LMFDB - Embedded newform 684.5.y.d.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,5,Mod(145,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("684.145");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	684.y (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:	$70.7050547493$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2826 x^{12} + 21668 x^{11} + 6144398 x^{10} + 32400228 x^{9} + 4476099452 x^{8} + \cdots + 21\!\cdots\!16 $ x^14 - 2x^13 + 2826x^12 + 21668x^11 + 6144398x^10 + 32400228x^9 + 4476099452x^8 + 1249545344x^7 + 2308151528484x^6 - 2140142598776x^5 + 625358881541536x^4 - 2569874136887808x^3 + 115090576468624800x^2 - 159892348486261824*x + 219826226298839616
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$0.702124 + 1.21611i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.d.217.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.297876 - 0.515937i) q^{5} -35.5020 q^{7} +O(q^{10})$	$q+(-0.297876 - 0.515937i) q^{5} -35.5020 q^{7} -68.6194 q^{11} +(103.682 + 59.8608i) q^{13} +(201.849 + 349.613i) q^{17} +(-22.5294 - 360.296i) q^{19} +(-256.177 + 443.711i) q^{23} +(312.323 - 540.959i) q^{25} +(228.822 + 132.110i) q^{29} +1205.84i q^{31} +(10.5752 + 18.3168i) q^{35} -1207.04i q^{37} +(1468.86 - 848.047i) q^{41} +(-1578.98 - 2734.88i) q^{43} +(-1135.48 + 1966.70i) q^{47} -1140.60 q^{49} +(-2175.85 - 1256.23i) q^{53} +(20.4401 + 35.4033i) q^{55} +(-3923.06 + 2264.98i) q^{59} +(2444.93 - 4234.75i) q^{61} -71.3245i q^{65} +(-2714.60 - 1567.27i) q^{67} +(6419.46 - 3706.28i) q^{71} +(732.965 + 1269.53i) q^{73} +2436.13 q^{77} +(4582.10 - 2645.47i) q^{79} -10712.4 q^{83} +(120.252 - 208.283i) q^{85} +(-581.235 - 335.576i) q^{89} +(-3680.92 - 2125.18i) q^{91} +(-179.179 + 118.948i) q^{95} +(-7638.32 + 4409.98i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) $ 14 * q - 12 * q^5 - 110 * q^7	$ 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) $ 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.297876	−	0.515937i	−0.0119151	−	0.0206375i	0.860006	−	0.510283i	$-0.170459\pi$
$5$	−0.297876	−	0.515937i	−0.0119151	−	0.0206375i	−0.871921	+	0.489646i	$0.837126\pi$
$6$		0			0
$7$	−35.5020			−0.724532			−0.362266	−	0.932075i	$-0.617997\pi$
$7$	−35.5020			−0.724532			−0.362266	+	0.932075i	$0.617997\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−68.6194			−0.567102			−0.283551	−	0.958957i	$-0.591513\pi$
$11$	−68.6194			−0.567102			−0.283551	+	0.958957i	$0.591513\pi$
$12$		0			0
$13$	103.682	+	59.8608i	0.613503	+	0.354206i	0.774335	−	0.632776i	$-0.218084\pi$
$13$	103.682	+	59.8608i	0.613503	+	0.354206i	−0.160832	+	0.986982i	$0.551418\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	201.849	+	349.613i	0.698440	+	1.20973i	0.969007	+	0.247032i	$0.0794554\pi$
$17$	201.849	+	349.613i	0.698440	+	1.20973i	−0.270567	+	0.962701i	$0.587211\pi$
$18$		0			0
$19$	−22.5294	−	360.296i	−0.0624082	−	0.998051i
$19$	−22.5294	−	360.296i	−0.0624082	−	0.998051i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−256.177	+	443.711i	−0.484266	+	0.838774i	−0.999837	−	0.0180736i	$-0.994247\pi$
$23$	−256.177	+	443.711i	−0.484266	+	0.838774i	0.515571	+	0.856847i	$0.327580\pi$
$24$		0			0
$25$	312.323	−	540.959i	0.499716	−	0.865534i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	228.822	+	132.110i	0.272083	+	0.157087i	0.629834	−	0.776730i	$-0.283123\pi$
$29$	228.822	+	132.110i	0.272083	+	0.157087i	−0.357751	+	0.933817i	$0.616456\pi$
$30$		0			0
$31$			1205.84i			1.25478i	0.778707	+	0.627388i	$0.215876\pi$
$31$			1205.84i			1.25478i	−0.778707	+	0.627388i	$0.784124\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	10.5752	+	18.3168i	0.00863283	+	0.0149525i
$36$		0			0
$37$		−	1207.04i		−	0.881696i	−0.897582	−	0.440848i	$-0.854678\pi$
$37$		−	1207.04i		−	0.881696i	0.897582	−	0.440848i	$-0.145322\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1468.86	−	848.047i	0.873802	−	0.504490i	0.00519221	−	0.999987i	$-0.498347\pi$
$41$	1468.86	−	848.047i	0.873802	−	0.504490i	0.868610	+	0.495497i	$0.165014\pi$
$42$		0			0
$43$	−1578.98	−	2734.88i	−0.853966	−	1.47911i	−0.877601	−	0.479392i	$-0.840857\pi$
$43$	−1578.98	−	2734.88i	−0.853966	−	1.47911i	0.0236354	−	0.999721i	$-0.492476\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1135.48	+	1966.70i	−0.514023	+	0.890314i	0.485845	+	0.874045i	$0.338512\pi$
$47$	−1135.48	+	1966.70i	−0.514023	+	0.890314i	−0.999868	+	0.0162686i	$0.994821\pi$
$48$		0			0
$49$	−1140.60			−0.475054
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2175.85	−	1256.23i	−0.774599	−	0.447215i	0.0599137	−	0.998204i	$-0.480917\pi$
$53$	−2175.85	−	1256.23i	−0.774599	−	0.447215i	−0.834513	+	0.550989i	$0.814251\pi$
$54$		0			0
$55$	20.4401	+	35.4033i	0.00675706	+	0.0117036i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3923.06	+	2264.98i	−1.12699	+	0.650669i	−0.943177	−	0.332292i	$-0.892178\pi$
$59$	−3923.06	+	2264.98i	−1.12699	+	0.650669i	−0.183815	+	0.982961i	$0.558845\pi$
$60$		0			0
$61$	2444.93	−	4234.75i	0.657063	−	1.13807i	−0.324309	−	0.945951i	$-0.605132\pi$
$61$	2444.93	−	4234.75i	0.657063	−	1.13807i	0.981372	−	0.192116i	$-0.0615349\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	71.3245i		−	0.0168815i
$66$		0			0
$67$	−2714.60	−	1567.27i	−0.604722	−	0.349137i	0.166175	−	0.986096i	$-0.446858\pi$
$67$	−2714.60	−	1567.27i	−0.604722	−	0.349137i	−0.770897	+	0.636960i	$0.780192\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6419.46	−	3706.28i	1.27345	−	0.735227i	0.297814	−	0.954624i	$-0.403742\pi$
$71$	6419.46	−	3706.28i	1.27345	−	0.735227i	0.975636	+	0.219397i	$0.0704090\pi$
$72$		0			0
$73$	732.965	+	1269.53i	0.137543	+	0.238231i	0.926566	−	0.376132i	$-0.122746\pi$
