LMFDB - Embedded newform 175.4.b.c.99.4

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			99.4
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.4.b.c.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.41421i q^{2} +4.65685i q^{3} -21.3137 q^{4} -25.2132 q^{6} -7.00000i q^{7} -72.0833i q^{8} +5.31371 q^{9} +O(q^{10})$	\(q+5.41421i q^{2} +4.65685i q^{3} -21.3137 q^{4} -25.2132 q^{6} -7.00000i q^{7} -72.0833i q^{8} +5.31371 q^{9} -52.2548 q^{11} -99.2548i q^{12} -30.6569i q^{13} +37.8995 q^{14} +219.765 q^{16} +37.2254i q^{17} +28.7696i q^{18} -80.2254 q^{19} +32.5980 q^{21} -282.919i q^{22} -25.8335i q^{23} +335.681 q^{24} +165.983 q^{26} +150.480i q^{27} +149.196i q^{28} -20.9411 q^{29} -314.558 q^{31} +613.186i q^{32} -243.343i q^{33} -201.546 q^{34} -113.255 q^{36} +197.147i q^{37} -434.357i q^{38} +142.765 q^{39} +11.3625 q^{41} +176.492i q^{42} +33.8335i q^{43} +1113.74 q^{44} +139.868 q^{46} -361.676i q^{47} +1023.41i q^{48} -49.0000 q^{49} -173.353 q^{51} +653.411i q^{52} -153.019i q^{53} -814.732 q^{54} -504.583 q^{56} -373.598i q^{57} -113.380i q^{58} +616.000 q^{59} +15.2649 q^{61} -1703.09i q^{62} -37.1960i q^{63} -1561.80 q^{64} +1317.51 q^{66} -166.510i q^{67} -793.411i q^{68} +120.303 q^{69} -952.000 q^{71} -383.029i q^{72} +148.489i q^{73} -1067.40 q^{74} +1709.90 q^{76} +365.784i q^{77} +772.958i q^{78} -857.725 q^{79} -557.294 q^{81} +61.5189i q^{82} -660.528i q^{83} -694.784 q^{84} -183.182 q^{86} -97.5198i q^{87} +3766.70i q^{88} +45.7746 q^{89} -214.598 q^{91} +550.607i q^{92} -1464.85i q^{93} +1958.19 q^{94} -2855.52 q^{96} +1682.13i q^{97} -265.296i q^{98} -277.667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.41421i	1.91421i	0.289735	+	0.957107i	$0.406433\pi$
$2$	5.41421i	1.91421i	−0.289735	+	0.957107i	$0.593567\pi$
$3$	4.65685i	0.896212i	0.893980	+	0.448106i	$0.147901\pi$
$3$	4.65685i	0.896212i	−0.893980	+	0.448106i	$0.852099\pi$
$4$	−21.3137	−2.66421
$5$	0	0
$5$	0	0
$6$	−25.2132	−1.71554
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	− 72.0833i	− 3.18566i
$9$	5.31371	0.196804
$10$	0	0
$11$	−52.2548	−1.43231	−0.716156	−	0.697941i	$-0.754100\pi$
$11$	−52.2548	−1.43231	−0.716156	+	0.697941i	$0.754100\pi$
$12$	− 99.2548i	− 2.38770i
$13$	− 30.6569i	− 0.654052i	−0.945015	−	0.327026i	$-0.893953\pi$
$13$	− 30.6569i	− 0.654052i	0.945015	−	0.327026i	$-0.106047\pi$
$14$	37.8995	0.723505
$15$	0	0
$16$	219.765	3.43382
$17$	37.2254i	0.531087i	0.964099	+	0.265544i	$0.0855514\pi$
$17$	37.2254i	0.531087i	−0.964099	+	0.265544i	$0.914449\pi$
$18$	28.7696i	0.376725i
$19$	−80.2254	−0.968683	−0.484341	−	0.874879i	$-0.660941\pi$
$19$	−80.2254	−0.968683	−0.484341	+	0.874879i	$0.660941\pi$
$20$	0	0
$21$	32.5980	0.338736
$22$	− 282.919i	− 2.74175i
$23$	− 25.8335i	− 0.234202i	−0.993120	−	0.117101i	$-0.962640\pi$
$23$	− 25.8335i	− 0.234202i	0.993120	−	0.117101i	$-0.0373602\pi$
$24$	335.681	2.85503
$25$	0	0
$26$	165.983	1.25200
$27$	150.480i	1.07259i
$28$	149.196i	1.00698i
$29$	−20.9411	−0.134092	−0.0670460	−	0.997750i	$-0.521357\pi$
$29$	−20.9411	−0.134092	−0.0670460	+	0.997750i	$0.521357\pi$
$30$	0	0
$31$	−314.558	−1.82246	−0.911232	−	0.411894i	$-0.864867\pi$
$31$	−314.558	−1.82246	−0.911232	+	0.411894i	$0.864867\pi$
$32$	613.186i	3.38741i
$33$	− 243.343i	− 1.28365i
$34$	−201.546	−1.01661
$35$	0	0
$36$	−113.255	−0.524328
$37$	197.147i	0.875968i	0.898983	+	0.437984i	$0.144307\pi$
$37$	197.147i	0.875968i	−0.898983	+	0.437984i	$0.855693\pi$
$38$	− 434.357i	− 1.85427i
$39$	142.765	0.586170
$40$	0	0
$41$	11.3625	0.0432810	0.0216405	−	0.999766i	$-0.493111\pi$
$41$	11.3625	0.0432810	0.0216405	+	0.999766i	$0.493111\pi$
$42$	176.492i	0.648414i
$43$	33.8335i	0.119990i	0.998199	+	0.0599948i	$0.0191084\pi$
$43$	33.8335i	0.119990i	−0.998199	+	0.0599948i	$0.980892\pi$
$44$	1113.74	3.81598
$45$	0	0
$46$	139.868	0.448313
$47$	− 361.676i	− 1.12247i	−0.827658	−	0.561233i	$-0.810327\pi$
$47$	− 361.676i	− 1.12247i	0.827658	−	0.561233i	$-0.189673\pi$
$48$	1023.41i	3.07743i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−173.353	−0.475967
$52$	653.411i	1.74254i
$53$	− 153.019i	− 0.396582i	−0.980143	−	0.198291i	$-0.936461\pi$
$53$	− 153.019i	− 0.396582i	0.980143	−	0.198291i	$-0.0635390\pi$
$54$	−814.732	−2.05317
$55$	0	0
$56$	−504.583	−1.20407
$57$	− 373.598i	− 0.868145i
$58$	− 113.380i	− 0.256681i
$59$	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
$61$	15.2649	0.0320406	0.0160203	−	0.999872i	$-0.494900\pi$
$61$	15.2649	0.0320406	0.0160203	+	0.999872i	$0.494900\pi$
$62$	− 1703.09i	− 3.48858i
$63$	− 37.1960i	− 0.0743849i
$64$	−1561.80	−3.05040
$65$	0	0
$66$	1317.51	2.45719
$67$	− 166.510i	− 0.303618i	−0.988410	−	0.151809i	$-0.951490\pi$
$67$	− 166.510i	− 0.303618i	0.988410	−	0.151809i	$-0.0485098\pi$
$68$	− 793.411i	− 1.41493i
$69$	120.303	0.209895
$70$	0	0
$71$	−952.000	−1.59129	−0.795645	−	0.605763i	$-0.792868\pi$
$71$	−952.000	−1.59129	−0.795645	+	0.605763i	$0.792868\pi$
$72$	− 383.029i	− 0.626951i
$73$	148.489i	0.238074i	0.992890	+	0.119037i	$0.0379807\pi$
$73$	148.489i	0.238074i	−0.992890	+	0.119037i	$0.962019\pi$
$74$	−1067.40	−1.67679
$75$	0	0
$76$	1709.90	2.58078
$77$	365.784i	0.541363i
$78$	772.958i	1.12205i
$79$	−857.725	−1.22154	−0.610770	−	0.791808i	$-0.709140\pi$
$79$	−857.725	−1.22154	−0.610770	+	0.791808i	$0.709140\pi$
$80$	0	0
$81$	−557.294	−0.764464
$82$	61.5189i	0.0828491i
$83$	− 660.528i	− 0.873523i	−0.899577	−	0.436761i	$-0.856125\pi$
