LMFDB - Embedded newform 175.4.b.c.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(99,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("175.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.b (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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.4.b.c.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58579i q^{2} +6.65685i q^{3} +1.31371 q^{4} +17.2132 q^{6} +7.00000i q^{7} -24.0833i q^{8} -17.3137 q^{9} +O(q^{10})$	\(q-2.58579i q^{2} +6.65685i q^{3} +1.31371 q^{4} +17.2132 q^{6} +7.00000i q^{7} -24.0833i q^{8} -17.3137 q^{9} +38.2548 q^{11} +8.74517i q^{12} +19.3431i q^{13} +18.1005 q^{14} -51.7645 q^{16} +87.2254i q^{17} +44.7696i q^{18} +44.2254 q^{19} -46.5980 q^{21} -98.9188i q^{22} +218.167i q^{23} +160.319 q^{24} +50.0172 q^{26} +64.4802i q^{27} +9.19596i q^{28} +46.9411 q^{29} +194.558 q^{31} -58.8141i q^{32} +254.657i q^{33} +225.546 q^{34} -22.7452 q^{36} -366.853i q^{37} -114.357i q^{38} -128.765 q^{39} -339.362 q^{41} +120.492i q^{42} -226.167i q^{43} +50.2557 q^{44} +564.132 q^{46} -11.6762i q^{47} -344.589i q^{48} -49.0000 q^{49} -580.647 q^{51} +25.4113i q^{52} -209.019i q^{53} +166.732 q^{54} +168.583 q^{56} +294.402i q^{57} -121.380i q^{58} +616.000 q^{59} +320.735 q^{61} -503.087i q^{62} -121.196i q^{63} -566.197 q^{64} +658.488 q^{66} -14.5097i q^{67} +114.589i q^{68} -1452.30 q^{69} -952.000 q^{71} +416.971i q^{72} +824.489i q^{73} -948.603 q^{74} +58.0993 q^{76} +267.784i q^{77} +332.958i q^{78} -156.275 q^{79} -896.706 q^{81} +877.519i q^{82} -1036.53i q^{83} -61.2162 q^{84} -584.818 q^{86} +312.480i q^{87} -921.301i q^{88} +170.225 q^{89} -135.402 q^{91} +286.607i q^{92} +1295.15i q^{93} -30.1921 q^{94} +391.517 q^{96} -1059.87i q^{97} +126.704i q^{98} -662.333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 40 q^{4} - 16 q^{6} - 24 q^{9}+O(q^{10}) $ 4 * q - 40 * q^4 - 16 * q^6 - 24 * q^9	$ 4 q - 40 q^{4} - 16 q^{6} - 24 q^{9} - 28 q^{11} + 112 q^{14} + 336 q^{16} - 72 q^{19} - 28 q^{21} + 992 q^{24} + 432 q^{26} + 52 q^{29} - 240 q^{31} + 48 q^{34} - 272 q^{36} + 28 q^{39} - 656 q^{41} + 2328 q^{44} + 1408 q^{46} - 196 q^{49} - 1508 q^{51} - 1296 q^{54} - 672 q^{56} + 2464 q^{59} + 672 q^{61} - 4256 q^{64} + 3952 q^{66} - 2664 q^{69} - 3808 q^{71} - 4032 q^{74} + 3536 q^{76} - 2028 q^{79} - 2908 q^{81} - 1512 q^{84} - 1536 q^{86} + 432 q^{89} - 700 q^{91} + 3856 q^{94} - 4928 q^{96} - 1880 q^{99}+O(q^{100}) $ 4 * q - 40 * q^4 - 16 * q^6 - 24 * q^9 - 28 * q^11 + 112 * q^14 + 336 * q^16 - 72 * q^19 - 28 * q^21 + 992 * q^24 + 432 * q^26 + 52 * q^29 - 240 * q^31 + 48 * q^34 - 272 * q^36 + 28 * q^39 - 656 * q^41 + 2328 * q^44 + 1408 * q^46 - 196 * q^49 - 1508 * q^51 - 1296 * q^54 - 672 * q^56 + 2464 * q^59 + 672 * q^61 - 4256 * q^64 + 3952 * q^66 - 2664 * q^69 - 3808 * q^71 - 4032 * q^74 + 3536 * q^76 - 2028 * q^79 - 2908 * q^81 - 1512 * q^84 - 1536 * q^86 + 432 * q^89 - 700 * q^91 + 3856 * q^94 - 4928 * q^96 - 1880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.58579i	− 0.914214i	−0.889412	−	0.457107i	$-0.848886\pi$
$2$	− 2.58579i	− 0.914214i	0.889412	−	0.457107i	$-0.151114\pi$
$3$	6.65685i	1.28111i	0.767911	+	0.640556i	$0.221296\pi$
$3$	6.65685i	1.28111i	−0.767911	+	0.640556i	$0.778704\pi$
$4$	1.31371	0.164214
$5$	0	0
$5$	0	0
$6$	17.2132	1.17121
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	− 24.0833i	− 1.06434i
$9$	−17.3137	−0.641248
$10$	0	0
$11$	38.2548	1.04857	0.524285	−	0.851543i	$-0.324333\pi$
$11$	38.2548	1.04857	0.524285	+	0.851543i	$0.324333\pi$
$12$	8.74517i	0.210376i
$13$	19.3431i	0.412679i	0.978480	+	0.206339i	$0.0661551\pi$
$13$	19.3431i	0.412679i	−0.978480	+	0.206339i	$0.933845\pi$
$14$	18.1005	0.345540
$15$	0	0
$16$	−51.7645	−0.808820
$17$	87.2254i	1.24443i	0.782847	+	0.622214i	$0.213767\pi$
$17$	87.2254i	1.24443i	−0.782847	+	0.622214i	$0.786233\pi$
$18$	44.7696i	0.586238i
$19$	44.2254	0.534000	0.267000	−	0.963697i	$-0.413968\pi$
$19$	44.2254	0.534000	0.267000	+	0.963697i	$0.413968\pi$
$20$	0	0
$21$	−46.5980	−0.484215
$22$	− 98.9188i	− 0.958617i
$23$	218.167i	1.97786i	0.148371	+	0.988932i	$0.452597\pi$
$23$	218.167i	1.97786i	−0.148371	+	0.988932i	$0.547403\pi$
$24$	160.319	1.36354
$25$	0	0
$26$	50.0172	0.377276
$27$	64.4802i	0.459601i
$28$	9.19596i	0.0620669i
$29$	46.9411	0.300578	0.150289	−	0.988642i	$-0.451980\pi$
$29$	46.9411	0.300578	0.150289	+	0.988642i	$0.451980\pi$
$30$	0	0
$31$	194.558	1.12722	0.563609	−	0.826042i	$-0.309413\pi$
$31$	194.558	1.12722	0.563609	+	0.826042i	$0.309413\pi$
$32$	− 58.8141i	− 0.324905i
$33$	254.657i	1.34334i
$34$	225.546	1.13767
$35$	0	0
$36$	−22.7452	−0.105302
$37$	− 366.853i	− 1.63001i	−0.579457	−	0.815003i	$-0.696735\pi$
$37$	− 366.853i	− 1.63001i	0.579457	−	0.815003i	$-0.303265\pi$
$38$	− 114.357i	− 0.488190i
$39$	−128.765	−0.528688
$40$	0	0
$41$	−339.362	−1.29267	−0.646336	−	0.763053i	$-0.723699\pi$
$41$	−339.362	−1.29267	−0.646336	+	0.763053i	$0.723699\pi$
$42$	120.492i	0.442676i
$43$	− 226.167i	− 0.802095i	−0.916057	−	0.401047i	$-0.868646\pi$
$43$	− 226.167i	− 0.802095i	0.916057	−	0.401047i	$-0.131354\pi$
$44$	50.2557	0.172189
$45$	0	0
$46$	564.132	1.80819
$47$	− 11.6762i	− 0.0362372i	−0.999836	−	0.0181186i	$-0.994232\pi$
$47$	− 11.6762i	− 0.0362372i	0.999836	−	0.0181186i	$-0.00576764\pi$
$48$	− 344.589i	− 1.03619i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−580.647	−1.59425
$52$	25.4113i	0.0677674i
$53$	− 209.019i	− 0.541717i	−0.962619	−	0.270859i	$-0.912692\pi$
$53$	− 209.019i	− 0.541717i	0.962619	−	0.270859i	$-0.0873076\pi$
$54$	166.732	0.420173
$55$	0	0
$56$	168.583	0.402283
$57$	294.402i	0.684114i
$58$	− 121.380i	− 0.274792i
$59$	616.000	1.35926	0.679630	−	0.733555i	$-0.262140\pi$