$73$	732.965	+	1269.53i	0.137543	+	0.238231i	−0.789023	+	0.614363i	$0.789413\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2436.13			0.410884
$78$		0			0
$79$	4582.10	−	2645.47i	0.734193	−	0.423886i	−0.0857614	−	0.996316i	$-0.527332\pi$
$79$	4582.10	−	2645.47i	0.734193	−	0.423886i	0.819954	+	0.572429i	$0.193999\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10712.4			−1.55499			−0.777497	−	0.628887i	$-0.783511\pi$
$83$	−10712.4			−1.55499			−0.777497	+	0.628887i	$0.783511\pi$
$84$		0			0
$85$	120.252	−	208.283i	0.0166439	−	0.0288281i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−581.235	−	335.576i	−0.0733790	−	0.0423654i	0.462862	−	0.886431i	$-0.346823\pi$
$89$	−581.235	−	335.576i	−0.0733790	−	0.0423654i	−0.536241	+	0.844065i	$0.680156\pi$
$90$		0			0
$91$	−3680.92	−	2125.18i	−0.444502	−	0.256633i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−179.179	+	118.948i	−0.0198537	+	0.0131798i
$96$		0			0
$97$	−7638.32	+	4409.98i	−0.811809	+	0.468698i	−0.847584	−	0.530661i	$-0.821944\pi$
$97$	−7638.32	+	4409.98i	−0.811809	+	0.468698i	0.0357744	+	0.999360i	$0.488610\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1635.82	+	2833.32i	−0.160359	+	0.277750i	−0.934997	−	0.354655i	$-0.884598\pi$
$101$	−1635.82	+	2833.32i	−0.160359	+	0.277750i	0.774639	+	0.632404i	$0.217932\pi$
$102$		0			0
$103$		−	5905.49i		−	0.556649i	−0.960487	−	0.278325i	$-0.910221\pi$
$103$		−	5905.49i		−	0.556649i	0.960487	−	0.278325i	$-0.0897791\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	19004.9i		−	1.65996i	−0.557791	−	0.829982i	$-0.688351\pi$
$107$		−	19004.9i		−	1.65996i	0.557791	−	0.829982i	$-0.311649\pi$
$108$		0			0
$109$	229.032	−	132.232i	0.0192771	−	0.0111297i	−0.490330	−	0.871537i	$-0.663124\pi$
$109$	229.032	−	132.232i	0.0192771	−	0.0111297i	0.509608	+	0.860407i	$0.329791\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	5997.99i		−	0.469731i	−0.972028	−	0.234865i	$-0.924535\pi$
$113$		−	5997.99i		−	0.469731i	0.972028	−	0.234865i	$-0.0754649\pi$
$114$		0			0
$115$	305.236			0.0230802
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7166.06	−	12412.0i	−0.506042	−	0.876490i
$120$		0			0
$121$	−9932.38			−0.678395
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−744.480			−0.0476467
$126$		0			0
$127$	13609.0	+	7857.17i	0.843761	+	0.487145i	0.858541	−	0.512745i	$-0.171372\pi$
$127$	13609.0	+	7857.17i	0.843761	+	0.487145i	−0.0147801	+	0.999891i	$0.504705\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13253.0	−	22954.9i	−0.772274	−	1.33762i	−0.936314	−	0.351164i	$-0.885786\pi$
$131$	−13253.0	−	22954.9i	−0.772274	−	1.33762i	0.164040	−	0.986454i	$-0.447547\pi$
$132$		0			0
$133$	799.838	+	12791.3i	0.0452167	+	0.723119i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10229.4	−	17717.9i	0.545016	−	0.943996i	−0.453590	−	0.891211i	$-0.649857\pi$
$137$	10229.4	−	17717.9i	0.545016	−	0.943996i	0.998606	−	0.0527850i	$-0.0168098\pi$
$138$		0			0
$139$	−14384.1	+	24914.1i	−0.744482	+	1.28948i	0.205954	+	0.978562i	$0.433970\pi$
$139$	−14384.1	+	24914.1i	−0.744482	+	1.28948i	−0.950436	+	0.310920i	$0.899363\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7114.59	−	4107.61i	−0.347919	−	0.200871i
$144$		0			0
$145$		−	157.410i		−	0.00748681i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11031.4	−	19106.9i	−0.496887	−	0.860633i	0.503107	−	0.864224i	$-0.332190\pi$
$149$	−11031.4	−	19106.9i	−0.496887	−	0.860633i	−0.999994	+	0.00359132i	$0.998857\pi$
$150$		0			0
$151$			2623.23i			0.115049i	0.998344	+	0.0575243i	$0.0183207\pi$
$151$			2623.23i			0.115049i	−0.998344	+	0.0575243i	$0.981679\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	622.137	−	359.191i	0.0258954	−	0.0149507i
$156$		0			0
$157$	−23860.0	−	41326.7i	−0.967990	−	1.67661i	−0.701358	−	0.712809i	$-0.747423\pi$
$157$	−23860.0	−	41326.7i	−0.967990	−	1.67661i	−0.266632	−	0.963798i	$-0.585911\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9094.80	−	15752.7i	0.350866	−	0.607718i
$162$		0			0
$163$	45267.5			1.70377			0.851885	−	0.523728i	$-0.175459\pi$
$163$	45267.5			1.70377			0.851885	+	0.523728i	$0.175459\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−42777.0	−	24697.3i	−1.53383	−	0.885557i	−0.999180	−	0.0404826i	$-0.987110\pi$
$167$	−42777.0	−	24697.3i	−1.53383	−	0.885557i	−0.534649	−	0.845074i	$-0.679556\pi$
$168$		0			0
$169$	−7113.86	−	12321.6i	−0.249076	−	0.431413i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	19915.5	−	11498.2i	0.665426	−	0.384184i	−0.128915	−	0.991656i	$-0.541150\pi$
$173$	19915.5	−	11498.2i	0.665426	−	0.384184i	0.794341	+	0.607472i	$0.207816\pi$
$174$		0			0
$175$	−11088.1	+	19205.1i	−0.362060	+	0.627106i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			11905.5i			0.371570i	0.982590	+	0.185785i	$0.0594827\pi$
$179$			11905.5i			0.371570i	−0.982590	+	0.185785i	$0.940517\pi$
$180$		0			0
$181$	−24156.9	−	13947.0i	−0.737368	−	0.425720i	0.0837436	−	0.996487i	$-0.473312\pi$
$181$	−24156.9	−	13947.0i	−0.737368	−	0.425720i	−0.821112	+	0.570768i	$0.806646\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−622.758	+	359.549i	−0.0181960	+	0.0105055i
$186$		0			0
$187$	−13850.8	−	23990.2i	−0.396087	−	0.686043i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−29874.9			−0.818917			−0.409458	−	0.912329i	$-0.634282\pi$
$191$	−29874.9			−0.818917			−0.409458	+	0.912329i	$0.634282\pi$
$192$		0			0
$193$	1529.72	−	883.186i	0.0410675	−	0.0237103i	−0.479326	−	0.877637i	$-0.659119\pi$
$193$	1529.72	−	883.186i	0.0410675	−	0.0237103i	0.520393	+	0.853927i	$0.325785\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16286.0			−0.419644			−0.209822	−	0.977740i	$-0.567289\pi$
$197$	−16286.0			−0.419644			−0.209822	+	0.977740i	$0.567289\pi$
$198$		0			0
$199$	5598.86	−	9697.50i	0.141382	−	0.244880i	−0.786635	−	0.617418i	$-0.788179\pi$
