0124i	0.785686	−	0.813323i
$92$	20.8289	−	36.0767i	0.226401	−	0.392138i
$93$	−136.206	+	36.2028i	−1.46458	+	0.389277i
$94$	−76.3027			−0.811731
$95$	−30.0406	−	17.3439i	−0.316217	−	0.182568i
$96$	75.9567	+	76.2629i	0.791215	+	0.794405i
$97$	90.1302	+	90.1302i	0.929177	+	0.929177i	0.997653	−	0.0684759i	$-0.0218136\pi$
$97$	90.1302	+	90.1302i	0.929177	+	0.929177i	−0.0684759	+	0.997653i	$0.521814\pi$
$98$	42.1035	+	11.2816i	0.429627	+	0.115118i
$99$	35.1253	−	34.8438i	0.354801	−	0.351958i
$100$	52.9235	+	91.6662i	0.529235	+	0.916662i
$101$	90.5960	−	52.3056i	0.896990	−	0.517877i	0.0207675	−	0.999784i	$-0.493389\pi$
$101$	90.5960	−	52.3056i	0.896990	−	0.517877i	0.876222	+	0.481907i	$0.160056\pi$
$102$	−111.010	+	110.564i	−1.08833	+	1.08396i
$103$	55.1145	−	31.8204i	0.535092	−	0.308936i	−0.207995	−	0.978130i	$-0.566694\pi$
$103$	55.1145	−	31.8204i	0.535092	−	0.308936i	0.743088	+	0.669194i	$0.233361\pi$
$104$	62.8449	−	65.0555i	0.604278	−	0.625534i
$105$	−77.3343	+	133.327i	−0.736517	+	1.26978i
$106$	46.7279	−	174.391i	0.440829	−	1.64520i
$107$	0.0803675	−	0.139201i	0.000751098	−	0.00130094i	−0.865650	−	0.500650i	$-0.833094\pi$
$107$	0.0803675	−	0.139201i	0.000751098	−	0.00130094i	0.866401	+	0.499349i	$0.166428\pi$
$108$	144.015	+	84.3096i	1.33347	+	0.780645i
$109$	−114.550	−	114.550i	−1.05092	−	1.05092i	−0.998632	−	0.0522892i	$-0.983348\pi$
$109$	−114.550	−	114.550i	−1.05092	−	1.05092i	−0.0522892	−	0.998632i	$-0.516652\pi$
$110$	80.5004	+	80.5004i	0.731822	+	0.731822i
$111$	−84.0571	+	83.7196i	−0.757271	+	0.754230i
$112$	−19.2835	−	5.16700i	−0.172174	−	0.0461339i
$113$	−17.2866	+	29.9413i	−0.152979	+	0.264967i	−0.932321	−	0.361631i	$-0.882220\pi$
$113$	−17.2866	+	29.9413i	−0.152979	+	0.264967i	0.779342	+	0.626598i	$0.215553\pi$
$114$	0.102902	−	51.1581i	0.000902652	−	0.448755i
$115$	−42.2548	−	11.3221i	−0.367433	−	0.0984534i
$116$			217.772i			1.87734i
$117$	−57.1514	+	102.092i	−0.488474	+	0.872579i
$118$	337.060			2.85644
$119$	33.5343	−	125.152i	0.281801	−	1.05169i
$120$	−67.9754	+	117.192i	−0.566462	+	0.976598i
$121$	−78.6172	−	45.3896i	−0.649729	−	0.375121i
$122$	−30.7645	+	114.815i	−0.252168	+	0.941104i
$123$	−63.1908	+	233.948i	−0.513746	+	1.90202i
$124$	205.314	−	205.314i	1.65576	−	1.65576i
$125$	−36.1394	+	36.1394i	−0.289115	+	0.289115i
$126$	−227.314	−	0.914469i	−1.80408	−	0.00725769i
$127$	−20.0101	−	11.5528i	−0.157560	−	0.0909672i	0.419147	−	0.907918i	$-0.362329\pi$
$127$	−20.0101	−	11.5528i	−0.157560	−	0.0909672i	−0.576707	+	0.816951i	$0.695663\pi$
$128$	−183.107	−	49.0632i	−1.43052	−	0.383307i
$129$	70.2353	−	40.3622i	0.544460	−	0.312885i
$130$	−235.441	−	130.560i	−1.81108	−	1.00431i
$131$	25.5029	+	44.1723i	0.194679	+	0.337193i	0.946795	−	0.321837i	$-0.104300\pi$
$131$	25.5029	+	44.1723i	0.194679	+	0.337193i	−0.752117	+	0.659030i	$0.770967\pi$
$132$	−26.5799	+	98.4052i	−0.201363	+	0.745494i
$133$	21.1531	+	36.6383i	0.159046	+	0.275476i
$134$	39.0244	−	22.5307i	0.291227	−	0.168140i
$135$	46.3764	−	168.993i	0.343529	−	1.25180i
$136$	29.4760	−	110.006i	0.216735	−	0.808867i
$137$	−36.6067	+	36.6067i	−0.267202	+	0.267202i	−0.827972	−	0.560770i	$-0.810505\pi$
$137$	−36.6067	+	36.6067i	−0.267202	+	0.267202i	0.560770	+	0.827972i	$0.310505\pi$
$138$	−16.5727	−	62.3514i	−0.120092	−	0.451822i
$139$	−43.3213	+	75.0347i	−0.311664	+	0.539818i	−0.978723	−	0.205187i	$-0.934220\pi$
$139$	−43.3213	+	75.0347i	−0.311664	+	0.539818i	0.667059	+	0.745005i	$0.267553\pi$
$140$		−	317.546i		−	2.26819i
$141$	−50.8311	+	50.6271i	−0.360505	+	0.359057i
$142$	184.970	+	106.792i	1.30260	+	0.752059i
$143$	−69.3396	−	17.3009i	−0.484892	−	0.120985i
$144$	22.6977	+	0.0913113i	0.157623	+	0.000634107i
$145$	220.893	−	59.1882i	1.52340	−	0.408194i
$146$	191.201	+	331.170i	1.30960	+	2.26829i
$147$	35.5337	−	20.4202i	0.241726	−	0.138913i
$148$	63.2598	−	236.089i	0.427431	−	1.59520i
$149$	91.9994	−	24.6512i	0.617445	−	0.165444i	0.0634792	−	0.997983i	$-0.479780\pi$
$149$	91.9994	−	24.6512i	0.617445	−	0.165444i	0.553966	+	0.832539i	$0.313114\pi$
$150$	158.256	+	42.7460i	1.05504	+	0.284974i
$151$	49.2708	+	183.881i	0.326296	+	1.21775i	0.913002	+	0.407955i	$0.133758\pi$
$151$	49.2708	+	183.881i	0.326296	+	1.21775i	−0.586706	+	0.809800i	$0.699575\pi$
$152$	18.5932	+	32.2043i	0.122324	+	0.211871i
$153$	−0.592619	+	147.310i	−0.00387333	+	0.962812i
$154$	−35.9365	−	134.117i	−0.233354	−	0.870889i
$155$	−264.059	−	152.455i	−1.70361	−	0.983578i
$156$	−3.68077	−	241.018i	−0.0235947	−	1.54499i
$157$	−52.8770	−	91.5856i	−0.336796	−	0.583348i	0.647032	−	0.762463i	$-0.276010\pi$
$157$	−52.8770	−	91.5856i	−0.336796	−	0.583348i	−0.983828	+	0.179115i	$0.942677\pi$
$158$	319.628	+	319.628i	2.02296	+	2.02296i
$159$	−84.5797	−	147.179i	−0.531948	−	0.925656i
$160$			232.867i			1.45542i
$161$	37.7263	+	37.7263i	0.234325	+	0.234325i
$162$	250.172	−	64.8806i	1.54427	−	0.400497i
$163$	−100.461	−	26.9184i	−0.616325	−	0.165144i	−0.0628683	−	0.998022i	$-0.520025\pi$
$163$	−100.461	−	26.9184i	−0.616325	−	0.165144i	−0.553456	+	0.832878i	$0.686691\pi$
$164$	−129.217	−	482.246i	−0.787911	−	2.94052i
$165$	107.040	+	0.215306i	0.648726	+	0.00130489i
$166$			32.2864i			0.194496i
$167$	141.028	−	141.028i	0.844481	−	0.844481i	−0.144957	−	0.989438i	$-0.546304\pi$
$167$	141.028	−	141.028i	0.844481	−	0.844481i	0.989438	+	0.144957i	$0.0463045\pi$
$168$	143.262	−	82.3289i	0.852753	−	0.490053i
$169$	168.899	−	5.84016i	0.999403	−	0.0345572i
$170$	−338.965			−1.99391
$171$	−33.8750	−	34.1486i	−0.198099	−	0.199699i
$172$	−83.4461	+	144.533i	−0.485152	+	0.840307i
$173$		−	107.754i		−	0.622856i	−0.950270	−	0.311428i	$-0.899193\pi$
$173$		−	107.754i		−	0.622856i	0.950270	−	0.311428i	$-0.100807\pi$
$174$	238.005	+	238.964i	1.36784	+	1.37336i
$175$	−130.944	+	35.0864i	−0.748252	+	0.200494i
$176$	3.58832	+	13.3918i	0.0203882	+	0.0760898i
$177$	224.542	−	223.641i	1.26860	−	1.26351i
$178$	−223.548			−1.25589
$179$	−128.017	−	73.9106i	−0.715178	−	0.412908i	0.0977974	−	0.995206i	$-0.468820\pi$
$179$	−128.017	−	73.9106i	−0.715178	−	0.412908i	−0.812975	+	0.582298i	$0.802154\pi$
$180$	92.0393	+	349.107i	0.511330	+	1.93948i
$181$		−	78.4431i		−	0.433387i	−0.976240	−	0.216694i	$-0.930473\pi$
$181$		−	78.4431i		−	0.433387i	0.976240	−	0.216694i	$-0.0695272\pi$
$182$	169.062	+	281.476i	0.928912	+	1.54657i
$183$	55.6852	+	96.8993i	0.304291	+	0.529504i
$184$	33.1607	+	33.1607i	0.180221	+	0.180221i
$185$	−256.666			−1.38738
$186$	0.904519	−	449.683i	0.00486300	−	2.41765i
$187$	−86.9140	+	23.2885i	−0.464781	+	0.124538i
$188$	38.2546	−	142.768i	0.203482	−	0.759405i
$189$	−152.038	+	150.214i	−0.804435	+	0.794785i
$190$	78.2620	−	78.2620i	0.411905	−	0.411905i
$191$	87.4407			0.457805			0.228902	−	0.973449i	$-0.426486\pi$
$191$	87.4407			0.457805			0.228902	+	0.973449i	$0.426486\pi$
$192$	−271.529	+	156.040i	−1.41421	+	0.812707i
$193$	−173.780	+	173.780i	−0.900412	+	0.900412i	−0.995472	−	0.0950594i	$-0.969696\pi$
$193$	−173.780	+	173.780i	−0.900412	+	0.900412i	0.0950594	+	0.995472i	$0.469696\pi$
$194$	−352.212	+	203.350i	−1.81552	+	1.04819i
$195$	−243.472	+	69.2398i	−1.24858	+	0.355076i
$196$	−42.2174	+	73.1227i	−0.215395	+	0.373075i
$197$	−194.514	+	52.1198i	−0.987379	+	0.264568i	−0.716149	−	0.697947i	$-0.754097\pi$
$197$	−194.514	+	52.1198i	−0.987379	+	0.264568i	−0.271230	+	0.962515i	$0.587430\pi$
$198$	78.3814	+	137.031i	0.395865	+	0.692074i
$199$	−16.6444	+	9.60968i	−0.0836404	+	0.0482898i	−0.541237	−	0.840870i	$-0.682044\pi$
$199$	−16.6444	+	9.60968i	−0.0836404	+	0.0482898i	0.457596	+	0.889160i	$0.348710\pi$
$200$	−115.097	+	30.8402i	−0.575487	+	0.154201i
$201$	11.0479	−	40.9022i	0.0549649	−	0.203494i
$202$	86.3898	+	322.411i	0.427672	+	1.59610i
$203$	−269.407	−	72.1874i	−1.32713	−	0.355603i
$204$	−151.218	−	263.139i	−0.741266	−	1.28990i
$205$	−454.038	+	262.139i	−2.21482	+	1.27873i
$206$	52.5557	+	196.140i	0.255125	+	0.952138i
$207$	−52.4107	−	30.5411i	−0.253192	−	0.147542i