$59$	616.000	1.35926	0.679630	+	0.733555i	$0.262140\pi$
$60$	0	0
$61$	320.735	0.673212	0.336606	−	0.941646i	$-0.390721\pi$
$61$	320.735	0.673212	0.336606	+	0.941646i	$0.390721\pi$
$62$	− 503.087i	− 1.03052i
$63$	− 121.196i	− 0.242369i
$64$	−566.197	−1.10585
$65$	0	0
$66$	658.488	1.22810
$67$	− 14.5097i	− 0.0264573i	−0.999912	−	0.0132286i	$-0.995789\pi$
$67$	− 14.5097i	− 0.0264573i	0.999912	−	0.0132286i	$-0.00421093\pi$
$68$	114.589i	0.204352i
$69$	−1452.30	−2.53387
$70$	0	0
$71$	−952.000	−1.59129	−0.795645	−	0.605763i	$-0.792868\pi$
$71$	−952.000	−1.59129	−0.795645	+	0.605763i	$0.792868\pi$
$72$	416.971i	0.682506i
$73$	824.489i	1.32191i	0.750427	+	0.660953i	$0.229848\pi$
$73$	824.489i	1.32191i	−0.750427	+	0.660953i	$0.770152\pi$
$74$	−948.603	−1.49017
$75$	0	0
$76$	58.0993	0.0876901
$77$	267.784i	0.396322i
$78$	332.958i	0.483334i
$79$	−156.275	−0.222561	−0.111280	−	0.993789i	$-0.535495\pi$
$79$	−156.275	−0.222561	−0.111280	+	0.993789i	$0.535495\pi$
$80$	0	0
$81$	−896.706	−1.23005
$82$	877.519i	1.18178i
$83$	− 1036.53i	− 1.37077i	−0.728182	−	0.685384i	$-0.759634\pi$
$83$	− 1036.53i	− 1.37077i	0.728182	−	0.685384i	$-0.240366\pi$
$84$	−61.2162	−0.0795147
$85$	0	0
$86$	−584.818	−0.733286
$87$	312.480i	0.385074i
$88$	− 921.301i	− 1.11603i
$89$	170.225	0.202740	0.101370	−	0.994849i	$-0.467677\pi$
$89$	170.225	0.202740	0.101370	+	0.994849i	$0.467677\pi$
$90$	0	0
$91$	−135.402	−0.155978
$92$	286.607i	0.324792i
$93$	1295.15i	1.44409i
$94$	−30.1921	−0.0331285
$95$	0	0
$96$	391.517	0.416240
$97$	− 1059.87i	− 1.10942i	−0.832044	−	0.554710i	$-0.812829\pi$
$97$	− 1059.87i	− 1.10942i	0.832044	−	0.554710i	$-0.187171\pi$
$98$	126.704i	0.130602i
$99$	−662.333	−0.672394
$100$	0	0
$101$	−241.833	−0.238251	−0.119125	−	0.992879i	$-0.538009\pi$
$101$	−241.833	−0.238251	−0.119125	+	0.992879i	$0.538009\pi$
$102$	1501.43i	1.45749i
$103$	− 1679.58i	− 1.60673i	−0.595484	−	0.803367i	$-0.703040\pi$
$103$	− 1679.58i	− 1.60673i	0.595484	−	0.803367i	$-0.296960\pi$
$104$	465.846	0.439230
$105$	0	0
$106$	−540.479	−0.495245
$107$	− 1506.88i	− 1.36146i	−0.732537	−	0.680728i	$-0.761664\pi$
$107$	− 1506.88i	− 1.36146i	0.732537	−	0.680728i	$-0.238336\pi$
$108$	84.7082i	0.0754727i
$109$	1252.41	1.10054	0.550271	−	0.834986i	$-0.314524\pi$
$109$	1252.41	1.10054	0.550271	+	0.834986i	$0.314524\pi$
$110$	0	0
$111$	2442.09	2.08822
$112$	− 362.352i	− 0.305705i
$113$	1370.20i	1.14069i	0.821405	+	0.570345i	$0.193190\pi$
$113$	1370.20i	1.14069i	−0.821405	+	0.570345i	$0.806810\pi$
$114$	761.261	0.625426
$115$	0	0
$116$	61.6670	0.0493589
$117$	− 334.902i	− 0.264630i
$118$	− 1592.84i	− 1.24265i
$119$	−610.578	−0.470349
$120$	0	0
$121$	132.432	0.0994984
$122$	− 829.352i	− 0.615459i
$123$	− 2259.09i	− 1.65606i
$124$	255.593	0.185104
$125$	0	0
$126$	−313.387	−0.221577
$127$	− 1213.49i	− 0.847873i	−0.905692	−	0.423936i	$-0.860648\pi$
$127$	− 1213.49i	− 0.847873i	0.905692	−	0.423936i	$-0.139352\pi$
$128$	993.551i	0.686081i
$129$	1505.56	1.02757
$130$	0	0
$131$	−1982.42	−1.32217	−0.661087	−	0.750309i	$-0.729904\pi$
$131$	−1982.42	−1.32217	−0.661087	+	0.750309i	$0.729904\pi$
$132$	334.545i	0.220594i
$133$	309.578i	0.201833i
$134$	−37.5189	−0.0241876
$135$	0	0
$136$	2100.67	1.32449
$137$	− 2210.95i	− 1.37879i	−0.724386	−	0.689394i	$-0.757877\pi$
$137$	− 2210.95i	− 1.37879i	0.724386	−	0.689394i	$-0.242123\pi$
$138$	3755.34i	2.31649i
$139$	−528.039	−0.322213	−0.161107	−	0.986937i	$-0.551506\pi$
$139$	−528.039	−0.322213	−0.161107	+	0.986937i	$0.551506\pi$
$140$	0	0
$141$	77.7267	0.0464239
$142$	2461.67i	1.45478i
$143$	739.969i	0.432722i
$144$	896.235	0.518655
$145$	0	0
$146$	2131.95	1.20851
$147$	− 326.186i	− 0.183016i
$148$	− 481.938i	− 0.267669i
$149$	328.372	0.180545	0.0902727	−	0.995917i	$-0.471226\pi$
$149$	328.372	0.180545	0.0902727	+	0.995917i	$0.471226\pi$
$150$	0	0
$151$	1029.43	0.554793	0.277396	−	0.960756i	$-0.410528\pi$
$151$	1029.43	0.554793	0.277396	+	0.960756i	$0.410528\pi$
$152$	− 1065.09i	− 0.568358i
$153$	− 1510.20i	− 0.797987i
$154$	692.432	0.362323
$155$	0	0
$156$	−169.159	−0.0868177
$157$	− 525.098i	− 0.266926i	−0.991054	−	0.133463i	$-0.957390\pi$
$157$	− 525.098i	− 0.266926i	0.991054	−	0.133463i	$-0.0426098\pi$
$158$	404.094i	0.203468i
$159$	1391.41	0.694001
$160$	0	0
$161$	−1527.17	−0.747562
$162$	2318.69i	1.12453i
$163$	1002.63i	0.481790i	0.970551	+	0.240895i	$0.0774409\pi$
$163$	1002.63i	0.481790i	−0.970551	+	0.240895i	$0.922559\pi$
$164$	−445.823	−0.212274
$165$	0	0
$166$	−2680.24	−1.25317
$167$	359.422i	0.166544i	0.996527	+	0.0832722i	$0.0265371\pi$
$167$	359.422i	0.166544i	−0.996527	+	0.0832722i	$0.973463\pi$
$168$	1122.23i	0.515369i
$169$	1822.84	0.829696
$170$	0	0
$171$	−765.706	−0.342427
$172$	− 297.117i	− 0.131715i
$173$	3293.65i	1.44747i	0.690080	+	0.723733i	$0.257575\pi$
$173$	3293.65i	1.44747i	−0.690080	+	0.723733i	$0.742425\pi$
$174$	808.007	0.352039
$175$	0	0
$176$	−1980.24	−0.848104
$177$	4100.62i	1.74137i
$178$	− 440.167i	− 0.185348i
$179$	−2978.82	−1.24384	−0.621921	−	0.783080i	$-0.713647\pi$
$179$	−2978.82	−1.24384	−0.621921	+	0.783080i	$0.713647\pi$
$180$	0	0
$181$	1462.31	0.600514	0.300257	−	0.953858i	$-0.402928\pi$
$181$	1462.31	0.600514	0.300257	+	0.953858i	$0.402928\pi$
$182$	350.121i	0.142597i
$183$	2135.09i	0.862460i
$184$	5254.16	2.10512
$185$	0	0
$186$	3348.97	1.32021
$187$	3336.79i	1.30487i
$188$	− 15.3391i	− 0.00595064i
$189$	−451.362	−0.173713
$190$	0	0
$191$	−374.923	−0.142034	−0.0710169	−	0.997475i	$-0.522624\pi$
$191$	−374.923	−0.142034	−0.0710169	+	0.997475i	$0.522624\pi$
$192$	− 3769.09i	− 1.41672i
$193$	733.028i	0.273391i	0.990613	+	0.136696i	$0.0436482\pi$
$193$	733.028i	0.273391i	−0.990613	+	0.136696i	$0.956352\pi$
$194$	−2740.61	−1.01425
$195$	0	0
