LMFDB - Embedded newform 117.3.bb.a.67.4

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			67.4
Character	$\chi$	$=$	117.67
Dual form			117.3.bb.a.7.4

$q$-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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$

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	−0.788987	−	0.614410i	$-0.789394\pi$
$2$	−0.825818	−	3.08200i	−0.412909	−	1.54100i	0.376078	−	0.926588i	$-0.377272\pi$
$3$	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	−0.902815	−	0.430029i	$-0.858503\pi$
$5$	−1.67984	−	6.26926i	−0.335969	−	1.25385i	0.566847	−	0.823823i	$-0.308163\pi$
$6$	−9.25095	−	2.45885i	−1.54183	−	0.409809i
$7$	5.59737	+	5.59737i	0.799624	+	0.799624i	0.983036	−	0.183412i	$-0.0587142\pi$
$7$	5.59737	+	5.59737i	0.799624	+	0.799624i	−0.183412	+	0.983036i	$0.558714\pi$
$8$	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	−0.491973	−	0.870610i	$-0.663724\pi$
$11$	−5.31002	+	1.42282i	−0.482729	+	0.129347i	0.00924404	+	0.999957i	$0.497057\pi$
$12$	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	0.855161	−	0.518363i	$-0.173458\pi$
$17$	14.1750	+	8.18397i	0.833826	+	0.481410i	−0.0213346	+	0.999772i	$0.506792\pi$
$18$	−20.2237	+	20.3871i	−1.12354	+	1.13262i
$19$	−1.38325	−	5.16237i	−0.0728028	−	0.271704i	0.919923	−	0.392098i	$-0.128251\pi$
$19$	−1.38325	−	5.16237i	−0.0728028	−	0.271704i	−0.992726	+	0.120395i	$0.961584\pi$
$20$	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	$-0.953192\pi$
$23$		−	6.74000i		−	0.293044i	0.989207	−	0.146522i	$-0.0468078\pi$
$24$	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	0.384164	+	0.923265i	$0.374490\pi$
$29$	−17.6172	+	30.5138i	−0.607489	+	1.05220i	−0.991653	+	0.128937i	$0.958844\pi$
$30$	0.124966	+	62.1271i	0.00416554	+	2.07090i
$31$	−12.1589	−	45.3776i	−0.392222	−	1.46379i	−0.826460	−	0.562996i	$-0.809649\pi$
$31$	−12.1589	−	45.3776i	−0.392222	−	1.46379i	0.434238	−	0.900798i	$-0.357018\pi$
$32$	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	−0.678120	−	0.734951i	$-0.737205\pi$
$37$	10.2351	−	38.1979i	0.276624	−	1.03238i	0.954745	−	0.297426i	$-0.0961281\pi$
$38$	−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	0.574906	−	0.818220i	$-0.305039\pi$
$41$	57.1181	−	57.1181i	1.39313	−	1.39313i	0.818220	−	0.574906i	$-0.194961\pi$
$42$	−38.0179	−	65.5441i	−0.905188	−	1.56057i
$43$			27.0023i			0.627960i	0.949430	+	0.313980i	$0.101662\pi$
$43$			27.0023i			0.627960i	−0.949430	+	0.313980i	$0.898338\pi$
$44$	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	−0.868300	−	0.496039i	$-0.834787\pi$
$47$	6.18939	−	23.0991i	0.131689	−	0.491471i	0.999990	+	0.00456799i	$0.00145404\pi$
$48$	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	0.198705	+	0.980059i	$0.436326\pi$
$59$	−27.3411	+	102.038i	−0.463408	+	1.72946i	−0.662113	+	0.749404i	$0.730340\pi$
$60$	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	−0.777693	−	0.628644i	$-0.783610\pi$
$67$	−9.98624	+	9.98624i	−0.149048	+	0.149048i	0.628644	+	0.777693i	$0.283610\pi$
$68$	−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	0.973875	+	0.227085i	$0.0729195\pi$
$71$	17.3252	+	64.6586i	0.244017	+	0.910684i	−0.729858	+	0.683599i	$0.760414\pi$
$72$	15.9641	−	60.5521i	0.221723	−	0.841001i
$73$	84.7455	+	84.7455i	1.16090	+	1.16090i	0.984279	+	0.176618i	$0.0565159\pi$
$73$	84.7455	+	84.7455i	1.16090	+	1.16090i	0.176618	+	0.984279i	$0.443484\pi$
$74$	−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	0.831772	+	0.555117i	$0.187327\pi$
$79$	70.8339	+	122.688i	0.896632	+	1.55301i	0.0648593	+	0.997894i	$0.479340\pi$
$80$	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	0.317218	−	0.948353i	$-0.397251\pi$
