LMFDB - Embedded newform 400.3.p.i.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(193,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("400.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.1
Root			$-3.70156i$ of defining polynomial
Character	$\chi$	$=$	400.193
Dual form			400.3.p.i.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.70156 - 3.70156i) q^{3} +(0.298438 - 0.298438i) q^{7} +18.4031i q^{9} +O(q^{10})$	$q+(-3.70156 - 3.70156i) q^{3} +(0.298438 - 0.298438i) q^{7} +18.4031i q^{9} -11.4031 q^{11} +(1.59688 + 1.59688i) q^{13} +(-10.4031 + 10.4031i) q^{17} +2.80625i q^{19} -2.20937 q^{21} +(19.1047 + 19.1047i) q^{23} +(34.8062 - 34.8062i) q^{27} -5.61250i q^{29} +15.4031 q^{31} +(42.2094 + 42.2094i) q^{33} +(40.6125 - 40.6125i) q^{37} -11.8219i q^{39} +70.6281 q^{41} +(20.2984 + 20.2984i) q^{43} +(-42.5078 + 42.5078i) q^{47} +48.8219i q^{49} +77.0156 q^{51} +(3.00000 + 3.00000i) q^{53} +(10.3875 - 10.3875i) q^{57} +66.8062i q^{59} -44.5969 q^{61} +(5.49219 + 5.49219i) q^{63} +(28.2984 - 28.2984i) q^{67} -141.434i q^{69} -32.5969 q^{71} +(-62.6125 - 62.6125i) q^{73} +(-3.40312 + 3.40312i) q^{77} +118.450i q^{79} -92.0469 q^{81} +(-11.2828 - 11.2828i) q^{83} +(-20.7750 + 20.7750i) q^{87} +11.2250i q^{89} +0.953136 q^{91} +(-57.0156 - 57.0156i) q^{93} +(-49.0000 + 49.0000i) q^{97} -209.853i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 14 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 + 14 * q^7	$ 4 q - 2 q^{3} + 14 q^{7} - 20 q^{11} + 32 q^{13} - 16 q^{17} + 68 q^{21} + 38 q^{23} + 88 q^{27} + 36 q^{31} + 92 q^{33} + 60 q^{37} + 52 q^{41} + 94 q^{43} - 106 q^{47} + 180 q^{51} + 12 q^{53} + 144 q^{57} - 204 q^{61} + 86 q^{63} + 126 q^{67} - 156 q^{71} - 148 q^{73} + 12 q^{77} + 16 q^{81} - 186 q^{83} - 288 q^{87} + 388 q^{91} - 100 q^{93} - 196 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 14 * q^7 - 20 * q^11 + 32 * q^13 - 16 * q^17 + 68 * q^21 + 38 * q^23 + 88 * q^27 + 36 * q^31 + 92 * q^33 + 60 * q^37 + 52 * q^41 + 94 * q^43 - 106 * q^47 + 180 * q^51 + 12 * q^53 + 144 * q^57 - 204 * q^61 + 86 * q^63 + 126 * q^67 - 156 * q^71 - 148 * q^73 + 12 * q^77 + 16 * q^81 - 186 * q^83 - 288 * q^87 + 388 * q^91 - 100 * q^93 - 196 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.70156	−	3.70156i	−1.23385	−	1.23385i	−0.962472	−	0.271382i	$-0.912519\pi$
$3$	−3.70156	−	3.70156i	−1.23385	−	1.23385i	−0.271382	−	0.962472i	$-0.587481\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.298438	−	0.298438i	0.0426340	−	0.0426340i	−0.685468	−	0.728102i	$-0.740403\pi$
$7$	0.298438	−	0.298438i	0.0426340	−	0.0426340i	0.728102	+	0.685468i	$0.240403\pi$
$8$		0			0
$9$			18.4031i			2.04479i
$10$		0			0
$11$	−11.4031			−1.03665			−0.518324	−	0.855184i	$-0.673444\pi$
$11$	−11.4031			−1.03665			−0.518324	+	0.855184i	$0.673444\pi$
$12$		0			0
$13$	1.59688	+	1.59688i	0.122837	+	0.122837i	0.765853	−	0.643016i	$-0.222317\pi$
$13$	1.59688	+	1.59688i	0.122837	+	0.122837i	−0.643016	+	0.765853i	$0.722317\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−10.4031	+	10.4031i	−0.611948	+	0.611948i	−0.943453	−	0.331505i	$-0.892444\pi$
$17$	−10.4031	+	10.4031i	−0.611948	+	0.611948i	0.331505	+	0.943453i	$0.392444\pi$
$18$		0			0
$19$			2.80625i			0.147697i	0.997269	+	0.0738486i	$0.0235282\pi$
$19$			2.80625i			0.147697i	−0.997269	+	0.0738486i	$0.976472\pi$
$20$		0			0
$21$	−2.20937			−0.105208
$22$		0			0
$23$	19.1047	+	19.1047i	0.830639	+	0.830639i	0.987604	−	0.156966i	$-0.0501712\pi$
$23$	19.1047	+	19.1047i	0.830639	+	0.830639i	−0.156966	+	0.987604i	$0.550171\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	34.8062	−	34.8062i	1.28912	−	1.28912i
$28$		0			0
$29$		−	5.61250i		−	0.193534i	−0.995307	−	0.0967672i	$-0.969150\pi$
$29$		−	5.61250i		−	0.193534i	0.995307	−	0.0967672i	$-0.0308502\pi$
$30$		0			0
$31$	15.4031			0.496875			0.248437	−	0.968648i	$-0.420083\pi$
$31$	15.4031			0.496875			0.248437	+	0.968648i	$0.420083\pi$
$32$		0			0
$33$	42.2094	+	42.2094i	1.27907	+	1.27907i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	40.6125	−	40.6125i	1.09764	−	1.09764i	0.102948	−	0.994687i	$-0.467172\pi$
$37$	40.6125	−	40.6125i	1.09764	−	1.09764i	0.994687	−	0.102948i	$-0.0328276\pi$
$38$		0			0
$39$		−	11.8219i		−	0.303125i
$40$		0			0
$41$	70.6281			1.72264			0.861319	−	0.508065i	$-0.169639\pi$
$41$	70.6281			1.72264			0.861319	+	0.508065i	$0.169639\pi$
$42$		0			0
$43$	20.2984	+	20.2984i	0.472057	+	0.472057i	0.902580	−	0.430523i	$-0.141671\pi$
$43$	20.2984	+	20.2984i	0.472057	+	0.472057i	−0.430523	+	0.902580i	$0.641671\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−42.5078	+	42.5078i	−0.904422	+	0.904422i	−0.995815	−	0.0913934i	$-0.970868\pi$
$47$	−42.5078	+	42.5078i	−0.904422	+	0.904422i	0.0913934	+	0.995815i	$0.470868\pi$
$48$		0			0
$49$			48.8219i			0.996365i
$50$		0			0
$51$	77.0156			1.51011
$52$		0			0
$53$	3.00000	+	3.00000i	0.0566038	+	0.0566038i	0.734842	−	0.678238i	$-0.237256\pi$
$53$	3.00000	+	3.00000i	0.0566038	+	0.0566038i	−0.678238	+	0.734842i	$0.737256\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	10.3875	−	10.3875i	0.182237	−	0.182237i
$58$		0			0
$59$			66.8062i			1.13231i	0.824299	+	0.566155i	$0.191570\pi$
$59$			66.8062i			1.13231i	−0.824299	+	0.566155i	$0.808430\pi$
$60$		0			0
$61$	−44.5969			−0.731096			−0.365548	−	0.930792i	$-0.619118\pi$
$61$	−44.5969			−0.731096			−0.365548	+	0.930792i	$0.619118\pi$
$62$		0			0
$63$	5.49219	+	5.49219i	0.0871776	+	0.0871776i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	28.2984	−	28.2984i	0.422365	−	0.422365i	−0.463652	−	0.886017i	$-0.653461\pi$
$67$	28.2984	−	28.2984i	0.422365	−	0.422365i	0.886017	+	0.463652i	$0.153461\pi$
$68$		0			0
$69$		−	141.434i		−	2.04977i
$70$		0			0
$71$	−32.5969			−0.459111			−0.229555	−	0.973296i	$-0.573727\pi$
$71$	−32.5969			−0.459111			−0.229555	+	0.973296i	$0.573727\pi$
$72$		0			0
$73$	−62.6125	−	62.6125i	−0.857705	−	0.857705i	0.133362	−	0.991067i	$-0.457423\pi$
