LMFDB - Embedded newform 1450.2.b.l.349.1

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:	6.0.24681024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 12x^{4} + 36x^{2} + 9 $ x^6 + 12x^4 + 36x^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			349.1
Root			$-2.66908i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.l.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.66908i q^{3} -1.00000 q^{4} -1.66908 q^{6} -3.21417i q^{7} +1.00000i q^{8} +0.214175 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.66908i q^{3} -1.00000 q^{4} -1.66908 q^{6} -3.21417i q^{7} +1.00000i q^{8} +0.214175 q^{9} +5.33816 q^{11} +1.66908i q^{12} +4.57889i q^{13} -3.21417 q^{14} +1.00000 q^{16} -4.12398i q^{17} -0.214175i q^{18} +6.24797 q^{19} -5.36471 q^{21} -5.33816i q^{22} -8.57889i q^{23} +1.66908 q^{24} +4.57889 q^{26} -5.36471i q^{27} +3.21417i q^{28} +1.00000 q^{29} +0.123983 q^{31} -1.00000i q^{32} -8.90981i q^{33} -4.12398 q^{34} -0.214175 q^{36} -4.42835i q^{37} -6.24797i q^{38} +7.64252 q^{39} -8.42835 q^{41} +5.36471i q^{42} +6.12398i q^{43} -5.33816 q^{44} -8.57889 q^{46} +10.6763i q^{47} -1.66908i q^{48} -3.33092 q^{49} -6.88325 q^{51} -4.57889i q^{52} +12.3719i q^{53} -5.36471 q^{54} +3.21417 q^{56} -10.4283i q^{57} -1.00000i q^{58} +13.9170 q^{59} -3.00724 q^{61} -0.123983i q^{62} -0.688396i q^{63} -1.00000 q^{64} -8.90981 q^{66} +5.58612i q^{67} +4.12398i q^{68} -14.3188 q^{69} -12.0000 q^{71} +0.214175i q^{72} +0.123983i q^{73} -4.42835 q^{74} -6.24797 q^{76} -17.1578i q^{77} -7.64252i q^{78} -12.8269 q^{79} -8.31160 q^{81} +8.42835i q^{82} -2.24797i q^{83} +5.36471 q^{84} +6.12398 q^{86} -1.66908i q^{87} +5.33816i q^{88} -5.33816 q^{89} +14.7173 q^{91} +8.57889i q^{92} -0.206938i q^{93} +10.6763 q^{94} -1.66908 q^{96} +0.578887i q^{97} +3.33092i q^{98} +1.14330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 6 q^{6} - 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 6 * q^6 - 12 * q^9	$ 6 q - 6 q^{4} + 6 q^{6} - 12 q^{9} - 6 q^{14} + 6 q^{16} - 24 q^{21} - 6 q^{24} + 6 q^{26} + 6 q^{29} - 18 q^{31} - 6 q^{34} + 12 q^{36} + 6 q^{39} - 24 q^{41} - 30 q^{46} - 36 q^{49} - 12 q^{51} - 24 q^{54} + 6 q^{56} + 30 q^{59} + 30 q^{61} - 6 q^{64} - 48 q^{66} + 18 q^{69} - 72 q^{71} - 18 q^{79} + 6 q^{81} + 24 q^{84} + 18 q^{86} - 48 q^{91} + 6 q^{96} + 60 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 6 * q^6 - 12 * q^9 - 6 * q^14 + 6 * q^16 - 24 * q^21 - 6 * q^24 + 6 * q^26 + 6 * q^29 - 18 * q^31 - 6 * q^34 + 12 * q^36 + 6 * q^39 - 24 * q^41 - 30 * q^46 - 36 * q^49 - 12 * q^51 - 24 * q^54 + 6 * q^56 + 30 * q^59 + 30 * q^61 - 6 * q^64 - 48 * q^66 + 18 * q^69 - 72 * q^71 - 18 * q^79 + 6 * q^81 + 24 * q^84 + 18 * q^86 - 48 * q^91 + 6 * q^96 + 60 * 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
$3$	− 1.66908i	− 0.963643i	−0.876269	−	0.481822i	$-0.839975\pi$
$3$	− 1.66908i	− 0.963643i	0.876269	−	0.481822i	$-0.160025\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.66908	−0.681399
$7$	− 3.21417i	− 1.21484i	−0.794379	−	0.607422i	$-0.792204\pi$
$7$	− 3.21417i	− 1.21484i	0.794379	−	0.607422i	$-0.207796\pi$
$8$	1.00000i	0.353553i
$9$	0.214175	0.0713917
$10$	0	0
$11$	5.33816	1.60952	0.804758	−	0.593604i	$-0.202295\pi$
$11$	5.33816	1.60952	0.804758	+	0.593604i	$0.202295\pi$
$12$	1.66908i	0.481822i
$13$	4.57889i	1.26995i	0.772531	+	0.634977i	$0.218991\pi$
$13$	4.57889i	1.26995i	−0.772531	+	0.634977i	$0.781009\pi$
$14$	−3.21417	−0.859024
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.12398i	− 1.00021i	−0.865964	−	0.500106i	$-0.833294\pi$
$17$	− 4.12398i	− 1.00021i	0.865964	−	0.500106i	$-0.166706\pi$
$18$	− 0.214175i	− 0.0504815i
$19$	6.24797	1.43338	0.716691	−	0.697391i	$-0.245656\pi$
$19$	6.24797	1.43338	0.716691	+	0.697391i	$0.245656\pi$
$20$	0	0
$21$	−5.36471	−1.17068
$22$	− 5.33816i	− 1.13810i
$23$	− 8.57889i	− 1.78882i	−0.447246	−	0.894411i	$-0.647595\pi$
$23$	− 8.57889i	− 1.78882i	0.447246	−	0.894411i	$-0.352405\pi$
$24$	1.66908	0.340699
$25$	0	0
$26$	4.57889	0.897994
$27$	− 5.36471i	− 1.03244i
$28$	3.21417i	0.607422i
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	0.123983	0.0222680	0.0111340	−	0.999938i	$-0.496456\pi$
$31$	0.123983	0.0222680	0.0111340	+	0.999938i	$0.496456\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 8.90981i	− 1.55100i
$34$	−4.12398	−0.707257
$35$	0	0
$36$	−0.214175	−0.0356958
$37$	− 4.42835i	− 0.728016i	−0.931396	−	0.364008i	$-0.881408\pi$
$37$	− 4.42835i	− 0.728016i	0.931396	−	0.364008i	$-0.118592\pi$
$38$	− 6.24797i	− 1.01355i
$39$	7.64252	1.22378
$40$	0	0
$41$	−8.42835	−1.31629	−0.658144	−	0.752892i	$-0.728658\pi$
$41$	−8.42835	−1.31629	−0.658144	+	0.752892i	$0.728658\pi$
$42$	5.36471i	0.827793i
$43$	6.12398i	0.933899i	0.884284	+	0.466949i	$0.154647\pi$
$43$	6.12398i	0.933899i	−0.884284	+	0.466949i	$0.845353\pi$
$44$	−5.33816	−0.804758
$45$	0	0
$46$	−8.57889	−1.26489
$47$	10.6763i	1.55730i	0.627458	+	0.778650i	$0.284095\pi$
$47$	10.6763i	1.55730i	−0.627458	+	0.778650i	$0.715905\pi$
$48$	− 1.66908i	− 0.240911i
$49$	−3.33092	−0.475846
$50$	0	0
$51$	−6.88325	−0.963848
$52$	− 4.57889i	− 0.634977i
$53$	12.3719i	1.69942i	0.527252	+	0.849709i	$0.323222\pi$
$53$	12.3719i	1.69942i	−0.527252	+	0.849709i	$0.676778\pi$
$54$	−5.36471	−0.730045
$55$	0	0
$56$	3.21417	0.429512
$57$	− 10.4283i	− 1.38127i
$58$	− 1.00000i	− 0.131306i
$59$	13.9170	1.81184	0.905922	−	0.423444i	$-0.139179\pi$
$59$	13.9170	1.81184	0.905922	+	0.423444i	$0.139179\pi$
$60$	0	0
$61$	−3.00724	−0.385037	−0.192519	−	0.981293i	$-0.561666\pi$
$61$	−3.00724	−0.385037	−0.192519	+	0.981293i	$0.561666\pi$
$62$	− 0.123983i	− 0.0157459i
