LMFDB - Embedded newform 3450.2.d.w.2899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, 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("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.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:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 37x^{2} + 324 $ x^4 + 37*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.2
Root			$-4.77200i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.w.2899.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +5.77200 q^{11} +1.00000i q^{12} +3.77200i q^{13} -3.00000 q^{14} +1.00000 q^{16} +0.772002i q^{17} +1.00000i q^{18} -7.77200 q^{19} -3.00000 q^{21} -5.77200i q^{22} -1.00000i q^{23} +1.00000 q^{24} +3.77200 q^{26} +1.00000i q^{27} +3.00000i q^{28} -3.00000 q^{29} -9.54400 q^{31} -1.00000i q^{32} -5.77200i q^{33} +0.772002 q^{34} +1.00000 q^{36} +6.77200i q^{37} +7.77200i q^{38} +3.77200 q^{39} -5.77200 q^{41} +3.00000i q^{42} -7.77200i q^{43} -5.77200 q^{44} -1.00000 q^{46} -8.77200i q^{47} -1.00000i q^{48} -2.00000 q^{49} +0.772002 q^{51} -3.77200i q^{52} -4.00000i q^{53} +1.00000 q^{54} +3.00000 q^{56} +7.77200i q^{57} +3.00000i q^{58} -6.00000 q^{59} -9.54400 q^{61} +9.54400i q^{62} +3.00000i q^{63} -1.00000 q^{64} -5.77200 q^{66} -9.54400i q^{67} -0.772002i q^{68} -1.00000 q^{69} -4.77200 q^{71} -1.00000i q^{72} -6.54400i q^{73} +6.77200 q^{74} +7.77200 q^{76} -17.3160i q^{77} -3.77200i q^{78} -2.22800 q^{79} +1.00000 q^{81} +5.77200i q^{82} +1.00000i q^{83} +3.00000 q^{84} -7.77200 q^{86} +3.00000i q^{87} +5.77200i q^{88} -16.7720 q^{89} +11.3160 q^{91} +1.00000i q^{92} +9.54400i q^{93} -8.77200 q^{94} -1.00000 q^{96} +17.5440i q^{97} +2.00000i q^{98} -5.77200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{11} - 12 q^{14} + 4 q^{16} - 14 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} - 4 q^{31} - 14 q^{34} + 4 q^{36} - 2 q^{39} - 6 q^{41} - 6 q^{44} - 4 q^{46} - 8 q^{49} - 14 q^{51} + 4 q^{54} + 12 q^{56} - 24 q^{59} - 4 q^{61} - 4 q^{64} - 6 q^{66} - 4 q^{69} - 2 q^{71} + 10 q^{74} + 14 q^{76} - 26 q^{79} + 4 q^{81} + 12 q^{84} - 14 q^{86} - 50 q^{89} - 6 q^{91} - 18 q^{94} - 4 q^{96} - 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 6 * q^11 - 12 * q^14 + 4 * q^16 - 14 * q^19 - 12 * q^21 + 4 * q^24 - 2 * q^26 - 12 * q^29 - 4 * q^31 - 14 * q^34 + 4 * q^36 - 2 * q^39 - 6 * q^41 - 6 * q^44 - 4 * q^46 - 8 * q^49 - 14 * q^51 + 4 * q^54 + 12 * q^56 - 24 * q^59 - 4 * q^61 - 4 * q^64 - 6 * q^66 - 4 * q^69 - 2 * q^71 + 10 * q^74 + 14 * q^76 - 26 * q^79 + 4 * q^81 + 12 * q^84 - 14 * q^86 - 50 * q^89 - 6 * q^91 - 18 * q^94 - 4 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

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
$7$	− 3.00000i	− 1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$	− 3.00000i	− 1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	5.77200	1.74032	0.870162	−	0.492766i	$-0.164014\pi$
$11$	5.77200	1.74032	0.870162	+	0.492766i	$0.164014\pi$
$12$	1.00000i	0.288675i
$13$	3.77200i	1.04617i	0.852282	+	0.523083i	$0.175218\pi$
$13$	3.77200i	1.04617i	−0.852282	+	0.523083i	$0.824782\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	0.772002i	0.187238i	0.995608	+	0.0936190i	$0.0298435\pi$
$17$	0.772002i	0.187238i	−0.995608	+	0.0936190i	$0.970156\pi$
$18$	1.00000i	0.235702i
$19$	−7.77200	−1.78302	−0.891510	−	0.453001i	$-0.850353\pi$
$19$	−7.77200	−1.78302	−0.891510	+	0.453001i	$0.850353\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	− 5.77200i	− 1.23059i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	1.00000	0.204124
$25$	0	0
$26$	3.77200	0.739750
$27$	1.00000i	0.192450i
$28$	3.00000i	0.566947i
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−9.54400	−1.71415	−0.857077	−	0.515189i	$-0.827722\pi$
$31$	−9.54400	−1.71415	−0.857077	+	0.515189i	$0.827722\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 5.77200i	− 1.00478i
$34$	0.772002	0.132397
$35$	0	0
$36$	1.00000	0.166667
$37$	6.77200i	1.11331i	0.830744	+	0.556655i	$0.187916\pi$
$37$	6.77200i	1.11331i	−0.830744	+	0.556655i	$0.812084\pi$
$38$	7.77200i	1.26079i
$39$	3.77200	0.604004
$40$	0	0
$41$	−5.77200	−0.901435	−0.450718	−	0.892667i	$-0.648832\pi$
$41$	−5.77200	−0.901435	−0.450718	+	0.892667i	$0.648832\pi$
$42$	3.00000i	0.462910i
$43$	− 7.77200i	− 1.18522i	−0.805490	−	0.592610i	$-0.798098\pi$
$43$	− 7.77200i	− 1.18522i	0.805490	−	0.592610i	$-0.201902\pi$
$44$	−5.77200	−0.870162
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 8.77200i	− 1.27953i	−0.768571	−	0.639764i	$-0.779032\pi$
$47$	− 8.77200i	− 1.27953i	0.768571	−	0.639764i	$-0.220968\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	0.772002	0.108102
$52$	− 3.77200i	− 0.523083i
$53$	− 4.00000i	− 0.549442i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	− 4.00000i	− 0.549442i	0.961524	−	0.274721i	$-0.0885855\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	7.77200i	1.02943i
$58$	3.00000i	0.393919i
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−9.54400	−1.22198	−0.610992	−	0.791637i	$-0.709229\pi$
$61$	−9.54400	−1.22198	−0.610992	+	0.791637i	$0.709229\pi$
$62$	9.54400i	1.21209i
$63$	3.00000i	0.377964i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.77200	−0.710484
$67$	− 9.54400i	− 1.16599i	−0.812477	−	0.582993i	$-0.801882\pi$
$67$	− 9.54400i	− 1.16599i	0.812477	−	0.582993i	$-0.198118\pi$
$68$	− 0.772002i	− 0.0936190i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−4.77200	−0.566332	−0.283166	−	0.959071i	$-0.591385\pi$
