LMFDB - Embedded newform 1450.2.b.j.349.6

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:	6.0.14077504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} + 33x^{2} + 16 $ x^6 + 11x^4 + 33x^2 + 16
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			349.6
Root			$-0.772866i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.j.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +3.40268i q^{3} -1.00000 q^{4} -3.40268 q^{6} -0.772866i q^{7} -1.00000i q^{8} -8.57822 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +3.40268i q^{3} -1.00000 q^{4} -3.40268 q^{6} -0.772866i q^{7} -1.00000i q^{8} -8.57822 q^{9} +1.54573 q^{11} -3.40268i q^{12} -3.85695i q^{13} +0.772866 q^{14} +1.00000 q^{16} -1.22713i q^{17} -8.57822i q^{18} -6.80536 q^{19} +2.62981 q^{21} +1.54573i q^{22} -3.40268i q^{23} +3.40268 q^{24} +3.85695 q^{26} -18.9809i q^{27} +0.772866i q^{28} -1.00000 q^{29} -9.12395 q^{31} +1.00000i q^{32} +5.25963i q^{33} +1.22713 q^{34} +8.57822 q^{36} -0.454269i q^{37} -6.80536i q^{38} +13.1240 q^{39} +3.54573 q^{41} +2.62981i q^{42} -3.86433i q^{43} -1.54573 q^{44} +3.40268 q^{46} -8.00000i q^{47} +3.40268i q^{48} +6.40268 q^{49} +4.17554 q^{51} +3.85695i q^{52} +0.318597i q^{53} +18.9809 q^{54} -0.772866 q^{56} -23.1564i q^{57} -1.00000i q^{58} -8.66231 q^{59} -1.40268 q^{61} -9.12395i q^{62} +6.62981i q^{63} -1.00000 q^{64} -5.25963 q^{66} +13.6107i q^{67} +1.22713i q^{68} +11.5782 q^{69} -13.6107 q^{71} +8.57822i q^{72} +9.92931i q^{73} +0.454269 q^{74} +6.80536 q^{76} -1.19464i q^{77} +13.1240i q^{78} -14.8452 q^{79} +38.8512 q^{81} +3.54573i q^{82} +14.8054i q^{83} -2.62981 q^{84} +3.86433 q^{86} -3.40268i q^{87} -1.54573i q^{88} +1.71390 q^{89} -2.98090 q^{91} +3.40268i q^{92} -31.0459i q^{93} +8.00000 q^{94} -3.40268 q^{96} +10.9484i q^{97} +6.40268i q^{98} -13.2596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9	$ 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9} + 4 q^{11} + 2 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{24} + 10 q^{26} - 6 q^{29} - 10 q^{31} + 10 q^{34} + 12 q^{36} + 34 q^{39} + 16 q^{41} - 4 q^{44} + 2 q^{46} + 20 q^{49} + 4 q^{51} + 56 q^{54} - 2 q^{56} - 2 q^{59} + 10 q^{61} - 6 q^{64} + 30 q^{69} - 8 q^{71} + 8 q^{74} + 4 q^{76} - 18 q^{79} + 70 q^{81} + 10 q^{86} - 16 q^{89} + 40 q^{91} + 48 q^{94} - 2 q^{96} - 48 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9 + 4 * q^11 + 2 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^24 + 10 * q^26 - 6 * q^29 - 10 * q^31 + 10 * q^34 + 12 * q^36 + 34 * q^39 + 16 * q^41 - 4 * q^44 + 2 * q^46 + 20 * q^49 + 4 * q^51 + 56 * q^54 - 2 * q^56 - 2 * q^59 + 10 * q^61 - 6 * q^64 + 30 * q^69 - 8 * q^71 + 8 * q^74 + 4 * q^76 - 18 * q^79 + 70 * q^81 + 10 * q^86 - 16 * q^89 + 40 * q^91 + 48 * q^94 - 2 * q^96 - 48 * 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
$3$	3.40268i	1.96454i	0.187478	+	0.982269i	$0.439969\pi$
$3$	3.40268i	1.96454i	−0.187478	+	0.982269i	$0.560031\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−3.40268	−1.38914
$7$	− 0.772866i	− 0.292116i	−0.989276	−	0.146058i	$-0.953341\pi$
$7$	− 0.772866i	− 0.292116i	0.989276	−	0.146058i	$-0.0466586\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−8.57822	−2.85941
$10$	0	0
$11$	1.54573	0.466055	0.233028	−	0.972470i	$-0.425137\pi$
$11$	1.54573	0.466055	0.233028	+	0.972470i	$0.425137\pi$
$12$	− 3.40268i	− 0.982269i
$13$	− 3.85695i	− 1.06972i	−0.844939	−	0.534862i	$-0.820363\pi$
$13$	− 3.85695i	− 1.06972i	0.844939	−	0.534862i	$-0.179637\pi$
$14$	0.772866	0.206557
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.22713i	− 0.297624i	−0.988866	−	0.148812i	$-0.952455\pi$
$17$	− 1.22713i	− 0.297624i	0.988866	−	0.148812i	$-0.0475449\pi$
$18$	− 8.57822i	− 2.02191i
$19$	−6.80536	−1.56126	−0.780628	−	0.624996i	$-0.785101\pi$
$19$	−6.80536	−1.56126	−0.780628	+	0.624996i	$0.785101\pi$
$20$	0	0
$21$	2.62981	0.573872
$22$	1.54573i	0.329551i
$23$	− 3.40268i	− 0.709508i	−0.934960	−	0.354754i	$-0.884565\pi$
$23$	− 3.40268i	− 0.709508i	0.934960	−	0.354754i	$-0.115435\pi$
$24$	3.40268	0.694569
$25$	0	0
$26$	3.85695	0.756410
$27$	− 18.9809i	− 3.65288i
$28$	0.772866i	0.146058i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−9.12395	−1.63871	−0.819355	−	0.573286i	$-0.805668\pi$
$31$	−9.12395	−1.63871	−0.819355	+	0.573286i	$0.805668\pi$
$32$	1.00000i	0.176777i
$33$	5.25963i	0.915583i
$34$	1.22713	0.210452
$35$	0	0
$36$	8.57822	1.42970
$37$	− 0.454269i	− 0.0746813i	−0.999303	−	0.0373407i	$-0.988111\pi$
$37$	− 0.454269i	− 0.0746813i	0.999303	−	0.0373407i	$-0.0118887\pi$
$38$	− 6.80536i	− 1.10397i
$39$	13.1240	2.10151
$40$	0	0
$41$	3.54573	0.553750	0.276875	−	0.960906i	$-0.410701\pi$
$41$	3.54573	0.553750	0.276875	+	0.960906i	$0.410701\pi$
$42$	2.62981i	0.405789i
$43$	− 3.86433i	− 0.589304i	−0.955605	−	0.294652i	$-0.904796\pi$
$43$	− 3.86433i	− 0.589304i	0.955605	−	0.294652i	$-0.0952038\pi$
$44$	−1.54573	−0.233028
$45$	0	0
$46$	3.40268	0.501698
$47$	− 8.00000i	− 1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$	− 8.00000i	− 1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	3.40268i	0.491134i
$49$	6.40268	0.914668
$50$	0	0
$51$	4.17554	0.584693
$52$	3.85695i	0.534862i
$53$	0.318597i	0.0437626i	0.999761	+	0.0218813i	$0.00696559\pi$
$53$	0.318597i	0.0437626i	−0.999761	+	0.0218813i	$0.993034\pi$
$54$	18.9809	2.58297
$55$	0	0
$56$	−0.772866	−0.103279
$57$	− 23.1564i	− 3.06715i
$58$	− 1.00000i	− 0.131306i
$59$	−8.66231	−1.12774	−0.563868	−	0.825865i	$-0.690687\pi$
$59$	−8.66231	−1.12774	−0.563868	+	0.825865i	$0.690687\pi$
$60$	0	0
$61$	−1.40268	−0.179595	−0.0897973	−	0.995960i	$-0.528622\pi$
