LMFDB - Embedded newform 351.4.r.a.10.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,4,Mod(10,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("351.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	351.r (of order $6$, degree $2$, not 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:	$20.7096704120$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.34
Character	$\chi$	$=$	351.10
Dual form			351.4.r.a.316.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.59109 + 2.07331i) q^{2} +(4.59727 + 7.96270i) q^{4} +(-4.17848 - 2.41245i) q^{5} -15.5822i q^{7} +4.95329i q^{8} +(-10.0035 - 17.3266i) q^{10} +(-39.1432 - 22.5993i) q^{11} +(21.5929 - 41.6022i) q^{13} +(32.3068 - 55.9571i) q^{14} +(26.5084 - 45.9139i) q^{16} +(1.85014 - 3.20453i) q^{17} +(-10.2746 - 5.93207i) q^{19} -44.3627i q^{20} +(-93.7110 - 162.312i) q^{22} +134.490 q^{23} +(-50.8602 - 88.0924i) q^{25} +(163.797 - 104.628i) q^{26} +(124.077 - 71.6356i) q^{28} +(-99.7201 + 172.720i) q^{29} +(-37.0698 - 21.4022i) q^{31} +(224.705 - 129.734i) q^{32} +(13.2880 - 7.67183i) q^{34} +(-37.5913 + 65.1100i) q^{35} +(-139.181 + 80.3560i) q^{37} +(-24.5981 - 42.6052i) q^{38} +(11.9496 - 20.6973i) q^{40} -369.833i q^{41} +210.696 q^{43} -415.580i q^{44} +(482.967 + 278.841i) q^{46} +(-160.177 + 92.4781i) q^{47} +100.195 q^{49} -421.797i q^{50} +(430.535 - 19.3187i) q^{52} +437.724 q^{53} +(109.039 + 188.862i) q^{55} +77.1833 q^{56} +(-716.207 + 413.502i) q^{58} +(-401.536 + 231.827i) q^{59} +495.381 q^{61} +(-88.7471 - 153.715i) q^{62} +651.781 q^{64} +(-190.589 + 121.742i) q^{65} -233.027i q^{67} +34.0223 q^{68} +(-269.987 + 155.877i) q^{70} +(-824.189 - 475.846i) q^{71} +885.664i q^{73} -666.413 q^{74} -109.085i q^{76} +(-352.147 + 609.937i) q^{77} +(-221.888 - 384.322i) q^{79} +(-221.530 + 127.900i) q^{80} +(766.781 - 1328.10i) q^{82} +(604.028 - 348.736i) q^{83} +(-15.4615 + 8.92672i) q^{85} +(756.628 + 436.839i) q^{86} +(111.941 - 193.888i) q^{88} +(-322.550 + 186.224i) q^{89} +(-648.255 - 336.466i) q^{91} +(618.289 + 1070.91i) q^{92} -766.944 q^{94} +(28.6216 + 49.5741i) q^{95} +135.651i q^{97} +(359.807 + 207.735i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 3 q^{2} + 153 q^{4} - 10 q^{10} + 3 q^{11} - 13 q^{13} - 126 q^{14} - 551 q^{16} + 138 q^{17} - 96 q^{19} - 31 q^{22} - 654 q^{23} + 798 q^{25} - 510 q^{26} + 18 q^{28} - 201 q^{29} - 180 q^{31}+ \cdots + 6339 q^{98}+O(q^{100}) $ 80 * q + 3 * q^2 + 153 * q^4 - 10 * q^10 + 3 * q^11 - 13 * q^13 - 126 * q^14 - 551 * q^16 + 138 * q^17 - 96 * q^19 - 31 * q^22 - 654 * q^23 + 798 * q^25 - 510 * q^26 + 18 * q^28 - 201 * q^29 - 180 * q^31 - 117 * q^32 - 24 * q^34 - 297 * q^35 + 246 * q^37 + 768 * q^38 + 328 * q^40 + 166 * q^43 - 6 * q^46 + 372 * q^47 - 3226 * q^49 + 186 * q^52 + 2568 * q^53 - 127 * q^55 - 4596 * q^56 - 3 * q^58 + 531 * q^59 + 838 * q^61 - 135 * q^62 - 3178 * q^64 + 2337 * q^65 + 3900 * q^68 + 1005 * q^70 + 2598 * q^71 + 942 * q^74 + 1584 * q^77 - 260 * q^79 + 1332 * q^80 - 1273 * q^82 + 1194 * q^83 + 3936 * q^85 - 2910 * q^86 + 781 * q^88 + 1056 * q^89 + 537 * q^91 - 1056 * q^92 - 1078 * q^94 + 5292 * q^95 + 6339 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	3.59109	+	2.07331i	1.26964	+	0.733027i	0.974920	−	0.222556i	$-0.0714400\pi$
$2$	3.59109	+	2.07331i	1.26964	+	0.733027i	0.294721	+	0.955583i	$0.404773\pi$
$3$		0			0
$3$		0			0
$4$	4.59727	+	7.96270i	0.574658	+	0.995338i
$5$	−4.17848	−	2.41245i	−0.373735	−	0.215776i	0.301354	−	0.953512i	$-0.402561\pi$
$5$	−4.17848	−	2.41245i	−0.373735	−	0.215776i	−0.675089	+	0.737736i	$0.735895\pi$
$6$		0			0
$7$		−	15.5822i		−	0.841361i	−0.907209	−	0.420680i	$-0.861791\pi$
$7$		−	15.5822i		−	0.841361i	0.907209	−	0.420680i	$-0.138209\pi$
$8$			4.95329i			0.218907i
$9$		0			0
$10$	−10.0035	−	17.3266i	−0.316339	−	0.547916i
$11$	−39.1432	−	22.5993i	−1.07292	−	0.619450i	−0.143941	−	0.989586i	$-0.545978\pi$
$11$	−39.1432	−	22.5993i	−1.07292	−	0.619450i	−0.928977	+	0.370136i	$0.879311\pi$
$12$		0			0
$13$	21.5929	−	41.6022i	0.460677	−	0.887568i
$13$	21.5929	−	41.6022i	0.460677	−	0.887568i
$14$	32.3068	−	55.9571i	0.616740	−	1.06823i
$15$		0			0
$16$	26.5084	−	45.9139i	0.414194	−	0.717405i
$17$	1.85014	−	3.20453i	0.0263955	−	0.0457184i	−0.852526	−	0.522685i	$-0.824930\pi$
$17$	1.85014	−	3.20453i	0.0263955	−	0.0457184i	0.878921	+	0.476967i	$0.158264\pi$
$18$		0			0
$19$	−10.2746	−	5.93207i	−0.124061	−	0.0716269i	0.436685	−	0.899614i	$-0.356152\pi$
$19$	−10.2746	−	5.93207i	−0.124061	−	0.0716269i	−0.560746	+	0.827988i	$0.689486\pi$
$20$		−	44.3627i		−	0.495990i
$21$		0			0
$22$	−93.7110	−	162.312i	−0.908148	−	1.57296i
$23$	134.490			1.21927			0.609635	−	0.792682i	$-0.291316\pi$
$23$	134.490			1.21927			0.609635	+	0.792682i	$0.291316\pi$
$24$		0			0
$25$	−50.8602	−	88.0924i	−0.406881	−	0.704739i
$26$	163.797	−	104.628i	1.23551	−	0.789204i
$27$		0			0
$28$	124.077	−	71.6356i	0.837438	−	0.483495i
$29$	−99.7201	+	172.720i	−0.638536	+	1.10598i	0.347218	+	0.937785i	$0.387126\pi$
$29$	−99.7201	+	172.720i	−0.638536	+	1.10598i	−0.985754	+	0.168193i	$0.946207\pi$
$30$		0			0
$31$	−37.0698	−	21.4022i	−0.214772	−	0.123999i	0.388755	−	0.921341i	$-0.372905\pi$
$31$	−37.0698	−	21.4022i	−0.214772	−	0.123999i	−0.603527	+	0.797342i	$0.706238\pi$
$32$	224.705	−	129.734i	1.24133	−	0.716684i
$33$		0			0
$34$	13.2880	−	7.67183i	0.0670257	−	0.0386973i
$35$	−37.5913	+	65.1100i	−0.181545	+	0.314446i
$36$		0			0
$37$	−139.181	+	80.3560i	−0.618410	+	0.357039i	−0.776250	−	0.630426i	$-0.782880\pi$
$37$	−139.181	+	80.3560i	−0.618410	+	0.357039i	0.157840	+	0.987465i	$0.449547\pi$
$38$	−24.5981	−	42.6052i	−0.105009	−	0.181881i
$39$		0			0
$40$	11.9496	−	20.6973i	0.0472348	−	0.0818131i
$41$		−	369.833i		−	1.40874i	−0.709834	−	0.704369i	$-0.751230\pi$
$41$		−	369.833i		−	1.40874i	0.709834	−	0.704369i	$-0.248770\pi$
$42$		0			0
$43$	210.696			0.747229			0.373614	−	0.927584i	$-0.378118\pi$
$43$	210.696			0.747229			0.373614	+	0.927584i	$0.378118\pi$
$44$		−	415.580i		−	1.42389i
$45$		0			0
$46$	482.967	+	278.841i	1.54803	+	0.893758i
$47$	−160.177	+	92.4781i	−0.497110	+	0.287007i	−0.727519	−	0.686087i	$-0.759327\pi$
$47$	−160.177	+	92.4781i	−0.497110	+	0.287007i	0.230409	+	0.973094i	$0.425994\pi$
$48$		0			0
$49$	100.195			0.292112
$50$		−	421.797i		−	1.19302i
$51$		0			0
$52$	430.535	−	19.3187i	1.14816	−	0.0515196i
$53$	437.724			1.13445			0.567227	−	0.823561i	$-0.308016\pi$
$53$	437.724			1.13445			0.567227	+	0.823561i	$0.308016\pi$
$54$		0			0
$55$	109.039	+	188.862i	0.267325	+	0.463020i
$56$	77.1833			0.184179
$57$		0			0
$58$	−716.207	+	413.502i	−1.62142	+	0.936129i
$59$	−401.536	+	231.827i	−0.886026	+	0.511547i	−0.872641	−	0.488363i	$-0.837594\pi$
$59$	−401.536	+	231.827i	−0.886026	+	0.511547i	−0.0133856	+	0.999910i	$0.504261\pi$
$60$		0			0
$61$	495.381			1.03979			0.519894	−	0.854231i	$-0.325971\pi$
$61$	495.381			1.03979			0.519894	+	0.854231i	$0.325971\pi$
$62$	−88.7471	−	153.715i	−0.181789	−	0.314867i
$63$		0			0
$64$	651.781			1.27301
$65$	−190.589	+	121.742i	−0.363687	+	0.232312i
$66$		0			0
$67$		−	233.027i		−	0.424907i	−0.977171	−	0.212453i	$-0.931855\pi$
$67$		−	233.027i		−	0.424907i	0.977171	−	0.212453i	$-0.0681453\pi$
