LMFDB - Embedded newform 252.4.x.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.37628 - 2.80147i) q^{3} +(-2.20656 + 3.82187i) q^{5} +(13.5618 - 12.6126i) q^{7} +(11.3036 + 24.5200i) q^{9} +O(q^{10})$	\(q+(-4.37628 - 2.80147i) q^{3} +(-2.20656 + 3.82187i) q^{5} +(13.5618 - 12.6126i) q^{7} +(11.3036 + 24.5200i) q^{9} +(-59.1776 + 34.1662i) q^{11} +(29.9666 + 17.3012i) q^{13} +(20.3633 - 10.5440i) q^{15} +21.8129 q^{17} -124.247i q^{19} +(-94.6839 + 17.2036i) q^{21} +(61.3750 + 35.4349i) q^{23} +(52.7622 + 91.3868i) q^{25} +(19.2243 - 138.973i) q^{27} +(187.759 - 108.403i) q^{29} +(242.498 + 140.006i) q^{31} +(354.693 + 16.2633i) q^{33} +(18.2791 + 79.6618i) q^{35} +150.970 q^{37} +(-82.6734 - 159.665i) q^{39} +(136.432 - 236.307i) q^{41} +(-136.727 - 236.817i) q^{43} +(-118.654 - 10.9039i) q^{45} +(97.3555 + 168.625i) q^{47} +(24.8427 - 342.099i) q^{49} +(-95.4592 - 61.1081i) q^{51} +520.567i q^{53} -301.559i q^{55} +(-348.073 + 543.738i) q^{57} +(301.275 - 521.824i) q^{59} +(145.594 - 84.0586i) q^{61} +(462.558 + 189.966i) q^{63} +(-132.246 + 76.3523i) q^{65} +(371.461 - 643.390i) q^{67} +(-169.324 - 327.013i) q^{69} +758.080i q^{71} +1159.14i q^{73} +(25.1151 - 547.746i) q^{75} +(-371.626 + 1209.74i) q^{77} +(78.6173 + 136.169i) q^{79} +(-473.458 + 554.327i) q^{81} +(-137.159 - 237.567i) q^{83} +(-48.1314 + 83.3660i) q^{85} +(-1125.37 - 51.6003i) q^{87} -1047.80 q^{89} +(624.614 - 143.323i) q^{91} +(-669.015 - 1292.06i) q^{93} +(474.855 + 274.158i) q^{95} +(211.382 - 122.041i) q^{97} +(-1506.67 - 1064.83i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.37628	−	2.80147i	−0.842215	−	0.539142i
$3$	−4.37628	−	2.80147i	−0.842215	−	0.539142i
$4$		0			0
$5$	−2.20656	+	3.82187i	−0.197360	+	0.341838i	−0.947672	−	0.319246i	$-0.896570\pi$
$5$	−2.20656	+	3.82187i	−0.197360	+	0.341838i	0.750311	+	0.661085i	$0.229904\pi$
$6$		0			0
$7$	13.5618	−	12.6126i	0.732266	−	0.681018i
$7$	13.5618	−	12.6126i	0.732266	−	0.681018i
$8$		0			0
$9$	11.3036	+	24.5200i	0.418651	+	0.908147i
$10$		0			0
$11$	−59.1776	+	34.1662i	−1.62207	+	0.936500i	−0.635698	+	0.771938i	$0.719288\pi$
$11$	−59.1776	+	34.1662i	−1.62207	+	0.936500i	−0.986367	+	0.164562i	$0.947379\pi$
$12$		0			0
$13$	29.9666	+	17.3012i	0.639326	+	0.369115i	0.784355	−	0.620312i	$-0.212994\pi$
$13$	29.9666	+	17.3012i	0.639326	+	0.369115i	−0.145029	+	0.989427i	$0.546327\pi$
$14$		0			0
$15$	20.3633	−	10.5440i	0.350519	−	0.181496i
$16$		0			0
$17$	21.8129			0.311200			0.155600	−	0.987820i	$-0.450269\pi$
$17$	21.8129			0.311200			0.155600	+	0.987820i	$0.450269\pi$
$18$		0			0
$19$		−	124.247i		−	1.50022i	−0.661313	−	0.750110i	$-0.730001\pi$
$19$		−	124.247i		−	1.50022i	0.661313	−	0.750110i	$-0.269999\pi$
$20$		0			0
$21$	−94.6839	+	17.2036i	−0.983891	+	0.178768i
$22$		0			0
$23$	61.3750	+	35.4349i	0.556416	+	0.321247i	0.751706	−	0.659498i	$-0.229231\pi$
$23$	61.3750	+	35.4349i	0.556416	+	0.321247i	−0.195289	+	0.980746i	$0.562565\pi$
$24$		0			0
$25$	52.7622	+	91.3868i	0.422098	+	0.731095i
$26$		0			0
$27$	19.2243	−	138.973i	0.137027	−	0.990567i
$28$		0			0
$29$	187.759	−	108.403i	1.20228	−	0.694134i	0.241215	−	0.970472i	$-0.422454\pi$
$29$	187.759	−	108.403i	1.20228	−	0.694134i	0.961061	+	0.276337i	$0.0891207\pi$
$30$		0			0
$31$	242.498	+	140.006i	1.40497	+	0.811157i	0.994897	−	0.100897i	$-0.0321713\pi$
$31$	242.498	+	140.006i	1.40497	+	0.811157i	0.410069	+	0.912055i	$0.365505\pi$
$32$		0			0
$33$	354.693	+	16.2633i	1.87103	+	0.0857902i
$34$		0			0
$35$	18.2791	+	79.6618i	0.0882778	+	0.384723i
$36$		0			0
$37$	150.970			0.670793			0.335397	−	0.942077i	$-0.391130\pi$
$37$	150.970			0.670793			0.335397	+	0.942077i	$0.391130\pi$
$38$		0			0
$39$	−82.6734	−	159.665i	−0.339444	−	0.655562i
$40$		0			0
$41$	136.432	−	236.307i	0.519685	−	0.900121i	−0.480053	−	0.877239i	$-0.659383\pi$
$41$	136.432	−	236.307i	0.519685	−	0.900121i	0.999738	−	0.0228815i	$-0.00728404\pi$
$42$		0			0
$43$	−136.727	−	236.817i	−0.484898	−	0.839867i	0.514952	−	0.857219i	$-0.327810\pi$
$43$	−136.727	−	236.817i	−0.484898	−	0.839867i	−0.999849	+	0.0173518i	$0.994476\pi$
$44$		0			0
$45$	−118.654	−	10.9039i	−0.393065	−	0.0361214i
$46$		0			0
$47$	97.3555	+	168.625i	0.302144	+	0.523328i	0.976621	−	0.214967i	$-0.0689644\pi$
$47$	97.3555	+	168.625i	0.302144	+	0.523328i	−0.674478	+	0.738295i	$0.735631\pi$
$48$		0			0
$49$	24.8427	−	342.099i	0.0724277	−	0.997374i
$50$		0			0
$51$	−95.4592	−	61.1081i	−0.262097	−	0.167781i
$52$		0			0
$53$			520.567i			1.34916i	0.738203	+	0.674579i	$0.235675\pi$
$53$			520.567i			1.34916i	−0.738203	+	0.674579i	$0.764325\pi$
$54$		0			0
$55$		−	301.559i		−	0.739312i
$56$		0			0
$57$	−348.073	+	543.738i	−0.808832	+	1.26351i
$58$		0			0
$59$	301.275	−	521.824i	0.664792	−	1.15145i	−0.314550	−	0.949241i	$-0.601854\pi$
$59$	301.275	−	521.824i	0.664792	−	1.15145i	0.979342	−	0.202212i	$-0.0648130\pi$
$60$		0			0
$61$	145.594	−	84.0586i	0.305596	−	0.176436i	−0.339358	−	0.940657i	$-0.610210\pi$
$61$	145.594	−	84.0586i	0.305596	−	0.176436i	0.644954	+	0.764221i	$0.276876\pi$
$62$		0			0
$63$	462.558	+	189.966i	0.925029	+	0.379896i
$64$		0			0
$65$	−132.246	+	76.3523i	−0.252355	+	0.145698i
$66$		0			0
$67$	371.461	−	643.390i	0.677332	−	1.17317i	−0.298450	−	0.954425i	$-0.596470\pi$
$67$	371.461	−	643.390i	0.677332	−	1.17317i	0.975782	−	0.218747i	$-0.0701970\pi$
$68$		0			0
$69$	−169.324	−	327.013i	−0.295424	−	0.570547i
$70$		0			0
$71$			758.080i			1.26715i	0.773682	+	0.633574i	$0.218413\pi$
$71$			758.080i			1.26715i	−0.773682	+	0.633574i	$0.781587\pi$
$72$		0			0
$73$			1159.14i			1.85845i	0.369520	+	0.929223i	$0.379522\pi$
$73$			1159.14i			1.85845i	−0.369520	+	0.929223i	$0.620478\pi$
$74$		0			0
$75$	25.1151	−	547.746i	0.0386672	−	0.843309i
$76$		0			0
$77$	−371.626	+	1209.74i	−0.550010	+	1.79042i
$78$		0			0
$79$	78.6173	+	136.169i	0.111964	+	0.193927i	0.916562	−	0.399893i	$-0.130953\pi$
$79$	78.6173	+	136.169i	0.111964	+	0.193927i	−0.804598	+	0.593820i	$0.797619\pi$
$80$		0			0
$81$	−473.458	+	554.327i	−0.649463	+	0.760394i
$82$		0			0
$83$	−137.159	−	237.567i	−0.181388	−	0.314173i	0.760965	−	0.648792i	$-0.224726\pi$
$83$	−137.159	−	237.567i	−0.181388	−	0.314173i	−0.942353	+	0.334619i	$0.891392\pi$
$84$		0			0
$85$	−48.1314	+	83.3660i	−0.0614186	+	0.106380i
$86$		0			0
$87$	−1125.37	−	51.6003i	−1.38681	−	0.0635878i
$88$		0			0
$89$	−1047.80			−1.24793			−0.623967	−	0.781451i	$-0.714480\pi$
$89$	−1047.80			−1.24793			−0.623967	+	0.781451i	$0.714480\pi$
