LMFDB - Embedded newform 76.5.h.a.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.h (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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} + \cdots + 90728724573 $ x^12 - 6x^11 + 631x^10 - 3100x^9 + 142264x^8 - 550522x^7 + 14083117x^6 - 40335478x^5 + 638031136x^4 - 1209472584x^3 + 12784623475x^2 - 12186518934*x + 90728724573
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.4
Root			$0.500000 - 4.96177i$ of defining polynomial
Character	$\chi$	$=$	76.65
Dual form			76.5.h.a.69.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.54702 + 2.04787i) q^{3} +(15.5891 - 27.0012i) q^{5} -2.67956 q^{7} +(-32.1124 - 55.6204i) q^{9} +O(q^{10})$	\(q+(3.54702 + 2.04787i) q^{3} +(15.5891 - 27.0012i) q^{5} -2.67956 q^{7} +(-32.1124 - 55.6204i) q^{9} +42.3332 q^{11} +(113.779 - 65.6905i) q^{13} +(110.590 - 63.8492i) q^{15} +(143.163 - 247.965i) q^{17} +(326.580 + 153.840i) q^{19} +(-9.50447 - 5.48741i) q^{21} +(-158.172 - 273.962i) q^{23} +(-173.542 - 300.584i) q^{25} -594.804i q^{27} +(-188.788 + 108.997i) q^{29} +475.836i q^{31} +(150.157 + 86.6931i) q^{33} +(-41.7721 + 72.3514i) q^{35} +1740.18i q^{37} +538.103 q^{39} +(-104.869 - 60.5462i) q^{41} +(-1237.98 + 2144.24i) q^{43} -2002.42 q^{45} +(168.749 + 292.282i) q^{47} -2393.82 q^{49} +(1015.60 - 586.359i) q^{51} +(-3656.19 + 2110.90i) q^{53} +(659.938 - 1143.05i) q^{55} +(843.340 + 1214.47i) q^{57} +(4911.88 + 2835.87i) q^{59} +(-1945.85 - 3370.31i) q^{61} +(86.0473 + 149.038i) q^{63} -4096.23i q^{65} +(2805.03 - 1619.49i) q^{67} -1295.67i q^{69} +(4050.68 + 2338.66i) q^{71} +(803.586 - 1391.85i) q^{73} -1421.57i q^{75} -113.435 q^{77} +(-2909.85 - 1680.00i) q^{79} +(-1383.02 + 2395.46i) q^{81} +6545.45 q^{83} +(-4463.57 - 7731.13i) q^{85} -892.849 q^{87} +(3179.74 - 1835.82i) q^{89} +(-304.879 + 176.022i) q^{91} +(-974.452 + 1687.80i) q^{93} +(9244.95 - 6419.80i) q^{95} +(4872.79 + 2813.31i) q^{97} +(-1359.42 - 2354.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9	$ 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9} + 6 q^{11} - 93 q^{13} - 741 q^{15} - 483 q^{17} - 533 q^{19} + 972 q^{21} + 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} - 1128 q^{35} - 2250 q^{39} - 1692 q^{41} - 63 q^{43} + 7976 q^{45} - 3471 q^{47} + 420 q^{49} + 6741 q^{51} - 3771 q^{53} - 2014 q^{55} + 7617 q^{57} - 9594 q^{59} + 1229 q^{61} + 1514 q^{63} + 7590 q^{67} + 963 q^{71} - 2838 q^{73} - 15408 q^{77} + 11073 q^{79} + 2086 q^{81} - 14202 q^{83} + 9455 q^{85} - 39510 q^{87} + 6525 q^{89} - 7686 q^{91} - 5316 q^{93} + 1521 q^{95} - 34110 q^{97} + 13220 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9 + 6 * q^11 - 93 * q^13 - 741 * q^15 - 483 * q^17 - 533 * q^19 + 972 * q^21 + 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 - 1128 * q^35 - 2250 * q^39 - 1692 * q^41 - 63 * q^43 + 7976 * q^45 - 3471 * q^47 + 420 * q^49 + 6741 * q^51 - 3771 * q^53 - 2014 * q^55 + 7617 * q^57 - 9594 * q^59 + 1229 * q^61 + 1514 * q^63 + 7590 * q^67 + 963 * q^71 - 2838 * q^73 - 15408 * q^77 + 11073 * q^79 + 2086 * q^81 - 14202 * q^83 + 9455 * q^85 - 39510 * q^87 + 6525 * q^89 - 7686 * q^91 - 5316 * q^93 + 1521 * q^95 - 34110 * q^97 + 13220 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	3.54702	+	2.04787i	0.394114	+	0.227542i	0.683941	−	0.729537i	$-0.260265\pi$
$3$	3.54702	+	2.04787i	0.394114	+	0.227542i	−0.289827	+	0.957079i	$0.593598\pi$
$4$		0			0
$5$	15.5891	−	27.0012i	0.623566	−	1.08005i	−0.365251	−	0.930909i	$-0.619017\pi$
$5$	15.5891	−	27.0012i	0.623566	−	1.08005i	0.988816	−	0.149138i	$-0.0476499\pi$
$6$		0			0
$7$	−2.67956			−0.0546850			−0.0273425	−	0.999626i	$-0.508704\pi$
$7$	−2.67956			−0.0546850			−0.0273425	+	0.999626i	$0.508704\pi$
$8$		0			0
$9$	−32.1124	−	55.6204i	−0.396450	−	0.686671i
$10$		0			0
$11$	42.3332			0.349861			0.174931	−	0.984581i	$-0.444030\pi$
$11$	42.3332			0.349861			0.174931	+	0.984581i	$0.444030\pi$
$12$		0			0
$13$	113.779	−	65.6905i	0.673250	−	0.388701i	−0.124057	−	0.992275i	$-0.539591\pi$
$13$	113.779	−	65.6905i	0.673250	−	0.388701i	0.797307	+	0.603574i	$0.206257\pi$
$14$		0			0
$15$	110.590	−	63.8492i	0.491511	−	0.283774i
$16$		0			0
$17$	143.163	−	247.965i	0.495373	−	0.858011i	−0.504613	−	0.863346i	$-0.668365\pi$
$17$	143.163	−	247.965i	0.495373	−	0.858011i	0.999986	+	0.00533450i	$0.00169803\pi$
$18$		0			0
$19$	326.580	+	153.840i	0.904653	+	0.426149i
$19$	326.580	+	153.840i	0.904653	+	0.426149i
$20$		0			0
$21$	−9.50447	−	5.48741i	−0.0215521	−	0.0124431i
$22$		0			0
$23$	−158.172	−	273.962i	−0.299002	−	0.517887i	0.676906	−	0.736070i	$-0.263321\pi$
$23$	−158.172	−	273.962i	−0.299002	−	0.517887i	−0.975908	+	0.218183i	$0.929987\pi$
$24$		0			0
$25$	−173.542	−	300.584i	−0.277668	−	0.480935i
$26$		0			0
$27$		−	594.804i		−	0.815918i
$28$		0			0
$29$	−188.788	+	108.997i	−0.224481	+	0.129604i	−0.608023	−	0.793919i	$-0.708037\pi$
$29$	−188.788	+	108.997i	−0.224481	+	0.129604i	0.383542	+	0.923523i	$0.374704\pi$
$30$		0			0
$31$			475.836i			0.495147i	0.968869	+	0.247573i	$0.0796331\pi$
$31$			475.836i			0.495147i	−0.968869	+	0.247573i	$0.920367\pi$
$32$		0			0
$33$	150.157	+	86.6931i	0.137885	+	0.0796080i
$34$		0			0
$35$	−41.7721	+	72.3514i	−0.0340997	+	0.0590623i
$36$		0			0
$37$			1740.18i			1.27114i	0.772045	+	0.635568i	$0.219234\pi$
$37$			1740.18i			1.27114i	−0.772045	+	0.635568i	$0.780766\pi$
$38$		0			0
$39$	538.103			0.353783
$40$		0			0
$41$	−104.869	−	60.5462i	−0.0623849	−	0.0360180i	0.468483	−	0.883472i	$-0.344801\pi$
$41$	−104.869	−	60.5462i	−0.0623849	−	0.0360180i	−0.530868	+	0.847454i	$0.678134\pi$
$42$		0			0
$43$	−1237.98	+	2144.24i	−0.669540	+	1.15968i	0.308493	+	0.951227i	$0.400175\pi$
$43$	−1237.98	+	2144.24i	−0.669540	+	1.15968i	−0.978033	+	0.208451i	$0.933158\pi$
$44$		0			0
$45$	−2002.42			−0.988849
$46$		0			0
$47$	168.749	+	292.282i	0.0763917	+	0.132314i	0.901691	−	0.432382i	$-0.142327\pi$
$47$	168.749	+	292.282i	0.0763917	+	0.132314i	−0.825299	+	0.564696i	$0.808993\pi$
$48$		0			0
$49$	−2393.82			−0.997010
$50$		0			0
$51$	1015.60	−	586.359i	0.390466	−	0.225436i
$52$		0			0
$53$	−3656.19	+	2110.90i	−1.30160	+	0.751477i	−0.980678	−	0.195630i	$-0.937325\pi$
$53$	−3656.19	+	2110.90i	−1.30160	+	0.751477i	−0.320919	+	0.947107i	$0.603992\pi$
$54$		0			0
$55$	659.938	−	1143.05i	0.218161	−	0.377867i
$56$		0			0
$57$	843.340	+	1214.47i	0.259569	+	0.373797i
$58$		0			0
$59$	4911.88	+	2835.87i	1.41105	+	0.814672i	0.995488	−	0.0948915i	$-0.0302504\pi$
$59$	4911.88	+	2835.87i	1.41105	+	0.814672i	0.415565	+	0.909563i	$0.363584\pi$
$60$		0			0