$68$	34.0223			0.0606737
$69$		0			0
$70$	−269.987	+	155.877i	−0.460995	+	0.266156i
$71$	−824.189	−	475.846i	−1.37765	−	0.795388i	−0.385775	−	0.922593i	$-0.626066\pi$
$71$	−824.189	−	475.846i	−1.37765	−	0.795388i	−0.991876	+	0.127205i	$0.959399\pi$
$72$		0			0
$73$			885.664i			1.41999i	0.704208	+	0.709994i	$0.251302\pi$
$73$			885.664i			1.41999i	−0.704208	+	0.709994i	$0.748698\pi$
$74$	−666.413			−1.04688
$75$		0			0
$76$		−	109.085i		−	0.164644i
$77$	−352.147	+	609.937i	−0.521181	+	0.902712i
$78$		0			0
$79$	−221.888	−	384.322i	−0.316005	−	0.547336i	0.663646	−	0.748047i	$-0.269008\pi$
$79$	−221.888	−	384.322i	−0.316005	−	0.547336i	−0.979651	+	0.200711i	$0.935675\pi$
$80$	−221.530	+	127.900i	−0.309597	+	0.178746i
$81$		0			0
$82$	766.781	−	1328.10i	1.03264	−	1.78859i
$83$	604.028	−	348.736i	0.798803	−	0.461189i	−0.0442492	−	0.999021i	$-0.514090\pi$
$83$	604.028	−	348.736i	0.798803	−	0.461189i	0.843053	+	0.537831i	$0.180756\pi$
$84$		0			0
$85$	−15.4615	+	8.92672i	−0.0197299	+	0.0113910i
$86$	756.628	+	436.839i	0.948712	+	0.547739i
$87$		0			0
$88$	111.941	−	193.888i	0.135602	−	0.234869i
$89$	−322.550	+	186.224i	−0.384160	+	0.221795i	−0.679626	−	0.733558i	$-0.737858\pi$
$89$	−322.550	+	186.224i	−0.384160	+	0.221795i	0.295467	+	0.955353i	$0.404525\pi$
$90$		0			0
$91$	−648.255	−	336.466i	−0.746765	−	0.387595i
$92$	618.289	+	1070.91i	0.700664	+	1.21358i
$93$		0			0
$94$	−766.944			−0.841535
$95$	28.6216	+	49.5741i	0.0309107	+	0.0535389i
$96$		0			0
$97$			135.651i			0.141993i	0.997477	+	0.0709965i	$0.0226179\pi$
$97$			135.651i			0.141993i	−0.997477	+	0.0709965i	$0.977382\pi$
$98$	359.807	+	207.735i	0.370878	+	0.214126i
$99$		0			0
$100$	467.636	−	809.969i	0.467636	−	0.809969i
$101$	383.501	−	664.244i	0.377820	−	0.654403i	−0.612925	−	0.790141i	$-0.710007\pi$
$101$	383.501	−	664.244i	0.377820	−	0.654403i	0.990745	+	0.135738i	$0.0433405\pi$
$102$		0			0
$103$	−190.422	+	329.821i	−0.182163	+	0.315516i	−0.942617	−	0.333876i	$-0.891643\pi$
$103$	−190.422	+	329.821i	−0.182163	+	0.315516i	0.760454	+	0.649392i	$0.224977\pi$
$104$	206.068	+	106.956i	0.194295	+	0.100845i
$105$		0			0
$106$	1571.91	+	907.540i	1.44035	+	0.831586i
$107$	249.465	+	432.086i	0.225389	+	0.390386i	0.956436	−	0.291941i	$-0.0943012\pi$
$107$	249.465	+	432.086i	0.225389	+	0.390386i	−0.731047	+	0.682327i	$0.760968\pi$
$108$		0			0
$109$			1867.86i			1.64136i	0.571388	+	0.820680i	$0.306405\pi$
$109$			1867.86i			1.64136i	−0.571388	+	0.820680i	$0.693595\pi$
$110$			904.292i			0.783826i
$111$		0			0
$112$	−715.440	−	413.060i	−0.603596	−	0.348486i
$113$	−904.664	−	1566.92i	−0.753129	−	1.30446i	−0.946299	−	0.323293i	$-0.895210\pi$
$113$	−904.664	−	1566.92i	−0.753129	−	1.30446i	0.193170	−	0.981165i	$-0.438123\pi$
$114$		0			0
$115$	−561.966	−	324.451i	−0.455684	−	0.263089i
$116$	−1833.76			−1.46776
$117$		0			0
$118$	−1922.60			−1.49991
$119$	−49.9337	−	28.8292i	−0.0384657	−	0.0222082i
$120$		0			0
$121$	355.958	+	616.537i	0.267436	+	0.463214i
$122$	1778.96	+	1027.08i	1.32016	+	0.762193i
$123$		0			0
$124$		−	393.567i		−	0.285027i
$125$			1093.90i			0.782733i
$126$		0			0
$127$	920.407	+	1594.19i	0.643094	+	1.11387i	0.984738	+	0.174042i	$0.0556829\pi$
$127$	920.407	+	1594.19i	0.643094	+	1.11387i	−0.341644	+	0.939829i	$0.610984\pi$
$128$	542.958	+	313.477i	0.374931	+	0.216466i
$129$		0			0
$130$	−936.832	+	42.0369i	−0.632043	+	0.0283606i
$131$	1036.68	−	1795.58i	0.691414	−	1.19756i	−0.279961	−	0.960011i	$-0.590322\pi$
$131$	1036.68	−	1795.58i	0.691414	−	1.19756i	0.971375	−	0.237552i	$-0.0763452\pi$
$132$		0			0
$133$	−92.4348	+	160.102i	−0.0602640	+	0.104380i
$134$	483.138	−	836.819i	0.311468	−	0.539479i
$135$		0			0
$136$	15.8730	+	9.16427i	0.0100081	+	0.00577816i
$137$			1009.61i			0.629609i	0.949157	+	0.314804i	$0.101939\pi$
$137$			1009.61i			0.629609i	−0.949157	+	0.314804i	$0.898061\pi$
$138$		0			0
$139$	938.027	+	1624.71i	0.572391	+	0.991411i	0.996320	+	0.0857152i	$0.0273175\pi$
$139$	938.027	+	1624.71i	0.572391	+	0.991411i	−0.423928	+	0.905696i	$0.639349\pi$
$140$	−691.269			−0.417306
$141$		0			0
$142$	−1973.16	−	3417.61i	−1.16608	−	2.01971i
$143$	−1785.40	+	1140.46i	−1.04407	+	0.666922i
$144$		0			0
$145$	833.357	−	481.139i	0.477287	−	0.275562i
$146$	−1836.26	+	3180.50i	−1.04089	+	1.80287i
$147$		0			0
$148$	−1279.70	−	738.836i	−0.710749	−	0.410351i
$149$	1970.39	−	1137.61i	1.08336	−	0.625479i	0.151561	−	0.988448i	$-0.451570\pi$
$149$	1970.39	−	1137.61i	1.08336	−	0.625479i	0.931801	+	0.362969i	$0.118237\pi$
$150$		0			0
$151$	124.588	−	71.9311i	0.0671447	−	0.0387660i	−0.466052	−	0.884757i	$-0.654324\pi$
$151$	124.588	−	71.9311i	0.0671447	−	0.0387660i	0.533197	+	0.845991i	$0.320991\pi$
$152$	29.3833	−	50.8933i	0.0156796	−	0.0271579i
$153$		0			0
$154$	−2529.18	+	1460.22i	−1.32342	+	0.764080i
$155$	103.264	+	178.858i	0.0535118	+	0.0926852i
$156$		0			0
$157$	1894.28	−	3280.98i	0.962928	−	1.66784i	0.247846	−	0.968799i	$-0.420277\pi$
$157$	1894.28	−	3280.98i	0.962928	−	1.66784i	0.715082	−	0.699041i	$-0.246389\pi$
$158$		−	1840.18i		−	0.926560i
$159$		0			0
$160$	−1251.90			−0.618573
$161$		−	2095.66i		−	1.02585i
$162$		0			0
$163$	−1676.30	−	967.813i	−0.805510	−	0.465061i	0.0398843	−	0.999204i	$-0.487301\pi$
$163$	−1676.30	−	967.813i	−0.805510	−	0.465061i	−0.845394	+	0.534143i	$0.820634\pi$
$164$	2944.87	−	1700.22i	1.40217	−	0.809543i
$165$		0			0
$166$	2892.16			1.35226
$167$			2197.30i			1.01816i	0.860720	+	0.509079i	$0.170014\pi$
$167$			2197.30i			1.01816i	−0.860720	+	0.509079i	$0.829986\pi$
$168$		0			0
$169$	−1264.49	−	1796.63i	−0.575554	−	0.817764i
$170$	−74.0316			−0.0333998
$171$		0			0
$172$	968.626	+	1677.71i	0.429401	+	0.743745i
$173$	2935.23			1.28995			0.644976	−	0.764203i	$-0.276868\pi$
$173$	2935.23			1.28995			0.644976	+	0.764203i	$0.276868\pi$
$174$		0			0
$175$	−1372.68	+	792.514i	−0.592940	+	0.342334i
$176$	−2075.25	+	1198.14i	−0.888793	+	0.513145i
$177$		0			0
$178$	−1544.41			−0.650326
$179$	−668.032	−	1157.07i	−0.278945	−	0.483146i	0.692178	−	0.721727i	$-0.256651\pi$
$179$	−668.032	−	1157.07i	−0.278945	−	0.483146i	−0.971123	+	0.238581i	$0.923318\pi$
$180$		0			0
$181$	−4103.79			−1.68526			−0.842630	−	0.538493i	$-0.818994\pi$
$181$	−4103.79			−1.68526			−0.842630	+	0.538493i	$0.818994\pi$
$182$	−1630.34	−	2552.31i	−0.664005	−	1.03951i
$183$		0			0
$184$			666.171i			0.266906i
$185$	775.419			0.308162
$186$		0			0
$187$	−144.840	+	83.6236i	−0.0566405	+	0.0327014i
$188$	−1472.75	−	850.293i	−0.571337	−	0.329862i
$189$		0			0
$190$			237.367i			0.0906336i
$191$	−1791.70			−0.678758			−0.339379	−	0.940650i	$-0.610217\pi$
$191$	−1791.70			−0.678758			−0.339379	+	0.940650i	$0.610217\pi$
$192$		0			0
$193$			2660.41i			0.992231i	0.868256	+	0.496116i	$0.165241\pi$
$193$			2660.41i			0.992231i	−0.868256	+	0.496116i	$0.834759\pi$
$194$	−281.248	+	487.136i	−0.104085	+	0.180280i
$195$		0			0
$196$	460.621	+	797.819i	0.167865	+	0.290750i
$197$	384.908	−	222.227i	0.139206	−	0.0803705i	−0.428780	−	0.903409i	$-0.641056\pi$
$197$	384.908	−	222.227i	0.139206	−	0.0803705i	0.567985	+	0.823039i	$0.307723\pi$
$198$		0			0
$199$	713.480	−	1235.78i	0.254157	−	0.440213i	−0.710509	−	0.703688i	$-0.751535\pi$
