LMFDB - Embedded newform 900.3.y.a.89.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(89,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.89");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.y (of order $10$, degree $4$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			89.20
Character	$\chi$	$=$	900.89
Dual form			900.3.y.a.809.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.98948 - 0.324198i) q^{5} -11.3476i q^{7} +O(q^{10})$	$q+(4.98948 - 0.324198i) q^{5} -11.3476i q^{7} +(9.57207 + 13.1748i) q^{11} +(-6.25783 + 8.61316i) q^{13} +(4.60448 + 14.1711i) q^{17} +(9.08119 + 27.9490i) q^{19} +(23.3479 - 16.9633i) q^{23} +(24.7898 - 3.23515i) q^{25} +(-23.1046 - 7.50712i) q^{29} +(5.24517 + 16.1430i) q^{31} +(-3.67887 - 56.6187i) q^{35} +(36.9930 - 50.9165i) q^{37} +(3.48701 - 4.79946i) q^{41} +27.1970i q^{43} +(11.8563 - 36.4901i) q^{47} -79.7683 q^{49} +(20.6965 - 63.6972i) q^{53} +(52.0309 + 62.6323i) q^{55} +(15.0057 - 20.6536i) q^{59} +(49.6277 - 36.0566i) q^{61} +(-28.4309 + 45.0040i) q^{65} +(-56.7309 + 18.4330i) q^{67} +(98.0388 + 31.8547i) q^{71} +(26.4085 + 36.3482i) q^{73} +(149.503 - 108.620i) q^{77} +(-33.1387 + 101.990i) q^{79} +(11.2956 + 34.7644i) q^{83} +(27.5682 + 69.2139i) q^{85} +(-45.8222 - 63.0688i) q^{89} +(97.7388 + 71.0114i) q^{91} +(54.3714 + 136.507i) q^{95} +(-22.2138 - 7.21769i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) $ 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.98948	−	0.324198i	0.997896	−	0.0648395i
$5$	4.98948	−	0.324198i	0.997896	−	0.0648395i
$6$		0			0
$7$		−	11.3476i		−	1.62109i	−0.585678	−	0.810544i	$-0.699172\pi$
$7$		−	11.3476i		−	1.62109i	0.585678	−	0.810544i	$-0.300828\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	9.57207	+	13.1748i	0.870188	+	1.19771i	0.979043	+	0.203654i	$0.0652816\pi$
$11$	9.57207	+	13.1748i	0.870188	+	1.19771i	−0.108855	+	0.994058i	$0.534718\pi$
$12$		0			0
$13$	−6.25783	+	8.61316i	−0.481372	+	0.662551i	−0.978768	−	0.204972i	$-0.934290\pi$
$13$	−6.25783	+	8.61316i	−0.481372	+	0.662551i	0.497396	+	0.867523i	$0.334290\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.60448	+	14.1711i	0.270852	+	0.833597i	0.990287	+	0.139037i	$0.0444007\pi$
$17$	4.60448	+	14.1711i	0.270852	+	0.833597i	−0.719435	+	0.694560i	$0.755599\pi$
$18$		0			0
$19$	9.08119	+	27.9490i	0.477957	+	1.47100i	0.841928	+	0.539590i	$0.181421\pi$
$19$	9.08119	+	27.9490i	0.477957	+	1.47100i	−0.363971	+	0.931410i	$0.618579\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	23.3479	−	16.9633i	1.01513	−	0.737533i	0.0498491	−	0.998757i	$-0.484126\pi$
$23$	23.3479	−	16.9633i	1.01513	−	0.737533i	0.965278	+	0.261224i	$0.0841260\pi$
$24$		0			0
$25$	24.7898	−	3.23515i	0.991592	−	0.129406i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−23.1046	−	7.50712i	−0.796709	−	0.258866i	−0.117750	−	0.993043i	$-0.537568\pi$
$29$	−23.1046	−	7.50712i	−0.796709	−	0.258866i	−0.678958	+	0.734177i	$0.737568\pi$
$30$		0			0
$31$	5.24517	+	16.1430i	0.169199	+	0.520741i	0.999321	−	0.0368407i	$-0.0117294\pi$
$31$	5.24517	+	16.1430i	0.169199	+	0.520741i	−0.830122	+	0.557581i	$0.811729\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.67887	−	56.6187i	−0.105110	−	1.61768i
$36$		0			0
$37$	36.9930	−	50.9165i	0.999810	−	1.37612i	0.0743682	−	0.997231i	$-0.476306\pi$
$37$	36.9930	−	50.9165i	0.999810	−	1.37612i	0.925442	−	0.378890i	$-0.123694\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.48701	−	4.79946i	0.0850491	−	0.117060i	−0.764372	−	0.644775i	$-0.776951\pi$
$41$	3.48701	−	4.79946i	0.0850491	−	0.117060i	0.849422	+	0.527715i	$0.176951\pi$
$42$		0			0
$43$			27.1970i			0.632489i	0.948678	+	0.316245i	$0.102422\pi$
$43$			27.1970i			0.632489i	−0.948678	+	0.316245i	$0.897578\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	11.8563	−	36.4901i	0.252263	−	0.776385i	−0.742094	−	0.670296i	$-0.766167\pi$
$47$	11.8563	−	36.4901i	0.252263	−	0.776385i	0.994357	−	0.106089i	$-0.0338328\pi$
$48$		0			0
$49$	−79.7683			−1.62792
$50$		0			0
$51$		0			0
$52$		0			0
$53$	20.6965	−	63.6972i	0.390500	−	1.20183i	−0.541912	−	0.840436i	$-0.682299\pi$
$53$	20.6965	−	63.6972i	0.390500	−	1.20183i	0.932411	−	0.361399i	$-0.117701\pi$
$54$		0			0
$55$	52.0309	+	62.6323i	0.946016	+	1.13877i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	15.0057	−	20.6536i	0.254334	−	0.350061i	−0.662689	−	0.748894i	$-0.730585\pi$
$59$	15.0057	−	20.6536i	0.254334	−	0.350061i	0.917023	+	0.398834i	$0.130585\pi$
$60$		0			0
$61$	49.6277	−	36.0566i	0.813569	−	0.591092i	−0.101294	−	0.994857i	$-0.532298\pi$
$61$	49.6277	−	36.0566i	0.813569	−	0.591092i	0.914863	+	0.403764i	$0.132298\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−28.4309	+	45.0040i	−0.437399	+	0.692369i
$66$		0			0
$67$	−56.7309	+	18.4330i	−0.846730	+	0.275119i	−0.700076	−	0.714068i	$-0.746851\pi$
$67$	−56.7309	+	18.4330i	−0.846730	+	0.275119i	−0.146654	+	0.989188i	$0.546851\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	98.0388	+	31.8547i	1.38083	+	0.448658i	0.902942	−	0.429763i	$-0.141403\pi$
$71$	98.0388	+	31.8547i	1.38083	+	0.448658i	0.477887	+	0.878422i	$0.341403\pi$
$72$		0			0
$73$	26.4085	+	36.3482i	0.361761	+	0.497921i	0.950638	−	0.310301i	$-0.100430\pi$
$73$	26.4085	+	36.3482i	0.361761	+	0.497921i	−0.588878	+	0.808222i	$0.700430\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	149.503	−	108.620i	1.94159	−	1.41065i
$78$		0			0
$79$	−33.1387	+	101.990i	−0.419477	+	1.29102i	0.488708	+	0.872447i	$0.337468\pi$
$79$	−33.1387	+	101.990i	−0.419477	+	1.29102i	−0.908185	+	0.418570i	$0.862532\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	11.2956	+	34.7644i	0.136092	+	0.418849i	0.995758	−	0.0920077i	$-0.0293284\pi$
$83$	11.2956	+	34.7644i	0.136092	+	0.418849i	−0.859666	+	0.510856i	$0.829328\pi$
$84$		0			0
