LMFDB - Embedded newform 525.4.d.g.274.4

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:	$4$
Coefficient field:	$\Q(i, \sqrt{57})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 29x^{2} + 196 $ x^4 + 29*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.4
Root			$4.27492i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.g.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.27492i q^{2} +3.00000i q^{3} -19.8248 q^{4} -15.8248 q^{6} -7.00000i q^{7} -62.3746i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+5.27492i q^{2} +3.00000i q^{3} -19.8248 q^{4} -15.8248 q^{6} -7.00000i q^{7} -62.3746i q^{8} -9.00000 q^{9} +34.7492 q^{11} -59.4743i q^{12} -37.2990i q^{13} +36.9244 q^{14} +170.423 q^{16} +10.5498i q^{17} -47.4743i q^{18} +58.5980 q^{19} +21.0000 q^{21} +183.299i q^{22} -125.347i q^{23} +187.124 q^{24} +196.749 q^{26} -27.0000i q^{27} +138.773i q^{28} +35.4020 q^{29} +291.794 q^{31} +399.969i q^{32} +104.248i q^{33} -55.6495 q^{34} +178.423 q^{36} +259.897i q^{37} +309.100i q^{38} +111.897 q^{39} -338.248 q^{41} +110.773i q^{42} +6.80397i q^{43} -688.894 q^{44} +661.196 q^{46} -250.694i q^{47} +511.268i q^{48} -49.0000 q^{49} -31.6495 q^{51} +739.444i q^{52} -536.900i q^{53} +142.423 q^{54} -436.622 q^{56} +175.794i q^{57} +186.743i q^{58} +35.8904 q^{59} +57.7940 q^{61} +1539.19i q^{62} +63.0000i q^{63} -746.423 q^{64} -549.897 q^{66} -481.691i q^{67} -209.148i q^{68} +376.042 q^{69} +363.752 q^{71} +561.371i q^{72} +581.299i q^{73} -1370.94 q^{74} -1161.69 q^{76} -243.244i q^{77} +590.248i q^{78} +693.691 q^{79} +81.0000 q^{81} -1784.23i q^{82} +1334.39i q^{83} -416.320 q^{84} -35.8904 q^{86} +106.206i q^{87} -2167.47i q^{88} +353.038 q^{89} -261.093 q^{91} +2484.98i q^{92} +875.382i q^{93} +1322.39 q^{94} -1199.91 q^{96} -1445.88i q^{97} -258.471i q^{98} -312.743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 34 q^{4} - 18 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q - 34 * q^4 - 18 * q^6 - 36 * q^9	$ 4 q - 34 q^{4} - 18 q^{6} - 36 q^{9} - 12 q^{11} + 42 q^{14} + 274 q^{16} - 128 q^{19} + 84 q^{21} + 522 q^{24} + 636 q^{26} + 504 q^{29} + 80 q^{31} - 132 q^{34} + 306 q^{36} - 96 q^{39} - 900 q^{41} - 1608 q^{44} + 1920 q^{46} - 196 q^{49} - 36 q^{51} + 162 q^{54} - 1218 q^{56} - 1608 q^{59} - 856 q^{61} - 2578 q^{64} - 1656 q^{66} - 36 q^{69} + 1908 q^{71} - 2796 q^{74} - 3016 q^{76} + 1144 q^{79} + 324 q^{81} - 714 q^{84} + 1608 q^{86} - 732 q^{89} + 224 q^{91} + 3840 q^{94} - 1674 q^{96} + 108 q^{99}+O(q^{100}) $ 4 * q - 34 * q^4 - 18 * q^6 - 36 * q^9 - 12 * q^11 + 42 * q^14 + 274 * q^16 - 128 * q^19 + 84 * q^21 + 522 * q^24 + 636 * q^26 + 504 * q^29 + 80 * q^31 - 132 * q^34 + 306 * q^36 - 96 * q^39 - 900 * q^41 - 1608 * q^44 + 1920 * q^46 - 196 * q^49 - 36 * q^51 + 162 * q^54 - 1218 * q^56 - 1608 * q^59 - 856 * q^61 - 2578 * q^64 - 1656 * q^66 - 36 * q^69 + 1908 * q^71 - 2796 * q^74 - 3016 * q^76 + 1144 * q^79 + 324 * q^81 - 714 * q^84 + 1608 * q^86 - 732 * q^89 + 224 * q^91 + 3840 * q^94 - 1674 * q^96 + 108 * 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 $

$2$	5.27492i	1.86496i	0.361215	+	0.932482i	$0.382362\pi$
$2$	5.27492i	1.86496i	−0.361215	+	0.932482i	$0.617638\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−19.8248	−2.47809
$5$	0	0
$5$	0	0
$6$	−15.8248	−1.07674
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	− 62.3746i	− 2.75659i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	34.7492	0.952479	0.476240	−	0.879316i	$-0.342000\pi$
$11$	34.7492	0.952479	0.476240	+	0.879316i	$0.342000\pi$
$12$	− 59.4743i	− 1.43073i
$13$	− 37.2990i	− 0.795760i	−0.917437	−	0.397880i	$-0.869746\pi$
$13$	− 37.2990i	− 0.795760i	0.917437	−	0.397880i	$-0.130254\pi$
$14$	36.9244	0.704890
$15$	0	0
$16$	170.423	2.66286
$17$	10.5498i	0.150512i	0.997164	+	0.0752562i	$0.0239775\pi$
$17$	10.5498i	0.150512i	−0.997164	+	0.0752562i	$0.976023\pi$
$18$	− 47.4743i	− 0.621655i
$19$	58.5980	0.707542	0.353771	−	0.935332i	$-0.384899\pi$
$19$	58.5980	0.707542	0.353771	+	0.935332i	$0.384899\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	183.299i	1.77634i
$23$	− 125.347i	− 1.13638i	−0.822898	−	0.568189i	$-0.807644\pi$
$23$	− 125.347i	− 1.13638i	0.822898	−	0.568189i	$-0.192356\pi$
$24$	187.124	1.59152
$25$	0	0
$26$	196.749	1.48406
$27$	− 27.0000i	− 0.192450i
$28$	138.773i	0.936631i
$29$	35.4020	0.226689	0.113345	−	0.993556i	$-0.463844\pi$
$29$	35.4020	0.226689	0.113345	+	0.993556i	$0.463844\pi$
$30$	0	0
$31$	291.794	1.69057	0.845286	−	0.534313i	$-0.179430\pi$
$31$	291.794	1.69057	0.845286	+	0.534313i	$0.179430\pi$
$32$	399.969i	2.20954i
$33$	104.248i	0.549914i
$34$	−55.6495	−0.280700
$35$	0	0
$36$	178.423	0.826031
$37$	259.897i	1.15478i	0.816469	+	0.577389i	$0.195928\pi$
$37$	259.897i	1.15478i	−0.816469	+	0.577389i	$0.804072\pi$
$38$	309.100i	1.31954i
$39$	111.897	0.459432
$40$	0	0
$41$	−338.248	−1.28842	−0.644212	−	0.764847i	$-0.722815\pi$
$41$	−338.248	−1.28842	−0.644212	+	0.764847i	$0.722815\pi$
$42$	110.773i	0.406969i
$43$	6.80397i	0.0241301i	0.999927	+	0.0120651i	$0.00384053\pi$
$43$	6.80397i	0.0241301i	−0.999927	+	0.0120651i	$0.996159\pi$
$44$	−688.894	−2.36033
$45$	0	0
$46$	661.196	2.11931
$47$	− 250.694i	− 0.778033i	−0.921231	−	0.389016i	$-0.872815\pi$
$47$	− 250.694i	− 0.778033i	0.921231	−	0.389016i	$-0.127185\pi$
$48$	511.268i	1.53740i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−31.6495	−0.0868984
$52$	739.444i	1.97197i
$53$	− 536.900i	− 1.39149i	−0.718289	−	0.695745i	$-0.755075\pi$
$53$	− 536.900i	− 1.39149i	0.718289	−	0.695745i	$-0.244925\pi$
$54$	142.423	0.358913
$55$	0	0
$56$	−436.622	−1.04189
$57$	175.794i	0.408500i
$58$	186.743i	0.422767i
$59$	35.8904	0.0791955	0.0395977	−	0.999216i	$-0.487392\pi$