$199$	713.480	−	1235.78i	0.254157	−	0.440213i	0.964666	+	0.263475i	$0.0848686\pi$
$200$	436.348	−	251.925i	0.154272	−	0.0890691i
$201$		0			0
$202$	2754.37	−	1590.24i	0.959391	−	0.553905i
$203$	2691.36	+	1553.86i	0.930526	+	0.537239i
$204$		0			0
$205$	−892.204	+	1545.34i	−0.303972	+	0.526495i
$206$	−1367.64	+	789.609i	−0.462564	+	0.267062i
$207$		0			0
$208$	−1337.73	−	2094.22i	−0.445936	−	0.698117i
$209$	268.121	+	464.400i	0.0887385	+	0.153700i
$210$		0			0
$211$	4491.04			1.46529			0.732645	−	0.680611i	$-0.238286\pi$
$211$	4491.04			1.46529			0.732645	+	0.680611i	$0.238286\pi$
$212$	2012.34	+	3485.47i	0.651924	+	1.12916i
$213$		0			0
$214$			2068.88i			0.660866i
$215$	−880.390	−	508.293i	−0.279266	−	0.161234i
$216$		0			0
$217$	−333.494	+	577.629i	−0.104327	+	0.180701i
$218$	−3872.65	+	6707.63i	−1.20316	+	2.08394i
$219$		0			0
$220$	−1002.57	+	1736.50i	−0.307241	+	0.532157i
$221$	−93.3658	−	146.165i	−0.0284184	−	0.0444892i
$222$		0			0
$223$	5100.14	+	2944.57i	1.53153	+	0.884228i	0.999292	+	0.0376324i	$0.0119816\pi$
$223$	5100.14	+	2944.57i	1.53153	+	0.884228i	0.532236	+	0.846596i	$0.321352\pi$
$224$	−2021.54	−	3501.41i	−0.602990	−	1.04441i
$225$		0			0
$226$		−	7502.61i		−	2.20826i
$227$		−	441.941i		−	0.129219i	−0.997911	−	0.0646094i	$-0.979420\pi$
$227$		−	441.941i		−	0.129219i	0.997911	−	0.0646094i	$-0.0205801\pi$
$228$		0			0
$229$	−827.880	−	477.977i	−0.238899	−	0.137928i	0.375772	−	0.926712i	$-0.377378\pi$
$229$	−827.880	−	477.977i	−0.238899	−	0.137928i	−0.614671	+	0.788784i	$0.710711\pi$
$230$	−1345.38	−	2330.27i	−0.385703	−	0.668057i
$231$		0			0
$232$	−855.534	−	493.943i	−0.242106	−	0.139780i
$233$	3455.74			0.971643			0.485822	−	0.874058i	$-0.338520\pi$
$233$	3455.74			0.971643			0.485822	+	0.874058i	$0.338520\pi$
$234$		0			0
$235$	892.394			0.247717
$236$	−3691.94	−	2131.54i	−1.01832	−	0.587930i
$237$		0			0
$238$	−119.544	−	207.057i	−0.0325584	−	0.0563928i
$239$	1556.43	+	898.605i	0.421243	+	0.243205i	0.695609	−	0.718421i	$-0.255135\pi$
$239$	1556.43	+	898.605i	0.421243	+	0.243205i	−0.274366	+	0.961625i	$0.588468\pi$
$240$		0			0
$241$			5699.63i			1.52343i	0.647915	+	0.761713i	$0.275641\pi$
$241$			5699.63i			1.52343i	−0.647915	+	0.761713i	$0.724359\pi$
$242$			2952.05i			0.784153i
$243$		0			0
$244$	2277.40	+	3944.57i	0.597523	+	1.03494i
$245$	−418.661	−	241.714i	−0.109173	−	0.0630308i
$246$		0			0
$247$	−468.647	+	299.358i	−0.120726	+	0.0771161i
$248$	106.012	−	183.617i	0.0271441	−	0.0470150i
$249$		0			0
$250$	−2268.00	+	3928.30i	−0.573765	+	0.993790i
$251$	1524.95	−	2641.30i	0.383483	−	0.664212i	−0.608075	−	0.793880i	$-0.708058\pi$
$251$	1524.95	−	2641.30i	0.383483	−	0.664212i	0.991557	+	0.129668i	$0.0413912\pi$
$252$		0			0
$253$	−5264.38	−	3039.39i	−1.30818	−	0.755277i
$254$			7633.18i			1.88562i
$255$		0			0
$256$	−1307.25	−	2264.22i	−0.319153	−	0.552789i
$257$	3374.76			0.819112			0.409556	−	0.912285i	$-0.365684\pi$
$257$	3374.76			0.819112			0.409556	+	0.912285i	$0.365684\pi$
$258$		0			0
$259$	1252.12	+	2168.74i	0.300399	+	0.520306i
$260$	−1845.59	−	957.920i	−0.440225	−	0.228491i
$261$		0			0
$262$	7445.62	−	4298.73i	1.75569	−	1.01365i
$263$	−2359.38	+	4086.57i	−0.553178	+	0.958133i	0.444865	+	0.895598i	$0.353252\pi$
$263$	−2359.38	+	4086.57i	−0.553178	+	0.958133i	−0.998043	+	0.0625348i	$0.980082\pi$
$264$		0			0
$265$	−1829.02	−	1055.99i	−0.423985	−	0.244788i
$266$	−663.883	+	383.293i	−0.153027	+	0.0883504i
$267$		0			0
$268$	1855.52	−	1071.29i	0.422925	−	0.244176i
$269$	318.110	−	550.982i	0.0721022	−	0.124885i	−0.827720	−	0.561141i	$-0.810363\pi$
$269$	318.110	−	550.982i	0.0721022	−	0.124885i	0.899822	+	0.436256i	$0.143696\pi$
$270$		0			0
$271$	1685.24	−	972.975i	0.377753	−	0.218096i	−0.299087	−	0.954226i	$-0.596682\pi$
$271$	1685.24	−	972.975i	0.377753	−	0.218096i	0.676840	+	0.736130i	$0.263349\pi$
$272$	−98.0883	−	169.894i	−0.0218657	−	0.0378726i
$273$		0			0
$274$	−2093.23	+	3625.58i	−0.461520	+	0.799377i
$275$			4597.62i			1.00817i
$276$		0			0
$277$	3079.00			0.667867			0.333933	−	0.942597i	$-0.391624\pi$
$277$	3079.00			0.667867			0.333933	+	0.942597i	$0.391624\pi$
$278$			7779.30i			1.67831i
$279$		0			0
$280$	−322.509	−	186.201i	−0.0688343	−	0.0397415i
$281$	8038.59	−	4641.08i	1.70655	−	0.985280i	0.767803	−	0.640686i	$-0.221350\pi$
$281$	8038.59	−	4641.08i	1.70655	−	0.985280i	0.938752	−	0.344594i	$-0.111983\pi$
$282$		0			0
$283$	3854.14			0.809557			0.404779	−	0.914415i	$-0.367349\pi$
$283$	3854.14			0.809557			0.404779	+	0.914415i	$0.367349\pi$
$284$		−	8750.36i		−	1.82830i
$285$		0			0
$286$	−8776.04	+	393.793i	−1.81447	+	0.0814177i
$287$	−5762.82			−1.18526
$288$		0			0
$289$	2449.65	+	4242.93i	0.498607	+	0.863612i
$290$	3990.21			0.807977
$291$		0			0
$292$	−7052.28	+	4071.63i	−1.41337	+	0.816008i
$293$	−6838.83	+	3948.40i	−1.36358	+	0.787263i	−0.990098	−	0.140375i	$-0.955169\pi$
$293$	−6838.83	+	3948.40i	−1.36358	+	0.787263i	−0.373481	+	0.927638i	$0.621836\pi$
$294$		0			0
$295$	2237.08			0.441519
$296$	−398.027	−	689.403i	−0.0781582	−	0.135374i
$297$		0			0
$298$	9434.47			1.83397
$299$	2904.04	−	5595.10i	0.561689	−	1.08218i
$300$		0			0
$301$		−	3283.11i		−	0.628689i
$302$	596.543			0.113666
$303$		0			0
$304$	−544.729	+	314.499i	−0.102771	+	0.0593348i
$305$	−2069.94	−	1195.08i	−0.388605	−	0.224361i
$306$		0			0
$307$		−	407.325i		−	0.0757241i	−0.999283	−	0.0378620i	$-0.987945\pi$
$307$		−	407.325i		−	0.0757241i	0.999283	−	0.0378620i	$-0.0120547\pi$
$308$	−6475.66			−1.19800
$309$		0			0
$310$			856.392i			0.156902i
$311$	3581.74	−	6203.75i	0.653060	−	1.13113i	−0.329317	−	0.944220i	$-0.606818\pi$
$311$	3581.74	−	6203.75i	0.653060	−	1.13113i	0.982376	−	0.186913i	$-0.0598483\pi$
$312$		0			0
$313$	3990.28	+	6911.36i	0.720587	+	1.24809i	0.960765	+	0.277364i	$0.0894609\pi$
$313$	3990.28	+	6911.36i	0.720587	+	1.24809i	−0.240178	+	0.970729i	$0.577206\pi$
$314$	13605.0	−	7854.86i	2.44515	−	1.41171i
$315$		0			0
$316$	2040.16	−	3533.66i	0.363189	−	0.629063i
$317$	1490.33	−	860.444i	0.264055	−	0.152452i	−0.362128	−	0.932128i	$-0.617950\pi$
$317$	1490.33	−	860.444i	0.264055	−	0.152452i	0.626183	+	0.779676i	$0.284616\pi$
$318$		0			0
$319$	7806.72	−	4507.21i	1.37020	−	0.791083i
$320$	−2723.45	−	1572.39i	−0.475768	−	0.274685i
$321$		0			0
$322$	4344.96	−	7525.70i	0.751973	−	1.30246i
$323$	−38.0190	+	21.9503i	−0.00654933	+	0.00378126i
$324$		0			0
$325$	−4763.06	+	213.725i	−0.812945	+	0.0364779i
$326$	−4013.16	−	6951.00i	−0.681805	−	1.18092i
$327$		0			0
$328$	1831.89			0.308382
$329$	1441.01	+	2495.91i	0.241476	+	0.418249i
$330$		0			0
$331$		−	8642.27i		−	1.43511i	−0.696501	−	0.717556i	$-0.745261\pi$
$331$		−	8642.27i		−	1.43511i	0.696501	−	0.717556i	$-0.254739\pi$
$332$	5553.76	+	3206.46i	0.918078	+	0.530053i
$333$		0			0
$334$	−4555.70	+	7890.70i	−0.746337	+	1.29269i
$335$	−562.165	+	973.698i	−0.0916846	+	0.158802i
$336$		0			0
$337$	4315.56	−	7474.77i	0.697577	−	1.20824i	−0.271727	−	0.962374i	$-0.587595\pi$
$337$	4315.56	−	7474.77i	0.697577	−	1.20824i	0.969304	−	0.245864i	$-0.0790718\pi$
$338$	−815.926	−	9073.53i	−0.131303	−	1.46016i
$339$		0			0
$340$	−142.162	−	82.0770i	−0.0226759	−	0.0130919i
$341$	967.352	+	1675.50i	0.153622	+	0.266081i
$342$		0			0
$343$		−	6905.95i		−	1.08713i
