LMFDB - Embedded newform 3610.2.a.bi.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.a (trivial)

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:	yes
Analytic conductor:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 $ x^9 - 24x^7 - 6x^6 + 183x^5 + 78x^4 - 455x^3 - 168x^2 + 228*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.31980$ of defining polynomial
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} -1.00000 q^{8} +2.38147 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} -1.00000 q^{8} +2.38147 q^{9} -1.00000 q^{10} +2.84657 q^{11} -2.31980 q^{12} -6.56179 q^{13} +4.91674 q^{14} -2.31980 q^{15} +1.00000 q^{16} -2.19123 q^{17} -2.38147 q^{18} +1.00000 q^{20} +11.4059 q^{21} -2.84657 q^{22} -2.65755 q^{23} +2.31980 q^{24} +1.00000 q^{25} +6.56179 q^{26} +1.43487 q^{27} -4.91674 q^{28} -7.60179 q^{29} +2.31980 q^{30} -5.41539 q^{31} -1.00000 q^{32} -6.60347 q^{33} +2.19123 q^{34} -4.91674 q^{35} +2.38147 q^{36} -2.06252 q^{37} +15.2220 q^{39} -1.00000 q^{40} -9.35729 q^{41} -11.4059 q^{42} +1.73409 q^{43} +2.84657 q^{44} +2.38147 q^{45} +2.65755 q^{46} -3.00499 q^{47} -2.31980 q^{48} +17.1744 q^{49} -1.00000 q^{50} +5.08321 q^{51} -6.56179 q^{52} -4.22215 q^{53} -1.43487 q^{54} +2.84657 q^{55} +4.91674 q^{56} +7.60179 q^{58} -0.964592 q^{59} -2.31980 q^{60} -7.49955 q^{61} +5.41539 q^{62} -11.7091 q^{63} +1.00000 q^{64} -6.56179 q^{65} +6.60347 q^{66} +1.91955 q^{67} -2.19123 q^{68} +6.16497 q^{69} +4.91674 q^{70} -6.16536 q^{71} -2.38147 q^{72} -3.97703 q^{73} +2.06252 q^{74} -2.31980 q^{75} -13.9959 q^{77} -15.2220 q^{78} +15.3229 q^{79} +1.00000 q^{80} -10.4730 q^{81} +9.35729 q^{82} -1.31206 q^{83} +11.4059 q^{84} -2.19123 q^{85} -1.73409 q^{86} +17.6346 q^{87} -2.84657 q^{88} -10.7763 q^{89} -2.38147 q^{90} +32.2626 q^{91} -2.65755 q^{92} +12.5626 q^{93} +3.00499 q^{94} +2.31980 q^{96} +2.05429 q^{97} -17.1744 q^{98} +6.77902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	$ 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) $ 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.31980	−1.33934	−0.669668	−	0.742660i	$-0.733564\pi$
$3$	−2.31980	−1.33934	−0.669668	+	0.742660i	$0.733564\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.31980	0.947054
$7$	−4.91674	−1.85835	−0.929177	−	0.369635i	$-0.879483\pi$
$7$	−4.91674	−1.85835	−0.929177	+	0.369635i	$0.879483\pi$
$8$	−1.00000	−0.353553
$9$	2.38147	0.793823
$10$	−1.00000	−0.316228
$11$	2.84657	0.858274	0.429137	−	0.903239i	$-0.358818\pi$
$11$	2.84657	0.858274	0.429137	+	0.903239i	$0.358818\pi$
$12$	−2.31980	−0.669668
$13$	−6.56179	−1.81991	−0.909956	−	0.414704i	$-0.863885\pi$
$13$	−6.56179	−1.81991	−0.909956	+	0.414704i	$0.863885\pi$
$14$	4.91674	1.31405
$15$	−2.31980	−0.598970
$16$	1.00000	0.250000
$17$	−2.19123	−0.531451	−0.265725	−	0.964049i	$-0.585611\pi$
$17$	−2.19123	−0.531451	−0.265725	+	0.964049i	$0.585611\pi$
$18$	−2.38147	−0.561317
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	11.4059	2.48896
