LMFDB - Embedded newform 1150.2.b.j.599.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1150.599");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.77580864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 19x^{4} + 105x^{2} + 144 $ x^6 + 19x^4 + 105x^2 + 144
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.6
Root			$3.11903i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.2.b.j.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +3.11903i q^{3} -1.00000 q^{4} -3.11903 q^{6} +4.50973i q^{7} -1.00000i q^{8} -6.72833 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +3.11903i q^{3} -1.00000 q^{4} -3.11903 q^{6} +4.50973i q^{7} -1.00000i q^{8} -6.72833 q^{9} +4.33763 q^{11} -3.11903i q^{12} +3.72833i q^{13} -4.50973 q^{14} +1.00000 q^{16} +1.11903i q^{17} -6.72833i q^{18} -4.50973 q^{19} -14.0660 q^{21} +4.33763i q^{22} +1.00000i q^{23} +3.11903 q^{24} -3.72833 q^{26} -11.6288i q^{27} -4.50973i q^{28} +8.23805 q^{29} +1.72833 q^{31} +1.00000i q^{32} +13.5292i q^{33} -1.11903 q^{34} +6.72833 q^{36} -0.781399i q^{37} -4.50973i q^{38} -11.6288 q^{39} +3.90043 q^{41} -14.0660i q^{42} -8.00000i q^{43} -4.33763 q^{44} -1.00000 q^{46} -11.4567i q^{47} +3.11903i q^{48} -13.3376 q^{49} -3.49027 q^{51} -3.72833i q^{52} +6.00000i q^{53} +11.6288 q^{54} +4.50973 q^{56} -14.0660i q^{57} +8.23805i q^{58} +2.23805 q^{59} +3.55623 q^{61} +1.72833i q^{62} -30.3429i q^{63} -1.00000 q^{64} -13.5292 q^{66} +2.43720i q^{67} -1.11903i q^{68} -3.11903 q^{69} +7.11903 q^{71} +6.72833i q^{72} +9.45665i q^{73} +0.781399 q^{74} +4.50973 q^{76} +19.5615i q^{77} -11.6288i q^{78} +14.9133 q^{79} +16.0854 q^{81} +3.90043i q^{82} -2.78140i q^{83} +14.0660 q^{84} +8.00000 q^{86} +25.6947i q^{87} -4.33763i q^{88} +7.69471 q^{89} -16.8137 q^{91} -1.00000i q^{92} +5.39070i q^{93} +11.4567 q^{94} -3.11903 q^{96} -0.642920i q^{97} -13.3376i q^{98} -29.1850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{6} - 20 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^6 - 20 * q^9	$ 6 q - 6 q^{4} + 2 q^{6} - 20 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} - 6 q^{19} - 44 q^{21} - 2 q^{24} - 2 q^{26} + 8 q^{29} - 10 q^{31} + 14 q^{34} + 20 q^{36} - 28 q^{39} + 2 q^{41} - 6 q^{44} - 6 q^{46} - 60 q^{49} - 42 q^{51} + 28 q^{54} + 6 q^{56} - 28 q^{59} + 2 q^{61} - 6 q^{64} - 18 q^{66} + 2 q^{69} + 22 q^{71} + 4 q^{74} + 6 q^{76} + 8 q^{79} + 14 q^{81} + 44 q^{84} + 48 q^{86} - 36 q^{89} + 2 q^{91} + 28 q^{94} + 2 q^{96} - 114 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^6 - 20 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 - 6 * q^19 - 44 * q^21 - 2 * q^24 - 2 * q^26 + 8 * q^29 - 10 * q^31 + 14 * q^34 + 20 * q^36 - 28 * q^39 + 2 * q^41 - 6 * q^44 - 6 * q^46 - 60 * q^49 - 42 * q^51 + 28 * q^54 + 6 * q^56 - 28 * q^59 + 2 * q^61 - 6 * q^64 - 18 * q^66 + 2 * q^69 + 22 * q^71 + 4 * q^74 + 6 * q^76 + 8 * q^79 + 14 * q^81 + 44 * q^84 + 48 * q^86 - 36 * q^89 + 2 * q^91 + 28 * q^94 + 2 * q^96 - 114 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	3.11903i	1.80077i	0.435093	+	0.900385i	$0.356715\pi$
$3$	3.11903i	1.80077i	−0.435093	+	0.900385i	$0.643285\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−3.11903	−1.27334
$7$	4.50973i	1.70452i	0.523122	+	0.852258i	$0.324767\pi$
$7$	4.50973i	1.70452i	−0.523122	+	0.852258i	$0.675233\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−6.72833	−2.24278
$10$	0	0
$11$	4.33763	1.30784	0.653922	−	0.756562i	$-0.273122\pi$
$11$	4.33763	1.30784	0.653922	+	0.756562i	$0.273122\pi$
$12$	− 3.11903i	− 0.900385i
$13$	3.72833i	1.03405i	0.855970	+	0.517026i	$0.172961\pi$
$13$	3.72833i	1.03405i	−0.855970	+	0.517026i	$0.827039\pi$
$14$	−4.50973	−1.20527
$15$	0	0
$16$	1.00000	0.250000
$17$	1.11903i	0.271404i	0.990750	+	0.135702i	$0.0433289\pi$
$17$	1.11903i	0.271404i	−0.990750	+	0.135702i	$0.956671\pi$
$18$	− 6.72833i	− 1.58588i
$19$	−4.50973	−1.03460	−0.517301	−	0.855803i	$-0.673063\pi$
$19$	−4.50973	−1.03460	−0.517301	+	0.855803i	$0.673063\pi$
$20$	0	0
$21$	−14.0660	−3.06944
$22$	4.33763i	0.924785i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	3.11903	0.636669
$25$	0	0
$26$	−3.72833	−0.731185
$27$	− 11.6288i	− 2.23795i
$28$	− 4.50973i	− 0.852258i
$29$	8.23805	1.52977	0.764884	−	0.644168i	$-0.222796\pi$
$29$	8.23805	1.52977	0.764884	+	0.644168i	$0.222796\pi$
$30$	0	0
$31$	1.72833	0.310417	0.155208	−	0.987882i	$-0.450395\pi$
$31$	1.72833	0.310417	0.155208	+	0.987882i	$0.450395\pi$
$32$	1.00000i	0.176777i
$33$	13.5292i	2.35513i
$34$	−1.11903	−0.191911
$35$	0	0
$36$	6.72833	1.12139
$37$	− 0.781399i	− 0.128461i	−0.997935	−	0.0642306i	$-0.979541\pi$
$37$	− 0.781399i	− 0.128461i	0.997935	−	0.0642306i	$-0.0204593\pi$
$38$	− 4.50973i	− 0.731574i
$39$	−11.6288	−1.86209
$40$	0	0
$41$	3.90043	0.609144	0.304572	−	0.952489i	$-0.401487\pi$
$41$	3.90043	0.609144	0.304572	+	0.952489i	$0.401487\pi$
$42$	− 14.0660i	− 2.17042i
$43$	− 8.00000i	− 1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$	− 8.00000i	− 1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$	−4.33763	−0.653922
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 11.4567i	− 1.67112i	−0.549396	−	0.835562i	$-0.685142\pi$
$47$	− 11.4567i	− 1.67112i	0.549396	−	0.835562i	$-0.314858\pi$
$48$	3.11903i	0.450193i
$49$	−13.3376	−1.90538
$50$	0	0
$51$	−3.49027	−0.488736
$52$	− 3.72833i	− 0.517026i
$53$	6.00000i	0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$	6.00000i	0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	11.6288	1.58247
$55$	0	0
$56$	4.50973	0.602637
$57$	− 14.0660i	− 1.86308i
$58$	8.23805i	1.08171i
$59$	2.23805	0.291370	0.145685	−	0.989331i	$-0.453461\pi$