$344$			1043.64i			0.163573i
$345$		0			0
$346$	10540.7	+	6085.66i	1.63777	+	0.945570i
$347$	−5717.41	−	9902.84i	−0.884514	−	1.53202i	−0.846270	−	0.532755i	$-0.821157\pi$
$347$	−5717.41	−	9902.84i	−0.884514	−	1.53202i	−0.0382445	−	0.999268i	$-0.512177\pi$
$348$		0			0
$349$	−4032.59	−	2328.21i	−0.618508	−	0.357096i	0.157780	−	0.987474i	$-0.449566\pi$
$349$	−4032.59	−	2328.21i	−0.618508	−	0.357096i	−0.776288	+	0.630378i	$0.782900\pi$
$350$	−6572.53			−1.00376
$351$		0			0
$352$	−11727.6			−1.77580
$353$	7582.18	+	4377.57i	1.14323	+	0.660042i	0.947227	−	0.320563i	$-0.103872\pi$
$353$	7582.18	+	4377.57i	1.14323	+	0.660042i	0.195998	+	0.980604i	$0.437205\pi$
$354$		0			0
$355$	2295.91	+	3976.63i	0.343251	+	0.594528i
$356$	−2965.69	−	1712.24i	−0.441521	−	0.254912i
$357$		0			0
$358$		−	5540.16i		−	0.817896i
$359$		−	9826.13i		−	1.44458i	−0.691591	−	0.722289i	$-0.743090\pi$
$359$		−	9826.13i		−	1.44458i	0.691591	−	0.722289i	$-0.256910\pi$
$360$		0			0
$361$	−3359.12	−	5818.17i	−0.489739	−	0.848253i
$362$	−14737.0	−	8508.44i	−2.13967	−	1.23534i
$363$		0			0
$364$	−301.028	−	6708.68i	−0.0433465	−	0.966018i
$365$	2136.62	−	3700.73i	0.306399	−	0.530699i
$366$		0			0
$367$	−3902.90	+	6760.02i	−0.555122	+	0.961499i	0.442772	+	0.896634i	$0.353995\pi$
$367$	−3902.90	+	6760.02i	−0.555122	+	0.961499i	−0.997894	+	0.0648650i	$0.979338\pi$
$368$	3565.13	−	6174.98i	0.505014	−	0.874710i
$369$		0			0
$370$	2784.60	+	1607.69i	0.391255	+	0.225891i
$371$		−	6820.72i		−	0.954485i
$372$		0			0
$373$	−1005.60	−	1741.75i	−0.139592	−	0.241781i	0.787750	−	0.615995i	$-0.211246\pi$
$373$	−1005.60	−	1741.75i	−0.139592	−	0.241781i	−0.927342	+	0.374214i	$0.877913\pi$
$374$	−693.512			−0.0958842
$375$		0			0
$376$	−458.071	−	793.402i	−0.0628277	−	0.108821i
$377$	5032.30	+	7878.11i	0.687471	+	1.07624i
$378$		0			0
$379$	8431.71	−	4868.05i	1.14276	−	0.659775i	0.195651	−	0.980674i	$-0.437318\pi$
$379$	8431.71	−	4868.05i	1.14276	−	0.659775i	0.947114	+	0.320898i	$0.103985\pi$
$380$	−263.163	+	455.811i	−0.0355262	+	0.0615332i
$381$		0			0
$382$	−6434.15	−	3714.76i	−0.861779	−	0.497548i
$383$	1112.25	−	642.160i	0.148390	−	0.0856733i	−0.423966	−	0.905678i	$-0.639363\pi$
$383$	1112.25	−	642.160i	0.148390	−	0.0856733i	0.572357	+	0.820005i	$0.306029\pi$
$384$		0			0
$385$	2942.88	−	1699.08i	0.389567	−	0.224917i
$386$	−5515.87	+	9553.77i	−0.727333	+	1.25978i
$387$		0			0
$388$	−1080.15	+	623.626i	−0.141331	+	0.0815974i
$389$	2696.83	+	4671.05i	0.351503	+	0.608822i	0.986513	−	0.163682i	$-0.0523373\pi$
$389$	2696.83	+	4671.05i	0.351503	+	0.608822i	−0.635010	+	0.772504i	$0.719004\pi$
$390$		0			0
$391$	248.826	−	430.979i	0.0321833	−	0.0557431i
$392$			496.293i			0.0639453i
$393$		0			0
$394$	1842.98			0.235655
$395$			2141.17i			0.272745i
$396$		0			0
$397$	8683.28	+	5013.29i	1.09774	+	0.633778i	0.935625	−	0.352994i	$-0.114837\pi$
$397$	8683.28	+	5013.29i	1.09774	+	0.633778i	0.162111	+	0.986773i	$0.448170\pi$
$398$	5124.34	−	2958.54i	0.645376	−	0.372608i
$399$		0			0
$400$	−5392.89			−0.674111
$401$			3025.48i			0.376771i	0.982095	+	0.188386i	$0.0603254\pi$
$401$			3025.48i			0.376771i	−0.982095	+	0.188386i	$0.939675\pi$
$402$		0			0
$403$	−1690.83	+	1080.05i	−0.208998	+	0.133501i
$404$	7052.23			0.868470
$405$		0			0
$406$	6443.28	+	11160.1i	0.787622	+	1.36420i
$407$	7263.96			0.884671
$408$		0			0
$409$	−10432.3	+	6023.11i	−1.26124	+	0.728175i	−0.973314	−	0.229479i	$-0.926298\pi$
$409$	−10432.3	+	6023.11i	−1.26124	+	0.728175i	−0.287922	+	0.957654i	$0.592964\pi$
$410$	−6407.96	+	3699.64i	−0.771870	+	0.445639i
$411$		0			0
$412$	−3501.68			−0.418727
$413$	3612.38	+	6256.82i	0.430396	+	0.745468i
$414$		0			0
$415$	−3365.23			−0.398054
$416$	−545.168	−	12149.6i	−0.0642525	−	1.43193i
$417$		0			0
$418$			2223.60i			0.260191i
$419$	−555.751			−0.0647977			−0.0323989	−	0.999475i	$-0.510315\pi$
$419$	−555.751			−0.0647977			−0.0323989	+	0.999475i	$0.510315\pi$
$420$		0			0
$421$	3191.54	−	1842.64i	0.369469	−	0.213313i	−0.303758	−	0.952749i	$-0.598241\pi$
$421$	3191.54	−	1842.64i	0.369469	−	0.213313i	0.673226	+	0.739437i	$0.264908\pi$
$422$	16127.7	+	9311.34i	1.86039	+	1.07410i
$423$		0			0
$424$			2168.18i			0.248340i
$425$	−376.393			−0.0429594
$426$		0			0
$427$		−	7719.14i		−	0.874837i
$428$	−2293.71	+	3972.83i	−0.259044	+	0.448677i
$429$		0			0
$430$	−2107.70	−	3650.65i	−0.236378	−	0.409419i
$431$	−9362.89	+	5405.67i	−1.04639	+	0.604134i	−0.921637	−	0.388053i	$-0.873148\pi$
$431$	−9362.89	+	5405.67i	−1.04639	+	0.604134i	−0.124754	+	0.992188i	$0.539814\pi$
$432$		0			0
$433$	−2665.15	+	4616.18i	−0.295795	+	0.512331i	−0.975169	−	0.221460i	$-0.928918\pi$
$433$	−2665.15	+	4616.18i	−0.295795	+	0.512331i	0.679375	+	0.733791i	$0.262251\pi$
$434$	−2395.21	+	1382.88i	−0.264917	+	0.152950i
$435$		0			0
$436$	−14873.2	+	8587.03i	−1.63371	+	0.943221i
$437$	−1381.84	−	797.807i	−0.151264	−	0.0873325i
$438$		0			0
$439$	3198.24	−	5539.51i	0.347707	−	0.602247i	−0.638134	−	0.769925i	$-0.720294\pi$
$439$	3198.24	−	5539.51i	0.347707	−	0.602247i	0.985842	+	0.167678i	$0.0536269\pi$
$440$	−935.487	+	540.104i	−0.101358	+	0.0585192i
$441$		0			0
$442$	−32.2386	−	718.468i	−0.00346931	−	0.0773168i
$443$	3255.46	+	5638.62i	0.349146	+	0.604738i	0.986098	−	0.166165i	$-0.0531386\pi$
$443$	3255.46	+	5638.62i	0.349146	+	0.604738i	−0.636952	+	0.770903i	$0.719805\pi$
$444$		0			0
$445$	1797.02			0.191432
$446$	12210.0	+	21148.4i	1.29633	+	2.24530i
$447$		0			0
$448$		−	10156.2i		−	1.07106i
$449$	9428.38	+	5443.48i	0.990986	+	0.572146i	0.905569	−	0.424199i	$-0.139444\pi$
$449$	9428.38	+	5443.48i	0.990986	+	0.572146i	0.0854173	+	0.996345i	$0.472778\pi$
$450$		0			0
$451$	−8357.98	+	14476.4i	−0.872643	+	1.51146i
$452$	8317.96	−	14407.1i	0.865584	−	1.49924i
$453$		0			0
$454$	916.283	−	1587.05i	0.0947209	−	0.164061i
$455$	1897.02	+	2969.80i	0.195458	+	0.305992i
$456$		0			0
$457$	−6900.23	−	3983.85i	−0.706300	−	0.407783i	0.103389	−	0.994641i	$-0.467031\pi$
$457$	−6900.23	−	3983.85i	−0.706300	−	0.407783i	−0.809690	+	0.586858i	$0.800365\pi$
$458$	−1981.99	−	3432.91i	−0.202210	−	0.350239i
$459$		0			0
$460$		−	5966.36i		−	0.604745i
$461$			16099.7i			1.62654i	0.581885	+	0.813271i	$0.302315\pi$
$461$			16099.7i			1.62654i	−0.581885	+	0.813271i	$0.697685\pi$
$462$		0			0
$463$	−14967.4	−	8641.42i	−1.50236	−	0.867388i	−0.999996	−	0.00273207i	$-0.999130\pi$
$463$	−14967.4	−	8641.42i	−1.50236	−	0.867388i	−0.502364	−	0.864656i	$-0.667536\pi$
$464$	5286.84	+	9157.08i	0.528956	+	0.916178i
$465$		0			0
$466$	12409.9	+	7164.83i	1.23364	+	0.712241i
$467$	−3133.28			−0.310473			−0.155237	−	0.987877i	$-0.549614\pi$
$467$	−3133.28			−0.310473			−0.155237	+	0.987877i	$0.549614\pi$
$468$		0			0
$469$	−3631.07			−0.357500
$470$	3204.66	+	1850.21i	0.314511	+	0.181583i
$471$		0			0
$472$	−1148.31	−	1988.93i	−0.111981	−	0.193957i
$473$	−8247.31	−	4761.59i	−0.801716	−	0.462871i
$474$		0			0
$475$			1206.82i			0.116575i
$476$		−	530.143i		−	0.0510484i
$477$		0			0
$478$	3726.18	+	6453.94i	0.356552	+	0.617565i
$479$	−9386.93	−	5419.55i	−0.895407	−	0.516964i	−0.0196998	−	0.999806i	$-0.506271\pi$
$479$	−9386.93	−	5419.55i	−0.895407	−	0.516964i	−0.875707	+	0.482842i	$0.839604\pi$
$480$		0			0
$481$	337.673	+	7525.35i	0.0320094	+	0.713360i