$61$	−1945.85	−	3370.31i	−0.522937	−	0.905754i	−0.999644	−	0.0266915i	$-0.991503\pi$
$61$	−1945.85	−	3370.31i	−0.522937	−	0.905754i	0.476706	−	0.879063i	$-0.341831\pi$
$62$		0			0
$63$	86.0473	+	149.038i	0.0216798	+	0.0375506i
$64$		0			0
$65$		−	4096.23i		−	0.969522i
$66$		0			0
$67$	2805.03	−	1619.49i	0.624868	−	0.360768i	−0.153894	−	0.988087i	$-0.549181\pi$
$67$	2805.03	−	1619.49i	0.624868	−	0.360768i	0.778762	+	0.627320i	$0.215848\pi$
$68$		0			0
$69$		−	1295.67i		−	0.272142i
$70$		0			0
$71$	4050.68	+	2338.66i	0.803546	+	0.463928i	0.844710	−	0.535225i	$-0.179773\pi$
$71$	4050.68	+	2338.66i	0.803546	+	0.463928i	−0.0411635	+	0.999152i	$0.513106\pi$
$72$		0			0
$73$	803.586	−	1391.85i	0.150795	−	0.261184i	−0.780725	−	0.624875i	$-0.785150\pi$
$73$	803.586	−	1391.85i	0.150795	−	0.261184i	0.931520	+	0.363690i	$0.118483\pi$
$74$		0			0
$75$		−	1421.57i		−	0.252724i
$76$		0			0
$77$	−113.435			−0.0191322
$78$		0			0
$79$	−2909.85	−	1680.00i	−0.466247	−	0.269188i	0.248420	−	0.968652i	$-0.420089\pi$
$79$	−2909.85	−	1680.00i	−0.466247	−	0.269188i	−0.714667	+	0.699464i	$0.753422\pi$
$80$		0			0
$81$	−1383.02	+	2395.46i	−0.210794	+	0.365107i
$82$		0			0
$83$	6545.45			0.950131			0.475065	−	0.879950i	$-0.342424\pi$
$83$	6545.45			0.950131			0.475065	+	0.879950i	$0.342424\pi$
$84$		0			0
$85$	−4463.57	−	7731.13i	−0.617795	−	1.07005i
$86$		0			0
$87$	−892.849			−0.117961
$88$		0			0
$89$	3179.74	−	1835.82i	0.401431	−	0.231766i	−0.285670	−	0.958328i	$-0.592216\pi$
$89$	3179.74	−	1835.82i	0.401431	−	0.231766i	0.687101	+	0.726562i	$0.258883\pi$
$90$		0			0
$91$	−304.879	+	176.022i	−0.0368166	+	0.0212561i
$92$		0			0
$93$	−974.452	+	1687.80i	−0.112666	+	0.195144i
$94$		0			0
$95$	9244.95	−	6419.80i	1.02437	−	0.711336i
$96$		0			0
$97$	4872.79	+	2813.31i	0.517886	+	0.299002i	0.736069	−	0.676906i	$-0.236680\pi$
$97$	4872.79	+	2813.31i	0.517886	+	0.299002i	−0.218183	+	0.975908i	$0.570013\pi$
$98$		0			0
$99$	−1359.42	−	2354.59i	−0.138702	−	0.240240i
$100$		0			0
$101$	2277.54	+	3944.81i	0.223266	+	0.386708i	0.955798	−	0.294025i	$-0.0949948\pi$
$101$	2277.54	+	3944.81i	0.223266	+	0.386708i	−0.732532	+	0.680733i	$0.761661\pi$
$102$		0			0
$103$		−	3792.04i		−	0.357436i	−0.983900	−	0.178718i	$-0.942805\pi$
$103$		−	3792.04i		−	0.357436i	0.983900	−	0.178718i	$-0.0571950\pi$
$104$		0			0
$105$	−296.333	+	171.088i	−0.0268783	+	0.0155182i
$106$		0			0
$107$			973.573i			0.0850357i	0.999096	+	0.0425178i	$0.0135379\pi$
$107$			973.573i			0.0850357i	−0.999096	+	0.0425178i	$0.986462\pi$
$108$		0			0
$109$	947.163	+	546.845i	0.0797208	+	0.0460268i	0.539331	−	0.842094i	$-0.318677\pi$
$109$	947.163	+	546.845i	0.0797208	+	0.0460268i	−0.459610	+	0.888121i	$0.652011\pi$
$110$		0			0
$111$	−3563.68	+	6172.47i	−0.289236	+	0.500972i
$112$		0			0
$113$			8095.59i			0.634003i	0.948425	+	0.317002i	$0.102676\pi$
$113$			8095.59i			0.634003i	−0.948425	+	0.317002i	$0.897324\pi$
$114$		0			0
$115$	−9863.08			−0.745790
$116$		0			0
$117$	−7307.45	−	4218.96i	−0.533819	−	0.308201i
$118$		0			0
$119$	−383.614	+	664.439i	−0.0270895	+	0.0469203i
$120$		0			0
$121$	−12848.9			−0.877597
$122$		0			0
$123$	−247.982	−	429.517i	−0.0163912	−	0.0283903i
$124$		0			0
$125$	8664.91			0.554555
$126$		0			0
$127$	−16925.5	+	9771.95i	−1.04938	+	0.605862i	−0.922477	−	0.386053i	$-0.873838\pi$
$127$	−16925.5	+	9771.95i	−1.04938	+	0.605862i	−0.126907	+	0.991915i	$0.540505\pi$
$128$		0			0
$129$	−8782.28	+	5070.45i	−0.527750	+	0.304696i
$130$		0			0
$131$	−4157.45	+	7200.92i	−0.242262	+	0.419610i	−0.961358	−	0.275301i	$-0.911223\pi$
$131$	−4157.45	+	7200.92i	−0.242262	+	0.419610i	0.719096	+	0.694910i	$0.244556\pi$
$132$		0			0
$133$	−875.091	−	412.224i	−0.0494709	−	0.0233040i
$134$		0			0
$135$	−16060.4	−	9272.49i	−0.881230	−	0.508778i
$136$		0			0
$137$	15897.5	+	27535.3i	0.847008	+	1.46706i	0.883866	+	0.467740i	$0.154932\pi$
$137$	15897.5	+	27535.3i	0.847008	+	1.46706i	−0.0368587	+	0.999320i	$0.511735\pi$
$138$		0			0
$139$	14915.2	+	25833.8i	0.771967	+	1.33709i	0.936483	+	0.350712i	$0.114060\pi$
$139$	14915.2	+	25833.8i	0.771967	+	1.33709i	−0.164516	+	0.986374i	$0.552606\pi$
$140$		0			0
$141$			1382.31i			0.0695292i
$142$		0			0
$143$	4816.64	−	2780.89i	0.235544	−	0.135991i
$144$		0			0
$145$			6796.68i			0.323267i
$146$		0			0
$147$	−8490.93	−	4902.24i	−0.392935	−	0.226861i
$148$		0			0
$149$	17689.6	−	30639.3i	0.796793	−	1.38009i	−0.124901	−	0.992169i	$-0.539861\pi$
$149$	17689.6	−	30639.3i	0.796793	−	1.38009i	0.921694	−	0.387917i	$-0.126805\pi$
$150$		0			0
$151$			13999.5i			0.613987i	0.951712	+	0.306994i	$0.0993230\pi$
$151$			13999.5i			0.613987i	−0.951712	+	0.306994i	$0.900677\pi$
$152$		0			0
$153$	−18389.2			−0.785562
$154$		0			0
$155$	12848.1	+	7417.87i	0.534782	+	0.308756i
$156$		0			0
$157$	17868.1	−	30948.5i	0.724902	−	1.25557i	−0.234112	−	0.972210i	$-0.575218\pi$
$157$	17868.1	−	30948.5i	0.724902	−	1.25557i	0.959014	−	0.283358i	$-0.0914485\pi$
$158$		0			0
$159$	−17291.4			−0.683969
$160$		0			0
$161$	423.833	+	734.099i	0.0163509	+	0.0283206i
$162$		0			0
$163$	−30641.7			−1.15329			−0.576644	−	0.816995i	$-0.695638\pi$
$163$	−30641.7			−1.15329			−0.576644	+	0.816995i	$0.695638\pi$
$164$		0			0
$165$	4681.63	−	2702.94i	0.171961	−	0.0992816i
$166$		0			0
$167$	35977.1	−	20771.4i	1.29001	−	0.744788i	0.311355	−	0.950294i	$-0.399217\pi$
$167$	35977.1	−	20771.4i	1.29001	−	0.744788i	0.978656	+	0.205506i	$0.0658840\pi$
$168$		0			0
$169$	−5650.02	+	9786.13i	−0.197823	+	0.342640i
$170$		0			0
$171$	−1930.63	−	23104.6i	−0.0660249	−	0.790146i
$172$		0			0
$173$	−27433.2	−	15838.6i	−0.916611	−	0.529205i	−0.0340586	−	0.999420i	$-0.510843\pi$
$173$	−27433.2	−	15838.6i	−0.916611	−	0.529205i	−0.882552	+	0.470214i	$0.844177\pi$
$174$		0			0
$175$	465.018	+	805.434i	0.0151843	+	0.0262999i
$176$		0			0
$177$	11615.0	+	20117.8i	0.370743	+	0.642146i
$178$		0			0
$179$		−	28590.1i		−	0.892298i	−0.894959	−	0.446149i	$-0.852795\pi$
$179$		−	28590.1i		−	0.892298i	0.894959	−	0.446149i	$-0.147205\pi$
$180$		0			0
$181$	32286.9	−	18640.9i	0.985529	−	0.568996i	0.0815944	−	0.996666i	$-0.473999\pi$
$181$	32286.9	−	18640.9i	0.985529	−	0.568996i	0.903935	+	0.427670i	$0.140665\pi$
$182$		0			0
$183$		−	15939.4i		−	0.475960i
$184$		0			0
$185$	46987.0	+	27128.0i	1.37289	+	0.792636i
$186$		0			0
$187$	6060.54	−	10497.2i	0.173312	−	0.300185i
$188$		0			0
$189$			1593.82i			0.0446184i
$190$		0			0
$191$	−8555.08			−0.234508			−0.117254	−	0.993102i	$-0.537409\pi$
$191$	−8555.08			−0.234508			−0.117254	+	0.993102i	$0.537409\pi$
$192$		0			0
$193$	20694.2	+	11947.8i	0.555563	+	0.320754i	0.751363	−	0.659890i	$-0.229397\pi$