$196$	−64.3717	−0.0234591
$197$	2093.24i	0.757043i	0.925593	+	0.378521i	$0.123567\pi$
$197$	2093.24i	0.757043i	−0.925593	+	0.378521i	$0.876433\pi$
$198$	1712.65i	0.614711i
$199$	−2865.04	−1.02059	−0.510295	−	0.860000i	$-0.670464\pi$
$199$	−2865.04	−1.02059	−0.510295	+	0.860000i	$0.670464\pi$
$200$	0	0
$201$	96.5887	0.0338948
$202$	625.330i	0.217812i
$203$	328.588i	0.113608i
$204$	−762.801	−0.261798
$205$	0	0
$206$	−4343.03	−1.46890
$207$	− 3777.27i	− 1.26830i
$208$	− 1001.29i	− 0.333783i
$209$	1691.84	0.559936
$210$	0	0
$211$	5643.65	1.84135	0.920674	−	0.390331i	$-0.127640\pi$
$211$	5643.65	1.84135	0.920674	+	0.390331i	$0.127640\pi$
$212$	− 274.590i	− 0.0889573i
$213$	− 6337.33i	− 2.03862i
$214$	−3896.47	−1.24466
$215$	0	0
$216$	1552.89	0.489172
$217$	1361.91i	0.426048i
$218$	− 3238.46i	− 1.00613i
$219$	−5488.51	−1.69351
$220$	0	0
$221$	−1687.21	−0.513549
$222$	− 6314.71i	− 1.90908i
$223$	− 6369.16i	− 1.91260i	−0.292381	−	0.956302i	$-0.594448\pi$
$223$	− 6369.16i	− 1.91260i	0.292381	−	0.956302i	$-0.405552\pi$
$224$	411.699	0.122803
$225$	0	0
$226$	3543.05	1.04283
$227$	1015.67i	0.296972i	0.988914	+	0.148486i	$0.0474400\pi$
$227$	1015.67i	0.296972i	−0.988914	+	0.148486i	$0.952560\pi$
$228$	386.758i	0.112341i
$229$	−4108.35	−1.18554	−0.592768	−	0.805373i	$-0.701965\pi$
$229$	−4108.35	−1.18554	−0.592768	+	0.805373i	$0.701965\pi$
$230$	0	0
$231$	−1782.60	−0.507733
$232$	− 1130.50i	− 0.319917i
$233$	608.431i	0.171071i	0.996335	+	0.0855357i	$0.0272602\pi$
$233$	608.431i	0.171071i	−0.996335	+	0.0855357i	$0.972740\pi$
$234$	−865.984	−0.241928
$235$	0	0
$236$	809.244	0.223209
$237$	− 1040.30i	− 0.285126i
$238$	1578.82i	0.430000i
$239$	5054.44	1.36797	0.683985	−	0.729496i	$-0.260245\pi$
$239$	5054.44	1.36797	0.683985	+	0.729496i	$0.260245\pi$
$240$	0	0
$241$	4.86782	0.00130109	0.000650547	−	1.00000i	$-0.499793\pi$
$241$	4.86782	0.00130109	0.000650547		1.00000i	$0.499793\pi$
$242$	− 342.442i	− 0.0909628i
$243$	− 4228.27i	− 1.11623i
$244$	421.352	0.110551
$245$	0	0
$246$	−5841.52	−1.51399
$247$	855.458i	0.220370i
$248$	− 4685.60i	− 1.19974i
$249$	6900.02	1.75611
$250$	0	0
$251$	−547.921	−0.137787	−0.0688934	−	0.997624i	$-0.521947\pi$
$251$	−547.921	−0.137787	−0.0688934	+	0.997624i	$0.521947\pi$
$252$	− 159.216i	− 0.0398003i
$253$	8345.92i	2.07393i
$254$	−3137.83	−0.775137
$255$	0	0
$256$	−1960.46	−0.478629
$257$	1774.61i	0.430729i	0.976534	+	0.215364i	$0.0690939\pi$
$257$	1774.61i	0.430729i	−0.976534	+	0.215364i	$0.930906\pi$
$258$	− 3893.05i	− 0.939421i
$259$	2567.97	0.616084
$260$	0	0
$261$	−812.725	−0.192745
$262$	5126.11i	1.20875i
$263$	− 1199.09i	− 0.281138i	−0.990071	−	0.140569i	$-0.955107\pi$
$263$	− 1199.09i	− 0.281138i	0.990071	−	0.140569i	$-0.0448932\pi$
$264$	6132.97	1.42977
$265$	0	0
$266$	800.502	0.184519
$267$	1133.17i	0.259733i
$268$	− 19.0615i	− 0.00434464i
$269$	−3250.29	−0.736706	−0.368353	−	0.929686i	$-0.620078\pi$
$269$	−3250.29	−0.736706	−0.368353	+	0.929686i	$0.620078\pi$
$270$	0	0
$271$	−896.143	−0.200874	−0.100437	−	0.994943i	$-0.532024\pi$
$271$	−896.143	−0.200874	−0.100437	+	0.994943i	$0.532024\pi$
$272$	− 4515.18i	− 1.00652i
$273$	− 901.352i	− 0.199825i
$274$	−5717.04	−1.26051
$275$	0	0
$276$	−1907.90	−0.416095
$277$	386.562i	0.0838492i	0.999121	+	0.0419246i	$0.0133489\pi$
$277$	386.562i	0.0838492i	−0.999121	+	0.0419246i	$0.986651\pi$
$278$	1365.40i	0.294572i
$279$	−3368.53	−0.722826
$280$	0	0
$281$	−3335.10	−0.708025	−0.354013	−	0.935241i	$-0.615183\pi$
$281$	−3335.10	−0.708025	−0.354013	+	0.935241i	$0.615183\pi$
$282$	− 200.985i	− 0.0424414i
$283$	5412.26i	1.13684i	0.822739	+	0.568419i	$0.192445\pi$
$283$	5412.26i	1.13684i	−0.822739	+	0.568419i	$0.807555\pi$
$284$	−1250.65	−0.261311
$285$	0	0
$286$	1913.40	0.395601
$287$	− 2375.54i	− 0.488584i
$288$	1018.29i	0.208345i
$289$	−2695.27	−0.548600
$290$	0	0
$291$	7055.42	1.42129
$292$	1083.14i	0.217075i
$293$	282.211i	0.0562695i	0.999604	+	0.0281347i	$0.00895675\pi$
$293$	282.211i	0.0562695i	−0.999604	+	0.0281347i	$0.991043\pi$
$294$	−843.447	−0.167316
$295$	0	0
$296$	−8835.01	−1.73488
$297$	2466.68i	0.481924i
$298$	− 849.099i	− 0.165057i
$299$	−4220.03	−0.816222
$300$	0	0
$301$	1583.17	0.303163
$302$	− 2661.88i	− 0.507199i
$303$	− 1609.85i	− 0.305226i
$304$	−2289.31	−0.431910
$305$	0	0
$306$	−3905.04	−0.729531
$307$	− 1919.67i	− 0.356878i	−0.983951	−	0.178439i	$-0.942895\pi$
$307$	− 1919.67i	− 0.356878i	0.983951	−	0.178439i	$-0.0571048\pi$
$308$	351.790i	0.0650815i
$309$	11180.7	2.05841
$310$	0	0
$311$	1213.31	0.221223	0.110612	−	0.993864i	$-0.464719\pi$
$311$	1213.31	0.221223	0.110612	+	0.993864i	$0.464719\pi$
$312$	3101.07i	0.562703i
$313$	− 1434.00i	− 0.258960i	−0.991582	−	0.129480i	$-0.958669\pi$
$313$	− 1434.00i	− 0.258960i	0.991582	−	0.129480i	$-0.0413309\pi$
$314$	−1357.79	−0.244028
$315$	0	0
$316$	−205.300	−0.0365475
$317$	− 6496.95i	− 1.15112i	−0.817760	−	0.575560i	$-0.804784\pi$
$317$	− 6496.95i	− 1.15112i	0.817760	−	0.575560i	$-0.195216\pi$
$318$	− 3597.89i	− 0.634465i
$319$	1795.72	0.315176
$320$	0	0
$321$	10031.1	1.74418
$322$	3948.92i	0.683432i
$323$	3857.58i	0.664524i
$324$	−1178.01	−0.201991
$325$	0	0
$326$	2592.58	0.440459
$327$	8337.11i	1.40992i
$328$	8172.96i	1.37584i
$329$	81.7333	0.0136964
$330$	0	0
$331$	−9683.88	−1.60808	−0.804039	−	0.594576i	$-0.797320\pi$
$331$	−9683.88	−1.60808	−0.804039	+	0.594576i	$0.797320\pi$
$332$	− 1361.70i	− 0.225099i
$333$	6351.58i	1.04524i
$334$	929.389	0.152257
$335$	0	0
$336$	2412.12	0.391643
$337$	− 29.1319i	− 0.00470895i	−0.999997	−	0.00235447i	$-0.999251\pi$
$337$	− 29.1319i	− 0.00470895i	0.999997	−	0.00235447i	$-0.000749453\pi$
$338$	− 4713.48i	− 0.758520i
$339$	−9121.24	−1.46135
$340$	0	0
$341$	7442.80	1.18197
$342$	1979.95i	0.313051i