$208$	−16.8811	−	28.1058i	−0.0811593	−	0.135124i
$209$	14.6902	−	25.4442i	0.0702880	−	0.121742i
$210$	−347.049	−	348.448i	−1.65261	−	1.65928i
$211$	207.378			0.982833			0.491417	−	0.870925i	$-0.336479\pi$
$211$	207.378			0.982833			0.491417	+	0.870925i	$0.336479\pi$
$212$	302.871	+	174.863i	1.42864	+	0.824824i
$213$	194.080	−	51.5853i	0.911173	−	0.242185i
$214$	0.362647	+	0.362647i	0.00169461	+	0.00169461i
$215$	169.284	+	45.3596i	0.787369	+	0.210975i
$216$	−133.639	+	132.035i	−0.618698	+	0.611275i
$217$	185.937	+	322.053i	0.856855	+	1.48412i
$218$	447.642	−	258.446i	2.05340	−	1.18553i
$219$	347.106	+	93.7554i	1.58496	+	0.428107i
$220$	−190.981	+	110.263i	−0.868097	+	0.501196i
$221$	182.410	−	109.560i	0.825382	−	0.495747i
$222$	−188.608	−	328.201i	−0.849583	−	1.47838i
$223$	−4.58807	+	17.1229i	−0.0205743	+	0.0767843i	−0.975450	−	0.220222i	$-0.929322\pi$
$223$	−4.58807	+	17.1229i	−0.0205743	+	0.0767843i	0.954875	+	0.297007i	$0.0959884\pi$
$224$	142.005	−	245.960i	0.633952	−	1.09804i
$225$	133.789	−	76.5271i	0.594618	−	0.340121i
$226$	−78.0033	−	78.0033i	−0.345147	−	0.345147i
$227$	−222.273	−	222.273i	−0.979175	−	0.979175i	0.0206130	−	0.999788i	$-0.493438\pi$
$227$	−222.273	−	222.273i	−0.979175	−	0.979175i	−0.999788	+	0.0206130i	$0.993438\pi$
$228$	95.6690	+	25.8408i	0.419601	+	0.113337i
$229$	19.3941	+	5.19664i	0.0846904	+	0.0226927i	0.300915	−	0.953651i	$-0.402708\pi$
$229$	19.3941	+	5.19664i	0.0846904	+	0.0226927i	−0.216225	+	0.976344i	$0.569374\pi$
$230$	69.7896	−	120.879i	0.303433	−	0.525561i
$231$	−112.927	−	65.5016i	−0.488861	−	0.283557i
$232$	−236.804	−	63.4514i	−1.02071	−	0.273497i
$233$			42.5489i			0.182613i	0.995823	+	0.0913066i	$0.0291043\pi$
$233$			42.5489i			0.182613i	−0.995823	+	0.0913066i	$0.970896\pi$
$234$	−267.449	−	260.450i	−1.14295	−	1.11303i
$235$	−155.212			−0.660475
$236$	−168.986	+	630.665i	−0.716044	+	2.67231i
$237$	425.002	+	0.854875i	1.79326	+	0.00360707i
$238$	358.024	+	206.705i	1.50430	+	0.868509i
$239$	110.626	−	412.860i	0.462868	−	1.72745i	−0.200993	−	0.979593i	$-0.564417\pi$
$239$	110.626	−	412.860i	0.462868	−	1.72745i	0.663862	−	0.747855i	$-0.268916\pi$
$240$	34.6534	+	34.7931i	0.144389	+	0.144971i
$241$	−211.492	+	211.492i	−0.877562	+	0.877562i	−0.993282	−	0.115720i	$-0.963083\pi$
$241$	−211.492	+	211.492i	−0.877562	+	0.877562i	0.115720	+	0.993282i	$0.463083\pi$
$242$	204.814	−	204.814i	0.846340	−	0.846340i
$243$	123.610	−	209.212i	0.508684	−	0.860953i
$244$	−199.403	−	115.125i	−0.817225	−	0.471825i
$245$	85.6450	+	22.9485i	0.349572	+	0.0936674i
$246$	−668.842	−	387.952i	−2.71887	−	1.57704i
$247$	−16.8199	+	67.4116i	−0.0680966	+	0.272921i
$248$	163.435	+	283.079i	0.659014	+	1.14145i
$249$	21.4221	+	21.5085i	0.0860326	+	0.0863794i
$250$	−81.5369	−	141.226i	−0.326147	−	0.564904i
$251$	−155.593	+	89.8316i	−0.619892	+	0.357895i	−0.776827	−	0.629714i	$-0.783172\pi$
$251$	−155.593	+	89.8316i	−0.619892	+	0.357895i	0.156935	+	0.987609i	$0.449839\pi$
$252$	115.676	−	424.863i	0.459030	−	1.68596i
$253$	9.58978	−	35.7895i	0.0379043	−	0.141461i
$254$	52.1305	−	52.1305i	0.205238	−	0.205238i
$255$	−225.811	+	224.904i	−0.885532	+	0.881977i
$256$	93.6446	−	162.197i	0.365799	−	0.633583i
$257$			227.751i			0.886192i	0.896474	+	0.443096i	$0.146120\pi$
$257$			227.751i			0.886192i	−0.896474	+	0.443096i	$0.853880\pi$
$258$	66.3946	+	249.797i	0.257343	+	0.968204i
$259$	271.098	+	156.518i	1.04671	+	0.604318i
$260$	362.326	−	375.071i	1.39356	−	1.44258i
$261$	317.107	+	1.27570i	1.21497	+	0.00488773i
$262$	−157.200	+	42.1215i	−0.599998	+	0.160769i
$263$	−130.865	−	226.666i	−0.497587	−	0.861847i	0.502409	−	0.864630i	$-0.332447\pi$
$263$	−130.865	−	226.666i	−0.497587	−	0.861847i	−0.999996	+	0.00278366i	$0.999114\pi$
$264$	−99.2606	−	57.5747i	−0.375987	−	0.218086i
$265$	95.0518	−	354.738i	0.358686	−	1.33863i
$266$	−130.388	+	34.9373i	−0.490179	+	0.131343i
$267$	−148.922	+	148.324i	−0.557761	+	0.555522i
$268$	22.5917	+	84.3133i	0.0842974	+	0.314602i
$269$	123.674	+	214.210i	0.459755	+	0.796320i	0.998948	−	0.0458628i	$-0.0146037\pi$
$269$	123.674	+	214.210i	0.459755	+	0.796320i	−0.539192	+	0.842183i	$0.681270\pi$
$270$	482.538	+	282.489i	1.78718	+	1.04626i
$271$	−81.9853	−	305.973i	−0.302529	−	1.12905i	−0.935052	−	0.354512i	$-0.884647\pi$
$271$	−81.9853	−	305.973i	−0.302529	−	1.12905i	0.632523	−	0.774542i	$-0.282020\pi$
$272$	−35.7493	−	20.6399i	−0.131431	−	0.0758819i
$273$	299.385	+	75.3396i	1.09665	+	0.275969i
$274$	−82.5912	−	143.052i	−0.301428	−	0.522088i
$275$	66.5703	+	66.5703i	0.242074	+	0.242074i
$276$	124.973	+	0.251378i	0.452801	+	0.000910790i
$277$		−	314.705i		−	1.13612i	−0.822987	−	0.568060i	$-0.807694\pi$
$277$		−	314.705i		−	1.13612i	0.822987	−	0.568060i	$-0.192306\pi$
$278$	−195.481	−	195.481i	−0.703169	−	0.703169i
$279$	−297.763	−	300.169i	−1.06725	−	1.07587i
$280$	345.298	+	92.5222i	1.23321	+	0.330437i
$281$	92.3077	+	344.497i	0.328497	+	1.22597i	0.910749	+	0.412960i	$0.135505\pi$
$281$	92.3077	+	344.497i	0.328497	+	1.22597i	−0.582252	+	0.813008i	$0.697828\pi$
$282$	−114.055	−	198.470i	−0.404451	−	0.703795i
$283$		−	245.100i		−	0.866078i	−0.901375	−	0.433039i	$-0.857441\pi$
$283$		−	245.100i		−	0.866078i	0.901375	−	0.433039i	$-0.142559\pi$
$284$	−292.552	+	292.552i	−1.03011	+	1.03011i
$285$	0.209319	−	104.063i	0.000734454	−	0.365135i
$286$	110.583	−	199.417i	0.386655	−	0.697262i
$287$	639.423			2.22795
$288$	−84.8286	+	311.566i	−0.294544	+	1.08182i
$289$	−10.5454	+	18.2651i	−0.0364891	+	0.0632010i
$290$			729.671i			2.51611i
$291$	−99.7125	+	369.160i	−0.342655	+	1.26859i
$292$	−715.503	+	191.718i	−2.45035	+	0.656570i
$293$	−78.7100	−	293.750i	−0.268635	−	1.00256i	−0.959988	−	0.280042i	$-0.909652\pi$
$293$	−78.7100	−	293.750i	−0.268635	−	1.00256i	0.691353	−	0.722517i	$-0.257015\pi$
$294$	33.5906	+	126.378i	0.114254	+	0.429858i
$295$	685.634			2.32418
$296$	238.290	+	137.577i	0.805033	+	0.464786i
$297$	143.136	+	39.2805i	0.481940	+	0.132257i
$298$			303.899i			1.01980i
$299$	1.51418	+	87.6069i	0.00506413	+	0.293000i
$300$	−159.323	+	274.679i	−0.531078	+	0.915596i
$301$	−151.142	−	151.142i	−0.502132	−	0.502132i
$302$	−607.409			−2.01129
$303$	271.472	+	157.463i	0.895946	+	0.519681i
$304$	13.0194	−	3.48855i	0.0428271	−	0.0114755i
$305$	−62.5798	+	233.551i	−0.205180	+	0.765741i
$306$	−453.520	−	123.478i	−1.48209	−	0.403523i
$307$	−28.5365	+	28.5365i	−0.0929529	+	0.0929529i	−0.752054	−	0.659101i	$-0.770937\pi$
$307$	−28.5365	+	28.5365i	−0.0929529	+	0.0929529i	0.659101	+	0.752054i	$0.270937\pi$
$308$	268.960			0.873245
$309$	165.151	+	95.7935i	0.534470	+	0.310011i
$310$	687.929	−	687.929i	2.21913	−	2.21913i
$311$	55.5350	−	32.0631i	0.178569	−	0.103097i	−0.408051	−	0.912959i	$-0.633791\pi$
$311$	55.5350	−	32.0631i	0.178569	−	0.103097i	0.586620	+	0.809862i	$0.300458\pi$
$312$	263.154	+	66.2221i	0.843442	+	0.212250i
$313$	−10.7968	+	18.7007i	−0.0344947	+	0.0597465i	−0.882757	−	0.469829i	$-0.844316\pi$
$313$	−10.7968	+	18.7007i	−0.0344947	+	0.0597465i	0.848263	+	0.529576i	$0.177649\pi$
$314$	325.933	−	87.3335i	1.03800	−	0.278132i
$315$	−462.392	−	1.86017i	−1.46791	−	0.00590531i
$316$	−758.294	+	437.801i	−2.39966	+	1.38545i
$317$	80.3280	−	21.5238i	0.253401	−	0.0678985i	−0.129882	−	0.991529i	$-0.541460\pi$
$317$	80.3280	−	21.5238i	0.253401	−	0.0678985i	0.383283	+	0.923631i	$0.374793\pi$
$318$	523.453	−	139.131i	1.64608	−	0.437519i
$319$	50.1320	+	187.095i	0.157154	+	0.586505i
$320$	−654.450	−	175.359i	−2.04516	−	0.547998i
$321$	0.482204		0.000969933i	0.00150219		3.02160e-6i
$322$	−147.427	+	85.1172i	−0.457849	+	0.264339i
$323$	22.6410	+	84.4973i	0.0700960	+	0.261602i
$324$	−4.02797	+	500.618i	−0.0124320	+	1.54512i
$325$	−194.699	−	107.967i	−0.599075	−	0.332207i
$326$	165.925	−	287.390i	0.508972	−	0.881566i
$327$	126.729	−	469.182i	0.387551	−	1.43481i
$328$	562.040			1.71354
$329$	163.939	+	94.6500i	0.498294	+	0.287690i
$330$	−89.0590	+	329.718i	−0.269876	+	0.999146i
