LMFDB - Embedded newform 4650.2.d.bc.3349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4650,2,Mod(3349,4650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4650, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4650.3349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4650.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$37.1304369399$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 186)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3349.1
Root			$-2.56155i$ of defining polynomial
Character	$\chi$	$=$	4650.3349
Dual form			4650.2.d.bc.3349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -5.12311i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -5.12311i q^{7} +1.00000i q^{8} -1.00000 q^{9} -2.56155 q^{11} +1.00000i q^{12} -0.561553i q^{13} -5.12311 q^{14} +1.00000 q^{16} -5.68466i q^{17} +1.00000i q^{18} +2.56155 q^{19} -5.12311 q^{21} +2.56155i q^{22} -8.00000i q^{23} +1.00000 q^{24} -0.561553 q^{26} +1.00000i q^{27} +5.12311i q^{28} +7.12311 q^{29} -1.00000 q^{31} -1.00000i q^{32} +2.56155i q^{33} -5.68466 q^{34} +1.00000 q^{36} -8.24621i q^{37} -2.56155i q^{38} -0.561553 q^{39} +4.24621 q^{41} +5.12311i q^{42} -9.12311i q^{43} +2.56155 q^{44} -8.00000 q^{46} +3.68466i q^{47} -1.00000i q^{48} -19.2462 q^{49} -5.68466 q^{51} +0.561553i q^{52} -2.00000i q^{53} +1.00000 q^{54} +5.12311 q^{56} -2.56155i q^{57} -7.12311i q^{58} +1.12311 q^{59} -0.561553 q^{61} +1.00000i q^{62} +5.12311i q^{63} -1.00000 q^{64} +2.56155 q^{66} -0.315342i q^{67} +5.68466i q^{68} -8.00000 q^{69} -1.43845 q^{71} -1.00000i q^{72} +10.0000i q^{73} -8.24621 q^{74} -2.56155 q^{76} +13.1231i q^{77} +0.561553i q^{78} +3.68466 q^{79} +1.00000 q^{81} -4.24621i q^{82} +12.8078i q^{83} +5.12311 q^{84} -9.12311 q^{86} -7.12311i q^{87} -2.56155i q^{88} +0.246211 q^{89} -2.87689 q^{91} +8.00000i q^{92} +1.00000i q^{93} +3.68466 q^{94} -1.00000 q^{96} +14.8078i q^{97} +19.2462i q^{98} +2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} - 2 q^{11} - 4 q^{14} + 4 q^{16} + 2 q^{19} - 4 q^{21} + 4 q^{24} + 6 q^{26} + 12 q^{29} - 4 q^{31} + 2 q^{34} + 4 q^{36} + 6 q^{39} - 16 q^{41} + 2 q^{44} - 32 q^{46} - 44 q^{49} + 2 q^{51} + 4 q^{54} + 4 q^{56} - 12 q^{59} + 6 q^{61} - 4 q^{64} + 2 q^{66} - 32 q^{69} - 14 q^{71} - 2 q^{76} - 10 q^{79} + 4 q^{81} + 4 q^{84} - 20 q^{86} - 32 q^{89} - 28 q^{91} - 10 q^{94} - 4 q^{96} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 - 2 * q^11 - 4 * q^14 + 4 * q^16 + 2 * q^19 - 4 * q^21 + 4 * q^24 + 6 * q^26 + 12 * q^29 - 4 * q^31 + 2 * q^34 + 4 * q^36 + 6 * q^39 - 16 * q^41 + 2 * q^44 - 32 * q^46 - 44 * q^49 + 2 * q^51 + 4 * q^54 + 4 * q^56 - 12 * q^59 + 6 * q^61 - 4 * q^64 + 2 * q^66 - 32 * q^69 - 14 * q^71 - 2 * q^76 - 10 * q^79 + 4 * q^81 + 4 * q^84 - 20 * q^86 - 32 * q^89 - 28 * q^91 - 10 * q^94 - 4 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4650\mathbb{Z}\right)^\times$.

$n$	$1801$	$2977$	$3101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	− 5.12311i	− 1.93635i	−0.250270	−	0.968176i	$-0.580520\pi$
$7$	− 5.12311i	− 1.93635i	0.250270	−	0.968176i	$-0.419480\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−2.56155	−0.772337	−0.386169	−	0.922428i	$-0.626202\pi$
$11$	−2.56155	−0.772337	−0.386169	+	0.922428i	$0.626202\pi$
$12$	1.00000i	0.288675i
$13$	− 0.561553i	− 0.155747i	−0.996963	−	0.0778734i	$-0.975187\pi$
$13$	− 0.561553i	− 0.155747i	0.996963	−	0.0778734i	$-0.0248130\pi$
$14$	−5.12311	−1.36921
$15$	0	0
$16$	1.00000	0.250000
$17$	− 5.68466i	− 1.37873i	−0.724413	−	0.689366i	$-0.757889\pi$
$17$	− 5.68466i	− 1.37873i	0.724413	−	0.689366i	$-0.242111\pi$
$18$	1.00000i	0.235702i
$19$	2.56155	0.587661	0.293830	−	0.955858i	$-0.405070\pi$
$19$	2.56155	0.587661	0.293830	+	0.955858i	$0.405070\pi$
$20$	0	0
$21$	−5.12311	−1.11795
$22$	2.56155i	0.546125i
$23$	− 8.00000i	− 1.66812i	−0.551677	−	0.834058i	$-0.686012\pi$
$23$	− 8.00000i	− 1.66812i	0.551677	−	0.834058i	$-0.313988\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−0.561553	−0.110130
$27$	1.00000i	0.192450i
$28$	5.12311i	0.968176i
$29$	7.12311	1.32273	0.661364	−	0.750065i	$-0.269978\pi$
$29$	7.12311	1.32273	0.661364	+	0.750065i	$0.269978\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	− 1.00000i	− 0.176777i
$33$	2.56155i	0.445909i
$34$	−5.68466	−0.974911
$35$	0	0
$36$	1.00000	0.166667
$37$	− 8.24621i	− 1.35567i	−0.735215	−	0.677834i	$-0.762919\pi$
$37$	− 8.24621i	− 1.35567i	0.735215	−	0.677834i	$-0.237081\pi$
$38$	− 2.56155i	− 0.415539i
$39$	−0.561553	−0.0899204
$40$	0	0
$41$	4.24621	0.663147	0.331573	−	0.943429i	$-0.392421\pi$
$41$	4.24621	0.663147	0.331573	+	0.943429i	$0.392421\pi$
$42$	5.12311i	0.790512i
$43$	− 9.12311i	− 1.39126i	−0.718400	−	0.695630i	$-0.755125\pi$
$43$	− 9.12311i	− 1.39126i	0.718400	−	0.695630i	$-0.244875\pi$
$44$	2.56155	0.386169
$45$	0	0
$46$	−8.00000	−1.17954
$47$	3.68466i	0.537463i	0.963215	+	0.268731i	$0.0866044\pi$
$47$	3.68466i	0.537463i	−0.963215	+	0.268731i	$0.913396\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−19.2462	−2.74946
$50$	0	0
$51$	−5.68466	−0.796011
$52$	0.561553i	0.0778734i
$53$	− 2.00000i	− 0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$	− 2.00000i	− 0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	5.12311	0.684604
$57$	− 2.56155i	− 0.339286i
$58$	− 7.12311i	− 0.935310i
$59$	1.12311	0.146216	0.0731079	−	0.997324i	$-0.476708\pi$
$59$	1.12311	0.146216	0.0731079	+	0.997324i	$0.476708\pi$
$60$	0	0
$61$	−0.561553	−0.0718995	−0.0359497	−	0.999354i	$-0.511446\pi$