$85$	27.5682	+	69.2139i	0.324332	+	0.814281i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−45.8222	−	63.0688i	−0.514856	−	0.708639i	0.469873	−	0.882734i	$-0.344300\pi$
$89$	−45.8222	−	63.0688i	−0.514856	−	0.708639i	−0.984729	+	0.174096i	$0.944300\pi$
$90$		0			0
$91$	97.7388	+	71.0114i	1.07405	+	0.780345i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	54.3714	+	136.507i	0.572330	+	1.43691i
$96$		0			0
$97$	−22.2138	−	7.21769i	−0.229008	−	0.0744092i	0.192265	−	0.981343i	$-0.438417\pi$
$97$	−22.2138	−	7.21769i	−0.229008	−	0.0744092i	−0.421273	+	0.906934i	$0.638417\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	92.0483i		−	0.911370i	−0.890141	−	0.455685i	$-0.849394\pi$
$101$		−	92.0483i		−	0.911370i	0.890141	−	0.455685i	$-0.150606\pi$
$102$		0			0
$103$	−114.930	−	37.3431i	−1.11583	−	0.362555i	−0.307654	−	0.951498i	$-0.599544\pi$
$103$	−114.930	−	37.3431i	−1.11583	−	0.362555i	−0.808174	+	0.588944i	$0.799544\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−56.7470			−0.530346			−0.265173	−	0.964201i	$-0.585429\pi$
$107$	−56.7470			−0.530346			−0.265173	+	0.964201i	$0.585429\pi$
$108$		0			0
$109$	3.69457	+	2.68426i	0.0338951	+	0.0246263i	0.604604	−	0.796526i	$-0.293331\pi$
$109$	3.69457	+	2.68426i	0.0338951	+	0.0246263i	−0.570709	+	0.821153i	$0.693331\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	37.0377	+	26.9094i	0.327767	+	0.238137i	0.739483	−	0.673176i	$-0.235070\pi$
$113$	37.0377	+	26.9094i	0.327767	+	0.238137i	−0.411716	+	0.911312i	$0.635070\pi$
$114$		0			0
$115$	110.995	−	92.2072i	0.965170	−	0.801802i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	160.809	−	52.2499i	1.35133	−	0.439075i
$120$		0			0
$121$	−44.5604	+	137.143i	−0.368268	+	1.13341i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	122.639	−	24.1785i	0.981114	−	0.193428i
$126$		0			0
$127$	34.1586	+	47.0152i	0.268965	+	0.370199i	0.922040	−	0.387095i	$-0.126521\pi$
$127$	34.1586	+	47.0152i	0.268965	+	0.370199i	−0.653075	+	0.757293i	$0.726521\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−175.693	+	57.0862i	−1.34117	+	0.435772i	−0.889713	−	0.456521i	$-0.849095\pi$
$131$	−175.693	+	57.0862i	−1.34117	+	0.435772i	−0.451456	+	0.892293i	$0.649095\pi$
$132$		0			0
$133$	317.155	−	103.050i	2.38462	−	0.774810i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	165.904	+	120.536i	1.21098	+	0.879828i	0.995319	−	0.0966402i	$-0.0308096\pi$
$137$	165.904	+	120.536i	1.21098	+	0.879828i	0.215660	+	0.976468i	$0.430810\pi$
$138$		0			0
$139$	213.514	−	155.127i	1.53607	−	1.11602i	0.583335	−	0.812232i	$-0.301748\pi$
$139$	213.514	−	155.127i	1.53607	−	1.11602i	0.952739	−	0.303791i	$-0.0982523\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−173.377			−1.21243
$144$		0			0
$145$	−117.713	−	29.9662i	−0.811817	−	0.206663i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	236.367i		−	1.58636i	−0.608988	−	0.793180i	$-0.708424\pi$
$149$		−	236.367i		−	1.58636i	0.608988	−	0.793180i	$-0.291576\pi$
$150$		0			0
$151$	−114.355			−0.757318			−0.378659	−	0.925536i	$-0.623615\pi$
$151$	−114.355			−0.757318			−0.378659	+	0.925536i	$0.623615\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	31.4042	+	78.8445i	0.202607	+	0.508674i
$156$		0			0
$157$		−	193.365i		−	1.23163i	−0.787893	−	0.615813i	$-0.788828\pi$
$157$		−	193.365i		−	1.23163i	0.787893	−	0.615813i	$-0.211172\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−192.493	−	264.943i	−1.19561	−	1.64561i
$162$		0			0
$163$	−17.1458	+	23.5992i	−0.105189	+	0.144780i	−0.858366	−	0.513037i	$-0.828520\pi$
$163$	−17.1458	+	23.5992i	−0.105189	+	0.144780i	0.753177	+	0.657818i	$0.228520\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−37.8127	−	116.375i	−0.226423	−	0.696859i	−0.998144	−	0.0608974i	$-0.980604\pi$
$167$	−37.8127	−	116.375i	−0.226423	−	0.696859i	0.771721	−	0.635961i	$-0.219396\pi$
$168$		0			0
$169$	17.1977	+	52.9291i	0.101762	+	0.313190i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−80.5288	+	58.5076i	−0.465484	+	0.338194i	−0.795679	−	0.605719i	$-0.792886\pi$
$173$	−80.5288	+	58.5076i	−0.465484	+	0.338194i	0.330194	+	0.943913i	$0.392886\pi$
$174$		0			0
$175$	−36.7113	−	281.305i	−0.209779	−	1.60746i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	213.798	+	69.4671i	1.19440	+	0.388084i	0.837698	−	0.546134i	$-0.183901\pi$
$179$	213.798	+	69.4671i	1.19440	+	0.388084i	0.356703	+	0.934218i	$0.383901\pi$
$180$		0			0
$181$	37.7178	+	116.083i	0.208385	+	0.641344i	0.999557	+	0.0297505i	$0.00947128\pi$
$181$	37.7178	+	116.083i	0.208385	+	0.641344i	−0.791172	+	0.611594i	$0.790529\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	168.069	−	266.040i	0.908479	−	1.43805i
$186$		0			0
$187$	−142.628	+	196.310i	−0.762716	+	1.04979i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−58.4915	+	80.5066i	−0.306238	+	0.421501i	−0.934203	−	0.356741i	$-0.883888\pi$
$191$	−58.4915	+	80.5066i	−0.306238	+	0.421501i	0.627965	+	0.778241i	$0.283888\pi$
$192$		0			0
$193$			318.469i			1.65010i	0.565059	+	0.825051i	$0.308853\pi$
$193$			318.469i			1.65010i	−0.565059	+	0.825051i	$0.691147\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−59.0075	+	181.606i	−0.299530	+	0.921859i	0.682132	+	0.731229i	$0.261053\pi$
$197$	−59.0075	+	181.606i	−0.299530	+	0.921859i	−0.981662	+	0.190630i	$0.938947\pi$
$198$		0			0
$199$	−366.115			−1.83977			−0.919886	−	0.392186i	$-0.871719\pi$
$199$	−366.115			−1.83977			−0.919886	+	0.392186i	$0.871719\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−85.1879	+	262.181i	−0.419645	+	1.29153i
$204$		0			0
$205$	15.8424	−	25.0773i	0.0772800	−	0.122328i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−281.298	+	387.173i	−1.34592	+	1.85250i
$210$		0			0
$211$	−240.157	+	174.484i	−1.13818	+	0.826940i	−0.986865	−	0.161545i	$-0.948352\pi$
$211$	−240.157	+	174.484i	−1.13818	+	0.826940i	−0.151319	+	0.988485i	$0.548352\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.81721	+	135.699i	0.0410103	+	0.631158i