$83$	9.77407	+	2.61895i	0.117760	+	0.0315537i	−0.199458	+	0.979906i	$0.563918\pi$
$84$	−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	−0.786083	−	0.618121i	$-0.787894\pi$
$89$	18.1333	−	67.6746i	0.203745	−	0.760388i	0.989828	−	0.142267i	$-0.0454392\pi$
$90$	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	−0.0684759	−	0.997653i	$-0.521814\pi$
$97$	90.1302	−	90.1302i	0.929177	−	0.929177i	0.997653	+	0.0684759i	$0.0218136\pi$
$98$	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	0.876222	−	0.481907i	$-0.160056\pi$
$101$	90.5960	+	52.3056i	0.896990	+	0.517877i	0.0207675	+	0.999784i	$0.493389\pi$
$102$	−111.010	−	110.564i	−1.08833	−	1.08396i
$103$	55.1145	+	31.8204i	0.535092	+	0.308936i	0.743088	−	0.669194i	$-0.233361\pi$
$103$	55.1145	+	31.8204i	0.535092	+	0.308936i	−0.207995	+	0.978130i	$0.566694\pi$
$104$	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	0.866401	−	0.499349i	$-0.166428\pi$
$107$	0.0803675	+	0.139201i	0.000751098	+	0.00130094i	−0.865650	+	0.500650i	$0.833094\pi$
$108$	144.015	−	84.3096i	1.33347	−	0.780645i
$109$	−114.550	+	114.550i	−1.05092	+	1.05092i	−0.0522892	+	0.998632i	$0.516652\pi$
$109$	−114.550	+	114.550i	−1.05092	+	1.05092i	−0.998632	+	0.0522892i	$0.983348\pi$
$110$	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	0.779342	−	0.626598i	$-0.215553\pi$
$113$	−17.2866	−	29.9413i	−0.152979	−	0.264967i	−0.932321	+	0.361631i	$0.882220\pi$
$114$	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	−0.576707	−	0.816951i	$-0.695663\pi$
$127$	−20.0101	+	11.5528i	−0.157560	+	0.0909672i	0.419147	+	0.907918i	$0.362329\pi$
$128$	−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	−0.752117	−	0.659030i	$-0.770967\pi$
$131$	25.5029	−	44.1723i	0.194679	−	0.337193i	0.946795	+	0.321837i	$0.104300\pi$
$132$	−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	0.560770	−	0.827972i	$-0.310505\pi$
$137$	−36.6067	−	36.6067i	−0.267202	−	0.267202i	−0.827972	+	0.560770i	$0.810505\pi$
$138$	−16.5727	+	62.3514i	−0.120092	+	0.451822i
$139$	−43.3213	−	75.0347i	−0.311664	−	0.539818i	0.667059	−	0.745005i	$-0.267553\pi$
$139$	−43.3213	−	75.0347i	−0.311664	−	0.539818i	−0.978723	+	0.205187i	$0.934220\pi$
$140$			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	0.553966	−	0.832539i	$-0.313114\pi$
$149$	91.9994	+	24.6512i	0.617445	+	0.165444i	0.0634792	+	0.997983i	$0.479780\pi$
$150$	158.256	−	42.7460i	1.05504	−	0.284974i
$151$	49.2708	−	183.881i	0.326296	−	1.21775i	−0.586706	−	0.809800i	$-0.699575\pi$
$151$	49.2708	−	183.881i	0.326296	−	1.21775i	0.913002	−	0.407955i	$-0.133758\pi$
$152$	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	−0.983828	−	0.179115i	$-0.942677\pi$
$157$	−52.8770	+	91.5856i	−0.336796	+	0.583348i	0.647032	+	0.762463i	$0.276010\pi$
$158$	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	−0.553456	−	0.832878i	$-0.686691\pi$
$163$	−100.461	+	26.9184i	−0.616325	+	0.165144i	−0.0628683	+	0.998022i	$0.520025\pi$
$164$	−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	0.989438	−	0.144957i	$-0.0463045\pi$
$167$	141.028	+	141.028i	0.844481	+	0.844481i	−0.144957	+	0.989438i	$0.546304\pi$
$168$	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	$0.100807\pi$
$173$			107.754i			0.622856i	−0.950270	+	0.311428i	$0.899193\pi$
$174$	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	−0.812975	−	0.582298i	$-0.802154\pi$
$179$	−128.017	+	73.9106i	−0.715178	+	0.412908i	0.0977974	+	0.995206i	$0.468820\pi$
$180$	92.0393	−	349.107i	0.511330	−	1.93948i
$181$			78.4431i			0.433387i	0.976240	+	0.216694i	$0.0695272\pi$
$181$			78.4431i			0.433387i	−0.976240	+	0.216694i	$0.930473\pi$
$182$	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	0.0950594	−	0.995472i	$-0.469696\pi$
