LMFDB - Embedded newform 825.4.c.p.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, 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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 54x^{6} + 913x^{4} + 5292x^{2} + 8464 $ x^8 + 54x^6 + 913x^4 + 5292*x^2 + 8464
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-4.17080i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.p.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.17080i q^{2} +3.00000i q^{3} -18.7372 q^{4} +15.5124 q^{6} +11.1745i q^{7} +55.5199i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-5.17080i q^{2} +3.00000i q^{3} -18.7372 q^{4} +15.5124 q^{6} +11.1745i q^{7} +55.5199i q^{8} -9.00000 q^{9} -11.0000 q^{11} -56.2116i q^{12} -89.5310i q^{13} +57.7813 q^{14} +137.185 q^{16} -58.3242i q^{17} +46.5372i q^{18} -24.5575 q^{19} -33.5236 q^{21} +56.8788i q^{22} -111.696i q^{23} -166.560 q^{24} -462.947 q^{26} -27.0000i q^{27} -209.379i q^{28} -109.954 q^{29} +119.547 q^{31} -265.196i q^{32} -33.0000i q^{33} -301.583 q^{34} +168.635 q^{36} +356.544i q^{37} +126.982i q^{38} +268.593 q^{39} +268.798 q^{41} +173.344i q^{42} +263.371i q^{43} +206.109 q^{44} -577.557 q^{46} +206.732i q^{47} +411.554i q^{48} +218.130 q^{49} +174.973 q^{51} +1677.56i q^{52} +223.749i q^{53} -139.612 q^{54} -620.408 q^{56} -73.6726i q^{57} +568.549i q^{58} -475.000 q^{59} -513.204 q^{61} -618.153i q^{62} -100.571i q^{63} -273.798 q^{64} -170.636 q^{66} +264.533i q^{67} +1092.83i q^{68} +335.087 q^{69} -1110.33 q^{71} -499.679i q^{72} +893.608i q^{73} +1843.62 q^{74} +460.139 q^{76} -122.920i q^{77} -1388.84i q^{78} -1303.66 q^{79} +81.0000 q^{81} -1389.90i q^{82} +1049.37i q^{83} +628.138 q^{84} +1361.84 q^{86} -329.862i q^{87} -610.718i q^{88} +1417.91 q^{89} +1000.47 q^{91} +2092.86i q^{92} +358.640i q^{93} +1068.97 q^{94} +795.587 q^{96} -85.8091i q^{97} -1127.91i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9	$ 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9} - 88 q^{11} + 104 q^{14} + 132 q^{16} - 272 q^{19} + 204 q^{21} - 288 q^{24} - 640 q^{26} - 104 q^{29} + 984 q^{31} - 488 q^{34} + 468 q^{36} - 12 q^{39} + 536 q^{41} + 572 q^{44} + 736 q^{46} + 992 q^{49} + 444 q^{51} - 216 q^{54} - 1704 q^{56} + 2064 q^{59} + 232 q^{61} + 1836 q^{64} - 264 q^{66} + 384 q^{69} - 1840 q^{71} + 5712 q^{74} + 3144 q^{76} - 2304 q^{79} + 648 q^{81} + 120 q^{84} + 472 q^{86} + 2128 q^{89} + 5560 q^{91} + 2864 q^{94} + 1248 q^{96} + 792 q^{99}+O(q^{100}) $ 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9 - 88 * q^11 + 104 * q^14 + 132 * q^16 - 272 * q^19 + 204 * q^21 - 288 * q^24 - 640 * q^26 - 104 * q^29 + 984 * q^31 - 488 * q^34 + 468 * q^36 - 12 * q^39 + 536 * q^41 + 572 * q^44 + 736 * q^46 + 992 * q^49 + 444 * q^51 - 216 * q^54 - 1704 * q^56 + 2064 * q^59 + 232 * q^61 + 1836 * q^64 - 264 * q^66 + 384 * q^69 - 1840 * q^71 + 5712 * q^74 + 3144 * q^76 - 2304 * q^79 + 648 * q^81 + 120 * q^84 + 472 * q^86 + 2128 * q^89 + 5560 * q^91 + 2864 * q^94 + 1248 * q^96 + 792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 5.17080i	− 1.82815i	−0.405540	−	0.914077i	$-0.632917\pi$
$2$	− 5.17080i	− 1.82815i	0.405540	−	0.914077i	$-0.367083\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−18.7372	−2.34215
$5$	0	0
$5$	0	0
$6$	15.5124	1.05549
$7$	11.1745i	0.603368i	0.953408	+	0.301684i	$0.0975487\pi$
$7$	11.1745i	0.603368i	−0.953408	+	0.301684i	$0.902451\pi$
$8$	55.5199i	2.45365i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	− 56.2116i	− 1.35224i
$13$	− 89.5310i	− 1.91011i	−0.296427	−	0.955056i	$-0.595795\pi$
$13$	− 89.5310i	− 1.91011i	0.296427	−	0.955056i	$-0.404205\pi$
$14$	57.7813	1.10305
$15$	0	0
$16$	137.185	2.14351
$17$	− 58.3242i	− 0.832100i	−0.909342	−	0.416050i	$-0.863414\pi$
$17$	− 58.3242i	− 0.832100i	0.909342	−	0.416050i	$-0.136586\pi$
$18$	46.5372i	0.609385i
$19$	−24.5575	−0.296520	−0.148260	−	0.988948i	$-0.547367\pi$
$19$	−24.5575	−0.296520	−0.148260	+	0.988948i	$0.547367\pi$
$20$	0	0
$21$	−33.5236	−0.348355
$22$	56.8788i	0.551209i
$23$	− 111.696i	− 1.01262i	−0.862353	−	0.506308i	$-0.831010\pi$
$23$	− 111.696i	− 1.01262i	0.862353	−	0.506308i	$-0.168990\pi$
$24$	−166.560	−1.41662
$25$	0	0
$26$	−462.947	−3.49198
$27$	− 27.0000i	− 0.192450i
$28$	− 209.379i	− 1.41318i
$29$	−109.954	−0.704066	−0.352033	−	0.935988i	$-0.614510\pi$
$29$	−109.954	−0.704066	−0.352033	+	0.935988i	$0.614510\pi$
$30$	0	0
$31$	119.547	0.692621	0.346310	−	0.938120i	$-0.387434\pi$
$31$	119.547	0.692621	0.346310	+	0.938120i	$0.387434\pi$
$32$	− 265.196i	− 1.46501i
$33$	− 33.0000i	− 0.174078i
$34$	−301.583	−1.52121
$35$	0	0
$36$	168.635	0.780716
$37$	356.544i	1.58420i	0.610391	+	0.792100i	$0.291012\pi$
$37$	356.544i	1.58420i	−0.610391	+	0.792100i	$0.708988\pi$
$38$	126.982i	0.542085i
$39$	268.593	1.10280
$40$	0	0
$41$	268.798	1.02388	0.511941	−	0.859021i	$-0.328927\pi$
$41$	268.798	1.02388	0.511941	+	0.859021i	$0.328927\pi$
$42$	173.344i	0.636846i
$43$	263.371i	0.934038i	0.884247	+	0.467019i	$0.154672\pi$
$43$	263.371i	0.934038i	−0.884247	+	0.467019i	$0.845328\pi$
$44$	206.109	0.706184
$45$	0	0
$46$	−577.557	−1.85122
$47$	206.732i	0.641594i	0.947148	+	0.320797i	$0.103951\pi$
$47$	206.732i	0.641594i	−0.947148	+	0.320797i	$0.896049\pi$
$48$	411.554i	1.23756i
$49$	218.130	0.635947
$50$	0	0
$51$	174.973	0.480413
$52$	1677.56i	4.47376i
$53$	223.749i	0.579891i	0.957043	+	0.289946i	$0.0936372\pi$
$53$	223.749i	0.579891i	−0.957043	+	0.289946i	$0.906363\pi$
$54$	−139.612	−0.351828
$55$	0	0
$56$	−620.408	−1.48046
$57$	− 73.6726i	− 0.171196i
$58$	568.549i	1.28714i
$59$	−475.000	−1.04813	−0.524066	−	0.851678i	$-0.675585\pi$