$193$	20694.2	+	11947.8i	0.555563	+	0.320754i	−0.195800	+	0.980644i	$0.562730\pi$
$194$		0			0
$195$	8388.57	−	14529.4i	0.220607	−	0.382102i
$196$		0			0
$197$	19842.4			0.511284			0.255642	−	0.966772i	$-0.417713\pi$
$197$	19842.4			0.511284			0.255642	+	0.966772i	$0.417713\pi$
$198$		0			0
$199$	−14300.1	−	24768.5i	−0.361104	−	0.625451i	0.627039	−	0.778988i	$-0.284267\pi$
$199$	−14300.1	−	24768.5i	−0.361104	−	0.625451i	−0.988143	+	0.153537i	$0.950933\pi$
$200$		0			0
$201$	13266.0			0.328359
$202$		0			0
$203$	505.870	−	292.064i	0.0122757	−	0.00708739i
$204$		0			0
$205$	−3269.64	+	1887.73i	−0.0778022	+	0.0449191i
$206$		0			0
$207$	−10158.6	+	17595.2i	−0.237079	+	0.410633i
$208$		0			0
$209$	13825.2	+	6512.54i	0.316503	+	0.149093i
$210$		0			0
$211$	−74772.9	−	43170.2i	−1.67950	−	0.969659i	−0.961981	−	0.273118i	$-0.911945\pi$
$211$	−74772.9	−	43170.2i	−1.67950	−	0.969659i	−0.717517	−	0.696541i	$-0.754722\pi$
$212$		0			0
$213$	9578.56	+	16590.5i	0.211126	+	0.365680i
$214$		0			0
$215$	38598.1	+	66853.8i	0.835004	+	1.44627i
$216$		0			0
$217$		−	1275.03i		−	0.0270771i
$218$		0			0
$219$	5700.67	−	3291.29i	0.118861	−	0.0686242i
$220$		0			0
$221$		−	37617.7i		−	0.770208i
$222$		0			0
$223$	−16078.0	−	9282.64i	−0.323313	−	0.186665i	0.329556	−	0.944136i	$-0.393101\pi$
$223$	−16078.0	−	9282.64i	−0.323313	−	0.186665i	−0.652868	+	0.757472i	$0.726434\pi$
$224$		0			0
$225$	−11145.7	+	19305.0i	−0.220163	+	0.381333i
$226$		0			0
$227$			43957.1i			0.853055i	0.904474	+	0.426528i	$0.140263\pi$
$227$			43957.1i			0.853055i	−0.904474	+	0.426528i	$0.859737\pi$
$228$		0			0
$229$	−93023.8			−1.77387			−0.886937	−	0.461890i	$-0.847172\pi$
$229$	−93023.8			−1.77387			−0.886937	+	0.461890i	$0.847172\pi$
$230$		0			0
$231$	−402.355	−	232.300i	−0.00754024	−	0.00435336i
$232$		0			0
$233$	12284.1	−	21276.6i	0.226272	−	0.391914i	−0.730429	−	0.682989i	$-0.760680\pi$
$233$	12284.1	−	21276.6i	0.226272	−	0.391914i	0.956700	+	0.291075i	$0.0940130\pi$
$234$		0			0
$235$	10522.6			0.190541
$236$		0			0
$237$	−6880.87	−	11918.0i	−0.122503	−	0.212181i
$238$		0			0
$239$	−61076.4			−1.06925			−0.534623	−	0.845091i	$-0.679546\pi$
$239$	−61076.4			−1.06925			−0.534623	+	0.845091i	$0.679546\pi$
$240$		0			0
$241$	24641.4	−	14226.7i	0.424260	−	0.244947i	−0.272638	−	0.962117i	$-0.587896\pi$
$241$	24641.4	−	14226.7i	0.424260	−	0.244947i	0.696898	+	0.717170i	$0.254563\pi$
$242$		0			0
$243$	−51535.6	+	29754.1i	−0.872760	+	0.503888i
$244$		0			0
$245$	−37317.6	+	64636.0i	−0.621701	+	1.07682i
$246$		0			0
$247$	47263.8	−	3949.38i	0.774702	−	0.0647344i
$248$		0			0
$249$	23216.9	+	13404.3i	0.374459	+	0.216194i
$250$		0			0
$251$	33418.7	+	57882.9i	0.530447	+	0.918762i	0.999369	+	0.0355218i	$0.0113093\pi$
$251$	33418.7	+	57882.9i	0.530447	+	0.918762i	−0.468922	+	0.883240i	$0.655357\pi$
$252$		0			0
$253$	−6695.94	−	11597.7i	−0.104609	−	0.181189i
$254$		0			0
$255$		−	36563.3i		−	0.562296i
$256$		0			0
$257$	100520.	−	58035.5i	1.52191	−	0.878673i	0.522241	−	0.852798i	$-0.325096\pi$
$257$	100520.	−	58035.5i	1.52191	−	0.878673i	0.999665	−	0.0258749i	$-0.00823716\pi$
$258$		0			0
$259$		−	4662.93i		−	0.0695120i
$260$		0			0
$261$	12124.9	+	7000.32i	0.177991	+	0.102763i
$262$		0			0
$263$	−43974.4	+	76165.9i	−0.635753	+	1.10116i	0.350602	+	0.936525i	$0.385977\pi$
$263$	−43974.4	+	76165.9i	−0.635753	+	1.10116i	−0.986355	+	0.164633i	$0.947356\pi$
$264$		0			0
$265$			131628.i			1.87438i
$266$		0			0
$267$	15038.1			0.210946
$268$		0			0
$269$	−106194.	−	61311.2i	−1.46756	−	0.847296i	−0.468219	−	0.883613i	$-0.655104\pi$
$269$	−106194.	−	61311.2i	−1.46756	−	0.847296i	−0.999340	+	0.0363169i	$0.988437\pi$
$270$		0			0
$271$	−22643.2	+	39219.1i	−0.308318	+	0.534022i	−0.977995	−	0.208631i	$-0.933099\pi$
$271$	−22643.2	+	39219.1i	−0.308318	+	0.534022i	0.669677	+	0.742653i	$0.266433\pi$
$272$		0			0
$273$	−1441.88			−0.0193466
$274$		0			0
$275$	−7346.61	−	12724.7i	−0.0971453	−	0.168261i
$276$		0			0
$277$	−90121.7			−1.17454			−0.587272	−	0.809389i	$-0.699798\pi$
$277$	−90121.7			−1.17454			−0.587272	+	0.809389i	$0.699798\pi$
$278$		0			0
$279$	26466.2	−	15280.2i	0.340003	−	0.196301i
$280$		0			0
$281$	−87904.2	+	50751.5i	−1.11326	+	0.642742i	−0.939672	−	0.342077i	$-0.888870\pi$
$281$	−87904.2	+	50751.5i	−1.11326	+	0.642742i	−0.173589	+	0.984818i	$0.555536\pi$
$282$		0			0
$283$	−959.420	+	1661.76i	−0.0119794	+	0.0207490i	−0.871953	−	0.489590i	$-0.837147\pi$
$283$	−959.420	+	1661.76i	−0.0119794	+	0.0207490i	0.859974	+	0.510339i	$0.170480\pi$
$284$		0			0
$285$	45939.0	−	3838.68i	0.565577	−	0.0472599i
$286$		0			0
$287$	281.003	+	162.237i	0.00341152	+	0.00196964i
$288$		0			0
$289$	769.316	+	1332.49i	0.00921104	+	0.0159540i
$290$		0			0
$291$	11522.6	+	19957.7i	0.136071	+	0.235681i
$292$		0			0
$293$		−	111146.i		−	1.29466i	−0.762208	−	0.647332i	$-0.775885\pi$
$293$		−	111146.i		−	1.29466i	0.762208	−	0.647332i	$-0.224115\pi$
$294$		0			0
$295$	153144.	−	88417.6i	1.75977	−	1.01600i
$296$		0			0
$297$		−	25180.0i		−	0.285458i
$298$		0			0
$299$	−35993.4	−	20780.8i	−0.402607	−	0.232445i
$300$		0			0
$301$	3317.24	−	5745.64i	0.0366138	−	0.0634169i
$302$		0			0
$303$			18656.4i			0.203209i
$304$		0			0
$305$	−121337.			−1.30434
$306$		0			0
$307$	94905.2	+	54793.5i	1.00696	+	0.581370i	0.910301	−	0.413948i	$-0.135850\pi$
$307$	94905.2	+	54793.5i	1.00696	+	0.581370i	0.0966613	+	0.995317i	$0.469184\pi$
$308$		0			0
$309$	7765.62	−	13450.5i	0.0813316	−	0.140870i
$310$		0			0
$311$	94945.0			0.981637			0.490819	−	0.871262i	$-0.336698\pi$
$311$	94945.0			0.981637			0.490819	+	0.871262i	$0.336698\pi$
$312$		0			0
$313$	10819.3	+	18739.5i	0.110436	+	0.191280i	0.915946	−	0.401302i	$-0.131442\pi$
$313$	10819.3	+	18739.5i	0.110436	+	0.191280i	−0.805510	+	0.592582i	$0.798109\pi$
$314$		0			0
$315$	5365.61			0.0540752
$316$		0			0
$317$	118433.	−	68377.5i	1.17857	−	0.680448i	0.222887	−	0.974844i	$-0.428452\pi$
$317$	118433.	−	68377.5i	1.17857	−	0.680448i	0.955683	+	0.294396i	$0.0951186\pi$
$318$		0			0
$319$	−7992.02	+	4614.20i	−0.0785372	+	0.0453435i
$320$		0			0
$321$	−1993.76	+	3453.29i	−0.0193491	+	0.0335137i
$322$		0			0
$323$	84901.0	−	58956.3i	0.813782	−	0.565099i
$324$		0			0
$325$	−39491.0	−	22800.2i	−0.373880	−	0.215860i
$326$		0			0
$327$	2239.74	+	3879.34i	0.0209460	+	0.0362796i
$328$		0			0
$329$	−452.174	−	783.189i	−0.00417748	−	0.00723561i
$330$		0			0
$331$		−	201597.i		−	1.84004i	−0.391869	−	0.920021i	$-0.628171\pi$
$331$		−	201597.i		−	1.84004i	0.391869	−	0.920021i	$-0.371829\pi$
$332$		0			0
$333$	96789.7	−	55881.6i	0.872852	−	0.503941i
$334$		0			0
