LMFDB - Embedded newform 1450.2.b.h.349.4

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:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.4
Root			$2.30278i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.h.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -3.30278i q^{7} -1.00000i q^{8} -2.30278 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -3.30278i q^{7} -1.00000i q^{8} -2.30278 q^{9} -2.60555 q^{11} -2.30278i q^{12} -2.30278i q^{13} +3.30278 q^{14} +1.00000 q^{16} -1.30278i q^{17} -2.30278i q^{18} +0.605551 q^{19} +7.60555 q^{21} -2.60555i q^{22} -6.90833i q^{23} +2.30278 q^{24} +2.30278 q^{26} +1.60555i q^{27} +3.30278i q^{28} +1.00000 q^{29} +6.69722 q^{31} +1.00000i q^{32} -6.00000i q^{33} +1.30278 q^{34} +2.30278 q^{36} +0.605551i q^{37} +0.605551i q^{38} +5.30278 q^{39} +8.60555 q^{41} +7.60555i q^{42} +3.30278i q^{43} +2.60555 q^{44} +6.90833 q^{46} -5.21110i q^{47} +2.30278i q^{48} -3.90833 q^{49} +3.00000 q^{51} +2.30278i q^{52} -13.3028i q^{53} -1.60555 q^{54} -3.30278 q^{56} +1.39445i q^{57} +1.00000i q^{58} +7.69722 q^{59} +0.302776 q^{61} +6.69722i q^{62} +7.60555i q^{63} -1.00000 q^{64} +6.00000 q^{66} +4.00000i q^{67} +1.30278i q^{68} +15.9083 q^{69} -5.21110 q^{71} +2.30278i q^{72} -13.1194i q^{73} -0.605551 q^{74} -0.605551 q^{76} +8.60555i q^{77} +5.30278i q^{78} -8.90833 q^{79} -10.6056 q^{81} +8.60555i q^{82} -13.8167i q^{83} -7.60555 q^{84} -3.30278 q^{86} +2.30278i q^{87} +2.60555i q^{88} -7.81665 q^{89} -7.60555 q^{91} +6.90833i q^{92} +15.4222i q^{93} +5.21110 q^{94} -2.30278 q^{96} +16.1194i q^{97} -3.90833i q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} + 4 q^{11} + 6 q^{14} + 4 q^{16} - 12 q^{19} + 16 q^{21} + 2 q^{24} + 2 q^{26} + 4 q^{29} + 34 q^{31} - 2 q^{34} + 2 q^{36} + 14 q^{39} + 20 q^{41} - 4 q^{44} + 6 q^{46} + 6 q^{49} + 12 q^{51} + 8 q^{54} - 6 q^{56} + 38 q^{59} - 6 q^{61} - 4 q^{64} + 24 q^{66} + 42 q^{69} + 8 q^{71} + 12 q^{74} + 12 q^{76} - 14 q^{79} - 28 q^{81} - 16 q^{84} - 6 q^{86} + 12 q^{89} - 16 q^{91} - 8 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 + 4 * q^11 + 6 * q^14 + 4 * q^16 - 12 * q^19 + 16 * q^21 + 2 * q^24 + 2 * q^26 + 4 * q^29 + 34 * q^31 - 2 * q^34 + 2 * q^36 + 14 * q^39 + 20 * q^41 - 4 * q^44 + 6 * q^46 + 6 * q^49 + 12 * q^51 + 8 * q^54 - 6 * q^56 + 38 * q^59 - 6 * q^61 - 4 * q^64 + 24 * q^66 + 42 * q^69 + 8 * q^71 + 12 * q^74 + 12 * q^76 - 14 * q^79 - 28 * q^81 - 16 * q^84 - 6 * q^86 + 12 * q^89 - 16 * q^91 - 8 * q^94 - 2 * q^96 + 24 * 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
$3$	2.30278i	1.32951i	0.747062	+	0.664754i	$0.231464\pi$
$3$	2.30278i	1.32951i	−0.747062	+	0.664754i	$0.768536\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−2.30278	−0.940104
$7$	− 3.30278i	− 1.24833i	−0.781292	−	0.624166i	$-0.785439\pi$
$7$	− 3.30278i	− 1.24833i	0.781292	−	0.624166i	$-0.214561\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−2.30278	−0.767592
$10$	0	0
$11$	−2.60555	−0.785603	−0.392802	−	0.919623i	$-0.628494\pi$
$11$	−2.60555	−0.785603	−0.392802	+	0.919623i	$0.628494\pi$
$12$	− 2.30278i	− 0.664754i
$13$	− 2.30278i	− 0.638675i	−0.947641	−	0.319338i	$-0.896540\pi$
$13$	− 2.30278i	− 0.638675i	0.947641	−	0.319338i	$-0.103460\pi$
$14$	3.30278	0.882704
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.30278i	− 0.315970i	−0.987442	−	0.157985i	$-0.949500\pi$
$17$	− 1.30278i	− 0.315970i	0.987442	−	0.157985i	$-0.0504997\pi$
$18$	− 2.30278i	− 0.542769i
$19$	0.605551	0.138923	0.0694615	−	0.997585i	$-0.477872\pi$
$19$	0.605551	0.138923	0.0694615	+	0.997585i	$0.477872\pi$
$20$	0	0
$21$	7.60555	1.65967
$22$	− 2.60555i	− 0.555505i
$23$	− 6.90833i	− 1.44049i	−0.693722	−	0.720243i	$-0.744030\pi$
$23$	− 6.90833i	− 1.44049i	0.693722	−	0.720243i	$-0.255970\pi$
$24$	2.30278	0.470052
$25$	0	0
$26$	2.30278	0.451611
$27$	1.60555i	0.308988i
$28$	3.30278i	0.624166i
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	6.69722	1.20286	0.601429	−	0.798927i	$-0.294598\pi$
$31$	6.69722	1.20286	0.601429	+	0.798927i	$0.294598\pi$
$32$	1.00000i	0.176777i
$33$	− 6.00000i	− 1.04447i
$34$	1.30278	0.223424
$35$	0	0
$36$	2.30278	0.383796
$37$	0.605551i	0.0995520i	0.998760	+	0.0497760i	$0.0158507\pi$
$37$	0.605551i	0.0995520i	−0.998760	+	0.0497760i	$0.984149\pi$
$38$	0.605551i	0.0982334i
$39$	5.30278	0.849124
$40$	0	0
$41$	8.60555	1.34396	0.671981	−	0.740569i	$-0.265444\pi$
$41$	8.60555	1.34396	0.671981	+	0.740569i	$0.265444\pi$
$42$	7.60555i	1.17356i
$43$	3.30278i	0.503669i	0.967770	+	0.251834i	$0.0810338\pi$
$43$	3.30278i	0.503669i	−0.967770	+	0.251834i	$0.918966\pi$
$44$	2.60555	0.392802
$45$	0	0
$46$	6.90833	1.01858
$47$	− 5.21110i	− 0.760117i	−0.924962	−	0.380059i	$-0.875904\pi$
$47$	− 5.21110i	− 0.760117i	0.924962	−	0.380059i	$-0.124096\pi$
$48$	2.30278i	0.332377i
$49$	−3.90833	−0.558332
$50$	0	0
$51$	3.00000	0.420084
$52$	2.30278i	0.319338i
$53$	− 13.3028i	− 1.82728i	−0.406528	−	0.913638i	$-0.633261\pi$
$53$	− 13.3028i	− 1.82728i	0.406528	−	0.913638i	$-0.366739\pi$
$54$	−1.60555	−0.218488
$55$	0	0
$56$	−3.30278	−0.441352
$57$	1.39445i	0.184699i
$58$	1.00000i	0.131306i
$59$	7.69722	1.00209	0.501047	−	0.865420i	$-0.332949\pi$
$59$	7.69722	1.00209	0.501047	+	0.865420i	$0.332949\pi$
$60$	0	0
$61$	0.302776	0.0387664	0.0193832	−	0.999812i	$-0.493830\pi$
$61$	0.302776	0.0387664	0.0193832	+	0.999812i	$0.493830\pi$
$62$	6.69722i	0.850548i
$63$	7.60555i	0.958209i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	1.30278i	0.157985i
$69$	15.9083	1.91514
$70$	0	0