$59$	−475.000	−1.04813	−0.524066	+	0.851678i	$0.675585\pi$
$60$	0	0
$61$	−513.204	−1.07720	−0.538598	−	0.842563i	$-0.681046\pi$
$61$	−513.204	−1.07720	−0.538598	+	0.842563i	$0.681046\pi$
$62$	− 618.153i	− 1.26622i
$63$	− 100.571i	− 0.201123i
$64$	−273.798	−0.534761
$65$	0	0
$66$	−170.636	−0.318241
$67$	264.533i	0.482355i	0.970481	+	0.241178i	$0.0775337\pi$
$67$	264.533i	0.482355i	−0.970481	+	0.241178i	$0.922466\pi$
$68$	1092.83i	1.94890i
$69$	335.087	0.584634
$70$	0	0
$71$	−1110.33	−1.85595	−0.927973	−	0.372648i	$-0.878450\pi$
$71$	−1110.33	−1.85595	−0.927973	+	0.372648i	$0.878450\pi$
$72$	− 499.679i	− 0.817885i
$73$	893.608i	1.43273i	0.697728	+	0.716363i	$0.254194\pi$
$73$	893.608i	1.43273i	−0.697728	+	0.716363i	$0.745806\pi$
$74$	1843.62	2.89616
$75$	0	0
$76$	460.139	0.694494
$77$	− 122.920i	− 0.181922i
$78$	− 1388.84i	− 2.01609i
$79$	−1303.66	−1.85663	−0.928314	−	0.371797i	$-0.878742\pi$
$79$	−1303.66	−1.85663	−0.928314	+	0.371797i	$0.878742\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 1389.90i	− 1.87181i
$83$	1049.37i	1.38775i	0.720098	+	0.693873i	$0.244097\pi$
$83$	1049.37i	1.38775i	−0.720098	+	0.693873i	$0.755903\pi$
$84$	628.138	0.815898
$85$	0	0
$86$	1361.84	1.70757
$87$	− 329.862i	− 0.406493i
$88$	− 610.718i	− 0.739805i
$89$	1417.91	1.68875	0.844374	−	0.535754i	$-0.179972\pi$
$89$	1417.91	1.68875	0.844374	+	0.535754i	$0.179972\pi$
$90$	0	0
$91$	1000.47	1.15250
$92$	2092.86i	2.37170i
$93$	358.640i	0.399885i
$94$	1068.97	1.17293
$95$	0	0
$96$	795.587	0.845826
$97$	− 85.8091i	− 0.0898206i	−0.998991	−	0.0449103i	$-0.985700\pi$
$97$	− 85.8091i	− 0.0898206i	0.998991	−	0.0449103i	$-0.0143002\pi$
$98$	− 1127.91i	− 1.16261i
$99$	99.0000	0.100504
$100$	0	0
$101$	137.761	0.135721	0.0678603	−	0.997695i	$-0.478383\pi$
$101$	137.761	0.135721	0.0678603	+	0.997695i	$0.478383\pi$
$102$	− 904.749i	− 0.878269i
$103$	419.397i	0.401208i	0.979672	+	0.200604i	$0.0642905\pi$
$103$	419.397i	0.401208i	−0.979672	+	0.200604i	$0.935710\pi$
$104$	4970.75	4.68675
$105$	0	0
$106$	1156.96	1.06013
$107$	1190.45i	1.07557i	0.843083	+	0.537783i	$0.180738\pi$
$107$	1190.45i	1.07557i	−0.843083	+	0.537783i	$0.819262\pi$
$108$	505.904i	0.450747i
$109$	−1033.37	−0.908066	−0.454033	−	0.890985i	$-0.650015\pi$
$109$	−1033.37	−0.908066	−0.454033	+	0.890985i	$0.650015\pi$
$110$	0	0
$111$	−1069.63	−0.914638
$112$	1532.97i	1.29333i
$113$	− 930.760i	− 0.774854i	−0.921900	−	0.387427i	$-0.873364\pi$
$113$	− 930.760i	− 0.774854i	0.921900	−	0.387427i	$-0.126636\pi$
$114$	−380.946	−0.312973
$115$	0	0
$116$	2060.23	1.64903
$117$	805.779i	0.636704i
$118$	2456.13i	1.91615i
$119$	651.746	0.502062
$120$	0	0
$121$	121.000	0.0909091
$122$	2653.68i	1.96928i
$123$	806.393i	0.591138i
$124$	−2239.97	−1.62222
$125$	0	0
$126$	−520.031	−0.367683
$127$	− 94.4315i	− 0.0659799i	−0.999456	−	0.0329899i	$-0.989497\pi$
$127$	− 94.4315i	− 0.0659799i	0.999456	−	0.0329899i	$-0.0105029\pi$
$128$	− 705.814i	− 0.487389i
$129$	−790.112	−0.539267
$130$	0	0
$131$	1318.12	0.879122	0.439561	−	0.898213i	$-0.355134\pi$
$131$	1318.12	0.879122	0.439561	+	0.898213i	$0.355134\pi$
$132$	618.327i	0.407716i
$133$	− 274.419i	− 0.178911i
$134$	1367.85	0.881820
$135$	0	0
$136$	3238.15	2.04169
$137$	− 2008.43i	− 1.25249i	−0.779624	−	0.626247i	$-0.784590\pi$
$137$	− 2008.43i	− 1.25249i	0.779624	−	0.626247i	$-0.215410\pi$
$138$	− 1732.67i	− 1.06880i
$139$	−2956.76	−1.80424	−0.902120	−	0.431486i	$-0.857989\pi$
$139$	−2956.76	−1.80424	−0.902120	+	0.431486i	$0.857989\pi$
$140$	0	0
$141$	−620.196	−0.370425
$142$	5741.30i	3.39295i
$143$	984.841i	0.575920i
$144$	−1234.66	−0.714504
$145$	0	0
$146$	4620.67	2.61924
$147$	654.390i	0.367164i
$148$	− 6680.62i	− 3.71043i
$149$	−878.768	−0.483164	−0.241582	−	0.970380i	$-0.577666\pi$
$149$	−878.768	−0.483164	−0.241582	+	0.970380i	$0.577666\pi$
$150$	0	0
$151$	−1679.35	−0.905058	−0.452529	−	0.891750i	$-0.649478\pi$
$151$	−1679.35	−0.905058	−0.452529	+	0.891750i	$0.649478\pi$
$152$	− 1363.43i	− 0.727558i
$153$	524.918i	0.277367i
$154$	−635.594	−0.332582
$155$	0	0
$156$	−5032.68	−2.58293
$157$	− 703.051i	− 0.357386i	−0.983905	−	0.178693i	$-0.942813\pi$
$157$	− 703.051i	− 0.357386i	0.983905	−	0.178693i	$-0.0571869\pi$
$158$	6740.99i	3.39420i
$159$	−671.246	−0.334800
$160$	0	0
$161$	1248.15	0.610980
$162$	− 418.835i	− 0.203128i
$163$	2934.66i	1.41019i	0.709114	+	0.705093i	$0.249095\pi$
$163$	2934.66i	1.41019i	−0.709114	+	0.705093i	$0.750905\pi$
$164$	−5036.51	−2.39808
$165$	0	0
$166$	5426.06	2.53701
$167$	2146.05i	0.994407i	0.867634	+	0.497204i	$0.165640\pi$
$167$	2146.05i	0.994407i	−0.867634	+	0.497204i	$0.834360\pi$
$168$	− 1861.22i	− 0.854742i
$169$	−5818.81	−2.64852
$170$	0	0
$171$	221.018	0.0988401
$172$	− 4934.82i	− 2.18766i
$173$	321.356i	0.141227i	0.997504	+	0.0706134i	$0.0224957\pi$
$173$	321.356i	0.141227i	−0.997504	+	0.0706134i	$0.977504\pi$
$174$	−1705.65	−0.743131
$175$	0	0
$176$	−1509.03	−0.646293
$177$	− 1425.00i	− 0.605139i
$178$	− 7331.75i	− 3.08729i
$179$	2662.08	1.11158	0.555791	−	0.831322i	$-0.312415\pi$
$179$	2662.08	1.11158	0.555791	+	0.831322i	$0.312415\pi$
$180$	0	0
$181$	3306.02	1.35765	0.678825	−	0.734300i	$-0.262490\pi$
$181$	3306.02	1.35765	0.678825	+	0.734300i	$0.262490\pi$
$182$	− 5173.22i	− 2.10695i
$183$	− 1539.61i	− 0.621920i
$184$	6201.33	2.48461
$185$	0	0
$186$	1854.46	0.731051
$187$	641.566i	0.250888i
$188$	− 3873.57i	− 1.50271i
$189$	301.712	0.116118
$190$	0	0
$191$	946.068	0.358404	0.179202	−	0.983812i	$-0.442648\pi$
$191$	946.068	0.358404	0.179202	+	0.983812i	$0.442648\pi$
$192$	− 821.393i	− 0.308744i
$193$	− 3692.54i	− 1.37717i	−0.725154	−	0.688587i	$-0.758231\pi$