$216$		0			0
$217$	183.184	−	59.5201i	0.844166	−	0.274286i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−150.872	−	49.0214i	−0.682681	−	0.221816i
$222$		0			0
$223$	70.6188	+	97.1984i	0.316676	+	0.435867i	0.937449	−	0.348123i	$-0.113181\pi$
$223$	70.6188	+	97.1984i	0.316676	+	0.435867i	−0.620773	+	0.783991i	$0.713181\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	137.120	−	99.6235i	0.604053	−	0.438870i	−0.243262	−	0.969961i	$-0.578218\pi$
$227$	137.120	−	99.6235i	0.604053	−	0.438870i	0.847315	+	0.531091i	$0.178218\pi$
$228$		0			0
$229$	−49.1720	+	151.336i	−0.214725	+	0.660855i	0.784448	+	0.620194i	$0.212946\pi$
$229$	−49.1720	+	151.336i	−0.214725	+	0.660855i	−0.999173	+	0.0406608i	$0.987054\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	72.6582	+	223.619i	0.311838	+	0.959738i	0.977037	+	0.213072i	$0.0683469\pi$
$233$	72.6582	+	223.619i	0.311838	+	0.959738i	−0.665199	+	0.746666i	$0.731653\pi$
$234$		0			0
$235$	47.3270	−	185.910i	0.201391	−	0.791107i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−257.121	−	353.897i	−1.07582	−	1.48074i	−0.864039	−	0.503425i	$-0.832073\pi$
$239$	−257.121	−	353.897i	−1.07582	−	1.48074i	−0.211783	−	0.977317i	$-0.567927\pi$
$240$		0			0
$241$	−300.281	−	218.167i	−1.24598	−	0.905257i	−0.247998	−	0.968761i	$-0.579772\pi$
$241$	−300.281	−	218.167i	−1.24598	−	0.905257i	−0.997982	+	0.0635038i	$0.979772\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−398.002	+	25.8607i	−1.62450	+	0.105554i
$246$		0			0
$247$	−297.558	−	96.6824i	−1.20469	−	0.391427i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			28.0840i			0.111889i	0.998434	+	0.0559443i	$0.0178169\pi$
$251$			28.0840i			0.111889i	−0.998434	+	0.0559443i	$0.982183\pi$
$252$		0			0
$253$	446.976	+	145.231i	1.76670	+	0.574037i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−320.361			−1.24654			−0.623271	−	0.782006i	$-0.714197\pi$
$257$	−320.361			−1.24654			−0.623271	+	0.782006i	$0.714197\pi$
$258$		0			0
$259$	−577.780	−	419.782i	−2.23081	−	1.62078i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	321.371	+	233.490i	1.22194	+	0.887793i	0.996260	−	0.0864078i	$-0.0275388\pi$
$263$	321.371	+	233.490i	1.22194	+	0.887793i	0.225682	+	0.974201i	$0.427539\pi$
$264$		0			0
$265$	82.6142	−	324.526i	0.311752	−	1.22463i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	247.488	−	80.4136i	0.920029	−	0.298935i	0.189550	−	0.981871i	$-0.439297\pi$
$269$	247.488	−	80.4136i	0.920029	−	0.298935i	0.730479	+	0.682936i	$0.239297\pi$
$270$		0			0
$271$	−132.589	+	408.066i	−0.489257	+	1.50578i	0.336463	+	0.941697i	$0.390769\pi$
$271$	−132.589	+	408.066i	−0.489257	+	1.50578i	−0.825720	+	0.564080i	$0.809231\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	279.912	+	295.634i	1.01786	+	1.07503i
$276$		0			0
$277$	−172.903	−	237.981i	−0.624200	−	0.859137i	0.373450	−	0.927650i	$-0.378175\pi$
$277$	−172.903	−	237.981i	−0.624200	−	0.859137i	−0.997650	+	0.0685128i	$0.978175\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.52683	+	0.496097i	−0.00543355	+	0.00176547i	−0.311733	−	0.950170i	$-0.600909\pi$
$281$	−1.52683	+	0.496097i	−0.00543355	+	0.00176547i	0.306299	+	0.951935i	$0.400909\pi$
$282$		0			0
$283$	382.584	−	124.309i	1.35189	−	0.439254i	0.458560	−	0.888664i	$-0.348366\pi$
$283$	382.584	−	124.309i	1.35189	−	0.439254i	0.893326	+	0.449409i	$0.148366\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−54.4624	−	39.5693i	−0.189765	−	0.137872i
$288$		0			0
$289$	54.1859	−	39.3683i	0.187494	−	0.136223i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−435.850			−1.48754			−0.743771	−	0.668434i	$-0.766965\pi$
$293$	−435.850			−1.48754			−0.743771	+	0.668434i	$0.766965\pi$
$294$		0			0
$295$	68.1748	−	107.915i	0.231101	−	0.365815i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			307.253i			1.02760i
$300$		0			0
$301$	308.621			1.02532
$302$		0			0
$303$		0			0
$304$		0			0
$305$	235.927	−	195.993i	0.773531	−	0.642600i
$306$		0			0
$307$		−	421.485i		−	1.37291i	−0.727170	−	0.686457i	$-0.759165\pi$
$307$		−	421.485i		−	1.37291i	0.727170	−	0.686457i	$-0.240835\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	231.294	+	318.349i	0.743710	+	1.02363i	0.998397	+	0.0566054i	$0.0180277\pi$
$311$	231.294	+	318.349i	0.743710	+	1.02363i	−0.254687	+	0.967024i	$0.581972\pi$
$312$		0			0
$313$	152.515	−	209.919i	0.487269	−	0.670669i	−0.492612	−	0.870249i	$-0.663958\pi$
$313$	152.515	−	209.919i	0.487269	−	0.670669i	0.979881	+	0.199580i	$0.0639579\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−115.605	−	355.794i	−0.364683	−	1.12238i	−0.950179	−	0.311704i	$-0.899100\pi$
$317$	−115.605	−	355.794i	−0.364683	−	1.12238i	0.585496	−	0.810675i	$-0.300900\pi$
$318$		0			0
$319$	−122.253	−	376.257i	−0.383239	−	1.17949i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−354.255	+	257.382i	−1.09677	+	0.796847i
$324$		0			0
$325$	−127.265	+	233.764i	−0.391586	+	0.719273i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−414.075	−	134.541i	−1.25859	−	0.408940i
$330$		0			0
$331$	25.3203	+	77.9280i	0.0764965	+	0.235432i	0.981992	−	0.188925i	$-0.0605003\pi$
$331$	25.3203	+	77.9280i	0.0764965	+	0.235432i	−0.905495	+	0.424357i	$0.860500\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−277.082	+	110.363i	−0.827110	+	0.329442i
$336$		0			0
$337$	241.253	−	332.056i	0.715883	−	0.985329i	−0.283767	−	0.958893i	$-0.591584\pi$
$337$	241.253	−	332.056i	0.715883	−	0.985329i	0.999651	−	0.0264355i	$-0.00841567\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−162.474	+	223.626i	−0.476462	+	0.655794i
$342$		0			0
$343$			349.146i			1.01792i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−108.046	+	332.530i	−0.311371	+	0.958300i	0.665852	+	0.746084i	$0.268068\pi$
