LMFDB - Embedded newform 525.4.d.o.274.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (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:	$30.9760027530$
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} + 40x^{6} + 488x^{4} + 1945x^{2} + 1936 $ x^8 + 40x^6 + 488x^4 + 1945*x^2 + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.5
Root			$1.21734i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.o.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.217342i q^{2} +3.00000i q^{3} +7.95276 q^{4} -0.652027 q^{6} +7.00000i q^{7} +3.46721i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+0.217342i q^{2} +3.00000i q^{3} +7.95276 q^{4} -0.652027 q^{6} +7.00000i q^{7} +3.46721i q^{8} -9.00000 q^{9} -30.6085 q^{11} +23.8583i q^{12} -25.3178i q^{13} -1.52140 q^{14} +62.8685 q^{16} +72.8676i q^{17} -1.95608i q^{18} -122.711 q^{19} -21.0000 q^{21} -6.65253i q^{22} +194.258i q^{23} -10.4016 q^{24} +5.50264 q^{26} -27.0000i q^{27} +55.6693i q^{28} -48.6103 q^{29} -288.907 q^{31} +41.4017i q^{32} -91.8255i q^{33} -15.8372 q^{34} -71.5749 q^{36} +15.8251i q^{37} -26.6702i q^{38} +75.9535 q^{39} +452.905 q^{41} -4.56419i q^{42} +152.574i q^{43} -243.422 q^{44} -42.2205 q^{46} -164.435i q^{47} +188.606i q^{48} -49.0000 q^{49} -218.603 q^{51} -201.347i q^{52} +591.600i q^{53} +5.86824 q^{54} -24.2705 q^{56} -368.132i q^{57} -10.5651i q^{58} +180.823 q^{59} +115.773 q^{61} -62.7918i q^{62} -63.0000i q^{63} +493.950 q^{64} +19.9576 q^{66} -605.264i q^{67} +579.499i q^{68} -582.774 q^{69} -990.917 q^{71} -31.2049i q^{72} +863.756i q^{73} -3.43947 q^{74} -975.889 q^{76} -214.260i q^{77} +16.5079i q^{78} -965.930 q^{79} +81.0000 q^{81} +98.4355i q^{82} +160.924i q^{83} -167.008 q^{84} -33.1608 q^{86} -145.831i q^{87} -106.126i q^{88} +51.6227 q^{89} +177.225 q^{91} +1544.89i q^{92} -866.722i q^{93} +35.7387 q^{94} -124.205 q^{96} -1497.31i q^{97} -10.6498i q^{98} +275.477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9	$ 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9} + 114 q^{11} + 84 q^{14} + 432 q^{16} + 24 q^{19} - 168 q^{21} - 558 q^{24} - 162 q^{26} - 756 q^{29} - 186 q^{31} - 1566 q^{34} + 288 q^{36} - 258 q^{39} - 930 q^{41} - 1362 q^{44} + 620 q^{46} - 392 q^{49} + 594 q^{51} - 324 q^{54} - 1302 q^{56} - 462 q^{59} - 2706 q^{61} - 6214 q^{64} - 246 q^{66} - 936 q^{69} - 3450 q^{71} + 3906 q^{74} - 6092 q^{76} - 3258 q^{79} + 648 q^{81} + 672 q^{84} - 9084 q^{86} + 1956 q^{89} - 602 q^{91} - 4960 q^{94} + 4140 q^{96} - 1026 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9 + 114 * q^11 + 84 * q^14 + 432 * q^16 + 24 * q^19 - 168 * q^21 - 558 * q^24 - 162 * q^26 - 756 * q^29 - 186 * q^31 - 1566 * q^34 + 288 * q^36 - 258 * q^39 - 930 * q^41 - 1362 * q^44 + 620 * q^46 - 392 * q^49 + 594 * q^51 - 324 * q^54 - 1302 * q^56 - 462 * q^59 - 2706 * q^61 - 6214 * q^64 - 246 * q^66 - 936 * q^69 - 3450 * q^71 + 3906 * q^74 - 6092 * q^76 - 3258 * q^79 + 648 * q^81 + 672 * q^84 - 9084 * q^86 + 1956 * q^89 - 602 * q^91 - 4960 * q^94 + 4140 * q^96 - 1026 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.217342i	0.0768421i	0.999262	+	0.0384211i	$0.0122328\pi$
$2$	0.217342i	0.0768421i	−0.999262	+	0.0384211i	$0.987767\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	7.95276	0.994095
$5$	0	0
$5$	0	0
$6$	−0.652027	−0.0443648
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	3.46721i	0.153231i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−30.6085	−0.838983	−0.419492	−	0.907759i	$-0.637792\pi$
$11$	−30.6085	−0.838983	−0.419492	+	0.907759i	$0.637792\pi$
$12$	23.8583i	0.573941i
$13$	− 25.3178i	− 0.540146i	−0.962840	−	0.270073i	$-0.912952\pi$
$13$	− 25.3178i	− 0.540146i	0.962840	−	0.270073i	$-0.0870479\pi$
$14$	−1.52140	−0.0290436
$15$	0	0
$16$	62.8685	0.982321
$17$	72.8676i	1.03959i	0.854292	+	0.519794i	$0.173991\pi$
$17$	72.8676i	1.03959i	−0.854292	+	0.519794i	$0.826009\pi$
$18$	− 1.95608i	− 0.0256140i
$19$	−122.711	−1.48167	−0.740836	−	0.671686i	$-0.765570\pi$
$19$	−122.711	−1.48167	−0.740836	+	0.671686i	$0.765570\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	− 6.65253i	− 0.0644692i
$23$	194.258i	1.76111i	0.473943	+	0.880556i	$0.342830\pi$
$23$	194.258i	1.76111i	−0.473943	+	0.880556i	$0.657170\pi$
$24$	−10.4016	−0.0884677
$25$	0	0
$26$	5.50264	0.0415060
$27$	− 27.0000i	− 0.192450i
$28$	55.6693i	0.375733i
$29$	−48.6103	−0.311266	−0.155633	−	0.987815i	$-0.549742\pi$
$29$	−48.6103	−0.311266	−0.155633	+	0.987815i	$0.549742\pi$
$30$	0	0
$31$	−288.907	−1.67385	−0.836924	−	0.547320i	$-0.815648\pi$
$31$	−288.907	−1.67385	−0.836924	+	0.547320i	$0.815648\pi$
$32$	41.4017i	0.228714i
$33$	− 91.8255i	− 0.484387i
$34$	−15.8372	−0.0798841
$35$	0	0
$36$	−71.5749	−0.331365
$37$	15.8251i	0.0703144i	0.999382	+	0.0351572i	$0.0111932\pi$
$37$	15.8251i	0.0703144i	−0.999382	+	0.0351572i	$0.988807\pi$
$38$	− 26.6702i	− 0.113855i
$39$	75.9535	0.311854
$40$	0	0
$41$	452.905	1.72517	0.862584	−	0.505914i	$-0.168845\pi$
$41$	452.905	1.72517	0.862584	+	0.505914i	$0.168845\pi$
$42$	− 4.56419i	− 0.0167683i
$43$	152.574i	0.541101i	0.962706	+	0.270550i	$0.0872057\pi$
$43$	152.574i	0.541101i	−0.962706	+	0.270550i	$0.912794\pi$
$44$	−243.422	−0.834029
$45$	0	0
$46$	−42.2205	−0.135328
$47$	− 164.435i	− 0.510325i	−0.966898	−	0.255163i	$-0.917871\pi$
$47$	− 164.435i	− 0.510325i	0.966898	−	0.255163i	$-0.0821290\pi$
$48$	188.606i	0.567143i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−218.603	−0.600206
$52$	− 201.347i	− 0.536957i
$53$	591.600i	1.53326i	0.642092	+	0.766628i	$0.278067\pi$
$53$	591.600i	1.53326i	−0.642092	+	0.766628i	$0.721933\pi$
$54$	5.86824	0.0147883
$55$	0	0
$56$	−24.2705	−0.0579157