$193$	− 3692.54i	− 1.37717i	0.725154	−	0.688587i	$-0.241769\pi$
$194$	−443.702	−0.164206
$195$	0	0
$196$	−4087.14	−1.48948
$197$	411.503i	0.148824i	0.997228	+	0.0744122i	$0.0237080\pi$
$197$	411.503i	0.148824i	−0.997228	+	0.0744122i	$0.976292\pi$
$198$	− 511.909i	− 0.183736i
$199$	−1491.28	−0.531226	−0.265613	−	0.964080i	$-0.585574\pi$
$199$	−1491.28	−0.531226	−0.265613	+	0.964080i	$0.585574\pi$
$200$	0	0
$201$	−793.598	−0.278488
$202$	− 712.337i	− 0.248118i
$203$	− 1228.68i	− 0.424811i
$204$	−3278.49	−1.12520
$205$	0	0
$206$	2168.62	0.733470
$207$	1005.26i	0.337539i
$208$	− 12282.3i	− 4.09434i
$209$	270.133	0.0894042
$210$	0	0
$211$	−899.947	−0.293625	−0.146813	−	0.989164i	$-0.546901\pi$
$211$	−899.947	−0.293625	−0.146813	+	0.989164i	$0.546901\pi$
$212$	− 4192.42i	− 1.35819i
$213$	− 3330.99i	− 1.07153i
$214$	6155.61	1.96630
$215$	0	0
$216$	1499.04	0.472206
$217$	1335.88i	0.417905i
$218$	5343.37i	1.66009i
$219$	−2680.82	−0.827184
$220$	0	0
$221$	−5221.83	−1.58940
$222$	5530.85i	1.67210i
$223$	1935.29i	0.581152i	0.956852	+	0.290576i	$0.0938469\pi$
$223$	1935.29i	0.581152i	−0.956852	+	0.290576i	$0.906153\pi$
$224$	2963.44	0.883942
$225$	0	0
$226$	−4812.77	−1.41655
$227$	2906.26i	0.849758i	0.905250	+	0.424879i	$0.139683\pi$
$227$	2906.26i	0.849758i	−0.905250	+	0.424879i	$0.860317\pi$
$228$	1380.42i	0.400966i
$229$	5411.89	1.56169	0.780846	−	0.624724i	$-0.214788\pi$
$229$	5411.89	1.56169	0.780846	+	0.624724i	$0.214788\pi$
$230$	0	0
$231$	368.759	0.105033
$232$	− 6104.62i	− 1.72753i
$233$	− 4778.90i	− 1.34368i	−0.740699	−	0.671838i	$-0.765505\pi$
$233$	− 4778.90i	− 1.34368i	0.740699	−	0.671838i	$-0.234495\pi$
$234$	4166.53	1.16399
$235$	0	0
$236$	8900.17	2.45488
$237$	− 3910.99i	− 1.07192i
$238$	− 3370.05i	− 0.917848i
$239$	−5883.88	−1.59245	−0.796227	−	0.604998i	$-0.793174\pi$
$239$	−5883.88	−1.59245	−0.796227	+	0.604998i	$0.793174\pi$
$240$	0	0
$241$	1806.96	0.482974	0.241487	−	0.970404i	$-0.422365\pi$
$241$	1806.96	0.482974	0.241487	+	0.970404i	$0.422365\pi$
$242$	− 625.667i	− 0.166196i
$243$	243.000i	0.0641500i
$244$	9616.00	2.52296
$245$	0	0
$246$	4169.70	1.08069
$247$	2198.66i	0.566386i
$248$	6637.22i	1.69945i
$249$	−3148.10	−0.801215
$250$	0	0
$251$	1265.10	0.318137	0.159069	−	0.987268i	$-0.449151\pi$
$251$	1265.10	0.318137	0.159069	+	0.987268i	$0.449151\pi$
$252$	1884.41i	0.471059i
$253$	1228.65i	0.305315i
$254$	−488.287	−0.120621
$255$	0	0
$256$	−5840.00	−1.42578
$257$	4366.53i	1.05983i	0.848050	+	0.529916i	$0.177777\pi$
$257$	4366.53i	1.05983i	−0.848050	+	0.529916i	$0.822223\pi$
$258$	4085.51i	0.985864i
$259$	−3984.21	−0.955855
$260$	0	0
$261$	989.585	0.234689
$262$	− 6815.76i	− 1.60717i
$263$	− 2950.96i	− 0.691878i	−0.938257	−	0.345939i	$-0.887560\pi$
$263$	− 2950.96i	− 0.691878i	0.938257	−	0.345939i	$-0.112440\pi$
$264$	1832.16	0.427126
$265$	0	0
$266$	−1418.97	−0.327076
$267$	4253.74i	0.974999i
$268$	− 4956.60i	− 1.12975i
$269$	6048.65	1.37098	0.685488	−	0.728084i	$-0.259589\pi$
$269$	6048.65	1.37098	0.685488	+	0.728084i	$0.259589\pi$
$270$	0	0
$271$	−2922.90	−0.655180	−0.327590	−	0.944820i	$-0.606236\pi$
$271$	−2922.90	−0.655180	−0.327590	+	0.944820i	$0.606236\pi$
$272$	− 8001.19i	− 1.78362i
$273$	3001.40i	0.665396i
$274$	−10385.2	−2.28975
$275$	0	0
$276$	−6278.59	−1.36930
$277$	5433.48i	1.17858i	0.807922	+	0.589289i	$0.200592\pi$
$277$	5433.48i	1.17858i	−0.807922	+	0.589289i	$0.799408\pi$
$278$	15288.8i	3.29843i
$279$	−1075.92	−0.230874
$280$	0	0
$281$	−7981.02	−1.69433	−0.847167	−	0.531327i	$-0.821693\pi$
$281$	−7981.02	−1.69433	−0.847167	+	0.531327i	$0.821693\pi$
$282$	3206.91i	0.677194i
$283$	− 2705.71i	− 0.568332i	−0.958775	−	0.284166i	$-0.908283\pi$
$283$	− 2705.71i	− 0.568332i	0.958775	−	0.284166i	$-0.0917167\pi$
$284$	20804.5	4.34690
$285$	0	0
$286$	5092.42	1.05287
$287$	3003.69i	0.617777i
$288$	2386.76i	0.488338i
$289$	1511.29	0.307610
$290$	0	0
$291$	257.427	0.0518579
$292$	− 16743.7i	− 3.35565i
$293$	2207.71i	0.440190i	0.975478	+	0.220095i	$0.0706367\pi$
$293$	2207.71i	0.440190i	−0.975478	+	0.220095i	$0.929363\pi$
$294$	3383.72	0.671233
$295$	0	0
$296$	−19795.2	−3.88708
$297$	297.000i	0.0580259i
$298$	4543.94i	0.883299i
$299$	−10000.2	−1.93421
$300$	0	0
$301$	−2943.04	−0.563569
$302$	8683.60i	1.65459i
$303$	413.284i	0.0783583i
$304$	−3368.92	−0.635594
$305$	0	0
$306$	2714.25	0.507069
$307$	3918.45i	0.728462i	0.931309	+	0.364231i	$0.118668\pi$
$307$	3918.45i	0.728462i	−0.931309	+	0.364231i	$0.881332\pi$
$308$	2303.17i	0.426089i
$309$	−1258.19	−0.231638
$310$	0	0
$311$	8769.03	1.59886	0.799431	−	0.600758i	$-0.205134\pi$
$311$	8769.03	1.59886	0.799431	+	0.600758i	$0.205134\pi$
$312$	14912.3i	2.70590i
$313$	− 5058.92i	− 0.913569i	−0.889577	−	0.456785i	$-0.849001\pi$
$313$	− 5058.92i	− 0.913569i	0.889577	−	0.456785i	$-0.150999\pi$
$314$	−3635.34	−0.653357
$315$	0	0
$316$	24427.0	4.34850
$317$	8329.52i	1.47581i	0.674904	+	0.737906i	$0.264185\pi$
$317$	8329.52i	1.47581i	−0.674904	+	0.737906i	$0.735815\pi$
$318$	3470.88i	0.612067i
$319$	1209.49	0.212284
$320$	0	0
$321$	−3571.36	−0.620979
$322$	− 6453.92i	− 1.11697i
$323$	1432.30i	0.246734i
$324$	−1517.71	−0.260239
$325$	0	0
$326$	15174.6	2.57804
$327$	− 3100.12i	− 0.524272i
$328$	14923.6i	2.51225i
$329$	−2310.13	−0.387118
$330$	0	0
$331$	2901.85	0.481874	0.240937	−	0.970541i	$-0.422545\pi$
$331$	2901.85	0.481874	0.240937	+	0.970541i	$0.422545\pi$
$332$	− 19662.2i	− 3.25030i
$333$	− 3208.89i	− 0.528067i
$334$	11096.8	1.81793
$335$	0	0
$336$	−4598.92	−0.746702
$337$	− 6000.75i	− 0.969976i	−0.874521	−	0.484988i	$-0.838824\pi$
$337$	− 6000.75i	− 0.969976i	0.874521	−	0.484988i	$-0.161176\pi$
