LMFDB - Embedded newform 3450.2.d.w.2899.1

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			2899.1
Root			$3.77200i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.w.2899.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -2.77200 q^{11} +1.00000i q^{12} -4.77200i q^{13} -3.00000 q^{14} +1.00000 q^{16} -7.77200i q^{17} +1.00000i q^{18} +0.772002 q^{19} -3.00000 q^{21} +2.77200i q^{22} -1.00000i q^{23} +1.00000 q^{24} -4.77200 q^{26} +1.00000i q^{27} +3.00000i q^{28} -3.00000 q^{29} +7.54400 q^{31} -1.00000i q^{32} +2.77200i q^{33} -7.77200 q^{34} +1.00000 q^{36} -1.77200i q^{37} -0.772002i q^{38} -4.77200 q^{39} +2.77200 q^{41} +3.00000i q^{42} +0.772002i q^{43} +2.77200 q^{44} -1.00000 q^{46} -0.227998i q^{47} -1.00000i q^{48} -2.00000 q^{49} -7.77200 q^{51} +4.77200i q^{52} -4.00000i q^{53} +1.00000 q^{54} +3.00000 q^{56} -0.772002i q^{57} +3.00000i q^{58} -6.00000 q^{59} +7.54400 q^{61} -7.54400i q^{62} +3.00000i q^{63} -1.00000 q^{64} +2.77200 q^{66} +7.54400i q^{67} +7.77200i q^{68} -1.00000 q^{69} +3.77200 q^{71} -1.00000i q^{72} +10.5440i q^{73} -1.77200 q^{74} -0.772002 q^{76} +8.31601i q^{77} +4.77200i q^{78} -10.7720 q^{79} +1.00000 q^{81} -2.77200i q^{82} +1.00000i q^{83} +3.00000 q^{84} +0.772002 q^{86} +3.00000i q^{87} -2.77200i q^{88} -8.22800 q^{89} -14.3160 q^{91} +1.00000i q^{92} -7.54400i q^{93} -0.227998 q^{94} -1.00000 q^{96} +0.455996i q^{97} +2.00000i q^{98} +2.77200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	−2.77200	−0.835790	−0.417895	−	0.908495i	$-0.637232\pi$
$11$	−2.77200	−0.835790	−0.417895	+	0.908495i	$0.637232\pi$
$12$	1.00000i	0.288675i
$13$	− 4.77200i	− 1.32352i	−0.749718	−	0.661758i	$-0.769811\pi$
$13$	− 4.77200i	− 1.32352i	0.749718	−	0.661758i	$-0.230189\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	− 7.77200i	− 1.88499i	−0.334224	−	0.942494i	$-0.608474\pi$
$17$	− 7.77200i	− 1.88499i	0.334224	−	0.942494i	$-0.391526\pi$
$18$	1.00000i	0.235702i
$19$	0.772002	0.177109	0.0885547	−	0.996071i	$-0.471775\pi$
$19$	0.772002	0.177109	0.0885547	+	0.996071i	$0.471775\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	2.77200i	0.590993i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	1.00000	0.204124
$25$	0	0
$26$	−4.77200	−0.935867
$27$	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
$31$	7.54400	1.35494	0.677472	−	0.735549i	$-0.263076\pi$
$31$	7.54400	1.35494	0.677472	+	0.735549i	$0.263076\pi$
$32$	− 1.00000i	− 0.176777i
$33$	2.77200i	0.482544i
$34$	−7.77200	−1.33289
$35$	0	0
$36$	1.00000	0.166667
$37$	− 1.77200i	− 0.291315i	−0.989335	−	0.145658i	$-0.953470\pi$
$37$	− 1.77200i	− 0.291315i	0.989335	−	0.145658i	$-0.0465298\pi$
$38$	− 0.772002i	− 0.125235i
$39$	−4.77200	−0.764132
$40$	0	0
$41$	2.77200	0.432914	0.216457	−	0.976292i	$-0.430550\pi$
$41$	2.77200	0.432914	0.216457	+	0.976292i	$0.430550\pi$
$42$	3.00000i	0.462910i
$43$	0.772002i	0.117729i	0.998266	+	0.0588646i	$0.0187480\pi$
$43$	0.772002i	0.117729i	−0.998266	+	0.0588646i	$0.981252\pi$
$44$	2.77200	0.417895
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 0.227998i	− 0.0332569i	−0.999862	−	0.0166285i	$-0.994707\pi$
$47$	− 0.227998i	− 0.0332569i	0.999862	−	0.0166285i	$-0.00529325\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	−7.77200	−1.08830
$52$	4.77200i	0.661758i
$53$	− 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
$57$	− 0.772002i	− 0.102254i
$58$	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
$61$	7.54400	0.965911	0.482955	−	0.875645i	$-0.339563\pi$
$61$	7.54400	0.965911	0.482955	+	0.875645i	$0.339563\pi$
$62$	− 7.54400i	− 0.958089i
$63$	3.00000i	0.377964i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.77200	0.341210
$67$	7.54400i	0.921647i	0.887492	+	0.460823i	$0.152446\pi$
$67$	7.54400i	0.921647i	−0.887492	+	0.460823i	$0.847554\pi$
$68$	7.77200i	0.942494i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	3.77200	0.447654	0.223827	−	0.974629i	$-0.428145\pi$
$71$	3.77200	0.447654	0.223827	+	0.974629i	$0.428145\pi$
$72$	− 1.00000i	− 0.117851i
$73$	10.5440i	1.23408i	0.786931	+	0.617041i	$0.211669\pi$
$73$	10.5440i	1.23408i	−0.786931	+	0.617041i	$0.788331\pi$
$74$	−1.77200	−0.205991
$75$	0	0
$76$	−0.772002	−0.0885547
$77$	8.31601i	0.947697i
$78$	4.77200i	0.540323i
$79$	−10.7720	−1.21194	−0.605972	−	0.795486i	$-0.707216\pi$
$79$	−10.7720	−1.21194	−0.605972	+	0.795486i	$0.707216\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 2.77200i	− 0.306116i
$83$	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
$86$	0.772002	0.0832471
$87$	3.00000i	0.321634i
$88$	− 2.77200i	− 0.295496i
$89$	−8.22800	−0.872166	−0.436083	−	0.899906i	$-0.643635\pi$
$89$	−8.22800	−0.872166	−0.436083	+	0.899906i	$0.643635\pi$
$90$	0	0
$91$	−14.3160	−1.50073
$92$	1.00000i	0.104257i
$93$	− 7.54400i	− 0.782277i
$94$	−0.227998	−0.0235162
$95$	0	0
$96$	−1.00000	−0.102062
$97$	0.455996i	0.0462994i	0.999732	+	0.0231497i	$0.00736944\pi$
$97$	0.455996i	0.0462994i	−0.999732	+	0.0231497i	$0.992631\pi$
$98$	2.00000i	0.202031i