$57$	− 368.132i	− 0.855443i
$58$	− 10.5651i	− 0.0239183i
$59$	180.823	0.399003	0.199501	−	0.979898i	$-0.436068\pi$
$59$	180.823	0.399003	0.199501	+	0.979898i	$0.436068\pi$
$60$	0	0
$61$	115.773	0.243004	0.121502	−	0.992591i	$-0.461229\pi$
$61$	115.773	0.243004	0.121502	+	0.992591i	$0.461229\pi$
$62$	− 62.7918i	− 0.128622i
$63$	− 63.0000i	− 0.125988i
$64$	493.950	0.964746
$65$	0	0
$66$	19.9576	0.0372213
$67$	− 605.264i	− 1.10365i	−0.833959	−	0.551827i	$-0.813931\pi$
$67$	− 605.264i	− 1.10365i	0.833959	−	0.551827i	$-0.186069\pi$
$68$	579.499i	1.03345i
$69$	−582.774	−1.01678
$70$	0	0
$71$	−990.917	−1.65634	−0.828170	−	0.560477i	$-0.810618\pi$
$71$	−990.917	−1.65634	−0.828170	+	0.560477i	$0.810618\pi$
$72$	− 31.2049i	− 0.0510768i
$73$	863.756i	1.38486i	0.721484	+	0.692431i	$0.243460\pi$
$73$	863.756i	1.38486i	−0.721484	+	0.692431i	$0.756540\pi$
$74$	−3.43947	−0.00540311
$75$	0	0
$76$	−975.889	−1.47292
$77$	− 214.260i	− 0.317106i
$78$	16.5079i	0.0239635i
$79$	−965.930	−1.37564	−0.687821	−	0.725881i	$-0.741432\pi$
$79$	−965.930	−1.37564	−0.687821	+	0.725881i	$0.741432\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	98.4355i	0.132566i
$83$	160.924i	0.212816i	0.994323	+	0.106408i	$0.0339350\pi$
$83$	160.924i	0.212816i	−0.994323	+	0.106408i	$0.966065\pi$
$84$	−167.008	−0.216929
$85$	0	0
$86$	−33.1608	−0.0415793
$87$	− 145.831i	− 0.179709i
$88$	− 106.126i	− 0.128558i
$89$	51.6227	0.0614831	0.0307415	−	0.999527i	$-0.490213\pi$
$89$	51.6227	0.0614831	0.0307415	+	0.999527i	$0.490213\pi$
$90$	0	0
$91$	177.225	0.204156
$92$	1544.89i	1.75071i
$93$	− 866.722i	− 0.966396i
$94$	35.7387	0.0392145
$95$	0	0
$96$	−124.205	−0.132048
$97$	− 1497.31i	− 1.56731i	−0.621195	−	0.783656i	$-0.713353\pi$
$97$	− 1497.31i	− 1.56731i	0.621195	−	0.783656i	$-0.286647\pi$
$98$	− 10.6498i	− 0.0109774i
$99$	275.477	0.279661
$100$	0	0
$101$	−485.333	−0.478143	−0.239071	−	0.971002i	$-0.576843\pi$
$101$	−485.333	−0.478143	−0.239071	+	0.971002i	$0.576843\pi$
$102$	− 47.5117i	− 0.0461211i
$103$	− 110.629i	− 0.105831i	−0.998599	−	0.0529156i	$-0.983149\pi$
$103$	− 110.629i	− 0.105831i	0.998599	−	0.0529156i	$-0.0168514\pi$
$104$	87.7822	0.0827669
$105$	0	0
$106$	−128.580	−0.117819
$107$	− 361.440i	− 0.326559i	−0.986580	−	0.163279i	$-0.947793\pi$
$107$	− 361.440i	− 0.326559i	0.986580	−	0.163279i	$-0.0522072\pi$
$108$	− 214.725i	− 0.191314i
$109$	−571.242	−0.501973	−0.250986	−	0.967991i	$-0.580755\pi$
$109$	−571.242	−0.501973	−0.250986	+	0.967991i	$0.580755\pi$
$110$	0	0
$111$	−47.4753	−0.0405960
$112$	440.080i	0.371282i
$113$	1389.82i	1.15702i	0.815677	+	0.578508i	$0.196365\pi$
$113$	1389.82i	1.15702i	−0.815677	+	0.578508i	$0.803635\pi$
$114$	80.0107	0.0657341
$115$	0	0
$116$	−386.586	−0.309428
$117$	227.860i	0.180049i
$118$	39.3005i	0.0306602i
$119$	−510.073	−0.392927
$120$	0	0
$121$	−394.119	−0.296107
$122$	25.1624i	0.0186729i
$123$	1358.72i	0.996026i
$124$	−2297.61	−1.66396
$125$	0	0
$126$	13.6926	0.00968120
$127$	777.868i	0.543501i	0.962368	+	0.271751i	$0.0876026\pi$
$127$	777.868i	0.543501i	−0.962368	+	0.271751i	$0.912397\pi$
$128$	438.570i	0.302847i
$129$	−457.722	−0.312405
$130$	0	0
$131$	−172.164	−0.114825	−0.0574125	−	0.998351i	$-0.518285\pi$
$131$	−172.164	−0.114825	−0.0574125	+	0.998351i	$0.518285\pi$
$132$	− 730.267i	− 0.481527i
$133$	− 858.975i	− 0.560019i
$134$	131.549	0.0848070
$135$	0	0
$136$	−252.647	−0.159297
$137$	2010.10i	1.25354i	0.779205	+	0.626769i	$0.215623\pi$
$137$	2010.10i	1.25354i	−0.779205	+	0.626769i	$0.784377\pi$
$138$	− 126.661i	− 0.0781314i
$139$	14.4226	0.00880080	0.00440040	−	0.999990i	$-0.498599\pi$
$139$	14.4226	0.00880080	0.00440040	+	0.999990i	$0.498599\pi$
$140$	0	0
$141$	493.305	0.294636
$142$	− 215.368i	− 0.127277i
$143$	774.941i	0.453174i
$144$	−565.817	−0.327440
$145$	0	0
$146$	−187.731	−0.106416
$147$	− 147.000i	− 0.0824786i
$148$	125.853i	0.0698992i
$149$	1286.13	0.707140	0.353570	−	0.935408i	$-0.384968\pi$
$149$	1286.13	0.707140	0.353570	+	0.935408i	$0.384968\pi$
$150$	0	0
$151$	3048.17	1.64276	0.821381	−	0.570380i	$-0.193204\pi$
$151$	3048.17	1.64276	0.821381	+	0.570380i	$0.193204\pi$
$152$	− 425.464i	− 0.227037i
$153$	− 655.809i	− 0.346529i
$154$	46.5677	0.0243671
$155$	0	0
$156$	604.040	0.310012
$157$	318.632i	0.161972i	0.996715	+	0.0809859i	$0.0258069\pi$
$157$	318.632i	0.161972i	−0.996715	+	0.0809859i	$0.974193\pi$
$158$	− 209.938i	− 0.105707i
$159$	−1774.80	−0.885226
$160$	0	0
$161$	−1359.80	−0.665638
$162$	17.6047i	0.00853801i
$163$	− 499.091i	− 0.239827i	−0.992784	−	0.119914i	$-0.961738\pi$
$163$	− 499.091i	− 0.239827i	0.992784	−	0.119914i	$-0.0382617\pi$
$164$	3601.85	1.71498
$165$	0	0
$166$	−34.9756	−0.0163532
$167$	− 1908.27i	− 0.884231i	−0.896958	−	0.442116i	$-0.854228\pi$
$167$	− 1908.27i	− 0.884231i	0.896958	−	0.442116i	$-0.145772\pi$
$168$	− 72.8114i	− 0.0334376i
$169$	1556.01	0.708242
$170$	0	0
$171$	1104.40	0.493890
$172$	1213.39i	0.537906i
$173$	− 1401.96i	− 0.616121i	−0.951367	−	0.308061i	$-0.900320\pi$
$173$	− 1401.96i	− 0.616121i	0.951367	−	0.308061i	$-0.0996800\pi$
$174$	31.6952	0.0138092
$175$	0	0
$176$	−1924.31	−0.824150
$177$	542.469i	0.230364i
$178$	11.2198i	0.00472449i
$179$	3529.16	1.47364	0.736821	−	0.676088i	$-0.236326\pi$
$179$	3529.16	1.47364	0.736821	+	0.676088i	$0.236326\pi$
$180$	0	0
$181$	4356.04	1.78885	0.894425	−	0.447217i	$-0.147585\pi$
$181$	4356.04	1.78885	0.894425	+	0.447217i	$0.147585\pi$
$182$	38.5185i	0.0156878i
$183$	347.319i	0.140298i
$184$	−673.533	−0.269856
$185$	0	0
$186$	188.375	0.0742599
$187$	− 2230.37i	− 0.872197i
$188$	− 1307.71i	− 0.507312i
$189$	189.000	0.0727393
$190$	0	0
$191$	1203.33	0.455864	0.227932	−	0.973677i	$-0.426804\pi$