$22$	−2.84657	−0.606891
$23$	−2.65755	−0.554137	−0.277068	−	0.960850i	$-0.589363\pi$
$23$	−2.65755	−0.554137	−0.277068	+	0.960850i	$0.589363\pi$
$24$	2.31980	0.473527
$25$	1.00000	0.200000
$26$	6.56179	1.28687
$27$	1.43487	0.276141
$28$	−4.91674	−0.929177
$29$	−7.60179	−1.41162	−0.705808	−	0.708403i	$-0.749416\pi$
$29$	−7.60179	−1.41162	−0.705808	+	0.708403i	$0.749416\pi$
$30$	2.31980	0.423535
$31$	−5.41539	−0.972632	−0.486316	−	0.873783i	$-0.661660\pi$
$31$	−5.41539	−0.972632	−0.486316	+	0.873783i	$0.661660\pi$
$32$	−1.00000	−0.176777
$33$	−6.60347	−1.14952
$34$	2.19123	0.375793
$35$	−4.91674	−0.831081
$36$	2.38147	0.396911
$37$	−2.06252	−0.339076	−0.169538	−	0.985524i	$-0.554228\pi$
$37$	−2.06252	−0.339076	−0.169538	+	0.985524i	$0.554228\pi$
$38$	0	0
$39$	15.2220	2.43748
$40$	−1.00000	−0.158114
$41$	−9.35729	−1.46136	−0.730682	−	0.682718i	$-0.760798\pi$
$41$	−9.35729	−1.46136	−0.730682	+	0.682718i	$0.760798\pi$
$42$	−11.4059	−1.75996
$43$	1.73409	0.264446	0.132223	−	0.991220i	$-0.457788\pi$
$43$	1.73409	0.264446	0.132223	+	0.991220i	$0.457788\pi$
$44$	2.84657	0.429137
$45$	2.38147	0.355008
$46$	2.65755	0.391834
$47$	−3.00499	−0.438323	−0.219162	−	0.975689i	$-0.570332\pi$
$47$	−3.00499	−0.438323	−0.219162	+	0.975689i	$0.570332\pi$
$48$	−2.31980	−0.334834
$49$	17.1744	2.45348
$50$	−1.00000	−0.141421
$51$	5.08321	0.711792
$52$	−6.56179	−0.909956
$53$	−4.22215	−0.579957	−0.289978	−	0.957033i	$-0.593648\pi$
$53$	−4.22215	−0.579957	−0.289978	+	0.957033i	$0.593648\pi$
$54$	−1.43487	−0.195261
$55$	2.84657	0.383832
$56$	4.91674	0.657027
$57$	0	0
$58$	7.60179	0.998163
$59$	−0.964592	−0.125579	−0.0627896	−	0.998027i	$-0.520000\pi$
$59$	−0.964592	−0.125579	−0.0627896	+	0.998027i	$0.520000\pi$
$60$	−2.31980	−0.299485
$61$	−7.49955	−0.960219	−0.480109	−	0.877209i	$-0.659403\pi$
$61$	−7.49955	−0.960219	−0.480109	+	0.877209i	$0.659403\pi$
$62$	5.41539	0.687755
$63$	−11.7091	−1.47520
$64$	1.00000	0.125000
$65$	−6.56179	−0.813890
$66$	6.60347	0.812832
$67$	1.91955	0.234510	0.117255	−	0.993102i	$-0.462590\pi$
$67$	1.91955	0.234510	0.117255	+	0.993102i	$0.462590\pi$
$68$	−2.19123	−0.265725
$69$	6.16497	0.742176
$70$	4.91674	0.587663
$71$	−6.16536	−0.731693	−0.365847	−	0.930675i	$-0.619221\pi$
$71$	−6.16536	−0.731693	−0.365847	+	0.930675i	$0.619221\pi$
$72$	−2.38147	−0.280659
$73$	−3.97703	−0.465477	−0.232738	−	0.972539i	$-0.574769\pi$
$73$	−3.97703	−0.465477	−0.232738	+	0.972539i	$0.574769\pi$
$74$	2.06252	0.239763
$75$	−2.31980	−0.267867
$76$	0	0
$77$	−13.9959	−1.59498
$78$	−15.2220	−1.72356
$79$	15.3229	1.72396	0.861981	−	0.506940i	$-0.169223\pi$
$79$	15.3229	1.72396	0.861981	+	0.506940i	$0.169223\pi$
$80$	1.00000	0.111803
$81$	−10.4730	−1.16367
$82$	9.35729	1.03334
$83$	−1.31206	−0.144018	−0.0720089	−	0.997404i	$-0.522941\pi$
$83$	−1.31206	−0.144018	−0.0720089	+	0.997404i	$0.522941\pi$
$84$	11.4059	1.24448
$85$	−2.19123	−0.237672
$86$	−1.73409	−0.186992
$87$	17.6346	1.89063
$88$	−2.84657	−0.303446