$59$	2.23805	0.291370	0.145685	+	0.989331i	$0.453461\pi$
$60$	0	0
$61$	3.55623	0.455329	0.227664	−	0.973740i	$-0.426891\pi$
$61$	3.55623	0.455329	0.227664	+	0.973740i	$0.426891\pi$
$62$	1.72833i	0.219498i
$63$	− 30.3429i	− 3.82285i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−13.5292	−1.66533
$67$	2.43720i	0.297752i	0.988856	+	0.148876i	$0.0475655\pi$
$67$	2.43720i	0.297752i	−0.988856	+	0.148876i	$0.952435\pi$
$68$	− 1.11903i	− 0.135702i
$69$	−3.11903	−0.375487
$70$	0	0
$71$	7.11903	0.844873	0.422437	−	0.906393i	$-0.361175\pi$
$71$	7.11903	0.844873	0.422437	+	0.906393i	$0.361175\pi$
$72$	6.72833i	0.792941i
$73$	9.45665i	1.10682i	0.832910	+	0.553409i	$0.186673\pi$
$73$	9.45665i	1.10682i	−0.832910	+	0.553409i	$0.813327\pi$
$74$	0.781399	0.0908357
$75$	0	0
$76$	4.50973	0.517301
$77$	19.5615i	2.22924i
$78$	− 11.6288i	− 1.31670i
$79$	14.9133	1.67788	0.838939	−	0.544225i	$-0.183176\pi$
$79$	14.9133	1.67788	0.838939	+	0.544225i	$0.183176\pi$
$80$	0	0
$81$	16.0854	1.78727
$82$	3.90043i	0.430730i
$83$	− 2.78140i	− 0.305298i	−0.988280	−	0.152649i	$-0.951220\pi$
$83$	− 2.78140i	− 0.305298i	0.988280	−	0.152649i	$-0.0487804\pi$
$84$	14.0660	1.53472
$85$	0	0
$86$	8.00000	0.862662
$87$	25.6947i	2.75476i
$88$	− 4.33763i	− 0.462393i
$89$	7.69471	0.815637	0.407819	−	0.913063i	$-0.366290\pi$
$89$	7.69471	0.815637	0.407819	+	0.913063i	$0.366290\pi$
$90$	0	0
$91$	−16.8137	−1.76256
$92$	− 1.00000i	− 0.104257i
$93$	5.39070i	0.558989i
$94$	11.4567	1.18166
$95$	0	0
$96$	−3.11903	−0.318334
$97$	− 0.642920i	− 0.0652786i	−0.999467	−	0.0326393i	$-0.989609\pi$
$97$	− 0.642920i	− 0.0652786i	0.999467	−	0.0326393i	$-0.0103913\pi$
$98$	− 13.3376i	− 1.34730i
$99$	−29.1850	−2.93320
$100$	0	0
$101$	−8.23805	−0.819717	−0.409858	−	0.912149i	$-0.634422\pi$
$101$	−8.23805	−0.819717	−0.409858	+	0.912149i	$0.634422\pi$
$102$	− 3.49027i	− 0.345589i
$103$	− 12.3376i	− 1.21566i	−0.794066	−	0.607831i	$-0.792040\pi$
$103$	− 12.3376i	− 1.21566i	0.794066	−	0.607831i	$-0.207960\pi$
$104$	3.72833	0.365593
$105$	0	0
$106$	−6.00000	−0.582772
$107$	− 15.9328i	− 1.54028i	−0.637876	−	0.770139i	$-0.720187\pi$
$107$	− 15.9328i	− 1.54028i	0.637876	−	0.770139i	$-0.279813\pi$
$108$	11.6288i	1.11898i
$109$	1.49027	0.142742	0.0713712	−	0.997450i	$-0.477263\pi$
$109$	1.49027	0.142742	0.0713712	+	0.997450i	$0.477263\pi$
$110$	0	0
$111$	2.43720	0.231329
$112$	4.50973i	0.426129i
$113$	6.00000i	0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$	6.00000i	0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	14.0660	1.31740
$115$	0	0
$116$	−8.23805	−0.764884
$117$	− 25.0854i	− 2.31915i
$118$	2.23805i	0.206030i
$119$	−5.04650	−0.462612
$120$	0	0
$121$	7.81502	0.710456
$122$	3.55623i	0.321966i
$123$	12.1655i	1.09693i
$124$	−1.72833	−0.155208
$125$	0	0
$126$	30.3429	2.70316
$127$	− 0.675256i	− 0.0599193i	−0.999551	−	0.0299597i	$-0.990462\pi$
$127$	− 0.675256i	− 0.0599193i	0.999551	−	0.0299597i	$-0.00953788\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	24.9522	2.19692
$130$	0	0
$131$	−13.6947	−1.19651	−0.598256	−	0.801305i	$-0.704139\pi$
$131$	−13.6947	−1.19651	−0.598256	+	0.801305i	$0.704139\pi$
$132$	− 13.5292i	− 1.17756i
$133$	− 20.3376i	− 1.76350i
$134$	−2.43720	−0.210542
$135$	0	0
$136$	1.11903	0.0959557
$137$	7.52918i	0.643261i	0.946865	+	0.321631i	$0.104231\pi$
$137$	7.52918i	0.643261i	−0.946865	+	0.321631i	$0.895769\pi$
$138$	− 3.11903i	− 0.265509i
$139$	−4.67526	−0.396550	−0.198275	−	0.980146i	$-0.563534\pi$
$139$	−4.67526	−0.396550	−0.198275	+	0.980146i	$0.563534\pi$
$140$	0	0
$141$	35.7336	3.00931
$142$	7.11903i	0.597415i
$143$	16.1721i	1.35238i
$144$	−6.72833	−0.560694
$145$	0	0
$146$	−9.45665	−0.782638
$147$	− 41.6004i	− 3.43114i
$148$	0.781399i	0.0642306i
$149$	−7.52918	−0.616814	−0.308407	−	0.951254i	$-0.599796\pi$
$149$	−7.52918	−0.616814	−0.308407	+	0.951254i	$0.599796\pi$
$150$	0	0
$151$	−13.3571	−1.08698	−0.543492	−	0.839414i	$-0.682898\pi$
$151$	−13.3571	−1.08698	−0.543492	+	0.839414i	$0.682898\pi$
$152$	4.50973i	0.365787i
$153$	− 7.52918i	− 0.608698i
$154$	−19.5615	−1.57631
$155$	0	0
$156$	11.6288	0.931045
$157$	16.2381i	1.29594i	0.761667	+	0.647969i	$0.224381\pi$
$157$	16.2381i	1.29594i	−0.761667	+	0.647969i	$0.775619\pi$
$158$	14.9133i	1.18644i
$159$	−18.7142	−1.48413
$160$	0	0
$161$	−4.50973	−0.355416
$162$	16.0854i	1.26379i
$163$	3.29112i	0.257781i	0.991659	+	0.128890i	$0.0411415\pi$
$163$	3.29112i	0.257781i	−0.991659	+	0.128890i	$0.958858\pi$
$164$	−3.90043	−0.304572
$165$	0	0
$166$	2.78140	0.215878
$167$	22.9133i	1.77309i	0.462647	+	0.886543i	$0.346900\pi$
$167$	22.9133i	1.77309i	−0.462647	+	0.886543i	$0.653100\pi$
$168$	14.0660i	1.08521i
$169$	−0.900425	−0.0692635
$170$	0	0
$171$	30.3429	2.32038
$172$	8.00000i	0.609994i
$173$	− 0.575681i	− 0.0437683i	−0.999761	−	0.0218841i	$-0.993034\pi$
$173$	− 0.575681i	− 0.0437683i	0.999761	−	0.0218841i	$-0.00696649\pi$
$174$	−25.6947	−1.94791
$175$	0	0
$176$	4.33763	0.326961
$177$	6.98055i	0.524690i
$178$	7.69471i	0.576743i
$179$	−5.01945	−0.375171	−0.187586	−	0.982248i	$-0.560066\pi$
$179$	−5.01945	−0.375171	−0.187586	+	0.982248i	$0.560066\pi$
$180$	0	0
$181$	−11.5292	−0.856957	−0.428479	−	0.903552i	$-0.640950\pi$
$181$	−11.5292	−0.856957	−0.428479	+	0.903552i	$0.640950\pi$
$182$	− 16.8137i	− 1.24632i
$183$	11.0920i	0.819942i
$184$	1.00000	0.0737210
$185$	0	0
$186$	−5.39070	−0.395265
$187$	4.85392i	0.354954i
$188$	11.4567i	0.835562i
$189$	52.4425	3.81463
$190$	0	0
$191$	−18.7142	−1.35411	−0.677055	−	0.735933i	$-0.736744\pi$
$191$	−18.7142	−1.35411	−0.677055	+	0.735933i	$0.736744\pi$
$192$	− 3.11903i	− 0.225096i