$331$	101.187	+	101.187i	0.305700	+	0.305700i	0.843239	−	0.537539i	$-0.180646\pi$
$331$	101.187	+	101.187i	0.305700	+	0.305700i	−0.537539	+	0.843239i	$0.680646\pi$
$332$	−60.4103	−	16.1869i	−0.181959	−	0.0487557i
$333$	−343.408	−	93.4982i	−1.03126	−	0.280775i
$334$	318.185	+	551.112i	0.952649	+	1.65004i
$335$	79.3816	−	45.8310i	0.236960	−	0.136809i
$336$	−15.3846	−	57.8815i	−0.0457875	−	0.172267i
$337$	−230.487	+	133.072i	−0.683937	+	0.394871i	−0.801337	−	0.598214i	$-0.795877\pi$
$337$	−230.487	+	133.072i	−0.683937	+	0.394871i	0.117400	+	0.993085i	$0.462544\pi$
$338$	−121.481	+	525.369i	−0.359410	+	1.55435i
$339$	−103.719	−	0.208627i	−0.305957	−	0.000615420i
$340$	169.941	−	634.229i	0.499827	−	1.86538i
$341$	129.128	−	223.656i	0.378674	−	0.655883i
$342$	133.220	−	76.2019i	0.389533	−	0.222813i
$343$	197.805	+	197.805i	0.576691	+	0.576691i
$344$	−132.851	−	132.851i	−0.386194	−	0.386194i
$345$	−33.7114	−	126.833i	−0.0977142	−	0.367631i
$346$	332.098	+	88.9853i	0.959820	+	0.257183i
$347$	89.1464	−	154.406i	0.256906	−	0.444974i	−0.708505	−	0.705705i	$-0.750630\pi$
$347$	89.1464	−	154.406i	0.256906	−	0.444974i	0.965412	+	0.260731i	$0.0839635\pi$
$348$	−566.444	+	325.519i	−1.62771	+	0.935400i
$349$	−624.529	−	167.342i	−1.78948	−	0.479490i	−0.797223	−	0.603684i	$-0.793699\pi$
$349$	−624.529	−	167.342i	−1.78948	−	0.479490i	−0.992258	+	0.124194i	$0.960365\pi$
$350$		−	432.544i		−	1.23584i
$351$	−350.978	+	3.94784i	−0.999937	+	0.0112474i
$352$	−197.237			−0.560331
$353$	−56.8274	+	212.083i	−0.160984	+	0.600801i	0.837534	+	0.546385i	$0.183996\pi$
$353$	−56.8274	+	212.083i	−0.160984	+	0.600801i	−0.998518	+	0.0544160i	$0.982670\pi$
$354$	503.828	+	876.724i	1.42324	+	2.47662i
$355$	376.258	+	217.232i	1.05988	+	0.611922i
$356$	112.076	−	418.274i	0.314821	−	1.17493i
$357$	375.657	−	99.8475i	1.05226	−	0.279685i
$358$	333.511	−	333.511i	0.931594	−	0.931594i
$359$	−124.833	+	124.833i	−0.347724	+	0.347724i	−0.859261	−	0.511537i	$-0.829076\pi$
$359$	−124.833	+	124.833i	−0.347724	+	0.347724i	0.511537	+	0.859261i	$0.329076\pi$
$360$	−406.434	−	1.63506i	−1.12898	−	0.00454182i
$361$	287.898	+	166.218i	0.797503	+	0.460438i
$362$	241.761	+	64.7797i	0.667848	+	0.178949i
$363$	0.547795	−	272.337i	0.00150908	−	0.750241i
$364$	−611.422	+	175.209i	−1.67973	+	0.481344i
$365$	388.933	+	673.651i	1.06557	+	1.84562i
$366$	−344.629	+	91.6005i	−0.941609	+	0.250274i
$367$	−107.120	−	185.537i	−0.291879	−	0.505550i	0.682375	−	0.731003i	$-0.260947\pi$
$367$	−107.120	−	185.537i	−0.291879	−	0.505550i	−0.974254	+	0.225453i	$0.927614\pi$
$368$	14.7209	−	8.49910i	0.0400024	−	0.0230954i
$369$	−702.975	+	185.334i	−1.90508	+	0.502259i
$370$	211.960	−	791.044i	0.572864	−	2.13796i
$371$	−316.720	+	316.720i	−0.853693	+	0.853693i
$372$	840.937	+	227.142i	2.26058	+	0.610598i
$373$	−31.1941	+	54.0297i	−0.0836302	+	0.144852i	−0.904807	−	0.425823i	$-0.859985\pi$
$373$	−31.1941	+	54.0297i	−0.0836302	+	0.144852i	0.821177	+	0.570674i	$0.193318\pi$
$374$		−	287.101i		−	0.767649i
$375$	−148.022	−	39.9816i	−0.394725	−	0.106618i
$376$	144.099	+	83.1956i	0.383242	+	0.221265i
$377$	−235.844	−	392.663i	−0.625581	−	1.04155i
$378$	−337.404	−	592.631i	−0.892603	−	1.56781i
$379$	−70.1295	+	18.7911i	−0.185038	+	0.0495808i	−0.350148	−	0.936694i	$-0.613869\pi$
$379$	−70.1295	+	18.7911i	−0.185038	+	0.0495808i	0.165110	+	0.986275i	$0.447202\pi$
$380$	107.197	+	185.671i	0.282098	+	0.488608i
$381$	0.139428	−	69.3169i	0.000365953	−	0.181934i
$382$	−72.2101	+	269.492i	−0.189032	+	0.705476i
$383$	−411.639	+	110.298i	−1.07478	+	0.287985i	−0.752454	−	0.658645i	$-0.771130\pi$
$383$	−411.639	+	110.298i	−1.07478	+	0.287985i	−0.322322	+	0.946630i	$0.604463\pi$
$384$	−146.084	−	549.614i	−0.380428	−	1.43129i
$385$	−73.1005	−	272.815i	−0.189871	−	0.708609i
$386$	−392.077	−	679.098i	−1.01574	−	1.75932i
$387$	209.971	+	122.356i	0.542562	+	0.316165i
$388$	−203.900	−	760.965i	−0.525515	−	1.96125i
$389$	184.185	+	106.339i	0.473482	+	0.273365i	0.717696	−	0.696356i	$-0.245197\pi$
$389$	184.185	+	106.339i	0.473482	+	0.273365i	−0.244214	+	0.969721i	$0.578530\pi$
$390$	−12.3328	−	807.560i	−0.0316227	−	2.07067i
$391$	55.1600	+	95.5398i	0.141074	+	0.244347i
$392$	−67.2124	−	67.2124i	−0.171460	−	0.171460i
$393$	−76.7751	+	132.363i	−0.195356	+	0.336801i
$394$		−	642.532i		−	1.63079i
$395$	650.173	+	650.173i	1.64601	+	1.64601i
$396$	−295.691	+	77.9567i	−0.746695	+	0.196860i
$397$	128.507	+	34.4334i	0.323696	+	0.0867340i	0.417008	−	0.908903i	$-0.363079\pi$
$397$	128.507	+	34.4334i	0.323696	+	0.0867340i	−0.0933120	+	0.995637i	$0.529745\pi$
$398$	−15.8717	−	59.2340i	−0.0398786	−	0.148829i
$399$	−63.6803	+	109.787i	−0.159600	+	0.275155i
$400$			43.1903i			0.107976i
$401$	19.6751	−	19.6751i	0.0490650	−	0.0490650i	−0.682149	−	0.731214i	$-0.738954\pi$
$401$	19.6751	−	19.6751i	0.0490650	−	0.0490650i	0.731214	+	0.682149i	$0.238954\pi$
$402$	116.937	+	67.8275i	0.290888	+	0.168725i
$403$	−147.848	+	592.552i	−0.366868	+	1.47035i
$404$	−646.568			−1.60041
$405$	508.888	−	131.977i	1.25651	−	0.325870i
$406$	444.963	−	770.698i	1.09597	−	1.89827i
$407$		−	217.394i		−	0.534139i
$408$	330.195	−	87.7640i	0.809301	−	0.215108i
$409$	−426.344	+	114.238i	−1.04241	+	0.279312i	−0.739110	−	0.673585i	$-0.764754\pi$
$409$	−426.344	+	114.238i	−1.04241	+	0.279312i	−0.303295	+	0.952897i	$0.598087\pi$
$410$	−432.958	−	1615.82i	−1.05600	−	3.94103i
$411$	−149.936	−	40.4986i	−0.364808	−	0.0985368i
$412$	−393.342			−0.954715
$413$	−724.184	−	418.108i	−1.75347	−	1.01237i
$414$	137.409	−	136.308i	0.331906	−	0.329247i
$415$			65.6756i			0.158254i
$416$	448.375	−	128.486i	1.07782	−	0.308861i
$417$	−259.927	−	0.522833i	−0.623327	−	0.00125380i
$418$	66.2874	+	66.2874i	0.158582	+	0.158582i
$419$	499.565			1.19228			0.596140	−	0.802881i	$-0.296700\pi$
$419$	499.565			1.19228			0.596140	+	0.802881i	$0.296700\pi$
$420$	825.966	−	474.659i	1.96659	−	1.13014i
$421$	315.600	−	84.5648i	0.749644	−	0.200866i	0.136284	−	0.990670i	$-0.456484\pi$
$421$	315.600	−	84.5648i	0.749644	−	0.200866i	0.613360	+	0.789803i	$0.289817\pi$
$422$	−171.256	+	639.137i	−0.405821	+	1.51454i
$423$	−207.666	−	56.5404i	−0.490937	−	0.133665i
$424$	−278.391	+	278.391i	−0.656582	+	0.656582i
$425$	−280.309			−0.659550
$426$	−1.28885	+	640.753i	−0.00302547	+	1.50412i
$427$	208.521	−	208.521i	0.488339	−	0.488339i
$428$	−0.860353	+	0.496725i	−0.00201017	+	0.00116057i
$429$	−58.6456	−	206.219i	−0.136703	−	0.480698i
$430$	−279.596	+	484.275i	−0.650223	+	1.12622i
$431$	−189.636	+	50.8128i	−0.439990	+	0.117895i	−0.472012	−	0.881592i	$-0.656472\pi$
$431$	−189.636	+	50.8128i	−0.439990	+	0.117895i	0.0320217	+	0.999487i	$0.489805\pi$
$432$	33.6904	+	59.1752i	0.0779869	+	0.136980i
$433$	−607.245	+	350.593i	−1.40241	+	0.809684i	−0.994640	−	0.103399i	$-0.967028\pi$
$433$	−607.245	+	350.593i	−1.40241	+	0.809684i	−0.407774	+	0.913083i	$0.633695\pi$
$434$	−1146.12	+	307.101i	−2.64082	+	0.707606i
$435$	484.139	+	486.090i	1.11296	+	1.11745i
$436$	259.145	+	967.144i	0.594370	+	2.21822i
$437$	−34.7944	−	9.32313i	−0.0796210	−	0.0213344i
$438$	−575.600	+	992.354i	−1.31416	+	2.26565i
$439$	43.3839	−	25.0477i	0.0988243	−	0.0570562i	−0.449773	−	0.893143i	$-0.648495\pi$
$439$	43.3839	−	25.0477i	0.0988243	−	0.0570562i	0.548598	+	0.836087i	$0.315162\pi$
$440$	−64.2539	−	239.799i	−0.146032	−	0.544997i
$441$	106.230	+	61.9028i	0.240883	+	0.140369i
$442$	187.027	+	652.662i	0.423138	+	1.47661i
$443$	80.7558	−	139.873i	0.182293	−	0.315741i	−0.760368	−	0.649492i	$-0.774981\pi$
$443$	80.7558	−	139.873i	0.182293	−	0.315741i	0.942661	+	0.333752i	$0.108315\pi$
$444$	708.647	−	188.354i	1.59605	−	0.424222i
$445$	−454.731			−1.02187
$446$	−48.9838	−	28.2808i	−0.109829	−	0.0634099i
$447$	201.638	+	202.451i	0.451091	+	0.452910i
$448$	584.312	+	584.312i	1.30427	+	1.30427i
$449$	219.030	+	58.6889i	0.487817	+	0.130710i	0.494340	−	0.869269i	$-0.335410\pi$
$449$	219.030	+	58.6889i	0.487817	+	0.130710i	−0.00652317	+	0.999979i	$0.502076\pi$