$193$	−173.780	−	173.780i	−0.900412	−	0.900412i	−0.995472	+	0.0950594i	$0.969696\pi$
$194$	−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	−0.271230	−	0.962515i	$-0.587430\pi$
$197$	−194.514	−	52.1198i	−0.987379	−	0.264568i	−0.716149	+	0.697947i	$0.754097\pi$
$198$	78.3814	−	137.031i	0.395865	−	0.692074i
$199$	−16.6444	−	9.60968i	−0.0836404	−	0.0482898i	0.457596	−	0.889160i	$-0.348710\pi$
$199$	−16.6444	−	9.60968i	−0.0836404	−	0.0482898i	−0.541237	+	0.840870i	$0.682044\pi$
$200$	−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	0.954875	−	0.297007i	$-0.0959884\pi$
$223$	−4.58807	−	17.1229i	−0.0205743	−	0.0767843i	−0.975450	+	0.220222i	$0.929322\pi$
$224$	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	−0.999788	−	0.0206130i	$-0.993438\pi$
$227$	−222.273	+	222.273i	−0.979175	+	0.979175i	0.0206130	+	0.999788i	$0.493438\pi$
$228$	95.6690	−	25.8408i	0.419601	−	0.113337i
$229$	19.3941	−	5.19664i	0.0846904	−	0.0226927i	−0.216225	−	0.976344i	$-0.569374\pi$
$229$	19.3941	−	5.19664i	0.0846904	−	0.0226927i	0.300915	+	0.953651i	$0.402708\pi$
$230$	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	$-0.970896\pi$
$233$		−	42.5489i		−	0.182613i	0.995823	−	0.0913066i	$-0.0291043\pi$
$234$	−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	0.663862	+	0.747855i	$0.268916\pi$
$239$	110.626	+	412.860i	0.462868	+	1.72745i	−0.200993	+	0.979593i	$0.564417\pi$
$240$	34.6534	−	34.7931i	0.144389	−	0.144971i
$241$	−211.492	−	211.492i	−0.877562	−	0.877562i	0.115720	−	0.993282i	$-0.463083\pi$
$241$	−211.492	−	211.492i	−0.877562	−	0.877562i	−0.993282	+	0.115720i	$0.963083\pi$
$242$	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	0.156935	−	0.987609i	$-0.449839\pi$
$251$	−155.593	−	89.8316i	−0.619892	−	0.357895i	−0.776827	+	0.629714i	$0.783172\pi$
$252$	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	$-0.853880\pi$
$257$		−	227.751i		−	0.886192i	0.896474	−	0.443096i	$-0.146120\pi$
$258$	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	−0.999996	−	0.00278366i	$-0.999114\pi$
$263$	−130.865	+	226.666i	−0.497587	+	0.861847i	0.502409	+	0.864630i	$0.332447\pi$
$264$	−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	−0.539192	−	0.842183i	$-0.681270\pi$
$269$	123.674	−	214.210i	0.459755	−	0.796320i	0.998948	+	0.0458628i	$0.0146037\pi$
$270$	482.538	−	282.489i	1.78718	−	1.04626i
$271$	−81.9853	+	305.973i	−0.302529	+	1.12905i	0.632523	+	0.774542i	$0.282020\pi$
$271$	−81.9853	+	305.973i	−0.302529	+	1.12905i	−0.935052	+	0.354512i	$0.884647\pi$
$272$	−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	$0.192306\pi$
$277$			314.705i			1.13612i	−0.822987	+	0.568060i	$0.807694\pi$
$278$	−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	−0.582252	−	0.813008i	$-0.697828\pi$
$281$	92.3077	−	344.497i	0.328497	−	1.22597i	0.910749	−	0.412960i	$-0.135505\pi$
$282$	−114.055	+	198.470i	−0.404451	+	0.703795i
$283$			245.100i			0.866078i	0.901375	+	0.433039i	$0.142559\pi$
$283$			245.100i			0.866078i	−0.901375	+	0.433039i	$0.857441\pi$
$284$	−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	0.691353	+	0.722517i	$0.257015\pi$
$293$	−78.7100	+	293.750i	−0.268635	+	1.00256i	−0.959988	+	0.280042i	$0.909652\pi$
$294$	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	0.659101	−	0.752054i	$-0.270937\pi$
$307$	−28.5365	−	28.5365i	−0.0929529	−	0.0929529i	−0.752054	+	0.659101i	$0.770937\pi$
$308$	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	0.586620	−	0.809862i	$-0.300458\pi$
$311$	55.5350	+	32.0631i	0.178569	+	0.103097i	−0.408051	+	0.912959i	$0.633791\pi$
$312$	263.154	−	66.2221i	0.843442	−	0.212250i
$313$	−10.7968	−	18.7007i	−0.0344947	−	0.0597465i	0.848263	−	0.529576i	$-0.177649\pi$