$347$	−108.046	+	332.530i	−0.311371	+	0.958300i	−0.977223	+	0.212216i	$0.931932\pi$
$348$		0			0
$349$	−391.807			−1.12266			−0.561328	−	0.827594i	$-0.689709\pi$
$349$	−391.807			−1.12266			−0.561328	+	0.827594i	$0.689709\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	24.6995	−	76.0173i	0.0699703	−	0.215346i	−0.909957	−	0.414703i	$-0.863885\pi$
$353$	24.6995	−	76.0173i	0.0699703	−	0.215346i	0.979927	+	0.199357i	$0.0638853\pi$
$354$		0			0
$355$	499.490	+	127.155i	1.40701	+	0.358182i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.7933	−	34.1251i	0.0690621	−	0.0950559i	−0.773089	−	0.634298i	$-0.781289\pi$
$359$	24.7933	−	34.1251i	0.0690621	−	0.0950559i	0.842151	+	0.539242i	$0.181289\pi$
$360$		0			0
$361$	−406.624	+	295.430i	−1.12638	+	0.818365i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	143.549	+	172.797i	0.393284	+	0.473417i
$366$		0			0
$367$	72.2962	−	23.4904i	0.196992	−	0.0640067i	−0.208859	−	0.977946i	$-0.566975\pi$
$367$	72.2962	−	23.4904i	0.196992	−	0.0640067i	0.405851	+	0.913939i	$0.366975\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−722.811	−	234.856i	−1.94828	−	0.633034i
$372$		0			0
$373$	−201.565	−	277.430i	−0.540388	−	0.743781i	0.448281	−	0.893893i	$-0.352037\pi$
$373$	−201.565	−	277.430i	−0.540388	−	0.743781i	−0.988669	+	0.150112i	$0.952037\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	209.244	−	152.025i	0.555025	−	0.403249i
$378$		0			0
$379$	−196.022	+	603.295i	−0.517210	+	1.59181i	0.262016	+	0.965064i	$0.415613\pi$
$379$	−196.022	+	603.295i	−0.517210	+	1.59181i	−0.779225	+	0.626744i	$0.784387\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−100.538	−	309.423i	−0.262500	−	0.807893i	−0.992259	−	0.124188i	$-0.960368\pi$
$383$	−100.538	−	309.423i	−0.262500	−	0.807893i	0.729759	−	0.683705i	$-0.239632\pi$
$384$		0			0
$385$	710.726	−	590.426i	1.84604	−	1.53357i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−437.452	−	602.101i	−1.12456	−	1.54782i	−0.798019	−	0.602633i	$-0.794118\pi$
$389$	−437.452	−	602.101i	−1.12456	−	1.54782i	−0.326536	−	0.945185i	$-0.605882\pi$
$390$		0			0
$391$	347.894	+	252.760i	0.889755	+	0.646445i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−132.280	+	519.622i	−0.334885	+	1.31550i
$396$		0			0
$397$	−630.649	−	204.910i	−1.58854	−	0.516147i	−0.624298	−	0.781186i	$-0.714615\pi$
$397$	−630.649	−	204.910i	−1.58854	−	0.516147i	−0.964238	+	0.265039i	$0.914615\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			234.752i			0.585417i	0.956202	+	0.292708i	$0.0945565\pi$
$401$			234.752i			0.585417i	−0.956202	+	0.292708i	$0.905443\pi$
$402$		0			0
$403$	−171.865	−	55.8424i	−0.426465	−	0.138567i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1024.91			2.51822
$408$		0			0
$409$	238.236	+	173.089i	0.582485	+	0.423200i	0.839619	−	0.543175i	$-0.182778\pi$
$409$	238.236	+	173.089i	0.582485	+	0.423200i	−0.257134	+	0.966376i	$0.582778\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−234.369	−	170.279i	−0.567479	−	0.412297i
$414$		0			0
$415$	67.6299	+	169.794i	0.162964	+	0.409143i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	201.255	−	65.3918i	0.480323	−	0.156066i	−0.0588407	−	0.998267i	$-0.518740\pi$
$419$	201.255	−	65.3918i	0.480323	−	0.156066i	0.539164	+	0.842201i	$0.318740\pi$
$420$		0			0
$421$	29.1646	−	89.7595i	0.0692747	−	0.213205i	−0.910426	−	0.413672i	$-0.864246\pi$
$421$	29.1646	−	89.7595i	0.0692747	−	0.213205i	0.979700	+	0.200467i	$0.0642459\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	159.990	+	336.404i	0.376447	+	0.791538i
$426$		0			0
$427$	−409.157	−	563.156i	−0.958212	−	1.31887i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−201.987	+	65.6296i	−0.468648	+	0.152273i	−0.533815	−	0.845602i	$-0.679242\pi$
$431$	−201.987	+	65.6296i	−0.468648	+	0.152273i	0.0651671	+	0.997874i	$0.479242\pi$
$432$		0			0
$433$	−620.886	+	201.738i	−1.43392	+	0.465908i	−0.919995	−	0.391930i	$-0.871808\pi$
$433$	−620.886	+	201.738i	−1.43392	+	0.465908i	−0.513921	+	0.857838i	$0.671808\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	686.133	+	498.505i	1.57010	+	1.14074i
$438$		0			0
$439$	−454.821	+	330.447i	−1.03604	+	0.752726i	−0.969508	−	0.245058i	$-0.921193\pi$
$439$	−454.821	+	330.447i	−1.03604	+	0.752726i	−0.0665306	+	0.997784i	$0.521193\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	644.774			1.45547			0.727736	−	0.685858i	$-0.240573\pi$
$443$	644.774			1.45547			0.727736	+	0.685858i	$0.240573\pi$
$444$		0			0
$445$	−249.076	−	299.825i	−0.559720	−	0.673764i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			23.3656i			0.0520392i	0.999661	+	0.0260196i	$0.00828323\pi$
$449$			23.3656i			0.0520392i	−0.999661	+	0.0260196i	$0.991717\pi$
$450$		0			0
$451$	96.6100			0.214213
$452$		0			0
$453$		0			0
$454$		0			0
$455$	510.687	+	322.623i	1.12239	+	0.709062i
$456$		0			0
$457$		−	450.231i		−	0.985188i	−0.870259	−	0.492594i	$-0.836049\pi$
$457$		−	450.231i		−	0.985188i	0.870259	−	0.492594i	$-0.163951\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−310.799	−	427.778i	−0.674184	−	0.927935i	0.325662	−	0.945486i	$-0.394413\pi$
$461$	−310.799	−	427.778i	−0.674184	−	0.927935i	−0.999846	+	0.0175513i	$0.994413\pi$
$462$		0			0
$463$	−216.231	+	297.616i	−0.467022	+	0.642800i	−0.975946	−	0.218011i	$-0.930043\pi$
$463$	−216.231	+	297.616i	−0.467022	+	0.642800i	0.508925	+	0.860811i	$0.330043\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−49.2624	−	151.614i	−0.105487	−	0.324655i	0.884357	−	0.466810i	$-0.154597\pi$
$467$	−49.2624	−	151.614i	−0.105487	−	0.324655i	−0.989844	+	0.142155i	$0.954597\pi$
$468$		0			0
$469$	209.170	+	643.761i	0.445992	+	1.37262i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−358.316	+	260.332i	−0.757539	+	0.550385i
$474$		0			0
$475$	315.540	+	663.471i	0.664295	+	1.39678i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	352.346	+	114.484i	0.735587	+	0.239007i	0.652768	−	0.757558i	$-0.273608\pi$
