LMFDB - Embedded newform 825.4.c.k.199.6

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:	$6$
Coefficient field:	6.0.36142572544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 53x^{4} + 632x^{2} + 484 $ x^6 + 53x^4 + 632x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$4.06484i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.k.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.06484i q^{2} +3.00000i q^{3} -17.6526 q^{4} -15.1945 q^{6} -27.4348i q^{7} -48.8887i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+5.06484i q^{2} +3.00000i q^{3} -17.6526 q^{4} -15.1945 q^{6} -27.4348i q^{7} -48.8887i q^{8} -9.00000 q^{9} +11.0000 q^{11} -52.9577i q^{12} +22.6949i q^{13} +138.953 q^{14} +106.392 q^{16} +41.1755i q^{17} -45.5835i q^{18} +142.128 q^{19} +82.3044 q^{21} +55.7132i q^{22} +176.166i q^{23} +146.666 q^{24} -114.946 q^{26} -27.0000i q^{27} +484.295i q^{28} -76.2044 q^{29} +197.373 q^{31} +147.751i q^{32} +33.0000i q^{33} -208.547 q^{34} +158.873 q^{36} -367.297i q^{37} +719.856i q^{38} -68.0846 q^{39} -238.279 q^{41} +416.858i q^{42} +30.2905i q^{43} -194.178 q^{44} -892.254 q^{46} -137.390i q^{47} +319.177i q^{48} -409.668 q^{49} -123.526 q^{51} -400.623i q^{52} +638.665i q^{53} +136.751 q^{54} -1341.25 q^{56} +426.385i q^{57} -385.963i q^{58} -103.146 q^{59} +605.596 q^{61} +999.662i q^{62} +246.913i q^{63} +102.804 q^{64} -167.140 q^{66} +704.925i q^{67} -726.852i q^{68} -528.499 q^{69} -782.162 q^{71} +439.998i q^{72} -243.132i q^{73} +1860.30 q^{74} -2508.93 q^{76} -301.783i q^{77} -344.837i q^{78} +532.874 q^{79} +81.0000 q^{81} -1206.84i q^{82} +1204.91i q^{83} -1452.88 q^{84} -153.416 q^{86} -228.613i q^{87} -537.775i q^{88} -1058.49 q^{89} +622.629 q^{91} -3109.79i q^{92} +592.119i q^{93} +695.857 q^{94} -443.254 q^{96} +85.1964i q^{97} -2074.90i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9	$ 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9} + 66 q^{11} + 136 q^{14} + 356 q^{16} + 116 q^{19} + 60 q^{21} - 108 q^{24} - 240 q^{26} + 440 q^{29} + 496 q^{31} + 160 q^{34} + 540 q^{36} - 684 q^{39} + 312 q^{41} - 660 q^{44} - 2512 q^{46} - 558 q^{49} - 624 q^{51} + 108 q^{54} - 3288 q^{56} - 1096 q^{59} + 828 q^{61} + 116 q^{64} - 132 q^{66} - 720 q^{69} - 1824 q^{71} + 3224 q^{74} - 5504 q^{76} + 1084 q^{79} + 486 q^{81} - 4056 q^{84} - 3096 q^{86} - 1580 q^{89} - 1544 q^{91} + 848 q^{94} - 1548 q^{96} - 594 q^{99}+O(q^{100}) $ 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9 + 66 * q^11 + 136 * q^14 + 356 * q^16 + 116 * q^19 + 60 * q^21 - 108 * q^24 - 240 * q^26 + 440 * q^29 + 496 * q^31 + 160 * q^34 + 540 * q^36 - 684 * q^39 + 312 * q^41 - 660 * q^44 - 2512 * q^46 - 558 * q^49 - 624 * q^51 + 108 * q^54 - 3288 * q^56 - 1096 * q^59 + 828 * q^61 + 116 * q^64 - 132 * q^66 - 720 * q^69 - 1824 * q^71 + 3224 * q^74 - 5504 * q^76 + 1084 * q^79 + 486 * q^81 - 4056 * q^84 - 3096 * q^86 - 1580 * q^89 - 1544 * q^91 + 848 * q^94 - 1548 * q^96 - 594 * 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 $

$2$	5.06484i	1.79069i	0.445373	+	0.895345i	$0.353071\pi$
$2$	5.06484i	1.79069i	−0.445373	+	0.895345i	$0.646929\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−17.6526	−2.20657
$5$	0	0
$5$	0	0
$6$	−15.1945	−1.03386
$7$	− 27.4348i	− 1.48134i	−0.671869	−	0.740670i	$-0.734508\pi$
$7$	− 27.4348i	− 1.48134i	0.671869	−	0.740670i	$-0.265492\pi$
$8$	− 48.8887i	− 2.16059i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	− 52.9577i	− 1.27396i
$13$	22.6949i	0.484187i	0.970253	+	0.242093i	$0.0778340\pi$
$13$	22.6949i	0.484187i	−0.970253	+	0.242093i	$0.922166\pi$
$14$	138.953	2.65262
$15$	0	0
$16$	106.392	1.66238
$17$	41.1755i	0.587442i	0.955891	+	0.293721i	$0.0948937\pi$
$17$	41.1755i	0.587442i	−0.955891	+	0.293721i	$0.905106\pi$
$18$	− 45.5835i	− 0.596897i
$19$	142.128	1.71613	0.858064	−	0.513542i	$-0.171667\pi$
$19$	142.128	1.71613	0.858064	+	0.513542i	$0.171667\pi$
$20$	0	0
$21$	82.3044	0.855252
$22$	55.7132i	0.539913i
$23$	176.166i	1.59710i	0.601931	+	0.798548i	$0.294398\pi$
$23$	176.166i	1.59710i	−0.601931	+	0.798548i	$0.705602\pi$
$24$	146.666	1.24742
$25$	0	0
$26$	−114.946	−0.867028
$27$	− 27.0000i	− 0.192450i
$28$	484.295i	3.26868i
$29$	−76.2044	−0.487959	−0.243979	−	0.969780i	$-0.578453\pi$
$29$	−76.2044	−0.487959	−0.243979	+	0.969780i	$0.578453\pi$
$30$	0	0
$31$	197.373	1.14352	0.571762	−	0.820420i	$-0.306260\pi$
$31$	197.373	1.14352	0.571762	+	0.820420i	$0.306260\pi$
$32$	147.751i	0.816218i
$33$	33.0000i	0.174078i
$34$	−208.547	−1.05193
$35$	0	0
$36$	158.873	0.735523
$37$	− 367.297i	− 1.63198i	−0.578067	−	0.815989i	$-0.696193\pi$
$37$	− 367.297i	− 1.63198i	0.578067	−	0.815989i	$-0.303807\pi$
$38$	719.856i	3.07305i
$39$	−68.0846	−0.279545
$40$	0	0
$41$	−238.279	−0.907633	−0.453817	−	0.891095i	$-0.649938\pi$
$41$	−238.279	−0.907633	−0.453817	+	0.891095i	$0.649938\pi$
$42$	416.858i	1.53149i
$43$	30.2905i	0.107425i	0.998556	+	0.0537123i	$0.0171054\pi$
$43$	30.2905i	0.107425i	−0.998556	+	0.0537123i	$0.982895\pi$
$44$	−194.178	−0.665306
$45$	0	0
$46$	−892.254	−2.85990
$47$	− 137.390i	− 0.426391i	−0.977010	−	0.213195i	$-0.931613\pi$
$47$	− 137.390i	− 0.426391i	0.977010	−	0.213195i	$-0.0683870\pi$
$48$	319.177i	0.959777i
$49$	−409.668	−1.19437
$50$	0	0
$51$	−123.526	−0.339160
$52$	− 400.623i	− 1.06839i
$53$	638.665i	1.65523i	0.561293	+	0.827617i	$0.310304\pi$
$53$	638.665i	1.65523i	−0.561293	+	0.827617i	$0.689696\pi$
$54$	136.751	0.344618
$55$	0	0
$56$	−1341.25	−3.20057
$57$	426.385i	0.990807i
$58$	− 385.963i	− 0.873783i
$59$	−103.146	−0.227601	−0.113800	−	0.993504i	$-0.536302\pi$