$71$	−5.21110	−0.618444	−0.309222	−	0.950990i	$-0.600069\pi$
$71$	−5.21110	−0.618444	−0.309222	+	0.950990i	$0.600069\pi$
$72$	2.30278i	0.271385i
$73$	− 13.1194i	− 1.53551i	−0.640742	−	0.767757i	$-0.721373\pi$
$73$	− 13.1194i	− 1.53551i	0.640742	−	0.767757i	$-0.278627\pi$
$74$	−0.605551	−0.0703939
$75$	0	0
$76$	−0.605551	−0.0694615
$77$	8.60555i	0.980694i
$78$	5.30278i	0.600421i
$79$	−8.90833	−1.00227	−0.501133	−	0.865371i	$-0.667083\pi$
$79$	−8.90833	−1.00227	−0.501133	+	0.865371i	$0.667083\pi$
$80$	0	0
$81$	−10.6056	−1.17839
$82$	8.60555i	0.950324i
$83$	− 13.8167i	− 1.51657i	−0.651920	−	0.758287i	$-0.726036\pi$
$83$	− 13.8167i	− 1.51657i	0.651920	−	0.758287i	$-0.273964\pi$
$84$	−7.60555	−0.829834
$85$	0	0
$86$	−3.30278	−0.356147
$87$	2.30278i	0.246883i
$88$	2.60555i	0.277753i
$89$	−7.81665	−0.828564	−0.414282	−	0.910149i	$-0.635967\pi$
$89$	−7.81665	−0.828564	−0.414282	+	0.910149i	$0.635967\pi$
$90$	0	0
$91$	−7.60555	−0.797278
$92$	6.90833i	0.720243i
$93$	15.4222i	1.59921i
$94$	5.21110	0.537484
$95$	0	0
$96$	−2.30278	−0.235026
$97$	16.1194i	1.63668i	0.574734	+	0.818340i	$0.305105\pi$
$97$	16.1194i	1.63668i	−0.574734	+	0.818340i	$0.694895\pi$
$98$	− 3.90833i	− 0.394801i
$99$	6.00000	0.603023
$100$	0	0
$101$	18.1194	1.80295	0.901475	−	0.432831i	$-0.142485\pi$
$101$	18.1194	1.80295	0.901475	+	0.432831i	$0.142485\pi$
$102$	3.00000i	0.297044i
$103$	18.4222i	1.81519i	0.419843	+	0.907597i	$0.362085\pi$
$103$	18.4222i	1.81519i	−0.419843	+	0.907597i	$0.637915\pi$
$104$	−2.30278	−0.225806
$105$	0	0
$106$	13.3028	1.29208
$107$	− 8.60555i	− 0.831930i	−0.909381	−	0.415965i	$-0.863444\pi$
$107$	− 8.60555i	− 0.831930i	0.909381	−	0.415965i	$-0.136556\pi$
$108$	− 1.60555i	− 0.154494i
$109$	0.605551	0.0580013	0.0290006	−	0.999579i	$-0.490768\pi$
$109$	0.605551	0.0580013	0.0290006	+	0.999579i	$0.490768\pi$
$110$	0	0
$111$	−1.39445	−0.132355
$112$	− 3.30278i	− 0.312083i
$113$	− 6.90833i	− 0.649881i	−0.945735	−	0.324940i	$-0.894656\pi$
$113$	− 6.90833i	− 0.649881i	0.945735	−	0.324940i	$-0.105344\pi$
$114$	−1.39445	−0.130602
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	5.30278i	0.490242i
$118$	7.69722i	0.708587i
$119$	−4.30278	−0.394435
$120$	0	0
$121$	−4.21110	−0.382828
$122$	0.302776i	0.0274120i
$123$	19.8167i	1.78681i
$124$	−6.69722	−0.601429
$125$	0	0
$126$	−7.60555	−0.677556
$127$	− 13.2111i	− 1.17230i	−0.810204	−	0.586148i	$-0.800644\pi$
$127$	− 13.2111i	− 1.17230i	0.810204	−	0.586148i	$-0.199356\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−7.60555	−0.669631
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	6.00000i	0.522233i
$133$	− 2.00000i	− 0.173422i
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−1.30278	−0.111712
$137$	12.1194i	1.03543i	0.855552	+	0.517716i	$0.173218\pi$
$137$	12.1194i	1.03543i	−0.855552	+	0.517716i	$0.826782\pi$
$138$	15.9083i	1.35421i
$139$	−22.3305	−1.89405	−0.947026	−	0.321158i	$-0.895928\pi$
$139$	−22.3305	−1.89405	−0.947026	+	0.321158i	$0.895928\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	− 5.21110i	− 0.437306i
$143$	6.00000i	0.501745i
$144$	−2.30278	−0.191898
$145$	0	0
$146$	13.1194	1.08577
$147$	− 9.00000i	− 0.742307i
$148$	− 0.605551i	− 0.0497760i
$149$	19.8167	1.62344	0.811722	−	0.584044i	$-0.198531\pi$
$149$	19.8167	1.62344	0.811722	+	0.584044i	$0.198531\pi$
$150$	0	0
$151$	−0.605551	−0.0492791	−0.0246395	−	0.999696i	$-0.507844\pi$
$151$	−0.605551	−0.0492791	−0.0246395	+	0.999696i	$0.507844\pi$
$152$	− 0.605551i	− 0.0491167i
$153$	3.00000i	0.242536i
$154$	−8.60555	−0.693455
$155$	0	0
$156$	−5.30278	−0.424562
$157$	− 7.21110i	− 0.575509i	−0.957704	−	0.287754i	$-0.907091\pi$
$157$	− 7.21110i	− 0.575509i	0.957704	−	0.287754i	$-0.0929087\pi$
$158$	− 8.90833i	− 0.708708i
$159$	30.6333	2.42938
$160$	0	0
$161$	−22.8167	−1.79820
$162$	− 10.6056i	− 0.833251i
$163$	13.2111i	1.03477i	0.855752	+	0.517387i	$0.173095\pi$
$163$	13.2111i	1.03477i	−0.855752	+	0.517387i	$0.826905\pi$
$164$	−8.60555	−0.671981
$165$	0	0
$166$	13.8167	1.07238
$167$	− 19.3028i	− 1.49369i	−0.664996	−	0.746847i	$-0.731567\pi$
$167$	− 19.3028i	− 1.49369i	0.664996	−	0.746847i	$-0.268433\pi$
$168$	− 7.60555i	− 0.586781i
$169$	7.69722	0.592094
$170$	0	0
$171$	−1.39445	−0.106636
$172$	− 3.30278i	− 0.251834i
$173$	3.51388i	0.267155i	0.991038	+	0.133578i	$0.0426465\pi$
$173$	3.51388i	0.267155i	−0.991038	+	0.133578i	$0.957353\pi$
$174$	−2.30278	−0.174573
$175$	0	0
$176$	−2.60555	−0.196401
$177$	17.7250i	1.33229i
$178$	− 7.81665i	− 0.585883i
$179$	−7.69722	−0.575318	−0.287659	−	0.957733i	$-0.592877\pi$
$179$	−7.69722	−0.575318	−0.287659	+	0.957733i	$0.592877\pi$
$180$	0	0
$181$	9.81665	0.729666	0.364833	−	0.931073i	$-0.381126\pi$
$181$	9.81665	0.729666	0.364833	+	0.931073i	$0.381126\pi$
$182$	− 7.60555i	− 0.563761i
$183$	0.697224i	0.0515403i
$184$	−6.90833	−0.509289
$185$	0	0
$186$	−15.4222	−1.13081
$187$	3.39445i	0.248227i
$188$	5.21110i	0.380059i
$189$	5.30278	0.385720
$190$	0	0
$191$	11.7250	0.848390	0.424195	−	0.905571i	$-0.360557\pi$
$191$	11.7250	0.848390	0.424195	+	0.905571i	$0.360557\pi$
$192$	− 2.30278i	− 0.166189i
$193$	− 7.51388i	− 0.540861i	−0.962740	−	0.270430i	$-0.912834\pi$
$193$	− 7.51388i	− 0.540861i	0.962740	−	0.270430i	$-0.0871660\pi$
$194$	−16.1194	−1.15731
$195$	0	0
$196$	3.90833	0.279166
$197$	− 21.1194i	− 1.50470i	−0.658765	−	0.752349i	$-0.728921\pi$
$197$	− 21.1194i	− 1.50470i	0.658765	−	0.752349i	$-0.271079\pi$
$198$	6.00000i	0.426401i
$199$	−5.39445	−0.382402	−0.191201	−	0.981551i	$-0.561238\pi$
$199$	−5.39445	−0.382402	−0.191201	+	0.981551i	$0.561238\pi$