$450$	125.371	+	475.534i	0.278602	+	1.05674i
$451$	−222.030	−	384.567i	−0.492306	−	0.852698i
$452$	185.057	−	106.843i	0.409418	−	0.236378i
$453$	−404.642	+	403.018i	−0.893250	+	0.889663i
$454$	868.600	−	501.486i	1.91322	−	1.10460i
$455$	343.899	+	572.565i	0.755821	+	1.25839i
$456$	−55.9738	+	96.5006i	−0.122750	+	0.211624i
$457$	154.163	−	575.345i	0.337338	−	1.25896i	−0.563975	−	0.825792i	$-0.690729\pi$
$457$	154.163	−	575.345i	0.337338	−	1.25896i	0.901313	−	0.433169i	$-0.142605\pi$
$458$	−32.0320	+	55.4811i	−0.0699389	+	0.121138i
$459$	−384.053	+	218.654i	−0.836716	+	0.476369i
$460$	191.185	+	191.185i	0.415619	+	0.415619i
$461$	340.923	+	340.923i	0.739529	+	0.739529i	0.972487	−	0.232958i	$-0.0748404\pi$
$461$	340.923	+	340.923i	0.739529	+	0.739529i	−0.232958	+	0.972487i	$0.574840\pi$
$462$	295.133	−	293.948i	0.638816	−	0.636251i
$463$	242.776	+	65.0516i	0.524354	+	0.140500i	0.511280	−	0.859414i	$-0.329172\pi$
$463$	242.776	+	65.0516i	0.524354	+	0.140500i	0.0130742	+	0.999915i	$0.495838\pi$
$464$	−44.4303	+	76.9555i	−0.0957549	+	0.165852i
$465$	1.83993	−	914.725i	0.00395684	−	1.96715i
$466$	−131.136	−	35.1377i	−0.281407	−	0.0754027i
$467$		−	196.958i		−	0.421752i	−0.977513	−	0.210876i	$-0.932368\pi$
$467$		−	196.958i		−	0.421752i	0.977513	−	0.210876i	$-0.0676317\pi$
$468$	621.407	−	369.841i	1.32779	−	0.790258i
$469$	−111.793			−0.238365
$470$	128.177	−	478.362i	0.272716	−	1.01779i
$471$	159.183	−	274.437i	0.337969	−	0.582669i
$472$	−636.544	−	367.509i	−1.34861	−	0.778621i
$473$	−38.4192	+	143.383i	−0.0812246	+	0.303134i
$474$	−353.610	+	1309.15i	−0.746012	+	2.76192i
$475$	64.7193	−	64.7193i	0.136251	−	0.136251i
$476$	−566.257	+	566.257i	−1.18962	+	1.18962i
$477$	256.399	−	439.999i	0.537524	−	0.922429i
$478$	1181.08	+	681.895i	2.47087	+	1.42656i
$479$	−908.793	−	243.510i	−1.89727	−	0.508373i	−0.997387	−	0.0722462i	$-0.976983\pi$
$479$	−908.793	−	243.510i	−1.89727	−	0.508373i	−0.899885	−	0.436126i	$-0.856350\pi$
$480$	−605.707	+	348.083i	−1.26189	+	0.725172i
$481$	141.618	+	494.200i	0.294424	+	1.02744i
$482$	−477.165	−	826.473i	−0.989968	−	1.71467i
$483$	−41.7372	+	154.522i	−0.0864125	+	0.319920i
$484$	280.538	+	485.907i	0.579625	+	1.00394i
$485$	−716.454	+	413.645i	−1.47722	+	0.852876i
$486$	542.710	+	553.737i	1.11669	+	1.13938i
$487$	−76.6653	+	286.119i	−0.157424	+	0.587513i	0.841462	+	0.540316i	$0.181695\pi$
$487$	−76.6653	+	286.119i	−0.157424	+	0.587513i	−0.998886	+	0.0471965i	$0.984971\pi$
$488$	183.286	−	183.286i	0.375586	−	0.375586i
$489$	−80.1489	−	301.545i	−0.163904	−	0.616656i
$490$	−141.454	+	245.006i	−0.288683	+	0.500013i
$491$			103.765i			0.211334i	0.994402	+	0.105667i	$0.0336977\pi$
$491$			103.765i			0.211334i	−0.994402	+	0.105667i	$0.966302\pi$
$492$	1061.21	−	1056.95i	2.15694	−	2.14828i
$493$	−499.449	−	288.357i	−1.01308	−	0.584902i
$494$	−193.872	−	107.508i	−0.392453	−	0.217628i
$495$	159.440	+	278.742i	0.322101	+	0.563115i
$496$	114.442	−	30.6646i	0.230729	−	0.0618237i
$497$	−264.942	−	458.893i	−0.533083	−	0.923327i
$498$	−83.9798	+	48.2608i	−0.168634	+	0.0969092i
$499$	112.532	−	419.975i	0.225515	−	0.841633i	−0.756683	−	0.653782i	$-0.773181\pi$
$499$	112.532	−	419.975i	0.225515	−	0.841633i	0.982198	−	0.187851i	$-0.0601522\pi$
$500$	305.123	−	81.7575i	0.610246	−	0.163515i
$501$	577.632	+	156.022i	1.15296	+	0.311421i
$502$	−148.369	−	553.721i	−0.295556	−	1.10303i
$503$	−391.281	−	677.719i	−0.777895	−	1.34735i	−0.933153	−	0.359480i	$-0.882954\pi$
$503$	−391.281	−	677.719i	−0.777895	−	1.34735i	0.155258	−	0.987874i	$-0.450379\pi$
$504$	428.289	+	249.576i	0.849780	+	0.495190i
$505$	175.730	+	655.835i	0.347981	+	1.29868i
$506$	102.384	+	59.1113i	0.202339	+	0.116821i
$507$	267.656	+	430.592i	0.527921	+	0.849293i
$508$	71.4043	+	123.676i	0.140560	+	0.243456i
$509$	−452.358	−	452.358i	−0.888719	−	0.888719i	0.105681	−	0.994400i	$-0.466298\pi$
$509$	−452.358	−	452.358i	−0.888719	−	0.888719i	−0.994400	+	0.105681i	$0.966298\pi$
$510$	−506.675	−	881.677i	−0.993480	−	1.72878i
$511$		−	948.704i		−	1.85656i
$512$	−113.615	−	113.615i	−0.221905	−	0.221905i
$513$	38.1882	−	139.156i	0.0744410	−	0.271259i
$514$	−701.928	−	188.081i	−1.36562	−	0.365917i
$515$	106.906	+	398.980i	0.207585	+	0.774719i
$516$	−500.675	−	1.00709i	−0.970301	−	0.00195172i
$517$		−	131.463i		−	0.254281i
$518$	−706.266	+	706.266i	−1.36345	+	1.36345i
$519$	280.278	−	161.068i	0.540035	−	0.310342i
$520$	302.280	+	503.274i	0.581308	+	0.967835i
$521$	497.305			0.954521			0.477260	−	0.878762i	$-0.341630\pi$
$521$	497.305			0.954521			0.477260	+	0.878762i	$0.341630\pi$
$522$	−265.804	+	976.267i	−0.509203	+	1.87024i
$523$	−38.3012	+	66.3397i	−0.0732337	+	0.126845i	−0.900317	−	0.435235i	$-0.856665\pi$
$523$	−38.3012	+	66.3397i	−0.0732337	+	0.126845i	0.827083	+	0.562080i	$0.189999\pi$
$524$		−	315.250i		−	0.601622i
$525$	−286.994	−	288.151i	−0.546656	−	0.548859i
$526$	806.654	−	216.142i	1.53356	−	0.410917i
$527$	199.016	+	742.738i	0.377639	+	1.40937i
$528$	−29.4695	+	29.3512i	−0.0558135	+	0.0555894i
$529$	483.572			0.914125
$530$	1014.81	+	585.898i	1.91473	+	1.10547i
$531$	917.348	+	249.762i	1.72758	+	0.470362i
$532$		−	261.481i		−	0.491506i
$533$	755.257	+	729.593i	1.41699	+	1.36884i
$534$	−334.152	−	581.467i	−0.625754	−	1.08889i
$535$	0.737680	+	0.737680i	0.00137884	+	0.00137884i
$536$	−98.2642			−0.183329
$537$	0.892006	−	443.462i	0.00166109	−	0.825815i
$538$	−762.327	+	204.265i	−1.41696	+	0.379674i
$539$	−19.4372	+	72.5407i	−0.0360617	+	0.134584i
$540$	−770.481	+	761.238i	−1.42682	+	1.40970i
$541$	425.851	−	425.851i	0.787155	−	0.787155i	−0.193872	−	0.981027i	$-0.562105\pi$
$541$	425.851	−	425.851i	0.787155	−	0.787155i	0.981027	+	0.193872i	$0.0621047\pi$
$542$	1010.71			1.86479
$543$	204.037	−	117.254i	0.375759	−	0.215938i
$544$	415.254	−	415.254i	0.763335	−	0.763335i
$545$	910.573	−	525.720i	1.67078	−	0.964623i
$546$	−479.434	+	860.487i	−0.878084	+	1.57598i
$547$	−287.949	+	498.743i	−0.526415	+	0.911778i	0.473111	+	0.881003i	$0.343131\pi$
$547$	−287.949	+	498.743i	−0.526415	+	0.911778i	−0.999526	+	0.0307753i	$0.990202\pi$
$548$	309.069	−	82.8147i	0.563994	−	0.151122i
$549$	−168.807	+	289.684i	−0.307481	+	0.527658i
$550$	−260.144	+	150.194i	−0.472990	+	0.273081i
$551$	181.893	−	48.7380i	0.330114	−	0.0884538i
$552$	−36.6862	+	135.821i	−0.0664606	+	0.246053i
$553$	−290.246	−	1083.21i	−0.524857	−	1.95879i
$554$	969.919	+	259.889i	1.75076	+	0.469114i
$555$	−383.657	−	667.611i	−0.691274	−	1.20290i
$556$	463.765	−	267.755i	0.834110	−	0.481573i
$557$	31.6421	+	118.090i	0.0568081	+	0.212011i	0.988495	−	0.151250i	$-0.0483300\pi$
$557$	31.6421	+	118.090i	0.0568081	+	0.212011i	−0.931687	+	0.363261i	$0.881663\pi$
$558$	1171.02	−	669.820i	2.09860	−	1.20039i
$559$	−6.06620	−	350.977i	−0.0108519	−	0.627866i
$560$	64.7865	−	112.213i	0.115690	−	0.200381i
$561$	−190.492	−	191.260i	−0.339558	−	0.340927i
$562$	−1137.97			−2.02485
$563$	708.691	+	409.163i	1.25878	+	0.726754i	0.972836	−	0.231493i	$-0.0743612\pi$
$563$	708.691	+	409.163i	1.25878	+	0.726754i	0.285939	+	0.958248i	$0.407694\pi$
$564$	428.534	−	113.902i	0.759813	−	0.201954i
$565$	−158.671	−	158.671i	−0.280833	−	0.280833i
$566$	755.397	+	202.408i	1.33462	+	0.357611i
$567$	−617.983	−	170.929i	−1.08992	−	0.301462i
$568$	−232.879	−	403.359i	−0.409999	−	0.710138i
$569$	−371.328	+	214.386i	−0.652597	+	0.376777i	−0.789451	−	0.613814i	$-0.789634\pi$
$569$	−371.328	+	214.386i	−0.652597	+	0.376777i	0.136853	+	0.990591i	$0.456301\pi$
$570$	320.550	+	86.5826i	0.562369	+	0.151899i
$571$	660.431	−	381.300i	1.15662	−	0.667776i	0.206130	−	0.978525i	$-0.433913\pi$
$571$	660.431	−	381.300i	1.15662	−	0.667776i	0.950492	+	0.310748i	$0.100580\pi$
$572$	317.683	+	306.888i	0.555389	+	0.536517i
$573$	130.704	+	227.441i	0.228104	+	0.396930i
$574$	−528.047	+	1970.70i	−0.919942	+	3.43327i
$575$	57.7129	−	99.9617i	0.100370	−	0.173846i
$576$	−811.746	−	473.026i	−1.40928	−	0.821226i