$59$	−103.146	−0.227601	−0.113800	+	0.993504i	$0.536302\pi$
$60$	0	0
$61$	605.596	1.27113	0.635563	−	0.772049i	$-0.280768\pi$
$61$	605.596	1.27113	0.635563	+	0.772049i	$0.280768\pi$
$62$	999.662i	2.04770i
$63$	246.913i	0.493780i
$64$	102.804	0.200789
$65$	0	0
$66$	−167.140	−0.311719
$67$	704.925i	1.28538i	0.766128	+	0.642688i	$0.222181\pi$
$67$	704.925i	1.28538i	−0.766128	+	0.642688i	$0.777819\pi$
$68$	− 726.852i	− 1.29623i
$69$	−528.499	−0.922084
$70$	0	0
$71$	−782.162	−1.30740	−0.653701	−	0.756753i	$-0.726785\pi$
$71$	−782.162	−1.30740	−0.653701	+	0.756753i	$0.726785\pi$
$72$	439.998i	0.720198i
$73$	− 243.132i	− 0.389814i	−0.980822	−	0.194907i	$-0.937560\pi$
$73$	− 243.132i	− 0.389814i	0.980822	−	0.194907i	$-0.0624404\pi$
$74$	1860.30	2.92237
$75$	0	0
$76$	−2508.93	−3.78676
$77$	− 301.783i	− 0.446641i
$78$	− 344.837i	− 0.500579i
$79$	532.874	0.758899	0.379449	−	0.925212i	$-0.376113\pi$
$79$	532.874	0.758899	0.379449	+	0.925212i	$0.376113\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 1206.84i	− 1.62529i
$83$	1204.91i	1.59344i	0.604345	+	0.796722i	$0.293435\pi$
$83$	1204.91i	1.59344i	−0.604345	+	0.796722i	$0.706565\pi$
$84$	−1452.88	−1.88717
$85$	0	0
$86$	−153.416	−0.192364
$87$	− 228.613i	− 0.281723i
$88$	− 537.775i	− 0.651443i
$89$	−1058.49	−1.26067	−0.630337	−	0.776322i	$-0.717083\pi$
$89$	−1058.49	−1.26067	−0.630337	+	0.776322i	$0.717083\pi$
$90$	0	0
$91$	622.629	0.717245
$92$	− 3109.79i	− 3.52411i
$93$	592.119i	0.660214i
$94$	695.857	0.763533
$95$	0	0
$96$	−443.254	−0.471244
$97$	85.1964i	0.0891792i	0.999005	+	0.0445896i	$0.0141980\pi$
$97$	85.1964i	0.0891792i	−0.999005	+	0.0445896i	$0.985802\pi$
$98$	− 2074.90i	− 2.13874i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−7.81823	−0.00770241	−0.00385120	−	0.999993i	$-0.501226\pi$
$101$	−7.81823	−0.00770241	−0.00385120	+	0.999993i	$0.501226\pi$
$102$	− 625.641i	− 0.607330i
$103$	12.4770i	0.0119359i	0.999982	+	0.00596794i	$0.00189967\pi$
$103$	12.4770i	0.0119359i	−0.999982	+	0.00596794i	$0.998100\pi$
$104$	1109.52	1.04613
$105$	0	0
$106$	−3234.73	−2.96401
$107$	1376.81i	1.24393i	0.783043	+	0.621967i	$0.213666\pi$
$107$	1376.81i	1.24393i	−0.783043	+	0.621967i	$0.786334\pi$
$108$	476.619i	0.424655i
$109$	−610.189	−0.536197	−0.268099	−	0.963391i	$-0.586395\pi$
$109$	−610.189	−0.536197	−0.268099	+	0.963391i	$0.586395\pi$
$110$	0	0
$111$	1101.89	0.942223
$112$	− 2918.86i	− 2.46255i
$113$	− 36.7727i	− 0.0306132i	−0.999883	−	0.0153066i	$-0.995128\pi$
$113$	− 36.7727i	− 0.0306132i	0.999883	−	0.0153066i	$-0.00487243\pi$
$114$	−2159.57	−1.77423
$115$	0	0
$116$	1345.20	1.07672
$117$	− 204.254i	− 0.161396i
$118$	− 522.416i	− 0.407562i
$119$	1129.64	0.870201
$120$	0	0
$121$	121.000	0.0909091
$122$	3067.25i	2.27619i
$123$	− 714.838i	− 0.524022i
$124$	−3484.14	−2.52326
$125$	0	0
$126$	−1250.57	−0.884207
$127$	54.5310i	0.0381011i	0.999819	+	0.0190506i	$0.00606435\pi$
$127$	54.5310i	0.0381011i	−0.999819	+	0.0190506i	$0.993936\pi$
$128$	1702.69i	1.17577i
$129$	−90.8715	−0.0620216
$130$	0	0
$131$	2377.83	1.58589	0.792947	−	0.609290i	$-0.208546\pi$
$131$	2377.83	1.58589	0.792947	+	0.609290i	$0.208546\pi$
$132$	− 582.535i	− 0.384115i
$133$	− 3899.26i	− 2.54217i
$134$	−3570.33	−2.30171
$135$	0	0
$136$	2013.01	1.26922
$137$	3078.41i	1.91976i	0.280417	+	0.959878i	$0.409527\pi$
$137$	3078.41i	1.91976i	−0.280417	+	0.959878i	$0.590473\pi$
$138$	− 2676.76i	− 1.65117i
$139$	1197.18	0.730530	0.365265	−	0.930904i	$-0.380978\pi$
$139$	1197.18	0.730530	0.365265	+	0.930904i	$0.380978\pi$
$140$	0	0
$141$	412.169	0.246177
$142$	− 3961.52i	− 2.34115i
$143$	249.644i	0.145988i
$144$	−957.532	−0.554128
$145$	0	0
$146$	1231.42	0.698035
$147$	− 1229.00i	− 0.689569i
$148$	6483.73i	3.60108i
$149$	749.456	0.412066	0.206033	−	0.978545i	$-0.433945\pi$
$149$	749.456	0.412066	0.206033	+	0.978545i	$0.433945\pi$
$150$	0	0
$151$	−2645.72	−1.42586	−0.712931	−	0.701234i	$-0.752633\pi$
$151$	−2645.72	−1.42586	−0.712931	+	0.701234i	$0.752633\pi$
$152$	− 6948.46i	− 3.70786i
$153$	− 370.579i	− 0.195814i
$154$	1528.48	0.799795
$155$	0	0
$156$	1201.87	0.616836
$157$	3475.74i	1.76684i	0.468578	+	0.883422i	$0.344767\pi$
$157$	3475.74i	1.76684i	−0.468578	+	0.883422i	$0.655233\pi$
$158$	2698.92i	1.35895i
$159$	−1916.00	−0.955650
$160$	0	0
$161$	4833.09	2.36584
$162$	410.252i	0.198966i
$163$	3518.89i	1.69092i	0.534035	+	0.845462i	$0.320675\pi$
$163$	3518.89i	1.69092i	−0.534035	+	0.845462i	$0.679325\pi$
$164$	4206.24	2.00276
$165$	0	0
$166$	−6102.67	−2.85337
$167$	− 250.304i	− 0.115983i	−0.998317	−	0.0579914i	$-0.981530\pi$
$167$	− 250.304i	− 0.115983i	0.998317	−	0.0579914i	$-0.0184696\pi$
$168$	− 4023.75i	− 1.84785i
$169$	1681.94	0.765563
$170$	0	0
$171$	−1279.15	−0.572043
$172$	− 534.705i	− 0.237040i
$173$	941.985i	0.413976i	0.978344	+	0.206988i	$0.0663660\pi$
$173$	941.985i	0.413976i	−0.978344	+	0.206988i	$0.933634\pi$
$174$	1157.89	0.504479
$175$	0	0
$176$	1170.32	0.501227
$177$	− 309.437i	− 0.131405i
$178$	− 5361.09i	− 2.25748i
$179$	−336.037	−0.140316	−0.0701582	−	0.997536i	$-0.522350\pi$
$179$	−336.037	−0.140316	−0.0701582	+	0.997536i	$0.522350\pi$
$180$	0	0
$181$	1107.45	0.454784	0.227392	−	0.973803i	$-0.426980\pi$
$181$	1107.45	0.454784	0.227392	+	0.973803i	$0.426980\pi$
$182$	3153.52i	1.28436i
$183$	1816.79i	0.733885i
$184$	8612.53	3.45068
$185$	0	0
$186$	−2998.98	−1.18224
$187$	452.930i	0.177120i
$188$	2425.28i	0.940861i
$189$	−740.740	−0.285084
$190$	0	0
$191$	−4243.01	−1.60740	−0.803700	−	0.595035i	$-0.797138\pi$
$191$	−4243.01	−1.60740	−0.803700	+	0.595035i	$0.797138\pi$
$192$	308.411i	0.115925i
$193$	− 3324.23i	− 1.23981i	−0.784677	−	0.619905i	$-0.787171\pi$