$193$	− 23.4956i	− 1.69125i	−0.533780	−	0.845624i	$-0.679229\pi$
$193$	− 23.4956i	− 1.69125i	0.533780	−	0.845624i	$-0.320771\pi$
$194$	0.642920	0.0461590
$195$	0	0
$196$	13.3376	0.952688
$197$	− 18.1385i	− 1.29231i	−0.763205	−	0.646157i	$-0.776375\pi$
$197$	− 18.1385i	− 1.29231i	0.763205	−	0.646157i	$-0.223625\pi$
$198$	− 29.1850i	− 2.07409i
$199$	23.2575	1.64868	0.824340	−	0.566094i	$-0.191546\pi$
$199$	23.2575	1.64868	0.824340	+	0.566094i	$0.191546\pi$
$200$	0	0
$201$	−7.60170	−0.536183
$202$	− 8.23805i	− 0.579627i
$203$	37.1514i	2.60751i
$204$	3.49027	0.244368
$205$	0	0
$206$	12.3376	0.859603
$207$	− 6.72833i	− 0.467651i
$208$	3.72833i	0.258513i
$209$	−19.5615	−1.35310
$210$	0	0
$211$	4.34420	0.299067	0.149533	−	0.988757i	$-0.452223\pi$
$211$	4.34420	0.299067	0.149533	+	0.988757i	$0.452223\pi$
$212$	− 6.00000i	− 0.412082i
$213$	22.2044i	1.52142i
$214$	15.9328	1.08914
$215$	0	0
$216$	−11.6288	−0.791236
$217$	7.79428i	0.529110i
$218$	1.49027i	0.100934i
$219$	−29.4956	−1.99313
$220$	0	0
$221$	−4.17210	−0.280646
$222$	2.43720i	0.163574i
$223$	− 12.4761i	− 0.835462i	−0.908571	−	0.417731i	$-0.862825\pi$
$223$	− 12.4761i	− 0.835462i	0.908571	−	0.417731i	$-0.137175\pi$
$224$	−4.50973	−0.301319
$225$	0	0
$226$	−6.00000	−0.399114
$227$	15.9328i	1.05749i	0.848779	+	0.528747i	$0.177338\pi$
$227$	15.9328i	1.05749i	−0.848779	+	0.528747i	$0.822662\pi$
$228$	14.0660i	0.931541i
$229$	3.56280	0.235436	0.117718	−	0.993047i	$-0.462442\pi$
$229$	3.56280	0.235436	0.117718	+	0.993047i	$0.462442\pi$
$230$	0	0
$231$	−61.0129	−4.01435
$232$	− 8.23805i	− 0.540855i
$233$	27.4956i	1.80129i	0.434552	+	0.900647i	$0.356907\pi$
$233$	27.4956i	1.80129i	−0.434552	+	0.900647i	$0.643093\pi$
$234$	25.0854	1.63988
$235$	0	0
$236$	−2.23805	−0.145685
$237$	46.5150i	3.02147i
$238$	− 5.04650i	− 0.327116i
$239$	−10.0389	−0.649363	−0.324681	−	0.945823i	$-0.605257\pi$
$239$	−10.0389	−0.649363	−0.324681	+	0.945823i	$0.605257\pi$
$240$	0	0
$241$	−23.6947	−1.52631	−0.763155	−	0.646215i	$-0.776351\pi$
$241$	−23.6947	−1.52631	−0.763155	+	0.646215i	$0.776351\pi$
$242$	7.81502i	0.502368i
$243$	15.2846i	0.980505i
$244$	−3.55623	−0.227664
$245$	0	0
$246$	−12.1655	−0.775646
$247$	− 16.8137i	− 1.06983i
$248$	− 1.72833i	− 0.109749i
$249$	8.67526	0.549772
$250$	0	0
$251$	12.4425	0.785363	0.392681	−	0.919675i	$-0.371548\pi$
$251$	12.4425	0.785363	0.392681	+	0.919675i	$0.371548\pi$
$252$	30.3429i	1.91142i
$253$	4.33763i	0.272704i
$254$	0.675256	0.0423693
$255$	0	0
$256$	1.00000	0.0625000
$257$	5.45665i	0.340377i	0.985412	+	0.170188i	$0.0544376\pi$
$257$	5.45665i	0.340377i	−0.985412	+	0.170188i	$0.945562\pi$
$258$	24.9522i	1.55346i
$259$	3.52389	0.218964
$260$	0	0
$261$	−55.4283	−3.43093
$262$	− 13.6947i	− 0.846062i
$263$	− 0.138479i	− 0.00853895i	−0.999991	−	0.00426948i	$-0.998641\pi$
$263$	− 0.138479i	− 0.00853895i	0.999991	−	0.00426948i	$-0.00135902\pi$
$264$	13.5292	0.832663
$265$	0	0
$266$	20.3376	1.24698
$267$	24.0000i	1.46878i
$268$	− 2.43720i	− 0.148876i
$269$	−14.6753	−0.894766	−0.447383	−	0.894342i	$-0.647644\pi$
$269$	−14.6753	−0.894766	−0.447383	+	0.894342i	$0.647644\pi$
$270$	0	0
$271$	−8.31058	−0.504832	−0.252416	−	0.967619i	$-0.581225\pi$
$271$	−8.31058	−0.504832	−0.252416	+	0.967619i	$0.581225\pi$
$272$	1.11903i	0.0678510i
$273$	− 52.4425i	− 3.17396i
$274$	−7.52918	−0.454854
$275$	0	0
$276$	3.11903	0.187743
$277$	12.9133i	0.775886i	0.921683	+	0.387943i	$0.126814\pi$
$277$	12.9133i	0.775886i	−0.921683	+	0.387943i	$0.873186\pi$
$278$	− 4.67526i	− 0.280403i
$279$	−11.6288	−0.696195
$280$	0	0
$281$	2.67526	0.159592	0.0797962	−	0.996811i	$-0.474573\pi$
$281$	2.67526	0.159592	0.0797962	+	0.996811i	$0.474573\pi$
$282$	35.7336i	2.12791i
$283$	− 0.742495i	− 0.0441367i	−0.999756	−	0.0220684i	$-0.992975\pi$
$283$	− 0.742495i	− 0.0441367i	0.999756	−	0.0220684i	$-0.00702515\pi$
$284$	−7.11903	−0.422437
$285$	0	0
$286$	−16.1721	−0.956276
$287$	17.5898i	1.03830i
$288$	− 6.72833i	− 0.396470i
$289$	15.7478	0.926340
$290$	0	0
$291$	2.00528	0.117552
$292$	− 9.45665i	− 0.553409i
$293$	6.00000i	0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$	6.00000i	0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	41.6004	2.42619
$295$	0	0
$296$	−0.781399	−0.0454179
$297$	− 50.4412i	− 2.92690i
$298$	− 7.52918i	− 0.436154i
$299$	−3.72833	−0.215615
$300$	0	0
$301$	36.0778	2.07949
$302$	− 13.3571i	− 0.768614i
$303$	− 25.6947i	− 1.47612i
$304$	−4.50973	−0.258651
$305$	0	0
$306$	7.52918	0.430414
$307$	30.5084i	1.74121i	0.491984	+	0.870604i	$0.336272\pi$
$307$	30.5084i	1.74121i	−0.491984	+	0.870604i	$0.663728\pi$
$308$	− 19.5615i	− 1.11462i
$309$	38.4814	2.18913
$310$	0	0
$311$	5.56280	0.315437	0.157719	−	0.987484i	$-0.449586\pi$
$311$	5.56280	0.315437	0.157719	+	0.987484i	$0.449586\pi$
$312$	11.6288i	0.658348i
$313$	− 4.07252i	− 0.230193i	−0.993354	−	0.115096i	$-0.963282\pi$
$313$	− 4.07252i	− 0.230193i	0.993354	−	0.115096i	$-0.0367177\pi$
$314$	−16.2381	−0.916366
$315$	0	0
$316$	−14.9133	−0.838939
$317$	− 6.16553i	− 0.346291i	−0.984896	−	0.173145i	$-0.944607\pi$
$317$	− 6.16553i	− 0.346291i	0.984896	−	0.173145i	$-0.0553930\pi$
$318$	− 18.7142i	− 1.04944i
$319$	35.7336	2.00070
$320$	0	0
$321$	49.6947	2.77369
$322$	− 4.50973i	− 0.251317i
$323$	− 5.04650i	− 0.280795i
$324$	−16.0854	−0.893634
$325$	0	0
$326$	−3.29112	−0.182279
$327$	4.64820i	0.257046i
$328$	− 3.90043i	− 0.215365i
$329$	51.6664	2.84846
$330$	0	0
$331$	27.5886	1.51640	0.758202	−	0.652019i	$-0.226078\pi$
$331$	27.5886	1.51640	0.758202	+	0.652019i	$0.226078\pi$
$332$	2.78140i	0.152649i
$333$	5.25751i	0.288110i
$334$	−22.9133	−1.25376
$335$	0	0
$336$	−14.0660	−0.767361