$482$	−11817.1	+	20467.9i	−1.11671	+	1.93420i
$483$		0			0
$484$	−3272.87	+	5668.77i	−0.307369	+	0.532379i
$485$	327.252	−	566.817i	0.0306387	−	0.0530677i
$486$		0			0
$487$	−1248.82	−	721.005i	−0.116200	−	0.0670880i	0.440774	−	0.897618i	$-0.354704\pi$
$487$	−1248.82	−	721.005i	−0.116200	−	0.0670880i	−0.556973	+	0.830530i	$0.688037\pi$
$488$			2453.77i			0.227617i
$489$		0			0
$490$	−1002.30	−	1736.03i	−0.0924066	−	0.160053i
$491$	−15805.4			−1.45273			−0.726363	−	0.687311i	$-0.758791\pi$
$491$	−15805.4			−1.45273			−0.726363	+	0.687311i	$0.758791\pi$
$492$		0			0
$493$	368.992	+	639.112i	0.0337090	+	0.0583857i
$494$	−2303.61	+	103.366i	−0.209807	+	0.00941431i
$495$		0			0
$496$	−1965.32	+	1134.68i	−0.177914	+	0.102719i
$497$	−7414.73	+	12842.7i	−0.669208	+	1.15910i
$498$		0			0
$499$	4054.09	+	2340.63i	0.363700	+	0.209982i	0.670702	−	0.741727i	$-0.265993\pi$
$499$	4054.09	+	2340.63i	0.363700	+	0.209982i	−0.307003	+	0.951709i	$0.599326\pi$
$500$	−8710.42	+	5028.96i	−0.779083	+	0.449804i
$501$		0			0
$502$	10952.5	−	6323.41i	0.973771	−	0.562207i
$503$	−6676.54	+	11564.1i	−0.591834	+	1.02509i	0.402152	+	0.915573i	$0.368262\pi$
$503$	−6676.54	+	11564.1i	−0.591834	+	1.02509i	−0.993985	+	0.109513i	$0.965071\pi$
$504$		0			0
$505$	−3204.91	+	1850.36i	−0.282409	+	0.163049i
$506$	−12603.2	−	21829.4i	−1.10728	−	1.91786i
$507$		0			0
$508$	−8462.72	+	14657.9i	−0.739119	+	1.28019i
$509$			4598.43i			0.400436i	0.979751	+	0.200218i	$0.0641651\pi$
$509$			4598.43i			0.400436i	−0.979751	+	0.200218i	$0.935835\pi$
$510$		0			0
$511$	13800.6			1.19472
$512$		−	15857.0i		−	1.36872i
$513$		0			0
$514$	12119.1	+	6996.94i	1.03998	+	0.600431i
$515$	1591.35	−	918.766i	0.136162	−	0.0786130i
$516$		0			0
$517$	8359.76			0.711145
$518$			10384.2i			0.880802i
$519$		0			0
$520$	−603.026	−	944.043i	−0.0508547	−	0.0796135i
$521$	−21107.9			−1.77496			−0.887482	−	0.460843i	$-0.847547\pi$
$521$	−21107.9			−1.77496			−0.887482	+	0.460843i	$0.847547\pi$
$522$		0			0
$523$	−551.772	−	955.697i	−0.0461325	−	0.0799039i	0.842037	−	0.539420i	$-0.181356\pi$
$523$	−551.772	−	955.697i	−0.0461325	−	0.0799039i	−0.888170	+	0.459516i	$0.848023\pi$
$524$	19063.6			1.58931
$525$		0			0
$526$	−16945.5	+	9783.49i	−1.40468	+	0.810989i
$527$	−137.168	+	79.1941i	−0.0113380	+	0.00654602i
$528$		0			0
$529$	5920.69			0.486619
$530$	−4378.79	−	7584.29i	−0.358873	−	0.621586i
$531$		0			0
$532$	−1699.79			−0.138525
$533$	−15385.9	−	7985.78i	−1.25035	−	0.648973i
$534$		0			0
$535$		−	2407.28i		−	0.194534i
$536$	1154.25			0.0930149
$537$		0			0
$538$	2284.72	−	1319.08i	0.183088	−	0.105706i
$539$	−3921.93	−	2264.33i	−0.313413	−	0.180949i
$540$		0			0
$541$		−	8406.46i		−	0.668063i	−0.942562	−	0.334031i	$-0.891591\pi$
$541$		−	8406.46i		−	0.668063i	0.942562	−	0.334031i	$-0.108409\pi$
$542$	8069.13			0.639481
$543$		0			0
$544$		−	960.100i		−	0.0756690i
$545$	4506.11	−	7804.81i	0.354166	−	0.613433i
$546$		0			0
$547$	−6012.48	−	10413.9i	−0.469972	−	0.814016i	0.529438	−	0.848349i	$-0.322403\pi$
$547$	−6012.48	−	10413.9i	−0.469972	−	0.814016i	−0.999410	+	0.0343326i	$0.989069\pi$
$548$	−8039.18	+	4641.42i	−0.626673	+	0.361810i
$549$		0			0
$550$	−9532.32	+	16510.5i	−0.739017	+	1.28001i
$551$	2049.18	−	1183.09i	0.158435	−	0.0914727i
$552$		0			0
$553$	−5988.58	+	3457.51i	−0.460507	+	0.265874i
$554$	11057.0	+	6383.73i	0.847951	+	0.489565i
$555$		0			0
$556$	−8624.72	+	14938.5i	−0.657859	+	1.13945i
$557$	8287.38	−	4784.72i	0.630427	−	0.363977i	−0.150491	−	0.988611i	$-0.548085\pi$
$557$	8287.38	−	4784.72i	0.630427	−	0.363977i	0.780917	+	0.624635i	$0.214752\pi$
$558$		0			0
$559$	4549.54	−	8765.43i	0.344231	−	0.663216i
$560$	1992.97	+	3451.93i	0.150390	+	0.260483i
$561$		0			0
$562$	38489.7			2.88895
$563$	1435.16	+	2485.77i	0.107433	+	0.186079i	0.914730	−	0.404067i	$-0.132404\pi$
$563$	1435.16	+	2485.77i	0.107433	+	0.186079i	−0.807297	+	0.590146i	$0.799070\pi$
$564$		0			0
$565$			8729.82i			0.650029i
$566$	13840.5	+	7990.84i	1.02785	+	0.593428i
$567$		0			0
$568$	2357.00	−	4082.45i	0.174116	−	0.301577i
$569$	3062.25	−	5303.98i	0.225617	−	0.390781i	−0.730887	−	0.682498i	$-0.760893\pi$
$569$	3062.25	−	5303.98i	0.225617	−	0.390781i	0.956505	+	0.291718i	$0.0942267\pi$
$570$		0			0
$571$	−6559.23	+	11360.9i	−0.480727	+	0.832644i	−0.999755	−	0.0221130i	$-0.992961\pi$
$571$	−6559.23	+	11360.9i	−0.480727	+	0.832644i	0.519028	+	0.854757i	$0.326294\pi$
$572$	−17289.1	−	8973.59i	−1.26380	−	0.655952i
$573$		0			0
$574$	−20694.8	−	11948.1i	−1.50485	−	0.868826i
$575$	−6840.21	−	11847.6i	−0.496098	−	0.859267i
$576$		0			0
$577$			19378.4i			1.39815i	0.715049	+	0.699074i	$0.246404\pi$
$577$			19378.4i			1.39815i	−0.715049	+	0.699074i	$0.753596\pi$
$578$			20315.6i			1.46197i
$579$		0			0
$580$	7662.33	+	4423.85i	0.548554	+	0.316708i
$581$	−5434.07	−	9412.09i	−0.388027	−	0.672082i
$582$		0			0
$583$	−17133.9	−	9892.27i	−1.21718	−	0.702738i
$584$	−4386.95			−0.310845
$585$		0			0
$586$	−32745.1			−2.30834
$587$	−2312.61	−	1335.18i	−0.162609	−	0.0938824i	0.416487	−	0.909142i	$-0.363261\pi$
$587$	−2312.61	−	1335.18i	−0.162609	−	0.0938824i	−0.579096	+	0.815259i	$0.696594\pi$
$588$		0			0
$589$	253.919	+	439.801i	0.0177633	+	0.0307669i
$590$	8033.56	+	4638.18i	0.560570	+	0.323645i
$591$		0			0
$592$			8520.44i			0.591533i
$593$			723.279i			0.0500869i	0.999686	+	0.0250434i	$0.00797241\pi$
$593$			723.279i			0.0500869i	−0.999686	+	0.0250434i	$0.992028\pi$
$594$		0			0
$595$	139.098	+	240.925i	0.00958397	+	0.0165999i
$596$	18116.9	+	10459.8i	1.24513	+	0.718874i
$597$		0			0
$598$	22029.1	−	14071.5i	1.50641	−	0.962252i
$599$	274.189	−	474.910i	0.0187030	−	0.0323945i	−0.856522	−	0.516110i	$-0.827380\pi$
$599$	274.189	−	474.910i	0.0187030	−	0.0323945i	0.875225	+	0.483715i	$0.160713\pi$
$600$		0			0
$601$	−10132.4	+	17549.9i	−0.687705	+	1.19114i	0.284874	+	0.958565i	$0.408048\pi$
$601$	−10132.4	+	17549.9i	−0.687705	+	1.19114i	−0.972579	+	0.232575i	$0.925285\pi$
$602$	6806.92	−	11789.9i	0.460846	−	0.798209i
$603$		0			0
$604$	1145.53	+	661.373i	0.0771705	+	0.0445544i
$605$		−	3434.92i		−	0.230825i
$606$		0			0
$607$	−11258.1	−	19499.6i	−0.752802	−	1.30389i	−0.946459	−	0.322823i	$-0.895368\pi$
$607$	−11258.1	−	19499.6i	−0.752802	−	1.30389i	0.193657	−	0.981069i	$-0.437965\pi$
$608$	−3078.36			−0.205335
$609$		0			0
$610$	−4955.56	−	8583.28i	−0.328926	−	0.569716i
$611$	388.612	+	8660.58i	0.0257309	+	0.573436i
$612$		0			0
$613$	12284.6	−	7092.50i	0.809411	−	0.467314i	−0.0373402	−	0.999303i	$-0.511889\pi$
$613$	12284.6	−	7092.50i	0.809411	−	0.467314i	0.846751	+	0.531989i	$0.178555\pi$
$614$	844.514	−	1462.74i	0.0555078	−	0.0961424i
$615$		0			0
$616$	−3021.20	−	1744.29i	−0.197610	−	0.114090i
$617$	3808.76	−	2198.99i	0.248517	−	0.143481i	−0.370568	−	0.928805i	$-0.620837\pi$
$617$	3808.76	−	2198.99i	0.248517	−	0.143481i	0.619085	+	0.785324i	$0.287504\pi$
$618$		0			0
$619$	3542.68	−	2045.37i	0.230036	−	0.132811i	−0.380553	−	0.924759i	$-0.624266\pi$
$619$	3542.68	−	2045.37i	0.230036	−	0.132811i	0.610589	+	0.791948i	$0.290933\pi$
$620$	−949.461	+	1644.51i	−0.0615020	+	0.106525i
$621$		0			0
$622$	25724.6	−	14852.1i	1.65830	−	0.957421i
$623$	2901.79	+	5026.04i	0.186609	+	0.323217i
