LMFDB - Embedded newform 275.4.b.b.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,4,Mod(199,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, 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("275.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	275.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:	$16.2255252516$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Root			$-2.56155i$ of defining polynomial
Character	$\chi$	$=$	275.199
Dual form			275.4.b.b.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.43845i q^{2} +0.561553i q^{3} +5.93087 q^{4} -0.807764 q^{6} +31.0540i q^{7} +20.0388i q^{8} +26.6847 q^{9} +O(q^{10})$	\(q+1.43845i q^{2} +0.561553i q^{3} +5.93087 q^{4} -0.807764 q^{6} +31.0540i q^{7} +20.0388i q^{8} +26.6847 q^{9} -11.0000 q^{11} +3.33050i q^{12} -45.6155i q^{13} -44.6695 q^{14} +18.6222 q^{16} +40.4536i q^{17} +38.3845i q^{18} -91.2699 q^{19} -17.4384 q^{21} -15.8229i q^{22} +32.2462i q^{23} -11.2529 q^{24} +65.6155 q^{26} +30.1468i q^{27} +184.177i q^{28} -35.8702 q^{29} +311.702 q^{31} +187.098i q^{32} -6.17708i q^{33} -58.1904 q^{34} +158.263 q^{36} +368.147i q^{37} -131.287i q^{38} +25.6155 q^{39} -393.602 q^{41} -25.0843i q^{42} -351.602i q^{43} -65.2396 q^{44} -46.3845 q^{46} +230.155i q^{47} +10.4573i q^{48} -621.349 q^{49} -22.7168 q^{51} -270.540i q^{52} +406.902i q^{53} -43.3645 q^{54} -622.285 q^{56} -51.2529i q^{57} -51.5975i q^{58} +368.725 q^{59} -322.825 q^{61} +448.366i q^{62} +828.665i q^{63} -120.153 q^{64} +8.88540 q^{66} -442.233i q^{67} +239.925i q^{68} -18.1080 q^{69} +667.745 q^{71} +534.729i q^{72} -84.5701i q^{73} -529.560 q^{74} -541.310 q^{76} -341.594i q^{77} +36.8466i q^{78} +411.983 q^{79} +703.557 q^{81} -566.176i q^{82} -835.619i q^{83} -103.425 q^{84} +505.761 q^{86} -20.1430i q^{87} -220.427i q^{88} +799.853 q^{89} +1416.54 q^{91} +191.248i q^{92} +175.037i q^{93} -331.066 q^{94} -105.065 q^{96} -768.945i q^{97} -893.778i q^{98} -293.531 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 34 q^{4} + 38 q^{6} + 82 q^{9}+O(q^{10}) $ 4 * q - 34 * q^4 + 38 * q^6 + 82 * q^9	$ 4 q - 34 q^{4} + 38 q^{6} + 82 q^{9} - 44 q^{11} - 22 q^{14} + 594 q^{16} + 6 q^{19} - 78 q^{21} - 614 q^{24} + 180 q^{26} + 442 q^{29} + 282 q^{31} - 1346 q^{34} - 340 q^{36} + 20 q^{39} - 288 q^{41} + 374 q^{44} - 268 q^{46} - 630 q^{49} + 742 q^{51} + 1550 q^{54} - 2250 q^{56} + 172 q^{59} - 310 q^{61} - 5618 q^{64} - 418 q^{66} + 76 q^{69} + 3174 q^{71} - 3182 q^{74} - 5406 q^{76} + 2588 q^{79} + 1132 q^{81} + 782 q^{84} - 2232 q^{86} + 3554 q^{89} + 2780 q^{91} + 1364 q^{94} + 6086 q^{96} - 902 q^{99}+O(q^{100}) $ 4 * q - 34 * q^4 + 38 * q^6 + 82 * q^9 - 44 * q^11 - 22 * q^14 + 594 * q^16 + 6 * q^19 - 78 * q^21 - 614 * q^24 + 180 * q^26 + 442 * q^29 + 282 * q^31 - 1346 * q^34 - 340 * q^36 + 20 * q^39 - 288 * q^41 + 374 * q^44 - 268 * q^46 - 630 * q^49 + 742 * q^51 + 1550 * q^54 - 2250 * q^56 + 172 * q^59 - 310 * q^61 - 5618 * q^64 - 418 * q^66 + 76 * q^69 + 3174 * q^71 - 3182 * q^74 - 5406 * q^76 + 2588 * q^79 + 1132 * q^81 + 782 * q^84 - 2232 * q^86 + 3554 * q^89 + 2780 * q^91 + 1364 * q^94 + 6086 * q^96 - 902 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.43845i	0.508568i	0.967130	+	0.254284i	$0.0818398\pi$
$2$	1.43845i	0.508568i	−0.967130	+	0.254284i	$0.918160\pi$
$3$	0.561553i	0.108071i	0.998539	+	0.0540354i	$0.0172084\pi$
$3$	0.561553i	0.108071i	−0.998539	+	0.0540354i	$0.982792\pi$
$4$	5.93087	0.741359
$5$	0	0
$5$	0	0
$6$	−0.807764	−0.0549614
$7$	31.0540i	1.67676i	0.545088	+	0.838379i	$0.316496\pi$
$7$	31.0540i	1.67676i	−0.545088	+	0.838379i	$0.683504\pi$
$8$	20.0388i	0.885599i
$9$	26.6847	0.988321
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	3.33050i	0.0801193i
$13$	− 45.6155i	− 0.973190i	−0.873628	−	0.486595i	$-0.838239\pi$
$13$	− 45.6155i	− 0.973190i	0.873628	−	0.486595i	$-0.161761\pi$
$14$	−44.6695	−0.852745
$15$	0	0
$16$	18.6222	0.290971
$17$	40.4536i	0.577144i	0.957458	+	0.288572i	$0.0931804\pi$
$17$	40.4536i	0.577144i	−0.957458	+	0.288572i	$0.906820\pi$
$18$	38.3845i	0.502628i
$19$	−91.2699	−1.10204	−0.551020	−	0.834492i	$-0.685761\pi$
$19$	−91.2699	−1.10204	−0.551020	+	0.834492i	$0.685761\pi$
$20$	0	0
$21$	−17.4384	−0.181209
$22$	− 15.8229i	− 0.153339i
$23$	32.2462i	0.292339i	0.989260	+	0.146170i	$0.0466945\pi$
$23$	32.2462i	0.292339i	−0.989260	+	0.146170i	$0.953305\pi$
$24$	−11.2529	−0.0957075
$25$	0	0
$26$	65.6155	0.494933
$27$	30.1468i	0.214880i
$28$	184.177i	1.24308i
$29$	−35.8702	−0.229688	−0.114844	−	0.993384i	$-0.536637\pi$
$29$	−35.8702	−0.229688	−0.114844	+	0.993384i	$0.536637\pi$
$30$	0	0
$31$	311.702	1.80591	0.902956	−	0.429733i	$-0.141392\pi$
$31$	311.702	1.80591	0.902956	+	0.429733i	$0.141392\pi$
$32$	187.098i	1.03358i
$33$	− 6.17708i	− 0.0325846i
$34$	−58.1904	−0.293517
$35$	0	0
$36$	158.263	0.732700
$37$	368.147i	1.63576i	0.575392	+	0.817878i	$0.304850\pi$
$37$	368.147i	1.63576i	−0.575392	+	0.817878i	$0.695150\pi$
$38$	− 131.287i	− 0.560462i
$39$	25.6155	0.105174
$40$	0	0
$41$	−393.602	−1.49928	−0.749638	−	0.661848i	$-0.769773\pi$
$41$	−393.602	−1.49928	−0.749638	+	0.661848i	$0.769773\pi$
$42$	− 25.0843i	− 0.0921569i
$43$	− 351.602i	− 1.24695i	−0.781843	−	0.623475i	$-0.785720\pi$
$43$	− 351.602i	− 1.24695i	0.781843	−	0.623475i	$-0.214280\pi$
$44$	−65.2396	−0.223528
$45$	0	0
$46$	−46.3845	−0.148674
$47$	230.155i	0.714289i	0.934049	+	0.357145i	$0.116250\pi$
$47$	230.155i	0.714289i	−0.934049	+	0.357145i	$0.883750\pi$
$48$	10.4573i	0.0314455i
$49$	−621.349	−1.81151
$50$	0	0
$51$	−22.7168	−0.0623724
$52$	− 270.540i	− 0.721483i
$53$	406.902i	1.05457i	0.849688	+	0.527286i	$0.176790\pi$
$53$	406.902i	1.05457i	−0.849688	+	0.527286i	$0.823210\pi$