$61$	−1.40268	−0.179595	−0.0897973	+	0.995960i	$0.528622\pi$
$62$	− 9.12395i	− 1.15874i
$63$	6.62981i	0.835278i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.25963	−0.647415
$67$	13.6107i	1.66281i	0.555664	+	0.831407i	$0.312464\pi$
$67$	13.6107i	1.66281i	−0.555664	+	0.831407i	$0.687536\pi$
$68$	1.22713i	0.148812i
$69$	11.5782	1.39385
$70$	0	0
$71$	−13.6107	−1.61529	−0.807647	−	0.589666i	$-0.799259\pi$
$71$	−13.6107	−1.61529	−0.807647	+	0.589666i	$0.799259\pi$
$72$	8.57822i	1.01095i
$73$	9.92931i	1.16214i	0.813854	+	0.581069i	$0.197365\pi$
$73$	9.92931i	1.16214i	−0.813854	+	0.581069i	$0.802635\pi$
$74$	0.454269	0.0528077
$75$	0	0
$76$	6.80536	0.780628
$77$	− 1.19464i	− 0.136142i
$78$	13.1240i	1.48600i
$79$	−14.8452	−1.67022	−0.835109	−	0.550084i	$-0.814596\pi$
$79$	−14.8452	−1.67022	−0.835109	+	0.550084i	$0.814596\pi$
$80$	0	0
$81$	38.8512	4.31680
$82$	3.54573i	0.391560i
$83$	14.8054i	1.62510i	0.582892	+	0.812550i	$0.301921\pi$
$83$	14.8054i	1.62510i	−0.582892	+	0.812550i	$0.698079\pi$
$84$	−2.62981	−0.286936
$85$	0	0
$86$	3.86433	0.416701
$87$	− 3.40268i	− 0.364805i
$88$	− 1.54573i	− 0.164775i
$89$	1.71390	0.181673	0.0908363	−	0.995866i	$-0.471046\pi$
$89$	1.71390	0.181673	0.0908363	+	0.995866i	$0.471046\pi$
$90$	0	0
$91$	−2.98090	−0.312483
$92$	3.40268i	0.354754i
$93$	− 31.0459i	− 3.21931i
$94$	8.00000	0.825137
$95$	0	0
$96$	−3.40268	−0.347284
$97$	10.9484i	1.11164i	0.831302	+	0.555821i	$0.187596\pi$
$97$	10.9484i	1.11164i	−0.831302	+	0.555821i	$0.812404\pi$
$98$	6.40268i	0.646768i
$99$	−13.2596	−1.33264
$100$	0	0
$101$	−11.2995	−1.12434	−0.562171	−	0.827021i	$-0.690034\pi$
$101$	−11.2995	−1.12434	−0.562171	+	0.827021i	$0.690034\pi$
$102$	4.17554i	0.413441i
$103$	− 14.5193i	− 1.43062i	−0.698805	−	0.715312i	$-0.746284\pi$
$103$	− 14.5193i	− 1.43062i	0.698805	−	0.715312i	$-0.253716\pi$
$104$	−3.85695	−0.378205
$105$	0	0
$106$	−0.318597	−0.0309448
$107$	12.4161i	1.20031i	0.799885	+	0.600154i	$0.204894\pi$
$107$	12.4161i	1.20031i	−0.799885	+	0.600154i	$0.795106\pi$
$108$	18.9809i	1.82644i
$109$	−1.36281	−0.130533	−0.0652666	−	0.997868i	$-0.520790\pi$
$109$	−1.36281	−0.130533	−0.0652666	+	0.997868i	$0.520790\pi$
$110$	0	0
$111$	1.54573	0.146714
$112$	− 0.772866i	− 0.0730289i
$113$	2.66231i	0.250449i	0.992128	+	0.125224i	$0.0399651\pi$
$113$	2.66231i	0.250449i	−0.992128	+	0.125224i	$0.960035\pi$
$114$	23.1564	2.16880
$115$	0	0
$116$	1.00000	0.0928477
$117$	33.0858i	3.05878i
$118$	− 8.66231i	− 0.797430i
$119$	−0.948410	−0.0869406
$120$	0	0
$121$	−8.61072	−0.782792
$122$	− 1.40268i	− 0.126993i
$123$	12.0650i	1.08786i
$124$	9.12395	0.819355
$125$	0	0
$126$	−6.62981	−0.590631
$127$	− 13.6107i	− 1.20776i	−0.797077	−	0.603878i	$-0.793621\pi$
$127$	− 13.6107i	− 1.20776i	0.797077	−	0.603878i	$-0.206379\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	13.1491	1.15771
$130$	0	0
$131$	−13.9618	−1.21985	−0.609924	−	0.792460i	$-0.708800\pi$
$131$	−13.9618	−1.21985	−0.609924	+	0.792460i	$0.708800\pi$
$132$	− 5.25963i	− 0.457792i
$133$	5.25963i	0.456067i
$134$	−13.6107	−1.17579
$135$	0	0
$136$	−1.22713	−0.105226
$137$	− 13.7538i	− 1.17506i	−0.809201	−	0.587532i	$-0.800100\pi$
$137$	− 13.7538i	− 1.17506i	0.809201	−	0.587532i	$-0.199900\pi$
$138$	11.5782i	0.985604i
$139$	18.0975	1.53501	0.767504	−	0.641044i	$-0.221498\pi$
$139$	18.0975	1.53501	0.767504	+	0.641044i	$0.221498\pi$
$140$	0	0
$141$	27.2214	2.29246
$142$	− 13.6107i	− 1.14219i
$143$	− 5.96180i	− 0.498551i
$144$	−8.57822	−0.714852
$145$	0	0
$146$	−9.92931	−0.821756
$147$	21.7863i	1.79690i
$148$	0.454269i	0.0373407i
$149$	6.41607	0.525625	0.262813	−	0.964847i	$-0.415350\pi$
$149$	6.41607	0.525625	0.262813	+	0.964847i	$0.415350\pi$
$150$	0	0
$151$	4.28610	0.348798	0.174399	−	0.984675i	$-0.444202\pi$
$151$	4.28610	0.348798	0.174399	+	0.984675i	$0.444202\pi$
$152$	6.80536i	0.551987i
$153$	10.5266i	0.851028i
$154$	1.19464	0.0962670
$155$	0	0
$156$	−13.1240	−1.05076
$157$	10.9085i	0.870596i	0.900286	+	0.435298i	$0.143357\pi$
$157$	10.9085i	0.870596i	−0.900286	+	0.435298i	$0.856643\pi$
$158$	− 14.8452i	− 1.18102i
$159$	−1.08408	−0.0859733
$160$	0	0
$161$	−2.62981	−0.207258
$162$	38.8512i	3.05244i
$163$	− 11.4278i	− 0.895094i	−0.894260	−	0.447547i	$-0.852298\pi$
$163$	− 11.4278i	− 0.895094i	0.894260	−	0.447547i	$-0.147702\pi$
$164$	−3.54573	−0.276875
$165$	0	0
$166$	−14.8054	−1.14912
$167$	− 8.77287i	− 0.678865i	−0.940630	−	0.339432i	$-0.889765\pi$
$167$	− 8.77287i	− 0.678865i	0.940630	−	0.339432i	$-0.110235\pi$
$168$	− 2.62981i	− 0.202894i
$169$	−1.87605	−0.144311
$170$	0	0
$171$	58.3779	4.46427
$172$	3.86433i	0.294652i
$173$	4.76549i	0.362313i	0.983454	+	0.181157i	$0.0579841\pi$
$173$	4.76549i	0.362313i	−0.983454	+	0.181157i	$0.942016\pi$
$174$	3.40268	0.257956
$175$	0	0
$176$	1.54573	0.116514
$177$	− 29.4750i	− 2.21548i
$178$	1.71390i	0.128462i
$179$	6.84523	0.511636	0.255818	−	0.966725i	$-0.417655\pi$
$179$	6.84523	0.511636	0.255818	+	0.966725i	$0.417655\pi$
$180$	0	0
$181$	19.3394	1.43748	0.718742	−	0.695277i	$-0.244718\pi$
$181$	19.3394	1.43748	0.718742	+	0.695277i	$0.244718\pi$
$182$	− 2.98090i	− 0.220959i
$183$	− 4.77287i	− 0.352820i
$184$	−3.40268	−0.250849
$185$	0	0
$186$	31.0459	2.27639
$187$	− 1.89682i	− 0.138709i
$188$	8.00000i	0.583460i
$189$	−14.6697	−1.06706
$190$	0	0
$191$	−5.05897	−0.366054	−0.183027	−	0.983108i	$-0.558590\pi$
$191$	−5.05897	−0.366054	−0.183027	+	0.983108i	$0.558590\pi$
$192$	− 3.40268i	− 0.245567i
$193$	14.3762i	1.03482i	0.855737	+	0.517411i	$0.173104\pi$
$193$	14.3762i	1.03482i	−0.855737	+	0.517411i	$0.826896\pi$
$194$	−10.9484	−0.786050
$195$	0	0