$83$	− 660.528i	− 0.873523i	0.899577	−	0.436761i	$-0.143875\pi$
$84$	−694.784	−0.902466
$85$	0	0
$86$	−183.182	−0.229686
$87$	− 97.5198i	− 0.120175i
$88$	3766.70i	4.56286i
$89$	45.7746	0.0545180	0.0272590	−	0.999628i	$-0.491322\pi$
$89$	45.7746	0.0545180	0.0272590	+	0.999628i	$0.491322\pi$
$90$	0	0
$91$	−214.598	−0.247209
$92$	550.607i	0.623965i
$93$	− 1464.85i	− 1.63331i
$94$	1958.19	2.14864
$95$	0	0
$96$	−2855.52	−3.03583
$97$	1682.13i	1.76076i	0.474265	+	0.880382i	$0.342714\pi$
$97$	1682.13i	1.76076i	−0.474265	+	0.880382i	$0.657286\pi$
$98$	− 265.296i	− 0.273459i
$99$	−277.667	−0.281885
$100$	0	0
$101$	−434.167	−0.427734	−0.213867	−	0.976863i	$-0.568606\pi$
$101$	−434.167	−0.427734	−0.213867	+	0.976863i	$0.568606\pi$
$102$	− 938.572i	− 0.911102i
$103$	− 345.577i	− 0.330589i	−0.986244	−	0.165295i	$-0.947142\pi$
$103$	− 345.577i	− 0.330589i	0.986244	−	0.165295i	$-0.0528575\pi$
$104$	−2209.85	−2.08359
$105$	0	0
$106$	828.479	0.759142
$107$	217.119i	0.196165i	0.995178	+	0.0980825i	$0.0312709\pi$
$107$	217.119i	0.196165i	−0.995178	+	0.0980825i	$0.968729\pi$
$108$	− 3207.29i	− 2.85761i
$109$	−1734.41	−1.52409	−0.762047	−	0.647521i	$-0.775806\pi$
$109$	−1734.41	−1.52409	−0.762047	+	0.647521i	$0.775806\pi$
$110$	0	0
$111$	−918.086	−0.785053
$112$	− 1538.35i	− 1.29786i
$113$	1854.20i	1.54362i	0.635855	+	0.771809i	$0.280648\pi$
$113$	1854.20i	1.54362i	−0.635855	+	0.771809i	$0.719352\pi$
$114$	2022.74	1.66181
$115$	0	0
$116$	446.333	0.357250
$117$	− 162.902i	− 0.128720i
$118$	3335.16i	2.60191i
$119$	260.578	0.200732
$120$	0	0
$121$	1399.57	1.05152
$122$	82.6476i	0.0613325i
$123$	52.9134i	0.0387890i
$124$	6704.41	4.85543
$125$	0	0
$126$	201.387	0.142389
$127$	1394.51i	0.974352i	0.873304	+	0.487176i	$0.161973\pi$
$127$	1394.51i	0.974352i	−0.873304	+	0.487176i	$0.838027\pi$
$128$	− 3550.45i	− 2.45171i
$129$	−157.558	−0.107536
$130$	0	0
$131$	1762.42	1.17544	0.587722	−	0.809063i	$-0.300025\pi$
$131$	1762.42	1.17544	0.587722	+	0.809063i	$0.300025\pi$
$132$	5186.54i	3.41993i
$133$	561.578i	0.366128i
$134$	901.519	0.581189
$135$	0	0
$136$	2683.33	1.69186
$137$	− 922.949i	− 0.575568i	−0.957695	−	0.287784i	$-0.907081\pi$
$137$	− 922.949i	− 0.575568i	0.957695	−	0.287784i	$-0.0929185\pi$
$138$	651.345i	0.401784i
$139$	196.039	0.119624	0.0598122	−	0.998210i	$-0.480950\pi$
$139$	196.039	0.119624	0.0598122	+	0.998210i	$0.480950\pi$
$140$	0	0
$141$	1684.27	1.00597
$142$	− 5154.33i	− 3.04607i
$143$	1601.97i	0.936807i
$144$	1167.76	0.675790
$145$	0	0
$146$	−803.954	−0.455724
$147$	− 228.186i	− 0.128030i
$148$	− 4201.94i	− 2.33376i
$149$	−780.372	−0.429064	−0.214532	−	0.976717i	$-0.568823\pi$
$149$	−780.372	−0.429064	−0.214532	+	0.976717i	$0.568823\pi$
$150$	0	0
$151$	−2319.43	−1.25002	−0.625008	−	0.780618i	$-0.714904\pi$
$151$	−2319.43	−1.25002	−0.625008	+	0.780618i	$0.714904\pi$
$152$	5782.91i	3.08589i
$153$	197.805i	0.104520i
$154$	−1980.43	−1.03628
$155$	0	0
$156$	−3042.84	−1.56168
$157$	1022.90i	0.519977i	0.965612	+	0.259989i	$0.0837188\pi$
$157$	1022.90i	0.519977i	−0.965612	+	0.259989i	$0.916281\pi$
$158$	− 4643.91i	− 2.33829i
$159$	712.589	0.355421
$160$	0	0
$161$	−180.834	−0.0885201
$162$	− 3017.31i	− 1.46335i
$163$	1350.63i	0.649013i	0.945883	+	0.324507i	$0.105198\pi$
$163$	1350.63i	0.649013i	−0.945883	+	0.324507i	$0.894802\pi$
$164$	−242.177	−0.115310
$165$	0	0
$166$	3576.24	1.67211
$167$	− 1230.58i	− 0.570209i	−0.958496	−	0.285105i	$-0.907972\pi$
$167$	− 1230.58i	− 0.570209i	0.958496	−	0.285105i	$-0.0920284\pi$
$168$	− 2349.77i	− 1.07910i
$169$	1257.16	0.572215
$170$	0	0
$171$	−426.294	−0.190641
$172$	− 721.117i	− 0.319678i
$173$	2487.65i	1.09325i	0.837377	+	0.546626i	$0.184088\pi$
$173$	2487.65i	1.09325i	−0.837377	+	0.546626i	$0.815912\pi$
$174$	527.993	0.230040
$175$	0	0
$176$	−11483.8	−4.91830
$177$	2868.62i	1.21819i
$178$	247.833i	0.104359i
$179$	−1621.18	−0.676941	−0.338471	−	0.940977i	$-0.609910\pi$
$179$	−1621.18	−0.676941	−0.338471	+	0.940977i	$0.609910\pi$
$180$	0	0
$181$	2593.69	1.06512	0.532561	−	0.846392i	$-0.321230\pi$
$181$	2593.69	1.06512	0.532561	+	0.846392i	$0.321230\pi$
$182$	− 1161.88i	− 0.473210i
$183$	71.0866i	0.0287151i
$184$	−1862.16	−0.746089
$185$	0	0
$186$	7931.03	3.12651
$187$	− 1945.21i	− 0.760682i
$188$	7708.66i	2.99049i
$189$	1053.36	0.405401
$190$	0	0
$191$	−1823.08	−0.690645	−0.345323	−	0.938484i	$-0.612231\pi$
$191$	−1823.08	−0.690645	−0.345323	+	0.938484i	$0.612231\pi$
$192$	− 7273.09i	− 2.73380i
$193$	1541.03i	0.574744i	0.957819	+	0.287372i	$0.0927816\pi$
$193$	1541.03i	0.574744i	−0.957819	+	0.287372i	$0.907218\pi$
$194$	−9107.39	−3.37048
$195$	0	0
$196$	1044.37	0.380602
$197$	701.243i	0.253612i	0.991928	+	0.126806i	$0.0404725\pi$
$197$	701.243i	0.253612i	−0.991928	+	0.126806i	$0.959527\pi$
$198$	− 1503.35i	− 0.539587i
$199$	−3294.96	−1.17374	−0.586868	−	0.809682i	$-0.699639\pi$
$199$	−3294.96	−1.17374	−0.586868	+	0.809682i	$0.699639\pi$
$200$	0	0
$201$	775.411	0.272106
$202$	− 2350.67i	− 0.818775i
$203$	146.588i	0.0506820i
$204$	3694.80	1.26808
$205$	0	0
$206$	1871.03	0.632819
$207$	− 137.272i	− 0.0460920i
$208$	− 6737.29i	− 2.24590i
$209$	4192.16	1.38746
$210$	0	0
$211$	4082.35	1.33195	0.665974	−	0.745975i	$-0.268016\pi$
$211$	4082.35	1.33195	0.665974	+	0.745975i	$0.268016\pi$
$212$	3261.41i	1.05658i
$213$	− 4433.33i	− 1.42613i
$214$	−1175.53	−0.375502
$215$	0	0
$216$	10847.1	3.41691
$217$	2201.91i	0.688826i