$200$	0	0
$201$	−9.21110	−0.649701
$202$	18.1194i	1.27488i
$203$	− 3.30278i	− 0.231809i
$204$	−3.00000	−0.210042
$205$	0	0
$206$	−18.4222	−1.28354
$207$	15.9083i	1.10571i
$208$	− 2.30278i	− 0.159669i
$209$	−1.57779	−0.109138
$210$	0	0
$211$	−11.8167	−0.813492	−0.406746	−	0.913541i	$-0.633337\pi$
$211$	−11.8167	−0.813492	−0.406746	+	0.913541i	$0.633337\pi$
$212$	13.3028i	0.913638i
$213$	− 12.0000i	− 0.822226i
$214$	8.60555	0.588263
$215$	0	0
$216$	1.60555	0.109244
$217$	− 22.1194i	− 1.50156i
$218$	0.605551i	0.0410131i
$219$	30.2111	2.04148
$220$	0	0
$221$	−3.00000	−0.201802
$222$	− 1.39445i	− 0.0935893i
$223$	− 26.5416i	− 1.77736i	−0.458529	−	0.888680i	$-0.651623\pi$
$223$	− 26.5416i	− 1.77736i	0.458529	−	0.888680i	$-0.348377\pi$
$224$	3.30278	0.220676
$225$	0	0
$226$	6.90833	0.459535
$227$	18.0000i	1.19470i	0.801980	+	0.597351i	$0.203780\pi$
$227$	18.0000i	1.19470i	−0.801980	+	0.597351i	$0.796220\pi$
$228$	− 1.39445i	− 0.0923496i
$229$	1.90833	0.126106	0.0630529	−	0.998010i	$-0.479916\pi$
$229$	1.90833	0.126106	0.0630529	+	0.998010i	$0.479916\pi$
$230$	0	0
$231$	−19.8167	−1.30384
$232$	− 1.00000i	− 0.0656532i
$233$	− 12.7889i	− 0.837829i	−0.908026	−	0.418914i	$-0.862411\pi$
$233$	− 12.7889i	− 0.837829i	0.908026	−	0.418914i	$-0.137589\pi$
$234$	−5.30278	−0.346653
$235$	0	0
$236$	−7.69722	−0.501047
$237$	− 20.5139i	− 1.33252i
$238$	− 4.30278i	− 0.278908i
$239$	−23.2111	−1.50140	−0.750701	−	0.660642i	$-0.770284\pi$
$239$	−23.2111	−1.50140	−0.750701	+	0.660642i	$0.770284\pi$
$240$	0	0
$241$	10.7250	0.690857	0.345428	−	0.938445i	$-0.387734\pi$
$241$	10.7250	0.690857	0.345428	+	0.938445i	$0.387734\pi$
$242$	− 4.21110i	− 0.270700i
$243$	− 19.6056i	− 1.25770i
$244$	−0.302776	−0.0193832
$245$	0	0
$246$	−19.8167	−1.26346
$247$	− 1.39445i	− 0.0887266i
$248$	− 6.69722i	− 0.425274i
$249$	31.8167	2.01630
$250$	0	0
$251$	19.0278	1.20102	0.600511	−	0.799617i	$-0.294964\pi$
$251$	19.0278	1.20102	0.600511	+	0.799617i	$0.294964\pi$
$252$	− 7.60555i	− 0.479105i
$253$	18.0000i	1.13165i
$254$	13.2111	0.828938
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 25.8167i	− 1.61040i	−0.593004	−	0.805199i	$-0.702058\pi$
$257$	− 25.8167i	− 1.61040i	0.593004	−	0.805199i	$-0.297942\pi$
$258$	− 7.60555i	− 0.473501i
$259$	2.00000	0.124274
$260$	0	0
$261$	−2.30278	−0.142538
$262$	− 6.00000i	− 0.370681i
$263$	6.78890i	0.418621i	0.977849	+	0.209311i	$0.0671220\pi$
$263$	6.78890i	0.418621i	−0.977849	+	0.209311i	$0.932878\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	2.00000	0.122628
$267$	− 18.0000i	− 1.10158i
$268$	− 4.00000i	− 0.244339i
$269$	20.3305	1.23957	0.619787	−	0.784770i	$-0.287219\pi$
$269$	20.3305	1.23957	0.619787	+	0.784770i	$0.287219\pi$
$270$	0	0
$271$	−10.7889	−0.655379	−0.327689	−	0.944786i	$-0.606270\pi$
$271$	−10.7889	−0.655379	−0.327689	+	0.944786i	$0.606270\pi$
$272$	− 1.30278i	− 0.0789924i
$273$	− 17.5139i	− 1.05999i
$274$	−12.1194	−0.732162
$275$	0	0
$276$	−15.9083	−0.957569
$277$	22.0000i	1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$	22.0000i	1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	− 22.3305i	− 1.33930i
$279$	−15.4222	−0.923303
$280$	0	0
$281$	15.1194	0.901950	0.450975	−	0.892537i	$-0.351076\pi$
$281$	15.1194	0.901950	0.450975	+	0.892537i	$0.351076\pi$
$282$	12.0000i	0.714590i
$283$	28.6056i	1.70042i	0.526441	+	0.850212i	$0.323526\pi$
$283$	28.6056i	1.70042i	−0.526441	+	0.850212i	$0.676474\pi$
$284$	5.21110	0.309222
$285$	0	0
$286$	−6.00000	−0.354787
$287$	− 28.4222i	− 1.67771i
$288$	− 2.30278i	− 0.135692i
$289$	15.3028	0.900163
$290$	0	0
$291$	−37.1194	−2.17598
$292$	13.1194i	0.767757i
$293$	19.0278i	1.11161i	0.831312	+	0.555807i	$0.187591\pi$
$293$	19.0278i	1.11161i	−0.831312	+	0.555807i	$0.812409\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	0.605551	0.0351970
$297$	− 4.18335i	− 0.242742i
$298$	19.8167i	1.14795i
$299$	−15.9083	−0.920002
$300$	0	0
$301$	10.9083	0.628746
$302$	− 0.605551i	− 0.0348456i
$303$	41.7250i	2.39704i
$304$	0.605551	0.0347307
$305$	0	0
$306$	−3.00000	−0.171499
$307$	− 1.21110i	− 0.0691213i	−0.999403	−	0.0345606i	$-0.988997\pi$
$307$	− 1.21110i	− 0.0691213i	0.999403	−	0.0345606i	$-0.0110032\pi$
$308$	− 8.60555i	− 0.490347i
$309$	−42.4222	−2.41331
$310$	0	0
$311$	11.0917	0.628951	0.314476	−	0.949266i	$-0.398171\pi$
$311$	11.0917	0.628951	0.314476	+	0.949266i	$0.398171\pi$
$312$	− 5.30278i	− 0.300211i
$313$	− 16.7889i	− 0.948965i	−0.880265	−	0.474482i	$-0.842635\pi$
$313$	− 16.7889i	− 0.948965i	0.880265	−	0.474482i	$-0.157365\pi$
$314$	7.21110	0.406946
$315$	0	0
$316$	8.90833	0.501133
$317$	− 4.18335i	− 0.234960i	−0.993075	−	0.117480i	$-0.962518\pi$
$317$	− 4.18335i	− 0.234960i	0.993075	−	0.117480i	$-0.0374816\pi$
$318$	30.6333i	1.71783i
$319$	−2.60555	−0.145883
$320$	0	0
$321$	19.8167	1.10606
$322$	− 22.8167i	− 1.27152i
$323$	− 0.788897i	− 0.0438954i
$324$	10.6056	0.589197
$325$	0	0
$326$	−13.2111	−0.731695
$327$	1.39445i	0.0771132i
$328$	− 8.60555i	− 0.475162i
$329$	−17.2111	−0.948879
$330$	0	0
$331$	−13.3944	−0.736225	−0.368113	−	0.929781i	$-0.619996\pi$
$331$	−13.3944	−0.736225	−0.368113	+	0.929781i	$0.619996\pi$
$332$	13.8167i	0.758287i
$333$	− 1.39445i	− 0.0764153i
$334$	19.3028	1.05620
$335$	0	0
$336$	7.60555	0.414917
$337$	− 13.4861i	− 0.734636i	−0.930095	−	0.367318i	$-0.880276\pi$
$337$	− 13.4861i	− 0.734636i	0.930095	−	0.367318i	$-0.119724\pi$
$338$	7.69722i	0.418674i
$339$	15.9083	0.864022
$340$	0	0
$341$	−17.4500	−0.944968
$342$	− 1.39445i	− 0.0754032i
$343$	− 10.2111i	− 0.551348i