$71$	−4.77200	−0.566332	−0.283166	+	0.959071i	$0.591385\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 6.54400i	− 0.765918i	−0.923765	−	0.382959i	$-0.874905\pi$
$73$	− 6.54400i	− 0.765918i	0.923765	−	0.382959i	$-0.125095\pi$
$74$	6.77200	0.787229
$75$	0	0
$76$	7.77200	0.891510
$77$	− 17.3160i	− 1.97334i
$78$	− 3.77200i	− 0.427095i
$79$	−2.22800	−0.250669	−0.125335	−	0.992115i	$-0.540000\pi$
$79$	−2.22800	−0.250669	−0.125335	+	0.992115i	$0.540000\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.77200i	0.637411i
$83$	1.00000i	0.109764i	0.998493	+	0.0548821i	$0.0174783\pi$
$83$	1.00000i	0.109764i	−0.998493	+	0.0548821i	$0.982522\pi$
$84$	3.00000	0.327327
$85$	0	0
$86$	−7.77200	−0.838077
$87$	3.00000i	0.321634i
$88$	5.77200i	0.615297i
$89$	−16.7720	−1.77783	−0.888914	−	0.458073i	$-0.848540\pi$
$89$	−16.7720	−1.77783	−0.888914	+	0.458073i	$0.848540\pi$
$90$	0	0
$91$	11.3160	1.18624
$92$	1.00000i	0.104257i
$93$	9.54400i	0.989667i
$94$	−8.77200	−0.904763
$95$	0	0
$96$	−1.00000	−0.102062
$97$	17.5440i	1.78132i	0.454666	+	0.890662i	$0.349759\pi$
$97$	17.5440i	1.78132i	−0.454666	+	0.890662i	$0.650241\pi$
$98$	2.00000i	0.202031i
$99$	−5.77200	−0.580108
$100$	0	0
$101$	14.3160	1.42450	0.712248	−	0.701928i	$-0.247677\pi$
$101$	14.3160	1.42450	0.712248	+	0.701928i	$0.247677\pi$
$102$	− 0.772002i	− 0.0764396i
$103$	− 11.0000i	− 1.08386i	−0.840423	−	0.541931i	$-0.817693\pi$
$103$	− 11.0000i	− 1.08386i	0.840423	−	0.541931i	$-0.182307\pi$
$104$	−3.77200	−0.369875
$105$	0	0
$106$	−4.00000	−0.388514
$107$	− 4.00000i	− 0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$	− 4.00000i	− 0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−14.7720	−1.41490	−0.707451	−	0.706763i	$-0.750155\pi$
$109$	−14.7720	−1.41490	−0.707451	+	0.706763i	$0.750155\pi$
$110$	0	0
$111$	6.77200	0.642770
$112$	− 3.00000i	− 0.283473i
$113$	− 4.77200i	− 0.448912i	−0.974484	−	0.224456i	$-0.927939\pi$
$113$	− 4.77200i	− 0.448912i	0.974484	−	0.224456i	$-0.0720605\pi$
$114$	7.77200	0.727915
$115$	0	0
$116$	3.00000	0.278543
$117$	− 3.77200i	− 0.348722i
$118$	6.00000i	0.552345i
$119$	2.31601	0.212308
$120$	0	0
$121$	22.3160	2.02873
$122$	9.54400i	0.864073i
$123$	5.77200i	0.520444i
$124$	9.54400	0.857077
$125$	0	0
$126$	3.00000	0.267261
$127$	4.45600i	0.395406i	0.980262	+	0.197703i	$0.0633481\pi$
$127$	4.45600i	0.395406i	−0.980262	+	0.197703i	$0.936652\pi$
$128$	1.00000i	0.0883883i
$129$	−7.77200	−0.684287
$130$	0	0
$131$	−19.0880	−1.66773	−0.833863	−	0.551971i	$-0.813876\pi$
$131$	−19.0880	−1.66773	−0.833863	+	0.551971i	$0.813876\pi$
$132$	5.77200i	0.502388i
$133$	23.3160i	2.02175i
$134$	−9.54400	−0.824476
$135$	0	0
$136$	−0.772002	−0.0661986
$137$	14.7720i	1.26206i	0.775760	+	0.631029i	$0.217367\pi$
$137$	14.7720i	1.26206i	−0.775760	+	0.631029i	$0.782633\pi$
$138$	1.00000i	0.0851257i
$139$	0.772002	0.0654803	0.0327402	−	0.999464i	$-0.489577\pi$
$139$	0.772002	0.0654803	0.0327402	+	0.999464i	$0.489577\pi$
$140$	0	0
$141$	−8.77200	−0.738736
$142$	4.77200i	0.400458i
$143$	21.7720i	1.82067i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−6.54400	−0.541586
$147$	2.00000i	0.164957i
$148$	− 6.77200i	− 0.556655i
$149$	11.0880	0.908365	0.454182	−	0.890909i	$-0.349931\pi$
$149$	11.0880	0.908365	0.454182	+	0.890909i	$0.349931\pi$
$150$	0	0
$151$	23.5440	1.91598	0.957992	−	0.286795i	$-0.0925899\pi$
$151$	23.5440	1.91598	0.957992	+	0.286795i	$0.0925899\pi$
$152$	− 7.77200i	− 0.630393i
$153$	− 0.772002i	− 0.0624127i
$154$	−17.3160	−1.39536
$155$	0	0
$156$	−3.77200	−0.302002
$157$	13.5440i	1.08093i	0.841367	+	0.540465i	$0.181752\pi$
$157$	13.5440i	1.08093i	−0.841367	+	0.540465i	$0.818248\pi$
$158$	2.22800i	0.177250i
$159$	−4.00000	−0.317221
$160$	0	0
$161$	−3.00000	−0.236433
$162$	− 1.00000i	− 0.0785674i
$163$	− 16.0000i	− 1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$	− 16.0000i	− 1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	5.77200	0.450718
$165$	0	0
$166$	1.00000	0.0776151
$167$	16.3160i	1.26257i	0.775551	+	0.631285i	$0.217472\pi$
$167$	16.3160i	1.26257i	−0.775551	+	0.631285i	$0.782528\pi$
$168$	− 3.00000i	− 0.231455i
$169$	−1.22800	−0.0944614
$170$	0	0
$171$	7.77200	0.594340
$172$	7.77200i	0.592610i
$173$	15.7720i	1.19912i	0.800329	+	0.599562i	$0.204658\pi$
$173$	15.7720i	1.19912i	−0.800329	+	0.599562i	$0.795342\pi$
$174$	3.00000	0.227429
$175$	0	0
$176$	5.77200	0.435081
$177$	6.00000i	0.450988i
$178$	16.7720i	1.25711i
$179$	−7.54400	−0.563865	−0.281933	−	0.959434i	$-0.590975\pi$
$179$	−7.54400	−0.563865	−0.281933	+	0.959434i	$0.590975\pi$
$180$	0	0
$181$	14.3160	1.06410	0.532050	−	0.846713i	$-0.321422\pi$
$181$	14.3160	1.06410	0.532050	+	0.846713i	$0.321422\pi$
$182$	− 11.3160i	− 0.838798i
$183$	9.54400i	0.705513i
$184$	1.00000	0.0737210
$185$	0	0
$186$	9.54400	0.699800
$187$	4.45600i	0.325855i
$188$	8.77200i	0.639764i
$189$	3.00000	0.218218
$190$	0	0
$191$	−7.31601	−0.529368	−0.264684	−	0.964335i	$-0.585268\pi$
$191$	−7.31601	−0.529368	−0.264684	+	0.964335i	$0.585268\pi$
$192$	1.00000i	0.0721688i
$193$	− 4.77200i	− 0.343496i	−0.985141	−	0.171748i	$-0.945058\pi$
$193$	− 4.77200i	− 0.343496i	0.985141	−	0.171748i	$-0.0549415\pi$
$194$	17.5440	1.25959
$195$	0	0
$196$	2.00000	0.142857
$197$	− 13.0000i	− 0.926212i	−0.886303	−	0.463106i	$-0.846735\pi$
$197$	− 13.0000i	− 0.926212i	0.886303	−	0.463106i	$-0.153265\pi$
$198$	5.77200i	0.410198i