$196$	−6.40268	−0.457334
$197$	− 27.5400i	− 1.96215i	−0.193639	−	0.981073i	$-0.562029\pi$
$197$	− 27.5400i	− 1.96215i	0.193639	−	0.981073i	$-0.437971\pi$
$198$	− 13.2596i	− 0.942321i
$199$	6.45427	0.457531	0.228765	−	0.973482i	$-0.426531\pi$
$199$	6.45427	0.457531	0.228765	+	0.973482i	$0.426531\pi$
$200$	0	0
$201$	−46.3129	−3.26666
$202$	− 11.2995i	− 0.795030i
$203$	0.772866i	0.0542445i
$204$	−4.17554	−0.292347
$205$	0	0
$206$	14.5193	1.01160
$207$	29.1889i	2.02877i
$208$	− 3.85695i	− 0.267431i
$209$	−10.5193	−0.727632
$210$	0	0
$211$	−1.54573	−0.106413	−0.0532063	−	0.998584i	$-0.516944\pi$
$211$	−1.54573	−0.106413	−0.0532063	+	0.998584i	$0.516944\pi$
$212$	− 0.318597i	− 0.0218813i
$213$	− 46.3129i	− 3.17331i
$214$	−12.4161	−0.848745
$215$	0	0
$216$	−18.9809	−1.29149
$217$	7.05159i	0.478693i
$218$	− 1.36281i	− 0.0923009i
$219$	−33.7863	−2.28306
$220$	0	0
$221$	−4.73299	−0.318376
$222$	1.54573i	0.103743i
$223$	− 9.01339i	− 0.603582i	−0.953374	−	0.301791i	$-0.902416\pi$
$223$	− 9.01339i	− 0.603582i	0.953374	−	0.301791i	$-0.0975844\pi$
$224$	0.772866	0.0516393
$225$	0	0
$226$	−2.66231	−0.177094
$227$	− 7.07670i	− 0.469697i	−0.972032	−	0.234849i	$-0.924541\pi$
$227$	− 7.07670i	− 0.469697i	0.972032	−	0.234849i	$-0.0754594\pi$
$228$	23.1564i	1.53357i
$229$	−4.94103	−0.326512	−0.163256	−	0.986584i	$-0.552200\pi$
$229$	−4.94103	−0.326512	−0.163256	+	0.986584i	$0.552200\pi$
$230$	0	0
$231$	4.06498	0.267456
$232$	1.00000i	0.0656532i
$233$	− 4.51925i	− 0.296066i	−0.988982	−	0.148033i	$-0.952706\pi$
$233$	− 4.51925i	− 0.296066i	0.988982	−	0.148033i	$-0.0472942\pi$
$234$	−33.0858	−2.16288
$235$	0	0
$236$	8.66231	0.563868
$237$	− 50.5135i	− 3.28121i
$238$	− 0.948410i	− 0.0614763i
$239$	−13.2596	−0.857694	−0.428847	−	0.903377i	$-0.641080\pi$
$239$	−13.2596	−0.857694	−0.428847	+	0.903377i	$0.641080\pi$
$240$	0	0
$241$	−18.3910	−1.18467	−0.592333	−	0.805693i	$-0.701793\pi$
$241$	−18.3910	−1.18467	−0.592333	+	0.805693i	$0.701793\pi$
$242$	− 8.61072i	− 0.553518i
$243$	75.2556i	4.82765i
$244$	1.40268	0.0897973
$245$	0	0
$246$	−12.0650	−0.769235
$247$	26.2479i	1.67011i
$248$	9.12395i	0.579372i
$249$	−50.3779	−3.19257
$250$	0	0
$251$	−6.10318	−0.385229	−0.192615	−	0.981274i	$-0.561697\pi$
$251$	−6.10318	−0.385229	−0.192615	+	0.981274i	$0.561697\pi$
$252$	− 6.62981i	− 0.417639i
$253$	− 5.25963i	− 0.330670i
$254$	13.6107	0.854012
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 4.45427i	− 0.277850i	−0.990303	−	0.138925i	$-0.955635\pi$
$257$	− 4.45427i	− 0.277850i	0.990303	−	0.138925i	$-0.0443646\pi$
$258$	13.1491i	0.818625i
$259$	−0.351089	−0.0218156
$260$	0	0
$261$	8.57822	0.530979
$262$	− 13.9618i	− 0.862563i
$263$	16.0000i	0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$	16.0000i	0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$	5.25963	0.323708
$265$	0	0
$266$	−5.25963	−0.322488
$267$	5.83184i	0.356903i
$268$	− 13.6107i	− 0.831407i
$269$	−3.12395	−0.190471	−0.0952354	−	0.995455i	$-0.530360\pi$
$269$	−3.12395	−0.190471	−0.0952354	+	0.995455i	$0.530360\pi$
$270$	0	0
$271$	−9.61072	−0.583809	−0.291905	−	0.956447i	$-0.594289\pi$
$271$	−9.61072	−0.583809	−0.291905	+	0.956447i	$0.594289\pi$
$272$	− 1.22713i	− 0.0744060i
$273$	− 10.1431i	− 0.613885i
$274$	13.7538	0.830895
$275$	0	0
$276$	−11.5782	−0.696927
$277$	− 10.7022i	− 0.643032i	−0.946904	−	0.321516i	$-0.895808\pi$
$277$	− 10.7022i	− 0.643032i	0.946904	−	0.321516i	$-0.104192\pi$
$278$	18.0975i	1.08541i
$279$	78.2673	4.68574
$280$	0	0
$281$	9.64321	0.575266	0.287633	−	0.957741i	$-0.407132\pi$
$281$	9.64321	0.575266	0.287633	+	0.957741i	$0.407132\pi$
$282$	27.2214i	1.62101i
$283$	− 29.1183i	− 1.73090i	−0.500995	−	0.865450i	$-0.667033\pi$
$283$	− 29.1183i	− 1.73090i	0.500995	−	0.865450i	$-0.332967\pi$
$284$	13.6107	0.807647
$285$	0	0
$286$	5.96180	0.352529
$287$	− 2.74037i	− 0.161759i
$288$	− 8.57822i	− 0.505477i
$289$	15.4941	0.911420
$290$	0	0
$291$	−37.2539	−2.18386
$292$	− 9.92931i	− 0.581069i
$293$	− 20.5842i	− 1.20254i	−0.799044	−	0.601272i	$-0.794661\pi$
$293$	− 20.5842i	− 1.20254i	0.799044	−	0.601272i	$-0.205339\pi$
$294$	−21.7863	−1.27060
$295$	0	0
$296$	−0.454269	−0.0264038
$297$	− 29.3394i	− 1.70244i
$298$	6.41607i	0.371673i
$299$	−13.1240	−0.758978
$300$	0	0
$301$	−2.98661	−0.172145
$302$	4.28610i	0.246638i
$303$	− 38.4486i	− 2.20881i
$304$	−6.80536	−0.390314
$305$	0	0
$306$	−10.5266	−0.601768
$307$	7.09146i	0.404731i	0.979310	+	0.202366i	$0.0648629\pi$
$307$	7.09146i	0.404731i	−0.979310	+	0.202366i	$0.935137\pi$
$308$	1.19464i	0.0680711i
$309$	49.4044	2.81052
$310$	0	0
$311$	−6.14305	−0.348341	−0.174170	−	0.984716i	$-0.555724\pi$
$311$	−6.14305	−0.348341	−0.174170	+	0.984716i	$0.555724\pi$
$312$	− 13.1240i	− 0.742998i
$313$	− 13.0915i	− 0.739973i	−0.929037	−	0.369987i	$-0.879362\pi$
$313$	− 13.0915i	− 0.739973i	0.929037	−	0.369987i	$-0.120638\pi$
$314$	−10.9085	−0.615604
$315$	0	0
$316$	14.8452	0.835109
$317$	− 3.19464i	− 0.179429i	−0.995968	−	0.0897145i	$-0.971405\pi$
$317$	− 3.19464i	− 0.179429i	0.995968	−	0.0897145i	$-0.0285955\pi$
$318$	− 1.08408i	− 0.0607923i
$319$	−1.54573	−0.0865443
$320$	0	0
$321$	−42.2479	−2.35805
$322$	− 2.62981i	− 0.146554i
$323$	8.35109i	0.464667i
$324$	−38.8512	−2.15840
$325$	0	0
$326$	11.4278	0.632927
$327$	− 4.63719i	− 0.256437i
$328$	− 3.54573i	− 0.195780i
$329$	−6.18292	−0.340876
$330$	0	0
$331$	6.45427	0.354759	0.177379	−	0.984143i	$-0.443238\pi$
$331$	6.45427	0.354759	0.177379	+	0.984143i	$0.443238\pi$
$332$	− 14.8054i	− 0.812550i
$333$	3.89682i	0.213544i
$334$	8.77287	0.480030
$335$	0	0
$336$	2.62981	0.143468
$337$	14.5015i	0.789948i	0.918692	+	0.394974i	$0.129246\pi$