$63$	− 0.688396i	− 0.0867297i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−8.90981	−1.09672
$67$	5.58612i	0.682454i	0.939981	+	0.341227i	$0.110842\pi$
$67$	5.58612i	0.682454i	−0.939981	+	0.341227i	$0.889158\pi$
$68$	4.12398i	0.500106i
$69$	−14.3188	−1.72379
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0.214175i	0.0252408i
$73$	0.123983i	0.0145111i	0.999974	+	0.00725557i	$0.00230954\pi$
$73$	0.123983i	0.0145111i	−0.999974	+	0.00725557i	$0.997690\pi$
$74$	−4.42835	−0.514785
$75$	0	0
$76$	−6.24797	−0.716691
$77$	− 17.1578i	− 1.95531i
$78$	− 7.64252i	− 0.865346i
$79$	−12.8269	−1.44313	−0.721567	−	0.692345i	$-0.756578\pi$
$79$	−12.8269	−1.44313	−0.721567	+	0.692345i	$0.756578\pi$
$80$	0	0
$81$	−8.31160	−0.923512
$82$	8.42835i	0.930756i
$83$	− 2.24797i	− 0.246746i	−0.992360	−	0.123373i	$-0.960629\pi$
$83$	− 2.24797i	− 0.246746i	0.992360	−	0.123373i	$-0.0393712\pi$
$84$	5.36471	0.585338
$85$	0	0
$86$	6.12398	0.660366
$87$	− 1.66908i	− 0.178944i
$88$	5.33816i	0.569050i
$89$	−5.33816	−0.565844	−0.282922	−	0.959143i	$-0.591304\pi$
$89$	−5.33816	−0.565844	−0.282922	+	0.959143i	$0.591304\pi$
$90$	0	0
$91$	14.7173	1.54280
$92$	8.57889i	0.894411i
$93$	− 0.206938i	− 0.0214584i
$94$	10.6763	1.10118
$95$	0	0
$96$	−1.66908	−0.170350
$97$	0.578887i	0.0587771i	0.999568	+	0.0293885i	$0.00935601\pi$
$97$	0.578887i	0.0587771i	−0.999568	+	0.0293885i	$0.990644\pi$
$98$	3.33092i	0.336474i
$99$	1.14330	0.114906
$100$	0	0
$101$	5.18762	0.516188	0.258094	−	0.966120i	$-0.416906\pi$
$101$	5.18762	0.516188	0.258094	+	0.966120i	$0.416906\pi$
$102$	6.88325i	0.681544i
$103$	− 11.7665i	− 1.15939i	−0.814834	−	0.579694i	$-0.803172\pi$
$103$	− 11.7665i	− 1.15939i	0.814834	−	0.579694i	$-0.196828\pi$
$104$	−4.57889	−0.448997
$105$	0	0
$106$	12.3719	1.20167
$107$	− 8.42835i	− 0.814799i	−0.913250	−	0.407400i	$-0.866436\pi$
$107$	− 8.42835i	− 0.814799i	0.913250	−	0.407400i	$-0.133564\pi$
$108$	5.36471i	0.516220i
$109$	−5.75203	−0.550945	−0.275472	−	0.961309i	$-0.588834\pi$
$109$	−5.75203	−0.550945	−0.275472	+	0.961309i	$0.588834\pi$
$110$	0	0
$111$	−7.39127	−0.701548
$112$	− 3.21417i	− 0.303711i
$113$	− 7.25520i	− 0.682512i	−0.939970	−	0.341256i	$-0.889148\pi$
$113$	− 7.25520i	− 0.682512i	0.939970	−	0.341256i	$-0.110852\pi$
$114$	−10.4283	−0.976704
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	0.980683i	0.0906642i
$118$	− 13.9170i	− 1.28117i
$119$	−13.2552	−1.21510
$120$	0	0
$121$	17.4959	1.59054
$122$	3.00724i	0.272262i
$123$	14.0676i	1.26843i
$124$	−0.123983	−0.0111340
$125$	0	0
$126$	−0.688396	−0.0613272
$127$	− 8.00000i	− 0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$	− 8.00000i	− 0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	1.00000i	0.0883883i
$129$	10.2214	0.899945
$130$	0	0
$131$	−11.8196	−1.03268	−0.516342	−	0.856382i	$-0.672707\pi$
$131$	−11.8196	−1.03268	−0.516342	+	0.856382i	$0.672707\pi$
$132$	8.90981i	0.775499i
$133$	− 20.0821i	− 1.74134i
$134$	5.58612	0.482568
$135$	0	0
$136$	4.12398	0.353629
$137$	− 3.42111i	− 0.292285i	−0.989264	−	0.146143i	$-0.953314\pi$
$137$	− 3.42111i	− 0.292285i	0.989264	−	0.146143i	$-0.0466859\pi$
$138$	14.3188i	1.21890i
$139$	7.64252	0.648231	0.324115	−	0.946018i	$-0.394933\pi$
$139$	7.64252	0.648231	0.324115	+	0.946018i	$0.394933\pi$
$140$	0	0
$141$	17.8196	1.50068
$142$	12.0000i	1.00702i
$143$	24.4428i	2.04401i
$144$	0.214175	0.0178479
$145$	0	0
$146$	0.123983	0.0102609
$147$	5.55957i	0.458546i
$148$	4.42835i	0.364008i
$149$	11.5185	0.943636	0.471818	−	0.881696i	$-0.343598\pi$
$149$	11.5185	0.943636	0.471818	+	0.881696i	$0.343598\pi$
$150$	0	0
$151$	−9.15777	−0.745249	−0.372625	−	0.927982i	$-0.621542\pi$
$151$	−9.15777	−0.745249	−0.372625	+	0.927982i	$0.621542\pi$
$152$	6.24797i	0.506777i
$153$	− 0.883254i	− 0.0714069i
$154$	−17.1578	−1.38261
$155$	0	0
$156$	−7.64252	−0.611892
$157$	10.0000i	0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$	10.0000i	0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$	12.8269i	1.02045i
$159$	20.6498	1.63763
$160$	0	0
$161$	−27.5740	−2.17314
$162$	8.31160i	0.653021i
$163$	18.6763i	1.46284i	0.681926	+	0.731421i	$0.261143\pi$
$163$	18.6763i	1.46284i	−0.681926	+	0.731421i	$0.738857\pi$
$164$	8.42835	0.658144
$165$	0	0
$166$	−2.24797	−0.174476
$167$	20.3188i	1.57232i	0.618024	+	0.786160i	$0.287934\pi$
$167$	20.3188i	1.57232i	−0.618024	+	0.786160i	$0.712066\pi$
$168$	− 5.36471i	− 0.413897i
$169$	−7.96621	−0.612785
$170$	0	0
$171$	1.33816	0.102332
$172$	− 6.12398i	− 0.466949i
$173$	7.91705i	0.601922i	0.953636	+	0.300961i	$0.0973074\pi$
$173$	7.91705i	0.601922i	−0.953636	+	0.300961i	$0.902693\pi$
$174$	−1.66908	−0.126533
$175$	0	0
$176$	5.33816	0.402379
$177$	− 23.2286i	− 1.74597i
$178$	5.33816i	0.400112i
$179$	−8.09743	−0.605230	−0.302615	−	0.953113i	$-0.597860\pi$
$179$	−8.09743	−0.605230	−0.302615	+	0.953113i	$0.597860\pi$
$180$	0	0
$181$	−6.24797	−0.464408	−0.232204	−	0.972667i	$-0.574594\pi$
$181$	−6.24797	−0.464408	−0.232204	+	0.972667i	$0.574594\pi$
$182$	− 14.7173i	− 1.09092i
$183$	5.01932i	0.371039i
$184$	8.57889	0.632444
$185$	0	0
$186$	−0.206938	−0.0151734
$187$	− 22.0145i	− 1.60986i
$188$	− 10.6763i	− 0.778650i
$189$	−17.2431	−1.25425
$190$	0	0
$191$	11.0483	0.799424	0.399712	−	0.916641i	$-0.369110\pi$
$191$	11.0483	0.799424	0.399712	+	0.916641i	$0.369110\pi$
$192$	1.66908i	0.120455i
$193$	0.0829546i	0.00597120i	0.999996	+	0.00298560i	$0.000950347\pi$
$193$	0.0829546i	0.00597120i	−0.999996	+	0.00298560i	$0.999050\pi$
$194$	0.578887	0.0415617
$195$	0	0
$196$	3.33092	0.237923
$197$	− 0.732717i	− 0.0522039i	−0.999659	−	0.0261020i	$-0.991691\pi$