$199$	−12.0880	−0.856896	−0.428448	−	0.903566i	$-0.640940\pi$
$199$	−12.0880	−0.856896	−0.428448	+	0.903566i	$0.640940\pi$
$200$	0	0
$201$	−9.54400	−0.673182
$202$	− 14.3160i	− 1.00727i
$203$	9.00000i	0.631676i
$204$	−0.772002	−0.0540509
$205$	0	0
$206$	−11.0000	−0.766406
$207$	1.00000i	0.0695048i
$208$	3.77200i	0.261541i
$209$	−44.8600	−3.10303
$210$	0	0
$211$	−10.3160	−0.710183	−0.355092	−	0.934832i	$-0.615550\pi$
$211$	−10.3160	−0.710183	−0.355092	+	0.934832i	$0.615550\pi$
$212$	4.00000i	0.274721i
$213$	4.77200i	0.326972i
$214$	−4.00000	−0.273434
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	28.6320i	1.94367i
$218$	14.7720i	1.00049i
$219$	−6.54400	−0.442203
$220$	0	0
$221$	−2.91199	−0.195882
$222$	− 6.77200i	− 0.454507i
$223$	− 10.0000i	− 0.669650i	−0.942280	−	0.334825i	$-0.891323\pi$
$223$	− 10.0000i	− 0.669650i	0.942280	−	0.334825i	$-0.108677\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	−4.77200	−0.317429
$227$	− 10.7720i	− 0.714963i	−0.933920	−	0.357481i	$-0.883636\pi$
$227$	− 10.7720i	− 0.714963i	0.933920	−	0.357481i	$-0.116364\pi$
$228$	− 7.77200i	− 0.514713i
$229$	6.45600	0.426624	0.213312	−	0.976984i	$-0.431575\pi$
$229$	6.45600	0.426624	0.213312	+	0.976984i	$0.431575\pi$
$230$	0	0
$231$	−17.3160	−1.13931
$232$	− 3.00000i	− 0.196960i
$233$	2.68399i	0.175834i	0.996128	+	0.0879172i	$0.0280211\pi$
$233$	2.68399i	0.175834i	−0.996128	+	0.0879172i	$0.971979\pi$
$234$	−3.77200	−0.246583
$235$	0	0
$236$	6.00000	0.390567
$237$	2.22800i	0.144724i
$238$	− 2.31601i	− 0.150124i
$239$	−22.7720	−1.47300	−0.736499	−	0.676438i	$-0.763522\pi$
$239$	−22.7720	−1.47300	−0.736499	+	0.676438i	$0.763522\pi$
$240$	0	0
$241$	−26.6320	−1.71552	−0.857759	−	0.514051i	$-0.828144\pi$
$241$	−26.6320	−1.71552	−0.857759	+	0.514051i	$0.828144\pi$
$242$	− 22.3160i	− 1.43453i
$243$	− 1.00000i	− 0.0641500i
$244$	9.54400	0.610992
$245$	0	0
$246$	5.77200	0.368009
$247$	− 29.3160i	− 1.86533i
$248$	− 9.54400i	− 0.606045i
$249$	1.00000	0.0633724
$250$	0	0
$251$	−3.68399	−0.232532	−0.116266	−	0.993218i	$-0.537092\pi$
$251$	−3.68399	−0.232532	−0.116266	+	0.993218i	$0.537092\pi$
$252$	− 3.00000i	− 0.188982i
$253$	− 5.77200i	− 0.362883i
$254$	4.45600	0.279594
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 9.08801i	− 0.566894i	−0.958988	−	0.283447i	$-0.908522\pi$
$257$	− 9.08801i	− 0.566894i	0.958988	−	0.283447i	$-0.0914781\pi$
$258$	7.77200i	0.483864i
$259$	20.3160	1.26238
$260$	0	0
$261$	3.00000	0.185695
$262$	19.0880i	1.17926i
$263$	6.45600i	0.398094i	0.979990	+	0.199047i	$0.0637846\pi$
$263$	6.45600i	0.398094i	−0.979990	+	0.199047i	$0.936215\pi$
$264$	5.77200	0.355242
$265$	0	0
$266$	23.3160	1.42960
$267$	16.7720i	1.02643i
$268$	9.54400i	0.582993i
$269$	26.8600	1.63768	0.818842	−	0.574019i	$-0.194617\pi$
$269$	26.8600	1.63768	0.818842	+	0.574019i	$0.194617\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	0.772002i	0.0468095i
$273$	− 11.3160i	− 0.684876i
$274$	14.7720	0.892409
$275$	0	0
$276$	1.00000	0.0601929
$277$	− 8.22800i	− 0.494372i	−0.968968	−	0.247186i	$-0.920494\pi$
$277$	− 8.22800i	− 0.494372i	0.968968	−	0.247186i	$-0.0795060\pi$
$278$	− 0.772002i	− 0.0463016i
$279$	9.54400	0.571385
$280$	0	0
$281$	15.8600	0.946129	0.473064	−	0.881028i	$-0.343148\pi$
$281$	15.8600	0.946129	0.473064	+	0.881028i	$0.343148\pi$
$282$	8.77200i	0.522365i
$283$	− 28.0000i	− 1.66443i	−0.554455	−	0.832214i	$-0.687073\pi$
$283$	− 28.0000i	− 1.66443i	0.554455	−	0.832214i	$-0.312927\pi$
$284$	4.77200	0.283166
$285$	0	0
$286$	21.7720	1.28741
$287$	17.3160i	1.02213i
$288$	1.00000i	0.0589256i
$289$	16.4040	0.964942
$290$	0	0
$291$	17.5440	1.02845
$292$	6.54400i	0.382959i
$293$	9.54400i	0.557567i	0.960354	+	0.278783i	$0.0899311\pi$
$293$	9.54400i	0.557567i	−0.960354	+	0.278783i	$0.910069\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	−6.77200	−0.393615
$297$	5.77200i	0.334926i
$298$	− 11.0880i	− 0.642311i
$299$	3.77200	0.218141
$300$	0	0
$301$	−23.3160	−1.34391
$302$	− 23.5440i	− 1.35481i
$303$	− 14.3160i	− 0.822433i
$304$	−7.77200	−0.445755
$305$	0	0
$306$	−0.772002	−0.0441324
$307$	− 20.3160i	− 1.15950i	−0.814796	−	0.579748i	$-0.803151\pi$
$307$	− 20.3160i	− 1.15950i	0.814796	−	0.579748i	$-0.196849\pi$
$308$	17.3160i	0.986671i
$309$	−11.0000	−0.625768
$310$	0	0
$311$	−17.8600	−1.01275	−0.506374	−	0.862314i	$-0.669015\pi$
$311$	−17.8600	−1.01275	−0.506374	+	0.862314i	$0.669015\pi$
$312$	3.77200i	0.213548i
$313$	8.00000i	0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$	8.00000i	0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	13.5440	0.764332
$315$	0	0
$316$	2.22800	0.125335
$317$	− 9.00000i	− 0.505490i	−0.967533	−	0.252745i	$-0.918667\pi$
$317$	− 9.00000i	− 0.505490i	0.967533	−	0.252745i	$-0.0813334\pi$
$318$	4.00000i	0.224309i
$319$	−17.3160	−0.969510
$320$	0	0
$321$	−4.00000	−0.223258
$322$	3.00000i	0.167183i
$323$	− 6.00000i	− 0.333849i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−16.0000	−0.886158
$327$	14.7720i	0.816894i
$328$	− 5.77200i	− 0.318705i
$329$	−26.3160	−1.45085
$330$	0	0
$331$	34.7720	1.91124	0.955621	−	0.294599i	$-0.0951860\pi$
$331$	34.7720	1.91124	0.955621	+	0.294599i	$0.0951860\pi$
$332$	− 1.00000i	− 0.0548821i
$333$	− 6.77200i	− 0.371103i
$334$	16.3160	0.892772
$335$	0	0
$336$	−3.00000	−0.163663
$337$	4.00000i	0.217894i	0.994048	+	0.108947i	$0.0347479\pi$
$337$	4.00000i	0.217894i	−0.994048	+	0.108947i	$0.965252\pi$
$338$	1.22800i	0.0667943i
$339$	−4.77200	−0.259180
$340$	0	0