$337$	− 17.4230i	− 0.949093i	−0.880230	−	0.474547i	$-0.842612\pi$
$337$	− 17.4230i	− 0.949093i	0.880230	−	0.474547i	$-0.157388\pi$
$338$	− 0.900425i	− 0.0489767i
$339$	−18.7142	−1.01641
$340$	0	0
$341$	7.49684	0.405977
$342$	30.3429i	1.64076i
$343$	− 28.5810i	− 1.54323i
$344$	−8.00000	−0.431331
$345$	0	0
$346$	0.575681	0.0309488
$347$	4.88097i	0.262024i	0.991381	+	0.131012i	$0.0418227\pi$
$347$	4.88097i	0.262024i	−0.991381	+	0.131012i	$0.958177\pi$
$348$	− 25.6947i	− 1.37738i
$349$	−24.0389	−1.28677	−0.643387	−	0.765542i	$-0.722471\pi$
$349$	−24.0389	−1.28677	−0.643387	+	0.765542i	$0.722471\pi$
$350$	0	0
$351$	43.3558	2.31416
$352$	4.33763i	0.231196i
$353$	14.3442i	0.763464i	0.924273	+	0.381732i	$0.124672\pi$
$353$	14.3442i	0.763464i	−0.924273	+	0.381732i	$0.875328\pi$
$354$	−6.98055	−0.371012
$355$	0	0
$356$	−7.69471	−0.407819
$357$	− 15.7402i	− 0.833059i
$358$	− 5.01945i	− 0.265286i
$359$	−26.7814	−1.41347	−0.706734	−	0.707479i	$-0.749832\pi$
$359$	−26.7814	−1.41347	−0.706734	+	0.707479i	$0.749832\pi$
$360$	0	0
$361$	1.33763	0.0704015
$362$	− 11.5292i	− 0.605960i
$363$	24.3752i	1.27937i
$364$	16.8137	0.881279
$365$	0	0
$366$	−11.0920	−0.579787
$367$	− 20.4761i	− 1.06884i	−0.845218	−	0.534422i	$-0.820529\pi$
$367$	− 20.4761i	− 1.06884i	0.845218	−	0.534422i	$-0.179471\pi$
$368$	1.00000i	0.0521286i
$369$	−26.2433	−1.36617
$370$	0	0
$371$	−27.0584	−1.40480
$372$	− 5.39070i	− 0.279495i
$373$	3.89386i	0.201616i	0.994906	+	0.100808i	$0.0321428\pi$
$373$	3.89386i	0.201616i	−0.994906	+	0.100808i	$0.967857\pi$
$374$	−4.85392	−0.250990
$375$	0	0
$376$	−11.4567	−0.590832
$377$	30.7142i	1.58186i
$378$	52.4425i	2.69735i
$379$	30.3765	1.56034	0.780169	−	0.625569i	$-0.215133\pi$
$379$	30.3765	1.56034	0.780169	+	0.625569i	$0.215133\pi$
$380$	0	0
$381$	2.10614	0.107901
$382$	− 18.7142i	− 0.957500i
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	3.11903	0.159167
$385$	0	0
$386$	23.4956	1.19589
$387$	53.8266i	2.73616i
$388$	0.642920i	0.0326393i
$389$	18.6818	0.947206	0.473603	−	0.880738i	$-0.342953\pi$
$389$	18.6818	0.947206	0.473603	+	0.880738i	$0.342953\pi$
$390$	0	0
$391$	−1.11903	−0.0565916
$392$	13.3376i	0.673652i
$393$	− 42.7142i	− 2.15464i
$394$	18.1385	0.913803
$395$	0	0
$396$	29.1850	1.46660
$397$	− 28.5757i	− 1.43417i	−0.696985	−	0.717086i	$-0.745475\pi$
$397$	− 28.5757i	− 1.43417i	0.696985	−	0.717086i	$-0.254525\pi$
$398$	23.2575i	1.16579i
$399$	63.4336	3.17565
$400$	0	0
$401$	12.1061	0.604552	0.302276	−	0.953220i	$-0.402254\pi$
$401$	12.1061	0.604552	0.302276	+	0.953220i	$0.402254\pi$
$402$	− 7.60170i	− 0.379138i
$403$	6.44377i	0.320987i
$404$	8.23805	0.409858
$405$	0	0
$406$	−37.1514	−1.84379
$407$	− 3.38942i	− 0.168007i
$408$	3.49027i	0.172794i
$409$	−25.2911	−1.25057	−0.625283	−	0.780398i	$-0.715016\pi$
$409$	−25.2911	−1.25057	−0.625283	+	0.780398i	$0.715016\pi$
$410$	0	0
$411$	−23.4837	−1.15837
$412$	12.3376i	0.607831i
$413$	10.0930i	0.496644i
$414$	6.72833	0.330679
$415$	0	0
$416$	−3.72833	−0.182796
$417$	− 14.5822i	− 0.714096i
$418$	− 19.5615i	− 0.956785i
$419$	17.3505	0.847628	0.423814	−	0.905749i	$-0.360691\pi$
$419$	17.3505	0.847628	0.423814	+	0.905749i	$0.360691\pi$
$420$	0	0
$421$	21.4230	1.04409	0.522047	−	0.852916i	$-0.325168\pi$
$421$	21.4230	1.04409	0.522047	+	0.852916i	$0.325168\pi$
$422$	4.34420i	0.211472i
$423$	77.0841i	3.74796i
$424$	6.00000	0.291386
$425$	0	0
$426$	−22.2044	−1.07581
$427$	16.0376i	0.776115i
$428$	15.9328i	0.770139i
$429$	−50.4412	−2.43532
$430$	0	0
$431$	22.5822	1.08775	0.543874	−	0.839167i	$-0.316957\pi$
$431$	22.5822	1.08775	0.543874	+	0.839167i	$0.316957\pi$
$432$	− 11.6288i	− 0.559489i
$433$	− 1.01417i	− 0.0487378i	−0.999703	−	0.0243689i	$-0.992242\pi$
$433$	− 1.01417i	− 0.0487378i	0.999703	−	0.0243689i	$-0.00775763\pi$
$434$	−7.79428	−0.374138
$435$	0	0
$436$	−1.49027	−0.0713712
$437$	− 4.50973i	− 0.215729i
$438$	− 29.4956i	− 1.40935i
$439$	26.7478	1.27660	0.638301	−	0.769787i	$-0.279638\pi$
$439$	26.7478	1.27660	0.638301	+	0.769787i	$0.279638\pi$
$440$	0	0
$441$	89.7399	4.27333
$442$	− 4.17210i	− 0.198446i
$443$	− 10.2044i	− 0.484827i	−0.970173	−	0.242414i	$-0.922061\pi$
$443$	− 10.2044i	− 0.484827i	0.970173	−	0.242414i	$-0.0779391\pi$
$444$	−2.43720	−0.115665
$445$	0	0
$446$	12.4761	0.590761
$447$	− 23.4837i	− 1.11074i
$448$	− 4.50973i	− 0.213065i
$449$	−38.7867	−1.83046	−0.915228	−	0.402936i	$-0.867990\pi$
$449$	−38.7867	−1.83046	−0.915228	+	0.402936i	$0.867990\pi$
$450$	0	0
$451$	16.9186	0.796665
$452$	− 6.00000i	− 0.282216i
$453$	− 41.6611i	− 1.95741i
$454$	−15.9328	−0.747762
$455$	0	0
$456$	−14.0660	−0.658699
$457$	34.9522i	1.63500i	0.575932	+	0.817498i	$0.304639\pi$
$457$	34.9522i	1.63500i	−0.575932	+	0.817498i	$0.695361\pi$
$458$	3.56280i	0.166479i
$459$	13.0129	0.607389
$460$	0	0
$461$	16.3700	0.762425	0.381213	−	0.924487i	$-0.375507\pi$
$461$	16.3700	0.762425	0.381213	+	0.924487i	$0.375507\pi$
$462$	− 61.0129i	− 2.83858i
$463$	− 29.2186i	− 1.35790i	−0.734183	−	0.678952i	$-0.762435\pi$
$463$	− 29.2186i	− 1.35790i	0.734183	−	0.678952i	$-0.237565\pi$
$464$	8.23805	0.382442
$465$	0	0
$466$	−27.4956	−1.27371
$467$	24.2770i	1.12340i	0.827340	+	0.561702i	$0.189853\pi$
$467$	24.2770i	1.12340i	−0.827340	+	0.561702i	$0.810147\pi$
$468$	25.0854i	1.15957i
$469$	−10.9911	−0.507523
$470$	0	0
$471$	−50.6469	−2.33369
$472$	− 2.23805i	− 0.103015i
$473$	− 34.7010i	− 1.59555i
$474$	−46.5150	−2.13651
$475$	0	0
$476$	5.04650	0.231306
$477$	− 40.3700i	− 1.84841i
$478$	− 10.0389i	− 0.459169i
$479$	−24.6080	−1.12437	−0.562185	−	0.827012i	$-0.690039\pi$
$479$	−24.6080	−1.12437	−0.562185	+	0.827012i	$0.690039\pi$
$480$	0	0
$481$	2.91331	0.132835
$482$	− 23.6947i	− 1.07926i