$337$	14.5015i	0.789948i	−0.918692	+	0.394974i	$0.870754\pi$
$338$	− 1.87605i	− 0.102043i
$339$	−9.05897	−0.492016
$340$	0	0
$341$	−14.1032	−0.763730
$342$	58.3779i	3.15671i
$343$	− 10.3585i	− 0.559305i
$344$	−3.86433	−0.208351
$345$	0	0
$346$	−4.76549	−0.256194
$347$	19.7139i	1.05830i	0.848529	+	0.529149i	$0.177489\pi$
$347$	19.7139i	1.05830i	−0.848529	+	0.529149i	$0.822511\pi$
$348$	3.40268i	0.182403i
$349$	9.64891	0.516494	0.258247	−	0.966079i	$-0.416855\pi$
$349$	9.64891	0.516494	0.258247	+	0.966079i	$0.416855\pi$
$350$	0	0
$351$	−73.2083	−3.90757
$352$	1.54573i	0.0823877i
$353$	− 23.9618i	− 1.27536i	−0.770302	−	0.637679i	$-0.779895\pi$
$353$	− 23.9618i	− 1.27536i	0.770302	−	0.637679i	$-0.220105\pi$
$354$	29.4750	1.56658
$355$	0	0
$356$	−1.71390	−0.0908363
$357$	− 3.22713i	− 0.170798i
$358$	6.84523i	0.361782i
$359$	14.1431	0.746442	0.373221	−	0.927743i	$-0.378253\pi$
$359$	14.1431	0.746442	0.373221	+	0.927743i	$0.378253\pi$
$360$	0	0
$361$	27.3129	1.43752
$362$	19.3394i	1.01645i
$363$	− 29.2995i	− 1.53782i
$364$	2.98090	0.156242
$365$	0	0
$366$	4.77287	0.249482
$367$	35.8439i	1.87103i	0.353281	+	0.935517i	$0.385066\pi$
$367$	35.8439i	1.87103i	−0.353281	+	0.935517i	$0.614934\pi$
$368$	− 3.40268i	− 0.177377i
$369$	−30.4161	−1.58340
$370$	0	0
$371$	0.246232	0.0127837
$372$	31.0459i	1.60965i
$373$	10.8378i	0.561163i	0.959830	+	0.280581i	$0.0905272\pi$
$373$	10.8378i	0.561163i	−0.959830	+	0.280581i	$0.909473\pi$
$374$	1.89682	0.0980822
$375$	0	0
$376$	−8.00000	−0.412568
$377$	3.85695i	0.198643i
$378$	− 14.6697i	− 0.754527i
$379$	10.2479	0.526400	0.263200	−	0.964741i	$-0.415222\pi$
$379$	10.2479	0.526400	0.263200	+	0.964741i	$0.415222\pi$
$380$	0	0
$381$	46.3129	2.37268
$382$	− 5.05897i	− 0.258839i
$383$	25.4750i	1.30171i	0.759200	+	0.650857i	$0.225590\pi$
$383$	25.4750i	1.30171i	−0.759200	+	0.650857i	$0.774410\pi$
$384$	3.40268	0.173642
$385$	0	0
$386$	−14.3762	−0.731729
$387$	33.1491i	1.68506i
$388$	− 10.9484i	− 0.555821i
$389$	5.22143	0.264737	0.132369	−	0.991201i	$-0.457742\pi$
$389$	5.22143	0.264737	0.132369	+	0.991201i	$0.457742\pi$
$390$	0	0
$391$	−4.17554	−0.211166
$392$	− 6.40268i	− 0.323384i
$393$	− 47.5075i	− 2.39644i
$394$	27.5400	1.38745
$395$	0	0
$396$	13.2596	0.666321
$397$	− 1.16215i	− 0.0583266i	−0.999575	−	0.0291633i	$-0.990716\pi$
$397$	− 1.16215i	− 0.0583266i	0.999575	−	0.0291633i	$-0.00928429\pi$
$398$	6.45427i	0.323523i
$399$	−17.8968	−0.895962
$400$	0	0
$401$	−17.6888	−0.883336	−0.441668	−	0.897179i	$-0.645613\pi$
$401$	−17.6888	−0.883336	−0.441668	+	0.897179i	$0.645613\pi$
$402$	− 46.3129i	− 2.30988i
$403$	35.1906i	1.75297i
$404$	11.2995	0.562171
$405$	0	0
$406$	−0.772866	−0.0383567
$407$	− 0.702178i	− 0.0348056i
$408$	− 4.17554i	− 0.206720i
$409$	−3.05327	−0.150974	−0.0754872	−	0.997147i	$-0.524051\pi$
$409$	−3.05327	−0.150974	−0.0754872	+	0.997147i	$0.524051\pi$
$410$	0	0
$411$	46.7997	2.30846
$412$	14.5193i	0.715312i
$413$	6.69480i	0.329429i
$414$	−29.1889	−1.43456
$415$	0	0
$416$	3.85695	0.189102
$417$	61.5799i	3.01558i
$418$	− 10.5193i	− 0.514513i
$419$	−14.8760	−0.726742	−0.363371	−	0.931644i	$-0.618374\pi$
$419$	−14.8760	−0.726742	−0.363371	+	0.931644i	$0.618374\pi$
$420$	0	0
$421$	−8.31289	−0.405146	−0.202573	−	0.979267i	$-0.564930\pi$
$421$	−8.31289	−0.405146	−0.202573	+	0.979267i	$0.564930\pi$
$422$	− 1.54573i	− 0.0752450i
$423$	68.6258i	3.33670i
$424$	0.318597	0.0154724
$425$	0	0
$426$	46.3129	2.24387
$427$	1.08408i	0.0524624i
$428$	− 12.4161i	− 0.600154i
$429$	20.2861	0.979422
$430$	0	0
$431$	−1.19464	−0.0575439	−0.0287719	−	0.999586i	$-0.509160\pi$
$431$	−1.19464	−0.0575439	−0.0287719	+	0.999586i	$0.509160\pi$
$432$	− 18.9809i	− 0.913219i
$433$	− 10.1300i	− 0.486815i	−0.969924	−	0.243408i	$-0.921735\pi$
$433$	− 10.1300i	− 0.486815i	0.969924	−	0.243408i	$-0.0782653\pi$
$434$	−7.05159	−0.338487
$435$	0	0
$436$	1.36281	0.0652666
$437$	23.1564i	1.10772i
$438$	− 33.7863i	− 1.61437i
$439$	−15.6489	−0.746882	−0.373441	−	0.927654i	$-0.621822\pi$
$439$	−15.6489	−0.746882	−0.373441	+	0.927654i	$0.621822\pi$
$440$	0	0
$441$	−54.9236	−2.61541
$442$	− 4.73299i	− 0.225126i
$443$	12.0251i	0.571330i	0.958329	+	0.285665i	$0.0922145\pi$
$443$	12.0251i	0.571330i	−0.958329	+	0.285665i	$0.907785\pi$
$444$	−1.54573	−0.0733572
$445$	0	0
$446$	9.01339	0.426797
$447$	21.8318i	1.03261i
$448$	0.772866i	0.0365145i
$449$	−28.2479	−1.33310	−0.666551	−	0.745460i	$-0.732230\pi$
$449$	−28.2479	−1.33310	−0.666551	+	0.745460i	$0.732230\pi$
$450$	0	0
$451$	5.48075	0.258078
$452$	− 2.66231i	− 0.125224i
$453$	14.5842i	0.685227i
$454$	7.07670	0.332126
$455$	0	0
$456$	−23.1564	−1.08440
$457$	3.27439i	0.153169i	0.997063	+	0.0765847i	$0.0244016\pi$
$457$	3.27439i	0.153169i	−0.997063	+	0.0765847i	$0.975598\pi$
$458$	− 4.94103i	− 0.230879i
$459$	−23.2921	−1.08718
$460$	0	0
$461$	−16.6697	−0.776385	−0.388192	−	0.921578i	$-0.626900\pi$
$461$	−16.6697	−0.776385	−0.388192	+	0.921578i	$0.626900\pi$
$462$	4.06498i	0.189120i
$463$	12.0000i	0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$	12.0000i	0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	4.51925	0.209350
$467$	− 28.8378i	− 1.33446i	−0.744853	−	0.667228i	$-0.767481\pi$
$467$	− 28.8378i	− 1.33446i	0.744853	−	0.667228i	$-0.232519\pi$
$468$	− 33.0858i	− 1.52939i
$469$	10.5193	0.485734
$470$	0	0
$471$	−37.1183	−1.71032
$472$	8.66231i	0.398715i
$473$	− 5.97321i	− 0.274649i
$474$	50.5135	2.32016
$475$	0	0
$476$	0.948410	0.0434703
$477$	− 2.73299i	− 0.125135i
$478$	− 13.2596i	− 0.606481i
$479$	−18.3688	−0.839293	−0.419646	−	0.907688i	$-0.637846\pi$
$479$	−18.3688	−0.839293	−0.419646	+	0.907688i	$0.637846\pi$