$197$	− 0.732717i	− 0.0522039i	0.999659	−	0.0261020i	$-0.00830945\pi$
$198$	− 1.14330i	− 0.0812508i
$199$	−4.60873	−0.326704	−0.163352	−	0.986568i	$-0.552231\pi$
$199$	−4.60873	−0.326704	−0.163352	+	0.986568i	$0.552231\pi$
$200$	0	0
$201$	9.32368	0.657642
$202$	− 5.18762i	− 0.365000i
$203$	− 3.21417i	− 0.225591i
$204$	6.88325	0.481924
$205$	0	0
$206$	−11.7665	−0.819811
$207$	− 1.83738i	− 0.127707i
$208$	4.57889i	0.317489i
$209$	33.3526	2.30705
$210$	0	0
$211$	2.66184	0.183249	0.0916244	−	0.995794i	$-0.470794\pi$
$211$	2.66184	0.183249	0.0916244	+	0.995794i	$0.470794\pi$
$212$	− 12.3719i	− 0.849709i
$213$	20.0289i	1.37236i
$214$	−8.42835	−0.576150
$215$	0	0
$216$	5.36471	0.365022
$217$	− 0.398504i	− 0.0270522i
$218$	5.75203i	0.389577i
$219$	0.206938	0.0139836
$220$	0	0
$221$	18.8833	1.27023
$222$	7.39127i	0.496069i
$223$	0.744796i	0.0498753i	0.999689	+	0.0249376i	$0.00793872\pi$
$223$	0.744796i	0.0498753i	−0.999689	+	0.0249376i	$0.992061\pi$
$224$	−3.21417	−0.214756
$225$	0	0
$226$	−7.25520	−0.482609
$227$	0.180384i	0.0119725i	0.999982	+	0.00598624i	$0.00190549\pi$
$227$	0.180384i	0.0119725i	−0.999982	+	0.00598624i	$0.998095\pi$
$228$	10.4283i	0.690634i
$229$	−10.1385	−0.669968	−0.334984	−	0.942224i	$-0.608731\pi$
$229$	−10.1385	−0.669968	−0.334984	+	0.942224i	$0.608731\pi$
$230$	0	0
$231$	−28.6377	−1.88422
$232$	1.00000i	0.0656532i
$233$	− 27.3526i	− 1.79193i	−0.444124	−	0.895965i	$-0.646485\pi$
$233$	− 27.3526i	− 1.79193i	0.444124	−	0.895965i	$-0.353515\pi$
$234$	0.980683	0.0641093
$235$	0	0
$236$	−13.9170	−0.905922
$237$	21.4090i	1.39067i
$238$	13.2552i	0.859207i
$239$	25.7665	1.66670	0.833348	−	0.552748i	$-0.186421\pi$
$239$	25.7665	1.66670	0.833348	+	0.552748i	$0.186421\pi$
$240$	0	0
$241$	6.34540	0.408743	0.204371	−	0.978893i	$-0.434485\pi$
$241$	6.34540	0.408743	0.204371	+	0.978893i	$0.434485\pi$
$242$	− 17.4959i	− 1.12468i
$243$	− 2.22141i	− 0.142504i
$244$	3.00724	0.192519
$245$	0	0
$246$	14.0676	0.896916
$247$	28.6087i	1.82033i
$248$	0.123983i	0.00787294i
$249$	−3.75203	−0.237775
$250$	0	0
$251$	19.1047	1.20588	0.602938	−	0.797788i	$-0.293997\pi$
$251$	19.1047	1.20588	0.602938	+	0.797788i	$0.293997\pi$
$252$	0.688396i	0.0433649i
$253$	− 45.7955i	− 2.87914i
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 19.1047i	− 1.19172i	−0.803090	−	0.595858i	$-0.796812\pi$
$257$	− 19.1047i	− 1.19172i	0.803090	−	0.595858i	$-0.203188\pi$
$258$	− 10.2214i	− 0.636357i
$259$	−14.2335	−0.884426
$260$	0	0
$261$	0.214175	0.0132571
$262$	11.8196i	0.730218i
$263$	− 12.0000i	− 0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$	− 12.0000i	− 0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$	8.90981	0.548361
$265$	0	0
$266$	−20.0821	−1.23131
$267$	8.90981i	0.545271i
$268$	− 5.58612i	− 0.341227i
$269$	19.2142	1.17151	0.585754	−	0.810489i	$-0.300798\pi$
$269$	19.2142	1.17151	0.585754	+	0.810489i	$0.300798\pi$
$270$	0	0
$271$	−1.09019	−0.0662244	−0.0331122	−	0.999452i	$-0.510542\pi$
$271$	−1.09019	−0.0662244	−0.0331122	+	0.999452i	$0.510542\pi$
$272$	− 4.12398i	− 0.250053i
$273$	− 24.5644i	− 1.48671i
$274$	−3.42111	−0.206677
$275$	0	0
$276$	14.3188	0.861893
$277$	25.5330i	1.53413i	0.641569	+	0.767065i	$0.278284\pi$
$277$	25.5330i	1.53413i	−0.641569	+	0.767065i	$0.721716\pi$
$278$	− 7.64252i	− 0.458368i
$279$	0.0265541	0.00158975
$280$	0	0
$281$	1.39456	0.0831924	0.0415962	−	0.999135i	$-0.486756\pi$
$281$	1.39456	0.0831924	0.0415962	+	0.999135i	$0.486756\pi$
$282$	− 17.8196i	− 1.06114i
$283$	10.2480i	0.609178i	0.952484	+	0.304589i	$0.0985192\pi$
$283$	10.2480i	0.609178i	−0.952484	+	0.304589i	$0.901481\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	24.4428	1.44533
$287$	27.0902i	1.59908i
$288$	− 0.214175i	− 0.0126204i
$289$	−0.00723726	−0.000425721 0
$290$	0	0
$291$	0.966209	0.0566402
$292$	− 0.123983i	− 0.00725557i
$293$	3.57165i	0.208658i	0.994543	+	0.104329i	$0.0332695\pi$
$293$	3.57165i	0.208658i	−0.994543	+	0.104329i	$0.966731\pi$
$294$	5.55957	0.324241
$295$	0	0
$296$	4.42835	0.257393
$297$	− 28.6377i	− 1.66173i
$298$	− 11.5185i	− 0.667251i
$299$	39.2818	2.27172
$300$	0	0
$301$	19.6836	1.13454
$302$	9.15777i	0.526971i
$303$	− 8.65855i	− 0.497421i
$304$	6.24797	0.358345
$305$	0	0
$306$	−0.883254	−0.0504923
$307$	− 12.4959i	− 0.713181i	−0.934261	−	0.356590i	$-0.883939\pi$
$307$	− 12.4959i	− 0.713181i	0.934261	−	0.356590i	$-0.116061\pi$
$308$	17.1578i	0.977655i
$309$	−19.6392	−1.11724
$310$	0	0
$311$	21.9846	1.24663	0.623317	−	0.781969i	$-0.285785\pi$
$311$	21.9846	1.24663	0.623317	+	0.781969i	$0.285785\pi$
$312$	7.64252i	0.432673i
$313$	17.1722i	0.970633i	0.874339	+	0.485316i	$0.161296\pi$
$313$	17.1722i	0.970633i	−0.874339	+	0.485316i	$0.838704\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	12.8269	0.721567
$317$	4.97739i	0.279558i	0.990183	+	0.139779i	$0.0446392\pi$
$317$	4.97739i	0.279558i	−0.990183	+	0.139779i	$0.955361\pi$
$318$	− 20.6498i	− 1.15798i
$319$	5.33816	0.298879
$320$	0	0
$321$	−14.0676	−0.785176
$322$	27.5740i	1.53664i
$323$	− 25.7665i	− 1.43369i
$324$	8.31160	0.461756
$325$	0	0
$326$	18.6763	1.03439
$327$	9.60060i	0.530914i
$328$	− 8.42835i	− 0.465378i
$329$	34.3155	1.89188
$330$	0	0
$331$	−20.0145	−1.10010	−0.550048	−	0.835133i	$-0.685390\pi$
$331$	−20.0145	−1.10010	−0.550048	+	0.835133i	$0.685390\pi$
$332$	2.24797i	0.123373i
$333$	− 0.948442i	− 0.0519743i
$334$	20.3188	1.11180
$335$	0	0
$336$	−5.36471	−0.292669
$337$	− 2.55233i	− 0.139034i	−0.997581	−	0.0695172i	$-0.977854\pi$
$337$	− 2.55233i	− 0.139034i	0.997581	−	0.0695172i	$-0.0221459\pi$
$338$	7.96621i	0.433305i
$339$	−12.1095	−0.657698
$340$	0	0
$341$	0.661842	0.0358407