$335$		−	100986.i		−	0.899850i
$336$		0			0
$337$	178761.	+	103208.i	1.57403	+	0.908766i	0.995668	+	0.0929845i	$0.0296407\pi$
$337$	178761.	+	103208.i	1.57403	+	0.908766i	0.578361	+	0.815781i	$0.303693\pi$
$338$		0			0
$339$	−16578.7	+	28715.2i	−0.144262	+	0.249869i
$340$		0			0
$341$			20143.7i			0.173233i
$342$		0			0
$343$	12848.0			0.109206
$344$		0			0
$345$	−34984.5	−	20198.3i	−0.293926	−	0.169698i
$346$		0			0
$347$	−610.820	+	1057.97i	−0.00507288	+	0.00878648i	−0.868551	−	0.495600i	$-0.834948\pi$
$347$	−610.820	+	1057.97i	−0.00507288	+	0.00878648i	0.863478	+	0.504387i	$0.168281\pi$
$348$		0			0
$349$	−205690.			−1.68874			−0.844368	−	0.535763i	$-0.820024\pi$
$349$	−205690.			−1.68874			−0.844368	+	0.535763i	$0.820024\pi$
$350$		0			0
$351$	−39073.0	−	67676.4i	−0.317148	−	0.549317i
$352$		0			0
$353$	−236605.			−1.89878			−0.949389	−	0.314101i	$-0.898297\pi$
$353$	−236605.			−1.89878			−0.949389	+	0.314101i	$0.898297\pi$
$354$		0			0
$355$	126293.	−	72915.4i	1.00213	−	0.578578i
$356$		0			0
$357$	−2721.37	+	1571.19i	−0.0213526	+	0.0123280i
$358$		0			0
$359$	−54382.0	+	94192.4i	−0.421955	+	0.730848i	−0.996131	−	0.0878842i	$-0.971989\pi$
$359$	−54382.0	+	94192.4i	−0.421955	+	0.730848i	0.574175	+	0.818732i	$0.305323\pi$
$360$		0			0
$361$	82987.6	+	100482.i	0.636793	+	0.771034i
$362$		0			0
$363$	−45575.3	−	26312.9i	−0.345873	−	0.199690i
$364$		0			0
$365$	−25054.4	−	43395.5i	−0.188061	−	0.325731i
$366$		0			0
$367$	93469.1	+	161893.i	0.693962	+	1.20198i	0.970529	+	0.240983i	$0.0774699\pi$
$367$	93469.1	+	161893.i	0.693962	+	1.20198i	−0.276567	+	0.960995i	$0.589197\pi$
$368$		0			0
$369$			7777.14i			0.0571172i
$370$		0			0
$371$	9796.98	−	5656.29i	0.0711778	−	0.0410945i
$372$		0			0
$373$		−	53955.4i		−	0.387808i	−0.981020	−	0.193904i	$-0.937885\pi$
$373$		−	53955.4i		−	0.387808i	0.981020	−	0.193904i	$-0.0621151\pi$
$374$		0			0
$375$	30734.6	+	17744.7i	0.218557	+	0.126184i
$376$		0			0
$377$	−14320.1	+	24803.2i	−0.100754	+	0.174512i
$378$		0			0
$379$			222631.i			1.54991i	0.632014	+	0.774957i	$0.282229\pi$
$379$			222631.i			1.54991i	−0.632014	+	0.774957i	$0.717771\pi$
$380$		0			0
$381$	−80046.9			−0.551435
$382$		0			0
$383$	28982.0	+	16732.7i	0.197574	+	0.114070i	0.595524	−	0.803338i	$-0.296945\pi$
$383$	28982.0	+	16732.7i	0.197574	+	0.114070i	−0.397949	+	0.917407i	$0.630278\pi$
$384$		0			0
$385$	−1768.35	+	3062.87i	−0.0119301	+	0.0206636i
$386$		0			0
$387$	159018.			1.06176
$388$		0			0
$389$	−41708.6	−	72241.3i	−0.275630	−	0.477405i	0.694664	−	0.719334i	$-0.255553\pi$
$389$	−41708.6	−	72241.3i	−0.275630	−	0.477405i	−0.970294	+	0.241930i	$0.922220\pi$
$390$		0			0
$391$	−90577.5			−0.592471
$392$		0			0
$393$	−29493.1	+	17027.9i	−0.190957	+	0.110249i
$394$		0			0
$395$	−90724.1	+	52379.6i	−0.581471	+	0.335713i
$396$		0			0
$397$	2130.79	−	3690.63i	0.0135194	−	0.0234164i	−0.859187	−	0.511662i	$-0.829030\pi$
$397$	2130.79	−	3690.63i	0.0135194	−	0.0234164i	0.872706	+	0.488246i	$0.162363\pi$
$398$		0			0
$399$	−2259.78	−	3254.24i	−0.0141945	−	0.0204411i
$400$		0			0
$401$	−81965.1	−	47322.6i	−0.509730	−	0.294293i	0.222993	−	0.974820i	$-0.428417\pi$
$401$	−81965.1	−	47322.6i	−0.509730	−	0.294293i	−0.732723	+	0.680527i	$0.761751\pi$
$402$		0			0
$403$	31257.9	+	54140.2i	0.192464	+	0.333357i
$404$		0			0
$405$	43120.2	+	74686.5i	0.262888	+	0.455336i
$406$		0			0
$407$			73667.6i			0.444721i
$408$		0			0
$409$	−3842.38	+	2218.40i	−0.0229696	+	0.0132615i	−0.511441	−	0.859318i	$-0.670888\pi$
$409$	−3842.38	+	2218.40i	−0.0229696	+	0.0132615i	0.488471	+	0.872580i	$0.337555\pi$
$410$		0			0
$411$			130224.i			0.770918i
$412$		0			0
$413$	−13161.7	−	7598.90i	−0.0771634	−	0.0445503i
$414$		0			0
$415$	102038.	−	176735.i	0.592469	−	1.02619i
$416$		0			0
$417$			122178.i			0.702618i
$418$		0			0
$419$	−316042.			−1.80019			−0.900093	−	0.435698i	$-0.856502\pi$
$419$	−316042.			−1.80019			−0.900093	+	0.435698i	$0.856502\pi$
$420$		0			0
$421$	76625.6	+	44239.8i	0.432324	+	0.249603i	0.700336	−	0.713813i	$-0.253033\pi$
$421$	76625.6	+	44239.8i	0.432324	+	0.249603i	−0.268012	+	0.963416i	$0.586367\pi$
$422$		0			0
$423$	10837.9	−	18771.8i	0.0605710	−	0.104912i
$424$		0			0
$425$	−99379.3			−0.550197
$426$		0			0
$427$	5214.03	+	9030.96i	0.0285968	+	0.0495311i
$428$		0			0
$429$	22779.6			0.123775
$430$		0			0
$431$	−279779.	+	161530.i	−1.50612	+	0.869560i	−0.506147	+	0.862447i	$0.668931\pi$
$431$	−279779.	+	161530.i	−1.50612	+	0.869560i	−0.999975	+	0.00711255i	$0.997736\pi$
$432$		0			0
$433$	77804.0	−	44920.2i	0.414979	−	0.239588i	−0.277948	−	0.960596i	$-0.589654\pi$
$433$	77804.0	−	44920.2i	0.414979	−	0.239588i	0.692927	+	0.721008i	$0.256321\pi$
$434$		0			0
$435$	−13918.7	+	24108.0i	−0.0735566	+	0.127404i
$436$		0			0
$437$	−9509.49	−	113804.i	−0.0497960	−	0.595928i
$438$		0			0
$439$	−314840.	−	181773.i	−1.63366	−	0.943192i	−0.982952	−	0.183862i	$-0.941140\pi$
$439$	−314840.	−	181773.i	−1.63366	−	0.943192i	−0.650705	−	0.759331i	$-0.725527\pi$
$440$		0			0
$441$	76871.4	+	133145.i	0.395264	+	0.684618i
$442$		0			0
$443$	102342.	+	177262.i	0.521492	+	0.903250i	0.999688	+	0.0249967i	$0.00795754\pi$
$443$	102342.	+	177262.i	0.521492	+	0.903250i	−0.478196	+	0.878253i	$0.658709\pi$
$444$		0			0
$445$		−	114476.i		−	0.578086i
$446$		0			0
$447$	125491.	−	72452.2i	0.628054	−	0.362607i
$448$		0			0
$449$		−	14073.0i		−	0.0698063i	−0.999391	−	0.0349031i	$-0.988888\pi$
$449$		−	14073.0i		−	0.0698063i	0.999391	−	0.0349031i	$-0.0111123\pi$
$450$		0			0
$451$	−4439.45	−	2563.12i	−0.0218261	−	0.0126013i
$452$		0			0
$453$	−28669.3	+	49656.6i	−0.139708	+	0.241981i
$454$		0			0
$455$			10976.1i			0.0530183i
$456$		0			0
$457$	209656.			1.00387			0.501933	−	0.864906i	$-0.332622\pi$
$457$	209656.			1.00387			0.501933	+	0.864906i	$0.332622\pi$
$458$		0			0
$459$	−147491.	−	85153.9i	−0.700067	−	0.404184i
$460$		0			0
$461$	91669.7	−	158777.i	0.431344	−	0.747110i	−0.565645	−	0.824649i	$-0.691373\pi$
$461$	91669.7	−	158777.i	0.431344	−	0.747110i	0.996989	+	0.0775385i	$0.0247061\pi$
$462$		0			0
$463$	−129586.			−0.604501			−0.302250	−	0.953229i	$-0.597738\pi$
$463$	−129586.			−0.604501			−0.302250	+	0.953229i	$0.597738\pi$
$464$		0			0
$465$	30381.7	+	52622.7i	0.140510	+	0.243370i
$466$		0			0
$467$	180073.			0.825686			0.412843	−	0.910802i	$-0.364536\pi$
$467$	180073.			0.825686			0.412843	+	0.910802i	$0.364536\pi$
$468$		0			0
$469$	−7516.26	+	4339.52i	−0.0341709	+	0.0197286i
$470$		0			0
$471$	126757.	−	73183.3i	0.571388	−	0.329891i
$472$		0			0
$473$	−52407.7	+	90772.7i	−0.234246	+	0.405726i
$474$		0			0
$475$	−10433.6	−	124862.i	−0.0462429	−	0.553407i