$73$	−62.6125	−	62.6125i	−0.857705	−	0.857705i	−0.991067	+	0.133362i	$0.957423\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.40312	+	3.40312i	−0.0441964	+	0.0441964i
$78$		0			0
$79$			118.450i			1.49937i	0.661797	+	0.749683i	$0.269794\pi$
$79$			118.450i			1.49937i	−0.661797	+	0.749683i	$0.730206\pi$
$80$		0			0
$81$	−92.0469			−1.13638
$82$		0			0
$83$	−11.2828	−	11.2828i	−0.135938	−	0.135938i	0.635864	−	0.771801i	$-0.280644\pi$
$83$	−11.2828	−	11.2828i	−0.135938	−	0.135938i	−0.771801	+	0.635864i	$0.780644\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−20.7750	+	20.7750i	−0.238793	+	0.238793i
$88$		0			0
$89$			11.2250i			0.126124i	0.998010	+	0.0630618i	$0.0200865\pi$
$89$			11.2250i			0.126124i	−0.998010	+	0.0630618i	$0.979913\pi$
$90$		0			0
$91$	0.953136			0.0104740
$92$		0			0
$93$	−57.0156	−	57.0156i	−0.613071	−	0.613071i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−49.0000	+	49.0000i	−0.505155	+	0.505155i	−0.913035	−	0.407881i	$-0.866268\pi$
$97$	−49.0000	+	49.0000i	−0.505155	+	0.505155i	0.407881	+	0.913035i	$0.366268\pi$
$98$		0			0
$99$		−	209.853i		−	2.11973i
$100$		0			0
$101$	−68.0312			−0.673577			−0.336788	−	0.941580i	$-0.609341\pi$
$101$	−68.0312			−0.673577			−0.336788	+	0.941580i	$0.609341\pi$
$102$		0			0
$103$	29.4922	+	29.4922i	0.286332	+	0.286332i	0.835628	−	0.549296i	$-0.185104\pi$
$103$	29.4922	+	29.4922i	0.286332	+	0.286332i	−0.549296	+	0.835628i	$0.685104\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−92.5391	+	92.5391i	−0.864851	+	0.864851i	−0.991897	−	0.127046i	$-0.959450\pi$
$107$	−92.5391	+	92.5391i	−0.864851	+	0.864851i	0.127046	+	0.991897i	$0.459450\pi$
$108$		0			0
$109$			173.047i			1.58759i	0.608188	+	0.793793i	$0.291897\pi$
$109$			173.047i			1.58759i	−0.608188	+	0.793793i	$0.708103\pi$
$110$		0			0
$111$	−300.659			−2.70864
$112$		0			0
$113$	80.8219	+	80.8219i	0.715238	+	0.715238i	0.967626	−	0.252388i	$-0.0812160\pi$
$113$	80.8219	+	80.8219i	0.715238	+	0.715238i	−0.252388	+	0.967626i	$0.581216\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−29.3875	+	29.3875i	−0.251175	+	0.251175i
$118$		0			0
$119$			6.20937i			0.0521796i
$120$		0			0
$121$	9.03124			0.0746384
$122$		0			0
$123$	−261.434	−	261.434i	−2.12548	−	2.12548i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.29844	−	8.29844i	0.0653420	−	0.0653420i	−0.673681	−	0.739023i	$-0.735288\pi$
$127$	8.29844	−	8.29844i	0.0653420	−	0.0653420i	0.739023	+	0.673681i	$0.235288\pi$
$128$		0			0
$129$		−	150.272i		−	1.16490i
$130$		0			0
$131$	107.884			0.823545			0.411772	−	0.911287i	$-0.364910\pi$
$131$	107.884			0.823545			0.411772	+	0.911287i	$0.364910\pi$
$132$		0			0
$133$	0.837491	+	0.837491i	0.00629692	+	0.00629692i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−35.3875	+	35.3875i	−0.258303	+	0.258303i	−0.824364	−	0.566061i	$-0.808467\pi$
$137$	−35.3875	+	35.3875i	−0.258303	+	0.258303i	0.566061	+	0.824364i	$0.308467\pi$
$138$		0			0
$139$		−	221.194i		−	1.59132i	−0.605742	−	0.795661i	$-0.707124\pi$
$139$		−	221.194i		−	1.59132i	0.605742	−	0.795661i	$-0.292876\pi$
$140$		0			0
$141$	314.691			2.23185
$142$		0			0
$143$	−18.2094	−	18.2094i	−0.127338	−	0.127338i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	180.717	−	180.717i	1.22937	−	1.22937i
$148$		0			0
$149$			95.8531i			0.643309i	0.946857	+	0.321655i	$0.104239\pi$
$149$			95.8531i			0.643309i	−0.946857	+	0.321655i	$0.895761\pi$
$150$		0			0
$151$	279.528			1.85118			0.925590	−	0.378528i	$-0.123570\pi$
$151$	279.528			1.85118			0.925590	+	0.378528i	$0.123570\pi$
$152$		0			0
$153$	−191.450	−	191.450i	−1.25131	−	1.25131i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−122.466	+	122.466i	−0.780036	+	0.780036i	−0.979837	−	0.199801i	$-0.935970\pi$
$157$	−122.466	+	122.466i	−0.780036	+	0.780036i	0.199801	+	0.979837i	$0.435970\pi$
$158$		0			0
$159$		−	22.2094i		−	0.139682i
$160$		0			0
$161$	11.4031			0.0708269
$162$		0			0
$163$	125.973	+	125.973i	0.772843	+	0.772843i	0.978603	−	0.205760i	$-0.0659665\pi$
$163$	125.973	+	125.973i	0.772843	+	0.772843i	−0.205760	+	0.978603i	$0.565966\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−81.6703	+	81.6703i	−0.489044	+	0.489044i	−0.908004	−	0.418961i	$-0.862395\pi$
$167$	−81.6703	+	81.6703i	−0.489044	+	0.489044i	0.418961	+	0.908004i	$0.362395\pi$
$168$		0			0
$169$		−	163.900i		−	0.969822i
$170$		0			0
$171$	−51.6437			−0.302010
$172$		0			0
$173$	117.388	+	117.388i	0.678540	+	0.678540i	0.959670	−	0.281129i	$-0.0907090\pi$
$173$	117.388	+	117.388i	0.678540	+	0.678540i	−0.281129	+	0.959670i	$0.590709\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	247.287	−	247.287i	1.39710	−	1.39710i
$178$		0			0
$179$			104.419i			0.583345i	0.956518	+	0.291672i	$0.0942117\pi$
$179$			104.419i			0.583345i	−0.956518	+	0.291672i	$0.905788\pi$
$180$		0			0
$181$	−139.612			−0.771340			−0.385670	−	0.922637i	$-0.626030\pi$
$181$	−139.612			−0.771340			−0.385670	+	0.922637i	$0.626030\pi$
$182$		0			0
$183$	165.078	+	165.078i	0.902066	+	0.902066i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	118.628	−	118.628i	0.634375	−	0.634375i
$188$		0			0
$189$		−	20.7750i		−	0.109921i
$190$		0			0
$191$	−317.497			−1.66229			−0.831144	−	0.556058i	$-0.812313\pi$
$191$	−317.497			−1.66229			−0.831144	+	0.556058i	$0.812313\pi$
$192$		0			0
$193$	−15.1781	−	15.1781i	−0.0786432	−	0.0786432i	0.666691	−	0.745334i	$-0.267710\pi$
$193$	−15.1781	−	15.1781i	−0.0786432	−	0.0786432i	−0.745334	+	0.666691i	$0.767710\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−221.837	+	221.837i	−1.12608	+	1.12608i	−0.135270	+	0.990809i	$0.543190\pi$
$197$	−221.837	+	221.837i	−1.12608	+	1.12608i	−0.990809	+	0.135270i	$0.956810\pi$
$198$		0			0
$199$		−	210.512i		−	1.05785i	−0.848668	−	0.528926i	$-0.822595\pi$
$199$		−	210.512i		−	1.05785i	0.848668	−	0.528926i	$-0.177405\pi$
$200$		0			0
$201$	−209.497			−1.04227
$202$		0			0