$338$	30087.9i	4.84191i
$339$	2792.28	0.447362
$340$	0	0
$341$	−1315.02	−0.208833
$342$	− 1142.84i	− 0.180695i
$343$	6270.36i	0.987078i
$344$	−14622.3	−2.29181
$345$	0	0
$346$	1661.67	0.258185
$347$	9059.04i	1.40148i	0.713415	+	0.700742i	$0.247148\pi$
$347$	9059.04i	1.40148i	−0.713415	+	0.700742i	$0.752852\pi$
$348$	6180.68i	0.952066i
$349$	9362.35	1.43597	0.717987	−	0.696057i	$-0.245064\pi$
$349$	9362.35	1.43597	0.717987	+	0.696057i	$0.245064\pi$
$350$	0	0
$351$	−2417.34	−0.367601
$352$	2917.15i	0.441718i
$353$	− 274.260i	− 0.0413524i	−0.999786	−	0.0206762i	$-0.993418\pi$
$353$	− 274.260i	− 0.0413524i	0.999786	−	0.0206762i	$-0.00658190\pi$
$354$	−7368.39	−1.10629
$355$	0	0
$356$	−26567.7	−3.95530
$357$	1955.24i	0.289866i
$358$	− 13765.1i	− 2.03214i
$359$	1394.51	0.205013	0.102506	−	0.994732i	$-0.467314\pi$
$359$	1394.51	0.205013	0.102506	+	0.994732i	$0.467314\pi$
$360$	0	0
$361$	−6255.93	−0.912076
$362$	− 17094.8i	− 2.48199i
$363$	363.000i	0.0524864i
$364$	−18745.9	−2.69933
$365$	0	0
$366$	−7961.03	−1.13697
$367$	− 11610.1i	− 1.65134i	−0.564155	−	0.825669i	$-0.690798\pi$
$367$	− 11610.1i	− 1.65134i	0.564155	−	0.825669i	$-0.309202\pi$
$368$	− 15322.9i	− 2.17055i
$369$	−2419.18	−0.341294
$370$	0	0
$371$	−2500.29	−0.349888
$372$	− 6719.91i	− 0.936590i
$373$	5068.89i	0.703639i	0.936068	+	0.351819i	$0.114437\pi$
$373$	5068.89i	0.703639i	−0.936068	+	0.351819i	$0.885563\pi$
$374$	3317.41	0.458661
$375$	0	0
$376$	−11477.7	−1.57425
$377$	9844.28i	1.34484i
$378$	− 1560.09i	− 0.212282i
$379$	−1623.62	−0.220052	−0.110026	−	0.993929i	$-0.535093\pi$
$379$	−1623.62	−0.220052	−0.110026	+	0.993929i	$0.535093\pi$
$380$	0	0
$381$	283.295	0.0380935
$382$	− 4891.93i	− 0.655217i
$383$	5513.47i	0.735575i	0.929910	+	0.367787i	$0.119885\pi$
$383$	5513.47i	0.735575i	−0.929910	+	0.367787i	$0.880115\pi$
$384$	2117.44	0.281394
$385$	0	0
$386$	−19093.4	−2.51769
$387$	− 2370.34i	− 0.311346i
$388$	1607.82i	0.210373i
$389$	−1591.80	−0.207474	−0.103737	−	0.994605i	$-0.533080\pi$
$389$	−1591.80	−0.207474	−0.103737	+	0.994605i	$0.533080\pi$
$390$	0	0
$391$	−6514.57	−0.842598
$392$	12110.5i	1.56039i
$393$	3954.37i	0.507561i
$394$	2127.80	0.272074
$395$	0	0
$396$	−1854.98	−0.235395
$397$	8032.19i	1.01543i	0.861526	+	0.507713i	$0.169509\pi$
$397$	8032.19i	1.01543i	−0.861526	+	0.507713i	$0.830491\pi$
$398$	7711.11i	0.971164i
$399$	823.256	0.103294
$400$	0	0
$401$	588.148	0.0732436	0.0366218	−	0.999329i	$-0.488340\pi$
$401$	588.148	0.0732436	0.0366218	+	0.999329i	$0.488340\pi$
$402$	4103.54i	0.509119i
$403$	− 10703.2i	− 1.32298i
$404$	−2581.26	−0.317878
$405$	0	0
$406$	−6353.27	−0.776620
$407$	− 3921.98i	− 0.477654i
$408$	9714.46i	1.17877i
$409$	−6945.63	−0.839705	−0.419853	−	0.907592i	$-0.637918\pi$
$409$	−6945.63	−0.839705	−0.419853	+	0.907592i	$0.637918\pi$
$410$	0	0
$411$	6025.29	0.723128
$412$	− 7858.33i	− 0.939689i
$413$	− 5307.90i	− 0.632409i
$414$	5198.01	0.617073
$415$	0	0
$416$	−23743.3	−2.79834
$417$	− 8870.28i	− 1.04168i
$418$	− 1396.80i	− 0.163445i
$419$	3310.93	0.386037	0.193018	−	0.981195i	$-0.438172\pi$
$419$	3310.93	0.386037	0.193018	+	0.981195i	$0.438172\pi$
$420$	0	0
$421$	−13906.6	−1.60989	−0.804946	−	0.593348i	$-0.797806\pi$
$421$	−13906.6	−1.60989	−0.804946	+	0.593348i	$0.797806\pi$
$422$	4653.45i	0.536792i
$423$	− 1860.59i	− 0.213865i
$424$	−12422.5	−1.42285
$425$	0	0
$426$	−17223.9	−1.95892
$427$	− 5734.81i	− 0.649946i
$428$	− 22305.8i	− 2.51914i
$429$	−2954.52	−0.332508
$430$	0	0
$431$	2713.07	0.303211	0.151606	−	0.988441i	$-0.451556\pi$
$431$	2713.07	0.303211	0.151606	+	0.988441i	$0.451556\pi$
$432$	− 3703.99i	− 0.412519i
$433$	668.058i	0.0741451i	0.999313	+	0.0370725i	$0.0118033\pi$
$433$	668.058i	0.0741451i	−0.999313	+	0.0370725i	$0.988197\pi$
$434$	6907.57	0.763995
$435$	0	0
$436$	19362.5	2.12683
$437$	2742.97i	0.300261i
$438$	13862.0i	1.51222i
$439$	−16512.6	−1.79522	−0.897611	−	0.440788i	$-0.854699\pi$
$439$	−16512.6	−1.79522	−0.897611	+	0.440788i	$0.854699\pi$
$440$	0	0
$441$	−1963.17	−0.211982
$442$	27001.0i	2.90567i
$443$	− 11305.6i	− 1.21252i	−0.795268	−	0.606258i	$-0.792670\pi$
$443$	− 11305.6i	− 1.21252i	0.795268	−	0.606258i	$-0.207330\pi$
$444$	20041.9	2.14222
$445$	0	0
$446$	10007.0	1.06244
$447$	− 2636.31i	− 0.278955i
$448$	− 3059.56i	− 0.322657i
$449$	−2103.65	−0.221108	−0.110554	−	0.993870i	$-0.535262\pi$
$449$	−2103.65	−0.221108	−0.110554	+	0.993870i	$0.535262\pi$
$450$	0	0
$451$	−2956.77	−0.308712
$452$	17439.8i	1.81482i
$453$	− 5038.06i	− 0.522536i
$454$	15027.7	1.55349
$455$	0	0
$456$	4090.29	0.420056
$457$	16013.6i	1.63914i	0.572979	+	0.819570i	$0.305788\pi$
$457$	16013.6i	1.63914i	−0.572979	+	0.819570i	$0.694212\pi$
$458$	− 27983.8i	− 2.85501i
$459$	−1574.75	−0.160138
$460$	0	0
$461$	13332.9	1.34702	0.673509	−	0.739179i	$-0.264786\pi$
$461$	13332.9	1.34702	0.673509	+	0.739179i	$0.264786\pi$
$462$	− 1906.78i	− 0.192016i
$463$	2453.48i	0.246270i	0.992390	+	0.123135i	$0.0392948\pi$
$463$	2453.48i	0.246270i	−0.992390	+	0.123135i	$0.960705\pi$
$464$	−15084.0	−1.50917
$465$	0	0
$466$	−24710.8	−2.45645
$467$	771.767i	0.0764735i	0.999269	+	0.0382367i	$0.0121741\pi$
$467$	771.767i	0.0764735i	−0.999269	+	0.0382367i	$0.987826\pi$
$468$	− 15098.0i	− 1.49125i
$469$	−2956.03	−0.291038
$470$	0	0
$471$	2109.15	0.206337
$472$	− 26371.9i	− 2.57175i
$473$	− 2897.08i	− 0.281623i
$474$	−20223.0	−1.95964
$475$	0	0
$476$	−12211.9	−1.17590
$477$	− 2013.74i	− 0.193297i
$478$	30424.4i	2.91125i
$479$	−2782.55	−0.265423	−0.132712	−	0.991155i	$-0.542368\pi$
$479$	−2782.55	−0.265423	−0.132712	+	0.991155i	$0.542368\pi$
$480$	0	0
