LMFDB - Embedded newform 1450.2.b.k.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.3
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.k.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.81361i q^{3} -1.00000 q^{4} +1.81361 q^{6} -2.52444i q^{7} +1.00000i q^{8} -0.289169 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.81361i q^{3} -1.00000 q^{4} +1.81361 q^{6} -2.52444i q^{7} +1.00000i q^{8} -0.289169 q^{9} -2.91638 q^{11} -1.81361i q^{12} +3.10278i q^{13} -2.52444 q^{14} +1.00000 q^{16} -6.91638i q^{17} +0.289169i q^{18} -1.81361 q^{19} +4.57834 q^{21} +2.91638i q^{22} -5.68111i q^{23} -1.81361 q^{24} +3.10278 q^{26} +4.91638i q^{27} +2.52444i q^{28} -1.00000 q^{29} -8.12193 q^{31} -1.00000i q^{32} -5.28917i q^{33} -6.91638 q^{34} +0.289169 q^{36} -7.39194i q^{37} +1.81361i q^{38} -5.62721 q^{39} +8.39194 q^{41} -4.57834i q^{42} -5.04888i q^{43} +2.91638 q^{44} -5.68111 q^{46} -4.86751i q^{47} +1.81361i q^{48} +0.627213 q^{49} +12.5436 q^{51} -3.10278i q^{52} +5.30833i q^{53} +4.91638 q^{54} +2.52444 q^{56} -3.28917i q^{57} +1.00000i q^{58} -2.60806 q^{59} -10.0680 q^{61} +8.12193i q^{62} +0.729988i q^{63} -1.00000 q^{64} -5.28917 q^{66} +2.68111i q^{67} +6.91638i q^{68} +10.3033 q^{69} +5.68111 q^{71} -0.289169i q^{72} -15.0680i q^{73} -7.39194 q^{74} +1.81361 q^{76} +7.36222i q^{77} +5.62721i q^{78} +1.73501 q^{79} -9.78389 q^{81} -8.39194i q^{82} -13.1219i q^{83} -4.57834 q^{84} -5.04888 q^{86} -1.81361i q^{87} -2.91638i q^{88} -5.23527 q^{89} +7.83276 q^{91} +5.68111i q^{92} -14.7300i q^{93} -4.86751 q^{94} +1.81361 q^{96} -1.27001i q^{97} -0.627213i q^{98} +0.843326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{6}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^6	$ 6 q - 6 q^{4} - 2 q^{6} + 10 q^{11} - 4 q^{14} + 6 q^{16} + 2 q^{19} + 24 q^{21} + 2 q^{24} + 4 q^{26} - 6 q^{29} + 8 q^{31} - 14 q^{34} - 8 q^{39} + 34 q^{41} - 10 q^{44} - 16 q^{46} - 22 q^{49} + 22 q^{51} + 2 q^{54} + 4 q^{56} - 32 q^{59} + 4 q^{61} - 6 q^{64} - 30 q^{66} - 12 q^{69} + 16 q^{71} - 28 q^{74} - 2 q^{76} - 26 q^{81} - 24 q^{84} - 8 q^{86} - 22 q^{89} - 8 q^{91} - 24 q^{94} - 2 q^{96} + 12 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^6 + 10 * q^11 - 4 * q^14 + 6 * q^16 + 2 * q^19 + 24 * q^21 + 2 * q^24 + 4 * q^26 - 6 * q^29 + 8 * q^31 - 14 * q^34 - 8 * q^39 + 34 * q^41 - 10 * q^44 - 16 * q^46 - 22 * q^49 + 22 * q^51 + 2 * q^54 + 4 * q^56 - 32 * q^59 + 4 * q^61 - 6 * q^64 - 30 * q^66 - 12 * q^69 + 16 * q^71 - 28 * q^74 - 2 * q^76 - 26 * q^81 - 24 * q^84 - 8 * q^86 - 22 * q^89 - 8 * q^91 - 24 * q^94 - 2 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	1.81361i	1.04709i	0.851999	+	0.523543i	$0.175390\pi$
$3$	1.81361i	1.04709i	−0.851999	+	0.523543i	$0.824610\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.81361	0.740402
$7$	− 2.52444i	− 0.954148i	−0.878863	−	0.477074i	$-0.841697\pi$
$7$	− 2.52444i	− 0.954148i	0.878863	−	0.477074i	$-0.158303\pi$
$8$	1.00000i	0.353553i
$9$	−0.289169	−0.0963895
$10$	0	0
$11$	−2.91638	−0.879322	−0.439661	−	0.898164i	$-0.644901\pi$
$11$	−2.91638	−0.879322	−0.439661	+	0.898164i	$0.644901\pi$
$12$	− 1.81361i	− 0.523543i
$13$	3.10278i	0.860555i	0.902697	+	0.430277i	$0.141584\pi$
$13$	3.10278i	0.860555i	−0.902697	+	0.430277i	$0.858416\pi$
$14$	−2.52444	−0.674684
$15$	0	0
$16$	1.00000	0.250000
$17$	− 6.91638i	− 1.67747i	−0.544541	−	0.838734i	$-0.683296\pi$
$17$	− 6.91638i	− 1.67747i	0.544541	−	0.838734i	$-0.316704\pi$
$18$	0.289169i	0.0681577i
$19$	−1.81361	−0.416070	−0.208035	−	0.978121i	$-0.566707\pi$
$19$	−1.81361	−0.416070	−0.208035	+	0.978121i	$0.566707\pi$
$20$	0	0
$21$	4.57834	0.999075
$22$	2.91638i	0.621775i
$23$	− 5.68111i	− 1.18459i	−0.805720	−	0.592297i	$-0.798221\pi$
$23$	− 5.68111i	− 1.18459i	0.805720	−	0.592297i	$-0.201779\pi$
$24$	−1.81361	−0.370201
$25$	0	0
$26$	3.10278	0.608504
$27$	4.91638i	0.946158i
$28$	2.52444i	0.477074i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−8.12193	−1.45874	−0.729371	−	0.684118i	$-0.760187\pi$
$31$	−8.12193	−1.45874	−0.729371	+	0.684118i	$0.760187\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 5.28917i	− 0.920726i
$34$	−6.91638	−1.18615
$35$	0	0
$36$	0.289169	0.0481948
$37$	− 7.39194i	− 1.21523i	−0.794232	−	0.607614i	$-0.792127\pi$
$37$	− 7.39194i	− 1.21523i	0.794232	−	0.607614i	$-0.207873\pi$
$38$	1.81361i	0.294206i
$39$	−5.62721	−0.901075
$40$	0	0
$41$	8.39194	1.31060	0.655301	−	0.755368i	$-0.272542\pi$
$41$	8.39194	1.31060	0.655301	+	0.755368i	$0.272542\pi$
$42$	− 4.57834i	− 0.706453i
$43$	− 5.04888i	− 0.769946i	−0.922928	−	0.384973i	$-0.874211\pi$
$43$	− 5.04888i	− 0.769946i	0.922928	−	0.384973i	$-0.125789\pi$
$44$	2.91638	0.439661
$45$	0	0
$46$	−5.68111	−0.837634
$47$	− 4.86751i	− 0.709999i	−0.934867	−	0.354999i	$-0.884481\pi$
$47$	− 4.86751i	− 0.709999i	0.934867	−	0.354999i	$-0.115519\pi$
$48$	1.81361i	0.261772i
$49$	0.627213	0.0896019
$50$	0	0
$51$	12.5436	1.75645
$52$	− 3.10278i	− 0.430277i
$53$	5.30833i	0.729155i	0.931173	+	0.364577i	$0.118786\pi$
$53$	5.30833i	0.729155i	−0.931173	+	0.364577i	$0.881214\pi$
$54$	4.91638	0.669035
$55$	0	0
$56$	2.52444	0.337342
$57$	− 3.28917i	− 0.435661i
$58$	1.00000i	0.131306i
$59$	−2.60806	−0.339540	−0.169770	−	0.985484i	$-0.554302\pi$
$59$	−2.60806	−0.339540	−0.169770	+	0.985484i	$0.554302\pi$
$60$	0	0
$61$	−10.0680	−1.28908	−0.644540	−	0.764571i	$-0.722951\pi$
$61$	−10.0680	−1.28908	−0.644540	+	0.764571i	$0.722951\pi$
$62$	8.12193i	1.03149i
$63$	0.729988i	0.0919699i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.28917	−0.651052