$343$	− 343.000i	− 0.0539949i
$344$	−5446.83	−0.853701
$345$	0	0
$346$	8516.68	1.32329
$347$	7848.58i	1.21422i	0.794618	+	0.607110i	$0.207671\pi$
$347$	7848.58i	1.21422i	−0.794618	+	0.607110i	$0.792329\pi$
$348$	410.508i	0.0632343i
$349$	10269.6	1.57513	0.787567	−	0.616229i	$-0.211341\pi$
$349$	10269.6	1.57513	0.787567	+	0.616229i	$0.211341\pi$
$350$	0	0
$351$	−1247.25	−0.189668
$352$	− 2249.93i	− 0.340686i
$353$	2799.93i	0.422168i	0.977468	+	0.211084i	$0.0676994\pi$
$353$	2799.93i	0.422168i	−0.977468	+	0.211084i	$0.932301\pi$
$354$	10603.3	1.59198
$355$	0	0
$356$	223.627	0.0332927
$357$	− 4064.53i	− 0.602570i
$358$	7702.60i	1.13714i
$359$	3163.29	0.465048	0.232524	−	0.972591i	$-0.425302\pi$
$359$	3163.29	0.465048	0.232524	+	0.972591i	$0.425302\pi$
$360$	0	0
$361$	−4903.11	−0.714844
$362$	− 3781.23i	− 0.548998i
$363$	881.583i	0.127469i
$364$	−177.879	−0.0256137
$365$	0	0
$366$	5520.88	0.788472
$367$	− 3182.85i	− 0.452706i	−0.974045	−	0.226353i	$-0.927320\pi$
$367$	− 3182.85i	− 0.452706i	0.974045	−	0.226353i	$-0.0726803\pi$
$368$	− 11293.3i	− 1.59974i
$369$	5875.62	0.828923
$370$	0	0
$371$	1463.14	0.204750
$372$	1701.45i	0.237139i
$373$	− 2615.14i	− 0.363021i	−0.983389	−	0.181510i	$-0.941901\pi$
$373$	− 2615.14i	− 0.363021i	0.983389	−	0.181510i	$-0.0580986\pi$
$374$	8628.23	1.19293
$375$	0	0
$376$	−281.201	−0.0385687
$377$	907.989i	0.124042i
$378$	1167.12i	0.158811i
$379$	672.434	0.0911362	0.0455681	−	0.998961i	$-0.485490\pi$
$379$	672.434	0.0911362	0.0455681	+	0.998961i	$0.485490\pi$
$380$	0	0
$381$	8078.03	1.08622
$382$	969.470i	0.129849i
$383$	1169.86i	0.156075i	0.996950	+	0.0780377i	$0.0248655\pi$
$383$	1169.86i	0.156075i	−0.996950	+	0.0780377i	$0.975135\pi$
$384$	−6613.92	−0.878946
$385$	0	0
$386$	1895.45	0.249938
$387$	3915.78i	0.514342i
$388$	− 1392.36i	− 0.182182i
$389$	1122.22	0.146269	0.0731347	−	0.997322i	$-0.476700\pi$
$389$	1122.22	0.146269	0.0731347	+	0.997322i	$0.476700\pi$
$390$	0	0
$391$	−19029.7	−2.46131
$392$	1180.08i	0.152049i
$393$	− 13196.7i	− 1.69385i
$394$	5412.68	0.692099
$395$	0	0
$396$	−870.113	−0.110416
$397$	1985.93i	0.251060i	0.992090	+	0.125530i	$0.0400631\pi$
$397$	1985.93i	0.251060i	−0.992090	+	0.125530i	$0.959937\pi$
$398$	7408.38i	0.933037i
$399$	−2060.81	−0.258571
$400$	0	0
$401$	−4172.38	−0.519597	−0.259799	−	0.965663i	$-0.583656\pi$
$401$	−4172.38	−0.519597	−0.259799	+	0.965663i	$0.583656\pi$
$402$	− 249.758i	− 0.0309870i
$403$	3763.37i	0.465178i
$404$	−317.699	−0.0391240
$405$	0	0
$406$	849.658	0.103862
$407$	− 14033.9i	− 1.70918i
$408$	13983.9i	1.69682i
$409$	11700.8	1.41459	0.707295	−	0.706919i	$-0.249915\pi$
$409$	11700.8	1.41459	0.707295	+	0.706919i	$0.249915\pi$
$410$	0	0
$411$	14718.0	1.76638
$412$	− 2206.47i	− 0.263848i
$413$	4312.00i	0.513752i
$414$	−9767.22	−1.15950
$415$	0	0
$416$	1137.65	0.134082
$417$	− 3515.08i	− 0.412791i
$418$	− 4374.72i	− 0.511901i
$419$	−2733.20	−0.318677	−0.159339	−	0.987224i	$-0.550936\pi$
$419$	−2733.20	−0.318677	−0.159339	+	0.987224i	$0.550936\pi$
$420$	0	0
$421$	13549.4	1.56854	0.784272	−	0.620417i	$-0.213037\pi$
$421$	13549.4	1.56854	0.784272	+	0.620417i	$0.213037\pi$
$422$	− 14593.3i	− 1.68339i
$423$	202.158i	0.0232370i
$424$	−5033.87	−0.576571
$425$	0	0
$426$	−16387.0	−1.86374
$427$	2245.15i	0.254450i
$428$	− 1979.60i	− 0.223569i
$429$	−4925.86	−0.554366
$430$	0	0
$431$	−6429.25	−0.718530	−0.359265	−	0.933236i	$-0.616973\pi$
$431$	−6429.25	−0.718530	−0.359265	+	0.933236i	$0.616973\pi$
$432$	− 3337.79i	− 0.371735i
$433$	8022.03i	0.890333i	0.895448	+	0.445166i	$0.146855\pi$
$433$	8022.03i	0.890333i	−0.895448	+	0.445166i	$0.853145\pi$
$434$	3521.61	0.389499
$435$	0	0
$436$	1645.30	0.180724
$437$	9648.50i	1.05618i
$438$	14192.1i	1.54823i
$439$	5569.88	0.605549	0.302774	−	0.953062i	$-0.402087\pi$
$439$	5569.88	0.605549	0.302774	+	0.953062i	$0.402087\pi$
$440$	0	0
$441$	848.372	0.0916069
$442$	4362.77i	0.469493i
$443$	− 5486.21i	− 0.588392i	−0.955745	−	0.294196i	$-0.904948\pi$
$443$	− 5486.21i	− 0.588392i	0.955745	−	0.294196i	$-0.0950519\pi$
$444$	3208.19	0.342914
$445$	0	0
$446$	−16469.3	−1.74853
$447$	2185.92i	0.231299i
$448$	− 3963.38i	− 0.417973i
$449$	7232.67	0.760203	0.380101	−	0.924945i	$-0.375889\pi$
$449$	7232.67	0.760203	0.380101	+	0.924945i	$0.375889\pi$
$450$	0	0
$451$	−12982.3	−1.35546
$452$	1800.05i	0.187317i
$453$	6852.76i	0.710752i
$454$	2626.32	0.271496
$455$	0	0
$456$	7090.16	0.728130
$457$	2900.51i	0.296893i	0.988920	+	0.148446i	$0.0474272\pi$
$457$	2900.51i	0.296893i	−0.988920	+	0.148446i	$0.952573\pi$
$458$	10623.3i	1.08383i
$459$	−5624.31	−0.571940
$460$	0	0
$461$	6073.57	0.613611	0.306805	−	0.951772i	$-0.400740\pi$
$461$	6073.57	0.613611	0.306805	+	0.951772i	$0.400740\pi$
$462$	4609.42i	0.464176i
$463$	− 18922.8i	− 1.89939i	−0.313183	−	0.949693i	$-0.601395\pi$
$463$	− 18922.8i	− 1.89939i	0.313183	−	0.949693i	$-0.398605\pi$
$464$	−2429.88	−0.243113
$465$	0	0
$466$	1573.27	0.156396
$467$	6776.71i	0.671496i	0.941952	+	0.335748i	$0.108989\pi$
$467$	6776.71i	0.671496i	−0.941952	+	0.335748i	$0.891011\pi$
$468$	− 439.963i	− 0.0434558i
$469$	101.568	0.00999991
$470$	0	0
$471$	3495.50	0.341962
$472$	− 14835.3i	− 1.44672i
$473$	− 8651.96i	− 0.841052i
$474$	−2689.99	−0.260666
$475$	0	0
$476$	−802.121	−0.0772377
$477$	3618.90i	0.347375i
$478$	− 13069.7i	− 1.25062i
$479$	−2397.32	−0.228677	−0.114338	−	0.993442i	$-0.536475\pi$
$479$	−2397.32	−0.228677	−0.114338	+	0.993442i	$0.536475\pi$
$480$	0	0
$481$	7096.09	0.672669
$482$	− 12.5871i	− 0.00118948i
$483$	− 10166.1i	− 0.957711i
$484$	173.977	0.0163390
$485$	0	0
$486$	−10933.4	−1.02047
$487$	− 5586.17i	− 0.519781i	−0.965638	−	0.259890i	$-0.916314\pi$
$487$	− 5586.17i	− 0.519781i	0.965638	−	0.259890i	$-0.0836865\pi$
$488$	− 7724.35i	− 0.716526i