$99$	2.77200	0.278597
$100$	0	0
$101$	−11.3160	−1.12598	−0.562992	−	0.826462i	$-0.690350\pi$
$101$	−11.3160	−1.12598	−0.562992	+	0.826462i	$0.690350\pi$
$102$	7.77200i	0.769543i
$103$	− 11.0000i	− 1.08386i	−0.840423	−	0.541931i	$-0.817693\pi$
$103$	− 11.0000i	− 1.08386i	0.840423	−	0.541931i	$-0.182307\pi$
$104$	4.77200	0.467933
$105$	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
$109$	−6.22800	−0.596534	−0.298267	−	0.954482i	$-0.596409\pi$
$109$	−6.22800	−0.596534	−0.298267	+	0.954482i	$0.596409\pi$
$110$	0	0
$111$	−1.77200	−0.168191
$112$	− 3.00000i	− 0.283473i
$113$	3.77200i	0.354840i	0.984135	+	0.177420i	$0.0567751\pi$
$113$	3.77200i	0.354840i	−0.984135	+	0.177420i	$0.943225\pi$
$114$	−0.772002	−0.0723046
$115$	0	0
$116$	3.00000	0.278543
$117$	4.77200i	0.441172i
$118$	6.00000i	0.552345i
$119$	−23.3160	−2.13737
$120$	0	0
$121$	−3.31601	−0.301455
$122$	− 7.54400i	− 0.683002i
$123$	− 2.77200i	− 0.249943i
$124$	−7.54400	−0.677472
$125$	0	0
$126$	3.00000	0.267261
$127$	21.5440i	1.91172i	0.293821	+	0.955861i	$0.405073\pi$
$127$	21.5440i	1.91172i	−0.293821	+	0.955861i	$0.594927\pi$
$128$	1.00000i	0.0883883i
$129$	0.772002	0.0679710
$130$	0	0
$131$	15.0880	1.31825	0.659123	−	0.752035i	$-0.270928\pi$
$131$	15.0880	1.31825	0.659123	+	0.752035i	$0.270928\pi$
$132$	− 2.77200i	− 0.241272i
$133$	− 2.31601i	− 0.200823i
$134$	7.54400	0.651703
$135$	0	0
$136$	7.77200	0.666444
$137$	6.22800i	0.532094i	0.963960	+	0.266047i	$0.0857176\pi$
$137$	6.22800i	0.532094i	−0.963960	+	0.266047i	$0.914282\pi$
$138$	1.00000i	0.0851257i
$139$	−7.77200	−0.659213	−0.329606	−	0.944118i	$-0.606916\pi$
$139$	−7.77200	−0.659213	−0.329606	+	0.944118i	$0.606916\pi$
$140$	0	0
$141$	−0.227998	−0.0192009
$142$	− 3.77200i	− 0.316539i
$143$	13.2280i	1.10618i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	10.5440	0.872628
$147$	2.00000i	0.164957i
$148$	1.77200i	0.145658i
$149$	−23.0880	−1.89144	−0.945722	−	0.324978i	$-0.894643\pi$
$149$	−23.0880	−1.89144	−0.945722	+	0.324978i	$0.894643\pi$
$150$	0	0
$151$	6.45600	0.525382	0.262691	−	0.964880i	$-0.415390\pi$
$151$	6.45600	0.525382	0.262691	+	0.964880i	$0.415390\pi$
$152$	0.772002i	0.0626176i
$153$	7.77200i	0.628329i
$154$	8.31601	0.670123
$155$	0	0
$156$	4.77200	0.382066
$157$	− 3.54400i	− 0.282842i	−0.989950	−	0.141421i	$-0.954833\pi$
$157$	− 3.54400i	− 0.282842i	0.989950	−	0.141421i	$-0.0451672\pi$
$158$	10.7720i	0.856974i
$159$	−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	$-0.215557\pi$
$164$	−2.77200	−0.216457
$165$	0	0
$166$	1.00000	0.0776151
$167$	− 9.31601i	− 0.720894i	−0.932780	−	0.360447i	$-0.882624\pi$
$167$	− 9.31601i	− 0.720894i	0.932780	−	0.360447i	$-0.117376\pi$
$168$	− 3.00000i	− 0.231455i
$169$	−9.77200	−0.751692
$170$	0	0
$171$	−0.772002	−0.0590365
$172$	− 0.772002i	− 0.0588646i
$173$	7.22800i	0.549535i	0.961511	+	0.274767i	$0.0886008\pi$
$173$	7.22800i	0.549535i	−0.961511	+	0.274767i	$0.911399\pi$
$174$	3.00000	0.227429
$175$	0	0
$176$	−2.77200	−0.208948
$177$	6.00000i	0.450988i
$178$	8.22800i	0.616715i
$179$	9.54400	0.713352	0.356676	−	0.934228i	$-0.383910\pi$
$179$	9.54400	0.713352	0.356676	+	0.934228i	$0.383910\pi$
$180$	0	0
$181$	−11.3160	−0.841112	−0.420556	−	0.907267i	$-0.638165\pi$
$181$	−11.3160	−0.841112	−0.420556	+	0.907267i	$0.638165\pi$
$182$	14.3160i	1.06117i
$183$	− 7.54400i	− 0.557669i
$184$	1.00000	0.0737210
$185$	0	0
$186$	−7.54400	−0.553153
$187$	21.5440i	1.57545i
$188$	0.227998i	0.0166285i
$189$	3.00000	0.218218
$190$	0	0
$191$	18.3160	1.32530	0.662650	−	0.748929i	$-0.269432\pi$
$191$	18.3160	1.32530	0.662650	+	0.748929i	$0.269432\pi$
$192$	1.00000i	0.0721688i
$193$	3.77200i	0.271515i	0.990742	+	0.135757i	$0.0433467\pi$
$193$	3.77200i	0.271515i	−0.990742	+	0.135757i	$0.956653\pi$
$194$	0.455996	0.0327386
$195$	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	$-0.153265\pi$
$198$	− 2.77200i	− 0.196998i
$199$	22.0880	1.56578	0.782889	−	0.622162i	$-0.213745\pi$
$199$	22.0880	1.56578	0.782889	+	0.622162i	$0.213745\pi$
$200$	0	0
$201$	7.54400	0.532113
$202$	11.3160i	0.796191i
$203$	9.00000i	0.631676i
$204$	7.77200	0.544149
$205$	0	0
$206$	−11.0000	−0.766406
$207$	1.00000i	0.0695048i
$208$	− 4.77200i	− 0.330879i
$209$	−2.13999	−0.148026
$210$	0	0
$211$	15.3160	1.05440	0.527199	−	0.849742i	$-0.323242\pi$
$211$	15.3160	1.05440	0.527199	+	0.849742i	$0.323242\pi$
$212$	4.00000i	0.274721i
$213$	− 3.77200i	− 0.258453i
$214$	−4.00000	−0.273434
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	− 22.6320i	− 1.53636i
$218$	6.22800i	0.421813i
$219$	10.5440	0.712498
$220$	0	0
$221$	−37.0880	−2.49481
$222$	1.77200i	0.118929i
$223$	− 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
$226$	3.77200	0.250910
$227$	− 2.22800i	− 0.147877i	−0.997263	−	0.0739387i	$-0.976443\pi$
$227$	− 2.22800i	− 0.147877i	0.997263	−	0.0739387i	$-0.0235569\pi$
$228$	0.772002i	0.0511271i
$229$	23.5440	1.55583	0.777916	−	0.628369i	$-0.216277\pi$
$229$	23.5440	1.55583	0.777916	+	0.628369i	$0.216277\pi$
$230$	0	0
$231$	8.31601	0.547153