$577$	−527.500	−	527.500i	−0.914211	−	0.914211i	0.0823891	−	0.996600i	$-0.473745\pi$
$577$	−527.500	−	527.500i	−0.914211	−	0.914211i	−0.996600	+	0.0823891i	$0.973745\pi$
$578$	−47.5844	−	47.5844i	−0.0823259	−	0.0823259i
$579$	−711.777	−	192.255i	−1.22932	−	0.332047i
$580$	−1365.27	−	365.823i	−2.35391	−	0.630729i
$581$	40.0498	−	69.3683i	0.0689326	−	0.119395i
$582$	−1055.41	−	612.173i	−1.81341	−	1.05184i
$583$	300.461	+	80.5082i	0.515370	+	0.138093i
$584$		−	833.893i		−	1.42790i
$585$	−544.034	−	529.795i	−0.929973	−	0.905633i
$586$	970.335			1.65586
$587$	−17.4441	+	65.1024i	−0.0297174	+	0.110907i	−0.979191	−	0.202939i	$-0.934951\pi$
$587$	−17.4441	+	65.1024i	−0.0297174	+	0.110907i	0.949474	+	0.313846i	$0.101617\pi$
$588$	−253.304	−	0.509510i	−0.430789	−	0.000866514i
$589$	−217.437	−	125.537i	−0.369163	−	0.213137i
$590$	−566.209	+	2113.12i	−0.959676	+	3.58156i
$591$	−426.322	−	428.040i	−0.721357	−	0.724264i
$592$	70.5219	−	70.5219i	0.119125	−	0.119125i
$593$	487.567	−	487.567i	0.822205	−	0.822205i	−0.164219	−	0.986424i	$-0.552510\pi$
$593$	487.567	−	487.567i	0.822205	−	0.822205i	0.986424	+	0.164219i	$0.0525105\pi$
$594$	−239.267	+	408.706i	−0.402806	+	0.688058i
$595$	728.276	+	420.470i	1.22399	+	0.706673i
$596$	−568.618	−	152.361i	−0.954057	−	0.255639i
$597$	−49.8753	−	28.9294i	−0.0835431	−	0.0484580i
$598$	−271.255	−	67.6807i	−0.453603	−	0.113178i
$599$	−481.068	−	833.235i	−0.803119	−	1.39104i	−0.917554	−	0.397612i	$-0.869839\pi$
$599$	−481.068	−	833.235i	−0.803119	−	1.39104i	0.114435	−	0.993431i	$-0.463494\pi$
$600$	−252.262	−	253.279i	−0.420437	−	0.422132i
$601$	270.547	+	468.601i	0.450162	+	0.779703i	0.998396	−	0.0566221i	$-0.0180330\pi$
$601$	270.547	+	468.601i	0.450162	+	0.779703i	−0.548234	+	0.836325i	$0.684700\pi$
$602$	590.634	−	341.002i	0.981119	−	0.566449i
$603$	122.904	−	32.4028i	0.203822	−	0.0537360i
$604$	304.526	−	1136.51i	0.504183	−	1.88164i
$605$	416.624	−	416.624i	0.688635	−	0.688635i
$606$	−709.487	+	706.639i	−1.17077	+	1.16607i
$607$	−501.663	+	868.907i	−0.826464	+	1.43148i	0.0743318	+	0.997234i	$0.476318\pi$
$607$	−501.663	+	868.907i	−0.826464	+	1.43148i	−0.900796	+	0.434244i	$0.857016\pi$
$608$			191.752i			0.315382i
$609$	−214.936	−	808.655i	−0.352933	−	1.32784i
$610$	−668.123	−	385.741i	−1.09528	−	0.632363i
$611$	85.6394	+	298.853i	0.140163	+	0.489122i
$612$	458.410	−	786.664i	0.749036	−	1.28540i
$613$	−818.083	+	219.205i	−1.33456	+	0.357593i	−0.854412	−	0.519596i	$-0.826082\pi$
$613$	−818.083	+	219.205i	−1.33456	+	0.357593i	−0.480144	+	0.877190i	$0.659416\pi$
$614$	−64.3835	−	111.516i	−0.104859	−	0.181621i
$615$	−1360.53	−	789.155i	−2.21224	−	1.28318i
$616$	−78.3657	+	292.465i	−0.127217	+	0.474780i
$617$	189.234	−	50.7050i	0.306700	−	0.0821800i	−0.102187	−	0.994765i	$-0.532584\pi$
$617$	189.234	−	50.7050i	0.306700	−	0.0821800i	0.408886	+	0.912585i	$0.365917\pi$
$618$	−431.620	+	429.887i	−0.698414	+	0.695610i
$619$	156.740	+	584.961i	0.253215	+	0.945010i	0.969075	+	0.246767i	$0.0793681\pi$
$619$	156.740	+	584.961i	0.253215	+	0.945010i	−0.715860	+	0.698244i	$0.753965\pi$
$620$	942.271	+	1632.06i	1.51979	+	2.63236i
$621$	1.09813	−	181.977i	0.00176832	−	0.293038i
$622$	52.9567	+	197.637i	0.0851393	+	0.317744i
$623$	480.299	+	277.301i	0.770945	+	0.445105i
$624$	47.8723	−	85.9211i	0.0767185	−	0.137694i
$625$	−379.927	−	658.054i	−0.607884	−	1.05289i
$626$	−48.7191	−	48.7191i	−0.0778261	−	0.0778261i
$627$	88.1410	+	0.177292i	0.140576	+	0.000282762i
$628$			653.630i			1.04081i
$629$	457.694	+	457.694i	0.727653	+	0.727653i
$630$	387.585	−	1423.55i	0.615214	−	2.25961i
$631$	−477.116	−	127.843i	−0.756127	−	0.202604i	−0.139893	−	0.990167i	$-0.544676\pi$
$631$	−477.116	−	127.843i	−0.756127	−	0.202604i	−0.616234	+	0.787563i	$0.711342\pi$
$632$	−255.121	−	952.124i	−0.403672	−	1.50652i
$633$	309.982	+	539.408i	0.489704	+	0.852145i
$634$			265.345i			0.418526i
$635$	106.042	−	106.042i	0.166995	−	0.166995i
$636$	−2.11037	+	1049.17i	−0.00331819	+	1.64964i
$637$	−3.06904	−	177.568i	−0.00481795	−	0.278756i
$638$	−618.026			−0.968693
$639$	424.283	+	427.710i	0.663979	+	0.669343i
$640$	615.180	−	1065.52i	0.961219	−	1.66488i
$641$			205.313i			0.320301i	0.987093	+	0.160151i	$0.0511980\pi$
$641$			205.313i			0.320301i	−0.987093	+	0.160151i	$0.948802\pi$
$642$	−0.401202	+	1.48535i	−0.000624925	+	0.00231363i
$643$	−1032.98	+	276.787i	−1.60651	+	0.430462i	−0.947000	−	0.321235i	$-0.895902\pi$
$643$	−1032.98	+	276.787i	−1.60651	+	0.430462i	−0.659508	+	0.751697i	$0.729235\pi$
$644$	−85.3475	−	318.521i	−0.132527	−	0.494598i
$645$	135.057	+	508.125i	0.209391	+	0.787791i
$646$	−279.118			−0.432071
$647$	305.804	+	176.556i	0.472649	+	0.272884i	0.717348	−	0.696715i	$-0.245356\pi$
$647$	305.804	+	176.556i	0.472649	+	0.272884i	−0.244699	+	0.969599i	$0.578689\pi$
$648$	−543.195	−	150.243i	−0.838264	−	0.231857i
$649$			580.727i			0.894802i
$650$	493.541	−	510.901i	0.759293	−	0.786002i
$651$	−559.755	+	965.035i	−0.859838	+	1.48239i
$652$	454.542	+	454.542i	0.697150	+	0.697150i
$653$	−102.524			−0.157004			−0.0785022	−	0.996914i	$-0.525014\pi$
$653$	−102.524			−0.157004			−0.0785022	+	0.996914i	$0.525014\pi$
$654$	1341.36	+	778.038i	2.05101	+	1.18966i
$655$	−319.769	+	85.6817i	−0.488196	+	0.130812i
$656$	52.7264	−	196.778i	0.0803756	−	0.299966i
$657$	274.978	+	1043.00i	0.418535	+	1.58751i
$658$	−427.095	+	427.095i	−0.649080	+	0.649080i
$659$	−1040.00			−1.57815			−0.789074	−	0.614298i	$-0.789439\pi$
$659$	−1040.00			−1.57815			−0.789074	+	0.614298i	$0.789439\pi$
$660$	−572.278	−	331.941i	−0.867087	−	0.502941i
$661$	52.6156	−	52.6156i	0.0796000	−	0.0796000i	−0.666186	−	0.745786i	$-0.732074\pi$
$661$	52.6156	−	52.6156i	0.0796000	−	0.0796000i	0.745786	+	0.666186i	$0.232074\pi$
$662$	−395.419	+	228.295i	−0.597310	+	0.344857i
$663$	557.636	+	310.696i	0.841080	+	0.468621i
$664$	35.2030	−	60.9734i	0.0530166	−	0.0918275i
$665$	−265.229	+	71.0678i	−0.398840	+	0.106869i
$666$	571.754	−	981.170i	0.858489	−	1.47323i
$667$	205.663	−	118.740i	0.308341	−	0.178021i
$668$	−1190.70	+	319.046i	−1.78248	+	0.477613i
$669$	−51.3963	+	13.6609i	−0.0768256	+	0.0204198i
$670$	75.6962	+	282.502i	0.112979	+	0.421645i
$671$	−197.816	−	53.0046i	−0.294808	−	0.0789935i
$672$	852.029	+	1.71382i	1.26790	+	0.00255033i
$673$	747.116	−	431.347i	1.11013	−	0.640932i	0.171265	−	0.985225i	$-0.445215\pi$
$673$	747.116	−	431.347i	1.11013	−	0.640932i	0.938862	+	0.344293i	$0.111881\pi$
$674$	−219.786	−	820.252i	−0.326092	−	1.21699i
$675$	399.038	+	233.606i	0.591167	+	0.346083i
$676$	−922.100	−	490.695i	−1.36405	−	0.725880i
$677$	−77.4425	+	134.134i	−0.114391	+	0.198131i	−0.917536	−	0.397653i	$-0.869825\pi$
$677$	−77.4425	+	134.134i	−0.114391	+	0.198131i	0.803145	+	0.595783i	$0.203158\pi$
$678$	86.2963	−	319.490i	0.127281	−	0.471225i
$679$	1008.98			1.48598
$680$	640.141	+	369.585i	0.941383	+	0.543508i
$681$	245.904	−	910.397i	0.361093	−	1.33685i
$682$	582.671	+	582.671i	0.854356	+	0.854356i
$683$	−171.212	−	45.8762i	−0.250677	−	0.0671686i	0.131293	−	0.991344i	$-0.458087\pi$
$683$	−171.212	−	45.8762i	−0.250677	−	0.0671686i	−0.381969	+	0.924175i	$0.624754\pi$
$684$	75.7890	+	287.469i	0.110803	+	0.420277i
$685$	−168.003	−	290.991i	−0.245261	−	0.424804i
$686$	−772.985	+	446.283i	−1.12680	+	0.650558i
$687$	15.4728	+	58.2136i	0.0225223	+	0.0847359i
$688$	−58.9758	+	34.0497i	−0.0857206	+	0.0494908i
$689$	−735.479	+	12.7118i	−1.06746	+	0.0184497i
$690$	418.737	+	0.842272i	0.606865	+	0.00122068i
$691$	−91.2918	+	340.706i	−0.132115	+	0.493062i	−0.999993	−	0.00371639i	$-0.998817\pi$
$691$	−91.2918	+	340.706i	−0.132115	+	0.493062i	0.867878	+	0.496778i	$0.165484\pi$
$692$	−332.996	+	576.767i	−0.481209	+	0.833478i
$693$	1.57555	−	391.643i	0.00227353	−	0.565141i
$694$	402.260	+	402.260i	0.579626	+	0.579626i
$695$	−397.639	−	397.639i	−0.572143	−	0.572143i
$696$	−188.925	−	710.792i	−0.271444	−	1.02125i
$697$	1277.11	+	342.199i	1.83229	+	0.490960i