$342$	− 1.33816i	− 0.0723593i
$343$	− 11.7931i	− 0.636766i
$344$	−6.12398	−0.330183
$345$	0	0
$346$	7.91705	0.425623
$347$	13.8872i	0.745504i	0.927931	+	0.372752i	$0.121586\pi$
$347$	13.8872i	0.745504i	−0.927931	+	0.372752i	$0.878414\pi$
$348$	1.66908i	0.0894720i
$349$	−26.0821	−1.39614	−0.698070	−	0.716029i	$-0.745958\pi$
$349$	−26.0821	−1.39614	−0.698070	+	0.716029i	$0.745958\pi$
$350$	0	0
$351$	24.5644	1.31115
$352$	− 5.33816i	− 0.284525i
$353$	19.4057i	1.03286i	0.856328	+	0.516432i	$0.172740\pi$
$353$	19.4057i	1.03286i	−0.856328	+	0.516432i	$0.827260\pi$
$354$	−23.2286	−1.23459
$355$	0	0
$356$	5.33816	0.282922
$357$	22.1240i	1.17093i
$358$	8.09743i	0.427962i
$359$	−16.1650	−0.853157	−0.426578	−	0.904451i	$-0.640281\pi$
$359$	−16.1650	−0.853157	−0.426578	+	0.904451i	$0.640281\pi$
$360$	0	0
$361$	20.0371	1.05458
$362$	6.24797i	0.328386i
$363$	− 29.2021i	− 1.53271i
$364$	−14.7173	−0.771398
$365$	0	0
$366$	5.01932	0.262364
$367$	− 1.51854i	− 0.0792672i	−0.999214	−	0.0396336i	$-0.987381\pi$
$367$	− 1.51854i	− 0.0792672i	0.999214	−	0.0396336i	$-0.0126191\pi$
$368$	− 8.57889i	− 0.447205i
$369$	−1.80514	−0.0939719
$370$	0	0
$371$	39.7656	2.06453
$372$	0.206938i	0.0107292i
$373$	− 7.16107i	− 0.370786i	−0.982664	−	0.185393i	$-0.940644\pi$
$373$	− 7.16107i	− 0.370786i	0.982664	−	0.185393i	$-0.0593558\pi$
$374$	−22.0145	−1.13834
$375$	0	0
$376$	−10.6763	−0.550589
$377$	4.57889i	0.235825i
$378$	17.2431i	0.886891i
$379$	−24.0145	−1.23354	−0.616770	−	0.787143i	$-0.711559\pi$
$379$	−24.0145	−1.23354	−0.616770	+	0.787143i	$0.711559\pi$
$380$	0	0
$381$	−13.3526	−0.684076
$382$	− 11.0483i	− 0.565278i
$383$	34.3864i	1.75706i	0.477683	+	0.878532i	$0.341477\pi$
$383$	34.3864i	1.75706i	−0.477683	+	0.878532i	$0.658523\pi$
$384$	1.66908	0.0851748
$385$	0	0
$386$	0.0829546	0.00422228
$387$	1.31160i	0.0666726i
$388$	− 0.578887i	− 0.0293885i
$389$	−5.63923	−0.285920	−0.142960	−	0.989728i	$-0.545662\pi$
$389$	−5.63923	−0.285920	−0.142960	+	0.989728i	$0.545662\pi$
$390$	0	0
$391$	−35.3792	−1.78920
$392$	− 3.33092i	− 0.168237i
$393$	19.7279i	0.995140i
$394$	−0.732717	−0.0369137
$395$	0	0
$396$	−1.14330	−0.0574530
$397$	10.9131i	0.547713i	0.961771	+	0.273856i	$0.0882993\pi$
$397$	10.9131i	0.547713i	−0.961771	+	0.273856i	$0.911701\pi$
$398$	4.60873i	0.231015i
$399$	−33.5185	−1.67803
$400$	0	0
$401$	21.9846	1.09786	0.548930	−	0.835868i	$-0.315035\pi$
$401$	21.9846	1.09786	0.548930	+	0.835868i	$0.315035\pi$
$402$	− 9.32368i	− 0.465023i
$403$	0.567705i	0.0282794i
$404$	−5.18762	−0.258094
$405$	0	0
$406$	−3.21417	−0.159517
$407$	− 23.6392i	− 1.17175i
$408$	− 6.88325i	− 0.340772i
$409$	5.58612	0.276216	0.138108	−	0.990417i	$-0.455898\pi$
$409$	5.58612	0.276216	0.138108	+	0.990417i	$0.455898\pi$
$410$	0	0
$411$	−5.71011	−0.281659
$412$	11.7665i	0.579694i
$413$	− 44.7318i	− 2.20111i
$414$	−1.83738	−0.0903025
$415$	0	0
$416$	4.57889	0.224498
$417$	− 12.7560i	− 0.624663i
$418$	− 33.3526i	− 1.63133i
$419$	12.2513	0.598513	0.299257	−	0.954173i	$-0.403261\pi$
$419$	12.2513	0.598513	0.299257	+	0.954173i	$0.403261\pi$
$420$	0	0
$421$	−2.85670	−0.139227	−0.0696135	−	0.997574i	$-0.522177\pi$
$421$	−2.85670	−0.139227	−0.0696135	+	0.997574i	$0.522177\pi$
$422$	− 2.66184i	− 0.129576i
$423$	2.28660i	0.111178i
$424$	−12.3719	−0.600835
$425$	0	0
$426$	20.0289	0.970406
$427$	9.66579i	0.467760i
$428$	8.42835i	0.407400i
$429$	40.7970	1.96970
$430$	0	0
$431$	−11.3382	−0.546140	−0.273070	−	0.961994i	$-0.588039\pi$
$431$	−11.3382	−0.546140	−0.273070	+	0.961994i	$0.588039\pi$
$432$	− 5.36471i	− 0.258110i
$433$	34.0289i	1.63533i	0.575696	+	0.817663i	$0.304731\pi$
$433$	34.0289i	1.63533i	−0.575696	+	0.817663i	$0.695269\pi$
$434$	−0.398504	−0.0191288
$435$	0	0
$436$	5.75203	0.275472
$437$	− 53.6006i	− 2.56406i
$438$	− 0.206938i	− 0.00988787i
$439$	−5.27058	−0.251551	−0.125775	−	0.992059i	$-0.540142\pi$
$439$	−5.27058	−0.251551	−0.125775	+	0.992059i	$0.540142\pi$
$440$	0	0
$441$	−0.713400	−0.0339714
$442$	− 18.8833i	− 0.898185i
$443$	13.1731i	0.625875i	0.949774	+	0.312938i	$0.101313\pi$
$443$	13.1731i	0.625875i	−0.949774	+	0.312938i	$0.898687\pi$
$444$	7.39127	0.350774
$445$	0	0
$446$	0.744796	0.0352671
$447$	− 19.2254i	− 0.909328i
$448$	3.21417i	0.151855i
$449$	−12.9243	−0.609935	−0.304967	−	0.952363i	$-0.598646\pi$
$449$	−12.9243	−0.609935	−0.304967	+	0.952363i	$0.598646\pi$
$450$	0	0
$451$	−44.9919	−2.11858
$452$	7.25520i	0.341256i
$453$	15.2850i	0.718154i
$454$	0.180384	0.00846582
$455$	0	0
$456$	10.4283	0.488352
$457$	14.4959i	0.678091i	0.940770	+	0.339046i	$0.110104\pi$
$457$	14.4959i	0.678091i	−0.940770	+	0.339046i	$0.889896\pi$
$458$	10.1385i	0.473739i
$459$	−22.1240	−1.03266
$460$	0	0
$461$	27.4621	1.27904	0.639520	−	0.768775i	$-0.279133\pi$
$461$	27.4621	1.27904	0.639520	+	0.768775i	$0.279133\pi$
$462$	28.6377i	1.33235i
$463$	− 2.41388i	− 0.112182i	−0.998426	−	0.0560912i	$-0.982136\pi$
$463$	− 2.41388i	− 0.112182i	0.998426	−	0.0560912i	$-0.0178637\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−27.3526	−1.26709
$467$	1.51525i	0.0701174i	0.999385	+	0.0350587i	$0.0111618\pi$
$467$	1.51525i	0.0701174i	−0.999385	+	0.0350587i	$0.988838\pi$
$468$	− 0.980683i	− 0.0453321i
$469$	17.9548	0.829075
$470$	0	0
$471$	16.6908	0.769071
$472$	13.9170i	0.640584i
$473$	32.6908i	1.50312i
$474$	21.4090	0.983349
$475$	0	0
$476$	13.2552	0.607551
$477$	2.64976i	0.121324i
$478$	− 25.7665i	− 1.17853i
$479$	20.6199	0.942148	0.471074	−	0.882094i	$-0.343866\pi$
$479$	20.6199	0.942148	0.471074	+	0.882094i	$0.343866\pi$
$480$	0	0
$481$	20.2769	0.924548
$482$	− 6.34540i	− 0.289025i
$483$	46.0233i	2.09413i
$484$	−17.4959	−0.795270