$61$	−0.561553	−0.0718995	−0.0359497	+	0.999354i	$0.511446\pi$
$62$	1.00000i	0.127000i
$63$	5.12311i	0.645451i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.56155	0.315305
$67$	− 0.315342i	− 0.0385251i	−0.999814	−	0.0192626i	$-0.993868\pi$
$67$	− 0.315342i	− 0.0385251i	0.999814	−	0.0192626i	$-0.00613184\pi$
$68$	5.68466i	0.689366i
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−1.43845	−0.170712	−0.0853561	−	0.996351i	$-0.527203\pi$
$71$	−1.43845	−0.170712	−0.0853561	+	0.996351i	$0.527203\pi$
$72$	− 1.00000i	− 0.117851i
$73$	10.0000i	1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$	10.0000i	1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	−8.24621	−0.958603
$75$	0	0
$76$	−2.56155	−0.293830
$77$	13.1231i	1.49552i
$78$	0.561553i	0.0635833i
$79$	3.68466	0.414556	0.207278	−	0.978282i	$-0.433539\pi$
$79$	3.68466	0.414556	0.207278	+	0.978282i	$0.433539\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 4.24621i	− 0.468916i
$83$	12.8078i	1.40583i	0.711272	+	0.702917i	$0.248120\pi$
$83$	12.8078i	1.40583i	−0.711272	+	0.702917i	$0.751880\pi$
$84$	5.12311	0.558977
$85$	0	0
$86$	−9.12311	−0.983770
$87$	− 7.12311i	− 0.763677i
$88$	− 2.56155i	− 0.273062i
$89$	0.246211	0.0260983	0.0130492	−	0.999915i	$-0.495846\pi$
$89$	0.246211	0.0260983	0.0130492	+	0.999915i	$0.495846\pi$
$90$	0	0
$91$	−2.87689	−0.301580
$92$	8.00000i	0.834058i
$93$	1.00000i	0.103695i
$94$	3.68466	0.380043
$95$	0	0
$96$	−1.00000	−0.102062
$97$	14.8078i	1.50350i	0.659448	+	0.751750i	$0.270790\pi$
$97$	14.8078i	1.50350i	−0.659448	+	0.751750i	$0.729210\pi$
$98$	19.2462i	1.94416i
$99$	2.56155	0.257446
$100$	0	0
$101$	16.2462	1.61656	0.808279	−	0.588799i	$-0.200399\pi$
$101$	16.2462	1.61656	0.808279	+	0.588799i	$0.200399\pi$
$102$	5.68466i	0.562865i
$103$	− 5.12311i	− 0.504795i	−0.967624	−	0.252397i	$-0.918781\pi$
$103$	− 5.12311i	− 0.504795i	0.967624	−	0.252397i	$-0.0812190\pi$
$104$	0.561553	0.0550648
$105$	0	0
$106$	−2.00000	−0.194257
$107$	4.00000i	0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$	4.00000i	0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	−8.24621	−0.782696
$112$	− 5.12311i	− 0.484088i
$113$	− 14.0000i	− 1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	− 14.0000i	− 1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	−2.56155	−0.239911
$115$	0	0
$116$	−7.12311	−0.661364
$117$	0.561553i	0.0519156i
$118$	− 1.12311i	− 0.103390i
$119$	−29.1231	−2.66971
$120$	0	0
$121$	−4.43845	−0.403495
$122$	0.561553i	0.0508406i
$123$	− 4.24621i	− 0.382868i
$124$	1.00000	0.0898027
$125$	0	0
$126$	5.12311	0.456403
$127$	− 10.2462i	− 0.909204i	−0.890695	−	0.454602i	$-0.849781\pi$
$127$	− 10.2462i	− 0.909204i	0.890695	−	0.454602i	$-0.150219\pi$
$128$	1.00000i	0.0883883i
$129$	−9.12311	−0.803245
$130$	0	0
$131$	17.1231	1.49605	0.748026	−	0.663669i	$-0.231002\pi$
$131$	17.1231	1.49605	0.748026	+	0.663669i	$0.231002\pi$
$132$	− 2.56155i	− 0.222955i
$133$	− 13.1231i	− 1.13792i
$134$	−0.315342	−0.0272414
$135$	0	0
$136$	5.68466	0.487455
$137$	6.00000i	0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$	6.00000i	0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$	8.00000i	0.681005i
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	3.68466	0.310304
$142$	1.43845i	0.120712i
$143$	1.43845i	0.120289i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	10.0000	0.827606
$147$	19.2462i	1.58740i
$148$	8.24621i	0.677834i
$149$	−9.68466	−0.793398	−0.396699	−	0.917949i	$-0.629844\pi$
$149$	−9.68466	−0.793398	−0.396699	+	0.917949i	$0.629844\pi$
$150$	0	0
$151$	5.93087	0.482647	0.241324	−	0.970445i	$-0.422418\pi$
$151$	5.93087	0.482647	0.241324	+	0.970445i	$0.422418\pi$
$152$	2.56155i	0.207769i
$153$	5.68466i	0.459577i
$154$	13.1231	1.05749
$155$	0	0
$156$	0.561553	0.0449602
$157$	9.36932i	0.747753i	0.927479	+	0.373876i	$0.121972\pi$
$157$	9.36932i	0.747753i	−0.927479	+	0.373876i	$0.878028\pi$
$158$	− 3.68466i	− 0.293136i
$159$	−2.00000	−0.158610
$160$	0	0
$161$	−40.9848	−3.23006
$162$	− 1.00000i	− 0.0785674i
$163$	− 23.0540i	− 1.80573i	−0.429928	−	0.902863i	$-0.641461\pi$
$163$	− 23.0540i	− 1.80573i	0.429928	−	0.902863i	$-0.358539\pi$
$164$	−4.24621	−0.331573
$165$	0	0
$166$	12.8078	0.994075
$167$	5.12311i	0.396438i	0.980158	+	0.198219i	$0.0635157\pi$
$167$	5.12311i	0.396438i	−0.980158	+	0.198219i	$0.936484\pi$
$168$	− 5.12311i	− 0.395256i
$169$	12.6847	0.975743
$170$	0	0
$171$	−2.56155	−0.195887
$172$	9.12311i	0.695630i
$173$	4.56155i	0.346808i	0.984851	+	0.173404i	$0.0554767\pi$
$173$	4.56155i	0.346808i	−0.984851	+	0.173404i	$0.944523\pi$
$174$	−7.12311	−0.540001
$175$	0	0
$176$	−2.56155	−0.193084
$177$	− 1.12311i	− 0.0844178i
$178$	− 0.246211i	− 0.0184543i
$179$	−23.0540	−1.72314	−0.861568	−	0.507643i	$-0.830517\pi$
$179$	−23.0540	−1.72314	−0.861568	+	0.507643i	$0.830517\pi$
$180$	0	0
$181$	−12.2462	−0.910254	−0.455127	−	0.890427i	$-0.650406\pi$
$181$	−12.2462	−0.910254	−0.455127	+	0.890427i	$0.650406\pi$
$182$	2.87689i	0.213250i
$183$	0.561553i	0.0415112i
$184$	8.00000	0.589768
$185$	0	0
$186$	1.00000	0.0733236
$187$	14.5616i	1.06485i
$188$	− 3.68466i	− 0.268731i
$189$	5.12311	0.372651
$190$	0	0
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	1.00000i	0.0721688i
$193$	24.5616i	1.76798i	0.467507	+	0.883990i	$0.345152\pi$
$193$	24.5616i	1.76798i	−0.467507	+	0.883990i	$0.654848\pi$
$194$	14.8078	1.06314
$195$	0	0
$196$	19.2462	1.37473
$197$	− 8.24621i	− 0.587518i	−0.955879	−	0.293759i	$-0.905094\pi$
$197$	− 8.24621i	− 0.587518i	0.955879	−	0.293759i	$-0.0949064\pi$
$198$	− 2.56155i	− 0.182042i