$193$	− 3324.23i	− 1.23981i	0.784677	−	0.619905i	$-0.212829\pi$
$194$	−431.506	−0.159692
$195$	0	0
$196$	7231.69	2.63546
$197$	− 2677.14i	− 0.968213i	−0.875009	−	0.484107i	$-0.839145\pi$
$197$	− 2677.14i	− 0.968213i	0.875009	−	0.484107i	$-0.160855\pi$
$198$	− 501.419i	− 0.179971i
$199$	−2779.90	−0.990261	−0.495131	−	0.868819i	$-0.664880\pi$
$199$	−2779.90	−0.990261	−0.495131	+	0.868819i	$0.664880\pi$
$200$	0	0
$201$	−2114.77	−0.742113
$202$	− 39.5981i	− 0.0137926i
$203$	2090.65i	0.722833i
$204$	2180.56	0.748380
$205$	0	0
$206$	−63.1940	−0.0213735
$207$	− 1585.50i	− 0.532365i
$208$	2414.56i	0.804903i
$209$	1563.41	0.517432
$210$	0	0
$211$	3056.15	0.997129	0.498564	−	0.866853i	$-0.333861\pi$
$211$	3056.15	0.997129	0.498564	+	0.866853i	$0.333861\pi$
$212$	− 11274.1i	− 3.65239i
$213$	− 2346.49i	− 0.754829i
$214$	−6973.30	−2.22750
$215$	0	0
$216$	−1319.99	−0.415806
$217$	− 5414.89i	− 1.69395i
$218$	− 3090.51i	− 0.960163i
$219$	729.395	0.225059
$220$	0	0
$221$	−934.472	−0.284432
$222$	5580.89i	1.68723i
$223$	571.375i	0.171579i	0.996313	+	0.0857895i	$0.0273412\pi$
$223$	571.375i	0.171579i	−0.996313	+	0.0857895i	$0.972659\pi$
$224$	4053.53	1.20910
$225$	0	0
$226$	186.248	0.0548187
$227$	1094.40i	0.319989i	0.987118	+	0.159995i	$0.0511477\pi$
$227$	1094.40i	0.319989i	−0.987118	+	0.159995i	$0.948852\pi$
$228$	− 7526.78i	− 2.18629i
$229$	645.240	0.186195	0.0930975	−	0.995657i	$-0.470323\pi$
$229$	645.240	0.186195	0.0930975	+	0.995657i	$0.470323\pi$
$230$	0	0
$231$	905.348	0.257868
$232$	3725.53i	1.05428i
$233$	− 2337.39i	− 0.657201i	−0.944469	−	0.328600i	$-0.893423\pi$
$233$	− 2337.39i	− 0.657201i	0.944469	−	0.328600i	$-0.106577\pi$
$234$	1034.51	0.289009
$235$	0	0
$236$	1820.79	0.502217
$237$	1598.62i	0.438151i
$238$	5721.44i	1.55826i
$239$	3656.91	0.989733	0.494866	−	0.868969i	$-0.335217\pi$
$239$	3656.91	0.989733	0.494866	+	0.868969i	$0.335217\pi$
$240$	0	0
$241$	−389.034	−0.103983	−0.0519914	−	0.998648i	$-0.516557\pi$
$241$	−389.034	−0.103983	−0.0519914	+	0.998648i	$0.516557\pi$
$242$	612.845i	0.162790i
$243$	243.000i	0.0641500i
$244$	−10690.3	−2.80483
$245$	0	0
$246$	3620.53	0.938361
$247$	3225.58i	0.830927i
$248$	− 9649.30i	− 2.47069i
$249$	−3614.73	−0.919976
$250$	0	0
$251$	2299.55	0.578271	0.289135	−	0.957288i	$-0.406632\pi$
$251$	2299.55	0.578271	0.289135	+	0.957288i	$0.406632\pi$
$252$	− 4358.65i	− 1.08956i
$253$	1937.83i	0.481543i
$254$	−276.191	−0.0682273
$255$	0	0
$256$	−7801.44	−1.90465
$257$	− 4921.61i	− 1.19456i	−0.802033	−	0.597279i	$-0.796248\pi$
$257$	− 4921.61i	− 1.19456i	0.802033	−	0.597279i	$-0.203752\pi$
$258$	− 460.249i	− 0.111062i
$259$	−10076.7	−2.41752
$260$	0	0
$261$	685.840	0.162653
$262$	12043.3i	2.83985i
$263$	− 2575.61i	− 0.603875i	−0.953328	−	0.301938i	$-0.902367\pi$
$263$	− 2575.61i	− 0.603875i	0.953328	−	0.301938i	$-0.0976334\pi$
$264$	1613.33	0.376111
$265$	0	0
$266$	19749.1	4.55224
$267$	− 3175.48i	− 0.727850i
$268$	− 12443.7i	− 2.83627i
$269$	4794.97	1.08682	0.543410	−	0.839468i	$-0.317133\pi$
$269$	4794.97	1.08682	0.543410	+	0.839468i	$0.317133\pi$
$270$	0	0
$271$	2729.47	0.611821	0.305910	−	0.952060i	$-0.401039\pi$
$271$	2729.47	0.611821	0.305910	+	0.952060i	$0.401039\pi$
$272$	4380.76i	0.976553i
$273$	1867.89i	0.414102i
$274$	−15591.7	−3.43769
$275$	0	0
$276$	9329.36	2.03464
$277$	3761.45i	0.815898i	0.913005	+	0.407949i	$0.133756\pi$
$277$	3761.45i	0.815898i	−0.913005	+	0.407949i	$0.866244\pi$
$278$	6063.53i	1.30815i
$279$	−1776.36	−0.381174
$280$	0	0
$281$	−6434.87	−1.36609	−0.683046	−	0.730375i	$-0.739345\pi$
$281$	−6434.87	−1.36609	−0.683046	+	0.730375i	$0.739345\pi$
$282$	2087.57i	0.440826i
$283$	3335.65i	0.700649i	0.936628	+	0.350325i	$0.113929\pi$
$283$	3335.65i	0.700649i	−0.936628	+	0.350325i	$0.886071\pi$
$284$	13807.2	2.88487
$285$	0	0
$286$	−1264.40	−0.261419
$287$	6537.14i	1.34451i
$288$	− 1329.76i	− 0.272073i
$289$	3217.58	0.654912
$290$	0	0
$291$	−255.589	−0.0514876
$292$	4291.89i	0.860151i
$293$	− 2878.93i	− 0.574023i	−0.957927	−	0.287012i	$-0.907338\pi$
$293$	− 2878.93i	− 0.574023i	0.957927	−	0.287012i	$-0.0926619\pi$
$294$	6224.71	1.23480
$295$	0	0
$296$	−17956.6	−3.52604
$297$	− 297.000i	− 0.0580259i
$298$	3795.87i	0.737883i
$299$	−3998.07	−0.773293
$300$	0	0
$301$	831.014	0.159132
$302$	− 13400.1i	− 2.55328i
$303$	− 23.4547i	− 0.00444699i
$304$	15121.4	2.85286
$305$	0	0
$306$	1876.92	0.350642
$307$	8154.28i	1.51593i	0.652297	+	0.757963i	$0.273805\pi$
$307$	8154.28i	1.51593i	−0.652297	+	0.757963i	$0.726195\pi$
$308$	5327.24i	0.985544i
$309$	−37.4310	−0.00689119
$310$	0	0
$311$	3818.24	0.696182	0.348091	−	0.937461i	$-0.386830\pi$
$311$	3818.24	0.696182	0.348091	+	0.937461i	$0.386830\pi$
$312$	3328.57i	0.603984i
$313$	2527.23i	0.456381i	0.973616	+	0.228191i	$0.0732810\pi$
$313$	2527.23i	0.456381i	−0.973616	+	0.228191i	$0.926719\pi$
$314$	−17604.1	−3.16387
$315$	0	0
$316$	−9406.59	−1.67456
$317$	11084.7i	1.96398i	0.188937	+	0.981989i	$0.439496\pi$
$317$	11084.7i	1.96398i	−0.188937	+	0.981989i	$0.560504\pi$
$318$	− 9704.20i	− 1.71127i
$319$	−838.249	−0.147125
$320$	0	0
$321$	−4130.42	−0.718186
$322$	24478.8i	4.23649i
$323$	5852.19i	1.00813i
$324$	−1429.86	−0.245174
$325$	0	0
$326$	−17822.6	−3.02792
$327$	− 1830.57i	− 0.309574i
$328$	11649.1i	1.96103i
$329$	−3769.26	−0.631629
$330$	0	0
$331$	−9417.70	−1.56388	−0.781939	−	0.623355i	$-0.785769\pi$
$331$	−9417.70	−1.56388	−0.781939	+	0.623355i	$0.785769\pi$
$332$	− 21269.7i	− 3.51605i
$333$	3305.67i	0.543993i
$334$	1267.75	0.207689
$335$	0	0
$336$	8756.57	1.42176
$337$	11263.2i	1.82061i	0.413938	+	0.910305i	$0.364153\pi$
$337$	11263.2i	1.82061i	−0.413938	+	0.910305i	$0.635847\pi$