$313$	−10.7968	−	18.7007i	−0.0344947	−	0.0597465i	−0.882757	+	0.469829i	$0.844316\pi$
$314$	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	0.383283	−	0.923631i	$-0.374793\pi$
$317$	80.3280	+	21.5238i	0.253401	+	0.0678985i	−0.129882	+	0.991529i	$0.541460\pi$
$318$	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	−0.537539	−	0.843239i	$-0.680646\pi$
$331$	101.187	−	101.187i	0.305700	−	0.305700i	0.843239	+	0.537539i	$0.180646\pi$
$332$	−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	0.117400	−	0.993085i	$-0.462544\pi$
$337$	−230.487	−	133.072i	−0.683937	−	0.394871i	−0.801337	+	0.598214i	$0.795877\pi$
$338$	−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	0.965412	−	0.260731i	$-0.0839635\pi$
$347$	89.1464	+	154.406i	0.256906	+	0.444974i	−0.708505	+	0.705705i	$0.750630\pi$
$348$	−566.444	−	325.519i	−1.62771	−	0.935400i
$349$	−624.529	+	167.342i	−1.78948	+	0.479490i	−0.992258	−	0.124194i	$-0.960365\pi$
$349$	−624.529	+	167.342i	−1.78948	+	0.479490i	−0.797223	+	0.603684i	$0.793699\pi$
$350$			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	−0.998518	−	0.0544160i	$-0.982670\pi$
$353$	−56.8274	−	212.083i	−0.160984	−	0.600801i	0.837534	−	0.546385i	$-0.183996\pi$
$354$	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	0.511537	−	0.859261i	$-0.329076\pi$
$359$	−124.833	−	124.833i	−0.347724	−	0.347724i	−0.859261	+	0.511537i	$0.829076\pi$
$360$	−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	−0.974254	−	0.225453i	$-0.927614\pi$
$367$	−107.120	+	185.537i	−0.291879	+	0.505550i	0.682375	+	0.731003i	$0.260947\pi$
$368$	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	0.821177	−	0.570674i	$-0.193318\pi$
$373$	−31.1941	−	54.0297i	−0.0836302	−	0.144852i	−0.904807	+	0.425823i	$0.859985\pi$
$374$			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	0.165110	−	0.986275i	$-0.447202\pi$
$379$	−70.1295	−	18.7911i	−0.185038	−	0.0495808i	−0.350148	+	0.936694i	$0.613869\pi$
$380$	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	−0.322322	−	0.946630i	$-0.604463\pi$
$383$	−411.639	−	110.298i	−1.07478	−	0.287985i	−0.752454	+	0.658645i	$0.771130\pi$
$384$	−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	−0.244214	−	0.969721i	$-0.578530\pi$
$389$	184.185	−	106.339i	0.473482	−	0.273365i	0.717696	+	0.696356i	$0.245197\pi$
$390$	−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	−0.0933120	−	0.995637i	$-0.529745\pi$
$397$	128.507	−	34.4334i	0.323696	−	0.0867340i	0.417008	+	0.908903i	$0.363079\pi$
$398$	−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	0.731214	−	0.682149i	$-0.238954\pi$
$401$	19.6751	+	19.6751i	0.0490650	+	0.0490650i	−0.682149	+	0.731214i	$0.738954\pi$
$402$	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	−0.303295	−	0.952897i	$-0.598087\pi$
$409$	−426.344	−	114.238i	−1.04241	−	0.279312i	−0.739110	+	0.673585i	$0.764754\pi$
$410$	−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	0.613360	−	0.789803i	$-0.289817\pi$
$421$	315.600	+	84.5648i	0.749644	+	0.200866i	0.136284	+	0.990670i	$0.456484\pi$
$422$	−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	0.0320217	−	0.999487i	$-0.489805\pi$
$431$	−189.636	−	50.8128i	−0.439990	−	0.117895i	−0.472012	+	0.881592i	$0.656472\pi$
$432$	33.6904	−	59.1752i	0.0779869	−	0.136980i
$433$	−607.245	−	350.593i	−1.40241	−	0.809684i	−0.407774	−	0.913083i	$-0.633695\pi$
$433$	−607.245	−	350.593i	−1.40241	−	0.809684i	−0.994640	+	0.103399i	$0.967028\pi$
$434$	−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	0.548598	−	0.836087i	$-0.315162\pi$
$439$	43.3839	+	25.0477i	0.0988243	+	0.0570562i	−0.449773	+	0.893143i	$0.648495\pi$
$440$	−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	0.942661	−	0.333752i	$-0.108315\pi$