$199$	−4.31534	−0.305906	−0.152953	−	0.988233i	$-0.548878\pi$
$199$	−4.31534	−0.305906	−0.152953	+	0.988233i	$0.548878\pi$
$200$	0	0
$201$	−0.315342	−0.0222425
$202$	− 16.2462i	− 1.14308i
$203$	− 36.4924i	− 2.56127i
$204$	5.68466	0.398006
$205$	0	0
$206$	−5.12311	−0.356944
$207$	8.00000i	0.556038i
$208$	− 0.561553i	− 0.0389367i
$209$	−6.56155	−0.453872
$210$	0	0
$211$	−1.75379	−0.120736	−0.0603679	−	0.998176i	$-0.519227\pi$
$211$	−1.75379	−0.120736	−0.0603679	+	0.998176i	$0.519227\pi$
$212$	2.00000i	0.137361i
$213$	1.43845i	0.0985608i
$214$	4.00000	0.273434
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	5.12311i	0.347779i
$218$	14.0000i	0.948200i
$219$	10.0000	0.675737
$220$	0	0
$221$	−3.19224	−0.214733
$222$	8.24621i	0.553449i
$223$	19.6847i	1.31818i	0.752063	+	0.659091i	$0.229059\pi$
$223$	19.6847i	1.31818i	−0.752063	+	0.659091i	$0.770941\pi$
$224$	−5.12311	−0.342302
$225$	0	0
$226$	−14.0000	−0.931266
$227$	19.3693i	1.28559i	0.766040	+	0.642793i	$0.222225\pi$
$227$	19.3693i	1.28559i	−0.766040	+	0.642793i	$0.777775\pi$
$228$	2.56155i	0.169643i
$229$	−17.6847	−1.16864	−0.584318	−	0.811525i	$-0.698638\pi$
$229$	−17.6847	−1.16864	−0.584318	+	0.811525i	$0.698638\pi$
$230$	0	0
$231$	13.1231	0.863437
$232$	7.12311i	0.467655i
$233$	11.6155i	0.760959i	0.924789	+	0.380479i	$0.124241\pi$
$233$	11.6155i	0.760959i	−0.924789	+	0.380479i	$0.875759\pi$
$234$	0.561553	0.0367099
$235$	0	0
$236$	−1.12311	−0.0731079
$237$	− 3.68466i	− 0.239344i
$238$	29.1231i	1.88777i
$239$	20.4924	1.32554	0.662772	−	0.748821i	$-0.269380\pi$
$239$	20.4924	1.32554	0.662772	+	0.748821i	$0.269380\pi$
$240$	0	0
$241$	7.75379	0.499465	0.249733	−	0.968315i	$-0.419657\pi$
$241$	7.75379	0.499465	0.249733	+	0.968315i	$0.419657\pi$
$242$	4.43845i	0.285314i
$243$	− 1.00000i	− 0.0641500i
$244$	0.561553	0.0359497
$245$	0	0
$246$	−4.24621	−0.270729
$247$	− 1.43845i	− 0.0915262i
$248$	− 1.00000i	− 0.0635001i
$249$	12.8078	0.811659
$250$	0	0
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	− 5.12311i	− 0.322725i
$253$	20.4924i	1.28835i
$254$	−10.2462	−0.642904
$255$	0	0
$256$	1.00000	0.0625000
$257$	16.8769i	1.05275i	0.850252	+	0.526376i	$0.176450\pi$
$257$	16.8769i	1.05275i	−0.850252	+	0.526376i	$0.823550\pi$
$258$	9.12311i	0.567980i
$259$	−42.2462	−2.62505
$260$	0	0
$261$	−7.12311	−0.440909
$262$	− 17.1231i	− 1.05787i
$263$	− 2.24621i	− 0.138507i	−0.997599	−	0.0692537i	$-0.977938\pi$
$263$	− 2.24621i	− 0.138507i	0.997599	−	0.0692537i	$-0.0220618\pi$
$264$	−2.56155	−0.157653
$265$	0	0
$266$	−13.1231	−0.804629
$267$	− 0.246211i	− 0.0150679i
$268$	0.315342i	0.0192626i
$269$	14.4924	0.883619	0.441809	−	0.897109i	$-0.354337\pi$
$269$	14.4924	0.883619	0.441809	+	0.897109i	$0.354337\pi$
$270$	0	0
$271$	−3.68466	−0.223827	−0.111914	−	0.993718i	$-0.535698\pi$
$271$	−3.68466	−0.223827	−0.111914	+	0.993718i	$0.535698\pi$
$272$	− 5.68466i	− 0.344683i
$273$	2.87689i	0.174118i
$274$	6.00000	0.362473
$275$	0	0
$276$	8.00000	0.481543
$277$	− 7.43845i	− 0.446933i	−0.974712	−	0.223466i	$-0.928263\pi$
$277$	− 7.43845i	− 0.446933i	0.974712	−	0.223466i	$-0.0717373\pi$
$278$	− 12.0000i	− 0.719712i
$279$	1.00000	0.0598684
$280$	0	0
$281$	14.4924	0.864545	0.432273	−	0.901743i	$-0.357712\pi$
$281$	14.4924	0.864545	0.432273	+	0.901743i	$0.357712\pi$
$282$	− 3.68466i	− 0.219418i
$283$	− 3.19224i	− 0.189759i	−0.995489	−	0.0948794i	$-0.969753\pi$
$283$	− 3.19224i	− 0.189759i	0.995489	−	0.0948794i	$-0.0302465\pi$
$284$	1.43845	0.0853561
$285$	0	0
$286$	1.43845	0.0850572
$287$	− 21.7538i	− 1.28409i
$288$	1.00000i	0.0589256i
$289$	−15.3153	−0.900902
$290$	0	0
$291$	14.8078	0.868047
$292$	− 10.0000i	− 0.585206i
$293$	6.00000i	0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$	6.00000i	0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	19.2462	1.12246
$295$	0	0
$296$	8.24621	0.479301
$297$	− 2.56155i	− 0.148636i
$298$	9.68466i	0.561017i
$299$	−4.49242	−0.259804
$300$	0	0
$301$	−46.7386	−2.69397
$302$	− 5.93087i	− 0.341283i
$303$	− 16.2462i	− 0.933320i
$304$	2.56155	0.146915
$305$	0	0
$306$	5.68466	0.324970
$307$	1.75379i	0.100094i	0.998747	+	0.0500470i	$0.0159371\pi$
$307$	1.75379i	0.100094i	−0.998747	+	0.0500470i	$0.984063\pi$
$308$	− 13.1231i	− 0.747758i
$309$	−5.12311	−0.291443
$310$	0	0
$311$	21.9309	1.24359	0.621793	−	0.783182i	$-0.286405\pi$
$311$	21.9309	1.24359	0.621793	+	0.783182i	$0.286405\pi$
$312$	− 0.561553i	− 0.0317917i
$313$	− 16.2462i	− 0.918290i	−0.888361	−	0.459145i	$-0.848156\pi$
$313$	− 16.2462i	− 0.918290i	0.888361	−	0.459145i	$-0.151844\pi$
$314$	9.36932	0.528741
$315$	0	0
$316$	−3.68466	−0.207278
$317$	− 10.3153i	− 0.579367i	−0.957122	−	0.289684i	$-0.906450\pi$
$317$	− 10.3153i	− 0.579367i	0.957122	−	0.289684i	$-0.0935501\pi$
$318$	2.00000i	0.112154i
$319$	−18.2462	−1.02159
$320$	0	0
$321$	4.00000	0.223258
$322$	40.9848i	2.28400i
$323$	− 14.5616i	− 0.810226i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−23.0540	−1.27684
$327$	14.0000i	0.774202i
$328$	4.24621i	0.234458i
$329$	18.8769	1.04072
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	− 12.8078i	− 0.702917i
$333$	8.24621i	0.451890i
$334$	5.12311	0.280324
$335$	0	0
$336$	−5.12311	−0.279488
$337$	27.1231i	1.47749i	0.673985	+	0.738745i	$0.264581\pi$
$337$	27.1231i	1.47749i	−0.673985	+	0.738745i	$0.735419\pi$
$338$	− 12.6847i	− 0.689954i
$339$	−14.0000	−0.760376
$340$	0	0
$341$	2.56155	0.138716
$342$	2.56155i	0.138513i
$343$	62.7386i	3.38757i
$344$	9.12311	0.491885
$345$	0	0
$346$	4.56155	0.245231
$347$	− 12.1771i	− 0.653700i	−0.945076	−	0.326850i	$-0.894013\pi$