$698$	1031.49	−	1786.60i	1.47779	−	2.55960i
$699$	−110.673	+	63.6009i	−0.158331	+	0.0909884i
$700$	809.322	+	216.857i	1.15617	+	0.309796i
$701$			921.277i			1.31423i	0.753789	+	0.657117i	$0.228224\pi$
$701$			921.277i			1.31423i	−0.753789	+	0.657117i	$0.771776\pi$
$702$	277.677	−	1084.97i	0.395551	−	1.54554i
$703$	−211.350			−0.300640
$704$	148.528	−	554.315i	0.210978	−	0.787379i
$705$	−232.006	−	403.719i	−0.329086	−	0.572651i
$706$	−606.709	−	350.283i	−0.859361	−	0.496152i
$707$	214.325	−	799.873i	0.303148	−	1.13136i
$708$	−1893.01	+	503.152i	−2.67375	+	0.710667i
$709$	21.9936	−	21.9936i	0.0310206	−	0.0310206i	−0.691426	−	0.722447i	$-0.743017\pi$
$709$	21.9936	−	21.9936i	0.0310206	−	0.0310206i	0.722447	+	0.691426i	$0.243017\pi$
$710$	−980.230	+	980.230i	−1.38061	+	1.38061i
$711$	633.058	+	1106.75i	0.890377	+	1.55661i
$712$	422.173	+	243.742i	0.592940	+	0.342334i
$713$	−305.845	−	81.9510i	−0.428955	−	0.114938i
$714$	−2.49467	+	1240.23i	−0.00349393	+	1.73701i
$715$	224.944	−	405.645i	0.314606	−	0.567336i
$716$	456.817	+	791.230i	0.638012	+	1.10507i
$717$	1239.25	−	329.385i	1.72838	−	0.459393i
$718$	−281.645	−	487.823i	−0.392263	−	0.679420i
$719$	812.194	−	468.921i	1.12962	−	0.652184i	0.185778	−	0.982592i	$-0.440519\pi$
$719$	812.194	−	468.921i	1.12962	−	0.652184i	0.943838	+	0.330407i	$0.107186\pi$
$720$	−38.7010	+	142.144i	−0.0537514	+	0.197423i
$721$	130.386	−	486.607i	0.180840	−	0.674905i
$722$	−750.036	+	750.036i	−1.03883	+	1.03883i
$723$	−866.243	−	233.978i	−1.19812	−	0.323621i
$724$	−242.415	+	419.876i	−0.334828	+	0.579939i
$725$			603.406i			0.832284i
$726$	838.890	+	226.589i	1.15550	+	0.312107i
$727$	−1178.78	−	680.570i	−1.62143	−	0.936135i	−0.986537	−	0.163538i	$-0.947709\pi$
$727$	−1178.78	−	680.570i	−1.62143	−	0.936135i	−0.634897	−	0.772597i	$-0.718957\pi$
$728$	−12.3735	−	715.906i	−0.0169966	−	0.983387i
$729$	728.947	+	8.79789i	0.999927	+	0.0120684i
$730$	−2397.38	+	642.375i	−3.28408	+	0.879966i
$731$	−220.986	−	382.758i	−0.302306	−	0.523609i
$732$	1.38942	−	690.751i	0.00189811	−	0.943649i
$733$	−81.8559	+	305.490i	−0.111672	+	0.416767i	−0.999016	−	0.0443408i	$-0.985881\pi$
$733$	−81.8559	+	305.490i	−0.111672	+	0.416767i	0.887344	+	0.461108i	$0.152548\pi$
$734$	660.285	−	176.923i	0.899571	−	0.241039i
$735$	68.3286	+	257.073i	0.0929641	+	0.349759i
$736$	62.5880	+	233.582i	0.0850381	+	0.317366i
$737$	38.8185	+	67.2357i	0.0526710	+	0.0912289i
$738$	9.33166	−	2319.62i	0.0126445	−	3.14311i
$739$	177.782	+	663.491i	0.240571	+	0.897823i	0.975558	+	0.219742i	$0.0705216\pi$
$739$	177.782	+	663.491i	0.240571	+	0.897823i	−0.734987	+	0.678081i	$0.762812\pi$
$740$	1373.84	+	793.185i	1.85654	+	1.07187i
$741$	−200.485	+	57.0149i	−0.270560	+	0.0769432i
$742$	−714.577	−	1237.68i	−0.963041	−	1.66804i
$743$	69.7919	+	69.7919i	0.0939325	+	0.0939325i	0.752512	−	0.658579i	$-0.228842\pi$
$743$	69.7919	+	69.7919i	0.0939325	+	0.0939325i	−0.658579	+	0.752512i	$0.728842\pi$
$744$	−492.014	+	848.248i	−0.661309	+	1.14012i
$745$			618.178i			0.829769i
$746$	−140.759	−	140.759i	−0.188685	−	0.188685i
$747$	−23.9243	+	87.8711i	−0.0320271	+	0.117632i
$748$	537.187	+	143.939i	0.718165	+	0.192432i
$749$	−0.329310	−	1.22900i	−0.000439667	−	0.00164086i
$750$	245.462	−	423.185i	0.327283	−	0.564247i
$751$			20.7896i			0.0276825i	0.999904	+	0.0138413i	$0.00440595\pi$
$751$			20.7896i			0.0276825i	−0.999904	+	0.0138413i	$0.995594\pi$
$752$	42.6461	−	42.6461i	0.0567103	−	0.0567103i
$753$	−466.236	−	270.433i	−0.619171	−	0.359141i
$754$	1404.95	−	402.602i	1.86333	−	0.533955i
$755$	−1235.56			−1.63651
$756$	1278.02	−	334.191i	1.69050	−	0.442051i
$757$	83.5383	−	144.693i	0.110354	−	0.191140i	−0.805559	−	0.592516i	$-0.798135\pi$
$757$	83.5383	−	144.693i	0.110354	−	0.191140i	0.915913	+	0.401376i	$0.131468\pi$
$758$		−	231.657i		−	0.305616i
$759$	107.426	−	28.5533i	0.141537	−	0.0376196i
$760$	−233.131	+	62.4673i	−0.306751	+	0.0821938i
$761$	−177.383	−	662.004i	−0.233093	−	0.869913i	−0.978999	−	0.203863i	$-0.934650\pi$
$761$	−177.383	−	662.004i	−0.233093	−	0.869913i	0.745907	−	0.666050i	$-0.232016\pi$
$762$	213.519	+	57.6729i	0.280209	+	0.0756862i
$763$	−1282.36			−1.68068
$764$	−468.037	−	270.221i	−0.612613	−	0.353693i
$765$	−922.531	−	251.173i	−1.20592	−	0.328331i
$766$		−	1359.76i		−	1.77514i
$767$	−378.304	−	1320.16i	−0.493226	−	1.72120i
$768$	561.867	+	1.13017i	0.731597	+	0.00147158i
$769$	212.632	+	212.632i	0.276505	+	0.276505i	0.831712	−	0.555207i	$-0.187361\pi$
$769$	212.632	+	212.632i	0.276505	+	0.276505i	−0.555207	+	0.831712i	$0.687361\pi$
$770$	901.181			1.17037
$771$	−592.401	+	340.436i	−0.768354	+	0.441551i
$772$	1467.21	−	393.138i	1.90053	−	0.509247i
$773$	129.778	−	484.339i	0.167889	−	0.626571i	−0.829765	−	0.558113i	$-0.811525\pi$
$773$	129.778	−	484.339i	0.167889	−	0.626571i	0.997654	−	0.0684578i	$-0.0218079\pi$
$774$	−550.499	+	546.087i	−0.711238	+	0.705539i
$775$	568.887	−	568.887i	0.734048	−	0.734048i
$776$	886.877			1.14288
$777$	−1.88898	+	939.108i	−0.00243112	+	1.20863i
$778$	−479.839	+	479.839i	−0.616760	+	0.616760i
$779$	−373.874	+	215.856i	−0.479941	+	0.277094i
$780$	1517.19	+	381.797i	1.94511	+	0.489483i
$781$	−183.994	+	318.688i	−0.235588	+	0.408051i
$782$	−340.005	+	91.1042i	−0.434790	+	0.116502i
$783$	470.684	+	826.729i	0.601128	+	1.05585i
$784$	−29.8373	+	17.2266i	−0.0380578	+	0.0219727i
$785$	662.999	−	177.650i	0.844585	−	0.226306i
$786$	−344.539	−	345.928i	−0.438345	−	0.440112i
$787$	296.540	+	1106.70i	0.376798	+	1.40623i	0.850700	+	0.525651i	$0.176178\pi$
$787$	296.540	+	1106.70i	0.376798	+	1.40623i	−0.473903	+	0.880577i	$0.657155\pi$
$788$	1202.23	+	322.135i	1.52567	+	0.408801i
$789$	393.963	−	679.206i	0.499320	−	0.860844i
$790$	−2540.75	+	1466.90i	−3.21614	+	1.85684i
$791$	70.8329	+	264.352i	0.0895485	+	0.334200i
$792$	1.38488	−	344.247i	0.00174859	−	0.434655i
$793$	484.221	−	8.36915i	0.610619	−	0.0105538i
$794$	−212.247	+	367.623i	−0.267314	+	0.463001i
$795$	1064.79	−	283.014i	1.33935	−	0.355993i
$796$	118.788			0.149232
$797$	−234.506	−	135.392i	−0.294236	−	0.169877i	0.345615	−	0.938377i	$-0.387670\pi$
$797$	−234.506	−	135.392i	−0.294236	−	0.169877i	−0.639851	+	0.768499i	$0.721004\pi$
$798$	−285.775	−	286.927i	−0.358113	−	0.359557i
$799$	276.777	+	276.777i	0.346405	+	0.346405i
$800$	−593.502	−	159.028i	−0.741877	−	0.198785i
$801$	−608.410	−	165.649i	−0.759563	−	0.206803i
$802$	44.3904	+	76.8865i	0.0553497	+	0.0958684i
$803$	−570.578	+	329.423i	−0.710558	+	0.410241i
$804$	−185.537	+	184.792i	−0.230767	+	0.229841i
$805$	−299.890	+	173.142i	−0.372534	+	0.215083i
$806$	−1704.15	−	945.007i	−2.11433	−	1.17246i
$807$	−372.315	+	641.883i	−0.461356	+	0.795393i
$808$	188.388	−	703.073i	0.233153	−	0.870140i
$809$	−615.609	+	1066.27i	−0.760951	+	1.31801i	0.181410	+	0.983408i	$0.441934\pi$
$809$	−615.609	+	1066.27i	−0.760951	+	1.31801i	−0.942361	+	0.334598i	$0.891400\pi$
$810$	−13.4962	+	1677.38i	−0.0166620	+	2.07084i
$811$	−249.991	−	249.991i	−0.308251	−	0.308251i	0.535980	−	0.844231i	$-0.319942\pi$
$811$	−249.991	−	249.991i	−0.308251	−	0.308251i	−0.844231	+	0.535980i	$0.819942\pi$
$812$	1218.95	+	1218.95i	1.50117	+	1.50117i
$813$	673.315	−	670.611i	0.828185	−	0.824860i
$814$	670.009	+	179.528i	0.823107	+	0.220551i
$815$	337.517	−	584.597i	0.414132	−	0.717297i
$816$	0.249097	−	123.839i	0.000305266	−	0.151763i
$817$	139.396	+	37.3510i	0.170619	+	0.0457172i
$818$		−	1408.33i		−	1.72167i
$819$	251.547	+	891.343i	0.307140	+	1.08833i
$820$	3240.39			3.95169
$821$	146.661	−	547.347i	0.178637	−	0.666684i	−0.817266	−	0.576261i	$-0.804511\pi$
$821$	146.661	−	547.347i	0.178637	−	0.666684i	0.995903	−	0.0904233i	$-0.0288220\pi$
$822$	248.636	−	428.657i	0.302477	−	0.521481i
$823$	958.015	+	553.110i	1.16405	+	0.672066i	0.952272	−	0.305251i	$-0.0987405\pi$
$823$	958.015	+	553.110i	1.16405	+	0.672066i	0.211780	+	0.977317i	$0.432074\pi$
$824$	114.607	−	427.718i	0.139086	−	0.519075i
$825$	−73.6478	+	272.663i	−0.0892701	+	0.330500i