$54$	−43.3645	−0.109281
$55$	0	0
$56$	−622.285	−1.48493
$57$	− 51.2529i	− 0.119098i
$58$	− 51.5975i	− 0.116812i
$59$	368.725	0.813626	0.406813	−	0.913511i	$-0.366640\pi$
$59$	368.725	0.813626	0.406813	+	0.913511i	$0.366640\pi$
$60$	0	0
$61$	−322.825	−0.677598	−0.338799	−	0.940859i	$-0.610021\pi$
$61$	−322.825	−0.677598	−0.338799	+	0.940859i	$0.610021\pi$
$62$	448.366i	0.918429i
$63$	828.665i	1.65717i
$64$	−120.153	−0.234673
$65$	0	0
$66$	8.88540	0.0165715
$67$	− 442.233i	− 0.806378i	−0.915117	−	0.403189i	$-0.867902\pi$
$67$	− 442.233i	− 0.806378i	0.915117	−	0.403189i	$-0.132098\pi$
$68$	239.925i	0.427870i
$69$	−18.1080	−0.0315933
$70$	0	0
$71$	667.745	1.11615	0.558076	−	0.829790i	$-0.311540\pi$
$71$	667.745	1.11615	0.558076	+	0.829790i	$0.311540\pi$
$72$	534.729i	0.875256i
$73$	− 84.5701i	− 0.135591i	−0.997699	−	0.0677957i	$-0.978403\pi$
$73$	− 84.5701i	− 0.135591i	0.997699	−	0.0677957i	$-0.0215966\pi$
$74$	−529.560	−0.831893
$75$	0	0
$76$	−541.310	−0.817006
$77$	− 341.594i	− 0.505561i
$78$	36.8466i	0.0534879i
$79$	411.983	0.586730	0.293365	−	0.956000i	$-0.405225\pi$
$79$	411.983	0.586730	0.293365	+	0.956000i	$0.405225\pi$
$80$	0	0
$81$	703.557	0.965098
$82$	− 566.176i	− 0.762484i
$83$	− 835.619i	− 1.10507i	−0.833488	−	0.552537i	$-0.813660\pi$
$83$	− 835.619i	− 1.10507i	0.833488	−	0.552537i	$-0.186340\pi$
$84$	−103.425	−0.134341
$85$	0	0
$86$	505.761	0.634159
$87$	− 20.1430i	− 0.0248225i
$88$	− 220.427i	− 0.267018i
$89$	799.853	0.952632	0.476316	−	0.879274i	$-0.341972\pi$
$89$	799.853	0.952632	0.476316	+	0.879274i	$0.341972\pi$
$90$	0	0
$91$	1416.54	1.63180
$92$	191.248i	0.216728i
$93$	175.037i	0.195167i
$94$	−331.066	−0.363265
$95$	0	0
$96$	−105.065	−0.111700
$97$	− 768.945i	− 0.804892i	−0.915444	−	0.402446i	$-0.868160\pi$
$97$	− 768.945i	− 0.804892i	0.915444	−	0.402446i	$-0.131840\pi$
$98$	− 893.778i	− 0.921278i
$99$	−293.531	−0.297990
$100$	0	0
$101$	−1412.31	−1.39139	−0.695696	−	0.718337i	$-0.744904\pi$
$101$	−1412.31	−1.39139	−0.695696	+	0.718337i	$0.744904\pi$
$102$	− 32.6770i	− 0.0317206i
$103$	24.4185i	0.0233595i	0.999932	+	0.0116797i	$0.00371786\pi$
$103$	24.4185i	0.0233595i	−0.999932	+	0.0116797i	$0.996282\pi$
$104$	914.081	0.861856
$105$	0	0
$106$	−585.308	−0.536322
$107$	− 532.155i	− 0.480798i	−0.970674	−	0.240399i	$-0.922722\pi$
$107$	− 532.155i	− 0.480798i	0.970674	−	0.240399i	$-0.0772783\pi$
$108$	178.797i	0.159303i
$109$	1234.62	1.08491	0.542455	−	0.840085i	$-0.317495\pi$
$109$	1234.62	1.08491	0.542455	+	0.840085i	$0.317495\pi$
$110$	0	0
$111$	−206.734	−0.176778
$112$	578.292i	0.487888i
$113$	− 1304.45i	− 1.08595i	−0.839748	−	0.542976i	$-0.817297\pi$
$113$	− 1304.45i	− 1.08595i	0.839748	−	0.542976i	$-0.182703\pi$
$114$	73.7245	0.0605696
$115$	0	0
$116$	−212.742	−0.170281
$117$	− 1217.23i	− 0.961824i
$118$	530.392i	0.413784i
$119$	−1256.25	−0.967729
$120$	0	0
$121$	121.000	0.0909091
$122$	− 464.366i	− 0.344605i
$123$	− 221.028i	− 0.162028i
$124$	1848.66	1.33883
$125$	0	0
$126$	−1191.99	−0.842785
$127$	− 1167.88i	− 0.816004i	−0.912981	−	0.408002i	$-0.866226\pi$
$127$	− 1167.88i	− 0.816004i	0.912981	−	0.408002i	$-0.133774\pi$
$128$	1323.95i	0.914231i
$129$	197.443	0.134759
$130$	0	0
$131$	1549.95	1.03374	0.516869	−	0.856065i	$-0.327098\pi$
$131$	1549.95	1.03374	0.516869	+	0.856065i	$0.327098\pi$
$132$	− 36.6355i	− 0.0241569i
$133$	− 2834.29i	− 1.84785i
$134$	636.129	0.410098
$135$	0	0
$136$	−810.642	−0.511118
$137$	2440.68i	1.52205i	0.648722	+	0.761026i	$0.275304\pi$
$137$	2440.68i	1.52205i	−0.648722	+	0.761026i	$0.724696\pi$
$138$	− 26.0473i	− 0.0160674i
$139$	1861.43	1.13586	0.567930	−	0.823077i	$-0.307744\pi$
$139$	1861.43	1.13586	0.567930	+	0.823077i	$0.307744\pi$
$140$	0	0
$141$	−129.244	−0.0771939
$142$	960.516i	0.567639i
$143$	501.771i	0.293428i
$144$	496.926	0.287573
$145$	0	0
$146$	121.650	0.0689575
$147$	− 348.920i	− 0.195772i
$148$	2183.43i	1.21268i
$149$	−814.376	−0.447760	−0.223880	−	0.974617i	$-0.571872\pi$
$149$	−814.376	−0.447760	−0.223880	+	0.974617i	$0.571872\pi$
$150$	0	0
$151$	3666.43	1.97596	0.987979	−	0.154591i	$-0.0494060\pi$
$151$	3666.43	1.97596	0.987979	+	0.154591i	$0.0494060\pi$
$152$	− 1828.94i	− 0.975965i
$153$	1079.49i	0.570403i
$154$	491.365	0.257112
$155$	0	0
$156$	151.922	0.0779713
$157$	− 2671.96i	− 1.35825i	−0.734021	−	0.679127i	$-0.762359\pi$
$157$	− 2671.96i	− 1.35825i	0.734021	−	0.679127i	$-0.237641\pi$
$158$	592.616i	0.298392i
$159$	−228.497	−0.113969
$160$	0	0
$161$	−1001.37	−0.490182
$162$	1012.03i	0.490818i
$163$	− 1728.53i	− 0.830605i	−0.909683	−	0.415302i	$-0.863676\pi$
$163$	− 1728.53i	− 0.830605i	0.909683	−	0.415302i	$-0.136324\pi$
$164$	−2334.40	−1.11150
$165$	0	0
$166$	1201.99	0.562005
$167$	0.0653990i	0 3.03037e-5i	1.00000		1.51519e-5i	$4.82299e-6\pi$
$167$	0.0653990i	0 3.03037e-5i	−1.00000		1.51519e-5i	$0.999995\pi$
$168$	− 349.446i	− 0.160478i
$169$	116.224	0.0529010
$170$	0	0
$171$	−2435.51	−1.08917
$172$	− 2085.31i	− 0.924437i
$173$	− 1816.75i	− 0.798411i	−0.916861	−	0.399205i	$-0.869286\pi$
$173$	− 1816.75i	− 0.798411i	0.916861	−	0.399205i	$-0.130714\pi$
$174$	28.9747	0.0126239
$175$	0	0
$176$	−204.844	−0.0877312
$177$	207.059i	0.0879293i
$178$	1150.55i	0.484478i
$179$	−2381.23	−0.994312	−0.497156	−	0.867661i	$-0.665622\pi$
$179$	−2381.23	−0.994312	−0.497156	+	0.867661i	$0.665622\pi$
$180$	0	0
$181$	1275.61	0.523840	0.261920	−	0.965090i	$-0.415644\pi$
$181$	1275.61	0.523840	0.261920	+	0.965090i	$0.415644\pi$
$182$	2037.62i	0.829883i
$183$	− 181.283i	− 0.0732286i
$184$	−646.176	−0.258895
$185$	0	0
$186$	−251.781	−0.0992554
$187$	− 444.990i	− 0.174015i
$188$	1365.02i	0.529545i
$189$	−936.177	−0.360301
$190$	0	0