$481$	31921.7	3.02600
$482$	− 9343.44i	− 0.882950i
$483$	3744.44i	0.352750i
$484$	−2267.20	−0.212923
$485$	0	0
$486$	1256.50	0.117276
$487$	9716.69i	0.904118i	0.891988	+	0.452059i	$0.149310\pi$
$487$	9716.69i	0.904118i	−0.891988	+	0.452059i	$0.850690\pi$
$488$	− 28493.0i	− 2.64307i
$489$	−8803.99	−0.814172
$490$	0	0
$491$	13582.7	1.24843	0.624213	−	0.781254i	$-0.285420\pi$
$491$	13582.7	1.24843	0.624213	+	0.781254i	$0.285420\pi$
$492$	− 15109.5i	− 1.38453i
$493$	6412.97i	0.585853i
$494$	11368.8	1.03544
$495$	0	0
$496$	16400.0	1.48464
$497$	− 12407.4i	− 1.11982i
$498$	16278.2i	1.46474i
$499$	−12177.8	−1.09249	−0.546244	−	0.837626i	$-0.683943\pi$
$499$	−12177.8	−1.09249	−0.546244	+	0.837626i	$0.683943\pi$
$500$	0	0
$501$	−6438.14	−0.574121
$502$	− 6541.59i	− 0.581604i
$503$	5799.88i	0.514123i	0.966395	+	0.257061i	$0.0827543\pi$
$503$	5799.88i	0.514123i	−0.966395	+	0.257061i	$0.917246\pi$
$504$	5583.67	0.493485
$505$	0	0
$506$	6353.12	0.558164
$507$	− 17456.4i	− 1.52913i
$508$	1769.38i	0.154535i
$509$	−19516.8	−1.69954	−0.849772	−	0.527151i	$-0.823260\pi$
$509$	−19516.8	−1.69954	−0.849772	+	0.527151i	$0.823260\pi$
$510$	0	0
$511$	−9985.65	−0.864460
$512$	24551.0i	2.11916i
$513$	663.053i	0.0570653i
$514$	22578.5	1.93754
$515$	0	0
$516$	14804.5	1.26304
$517$	− 2274.05i	− 0.193448i
$518$	20601.5i	1.74745i
$519$	−964.068	−0.0815374
$520$	0	0
$521$	9489.76	0.797993	0.398996	−	0.916953i	$-0.369359\pi$
$521$	9489.76	0.797993	0.398996	+	0.916953i	$0.369359\pi$
$522$	− 5116.95i	− 0.429047i
$523$	5714.17i	0.477750i	0.971050	+	0.238875i	$0.0767786\pi$
$523$	5714.17i	0.477750i	−0.971050	+	0.238875i	$0.923221\pi$
$524$	−24697.9	−2.05903
$525$	0	0
$526$	−15258.8	−1.26486
$527$	− 6972.47i	− 0.576330i
$528$	− 4527.09i	− 0.373137i
$529$	−308.942	−0.0253918
$530$	0	0
$531$	4275.00	0.349377
$532$	5141.84i	0.419036i
$533$	− 24065.7i	− 1.95573i
$534$	21995.3	1.78245
$535$	0	0
$536$	−14686.8	−1.18353
$537$	7986.24i	0.641772i
$538$	− 31276.4i	− 2.50636i
$539$	−2399.43	−0.191745
$540$	0	0
$541$	−2530.63	−0.201110	−0.100555	−	0.994932i	$-0.532062\pi$
$541$	−2530.63	−0.201110	−0.100555	+	0.994932i	$0.532062\pi$
$542$	15113.8i	1.19777i
$543$	9918.06i	0.783839i
$544$	−15467.3	−1.21904
$545$	0	0
$546$	15519.7	1.21645
$547$	− 18910.4i	− 1.47816i	−0.673619	−	0.739079i	$-0.735261\pi$
$547$	− 18910.4i	− 1.47816i	0.673619	−	0.739079i	$-0.264739\pi$
$548$	37632.3i	2.93353i
$549$	4618.83	0.359066
$550$	0	0
$551$	2700.19	0.208770
$552$	18604.0i	1.43449i
$553$	− 14567.8i	− 1.12023i
$554$	28095.4	2.15462
$555$	0	0
$556$	55401.4	4.22580
$557$	− 4480.34i	− 0.340823i	−0.985373	−	0.170411i	$-0.945490\pi$
$557$	− 4480.34i	− 0.340823i	0.985373	−	0.170411i	$-0.0545096\pi$
$558$	5563.38i	0.422073i
$559$	23579.8	1.78412
$560$	0	0
$561$	−1924.70	−0.144850
$562$	41268.3i	3.09750i
$563$	1726.52i	0.129244i	0.997910	+	0.0646218i	$0.0205841\pi$
$563$	1726.52i	0.129244i	−0.997910	+	0.0646218i	$0.979416\pi$
$564$	11620.7	0.867590
$565$	0	0
$566$	−13990.7	−1.03900
$567$	905.137i	0.0670409i
$568$	− 61645.5i	− 4.55385i
$569$	10862.7	0.800327	0.400164	−	0.916444i	$-0.368953\pi$
$569$	10862.7	0.800327	0.400164	+	0.916444i	$0.368953\pi$
$570$	0	0
$571$	14448.8	1.05895	0.529477	−	0.848324i	$-0.322388\pi$
$571$	14448.8	1.05895	0.529477	+	0.848324i	$0.322388\pi$
$572$	− 18453.2i	− 1.34889i
$573$	2838.20i	0.206924i
$574$	15531.5	1.12939
$575$	0	0
$576$	2464.18	0.178254
$577$	5335.95i	0.384988i	0.981298	+	0.192494i	$0.0616577\pi$
$577$	5335.95i	0.384988i	−0.981298	+	0.192494i	$0.938342\pi$
$578$	− 7814.56i	− 0.562358i
$579$	11077.6	0.795112
$580$	0	0
$581$	−11726.2	−0.837321
$582$	− 1331.11i	− 0.0948043i
$583$	− 2461.23i	− 0.174844i
$584$	−49613.0	−3.51541
$585$	0	0
$586$	11415.6	0.804735
$587$	− 25633.8i	− 1.80242i	−0.433386	−	0.901208i	$-0.642681\pi$
$587$	− 25633.8i	− 1.80242i	0.433386	−	0.901208i	$-0.357319\pi$
$588$	− 12261.4i	− 0.859953i
$589$	−2935.77	−0.205376
$590$	0	0
$591$	−1234.51	−0.0859238
$592$	48912.3i	3.39575i
$593$	− 16094.8i	− 1.11456i	−0.830324	−	0.557282i	$-0.811844\pi$
$593$	− 16094.8i	− 1.11456i	0.830324	−	0.557282i	$-0.188156\pi$
$594$	1535.73	0.106080
$595$	0	0
$596$	16465.6	1.13164
$597$	− 4473.84i	− 0.306704i
$598$	51709.2i	3.53603i
$599$	17160.5	1.17055	0.585275	−	0.810835i	$-0.300986\pi$
$599$	17160.5	1.17055	0.585275	+	0.810835i	$0.300986\pi$
$600$	0	0
$601$	−14563.2	−0.988426	−0.494213	−	0.869341i	$-0.664544\pi$
$601$	−14563.2	−0.988426	−0.494213	+	0.869341i	$0.664544\pi$
$602$	15217.9i	1.03029i
$603$	− 2380.79i	− 0.160785i
$604$	31466.3	2.11978
$605$	0	0
$606$	2137.01	0.143251
$607$	12834.7i	0.858230i	0.903250	+	0.429115i	$0.141175\pi$
$607$	12834.7i	0.858230i	−0.903250	+	0.429115i	$0.858825\pi$
$608$	6512.55i	0.434406i
$609$	3686.05	0.245265
$610$	0	0
$611$	18508.9	1.22552
$612$	− 9835.48i	− 0.649634i
$613$	− 10814.5i	− 0.712548i	−0.934381	−	0.356274i	$-0.884047\pi$
$613$	− 10814.5i	− 0.712548i	0.934381	−	0.356274i	$-0.115953\pi$
$614$	20261.5	1.33174
$615$	0	0
$616$	6824.49	0.446374
$617$	− 5118.52i	− 0.333977i	−0.985959	−	0.166988i	$-0.946596\pi$
$617$	− 5118.52i	− 0.333977i	0.985959	−	0.166988i	$-0.0534042\pi$
$618$	6505.86i	0.423469i
$619$	−26144.1	−1.69761	−0.848804	−	0.528708i	$-0.822677\pi$
$619$	−26144.1	−1.69761	−0.848804	+	0.528708i	$0.822677\pi$
$620$	0	0
$621$	−3015.79	−0.194878
$622$	− 45342.9i	− 2.92297i
$623$	15844.5i	1.01894i
$624$	36846.9	2.36387
$625$	0	0
$626$	−26158.7	−1.67015
$627$	810.398i	0.0516175i
$628$	13173.2i	0.837051i
$629$	20795.1	1.31821
$630$	0	0
$631$	−15147.2	−0.955626	−0.477813	−	0.878462i	$-0.658570\pi$
$631$	−15147.2	−0.955626	−0.477813	+	0.878462i	$0.658570\pi$
