LMFDB - Embedded newform 416.3.bb.c.159.7

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)

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")

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);

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			159.7
Character	$\chi$	$=$	416.159
Dual form			416.3.bb.c.191.7

$q$-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 $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

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

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			0
$2$		0			0
$3$	−0.576566	+	0.332881i	−0.192189	+	0.110960i	−0.593007	−	0.805197i	$-0.702059\pi$
$3$	−0.576566	+	0.332881i	−0.192189	+	0.110960i	0.400818	+	0.916158i	$0.368726\pi$
$4$		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	0.616716	−	0.787186i	$-0.288463\pi$
$7$	1.70346	+	0.983494i	0.243352	+	0.140499i	−0.373365	+	0.927685i	$0.621796\pi$
$8$		0			0
$9$	−4.27838	+	7.41037i	−0.475376	+	0.823375i
$10$		0			0
$11$	−5.88030	+	3.39500i	−0.534573	+	0.308636i	−0.742877	−	0.669428i	$-0.766539\pi$
$11$	−5.88030	+	3.39500i	−0.534573	+	0.308636i	0.208304	+	0.978064i	$0.433206\pi$
$12$		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	0.121274	−	0.992619i	$-0.461302\pi$
$17$	15.6446	−	27.0972i	0.920270	−	1.59395i	0.798997	−	0.601336i	$-0.205365\pi$
$18$		0			0
$19$	−22.2355	−	12.8377i	−1.17029	−	0.675668i	−0.216542	−	0.976273i	$-0.569478\pi$
$19$	−22.2355	−	12.8377i	−1.17029	−	0.675668i	−0.953748	+	0.300606i	$0.902811\pi$
$20$		0			0
$21$	−1.30955			−0.0623593
$22$		0			0
$23$	−22.3874	+	12.9254i	−0.973364	+	0.561972i	−0.900260	−	0.435352i	$-0.856624\pi$
$23$	−22.3874	+	12.9254i	−0.973364	+	0.561972i	−0.0731040	+	0.997324i	$0.523291\pi$
$24$		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	0.750888	−	0.660429i	$-0.229626\pi$
$29$	−5.69864	−	9.87033i	−0.196505	−	0.340356i	−0.947393	+	0.320073i	$0.896292\pi$
$30$		0			0
$31$			48.9377i			1.57863i	0.613985	+	0.789317i	$0.289565\pi$
$31$			48.9377i			1.57863i	−0.613985	+	0.789317i	$0.710435\pi$
$32$		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	−0.999996	−	0.00269853i	$-0.999141\pi$
$37$	−18.5864	−	32.1926i	−0.502335	−	0.870070i	0.497661	−	0.867372i	$-0.334192\pi$
$38$		0			0
$39$	1.00178	+	8.59673i	0.0256867	+	0.220429i
$40$		0			0
$41$	−3.15967	−	5.47272i	−0.0770652	−	0.133481i	0.824917	−	0.565253i	$-0.191222\pi$
$41$	−3.15967	−	5.47272i	−0.0770652	−	0.133481i	−0.901983	+	0.431773i	$0.857888\pi$
$42$		0			0
$43$	−70.4488	−	40.6737i	−1.63835	−	0.945899i	−0.981403	−	0.191958i	$-0.938516\pi$
$43$	−70.4488	−	40.6737i	−1.63835	−	0.945899i	−0.656942	−	0.753941i	$-0.728150\pi$
$44$		0			0
$45$	9.48892	−	16.4353i	0.210865	−	0.365229i
$46$		0			0
$47$		−	48.9746i		−	1.04201i	−0.853553	−	0.521006i	$-0.825557\pi$
$47$		−	48.9746i		−	1.04201i	0.853553	−	0.521006i	$-0.174443\pi$
$48$		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	0.476273	−	0.879297i	$-0.341987\pi$
$59$	−2.77794	−	1.60385i	−0.0470837	−	0.0271838i	−0.523357	+	0.852113i	$0.675321\pi$
$60$		0			0
$61$	−8.27717	+	14.3365i	−0.135691	+	0.235024i	−0.925861	−	0.377863i	$-0.876659\pi$
$61$	−8.27717	+	14.3365i	−0.135691	+	0.235024i	0.790170	+	0.612888i	$0.209992\pi$
$62$		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	−0.808946	−	0.587883i	$-0.799962\pi$
$67$	−47.1880	+	27.2440i	−0.704298	+	0.406627i	0.104648	+	0.994509i	$0.466628\pi$
$68$		0			0