$338$	8518.76i	1.37089i
$339$	110.318	0.0176745
$340$	0	0
$341$	2171.10	0.344785
$342$	− 6478.70i	− 1.02435i
$343$	1829.03i	0.287925i
$344$	1480.86	0.232101
$345$	0	0
$346$	−4771.00	−0.741302
$347$	4213.25i	0.651814i	0.945402	+	0.325907i	$0.105670\pi$
$347$	4213.25i	0.651814i	−0.945402	+	0.325907i	$0.894330\pi$
$348$	4035.61i	0.621642i
$349$	−4987.07	−0.764905	−0.382452	−	0.923975i	$-0.624920\pi$
$349$	−4987.07	−0.764905	−0.382452	+	0.923975i	$0.624920\pi$
$350$	0	0
$351$	612.762	0.0931817
$352$	1625.26i	0.246099i
$353$	− 7633.47i	− 1.15096i	−0.817816	−	0.575480i	$-0.804815\pi$
$353$	− 7633.47i	− 1.15096i	0.817816	−	0.575480i	$-0.195185\pi$
$354$	1567.25	0.235306
$355$	0	0
$356$	18685.1	2.78177
$357$	3388.92i	0.502411i
$358$	− 1701.97i	− 0.251263i
$359$	3114.76	0.457913	0.228957	−	0.973437i	$-0.426469\pi$
$359$	3114.76	0.457913	0.228957	+	0.973437i	$0.426469\pi$
$360$	0	0
$361$	13341.4	1.94510
$362$	5609.04i	0.814378i
$363$	363.000i	0.0524864i
$364$	−10991.0	−1.58265
$365$	0	0
$366$	−9201.74	−1.31416
$367$	− 5931.48i	− 0.843653i	−0.906677	−	0.421827i	$-0.861389\pi$
$367$	− 5931.48i	− 0.843653i	0.906677	−	0.421827i	$-0.138611\pi$
$368$	18742.8i	2.65499i
$369$	2144.51	0.302544
$370$	0	0
$371$	17521.7	2.45196
$372$	− 10452.4i	− 1.45681i
$373$	13918.9i	1.93215i	0.258267	+	0.966073i	$0.416848\pi$
$373$	13918.9i	1.93215i	−0.258267	+	0.966073i	$0.583152\pi$
$374$	−2294.02	−0.317168
$375$	0	0
$376$	−6716.80	−0.921257
$377$	− 1729.45i	− 0.236263i
$378$	− 3751.72i	− 0.510497i
$379$	12267.3	1.66261	0.831303	−	0.555820i	$-0.187596\pi$
$379$	12267.3	1.66261	0.831303	+	0.555820i	$0.187596\pi$
$380$	0	0
$381$	−163.593	−0.0219977
$382$	− 21490.1i	− 2.87835i
$383$	− 6935.04i	− 0.925233i	−0.886559	−	0.462616i	$-0.846911\pi$
$383$	− 6935.04i	− 0.925233i	0.886559	−	0.462616i	$-0.153089\pi$
$384$	−5108.08	−0.678830
$385$	0	0
$386$	16836.7	2.22012
$387$	− 272.615i	− 0.0358082i
$388$	− 1503.93i	− 0.196780i
$389$	−2775.18	−0.361715	−0.180858	−	0.983509i	$-0.557887\pi$
$389$	−2775.18	−0.361715	−0.180858	+	0.983509i	$0.557887\pi$
$390$	0	0
$391$	−7253.73	−0.938202
$392$	20028.1i	2.58054i
$393$	7133.50i	0.915617i
$394$	13559.3	1.73377
$395$	0	0
$396$	1747.60	0.221769
$397$	− 10539.5i	− 1.33240i	−0.745775	−	0.666198i	$-0.767921\pi$
$397$	− 10539.5i	− 1.33240i	0.745775	−	0.666198i	$-0.232079\pi$
$398$	− 14079.7i	− 1.77325i
$399$	11697.8	1.46772
$400$	0	0
$401$	−12295.3	−1.53117	−0.765585	−	0.643334i	$-0.777550\pi$
$401$	−12295.3	−1.53117	−0.765585	+	0.643334i	$0.777550\pi$
$402$	− 10711.0i	− 1.32889i
$403$	4479.35i	0.553679i
$404$	138.012	0.0169959
$405$	0	0
$406$	−10588.8	−1.29437
$407$	− 4040.26i	− 0.492060i
$408$	6039.04i	0.732787i
$409$	11545.7	1.39584	0.697918	−	0.716178i	$-0.254110\pi$
$409$	11545.7	1.39584	0.697918	+	0.716178i	$0.254110\pi$
$410$	0	0
$411$	−9235.24	−1.10837
$412$	− 220.251i	− 0.0263374i
$413$	2829.78i	0.337154i
$414$	8030.28	0.953301
$415$	0	0
$416$	−3353.20	−0.395202
$417$	3591.55i	0.421772i
$418$	7918.42i	0.926561i
$419$	−1851.51	−0.215876	−0.107938	−	0.994158i	$-0.534425\pi$
$419$	−1851.51	−0.215876	−0.107938	+	0.994158i	$0.534425\pi$
$420$	0	0
$421$	−1303.60	−0.150911	−0.0754557	−	0.997149i	$-0.524041\pi$
$421$	−1303.60	−0.150911	−0.0754557	+	0.997149i	$0.524041\pi$
$422$	15478.9i	1.78555i
$423$	1236.51i	0.142130i
$424$	31223.5	3.57629
$425$	0	0
$426$	11884.6	1.35166
$427$	− 16614.4i	− 1.88297i
$428$	− 24304.2i	− 2.74483i
$429$	−748.931	−0.0842861
$430$	0	0
$431$	8228.85	0.919652	0.459826	−	0.888009i	$-0.347912\pi$
$431$	8228.85	0.919652	0.459826	+	0.888009i	$0.347912\pi$
$432$	− 2872.60i	− 0.319926i
$433$	5830.21i	0.647072i	0.946216	+	0.323536i	$0.104872\pi$
$433$	5830.21i	0.647072i	−0.946216	+	0.323536i	$0.895128\pi$
$434$	27425.5	3.03333
$435$	0	0
$436$	10771.4	1.18316
$437$	25038.2i	2.74082i
$438$	3694.26i	0.403011i
$439$	−14261.0	−1.55044	−0.775218	−	0.631694i	$-0.782360\pi$
$439$	−14261.0	−1.55044	−0.775218	+	0.631694i	$0.782360\pi$
$440$	0	0
$441$	3687.01	0.398123
$442$	− 4732.95i	− 0.509329i
$443$	12025.7i	1.28975i	0.764288	+	0.644875i	$0.223090\pi$
$443$	12025.7i	1.28975i	−0.764288	+	0.644875i	$0.776910\pi$
$444$	−19451.2	−2.07908
$445$	0	0
$446$	−2893.92	−0.307245
$447$	2248.37i	0.237907i
$448$	− 2820.40i	− 0.297436i
$449$	7073.28	0.743449	0.371725	−	0.928343i	$-0.378767\pi$
$449$	7073.28	0.743449	0.371725	+	0.928343i	$0.378767\pi$
$450$	0	0
$451$	−2621.07	−0.273662
$452$	649.133i	0.0675501i
$453$	− 7937.15i	− 0.823222i
$454$	−5542.93	−0.573001
$455$	0	0
$456$	20845.4	2.14073
$457$	− 2732.31i	− 0.279677i	−0.990174	−	0.139838i	$-0.955342\pi$
$457$	− 2732.31i	− 0.279677i	0.990174	−	0.139838i	$-0.0446583\pi$
$458$	3268.04i	0.333418i
$459$	1111.74	0.113053
$460$	0	0
$461$	−332.708	−0.0336134	−0.0168067	−	0.999859i	$-0.505350\pi$
$461$	−332.708	−0.0336134	−0.0168067	+	0.999859i	$0.505350\pi$
$462$	4585.44i	0.461762i
$463$	8248.39i	0.827937i	0.910291	+	0.413969i	$0.135858\pi$
$463$	8248.39i	0.827937i	−0.910291	+	0.413969i	$0.864142\pi$
$464$	−8107.58	−0.811174
$465$	0	0
$466$	11838.5	1.17684
$467$	− 7359.35i	− 0.729229i	−0.931158	−	0.364615i	$-0.881201\pi$
$467$	− 7359.35i	− 0.729229i	0.931158	−	0.364615i	$-0.118799\pi$
$468$	3605.60i	0.356131i
$469$	19339.5	1.90408
$470$	0	0
$471$	−10427.2	−1.02009
$472$	5042.66i	0.491752i
$473$	333.196i	0.0323897i
$474$	−8096.76	−0.784592
$475$	0	0
$476$	−19941.0	−1.92016
$477$	− 5747.99i	− 0.551745i
$478$	18521.7i	1.77230i
$479$	10327.6	0.985140	0.492570	−	0.870273i	$-0.336058\pi$
$479$	10327.6	0.985140	0.492570	+	0.870273i	$0.336058\pi$
$480$	0	0
$481$	8335.75	0.790182
$482$	− 1970.39i	− 0.186201i