$90$		0			0
$91$	624.614	−	143.323i	0.719531	−	0.165102i
$92$		0			0
$93$	−669.015	−	1292.06i	−0.745953	−	1.44065i
$94$		0			0
$95$	474.855	+	274.158i	0.512833	+	0.296084i
$96$		0			0
$97$	211.382	−	122.041i	0.221264	−	0.127747i	−0.385272	−	0.922803i	$-0.625892\pi$
$97$	211.382	−	122.041i	0.221264	−	0.127747i	0.606535	+	0.795057i	$0.292559\pi$
$98$		0			0
$99$	−1506.67	−	1064.83i	−1.52956	−	1.08101i
$100$		0			0
$101$	525.022	+	909.365i	0.517244	+	0.895893i	0.999799	+	0.0200273i	$0.00637530\pi$
$101$	525.022	+	909.365i	0.517244	+	0.895893i	−0.482556	+	0.875865i	$0.660291\pi$
$102$		0			0
$103$	−373.861	−	215.849i	−0.357647	−	0.206488i	0.310401	−	0.950606i	$-0.399537\pi$
$103$	−373.861	−	215.849i	−0.357647	−	0.206488i	−0.668048	+	0.744118i	$0.732870\pi$
$104$		0			0
$105$	143.176	−	399.830i	0.133071	−	0.371613i
$106$		0			0
$107$			12.0965i			0.0109291i	0.999985	+	0.00546455i	$0.00173943\pi$
$107$			12.0965i			0.0109291i	−0.999985	+	0.00546455i	$0.998261\pi$
$108$		0			0
$109$	−877.008			−0.770662			−0.385331	−	0.922778i	$-0.625913\pi$
$109$	−877.008			−0.770662			−0.385331	+	0.922778i	$0.625913\pi$
$110$		0			0
$111$	−660.687	−	422.938i	−0.564952	−	0.361653i
$112$		0			0
$113$	1041.65	+	601.395i	0.867167	+	0.500659i	0.866406	−	0.499340i	$-0.166424\pi$
$113$	1041.65	+	601.395i	0.867167	+	0.500659i	0.000761396		1.00000i	$0.499758\pi$
$114$		0			0
$115$	−270.855	+	156.378i	−0.219629	+	0.126803i
$116$		0			0
$117$	−85.4958	+	930.346i	−0.0675563	+	0.735133i
$118$		0			0
$119$	295.821	−	275.118i	0.227881	−	0.211933i
$120$		0			0
$121$	1669.16	−	2891.07i	1.25406	−	2.17210i
$122$		0			0
$123$	−1259.07	+	651.935i	−0.922980	+	0.477911i
$124$		0			0
$125$	−1017.33			−0.727942
$126$		0			0
$127$	2508.88			1.75297			0.876485	−	0.481429i	$-0.159882\pi$
$127$	2508.88			1.75297			0.876485	+	0.481429i	$0.159882\pi$
$128$		0			0
$129$	−65.0826	+	1419.41i	−0.0444202	+	0.968777i
$130$		0			0
$131$	−203.928	+	353.215i	−0.136010	+	0.235576i	−0.925983	−	0.377566i	$-0.876761\pi$
$131$	−203.928	+	353.215i	−0.136010	+	0.235576i	0.789973	+	0.613142i	$0.210095\pi$
$132$		0			0
$133$	−1567.08	−	1685.01i	−1.02168	−	1.09856i
$134$		0			0
$135$	488.716	+	380.124i	0.311570	+	0.242340i
$136$		0			0
$137$	−1998.46	+	1153.81i	−1.24628	+	0.719540i	−0.970365	−	0.241642i	$-0.922314\pi$
$137$	−1998.46	+	1153.81i	−1.24628	+	0.719540i	−0.275914	+	0.961182i	$0.588981\pi$
$138$		0			0
$139$	35.4504	+	20.4673i	0.0216321	+	0.0124893i	0.510777	−	0.859713i	$-0.329358\pi$
$139$	35.4504	+	20.4673i	0.0216321	+	0.0124893i	−0.489145	+	0.872203i	$0.662691\pi$
$140$		0			0
$141$	46.3417	−	1010.69i	0.0276786	−	0.603653i
$142$		0			0
$143$	−2364.47			−1.38271
$144$		0			0
$145$			956.788i			0.547979i
$146$		0			0
$147$	−1067.10	+	1427.52i	−0.598726	+	0.800954i
$148$		0			0
$149$	2458.97	+	1419.69i	1.35199	+	0.780573i	0.988528	−	0.151035i	$-0.0482605\pi$
$149$	2458.97	+	1419.69i	1.35199	+	0.780573i	0.363464	+	0.931608i	$0.381594\pi$
$150$		0			0
$151$	383.904	+	664.941i	0.206898	+	0.358359i	0.950736	−	0.310002i	$-0.100330\pi$
$151$	383.904	+	664.941i	0.206898	+	0.358359i	−0.743837	+	0.668361i	$0.766996\pi$
$152$		0			0
$153$	246.564	+	534.851i	0.130284	+	0.282616i
$154$		0			0
$155$	−1070.17	+	617.864i	−0.554569	+	0.320181i
$156$		0			0
$157$	−121.383	−	70.0804i	−0.0617032	−	0.0356243i	0.468831	−	0.883288i	$-0.344675\pi$
$157$	−121.383	−	70.0804i	−0.0617032	−	0.0356243i	−0.530534	+	0.847664i	$0.678009\pi$
$158$		0			0
$159$	1458.35	−	2278.15i	0.727388	−	1.13628i
$160$		0			0
$161$	1279.28	−	293.542i	0.626220	−	0.143691i
$162$		0			0
$163$	−702.905			−0.337765			−0.168883	−	0.985636i	$-0.554016\pi$
$163$	−702.905			−0.337765			−0.168883	+	0.985636i	$0.554016\pi$
$164$		0			0
$165$	−844.806	+	1319.70i	−0.398594	+	0.622659i
$166$		0			0
$167$	1094.61	−	1895.92i	0.507206	−	0.878506i	−0.492759	−	0.870166i	$-0.664012\pi$
$167$	1094.61	−	1895.92i	0.507206	−	0.878506i	0.999965	−	0.00834081i	$-0.00265499\pi$
$168$		0			0
$169$	−499.835	−	865.739i	−0.227508	−	0.394055i
$170$		0			0
$171$	3046.53	−	1404.43i	1.36242	−	0.628068i
$172$		0			0
$173$	−900.641	−	1559.96i	−0.395806	−	0.685557i	0.597397	−	0.801945i	$-0.296202\pi$
$173$	−900.641	−	1559.96i	−0.395806	−	0.685557i	−0.993204	+	0.116389i	$0.962868\pi$
$174$		0			0
$175$	1868.18	+	573.896i	0.806977	+	0.247900i
$176$		0			0
$177$	−2780.34	+	1439.63i	−1.18069	+	0.611353i
$178$		0			0
$179$			2708.76i			1.13107i	0.824723	+	0.565537i	$0.191331\pi$
$179$			2708.76i			1.13107i	−0.824723	+	0.565537i	$0.808669\pi$
$180$		0			0
$181$		−	466.672i		−	0.191644i	−0.995399	−	0.0958218i	$-0.969452\pi$
$181$		−	466.672i		−	0.191644i	0.995399	−	0.0958218i	$-0.0305479\pi$
$182$		0			0
$183$	−872.646	−	40.0124i	−0.352502	−	0.0161628i
$184$		0			0
$185$	−333.124	+	576.988i	−0.132388	+	0.229303i
$186$		0			0
$187$	−1290.83	+	745.263i	−0.504787	+	0.291439i
$188$		0			0
$189$	−1492.10	−	2127.18i	−0.574255	−	0.818677i
$190$		0			0
$191$	2131.65	−	1230.71i	0.807544	−	0.466236i	−0.0385584	−	0.999256i	$-0.512277\pi$
$191$	2131.65	−	1230.71i	0.807544	−	0.466236i	0.846102	+	0.533021i	$0.178943\pi$
$192$		0			0
$193$	−821.546	+	1422.96i	−0.306405	+	0.530709i	−0.977573	−	0.210596i	$-0.932460\pi$
$193$	−821.546	+	1422.96i	−0.306405	+	0.530709i	0.671168	+	0.741305i	$0.265793\pi$
$194$		0			0
$195$	792.644	+	36.3441i	0.291089	+	0.0133470i
$196$		0			0
$197$		−	528.765i		−	0.191233i	−0.995418	−	0.0956166i	$-0.969518\pi$
$197$		−	528.765i		−	0.191233i	0.995418	−	0.0956166i	$-0.0304823\pi$
$198$		0			0
$199$		−	3314.80i		−	1.18080i	−0.807109	−	0.590402i	$-0.798969\pi$
$199$		−	3314.80i		−	1.18080i	0.807109	−	0.590402i	$-0.201031\pi$
$200$		0			0
$201$	−3428.05	+	1775.01i	−1.20297	+	0.622885i
$202$		0			0
$203$	1179.10	−	3838.27i	0.407668	−	1.32706i
$204$		0			0
$205$	602.090	+	1042.85i	0.205131	+	0.355297i
$206$		0			0
$207$	−175.105	+	1905.46i	−0.0587954	+	0.639799i
$208$		0			0
$209$	4245.04	+	7352.63i	1.40496	+	2.43345i
$210$		0			0
$211$	−2475.87	+	4288.34i	−0.807801	+	1.39915i	0.106582	+	0.994304i	$0.466009\pi$
$211$	−2475.87	+	4288.34i	−0.807801	+	1.39915i	−0.914384	+	0.404849i	$0.867324\pi$
$212$		0			0
$213$	2123.73	−	3317.57i	0.683173	−	1.06721i
$214$		0			0
$215$	1206.78			0.382798
$216$		0			0
$217$	5054.55	−	1159.81i	1.58122	−	0.362824i
$218$		0			0
$219$	3247.28	−	5072.70i	1.00197	−	1.56521i
$220$		0			0
$221$	653.658	+	377.390i	0.198958	+	0.114869i
$222$		0			0