$59$	35.8904	0.0791955	0.0395977	+	0.999216i	$0.487392\pi$
$60$	0	0
$61$	57.7940	0.121308	0.0606538	−	0.998159i	$-0.480681\pi$
$61$	57.7940	0.121308	0.0606538	+	0.998159i	$0.480681\pi$
$62$	1539.19i	3.15286i
$63$	63.0000i	0.125988i
$64$	−746.423	−1.45786
$65$	0	0
$66$	−549.897	−1.02557
$67$	− 481.691i	− 0.878327i	−0.898407	−	0.439164i	$-0.855275\pi$
$67$	− 481.691i	− 0.878327i	0.898407	−	0.439164i	$-0.144725\pi$
$68$	− 209.148i	− 0.372984i
$69$	376.042	0.656088
$70$	0	0
$71$	363.752	0.608021	0.304010	−	0.952669i	$-0.401674\pi$
$71$	363.752	0.608021	0.304010	+	0.952669i	$0.401674\pi$
$72$	561.371i	0.918864i
$73$	581.299i	0.931999i	0.884785	+	0.465999i	$0.154305\pi$
$73$	581.299i	0.931999i	−0.884785	+	0.465999i	$0.845695\pi$
$74$	−1370.94	−2.15362
$75$	0	0
$76$	−1161.69	−1.75336
$77$	− 243.244i	− 0.360003i
$78$	590.248i	0.856825i
$79$	693.691	0.987928	0.493964	−	0.869482i	$-0.335547\pi$
$79$	693.691	0.987928	0.493964	+	0.869482i	$0.335547\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 1784.23i	− 2.40287i
$83$	1334.39i	1.76468i	0.470611	+	0.882341i	$0.344033\pi$
$83$	1334.39i	1.76468i	−0.470611	+	0.882341i	$0.655967\pi$
$84$	−416.320	−0.540764
$85$	0	0
$86$	−35.8904	−0.0450019
$87$	106.206i	0.130879i
$88$	− 2167.47i	− 2.62560i
$89$	353.038	0.420472	0.210236	−	0.977651i	$-0.432577\pi$
$89$	353.038	0.420472	0.210236	+	0.977651i	$0.432577\pi$
$90$	0	0
$91$	−261.093	−0.300769
$92$	2484.98i	2.81605i
$93$	875.382i	0.976053i
$94$	1322.39	1.45100
$95$	0	0
$96$	−1199.91	−1.27568
$97$	− 1445.88i	− 1.51347i	−0.653722	−	0.756735i	$-0.726793\pi$
$97$	− 1445.88i	− 1.51347i	0.653722	−	0.756735i	$-0.273207\pi$
$98$	− 258.471i	− 0.266424i
$99$	−312.743	−0.317493
$100$	0	0
$101$	474.852	0.467817	0.233909	−	0.972259i	$-0.424848\pi$
$101$	474.852	0.467817	0.233909	+	0.972259i	$0.424848\pi$
$102$	− 166.949i	− 0.162062i
$103$	− 1999.59i	− 1.91287i	−0.291951	−	0.956433i	$-0.594304\pi$
$103$	− 1999.59i	− 1.91287i	0.291951	−	0.956433i	$-0.405696\pi$
$104$	−2326.51	−2.19359
$105$	0	0
$106$	2832.10	2.59508
$107$	− 1166.74i	− 1.05414i	−0.849823	−	0.527068i	$-0.823291\pi$
$107$	− 1166.74i	− 1.05414i	0.849823	−	0.527068i	$-0.176709\pi$
$108$	535.268i	0.476909i
$109$	1337.18	1.17503	0.587515	−	0.809213i	$-0.300106\pi$
$109$	1337.18	1.17503	0.587515	+	0.809213i	$0.300106\pi$
$110$	0	0
$111$	−779.691	−0.666712
$112$	− 1192.96i	− 1.00646i
$113$	906.578i	0.754723i	0.926066	+	0.377361i	$0.123169\pi$
$113$	906.578i	0.754723i	−0.926066	+	0.377361i	$0.876831\pi$
$114$	−927.299	−0.761838
$115$	0	0
$116$	−701.836	−0.561757
$117$	335.691i	0.265253i
$118$	189.319i	0.147697i
$119$	73.8488	0.0568883
$120$	0	0
$121$	−123.495	−0.0927836
$122$	304.859i	0.226235i
$123$	− 1014.74i	− 0.743872i
$124$	−5784.74	−4.18940
$125$	0	0
$126$	−332.320	−0.234963
$127$	1714.89i	1.19820i	0.800674	+	0.599101i	$0.204475\pi$
$127$	1714.89i	1.19820i	−0.800674	+	0.599101i	$0.795525\pi$
$128$	− 737.564i	− 0.509313i
$129$	−20.4119	−0.0139315
$130$	0	0
$131$	470.611	0.313874	0.156937	−	0.987609i	$-0.449838\pi$
$131$	470.611	0.313874	0.156937	+	0.987609i	$0.449838\pi$
$132$	− 2066.68i	− 1.36274i
$133$	− 410.186i	− 0.267426i
$134$	2540.88	1.63805
$135$	0	0
$136$	658.042	0.414901
$137$	443.910i	0.276831i	0.990374	+	0.138415i	$0.0442009\pi$
$137$	443.910i	0.276831i	−0.990374	+	0.138415i	$0.955799\pi$
$138$	1983.59i	1.22358i
$139$	−1669.98	−1.01904	−0.509518	−	0.860460i	$-0.670176\pi$
$139$	−1669.98	−1.01904	−0.509518	+	0.860460i	$0.670176\pi$
$140$	0	0
$141$	752.083	0.449197
$142$	1918.76i	1.13394i
$143$	− 1296.11i	− 0.757945i
$144$	−1533.80	−0.887619
$145$	0	0
$146$	−3066.30	−1.73814
$147$	− 147.000i	− 0.0824786i
$148$	− 5152.39i	− 2.86165i
$149$	−743.871	−0.408995	−0.204497	−	0.978867i	$-0.565556\pi$
$149$	−743.871	−0.408995	−0.204497	+	0.978867i	$0.565556\pi$
$150$	0	0
$151$	606.764	0.327005	0.163503	−	0.986543i	$-0.447721\pi$
$151$	606.764	0.327005	0.163503	+	0.986543i	$0.447721\pi$
$152$	− 3655.03i	− 1.95041i
$153$	− 94.9485i	− 0.0501708i
$154$	1283.09	0.671393
$155$	0	0
$156$	−2218.33	−1.13852
$157$	− 3114.78i	− 1.58336i	−0.610939	−	0.791678i	$-0.709208\pi$
$157$	− 3114.78i	− 1.58336i	0.610939	−	0.791678i	$-0.290792\pi$
$158$	3659.16i	1.84245i
$159$	1610.70	0.803377
$160$	0	0
$161$	−877.430	−0.429511
$162$	427.268i	0.207218i
$163$	2413.07i	1.15955i	0.814777	+	0.579774i	$0.196859\pi$
$163$	2413.07i	1.15955i	−0.814777	+	0.579774i	$0.803141\pi$
$164$	6705.67	3.19284
$165$	0	0
$166$	−7038.81	−3.29107
$167$	610.475i	0.282874i	0.989947	+	0.141437i	$0.0451723\pi$
$167$	610.475i	0.282874i	−0.989947	+	0.141437i	$0.954828\pi$
$168$	− 1309.87i	− 0.601538i
$169$	805.784	0.366766
$170$	0	0
$171$	−527.382	−0.235847
$172$	− 134.887i	− 0.0597968i
$173$	3793.81i	1.66727i	0.552315	+	0.833636i	$0.313745\pi$
$173$	3793.81i	1.66727i	−0.552315	+	0.833636i	$0.686255\pi$
$174$	−560.228	−0.244085
$175$	0	0
$176$	5922.05	2.53631
$177$	107.671i	0.0457235i
$178$	1862.25i	0.784165i
$179$	2804.68	1.17112	0.585562	−	0.810627i	$-0.300874\pi$
$179$	2804.68	1.17112	0.585562	+	0.810627i	$0.300874\pi$
$180$	0	0
$181$	3106.04	1.27553	0.637763	−	0.770232i	$-0.279860\pi$
$181$	3106.04	1.27553	0.637763	+	0.770232i	$0.279860\pi$
$182$	− 1377.24i	− 0.560924i
$183$	173.382i	0.0700370i
$184$	−7818.48	−3.13253
$185$	0	0
$186$	−4617.57	−1.82030
$187$	366.598i	0.143360i
$188$	4969.95i	1.92804i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	261.952	0.0992365	0.0496182	−	0.998768i	$-0.484200\pi$
$191$	261.952	0.0992365	0.0496182	+	0.998768i	$0.484200\pi$
$192$	− 2239.27i	− 0.841694i
$193$	4051.07i	1.51089i	0.655210	+	0.755447i	$0.272580\pi$
$193$	4051.07i	1.51089i	−0.655210	+	0.755447i	$0.727420\pi$
$194$	7626.88	2.82257
$195$	0	0
$196$	971.413	0.354013
$197$	2874.83i	1.03971i	0.854254	+	0.519855i	$0.174014\pi$