$483$	14499.3i	1.36592i
$484$	−2135.96	−0.200597
$485$	0	0
$486$	−1230.76	−0.114873
$487$	− 9622.57i	− 0.895360i	−0.894194	−	0.447680i	$-0.852250\pi$
$487$	− 9622.57i	− 0.895360i	0.894194	−	0.447680i	$-0.147750\pi$
$488$	− 29606.8i	− 2.74639i
$489$	−10556.7	−0.976256
$490$	0	0
$491$	−8993.59	−0.826629	−0.413315	−	0.910588i	$-0.635629\pi$
$491$	−8993.59	−0.826629	−0.413315	+	0.910588i	$0.635629\pi$
$492$	12618.7i	1.15629i
$493$	− 3137.75i	− 0.286648i
$494$	−16337.0	−1.48793
$495$	0	0
$496$	20999.0	1.90097
$497$	21458.5i	1.93671i
$498$	− 18308.0i	− 1.64739i
$499$	−2623.70	−0.235377	−0.117688	−	0.993051i	$-0.537548\pi$
$499$	−2623.70	−0.235377	−0.117688	+	0.993051i	$0.537548\pi$
$500$	0	0
$501$	750.912	0.0669627
$502$	11646.8i	1.03550i
$503$	13234.5i	1.17316i	0.809892	+	0.586579i	$0.199526\pi$
$503$	13234.5i	1.17316i	−0.809892	+	0.586579i	$0.800474\pi$
$504$	12071.3	1.06686
$505$	0	0
$506$	−9814.79	−0.862294
$507$	5045.83i	0.441998i
$508$	− 962.612i	− 0.0840728i
$509$	12810.3	1.11553	0.557765	−	0.829999i	$-0.311659\pi$
$509$	12810.3	1.11553	0.557765	+	0.829999i	$0.311659\pi$
$510$	0	0
$511$	−6670.26	−0.577446
$512$	− 25891.5i	− 2.23487i
$513$	− 3837.46i	− 0.330269i
$514$	24927.1	2.13908
$515$	0	0
$516$	1604.12	0.136855
$517$	− 1511.29i	− 0.128562i
$518$	− 51036.9i	− 4.32902i
$519$	−2825.95	−0.239009
$520$	0	0
$521$	1151.47	0.0968268	0.0484134	−	0.998827i	$-0.484584\pi$
$521$	1151.47	0.0968268	0.0484134	+	0.998827i	$0.484584\pi$
$522$	3473.67i	0.291261i
$523$	− 17319.1i	− 1.44801i	−0.689794	−	0.724005i	$-0.742299\pi$
$523$	− 17319.1i	− 1.44801i	0.689794	−	0.724005i	$-0.257701\pi$
$524$	−41974.8	−3.49939
$525$	0	0
$526$	13045.1	1.08135
$527$	8126.92i	0.671754i
$528$	3510.95i	0.289384i
$529$	−18867.6	−1.55072
$530$	0	0
$531$	928.312	0.0758669
$532$	68831.9i	5.60948i
$533$	− 5407.72i	− 0.439464i
$534$	16083.3	1.30335
$535$	0	0
$536$	34462.8	2.77718
$537$	− 1008.11i	− 0.0810117i
$538$	24285.7i	1.94616i
$539$	−4506.35	−0.360115
$540$	0	0
$541$	−7190.73	−0.571449	−0.285724	−	0.958312i	$-0.592234\pi$
$541$	−7190.73	−0.571449	−0.285724	+	0.958312i	$0.592234\pi$
$542$	13824.3i	1.09558i
$543$	3322.34i	0.262570i
$544$	−6083.73	−0.479481
$545$	0	0
$546$	−9460.55	−0.741527
$547$	− 18670.5i	− 1.45940i	−0.683766	−	0.729701i	$-0.739659\pi$
$547$	− 18670.5i	− 1.45940i	0.683766	−	0.729701i	$-0.260341\pi$
$548$	− 54341.9i	− 4.23608i
$549$	−5450.37	−0.423709
$550$	0	0
$551$	−10830.8	−0.837400
$552$	25837.6i	1.99225i
$553$	− 14619.3i	− 1.12419i
$554$	−19051.1	−1.46102
$555$	0	0
$556$	−21133.3	−1.61197
$557$	5510.44i	0.419183i	0.977789	+	0.209591i	$0.0672134\pi$
$557$	5510.44i	0.419183i	−0.977789	+	0.209591i	$0.932787\pi$
$558$	− 8996.95i	− 0.682565i
$559$	−687.439	−0.0520136
$560$	0	0
$561$	−1358.79	−0.102261
$562$	− 32591.5i	− 2.44625i
$563$	3576.57i	0.267734i	0.990999	+	0.133867i	$0.0427395\pi$
$563$	3576.57i	0.267734i	−0.990999	+	0.133867i	$0.957260\pi$
$564$	−7275.84	−0.543206
$565$	0	0
$566$	−16894.5	−1.25465
$567$	− 2222.22i	− 0.164593i
$568$	38238.8i	2.82476i
$569$	−12285.2	−0.905138	−0.452569	−	0.891729i	$-0.649492\pi$
$569$	−12285.2	−0.905138	−0.452569	+	0.891729i	$0.649492\pi$
$570$	0	0
$571$	13889.5	1.01797	0.508983	−	0.860777i	$-0.330022\pi$
$571$	13889.5	1.01797	0.508983	+	0.860777i	$0.330022\pi$
$572$	− 4406.85i	− 0.322132i
$573$	− 12729.0i	− 0.928032i
$574$	−33109.5	−2.40761
$575$	0	0
$576$	−925.234	−0.0669296
$577$	− 11579.4i	− 0.835457i	−0.908572	−	0.417728i	$-0.862826\pi$
$577$	− 11579.4i	− 0.835457i	0.908572	−	0.417728i	$-0.137174\pi$
$578$	16296.5i	1.17274i
$579$	9972.69	0.715805
$580$	0	0
$581$	33056.4	2.36043
$582$	− 1294.52i	− 0.0921984i
$583$	7025.32i	0.499072i
$584$	−11886.4	−0.842229
$585$	0	0
$586$	14581.3	1.02790
$587$	− 26468.0i	− 1.86107i	−0.366199	−	0.930537i	$-0.619341\pi$
$587$	− 26468.0i	− 1.86107i	0.366199	−	0.930537i	$-0.380659\pi$
$588$	21695.1i	1.52158i
$589$	28052.3	1.96243
$590$	0	0
$591$	8031.41	0.558998
$592$	− 39077.6i	− 2.71297i
$593$	1059.52i	0.0733716i	0.999327	+	0.0366858i	$0.0116801\pi$
$593$	1059.52i	0.0733716i	−0.999327	+	0.0366858i	$0.988320\pi$
$594$	1504.26	0.103906
$595$	0	0
$596$	−13229.8	−0.909253
$597$	− 8339.70i	− 0.571728i
$598$	− 20249.6i	− 1.38473i
$599$	17858.7	1.21817	0.609086	−	0.793104i	$-0.291536\pi$
$599$	17858.7	1.21817	0.609086	+	0.793104i	$0.291536\pi$
$600$	0	0
$601$	−9650.91	−0.655023	−0.327511	−	0.944847i	$-0.606210\pi$
$601$	−9650.91	−0.655023	−0.327511	+	0.944847i	$0.606210\pi$
$602$	4208.95i	0.284957i
$603$	− 6344.32i	− 0.428459i
$604$	46703.7	3.14627
$605$	0	0
$606$	118.794	0.00796318
$607$	− 22754.9i	− 1.52157i	−0.649002	−	0.760786i	$-0.724813\pi$
$607$	− 22754.9i	− 1.52157i	0.649002	−	0.760786i	$-0.275187\pi$
$608$	20999.6i	1.40074i
$609$	−6271.96	−0.417328
$610$	0	0
$611$	3118.04	0.206453
$612$	6541.67i	0.432077i
$613$	13074.5i	0.861459i	0.902481	+	0.430729i	$0.141744\pi$
$613$	13074.5i	0.861459i	−0.902481	+	0.430729i	$0.858256\pi$
$614$	−41300.1	−2.71455
$615$	0	0
$616$	−14753.8	−0.965009
$617$	13393.0i	0.873878i	0.899491	+	0.436939i	$0.143937\pi$
$617$	13393.0i	0.873878i	−0.899491	+	0.436939i	$0.856063\pi$
$618$	− 189.582i	− 0.0123400i
$619$	15965.3	1.03667	0.518336	−	0.855177i	$-0.326552\pi$
$619$	15965.3	1.03667	0.518336	+	0.855177i	$0.326552\pi$
$620$	0	0
$621$	4756.49	0.307361
$622$	19338.8i	1.24665i
$623$	29039.5i	1.86749i
$624$	−7243.69	−0.464711
$625$	0	0
$626$	−12800.0	−0.817237
$627$	4690.23i	0.298740i
$628$	− 61355.8i	− 3.89867i
$629$	15123.6	0.958693
$630$	0	0
$631$	17698.3	1.11657	0.558287	−	0.829648i	$-0.311459\pi$
$631$	17698.3	1.11657	0.558287	+	0.829648i	$0.311459\pi$