$191$	1203.33	0.455864	0.227932	+	0.973677i	$0.426804\pi$
$192$	1481.85i	0.556996i
$193$	1553.31i	0.579323i	0.957129	+	0.289662i	$0.0935428\pi$
$193$	1553.31i	0.579323i	−0.957129	+	0.289662i	$0.906457\pi$
$194$	325.430	0.120436
$195$	0	0
$196$	−389.685	−0.142014
$197$	1826.02i	0.660397i	0.943912	+	0.330199i	$0.107116\pi$
$197$	1826.02i	0.660397i	−0.943912	+	0.330199i	$0.892884\pi$
$198$	59.8727i	0.0214897i
$199$	−596.394	−0.212448	−0.106224	−	0.994342i	$-0.533876\pi$
$199$	−596.394	−0.212448	−0.106224	+	0.994342i	$0.533876\pi$
$200$	0	0
$201$	1815.79	0.637194
$202$	− 105.483i	− 0.0367415i
$203$	− 340.272i	− 0.117647i
$204$	−1738.50	−0.596662
$205$	0	0
$206$	24.0444	0.00813229
$207$	− 1748.32i	− 0.587037i
$208$	− 1591.69i	− 0.530597i
$209$	3755.99	1.24310
$210$	0	0
$211$	122.070	0.0398276	0.0199138	−	0.999802i	$-0.493661\pi$
$211$	122.070	0.0398276	0.0199138	+	0.999802i	$0.493661\pi$
$212$	4704.86i	1.52420i
$213$	− 2972.75i	− 0.956288i
$214$	78.5563	0.0250935
$215$	0	0
$216$	93.6147	0.0294892
$217$	− 2022.35i	− 0.632655i
$218$	− 124.155i	− 0.0385726i
$219$	−2591.27	−0.799551
$220$	0	0
$221$	1844.85	0.561530
$222$	− 10.3184i	− 0.00311948i
$223$	− 3619.02i	− 1.08676i	−0.839487	−	0.543380i	$-0.817144\pi$
$223$	− 3619.02i	− 1.08676i	0.839487	−	0.543380i	$-0.182856\pi$
$224$	−289.812	−0.0864458
$225$	0	0
$226$	−302.066	−0.0889076
$227$	− 5648.79i	− 1.65165i	−0.563929	−	0.825823i	$-0.690711\pi$
$227$	− 5648.79i	− 1.65165i	0.563929	−	0.825823i	$-0.309289\pi$
$228$	− 2927.67i	− 0.850392i
$229$	619.352	0.178725	0.0893623	−	0.995999i	$-0.471517\pi$
$229$	619.352	0.178725	0.0893623	+	0.995999i	$0.471517\pi$
$230$	0	0
$231$	642.779	0.183081
$232$	− 168.542i	− 0.0476954i
$233$	675.465i	0.189919i	0.995481	+	0.0949597i	$0.0302722\pi$
$233$	675.465i	0.189919i	−0.995481	+	0.0949597i	$0.969728\pi$
$234$	−49.5237	−0.0138353
$235$	0	0
$236$	1438.04	0.396647
$237$	− 2897.79i	− 0.794227i
$238$	− 110.861i	− 0.0301934i
$239$	5799.50	1.56962	0.784809	−	0.619738i	$-0.212761\pi$
$239$	5799.50	1.56962	0.784809	+	0.619738i	$0.212761\pi$
$240$	0	0
$241$	−2855.14	−0.763136	−0.381568	−	0.924341i	$-0.624616\pi$
$241$	−2855.14	−0.763136	−0.381568	+	0.924341i	$0.624616\pi$
$242$	− 85.6587i	− 0.0227535i
$243$	243.000i	0.0641500i
$244$	920.716	0.241569
$245$	0	0
$246$	−295.306	−0.0765368
$247$	3106.77i	0.800319i
$248$	− 1001.70i	− 0.256484i
$249$	−482.773	−0.122869
$250$	0	0
$251$	−6378.07	−1.60390	−0.801952	−	0.597388i	$-0.796205\pi$
$251$	−6378.07	−1.60390	−0.801952	+	0.597388i	$0.796205\pi$
$252$	− 501.024i	− 0.125244i
$253$	− 5945.94i	− 1.47754i
$254$	−169.064	−0.0417638
$255$	0	0
$256$	3856.28	0.941474
$257$	7570.27i	1.83743i	0.394918	+	0.918716i	$0.370773\pi$
$257$	7570.27i	1.83743i	−0.394918	+	0.918716i	$0.629227\pi$
$258$	− 99.4824i	− 0.0240058i
$259$	−110.776	−0.0265763
$260$	0	0
$261$	437.492	0.103755
$262$	− 37.4186i	− 0.00882339i
$263$	4258.56i	0.998456i	0.866471	+	0.499228i	$0.166383\pi$
$263$	4258.56i	0.998456i	−0.866471	+	0.499228i	$0.833617\pi$
$264$	318.379	0.0742229
$265$	0	0
$266$	186.692	0.0430331
$267$	154.868i	0.0354973i
$268$	− 4813.52i	− 1.09714i
$269$	6518.96	1.47758	0.738788	−	0.673938i	$-0.235399\pi$
$269$	6518.96	1.47758	0.738788	+	0.673938i	$0.235399\pi$
$270$	0	0
$271$	1565.51	0.350914	0.175457	−	0.984487i	$-0.443860\pi$
$271$	1565.51	0.350914	0.175457	+	0.984487i	$0.443860\pi$
$272$	4581.08i	1.02121i
$273$	531.674i	0.117870i
$274$	−436.881	−0.0963245
$275$	0	0
$276$	−4634.66	−1.01077
$277$	2396.83i	0.519897i	0.965623	+	0.259948i	$0.0837055\pi$
$277$	2396.83i	0.519897i	−0.965623	+	0.259948i	$0.916294\pi$
$278$	3.13465i	0 0.000676272i
$279$	2600.16	0.557949
$280$	0	0
$281$	774.094	0.164336	0.0821682	−	0.996618i	$-0.473816\pi$
$281$	774.094	0.164336	0.0821682	+	0.996618i	$0.473816\pi$
$282$	107.216i	0.0226405i
$283$	− 4711.07i	− 0.989554i	−0.869020	−	0.494777i	$-0.835250\pi$
$283$	− 4711.07i	− 0.989554i	0.869020	−	0.494777i	$-0.164750\pi$
$284$	−7880.52	−1.64656
$285$	0	0
$286$	−168.428	−0.0348228
$287$	3170.34i	0.652052i
$288$	− 372.615i	− 0.0762380i
$289$	−396.690	−0.0807428
$290$	0	0
$291$	4491.94	0.904888
$292$	6869.24i	1.37668i
$293$	1141.66i	0.227634i	0.993502	+	0.113817i	$0.0363077\pi$
$293$	1141.66i	0.227634i	−0.993502	+	0.113817i	$0.963692\pi$
$294$	31.9493	0.00633783
$295$	0	0
$296$	−54.8690	−0.0107743
$297$	826.430i	0.161462i
$298$	279.531i	0.0543382i
$299$	4918.19	0.951258
$300$	0	0
$301$	−1068.02	−0.204517
$302$	662.498i	0.126233i
$303$	− 1456.00i	− 0.276056i
$304$	−7714.64	−1.45548
$305$	0	0
$306$	142.535	0.0266280
$307$	− 8177.38i	− 1.52022i	−0.649795	−	0.760110i	$-0.725145\pi$
$307$	− 8177.38i	− 1.52022i	0.649795	−	0.760110i	$-0.274855\pi$
$308$	− 1703.96i	− 0.315233i
$309$	331.887	0.0611016
$310$	0	0
$311$	728.496	0.132827	0.0664136	−	0.997792i	$-0.478844\pi$
$311$	728.496	0.132827	0.0664136	+	0.997792i	$0.478844\pi$
$312$	263.347i	0.0477855i
$313$	5505.37i	0.994191i	0.867696	+	0.497096i	$0.165600\pi$
$313$	5505.37i	0.994191i	−0.867696	+	0.497096i	$0.834400\pi$
$314$	−69.2521	−0.0124463
$315$	0	0
$316$	−7681.81	−1.36752
$317$	− 4947.15i	− 0.876529i	−0.898846	−	0.438264i	$-0.855593\pi$
$317$	− 4947.15i	− 0.876529i	0.898846	−	0.438264i	$-0.144407\pi$
$318$	− 385.739i	− 0.0680226i
$319$	1487.89	0.261146
$320$	0	0
$321$	1084.32	0.188539
$322$	− 295.543i	− 0.0511490i
$323$	− 8941.63i	− 1.54033i
$324$	644.174	0.110455
$325$	0	0
$326$	108.474	0.0184288
$327$	− 1713.72i	− 0.289814i
$328$	1570.32i	0.264348i
$329$	1151.04	0.192885
$330$	0	0
$331$	5893.79	0.978707	0.489353	−	0.872086i	$-0.337233\pi$
$331$	5893.79	0.978707	0.489353	+	0.872086i	$0.337233\pi$
$332$	1279.79i	0.211559i
$333$	− 142.426i	− 0.0234381i
$334$	414.749	0.0679462