$223$	1349.02	−	778.858i	0.405100	−	0.233884i	−0.283582	−	0.958948i	$-0.591523\pi$
$223$	1349.02	−	778.858i	0.405100	−	0.233884i	0.688682	+	0.725064i	$0.258190\pi$
$224$		0			0
$225$	−1644.40	+	2326.73i	−0.487230	+	0.689400i
$226$		0			0
$227$	125.360	+	217.131i	0.0366540	+	0.0634866i	0.883770	−	0.467921i	$-0.154997\pi$
$227$	125.360	+	217.131i	0.0366540	+	0.0634866i	−0.847116	+	0.531407i	$0.821663\pi$
$228$		0			0
$229$	4341.47	+	2506.55i	1.25281	+	0.723308i	0.971666	−	0.236359i	$-0.0759542\pi$
$229$	4341.47	+	2506.55i	1.25281	+	0.723308i	0.281140	+	0.959667i	$0.409288\pi$
$230$		0			0
$231$	5015.38	−	4253.05i	1.42852	−	1.21139i
$232$		0			0
$233$		−	3160.66i		−	0.888676i	−0.895859	−	0.444338i	$-0.853439\pi$
$233$		−	3160.66i		−	0.888676i	0.895859	−	0.444338i	$-0.146561\pi$
$234$		0			0
$235$	−859.281			−0.238525
$236$		0			0
$237$	37.4223	−	816.157i	0.0102567	−	0.223692i
$238$		0			0
$239$	−504.538	−	291.295i	−0.136552	−	0.0788382i	0.430168	−	0.902749i	$-0.358454\pi$
$239$	−504.538	−	291.295i	−0.136552	−	0.0788382i	−0.566720	+	0.823911i	$0.691788\pi$
$240$		0			0
$241$	2813.68	−	1624.48i	0.752054	−	0.434198i	−0.0743818	−	0.997230i	$-0.523698\pi$
$241$	2813.68	−	1624.48i	0.752054	−	0.434198i	0.826435	+	0.563031i	$0.190365\pi$
$242$		0			0
$243$	3624.91	−	1099.51i	0.956947	−	0.290262i
$244$		0			0
$245$	1252.64	+	849.807i	0.326646	+	0.221601i
$246$		0			0
$247$	2149.62	−	3723.26i	0.553754	−	0.959130i
$248$		0			0
$249$	−65.2887	+	1423.91i	−0.0166165	+	0.362395i
$250$		0			0
$251$	−4222.39			−1.06181			−0.530907	−	0.847430i	$-0.678148\pi$
$251$	−4222.39			−1.06181			−0.530907	+	0.847430i	$0.678148\pi$
$252$		0			0
$253$	−4842.70			−1.20339
$254$		0			0
$255$	444.183	−	229.994i	0.109082	−	0.0564815i
$256$		0			0
$257$	3840.77	−	6652.41i	0.932220	−	1.61465i	0.152704	−	0.988272i	$-0.451202\pi$
$257$	3840.77	−	6652.41i	0.932220	−	1.61465i	0.779517	−	0.626381i	$-0.215465\pi$
$258$		0			0
$259$	2047.42	−	1904.13i	0.491199	−	0.456823i
$260$		0			0
$261$	4780.38	+	3378.51i	1.13371	+	0.801243i
$262$		0			0
$263$	−5082.39	+	2934.32i	−1.19161	+	0.687976i	−0.958671	−	0.284515i	$-0.908167\pi$
$263$	−5082.39	+	2934.32i	−1.19161	+	0.687976i	−0.232938	+	0.972492i	$0.574834\pi$
$264$		0			0
$265$	−1989.54	−	1148.66i	−0.461194	−	0.266270i
$266$		0			0
$267$	4585.44	+	2935.36i	1.05103	+	0.672814i
$268$		0			0
$269$	−810.599			−0.183729			−0.0918645	−	0.995772i	$-0.529283\pi$
$269$	−810.599			−0.183729			−0.0918645	+	0.995772i	$0.529283\pi$
$270$		0			0
$271$			6222.78i			1.39486i	0.716653	+	0.697430i	$0.245673\pi$
$271$			6222.78i			1.39486i	−0.716653	+	0.697430i	$0.754327\pi$
$272$		0			0
$273$	−3135.00	−	1122.62i	−0.695014	−	0.248878i
$274$		0			0
$275$	−6244.68	−	3605.37i	−1.36934	−	0.790589i
$276$		0			0
$277$	285.059	+	493.737i	0.0618323	+	0.107097i	0.895284	−	0.445495i	$-0.146972\pi$
$277$	285.059	+	493.737i	0.0618323	+	0.107097i	−0.833452	+	0.552592i	$0.813639\pi$
$278$		0			0
$279$	−691.856	+	7528.62i	−0.148460	+	1.61551i
$280$		0			0
$281$	2609.79	−	1506.76i	0.554047	−	0.319879i	−0.196706	−	0.980463i	$-0.563024\pi$
$281$	2609.79	−	1506.76i	0.554047	−	0.319879i	0.750753	+	0.660584i	$0.229691\pi$
$282$		0			0
$283$	−5937.64	−	3428.10i	−1.24719	−	0.720068i	−0.276646	−	0.960972i	$-0.589223\pi$
$283$	−5937.64	−	3428.10i	−1.24719	−	0.720068i	−0.970549	+	0.240904i	$0.922556\pi$
$284$		0			0
$285$	−1310.05	−	2530.08i	−0.272284	−	0.525856i
$286$		0			0
$287$	−1130.20	−	4925.51i	−0.232451	−	1.01304i
$288$		0			0
$289$	−4437.20			−0.903154
$290$		0			0
$291$	−1266.96	−	58.0924i	−0.255225	−	0.0117025i
$292$		0			0
$293$	507.694	−	879.352i	0.101228	−	0.175332i	−0.810963	−	0.585098i	$-0.801056\pi$
$293$	507.694	−	879.352i	0.101228	−	0.175332i	0.912191	+	0.409766i	$0.134390\pi$
$294$		0			0
$295$	1329.56	+	2302.87i	0.262407	+	0.454503i
$296$		0			0
$297$	3610.52	+	8880.89i	0.705400	+	1.73509i
$298$		0			0
$299$	1226.13	+	2123.73i	0.237155	+	0.410764i
$300$		0			0
$301$	−4841.14	−	1487.18i	−0.927039	−	0.284782i
$302$		0			0
$303$	249.913	−	5450.46i	0.0473833	−	1.03340i
$304$		0			0
$305$			741.920i			0.139286i
$306$		0			0
$307$		−	313.327i		−	0.0582493i	−0.999576	−	0.0291246i	$-0.990728\pi$
$307$		−	313.327i		−	0.0582493i	0.999576	−	0.0291246i	$-0.00927197\pi$
$308$		0			0
$309$	1031.43	+	1991.98i	0.189889	+	0.366730i
$310$		0			0
$311$	2117.00	−	3666.76i	0.385994	−	0.668562i	−0.605912	−	0.795531i	$-0.707192\pi$
$311$	2117.00	−	3666.76i	0.385994	−	0.668562i	0.991907	+	0.126970i	$0.0405251\pi$
$312$		0			0
$313$	−2846.33	+	1643.33i	−0.514007	+	0.296762i	−0.734479	−	0.678631i	$-0.762573\pi$
$313$	−2846.33	+	1643.33i	−0.514007	+	0.296762i	0.220472	+	0.975393i	$0.429240\pi$
$314$		0			0
$315$	−1746.69	+	1348.66i	−0.312427	+	0.241234i
$316$		0			0
$317$	5320.94	−	3072.05i	0.942757	−	0.544301i	0.0519334	−	0.998651i	$-0.483462\pi$
$317$	5320.94	−	3072.05i	0.942757	−	0.544301i	0.890823	+	0.454350i	$0.150128\pi$
$318$		0			0
$319$	−7407.42	+	12830.0i	−1.30011	+	2.25186i
$320$		0			0
$321$	33.8880	−	52.9377i	0.00589234	−	0.00920465i
$322$		0			0
$323$		−	2710.18i		−	0.466869i
$324$		0			0
$325$			3651.41i			0.623211i
$326$		0			0
$327$	3838.03	+	2456.91i	0.649063	+	0.415497i
$328$		0			0
$329$	3447.11	+	1058.94i	0.577646	+	0.177450i
$330$		0			0
$331$	3009.90	+	5213.30i	0.499816	+	0.865707i	1.00000		0.000212000i	$-6.74816e-5\pi$
$331$	3009.90	+	5213.30i	0.499816	+	0.865707i	−0.500184	+	0.865919i	$0.666734\pi$
$332$		0			0
$333$	1706.50	+	3701.79i	0.280828	+	0.609179i
$334$		0			0
$335$	1639.30	+	2839.35i	0.267357	+	0.463076i
$336$		0			0
$337$	−130.124	+	225.382i	−0.0210336	+	0.0364313i	−0.876351	−	0.481674i	$-0.840029\pi$
$337$	−130.124	+	225.382i	−0.0210336	+	0.0364313i	0.855317	+	0.518105i	$0.173362\pi$
$338$		0			0
$339$	−2873.75	−	5550.01i	−0.460414	−	0.889189i
$340$		0			0
$341$	−19133.9			−3.03859
$342$		0			0
$343$	−3977.86	−	4952.80i	−0.626194	−	0.779668i
$344$		0			0
$345$	1623.42	+	74.4369i	0.253340	+	0.0116161i
$346$		0			0
$347$	−7714.97	−	4454.24i	−1.19355	−	0.689096i	−0.234439	−	0.972131i	$-0.575325\pi$
$347$	−7714.97	−	4454.24i	−1.19355	−	0.689096i	−0.959110	+	0.283035i	$0.908659\pi$
$348$		0			0
$349$	−2449.08	+	1413.98i	−0.375635	+	0.216873i	−0.675917	−	0.736978i	$-0.736252\pi$
$349$	−2449.08	+	1413.98i	−0.375635	+	0.216873i	0.300283	+	0.953850i	$0.402919\pi$
$350$		0			0
$351$	2980.49	−	3831.94i	0.453238	−	0.582717i
$352$		0			0