$632$	− 26051.5i	− 1.63967i
$633$	9168.45i	0.575693i
$634$	−56142.4	−3.51688
$635$	0	0
$636$	33822.2	2.10871
$637$	− 9297.37i	− 0.578297i
$638$	− 4245.59i	− 0.263455i
$639$	7039.46	0.435801
$640$	0	0
$641$	18264.8	1.12546	0.562728	−	0.826642i	$-0.309752\pi$
$641$	18264.8	1.12546	0.562728	+	0.826642i	$0.309752\pi$
$642$	− 20919.9i	− 1.28605i
$643$	− 15730.5i	− 0.964778i	−0.875957	−	0.482389i	$-0.839769\pi$
$643$	− 15730.5i	− 0.964778i	0.875957	−	0.482389i	$-0.160231\pi$
$644$	−85316.4	−5.22040
$645$	0	0
$646$	−29640.4	−1.80524
$647$	− 21176.6i	− 1.28676i	−0.765545	−	0.643382i	$-0.777531\pi$
$647$	− 21176.6i	− 1.28676i	0.765545	−	0.643382i	$-0.222469\pi$
$648$	− 3959.98i	− 0.240066i
$649$	−1134.60	−0.0686242
$650$	0	0
$651$	16244.7	0.978001
$652$	− 62117.4i	− 3.73114i
$653$	− 28293.6i	− 1.69558i	−0.530331	−	0.847791i	$-0.677932\pi$
$653$	− 28293.6i	− 1.69558i	0.530331	−	0.847791i	$-0.322068\pi$
$654$	9271.52	0.554350
$655$	0	0
$656$	−25351.1	−1.50883
$657$	2188.18i	0.129938i
$658$	− 19090.7i	− 1.13105i
$659$	3894.19	0.230191	0.115096	−	0.993354i	$-0.463283\pi$
$659$	3894.19	0.230191	0.115096	+	0.993354i	$0.463283\pi$
$660$	0	0
$661$	−6063.63	−0.356805	−0.178402	−	0.983958i	$-0.557093\pi$
$661$	−6063.63	−0.356805	−0.178402	+	0.983958i	$0.557093\pi$
$662$	− 47699.1i	− 2.80042i
$663$	− 2803.42i	− 0.164217i
$664$	58906.4	3.44279
$665$	0	0
$666$	−16742.7	−0.974123
$667$	− 13424.7i	− 0.779317i
$668$	4418.51i	0.255924i
$669$	−1714.13	−0.0990612
$670$	0	0
$671$	6661.56	0.383259
$672$	12160.6i	0.698072i
$673$	17297.1i	0.990719i	0.868688	+	0.495360i	$0.164964\pi$
$673$	17297.1i	0.990719i	−0.868688	+	0.495360i	$0.835036\pi$
$674$	−57046.3	−3.26015
$675$	0	0
$676$	−29690.6	−1.68927
$677$	4640.36i	0.263432i	0.991287	+	0.131716i	$0.0420487\pi$
$677$	4640.36i	0.263432i	−0.991287	+	0.131716i	$0.957951\pi$
$678$	558.744i	0.0316496i
$679$	2337.35	0.132105
$680$	0	0
$681$	−3283.19	−0.184746
$682$	10996.3i	0.617404i
$683$	− 14694.9i	− 0.823256i	−0.911352	−	0.411628i	$-0.864960\pi$
$683$	− 14694.9i	− 0.823256i	0.911352	−	0.411628i	$-0.135040\pi$
$684$	22580.3	1.26225
$685$	0	0
$686$	−9263.73	−0.515584
$687$	1935.72i	0.107500i
$688$	3222.68i	0.178581i
$689$	−14494.4	−0.801442
$690$	0	0
$691$	−9905.09	−0.545307	−0.272654	−	0.962112i	$-0.587901\pi$
$691$	−9905.09	−0.545307	−0.272654	+	0.962112i	$0.587901\pi$
$692$	− 16628.4i	− 0.913466i
$693$	2716.05i	0.148880i
$694$	−21339.4	−1.16720
$695$	0	0
$696$	−11176.6	−0.608689
$697$	− 9811.25i	− 0.533182i
$698$	− 25258.7i	− 1.36971i
$699$	7012.18	0.379435
$700$	0	0
$701$	−947.946	−0.0510748	−0.0255374	−	0.999674i	$-0.508130\pi$
$701$	−947.946	−0.0510748	−0.0255374	+	0.999674i	$0.508130\pi$
$702$	3103.54i	0.166860i
$703$	− 52203.2i	− 2.80069i
$704$	1130.84	0.0605401
$705$	0	0
$706$	38662.3	2.06101
$707$	214.492i	0.0114099i
$708$	5462.36i	0.289955i
$709$	3310.76	0.175371	0.0876855	−	0.996148i	$-0.472053\pi$
$709$	3310.76	0.175371	0.0876855	+	0.996148i	$0.472053\pi$
$710$	0	0
$711$	−4795.87	−0.252966
$712$	51748.3i	2.72380i
$713$	34770.5i	1.82632i
$714$	−17164.3	−0.899662
$715$	0	0
$716$	5931.92	0.309618
$717$	10970.7i	0.571423i
$718$	15775.8i	0.819981i
$719$	−3061.15	−0.158778	−0.0793892	−	0.996844i	$-0.525297\pi$
$719$	−3061.15	−0.158778	−0.0793892	+	0.996844i	$0.525297\pi$
$720$	0	0
$721$	342.304	0.0176811
$722$	67572.1i	3.48307i
$723$	− 1167.10i	− 0.0600345i
$724$	−19549.3	−1.00351
$725$	0	0
$726$	−1838.54	−0.0939868
$727$	7405.09i	0.377771i	0.981999	+	0.188886i	$0.0604875\pi$
$727$	7405.09i	0.377771i	−0.981999	+	0.188886i	$0.939512\pi$
$728$	− 30439.5i	− 1.54967i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−1247.23	−0.0631057
$732$	− 32071.0i	− 1.61937i
$733$	29791.4i	1.50119i	0.660765	+	0.750593i	$0.270232\pi$
$733$	29791.4i	1.50119i	−0.660765	+	0.750593i	$0.729768\pi$
$734$	30042.0	1.51072
$735$	0	0
$736$	−26028.8	−1.30358
$737$	7754.17i	0.387556i
$738$	10861.6i	0.541763i
$739$	7150.93	0.355955	0.177978	−	0.984035i	$-0.443045\pi$
$739$	7150.93	0.355955	0.177978	+	0.984035i	$0.443045\pi$
$740$	0	0
$741$	−9676.75	−0.479736
$742$	88744.3i	4.39071i
$743$	− 1940.69i	− 0.0958239i	−0.998852	−	0.0479120i	$-0.984743\pi$
$743$	− 1940.69i	− 0.0958239i	0.998852	−	0.0479120i	$-0.0152567\pi$
$744$	28947.9	1.42645
$745$	0	0
$746$	−70496.7	−3.45988
$747$	− 10844.2i	− 0.531148i
$748$	− 7995.38i	− 0.390829i
$749$	37772.4	1.84269
$750$	0	0
$751$	−29491.2	−1.43295	−0.716476	−	0.697611i	$-0.754246\pi$
$751$	−29491.2	−1.43295	−0.716476	+	0.697611i	$0.754246\pi$
$752$	− 14617.2i	− 0.708824i
$753$	6898.64i	0.333865i
$754$	8759.38	0.423074
$755$	0	0
$756$	13076.0	0.629058
$757$	− 3542.54i	− 0.170087i	−0.996377	−	0.0850436i	$-0.972897\pi$
$757$	− 3542.54i	− 0.170087i	0.996377	−	0.0850436i	$-0.0271030\pi$
$758$	62131.7i	2.97721i
$759$	−5813.49	−0.278019
$760$	0	0
$761$	8552.86	0.407412	0.203706	−	0.979032i	$-0.434701\pi$
$761$	8552.86	0.407412	0.203706	+	0.979032i	$0.434701\pi$
$762$	− 828.572i	− 0.0393911i
$763$	16740.4i	0.794290i
$764$	74900.0	3.54684
$765$	0	0
$766$	35124.9	1.65680
$767$	− 2340.88i	− 0.110201i
$768$	− 23404.3i	− 1.09965i
$769$	3128.73	0.146716	0.0733582	−	0.997306i	$-0.476628\pi$
$769$	3128.73	0.146716	0.0733582	+	0.997306i	$0.476628\pi$
$770$	0	0
$771$	14764.8	0.689679
$772$	58681.2i	2.73573i
$773$	− 5364.51i	− 0.249609i	−0.992181	−	0.124805i	$-0.960170\pi$
$773$	− 5364.51i	− 0.249609i	0.992181	−	0.124805i	$-0.0398304\pi$
$774$	1380.75	0.0641214
$775$	0	0
$776$	4165.14	0.192680
$777$	− 30230.1i	− 1.39575i
$778$	− 14055.8i	− 0.647719i
$779$	−33866.2	−1.55762
$780$	0	0
$781$	−8603.78	−0.394197
$782$	− 36738.9i	− 1.68003i
