LMFDB - Embedded newform 416.3.bb.c.191.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,3,Mod(159,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.159"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	416.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,-8,0,0,0,80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$11.3351789974$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.7
Character	$\chi$	$=$	416.191
Dual form			416.3.bb.c.159.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.576566 - 0.332881i) q^{3} -2.21788 q^{5} +(1.70346 - 0.983494i) q^{7} +(-4.27838 - 7.41037i) q^{9} +(-5.88030 - 3.39500i) q^{11} +(5.15319 + 11.9350i) q^{13} +(1.27875 + 0.738289i) q^{15} +(15.6446 + 27.0972i) q^{17} +(-22.2355 + 12.8377i) q^{19} -1.30955 q^{21} +(-22.3874 - 12.9254i) q^{23} -20.0810 q^{25} +11.6886i q^{27} +(-5.69864 + 9.87033i) q^{29} -48.9377i q^{31} +(2.26026 + 3.91488i) q^{33} +(-3.77807 + 2.18127i) q^{35} +(-18.5864 + 32.1926i) q^{37} +(1.00178 - 8.59673i) q^{39} +(-3.15967 + 5.47272i) q^{41} +(-70.4488 + 40.6737i) q^{43} +(9.48892 + 16.4353i) q^{45} +48.9746i q^{47} +(-22.5655 + 39.0846i) q^{49} -20.8311i q^{51} +20.7411 q^{53} +(13.0418 + 7.52968i) q^{55} +17.0937 q^{57} +(-2.77794 + 1.60385i) q^{59} +(-8.27717 - 14.3365i) q^{61} +(-14.5761 - 8.41553i) q^{63} +(-11.4291 - 26.4704i) q^{65} +(-47.1880 - 27.2440i) q^{67} +(8.60520 + 14.9047i) q^{69} +(67.4819 - 38.9607i) q^{71} +56.2186 q^{73} +(11.5780 + 6.68458i) q^{75} -13.3558 q^{77} -126.553i q^{79} +(-34.6145 + 59.9541i) q^{81} +146.677i q^{83} +(-34.6978 - 60.0983i) q^{85} +(6.57128 - 3.79393i) q^{87} +(25.8544 - 44.7812i) q^{89} +(20.5163 + 15.2627i) q^{91} +(-16.2904 + 28.2158i) q^{93} +(49.3157 - 28.4724i) q^{95} +(-35.3285 - 61.1907i) q^{97} +58.1003i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{5} + 80 q^{9} - 44 q^{13} + 16 q^{17} - 128 q^{21} + 272 q^{25} - 52 q^{29} - 72 q^{33} + 148 q^{37} + 72 q^{41} - 116 q^{45} + 328 q^{49} - 152 q^{53} - 224 q^{57} + 228 q^{61} - 352 q^{65}+ \cdots - 352 q^{97}+O(q^{100}) $ 32 * q - 8 * q^5 + 80 * q^9 - 44 * q^13 + 16 * q^17 - 128 * q^21 + 272 * q^25 - 52 * q^29 - 72 * q^33 + 148 * q^37 + 72 * q^41 - 116 * q^45 + 328 * q^49 - 152 * q^53 - 224 * q^57 + 228 * q^61 - 352 * q^65 + 200 * q^69 + 224 * q^73 + 832 * q^77 - 696 * q^81 - 84 * q^85 - 112 * q^89 + 152 * q^93 - 352 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	−0.576566	−	0.332881i	−0.192189	−	0.110960i	0.400818	−	0.916158i	$-0.368726\pi$
$3$	−0.576566	−	0.332881i	−0.192189	−	0.110960i	−0.593007	+	0.805197i	$0.702059\pi$
$4$		0			0
$5$	−2.21788			−0.443576			−0.221788	−	0.975095i	$-0.571189\pi$
$5$	−2.21788			−0.443576			−0.221788	+	0.975095i	$0.571189\pi$
$6$		0			0
$7$	1.70346	−	0.983494i	0.243352	−	0.140499i	−0.373365	−	0.927685i	$-0.621796\pi$
$7$	1.70346	−	0.983494i	0.243352	−	0.140499i	0.616716	+	0.787186i	$0.288463\pi$
$8$		0			0
$9$	−4.27838	−	7.41037i	−0.475376	−	0.823375i
$10$		0			0
$11$	−5.88030	−	3.39500i	−0.534573	−	0.308636i	0.208304	−	0.978064i	$-0.433206\pi$
$11$	−5.88030	−	3.39500i	−0.534573	−	0.308636i	−0.742877	+	0.669428i	$0.766539\pi$
$12$		0			0
$13$	5.15319	+	11.9350i	0.396399	+	0.918078i
$13$	5.15319	+	11.9350i	0.396399	+	0.918078i
$14$		0			0
$15$	1.27875	+	0.738289i	0.0852502	+	0.0492192i
$16$		0			0
$17$	15.6446	+	27.0972i	0.920270	+	1.59395i	0.798997	+	0.601336i	$0.205365\pi$
$17$	15.6446	+	27.0972i	0.920270	+	1.59395i	0.121274	+	0.992619i	$0.461302\pi$
$18$		0			0
$19$	−22.2355	+	12.8377i	−1.17029	+	0.675668i	−0.953748	−	0.300606i	$-0.902811\pi$
$19$	−22.2355	+	12.8377i	−1.17029	+	0.675668i	−0.216542	+	0.976273i	$0.569478\pi$
$20$		0			0
$21$	−1.30955			−0.0623593
$22$		0			0
$23$	−22.3874	−	12.9254i	−0.973364	−	0.561972i	−0.0731040	−	0.997324i	$-0.523291\pi$
$23$	−22.3874	−	12.9254i	−0.973364	−	0.561972i	−0.900260	+	0.435352i	$0.856624\pi$
$24$		0			0
$25$	−20.0810			−0.803241
$26$		0			0
$27$			11.6886i			0.432912i
$28$		0			0
$29$	−5.69864	+	9.87033i	−0.196505	+	0.340356i	−0.947393	−	0.320073i	$-0.896292\pi$
$29$	−5.69864	+	9.87033i	−0.196505	+	0.340356i	0.750888	+	0.660429i	$0.229626\pi$
$30$		0			0
$31$		−	48.9377i		−	1.57863i	−0.613985	−	0.789317i	$-0.710435\pi$
$31$		−	48.9377i		−	1.57863i	0.613985	−	0.789317i	$-0.289565\pi$
$32$		0			0
$33$	2.26026	+	3.91488i	0.0684926	+	0.118633i
$34$		0			0
$35$	−3.77807	+	2.18127i	−0.107945	+	0.0623220i
$36$		0			0
$37$	−18.5864	+	32.1926i	−0.502335	+	0.870070i	0.497661	+	0.867372i	$0.334192\pi$
$37$	−18.5864	+	32.1926i	−0.502335	+	0.870070i	−0.999996	+	0.00269853i	$0.999141\pi$
$38$		0			0
$39$	1.00178	−	8.59673i	0.0256867	−	0.220429i
$40$		0			0
$41$	−3.15967	+	5.47272i	−0.0770652	+	0.133481i	−0.901983	−	0.431773i	$-0.857888\pi$
$41$	−3.15967	+	5.47272i	−0.0770652	+	0.133481i	0.824917	+	0.565253i	$0.191222\pi$
$42$		0			0
$43$	−70.4488	+	40.6737i	−1.63835	+	0.945899i	−0.656942	+	0.753941i	$0.728150\pi$
$43$	−70.4488	+	40.6737i	−1.63835	+	0.945899i	−0.981403	+	0.191958i	$0.938516\pi$
$44$		0			0
$45$	9.48892	+	16.4353i	0.210865	+	0.365229i
$46$		0			0
$47$			48.9746i			1.04201i	0.853553	+	0.521006i	$0.174443\pi$
$47$			48.9746i			1.04201i	−0.853553	+	0.521006i	$0.825557\pi$
$48$		0			0
$49$	−22.5655	+	39.0846i	−0.460520	+	0.797644i
$50$		0			0
$51$		−	20.8311i		−	0.408454i
$52$		0			0
$53$	20.7411			0.391341			0.195671	−	0.980670i	$-0.437312\pi$
$53$	20.7411			0.391341			0.195671	+	0.980670i	$0.437312\pi$
$54$		0			0
$55$	13.0418	+	7.52968i	0.237124	+	0.136903i
$56$		0			0
$57$	17.0937			0.299889
$58$		0			0
$59$	−2.77794	+	1.60385i	−0.0470837	+	0.0271838i	−0.523357	−	0.852113i	$-0.675321\pi$
$59$	−2.77794	+	1.60385i	−0.0470837	+	0.0271838i	0.476273	+	0.879297i	$0.341987\pi$
$60$		0			0
$61$	−8.27717	−	14.3365i	−0.135691	−	0.235024i	0.790170	−	0.612888i	$-0.209992\pi$
$61$	−8.27717	−	14.3365i	−0.135691	−	0.235024i	−0.925861	+	0.377863i	$0.876659\pi$
$62$		0			0
$63$	−14.5761	−	8.41553i	−0.231367	−	0.133580i
$64$		0			0
$65$	−11.4291	−	26.4704i	−0.175833	−	0.407237i
$66$		0			0
$67$	−47.1880	−	27.2440i	−0.704298	−	0.406627i	0.104648	−	0.994509i	$-0.466628\pi$
$67$	−47.1880	−	27.2440i	−0.704298	−	0.406627i	−0.808946	+	0.587883i	$0.799962\pi$
$68$		0			0
$69$	8.60520	+	14.9047i	0.124713	+	0.216009i
$70$		0			0
$71$	67.4819	−	38.9607i	0.950449	−	0.548742i	0.0572288	−	0.998361i	$-0.481774\pi$
$71$	67.4819	−	38.9607i	0.950449	−	0.548742i	0.893220	+	0.449619i	$0.148440\pi$