$353$	−792.030	−	1371.84i	−0.119421	−	0.206843i	0.800118	−	0.599843i	$-0.204770\pi$
$353$	−792.030	−	1371.84i	−0.119421	−	0.206843i	−0.919538	+	0.393001i	$0.871437\pi$
$354$		0			0
$355$	−2897.28	−	1672.75i	−0.433160	−	0.250085i
$356$		0			0
$357$	−2065.33	+	375.260i	−0.306187	+	0.0556326i
$358$		0			0
$359$		−	7054.16i		−	1.03706i	−0.855060	−	0.518529i	$-0.826480\pi$
$359$		−	7054.16i		−	1.03706i	0.855060	−	0.518529i	$-0.173520\pi$
$360$		0			0
$361$	−8578.27			−1.25066
$362$		0			0
$363$	−15403.9	+	7976.02i	−2.22726	+	1.15326i
$364$		0			0
$365$	−4430.06	−	2557.70i	−0.635288	−	0.366784i
$366$		0			0
$367$	−4786.15	+	2763.29i	−0.680749	+	0.393031i	−0.800137	−	0.599817i	$-0.795240\pi$
$367$	−4786.15	+	2763.29i	−0.680749	+	0.393031i	0.119388	+	0.992848i	$0.461907\pi$
$368$		0			0
$369$	7336.41	+	674.192i	1.03501	+	0.0951140i
$370$		0			0
$371$	6565.72	+	7059.81i	0.918802	+	0.987943i
$372$		0			0
$373$	−117.016	+	202.678i	−0.0162436	+	0.0281348i	−0.874033	−	0.485867i	$-0.838504\pi$
$373$	−117.016	+	202.678i	−0.0162436	+	0.0281348i	0.857789	+	0.514001i	$0.171837\pi$
$374$		0			0
$375$	4452.12	+	2850.02i	0.613084	+	0.392465i
$376$		0			0
$377$	7502.01			1.02486
$378$		0			0
$379$	5344.34			0.724328			0.362164	−	0.932114i	$-0.382038\pi$
$379$	5344.34			0.724328			0.362164	+	0.932114i	$0.382038\pi$
$380$		0			0
$381$	−10979.6	−	7028.55i	−1.47638	−	0.945101i
$382$		0			0
$383$	−1223.32	+	2118.85i	−0.163208	+	0.282684i	−0.936017	−	0.351954i	$-0.885517\pi$
$383$	−1223.32	+	2118.85i	−0.163208	+	0.282684i	0.772810	+	0.634638i	$0.218851\pi$
$384$		0			0
$385$	−3803.45	−	4089.67i	−0.503485	−	0.541373i
$386$		0			0
$387$	4261.25	−	6029.41i	0.559720	−	0.791970i
$388$		0			0
$389$	168.902	−	97.5154i	0.0220145	−	0.0127101i	−0.488952	−	0.872310i	$-0.662621\pi$
$389$	168.902	−	97.5154i	0.0220145	−	0.0127101i	0.510967	+	0.859600i	$0.329287\pi$
$390$		0			0
$391$	1338.77	+	772.937i	0.173157	+	0.0999722i
$392$		0			0
$393$	1881.97	−	974.465i	0.241559	−	0.125077i
$394$		0			0
$395$	−693.894			−0.0883889
$396$		0			0
$397$		−	3572.40i		−	0.451621i	−0.974171	−	0.225810i	$-0.927497\pi$
$397$		−	3572.40i		−	0.451621i	0.974171	−	0.225810i	$-0.0725029\pi$
$398$		0			0
$399$	2137.49	+	11764.2i	0.268191	+	1.47605i
$400$		0			0
$401$	1583.57	+	914.277i	0.197207	+	0.113857i	0.595352	−	0.803465i	$-0.297013\pi$
$401$	1583.57	+	914.277i	0.197207	+	0.113857i	−0.398145	+	0.917322i	$0.630346\pi$
$402$		0			0
$403$	4844.56	+	8391.03i	0.598821	+	1.03719i
$404$		0			0
$405$	−1073.85	−	3032.65i	−0.131753	−	0.372083i
$406$		0			0
$407$	−8934.05	+	5158.08i	−1.08807	+	0.628198i
$408$		0			0
$409$	10364.8	+	5984.12i	1.25307	+	0.723461i	0.971718	−	0.236143i	$-0.0758833\pi$
$409$	10364.8	+	5984.12i	1.25307	+	0.723461i	0.281353	+	0.959604i	$0.409217\pi$
$410$		0			0
$411$	11978.2	+	549.222i	1.43757	+	0.0659151i
$412$		0			0
$413$	−2495.76	−	10876.7i	−0.297356	−	1.29591i
$414$		0			0
$415$	1210.60			0.143195
$416$		0			0
$417$	−97.8023	−	188.884i	−0.0114854	−	0.0221815i
$418$		0			0
$419$	895.525	−	1551.09i	0.104413	−	0.180849i	−0.809085	−	0.587692i	$-0.800037\pi$
$419$	895.525	−	1551.09i	0.104413	−	0.180849i	0.913498	+	0.406842i	$0.133370\pi$
$420$		0			0
$421$	−3886.50	−	6731.62i	−0.449920	−	0.779285i	0.548460	−	0.836177i	$-0.315214\pi$
$421$	−3886.50	−	6731.62i	−0.449920	−	0.779285i	−0.998380	+	0.0568918i	$0.981881\pi$
$422$		0			0
$423$	−3034.21	+	4293.21i	−0.348766	+	0.493483i
$424$		0			0
$425$	1150.90	+	1993.41i	0.131357	+	0.227517i
$426$		0			0
$427$	914.307	−	2976.30i	0.103622	−	0.337315i
$428$		0			0
$429$	10347.6	+	6623.98i	1.16453	+	0.745475i
$430$		0			0
$431$		−	11600.3i		−	1.29644i	−0.761453	−	0.648221i	$-0.775513\pi$
$431$		−	11600.3i		−	1.29644i	0.761453	−	0.648221i	$-0.224487\pi$
$432$		0			0
$433$		−	12453.9i		−	1.38221i	−0.722755	−	0.691105i	$-0.757124\pi$
$433$		−	12453.9i		−	1.38221i	0.722755	−	0.691105i	$-0.242876\pi$
$434$		0			0
$435$	2680.41	−	4187.17i	0.295438	−	0.461516i
$436$		0			0
$437$	4402.67	−	7625.65i	0.481941	−	0.834747i
$438$		0			0
$439$	−10941.0	+	6316.81i	−1.18949	+	0.686754i	−0.958191	−	0.286128i	$-0.907632\pi$
$439$	−10941.0	+	6316.81i	−1.18949	+	0.686754i	−0.231301	+	0.972882i	$0.574298\pi$
$440$		0			0
$441$	8669.07	−	3257.80i	0.936084	−	0.351777i
$442$		0			0
$443$	−11050.1	+	6379.76i	−1.18511	+	0.684224i	−0.957191	−	0.289456i	$-0.906526\pi$
$443$	−11050.1	+	6379.76i	−1.18511	+	0.684224i	−0.227920	+	0.973680i	$0.573192\pi$
$444$		0			0
$445$	2312.02	−	4004.54i	0.246293	−	0.426592i
$446$		0			0
$447$	−6783.93	−	13101.7i	−0.717828	−	1.38633i
$448$		0			0
$449$			3363.17i			0.353492i	0.984256	+	0.176746i	$0.0565571\pi$
$449$			3363.17i			0.353492i	−0.984256	+	0.176746i	$0.943443\pi$
$450$		0			0
$451$			18645.4i			1.94674i
$452$		0			0
$453$	182.740	−	3985.46i	0.0189534	−	0.413363i
$454$		0			0
$455$	−830.486	+	2703.44i	−0.0855687	+	0.278548i
$456$		0			0
$457$	−1125.50	−	1949.43i	−0.115205	−	0.199541i	0.802657	−	0.596441i	$-0.203419\pi$
$457$	−1125.50	−	1949.43i	−0.115205	−	0.199541i	−0.917862	+	0.396900i	$0.870086\pi$
$458$		0			0
$459$	419.337	−	3031.40i	0.0426427	−	0.308265i
$460$		0			0
$461$	907.079	+	1571.11i	0.0916418	+	0.158728i	0.908202	−	0.418532i	$-0.137455\pi$
$461$	907.079	+	1571.11i	0.0916418	+	0.158728i	−0.816560	+	0.577260i	$0.804122\pi$
$462$		0			0
$463$	−4184.81	+	7248.31i	−0.420053	+	0.727554i	−0.995944	−	0.0899729i	$-0.971322\pi$
$463$	−4184.81	+	7248.31i	−0.420053	+	0.727554i	0.575891	+	0.817527i	$0.304655\pi$
$464$		0			0
$465$	6414.29	+	294.107i	0.639689	+	0.0293309i
$466$		0			0
$467$	−8185.98			−0.811139			−0.405569	−	0.914064i	$-0.632927\pi$
$467$	−8185.98			−0.811139			−0.405569	+	0.914064i	$0.632927\pi$
$468$		0			0
$469$	−3077.17	−	13410.6i	−0.302965	−	1.32035i
$470$		0			0
$471$	334.877	+	646.741i	0.0327607	+	0.0632701i
$472$		0			0
$473$	16182.3	+	9342.85i	1.57307	+	0.908213i
$474$		0			0
$475$	11354.5	−	6555.54i	1.09680	−	0.633239i
$476$		0			0
$477$	−12764.3	+	5884.27i	−1.22523	+	0.564826i
$478$		0			0
$479$	−576.208	−	998.022i	−0.0549637	−	0.0952000i	0.837234	−	0.546844i	$-0.184171\pi$
$479$	−576.208	−	998.022i	−0.0549637	−	0.0952000i	−0.892198	+	0.451644i	$0.850838\pi$
$480$		0			0
$481$	4524.07	+	2611.97i	0.428856	+	0.247600i
$482$		0			0
$483$	−6420.83	−	2299.24i	−0.604882	−	0.216603i
$484$		0			0
$485$			1077.17i			0.100849i
$486$		0			0
$487$	−336.704			−0.0313296			−0.0156648	−	0.999877i	$-0.504986\pi$
$487$	−336.704			−0.0313296			−0.0156648	+	0.999877i	$0.504986\pi$