$89$	−10.7763	−1.14228	−0.571142	−	0.820851i	$-0.693500\pi$
$89$	−10.7763	−1.14228	−0.571142	+	0.820851i	$0.693500\pi$
$90$	−2.38147	−0.251029
$91$	32.2626	3.38204
$92$	−2.65755	−0.277068
$93$	12.5626	1.30268
$94$	3.00499	0.309941
$95$	0	0
$96$	2.31980	0.236764
$97$	2.05429	0.208582	0.104291	−	0.994547i	$-0.466743\pi$
$97$	2.05429	0.208582	0.104291	+	0.994547i	$0.466743\pi$
$98$	−17.1744	−1.73487
$99$	6.77902	0.681317
$100$	1.00000	0.100000
$101$	−5.00966	−0.498480	−0.249240	−	0.968442i	$-0.580181\pi$
$101$	−5.00966	−0.498480	−0.249240	+	0.968442i	$0.580181\pi$
$102$	−5.08321	−0.503313
$103$	−9.03489	−0.890234	−0.445117	−	0.895472i	$-0.646838\pi$
$103$	−9.03489	−0.890234	−0.445117	+	0.895472i	$0.646838\pi$
$104$	6.56179	0.643436
$105$	11.4059	1.11310
$106$	4.22215	0.410091
$107$	5.96783	0.576932	0.288466	−	0.957490i	$-0.406855\pi$
$107$	5.96783	0.576932	0.288466	+	0.957490i	$0.406855\pi$
$108$	1.43487	0.138070
$109$	−15.8300	−1.51624	−0.758118	−	0.652118i	$-0.773881\pi$
$109$	−15.8300	−1.51624	−0.758118	+	0.652118i	$0.773881\pi$
$110$	−2.84657	−0.271410
$111$	4.78463	0.454137
$112$	−4.91674	−0.464589
$113$	18.2051	1.71259	0.856296	−	0.516485i	$-0.172760\pi$
$113$	18.2051	1.71259	0.856296	+	0.516485i	$0.172760\pi$
$114$	0	0
$115$	−2.65755	−0.247817
$116$	−7.60179	−0.705808
$117$	−15.6267	−1.44469
$118$	0.964592	0.0887979
$119$	10.7737	0.987624
$120$	2.31980	0.211768
$121$	−2.89703	−0.263366
$122$	7.49955	0.678977
$123$	21.7070	1.95726
$124$	−5.41539	−0.486316
$125$	1.00000	0.0894427
$126$	11.7091	1.04313
$127$	7.64954	0.678787	0.339394	−	0.940644i	$-0.389778\pi$
$127$	7.64954	0.678787	0.339394	+	0.940644i	$0.389778\pi$
$128$	−1.00000	−0.0883883
$129$	−4.02274	−0.354182
$130$	6.56179	0.575507
$131$	−13.3148	−1.16332	−0.581659	−	0.813433i	$-0.697596\pi$
$131$	−13.3148	−1.16332	−0.581659	+	0.813433i	$0.697596\pi$
$132$	−6.60347	−0.574759
$133$	0	0
$134$	−1.91955	−0.165824
$135$	1.43487	0.123494
$136$	2.19123	0.187896
$137$	−7.22627	−0.617382	−0.308691	−	0.951162i	$-0.599891\pi$
$137$	−7.22627	−0.617382	−0.308691	+	0.951162i	$0.599891\pi$
$138$	−6.16497	−0.524797
$139$	−2.41177	−0.204564	−0.102282	−	0.994755i	$-0.532614\pi$
$139$	−2.41177	−0.204564	−0.102282	+	0.994755i	$0.532614\pi$
$140$	−4.91674	−0.415541
$141$	6.97098	0.587063
$142$	6.16536	0.517385
$143$	−18.6786	−1.56198
$144$	2.38147	0.198456
$145$	−7.60179	−0.631294
$146$	3.97703	0.329142
$147$	−39.8411	−3.28604
$148$	−2.06252	−0.169538
$149$	−6.97873	−0.571720	−0.285860	−	0.958271i	$-0.592279\pi$
$149$	−6.97873	−0.571720	−0.285860	+	0.958271i	$0.592279\pi$
$150$	2.31980	0.189411
$151$	−5.69362	−0.463340	−0.231670	−	0.972794i	$-0.574419\pi$
$151$	−5.69362	−0.463340	−0.231670	+	0.972794i	$0.574419\pi$
$152$	0	0
$153$	−5.21834	−0.421878
$154$	13.9959	1.12782
$155$	−5.41539	−0.434974
$156$	15.2220	1.21874
$157$	−5.31383	−0.424090	−0.212045	−	0.977260i	$-0.568012\pi$
$157$	−5.31383	−0.424090	−0.212045	+	0.977260i	$0.568012\pi$
$158$	−15.3229	−1.21903