$72$		0			0
$73$	56.2186			0.770118			0.385059	−	0.922892i	$-0.374181\pi$
$73$	56.2186			0.770118			0.385059	+	0.922892i	$0.374181\pi$
$74$		0			0
$75$	11.5780	+	6.68458i	0.154374	+	0.0891278i
$76$		0			0
$77$	−13.3558			−0.173452
$78$		0			0
$79$		−	126.553i		−	1.60193i	−0.598711	−	0.800965i	$-0.704320\pi$
$79$		−	126.553i		−	1.60193i	0.598711	−	0.800965i	$-0.295680\pi$
$80$		0			0
$81$	−34.6145	+	59.9541i	−0.427340	+	0.740174i
$82$		0			0
$83$			146.677i			1.76719i	0.468252	+	0.883595i	$0.344884\pi$
$83$			146.677i			1.76719i	−0.468252	+	0.883595i	$0.655116\pi$
$84$		0			0
$85$	−34.6978	−	60.0983i	−0.408209	−	0.707039i
$86$		0			0
$87$	6.57128	−	3.79393i	0.0755320	−	0.0436084i
$88$		0			0
$89$	25.8544	−	44.7812i	0.290499	−	0.503159i	−0.683429	−	0.730017i	$-0.739512\pi$
$89$	25.8544	−	44.7812i	0.290499	−	0.503159i	0.973928	+	0.226858i	$0.0728454\pi$
$90$		0			0
$91$	20.5163	+	15.2627i	0.225454	+	0.167722i
$92$		0			0
$93$	−16.2904	+	28.2158i	−0.175166	+	0.303396i
$94$		0			0
$95$	49.3157	−	28.4724i	0.519112	−	0.299710i
$96$		0			0
$97$	−35.3285	−	61.1907i	−0.364211	−	0.630832i	0.624438	−	0.781074i	$-0.285328\pi$
$97$	−35.3285	−	61.1907i	−0.364211	−	0.630832i	−0.988649	+	0.150242i	$0.951995\pi$
$98$		0			0
$99$			58.1003i			0.586872i
$100$		0			0
$101$	38.3011	−	66.3394i	0.379219	−	0.656826i	−0.611730	−	0.791067i	$-0.709526\pi$
$101$	38.3011	−	66.3394i	0.379219	−	0.656826i	0.990949	+	0.134240i	$0.0428595\pi$
$102$		0			0
$103$		−	15.4021i		−	0.149535i	−0.997201	−	0.0747674i	$-0.976179\pi$
$103$		−	15.4021i		−	0.149535i	0.997201	−	0.0747674i	$-0.0238214\pi$
$104$		0			0
$105$	2.90441			0.0276611
$106$		0			0
$107$	−79.1106	−	45.6746i	−0.739352	−	0.426865i	0.0824818	−	0.996593i	$-0.473715\pi$
$107$	−79.1106	−	45.6746i	−0.739352	−	0.426865i	−0.821834	+	0.569728i	$0.807049\pi$
$108$		0			0
$109$	−9.13850			−0.0838394			−0.0419197	−	0.999121i	$-0.513347\pi$
$109$	−9.13850			−0.0838394			−0.0419197	+	0.999121i	$0.513347\pi$
$110$		0			0
$111$	21.4326	−	12.3741i	0.193086	−	0.111478i
$112$		0			0
$113$	35.4919	+	61.4738i	0.314088	+	0.544016i	0.979243	−	0.202689i	$-0.0649681\pi$
$113$	35.4919	+	61.4738i	0.314088	+	0.544016i	−0.665155	+	0.746705i	$0.731635\pi$
$114$		0			0
$115$	49.6525	+	28.6669i	0.431761	+	0.249277i
$116$		0			0
$117$	66.3956	−	89.2496i	0.567484	−	0.762817i
$118$		0			0
$119$	53.2999	+	30.7727i	0.447899	+	0.258594i
$120$		0			0
$121$	−37.4480	−	64.8619i	−0.309488	−	0.536048i
$122$		0			0
$123$	3.64352	−	2.10359i	0.0296221	−	0.0171024i
$124$		0			0
$125$	99.9842			0.799873
$126$		0			0
$127$	165.732	+	95.6854i	1.30498	+	0.753428i	0.981253	−	0.192723i	$-0.0617320\pi$
$127$	165.732	+	95.6854i	1.30498	+	0.753428i	0.323723	+	0.946152i	$0.395065\pi$
$128$		0			0
$129$	54.1579			0.419829
$130$		0			0
$131$			40.2174i			0.307003i	0.988148	+	0.153502i	$0.0490550\pi$
$131$			40.2174i			0.307003i	−0.988148	+	0.153502i	$0.950945\pi$
$132$		0			0
$133$	−25.2516	+	43.7370i	−0.189861	+	0.328850i
$134$		0			0
$135$		−	25.9239i		−	0.192029i
$136$		0			0
$137$	−61.1993	−	106.000i	−0.446710	−	0.773724i	0.551460	−	0.834202i	$-0.314071\pi$
$137$	−61.1993	−	106.000i	−0.446710	−	0.773724i	−0.998170	+	0.0604771i	$0.980738\pi$
$138$		0			0
$139$	100.067	−	57.7738i	0.719908	−	0.415639i	−0.0948110	−	0.995495i	$-0.530225\pi$
$139$	100.067	−	57.7738i	0.719908	−	0.415639i	0.814719	+	0.579856i	$0.196891\pi$
$140$		0			0
$141$	16.3027	−	28.2371i	0.115622	−	0.200263i
$142$		0			0
$143$	10.2170	−	87.6766i	0.0714476	−	0.613123i
$144$		0			0
$145$	12.6389	−	21.8912i	0.0871647	−	0.150974i
$146$		0			0
$147$	26.0210	−	15.0232i	0.177014	−	0.102199i
$148$		0			0
$149$	−96.4775	−	167.104i	−0.647500	−	1.12150i	−0.983718	−	0.179719i	$-0.942481\pi$
$149$	−96.4775	−	167.104i	−0.647500	−	1.12150i	0.336218	−	0.941784i	$-0.390852\pi$
$150$		0			0
$151$		−	36.3232i		−	0.240551i	−0.992741	−	0.120276i	$-0.961622\pi$
$151$		−	36.3232i		−	0.240551i	0.992741	−	0.120276i	$-0.0383778\pi$
$152$		0			0
$153$	133.867	−	231.865i	0.874948	−	1.51545i
$154$		0			0
$155$			108.538i			0.700244i
$156$		0			0
$157$	−198.926			−1.26705			−0.633524	−	0.773723i	$-0.718392\pi$
$157$	−198.926			−1.26705			−0.633524	+	0.773723i	$0.718392\pi$
$158$		0			0
$159$	−11.9586	−	6.90431i	−0.0752114	−	0.0434233i
$160$		0			0
$161$	−50.8481			−0.315826
$162$		0			0
$163$	146.565	−	84.6196i	0.899174	−	0.519138i	0.0222420	−	0.999753i	$-0.492920\pi$
$163$	146.565	−	84.6196i	0.899174	−	0.519138i	0.876932	+	0.480614i	$0.159586\pi$
$164$		0			0
$165$	−5.01297	−	8.68272i	−0.0303817	−	0.0526226i
$166$		0			0
$167$	175.923	+	101.569i	1.05343	+	0.608199i	0.923608	−	0.383338i	$-0.125226\pi$
$167$	175.923	+	101.569i	1.05343	+	0.608199i	0.129824	+	0.991537i	$0.458559\pi$
$168$		0			0
$169$	−115.889	+	123.007i	−0.685735	+	0.727851i
$170$		0			0
$171$	190.264	+	109.849i	1.11266	+	0.642392i
$172$		0			0
$173$	77.0704	+	133.490i	0.445493	+	0.771617i	0.998086	−	0.0618339i	$-0.0196949\pi$
$173$	77.0704	+	133.490i	0.445493	+	0.771617i	−0.552593	+	0.833451i	$0.686362\pi$
$174$		0			0
$175$	−34.2073	+	19.7496i	−0.195470	+	0.112855i
$176$		0			0
$177$	2.13556			0.0120653
$178$		0			0
$179$	−85.1909	−	49.1850i	−0.475927	−	0.274776i	0.242791	−	0.970079i	$-0.421937\pi$
$179$	−85.1909	−	49.1850i	−0.475927	−	0.274776i	−0.718717	+	0.695302i	$0.755271\pi$
$180$		0			0
$181$	188.078			1.03911			0.519554	−	0.854438i	$-0.326098\pi$
$181$	188.078			1.03911			0.519554	+	0.854438i	$0.326098\pi$
$182$		0			0
$183$			11.0212i			0.0602254i
$184$		0			0
$185$	41.2224	−	71.3992i	0.222824	−	0.385942i
$186$		0			0
$187$		−	212.453i		−	1.13611i
$188$		0			0
$189$	11.4957	+	19.9111i	0.0608237	+	0.105350i
$190$		0			0
$191$	−211.924	+	122.355i	−1.10955	+	0.640600i	−0.938713	−	0.344699i	$-0.887981\pi$
$191$	−211.924	+	122.355i	−1.10955	+	0.640600i	−0.170839	+	0.985299i	$0.554648\pi$
$192$		0			0
$193$	−101.903	+	176.501i	−0.527996	+	0.914515i	0.471472	+	0.881881i	$0.343723\pi$
$193$	−101.903	+	176.501i	−0.527996	+	0.914515i	−0.999467	+	0.0326342i	$0.989610\pi$
$194$		0			0
$195$	−2.22183	+	19.0665i	−0.0113940	+	0.0977768i
$196$		0			0
$197$	106.116	−	183.798i	0.538660	−	0.932986i	−0.460317	−	0.887755i	$-0.652264\pi$
$197$	106.116	−	183.798i	0.538660	−	0.932986i	0.998977	−	0.0452315i	$-0.0144025\pi$
$198$		0			0
$199$	−273.754	+	158.052i	−1.37565	+	0.794232i	−0.991632	−	0.129094i	$-0.958793\pi$