$443$	80.7558	+	139.873i	0.182293	+	0.315741i	−0.760368	+	0.649492i	$0.774981\pi$
$444$	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	−0.00652317	−	0.999979i	$-0.502076\pi$
$449$	219.030	−	58.6889i	0.487817	−	0.130710i	0.494340	+	0.869269i	$0.335410\pi$
$450$	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	0.901313	+	0.433169i	$0.142605\pi$
$457$	154.163	+	575.345i	0.337338	+	1.25896i	−0.563975	+	0.825792i	$0.690729\pi$
$458$	−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	−0.232958	−	0.972487i	$-0.574840\pi$
$461$	340.923	−	340.923i	0.739529	−	0.739529i	0.972487	+	0.232958i	$0.0748404\pi$
$462$	295.133	+	293.948i	0.638816	+	0.636251i
$463$	242.776	−	65.0516i	0.524354	−	0.140500i	0.0130742	−	0.999915i	$-0.495838\pi$
$463$	242.776	−	65.0516i	0.524354	−	0.140500i	0.511280	+	0.859414i	$0.329172\pi$
$464$	−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	$0.0676317\pi$
$467$			196.958i			0.421752i	−0.977513	+	0.210876i	$0.932368\pi$
$468$	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	−0.899885	+	0.436126i	$0.856350\pi$
$479$	−908.793	+	243.510i	−1.89727	+	0.508373i	−0.997387	+	0.0722462i	$0.976983\pi$
$480$	−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	−0.998886	−	0.0471965i	$-0.984971\pi$
$487$	−76.6653	−	286.119i	−0.157424	−	0.587513i	0.841462	−	0.540316i	$-0.181695\pi$
$488$	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	$-0.966302\pi$
$491$		−	103.765i		−	0.211334i	0.994402	−	0.105667i	$-0.0336977\pi$
$492$	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	0.982198	+	0.187851i	$0.0601522\pi$
$499$	112.532	+	419.975i	0.225515	+	0.841633i	−0.756683	+	0.653782i	$0.773181\pi$
$500$	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	0.155258	+	0.987874i	$0.450379\pi$
$503$	−391.281	+	677.719i	−0.777895	+	1.34735i	−0.933153	+	0.359480i	$0.882954\pi$
$504$	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	−0.994400	−	0.105681i	$-0.966298\pi$
$509$	−452.358	+	452.358i	−0.888719	+	0.888719i	0.105681	+	0.994400i	$0.466298\pi$
$510$	−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	0.827083	−	0.562080i	$-0.189999\pi$
$523$	−38.3012	−	66.3397i	−0.0732337	−	0.126845i	−0.900317	+	0.435235i	$0.856665\pi$
$524$			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	0.981027	−	0.193872i	$-0.0621047\pi$
$541$	425.851	+	425.851i	0.787155	+	0.787155i	−0.193872	+	0.981027i	$0.562105\pi$
$542$	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	−0.999526	−	0.0307753i	$-0.990202\pi$
$547$	−287.949	−	498.743i	−0.526415	−	0.911778i	0.473111	−	0.881003i	$-0.343131\pi$
$548$	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	−0.931687	−	0.363261i	$-0.881663\pi$
$557$	31.6421	−	118.090i	0.0568081	−	0.212011i	0.988495	+	0.151250i	$0.0483300\pi$
$558$	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	0.285939	−	0.958248i	$-0.407694\pi$
$563$	708.691	−	409.163i	1.25878	−	0.726754i	0.972836	+	0.231493i	$0.0743612\pi$
$564$	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	0.136853	−	0.990591i	$-0.456301\pi$
$569$	−371.328	−	214.386i	−0.652597	−	0.376777i	−0.789451	+	0.613814i	$0.789634\pi$
$570$	320.550	−	86.5826i	0.562369	−	0.151899i
$571$	660.431	+	381.300i	1.15662	+	0.667776i	0.950492	−	0.310748i	$-0.100580\pi$
$571$	660.431	+	381.300i	1.15662	+	0.667776i	0.206130	+	0.978525i	$0.433913\pi$
$572$	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	−0.996600	−	0.0823891i	$-0.973745\pi$
$577$	−527.500	+	527.500i	−0.914211	+	0.914211i	0.0823891	+	0.996600i	$0.473745\pi$
$578$	−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	0.949474	−	0.313846i	$-0.101617\pi$
$587$	−17.4441	−	65.1024i	−0.0297174	−	0.110907i	−0.979191	+	0.202939i	$0.934951\pi$