$344$	3.30278	0.178074
$345$	0	0
$346$	−3.51388	−0.188907
$347$	13.8167i	0.741717i	0.928689	+	0.370858i	$0.120936\pi$
$347$	13.8167i	0.741717i	−0.928689	+	0.370858i	$0.879064\pi$
$348$	− 2.30278i	− 0.123442i
$349$	19.6333	1.05095	0.525473	−	0.850810i	$-0.323888\pi$
$349$	19.6333	1.05095	0.525473	+	0.850810i	$0.323888\pi$
$350$	0	0
$351$	3.69722	0.197343
$352$	− 2.60555i	− 0.138876i
$353$	22.4222i	1.19341i	0.802459	+	0.596707i	$0.203524\pi$
$353$	22.4222i	1.19341i	−0.802459	+	0.596707i	$0.796476\pi$
$354$	−17.7250	−0.942072
$355$	0	0
$356$	7.81665	0.414282
$357$	− 9.90833i	− 0.524404i
$358$	− 7.69722i	− 0.406811i
$359$	−11.0917	−0.585396	−0.292698	−	0.956205i	$-0.594553\pi$
$359$	−11.0917	−0.585396	−0.292698	+	0.956205i	$0.594553\pi$
$360$	0	0
$361$	−18.6333	−0.980700
$362$	9.81665i	0.515952i
$363$	− 9.69722i	− 0.508972i
$364$	7.60555	0.398639
$365$	0	0
$366$	−0.697224	−0.0364445
$367$	2.18335i	0.113970i	0.998375	+	0.0569849i	$0.0181487\pi$
$367$	2.18335i	0.113970i	−0.998375	+	0.0569849i	$0.981851\pi$
$368$	− 6.90833i	− 0.360121i
$369$	−19.8167	−1.03161
$370$	0	0
$371$	−43.9361	−2.28105
$372$	− 15.4222i	− 0.799604i
$373$	− 3.72498i	− 0.192872i	−0.995339	−	0.0964361i	$-0.969256\pi$
$373$	− 3.72498i	− 0.192872i	0.995339	−	0.0964361i	$-0.0307443\pi$
$374$	−3.39445	−0.175523
$375$	0	0
$376$	−5.21110	−0.268742
$377$	− 2.30278i	− 0.118599i
$378$	5.30278i	0.272745i
$379$	23.8167	1.22338	0.611690	−	0.791098i	$-0.290490\pi$
$379$	23.8167	1.22338	0.611690	+	0.791098i	$0.290490\pi$
$380$	0	0
$381$	30.4222	1.55858
$382$	11.7250i	0.599902i
$383$	7.30278i	0.373154i	0.982440	+	0.186577i	$0.0597394\pi$
$383$	7.30278i	0.373154i	−0.982440	+	0.186577i	$0.940261\pi$
$384$	2.30278	0.117513
$385$	0	0
$386$	7.51388	0.382446
$387$	− 7.60555i	− 0.386612i
$388$	− 16.1194i	− 0.818340i
$389$	−4.42221	−0.224215	−0.112107	−	0.993696i	$-0.535760\pi$
$389$	−4.42221	−0.224215	−0.112107	+	0.993696i	$0.535760\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	3.90833i	0.197400i
$393$	− 13.8167i	− 0.696958i
$394$	21.1194	1.06398
$395$	0	0
$396$	−6.00000	−0.301511
$397$	2.69722i	0.135370i	0.997707	+	0.0676849i	$0.0215613\pi$
$397$	2.69722i	0.135370i	−0.997707	+	0.0676849i	$0.978439\pi$
$398$	− 5.39445i	− 0.270399i
$399$	4.60555	0.230566
$400$	0	0
$401$	−6.11943	−0.305590	−0.152795	−	0.988258i	$-0.548827\pi$
$401$	−6.11943	−0.305590	−0.152795	+	0.988258i	$0.548827\pi$
$402$	− 9.21110i	− 0.459408i
$403$	− 15.4222i	− 0.768235i
$404$	−18.1194	−0.901475
$405$	0	0
$406$	3.30278	0.163914
$407$	− 1.57779i	− 0.0782084i
$408$	− 3.00000i	− 0.148522i
$409$	−25.2111	−1.24661	−0.623304	−	0.781979i	$-0.714210\pi$
$409$	−25.2111	−1.24661	−0.623304	+	0.781979i	$0.714210\pi$
$410$	0	0
$411$	−27.9083	−1.37662
$412$	− 18.4222i	− 0.907597i
$413$	− 25.4222i	− 1.25094i
$414$	−15.9083	−0.781852
$415$	0	0
$416$	2.30278	0.112903
$417$	− 51.4222i	− 2.51816i
$418$	− 1.57779i	− 0.0771725i
$419$	−30.5139	−1.49070	−0.745350	−	0.666673i	$-0.767718\pi$
$419$	−30.5139	−1.49070	−0.745350	+	0.666673i	$0.767718\pi$
$420$	0	0
$421$	17.6333	0.859395	0.429697	−	0.902973i	$-0.358620\pi$
$421$	17.6333	0.859395	0.429697	+	0.902973i	$0.358620\pi$
$422$	− 11.8167i	− 0.575226i
$423$	12.0000i	0.583460i
$424$	−13.3028	−0.646040
$425$	0	0
$426$	12.0000	0.581402
$427$	− 1.00000i	− 0.0483934i
$428$	8.60555i	0.415965i
$429$	−13.8167	−0.667074
$430$	0	0
$431$	8.60555	0.414515	0.207257	−	0.978286i	$-0.433546\pi$
$431$	8.60555	0.414515	0.207257	+	0.978286i	$0.433546\pi$
$432$	1.60555i	0.0772471i
$433$	29.6333i	1.42409i	0.702136	+	0.712043i	$0.252230\pi$
$433$	29.6333i	1.42409i	−0.702136	+	0.712043i	$0.747770\pi$
$434$	22.1194	1.06177
$435$	0	0
$436$	−0.605551	−0.0290006
$437$	− 4.18335i	− 0.200117i
$438$	30.2111i	1.44354i
$439$	−22.8444	−1.09030	−0.545152	−	0.838337i	$-0.683528\pi$
$439$	−22.8444	−1.09030	−0.545152	+	0.838337i	$0.683528\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	− 3.00000i	− 0.142695i
$443$	− 17.0917i	− 0.812050i	−0.913862	−	0.406025i	$-0.866915\pi$
$443$	− 17.0917i	− 0.812050i	0.913862	−	0.406025i	$-0.133085\pi$
$444$	1.39445	0.0661776
$445$	0	0
$446$	26.5416	1.25678
$447$	45.6333i	2.15838i
$448$	3.30278i	0.156041i
$449$	−24.2389	−1.14390	−0.571951	−	0.820288i	$-0.693813\pi$
$449$	−24.2389	−1.14390	−0.571951	+	0.820288i	$0.693813\pi$
$450$	0	0
$451$	−22.4222	−1.05582
$452$	6.90833i	0.324940i
$453$	− 1.39445i	− 0.0655169i
$454$	−18.0000	−0.844782
$455$	0	0
$456$	1.39445	0.0653010
$457$	10.0000i	0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$	10.0000i	0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	1.90833i	0.0891703i
$459$	2.09167	0.0976309
$460$	0	0
$461$	17.7250	0.825535	0.412767	−	0.910837i	$-0.364562\pi$
$461$	17.7250	0.825535	0.412767	+	0.910837i	$0.364562\pi$
$462$	− 19.8167i	− 0.921954i
$463$	20.0000i	0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$463$	20.0000i	0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	12.7889	0.592434
$467$	16.6972i	0.772655i	0.922362	+	0.386328i	$0.126257\pi$
$467$	16.6972i	0.772655i	−0.922362	+	0.386328i	$0.873743\pi$
$468$	− 5.30278i	− 0.245121i
$469$	13.2111	0.610032
$470$	0	0
$471$	16.6056	0.765143
$472$	− 7.69722i	− 0.354293i
$473$	− 8.60555i	− 0.395684i
$474$	20.5139	0.942234
$475$	0	0
$476$	4.30278	0.197217
$477$	30.6333i	1.40260i
$478$	− 23.2111i	− 1.06165i
$479$	−42.5139	−1.94251	−0.971254	−	0.238044i	$-0.923494\pi$
$479$	−42.5139	−1.94251	−0.971254	+	0.238044i	$0.923494\pi$
$480$	0	0
$481$	1.39445	0.0635814
$482$	10.7250i	0.488509i