$483$	− 14.0660i	− 0.640023i
$484$	−7.81502	−0.355228
$485$	0	0
$486$	−15.2846	−0.693322
$487$	− 30.2381i	− 1.37022i	−0.728441	−	0.685108i	$-0.759755\pi$
$487$	− 30.2381i	− 1.37022i	0.728441	−	0.685108i	$-0.240245\pi$
$488$	− 3.55623i	− 0.160983i
$489$	−10.2651	−0.464204
$490$	0	0
$491$	12.3311	0.556493	0.278246	−	0.960510i	$-0.410247\pi$
$491$	12.3311	0.556493	0.278246	+	0.960510i	$0.410247\pi$
$492$	− 12.1655i	− 0.548464i
$493$	9.21860i	0.415185i
$494$	16.8137	0.756486
$495$	0	0
$496$	1.72833	0.0776042
$497$	32.1049i	1.44010i
$498$	8.67526i	0.388748i
$499$	26.9133	1.20481	0.602403	−	0.798192i	$-0.294210\pi$
$499$	26.9133	1.20481	0.602403	+	0.798192i	$0.294210\pi$
$500$	0	0
$501$	−71.4672	−3.19292
$502$	12.4425i	0.555335i
$503$	− 20.5097i	− 0.914483i	−0.889342	−	0.457242i	$-0.848837\pi$
$503$	− 20.5097i	− 0.914483i	0.889342	−	0.457242i	$-0.151163\pi$
$504$	−30.3429	−1.35158
$505$	0	0
$506$	−4.33763	−0.192831
$507$	− 2.80845i	− 0.124728i
$508$	0.675256i	0.0299597i
$509$	36.7142	1.62733	0.813663	−	0.581336i	$-0.197470\pi$
$509$	36.7142	1.62733	0.813663	+	0.581336i	$0.197470\pi$
$510$	0	0
$511$	−42.6469	−1.88659
$512$	1.00000i	0.0441942i
$513$	52.4425i	2.31539i
$514$	−5.45665	−0.240683
$515$	0	0
$516$	−24.9522	−1.09846
$517$	− 49.6947i	− 2.18557i
$518$	3.52389i	0.154831i
$519$	1.79557	0.0788166
$520$	0	0
$521$	−4.91331	−0.215256	−0.107628	−	0.994191i	$-0.534326\pi$
$521$	−4.91331	−0.215256	−0.107628	+	0.994191i	$0.534326\pi$
$522$	− 55.4283i	− 2.42603i
$523$	0.344196i	0.0150506i	0.999972	+	0.00752531i	$0.00239540\pi$
$523$	0.344196i	0.0150506i	−0.999972	+	0.00752531i	$0.997605\pi$
$524$	13.6947	0.598256
$525$	0	0
$526$	0.138479	0.00603795
$527$	1.93404i	0.0842483i
$528$	13.5292i	0.588782i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	−15.0584	−0.653477
$532$	20.3376i	0.881748i
$533$	14.5421i	0.629887i
$534$	−24.0000	−1.03858
$535$	0	0
$536$	2.43720	0.105271
$537$	− 15.6558i	− 0.675598i
$538$	− 14.6753i	− 0.632695i
$539$	−57.8537	−2.49193
$540$	0	0
$541$	−6.13191	−0.263631	−0.131816	−	0.991274i	$-0.542081\pi$
$541$	−6.13191	−0.263631	−0.131816	+	0.991274i	$0.542081\pi$
$542$	− 8.31058i	− 0.356970i
$543$	− 35.9598i	− 1.54318i
$544$	−1.11903	−0.0479779
$545$	0	0
$546$	52.4425	2.24433
$547$	− 9.18498i	− 0.392721i	−0.980532	−	0.196361i	$-0.937088\pi$
$547$	− 9.18498i	− 0.392721i	0.980532	−	0.196361i	$-0.0629124\pi$
$548$	− 7.52918i	− 0.321631i
$549$	−23.9275	−1.02120
$550$	0	0
$551$	−37.1514	−1.58270
$552$	3.11903i	0.132755i
$553$	67.2549i	2.85997i
$554$	−12.9133	−0.548634
$555$	0	0
$556$	4.67526	0.198275
$557$	− 4.30529i	− 0.182421i	−0.995832	−	0.0912105i	$-0.970926\pi$
$557$	− 4.30529i	− 0.182421i	0.995832	−	0.0912105i	$-0.0290736\pi$
$558$	− 11.6288i	− 0.492284i
$559$	29.8266	1.26153
$560$	0	0
$561$	−15.1395	−0.639191
$562$	2.67526i	0.112849i
$563$	− 11.1256i	− 0.468888i	−0.972130	−	0.234444i	$-0.924673\pi$
$563$	− 11.1256i	− 0.468888i	0.972130	−	0.234444i	$-0.0753269\pi$
$564$	−35.7336	−1.50466
$565$	0	0
$566$	0.742495	0.0312094
$567$	72.5408i	3.04643i
$568$	− 7.11903i	− 0.298708i
$569$	16.0389	0.672386	0.336193	−	0.941793i	$-0.390861\pi$
$569$	16.0389	0.672386	0.336193	+	0.941793i	$0.390861\pi$
$570$	0	0
$571$	17.9004	0.749109	0.374555	−	0.927205i	$-0.377796\pi$
$571$	17.9004	0.749109	0.374555	+	0.927205i	$0.377796\pi$
$572$	− 16.1721i	− 0.676189i
$573$	− 58.3700i	− 2.43844i
$574$	−17.5898	−0.734186
$575$	0	0
$576$	6.72833	0.280347
$577$	− 9.12559i	− 0.379903i	−0.981793	−	0.189952i	$-0.939167\pi$
$577$	− 9.12559i	− 0.379903i	0.981793	−	0.189952i	$-0.0608332\pi$
$578$	15.7478i	0.655021i
$579$	73.2833	3.04555
$580$	0	0
$581$	12.5433	0.520386
$582$	2.00528i	0.0831217i
$583$	26.0258i	1.07788i
$584$	9.45665	0.391319
$585$	0	0
$586$	−6.00000	−0.247858
$587$	− 33.6340i	− 1.38823i	−0.719866	−	0.694113i	$-0.755797\pi$
$587$	− 33.6340i	− 1.38823i	0.719866	−	0.694113i	$-0.244203\pi$
$588$	41.6004i	1.71557i
$589$	−7.79428	−0.321158
$590$	0	0
$591$	56.5744	2.32716
$592$	− 0.781399i	− 0.0321153i
$593$	17.4567i	0.716859i	0.933557	+	0.358429i	$0.116688\pi$
$593$	17.4567i	0.716859i	−0.933557	+	0.358429i	$0.883312\pi$
$594$	50.4412	2.06963
$595$	0	0
$596$	7.52918	0.308407
$597$	72.5408i	2.96890i
$598$	− 3.72833i	− 0.152463i
$599$	11.5951	0.473764	0.236882	−	0.971538i	$-0.423874\pi$
$599$	11.5951	0.473764	0.236882	+	0.971538i	$0.423874\pi$
$600$	0	0
$601$	−31.6611	−1.29148	−0.645741	−	0.763556i	$-0.723452\pi$
$601$	−31.6611	−1.29148	−0.645741	+	0.763556i	$0.723452\pi$
$602$	36.0778i	1.47042i
$603$	− 16.3983i	− 0.667790i
$604$	13.3571	0.543492
$605$	0	0
$606$	25.6947	1.04378
$607$	− 36.0778i	− 1.46435i	−0.681115	−	0.732177i	$-0.738505\pi$
$607$	− 36.0778i	− 1.46435i	0.681115	−	0.732177i	$-0.261495\pi$
$608$	− 4.50973i	− 0.182894i
$609$	−115.876	−4.69554
$610$	0	0
$611$	42.7142	1.72803
$612$	7.52918i	0.304349i
$613$	32.0389i	1.29404i	0.762473	+	0.647020i	$0.223985\pi$
$613$	32.0389i	1.29404i	−0.762473	+	0.647020i	$0.776015\pi$
$614$	−30.5084	−1.23122
$615$	0	0
$616$	19.5615	0.788156
$617$	− 13.3960i	− 0.539302i	−0.962958	−	0.269651i	$-0.913092\pi$
$617$	− 13.3960i	− 0.539302i	0.962958	−	0.269651i	$-0.0869083\pi$
$618$	38.4814i	1.54795i
$619$	−37.1309	−1.49242	−0.746208	−	0.665713i	$-0.768128\pi$
$619$	−37.1309	−1.49242	−0.746208	+	0.665713i	$0.768128\pi$
$620$	0	0
$621$	11.6288	0.466646
$622$	5.56280i	0.223048i
$623$	34.7010i	1.39027i
$624$	−11.6288	−0.465523
$625$	0	0
$626$	4.07252	0.162771
$627$	− 61.0129i	− 2.43662i
$628$	− 16.2381i	− 0.647969i
$629$	0.874406	0.0348648
$630$	0	0
$631$	11.1125	0.442380	0.221190	−	0.975231i	$-0.429006\pi$
$631$	11.1125	0.442380	0.221190	+	0.975231i	$0.429006\pi$