$347$	− 12.1771i	− 0.653700i	0.945076	−	0.326850i	$-0.105987\pi$
$348$	7.12311i	0.381839i
$349$	−15.6155	−0.835880	−0.417940	−	0.908475i	$-0.637248\pi$
$349$	−15.6155	−0.835880	−0.417940	+	0.908475i	$0.637248\pi$
$350$	0	0
$351$	0.561553	0.0299735
$352$	2.56155i	0.136531i
$353$	18.8078i	1.00104i	0.865726	+	0.500518i	$0.166857\pi$
$353$	18.8078i	1.00104i	−0.865726	+	0.500518i	$0.833143\pi$
$354$	−1.12311	−0.0596924
$355$	0	0
$356$	−0.246211	−0.0130492
$357$	29.1231i	1.54136i
$358$	23.0540i	1.21844i
$359$	−29.3002	−1.54640	−0.773202	−	0.634159i	$-0.781346\pi$
$359$	−29.3002	−1.54640	−0.773202	+	0.634159i	$0.781346\pi$
$360$	0	0
$361$	−12.4384	−0.654655
$362$	12.2462i	0.643647i
$363$	4.43845i	0.232958i
$364$	2.87689	0.150790
$365$	0	0
$366$	0.561553	0.0293528
$367$	− 32.8078i	− 1.71255i	−0.516519	−	0.856276i	$-0.672772\pi$
$367$	− 32.8078i	− 1.71255i	0.516519	−	0.856276i	$-0.327228\pi$
$368$	− 8.00000i	− 0.417029i
$369$	−4.24621	−0.221049
$370$	0	0
$371$	−10.2462	−0.531957
$372$	− 1.00000i	− 0.0518476i
$373$	3.12311i	0.161708i	0.996726	+	0.0808541i	$0.0257648\pi$
$373$	3.12311i	0.161708i	−0.996726	+	0.0808541i	$0.974235\pi$
$374$	14.5616	0.752960
$375$	0	0
$376$	−3.68466	−0.190022
$377$	− 4.00000i	− 0.206010i
$378$	− 5.12311i	− 0.263504i
$379$	17.9309	0.921047	0.460523	−	0.887648i	$-0.347662\pi$
$379$	17.9309	0.921047	0.460523	+	0.887648i	$0.347662\pi$
$380$	0	0
$381$	−10.2462	−0.524929
$382$	− 16.0000i	− 0.818631i
$383$	− 17.6155i	− 0.900111i	−0.893000	−	0.450056i	$-0.851404\pi$
$383$	− 17.6155i	− 0.900111i	0.893000	−	0.450056i	$-0.148596\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	24.5616	1.25015
$387$	9.12311i	0.463754i
$388$	− 14.8078i	− 0.751750i
$389$	12.2462	0.620908	0.310454	−	0.950588i	$-0.399519\pi$
$389$	12.2462	0.620908	0.310454	+	0.950588i	$0.399519\pi$
$390$	0	0
$391$	−45.4773	−2.29988
$392$	− 19.2462i	− 0.972080i
$393$	− 17.1231i	− 0.863746i
$394$	−8.24621	−0.415438
$395$	0	0
$396$	−2.56155	−0.128723
$397$	− 12.7386i	− 0.639334i	−0.947530	−	0.319667i	$-0.896429\pi$
$397$	− 12.7386i	− 0.639334i	0.947530	−	0.319667i	$-0.103571\pi$
$398$	4.31534i	0.216309i
$399$	−13.1231	−0.656977
$400$	0	0
$401$	−27.9309	−1.39480	−0.697401	−	0.716682i	$-0.745660\pi$
$401$	−27.9309	−1.39480	−0.697401	+	0.716682i	$0.745660\pi$
$402$	0.315342i	0.0157278i
$403$	0.561553i	0.0279729i
$404$	−16.2462	−0.808279
$405$	0	0
$406$	−36.4924	−1.81109
$407$	21.1231i	1.04703i
$408$	− 5.68466i	− 0.281433i
$409$	−4.24621	−0.209962	−0.104981	−	0.994474i	$-0.533478\pi$
$409$	−4.24621	−0.209962	−0.104981	+	0.994474i	$0.533478\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	5.12311i	0.252397i
$413$	− 5.75379i	− 0.283125i
$414$	8.00000	0.393179
$415$	0	0
$416$	−0.561553	−0.0275324
$417$	− 12.0000i	− 0.587643i
$418$	6.56155i	0.320936i
$419$	6.24621	0.305147	0.152574	−	0.988292i	$-0.451244\pi$
$419$	6.24621	0.305147	0.152574	+	0.988292i	$0.451244\pi$
$420$	0	0
$421$	−24.7386	−1.20569	−0.602844	−	0.797859i	$-0.705966\pi$
$421$	−24.7386	−1.20569	−0.602844	+	0.797859i	$0.705966\pi$
$422$	1.75379i	0.0853731i
$423$	− 3.68466i	− 0.179154i
$424$	2.00000	0.0971286
$425$	0	0
$426$	1.43845	0.0696930
$427$	2.87689i	0.139223i
$428$	− 4.00000i	− 0.193347i
$429$	1.43845	0.0694489
$430$	0	0
$431$	40.9848	1.97417	0.987085	−	0.160196i	$-0.0512126\pi$
$431$	40.9848	1.97417	0.987085	+	0.160196i	$0.0512126\pi$
$432$	1.00000i	0.0481125i
$433$	35.6155i	1.71157i	0.517329	+	0.855787i	$0.326926\pi$
$433$	35.6155i	1.71157i	−0.517329	+	0.855787i	$0.673074\pi$
$434$	5.12311	0.245917
$435$	0	0
$436$	14.0000	0.670478
$437$	− 20.4924i	− 0.980286i
$438$	− 10.0000i	− 0.477818i
$439$	38.7386	1.84889	0.924447	−	0.381310i	$-0.124527\pi$
$439$	38.7386	1.84889	0.924447	+	0.381310i	$0.124527\pi$
$440$	0	0
$441$	19.2462	0.916486
$442$	3.19224i	0.151839i
$443$	− 11.3693i	− 0.540173i	−0.962836	−	0.270086i	$-0.912948\pi$
$443$	− 11.3693i	− 0.540173i	0.962836	−	0.270086i	$-0.0870522\pi$
$444$	8.24621	0.391348
$445$	0	0
$446$	19.6847	0.932096
$447$	9.68466i	0.458069i
$448$	5.12311i	0.242044i
$449$	−2.80776	−0.132507	−0.0662533	−	0.997803i	$-0.521105\pi$
$449$	−2.80776	−0.132507	−0.0662533	+	0.997803i	$0.521105\pi$
$450$	0	0
$451$	−10.8769	−0.512173
$452$	14.0000i	0.658505i
$453$	− 5.93087i	− 0.278657i
$454$	19.3693	0.909047
$455$	0	0
$456$	2.56155	0.119956
$457$	0.246211i	0.0115173i	0.999983	+	0.00575864i	$0.00183304\pi$
$457$	0.246211i	0.0115173i	−0.999983	+	0.00575864i	$0.998167\pi$
$458$	17.6847i	0.826350i
$459$	5.68466	0.265337
$460$	0	0
$461$	32.2462	1.50186	0.750928	−	0.660384i	$-0.229607\pi$
$461$	32.2462	1.50186	0.750928	+	0.660384i	$0.229607\pi$
$462$	− 13.1231i	− 0.610542i
$463$	− 13.9309i	− 0.647422i	−0.946156	−	0.323711i	$-0.895069\pi$
$463$	− 13.9309i	− 0.647422i	0.946156	−	0.323711i	$-0.104931\pi$
$464$	7.12311	0.330682
$465$	0	0
$466$	11.6155	0.538079
$467$	22.2462i	1.02943i	0.857361	+	0.514716i	$0.172103\pi$
$467$	22.2462i	1.02943i	−0.857361	+	0.514716i	$0.827897\pi$
$468$	− 0.561553i	− 0.0259578i
$469$	−1.61553	−0.0745982
$470$	0	0
$471$	9.36932	0.431715
$472$	1.12311i	0.0516951i
$473$	23.3693i	1.07452i
$474$	−3.68466	−0.169242
$475$	0	0
$476$	29.1231	1.33486
$477$	2.00000i	0.0915737i
$478$	− 20.4924i	− 0.937302i
$479$	−29.9309	−1.36758	−0.683788	−	0.729681i	$-0.739669\pi$
$479$	−29.9309	−1.36758	−0.683788	+	0.729681i	$0.739669\pi$
$480$	0	0
$481$	−4.63068	−0.211141
$482$	− 7.75379i	− 0.353175i
$483$	40.9848i	1.86488i
$484$	4.43845	0.201748
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	11.6847i	0.529482i	0.964319	+	0.264741i	$0.0852865\pi$