$488$		0			0
$489$	3076.10	+	1969.16i	0.284471	+	0.182104i
$490$		0			0
$491$	−2081.98	−	1202.03i	−0.191361	−	0.110483i	0.401258	−	0.915965i	$-0.368573\pi$
$491$	−2081.98	−	1202.03i	−0.191361	−	0.110483i	−0.592620	+	0.805482i	$0.701906\pi$
$492$		0			0
$493$	4095.57	−	2364.58i	0.374148	−	0.216015i
$494$		0			0
$495$	7394.21	−	3408.69i	0.671404	−	0.309514i
$496$		0			0
$497$	9561.39	+	10280.9i	0.862951	+	0.927890i
$498$		0			0
$499$	−3839.68	+	6650.52i	−0.344464	+	0.596630i	−0.985256	−	0.171085i	$-0.945273\pi$
$499$	−3839.68	+	6650.52i	−0.344464	+	0.596630i	0.640792	+	0.767715i	$0.278606\pi$
$500$		0			0
$501$	−10101.7	+	5230.55i	−0.900816	+	0.466435i
$502$		0			0
$503$	13936.7			1.23540			0.617699	−	0.786414i	$-0.288065\pi$
$503$	13936.7			1.23540			0.617699	+	0.786414i	$0.288065\pi$
$504$		0			0
$505$	−4633.96			−0.408334
$506$		0			0
$507$	−237.924	+	5188.98i	−0.0208414	+	0.454538i
$508$		0			0
$509$	9073.41	−	15715.6i	0.790122	−	1.36853i	−0.135770	−	0.990740i	$-0.543351\pi$
$509$	9073.41	−	15715.6i	0.790122	−	1.36853i	0.925891	−	0.377790i	$-0.123316\pi$
$510$		0			0
$511$	14619.8	+	15719.9i	1.26564	+	1.36088i
$512$		0			0
$513$	−17266.9	−	2388.56i	−1.48607	−	0.205570i
$514$		0			0
$515$	1649.89	−	952.566i	0.141171	−	0.0815050i
$516$		0			0
$517$	−11522.5	−	6652.53i	−0.980193	−	0.565915i
$518$		0			0
$519$	−428.710	+	9349.92i	−0.0362588	+	0.790782i
$520$		0			0
$521$	−3194.77			−0.268648			−0.134324	−	0.990937i	$-0.542886\pi$
$521$	−3194.77			−0.268648			−0.134324	+	0.990937i	$0.542886\pi$
$522$		0			0
$523$			10093.3i			0.843884i	0.906623	+	0.421942i	$0.138651\pi$
$523$			10093.3i			0.843884i	−0.906623	+	0.421942i	$0.861349\pi$
$524$		0			0
$525$	−6567.91	−	7745.16i	−0.545995	−	0.643860i
$526$		0			0
$527$	5289.58	+	3053.94i	0.437226	+	0.252432i
$528$		0			0
$529$	−3572.24	−	6187.30i	−0.293600	−	0.508531i
$530$		0			0
$531$	16200.6	+	1488.78i	1.32400	+	0.121672i
$532$		0			0
$533$	8176.81	−	4720.88i	0.664497	−	0.383647i
$534$		0			0
$535$	−46.2313	−	26.6916i	−0.00373599	−	0.00215697i
$536$		0			0
$537$	7588.50	−	11854.3i	0.609810	−	0.952607i
$538$		0			0
$539$	10218.1	+	21093.4i	0.816558	+	1.68563i
$540$		0			0
$541$	13231.5			1.05151			0.525754	−	0.850636i	$-0.323783\pi$
$541$	13231.5			1.05151			0.525754	+	0.850636i	$0.323783\pi$
$542$		0			0
$543$	−1307.37	+	2042.29i	−0.103323	+	0.161405i
$544$		0			0
$545$	1935.17	−	3351.81i	0.152098	−	0.263442i
$546$		0			0
$547$	3714.66	+	6433.98i	0.290361	+	0.502920i	0.973895	−	0.226999i	$-0.0728913\pi$
$547$	3714.66	+	6433.98i	0.290361	+	0.502920i	−0.683534	+	0.729918i	$0.739558\pi$
$548$		0			0
$549$	3706.85	+	2619.79i	0.288168	+	0.203661i
$550$		0			0
$551$	−13468.7	−	23328.5i	−1.04135	−	1.80368i
$552$		0			0
$553$	2783.64	+	855.122i	0.214055	+	0.0657567i
$554$		0			0
$555$	3074.26	−	1591.82i	0.235126	−	0.121746i
$556$		0			0
$557$			9964.28i			0.757990i	0.925399	+	0.378995i	$0.123730\pi$
$557$			9964.28i			0.757990i	−0.925399	+	0.378995i	$0.876270\pi$
$558$		0			0
$559$		−	9462.15i		−	0.715933i
$560$		0			0
$561$	7736.88	+	354.750i	0.582266	+	0.0266979i
$562$		0			0
$563$	−376.346	+	651.850i	−0.0281724	+	0.0487961i	−0.879768	−	0.475403i	$-0.842302\pi$
$563$	−376.346	+	651.850i	−0.0281724	+	0.0487961i	0.851595	+	0.524200i	$0.175635\pi$
$564$		0			0
$565$	−4596.91	+	2654.03i	−0.342289	+	0.197621i
$566$		0			0
$567$	570.597	+	13489.2i	0.0422625	+	0.999107i
$568$		0			0
$569$	4971.12	−	2870.08i	0.366257	−	0.211459i	−0.305565	−	0.952171i	$-0.598845\pi$
$569$	4971.12	−	2870.08i	0.366257	−	0.211459i	0.671822	+	0.740713i	$0.265512\pi$
$570$		0			0
$571$	8003.90	−	13863.2i	0.586608	−	1.01603i	−0.408065	−	0.912953i	$-0.633796\pi$
$571$	8003.90	−	13863.2i	0.586608	−	1.01603i	0.994673	−	0.103081i	$-0.0328702\pi$
$572$		0			0
$573$	−12776.5	−	585.824i	−0.931493	−	0.0427106i
$574$		0			0
$575$			7478.49i			0.542391i
$576$		0			0
$577$		−	970.474i		−	0.0700197i	−0.999387	−	0.0350099i	$-0.988854\pi$
$577$		−	970.474i		−	0.0700197i	0.999387	−	0.0350099i	$-0.0111463\pi$
$578$		0			0
$579$	7581.69	−	3925.73i	0.544187	−	0.281775i
$580$		0			0
$581$	−4856.47	−	1491.89i	−0.346782	−	0.106530i
$582$		0			0
$583$	−17785.8	−	30805.9i	−1.26349	−	2.18842i
$584$		0			0
$585$	−3367.01	−	2379.62i	−0.237964	−	0.168180i
$586$		0			0
$587$	3363.90	+	5826.44i	0.236530	+	0.409681i	0.959716	−	0.280971i	$-0.0906566\pi$
$587$	3363.90	+	5826.44i	0.236530	+	0.409681i	−0.723187	+	0.690653i	$0.757323\pi$
$588$		0			0
$589$	17395.3	−	30129.6i	1.21691	−	2.10776i
$590$		0			0
$591$	−1481.32	+	2314.02i	−0.103102	+	0.161059i
$592$		0			0
$593$	−20829.3			−1.44242			−0.721211	−	0.692716i	$-0.756414\pi$
$593$	−20829.3			−1.44242			−0.721211	+	0.692716i	$0.756414\pi$
$594$		0			0
$595$	398.719	+	1737.65i	0.0274721	+	0.119726i
$596$		0			0
$597$	−9286.30	+	14506.5i	−0.636622	+	0.994491i
$598$		0			0
$599$	−3804.23	−	2196.37i	−0.259494	−	0.149819i	0.364610	−	0.931160i	$-0.381202\pi$
$599$	−3804.23	−	2196.37i	−0.259494	−	0.149819i	−0.624104	+	0.781342i	$0.714536\pi$
$600$		0			0
$601$	24379.1	−	14075.3i	1.65465	−	0.955312i	0.679526	−	0.733652i	$-0.262186\pi$
$601$	24379.1	−	14075.3i	1.65465	−	0.955312i	0.975124	−	0.221661i	$-0.0711477\pi$
$602$		0			0
$603$	19974.7	+	1835.61i	1.34898	+	0.123967i
$604$		0			0
$605$	7366.19	+	12758.6i	0.495005	+	0.857374i
$606$		0			0
$607$	23547.8	+	13595.3i	1.57459	+	0.909091i	0.995595	+	0.0937614i	$0.0298891\pi$
$607$	23547.8	+	13595.3i	1.57459	+	0.909091i	0.578997	+	0.815330i	$0.303444\pi$
$608$		0			0
$609$	−15912.8	+	13494.1i	−1.05882	+	0.897881i
$610$		0			0
$611$			6737.48i			0.446103i
$612$		0			0
$613$	20898.3			1.37696			0.688478	−	0.725257i	$-0.258279\pi$
$613$	20898.3			1.37696			0.688478	+	0.725257i	$0.258279\pi$
$614$		0			0
$615$	286.598	−	6250.53i	0.0187915	−	0.409831i
$616$		0			0
$617$	4534.89	+	2618.22i	0.295896	+	0.170836i	0.640598	−	0.767877i	$-0.278687\pi$
$617$	4534.89	+	2618.22i	0.295896	+	0.170836i	−0.344702	+	0.938712i	$0.612020\pi$
$618$		0			0
$619$	−1232.96	+	711.851i	−0.0800596	+	0.0462224i	−0.539495	−	0.841989i	$-0.681385\pi$
$619$	−1232.96	+	711.851i	−0.0800596	+	0.0462224i	0.459436	+	0.888211i	$0.348052\pi$
$620$		0			0
$621$	6104.38	−	7848.25i	0.394461	−	0.507149i
$622$		0			0
$623$	−14210.0	+	13215.5i	−0.913820	+	0.849866i
$624$		0			0
$625$	−4350.48	+	7535.25i	−0.278431	+	0.482256i
$626$		0			0
$627$	2020.66	−	44069.5i	0.128704	−	2.80696i
$628$		0			0