$199$	5598.86	−	9697.50i	0.141382	−	0.244880i	0.928017	+	0.372537i	$0.121512\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8123.64	−	4690.19i	−0.197133	−	0.113815i
$204$		0			0
$205$	−875.078	−	505.227i	−0.0208228	−	0.0120220i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1545.95	+	24723.3i	0.0353918	+	0.565997i
$210$		0			0
$211$	8025.80	−	4633.70i	0.180270	−	0.104079i	−0.407149	−	0.913362i	$-0.633477\pi$
$211$	8025.80	−	4633.70i	0.180270	−	0.104079i	0.587420	+	0.809283i	$0.300144\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−940.683	+	1629.31i	−0.0203501	+	0.0352474i
$216$		0			0
$217$		−	42809.8i		−	0.909124i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			48331.4i			0.989567i
$222$		0			0
$223$	−3922.37	+	2264.58i	−0.0788750	+	0.0455385i	−0.538919	−	0.842358i	$-0.681167\pi$
$223$	−3922.37	+	2264.58i	−0.0788750	+	0.0455385i	0.460044	+	0.887896i	$0.347834\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	67829.6i		−	1.31634i	−0.752870	−	0.658169i	$-0.771331\pi$
$227$		−	67829.6i		−	1.31634i	0.752870	−	0.658169i	$-0.228669\pi$
$228$		0			0
$229$	13397.6			0.255479			0.127739	−	0.991808i	$-0.459228\pi$
$229$	13397.6			0.255479			0.127739	+	0.991808i	$0.459228\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6591.92	−	11417.5i	−0.121423	−	0.210310i	0.798906	−	0.601456i	$-0.205412\pi$
$233$	−6591.92	−	11417.5i	−0.121423	−	0.210310i	−0.920329	+	0.391145i	$0.872079\pi$
$234$		0			0
$235$	1352.93			0.0244984
$236$		0			0
$237$		0			0
$238$		0			0
$239$	61880.1			1.08332			0.541658	−	0.840599i	$-0.317797\pi$
$239$	61880.1			1.08332			0.541658	+	0.840599i	$0.317797\pi$
$240$		0			0
$241$	−31189.8	−	18007.5i	−0.537006	−	0.310040i	0.206859	−	0.978371i	$-0.433676\pi$
$241$	−31189.8	−	18007.5i	−0.537006	−	0.310040i	−0.743865	+	0.668330i	$0.767009\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	339.759	+	588.480i	0.00566030	+	0.00980392i
$246$		0			0
$247$	19231.7	−	38704.9i	0.315228	−	0.634412i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−53754.1	+	93104.8i	−0.853226	+	1.47783i	0.0250556	+	0.999686i	$0.492024\pi$
$251$	−53754.1	+	93104.8i	−0.853226	+	1.47783i	−0.878281	+	0.478144i	$0.841310\pi$
$252$		0			0
$253$	17578.7	−	30447.2i	0.274628	−	0.475671i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	101714.	+	58724.7i	1.53998	+	0.889108i	0.998839	+	0.0481766i	$0.0153410\pi$
$257$	101714.	+	58724.7i	1.53998	+	0.889108i	0.541142	+	0.840931i	$0.317992\pi$
$258$		0			0
$259$			42852.5i			0.638817i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−26325.6	−	45597.2i	−0.380598	−	0.659214i	0.610550	−	0.791978i	$-0.290948\pi$
$263$	−26325.6	−	45597.2i	−0.380598	−	0.659214i	−0.991148	+	0.132763i	$0.957615\pi$
$264$		0			0
$265$			1496.80i			0.0213144i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8265.47	+	4772.07i	−0.114225	+	0.0659481i	−0.556024	−	0.831166i	$-0.687674\pi$
$269$	−8265.47	+	4772.07i	−0.114225	+	0.0659481i	0.441799	+	0.897114i	$0.354341\pi$
$270$		0			0
$271$	−7879.63	−	13647.9i	−0.107292	−	0.185835i	0.807380	−	0.590031i	$-0.200885\pi$
$271$	−7879.63	−	13647.9i	−0.107292	−	0.185835i	−0.914672	+	0.404196i	$0.867551\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−21431.4	+	37120.2i	−0.283390	+	0.490846i
$276$		0			0
$277$	−26900.5			−0.350591			−0.175295	−	0.984516i	$-0.556088\pi$
$277$	−26900.5			−0.350591			−0.175295	+	0.984516i	$0.556088\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	59947.4	+	34610.6i	0.759202	+	0.438326i	0.829009	−	0.559235i	$-0.188905\pi$
$281$	59947.4	+	34610.6i	0.759202	+	0.438326i	−0.0698069	+	0.997561i	$0.522238\pi$
$282$		0			0
$283$	−34870.0	−	60396.6i	−0.435391	−	0.754118i	0.561937	−	0.827180i	$-0.310056\pi$
$283$	−34870.0	−	60396.6i	−0.435391	−	0.754118i	−0.997327	+	0.0730616i	$0.976723\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−52147.6	+	30107.4i	−0.633097	+	0.365519i
$288$		0			0
$289$	−39725.6	+	68806.8i	−0.475637	+	0.823827i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			7422.09i			0.0864552i	0.999065	+	0.0432276i	$0.0137641\pi$
$293$			7422.09i			0.0864552i	−0.999065	+	0.0432276i	$0.986236\pi$
$294$		0			0
$295$	2337.17	+	1349.37i	0.0268563	+	0.0155055i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−53121.8	+	30669.9i	−0.594197	+	0.343060i
$300$		0			0
$301$	56057.1	+	97093.8i	0.618725	+	1.07166i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2913.15			−0.0313158
$306$		0			0
$307$	34784.4	−	20082.8i	0.369069	−	0.213082i	−0.303983	−	0.952678i	$-0.598317\pi$
$307$	34784.4	−	20082.8i	0.369069	−	0.213082i	0.673052	+	0.739596i	$0.264983\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−82135.8			−0.849203			−0.424602	−	0.905380i	$-0.639586\pi$
$311$	−82135.8			−0.849203			−0.424602	+	0.905380i	$0.639586\pi$
$312$		0			0
$313$	15991.5	−	27698.1i	0.163230	−	0.282723i	−0.772795	−	0.634655i	$-0.781142\pi$
$313$	15991.5	−	27698.1i	0.163230	−	0.282723i	0.936025	+	0.351933i	$0.114475\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	113957.	+	65793.2i	1.13403	+	0.654730i	0.944944	−	0.327231i	$-0.106116\pi$
$317$	113957.	+	65793.2i	1.13403	+	0.654730i	0.189082	+	0.981961i	$0.439449\pi$
$318$		0			0
$319$	−15701.6	−	9065.33i	−0.154299	−	0.0890846i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	121417.	−	80602.1i	1.16379	−	0.772576i
$324$		0			0
$325$	64764.4	−	37391.8i	0.613154	−	0.354005i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	40311.7	−	69822.0i	0.372426	−	0.645060i
$330$		0			0
$331$			23205.7i			0.211806i	0.994376	+	0.105903i	$0.0337734\pi$
$331$			23205.7i			0.211806i	−0.994376	+	0.105903i	$0.966227\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			1867.42i			0.0166399i
$336$		0			0