$203$	−1.67498	−	1.67498i	−0.00825114	−	0.00825114i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−351.586	+	351.586i	−1.69848	+	1.69848i
$208$		0			0
$209$		−	32.0000i		−	0.153110i
$210$		0			0
$211$	217.372			1.03020			0.515099	−	0.857131i	$-0.327755\pi$
$211$	217.372			1.03020			0.515099	+	0.857131i	$0.327755\pi$
$212$		0			0
$213$	120.659	+	120.659i	0.566476	+	0.566476i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.59688	−	4.59688i	0.0211838	−	0.0211838i
$218$		0			0
$219$			463.528i			2.11657i
$220$		0			0
$221$	−33.2250			−0.150339
$222$		0			0
$223$	−228.602	−	228.602i	−1.02512	−	1.02512i	−0.999676	−	0.0254427i	$-0.991900\pi$
$223$	−228.602	−	228.602i	−1.02512	−	1.02512i	−0.0254427	−	0.999676i	$-0.508100\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	123.167	−	123.167i	0.542587	−	0.542587i	−0.381700	−	0.924286i	$-0.624661\pi$
$227$	123.167	−	123.167i	0.542587	−	0.542587i	0.924286	+	0.381700i	$0.124661\pi$
$228$		0			0
$229$			60.0625i			0.262282i	0.991364	+	0.131141i	$0.0418640\pi$
$229$			60.0625i			0.262282i	−0.991364	+	0.131141i	$0.958136\pi$
$230$		0			0
$231$	25.1938			0.109064
$232$		0			0
$233$	99.2094	+	99.2094i	0.425791	+	0.425791i	0.887192	−	0.461401i	$-0.152653\pi$
$233$	99.2094	+	99.2094i	0.425791	+	0.425791i	−0.461401	+	0.887192i	$0.652653\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	438.450	−	438.450i	1.85000	−	1.85000i
$238$		0			0
$239$			229.612i			0.960722i	0.877071	+	0.480361i	$0.159494\pi$
$239$			229.612i			0.960722i	−0.877071	+	0.480361i	$0.840506\pi$
$240$		0			0
$241$	0.178130			0.000739130			0.000369565	−	1.00000i	$-0.499882\pi$
$241$	0.178130			0.000739130			0.000369565		1.00000i	$0.499882\pi$
$242$		0			0
$243$	27.4609	+	27.4609i	0.113008	+	0.113008i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.48123	+	4.48123i	−0.0181426	+	0.0181426i
$248$		0			0
$249$			83.5281i			0.335454i
$250$		0			0
$251$	−263.466			−1.04966			−0.524832	−	0.851206i	$-0.675872\pi$
$251$	−263.466			−1.04966			−0.524832	+	0.851206i	$0.675872\pi$
$252$		0			0
$253$	−217.853	−	217.853i	−0.861079	−	0.861079i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	19.9219	−	19.9219i	0.0775171	−	0.0775171i	−0.667285	−	0.744802i	$-0.732544\pi$
$257$	19.9219	−	19.9219i	0.0775171	−	0.0775171i	0.744802	+	0.667285i	$0.232544\pi$
$258$		0			0
$259$		−	24.2406i		−	0.0935931i
$260$		0			0
$261$	103.287			0.395737
$262$		0			0
$263$	220.361	+	220.361i	0.837874	+	0.837874i	0.988579	−	0.150705i	$-0.0481542\pi$
$263$	220.361	+	220.361i	0.837874	+	0.837874i	−0.150705	+	0.988579i	$0.548154\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	41.5500	−	41.5500i	0.155618	−	0.155618i
$268$		0			0
$269$			210.953i			0.784212i	0.919920	+	0.392106i	$0.128253\pi$
$269$			210.953i			0.784212i	−0.919920	+	0.392106i	$0.871747\pi$
$270$		0			0
$271$	373.016			1.37644			0.688221	−	0.725501i	$-0.258392\pi$
$271$	373.016			1.37644			0.688221	+	0.725501i	$0.258392\pi$
$272$		0			0
$273$	−3.52809	−	3.52809i	−0.0129234	−	0.0129234i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−22.4031	+	22.4031i	−0.0808777	+	0.0808777i	−0.746388	−	0.665511i	$-0.768214\pi$
$277$	−22.4031	+	22.4031i	−0.0808777	+	0.0808777i	0.665511	+	0.746388i	$0.268214\pi$
$278$		0			0
$279$			283.466i			1.01601i
$280$		0			0
$281$	−153.372			−0.545807			−0.272904	−	0.962041i	$-0.587984\pi$
$281$	−153.372			−0.545807			−0.272904	+	0.962041i	$0.587984\pi$
$282$		0			0
$283$	55.9422	+	55.9422i	0.197676	+	0.197676i	0.799003	−	0.601327i	$-0.205361\pi$
$283$	55.9422	+	55.9422i	0.197676	+	0.197676i	−0.601327	+	0.799003i	$0.705361\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	21.0781	−	21.0781i	0.0734429	−	0.0734429i
$288$		0			0
$289$			72.5500i			0.251038i
$290$		0			0
$291$	362.753			1.24657
$292$		0			0
$293$	−237.691	−	237.691i	−0.811231	−	0.811231i	0.173588	−	0.984818i	$-0.444464\pi$
$293$	−237.691	−	237.691i	−0.811231	−	0.811231i	−0.984818	+	0.173588i	$0.944464\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−396.900	+	396.900i	−1.33636	+	1.33636i
$298$		0			0
$299$			61.0156i			0.204066i
$300$		0			0
$301$	12.1156			0.0402513
$302$		0			0
$303$	251.822	+	251.822i	0.831095	+	0.831095i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−115.702	+	115.702i	−0.376878	+	0.376878i	−0.869975	−	0.493097i	$-0.835865\pi$
$307$	−115.702	+	115.702i	−0.376878	+	0.376878i	0.493097	+	0.869975i	$0.335865\pi$
$308$		0			0
$309$		−	218.334i		−	0.706584i
$310$		0			0
$311$	−57.3094			−0.184275			−0.0921373	−	0.995746i	$-0.529370\pi$
$311$	−57.3094			−0.184275			−0.0921373	+	0.995746i	$0.529370\pi$
$312$		0			0
$313$	251.334	+	251.334i	0.802985	+	0.802985i	0.983561	−	0.180576i	$-0.0577962\pi$
$313$	251.334	+	251.334i	0.802985	+	0.802985i	−0.180576	+	0.983561i	$0.557796\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	36.1093	−	36.1093i	0.113910	−	0.113910i	−0.647854	−	0.761764i	$-0.724334\pi$
$317$	36.1093	−	36.1093i	0.113910	−	0.113910i	0.761764	+	0.647854i	$0.224334\pi$
$318$		0			0
$319$			64.0000i			0.200627i
$320$		0			0
$321$	685.078			2.13420
$322$		0			0
$323$	−29.1938	−	29.1938i	−0.0903831	−	0.0903831i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	640.544	−	640.544i	1.95885	−	1.95885i
$328$		0			0
$329$			25.3719i			0.0771182i
$330$		0			0
$331$	−333.078			−1.00628			−0.503139	−	0.864205i	$-0.667822\pi$
$331$	−333.078			−1.00628			−0.503139	+	0.864205i	$0.667822\pi$
$332$		0			0
$333$	747.397	+	747.397i	2.24443	+	2.24443i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	368.675	−	368.675i	1.09399	−	1.09399i	0.0988930	−	0.995098i	$-0.468470\pi$
$337$	368.675	−	368.675i	1.09399	−	1.09399i	0.995098	−	0.0988930i	$-0.0315301\pi$
$338$		0			0
$339$		−	598.334i		−	1.76500i
$340$		0			0
$341$	−175.644			−0.515084
$342$		0			0
$343$	29.1938	+	29.1938i	0.0851130	+	0.0851130i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−160.183	+	160.183i	−0.461622	+	0.461622i	−0.899187	−	0.437565i	$-0.855841\pi$
$347$	−160.183	+	160.183i	−0.461622	+	0.461622i	0.437565	+	0.899187i	$0.355841\pi$