$487$	11.6847i	0.529482i	−0.964319	+	0.264741i	$0.914713\pi$
$488$	− 0.561553i	− 0.0254203i
$489$	−23.0540	−1.04254
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	4.24621i	0.191434i
$493$	− 40.4924i	− 1.82369i
$494$	−1.43845	−0.0647188
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	7.36932i	0.330559i
$498$	− 12.8078i	− 0.573930i
$499$	−1.75379	−0.0785104	−0.0392552	−	0.999229i	$-0.512499\pi$
$499$	−1.75379	−0.0785104	−0.0392552	+	0.999229i	$0.512499\pi$
$500$	0	0
$501$	5.12311	0.228883
$502$	− 20.0000i	− 0.892644i
$503$	− 32.1771i	− 1.43471i	−0.696710	−	0.717353i	$-0.745354\pi$
$503$	− 32.1771i	− 1.43471i	0.696710	−	0.717353i	$-0.254646\pi$
$504$	−5.12311	−0.228201
$505$	0	0
$506$	20.4924	0.910999
$507$	− 12.6847i	− 0.563345i
$508$	10.2462i	0.454602i
$509$	37.8617	1.67819	0.839096	−	0.543983i	$-0.183085\pi$
$509$	37.8617	1.67819	0.839096	+	0.543983i	$0.183085\pi$
$510$	0	0
$511$	51.2311	2.26633
$512$	− 1.00000i	− 0.0441942i
$513$	2.56155i	0.113095i
$514$	16.8769	0.744408
$515$	0	0
$516$	9.12311	0.401622
$517$	− 9.43845i	− 0.415102i
$518$	42.2462i	1.85619i
$519$	4.56155	0.200230
$520$	0	0
$521$	−23.6155	−1.03462	−0.517308	−	0.855800i	$-0.673066\pi$
$521$	−23.6155	−1.03462	−0.517308	+	0.855800i	$0.673066\pi$
$522$	7.12311i	0.311770i
$523$	− 25.1231i	− 1.09856i	−0.835639	−	0.549278i	$-0.814903\pi$
$523$	− 25.1231i	− 1.09856i	0.835639	−	0.549278i	$-0.185097\pi$
$524$	−17.1231	−0.748026
$525$	0	0
$526$	−2.24621	−0.0979395
$527$	5.68466i	0.247628i
$528$	2.56155i	0.111477i
$529$	−41.0000	−1.78261
$530$	0	0
$531$	−1.12311	−0.0487386
$532$	13.1231i	0.568959i
$533$	− 2.38447i	− 0.103283i
$534$	−0.246211	−0.0106546
$535$	0	0
$536$	0.315342	0.0136207
$537$	23.0540i	0.994852i
$538$	− 14.4924i	− 0.624813i
$539$	49.3002	2.12351
$540$	0	0
$541$	−41.3693	−1.77861	−0.889303	−	0.457319i	$-0.848810\pi$
$541$	−41.3693	−1.77861	−0.889303	+	0.457319i	$0.848810\pi$
$542$	3.68466i	0.158270i
$543$	12.2462i	0.525535i
$544$	−5.68466	−0.243728
$545$	0	0
$546$	2.87689	0.123120
$547$	26.7386i	1.14326i	0.820511	+	0.571631i	$0.193689\pi$
$547$	26.7386i	1.14326i	−0.820511	+	0.571631i	$0.806311\pi$
$548$	− 6.00000i	− 0.256307i
$549$	0.561553	0.0239665
$550$	0	0
$551$	18.2462	0.777315
$552$	− 8.00000i	− 0.340503i
$553$	− 18.8769i	− 0.802727i
$554$	−7.43845	−0.316029
$555$	0	0
$556$	−12.0000	−0.508913
$557$	17.3693i	0.735962i	0.929833	+	0.367981i	$0.119951\pi$
$557$	17.3693i	0.735962i	−0.929833	+	0.367981i	$0.880049\pi$
$558$	− 1.00000i	− 0.0423334i
$559$	−5.12311	−0.216684
$560$	0	0
$561$	14.5616	0.614789
$562$	− 14.4924i	− 0.611326i
$563$	− 12.0000i	− 0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$	− 12.0000i	− 0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$	−3.68466	−0.155152
$565$	0	0
$566$	−3.19224	−0.134180
$567$	− 5.12311i	− 0.215150i
$568$	− 1.43845i	− 0.0603559i
$569$	−4.24621	−0.178010	−0.0890052	−	0.996031i	$-0.528369\pi$
$569$	−4.24621	−0.178010	−0.0890052	+	0.996031i	$0.528369\pi$
$570$	0	0
$571$	28.9848	1.21298	0.606489	−	0.795092i	$-0.292577\pi$
$571$	28.9848	1.21298	0.606489	+	0.795092i	$0.292577\pi$
$572$	− 1.43845i	− 0.0601445i
$573$	− 16.0000i	− 0.668410i
$574$	−21.7538	−0.907986
$575$	0	0
$576$	1.00000	0.0416667
$577$	7.43845i	0.309667i	0.987941	+	0.154833i	$0.0494840\pi$
$577$	7.43845i	0.309667i	−0.987941	+	0.154833i	$0.950516\pi$
$578$	15.3153i	0.637034i
$579$	24.5616	1.02074
$580$	0	0
$581$	65.6155	2.72219
$582$	− 14.8078i	− 0.613802i
$583$	5.12311i	0.212177i
$584$	−10.0000	−0.413803
$585$	0	0
$586$	6.00000	0.247858
$587$	− 25.3002i	− 1.04425i	−0.852869	−	0.522125i	$-0.825139\pi$
$587$	− 25.3002i	− 1.04425i	0.852869	−	0.522125i	$-0.174861\pi$
$588$	− 19.2462i	− 0.793700i
$589$	−2.56155	−0.105547
$590$	0	0
$591$	−8.24621	−0.339204
$592$	− 8.24621i	− 0.338917i
$593$	− 34.4924i	− 1.41643i	−0.705995	−	0.708217i	$-0.749500\pi$
$593$	− 34.4924i	− 1.41643i	0.705995	−	0.708217i	$-0.250500\pi$
$594$	−2.56155	−0.105102
$595$	0	0
$596$	9.68466	0.396699
$597$	4.31534i	0.176615i
$598$	4.49242i	0.183709i
$599$	20.3153	0.830062	0.415031	−	0.909807i	$-0.363771\pi$
$599$	20.3153	0.830062	0.415031	+	0.909807i	$0.363771\pi$
$600$	0	0
$601$	−11.7538	−0.479447	−0.239724	−	0.970841i	$-0.577057\pi$
$601$	−11.7538	−0.479447	−0.239724	+	0.970841i	$0.577057\pi$
$602$	46.7386i	1.90492i
$603$	0.315342i	0.0128417i
$604$	−5.93087	−0.241324
$605$	0	0
$606$	−16.2462	−0.659957
$607$	− 7.36932i	− 0.299111i	−0.988753	−	0.149556i	$-0.952216\pi$
$607$	− 7.36932i	− 0.299111i	0.988753	−	0.149556i	$-0.0477843\pi$
$608$	− 2.56155i	− 0.103885i
$609$	−36.4924	−1.47875
$610$	0	0
$611$	2.06913	0.0837081
$612$	− 5.68466i	− 0.229789i
$613$	13.1922i	0.532829i	0.963859	+	0.266415i	$0.0858391\pi$
$613$	13.1922i	0.532829i	−0.963859	+	0.266415i	$0.914161\pi$
$614$	1.75379	0.0707772
$615$	0	0
$616$	−13.1231	−0.528745
$617$	22.0000i	0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$	22.0000i	0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$	5.12311i	0.206082i
$619$	−9.75379	−0.392038	−0.196019	−	0.980600i	$-0.562801\pi$
$619$	−9.75379	−0.392038	−0.196019	+	0.980600i	$0.562801\pi$
$620$	0	0
$621$	8.00000	0.321029
$622$	− 21.9309i	− 0.879348i
$623$	− 1.26137i	− 0.0505356i
$624$	−0.561553	−0.0224801
$625$	0	0
$626$	−16.2462	−0.649329
$627$	6.56155i	0.262043i
$628$	− 9.36932i	− 0.373876i
$629$	−46.8769	−1.86910
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	3.68466i	0.146568i
$633$	1.75379i	0.0697068i
$634$	−10.3153	−0.409675
$635$	0	0