$480$	0	0
$481$	−1.75209	−0.0798885
$482$	− 18.3910i	− 0.837685i
$483$	− 8.94841i	− 0.407167i
$484$	8.61072	0.391396
$485$	0	0
$486$	−75.2556	−3.41366
$487$	− 28.2348i	− 1.27944i	−0.768607	−	0.639721i	$-0.779050\pi$
$487$	− 28.2348i	− 1.27944i	0.768607	−	0.639721i	$-0.220950\pi$
$488$	1.40268i	0.0634963i
$489$	38.8851	1.75845
$490$	0	0
$491$	16.0000	0.722070	0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000	0.722070	0.361035	+	0.932552i	$0.382424\pi$
$492$	− 12.0650i	− 0.543931i
$493$	1.22713i	0.0552674i
$494$	−26.2479	−1.18095
$495$	0	0
$496$	−9.12395	−0.409678
$497$	10.5193i	0.471853i
$498$	− 50.3779i	− 2.25749i
$499$	24.0901	1.07842	0.539210	−	0.842171i	$-0.318723\pi$
$499$	24.0901	1.07842	0.539210	+	0.842171i	$0.318723\pi$
$500$	0	0
$501$	29.8512	1.33366
$502$	− 6.10318i	− 0.272398i
$503$	− 8.70218i	− 0.388011i	−0.981000	−	0.194005i	$-0.937852\pi$
$503$	− 8.70218i	− 0.388011i	0.981000	−	0.194005i	$-0.0621480\pi$
$504$	6.62981	0.295315
$505$	0	0
$506$	5.25963	0.233819
$507$	− 6.38358i	− 0.283505i
$508$	13.6107i	0.603878i
$509$	−23.5457	−1.04365	−0.521823	−	0.853054i	$-0.674748\pi$
$509$	−23.5457	−1.04365	−0.521823	+	0.853054i	$0.674748\pi$
$510$	0	0
$511$	7.67402	0.339479
$512$	1.00000i	0.0441942i
$513$	129.172i	5.70308i
$514$	4.45427	0.196469
$515$	0	0
$516$	−13.1491	−0.578855
$517$	− 12.3658i	− 0.543849i
$518$	− 0.351089i	− 0.0154260i
$519$	−16.2154	−0.711778
$520$	0	0
$521$	−22.6167	−0.990857	−0.495428	−	0.868649i	$-0.664989\pi$
$521$	−22.6167	−0.990857	−0.495428	+	0.868649i	$0.664989\pi$
$522$	8.57822i	0.375459i
$523$	− 6.80536i	− 0.297578i	−0.988869	−	0.148789i	$-0.952463\pi$
$523$	− 6.80536i	− 0.297578i	0.988869	−	0.148789i	$-0.0475374\pi$
$524$	13.9618	0.609924
$525$	0	0
$526$	−16.0000	−0.697633
$527$	11.1963i	0.487719i
$528$	5.25963i	0.228896i
$529$	11.4218	0.496599
$530$	0	0
$531$	74.3072	3.22466
$532$	− 5.25963i	− 0.228034i
$533$	− 13.6757i	− 0.592360i
$534$	−5.83184	−0.252368
$535$	0	0
$536$	13.6107	0.587893
$537$	23.2921i	1.00513i
$538$	− 3.12395i	− 0.134683i
$539$	9.89682	0.426286
$540$	0	0
$541$	10.5517	0.453655	0.226827	−	0.973935i	$-0.427165\pi$
$541$	10.5517	0.453655	0.226827	+	0.973935i	$0.427165\pi$
$542$	− 9.61072i	− 0.412816i
$543$	65.8057i	2.82399i
$544$	1.22713	0.0526130
$545$	0	0
$546$	10.1431	0.434083
$547$	16.6224i	0.710724i	0.934729	+	0.355362i	$0.115642\pi$
$547$	16.6224i	0.710724i	−0.934729	+	0.355362i	$0.884358\pi$
$548$	13.7538i	0.587532i
$549$	12.0325	0.513534
$550$	0	0
$551$	6.80536	0.289918
$552$	− 11.5782i	− 0.492802i
$553$	11.4734i	0.487897i
$554$	10.7022	0.454692
$555$	0	0
$556$	−18.0975	−0.767504
$557$	2.66231i	0.112805i	0.998408	+	0.0564027i	$0.0179631\pi$
$557$	2.66231i	0.112805i	−0.998408	+	0.0564027i	$0.982037\pi$
$558$	78.2673i	3.31332i
$559$	−14.9045	−0.630394
$560$	0	0
$561$	6.45427	0.272499
$562$	9.64321i	0.406774i
$563$	− 12.0251i	− 0.506798i	−0.967362	−	0.253399i	$-0.918451\pi$
$563$	− 12.0251i	− 0.506798i	0.967362	−	0.253399i	$-0.0815486\pi$
$564$	−27.2214	−1.14623
$565$	0	0
$566$	29.1183	1.22393
$567$	− 30.0268i	− 1.26101i
$568$	13.6107i	0.571093i
$569$	6.92330	0.290240	0.145120	−	0.989414i	$-0.453643\pi$
$569$	6.92330	0.290240	0.145120	+	0.989414i	$0.453643\pi$
$570$	0	0
$571$	25.9869	1.08752	0.543759	−	0.839241i	$-0.317000\pi$
$571$	25.9869	1.08752	0.543759	+	0.839241i	$0.317000\pi$
$572$	5.96180i	0.249276i
$573$	− 17.2141i	− 0.719127i
$574$	2.74037	0.114381
$575$	0	0
$576$	8.57822	0.357426
$577$	16.1772i	0.673467i	0.941600	+	0.336733i	$0.109322\pi$
$577$	16.1772i	0.673467i	−0.941600	+	0.336733i	$0.890678\pi$
$578$	15.4941i	0.644471i
$579$	−48.9176	−2.03295
$580$	0	0
$581$	11.4426	0.474717
$582$	− 37.2539i	− 1.54422i
$583$	0.492465i	0.0203958i
$584$	9.92931	0.410878
$585$	0	0
$586$	20.5842	0.850327
$587$	41.0533i	1.69445i	0.531235	+	0.847225i	$0.321728\pi$
$587$	41.0533i	1.69445i	−0.531235	+	0.847225i	$0.678272\pi$
$588$	− 21.7863i	− 0.898450i
$589$	62.0918	2.55845
$590$	0	0
$591$	93.7099	3.85471
$592$	− 0.454269i	− 0.0186703i
$593$	− 8.23315i	− 0.338095i	−0.985608	−	0.169047i	$-0.945931\pi$
$593$	− 8.23315i	− 0.338095i	0.985608	−	0.169047i	$-0.0540691\pi$
$594$	29.3394	1.20381
$595$	0	0
$596$	−6.41607	−0.262813
$597$	21.9618i	0.898837i
$598$	− 13.1240i	− 0.536678i
$599$	−24.9826	−1.02076	−0.510380	−	0.859949i	$-0.670495\pi$
$599$	−24.9826	−1.02076	−0.510380	+	0.859949i	$0.670495\pi$
$600$	0	0
$601$	14.9883	0.611385	0.305692	−	0.952130i	$-0.401112\pi$
$601$	14.9883	0.611385	0.305692	+	0.952130i	$0.401112\pi$
$602$	− 2.98661i	− 0.121725i
$603$	− 116.756i	− 4.75466i
$604$	−4.28610	−0.174399
$605$	0	0
$606$	38.4486	1.56187
$607$	− 8.00000i	− 0.324710i	−0.986732	−	0.162355i	$-0.948091\pi$
$607$	− 8.00000i	− 0.324710i	0.986732	−	0.162355i	$-0.0519090\pi$
$608$	− 6.80536i	− 0.275994i
$609$	−2.62981	−0.106565
$610$	0	0
$611$	−30.8556	−1.24828
$612$	− 10.5266i	− 0.425514i
$613$	23.2037i	0.937189i	0.883413	+	0.468594i	$0.155239\pi$
$613$	23.2037i	0.937189i	−0.883413	+	0.468594i	$0.844761\pi$
$614$	−7.09146	−0.286188
$615$	0	0
$616$	−1.19464	−0.0481335
$617$	29.9293i	1.20491i	0.798153	+	0.602454i	$0.205810\pi$
$617$	29.9293i	1.20491i	−0.798153	+	0.602454i	$0.794190\pi$
$618$	49.4044i	1.98733i
$619$	−18.2981	−0.735464	−0.367732	−	0.929932i	$-0.619866\pi$
$619$	−18.2981	−0.735464	−0.367732	+	0.929932i	$0.619866\pi$
$620$	0	0
$621$	−64.5859	−2.59174
$622$	− 6.14305i	− 0.246314i
$623$	− 1.32461i	− 0.0530694i
$624$	13.1240	0.525379
$625$	0	0
$626$	13.0915	0.523240
$627$	− 35.7936i	− 1.42946i
$628$	− 10.9085i	− 0.435298i
$629$	−0.557449	−0.0222269
$630$	0	0