$218$	− 9390.46i	− 2.91744i
$219$	−691.494	−0.213364
$220$	0	0
$221$	1141.21	0.347359
$222$	− 4970.71i	− 1.50276i
$223$	− 747.161i	− 0.224366i	−0.993688	−	0.112183i	$-0.964216\pi$
$223$	− 747.161i	− 0.224366i	0.993688	−	0.112183i	$-0.0357843\pi$
$224$	4292.30	1.28032
$225$	0	0
$226$	−10039.1	−2.95481
$227$	1665.67i	0.487025i	0.969898	+	0.243513i	$0.0782997\pi$
$227$	1665.67i	0.487025i	−0.969898	+	0.243513i	$0.921700\pi$
$228$	7962.76i	2.31292i
$229$	6628.35	1.91272	0.956362	−	0.292183i	$-0.0943816\pi$
$229$	6628.35	1.91272	0.956362	+	0.292183i	$0.0943816\pi$
$230$	0	0
$231$	−1703.40	−0.485176
$232$	1509.50i	0.427172i
$233$	432.431i	0.121586i	0.998150	+	0.0607929i	$0.0193629\pi$
$233$	432.431i	0.121586i	−0.998150	+	0.0607929i	$0.980637\pi$
$234$	881.984	0.246398
$235$	0	0
$236$	−13129.2	−3.62136
$237$	− 3994.30i	− 1.09476i
$238$	1410.82i	0.384244i
$239$	−5580.44	−1.51033	−0.755165	−	0.655535i	$-0.772443\pi$
$239$	−5580.44	−1.51033	−0.755165	+	0.655535i	$0.772443\pi$
$240$	0	0
$241$	−6296.87	−1.68306	−0.841529	−	0.540212i	$-0.818344\pi$
$241$	−6296.87	−1.68306	−0.841529	+	0.540212i	$0.818344\pi$
$242$	7577.56i	2.01283i
$243$	1467.73i	0.387468i
$244$	−325.352	−0.0853629
$245$	0	0
$246$	−286.485	−0.0742504
$247$	2459.46i	0.633569i
$248$	22674.4i	5.80575i
$249$	3075.98	0.782862
$250$	0	0
$251$	311.921	0.0784393	0.0392197	−	0.999231i	$-0.487513\pi$
$251$	311.921	0.0784393	0.0392197	+	0.999231i	$0.487513\pi$
$252$	792.784i	0.198177i
$253$	1349.92i	0.335451i
$254$	−7550.17	−1.86512
$255$	0	0
$256$	6728.46	1.64269
$257$	− 7861.39i	− 1.90809i	−0.299659	−	0.954046i	$-0.596873\pi$
$257$	− 7861.39i	− 1.90809i	0.299659	−	0.954046i	$-0.403127\pi$
$258$	− 853.050i	− 0.205847i
$259$	1380.03	0.331085
$260$	0	0
$261$	−111.275	−0.0263899
$262$	9542.11i	2.25005i
$263$	− 5227.09i	− 1.22554i	−0.790262	−	0.612769i	$-0.790056\pi$
$263$	− 5227.09i	− 1.22554i	0.790262	−	0.612769i	$-0.209944\pi$
$264$	−17541.0	−4.08929
$265$	0	0
$266$	−3040.50	−0.700846
$267$	213.166i	0.0488596i
$268$	3548.94i	0.808903i
$269$	−1281.71	−0.290510	−0.145255	−	0.989394i	$-0.546400\pi$
$269$	−1281.71	−0.290510	−0.145255	+	0.989394i	$0.546400\pi$
$270$	0	0
$271$	4704.14	1.05445	0.527226	−	0.849725i	$-0.323232\pi$
$271$	4704.14	1.05445	0.527226	+	0.849725i	$0.323232\pi$
$272$	8180.82i	1.82366i
$273$	− 999.352i	− 0.221551i
$274$	4997.04	1.10176
$275$	0	0
$276$	−2564.10	−0.559205
$277$	8958.56i	1.94321i	0.236619	+	0.971603i	$0.423961\pi$
$277$	8958.56i	1.94321i	−0.236619	+	0.971603i	$0.576039\pi$
$278$	1061.40i	0.228987i
$279$	−1671.47	−0.358668
$280$	0	0
$281$	−370.904	−0.0787412	−0.0393706	−	0.999225i	$-0.512535\pi$
$281$	−370.904	−0.0787412	−0.0393706	+	0.999225i	$0.512535\pi$
$282$	9119.02i	1.92564i
$283$	5822.26i	1.22296i	0.791261	+	0.611479i	$0.209425\pi$
$283$	5822.26i	1.22296i	−0.791261	+	0.611479i	$0.790575\pi$
$284$	20290.7	4.23954
$285$	0	0
$286$	−8673.40	−1.79325
$287$	− 79.5374i	− 0.0163587i
$288$	3258.29i	0.666655i
$289$	3527.27	0.717946
$290$	0	0
$291$	−7833.42	−1.57802
$292$	− 3164.86i	− 0.634279i
$293$	− 7443.79i	− 1.48420i	−0.670289	−	0.742100i	$-0.733830\pi$
$293$	− 7443.79i	− 1.48420i	0.670289	−	0.742100i	$-0.266170\pi$
$294$	1235.45	0.245077
$295$	0	0
$296$	14211.0	2.79053
$297$	− 7863.32i	− 1.53628i
$298$	− 4225.10i	− 0.821320i
$299$	−791.973	−0.153181
$300$	0	0
$301$	236.834	0.0453518
$302$	− 12557.9i	− 2.39280i
$303$	− 2021.85i	− 0.383341i
$304$	−17630.7	−3.32628
$305$	0	0
$306$	−1070.96	−0.200074
$307$	− 761.674i	− 0.141600i	−0.997491	−	0.0707998i	$-0.977445\pi$
$307$	− 761.674i	− 0.141600i	0.997491	−	0.0707998i	$-0.0225551\pi$
$308$	− 7796.21i	− 1.44231i
$309$	1609.30	0.296278
$310$	0	0
$311$	7718.69	1.40735	0.703677	−	0.710520i	$-0.251540\pi$
$311$	7718.69	1.40735	0.703677	+	0.710520i	$0.251540\pi$
$312$	− 10290.9i	− 1.86734i
$313$	− 8556.00i	− 1.54509i	−0.634959	−	0.772546i	$-0.718983\pi$
$313$	− 8556.00i	− 1.54509i	0.634959	−	0.772546i	$-0.281017\pi$
$314$	−5538.21	−0.995348
$315$	0	0
$316$	18281.3	3.25444
$317$	− 7780.95i	− 1.37862i	−0.724468	−	0.689309i	$-0.757914\pi$
$317$	− 7780.95i	− 1.37862i	0.724468	−	0.689309i	$-0.242086\pi$
$318$	3858.11i	0.680352i
$319$	1094.28	0.192062
$320$	0	0
$321$	−1011.09	−0.175805
$322$	− 979.076i	− 0.169446i
$323$	− 2986.42i	− 0.514455i
$324$	11878.0	2.03670
$325$	0	0
$326$	−7312.58	−1.24235
$327$	− 8076.89i	− 1.36591i
$328$	− 819.045i	− 0.137879i
$329$	−2531.73	−0.424252
$330$	0	0
$331$	−4932.12	−0.819015	−0.409507	−	0.912307i	$-0.634299\pi$
$331$	−4932.12	−0.819015	−0.409507	+	0.912307i	$0.634299\pi$
$332$	14078.3i	2.32725i
$333$	1047.58i	0.172394i
$334$	6662.61	1.09150
$335$	0	0
$336$	7163.88	1.16316
$337$	− 7121.13i	− 1.15108i	−0.817775	−	0.575538i	$-0.804793\pi$
$337$	− 7121.13i	− 1.15108i	0.817775	−	0.575538i	$-0.195207\pi$
$338$	6806.52i	1.09534i
$339$	−8634.76	−1.38341
$340$	0	0
$341$	16437.2	2.61034
$342$	− 2308.05i	− 0.364927i
$343$	343.000i	0.0539949i
$344$	2438.83	0.382246
$345$	0	0
$346$	−13468.7	−2.09272
$347$	9540.58i	1.47598i	0.674811	+	0.737991i	$0.264225\pi$
$347$	9540.58i	1.47598i	−0.674811	+	0.737991i	$0.735775\pi$
$348$	2078.51i	0.320172i
$349$	−1281.65	−0.196576	−0.0982880	−	0.995158i	$-0.531337\pi$
$349$	−1281.65	−0.196576	−0.0982880	+	0.995158i	$0.531337\pi$
$350$	0	0
$351$	4613.25	0.701530
$352$	− 32041.9i	− 4.85182i
$353$	− 5798.07i	− 0.874221i	−0.899408	−	0.437110i	$-0.856002\pi$