$476$		0			0
$477$	234818.	+	135572.i	1.03204	+	0.595846i
$478$		0			0
$479$	98408.8	+	170449.i	0.428907	+	0.742889i	0.996776	−	0.0802301i	$-0.0255655\pi$
$479$	98408.8	+	170449.i	0.428907	+	0.742889i	−0.567869	+	0.823119i	$0.692232\pi$
$480$		0			0
$481$	114314.	+	197997.i	0.494092	+	0.855792i
$482$		0			0
$483$			3471.82i			0.0148821i
$484$		0			0
$485$	151925.	−	87714.1i	0.645872	−	0.372894i
$486$		0			0
$487$		−	170934.i		−	0.720728i	−0.932812	−	0.360364i	$-0.882652\pi$
$487$		−	170934.i		−	0.720728i	0.932812	−	0.360364i	$-0.117348\pi$
$488$		0			0
$489$	−108687.	−	62750.4i	−0.454527	−	0.262421i
$490$		0			0
$491$	69546.2	−	120458.i	0.288476	−	0.499656i	−0.684970	−	0.728571i	$-0.740185\pi$
$491$	69546.2	−	120458.i	0.288476	−	0.499656i	0.973446	+	0.228916i	$0.0735180\pi$
$492$		0			0
$493$			62417.3i			0.256809i
$494$		0			0
$495$	−84768.9			−0.345960
$496$		0			0
$497$	−10854.0	−	6266.58i	−0.0439419	−	0.0253699i
$498$		0			0
$499$	131082.	−	227041.i	0.526432	−	0.911807i	−0.473094	−	0.881012i	$-0.656863\pi$
$499$	131082.	−	227041.i	0.526432	−	0.911807i	0.999526	−	0.0307946i	$-0.00980377\pi$
$500$		0			0
$501$	170149.			0.677881
$502$		0			0
$503$	−165915.	−	287373.i	−0.655767	−	1.13582i	−0.981701	−	0.190430i	$-0.939012\pi$
$503$	−165915.	−	287373.i	−0.655767	−	1.13582i	0.325933	−	0.945393i	$-0.394322\pi$
$504$		0			0
$505$	142019.			0.556884
$506$		0			0
$507$	−40081.5	+	23141.1i	−0.155929	+	0.0900259i
$508$		0			0
$509$	−84260.9	+	48648.0i	−0.325230	+	0.187772i	−0.653721	−	0.756735i	$-0.726793\pi$
$509$	−84260.9	+	48648.0i	−0.325230	+	0.187772i	0.328491	+	0.944507i	$0.393460\pi$
$510$		0			0
$511$	−2153.26	+	3729.55i	−0.00824621	+	0.0142829i
$512$		0			0
$513$	91504.7	−	194251.i	0.347703	−	0.738123i
$514$		0			0
$515$	−102390.	−	59114.6i	−0.386048	−	0.222885i
$516$		0			0
$517$	7143.70	+	12373.3i	0.0267265	+	0.0462917i
$518$		0			0
$519$	−64870.9	−	112360.i	−0.240832	−	0.417134i
$520$		0			0
$521$		−	147455.i		−	0.543231i	−0.962406	−	0.271615i	$-0.912442\pi$
$521$		−	147455.i		−	0.543231i	0.962406	−	0.271615i	$-0.0875578\pi$
$522$		0			0
$523$	−304145.	+	175598.i	−1.11193	+	0.641973i	−0.939329	−	0.343019i	$-0.888551\pi$
$523$	−304145.	+	175598.i	−1.11193	+	0.641973i	−0.172601	+	0.984992i	$0.555217\pi$
$524$		0			0
$525$			3809.19i			0.0138202i
$526$		0			0
$527$	117991.	+	68122.0i	0.424841	+	0.245282i
$528$		0			0
$529$	89883.6	−	155683.i	0.321195	−	0.556326i
$530$		0			0
$531$		−	364267.i		−	1.29191i
$532$		0			0
$533$	−15909.2			−0.0560009
$534$		0			0
$535$	26287.6	+	15177.2i	0.0918425	+	0.0530253i
$536$		0			0
$537$	58548.9	−	101410.i	0.203035	−	0.351667i
$538$		0			0
$539$	−101338.			−0.348815
$540$		0			0
$541$	41571.0	+	72003.1i	0.142035	+	0.246012i	0.928263	−	0.371925i	$-0.121302\pi$
$541$	41571.0	+	72003.1i	0.142035	+	0.246012i	−0.786228	+	0.617937i	$0.787969\pi$
$542$		0			0
$543$	152697.			0.517881
$544$		0			0
$545$	29530.9	−	17049.7i	0.0994223	−	0.0574015i
$546$		0			0
$547$	260352.	−	150314.i	0.870135	−	0.502373i	0.00274192	−	0.999996i	$-0.499127\pi$
$547$	260352.	−	150314.i	0.870135	−	0.502373i	0.867393	+	0.497624i	$0.165794\pi$
$548$		0			0
$549$	−124972.	+	216458.i	−0.414637	+	0.718172i
$550$		0			0
$551$	−78422.5	+	6553.02i	−0.258308	+	0.0215843i
$552$		0			0
$553$	7797.12	+	4501.67i	0.0254967	+	0.0147205i
$554$		0			0
$555$	111109.	+	192447.i	0.360715	+	0.624777i
$556$		0			0
$557$	79597.5	+	137867.i	0.256560	+	0.444375i	0.965318	−	0.261077i	$-0.0840775\pi$
$557$	79597.5	+	137867.i	0.256560	+	0.444375i	−0.708758	+	0.705452i	$0.750744\pi$
$558$		0			0
$559$			325294.i			1.04100i
$560$		0			0
$561$	42993.8	−	24822.5i	0.136609	−	0.0788713i
$562$		0			0
$563$			325284.i			1.02623i	0.858319	+	0.513117i	$0.171509\pi$
$563$			325284.i			1.02623i	−0.858319	+	0.513117i	$0.828491\pi$
$564$		0			0
$565$	218590.	+	126203.i	0.684753	+	0.395343i
$566$		0			0
$567$	3705.89	−	6418.80i	0.0115273	−	0.0199658i
$568$		0			0
$569$		−	489736.i		−	1.51265i	−0.654199	−	0.756323i	$-0.726994\pi$
$569$		−	489736.i		−	1.51265i	0.654199	−	0.756323i	$-0.273006\pi$
$570$		0			0
$571$	−307676.			−0.943672			−0.471836	−	0.881686i	$-0.656409\pi$
$571$	−307676.			−0.943672			−0.471836	+	0.881686i	$0.656409\pi$
$572$		0			0
$573$	−30345.1	−	17519.7i	−0.0924227	−	0.0533603i
$574$		0			0
$575$	−54899.2	+	95088.2i	−0.166047	+	0.287601i
$576$		0			0
$577$	−20529.7			−0.0616638			−0.0308319	−	0.999525i	$-0.509816\pi$
$577$	−20529.7			−0.0616638			−0.0308319	+	0.999525i	$0.509816\pi$
$578$		0			0
$579$	48935.1	+	84758.0i	0.145970	+	0.252827i
$580$		0			0
$581$	−17538.9			−0.0519579
$582$		0			0
$583$	−154778.	+	89361.2i	−0.455378	+	0.262913i
$584$		0			0
$585$	−227834.	+	131540.i	−0.665743	+	0.384367i
$586$		0			0
$587$	−18925.0	+	32779.0i	−0.0549236	+	0.0951305i	−0.892180	−	0.451680i	$-0.850825\pi$
$587$	−18925.0	+	32779.0i	−0.0549236	+	0.0951305i	0.837256	+	0.546811i	$0.184158\pi$
$588$		0			0
$589$	−73202.6	+	155398.i	−0.211006	+	0.447936i
$590$		0			0
$591$	70381.5	+	40634.8i	0.201504	+	0.116338i
$592$		0			0
$593$	−153015.	−	265029.i	−0.435134	−	0.753675i	0.562172	−	0.827020i	$-0.309966\pi$
$593$	−153015.	−	265029.i	−0.435134	−	0.753675i	−0.997307	+	0.0733454i	$0.976632\pi$
$594$		0			0
$595$	11960.4	+	20716.0i	0.0337841	+	0.0585158i
$596$		0			0
$597$		−	117139.i		−	0.328665i
$598$		0			0
$599$	−121787.	+	70313.5i	−0.339427	+	0.195968i	−0.660018	−	0.751249i	$-0.729452\pi$
$599$	−121787.	+	70313.5i	−0.339427	+	0.195968i	0.320592	+	0.947217i	$0.396118\pi$
$600$		0			0
$601$			210748.i			0.583464i	0.956500	+	0.291732i	$0.0942315\pi$
$601$			210748.i			0.583464i	−0.956500	+	0.291732i	$0.905768\pi$
$602$		0			0
$603$	−180153.	−	104011.i	−0.495458	−	0.286053i
$604$		0			0
$605$	−200303.	+	346935.i	−0.547239	+	0.947846i
$606$		0			0
$607$			432873.i			1.17485i	0.809278	+	0.587426i	$0.199859\pi$
$607$			432873.i			1.17485i	−0.809278	+	0.587426i	$0.800141\pi$
$608$		0			0
$609$	2392.44			0.00645071
$610$		0			0
$611$	38400.3	+	22170.4i	0.102861	+	0.0593871i
$612$		0			0
$613$	−358892.	+	621619.i	−0.955087	+	1.65426i	−0.220918	+	0.975292i	$0.570905\pi$
$613$	−358892.	+	621619.i	−0.955087	+	1.65426i	−0.734169	+	0.678967i	$0.762428\pi$
$614$		0			0
$615$	−15463.3			−0.0408839
$616$		0			0
$617$	−83115.0	−	143959.i	−0.218328	−	0.378155i	0.735969	−	0.677015i	$-0.236727\pi$
$617$	−83115.0	−	143959.i	−0.218328	−	0.378155i	−0.954297	+	0.298860i	$0.903394\pi$
$618$		0			0
$619$	−475284.			−1.24043			−0.620214	−	0.784433i	$-0.712954\pi$
$619$	−475284.			−1.24043			−0.620214	+	0.784433i	$0.712954\pi$
$620$		0			0