$69$	8.60520	−	14.9047i	0.124713	−	0.216009i
$70$		0			0
$71$	67.4819	+	38.9607i	0.950449	+	0.548742i	0.893220	−	0.449619i	$-0.148440\pi$
$71$	67.4819	+	38.9607i	0.950449	+	0.548742i	0.0572288	+	0.998361i	$0.481774\pi$
$72$		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	$0.295680\pi$
$79$			126.553i			1.60193i	−0.598711	+	0.800965i	$0.704320\pi$
$80$		0			0
$81$	−34.6145	−	59.9541i	−0.427340	−	0.740174i
$82$		0			0
$83$		−	146.677i		−	1.76719i	−0.468252	−	0.883595i	$-0.655116\pi$
$83$		−	146.677i		−	1.76719i	0.468252	−	0.883595i	$-0.344884\pi$
$84$		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	0.973928	−	0.226858i	$-0.0728454\pi$
$89$	25.8544	+	44.7812i	0.290499	+	0.503159i	−0.683429	+	0.730017i	$0.739512\pi$
$90$		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	−0.988649	−	0.150242i	$-0.951995\pi$
$97$	−35.3285	+	61.1907i	−0.364211	+	0.630832i	0.624438	+	0.781074i	$0.285328\pi$
$98$		0			0
$99$		−	58.1003i		−	0.586872i
$100$		0			0
$101$	38.3011	+	66.3394i	0.379219	+	0.656826i	0.990949	−	0.134240i	$-0.0428595\pi$
$101$	38.3011	+	66.3394i	0.379219	+	0.656826i	−0.611730	+	0.791067i	$0.709526\pi$
$102$		0			0
$103$			15.4021i			0.149535i	0.997201	+	0.0747674i	$0.0238214\pi$
$103$			15.4021i			0.149535i	−0.997201	+	0.0747674i	$0.976179\pi$
$104$		0			0
$105$	2.90441			0.0276611
$106$		0			0
$107$	−79.1106	+	45.6746i	−0.739352	+	0.426865i	−0.821834	−	0.569728i	$-0.807049\pi$
$107$	−79.1106	+	45.6746i	−0.739352	+	0.426865i	0.0824818	+	0.996593i	$0.473715\pi$
$108$		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	−0.665155	−	0.746705i	$-0.731635\pi$
$113$	35.4919	−	61.4738i	0.314088	−	0.544016i	0.979243	+	0.202689i	$0.0649681\pi$
$114$		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	0.323723	−	0.946152i	$-0.395065\pi$
$127$	165.732	−	95.6854i	1.30498	−	0.753428i	0.981253	+	0.192723i	$0.0617320\pi$
$128$		0			0
$129$	54.1579			0.419829
$130$		0			0
$131$		−	40.2174i		−	0.307003i	−0.988148	−	0.153502i	$-0.950945\pi$
$131$		−	40.2174i		−	0.307003i	0.988148	−	0.153502i	$-0.0490550\pi$
$132$		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	−0.998170	−	0.0604771i	$-0.980738\pi$
$137$	−61.1993	+	106.000i	−0.446710	+	0.773724i	0.551460	+	0.834202i	$0.314071\pi$
$138$		0			0
$139$	100.067	+	57.7738i	0.719908	+	0.415639i	0.814719	−	0.579856i	$-0.196891\pi$
$139$	100.067	+	57.7738i	0.719908	+	0.415639i	−0.0948110	+	0.995495i	$0.530225\pi$
$140$		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	0.336218	+	0.941784i	$0.390852\pi$
$149$	−96.4775	+	167.104i	−0.647500	+	1.12150i	−0.983718	+	0.179719i	$0.942481\pi$
$150$		0			0
$151$			36.3232i			0.240551i	0.992741	+	0.120276i	$0.0383778\pi$
$151$			36.3232i			0.240551i	−0.992741	+	0.120276i	$0.961622\pi$
$152$		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	0.876932	−	0.480614i	$-0.159586\pi$
$163$	146.565	+	84.6196i	0.899174	+	0.519138i	0.0222420	+	0.999753i	$0.492920\pi$
$164$		0			0
$165$	−5.01297	+	8.68272i	−0.0303817	+	0.0526226i
$166$		0			0
$167$	175.923	−	101.569i	1.05343	−	0.608199i	0.129824	−	0.991537i	$-0.458559\pi$
$167$	175.923	−	101.569i	1.05343	−	0.608199i	0.923608	+	0.383338i	$0.125226\pi$
$168$		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	−0.552593	−	0.833451i	$-0.686362\pi$
$173$	77.0704	−	133.490i	0.445493	−	0.771617i	0.998086	+	0.0618339i	$0.0196949\pi$
$174$		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	−0.718717	−	0.695302i	$-0.755271\pi$