$199$	−273.754	+	158.052i	−1.37565	+	0.794232i	−0.384018	+	0.923326i	$0.625460\pi$
$200$		0			0
$201$	18.1380	+	31.4159i	0.0902387	+	0.156298i
$202$		0			0
$203$			22.4183i			0.110435i
$204$		0			0
$205$	7.00777	−	12.1378i	0.0341842	−	0.0592089i
$206$		0			0
$207$			221.198i			1.06859i
$208$		0			0
$209$	174.336			0.834141
$210$		0			0
$211$	−291.910	−	168.534i	−1.38346	−	0.798741i	−0.390893	−	0.920436i	$-0.627834\pi$
$211$	−291.910	−	168.534i	−1.38346	−	0.798741i	−0.992568	+	0.121695i	$0.961167\pi$
$212$		0			0
$213$	−51.8770			−0.243554
$214$		0			0
$215$	156.247	−	90.2092i	0.726730	−	0.419578i
$216$		0			0
$217$	−48.1299	−	83.3635i	−0.221797	−	0.384163i
$218$		0			0
$219$	−32.4137	−	18.7141i	−0.148008	−	0.0854524i
$220$		0			0
$221$	−242.786	+	326.356i	−1.09858	+	1.47672i
$222$		0			0
$223$	−128.077	−	73.9456i	−0.574339	−	0.331595i	0.184542	−	0.982825i	$-0.440920\pi$
$223$	−128.077	−	73.9456i	−0.574339	−	0.331595i	−0.758880	+	0.651230i	$0.774253\pi$
$224$		0			0
$225$	85.9142	+	148.808i	0.381841	+	0.661368i
$226$		0			0
$227$	299.989	−	173.199i	1.32154	−	0.762991i	0.337565	−	0.941302i	$-0.390397\pi$
$227$	299.989	−	173.199i	1.32154	−	0.762991i	0.983974	+	0.178311i	$0.0570633\pi$
$228$		0			0
$229$	−140.263			−0.612501			−0.306251	−	0.951951i	$-0.599075\pi$
$229$	−140.263			−0.612501			−0.306251	+	0.951951i	$0.599075\pi$
$230$		0			0
$231$	7.70052	+	4.44590i	0.0333356	+	0.0192463i
$232$		0			0
$233$	−37.6195			−0.161457			−0.0807285	−	0.996736i	$-0.525725\pi$
$233$	−37.6195			−0.161457			−0.0807285	+	0.996736i	$0.525725\pi$
$234$		0			0
$235$		−	108.620i		−	0.462211i
$236$		0			0
$237$	−42.1269	+	72.9659i	−0.177751	+	0.307873i
$238$		0			0
$239$			141.695i			0.592865i	0.955054	+	0.296433i	$0.0957970\pi$
$239$			141.695i			0.592865i	−0.955054	+	0.296433i	$0.904203\pi$
$240$		0			0
$241$	−51.0492	−	88.4197i	−0.211822	−	0.366887i	0.740463	−	0.672098i	$-0.234606\pi$
$241$	−51.0492	−	88.4197i	−0.211822	−	0.366887i	−0.952285	+	0.305211i	$0.901273\pi$
$242$		0			0
$243$	131.019	−	75.6438i	0.539172	−	0.311291i
$244$		0			0
$245$	50.0475	−	86.6848i	0.204275	−	0.353815i
$246$		0			0
$247$	−267.802	−	199.226i	−1.08422	−	0.806584i
$248$		0			0
$249$	48.8259	−	84.5689i	0.196088	−	0.339634i
$250$		0			0
$251$	−149.068	+	86.0642i	−0.593895	+	0.342885i	−0.766636	−	0.642082i	$-0.778071\pi$
$251$	−149.068	+	86.0642i	−0.593895	+	0.342885i	0.172741	+	0.984967i	$0.444738\pi$
$252$		0			0
$253$	87.7631	+	152.010i	0.346890	+	0.600830i
$254$		0			0
$255$			46.2009i			0.181180i
$256$		0			0
$257$	−85.5022	+	148.094i	−0.332693	+	0.576242i	−0.983039	−	0.183396i	$-0.941291\pi$
$257$	−85.5022	+	148.094i	−0.332693	+	0.576242i	0.650346	+	0.759639i	$0.274624\pi$
$258$		0			0
$259$			73.1185i			0.282311i
$260$		0			0
$261$	97.5237			0.373654
$262$		0			0
$263$	−128.083	−	73.9485i	−0.487006	−	0.281173i	0.236326	−	0.971674i	$-0.424057\pi$
$263$	−128.083	−	73.9485i	−0.487006	−	0.281173i	−0.723332	+	0.690501i	$0.757390\pi$
$264$		0			0
$265$	−46.0012			−0.173589
$266$		0			0
$267$	−29.8136	+	17.2129i	−0.111661	+	0.0644677i
$268$		0			0
$269$	161.211	+	279.226i	0.599298	+	1.03802i	0.992925	+	0.118745i	$0.0378871\pi$
$269$	161.211	+	279.226i	0.599298	+	1.03802i	−0.393626	+	0.919271i	$0.628780\pi$
$270$		0			0
$271$	−123.017	−	71.0240i	−0.453938	−	0.262081i	0.255554	−	0.966795i	$-0.417742\pi$
$271$	−123.017	−	71.0240i	−0.453938	−	0.262081i	−0.709492	+	0.704714i	$0.751075\pi$
$272$		0			0
$273$	−6.74833	−	15.6294i	−0.0247192	−	0.0572507i
$274$		0			0
$275$	118.083	+	68.1750i	0.429391	+	0.247909i
$276$		0			0
$277$	46.7361	+	80.9493i	0.168722	+	0.292236i	0.937971	−	0.346714i	$-0.112703\pi$
$277$	46.7361	+	80.9493i	0.168722	+	0.292236i	−0.769249	+	0.638950i	$0.779369\pi$
$278$		0			0
$279$	−362.646	+	209.374i	−1.29981	+	0.750444i
$280$		0			0
$281$	373.711			1.32993			0.664966	−	0.746874i	$-0.268446\pi$
$281$	373.711			1.32993			0.664966	+	0.746874i	$0.268446\pi$
$282$		0			0
$283$	−80.8275	−	46.6658i	−0.285610	−	0.164897i	0.350351	−	0.936619i	$-0.386062\pi$
$283$	−80.8275	−	46.6658i	−0.285610	−	0.164897i	−0.635960	+	0.771722i	$0.719396\pi$
$284$		0			0
$285$	−37.9117			−0.133023
$286$		0			0
$287$			12.4301i			0.0433104i
$288$		0			0
$289$	−345.007	+	597.569i	−1.19379	+	2.06771i
$290$		0			0
$291$			47.0407i			0.161652i
$292$		0			0
$293$	−243.521	−	421.790i	−0.831128	−	1.43956i	−0.897144	−	0.441738i	$-0.854362\pi$
$293$	−243.521	−	421.790i	−0.831128	−	1.43956i	0.0660162	−	0.997819i	$-0.478971\pi$
$294$		0			0
$295$	6.16113	−	3.55713i	0.0208852	−	0.0120581i
$296$		0			0
$297$	39.6828	−	68.7326i	0.133612	−	0.231423i
$298$		0			0
$299$	38.8980	−	333.801i	0.130094	−	1.11639i
$300$		0			0
$301$	−80.0046	+	138.572i	−0.265796	+	0.460372i
$302$		0			0
$303$	−44.1662	+	25.4994i	−0.145763	+	0.0841564i
$304$		0			0
$305$	18.3578	+	31.7966i	0.0601894	+	0.104251i
$306$		0			0
$307$			25.1356i			0.0818749i	0.999162	+	0.0409374i	$0.0130344\pi$
$307$			25.1356i			0.0818749i	−0.999162	+	0.0409374i	$0.986966\pi$
$308$		0			0
$309$	−5.12705	+	8.88032i	−0.0165924	+	0.0287389i
$310$		0			0
$311$			272.009i			0.874627i	0.899309	+	0.437313i	$0.144070\pi$
$311$			272.009i			0.874627i	−0.899309	+	0.437313i	$0.855930\pi$
$312$		0			0
$313$	−450.157			−1.43820			−0.719101	−	0.694905i	$-0.755446\pi$
$313$	−450.157			−1.43820			−0.719101	+	0.694905i	$0.755446\pi$
$314$		0			0
$315$	32.3280	+	18.6646i	0.102629	+	0.0592527i
$316$		0			0
$317$	369.276			1.16491			0.582454	−	0.812863i	$-0.302092\pi$
$317$	369.276			1.16491			0.582454	+	0.812863i	$0.302092\pi$
$318$		0			0
$319$	67.0194	−	38.6937i	0.210092	−	0.121297i
$320$		0			0
$321$	30.4084	+	52.6688i	0.0947301	+	0.164077i
$322$		0			0
$323$	−695.731	−	401.681i	−2.15397	−	1.24359i
$324$		0			0
$325$	−103.481	−	239.667i	−0.318404	−	0.737438i
$326$		0			0
$327$	5.26895	+	3.04203i	0.0161130	+	0.00930284i
$328$		0			0
$329$	48.1662	+	83.4263i	0.146402	+	0.253575i
$330$		0			0
$331$	304.135	−	175.592i	0.918837	−	0.530491i	0.0355728	−	0.999367i	$-0.488674\pi$
$331$	304.135	−	175.592i	0.918837	−	0.530491i	0.883264	+	0.468877i	$0.155341\pi$
$332$		0			0
$333$	318.079			0.955192
$334$		0			0
$335$	104.657	+	60.4238i	0.312409	+	0.180370i
$336$		0			0
$337$	354.356			1.05150			0.525751	−	0.850638i	$-0.323784\pi$
$337$	354.356			1.05150			0.525751	+	0.850638i	$0.323784\pi$
$338$		0			0
$339$		−	47.2583i		−	0.139405i
$340$		0			0
$341$	−166.143	+	287.768i	−0.487223	+	0.843896i