$159$	9.79454	0.776758
$160$	−1.00000	−0.0790569
$161$	13.0665	1.02978
$162$	10.4730	0.822838
$163$	−4.47359	−0.350398	−0.175199	−	0.984533i	$-0.556057\pi$
$163$	−4.47359	−0.350398	−0.175199	+	0.984533i	$0.556057\pi$
$164$	−9.35729	−0.730682
$165$	−6.60347	−0.514080
$166$	1.31206	0.101836
$167$	3.64877	0.282350	0.141175	−	0.989985i	$-0.454912\pi$
$167$	3.64877	0.282350	0.141175	+	0.989985i	$0.454912\pi$
$168$	−11.4059	−0.879981
$169$	30.0571	2.31208
$170$	2.19123	0.168060
$171$	0	0
$172$	1.73409	0.132223
$173$	−1.17631	−0.0894333	−0.0447167	−	0.999000i	$-0.514239\pi$
$173$	−1.17631	−0.0894333	−0.0447167	+	0.999000i	$0.514239\pi$
$174$	−17.6346	−1.33688
$175$	−4.91674	−0.371671
$176$	2.84657	0.214568
$177$	2.23766	0.168193
$178$	10.7763	0.807717
$179$	4.33057	0.323682	0.161841	−	0.986817i	$-0.448257\pi$
$179$	4.33057	0.323682	0.161841	+	0.986817i	$0.448257\pi$
$180$	2.38147	0.177504
$181$	1.36920	0.101771	0.0508857	−	0.998704i	$-0.483796\pi$
$181$	1.36920	0.101771	0.0508857	+	0.998704i	$0.483796\pi$
$182$	−32.2626	−2.39147
$183$	17.3974	1.28606
$184$	2.65755	0.195917
$185$	−2.06252	−0.151640
$186$	−12.5626	−0.921135
$187$	−6.23749	−0.456130
$188$	−3.00499	−0.219162
$189$	−7.05488	−0.513167
$190$	0	0
$191$	13.6338	0.986505	0.493252	−	0.869886i	$-0.335808\pi$
$191$	13.6338	0.986505	0.493252	+	0.869886i	$0.335808\pi$
$192$	−2.31980	−0.167417
$193$	−5.21947	−0.375706	−0.187853	−	0.982197i	$-0.560153\pi$
$193$	−5.21947	−0.375706	−0.187853	+	0.982197i	$0.560153\pi$
$194$	−2.05429	−0.147490
$195$	15.2220	1.09007
$196$	17.1744	1.22674
$197$	2.85541	0.203440	0.101720	−	0.994813i	$-0.467565\pi$
$197$	2.85541	0.203440	0.101720	+	0.994813i	$0.467565\pi$
$198$	−6.77902	−0.481764
$199$	−1.46463	−0.103825	−0.0519123	−	0.998652i	$-0.516532\pi$
$199$	−1.46463	−0.103825	−0.0519123	+	0.998652i	$0.516532\pi$
$200$	−1.00000	−0.0707107
$201$	−4.45297	−0.314088
$202$	5.00966	0.352478
$203$	37.3760	2.62328
$204$	5.08321	0.355896
$205$	−9.35729	−0.653542
$206$	9.03489	0.629490
$207$	−6.32886	−0.439886
$208$	−6.56179	−0.454978
$209$	0	0
$210$	−11.4059	−0.787079
$211$	1.31050	0.0902188	0.0451094	−	0.998982i	$-0.485636\pi$
$211$	1.31050	0.0902188	0.0451094	+	0.998982i	$0.485636\pi$
$212$	−4.22215	−0.289978
$213$	14.3024	0.979984
$214$	−5.96783	−0.407952
$215$	1.73409	0.118264
$216$	−1.43487	−0.0976305
$217$	26.6261	1.80749
$218$	15.8300	1.07214
$219$	9.22592	0.623430
$220$	2.84657	0.191916
$221$	14.3784	0.967194
$222$	−4.78463	−0.321124
$223$	28.1303	1.88375	0.941874	−	0.335967i	$-0.109063\pi$
$223$	28.1303	1.88375	0.941874	+	0.335967i	$0.109063\pi$
$224$	4.91674	0.328514
$225$	2.38147	0.158765
$226$	−18.2051	−1.21099
$227$	12.6466	0.839382	0.419691	−	0.907667i	$-0.362138\pi$
$227$	12.6466	0.839382	0.419691	+	0.907667i	$0.362138\pi$
$228$	0	0
$229$	13.7440	0.908227	0.454113	−	0.890944i	$-0.349956\pi$
$229$	13.7440	0.908227	0.454113	+	0.890944i	$0.349956\pi$
$230$	2.65755	0.175233
$231$	32.4676	2.13621
$232$	7.60179	0.499082