$489$	−6674.33	−0.617227
$490$	0	0
$491$	537.392	0.0493934	0.0246967	−	0.999695i	$-0.492138\pi$
$491$	537.392	0.0493934	0.0246967	+	0.999695i	$0.492138\pi$
$492$	− 2967.78i	− 0.271947i
$493$	4094.46i	0.374047i
$494$	2212.03	0.201466
$495$	0	0
$496$	−10071.2	−0.911716
$497$	− 6664.00i	− 0.601451i
$498$	− 17842.0i	− 1.60546i
$499$	−598.965	−0.0537342	−0.0268671	−	0.999639i	$-0.508553\pi$
$499$	−598.965	−0.0537342	−0.0268671	+	0.999639i	$0.508553\pi$
$500$	0	0
$501$	−2392.62	−0.213362
$502$	1416.81i	0.125966i
$503$	4426.76i	0.392405i	0.980563	+	0.196202i	$0.0628610\pi$
$503$	4426.76i	0.392405i	−0.980563	+	0.196202i	$0.937139\pi$
$504$	−2918.79	−0.257963
$505$	0	0
$506$	21580.8	1.89601
$507$	12134.4i	1.06293i
$508$	− 1594.17i	− 0.139232i
$509$	−17727.7	−1.54374	−0.771872	−	0.635779i	$-0.780679\pi$
$509$	−17727.7	−1.54374	−0.771872	+	0.635779i	$0.780679\pi$
$510$	0	0
$511$	−5771.43	−0.499634
$512$	13017.7i	1.12365i
$513$	2851.66i	0.245427i
$514$	4588.77	0.393778
$515$	0	0
$516$	1977.86	0.168741
$517$	− 446.671i	− 0.0379972i
$518$	− 6640.22i	− 0.563233i
$519$	−21925.4	−1.85437
$520$	0	0
$521$	8662.79	0.728453	0.364226	−	0.931310i	$-0.381333\pi$
$521$	8662.79	0.728453	0.364226	+	0.931310i	$0.381333\pi$
$522$	2101.53i	0.176210i
$523$	− 7770.40i	− 0.649667i	−0.945771	−	0.324833i	$-0.894692\pi$
$523$	− 7770.40i	− 0.649667i	0.945771	−	0.324833i	$-0.105308\pi$
$524$	−2604.32	−0.217119
$525$	0	0
$526$	−3100.60	−0.257020
$527$	16970.4i	1.40274i
$528$	− 13182.2i	− 1.08652i
$529$	−35429.6	−2.91194
$530$	0	0
$531$	−10665.2	−0.871624
$532$	406.695i	0.0331437i
$533$	− 6564.34i	− 0.533458i
$534$	2930.12	0.237451
$535$	0	0
$536$	−349.440	−0.0281595
$537$	− 19829.6i	− 1.59350i
$538$	8404.56i	0.673506i
$539$	−1874.49	−0.149796
$540$	0	0
$541$	21641.0	1.71981	0.859906	−	0.510453i	$-0.170522\pi$
$541$	21641.0	1.71981	0.859906	+	0.510453i	$0.170522\pi$
$542$	2317.23i	0.183642i
$543$	9734.41i	0.769325i
$544$	5130.09	0.404321
$545$	0	0
$546$	−2330.70	−0.182683
$547$	− 7489.29i	− 0.585409i	−0.956203	−	0.292705i	$-0.905445\pi$
$547$	− 7489.29i	− 0.585409i	0.956203	−	0.292705i	$-0.0945552\pi$
$548$	− 2904.54i	− 0.226416i
$549$	−5553.11	−0.431696
$550$	0	0
$551$	2075.99	0.160508
$552$	34976.2i	2.69689i
$553$	− 1093.93i	− 0.0841201i
$554$	999.566	0.0766561
$555$	0	0
$556$	−693.689	−0.0529118
$557$	− 25297.9i	− 1.92443i	−0.272295	−	0.962214i	$-0.587783\pi$
$557$	− 25297.9i	− 1.92443i	0.272295	−	0.962214i	$-0.412217\pi$
$558$	8710.29i	0.660817i
$559$	4374.77	0.331007
$560$	0	0
$561$	−22212.5	−1.67168
$562$	8623.85i	0.647286i
$563$	15661.3i	1.17237i	0.810177	+	0.586186i	$0.199371\pi$
$563$	15661.3i	1.17237i	−0.810177	+	0.586186i	$0.800629\pi$
$564$	102.110	0.00762343
$565$	0	0
$566$	13994.9	1.03931
$567$	− 6276.94i	− 0.464915i
$568$	22927.3i	1.69367i
$569$	9982.75	0.735498	0.367749	−	0.929925i	$-0.380129\pi$
$569$	9982.75	0.735498	0.367749	+	0.929925i	$0.380129\pi$
$570$	0	0
$571$	−11583.6	−0.848966	−0.424483	−	0.905436i	$-0.639544\pi$
$571$	−11583.6	−0.848966	−0.424483	+	0.905436i	$0.639544\pi$
$572$	972.103i	0.0710589i
$573$	− 2495.81i	− 0.181961i
$574$	−6142.63	−0.446670
$575$	0	0
$576$	9802.97	0.709127
$577$	595.378i	0.0429565i	0.999769	+	0.0214783i	$0.00683727\pi$
$577$	595.378i	0.0429565i	−0.999769	+	0.0214783i	$0.993163\pi$
$578$	6969.39i	0.501537i
$579$	−4879.66	−0.350245
$580$	0	0
$581$	7255.70	0.518102
$582$	− 18243.8i	− 1.29936i
$583$	− 7996.00i	− 0.568028i
$584$	19856.4	1.40696
$585$	0	0
$586$	729.738	0.0514423
$587$	15750.3i	1.10747i	0.832693	+	0.553736i	$0.186798\pi$
$587$	15750.3i	1.10747i	−0.832693	+	0.553736i	$0.813202\pi$
$588$	− 428.513i	− 0.0300537i
$589$	8604.42	0.601934
$590$	0	0
$591$	−13934.4	−0.969856
$592$	18990.0i	1.31838i
$593$	− 417.878i	− 0.0289379i	−0.999895	−	0.0144690i	$-0.995394\pi$
$593$	− 417.878i	− 0.0289379i	0.999895	−	0.0144690i	$-0.00460577\pi$
$594$	6378.31	0.440581
$595$	0	0
$596$	431.385	0.0296480
$597$	− 19072.2i	− 1.30749i
$598$	10912.1i	0.746201i
$599$	19997.3	1.36406	0.682028	−	0.731326i	$-0.261098\pi$
$599$	19997.3	1.36406	0.682028	+	0.731326i	$0.261098\pi$
$600$	0	0
$601$	−15992.6	−1.08545	−0.542723	−	0.839912i	$-0.682607\pi$
$601$	−15992.6	−1.08545	−0.542723	+	0.839912i	$0.682607\pi$
$602$	− 4093.73i	− 0.277156i
$603$	251.216i	0.0169657i
$604$	1352.37	0.0911045
$605$	0	0
$606$	−4162.73	−0.279042
$607$	− 14159.2i	− 0.946793i	−0.880850	−	0.473396i	$-0.843028\pi$
$607$	− 14159.2i	− 0.946793i	0.880850	−	0.473396i	$-0.156972\pi$
$608$	− 2601.08i	− 0.173499i
$609$	−2187.36	−0.145544
$610$	0	0
$611$	225.854	0.0149543
$612$	− 1983.96i	− 0.131040i
$613$	− 4629.41i	− 0.305025i	−0.988302	−	0.152512i	$-0.951264\pi$
$613$	− 4629.41i	− 0.305025i	0.988302	−	0.152512i	$-0.0487364\pi$
$614$	−4963.87	−0.326263
$615$	0	0
$616$	6449.11	0.421821
$617$	23165.3i	1.51151i	0.654857	+	0.755753i	$0.272729\pi$
$617$	23165.3i	1.51151i	−0.654857	+	0.755753i	$0.727271\pi$
$618$	− 28910.9i	− 1.88182i
$619$	−12370.6	−0.803258	−0.401629	−	0.915803i	$-0.631556\pi$
$619$	−12370.6	−0.803258	−0.401629	+	0.915803i	$0.631556\pi$
$620$	0	0
$621$	−14067.4	−0.909028
$622$	− 3137.36i	− 0.202245i
$623$	1191.58i	0.0766285i
$624$	6665.43	0.427613
$625$	0	0
$626$	−3708.02	−0.236745
$627$	11262.3i	0.717341i
$628$	− 689.826i	− 0.0438329i
$629$	31998.9	2.02842
$630$	0	0
$631$	13980.2	0.882002	0.441001	−	0.897507i	$-0.354623\pi$
$631$	13980.2	0.882002	0.441001	+	0.897507i	$0.354623\pi$
$632$	3763.61i	0.236880i
$633$	37568.9i	2.35897i
$634$	−16799.7	−1.05237
$635$	0	0
$636$	1827.91	0.113964
$637$	− 947.814i	− 0.0589541i
$638$	− 4643.36i	− 0.288139i
$639$	16482.7	1.02041
$640$	0	0
$641$	−16060.9	−0.989655	−0.494828	−	0.868991i	$-0.664769\pi$
$641$	−16060.9	−0.989655	−0.494828	+	0.868991i	$0.664769\pi$