$621$	−162954.	+	94081.6i	−0.422554	+	0.243961i
$622$		0			0
$623$	−8520.30	+	4919.20i	−0.0219523	+	0.0126741i
$624$		0			0
$625$	243543.	−	421828.i	0.623469	−	1.07988i
$626$		0			0
$627$	35701.3	+	51412.3i	0.0908132	+	0.130777i
$628$		0			0
$629$	431505.	+	249130.i	1.09065	+	0.629686i
$630$		0			0
$631$	−235600.	−	408071.i	−0.591720	−	1.02489i	−0.994001	−	0.109372i	$-0.965116\pi$
$631$	−235600.	−	408071.i	−0.591720	−	1.02489i	0.402281	−	0.915516i	$-0.368217\pi$
$632$		0			0
$633$	−176814.	−	306251.i	−0.441275	−	0.764311i
$634$		0			0
$635$			609345.i			1.51118i
$636$		0			0
$637$	−272367.	+	157251.i	−0.671237	+	0.387539i
$638$		0			0
$639$		−	300400.i		−	0.735696i
$640$		0			0
$641$	−172675.	−	99693.7i	−0.420254	−	0.242634i	0.274932	−	0.961464i	$-0.411345\pi$
$641$	−172675.	−	99693.7i	−0.420254	−	0.242634i	−0.695186	+	0.718830i	$0.744678\pi$
$642$		0			0
$643$	205975.	−	356759.i	0.498187	−	0.862885i	−0.501811	−	0.864977i	$-0.667333\pi$
$643$	205975.	−	356759.i	0.498187	−	0.862885i	0.999998	+	0.00209261i	$0.000666100\pi$
$644$		0			0
$645$			316176.i			0.759993i
$646$		0			0
$647$	438545.			1.04762			0.523812	−	0.851834i	$-0.324509\pi$
$647$	438545.			1.04762			0.523812	+	0.851834i	$0.324509\pi$
$648$		0			0
$649$	207936.	+	120052.i	0.493673	+	0.285022i
$650$		0			0
$651$	2611.11	−	4522.57i	0.00616116	−	0.0106714i
$652$		0			0
$653$	282897.			0.663440			0.331720	−	0.943378i	$-0.392371\pi$
$653$	282897.			0.663440			0.331720	+	0.943378i	$0.392371\pi$
$654$		0			0
$655$	129622.	+	224512.i	0.302132	+	0.523308i
$656$		0			0
$657$	−103220.			−0.239130
$658$		0			0
$659$	612072.	−	353380.i	1.40939	−	0.813712i	0.414061	−	0.910249i	$-0.364110\pi$
$659$	612072.	−	353380.i	1.40939	−	0.813712i	0.995329	+	0.0965371i	$0.0307766\pi$
$660$		0			0
$661$	−213537.	+	123285.i	−0.488730	+	0.282169i	−0.724048	−	0.689750i	$-0.757720\pi$
$661$	−213537.	+	123285.i	−0.488730	+	0.282169i	0.235317	+	0.971919i	$0.424387\pi$
$662$		0			0
$663$	77036.4	−	133431.i	0.175254	−	0.303549i
$664$		0			0
$665$	−24772.4	+	17202.3i	−0.0560177	+	0.0388994i
$666$		0			0
$667$	59722.2	+	34480.6i	0.134241	+	0.0775039i
$668$		0			0
$669$	−38019.4	−	65851.5i	−0.0849479	−	0.147134i
$670$		0			0
$671$	−82374.1	−	142676.i	−0.182956	−	0.316888i
$672$		0			0
$673$		−	717726.i		−	1.58463i	−0.610110	−	0.792316i	$-0.708875\pi$
$673$		−	717726.i		−	1.58463i	0.610110	−	0.792316i	$-0.291125\pi$
$674$		0			0
$675$	−178789.	+	103224.i	−0.392404	+	0.226554i
$676$		0			0
$677$			3440.63i			0.00750690i	0.999993	+	0.00375345i	$0.00119476\pi$
$677$			3440.63i			0.00750690i	−0.999993	+	0.00375345i	$0.998805\pi$
$678$		0			0
$679$	−13057.0	−	7538.43i	−0.0283206	−	0.0163509i
$680$		0			0
$681$	−90018.6	+	155917.i	−0.194106	+	0.336201i
$682$		0			0
$683$		−	399217.i		−	0.855792i	−0.903828	−	0.427896i	$-0.859255\pi$
$683$		−	399217.i		−	0.855792i	0.903828	−	0.427896i	$-0.140745\pi$
$684$		0			0
$685$	991312.			2.11266
$686$		0			0
$687$	−329957.	−	190501.i	−0.699108	−	0.403630i
$688$		0			0
$689$	−277332.	+	480353.i	−0.584200	+	1.01186i
$690$		0			0
$691$	−523284.			−1.09593			−0.547963	−	0.836503i	$-0.684596\pi$
$691$	−523284.			−1.09593			−0.547963	+	0.836503i	$0.684596\pi$
$692$		0			0
$693$	3642.66	+	6309.27i	0.00758494	+	0.0131375i
$694$		0			0
$695$	930059.			1.92549
$696$		0			0
$697$	−30026.7	+	17335.9i	−0.0618076	+	0.0356847i
$698$		0			0
$699$	87143.6	−	50312.4i	0.178353	−	0.102972i
$700$		0			0
$701$	188003.	−	325630.i	0.382585	−	0.662657i	−0.608846	−	0.793289i	$-0.708367\pi$
$701$	188003.	−	325630.i	0.382585	−	0.662657i	0.991431	+	0.130632i	$0.0417005\pi$
$702$		0			0
$703$	−267710.	+	568309.i	−0.541694	+	1.14994i
$704$		0			0
$705$	37324.0	+	21549.0i	0.0750948	+	0.0433560i
$706$		0			0
$707$	−6102.81	−	10570.4i	−0.0122093	−	0.0211471i
$708$		0			0
$709$	−443869.	−	768803.i	−0.883003	−	1.52941i	−0.847986	−	0.530019i	$-0.822185\pi$
$709$	−443869.	−	768803.i	−0.883003	−	1.52941i	−0.0350172	−	0.999387i	$-0.511149\pi$
$710$		0			0
$711$			215796.i			0.426878i
$712$		0			0
$713$	130361.	−	75264.0i	0.256430	−	0.148050i
$714$		0			0
$715$		−	173407.i		−	0.339198i
$716$		0			0
$717$	−216639.	−	125077.i	−0.421404	−	0.243298i
$718$		0			0
$719$	−3549.67	+	6148.21i	−0.00686642	+	0.0118930i	−0.869438	−	0.494042i	$-0.835519\pi$
$719$	−3549.67	+	6148.21i	−0.00686642	+	0.0118930i	0.862572	+	0.505935i	$0.168852\pi$
$720$		0			0
$721$			10161.0i			0.0195464i
$722$		0			0
$723$	116538.			0.222942
$724$		0			0
$725$	65525.6	+	37831.2i	0.124662	+	0.0719738i
$726$		0			0
$727$	401282.	−	695041.i	0.759243	−	1.31505i	−0.183994	−	0.982927i	$-0.558903\pi$
$727$	401282.	−	695041.i	0.759243	−	1.31505i	0.943237	−	0.332120i	$-0.107764\pi$
$728$		0			0
$729$	−19680.9			−0.0370331
$730$		0			0
$731$	354465.	+	613952.i	0.663344	+	1.14895i
$732$		0			0
$733$	−407403.			−0.758257			−0.379128	−	0.925344i	$-0.623776\pi$
$733$	−407403.			−0.758257			−0.379128	+	0.925344i	$0.623776\pi$
$734$		0			0
$735$	−264733.	+	152843.i	−0.490041	+	0.282926i
$736$		0			0
$737$	118746.	−	68558.1i	0.218617	−	0.126219i
$738$		0			0
$739$	417909.	−	723839.i	0.765231	−	1.32542i	−0.174894	−	0.984587i	$-0.555958\pi$
$739$	417909.	−	723839.i	0.765231	−	1.32542i	0.940125	−	0.340831i	$-0.110708\pi$
$740$		0			0
$741$	175734.	+	82781.8i	0.320050	+	0.150764i
$742$		0			0
$743$	615115.	+	355137.i	1.11424	+	0.643307i	0.939924	−	0.341383i	$-0.110895\pi$
$743$	615115.	+	355137.i	1.11424	+	0.643307i	0.174316	+	0.984690i	$0.444229\pi$
$744$		0			0
$745$	−551531.	−	955280.i	−0.993706	−	1.72115i
$746$		0			0
$747$	−210190.	−	364060.i	−0.376679	−	0.652427i
$748$		0			0
$749$		−	2608.75i		−	0.00465017i
$750$		0			0
$751$	−49411.3	+	28527.6i	−0.0876085	+	0.0505808i	−0.543164	−	0.839626i	$-0.682774\pi$
$751$	−49411.3	+	28527.6i	−0.0876085	+	0.0505808i	0.455556	+	0.890207i	$0.349441\pi$
$752$		0			0
$753$			273749.i			0.482795i
$754$		0			0
$755$	378004.	+	218241.i	0.663135	+	0.382861i
$756$		0			0
$757$	−184006.	+	318708.i	−0.321100	+	0.556162i	−0.980715	−	0.195441i	$-0.937386\pi$
$757$	−184006.	+	318708.i	−0.321100	+	0.556162i	0.659615	+	0.751604i	$0.270719\pi$
$758$		0			0
$759$		−	54849.8i		−	0.0952119i
$760$		0			0
$761$	216648.			0.374097			0.187049	−	0.982351i	$-0.440108\pi$
$761$	216648.			0.374097			0.187049	+	0.982351i	$0.440108\pi$
$762$		0			0
$763$	−2537.98	−	1465.31i	−0.00435953	−	0.00251698i
$764$		0			0
$765$	−286672.	+	496531.i	−0.489849	+	0.848444i
$766$		0			0
$767$	745159.			1.26666
$768$		0			0
$769$	72005.9	+	124718.i	0.121763	+	0.210900i	0.920463	−	0.390830i	$-0.127812\pi$
$769$	72005.9	+	124718.i	0.121763	+	0.210900i	−0.798700	+	0.601729i	$0.794479\pi$