$197$	2874.83i	1.03971i	−0.854254	+	0.519855i	$0.825986\pi$
$198$	− 1649.69i	− 0.592113i
$199$	3066.97	1.09252	0.546261	−	0.837615i	$-0.316051\pi$
$199$	3066.97	1.09252	0.546261	+	0.837615i	$0.316051\pi$
$200$	0	0
$201$	1445.07	0.507103
$202$	2504.81i	0.872463i
$203$	− 247.814i	− 0.0856804i
$204$	627.444	0.215342
$205$	0	0
$206$	10547.7	3.56743
$207$	1128.12i	0.378793i
$208$	− 6356.60i	− 2.11899i
$209$	2036.23	0.673919
$210$	0	0
$211$	595.422	0.194268	0.0971340	−	0.995271i	$-0.469032\pi$
$211$	595.422	0.194268	0.0971340	+	0.995271i	$0.469032\pi$
$212$	10643.9i	3.44824i
$213$	1091.26i	0.351041i
$214$	6154.44	1.96593
$215$	0	0
$216$	−1684.11	−0.530507
$217$	− 2042.56i	− 0.638976i
$218$	7053.49i	2.19139i
$219$	−1743.90	−0.538090
$220$	0	0
$221$	393.498	0.119772
$222$	− 4112.81i	− 1.24339i
$223$	− 3779.79i	− 1.13504i	−0.823360	−	0.567520i	$-0.807903\pi$
$223$	− 3779.79i	− 1.13504i	0.823360	−	0.567520i	$-0.192097\pi$
$224$	2799.79	0.835127
$225$	0	0
$226$	−4782.12	−1.40753
$227$	− 1827.62i	− 0.534376i	−0.963644	−	0.267188i	$-0.913906\pi$
$227$	− 1827.62i	− 0.534376i	0.963644	−	0.267188i	$-0.0860944\pi$
$228$	− 3485.07i	− 1.01230i
$229$	850.249	0.245354	0.122677	−	0.992447i	$-0.460852\pi$
$229$	850.249	0.245354	0.122677	+	0.992447i	$0.460852\pi$
$230$	0	0
$231$	729.733	0.207848
$232$	− 2208.18i	− 0.624890i
$233$	− 6591.10i	− 1.85321i	−0.376039	−	0.926604i	$-0.622714\pi$
$233$	− 6591.10i	− 1.85321i	0.376039	−	0.926604i	$-0.377286\pi$
$234$	−1770.74	−0.494688
$235$	0	0
$236$	−711.518	−0.196254
$237$	2081.07i	0.570381i
$238$	389.547i	0.106095i
$239$	182.556	0.0494083	0.0247042	−	0.999695i	$-0.492136\pi$
$239$	182.556	0.0494083	0.0247042	+	0.999695i	$0.492136\pi$
$240$	0	0
$241$	1523.90	0.407315	0.203657	−	0.979042i	$-0.434717\pi$
$241$	1523.90	0.407315	0.203657	+	0.979042i	$0.434717\pi$
$242$	− 651.426i	− 0.173038i
$243$	243.000i	0.0641500i
$244$	−1145.75	−0.300612
$245$	0	0
$246$	5352.68	1.38730
$247$	− 2185.65i	− 0.563034i
$248$	− 18200.5i	− 4.66022i
$249$	−4003.18	−1.01884
$250$	0	0
$251$	2357.73	0.592903	0.296451	−	0.955048i	$-0.404197\pi$
$251$	2357.73	0.592903	0.296451	+	0.955048i	$0.404197\pi$
$252$	− 1248.96i	− 0.312210i
$253$	− 4355.71i	− 1.08238i
$254$	−9045.89	−2.23460
$255$	0	0
$256$	−2080.79	−0.508006
$257$	− 2782.55i	− 0.675372i	−0.941259	−	0.337686i	$-0.890356\pi$
$257$	− 2782.55i	− 0.675372i	0.941259	−	0.337686i	$-0.109644\pi$
$258$	− 107.671i	− 0.0259818i
$259$	1819.28	0.436465
$260$	0	0
$261$	−318.618	−0.0755630
$262$	2482.44i	0.585364i
$263$	2043.78i	0.479183i	0.970874	+	0.239591i	$0.0770135\pi$
$263$	2043.78i	0.479183i	−0.970874	+	0.239591i	$0.922987\pi$
$264$	6502.40	1.51589
$265$	0	0
$266$	2163.70	0.498740
$267$	1059.11i	0.242759i
$268$	9549.41i	2.17658i
$269$	−3452.84	−0.782614	−0.391307	−	0.920260i	$-0.627977\pi$
$269$	−3452.84	−0.782614	−0.391307	+	0.920260i	$0.627977\pi$
$270$	0	0
$271$	2644.29	0.592728	0.296364	−	0.955075i	$-0.404226\pi$
$271$	2644.29	0.592728	0.296364	+	0.955075i	$0.404226\pi$
$272$	1797.93i	0.400793i
$273$	− 783.279i	− 0.173649i
$274$	−2341.59	−0.516280
$275$	0	0
$276$	−7454.93	−1.62585
$277$	− 2679.49i	− 0.581208i	−0.956843	−	0.290604i	$-0.906144\pi$
$277$	− 2679.49i	− 0.581208i	0.956843	−	0.290604i	$-0.0938562\pi$
$278$	− 8809.01i	− 1.90046i
$279$	−2626.15	−0.563524
$280$	0	0
$281$	−1019.69	−0.216476	−0.108238	−	0.994125i	$-0.534521\pi$
$281$	−1019.69	−0.216476	−0.108238	+	0.994125i	$0.534521\pi$
$282$	3967.18i	0.837737i
$283$	432.206i	0.0907844i	0.998969	+	0.0453922i	$0.0144537\pi$
$283$	432.206i	0.0907844i	−0.998969	+	0.0453922i	$0.985546\pi$
$284$	−7211.30	−1.50673
$285$	0	0
$286$	6836.87	1.41354
$287$	2367.73i	0.486979i
$288$	− 3599.72i	− 0.736513i
$289$	4801.70	0.977346
$290$	0	0
$291$	4337.63	0.873802
$292$	− 11524.1i	− 2.30958i
$293$	− 2245.92i	− 0.447809i	−0.974611	−	0.223904i	$-0.928120\pi$
$293$	− 2245.92i	− 0.447809i	0.974611	−	0.223904i	$-0.0718803\pi$
$294$	775.413	0.153820
$295$	0	0
$296$	16211.0	3.18325
$297$	− 938.228i	− 0.183305i
$298$	− 3923.86i	− 0.762761i
$299$	−4675.33	−0.904284
$300$	0	0
$301$	47.6278	0.00912034
$302$	3200.63i	0.609853i
$303$	1424.56i	0.270094i
$304$	9986.44	1.88408
$305$	0	0
$306$	500.846	0.0935668
$307$	3197.08i	0.594354i	0.954822	+	0.297177i	$0.0960452\pi$
$307$	3197.08i	0.594354i	−0.954822	+	0.297177i	$0.903955\pi$
$308$	4822.26i	0.892122i
$309$	5998.76	1.10439
$310$	0	0
$311$	−3355.60	−0.611829	−0.305915	−	0.952059i	$-0.598962\pi$
$311$	−3355.60	−0.611829	−0.305915	+	0.952059i	$0.598962\pi$
$312$	− 6979.53i	− 1.26647i
$313$	− 2256.39i	− 0.407472i	−0.979026	−	0.203736i	$-0.934692\pi$
$313$	− 2256.39i	− 0.407472i	0.979026	−	0.203736i	$-0.0653085\pi$
$314$	16430.2	2.95290
$315$	0	0
$316$	−13752.3	−2.44818
$317$	6139.19i	1.08773i	0.839172	+	0.543866i	$0.183040\pi$
$317$	6139.19i	1.08773i	−0.839172	+	0.543866i	$0.816960\pi$
$318$	8496.31i	1.49827i
$319$	1230.19	0.215917
$320$	0	0
$321$	3500.21	0.608606
$322$	− 4628.37i	− 0.801022i
$323$	618.199i	0.106494i
$324$	−1605.80	−0.275344
$325$	0	0
$326$	−12728.8	−2.16252
$327$	4011.53i	0.678404i
$328$	21098.0i	3.55166i
$329$	−1754.86	−0.294069
$330$	0	0
$331$	7029.81	1.16735	0.583676	−	0.811987i	$-0.301614\pi$
$331$	7029.81	1.16735	0.583676	+	0.811987i	$0.301614\pi$
$332$	− 26454.0i	− 4.37305i
$333$	− 2339.07i	− 0.384926i
$334$	−3220.21	−0.527550
$335$	0	0
$336$	3578.88	0.581083
$337$	− 10328.4i	− 1.66951i	−0.550619	−	0.834757i	$-0.685608\pi$
$337$	− 10328.4i	− 1.66951i	0.550619	−	0.834757i	$-0.314392\pi$
$338$	4250.44i	0.684005i
$339$	−2719.73	−0.435740
$340$	0	0
$341$	10139.6	1.61024
$342$	− 2781.90i	− 0.439847i
$343$	343.000i	0.0539949i
$344$	424.395	0.0665170
$345$	0	0
$346$	−20012.0	−3.10940
$347$	− 1967.54i	− 0.304389i	−0.988351	−	0.152194i	$-0.951366\pi$