$348$		0			0
$349$		−	424.962i		−	1.21766i	−0.793302	−	0.608829i	$-0.791640\pi$
$349$		−	424.962i		−	1.21766i	0.793302	−	0.608829i	$-0.208360\pi$
$350$		0			0
$351$	111.163			0.316702
$352$		0			0
$353$	267.900	+	267.900i	0.758923	+	0.758923i	0.976126	−	0.217203i	$-0.0696934\pi$
$353$	267.900	+	267.900i	0.758923	+	0.758923i	−0.217203	+	0.976126i	$0.569693\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	22.9844	−	22.9844i	0.0643820	−	0.0643820i
$358$		0			0
$359$		−	545.675i		−	1.51999i	−0.649931	−	0.759993i	$-0.725202\pi$
$359$		−	545.675i		−	1.51999i	0.649931	−	0.759993i	$-0.274798\pi$
$360$		0			0
$361$	353.125			0.978186
$362$		0			0
$363$	−33.4297	−	33.4297i	−0.0920929	−	0.0920929i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	355.523	−	355.523i	0.968729	−	0.968729i	−0.0307970	−	0.999526i	$-0.509805\pi$
$367$	355.523	−	355.523i	0.968729	−	0.968729i	0.999526	+	0.0307970i	$0.00980453\pi$
$368$		0			0
$369$			1299.78i			3.52243i
$370$		0			0
$371$	1.79063			0.00482649
$372$		0			0
$373$	−304.350	−	304.350i	−0.815952	−	0.815952i	0.169567	−	0.985519i	$-0.445763\pi$
$373$	−304.350	−	304.350i	−0.815952	−	0.815952i	−0.985519	+	0.169567i	$0.945763\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.96246	−	8.96246i	0.0237731	−	0.0237731i
$378$		0			0
$379$		−	550.156i		−	1.45160i	−0.687906	−	0.725800i	$-0.741470\pi$
$379$		−	550.156i		−	1.45160i	0.687906	−	0.725800i	$-0.258530\pi$
$380$		0			0
$381$	−61.4344			−0.161245
$382$		0			0
$383$	−215.702	−	215.702i	−0.563189	−	0.563189i	0.367023	−	0.930212i	$-0.380377\pi$
$383$	−215.702	−	215.702i	−0.563189	−	0.563189i	−0.930212	+	0.367023i	$0.880377\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−373.555	+	373.555i	−0.965258	+	0.965258i
$388$		0			0
$389$		−	308.628i		−	0.793388i	−0.917951	−	0.396694i	$-0.870157\pi$
$389$		−	308.628i		−	0.793388i	0.917951	−	0.396694i	$-0.129843\pi$
$390$		0			0
$391$	−397.497			−1.01662
$392$		0			0
$393$	−399.341	−	399.341i	−1.01613	−	1.01613i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	22.2250	−	22.2250i	0.0559824	−	0.0559824i	−0.678561	−	0.734544i	$-0.737396\pi$
$397$	22.2250	−	22.2250i	0.0559824	−	0.0559824i	0.734544	+	0.678561i	$0.237396\pi$
$398$		0			0
$399$		−	6.20005i		−	0.0155390i
$400$		0			0
$401$	91.8000			0.228928			0.114464	−	0.993427i	$-0.463485\pi$
$401$	91.8000			0.228928			0.114464	+	0.993427i	$0.463485\pi$
$402$		0			0
$403$	24.5969	+	24.5969i	0.0610344	+	0.0610344i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−463.109	+	463.109i	−1.13786	+	1.13786i
$408$		0			0
$409$		−	342.597i		−	0.837645i	−0.908068	−	0.418823i	$-0.862443\pi$
$409$		−	342.597i		−	0.837645i	0.908068	−	0.418823i	$-0.137557\pi$
$410$		0			0
$411$	261.978			0.637416
$412$		0			0
$413$	19.9375	+	19.9375i	0.0482749	+	0.0482749i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−818.762	+	818.762i	−1.96346	+	1.96346i
$418$		0			0
$419$			588.356i			1.40419i	0.712083	+	0.702096i	$0.247752\pi$
$419$			588.356i			1.40419i	−0.712083	+	0.702096i	$0.752248\pi$
$420$		0			0
$421$	−52.7218			−0.125230			−0.0626150	−	0.998038i	$-0.519944\pi$
$421$	−52.7218			−0.125230			−0.0626150	+	0.998038i	$0.519944\pi$
$422$		0			0
$423$	−782.277	−	782.277i	−1.84935	−	1.84935i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−13.3094	+	13.3094i	−0.0311695	+	0.0311695i
$428$		0			0
$429$			134.806i			0.314234i
$430$		0			0
$431$	−342.209			−0.793989			−0.396995	−	0.917821i	$-0.629947\pi$
$431$	−342.209			−0.793989			−0.396995	+	0.917821i	$0.629947\pi$
$432$		0			0
$433$	−4.34996	−	4.34996i	−0.0100461	−	0.0100461i	0.702066	−	0.712112i	$-0.252261\pi$
$433$	−4.34996	−	4.34996i	−0.0100461	−	0.0100461i	−0.712112	+	0.702066i	$0.752261\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−53.6125	+	53.6125i	−0.122683	+	0.122683i
$438$		0			0
$439$			593.925i			1.35290i	0.736487	+	0.676452i	$0.236483\pi$
$439$			593.925i			1.35290i	−0.736487	+	0.676452i	$0.763517\pi$
$440$		0			0
$441$	−898.475			−2.03736
$442$		0			0
$443$	449.492	+	449.492i	1.01466	+	1.01466i	0.999891	+	0.0147640i	$0.00469971\pi$
$443$	449.492	+	449.492i	1.01466	+	1.01466i	0.0147640	+	0.999891i	$0.495300\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	354.806	−	354.806i	0.793750	−	0.793750i
$448$		0			0
$449$		−	366.428i		−	0.816098i	−0.912960	−	0.408049i	$-0.866209\pi$
$449$		−	366.428i		−	0.816098i	0.912960	−	0.408049i	$-0.133791\pi$
$450$		0			0
$451$	−805.381			−1.78577
$452$		0			0
$453$	−1034.69	−	1034.69i	−2.28409	−	2.28409i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	147.209	−	147.209i	0.322121	−	0.322121i	−0.527459	−	0.849580i	$-0.676855\pi$
$457$	147.209	−	147.209i	0.322121	−	0.322121i	0.849580	+	0.527459i	$0.176855\pi$
$458$		0			0
$459$			724.187i			1.57775i
$460$		0			0
$461$	−804.281			−1.74464			−0.872322	−	0.488931i	$-0.837387\pi$
$461$	−804.281			−1.74464			−0.872322	+	0.488931i	$0.837387\pi$
$462$		0			0
$463$	−185.670	−	185.670i	−0.401016	−	0.401016i	0.477575	−	0.878591i	$-0.341516\pi$
$463$	−185.670	−	185.670i	−0.401016	−	0.401016i	−0.878591	+	0.477575i	$0.841516\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−135.345	+	135.345i	−0.289819	+	0.289819i	−0.837009	−	0.547190i	$-0.815698\pi$
$467$	−135.345	+	135.345i	−0.289819	+	0.289819i	0.547190	+	0.837009i	$0.315698\pi$
$468$		0			0
$469$		−	16.8907i		−	0.0360142i
$470$		0			0
$471$	906.628			1.92490
$472$		0			0
$473$	−231.466	−	231.466i	−0.489356	−	0.489356i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−55.2094	+	55.2094i	−0.115743	+	0.115743i
$478$		0			0
$479$		−	629.862i		−	1.31495i	−0.753475	−	0.657476i	$-0.771624\pi$
$479$		−	629.862i		−	1.31495i	0.753475	−	0.657476i	$-0.228376\pi$
$480$		0			0
$481$	129.706			0.269660
$482$		0			0
$483$	−42.2094	−	42.2094i	−0.0873900	−	0.0873900i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−174.864	+	174.864i	−0.359064	+	0.359064i	−0.863468	−	0.504404i	$-0.831712\pi$