$632$	− 72379.2i	− 4.55552i
$633$	− 2699.84i	− 0.169525i
$634$	43070.3	2.69801
$635$	0	0
$636$	12577.3	0.784152
$637$	− 19529.4i	− 1.21473i
$638$	− 6254.04i	− 0.388088i
$639$	9992.98	0.618648
$640$	0	0
$641$	6959.04	0.428807	0.214404	−	0.976745i	$-0.431219\pi$
$641$	6959.04	0.428807	0.214404	+	0.976745i	$0.431219\pi$
$642$	18466.8i	1.13524i
$643$	50.7662i	0.00311357i	0.999999	+	0.00155678i	$0.000495540\pi$
$643$	50.7662i	0.00311357i	−0.999999	+	0.00155678i	$0.999504\pi$
$644$	−23386.8	−1.43101
$645$	0	0
$646$	7406.13	0.451069
$647$	14853.2i	0.902537i	0.892388	+	0.451268i	$0.149028\pi$
$647$	14853.2i	0.902537i	−0.892388	+	0.451268i	$0.850972\pi$
$648$	4497.11i	0.272628i
$649$	5225.00	0.316023
$650$	0	0
$651$	−4007.64	−0.241278
$652$	− 54987.3i	− 3.30287i
$653$	18366.0i	1.10064i	0.834953	+	0.550321i	$0.185495\pi$
$653$	18366.0i	1.10064i	−0.834953	+	0.550321i	$0.814505\pi$
$654$	−16030.1	−0.958451
$655$	0	0
$656$	36874.9	2.19470
$657$	− 8042.47i	− 0.477575i
$658$	11945.2i	0.707711i
$659$	8660.13	0.511913	0.255957	−	0.966688i	$-0.417610\pi$
$659$	8660.13	0.511913	0.255957	+	0.966688i	$0.417610\pi$
$660$	0	0
$661$	−11057.5	−0.650661	−0.325331	−	0.945600i	$-0.605476\pi$
$661$	−11057.5	−0.650661	−0.325331	+	0.945600i	$0.605476\pi$
$662$	− 15004.9i	− 0.880940i
$663$	− 15665.5i	− 0.917642i
$664$	−58260.6	−3.40505
$665$	0	0
$666$	−16592.5	−0.965387
$667$	12281.4i	0.712949i
$668$	− 40210.9i	− 2.32905i
$669$	−5805.88	−0.335528
$670$	0	0
$671$	5645.24	0.324787
$672$	8890.32i	0.510344i
$673$	1921.35i	0.110048i	0.998485	+	0.0550241i	$0.0175236\pi$
$673$	1921.35i	0.110048i	−0.998485	+	0.0550241i	$0.982476\pi$
$674$	−31028.7	−1.77327
$675$	0	0
$676$	109028.	6.20324
$677$	− 25838.8i	− 1.46686i	−0.679764	−	0.733431i	$-0.737918\pi$
$677$	− 25838.8i	− 1.46686i	0.679764	−	0.733431i	$-0.262082\pi$
$678$	− 14438.3i	− 0.817847i
$679$	958.877	0.0541948
$680$	0	0
$681$	−8718.78	−0.490608
$682$	6799.68i	0.381779i
$683$	− 33038.7i	− 1.85094i	−0.378823	−	0.925469i	$-0.623671\pi$
$683$	− 33038.7i	− 1.85094i	0.378823	−	0.925469i	$-0.376329\pi$
$684$	−4141.25	−0.231498
$685$	0	0
$686$	32422.8	1.80453
$687$	16235.7i	0.901643i
$688$	36130.4i	2.00212i
$689$	20032.4	1.10766
$690$	0	0
$691$	−2065.11	−0.113691	−0.0568454	−	0.998383i	$-0.518104\pi$
$691$	−2065.11	−0.113691	−0.0568454	+	0.998383i	$0.518104\pi$
$692$	− 6021.31i	− 0.330774i
$693$	1106.28i	0.0606408i
$694$	46842.5	2.56213
$695$	0	0
$696$	18313.9	0.997393
$697$	− 15677.4i	− 0.851972i
$698$	− 48410.8i	− 2.62518i
$699$	14336.7	0.775771
$700$	0	0
$701$	−23504.1	−1.26639	−0.633194	−	0.773993i	$-0.718257\pi$
$701$	−23504.1	−1.26639	−0.633194	+	0.773993i	$0.718257\pi$
$702$	12499.6i	0.672031i
$703$	− 8755.83i	− 0.469747i
$704$	3011.77	0.161236
$705$	0	0
$706$	−1418.14	−0.0755985
$707$	1539.42i	0.0818894i
$708$	26700.5i	1.41732i
$709$	135.537	0.00717943	0.00358971	−	0.999994i	$-0.498857\pi$
$709$	135.537	0.00717943	0.00358971	+	0.999994i	$0.498857\pi$
$710$	0	0
$711$	11733.0	0.618876
$712$	78722.4i	4.14361i
$713$	− 13352.9i	− 0.701359i
$714$	10110.1	0.529920
$715$	0	0
$716$	−49879.9	−2.60349
$717$	− 17651.6i	− 0.919404i
$718$	− 7210.75i	− 0.374795i
$719$	−10752.3	−0.557711	−0.278856	−	0.960333i	$-0.589955\pi$
$719$	−10752.3	−0.557711	−0.278856	+	0.960333i	$0.589955\pi$
$720$	0	0
$721$	−4686.57	−0.242076
$722$	32348.2i	1.66742i
$723$	5420.88i	0.278845i
$724$	−61945.5	−3.17982
$725$	0	0
$726$	1877.00	0.0959532
$727$	7521.06i	0.383687i	0.981425	+	0.191844i	$0.0614467\pi$
$727$	7521.06i	0.383687i	−0.981425	+	0.191844i	$0.938553\pi$
$728$	55545.8i	2.82784i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	15360.9	0.777213
$732$	28848.0i	1.45663i
$733$	− 5330.33i	− 0.268595i	−0.990941	−	0.134298i	$-0.957122\pi$
$733$	− 5330.33i	− 0.268595i	0.990941	−	0.134298i	$-0.0428778\pi$
$734$	−60033.4	−3.01890
$735$	0	0
$736$	−29621.2	−1.48350
$737$	− 2909.86i	− 0.145436i
$738$	12509.1i	0.623938i
$739$	−29328.0	−1.45988	−0.729938	−	0.683513i	$-0.760451\pi$
$739$	−29328.0	−1.45988	−0.729938	+	0.683513i	$0.760451\pi$
$740$	0	0
$741$	−6595.98	−0.327003
$742$	12928.5i	0.639649i
$743$	− 1378.56i	− 0.0680679i	−0.999421	−	0.0340340i	$-0.989165\pi$
$743$	− 1378.56i	− 0.0680679i	0.999421	−	0.0340340i	$-0.0108354\pi$
$744$	−19911.7	−0.981179
$745$	0	0
$746$	26210.2	1.28636
$747$	− 9444.29i	− 0.462582i
$748$	− 12021.1i	− 0.587616i
$749$	−13302.8	−0.648962
$750$	0	0
$751$	−31066.4	−1.50950	−0.754748	−	0.656015i	$-0.772241\pi$
$751$	−31066.4	−1.50950	−0.754748	+	0.656015i	$0.772241\pi$
$752$	28360.4i	1.37526i
$753$	3795.30i	0.183677i
$754$	50902.8	2.45858
$755$	0	0
$756$	−5653.24	−0.271966
$757$	− 21971.1i	− 1.05489i	−0.849589	−	0.527445i	$-0.823150\pi$
$757$	− 21971.1i	− 1.05489i	0.849589	−	0.527445i	$-0.176850\pi$
$758$	8395.42i	0.402290i
$759$	−3685.96	−0.176274
$760$	0	0
$761$	−35175.8	−1.67559	−0.837794	−	0.545987i	$-0.816155\pi$
$761$	−35175.8	−1.67559	−0.837794	+	0.545987i	$0.816155\pi$
$762$	− 1464.86i	− 0.0696408i
$763$	− 11547.5i	− 0.547898i
$764$	−17726.7	−0.839435
$765$	0	0
$766$	28509.1	1.34474
$767$	42527.3i	2.00205i
$768$	− 17520.0i	− 0.823176i
$769$	−32952.5	−1.54525	−0.772626	−	0.634862i	$-0.781057\pi$
$769$	−32952.5	−1.54525	−0.772626	+	0.634862i	$0.781057\pi$
$770$	0	0
$771$	−13099.6	−0.611894
$772$	69187.7i	3.22554i
$773$	− 11158.7i	− 0.519213i	−0.965714	−	0.259607i	$-0.916407\pi$
$773$	− 11158.7i	− 0.519213i	0.965714	−	0.259607i	$-0.0835929\pi$
$774$	−12256.5	−0.569189
$775$	0	0
$776$	4764.11	0.220389
$777$	− 11952.6i	− 0.551863i
$778$	8230.86i	0.379294i
$779$	−6601.00	−0.303601
$780$	0	0
$781$	12213.6	0.559589
$782$	33685.5i	1.54040i