$232$	− 3.00000i	− 0.196960i
$233$	28.3160i	1.85504i	0.373770	+	0.927522i	$0.378065\pi$
$233$	28.3160i	1.85504i	−0.373770	+	0.927522i	$0.621935\pi$
$234$	4.77200	0.311956
$235$	0	0
$236$	6.00000	0.390567
$237$	10.7720i	0.699717i
$238$	23.3160i	1.51135i
$239$	−14.2280	−0.920333	−0.460166	−	0.887833i	$-0.652210\pi$
$239$	−14.2280	−0.920333	−0.460166	+	0.887833i	$0.652210\pi$
$240$	0	0
$241$	24.6320	1.58669	0.793344	−	0.608774i	$-0.208338\pi$
$241$	24.6320	1.58669	0.793344	+	0.608774i	$0.208338\pi$
$242$	3.31601i	0.213161i
$243$	− 1.00000i	− 0.0641500i
$244$	−7.54400	−0.482955
$245$	0	0
$246$	−2.77200	−0.176736
$247$	− 3.68399i	− 0.234407i
$248$	7.54400i	0.479045i
$249$	1.00000	0.0633724
$250$	0	0
$251$	−29.3160	−1.85041	−0.925205	−	0.379468i	$-0.876107\pi$
$251$	−29.3160	−1.85041	−0.925205	+	0.379468i	$0.876107\pi$
$252$	− 3.00000i	− 0.188982i
$253$	2.77200i	0.174274i
$254$	21.5440	1.35179
$255$	0	0
$256$	1.00000	0.0625000
$257$	25.0880i	1.56495i	0.622684	+	0.782473i	$0.286042\pi$
$257$	25.0880i	1.56495i	−0.622684	+	0.782473i	$0.713958\pi$
$258$	− 0.772002i	− 0.0480627i
$259$	−5.31601	−0.330321
$260$	0	0
$261$	3.00000	0.185695
$262$	− 15.0880i	− 0.932140i
$263$	23.5440i	1.45179i	0.687808	+	0.725893i	$0.258573\pi$
$263$	23.5440i	1.45179i	−0.687808	+	0.725893i	$0.741427\pi$
$264$	−2.77200	−0.170605
$265$	0	0
$266$	−2.31601	−0.142003
$267$	8.22800i	0.503545i
$268$	− 7.54400i	− 0.460823i
$269$	−15.8600	−0.967002	−0.483501	−	0.875344i	$-0.660635\pi$
$269$	−15.8600	−0.967002	−0.483501	+	0.875344i	$0.660635\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	− 7.77200i	− 0.471247i
$273$	14.3160i	0.866444i
$274$	6.22800	0.376247
$275$	0	0
$276$	1.00000	0.0601929
$277$	− 16.7720i	− 1.00773i	−0.863782	−	0.503866i	$-0.831911\pi$
$277$	− 16.7720i	− 1.00773i	0.863782	−	0.503866i	$-0.168089\pi$
$278$	7.77200i	0.466134i
$279$	−7.54400	−0.451648
$280$	0	0
$281$	−26.8600	−1.60233	−0.801167	−	0.598441i	$-0.795787\pi$
$281$	−26.8600	−1.60233	−0.801167	+	0.598441i	$0.795787\pi$
$282$	0.227998i	0.0135771i
$283$	− 28.0000i	− 1.66443i	−0.554455	−	0.832214i	$-0.687073\pi$
$283$	− 28.0000i	− 1.66443i	0.554455	−	0.832214i	$-0.312927\pi$
$284$	−3.77200	−0.223827
$285$	0	0
$286$	13.2280	0.782188
$287$	− 8.31601i	− 0.490878i
$288$	1.00000i	0.0589256i
$289$	−43.4040	−2.55318
$290$	0	0
$291$	0.455996	0.0267310
$292$	− 10.5440i	− 0.617041i
$293$	− 7.54400i	− 0.440725i	−0.975418	−	0.220363i	$-0.929276\pi$
$293$	− 7.54400i	− 0.440725i	0.975418	−	0.220363i	$-0.0707241\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	1.77200	0.102996
$297$	− 2.77200i	− 0.160848i
$298$	23.0880i	1.33745i
$299$	−4.77200	−0.275972
$300$	0	0
$301$	2.31601	0.133492
$302$	− 6.45600i	− 0.371501i
$303$	11.3160i	0.650088i
$304$	0.772002	0.0442773
$305$	0	0
$306$	7.77200	0.444296
$307$	5.31601i	0.303400i	0.988427	+	0.151700i	$0.0484748\pi$
$307$	5.31601i	0.303400i	−0.988427	+	0.151700i	$0.951525\pi$
$308$	− 8.31601i	− 0.473848i
$309$	−11.0000	−0.625768
$310$	0	0
$311$	24.8600	1.40968	0.704841	−	0.709365i	$-0.251018\pi$
$311$	24.8600	1.40968	0.704841	+	0.709365i	$0.251018\pi$
$312$	− 4.77200i	− 0.270161i
$313$	8.00000i	0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$	8.00000i	0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	−3.54400	−0.200000
$315$	0	0
$316$	10.7720	0.605972
$317$	− 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
$319$	8.31601	0.465607
$320$	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
$327$	6.22800i	0.344409i
$328$	2.77200i	0.153058i
$329$	−0.683994	−0.0377098
$330$	0	0
$331$	26.2280	1.44162	0.720811	−	0.693132i	$-0.243770\pi$
$331$	26.2280	1.44162	0.720811	+	0.693132i	$0.243770\pi$
$332$	− 1.00000i	− 0.0548821i
$333$	1.77200i	0.0971051i
$334$	−9.31601	−0.509749
$335$	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	$0.965252\pi$
$338$	9.77200i	0.531527i
$339$	3.77200	0.204867
$340$	0	0
$341$	−20.9120	−1.13245
$342$	0.772002i	0.0417451i
$343$	− 15.0000i	− 0.809924i
$344$	−0.772002	−0.0416236
$345$	0	0
$346$	7.22800	0.388580
$347$	− 7.54400i	− 0.404983i	−0.979284	−	0.202492i	$-0.935096\pi$
$347$	− 7.54400i	− 0.404983i	0.979284	−	0.202492i	$-0.0649039\pi$
$348$	− 3.00000i	− 0.160817i
$349$	8.77200	0.469554	0.234777	−	0.972049i	$-0.424564\pi$
$349$	8.77200	0.469554	0.234777	+	0.972049i	$0.424564\pi$
$350$	0	0
$351$	4.77200	0.254711
$352$	2.77200i	0.147748i
$353$	− 23.8600i	− 1.26994i	−0.772537	−	0.634970i	$-0.781012\pi$
$353$	− 23.8600i	− 1.26994i	0.772537	−	0.634970i	$-0.218988\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	8.22800	0.436083
$357$	23.3160i	1.23401i
$358$	− 9.54400i	− 0.504416i
$359$	18.7720	0.990748	0.495374	−	0.868680i	$-0.335031\pi$
$359$	18.7720	0.990748	0.495374	+	0.868680i	$0.335031\pi$
$360$	0	0
$361$	−18.4040	−0.968632
$362$	11.3160i	0.594756i
$363$	3.31601i	0.174045i
$364$	14.3160	0.750363
$365$	0	0
$366$	−7.54400	−0.394331
$367$	7.68399i	0.401101i	0.979683	+	0.200551i	$0.0642731\pi$