$636$	2.00000	0.0793052
$637$	10.8078i	0.428219i
$638$	18.2462i	0.722374i
$639$	1.43845	0.0569041
$640$	0	0
$641$	−10.3153	−0.407431	−0.203716	−	0.979030i	$-0.565302\pi$
$641$	−10.3153	−0.407431	−0.203716	+	0.979030i	$0.565302\pi$
$642$	− 4.00000i	− 0.157867i
$643$	− 20.0000i	− 0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$	− 20.0000i	− 0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$	40.9848	1.61503
$645$	0	0
$646$	−14.5616	−0.572917
$647$	35.8617i	1.40987i	0.709272	+	0.704935i	$0.249024\pi$
$647$	35.8617i	1.40987i	−0.709272	+	0.704935i	$0.750976\pi$
$648$	1.00000i	0.0392837i
$649$	−2.87689	−0.112928
$650$	0	0
$651$	5.12311	0.200790
$652$	23.0540i	0.902863i
$653$	− 33.5464i	− 1.31277i	−0.754425	−	0.656386i	$-0.772084\pi$
$653$	− 33.5464i	− 1.31277i	0.754425	−	0.656386i	$-0.227916\pi$
$654$	14.0000	0.547443
$655$	0	0
$656$	4.24621	0.165787
$657$	− 10.0000i	− 0.390137i
$658$	− 18.8769i	− 0.735898i
$659$	19.3693	0.754521	0.377261	−	0.926107i	$-0.376866\pi$
$659$	19.3693	0.754521	0.377261	+	0.926107i	$0.376866\pi$
$660$	0	0
$661$	44.1080	1.71560	0.857800	−	0.513983i	$-0.171831\pi$
$661$	44.1080	1.71560	0.857800	+	0.513983i	$0.171831\pi$
$662$	12.0000i	0.466393i
$663$	3.19224i	0.123976i
$664$	−12.8078	−0.497038
$665$	0	0
$666$	8.24621	0.319534
$667$	− 56.9848i	− 2.20646i
$668$	− 5.12311i	− 0.198219i
$669$	19.6847	0.761053
$670$	0	0
$671$	1.43845	0.0555306
$672$	5.12311i	0.197628i
$673$	− 0.876894i	− 0.0338018i	−0.999857	−	0.0169009i	$-0.994620\pi$
$673$	− 0.876894i	− 0.0338018i	0.999857	−	0.0169009i	$-0.00537998\pi$
$674$	27.1231	1.04474
$675$	0	0
$676$	−12.6847	−0.487871
$677$	− 0.876894i	− 0.0337018i	−0.999858	−	0.0168509i	$-0.994636\pi$
$677$	− 0.876894i	− 0.0337018i	0.999858	−	0.0168509i	$-0.00536406\pi$
$678$	14.0000i	0.537667i
$679$	75.8617	2.91131
$680$	0	0
$681$	19.3693	0.742234
$682$	− 2.56155i	− 0.0980869i
$683$	− 50.7386i	− 1.94146i	−0.240174	−	0.970730i	$-0.577204\pi$
$683$	− 50.7386i	− 1.94146i	0.240174	−	0.970730i	$-0.422796\pi$
$684$	2.56155	0.0979434
$685$	0	0
$686$	62.7386	2.39537
$687$	17.6847i	0.674712i
$688$	− 9.12311i	− 0.347815i
$689$	−1.12311	−0.0427869
$690$	0	0
$691$	−4.17708	−0.158904	−0.0794518	−	0.996839i	$-0.525317\pi$
$691$	−4.17708	−0.158904	−0.0794518	+	0.996839i	$0.525317\pi$
$692$	− 4.56155i	− 0.173404i
$693$	− 13.1231i	− 0.498506i
$694$	−12.1771	−0.462236
$695$	0	0
$696$	7.12311	0.270001
$697$	− 24.1383i	− 0.914302i
$698$	15.6155i	0.591056i
$699$	11.6155	0.439340
$700$	0	0
$701$	−4.06913	−0.153689	−0.0768445	−	0.997043i	$-0.524484\pi$
$701$	−4.06913	−0.153689	−0.0768445	+	0.997043i	$0.524484\pi$
$702$	− 0.561553i	− 0.0211944i
$703$	− 21.1231i	− 0.796673i
$704$	2.56155	0.0965422
$705$	0	0
$706$	18.8078	0.707840
$707$	− 83.2311i	− 3.13023i
$708$	1.12311i	0.0422089i
$709$	20.4233	0.767013	0.383506	−	0.923538i	$-0.374716\pi$
$709$	20.4233	0.767013	0.383506	+	0.923538i	$0.374716\pi$
$710$	0	0
$711$	−3.68466	−0.138185
$712$	0.246211i	0.00922716i
$713$	8.00000i	0.299602i
$714$	29.1231	1.08990
$715$	0	0
$716$	23.0540	0.861568
$717$	− 20.4924i	− 0.765304i
$718$	29.3002i	1.09347i
$719$	−4.49242	−0.167539	−0.0837695	−	0.996485i	$-0.526696\pi$
$719$	−4.49242	−0.167539	−0.0837695	+	0.996485i	$0.526696\pi$
$720$	0	0
$721$	−26.2462	−0.977460
$722$	12.4384i	0.462911i
$723$	− 7.75379i	− 0.288367i
$724$	12.2462	0.455127
$725$	0	0
$726$	4.43845	0.164726
$727$	13.7538i	0.510100i	0.966928	+	0.255050i	$0.0820919\pi$
$727$	13.7538i	0.510100i	−0.966928	+	0.255050i	$0.917908\pi$
$728$	− 2.87689i	− 0.106625i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−51.8617	−1.91818
$732$	− 0.561553i	− 0.0207556i
$733$	8.24621i	0.304581i	0.988336	+	0.152290i	$0.0486649\pi$
$733$	8.24621i	0.304581i	−0.988336	+	0.152290i	$0.951335\pi$
$734$	−32.8078	−1.21096
$735$	0	0
$736$	−8.00000	−0.294884
$737$	0.807764i	0.0297544i
$738$	4.24621i	0.156305i
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	0	0
$741$	−1.43845	−0.0528427
$742$	10.2462i	0.376150i
$743$	− 8.00000i	− 0.293492i	−0.989174	−	0.146746i	$-0.953120\pi$
$743$	− 8.00000i	− 0.293492i	0.989174	−	0.146746i	$-0.0468799\pi$
$744$	−1.00000	−0.0366618
$745$	0	0
$746$	3.12311	0.114345
$747$	− 12.8078i	− 0.468612i
$748$	− 14.5616i	− 0.532423i
$749$	20.4924	0.748777
$750$	0	0
$751$	−18.8769	−0.688828	−0.344414	−	0.938818i	$-0.611922\pi$
$751$	−18.8769	−0.688828	−0.344414	+	0.938818i	$0.611922\pi$
$752$	3.68466i	0.134366i
$753$	− 20.0000i	− 0.728841i
$754$	−4.00000	−0.145671
$755$	0	0
$756$	−5.12311	−0.186326
$757$	− 40.2462i	− 1.46277i	−0.681963	−	0.731387i	$-0.738873\pi$
$757$	− 40.2462i	− 1.46277i	0.681963	−	0.731387i	$-0.261127\pi$
$758$	− 17.9309i	− 0.651279i
$759$	20.4924	0.743828
$760$	0	0
$761$	−40.4233	−1.46534	−0.732672	−	0.680582i	$-0.761727\pi$
$761$	−40.4233	−1.46534	−0.732672	+	0.680582i	$0.761727\pi$
$762$	10.2462i	0.371181i
$763$	71.7235i	2.59656i
$764$	−16.0000	−0.578860
$765$	0	0
$766$	−17.6155	−0.636475
$767$	− 0.630683i	− 0.0227726i
$768$	− 1.00000i	− 0.0360844i
$769$	−7.75379	−0.279609	−0.139804	−	0.990179i	$-0.544647\pi$
$769$	−7.75379	−0.279609	−0.139804	+	0.990179i	$0.544647\pi$
$770$	0	0
$771$	16.8769	0.607807
$772$	− 24.5616i	− 0.883990i
$773$	31.6155i	1.13713i	0.822638	+	0.568566i	$0.192502\pi$
$773$	31.6155i	1.13713i	−0.822638	+	0.568566i	$0.807498\pi$
$774$	9.12311	0.327923
$775$	0	0
$776$	−14.8078	−0.531568
$777$	42.2462i	1.51557i
$778$	− 12.2462i	− 0.439048i
$779$	10.8769	0.389705
$780$	0	0
$781$	3.68466	0.131847
$782$	45.4773i	1.62626i
$783$	7.12311i	0.254559i
$784$	−19.2462	−0.687365