$783$	2968.75i	0.135498i
$784$	29924.1	1.36316
$785$	0	0
$786$	20447.3	0.927901
$787$	− 17308.9i	− 0.783985i	−0.919968	−	0.391993i	$-0.871786\pi$
$787$	− 17308.9i	− 0.783985i	0.919968	−	0.391993i	$-0.128214\pi$
$788$	− 7710.41i	− 0.348569i
$789$	8852.87	0.399456
$790$	0	0
$791$	10400.8	0.467522
$792$	5496.47i	0.246602i
$793$	45947.7i	2.05757i
$794$	41532.9	1.85636
$795$	0	0
$796$	27942.4	1.24421
$797$	14802.4i	0.657876i	0.944351	+	0.328938i	$0.106691\pi$
$797$	14802.4i	0.657876i	−0.944351	+	0.328938i	$0.893309\pi$
$798$	− 4256.90i	− 0.188838i
$799$	12057.5	0.533871
$800$	0	0
$801$	−12761.2	−0.562916
$802$	− 3041.19i	− 0.133901i
$803$	− 9829.69i	− 0.431983i
$804$	14869.8	0.652260
$805$	0	0
$806$	−55343.9	−2.41862
$807$	18146.0i	0.791534i
$808$	7648.50i	0.333011i
$809$	8999.53	0.391108	0.195554	−	0.980693i	$-0.437349\pi$
$809$	8999.53	0.391108	0.195554	+	0.980693i	$0.437349\pi$
$810$	0	0
$811$	−41368.5	−1.79117	−0.895587	−	0.444886i	$-0.853244\pi$
$811$	−41368.5	−1.79117	−0.895587	+	0.444886i	$0.853244\pi$
$812$	23022.1i	0.994970i
$813$	− 8768.71i	− 0.378268i
$814$	−20279.8	−0.873226
$815$	0	0
$816$	24003.6	1.02977
$817$	− 6467.73i	− 0.276961i
$818$	35914.5i	1.53511i
$819$	−9004.21	−0.384167
$820$	0	0
$821$	27772.2	1.18058	0.590289	−	0.807192i	$-0.299014\pi$
$821$	27772.2	1.18058	0.590289	+	0.807192i	$0.299014\pi$
$822$	− 31155.6i	− 1.32199i
$823$	− 9315.89i	− 0.394571i	−0.980346	−	0.197285i	$-0.936787\pi$
$823$	− 9315.89i	− 0.394571i	0.980346	−	0.197285i	$-0.0632125\pi$
$824$	−23284.9	−0.984426
$825$	0	0
$826$	−27446.1	−1.15614
$827$	20344.6i	0.855443i	0.903911	+	0.427721i	$0.140684\pi$
$827$	20344.6i	0.855443i	−0.903911	+	0.427721i	$0.859316\pi$
$828$	− 18835.8i	− 0.790566i
$829$	−16916.7	−0.708737	−0.354368	−	0.935106i	$-0.615304\pi$
$829$	−16916.7	−0.708737	−0.354368	+	0.935106i	$0.615304\pi$
$830$	0	0
$831$	−16300.4	−0.680452
$832$	24513.4i	1.02145i
$833$	− 12722.3i	− 0.529172i
$834$	−45866.5	−1.90435
$835$	0	0
$836$	−5061.53	−0.209398
$837$	− 3227.76i	− 0.133295i
$838$	− 17120.2i	− 0.705735i
$839$	−23690.7	−0.974844	−0.487422	−	0.873167i	$-0.662063\pi$
$839$	−23690.7	−0.974844	−0.487422	+	0.873167i	$0.662063\pi$
$840$	0	0
$841$	−12299.2	−0.504291
$842$	71908.1i	2.94313i
$843$	− 23943.1i	− 0.978224i
$844$	16862.5	0.687714
$845$	0	0
$846$	−9620.72	−0.390978
$847$	1352.12i	0.0548516i
$848$	30694.9i	1.24300i
$849$	8117.14	0.328127
$850$	0	0
$851$	39824.4	1.60419
$852$	62413.5i	2.50968i
$853$	− 3804.67i	− 0.152719i	−0.997080	−	0.0763596i	$-0.975670\pi$
$853$	− 3804.67i	− 0.152719i	0.997080	−	0.0763596i	$-0.0243297\pi$
$854$	−29653.6	−1.18820
$855$	0	0
$856$	−66093.9	−2.63907
$857$	3125.89i	0.124596i	0.998058	+	0.0622978i	$0.0198429\pi$
$857$	3125.89i	0.124596i	−0.998058	+	0.0622978i	$0.980157\pi$
$858$	15277.3i	0.607875i
$859$	38044.2	1.51112	0.755559	−	0.655081i	$-0.227365\pi$
$859$	38044.2	1.51112	0.755559	+	0.655081i	$0.227365\pi$
$860$	0	0
$861$	−9011.06	−0.356674
$862$	− 14028.8i	− 0.554317i
$863$	728.739i	0.0287446i	0.999897	+	0.0143723i	$0.00457500\pi$
$863$	728.739i	0.0287446i	−0.999897	+	0.0143723i	$0.995425\pi$
$864$	−7160.29	−0.281942
$865$	0	0
$866$	3454.39	0.135549
$867$	4533.86i	0.177599i
$868$	− 25030.6i	− 0.978796i
$869$	14340.3	0.559795
$870$	0	0
$871$	23683.9	0.921352
$872$	− 57372.7i	− 2.22808i
$873$	772.282i	0.0299402i
$874$	14183.4	0.548924
$875$	0	0
$876$	50231.1	1.93739
$877$	− 18861.7i	− 0.726241i	−0.931742	−	0.363120i	$-0.881711\pi$
$877$	− 18861.7i	− 0.726241i	0.931742	−	0.363120i	$-0.118289\pi$
$878$	85383.3i	3.28194i
$879$	−6623.12	−0.254144
$880$	0	0
$881$	24435.2	0.934442	0.467221	−	0.884141i	$-0.345255\pi$
$881$	24435.2	0.934442	0.467221	+	0.884141i	$0.345255\pi$
$882$	10151.2i	0.387537i
$883$	3101.93i	0.118220i	0.998251	+	0.0591101i	$0.0188263\pi$
$883$	3101.93i	0.118220i	−0.998251	+	0.0591101i	$0.981174\pi$
$884$	97842.4	3.72262
$885$	0	0
$886$	−58458.9	−2.21667
$887$	− 2129.33i	− 0.0806043i	−0.999188	−	0.0403021i	$-0.987168\pi$
$887$	− 2129.33i	− 0.0806043i	0.999188	−	0.0403021i	$-0.0128320\pi$
$888$	− 59385.7i	− 2.24421i
$889$	1055.23	0.0398101
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 36262.0i	− 1.36114i
$893$	− 5076.82i	− 0.190246i
$894$	−13631.8	−0.509973
$895$	0	0
$896$	7887.14	0.294075
$897$	− 30000.7i	− 1.11672i
$898$	10877.5i	0.404219i
$899$	−13144.6	−0.487651
$900$	0	0
$901$	13050.0	0.482527
$902$	15288.9i	0.564373i
$903$	− 8829.13i	− 0.325376i
$904$	51675.6	1.90122
$905$	0	0
$906$	−26050.8	−0.955276
$907$	− 33678.6i	− 1.23294i	−0.787378	−	0.616471i	$-0.788562\pi$
$907$	− 33678.6i	− 1.23294i	0.787378	−	0.616471i	$-0.211438\pi$
$908$	− 54455.1i	− 1.99026i
$909$	−1239.85	−0.0452402
$910$	0	0
$911$	−28917.6	−1.05168	−0.525841	−	0.850583i	$-0.676249\pi$
$911$	−28917.6	−1.05168	−0.525841	+	0.850583i	$0.676249\pi$
$912$	− 10106.7i	− 0.366960i
$913$	− 11543.0i	− 0.418421i
$914$	82803.4	2.99660
$915$	0	0
$916$	−101404.	−3.65771
$917$	14729.4i	0.530434i
$918$	8142.74i	0.292756i
$919$	8611.83	0.309117	0.154558	−	0.987984i	$-0.450605\pi$
$919$	8611.83	0.309117	0.154558	+	0.987984i	$0.450605\pi$
$920$	0	0
$921$	−11755.4	−0.420578
$922$	− 68941.8i	− 2.46256i
$923$	99409.2i	3.54506i
$924$	−6909.52	−0.246003
$925$	0	0
$926$	12686.5	0.450219
$927$	− 3774.58i	− 0.133736i
$928$	29159.3i	1.03147i
$929$	31195.3	1.10171	0.550853	−	0.834602i	$-0.314302\pi$
$929$	31195.3	1.10171	0.550853	+	0.834602i	$0.314302\pi$
$930$	0	0
$931$	−5356.73	−0.188571
$932$	89543.2i	3.14709i
$933$	26307.1i	0.923103i
$934$	3990.65	0.139805
$935$	0	0
$936$	−44736.8	−1.56225
$937$	− 24625.3i	− 0.858561i	−0.903171	−	0.429281i	$-0.858767\pi$