$629$	3293.10			0.208751
$630$		0			0
$631$	−1055.32			−0.0665793			−0.0332896	−	0.999446i	$-0.510598\pi$
$631$	−1055.32			−0.0665793			−0.0332896	+	0.999446i	$0.510598\pi$
$632$		0			0
$633$	22848.7	−	11830.9i	1.43468	−	0.742867i
$634$		0			0
$635$	−5535.99	+	9588.62i	−0.345967	+	0.599232i
$636$		0			0
$637$	6663.19	−	9821.74i	0.414451	−	0.610913i
$638$		0			0
$639$	−18588.1	+	8569.01i	−1.15076	+	0.530493i
$640$		0			0
$641$	−4293.85	+	2479.06i	−0.264582	+	0.152756i	−0.626423	−	0.779483i	$-0.715482\pi$
$641$	−4293.85	+	2479.06i	−0.264582	+	0.152756i	0.361841	+	0.932240i	$0.382148\pi$
$642$		0			0
$643$	−10203.4	−	5890.91i	−0.625787	−	0.361299i	0.153331	−	0.988175i	$-0.451000\pi$
$643$	−10203.4	−	5890.91i	−0.625787	−	0.361299i	−0.779119	+	0.626876i	$0.784333\pi$
$644$		0			0
$645$	−5281.20	−	3380.75i	−0.322398	−	0.206383i
$646$		0			0
$647$	−23017.2			−1.39861			−0.699305	−	0.714824i	$-0.746507\pi$
$647$	−23017.2			−1.39861			−0.699305	+	0.714824i	$0.746507\pi$
$648$		0			0
$649$			41173.7i			2.49031i
$650$		0			0
$651$	−25369.3	−	9084.51i	−1.52734	−	0.546928i
$652$		0			0
$653$	13803.0	+	7969.16i	0.827187	+	0.477576i	0.852888	−	0.522093i	$-0.174849\pi$
$653$	13803.0	+	7969.16i	0.827187	+	0.477576i	−0.0257018	+	0.999670i	$0.508182\pi$
$654$		0			0
$655$	−899.960	−	1558.78i	−0.0536860	−	0.0929869i
$656$		0			0
$657$	−28422.0	+	13102.4i	−1.68774	+	0.778040i
$658$		0			0
$659$	9563.07	−	5521.24i	0.565287	−	0.326369i	−0.189978	−	0.981788i	$-0.560842\pi$
$659$	9563.07	−	5521.24i	0.565287	−	0.326369i	0.755265	+	0.655420i	$0.227508\pi$
$660$		0			0
$661$	−16985.4	−	9806.51i	−0.999477	−	0.577048i	−0.0913835	−	0.995816i	$-0.529129\pi$
$661$	−16985.4	−	9806.51i	−0.999477	−	0.577048i	−0.908094	+	0.418767i	$0.862462\pi$
$662$		0			0
$663$	−1803.34	−	3482.76i	−0.105635	−	0.204011i
$664$		0			0
$665$	9897.72	−	2271.11i	0.577169	−	0.132436i
$666$		0			0
$667$	15365.0			0.891955
$668$		0			0
$669$	−8085.64	−	370.741i	−0.467278	−	0.0214255i
$670$		0			0
$671$	−5743.93	+	9948.77i	−0.330465	+	0.572382i
$672$		0			0
$673$	3041.11	+	5267.35i	0.174184	+	0.301696i	0.939879	−	0.341508i	$-0.110938\pi$
$673$	3041.11	+	5267.35i	0.174184	+	0.301696i	−0.765694	+	0.643205i	$0.777604\pi$
$674$		0			0
$675$	13714.6	−	5575.66i	0.782037	−	0.317937i
$676$		0			0
$677$	−8417.11	−	14578.9i	−0.477837	−	0.827638i	0.521840	−	0.853043i	$-0.325246\pi$
$677$	−8417.11	−	14578.9i	−0.477837	−	0.827638i	−0.999677	+	0.0254051i	$0.991912\pi$
$678$		0			0
$679$	1327.45	−	4321.18i	0.0750261	−	0.244229i
$680$		0			0
$681$	59.6723	−	1301.42i	0.00335778	−	0.0732311i
$682$		0			0
$683$		−	6568.11i		−	0.367968i	−0.982929	−	0.183984i	$-0.941101\pi$
$683$		−	6568.11i		−	0.367968i	0.982929	−	0.183984i	$-0.0588994\pi$
$684$		0			0
$685$		−	10183.8i		−	0.568035i
$686$		0			0
$687$	−11977.5	−	23131.8i	−0.665165	−	1.28462i
$688$		0			0
$689$	−9006.45	+	15599.6i	−0.497995	+	0.862553i
$690$		0			0
$691$	−8934.79	+	5158.50i	−0.491889	+	0.283992i	−0.725358	−	0.688372i	$-0.758326\pi$
$691$	−8934.79	+	5158.50i	−0.491889	+	0.283992i	0.233469	+	0.972364i	$0.424992\pi$
$692$		0			0
$693$	−33863.5	+	4562.11i	−1.85623	+	0.250073i
$694$		0			0
$695$	−156.447	+	90.3246i	−0.00853865	+	0.00492979i
$696$		0			0
$697$	2975.97	−	5154.54i	0.161726	−	0.280118i
$698$		0			0
$699$	−8854.47	+	13831.9i	−0.479123	+	0.748456i
$700$		0			0
$701$			10545.7i			0.568195i	0.958795	+	0.284098i	$0.0916940\pi$
$701$			10545.7i			0.568195i	−0.958795	+	0.284098i	$0.908306\pi$
$702$		0			0
$703$		−	18757.6i		−	1.00634i
$704$		0			0
$705$	3760.45	+	2407.25i	0.200889	+	0.128599i
$706$		0			0
$707$	18589.7	+	5710.67i	0.988880	+	0.303779i
$708$		0			0
$709$	3965.20	+	6867.93i	0.210037	+	0.363795i	0.951726	−	0.306949i	$-0.0993082\pi$
$709$	3965.20	+	6867.93i	0.210037	+	0.363795i	−0.741689	+	0.670744i	$0.765975\pi$
$710$		0			0
$711$	−2450.21	+	3466.89i	−0.129240	+	0.182867i
$712$		0			0
$713$	9922.22	+	17185.8i	0.521164	+	0.902683i
$714$		0			0
$715$	5217.34	−	9036.69i	0.272891	−	0.472662i
$716$		0			0
$717$	1391.94	+	2688.23i	0.0725009	+	0.140019i
$718$		0			0
$719$	15064.3			0.781368			0.390684	−	0.920525i	$-0.372238\pi$
$719$	15064.3			0.781368			0.390684	+	0.920525i	$0.372238\pi$
$720$		0			0
$721$	−7792.65	+	1788.09i	−0.402515	+	0.0923604i
$722$		0			0
$723$	−16864.4	−	773.260i	−0.867485	−	0.0397757i
$724$		0			0
$725$	19813.2	+	11439.1i	1.01496	+	0.585985i
$726$		0			0
$727$	−21471.0	+	12396.3i	−1.09535	+	0.632398i	−0.934995	−	0.354662i	$-0.884596\pi$
$727$	−21471.0	+	12396.3i	−1.09535	+	0.632398i	−0.160351	+	0.987060i	$0.551263\pi$
$728$		0			0
$729$	−18943.9	−	5343.31i	−0.962447	−	0.271468i
$730$		0			0
$731$	−2982.40	−	5165.67i	−0.150900	−	0.261367i
$732$		0			0
$733$	−7401.55	−	4273.28i	−0.372964	−	0.215331i	0.301789	−	0.953375i	$-0.402416\pi$
$733$	−7401.55	−	4273.28i	−0.372964	−	0.215331i	−0.674752	+	0.738044i	$0.735750\pi$
$734$		0			0
$735$	−3101.20	−	7228.22i	−0.155632	−	0.362744i
$736$		0			0
$737$			50765.7i			2.53728i
$738$		0			0
$739$	17244.9			0.858410			0.429205	−	0.903207i	$-0.358794\pi$
$739$	17244.9			0.858410			0.429205	+	0.903207i	$0.358794\pi$
$740$		0			0
$741$	−19837.9	+	10271.9i	−0.983487	+	0.509241i
$742$		0			0
$743$	−10003.9	−	5775.74i	−0.493952	−	0.285183i	0.232260	−	0.972654i	$-0.425388\pi$
$743$	−10003.9	−	5775.74i	−0.493952	−	0.285183i	−0.726213	+	0.687470i	$0.758721\pi$
$744$		0			0
$745$	−10851.7	+	6265.25i	−0.533660	+	0.308109i
$746$		0			0
$747$	4274.75	−	6048.51i	0.209377	−	0.296256i
$748$		0			0
$749$	152.569	+	164.050i	0.00744292	+	0.00800301i
$750$		0			0
$751$	−7899.58	+	13682.5i	−0.383835	+	0.664821i	−0.991607	−	0.129290i	$-0.958730\pi$
$751$	−7899.58	+	13682.5i	−0.383835	+	0.664821i	0.607772	+	0.794112i	$0.292063\pi$
$752$		0			0
$753$	18478.4	+	11828.9i	0.894274	+	0.572468i
$754$		0			0
$755$	−3388.42			−0.163334
$756$		0			0
$757$	−15294.2			−0.734318			−0.367159	−	0.930158i	$-0.619669\pi$
$757$	−15294.2			−0.734318			−0.367159	+	0.930158i	$0.619669\pi$
$758$		0			0
$759$	21193.0	+	13566.7i	1.01351	+	0.648799i
$760$		0			0
$761$	−8139.52	+	14098.1i	−0.387723	+	0.671556i	−0.992143	−	0.125110i	$-0.960072\pi$
$761$	−8139.52	+	14098.1i	−0.387723	+	0.671556i	0.604420	+	0.796666i	$0.293405\pi$
$762$		0			0
$763$	−11893.8	+	11061.4i	−0.564330	+	0.524835i
$764$		0			0
$765$	−2588.19	−	237.846i	−0.122322	−	0.0112410i
$766$		0			0
$767$	18056.4	−	10424.9i	0.850038	−	0.490770i
$768$		0			0