$341$	−55.0880	−2.98318
$342$	− 7.77200i	− 0.420262i
$343$	− 15.0000i	− 0.809924i
$344$	7.77200	0.419038
$345$	0	0
$346$	15.7720	0.847908
$347$	9.54400i	0.512349i	0.966631	+	0.256174i	$0.0824622\pi$
$347$	9.54400i	0.512349i	−0.966631	+	0.256174i	$0.917538\pi$
$348$	− 3.00000i	− 0.160817i
$349$	0.227998	0.0122045	0.00610223	−	0.999981i	$-0.498058\pi$
$349$	0.227998	0.0122045	0.00610223	+	0.999981i	$0.498058\pi$
$350$	0	0
$351$	−3.77200	−0.201335
$352$	− 5.77200i	− 0.307649i
$353$	18.8600i	1.00382i	0.864921	+	0.501909i	$0.167369\pi$
$353$	18.8600i	1.00382i	−0.864921	+	0.501909i	$0.832631\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	16.7720	0.888914
$357$	− 2.31601i	− 0.122576i
$358$	7.54400i	0.398713i
$359$	10.2280	0.539813	0.269907	−	0.962887i	$-0.413007\pi$
$359$	10.2280	0.539813	0.269907	+	0.962887i	$0.413007\pi$
$360$	0	0
$361$	41.4040	2.17916
$362$	− 14.3160i	− 0.752433i
$363$	− 22.3160i	− 1.17129i
$364$	−11.3160	−0.593120
$365$	0	0
$366$	9.54400	0.498873
$367$	33.3160i	1.73908i	0.493861	+	0.869541i	$0.335585\pi$
$367$	33.3160i	1.73908i	−0.493861	+	0.869541i	$0.664415\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	5.77200	0.300478
$370$	0	0
$371$	−12.0000	−0.623009
$372$	− 9.54400i	− 0.494834i
$373$	12.7720i	0.661309i	0.943752	+	0.330655i	$0.107270\pi$
$373$	12.7720i	0.661309i	−0.943752	+	0.330655i	$0.892730\pi$
$374$	4.45600	0.230414
$375$	0	0
$376$	8.77200	0.452381
$377$	− 11.3160i	− 0.582804i
$378$	− 3.00000i	− 0.154303i
$379$	23.0880	1.18595	0.592976	−	0.805220i	$-0.297953\pi$
$379$	23.0880	1.18595	0.592976	+	0.805220i	$0.297953\pi$
$380$	0	0
$381$	4.45600	0.228288
$382$	7.31601i	0.374319i
$383$	− 13.7720i	− 0.703716i	−0.936053	−	0.351858i	$-0.885550\pi$
$383$	− 13.7720i	− 0.703716i	0.936053	−	0.351858i	$-0.114450\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−4.77200	−0.242889
$387$	7.77200i	0.395073i
$388$	− 17.5440i	− 0.890662i
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	0.772002	0.0390418
$392$	− 2.00000i	− 0.101015i
$393$	19.0880i	0.962863i
$394$	−13.0000	−0.654931
$395$	0	0
$396$	5.77200	0.290054
$397$	− 14.6320i	− 0.734360i	−0.930150	−	0.367180i	$-0.880323\pi$
$397$	− 14.6320i	− 0.734360i	0.930150	−	0.367180i	$-0.119677\pi$
$398$	12.0880i	0.605917i
$399$	23.3160	1.16726
$400$	0	0
$401$	−28.6320	−1.42981	−0.714907	−	0.699219i	$-0.753531\pi$
$401$	−28.6320	−1.42981	−0.714907	+	0.699219i	$0.753531\pi$
$402$	9.54400i	0.476012i
$403$	− 36.0000i	− 1.79329i
$404$	−14.3160	−0.712248
$405$	0	0
$406$	9.00000	0.446663
$407$	39.0880i	1.93752i
$408$	0.772002i	0.0382198i
$409$	23.0000	1.13728	0.568638	−	0.822588i	$-0.307470\pi$
$409$	23.0000	1.13728	0.568638	+	0.822588i	$0.307470\pi$
$410$	0	0
$411$	14.7720	0.728649
$412$	11.0000i	0.541931i
$413$	18.0000i	0.885722i
$414$	1.00000	0.0491473
$415$	0	0
$416$	3.77200	0.184938
$417$	− 0.772002i	− 0.0378051i
$418$	44.8600i	2.19417i
$419$	−25.6320	−1.25221	−0.626103	−	0.779740i	$-0.715351\pi$
$419$	−25.6320	−1.25221	−0.626103	+	0.779740i	$0.715351\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	10.3160i	0.502175i
$423$	8.77200i	0.426509i
$424$	4.00000	0.194257
$425$	0	0
$426$	4.77200	0.231204
$427$	28.6320i	1.38560i
$428$	4.00000i	0.193347i
$429$	21.7720	1.05116
$430$	0	0
$431$	24.6320	1.18648	0.593241	−	0.805025i	$-0.297848\pi$
$431$	24.6320	1.18648	0.593241	+	0.805025i	$0.297848\pi$
$432$	1.00000i	0.0481125i
$433$	− 6.45600i	− 0.310255i	−0.987894	−	0.155128i	$-0.950421\pi$
$433$	− 6.45600i	− 0.310255i	0.987894	−	0.155128i	$-0.0495789\pi$
$434$	28.6320	1.37438
$435$	0	0
$436$	14.7720	0.707451
$437$	7.77200i	0.371785i
$438$	6.54400i	0.312685i
$439$	12.0000	0.572729	0.286364	−	0.958121i	$-0.407553\pi$
$439$	12.0000	0.572729	0.286364	+	0.958121i	$0.407553\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	2.91199i	0.138509i
$443$	− 24.0000i	− 1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$	− 24.0000i	− 1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$	−6.77200	−0.321385
$445$	0	0
$446$	−10.0000	−0.473514
$447$	− 11.0880i	− 0.524445i
$448$	3.00000i	0.141737i
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	0	0
$451$	−33.3160	−1.56879
$452$	4.77200i	0.224456i
$453$	− 23.5440i	− 1.10619i
$454$	−10.7720	−0.505555
$455$	0	0
$456$	−7.77200	−0.363957
$457$	− 30.6320i	− 1.43291i	−0.697636	−	0.716453i	$-0.745765\pi$
$457$	− 30.6320i	− 1.43291i	0.697636	−	0.716453i	$-0.254235\pi$
$458$	− 6.45600i	− 0.301669i
$459$	−0.772002	−0.0360340
$460$	0	0
$461$	12.5440	0.584232	0.292116	−	0.956383i	$-0.405641\pi$
$461$	12.5440	0.584232	0.292116	+	0.956383i	$0.405641\pi$
$462$	17.3160i	0.805613i
$463$	− 0.911993i	− 0.0423839i	−0.999775	−	0.0211919i	$-0.993254\pi$
$463$	− 0.911993i	− 0.0423839i	0.999775	−	0.0211919i	$-0.00674611\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	2.68399	0.124334
$467$	18.5440i	0.858114i	0.903277	+	0.429057i	$0.141154\pi$
$467$	18.5440i	0.858114i	−0.903277	+	0.429057i	$0.858846\pi$
$468$	3.77200i	0.174361i
$469$	−28.6320	−1.32210
$470$	0	0
$471$	13.5440	0.624075
$472$	− 6.00000i	− 0.276172i
$473$	− 44.8600i	− 2.06267i
$474$	2.22800	0.102335
$475$	0	0
$476$	−2.31601	−0.106154
$477$	4.00000i	0.183147i
$478$	22.7720i	1.04157i
$479$	35.3160	1.61363	0.806815	−	0.590805i	$-0.201190\pi$
$479$	35.3160	1.61363	0.806815	+	0.590805i	$0.201190\pi$
$480$	0	0
$481$	−25.5440	−1.16471
$482$	26.6320i	1.21305i
$483$	3.00000i	0.136505i
$484$	−22.3160	−1.01436