$367$	7.68399i	0.401101i	−0.979683	+	0.200551i	$0.935727\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	−2.77200	−0.144305
$370$	0	0
$371$	−12.0000	−0.623009
$372$	7.54400i	0.391138i
$373$	4.22800i	0.218917i	0.993991	+	0.109459i	$0.0349117\pi$
$373$	4.22800i	0.218917i	−0.993991	+	0.109459i	$0.965088\pi$
$374$	21.5440	1.11401
$375$	0	0
$376$	0.227998	0.0117581
$377$	14.3160i	0.737312i
$378$	− 3.00000i	− 0.154303i
$379$	−11.0880	−0.569553	−0.284776	−	0.958594i	$-0.591919\pi$
$379$	−11.0880	−0.569553	−0.284776	+	0.958594i	$0.591919\pi$
$380$	0	0
$381$	21.5440	1.10373
$382$	− 18.3160i	− 0.937128i
$383$	− 5.22800i	− 0.267138i	−0.991040	−	0.133569i	$-0.957356\pi$
$383$	− 5.22800i	− 0.267138i	0.991040	−	0.133569i	$-0.0426438\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	3.77200	0.191990
$387$	− 0.772002i	− 0.0392431i
$388$	− 0.455996i	− 0.0231497i
$389$	−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
$391$	−7.77200	−0.393047
$392$	− 2.00000i	− 0.101015i
$393$	− 15.0880i	− 0.761089i
$394$	−13.0000	−0.654931
$395$	0	0
$396$	−2.77200	−0.139298
$397$	36.6320i	1.83851i	0.393665	+	0.919254i	$0.371207\pi$
$397$	36.6320i	1.83851i	−0.393665	+	0.919254i	$0.628793\pi$
$398$	− 22.0880i	− 1.10717i
$399$	−2.31601	−0.115945
$400$	0	0
$401$	22.6320	1.13019	0.565094	−	0.825026i	$-0.308840\pi$
$401$	22.6320	1.13019	0.565094	+	0.825026i	$0.308840\pi$
$402$	− 7.54400i	− 0.376261i
$403$	− 36.0000i	− 1.79329i
$404$	11.3160	0.562992
$405$	0	0
$406$	9.00000	0.446663
$407$	4.91199i	0.243478i
$408$	− 7.77200i	− 0.384771i
$409$	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
$411$	6.22800	0.307204
$412$	11.0000i	0.541931i
$413$	18.0000i	0.885722i
$414$	1.00000	0.0491473
$415$	0	0
$416$	−4.77200	−0.233967
$417$	7.77200i	0.380597i
$418$	2.13999i	0.104670i
$419$	25.6320	1.25221	0.626103	−	0.779740i	$-0.284649\pi$
$419$	25.6320	1.25221	0.626103	+	0.779740i	$0.284649\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	− 15.3160i	− 0.745571i
$423$	0.227998i	0.0110856i
$424$	4.00000	0.194257
$425$	0	0
$426$	−3.77200	−0.182754
$427$	− 22.6320i	− 1.09524i
$428$	4.00000i	0.193347i
$429$	13.2280	0.638654
$430$	0	0
$431$	−26.6320	−1.28282	−0.641409	−	0.767199i	$-0.721650\pi$
$431$	−26.6320	−1.28282	−0.641409	+	0.767199i	$0.721650\pi$
$432$	1.00000i	0.0481125i
$433$	− 23.5440i	− 1.13145i	−0.824593	−	0.565726i	$-0.808596\pi$
$433$	− 23.5440i	− 1.13145i	0.824593	−	0.565726i	$-0.191404\pi$
$434$	−22.6320	−1.08637
$435$	0	0
$436$	6.22800	0.298267
$437$	− 0.772002i	− 0.0369299i
$438$	− 10.5440i	− 0.503812i
$439$	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
$442$	37.0880i	1.76410i
$443$	− 24.0000i	− 1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$	− 24.0000i	− 1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$	1.77200	0.0840955
$445$	0	0
$446$	−10.0000	−0.473514
$447$	23.0880i	1.09203i
$448$	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
$451$	−7.68399	−0.361825
$452$	− 3.77200i	− 0.177420i
$453$	− 6.45600i	− 0.303329i
$454$	−2.22800	−0.104565
$455$	0	0
$456$	0.772002	0.0361523
$457$	20.6320i	0.965125i	0.875862	+	0.482562i	$0.160294\pi$
$457$	20.6320i	0.965125i	−0.875862	+	0.482562i	$0.839706\pi$
$458$	− 23.5440i	− 1.10014i
$459$	7.77200	0.362766
$460$	0	0
$461$	−4.54400	−0.211635	−0.105818	−	0.994386i	$-0.533746\pi$
$461$	−4.54400	−0.211635	−0.105818	+	0.994386i	$0.533746\pi$
$462$	− 8.31601i	− 0.386896i
$463$	− 35.0880i	− 1.63068i	−0.578984	−	0.815339i	$-0.696551\pi$
$463$	− 35.0880i	− 1.63068i	0.578984	−	0.815339i	$-0.303449\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	28.3160	1.31171
$467$	1.45600i	0.0673755i	0.999432	+	0.0336877i	$0.0107252\pi$
$467$	1.45600i	0.0673755i	−0.999432	+	0.0336877i	$0.989275\pi$
$468$	− 4.77200i	− 0.220586i
$469$	22.6320	1.04505
$470$	0	0
$471$	−3.54400	−0.163299
$472$	− 6.00000i	− 0.276172i
$473$	− 2.13999i	− 0.0983969i
$474$	10.7720	0.494774
$475$	0	0
$476$	23.3160	1.06869
$477$	4.00000i	0.183147i
$478$	14.2280i	0.650773i
$479$	9.68399	0.442473	0.221236	−	0.975220i	$-0.428991\pi$
$479$	9.68399	0.442473	0.221236	+	0.975220i	$0.428991\pi$
$480$	0	0
$481$	−8.45600	−0.385560
$482$	− 24.6320i	− 1.12196i
$483$	3.00000i	0.136505i
$484$	3.31601	0.150728
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	29.5440i	1.33877i	0.742917	+	0.669383i	$0.233442\pi$
$487$	29.5440i	1.33877i	−0.742917	+	0.669383i	$0.766558\pi$
$488$	7.54400i	0.341501i
$489$	−16.0000	−0.723545
$490$	0	0
$491$	−27.5440	−1.24304	−0.621522	−	0.783397i	$-0.713485\pi$
$491$	−27.5440	−1.24304	−0.621522	+	0.783397i	$0.713485\pi$
$492$	2.77200i	0.124971i
$493$	23.3160i	1.05010i
$494$	−3.68399	−0.165751
$495$	0	0
$496$	7.54400	0.338736
$497$	− 11.3160i	− 0.507592i
$498$	− 1.00000i	− 0.0448111i
$499$	35.3160	1.58096	0.790481	−	0.612487i	$-0.209831\pi$
$499$	35.3160	1.58096	0.790481	+	0.612487i	$0.209831\pi$
$500$	0	0
$501$	−9.31601	−0.416208
$502$	29.3160i	1.30844i
$503$	− 36.9480i	− 1.64743i	−0.567004	−	0.823715i	$-0.691897\pi$
$503$	− 36.9480i	− 1.64743i	0.567004	−	0.823715i	$-0.308103\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	2.77200	0.123231