$67$	2.68111i	0.327550i	0.986498	+	0.163775i	$0.0523671\pi$
$67$	2.68111i	0.327550i	−0.986498	+	0.163775i	$0.947633\pi$
$68$	6.91638i	0.838734i
$69$	10.3033	1.24037
$70$	0	0
$71$	5.68111	0.674224	0.337112	−	0.941465i	$-0.390550\pi$
$71$	5.68111	0.674224	0.337112	+	0.941465i	$0.390550\pi$
$72$	− 0.289169i	− 0.0340788i
$73$	− 15.0680i	− 1.76358i	−0.471642	−	0.881790i	$-0.656339\pi$
$73$	− 15.0680i	− 1.76358i	0.471642	−	0.881790i	$-0.343661\pi$
$74$	−7.39194	−0.859296
$75$	0	0
$76$	1.81361	0.208035
$77$	7.36222i	0.839003i
$78$	5.62721i	0.637156i
$79$	1.73501	0.195204	0.0976020	−	0.995226i	$-0.468883\pi$
$79$	1.73501	0.195204	0.0976020	+	0.995226i	$0.468883\pi$
$80$	0	0
$81$	−9.78389	−1.08710
$82$	− 8.39194i	− 0.926735i
$83$	− 13.1219i	− 1.44032i	−0.693808	−	0.720160i	$-0.744069\pi$
$83$	− 13.1219i	− 1.44032i	0.693808	−	0.720160i	$-0.255931\pi$
$84$	−4.57834	−0.499538
$85$	0	0
$86$	−5.04888	−0.544434
$87$	− 1.81361i	− 0.194439i
$88$	− 2.91638i	− 0.310887i
$89$	−5.23527	−0.554937	−0.277469	−	0.960735i	$-0.589495\pi$
$89$	−5.23527	−0.554937	−0.277469	+	0.960735i	$0.589495\pi$
$90$	0	0
$91$	7.83276	0.821097
$92$	5.68111i	0.592297i
$93$	− 14.7300i	− 1.52743i
$94$	−4.86751	−0.502045
$95$	0	0
$96$	1.81361	0.185100
$97$	− 1.27001i	− 0.128950i	−0.997919	−	0.0644751i	$-0.979463\pi$
$97$	− 1.27001i	− 0.128950i	0.997919	−	0.0644751i	$-0.0205373\pi$
$98$	− 0.627213i	− 0.0633581i
$99$	0.843326	0.0847574
$100$	0	0
$101$	5.39194	0.536518	0.268259	−	0.963347i	$-0.413552\pi$
$101$	5.39194	0.536518	0.268259	+	0.963347i	$0.413552\pi$
$102$	− 12.5436i	− 1.24200i
$103$	− 17.6116i	− 1.73533i	−0.497154	−	0.867663i	$-0.665621\pi$
$103$	− 17.6116i	− 1.73533i	0.497154	−	0.867663i	$-0.334379\pi$
$104$	−3.10278	−0.304252
$105$	0	0
$106$	5.30833	0.515590
$107$	− 4.30833i	− 0.416502i	−0.978075	−	0.208251i	$-0.933223\pi$
$107$	− 4.30833i	− 0.416502i	0.978075	−	0.208251i	$-0.0667770\pi$
$108$	− 4.91638i	− 0.473079i
$109$	7.57331	0.725392	0.362696	−	0.931908i	$-0.381856\pi$
$109$	7.57331	0.725392	0.362696	+	0.931908i	$0.381856\pi$
$110$	0	0
$111$	13.4061	1.27245
$112$	− 2.52444i	− 0.238537i
$113$	− 5.60806i	− 0.527562i	−0.964583	−	0.263781i	$-0.915030\pi$
$113$	− 5.60806i	− 0.527562i	0.964583	−	0.263781i	$-0.0849696\pi$
$114$	−3.28917	−0.308059
$115$	0	0
$116$	1.00000	0.0928477
$117$	− 0.897225i	− 0.0829485i
$118$	2.60806i	0.240091i
$119$	−17.4600	−1.60055
$120$	0	0
$121$	−2.49472	−0.226793
$122$	10.0680i	0.911517i
$123$	15.2197i	1.37231i
$124$	8.12193	0.729371
$125$	0	0
$126$	0.729988	0.0650325
$127$	− 2.12193i	− 0.188291i	−0.995558	−	0.0941455i	$-0.969988\pi$
$127$	− 2.12193i	− 0.188291i	0.995558	−	0.0941455i	$-0.0300119\pi$
$128$	1.00000i	0.0883883i
$129$	9.15667	0.806200
$130$	0	0
$131$	3.74055	0.326813	0.163407	−	0.986559i	$-0.447752\pi$
$131$	3.74055	0.326813	0.163407	+	0.986559i	$0.447752\pi$
$132$	5.28917i	0.460363i
$133$	4.57834i	0.396992i
$134$	2.68111	0.231613
$135$	0	0
$136$	6.91638	0.593075
$137$	− 11.7980i	− 1.00797i	−0.863712	−	0.503986i	$-0.831866\pi$
$137$	− 11.7980i	− 1.00797i	0.863712	−	0.503986i	$-0.168134\pi$
$138$	− 10.3033i	− 0.877075i
$139$	−12.3083	−1.04398	−0.521989	−	0.852952i	$-0.674810\pi$
$139$	−12.3083	−1.04398	−0.521989	+	0.852952i	$0.674810\pi$
$140$	0	0
$141$	8.82774	0.743430
$142$	− 5.68111i	− 0.476748i
$143$	− 9.04888i	− 0.756705i
$144$	−0.289169	−0.0240974
$145$	0	0
$146$	−15.0680	−1.24704
$147$	1.13752i	0.0938209i
$148$	7.39194i	0.607614i
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	−8.89722	−0.724046	−0.362023	−	0.932169i	$-0.617914\pi$
$151$	−8.89722	−0.724046	−0.362023	+	0.932169i	$0.617914\pi$
$152$	− 1.81361i	− 0.147103i
$153$	2.00000i	0.161690i
$154$	7.36222	0.593265
$155$	0	0
$156$	5.62721	0.450538
$157$	17.4897i	1.39583i	0.716181	+	0.697915i	$0.245889\pi$
$157$	17.4897i	1.39583i	−0.716181	+	0.697915i	$0.754111\pi$
$158$	− 1.73501i	− 0.138030i
$159$	−9.62721	−0.763488
$160$	0	0
$161$	−14.3416	−1.13028
$162$	9.78389i	0.768695i
$163$	− 3.02972i	− 0.237306i	−0.992936	−	0.118653i	$-0.962142\pi$
$163$	− 3.02972i	− 0.237306i	0.992936	−	0.118653i	$-0.0378576\pi$
$164$	−8.39194	−0.655301
$165$	0	0
$166$	−13.1219	−1.01846
$167$	23.9305i	1.85180i	0.377770	+	0.925899i	$0.376691\pi$
$167$	23.9305i	1.85180i	−0.377770	+	0.925899i	$0.623309\pi$
$168$	4.57834i	0.353226i
$169$	3.37279	0.259445
$170$	0	0
$171$	0.524438	0.0401048
$172$	5.04888i	0.384973i
$173$	11.5194i	0.875805i	0.899022	+	0.437902i	$0.144278\pi$
$173$	11.5194i	0.875805i	−0.899022	+	0.437902i	$0.855722\pi$
$174$	−1.81361	−0.137489
$175$	0	0
$176$	−2.91638	−0.219831
$177$	− 4.72999i	− 0.355528i
$178$	5.23527i	0.392400i
$179$	−8.30833	−0.620993	−0.310497	−	0.950574i	$-0.600495\pi$
$179$	−8.30833	−0.620993	−0.310497	+	0.950574i	$0.600495\pi$
$180$	0	0
$181$	17.7194	1.31707	0.658537	−	0.752548i	$-0.271175\pi$
$181$	17.7194	1.31707	0.658537	+	0.752548i	$0.271175\pi$
$182$	− 7.83276i	− 0.580603i
$183$	− 18.2594i	− 1.34978i
$184$	5.68111	0.418817
$185$	0	0
$186$	−14.7300	−1.08006
$187$	20.1708i	1.47504i
$188$	4.86751i	0.354999i
$189$	12.4111	0.902775
$190$	0	0
$191$	17.1708	1.24244	0.621218	−	0.783638i	$-0.286638\pi$
$191$	17.1708	1.24244	0.621218	+	0.783638i	$0.286638\pi$
$192$	− 1.81361i	− 0.130886i
$193$	7.06803i	0.508768i	0.967103	+	0.254384i	$0.0818727\pi$
$193$	7.06803i	0.508768i	−0.967103	+	0.254384i	$0.918127\pi$
$194$	−1.27001	−0.0911815
$195$	0	0
$196$	−0.627213	−0.0448009
$197$	16.1361i	1.14965i	0.818277	+	0.574824i	$0.194929\pi$
$197$	16.1361i	1.14965i	−0.818277	+	0.574824i	$0.805071\pi$