$335$	0	0
$336$	−1320.24	−0.214360
$337$	− 10148.7i	− 1.64046i	−0.572033	−	0.820231i	$-0.693845\pi$
$337$	− 10148.7i	− 1.64046i	0.572033	−	0.820231i	$-0.306155\pi$
$338$	338.186i	0.0544228i
$339$	−4169.45	−0.668004
$340$	0	0
$341$	8843.02	1.40433
$342$	240.032i	0.0379516i
$343$	− 343.000i	− 0.0539949i
$344$	−529.007	−0.0829131
$345$	0	0
$346$	304.705	0.0473441
$347$	9389.81i	1.45266i	0.687349	+	0.726328i	$0.258774\pi$
$347$	9389.81i	1.45266i	−0.687349	+	0.726328i	$0.741226\pi$
$348$	− 1159.76i	− 0.178648i
$349$	1302.83	0.199825	0.0999127	−	0.994996i	$-0.468144\pi$
$349$	1302.83	0.199825	0.0999127	+	0.994996i	$0.468144\pi$
$350$	0	0
$351$	−683.581	−0.103951
$352$	− 1267.24i	− 0.191887i
$353$	9448.64i	1.42465i	0.701851	+	0.712323i	$0.252357\pi$
$353$	9448.64i	1.42465i	−0.701851	+	0.712323i	$0.747643\pi$
$354$	−117.902	−0.0177017
$355$	0	0
$356$	410.543	0.0611201
$357$	− 1530.22i	− 0.226857i
$358$	767.036i	0.113238i
$359$	7937.83	1.16697	0.583486	−	0.812124i	$-0.301688\pi$
$359$	7937.83	1.16697	0.583486	+	0.812124i	$0.301688\pi$
$360$	0	0
$361$	8198.90	1.19535
$362$	946.752i	0.137459i
$363$	− 1182.36i	− 0.170958i
$364$	1409.43	0.202951
$365$	0	0
$366$	−75.4872	−0.0107808
$367$	− 2030.61i	− 0.288821i	−0.989518	−	0.144410i	$-0.953871\pi$
$367$	− 2030.61i	− 0.288821i	0.989518	−	0.144410i	$-0.0461285\pi$
$368$	12212.7i	1.72998i
$369$	−4076.15	−0.575056
$370$	0	0
$371$	−4141.20	−0.579516
$372$	− 6892.83i	− 0.960690i
$373$	10507.7i	1.45863i	0.684179	+	0.729314i	$0.260161\pi$
$373$	10507.7i	1.45863i	−0.684179	+	0.729314i	$0.739839\pi$
$374$	484.754	0.0670214
$375$	0	0
$376$	570.130	0.0781974
$377$	1230.71i	0.168129i
$378$	41.0777i	0.00558944i
$379$	−10524.4	−1.42639	−0.713196	−	0.700965i	$-0.752753\pi$
$379$	−10524.4	−1.42639	−0.713196	+	0.700965i	$0.752753\pi$
$380$	0	0
$381$	−2333.60	−0.313791
$382$	261.535i	0.0350296i
$383$	10464.3i	1.39609i	0.716053	+	0.698045i	$0.245947\pi$
$383$	10464.3i	1.39609i	−0.716053	+	0.698045i	$0.754053\pi$
$384$	−1315.71	−0.174849
$385$	0	0
$386$	−337.599	−0.0445164
$387$	− 1373.17i	− 0.180367i
$388$	− 11907.8i	− 1.55806i
$389$	−7674.91	−1.00034	−0.500172	−	0.865926i	$-0.666730\pi$
$389$	−7674.91	−1.00034	−0.500172	+	0.865926i	$0.666730\pi$
$390$	0	0
$391$	−14155.1	−1.83083
$392$	− 169.893i	− 0.0218901i
$393$	− 516.493i	− 0.0662942i
$394$	−396.870	−0.0507463
$395$	0	0
$396$	2190.80	0.278010
$397$	7.14346i	0 0.000903072i	1.00000		0.000451536i	$0.000143728\pi$
$397$	7.14346i	0 0.000903072i	−1.00000		0.000451536i	$0.999856\pi$
$398$	− 129.622i	− 0.0163250i
$399$	2576.92	0.323327
$400$	0	0
$401$	1756.24	0.218709	0.109355	−	0.994003i	$-0.465122\pi$
$401$	1756.24	0.218709	0.109355	+	0.994003i	$0.465122\pi$
$402$	394.648i	0.0489634i
$403$	7314.50i	0.904122i
$404$	−3859.74	−0.475320
$405$	0	0
$406$	73.9555	0.00904027
$407$	− 484.383i	− 0.0589926i
$408$	− 757.942i	− 0.0919699i
$409$	11484.0	1.38838	0.694192	−	0.719790i	$-0.255762\pi$
$409$	11484.0	1.38838	0.694192	+	0.719790i	$0.255762\pi$
$410$	0	0
$411$	−6030.31	−0.723731
$412$	− 879.807i	− 0.105206i
$413$	1265.76i	0.150809i
$414$	379.984	0.0451092
$415$	0	0
$416$	1048.20	0.123539
$417$	43.2679i	0.00508114i
$418$	816.336i	0.0955222i
$419$	3229.63	0.376558	0.188279	−	0.982116i	$-0.439709\pi$
$419$	3229.63	0.376558	0.188279	+	0.982116i	$0.439709\pi$
$420$	0	0
$421$	11091.5	1.28400	0.642001	−	0.766703i	$-0.278104\pi$
$421$	11091.5	1.28400	0.642001	+	0.766703i	$0.278104\pi$
$422$	26.5309i	0.00306044i
$423$	1479.91i	0.170108i
$424$	−2051.20	−0.234942
$425$	0	0
$426$	646.104	0.0734832
$427$	810.411i	0.0918467i
$428$	− 2874.45i	− 0.324630i
$429$	−2324.82	−0.261640
$430$	0	0
$431$	12807.8	1.43139	0.715695	−	0.698413i	$-0.246110\pi$
$431$	12807.8	1.43139	0.715695	+	0.698413i	$0.246110\pi$
$432$	− 1697.45i	− 0.189048i
$433$	− 7189.27i	− 0.797908i	−0.916971	−	0.398954i	$-0.869373\pi$
$433$	− 7189.27i	− 0.797908i	0.916971	−	0.398954i	$-0.130627\pi$
$434$	439.542	0.0486145
$435$	0	0
$436$	−4542.95	−0.499009
$437$	− 23837.5i	− 2.60939i
$438$	− 563.192i	− 0.0614392i
$439$	−4112.88	−0.447146	−0.223573	−	0.974687i	$-0.571772\pi$
$439$	−4112.88	−0.447146	−0.223573	+	0.974687i	$0.571772\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	400.964i	0.0431491i
$443$	8575.57i	0.919724i	0.887991	+	0.459862i	$0.152101\pi$
$443$	8575.57i	0.919724i	−0.887991	+	0.459862i	$0.847899\pi$
$444$	−377.560	−0.0403563
$445$	0	0
$446$	786.566	0.0835089
$447$	3858.39i	0.408268i
$448$	3457.65i	0.364640i
$449$	−17872.4	−1.87850	−0.939252	−	0.343227i	$-0.888480\pi$
$449$	−17872.4	−1.87850	−0.939252	+	0.343227i	$0.888480\pi$
$450$	0	0
$451$	−13862.8	−1.44739
$452$	11052.9i	1.15018i
$453$	9144.52i	0.948449i
$454$	1227.72	0.126916
$455$	0	0
$456$	1276.39	0.131080
$457$	12602.8i	1.29000i	0.764181	+	0.645002i	$0.223144\pi$
$457$	12602.8i	1.29000i	−0.764181	+	0.645002i	$0.776856\pi$
$458$	134.611i	0.0137336i
$459$	1967.43	0.200069
$460$	0	0
$461$	−18008.7	−1.81941	−0.909703	−	0.415259i	$-0.863691\pi$
$461$	−18008.7	−1.81941	−0.909703	+	0.415259i	$0.863691\pi$
$462$	139.703i	0.0140683i
$463$	15173.3i	1.52303i	0.648150	+	0.761513i	$0.275543\pi$
$463$	15173.3i	1.52303i	−0.648150	+	0.761513i	$0.724457\pi$
$464$	−3056.06	−0.305763
$465$	0	0
$466$	−146.807	−0.0145938
$467$	− 8759.79i	− 0.867998i	−0.900913	−	0.433999i	$-0.857102\pi$
$467$	− 8759.79i	− 0.867998i	0.900913	−	0.433999i	$-0.142898\pi$
$468$	1812.12i	0.178986i
$469$	4236.85	0.417142
$470$	0	0
$471$	−955.895	−0.0935144
$472$	626.952i	0.0611394i
$473$	− 4670.07i	− 0.453974i
$474$	629.813	0.0610301
$475$	0	0
$476$	−4056.49	−0.390607
$477$	− 5324.40i	− 0.511085i
$478$	1260.48i	0.120613i
$479$	−9047.02	−0.862983	−0.431491	−	0.902117i	$-0.642012\pi$