$347$	− 1967.54i	− 0.304389i	0.988351	−	0.152194i	$-0.0486340\pi$
$348$	− 2105.51i	− 0.324330i
$349$	4365.46	0.669564	0.334782	−	0.942296i	$-0.391337\pi$
$349$	4365.46	0.669564	0.334782	+	0.942296i	$0.391337\pi$
$350$	0	0
$351$	−1007.07	−0.153144
$352$	13898.6i	2.10454i
$353$	− 6071.59i	− 0.915462i	−0.889091	−	0.457731i	$-0.848662\pi$
$353$	− 6071.59i	− 0.915462i	0.889091	−	0.457731i	$-0.151338\pi$
$354$	−567.957	−0.0852728
$355$	0	0
$356$	−6998.90	−1.04197
$357$	221.547i	0.0328445i
$358$	14794.4i	2.18411i
$359$	−9638.04	−1.41693	−0.708463	−	0.705748i	$-0.750611\pi$
$359$	−9638.04	−1.41693	−0.708463	+	0.705748i	$0.750611\pi$
$360$	0	0
$361$	−3425.27	−0.499384
$362$	16384.1i	2.37881i
$363$	− 370.485i	− 0.0535687i
$364$	5176.10	0.745334
$365$	0	0
$366$	−914.576	−0.130617
$367$	− 522.725i	− 0.0743488i	−0.999309	−	0.0371744i	$-0.988164\pi$
$367$	− 522.725i	− 0.0743488i	0.999309	−	0.0371744i	$-0.0118357\pi$
$368$	− 21362.0i	− 3.02601i
$369$	3044.23	0.429475
$370$	0	0
$371$	−3758.30	−0.525934
$372$	− 17354.2i	− 2.41875i
$373$	3229.84i	0.448351i	0.974549	+	0.224175i	$0.0719688\pi$
$373$	3229.84i	0.448351i	−0.974549	+	0.224175i	$0.928031\pi$
$374$	−1933.77	−0.267361
$375$	0	0
$376$	−15637.0	−2.14472
$377$	− 1320.46i	− 0.180390i
$378$	− 996.959i	− 0.135656i
$379$	−6639.71	−0.899892	−0.449946	−	0.893056i	$-0.648557\pi$
$379$	−6639.71	−0.899892	−0.449946	+	0.893056i	$0.648557\pi$
$380$	0	0
$381$	−5144.66	−0.691782
$382$	1381.77i	0.185073i
$383$	− 14224.4i	− 1.89774i	−0.315664	−	0.948871i	$-0.602227\pi$
$383$	− 14224.4i	− 1.89774i	0.315664	−	0.948871i	$-0.397773\pi$
$384$	2212.69	0.294052
$385$	0	0
$386$	−21369.1	−2.81777
$387$	− 61.2358i	− 0.00804338i
$388$	28664.2i	3.75052i
$389$	−2921.82	−0.380828	−0.190414	−	0.981704i	$-0.560983\pi$
$389$	−2921.82	−0.380828	−0.190414	+	0.981704i	$0.560983\pi$
$390$	0	0
$391$	1322.39	0.171039
$392$	3056.35i	0.393799i
$393$	1411.83i	0.181215i
$394$	−15164.5	−1.93902
$395$	0	0
$396$	6200.04	0.786778
$397$	− 811.940i	− 0.102645i	−0.998682	−	0.0513226i	$-0.983656\pi$
$397$	− 811.940i	− 0.102645i	0.998682	−	0.0513226i	$-0.0163437\pi$
$398$	16178.0i	2.03751i
$399$	1230.56	0.154398
$400$	0	0
$401$	2338.63	0.291237	0.145618	−	0.989341i	$-0.453483\pi$
$401$	2338.63	0.291237	0.145618	+	0.989341i	$0.453483\pi$
$402$	7622.64i	0.945728i
$403$	− 10883.6i	− 1.34529i
$404$	−9413.83	−1.15930
$405$	0	0
$406$	1307.20	0.159791
$407$	9031.21i	1.09990i
$408$	1974.12i	0.239543i
$409$	2727.57	0.329755	0.164877	−	0.986314i	$-0.447277\pi$
$409$	2727.57	0.329755	0.164877	+	0.986314i	$0.447277\pi$
$410$	0	0
$411$	−1331.73	−0.159828
$412$	39641.3i	4.74026i
$413$	− 251.233i	− 0.0299331i
$414$	−5950.76	−0.706435
$415$	0	0
$416$	14918.5	1.75826
$417$	− 5009.94i	− 0.588340i
$418$	10741.0i	1.25684i
$419$	−13306.3	−1.55144	−0.775721	−	0.631076i	$-0.782614\pi$
$419$	−13306.3	−1.55144	−0.775721	+	0.631076i	$0.782614\pi$
$420$	0	0
$421$	−11007.5	−1.27428	−0.637138	−	0.770750i	$-0.719882\pi$
$421$	−11007.5	−1.27428	−0.637138	+	0.770750i	$0.719882\pi$
$422$	3140.80i	0.362303i
$423$	2256.25i	0.259344i
$424$	−33488.9	−3.83577
$425$	0	0
$426$	−5756.29	−0.654679
$427$	− 404.558i	− 0.0458500i
$428$	23130.2i	2.61225i
$429$	3888.33	0.437600
$430$	0	0
$431$	−6525.62	−0.729300	−0.364650	−	0.931145i	$-0.618811\pi$
$431$	−6525.62	−0.729300	−0.364650	+	0.931145i	$0.618811\pi$
$432$	− 4601.41i	− 0.512467i
$433$	− 11716.3i	− 1.30034i	−0.759788	−	0.650171i	$-0.774697\pi$
$433$	− 11716.3i	− 1.30034i	0.759788	−	0.650171i	$-0.225303\pi$
$434$	10774.3	1.19167
$435$	0	0
$436$	−26509.2	−2.91183
$437$	− 7345.10i	− 0.804036i
$438$	− 9198.91i	− 1.00352i
$439$	14611.4	1.58853	0.794264	−	0.607573i	$-0.207857\pi$
$439$	14611.4	1.58853	0.794264	+	0.607573i	$0.207857\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	2075.67i	0.223370i
$443$	− 15239.8i	− 1.63446i	−0.576314	−	0.817228i	$-0.695510\pi$
$443$	− 15239.8i	− 1.63446i	0.576314	−	0.817228i	$-0.304490\pi$
$444$	15457.2	1.65217
$445$	0	0
$446$	19938.1	2.11681
$447$	− 2231.61i	− 0.236133i
$448$	5224.96i	0.551018i
$449$	−10678.8	−1.12241	−0.561206	−	0.827676i	$-0.689662\pi$
$449$	−10678.8	−1.12241	−0.561206	+	0.827676i	$0.689662\pi$
$450$	0	0
$451$	−11753.8	−1.22720
$452$	− 17972.7i	− 1.87027i
$453$	1820.29i	0.188796i
$454$	9640.53	0.996592
$455$	0	0
$456$	10965.1	1.12607
$457$	− 4228.23i	− 0.432797i	−0.976305	−	0.216399i	$-0.930569\pi$
$457$	− 4228.23i	− 0.432797i	0.976305	−	0.216399i	$-0.0694311\pi$
$458$	4484.99i	0.457577i
$459$	284.846	0.0289661
$460$	0	0
$461$	910.121	0.0919492	0.0459746	−	0.998943i	$-0.485361\pi$
$461$	910.121	0.0919492	0.0459746	+	0.998943i	$0.485361\pi$
$462$	3849.28i	0.387629i
$463$	4456.16i	0.447290i	0.974671	+	0.223645i	$0.0717957\pi$
$463$	4456.16i	0.447290i	−0.974671	+	0.223645i	$0.928204\pi$
$464$	6033.30	0.603640
$465$	0	0
$466$	34767.5	3.45617
$467$	4429.42i	0.438907i	0.975623	+	0.219453i	$0.0704273\pi$
$467$	4429.42i	0.438907i	−0.975623	+	0.219453i	$0.929573\pi$
$468$	− 6654.99i	− 0.657323i
$469$	−3371.84	−0.331977
$470$	0	0
$471$	9344.35	0.914151
$472$	− 2238.65i	− 0.218310i
$473$	236.432i	0.0229835i
$474$	−10977.5	−1.06374
$475$	0	0
$476$	−1464.03	−0.140975
$477$	4832.10i	0.463830i
$478$	962.970i	0.0921448i
$479$	−2752.85	−0.262591	−0.131296	−	0.991343i	$-0.541914\pi$
$479$	−2752.85	−0.262591	−0.131296	+	0.991343i	$0.541914\pi$
$480$	0	0
$481$	9693.90	0.918927
$482$	8038.43i	0.759628i
$483$	− 2632.29i	− 0.247978i
$484$	2448.26	0.229927
$485$	0	0
$486$	−1281.80	−0.119638
$487$	670.598i	0.0623977i	0.999513	+	0.0311989i	$0.00993252\pi$
$487$	670.598i	0.0623977i	−0.999513	+	0.0311989i	$0.990067\pi$
$488$	− 3604.88i	− 0.334396i
$489$	−7239.22	−0.669466
$490$	0	0
$491$	−8244.70	−0.757797	−0.378898	−	0.925438i	$-0.623697\pi$