$198$	− 0.843326i	− 0.0599326i
$199$	−8.25945	−0.585497	−0.292748	−	0.956190i	$-0.594570\pi$
$199$	−8.25945	−0.585497	−0.292748	+	0.956190i	$0.594570\pi$
$200$	0	0
$201$	−4.86248	−0.342973
$202$	− 5.39194i	− 0.379376i
$203$	2.52444i	0.177181i
$204$	−12.5436	−0.878227
$205$	0	0
$206$	−17.6116	−1.22706
$207$	1.64280i	0.114182i
$208$	3.10278i	0.215139i
$209$	5.28917	0.365859
$210$	0	0
$211$	−12.2302	−0.841965	−0.420982	−	0.907069i	$-0.638315\pi$
$211$	−12.2302	−0.841965	−0.420982	+	0.907069i	$0.638315\pi$
$212$	− 5.30833i	− 0.364577i
$213$	10.3033i	0.705971i
$214$	−4.30833	−0.294511
$215$	0	0
$216$	−4.91638	−0.334517
$217$	20.5033i	1.39186i
$218$	− 7.57331i	− 0.512930i
$219$	27.3275	1.84662
$220$	0	0
$221$	21.4600	1.44355
$222$	− 13.4061i	− 0.899757i
$223$	11.2544i	0.753652i	0.926284	+	0.376826i	$0.122985\pi$
$223$	11.2544i	0.753652i	−0.926284	+	0.376826i	$0.877015\pi$
$224$	−2.52444	−0.168671
$225$	0	0
$226$	−5.60806	−0.373042
$227$	19.7647i	1.31183i	0.754834	+	0.655916i	$0.227717\pi$
$227$	19.7647i	1.31183i	−0.754834	+	0.655916i	$0.772283\pi$
$228$	3.28917i	0.217831i
$229$	23.7250	1.56779	0.783895	−	0.620894i	$-0.213230\pi$
$229$	23.7250	1.56779	0.783895	+	0.620894i	$0.213230\pi$
$230$	0	0
$231$	−13.3522	−0.878509
$232$	− 1.00000i	− 0.0656532i
$233$	24.0625i	1.57639i	0.615428	+	0.788193i	$0.288983\pi$
$233$	24.0625i	1.57639i	−0.615428	+	0.788193i	$0.711017\pi$
$234$	−0.897225	−0.0586534
$235$	0	0
$236$	2.60806	0.169770
$237$	3.14663i	0.204395i
$238$	17.4600i	1.13176i
$239$	4.31335	0.279007	0.139504	−	0.990222i	$-0.455449\pi$
$239$	4.31335	0.279007	0.139504	+	0.990222i	$0.455449\pi$
$240$	0	0
$241$	−27.7144	−1.78524	−0.892621	−	0.450808i	$-0.851136\pi$
$241$	−27.7144	−1.78524	−0.892621	+	0.450808i	$0.851136\pi$
$242$	2.49472i	0.160367i
$243$	− 2.99498i	− 0.192128i
$244$	10.0680	0.644540
$245$	0	0
$246$	15.2197	0.970372
$247$	− 5.62721i	− 0.358051i
$248$	− 8.12193i	− 0.515743i
$249$	23.7980	1.50814
$250$	0	0
$251$	−21.7542	−1.37311	−0.686555	−	0.727077i	$-0.740878\pi$
$251$	−21.7542	−1.37311	−0.686555	+	0.727077i	$0.740878\pi$
$252$	− 0.729988i	− 0.0459849i
$253$	16.5683i	1.04164i
$254$	−2.12193	−0.133142
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 5.83276i	− 0.363838i	−0.983314	−	0.181919i	$-0.941769\pi$
$257$	− 5.83276i	− 0.363838i	0.983314	−	0.181919i	$-0.0582308\pi$
$258$	− 9.15667i	− 0.570070i
$259$	−18.6605	−1.15951
$260$	0	0
$261$	0.289169	0.0178991
$262$	− 3.74055i	− 0.231092i
$263$	20.8675i	1.28675i	0.765553	+	0.643373i	$0.222465\pi$
$263$	20.8675i	1.28675i	−0.765553	+	0.643373i	$0.777535\pi$
$264$	5.28917	0.325526
$265$	0	0
$266$	4.57834	0.280716
$267$	− 9.49472i	− 0.581067i
$268$	− 2.68111i	− 0.163775i
$269$	−0.548618	−0.0334498	−0.0167249	−	0.999860i	$-0.505324\pi$
$269$	−0.548618	−0.0334498	−0.0167249	+	0.999860i	$0.505324\pi$
$270$	0	0
$271$	5.00357	0.303945	0.151973	−	0.988385i	$-0.451437\pi$
$271$	5.00357	0.303945	0.151973	+	0.988385i	$0.451437\pi$
$272$	− 6.91638i	− 0.419367i
$273$	14.2056i	0.859759i
$274$	−11.7980	−0.712744
$275$	0	0
$276$	−10.3033	−0.620186
$277$	− 0.632236i	− 0.0379874i	−0.999820	−	0.0189937i	$-0.993954\pi$
$277$	− 0.632236i	− 0.0379874i	0.999820	−	0.0189937i	$-0.00604625\pi$
$278$	12.3083i	0.738204i
$279$	2.34861	0.140607
$280$	0	0
$281$	30.9653	1.84723	0.923616	−	0.383319i	$-0.125219\pi$
$281$	30.9653	1.84723	0.923616	+	0.383319i	$0.125219\pi$
$282$	− 8.82774i	− 0.525684i
$283$	− 6.33804i	− 0.376758i	−0.982096	−	0.188379i	$-0.939677\pi$
$283$	− 6.33804i	− 0.376758i	0.982096	−	0.188379i	$-0.0603233\pi$
$284$	−5.68111	−0.337112
$285$	0	0
$286$	−9.04888	−0.535071
$287$	− 21.1849i	− 1.25051i
$288$	0.289169i	0.0170394i
$289$	−30.8363	−1.81390
$290$	0	0
$291$	2.30330	0.135022
$292$	15.0680i	0.881790i
$293$	− 28.4197i	− 1.66030i	−0.557543	−	0.830148i	$-0.688256\pi$
$293$	− 28.4197i	− 1.66030i	0.557543	−	0.830148i	$-0.311744\pi$
$294$	1.13752	0.0663414
$295$	0	0
$296$	7.39194	0.429648
$297$	− 14.3380i	− 0.831978i
$298$	2.00000i	0.115857i
$299$	17.6272	1.01941
$300$	0	0
$301$	−12.7456	−0.734643
$302$	8.89722i	0.511978i
$303$	9.77886i	0.561781i
$304$	−1.81361	−0.104017
$305$	0	0
$306$	2.00000	0.114332
$307$	− 22.6797i	− 1.29440i	−0.762322	−	0.647198i	$-0.775941\pi$
$307$	− 22.6797i	− 1.29440i	0.762322	−	0.647198i	$-0.224059\pi$
$308$	− 7.36222i	− 0.419502i
$309$	31.9406	1.81704
$310$	0	0
$311$	−9.08719	−0.515287	−0.257644	−	0.966240i	$-0.582946\pi$
$311$	−9.08719	−0.515287	−0.257644	+	0.966240i	$0.582946\pi$
$312$	− 5.62721i	− 0.318578i
$313$	25.0630i	1.41665i	0.705889	+	0.708323i	$0.250548\pi$
$313$	25.0630i	1.41665i	−0.705889	+	0.708323i	$0.749452\pi$
$314$	17.4897	0.987001
$315$	0	0
$316$	−1.73501	−0.0976020
$317$	14.9497i	0.839657i	0.907603	+	0.419829i	$0.137910\pi$
$317$	14.9497i	0.839657i	−0.907603	+	0.419829i	$0.862090\pi$
$318$	9.62721i	0.539867i
$319$	2.91638	0.163286
$320$	0	0
$321$	7.81361	0.436113
$322$	14.3416i	0.799227i
$323$	12.5436i	0.697944i
$324$	9.78389	0.543549
$325$	0	0
$326$	−3.02972	−0.167801
$327$	13.7350i	0.759548i
$328$	8.39194i	0.463368i
$329$	−12.2877	−0.677444
$330$	0	0
$331$	−18.1270	−0.996348	−0.498174	−	0.867077i	$-0.665996\pi$
$331$	−18.1270	−0.996348	−0.498174	+	0.867077i	$0.665996\pi$
$332$	13.1219i	0.720160i
$333$	2.13752i	0.117135i
$334$	23.9305	1.30942
$335$	0	0
$336$	4.57834	0.249769
$337$	− 9.08362i	− 0.494816i	−0.968911	−	0.247408i	$-0.920421\pi$
$337$	− 9.08362i	− 0.494816i	0.968911	−	0.247408i	$-0.0795788\pi$
$338$	− 3.37279i	− 0.183455i
$339$	10.1708	0.552402
$340$	0	0
$341$	23.6867	1.28270