$483$	− 52.5416i	− 2.39073i
$484$	4.21110	0.191414
$485$	0	0
$486$	19.6056	0.889326
$487$	36.7250i	1.66417i	0.554650	+	0.832084i	$0.312852\pi$
$487$	36.7250i	1.66417i	−0.554650	+	0.832084i	$0.687148\pi$
$488$	− 0.302776i	− 0.0137060i
$489$	−30.4222	−1.37574
$490$	0	0
$491$	17.2111	0.776726	0.388363	−	0.921506i	$-0.373041\pi$
$491$	17.2111	0.776726	0.388363	+	0.921506i	$0.373041\pi$
$492$	− 19.8167i	− 0.893404i
$493$	− 1.30278i	− 0.0586741i
$494$	1.39445	0.0627392
$495$	0	0
$496$	6.69722	0.300714
$497$	17.2111i	0.772023i
$498$	31.8167i	1.42574i
$499$	25.5139	1.14216	0.571079	−	0.820895i	$-0.306525\pi$
$499$	25.5139	1.14216	0.571079	+	0.820895i	$0.306525\pi$
$500$	0	0
$501$	44.4500	1.98588
$502$	19.0278i	0.849250i
$503$	− 34.4222i	− 1.53481i	−0.641163	−	0.767405i	$-0.721548\pi$
$503$	− 34.4222i	− 1.53481i	0.641163	−	0.767405i	$-0.278452\pi$
$504$	7.60555	0.338778
$505$	0	0
$506$	−18.0000	−0.800198
$507$	17.7250i	0.787194i
$508$	13.2111i	0.586148i
$509$	1.81665	0.0805218	0.0402609	−	0.999189i	$-0.487181\pi$
$509$	1.81665	0.0805218	0.0402609	+	0.999189i	$0.487181\pi$
$510$	0	0
$511$	−43.3305	−1.91683
$512$	1.00000i	0.0441942i
$513$	0.972244i	0.0429256i
$514$	25.8167	1.13872
$515$	0	0
$516$	7.60555	0.334816
$517$	13.5778i	0.597151i
$518$	2.00000i	0.0878750i
$519$	−8.09167	−0.355185
$520$	0	0
$521$	25.5416	1.11900	0.559500	−	0.828831i	$-0.310993\pi$
$521$	25.5416	1.11900	0.559500	+	0.828831i	$0.310993\pi$
$522$	− 2.30278i	− 0.100790i
$523$	15.0278i	0.657118i	0.944483	+	0.328559i	$0.106563\pi$
$523$	15.0278i	0.657118i	−0.944483	+	0.328559i	$0.893437\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	−6.78890	−0.296010
$527$	− 8.72498i	− 0.380066i
$528$	− 6.00000i	− 0.261116i
$529$	−24.7250	−1.07500
$530$	0	0
$531$	−17.7250	−0.769199
$532$	2.00000i	0.0867110i
$533$	− 19.8167i	− 0.858355i
$534$	18.0000	0.778936
$535$	0	0
$536$	4.00000	0.172774
$537$	− 17.7250i	− 0.764889i
$538$	20.3305i	0.876511i
$539$	10.1833	0.438628
$540$	0	0
$541$	15.3028	0.657918	0.328959	−	0.944344i	$-0.393302\pi$
$541$	15.3028	0.657918	0.328959	+	0.944344i	$0.393302\pi$
$542$	− 10.7889i	− 0.463423i
$543$	22.6056i	0.970097i
$544$	1.30278	0.0558560
$545$	0	0
$546$	17.5139	0.749525
$547$	− 23.3944i	− 1.00027i	−0.865946	−	0.500137i	$-0.833283\pi$
$547$	− 23.3944i	− 1.00027i	0.865946	−	0.500137i	$-0.166717\pi$
$548$	− 12.1194i	− 0.517716i
$549$	−0.697224	−0.0297568
$550$	0	0
$551$	0.605551	0.0257974
$552$	− 15.9083i	− 0.677103i
$553$	29.4222i	1.25116i
$554$	−22.0000	−0.934690
$555$	0	0
$556$	22.3305	0.947026
$557$	34.5416i	1.46358i	0.681532	+	0.731788i	$0.261314\pi$
$557$	34.5416i	1.46358i	−0.681532	+	0.731788i	$0.738686\pi$
$558$	− 15.4222i	− 0.652874i
$559$	7.60555	0.321681
$560$	0	0
$561$	−7.81665	−0.330019
$562$	15.1194i	0.637775i
$563$	− 6.90833i	− 0.291151i	−0.989347	−	0.145576i	$-0.953497\pi$
$563$	− 6.90833i	− 0.291151i	0.989347	−	0.145576i	$-0.0465034\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	−28.6056	−1.20238
$567$	35.0278i	1.47103i
$568$	5.21110i	0.218653i
$569$	3.63331	0.152316	0.0761581	−	0.997096i	$-0.475735\pi$
$569$	3.63331	0.152316	0.0761581	+	0.997096i	$0.475735\pi$
$570$	0	0
$571$	−4.66947	−0.195411	−0.0977056	−	0.995215i	$-0.531150\pi$
$571$	−4.66947	−0.195411	−0.0977056	+	0.995215i	$0.531150\pi$
$572$	− 6.00000i	− 0.250873i
$573$	27.0000i	1.12794i
$574$	28.4222	1.18632
$575$	0	0
$576$	2.30278	0.0959490
$577$	38.6972i	1.61099i	0.592605	+	0.805493i	$0.298100\pi$
$577$	38.6972i	1.61099i	−0.592605	+	0.805493i	$0.701900\pi$
$578$	15.3028i	0.636512i
$579$	17.3028	0.719079
$580$	0	0
$581$	−45.6333	−1.89319
$582$	− 37.1194i	− 1.53865i
$583$	34.6611i	1.43551i
$584$	−13.1194	−0.542886
$585$	0	0
$586$	−19.0278	−0.786029
$587$	18.0000i	0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$	18.0000i	0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$	9.00000i	0.371154i
$589$	4.05551	0.167104
$590$	0	0
$591$	48.6333	2.00051
$592$	0.605551i	0.0248880i
$593$	− 33.3944i	− 1.37135i	−0.727910	−	0.685673i	$-0.759508\pi$
$593$	− 33.3944i	− 1.37135i	0.727910	−	0.685673i	$-0.240492\pi$
$594$	4.18335	0.171645
$595$	0	0
$596$	−19.8167	−0.811722
$597$	− 12.4222i	− 0.508407i
$598$	− 15.9083i	− 0.650540i
$599$	−34.6972	−1.41769	−0.708845	−	0.705364i	$-0.750783\pi$
$599$	−34.6972	−1.41769	−0.708845	+	0.705364i	$0.750783\pi$
$600$	0	0
$601$	12.1833	0.496969	0.248485	−	0.968636i	$-0.420067\pi$
$601$	12.1833	0.496969	0.248485	+	0.968636i	$0.420067\pi$
$602$	10.9083i	0.444590i
$603$	− 9.21110i	− 0.375105i
$604$	0.605551	0.0246395
$605$	0	0
$606$	−41.7250	−1.69496
$607$	16.0000i	0.649420i	0.945814	+	0.324710i	$0.105267\pi$
$607$	16.0000i	0.649420i	−0.945814	+	0.324710i	$0.894733\pi$
$608$	0.605551i	0.0245583i
$609$	7.60555	0.308192
$610$	0	0
$611$	−12.0000	−0.485468
$612$	− 3.00000i	− 0.121268i
$613$	30.6972i	1.23985i	0.784661	+	0.619925i	$0.212837\pi$
$613$	30.6972i	1.23985i	−0.784661	+	0.619925i	$0.787163\pi$
$614$	1.21110	0.0488761
$615$	0	0
$616$	8.60555	0.346728
$617$	− 19.5416i	− 0.786717i	−0.919385	−	0.393358i	$-0.871313\pi$
$617$	− 19.5416i	− 0.786717i	0.919385	−	0.393358i	$-0.128687\pi$
$618$	− 42.4222i	− 1.70647i
$619$	28.7889	1.15712	0.578562	−	0.815639i	$-0.303614\pi$
$619$	28.7889	1.15712	0.578562	+	0.815639i	$0.303614\pi$
$620$	0	0
$621$	11.0917	0.445094
$622$	11.0917i	0.444736i
$623$	25.8167i	1.03432i
$624$	5.30278	0.212281
$625$	0	0
$626$	16.7889	0.671019
$627$	− 3.63331i	− 0.145100i
$628$	7.21110i	0.287754i
$629$	0.788897	0.0314554
$630$	0	0
$631$	−20.4222	−0.812995	−0.406498	−	0.913652i	$-0.633250\pi$