$487$	−174.864	+	174.864i	−0.359064	+	0.359064i	0.504404	+	0.863468i	$0.331712\pi$
$488$		0			0
$489$		−	932.597i		−	1.90715i
$490$		0			0
$491$	555.047			1.13044			0.565221	−	0.824940i	$-0.308791\pi$
$491$	555.047			1.13044			0.565221	+	0.824940i	$0.308791\pi$
$492$		0			0
$493$	58.3875	+	58.3875i	0.118433	+	0.118433i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.72814	+	9.72814i	−0.0195737	+	0.0195737i
$498$		0			0
$499$			391.831i			0.785233i	0.919702	+	0.392616i	$0.128430\pi$
$499$			391.831i			0.785233i	−0.919702	+	0.392616i	$0.871570\pi$
$500$		0			0
$501$	604.616			1.20682
$502$		0			0
$503$	−103.283	−	103.283i	−0.205334	−	0.205334i	0.596947	−	0.802281i	$-0.296380\pi$
$503$	−103.283	−	103.283i	−0.205334	−	0.205334i	−0.802281	+	0.596947i	$0.796380\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−606.686	+	606.686i	−1.19662	+	1.19662i
$508$		0			0
$509$			349.737i			0.687107i	0.939133	+	0.343554i	$0.111631\pi$
$509$			349.737i			0.687107i	−0.939133	+	0.343554i	$0.888369\pi$
$510$		0			0
$511$	−37.3719			−0.0731348
$512$		0			0
$513$	97.6750	+	97.6750i	0.190400	+	0.190400i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	484.722	−	484.722i	0.937566	−	0.937566i
$518$		0			0
$519$		−	869.034i		−	1.67444i
$520$		0			0
$521$	−72.0937			−0.138376			−0.0691878	−	0.997604i	$-0.522041\pi$
$521$	−72.0937			−0.138376			−0.0691878	+	0.997604i	$0.522041\pi$
$522$		0			0
$523$	−383.345	−	383.345i	−0.732974	−	0.732974i	0.238234	−	0.971208i	$-0.423431\pi$
$523$	−383.345	−	383.345i	−0.732974	−	0.732974i	−0.971208	+	0.238234i	$0.923431\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−160.241	+	160.241i	−0.304062	+	0.304062i
$528$		0			0
$529$			200.978i			0.379921i
$530$		0			0
$531$	−1229.44			−2.31534
$532$		0			0
$533$	112.784	+	112.784i	0.211603	+	0.211603i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	386.512	−	386.512i	0.719763	−	0.719763i
$538$		0			0
$539$		−	556.722i		−	1.03288i
$540$		0			0
$541$	43.9688			0.0812731			0.0406366	−	0.999174i	$-0.487061\pi$
$541$	43.9688			0.0812731			0.0406366	+	0.999174i	$0.487061\pi$
$542$		0			0
$543$	516.784	+	516.784i	0.951721	+	0.951721i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	111.942	−	111.942i	0.204647	−	0.204647i	−0.597340	−	0.801988i	$-0.703776\pi$
$547$	111.942	−	111.942i	0.204647	−	0.204647i	0.801988	+	0.597340i	$0.203776\pi$
$548$		0			0
$549$		−	820.722i		−	1.49494i
$550$		0			0
$551$	15.7501			0.0285845
$552$		0			0
$553$	35.3500	+	35.3500i	0.0639240	+	0.0639240i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−275.575	+	275.575i	−0.494749	+	0.494749i	−0.909799	−	0.415050i	$-0.863764\pi$
$557$	−275.575	+	275.575i	−0.494749	+	0.494749i	0.415050	+	0.909799i	$0.363764\pi$
$558$		0			0
$559$			64.8282i			0.115972i
$560$		0			0
$561$	−878.219			−1.56545
$562$		0			0
$563$	240.236	+	240.236i	0.426707	+	0.426707i	0.887505	−	0.460798i	$-0.152437\pi$
$563$	240.236	+	240.236i	0.426707	+	0.426707i	−0.460798	+	0.887505i	$0.652437\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−27.4703	+	27.4703i	−0.0484484	+	0.0484484i
$568$		0			0
$569$		−	108.753i		−	0.191130i	−0.995423	−	0.0955651i	$-0.969534\pi$
$569$		−	108.753i		−	0.191130i	0.995423	−	0.0955651i	$-0.0304658\pi$
$570$		0			0
$571$	80.0718			0.140231			0.0701154	−	0.997539i	$-0.477663\pi$
$571$	80.0718			0.140231			0.0701154	+	0.997539i	$0.477663\pi$
$572$		0			0
$573$	1175.23	+	1175.23i	2.05102	+	2.05102i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	484.172	−	484.172i	0.839119	−	0.839119i	−0.149624	−	0.988743i	$-0.547806\pi$
$577$	484.172	−	484.172i	0.839119	−	0.839119i	0.988743	+	0.149624i	$0.0478062\pi$
$578$		0			0
$579$			112.366i			0.194068i
$580$		0			0
$581$	−6.73444			−0.0115911
$582$		0			0
$583$	−34.2094	−	34.2094i	−0.0586782	−	0.0586782i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	342.517	−	342.517i	0.583504	−	0.583504i	−0.352360	−	0.935865i	$-0.614621\pi$
$587$	342.517	−	342.517i	0.583504	−	0.583504i	0.935865	+	0.352360i	$0.114621\pi$
$588$		0			0
$589$			43.2250i			0.0733871i
$590$		0			0
$591$	1642.29			2.77883
$592$		0			0
$593$	−39.4500	−	39.4500i	−0.0665261	−	0.0665261i	0.673061	−	0.739587i	$-0.264979\pi$
$593$	−39.4500	−	39.4500i	−0.0665261	−	0.0665261i	−0.739587	+	0.673061i	$0.764979\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−779.225	+	779.225i	−1.30523	+	1.30523i
$598$		0			0
$599$			589.987i			0.984954i	0.870325	+	0.492477i	$0.163908\pi$
$599$			589.987i			0.984954i	−0.870325	+	0.492477i	$0.836092\pi$
$600$		0			0
$601$	806.628			1.34214			0.671072	−	0.741393i	$-0.265834\pi$
$601$	806.628			1.34214			0.671072	+	0.741393i	$0.265834\pi$
$602$		0			0
$603$	520.780	+	520.780i	0.863648	+	0.863648i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	391.167	−	391.167i	0.644427	−	0.644427i	−0.307214	−	0.951641i	$-0.599397\pi$
$607$	391.167	−	391.167i	0.644427	−	0.644427i	0.951641	+	0.307214i	$0.0993966\pi$
$608$		0			0
$609$			12.4001i			0.0203614i
$610$		0			0
$611$	−135.759			−0.222192
$612$		0			0
$613$	111.209	+	111.209i	0.181418	+	0.181418i	0.791974	−	0.610555i	$-0.209054\pi$
$613$	111.209	+	111.209i	0.181418	+	0.181418i	−0.610555	+	0.791974i	$0.709054\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−286.466	+	286.466i	−0.464288	+	0.464288i	−0.900058	−	0.435770i	$-0.856476\pi$
$617$	−286.466	+	286.466i	−0.464288	+	0.464288i	0.435770	+	0.900058i	$0.356476\pi$
$618$		0			0
$619$			233.006i			0.376424i	0.982128	+	0.188212i	$0.0602692\pi$
$619$			233.006i			0.376424i	−0.982128	+	0.188212i	$0.939731\pi$
$620$		0			0
$621$	1329.92			2.14159
$622$		0			0
$623$	3.34996	+	3.34996i	0.00537715	+	0.00537715i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−118.450	+	118.450i	−0.188915	+	0.188915i
$628$		0			0
$629$			844.994i			1.34339i
$630$		0			0
$631$	−79.7594			−0.126402			−0.0632008	−	0.998001i	$-0.520131\pi$
$631$	−79.7594			−0.126402			−0.0632008	+	0.998001i	$0.520131\pi$
$632$		0			0