$337$	85630.1	−	49438.5i	0.753991	−	0.435317i	−0.0731428	−	0.997321i	$-0.523303\pi$
$337$	85630.1	−	49438.5i	0.753991	−	0.435317i	0.827134	+	0.562004i	$0.189970\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	82744.0i		−	0.711586i
$342$		0			0
$343$	125734.			1.06872
$344$		0			0
$345$		0			0
$346$		0			0
$347$	970.720	+	1681.34i	0.00806186	+	0.0139635i	0.870028	−	0.493002i	$-0.164100\pi$
$347$	970.720	+	1681.34i	0.00806186	+	0.0139635i	−0.861966	+	0.506966i	$0.830767\pi$
$348$		0			0
$349$	−53578.4			−0.439884			−0.219942	−	0.975513i	$-0.570587\pi$
$349$	−53578.4			−0.439884			−0.219942	+	0.975513i	$0.570587\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−158947.			−1.27557			−0.637783	−	0.770216i	$-0.720148\pi$
$353$	−158947.			−1.27557			−0.637783	+	0.770216i	$0.720148\pi$
$354$		0			0
$355$	−3824.41	−	2208.03i	−0.0303465	−	0.0175205i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	61862.3	+	107149.i	0.479995	+	0.831376i	0.999737	−	0.0229475i	$-0.00730506\pi$
$359$	61862.3	+	107149.i	0.479995	+	0.831376i	−0.519741	+	0.854324i	$0.673972\pi$
$360$		0			0
$361$	−129306.	+	16234.5i	−0.992210	+	0.124573i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	436.666	−	756.328i	0.00327766	−	0.00567707i
$366$		0			0
$367$	−74531.3	+	129092.i	−0.553358	+	0.958444i	0.444671	+	0.895694i	$0.353321\pi$
$367$	−74531.3	+	129092.i	−0.553358	+	0.958444i	−0.998029	+	0.0627505i	$0.980013\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	77247.1	+	44598.6i	0.561222	+	0.324021i
$372$		0			0
$373$			48416.5i			0.347997i	0.984746	+	0.173998i	$0.0556688\pi$
$373$			48416.5i			0.347997i	−0.984746	+	0.173998i	$0.944331\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15816.5	+	27394.9i	0.111282	+	0.192747i
$378$		0			0
$379$			210471.i			1.46526i	0.680628	+	0.732629i	$0.261707\pi$
$379$			210471.i			1.46526i	−0.680628	+	0.732629i	$0.738293\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−52827.7	+	30500.1i	−0.360134	+	0.207923i	−0.669139	−	0.743137i	$-0.733337\pi$
$383$	−52827.7	+	30500.1i	−0.360134	+	0.207923i	0.309006	+	0.951060i	$0.400004\pi$
$384$		0			0
$385$	−725.665	−	1256.89i	−0.00489570	−	0.00847960i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−23337.5	+	40421.7i	−0.154225	+	0.267125i	−0.932777	−	0.360455i	$-0.882621\pi$
$389$	−23337.5	+	40421.7i	−0.154225	+	0.267125i	0.778552	+	0.627581i	$0.215955\pi$
$390$		0			0
$391$	−206836.			−1.35292
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2729.80	−	1576.05i	−0.0174959	−	0.0101013i
$396$		0			0
$397$	144820.	+	250835.i	0.918855	+	1.59150i	0.801158	+	0.598454i	$0.204218\pi$
$397$	144820.	+	250835.i	0.918855	+	1.59150i	0.117697	+	0.993050i	$0.462449\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	116750.	−	67405.8i	0.726054	−	0.419188i	−0.0909226	−	0.995858i	$-0.528982\pi$
$401$	116750.	−	67405.8i	0.726054	−	0.419188i	0.816977	+	0.576670i	$0.195648\pi$
$402$		0			0
$403$	−72182.5	+	125024.i	−0.444449	+	0.769808i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			82826.5i			0.500012i
$408$		0			0
$409$	278613.	+	160857.i	1.66554	+	0.961598i	0.969999	+	0.243108i	$0.0781669\pi$
$409$	278613.	+	160857.i	1.66554	+	0.961598i	0.695537	+	0.718490i	$0.255166\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	139277.	−	80411.4i	0.816541	−	0.471430i
$414$		0			0
$415$	3190.96	+	5526.90i	0.0185278	+	0.0320912i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	95461.2			0.543750			0.271875	−	0.962333i	$-0.412356\pi$
$419$	95461.2			0.543750			0.271875	+	0.962333i	$0.412356\pi$
$420$		0			0
$421$	143000.	−	82561.2i	0.806812	−	0.465813i	−0.0390355	−	0.999238i	$-0.512429\pi$
$421$	143000.	−	82561.2i	0.806812	−	0.465813i	0.845848	+	0.533425i	$0.179095\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	252168.			1.39609
$426$		0			0
$427$	−86800.1	+	150342.i	−0.476063	+	0.824566i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−147998.	−	85446.4i	−0.796709	−	0.459980i	0.0456099	−	0.998959i	$-0.485477\pi$
$431$	−147998.	−	85446.4i	−0.796709	−	0.459980i	−0.842319	+	0.538979i	$0.818810\pi$
$432$		0			0
$433$	29748.6	+	17175.3i	0.158668	+	0.0916072i	0.577232	−	0.816580i	$-0.304133\pi$
$433$	29748.6	+	17175.3i	0.158668	+	0.0916072i	−0.418563	+	0.908188i	$0.637466\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	165639.	+	82303.0i	0.867361	+	0.430976i
$438$		0			0
$439$	275154.	−	158860.i	1.42773	−	0.824302i	0.430792	−	0.902451i	$-0.358234\pi$
$439$	275154.	−	158860.i	1.42773	−	0.824302i	0.996942	+	0.0781492i	$0.0249010\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−175310.	+	303646.i	−0.893304	+	1.54725i	−0.0574146	+	0.998350i	$0.518286\pi$
$443$	−175310.	+	303646.i	−0.893304	+	1.54725i	−0.835890	+	0.548898i	$0.815048\pi$
$444$		0			0
$445$			399.841i			0.00201914i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	27376.3i		−	0.135795i	−0.997692	−	0.0678973i	$-0.978371\pi$
$449$		−	27376.3i		−	0.135795i	0.997692	−	0.0678973i	$-0.0216290\pi$
$450$		0			0
$451$	−100792.	+	58192.5i	−0.495535	+	0.286097i
$452$		0			0
$453$		0			0
$454$		0			0
$455$			2532.17i			0.0122312i
$456$		0			0
$457$	−153133.			−0.733221			−0.366611	−	0.930374i	$-0.619482\pi$
$457$	−153133.			−0.733221			−0.366611	+	0.930374i	$0.619482\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	58770.8	+	101794.i	0.276541	+	0.478983i	0.970523	−	0.241009i	$-0.0774785\pi$
$461$	58770.8	+	101794.i	0.276541	+	0.478983i	−0.693982	+	0.719993i	$0.744145\pi$
$462$		0			0
$463$	111195.			0.518710			0.259355	−	0.965782i	$-0.416490\pi$
$463$	111195.			0.518710			0.259355	+	0.965782i	$0.416490\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	98047.3			0.449575			0.224787	−	0.974408i	$-0.427831\pi$
$467$	98047.3			0.449575			0.224787	+	0.974408i	$0.427831\pi$
$468$		0			0