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	12.4560i	0.564435i	0.959350	+	0.282218i	$0.0910700\pi$
$487$	12.4560i	0.564435i	−0.959350	+	0.282218i	$0.908930\pi$
$488$	− 9.54400i	− 0.432037i
$489$	−16.0000	−0.723545
$490$	0	0
$491$	−10.4560	−0.471873	−0.235936	−	0.971769i	$-0.575816\pi$
$491$	−10.4560	−0.471873	−0.235936	+	0.971769i	$0.575816\pi$
$492$	− 5.77200i	− 0.260222i
$493$	− 2.31601i	− 0.104308i
$494$	−29.3160	−1.31899
$495$	0	0
$496$	−9.54400	−0.428538
$497$	14.3160i	0.642161i
$498$	− 1.00000i	− 0.0448111i
$499$	9.68399	0.433515	0.216758	−	0.976225i	$-0.430452\pi$
$499$	9.68399	0.433515	0.216758	+	0.976225i	$0.430452\pi$
$500$	0	0
$501$	16.3160	0.728945
$502$	3.68399i	0.164425i
$503$	39.9480i	1.78119i	0.454793	+	0.890597i	$0.349713\pi$
$503$	39.9480i	1.78119i	−0.454793	+	0.890597i	$0.650287\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−5.77200	−0.256597
$507$	1.22800i	0.0545373i
$508$	− 4.45600i	− 0.197703i
$509$	−27.8600	−1.23487	−0.617437	−	0.786621i	$-0.711829\pi$
$509$	−27.8600	−1.23487	−0.617437	+	0.786621i	$0.711829\pi$
$510$	0	0
$511$	−19.6320	−0.868469
$512$	− 1.00000i	− 0.0441942i
$513$	− 7.77200i	− 0.343142i
$514$	−9.08801	−0.400855
$515$	0	0
$516$	7.77200	0.342143
$517$	− 50.6320i	− 2.22679i
$518$	− 20.3160i	− 0.892634i
$519$	15.7720	0.692314
$520$	0	0
$521$	6.77200	0.296687	0.148343	−	0.988936i	$-0.452606\pi$
$521$	6.77200	0.296687	0.148343	+	0.988936i	$0.452606\pi$
$522$	− 3.00000i	− 0.131306i
$523$	13.3160i	0.582268i	0.956682	+	0.291134i	$0.0940326\pi$
$523$	13.3160i	0.582268i	−0.956682	+	0.291134i	$0.905967\pi$
$524$	19.0880	0.833863
$525$	0	0
$526$	6.45600	0.281495
$527$	− 7.36799i	− 0.320955i
$528$	− 5.77200i	− 0.251194i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	6.00000	0.260378
$532$	− 23.3160i	− 1.01088i
$533$	− 21.7720i	− 0.943050i
$534$	16.7720	0.725796
$535$	0	0
$536$	9.54400	0.412238
$537$	7.54400i	0.325548i
$538$	− 26.8600i	− 1.15802i
$539$	−11.5440	−0.497235
$540$	0	0
$541$	−10.6840	−0.459341	−0.229670	−	0.973268i	$-0.573765\pi$
$541$	−10.6840	−0.459341	−0.229670	+	0.973268i	$0.573765\pi$
$542$	− 16.0000i	− 0.687259i
$543$	− 14.3160i	− 0.614359i
$544$	0.772002	0.0330993
$545$	0	0
$546$	−11.3160	−0.484280
$547$	11.8600i	0.507097i	0.967323	+	0.253549i	$0.0815978\pi$
$547$	11.8600i	0.507097i	−0.967323	+	0.253549i	$0.918402\pi$
$548$	− 14.7720i	− 0.631029i
$549$	9.54400	0.407328
$550$	0	0
$551$	23.3160	0.993295
$552$	− 1.00000i	− 0.0425628i
$553$	6.68399i	0.284232i
$554$	−8.22800	−0.349574
$555$	0	0
$556$	−0.772002	−0.0327402
$557$	− 21.0880i	− 0.893528i	−0.894652	−	0.446764i	$-0.852576\pi$
$557$	− 21.0880i	− 0.893528i	0.894652	−	0.446764i	$-0.147424\pi$
$558$	− 9.54400i	− 0.404030i
$559$	29.3160	1.23993
$560$	0	0
$561$	4.45600	0.188132
$562$	− 15.8600i	− 0.669014i
$563$	− 43.9480i	− 1.85219i	−0.377293	−	0.926094i	$-0.623145\pi$
$563$	− 43.9480i	− 1.85219i	0.377293	−	0.926094i	$-0.376855\pi$
$564$	8.77200	0.369368
$565$	0	0
$566$	−28.0000	−1.17693
$567$	− 3.00000i	− 0.125988i
$568$	− 4.77200i	− 0.200229i
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	12.6320	0.528633	0.264317	−	0.964436i	$-0.414854\pi$
$571$	12.6320	0.528633	0.264317	+	0.964436i	$0.414854\pi$
$572$	− 21.7720i	− 0.910333i
$573$	7.31601i	0.305631i
$574$	17.3160	0.722756
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 31.3160i	− 1.30370i	−0.758347	−	0.651851i	$-0.773993\pi$
$577$	− 31.3160i	− 1.30370i	0.758347	−	0.651851i	$-0.226007\pi$
$578$	− 16.4040i	− 0.682317i
$579$	−4.77200	−0.198318
$580$	0	0
$581$	3.00000	0.124461
$582$	− 17.5440i	− 0.727222i
$583$	− 23.0880i	− 0.956208i
$584$	6.54400	0.270793
$585$	0	0
$586$	9.54400	0.394259
$587$	24.4560i	1.00941i	0.863293	+	0.504703i	$0.168398\pi$
$587$	24.4560i	1.00941i	−0.863293	+	0.504703i	$0.831602\pi$
$588$	− 2.00000i	− 0.0824786i
$589$	74.1760	3.05637
$590$	0	0
$591$	−13.0000	−0.534749
$592$	6.77200i	0.278328i
$593$	− 41.3160i	− 1.69664i	−0.529480	−	0.848322i	$-0.677613\pi$
$593$	− 41.3160i	− 1.69664i	0.529480	−	0.848322i	$-0.322387\pi$
$594$	5.77200	0.236828
$595$	0	0
$596$	−11.0880	−0.454182
$597$	12.0880i	0.494729i
$598$	− 3.77200i	− 0.154249i
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	0	0
$601$	−32.7720	−1.33680	−0.668399	−	0.743803i	$-0.733020\pi$
$601$	−32.7720	−1.33680	−0.668399	+	0.743803i	$0.733020\pi$
$602$	23.3160i	0.950289i
$603$	9.54400i	0.388662i
$604$	−23.5440	−0.957992
$605$	0	0
$606$	−14.3160	−0.581548
$607$	5.08801i	0.206516i	0.994655	+	0.103258i	$0.0329267\pi$
$607$	5.08801i	0.206516i	−0.994655	+	0.103258i	$0.967073\pi$
$608$	7.77200i	0.315196i
$609$	9.00000	0.364698
$610$	0	0
$611$	33.0880	1.33860
$612$	0.772002i	0.0312063i
$613$	− 20.7720i	− 0.838973i	−0.907762	−	0.419487i	$-0.862210\pi$
$613$	− 20.7720i	− 0.838973i	0.907762	−	0.419487i	$-0.137790\pi$
$614$	−20.3160	−0.819887
$615$	0	0
$616$	17.3160	0.697682
$617$	− 18.0000i	− 0.724653i	−0.932051	−	0.362326i	$-0.881983\pi$
$617$	− 18.0000i	− 0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$	11.0000i	0.442485i
$619$	0.911993	0.0366561	0.0183280	−	0.999832i	$-0.494166\pi$
$619$	0.911993	0.0366561	0.0183280	+	0.999832i	$0.494166\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	17.8600i	0.716121i
$623$	50.3160i	2.01587i
$624$	3.77200	0.151001
$625$	0	0
$626$	8.00000	0.319744
$627$	44.8600i	1.79154i
$628$	− 13.5440i	− 0.540465i
$629$	−5.22800	−0.208454
$630$	0	0
$631$	14.0880	0.560835	0.280417	−	0.959878i	$-0.409527\pi$