$342$	− 0.524438i	− 0.0283584i
$343$	− 19.2544i	− 1.03964i
$344$	5.04888	0.272217
$345$	0	0
$346$	11.5194	0.619288
$347$	30.7194i	1.64911i	0.565785	+	0.824553i	$0.308573\pi$
$347$	30.7194i	1.64911i	−0.565785	+	0.824553i	$0.691427\pi$
$348$	1.81361i	0.0972195i
$349$	−15.7789	−0.844623	−0.422312	−	0.906451i	$-0.638781\pi$
$349$	−15.7789	−0.844623	−0.422312	+	0.906451i	$0.638781\pi$
$350$	0	0
$351$	−15.2544	−0.814221
$352$	2.91638i	0.155444i
$353$	− 31.6797i	− 1.68614i	−0.537805	−	0.843069i	$-0.680746\pi$
$353$	− 31.6797i	− 1.68614i	0.537805	−	0.843069i	$-0.319254\pi$
$354$	−4.72999	−0.251396
$355$	0	0
$356$	5.23527	0.277469
$357$	− 31.6655i	− 1.67592i
$358$	8.30833i	0.439109i
$359$	27.1013	1.43035	0.715177	−	0.698944i	$-0.246346\pi$
$359$	27.1013	1.43035	0.715177	+	0.698944i	$0.246346\pi$
$360$	0	0
$361$	−15.7108	−0.826886
$362$	− 17.7194i	− 0.931312i
$363$	− 4.52444i	− 0.237471i
$364$	−7.83276	−0.410548
$365$	0	0
$366$	−18.2594	−0.954437
$367$	− 31.8953i	− 1.66492i	−0.554086	−	0.832459i	$-0.686932\pi$
$367$	− 31.8953i	− 1.66492i	0.554086	−	0.832459i	$-0.313068\pi$
$368$	− 5.68111i	− 0.296148i
$369$	−2.42669	−0.126328
$370$	0	0
$371$	13.4005	0.695721
$372$	14.7300i	0.763714i
$373$	28.0383i	1.45177i	0.687817	+	0.725884i	$0.258569\pi$
$373$	28.0383i	1.45177i	−0.687817	+	0.725884i	$0.741431\pi$
$374$	20.1708	1.04301
$375$	0	0
$376$	4.86751	0.251022
$377$	− 3.10278i	− 0.159801i
$378$	− 12.4111i	− 0.638358i
$379$	−8.69525	−0.446645	−0.223322	−	0.974745i	$-0.571690\pi$
$379$	−8.69525	−0.446645	−0.223322	+	0.974745i	$0.571690\pi$
$380$	0	0
$381$	3.84835	0.197157
$382$	− 17.1708i	− 0.878535i
$383$	14.8917i	0.760930i	0.924795	+	0.380465i	$0.124236\pi$
$383$	14.8917i	0.760930i	−0.924795	+	0.380465i	$0.875764\pi$
$384$	−1.81361	−0.0925502
$385$	0	0
$386$	7.06803	0.359753
$387$	1.45998i	0.0742148i
$388$	1.27001i	0.0644751i
$389$	1.93197	0.0979546	0.0489773	−	0.998800i	$-0.484404\pi$
$389$	1.93197	0.0979546	0.0489773	+	0.998800i	$0.484404\pi$
$390$	0	0
$391$	−39.2927	−1.98712
$392$	0.627213i	0.0316790i
$393$	6.78389i	0.342202i
$394$	16.1361	0.812923
$395$	0	0
$396$	−0.843326	−0.0423787
$397$	− 19.2983i	− 0.968553i	−0.874915	−	0.484276i	$-0.839083\pi$
$397$	− 19.2983i	− 0.968553i	0.874915	−	0.484276i	$-0.160917\pi$
$398$	8.25945i	0.414009i
$399$	−8.30330	−0.415685
$400$	0	0
$401$	16.7250	0.835205	0.417602	−	0.908630i	$-0.362870\pi$
$401$	16.7250	0.835205	0.417602	+	0.908630i	$0.362870\pi$
$402$	4.86248i	0.242519i
$403$	− 25.2005i	− 1.25533i
$404$	−5.39194	−0.268259
$405$	0	0
$406$	2.52444	0.125286
$407$	21.5577i	1.06858i
$408$	12.5436i	0.621000i
$409$	26.4842	1.30956	0.654779	−	0.755821i	$-0.272762\pi$
$409$	26.4842	1.30956	0.654779	+	0.755821i	$0.272762\pi$
$410$	0	0
$411$	21.3970	1.05543
$412$	17.6116i	0.867663i
$413$	6.58388i	0.323971i
$414$	1.64280	0.0807392
$415$	0	0
$416$	3.10278	0.152126
$417$	− 22.3225i	− 1.09314i
$418$	− 5.28917i	− 0.258702i
$419$	6.94610	0.339339	0.169670	−	0.985501i	$-0.445730\pi$
$419$	6.94610	0.339339	0.169670	+	0.985501i	$0.445730\pi$
$420$	0	0
$421$	−2.71585	−0.132363	−0.0661813	−	0.997808i	$-0.521082\pi$
$421$	−2.71585	−0.132363	−0.0661813	+	0.997808i	$0.521082\pi$
$422$	12.2302i	0.595359i
$423$	1.40753i	0.0684364i
$424$	−5.30833	−0.257795
$425$	0	0
$426$	10.3033	0.499197
$427$	25.4161i	1.22997i
$428$	4.30833i	0.208251i
$429$	16.4111	0.792335
$430$	0	0
$431$	16.2978	0.785036	0.392518	−	0.919744i	$-0.371604\pi$
$431$	16.2978	0.785036	0.392518	+	0.919744i	$0.371604\pi$
$432$	4.91638i	0.236540i
$433$	− 10.1169i	− 0.486188i	−0.970003	−	0.243094i	$-0.921838\pi$
$433$	− 10.1169i	− 0.486188i	0.970003	−	0.243094i	$-0.0781623\pi$
$434$	20.5033	0.984190
$435$	0	0
$436$	−7.57331	−0.362696
$437$	10.3033i	0.492874i
$438$	− 27.3275i	− 1.30576i
$439$	−9.79445	−0.467464	−0.233732	−	0.972301i	$-0.575094\pi$
$439$	−9.79445	−0.467464	−0.233732	+	0.972301i	$0.575094\pi$
$440$	0	0
$441$	−0.181370	−0.00863668
$442$	− 21.4600i	− 1.02075i
$443$	− 21.7980i	− 1.03566i	−0.855485	−	0.517828i	$-0.826741\pi$
$443$	− 21.7980i	− 1.03566i	0.855485	−	0.517828i	$-0.173259\pi$
$444$	−13.4061	−0.636224
$445$	0	0
$446$	11.2544	0.532913
$447$	− 3.62721i	− 0.171561i
$448$	2.52444i	0.119268i
$449$	22.2686	1.05092	0.525459	−	0.850819i	$-0.323894\pi$
$449$	22.2686	1.05092	0.525459	+	0.850819i	$0.323894\pi$
$450$	0	0
$451$	−24.4741	−1.15244
$452$	5.60806i	0.263781i
$453$	− 16.1361i	− 0.758138i
$454$	19.7647	0.927605
$455$	0	0
$456$	3.28917	0.154029
$457$	29.8958i	1.39847i	0.714894	+	0.699233i	$0.246475\pi$
$457$	29.8958i	1.39847i	−0.714894	+	0.699233i	$0.753525\pi$
$458$	− 23.7250i	− 1.10859i
$459$	34.0036	1.58715
$460$	0	0
$461$	33.2927	1.55060	0.775299	−	0.631595i	$-0.217599\pi$
$461$	33.2927	1.55060	0.775299	+	0.631595i	$0.217599\pi$
$462$	13.3522i	0.621200i
$463$	13.1184i	0.609662i	0.952406	+	0.304831i	$0.0986000\pi$
$463$	13.1184i	0.609662i	−0.952406	+	0.304831i	$0.901400\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	24.0625	1.11467
$467$	4.15165i	0.192115i	0.995376	+	0.0960577i	$0.0306233\pi$
$467$	4.15165i	0.192115i	−0.995376	+	0.0960577i	$0.969377\pi$
$468$	0.897225i	0.0414742i
$469$	6.76830	0.312531
$470$	0	0
$471$	−31.7194	−1.46155
$472$	− 2.60806i	− 0.120046i
$473$	14.7244i	0.677031i
$474$	3.14663	0.144529
$475$	0	0
$476$	17.4600	0.800277
$477$	− 1.53500i	− 0.0702829i
$478$	− 4.31335i	− 0.197288i
$479$	−42.7144	−1.95167	−0.975835	−	0.218507i	$-0.929881\pi$
$479$	−42.7144	−1.95167	−0.975835	+	0.218507i	$0.929881\pi$
$480$	0	0
$481$	22.9355	1.04577
$482$	27.7144i	1.26236i