$770$		0			0
$771$	475397.			0.799738
$772$		0			0
$773$	386420.	−	223100.i	0.646697	−	0.373371i	−0.140492	−	0.990082i	$-0.544869\pi$
$773$	386420.	−	223100.i	0.646697	−	0.373371i	0.787190	+	0.616711i	$0.211535\pi$
$774$		0			0
$775$	143029.	−	82577.7i	0.238133	−	0.137486i
$776$		0			0
$777$	9549.10	−	16539.5i	0.0158169	−	0.0273956i
$778$		0			0
$779$	−24933.7	−	35906.2i	−0.0410877	−	0.0591691i
$780$		0			0
$781$	171478.	+	99003.0i	0.281130	+	0.162310i
$782$		0			0
$783$	64831.9	+	112292.i	0.105746	+	0.183158i
$784$		0			0
$785$	−557097.	−	964921.i	−0.904048	−	1.56586i
$786$		0			0
$787$			766710.i			1.23789i	0.785435	+	0.618944i	$0.212439\pi$
$787$			766710.i			1.23789i	−0.785435	+	0.618944i	$0.787561\pi$
$788$		0			0
$789$	−311957.	+	180108.i	−0.501118	+	0.289321i
$790$		0			0
$791$		−	21692.6i		−	0.0346704i
$792$		0			0
$793$	−442795.	−	255648.i	−0.704135	−	0.406533i
$794$		0			0
$795$	−269558.	+	466889.i	−0.426500	+	0.738719i
$796$		0			0
$797$		−	367354.i		−	0.578320i	−0.957281	−	0.289160i	$-0.906624\pi$
$797$		−	367354.i		−	0.578320i	0.957281	−	0.289160i	$-0.0933760\pi$
$798$		0			0
$799$	96634.5			0.151370
$800$		0			0
$801$	−204218.	−	117905.i	−0.318295	−	0.183767i
$802$		0			0
$803$	34018.4	−	58921.6i	0.0527573	−	0.0913783i
$804$		0			0
$805$	26428.7			0.0407835
$806$		0			0
$807$	−251115.	−	434944.i	−0.385590	−	0.667861i
$808$		0			0
$809$	−76993.0			−0.117640			−0.0588199	−	0.998269i	$-0.518734\pi$
$809$	−76993.0			−0.117640			−0.0588199	+	0.998269i	$0.518734\pi$
$810$		0			0
$811$	32488.6	−	18757.3i	0.0493958	−	0.0285187i	−0.475099	−	0.879932i	$-0.657588\pi$
$811$	32488.6	−	18757.3i	0.0493958	−	0.0285187i	0.524495	+	0.851414i	$0.324254\pi$
$812$		0			0
$813$	−160632.	+	92740.7i	−0.243024	+	0.140310i
$814$		0			0
$815$	−477678.	+	827363.i	−0.719151	+	1.24561i
$816$		0			0
$817$	−734169.	+	509816.i	−1.09990	+	0.763781i
$818$		0			0
$819$	19580.8	+	11305.0i	0.0291919	+	0.0168539i
$820$		0			0
$821$	−193430.	−	335030.i	−0.286970	−	0.497047i	0.686115	−	0.727493i	$-0.259315\pi$
$821$	−193430.	−	335030.i	−0.286970	−	0.497047i	−0.973085	+	0.230446i	$0.925981\pi$
$822$		0			0
$823$	−32063.3	−	55535.3i	−0.0473379	−	0.0819916i	0.841386	−	0.540435i	$-0.181740\pi$
$823$	−32063.3	−	55535.3i	−0.0473379	−	0.0819916i	−0.888723	+	0.458444i	$0.848407\pi$
$824$		0			0
$825$		−	60179.7i		−	0.0884183i
$826$		0			0
$827$	−733365.	+	423408.i	−1.07228	+	0.619082i	−0.928804	−	0.370571i	$-0.879162\pi$
$827$	−733365.	+	423408.i	−1.07228	+	0.619082i	−0.143478	+	0.989653i	$0.545829\pi$
$828$		0			0
$829$			1.00726e6i			1.46566i	0.680413	+	0.732829i	$0.261800\pi$
$829$			1.00726e6i			1.46566i	−0.680413	+	0.732829i	$0.738200\pi$
$830$		0			0
$831$	−319663.	−	184558.i	−0.462904	−	0.267258i
$832$		0			0
$833$	−342706.	+	593584.i	−0.493892	+	0.855445i
$834$		0			0
$835$		−	1.29523e6i		−	1.85770i
$836$		0			0
$837$	283029.			0.403999
$838$		0			0
$839$	453943.	+	262084.i	0.644878	+	0.372321i	0.786491	−	0.617602i	$-0.211896\pi$
$839$	453943.	+	262084.i	0.644878	+	0.372321i	−0.141613	+	0.989922i	$0.545229\pi$
$840$		0			0
$841$	−329880.	+	571369.i	−0.466406	+	0.807838i
$842$		0			0
$843$	−415731.			−0.585002
$844$		0			0
$845$	176158.	+	305115.i	0.246711	+	0.427316i
$846$		0			0
$847$	34429.4			0.0479914
$848$		0			0
$849$	−6806.17	+	3929.54i	−0.00944250	+	0.00545163i
$850$		0			0
$851$	476745.	−	275249.i	0.658305	−	0.380073i
$852$		0			0
$853$	124659.	−	215915.i	0.171327	−	0.296747i	−0.767557	−	0.640980i	$-0.778528\pi$
$853$	124659.	−	215915.i	0.171327	−	0.296747i	0.938884	+	0.344234i	$0.111861\pi$
$854$		0			0
$855$	−653950.	−	308052.i	−0.894565	−	0.421398i
$856$		0			0
$857$	364453.	+	210417.i	0.496227	+	0.286497i	0.727154	−	0.686474i	$-0.240843\pi$
$857$	364453.	+	210417.i	0.496227	+	0.286497i	−0.230927	+	0.972971i	$0.574176\pi$
$858$		0			0
$859$	668834.	+	1.15845e6i	0.906426	+	1.56998i	0.818992	+	0.573805i	$0.194533\pi$
$859$	668834.	+	1.15845e6i	0.906426	+	1.56998i	0.0874335	+	0.996170i	$0.472133\pi$
$860$		0			0
$861$	664.483	+	1150.92i	0.000896350	+	0.00155252i
$862$		0			0
$863$			1.05678e6i			1.41894i	0.704734	+	0.709472i	$0.251066\pi$
$863$			1.05678e6i			1.41894i	−0.704734	+	0.709472i	$0.748934\pi$
$864$		0			0
$865$	−855321.	+	493820.i	−1.14313	+	0.659989i
$866$		0			0
$867$			6301.85i			0.00838358i
$868$		0			0
$869$	−123183.	−	71119.9i	−0.163122	−	0.0941785i
$870$		0			0
$871$	212770.	−	368528.i	0.280462	−	0.485774i
$872$		0			0
$873$		−	361369.i		−	0.474157i
$874$		0			0
$875$	−23218.2			−0.0303258
$876$		0			0
$877$	443505.	+	256058.i	0.576633	+	0.332919i	0.759794	−	0.650164i	$-0.225300\pi$
$877$	443505.	+	256058.i	0.576633	+	0.332919i	−0.183161	+	0.983083i	$0.558633\pi$
$878$		0			0
$879$	227612.	−	394236.i	0.294590	−	0.510244i
$880$		0			0
$881$	692838.			0.892647			0.446323	−	0.894872i	$-0.352733\pi$
$881$	692838.			0.892647			0.446323	+	0.894872i	$0.352733\pi$
$882$		0			0
$883$	437281.	+	757394.i	0.560841	+	0.971405i	0.997423	+	0.0717406i	$0.0228554\pi$
$883$	437281.	+	757394.i	0.560841	+	0.971405i	−0.436583	+	0.899664i	$0.643811\pi$
$884$		0			0
$885$	724273.			0.924731
$886$		0			0
$887$	−1.16648e6	+	673468.i	−1.48262	+	0.855992i	−0.999805	−	0.0197298i	$-0.993719\pi$
$887$	−1.16648e6	+	673468.i	−1.48262	+	0.855992i	−0.482816	+	0.875722i	$0.660386\pi$
$888$		0			0
$889$	45353.0	−	26184.6i	0.0573855	−	0.0331315i
$890$		0			0
$891$	−58547.8	+	101408.i	−0.0737488	+	0.127737i
$892$		0			0
$893$	10145.4	+	121414.i	0.0127223	+	0.152253i
$894$		0			0
$895$	−771967.	−	445695.i	−0.963723	−	0.556406i
$896$		0			0
$897$	−85113.0	−	147420.i	−0.105782	−	0.183219i
$898$		0			0
$899$	−51864.7	−	89832.3i	−0.0641730	−	0.111151i
$900$		0			0
$901$			1.20881e6i			1.48905i
$902$		0			0
$903$	23532.7	−	13586.6i	0.0288600	−	0.0166623i
$904$		0			0
$905$		−	1.16238e6i		−	1.41922i
$906$		0			0
$907$	−1.04154e6	−	601332.i	−1.26608	−	0.730971i	−0.291835	−	0.956469i	$-0.594266\pi$
$907$	−1.04154e6	−	601332.i	−1.26608	−	0.730971i	−0.974244	+	0.225498i	$0.927599\pi$
$908$		0			0
$909$	146275.	−	253355.i	0.177028	−	0.306621i
$910$		0			0
$911$		−	1.13879e6i		−	1.37216i	−0.727526	−	0.686080i	$-0.759330\pi$
$911$		−	1.13879e6i		−	1.37216i	0.727526	−	0.686080i	$-0.240670\pi$
$912$		0			0
$913$	277090.			0.332414
$914$		0			0
$915$	−430383.	−	248482.i	−0.514059	−	0.296792i
$916$		0			0
$917$	11140.2	−	19295.3i	0.0132481	−	0.0229463i
$918$		0			0
$919$	558543.			0.661341			0.330671	−	0.943746i	$-0.392725\pi$
$919$	558543.			0.661341			0.330671	+	0.943746i	$0.392725\pi$
$920$		0			0
$921$	224420.	+	388708.i	0.264572	+	0.458251i