$633$	−804.616	−	804.616i	−1.27111	−	1.27111i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−77.9625	+	77.9625i	−0.122390	+	0.122390i
$638$		0			0
$639$		−	599.884i		−	0.938786i
$640$		0			0
$641$	736.178			1.14848			0.574242	−	0.818686i	$-0.305297\pi$
$641$	736.178			1.14848			0.574242	+	0.818686i	$0.305297\pi$
$642$		0			0
$643$	−580.245	−	580.245i	−0.902403	−	0.902403i	0.0932404	−	0.995644i	$-0.470277\pi$
$643$	−580.245	−	580.245i	−0.902403	−	0.902403i	−0.995644	+	0.0932404i	$0.970277\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	711.586	−	711.586i	1.09982	−	1.09982i	0.105393	−	0.994431i	$-0.466390\pi$
$647$	711.586	−	711.586i	1.09982	−	1.09982i	0.994431	−	0.105393i	$-0.0336101\pi$
$648$		0			0
$649$		−	761.800i		−	1.17381i
$650$		0			0
$651$	−34.0312			−0.0522753
$652$		0			0
$653$	−521.187	−	521.187i	−0.798143	−	0.798143i	0.184659	−	0.982803i	$-0.440882\pi$
$653$	−521.187	−	521.187i	−0.798143	−	0.798143i	−0.982803	+	0.184659i	$0.940882\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1152.27	−	1152.27i	1.75383	−	1.75383i
$658$		0			0
$659$			444.606i			0.674668i	0.941385	+	0.337334i	$0.109525\pi$
$659$			444.606i			0.674668i	−0.941385	+	0.337334i	$0.890475\pi$
$660$		0			0
$661$	−479.947			−0.726092			−0.363046	−	0.931771i	$-0.618263\pi$
$661$	−479.947			−0.726092			−0.363046	+	0.931771i	$0.618263\pi$
$662$		0			0
$663$	122.984	+	122.984i	0.185497	+	0.185497i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	107.225	−	107.225i	0.160757	−	0.160757i
$668$		0			0
$669$			1692.37i			2.52969i
$670$		0			0
$671$	508.544			0.757889
$672$		0			0
$673$	440.550	+	440.550i	0.654606	+	0.654606i	0.954099	−	0.299492i	$-0.0968173\pi$
$673$	440.550	+	440.550i	0.654606	+	0.654606i	−0.299492	+	0.954099i	$0.596817\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−494.087	+	494.087i	−0.729819	+	0.729819i	−0.970584	−	0.240765i	$-0.922602\pi$
$677$	−494.087	+	494.087i	−0.729819	+	0.729819i	0.240765	+	0.970584i	$0.422602\pi$
$678$		0			0
$679$			29.2469i			0.0430735i
$680$		0			0
$681$	−911.822			−1.33895
$682$		0			0
$683$	362.748	+	362.748i	0.531110	+	0.531110i	0.920903	−	0.389792i	$-0.127453\pi$
$683$	362.748	+	362.748i	0.531110	+	0.531110i	−0.389792	+	0.920903i	$0.627453\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	222.325	−	222.325i	0.323617	−	0.323617i
$688$		0			0
$689$			9.58125i			0.0139060i
$690$		0			0
$691$	228.597			0.330820			0.165410	−	0.986225i	$-0.447105\pi$
$691$	228.597			0.330820			0.165410	+	0.986225i	$0.447105\pi$
$692$		0			0
$693$	−62.6281	−	62.6281i	−0.0903725	−	0.0903725i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−734.753	+	734.753i	−1.05417	+	1.05417i
$698$		0			0
$699$		−	734.459i		−	1.05073i
$700$		0			0
$701$	264.178			0.376859			0.188429	−	0.982087i	$-0.439660\pi$
$701$	264.178			0.376859			0.188429	+	0.982087i	$0.439660\pi$
$702$		0			0
$703$	113.969	+	113.969i	0.162118	+	0.162118i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−20.3031	+	20.3031i	−0.0287173	+	0.0287173i
$708$		0			0
$709$			1122.76i			1.58359i	0.610790	+	0.791793i	$0.290852\pi$
$709$			1122.76i			1.58359i	−0.610790	+	0.791793i	$0.709148\pi$
$710$		0			0
$711$	−2179.85			−3.06589
$712$		0			0
$713$	294.272	+	294.272i	0.412724	+	0.412724i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	849.925	−	849.925i	1.18539	−	1.18539i
$718$		0			0
$719$		−	320.588i		−	0.445880i	−0.974832	−	0.222940i	$-0.928435\pi$
$719$		−	320.588i		−	0.445880i	0.974832	−	0.222940i	$-0.0715654\pi$
$720$		0			0
$721$	17.6032			0.0244149
$722$		0			0
$723$	−0.659361	−	0.659361i	−0.000911979	−	0.000911979i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−521.502	+	521.502i	−0.717334	+	0.717334i	−0.968058	−	0.250725i	$-0.919331\pi$
$727$	−521.502	+	521.502i	−0.717334	+	0.717334i	0.250725	+	0.968058i	$0.419331\pi$
$728$		0			0
$729$			625.125i			0.857510i
$730$		0			0
$731$	−422.334			−0.577749
$732$		0			0
$733$	680.737	+	680.737i	0.928700	+	0.928700i	0.997622	−	0.0689216i	$-0.0219558\pi$
$733$	680.737	+	680.737i	0.928700	+	0.928700i	−0.0689216	+	0.997622i	$0.521956\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−322.691	+	322.691i	−0.437843	+	0.437843i
$738$		0			0
$739$			408.669i			0.553002i	0.961014	+	0.276501i	$0.0891750\pi$
$739$			408.669i			0.553002i	−0.961014	+	0.276501i	$0.910825\pi$
$740$		0			0
$741$	33.1751			0.0447707
$742$		0			0
$743$	−819.301	−	819.301i	−1.10269	−	1.10269i	−0.994085	−	0.108609i	$-0.965360\pi$
$743$	−819.301	−	819.301i	−1.10269	−	1.10269i	−0.108609	−	0.994085i	$-0.534640\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	207.639	−	207.639i	0.277964	−	0.277964i
$748$		0			0
$749$			55.2343i			0.0737441i
$750$		0			0
$751$	−48.5969			−0.0647096			−0.0323548	−	0.999476i	$-0.510301\pi$
$751$	−48.5969			−0.0647096			−0.0323548	+	0.999476i	$0.510301\pi$
$752$		0			0
$753$	975.234	+	975.234i	1.29513	+	1.29513i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−481.628	+	481.628i	−0.636233	+	0.636233i	−0.949624	−	0.313391i	$-0.898535\pi$
$757$	−481.628	+	481.628i	−0.636233	+	0.636233i	0.313391	+	0.949624i	$0.398535\pi$
$758$		0			0
$759$			1612.79i			2.12489i
$760$		0			0
$761$	−588.325			−0.773095			−0.386547	−	0.922270i	$-0.626332\pi$
$761$	−588.325			−0.773095			−0.386547	+	0.922270i	$0.626332\pi$
$762$		0			0
$763$	51.6437	+	51.6437i	0.0676851	+	0.0676851i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−106.681	+	106.681i	−0.139089	+	0.139089i
$768$		0			0
$769$		−	65.6750i		−	0.0854031i	−0.999088	−	0.0427015i	$-0.986404\pi$
$769$		−	65.6750i		−	0.0854031i	0.999088	−	0.0427015i	$-0.0135965\pi$
$770$		0			0
$771$	−147.484			−0.191290
$772$		0			0
$773$	703.459	+	703.459i	0.910038	+	0.910038i	0.996275	−	0.0862368i	$-0.0274841\pi$
$773$	703.459	+	703.459i	0.910038	+	0.910038i	−0.0862368	+	0.996275i	$0.527484\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−89.7281	+	89.7281i	−0.115480	+	0.115480i
$778$		0			0
$779$			198.200i			0.254429i
$780$		0			0