$485$	0	0
$486$	−2.22141	−0.100765
$487$	17.7367i	0.803725i	0.915700	+	0.401862i	$0.131637\pi$
$487$	17.7367i	0.803725i	−0.915700	+	0.401862i	$0.868363\pi$
$488$	− 3.00724i	− 0.136131i
$489$	31.1722	1.40966
$490$	0	0
$491$	22.4139	1.01152	0.505762	−	0.862673i	$-0.331211\pi$
$491$	22.4139	1.01152	0.505762	+	0.862673i	$0.331211\pi$
$492$	− 14.0676i	− 0.634216i
$493$	− 4.12398i	− 0.185735i
$494$	28.6087	1.28717
$495$	0	0
$496$	0.123983	0.00556701
$497$	38.5701i	1.73011i
$498$	3.75203i	0.168133i
$499$	−14.7737	−0.661364	−0.330682	−	0.943742i	$-0.607279\pi$
$499$	−14.7737	−0.661364	−0.330682	+	0.943742i	$0.607279\pi$
$500$	0	0
$501$	33.9138	1.51515
$502$	− 19.1047i	− 0.852683i
$503$	− 21.3526i	− 0.952067i	−0.879427	−	0.476033i	$-0.842074\pi$
$503$	− 21.3526i	− 0.952067i	0.879427	−	0.476033i	$-0.157926\pi$
$504$	0.688396	0.0306636
$505$	0	0
$506$	−45.7955	−2.03586
$507$	13.2962i	0.590506i
$508$	8.00000i	0.354943i
$509$	−19.1047	−0.846799	−0.423400	−	0.905943i	$-0.639163\pi$
$509$	−19.1047	−0.846799	−0.423400	+	0.905943i	$0.639163\pi$
$510$	0	0
$511$	0.398504	0.0176288
$512$	− 1.00000i	− 0.0441942i
$513$	− 33.5185i	− 1.47988i
$514$	−19.1047	−0.842671
$515$	0	0
$516$	−10.2214	−0.449973
$517$	56.9919i	2.50650i
$518$	14.2335i	0.625384i
$519$	13.2142	0.580038
$520$	0	0
$521$	22.7472	0.996573	0.498286	−	0.867013i	$-0.333963\pi$
$521$	22.7472	0.996573	0.498286	+	0.867013i	$0.333963\pi$
$522$	− 0.214175i	− 0.00937418i
$523$	25.7810i	1.12732i	0.826006	+	0.563662i	$0.190608\pi$
$523$	25.7810i	1.12732i	−0.826006	+	0.563662i	$0.809392\pi$
$524$	11.8196	0.516342
$525$	0	0
$526$	−12.0000	−0.523225
$527$	− 0.511305i	− 0.0222728i
$528$	− 8.90981i	− 0.387750i
$529$	−50.5973	−2.19988
$530$	0	0
$531$	2.98068	0.129351
$532$	20.0821i	0.870668i
$533$	− 38.5925i	− 1.67163i
$534$	8.90981	0.385565
$535$	0	0
$536$	−5.58612	−0.241284
$537$	13.5152i	0.583226i
$538$	− 19.2142i	− 0.828382i
$539$	−17.7810	−0.765881
$540$	0	0
$541$	−21.5297	−0.925635	−0.462818	−	0.886454i	$-0.653161\pi$
$541$	−21.5297	−0.925635	−0.462818	+	0.886454i	$0.653161\pi$
$542$	1.09019i	0.0468277i
$543$	10.4283i	0.447523i
$544$	−4.12398	−0.176814
$545$	0	0
$546$	−24.5644	−1.05126
$547$	− 21.8872i	− 0.935829i	−0.883774	−	0.467915i	$-0.845006\pi$
$547$	− 21.8872i	− 0.935829i	0.883774	−	0.467915i	$-0.154994\pi$
$548$	3.42111i	0.146143i
$549$	−0.644075	−0.0274885
$550$	0	0
$551$	6.24797	0.266172
$552$	− 14.3188i	− 0.609450i
$553$	41.2278i	1.75318i
$554$	25.5330	1.08479
$555$	0	0
$556$	−7.64252	−0.324115
$557$	− 9.24073i	− 0.391542i	−0.980650	−	0.195771i	$-0.937279\pi$
$557$	− 9.24073i	− 0.391542i	0.980650	−	0.195771i	$-0.0627210\pi$
$558$	− 0.0265541i	− 0.00112412i
$559$	−28.0410	−1.18601
$560$	0	0
$561$	−36.7439	−1.55133
$562$	− 1.39456i	− 0.0588259i
$563$	23.1876i	0.977242i	0.872496	+	0.488621i	$0.162500\pi$
$563$	23.1876i	0.977242i	−0.872496	+	0.488621i	$0.837500\pi$
$564$	−17.8196	−0.750341
$565$	0	0
$566$	10.2480	0.430754
$567$	26.7150i	1.12192i
$568$	− 12.0000i	− 0.503509i
$569$	−2.90981	−0.121986	−0.0609928	−	0.998138i	$-0.519427\pi$
$569$	−2.90981	−0.121986	−0.0609928	+	0.998138i	$0.519427\pi$
$570$	0	0
$571$	26.4130	1.10535	0.552674	−	0.833397i	$-0.313607\pi$
$571$	26.4130	1.10535	0.552674	+	0.833397i	$0.313607\pi$
$572$	− 24.4428i	− 1.02201i
$573$	− 18.4404i	− 0.770360i
$574$	27.0902	1.13072
$575$	0	0
$576$	−0.214175	−0.00892396
$577$	− 9.47662i	− 0.394517i	−0.980352	−	0.197258i	$-0.936796\pi$
$577$	− 9.47662i	− 0.394517i	0.980352	−	0.197258i	$-0.0632038\pi$
$578$	0.00723726i	0 0.000301031i
$579$	0.138458	0.00575411
$580$	0	0
$581$	−7.22536	−0.299758
$582$	− 0.966209i	− 0.0400506i
$583$	66.0434i	2.73524i
$584$	−0.123983	−0.00513046
$585$	0	0
$586$	3.57165	0.147544
$587$	1.50407i	0.0620795i	0.999518	+	0.0310398i	$0.00988185\pi$
$587$	1.50407i	0.0620795i	−0.999518	+	0.0310398i	$0.990118\pi$
$588$	− 5.55957i	− 0.229273i
$589$	0.774643	0.0319186
$590$	0	0
$591$	−1.22296	−0.0503059
$592$	− 4.42835i	− 0.182004i
$593$	20.5104i	0.842261i	0.907000	+	0.421131i	$0.138367\pi$
$593$	20.5104i	0.842261i	−0.907000	+	0.421131i	$0.861633\pi$
$594$	−28.6377	−1.17502
$595$	0	0
$596$	−11.5185	−0.471818
$597$	7.69234i	0.314827i
$598$	− 39.2818i	− 1.60635i
$599$	7.51525	0.307065	0.153532	−	0.988144i	$-0.450935\pi$
$599$	7.51525	0.307065	0.153532	+	0.988144i	$0.450935\pi$
$600$	0	0
$601$	4.51041	0.183983	0.0919917	−	0.995760i	$-0.470677\pi$
$601$	4.51041	0.183983	0.0919917	+	0.995760i	$0.470677\pi$
$602$	− 19.6836i	− 0.802242i
$603$	1.19641i	0.0487215i
$604$	9.15777	0.372625
$605$	0	0
$606$	−8.65855	−0.351730
$607$	30.2093i	1.22616i	0.790021	+	0.613079i	$0.210069\pi$
$607$	30.2093i	1.22616i	−0.790021	+	0.613079i	$0.789931\pi$
$608$	− 6.24797i	− 0.253388i
$609$	−5.36471	−0.217389
$610$	0	0
$611$	−48.8856	−1.97770
$612$	0.883254i	0.0357034i
$613$	− 31.1611i	− 1.25858i	−0.777169	−	0.629292i	$-0.783345\pi$
$613$	− 31.1611i	− 1.25858i	0.777169	−	0.629292i	$-0.216655\pi$
$614$	−12.4959	−0.504295
$615$	0	0
$616$	17.1578	0.691306
$617$	− 19.8760i	− 0.800178i	−0.916476	−	0.400089i	$-0.868979\pi$
$617$	− 19.8760i	− 0.800178i	0.916476	−	0.400089i	$-0.131021\pi$
$618$	19.6392i	0.790006i
$619$	15.2175	0.611642	0.305821	−	0.952089i	$-0.401069\pi$
$619$	15.2175	0.611642	0.305821	+	0.952089i	$0.401069\pi$
$620$	0	0
$621$	−46.0233	−1.84685
$622$	− 21.9846i	− 0.881503i
$623$	17.1578i	0.687412i
$624$	7.64252	0.305946
$625$	0	0
$626$	17.1722	0.686341
$627$	− 55.6682i	− 2.22317i
$628$	− 10.0000i	− 0.399043i
$629$	−18.2624	−0.728171
$630$	0	0
$631$	−8.05311	−0.320589	−0.160295	−	0.987069i	$-0.551244\pi$
$631$	−8.05311	−0.320589	−0.160295	+	0.987069i	$0.551244\pi$