$922$		0			0
$923$	614510.			0.721317
$924$		0			0
$925$	523072.	−	301996.i	0.611334	−	0.352954i
$926$		0			0
$927$	−210915.	+	121772.i	−0.245441	+	0.141705i
$928$		0			0
$929$	329379.	−	570502.i	0.381650	−	0.661036i	−0.609649	−	0.792672i	$-0.708689\pi$
$929$	329379.	−	570502.i	0.381650	−	0.661036i	0.991298	+	0.131635i	$0.0420228\pi$
$930$		0			0
$931$	−781773.	−	368265.i	−0.901947	−	0.424875i
$932$		0			0
$933$	336772.	+	194435.i	0.386877	+	0.223363i
$934$		0			0
$935$	−188957.	−	327284.i	−0.216143	−	0.374370i
$936$		0			0
$937$	−117517.	−	203546.i	−0.133851	−	0.231837i	0.791307	−	0.611419i	$-0.209401\pi$
$937$	−117517.	−	203546.i	−0.133851	−	0.231837i	−0.925158	+	0.379582i	$0.876068\pi$
$938$		0			0
$939$			88625.9i			0.100515i
$940$		0			0
$941$	−503887.	+	290919.i	−0.569055	+	0.328544i	−0.756772	−	0.653679i	$-0.773225\pi$
$941$	−503887.	+	290919.i	−0.569055	+	0.328544i	0.187717	+	0.982223i	$0.439891\pi$
$942$		0			0
$943$			38306.9i			0.0430778i
$944$		0			0
$945$	43034.9	+	24846.2i	0.0481900	+	0.0278225i
$946$		0			0
$947$	468017.	−	810629.i	0.521869	−	0.903904i	−0.477807	−	0.878465i	$-0.658568\pi$
$947$	468017.	−	810629.i	0.521869	−	0.903904i	0.999676	−	0.0254391i	$-0.00809839\pi$
$948$		0			0
$949$		−	211152.i		−	0.234457i
$950$		0			0
$951$	560114.			0.619321
$952$		0			0
$953$	−26206.7	−	15130.5i	−0.0288554	−	0.0166597i	0.485503	−	0.874235i	$-0.338637\pi$
$953$	−26206.7	−	15130.5i	−0.0288554	−	0.0166597i	−0.514358	+	0.857575i	$0.671970\pi$
$954$		0			0
$955$	−133366.	+	230997.i	−0.146231	+	0.253280i
$956$		0			0
$957$	−37797.2			−0.0412701
$958$		0			0
$959$	−42598.3	−	73782.4i	−0.0463186	−	0.0802261i
$960$		0			0
$961$	697101.			0.754830
$962$		0			0
$963$	54150.5	−	31263.8i	0.0583915	−	0.0337124i
$964$		0			0
$965$	645208.	−	372511.i	0.692859	−	0.400023i
$966$		0			0
$967$	163335.	−	282905.i	0.174673	−	0.302543i	−0.765375	−	0.643585i	$-0.777446\pi$
$967$	163335.	−	282905.i	0.174673	−	0.302543i	0.940048	+	0.341042i	$0.110780\pi$
$968$		0			0
$969$	421881.	−	35252.5i	0.449306	−	0.0375442i
$970$		0			0
$971$	−882382.	−	509444.i	−0.935876	−	0.540328i	−0.0472107	−	0.998885i	$-0.515033\pi$
$971$	−882382.	−	509444.i	−0.935876	−	0.540328i	−0.888665	+	0.458557i	$0.848367\pi$
$972$		0			0
$973$	−39966.2	−	69223.4i	−0.0422150	−	0.0731185i
$974$		0			0
$975$	−93383.7	−	161745.i	−0.0982340	−	0.170146i
$976$		0			0
$977$			411302.i			0.430895i	0.976515	+	0.215448i	$0.0691210\pi$
$977$			411302.i			0.430895i	−0.976515	+	0.215448i	$0.930879\pi$
$978$		0			0
$979$	134609.	−	77716.3i	0.140445	−	0.0810861i
$980$		0			0
$981$		−	70242.1i		−	0.0729893i
$982$		0			0
$983$	195401.	+	112815.i	0.202218	+	0.116751i	0.597690	−	0.801728i	$-0.296085\pi$
$983$	195401.	+	112815.i	0.202218	+	0.116751i	−0.395472	+	0.918478i	$0.629419\pi$
$984$		0			0
$985$	309326.	−	535769.i	0.318819	−	0.552211i
$986$		0			0
$987$		−	3703.99i		−	0.00380220i
$988$		0			0
$989$	783256.			0.800776
$990$		0			0
$991$	464516.	+	268188.i	0.472991	+	0.273082i	0.717491	−	0.696568i	$-0.245290\pi$
$991$	464516.	+	268188.i	0.472991	+	0.273082i	−0.244500	+	0.969649i	$0.578624\pi$
$992$		0			0
$993$	412845.	−	715068.i	0.418686	−	0.725185i
$994$		0			0
$995$	−891704.			−0.900689
$996$		0			0
$997$	−270086.	−	467803.i	−0.271714	−	0.470623i	0.697587	−	0.716500i	$-0.254257\pi$
$997$	−270086.	−	467803.i	−0.271714	−	0.470623i	−0.969301	+	0.245878i	$0.920924\pi$
$998$		0			0
$999$	1.03507e6			1.03714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.h.a.65.4	✓	12
3.2	odd	2		684.5.y.c.217.2		12
4.3	odd	2		304.5.r.b.65.3		12
19.12	odd	6	inner	76.5.h.a.69.4	yes	12
57.50	even	6		684.5.y.c.145.2		12
76.31	even	6		304.5.r.b.145.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.4	✓	12	1.1	even	1	trivial
76.5.h.a.69.4	yes	12	19.12	odd	6	inner
304.5.r.b.65.3		12	4.3	odd	2
304.5.r.b.145.3		12	76.31	even	6
684.5.y.c.145.2		12	57.50	even	6
684.5.y.c.217.2		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.54702 + 2.04787i) q^{3} +(15.5891 - 27.0012i) q^{5} -2.67956 q^{7} +(-32.1124 - 55.6204i) q^{9} +O(q^{10})\)	\(q+(3.54702 + 2.04787i) q^{3} +(15.5891 - 27.0012i) q^{5} -2.67956 q^{7} +(-32.1124 - 55.6204i) q^{9} +42.3332 q^{11} +(113.779 - 65.6905i) q^{13} +(110.590 - 63.8492i) q^{15} +(143.163 - 247.965i) q^{17} +(326.580 + 153.840i) q^{19} +(-9.50447 - 5.48741i) q^{21} +(-158.172 - 273.962i) q^{23} +(-173.542 - 300.584i) q^{25} -594.804i q^{27} +(-188.788 + 108.997i) q^{29} +475.836i q^{31} +(150.157 + 86.6931i) q^{33} +(-41.7721 + 72.3514i) q^{35} +1740.18i q^{37} +538.103 q^{39} +(-104.869 - 60.5462i) q^{41} +(-1237.98 + 2144.24i) q^{43} -2002.42 q^{45} +(168.749 + 292.282i) q^{47} -2393.82 q^{49} +(1015.60 - 586.359i) q^{51} +(-3656.19 + 2110.90i) q^{53} +(659.938 - 1143.05i) q^{55} +(843.340 + 1214.47i) q^{57} +(4911.88 + 2835.87i) q^{59} +(-1945.85 - 3370.31i) q^{61} +(86.0473 + 149.038i) q^{63} -4096.23i q^{65} +(2805.03 - 1619.49i) q^{67} -1295.67i q^{69} +(4050.68 + 2338.66i) q^{71} +(803.586 - 1391.85i) q^{73} -1421.57i q^{75} -113.435 q^{77} +(-2909.85 - 1680.00i) q^{79} +(-1383.02 + 2395.46i) q^{81} +6545.45 q^{83} +(-4463.57 - 7731.13i) q^{85} -892.849 q^{87} +(3179.74 - 1835.82i) q^{89} +(-304.879 + 176.022i) q^{91} +(-974.452 + 1687.80i) q^{93} +(9244.95 - 6419.80i) q^{95} +(4872.79 + 2813.31i) q^{97} +(-1359.42 - 2354.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9} + 6 q^{11} - 93 q^{13} - 741 q^{15} - 483 q^{17} - 533 q^{19} + 972 q^{21} + 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} - 1128 q^{35} - 2250 q^{39} - 1692 q^{41} - 63 q^{43} + 7976 q^{45} - 3471 q^{47} + 420 q^{49} + 6741 q^{51} - 3771 q^{53} - 2014 q^{55} + 7617 q^{57} - 9594 q^{59} + 1229 q^{61} + 1514 q^{63} + 7590 q^{67} + 963 q^{71} - 2838 q^{73} - 15408 q^{77} + 11073 q^{79} + 2086 q^{81} - 14202 q^{83} + 9455 q^{85} - 39510 q^{87} + 6525 q^{89} - 7686 q^{91} - 5316 q^{93} + 1521 q^{95} - 34110 q^{97} + 13220 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9 + 6 * q^11 - 93 * q^13 - 741 * q^15 - 483 * q^17 - 533 * q^19 + 972 * q^21 + 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 - 1128 * q^35 - 2250 * q^39 - 1692 * q^41 - 63 * q^43 + 7976 * q^45 - 3471 * q^47 + 420 * q^49 + 6741 * q^51 - 3771 * q^53 - 2014 * q^55 + 7617 * q^57 - 9594 * q^59 + 1229 * q^61 + 1514 * q^63 + 7590 * q^67 + 963 * q^71 - 2838 * q^73 - 15408 * q^77 + 11073 * q^79 + 2086 * q^81 - 14202 * q^83 + 9455 * q^85 - 39510 * q^87 + 6525 * q^89 - 7686 * q^91 - 5316 * q^93 + 1521 * q^95 - 34110 * q^97 + 13220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more