$507$	9.77200i	0.433990i
$508$	− 21.5440i	− 0.955861i
$509$	14.8600	0.658658	0.329329	−	0.944215i	$-0.393177\pi$
$509$	14.8600	0.658658	0.329329	+	0.944215i	$0.393177\pi$
$510$	0	0
$511$	31.6320	1.39932
$512$	− 1.00000i	− 0.0441942i
$513$	0.772002i	0.0340847i
$514$	25.0880	1.10658
$515$	0	0
$516$	−0.772002	−0.0339855
$517$	0.632011i	0.0277958i
$518$	5.31601i	0.233572i
$519$	7.22800	0.317274
$520$	0	0
$521$	−1.77200	−0.0776328	−0.0388164	−	0.999246i	$-0.512359\pi$
$521$	−1.77200	−0.0776328	−0.0388164	+	0.999246i	$0.512359\pi$
$522$	− 3.00000i	− 0.131306i
$523$	− 12.3160i	− 0.538541i	−0.963065	−	0.269271i	$-0.913217\pi$
$523$	− 12.3160i	− 0.538541i	0.963065	−	0.269271i	$-0.0867826\pi$
$524$	−15.0880	−0.659123
$525$	0	0
$526$	23.5440	1.02657
$527$	− 58.6320i	− 2.55405i
$528$	2.77200i	0.120636i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	6.00000	0.260378
$532$	2.31601i	0.100412i
$533$	− 13.2280i	− 0.572968i
$534$	8.22800	0.356060
$535$	0	0
$536$	−7.54400	−0.325851
$537$	− 9.54400i	− 0.411854i
$538$	15.8600i	0.683774i
$539$	5.54400	0.238797
$540$	0	0
$541$	−36.3160	−1.56135	−0.780674	−	0.624939i	$-0.785124\pi$
$541$	−36.3160	−1.56135	−0.780674	+	0.624939i	$0.785124\pi$
$542$	− 16.0000i	− 0.687259i
$543$	11.3160i	0.485616i
$544$	−7.77200	−0.333222
$545$	0	0
$546$	14.3160	0.612668
$547$	− 30.8600i	− 1.31948i	−0.751494	−	0.659739i	$-0.770667\pi$
$547$	− 30.8600i	− 1.31948i	0.751494	−	0.659739i	$-0.229333\pi$
$548$	− 6.22800i	− 0.266047i
$549$	−7.54400	−0.321970
$550$	0	0
$551$	−2.31601	−0.0986652
$552$	− 1.00000i	− 0.0425628i
$553$	32.3160i	1.37422i
$554$	−16.7720	−0.712574
$555$	0	0
$556$	7.77200	0.329606
$557$	13.0880i	0.554557i	0.960790	+	0.277278i	$0.0894324\pi$
$557$	13.0880i	0.554557i	−0.960790	+	0.277278i	$0.910568\pi$
$558$	7.54400i	0.319363i
$559$	3.68399	0.155816
$560$	0	0
$561$	21.5440	0.909589
$562$	26.8600i	1.13302i
$563$	32.9480i	1.38859i	0.719689	+	0.694297i	$0.244284\pi$
$563$	32.9480i	1.38859i	−0.719689	+	0.694297i	$0.755716\pi$
$564$	0.227998	0.00960045
$565$	0	0
$566$	−28.0000	−1.17693
$567$	− 3.00000i	− 0.125988i
$568$	3.77200i	0.158270i
$569$	−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
$571$	−38.6320	−1.61670	−0.808350	−	0.588703i	$-0.799639\pi$
$571$	−38.6320	−1.61670	−0.808350	+	0.588703i	$0.799639\pi$
$572$	− 13.2280i	− 0.553090i
$573$	− 18.3160i	− 0.765162i
$574$	−8.31601	−0.347103
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 5.68399i	− 0.236628i	−0.992976	−	0.118314i	$-0.962251\pi$
$577$	− 5.68399i	− 0.236628i	0.992976	−	0.118314i	$-0.0377489\pi$
$578$	43.4040i	1.80537i
$579$	3.77200	0.156759
$580$	0	0
$581$	3.00000	0.124461
$582$	− 0.455996i	− 0.0189017i
$583$	11.0880i	0.459218i
$584$	−10.5440	−0.436314
$585$	0	0
$586$	−7.54400	−0.311640
$587$	41.5440i	1.71470i	0.514730	+	0.857352i	$0.327892\pi$
$587$	41.5440i	1.71470i	−0.514730	+	0.857352i	$0.672108\pi$
$588$	− 2.00000i	− 0.0824786i
$589$	5.82399	0.239973
$590$	0	0
$591$	−13.0000	−0.534749
$592$	− 1.77200i	− 0.0728288i
$593$	− 15.6840i	− 0.644064i	−0.946729	−	0.322032i	$-0.895634\pi$
$593$	− 15.6840i	− 0.644064i	0.946729	−	0.322032i	$-0.104366\pi$
$594$	−2.77200	−0.113737
$595$	0	0
$596$	23.0880	0.945722
$597$	− 22.0880i	− 0.904002i
$598$	4.77200i	0.195142i
$599$	−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
$601$	−24.2280	−0.988281	−0.494140	−	0.869382i	$-0.664517\pi$
$601$	−24.2280	−0.988281	−0.494140	+	0.869382i	$0.664517\pi$
$602$	− 2.31601i	− 0.0943933i
$603$	− 7.54400i	− 0.307216i
$604$	−6.45600	−0.262691
$605$	0	0
$606$	11.3160	0.459681
$607$	− 29.0880i	− 1.18065i	−0.807167	−	0.590323i	$-0.799000\pi$
$607$	− 29.0880i	− 1.18065i	0.807167	−	0.590323i	$-0.201000\pi$
$608$	− 0.772002i	− 0.0313088i
$609$	9.00000	0.364698
$610$	0	0
$611$	−1.08801	−0.0440161
$612$	− 7.77200i	− 0.314165i
$613$	− 12.2280i	− 0.493884i	−0.969030	−	0.246942i	$-0.920574\pi$
$613$	− 12.2280i	− 0.493884i	0.969030	−	0.246942i	$-0.0794257\pi$
$614$	5.31601	0.214537
$615$	0	0
$616$	−8.31601	−0.335061
$617$	− 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
$619$	35.0880	1.41031	0.705153	−	0.709055i	$-0.250878\pi$
$619$	35.0880	1.41031	0.705153	+	0.709055i	$0.250878\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	− 24.8600i	− 0.996796i
$623$	24.6840i	0.988943i
$624$	−4.77200	−0.191033
$625$	0	0
$626$	8.00000	0.319744
$627$	2.13999i	0.0854630i
$628$	3.54400i	0.141421i
$629$	−13.7720	−0.549126
$630$	0	0
$631$	−20.0880	−0.799691	−0.399845	−	0.916583i	$-0.630936\pi$
$631$	−20.0880	−0.799691	−0.399845	+	0.916583i	$0.630936\pi$
$632$	− 10.7720i	− 0.428487i
$633$	− 15.3160i	− 0.608757i
$634$	−9.00000	−0.357436
$635$	0	0
$636$	4.00000	0.158610
$637$	9.54400i	0.378147i
$638$	− 8.31601i	− 0.329234i
$639$	−3.77200	−0.149218
$640$	0	0
$641$	24.8600	0.981911	0.490956	−	0.871185i	$-0.336648\pi$
$641$	24.8600	0.981911	0.490956	+	0.871185i	$0.336648\pi$
$642$	4.00000i	0.157867i
$643$	− 6.31601i	− 0.249079i	−0.992215	−	0.124539i	$-0.960255\pi$