$479$	−9047.02	−0.862983	−0.431491	+	0.902117i	$0.642012\pi$
$480$	0	0
$481$	400.657	0.0379800
$482$	− 620.543i	− 0.0586410i
$483$	− 4079.41i	− 0.384306i
$484$	−3134.33	−0.294359
$485$	0	0
$486$	−52.8142	−0.00492942
$487$	1832.63i	0.170523i	0.996359	+	0.0852614i	$0.0271725\pi$
$487$	1832.63i	0.170523i	−0.996359	+	0.0852614i	$0.972827\pi$
$488$	401.410i	0.0372356i
$489$	1497.27	0.138464
$490$	0	0
$491$	−20593.6	−1.89282	−0.946411	−	0.322964i	$-0.895321\pi$
$491$	−20593.6	−1.89282	−0.946411	+	0.322964i	$0.895321\pi$
$492$	10805.5i	0.990145i
$493$	− 3542.11i	− 0.323588i
$494$	−675.232	−0.0614982
$495$	0	0
$496$	−18163.2	−1.64425
$497$	− 6936.42i	− 0.626038i
$498$	− 104.927i	− 0.00944154i
$499$	−4863.99	−0.436357	−0.218178	−	0.975909i	$-0.570011\pi$
$499$	−4863.99	−0.436357	−0.218178	+	0.975909i	$0.570011\pi$
$500$	0	0
$501$	5724.82	0.510511
$502$	− 1386.22i	− 0.123247i
$503$	− 11688.3i	− 1.03609i	−0.855352	−	0.518047i	$-0.826659\pi$
$503$	− 11688.3i	− 1.03609i	0.855352	−	0.518047i	$-0.173341\pi$
$504$	218.434	0.0193052
$505$	0	0
$506$	1292.31	0.113538
$507$	4668.02i	0.408904i
$508$	6186.20i	0.540292i
$509$	16917.0	1.47315	0.736573	−	0.676358i	$-0.236443\pi$
$509$	16917.0	1.47315	0.736573	+	0.676358i	$0.236443\pi$
$510$	0	0
$511$	−6046.29	−0.523429
$512$	4346.69i	0.375192i
$513$	3313.19i	0.285148i
$514$	−1645.34	−0.141192
$515$	0	0
$516$	−3640.16	−0.310560
$517$	5033.11i	0.428154i
$518$	− 24.0763i	− 0.00204218i
$519$	4205.88	0.355718
$520$	0	0
$521$	−13797.3	−1.16022	−0.580108	−	0.814540i	$-0.696990\pi$
$521$	−13797.3	−1.16022	−0.580108	+	0.814540i	$0.696990\pi$
$522$	95.0856i	0.00797277i
$523$	19819.3i	1.65705i	0.559953	+	0.828524i	$0.310819\pi$
$523$	19819.3i	1.65705i	−0.559953	+	0.828524i	$0.689181\pi$
$524$	−1369.18	−0.114147
$525$	0	0
$526$	−925.565	−0.0767234
$527$	− 21052.0i	− 1.74011i
$528$	− 5772.94i	− 0.475823i
$529$	−25569.1	−2.10151
$530$	0	0
$531$	−1627.41	−0.133001
$532$	− 6831.22i	− 0.556712i
$533$	− 11466.6i	− 0.931843i
$534$	−33.6594	−0.00272769
$535$	0	0
$536$	2098.58	0.169113
$537$	10587.5i	0.850807i
$538$	1416.85i	0.113540i
$539$	1499.82	0.119855
$540$	0	0
$541$	14896.9	1.18386	0.591930	−	0.805989i	$-0.298366\pi$
$541$	14896.9	1.18386	0.591930	+	0.805989i	$0.298366\pi$
$542$	340.251i	0.0269650i
$543$	13068.1i	1.03279i
$544$	−3016.84	−0.237768
$545$	0	0
$546$	−115.555	−0.00905735
$547$	− 17673.2i	− 1.38145i	−0.723119	−	0.690724i	$-0.757292\pi$
$547$	− 17673.2i	− 1.38145i	0.723119	−	0.690724i	$-0.242708\pi$
$548$	15985.9i	1.24614i
$549$	−1041.96	−0.0810012
$550$	0	0
$551$	5965.00	0.461193
$552$	− 2020.60i	− 0.155801i
$553$	− 6761.51i	− 0.519944i
$554$	−520.932	−0.0399500
$555$	0	0
$556$	114.700	0.00874883
$557$	10008.9i	0.761382i	0.924702	+	0.380691i	$0.124314\pi$
$557$	10008.9i	0.761382i	−0.924702	+	0.380691i	$0.875686\pi$
$558$	565.126i	0.0428740i
$559$	3862.84	0.292274
$560$	0	0
$561$	6691.11	0.503563
$562$	168.243i	0.0126280i
$563$	− 5504.86i	− 0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$563$	− 5504.86i	− 0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$564$	3923.13	0.292897
$565$	0	0
$566$	1023.91	0.0760394
$567$	567.000i	0.0419961i
$568$	− 3435.72i	− 0.253802i
$569$	−9097.13	−0.670248	−0.335124	−	0.942174i	$-0.608778\pi$
$569$	−9097.13	−0.670248	−0.335124	+	0.942174i	$0.608778\pi$
$570$	0	0
$571$	21105.4	1.54682	0.773408	−	0.633908i	$-0.218550\pi$
$571$	21105.4	1.54682	0.773408	+	0.633908i	$0.218550\pi$
$572$	6162.92i	0.450498i
$573$	3609.99i	0.263193i
$574$	−689.048	−0.0501051
$575$	0	0
$576$	−4445.55	−0.321582
$577$	7916.35i	0.571165i	0.958354	+	0.285582i	$0.0921870\pi$
$577$	7916.35i	0.571165i	−0.958354	+	0.285582i	$0.907813\pi$
$578$	− 86.2174i	− 0.00620445i
$579$	−4659.92	−0.334472
$580$	0	0
$581$	−1126.47	−0.0804369
$582$	976.289i	0.0695335i
$583$	− 18108.0i	− 1.28638i
$584$	−2994.82	−0.212203
$585$	0	0
$586$	−248.132	−0.0174919
$587$	− 4843.75i	− 0.340584i	−0.985394	−	0.170292i	$-0.945529\pi$
$587$	− 4843.75i	− 0.340584i	0.985394	−	0.170292i	$-0.0544711\pi$
$588$	− 1169.06i	− 0.0819916i
$589$	35452.0	2.48009
$590$	0	0
$591$	−5478.05	−0.381280
$592$	994.901i	0.0690713i
$593$	− 24436.8i	− 1.69224i	−0.532989	−	0.846122i	$-0.678931\pi$
$593$	− 24436.8i	− 1.69224i	0.532989	−	0.846122i	$-0.321069\pi$
$594$	−179.618	−0.0124071
$595$	0	0
$596$	10228.3	0.702965
$597$	− 1789.18i	− 0.122657i
$598$	1068.93i	0.0730967i
$599$	−19665.1	−1.34139	−0.670695	−	0.741733i	$-0.734004\pi$
$599$	−19665.1	−1.34139	−0.670695	+	0.741733i	$0.734004\pi$
$600$	0	0
$601$	5290.41	0.359069	0.179534	−	0.983752i	$-0.442541\pi$
$601$	5290.41	0.359069	0.179534	+	0.983752i	$0.442541\pi$
$602$	− 232.126i	− 0.0157155i
$603$	5447.38i	0.367884i
$604$	24241.4	1.63306
$605$	0	0
$606$	316.450	0.0212127
$607$	13324.8i	0.890997i	0.895283	+	0.445499i	$0.146974\pi$
$607$	13324.8i	0.890997i	−0.895283	+	0.445499i	$0.853026\pi$
$608$	− 5080.43i	− 0.338879i
$609$	1020.82	0.0679237
$610$	0	0
$611$	−4163.13	−0.275650
$612$	− 5215.49i	− 0.344483i
$613$	9606.30i	0.632944i	0.948602	+	0.316472i	$0.102498\pi$
$613$	9606.30i	0.632944i	−0.948602	+	0.316472i	$0.897502\pi$
$614$	1777.29	0.116817
$615$	0	0
$616$	742.883	0.0485903
$617$	− 7675.38i	− 0.500809i	−0.968141	−	0.250404i	$-0.919436\pi$
$617$	− 7675.38i	− 0.500809i	0.968141	−	0.250404i	$-0.0805636\pi$
$618$	72.1332i	0.00469518i
$619$	−8301.91	−0.539066	−0.269533	−	0.962991i	$-0.586869\pi$
$619$	−8301.91	−0.539066	−0.269533	+	0.962991i	$0.586869\pi$
$620$	0	0
$621$	5244.96	0.338926
$622$	158.333i	0.0102067i
$623$	361.359i	0.0232384i
$624$	4775.08	0.306340
$625$	0	0
$626$	−1196.55	−0.0763958
$627$	11268.0i	0.717702i
$628$	2534.00i	0.161015i