$353$	− 5798.07i	− 0.874221i	0.899408	−	0.437110i	$-0.143998\pi$
$354$	−15531.3	−2.33187
$355$	0	0
$356$	−975.627	−0.145247
$357$	1213.47i	0.179899i
$358$	− 8777.40i	− 1.29581i
$359$	−2267.29	−0.333323	−0.166662	−	0.986014i	$-0.553299\pi$
$359$	−2267.29	−0.333323	−0.166662	+	0.986014i	$0.553299\pi$
$360$	0	0
$361$	−422.886	−0.0616541
$362$	14042.8i	2.03887i
$363$	6517.58i	0.942381i
$364$	4573.88	0.658616
$365$	0	0
$366$	−384.878	−0.0549669
$367$	− 7372.85i	− 1.04866i	−0.851514	−	0.524332i	$-0.824315\pi$
$367$	− 7372.85i	− 1.04866i	0.851514	−	0.524332i	$-0.175685\pi$
$368$	− 5677.28i	− 0.804209i
$369$	60.3769	0.00851788
$370$	0	0
$371$	−1071.14	−0.149894
$372$	31221.4i	4.35150i
$373$	− 6447.14i	− 0.894961i	−0.894294	−	0.447480i	$-0.852321\pi$
$373$	− 6447.14i	− 0.894961i	0.894294	−	0.447480i	$-0.147679\pi$
$374$	10531.8	1.45611
$375$	0	0
$376$	−26070.8	−3.57579
$377$	641.989i	0.0877032i
$378$	5703.12i	0.776024i
$379$	4247.57	0.575680	0.287840	−	0.957678i	$-0.407063\pi$
$379$	4247.57	0.575680	0.287840	+	0.957678i	$0.407063\pi$
$380$	0	0
$381$	−6494.03	−0.873226
$382$	− 9870.53i	− 1.32204i
$383$	6681.86i	0.891454i	0.895169	+	0.445727i	$0.147055\pi$
$383$	6681.86i	0.891454i	−0.895169	+	0.445727i	$0.852945\pi$
$384$	16533.9	2.19725
$385$	0	0
$386$	−8343.45	−1.10018
$387$	179.781i	0.0236145i
$388$	− 35852.4i	− 4.69105i
$389$	6371.78	0.830494	0.415247	−	0.909709i	$-0.363695\pi$
$389$	6371.78	0.830494	0.415247	+	0.909709i	$0.363695\pi$
$390$	0	0
$391$	961.661	0.124382
$392$	3532.08i	0.455094i
$393$	8207.33i	1.05345i
$394$	−3796.68	−0.485467
$395$	0	0
$396$	5918.11	0.751001
$397$	4247.93i	0.537021i	0.963277	+	0.268510i	$0.0865314\pi$
$397$	4247.93i	0.537021i	−0.963277	+	0.268510i	$0.913469\pi$
$398$	− 17839.6i	− 2.24678i
$399$	−2615.19	−0.328128
$400$	0	0
$401$	−8833.62	−1.10008	−0.550038	−	0.835140i	$-0.685387\pi$
$401$	−8833.62	−1.10008	−0.550038	+	0.835140i	$0.685387\pi$
$402$	4198.24i	0.520869i
$403$	9643.37i	1.19199i
$404$	9253.70	1.13958
$405$	0	0
$406$	−793.658	−0.0970162
$407$	− 10301.9i	− 1.25466i
$408$	12495.9i	1.51627i
$409$	319.205	0.0385908	0.0192954	−	0.999814i	$-0.493858\pi$
$409$	319.205	0.0385908	0.0192954	+	0.999814i	$0.493858\pi$
$410$	0	0
$411$	4298.04	0.515831
$412$	7365.53i	0.880761i
$413$	− 4312.00i	− 0.513752i
$414$	743.218	0.0882298
$415$	0	0
$416$	18798.3	2.21554
$417$	912.924i	0.107209i
$418$	22697.3i	2.65589i
$419$	12789.2	1.49115	0.745577	−	0.666420i	$-0.232174\pi$
$419$	12789.2	1.49115	0.745577	+	0.666420i	$0.232174\pi$
$420$	0	0
$421$	−6747.40	−0.781112	−0.390556	−	0.920579i	$-0.627717\pi$
$421$	−6747.40	−0.781112	−0.390556	+	0.920579i	$0.627717\pi$
$422$	22102.7i	2.54963i
$423$	− 1921.84i	− 0.220906i
$424$	−11030.1	−1.26337
$425$	0	0
$426$	24003.0	2.72992
$427$	− 106.855i	− 0.0121102i
$428$	− 4627.60i	− 0.522625i
$429$	−7460.14	−0.839577
$430$	0	0
$431$	−5184.75	−0.579444	−0.289722	−	0.957111i	$-0.593563\pi$
$431$	−5184.75	−0.579444	−0.289722	+	0.957111i	$0.593563\pi$
$432$	33070.2i	3.68308i
$433$	4242.03i	0.470806i	0.971898	+	0.235403i	$0.0756410\pi$
$433$	4242.03i	0.470806i	−0.971898	+	0.235403i	$0.924359\pi$
$434$	−11921.6	−1.31856
$435$	0	0
$436$	36966.7	4.06051
$437$	2072.50i	0.226868i
$438$	− 3743.90i	− 0.408425i
$439$	5434.12	0.590789	0.295394	−	0.955375i	$-0.404549\pi$
$439$	5434.12	0.590789	0.295394	+	0.955375i	$0.404549\pi$
$440$	0	0
$441$	−260.372	−0.0281149
$442$	6178.77i	0.664919i
$443$	11493.8i	1.23270i	0.787472	+	0.616350i	$0.211389\pi$
$443$	11493.8i	1.23270i	−0.787472	+	0.616350i	$0.788611\pi$
$444$	19567.8	2.09155
$445$	0	0
$446$	4045.29	0.429484
$447$	− 3634.08i	− 0.384532i
$448$	10932.6i	1.15294i
$449$	16849.3	1.77098	0.885489	−	0.464661i	$-0.153824\pi$
$449$	16849.3	1.77098	0.885489	+	0.464661i	$0.153824\pi$
$450$	0	0
$451$	−593.745	−0.0619919
$452$	− 39520.0i	− 4.11253i
$453$	− 10801.2i	− 1.12028i
$454$	−9018.32	−0.932270
$455$	0	0
$456$	−26930.2	−2.76561
$457$	15348.5i	1.57106i	0.618826	+	0.785528i	$0.287609\pi$
$457$	15348.5i	1.57106i	−0.618826	+	0.785528i	$0.712391\pi$
$458$	35887.3i	3.66136i
$459$	−5601.69	−0.569639
$460$	0	0
$461$	14038.4	1.41830	0.709148	−	0.705059i	$-0.249080\pi$
$461$	14038.4	1.41830	0.709148	+	0.705059i	$0.249080\pi$
$462$	− 9222.58i	− 0.928730i
$463$	8661.23i	0.869377i	0.900581	+	0.434689i	$0.143142\pi$
$463$	8661.23i	0.869377i	−0.900581	+	0.434689i	$0.856858\pi$
$464$	−4602.12	−0.460448
$465$	0	0
$466$	−2341.27	−0.232741
$467$	7014.71i	0.695079i	0.937665	+	0.347539i	$0.112983\pi$
$467$	7014.71i	0.695079i	−0.937665	+	0.347539i	$0.887017\pi$
$468$	3472.04i	0.342938i
$469$	−1165.57	−0.114757
$470$	0	0
$471$	−4763.50	−0.466010
$472$	− 44403.3i	− 4.33014i
$473$	− 1767.96i	− 0.171863i
$474$	21626.0	2.09560
$475$	0	0
$476$	−5553.88	−0.534793
$477$	− 813.100i	− 0.0780488i
$478$	− 30213.7i	− 2.89109i
$479$	−18134.7	−1.72984	−0.864922	−	0.501907i	$-0.832632\pi$
$479$	−18134.7	−1.72984	−0.864922	+	0.501907i	$0.832632\pi$
$480$	0	0
$481$	6043.91	0.572929
$482$	− 34092.6i	− 3.22173i
$483$	− 842.119i	− 0.0793328i
$484$	−29830.0	−2.80146
$485$	0	0
$486$	−7946.59	−0.741697
$487$	16537.8i	1.53881i	0.638761	+	0.769405i	$0.279447\pi$
$487$	16537.8i	1.53881i	−0.638761	+	0.769405i	$0.720553\pi$
$488$	− 1100.35i	− 0.102070i
$489$	−6289.67	−0.581654
$490$	0	0
$491$	220.608	0.0202768	0.0101384	−	0.999949i	$-0.496773\pi$
$491$	220.608	0.0202768	0.0101384	+	0.999949i	$0.496773\pi$
$492$	− 1127.78i	− 0.103342i