$785$	0	0
$786$	−17.1231	−0.610761
$787$	15.5076i	0.552785i	0.961045	+	0.276393i	$0.0891390\pi$
$787$	15.5076i	0.552785i	−0.961045	+	0.276393i	$0.910861\pi$
$788$	8.24621i	0.293759i
$789$	−2.24621	−0.0799672
$790$	0	0
$791$	−71.7235	−2.55019
$792$	2.56155i	0.0910208i
$793$	0.315342i	0.0111981i
$794$	−12.7386	−0.452077
$795$	0	0
$796$	4.31534	0.152953
$797$	− 54.3542i	− 1.92532i	−0.270708	−	0.962662i	$-0.587258\pi$
$797$	− 54.3542i	− 1.92532i	0.270708	−	0.962662i	$-0.412742\pi$
$798$	13.1231i	0.464553i
$799$	20.9460	0.741017
$800$	0	0
$801$	−0.246211	−0.00869945
$802$	27.9309i	0.986273i
$803$	− 25.6155i	− 0.903952i
$804$	0.315342	0.0111212
$805$	0	0
$806$	0.561553	0.0197799
$807$	− 14.4924i	− 0.510157i
$808$	16.2462i	0.571540i
$809$	17.0540	0.599586	0.299793	−	0.954004i	$-0.403082\pi$
$809$	17.0540	0.599586	0.299793	+	0.954004i	$0.403082\pi$
$810$	0	0
$811$	16.4924	0.579127	0.289564	−	0.957159i	$-0.406490\pi$
$811$	16.4924	0.579127	0.289564	+	0.957159i	$0.406490\pi$
$812$	36.4924i	1.28063i
$813$	3.68466i	0.129227i
$814$	21.1231	0.740364
$815$	0	0
$816$	−5.68466	−0.199003
$817$	− 23.3693i	− 0.817589i
$818$	4.24621i	0.148465i
$819$	2.87689	0.100527
$820$	0	0
$821$	−2.00000	−0.0698005	−0.0349002	−	0.999391i	$-0.511111\pi$
$821$	−2.00000	−0.0698005	−0.0349002	+	0.999391i	$0.511111\pi$
$822$	− 6.00000i	− 0.209274i
$823$	11.6847i	0.407302i	0.979044	+	0.203651i	$0.0652807\pi$
$823$	11.6847i	0.407302i	−0.979044	+	0.203651i	$0.934719\pi$
$824$	5.12311	0.178472
$825$	0	0
$826$	−5.75379	−0.200200
$827$	30.4233i	1.05792i	0.848646	+	0.528961i	$0.177418\pi$
$827$	30.4233i	1.05792i	−0.848646	+	0.528961i	$0.822582\pi$
$828$	− 8.00000i	− 0.278019i
$829$	4.24621	0.147477	0.0737385	−	0.997278i	$-0.476507\pi$
$829$	4.24621	0.147477	0.0737385	+	0.997278i	$0.476507\pi$
$830$	0	0
$831$	−7.43845	−0.258037
$832$	0.561553i	0.0194683i
$833$	109.408i	3.79077i
$834$	−12.0000	−0.415526
$835$	0	0
$836$	6.56155	0.226936
$837$	− 1.00000i	− 0.0345651i
$838$	− 6.24621i	− 0.215772i
$839$	13.7538	0.474834	0.237417	−	0.971408i	$-0.423699\pi$
$839$	13.7538	0.474834	0.237417	+	0.971408i	$0.423699\pi$
$840$	0	0
$841$	21.7386	0.749608
$842$	24.7386i	0.852550i
$843$	− 14.4924i	− 0.499146i
$844$	1.75379	0.0603679
$845$	0	0
$846$	−3.68466	−0.126681
$847$	22.7386i	0.781309i
$848$	− 2.00000i	− 0.0686803i
$849$	−3.19224	−0.109557
$850$	0	0
$851$	−65.9697	−2.26141
$852$	− 1.43845i	− 0.0492804i
$853$	− 29.2311i	− 1.00085i	−0.865779	−	0.500426i	$-0.833177\pi$
$853$	− 29.2311i	− 1.00085i	0.865779	−	0.500426i	$-0.166823\pi$
$854$	2.87689	0.0984453
$855$	0	0
$856$	−4.00000	−0.136717
$857$	28.1080i	0.960149i	0.877228	+	0.480075i	$0.159390\pi$
$857$	28.1080i	0.960149i	−0.877228	+	0.480075i	$0.840610\pi$
$858$	− 1.43845i	− 0.0491078i
$859$	−58.1080	−1.98262	−0.991309	−	0.131555i	$-0.958003\pi$
$859$	−58.1080	−1.98262	−0.991309	+	0.131555i	$0.958003\pi$
$860$	0	0
$861$	−21.7538	−0.741367
$862$	− 40.9848i	− 1.39595i
$863$	17.6155i	0.599640i	0.953996	+	0.299820i	$0.0969265\pi$
$863$	17.6155i	0.599640i	−0.953996	+	0.299820i	$0.903073\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	35.6155	1.21026
$867$	15.3153i	0.520136i
$868$	− 5.12311i	− 0.173890i
$869$	−9.43845	−0.320177
$870$	0	0
$871$	−0.177081	−0.00600016
$872$	− 14.0000i	− 0.474100i
$873$	− 14.8078i	− 0.501167i
$874$	−20.4924	−0.693167
$875$	0	0
$876$	−10.0000	−0.337869
$877$	− 31.6155i	− 1.06758i	−0.845617	−	0.533790i	$-0.820767\pi$
$877$	− 31.6155i	− 1.06758i	0.845617	−	0.533790i	$-0.179233\pi$
$878$	− 38.7386i	− 1.30737i
$879$	6.00000	0.202375
$880$	0	0
$881$	47.9309	1.61483	0.807416	−	0.589983i	$-0.200865\pi$
$881$	47.9309	1.61483	0.807416	+	0.589983i	$0.200865\pi$
$882$	− 19.2462i	− 0.648054i
$883$	14.8769i	0.500647i	0.968162	+	0.250324i	$0.0805370\pi$
$883$	14.8769i	0.500647i	−0.968162	+	0.250324i	$0.919463\pi$
$884$	3.19224	0.107367
$885$	0	0
$886$	−11.3693	−0.381960
$887$	− 28.4924i	− 0.956682i	−0.878174	−	0.478341i	$-0.841238\pi$
$887$	− 28.4924i	− 0.956682i	0.878174	−	0.478341i	$-0.158762\pi$
$888$	− 8.24621i	− 0.276725i
$889$	−52.4924	−1.76054
$890$	0	0
$891$	−2.56155	−0.0858152
$892$	− 19.6847i	− 0.659091i
$893$	9.43845i	0.315846i
$894$	9.68466	0.323903
$895$	0	0
$896$	5.12311	0.171151
$897$	4.49242i	0.149998i
$898$	2.80776i	0.0936963i
$899$	−7.12311	−0.237569
$900$	0	0
$901$	−11.3693	−0.378767
$902$	10.8769i	0.362161i
$903$	46.7386i	1.55536i
$904$	14.0000	0.465633
$905$	0	0
$906$	−5.93087	−0.197040
$907$	− 5.43845i	− 0.180581i	−0.995915	−	0.0902903i	$-0.971220\pi$
$907$	− 5.43845i	− 0.180581i	0.995915	−	0.0902903i	$-0.0287795\pi$
$908$	− 19.3693i	− 0.642793i
$909$	−16.2462	−0.538853
$910$	0	0
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	− 2.56155i	− 0.0848215i
$913$	− 32.8078i	− 1.08578i
$914$	0.246211	0.00814394
$915$	0	0
$916$	17.6847	0.584318
$917$	− 87.7235i	− 2.89688i
$918$	− 5.68466i	− 0.187622i
$919$	−44.4924	−1.46767	−0.733835	−	0.679328i	$-0.762271\pi$
$919$	−44.4924	−1.46767	−0.733835	+	0.679328i	$0.762271\pi$
$920$	0	0
$921$	1.75379	0.0577893
$922$	− 32.2462i	− 1.06197i
$923$	0.807764i	0.0265879i
$924$	−13.1231	−0.431718
$925$	0	0
$926$	−13.9309	−0.457797
$927$	5.12311i	0.168265i
$928$	− 7.12311i	− 0.233827i
$929$	−6.49242	−0.213009	−0.106505	−	0.994312i	$-0.533966\pi$
$929$	−6.49242	−0.213009	−0.106505	+	0.994312i	$0.533966\pi$
$930$	0	0
$931$	−49.3002	−1.61575
$932$	− 11.6155i	− 0.380479i
$933$	− 21.9309i	− 0.717984i
$934$	22.2462	0.727918
$935$	0	0
$936$	−0.561553	−0.0183549
$937$	1.05398i	0.0344319i	0.999852	+	0.0172159i	$0.00548027\pi$