$191$	−3699.04	−1.40133	−0.700663	−	0.713492i	$-0.747112\pi$
$191$	−3699.04	−1.40133	−0.700663	+	0.713492i	$0.747112\pi$
$192$	− 67.4720i	− 0.0253613i
$193$	1231.22i	0.459196i	0.973285	+	0.229598i	$0.0737412\pi$
$193$	1231.22i	0.459196i	−0.973285	+	0.229598i	$0.926259\pi$
$194$	1106.09	0.409342
$195$	0	0
$196$	−3685.14	−1.34298
$197$	− 728.087i	− 0.263320i	−0.991295	−	0.131660i	$-0.957969\pi$
$197$	− 728.087i	− 0.263320i	0.991295	−	0.131660i	$-0.0420307\pi$
$198$	− 422.229i	− 0.151548i
$199$	1650.81	0.588055	0.294027	−	0.955797i	$-0.405004\pi$
$199$	1650.81	0.588055	0.294027	+	0.955797i	$0.405004\pi$
$200$	0	0
$201$	248.337	0.0871460
$202$	− 2031.54i	− 0.707617i
$203$	− 1113.91i	− 0.385130i
$204$	−134.731	−0.0462403
$205$	0	0
$206$	−35.1247	−0.0118799
$207$	860.479i	0.288925i
$208$	− 849.460i	− 0.283171i
$209$	1003.97	0.332277
$210$	0	0
$211$	1587.01	0.517792	0.258896	−	0.965905i	$-0.416641\pi$
$211$	1587.01	0.517792	0.258896	+	0.965905i	$0.416641\pi$
$212$	2413.29i	0.781817i
$213$	374.974i	0.120624i
$214$	765.477	0.244518
$215$	0	0
$216$	−604.106	−0.190297
$217$	9679.58i	3.02808i
$218$	1775.94i	0.551751i
$219$	47.4906	0.0146535
$220$	0	0
$221$	1845.31	0.561670
$222$	− 297.376i	− 0.0899034i
$223$	− 1998.59i	− 0.600160i	−0.953914	−	0.300080i	$-0.902987\pi$
$223$	− 1998.59i	− 0.600160i	0.953914	−	0.300080i	$-0.0970135\pi$
$224$	−5810.12	−1.73306
$225$	0	0
$226$	1876.39	0.552280
$227$	− 4212.00i	− 1.23154i	−0.787925	−	0.615771i	$-0.788845\pi$
$227$	− 4212.00i	− 1.23154i	0.787925	−	0.615771i	$-0.211155\pi$
$228$	− 303.974i	− 0.0882946i
$229$	−1371.82	−0.395863	−0.197931	−	0.980216i	$-0.563422\pi$
$229$	−1371.82	−0.395863	−0.197931	+	0.980216i	$0.563422\pi$
$230$	0	0
$231$	191.823	0.0546365
$232$	− 718.797i	− 0.203411i
$233$	− 1718.37i	− 0.483152i	−0.970382	−	0.241576i	$-0.922336\pi$
$233$	− 1718.37i	− 0.483152i	0.970382	−	0.241576i	$-0.0776643\pi$
$234$	1750.93	0.489153
$235$	0	0
$236$	2186.86	0.603189
$237$	231.350i	0.0634085i
$238$	− 1807.04i	− 0.492156i
$239$	1794.77	0.485749	0.242875	−	0.970058i	$-0.421910\pi$
$239$	1794.77	0.485749	0.242875	+	0.970058i	$0.421910\pi$
$240$	0	0
$241$	5185.02	1.38588	0.692939	−	0.720996i	$-0.256315\pi$
$241$	5185.02	1.38588	0.692939	+	0.720996i	$0.256315\pi$
$242$	174.052i	0.0462334i
$243$	1209.05i	0.319179i
$244$	−1914.63	−0.502343
$245$	0	0
$246$	317.938	0.0824023
$247$	4163.32i	1.07249i
$248$	6246.13i	1.59931i
$249$	469.244	0.119426
$250$	0	0
$251$	−3827.69	−0.962556	−0.481278	−	0.876568i	$-0.659827\pi$
$251$	−3827.69	−0.962556	−0.481278	+	0.876568i	$0.659827\pi$
$252$	4914.70i	1.22856i
$253$	− 354.708i	− 0.0881436i
$254$	1679.93	0.414993
$255$	0	0
$256$	−2865.65	−0.699621
$257$	2671.37i	0.648387i	0.945991	+	0.324193i	$0.105093\pi$
$257$	2671.37i	0.648387i	−0.945991	+	0.324193i	$0.894907\pi$
$258$	284.012i	0.0685341i
$259$	−11432.4	−2.74276
$260$	0	0
$261$	−957.185	−0.227005
$262$	2229.52i	0.525726i
$263$	6659.10i	1.56128i	0.624979	+	0.780642i	$0.285108\pi$
$263$	6659.10i	1.56128i	−0.624979	+	0.780642i	$0.714892\pi$
$264$	123.781	0.0288569
$265$	0	0
$266$	4076.98	0.939758
$267$	449.160i	0.102952i
$268$	− 2622.83i	− 0.597816i
$269$	−8473.05	−1.92049	−0.960244	−	0.279162i	$-0.909943\pi$
$269$	−8473.05	−1.92049	−0.960244	+	0.279162i	$0.909943\pi$
$270$	0	0
$271$	−2643.21	−0.592486	−0.296243	−	0.955113i	$-0.595734\pi$
$271$	−2643.21	−0.592486	−0.296243	+	0.955113i	$0.595734\pi$
$272$	753.334i	0.167932i
$273$	795.464i	0.176350i
$274$	−3510.78	−0.774066
$275$	0	0
$276$	−107.396	−0.0234220
$277$	386.962i	0.0839361i	0.999119	+	0.0419680i	$0.0133628\pi$
$277$	386.962i	0.0839361i	−0.999119	+	0.0419680i	$0.986637\pi$
$278$	2677.57i	0.577662i
$279$	8317.65	1.78482
$280$	0	0
$281$	−1106.42	−0.234887	−0.117444	−	0.993080i	$-0.537470\pi$
$281$	−1106.42	−0.234887	−0.117444	+	0.993080i	$0.537470\pi$
$282$	− 185.911i	− 0.0392583i
$283$	1165.71i	0.244855i	0.992477	+	0.122428i	$0.0390679\pi$
$283$	1165.71i	0.244855i	−0.992477	+	0.122428i	$0.960932\pi$
$284$	3960.31	0.827469
$285$	0	0
$286$	−721.771	−0.149228
$287$	− 12222.9i	− 2.51392i
$288$	4992.63i	1.02151i
$289$	3276.51	0.666905
$290$	0	0
$291$	431.803	0.0869854
$292$	− 501.574i	− 0.100522i
$293$	− 3646.82i	− 0.727131i	−0.931569	−	0.363566i	$-0.881559\pi$
$293$	− 3646.82i	− 0.727131i	0.931569	−	0.363566i	$-0.118441\pi$
$294$	501.904	0.0995633
$295$	0	0
$296$	−7377.23	−1.44862
$297$	− 331.614i	− 0.0647886i
$298$	− 1171.44i	− 0.227716i
$299$	1470.93	0.284502
$300$	0	0
$301$	10918.6	2.09083
$302$	5273.96i	1.00491i
$303$	− 793.089i	− 0.150369i
$304$	−1699.64	−0.320662
$305$	0	0
$306$	−1552.79	−0.290089
$307$	816.066i	0.151711i	0.997119	+	0.0758556i	$0.0241688\pi$
$307$	816.066i	0.151711i	−0.997119	+	0.0758556i	$0.975831\pi$
$308$	− 2025.95i	− 0.374802i
$309$	−13.7123	−0.00252448
$310$	0	0
$311$	3146.99	0.573793	0.286896	−	0.957962i	$-0.407376\pi$
$311$	3146.99	0.573793	0.286896	+	0.957962i	$0.407376\pi$
$312$	513.305i	0.0931416i
$313$	− 5085.49i	− 0.918367i	−0.888341	−	0.459184i	$-0.848142\pi$
$313$	− 5085.49i	− 0.918367i	0.888341	−	0.459184i	$-0.151858\pi$
$314$	3843.48	0.690764
$315$	0	0
$316$	2443.42	0.434978
$317$	4801.89i	0.850791i	0.905007	+	0.425396i	$0.139865\pi$
$317$	4801.89i	0.850791i	−0.905007	+	0.425396i	$0.860135\pi$
$318$	− 328.681i	− 0.0579608i
$319$	394.573	0.0692534
$320$	0	0
$321$	298.833	0.0519603
$322$	− 1440.42i	− 0.249291i
$323$	− 3692.20i	− 0.636035i
$324$	4172.70	0.715484
$325$	0	0
$326$	2486.39	0.422419
$327$	693.305i	0.117247i
$328$	− 7887.32i	− 1.32776i
$329$	−7147.24	−1.19769
$330$	0	0
$331$	−2597.31	−0.431302	−0.215651	−	0.976470i	$-0.569187\pi$
$331$	−2597.31	−0.431302	−0.215651	+	0.976470i	$0.569187\pi$
$332$	− 4955.95i	− 0.819256i
$333$	9823.87i	1.61665i