$624$		0			0
$625$	−3718.54	+	6440.70i	−0.237987	+	0.412205i
$626$			33092.4i			2.11284i
$627$		0			0
$628$	34834.0			2.21342
$629$			594.678i			0.0376969i
$630$		0			0
$631$	−21280.2	−	12286.1i	−1.34255	−	0.775122i	−0.355370	−	0.934726i	$-0.615645\pi$
$631$	−21280.2	−	12286.1i	−1.34255	−	0.775122i	−0.987181	+	0.159603i	$0.948979\pi$
$632$	1903.66	−	1099.08i	0.119816	−	0.0691755i
$633$		0			0
$634$	7135.89			0.447007
$635$		−	8881.74i		−	0.555057i
$636$		0			0
$637$	2163.49	−	4168.32i	0.134569	−	0.259270i
$638$	37379.5			2.31954
$639$		0			0
$640$	−1512.49	−	2619.72i	−0.0934165	−	0.161802i
$641$	−27091.7			−1.66935			−0.834677	−	0.550739i	$-0.814346\pi$
$641$	−27091.7			−1.66935			−0.834677	+	0.550739i	$0.814346\pi$
$642$		0			0
$643$	−10565.8	+	6100.14i	−0.648013	+	0.374131i	−0.787695	−	0.616066i	$-0.788726\pi$
$643$	−10565.8	+	6100.14i	−0.648013	+	0.374131i	0.139681	+	0.990197i	$0.455392\pi$
$644$	16687.1	−	9634.31i	1.02106	−	0.589511i
$645$		0			0
$646$	−182.039			−0.0110871
$647$	8686.06	+	15044.7i	0.527796	+	0.914170i	0.999475	+	0.0323993i	$0.0103148\pi$
$647$	8686.06	+	15044.7i	0.527796	+	0.914170i	−0.471679	+	0.881770i	$0.656352\pi$
$648$		0			0
$649$	20956.5			1.26751
$650$	−17547.7	−	9107.82i	−1.05889	−	0.549597i
$651$		0			0
$652$		−	17797.2i		−	1.06901i
$653$	17666.7			1.05873			0.529367	−	0.848393i	$-0.322429\pi$
$653$	17666.7			1.05873			0.529367	+	0.848393i	$0.322429\pi$
$654$		0			0
$655$	−8663.51	+	5001.88i	−0.516811	+	0.298381i
$656$	−16980.5	−	9803.69i	−1.01064	−	0.583491i
$657$		0			0
$658$			11950.7i			0.708034i
$659$	3389.99			0.200388			0.100194	−	0.994968i	$-0.468054\pi$
$659$	3389.99			0.200388			0.100194	+	0.994968i	$0.468054\pi$
$660$		0			0
$661$			4621.97i			0.271973i	0.990711	+	0.135986i	$0.0434203\pi$
$661$			4621.97i			0.271973i	−0.990711	+	0.135986i	$0.956580\pi$
$662$	17918.1	−	31035.1i	1.05198	−	1.82208i
$663$		0			0
$664$	1727.39	+	2991.93i	0.100957	+	0.174863i
$665$	772.475	−	445.989i	0.0450455	−	0.0260071i
$666$		0			0
$667$	−13411.4	+	23229.2i	−0.778548	+	1.34848i
$668$	−17496.5	+	10101.6i	−1.01341	+	0.585093i
$669$		0			0
$670$	−4037.57	+	2331.09i	−0.232813	+	0.134415i
$671$	−19390.8	−	11195.3i	−1.11561	−	0.644097i
$672$		0			0
$673$	−7660.42	+	13268.2i	−0.438763	+	0.759959i	−0.997594	−	0.0693218i	$-0.977916\pi$
$673$	−7660.42	+	13268.2i	−0.438763	+	0.759959i	0.558832	+	0.829281i	$0.311250\pi$
$674$	30995.1	−	17895.0i	1.77134	−	1.02269i
$675$		0			0
$676$	8492.80	−	18328.3i	0.483204	−	1.04281i
$677$	4939.85	+	8556.07i	0.280434	+	0.485726i	0.971492	−	0.237074i	$-0.0761883\pi$
$677$	4939.85	+	8556.07i	0.280434	+	0.485726i	−0.691058	+	0.722800i	$0.742855\pi$
$678$		0			0
$679$	2113.75			0.119467
$680$	−44.2167	−	76.5855i	−0.00249358	−	0.00431900i
$681$		0			0
$682$			8022.50i			0.450436i
$683$	−9566.46	−	5523.20i	−0.535945	−	0.309428i	0.207489	−	0.978237i	$-0.433471\pi$
$683$	−9566.46	−	5523.20i	−0.535945	−	0.309428i	−0.743434	+	0.668809i	$0.766804\pi$
$684$		0			0
$685$	2435.62	−	4218.62i	0.135854	−	0.235307i
$686$	14318.2	−	24799.9i	0.796898	−	1.38027i
$687$		0			0
$688$	5585.22	−	9673.88i	0.309498	−	0.536066i
$689$	9451.75	−	18210.3i	0.522617	−	1.00691i
$690$		0			0
$691$	−15283.1	−	8823.71i	−0.841385	−	0.485774i	0.0163498	−	0.999866i	$-0.494795\pi$
$691$	−15283.1	−	8823.71i	−0.841385	−	0.485774i	−0.857735	+	0.514092i	$0.828129\pi$
$692$	13494.0	+	23372.4i	0.741281	+	1.28394i
$693$		0			0
$694$		−	47415.9i		−	2.59349i
$695$		−	9051.77i		−	0.494033i
$696$		0			0
$697$	−1185.14	−	684.242i	−0.0644053	−	0.0371844i
$698$	−9654.24	−	16721.6i	−0.523522	−	0.906767i
$699$		0			0
$700$	−12621.1	−	7286.80i	−0.681476	−	0.393450i
$701$	10173.6			0.548149			0.274075	−	0.961708i	$-0.411628\pi$
$701$	10173.6			0.548149			0.274075	+	0.961708i	$0.411628\pi$
$702$		0			0
$703$	1906.71			0.102294
$704$	−25512.8	−	14729.8i	−1.36584	−	0.788565i
$705$		0			0
$706$	18152.2	+	31440.5i	0.967657	+	1.67603i
$707$	−10350.4	−	5975.80i	−0.550589	−	0.317883i
$708$		0			0
$709$			25991.1i			1.37675i	0.725354	+	0.688376i	$0.241676\pi$
$709$			25991.1i			1.37675i	−0.725354	+	0.688376i	$0.758324\pi$
$710$			19040.6i			1.00645i
$711$		0			0
$712$	−922.423	−	1597.68i	−0.0485523	−	0.0840951i
$713$	−4985.53	−	2878.40i	−0.261865	−	0.151188i
$714$		0			0
$715$	10211.5	−	458.206i	0.534112	−	0.0239663i
$716$	6142.24	−	10638.7i	0.320596	−	0.555288i
$717$		0			0
$718$	20372.7	−	35286.5i	1.05892	−	1.83409i
$719$	−4071.16	+	7051.46i	−0.211167	+	0.365751i	−0.952080	−	0.305849i	$-0.901060\pi$
$719$	−4071.16	+	7051.46i	−0.211167	+	0.365751i	0.740913	+	0.671601i	$0.234393\pi$
$720$		0			0
$721$	5139.33	+	2967.20i	0.265463	+	0.153265i
$722$		−	27858.1i		−	1.43597i
$723$		0			0
$724$	−18866.2	−	32677.2i	−0.968449	−	1.67740i
$725$	20287.1			1.03923
$726$		0			0
$727$	−18580.0	−	32181.5i	−0.947858	−	1.64174i	−0.749925	−	0.661523i	$-0.769910\pi$
$727$	−18580.0	−	32181.5i	−0.947858	−	1.64174i	−0.197933	−	0.980215i	$-0.563423\pi$
$728$	1666.61	−	3211.00i	0.0848472	−	0.163472i
$729$		0			0
$730$	15345.6	−	8859.76i	0.778034	−	0.449198i
$731$	389.816	−	675.182i	0.0197235	−	0.0341621i
$732$		0			0
$733$	−10221.9	−	5901.60i	−0.515079	−	0.297381i	0.219840	−	0.975536i	$-0.429447\pi$
$733$	−10221.9	−	5901.60i	−0.515079	−	0.297381i	−0.734919	+	0.678155i	$0.762780\pi$
$734$	−28031.3	+	16183.9i	−1.40961	+	0.813839i
$735$		0			0
$736$	30220.7	−	17447.9i	1.51352	−	0.873831i
$737$	−5266.24	+	9121.40i	−0.263208	+	0.455890i
$738$		0			0
$739$	−7857.56	+	4536.57i	−0.391130	+	0.225819i	−0.682650	−	0.730746i	$-0.739172\pi$
$739$	−7857.56	+	4536.57i	−0.391130	+	0.225819i	0.291520	+	0.956565i	$0.405839\pi$
$740$	3564.81	+	6174.43i	0.177088	+	0.306725i
$741$		0			0
$742$	14141.5	−	24493.8i	0.699664	−	1.21185i
$743$		−	26844.1i		−	1.32546i	−0.748859	−	0.662729i	$-0.769398\pi$
$743$		−	26844.1i		−	1.32546i	0.748859	−	0.662729i	$-0.230602\pi$
$744$		0			0
$745$	−10977.7			−0.539854
$746$		−	8339.69i		−	0.409300i
$747$		0			0
$748$	−1331.74	−	768.880i	−0.0650979	−	0.0375843i
$749$	6732.85	−	3887.21i	0.328455	−	0.189634i
$750$		0			0
$751$	6213.29			0.301899			0.150950	−	0.988541i	$-0.451767\pi$
$751$	6213.29			0.301899			0.150950	+	0.988541i	$0.451767\pi$
$752$			9805.78i			0.475505i
$753$		0			0
$754$	1737.62	+	38724.5i	0.0839263	+	1.87038i
$755$	−694.120			−0.0334591
$756$		0			0
$757$	−19308.9	−	33444.0i	−0.927073	−	1.60574i	−0.788192	−	0.615429i	$-0.788983\pi$
$757$	−19308.9	−	33444.0i	−0.927073	−	1.60574i	−0.138881	−	0.990309i	$-0.544351\pi$
$758$	40372.0			1.93453
$759$		0			0
$760$	−245.555	+	141.771i	−0.0117200	+	0.00676656i
$761$	−9743.29	+	5625.29i	−0.464118	+	0.267959i	−0.713774	−	0.700376i	$-0.753016\pi$
$761$	−9743.29	+	5625.29i	−0.464118	+	0.267959i	0.249656	+	0.968335i	$0.419682\pi$
$762$		0			0
$763$	29105.3			1.38098
$764$	−8236.92	−	14266.8i	−0.390054	−	0.675593i
$765$		0			0
$766$	5325.60			0.251203
$767$	974.185	+	21710.6i	0.0458615	+	1.02207i
$768$		0			0
$769$		−	8776.63i		−	0.411565i	−0.978598	−	0.205783i	$-0.934026\pi$
$769$		−	8776.63i		−	0.411565i	0.978598	−	0.205783i	$-0.0659739\pi$
$770$	14090.9			0.659480
$771$		0			0
$772$	−21184.1	+	12230.6i	−0.987605	+	0.570194i