$491$	−8244.70	−0.757797	−0.378898	+	0.925438i	$0.623697\pi$
$492$	20117.0i	1.84338i
$493$	373.485i	0.0341195i
$494$	11529.1	1.05004
$495$	0	0
$496$	49728.3	4.50175
$497$	− 2546.27i	− 0.229810i
$498$	− 21116.4i	− 1.90010i
$499$	−8164.91	−0.732488	−0.366244	−	0.930519i	$-0.619356\pi$
$499$	−8164.91	−0.732488	−0.366244	+	0.930519i	$0.619356\pi$
$500$	0	0
$501$	−1831.43	−0.163317
$502$	12436.8i	1.10574i
$503$	8175.59i	0.724715i	0.932039	+	0.362357i	$0.118028\pi$
$503$	8175.59i	0.724715i	−0.932039	+	0.362357i	$0.881972\pi$
$504$	3929.60	0.347298
$505$	0	0
$506$	22976.0	2.01859
$507$	2417.35i	0.211752i
$508$	− 33997.2i	− 2.96926i
$509$	878.448	0.0764961	0.0382480	−	0.999268i	$-0.487822\pi$
$509$	878.448	0.0764961	0.0382480	+	0.999268i	$0.487822\pi$
$510$	0	0
$511$	4069.09	0.352262
$512$	− 16876.5i	− 1.45673i
$513$	− 1582.15i	− 0.136167i
$514$	14677.7	1.25955
$515$	0	0
$516$	404.661	0.0345237
$517$	− 8711.42i	− 0.741060i
$518$	9596.55i	0.813992i
$519$	−11381.4	−0.962600
$520$	0	0
$521$	11712.6	0.984910	0.492455	−	0.870338i	$-0.336100\pi$
$521$	11712.6	0.984910	0.492455	+	0.870338i	$0.336100\pi$
$522$	− 1680.68i	− 0.140922i
$523$	− 7341.82i	− 0.613834i	−0.951736	−	0.306917i	$-0.900703\pi$
$523$	− 7341.82i	− 0.613834i	0.951736	−	0.306917i	$-0.0992975\pi$
$524$	−9329.75	−0.777809
$525$	0	0
$526$	−10780.8	−0.893659
$527$	3078.38i	0.254452i
$528$	17766.1i	1.46434i
$529$	−3544.92	−0.291355
$530$	0	0
$531$	−323.014	−0.0263985
$532$	8131.84i	0.662707i
$533$	12616.3i	1.02528i
$534$	−5586.74	−0.452738
$535$	0	0
$536$	−30045.3	−2.42119
$537$	8414.03i	0.676149i
$538$	− 18213.4i	− 1.45955i
$539$	−1702.71	−0.136068
$540$	0	0
$541$	−15868.7	−1.26109	−0.630545	−	0.776153i	$-0.717169\pi$
$541$	−15868.7	−1.26109	−0.630545	+	0.776153i	$0.717169\pi$
$542$	13948.4i	1.10542i
$543$	9318.13i	0.736426i
$544$	−4219.61	−0.332563
$545$	0	0
$546$	4131.73	0.323850
$547$	− 2315.26i	− 0.180975i	−0.995898	−	0.0904875i	$-0.971157\pi$
$547$	− 2315.26i	− 0.180975i	0.995898	−	0.0904875i	$-0.0288425\pi$
$548$	− 8800.41i	− 0.686013i
$549$	−520.146	−0.0404359
$550$	0	0
$551$	2074.49	0.160392
$552$	− 23455.4i	− 1.80857i
$553$	− 4855.84i	− 0.373402i
$554$	14134.1	1.08393
$555$	0	0
$556$	33106.9	2.52526
$557$	4819.05i	0.366588i	0.983058	+	0.183294i	$0.0586760\pi$
$557$	4819.05i	0.366588i	−0.983058	+	0.183294i	$0.941324\pi$
$558$	− 13852.7i	− 1.05095i
$559$	253.781	0.0192018
$560$	0	0
$561$	−1099.79	−0.0827689
$562$	− 5378.79i	− 0.403720i
$563$	2540.86i	0.190203i	0.995468	+	0.0951017i	$0.0303176\pi$
$563$	2540.86i	0.190203i	−0.995468	+	0.0951017i	$0.969682\pi$
$564$	−14909.9	−1.11315
$565$	0	0
$566$	−2279.85	−0.169310
$567$	− 567.000i	− 0.0419961i
$568$	− 22688.9i	− 1.67607i
$569$	24220.0	1.78445	0.892227	−	0.451587i	$-0.149142\pi$
$569$	24220.0	1.78445	0.892227	+	0.451587i	$0.149142\pi$
$570$	0	0
$571$	−11772.1	−0.862778	−0.431389	−	0.902166i	$-0.641976\pi$
$571$	−11772.1	−0.862778	−0.431389	+	0.902166i	$0.641976\pi$
$572$	25695.1i	1.87826i
$573$	785.855i	0.0572942i
$574$	−12489.6	−0.908198
$575$	0	0
$576$	6717.80	0.485952
$577$	− 10584.3i	− 0.763655i	−0.924234	−	0.381827i	$-0.875295\pi$
$577$	− 10584.3i	− 0.763655i	0.924234	−	0.381827i	$-0.124705\pi$
$578$	25328.6i	1.82272i
$579$	−12153.2	−0.872315
$580$	0	0
$581$	9340.74	0.666987
$582$	22880.6i	1.62961i
$583$	− 18656.8i	− 1.32536i
$584$	36258.3	2.56914
$585$	0	0
$586$	11847.0	0.835148
$587$	8712.63i	0.612621i	0.951932	+	0.306311i	$0.0990946\pi$
$587$	8712.63i	0.612621i	−0.951932	+	0.306311i	$0.900905\pi$
$588$	2914.24i	0.204390i
$589$	17098.6	1.19615
$590$	0	0
$591$	−8624.48	−0.600277
$592$	44292.4i	3.07501i
$593$	− 15362.9i	− 1.06387i	−0.846784	−	0.531937i	$-0.821464\pi$
$593$	− 15362.9i	− 1.06387i	0.846784	−	0.531937i	$-0.178536\pi$
$594$	4949.07	0.341857
$595$	0	0
$596$	14747.0	1.01353
$597$	9200.91i	0.630768i
$598$	− 24662.0i	− 1.68646i
$599$	−26003.8	−1.77377	−0.886883	−	0.461994i	$-0.847134\pi$
$599$	−26003.8	−1.77377	−0.886883	+	0.461994i	$0.847134\pi$
$600$	0	0
$601$	20567.7	1.39596	0.697982	−	0.716115i	$-0.254082\pi$
$601$	20567.7	1.39596	0.697982	+	0.716115i	$0.254082\pi$
$602$	251.233i	0.0170091i
$603$	4335.22i	0.292776i
$604$	−12029.0	−0.810349
$605$	0	0
$606$	−7514.42	−0.503717
$607$	− 19642.1i	− 1.31342i	−0.754142	−	0.656711i	$-0.771947\pi$
$607$	− 19642.1i	− 1.31342i	0.754142	−	0.656711i	$-0.228053\pi$
$608$	23437.4i	1.56334i
$609$	743.442	0.0494676
$610$	0	0
$611$	−9350.65	−0.619127
$612$	1882.33i	0.124328i
$613$	8454.59i	0.557060i	0.960428	+	0.278530i	$0.0898471\pi$
$613$	8454.59i	0.557060i	−0.960428	+	0.278530i	$0.910153\pi$
$614$	−16864.3	−1.10845
$615$	0	0
$616$	−15172.3	−0.992383
$617$	24168.4i	1.57696i	0.615061	+	0.788479i	$0.289131\pi$
$617$	24168.4i	1.57696i	−0.615061	+	0.788479i	$0.710869\pi$
$618$	31643.0i	2.05966i
$619$	2037.56	0.132305	0.0661523	−	0.997810i	$-0.478928\pi$
$619$	2037.56	0.132305	0.0661523	+	0.997810i	$0.478928\pi$
$620$	0	0
$621$	−3384.37	−0.218696
$622$	− 17700.5i	− 1.14104i
$623$	− 2471.27i	− 0.158923i
$624$	19069.8	1.22340
$625$	0	0
$626$	11902.3	0.759921
$627$	6108.70i	0.389088i
$628$	61749.8i	3.92370i
$629$	−2741.87	−0.173808
$630$	0	0
$631$	12339.5	0.778489	0.389244	−	0.921135i	$-0.372736\pi$
$631$	12339.5	0.778489	0.389244	+	0.921135i	$0.372736\pi$
$632$	− 43268.7i	− 2.72332i
$633$	1786.27i	0.112161i
$634$	−32383.7	−2.02858
$635$	0	0
$636$	−31931.7	−1.99084
$637$	1827.65i	0.113680i
$638$	6489.15i	0.402677i
$639$	−3273.77	−0.202674
$640$	0	0
$641$	−10222.6	−0.629906	−0.314953	−	0.949107i	$-0.601989\pi$
$641$	−10222.6	−0.629906	−0.314953	+	0.949107i	$0.601989\pi$
$642$	18463.3i	1.13503i
$643$	− 1211.75i	− 0.0743187i	−0.999309	−	0.0371594i	$-0.988169\pi$
$643$	− 1211.75i	− 0.0743187i	0.999309	−	0.0371594i	$-0.0118309\pi$
$644$	17394.8	1.06437