$483$	− 26.0100i	− 1.18350i
$484$	2.49472	0.113396
$485$	0	0
$486$	−2.99498	−0.135855
$487$	− 18.3728i	− 0.832550i	−0.909239	−	0.416275i	$-0.863335\pi$
$487$	− 18.3728i	− 0.832550i	0.909239	−	0.416275i	$-0.136665\pi$
$488$	− 10.0680i	− 0.455758i
$489$	5.49472	0.248480
$490$	0	0
$491$	−0.881639	−0.0397878	−0.0198939	−	0.999802i	$-0.506333\pi$
$491$	−0.881639	−0.0397878	−0.0198939	+	0.999802i	$0.506333\pi$
$492$	− 15.2197i	− 0.686156i
$493$	6.91638i	0.311498i
$494$	−5.62721	−0.253180
$495$	0	0
$496$	−8.12193	−0.364685
$497$	− 14.3416i	− 0.643309i
$498$	− 23.7980i	− 1.06641i
$499$	−32.4791	−1.45397	−0.726983	−	0.686656i	$-0.759078\pi$
$499$	−32.4791	−1.45397	−0.726983	+	0.686656i	$0.759078\pi$
$500$	0	0
$501$	−43.4005	−1.93899
$502$	21.7542i	0.970936i
$503$	32.6620i	1.45632i	0.685405	+	0.728162i	$0.259625\pi$
$503$	32.6620i	1.45632i	−0.685405	+	0.728162i	$0.740375\pi$
$504$	−0.729988	−0.0325163
$505$	0	0
$506$	16.5683	0.736550
$507$	6.11691i	0.271661i
$508$	2.12193i	0.0941455i
$509$	−27.3311	−1.21143	−0.605714	−	0.795683i	$-0.707112\pi$
$509$	−27.3311	−1.21143	−0.605714	+	0.795683i	$0.707112\pi$
$510$	0	0
$511$	−38.0383	−1.68272
$512$	− 1.00000i	− 0.0441942i
$513$	− 8.91638i	− 0.393668i
$514$	−5.83276	−0.257272
$515$	0	0
$516$	−9.15667	−0.403100
$517$	14.1955i	0.624318i
$518$	18.6605i	0.819895i
$519$	−20.8917	−0.917043
$520$	0	0
$521$	11.5400	0.505578	0.252789	−	0.967521i	$-0.418652\pi$
$521$	11.5400	0.505578	0.252789	+	0.967521i	$0.418652\pi$
$522$	− 0.289169i	− 0.0126566i
$523$	− 19.4056i	− 0.848546i	−0.905534	−	0.424273i	$-0.860530\pi$
$523$	− 19.4056i	− 0.848546i	0.905534	−	0.424273i	$-0.139470\pi$
$524$	−3.74055	−0.163407
$525$	0	0
$526$	20.8675	0.909866
$527$	56.1744i	2.44699i
$528$	− 5.28917i	− 0.230182i
$529$	−9.27504	−0.403262
$530$	0	0
$531$	0.754168	0.0327281
$532$	− 4.57834i	− 0.198496i
$533$	26.0383i	1.12784i
$534$	−9.49472	−0.410877
$535$	0	0
$536$	−2.68111	−0.115806
$537$	− 15.0680i	− 0.650234i
$538$	0.548618i	0.0236526i
$539$	−1.82919	−0.0787889
$540$	0	0
$541$	26.7230	1.14891	0.574456	−	0.818536i	$-0.305214\pi$
$541$	26.7230	1.14891	0.574456	+	0.818536i	$0.305214\pi$
$542$	− 5.00357i	− 0.214922i
$543$	32.1361i	1.37909i
$544$	−6.91638	−0.296537
$545$	0	0
$546$	14.2056	0.607941
$547$	− 20.7875i	− 0.888808i	−0.895827	−	0.444404i	$-0.853416\pi$
$547$	− 20.7875i	− 0.888808i	0.895827	−	0.444404i	$-0.146584\pi$
$548$	11.7980i	0.503986i
$549$	2.91136	0.124254
$550$	0	0
$551$	1.81361	0.0772622
$552$	10.3033i	0.438538i
$553$	− 4.37993i	− 0.186253i
$554$	−0.632236	−0.0268611
$555$	0	0
$556$	12.3083	0.521989
$557$	− 11.0489i	− 0.468156i	−0.972218	−	0.234078i	$-0.924793\pi$
$557$	− 11.0489i	− 0.468156i	0.972218	−	0.234078i	$-0.0752071\pi$
$558$	− 2.34861i	− 0.0994245i
$559$	15.6655	0.662581
$560$	0	0
$561$	−36.5819	−1.54449
$562$	− 30.9653i	− 1.30619i
$563$	− 27.3311i	− 1.15187i	−0.817497	−	0.575933i	$-0.804639\pi$
$563$	− 27.3311i	− 1.15187i	0.817497	−	0.575933i	$-0.195361\pi$
$564$	−8.82774	−0.371715
$565$	0	0
$566$	−6.33804	−0.266408
$567$	24.6988i	1.03725i
$568$	5.68111i	0.238374i
$569$	6.54359	0.274322	0.137161	−	0.990549i	$-0.456202\pi$
$569$	6.54359	0.274322	0.137161	+	0.990549i	$0.456202\pi$
$570$	0	0
$571$	46.4691	1.94467	0.972335	−	0.233589i	$-0.0750471\pi$
$571$	46.4691	1.94467	0.972335	+	0.233589i	$0.0750471\pi$
$572$	9.04888i	0.378353i
$573$	31.1411i	1.30094i
$574$	−21.1849	−0.884242
$575$	0	0
$576$	0.289169	0.0120487
$577$	− 40.4585i	− 1.68431i	−0.539235	−	0.842155i	$-0.681287\pi$
$577$	− 40.4585i	− 1.68431i	0.539235	−	0.842155i	$-0.318713\pi$
$578$	30.8363i	1.28262i
$579$	−12.8186	−0.532724
$580$	0	0
$581$	−33.1255	−1.37428
$582$	− 2.30330i	− 0.0954749i
$583$	− 15.4811i	− 0.641162i
$584$	15.0680	0.623520
$585$	0	0
$586$	−28.4197	−1.17401
$587$	− 15.1900i	− 0.626957i	−0.949595	−	0.313478i	$-0.898506\pi$
$587$	− 15.1900i	− 0.626957i	0.949595	−	0.313478i	$-0.101494\pi$
$588$	− 1.13752i	− 0.0469104i
$589$	14.7300	0.606939
$590$	0	0
$591$	−29.2645	−1.20378
$592$	− 7.39194i	− 0.303807i
$593$	− 2.21611i	− 0.0910048i	−0.998964	−	0.0455024i	$-0.985511\pi$
$593$	− 2.21611i	− 0.0910048i	0.998964	−	0.0455024i	$-0.0144889\pi$
$594$	−14.3380	−0.588297
$595$	0	0
$596$	2.00000	0.0819232
$597$	− 14.9794i	− 0.613066i
$598$	− 17.6272i	− 0.720830i
$599$	39.8852	1.62967	0.814833	−	0.579696i	$-0.196829\pi$
$599$	39.8852	1.62967	0.814833	+	0.579696i	$0.196829\pi$
$600$	0	0
$601$	20.6897	0.843951	0.421975	−	0.906607i	$-0.361337\pi$
$601$	20.6897	0.843951	0.421975	+	0.906607i	$0.361337\pi$
$602$	12.7456i	0.519471i
$603$	− 0.775293i	− 0.0315724i
$604$	8.89722	0.362023
$605$	0	0
$606$	9.77886	0.397239
$607$	16.6025i	0.673875i	0.941527	+	0.336938i	$0.109391\pi$
$607$	16.6025i	0.673875i	−0.941527	+	0.336938i	$0.890609\pi$
$608$	1.81361i	0.0735515i
$609$	−4.57834	−0.185524
$610$	0	0
$611$	15.1028	0.610993
$612$	− 2.00000i	− 0.0808452i
$613$	8.13607i	0.328613i	0.986409	+	0.164306i	$0.0525385\pi$
$613$	8.13607i	0.328613i	−0.986409	+	0.164306i	$0.947461\pi$
$614$	−22.6797	−0.915277
$615$	0	0
$616$	−7.36222	−0.296632
$617$	− 36.0822i	− 1.45261i	−0.687371	−	0.726307i	$-0.741235\pi$
$617$	− 36.0822i	− 1.45261i	0.687371	−	0.726307i	$-0.258765\pi$
$618$	− 31.9406i	− 1.28484i
$619$	−13.9617	−0.561168	−0.280584	−	0.959830i	$-0.590528\pi$
$619$	−13.9617	−0.561168	−0.280584	+	0.959830i	$0.590528\pi$
$620$	0	0
$621$	27.9305	1.12081
$622$	9.08719i	0.364363i
$623$	13.2161i	0.529492i
$624$	−5.62721	−0.225269
$625$	0	0
$626$	25.0630	1.00172
$627$	9.59247i	0.383086i
$628$	− 17.4897i	− 0.697915i
$629$	−51.1255	−2.03851