$631$	14.0880	0.560835	0.280417	+	0.959878i	$0.409527\pi$
$632$	− 2.22800i	− 0.0886250i
$633$	10.3160i	0.410024i
$634$	−9.00000	−0.357436
$635$	0	0
$636$	4.00000	0.158610
$637$	− 7.54400i	− 0.298904i
$638$	17.3160i	0.685547i
$639$	4.77200	0.188777
$640$	0	0
$641$	−17.8600	−0.705428	−0.352714	−	0.935731i	$-0.614741\pi$
$641$	−17.8600	−0.705428	−0.352714	+	0.935731i	$0.614741\pi$
$642$	4.00000i	0.157867i
$643$	19.3160i	0.761749i	0.924627	+	0.380874i	$0.124377\pi$
$643$	19.3160i	0.761749i	−0.924627	+	0.380874i	$0.875623\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−6.00000	−0.236067
$647$	− 30.7720i	− 1.20977i	−0.796312	−	0.604886i	$-0.793219\pi$
$647$	− 30.7720i	− 1.20977i	0.796312	−	0.604886i	$-0.206781\pi$
$648$	1.00000i	0.0392837i
$649$	−34.6320	−1.35943
$650$	0	0
$651$	28.6320	1.12218
$652$	16.0000i	0.626608i
$653$	− 23.4560i	− 0.917904i	−0.888461	−	0.458952i	$-0.848225\pi$
$653$	− 23.4560i	− 0.917904i	0.888461	−	0.458952i	$-0.151775\pi$
$654$	14.7720	0.577631
$655$	0	0
$656$	−5.77200	−0.225359
$657$	6.54400i	0.255306i
$658$	26.3160i	1.02590i
$659$	43.6320	1.69966	0.849831	−	0.527055i	$-0.176704\pi$
$659$	43.6320	1.69966	0.849831	+	0.527055i	$0.176704\pi$
$660$	0	0
$661$	−17.8600	−0.694674	−0.347337	−	0.937740i	$-0.612914\pi$
$661$	−17.8600	−0.694674	−0.347337	+	0.937740i	$0.612914\pi$
$662$	− 34.7720i	− 1.35145i
$663$	2.91199i	0.113092i
$664$	−1.00000	−0.0388075
$665$	0	0
$666$	−6.77200	−0.262410
$667$	3.00000i	0.116160i
$668$	− 16.3160i	− 0.631285i
$669$	−10.0000	−0.386622
$670$	0	0
$671$	−55.0880	−2.12665
$672$	3.00000i	0.115728i
$673$	26.5440i	1.02320i	0.859225	+	0.511598i	$0.170946\pi$
$673$	26.5440i	1.02320i	−0.859225	+	0.511598i	$0.829054\pi$
$674$	4.00000	0.154074
$675$	0	0
$676$	1.22800	0.0472307
$677$	− 48.0000i	− 1.84479i	−0.386248	−	0.922395i	$-0.626229\pi$
$677$	− 48.0000i	− 1.84479i	0.386248	−	0.922395i	$-0.373771\pi$
$678$	4.77200i	0.183268i
$679$	52.6320	2.01983
$680$	0	0
$681$	−10.7720	−0.412784
$682$	55.0880i	2.10943i
$683$	26.6320i	1.01905i	0.860457	+	0.509523i	$0.170178\pi$
$683$	26.6320i	1.01905i	−0.860457	+	0.509523i	$0.829822\pi$
$684$	−7.77200	−0.297170
$685$	0	0
$686$	−15.0000	−0.572703
$687$	− 6.45600i	− 0.246312i
$688$	− 7.77200i	− 0.296305i
$689$	15.0880	0.574807
$690$	0	0
$691$	−39.2280	−1.49230	−0.746152	−	0.665776i	$-0.768101\pi$
$691$	−39.2280	−1.49230	−0.746152	+	0.665776i	$0.768101\pi$
$692$	− 15.7720i	− 0.599562i
$693$	17.3160i	0.657781i
$694$	9.54400	0.362285
$695$	0	0
$696$	−3.00000	−0.113715
$697$	− 4.45600i	− 0.168783i
$698$	− 0.227998i	− 0.00862986i
$699$	2.68399	0.101518
$700$	0	0
$701$	1.54400	0.0583162	0.0291581	−	0.999575i	$-0.490717\pi$
$701$	1.54400	0.0583162	0.0291581	+	0.999575i	$0.490717\pi$
$702$	3.77200i	0.142365i
$703$	− 52.6320i	− 1.98505i
$704$	−5.77200	−0.217541
$705$	0	0
$706$	18.8600	0.709806
$707$	− 42.9480i	− 1.61523i
$708$	− 6.00000i	− 0.225494i
$709$	−24.3160	−0.913207	−0.456603	−	0.889670i	$-0.650934\pi$
$709$	−24.3160	−0.913207	−0.456603	+	0.889670i	$0.650934\pi$
$710$	0	0
$711$	2.22800	0.0835565
$712$	− 16.7720i	− 0.628557i
$713$	9.54400i	0.357426i
$714$	−2.31601	−0.0866743
$715$	0	0
$716$	7.54400	0.281933
$717$	22.7720i	0.850436i
$718$	− 10.2280i	− 0.381705i
$719$	30.3160	1.13060	0.565298	−	0.824887i	$-0.308761\pi$
$719$	30.3160	1.13060	0.565298	+	0.824887i	$0.308761\pi$
$720$	0	0
$721$	−33.0000	−1.22898
$722$	− 41.4040i	− 1.54090i
$723$	26.6320i	0.990455i
$724$	−14.3160	−0.532050
$725$	0	0
$726$	−22.3160	−0.828225
$727$	8.00000i	0.296704i	0.988935	+	0.148352i	$0.0473968\pi$
$727$	8.00000i	0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$	11.3160i	0.419399i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	6.00000	0.221918
$732$	− 9.54400i	− 0.352757i
$733$	− 17.2280i	− 0.636331i	−0.948035	−	0.318165i	$-0.896933\pi$
$733$	− 17.2280i	− 0.636331i	0.948035	−	0.318165i	$-0.103067\pi$
$734$	33.3160	1.22972
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	− 55.0880i	− 2.02919i
$738$	− 5.77200i	− 0.212470i
$739$	−17.2280	−0.633742	−0.316871	−	0.948469i	$-0.602632\pi$
$739$	−17.2280	−0.633742	−0.316871	+	0.948469i	$0.602632\pi$
$740$	0	0
$741$	−29.3160	−1.07695
$742$	12.0000i	0.440534i
$743$	− 20.2280i	− 0.742093i	−0.928614	−	0.371047i	$-0.878999\pi$
$743$	− 20.2280i	− 0.742093i	0.928614	−	0.371047i	$-0.121001\pi$
$744$	−9.54400	−0.349900
$745$	0	0
$746$	12.7720	0.467616
$747$	− 1.00000i	− 0.0365881i
$748$	− 4.45600i	− 0.162927i
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−26.5440	−0.968604	−0.484302	−	0.874901i	$-0.660926\pi$
$751$	−26.5440	−0.968604	−0.484302	+	0.874901i	$0.660926\pi$
$752$	− 8.77200i	− 0.319882i
$753$	3.68399i	0.134252i
$754$	−11.3160	−0.412105
$755$	0	0
$756$	−3.00000	−0.109109
$757$	− 41.2280i	− 1.49846i	−0.662312	−	0.749229i	$-0.730424\pi$
$757$	− 41.2280i	− 1.49846i	0.662312	−	0.749229i	$-0.269576\pi$
$758$	− 23.0880i	− 0.838594i
$759$	−5.77200	−0.209510
$760$	0	0
$761$	−14.8600	−0.538675	−0.269337	−	0.963046i	$-0.586805\pi$
$761$	−14.8600	−0.538675	−0.269337	+	0.963046i	$0.586805\pi$
$762$	− 4.45600i	− 0.161424i
$763$	44.3160i	1.60435i
$764$	7.31601	0.264684
$765$	0	0
$766$	−13.7720	−0.497603
$767$	− 22.6320i	− 0.817195i
$768$	− 1.00000i	− 0.0360844i
$769$	9.08801	0.327722	0.163861	−	0.986483i	$-0.447605\pi$
$769$	9.08801	0.327722	0.163861	+	0.986483i	$0.447605\pi$
$770$	0	0
$771$	−9.08801	−0.327297
$772$	4.77200i	0.171748i
$773$	14.4560i	0.519946i	0.965616	+	0.259973i	$0.0837137\pi$