$479$	352.346	+	114.484i	0.735587	+	0.239007i	0.0828189	+	0.996565i	$0.473608\pi$
$480$		0			0
$481$	207.056	+	637.253i	0.430470	+	1.32485i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−113.175	−	28.8109i	−0.233351	−	0.0594038i
$486$		0			0
$487$	−346.680	+	477.164i	−0.711868	+	0.979802i	0.287887	+	0.957664i	$0.407047\pi$
$487$	−346.680	+	477.164i	−0.711868	+	0.979802i	−0.999755	+	0.0221379i	$0.992953\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−81.6196	+	112.340i	−0.166231	+	0.228798i	−0.884004	−	0.467480i	$-0.845162\pi$
$491$	−81.6196	+	112.340i	−0.166231	+	0.228798i	0.717772	+	0.696278i	$0.245162\pi$
$492$		0			0
$493$		−	361.984i		−	0.734248i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	361.475	−	1112.51i	0.727314	−	2.23844i
$498$		0			0
$499$	−426.207			−0.854122			−0.427061	−	0.904223i	$-0.640451\pi$
$499$	−426.207			−0.854122			−0.427061	+	0.904223i	$0.640451\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−109.796	+	337.918i	−0.218282	+	0.671804i	0.780622	+	0.625004i	$0.214903\pi$
$503$	−109.796	+	337.918i	−0.218282	+	0.671804i	−0.998904	+	0.0468006i	$0.985097\pi$
$504$		0			0
$505$	−29.8418	−	459.273i	−0.0590928	−	0.909452i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	579.155	−	797.139i	1.13783	−	1.56609i	0.365565	−	0.930786i	$-0.380876\pi$
$509$	579.155	−	797.139i	1.13783	−	1.56609i	0.772264	−	0.635302i	$-0.219124\pi$
$510$		0			0
$511$	412.465	−	299.674i	0.807173	−	0.586445i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−585.549	−	149.063i	−1.13699	−	0.289442i
$516$		0			0
$517$	594.240	−	193.080i	1.14940	−	0.373463i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−254.622	−	82.7318i	−0.488718	−	0.158794i	0.0542837	−	0.998526i	$-0.482712\pi$
$521$	−254.622	−	82.7318i	−0.488718	−	0.158794i	−0.543002	+	0.839731i	$0.682712\pi$
$522$		0			0
$523$	309.408	+	425.864i	0.591603	+	0.814271i	0.994907	−	0.100795i	$-0.0321385\pi$
$523$	309.408	+	425.864i	0.591603	+	0.814271i	−0.403305	+	0.915066i	$0.632138\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−204.613	+	148.660i	−0.388260	+	0.282087i
$528$		0			0
$529$	93.9035	−	289.005i	0.177511	−	0.546324i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	19.5174	+	60.0684i	0.0366180	+	0.112699i
$534$		0			0
$535$	−283.138	+	18.3972i	−0.529230	+	0.0343874i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−763.547	−	1050.93i	−1.41660	−	1.94978i
$540$		0			0
$541$	625.475	+	454.434i	1.15615	+	0.839989i	0.989286	−	0.145992i	$-0.0466372\pi$
$541$	625.475	+	454.434i	1.15615	+	0.839989i	0.166860	+	0.985981i	$0.446637\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	19.3042	+	12.1953i	0.0354206	+	0.0223767i
$546$		0			0
$547$	−95.2535	−	30.9497i	−0.174138	−	0.0565809i	0.220650	−	0.975353i	$-0.429182\pi$
$547$	−95.2535	−	30.9497i	−0.174138	−	0.0565809i	−0.394788	+	0.918772i	$0.629182\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	713.923i		−	1.29569i
$552$		0			0
$553$	1157.35	+	376.045i	2.09285	+	0.680009i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	399.252			0.716790			0.358395	−	0.933570i	$-0.383324\pi$
$557$	399.252			0.716790			0.358395	+	0.933570i	$0.383324\pi$
$558$		0			0
$559$	−234.253	−	170.194i	−0.419056	−	0.304462i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	241.225	+	175.260i	0.428463	+	0.311296i	0.781034	−	0.624489i	$-0.214693\pi$
$563$	241.225	+	175.260i	0.428463	+	0.311296i	−0.352571	+	0.935785i	$0.614693\pi$
$564$		0			0
$565$	193.523	+	122.257i	0.342518	+	0.216383i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−184.352	+	59.8996i	−0.323993	+	0.105272i	−0.466498	−	0.884522i	$-0.654484\pi$
$569$	−184.352	+	59.8996i	−0.323993	+	0.105272i	0.142505	+	0.989794i	$0.454484\pi$
$570$		0			0
$571$	91.2850	−	280.946i	0.159869	−	0.492025i	−0.838753	−	0.544512i	$-0.816715\pi$
$571$	91.2850	−	280.946i	0.159869	−	0.492025i	0.998622	+	0.0524872i	$0.0167149\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	523.912	−	496.050i	0.911151	−	0.862696i
$576$		0			0
$577$	302.071	+	415.765i	0.523520	+	0.720563i	0.986126	−	0.166001i	$-0.0530855\pi$
$577$	302.071	+	415.765i	0.523520	+	0.720563i	−0.462606	+	0.886564i	$0.653086\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	394.493	−	128.179i	0.678990	−	0.220617i
$582$		0			0
$583$	1037.31	−	337.042i	1.77926	−	0.578116i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	95.4351	+	69.3377i	0.162581	+	0.118122i	0.666101	−	0.745861i	$-0.267962\pi$
$587$	95.4351	+	69.3377i	0.162581	+	0.118122i	−0.503520	+	0.863984i	$0.667962\pi$
$588$		0			0
$589$	−403.548	+	293.195i	−0.685140	+	0.497784i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	179.491			0.302682			0.151341	−	0.988482i	$-0.451641\pi$
$593$	179.491			0.302682			0.151341	+	0.988482i	$0.451641\pi$
$594$		0			0
$595$	785.412	−	312.833i	1.32002	−	0.525770i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	228.015i		−	0.380660i	−0.981720	−	0.190330i	$-0.939044\pi$
$599$		−	228.015i		−	0.380660i	0.981720	−	0.190330i	$-0.0609558\pi$
$600$		0			0
$601$	−908.065			−1.51092			−0.755462	−	0.655193i	$-0.772587\pi$
$601$	−908.065			−1.51092			−0.755462	+	0.655193i	$0.772587\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−177.872	+	698.718i	−0.294003	+	1.15490i
$606$		0			0
$607$		−	31.5495i		−	0.0519760i	−0.999662	−	0.0259880i	$-0.991727\pi$
$607$		−	31.5495i		−	0.0519760i	0.999662	−	0.0259880i	$-0.00827317\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	240.100	+	330.469i	0.392962	+	0.540866i
$612$		0			0
$613$	−444.428	+	611.702i	−0.725004	+	0.997883i	0.274338	+	0.961633i	$0.411541\pi$
$613$	−444.428	+	611.702i	−0.725004	+	0.997883i	−0.999343	+	0.0362497i	$0.988459\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.9732	+	61.4711i	0.0323714	+	0.0996290i	0.965937	−	0.258778i	$-0.0833199\pi$