$630$	0	0
$631$	−5.49829	−0.218883	−0.109442	−	0.993993i	$-0.534906\pi$
$631$	−5.49829	−0.218883	−0.109442	+	0.993993i	$0.534906\pi$
$632$	1.73501i	0.0690150i
$633$	− 22.1809i	− 0.881610i
$634$	14.9497	0.593727
$635$	0	0
$636$	9.62721	0.381744
$637$	1.94610i	0.0771073i
$638$	− 2.91638i	− 0.115461i
$639$	−1.64280	−0.0649881
$640$	0	0
$641$	18.5033	0.730837	0.365418	−	0.930843i	$-0.380926\pi$
$641$	18.5033	0.730837	0.365418	+	0.930843i	$0.380926\pi$
$642$	− 7.81361i	− 0.308378i
$643$	25.3608i	1.00013i	0.865988	+	0.500066i	$0.166691\pi$
$643$	25.3608i	1.00013i	−0.865988	+	0.500066i	$0.833309\pi$
$644$	14.3416	0.565139
$645$	0	0
$646$	12.5436	0.493521
$647$	− 36.6761i	− 1.44189i	−0.692994	−	0.720943i	$-0.743709\pi$
$647$	− 36.6761i	− 1.44189i	0.692994	−	0.720943i	$-0.256291\pi$
$648$	− 9.78389i	− 0.384347i
$649$	7.60609	0.298565
$650$	0	0
$651$	−37.1849	−1.45739
$652$	3.02972i	0.118653i
$653$	4.47913i	0.175282i	0.996152	+	0.0876410i	$0.0279328\pi$
$653$	4.47913i	0.175282i	−0.996152	+	0.0876410i	$0.972067\pi$
$654$	13.7350	0.537081
$655$	0	0
$656$	8.39194	0.327650
$657$	4.35720i	0.169991i
$658$	12.2877i	0.479025i
$659$	16.0630	0.625726	0.312863	−	0.949798i	$-0.398712\pi$
$659$	16.0630	0.625726	0.312863	+	0.949798i	$0.398712\pi$
$660$	0	0
$661$	−22.5244	−0.876099	−0.438050	−	0.898951i	$-0.644331\pi$
$661$	−22.5244	−0.876099	−0.438050	+	0.898951i	$0.644331\pi$
$662$	18.1270i	0.704524i
$663$	38.9200i	1.51153i
$664$	13.1219	0.509230
$665$	0	0
$666$	2.13752	0.0828271
$667$	5.68111i	0.219974i
$668$	− 23.9305i	− 0.925899i
$669$	−20.4111	−0.789139
$670$	0	0
$671$	29.3622	1.13352
$672$	− 4.57834i	− 0.176613i
$673$	− 41.2474i	− 1.58997i	−0.606628	−	0.794986i	$-0.707478\pi$
$673$	− 41.2474i	− 1.58997i	0.606628	−	0.794986i	$-0.292522\pi$
$674$	−9.08362	−0.349888
$675$	0	0
$676$	−3.37279	−0.129723
$677$	− 17.1653i	− 0.659715i	−0.944031	−	0.329857i	$-0.892999\pi$
$677$	− 17.1653i	− 0.659715i	0.944031	−	0.329857i	$-0.107001\pi$
$678$	− 10.1708i	− 0.390608i
$679$	−3.20607	−0.123038
$680$	0	0
$681$	−35.8454	−1.37360
$682$	− 23.6867i	− 0.907009i
$683$	− 20.2786i	− 0.775939i	−0.921672	−	0.387970i	$-0.873177\pi$
$683$	− 20.2786i	− 0.775939i	0.921672	−	0.387970i	$-0.126823\pi$
$684$	−0.524438	−0.0200524
$685$	0	0
$686$	−19.2544	−0.735137
$687$	43.0278i	1.64161i
$688$	− 5.04888i	− 0.192487i
$689$	−16.4705	−0.627478
$690$	0	0
$691$	22.2106	0.844930	0.422465	−	0.906379i	$-0.361165\pi$
$691$	22.2106	0.844930	0.422465	+	0.906379i	$0.361165\pi$
$692$	− 11.5194i	− 0.437902i
$693$	− 2.12892i	− 0.0808711i
$694$	30.7194	1.16609
$695$	0	0
$696$	1.81361	0.0687446
$697$	− 58.0419i	− 2.19849i
$698$	15.7789i	0.597239i
$699$	−43.6399	−1.65061
$700$	0	0
$701$	−11.4005	−0.430592	−0.215296	−	0.976549i	$-0.569072\pi$
$701$	−11.4005	−0.430592	−0.215296	+	0.976549i	$0.569072\pi$
$702$	15.2544i	0.575741i
$703$	13.4061i	0.505620i
$704$	2.91638	0.109915
$705$	0	0
$706$	−31.6797	−1.19228
$707$	− 13.6116i	− 0.511918i
$708$	4.72999i	0.177764i
$709$	−37.3311	−1.40200	−0.700999	−	0.713163i	$-0.747262\pi$
$709$	−37.3311	−1.40200	−0.700999	+	0.713163i	$0.747262\pi$
$710$	0	0
$711$	−0.501711	−0.0188156
$712$	− 5.23527i	− 0.196200i
$713$	46.1416i	1.72802i
$714$	−31.6655	−1.18505
$715$	0	0
$716$	8.30833	0.310497
$717$	7.82272i	0.292145i
$718$	− 27.1013i	− 1.01141i
$719$	−18.5839	−0.693062	−0.346531	−	0.938039i	$-0.612640\pi$
$719$	−18.5839	−0.693062	−0.346531	+	0.938039i	$0.612640\pi$
$720$	0	0
$721$	−44.4595	−1.65576
$722$	15.7108i	0.584697i
$723$	− 50.2630i	− 1.86930i
$724$	−17.7194	−0.658537
$725$	0	0
$726$	−4.52444	−0.167918
$727$	29.8227i	1.10606i	0.833160	+	0.553032i	$0.186529\pi$
$727$	29.8227i	1.10606i	−0.833160	+	0.553032i	$0.813471\pi$
$728$	7.83276i	0.290302i
$729$	−23.9200	−0.885924
$730$	0	0
$731$	−34.9200	−1.29156
$732$	18.2594i	0.674889i
$733$	− 32.2056i	− 1.18954i	−0.803896	−	0.594770i	$-0.797243\pi$
$733$	− 32.2056i	− 1.18954i	0.803896	−	0.594770i	$-0.202757\pi$
$734$	−31.8953	−1.17728
$735$	0	0
$736$	−5.68111	−0.209409
$737$	− 7.81915i	− 0.288022i
$738$	2.42669i	0.0893276i
$739$	−27.8328	−1.02384	−0.511922	−	0.859032i	$-0.671066\pi$
$739$	−27.8328	−1.02384	−0.511922	+	0.859032i	$0.671066\pi$
$740$	0	0
$741$	10.2056	0.374910
$742$	− 13.4005i	− 0.491949i
$743$	31.4288i	1.15301i	0.817093	+	0.576506i	$0.195584\pi$
$743$	31.4288i	1.15301i	−0.817093	+	0.576506i	$0.804416\pi$
$744$	14.7300	0.540028
$745$	0	0
$746$	28.0383	1.02656
$747$	3.79445i	0.138832i
$748$	− 20.1708i	− 0.737518i
$749$	−10.8761	−0.397404
$750$	0	0
$751$	14.4635	0.527782	0.263891	−	0.964552i	$-0.414994\pi$
$751$	14.4635	0.527782	0.263891	+	0.964552i	$0.414994\pi$
$752$	− 4.86751i	− 0.177500i
$753$	− 39.4535i	− 1.43777i
$754$	−3.10278	−0.112996
$755$	0	0
$756$	−12.4111	−0.451387
$757$	34.0071i	1.23601i	0.786174	+	0.618005i	$0.212059\pi$
$757$	34.0071i	1.23601i	−0.786174	+	0.618005i	$0.787941\pi$
$758$	8.69525i	0.315826i
$759$	−30.0484	−1.09069
$760$	0	0
$761$	13.0594	0.473404	0.236702	−	0.971582i	$-0.423933\pi$
$761$	13.0594	0.473404	0.236702	+	0.971582i	$0.423933\pi$
$762$	− 3.84835i	− 0.139411i
$763$	− 19.1184i	− 0.692131i
$764$	−17.1708	−0.621218
$765$	0	0
$766$	14.8917	0.538058
$767$	− 8.09221i	− 0.292193i
$768$	1.81361i	0.0654429i
$769$	−47.2525	−1.70397	−0.851984	−	0.523568i	$-0.824600\pi$
$769$	−47.2525	−1.70397	−0.851984	+	0.523568i	$0.824600\pi$
$770$	0	0
$771$	10.5783	0.380970
$772$	− 7.06803i	− 0.254384i
$773$	− 12.6675i	− 0.455618i	−0.973706	−	0.227809i	$-0.926844\pi$
$773$	− 12.6675i	− 0.455618i	0.973706	−	0.227809i	$-0.0731562\pi$