$469$	96373.8	+	55641.4i	0.438140	+	0.252960i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	108349.	+	187666.i	0.484286	+	0.838808i
$474$		0			0
$475$	−201942.	−	100341.i	−0.895033	−	0.444726i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	119024.	−	206155.i	0.518755	−	0.898510i	−0.481007	−	0.876717i	$-0.659729\pi$
$479$	119024.	−	206155.i	0.518755	−	0.898510i	0.999762	−	0.0217938i	$-0.00693772\pi$
$480$		0			0
$481$	72254.6	−	125149.i	0.312302	−	0.540923i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4550.55	+	2627.26i	0.0193455	+	0.0111691i
$486$		0			0
$487$		−	194469.i		−	0.819959i	−0.912095	−	0.409979i	$-0.865536\pi$
$487$		−	194469.i		−	0.819959i	0.912095	−	0.409979i	$-0.134464\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−35535.1	−	61548.6i	−0.147399	−	0.255303i	0.782866	−	0.622190i	$-0.213757\pi$
$491$	−35535.1	−	61548.6i	−0.147399	−	0.255303i	−0.930265	+	0.366887i	$0.880423\pi$
$492$		0			0
$493$			106665.i			0.438864i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−227904.	+	131580.i	−0.922655	+	0.532695i
$498$		0			0
$499$	−5420.95	−	9389.37i	−0.0217708	−	0.0377081i	0.854935	−	0.518736i	$-0.173597\pi$
$499$	−5420.95	−	9389.37i	−0.0217708	−	0.0377081i	−0.876706	+	0.481027i	$0.840264\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−94208.6	+	163174.i	−0.372353	+	0.644934i	−0.989927	−	0.141579i	$-0.954782\pi$
$503$	−94208.6	+	163174.i	−0.372353	+	0.644934i	0.617574	+	0.786513i	$0.288116\pi$
$504$		0			0
$505$	1949.09			0.00764274
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−234963.	−	135656.i	−0.906908	−	0.523604i	−0.0274732	−	0.999623i	$-0.508746\pi$
$509$	−234963.	−	135656.i	−0.906908	−	0.523604i	−0.879435	+	0.476019i	$0.842079\pi$
$510$		0			0
$511$	−26021.8	−	45071.0i	−0.0996540	−	0.172606i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3046.86	+	1759.11i	−0.0114878	+	0.00663251i
$516$		0			0
$517$	77915.7	−	134954.i	0.291504	−	0.504899i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			403279.i			1.48570i	0.669461	+	0.742848i	$0.266525\pi$
$521$			403279.i			1.48570i	−0.669461	+	0.742848i	$0.733475\pi$
$522$		0			0
$523$	−409059.	−	236171.i	−1.49549	−	0.863421i	−0.495502	−	0.868607i	$-0.665016\pi$
$523$	−409059.	−	236171.i	−1.49549	−	0.863421i	−0.999987	+	0.00518639i	$0.998349\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−421577.	+	243398.i	−1.51794	+	0.876385i
$528$		0			0
$529$	8667.42	+	15012.4i	0.0309727	+	0.0536462i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	203059.			0.714773
$534$		0			0
$535$	−9805.34	+	5661.12i	−0.0342575	+	0.0197786i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	78267.6			0.269404
$540$		0			0
$541$	87317.7	−	151239.i	0.298337	−	0.516735i	−0.677418	−	0.735598i	$-0.736901\pi$
$541$	87317.7	−	151239.i	0.298337	−	0.516735i	0.975756	+	0.218863i	$0.0702346\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−136.446	−	78.7773i	−0.000459376	−	0.000265221i
$546$		0			0
$547$	−75825.5	−	43777.9i	−0.253420	−	0.146312i	0.367909	−	0.929862i	$-0.380074\pi$
$547$	−75825.5	−	43777.9i	−0.253420	−	0.146312i	−0.621329	+	0.783550i	$0.713407\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	42443.7	−	85420.0i	0.139801	−	0.281356i
$552$		0			0
$553$	−162674.	+	93919.8i	−0.531946	+	0.307119i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19609.3	+	33964.2i	−0.0632049	+	0.109474i	−0.895896	−	0.444263i	$-0.853466\pi$
$557$	−19609.3	+	33964.2i	−0.0632049	+	0.109474i	0.832691	+	0.553737i	$0.186799\pi$
$558$		0			0
$559$		−	378077.i		−	1.20992i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	50390.3i		−	0.158976i	−0.996836	−	0.0794878i	$-0.974672\pi$
$563$		−	50390.3i		−	0.158976i	0.996836	−	0.0794878i	$-0.0253285\pi$
$564$		0			0
$565$	−3094.59	+	1786.66i	−0.00969406	+	0.00559687i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	353187.i		−	1.09089i	−0.838147	−	0.545444i	$-0.816361\pi$
$569$		−	353187.i		−	1.09089i	0.838147	−	0.545444i	$-0.183639\pi$
$570$		0			0
$571$	−13123.9			−0.0402524			−0.0201262	−	0.999797i	$-0.506407\pi$
$571$	−13123.9			−0.0402524			−0.0201262	+	0.999797i	$0.506407\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	160020.	+	277162.i	0.483991	+	0.838297i
$576$		0			0
$577$	521963.			1.56779			0.783896	−	0.620892i	$-0.213229\pi$
$577$	521963.			1.56779			0.783896	+	0.620892i	$0.213229\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	380310.			1.12664
$582$		0			0
$583$	149305.	+	86201.5i	0.439277	+	0.253617i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9586.84	−	16604.9i	−0.0278227	−	0.0481903i	0.851779	−	0.523902i	$-0.175524\pi$
$587$	−9586.84	−	16604.9i	−0.0278227	−	0.0481903i	−0.879601	+	0.475711i	$0.842191\pi$
$588$		0			0
$589$	434459.	−	27166.8i	1.25233	−	0.0783083i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	35223.9	−	61009.5i	0.100168	−	0.173496i	−0.811586	−	0.584233i	$-0.801395\pi$
$593$	35223.9	−	61009.5i	0.100168	−	0.173496i	0.911754	+	0.410738i	$0.134729\pi$
$594$		0			0
$595$	−4269.20	+	7394.47i	−0.0120590	+	0.0208869i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	112276.	+	64822.7i	0.312920	+	0.180665i	0.648233	−	0.761442i	$-0.275508\pi$
$599$	112276.	+	64822.7i	0.312920	+	0.180665i	−0.335312	+	0.942107i	$0.608842\pi$
$600$		0			0
$601$			219277.i			0.607078i	0.952819	+	0.303539i	$0.0981682\pi$
$601$			219277.i			0.607078i	−0.952819	+	0.303539i	$0.901832\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2958.62	+	5124.48i	0.00808311	+	0.0140004i
$606$		0			0
$607$			101938.i			0.276668i	0.990386	+	0.138334i	$0.0441747\pi$
$607$			101938.i			0.276668i	−0.990386	+	0.138334i	$0.955825\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−235457.	+	135941.i	−0.630709	+	0.364140i
$612$		0			0