$334$	−0.0940730	−1.54115e−5 0
$335$	0	0
$336$	−324.742	−0.0527265
$337$	− 2695.45i	− 0.435698i	−0.975982	−	0.217849i	$-0.930096\pi$
$337$	− 2695.45i	− 0.435698i	0.975982	−	0.217849i	$-0.0699041\pi$
$338$	167.182i	0.0269038i
$339$	732.519	0.117360
$340$	0	0
$341$	−3428.72	−0.544503
$342$	− 3503.35i	− 0.553916i
$343$	− 8643.85i	− 1.36071i
$344$	7045.69	1.10430
$345$	0	0
$346$	2613.30	0.406046
$347$	9239.79i	1.42945i	0.699407	+	0.714723i	$0.253447\pi$
$347$	9239.79i	1.42945i	−0.699407	+	0.714723i	$0.746553\pi$
$348$	− 119.466i	− 0.0184024i
$349$	−3857.67	−0.591680	−0.295840	−	0.955237i	$-0.595600\pi$
$349$	−3857.67	−0.591680	−0.295840	+	0.955237i	$0.595600\pi$
$350$	0	0
$351$	1375.16	0.209119
$352$	− 2058.07i	− 0.311635i
$353$	− 3378.21i	− 0.509360i	−0.967025	−	0.254680i	$-0.918030\pi$
$353$	− 3378.21i	− 0.509360i	0.967025	−	0.254680i	$-0.0819701\pi$
$354$	−297.843	−0.0447180
$355$	0	0
$356$	4743.83	0.706242
$357$	− 705.448i	− 0.104583i
$358$	− 3425.28i	− 0.505675i
$359$	9892.96	1.45440	0.727201	−	0.686425i	$-0.240821\pi$
$359$	9892.96	1.45440	0.727201	+	0.686425i	$0.240821\pi$
$360$	0	0
$361$	1471.19	0.214491
$362$	1834.89i	0.266408i
$363$	67.9479i	0.00982463i
$364$	8401.33	1.20975
$365$	0	0
$366$	260.766	0.0372417
$367$	− 5295.58i	− 0.753208i	−0.926374	−	0.376604i	$-0.877092\pi$
$367$	− 5295.58i	− 0.753208i	0.926374	−	0.376604i	$-0.122908\pi$
$368$	600.495i	0.0850623i
$369$	−10503.1	−1.48177
$370$	0	0
$371$	−12635.9	−1.76826
$372$	1038.12i	0.144688i
$373$	7786.10i	1.08083i	0.841399	+	0.540414i	$0.181732\pi$
$373$	7786.10i	1.08083i	−0.841399	+	0.540414i	$0.818268\pi$
$374$	640.094	0.0884986
$375$	0	0
$376$	−4612.04	−0.632574
$377$	1636.24i	0.223530i
$378$	− 1346.64i	− 0.183237i
$379$	1940.17	0.262955	0.131477	−	0.991319i	$-0.458028\pi$
$379$	1940.17	0.262955	0.131477	+	0.991319i	$0.458028\pi$
$380$	0	0
$381$	655.826	0.0881863
$382$	− 5320.88i	− 0.712669i
$383$	10805.6i	1.44161i	0.693136	+	0.720807i	$0.256228\pi$
$383$	10805.6i	1.44161i	−0.693136	+	0.720807i	$0.743772\pi$
$384$	−743.466	−0.0988017
$385$	0	0
$386$	−1771.04	−0.233533
$387$	− 9382.39i	− 1.23239i
$388$	− 4560.51i	− 0.596714i
$389$	9225.11	1.20239	0.601197	−	0.799101i	$-0.294691\pi$
$389$	9225.11	1.20239	0.601197	+	0.799101i	$0.294691\pi$
$390$	0	0
$391$	−1304.48	−0.168722
$392$	− 12451.1i	− 1.60428i
$393$	870.378i	0.111717i
$394$	1047.31	0.133916
$395$	0	0
$396$	−1740.90	−0.220917
$397$	− 13364.3i	− 1.68951i	−0.535156	−	0.844753i	$-0.679747\pi$
$397$	− 13364.3i	− 1.68951i	0.535156	−	0.844753i	$-0.320253\pi$
$398$	2374.61i	0.299066i
$399$	1591.60	0.199699
$400$	0	0
$401$	−6030.88	−0.751042	−0.375521	−	0.926814i	$-0.622536\pi$
$401$	−6030.88	−0.751042	−0.375521	+	0.926814i	$0.622536\pi$
$402$	357.220i	0.0443197i
$403$	− 14218.4i	− 1.75750i
$404$	−8376.25	−1.03152
$405$	0	0
$406$	1602.31	0.195865
$407$	− 4049.61i	− 0.493199i
$408$	− 455.219i	− 0.0552370i
$409$	−931.381	−0.112601	−0.0563005	−	0.998414i	$-0.517931\pi$
$409$	−931.381	−0.112601	−0.0563005	+	0.998414i	$0.517931\pi$
$410$	0	0
$411$	−1370.57	−0.164489
$412$	144.823i	0.0173178i
$413$	11450.4i	1.36425i
$414$	−1237.75	−0.146938
$415$	0	0
$416$	8534.55	1.00587
$417$	1045.29i	0.122753i
$418$	1444.16i	0.168986i
$419$	13161.8	1.53460	0.767300	−	0.641289i	$-0.221600\pi$
$419$	13161.8	1.53460	0.767300	+	0.641289i	$0.221600\pi$
$420$	0	0
$421$	−1127.05	−0.130473	−0.0652365	−	0.997870i	$-0.520780\pi$
$421$	−1127.05	−0.130473	−0.0652365	+	0.997870i	$0.520780\pi$
$422$	2282.83i	0.263332i
$423$	6141.62i	0.705947i
$424$	−8153.84	−0.933929
$425$	0	0
$426$	−539.381	−0.0613453
$427$	− 10025.0i	− 1.13617i
$428$	− 3156.14i	− 0.356444i
$429$	−281.771	−0.0317110
$430$	0	0
$431$	−4386.13	−0.490191	−0.245096	−	0.969499i	$-0.578819\pi$
$431$	−4386.13	−0.490191	−0.245096	+	0.969499i	$0.578819\pi$
$432$	561.398i	0.0625238i
$433$	10905.5i	1.21035i	0.796091	+	0.605177i	$0.206898\pi$
$433$	10905.5i	1.21035i	−0.796091	+	0.605177i	$0.793102\pi$
$434$	−13923.6	−1.53998
$435$	0	0
$436$	7322.38	0.804308
$437$	− 2943.11i	− 0.322169i
$438$	68.3127i	0.00745229i
$439$	3900.94	0.424104	0.212052	−	0.977258i	$-0.431985\pi$
$439$	3900.94	0.424104	0.212052	+	0.977258i	$0.431985\pi$
$440$	0	0
$441$	−16580.5	−1.79036
$442$	2654.38i	0.285647i
$443$	− 15537.5i	− 1.66638i	−0.552985	−	0.833192i	$-0.686511\pi$
$443$	− 15537.5i	− 1.66638i	0.552985	−	0.833192i	$-0.313489\pi$
$444$	−1226.11	−0.131056
$445$	0	0
$446$	2874.87	0.305222
$447$	− 457.315i	− 0.0483898i
$448$	− 3731.22i	− 0.393490i
$449$	3464.47	0.364139	0.182070	−	0.983286i	$-0.441720\pi$
$449$	3464.47	0.364139	0.182070	+	0.983286i	$0.441720\pi$
$450$	0	0
$451$	4329.62	0.452049
$452$	− 7736.54i	− 0.805080i
$453$	2058.89i	0.213543i
$454$	6058.74	0.626323
$455$	0	0
$456$	1027.05	0.105473
$457$	14410.6i	1.47506i	0.675317	+	0.737528i	$0.264007\pi$
$457$	14410.6i	1.47506i	−0.675317	+	0.737528i	$0.735993\pi$
$458$	− 1973.29i	− 0.201323i
$459$	−1219.55	−0.124016
$460$	0	0
$461$	−3219.12	−0.325226	−0.162613	−	0.986690i	$-0.551992\pi$
$461$	−3219.12	−0.325226	−0.162613	+	0.986690i	$0.551992\pi$
$462$	275.927i	0.0277863i
$463$	− 1338.77i	− 0.134380i	−0.997740	−	0.0671899i	$-0.978597\pi$
$463$	− 1338.77i	− 0.134380i	0.997740	−	0.0671899i	$-0.0214033\pi$
$464$	−667.982	−0.0668325
$465$	0	0
$466$	2471.79	0.245716
$467$	12221.6i	1.21102i	0.795836	+	0.605512i	$0.207032\pi$
$467$	12221.6i	1.21102i	−0.795836	+	0.605512i	$0.792968\pi$
$468$	− 7219.26i	− 0.713057i
$469$	13733.1	1.35210
$470$	0	0
$471$	1500.45	0.146788
$472$	7388.82i	0.720547i
$473$	3867.62i	0.375969i
$474$	−332.785	−0.0322475
$475$	0	0
$476$	−7450.63	−0.717435
$477$	10858.1i	1.04226i
$478$	2581.68i	0.247036i
$479$	20290.0	1.93544	0.967718	−	0.252036i	$-0.0811001\pi$