$774$	1.45998	0.0524778
$775$	0	0
$776$	1.27001	0.0455908
$777$	− 33.8428i	− 1.21410i
$778$	− 1.93197i	− 0.0692644i
$779$	−15.2197	−0.545302
$780$	0	0
$781$	−16.5683	−0.592860
$782$	39.2927i	1.40511i
$783$	− 4.91638i	− 0.175697i
$784$	0.627213	0.0224005
$785$	0	0
$786$	6.78389	0.241973
$787$	30.0297i	1.07044i	0.844711	+	0.535222i	$0.179772\pi$
$787$	30.0297i	1.07044i	−0.844711	+	0.535222i	$0.820228\pi$
$788$	− 16.1361i	− 0.574824i
$789$	−37.8454	−1.34733
$790$	0	0
$791$	−14.1572	−0.503372
$792$	0.843326i	0.0299663i
$793$	− 31.2388i	− 1.10932i
$794$	−19.2983	−0.684870
$795$	0	0
$796$	8.25945	0.292748
$797$	− 43.9094i	− 1.55535i	−0.628666	−	0.777675i	$-0.716399\pi$
$797$	− 43.9094i	− 1.55535i	0.628666	−	0.777675i	$-0.283601\pi$
$798$	8.30330i	0.293934i
$799$	−33.6655	−1.19100
$800$	0	0
$801$	1.51388	0.0534902
$802$	− 16.7250i	− 0.590579i
$803$	43.9441i	1.55075i
$804$	4.86248	0.171487
$805$	0	0
$806$	−25.2005	−0.887651
$807$	− 0.994977i	− 0.0350248i
$808$	5.39194i	0.189688i
$809$	53.3794	1.87672	0.938360	−	0.345659i	$-0.112345\pi$
$809$	53.3794	1.87672	0.938360	+	0.345659i	$0.112345\pi$
$810$	0	0
$811$	−7.53806	−0.264697	−0.132348	−	0.991203i	$-0.542252\pi$
$811$	−7.53806	−0.264697	−0.132348	+	0.991203i	$0.542252\pi$
$812$	− 2.52444i	− 0.0885904i
$813$	9.07451i	0.318257i
$814$	21.5577	0.755598
$815$	0	0
$816$	12.5436	0.439114
$817$	9.15667i	0.320351i
$818$	− 26.4842i	− 0.925997i
$819$	−2.26499	−0.0791451
$820$	0	0
$821$	4.08217	0.142469	0.0712343	−	0.997460i	$-0.477306\pi$
$821$	4.08217	0.142469	0.0712343	+	0.997460i	$0.477306\pi$
$822$	− 21.3970i	− 0.746305i
$823$	34.2338i	1.19332i	0.802496	+	0.596658i	$0.203505\pi$
$823$	34.2338i	1.19332i	−0.802496	+	0.596658i	$0.796495\pi$
$824$	17.6116	0.613530
$825$	0	0
$826$	6.58388	0.229082
$827$	45.9935i	1.59935i	0.600432	+	0.799676i	$0.294995\pi$
$827$	45.9935i	1.59935i	−0.600432	+	0.799676i	$0.705005\pi$
$828$	− 1.64280i	− 0.0570912i
$829$	6.30330	0.218923	0.109461	−	0.993991i	$-0.465087\pi$
$829$	6.30330	0.218923	0.109461	+	0.993991i	$0.465087\pi$
$830$	0	0
$831$	1.14663	0.0397761
$832$	− 3.10278i	− 0.107569i
$833$	− 4.33804i	− 0.150304i
$834$	−22.3225	−0.772964
$835$	0	0
$836$	−5.28917	−0.182930
$837$	− 39.9305i	− 1.38020i
$838$	− 6.94610i	− 0.239949i
$839$	−40.6902	−1.40478	−0.702391	−	0.711791i	$-0.747884\pi$
$839$	−40.6902	−1.40478	−0.702391	+	0.711791i	$0.747884\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	2.71585i	0.0935945i
$843$	56.1588i	1.93421i
$844$	12.2302	0.420982
$845$	0	0
$846$	1.40753	0.0483919
$847$	6.29776i	0.216394i
$848$	5.30833i	0.182289i
$849$	11.4947	0.394498
$850$	0	0
$851$	−41.9945	−1.43955
$852$	− 10.3033i	− 0.352985i
$853$	52.1250i	1.78473i	0.451319	+	0.892363i	$0.350954\pi$
$853$	52.1250i	1.78473i	−0.451319	+	0.892363i	$0.649046\pi$
$854$	25.4161	0.869722
$855$	0	0
$856$	4.30833	0.147256
$857$	48.5608i	1.65880i	0.558652	+	0.829402i	$0.311319\pi$
$857$	48.5608i	1.65880i	−0.558652	+	0.829402i	$0.688681\pi$
$858$	− 16.4111i	− 0.560266i
$859$	43.6308	1.48866	0.744332	−	0.667810i	$-0.232768\pi$
$859$	43.6308	1.48866	0.744332	+	0.667810i	$0.232768\pi$
$860$	0	0
$861$	38.4211	1.30939
$862$	− 16.2978i	− 0.555104i
$863$	10.5839i	0.360279i	0.983641	+	0.180140i	$0.0576550\pi$
$863$	10.5839i	0.360279i	−0.983641	+	0.180140i	$0.942345\pi$
$864$	4.91638	0.167259
$865$	0	0
$866$	−10.1169	−0.343787
$867$	− 55.9250i	− 1.89931i
$868$	− 20.5033i	− 0.695928i
$869$	−5.05995	−0.171647
$870$	0	0
$871$	−8.31889	−0.281875
$872$	7.57331i	0.256465i
$873$	0.367248i	0.0124294i
$874$	10.3033	0.348514
$875$	0	0
$876$	−27.3275	−0.923310
$877$	− 45.6938i	− 1.54297i	−0.636248	−	0.771485i	$-0.719514\pi$
$877$	− 45.6938i	− 1.54297i	0.636248	−	0.771485i	$-0.280486\pi$
$878$	9.79445i	0.330547i
$879$	51.5421	1.73847
$880$	0	0
$881$	4.55721	0.153536	0.0767682	−	0.997049i	$-0.475540\pi$
$881$	4.55721	0.153536	0.0767682	+	0.997049i	$0.475540\pi$
$882$	0.181370i	0.00610705i
$883$	− 45.6222i	− 1.53531i	−0.640864	−	0.767654i	$-0.721424\pi$
$883$	− 45.6222i	− 1.53531i	0.640864	−	0.767654i	$-0.278576\pi$
$884$	−21.4600	−0.721777
$885$	0	0
$886$	−21.7980	−0.732319
$887$	− 24.8122i	− 0.833111i	−0.909110	−	0.416555i	$-0.863237\pi$
$887$	− 24.8122i	− 0.833111i	0.909110	−	0.416555i	$-0.136763\pi$
$888$	13.4061i	0.449878i
$889$	−5.35668	−0.179657
$890$	0	0
$891$	28.5335	0.955910
$892$	− 11.2544i	− 0.376826i
$893$	8.82774i	0.295409i
$894$	−3.62721	−0.121312
$895$	0	0
$896$	2.52444	0.0843356
$897$	31.9688i	1.06741i
$898$	− 22.2686i	− 0.743111i
$899$	8.12193	0.270882
$900$	0	0
$901$	36.7144	1.22313
$902$	24.4741i	0.814899i
$903$	− 23.1155i	− 0.769234i
$904$	5.60806	0.186521
$905$	0	0
$906$	−16.1361	−0.536085
$907$	14.8277i	0.492347i	0.969226	+	0.246174i	$0.0791733\pi$
$907$	14.8277i	0.492347i	−0.969226	+	0.246174i	$0.920827\pi$
$908$	− 19.7647i	− 0.655916i
$909$	−1.55918	−0.0517148
$910$	0	0
$911$	3.40753	0.112896	0.0564482	−	0.998406i	$-0.482022\pi$
$911$	3.40753	0.112896	0.0564482	+	0.998406i	$0.482022\pi$
$912$	− 3.28917i	− 0.108915i
$913$	38.2686i	1.26650i
$914$	29.8958	0.988864
$915$	0	0
$916$	−23.7250	−0.783895
$917$	− 9.44279i	− 0.311828i
$918$	− 34.0036i	− 1.12229i
$919$	−2.59392	−0.0855656	−0.0427828	−	0.999084i	$-0.513622\pi$
$919$	−2.59392	−0.0855656	−0.0427828	+	0.999084i	$0.513622\pi$
$920$	0	0
$921$	41.1320	1.35534
$922$	− 33.2927i	− 1.09644i
$923$	17.6272i	0.580207i
$924$	13.3522	0.439254
$925$	0	0
$926$	13.1184	0.431096
$927$	5.09273i	0.167267i
$928$	1.00000i	0.0328266i
$929$	−8.56420	−0.280982	−0.140491	−	0.990082i	$-0.544868\pi$