$629$	−1153.14	−0.0730980
$630$	0	0
$631$	−18189.1	−1.14754	−0.573768	−	0.819018i	$-0.694519\pi$
$631$	−18189.1	−1.14754	−0.573768	+	0.819018i	$0.694519\pi$
$632$	− 3349.08i	− 0.210790i
$633$	366.209i	0.0229945i
$634$	1075.23	0.0673543
$635$	0	0
$636$	−14114.6	−0.879999
$637$	1240.57i	0.0771638i
$638$	323.381i	0.0200671i
$639$	8918.25	0.552113
$640$	0	0
$641$	7924.18	0.488278	0.244139	−	0.969740i	$-0.421495\pi$
$641$	7924.18	0.488278	0.244139	+	0.969740i	$0.421495\pi$
$642$	235.669i	0.0144877i
$643$	18621.9i	1.14211i	0.820913	+	0.571054i	$0.193465\pi$
$643$	18621.9i	1.14211i	−0.820913	+	0.571054i	$0.806535\pi$
$644$	−10814.2	−0.661707
$645$	0	0
$646$	1943.40	0.118362
$647$	− 13479.1i	− 0.819039i	−0.912301	−	0.409520i	$-0.865696\pi$
$647$	− 13479.1i	− 0.819039i	0.912301	−	0.409520i	$-0.134304\pi$
$648$	280.844i	0.0170256i
$649$	−5534.73	−0.334757
$650$	0	0
$651$	6067.05	0.365263
$652$	− 3969.15i	− 0.238411i
$653$	1979.08i	0.118602i	0.998240	+	0.0593011i	$0.0188872\pi$
$653$	1979.08i	0.118602i	−0.998240	+	0.0593011i	$0.981113\pi$
$654$	372.465	0.0222699
$655$	0	0
$656$	28473.5	1.69467
$657$	− 7773.80i	− 0.461621i
$658$	250.171i	0.0148217i
$659$	11366.4	0.671882	0.335941	−	0.941883i	$-0.390946\pi$
$659$	11366.4	0.671882	0.335941	+	0.941883i	$0.390946\pi$
$660$	0	0
$661$	−7806.27	−0.459348	−0.229674	−	0.973268i	$-0.573766\pi$
$661$	−7806.27	−0.459348	−0.229674	+	0.973268i	$0.573766\pi$
$662$	1280.97i	0.0752059i
$663$	5534.55i	0.324199i
$664$	−557.958	−0.0326099
$665$	0	0
$666$	30.9552	0.00180104
$667$	− 9442.93i	− 0.548173i
$668$	− 15176.0i	− 0.879010i
$669$	10857.1	0.627441
$670$	0	0
$671$	−3543.64	−0.203876
$672$	− 869.435i	− 0.0499095i
$673$	− 8629.80i	− 0.494286i	−0.968979	−	0.247143i	$-0.920508\pi$
$673$	− 8629.80i	− 0.494286i	0.968979	−	0.247143i	$-0.0794917\pi$
$674$	2205.74	0.126057
$675$	0	0
$676$	12374.6	0.704060
$677$	2482.54i	0.140933i	0.997514	+	0.0704666i	$0.0224488\pi$
$677$	2482.54i	0.140933i	−0.997514	+	0.0704666i	$0.977551\pi$
$678$	− 906.197i	− 0.0513308i
$679$	10481.2	0.592388
$680$	0	0
$681$	16946.4	0.953578
$682$	1921.96i	0.107912i
$683$	21007.2i	1.17689i	0.808536	+	0.588446i	$0.200260\pi$
$683$	21007.2i	1.17689i	−0.808536	+	0.588446i	$0.799740\pi$
$684$	8783.00	0.490974
$685$	0	0
$686$	74.5484	0.00414908
$687$	1858.06i	0.103187i
$688$	9592.11i	0.531534i
$689$	14978.0	0.828182
$690$	0	0
$691$	28126.3	1.54844	0.774222	−	0.632914i	$-0.218142\pi$
$691$	28126.3	1.54844	0.774222	+	0.632914i	$0.218142\pi$
$692$	− 11149.4i	− 0.612483i
$693$	1928.34i	0.105702i
$694$	−2040.80	−0.111625
$695$	0	0
$696$	505.626	0.0275369
$697$	33002.1i	1.79346i
$698$	283.161i	0.0153550i
$699$	−2026.40	−0.109650
$700$	0	0
$701$	6685.41	0.360206	0.180103	−	0.983648i	$-0.442357\pi$
$701$	6685.41	0.360206	0.180103	+	0.983648i	$0.442357\pi$
$702$	− 148.571i	− 0.00798783i
$703$	− 1941.91i	− 0.104183i
$704$	−15119.1	−0.809405
$705$	0	0
$706$	−2053.59	−0.109473
$707$	− 3397.33i	− 0.180721i
$708$	4314.13i	0.229004i
$709$	−6066.14	−0.321324	−0.160662	−	0.987009i	$-0.551363\pi$
$709$	−6066.14	−0.321324	−0.160662	+	0.987009i	$0.551363\pi$
$710$	0	0
$711$	8693.37	0.458547
$712$	178.987i	0.00942109i
$713$	− 56122.5i	− 2.94783i
$714$	332.582	0.0174321
$715$	0	0
$716$	28066.6	1.46494
$717$	17398.5i	0.906219i
$718$	1725.23i	0.0896725i
$719$	−33959.8	−1.76146	−0.880728	−	0.473623i	$-0.842946\pi$
$719$	−33959.8	−1.76146	−0.880728	+	0.473623i	$0.842946\pi$
$720$	0	0
$721$	774.404	0.0400004
$722$	1781.97i	0.0918532i
$723$	− 8565.42i	− 0.440597i
$724$	34642.6	1.77829
$725$	0	0
$726$	256.976	0.0131368
$727$	− 1200.78i	− 0.0612578i	−0.999531	−	0.0306289i	$-0.990249\pi$
$727$	− 1200.78i	− 0.0612578i	0.999531	−	0.0306289i	$-0.00975101\pi$
$728$	614.476i	0.0312829i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−11117.7	−0.562522
$732$	2762.15i	0.139470i
$733$	− 14536.9i	− 0.732513i	−0.930514	−	0.366257i	$-0.880639\pi$
$733$	− 14536.9i	− 0.732513i	0.930514	−	0.366257i	$-0.119361\pi$
$734$	441.338	0.0221936
$735$	0	0
$736$	−8042.60	−0.402791
$737$	18526.2i	0.925946i
$738$	− 885.919i	− 0.0441885i
$739$	33712.0	1.67810	0.839049	−	0.544056i	$-0.183112\pi$
$739$	33712.0	1.67810	0.839049	+	0.544056i	$0.183112\pi$
$740$	0	0
$741$	−9320.30	−0.462065
$742$	− 900.059i	− 0.0445313i
$743$	− 34986.0i	− 1.72747i	−0.503944	−	0.863737i	$-0.668118\pi$
$743$	− 34986.0i	− 1.72747i	0.503944	−	0.863737i	$-0.331882\pi$
$744$	3005.11	0.148081
$745$	0	0
$746$	−2283.77	−0.112084
$747$	− 1448.32i	− 0.0709386i
$748$	− 17737.6i	− 0.867047i
$749$	2530.08	0.123428
$750$	0	0
$751$	−23260.7	−1.13022	−0.565109	−	0.825016i	$-0.691166\pi$
$751$	−23260.7	−1.13022	−0.565109	+	0.825016i	$0.691166\pi$
$752$	− 10337.8i	− 0.501303i
$753$	− 19134.2i	− 0.926015i
$754$	−267.485	−0.0129194
$755$	0	0
$756$	1503.07	0.0723098
$757$	27313.4i	1.31139i	0.755026	+	0.655694i	$0.227624\pi$
$757$	27313.4i	1.31139i	−0.755026	+	0.655694i	$0.772376\pi$
$758$	− 2287.40i	− 0.109607i
$759$	17837.8	0.853060
$760$	0	0
$761$	24853.4	1.18389	0.591943	−	0.805980i	$-0.298361\pi$
$761$	24853.4	1.18389	0.591943	+	0.805980i	$0.298361\pi$
$762$	− 507.191i	− 0.0241123i
$763$	− 3998.69i	− 0.189728i
$764$	9569.81	0.453172
$765$	0	0
$766$	−2274.34	−0.107279
$767$	− 4578.05i	− 0.215520i
$768$	11568.8i	0.543561i
$769$	−8507.18	−0.398929	−0.199465	−	0.979905i	$-0.563920\pi$
$769$	−8507.18	−0.398929	−0.199465	+	0.979905i	$0.563920\pi$
$770$	0	0
$771$	−22710.8	−1.06084
$772$	12353.1i	0.575903i
$773$	− 1265.93i	− 0.0589032i	−0.999566	−	0.0294516i	$-0.990624\pi$
$773$	− 1265.93i	− 0.0589032i	0.999566	−	0.0294516i	$-0.00937610\pi$
$774$	298.447	0.0138598
$775$	0	0
$776$	5191.50	0.240160
$777$	− 332.327i	− 0.0153439i