$631$	−20.4222	−0.812995	−0.406498	+	0.913652i	$0.633250\pi$
$632$	8.90833i	0.354354i
$633$	− 27.2111i	− 1.08154i
$634$	4.18335	0.166142
$635$	0	0
$636$	−30.6333	−1.21469
$637$	9.00000i	0.356593i
$638$	− 2.60555i	− 0.103155i
$639$	12.0000	0.474713
$640$	0	0
$641$	−41.4500	−1.63718	−0.818588	−	0.574382i	$-0.805242\pi$
$641$	−41.4500	−1.63718	−0.818588	+	0.574382i	$0.805242\pi$
$642$	19.8167i	0.782101i
$643$	− 11.8167i	− 0.466003i	−0.972476	−	0.233002i	$-0.925145\pi$
$643$	− 11.8167i	− 0.466003i	0.972476	−	0.233002i	$-0.0748548\pi$
$644$	22.8167	0.899102
$645$	0	0
$646$	0.788897	0.0310388
$647$	41.2111i	1.62018i	0.586309	+	0.810088i	$0.300581\pi$
$647$	41.2111i	1.62018i	−0.586309	+	0.810088i	$0.699419\pi$
$648$	10.6056i	0.416625i
$649$	−20.0555	−0.787248
$650$	0	0
$651$	50.9361	1.99634
$652$	− 13.2111i	− 0.517387i
$653$	6.23886i	0.244145i	0.992521	+	0.122073i	$0.0389541\pi$
$653$	6.23886i	0.244145i	−0.992521	+	0.122073i	$0.961046\pi$
$654$	−1.39445	−0.0545273
$655$	0	0
$656$	8.60555	0.335990
$657$	30.2111i	1.17865i
$658$	− 17.2111i	− 0.670959i
$659$	19.8167	0.771947	0.385974	−	0.922510i	$-0.373866\pi$
$659$	19.8167	0.771947	0.385974	+	0.922510i	$0.373866\pi$
$660$	0	0
$661$	−46.2389	−1.79848	−0.899242	−	0.437452i	$-0.855881\pi$
$661$	−46.2389	−1.79848	−0.899242	+	0.437452i	$0.855881\pi$
$662$	− 13.3944i	− 0.520590i
$663$	− 6.90833i	− 0.268297i
$664$	−13.8167	−0.536190
$665$	0	0
$666$	1.39445	0.0540338
$667$	− 6.90833i	− 0.267491i
$668$	19.3028i	0.746847i
$669$	61.1194	2.36301
$670$	0	0
$671$	−0.788897	−0.0304550
$672$	7.60555i	0.293391i
$673$	− 0.605551i	− 0.0233423i	−0.999932	−	0.0116711i	$-0.996285\pi$
$673$	− 0.605551i	− 0.0233423i	0.999932	−	0.0116711i	$-0.00371512\pi$
$674$	13.4861	0.519466
$675$	0	0
$676$	−7.69722	−0.296047
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	15.9083i	0.610956i
$679$	53.2389	2.04312
$680$	0	0
$681$	−41.4500	−1.58837
$682$	− 17.4500i	− 0.668194i
$683$	46.6611i	1.78544i	0.450616	+	0.892718i	$0.351204\pi$
$683$	46.6611i	1.78544i	−0.450616	+	0.892718i	$0.648796\pi$
$684$	1.39445	0.0533181
$685$	0	0
$686$	10.2111	0.389862
$687$	4.39445i	0.167659i
$688$	3.30278i	0.125917i
$689$	−30.6333	−1.16704
$690$	0	0
$691$	5.11943	0.194752	0.0973761	−	0.995248i	$-0.468955\pi$
$691$	5.11943	0.194752	0.0973761	+	0.995248i	$0.468955\pi$
$692$	− 3.51388i	− 0.133578i
$693$	− 19.8167i	− 0.752772i
$694$	−13.8167	−0.524473
$695$	0	0
$696$	2.30278	0.0872865
$697$	− 11.2111i	− 0.424651i
$698$	19.6333i	0.743132i
$699$	29.4500	1.11390
$700$	0	0
$701$	−13.0278	−0.492052	−0.246026	−	0.969263i	$-0.579125\pi$
$701$	−13.0278	−0.492052	−0.246026	+	0.969263i	$0.579125\pi$
$702$	3.69722i	0.139543i
$703$	0.366692i	0.0138301i
$704$	2.60555	0.0982004
$705$	0	0
$706$	−22.4222	−0.843871
$707$	− 59.8444i	− 2.25068i
$708$	− 17.7250i	− 0.666146i
$709$	23.8167	0.894453	0.447227	−	0.894421i	$-0.352412\pi$
$709$	23.8167	0.894453	0.447227	+	0.894421i	$0.352412\pi$
$710$	0	0
$711$	20.5139	0.769331
$712$	7.81665i	0.292941i
$713$	− 46.2666i	− 1.73270i
$714$	9.90833	0.370810
$715$	0	0
$716$	7.69722	0.287659
$717$	− 53.4500i	− 1.99613i
$718$	− 11.0917i	− 0.413938i
$719$	1.81665	0.0677498	0.0338749	−	0.999426i	$-0.489215\pi$
$719$	1.81665	0.0677498	0.0338749	+	0.999426i	$0.489215\pi$
$720$	0	0
$721$	60.8444	2.26596
$722$	− 18.6333i	− 0.693460i
$723$	24.6972i	0.918500i
$724$	−9.81665	−0.364833
$725$	0	0
$726$	9.69722	0.359898
$727$	8.18335i	0.303504i	0.988419	+	0.151752i	$0.0484914\pi$
$727$	8.18335i	0.303504i	−0.988419	+	0.151752i	$0.951509\pi$
$728$	7.60555i	0.281880i
$729$	13.3305	0.493723
$730$	0	0
$731$	4.30278	0.159144
$732$	− 0.697224i	− 0.0257702i
$733$	− 33.2111i	− 1.22668i	−0.789819	−	0.613340i	$-0.789826\pi$
$733$	− 33.2111i	− 1.22668i	0.789819	−	0.613340i	$-0.210174\pi$
$734$	−2.18335	−0.0805888
$735$	0	0
$736$	6.90833	0.254644
$737$	− 10.4222i	− 0.383907i
$738$	− 19.8167i	− 0.729461i
$739$	22.7889	0.838303	0.419152	−	0.907916i	$-0.362328\pi$
$739$	22.7889	0.838303	0.419152	+	0.907916i	$0.362328\pi$
$740$	0	0
$741$	3.21110	0.117963
$742$	− 43.9361i	− 1.61294i
$743$	− 26.0555i	− 0.955884i	−0.878391	−	0.477942i	$-0.841383\pi$
$743$	− 26.0555i	− 0.955884i	0.878391	−	0.477942i	$-0.158617\pi$
$744$	15.4222	0.565405
$745$	0	0
$746$	3.72498	0.136381
$747$	31.8167i	1.16411i
$748$	− 3.39445i	− 0.124113i
$749$	−28.4222	−1.03852
$750$	0	0
$751$	51.2666	1.87075	0.935373	−	0.353664i	$-0.115064\pi$
$751$	51.2666	1.87075	0.935373	+	0.353664i	$0.115064\pi$
$752$	− 5.21110i	− 0.190029i
$753$	43.8167i	1.59677i
$754$	2.30278	0.0838621
$755$	0	0
$756$	−5.30278	−0.192860
$757$	33.4500i	1.21576i	0.794029	+	0.607880i	$0.207980\pi$
$757$	33.4500i	1.21576i	−0.794029	+	0.607880i	$0.792020\pi$
$758$	23.8167i	0.865060i
$759$	−41.4500	−1.50454
$760$	0	0
$761$	−11.4861	−0.416372	−0.208186	−	0.978089i	$-0.566756\pi$
$761$	−11.4861	−0.416372	−0.208186	+	0.978089i	$0.566756\pi$
$762$	30.4222i	1.10208i
$763$	− 2.00000i	− 0.0724049i
$764$	−11.7250	−0.424195
$765$	0	0
$766$	−7.30278	−0.263860
$767$	− 17.7250i	− 0.640012i
$768$	2.30278i	0.0830943i
$769$	5.02776	0.181306	0.0906528	−	0.995883i	$-0.471105\pi$
$769$	5.02776	0.181306	0.0906528	+	0.995883i	$0.471105\pi$
$770$	0	0
$771$	59.4500	2.14104
$772$	7.51388i	0.270430i
$773$	− 42.0000i	− 1.51064i	−0.655359	−	0.755318i	$-0.727483\pi$
$773$	− 42.0000i	− 1.51064i	0.655359	−	0.755318i	$-0.272517\pi$
$774$	7.60555	0.273376
$775$	0	0
$776$	16.1194	0.578654
$777$	4.60555i	0.165223i
$778$	− 4.42221i	− 0.158544i
$779$	5.21110	0.186707