$781$	371.706			0.475936
$782$		0			0
$783$	−195.350	−	195.350i	−0.249489	−	0.249489i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1012.79	+	1012.79i	−1.28690	+	1.28690i	−0.350237	+	0.936661i	$0.613899\pi$
$787$	−1012.79	+	1012.79i	−1.28690	+	1.28690i	−0.936661	+	0.350237i	$0.886101\pi$
$788$		0			0
$789$		−	1631.36i		−	2.06763i
$790$		0			0
$791$	48.2406			0.0609869
$792$		0			0
$793$	−71.2157	−	71.2157i	−0.0898054	−	0.0898054i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	996.109	−	996.109i	1.24982	−	1.24982i	0.294026	−	0.955797i	$-0.405005\pi$
$797$	996.109	−	996.109i	1.24982	−	1.24982i	0.955797	−	0.294026i	$-0.0949953\pi$
$798$		0			0
$799$		−	884.428i		−	1.10692i
$800$		0			0
$801$	−206.575			−0.257896
$802$		0			0
$803$	713.978	+	713.978i	0.889138	+	0.889138i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	780.856	−	780.856i	0.967604	−	0.967604i
$808$		0			0
$809$			1105.92i			1.36703i	0.729938	+	0.683514i	$0.239549\pi$
$809$			1105.92i			1.36703i	−0.729938	+	0.683514i	$0.760451\pi$
$810$		0			0
$811$	697.034			0.859475			0.429738	−	0.902954i	$-0.358606\pi$
$811$	697.034			0.859475			0.429738	+	0.902954i	$0.358606\pi$
$812$		0			0
$813$	−1380.74	−	1380.74i	−1.69833	−	1.69833i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−56.9625	+	56.9625i	−0.0697215	+	0.0697215i
$818$		0			0
$819$			17.5407i			0.0214172i
$820$		0			0
$821$	−1091.30			−1.32923			−0.664614	−	0.747187i	$-0.731404\pi$
$821$	−1091.30			−1.32923			−0.664614	+	0.747187i	$0.731404\pi$
$822$		0			0
$823$	1147.48	+	1147.48i	1.39426	+	1.39426i	0.815482	+	0.578782i	$0.196472\pi$
$823$	1147.48	+	1147.48i	1.39426	+	1.39426i	0.578782	+	0.815482i	$0.303528\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	673.492	−	673.492i	0.814380	−	0.814380i	−0.170907	−	0.985287i	$-0.554670\pi$
$827$	673.492	−	673.492i	0.814380	−	0.814380i	0.985287	+	0.170907i	$0.0546698\pi$
$828$		0			0
$829$		−	586.197i		−	0.707113i	−0.935413	−	0.353557i	$-0.884972\pi$
$829$		−	586.197i		−	0.707113i	0.935413	−	0.353557i	$-0.115028\pi$
$830$		0			0
$831$	165.853			0.199583
$832$		0			0
$833$	−507.900	−	507.900i	−0.609724	−	0.609724i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	536.125	−	536.125i	0.640532	−	0.640532i
$838$		0			0
$839$		−	306.512i		−	0.365331i	−0.983175	−	0.182665i	$-0.941528\pi$
$839$		−	306.512i		−	0.365331i	0.983175	−	0.182665i	$-0.0584725\pi$
$840$		0			0
$841$	809.500			0.962544
$842$		0			0
$843$	567.716	+	567.716i	0.673447	+	0.673447i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.69526	−	2.69526i	0.00318213	−	0.00318213i
$848$		0			0
$849$		−	414.147i		−	0.487806i
$850$		0			0
$851$	1551.78			1.82348
$852$		0			0
$853$	−4.14059	−	4.14059i	−0.00485415	−	0.00485415i	0.704676	−	0.709530i	$-0.251093\pi$
$853$	−4.14059	−	4.14059i	−0.00485415	−	0.00485415i	−0.709530	+	0.704676i	$0.751093\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	644.737	−	644.737i	0.752319	−	0.752319i	−0.222592	−	0.974912i	$-0.571452\pi$
$857$	644.737	−	644.737i	0.752319	−	0.752319i	0.974912	+	0.222592i	$0.0714519\pi$
$858$		0			0
$859$		−	170.094i		−	0.198014i	−0.995087	−	0.0990068i	$-0.968433\pi$
$859$		−	170.094i		−	0.198014i	0.995087	−	0.0990068i	$-0.0315666\pi$
$860$		0			0
$861$	−156.044			−0.181236
$862$		0			0
$863$	−412.183	−	412.183i	−0.477616	−	0.477616i	0.426752	−	0.904369i	$-0.359658\pi$
$863$	−412.183	−	412.183i	−0.477616	−	0.477616i	−0.904369	+	0.426752i	$0.859658\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	268.548	−	268.548i	0.309744	−	0.309744i
$868$		0			0
$869$		−	1350.70i		−	1.55432i
$870$		0			0
$871$	90.3782			0.103764
$872$		0			0
$873$	−901.753	−	901.753i	−1.03294	−	1.03294i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−882.841	+	882.841i	−1.00666	+	1.00666i	−0.00668198	+	0.999978i	$0.502127\pi$
$877$	−882.841	+	882.841i	−1.00666	+	1.00666i	−0.999978	+	0.00668198i	$0.997873\pi$
$878$		0			0
$879$			1759.65i			2.00188i
$880$		0			0
$881$	685.078			0.777614			0.388807	−	0.921319i	$-0.372887\pi$
$881$	685.078			0.777614			0.388807	+	0.921319i	$0.372887\pi$
$882$		0			0
$883$	−742.214	−	742.214i	−0.840559	−	0.840559i	0.148372	−	0.988932i	$-0.452597\pi$
$883$	−742.214	−	742.214i	−0.840559	−	0.840559i	−0.988932	+	0.148372i	$0.952597\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−882.464	+	882.464i	−0.994886	+	0.994886i	−0.999987	−	0.00510089i	$-0.998376\pi$
$887$	−882.464	+	882.464i	−0.994886	+	0.994886i	0.00510089	+	0.999987i	$0.498376\pi$
$888$		0			0
$889$		−	4.95314i		−	0.00557158i
$890$		0			0
$891$	1049.62			1.17803
$892$		0			0
$893$	−119.287	−	119.287i	−0.133581	−	0.133581i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	225.853	−	225.853i	0.251787	−	0.251787i
$898$		0			0
$899$		−	86.4500i		−	0.0961624i
$900$		0			0
$901$	−62.4187			−0.0692772
$902$		0			0
$903$	−44.8468	−	44.8468i	−0.0496642	−	0.0496642i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−457.439	+	457.439i	−0.504343	+	0.504343i	−0.912784	−	0.408442i	$-0.866072\pi$
$907$	−457.439	+	457.439i	−0.504343	+	0.504343i	0.408442	+	0.912784i	$0.366072\pi$
$908$		0			0
$909$		−	1251.99i		−	1.37732i
$910$		0			0
$911$	591.903			0.649729			0.324864	−	0.945761i	$-0.394681\pi$
$911$	591.903			0.649729			0.324864	+	0.945761i	$0.394681\pi$
$912$		0			0
$913$	128.659	+	128.659i	0.140919	+	0.140919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	32.1968	−	32.1968i	0.0351110	−	0.0351110i
$918$		0			0
$919$			1391.66i			1.51432i	0.653228	+	0.757161i	$0.273414\pi$
$919$			1391.66i			1.51432i	−0.653228	+	0.757161i	$0.726586\pi$
$920$		0			0
$921$	856.553			0.930025
$922$		0			0
$923$	−52.0532	−	52.0532i	−0.0563956	−	0.0563956i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−542.748	+	542.748i	−0.585489	+	0.585489i
$928$		0			0
$929$		−	81.5719i		−	0.0878062i	−0.999036	−	0.0439031i	$-0.986021\pi$
$929$		−	81.5719i		−	0.0878062i	0.999036	−	0.0439031i	$-0.0139793\pi$
$930$		0			0
$931$	−137.006			−0.147160