$778$	− 1668.08i	− 0.0768685i
$779$	−55576.3	−2.55613
$780$	0	0
$781$	30330.5	1.38964
$782$	− 3076.50i	− 0.140685i
$783$	1312.48i	0.0599031i
$784$	−3080.56	−0.140332
$785$	0	0
$786$	112.256	0.00509419
$787$	1435.78i	0.0650316i	0.999471	+	0.0325158i	$0.0103519\pi$
$787$	1435.78i	0.0650316i	−0.999471	+	0.0325158i	$0.989648\pi$
$788$	14521.9i	0.656498i
$789$	−12775.7	−0.576459
$790$	0	0
$791$	−9728.71	−0.437311
$792$	955.136i	0.0428526i
$793$	− 2931.12i	− 0.131258i
$794$	−1.55258	−6.93940e−5 0
$795$	0	0
$796$	−4742.98	−0.211194
$797$	23340.9i	1.03736i	0.854968	+	0.518680i	$0.173576\pi$
$797$	23340.9i	1.03736i	−0.854968	+	0.518680i	$0.826424\pi$
$798$	560.075i	0.0248451i
$799$	11982.0	0.530528
$800$	0	0
$801$	−464.604	−0.0204944
$802$	381.705i	0.0168061i
$803$	− 26438.3i	− 1.16188i
$804$	14440.6	0.633432
$805$	0	0
$806$	−1589.75	−0.0694747
$807$	19556.9i	0.853079i
$808$	− 1682.75i	− 0.0732661i
$809$	−1425.33	−0.0619430	−0.0309715	−	0.999520i	$-0.509860\pi$
$809$	−1425.33	−0.0619430	−0.0309715	+	0.999520i	$0.509860\pi$
$810$	0	0
$811$	5914.80	0.256099	0.128050	−	0.991768i	$-0.459128\pi$
$811$	5914.80	0.256099	0.128050	+	0.991768i	$0.459128\pi$
$812$	− 2706.10i	− 0.116953i
$813$	4696.52i	0.202600i
$814$	105.277	0.00453311
$815$	0	0
$816$	−13743.2	−0.589595
$817$	− 18722.5i	− 0.801733i
$818$	2495.97i	0.106686i
$819$	−1595.02	−0.0680520
$820$	0	0
$821$	561.660	0.0238759	0.0119379	−	0.999929i	$-0.496200\pi$
$821$	561.660	0.0238759	0.0119379	+	0.999929i	$0.496200\pi$
$822$	− 1310.64i	− 0.0556130i
$823$	− 28178.0i	− 1.19347i	−0.802439	−	0.596734i	$-0.796465\pi$
$823$	− 28178.0i	− 1.19347i	0.802439	−	0.596734i	$-0.203535\pi$
$824$	383.574	0.0162166
$825$	0	0
$826$	−275.104	−0.0115885
$827$	− 12836.7i	− 0.539754i	−0.962895	−	0.269877i	$-0.913017\pi$
$827$	− 12836.7i	− 0.539754i	0.962895	−	0.269877i	$-0.0869830\pi$
$828$	− 13904.0i	− 0.583571i
$829$	−1411.97	−0.0591552	−0.0295776	−	0.999562i	$-0.509416\pi$
$829$	−1411.97	−0.0591552	−0.0295776	+	0.999562i	$0.509416\pi$
$830$	0	0
$831$	−7190.48	−0.300162
$832$	− 12505.7i	− 0.521104i
$833$	− 3570.51i	− 0.148513i
$834$	−9.40394	−0.000390446 0
$835$	0	0
$836$	29870.5	1.23576
$837$	7800.49i	0.322132i
$838$	701.935i	0.0289355i
$839$	−23633.2	−0.972476	−0.486238	−	0.873826i	$-0.661631\pi$
$839$	−23633.2	−0.972476	−0.486238	+	0.873826i	$0.661631\pi$
$840$	0	0
$841$	−22026.0	−0.903114
$842$	2410.65i	0.0986655i
$843$	2322.28i	0.0948797i
$844$	970.791	0.0395924
$845$	0	0
$846$	−321.648	−0.0130715
$847$	− 2758.83i	− 0.111918i
$848$	37193.0i	1.50615i
$849$	14133.2	0.571319
$850$	0	0
$851$	−3074.15	−0.123831
$852$	− 23641.6i	− 0.950642i
$853$	− 22987.9i	− 0.922734i	−0.887210	−	0.461367i	$-0.847359\pi$
$853$	− 22987.9i	− 0.922734i	0.887210	−	0.461367i	$-0.152641\pi$
$854$	−176.137	−0.00705770
$855$	0	0
$856$	1253.19	0.0500387
$857$	10505.6i	0.418745i	0.977836	+	0.209372i	$0.0671421\pi$
$857$	10505.6i	0.418745i	−0.977836	+	0.209372i	$0.932858\pi$
$858$	− 505.283i	− 0.0201050i
$859$	4159.29	0.165207	0.0826037	−	0.996582i	$-0.473676\pi$
$859$	4159.29	0.165207	0.0826037	+	0.996582i	$0.473676\pi$
$860$	0	0
$861$	−9511.01	−0.376463
$862$	2783.67i	0.109991i
$863$	1464.49i	0.0577657i	0.999583	+	0.0288828i	$0.00919497\pi$
$863$	1464.49i	0.0577657i	−0.999583	+	0.0288828i	$0.990805\pi$
$864$	1117.85	0.0440161
$865$	0	0
$866$	1562.53	0.0613129
$867$	− 1190.07i	− 0.0466169i
$868$	− 16083.3i	− 0.628919i
$869$	29565.7	1.15414
$870$	0	0
$871$	−15324.0	−0.596134
$872$	− 1980.62i	− 0.0769175i
$873$	13475.8i	0.522437i
$874$	5180.90	0.200511
$875$	0	0
$876$	−20607.7	−0.794829
$877$	− 16909.1i	− 0.651062i	−0.945531	−	0.325531i	$-0.894457\pi$
$877$	− 16909.1i	− 0.651062i	0.945531	−	0.325531i	$-0.105543\pi$
$878$	− 893.904i	− 0.0343597i
$879$	−3424.99	−0.131424
$880$	0	0
$881$	16144.3	0.617384	0.308692	−	0.951162i	$-0.400109\pi$
$881$	16144.3	0.617384	0.308692	+	0.951162i	$0.400109\pi$
$882$	95.8480i	0.00365915i
$883$	12346.9i	0.470562i	0.971927	+	0.235281i	$0.0756010\pi$
$883$	12346.9i	0.470562i	−0.971927	+	0.235281i	$0.924399\pi$
$884$	14671.7	0.558214
$885$	0	0
$886$	−1863.83	−0.0706735
$887$	37140.9i	1.40594i	0.711219	+	0.702971i	$0.248144\pi$
$887$	37140.9i	1.40594i	−0.711219	+	0.702971i	$0.751856\pi$
$888$	− 164.607i	− 0.00622055i
$889$	−5445.08	−0.205424
$890$	0	0
$891$	−2479.29	−0.0932203
$892$	− 28781.2i	− 1.08034i
$893$	20177.9i	0.756134i
$894$	−838.592	−0.0313722
$895$	0	0
$896$	−3069.99	−0.114466
$897$	14754.6i	0.549209i
$898$	− 3884.42i	− 0.144348i
$899$	14043.9	0.521011
$900$	0	0
$901$	−43108.5	−1.59395
$902$	− 3012.96i	− 0.111220i
$903$	− 3204.06i	− 0.118078i
$904$	−4818.78	−0.177290
$905$	0	0
$906$	−1987.49	−0.0728808
$907$	44511.9i	1.62954i	0.579784	+	0.814770i	$0.303137\pi$
$907$	44511.9i	1.62954i	−0.579784	+	0.814770i	$0.696863\pi$
$908$	− 44923.5i	− 1.64189i
$909$	4368.00	0.159381
$910$	0	0
$911$	33943.4	1.23446	0.617232	−	0.786781i	$-0.288254\pi$
$911$	33943.4	1.23446	0.617232	+	0.786781i	$0.288254\pi$
$912$	− 23143.9i	− 0.840320i
$913$	− 4925.65i	− 0.178549i
$914$	−2739.11	−0.0991267
$915$	0	0
$916$	4925.56	0.177669
$917$	− 1205.15i	− 0.0433998i
$918$	427.605i	0.0153737i
$919$	−14553.6	−0.522392	−0.261196	−	0.965286i	$-0.584117\pi$
$919$	−14553.6	−0.522392	−0.261196	+	0.965286i	$0.584117\pi$
$920$	0	0
$921$	24532.1	0.877699
$922$	− 3914.04i	− 0.139807i
$923$	25087.9i	0.894666i
$924$	5111.87	0.182000
$925$	0	0
$926$	−3297.79	−0.117033
$927$	995.662i	0.0352771i
$928$	− 2012.55i	− 0.0711908i
$929$	38414.8	1.35667	0.678335	−	0.734752i	$-0.262702\pi$
$929$	38414.8	1.35667	0.678335	+	0.734752i	$0.262702\pi$
$930$	0	0
$931$	6012.82	0.211667
$932$	5371.82i	0.188798i
$933$	2185.49i	0.0766878i