$493$	− 779.542i	− 0.0712146i
$494$	−13316.0	−1.21279
$495$	0	0
$496$	−69128.8	−6.25801
$497$	6664.00i	0.601451i
$498$	16654.0i	1.49856i
$499$	−5939.04	−0.532801	−0.266401	−	0.963862i	$-0.585834\pi$
$499$	−5939.04	−0.532801	−0.266401	+	0.963862i	$0.585834\pi$
$500$	0	0
$501$	5730.62	0.511029
$502$	1688.81i	0.150150i
$503$	11604.8i	1.02869i	0.857584	+	0.514345i	$0.171965\pi$
$503$	11604.8i	1.02869i	−0.857584	+	0.514345i	$0.828035\pi$
$504$	−2681.21	−0.236965
$505$	0	0
$506$	−7308.78	−0.642124
$507$	5854.40i	0.512826i
$508$	− 29722.2i	− 2.59588i
$509$	1867.67	0.162639	0.0813193	−	0.996688i	$-0.474087\pi$
$509$	1867.67	0.162639	0.0813193	+	0.996688i	$0.474087\pi$
$510$	0	0
$511$	1039.43	0.0899834
$512$	8025.75i	0.692757i
$513$	− 12072.3i	− 1.03900i
$514$	42563.2	3.65250
$515$	0	0
$516$	3358.14	0.286499
$517$	18899.3i	1.60772i
$518$	7471.78i	0.633767i
$519$	−11584.6	−0.979786
$520$	0	0
$521$	6117.21	0.514395	0.257197	−	0.966359i	$-0.417201\pi$
$521$	6117.21	0.514395	0.257197	+	0.966359i	$0.417201\pi$
$522$	− 602.467i	− 0.0505158i
$523$	16685.6i	1.39505i	0.716561	+	0.697524i	$0.245715\pi$
$523$	16685.6i	1.39505i	−0.716561	+	0.697524i	$0.754285\pi$
$524$	−37563.7	−3.13164
$525$	0	0
$526$	28300.6	2.34594
$527$	− 11709.6i	− 0.967887i
$528$	− 53478.2i	− 4.40784i
$529$	11499.6	0.945149
$530$	0	0
$531$	3273.24	0.267508
$532$	− 11969.3i	− 0.975442i
$533$	− 348.338i	− 0.0283081i
$534$	−1154.12	−0.0935278
$535$	0	0
$536$	−12002.6	−0.967223
$537$	− 7549.59i	− 0.606683i
$538$	− 6939.44i	− 0.556097i
$539$	2560.49	0.204616
$540$	0	0
$541$	9309.03	0.739790	0.369895	−	0.929074i	$-0.379394\pi$
$541$	9309.03	0.739790	0.369895	+	0.929074i	$0.379394\pi$
$542$	25469.2i	2.01845i
$543$	12078.4i	0.954575i
$544$	−22826.1	−1.79901
$545$	0	0
$546$	5410.70	0.424097
$547$	10894.7i	0.851598i	0.904818	+	0.425799i	$0.140007\pi$
$547$	10894.7i	0.851598i	−0.904818	+	0.425799i	$0.859993\pi$
$548$	19671.5i	1.53344i
$549$	81.1134	0.00630571
$550$	0	0
$551$	1680.01	0.129893
$552$	− 8671.81i	− 0.668654i
$553$	6004.07i	0.461698i
$554$	−48503.6	−3.71971
$555$	0	0
$556$	−4178.31	−0.318705
$557$	− 7873.90i	− 0.598973i	−0.954101	−	0.299486i	$-0.903185\pi$
$557$	− 7873.90i	− 0.598973i	0.954101	−	0.299486i	$-0.0968153\pi$
$558$	− 9049.71i	− 0.686567i
$559$	1037.23	0.0784796
$560$	0	0
$561$	9058.55	0.681733
$562$	− 2008.15i	− 0.150728i
$563$	− 21770.7i	− 1.62971i	−0.579666	−	0.814854i	$-0.696817\pi$
$563$	− 21770.7i	− 1.62971i	0.579666	−	0.814854i	$-0.303183\pi$
$564$	−35898.1	−2.68011
$565$	0	0
$566$	−31522.9	−2.34100
$567$	3901.06i	0.288940i
$568$	68623.3i	5.06931i
$569$	12381.3	0.912213	0.456106	−	0.889925i	$-0.349244\pi$
$569$	12381.3	0.912213	0.456106	+	0.889925i	$0.349244\pi$
$570$	0	0
$571$	−5768.38	−0.422765	−0.211383	−	0.977403i	$-0.567797\pi$
$571$	−5768.38	−0.422765	−0.211383	+	0.977403i	$0.567797\pi$
$572$	− 34143.9i	− 2.49585i
$573$	− 8489.81i	− 0.618965i
$574$	430.632	0.0313140
$575$	0	0
$576$	−8298.97	−0.600330
$577$	4733.38i	0.341513i	0.985313	+	0.170757i	$0.0546212\pi$
$577$	4733.38i	0.341513i	−0.985313	+	0.170757i	$0.945379\pi$
$578$	19097.4i	1.37430i
$579$	−7176.34	−0.515093
$580$	0	0
$581$	−4623.70	−0.330161
$582$	− 42411.8i	− 3.02066i
$583$	7996.00i	0.568028i
$584$	10703.6	0.758422
$585$	0	0
$586$	40302.3	2.84108
$587$	− 8441.67i	− 0.593569i	−0.954944	−	0.296785i	$-0.904086\pi$
$587$	− 8441.67i	− 0.593569i	0.954944	−	0.296785i	$-0.0959143\pi$
$588$	4863.49i	0.341100i
$589$	25235.6	1.76539
$590$	0	0
$591$	−3265.59	−0.227290
$592$	43326.0i	3.00792i
$593$	− 18939.9i	− 1.31158i	−0.754943	−	0.655791i	$-0.772335\pi$
$593$	− 18939.9i	− 1.31158i	0.754943	−	0.655791i	$-0.227665\pi$
$594$	42573.7	2.94077
$595$	0	0
$596$	16632.6	1.14312
$597$	− 15344.2i	− 1.05192i
$598$	− 4287.91i	− 0.293220i
$599$	−22655.3	−1.54536	−0.772681	−	0.634794i	$-0.781085\pi$
$599$	−22655.3	−1.54536	−0.772681	+	0.634794i	$0.781085\pi$
$600$	0	0
$601$	−15947.4	−1.08237	−0.541187	−	0.840902i	$-0.682025\pi$
$601$	−15947.4	−1.08237	−0.541187	+	0.840902i	$0.682025\pi$
$602$	1282.27i	0.0868131i
$603$	− 884.784i	− 0.0597532i
$604$	49435.6	3.33031
$605$	0	0
$606$	10946.7	0.733796
$607$	− 25993.2i	− 1.73811i	−0.494719	−	0.869053i	$-0.664729\pi$
$607$	− 25993.2i	− 1.73811i	0.494719	−	0.869053i	$-0.335271\pi$
$608$	− 49193.1i	− 3.28132i
$609$	−682.638	−0.0454218
$610$	0	0
$611$	−11087.9	−0.734152
$612$	− 4215.96i	− 0.278464i
$613$	− 665.408i	− 0.0438427i	−0.999760	−	0.0219213i	$-0.993022\pi$
$613$	− 665.408i	− 0.0438427i	0.999760	−	0.0219213i	$-0.00697834\pi$
$614$	4123.87	0.271052
$615$	0	0
$616$	26366.9	1.72460
$617$	18401.3i	1.20066i	0.799752	+	0.600330i	$0.204964\pi$
$617$	18401.3i	1.20066i	−0.799752	+	0.600330i	$0.795036\pi$
$618$	8713.10i	0.567140i
$619$	11150.6	0.724040	0.362020	−	0.932170i	$-0.382087\pi$
$619$	11150.6	0.724040	0.362020	+	0.932170i	$0.382087\pi$
$620$	0	0
$621$	3887.43	0.251203
$622$	41790.6i	2.69397i
$623$	− 320.422i	− 0.0206059i
$624$	31374.6	2.01280
$625$	0	0
$626$	46324.0	2.95764
$627$	19522.3i	1.24345i
$628$	− 21801.8i	− 1.38533i
$629$	−7338.88	−0.465215
$630$	0	0
$631$	5381.79	0.339534	0.169767	−	0.985484i	$-0.445699\pi$
$631$	5381.79	0.339534	0.169767	+	0.985484i	$0.445699\pi$
$632$	61827.6i	3.89141i
$633$	19010.9i	1.19371i
$634$	42127.7	2.63897
$635$	0	0
$636$	−15187.9	−0.946918
$637$	1502.19i	0.0934361i
$638$	5924.64i	0.367647i
$639$	−5058.65	−0.313172
$640$	0	0
$641$	−19455.1	−1.19880	−0.599398	−	0.800451i	$-0.704593\pi$