$342$		0			0
$343$			185.155i			0.539809i
$344$		0			0
$345$	−19.0853	−	33.0567i	−0.0553197	−	0.0958165i
$346$		0			0
$347$	−66.0668	+	38.1437i	−0.190394	+	0.109924i	−0.592167	−	0.805815i	$-0.701727\pi$
$347$	−66.0668	+	38.1437i	−0.190394	+	0.109924i	0.401773	+	0.915739i	$0.368394\pi$
$348$		0			0
$349$	−341.837	+	592.079i	−0.979475	+	1.69650i	−0.315178	+	0.949032i	$0.602064\pi$
$349$	−341.837	+	592.079i	−0.979475	+	1.69650i	−0.664297	+	0.747469i	$0.731269\pi$
$350$		0			0
$351$	−139.504	+	60.2336i	−0.397447	+	0.171606i
$352$		0			0
$353$	−179.201	+	310.386i	−0.507653	+	0.879280i	0.492308	+	0.870421i	$0.336153\pi$
$353$	−179.201	+	310.386i	−0.507653	+	0.879280i	−0.999961	+	0.00885925i	$0.997180\pi$
$354$		0			0
$355$	−149.667	+	86.4100i	−0.421596	+	0.243409i
$356$		0			0
$357$	−20.4873	−	35.4850i	−0.0573874	−	0.0993979i
$358$		0			0
$359$			704.809i			1.96326i	0.190806	+	0.981628i	$0.438890\pi$
$359$			704.809i			1.96326i	−0.190806	+	0.981628i	$0.561110\pi$
$360$		0			0
$361$	149.112	−	258.270i	0.413053	−	0.715429i
$362$		0			0
$363$			49.8629i			0.137363i
$364$		0			0
$365$	−124.686			−0.341605
$366$		0			0
$367$	−348.259	−	201.067i	−0.948933	−	0.547867i	−0.0561839	−	0.998420i	$-0.517893\pi$
$367$	−348.259	−	201.067i	−0.948933	−	0.547867i	−0.892749	+	0.450554i	$0.851227\pi$
$368$		0			0
$369$	54.0732			0.146540
$370$		0			0
$371$	35.3317	−	20.3988i	0.0952336	−	0.0549832i
$372$		0			0
$373$	−149.107	−	258.260i	−0.399749	−	0.692386i	0.593945	−	0.804505i	$-0.297570\pi$
$373$	−149.107	−	258.260i	−0.399749	−	0.692386i	−0.993695	+	0.112119i	$0.964236\pi$
$374$		0			0
$375$	−57.6475	−	33.2828i	−0.153727	−	0.0887541i
$376$		0			0
$377$	−147.169	−	17.1496i	−0.390368	−	0.0454898i
$378$		0			0
$379$	−20.1610	−	11.6399i	−0.0531952	−	0.0307122i	0.473167	−	0.880973i	$-0.343111\pi$
$379$	−20.1610	−	11.6399i	−0.0531952	−	0.0307122i	−0.526362	+	0.850261i	$0.676444\pi$
$380$		0			0
$381$	−63.7037	−	110.338i	−0.167201	−	0.289601i
$382$		0			0
$383$	32.6408	−	18.8452i	0.0852239	−	0.0492041i	−0.456782	−	0.889578i	$-0.650998\pi$
$383$	32.6408	−	18.8452i	0.0852239	−	0.0492041i	0.542006	+	0.840374i	$0.317665\pi$
$384$		0			0
$385$	29.6216			0.0769392
$386$		0			0
$387$	602.814	+	348.035i	1.55766	+	0.899315i
$388$		0			0
$389$	318.795			0.819525			0.409762	−	0.912192i	$-0.365612\pi$
$389$	318.795			0.819525			0.409762	+	0.912192i	$0.365612\pi$
$390$		0			0
$391$		−	808.848i		−	2.06866i
$392$		0			0
$393$	13.3876	−	23.1880i	0.0340652	−	0.0590026i
$394$		0			0
$395$			280.678i			0.710577i
$396$		0			0
$397$	−180.443	−	312.537i	−0.454516	−	0.787246i	0.544144	−	0.838992i	$-0.316855\pi$
$397$	−180.443	−	312.537i	−0.454516	−	0.787246i	−0.998660	+	0.0517464i	$0.983521\pi$
$398$		0			0
$399$	29.1184	−	16.8115i	0.0729785	−	0.0421341i
$400$		0			0
$401$	14.5528	−	25.2062i	0.0362913	−	0.0628585i	−0.847309	−	0.531100i	$-0.821779\pi$
$401$	14.5528	−	25.2062i	0.0362913	−	0.0628585i	0.883601	+	0.468241i	$0.155112\pi$
$402$		0			0
$403$	584.072	−	252.185i	1.44931	−	0.625770i
$404$		0			0
$405$	76.7708	−	132.971i	0.189557	−	0.328323i
$406$		0			0
$407$	218.587	−	126.201i	0.537070	−	0.310077i
$408$		0			0
$409$	−24.4161	−	42.2899i	−0.0596971	−	0.103398i	0.834632	−	0.550807i	$-0.185680\pi$
$409$	−24.4161	−	42.2899i	−0.0596971	−	0.103398i	−0.894329	+	0.447409i	$0.852347\pi$
$410$		0			0
$411$			81.4882i			0.198268i
$412$		0			0
$413$	−3.15475	+	5.46418i	−0.00763861	+	0.0132305i
$414$		0			0
$415$		−	325.311i		−	0.783882i
$416$		0			0
$417$	−76.9271			−0.184478
$418$		0			0
$419$	−288.275	−	166.436i	−0.688008	−	0.397221i	0.114858	−	0.993382i	$-0.463359\pi$
$419$	−288.275	−	166.436i	−0.688008	−	0.397221i	−0.802865	+	0.596161i	$0.796692\pi$
$420$		0			0
$421$	103.721			0.246367			0.123184	−	0.992384i	$-0.460690\pi$
$421$	103.721			0.246367			0.123184	+	0.992384i	$0.460690\pi$
$422$		0			0
$423$	362.920	−	209.532i	0.857966	−	0.495347i
$424$		0			0
$425$	−314.159	−	544.140i	−0.739199	−	1.28033i
$426$		0			0
$427$	−28.1997	−	16.2811i	−0.0660415	−	0.0381291i
$428$		0			0
$429$	−35.0766	+	47.1503i	−0.0817637	+	0.109908i
$430$		0			0
$431$	260.403	+	150.344i	0.604183	+	0.348825i	0.770685	−	0.637216i	$-0.219914\pi$
$431$	260.403	+	150.344i	0.604183	+	0.348825i	−0.166502	+	0.986041i	$0.553247\pi$
$432$		0			0
$433$	180.652	+	312.898i	0.417210	+	0.722629i	0.995658	−	0.0930905i	$-0.0296746\pi$
$433$	180.652	+	312.898i	0.417210	+	0.722629i	−0.578448	+	0.815720i	$0.696341\pi$
$434$		0			0
$435$	−14.5743	+	8.41447i	−0.0335041	+	0.0193436i
$436$		0			0
$437$	663.727			1.51883
$438$		0			0
$439$	−71.4908	−	41.2752i	−0.162849	−	0.0940210i	0.416361	−	0.909200i	$-0.363305\pi$
$439$	−71.4908	−	41.2752i	−0.162849	−	0.0940210i	−0.579210	+	0.815179i	$0.696639\pi$
$440$		0			0
$441$	386.175			0.875680
$442$		0			0
$443$			384.913i			0.868877i	0.900701	+	0.434439i	$0.143053\pi$
$443$			384.913i			0.868877i	−0.900701	+	0.434439i	$0.856947\pi$
$444$		0			0
$445$	−57.3419	+	99.3191i	−0.128858	+	0.223189i
$446$		0			0
$447$			128.462i			0.287387i
$448$		0			0
$449$	−176.746	−	306.133i	−0.393644	−	0.681812i	0.599283	−	0.800537i	$-0.295452\pi$
$449$	−176.746	−	306.133i	−0.393644	−	0.681812i	−0.992927	+	0.118726i	$0.962119\pi$
$450$		0			0
$451$	37.1597	−	21.4542i	0.0823940	−	0.0475702i
$452$		0			0
$453$	−12.0913	+	20.9427i	−0.0266916	+	0.0462312i
$454$		0			0
$455$	−45.5026	−	33.8508i	−0.100006	−	0.0743974i
$456$		0			0
$457$	351.369	−	608.589i	0.768860	−	1.33171i	−0.169321	−	0.985561i	$-0.554157\pi$
$457$	351.369	−	608.589i	0.768860	−	1.33171i	0.938181	−	0.346144i	$-0.112509\pi$
$458$		0			0
$459$	−316.729	+	182.864i	−0.690042	+	0.398396i
$460$		0			0
$461$	−181.475	−	314.324i	−0.393655	−	0.681831i	0.599273	−	0.800544i	$-0.295456\pi$
$461$	−181.475	−	314.324i	−0.393655	−	0.681831i	−0.992929	+	0.118714i	$0.962123\pi$
$462$		0			0
$463$			661.323i			1.42834i	0.699970	+	0.714172i	$0.253197\pi$
$463$			661.323i			1.42834i	−0.699970	+	0.714172i	$0.746803\pi$
$464$		0			0
$465$	36.1301	−	62.5792i	0.0776992	−	0.134579i
$466$		0			0
$467$			466.706i			0.999371i	0.866207	+	0.499686i	$0.166551\pi$
$467$			466.706i			0.999371i	−0.866207	+	0.499686i	$0.833449\pi$
$468$		0			0
$469$	−107.177			−0.228523
$470$		0			0
$471$	114.694	+	66.2188i	0.243512	+	0.140592i
$472$		0			0
$473$	552.348			1.16775
$474$		0			0
$475$	446.512	−	257.794i	0.940025	−	0.542724i
$476$		0			0
$477$	−88.7383	−	153.699i	−0.186034	−	0.322221i