$632$	− 14.9133i	− 0.593220i
$633$	13.5497i	0.538551i
$634$	6.16553	0.244864
$635$	0	0
$636$	18.7142	0.742065
$637$	− 49.7270i	− 1.97026i
$638$	35.7336i	1.41471i
$639$	−47.8991	−1.89486
$640$	0	0
$641$	12.3831	0.489103	0.244552	−	0.969636i	$-0.421359\pi$
$641$	12.3831	0.489103	0.244552	+	0.969636i	$0.421359\pi$
$642$	49.6947i	1.96129i
$643$	37.4956i	1.47868i	0.673332	+	0.739340i	$0.264862\pi$
$643$	37.4956i	1.47868i	−0.673332	+	0.739340i	$0.735138\pi$
$644$	4.50973	0.177708
$645$	0	0
$646$	5.04650	0.198552
$647$	14.5691i	0.572771i	0.958114	+	0.286385i	$0.0924538\pi$
$647$	14.5691i	0.572771i	−0.958114	+	0.286385i	$0.907546\pi$
$648$	− 16.0854i	− 0.631894i
$649$	9.70784	0.381066
$650$	0	0
$651$	−24.3106	−0.952807
$652$	− 3.29112i	− 0.128890i
$653$	4.41672i	0.172840i	0.996259	+	0.0864198i	$0.0275426\pi$
$653$	4.41672i	0.172840i	−0.996259	+	0.0864198i	$0.972457\pi$
$654$	−4.64820	−0.181759
$655$	0	0
$656$	3.90043	0.152286
$657$	− 63.6275i	− 2.48234i
$658$	51.6664i	2.01416i
$659$	31.8655	1.24130	0.620652	−	0.784086i	$-0.286868\pi$
$659$	31.8655	1.24130	0.620652	+	0.784086i	$0.286868\pi$
$660$	0	0
$661$	33.1190	1.28818	0.644090	−	0.764949i	$-0.277236\pi$
$661$	33.1190	1.28818	0.644090	+	0.764949i	$0.277236\pi$
$662$	27.5886i	1.07226i
$663$	− 13.0129i	− 0.505379i
$664$	−2.78140	−0.107939
$665$	0	0
$666$	−5.25751	−0.203724
$667$	8.23805i	0.318979i
$668$	− 22.9133i	− 0.886543i
$669$	38.9133	1.50448
$670$	0	0
$671$	15.4256	0.595499
$672$	− 14.0660i	− 0.542606i
$673$	− 19.3505i	− 0.745907i	−0.927850	−	0.372954i	$-0.878345\pi$
$673$	− 19.3505i	− 0.745907i	0.927850	−	0.372954i	$-0.121655\pi$
$674$	17.4230	0.671110
$675$	0	0
$676$	0.900425	0.0346317
$677$	− 6.00000i	− 0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$	− 6.00000i	− 0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$	− 18.7142i	− 0.718713i
$679$	2.89939	0.111268
$680$	0	0
$681$	−49.6947	−1.90431
$682$	7.49684i	0.287069i
$683$	− 38.3495i	− 1.46740i	−0.679472	−	0.733701i	$-0.737791\pi$
$683$	− 38.3495i	− 1.46740i	0.679472	−	0.733701i	$-0.262209\pi$
$684$	−30.3429	−1.16019
$685$	0	0
$686$	28.5810	1.09123
$687$	11.1125i	0.423967i
$688$	− 8.00000i	− 0.304997i
$689$	−22.3700	−0.852228
$690$	0	0
$691$	−21.0195	−0.799618	−0.399809	−	0.916599i	$-0.630923\pi$
$691$	−21.0195	−0.799618	−0.399809	+	0.916599i	$0.630923\pi$
$692$	0.575681i	0.0218841i
$693$	− 131.616i	− 4.99969i
$694$	−4.88097	−0.185279
$695$	0	0
$696$	25.6947	0.973955
$697$	4.36468i	0.165324i
$698$	− 24.0389i	− 0.909886i
$699$	−85.7594	−3.24372
$700$	0	0
$701$	19.3169	0.729589	0.364794	−	0.931088i	$-0.381139\pi$
$701$	19.3169	0.729589	0.364794	+	0.931088i	$0.381139\pi$
$702$	43.3558i	1.63636i
$703$	3.52389i	0.132906i
$704$	−4.33763	−0.163481
$705$	0	0
$706$	−14.3442	−0.539851
$707$	− 37.1514i	− 1.39722i
$708$	− 6.98055i	− 0.262345i
$709$	−12.2315	−0.459363	−0.229682	−	0.973266i	$-0.573768\pi$
$709$	−12.2315	−0.459363	−0.229682	+	0.973266i	$0.573768\pi$
$710$	0	0
$711$	−100.342	−3.76311
$712$	− 7.69471i	− 0.288371i
$713$	1.72833i	0.0647264i
$714$	15.7402	0.589061
$715$	0	0
$716$	5.01945	0.187586
$717$	− 31.3116i	− 1.16935i
$718$	− 26.7814i	− 0.999473i
$719$	40.6416	1.51568	0.757839	−	0.652442i	$-0.226255\pi$
$719$	40.6416	1.51568	0.757839	+	0.652442i	$0.226255\pi$
$720$	0	0
$721$	55.6393	2.07212
$722$	1.33763i	0.0497814i
$723$	− 73.9044i	− 2.74854i
$724$	11.5292	0.428479
$725$	0	0
$726$	−24.3752	−0.904650
$727$	− 23.4501i	− 0.869716i	−0.900499	−	0.434858i	$-0.856799\pi$
$727$	− 23.4501i	− 0.869716i	0.900499	−	0.434858i	$-0.143201\pi$
$728$	16.8137i	0.623158i
$729$	0.583281	0.0216030
$730$	0	0
$731$	8.95221	0.331110
$732$	− 11.0920i	− 0.409971i
$733$	12.5150i	0.462252i	0.972924	+	0.231126i	$0.0742410\pi$
$733$	12.5150i	0.462252i	−0.972924	+	0.231126i	$0.925759\pi$
$734$	20.4761	0.755787
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	10.5717i	0.389413i
$738$	− 26.2433i	− 0.966031i
$739$	21.3505	0.785391	0.392696	−	0.919668i	$-0.371543\pi$
$739$	21.3505	0.785391	0.392696	+	0.919668i	$0.371543\pi$
$740$	0	0
$741$	52.4425	1.92652
$742$	− 27.0584i	− 0.993343i
$743$	− 24.9858i	− 0.916641i	−0.888787	−	0.458321i	$-0.848451\pi$
$743$	− 24.9858i	− 0.916641i	0.888787	−	0.458321i	$-0.151549\pi$
$744$	5.39070	0.197633
$745$	0	0
$746$	−3.89386	−0.142564
$747$	18.7142i	0.684715i
$748$	− 4.85392i	− 0.177477i
$749$	71.8524	2.62543
$750$	0	0
$751$	−33.6275	−1.22708	−0.613542	−	0.789662i	$-0.710256\pi$
$751$	−33.6275	−1.22708	−0.613542	+	0.789662i	$0.710256\pi$
$752$	− 11.4567i	− 0.417781i
$753$	38.8085i	1.41426i
$754$	−30.7142	−1.11854
$755$	0	0
$756$	−52.4425	−1.90731
$757$	− 37.1230i	− 1.34926i	−0.738156	−	0.674630i	$-0.764303\pi$
$757$	− 37.1230i	− 1.34926i	0.738156	−	0.674630i	$-0.235697\pi$
$758$	30.3765i	1.10333i
$759$	−13.5292	−0.491078
$760$	0	0
$761$	−3.87337	−0.140410	−0.0702048	−	0.997533i	$-0.522365\pi$
$761$	−3.87337	−0.140410	−0.0702048	+	0.997533i	$0.522365\pi$
$762$	2.10614i	0.0762975i
$763$	6.72073i	0.243307i
$764$	18.7142	0.677055
$765$	0	0
$766$	0	0
$767$	8.34420i	0.301291i
$768$	3.11903i	0.112548i
$769$	−23.1645	−0.835333	−0.417667	−	0.908600i	$-0.637152\pi$
$769$	−23.1645	−0.835333	−0.417667	+	0.908600i	$0.637152\pi$
$770$	0	0
$771$	−17.0195	−0.612941
$772$	23.4956i	0.845624i
$773$	8.78140i	0.315845i	0.987452	+	0.157922i	$0.0504796\pi$
$773$	8.78140i	0.315845i	−0.987452	+	0.157922i	$0.949520\pi$
$774$	−53.8266	−1.93476
$775$	0	0
$776$	−0.642920	−0.0230795
$777$	10.9911i	0.394304i
$778$	18.6818i	0.669776i
$779$	−17.5898	−0.630222
$780$	0	0
$781$	30.8797	1.10496
$782$	− 1.11903i	− 0.0400163i
$783$	− 95.7983i	− 3.42355i