$233$	24.6181	1.61279	0.806394	−	0.591379i	$-0.201416\pi$
$233$	24.6181	1.61279	0.806394	+	0.591379i	$0.201416\pi$
$234$	15.6267	1.02155
$235$	−3.00499	−0.196024
$236$	−0.964592	−0.0627896
$237$	−35.5461	−2.30897
$238$	−10.7737	−0.698356
$239$	−16.2940	−1.05397	−0.526984	−	0.849875i	$-0.676677\pi$
$239$	−16.2940	−1.05397	−0.526984	+	0.849875i	$0.676677\pi$
$240$	−2.31980	−0.149742
$241$	−19.2548	−1.24031	−0.620155	−	0.784479i	$-0.712930\pi$
$241$	−19.2548	−1.24031	−0.620155	+	0.784479i	$0.712930\pi$
$242$	2.89703	0.186228
$243$	19.9907	1.28240
$244$	−7.49955	−0.480109
$245$	17.1744	1.09723
$246$	−21.7070	−1.38399
$247$	0	0
$248$	5.41539	0.343877
$249$	3.04373	0.192888
$250$	−1.00000	−0.0632456
$251$	−27.7701	−1.75283	−0.876416	−	0.481555i	$-0.840072\pi$
$251$	−27.7701	−1.75283	−0.876416	+	0.481555i	$0.840072\pi$
$252$	−11.7091	−0.737602
$253$	−7.56490	−0.475601
$254$	−7.64954	−0.479975
$255$	5.08321	0.318323
$256$	1.00000	0.0625000
$257$	13.0703	0.815301	0.407650	−	0.913138i	$-0.366348\pi$
$257$	13.0703	0.815301	0.407650	+	0.913138i	$0.366348\pi$
$258$	4.02274	0.250445
$259$	10.1409	0.630124
$260$	−6.56179	−0.406945
$261$	−18.1034	−1.12057
$262$	13.3148	0.822589
$263$	15.0560	0.928392	0.464196	−	0.885733i	$-0.346343\pi$
$263$	15.0560	0.928392	0.464196	+	0.885733i	$0.346343\pi$
$264$	6.60347	0.406416
$265$	−4.22215	−0.259365
$266$	0	0
$267$	24.9988	1.52990
$268$	1.91955	0.117255
$269$	24.4553	1.49107	0.745533	−	0.666468i	$-0.232195\pi$
$269$	24.4553	1.49107	0.745533	+	0.666468i	$0.232195\pi$
$270$	−1.43487	−0.0873233
$271$	8.95074	0.543719	0.271859	−	0.962337i	$-0.412361\pi$
$271$	8.95074	0.543719	0.271859	+	0.962337i	$0.412361\pi$
$272$	−2.19123	−0.132863
$273$	−74.8428	−4.52969
$274$	7.22627	0.436555
$275$	2.84657	0.171655
$276$	6.16497	0.371088
$277$	−7.80141	−0.468741	−0.234371	−	0.972147i	$-0.575303\pi$
$277$	−7.80141	−0.468741	−0.234371	+	0.972147i	$0.575303\pi$
$278$	2.41177	0.144648
$279$	−12.8966	−0.772098
$280$	4.91674	0.293832
$281$	18.2982	1.09158	0.545791	−	0.837921i	$-0.316229\pi$
$281$	18.2982	1.09158	0.545791	+	0.837921i	$0.316229\pi$
$282$	−6.97098	−0.415116
$283$	7.22803	0.429662	0.214831	−	0.976651i	$-0.431080\pi$
$283$	7.22803	0.429662	0.214831	+	0.976651i	$0.431080\pi$
$284$	−6.16536	−0.365847
$285$	0	0
$286$	18.6786	1.10449
$287$	46.0074	2.71573
$288$	−2.38147	−0.140329
$289$	−12.1985	−0.717560
$290$	7.60179	0.446392
$291$	−4.76555	−0.279361
$292$	−3.97703	−0.232738
$293$	11.3866	0.665212	0.332606	−	0.943066i	$-0.392072\pi$
$293$	11.3866	0.665212	0.332606	+	0.943066i	$0.392072\pi$
$294$	39.8411	2.32358
$295$	−0.964592	−0.0561607
$296$	2.06252	0.119882
$297$	4.08446	0.237004
$298$	6.97873	0.404267
$299$	17.4383	1.00848
$300$	−2.31980	−0.133934
$301$	−8.52607	−0.491434
$302$	5.69362	0.327631
$303$	11.6214	0.667632
$304$	0	0
$305$	−7.49955	−0.429423
$306$	5.21834	0.298313
$307$	4.94292	0.282107	0.141054	−	0.990002i	$-0.454951\pi$
$307$	4.94292	0.282107	0.141054	+	0.990002i	$0.454951\pi$
$308$	−13.9959	−0.797488