$642$	− 25938.3i	− 1.59455i
$643$	− 4502.17i	− 0.276125i	−0.990424	−	0.138063i	$-0.955913\pi$
$643$	− 4502.17i	− 0.276125i	0.990424	−	0.138063i	$-0.0440875\pi$
$644$	−2006.25	−0.122760
$645$	0	0
$646$	9974.87	0.607517
$647$	− 29414.8i	− 1.78735i	−0.448715	−	0.893675i	$-0.648118\pi$
$647$	− 29414.8i	− 1.78735i	0.448715	−	0.893675i	$-0.351882\pi$
$648$	21595.6i	1.30919i
$649$	23565.0	1.42528
$650$	0	0
$651$	−9066.03	−0.545815
$652$	1317.16i	0.0791164i
$653$	13013.6i	0.779882i	0.920840	+	0.389941i	$0.127505\pi$
$653$	13013.6i	0.779882i	−0.920840	+	0.389941i	$0.872495\pi$
$654$	21558.0	1.28897
$655$	0	0
$656$	17566.9	1.04554
$657$	− 14275.0i	− 0.847671i
$658$	− 211.345i	− 0.0125214i
$659$	−23474.2	−1.38759	−0.693797	−	0.720171i	$-0.744063\pi$
$659$	−23474.2	−1.38759	−0.693797	+	0.720171i	$0.744063\pi$
$660$	0	0
$661$	−9266.36	−0.545264	−0.272632	−	0.962118i	$-0.587894\pi$
$661$	−9266.36	−0.545264	−0.272632	+	0.962118i	$0.587894\pi$
$662$	25040.4i	1.47013i
$663$	− 11231.5i	− 0.657914i
$664$	−24963.0	−1.45896
$665$	0	0
$666$	16423.8	0.955572
$667$	10241.0i	0.594501i
$668$	472.176i	0.0273489i
$669$	42398.6	2.45026
$670$	0	0
$671$	12269.7	0.705909
$672$	2740.62i	0.157324i
$673$	− 25067.2i	− 1.43576i	−0.696164	−	0.717882i	$-0.745112\pi$
$673$	− 25067.2i	− 1.43576i	0.696164	−	0.717882i	$-0.254888\pi$
$674$	−75.3288	−0.00430498
$675$	0	0
$676$	2394.68	0.136247
$677$	22409.6i	1.27219i	0.771613	+	0.636093i	$0.219450\pi$
$677$	22409.6i	1.27219i	−0.771613	+	0.636093i	$0.780550\pi$
$678$	23585.6i	1.33599i
$679$	7419.11	0.419322
$680$	0	0
$681$	−6761.20	−0.380455
$682$	− 19245.5i	− 1.08057i
$683$	− 8757.53i	− 0.490626i	−0.969444	−	0.245313i	$-0.921109\pi$
$683$	− 8757.53i	− 0.490626i	0.969444	−	0.245313i	$-0.0788908\pi$
$684$	−1005.91	−0.0562311
$685$	0	0
$686$	−886.925	−0.0493629
$687$	− 27348.7i	− 1.51880i
$688$	11707.4i	0.648750i
$689$	4043.09	0.223555
$690$	0	0
$691$	8468.42	0.466214	0.233107	−	0.972451i	$-0.425111\pi$
$691$	8468.42	0.466214	0.233107	+	0.972451i	$0.425111\pi$
$692$	4326.90i	0.237694i
$693$	− 4636.33i	− 0.254141i
$694$	20294.8	1.11006
$695$	0	0
$696$	7525.54	0.409849
$697$	− 29601.0i	− 1.60864i
$698$	− 26555.1i	− 1.44001i
$699$	−4050.23	−0.219162
$700$	0	0
$701$	15996.9	0.861906	0.430953	−	0.902374i	$-0.358177\pi$
$701$	15996.9	0.861906	0.430953	+	0.902374i	$0.358177\pi$
$702$	3225.12i	0.173397i
$703$	− 16224.2i	− 0.870423i
$704$	−21659.8	−1.15956
$705$	0	0
$706$	7240.03	0.385952
$707$	− 1692.83i	− 0.0900503i
$708$	5387.02i	0.285956i
$709$	−19903.0	−1.05426	−0.527131	−	0.849784i	$-0.676732\pi$
$709$	−19903.0	−1.05426	−0.527131	+	0.849784i	$0.676732\pi$
$710$	0	0
$711$	2705.70	0.142717
$712$	− 4099.58i	− 0.215784i
$713$	42446.1i	2.22948i
$714$	−10510.0	−0.550878
$715$	0	0
$716$	−3913.30	−0.204256
$717$	33646.7i	1.75252i
$718$	− 8179.59i	− 0.425153i
$719$	11073.1	0.574347	0.287174	−	0.957879i	$-0.407284\pi$
$719$	11073.1	0.574347	0.287174	+	0.957879i	$0.407284\pi$
$720$	0	0
$721$	11757.0	0.607288
$722$	12678.4i	0.653520i
$723$	32.4043i	0.00166685i
$724$	1921.06	0.0986125
$725$	0	0
$726$	2279.58	0.116533
$727$	− 31652.7i	− 1.61476i	−0.590029	−	0.807382i	$-0.700884\pi$
$727$	− 31652.7i	− 1.61476i	0.590029	−	0.807382i	$-0.299116\pi$
$728$	3260.92i	0.166013i
$729$	3935.94	0.199967
$730$	0	0
$731$	19727.5	0.998149
$732$	2804.88i	0.141628i
$733$	16958.3i	0.854528i	0.904127	+	0.427264i	$0.140523\pi$
$733$	16958.3i	0.854528i	−0.904127	+	0.427264i	$0.859477\pi$
$734$	−8230.16	−0.413870
$735$	0	0
$736$	12831.3	0.642618
$737$	− 555.065i	− 0.0277423i
$738$	− 15193.1i	− 0.757813i
$739$	11616.6	0.578245	0.289123	−	0.957292i	$-0.406636\pi$
$739$	11616.6	0.578245	0.289123	+	0.957292i	$0.406636\pi$
$740$	0	0
$741$	−5694.66	−0.282319
$742$	− 3783.36i	− 0.187185i
$743$	15928.0i	0.786464i	0.919439	+	0.393232i	$0.128643\pi$
$743$	15928.0i	0.786464i	−0.919439	+	0.393232i	$0.871357\pi$
$744$	31191.4	1.53700
$745$	0	0
$746$	−6762.19	−0.331879
$747$	17946.1i	0.879003i
$748$	4383.57i	0.214277i
$749$	10548.2	0.514582
$750$	0	0
$751$	25571.9	1.24252	0.621260	−	0.783604i	$-0.286621\pi$
$751$	25571.9	1.24252	0.621260	+	0.783604i	$0.286621\pi$
$752$	604.412i	0.0293094i
$753$	− 3647.43i	− 0.176520i
$754$	2347.87	0.113401
$755$	0	0
$756$	−592.958	−0.0285260
$757$	− 6202.41i	− 0.297794i	−0.988853	−	0.148897i	$-0.952428\pi$
$757$	− 6202.41i	− 0.297794i	0.988853	−	0.148897i	$-0.0475723\pi$
$758$	− 1738.77i	− 0.0833179i
$759$	−55557.6	−2.65693
$760$	0	0
$761$	−29199.1	−1.39089	−0.695444	−	0.718580i	$-0.744792\pi$
$761$	−29199.1	−1.39089	−0.695444	+	0.718580i	$0.744792\pi$
$762$	− 20888.1i	− 0.993037i
$763$	8766.87i	0.415966i
$764$	−492.539	−0.0233239
$765$	0	0
$766$	3025.00	0.142686
$767$	11915.4i	0.560938i
$768$	− 13050.5i	− 0.613177i
$769$	−21838.2	−1.02407	−0.512033	−	0.858966i	$-0.671108\pi$
$769$	−21838.2	−1.02407	−0.512033	+	0.858966i	$0.671108\pi$
$770$	0	0
$771$	−11813.3	−0.551812
$772$	962.985i	0.0448945i
$773$	− 25544.8i	− 1.18859i	−0.804246	−	0.594296i	$-0.797431\pi$
$773$	− 25544.8i	− 1.18859i	0.804246	−	0.594296i	$-0.202569\pi$
$774$	10125.4	0.470218
$775$	0	0
$776$	−25525.2	−1.18080
$777$	17094.6i	0.789273i
$778$	− 2901.82i	− 0.133721i
$779$	−15008.4	−0.690286
$780$	0	0
$781$	−36418.6	−1.66858
$782$	49206.6i	2.25016i
$783$	3026.77i	0.138146i
$784$	2536.46	0.115546
$785$	0	0
$786$	−34123.8	−1.54854
$787$	37223.2i	1.68598i	0.537931	+	0.842989i	$0.319206\pi$
$787$	37223.2i	1.68598i	−0.537931	+	0.842989i	$0.680794\pi$
$788$	2749.91i	0.124317i
$789$	7982.19	0.360169
$790$	0	0
$791$	−9591.42	−0.431140
$792$	15951.1i	0.715655i
$793$	6204.03i	0.277820i
$794$	5135.18	0.229522
$795$	0	0
$796$	−3763.83	−0.167595
$797$	40384.6i	1.79485i	0.441168	+	0.897425i	$0.354564\pi$