$588$	−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	0.986424	−	0.164219i	$-0.0525105\pi$
$593$	487.567	+	487.567i	0.822205	+	0.822205i	−0.164219	+	0.986424i	$0.552510\pi$
$594$	−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	0.114435	+	0.993431i	$0.463494\pi$
$599$	−481.068	+	833.235i	−0.803119	+	1.39104i	−0.917554	+	0.397612i	$0.869839\pi$
$600$	−252.262	+	253.279i	−0.420437	+	0.422132i
$601$	270.547	−	468.601i	0.450162	−	0.779703i	−0.548234	−	0.836325i	$-0.684700\pi$
$601$	270.547	−	468.601i	0.450162	−	0.779703i	0.998396	+	0.0566221i	$0.0180330\pi$
$602$	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	−0.900796	−	0.434244i	$-0.857016\pi$
$607$	−501.663	−	868.907i	−0.826464	−	1.43148i	0.0743318	−	0.997234i	$-0.476318\pi$
$608$		−	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	−0.480144	−	0.877190i	$-0.659416\pi$
$613$	−818.083	−	219.205i	−1.33456	−	0.357593i	−0.854412	+	0.519596i	$0.826082\pi$
$614$	−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	0.408886	−	0.912585i	$-0.365917\pi$
$617$	189.234	+	50.7050i	0.306700	+	0.0821800i	−0.102187	+	0.994765i	$0.532584\pi$
$618$	−431.620	−	429.887i	−0.698414	−	0.695610i
$619$	156.740	−	584.961i	0.253215	−	0.945010i	−0.715860	−	0.698244i	$-0.753965\pi$
$619$	156.740	−	584.961i	0.253215	−	0.945010i	0.969075	−	0.246767i	$-0.0793681\pi$
$620$	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	−0.616234	−	0.787563i	$-0.711342\pi$
$631$	−477.116	+	127.843i	−0.756127	+	0.202604i	−0.139893	+	0.990167i	$0.544676\pi$
$632$	−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	$-0.948802\pi$
$641$		−	205.313i		−	0.320301i	0.987093	−	0.160151i	$-0.0511980\pi$
$642$	−0.401202	−	1.48535i	−0.000624925	−	0.00231363i
$643$	−1032.98	−	276.787i	−1.60651	−	0.430462i	−0.659508	−	0.751697i	$-0.729235\pi$
$643$	−1032.98	−	276.787i	−1.60651	−	0.430462i	−0.947000	+	0.321235i	$0.895902\pi$
$644$	−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	−0.244699	−	0.969599i	$-0.578689\pi$
$647$	305.804	−	176.556i	0.472649	−	0.272884i	0.717348	+	0.696715i	$0.245356\pi$
$648$	−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	0.745786	−	0.666186i	$-0.232074\pi$
$661$	52.6156	+	52.6156i	0.0796000	+	0.0796000i	−0.666186	+	0.745786i	$0.732074\pi$
$662$	−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	0.938862	−	0.344293i	$-0.111881\pi$
$673$	747.116	+	431.347i	1.11013	+	0.640932i	0.171265	+	0.985225i	$0.445215\pi$
$674$	−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	0.803145	−	0.595783i	$-0.203158\pi$
$677$	−77.4425	−	134.134i	−0.114391	−	0.198131i	−0.917536	+	0.397653i	$0.869825\pi$
$678$	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	−0.381969	−	0.924175i	$-0.624754\pi$
$683$	−171.212	+	45.8762i	−0.250677	+	0.0671686i	0.131293	+	0.991344i	$0.458087\pi$
$684$	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	0.867878	−	0.496778i	$-0.165484\pi$
$691$	−91.2918	−	340.706i	−0.132115	−	0.493062i	−0.999993	+	0.00371639i	$0.998817\pi$
$692$	−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	$-0.771776\pi$
$701$		−	921.277i		−	1.31423i	0.753789	−	0.657117i	$-0.228224\pi$
$702$	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	0.722447	−	0.691426i	$-0.243017\pi$
$709$	21.9936	+	21.9936i	0.0310206	+	0.0310206i	−0.691426	+	0.722447i	$0.743017\pi$
$710$	−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	0.943838	−	0.330407i	$-0.107186\pi$
$719$	812.194	+	468.921i	1.12962	+	0.652184i	0.185778	+	0.982592i	$0.440519\pi$
$720$	−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	−0.634897	+	0.772597i	$0.718957\pi$
$727$	−1178.78	+	680.570i	−1.62143	+	0.936135i	−0.986537	+	0.163538i	$0.947709\pi$