$937$	− 24625.3i	− 0.858561i	0.903171	−	0.429281i	$-0.141233\pi$
$938$	15285.0i	0.532062i
$939$	15176.8	0.527449
$940$	0	0
$941$	3605.28	0.124898	0.0624488	−	0.998048i	$-0.480109\pi$
$941$	3605.28	0.124898	0.0624488	+	0.998048i	$0.480109\pi$
$942$	− 10906.0i	− 0.377216i
$943$	− 30023.6i	− 1.03680i
$944$	−65162.7	−2.24668
$945$	0	0
$946$	−14980.2	−0.514850
$947$	− 11634.6i	− 0.399231i	−0.979874	−	0.199616i	$-0.936031\pi$
$947$	− 11634.6i	− 0.399231i	0.979874	−	0.199616i	$-0.0639694\pi$
$948$	73281.0i	2.51061i
$949$	80005.7	2.73666
$950$	0	0
$951$	−24988.6	−0.852060
$952$	36184.8i	1.23189i
$953$	27302.2i	0.928021i	0.885830	+	0.464010i	$0.153590\pi$
$953$	27302.2i	0.928021i	−0.885830	+	0.464010i	$0.846410\pi$
$954$	−10412.6	−0.353377
$955$	0	0
$956$	110247.	3.72976
$957$	3628.48i	0.122562i
$958$	14388.0i	0.485235i
$959$	22443.3	0.755715
$960$	0	0
$961$	−15499.6	−0.520276
$962$	− 165061.i	− 5.53199i
$963$	− 10714.1i	− 0.358522i
$964$	−33857.4	−1.13120
$965$	0	0
$966$	19361.8	0.644881
$967$	19429.3i	0.646125i	0.946378	+	0.323063i	$0.104712\pi$
$967$	19429.3i	0.646125i	−0.946378	+	0.323063i	$0.895288\pi$
$968$	6717.90i	0.223059i
$969$	−4296.90	−0.142452
$970$	0	0
$971$	42852.0	1.41626	0.708129	−	0.706083i	$-0.249539\pi$
$971$	42852.0	1.41626	0.708129	+	0.706083i	$0.249539\pi$
$972$	− 4553.14i	− 0.150249i
$973$	− 33040.4i	− 1.08862i
$974$	50243.1	1.65287
$975$	0	0
$976$	−70403.7	−2.30898
$977$	− 6559.02i	− 0.214782i	−0.994217	−	0.107391i	$-0.965750\pi$
$977$	− 6559.02i	− 0.214782i	0.994217	−	0.107391i	$-0.0342496\pi$
$978$	45523.7i	1.48843i
$979$	−15597.1	−0.509177
$980$	0	0
$981$	9300.36	0.302689
$982$	− 70233.3i	− 2.28232i
$983$	− 15077.3i	− 0.489208i	−0.969623	−	0.244604i	$-0.921342\pi$
$983$	− 15077.3i	− 0.489208i	0.969623	−	0.244604i	$-0.0786579\pi$
$984$	−44770.8	−1.45045
$985$	0	0
$986$	33160.2	1.07103
$987$	− 6930.39i	− 0.223502i
$988$	− 41196.7i	− 1.32656i
$989$	29417.4	0.945822
$990$	0	0
$991$	45239.3	1.45013	0.725063	−	0.688683i	$-0.241811\pi$
$991$	45239.3	1.45013	0.725063	+	0.688683i	$0.241811\pi$
$992$	− 31703.3i	− 1.01470i
$993$	8705.56i	0.278210i
$994$	−64156.4	−2.04720
$995$	0	0
$996$	58986.5	1.87656
$997$	− 30975.1i	− 0.983942i	−0.870612	−	0.491971i	$-0.836277\pi$
$997$	− 30975.1i	− 0.983942i	0.870612	−	0.491971i	$-0.163723\pi$
$998$	62968.8i	1.99724i
$999$	9626.68	0.304879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.p.199.1		8
5.2	odd	4		165.4.a.h.1.4	✓	4
5.3	odd	4		825.4.a.t.1.1		4
5.4	even	2	inner	825.4.c.p.199.8		8
15.2	even	4		495.4.a.m.1.1		4
15.8	even	4		2475.4.a.be.1.4		4
55.32	even	4		1815.4.a.t.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.h.1.4	✓	4	5.2	odd	4
495.4.a.m.1.1		4	15.2	even	4
825.4.a.t.1.1		4	5.3	odd	4
825.4.c.p.199.1		8	1.1	even	1	trivial
825.4.c.p.199.8		8	5.4	even	2	inner
1815.4.a.t.1.1		4	55.32	even	4
2475.4.a.be.1.4		4	15.8	even	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-5.17080i q^{2} +3.00000i q^{3} -18.7372 q^{4} +15.5124 q^{6} +11.1745i q^{7} +55.5199i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-5.17080i q^{2} +3.00000i q^{3} -18.7372 q^{4} +15.5124 q^{6} +11.1745i q^{7} +55.5199i q^{8} -9.00000 q^{9} -11.0000 q^{11} -56.2116i q^{12} -89.5310i q^{13} +57.7813 q^{14} +137.185 q^{16} -58.3242i q^{17} +46.5372i q^{18} -24.5575 q^{19} -33.5236 q^{21} +56.8788i q^{22} -111.696i q^{23} -166.560 q^{24} -462.947 q^{26} -27.0000i q^{27} -209.379i q^{28} -109.954 q^{29} +119.547 q^{31} -265.196i q^{32} -33.0000i q^{33} -301.583 q^{34} +168.635 q^{36} +356.544i q^{37} +126.982i q^{38} +268.593 q^{39} +268.798 q^{41} +173.344i q^{42} +263.371i q^{43} +206.109 q^{44} -577.557 q^{46} +206.732i q^{47} +411.554i q^{48} +218.130 q^{49} +174.973 q^{51} +1677.56i q^{52} +223.749i q^{53} -139.612 q^{54} -620.408 q^{56} -73.6726i q^{57} +568.549i q^{58} -475.000 q^{59} -513.204 q^{61} -618.153i q^{62} -100.571i q^{63} -273.798 q^{64} -170.636 q^{66} +264.533i q^{67} +1092.83i q^{68} +335.087 q^{69} -1110.33 q^{71} -499.679i q^{72} +893.608i q^{73} +1843.62 q^{74} +460.139 q^{76} -122.920i q^{77} -1388.84i q^{78} -1303.66 q^{79} +81.0000 q^{81} -1389.90i q^{82} +1049.37i q^{83} +628.138 q^{84} +1361.84 q^{86} -329.862i q^{87} -610.718i q^{88} +1417.91 q^{89} +1000.47 q^{91} +2092.86i q^{92} +358.640i q^{93} +1068.97 q^{94} +795.587 q^{96} -85.8091i q^{97} -1127.91i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9	\( 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9} - 88 q^{11} + 104 q^{14} + 132 q^{16} - 272 q^{19} + 204 q^{21} - 288 q^{24} - 640 q^{26} - 104 q^{29} + 984 q^{31} - 488 q^{34} + 468 q^{36} - 12 q^{39} + 536 q^{41} + 572 q^{44} + 736 q^{46} + 992 q^{49} + 444 q^{51} - 216 q^{54} - 1704 q^{56} + 2064 q^{59} + 232 q^{61} + 1836 q^{64} - 264 q^{66} + 384 q^{69} - 1840 q^{71} + 5712 q^{74} + 3144 q^{76} - 2304 q^{79} + 648 q^{81} + 120 q^{84} + 472 q^{86} + 2128 q^{89} + 5560 q^{91} + 2864 q^{94} + 1248 q^{96} + 792 q^{99}+O(q^{100}) \) 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9 - 88 * q^11 + 104 * q^14 + 132 * q^16 - 272 * q^19 + 204 * q^21 - 288 * q^24 - 640 * q^26 - 104 * q^29 + 984 * q^31 - 488 * q^34 + 468 * q^36 - 12 * q^39 + 536 * q^41 + 572 * q^44 + 736 * q^46 + 992 * q^49 + 444 * q^51 - 216 * q^54 - 1704 * q^56 + 2064 * q^59 + 232 * q^61 + 1836 * q^64 - 264 * q^66 + 384 * q^69 - 1840 * q^71 + 5712 * q^74 + 3144 * q^76 - 2304 * q^79 + 648 * q^81 + 120 * q^84 + 472 * q^86 + 2128 * q^89 + 5560 * q^91 + 2864 * q^94 + 1248 * q^96 + 792 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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