$797$	40384.6i	1.79485i	−0.441168	+	0.897425i	$0.645436\pi$
$798$	5328.83i	0.236389i
$799$	1018.46	0.0450945
$800$	0	0
$801$	−2947.23	−0.130007
$802$	10788.9i	0.475023i
$803$	31540.7i	1.38611i
$804$	126.889	0.00556598
$805$	0	0
$806$	9731.28	0.425272
$807$	− 21636.7i	− 0.943803i
$808$	5824.14i	0.253580i
$809$	1955.76	0.0849948	0.0424974	−	0.999097i	$-0.486469\pi$
$809$	1955.76	0.0849948	0.0424974	+	0.999097i	$0.486469\pi$
$810$	0	0
$811$	−34301.8	−1.48520	−0.742600	−	0.669735i	$-0.766408\pi$
$811$	−34301.8	−1.48520	−0.742600	+	0.669735i	$0.766408\pi$
$812$	431.669i	0.0186559i
$813$	− 5965.49i	− 0.257342i
$814$	−36288.7	−1.56255
$815$	0	0
$816$	30056.9	1.28946
$817$	− 10002.3i	− 0.428319i
$818$	− 30255.8i	− 1.29324i
$819$	2344.31	0.100021
$820$	0	0
$821$	−13665.6	−0.580918	−0.290459	−	0.956887i	$-0.593808\pi$
$821$	−13665.6	−0.580918	−0.290459	+	0.956887i	$0.593808\pi$
$822$	− 38057.5i	− 1.61485i
$823$	− 21519.5i	− 0.911449i	−0.890121	−	0.455724i	$-0.849380\pi$
$823$	− 21519.5i	− 0.911449i	0.890121	−	0.455724i	$-0.150620\pi$
$824$	−40449.7	−1.71011
$825$	0	0
$826$	11149.9	0.469679
$827$	− 35220.6i	− 1.48094i	−0.672088	−	0.740471i	$-0.734602\pi$
$827$	− 35220.6i	− 1.48094i	0.672088	−	0.740471i	$-0.265398\pi$
$828$	− 4962.23i	− 0.208272i
$829$	−31365.5	−1.31408	−0.657039	−	0.753857i	$-0.728191\pi$
$829$	−31365.5	−1.31408	−0.657039	+	0.753857i	$0.728191\pi$
$830$	0	0
$831$	−2573.28	−0.107420
$832$	− 10952.0i	− 0.456362i
$833$	− 4274.04i	− 0.177775i
$834$	−9089.24	−0.377380
$835$	0	0
$836$	2222.58	0.0919491
$837$	12545.2i	0.518070i
$838$	7067.48i	0.291339i
$839$	28287.1	1.16398	0.581990	−	0.813196i	$-0.302274\pi$
$839$	28287.1	1.16398	0.581990	+	0.813196i	$0.302274\pi$
$840$	0	0
$841$	−22185.5	−0.909653
$842$	− 35035.8i	− 1.43398i
$843$	− 22201.2i	− 0.907060i
$844$	7414.11	0.302374
$845$	0	0
$846$	522.738	0.0212436
$847$	927.026i	0.0376068i
$848$	10819.8i	0.438152i
$849$	−36028.6	−1.45642
$850$	0	0
$851$	80035.0	3.22393
$852$	− 8325.40i	− 0.334769i
$853$	9405.41i	0.377533i	0.982022	+	0.188766i	$0.0604489\pi$
$853$	9405.41i	0.377533i	−0.982022	+	0.188766i	$0.939551\pi$
$854$	5805.47	0.232622
$855$	0	0
$856$	−36290.6	−1.44905
$857$	27966.9i	1.11474i	0.830265	+	0.557369i	$0.188189\pi$
$857$	27966.9i	1.11474i	−0.830265	+	0.557369i	$0.811811\pi$
$858$	12737.2i	0.506809i
$859$	−6281.11	−0.249486	−0.124743	−	0.992189i	$-0.539811\pi$
$859$	−6281.11	−0.249486	−0.124743	+	0.992189i	$0.539811\pi$
$860$	0	0
$861$	15813.6	0.625931
$862$	16624.7i	0.656890i
$863$	− 4757.13i	− 0.187642i	−0.995589	−	0.0938208i	$-0.970092\pi$
$863$	− 4757.13i	− 0.187642i	0.995589	−	0.0938208i	$-0.0299081\pi$
$864$	3792.35	0.149327
$865$	0	0
$866$	20743.3	0.813954
$867$	− 17942.0i	− 0.702818i
$868$	1789.15i	0.0699629i
$869$	−5978.28	−0.233371
$870$	0	0
$871$	280.663	0.0109184
$872$	− 30162.1i	− 1.17135i
$873$	18350.3i	0.711414i
$874$	24949.0	0.965574
$875$	0	0
$876$	−7210.30	−0.278097
$877$	30240.5i	1.16437i	0.813057	+	0.582184i	$0.197802\pi$
$877$	30240.5i	1.16437i	−0.813057	+	0.582184i	$0.802198\pi$
$878$	− 14402.5i	− 0.553601i
$879$	−1878.64	−0.0720875
$880$	0	0
$881$	44875.5	1.71611	0.858056	−	0.513556i	$-0.171672\pi$
$881$	44875.5	1.71611	0.858056	+	0.513556i	$0.171672\pi$
$882$	− 2193.71i	− 0.0837483i
$883$	4892.13i	0.186448i	0.995645	+	0.0932238i	$0.0297172\pi$
$883$	4892.13i	0.186448i	−0.995645	+	0.0932238i	$0.970283\pi$
$884$	−2216.51	−0.0843317
$885$	0	0
$886$	−14186.2	−0.537916
$887$	− 1761.40i	− 0.0666765i	−0.999444	−	0.0333382i	$-0.989386\pi$
$887$	− 1761.40i	− 0.0666765i	0.999444	−	0.0333382i	$-0.0106139\pi$
$888$	− 58813.4i	− 2.22258i
$889$	8494.43	0.320466
$890$	0	0
$891$	−34303.3	−1.28979
$892$	− 8367.22i	− 0.314075i
$893$	− 516.384i	− 0.0193507i
$894$	5652.33	0.211457
$895$	0	0
$896$	−6954.86	−0.259314
$897$	− 28092.1i	− 1.04567i
$898$	− 18702.2i	− 0.694988i
$899$	9132.79	0.338816
$900$	0	0
$901$	18231.8	0.674128
$902$	33569.3i	1.23918i
$903$	10538.9i	0.388386i
$904$	32999.0	1.21408
$905$	0	0
$906$	17719.8	0.649779
$907$	− 23689.1i	− 0.867238i	−0.901096	−	0.433619i	$-0.857236\pi$
$907$	− 23689.1i	− 0.867238i	0.901096	−	0.433619i	$-0.142764\pi$
$908$	1334.30i	0.0487669i
$909$	4187.03	0.152778
$910$	0	0
$911$	−13877.3	−0.504692	−0.252346	−	0.967637i	$-0.581202\pi$
$911$	−13877.3	−0.504692	−0.252346	+	0.967637i	$0.581202\pi$
$912$	− 15239.6i	− 0.553325i
$913$	− 39652.2i	− 1.43735i
$914$	7500.09	0.271423
$915$	0	0
$916$	−5397.18	−0.194681
$917$	− 13876.9i	− 0.499735i
$918$	14543.3i	0.522875i
$919$	−14331.6	−0.514426	−0.257213	−	0.966355i	$-0.582804\pi$
$919$	−14331.6	−0.514426	−0.257213	+	0.966355i	$0.582804\pi$
$920$	0	0
$921$	12779.0	0.457201
$922$	− 15705.0i	− 0.560971i
$923$	− 18414.7i	− 0.656692i
$924$	−2341.81	−0.0833767
$925$	0	0
$926$	−48930.2	−1.73644
$927$	29079.7i	1.03032i
$928$	− 2760.80i	− 0.0976592i
$929$	−16668.4	−0.588668	−0.294334	−	0.955703i	$-0.595098\pi$
$929$	−16668.4	−0.588668	−0.294334	+	0.955703i	$0.595098\pi$
$930$	0	0
$931$	−2167.04	−0.0762857
$932$	799.300i	0.0280922i
$933$	8076.82i	0.283412i
$934$	17523.1	0.613891
$935$	0	0
$936$	−8065.52	−0.281656
$937$	− 30384.9i	− 1.05937i	−0.848194	−	0.529685i	$-0.822310\pi$
$937$	− 30384.9i	− 1.05937i	0.848194	−	0.529685i	$-0.177690\pi$
$938$	− 262.632i	− 0.00914206i
$939$	9545.94	0.331757
$940$	0	0
$941$	−1196.35	−0.0414452	−0.0207226	−	0.999785i	$-0.506597\pi$
$941$	−1196.35	−0.0414452	−0.0207226	+	0.999785i	$0.506597\pi$
$942$	− 9038.63i	− 0.312627i
$943$	− 74037.5i	− 2.55673i
$944$	−31886.9	−1.09940
$945$	0	0
$946$	−22372.1	−0.768901
$947$	− 1788.41i	− 0.0613681i	−0.999529	−	0.0306840i	$-0.990231\pi$
$947$	− 1788.41i	− 0.0613681i	0.999529	−	0.0306840i	$-0.00976856\pi$
$948$	− 1366.65i	− 0.0468215i
$949$	−15948.2	−0.545523