$179$	−85.1909	+	49.1850i	−0.475927	+	0.274776i	0.242791	+	0.970079i	$0.421937\pi$
$180$		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	−0.170839	−	0.985299i	$-0.554648\pi$
$191$	−211.924	−	122.355i	−1.10955	−	0.640600i	−0.938713	+	0.344699i	$0.887981\pi$
$192$		0			0
$193$	−101.903	−	176.501i	−0.527996	−	0.914515i	−0.999467	−	0.0326342i	$-0.989610\pi$
$193$	−101.903	−	176.501i	−0.527996	−	0.914515i	0.471472	−	0.881881i	$-0.343723\pi$
$194$		0			0
$195$	−2.22183	−	19.0665i	−0.0113940	−	0.0977768i
$196$		0			0
$197$	106.116	+	183.798i	0.538660	+	0.932986i	0.998977	+	0.0452315i	$0.0144025\pi$
$197$	106.116	+	183.798i	0.538660	+	0.932986i	−0.460317	+	0.887755i	$0.652264\pi$
$198$		0			0
$199$	−273.754	−	158.052i	−1.37565	−	0.794232i	−0.384018	−	0.923326i	$-0.625460\pi$
$199$	−273.754	−	158.052i	−1.37565	−	0.794232i	−0.991632	+	0.129094i	$0.958793\pi$
$200$		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	−0.992568	−	0.121695i	$-0.961167\pi$
$211$	−291.910	+	168.534i	−1.38346	+	0.798741i	−0.390893	+	0.920436i	$0.627834\pi$
$212$		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	−0.758880	−	0.651230i	$-0.774253\pi$
$223$	−128.077	+	73.9456i	−0.574339	+	0.331595i	0.184542	+	0.982825i	$0.440920\pi$
$224$		0			0
$225$	85.9142	−	148.808i	0.381841	−	0.661368i
$226$		0			0
$227$	299.989	+	173.199i	1.32154	+	0.762991i	0.983974	−	0.178311i	$-0.0570633\pi$
$227$	299.989	+	173.199i	1.32154	+	0.762991i	0.337565	+	0.941302i	$0.390397\pi$
$228$		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	$-0.904203\pi$
$239$		−	141.695i		−	0.592865i	0.955054	−	0.296433i	$-0.0957970\pi$
$240$		0			0
$241$	−51.0492	+	88.4197i	−0.211822	+	0.366887i	−0.952285	−	0.305211i	$-0.901273\pi$
$241$	−51.0492	+	88.4197i	−0.211822	+	0.366887i	0.740463	+	0.672098i	$0.234606\pi$
$242$		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	0.172741	−	0.984967i	$-0.444738\pi$
$251$	−149.068	−	86.0642i	−0.593895	−	0.342885i	−0.766636	+	0.642082i	$0.778071\pi$
$252$		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	0.650346	−	0.759639i	$-0.274624\pi$
$257$	−85.5022	−	148.094i	−0.332693	−	0.576242i	−0.983039	+	0.183396i	$0.941291\pi$
$258$		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	−0.723332	−	0.690501i	$-0.757390\pi$
$263$	−128.083	+	73.9485i	−0.487006	+	0.281173i	0.236326	+	0.971674i	$0.424057\pi$
$264$		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	−0.393626	−	0.919271i	$-0.628780\pi$
$269$	161.211	−	279.226i	0.599298	−	1.03802i	0.992925	−	0.118745i	$-0.0378871\pi$
$270$		0			0
$271$	−123.017	+	71.0240i	−0.453938	+	0.262081i	−0.709492	−	0.704714i	$-0.751075\pi$
$271$	−123.017	+	71.0240i	−0.453938	+	0.262081i	0.255554	+	0.966795i	$0.417742\pi$
$272$		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	−0.769249	−	0.638950i	$-0.779369\pi$
$277$	46.7361	−	80.9493i	0.168722	−	0.292236i	0.937971	+	0.346714i	$0.112703\pi$
$278$		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	−0.635960	−	0.771722i	$-0.719396\pi$
$283$	−80.8275	+	46.6658i	−0.285610	+	0.164897i	0.350351	+	0.936619i	$0.386062\pi$
$284$		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	0.0660162	+	0.997819i	$0.478971\pi$
$293$	−243.521	+	421.790i	−0.831128	+	1.43956i	−0.897144	+	0.441738i	$0.854362\pi$
$294$		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	$-0.986966\pi$
$307$		−	25.1356i		−	0.0818749i	0.999162	−	0.0409374i	$-0.0130344\pi$