$783$	2057.52i	0.0939077i
$784$	−43585.6	−1.98550
$785$	0	0
$786$	−36130.0	−1.63959
$787$	− 12160.9i	− 0.550813i	−0.961328	−	0.275406i	$-0.911188\pi$
$787$	− 12160.9i	− 0.550813i	0.961328	−	0.275406i	$-0.0888124\pi$
$788$	47258.3i	2.13643i
$789$	7726.84	0.348648
$790$	0	0
$791$	−1008.85	−0.0453485
$792$	4839.98i	0.217148i
$793$	13743.9i	0.615462i
$794$	53380.7	2.38591
$795$	0	0
$796$	49072.4	2.18508
$797$	581.179i	0.0258299i	0.999917	+	0.0129149i	$0.00411107\pi$
$797$	581.179i	0.0258299i	−0.999917	+	0.0129149i	$0.995889\pi$
$798$	59247.3i	2.62824i
$799$	5657.09	0.250480
$800$	0	0
$801$	9526.43	0.420225
$802$	− 62273.8i	− 2.74185i
$803$	− 2674.45i	− 0.117533i
$804$	37331.2	1.63752
$805$	0	0
$806$	−22687.2	−0.991467
$807$	14384.9i	0.627475i
$808$	382.223i	0.0166418i
$809$	−4763.37	−0.207010	−0.103505	−	0.994629i	$-0.533006\pi$
$809$	−4763.37	−0.207010	−0.103505	+	0.994629i	$0.533006\pi$
$810$	0	0
$811$	−18055.4	−0.781762	−0.390881	−	0.920441i	$-0.627830\pi$
$811$	−18055.4	−0.781762	−0.390881	+	0.920441i	$0.627830\pi$
$812$	− 36905.4i	− 1.59498i
$813$	8188.40i	0.353235i
$814$	20463.3	0.881127
$815$	0	0
$816$	−13142.3	−0.563813
$817$	4305.14i	0.184354i
$818$	58476.9i	2.49951i
$819$	−5603.66	−0.239082
$820$	0	0
$821$	1128.04	0.0479522	0.0239761	−	0.999713i	$-0.492367\pi$
$821$	1128.04	0.0479522	0.0239761	+	0.999713i	$0.492367\pi$
$822$	− 46775.0i	− 1.98475i
$823$	− 32124.2i	− 1.36061i	−0.732930	−	0.680304i	$-0.761848\pi$
$823$	− 32124.2i	− 1.36061i	0.732930	−	0.680304i	$-0.238152\pi$
$824$	609.984	0.0257886
$825$	0	0
$826$	−14332.4	−0.603738
$827$	− 11914.2i	− 0.500964i	−0.968121	−	0.250482i	$-0.919411\pi$
$827$	− 11914.2i	− 0.500964i	0.968121	−	0.250482i	$-0.0805891\pi$
$828$	27988.1i	1.17470i
$829$	37721.6	1.58037	0.790185	−	0.612868i	$-0.209984\pi$
$829$	37721.6	1.58037	0.790185	+	0.612868i	$0.209984\pi$
$830$	0	0
$831$	−11284.4	−0.471059
$832$	2333.12i	0.0972192i
$833$	− 16868.3i	− 0.701622i
$834$	−18190.6	−0.755262
$835$	0	0
$836$	−27598.2	−1.14175
$837$	− 5329.07i	− 0.220071i
$838$	− 9377.57i	− 0.386567i
$839$	16550.5	0.681034	0.340517	−	0.940238i	$-0.389398\pi$
$839$	16550.5	0.681034	0.340517	+	0.940238i	$0.389398\pi$
$840$	0	0
$841$	−18581.9	−0.761896
$842$	− 6602.53i	− 0.270236i
$843$	− 19304.6i	− 0.788714i
$844$	−53948.9	−2.20023
$845$	0	0
$846$	−6262.71	−0.254511
$847$	− 3319.61i	− 0.134667i
$848$	67949.2i	2.75163i
$849$	−10006.9	−0.404520
$850$	0	0
$851$	64705.3	2.60643
$852$	41421.5i	1.66558i
$853$	1045.52i	0.0419672i	0.999780	+	0.0209836i	$0.00667977\pi$
$853$	1045.52i	0.0419672i	−0.999780	+	0.0209836i	$0.993320\pi$
$854$	84149.3	3.37181
$855$	0	0
$856$	67310.2	2.68764
$857$	14016.5i	0.558688i	0.960191	+	0.279344i	$0.0901169\pi$
$857$	14016.5i	0.558688i	−0.960191	+	0.279344i	$0.909883\pi$
$858$	− 3793.21i	− 0.150930i
$859$	20476.3	0.813319	0.406660	−	0.913580i	$-0.366694\pi$
$859$	20476.3	0.813319	0.406660	+	0.913580i	$0.366694\pi$
$860$	0	0
$861$	−19611.4	−0.776255
$862$	41677.8i	1.64681i
$863$	24083.0i	0.949936i	0.880003	+	0.474968i	$0.157540\pi$
$863$	24083.0i	0.949936i	−0.880003	+	0.474968i	$0.842460\pi$
$864$	3989.29	0.157081
$865$	0	0
$866$	−29529.1	−1.15871
$867$	9652.75i	0.378114i
$868$	95586.6i	3.73781i
$869$	5861.61	0.228817
$870$	0	0
$871$	−15998.2	−0.622362
$872$	29831.3i	1.15850i
$873$	− 766.768i	− 0.0297264i
$874$	−126814.	−4.90796
$875$	0	0
$876$	−12875.7	−0.496608
$877$	− 30432.5i	− 1.17176i	−0.810399	−	0.585879i	$-0.800750\pi$
$877$	− 30432.5i	− 1.17176i	0.810399	−	0.585879i	$-0.199250\pi$
$878$	− 72229.7i	− 2.77635i
$879$	8636.79	0.331413
$880$	0	0
$881$	24559.2	0.939183	0.469592	−	0.882884i	$-0.344401\pi$
$881$	24559.2	0.939183	0.469592	+	0.882884i	$0.344401\pi$
$882$	18674.1i	0.712914i
$883$	6013.88i	0.229200i	0.993412	+	0.114600i	$0.0365586\pi$
$883$	6013.88i	0.229200i	−0.993412	+	0.114600i	$0.963441\pi$
$884$	16495.8	0.627618
$885$	0	0
$886$	−60908.3	−2.30954
$887$	− 13395.5i	− 0.507075i	−0.967325	−	0.253538i	$-0.918406\pi$
$887$	− 13395.5i	− 0.507075i	0.967325	−	0.253538i	$-0.0815942\pi$
$888$	− 53869.9i	− 2.03576i
$889$	1496.05	0.0564407
$890$	0	0
$891$	891.000	0.0335013
$892$	− 10086.2i	− 0.378601i
$893$	− 19527.0i	− 0.731741i
$894$	−11387.6	−0.426017
$895$	0	0
$896$	46713.1	1.74171
$897$	− 11994.2i	− 0.446461i
$898$	35825.0i	1.33129i
$899$	−15040.7	−0.557992
$900$	0	0
$901$	−26297.3	−0.972354
$902$	− 13275.3i	− 0.490043i
$903$	2493.04i	0.0918751i
$904$	−1797.77	−0.0661426
$905$	0	0
$906$	40200.3	1.47414
$907$	32078.9i	1.17438i	0.809450	+	0.587189i	$0.199766\pi$
$907$	32078.9i	1.17438i	−0.809450	+	0.587189i	$0.800234\pi$
$908$	− 19318.9i	− 0.706079i
$909$	70.3641	0.00256747
$910$	0	0
$911$	−15992.0	−0.581600	−0.290800	−	0.956784i	$-0.593921\pi$
$911$	−15992.0	−0.581600	−0.290800	+	0.956784i	$0.593921\pi$
$912$	45364.1i	1.64710i
$913$	13254.0i	0.480442i
$914$	13838.7	0.500814
$915$	0	0
$916$	−11390.1	−0.410852
$917$	− 65235.4i	− 2.34925i
$918$	5630.77i	0.202443i
$919$	−33876.1	−1.21596	−0.607980	−	0.793952i	$-0.708020\pi$
$919$	−33876.1	−1.21596	−0.607980	+	0.793952i	$0.708020\pi$
$920$	0	0
$921$	−24462.8	−0.875220
$922$	− 1685.11i	− 0.0601912i
$923$	− 17751.1i	− 0.633026i
$924$	−15981.7	−0.569004
$925$	0	0
$926$	−41776.7	−1.48258
$927$	− 112.293i	− 0.00397863i
$928$	− 11259.3i	− 0.398281i
$929$	−21163.4	−0.747416	−0.373708	−	0.927546i	$-0.621914\pi$
$929$	−21163.4	−0.747416	−0.373708	+	0.927546i	$0.621914\pi$
$930$	0	0
$931$	−58225.4	−2.04969
$932$	41261.0i	1.45016i
$933$	11454.7i	0.401941i
$934$	37273.9	1.30582
$935$	0	0
$936$	−9985.70	−0.348710
$937$	49771.9i	1.73530i	0.497175	+	0.867650i	$0.334371\pi$