$728$	−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	0.887344	−	0.461108i	$-0.152548\pi$
$733$	−81.8559	−	305.490i	−0.111672	−	0.416767i	−0.999016	+	0.0443408i	$0.985881\pi$
$734$	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	−0.734987	−	0.678081i	$-0.762812\pi$
$739$	177.782	−	663.491i	0.240571	−	0.897823i	0.975558	−	0.219742i	$-0.0705216\pi$
$740$	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	−0.658579	−	0.752512i	$-0.728842\pi$
$743$	69.7919	−	69.7919i	0.0939325	−	0.0939325i	0.752512	+	0.658579i	$0.228842\pi$
$744$	−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	$-0.995594\pi$
$751$		−	20.7896i		−	0.0276825i	0.999904	−	0.0138413i	$-0.00440595\pi$
$752$	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	0.915913	−	0.401376i	$-0.131468\pi$
$757$	83.5383	+	144.693i	0.110354	+	0.191140i	−0.805559	+	0.592516i	$0.798135\pi$
$758$			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	0.745907	+	0.666050i	$0.232016\pi$
$761$	−177.383	+	662.004i	−0.233093	+	0.869913i	−0.978999	+	0.203863i	$0.934650\pi$
$762$	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	−0.555207	−	0.831712i	$-0.687361\pi$
$769$	212.632	−	212.632i	0.276505	−	0.276505i	0.831712	+	0.555207i	$0.187361\pi$
$770$	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	0.997654	+	0.0684578i	$0.0218079\pi$
$773$	129.778	+	484.339i	0.167889	+	0.626571i	−0.829765	+	0.558113i	$0.811525\pi$
$774$	−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	−0.473903	−	0.880577i	$-0.657155\pi$
$787$	296.540	−	1106.70i	0.376798	−	1.40623i	0.850700	−	0.525651i	$-0.176178\pi$
$788$	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	−0.639851	−	0.768499i	$-0.721004\pi$
$797$	−234.506	+	135.392i	−0.294236	+	0.169877i	0.345615	+	0.938377i	$0.387670\pi$
$798$	−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	−0.942361	−	0.334598i	$-0.891400\pi$
$809$	−615.609	−	1066.27i	−0.760951	−	1.31801i	0.181410	−	0.983408i	$-0.441934\pi$
$810$	−13.4962	−	1677.38i	−0.0166620	−	2.07084i
$811$	−249.991	+	249.991i	−0.308251	+	0.308251i	−0.844231	−	0.535980i	$-0.819942\pi$
$811$	−249.991	+	249.991i	−0.308251	+	0.308251i	0.535980	+	0.844231i	$0.319942\pi$
$812$	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	0.995903	+	0.0904233i	$0.0288220\pi$
$821$	146.661	+	547.347i	0.178637	+	0.666684i	−0.817266	+	0.576261i	$0.804511\pi$
$822$	248.636	+	428.657i	0.302477	+	0.521481i
$823$	958.015	−	553.110i	1.16405	−	0.672066i	0.211780	−	0.977317i	$-0.432074\pi$
$823$	958.015	−	553.110i	1.16405	−	0.672066i	0.952272	+	0.305251i	$0.0987405\pi$
$824$	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	0.538353	−	0.842720i	$-0.319047\pi$
$827$	−251.711	−	251.711i	−0.304367	−	0.304367i	−0.842720	+	0.538353i	$0.819047\pi$
$828$	186.152	−	325.441i	0.224821	−	0.393045i
$829$	720.778	−	416.141i	0.869454	−	0.501980i	0.00228740	−	0.999997i	$-0.499272\pi$
$829$	720.778	−	416.141i	0.869454	−	0.501980i	0.867167	+	0.498018i	$0.165939\pi$
$830$	−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	0.956878	−	0.290492i	$-0.0938189\pi$
$839$	559.098	+	559.098i	0.666386	+	0.666386i	−0.290492	+	0.956878i	$0.593819\pi$
$840$	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	0.393970	+	0.919123i	$0.371101\pi$
$853$	−346.983	+	1294.96i	−0.406780	+	1.51812i	−0.800750	+	0.598999i	$0.795565\pi$
$854$	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	0.247485	−	0.968892i	$-0.420396\pi$
$857$	1037.24	−	598.850i	1.21031	−	0.698774i	0.962827	+	0.270117i	$0.0870625\pi$
$858$	683.997	+	10.4458i	0.797200	+	0.0121746i
$859$	127.231	−	220.371i	0.148116	−	0.256544i	−0.782415	−	0.622757i	$-0.786013\pi$
$859$	127.231	−	220.371i	0.148116	−	0.256544i	0.930531	+	0.366213i	$0.119346\pi$