$308$		0			0
$309$	−5.12705	−	8.88032i	−0.0165924	−	0.0287389i
$310$		0			0
$311$		−	272.009i		−	0.874627i	−0.899309	−	0.437313i	$-0.855930\pi$
$311$		−	272.009i		−	0.874627i	0.899309	−	0.437313i	$-0.144070\pi$
$312$		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	0.883264	−	0.468877i	$-0.155341\pi$
$331$	304.135	+	175.592i	0.918837	+	0.530491i	0.0355728	+	0.999367i	$0.488674\pi$
$332$		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	0.401773	−	0.915739i	$-0.368394\pi$
$347$	−66.0668	−	38.1437i	−0.190394	−	0.109924i	−0.592167	+	0.805815i	$0.701727\pi$
$348$		0			0
$349$	−341.837	−	592.079i	−0.979475	−	1.69650i	−0.664297	−	0.747469i	$-0.731269\pi$
$349$	−341.837	−	592.079i	−0.979475	−	1.69650i	−0.315178	−	0.949032i	$-0.602064\pi$
$350$		0			0
$351$	−139.504	−	60.2336i	−0.397447	−	0.171606i
$352$		0			0
$353$	−179.201	−	310.386i	−0.507653	−	0.879280i	−0.999961	−	0.00885925i	$-0.997180\pi$
$353$	−179.201	−	310.386i	−0.507653	−	0.879280i	0.492308	−	0.870421i	$-0.336153\pi$
$354$		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	$-0.561110\pi$
$359$		−	704.809i		−	1.96326i	0.190806	−	0.981628i	$-0.438890\pi$
$360$		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	−0.892749	−	0.450554i	$-0.851227\pi$
$367$	−348.259	+	201.067i	−0.948933	+	0.547867i	−0.0561839	+	0.998420i	$0.517893\pi$
$368$		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	−0.993695	−	0.112119i	$-0.964236\pi$
$373$	−149.107	+	258.260i	−0.399749	+	0.692386i	0.593945	+	0.804505i	$0.297570\pi$
$374$		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	−0.526362	−	0.850261i	$-0.676444\pi$
$379$	−20.1610	+	11.6399i	−0.0531952	+	0.0307122i	0.473167	+	0.880973i	$0.343111\pi$
$380$		0			0
$381$	−63.7037	+	110.338i	−0.167201	+	0.289601i
$382$		0			0
$383$	32.6408	+	18.8452i	0.0852239	+	0.0492041i	0.542006	−	0.840374i	$-0.317665\pi$
$383$	32.6408	+	18.8452i	0.0852239	+	0.0492041i	−0.456782	+	0.889578i	$0.650998\pi$
$384$		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	−0.998660	−	0.0517464i	$-0.983521\pi$
$397$	−180.443	+	312.537i	−0.454516	+	0.787246i	0.544144	+	0.838992i	$0.316855\pi$
$398$		0			0
$399$	29.1184	+	16.8115i	0.0729785	+	0.0421341i
$400$		0			0
$401$	14.5528	+	25.2062i	0.0362913	+	0.0628585i	0.883601	−	0.468241i	$-0.155112\pi$
$401$	14.5528	+	25.2062i	0.0362913	+	0.0628585i	−0.847309	+	0.531100i	$0.821779\pi$
$402$		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	−0.894329	−	0.447409i	$-0.852347\pi$
$409$	−24.4161	+	42.2899i	−0.0596971	+	0.103398i	0.834632	+	0.550807i	$0.185680\pi$
$410$		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	−0.802865	−	0.596161i	$-0.796692\pi$
$419$	−288.275	+	166.436i	−0.688008	+	0.397221i	0.114858	+	0.993382i	$0.463359\pi$
$420$		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	−0.166502	−	0.986041i	$-0.553247\pi$
$431$	260.403	−	150.344i	0.604183	−	0.348825i	0.770685	+	0.637216i	$0.219914\pi$
$432$		0			0
$433$	180.652	−	312.898i	0.417210	−	0.722629i	−0.578448	−	0.815720i	$-0.696341\pi$
$433$	180.652	−	312.898i	0.417210	−	0.722629i	0.995658	+	0.0930905i	$0.0296746\pi$
$434$		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	−0.579210	−	0.815179i	$-0.696639\pi$
$439$	−71.4908	+	41.2752i	−0.162849	+	0.0940210i	0.416361	+	0.909200i	$0.363305\pi$
$440$		0			0
$441$	386.175			0.875680
$442$		0			0
$443$		−	384.913i		−	0.868877i	−0.900701	−	0.434439i	$-0.856947\pi$