$643$	− 6.31601i	− 0.249079i	0.992215	−	0.124539i	$-0.0397453\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−6.00000	−0.236067
$647$	− 22.2280i	− 0.873873i	−0.899492	−	0.436936i	$-0.856063\pi$
$647$	− 22.2280i	− 0.873873i	0.899492	−	0.436936i	$-0.143937\pi$
$648$	1.00000i	0.0392837i
$649$	16.6320	0.652864
$650$	0	0
$651$	−22.6320	−0.887018
$652$	16.0000i	0.626608i
$653$	− 40.5440i	− 1.58661i	−0.608825	−	0.793305i	$-0.708359\pi$
$653$	− 40.5440i	− 1.58661i	0.608825	−	0.793305i	$-0.291641\pi$
$654$	6.22800	0.243534
$655$	0	0
$656$	2.77200	0.108228
$657$	− 10.5440i	− 0.411361i
$658$	0.683994i	0.0266649i
$659$	−7.63201	−0.297301	−0.148650	−	0.988890i	$-0.547493\pi$
$659$	−7.63201	−0.297301	−0.148650	+	0.988890i	$0.547493\pi$
$660$	0	0
$661$	24.8600	0.966942	0.483471	−	0.875360i	$-0.339376\pi$
$661$	24.8600	0.966942	0.483471	+	0.875360i	$0.339376\pi$
$662$	− 26.2280i	− 1.01938i
$663$	37.0880i	1.44038i
$664$	−1.00000	−0.0388075
$665$	0	0
$666$	1.77200	0.0686637
$667$	3.00000i	0.116160i
$668$	9.31601i	0.360447i
$669$	−10.0000	−0.386622
$670$	0	0
$671$	−20.9120	−0.807299
$672$	3.00000i	0.115728i
$673$	9.45600i	0.364502i	0.983252	+	0.182251i	$0.0583383\pi$
$673$	9.45600i	0.364502i	−0.983252	+	0.182251i	$0.941662\pi$
$674$	4.00000	0.154074
$675$	0	0
$676$	9.77200	0.375846
$677$	− 48.0000i	− 1.84479i	−0.386248	−	0.922395i	$-0.626229\pi$
$677$	− 48.0000i	− 1.84479i	0.386248	−	0.922395i	$-0.373771\pi$
$678$	− 3.77200i	− 0.144863i
$679$	1.36799	0.0524986
$680$	0	0
$681$	−2.22800	−0.0853771
$682$	20.9120i	0.800762i
$683$	− 24.6320i	− 0.942518i	−0.881995	−	0.471259i	$-0.843800\pi$
$683$	− 24.6320i	− 0.942518i	0.881995	−	0.471259i	$-0.156200\pi$
$684$	0.772002	0.0295182
$685$	0	0
$686$	−15.0000	−0.572703
$687$	− 23.5440i	− 0.898260i
$688$	0.772002i	0.0294323i
$689$	−19.0880	−0.727195
$690$	0	0
$691$	−47.7720	−1.81733	−0.908666	−	0.417523i	$-0.862898\pi$
$691$	−47.7720	−1.81733	−0.908666	+	0.417523i	$0.862898\pi$
$692$	− 7.22800i	− 0.274767i
$693$	− 8.31601i	− 0.315899i
$694$	−7.54400	−0.286366
$695$	0	0
$696$	−3.00000	−0.113715
$697$	− 21.5440i	− 0.816037i
$698$	− 8.77200i	− 0.332025i
$699$	28.3160	1.07101
$700$	0	0
$701$	−15.5440	−0.587089	−0.293544	−	0.955945i	$-0.594835\pi$
$701$	−15.5440	−0.587089	−0.293544	+	0.955945i	$0.594835\pi$
$702$	− 4.77200i	− 0.180108i
$703$	− 1.36799i	− 0.0515947i
$704$	2.77200	0.104474
$705$	0	0
$706$	−23.8600	−0.897983
$707$	33.9480i	1.27675i
$708$	− 6.00000i	− 0.225494i
$709$	1.31601	0.0494236	0.0247118	−	0.999695i	$-0.492133\pi$
$709$	1.31601	0.0494236	0.0247118	+	0.999695i	$0.492133\pi$
$710$	0	0
$711$	10.7720	0.403982
$712$	− 8.22800i	− 0.308357i
$713$	− 7.54400i	− 0.282525i
$714$	23.3160	0.872580
$715$	0	0
$716$	−9.54400	−0.356676
$717$	14.2280i	0.531354i
$718$	− 18.7720i	− 0.700565i
$719$	4.68399	0.174684	0.0873418	−	0.996178i	$-0.472163\pi$
$719$	4.68399	0.174684	0.0873418	+	0.996178i	$0.472163\pi$
$720$	0	0
$721$	−33.0000	−1.22898
$722$	18.4040i	0.684926i
$723$	− 24.6320i	− 0.916074i
$724$	11.3160	0.420556
$725$	0	0
$726$	3.31601	0.123069
$727$	8.00000i	0.296704i	0.988935	+	0.148352i	$0.0473968\pi$
$727$	8.00000i	0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$	− 14.3160i	− 0.530586i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	6.00000	0.221918
$732$	7.54400i	0.278834i
$733$	− 25.7720i	− 0.951911i	−0.879469	−	0.475955i	$-0.842102\pi$
$733$	− 25.7720i	− 0.951911i	0.879469	−	0.475955i	$-0.157898\pi$
$734$	7.68399	0.283621
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	− 20.9120i	− 0.770303i
$738$	2.77200i	0.102039i
$739$	−25.7720	−0.948038	−0.474019	−	0.880515i	$-0.657197\pi$
$739$	−25.7720	−0.948038	−0.474019	+	0.880515i	$0.657197\pi$
$740$	0	0
$741$	−3.68399	−0.135335
$742$	12.0000i	0.440534i
$743$	− 28.7720i	− 1.05554i	−0.849387	−	0.527771i	$-0.823028\pi$
$743$	− 28.7720i	− 1.05554i	0.849387	−	0.527771i	$-0.176972\pi$
$744$	7.54400	0.276577
$745$	0	0
$746$	4.22800	0.154798
$747$	− 1.00000i	− 0.0365881i
$748$	− 21.5440i	− 0.787727i
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−9.45600	−0.345054	−0.172527	−	0.985005i	$-0.555193\pi$
$751$	−9.45600	−0.345054	−0.172527	+	0.985005i	$0.555193\pi$
$752$	− 0.227998i	− 0.00831424i
$753$	29.3160i	1.06833i
$754$	14.3160	0.521358
$755$	0	0
$756$	−3.00000	−0.109109
$757$	− 49.7720i	− 1.80899i	−0.426480	−	0.904497i	$-0.640246\pi$
$757$	− 49.7720i	− 1.80899i	0.426480	−	0.904497i	$-0.359754\pi$
$758$	11.0880i	0.402735i
$759$	2.77200	0.100617
$760$	0	0
$761$	27.8600	1.00992	0.504962	−	0.863141i	$-0.331506\pi$
$761$	27.8600	1.00992	0.504962	+	0.863141i	$0.331506\pi$
$762$	− 21.5440i	− 0.780457i
$763$	18.6840i	0.676406i
$764$	−18.3160	−0.662650
$765$	0	0
$766$	−5.22800	−0.188895
$767$	28.6320i	1.03384i
$768$	− 1.00000i	− 0.0360844i
$769$	−25.0880	−0.904697	−0.452348	−	0.891841i	$-0.649414\pi$
$769$	−25.0880	−0.904697	−0.452348	+	0.891841i	$0.649414\pi$
$770$	0	0
$771$	25.0880	0.903523
$772$	− 3.77200i	− 0.135757i
$773$	31.5440i	1.13456i	0.823525	+	0.567279i	$0.192004\pi$