$631$	−25.0533	−0.997355	−0.498677	−	0.866788i	$-0.666181\pi$
$631$	−25.0533	−0.997355	−0.498677	+	0.866788i	$0.666181\pi$
$632$	14.8452i	0.590512i
$633$	− 5.25963i	− 0.209051i
$634$	3.19464	0.126875
$635$	0	0
$636$	1.08408	0.0429867
$637$	− 24.6948i	− 0.978444i
$638$	− 1.54573i	− 0.0611961i
$639$	116.756	4.61879
$640$	0	0
$641$	−15.6757	−0.619153	−0.309576	−	0.950875i	$-0.600187\pi$
$641$	−15.6757	−0.619153	−0.309576	+	0.950875i	$0.600187\pi$
$642$	− 42.2479i	− 1.66739i
$643$	47.1564i	1.85967i	0.367978	+	0.929834i	$0.380050\pi$
$643$	47.1564i	1.85967i	−0.367978	+	0.929834i	$0.619950\pi$
$644$	2.62981	0.103629
$645$	0	0
$646$	−8.35109	−0.328569
$647$	− 20.1300i	− 0.791391i	−0.918382	−	0.395695i	$-0.870504\pi$
$647$	− 20.1300i	− 0.791391i	0.918382	−	0.395695i	$-0.129496\pi$
$648$	− 38.8512i	− 1.52622i
$649$	−13.3896	−0.525588
$650$	0	0
$651$	−23.9943	−0.940411
$652$	11.4278i	0.447547i
$653$	− 25.1712i	− 0.985025i	−0.870305	−	0.492513i	$-0.836079\pi$
$653$	− 25.1712i	− 0.985025i	0.870305	−	0.492513i	$-0.163921\pi$
$654$	4.63719	0.181329
$655$	0	0
$656$	3.54573	0.138438
$657$	− 85.1759i	− 3.32303i
$658$	− 6.18292i	− 0.241035i
$659$	−33.5457	−1.30676	−0.653378	−	0.757032i	$-0.726649\pi$
$659$	−33.5457	−1.30676	−0.653378	+	0.757032i	$0.726649\pi$
$660$	0	0
$661$	−19.3246	−0.751640	−0.375820	−	0.926693i	$-0.622639\pi$
$661$	−19.3246	−0.751640	−0.375820	+	0.926693i	$0.622639\pi$
$662$	6.45427i	0.250852i
$663$	− 16.1049i	− 0.625461i
$664$	14.8054	0.574559
$665$	0	0
$666$	−3.89682	−0.150999
$667$	3.40268i	0.131752i
$668$	8.77287i	0.339432i
$669$	30.6697	1.18576
$670$	0	0
$671$	−2.16816	−0.0837011
$672$	2.62981i	0.101447i
$673$	1.36281i	0.0525323i	0.999655	+	0.0262662i	$0.00836174\pi$
$673$	1.36281i	0.0525323i	−0.999655	+	0.0262662i	$0.991638\pi$
$674$	−14.5015	−0.558578
$675$	0	0
$676$	1.87605	0.0721556
$677$	24.1682i	0.928858i	0.885610	+	0.464429i	$0.153740\pi$
$677$	24.1682i	0.928858i	−0.885610	+	0.464429i	$0.846260\pi$
$678$	− 9.05897i	− 0.347908i
$679$	8.46165	0.324728
$680$	0	0
$681$	24.0797	0.922738
$682$	− 14.1032i	− 0.540039i
$683$	− 12.9883i	− 0.496983i	−0.968634	−	0.248491i	$-0.920065\pi$
$683$	− 12.9883i	− 0.496983i	0.968634	−	0.248491i	$-0.0799348\pi$
$684$	−58.3779	−2.23213
$685$	0	0
$686$	10.3585	0.395488
$687$	− 16.8127i	− 0.641446i
$688$	− 3.86433i	− 0.147326i
$689$	1.22881	0.0468140
$690$	0	0
$691$	48.5517	1.84700	0.923498	−	0.383604i	$-0.125317\pi$
$691$	48.5517	1.84700	0.923498	+	0.383604i	$0.125317\pi$
$692$	− 4.76549i	− 0.181157i
$693$	10.2479i	0.389286i
$694$	−19.7139	−0.748329
$695$	0	0
$696$	−3.40268	−0.128978
$697$	− 4.35109i	− 0.164809i
$698$	9.64891i	0.365217i
$699$	15.3776	0.581633
$700$	0	0
$701$	−42.7819	−1.61585	−0.807925	−	0.589285i	$-0.799410\pi$
$701$	−42.7819	−1.61585	−0.807925	+	0.589285i	$0.799410\pi$
$702$	− 73.2083i	− 2.76307i
$703$	3.09146i	0.116597i
$704$	−1.54573	−0.0582569
$705$	0	0
$706$	23.9618	0.901814
$707$	8.73299i	0.328438i
$708$	29.4750i	1.10774i
$709$	48.2331	1.81143	0.905717	−	0.423883i	$-0.139333\pi$
$709$	48.2331	1.81143	0.905717	+	0.423883i	$0.139333\pi$
$710$	0	0
$711$	127.346	4.77584
$712$	− 1.71390i	− 0.0642309i
$713$	31.0459i	1.16268i
$714$	3.22713	0.120772
$715$	0	0
$716$	−6.84523	−0.255818
$717$	− 45.1183i	− 1.68497i
$718$	14.1431i	0.527814i
$719$	22.8054	0.850496	0.425248	−	0.905077i	$-0.360187\pi$
$719$	22.8054	0.850496	0.425248	+	0.905077i	$0.360187\pi$
$720$	0	0
$721$	−11.2214	−0.417908
$722$	27.3129i	1.01648i
$723$	− 62.5785i	− 2.32732i
$724$	−19.3394	−0.718742
$725$	0	0
$726$	29.2995	1.08741
$727$	− 12.0650i	− 0.447465i	−0.974651	−	0.223733i	$-0.928176\pi$
$727$	− 12.0650i	− 0.447465i	0.974651	−	0.223733i	$-0.0718243\pi$
$728$	2.98090i	0.110480i
$729$	−139.517	−5.16729
$730$	0	0
$731$	−4.74205	−0.175391
$732$	4.77287i	0.176410i
$733$	26.3511i	0.973300i	0.873597	+	0.486650i	$0.161781\pi$
$733$	26.3511i	0.973300i	−0.873597	+	0.486650i	$0.838219\pi$
$734$	−35.8439	−1.32302
$735$	0	0
$736$	3.40268	0.125424
$737$	21.0385i	0.774963i
$738$	− 30.4161i	− 1.11963i
$739$	1.81708	0.0668422	0.0334211	−	0.999441i	$-0.489360\pi$
$739$	1.81708	0.0668422	0.0334211	+	0.999441i	$0.489360\pi$
$740$	0	0
$741$	−89.3132	−3.28100
$742$	0.246232i	0.00903948i
$743$	4.90854i	0.180077i	0.995938	+	0.0900384i	$0.0286990\pi$
$743$	4.90854i	0.180077i	−0.995938	+	0.0900384i	$0.971301\pi$
$744$	−31.0459	−1.13820
$745$	0	0
$746$	−10.8378	−0.396802
$747$	− 127.004i	− 4.64682i
$748$	1.89682i	0.0693546i
$749$	9.59596	0.350629
$750$	0	0
$751$	10.1829	0.371580	0.185790	−	0.982589i	$-0.440516\pi$
$751$	10.1829	0.371580	0.185790	+	0.982589i	$0.440516\pi$
$752$	− 8.00000i	− 0.291730i
$753$	− 20.7672i	− 0.756797i
$754$	−3.85695	−0.140462
$755$	0	0
$756$	14.6697	0.533531
$757$	29.8586i	1.08523i	0.839981	+	0.542615i	$0.182566\pi$
$757$	29.8586i	1.08523i	−0.839981	+	0.542615i	$0.817434\pi$
$758$	10.2479i	0.372221i
$759$	17.8968	0.649613
$760$	0	0
$761$	39.5253	1.43279	0.716395	−	0.697695i	$-0.245791\pi$
$761$	39.5253	1.43279	0.716395	+	0.697695i	$0.245791\pi$
$762$	46.3129i	1.67774i
$763$	1.05327i	0.0381308i
$764$	5.05897	0.183027
$765$	0	0
$766$	−25.4750	−0.920451
$767$	33.4101i	1.20637i
$768$	3.40268i	0.122784i
$769$	−24.9353	−0.899191	−0.449595	−	0.893232i	$-0.648432\pi$
$769$	−24.9353	−0.899191	−0.449595	+	0.893232i	$0.648432\pi$
$770$	0	0
$771$	15.1564	0.545846
$772$	− 14.3762i	− 0.517411i
$773$	− 2.20636i	− 0.0793573i	−0.999212	−	0.0396786i	$-0.987367\pi$
$773$	− 2.20636i	− 0.0793573i	0.999212	−	0.0396786i	$-0.0126334\pi$
$774$	−33.1491	−1.19152
$775$	0	0
$776$	10.9484	0.393025
$777$	− 1.19464i	− 0.0428576i
$778$	5.22143i	0.187197i
$779$	−24.1300	−0.864546