$479$	20290.0	1.93544	0.967718	+	0.252036i	$0.0811001\pi$
$480$	0	0
$481$	16793.2	1.59190
$482$	7458.38i	0.704813i
$483$	− 562.324i	− 0.0529744i
$484$	717.635	0.0673962
$485$	0	0
$486$	−1739.15	−0.162324
$487$	− 17360.7i	− 1.61538i	−0.589610	−	0.807688i	$-0.700718\pi$
$487$	− 17360.7i	− 1.61538i	0.589610	−	0.807688i	$-0.299282\pi$
$488$	− 6469.03i	− 0.600080i
$489$	970.658	0.0897642
$490$	0	0
$491$	5129.01	0.471424	0.235712	−	0.971823i	$-0.424258\pi$
$491$	5129.01	0.471424	0.235712	+	0.971823i	$0.424258\pi$
$492$	− 1310.89i	− 0.120121i
$493$	− 1451.08i	− 0.132563i
$494$	−5988.72	−0.545436
$495$	0	0
$496$	5804.56	0.525469
$497$	20736.1i	1.87152i
$498$	674.983i	0.0607364i
$499$	−13009.6	−1.16712	−0.583558	−	0.812072i	$-0.698340\pi$
$499$	−13009.6	−1.16712	−0.583558	+	0.812072i	$0.698340\pi$
$500$	0	0
$501$	−0.0367250	−3.27495e−6 0
$502$	− 5505.93i	− 0.489525i
$503$	3972.02i	0.352095i	0.984382	+	0.176047i	$0.0563312\pi$
$503$	3972.02i	0.352095i	−0.984382	+	0.176047i	$0.943669\pi$
$504$	−16605.5	−1.46759
$505$	0	0
$506$	510.229	0.0448270
$507$	65.2657i	0.00571706i
$508$	− 6926.54i	− 0.604952i
$509$	−11174.1	−0.973048	−0.486524	−	0.873667i	$-0.661735\pi$
$509$	−11174.1	−0.973048	−0.486524	+	0.873667i	$0.661735\pi$
$510$	0	0
$511$	2626.24	0.227354
$512$	6469.49i	0.558426i
$513$	− 2751.49i	− 0.236806i
$514$	−3842.62	−0.329749
$515$	0	0
$516$	1171.01	0.0999047
$517$	− 2531.71i	− 0.215366i
$518$	− 16444.9i	− 1.39488i
$519$	1020.20	0.0862850
$520$	0	0
$521$	−18614.6	−1.56530	−0.782648	−	0.622464i	$-0.786132\pi$
$521$	−18614.6	−1.56530	−0.782648	+	0.622464i	$0.786132\pi$
$522$	− 1376.86i	− 0.115447i
$523$	3792.30i	0.317066i	0.987354	+	0.158533i	$0.0506765\pi$
$523$	3792.30i	0.317066i	−0.987354	+	0.158533i	$0.949324\pi$
$524$	9192.54	0.766370
$525$	0	0
$526$	−9578.76	−0.794019
$527$	12609.5i	1.04227i
$528$	− 115.031i	− 0.00948119i
$529$	11127.2	0.914538
$530$	0	0
$531$	9839.31	0.804124
$532$	− 16809.8i	− 1.36992i
$533$	17954.4i	1.45908i
$534$	−646.093	−0.0523580
$535$	0	0
$536$	8861.83	0.714128
$537$	− 1337.19i	− 0.107456i
$538$	− 12188.0i	− 0.976698i
$539$	6834.84	0.546192
$540$	0	0
$541$	5187.61	0.412260	0.206130	−	0.978525i	$-0.433913\pi$
$541$	5187.61	0.412260	0.206130	+	0.978525i	$0.433913\pi$
$542$	− 3802.12i	− 0.301319i
$543$	716.320i	0.0566119i
$544$	−7568.77	−0.596523
$545$	0	0
$546$	−1144.23	−0.0896862
$547$	15642.1i	1.22268i	0.791366	+	0.611342i	$0.209370\pi$
$547$	15642.1i	1.22268i	−0.791366	+	0.611342i	$0.790630\pi$
$548$	14475.3i	1.12839i
$549$	−8614.47	−0.669684
$550$	0	0
$551$	3273.87	0.253125
$552$	− 362.862i	− 0.0279790i
$553$	12793.7i	0.983804i
$554$	−556.624	−0.0426872
$555$	0	0
$556$	11039.9	0.842080
$557$	− 15798.8i	− 1.20182i	−0.799315	−	0.600912i	$-0.794804\pi$
$557$	− 15798.8i	− 1.20182i	0.799315	−	0.600912i	$-0.205196\pi$
$558$	11964.5i	0.907702i
$559$	−16038.5	−1.21352
$560$	0	0
$561$	249.885	0.0188060
$562$	− 1591.52i	− 0.119456i
$563$	5028.68i	0.376436i	0.982127	+	0.188218i	$0.0602712\pi$
$563$	5028.68i	0.376436i	−0.982127	+	0.188218i	$0.939729\pi$
$564$	−766.531	−0.0572284
$565$	0	0
$566$	−1676.81	−0.124526
$567$	21848.2i	1.61824i
$568$	13380.8i	0.988463i
$569$	−24194.1	−1.78255	−0.891273	−	0.453467i	$-0.850187\pi$
$569$	−24194.1	−1.78255	−0.891273	+	0.453467i	$0.850187\pi$
$570$	0	0
$571$	−8184.61	−0.599852	−0.299926	−	0.953963i	$-0.596962\pi$
$571$	−8184.61	−0.599852	−0.299926	+	0.953963i	$0.596962\pi$
$572$	2975.94i	0.217535i
$573$	− 2077.21i	− 0.151443i
$574$	17582.0	1.27850
$575$	0	0
$576$	−3206.23	−0.231932
$577$	− 550.908i	− 0.0397480i	−0.999802	−	0.0198740i	$-0.993673\pi$
$577$	− 550.908i	− 0.0397480i	0.999802	−	0.0198740i	$-0.00632651\pi$
$578$	4713.08i	0.339167i
$579$	−691.393	−0.0496258
$580$	0	0
$581$	25949.3	1.85294
$582$	621.126i	0.0442380i
$583$	− 4475.93i	− 0.317966i
$584$	1694.68	0.120080
$585$	0	0
$586$	5245.76	0.369796
$587$	− 3080.03i	− 0.216570i	−0.994120	−	0.108285i	$-0.965464\pi$
$587$	− 3080.03i	− 0.216570i	0.994120	−	0.108285i	$-0.0345359\pi$
$588$	− 2069.40i	− 0.145137i
$589$	−28449.0	−1.99019
$590$	0	0
$591$	408.859	0.0284572
$592$	6855.69i	0.475958i
$593$	5257.89i	0.364108i	0.983289	+	0.182054i	$0.0582745\pi$
$593$	5257.89i	0.364108i	−0.983289	+	0.182054i	$0.941726\pi$
$594$	477.010	0.0329494
$595$	0	0
$596$	−4829.96	−0.331951
$597$	927.018i	0.0635516i
$598$	2115.85i	0.144688i
$599$	1181.80	0.0806125	0.0403062	−	0.999187i	$-0.487167\pi$
$599$	1181.80	0.0806125	0.0403062	+	0.999187i	$0.487167\pi$
$600$	0	0
$601$	−27879.8	−1.89225	−0.946123	−	0.323807i	$-0.895037\pi$
$601$	−27879.8	−1.89225	−0.946123	+	0.323807i	$0.895037\pi$
$602$	15705.9i	1.06333i
$603$	− 11800.8i	− 0.796960i
$604$	21745.1	1.46489
$605$	0	0
$606$	1140.82	0.0764728
$607$	4500.25i	0.300922i	0.988616	+	0.150461i	$0.0480757\pi$
$607$	4500.25i	0.300922i	−0.988616	+	0.150461i	$0.951924\pi$
$608$	− 17076.4i	− 1.13904i
$609$	625.521	0.0416214
$610$	0	0
$611$	10498.7	0.695139
$612$	6402.32i	0.422873i
$613$	8963.16i	0.590569i	0.955409	+	0.295284i	$0.0954144\pi$
$613$	8963.16i	0.590569i	−0.955409	+	0.295284i	$0.904586\pi$
$614$	−1173.87	−0.0771555
$615$	0	0
$616$	6845.14	0.447725
$617$	9394.42i	0.612974i	0.951875	+	0.306487i	$0.0991537\pi$
$617$	9394.42i	0.612974i	−0.951875	+	0.306487i	$0.900846\pi$
$618$	− 19.7244i	− 0.00128387i
$619$	−4816.38	−0.312741	−0.156371	−	0.987698i	$-0.549979\pi$
$619$	−4816.38	−0.312741	−0.156371	+	0.987698i	$0.549979\pi$
$620$	0	0
$621$	−972.119	−0.0628177
$622$	4526.78i	0.291813i
$623$	24838.6i	1.59733i
$624$	477.017	0.0306025
$625$	0	0
$626$	7315.21	0.467052
$627$	563.781i	0.0359095i
$628$	− 15847.1i	− 1.00695i
$629$	−14892.9	−0.944066
$630$	0	0