$937$	49771.9i	1.73530i	−0.497175	+	0.867650i	$0.665629\pi$
$938$	97951.2i	3.40962i
$939$	−7581.68	−0.263492
$940$	0	0
$941$	32194.6	1.11532	0.557659	−	0.830070i	$-0.311700\pi$
$941$	32194.6	1.11532	0.557659	+	0.830070i	$0.311700\pi$
$942$	− 52812.2i	− 1.82666i
$943$	− 41976.8i	− 1.44958i
$944$	−10973.9	−0.378359
$945$	0	0
$946$	−1687.58	−0.0580000
$947$	30091.9i	1.03258i	0.856413	+	0.516291i	$0.172688\pi$
$947$	30091.9i	1.03258i	−0.856413	+	0.516291i	$0.827312\pi$
$948$	− 28219.8i	− 0.966810i
$949$	5517.84	0.188742
$950$	0	0
$951$	−33254.2	−1.13390
$952$	− 55226.6i	− 1.88015i
$953$	5710.17i	0.194093i	0.995280	+	0.0970465i	$0.0309395\pi$
$953$	5710.17i	0.194093i	−0.995280	+	0.0970465i	$0.969060\pi$
$954$	29112.6	0.988004
$955$	0	0
$956$	−64553.9	−2.18392
$957$	− 2514.75i	− 0.0849427i
$958$	52307.8i	1.76408i
$959$	84455.7	2.84381
$960$	0	0
$961$	9165.07	0.307646
$962$	42219.2i	1.41497i
$963$	− 12391.3i	− 0.414645i
$964$	6867.44	0.229445
$965$	0	0
$966$	−73436.4	−2.44594
$967$	− 29638.4i	− 0.985634i	−0.870133	−	0.492817i	$-0.835967\pi$
$967$	− 29638.4i	− 0.985634i	0.870133	−	0.492817i	$-0.164033\pi$
$968$	− 5915.53i	− 0.196418i
$969$	−17556.6	−0.582042
$970$	0	0
$971$	21416.3	0.707808	0.353904	−	0.935282i	$-0.384854\pi$
$971$	21416.3	0.707808	0.353904	+	0.935282i	$0.384854\pi$
$972$	− 4289.57i	− 0.141552i
$973$	− 32844.5i	− 1.08216i
$974$	48736.7	1.60331
$975$	0	0
$976$	64430.9	2.11310
$977$	− 1038.84i	− 0.0340177i	−0.999855	−	0.0170088i	$-0.994586\pi$
$977$	− 1038.84i	− 0.0340177i	0.999855	−	0.0170088i	$-0.00541434\pi$
$978$	− 53467.8i	− 1.74817i
$979$	−11643.4	−0.380107
$980$	0	0
$981$	5491.70	0.178732
$982$	− 45551.1i	− 1.48024i
$983$	− 44173.6i	− 1.43329i	−0.697440	−	0.716643i	$-0.745678\pi$
$983$	− 44173.6i	− 1.43329i	0.697440	−	0.716643i	$-0.254322\pi$
$984$	−34947.4	−1.13220
$985$	0	0
$986$	15892.2	0.513297
$987$	− 11307.8i	− 0.364671i
$988$	− 56939.8i	− 1.83350i
$989$	−5336.17	−0.171567
$990$	0	0
$991$	−23940.9	−0.767414	−0.383707	−	0.923455i	$-0.625353\pi$
$991$	−23940.9	−0.767414	−0.383707	+	0.923455i	$0.625353\pi$
$992$	29162.1i	0.933365i
$993$	− 28253.1i	− 0.902905i
$994$	−108684.	−3.46804
$995$	0	0
$996$	63809.2	2.02999
$997$	− 13557.9i	− 0.430674i	−0.976540	−	0.215337i	$-0.930915\pi$
$997$	− 13557.9i	− 0.430674i	0.976540	−	0.215337i	$-0.0690849\pi$
$998$	− 13288.6i	− 0.421487i
$999$	−9917.01	−0.314074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.k.199.6		6
5.2	odd	4		165.4.a.e.1.1	✓	3
5.3	odd	4		825.4.a.r.1.3		3
5.4	even	2	inner	825.4.c.k.199.1		6
15.2	even	4		495.4.a.k.1.3		3
15.8	even	4		2475.4.a.t.1.1		3
55.32	even	4		1815.4.a.r.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.1	✓	3	5.2	odd	4
495.4.a.k.1.3		3	15.2	even	4
825.4.a.r.1.3		3	5.3	odd	4
825.4.c.k.199.1		6	5.4	even	2	inner
825.4.c.k.199.6		6	1.1	even	1	trivial
1815.4.a.r.1.3		3	55.32	even	4
2475.4.a.t.1.1		3	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)

\(f(q)\)	\(=\)	\(q+5.06484i q^{2} +3.00000i q^{3} -17.6526 q^{4} -15.1945 q^{6} -27.4348i q^{7} -48.8887i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+5.06484i q^{2} +3.00000i q^{3} -17.6526 q^{4} -15.1945 q^{6} -27.4348i q^{7} -48.8887i q^{8} -9.00000 q^{9} +11.0000 q^{11} -52.9577i q^{12} +22.6949i q^{13} +138.953 q^{14} +106.392 q^{16} +41.1755i q^{17} -45.5835i q^{18} +142.128 q^{19} +82.3044 q^{21} +55.7132i q^{22} +176.166i q^{23} +146.666 q^{24} -114.946 q^{26} -27.0000i q^{27} +484.295i q^{28} -76.2044 q^{29} +197.373 q^{31} +147.751i q^{32} +33.0000i q^{33} -208.547 q^{34} +158.873 q^{36} -367.297i q^{37} +719.856i q^{38} -68.0846 q^{39} -238.279 q^{41} +416.858i q^{42} +30.2905i q^{43} -194.178 q^{44} -892.254 q^{46} -137.390i q^{47} +319.177i q^{48} -409.668 q^{49} -123.526 q^{51} -400.623i q^{52} +638.665i q^{53} +136.751 q^{54} -1341.25 q^{56} +426.385i q^{57} -385.963i q^{58} -103.146 q^{59} +605.596 q^{61} +999.662i q^{62} +246.913i q^{63} +102.804 q^{64} -167.140 q^{66} +704.925i q^{67} -726.852i q^{68} -528.499 q^{69} -782.162 q^{71} +439.998i q^{72} -243.132i q^{73} +1860.30 q^{74} -2508.93 q^{76} -301.783i q^{77} -344.837i q^{78} +532.874 q^{79} +81.0000 q^{81} -1206.84i q^{82} +1204.91i q^{83} -1452.88 q^{84} -153.416 q^{86} -228.613i q^{87} -537.775i q^{88} -1058.49 q^{89} +622.629 q^{91} -3109.79i q^{92} +592.119i q^{93} +695.857 q^{94} -443.254 q^{96} +85.1964i q^{97} -2074.90i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9	\( 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9} + 66 q^{11} + 136 q^{14} + 356 q^{16} + 116 q^{19} + 60 q^{21} - 108 q^{24} - 240 q^{26} + 440 q^{29} + 496 q^{31} + 160 q^{34} + 540 q^{36} - 684 q^{39} + 312 q^{41} - 660 q^{44} - 2512 q^{46} - 558 q^{49} - 624 q^{51} + 108 q^{54} - 3288 q^{56} - 1096 q^{59} + 828 q^{61} + 116 q^{64} - 132 q^{66} - 720 q^{69} - 1824 q^{71} + 3224 q^{74} - 5504 q^{76} + 1084 q^{79} + 486 q^{81} - 4056 q^{84} - 3096 q^{86} - 1580 q^{89} - 1544 q^{91} + 848 q^{94} - 1548 q^{96} - 594 q^{99}+O(q^{100}) \) 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9 + 66 * q^11 + 136 * q^14 + 356 * q^16 + 116 * q^19 + 60 * q^21 - 108 * q^24 - 240 * q^26 + 440 * q^29 + 496 * q^31 + 160 * q^34 + 540 * q^36 - 684 * q^39 + 312 * q^41 - 660 * q^44 - 2512 * q^46 - 558 * q^49 - 624 * q^51 + 108 * q^54 - 3288 * q^56 - 1096 * q^59 + 828 * q^61 + 116 * q^64 - 132 * q^66 - 720 * q^69 - 1824 * q^71 + 3224 * q^74 - 5504 * q^76 + 1084 * q^79 + 486 * q^81 - 4056 * q^84 - 3096 * q^86 - 1580 * q^89 - 1544 * q^91 + 848 * q^94 - 1548 * q^96 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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