$309$	20.9591	1.19232
$310$	5.41539	0.307573
$311$	24.1172	1.36756	0.683782	−	0.729687i	$-0.260334\pi$
$311$	24.1172	1.36756	0.683782	+	0.729687i	$0.260334\pi$
$312$	−15.2220	−0.861778
$313$	−30.9756	−1.75084	−0.875422	−	0.483359i	$-0.839416\pi$
$313$	−30.9756	−1.75084	−0.875422	+	0.483359i	$0.839416\pi$
$314$	5.31383	0.299877
$315$	−11.7091	−0.659731
$316$	15.3229	0.861981
$317$	−6.91053	−0.388134	−0.194067	−	0.980988i	$-0.562168\pi$
$317$	−6.91053	−0.388134	−0.194067	+	0.980988i	$0.562168\pi$
$318$	−9.79454	−0.549251
$319$	−21.6390	−1.21155
$320$	1.00000	0.0559017
$321$	−13.8442	−0.772706
$322$	−13.0665	−0.728166
$323$	0	0
$324$	−10.4730	−0.581834
$325$	−6.56179	−0.363983
$326$	4.47359	0.247769
$327$	36.7223	2.03075
$328$	9.35729	0.516670
$329$	14.7748	0.814560
$330$	6.60347	0.363509
$331$	4.17886	0.229691	0.114845	−	0.993383i	$-0.463363\pi$
$331$	4.17886	0.229691	0.114845	+	0.993383i	$0.463363\pi$
$332$	−1.31206	−0.0720089
$333$	−4.91183	−0.269167
$334$	−3.64877	−0.199652
$335$	1.91955	0.104876
$336$	11.4059	0.622240
$337$	17.2012	0.937008	0.468504	−	0.883461i	$-0.344793\pi$
$337$	17.2012	0.937008	0.468504	+	0.883461i	$0.344793\pi$
$338$	−30.0571	−1.63489
$339$	−42.2322	−2.29374
$340$	−2.19123	−0.118836
$341$	−15.4153	−0.834784
$342$	0	0
$343$	−50.0247	−2.70108
$344$	−1.73409	−0.0934958
$345$	6.16497	0.331911
$346$	1.17631	0.0632389
$347$	18.4628	0.991137	0.495568	−	0.868569i	$-0.334960\pi$
$347$	18.4628	0.991137	0.495568	+	0.868569i	$0.334960\pi$
$348$	17.6346	0.945315
$349$	24.7409	1.32435	0.662174	−	0.749350i	$-0.269634\pi$
$349$	24.7409	1.32435	0.662174	+	0.749350i	$0.269634\pi$
$350$	4.91674	0.262811
$351$	−9.41531	−0.502552
$352$	−2.84657	−0.151723
$353$	−6.40992	−0.341165	−0.170583	−	0.985343i	$-0.554565\pi$
$353$	−6.40992	−0.341165	−0.170583	+	0.985343i	$0.554565\pi$
$354$	−2.23766	−0.118930
$355$	−6.16536	−0.327223
$356$	−10.7763	−0.571142
$357$	−24.9928	−1.32276
$358$	−4.33057	−0.228878
$359$	−36.8154	−1.94304	−0.971522	−	0.236948i	$-0.923853\pi$
$359$	−36.8154	−1.94304	−0.971522	+	0.236948i	$0.923853\pi$
$360$	−2.38147	−0.125514
$361$	0	0
$362$	−1.36920	−0.0719633
$363$	6.72053	0.352736
$364$	32.2626	1.69102
$365$	−3.97703	−0.208167
$366$	−17.3974	−0.909379
$367$	14.6238	0.763356	0.381678	−	0.924295i	$-0.375346\pi$
$367$	14.6238	0.763356	0.381678	+	0.924295i	$0.375346\pi$
$368$	−2.65755	−0.138534
$369$	−22.2841	−1.16006
$370$	2.06252	0.107225
$371$	20.7592	1.07777
$372$	12.5626	0.651341
$373$	−13.5574	−0.701977	−0.350989	−	0.936380i	$-0.614154\pi$
$373$	−13.5574	−0.701977	−0.350989	+	0.936380i	$0.614154\pi$
$374$	6.23749	0.322533
$375$	−2.31980	−0.119794
$376$	3.00499	0.154971
$377$	49.8813	2.56902
$378$	7.05488	0.362864
$379$	30.2899	1.55589	0.777944	−	0.628333i	$-0.216262\pi$
$379$	30.2899	1.55589	0.777944	+	0.628333i	$0.216262\pi$
$380$	0	0
$381$	−17.7454	−0.909124
$382$	−13.6338	−0.697564
$383$	−28.6630	−1.46461	−0.732305	−	0.680977i	$-0.761555\pi$