$631$	−24847.7	−1.56763	−0.783814	−	0.620996i	$-0.786728\pi$
$631$	−24847.7	−1.56763	−0.783814	+	0.620996i	$0.786728\pi$
$632$	8255.65i	0.519608i
$633$	891.189i	0.0559583i
$634$	−6907.26	−0.432685
$635$	0	0
$636$	−1355.19	−0.0844916
$637$	28343.2i	1.76295i
$638$	567.572i	0.0352201i
$639$	17818.6	1.10312
$640$	0	0
$641$	−30497.0	−1.87919	−0.939594	−	0.342290i	$-0.888798\pi$
$641$	−30497.0	−1.87919	−0.939594	+	0.342290i	$0.888798\pi$
$642$	429.856i	0.0264253i
$643$	5407.75i	0.331665i	0.986154	+	0.165833i	$0.0530311\pi$
$643$	5407.75i	0.331665i	−0.986154	+	0.165833i	$0.946969\pi$
$644$	−5939.01	−0.363400
$645$	0	0
$646$	5311.03	0.323467
$647$	− 22118.8i	− 1.34402i	−0.740542	−	0.672011i	$-0.765431\pi$
$647$	− 22118.8i	− 1.34402i	0.740542	−	0.672011i	$-0.234569\pi$
$648$	14098.4i	0.854690i
$649$	−4055.98	−0.245318
$650$	0	0
$651$	−5435.59	−0.327247
$652$	− 10251.7i	− 0.615776i
$653$	− 12862.4i	− 0.770817i	−0.922746	−	0.385409i	$-0.874060\pi$
$653$	− 12862.4i	− 0.770817i	0.922746	−	0.385409i	$-0.125940\pi$
$654$	−997.283	−0.0596282
$655$	0	0
$656$	−7329.73	−0.436247
$657$	− 2256.72i	− 0.134008i
$658$	− 10280.9i	− 0.609106i
$659$	−13216.0	−0.781218	−0.390609	−	0.920557i	$-0.627736\pi$
$659$	−13216.0	−0.781218	−0.390609	+	0.920557i	$0.627736\pi$
$660$	0	0
$661$	32098.3	1.88878	0.944388	−	0.328833i	$-0.106655\pi$
$661$	32098.3	1.88878	0.944388	+	0.328833i	$0.106655\pi$
$662$	− 3736.09i	− 0.219347i
$663$	1036.24i	0.0607002i
$664$	16744.8	0.978652
$665$	0	0
$666$	−14131.1	−0.822177
$667$	− 1156.68i	− 0.0671466i
$668$	0.387873i	0 2.24659e-5i
$669$	1122.32	0.0648599
$670$	0	0
$671$	3551.07	0.204303
$672$	− 3262.69i	− 0.187293i
$673$	− 19956.4i	− 1.14304i	−0.820590	−	0.571518i	$-0.806355\pi$
$673$	− 19956.4i	− 1.14304i	0.820590	−	0.571518i	$-0.193645\pi$
$674$	3877.26	0.221582
$675$	0	0
$676$	689.307	0.0392186
$677$	1483.58i	0.0842223i	0.999113	+	0.0421111i	$0.0134084\pi$
$677$	1483.58i	0.0842223i	−0.999113	+	0.0421111i	$0.986592\pi$
$678$	1053.69i	0.0596854i
$679$	23878.8	1.34961
$680$	0	0
$681$	2365.26	0.133094
$682$	− 4932.03i	− 0.276917i
$683$	23228.2i	1.30132i	0.759370	+	0.650659i	$0.225507\pi$
$683$	23228.2i	1.30132i	−0.759370	+	0.650659i	$0.774493\pi$
$684$	−14444.7	−0.807464
$685$	0	0
$686$	12433.7	0.692015
$687$	− 770.350i	− 0.0427812i
$688$	− 6547.60i	− 0.362827i
$689$	18561.1	1.02630
$690$	0	0
$691$	−7333.20	−0.403717	−0.201858	−	0.979415i	$-0.564698\pi$
$691$	−7333.20	−0.403717	−0.201858	+	0.979415i	$0.564698\pi$
$692$	− 10774.9i	− 0.591909i
$693$	− 9115.31i	− 0.499657i
$694$	−13290.9	−0.726971
$695$	0	0
$696$	403.643	0.0219828
$697$	− 15922.6i	− 0.865298i
$698$	− 5549.06i	− 0.300909i
$699$	964.958	0.0522147
$700$	0	0
$701$	−19481.6	−1.04966	−0.524829	−	0.851208i	$-0.675871\pi$
$701$	−19481.6	−1.04966	−0.524829	+	0.851208i	$0.675871\pi$
$702$	1978.10i	0.106351i
$703$	− 33600.7i	− 1.80267i
$704$	1321.68	0.0707566
$705$	0	0
$706$	4859.38	0.259044
$707$	− 43858.0i	− 2.33303i
$708$	1228.04i	0.0651872i
$709$	−14807.5	−0.784353	−0.392177	−	0.919890i	$-0.628278\pi$
$709$	−14807.5	−0.784353	−0.392177	+	0.919890i	$0.628278\pi$
$710$	0	0
$711$	10993.6	0.579878
$712$	16028.1i	0.843650i
$713$	10051.2i	0.527939i
$714$	1014.75	0.0531877
$715$	0	0
$716$	−14122.8	−0.737142
$717$	1007.86i	0.0524953i
$718$	14230.5i	0.739662i
$719$	−22891.1	−1.18734	−0.593669	−	0.804709i	$-0.702321\pi$
$719$	−22891.1	−1.18734	−0.593669	+	0.804709i	$0.702321\pi$
$720$	0	0
$721$	−758.292	−0.0391682
$722$	2116.23i	0.109083i
$723$	2911.66i	0.149773i
$724$	7565.45	0.388353
$725$	0	0
$726$	−97.7395	−0.00499649
$727$	− 24318.7i	− 1.24062i	−0.784357	−	0.620309i	$-0.787007\pi$
$727$	− 24318.7i	− 1.24062i	0.784357	−	0.620309i	$-0.212993\pi$
$728$	28385.9i	1.44512i
$729$	18317.1	0.930605
$730$	0	0
$731$	14223.6	0.719669
$732$	− 1075.17i	− 0.0542887i
$733$	− 34939.0i	− 1.76057i	−0.474441	−	0.880287i	$-0.657350\pi$
$733$	− 34939.0i	− 1.76057i	0.474441	−	0.880287i	$-0.342650\pi$
$734$	7617.42	0.383057
$735$	0	0
$736$	−6033.19	−0.302155
$737$	4864.56i	0.243132i
$738$	− 15108.2i	− 0.753579i
$739$	12663.1	0.630337	0.315168	−	0.949036i	$-0.397939\pi$
$739$	12663.1	0.630337	0.315168	+	0.949036i	$0.397939\pi$
$740$	0	0
$741$	−2337.93	−0.115905
$742$	− 18176.1i	− 0.899281i
$743$	− 1711.32i	− 0.0844985i	−0.999107	−	0.0422492i	$-0.986548\pi$
$743$	− 1711.32i	− 0.0844985i	0.999107	−	0.0422492i	$-0.0134524\pi$
$744$	−3507.53	−0.172839
$745$	0	0
$746$	−11199.9	−0.549675
$747$	− 22298.2i	− 1.09217i
$748$	− 2639.18i	− 0.129008i
$749$	16525.5	0.806182
$750$	0	0
$751$	−5165.32	−0.250979	−0.125489	−	0.992095i	$-0.540050\pi$
$751$	−5165.32	−0.250979	−0.125489	+	0.992095i	$0.540050\pi$
$752$	4285.99i	0.207838i
$753$	− 2149.45i	− 0.104024i
$754$	−2353.65	−0.113680
$755$	0	0
$756$	−5552.34	−0.267112
$757$	40684.0i	1.95335i	0.214722	+	0.976675i	$0.431115\pi$
$757$	40684.0i	1.95335i	−0.214722	+	0.976675i	$0.568885\pi$
$758$	2790.83i	0.133730i
$759$	199.187	0.00952575
$760$	0	0
$761$	26564.1	1.26537	0.632687	−	0.774408i	$-0.281952\pi$
$761$	26564.1	1.26537	0.632687	+	0.774408i	$0.281952\pi$
$762$	943.370i	0.0448487i
$763$	38339.9i	1.81913i
$764$	−21938.5	−1.03889
$765$	0	0
$766$	−15543.2	−0.733158
$767$	− 16819.6i	− 0.791813i
$768$	− 1609.21i	− 0.0756087i
$769$	−24381.9	−1.14335	−0.571674	−	0.820481i	$-0.693706\pi$
$769$	−24381.9	−1.14335	−0.571674	+	0.820481i	$0.693706\pi$
$770$	0	0
$771$	−1500.11	−0.0700717
$772$	7302.19i	0.340429i
$773$	− 18945.0i	− 0.881508i	−0.897628	−	0.440754i	$-0.854711\pi$
$773$	− 18945.0i	− 0.881508i	0.897628	−	0.440754i	$-0.145289\pi$
$774$	13496.1	0.626752
$775$	0	0
$776$	15408.8	0.712812
$777$	− 6419.91i	− 0.296413i
$778$	13269.8i	0.611499i
$779$	35924.0	1.65226
$780$	0	0
$781$	−7345.20	−0.336532