$617$	19.9732	+	61.4711i	0.0323714	+	0.0996290i	−0.933565	+	0.358407i	$0.883320\pi$
$618$		0			0
$619$	−64.5851	−	198.773i	−0.104338	−	0.321119i	0.885237	−	0.465141i	$-0.153996\pi$
$619$	−64.5851	−	198.773i	−0.104338	−	0.321119i	−0.989574	+	0.144022i	$0.953996\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−715.680	+	519.972i	−1.14876	+	0.834626i
$624$		0			0
$625$	604.068	−	160.398i	0.966508	−	0.256636i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	891.878	+	289.789i	1.41793	+	0.460713i
$630$		0			0
$631$	−35.2315	−	108.432i	−0.0558345	−	0.171841i	0.919250	−	0.393674i	$-0.128796\pi$
$631$	−35.2315	−	108.432i	−0.0558345	−	0.171841i	−0.975085	+	0.221833i	$0.928796\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	185.676	+	223.507i	0.292402	+	0.351980i
$636$		0			0
$637$	499.176	−	687.057i	0.783636	−	1.07858i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	480.322	−	661.107i	0.749333	−	1.03137i	−0.248694	−	0.968582i	$-0.580001\pi$
$641$	480.322	−	661.107i	0.749333	−	1.03137i	0.998027	−	0.0627860i	$-0.0199986\pi$
$642$		0			0
$643$		−	591.812i		−	0.920392i	−0.887817	−	0.460196i	$-0.847779\pi$
$643$		−	591.812i		−	0.920392i	0.887817	−	0.460196i	$-0.152221\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.7782	+	42.4050i	−0.0212956	+	0.0655410i	−0.961140	−	0.276063i	$-0.910970\pi$
$647$	−13.7782	+	42.4050i	−0.0212956	+	0.0655410i	0.939844	+	0.341604i	$0.110970\pi$
$648$		0			0
$649$	415.743			0.640590
$650$		0			0
$651$		0			0
$652$		0			0
$653$	204.642	−	629.824i	0.313388	−	0.964508i	−0.663025	−	0.748597i	$-0.730728\pi$
$653$	204.642	−	629.824i	0.313388	−	0.964508i	0.976413	−	0.215911i	$-0.0692721\pi$
$654$		0			0
$655$	−858.110	+	341.789i	−1.31009	+	0.521816i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	113.838	−	156.685i	0.172744	−	0.237761i	−0.713863	−	0.700285i	$-0.753056\pi$
$659$	113.838	−	156.685i	0.172744	−	0.237761i	0.886607	+	0.462524i	$0.153056\pi$
$660$		0			0
$661$	−324.058	+	235.442i	−0.490255	+	0.356191i	−0.805282	−	0.592892i	$-0.797986\pi$
$661$	−324.058	+	235.442i	−0.490255	+	0.356191i	0.315028	+	0.949083i	$0.397986\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1549.03	−	616.985i	2.32936	−	0.927797i
$666$		0			0
$667$	−666.789	+	216.653i	−0.999683	+	0.324817i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	950.080	+	308.700i	1.41592	+	0.460059i
$672$		0			0
$673$	326.971	+	450.037i	0.485841	+	0.668703i	0.979614	−	0.200888i	$-0.0643827\pi$
$673$	326.971	+	450.037i	0.485841	+	0.668703i	−0.493773	+	0.869591i	$0.664383\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	587.024	−	426.498i	0.867097	−	0.629982i	−0.0627098	−	0.998032i	$-0.519974\pi$
$677$	587.024	−	426.498i	0.867097	−	0.629982i	0.929806	+	0.368049i	$0.119974\pi$
$678$		0			0
$679$	−81.9035	+	252.073i	−0.120624	+	0.371242i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−168.713	−	519.246i	−0.247018	−	0.760244i	−0.995298	−	0.0968605i	$-0.969120\pi$
$683$	−168.713	−	519.246i	−0.247018	−	0.760244i	0.748280	−	0.663383i	$-0.230880\pi$
$684$		0			0
$685$	866.853	+	547.628i	1.26548	+	0.799457i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	419.120	+	576.869i	0.608301	+	0.837255i
$690$		0			0
$691$	−152.710	−	110.950i	−0.220998	−	0.160564i	0.471778	−	0.881717i	$-0.343612\pi$
$691$	−152.710	−	110.950i	−0.220998	−	0.160564i	−0.692776	+	0.721153i	$0.743612\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1015.03	−	843.224i	1.46048	−	1.21327i
$696$		0			0
$697$	84.0698	+	27.3159i	0.120617	+	0.0391907i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1215.56i			1.73404i	0.498276	+	0.867019i	$0.333967\pi$
$701$			1215.56i			1.73404i	−0.498276	+	0.867019i	$0.666033\pi$
$702$		0			0
$703$	1759.00	+	571.535i	2.50214	+	0.812995i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1044.53			−1.47741
$708$		0			0
$709$	−315.483	−	229.212i	−0.444969	−	0.323289i	0.342637	−	0.939468i	$-0.388680\pi$
$709$	−315.483	−	229.212i	−0.444969	−	0.323289i	−0.787606	+	0.616179i	$0.788680\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	396.301	+	287.930i	0.555822	+	0.403828i
$714$		0			0
$715$	−865.062	+	56.2085i	−1.20988	+	0.0786133i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−762.697	+	247.815i	−1.06078	+	0.344667i	−0.786888	−	0.617095i	$-0.788309\pi$
$719$	−762.697	+	247.815i	−1.06078	+	0.344667i	−0.273887	+	0.961762i	$0.588309\pi$
$720$		0			0
$721$	−423.755	+	1304.18i	−0.587732	+	1.80885i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−597.044	−	111.353i	−0.823509	−	0.153591i
$726$		0			0
$727$	151.625	+	208.694i	0.208563	+	0.287062i	0.900464	−	0.434930i	$-0.143227\pi$
$727$	151.625	+	208.694i	0.208563	+	0.287062i	−0.691902	+	0.721992i	$0.743227\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−385.413	+	125.228i	−0.527241	+	0.171311i
$732$		0			0
$733$	−582.668	+	189.320i	−0.794909	+	0.258281i	−0.678193	−	0.734884i	$-0.737237\pi$
$733$	−582.668	+	189.320i	−0.794909	+	0.258281i	−0.116716	+	0.993165i	$0.537237\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−785.884	−	570.978i	−1.06633	−	0.774733i
$738$		0			0
$739$	190.818	−	138.638i	0.258212	−	0.187602i	−0.451147	−	0.892450i	$-0.648985\pi$
$739$	190.818	−	138.638i	0.258212	−	0.187602i	0.709358	+	0.704848i	$0.248985\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1079.08			1.45232			0.726162	−	0.687524i	$-0.241302\pi$
$743$	1079.08			1.45232			0.726162	+	0.687524i	$0.241302\pi$
$744$		0			0
$745$	−76.6298	−	1179.35i	−0.102859	−	1.58302i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			643.943i			0.859737i
$750$		0			0
$751$	−952.678			−1.26855			−0.634273	−	0.773109i	$-0.718700\pi$
$751$	−952.678			−1.26855			−0.634273	+	0.773109i	$0.718700\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−570.572	+	37.0736i	−0.755725	+	0.0491042i
$756$		0			0