$383$	−28.6630	−1.46461	−0.732305	+	0.680977i	$0.761555\pi$
$384$	2.31980	0.118382
$385$	−13.9959	−0.713295
$386$	5.21947	0.265664
$387$	4.12968	0.209923
$388$	2.05429	0.104291
$389$	17.1263	0.868337	0.434168	−	0.900832i	$-0.357042\pi$
$389$	17.1263	0.868337	0.434168	+	0.900832i	$0.357042\pi$
$390$	−15.2220	−0.770798
$391$	5.82329	0.294496
$392$	−17.1744	−0.867436
$393$	30.8876	1.55807
$394$	−2.85541	−0.143854
$395$	15.3229	0.770980
$396$	6.77902	0.340659
$397$	26.1050	1.31017	0.655085	−	0.755555i	$-0.272633\pi$
$397$	26.1050	1.31017	0.655085	+	0.755555i	$0.272633\pi$
$398$	1.46463	0.0734151
$399$	0	0
$400$	1.00000	0.0500000
$401$	−9.31093	−0.464966	−0.232483	−	0.972600i	$-0.574685\pi$
$401$	−9.31093	−0.464966	−0.232483	+	0.972600i	$0.574685\pi$
$402$	4.45297	0.222094
$403$	35.5346	1.77011
$404$	−5.00966	−0.249240
$405$	−10.4730	−0.520408
$406$	−37.3760	−1.85494
$407$	−5.87111	−0.291020
$408$	−5.08321	−0.251656
$409$	14.5798	0.720925	0.360462	−	0.932774i	$-0.382619\pi$
$409$	14.5798	0.720925	0.360462	+	0.932774i	$0.382619\pi$
$410$	9.35729	0.462124
$411$	16.7635	0.826882
$412$	−9.03489	−0.445117
$413$	4.74265	0.233371
$414$	6.32886	0.311047
$415$	−1.31206	−0.0644067
$416$	6.56179	0.321718
$417$	5.59483	0.273980
$418$	0	0
$419$	14.5969	0.713103	0.356552	−	0.934276i	$-0.383952\pi$
$419$	14.5969	0.713103	0.356552	+	0.934276i	$0.383952\pi$
$420$	11.4059	0.556549
$421$	−39.2412	−1.91250	−0.956249	−	0.292555i	$-0.905494\pi$
$421$	−39.2412	−1.91250	−0.956249	+	0.292555i	$0.905494\pi$
$422$	−1.31050	−0.0637943
$423$	−7.15630	−0.347951
$424$	4.22215	0.205046
$425$	−2.19123	−0.106290
$426$	−14.3024	−0.692953
$427$	36.8734	1.78443
$428$	5.96783	0.288466
$429$	43.3306	2.09202
$430$	−1.73409	−0.0836252
$431$	21.8767	1.05376	0.526881	−	0.849939i	$-0.323361\pi$
$431$	21.8767	1.05376	0.526881	+	0.849939i	$0.323361\pi$
$432$	1.43487	0.0690352
$433$	−1.10168	−0.0529436	−0.0264718	−	0.999650i	$-0.508427\pi$
$433$	−1.10168	−0.0529436	−0.0264718	+	0.999650i	$0.508427\pi$
$434$	−26.6261	−1.27809
$435$	17.6346	0.845515
$436$	−15.8300	−0.758118
$437$	0	0
$438$	−9.22592	−0.440832
$439$	−4.21717	−0.201275	−0.100637	−	0.994923i	$-0.532088\pi$
$439$	−4.21717	−0.201275	−0.100637	+	0.994923i	$0.532088\pi$
$440$	−2.84657	−0.135705
$441$	40.9002	1.94763
$442$	−14.3784	−0.683910
$443$	7.58310	0.360284	0.180142	−	0.983641i	$-0.442344\pi$
$443$	7.58310	0.360284	0.180142	+	0.983641i	$0.442344\pi$
$444$	4.78463	0.227069
$445$	−10.7763	−0.510845
$446$	−28.1303	−1.33201
$447$	16.1893	0.765726
$448$	−4.91674	−0.232294
$449$	29.6975	1.40151	0.700756	−	0.713401i	$-0.252846\pi$
$449$	29.6975	1.40151	0.700756	+	0.713401i	$0.252846\pi$
$450$	−2.38147	−0.112263
$451$	−26.6362	−1.25425
$452$	18.2051	0.856296
$453$	13.2080	0.620568
$454$	−12.6466	−0.593533
$455$	32.2626	1.51250
$456$	0	0
$457$	9.12576	0.426885	0.213442	−	0.976956i	$-0.431532\pi$
$457$	9.12576	0.426885	0.213442	+	0.976956i	$0.431532\pi$
$458$	−13.7440	−0.642213
$459$	−3.14413	−0.146755
$460$	−2.65755	−0.123909