$780$	0	0
$781$	−21.0385	−0.752817
$782$	− 4.17554i	− 0.149317i
$783$	18.9809i	0.678322i
$784$	6.40268	0.228667
$785$	0	0
$786$	47.5075	1.69454
$787$	− 43.2717i	− 1.54247i	−0.636552	−	0.771234i	$-0.719640\pi$
$787$	− 43.2717i	− 1.54247i	0.636552	−	0.771234i	$-0.280360\pi$
$788$	27.5400i	0.981073i
$789$	−54.4429	−1.93822
$790$	0	0
$791$	2.05760	0.0731600
$792$	13.2596i	0.471160i
$793$	5.41006i	0.192117i
$794$	1.16215	0.0412432
$795$	0	0
$796$	−6.45427	−0.228765
$797$	− 51.1832i	− 1.81300i	−0.422202	−	0.906502i	$-0.638743\pi$
$797$	− 51.1832i	− 1.81300i	0.422202	−	0.906502i	$-0.361257\pi$
$798$	− 17.8968i	− 0.633541i
$799$	−9.81708	−0.347303
$800$	0	0
$801$	−14.7022	−0.519476
$802$	− 17.6888i	− 0.624613i
$803$	15.3480i	0.541621i
$804$	46.3129	1.63333
$805$	0	0
$806$	−35.1906	−1.23954
$807$	− 10.6298i	− 0.374187i
$808$	11.2995i	0.397515i
$809$	4.37452	0.153800	0.0769000	−	0.997039i	$-0.475498\pi$
$809$	4.37452	0.153800	0.0769000	+	0.997039i	$0.475498\pi$
$810$	0	0
$811$	−37.6198	−1.32101	−0.660504	−	0.750822i	$-0.729658\pi$
$811$	−37.6198	−1.32101	−0.660504	+	0.750822i	$0.729658\pi$
$812$	− 0.772866i	− 0.0271223i
$813$	− 32.7022i	− 1.14692i
$814$	0.702178	0.0246113
$815$	0	0
$816$	4.17554	0.146173
$817$	26.2981i	0.920055i
$818$	− 3.05327i	− 0.106755i
$819$	25.5708	0.893518
$820$	0	0
$821$	23.1946	0.809499	0.404749	−	0.914428i	$-0.367359\pi$
$821$	23.1946	0.809499	0.404749	+	0.914428i	$0.367359\pi$
$822$	46.7997i	1.63233i
$823$	23.2067i	0.808934i	0.914553	+	0.404467i	$0.132543\pi$
$823$	23.2067i	0.808934i	−0.914553	+	0.404467i	$0.867457\pi$
$824$	−14.5193	−0.505802
$825$	0	0
$826$	−6.69480	−0.232942
$827$	− 27.8643i	− 0.968938i	−0.874809	−	0.484469i	$-0.839013\pi$
$827$	− 27.8643i	− 0.968938i	0.874809	−	0.484469i	$-0.160987\pi$
$828$	− 29.1889i	− 1.01439i
$829$	45.1360	1.56764	0.783819	−	0.620990i	$-0.213269\pi$
$829$	45.1360	1.56764	0.783819	+	0.620990i	$0.213269\pi$
$830$	0	0
$831$	36.4161	1.26326
$832$	3.85695i	0.133716i
$833$	− 7.85695i	− 0.272227i
$834$	−61.5799	−2.13234
$835$	0	0
$836$	10.5193	0.363816
$837$	173.181i	5.98601i
$838$	− 14.8760i	− 0.513884i
$839$	−29.9766	−1.03491	−0.517453	−	0.855712i	$-0.673120\pi$
$839$	−29.9766	−1.03491	−0.517453	+	0.855712i	$0.673120\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 8.31289i	− 0.286481i
$843$	32.8127i	1.13013i
$844$	1.54573	0.0532063
$845$	0	0
$846$	−68.6258	−2.35940
$847$	6.65493i	0.228666i
$848$	0.318597i	0.0109407i
$849$	99.0801	3.40042
$850$	0	0
$851$	−1.54573	−0.0529870
$852$	46.3129i	1.58665i
$853$	− 42.2245i	− 1.44574i	−0.690985	−	0.722869i	$-0.742823\pi$
$853$	− 42.2245i	− 1.44574i	0.690985	−	0.722869i	$-0.257177\pi$
$854$	−1.08408	−0.0370965
$855$	0	0
$856$	12.4161	0.424373
$857$	11.8968i	0.406388i	0.979139	+	0.203194i	$0.0651321\pi$
$857$	11.8968i	0.406388i	−0.979139	+	0.203194i	$0.934868\pi$
$858$	20.2861i	0.692556i
$859$	−29.6905	−1.01303	−0.506513	−	0.862232i	$-0.669066\pi$
$859$	−29.6905	−1.01303	−0.506513	+	0.862232i	$0.669066\pi$
$860$	0	0
$861$	9.32461	0.317782
$862$	− 1.19464i	− 0.0406897i
$863$	41.0134i	1.39611i	0.716043	+	0.698056i	$0.245951\pi$
$863$	41.0134i	1.39611i	−0.716043	+	0.698056i	$0.754049\pi$
$864$	18.9809	0.645743
$865$	0	0
$866$	10.1300	0.344230
$867$	52.7216i	1.79052i
$868$	− 7.05159i	− 0.239347i
$869$	−22.9467	−0.778415
$870$	0	0
$871$	52.4958	1.77875
$872$	1.36281i	0.0461505i
$873$	− 93.9179i	− 3.17864i
$874$	−23.1564	−0.783278
$875$	0	0
$876$	33.7863	1.14153
$877$	− 13.3377i	− 0.450382i	−0.974315	−	0.225191i	$-0.927699\pi$
$877$	− 13.3377i	− 0.450382i	0.974315	−	0.225191i	$-0.0723006\pi$
$878$	− 15.6489i	− 0.528125i
$879$	70.0415	2.36244
$880$	0	0
$881$	13.4928	0.454583	0.227292	−	0.973827i	$-0.427013\pi$
$881$	13.4928	0.454583	0.227292	+	0.973827i	$0.427013\pi$
$882$	− 54.9236i	− 1.84937i
$883$	14.2331i	0.478984i	0.970898	+	0.239492i	$0.0769808\pi$
$883$	14.2331i	0.478984i	−0.970898	+	0.239492i	$0.923019\pi$
$884$	4.73299	0.159188
$885$	0	0
$886$	−12.0251	−0.403992
$887$	− 55.0151i	− 1.84723i	−0.383327	−	0.923613i	$-0.625222\pi$
$887$	− 55.0151i	− 1.84723i	0.383327	−	0.923613i	$-0.374778\pi$
$888$	− 1.54573i	− 0.0518713i
$889$	−10.5193	−0.352804
$890$	0	0
$891$	60.0536	2.01187
$892$	9.01339i	0.301791i
$893$	54.4429i	1.82186i
$894$	−21.8318	−0.730166
$895$	0	0
$896$	−0.772866	−0.0258196
$897$	− 44.6566i	− 1.49104i
$898$	− 28.2479i	− 0.942645i
$899$	9.12395	0.304301
$900$	0	0
$901$	0.390961	0.0130248
$902$	5.48075i	0.182489i
$903$	− 10.1625i	− 0.338186i
$904$	2.66231	0.0885470
$905$	0	0
$906$	−14.5842	−0.484529
$907$	− 48.9028i	− 1.62379i	−0.583802	−	0.811896i	$-0.698436\pi$
$907$	− 48.9028i	− 1.62379i	0.583802	−	0.811896i	$-0.301564\pi$
$908$	7.07670i	0.234849i
$909$	96.9296	3.21495
$910$	0	0
$911$	0.742050	0.0245852	0.0122926	−	0.999924i	$-0.496087\pi$
$911$	0.742050	0.0245852	0.0122926	+	0.999924i	$0.496087\pi$
$912$	− 23.1564i	− 0.766787i
$913$	22.8851i	0.757386i
$914$	−3.27439	−0.108307
$915$	0	0
$916$	4.94103	0.163256
$917$	10.7906i	0.356337i
$918$	− 23.2921i	− 0.768754i
$919$	−9.81708	−0.323835	−0.161918	−	0.986804i	$-0.551768\pi$
$919$	−9.81708	−0.323835	−0.161918	+	0.986804i	$0.551768\pi$
$920$	0	0
$921$	−24.1300	−0.795109
$922$	− 16.6697i	− 0.548987i
$923$	52.4958i	1.72792i
$924$	−4.06498	−0.133728
$925$	0	0
$926$	−12.0000	−0.394344
$927$	124.549i	4.09074i
$928$	− 1.00000i	− 0.0328266i
$929$	−18.6167	−0.610795	−0.305398	−	0.952225i	$-0.598789\pi$
$929$	−18.6167	−0.610795	−0.305398	+	0.952225i	$0.598789\pi$
$930$	0	0
$931$	−43.5725	−1.42803
$932$	4.51925i	0.148033i
$933$	− 20.9028i	− 0.684328i
$934$	28.8378	0.943603
$935$	0	0
$936$	33.0858	1.08144