$632$	− 12.8269i	− 0.510225i
$633$	− 4.44282i	− 0.176586i
$634$	4.97739	0.197677
$635$	0	0
$636$	−20.6498	−0.818816
$637$	− 15.2519i	− 0.604303i
$638$	− 5.33816i	− 0.211340i
$639$	−2.57010	−0.101672
$640$	0	0
$641$	−22.2769	−0.879885	−0.439943	−	0.898026i	$-0.645001\pi$
$641$	−22.2769	−0.879885	−0.439943	+	0.898026i	$0.645001\pi$
$642$	14.0676i	0.555203i
$643$	− 16.4815i	− 0.649965i	−0.945720	−	0.324983i	$-0.894642\pi$
$643$	− 16.4815i	− 0.649965i	0.945720	−	0.324983i	$-0.105358\pi$
$644$	27.5740	1.08657
$645$	0	0
$646$	−25.7665	−1.01377
$647$	− 11.9017i	− 0.467903i	−0.972248	−	0.233952i	$-0.924834\pi$
$647$	− 11.9017i	− 0.467903i	0.972248	−	0.233952i	$-0.0751657\pi$
$648$	− 8.31160i	− 0.326511i
$649$	74.2914	2.91619
$650$	0	0
$651$	−0.665134	−0.0260687
$652$	− 18.6763i	− 0.731421i
$653$	− 38.3300i	− 1.49997i	−0.661455	−	0.749985i	$-0.730061\pi$
$653$	− 38.3300i	− 1.49997i	0.661455	−	0.749985i	$-0.269939\pi$
$654$	9.60060	0.375413
$655$	0	0
$656$	−8.42835	−0.329072
$657$	0.0265541i	0.00103597i
$658$	− 34.3155i	− 1.33776i
$659$	15.6537	0.609782	0.304891	−	0.952387i	$-0.401380\pi$
$659$	15.6537	0.609782	0.304891	+	0.952387i	$0.401380\pi$
$660$	0	0
$661$	−15.1578	−0.589569	−0.294785	−	0.955564i	$-0.595248\pi$
$661$	−15.1578	−0.589569	−0.294785	+	0.955564i	$0.595248\pi$
$662$	20.0145i	0.777885i
$663$	− 31.5176i	− 1.22404i
$664$	2.24797	0.0872380
$665$	0	0
$666$	−0.948442	−0.0367514
$667$	− 8.57889i	− 0.332176i
$668$	− 20.3188i	− 0.786160i
$669$	1.24312	0.0480620
$670$	0	0
$671$	−16.0531	−0.619723
$672$	5.36471i	0.206948i
$673$	− 22.3831i	− 0.862806i	−0.902159	−	0.431403i	$-0.858019\pi$
$673$	− 22.3831i	− 0.862806i	0.902159	−	0.431403i	$-0.141981\pi$
$674$	−2.55233	−0.0983122
$675$	0	0
$676$	7.96621	0.306393
$677$	− 41.1191i	− 1.58034i	−0.612890	−	0.790168i	$-0.709993\pi$
$677$	− 41.1191i	− 1.58034i	0.612890	−	0.790168i	$-0.290007\pi$
$678$	12.1095i	0.465063i
$679$	1.86064	0.0714050
$680$	0	0
$681$	0.301075	0.0115372
$682$	− 0.661842i	− 0.0253432i
$683$	50.7728i	1.94277i	0.237512	+	0.971385i	$0.423668\pi$
$683$	50.7728i	1.94277i	−0.237512	+	0.971385i	$0.576332\pi$
$684$	−1.33816	−0.0511658
$685$	0	0
$686$	−11.7931	−0.450261
$687$	16.9219i	0.645610i
$688$	6.12398i	0.233475i
$689$	−56.6498	−2.15818
$690$	0	0
$691$	−3.14659	−0.119702	−0.0598510	−	0.998207i	$-0.519063\pi$
$691$	−3.14659	−0.119702	−0.0598510	+	0.998207i	$0.519063\pi$
$692$	− 7.91705i	− 0.300961i
$693$	− 3.67477i	− 0.139593i
$694$	13.8872	0.527151
$695$	0	0
$696$	1.66908	0.0632663
$697$	34.7584i	1.31657i
$698$	26.0821i	0.987220i
$699$	−45.6537	−1.72678
$700$	0	0
$701$	18.6618	0.704848	0.352424	−	0.935840i	$-0.385357\pi$
$701$	18.6618	0.704848	0.352424	+	0.935840i	$0.385357\pi$
$702$	− 24.5644i	− 0.927124i
$703$	− 27.6682i	− 1.04353i
$704$	−5.33816	−0.201189
$705$	0	0
$706$	19.4057	0.730345
$707$	− 16.6739i	− 0.627087i
$708$	23.2286i	0.872986i
$709$	44.5394	1.67271	0.836355	−	0.548188i	$-0.184682\pi$
$709$	44.5394	1.67271	0.836355	+	0.548188i	$0.184682\pi$
$710$	0	0
$711$	−2.74719	−0.103028
$712$	− 5.33816i	− 0.200056i
$713$	− 1.06364i	− 0.0398335i
$714$	22.1240	0.827969
$715$	0	0
$716$	8.09743	0.302615
$717$	− 43.0063i	− 1.60610i
$718$	16.1650i	0.603273i
$719$	49.5475	1.84781	0.923905	−	0.382622i	$-0.124979\pi$
$719$	49.5475	1.84781	0.923905	+	0.382622i	$0.124979\pi$
$720$	0	0
$721$	−37.8196	−1.40848
$722$	− 20.0371i	− 0.745703i
$723$	− 10.5910i	− 0.393882i
$724$	6.24797	0.232204
$725$	0	0
$726$	−29.2021	−1.08379
$727$	1.21088i	0.0449092i	0.999748	+	0.0224546i	$0.00714811\pi$
$727$	1.21088i	0.0449092i	−0.999748	+	0.0224546i	$0.992852\pi$
$728$	14.7173i	0.545461i
$729$	−28.6425	−1.06083
$730$	0	0
$731$	25.2552	0.934097
$732$	− 5.01932i	− 0.185519i
$733$	23.2706i	0.859518i	0.902944	+	0.429759i	$0.141402\pi$
$733$	23.2706i	0.859518i	−0.902944	+	0.429759i	$0.858598\pi$
$734$	−1.51854	−0.0560504
$735$	0	0
$736$	−8.57889	−0.316222
$737$	29.8196i	1.09842i
$738$	1.80514i	0.0664482i
$739$	23.7665	0.874265	0.437133	−	0.899397i	$-0.355994\pi$
$739$	23.7665	0.874265	0.437133	+	0.899397i	$0.355994\pi$
$740$	0	0
$741$	47.7502	1.75415
$742$	− 39.7656i	− 1.45984i
$743$	46.6763i	1.71239i	0.516654	+	0.856194i	$0.327177\pi$
$743$	46.6763i	1.71239i	−0.516654	+	0.856194i	$0.672823\pi$
$744$	0.206938	0.00758671
$745$	0	0
$746$	−7.16107	−0.262185
$747$	− 0.481458i	− 0.0176156i
$748$	22.0145i	0.804929i
$749$	−27.0902	−0.989854
$750$	0	0
$751$	−2.41388	−0.0880836	−0.0440418	−	0.999030i	$-0.514023\pi$
$751$	−2.41388	−0.0880836	−0.0440418	+	0.999030i	$0.514023\pi$
$752$	10.6763i	0.389325i
$753$	− 31.8872i	− 1.16203i
$754$	4.57889	0.166753
$755$	0	0
$756$	17.2431	0.627126
$757$	− 11.5717i	− 0.420579i	−0.977639	−	0.210289i	$-0.932559\pi$
$757$	− 11.5717i	− 0.420579i	0.977639	−	0.210289i	$-0.0674406\pi$
$758$	24.0145i	0.872245i
$759$	−76.4362	−2.77446
$760$	0	0
$761$	3.10137	0.112425	0.0562124	−	0.998419i	$-0.482098\pi$
$761$	3.10137	0.112425	0.0562124	+	0.998419i	$0.482098\pi$
$762$	13.3526i	0.483715i
$763$	18.4880i	0.669312i
$764$	−11.0483	−0.399712
$765$	0	0
$766$	34.3864	1.24243
$767$	63.7246i	2.30096i
$768$	− 1.66908i	− 0.0602277i
$769$	43.6537	1.57419	0.787096	−	0.616830i	$-0.211583\pi$
$769$	43.6537	1.57419	0.787096	+	0.616830i	$0.211583\pi$
$770$	0	0
$771$	−31.8872	−1.14839
$772$	− 0.0829546i	− 0.00298560i
$773$	− 13.6682i	− 0.491610i	−0.969319	−	0.245805i	$-0.920948\pi$
$773$	− 13.6682i	− 0.491610i	0.969319	−	0.245805i	$-0.0790523\pi$
$774$	1.31160	0.0471446
$775$	0	0
$776$	−0.578887	−0.0207808
$777$	23.7568i	0.852271i
$778$	5.63923i	0.202176i
$779$	−52.6600	−1.88674
$780$	0	0