$773$	31.5440i	1.13456i	−0.823525	+	0.567279i	$0.807996\pi$
$774$	−0.772002	−0.0277490
$775$	0	0
$776$	−0.455996	−0.0163693
$777$	5.31601i	0.190711i
$778$	18.0000i	0.645331i
$779$	2.13999	0.0766731
$780$	0	0
$781$	−10.4560	−0.374145
$782$	7.77200i	0.277926i
$783$	− 3.00000i	− 0.107211i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	−15.0880	−0.538171
$787$	13.2280i	0.471527i	0.971810	+	0.235764i	$0.0757591\pi$
$787$	13.2280i	0.471527i	−0.971810	+	0.235764i	$0.924241\pi$
$788$	13.0000i	0.463106i
$789$	23.5440	0.838189
$790$	0	0
$791$	11.3160	0.402351
$792$	2.77200i	0.0984988i
$793$	− 36.0000i	− 1.27840i
$794$	36.6320	1.30002
$795$	0	0
$796$	−22.0880	−0.782889
$797$	− 37.0880i	− 1.31372i	−0.754011	−	0.656862i	$-0.771883\pi$
$797$	− 37.0880i	− 1.31372i	0.754011	−	0.656862i	$-0.228117\pi$
$798$	2.31601i	0.0819857i
$799$	−1.77200	−0.0626889
$800$	0	0
$801$	8.22800	0.290722
$802$	− 22.6320i	− 0.799164i
$803$	− 29.2280i	− 1.03143i
$804$	−7.54400	−0.266056
$805$	0	0
$806$	−36.0000	−1.26805
$807$	15.8600i	0.558299i
$808$	− 11.3160i	− 0.398096i
$809$	−21.6840	−0.762369	−0.381184	−	0.924499i	$-0.624484\pi$
$809$	−21.6840	−0.762369	−0.381184	+	0.924499i	$0.624484\pi$
$810$	0	0
$811$	12.6320	0.443570	0.221785	−	0.975096i	$-0.428812\pi$
$811$	12.6320	0.443570	0.221785	+	0.975096i	$0.428812\pi$
$812$	− 9.00000i	− 0.315838i
$813$	− 16.0000i	− 0.561144i
$814$	4.91199	0.172165
$815$	0	0
$816$	−7.77200	−0.272074
$817$	0.595987i	0.0208509i
$818$	− 23.0000i	− 0.804176i
$819$	14.3160	0.500242
$820$	0	0
$821$	−20.7720	−0.724948	−0.362474	−	0.931994i	$-0.618068\pi$
$821$	−20.7720	−0.724948	−0.362474	+	0.931994i	$0.618068\pi$
$822$	− 6.22800i	− 0.217226i
$823$	6.45600i	0.225042i	0.993649	+	0.112521i	$0.0358925\pi$
$823$	6.45600i	0.225042i	−0.993649	+	0.112521i	$0.964107\pi$
$824$	11.0000	0.383203
$825$	0	0
$826$	18.0000	0.626300
$827$	− 0.367989i	− 0.0127962i	−0.999980	−	0.00639811i	$-0.997963\pi$
$827$	− 0.367989i	− 0.0127962i	0.999980	−	0.00639811i	$-0.00203660\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	−21.4040	−0.743392	−0.371696	−	0.928354i	$-0.621224\pi$
$829$	−21.4040	−0.743392	−0.371696	+	0.928354i	$0.621224\pi$
$830$	0	0
$831$	−16.7720	−0.581814
$832$	4.77200i	0.165439i
$833$	15.5440i	0.538568i
$834$	7.77200	0.269122
$835$	0	0
$836$	2.13999	0.0740131
$837$	7.54400i	0.260759i
$838$	− 25.6320i	− 0.885443i
$839$	27.4040	0.946092	0.473046	−	0.881038i	$-0.343155\pi$
$839$	27.4040	0.946092	0.473046	+	0.881038i	$0.343155\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	− 22.0000i	− 0.758170i
$843$	26.8600i	0.925108i
$844$	−15.3160	−0.527199
$845$	0	0
$846$	0.227998	0.00783874
$847$	9.94802i	0.341818i
$848$	− 4.00000i	− 0.137361i
$849$	−28.0000	−0.960958
$850$	0	0
$851$	−1.77200	−0.0607434
$852$	3.77200i	0.129227i
$853$	33.8600i	1.15934i	0.814850	+	0.579672i	$0.196819\pi$
$853$	33.8600i	1.15934i	−0.814850	+	0.579672i	$0.803181\pi$
$854$	−22.6320	−0.774451
$855$	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	$0.967323\pi$
$858$	− 13.2280i	− 0.451596i
$859$	41.5440	1.41746	0.708732	−	0.705478i	$-0.249268\pi$
$859$	41.5440	1.41746	0.708732	+	0.705478i	$0.249268\pi$
$860$	0	0
$861$	−8.31601	−0.283409
$862$	26.6320i	0.907090i
$863$	23.3160i	0.793686i	0.917886	+	0.396843i	$0.129894\pi$
$863$	23.3160i	0.793686i	−0.917886	+	0.396843i	$0.870106\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−23.5440	−0.800058
$867$	43.4040i	1.47408i
$868$	22.6320i	0.768181i
$869$	29.8600	1.01293
$870$	0	0
$871$	36.0000	1.21981
$872$	− 6.22800i	− 0.210907i
$873$	− 0.455996i	− 0.0154331i
$874$	−0.772002	−0.0261134
$875$	0	0
$876$	−10.5440	−0.356249
$877$	− 55.2640i	− 1.86613i	−0.359703	−	0.933067i	$-0.617122\pi$
$877$	− 55.2640i	− 1.86613i	0.359703	−	0.933067i	$-0.382878\pi$
$878$	− 12.0000i	− 0.404980i
$879$	−7.54400	−0.254453
$880$	0	0
$881$	27.5440	0.927981	0.463991	−	0.885840i	$-0.346417\pi$
$881$	27.5440	0.927981	0.463991	+	0.885840i	$0.346417\pi$
$882$	− 2.00000i	− 0.0673435i
$883$	2.22800i	0.0749781i	0.999297	+	0.0374891i	$0.0119359\pi$
$883$	2.22800i	0.0749781i	−0.999297	+	0.0374891i	$0.988064\pi$
$884$	37.0880	1.24740
$885$	0	0
$886$	−24.0000	−0.806296
$887$	29.9480i	1.00556i	0.864416	+	0.502778i	$0.167689\pi$
$887$	29.9480i	1.00556i	−0.864416	+	0.502778i	$0.832311\pi$
$888$	− 1.77200i	− 0.0594645i
$889$	64.6320	2.16769
$890$	0	0
$891$	−2.77200	−0.0928656
$892$	10.0000i	0.334825i
$893$	− 0.176015i	− 0.00589012i
$894$	23.0880	0.772178
$895$	0	0
$896$	3.00000	0.100223
$897$	4.77200i	0.159333i
$898$	− 2.00000i	− 0.0667409i
$899$	−22.6320	−0.754820
$900$	0	0
$901$	−31.0880	−1.03569
$902$	7.68399i	0.255849i
$903$	− 2.31601i	− 0.0770718i
$904$	−3.77200	−0.125455
$905$	0	0
$906$	−6.45600	−0.214486
$907$	− 25.4040i	− 0.843526i	−0.906706	−	0.421763i	$-0.861411\pi$
$907$	− 25.4040i	− 0.843526i	0.906706	−	0.421763i	$-0.138589\pi$
$908$	2.22800i	0.0739387i
$909$	11.3160	0.375328
$910$	0	0
$911$	−2.77200	−0.0918405	−0.0459203	−	0.998945i	$-0.514622\pi$