$934$	1903.87	0.0666988
$935$	0	0
$936$	−790.040	−0.0275890
$937$	− 31745.6i	− 1.10681i	−0.832911	−	0.553407i	$-0.813328\pi$
$937$	− 31745.6i	− 1.10681i	0.832911	−	0.553407i	$-0.186672\pi$
$938$	920.846i	0.0320541i
$939$	−16516.1	−0.573997
$940$	0	0
$941$	−45611.1	−1.58011	−0.790053	−	0.613039i	$-0.789947\pi$
$941$	−45611.1	−1.58011	−0.790053	+	0.613039i	$0.789947\pi$
$942$	− 207.756i	− 0.00718585i
$943$	87980.4i	3.03821i
$944$	11368.1	0.391949
$945$	0	0
$946$	1015.00	0.0348844
$947$	− 29473.9i	− 1.01138i	−0.862716	−	0.505689i	$-0.831238\pi$
$947$	− 29473.9i	− 1.01138i	0.862716	−	0.505689i	$-0.168762\pi$
$948$	− 23045.4i	− 0.789537i
$949$	21868.4	0.748028
$950$	0	0
$951$	14841.4	0.506064
$952$	− 1768.53i	− 0.0602084i
$953$	− 15280.3i	− 0.519390i	−0.965691	−	0.259695i	$-0.916378\pi$
$953$	− 15280.3i	− 0.519390i	0.965691	−	0.259695i	$-0.0836221\pi$
$954$	1157.22	0.0392729
$955$	0	0
$956$	46122.1	1.56035
$957$	4463.66i	0.150773i
$958$	− 1966.30i	− 0.0663134i
$959$	−14070.7	−0.473793
$960$	0	0
$961$	53676.4	1.80176
$962$	87.0798i	0.00291847i
$963$	3252.96i	0.108853i
$964$	−22706.3	−0.758630
$965$	0	0
$966$	886.630	0.0295309
$967$	35221.4i	1.17130i	0.810565	+	0.585648i	$0.199160\pi$
$967$	35221.4i	1.17130i	−0.810565	+	0.585648i	$0.800840\pi$
$968$	− 1366.49i	− 0.0453727i
$969$	26824.9	0.889308
$970$	0	0
$971$	−20190.6	−0.667298	−0.333649	−	0.942697i	$-0.608280\pi$
$971$	−20190.6	−0.667298	−0.333649	+	0.942697i	$0.608280\pi$
$972$	1932.52i	0.0637712i
$973$	100.958i	0.00332639i
$974$	−398.309	−0.0131033
$975$	0	0
$976$	7278.48	0.238707
$977$	− 54320.0i	− 1.77876i	−0.457165	−	0.889382i	$-0.651135\pi$
$977$	− 54320.0i	− 1.77876i	0.457165	−	0.889382i	$-0.348865\pi$
$978$	325.421i	0.0106399i
$979$	−1580.09	−0.0515833
$980$	0	0
$981$	5141.17	0.167324
$982$	− 4475.86i	− 0.145449i
$983$	22357.2i	0.725415i	0.931903	+	0.362707i	$0.118148\pi$
$983$	22357.2i	0.725415i	−0.931903	+	0.362707i	$0.881852\pi$
$984$	−4710.95	−0.152622
$985$	0	0
$986$	769.851	0.0248652
$987$	3453.13i	0.111362i
$988$	24707.4i	0.795594i
$989$	−29638.7	−0.952939
$990$	0	0
$991$	−35261.4	−1.13029	−0.565144	−	0.824993i	$-0.691179\pi$
$991$	−35261.4	−1.13029	−0.565144	+	0.824993i	$0.691179\pi$
$992$	− 11961.2i	− 0.382833i
$993$	17681.4i	0.565057i
$994$	1507.58	0.0481061
$995$	0	0
$996$	−3839.38	−0.122144
$997$	15862.5i	0.503881i	0.967743	+	0.251940i	$0.0810687\pi$
$997$	15862.5i	0.503881i	−0.967743	+	0.251940i	$0.918931\pi$
$998$	− 1057.15i	− 0.0335306i
$999$	427.278	0.0135320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.o.274.5		8
5.2	odd	4		525.4.a.v.1.2	yes	4
5.3	odd	4		525.4.a.s.1.3	✓	4
5.4	even	2	inner	525.4.d.o.274.4		8
15.2	even	4		1575.4.a.bf.1.3		4
15.8	even	4		1575.4.a.bm.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.s.1.3	✓	4	5.3	odd	4
525.4.a.v.1.2	yes	4	5.2	odd	4
525.4.d.o.274.4		8	5.4	even	2	inner
525.4.d.o.274.5		8	1.1	even	1	trivial
1575.4.a.bf.1.3		4	15.2	even	4
1575.4.a.bm.1.2		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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.217342i q^{2} +3.00000i q^{3} +7.95276 q^{4} -0.652027 q^{6} +7.00000i q^{7} +3.46721i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+0.217342i q^{2} +3.00000i q^{3} +7.95276 q^{4} -0.652027 q^{6} +7.00000i q^{7} +3.46721i q^{8} -9.00000 q^{9} -30.6085 q^{11} +23.8583i q^{12} -25.3178i q^{13} -1.52140 q^{14} +62.8685 q^{16} +72.8676i q^{17} -1.95608i q^{18} -122.711 q^{19} -21.0000 q^{21} -6.65253i q^{22} +194.258i q^{23} -10.4016 q^{24} +5.50264 q^{26} -27.0000i q^{27} +55.6693i q^{28} -48.6103 q^{29} -288.907 q^{31} +41.4017i q^{32} -91.8255i q^{33} -15.8372 q^{34} -71.5749 q^{36} +15.8251i q^{37} -26.6702i q^{38} +75.9535 q^{39} +452.905 q^{41} -4.56419i q^{42} +152.574i q^{43} -243.422 q^{44} -42.2205 q^{46} -164.435i q^{47} +188.606i q^{48} -49.0000 q^{49} -218.603 q^{51} -201.347i q^{52} +591.600i q^{53} +5.86824 q^{54} -24.2705 q^{56} -368.132i q^{57} -10.5651i q^{58} +180.823 q^{59} +115.773 q^{61} -62.7918i q^{62} -63.0000i q^{63} +493.950 q^{64} +19.9576 q^{66} -605.264i q^{67} +579.499i q^{68} -582.774 q^{69} -990.917 q^{71} -31.2049i q^{72} +863.756i q^{73} -3.43947 q^{74} -975.889 q^{76} -214.260i q^{77} +16.5079i q^{78} -965.930 q^{79} +81.0000 q^{81} +98.4355i q^{82} +160.924i q^{83} -167.008 q^{84} -33.1608 q^{86} -145.831i q^{87} -106.126i q^{88} +51.6227 q^{89} +177.225 q^{91} +1544.89i q^{92} -866.722i q^{93} +35.7387 q^{94} -124.205 q^{96} -1497.31i q^{97} -10.6498i q^{98} +275.477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9} + 114 q^{11} + 84 q^{14} + 432 q^{16} + 24 q^{19} - 168 q^{21} - 558 q^{24} - 162 q^{26} - 756 q^{29} - 186 q^{31} - 1566 q^{34} + 288 q^{36} - 258 q^{39} - 930 q^{41} - 1362 q^{44} + 620 q^{46} - 392 q^{49} + 594 q^{51} - 324 q^{54} - 1302 q^{56} - 462 q^{59} - 2706 q^{61} - 6214 q^{64} - 246 q^{66} - 936 q^{69} - 3450 q^{71} + 3906 q^{74} - 6092 q^{76} - 3258 q^{79} + 648 q^{81} + 672 q^{84} - 9084 q^{86} + 1956 q^{89} - 602 q^{91} - 4960 q^{94} + 4140 q^{96} - 1026 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9 + 114 * q^11 + 84 * q^14 + 432 * q^16 + 24 * q^19 - 168 * q^21 - 558 * q^24 - 162 * q^26 - 756 * q^29 - 186 * q^31 - 1566 * q^34 + 288 * q^36 - 258 * q^39 - 930 * q^41 - 1362 * q^44 + 620 * q^46 - 392 * q^49 + 594 * q^51 - 324 * q^54 - 1302 * q^56 - 462 * q^59 - 2706 * q^61 - 6214 * q^64 - 246 * q^66 - 936 * q^69 - 3450 * q^71 + 3906 * q^74 - 6092 * q^76 - 3258 * q^79 + 648 * q^81 + 672 * q^84 - 9084 * q^86 + 1956 * q^89 - 602 * q^91 - 4960 * q^94 + 4140 * q^96 - 1026 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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