$781$	−64.0579	−2.29217
$782$	35.3792i	1.26516i
$783$	− 5.36471i	− 0.191719i
$784$	−3.33092	−0.118961
$785$	0	0
$786$	19.7279	0.703670
$787$	− 9.28505i	− 0.330976i	−0.986212	−	0.165488i	$-0.947080\pi$
$787$	− 9.28505i	− 0.330976i	0.986212	−	0.165488i	$-0.0529200\pi$
$788$	0.732717i	0.0261020i
$789$	−20.0289	−0.713049
$790$	0	0
$791$	−23.3195	−0.829146
$792$	1.14330i	0.0406254i
$793$	− 13.7698i	− 0.488980i
$794$	10.9131	0.387291
$795$	0	0
$796$	4.60873	0.163352
$797$	− 25.9469i	− 0.919086i	−0.888156	−	0.459543i	$-0.848013\pi$
$797$	− 25.9469i	− 0.919086i	0.888156	−	0.459543i	$-0.151987\pi$
$798$	33.5185i	1.18654i
$799$	44.0289	1.55763
$800$	0	0
$801$	−1.14330	−0.0403965
$802$	− 21.9846i	− 0.776304i
$803$	0.661842i	0.0233559i
$804$	−9.32368	−0.328821
$805$	0	0
$806$	0.567705	0.0199966
$807$	− 32.0700i	− 1.12892i
$808$	5.18762i	0.182500i
$809$	6.08206	0.213834	0.106917	−	0.994268i	$-0.465902\pi$
$809$	6.08206	0.213834	0.106917	+	0.994268i	$0.465902\pi$
$810$	0	0
$811$	−47.9194	−1.68268	−0.841340	−	0.540507i	$-0.818232\pi$
$811$	−47.9194	−1.68268	−0.841340	+	0.540507i	$0.818232\pi$
$812$	3.21417i	0.112795i
$813$	1.81962i	0.0638167i
$814$	−23.6392	−0.828555
$815$	0	0
$816$	−6.88325	−0.240962
$817$	38.2624i	1.33863i
$818$	− 5.58612i	− 0.195314i
$819$	3.15209	0.110143
$820$	0	0
$821$	−7.98553	−0.278697	−0.139348	−	0.990243i	$-0.544501\pi$
$821$	−7.98553	−0.278697	−0.139348	+	0.990243i	$0.544501\pi$
$822$	5.71011i	0.199163i
$823$	− 12.3077i	− 0.429018i	−0.976722	−	0.214509i	$-0.931185\pi$
$823$	− 12.3077i	− 0.429018i	0.976722	−	0.214509i	$-0.0688151\pi$
$824$	11.7665	0.409906
$825$	0	0
$826$	−44.7318	−1.55642
$827$	− 34.8679i	− 1.21248i	−0.795284	−	0.606238i	$-0.792678\pi$
$827$	− 34.8679i	− 1.21248i	0.795284	−	0.606238i	$-0.207322\pi$
$828$	1.83738i	0.0638535i
$829$	−45.7777	−1.58992	−0.794962	−	0.606659i	$-0.792509\pi$
$829$	−45.7777	−1.58992	−0.794962	+	0.606659i	$0.792509\pi$
$830$	0	0
$831$	42.6166	1.47835
$832$	− 4.57889i	− 0.158744i
$833$	13.7367i	0.475947i
$834$	−12.7560	−0.441703
$835$	0	0
$836$	−33.3526	−1.15352
$837$	− 0.665134i	− 0.0229904i
$838$	− 12.2513i	− 0.423213i
$839$	47.9017	1.65375	0.826875	−	0.562386i	$-0.190117\pi$
$839$	47.9017	1.65375	0.826875	+	0.562386i	$0.190117\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	2.85670i	0.0984484i
$843$	− 2.32763i	− 0.0801678i
$844$	−2.66184	−0.0916244
$845$	0	0
$846$	2.28660	0.0786149
$847$	− 56.2350i	− 1.93226i
$848$	12.3719i	0.424854i
$849$	17.1047	0.587031
$850$	0	0
$851$	−37.9903	−1.30229
$852$	− 20.0289i	− 0.686180i
$853$	5.03050i	0.172241i	0.996285	+	0.0861205i	$0.0274470\pi$
$853$	5.03050i	0.172241i	−0.996285	+	0.0861205i	$0.972553\pi$
$854$	9.66579	0.330756
$855$	0	0
$856$	8.42835	0.288075
$857$	8.51041i	0.290710i	0.989380	+	0.145355i	$0.0464324\pi$
$857$	8.51041i	0.290710i	−0.989380	+	0.145355i	$0.953568\pi$
$858$	− 40.7970i	− 1.39279i
$859$	25.7520	0.878648	0.439324	−	0.898329i	$-0.355218\pi$
$859$	25.7520	0.878648	0.439324	+	0.898329i	$0.355218\pi$
$860$	0	0
$861$	45.2157	1.54095
$862$	11.3382i	0.386179i
$863$	− 2.45820i	− 0.0836780i	−0.999124	−	0.0418390i	$-0.986678\pi$
$863$	− 2.45820i	− 0.0836780i	0.999124	−	0.0418390i	$-0.0133217\pi$
$864$	−5.36471	−0.182511
$865$	0	0
$866$	34.0289	1.15635
$867$	0.0120796i	0 0.000410244i
$868$	0.398504i	0.0135261i
$869$	−68.4718	−2.32275
$870$	0	0
$871$	−25.5782	−0.866685
$872$	− 5.75203i	− 0.194788i
$873$	0.123983i	0.00419619i
$874$	−53.6006	−1.81307
$875$	0	0
$876$	−0.206938	−0.00699178
$877$	49.4645i	1.67030i	0.550023	+	0.835149i	$0.314619\pi$
$877$	49.4645i	1.67030i	−0.550023	+	0.835149i	$0.685381\pi$
$878$	5.27058i	0.177873i
$879$	5.96137	0.201072
$880$	0	0
$881$	41.0594	1.38333	0.691664	−	0.722219i	$-0.256878\pi$
$881$	41.0594	1.38333	0.691664	+	0.722219i	$0.256878\pi$
$882$	0.713400i	0.0240214i
$883$	29.3913i	0.989095i	0.869151	+	0.494547i	$0.164666\pi$
$883$	29.3913i	0.989095i	−0.869151	+	0.494547i	$0.835334\pi$
$884$	−18.8833	−0.635113
$885$	0	0
$886$	13.1731	0.442561
$887$	− 4.85670i	− 0.163072i	−0.996670	−	0.0815360i	$-0.974017\pi$
$887$	− 4.85670i	− 0.163072i	0.996670	−	0.0815360i	$-0.0259826\pi$
$888$	− 7.39127i	− 0.248035i
$889$	−25.7134	−0.862400
$890$	0	0
$891$	−44.3687	−1.48641
$892$	− 0.744796i	− 0.0249376i
$893$	66.7053i	2.23221i
$894$	−19.2254	−0.642992
$895$	0	0
$896$	3.21417	0.107378
$897$	− 65.5644i	− 2.18913i
$898$	12.9243i	0.431289i
$899$	0.123983	0.00413507
$900$	0	0
$901$	51.0217	1.69978
$902$	44.9919i	1.49807i
$903$	− 32.8534i	− 1.09329i
$904$	7.25520	0.241304
$905$	0	0
$906$	15.2850	0.507812
$907$	− 42.8679i	− 1.42340i	−0.702481	−	0.711702i	$-0.747924\pi$
$907$	− 42.8679i	− 1.42340i	0.702481	−	0.711702i	$-0.252076\pi$
$908$	− 0.180384i	− 0.00598624i
$909$	1.11106	0.0368515
$910$	0	0
$911$	−20.3599	−0.674553	−0.337276	−	0.941406i	$-0.609506\pi$
$911$	−20.3599	−0.674553	−0.337276	+	0.941406i	$0.609506\pi$
$912$	− 10.4283i	− 0.345317i
$913$	− 12.0000i	− 0.397142i
$914$	14.4959	0.479483
$915$	0	0
$916$	10.1385	0.334984
$917$	37.9903i	1.25455i
$918$	22.1240i	0.730200i
$919$	−44.0000	−1.45143	−0.725713	−	0.687998i	$-0.758490\pi$
$919$	−44.0000	−1.45143	−0.725713	+	0.687998i	$0.758490\pi$
$920$	0	0
$921$	−20.8567	−0.687252
$922$	− 27.4621i	− 0.904417i
$923$	− 54.9466i	− 1.80859i
$924$	28.6377	0.942111
$925$	0	0
$926$	−2.41388	−0.0793249
$927$	− 2.52009i	− 0.0827707i
$928$	− 1.00000i	− 0.0328266i
$929$	40.5668	1.33095	0.665477	−	0.746418i	$-0.268228\pi$
$929$	40.5668	1.33095	0.665477	+	0.746418i	$0.268228\pi$
$930$	0	0
$931$	−20.8115	−0.682069
$932$	27.3526i	0.895965i
$933$	− 36.6941i	− 1.20131i
$934$	1.51525	0.0495805
$935$	0	0