$645$	0	0
$646$	−3260.95	−0.198607
$647$	2817.22i	0.171184i	0.996330	+	0.0855922i	$0.0272782\pi$
$647$	2817.22i	0.171184i	−0.996330	+	0.0855922i	$0.972722\pi$
$648$	− 5052.34i	− 0.306288i
$649$	1247.16	0.0754320
$650$	0	0
$651$	6127.67	0.368913
$652$	− 47838.6i	− 2.87347i
$653$	20986.2i	1.25766i	0.777542	+	0.628831i	$0.216466\pi$
$653$	20986.2i	1.25766i	−0.777542	+	0.628831i	$0.783534\pi$
$654$	−21160.5	−1.26520
$655$	0	0
$656$	−57645.1	−3.43089
$657$	− 5231.69i	− 0.310666i
$658$	− 9256.74i	− 0.548428i
$659$	2384.09	0.140927	0.0704635	−	0.997514i	$-0.477552\pi$
$659$	2384.09	0.140927	0.0704635	+	0.997514i	$0.477552\pi$
$660$	0	0
$661$	−7577.10	−0.445862	−0.222931	−	0.974834i	$-0.571562\pi$
$661$	−7577.10	−0.445862	−0.222931	+	0.974834i	$0.571562\pi$
$662$	37081.7i	2.17707i
$663$	1180.50i	0.0691503i
$664$	83232.2	4.86451
$665$	0	0
$666$	12338.4	0.717874
$667$	− 4437.54i	− 0.257605i
$668$	− 12102.5i	− 0.700989i
$669$	11339.4	0.655315
$670$	0	0
$671$	2008.30	0.115543
$672$	8399.36i	0.482161i
$673$	11724.6i	0.671547i	0.941943	+	0.335774i	$0.108998\pi$
$673$	11724.6i	0.671547i	−0.941943	+	0.335774i	$0.891002\pi$
$674$	54481.7	3.11358
$675$	0	0
$676$	−15974.5	−0.908880
$677$	− 32304.3i	− 1.83390i	−0.398997	−	0.916952i	$-0.630642\pi$
$677$	− 32304.3i	− 1.83390i	0.398997	−	0.916952i	$-0.369358\pi$
$678$	− 14346.4i	− 0.812639i
$679$	−10121.1	−0.572038
$680$	0	0
$681$	5482.85	0.308522
$682$	53485.6i	3.00303i
$683$	33367.1i	1.86934i	0.355519	+	0.934669i	$0.384304\pi$
$683$	33367.1i	1.86934i	−0.355519	+	0.934669i	$0.615696\pi$
$684$	10455.2	0.584452
$685$	0	0
$686$	−1809.30	−0.100699
$687$	2550.75i	0.141655i
$688$	1159.55i	0.0642551i
$689$	−20025.8	−1.10729
$690$	0	0
$691$	−1043.67	−0.0574577	−0.0287288	−	0.999587i	$-0.509146\pi$
$691$	−1043.67	−0.0574577	−0.0287288	+	0.999587i	$0.509146\pi$
$692$	− 75211.3i	− 4.13166i
$693$	2189.20i	0.120001i
$694$	10378.6	0.567674
$695$	0	0
$696$	6624.55	0.360780
$697$	− 3568.46i	− 0.193924i
$698$	23027.4i	1.24871i
$699$	19773.3	1.06995
$700$	0	0
$701$	−11305.7	−0.609143	−0.304572	−	0.952489i	$-0.598513\pi$
$701$	−11305.7	−0.609143	−0.304572	+	0.952489i	$0.598513\pi$
$702$	− 5312.23i	− 0.285608i
$703$	15229.4i	0.817055i
$704$	−25937.6	−1.38858
$705$	0	0
$706$	32027.1	1.70730
$707$	− 3323.97i	− 0.176818i
$708$	− 2134.55i	− 0.113307i
$709$	13306.8	0.704860	0.352430	−	0.935838i	$-0.385355\pi$
$709$	13306.8	0.704860	0.352430	+	0.935838i	$0.385355\pi$
$710$	0	0
$711$	−6243.22	−0.329309
$712$	− 22020.6i	− 1.15907i
$713$	− 36575.6i	− 1.92113i
$714$	−1168.64	−0.0612538
$715$	0	0
$716$	−55602.0	−2.90216
$717$	547.669i	0.0285259i
$718$	− 50839.9i	− 2.64252i
$719$	−10701.2	−0.555062	−0.277531	−	0.960717i	$-0.589516\pi$
$719$	−10701.2	−0.555062	−0.277531	+	0.960717i	$0.589516\pi$
$720$	0	0
$721$	−13997.1	−0.722996
$722$	− 18068.0i	− 0.931333i
$723$	4571.69i	0.235163i
$724$	−61576.5	−3.16088
$725$	0	0
$726$	1954.28	0.0999037
$727$	2121.14i	0.108210i	0.998535	+	0.0541051i	$0.0172306\pi$
$727$	2121.14i	0.108210i	−0.998535	+	0.0541051i	$0.982769\pi$
$728$	16285.6i	0.829098i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−71.7808	−0.00363189
$732$	− 3437.26i	− 0.173558i
$733$	− 21584.0i	− 1.08762i	−0.839209	−	0.543809i	$-0.816981\pi$
$733$	− 21584.0i	− 1.08762i	0.839209	−	0.543809i	$-0.183019\pi$
$734$	2757.33	0.138658
$735$	0	0
$736$	50135.0	2.51087
$737$	− 16738.4i	− 0.836588i
$738$	16058.0i	0.800955i
$739$	9945.21	0.495048	0.247524	−	0.968882i	$-0.420383\pi$
$739$	9945.21	0.495048	0.247524	+	0.968882i	$0.420383\pi$
$740$	0	0
$741$	6556.94	0.325068
$742$	− 19824.7i	− 0.980848i
$743$	2867.01i	0.141562i	0.997492	+	0.0707808i	$0.0225491\pi$
$743$	2867.01i	0.141562i	−0.997492	+	0.0707808i	$0.977451\pi$
$744$	54601.6	2.69058
$745$	0	0
$746$	−17037.1	−0.836158
$747$	− 12009.5i	− 0.588227i
$748$	− 7267.71i	− 0.355259i
$749$	−8167.15	−0.398426
$750$	0	0
$751$	−10824.1	−0.525934	−0.262967	−	0.964805i	$-0.584701\pi$
$751$	−10824.1	−0.525934	−0.262967	+	0.964805i	$0.584701\pi$
$752$	− 42724.0i	− 2.07179i
$753$	7073.19i	0.342313i
$754$	6965.31	0.336421
$755$	0	0
$756$	3746.88	0.180255
$757$	14512.0i	0.696761i	0.937353	+	0.348381i	$0.113268\pi$
$757$	14512.0i	0.696761i	−0.937353	+	0.348381i	$0.886732\pi$
$758$	− 35023.9i	− 1.67827i
$759$	13067.1	0.624910
$760$	0	0
$761$	−33075.8	−1.57556	−0.787778	−	0.615959i	$-0.788769\pi$
$761$	−33075.8	−1.57556	−0.787778	+	0.615959i	$0.788769\pi$
$762$	− 27137.7i	− 1.29015i
$763$	− 9360.23i	− 0.444120i
$764$	−5193.13	−0.245917
$765$	0	0
$766$	75032.8	3.53922
$767$	− 1338.68i	− 0.0630206i
$768$	− 6242.38i	− 0.293297i
$769$	−6728.44	−0.315518	−0.157759	−	0.987478i	$-0.550427\pi$
$769$	−6728.44	−0.315518	−0.157759	+	0.987478i	$0.550427\pi$
$770$	0	0
$771$	8347.65	0.389926
$772$	− 80311.5i	− 3.74414i
$773$	− 24233.3i	− 1.12757i	−0.825922	−	0.563784i	$-0.809345\pi$
$773$	− 24233.3i	− 1.12757i	0.825922	−	0.563784i	$-0.190655\pi$
$774$	323.014	0.0150006
$775$	0	0
$776$	−90186.0	−4.17202
$777$	5457.84i	0.251993i
$778$	− 15412.4i	− 0.710231i
$779$	−19820.6	−0.911615
$780$	0	0
$781$	12640.1	0.579127
$782$	6975.51i	0.318982i
$783$	− 955.854i	− 0.0436263i
$784$	−8350.72	−0.380408
$785$	0	0
$786$	−7447.31	−0.337960
$787$	17200.4i	0.779069i	0.921012	+	0.389535i	$0.127364\pi$
$787$	17200.4i	0.779069i	−0.921012	+	0.389535i	$0.872636\pi$
$788$	− 56992.7i	− 2.57650i
$789$	−6131.35	−0.276656
$790$	0	0
$791$	6346.05	0.285258
$792$	19507.2i	0.875199i
$793$	− 2155.66i	− 0.0965318i
$794$	4282.92	0.191430
$795$	0	0
$796$	−60801.9	−2.70737
$797$	4208.87i	0.187059i	0.995617	+	0.0935295i	$0.0298149\pi$
$797$	4208.87i	0.187059i	−0.995617	+	0.0935295i	$0.970185\pi$
$798$	6491.09i	0.287948i
$799$	2644.78	0.117104
$800$	0	0
$801$	−3177.34	−0.140157
$802$	12336.1i	0.543146i