$769$	20947.3	+	12093.9i	0.982286	+	0.567123i	0.902960	−	0.429726i	$-0.141390\pi$
$769$	20947.3	+	12093.9i	0.982286	+	0.567123i	0.0793265	+	0.996849i	$0.474723\pi$
$770$		0			0
$771$	−35444.8	+	18353.0i	−1.65566	+	0.857285i
$772$		0			0
$773$	−31168.4			−1.45026			−0.725128	−	0.688614i	$-0.758219\pi$
$773$	−31168.4			−1.45026			−0.725128	+	0.688614i	$0.758219\pi$
$774$		0			0
$775$			29548.2i			1.36955i
$776$		0			0
$777$	−14294.4	+	2597.23i	−0.659988	+	0.119916i
$778$		0			0
$779$	−29360.4	−	16951.2i	−1.35038	−	0.779642i
$780$		0			0
$781$	−25900.7	−	44861.3i	−1.18668	−	2.05540i
$782$		0			0
$783$	−11455.5	−	28177.4i	−0.522843	−	1.28605i
$784$		0			0
$785$	535.676	−	309.273i	0.0243555	−	0.0140617i
$786$		0			0
$787$	2609.54	+	1506.62i	0.118196	+	0.0682403i	0.557932	−	0.829886i	$-0.311595\pi$
$787$	2609.54	+	1506.62i	0.118196	+	0.0682403i	−0.439737	+	0.898127i	$0.644928\pi$
$788$		0			0
$789$	30462.3	+	1396.75i	1.37451	+	0.0630236i
$790$		0			0
$791$	21711.7	−	4981.94i	0.975955	−	0.223941i
$792$		0			0
$793$	5817.27			0.260501
$794$		0			0
$795$	5488.84	+	10600.5i	0.244867	+	0.472906i
$796$		0			0
$797$	−8179.07	+	14166.6i	−0.363510	+	0.629618i	−0.988536	−	0.150986i	$-0.951755\pi$
$797$	−8179.07	+	14166.6i	−0.363510	+	0.629618i	0.625026	+	0.780604i	$0.285088\pi$
$798$		0			0
$799$	2123.60	+	3678.19i	0.0940271	+	0.162860i
$800$		0			0
$801$	−11843.8	−	25691.9i	−0.522449	−	1.13331i
$802$		0			0
$803$	−39603.3	−	68594.8i	−1.74043	−	3.01452i
$804$		0			0
$805$	−1700.93	+	5536.96i	−0.0744719	+	0.242425i
$806$		0			0
$807$	3547.40	+	2270.86i	0.154739	+	0.0990561i
$808$		0			0
$809$		−	35491.9i		−	1.54243i	−0.636573	−	0.771217i	$-0.719648\pi$
$809$		−	35491.9i		−	1.54243i	0.636573	−	0.771217i	$-0.280352\pi$
$810$		0			0
$811$		−	24897.6i		−	1.07802i	−0.842300	−	0.539010i	$-0.818799\pi$
$811$		−	24897.6i		−	1.07802i	0.842300	−	0.539010i	$-0.181201\pi$
$812$		0			0
$813$	17432.9	−	27232.6i	0.752028	−	1.17477i
$814$		0			0
$815$	1551.00	−	2686.41i	0.0666615	−	0.115461i
$816$		0			0
$817$	−29423.8	+	16987.8i	−1.25999	+	0.727453i
$818$		0			0
$819$	10574.6	+	13695.5i	0.451170	+	0.584320i
$820$		0			0
$821$	−19778.3	+	11419.0i	−0.840764	+	0.485415i	−0.857524	−	0.514444i	$-0.827998\pi$
$821$	−19778.3	+	11419.0i	−0.840764	+	0.485415i	0.0167601	+	0.999860i	$0.494665\pi$
$822$		0			0
$823$	20777.9	−	35988.3i	0.880038	−	1.52427i	0.0287410	−	0.999587i	$-0.490850\pi$
$823$	20777.9	−	35988.3i	0.880038	−	1.52427i	0.851297	−	0.524684i	$-0.175816\pi$
$824$		0			0
$825$	17228.1	+	33272.4i	0.727038	+	1.40411i
$826$		0			0
$827$			35202.3i			1.48017i	0.672512	+	0.740087i	$0.265215\pi$
$827$			35202.3i			1.48017i	−0.672512	+	0.740087i	$0.734785\pi$
$828$		0			0
$829$			24265.7i			1.01663i	0.861173	+	0.508313i	$0.169731\pi$
$829$			24265.7i			1.01663i	−0.861173	+	0.508313i	$0.830269\pi$
$830$		0			0
$831$	135.690	−	2959.31i	0.00566429	−	0.123535i
$832$		0			0
$833$	541.891	−	7462.17i	0.0225395	−	0.310383i
$834$		0			0
$835$	4830.63	+	8366.90i	0.200205	+	0.346765i
$836$		0			0
$837$	24118.9	−	31009.1i	0.996024	−	1.28056i
$838$		0			0
$839$	16940.7	+	29342.1i	0.697088	+	1.20739i	0.969472	+	0.245204i	$0.0788549\pi$
$839$	16940.7	+	29342.1i	0.697088	+	1.20739i	−0.272383	+	0.962189i	$0.587812\pi$
$840$		0			0
$841$	11307.8	−	19585.7i	0.463645	−	0.803056i
$842$		0			0
$843$	−15642.3	−	717.228i	−0.639087	−	0.0293033i
$844$		0			0
$845$	4411.65			0.179604
$846$		0			0
$847$	−13827.3	−	60260.5i	−0.560933	−	2.44460i
$848$		0			0
$849$	16381.1	+	31636.4i	0.662186	+	1.27887i
$850$		0			0
$851$	9265.80	+	5349.61i	0.373240	+	0.215490i
$852$		0			0
$853$	−11908.8	+	6875.53i	−0.478017	+	0.275983i	−0.719590	−	0.694400i	$-0.755670\pi$
$853$	−11908.8	+	6875.53i	−0.478017	+	0.275983i	0.241573	+	0.970383i	$0.422337\pi$
$854$		0			0
$855$	−1354.78	+	14742.4i	−0.0541900	+	0.589683i
$856$		0			0
$857$	−11963.0	−	20720.5i	−0.476834	−	0.825901i	0.522813	−	0.852447i	$-0.324882\pi$
$857$	−11963.0	−	20720.5i	−0.476834	−	0.825901i	−0.999648	+	0.0265460i	$0.991549\pi$
$858$		0			0
$859$	23691.7	+	13678.4i	0.941038	+	0.543309i	0.890286	−	0.455403i	$-0.150505\pi$
$859$	23691.7	+	13678.4i	0.941038	+	0.543309i	0.0507527	+	0.998711i	$0.483838\pi$
$860$		0			0
$861$	−8852.58	+	24721.6i	−0.350401	+	0.978524i
$862$		0			0
$863$		−	14465.7i		−	0.570587i	−0.958440	−	0.285294i	$-0.907909\pi$
$863$		−	14465.7i		−	0.570587i	0.958440	−	0.285294i	$-0.0920911\pi$
$864$		0			0
$865$	7949.27			0.312466
$866$		0			0
$867$	19418.4	+	12430.7i	0.760650	+	0.486929i
$868$		0			0
$869$	−9304.76	−	5372.11i	−0.363225	−	0.209708i
$870$		0			0
$871$	22262.9	−	12853.5i	0.866072	−	0.500027i
$872$		0			0
$873$	5381.82	+	3803.57i	0.208645	+	0.147459i
$874$		0			0
$875$	−13796.8	+	12831.2i	−0.533048	+	0.495742i
$876$		0			0
$877$	−11061.9	+	19159.7i	−0.425921	+	0.737717i	−0.996506	−	0.0835218i	$-0.973383\pi$
$877$	−11061.9	+	19159.7i	−0.425921	+	0.737717i	0.570585	+	0.821239i	$0.306717\pi$
$878$		0			0
$879$	−4685.28	+	2426.00i	−0.179785	+	0.0930909i
$880$		0			0
$881$	32407.6			1.23932			0.619659	−	0.784871i	$-0.287271\pi$
$881$	32407.6			1.23932			0.619659	+	0.784871i	$0.287271\pi$
$882$		0			0
$883$	26453.8			1.00820			0.504100	−	0.863645i	$-0.331824\pi$
$883$	26453.8			1.00820			0.504100	+	0.863645i	$0.331824\pi$
$884$		0			0
$885$	632.879	−	13802.7i	0.0240384	−	0.524264i
$886$		0			0
$887$	−5919.53	+	10252.9i	−0.224079	+	0.388117i	−0.956043	−	0.293227i	$-0.905271\pi$
$887$	−5919.53	+	10252.9i	−0.224079	+	0.388117i	0.731964	+	0.681344i	$0.238604\pi$
$888$		0			0
$889$	34024.9	−	31643.6i	1.28364	−	1.19381i
$890$		0			0
$891$	9078.88	−	48980.0i	0.341362	−	1.84163i
$892$		0			0
$893$	20951.1	−	12096.1i	0.785107	−	0.453282i
$894$		0			0
$895$	−10352.5	−	5977.03i	−0.386644	−	0.223229i
$896$		0			0
$897$	583.647	−	12729.0i	0.0217251	−	0.473811i
$898$		0			0
$899$	60708.3			2.25221
$900$		0			0
$901$			11355.1i			0.419858i
$902$		0			0
$903$	17019.9	+	20070.6i	0.627228	+	0.739654i
$904$		0			0
$905$	1783.56	+	1029.74i	0.0655111	+	0.0378229i
$906$		0			0
$907$	13677.0	+	23689.2i	0.500702	+	0.867241i	1.00000		0.000810516i	$0.000257995\pi$
$907$	13677.0	+	23689.2i	0.500702	+	0.867241i	−0.499298	+	0.866430i	$0.666409\pi$
$908$		0			0
$909$	−16363.0	+	23152.6i	−0.597058	+	0.844800i
$910$		0			0
$911$	44979.8	−	25969.1i	1.63584	−	0.944451i	0.653593	−	0.756846i	$-0.273261\pi$
$911$	44979.8	−	25969.1i	1.63584	−	0.944451i	0.982245	−	0.187605i	$-0.0600724\pi$
$912$		0			0