$443$		−	384.913i		−	0.868877i	0.900701	−	0.434439i	$-0.143053\pi$
$444$		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	−0.992927	−	0.118726i	$-0.962119\pi$
$449$	−176.746	+	306.133i	−0.393644	+	0.681812i	0.599283	+	0.800537i	$0.295452\pi$
$450$		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	0.938181	+	0.346144i	$0.112509\pi$
$457$	351.369	+	608.589i	0.768860	+	1.33171i	−0.169321	+	0.985561i	$0.554157\pi$
$458$		0			0
$459$	−316.729	−	182.864i	−0.690042	−	0.398396i
$460$		0			0
$461$	−181.475	+	314.324i	−0.393655	+	0.681831i	−0.992929	−	0.118714i	$-0.962123\pi$
$461$	−181.475	+	314.324i	−0.393655	+	0.681831i	0.599273	+	0.800544i	$0.295456\pi$
$462$		0			0
$463$		−	661.323i		−	1.42834i	−0.699970	−	0.714172i	$-0.746803\pi$
$463$		−	661.323i		−	1.42834i	0.699970	−	0.714172i	$-0.253197\pi$
$464$		0			0
$465$	36.1301	+	62.5792i	0.0776992	+	0.134579i
$466$		0			0
$467$		−	466.706i		−	0.999371i	−0.866207	−	0.499686i	$-0.833449\pi$
$467$		−	466.706i		−	0.999371i	0.866207	−	0.499686i	$-0.166551\pi$
$468$		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	0.0905462	−	0.995892i	$-0.471139\pi$
$479$	478.180	−	276.077i	0.998287	−	0.576361i	0.907741	+	0.419531i	$0.137805\pi$
$480$		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	0.491257	−	0.871015i	$-0.336538\pi$
$487$	−8.49135	−	4.90248i	−0.0174360	−	0.0100667i	−0.508693	+	0.860948i	$0.669871\pi$
$488$		0			0
$489$	−112.673			−0.230415
$490$		0			0
$491$	39.5580	−	22.8388i	0.0805661	−	0.0465149i	−0.459176	−	0.888345i	$-0.651855\pi$
$491$	39.5580	−	22.8388i	0.0805661	−	0.0465149i	0.539742	+	0.841831i	$0.318522\pi$
$492$		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	$0.122753\pi$
$499$			375.399i			0.752303i	−0.926558	+	0.376151i	$0.877247\pi$
$500$		0			0
$501$	−67.6209	+	117.123i	−0.134972	+	0.233778i
$502$		0			0
$503$	544.647	+	314.452i	1.08280	+	0.625153i	0.931649	−	0.363359i	$-0.118370\pi$
$503$	544.647	+	314.452i	1.08280	+	0.625153i	0.151147	+	0.988511i	$0.451703\pi$
$504$		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	0.965755	+	0.259457i	$0.0835434\pi$
$509$	360.155	+	623.807i	0.707573	+	1.22555i	−0.258181	+	0.966096i	$0.583123\pi$
$510$		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	−0.940191	−	0.340648i	$-0.889353\pi$
$523$	−583.289	+	336.762i	−1.11528	+	0.643905i	−0.175085	+	0.984553i	$0.556020\pi$
$524$		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	$-0.743356\pi$
$547$		−	789.553i		−	1.44342i	0.692194	−	0.721712i	$-0.256644\pi$
$548$		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	0.981578	−	0.191059i	$-0.0611923\pi$
$557$	181.207	+	313.860i	0.325327	+	0.563483i	−0.656252	+	0.754542i	$0.727859\pi$
$558$		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	−0.997998	−	0.0632396i	$-0.979857\pi$
$563$	−873.644	−	504.398i	−1.55176	−	0.895912i	−0.553766	−	0.832672i	$-0.686810\pi$
$564$		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	0.950336	−	0.311226i	$-0.100740\pi$
$569$	117.008	+	202.664i	0.205638	+	0.356176i	−0.744698	+	0.667402i	$0.767406\pi$
$570$		0			0
$571$		−	1064.96i		−	1.86508i	−0.361064	−	0.932541i	$-0.617586\pi$
$571$		−	1064.96i		−	1.86508i	0.361064	−	0.932541i	$-0.382414\pi$
$572$		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	−0.0278022	−	0.999613i	$-0.508851\pi$
$587$	483.681	−	279.253i	0.823987	−	0.475729i	0.851790	+	0.523884i	$0.175518\pi$
$588$		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	$0.147301\pi$