$613$	−107916.	−	186917.i	−0.287188	−	0.497424i	0.685949	−	0.727649i	$-0.259387\pi$
$613$	−107916.	−	186917.i	−0.287188	−	0.497424i	−0.973137	+	0.230225i	$0.926054\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	43031.3	−	74532.4i	0.113035	−	0.195783i	−0.803957	−	0.594687i	$-0.797276\pi$
$617$	43031.3	−	74532.4i	0.113035	−	0.195783i	0.916993	+	0.398904i	$0.130609\pi$
$618$		0			0
$619$	−711768.			−1.85762			−0.928811	−	0.370555i	$-0.879168\pi$
$619$	−711768.			−1.85762			−0.928811	+	0.370555i	$0.879168\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	20635.0	+	11913.6i	0.0531654	+	0.0306950i
$624$		0			0
$625$	−194980.	−	337715.i	−0.499148	−	0.864550i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	421998.	−	243640.i	1.06662	−	0.615812i
$630$		0			0
$631$	39491.0	−	68400.3i	0.0991834	−	0.171791i	−0.812163	−	0.583430i	$-0.801710\pi$
$631$	39491.0	−	68400.3i	0.0991834	−	0.171791i	0.911347	+	0.411639i	$0.135044\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		−	9361.86i		−	0.0232175i
$636$		0			0
$637$	−118260.	−	68277.5i	−0.291447	−	0.168267i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−199313.	+	115073.i	−0.485087	+	0.280065i	−0.722534	−	0.691335i	$-0.757023\pi$
$641$	−199313.	+	115073.i	−0.485087	+	0.280065i	0.237447	+	0.971400i	$0.423689\pi$
$642$		0			0
$643$	221676.	+	383955.i	0.536163	+	0.928662i	0.999106	+	0.0422741i	$0.0134603\pi$
$643$	221676.	+	383955.i	0.536163	+	0.928662i	−0.462943	+	0.886388i	$0.653206\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−337930.			−0.807268			−0.403634	−	0.914920i	$-0.632253\pi$
$647$	−337930.			−0.807268			−0.403634	+	0.914920i	$0.632253\pi$
$648$		0			0
$649$	269198.	−	155422.i	0.639120	−	0.368996i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−669034.			−1.56900			−0.784498	−	0.620131i	$-0.787080\pi$
$653$	−669034.			−1.56900			−0.784498	+	0.620131i	$0.787080\pi$
$654$		0			0
$655$	−7895.51	+	13675.4i	−0.0184034	+	0.0318756i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−42834.3	−	24730.4i	−0.0986327	−	0.0569456i	0.449872	−	0.893093i	$-0.351469\pi$
$659$	−42834.3	−	24730.4i	−0.0986327	−	0.0569456i	−0.548505	+	0.836147i	$0.684803\pi$
$660$		0			0
$661$	−656611.	−	379095.i	−1.50281	−	0.867650i	−0.999995	−	0.00325898i	$-0.998963\pi$
$661$	−656611.	−	379095.i	−1.50281	−	0.867650i	−0.502820	−	0.864391i	$-0.667704\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6361.23	−	4222.88i	0.0143846	−	0.00954917i
$666$		0			0
$667$	−117238.	+	67687.2i	−0.263521	+	0.152144i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−167770.	+	290586.i	−0.372622	+	0.645401i
$672$		0			0
$673$			749614.i			1.65504i	0.561439	+	0.827518i	$0.310248\pi$
$673$			749614.i			1.65504i	−0.561439	+	0.827518i	$0.689752\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	683204.i		−	1.49064i	−0.666706	−	0.745321i	$-0.732296\pi$
$677$		−	683204.i		−	1.49064i	0.666706	−	0.745321i	$-0.267704\pi$
$678$		0			0
$679$	271176.	−	156563.i	0.588182	−	0.339587i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	437561.i		−	0.937988i	−0.883201	−	0.468994i	$-0.844617\pi$
$683$		−	437561.i		−	0.937988i	0.883201	−	0.468994i	$-0.155383\pi$
$684$		0			0
$685$	−12188.4			−0.0259756
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−150398.	−	260496.i	−0.316813	−	0.548735i
$690$		0			0
$691$	−477056.			−0.999110			−0.499555	−	0.866282i	$-0.666503\pi$
$691$	−477056.			−0.999110			−0.499555	+	0.866282i	$0.666503\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17138.8			0.0354822
$696$		0			0
$697$	592977.	+	342355.i	1.22060	+	0.704712i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−154603.	−	267780.i	−0.314617	−	0.544932i	0.664739	−	0.747075i	$-0.268543\pi$
$701$	−154603.	−	267780.i	−0.314617	−	0.544932i	−0.979356	+	0.202143i	$0.935209\pi$
$702$		0			0
$703$	−434893.	+	27193.9i	−0.879978	+	0.0550251i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	58075.0	−	100589.i	0.116185	−	0.201238i
$708$		0			0
$709$	461595.	−	799507.i	0.918267	−	1.59049i	0.116221	−	0.993223i	$-0.462922\pi$
$709$	461595.	−	799507.i	0.918267	−	1.59049i	0.802046	−	0.597262i	$-0.203745\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−535044.	−	308908.i	−1.05247	−	0.607645i
$714$		0			0
$715$			4894.24i			0.00957356i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−372020.	−	644358.i	−0.719630	−	1.24644i	−0.961147	−	0.276039i	$-0.910978\pi$
$719$	−372020.	−	644358.i	−0.719630	−	1.24644i	0.241517	−	0.970397i	$-0.422355\pi$
$720$		0			0
$721$			209657.i			0.403310i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	142932.	−	82522.1i	0.271929	−	0.156998i
$726$		0			0
$727$	−452677.	−	784060.i	−0.856485	−	1.48348i	−0.875261	−	0.483652i	$-0.839310\pi$
$727$	−452677.	−	784060.i	−0.856485	−	1.48348i	0.0187758	−	0.999824i	$-0.494023\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	637433.	−	1.10407e6i	1.19289	−	2.06614i
$732$		0			0
$733$	−514665.			−0.957893			−0.478947	−	0.877844i	$-0.658981\pi$
$733$	−514665.			−0.957893			−0.478947	+	0.877844i	$0.658981\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	186274.	+	107545.i	0.342939	+	0.197996i
$738$		0			0
$739$	98335.0	+	170321.i	0.180061	+	0.311875i	0.941901	−	0.335890i	$-0.109037\pi$
$739$	98335.0	+	170321.i	0.180061	+	0.311875i	−0.761840	+	0.647765i	$0.775704\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−243158.	+	140387.i	−0.440464	+	0.254302i	−0.703794	−	0.710404i	$-0.748512\pi$
$743$	−243158.	+	140387.i	−0.440464	+	0.254302i	0.263330	+	0.964706i	$0.415179\pi$
$744$		0			0
$745$	−6571.98	+	11383.0i	−0.0118409	+	0.0205090i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			674713.i			1.20270i
$750$		0			0
$751$	273584.	+	157954.i	0.485078	+	0.280060i	0.722530	−	0.691339i	$-0.242979\pi$