$826$	1886.65	−	1886.65i	2.28408	−	2.28408i
$827$	−251.711	+	251.711i	−0.304367	+	0.304367i	−0.842720	−	0.538353i	$-0.819047\pi$
$827$	−251.711	+	251.711i	−0.304367	+	0.304367i	0.538353	+	0.842720i	$0.319047\pi$
$828$	186.152	+	325.441i	0.224821	+	0.393045i
$829$	720.778	+	416.141i	0.869454	+	0.501980i	0.867167	−	0.498018i	$-0.165939\pi$
$829$	720.778	+	416.141i	0.869454	+	0.501980i	0.00228740	+	0.999997i	$0.499272\pi$
$830$	−202.412	−	54.2361i	−0.243870	−	0.0653447i
$831$	818.575	−	470.412i	0.985049	−	0.566079i
$832$	23.4518	+	1356.87i	0.0281873	+	1.63086i
$833$	−111.802	−	193.647i	−0.134216	−	0.232469i
$834$	216.264	−	800.663i	0.259309	−	0.960028i
$835$	647.237	+	1121.05i	0.775135	+	1.34257i
$836$	−157.262	+	90.7953i	−0.188113	+	0.108607i
$837$	335.677	−	1223.19i	0.401048	−	1.46140i
$838$	−412.550	+	1539.66i	−0.492303	+	1.83730i
$839$	559.098	−	559.098i	0.666386	−	0.666386i	−0.290492	−	0.956878i	$-0.593819\pi$
$839$	559.098	−	559.098i	0.666386	−	0.666386i	0.956878	+	0.290492i	$0.0938189\pi$
$840$	275.483	+	1036.45i	0.327955	+	1.23387i
$841$	−200.230	+	346.808i	−0.238085	+	0.412376i
$842$			1042.51i			1.23814i
$843$	−758.088	+	755.045i	−0.899274	+	0.895664i
$844$	−1110.01	−	640.867i	−1.31518	−	0.759321i
$845$	−247.110	+	1068.68i	−0.292438	+	1.26471i
$846$	345.752	−	593.335i	0.408690	−	0.701341i
$847$	−694.112	+	185.987i	−0.819495	+	0.219583i
$848$	71.3517	+	123.585i	0.0841412	+	0.145737i
$849$	637.527	−	366.368i	0.750915	−	0.431529i
$850$	231.484	−	863.911i	0.272334	−	1.01637i
$851$	−257.454	+	68.9846i	−0.302531	+	0.0810630i
$852$	−1198.25	−	323.655i	−1.40640	−	0.379877i
$853$	−346.983	−	1294.96i	−0.406780	−	1.51812i	−0.800750	−	0.598999i	$-0.795565\pi$
$853$	−346.983	−	1294.96i	−0.406780	−	1.51812i	0.393970	−	0.919123i	$-0.371101\pi$
$854$	470.460	+	814.860i	0.550890	+	0.954169i
$855$	270.991	−	155.007i	0.316949	−	0.181294i
$856$	−0.289458	−	1.08027i	−0.000338151	−	0.00126200i
$857$	1037.24	+	598.850i	1.21031	+	0.698774i	0.962827	−	0.270117i	$-0.0870625\pi$
$857$	1037.24	+	598.850i	1.21031	+	0.698774i	0.247485	+	0.968892i	$0.420396\pi$
$858$	683.997	−	10.4458i	0.797200	−	0.0121746i
$859$	127.231	+	220.371i	0.148116	+	0.256544i	0.930531	−	0.366213i	$-0.119346\pi$
$859$	127.231	+	220.371i	0.148116	+	0.256544i	−0.782415	+	0.622757i	$0.786013\pi$
$860$	−765.938	−	765.938i	−0.890625	−	0.890625i
$861$	955.791	+	1663.19i	1.11009	+	1.93170i
$862$		−	626.419i		−	0.726704i
$863$	−219.545	−	219.545i	−0.254397	−	0.254397i	0.568374	−	0.822771i	$-0.307573\pi$
$863$	−219.545	−	219.545i	−0.254397	−	0.254397i	−0.822771	+	0.568374i	$0.807573\pi$
$864$	−937.209	+	245.073i	−1.08473	+	0.283649i
$865$	675.539	+	181.010i	0.780970	+	0.209260i
$866$	−579.052	−	2161.05i	−0.668652	−	2.49544i
$867$	−63.2720	−	0.127269i	−0.0729781	−	0.000146792i
$868$		−	2298.44i		−	2.64797i
$869$	−550.692	+	550.692i	−0.633707	+	0.633707i
$870$	−1897.94	+	1090.69i	−2.18154	+	1.25367i
$871$	−132.045	−	127.558i	−0.151602	−	0.146450i
$872$	−1127.17			−1.29263
$873$	−1109.27	+	292.449i	−1.27064	+	0.334993i
$874$	57.4677	−	99.5369i	0.0657525	−	0.113887i
$875$			404.571i			0.462367i
$876$	−1568.19	−	1574.51i	−1.79017	−	1.79739i
$877$	−767.777	+	205.725i	−0.875459	+	0.234579i	−0.668447	−	0.743760i	$-0.733041\pi$
$877$	−767.777	+	205.725i	−0.875459	+	0.234579i	−0.207012	+	0.978338i	$0.566374\pi$
$878$	41.3697	+	154.394i	0.0471181	+	0.175847i
$879$	646.415	−	643.820i	0.735399	−	0.732446i
$880$	−89.9845			−0.102255
$881$	−861.530	−	497.405i	−0.977901	−	0.564591i	−0.0762650	−	0.997088i	$-0.524299\pi$
$881$	−861.530	−	497.405i	−0.977901	−	0.564591i	−0.901636	+	0.432496i	$0.857633\pi$
$882$	−278.511	+	276.279i	−0.315772	+	0.313241i
$883$			1275.83i			1.44488i	0.691435	+	0.722438i	$0.256979\pi$
$883$			1275.83i			1.44488i	−0.691435	+	0.722438i	$0.743021\pi$
$884$	−1314.95	+	22.7272i	−1.48750	+	0.0257095i
$885$	1024.87	+	1783.39i	1.15804	+	2.01513i
$886$	364.399	+	364.399i	0.411285	+	0.411285i
$887$	−88.8892			−0.100213			−0.0501067	−	0.998744i	$-0.515956\pi$
$887$	−88.8892			−0.100213			−0.0501067	+	0.998744i	$0.515956\pi$
$888$	−1.66037	+	825.458i	−0.00186979	+	0.929570i
$889$	−176.669	+	47.3384i	−0.198728	+	0.0532491i
$890$	375.525	−	1401.48i	0.421938	−	1.57469i
$891$	111.784	+	431.025i	0.125459	+	0.483754i
$892$	77.4737	−	77.4737i	0.0868539	−	0.0868539i
$893$	−127.808			−0.143122
$894$	−790.468	+	454.259i	−0.884193	+	0.508120i
$895$	678.413	−	678.413i	0.758003	−	0.758003i
$896$	−1299.54	+	750.290i	−1.45038	+	0.837377i
$897$	−225.610	+	134.891i	−0.251516	+	0.150380i
$898$	−361.758	+	626.583i	−0.402848	+	0.697753i
$899$	1598.85	−	428.411i	1.77848	−	0.476541i
$900$	−952.616	−	3.83231i	−1.05846	−	0.00425812i
$901$	−802.077	+	463.079i	−0.890208	+	0.513962i
$902$	1368.59	−	366.713i	1.51728	−	0.406555i
$903$	167.211	−	619.055i	0.185172	−	0.685554i
$904$	62.2607	+	232.360i	0.0688725	+	0.257036i
$905$	491.780	+	131.772i	0.543403	+	0.145604i
$906$	−907.937	−	1579.92i	−1.00214	−	1.74385i
$907$	414.470	−	239.295i	0.456969	−	0.263831i	−0.253800	−	0.967257i	$-0.581681\pi$
$907$	414.470	−	239.295i	0.456969	−	0.263831i	0.710769	+	0.703426i	$0.248347\pi$
$908$	502.844	+	1876.64i	0.553792	+	2.06678i
$909$	−3.78756	+	941.493i	−0.00416674	+	1.03575i
$910$	−2048.64	+	587.059i	−2.25125	+	0.645120i
$911$	351.455	−	608.738i	0.385791	−	0.668209i	−0.606088	−	0.795398i	$-0.707262\pi$
$911$	351.455	−	608.738i	0.385791	−	0.668209i	0.991879	+	0.127189i	$0.0405954\pi$
$912$	28.5351	+	28.6501i	0.0312885	+	0.0314146i
$913$	−55.6268			−0.0609275
$914$	1645.90	+	950.261i	1.80077	+	1.03967i
$915$	−701.029	+	186.330i	−0.766152	+	0.203639i
$916$	−87.7499	−	87.7499i	−0.0957968	−	0.0957968i
$917$	389.998	+	104.500i	0.425298	+	0.113958i
$918$	−356.732	−	1364.22i	−0.388597	−	1.48607i
$919$	177.954	+	308.225i	0.193639	+	0.335392i	0.946453	−	0.322841i	$-0.104638\pi$
$919$	177.954	+	308.225i	0.193639	+	0.335392i	−0.752815	+	0.658232i	$0.771304\pi$
$920$	−263.598	+	152.188i	−0.286519	+	0.165422i
$921$	−116.882	−	31.5705i	−0.126907	−	0.0342785i
$922$	−1332.26	+	769.183i	−1.44497	+	0.834254i
$923$	210.668	−	844.328i	0.228243	−	0.914765i
$924$	402.033	+	699.588i	0.435101	+	0.757129i
$925$	175.281	−	654.159i	0.189493	−	0.707198i
$926$	−400.978	+	694.513i	−0.433021	+	0.750015i
$927$	−2.30418	+	572.762i	−0.00248563	+	0.617866i
$928$	−893.895	−	893.895i	−0.963248	−	0.963248i
$929$	−151.399	−	151.399i	−0.162970	−	0.162970i	0.620911	−	0.783881i	$-0.286763\pi$
$929$	−151.399	−	151.399i	−0.162970	−	0.162970i	−0.783881	+	0.620911i	$0.786763\pi$
$930$	2817.66	+	761.068i	3.02974	+	0.818352i
$931$	70.5237	+	18.8968i	0.0757505	+	0.0202973i
$932$	131.490	−	227.748i	0.141084	−	0.244365i
$933$	166.411	+	96.5244i	0.178361	+	0.103456i
$934$	607.025	+	162.652i	0.649920	+	0.174145i
$935$		−	584.008i		−	0.624607i
$936$	221.105	+	783.473i	0.236224	+	0.837044i
$937$	−1654.06			−1.76527			−0.882634	−	0.470060i	$-0.844232\pi$
$937$	−1654.06			−1.76527			−0.882634	+	0.470060i	$0.844232\pi$
$938$	92.3210	−	344.547i	0.0984232	−	0.367320i
$939$	−64.7809	−	0.130304i	−0.0689892	−	0.000138769i
$940$	830.789	+	479.656i	0.883818	+	0.510272i
$941$	−81.6015	+	304.541i	−0.0867179	+	0.323636i	−0.995634	−	0.0933435i	$-0.970245\pi$
$941$	−81.6015	+	304.541i	−0.0867179	+	0.323636i	0.908916	+	0.416979i	$0.136911\pi$
$942$	714.358	+	717.237i	0.758342	+	0.761399i
$943$	−384.976	+	384.976i	−0.408246	+	0.408246i
$944$	−188.385	+	188.385i	−0.199561	+	0.199561i
$945$	−686.332	−	1205.50i	−0.726277	−	1.27567i
$946$	−410.177	−	236.816i	−0.433591	−	0.250334i
$947$	−522.550	−	140.017i	−0.551795	−	0.147853i	−0.0278610	−	0.999612i	$-0.508870\pi$
$947$	−522.550	−	140.017i	−0.551795	−	0.147853i	−0.523934	+	0.851759i	$0.675536\pi$
$948$	−2272.23	−	1317.98i	−2.39687	−	1.39027i
$949$	1082.49	−	1120.57i	1.14066	−	1.18079i
$950$	146.018	+	252.911i	0.153703	+	0.266222i
$951$	176.057	+	176.767i	0.185129	+	0.185875i
$952$	−450.756	−	780.732i	−0.473483	−	0.820097i