$641$	−19455.1	−1.19880	−0.599398	+	0.800451i	$0.704593\pi$
$642$	− 5474.26i	− 0.336529i
$643$	14695.8i	0.901317i	0.892696	+	0.450658i	$0.148811\pi$
$643$	14695.8i	0.901317i	−0.892696	+	0.450658i	$0.851189\pi$
$644$	3854.25	0.235837
$645$	0	0
$646$	16169.1	0.984777
$647$	− 12694.8i	− 0.771383i	−0.922628	−	0.385691i	$-0.873963\pi$
$647$	− 12694.8i	− 0.771383i	0.922628	−	0.385691i	$-0.126037\pi$
$648$	40171.6i	2.43532i
$649$	−32189.0	−1.94688
$650$	0	0
$651$	−10254.0	−0.617334
$652$	− 28786.8i	− 1.72911i
$653$	12385.6i	0.742247i	0.928583	+	0.371124i	$0.121027\pi$
$653$	12385.6i	0.742247i	−0.928583	+	0.371124i	$0.878973\pi$
$654$	43730.0	2.61465
$655$	0	0
$656$	2497.07	0.148619
$657$	789.030i	0.0468539i
$658$	− 13707.3i	− 0.812109i
$659$	2072.18	0.122489	0.0612447	−	0.998123i	$-0.480493\pi$
$659$	2072.18	0.122489	0.0612447	+	0.998123i	$0.480493\pi$
$660$	0	0
$661$	1074.36	0.0632193	0.0316096	−	0.999500i	$-0.489937\pi$
$661$	1074.36	0.0632193	0.0316096	+	0.999500i	$0.489937\pi$
$662$	− 26703.6i	− 1.56777i
$663$	5314.47i	0.311307i
$664$	−47613.0	−2.78275
$665$	0	0
$666$	−5671.84	−0.329999
$667$	540.982i	0.0314047i
$668$	26228.2i	1.51916i
$669$	3479.42	0.201080
$670$	0	0
$671$	−797.667	−0.0458921
$672$	19988.6i	1.14744i
$673$	− 26195.2i	− 1.50037i	−0.661226	−	0.750186i	$-0.729964\pi$
$673$	− 26195.2i	− 1.50037i	0.661226	−	0.750186i	$-0.270036\pi$
$674$	38555.3	2.20341
$675$	0	0
$676$	−26794.7	−1.52450
$677$	− 4228.44i	− 0.240047i	−0.992771	−	0.120024i	$-0.961703\pi$
$677$	− 4228.44i	− 0.240047i	0.992771	−	0.120024i	$-0.0382970\pi$
$678$	− 46750.4i	− 2.64814i
$679$	11774.9	0.665506
$680$	0	0
$681$	−7756.80	−0.436478
$682$	88994.5i	4.99674i
$683$	− 27525.5i	− 1.54207i	−0.636792	−	0.771036i	$-0.719739\pi$
$683$	− 27525.5i	− 1.54207i	0.636792	−	0.771036i	$-0.280261\pi$
$684$	9085.91	0.507907
$685$	0	0
$686$	−1857.08	−0.103358
$687$	30867.3i	1.71421i
$688$	7435.40i	0.412023i
$689$	−4691.09	−0.259385
$690$	0	0
$691$	−33324.4	−1.83462	−0.917309	−	0.398177i	$-0.869643\pi$
$691$	−33324.4	−1.83462	−0.917309	+	0.398177i	$0.869643\pi$
$692$	− 53021.1i	− 2.91266i
$693$	1943.67i	0.106542i
$694$	−51654.8	−2.82534
$695$	0	0
$696$	−7029.54	−0.382836
$697$	422.973i	0.0229860i
$698$	− 6939.12i	− 0.376289i
$699$	−2013.77	−0.108967
$700$	0	0
$701$	−33262.9	−1.79219	−0.896094	−	0.443864i	$-0.853607\pi$
$701$	−33262.9	−1.79219	−0.896094	+	0.443864i	$0.853607\pi$
$702$	24977.1i	1.34288i
$703$	− 15816.2i	− 0.848534i
$704$	81611.8	4.36912
$705$	0	0
$706$	31392.0	1.67345
$707$	3039.17i	0.161668i
$708$	− 61141.0i	− 3.24551i
$709$	−13703.0	−0.725851	−0.362926	−	0.931818i	$-0.618222\pi$
$709$	−13703.0	−0.725851	−0.362926	+	0.931818i	$0.618222\pi$
$710$	0	0
$711$	−4557.70	−0.240404
$712$	− 3299.58i	− 0.173676i
$713$	8126.14i	0.426825i
$714$	−6570.00	−0.344364
$715$	0	0
$716$	34553.3	1.80352
$717$	− 25987.3i	− 1.35358i
$718$	− 12275.6i	− 0.638052i
$719$	8074.93	0.418838	0.209419	−	0.977826i	$-0.432843\pi$
$719$	8074.93	0.418838	0.209419	+	0.977826i	$0.432843\pi$
$720$	0	0
$721$	−2419.04	−0.124951
$722$	− 2289.59i	− 0.118019i
$723$	− 29323.6i	− 1.50838i
$724$	−55281.1	−2.83771
$725$	0	0
$726$	−35287.6	−1.80392
$727$	− 3668.70i	− 0.187159i	−0.995612	−	0.0935794i	$-0.970169\pi$
$727$	− 3668.70i	− 0.187159i	0.995612	−	0.0935794i	$-0.0298309\pi$
$728$	15468.9i	0.787523i
$729$	−21881.9	−1.11172
$730$	0	0
$731$	−1259.46	−0.0637250
$732$	− 1515.12i	− 0.0765033i
$733$	14980.3i	0.754857i	0.926039	+	0.377428i	$0.123192\pi$
$733$	14980.3i	0.754857i	−0.926039	+	0.377428i	$0.876808\pi$
$734$	39918.2	2.00737
$735$	0	0
$736$	15840.7	0.793338
$737$	8700.94i	0.434875i
$738$	326.894i	0.0163050i
$739$	−6530.59	−0.325077	−0.162538	−	0.986702i	$-0.551968\pi$
$739$	−6530.59	−0.325077	−0.162538	+	0.986702i	$0.551968\pi$
$740$	0	0
$741$	−11453.3	−0.567812
$742$	− 5799.36i	− 0.286929i
$743$	− 25952.0i	− 1.28141i	−0.767788	−	0.640704i	$-0.778643\pi$
$743$	− 25952.0i	− 1.28141i	0.767788	−	0.640704i	$-0.221357\pi$
$744$	−105591.	−5.20318
$745$	0	0
$746$	34906.2	1.71315
$747$	− 3509.85i	− 0.171913i
$748$	41459.6i	2.02662i
$749$	1519.83	0.0741434
$750$	0	0
$751$	−14093.9	−0.684813	−0.342407	−	0.939552i	$-0.611242\pi$
$751$	−14093.9	−0.684813	−0.342407	+	0.939552i	$0.611242\pi$
$752$	− 79483.6i	− 3.85435i
$753$	1452.57i	0.0702983i
$754$	−3475.87	−0.167883
$755$	0	0
$756$	−22451.0	−1.08007
$757$	− 2554.41i	− 0.122644i	−0.998118	−	0.0613220i	$-0.980468\pi$
$757$	− 2554.41i	− 0.122644i	0.998118	−	0.0613220i	$-0.0195316\pi$
$758$	22997.2i	1.10197i
$759$	−6286.40	−0.300635
$760$	0	0
$761$	2219.08	0.105705	0.0528527	−	0.998602i	$-0.483169\pi$
$761$	2219.08	0.105705	0.0528527	+	0.998602i	$0.483169\pi$
$762$	− 35160.1i	− 1.67154i
$763$	12140.9i	0.576054i
$764$	38856.5	1.84003
$765$	0	0
$766$	−36177.0	−1.70643
$767$	− 18884.6i	− 0.889028i
$768$	31333.5i	1.47220i
$769$	22466.2	1.05352	0.526758	−	0.850015i	$-0.323408\pi$
$769$	22466.2	1.05352	0.526758	+	0.850015i	$0.323408\pi$
$770$	0	0
$771$	36609.3	1.71006
$772$	− 32845.0i	− 1.53124i
$773$	− 9674.79i	− 0.450165i	−0.974340	−	0.225083i	$-0.927735\pi$
$773$	− 9674.79i	− 0.450165i	0.974340	−	0.225083i	$-0.0722652\pi$
$774$	−973.374	−0.0452031
$775$	0	0
$776$	121253.	5.60920
$777$	6426.60i	0.296722i
$778$	34498.2i	1.58974i
$779$	−911.560	−0.0419256
$780$	0	0
$781$	49746.6	2.27922
$782$	5206.64i	0.238093i
$783$	− 3151.23i	− 0.143826i
$784$	−10768.5	−0.490546