$599$			534.811i			0.892840i	−0.894824	+	0.446420i	$0.852699\pi$
$600$		0			0
$601$	−236.885	−	410.297i	−0.394151	−	0.682690i	0.598841	−	0.800868i	$-0.295628\pi$
$601$	−236.885	−	410.297i	−0.394151	−	0.682690i	−0.992992	+	0.118178i	$0.962295\pi$
$602$		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	0.579562	−	0.814928i	$-0.303224\pi$
$607$	99.3019	+	57.3320i	0.163595	+	0.0944514i	−0.415967	+	0.909380i	$0.636557\pi$
$608$		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	0.819540	−	0.573022i	$-0.194229\pi$
$613$	−53.0135	−	91.8221i	−0.0864820	−	0.149791i	−0.906022	+	0.423231i	$0.860896\pi$
$614$		0			0
$615$	−8.08089	−	4.66550i	−0.0131397	−	0.00758618i
$616$		0			0
$617$	−190.348	+	329.692i	−0.308506	+	0.534348i	−0.978036	−	0.208437i	$-0.933162\pi$
$617$	−190.348	+	329.692i	−0.308506	+	0.534348i	0.669530	+	0.742785i	$0.266496\pi$
$618$		0			0
$619$			340.038i			0.549334i	0.961539	+	0.274667i	$0.0885676\pi$
$619$			340.038i			0.549334i	−0.961539	+	0.274667i	$0.911432\pi$
$620$		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	0.545484	−	0.838121i	$-0.316346\pi$
$631$	58.2989	+	33.6589i	0.0923912	+	0.0533421i	−0.453093	+	0.891463i	$0.649679\pi$
$632$		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	−0.809830	−	0.586664i	$-0.800441\pi$
$641$	66.1196	−	114.522i	0.103151	−	0.178662i	0.912981	+	0.408002i	$0.133774\pi$
$642$		0			0
$643$	391.462	+	226.011i	0.608805	+	0.351494i	0.772498	−	0.635017i	$-0.219007\pi$
$643$	391.462	+	226.011i	0.608805	+	0.351494i	−0.163692	+	0.986511i	$0.552340\pi$
$644$		0			0
$645$	−120.116			−0.186226
$646$		0			0
$647$	776.369	−	448.237i	1.19995	−	0.692793i	0.239408	−	0.970919i	$-0.423047\pi$
$647$	776.369	−	448.237i	1.19995	−	0.692793i	0.960545	+	0.278126i	$0.0897133\pi$
$648$		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	−0.999750	−	0.0223805i	$-0.992875\pi$
$653$	−339.075	−	587.295i	−0.519257	−	0.899379i	0.480493	−	0.876999i	$-0.340458\pi$
$654$		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	0.257059	−	0.966396i	$-0.417246\pi$
$659$	−297.429	−	171.721i	−0.451334	−	0.260578i	−0.708394	+	0.705818i	$0.750580\pi$
$660$		0			0
$661$	428.396	+	742.004i	0.648103	+	1.12255i	0.983575	+	0.180497i	$0.0577707\pi$
$661$	428.396	+	742.004i	0.648103	+	1.12255i	−0.335472	+	0.942050i	$0.608896\pi$
$662$		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	0.663156	−	0.748481i	$-0.269217\pi$
$673$	−213.089	−	369.081i	−0.316626	−	0.548412i	−0.979782	+	0.200069i	$0.935883\pi$
$674$		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	−0.234985	−	0.971999i	$-0.575504\pi$
$683$	−815.675	−	470.930i	−1.19425	−	0.689502i	−0.959268	+	0.282497i	$0.908837\pi$
$684$		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	−0.196685	−	0.980467i	$-0.563018\pi$
$691$	382.870	−	221.050i	0.554081	−	0.319899i	0.750767	+	0.660568i	$0.229684\pi$
$692$		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	−0.931661	−	0.363328i	$-0.881640\pi$
$709$	−107.186	+	185.652i	−0.151179	+	0.261850i	0.780482	+	0.625178i	$0.214974\pi$
$710$		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	0.0229170	−	0.999737i	$-0.492705\pi$
$719$	−597.793	−	345.136i	−0.831422	−	0.480022i	−0.854339	+	0.519715i	$0.826038\pi$
$720$		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	$0.0833416\pi$
$727$			376.359i			0.517688i	−0.965919	+	0.258844i	$0.916658\pi$