$950$	0	0
$951$	43249.2	1.47471
$952$	14704.7i	0.500612i
$953$	8578.60i	0.291593i	0.989315	+	0.145796i	$0.0465744\pi$
$953$	8578.60i	0.291593i	−0.989315	+	0.145796i	$0.953426\pi$
$954$	9357.70	0.317575
$955$	0	0
$956$	6640.06	0.224639
$957$	11953.9i	0.403776i
$958$	6198.95i	0.209059i
$959$	15476.6	0.521133
$960$	0	0
$961$	8061.99	0.270618
$962$	− 18349.0i	− 0.614963i
$963$	26089.7i	0.873031i
$964$	6.39489	0.000213657 0
$965$	0	0
$966$	−26287.4	−0.875552
$967$	55459.3i	1.84431i	0.386818	+	0.922156i	$0.373574\pi$
$967$	55459.3i	1.84431i	−0.386818	+	0.922156i	$0.626426\pi$
$968$	− 3189.40i	− 0.105900i
$969$	−25679.3	−0.851330
$970$	0	0
$971$	22047.3	0.728662	0.364331	−	0.931270i	$-0.381298\pi$
$971$	22047.3	0.728662	0.364331	+	0.931270i	$0.381298\pi$
$972$	− 5554.72i	− 0.183300i
$973$	− 3696.27i	− 0.121785i
$974$	−14444.6	−0.475191
$975$	0	0
$976$	−16602.7	−0.544507
$977$	− 14402.3i	− 0.471617i	−0.971800	−	0.235809i	$-0.924226\pi$
$977$	− 14402.3i	− 0.471617i	0.971800	−	0.235809i	$-0.0757738\pi$
$978$	17258.4i	0.564277i
$979$	6511.94	0.212587
$980$	0	0
$981$	−21683.9	−0.705721
$982$	− 1389.58i	− 0.0451561i
$983$	7817.11i	0.253639i	0.991926	+	0.126819i	$0.0404769\pi$
$983$	7817.11i	0.253639i	−0.991926	+	0.126819i	$0.959523\pi$
$984$	−54406.2	−1.76261
$985$	0	0
$986$	10587.4	0.341959
$987$	544.087i	0.0175466i
$988$	1123.82i	0.0361878i
$989$	49342.0	1.58643
$990$	0	0
$991$	24501.6	0.785386	0.392693	−	0.919670i	$-0.371543\pi$
$991$	24501.6	0.785386	0.392693	+	0.919670i	$0.371543\pi$
$992$	− 11442.8i	− 0.366239i
$993$	− 64464.2i	− 2.06013i
$994$	−17231.7	−0.549855
$995$	0	0
$996$	9064.61	0.288377
$997$	50696.0i	1.61039i	0.593010	+	0.805195i	$0.297940\pi$
$997$	50696.0i	1.61039i	−0.593010	+	0.805195i	$0.702060\pi$
$998$	1548.80i	0.0491245i
$999$	23654.8	0.749152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.b.c.99.2		4
5.2	odd	4		35.4.a.b.1.1	✓	2
5.3	odd	4		175.4.a.c.1.2		2
5.4	even	2	inner	175.4.b.c.99.3		4
15.2	even	4		315.4.a.f.1.2		2
15.8	even	4		1575.4.a.z.1.1		2
20.7	even	4		560.4.a.r.1.1		2
35.2	odd	12		245.4.e.h.116.2		4
35.12	even	12		245.4.e.i.116.2		4
35.13	even	4		1225.4.a.m.1.2		2
35.17	even	12		245.4.e.i.226.2		4
35.27	even	4		245.4.a.k.1.1		2
35.32	odd	12		245.4.e.h.226.2		4
40.27	even	4		2240.4.a.bo.1.2		2
40.37	odd	4		2240.4.a.bn.1.1		2
105.62	odd	4		2205.4.a.u.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.b.1.1	✓	2	5.2	odd	4
175.4.a.c.1.2		2	5.3	odd	4
175.4.b.c.99.2		4	1.1	even	1	trivial
175.4.b.c.99.3		4	5.4	even	2	inner
245.4.a.k.1.1		2	35.27	even	4
245.4.e.h.116.2		4	35.2	odd	12
245.4.e.h.226.2		4	35.32	odd	12
245.4.e.i.116.2		4	35.12	even	12
245.4.e.i.226.2		4	35.17	even	12
315.4.a.f.1.2		2	15.2	even	4
560.4.a.r.1.1		2	20.7	even	4
1225.4.a.m.1.2		2	35.13	even	4
1575.4.a.z.1.1		2	15.8	even	4
2205.4.a.u.1.2		2	105.62	odd	4
2240.4.a.bn.1.1		2	40.37	odd	4
2240.4.a.bo.1.2		2	40.27	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.58579i q^{2} +6.65685i q^{3} +1.31371 q^{4} +17.2132 q^{6} +7.00000i q^{7} -24.0833i q^{8} -17.3137 q^{9} +O(q^{10})\)	\(q-2.58579i q^{2} +6.65685i q^{3} +1.31371 q^{4} +17.2132 q^{6} +7.00000i q^{7} -24.0833i q^{8} -17.3137 q^{9} +38.2548 q^{11} +8.74517i q^{12} +19.3431i q^{13} +18.1005 q^{14} -51.7645 q^{16} +87.2254i q^{17} +44.7696i q^{18} +44.2254 q^{19} -46.5980 q^{21} -98.9188i q^{22} +218.167i q^{23} +160.319 q^{24} +50.0172 q^{26} +64.4802i q^{27} +9.19596i q^{28} +46.9411 q^{29} +194.558 q^{31} -58.8141i q^{32} +254.657i q^{33} +225.546 q^{34} -22.7452 q^{36} -366.853i q^{37} -114.357i q^{38} -128.765 q^{39} -339.362 q^{41} +120.492i q^{42} -226.167i q^{43} +50.2557 q^{44} +564.132 q^{46} -11.6762i q^{47} -344.589i q^{48} -49.0000 q^{49} -580.647 q^{51} +25.4113i q^{52} -209.019i q^{53} +166.732 q^{54} +168.583 q^{56} +294.402i q^{57} -121.380i q^{58} +616.000 q^{59} +320.735 q^{61} -503.087i q^{62} -121.196i q^{63} -566.197 q^{64} +658.488 q^{66} -14.5097i q^{67} +114.589i q^{68} -1452.30 q^{69} -952.000 q^{71} +416.971i q^{72} +824.489i q^{73} -948.603 q^{74} +58.0993 q^{76} +267.784i q^{77} +332.958i q^{78} -156.275 q^{79} -896.706 q^{81} +877.519i q^{82} -1036.53i q^{83} -61.2162 q^{84} -584.818 q^{86} +312.480i q^{87} -921.301i q^{88} +170.225 q^{89} -135.402 q^{91} +286.607i q^{92} +1295.15i q^{93} -30.1921 q^{94} +391.517 q^{96} -1059.87i q^{97} +126.704i q^{98} -662.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 40 q^{4} - 16 q^{6} - 24 q^{9}+O(q^{10}) \) 4 * q - 40 * q^4 - 16 * q^6 - 24 * q^9	\( 4 q - 40 q^{4} - 16 q^{6} - 24 q^{9} - 28 q^{11} + 112 q^{14} + 336 q^{16} - 72 q^{19} - 28 q^{21} + 992 q^{24} + 432 q^{26} + 52 q^{29} - 240 q^{31} + 48 q^{34} - 272 q^{36} + 28 q^{39} - 656 q^{41} + 2328 q^{44} + 1408 q^{46} - 196 q^{49} - 1508 q^{51} - 1296 q^{54} - 672 q^{56} + 2464 q^{59} + 672 q^{61} - 4256 q^{64} + 3952 q^{66} - 2664 q^{69} - 3808 q^{71} - 4032 q^{74} + 3536 q^{76} - 2028 q^{79} - 2908 q^{81} - 1512 q^{84} - 1536 q^{86} + 432 q^{89} - 700 q^{91} + 3856 q^{94} - 4928 q^{96} - 1880 q^{99}+O(q^{100}) \) 4 * q - 40 * q^4 - 16 * q^6 - 24 * q^9 - 28 * q^11 + 112 * q^14 + 336 * q^16 - 72 * q^19 - 28 * q^21 + 992 * q^24 + 432 * q^26 + 52 * q^29 - 240 * q^31 + 48 * q^34 - 272 * q^36 + 28 * q^39 - 656 * q^41 + 2328 * q^44 + 1408 * q^46 - 196 * q^49 - 1508 * q^51 - 1296 * q^54 - 672 * q^56 + 2464 * q^59 + 672 * q^61 - 4256 * q^64 + 3952 * q^66 - 2664 * q^69 - 3808 * q^71 - 4032 * q^74 + 3536 * q^76 - 2028 * q^79 - 2908 * q^81 - 1512 * q^84 - 1536 * q^86 + 432 * q^89 - 700 * q^91 + 3856 * q^94 - 4928 * q^96 - 1880 * q^99

Introduction

L-functions

Modular forms

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Database

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