$953$	−129.908	+	75.0025i	−0.136315	+	0.0787015i	−0.566607	−	0.823988i	$-0.691744\pi$
$953$	−129.908	+	75.0025i	−0.136315	+	0.0787015i	0.430292	+	0.902690i	$0.358411\pi$
$954$	1144.33	+	1153.58i	1.19951	+	1.20920i
$955$	−146.887	+	548.188i	−0.153808	+	0.574019i
$956$	−1868.01	+	1868.01i	−1.95399	+	1.95399i
$957$	−411.715	+	410.062i	−0.430214	+	0.428487i
$958$	1501.00	−	2599.80i	1.56680	−	2.71378i
$959$			409.803i			0.427323i
$960$	−522.128	−	1964.41i	−0.543883	−	2.04626i
$961$	−1079.04	−	622.983i	−1.12283	−	0.648266i
$962$	−1640.07	+	28.3466i	−1.70486	+	0.0294663i
$963$	0.718261	+	1.25570i	0.000745858	+	0.00130395i
$964$	1785.62	−	478.456i	1.85230	−	0.496323i
$965$	−797.547	−	1381.39i	−0.826473	−	1.43149i
$966$	−441.767	−	256.241i	−0.457316	−	0.265259i
$967$	18.7917	−	70.1315i	0.0194330	−	0.0725249i	−0.955528	−	0.294899i	$-0.904714\pi$
$967$	18.7917	−	70.1315i	0.0194330	−	0.0725249i	0.974961	+	0.222374i	$0.0713807\pi$
$968$	−610.111	+	163.479i	−0.630280	+	0.168883i
$969$	−185.942	+	185.195i	−0.191891	+	0.191120i
$970$	−683.191	−	2549.70i	−0.704320	−	2.62856i
$971$	−228.965	−	396.580i	−0.235804	−	0.408424i	0.723702	−	0.690112i	$-0.242439\pi$
$971$	−228.965	−	396.580i	−0.235804	−	0.408424i	−0.959506	+	0.281688i	$0.909106\pi$
$972$	−1308.17	+	737.832i	−1.34586	+	0.759087i
$973$	177.512	+	662.483i	0.182437	+	0.680866i
$974$	−818.505	−	472.564i	−0.840354	−	0.485179i
$975$	−10.1987	−	667.816i	−0.0104602	−	0.684940i
$976$	−46.9762	−	81.3652i	−0.0481314	−	0.0833660i
$977$	−104.027	−	104.027i	−0.106476	−	0.106476i	0.651862	−	0.758338i	$-0.273988\pi$
$977$	−104.027	−	104.027i	−0.106476	−	0.106476i	−0.758338	+	0.651862i	$0.773988\pi$
$978$	995.548	+	2.00250i	1.01794	+	0.00204755i
$979$		−	385.154i		−	0.393415i
$980$	−387.506	−	387.506i	−0.395415	−	0.395415i
$981$	1409.82	−	371.687i	1.43712	−	0.378886i
$982$	−319.803	−	85.6909i	−0.325665	−	0.0872616i
$983$	101.918	+	380.363i	0.103681	+	0.386941i	0.998192	−	0.0601037i	$-0.0191432\pi$
$983$	101.918	+	380.363i	0.103681	+	0.386941i	−0.894512	+	0.447045i	$0.852476\pi$
$984$	840.122	+	1461.92i	0.853782	+	1.48569i
$985$		−	1307.01i		−	1.32691i
$986$	1301.17	−	1301.17i	1.31964	−	1.31964i
$987$	−1.14231	+	567.899i	−0.00115735	+	0.575379i
$988$	298.355	−	308.849i	0.301978	−	0.312601i
$989$	181.995			0.184020
$990$	−990.749	+	261.203i	−1.00076	+	0.263842i
$991$	−472.932	+	819.142i	−0.477227	+	0.826581i	−0.999659	−	0.0260997i	$-0.991691\pi$
$991$	−472.932	+	819.142i	−0.477227	+	0.826581i	0.522433	+	0.852681i	$0.325025\pi$
$992$			1685.52i			1.69911i
$993$	−111.945	+	414.447i	−0.112734	+	0.417369i
$994$	1633.10	−	437.588i	1.64296	−	0.440230i
$995$	−32.2855	−	120.491i	−0.0324477	−	0.121097i
$996$	−48.1960	−	181.328i	−0.0483896	−	0.182056i
$997$	439.330			0.440651			0.220326	−	0.975426i	$-0.429288\pi$
$997$	439.330			0.440651			0.220326	+	0.975426i	$0.429288\pi$
$998$	1201.43	+	693.646i	1.20384	+	0.695036i
$999$	−270.119	−	1032.99i	−0.270390	−	1.03403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.bb.a.7.4	yes	104
3.2	odd	2		351.3.be.a.46.23		104
9.4	even	3		117.3.w.a.85.4	✓	104
9.5	odd	6		351.3.z.a.280.23		104
13.2	odd	12		117.3.w.a.106.4	yes	104
39.2	even	12		351.3.z.a.262.23		104
117.41	even	12		351.3.be.a.145.23		104
117.67	odd	12	inner	117.3.bb.a.67.4	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.w.a.85.4	✓	104	9.4	even	3
117.3.w.a.106.4	yes	104	13.2	odd	12
117.3.bb.a.7.4	yes	104	1.1	even	1	trivial
117.3.bb.a.67.4	yes	104	117.67	odd	12	inner
351.3.z.a.262.23		104	39.2	even	12
351.3.z.a.280.23		104	9.5	odd	6
351.3.be.a.46.23		104	3.2	odd	2
351.3.be.a.145.23		104	117.41	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.825818 + 3.08200i) q^{2} +(1.49477 + 2.60109i) q^{3} +(-5.35262 - 3.09034i) q^{4} +(-1.67984 + 6.26926i) q^{5} +(-9.25095 + 2.45885i) q^{6} +(5.59737 - 5.59737i) q^{7} +(4.91998 - 4.91998i) q^{8} +(-4.53132 + 7.77606i) q^{9} +(-17.9346 - 10.3545i) q^{10} +(-5.31002 - 1.42282i) q^{11} +(0.0372964 - 18.5420i) q^{12} +(12.9981 - 0.224655i) q^{13} +(12.6287 + 21.8735i) q^{14} +(-18.8179 + 5.00169i) q^{15} +(-1.26099 - 2.18411i) q^{16} +(14.1750 - 8.18397i) q^{17} +(-20.2237 - 20.3871i) q^{18} +(-1.38325 + 5.16237i) q^{19} +(28.3657 - 28.3657i) q^{20} +(22.9260 + 6.19247i) q^{21} +(8.77022 - 15.1905i) q^{22} +6.74000i q^{23} +(20.1515 + 5.44306i) q^{24} +(-14.8311 - 8.56275i) q^{25} +(-10.0416 + 40.2455i) q^{26} +(-26.9995 - 0.162927i) q^{27} +(-47.2583 + 12.6628i) q^{28} +(-17.6172 - 30.5138i) q^{29} +(0.124966 - 62.1271i) q^{30} +(-12.1589 + 45.3776i) q^{31} +(34.6560 - 9.28606i) q^{32} +(-4.23639 - 15.9386i) q^{33} +(13.5169 + 50.4459i) q^{34} +(25.6887 + 44.4941i) q^{35} +(48.2851 - 27.6190i) q^{36} +(10.2351 + 38.1979i) q^{37} +(-14.7681 - 8.52636i) q^{38} +(20.0135 + 33.4733i) q^{39} +(22.5798 + 39.1094i) q^{40} +(57.1181 + 57.1181i) q^{41} +(-38.0179 + 65.5441i) q^{42} -27.0023i q^{43} +(24.0255 + 24.0255i) q^{44} +(-41.1383 - 41.4706i) q^{45} +(-20.7727 - 5.56602i) q^{46} +(6.18939 + 23.0991i) q^{47} +(3.79615 - 6.54469i) q^{48} -13.6611i q^{49} +(38.6381 - 38.6381i) q^{50} +(42.4757 + 24.6374i) q^{51} +(-70.2679 - 38.9659i) q^{52} -56.5837 q^{53} +(22.7988 - 83.0778i) q^{54} +(17.8400 - 30.8998i) q^{55} -55.0779i q^{56} +(-15.4954 + 4.11860i) q^{57} +(108.592 - 29.0972i) q^{58} +(-27.3411 - 102.038i) q^{59} +(116.182 + 31.3814i) q^{60} +37.2534 q^{61} +(-129.813 - 74.9473i) q^{62} +(18.1620 + 68.8890i) q^{63} +104.390i q^{64} +(-20.4263 + 81.8656i) q^{65} +(52.6212 + 0.105845i) q^{66} +(-9.98624 - 9.98624i) q^{67} -101.165 q^{68} +(-17.5313 + 10.0748i) q^{69} +(-158.345 + 42.4283i) q^{70} +(17.3252 - 64.6586i) q^{71} +(15.9641 + 60.5521i) q^{72} +(84.7455 - 84.7455i) q^{73} -126.178 q^{74} +(0.103341 - 51.3764i) q^{75} +(23.3575 - 23.3575i) q^{76} +(-37.6862 + 21.7581i) q^{77} +(-119.692 + 34.0386i) q^{78} +(70.8339 - 122.688i) q^{79} +(15.8110 - 4.23654i) q^{80} +(-39.9343 - 70.4716i) q^{81} +(-223.207 + 128.869i) q^{82} +(9.77407 - 2.61895i) q^{83} +(-103.578 - 103.995i) q^{84} +(27.4956 + 102.615i) q^{85} +(83.2209 + 22.2990i) q^{86} +(53.0355 - 91.4350i) q^{87} +(-33.1254 + 19.1250i) q^{88} +(18.1333 + 67.6746i) q^{89} +(161.785 - 92.5407i) q^{90} +(71.4975 - 74.0124i) q^{91} +(20.8289 - 36.0767i) q^{92} +(-136.206 + 36.2028i) q^{93} -76.3027 q^{94} +(-30.0406 - 17.3439i) q^{95} +(75.9567 + 76.2629i) q^{96} +(90.1302 + 90.1302i) q^{97} +(42.1035 + 11.2816i) q^{98} +(35.1253 - 34.8438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 2 q^{5} + 10 q^{6} - 6 q^{7} + 18 q^{8} - 2 q^{9} - 12 q^{10} - 14 q^{11} - 54 q^{12} - 2 q^{13} - 4 q^{14} - 44 q^{15} + 162 q^{16} - 12 q^{17} + 34 q^{18} - 36 q^{19}+ \cdots - 524 q^{99}+O(q^{100}) \) 104 * q - 2 * q^2 - 2 * q^3 - 6 * q^4 - 2 * q^5 + 10 * q^6 - 6 * q^7 + 18 * q^8 - 2 * q^9 - 12 * q^10 - 14 * q^11 - 54 * q^12 - 2 * q^13 - 4 * q^14 - 44 * q^15 + 162 * q^16 - 12 * q^17 + 34 * q^18 - 36 * q^19 - 82 * q^20 + 106 * q^21 + 2 * q^22 - 66 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 + 74 * q^29 - 438 * q^30 - 34 * q^31 + 22 * q^32 - 68 * q^33 + 6 * q^34 - 106 * q^35 - 6 * q^36 + 14 * q^37 - 216 * q^38 - 176 * q^39 - 36 * q^40 - 26 * q^41 - 220 * q^42 + 496 * q^44 - 50 * q^45 + 118 * q^47 + 130 * q^48 + 92 * q^50 + 76 * q^52 - 208 * q^53 + 904 * q^54 - 4 * q^55 - 86 * q^57 - 76 * q^58 + 430 * q^59 - 358 * q^60 - 4 * q^61 - 282 * q^62 - 326 * q^63 + 406 * q^65 - 412 * q^66 - 72 * q^67 - 1068 * q^68 + 204 * q^69 - 106 * q^70 - 8 * q^71 - 642 * q^72 + 90 * q^73 + 356 * q^74 + 204 * q^75 - 194 * q^76 + 432 * q^77 + 646 * q^78 - 16 * q^79 - 278 * q^80 - 182 * q^81 - 12 * q^82 - 536 * q^83 + 310 * q^84 - 234 * q^85 + 414 * q^86 + 434 * q^87 - 6 * q^88 + 400 * q^89 + 798 * q^90 + 120 * q^91 + 48 * q^92 - 116 * q^93 - 244 * q^94 + 858 * q^95 + 1528 * q^96 + 344 * q^97 + 280 * q^98 - 524 * q^99

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