$478$		0			0
$479$	478.180	+	276.077i	0.998287	+	0.576361i	0.907741	−	0.419531i	$-0.137805\pi$
$479$	478.180	+	276.077i	0.998287	+	0.576361i	0.0905462	+	0.995892i	$0.471139\pi$
$480$		0			0
$481$	−479.998	−	55.9345i	−0.997918	−	0.116288i
$482$		0			0
$483$	29.3173	+	16.9263i	0.0606983	+	0.0350442i
$484$		0			0
$485$	78.3542	+	135.713i	0.161555	+	0.279822i
$486$		0			0
$487$	−8.49135	+	4.90248i	−0.0174360	+	0.0100667i	−0.508693	−	0.860948i	$-0.669871\pi$
$487$	−8.49135	+	4.90248i	−0.0174360	+	0.0100667i	0.491257	+	0.871015i	$0.336538\pi$
$488$		0			0
$489$	−112.673			−0.230415
$490$		0			0
$491$	39.5580	+	22.8388i	0.0805661	+	0.0465149i	0.539742	−	0.841831i	$-0.318522\pi$
$491$	39.5580	+	22.8388i	0.0805661	+	0.0465149i	−0.459176	+	0.888345i	$0.651855\pi$
$492$		0			0
$493$	−356.611			−0.723350
$494$		0			0
$495$		−	128.859i		−	0.260322i
$496$		0			0
$497$	76.6352	−	132.736i	0.154196	−	0.267075i
$498$		0			0
$499$		−	375.399i		−	0.752303i	−0.926558	−	0.376151i	$-0.877247\pi$
$499$		−	375.399i		−	0.752303i	0.926558	−	0.376151i	$-0.122753\pi$
$500$		0			0
$501$	−67.6209	−	117.123i	−0.134972	−	0.233778i
$502$		0			0
$503$	544.647	−	314.452i	1.08280	−	0.625153i	0.151147	−	0.988511i	$-0.451703\pi$
$503$	544.647	−	314.452i	1.08280	−	0.625153i	0.931649	+	0.363359i	$0.118370\pi$
$504$		0			0
$505$	−84.9471	+	147.133i	−0.168212	+	0.291352i
$506$		0			0
$507$	107.764	−	32.3443i	0.212553	−	0.0637954i
$508$		0			0
$509$	360.155	−	623.807i	0.707573	−	1.22555i	−0.258181	−	0.966096i	$-0.583123\pi$
$509$	360.155	−	623.807i	0.707573	−	1.22555i	0.965755	−	0.259457i	$-0.0835434\pi$
$510$		0			0
$511$	95.7662	−	55.2907i	0.187409	−	0.108201i
$512$		0			0
$513$	−150.055	−	259.902i	−0.292504	−	0.506632i
$514$		0			0
$515$			34.1599i			0.0663299i
$516$		0			0
$517$	166.268	−	287.985i	0.321602	−	0.557032i
$518$		0			0
$519$		−	102.621i		−	0.197728i
$520$		0			0
$521$	−168.221			−0.322880			−0.161440	−	0.986883i	$-0.551614\pi$
$521$	−168.221			−0.322880			−0.161440	+	0.986883i	$0.551614\pi$
$522$		0			0
$523$	−583.289	−	336.762i	−1.11528	−	0.643905i	−0.175085	−	0.984553i	$-0.556020\pi$
$523$	−583.289	−	336.762i	−1.11528	−	0.643905i	−0.940191	+	0.340648i	$0.889353\pi$
$524$		0			0
$525$	26.2970			0.0500895
$526$		0			0
$527$	1326.08	−	765.610i	2.51627	−	1.45277i
$528$		0			0
$529$	69.6298	+	120.602i	0.131625	+	0.227982i
$530$		0			0
$531$	23.7702	+	13.7237i	0.0447649	+	0.0258450i
$532$		0			0
$533$	−81.5994	−	9.50882i	−0.153094	−	0.0178402i
$534$		0			0
$535$	175.458	+	101.301i	0.327958	+	0.189347i
$536$		0			0
$537$	32.7455	+	56.7168i	0.0609785	+	0.105618i
$538$		0			0
$539$	265.384	−	153.219i	0.492363	−	0.284266i
$540$		0			0
$541$	−293.373			−0.542279			−0.271140	−	0.962540i	$-0.587401\pi$
$541$	−293.373			−0.542279			−0.271140	+	0.962540i	$0.587401\pi$
$542$		0			0
$543$	−108.440	−	62.6077i	−0.199705	−	0.115300i
$544$		0			0
$545$	20.2681			0.0371891
$546$		0			0
$547$			789.553i			1.44342i	0.692194	+	0.721712i	$0.256644\pi$
$547$			789.553i			1.44342i	−0.692194	+	0.721712i	$0.743356\pi$
$548$		0			0
$549$	−70.8258	+	122.674i	−0.129009	+	0.223450i
$550$		0			0
$551$		−	292.629i		−	0.531087i
$552$		0			0
$553$	−124.464	−	215.577i	−0.225070	−	0.389833i
$554$		0			0
$555$	−47.5348	+	27.4443i	−0.0856484	+	0.0494491i
$556$		0			0
$557$	181.207	−	313.860i	0.325327	−	0.563483i	−0.656252	−	0.754542i	$-0.727859\pi$
$557$	181.207	−	313.860i	0.325327	−	0.563483i	0.981578	+	0.191059i	$0.0611923\pi$
$558$		0			0
$559$	−848.477	−	631.209i	−1.51785	−	1.12918i
$560$		0			0
$561$	−70.7216	+	122.493i	−0.126063	+	0.218348i
$562$		0			0
$563$	−873.644	+	504.398i	−1.55176	+	0.895912i	−0.553766	+	0.832672i	$0.686810\pi$
$563$	−873.644	+	504.398i	−1.55176	+	0.895912i	−0.997998	+	0.0632396i	$0.979857\pi$
$564$		0			0
$565$	−78.7167	−	136.341i	−0.139322	−	0.241312i
$566$		0			0
$567$			136.173i			0.240164i
$568$		0			0
$569$	117.008	−	202.664i	0.205638	−	0.356176i	−0.744698	−	0.667402i	$-0.767406\pi$
$569$	117.008	−	202.664i	0.205638	−	0.356176i	0.950336	+	0.311226i	$0.100740\pi$
$570$		0			0
$571$			1064.96i			1.86508i	0.361064	+	0.932541i	$0.382414\pi$
$571$			1064.96i			1.86508i	−0.361064	+	0.932541i	$0.617586\pi$
$572$		0			0
$573$	162.918			0.284325
$574$		0			0
$575$	449.561	+	259.554i	0.781846	+	0.451399i
$576$		0			0
$577$	−449.468			−0.778974			−0.389487	−	0.921032i	$-0.627348\pi$
$577$	−449.468			−0.778974			−0.389487	+	0.921032i	$0.627348\pi$
$578$		0			0
$579$	117.508	−	67.8432i	0.202950	−	0.117173i
$580$		0			0
$581$	144.256	+	249.858i	0.248289	+	0.430049i
$582$		0			0
$583$	−121.964	−	70.4159i	−0.209201	−	0.120782i
$584$		0			0
$585$	−147.257	+	197.945i	−0.251722	+	0.338367i
$586$		0			0
$587$	483.681	+	279.253i	0.823987	+	0.475729i	0.851790	−	0.523884i	$-0.175518\pi$
$587$	483.681	+	279.253i	0.823987	+	0.475729i	−0.0278022	+	0.999613i	$0.508851\pi$
$588$		0			0
$589$	628.246	+	1088.15i	1.06663	+	1.84746i
$590$		0			0
$591$	−122.366	+	70.6479i	−0.207049	+	0.119540i
$592$		0			0
$593$	1072.40			1.80844			0.904218	−	0.427070i	$-0.140454\pi$
$593$	1072.40			1.80844			0.904218	+	0.427070i	$0.140454\pi$
$594$		0			0
$595$	−118.213	−	68.2502i	−0.198677	−	0.114706i
$596$		0			0
$597$	210.450			0.352513
$598$		0			0
$599$		−	534.811i		−	0.892840i	−0.894824	−	0.446420i	$-0.852699\pi$
$599$		−	534.811i		−	0.892840i	0.894824	−	0.446420i	$-0.147301\pi$
$600$		0			0
$601$	−236.885	+	410.297i	−0.394151	+	0.682690i	−0.992992	−	0.118178i	$-0.962295\pi$
$601$	−236.885	+	410.297i	−0.394151	+	0.682690i	0.598841	+	0.800868i	$0.295628\pi$
$602$		0			0
$603$			466.240i			0.773201i
$604$		0			0
$605$	83.0551	+	143.856i	0.137281	+	0.237778i
$606$		0			0
$607$	99.3019	−	57.3320i	0.163595	−	0.0944514i	−0.415967	−	0.909380i	$-0.636557\pi$
$607$	99.3019	−	57.3320i	0.163595	−	0.0944514i	0.579562	+	0.814928i	$0.303224\pi$
$608$		0			0
$609$	7.46262	−	12.9256i	0.0122539	−	0.0212244i
$610$		0			0
$611$	−584.512	+	252.375i	−0.956648	+	0.413053i
$612$		0			0
$613$	−53.0135	+	91.8221i	−0.0864820	+	0.149791i	−0.906022	−	0.423231i	$-0.860896\pi$
$613$	−53.0135	+	91.8221i	−0.0864820	+	0.149791i	0.819540	+	0.573022i	$0.194229\pi$
$614$		0			0
$615$	−8.08089	+	4.66550i	−0.0131397	+	0.00758618i
$616$		0			0
$617$	−190.348	−	329.692i	−0.308506	−	0.534348i	0.669530	−	0.742785i	$-0.266496\pi$
$617$	−190.348	−	329.692i	−0.308506	−	0.534348i	−0.978036	+	0.208437i	$0.933162\pi$
$618$		0			0