$773$	16628.3	+	9600.38i	0.773712	+	0.446703i	0.834197	−	0.551466i	$-0.185931\pi$
$773$	16628.3	+	9600.38i	0.773712	+	0.446703i	−0.0604849	+	0.998169i	$0.519265\pi$
$774$		0			0
$775$			4354.09i			0.201811i
$776$	−671.921			−0.0310832
$777$		0			0
$778$			22365.5i			1.03065i
$779$	−2193.88	+	3799.91i	−0.100904	+	0.174770i
$780$		0			0
$781$	21507.6	+	37252.2i	0.985406	+	1.70677i
$782$	1787.11	−	1031.79i	0.0817224	−	0.0471824i
$783$		0			0
$784$	2656.00	−	4600.32i	0.120991	−	0.209563i
$785$	−15830.4	+	9139.69i	−0.719760	+	0.415553i
$786$		0			0
$787$	21294.7	−	12294.5i	0.964517	−	0.556864i	0.0669566	−	0.997756i	$-0.478671\pi$
$787$	21294.7	−	12294.5i	0.964517	−	0.556864i	0.897560	+	0.440892i	$0.145338\pi$
$788$	3539.05	+	2043.27i	0.159992	+	0.0923712i
$789$		0			0
$790$	−4439.33	+	7689.14i	−0.199929	+	0.346288i
$791$	−24416.1	+	14096.7i	−1.09752	+	0.633653i
$792$		0			0
$793$	10696.7	−	20609.0i	0.479006	−	0.922883i
$794$	20788.3	+	36006.3i	0.929154	+	1.60934i
$795$		0			0
$796$	13120.2			0.584214
$797$	−12934.6	−	22403.3i	−0.574863	−	0.995691i	−0.996057	−	0.0887205i	$-0.971722\pi$
$797$	−12934.6	−	22403.3i	−0.574863	−	0.995691i	0.421194	−	0.906971i	$-0.361611\pi$
$798$		0			0
$799$			684.388i			0.0303028i
$800$	−22857.1	−	13196.6i	−1.01015	−	0.583211i
$801$		0			0
$802$	−6272.77	+	10864.8i	−0.276183	+	0.478364i
$803$	20015.4	−	34667.7i	0.879611	−	1.52353i
$804$		0			0
$805$	−5055.67	+	8756.68i	−0.221353	+	0.383394i
$806$	−8311.18	+	372.934i	−0.363212	+	0.0162978i
$807$		0			0
$808$	3290.20	+	1899.60i	0.143253	+	0.0827073i
$809$	−6856.33	−	11875.5i	−0.297967	−	0.516095i	0.677703	−	0.735335i	$-0.262975\pi$
$809$	−6856.33	−	11875.5i	−0.297967	−	0.516095i	−0.975671	+	0.219241i	$0.929642\pi$
$810$		0			0
$811$			13848.1i			0.599595i	0.954003	+	0.299797i	$0.0969190\pi$
$811$			13848.1i			0.599595i	−0.954003	+	0.299797i	$0.903081\pi$
$812$			28574.0i			1.23492i
$813$		0			0
$814$	26085.5	+	15060.5i	1.12321	+	0.648488i
$815$	4669.60	+	8087.98i	0.200698	+	0.347619i
$816$		0			0
$817$	−2164.83	−	1249.86i	−0.0927022	−	0.0535217i
$818$	−49951.2			−2.13509
$819$		0			0
$820$	−16406.8			−0.698720
$821$	−16728.7	−	9658.29i	−0.711125	−	0.410568i	0.100352	−	0.994952i	$-0.468003\pi$
$821$	−16728.7	−	9658.29i	−0.711125	−	0.410568i	−0.811478	+	0.584384i	$0.801336\pi$
$822$		0			0
$823$	6071.20	+	10515.6i	0.257143	+	0.445385i	0.965475	−	0.260494i	$-0.0838855\pi$
$823$	6071.20	+	10515.6i	0.257143	+	0.445385i	−0.708332	+	0.705879i	$0.750552\pi$
$824$	−1633.70	−	943.216i	−0.0690686	−	0.0398768i
$825$		0			0
$826$			29958.4i			1.26197i
$827$		−	42693.9i		−	1.79518i	−0.440835	−	0.897588i	$-0.645317\pi$
$827$		−	42693.9i		−	1.79518i	0.440835	−	0.897588i	$-0.354683\pi$
$828$		0			0
$829$	3307.74	+	5729.18i	0.138580	+	0.240027i	0.926959	−	0.375162i	$-0.122413\pi$
$829$	3307.74	+	5729.18i	0.138580	+	0.240027i	−0.788380	+	0.615189i	$0.789080\pi$
$830$	−12084.8	−	6977.18i	−0.505386	−	0.291785i
$831$		0			0
$832$	14073.8	−	27115.5i	0.586446	−	1.12988i
$833$	185.374	−	321.076i	0.00771046	−	0.0133549i
$834$		0			0
$835$	5300.88	−	9181.39i	0.219694	−	0.380521i
$836$	−2465.25	+	4269.94i	−0.101989	+	0.176650i
$837$		0			0
$838$	−1995.75	−	1152.25i	−0.0822698	−	0.0474985i
$839$			30267.8i			1.24548i	0.782428	+	0.622741i	$0.213981\pi$
$839$			30267.8i			1.24548i	−0.782428	+	0.622741i	$0.786019\pi$
$840$		0			0
$841$	−7693.69	−	13325.9i	−0.315457	−	0.546388i
$842$	15281.5			0.625457
$843$		0			0
$844$	20646.5	+	35760.8i	0.842041	+	1.45846i
$845$	949.388	+	10557.7i	0.0386508	+	0.429818i
$846$		0			0
$847$	9607.02	−	5546.61i	0.389730	−	0.225011i
$848$	11603.4	−	20097.6i	0.469884	−	0.813863i
$849$		0			0
$850$	−1351.66	−	780.381i	−0.0545430	−	0.0314904i
$851$	−18718.5	+	10807.1i	−0.754008	+	0.435327i
$852$		0			0
$853$	−32920.6	+	19006.7i	−1.32143	+	0.762928i	−0.983957	−	0.178407i	$-0.942906\pi$
$853$	−32920.6	+	19006.7i	−1.32143	+	0.762928i	−0.337474	+	0.941335i	$0.609572\pi$
$854$	16004.2	−	27720.1i	0.641279	−	1.11073i
$855$		0			0
$856$	−2140.25	+	1235.67i	−0.0854581	+	0.0493392i
$857$	21594.2	+	37402.2i	0.860728	+	1.49082i	0.871228	+	0.490879i	$0.163324\pi$
$857$	21594.2	+	37402.2i	0.860728	+	1.49082i	−0.0105002	+	0.999945i	$0.503342\pi$
$858$		0			0
$859$	−6630.09	+	11483.6i	−0.263348	+	0.456132i	−0.967129	−	0.254285i	$-0.918160\pi$
$859$	−6630.09	+	11483.6i	−0.263348	+	0.456132i	0.703782	+	0.710416i	$0.251493\pi$
$860$		−	9347.04i		−	0.370618i
$861$		0			0
$862$	−44830.6			−1.77139
$863$			18526.0i			0.730746i	0.930861	+	0.365373i	$0.119059\pi$
$863$			18526.0i			0.730746i	−0.930861	+	0.365373i	$0.880941\pi$
$864$		0			0
$865$	−12264.8	−	7081.10i	−0.482100	−	0.278340i
$866$	−19141.6	+	11051.4i	−0.751106	+	0.433651i
$867$		0			0
$868$	−6132.65			−0.239811
$869$			20058.1i			0.782996i
$870$		0			0
$871$	−9694.43	−	5031.73i	−0.377133	−	0.195745i
$872$	−9252.04			−0.359305
$873$		0			0
$874$	−3308.21	−	5729.99i	−0.128034	−	0.221762i
$875$	17045.4			0.658561
$876$		0			0
$877$	−20484.8	+	11826.9i	−0.788738	+	0.455378i	−0.839518	−	0.543332i	$-0.817163\pi$
$877$	−20484.8	+	11826.9i	−0.788738	+	0.455378i	0.0507799	+	0.998710i	$0.483829\pi$
$878$	22970.3	−	13261.9i	0.882927	−	0.509758i
$879$		0			0
$880$	11561.8			0.442897
$881$	8034.27	+	13915.8i	0.307243	+	0.532161i	0.977758	−	0.209735i	$-0.0672601\pi$
$881$	8034.27	+	13915.8i	0.307243	+	0.532161i	−0.670515	+	0.741896i	$0.733927\pi$
$882$		0			0
$883$	30283.3			1.15415			0.577075	−	0.816691i	$-0.304194\pi$
$883$	30283.3			1.15415			0.577075	+	0.816691i	$0.304194\pi$
$884$	734.640	−	1415.40i	0.0279509	−	0.0538520i
$885$		0			0
$886$			26998.4i			1.02373i
$887$	15006.7			0.568067			0.284034	−	0.958814i	$-0.408327\pi$
$887$	15006.7			0.568067			0.284034	+	0.958814i	$0.408327\pi$
$888$		0			0
$889$	24841.0	−	14342.0i	0.937168	−	0.541074i
$890$	6453.27	+	3725.80i	0.243050	+	0.140325i
$891$		0			0
$892$			54147.9i			2.03252i
$893$	2194.35			0.0822295
$894$		0			0
$895$			6446.37i			0.240758i
$896$	4884.66	−	8460.49i	0.182126	−	0.315452i
$897$		0			0
$898$	22572.1	+	39096.0i	0.838798	+	1.45284i
$899$	7393.20	−	4268.47i	0.274279	−	0.158355i
$900$		0			0
$901$	809.850	−	1402.70i	0.0299445	−	0.0518654i
$902$	−60028.5	+	34657.4i	−2.21589	+	1.27934i
$903$		0			0
$904$	7761.43	−	4481.06i	0.285555	−	0.164865i
$905$	17147.6	+	9900.17i	0.629840	+	0.363638i
$906$		0			0
$907$	7142.03	−	12370.4i	0.261463	−	0.452868i	−0.705168	−	0.709041i	$-0.749128\pi$
$907$	7142.03	−	12370.4i	0.261463	−	0.452868i	0.966631	+	0.256173i	$0.0824616\pi$
$908$	3519.05	−	2031.72i	0.128616	−	0.0742567i
$909$		0			0
$910$	655.028	+	14597.9i	0.0238615	+	0.531776i
$911$	−7540.95	−	13061.3i	−0.274251	−	0.475017i	0.695695	−	0.718338i	$-0.255097\pi$
$911$	−7540.95	−	13061.3i	−0.274251	−	0.475017i	−0.969946	+	0.243320i	$0.921763\pi$
$912$		0			0
$913$	−31524.7			−1.14273
$914$	−16519.6	−	28612.7i	−0.597832	−	1.03548i
$915$		0			0
$916$		−	8789.54i		−	0.317047i
$917$	−27979.2	−	16153.8i	−1.00758	−	0.581728i
$918$		0			0
$919$	12553.0	−	21742.4i	0.450582	−	0.780431i	−0.547840	−	0.836583i	$-0.684550\pi$
$919$	12553.0	−	21742.4i	0.450582	−	0.780431i	0.998422	+	0.0561523i	$0.0178832\pi$
$920$	1607.10	−	2783.58i	0.0575920	−	0.0997522i
$921$		0			0
$922$	−33379.7	+	57815.3i	−1.19230	+	2.06512i