$784$	−13.3376	−0.476344
$785$	0	0
$786$	42.7142	1.52356
$787$	49.6275i	1.76903i	0.466513	+	0.884514i	$0.345510\pi$
$787$	49.6275i	1.76903i	−0.466513	+	0.884514i	$0.654490\pi$
$788$	18.1385i	0.646157i
$789$	0.431918	0.0153767
$790$	0	0
$791$	−27.0584	−0.962084
$792$	29.1850i	1.03704i
$793$	13.2588i	0.470833i
$794$	28.5757	1.01411
$795$	0	0
$796$	−23.2575	−0.824340
$797$	18.3311i	0.649319i	0.945831	+	0.324660i	$0.105250\pi$
$797$	18.3311i	0.649319i	−0.945831	+	0.324660i	$0.894750\pi$
$798$	63.4336i	2.24553i
$799$	12.8203	0.453550
$800$	0	0
$801$	−51.7725	−1.82929
$802$	12.1061i	0.427483i
$803$	41.0195i	1.44755i
$804$	7.60170	0.268091
$805$	0	0
$806$	−6.44377	−0.226972
$807$	− 45.7725i	− 1.61127i
$808$	8.23805i	0.289814i
$809$	1.93933	0.0681832	0.0340916	−	0.999419i	$-0.489146\pi$
$809$	1.93933	0.0681832	0.0340916	+	0.999419i	$0.489146\pi$
$810$	0	0
$811$	−5.41775	−0.190243	−0.0951215	−	0.995466i	$-0.530324\pi$
$811$	−5.41775	−0.190243	−0.0951215	+	0.995466i	$0.530324\pi$
$812$	− 37.1514i	− 1.30376i
$813$	− 25.9209i	− 0.909086i
$814$	3.38942	0.118799
$815$	0	0
$816$	−3.49027	−0.122184
$817$	36.0778i	1.26220i
$818$	− 25.2911i	− 0.884283i
$819$	113.128	3.95302
$820$	0	0
$821$	37.8655	1.32152	0.660758	−	0.750599i	$-0.270235\pi$
$821$	37.8655	1.32152	0.660758	+	0.750599i	$0.270235\pi$
$822$	− 23.4837i	− 0.819088i
$823$	− 43.7336i	− 1.52446i	−0.647308	−	0.762229i	$-0.724105\pi$
$823$	− 43.7336i	− 1.52446i	0.647308	−	0.762229i	$-0.275895\pi$
$824$	−12.3376	−0.429802
$825$	0	0
$826$	−10.0930	−0.351181
$827$	28.1991i	0.980581i	0.871559	+	0.490290i	$0.163109\pi$
$827$	28.1991i	0.980581i	−0.871559	+	0.490290i	$0.836891\pi$
$828$	6.72833i	0.233826i
$829$	−1.12559	−0.0390935	−0.0195468	−	0.999809i	$-0.506222\pi$
$829$	−1.12559	−0.0390935	−0.0195468	+	0.999809i	$0.506222\pi$
$830$	0	0
$831$	−40.2770	−1.39719
$832$	− 3.72833i	− 0.129256i
$833$	− 14.9252i	− 0.517126i
$834$	14.5822	0.504942
$835$	0	0
$836$	19.5615	0.676549
$837$	− 20.0983i	− 0.694699i
$838$	17.3505i	0.599364i
$839$	−39.9328	−1.37863	−0.689316	−	0.724461i	$-0.742089\pi$
$839$	−39.9328	−1.37863	−0.689316	+	0.724461i	$0.742089\pi$
$840$	0	0
$841$	38.8655	1.34019
$842$	21.4230i	0.738287i
$843$	8.34420i	0.287389i
$844$	−4.34420	−0.149533
$845$	0	0
$846$	−77.0841	−2.65021
$847$	35.2436i	1.21098i
$848$	6.00000i	0.206041i
$849$	2.31586	0.0794801
$850$	0	0
$851$	0.781399	0.0267860
$852$	− 22.2044i	− 0.760711i
$853$	− 47.9921i	− 1.64322i	−0.570050	−	0.821610i	$-0.693076\pi$
$853$	− 47.9921i	− 1.64322i	0.570050	−	0.821610i	$-0.306924\pi$
$854$	−16.0376	−0.548796
$855$	0	0
$856$	−15.9328	−0.544571
$857$	− 43.4283i	− 1.48348i	−0.670686	−	0.741742i	$-0.734000\pi$
$857$	− 43.4283i	− 1.48348i	0.670686	−	0.741742i	$-0.266000\pi$
$858$	− 50.4412i	− 1.72203i
$859$	−32.5433	−1.11036	−0.555182	−	0.831729i	$-0.687352\pi$
$859$	−32.5433	−1.11036	−0.555182	+	0.831729i	$0.687352\pi$
$860$	0	0
$861$	−54.8632	−1.86973
$862$	22.5822i	0.769154i
$863$	− 46.1036i	− 1.56938i	−0.619886	−	0.784692i	$-0.712821\pi$
$863$	− 46.1036i	− 1.56938i	0.619886	−	0.784692i	$-0.287179\pi$
$864$	11.6288	0.395618
$865$	0	0
$866$	1.01417	0.0344628
$867$	49.1177i	1.66813i
$868$	− 7.79428i	− 0.264555i
$869$	64.6884	2.19440
$870$	0	0
$871$	−9.08669	−0.307891
$872$	− 1.49027i	− 0.0504670i
$873$	4.32578i	0.146405i
$874$	4.50973	0.152544
$875$	0	0
$876$	29.4956	0.996563
$877$	− 24.0996i	− 0.813785i	−0.913476	−	0.406892i	$-0.866612\pi$
$877$	− 24.0996i	− 0.813785i	0.913476	−	0.406892i	$-0.133388\pi$
$878$	26.7478i	0.902694i
$879$	−18.7142	−0.631213
$880$	0	0
$881$	2.34420	0.0789780	0.0394890	−	0.999220i	$-0.487427\pi$
$881$	2.34420	0.0789780	0.0394890	+	0.999220i	$0.487427\pi$
$882$	89.7399i	3.02170i
$883$	41.0505i	1.38146i	0.723113	+	0.690730i	$0.242711\pi$
$883$	41.0505i	1.38146i	−0.723113	+	0.690730i	$0.757289\pi$
$884$	4.17210	0.140323
$885$	0	0
$886$	10.2044	0.342825
$887$	54.7788i	1.83929i	0.392747	+	0.919647i	$0.371525\pi$
$887$	54.7788i	1.83929i	−0.392747	+	0.919647i	$0.628475\pi$
$888$	− 2.43720i	− 0.0817872i
$889$	3.04522	0.102133
$890$	0	0
$891$	69.7725	2.33747
$892$	12.4761i	0.417731i
$893$	51.6664i	1.72895i
$894$	23.4837	0.785413
$895$	0	0
$896$	4.50973	0.150659
$897$	− 11.6288i	− 0.388273i
$898$	− 38.7867i	− 1.29433i
$899$	14.2381	0.474866
$900$	0	0
$901$	−6.71416	−0.223681
$902$	16.9186i	0.563328i
$903$	112.528i	3.74469i
$904$	6.00000	0.199557
$905$	0	0
$906$	41.6611	1.38410
$907$	− 10.1061i	− 0.335569i	−0.985824	−	0.167784i	$-0.946339\pi$
$907$	− 10.1061i	− 0.335569i	0.985824	−	0.167784i	$-0.0536613\pi$
$908$	− 15.9328i	− 0.528747i
$909$	55.4283	1.83844
$910$	0	0
$911$	−25.4178	−0.842128	−0.421064	−	0.907031i	$-0.638343\pi$
$911$	−25.4178	−0.842128	−0.421064	+	0.907031i	$0.638343\pi$
$912$	− 14.0660i	− 0.465770i
$913$	− 12.0647i	− 0.399282i
$914$	−34.9522	−1.15612
$915$	0	0
$916$	−3.56280	−0.117718
$917$	− 61.7594i	− 2.03947i
$918$	13.0129i	0.429489i
$919$	−23.6017	−0.778548	−0.389274	−	0.921122i	$-0.627274\pi$
$919$	−23.6017	−0.778548	−0.389274	+	0.921122i	$0.627274\pi$
$920$	0	0
$921$	−95.1566	−3.13552
$922$	16.3700i	0.539116i
$923$	26.5421i	0.873643i
$924$	61.0129	2.00718
$925$	0	0
$926$	29.2186	0.960183
$927$	83.0116i	2.72646i
$928$	8.23805i	0.270427i
$929$	7.08669	0.232507	0.116253	−	0.993220i	$-0.462912\pi$
$929$	7.08669	0.232507	0.116253	+	0.993220i	$0.462912\pi$
$930$	0	0
$931$	60.1490	1.97131
$932$	− 27.4956i	− 0.900647i
$933$	17.3505i	0.568030i
$934$	−24.2770	−0.794366
$935$	0	0
$936$	−25.0854	−0.819942
$937$	27.3169i	0.892404i	0.894932	+	0.446202i	$0.147224\pi$
$937$	27.3169i	0.892404i	−0.894932	+	0.446202i	$0.852776\pi$
$938$	− 10.9911i	− 0.358873i