$619$		−	340.038i		−	0.549334i	−0.961539	−	0.274667i	$-0.911432\pi$
$619$		−	340.038i		−	0.549334i	0.961539	−	0.274667i	$-0.0885676\pi$
$620$		0			0
$621$	151.080	−	261.677i	0.243284	−	0.421381i
$622$		0			0
$623$		−	101.711i		−	0.163260i
$624$		0			0
$625$	280.273			0.448437
$626$		0			0
$627$	−100.516	−	58.0329i	−0.160313	−	0.0925565i
$628$		0			0
$629$	−1163.11			−1.84914
$630$		0			0
$631$	58.2989	−	33.6589i	0.0923912	−	0.0533421i	−0.453093	−	0.891463i	$-0.649679\pi$
$631$	58.2989	−	33.6589i	0.0923912	−	0.0533421i	0.545484	+	0.838121i	$0.316346\pi$
$632$		0			0
$633$	112.204	+	194.342i	0.177257	+	0.307018i
$634$		0			0
$635$	−367.573	−	212.219i	−0.578856	−	0.334202i
$636$		0			0
$637$	−582.759	−	67.9092i	−0.914849	−	0.106608i
$638$		0			0
$639$	−577.426	−	333.377i	−0.903641	−	0.521717i
$640$		0			0
$641$	66.1196	+	114.522i	0.103151	+	0.178662i	0.912981	−	0.408002i	$-0.133774\pi$
$641$	66.1196	+	114.522i	0.103151	+	0.178662i	−0.809830	+	0.586664i	$0.800441\pi$
$642$		0			0
$643$	391.462	−	226.011i	0.608805	−	0.351494i	−0.163692	−	0.986511i	$-0.552340\pi$
$643$	391.462	−	226.011i	0.608805	−	0.351494i	0.772498	+	0.635017i	$0.219007\pi$
$644$		0			0
$645$	−120.116			−0.186226
$646$		0			0
$647$	776.369	+	448.237i	1.19995	+	0.692793i	0.960545	−	0.278126i	$-0.0897133\pi$
$647$	776.369	+	448.237i	1.19995	+	0.692793i	0.239408	+	0.970919i	$0.423047\pi$
$648$		0			0
$649$	21.7802			0.0335596
$650$		0			0
$651$			64.0861i			0.0984425i
$652$		0			0
$653$	−339.075	+	587.295i	−0.519257	+	0.899379i	0.480493	+	0.876999i	$0.340458\pi$
$653$	−339.075	+	587.295i	−0.519257	+	0.899379i	−0.999750	+	0.0223805i	$0.992875\pi$
$654$		0			0
$655$		−	89.1973i		−	0.136179i
$656$		0			0
$657$	−240.525	−	416.601i	−0.366095	−	0.634095i
$658$		0			0
$659$	−297.429	+	171.721i	−0.451334	+	0.260578i	−0.708394	−	0.705818i	$-0.750580\pi$
$659$	−297.429	+	171.721i	−0.451334	+	0.260578i	0.257059	+	0.966396i	$0.417246\pi$
$660$		0			0
$661$	428.396	−	742.004i	0.648103	−	1.12255i	−0.335472	−	0.942050i	$-0.608896\pi$
$661$	428.396	−	742.004i	0.648103	−	1.12255i	0.983575	−	0.180497i	$-0.0577707\pi$
$662$		0			0
$663$	248.620	−	107.347i	0.374992	−	0.161911i
$664$		0			0
$665$	56.0049	−	97.0033i	0.0842179	−	0.145870i
$666$		0			0
$667$	255.155	−	147.314i	0.382541	−	0.220860i
$668$		0			0
$669$	49.2301	+	85.2690i	0.0735876	+	0.127457i
$670$		0			0
$671$			112.404i			0.167517i
$672$		0			0
$673$	−213.089	+	369.081i	−0.316626	+	0.548412i	−0.979782	−	0.200069i	$-0.935883\pi$
$673$	−213.089	+	369.081i	−0.316626	+	0.548412i	0.663156	+	0.748481i	$0.269217\pi$
$674$		0			0
$675$		−	234.719i		−	0.347732i
$676$		0			0
$677$	−912.853			−1.34838			−0.674190	−	0.738558i	$-0.735507\pi$
$677$	−912.853			−1.34838			−0.674190	+	0.738558i	$0.735507\pi$
$678$		0			0
$679$	−120.361	−	69.4907i	−0.177263	−	0.102343i
$680$		0			0
$681$	−230.618			−0.338647
$682$		0			0
$683$	−815.675	+	470.930i	−1.19425	+	0.689502i	−0.959268	−	0.282497i	$-0.908837\pi$
$683$	−815.675	+	470.930i	−1.19425	+	0.689502i	−0.234985	+	0.971999i	$0.575504\pi$
$684$		0			0
$685$	135.732	+	235.096i	0.198150	+	0.343205i
$686$		0			0
$687$	80.8708	+	46.6908i	0.117716	+	0.0679633i
$688$		0			0
$689$	106.883	+	247.545i	0.155127	+	0.359282i
$690$		0			0
$691$	382.870	+	221.050i	0.554081	+	0.319899i	0.750767	−	0.660568i	$-0.229684\pi$
$691$	382.870	+	221.050i	0.554081	+	0.319899i	−0.196685	+	0.980467i	$0.563018\pi$
$692$		0			0
$693$	57.1413	+	98.9717i	0.0824551	+	0.142816i
$694$		0			0
$695$	−221.937	+	128.135i	−0.319333	+	0.184367i
$696$		0			0
$697$	−197.727			−0.283683
$698$		0			0
$699$	21.6901	+	12.5228i	0.0310302	+	0.0179153i
$700$		0			0
$701$	1153.24			1.64514			0.822569	−	0.568666i	$-0.192540\pi$
$701$	1153.24			1.64514			0.822569	+	0.568666i	$0.192540\pi$
$702$		0			0
$703$		−	954.425i		−	1.35765i
$704$		0			0
$705$	−36.1574	+	62.6264i	−0.0512870	+	0.0888317i
$706$		0			0
$707$		−	150.676i		−	0.213120i
$708$		0			0
$709$	−107.186	−	185.652i	−0.151179	−	0.261850i	0.780482	−	0.625178i	$-0.214974\pi$
$709$	−107.186	−	185.652i	−0.151179	−	0.261850i	−0.931661	+	0.363328i	$0.881640\pi$
$710$		0			0
$711$	−937.801	+	541.440i	−1.31899	+	0.761519i
$712$		0			0
$713$	−632.537	+	1095.59i	−0.887149	+	1.53659i
$714$		0			0
$715$	−22.6601	+	194.456i	−0.0316924	+	0.271966i
$716$		0			0
$717$	47.1675	−	81.6965i	0.0657845	−	0.113942i
$718$		0			0
$719$	−597.793	+	345.136i	−0.831422	+	0.480022i	−0.854339	−	0.519715i	$-0.826038\pi$
$719$	−597.793	+	345.136i	−0.831422	+	0.480022i	0.0229170	+	0.999737i	$0.492705\pi$
$720$		0			0
$721$	−15.1479	−	26.2369i	−0.0210095	−	0.0363895i
$722$		0			0
$723$			67.9731i			0.0940154i
$724$		0			0
$725$	114.434	−	198.206i	0.157841	−	0.273388i
$726$		0			0
$727$		−	376.359i		−	0.517688i	−0.965919	−	0.258844i	$-0.916658\pi$
$727$		−	376.359i		−	0.517688i	0.965919	−	0.258844i	$-0.0833416\pi$
$728$		0			0
$729$	522.340			0.716516
$730$		0			0
$731$	−2204.29	−	1272.65i	−3.01544	−	1.74097i
$732$		0			0
$733$	873.660			1.19190			0.595948	−	0.803023i	$-0.296776\pi$
$733$	873.660			1.19190			0.595948	+	0.803023i	$0.296776\pi$
$734$		0			0
$735$	−57.7114	+	33.3197i	−0.0785189	+	0.0453329i
$736$		0			0
$737$	184.986	+	320.406i	0.250999	+	0.434743i
$738$		0			0
$739$	66.3127	+	38.2857i	0.0897331	+	0.0518074i	0.544195	−	0.838959i	$-0.316835\pi$
$739$	66.3127	+	38.2857i	0.0897331	+	0.0518074i	−0.454462	+	0.890766i	$0.650168\pi$
$740$		0			0
$741$	88.0869	+	204.013i	0.118876	+	0.275321i
$742$		0			0
$743$	−689.527	−	398.099i	−0.928031	−	0.535799i	−0.0418426	−	0.999124i	$-0.513323\pi$
$743$	−689.527	−	398.099i	−0.928031	−	0.535799i	−0.886188	+	0.463325i	$0.846656\pi$
$744$		0			0
$745$	213.975	+	370.616i	0.287215	+	0.497471i
$746$		0			0
$747$	1086.93	−	627.539i	1.45506	−	0.840079i
$748$		0			0
$749$	−179.683			−0.239897
$750$		0			0
$751$	856.943	+	494.756i	1.14107	+	0.658796i	0.946695	−	0.322131i	$-0.104399\pi$
$751$	856.943	+	494.756i	1.14107	+	0.658796i	0.194374	+	0.980928i	$0.437733\pi$
$752$		0			0
$753$	114.596			0.152186
$754$		0			0
$755$			80.5604i			0.106703i
$756$		0			0
$757$	−276.505	+	478.921i	−0.365264	+	0.632656i	−0.988819	−	0.149124i	$-0.952355\pi$
$757$	−276.505	+	478.921i	−0.365264	+	0.632656i	0.623554	+	0.781780i	$0.285688\pi$
$758$		0			0
$759$		−	116.859i		−	0.153964i
$760$		0			0
$761$	84.2955	+	146.004i	0.110769	+	0.191858i	0.916081	−	0.400994i	$-0.131335\pi$