$773$	14.4560i	0.519946i	−0.965616	+	0.259973i	$0.916286\pi$
$774$	7.77200	0.279359
$775$	0	0
$776$	−17.5440	−0.629793
$777$	− 20.3160i	− 0.728833i
$778$	18.0000i	0.645331i
$779$	44.8600	1.60728
$780$	0	0
$781$	−27.5440	−0.985602
$782$	− 0.772002i	− 0.0276067i
$783$	− 3.00000i	− 0.107211i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	19.0880	0.680847
$787$	21.7720i	0.776088i	0.921641	+	0.388044i	$0.126849\pi$
$787$	21.7720i	0.776088i	−0.921641	+	0.388044i	$0.873151\pi$
$788$	13.0000i	0.463106i
$789$	6.45600	0.229840
$790$	0	0
$791$	−14.3160	−0.509019
$792$	− 5.77200i	− 0.205099i
$793$	− 36.0000i	− 1.27840i
$794$	−14.6320	−0.519271
$795$	0	0
$796$	12.0880	0.428448
$797$	− 2.91199i	− 0.103148i	−0.998669	−	0.0515740i	$-0.983576\pi$
$797$	− 2.91199i	− 0.103148i	0.998669	−	0.0515740i	$-0.0164238\pi$
$798$	− 23.3160i	− 0.825378i
$799$	6.77200	0.239576
$800$	0	0
$801$	16.7720	0.592610
$802$	28.6320i	1.01103i
$803$	− 37.7720i	− 1.33294i
$804$	9.54400	0.336591
$805$	0	0
$806$	−36.0000	−1.26805
$807$	− 26.8600i	− 0.945517i
$808$	14.3160i	0.503635i
$809$	−47.3160	−1.66354	−0.831771	−	0.555119i	$-0.812673\pi$
$809$	−47.3160	−1.66354	−0.831771	+	0.555119i	$0.812673\pi$
$810$	0	0
$811$	−38.6320	−1.35655	−0.678277	−	0.734807i	$-0.737273\pi$
$811$	−38.6320	−1.35655	−0.678277	+	0.734807i	$0.737273\pi$
$812$	− 9.00000i	− 0.315838i
$813$	− 16.0000i	− 0.561144i
$814$	39.0880	1.37003
$815$	0	0
$816$	0.772002	0.0270255
$817$	60.4040i	2.11327i
$818$	− 23.0000i	− 0.804176i
$819$	−11.3160	−0.395413
$820$	0	0
$821$	−12.2280	−0.426760	−0.213380	−	0.976969i	$-0.568447\pi$
$821$	−12.2280	−0.426760	−0.213380	+	0.976969i	$0.568447\pi$
$822$	− 14.7720i	− 0.515233i
$823$	23.5440i	0.820692i	0.911930	+	0.410346i	$0.134592\pi$
$823$	23.5440i	0.820692i	−0.911930	+	0.410346i	$0.865408\pi$
$824$	11.0000	0.383203
$825$	0	0
$826$	18.0000	0.626300
$827$	− 51.6320i	− 1.79542i	−0.440586	−	0.897710i	$-0.645229\pi$
$827$	− 51.6320i	− 1.79542i	0.440586	−	0.897710i	$-0.354771\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	38.4040	1.33383	0.666913	−	0.745135i	$-0.267615\pi$
$829$	38.4040	1.33383	0.666913	+	0.745135i	$0.267615\pi$
$830$	0	0
$831$	−8.22800	−0.285426
$832$	− 3.77200i	− 0.130771i
$833$	− 1.54400i	− 0.0534966i
$834$	−0.772002	−0.0267322
$835$	0	0
$836$	44.8600	1.55152
$837$	− 9.54400i	− 0.329889i
$838$	25.6320i	0.885443i
$839$	−32.4040	−1.11871	−0.559355	−	0.828928i	$-0.688951\pi$
$839$	−32.4040	−1.11871	−0.559355	+	0.828928i	$0.688951\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	− 22.0000i	− 0.758170i
$843$	− 15.8600i	− 0.546248i
$844$	10.3160	0.355092
$845$	0	0
$846$	8.77200	0.301588
$847$	− 66.9480i	− 2.30036i
$848$	− 4.00000i	− 0.137361i
$849$	−28.0000	−0.960958
$850$	0	0
$851$	6.77200	0.232141
$852$	− 4.77200i	− 0.163486i
$853$	− 8.86001i	− 0.303361i	−0.988430	−	0.151680i	$-0.951532\pi$
$853$	− 8.86001i	− 0.303361i	0.988430	−	0.151680i	$-0.0484685\pi$
$854$	28.6320	0.979767
$855$	0	0
$856$	4.00000	0.136717
$857$	6.00000i	0.204956i	0.994735	+	0.102478i	$0.0326771\pi$
$857$	6.00000i	0.204956i	−0.994735	+	0.102478i	$0.967323\pi$
$858$	− 21.7720i	− 0.743284i
$859$	24.4560	0.834428	0.417214	−	0.908808i	$-0.363007\pi$
$859$	24.4560	0.834428	0.417214	+	0.908808i	$0.363007\pi$
$860$	0	0
$861$	17.3160	0.590128
$862$	− 24.6320i	− 0.838970i
$863$	− 2.31601i	− 0.0788377i	−0.999223	−	0.0394189i	$-0.987449\pi$
$863$	− 2.31601i	− 0.0788377i	0.999223	−	0.0394189i	$-0.0125507\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−6.45600	−0.219384
$867$	− 16.4040i	− 0.557109i
$868$	− 28.6320i	− 0.971834i
$869$	−12.8600	−0.436246
$870$	0	0
$871$	36.0000	1.21981
$872$	− 14.7720i	− 0.500243i
$873$	− 17.5440i	− 0.593775i
$874$	7.77200	0.262892
$875$	0	0
$876$	6.54400	0.221101
$877$	47.2640i	1.59599i	0.602662	+	0.797996i	$0.294107\pi$
$877$	47.2640i	1.59599i	−0.602662	+	0.797996i	$0.705893\pi$
$878$	− 12.0000i	− 0.404980i
$879$	9.54400	0.321911
$880$	0	0
$881$	10.4560	0.352271	0.176136	−	0.984366i	$-0.443640\pi$
$881$	10.4560	0.352271	0.176136	+	0.984366i	$0.443640\pi$
$882$	− 2.00000i	− 0.0673435i
$883$	10.7720i	0.362507i	0.983436	+	0.181253i	$0.0580154\pi$
$883$	10.7720i	0.362507i	−0.983436	+	0.181253i	$0.941985\pi$
$884$	2.91199	0.0979409
$885$	0	0
$886$	−24.0000	−0.806296
$887$	− 46.9480i	− 1.57636i	−0.615445	−	0.788180i	$-0.711024\pi$
$887$	− 46.9480i	− 1.57636i	0.615445	−	0.788180i	$-0.288976\pi$
$888$	6.77200i	0.227254i
$889$	13.3680	0.448348
$890$	0	0
$891$	5.77200	0.193369
$892$	10.0000i	0.334825i
$893$	68.1760i	2.28142i
$894$	−11.0880	−0.370838
$895$	0	0
$896$	3.00000	0.100223
$897$	− 3.77200i	− 0.125943i
$898$	− 2.00000i	− 0.0667409i
$899$	28.6320	0.954931
$900$	0	0
$901$	3.08801	0.102876
$902$	33.3160i	1.10930i
$903$	23.3160i	0.775908i
$904$	4.77200	0.158714
$905$	0	0
$906$	−23.5440	−0.782197
$907$	34.4040i	1.14237i	0.820823	+	0.571183i	$0.193515\pi$
$907$	34.4040i	1.14237i	−0.820823	+	0.571183i	$0.806485\pi$
$908$	10.7720i	0.357481i
$909$	−14.3160	−0.474832
$910$	0	0
$911$	5.77200	0.191235	0.0956175	−	0.995418i	$-0.469517\pi$
$911$	5.77200	0.191235	0.0956175	+	0.995418i	$0.469517\pi$
$912$	7.77200i	0.257357i
$913$	5.77200i	0.191025i
$914$	−30.6320	−1.01322
$915$	0	0
$916$	−6.45600	−0.213312
$917$	57.2640i	1.89102i
$918$	0.772002i	0.0254799i
$919$	−20.3160	−0.670163	−0.335082	−	0.942189i	$-0.608764\pi$
$919$	−20.3160	−0.670163	−0.335082	+	0.942189i	$0.608764\pi$
$920$	0	0
$921$	−20.3160	−0.669435