$803$	20199.7i	0.887709i
$804$	−28648.2	−1.25665
$805$	0	0
$806$	57410.2	2.50892
$807$	− 10358.5i	− 0.451842i
$808$	− 29618.7i	− 1.28958i
$809$	23632.1	1.02702	0.513511	−	0.858083i	$-0.328344\pi$
$809$	23632.1	1.02702	0.513511	+	0.858083i	$0.328344\pi$
$810$	0	0
$811$	28425.1	1.23075	0.615377	−	0.788233i	$-0.289004\pi$
$811$	28425.1	1.23075	0.615377	+	0.788233i	$0.289004\pi$
$812$	4912.85i	0.212324i
$813$	7932.88i	0.342212i
$814$	−47638.9	−2.05128
$815$	0	0
$816$	−5393.80	−0.231398
$817$	398.699i	0.0170731i
$818$	14387.7i	0.614981i
$819$	2349.84	0.100256
$820$	0	0
$821$	39409.6	1.67528	0.837640	−	0.546223i	$-0.183935\pi$
$821$	39409.6	1.67528	0.837640	+	0.546223i	$0.183935\pi$
$822$	− 7024.77i	− 0.298074i
$823$	16346.6i	0.692352i	0.938170	+	0.346176i	$0.112520\pi$
$823$	16346.6i	0.692352i	−0.938170	+	0.346176i	$0.887480\pi$
$824$	−124723.	−5.27300
$825$	0	0
$826$	1325.23	0.0558241
$827$	3738.87i	0.157211i	0.996906	+	0.0786054i	$0.0250467\pi$
$827$	3738.87i	0.157211i	−0.996906	+	0.0786054i	$0.974953\pi$
$828$	− 22364.8i	− 0.938684i
$829$	45196.2	1.89352	0.946761	−	0.321937i	$-0.104334\pi$
$829$	45196.2	1.89352	0.946761	+	0.321937i	$0.104334\pi$
$830$	0	0
$831$	8038.46	0.335561
$832$	27840.8i	1.16010i
$833$	− 516.942i	− 0.0215018i
$834$	26427.0	1.09723
$835$	0	0
$836$	−40367.8	−1.67004
$837$	− 7878.44i	− 0.325351i
$838$	− 70189.5i	− 2.89338i
$839$	−15899.7	−0.654254	−0.327127	−	0.944980i	$-0.606080\pi$
$839$	−15899.7	−0.654254	−0.327127	+	0.944980i	$0.606080\pi$
$840$	0	0
$841$	−23135.7	−0.948612
$842$	− 58063.4i	− 2.37648i
$843$	− 3059.07i	− 0.124982i
$844$	−11804.1	−0.481414
$845$	0	0
$846$	−11901.5	−0.483668
$847$	864.465i	0.0350689i
$848$	− 91500.0i	− 3.70534i
$849$	−1296.62	−0.0524144
$850$	0	0
$851$	32577.4	1.31227
$852$	− 21633.9i	− 0.869913i
$853$	33926.7i	1.36182i	0.732369	+	0.680908i	$0.238415\pi$
$853$	33926.7i	1.36182i	−0.732369	+	0.680908i	$0.761585\pi$
$854$	2134.01	0.0855086
$855$	0	0
$856$	−72774.7	−2.90583
$857$	35432.4i	1.41231i	0.708058	+	0.706154i	$0.249572\pi$
$857$	35432.4i	1.41231i	−0.708058	+	0.706154i	$0.750428\pi$
$858$	20510.6i	0.816108i
$859$	6780.17	0.269309	0.134655	−	0.990893i	$-0.457008\pi$
$859$	6780.17	0.269309	0.134655	+	0.990893i	$0.457008\pi$
$860$	0	0
$861$	−7103.20	−0.281157
$862$	− 34422.1i	− 1.36012i
$863$	− 30675.1i	− 1.20995i	−0.796243	−	0.604977i	$-0.793182\pi$
$863$	− 30675.1i	− 1.20995i	0.796243	−	0.604977i	$-0.206818\pi$
$864$	10799.2	0.425226
$865$	0	0
$866$	61802.4	2.42509
$867$	14405.1i	0.564271i
$868$	40493.2i	1.58344i
$869$	24105.2	0.940981
$870$	0	0
$871$	−17966.6	−0.698938
$872$	− 83405.8i	− 3.23908i
$873$	13012.9i	0.504490i
$874$	38744.8	1.49950
$875$	0	0
$876$	34572.3	1.33344
$877$	− 40861.3i	− 1.57330i	−0.617397	−	0.786652i	$-0.711813\pi$
$877$	− 40861.3i	− 1.57330i	0.617397	−	0.786652i	$-0.288187\pi$
$878$	77073.9i	2.96255i
$879$	6737.76	0.258543
$880$	0	0
$881$	−43839.0	−1.67647	−0.838236	−	0.545308i	$-0.816413\pi$
$881$	−43839.0	−1.67647	−0.838236	+	0.545308i	$0.816413\pi$
$882$	2326.24i	0.0888079i
$883$	44625.1i	1.70074i	0.526183	+	0.850371i	$0.323623\pi$
$883$	44625.1i	1.70074i	−0.526183	+	0.850371i	$0.676377\pi$
$884$	−7801.01	−0.296806
$885$	0	0
$886$	80388.6	3.04820
$887$	43967.5i	1.66436i	0.554509	+	0.832178i	$0.312906\pi$
$887$	43967.5i	1.66436i	−0.554509	+	0.832178i	$0.687094\pi$
$888$	48632.9i	1.83785i
$889$	12004.2	0.452878
$890$	0	0
$891$	2814.68	0.105831
$892$	74933.5i	2.81273i
$893$	− 14690.2i	− 0.550491i
$894$	11771.6	0.440380
$895$	0	0
$896$	−5162.95	−0.192502
$897$	− 14026.0i	− 0.522089i
$898$	− 56329.7i	− 2.09326i
$899$	10330.1	0.383234
$900$	0	0
$901$	5664.21	0.209436
$902$	− 62000.4i	− 2.28868i
$903$	142.883i	0.00526563i
$904$	56547.4	2.08046
$905$	0	0
$906$	−9601.89	−0.352099
$907$	13584.3i	0.497309i	0.968592	+	0.248654i	$0.0799883\pi$
$907$	13584.3i	0.497309i	−0.968592	+	0.248654i	$0.920012\pi$
$908$	36232.1i	1.32423i
$909$	−4273.67	−0.155939
$910$	0	0
$911$	−16421.6	−0.597226	−0.298613	−	0.954374i	$-0.596524\pi$
$911$	−16421.6	−0.597226	−0.298613	+	0.954374i	$0.596524\pi$
$912$	29959.3i	1.08778i
$913$	46369.0i	1.68082i
$914$	22303.6	0.807152
$915$	0	0
$916$	−16856.0	−0.608010
$917$	− 3294.28i	− 0.118633i
$918$	1502.54i	0.0540208i
$919$	29487.3	1.05843	0.529214	−	0.848488i	$-0.322487\pi$
$919$	29487.3	1.05843	0.529214	+	0.848488i	$0.322487\pi$
$920$	0	0
$921$	−9591.23	−0.343151
$922$	4800.81i	0.171482i
$923$	− 13567.6i	− 0.483839i
$924$	−14466.8	−0.515067
$925$	0	0
$926$	−23505.9	−0.834181
$927$	17996.3i	0.637622i
$928$	14159.7i	0.500878i
$929$	−3441.85	−0.121554	−0.0607769	−	0.998151i	$-0.519358\pi$
$929$	−3441.85	−0.121554	−0.0607769	+	0.998151i	$0.519358\pi$
$930$	0	0
$931$	−2871.30	−0.101077
$932$	130667.i	4.59242i
$933$	− 10066.8i	− 0.353240i
$934$	−23364.8	−0.818545
$935$	0	0
$936$	20938.6	0.731196
$937$	− 5646.60i	− 0.196869i	−0.995144	−	0.0984346i	$-0.968616\pi$
$937$	− 5646.60i	− 0.196869i	0.995144	−	0.0984346i	$-0.0313835\pi$
$938$	− 17786.2i	− 0.619125i
$939$	6769.18	0.235254
$940$	0	0
$941$	−44680.1	−1.54785	−0.773927	−	0.633275i	$-0.781710\pi$
$941$	−44680.1	−1.54785	−0.773927	+	0.633275i	$0.781710\pi$
$942$	49290.7i	1.70486i
$943$	42398.4i	1.46414i
$944$	6116.54	0.210886
$945$	0	0
$946$	−1247.16	−0.0428633
$947$	48924.6i	1.67881i	0.543505	+	0.839406i	$0.317097\pi$
$947$	48924.6i	1.67881i	−0.543505	+	0.839406i	$0.682903\pi$
$948$	− 41256.8i	− 1.41346i
$949$	21681.9	0.741647
$950$	0	0
$951$	−18417.6	−0.628002
$952$	− 4606.29i	− 0.156818i
$953$	52014.3i	1.76801i	0.467482	+	0.884003i	$0.345161\pi$
$953$	52014.3i	1.76801i	−0.467482	+	0.884003i	$0.654839\pi$
$954$	−25488.9	−0.865026
$955$	0	0
$956$	−3619.14	−0.122439
$957$	3690.57i	0.124660i
$958$	− 14521.1i	− 0.489723i
$959$	3107.37	0.104632
$960$	0	0