$923$	−37592.9	+	24013.2i	−1.34061	+	0.856343i
$924$		0			0
$925$	14157.5	+	8173.84i	0.503239	+	0.290545i
$926$	−35832.8	−	62064.2i	−1.27164	−	2.20254i
$927$		0			0
$928$			51748.2i			1.83052i
$929$			44786.2i			1.58169i	0.612017	+	0.790844i	$0.290358\pi$
$929$			44786.2i			1.58169i	−0.612017	+	0.790844i	$0.709642\pi$
$930$		0			0
$931$	−1029.46	−	594.361i	−0.0362399	−	0.0209231i
$932$	15887.0	+	27517.0i	0.558363	+	0.967113i
$933$		0			0
$934$	−11251.9	−	6496.29i	−0.394190	−	0.227586i
$935$	806.951			0.0282247
$936$		0			0
$937$	50350.7			1.75548			0.877740	−	0.479138i	$-0.159051\pi$
$937$	50350.7			1.75548			0.877740	+	0.479138i	$0.159051\pi$
$938$	−13039.5	−	7528.36i	−0.453896	−	0.262057i
$939$		0			0
$940$	4102.57	+	7105.87i	0.142352	+	0.246562i
$941$	10299.0	+	5946.14i	0.356789	+	0.205992i	0.667671	−	0.744456i	$-0.267291\pi$
$941$	10299.0	+	5946.14i	0.356789	+	0.205992i	−0.310882	+	0.950448i	$0.600625\pi$
$942$		0			0
$943$		−	49739.1i		−	1.71763i
$944$			24581.5i			0.847519i
$945$		0			0
$946$	−19744.5	−	34198.5i	−0.678594	−	1.17536i
$947$	6876.57	+	3970.19i	0.235965	+	0.136234i	0.613321	−	0.789834i	$-0.289833\pi$
$947$	6876.57	+	3970.19i	0.235965	+	0.136234i	−0.377356	+	0.926068i	$0.623167\pi$
$948$		0			0
$949$	36845.6	+	19124.1i	1.26034	+	0.654155i
$950$	−2502.13	+	4333.81i	−0.0854524	+	0.148008i
$951$		0			0
$952$	142.800	−	247.336i	0.00486152	−	0.00842039i
$953$	−5556.35	+	9623.87i	−0.188864	+	0.327123i	−0.944872	−	0.327440i	$-0.893814\pi$
$953$	−5556.35	+	9623.87i	−0.188864	+	0.327123i	0.756008	+	0.654563i	$0.227147\pi$
$954$		0			0
$955$	7486.59	+	4322.38i	0.253676	+	0.146460i
$956$			16524.5i			0.559039i
$957$		0			0
$958$	−22472.9	−	38924.1i	−0.757897	−	1.31272i
$959$	15731.9			0.529728
$960$		0			0
$961$	−13979.4	−	24213.0i	−0.469249	−	0.812763i
$962$	−14389.8	+	27724.3i	−0.482272	+	0.929175i
$963$		0			0
$964$	−45384.5	+	26202.7i	−1.51632	+	0.875450i
$965$	6418.11	−	11116.5i	0.214100	−	0.370831i
$966$		0			0
$967$	23614.5	+	13633.8i	0.785307	+	0.453397i	0.838308	−	0.545197i	$-0.183545\pi$
$967$	23614.5	+	13633.8i	0.785307	+	0.453397i	−0.0530008	+	0.998594i	$0.516879\pi$
$968$	−3053.89	+	1763.16i	−0.101401	+	0.0585436i
$969$		0			0
$970$	2350.38	−	1356.99i	0.0778002	−	0.0449179i
$971$	2589.60	−	4485.33i	0.0855863	−	0.148240i	−0.820055	−	0.572285i	$-0.806057\pi$
$971$	2589.60	−	4485.33i	0.0855863	−	0.148240i	0.905641	+	0.424045i	$0.139390\pi$
$972$		0			0
$973$	25316.6	−	14616.5i	0.834134	−	0.481588i
$974$	−2989.74	−	5178.38i	−0.0983547	−	0.170355i
$975$		0			0
$976$	13131.8	−	22744.9i	0.430674	−	0.745949i
$977$		−	1148.38i		−	0.0376047i	−0.999823	−	0.0188024i	$-0.994015\pi$
$977$		−	1148.38i		−	0.0376047i	0.999823	−	0.0188024i	$-0.00598533\pi$
$978$		0			0
$979$	16834.2			0.549563
$980$		−	4444.90i		−	0.144885i
$981$		0			0
$982$	−56758.6	−	32769.6i	−1.84444	−	1.06489i
$983$	46109.2	−	26621.2i	1.49609	−	0.863767i	0.496098	−	0.868266i	$-0.334766\pi$
$983$	46109.2	−	26621.2i	1.49609	−	0.863767i	0.999990	+	0.00449948i	$0.00143223\pi$
$984$		0			0
$985$	−2144.44			−0.0693681
$986$			3060.14i			0.0988385i
$987$		0			0
$988$	−4538.19	−	2355.47i	−0.146133	−	0.0758476i
$989$	28336.6			0.911074
$990$		0			0
$991$	−25165.1	−	43587.2i	−0.806656	−	1.39717i	−0.915168	−	0.403074i	$-0.867942\pi$
$991$	−25165.1	−	43587.2i	−0.806656	−	1.39717i	0.108512	−	0.994095i	$-0.465392\pi$
$992$	−11106.4			−0.355471
$993$		0			0
$994$	−53253.9	+	30746.2i	−1.69931	+	0.981095i
$995$	−5962.53	+	3442.47i	−0.189975	+	0.109682i
$996$		0			0
$997$	11360.4			0.360872			0.180436	−	0.983587i	$-0.442249\pi$
$997$	11360.4			0.360872			0.180436	+	0.983587i	$0.442249\pi$
$998$	9705.73	+	16810.8i	0.307845	+	0.533204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.4.r.a.10.34		80
3.2	odd	2		117.4.r.a.49.7	yes	80
9.2	odd	6		117.4.l.a.88.34	yes	80
9.7	even	3		351.4.l.a.127.7		80
13.4	even	6		351.4.l.a.199.34		80
39.17	odd	6		117.4.l.a.4.7	✓	80
117.43	even	6	inner	351.4.r.a.316.34		80
117.56	odd	6		117.4.r.a.43.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.7	✓	80	39.17	odd	6
117.4.l.a.88.34	yes	80	9.2	odd	6
117.4.r.a.43.7	yes	80	117.56	odd	6
117.4.r.a.49.7	yes	80	3.2	odd	2
351.4.l.a.127.7		80	9.7	even	3
351.4.l.a.199.34		80	13.4	even	6
351.4.r.a.10.34		80	1.1	even	1	trivial
351.4.r.a.316.34		80	117.43	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	351.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.59109 + 2.07331i) q^{2} +(4.59727 + 7.96270i) q^{4} +(-4.17848 - 2.41245i) q^{5} -15.5822i q^{7} +4.95329i q^{8} +(-10.0035 - 17.3266i) q^{10} +(-39.1432 - 22.5993i) q^{11} +(21.5929 - 41.6022i) q^{13} +(32.3068 - 55.9571i) q^{14} +(26.5084 - 45.9139i) q^{16} +(1.85014 - 3.20453i) q^{17} +(-10.2746 - 5.93207i) q^{19} -44.3627i q^{20} +(-93.7110 - 162.312i) q^{22} +134.490 q^{23} +(-50.8602 - 88.0924i) q^{25} +(163.797 - 104.628i) q^{26} +(124.077 - 71.6356i) q^{28} +(-99.7201 + 172.720i) q^{29} +(-37.0698 - 21.4022i) q^{31} +(224.705 - 129.734i) q^{32} +(13.2880 - 7.67183i) q^{34} +(-37.5913 + 65.1100i) q^{35} +(-139.181 + 80.3560i) q^{37} +(-24.5981 - 42.6052i) q^{38} +(11.9496 - 20.6973i) q^{40} -369.833i q^{41} +210.696 q^{43} -415.580i q^{44} +(482.967 + 278.841i) q^{46} +(-160.177 + 92.4781i) q^{47} +100.195 q^{49} -421.797i q^{50} +(430.535 - 19.3187i) q^{52} +437.724 q^{53} +(109.039 + 188.862i) q^{55} +77.1833 q^{56} +(-716.207 + 413.502i) q^{58} +(-401.536 + 231.827i) q^{59} +495.381 q^{61} +(-88.7471 - 153.715i) q^{62} +651.781 q^{64} +(-190.589 + 121.742i) q^{65} -233.027i q^{67} +34.0223 q^{68} +(-269.987 + 155.877i) q^{70} +(-824.189 - 475.846i) q^{71} +885.664i q^{73} -666.413 q^{74} -109.085i q^{76} +(-352.147 + 609.937i) q^{77} +(-221.888 - 384.322i) q^{79} +(-221.530 + 127.900i) q^{80} +(766.781 - 1328.10i) q^{82} +(604.028 - 348.736i) q^{83} +(-15.4615 + 8.92672i) q^{85} +(756.628 + 436.839i) q^{86} +(111.941 - 193.888i) q^{88} +(-322.550 + 186.224i) q^{89} +(-648.255 - 336.466i) q^{91} +(618.289 + 1070.91i) q^{92} -766.944 q^{94} +(28.6216 + 49.5741i) q^{95} +135.651i q^{97} +(359.807 + 207.735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 3 q^{2} + 153 q^{4} - 10 q^{10} + 3 q^{11} - 13 q^{13} - 126 q^{14} - 551 q^{16} + 138 q^{17} - 96 q^{19} - 31 q^{22} - 654 q^{23} + 798 q^{25} - 510 q^{26} + 18 q^{28} - 201 q^{29} - 180 q^{31}+ \cdots + 6339 q^{98}+O(q^{100}) \) 80 * q + 3 * q^2 + 153 * q^4 - 10 * q^10 + 3 * q^11 - 13 * q^13 - 126 * q^14 - 551 * q^16 + 138 * q^17 - 96 * q^19 - 31 * q^22 - 654 * q^23 + 798 * q^25 - 510 * q^26 + 18 * q^28 - 201 * q^29 - 180 * q^31 - 117 * q^32 - 24 * q^34 - 297 * q^35 + 246 * q^37 + 768 * q^38 + 328 * q^40 + 166 * q^43 - 6 * q^46 + 372 * q^47 - 3226 * q^49 + 186 * q^52 + 2568 * q^53 - 127 * q^55 - 4596 * q^56 - 3 * q^58 + 531 * q^59 + 838 * q^61 - 135 * q^62 - 3178 * q^64 + 2337 * q^65 + 3900 * q^68 + 1005 * q^70 + 2598 * q^71 + 942 * q^74 + 1584 * q^77 - 260 * q^79 + 1332 * q^80 - 1273 * q^82 + 1194 * q^83 + 3936 * q^85 - 2910 * q^86 + 781 * q^88 + 1056 * q^89 + 537 * q^91 - 1056 * q^92 - 1078 * q^94 + 5292 * q^95 + 6339 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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