$913$	16233.5	+	9372.44i	0.588447	+	0.339740i
$914$		0			0
$915$	2078.46	−	3246.85i	0.0750950	−	0.117309i
$916$		0			0
$917$	1689.34	+	7362.29i	0.0608362	+	0.265130i
$918$		0			0
$919$	−35791.5			−1.28471			−0.642357	−	0.766405i	$-0.722044\pi$
$919$	−35791.5			−1.28471			−0.642357	+	0.766405i	$0.722044\pi$
$920$		0			0
$921$	−877.776	+	1371.21i	−0.0314047	+	0.0490584i
$922$		0			0
$923$	−13115.7	+	22717.1i	−0.467724	+	0.810121i
$924$		0			0
$925$	7965.52	+	13796.7i	0.283140	+	0.490413i
$926$		0			0
$927$	1066.64	−	11606.9i	0.0377919	−	0.411243i
$928$		0			0
$929$	9833.15	+	17031.5i	0.347271	+	0.601492i	0.985764	−	0.168137i	$-0.0537749\pi$
$929$	9833.15	+	17031.5i	0.347271	+	0.601492i	−0.638492	+	0.769628i	$0.720442\pi$
$930$		0			0
$931$	−42504.7	−	3086.63i	−1.49628	−	0.108657i
$932$		0			0
$933$	−19536.9	+	10116.0i	−0.685540	+	0.354967i
$934$		0			0
$935$		−	6577.86i		−	0.230074i
$936$		0			0
$937$		−	6612.53i		−	0.230546i	−0.993334	−	0.115273i	$-0.963226\pi$
$937$		−	6612.53i		−	0.230546i	0.993334	−	0.115273i	$-0.0367744\pi$
$938$		0			0
$939$	17060.1	+	782.234i	0.592901	+	0.0271856i
$940$		0			0
$941$	15396.3	−	26667.2i	0.533374	−	0.923832i	−0.465866	−	0.884855i	$-0.654257\pi$
$941$	15396.3	−	26667.2i	0.533374	−	0.923832i	0.999240	−	0.0389761i	$-0.0124096\pi$
$942$		0			0
$943$	16747.0	−	9668.90i	0.578323	−	0.333895i
$944$		0			0
$945$	11422.2	−	1008.85i	0.393190	−	0.0347279i
$946$		0			0
$947$	−3307.77	+	1909.74i	−0.113504	+	0.0655314i	−0.555677	−	0.831398i	$-0.687541\pi$
$947$	−3307.77	+	1909.74i	−0.113504	+	0.0655314i	0.442173	+	0.896930i	$0.354208\pi$
$948$		0			0
$949$	−20054.5	+	34735.4i	−0.685981	+	1.18815i
$950$		0			0
$951$	−31892.1	−	1462.31i	−1.08746	−	0.0498619i
$952$		0			0
$953$		−	43050.4i		−	1.46332i	−0.681672	−	0.731658i	$-0.738747\pi$
$953$		−	43050.4i		−	1.46332i	0.681672	−	0.731658i	$-0.261253\pi$
$954$		0			0
$955$			10862.5i			0.368066i
$956$		0			0
$957$	68359.8	−	35396.1i	2.30905	−	1.19561i
$958$		0			0
$959$	−12550.1	+	40853.6i	−0.422589	+	1.37563i
$960$		0			0
$961$	24308.0	+	42102.8i	0.815952	+	1.41327i
$962$		0			0
$963$	−296.606	+	136.734i	−0.00992523	+	0.00457548i
$964$		0			0
$965$	−3625.58	−	6279.68i	−0.120945	−	0.209482i
$966$		0			0
$967$	−25827.9	+	44735.3i	−0.858914	+	1.48768i	0.0140515	+	0.999901i	$0.495527\pi$
$967$	−25827.9	+	44735.3i	−0.858914	+	1.48768i	−0.872966	+	0.487782i	$0.837806\pi$
$968$		0			0
$969$	−7592.48	+	11860.5i	−0.251709	+	0.393203i
$970$		0			0
$971$	−44241.3			−1.46217			−0.731086	−	0.682285i	$-0.760986\pi$
$971$	−44241.3			−1.46217			−0.731086	+	0.682285i	$0.760986\pi$
$972$		0			0
$973$	738.917	−	169.551i	0.0243459	−	0.00558637i
$974$		0			0
$975$	10229.3	−	15979.6i	0.335999	−	0.524877i
$976$		0			0
$977$	−50545.7	−	29182.6i	−1.65517	−	0.955613i	−0.974897	−	0.222654i	$-0.928528\pi$
$977$	−50545.7	−	29182.6i	−1.65517	−	0.955613i	−0.680273	−	0.732959i	$-0.738139\pi$
$978$		0			0
$979$	62006.0	−	35799.2i	2.02423	−	1.16869i
$980$		0			0
$981$	−9913.33	−	21504.2i	−0.322638	−	0.699874i
$982$		0			0
$983$	−29934.2	−	51847.6i	−0.971265	−	1.68228i	−0.691746	−	0.722141i	$-0.743158\pi$
$983$	−29934.2	−	51847.6i	−0.971265	−	1.68228i	−0.279519	−	0.960140i	$-0.590175\pi$
$984$		0			0
$985$	2020.87	+	1166.75i	0.0653709	+	0.0377419i
$986$		0			0
$987$	−12118.9	−	14291.2i	−0.390831	−	0.460884i
$988$		0			0
$989$		−	19379.6i		−	0.623088i
$990$		0			0
$991$	−24705.3			−0.791918			−0.395959	−	0.918268i	$-0.629588\pi$
$991$	−24705.3			−0.791918			−0.395959	+	0.918268i	$0.629588\pi$
$992$		0			0
$993$	1432.73	−	31247.0i	0.0457868	−	0.998584i
$994$		0			0
$995$	12668.7	+	7314.30i	0.403644	+	0.233044i
$996$		0			0
$997$	−1156.40	+	667.649i	−0.0367338	+	0.0212083i	−0.518254	−	0.855226i	$-0.673418\pi$
$997$	−1156.40	+	667.649i	−0.0367338	+	0.0212083i	0.481521	+	0.876435i	$0.340085\pi$
$998$		0			0
$999$	2902.30	−	20980.7i	0.0919165	−	0.664466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.41.5	✓	48
3.2	odd	2		756.4.x.a.125.14		48
7.6	odd	2	inner	252.4.x.a.41.20	yes	48
9.2	odd	6	inner	252.4.x.a.209.20	yes	48
9.4	even	3		2268.4.f.a.1133.28		48
9.5	odd	6		2268.4.f.a.1133.21		48
9.7	even	3		756.4.x.a.629.11		48
21.20	even	2		756.4.x.a.125.11		48
63.13	odd	6		2268.4.f.a.1133.22		48
63.20	even	6	inner	252.4.x.a.209.5	yes	48
63.34	odd	6		756.4.x.a.629.14		48
63.41	even	6		2268.4.f.a.1133.27		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.5	✓	48	1.1	even	1	trivial
252.4.x.a.41.20	yes	48	7.6	odd	2	inner
252.4.x.a.209.5	yes	48	63.20	even	6	inner
252.4.x.a.209.20	yes	48	9.2	odd	6	inner
756.4.x.a.125.11		48	21.20	even	2
756.4.x.a.125.14		48	3.2	odd	2
756.4.x.a.629.11		48	9.7	even	3
756.4.x.a.629.14		48	63.34	odd	6
2268.4.f.a.1133.21		48	9.5	odd	6
2268.4.f.a.1133.22		48	63.13	odd	6
2268.4.f.a.1133.27		48	63.41	even	6
2268.4.f.a.1133.28		48	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.37628 - 2.80147i) q^{3} +(-2.20656 + 3.82187i) q^{5} +(13.5618 - 12.6126i) q^{7} +(11.3036 + 24.5200i) q^{9} +O(q^{10})\)	\(q+(-4.37628 - 2.80147i) q^{3} +(-2.20656 + 3.82187i) q^{5} +(13.5618 - 12.6126i) q^{7} +(11.3036 + 24.5200i) q^{9} +(-59.1776 + 34.1662i) q^{11} +(29.9666 + 17.3012i) q^{13} +(20.3633 - 10.5440i) q^{15} +21.8129 q^{17} -124.247i q^{19} +(-94.6839 + 17.2036i) q^{21} +(61.3750 + 35.4349i) q^{23} +(52.7622 + 91.3868i) q^{25} +(19.2243 - 138.973i) q^{27} +(187.759 - 108.403i) q^{29} +(242.498 + 140.006i) q^{31} +(354.693 + 16.2633i) q^{33} +(18.2791 + 79.6618i) q^{35} +150.970 q^{37} +(-82.6734 - 159.665i) q^{39} +(136.432 - 236.307i) q^{41} +(-136.727 - 236.817i) q^{43} +(-118.654 - 10.9039i) q^{45} +(97.3555 + 168.625i) q^{47} +(24.8427 - 342.099i) q^{49} +(-95.4592 - 61.1081i) q^{51} +520.567i q^{53} -301.559i q^{55} +(-348.073 + 543.738i) q^{57} +(301.275 - 521.824i) q^{59} +(145.594 - 84.0586i) q^{61} +(462.558 + 189.966i) q^{63} +(-132.246 + 76.3523i) q^{65} +(371.461 - 643.390i) q^{67} +(-169.324 - 327.013i) q^{69} +758.080i q^{71} +1159.14i q^{73} +(25.1151 - 547.746i) q^{75} +(-371.626 + 1209.74i) q^{77} +(78.6173 + 136.169i) q^{79} +(-473.458 + 554.327i) q^{81} +(-137.159 - 237.567i) q^{83} +(-48.1314 + 83.3660i) q^{85} +(-1125.37 - 51.6003i) q^{87} -1047.80 q^{89} +(624.614 - 143.323i) q^{91} +(-669.015 - 1292.06i) q^{93} +(474.855 + 274.158i) q^{95} +(211.382 - 122.041i) q^{97} +(-1506.67 - 1064.83i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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