$751$	273584.	+	157954.i	0.485078	+	0.280060i	−0.237452	+	0.971399i	$0.576312\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1353.42	−	781.397i	0.00237432	−	0.00137081i
$756$		0			0
$757$	517523.	+	896376.i	0.903104	+	1.56422i	0.823442	+	0.567400i	$0.192051\pi$
$757$	517523.	+	896376.i	0.903104	+	1.56422i	0.0796622	+	0.996822i	$0.474616\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	655827.			1.13245			0.566226	−	0.824250i	$-0.308403\pi$
$761$	655827.			1.13245			0.566226	+	0.824250i	$0.308403\pi$
$762$		0			0
$763$	−8131.09	+	4694.49i	−0.0139669	+	0.00806379i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−542334.			−0.921884
$768$		0			0
$769$	216433.	−	374874.i	0.365992	−	0.633917i	−0.622943	−	0.782267i	$-0.714063\pi$
$769$	216433.	−	374874.i	0.365992	−	0.633917i	0.988935	+	0.148351i	$0.0473964\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−455467.	−	262964.i	−0.762251	−	0.440086i	0.0678524	−	0.997695i	$-0.478385\pi$
$773$	−455467.	−	262964.i	−0.762251	−	0.440086i	−0.830103	+	0.557610i	$0.811719\pi$
$774$		0			0
$775$	652309.	+	376611.i	1.08605	+	0.627031i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−338641.	−	510119.i	−0.558039	−	0.840614i
$780$		0			0
$781$	−440500.	+	254323.i	−0.722177	+	0.416949i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−14214.7	+	24620.5i	−0.0230673	+	0.0399537i
$786$		0			0
$787$		−	454894.i		−	0.734448i	−0.930132	−	0.367224i	$-0.880308\pi$
$787$		−	454894.i		−	0.734448i	0.930132	−	0.367224i	$-0.119692\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			212941.i			0.340335i
$792$		0			0
$793$	506991.	−	292711.i	0.806220	−	0.465472i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	1.06757e6i		−	1.68065i	−0.542080	−	0.840327i	$-0.682363\pi$
$797$		−	1.06757e6i		−	1.68065i	0.542080	−	0.840327i	$-0.317637\pi$
$798$		0			0
$799$	−916780.			−1.43606
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−50295.6	−	87114.6i	−0.0780008	−	0.135101i
$804$		0			0
$805$	−10836.5			−0.0167224
$806$		0			0
$807$		0			0
$808$		0			0
$809$	637963.			0.974762			0.487381	−	0.873189i	$-0.337952\pi$
$809$	637963.			0.974762			0.487381	+	0.873189i	$0.337952\pi$
$810$		0			0
$811$	185580.	+	107145.i	0.282157	+	0.162903i	0.634399	−	0.773006i	$-0.281248\pi$
$811$	185580.	+	107145.i	0.282157	+	0.162903i	−0.352243	+	0.935909i	$0.614581\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−13484.1	−	23355.2i	−0.0203005	−	0.0351615i
$816$		0			0
$817$	−949793.	+	630517.i	−1.42293	+	0.944610i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	415898.	−	720356.i	0.617022	−	1.06871i	−0.373005	−	0.927830i	$-0.621672\pi$
$821$	415898.	−	720356.i	0.617022	−	1.06871i	0.990026	−	0.140883i	$-0.0449943\pi$
$822$		0			0
$823$	195874.	−	339263.i	0.289186	−	0.500884i	−0.684430	−	0.729079i	$-0.739949\pi$
$823$	195874.	−	339263.i	0.289186	−	0.500884i	0.973616	+	0.228194i	$0.0732822\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−690088.	−	398423.i	−1.00901	−	0.582550i	−0.0981052	−	0.995176i	$-0.531278\pi$
$827$	−690088.	−	398423.i	−1.00901	−	0.582550i	−0.910900	+	0.412626i	$0.864611\pi$
$828$		0			0
$829$			1.01961e6i			1.48363i	0.670605	+	0.741814i	$0.266034\pi$
$829$			1.01961e6i			1.48363i	−0.670605	+	0.741814i	$0.733966\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−230230.	−	398770.i	−0.331797	−	0.574689i
$834$		0			0
$835$			29427.0i			0.0422058i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−992539.	+	573043.i	−1.41002	+	0.814073i	−0.995389	−	0.0959190i	$-0.969421\pi$
$839$	−992539.	+	573043.i	−1.41002	+	0.814073i	−0.414626	+	0.909992i	$0.636088\pi$
$840$		0			0
$841$	−318734.	−	552064.i	−0.450647	−	0.780544i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4238.10	+	7340.61i	−0.00593551	+	0.0102806i
$846$		0			0
$847$	352620.			0.491518
$848$		0			0
$849$		0			0
$850$		0			0
$851$	535578.	+	309216.i	0.739544	+	0.426976i
$852$		0			0
$853$	−345351.	−	598165.i	−0.474638	−	0.822097i	0.524940	−	0.851139i	$-0.324088\pi$
$853$	−345351.	−	598165.i	−0.474638	−	0.822097i	−0.999578	+	0.0290421i	$0.990754\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−426307.	+	246129.i	−0.580445	+	0.335120i	−0.761310	−	0.648388i	$-0.775444\pi$
$857$	−426307.	+	246129.i	−0.580445	+	0.335120i	0.180865	+	0.983508i	$0.442110\pi$
$858$		0			0
$859$	−559855.	+	969698.i	−0.758734	+	1.31417i	0.184762	+	0.982783i	$0.440848\pi$
$859$	−559855.	+	969698.i	−0.758734	+	1.31417i	−0.943496	+	0.331383i	$0.892485\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1.18127e6i		−	1.58609i	−0.609166	−	0.793043i	$-0.708496\pi$
$863$		−	1.18127e6i		−	1.58609i	0.609166	−	0.793043i	$-0.291504\pi$
$864$		0			0
$865$	−11864.7	−	6850.11i	−0.0158572	−	0.00915515i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−314421.	+	181531.i	−0.416362	+	0.240387i
$870$		0			0
$871$	−187637.	−	324996.i	−0.247333	−	0.428393i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	26430.5			0.0345215
$876$		0			0
$877$	−130845.	+	75543.5i	−0.170121	+	0.0982195i	−0.582643	−	0.812728i	$-0.697981\pi$
$877$	−130845.	+	75543.5i	−0.170121	+	0.0982195i	0.412522	+	0.910948i	$0.364648\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	648551.			0.835588			0.417794	−	0.908542i	$-0.362803\pi$
$881$	648551.			0.835588			0.417794	+	0.908542i	$0.362803\pi$
$882$		0			0
$883$	311217.	−	539043.i	0.399155	−	0.691357i	−0.594467	−	0.804120i	$-0.702637\pi$
$883$	311217.	−	539043.i	0.399155	−	0.691357i	0.993622	+	0.112763i	$0.0359702\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.15378e6	−	666136.i	−1.46648	−	0.846672i	−0.467183	−	0.884161i	$-0.654731\pi$
$887$	−1.15378e6	−	666136.i	−1.46648	−	0.846672i	−0.999297	+	0.0374885i	$0.988064\pi$
$888$		0			0