$782$	− 1876.42i	− 0.0858064i
$783$	− 1081.37i	− 0.0493552i
$784$	−11570.9	−0.527099
$785$	0	0
$786$	−1251.99	−0.0568156
$787$	7610.70i	0.344717i	0.985034	+	0.172359i	$0.0551388\pi$
$787$	7610.70i	0.344717i	−0.985034	+	0.172359i	$0.944861\pi$
$788$	− 4318.19i	− 0.195215i
$789$	−3739.44	−0.168729
$790$	0	0
$791$	40508.4	1.82088
$792$	− 5882.02i	− 0.263900i
$793$	14725.8i	0.659432i
$794$	19223.8	0.859229
$795$	0	0
$796$	9790.75	0.435960
$797$	− 3732.50i	− 0.165887i	−0.996554	−	0.0829435i	$-0.973568\pi$
$797$	− 3732.50i	− 0.165887i	0.996554	−	0.0829435i	$-0.0264321\pi$
$798$	2289.44i	0.101561i
$799$	−9310.61	−0.412247
$800$	0	0
$801$	21343.8	0.941506
$802$	− 8675.11i	− 0.381956i
$803$	930.271i	0.0408824i
$804$	1472.86	0.0646065
$805$	0	0
$806$	20452.5	0.893806
$807$	− 4758.07i	− 0.207549i
$808$	− 28301.1i	− 1.23221i
$809$	27621.8	1.20041	0.600204	−	0.799847i	$-0.295086\pi$
$809$	27621.8	1.20041	0.600204	+	0.799847i	$0.295086\pi$
$810$	0	0
$811$	−29996.0	−1.29877	−0.649384	−	0.760461i	$-0.724973\pi$
$811$	−29996.0	−1.29877	−0.649384	+	0.760461i	$0.724973\pi$
$812$	− 6606.48i	− 0.285520i
$813$	− 1484.30i	− 0.0640305i
$814$	5825.16	0.250825
$815$	0	0
$816$	−423.037	−0.0181486
$817$	32090.7i	1.37419i
$818$	− 1339.74i	− 0.0572653i
$819$	37800.0	1.61275
$820$	0	0
$821$	18075.1	0.768362	0.384181	−	0.923258i	$-0.374484\pi$
$821$	18075.1	0.768362	0.384181	+	0.923258i	$0.374484\pi$
$822$	− 1971.49i	− 0.0836540i
$823$	− 26723.7i	− 1.13187i	−0.824450	−	0.565935i	$-0.808515\pi$
$823$	− 26723.7i	− 1.13187i	0.824450	−	0.565935i	$-0.191485\pi$
$824$	−489.318	−0.0206871
$825$	0	0
$826$	−16470.8	−0.693816
$827$	− 36788.1i	− 1.54685i	−0.633885	−	0.773427i	$-0.718541\pi$
$827$	− 36788.1i	− 1.54685i	0.633885	−	0.773427i	$-0.281459\pi$
$828$	5103.39i	0.214197i
$829$	1260.15	0.0527948	0.0263974	−	0.999652i	$-0.491596\pi$
$829$	1260.15	0.0527948	0.0263974	+	0.999652i	$0.491596\pi$
$830$	0	0
$831$	−217.300	−0.00907105
$832$	5480.82i	0.228381i
$833$	− 25135.8i	− 1.04550i
$834$	−1503.60	−0.0624284
$835$	0	0
$836$	5954.41	0.246337
$837$	9396.80i	0.388054i
$838$	18932.6i	0.780448i
$839$	4023.16	0.165548	0.0827742	−	0.996568i	$-0.473622\pi$
$839$	4023.16	0.165548	0.0827742	+	0.996568i	$0.473622\pi$
$840$	0	0
$841$	−23102.3	−0.947244
$842$	− 1621.20i	− 0.0663543i
$843$	− 621.312i	− 0.0253845i
$844$	9412.34	0.383870
$845$	0	0
$846$	−8834.39	−0.359022
$847$	3757.53i	0.152432i
$848$	7577.41i	0.306851i
$849$	−654.605	−0.0264617
$850$	0	0
$851$	−11871.3	−0.478195
$852$	2223.92i	0.0894253i
$853$	40707.7i	1.63400i	0.576636	+	0.817001i	$0.304365\pi$
$853$	40707.7i	1.63400i	−0.576636	+	0.817001i	$0.695635\pi$
$854$	14420.4	0.577818
$855$	0	0
$856$	10663.8	0.425794
$857$	− 24321.4i	− 0.969431i	−0.874672	−	0.484715i	$-0.838923\pi$
$857$	− 24321.4i	− 0.969431i	0.874672	−	0.484715i	$-0.161077\pi$
$858$	− 405.312i	− 0.0161272i
$859$	−16912.7	−0.671776	−0.335888	−	0.941902i	$-0.609036\pi$
$859$	−16912.7	−0.671776	−0.335888	+	0.941902i	$0.609036\pi$
$860$	0	0
$861$	6863.81	0.271682
$862$	− 6309.22i	− 0.249295i
$863$	− 25793.8i	− 1.01742i	−0.860939	−	0.508708i	$-0.830123\pi$
$863$	− 25793.8i	− 1.01742i	0.860939	−	0.508708i	$-0.169877\pi$
$864$	−5640.39	−0.222095
$865$	0	0
$866$	−15686.9	−0.615547
$867$	1839.93i	0.0720731i
$868$	57408.3i	2.24489i
$869$	−4531.81	−0.176906
$870$	0	0
$871$	−20172.7	−0.784759
$872$	24740.4i	0.960796i
$873$	− 20519.0i	− 0.795492i
$874$	4233.51	0.163845
$875$	0	0
$876$	281.660	0.0108635
$877$	− 20143.8i	− 0.775607i	−0.921742	−	0.387803i	$-0.873234\pi$
$877$	− 20143.8i	− 0.775607i	0.921742	−	0.387803i	$-0.126766\pi$
$878$	5611.30i	0.215686i
$879$	2047.88	0.0785817
$880$	0	0
$881$	−18231.3	−0.697196	−0.348598	−	0.937272i	$-0.613342\pi$
$881$	−18231.3	−0.697196	−0.348598	+	0.937272i	$0.613342\pi$
$882$	− 23850.2i	− 0.910518i
$883$	− 34487.5i	− 1.31438i	−0.753725	−	0.657189i	$-0.771745\pi$
$883$	− 34487.5i	− 1.31438i	0.753725	−	0.657189i	$-0.228255\pi$
$884$	10944.3	0.416399
$885$	0	0
$886$	22349.8	0.847469
$887$	16039.9i	0.607180i	0.952803	+	0.303590i	$0.0981852\pi$
$887$	16039.9i	0.607180i	−0.952803	+	0.303590i	$0.901815\pi$
$888$	− 4142.70i	− 0.156554i
$889$	36267.3	1.36824
$890$	0	0
$891$	−7739.12	−0.290988
$892$	− 11853.4i	− 0.444934i
$893$	− 21006.2i	− 0.787175i
$894$	657.824	0.0246095
$895$	0	0
$896$	−41113.8	−1.53294
$897$	826.004i	0.0307463i
$898$	4983.46i	0.185189i
$899$	−11180.8	−0.414795
$900$	0	0
$901$	−16460.7	−0.608640
$902$	6227.94i	0.229898i
$903$	6131.40i	0.225958i
$904$	26139.7	0.961718
$905$	0	0
$906$	−2961.61	−0.108601
$907$	23029.2i	0.843077i	0.906810	+	0.421539i	$0.138510\pi$
$907$	23029.2i	0.843077i	−0.906810	+	0.421539i	$0.861490\pi$
$908$	− 24980.8i	− 0.913015i
$909$	−37687.1	−1.37514
$910$	0	0
$911$	−9206.00	−0.334806	−0.167403	−	0.985889i	$-0.553538\pi$
$911$	−9206.00	−0.334806	−0.167403	+	0.985889i	$0.553538\pi$
$912$	− 954.440i	− 0.0346542i
$913$	9191.81i	0.333192i
$914$	−20728.9	−0.750166
$915$	0	0
$916$	−8136.10	−0.293476
$917$	48132.0i	1.73333i
$918$	− 1754.25i	− 0.0630707i
$919$	−13329.5	−0.478456	−0.239228	−	0.970963i	$-0.576894\pi$
$919$	−13329.5	−0.478456	−0.239228	+	0.970963i	$0.576894\pi$
$920$	0	0
$921$	−458.264	−0.0163956
$922$	− 4630.53i	− 0.165400i
$923$	− 30459.6i	− 1.08623i
$924$	1137.68	0.0405052
$925$	0	0
$926$	1925.75	0.0683412
$927$	651.600i	0.0230867i
$928$	− 6711.24i	− 0.237400i
$929$	−1819.10	−0.0642442	−0.0321221	−	0.999484i	$-0.510227\pi$
$929$	−1819.10	−0.0642442	−0.0321221	+	0.999484i	$0.510227\pi$
$930$	0	0
$931$	56710.5	1.99636
$932$	− 10191.5i	− 0.358189i
$933$	1767.20i	0.0620103i
$934$	−17580.1	−0.615888
$935$	0	0
$936$	24391.9	0.851790
$937$	− 4012.08i	− 0.139882i	−0.997551	−	0.0699408i	$-0.977719\pi$