$860$	−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	−0.822771	−	0.568374i	$-0.807573\pi$
$863$	−219.545	+	219.545i	−0.254397	+	0.254397i	0.568374	+	0.822771i	$0.307573\pi$
$864$	−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	−0.207012	−	0.978338i	$-0.566374\pi$
$877$	−767.777	−	205.725i	−0.875459	−	0.234579i	−0.668447	+	0.743760i	$0.733041\pi$
$878$	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	−0.901636	−	0.432496i	$-0.857633\pi$
$881$	−861.530	+	497.405i	−0.977901	+	0.564591i	−0.0762650	+	0.997088i	$0.524299\pi$
$882$	−278.511	−	276.279i	−0.315772	−	0.313241i
$883$		−	1275.83i		−	1.44488i	−0.691435	−	0.722438i	$-0.743021\pi$
$883$		−	1275.83i		−	1.44488i	0.691435	−	0.722438i	$-0.256979\pi$
$884$	−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	0.710769	−	0.703426i	$-0.248347\pi$
$907$	414.470	+	239.295i	0.456969	+	0.263831i	−0.253800	+	0.967257i	$0.581681\pi$
$908$	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	0.991879	−	0.127189i	$-0.0405954\pi$
$911$	351.455	+	608.738i	0.385791	+	0.668209i	−0.606088	+	0.795398i	$0.707262\pi$
$912$	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	−0.752815	−	0.658232i	$-0.771304\pi$
$919$	177.954	−	308.225i	0.193639	−	0.335392i	0.946453	+	0.322841i	$0.104638\pi$
$920$	−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	−0.783881	−	0.620911i	$-0.786763\pi$
$929$	−151.399	+	151.399i	−0.162970	+	0.162970i	0.620911	+	0.783881i	$0.286763\pi$
$930$	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	0.908916	−	0.416979i	$-0.136911\pi$
$941$	−81.6015	−	304.541i	−0.0867179	−	0.323636i	−0.995634	+	0.0933435i	$0.970245\pi$
$942$	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	−0.523934	−	0.851759i	$-0.675536\pi$
$947$	−522.550	+	140.017i	−0.551795	+	0.147853i	−0.0278610	+	0.999612i	$0.508870\pi$
$948$	−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	0.430292	−	0.902690i	$-0.358411\pi$
$953$	−129.908	−	75.0025i	−0.136315	−	0.0787015i	−0.566607	+	0.823988i	$0.691744\pi$
$954$	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	0.974961	−	0.222374i	$-0.0713807\pi$
$967$	18.7917	+	70.1315i	0.0194330	+	0.0725249i	−0.955528	+	0.294899i	$0.904714\pi$
$968$	−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	−0.959506	−	0.281688i	$-0.909106\pi$
$971$	−228.965	+	396.580i	−0.235804	+	0.408424i	0.723702	+	0.690112i	$0.242439\pi$
$972$	−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	−0.758338	−	0.651862i	$-0.773988\pi$
$977$	−104.027	+	104.027i	−0.106476	+	0.106476i	0.651862	+	0.758338i	$0.273988\pi$
$978$	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	−0.894512	−	0.447045i	$-0.852476\pi$
$983$	101.918	−	380.363i	0.103681	−	0.386941i	0.998192	+	0.0601037i	$0.0191432\pi$
$984$	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	0.522433	−	0.852681i	$-0.325025\pi$
$991$	−472.932	−	819.142i	−0.477227	−	0.826581i	−0.999659	+	0.0260997i	$0.991691\pi$
$992$		−	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.67.4	yes	104
3.2	odd	2		351.3.be.a.145.23		104
9.2	odd	6		351.3.z.a.262.23		104
9.7	even	3		117.3.w.a.106.4	yes	104
13.7	odd	12		117.3.w.a.85.4	✓	104
39.20	even	12		351.3.z.a.280.23		104
117.7	odd	12	inner	117.3.bb.a.7.4	yes	104
117.20	even	12		351.3.be.a.46.23		104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.w.a.85.4	✓	104	13.7	odd	12
117.3.w.a.106.4	yes	104	9.7	even	3
117.3.bb.a.7.4	yes	104	117.7	odd	12	inner
117.3.bb.a.67.4	yes	104	1.1	even	1	trivial
351.3.z.a.262.23		104	9.2	odd	6
351.3.z.a.280.23		104	39.20	even	12
351.3.be.a.46.23		104	117.20	even	12
351.3.be.a.145.23		104	3.2	odd	2

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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