$785$	0	0
$786$	−44436.2	−2.01652
$787$	− 20942.8i	− 0.948577i	−0.880370	−	0.474288i	$-0.842705\pi$
$787$	− 20942.8i	− 0.948577i	0.880370	−	0.474288i	$-0.157295\pi$
$788$	− 14946.1i	− 0.675676i
$789$	24341.8	1.09834
$790$	0	0
$791$	12979.4	0.583433
$792$	20015.1i	0.897989i
$793$	− 467.975i	− 0.0209562i
$794$	−22999.2	−1.02797
$795$	0	0
$796$	70227.8	3.12708
$797$	23526.6i	1.04561i	0.852451	+	0.522807i	$0.175115\pi$
$797$	23526.6i	1.04561i	−0.852451	+	0.522807i	$0.824885\pi$
$798$	− 14159.2i	− 0.628107i
$799$	13463.5	0.596127
$800$	0	0
$801$	243.233	0.0107294
$802$	− 47827.1i	− 2.10578i
$803$	− 7759.29i	− 0.340996i
$804$	−16526.9	−0.724948
$805$	0	0
$806$	−52211.3	−2.28172
$807$	− 5968.72i	− 0.260358i
$808$	31296.1i	1.36262i
$809$	18202.2	0.791047	0.395523	−	0.918456i	$-0.370563\pi$
$809$	18202.2	0.791047	0.395523	+	0.918456i	$0.370563\pi$
$810$	0	0
$811$	−2510.24	−0.108689	−0.0543443	−	0.998522i	$-0.517307\pi$
$811$	−2510.24	−0.108689	−0.0543443	+	0.998522i	$0.517307\pi$
$812$	− 3124.33i	− 0.135028i
$813$	21906.5i	0.945012i
$814$	55776.7	2.40168
$815$	0	0
$816$	−38096.9	−1.63438
$817$	− 2714.30i	− 0.116232i
$818$	1728.24i	0.0738711i
$819$	−1140.31	−0.0486516
$820$	0	0
$821$	17899.6	0.760903	0.380451	−	0.924801i	$-0.375769\pi$
$821$	17899.6	0.760903	0.380451	+	0.924801i	$0.375769\pi$
$822$	23270.5i	0.987411i
$823$	− 14039.5i	− 0.594637i	−0.954778	−	0.297318i	$-0.903908\pi$
$823$	− 14039.5i	− 0.594637i	0.954778	−	0.297318i	$-0.0960923\pi$
$824$	−24910.3	−1.05315
$825$	0	0
$826$	23346.1	0.983431
$827$	15127.4i	0.636073i	0.948079	+	0.318036i	$0.103023\pi$
$827$	15127.4i	0.636073i	−0.948079	+	0.318036i	$0.896977\pi$
$828$	2925.77i	0.122799i
$829$	−21986.5	−0.921136	−0.460568	−	0.887624i	$-0.652354\pi$
$829$	−21986.5	−0.921136	−0.460568	+	0.887624i	$0.652354\pi$
$830$	0	0
$831$	−41718.7	−1.74152
$832$	47880.0i	1.99512i
$833$	− 1824.04i	− 0.0758696i
$834$	−4942.76	−0.205220
$835$	0	0
$836$	−89350.6	−3.69648
$837$	− 47334.8i	− 1.95476i
$838$	69243.5i	2.85439i
$839$	2276.89	0.0936914	0.0468457	−	0.998902i	$-0.485083\pi$
$839$	2276.89	0.0936914	0.0468457	+	0.998902i	$0.485083\pi$
$840$	0	0
$841$	−23950.5	−0.982019
$842$	− 36531.8i	− 1.49521i
$843$	− 1727.25i	− 0.0705688i
$844$	−87010.1	−3.54859
$845$	0	0
$846$	10405.3	0.422861
$847$	− 9796.97i	− 0.397436i
$848$	− 33628.2i	− 1.36179i
$849$	−27113.4	−1.09603
$850$	0	0
$851$	5093.00	0.205154
$852$	94490.6i	3.79952i
$853$	− 13342.6i	− 0.535570i	−0.963479	−	0.267785i	$-0.913708\pi$
$853$	− 13342.6i	− 0.535570i	0.963479	−	0.267785i	$-0.0862917\pi$
$854$	578.533	0.0231815
$855$	0	0
$856$	15650.6	0.624915
$857$	18690.9i	0.745003i	0.928032	+	0.372502i	$0.121500\pi$
$857$	18690.9i	0.745003i	−0.928032	+	0.372502i	$0.878500\pi$
$858$	− 40390.8i	− 1.60713i
$859$	−18318.9	−0.727628	−0.363814	−	0.931472i	$-0.618526\pi$
$859$	−18318.9	−0.727628	−0.363814	+	0.931472i	$0.618526\pi$
$860$	0	0
$861$	370.394	0.0146609
$862$	− 28071.3i	− 1.10918i
$863$	− 38133.1i	− 1.50413i	−0.659087	−	0.752067i	$-0.729057\pi$
$863$	− 38133.1i	− 1.50413i	0.659087	−	0.752067i	$-0.270943\pi$
$864$	−92272.3	−3.63330
$865$	0	0
$866$	−22967.3	−0.901223
$867$	16426.0i	0.643432i
$868$	− 46930.8i	− 1.83518i
$869$	44820.3	1.74962
$870$	0	0
$871$	−5104.66	−0.198582
$872$	125022.i	4.85525i
$873$	8938.33i	0.346525i
$874$	−11221.0	−0.434273
$875$	0	0
$876$	14738.3	0.568449
$877$	− 19707.5i	− 0.758807i	−0.925231	−	0.379404i	$-0.876129\pi$
$877$	− 19707.5i	− 0.758807i	0.925231	−	0.379404i	$-0.123871\pi$
$878$	29421.5i	1.13090i
$879$	34664.6	1.33016
$880$	0	0
$881$	−14091.5	−0.538883	−0.269441	−	0.963017i	$-0.586839\pi$
$881$	−14091.5	−0.538883	−0.269441	+	0.963017i	$0.586839\pi$
$882$	− 1409.71i	− 0.0538178i
$883$	− 3115.87i	− 0.118751i	−0.998236	−	0.0593757i	$-0.981089\pi$
$883$	− 3115.87i	− 0.118751i	0.998236	−	0.0593757i	$-0.0189110\pi$
$884$	−24323.5	−0.925438
$885$	0	0
$886$	−62229.8	−2.35965
$887$	38734.6i	1.46627i	0.680084	+	0.733134i	$0.261943\pi$
$887$	38734.6i	1.46627i	−0.680084	+	0.733134i	$0.738057\pi$
$888$	66178.6i	2.50091i
$889$	9761.57	0.368270
$890$	0	0
$891$	29121.3	1.09495
$892$	15924.8i	0.597759i
$893$	29015.6i	1.08731i
$894$	19675.7	0.736077
$895$	0	0
$896$	−24853.1	−0.926658
$897$	− 3688.10i	− 0.137282i
$898$	91225.8i	3.39003i
$899$	6587.21	0.244378
$900$	0	0
$901$	5696.21	0.210619
$902$	− 3214.66i	− 0.118666i
$903$	1102.90i	0.0406449i
$904$	133657.	4.91744
$905$	0	0
$906$	58480.2	2.14445
$907$	19242.9i	0.704464i	0.935913	+	0.352232i	$0.114577\pi$
$907$	19242.9i	0.704464i	−0.935913	+	0.352232i	$0.885423\pi$
$908$	− 35501.7i	− 1.29754i
$909$	−2307.03	−0.0841799
$910$	0	0
$911$	34613.3	1.25882	0.629412	−	0.777072i	$-0.283296\pi$
$911$	34613.3	1.25882	0.629412	+	0.777072i	$0.283296\pi$
$912$	− 82103.6i	− 2.98105i
$913$	34515.8i	1.25116i
$914$	−83100.1	−3.00734
$915$	0	0
$916$	−141275.	−5.09591
$917$	− 12336.9i	− 0.444276i
$918$	− 30328.7i	− 1.09041i
$919$	−25826.4	−0.927022	−0.463511	−	0.886091i	$-0.653411\pi$
$919$	−25826.4	−0.927022	−0.463511	+	0.886091i	$0.653411\pi$
$920$	0	0
$921$	3547.01	0.126903
$922$	76007.0i	2.71492i
$923$	29185.3i	1.04079i
$924$	36305.8	1.29261
$925$	0	0
$926$	−46893.8	−1.66417
$927$	− 1836.29i	− 0.0650613i
$928$	− 12840.8i	− 0.454224i
$929$	−19451.6	−0.686960	−0.343480	−	0.939160i	$-0.611606\pi$
$929$	−19451.6	−0.686960	−0.343480	+	0.939160i	$0.611606\pi$
$930$	0	0
$931$	3931.04	0.138383
$932$	− 9216.70i	− 0.323930i