$936$	−0.980683	−0.0320546
$937$	34.7439i	1.13503i	0.823362	+	0.567517i	$0.192096\pi$
$937$	34.7439i	1.13503i	−0.823362	+	0.567517i	$0.807904\pi$
$938$	− 17.9548i	− 0.586244i
$939$	28.6618	0.935344
$940$	0	0
$941$	−18.0821	−0.589458	−0.294729	−	0.955581i	$-0.595229\pi$
$941$	−18.0821	−0.589458	−0.294729	+	0.955581i	$0.595229\pi$
$942$	− 16.6908i	− 0.543815i
$943$	72.3059i	2.35460i
$944$	13.9170	0.452961
$945$	0	0
$946$	32.6908	1.06287
$947$	48.3743i	1.57195i	0.618255	+	0.785977i	$0.287840\pi$
$947$	48.3743i	1.57195i	−0.618255	+	0.785977i	$0.712160\pi$
$948$	− 21.4090i	− 0.695333i
$949$	−0.567705	−0.0184285
$950$	0	0
$951$	8.30766	0.269394
$952$	− 13.2552i	− 0.429604i
$953$	14.0289i	0.454442i	0.973843	+	0.227221i	$0.0729640\pi$
$953$	14.0289i	0.454442i	−0.973843	+	0.227221i	$0.927036\pi$
$954$	2.64976	0.0857892
$955$	0	0
$956$	−25.7665	−0.833348
$957$	− 8.90981i	− 0.288013i
$958$	− 20.6199i	− 0.666199i
$959$	−10.9961	−0.355081
$960$	0	0
$961$	−30.9846	−0.999504
$962$	− 20.2769i	− 0.653754i
$963$	− 1.80514i	− 0.0581699i
$964$	−6.34540	−0.204371
$965$	0	0
$966$	46.0233	1.48077
$967$	− 25.9614i	− 0.834861i	−0.908709	−	0.417431i	$-0.862931\pi$
$967$	− 25.9614i	− 0.834861i	0.908709	−	0.417431i	$-0.137069\pi$
$968$	17.4959i	0.562341i
$969$	−43.0063	−1.38156
$970$	0	0
$971$	21.7520	0.698056	0.349028	−	0.937112i	$-0.386512\pi$
$971$	21.7520	0.698056	0.349028	+	0.937112i	$0.386512\pi$
$972$	2.22141i	0.0712518i
$973$	− 24.5644i	− 0.787499i
$974$	17.7367	0.568319
$975$	0	0
$976$	−3.00724	−0.0962593
$977$	− 26.6908i	− 0.853914i	−0.904272	−	0.426957i	$-0.859586\pi$
$977$	− 26.6908i	− 0.853914i	0.904272	−	0.426957i	$-0.140414\pi$
$978$	− 31.1722i	− 0.996779i
$979$	−28.4959	−0.910734
$980$	0	0
$981$	−1.23194	−0.0393329
$982$	− 22.4139i	− 0.715256i
$983$	37.0450i	1.18155i	0.806836	+	0.590776i	$0.201178\pi$
$983$	37.0450i	1.18155i	−0.806836	+	0.590776i	$0.798822\pi$
$984$	−14.0676	−0.448458
$985$	0	0
$986$	−4.12398	−0.131334
$987$	− 57.2754i	− 1.82309i
$988$	− 28.6087i	− 0.910165i
$989$	52.5370	1.67058
$990$	0	0
$991$	−30.4283	−0.966588	−0.483294	−	0.875458i	$-0.660560\pi$
$991$	−30.4283	−0.966588	−0.483294	+	0.875458i	$0.660560\pi$
$992$	− 0.123983i	− 0.00393647i
$993$	33.4057i	1.06010i
$994$	38.5701	1.22337
$995$	0	0
$996$	3.75203	0.118888
$997$	− 15.0226i	− 0.475771i	−0.971293	−	0.237885i	$-0.923546\pi$
$997$	− 15.0226i	− 0.475771i	0.971293	−	0.237885i	$-0.0764543\pi$
$998$	14.7737i	0.467655i
$999$	−23.7568	−0.751633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.l.349.1		6
5.2	odd	4		290.2.a.e.1.1	✓	3
5.3	odd	4		1450.2.a.p.1.3		3
5.4	even	2	inner	1450.2.b.l.349.6		6
15.2	even	4		2610.2.a.x.1.2		3
20.7	even	4		2320.2.a.l.1.3		3
40.27	even	4		9280.2.a.by.1.1		3
40.37	odd	4		9280.2.a.bf.1.3		3
145.57	odd	4		8410.2.a.v.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.e.1.1	✓	3	5.2	odd	4
1450.2.a.p.1.3		3	5.3	odd	4
1450.2.b.l.349.1		6	1.1	even	1	trivial
1450.2.b.l.349.6		6	5.4	even	2	inner
2320.2.a.l.1.3		3	20.7	even	4
2610.2.a.x.1.2		3	15.2	even	4
8410.2.a.v.1.3		3	145.57	odd	4
9280.2.a.bf.1.3		3	40.37	odd	4
9280.2.a.by.1.1		3	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.66908i q^{3} -1.00000 q^{4} -1.66908 q^{6} -3.21417i q^{7} +1.00000i q^{8} +0.214175 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.66908i q^{3} -1.00000 q^{4} -1.66908 q^{6} -3.21417i q^{7} +1.00000i q^{8} +0.214175 q^{9} +5.33816 q^{11} +1.66908i q^{12} +4.57889i q^{13} -3.21417 q^{14} +1.00000 q^{16} -4.12398i q^{17} -0.214175i q^{18} +6.24797 q^{19} -5.36471 q^{21} -5.33816i q^{22} -8.57889i q^{23} +1.66908 q^{24} +4.57889 q^{26} -5.36471i q^{27} +3.21417i q^{28} +1.00000 q^{29} +0.123983 q^{31} -1.00000i q^{32} -8.90981i q^{33} -4.12398 q^{34} -0.214175 q^{36} -4.42835i q^{37} -6.24797i q^{38} +7.64252 q^{39} -8.42835 q^{41} +5.36471i q^{42} +6.12398i q^{43} -5.33816 q^{44} -8.57889 q^{46} +10.6763i q^{47} -1.66908i q^{48} -3.33092 q^{49} -6.88325 q^{51} -4.57889i q^{52} +12.3719i q^{53} -5.36471 q^{54} +3.21417 q^{56} -10.4283i q^{57} -1.00000i q^{58} +13.9170 q^{59} -3.00724 q^{61} -0.123983i q^{62} -0.688396i q^{63} -1.00000 q^{64} -8.90981 q^{66} +5.58612i q^{67} +4.12398i q^{68} -14.3188 q^{69} -12.0000 q^{71} +0.214175i q^{72} +0.123983i q^{73} -4.42835 q^{74} -6.24797 q^{76} -17.1578i q^{77} -7.64252i q^{78} -12.8269 q^{79} -8.31160 q^{81} +8.42835i q^{82} -2.24797i q^{83} +5.36471 q^{84} +6.12398 q^{86} -1.66908i q^{87} +5.33816i q^{88} -5.33816 q^{89} +14.7173 q^{91} +8.57889i q^{92} -0.206938i q^{93} +10.6763 q^{94} -1.66908 q^{96} +0.578887i q^{97} +3.33092i q^{98} +1.14330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 6 q^{6} - 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 6 * q^6 - 12 * q^9	\( 6 q - 6 q^{4} + 6 q^{6} - 12 q^{9} - 6 q^{14} + 6 q^{16} - 24 q^{21} - 6 q^{24} + 6 q^{26} + 6 q^{29} - 18 q^{31} - 6 q^{34} + 12 q^{36} + 6 q^{39} - 24 q^{41} - 30 q^{46} - 36 q^{49} - 12 q^{51} - 24 q^{54} + 6 q^{56} + 30 q^{59} + 30 q^{61} - 6 q^{64} - 48 q^{66} + 18 q^{69} - 72 q^{71} - 18 q^{79} + 6 q^{81} + 24 q^{84} + 18 q^{86} - 48 q^{91} + 6 q^{96} + 60 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 6 * q^6 - 12 * q^9 - 6 * q^14 + 6 * q^16 - 24 * q^21 - 6 * q^24 + 6 * q^26 + 6 * q^29 - 18 * q^31 - 6 * q^34 + 12 * q^36 + 6 * q^39 - 24 * q^41 - 30 * q^46 - 36 * q^49 - 12 * q^51 - 24 * q^54 + 6 * q^56 + 30 * q^59 + 30 * q^61 - 6 * q^64 - 48 * q^66 + 18 * q^69 - 72 * q^71 - 18 * q^79 + 6 * q^81 + 24 * q^84 + 18 * q^86 - 48 * q^91 + 6 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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