$937$	1.05398i	0.0344319i	−0.999852	+	0.0172159i	$0.994520\pi$
$938$	1.61553i	0.0527489i
$939$	−16.2462	−0.530175
$940$	0	0
$941$	−2.63068	−0.0857578	−0.0428789	−	0.999080i	$-0.513653\pi$
$941$	−2.63068	−0.0857578	−0.0428789	+	0.999080i	$0.513653\pi$
$942$	− 9.36932i	− 0.305269i
$943$	− 33.9697i	− 1.10621i
$944$	1.12311	0.0365540
$945$	0	0
$946$	23.3693	0.759802
$947$	− 34.5616i	− 1.12310i	−0.827443	−	0.561550i	$-0.810205\pi$
$947$	− 34.5616i	− 1.12310i	0.827443	−	0.561550i	$-0.189795\pi$
$948$	3.68466i	0.119672i
$949$	5.61553	0.182288
$950$	0	0
$951$	−10.3153	−0.334498
$952$	− 29.1231i	− 0.943885i
$953$	− 21.5464i	− 0.697956i	−0.937131	−	0.348978i	$-0.886529\pi$
$953$	− 21.5464i	− 0.697956i	0.937131	−	0.348978i	$-0.113471\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	−20.4924	−0.662772
$957$	18.2462i	0.589816i
$958$	29.9309i	0.967023i
$959$	30.7386	0.992602
$960$	0	0
$961$	1.00000	0.0322581
$962$	4.63068i	0.149299i
$963$	− 4.00000i	− 0.128898i
$964$	−7.75379	−0.249733
$965$	0	0
$966$	40.9848	1.31867
$967$	− 46.5616i	− 1.49732i	−0.662955	−	0.748659i	$-0.730698\pi$
$967$	− 46.5616i	− 1.49732i	0.662955	−	0.748659i	$-0.269302\pi$
$968$	− 4.43845i	− 0.142657i
$969$	−14.5616	−0.467784
$970$	0	0
$971$	−18.3845	−0.589986	−0.294993	−	0.955499i	$-0.595317\pi$
$971$	−18.3845	−0.589986	−0.294993	+	0.955499i	$0.595317\pi$
$972$	1.00000i	0.0320750i
$973$	− 61.4773i	− 1.97087i
$974$	11.6847	0.374401
$975$	0	0
$976$	−0.561553	−0.0179749
$977$	− 44.2462i	− 1.41556i	−0.706432	−	0.707781i	$-0.749696\pi$
$977$	− 44.2462i	− 1.41556i	0.706432	−	0.707781i	$-0.250304\pi$
$978$	23.0540i	0.737185i
$979$	−0.630683	−0.0201567
$980$	0	0
$981$	14.0000	0.446986
$982$	− 20.0000i	− 0.638226i
$983$	− 18.2462i	− 0.581964i	−0.956729	−	0.290982i	$-0.906018\pi$
$983$	− 18.2462i	− 0.581964i	0.956729	−	0.290982i	$-0.0939819\pi$
$984$	4.24621	0.135364
$985$	0	0
$986$	−40.4924	−1.28954
$987$	− 18.8769i	− 0.600858i
$988$	1.43845i	0.0457631i
$989$	−72.9848	−2.32078
$990$	0	0
$991$	46.7386	1.48470	0.742351	−	0.670011i	$-0.233711\pi$
$991$	46.7386	1.48470	0.742351	+	0.670011i	$0.233711\pi$
$992$	1.00000i	0.0317500i
$993$	12.0000i	0.380808i
$994$	7.36932	0.233741
$995$	0	0
$996$	−12.8078	−0.405830
$997$	26.0000i	0.823428i	0.911313	+	0.411714i	$0.135070\pi$
$997$	26.0000i	0.823428i	−0.911313	+	0.411714i	$0.864930\pi$
$998$	1.75379i	0.0555152i
$999$	8.24621	0.260899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4650.2.d.bc.3349.1		4
5.2	odd	4		186.2.a.d.1.1	✓	2
5.3	odd	4		4650.2.a.cd.1.1		2
5.4	even	2	inner	4650.2.d.bc.3349.4		4
15.2	even	4		558.2.a.i.1.2		2
20.7	even	4		1488.2.a.r.1.1		2
35.27	even	4		9114.2.a.be.1.2		2
40.27	even	4		5952.2.a.bk.1.2		2
40.37	odd	4		5952.2.a.bs.1.2		2
60.47	odd	4		4464.2.a.bb.1.2		2
155.92	even	4		5766.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.a.d.1.1	✓	2	5.2	odd	4
558.2.a.i.1.2		2	15.2	even	4
1488.2.a.r.1.1		2	20.7	even	4
4464.2.a.bb.1.2		2	60.47	odd	4
4650.2.a.cd.1.1		2	5.3	odd	4
4650.2.d.bc.3349.1		4	1.1	even	1	trivial
4650.2.d.bc.3349.4		4	5.4	even	2	inner
5766.2.a.v.1.1		2	155.92	even	4
5952.2.a.bk.1.2		2	40.27	even	4
5952.2.a.bs.1.2		2	40.37	odd	4
9114.2.a.be.1.2		2	35.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -5.12311i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -5.12311i q^{7} +1.00000i q^{8} -1.00000 q^{9} -2.56155 q^{11} +1.00000i q^{12} -0.561553i q^{13} -5.12311 q^{14} +1.00000 q^{16} -5.68466i q^{17} +1.00000i q^{18} +2.56155 q^{19} -5.12311 q^{21} +2.56155i q^{22} -8.00000i q^{23} +1.00000 q^{24} -0.561553 q^{26} +1.00000i q^{27} +5.12311i q^{28} +7.12311 q^{29} -1.00000 q^{31} -1.00000i q^{32} +2.56155i q^{33} -5.68466 q^{34} +1.00000 q^{36} -8.24621i q^{37} -2.56155i q^{38} -0.561553 q^{39} +4.24621 q^{41} +5.12311i q^{42} -9.12311i q^{43} +2.56155 q^{44} -8.00000 q^{46} +3.68466i q^{47} -1.00000i q^{48} -19.2462 q^{49} -5.68466 q^{51} +0.561553i q^{52} -2.00000i q^{53} +1.00000 q^{54} +5.12311 q^{56} -2.56155i q^{57} -7.12311i q^{58} +1.12311 q^{59} -0.561553 q^{61} +1.00000i q^{62} +5.12311i q^{63} -1.00000 q^{64} +2.56155 q^{66} -0.315342i q^{67} +5.68466i q^{68} -8.00000 q^{69} -1.43845 q^{71} -1.00000i q^{72} +10.0000i q^{73} -8.24621 q^{74} -2.56155 q^{76} +13.1231i q^{77} +0.561553i q^{78} +3.68466 q^{79} +1.00000 q^{81} -4.24621i q^{82} +12.8078i q^{83} +5.12311 q^{84} -9.12311 q^{86} -7.12311i q^{87} -2.56155i q^{88} +0.246211 q^{89} -2.87689 q^{91} +8.00000i q^{92} +1.00000i q^{93} +3.68466 q^{94} -1.00000 q^{96} +14.8078i q^{97} +19.2462i q^{98} +2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} - 2 q^{11} - 4 q^{14} + 4 q^{16} + 2 q^{19} - 4 q^{21} + 4 q^{24} + 6 q^{26} + 12 q^{29} - 4 q^{31} + 2 q^{34} + 4 q^{36} + 6 q^{39} - 16 q^{41} + 2 q^{44} - 32 q^{46} - 44 q^{49} + 2 q^{51} + 4 q^{54} + 4 q^{56} - 12 q^{59} + 6 q^{61} - 4 q^{64} + 2 q^{66} - 32 q^{69} - 14 q^{71} - 2 q^{76} - 10 q^{79} + 4 q^{81} + 4 q^{84} - 20 q^{86} - 32 q^{89} - 28 q^{91} - 10 q^{94} - 4 q^{96} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 - 2 * q^11 - 4 * q^14 + 4 * q^16 + 2 * q^19 - 4 * q^21 + 4 * q^24 + 6 * q^26 + 12 * q^29 - 4 * q^31 + 2 * q^34 + 4 * q^36 + 6 * q^39 - 16 * q^41 + 2 * q^44 - 32 * q^46 - 44 * q^49 + 2 * q^51 + 4 * q^54 + 4 * q^56 - 12 * q^59 + 6 * q^61 - 4 * q^64 + 2 * q^66 - 32 * q^69 - 14 * q^71 - 2 * q^76 - 10 * q^79 + 4 * q^81 + 4 * q^84 - 20 * q^86 - 32 * q^89 - 28 * q^91 - 10 * q^94 - 4 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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