$932$		0			0
$933$	212.134	+	212.134i	0.227368	+	0.227368i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1126.84	+	1126.84i	−1.20260	+	1.20260i	−0.229233	+	0.973372i	$0.573622\pi$
$937$	−1126.84	+	1126.84i	−1.20260	+	1.20260i	−0.973372	+	0.229233i	$0.926378\pi$
$938$		0			0
$939$		−	1860.66i		−	1.98153i
$940$		0			0
$941$	983.987			1.04568			0.522841	−	0.852430i	$-0.324872\pi$
$941$	983.987			1.04568			0.522841	+	0.852430i	$0.324872\pi$
$942$		0			0
$943$	1349.33	+	1349.33i	1.43089	+	1.43089i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	301.973	−	301.973i	0.318874	−	0.318874i	−0.529461	−	0.848334i	$-0.677606\pi$
$947$	301.973	−	301.973i	0.318874	−	0.318874i	0.848334	+	0.529461i	$0.177606\pi$
$948$		0			0
$949$		−	199.969i		−	0.210715i
$950$		0			0
$951$	−267.322			−0.281096
$952$		0			0
$953$	531.459	+	531.459i	0.557670	+	0.557670i	0.928643	−	0.370974i	$-0.120976\pi$
$953$	531.459	+	531.459i	0.557670	+	0.557670i	−0.370974	+	0.928643i	$0.620976\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	236.900	−	236.900i	0.247544	−	0.247544i
$958$		0			0
$959$			21.1219i			0.0220250i
$960$		0			0
$961$	−723.744			−0.753115
$962$		0			0
$963$	−1703.01	−	1703.01i	−1.76844	−	1.76844i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	74.3922	−	74.3922i	0.0769309	−	0.0769309i	−0.667594	−	0.744525i	$-0.732676\pi$
$967$	74.3922	−	74.3922i	0.0769309	−	0.0769309i	0.744525	+	0.667594i	$0.232676\pi$
$968$		0			0
$969$			216.125i			0.223039i
$970$		0			0
$971$	169.959			0.175035			0.0875177	−	0.996163i	$-0.472107\pi$
$971$	169.959			0.175035			0.0875177	+	0.996163i	$0.472107\pi$
$972$		0			0
$973$	−66.0126	−	66.0126i	−0.0678444	−	0.0678444i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	287.000	−	287.000i	0.293756	−	0.293756i	−0.544806	−	0.838562i	$-0.683397\pi$
$977$	287.000	−	287.000i	0.293756	−	0.293756i	0.838562	+	0.544806i	$0.183397\pi$
$978$		0			0
$979$		−	128.000i		−	0.130746i
$980$		0			0
$981$	−3184.60			−3.24628
$982$		0			0
$983$	−772.477	−	772.477i	−0.785836	−	0.785836i	0.194973	−	0.980809i	$-0.437538\pi$
$983$	−772.477	−	772.477i	−0.785836	−	0.785836i	−0.980809	+	0.194973i	$0.937538\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	93.9156	−	93.9156i	0.0951526	−	0.0951526i
$988$		0			0
$989$			775.591i			0.784217i
$990$		0			0
$991$	−1541.28			−1.55528			−0.777641	−	0.628709i	$-0.783584\pi$
$991$	−1541.28			−1.55528			−0.777641	+	0.628709i	$0.783584\pi$
$992$		0			0
$993$	1232.91	+	1232.91i	1.24160	+	1.24160i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1248.55	−	1248.55i	1.25230	−	1.25230i	0.297619	−	0.954685i	$-0.403808\pi$
$997$	1248.55	−	1248.55i	1.25230	−	1.25230i	0.954685	−	0.297619i	$-0.0961925\pi$
$998$		0			0
$999$		−	2827.14i		−	2.82997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.p.i.193.1		4
4.3	odd	2		200.3.l.e.193.2		4
5.2	odd	4	inner	400.3.p.i.257.1		4
5.3	odd	4		80.3.p.d.17.2		4
5.4	even	2		80.3.p.d.33.2		4
12.11	even	2		1800.3.v.k.793.2		4
15.8	even	4		720.3.bh.l.577.1		4
15.14	odd	2		720.3.bh.l.433.1		4
20.3	even	4		40.3.l.b.17.1	✓	4
20.7	even	4		200.3.l.e.57.2		4
20.19	odd	2		40.3.l.b.33.1	yes	4
40.3	even	4		320.3.p.l.257.2		4
40.13	odd	4		320.3.p.i.257.1		4
40.19	odd	2		320.3.p.l.193.2		4
40.29	even	2		320.3.p.i.193.1		4
60.23	odd	4		360.3.v.c.217.1		4
60.47	odd	4		1800.3.v.k.1657.2		4
60.59	even	2		360.3.v.c.73.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.l.b.17.1	✓	4	20.3	even	4
40.3.l.b.33.1	yes	4	20.19	odd	2
80.3.p.d.17.2		4	5.3	odd	4
80.3.p.d.33.2		4	5.4	even	2
200.3.l.e.57.2		4	20.7	even	4
200.3.l.e.193.2		4	4.3	odd	2
320.3.p.i.193.1		4	40.29	even	2
320.3.p.i.257.1		4	40.13	odd	4
320.3.p.l.193.2		4	40.19	odd	2
320.3.p.l.257.2		4	40.3	even	4
360.3.v.c.73.1		4	60.59	even	2
360.3.v.c.217.1		4	60.23	odd	4
400.3.p.i.193.1		4	1.1	even	1	trivial
400.3.p.i.257.1		4	5.2	odd	4	inner
720.3.bh.l.433.1		4	15.14	odd	2
720.3.bh.l.577.1		4	15.8	even	4
1800.3.v.k.793.2		4	12.11	even	2
1800.3.v.k.1657.2		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.70156 - 3.70156i) q^{3} +(0.298438 - 0.298438i) q^{7} +18.4031i q^{9} +O(q^{10})\)	\(q+(-3.70156 - 3.70156i) q^{3} +(0.298438 - 0.298438i) q^{7} +18.4031i q^{9} -11.4031 q^{11} +(1.59688 + 1.59688i) q^{13} +(-10.4031 + 10.4031i) q^{17} +2.80625i q^{19} -2.20937 q^{21} +(19.1047 + 19.1047i) q^{23} +(34.8062 - 34.8062i) q^{27} -5.61250i q^{29} +15.4031 q^{31} +(42.2094 + 42.2094i) q^{33} +(40.6125 - 40.6125i) q^{37} -11.8219i q^{39} +70.6281 q^{41} +(20.2984 + 20.2984i) q^{43} +(-42.5078 + 42.5078i) q^{47} +48.8219i q^{49} +77.0156 q^{51} +(3.00000 + 3.00000i) q^{53} +(10.3875 - 10.3875i) q^{57} +66.8062i q^{59} -44.5969 q^{61} +(5.49219 + 5.49219i) q^{63} +(28.2984 - 28.2984i) q^{67} -141.434i q^{69} -32.5969 q^{71} +(-62.6125 - 62.6125i) q^{73} +(-3.40312 + 3.40312i) q^{77} +118.450i q^{79} -92.0469 q^{81} +(-11.2828 - 11.2828i) q^{83} +(-20.7750 + 20.7750i) q^{87} +11.2250i q^{89} +0.953136 q^{91} +(-57.0156 - 57.0156i) q^{93} +(-49.0000 + 49.0000i) q^{97} -209.853i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 14 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 + 14 * q^7	\( 4 q - 2 q^{3} + 14 q^{7} - 20 q^{11} + 32 q^{13} - 16 q^{17} + 68 q^{21} + 38 q^{23} + 88 q^{27} + 36 q^{31} + 92 q^{33} + 60 q^{37} + 52 q^{41} + 94 q^{43} - 106 q^{47} + 180 q^{51} + 12 q^{53} + 144 q^{57} - 204 q^{61} + 86 q^{63} + 126 q^{67} - 156 q^{71} - 148 q^{73} + 12 q^{77} + 16 q^{81} - 186 q^{83} - 288 q^{87} + 388 q^{91} - 100 q^{93} - 196 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 14 * q^7 - 20 * q^11 + 32 * q^13 - 16 * q^17 + 68 * q^21 + 38 * q^23 + 88 * q^27 + 36 * q^31 + 92 * q^33 + 60 * q^37 + 52 * q^41 + 94 * q^43 - 106 * q^47 + 180 * q^51 + 12 * q^53 + 144 * q^57 - 204 * q^61 + 86 * q^63 + 126 * q^67 - 156 * q^71 - 148 * q^73 + 12 * q^77 + 16 * q^81 - 186 * q^83 - 288 * q^87 + 388 * q^91 - 100 * q^93 - 196 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more