$780$	0	0
$781$	13.5778	0.485852
$782$	− 9.00000i	− 0.321839i
$783$	1.60555i	0.0573777i
$784$	−3.90833	−0.139583
$785$	0	0
$786$	13.8167	0.492824
$787$	− 27.0278i	− 0.963435i	−0.876326	−	0.481718i	$-0.840013\pi$
$787$	− 27.0278i	− 0.963435i	0.876326	−	0.481718i	$-0.159987\pi$
$788$	21.1194i	0.752349i
$789$	−15.6333	−0.556560
$790$	0	0
$791$	−22.8167	−0.811267
$792$	− 6.00000i	− 0.213201i
$793$	− 0.697224i	− 0.0247592i
$794$	−2.69722	−0.0957209
$795$	0	0
$796$	5.39445	0.191201
$797$	− 39.6333i	− 1.40388i	−0.712234	−	0.701942i	$-0.752317\pi$
$797$	− 39.6333i	− 1.40388i	0.712234	−	0.701942i	$-0.247683\pi$
$798$	4.60555i	0.163035i
$799$	−6.78890	−0.240174
$800$	0	0
$801$	18.0000	0.635999
$802$	− 6.11943i	− 0.216085i
$803$	34.1833i	1.20630i
$804$	9.21110	0.324851
$805$	0	0
$806$	15.4222	0.543224
$807$	46.8167i	1.64802i
$808$	− 18.1194i	− 0.637439i
$809$	3.63331	0.127740	0.0638701	−	0.997958i	$-0.479656\pi$
$809$	3.63331	0.127740	0.0638701	+	0.997958i	$0.479656\pi$
$810$	0	0
$811$	22.8806	0.803445	0.401723	−	0.915761i	$-0.368412\pi$
$811$	22.8806	0.803445	0.401723	+	0.915761i	$0.368412\pi$
$812$	3.30278i	0.115905i
$813$	− 24.8444i	− 0.871332i
$814$	1.57779	0.0553017
$815$	0	0
$816$	3.00000	0.105021
$817$	2.00000i	0.0699711i
$818$	− 25.2111i	− 0.881486i
$819$	17.5139	0.611984
$820$	0	0
$821$	−30.2389	−1.05534	−0.527672	−	0.849448i	$-0.676935\pi$
$821$	−30.2389	−1.05534	−0.527672	+	0.849448i	$0.676935\pi$
$822$	− 27.9083i	− 0.973415i
$823$	29.6333i	1.03295i	0.856302	+	0.516476i	$0.172756\pi$
$823$	29.6333i	1.03295i	−0.856302	+	0.516476i	$0.827244\pi$
$824$	18.4222	0.641768
$825$	0	0
$826$	25.4222	0.884552
$827$	40.1472i	1.39605i	0.716071	+	0.698027i	$0.245939\pi$
$827$	40.1472i	1.39605i	−0.716071	+	0.698027i	$0.754061\pi$
$828$	− 15.9083i	− 0.552853i
$829$	25.9083	0.899833	0.449917	−	0.893071i	$-0.351454\pi$
$829$	25.9083	0.899833	0.449917	+	0.893071i	$0.351454\pi$
$830$	0	0
$831$	−50.6611	−1.75741
$832$	2.30278i	0.0798344i
$833$	5.09167i	0.176416i
$834$	51.4222	1.78061
$835$	0	0
$836$	1.57779	0.0545692
$837$	10.7527i	0.371669i
$838$	− 30.5139i	− 1.05408i
$839$	−8.36669	−0.288850	−0.144425	−	0.989516i	$-0.546133\pi$
$839$	−8.36669	−0.288850	−0.144425	+	0.989516i	$0.546133\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	17.6333i	0.607684i
$843$	34.8167i	1.19915i
$844$	11.8167	0.406746
$845$	0	0
$846$	−12.0000	−0.412568
$847$	13.9083i	0.477896i
$848$	− 13.3028i	− 0.456819i
$849$	−65.8722	−2.26073
$850$	0	0
$851$	4.18335	0.143403
$852$	12.0000i	0.411113i
$853$	4.60555i	0.157691i	0.996887	+	0.0788455i	$0.0251234\pi$
$853$	4.60555i	0.157691i	−0.996887	+	0.0788455i	$0.974877\pi$
$854$	1.00000	0.0342193
$855$	0	0
$856$	−8.60555	−0.294132
$857$	9.39445i	0.320908i	0.987043	+	0.160454i	$0.0512959\pi$
$857$	9.39445i	0.320908i	−0.987043	+	0.160454i	$0.948704\pi$
$858$	− 13.8167i	− 0.471693i
$859$	−12.9722	−0.442607	−0.221304	−	0.975205i	$-0.571031\pi$
$859$	−12.9722	−0.442607	−0.221304	+	0.975205i	$0.571031\pi$
$860$	0	0
$861$	65.4500	2.23053
$862$	8.60555i	0.293106i
$863$	58.5416i	1.99278i	0.0848914	+	0.996390i	$0.472946\pi$
$863$	58.5416i	1.99278i	−0.0848914	+	0.996390i	$0.527054\pi$
$864$	−1.60555	−0.0546220
$865$	0	0
$866$	−29.6333	−1.00698
$867$	35.2389i	1.19677i
$868$	22.1194i	0.750782i
$869$	23.2111	0.787383
$870$	0	0
$871$	9.21110	0.312106
$872$	− 0.605551i	− 0.0205066i
$873$	− 37.1194i	− 1.25630i
$874$	4.18335	0.141504
$875$	0	0
$876$	−30.2111	−1.02074
$877$	− 18.3028i	− 0.618041i	−0.951055	−	0.309020i	$-0.899999\pi$
$877$	− 18.3028i	− 0.618041i	0.951055	−	0.309020i	$-0.100001\pi$
$878$	− 22.8444i	− 0.770962i
$879$	−43.8167	−1.47790
$880$	0	0
$881$	10.1833	0.343086	0.171543	−	0.985177i	$-0.445125\pi$
$881$	10.1833	0.343086	0.171543	+	0.985177i	$0.445125\pi$
$882$	9.00000i	0.303046i
$883$	32.2389i	1.08492i	0.840080	+	0.542462i	$0.182508\pi$
$883$	32.2389i	1.08492i	−0.840080	+	0.542462i	$0.817492\pi$
$884$	3.00000	0.100901
$885$	0	0
$886$	17.0917	0.574206
$887$	26.0555i	0.874858i	0.899253	+	0.437429i	$0.144111\pi$
$887$	26.0555i	0.874858i	−0.899253	+	0.437429i	$0.855889\pi$
$888$	1.39445i	0.0467946i
$889$	−43.6333	−1.46341
$890$	0	0
$891$	27.6333	0.925751
$892$	26.5416i	0.888680i
$893$	− 3.15559i	− 0.105598i
$894$	−45.6333	−1.52621
$895$	0	0
$896$	−3.30278	−0.110338
$897$	− 36.6333i	− 1.22315i
$898$	− 24.2389i	− 0.808861i
$899$	6.69722	0.223365
$900$	0	0
$901$	−17.3305	−0.577364
$902$	− 22.4222i	− 0.746578i
$903$	25.1194i	0.835922i
$904$	−6.90833	−0.229768
$905$	0	0
$906$	1.39445	0.0463275
$907$	21.7250i	0.721366i	0.932688	+	0.360683i	$0.117456\pi$
$907$	21.7250i	0.721366i	−0.932688	+	0.360683i	$0.882544\pi$
$908$	− 18.0000i	− 0.597351i
$909$	−41.7250	−1.38393
$910$	0	0
$911$	54.3583	1.80097	0.900485	−	0.434887i	$-0.143212\pi$
$911$	54.3583	1.80097	0.900485	+	0.434887i	$0.143212\pi$
$912$	1.39445i	0.0461748i
$913$	36.0000i	1.19143i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	−1.90833	−0.0630529
$917$	19.8167i	0.654404i
$918$	2.09167i	0.0690355i
$919$	45.2111	1.49138	0.745688	−	0.666295i	$-0.232121\pi$
$919$	45.2111	1.49138	0.745688	+	0.666295i	$0.232121\pi$
$920$	0	0
$921$	2.78890	0.0918973
$922$	17.7250i	0.583741i
$923$	12.0000i	0.394985i
$924$	19.8167	0.651920
$925$	0	0
$926$	−20.0000	−0.657241
$927$	− 42.4222i	− 1.39333i
$928$	1.00000i	0.0328266i
$929$	6.27502	0.205877	0.102938	−	0.994688i	$-0.467176\pi$
$929$	6.27502	0.205877	0.102938	+	0.994688i	$0.467176\pi$
$930$	0	0
$931$	−2.36669	−0.0775652
$932$	12.7889i	0.418914i
$933$	25.5416i	0.836196i