$757$			716.186i			0.946085i	0.881040	+	0.473042i	$0.156844\pi$
$757$			716.186i			0.946085i	−0.881040	+	0.473042i	$0.843156\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−553.974	−	762.479i	−0.727955	−	1.00194i	−0.999222	−	0.0394398i	$-0.987443\pi$
$761$	−553.974	−	762.479i	−0.727955	−	1.00194i	0.271267	−	0.962504i	$-0.412557\pi$
$762$		0			0
$763$	30.4600	−	41.9245i	0.0399213	−	0.0549470i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	83.9895	+	258.493i	0.109504	+	0.337018i
$768$		0			0
$769$	−346.913	−	1067.69i	−0.451122	−	1.38841i	−0.875628	−	0.482986i	$-0.839552\pi$
$769$	−346.913	−	1067.69i	−0.451122	−	1.38841i	0.424506	−	0.905425i	$-0.360448\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−542.077	+	393.842i	−0.701264	+	0.509498i	−0.880344	−	0.474336i	$-0.842688\pi$
$773$	−542.077	+	393.842i	−0.701264	+	0.509498i	0.179079	+	0.983835i	$0.442688\pi$
$774$		0			0
$775$	182.252	+	383.212i	0.235163	+	0.494467i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	165.806	+	53.8738i	0.212845	+	0.0691576i
$780$		0			0
$781$	518.754	+	1596.56i	0.664217	+	2.04425i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−62.6885	−	964.791i	−0.0798580	−	1.22903i
$786$		0			0
$787$	147.660	−	203.236i	0.187623	−	0.258241i	−0.704835	−	0.709371i	$-0.748979\pi$
$787$	147.660	−	203.236i	0.187623	−	0.258241i	0.892458	+	0.451130i	$0.148979\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	305.358	−	420.289i	0.386040	−	0.531339i
$792$		0			0
$793$			653.088i			0.823566i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−247.956	+	763.129i	−0.311111	+	0.957502i	0.666214	+	0.745760i	$0.267914\pi$
$797$	−247.956	+	763.129i	−0.311111	+	0.957502i	−0.977326	+	0.211742i	$0.932086\pi$
$798$		0			0
$799$	571.698			0.715517
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−226.097	+	695.855i	−0.281565	+	0.866569i
$804$		0			0
$805$	−1046.33	−	1259.52i	−1.29979	−	1.56462i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	433.364	−	596.475i	0.535679	−	0.737299i	−0.452304	−	0.891864i	$-0.649398\pi$
$809$	433.364	−	596.475i	0.535679	−	0.737299i	0.987983	+	0.154565i	$0.0493977\pi$
$810$		0			0
$811$	−470.143	+	341.579i	−0.579708	+	0.421183i	−0.838619	−	0.544719i	$-0.816637\pi$
$811$	−470.143	+	341.579i	−0.579708	+	0.421183i	0.258911	+	0.965901i	$0.416637\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−77.8979	+	123.306i	−0.0955802	+	0.151296i
$816$		0			0
$817$	−760.130	+	246.981i	−0.930392	+	0.302303i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1170.26	−	380.241i	−1.42541	−	0.463143i	−0.508092	−	0.861303i	$-0.669649\pi$
$821$	−1170.26	−	380.241i	−1.42541	−	0.463143i	−0.917316	+	0.398159i	$0.869649\pi$
$822$		0			0
$823$	−78.3919	−	107.897i	−0.0952514	−	0.131102i	0.758731	−	0.651404i	$-0.225820\pi$
$823$	−78.3919	−	107.897i	−0.0952514	−	0.131102i	−0.853983	+	0.520301i	$0.825820\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	777.880	−	565.163i	0.940604	−	0.683389i	−0.00796199	−	0.999968i	$-0.502534\pi$
$827$	777.880	−	565.163i	0.940604	−	0.683389i	0.948566	+	0.316579i	$0.102534\pi$
$828$		0			0
$829$	73.2358	−	225.397i	0.0883423	−	0.271890i	−0.897119	−	0.441789i	$-0.854344\pi$
$829$	73.2358	−	225.397i	0.0883423	−	0.271890i	0.985461	+	0.169899i	$0.0543441\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−367.292	−	1130.41i	−0.440926	−	1.35703i
$834$		0			0
$835$	−226.394	−	568.394i	−0.271131	−	0.680711i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	773.325	+	1064.39i	0.921722	+	1.26864i	0.963002	+	0.269494i	$0.0868565\pi$
$839$	773.325	+	1064.39i	0.921722	+	1.26864i	−0.0412798	+	0.999148i	$0.513143\pi$
$840$		0			0
$841$	−202.920	−	147.430i	−0.241284	−	0.175303i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	102.967	+	258.513i	0.121855	+	0.305933i
$846$		0			0
$847$	1556.24	+	505.654i	1.83736	+	0.596994i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	1816.32i		−	2.13433i
$852$		0			0
$853$	−1544.51	−	501.843i	−1.81068	−	0.588327i	−0.999996	−	0.00284777i	$-0.999094\pi$
$853$	−1544.51	−	501.843i	−1.81068	−	0.588327i	−0.810688	−	0.585479i	$-0.800906\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1043.27			−1.21735			−0.608675	−	0.793419i	$-0.708299\pi$
$857$	−1043.27			−1.21735			−0.608675	+	0.793419i	$0.708299\pi$
$858$		0			0
$859$	502.133	+	364.821i	0.584556	+	0.424705i	0.840364	−	0.542023i	$-0.182341\pi$
$859$	502.133	+	364.821i	0.584556	+	0.424705i	−0.255808	+	0.966728i	$0.582341\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	703.584	+	511.183i	0.815276	+	0.592333i	0.915356	−	0.402647i	$-0.131910\pi$
$863$	703.584	+	511.183i	0.815276	+	0.592333i	−0.100079	+	0.994979i	$0.531910\pi$
$864$		0			0
$865$	−382.829	+	318.030i	−0.442577	+	0.367664i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1660.91	+	539.663i	−1.91129	+	0.621016i
$870$		0			0
$871$	196.246	−	603.983i	0.225311	−	0.693437i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−274.368	−	1391.66i	−0.313564	−	1.59047i
$876$		0			0
$877$	−28.0973	−	38.6726i	−0.0320380	−	0.0440965i	0.792698	−	0.609615i	$-0.208676\pi$
$877$	−28.0973	−	38.6726i	−0.0320380	−	0.0440965i	−0.824735	+	0.565519i	$0.808676\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1172.64	+	381.015i	−1.33104	+	0.432480i	−0.886271	−	0.463167i	$-0.846713\pi$
$881$	−1172.64	+	381.015i	−1.33104	+	0.432480i	−0.444766	+	0.895647i	$0.646713\pi$
$882$		0			0
$883$	921.979	−	299.569i	1.04414	−	0.339263i	0.263776	−	0.964584i	$-0.415032\pi$
$883$	921.979	−	299.569i	1.04414	−	0.339263i	0.780368	+	0.625321i	$0.215032\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1081.95	−	786.086i	−1.21979	−	0.886230i	−0.223708	−	0.974656i	$-0.571816\pi$
$887$	−1081.95	−	786.086i	−1.21979	−	0.886230i	−0.996083	+	0.0884267i	$0.971816\pi$
$888$		0			0