$889$	−483148.	−	278946.i	−0.611331	−	0.352952i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	734177.	+	364799.i	0.920657	+	0.457458i
$894$		0			0
$895$	6142.47	−	3546.36i	0.00766826	−	0.00442727i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−159304.	+	275922.i	−0.197109	+	0.341403i
$900$		0			0
$901$		−	1.01427e6i		−	1.24941i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			16617.9i			0.0202899i
$906$		0			0
$907$	455391.	−	262920.i	0.553566	−	0.319602i	−0.196993	−	0.980405i	$-0.563118\pi$
$907$	455391.	−	262920.i	0.553566	−	0.319602i	0.750559	+	0.660803i	$0.229784\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			946777.i			1.14080i	0.821366	+	0.570402i	$0.193212\pi$
$911$			946777.i			1.14080i	−0.821366	+	0.570402i	$0.806788\pi$
$912$		0			0
$913$	735075.			0.881841
$914$		0			0
$915$		0			0
$916$		0			0
$917$	470508.	+	814944.i	0.559537	+	0.969146i
$918$		0			0
$919$	748658.			0.886447			0.443223	−	0.896411i	$-0.353835\pi$
$919$	748658.			0.886447			0.443223	+	0.896411i	$0.353835\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	887443.			1.04169
$924$		0			0
$925$	−652960.	−	376987.i	−0.763138	−	0.440598i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	656093.	+	1.13639e6i	0.760211	+	1.31672i	0.942742	+	0.333524i	$0.108238\pi$
$929$	656093.	+	1.13639e6i	0.760211	+	1.31672i	−0.182531	+	0.983200i	$0.558429\pi$
$930$		0			0
$931$	25697.1	+	410956.i	0.0296473	+	0.474128i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8251.63	+	14292.2i	−0.00943880	+	0.0163485i
$936$		0			0
$937$	653872.	−	1.13254e6i	0.744756	−	1.28995i	−0.205553	−	0.978646i	$-0.565899\pi$
$937$	653872.	−	1.13254e6i	0.744756	−	1.28995i	0.950309	−	0.311309i	$-0.100767\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.30830e6	+	755349.i	1.47751	+	0.853038i	0.999677	−	0.0254148i	$-0.00809066\pi$
$941$	1.30830e6	+	755349.i	1.47751	+	0.853038i	0.477829	+	0.878453i	$0.341424\pi$
$942$		0			0
$943$			869000.i			0.977229i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−94321.1	−	163369.i	−0.105174	−	0.182167i	0.808635	−	0.588310i	$-0.200207\pi$
$947$	−94321.1	−	163369.i	−0.105174	−	0.182167i	−0.913809	+	0.406143i	$0.866873\pi$
$948$		0			0
$949$			175504.i			0.194874i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.43522e6	+	828625.i	−1.58027	+	0.912372i	−0.585457	+	0.810704i	$0.699085\pi$
$953$	−1.43522e6	+	828625.i	−1.58027	+	0.912372i	−0.994818	+	0.101668i	$0.967582\pi$
$954$		0			0
$955$	8899.03	+	15413.6i	0.00975744	+	0.0169004i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−363165.	+	629020.i	−0.394881	+	0.683955i
$960$		0			0
$961$	−530527.			−0.574461
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−911.337	−	526.160i	−0.000978643	−	0.000565020i
$966$		0			0
$967$	154209.	+	267098.i	0.164914	+	0.285639i	0.936625	−	0.350335i	$-0.113932\pi$
$967$	154209.	+	267098.i	0.164914	+	0.285639i	−0.771711	+	0.635973i	$0.780599\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−149267.	+	86179.3i	−0.158316	+	0.0914038i	−0.577065	−	0.816698i	$-0.695802\pi$
$971$	−149267.	+	86179.3i	−0.158316	+	0.0914038i	0.418749	+	0.908102i	$0.362469\pi$
$972$		0			0
$973$	510667.	−	884500.i	0.539401	−	0.934270i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	734974.i		−	0.769986i	−0.922919	−	0.384993i	$-0.874204\pi$
$977$		−	734974.i		−	0.769986i	0.922919	−	0.384993i	$-0.125796\pi$
$978$		0			0
$979$	39884.0	+	23027.0i	0.0416134	+	0.0240255i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.26662e6	+	731283.i	−1.31081	+	0.756795i	−0.982230	−	0.187681i	$-0.939903\pi$
$983$	−1.26662e6	+	731283.i	−1.31081	+	0.756795i	−0.328578	+	0.944477i	$0.606569\pi$
$984$		0			0
$985$	4851.21	+	8402.54i	0.00500009	+	0.00866040i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.61799e6			1.65419
$990$		0			0
$991$	1.32563e6	−	765353.i	1.34982	−	0.779318i	0.361595	−	0.932335i	$-0.382232\pi$
$991$	1.32563e6	−	765353.i	1.34982	−	0.779318i	0.988223	+	0.153017i	$0.0488991\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6671.07			−0.00673828
$996$		0			0
$997$	−448104.	+	776138.i	−0.450805	+	0.780816i	−0.998436	−	0.0559032i	$-0.982196\pi$
$997$	−448104.	+	776138.i	−0.450805	+	0.780816i	0.547632	+	0.836720i	$0.315530\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.5.y.d.145.4		14
3.2	odd	2		228.5.l.b.145.4	✓	14
19.8	odd	6	inner	684.5.y.d.217.4		14
57.8	even	6		228.5.l.b.217.4	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.5.l.b.145.4	✓	14	3.2	odd	2
228.5.l.b.217.4	yes	14	57.8	even	6
684.5.y.d.145.4		14	1.1	even	1	trivial
684.5.y.d.217.4		14	19.8	odd	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	684.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.297876 - 0.515937i) q^{5} -35.5020 q^{7} +O(q^{10})\)	\(q+(-0.297876 - 0.515937i) q^{5} -35.5020 q^{7} -68.6194 q^{11} +(103.682 + 59.8608i) q^{13} +(201.849 + 349.613i) q^{17} +(-22.5294 - 360.296i) q^{19} +(-256.177 + 443.711i) q^{23} +(312.323 - 540.959i) q^{25} +(228.822 + 132.110i) q^{29} +1205.84i q^{31} +(10.5752 + 18.3168i) q^{35} -1207.04i q^{37} +(1468.86 - 848.047i) q^{41} +(-1578.98 - 2734.88i) q^{43} +(-1135.48 + 1966.70i) q^{47} -1140.60 q^{49} +(-2175.85 - 1256.23i) q^{53} +(20.4401 + 35.4033i) q^{55} +(-3923.06 + 2264.98i) q^{59} +(2444.93 - 4234.75i) q^{61} -71.3245i q^{65} +(-2714.60 - 1567.27i) q^{67} +(6419.46 - 3706.28i) q^{71} +(732.965 + 1269.53i) q^{73} +2436.13 q^{77} +(4582.10 - 2645.47i) q^{79} -10712.4 q^{83} +(120.252 - 208.283i) q^{85} +(-581.235 - 335.576i) q^{89} +(-3680.92 - 2125.18i) q^{91} +(-179.179 + 118.948i) q^{95} +(-7638.32 + 4409.98i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) \) 14 * q - 12 * q^5 - 110 * q^7	\( 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) \) 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more