$761$	84.2955	+	146.004i	0.110769	+	0.191858i	−0.805311	+	0.592852i	$0.798002\pi$
$762$		0			0
$763$	−15.5671	+	8.98766i	−0.0204025	+	0.0117794i
$764$		0			0
$765$	−296.901	+	514.247i	−0.388106	+	0.672219i
$766$		0			0
$767$	−33.4572	−	24.8899i	−0.0436208	−	0.0324509i
$768$		0			0
$769$	−304.996	+	528.269i	−0.396614	+	0.686956i	−0.993306	−	0.115515i	$-0.963148\pi$
$769$	−304.996	+	528.269i	−0.396614	+	0.686956i	0.596692	+	0.802471i	$0.296482\pi$
$770$		0			0
$771$	98.5954	−	56.9241i	0.127880	−	0.0738315i
$772$		0			0
$773$	554.353	+	960.168i	0.717145	+	1.24213i	0.962126	+	0.272604i	$0.0878848\pi$
$773$	554.353	+	960.168i	0.717145	+	1.24213i	−0.244981	+	0.969528i	$0.578782\pi$
$774$		0			0
$775$			982.718i			1.26802i
$776$		0			0
$777$	24.3397	−	42.1576i	0.0313253	−	0.0542569i
$778$		0			0
$779$		−	162.252i		−	0.208282i
$780$		0			0
$781$	−529.085			−0.677446
$782$		0			0
$783$	−115.370	−	66.6091i	−0.147344	−	0.0850692i
$784$		0			0
$785$	441.194			0.562031
$786$		0			0
$787$	−285.999	+	165.122i	−0.363404	+	0.209812i	−0.670573	−	0.741843i	$-0.733952\pi$
$787$	−285.999	+	165.122i	−0.363404	+	0.209812i	0.307169	+	0.951655i	$0.400618\pi$
$788$		0			0
$789$	49.2321	+	85.2724i	0.0623980	+	0.108077i
$790$		0			0
$791$	120.918	+	69.8122i	0.152868	+	0.0882581i
$792$		0			0
$793$	128.452	−	172.667i	0.161983	−	0.217739i
$794$		0			0
$795$	26.5227	+	15.3129i	0.0333619	+	0.0192615i
$796$		0			0
$797$	−632.672	−	1095.82i	−0.793817	−	1.37493i	−0.923588	−	0.383387i	$-0.874758\pi$
$797$	−632.672	−	1095.82i	−0.793817	−	1.37493i	0.129771	−	0.991544i	$-0.458576\pi$
$798$		0			0
$799$	−1327.07	+	766.187i	−1.66092	+	0.958932i
$800$		0			0
$801$	−442.460			−0.552385
$802$		0			0
$803$	−330.582	−	190.862i	−0.411684	−	0.237686i
$804$		0			0
$805$	112.775			0.140093
$806$		0			0
$807$		−	214.657i		−	0.265993i
$808$		0			0
$809$	−719.267	+	1245.81i	−0.889081	+	1.53993i	−0.0481182	+	0.998842i	$0.515322\pi$
$809$	−719.267	+	1245.81i	−0.889081	+	1.53993i	−0.840963	+	0.541092i	$0.818011\pi$
$810$		0			0
$811$			492.383i			0.607131i	0.952811	+	0.303566i	$0.0981771\pi$
$811$			492.383i			0.607131i	−0.952811	+	0.303566i	$0.901823\pi$
$812$		0			0
$813$	47.2850	+	81.9001i	0.0581612	+	0.100738i
$814$		0			0
$815$	−325.064	+	187.676i	−0.398852	+	0.230277i
$816$		0			0
$817$	1044.31	−	1808.80i	1.27823	−	2.21395i
$818$		0			0
$819$	25.3259	−	217.333i	0.0309230	−	0.265364i
$820$		0			0
$821$	−560.611	+	971.006i	−0.682839	+	1.18271i	0.291272	+	0.956640i	$0.405922\pi$
$821$	−560.611	+	971.006i	−0.682839	+	1.18271i	−0.974111	+	0.226071i	$0.927412\pi$
$822$		0			0
$823$	−330.419	+	190.767i	−0.401481	+	0.231795i	−0.687123	−	0.726541i	$-0.741127\pi$
$823$	−330.419	+	190.767i	−0.401481	+	0.231795i	0.285642	+	0.958336i	$0.407793\pi$
$824$		0			0
$825$	−45.3883	−	78.6148i	−0.0550161	−	0.0952906i
$826$		0			0
$827$		−	389.604i		−	0.471105i	−0.971862	−	0.235553i	$-0.924310\pi$
$827$		−	389.604i		−	0.471105i	0.971862	−	0.235553i	$-0.0756900\pi$
$828$		0			0
$829$	−339.169	+	587.457i	−0.409130	+	0.708634i	−0.994792	−	0.101921i	$-0.967501\pi$
$829$	−339.169	+	587.457i	−0.409130	+	0.708634i	0.585663	+	0.810555i	$0.300834\pi$
$830$		0			0
$831$		−	62.2302i		−	0.0748859i
$832$		0			0
$833$	−1412.11			−1.69521
$834$		0			0
$835$	−390.176	−	225.268i	−0.467276	−	0.269782i
$836$		0			0
$837$	572.014			0.683409
$838$		0			0
$839$	145.458	−	83.9804i	0.173371	−	0.100096i	−0.410803	−	0.911724i	$-0.634752\pi$
$839$	145.458	−	83.9804i	0.173371	−	0.100096i	0.584174	+	0.811628i	$0.301418\pi$
$840$		0			0
$841$	355.551	+	615.833i	0.422772	+	0.732262i
$842$		0			0
$843$	−215.469	−	124.401i	−0.255598	−	0.147570i
$844$		0			0
$845$	257.028	−	272.814i	0.304175	−	0.322857i
$846$		0			0
$847$	−127.583	−	73.6598i	−0.150629	−	0.0869655i
$848$		0			0
$849$	31.0683	+	53.8118i	0.0365940	+	0.0633826i
$850$		0			0
$851$	832.202	−	480.472i	0.977910	−	0.564597i
$852$		0			0
$853$	1362.92			1.59779			0.798896	−	0.601469i	$-0.205418\pi$
$853$	1362.92			1.59779			0.798896	+	0.601469i	$0.205418\pi$
$854$		0			0
$855$	−421.982	−	243.632i	−0.493547	−	0.284949i
$856$		0			0
$857$	387.158			0.451759			0.225880	−	0.974155i	$-0.427474\pi$
$857$	387.158			0.451759			0.225880	+	0.974155i	$0.427474\pi$
$858$		0			0
$859$			383.890i			0.446904i	0.974715	+	0.223452i	$0.0717326\pi$
$859$			383.890i			0.446904i	−0.974715	+	0.223452i	$0.928267\pi$
$860$		0			0
$861$	4.13774	−	7.16677i	0.00480573	−	0.00832377i
$862$		0			0
$863$		−	607.026i		−	0.703390i	−0.936115	−	0.351695i	$-0.885605\pi$
$863$		−	607.026i		−	0.703390i	0.936115	−	0.351695i	$-0.114395\pi$
$864$		0			0
$865$	−170.933	−	296.064i	−0.197610	−	0.342271i
$866$		0			0
$867$	397.838	−	229.692i	0.458868	−	0.264927i
$868$		0			0
$869$	−429.645	+	744.167i	−0.494413	+	0.856349i
$870$		0			0
$871$	81.9889	−	703.582i	0.0941319	−	0.807787i
$872$		0			0
$873$	−302.297	+	523.594i	−0.346274	+	0.599764i
$874$		0			0
$875$	170.319	−	98.3339i	0.194651	−	0.112382i
$876$		0			0
$877$	−721.043	−	1248.88i	−0.822170	−	1.42404i	−0.904063	−	0.427399i	$-0.859430\pi$
$877$	−721.043	−	1248.88i	−0.822170	−	1.42404i	0.0818934	−	0.996641i	$-0.473903\pi$
$878$		0			0
$879$			324.253i			0.368889i
$880$		0			0
$881$	531.728	−	920.980i	0.603551	−	1.04538i	−0.388728	−	0.921353i	$-0.627085\pi$
$881$	531.728	−	920.980i	0.603551	−	1.04538i	0.992279	−	0.124028i	$-0.0395813\pi$
$882$		0			0
$883$			709.951i			0.804021i	0.915635	+	0.402011i	$0.131689\pi$
$883$			709.951i			0.804021i	−0.915635	+	0.402011i	$0.868311\pi$
$884$		0			0
$885$	−4.73640			−0.00535187
$886$		0			0
$887$	1013.11	+	584.919i	1.14218	+	0.659436i	0.946968	−	0.321326i	$-0.104129\pi$
$887$	1013.11	+	584.919i	1.14218	+	0.659436i	0.195207	+	0.980762i	$0.437462\pi$
$888$		0			0
$889$	376.424			0.423424
$890$		0			0
$891$	407.088	−	235.032i	0.456889	−	0.263785i
$892$		0			0
$893$	−628.720	−	1088.97i	−0.704054	−	1.21946i
$894$		0			0
$895$	188.943	+	109.086i	0.211109	+	0.121884i
$896$		0			0
$897$	−133.543	+	179.510i	−0.148877	+	0.200122i
$898$		0			0
$899$	483.031	+	278.878i	0.537298	+	0.310209i
$900$		0			0
$901$	324.486	+	562.026i	0.360140	+	0.623781i
$902$		0			0
$903$	92.2559	−	53.2640i	0.102166	−	0.0589856i
$904$		0			0
$905$	−417.135			−0.460922
$906$		0			0
$907$	226.051	+	130.511i	0.249229	+	0.143893i	0.619411	−	0.785067i	$-0.287371\pi$
$907$	226.051	+	130.511i	0.249229	+	0.143893i	−0.370182	+	0.928959i	$0.620705\pi$
$908$		0			0
$909$	−655.467			−0.721085
$910$		0			0