$728$		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	−0.454462	−	0.890766i	$-0.650168\pi$
$739$	66.3127	−	38.2857i	0.0897331	−	0.0518074i	0.544195	+	0.838959i	$0.316835\pi$
$740$		0			0
$741$	88.0869	−	204.013i	0.118876	−	0.275321i
$742$		0			0
$743$	−689.527	+	398.099i	−0.928031	+	0.535799i	−0.886188	−	0.463325i	$-0.846656\pi$
$743$	−689.527	+	398.099i	−0.928031	+	0.535799i	−0.0418426	+	0.999124i	$0.513323\pi$
$744$		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	0.194374	−	0.980928i	$-0.437733\pi$
$751$	856.943	−	494.756i	1.14107	−	0.658796i	0.946695	+	0.322131i	$0.104399\pi$
$752$		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	0.623554	−	0.781780i	$-0.285688\pi$
$757$	−276.505	−	478.921i	−0.365264	−	0.632656i	−0.988819	+	0.149124i	$0.952355\pi$
$758$		0			0
$759$			116.859i			0.153964i
$760$		0			0
$761$	84.2955	−	146.004i	0.110769	−	0.191858i	−0.805311	−	0.592852i	$-0.798002\pi$
$761$	84.2955	−	146.004i	0.110769	−	0.191858i	0.916081	+	0.400994i	$0.131335\pi$
$762$		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	0.596692	−	0.802471i	$-0.296482\pi$
$769$	−304.996	−	528.269i	−0.396614	−	0.686956i	−0.993306	+	0.115515i	$0.963148\pi$
$770$		0			0
$771$	98.5954	+	56.9241i	0.127880	+	0.0738315i
$772$		0			0
$773$	554.353	−	960.168i	0.717145	−	1.24213i	−0.244981	−	0.969528i	$-0.578782\pi$
$773$	554.353	−	960.168i	0.717145	−	1.24213i	0.962126	−	0.272604i	$-0.0878848\pi$
$774$		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	0.307169	−	0.951655i	$-0.400618\pi$
$787$	−285.999	−	165.122i	−0.363404	−	0.209812i	−0.670573	+	0.741843i	$0.733952\pi$
$788$		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	0.129771	+	0.991544i	$0.458576\pi$
$797$	−632.672	+	1095.82i	−0.793817	+	1.37493i	−0.923588	+	0.383387i	$0.874758\pi$
$798$		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	−0.840963	−	0.541092i	$-0.818011\pi$
$809$	−719.267	−	1245.81i	−0.889081	−	1.53993i	−0.0481182	−	0.998842i	$-0.515322\pi$
$810$		0			0
$811$		−	492.383i		−	0.607131i	−0.952811	−	0.303566i	$-0.901823\pi$
$811$		−	492.383i		−	0.607131i	0.952811	−	0.303566i	$-0.0981771\pi$
$812$		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	−0.974111	−	0.226071i	$-0.927412\pi$
$821$	−560.611	−	971.006i	−0.682839	−	1.18271i	0.291272	−	0.956640i	$-0.405922\pi$
$822$		0			0
$823$	−330.419	−	190.767i	−0.401481	−	0.231795i	0.285642	−	0.958336i	$-0.407793\pi$
$823$	−330.419	−	190.767i	−0.401481	−	0.231795i	−0.687123	+	0.726541i	$0.741127\pi$
$824$		0			0
$825$	−45.3883	+	78.6148i	−0.0550161	+	0.0952906i
$826$		0			0
$827$			389.604i			0.471105i	0.971862	+	0.235553i	$0.0756900\pi$
$827$			389.604i			0.471105i	−0.971862	+	0.235553i	$0.924310\pi$
$828$		0			0
$829$	−339.169	−	587.457i	−0.409130	−	0.708634i	0.585663	−	0.810555i	$-0.300834\pi$
$829$	−339.169	−	587.457i	−0.409130	−	0.708634i	−0.994792	+	0.101921i	$0.967501\pi$
$830$		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	0.584174	−	0.811628i	$-0.301418\pi$
$839$	145.458	+	83.9804i	0.173371	+	0.100096i	−0.410803	+	0.911724i	$0.634752\pi$
$840$		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	$-0.928267\pi$
$859$		−	383.890i		−	0.446904i	0.974715	−	0.223452i	$-0.0717326\pi$
$860$		0			0
$861$	4.13774	+	7.16677i	0.00480573	+	0.00832377i
$862$		0			0
$863$			607.026i			0.703390i	0.936115	+	0.351695i	$0.114395\pi$
$863$			607.026i			0.703390i	−0.936115	+	0.351695i	$0.885605\pi$