$929$	−8.56420	−0.280982	−0.140491	+	0.990082i	$0.544868\pi$
$930$	0	0
$931$	−1.13752	−0.0372806
$932$	− 24.0625i	− 0.788193i
$933$	− 16.4806i	− 0.539550i
$934$	4.15165	0.135846
$935$	0	0
$936$	0.897225	0.0293267
$937$	0.498289i	0.0162784i	0.999967	+	0.00813920i	$0.00259082\pi$
$937$	0.498289i	0.0162784i	−0.999967	+	0.00813920i	$0.997409\pi$
$938$	− 6.76830i	− 0.220993i
$939$	−45.4544	−1.48335
$940$	0	0
$941$	13.1028	0.427138	0.213569	−	0.976928i	$-0.431491\pi$
$941$	13.1028	0.427138	0.213569	+	0.976928i	$0.431491\pi$
$942$	31.7194i	1.03347i
$943$	− 47.6756i	− 1.55253i
$944$	−2.60806	−0.0848850
$945$	0	0
$946$	14.7244	0.478733
$947$	− 5.67107i	− 0.184285i	−0.995746	−	0.0921424i	$-0.970628\pi$
$947$	− 5.67107i	− 0.184285i	0.995746	−	0.0921424i	$-0.0293715\pi$
$948$	− 3.14663i	− 0.102198i
$949$	46.7527	1.51766
$950$	0	0
$951$	−27.1128	−0.879193
$952$	− 17.4600i	− 0.565881i
$953$	− 31.9824i	− 1.03601i	−0.855377	−	0.518007i	$-0.826674\pi$
$953$	− 31.9824i	− 1.03601i	0.855377	−	0.518007i	$-0.173326\pi$
$954$	−1.53500	−0.0496975
$955$	0	0
$956$	−4.31335	−0.139504
$957$	5.28917i	0.170975i
$958$	42.7144i	1.38004i
$959$	−29.7834	−0.961755
$960$	0	0
$961$	34.9658	1.12793
$962$	− 22.9355i	− 0.739471i
$963$	1.24583i	0.0401464i
$964$	27.7144	0.892621
$965$	0	0
$966$	−26.0100	−0.836860
$967$	14.0484i	0.451765i	0.974155	+	0.225882i	$0.0725265\pi$
$967$	14.0484i	0.451765i	−0.974155	+	0.225882i	$0.927473\pi$
$968$	− 2.49472i	− 0.0801833i
$969$	−22.7491	−0.730808
$970$	0	0
$971$	46.7436	1.50007	0.750037	−	0.661396i	$-0.230036\pi$
$971$	46.7436	1.50007	0.750037	+	0.661396i	$0.230036\pi$
$972$	2.99498i	0.0960639i
$973$	31.0716i	0.996110i
$974$	−18.3728	−0.588702
$975$	0	0
$976$	−10.0680	−0.322270
$977$	− 32.8016i	− 1.04942i	−0.851282	−	0.524708i	$-0.824175\pi$
$977$	− 32.8016i	− 1.04942i	0.851282	−	0.524708i	$-0.175825\pi$
$978$	− 5.49472i	− 0.175702i
$979$	15.2680	0.487969
$980$	0	0
$981$	−2.18996	−0.0699202
$982$	0.881639i	0.0281342i
$983$	− 47.5225i	− 1.51573i	−0.652411	−	0.757866i	$-0.726242\pi$
$983$	− 47.5225i	− 1.51573i	0.652411	−	0.757866i	$-0.273758\pi$
$984$	−15.2197	−0.485186
$985$	0	0
$986$	6.91638	0.220262
$987$	− 22.2851i	− 0.709342i
$988$	5.62721i	0.179025i
$989$	−28.6832	−0.912074
$990$	0	0
$991$	3.00052	0.0953145	0.0476573	−	0.998864i	$-0.484824\pi$
$991$	3.00052	0.0953145	0.0476573	+	0.998864i	$0.484824\pi$
$992$	8.12193i	0.257872i
$993$	− 32.8752i	− 1.04326i
$994$	−14.3416	−0.454888
$995$	0	0
$996$	−23.7980	−0.754069
$997$	42.3502i	1.34124i	0.741799	+	0.670622i	$0.233973\pi$
$997$	42.3502i	1.34124i	−0.741799	+	0.670622i	$0.766027\pi$
$998$	32.4791i	1.02811i
$999$	36.3416	1.14980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.k.349.3		6
5.2	odd	4		1450.2.a.s.1.3	yes	3
5.3	odd	4		1450.2.a.q.1.1	✓	3
5.4	even	2	inner	1450.2.b.k.349.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.a.q.1.1	✓	3	5.3	odd	4
1450.2.a.s.1.3	yes	3	5.2	odd	4
1450.2.b.k.349.3		6	1.1	even	1	trivial
1450.2.b.k.349.4		6	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.81361i q^{3} -1.00000 q^{4} +1.81361 q^{6} -2.52444i q^{7} +1.00000i q^{8} -0.289169 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.81361i q^{3} -1.00000 q^{4} +1.81361 q^{6} -2.52444i q^{7} +1.00000i q^{8} -0.289169 q^{9} -2.91638 q^{11} -1.81361i q^{12} +3.10278i q^{13} -2.52444 q^{14} +1.00000 q^{16} -6.91638i q^{17} +0.289169i q^{18} -1.81361 q^{19} +4.57834 q^{21} +2.91638i q^{22} -5.68111i q^{23} -1.81361 q^{24} +3.10278 q^{26} +4.91638i q^{27} +2.52444i q^{28} -1.00000 q^{29} -8.12193 q^{31} -1.00000i q^{32} -5.28917i q^{33} -6.91638 q^{34} +0.289169 q^{36} -7.39194i q^{37} +1.81361i q^{38} -5.62721 q^{39} +8.39194 q^{41} -4.57834i q^{42} -5.04888i q^{43} +2.91638 q^{44} -5.68111 q^{46} -4.86751i q^{47} +1.81361i q^{48} +0.627213 q^{49} +12.5436 q^{51} -3.10278i q^{52} +5.30833i q^{53} +4.91638 q^{54} +2.52444 q^{56} -3.28917i q^{57} +1.00000i q^{58} -2.60806 q^{59} -10.0680 q^{61} +8.12193i q^{62} +0.729988i q^{63} -1.00000 q^{64} -5.28917 q^{66} +2.68111i q^{67} +6.91638i q^{68} +10.3033 q^{69} +5.68111 q^{71} -0.289169i q^{72} -15.0680i q^{73} -7.39194 q^{74} +1.81361 q^{76} +7.36222i q^{77} +5.62721i q^{78} +1.73501 q^{79} -9.78389 q^{81} -8.39194i q^{82} -13.1219i q^{83} -4.57834 q^{84} -5.04888 q^{86} -1.81361i q^{87} -2.91638i q^{88} -5.23527 q^{89} +7.83276 q^{91} +5.68111i q^{92} -14.7300i q^{93} -4.86751 q^{94} +1.81361 q^{96} -1.27001i q^{97} -0.627213i q^{98} +0.843326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{6}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^6	\( 6 q - 6 q^{4} - 2 q^{6} + 10 q^{11} - 4 q^{14} + 6 q^{16} + 2 q^{19} + 24 q^{21} + 2 q^{24} + 4 q^{26} - 6 q^{29} + 8 q^{31} - 14 q^{34} - 8 q^{39} + 34 q^{41} - 10 q^{44} - 16 q^{46} - 22 q^{49} + 22 q^{51} + 2 q^{54} + 4 q^{56} - 32 q^{59} + 4 q^{61} - 6 q^{64} - 30 q^{66} - 12 q^{69} + 16 q^{71} - 28 q^{74} - 2 q^{76} - 26 q^{81} - 24 q^{84} - 8 q^{86} - 22 q^{89} - 8 q^{91} - 24 q^{94} - 2 q^{96} + 12 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^6 + 10 * q^11 - 4 * q^14 + 6 * q^16 + 2 * q^19 + 24 * q^21 + 2 * q^24 + 4 * q^26 - 6 * q^29 + 8 * q^31 - 14 * q^34 - 8 * q^39 + 34 * q^41 - 10 * q^44 - 16 * q^46 - 22 * q^49 + 22 * q^51 + 2 * q^54 + 4 * q^56 - 32 * q^59 + 4 * q^61 - 6 * q^64 - 30 * q^66 - 12 * q^69 + 16 * q^71 - 28 * q^74 - 2 * q^76 - 26 * q^81 - 24 * q^84 - 8 * q^86 - 22 * q^89 - 8 * q^91 - 24 * q^94 - 2 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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