$911$		−	520.587i		−	0.571446i	−0.958312	−	0.285723i	$-0.907766\pi$
$911$		−	520.587i		−	0.571446i	0.958312	−	0.285723i	$-0.0922338\pi$
$912$		0			0
$913$	497.967	−	862.504i	0.545418	−	0.944692i
$914$		0			0
$915$		−	24.4438i		−	0.0267145i
$916$		0			0
$917$	39.5536	+	68.5089i	0.0431337	+	0.0747098i
$918$		0			0
$919$	−799.452	+	461.564i	−0.869915	+	0.502246i	−0.867320	−	0.497751i	$-0.834159\pi$
$919$	−799.452	+	461.564i	−0.869915	+	0.502246i	−0.00259493	+	0.999997i	$0.500826\pi$
$920$		0			0
$921$	8.36715	−	14.4923i	0.00908486	−	0.0157354i
$922$		0			0
$923$	812.744	+	604.626i	0.880546	+	0.655066i
$924$		0			0
$925$	373.234	−	646.460i	0.403496	−	0.698876i
$926$		0			0
$927$	−114.135	+	65.8960i	−0.123123	+	0.0710852i
$928$		0			0
$929$	−180.089	−	311.923i	−0.193853	−	0.335762i	0.752671	−	0.658397i	$-0.228765\pi$
$929$	−180.089	−	311.923i	−0.193853	−	0.335762i	−0.946524	+	0.322634i	$0.895432\pi$
$930$		0			0
$931$		−	1158.75i		−	1.24463i
$932$		0			0
$933$	90.5465	−	156.831i	0.0970488	−	0.168093i
$934$		0			0
$935$			471.195i			0.503952i
$936$		0			0
$937$	143.237			0.152868			0.0764339	−	0.997075i	$-0.475647\pi$
$937$	143.237			0.152868			0.0764339	+	0.997075i	$0.475647\pi$
$938$		0			0
$939$	259.546	+	149.849i	0.276406	+	0.159583i
$940$		0			0
$941$	−318.618			−0.338595			−0.169297	−	0.985565i	$-0.554150\pi$
$941$	−318.618			−0.338595			−0.169297	+	0.985565i	$0.554150\pi$
$942$		0			0
$943$	141.474	−	81.6798i	0.150025	−	0.0866170i
$944$		0			0
$945$	−25.4960	−	44.1604i	−0.0269799	−	0.0467306i
$946$		0			0
$947$	−412.918	−	238.398i	−0.436028	−	0.251741i	0.265884	−	0.964005i	$-0.414336\pi$
$947$	−412.918	−	238.398i	−0.436028	−	0.251741i	−0.701911	+	0.712264i	$0.747670\pi$
$948$		0			0
$949$	289.705	+	670.970i	0.305274	+	0.707028i
$950$		0			0
$951$	−212.912	−	122.925i	−0.223882	−	0.129259i
$952$		0			0
$953$	45.8183	+	79.3596i	0.0480779	+	0.0832734i	0.889063	−	0.457785i	$-0.151357\pi$
$953$	45.8183	+	79.3596i	0.0480779	+	0.0832734i	−0.840985	+	0.541058i	$0.818024\pi$
$954$		0			0
$955$	470.022	−	271.368i	0.492170	−	0.284155i
$956$		0			0
$957$	−51.5215			−0.0538365
$958$		0			0
$959$	−208.501	−	120.378i	−0.217415	−	0.125525i
$960$		0			0
$961$	−1433.90			−1.49209
$962$		0			0
$963$			781.653i			0.811685i
$964$		0			0
$965$	226.009	−	391.459i	0.234206	−	0.405657i
$966$		0			0
$967$			1374.98i			1.42191i	0.703240	+	0.710953i	$0.251736\pi$
$967$			1374.98i			1.42191i	−0.703240	+	0.710953i	$0.748264\pi$
$968$		0			0
$969$	267.423	+	463.191i	0.275979	+	0.478009i
$970$		0			0
$971$	743.910	−	429.497i	0.766128	−	0.442324i	−0.0653638	−	0.997862i	$-0.520821\pi$
$971$	743.910	−	429.497i	0.766128	−	0.442324i	0.831492	+	0.555537i	$0.187487\pi$
$972$		0			0
$973$	113.640	−	196.831i	0.116794	−	0.202293i
$974$		0			0
$975$	−20.1168	+	172.631i	−0.0206326	+	0.177057i
$976$		0			0
$977$	747.534	−	1294.77i	0.765132	−	1.32525i	−0.175045	−	0.984560i	$-0.556007\pi$
$977$	747.534	−	1294.77i	0.765132	−	1.32525i	0.940177	−	0.340687i	$-0.110660\pi$
$978$		0			0
$979$	−304.064	+	175.551i	−0.310586	+	0.179317i
$980$		0			0
$981$	39.0980	+	67.7197i	0.0398552	+	0.0690313i
$982$		0			0
$983$			1629.77i			1.65796i	0.559281	+	0.828978i	$0.311077\pi$
$983$			1629.77i			1.65796i	−0.559281	+	0.828978i	$0.688923\pi$
$984$		0			0
$985$	−235.352	+	407.642i	−0.238936	+	0.413850i
$986$		0			0
$987$		−	64.1344i		−	0.0649791i
$988$		0			0
$989$	2102.89			2.12628
$990$		0			0
$991$	1498.34	+	865.070i	1.51195	+	0.872926i	0.999902	+	0.0139703i	$0.00444702\pi$
$991$	1498.34	+	865.070i	1.51195	+	0.872926i	0.512050	+	0.858956i	$0.328886\pi$
$992$		0			0
$993$	−233.805			−0.235453
$994$		0			0
$995$	607.154	−	350.540i	0.610205	−	0.352302i
$996$		0			0
$997$	56.4324	+	97.7438i	0.0566022	+	0.0980379i	0.892938	−	0.450179i	$-0.148640\pi$
$997$	56.4324	+	97.7438i	0.0566022	+	0.0980379i	−0.836336	+	0.548217i	$0.815307\pi$
$998$		0			0
$999$	−376.287	−	217.249i	−0.376663	−	0.217467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.3.bb.c.191.7	yes	32
4.3	odd	2	inner	416.3.bb.c.191.10	yes	32
13.3	even	3	inner	416.3.bb.c.159.10	yes	32
52.3	odd	6	inner	416.3.bb.c.159.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.3.bb.c.159.7	✓	32	52.3	odd	6	inner
416.3.bb.c.159.10	yes	32	13.3	even	3	inner
416.3.bb.c.191.7	yes	32	1.1	even	1	trivial
416.3.bb.c.191.10	yes	32	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	416.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576566 - 0.332881i) q^{3} -2.21788 q^{5} +(1.70346 - 0.983494i) q^{7} +(-4.27838 - 7.41037i) q^{9} +(-5.88030 - 3.39500i) q^{11} +(5.15319 + 11.9350i) q^{13} +(1.27875 + 0.738289i) q^{15} +(15.6446 + 27.0972i) q^{17} +(-22.2355 + 12.8377i) q^{19} -1.30955 q^{21} +(-22.3874 - 12.9254i) q^{23} -20.0810 q^{25} +11.6886i q^{27} +(-5.69864 + 9.87033i) q^{29} -48.9377i q^{31} +(2.26026 + 3.91488i) q^{33} +(-3.77807 + 2.18127i) q^{35} +(-18.5864 + 32.1926i) q^{37} +(1.00178 - 8.59673i) q^{39} +(-3.15967 + 5.47272i) q^{41} +(-70.4488 + 40.6737i) q^{43} +(9.48892 + 16.4353i) q^{45} +48.9746i q^{47} +(-22.5655 + 39.0846i) q^{49} -20.8311i q^{51} +20.7411 q^{53} +(13.0418 + 7.52968i) q^{55} +17.0937 q^{57} +(-2.77794 + 1.60385i) q^{59} +(-8.27717 - 14.3365i) q^{61} +(-14.5761 - 8.41553i) q^{63} +(-11.4291 - 26.4704i) q^{65} +(-47.1880 - 27.2440i) q^{67} +(8.60520 + 14.9047i) q^{69} +(67.4819 - 38.9607i) q^{71} +56.2186 q^{73} +(11.5780 + 6.68458i) q^{75} -13.3558 q^{77} -126.553i q^{79} +(-34.6145 + 59.9541i) q^{81} +146.677i q^{83} +(-34.6978 - 60.0983i) q^{85} +(6.57128 - 3.79393i) q^{87} +(25.8544 - 44.7812i) q^{89} +(20.5163 + 15.2627i) q^{91} +(-16.2904 + 28.2158i) q^{93} +(49.3157 - 28.4724i) q^{95} +(-35.3285 - 61.1907i) q^{97} +58.1003i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{5} + 80 q^{9} - 44 q^{13} + 16 q^{17} - 128 q^{21} + 272 q^{25} - 52 q^{29} - 72 q^{33} + 148 q^{37} + 72 q^{41} - 116 q^{45} + 328 q^{49} - 152 q^{53} - 224 q^{57} + 228 q^{61} - 352 q^{65}+ \cdots - 352 q^{97}+O(q^{100}) \) 32 * q - 8 * q^5 + 80 * q^9 - 44 * q^13 + 16 * q^17 - 128 * q^21 + 272 * q^25 - 52 * q^29 - 72 * q^33 + 148 * q^37 + 72 * q^41 - 116 * q^45 + 328 * q^49 - 152 * q^53 - 224 * q^57 + 228 * q^61 - 352 * q^65 + 200 * q^69 + 224 * q^73 + 832 * q^77 - 696 * q^81 - 84 * q^85 - 112 * q^89 + 152 * q^93 - 352 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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