$911$	−2.77200	−0.0918405	−0.0459203	+	0.998945i	$0.514622\pi$
$912$	− 0.772002i	− 0.0255635i
$913$	− 2.77200i	− 0.0917399i
$914$	20.6320	0.682446
$915$	0	0
$916$	−23.5440	−0.777916
$917$	− 45.2640i	− 1.49475i
$918$	− 7.77200i	− 0.256514i
$919$	5.31601	0.175359	0.0876794	−	0.996149i	$-0.472055\pi$
$919$	5.31601	0.175359	0.0876794	+	0.996149i	$0.472055\pi$
$920$	0	0
$921$	5.31601	0.175168
$922$	4.54400i	0.149649i
$923$	− 18.0000i	− 0.592477i
$924$	−8.31601	−0.273576
$925$	0	0
$926$	−35.0880	−1.15306
$927$	11.0000i	0.361287i
$928$	3.00000i	0.0984798i
$929$	−50.3160	−1.65081	−0.825407	−	0.564538i	$-0.809054\pi$
$929$	−50.3160	−1.65081	−0.825407	+	0.564538i	$0.809054\pi$
$930$	0	0
$931$	−1.54400	−0.0506027
$932$	− 28.3160i	− 0.927522i
$933$	− 24.8600i	− 0.813880i
$934$	1.45600	0.0476417
$935$	0	0
$936$	−4.77200	−0.155978
$937$	− 42.6320i	− 1.39273i	−0.717689	−	0.696364i	$-0.754800\pi$
$937$	− 42.6320i	− 1.39273i	0.717689	−	0.696364i	$-0.245200\pi$
$938$	− 22.6320i	− 0.738961i
$939$	8.00000	0.261070
$940$	0	0
$941$	−30.6320	−0.998575	−0.499288	−	0.866436i	$-0.666405\pi$
$941$	−30.6320	−0.998575	−0.499288	+	0.866436i	$0.666405\pi$
$942$	3.54400i	0.115470i
$943$	− 2.77200i	− 0.0902688i
$944$	−6.00000	−0.195283
$945$	0	0
$946$	−2.13999	−0.0695771
$947$	− 3.08801i	− 0.100347i	−0.998741	−	0.0501734i	$-0.984023\pi$
$947$	− 3.08801i	− 0.100347i	0.998741	−	0.0501734i	$-0.0159774\pi$
$948$	− 10.7720i	− 0.349858i
$949$	50.3160	1.63333
$950$	0	0
$951$	−9.00000	−0.291845
$952$	− 23.3160i	− 0.755676i
$953$	38.2280i	1.23833i	0.785262	+	0.619163i	$0.212528\pi$
$953$	38.2280i	1.23833i	−0.785262	+	0.619163i	$0.787472\pi$
$954$	4.00000	0.129505
$955$	0	0
$956$	14.2280	0.460166
$957$	− 8.31601i	− 0.268818i
$958$	− 9.68399i	− 0.312876i
$959$	18.6840	0.603338
$960$	0	0
$961$	25.9120	0.835871
$962$	8.45600i	0.272632i
$963$	4.00000i	0.128898i
$964$	−24.6320	−0.793344
$965$	0	0
$966$	3.00000	0.0965234
$967$	− 42.6320i	− 1.37095i	−0.728095	−	0.685477i	$-0.759594\pi$
$967$	− 42.6320i	− 1.37095i	0.728095	−	0.685477i	$-0.240406\pi$
$968$	− 3.31601i	− 0.106580i
$969$	−6.00000	−0.192748
$970$	0	0
$971$	19.6320	0.630021	0.315011	−	0.949088i	$-0.397992\pi$
$971$	19.6320	0.630021	0.315011	+	0.949088i	$0.397992\pi$
$972$	1.00000i	0.0320750i
$973$	23.3160i	0.747477i
$974$	29.5440	0.946651
$975$	0	0
$976$	7.54400	0.241478
$977$	− 34.6840i	− 1.10964i	−0.831971	−	0.554820i	$-0.812787\pi$
$977$	− 34.6840i	− 1.10964i	0.831971	−	0.554820i	$-0.187213\pi$
$978$	16.0000i	0.511624i
$979$	22.8080	0.728948
$980$	0	0
$981$	6.22800	0.198845
$982$	27.5440i	0.878964i
$983$	51.4040i	1.63953i	0.572698	+	0.819767i	$0.305897\pi$
$983$	51.4040i	1.63953i	−0.572698	+	0.819767i	$0.694103\pi$
$984$	2.77200	0.0883682
$985$	0	0
$986$	23.3160	0.742533
$987$	0.683994i	0.0217718i
$988$	3.68399i	0.117203i
$989$	0.772002	0.0245482
$990$	0	0
$991$	−38.1760	−1.21270	−0.606351	−	0.795197i	$-0.707367\pi$
$991$	−38.1760	−1.21270	−0.606351	+	0.795197i	$0.707367\pi$
$992$	− 7.54400i	− 0.239522i
$993$	− 26.2280i	− 0.832320i
$994$	−11.3160	−0.358922
$995$	0	0
$996$	−1.00000	−0.0316862
$997$	− 8.77200i	− 0.277812i	−0.990306	−	0.138906i	$-0.955641\pi$
$997$	− 8.77200i	− 0.277812i	0.990306	−	0.138906i	$-0.0443586\pi$
$998$	− 35.3160i	− 1.11791i
$999$	1.77200	0.0560637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.w.2899.1		4
5.2	odd	4		3450.2.a.bj.1.1	yes	2
5.3	odd	4		3450.2.a.bh.1.1	✓	2
5.4	even	2	inner	3450.2.d.w.2899.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bh.1.1	✓	2	5.3	odd	4
3450.2.a.bj.1.1	yes	2	5.2	odd	4
3450.2.d.w.2899.1		4	1.1	even	1	trivial
3450.2.d.w.2899.3		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -2.77200 q^{11} +1.00000i q^{12} -4.77200i q^{13} -3.00000 q^{14} +1.00000 q^{16} -7.77200i q^{17} +1.00000i q^{18} +0.772002 q^{19} -3.00000 q^{21} +2.77200i q^{22} -1.00000i q^{23} +1.00000 q^{24} -4.77200 q^{26} +1.00000i q^{27} +3.00000i q^{28} -3.00000 q^{29} +7.54400 q^{31} -1.00000i q^{32} +2.77200i q^{33} -7.77200 q^{34} +1.00000 q^{36} -1.77200i q^{37} -0.772002i q^{38} -4.77200 q^{39} +2.77200 q^{41} +3.00000i q^{42} +0.772002i q^{43} +2.77200 q^{44} -1.00000 q^{46} -0.227998i q^{47} -1.00000i q^{48} -2.00000 q^{49} -7.77200 q^{51} +4.77200i q^{52} -4.00000i q^{53} +1.00000 q^{54} +3.00000 q^{56} -0.772002i q^{57} +3.00000i q^{58} -6.00000 q^{59} +7.54400 q^{61} -7.54400i q^{62} +3.00000i q^{63} -1.00000 q^{64} +2.77200 q^{66} +7.54400i q^{67} +7.77200i q^{68} -1.00000 q^{69} +3.77200 q^{71} -1.00000i q^{72} +10.5440i q^{73} -1.77200 q^{74} -0.772002 q^{76} +8.31601i q^{77} +4.77200i q^{78} -10.7720 q^{79} +1.00000 q^{81} -2.77200i q^{82} +1.00000i q^{83} +3.00000 q^{84} +0.772002 q^{86} +3.00000i q^{87} -2.77200i q^{88} -8.22800 q^{89} -14.3160 q^{91} +1.00000i q^{92} -7.54400i q^{93} -0.227998 q^{94} -1.00000 q^{96} +0.455996i q^{97} +2.00000i q^{98} +2.77200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 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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