$933$	35944.8i	1.26129i
$934$	−37979.1	−1.33053
$935$	0	0
$936$	−11742.5	−0.410059
$937$	34469.1i	1.20177i	0.799336	+	0.600884i	$0.205185\pi$
$937$	34469.1i	1.20177i	−0.799336	+	0.600884i	$0.794815\pi$
$938$	− 6310.63i	− 0.219669i
$939$	39844.1	1.38473
$940$	0	0
$941$	14156.4	0.490419	0.245209	−	0.969470i	$-0.421143\pi$
$941$	14156.4	0.490419	0.245209	+	0.969470i	$0.421143\pi$
$942$	− 25790.6i	− 0.892042i
$943$	− 293.532i	− 0.0101365i
$944$	135375.	4.66746
$945$	0	0
$946$	9572.13	0.328982
$947$	− 38092.4i	− 1.30711i	−0.756877	−	0.653557i	$-0.773276\pi$
$947$	− 38092.4i	− 1.30711i	0.756877	−	0.653557i	$-0.226724\pi$
$948$	85133.3i	2.91667i
$949$	4552.22	0.155713
$950$	0	0
$951$	36234.8	1.23553
$952$	− 18783.3i	− 0.639464i
$953$	− 5037.40i	− 0.171225i	−0.996329	−	0.0856126i	$-0.972715\pi$
$953$	− 5037.40i	− 0.171225i	0.996329	−	0.0856126i	$-0.0272847\pi$
$954$	4402.30	0.149402
$955$	0	0
$956$	118940.	4.02384
$957$	5095.88i	0.172128i
$958$	− 98185.1i	− 3.31129i
$959$	−6460.64	−0.217544
$960$	0	0
$961$	69156.0	2.32137
$962$	32723.0i	1.09671i
$963$	1153.71i	0.0386060i
$964$	134210.	4.48403
$965$	0	0
$966$	4559.41	0.151860
$967$	11495.3i	0.382278i	0.981563	+	0.191139i	$0.0612181\pi$
$967$	11495.3i	0.382278i	−0.981563	+	0.191139i	$0.938782\pi$
$968$	− 100885.i	− 3.34977i
$969$	13907.3	0.461061
$970$	0	0
$971$	22352.7	0.738757	0.369379	−	0.929279i	$-0.379571\pi$
$971$	22352.7	0.738757	0.369379	+	0.929279i	$0.379571\pi$
$972$	− 31282.7i	− 1.03230i
$973$	− 1372.27i	− 0.0452138i
$974$	−89539.4	−2.94561
$975$	0	0
$976$	3354.69	0.110022
$977$	14345.7i	0.469765i	0.972024	+	0.234882i	$0.0754705\pi$
$977$	14345.7i	0.469765i	−0.972024	+	0.234882i	$0.924530\pi$
$978$	− 34053.6i	− 1.11341i
$979$	−2391.94	−0.0780867
$980$	0	0
$981$	−9216.15	−0.299948
$982$	1194.42i	0.0388141i
$983$	− 34460.9i	− 1.11814i	−0.829120	−	0.559070i	$-0.811158\pi$
$983$	− 34460.9i	− 1.11814i	0.829120	−	0.559070i	$-0.188842\pi$
$984$	3814.17	0.123568
$985$	0	0
$986$	4220.61	0.136320
$987$	− 11789.9i	− 0.380220i
$988$	− 52420.2i	− 1.68796i
$989$	874.036	0.0281019
$990$	0	0
$991$	−35189.6	−1.12799	−0.563993	−	0.825780i	$-0.690735\pi$
$991$	−35189.6	−1.12799	−0.563993	+	0.825780i	$0.690735\pi$
$992$	− 192883.i	− 6.17342i
$993$	− 22968.2i	− 0.734011i
$994$	−36080.3	−1.15131
$995$	0	0
$996$	−65560.6	−2.08571
$997$	− 50730.0i	− 1.61147i	−0.592277	−	0.805734i	$-0.701771\pi$
$997$	− 50730.0i	− 1.61147i	0.592277	−	0.805734i	$-0.298229\pi$
$998$	− 32155.2i	− 1.01990i
$999$	−29666.8	−0.939554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.b.c.99.4		4
5.2	odd	4		175.4.a.c.1.1		2
5.3	odd	4		35.4.a.b.1.2	✓	2
5.4	even	2	inner	175.4.b.c.99.1		4
15.2	even	4		1575.4.a.z.1.2		2
15.8	even	4		315.4.a.f.1.1		2
20.3	even	4		560.4.a.r.1.2		2
35.3	even	12		245.4.e.i.226.1		4
35.13	even	4		245.4.a.k.1.2		2
35.18	odd	12		245.4.e.h.226.1		4
35.23	odd	12		245.4.e.h.116.1		4
35.27	even	4		1225.4.a.m.1.1		2
35.33	even	12		245.4.e.i.116.1		4
40.3	even	4		2240.4.a.bo.1.1		2
40.13	odd	4		2240.4.a.bn.1.2		2
105.83	odd	4		2205.4.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.b.1.2	✓	2	5.3	odd	4
175.4.a.c.1.1		2	5.2	odd	4
175.4.b.c.99.1		4	5.4	even	2	inner
175.4.b.c.99.4		4	1.1	even	1	trivial
245.4.a.k.1.2		2	35.13	even	4
245.4.e.h.116.1		4	35.23	odd	12
245.4.e.h.226.1		4	35.18	odd	12
245.4.e.i.116.1		4	35.33	even	12
245.4.e.i.226.1		4	35.3	even	12
315.4.a.f.1.1		2	15.8	even	4
560.4.a.r.1.2		2	20.3	even	4
1225.4.a.m.1.1		2	35.27	even	4
1575.4.a.z.1.2		2	15.2	even	4
2205.4.a.u.1.1		2	105.83	odd	4
2240.4.a.bn.1.2		2	40.13	odd	4
2240.4.a.bo.1.1		2	40.3	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)

\(f(q)\)	\(=\)	\(q+5.41421i q^{2} +4.65685i q^{3} -21.3137 q^{4} -25.2132 q^{6} -7.00000i q^{7} -72.0833i q^{8} +5.31371 q^{9} +O(q^{10})\)	\(q+5.41421i q^{2} +4.65685i q^{3} -21.3137 q^{4} -25.2132 q^{6} -7.00000i q^{7} -72.0833i q^{8} +5.31371 q^{9} -52.2548 q^{11} -99.2548i q^{12} -30.6569i q^{13} +37.8995 q^{14} +219.765 q^{16} +37.2254i q^{17} +28.7696i q^{18} -80.2254 q^{19} +32.5980 q^{21} -282.919i q^{22} -25.8335i q^{23} +335.681 q^{24} +165.983 q^{26} +150.480i q^{27} +149.196i q^{28} -20.9411 q^{29} -314.558 q^{31} +613.186i q^{32} -243.343i q^{33} -201.546 q^{34} -113.255 q^{36} +197.147i q^{37} -434.357i q^{38} +142.765 q^{39} +11.3625 q^{41} +176.492i q^{42} +33.8335i q^{43} +1113.74 q^{44} +139.868 q^{46} -361.676i q^{47} +1023.41i q^{48} -49.0000 q^{49} -173.353 q^{51} +653.411i q^{52} -153.019i q^{53} -814.732 q^{54} -504.583 q^{56} -373.598i q^{57} -113.380i q^{58} +616.000 q^{59} +15.2649 q^{61} -1703.09i q^{62} -37.1960i q^{63} -1561.80 q^{64} +1317.51 q^{66} -166.510i q^{67} -793.411i q^{68} +120.303 q^{69} -952.000 q^{71} -383.029i q^{72} +148.489i q^{73} -1067.40 q^{74} +1709.90 q^{76} +365.784i q^{77} +772.958i q^{78} -857.725 q^{79} -557.294 q^{81} +61.5189i q^{82} -660.528i q^{83} -694.784 q^{84} -183.182 q^{86} -97.5198i q^{87} +3766.70i q^{88} +45.7746 q^{89} -214.598 q^{91} +550.607i q^{92} -1464.85i q^{93} +1958.19 q^{94} -2855.52 q^{96} +1682.13i q^{97} -265.296i q^{98} -277.667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 40 q^{4} - 16 q^{6} - 24 q^{9}+O(q^{10}) \) 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

Varieties

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Representations

Groups

Database

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