$939$	12.7023	0.414524
$940$	0	0
$941$	55.8979	1.82222	0.911109	−	0.412165i	$-0.135227\pi$
$941$	55.8979	1.82222	0.911109	+	0.412165i	$0.135227\pi$
$942$	− 50.6469i	− 1.65017i
$943$	3.90043i	0.127015i
$944$	2.23805	0.0728424
$945$	0	0
$946$	34.7010	1.12823
$947$	37.5939i	1.22164i	0.791771	+	0.610818i	$0.209159\pi$
$947$	37.5939i	1.22164i	−0.791771	+	0.610818i	$0.790841\pi$
$948$	− 46.5150i	− 1.51074i
$949$	−35.2575	−1.14451
$950$	0	0
$951$	19.2305	0.623590
$952$	5.04650i	0.163558i
$953$	29.3828i	0.951804i	0.879498	+	0.475902i	$0.157878\pi$
$953$	29.3828i	0.951804i	−0.879498	+	0.475902i	$0.842122\pi$
$954$	40.3700	1.30703
$955$	0	0
$956$	10.0389	0.324681
$957$	111.454i	3.60280i
$958$	− 24.6080i	− 0.795049i
$959$	−33.9545	−1.09645
$960$	0	0
$961$	−28.0129	−0.903641
$962$	2.91331i	0.0939289i
$963$	107.201i	3.45450i
$964$	23.6947	0.763155
$965$	0	0
$966$	14.0660	0.452565
$967$	− 49.2292i	− 1.58310i	−0.611102	−	0.791552i	$-0.709274\pi$
$967$	− 49.2292i	− 1.58310i	0.611102	−	0.791552i	$-0.290726\pi$
$968$	− 7.81502i	− 0.251184i
$969$	15.7402	0.505647
$970$	0	0
$971$	9.62347	0.308832	0.154416	−	0.988006i	$-0.450650\pi$
$971$	9.62347	0.308832	0.154416	+	0.988006i	$0.450650\pi$
$972$	− 15.2846i	− 0.490252i
$973$	− 21.0841i	− 0.675926i
$974$	30.2381	0.968890
$975$	0	0
$976$	3.55623	0.113832
$977$	18.9858i	0.607411i	0.952766	+	0.303705i	$0.0982238\pi$
$977$	18.9858i	0.607411i	−0.952766	+	0.303705i	$0.901776\pi$
$978$	− 10.2651i	− 0.328242i
$979$	33.3768	1.06673
$980$	0	0
$981$	−10.0271	−0.320139
$982$	12.3311i	0.393500i
$983$	− 4.33763i	− 0.138349i	−0.997605	−	0.0691744i	$-0.977963\pi$
$983$	− 4.33763i	− 0.138349i	0.997605	−	0.0691744i	$-0.0220365\pi$
$984$	12.1655	0.387823
$985$	0	0
$986$	−9.21860	−0.293580
$987$	161.149i	5.12942i
$988$	16.8137i	0.534916i
$989$	8.00000	0.254385
$990$	0	0
$991$	1.96766	0.0625049	0.0312524	−	0.999512i	$-0.490050\pi$
$991$	1.96766	0.0625049	0.0312524	+	0.999512i	$0.490050\pi$
$992$	1.72833i	0.0548744i
$993$	86.0495i	2.73070i
$994$	−32.1049	−1.01830
$995$	0	0
$996$	−8.67526	−0.274886
$997$	3.96110i	0.125449i	0.998031	+	0.0627246i	$0.0199790\pi$
$997$	3.96110i	0.125449i	−0.998031	+	0.0627246i	$0.980021\pi$
$998$	26.9133i	0.851926i
$999$	−9.08669	−0.287490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.b.j.599.6		6
5.2	odd	4		1150.2.a.q.1.3		3
5.3	odd	4		230.2.a.d.1.1	✓	3
5.4	even	2	inner	1150.2.b.j.599.1		6
15.8	even	4		2070.2.a.z.1.3		3
20.3	even	4		1840.2.a.r.1.3		3
20.7	even	4		9200.2.a.cf.1.1		3
40.3	even	4		7360.2.a.ce.1.1		3
40.13	odd	4		7360.2.a.bz.1.3		3
115.68	even	4		5290.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.1	✓	3	5.3	odd	4
1150.2.a.q.1.3		3	5.2	odd	4
1150.2.b.j.599.1		6	5.4	even	2	inner
1150.2.b.j.599.6		6	1.1	even	1	trivial
1840.2.a.r.1.3		3	20.3	even	4
2070.2.a.z.1.3		3	15.8	even	4
5290.2.a.r.1.1		3	115.68	even	4
7360.2.a.bz.1.3		3	40.13	odd	4
7360.2.a.ce.1.1		3	40.3	even	4
9200.2.a.cf.1.1		3	20.7	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +3.11903i q^{3} -1.00000 q^{4} -3.11903 q^{6} +4.50973i q^{7} -1.00000i q^{8} -6.72833 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +3.11903i q^{3} -1.00000 q^{4} -3.11903 q^{6} +4.50973i q^{7} -1.00000i q^{8} -6.72833 q^{9} +4.33763 q^{11} -3.11903i q^{12} +3.72833i q^{13} -4.50973 q^{14} +1.00000 q^{16} +1.11903i q^{17} -6.72833i q^{18} -4.50973 q^{19} -14.0660 q^{21} +4.33763i q^{22} +1.00000i q^{23} +3.11903 q^{24} -3.72833 q^{26} -11.6288i q^{27} -4.50973i q^{28} +8.23805 q^{29} +1.72833 q^{31} +1.00000i q^{32} +13.5292i q^{33} -1.11903 q^{34} +6.72833 q^{36} -0.781399i q^{37} -4.50973i q^{38} -11.6288 q^{39} +3.90043 q^{41} -14.0660i q^{42} -8.00000i q^{43} -4.33763 q^{44} -1.00000 q^{46} -11.4567i q^{47} +3.11903i q^{48} -13.3376 q^{49} -3.49027 q^{51} -3.72833i q^{52} +6.00000i q^{53} +11.6288 q^{54} +4.50973 q^{56} -14.0660i q^{57} +8.23805i q^{58} +2.23805 q^{59} +3.55623 q^{61} +1.72833i q^{62} -30.3429i q^{63} -1.00000 q^{64} -13.5292 q^{66} +2.43720i q^{67} -1.11903i q^{68} -3.11903 q^{69} +7.11903 q^{71} +6.72833i q^{72} +9.45665i q^{73} +0.781399 q^{74} +4.50973 q^{76} +19.5615i q^{77} -11.6288i q^{78} +14.9133 q^{79} +16.0854 q^{81} +3.90043i q^{82} -2.78140i q^{83} +14.0660 q^{84} +8.00000 q^{86} +25.6947i q^{87} -4.33763i q^{88} +7.69471 q^{89} -16.8137 q^{91} -1.00000i q^{92} +5.39070i q^{93} +11.4567 q^{94} -3.11903 q^{96} -0.642920i q^{97} -13.3376i q^{98} -29.1850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{6} - 20 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^6 - 20 * q^9	\( 6 q - 6 q^{4} + 2 q^{6} - 20 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} - 6 q^{19} - 44 q^{21} - 2 q^{24} - 2 q^{26} + 8 q^{29} - 10 q^{31} + 14 q^{34} + 20 q^{36} - 28 q^{39} + 2 q^{41} - 6 q^{44} - 6 q^{46} - 60 q^{49} - 42 q^{51} + 28 q^{54} + 6 q^{56} - 28 q^{59} + 2 q^{61} - 6 q^{64} - 18 q^{66} + 2 q^{69} + 22 q^{71} + 4 q^{74} + 6 q^{76} + 8 q^{79} + 14 q^{81} + 44 q^{84} + 48 q^{86} - 36 q^{89} + 2 q^{91} + 28 q^{94} + 2 q^{96} - 114 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^6 - 20 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 - 6 * q^19 - 44 * q^21 - 2 * q^24 - 2 * q^26 + 8 * q^29 - 10 * q^31 + 14 * q^34 + 20 * q^36 - 28 * q^39 + 2 * q^41 - 6 * q^44 - 6 * q^46 - 60 * q^49 - 42 * q^51 + 28 * q^54 + 6 * q^56 - 28 * q^59 + 2 * q^61 - 6 * q^64 - 18 * q^66 + 2 * q^69 + 22 * q^71 + 4 * q^74 + 6 * q^76 + 8 * q^79 + 14 * q^81 + 44 * q^84 + 48 * q^86 - 36 * q^89 + 2 * q^91 + 28 * q^94 + 2 * q^96 - 114 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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