$864$		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	0.0818934	+	0.996641i	$0.473903\pi$
$877$	−721.043	+	1248.88i	−0.822170	+	1.42404i	−0.904063	+	0.427399i	$0.859430\pi$
$878$		0			0
$879$		−	324.253i		−	0.368889i
$880$		0			0
$881$	531.728	+	920.980i	0.603551	+	1.04538i	0.992279	+	0.124028i	$0.0395813\pi$
$881$	531.728	+	920.980i	0.603551	+	1.04538i	−0.388728	+	0.921353i	$0.627085\pi$
$882$		0			0
$883$		−	709.951i		−	0.804021i	−0.915635	−	0.402011i	$-0.868311\pi$
$883$		−	709.951i		−	0.804021i	0.915635	−	0.402011i	$-0.131689\pi$
$884$		0			0
$885$	−4.73640			−0.00535187
$886$		0			0
$887$	1013.11	−	584.919i	1.14218	−	0.659436i	0.195207	−	0.980762i	$-0.437462\pi$
$887$	1013.11	−	584.919i	1.14218	−	0.659436i	0.946968	+	0.321326i	$0.104129\pi$
$888$		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	−0.370182	−	0.928959i	$-0.620705\pi$
$907$	226.051	−	130.511i	0.249229	−	0.143893i	0.619411	+	0.785067i	$0.287371\pi$
$908$		0			0
$909$	−655.467			−0.721085
$910$		0			0
$911$			520.587i			0.571446i	0.958312	+	0.285723i	$0.0922338\pi$
$911$			520.587i			0.571446i	−0.958312	+	0.285723i	$0.907766\pi$
$912$		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	−0.00259493	−	0.999997i	$-0.500826\pi$
$919$	−799.452	−	461.564i	−0.869915	−	0.502246i	−0.867320	+	0.497751i	$0.834159\pi$
$920$		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	−0.946524	−	0.322634i	$-0.895432\pi$
$929$	−180.089	+	311.923i	−0.193853	+	0.335762i	0.752671	+	0.658397i	$0.228765\pi$
$930$		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	−0.701911	−	0.712264i	$-0.747670\pi$
$947$	−412.918	+	238.398i	−0.436028	+	0.251741i	0.265884	+	0.964005i	$0.414336\pi$
$948$		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	−0.840985	−	0.541058i	$-0.818024\pi$
$953$	45.8183	−	79.3596i	0.0480779	−	0.0832734i	0.889063	+	0.457785i	$0.151357\pi$
$954$		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	$-0.748264\pi$
$967$		−	1374.98i		−	1.42191i	0.703240	−	0.710953i	$-0.251736\pi$
$968$		0			0
$969$	267.423	−	463.191i	0.275979	−	0.478009i
$970$		0			0
$971$	743.910	+	429.497i	0.766128	+	0.442324i	0.831492	−	0.555537i	$-0.187487\pi$
$971$	743.910	+	429.497i	0.766128	+	0.442324i	−0.0653638	+	0.997862i	$0.520821\pi$
$972$		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	0.940177	+	0.340687i	$0.110660\pi$
$977$	747.534	+	1294.77i	0.765132	+	1.32525i	−0.175045	+	0.984560i	$0.556007\pi$
$978$		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	$-0.688923\pi$
$983$		−	1629.77i		−	1.65796i	0.559281	−	0.828978i	$-0.311077\pi$
$984$		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	0.512050	−	0.858956i	$-0.328886\pi$
$991$	1498.34	−	865.070i	1.51195	−	0.872926i	0.999902	−	0.0139703i	$-0.00444702\pi$
$992$		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	−0.836336	−	0.548217i	$-0.815307\pi$
$997$	56.4324	−	97.7438i	0.0566022	−	0.0980379i	0.892938	+	0.450179i	$0.148640\pi$
$998$		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.159.7	✓	32
4.3	odd	2	inner	416.3.bb.c.159.10	yes	32
13.9	even	3	inner	416.3.bb.c.191.10	yes	32
52.35	odd	6	inner	416.3.bb.c.191.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.3.bb.c.159.7	✓	32	1.1	even	1	trivial
416.3.bb.c.159.10	yes	32	4.3	odd	2	inner
416.3.bb.c.191.7	yes	32	52.35	odd	6	inner
416.3.bb.c.191.10	yes	32	13.9	even	3	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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