$937$	− 43.4693i	− 1.42008i	−0.704161	−	0.710041i	$-0.748677\pi$
$937$	− 43.4693i	− 1.42008i	0.704161	−	0.710041i	$-0.251323\pi$
$938$	10.5193i	0.343466i
$939$	44.5460	1.45371
$940$	0	0
$941$	53.2067	1.73449	0.867244	−	0.497883i	$-0.165889\pi$
$941$	53.2067	1.73449	0.867244	+	0.497883i	$0.165889\pi$
$942$	− 37.1183i	− 1.20938i
$943$	− 12.0650i	− 0.392890i
$944$	−8.66231	−0.281934
$945$	0	0
$946$	5.97321	0.194206
$947$	− 16.8834i	− 0.548638i	−0.961639	−	0.274319i	$-0.911548\pi$
$947$	− 16.8834i	− 0.548638i	0.961639	−	0.274319i	$-0.0884524\pi$
$948$	50.5135i	1.64060i
$949$	38.2968	1.24317
$950$	0	0
$951$	10.8703	0.352495
$952$	0.948410i	0.0307381i
$953$	24.1065i	0.780887i	0.920627	+	0.390444i	$0.127678\pi$
$953$	24.1065i	0.780887i	−0.920627	+	0.390444i	$0.872322\pi$
$954$	2.73299	0.0884839
$955$	0	0
$956$	13.2596	0.428847
$957$	− 5.25963i	− 0.170020i
$958$	− 18.3688i	− 0.593470i
$959$	−10.6298	−0.343255
$960$	0	0
$961$	52.2465	1.68537
$962$	− 1.75209i	− 0.0564897i
$963$	− 106.508i	− 3.43217i
$964$	18.3910	0.592333
$965$	0	0
$966$	8.94841	0.287910
$967$	18.1179i	0.582634i	0.956627	+	0.291317i	$0.0940934\pi$
$967$	18.1179i	0.582634i	−0.956627	+	0.291317i	$0.905907\pi$
$968$	8.61072i	0.276759i
$969$	−28.4161	−0.912856
$970$	0	0
$971$	1.32461	0.0425088	0.0212544	−	0.999774i	$-0.493234\pi$
$971$	1.32461	0.0425088	0.0212544	+	0.999774i	$0.493234\pi$
$972$	− 75.2556i	− 2.41382i
$973$	− 13.9869i	− 0.448400i
$974$	28.2348	0.904702
$975$	0	0
$976$	−1.40268	−0.0448987
$977$	13.1712i	0.421384i	0.977552	+	0.210692i	$0.0675718\pi$
$977$	13.1712i	0.421384i	−0.977552	+	0.210692i	$0.932428\pi$
$978$	38.8851i	1.24341i
$979$	2.64922	0.0846695
$980$	0	0
$981$	11.6905	0.373248
$982$	16.0000i	0.510581i
$983$	54.0918i	1.72526i	0.505836	+	0.862630i	$0.331184\pi$
$983$	54.0918i	1.72526i	−0.505836	+	0.862630i	$0.668816\pi$
$984$	12.0650	0.384618
$985$	0	0
$986$	−1.22713	−0.0390799
$987$	− 21.0385i	− 0.669663i
$988$	− 26.2479i	− 0.835057i
$989$	−13.1491	−0.418116
$990$	0	0
$991$	47.3159	1.50304	0.751520	−	0.659710i	$-0.229321\pi$
$991$	47.3159	1.50304	0.751520	+	0.659710i	$0.229321\pi$
$992$	− 9.12395i	− 0.289686i
$993$	21.9618i	0.696937i
$994$	−10.5193	−0.333650
$995$	0	0
$996$	50.3779	1.59628
$997$	− 7.11825i	− 0.225437i	−0.993627	−	0.112719i	$-0.964044\pi$
$997$	− 7.11825i	− 0.225437i	0.993627	−	0.112719i	$-0.0359559\pi$
$998$	24.0901i	0.762559i
$999$	−8.62243	−0.272802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.j.349.6		6
5.2	odd	4		1450.2.a.r.1.3		3
5.3	odd	4		290.2.a.d.1.1	✓	3
5.4	even	2	inner	1450.2.b.j.349.1		6
15.8	even	4		2610.2.a.w.1.2		3
20.3	even	4		2320.2.a.q.1.3		3
40.3	even	4		9280.2.a.bn.1.1		3
40.13	odd	4		9280.2.a.bp.1.3		3
145.28	odd	4		8410.2.a.w.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.d.1.1	✓	3	5.3	odd	4
1450.2.a.r.1.3		3	5.2	odd	4
1450.2.b.j.349.1		6	5.4	even	2	inner
1450.2.b.j.349.6		6	1.1	even	1	trivial
2320.2.a.q.1.3		3	20.3	even	4
2610.2.a.w.1.2		3	15.8	even	4
8410.2.a.w.1.3		3	145.28	odd	4
9280.2.a.bn.1.1		3	40.3	even	4
9280.2.a.bp.1.3		3	40.13	odd	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +3.40268i q^{3} -1.00000 q^{4} -3.40268 q^{6} -0.772866i q^{7} -1.00000i q^{8} -8.57822 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +3.40268i q^{3} -1.00000 q^{4} -3.40268 q^{6} -0.772866i q^{7} -1.00000i q^{8} -8.57822 q^{9} +1.54573 q^{11} -3.40268i q^{12} -3.85695i q^{13} +0.772866 q^{14} +1.00000 q^{16} -1.22713i q^{17} -8.57822i q^{18} -6.80536 q^{19} +2.62981 q^{21} +1.54573i q^{22} -3.40268i q^{23} +3.40268 q^{24} +3.85695 q^{26} -18.9809i q^{27} +0.772866i q^{28} -1.00000 q^{29} -9.12395 q^{31} +1.00000i q^{32} +5.25963i q^{33} +1.22713 q^{34} +8.57822 q^{36} -0.454269i q^{37} -6.80536i q^{38} +13.1240 q^{39} +3.54573 q^{41} +2.62981i q^{42} -3.86433i q^{43} -1.54573 q^{44} +3.40268 q^{46} -8.00000i q^{47} +3.40268i q^{48} +6.40268 q^{49} +4.17554 q^{51} +3.85695i q^{52} +0.318597i q^{53} +18.9809 q^{54} -0.772866 q^{56} -23.1564i q^{57} -1.00000i q^{58} -8.66231 q^{59} -1.40268 q^{61} -9.12395i q^{62} +6.62981i q^{63} -1.00000 q^{64} -5.25963 q^{66} +13.6107i q^{67} +1.22713i q^{68} +11.5782 q^{69} -13.6107 q^{71} +8.57822i q^{72} +9.92931i q^{73} +0.454269 q^{74} +6.80536 q^{76} -1.19464i q^{77} +13.1240i q^{78} -14.8452 q^{79} +38.8512 q^{81} +3.54573i q^{82} +14.8054i q^{83} -2.62981 q^{84} +3.86433 q^{86} -3.40268i q^{87} -1.54573i q^{88} +1.71390 q^{89} -2.98090 q^{91} +3.40268i q^{92} -31.0459i q^{93} +8.00000 q^{94} -3.40268 q^{96} +10.9484i q^{97} +6.40268i q^{98} -13.2596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9	\( 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9} + 4 q^{11} + 2 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{24} + 10 q^{26} - 6 q^{29} - 10 q^{31} + 10 q^{34} + 12 q^{36} + 34 q^{39} + 16 q^{41} - 4 q^{44} + 2 q^{46} + 20 q^{49} + 4 q^{51} + 56 q^{54} - 2 q^{56} - 2 q^{59} + 10 q^{61} - 6 q^{64} + 30 q^{69} - 8 q^{71} + 8 q^{74} + 4 q^{76} - 18 q^{79} + 70 q^{81} + 10 q^{86} - 16 q^{89} + 40 q^{91} + 48 q^{94} - 2 q^{96} - 48 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9 + 4 * q^11 + 2 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^24 + 10 * q^26 - 6 * q^29 - 10 * q^31 + 10 * q^34 + 12 * q^36 + 34 * q^39 + 16 * q^41 - 4 * q^44 + 2 * q^46 + 20 * q^49 + 4 * q^51 + 56 * q^54 - 2 * q^56 - 2 * q^59 + 10 * q^61 - 6 * q^64 + 30 * q^69 - 8 * q^71 + 8 * q^74 + 4 * q^76 - 18 * q^79 + 70 * q^81 + 10 * q^86 - 16 * q^89 + 40 * q^91 + 48 * q^94 - 2 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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