$889$	533.510	−	387.618i	0.600124	−	0.436016i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1127.53			1.26263
$894$		0			0
$895$	1089.26	+	277.292i	1.21705	+	0.309823i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	412.352i		−	0.458679i
$900$		0			0
$901$	997.959			1.10761
$902$		0			0
$903$		0			0
$904$		0			0
$905$	225.826	+	566.967i	0.249531	+	0.626483i
$906$		0			0
$907$		−	585.205i		−	0.645210i	−0.946534	−	0.322605i	$-0.895441\pi$
$907$		−	585.205i		−	0.645210i	0.946534	−	0.322605i	$-0.104559\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	470.610	+	647.740i	0.516587	+	0.711020i	0.985013	−	0.172482i	$-0.0551788\pi$
$911$	470.610	+	647.740i	0.516587	+	0.711020i	−0.468426	+	0.883503i	$0.655179\pi$
$912$		0			0
$913$	−349.892	+	481.586i	−0.383234	+	0.527476i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	647.791	+	1993.70i	0.706425	+	2.17415i
$918$		0			0
$919$	60.2788	+	185.519i	0.0655917	+	0.201870i	0.978481	−	0.206337i	$-0.0661542\pi$
$919$	60.2788	+	185.519i	0.0655917	+	0.201870i	−0.912889	+	0.408207i	$0.866154\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−887.880	+	645.083i	−0.961950	+	0.698898i
$924$		0			0
$925$	752.326	−	1381.89i	0.813325	−	1.49393i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	238.257	+	77.4145i	0.256466	+	0.0833310i	0.434428	−	0.900706i	$-0.356950\pi$
$929$	238.257	+	77.4145i	0.256466	+	0.0833310i	−0.177962	+	0.984037i	$0.556950\pi$
$930$		0			0
$931$	−724.390	−	2229.44i	−0.778078	−	2.39468i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−647.995	+	1025.73i	−0.693043	+	1.09703i
$936$		0			0
$937$	−228.313	+	314.246i	−0.243664	+	0.335375i	−0.913280	−	0.407333i	$-0.866459\pi$
$937$	−228.313	+	314.246i	−0.243664	+	0.335375i	0.669616	+	0.742708i	$0.266459\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−529.899	+	729.344i	−0.563124	+	0.775073i	−0.991719	−	0.128423i	$-0.959008\pi$
$941$	−529.899	+	729.344i	−0.563124	+	0.775073i	0.428596	+	0.903496i	$0.359008\pi$
$942$		0			0
$943$		−	171.209i		−	0.181557i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	310.853	−	956.707i	0.328250	−	1.01025i	−0.641702	−	0.766954i	$-0.721771\pi$
$947$	310.853	−	956.707i	0.328250	−	1.01025i	0.969952	−	0.243296i	$-0.0782288\pi$
$948$		0			0
$949$	−478.333			−0.504039
$950$		0			0
$951$		0			0
$952$		0			0
$953$	184.380	−	567.464i	0.193473	−	0.595450i	−0.806518	−	0.591210i	$-0.798650\pi$
$953$	184.380	−	567.464i	0.193473	−	0.595450i	0.999991	−	0.00423997i	$-0.00134963\pi$
$954$		0			0
$955$	−265.742	+	420.649i	−0.278264	+	0.440470i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1367.80	−	1882.62i	1.42628	−	1.96310i
$960$		0			0
$961$	544.382	−	395.517i	0.566474	−	0.411568i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	103.247	+	1589.00i	0.106992	+	1.64663i
$966$		0			0
$967$	−1500.73	+	487.616i	−1.55194	+	0.504256i	−0.954640	−	0.297762i	$-0.903760\pi$
$967$	−1500.73	+	487.616i	−1.55194	+	0.504256i	−0.597300	+	0.802018i	$0.703760\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1237.54	+	402.103i	1.27451	+	0.414112i	0.866642	−	0.498931i	$-0.166274\pi$
$971$	1237.54	+	402.103i	1.27451	+	0.414112i	0.407864	+	0.913043i	$0.366274\pi$
$972$		0			0
$973$	−1760.32	−	2422.88i	−1.80917	−	2.49011i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1413.21	+	1026.75i	−1.44647	+	1.05093i	−0.459835	+	0.888004i	$0.652092\pi$
$977$	−1413.21	+	1026.75i	−1.44647	+	1.05093i	−0.986639	+	0.162921i	$0.947908\pi$
$978$		0			0
$979$	392.308	−	1207.40i	0.400723	−	1.23330i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−145.331	−	447.282i	−0.147844	−	0.455017i	0.849522	−	0.527554i	$-0.176891\pi$
$983$	−145.331	−	447.282i	−0.147844	−	0.455017i	−0.997366	+	0.0725365i	$0.976891\pi$
$984$		0			0
$985$	−235.540	+	925.251i	−0.239127	+	0.939341i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	461.351	+	634.995i	0.466482	+	0.642057i
$990$		0			0
$991$	−488.860	−	355.178i	−0.493300	−	0.358403i	0.313152	−	0.949703i	$-0.398615\pi$
$991$	−488.860	−	355.178i	−0.493300	−	0.358403i	−0.806452	+	0.591300i	$0.798615\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1826.72	+	118.693i	−1.83590	+	0.119290i
$996$		0			0
$997$	−148.918	−	48.3863i	−0.149366	−	0.0485319i	0.233380	−	0.972386i	$-0.425021\pi$
$997$	−148.918	−	48.3863i	−0.149366	−	0.0485319i	−0.382746	+	0.923854i	$0.625021\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.y.a.89.20	yes	80
3.2	odd	2	inner	900.3.y.a.89.1	✓	80
25.9	even	10	inner	900.3.y.a.809.1	yes	80
75.59	odd	10	inner	900.3.y.a.809.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.y.a.89.1	✓	80	3.2	odd	2	inner
900.3.y.a.89.20	yes	80	1.1	even	1	trivial
900.3.y.a.809.1	yes	80	25.9	even	10	inner
900.3.y.a.809.20	yes	80	75.59	odd	10	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.98948 - 0.324198i) q^{5} -11.3476i q^{7} +O(q^{10})\)	\(q+(4.98948 - 0.324198i) q^{5} -11.3476i q^{7} +(9.57207 + 13.1748i) q^{11} +(-6.25783 + 8.61316i) q^{13} +(4.60448 + 14.1711i) q^{17} +(9.08119 + 27.9490i) q^{19} +(23.3479 - 16.9633i) q^{23} +(24.7898 - 3.23515i) q^{25} +(-23.1046 - 7.50712i) q^{29} +(5.24517 + 16.1430i) q^{31} +(-3.67887 - 56.6187i) q^{35} +(36.9930 - 50.9165i) q^{37} +(3.48701 - 4.79946i) q^{41} +27.1970i q^{43} +(11.8563 - 36.4901i) q^{47} -79.7683 q^{49} +(20.6965 - 63.6972i) q^{53} +(52.0309 + 62.6323i) q^{55} +(15.0057 - 20.6536i) q^{59} +(49.6277 - 36.0566i) q^{61} +(-28.4309 + 45.0040i) q^{65} +(-56.7309 + 18.4330i) q^{67} +(98.0388 + 31.8547i) q^{71} +(26.4085 + 36.3482i) q^{73} +(149.503 - 108.620i) q^{77} +(-33.1387 + 101.990i) q^{79} +(11.2956 + 34.7644i) q^{83} +(27.5682 + 69.2139i) q^{85} +(-45.8222 - 63.0688i) q^{89} +(97.7388 + 71.0114i) q^{91} +(54.3714 + 136.507i) q^{95} +(-22.2138 - 7.21769i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Introduction

L-functions

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