$934$	−16.6972	−0.546350
$935$	0	0
$936$	5.30278	0.173327
$937$	− 37.4500i	− 1.22344i	−0.791076	−	0.611718i	$-0.790479\pi$
$937$	− 37.4500i	− 1.22344i	0.791076	−	0.611718i	$-0.209521\pi$
$938$	13.2111i	0.431358i
$939$	38.6611	1.26166
$940$	0	0
$941$	12.0000	0.391189	0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000	0.391189	0.195594	+	0.980685i	$0.437336\pi$
$942$	16.6056i	0.541038i
$943$	− 59.4500i	− 1.93596i
$944$	7.69722	0.250523
$945$	0	0
$946$	8.60555	0.279791
$947$	− 8.72498i	− 0.283524i	−0.989901	−	0.141762i	$-0.954723\pi$
$947$	− 8.72498i	− 0.283524i	0.989901	−	0.141762i	$-0.0452767\pi$
$948$	20.5139i	0.666260i
$949$	−30.2111	−0.980694
$950$	0	0
$951$	9.63331	0.312381
$952$	4.30278i	0.139454i
$953$	− 2.36669i	− 0.0766647i	−0.999265	−	0.0383323i	$-0.987795\pi$
$953$	− 2.36669i	− 0.0766647i	0.999265	−	0.0383323i	$-0.0122046\pi$
$954$	−30.6333	−0.991790
$955$	0	0
$956$	23.2111	0.750701
$957$	− 6.00000i	− 0.193952i
$958$	− 42.5139i	− 1.37356i
$959$	40.0278	1.29256
$960$	0	0
$961$	13.8528	0.446865
$962$	1.39445i	0.0449588i
$963$	19.8167i	0.638583i
$964$	−10.7250	−0.345428
$965$	0	0
$966$	52.5416	1.69050
$967$	− 36.1833i	− 1.16358i	−0.813340	−	0.581789i	$-0.802353\pi$
$967$	− 36.1833i	− 1.16358i	0.813340	−	0.581789i	$-0.197647\pi$
$968$	4.21110i	0.135350i
$969$	1.81665	0.0583593
$970$	0	0
$971$	−36.2389	−1.16296	−0.581480	−	0.813561i	$-0.697526\pi$
$971$	−36.2389	−1.16296	−0.581480	+	0.813561i	$0.697526\pi$
$972$	19.6056i	0.628848i
$973$	73.7527i	2.36440i
$974$	−36.7250	−1.17674
$975$	0	0
$976$	0.302776	0.00969161
$977$	− 2.60555i	− 0.0833590i	−0.999131	−	0.0416795i	$-0.986729\pi$
$977$	− 2.60555i	− 0.0833590i	0.999131	−	0.0416795i	$-0.0132708\pi$
$978$	− 30.4222i	− 0.972795i
$979$	20.3667	0.650922
$980$	0	0
$981$	−1.39445	−0.0445213
$982$	17.2111i	0.549228i
$983$	− 33.6333i	− 1.07274i	−0.843984	−	0.536368i	$-0.819796\pi$
$983$	− 33.6333i	− 1.07274i	0.843984	−	0.536368i	$-0.180204\pi$
$984$	19.8167	0.631732
$985$	0	0
$986$	1.30278	0.0414888
$987$	− 39.6333i	− 1.26154i
$988$	1.39445i	0.0443633i
$989$	22.8167	0.725527
$990$	0	0
$991$	−15.4500	−0.490784	−0.245392	−	0.969424i	$-0.578917\pi$
$991$	−15.4500	−0.490784	−0.245392	+	0.969424i	$0.578917\pi$
$992$	6.69722i	0.212637i
$993$	− 30.8444i	− 0.978818i
$994$	−17.2111	−0.545903
$995$	0	0
$996$	−31.8167	−1.00815
$997$	58.2389i	1.84444i	0.386662	+	0.922222i	$0.373628\pi$
$997$	58.2389i	1.84444i	−0.386662	+	0.922222i	$0.626372\pi$
$998$	25.5139i	0.807628i
$999$	−0.972244	−0.0307604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.h.349.4		4
5.2	odd	4		290.2.a.c.1.2	✓	2
5.3	odd	4		1450.2.a.n.1.1		2
5.4	even	2	inner	1450.2.b.h.349.1		4
15.2	even	4		2610.2.a.s.1.2		2
20.7	even	4		2320.2.a.j.1.1		2
40.27	even	4		9280.2.a.bb.1.2		2
40.37	odd	4		9280.2.a.x.1.1		2
145.57	odd	4		8410.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.c.1.2	✓	2	5.2	odd	4
1450.2.a.n.1.1		2	5.3	odd	4
1450.2.b.h.349.1		4	5.4	even	2	inner
1450.2.b.h.349.4		4	1.1	even	1	trivial
2320.2.a.j.1.1		2	20.7	even	4
2610.2.a.s.1.2		2	15.2	even	4
8410.2.a.s.1.1		2	145.57	odd	4
9280.2.a.x.1.1		2	40.37	odd	4
9280.2.a.bb.1.2		2	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -3.30278i q^{7} -1.00000i q^{8} -2.30278 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -3.30278i q^{7} -1.00000i q^{8} -2.30278 q^{9} -2.60555 q^{11} -2.30278i q^{12} -2.30278i q^{13} +3.30278 q^{14} +1.00000 q^{16} -1.30278i q^{17} -2.30278i q^{18} +0.605551 q^{19} +7.60555 q^{21} -2.60555i q^{22} -6.90833i q^{23} +2.30278 q^{24} +2.30278 q^{26} +1.60555i q^{27} +3.30278i q^{28} +1.00000 q^{29} +6.69722 q^{31} +1.00000i q^{32} -6.00000i q^{33} +1.30278 q^{34} +2.30278 q^{36} +0.605551i q^{37} +0.605551i q^{38} +5.30278 q^{39} +8.60555 q^{41} +7.60555i q^{42} +3.30278i q^{43} +2.60555 q^{44} +6.90833 q^{46} -5.21110i q^{47} +2.30278i q^{48} -3.90833 q^{49} +3.00000 q^{51} +2.30278i q^{52} -13.3028i q^{53} -1.60555 q^{54} -3.30278 q^{56} +1.39445i q^{57} +1.00000i q^{58} +7.69722 q^{59} +0.302776 q^{61} +6.69722i q^{62} +7.60555i q^{63} -1.00000 q^{64} +6.00000 q^{66} +4.00000i q^{67} +1.30278i q^{68} +15.9083 q^{69} -5.21110 q^{71} +2.30278i q^{72} -13.1194i q^{73} -0.605551 q^{74} -0.605551 q^{76} +8.60555i q^{77} +5.30278i q^{78} -8.90833 q^{79} -10.6056 q^{81} +8.60555i q^{82} -13.8167i q^{83} -7.60555 q^{84} -3.30278 q^{86} +2.30278i q^{87} +2.60555i q^{88} -7.81665 q^{89} -7.60555 q^{91} +6.90833i q^{92} +15.4222i q^{93} +5.21110 q^{94} -2.30278 q^{96} +16.1194i q^{97} -3.90833i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} + 4 q^{11} + 6 q^{14} + 4 q^{16} - 12 q^{19} + 16 q^{21} + 2 q^{24} + 2 q^{26} + 4 q^{29} + 34 q^{31} - 2 q^{34} + 2 q^{36} + 14 q^{39} + 20 q^{41} - 4 q^{44} + 6 q^{46} + 6 q^{49} + 12 q^{51} + 8 q^{54} - 6 q^{56} + 38 q^{59} - 6 q^{61} - 4 q^{64} + 24 q^{66} + 42 q^{69} + 8 q^{71} + 12 q^{74} + 12 q^{76} - 14 q^{79} - 28 q^{81} - 16 q^{84} - 6 q^{86} + 12 q^{89} - 16 q^{91} - 8 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 + 4 * q^11 + 6 * q^14 + 4 * q^16 - 12 * q^19 + 16 * q^21 + 2 * q^24 + 2 * q^26 + 4 * q^29 + 34 * q^31 - 2 * q^34 + 2 * q^36 + 14 * q^39 + 20 * q^41 - 4 * q^44 + 6 * q^46 + 6 * q^49 + 12 * q^51 + 8 * q^54 - 6 * q^56 + 38 * q^59 - 6 * q^61 - 4 * q^64 + 24 * q^66 + 42 * q^69 + 8 * q^71 + 12 * q^74 + 12 * q^76 - 14 * q^79 - 28 * q^81 - 16 * q^84 - 6 * q^86 + 12 * q^89 - 16 * q^91 - 8 * q^94 - 2 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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