$961$	55352.8	1.85804
$962$	51134.5i	1.71377i
$963$	10500.6i	0.351379i
$964$	−30210.9	−1.00936
$965$	0	0
$966$	13885.1	0.462470
$967$	47117.7i	1.56691i	0.621448	+	0.783456i	$0.286545\pi$
$967$	47117.7i	1.56691i	−0.621448	+	0.783456i	$0.713455\pi$
$968$	7702.95i	0.255767i
$969$	−1854.60	−0.0614843
$970$	0	0
$971$	−8195.04	−0.270846	−0.135423	−	0.990788i	$-0.543239\pi$
$971$	−8195.04	−0.270846	−0.135423	+	0.990788i	$0.543239\pi$
$972$	− 4817.41i	− 0.158970i
$973$	11689.9i	0.385159i
$974$	−3537.35	−0.116370
$975$	0	0
$976$	9849.42	0.323025
$977$	− 4643.51i	− 0.152056i	−0.997106	−	0.0760282i	$-0.975776\pi$
$977$	− 4643.51i	− 0.152056i	0.997106	−	0.0760282i	$-0.0242239\pi$
$978$	− 38186.3i	− 1.24853i
$979$	12267.8	0.400490
$980$	0	0
$981$	−12034.6	−0.391677
$982$	− 43490.1i	− 1.41326i
$983$	43986.5i	1.42721i	0.700546	+	0.713607i	$0.252940\pi$
$983$	43986.5i	1.42721i	−0.700546	+	0.713607i	$0.747060\pi$
$984$	−63294.1	−2.05055
$985$	0	0
$986$	−1970.10	−0.0636317
$987$	− 5264.58i	− 0.169781i
$988$	43329.9i	1.39525i
$989$	852.859	0.0274210
$990$	0	0
$991$	1595.21	0.0511337	0.0255668	−	0.999673i	$-0.491861\pi$
$991$	1595.21	0.0511337	0.0255668	+	0.999673i	$0.491861\pi$
$992$	116709.i	3.73539i
$993$	21089.4i	0.673971i
$994$	13431.3	0.428588
$995$	0	0
$996$	79362.0	2.52478
$997$	− 21501.2i	− 0.682998i	−0.939882	−	0.341499i	$-0.889065\pi$
$997$	− 21501.2i	− 0.682998i	0.939882	−	0.341499i	$-0.110935\pi$
$998$	− 43069.2i	− 1.36606i
$999$	7017.22	0.222237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.g.274.4		4
5.2	odd	4		21.4.a.c.1.1	✓	2
5.3	odd	4		525.4.a.n.1.2		2
5.4	even	2	inner	525.4.d.g.274.1		4
15.2	even	4		63.4.a.e.1.2		2
15.8	even	4		1575.4.a.p.1.1		2
20.7	even	4		336.4.a.m.1.2		2
35.2	odd	12		147.4.e.l.67.2		4
35.12	even	12		147.4.e.m.67.2		4
35.17	even	12		147.4.e.m.79.2		4
35.27	even	4		147.4.a.i.1.1		2
35.32	odd	12		147.4.e.l.79.2		4
40.27	even	4		1344.4.a.bo.1.1		2
40.37	odd	4		1344.4.a.bg.1.1		2
60.47	odd	4		1008.4.a.ba.1.1		2
105.2	even	12		441.4.e.q.361.1		4
105.17	odd	12		441.4.e.p.226.1		4
105.32	even	12		441.4.e.q.226.1		4
105.47	odd	12		441.4.e.p.361.1		4
105.62	odd	4		441.4.a.r.1.2		2
140.27	odd	4		2352.4.a.bz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.1	✓	2	5.2	odd	4
63.4.a.e.1.2		2	15.2	even	4
147.4.a.i.1.1		2	35.27	even	4
147.4.e.l.67.2		4	35.2	odd	12
147.4.e.l.79.2		4	35.32	odd	12
147.4.e.m.67.2		4	35.12	even	12
147.4.e.m.79.2		4	35.17	even	12
336.4.a.m.1.2		2	20.7	even	4
441.4.a.r.1.2		2	105.62	odd	4
441.4.e.p.226.1		4	105.17	odd	12
441.4.e.p.361.1		4	105.47	odd	12
441.4.e.q.226.1		4	105.32	even	12
441.4.e.q.361.1		4	105.2	even	12
525.4.a.n.1.2		2	5.3	odd	4
525.4.d.g.274.1		4	5.4	even	2	inner
525.4.d.g.274.4		4	1.1	even	1	trivial
1008.4.a.ba.1.1		2	60.47	odd	4
1344.4.a.bg.1.1		2	40.37	odd	4
1344.4.a.bo.1.1		2	40.27	even	4
1575.4.a.p.1.1		2	15.8	even	4
2352.4.a.bz.1.1		2	140.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+5.27492i q^{2} +3.00000i q^{3} -19.8248 q^{4} -15.8248 q^{6} -7.00000i q^{7} -62.3746i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+5.27492i q^{2} +3.00000i q^{3} -19.8248 q^{4} -15.8248 q^{6} -7.00000i q^{7} -62.3746i q^{8} -9.00000 q^{9} +34.7492 q^{11} -59.4743i q^{12} -37.2990i q^{13} +36.9244 q^{14} +170.423 q^{16} +10.5498i q^{17} -47.4743i q^{18} +58.5980 q^{19} +21.0000 q^{21} +183.299i q^{22} -125.347i q^{23} +187.124 q^{24} +196.749 q^{26} -27.0000i q^{27} +138.773i q^{28} +35.4020 q^{29} +291.794 q^{31} +399.969i q^{32} +104.248i q^{33} -55.6495 q^{34} +178.423 q^{36} +259.897i q^{37} +309.100i q^{38} +111.897 q^{39} -338.248 q^{41} +110.773i q^{42} +6.80397i q^{43} -688.894 q^{44} +661.196 q^{46} -250.694i q^{47} +511.268i q^{48} -49.0000 q^{49} -31.6495 q^{51} +739.444i q^{52} -536.900i q^{53} +142.423 q^{54} -436.622 q^{56} +175.794i q^{57} +186.743i q^{58} +35.8904 q^{59} +57.7940 q^{61} +1539.19i q^{62} +63.0000i q^{63} -746.423 q^{64} -549.897 q^{66} -481.691i q^{67} -209.148i q^{68} +376.042 q^{69} +363.752 q^{71} +561.371i q^{72} +581.299i q^{73} -1370.94 q^{74} -1161.69 q^{76} -243.244i q^{77} +590.248i q^{78} +693.691 q^{79} +81.0000 q^{81} -1784.23i q^{82} +1334.39i q^{83} -416.320 q^{84} -35.8904 q^{86} +106.206i q^{87} -2167.47i q^{88} +353.038 q^{89} -261.093 q^{91} +2484.98i q^{92} +875.382i q^{93} +1322.39 q^{94} -1199.91 q^{96} -1445.88i q^{97} -258.471i q^{98} -312.743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 34 q^{4} - 18 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q - 34 * q^4 - 18 * q^6 - 36 * q^9	\( 4 q - 34 q^{4} - 18 q^{6} - 36 q^{9} - 12 q^{11} + 42 q^{14} + 274 q^{16} - 128 q^{19} + 84 q^{21} + 522 q^{24} + 636 q^{26} + 504 q^{29} + 80 q^{31} - 132 q^{34} + 306 q^{36} - 96 q^{39} - 900 q^{41} - 1608 q^{44} + 1920 q^{46} - 196 q^{49} - 36 q^{51} + 162 q^{54} - 1218 q^{56} - 1608 q^{59} - 856 q^{61} - 2578 q^{64} - 1656 q^{66} - 36 q^{69} + 1908 q^{71} - 2796 q^{74} - 3016 q^{76} + 1144 q^{79} + 324 q^{81} - 714 q^{84} + 1608 q^{86} - 732 q^{89} + 224 q^{91} + 3840 q^{94} - 1674 q^{96} + 108 q^{99}+O(q^{100}) \) 4 * q - 34 * q^4 - 18 * q^6 - 36 * q^9 - 12 * q^11 + 42 * q^14 + 274 * q^16 - 128 * q^19 + 84 * q^21 + 522 * q^24 + 636 * q^26 + 504 * q^29 + 80 * q^31 - 132 * q^34 + 306 * q^36 - 96 * q^39 - 900 * q^41 - 1608 * q^44 + 1920 * q^46 - 196 * q^49 - 36 * q^51 + 162 * q^54 - 1218 * q^56 - 1608 * q^59 - 856 * q^61 - 2578 * q^64 - 1656 * q^66 - 36 * q^69 + 1908 * q^71 - 2796 * q^74 - 3016 * q^76 + 1144 * q^79 + 324 * q^81 - 714 * q^84 + 1608 * q^86 - 732 * q^89 + 224 * q^91 + 3840 * q^94 - 1674 * q^96 + 108 * q^99

Introduction

L-functions

Modular forms

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Database

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