$937$	− 4012.08i	− 0.139882i	0.997551	−	0.0699408i	$-0.0222810\pi$
$938$	19754.3i	0.687635i
$939$	2855.77	0.0992488
$940$	0	0
$941$	8444.53	0.292544	0.146272	−	0.989244i	$-0.453273\pi$
$941$	8444.53	0.292544	0.146272	+	0.989244i	$0.453273\pi$
$942$	2158.32i	0.0746515i
$943$	− 12692.2i	− 0.438297i
$944$	6866.47	0.236742
$945$	0	0
$946$	−5563.37	−0.191206
$947$	− 45316.0i	− 1.55499i	−0.628892	−	0.777493i	$-0.716491\pi$
$947$	− 45316.0i	− 1.55499i	0.628892	−	0.777493i	$-0.283509\pi$
$948$	1372.11i	0.0470084i
$949$	−3857.71	−0.131956
$950$	0	0
$951$	−2696.51	−0.0919458
$952$	− 25173.7i	− 0.857020i
$953$	96.7143i	0.00328739i	0.999999	+	0.00164370i	$0.000523205\pi$
$953$	96.7143i	0.00328739i	−0.999999	+	0.00164370i	$0.999477\pi$
$954$	−15618.7	−0.530058
$955$	0	0
$956$	10644.6	0.360114
$957$	221.573i	0.00748428i
$958$	29186.1i	0.984300i
$959$	−75792.7	−2.55211
$960$	0	0
$961$	67366.9	2.26132
$962$	24156.1i	0.809590i
$963$	− 14200.4i	− 0.475183i
$964$	30751.7	1.02743
$965$	0	0
$966$	808.873	0.0269411
$967$	− 7666.63i	− 0.254956i	−0.991841	−	0.127478i	$-0.959312\pi$
$967$	− 7666.63i	− 0.254956i	0.991841	−	0.127478i	$-0.0406882\pi$
$968$	2424.70i	0.0805090i
$969$	2073.36	0.0687368
$970$	0	0
$971$	−5221.18	−0.172560	−0.0862799	−	0.996271i	$-0.527498\pi$
$971$	−5221.18	−0.172560	−0.0862799	+	0.996271i	$0.527498\pi$
$972$	7170.70i	0.236626i
$973$	57804.9i	1.90456i
$974$	24972.4	0.821529
$975$	0	0
$976$	−6011.70	−0.197162
$977$	45769.9i	1.49878i	0.662129	+	0.749390i	$0.269653\pi$
$977$	45769.9i	1.49878i	−0.662129	+	0.749390i	$0.730347\pi$
$978$	1396.24i	0.0456512i
$979$	−8798.39	−0.287229
$980$	0	0
$981$	32945.4	1.07224
$982$	7377.81i	0.239751i
$983$	− 14777.8i	− 0.479488i	−0.970836	−	0.239744i	$-0.922936\pi$
$983$	− 14777.8i	− 0.479488i	0.970836	−	0.239744i	$-0.0770636\pi$
$984$	4429.15	0.143492
$985$	0	0
$986$	2087.30	0.0674171
$987$	− 4013.55i	− 0.129435i
$988$	24692.1i	0.795103i
$989$	11337.8	0.364532
$990$	0	0
$991$	−16783.9	−0.538001	−0.269001	−	0.963140i	$-0.586693\pi$
$991$	−16783.9	−0.538001	−0.269001	+	0.963140i	$0.586693\pi$
$992$	58318.6i	1.86655i
$993$	− 1458.53i	− 0.0466112i
$994$	−29827.9	−0.951793
$995$	0	0
$996$	2783.03	0.0885377
$997$	8720.36i	0.277008i	0.990362	+	0.138504i	$0.0442293\pi$
$997$	8720.36i	0.277008i	−0.990362	+	0.138504i	$0.955771\pi$
$998$	− 18713.7i	− 0.593557i
$999$	−11098.4	−0.351490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.4.b.b.199.3		4
5.2	odd	4		55.4.a.b.1.2	✓	2
5.3	odd	4		275.4.a.c.1.1		2
5.4	even	2	inner	275.4.b.b.199.2		4
15.2	even	4		495.4.a.e.1.1		2
15.8	even	4		2475.4.a.l.1.2		2
20.7	even	4		880.4.a.r.1.1		2
55.32	even	4		605.4.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.4.a.b.1.2	✓	2	5.2	odd	4
275.4.a.c.1.1		2	5.3	odd	4
275.4.b.b.199.2		4	5.4	even	2	inner
275.4.b.b.199.3		4	1.1	even	1	trivial
495.4.a.e.1.1		2	15.2	even	4
605.4.a.g.1.1		2	55.32	even	4
880.4.a.r.1.1		2	20.7	even	4
2475.4.a.l.1.2		2	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.43845i q^{2} +0.561553i q^{3} +5.93087 q^{4} -0.807764 q^{6} +31.0540i q^{7} +20.0388i q^{8} +26.6847 q^{9} +O(q^{10})\)	\(q+1.43845i q^{2} +0.561553i q^{3} +5.93087 q^{4} -0.807764 q^{6} +31.0540i q^{7} +20.0388i q^{8} +26.6847 q^{9} -11.0000 q^{11} +3.33050i q^{12} -45.6155i q^{13} -44.6695 q^{14} +18.6222 q^{16} +40.4536i q^{17} +38.3845i q^{18} -91.2699 q^{19} -17.4384 q^{21} -15.8229i q^{22} +32.2462i q^{23} -11.2529 q^{24} +65.6155 q^{26} +30.1468i q^{27} +184.177i q^{28} -35.8702 q^{29} +311.702 q^{31} +187.098i q^{32} -6.17708i q^{33} -58.1904 q^{34} +158.263 q^{36} +368.147i q^{37} -131.287i q^{38} +25.6155 q^{39} -393.602 q^{41} -25.0843i q^{42} -351.602i q^{43} -65.2396 q^{44} -46.3845 q^{46} +230.155i q^{47} +10.4573i q^{48} -621.349 q^{49} -22.7168 q^{51} -270.540i q^{52} +406.902i q^{53} -43.3645 q^{54} -622.285 q^{56} -51.2529i q^{57} -51.5975i q^{58} +368.725 q^{59} -322.825 q^{61} +448.366i q^{62} +828.665i q^{63} -120.153 q^{64} +8.88540 q^{66} -442.233i q^{67} +239.925i q^{68} -18.1080 q^{69} +667.745 q^{71} +534.729i q^{72} -84.5701i q^{73} -529.560 q^{74} -541.310 q^{76} -341.594i q^{77} +36.8466i q^{78} +411.983 q^{79} +703.557 q^{81} -566.176i q^{82} -835.619i q^{83} -103.425 q^{84} +505.761 q^{86} -20.1430i q^{87} -220.427i q^{88} +799.853 q^{89} +1416.54 q^{91} +191.248i q^{92} +175.037i q^{93} -331.066 q^{94} -105.065 q^{96} -768.945i q^{97} -893.778i q^{98} -293.531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 34 q^{4} + 38 q^{6} + 82 q^{9}+O(q^{10}) \) 4 * q - 34 * q^4 + 38 * q^6 + 82 * q^9	\( 4 q - 34 q^{4} + 38 q^{6} + 82 q^{9} - 44 q^{11} - 22 q^{14} + 594 q^{16} + 6 q^{19} - 78 q^{21} - 614 q^{24} + 180 q^{26} + 442 q^{29} + 282 q^{31} - 1346 q^{34} - 340 q^{36} + 20 q^{39} - 288 q^{41} + 374 q^{44} - 268 q^{46} - 630 q^{49} + 742 q^{51} + 1550 q^{54} - 2250 q^{56} + 172 q^{59} - 310 q^{61} - 5618 q^{64} - 418 q^{66} + 76 q^{69} + 3174 q^{71} - 3182 q^{74} - 5406 q^{76} + 2588 q^{79} + 1132 q^{81} + 782 q^{84} - 2232 q^{86} + 3554 q^{89} + 2780 q^{91} + 1364 q^{94} + 6086 q^{96} - 902 q^{99}+O(q^{100}) \) 4 * q - 34 * q^4 + 38 * q^6 + 82 * q^9 - 44 * q^11 - 22 * q^14 + 594 * q^16 + 6 * q^19 - 78 * q^21 - 614 * q^24 + 180 * q^26 + 442 * q^29 + 282 * q^31 - 1346 * q^34 - 340 * q^36 + 20 * q^39 - 288 * q^41 + 374 * q^44 - 268 * q^46 - 630 * q^49 + 742 * q^51 + 1550 * q^54 - 2250 * q^56 + 172 * q^59 - 310 * q^61 - 5618 * q^64 - 418 * q^66 + 76 * q^69 + 3174 * q^71 - 3182 * q^74 - 5406 * q^76 + 2588 * q^79 + 1132 * q^81 + 782 * q^84 - 2232 * q^86 + 3554 * q^89 + 2780 * q^91 + 1364 * q^94 + 6086 * q^96 - 902 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more