$922$	− 12.5440i	− 0.413115i
$923$	− 18.0000i	− 0.592477i
$924$	17.3160	0.569655
$925$	0	0
$926$	−0.911993	−0.0299699
$927$	11.0000i	0.361287i
$928$	3.00000i	0.0984798i
$929$	−24.6840	−0.809856	−0.404928	−	0.914349i	$-0.632703\pi$
$929$	−24.6840	−0.809856	−0.404928	+	0.914349i	$0.632703\pi$
$930$	0	0
$931$	15.5440	0.509434
$932$	− 2.68399i	− 0.0879172i
$933$	17.8600i	0.584710i
$934$	18.5440	0.606778
$935$	0	0
$936$	3.77200	0.123292
$937$	8.63201i	0.281996i	0.990010	+	0.140998i	$0.0450310\pi$
$937$	8.63201i	0.281996i	−0.990010	+	0.140998i	$0.954969\pi$
$938$	28.6320i	0.934868i
$939$	8.00000	0.261070
$940$	0	0
$941$	20.6320	0.672584	0.336292	−	0.941758i	$-0.390827\pi$
$941$	20.6320	0.672584	0.336292	+	0.941758i	$0.390827\pi$
$942$	− 13.5440i	− 0.441287i
$943$	5.77200i	0.187962i
$944$	−6.00000	−0.195283
$945$	0	0
$946$	−44.8600	−1.45852
$947$	31.0880i	1.01022i	0.863054	+	0.505112i	$0.168549\pi$
$947$	31.0880i	1.01022i	−0.863054	+	0.505112i	$0.831451\pi$
$948$	− 2.22800i	− 0.0723620i
$949$	24.6840	0.801276
$950$	0	0
$951$	−9.00000	−0.291845
$952$	2.31601i	0.0750622i
$953$	46.7720i	1.51509i	0.652781	+	0.757547i	$0.273602\pi$
$953$	46.7720i	1.51509i	−0.652781	+	0.757547i	$0.726398\pi$
$954$	4.00000	0.129505
$955$	0	0
$956$	22.7720	0.736499
$957$	17.3160i	0.559747i
$958$	− 35.3160i	− 1.14101i
$959$	44.3160	1.43104
$960$	0	0
$961$	60.0880	1.93832
$962$	25.5440i	0.823572i
$963$	4.00000i	0.128898i
$964$	26.6320	0.857759
$965$	0	0
$966$	3.00000	0.0965234
$967$	8.63201i	0.277587i	0.990321	+	0.138793i	$0.0443224\pi$
$967$	8.63201i	0.277587i	−0.990321	+	0.138793i	$0.955678\pi$
$968$	22.3160i	0.717264i
$969$	−6.00000	−0.192748
$970$	0	0
$971$	−31.6320	−1.01512	−0.507560	−	0.861617i	$-0.669452\pi$
$971$	−31.6320	−1.01512	−0.507560	+	0.861617i	$0.669452\pi$
$972$	1.00000i	0.0320750i
$973$	− 2.31601i	− 0.0742477i
$974$	12.4560	0.399116
$975$	0	0
$976$	−9.54400	−0.305496
$977$	− 60.3160i	− 1.92968i	−0.262838	−	0.964840i	$-0.584658\pi$
$977$	− 60.3160i	− 1.92968i	0.262838	−	0.964840i	$-0.415342\pi$
$978$	16.0000i	0.511624i
$979$	−96.8080	−3.09400
$980$	0	0
$981$	14.7720	0.471634
$982$	10.4560i	0.333664i
$983$	− 8.40401i	− 0.268046i	−0.990978	−	0.134023i	$-0.957210\pi$
$983$	− 8.40401i	− 0.268046i	0.990978	−	0.134023i	$-0.0427897\pi$
$984$	−5.77200	−0.184005
$985$	0	0
$986$	−2.31601	−0.0737566
$987$	26.3160i	0.837648i
$988$	29.3160i	0.932666i
$989$	−7.77200	−0.247135
$990$	0	0
$991$	30.1760	0.958573	0.479286	−	0.877659i	$-0.340896\pi$
$991$	30.1760	0.958573	0.479286	+	0.877659i	$0.340896\pi$
$992$	9.54400i	0.303022i
$993$	− 34.7720i	− 1.10346i
$994$	14.3160	0.454076
$995$	0	0
$996$	−1.00000	−0.0316862
$997$	− 0.227998i	− 0.00722077i	−0.999993	−	0.00361039i	$-0.998851\pi$
$997$	− 0.227998i	− 0.00722077i	0.999993	−	0.00361039i	$-0.00114922\pi$
$998$	− 9.68399i	− 0.306541i
$999$	−6.77200	−0.214257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.w.2899.2		4
5.2	odd	4		3450.2.a.bj.1.2	yes	2
5.3	odd	4		3450.2.a.bh.1.2	✓	2
5.4	even	2	inner	3450.2.d.w.2899.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bh.1.2	✓	2	5.3	odd	4
3450.2.a.bj.1.2	yes	2	5.2	odd	4
3450.2.d.w.2899.2		4	1.1	even	1	trivial
3450.2.d.w.2899.4		4	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +5.77200 q^{11} +1.00000i q^{12} +3.77200i q^{13} -3.00000 q^{14} +1.00000 q^{16} +0.772002i q^{17} +1.00000i q^{18} -7.77200 q^{19} -3.00000 q^{21} -5.77200i q^{22} -1.00000i q^{23} +1.00000 q^{24} +3.77200 q^{26} +1.00000i q^{27} +3.00000i q^{28} -3.00000 q^{29} -9.54400 q^{31} -1.00000i q^{32} -5.77200i q^{33} +0.772002 q^{34} +1.00000 q^{36} +6.77200i q^{37} +7.77200i q^{38} +3.77200 q^{39} -5.77200 q^{41} +3.00000i q^{42} -7.77200i q^{43} -5.77200 q^{44} -1.00000 q^{46} -8.77200i q^{47} -1.00000i q^{48} -2.00000 q^{49} +0.772002 q^{51} -3.77200i q^{52} -4.00000i q^{53} +1.00000 q^{54} +3.00000 q^{56} +7.77200i q^{57} +3.00000i q^{58} -6.00000 q^{59} -9.54400 q^{61} +9.54400i q^{62} +3.00000i q^{63} -1.00000 q^{64} -5.77200 q^{66} -9.54400i q^{67} -0.772002i q^{68} -1.00000 q^{69} -4.77200 q^{71} -1.00000i q^{72} -6.54400i q^{73} +6.77200 q^{74} +7.77200 q^{76} -17.3160i q^{77} -3.77200i q^{78} -2.22800 q^{79} +1.00000 q^{81} +5.77200i q^{82} +1.00000i q^{83} +3.00000 q^{84} -7.77200 q^{86} +3.00000i q^{87} +5.77200i q^{88} -16.7720 q^{89} +11.3160 q^{91} +1.00000i q^{92} +9.54400i q^{93} -8.77200 q^{94} -1.00000 q^{96} +17.5440i q^{97} +2.00000i q^{98} -5.77200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 6 q^{11} - 12 q^{14} + 4 q^{16} - 14 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} - 4 q^{31} - 14 q^{34} + 4 q^{36} - 2 q^{39} - 6 q^{41} - 6 q^{44} - 4 q^{46} - 8 q^{49} - 14 q^{51} + 4 q^{54} + 12 q^{56} - 24 q^{59} - 4 q^{61} - 4 q^{64} - 6 q^{66} - 4 q^{69} - 2 q^{71} + 10 q^{74} + 14 q^{76} - 26 q^{79} + 4 q^{81} + 12 q^{84} - 14 q^{86} - 50 q^{89} - 6 q^{91} - 18 q^{94} - 4 q^{96} - 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 6 * q^11 - 12 * q^14 + 4 * q^16 - 14 * q^19 - 12 * q^21 + 4 * q^24 - 2 * q^26 - 12 * q^29 - 4 * q^31 - 14 * q^34 + 4 * q^36 - 2 * q^39 - 6 * q^41 - 6 * q^44 - 4 * q^46 - 8 * q^49 - 14 * q^51 + 4 * q^54 + 12 * q^56 - 24 * q^59 - 4 * q^61 - 4 * q^64 - 6 * q^66 - 4 * q^69 - 2 * q^71 + 10 * q^74 + 14 * q^76 - 26 * q^79 + 4 * q^81 + 12 * q^84 - 14 * q^86 - 50 * q^89 - 6 * q^91 - 18 * q^94 - 4 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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