$461$	−26.3855	−1.22890	−0.614449	−	0.788957i	$-0.710621\pi$
$461$	−26.3855	−1.22890	−0.614449	+	0.788957i	$0.710621\pi$
$462$	−32.4676	−1.51053
$463$	−15.7219	−0.730658	−0.365329	−	0.930878i	$-0.619044\pi$
$463$	−15.7219	−0.730658	−0.365329	+	0.930878i	$0.619044\pi$
$464$	−7.60179	−0.352904
$465$	12.5626	0.582577
$466$	−24.6181	−1.14041
$467$	−6.89932	−0.319263	−0.159631	−	0.987177i	$-0.551031\pi$
$467$	−6.89932	−0.319263	−0.159631	+	0.987177i	$0.551031\pi$
$468$	−15.6267	−0.722344
$469$	−9.43794	−0.435803
$470$	3.00499	0.138610
$471$	12.3270	0.567999
$472$	0.964592	0.0443989
$473$	4.93621	0.226967
$474$	35.5461	1.63269
$475$	0	0
$476$	10.7737	0.493812
$477$	−10.0549	−0.460383
$478$	16.2940	0.745268
$479$	−3.64861	−0.166709	−0.0833547	−	0.996520i	$-0.526563\pi$
$479$	−3.64861	−0.166709	−0.0833547	+	0.996520i	$0.526563\pi$
$480$	2.31980	0.105884
$481$	13.5338	0.617089
$482$	19.2548	0.877032
$483$	−30.3116	−1.37922
$484$	−2.89703	−0.131683
$485$	2.05429	0.0932806
$486$	−19.9907	−0.906796
$487$	−22.5151	−1.02026	−0.510128	−	0.860098i	$-0.670402\pi$
$487$	−22.5151	−1.02026	−0.510128	+	0.860098i	$0.670402\pi$
$488$	7.49955	0.339489
$489$	10.3778	0.469301
$490$	−17.1744	−0.775859
$491$	25.1612	1.13551	0.567753	−	0.823199i	$-0.307813\pi$
$491$	25.1612	1.13551	0.567753	+	0.823199i	$0.307813\pi$
$492$	21.7070	0.978629
$493$	16.6573	0.750205
$494$	0	0
$495$	6.77902	0.304694
$496$	−5.41539	−0.243158
$497$	30.3135	1.35975
$498$	−3.04373	−0.136393
$499$	31.7722	1.42232	0.711159	−	0.703032i	$-0.248171\pi$
$499$	31.7722	1.42232	0.711159	+	0.703032i	$0.248171\pi$
$500$	1.00000	0.0447214
$501$	−8.46441	−0.378162
$502$	27.7701	1.23944
$503$	−25.5621	−1.13976	−0.569878	−	0.821729i	$-0.693010\pi$
$503$	−25.5621	−1.13976	−0.569878	+	0.821729i	$0.693010\pi$
$504$	11.7091	0.521563
$505$	−5.00966	−0.222927
$506$	7.56490	0.336301
$507$	−69.7264	−3.09666
$508$	7.64954	0.339394
$509$	9.88190	0.438007	0.219004	−	0.975724i	$-0.429719\pi$
$509$	9.88190	0.438007	0.219004	+	0.975724i	$0.429719\pi$
$510$	−5.08321	−0.225088
$511$	19.5541	0.865020
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−13.0703	−0.576505
$515$	−9.03489	−0.398125
$516$	−4.02274	−0.177091
$517$	−8.55393	−0.376201
$518$	−10.1409	−0.445565
$519$	2.72881	0.119781
$520$	6.56179	0.287753
$521$	−4.29775	−0.188288	−0.0941440	−	0.995559i	$-0.530011\pi$
$521$	−4.29775	−0.188288	−0.0941440	+	0.995559i	$0.530011\pi$
$522$	18.1034	0.792365
$523$	24.9031	1.08893	0.544467	−	0.838782i	$-0.316732\pi$
$523$	24.9031	1.08893	0.544467	+	0.838782i	$0.316732\pi$
$524$	−13.3148	−0.581659
$525$	11.4059	0.497792
$526$	−15.0560	−0.656472
$527$	11.8663	0.516906
$528$	−6.60347	−0.287379
$529$	−15.9374	−0.692933
$530$	4.22215	0.183398
$531$	−2.29714	−0.0996876
$532$	0	0
$533$	61.4006	2.65955
$534$	−24.9988	−1.08181
$535$	5.96783	0.258012
$536$	−1.91955	−0.0829120
$537$	−10.0461	−0.433519
$538$	−24.4553	−1.05434
$539$	48.8880	2.10576
$540$	1.43487	0.0617469
$541$	−21.8913	−0.941181	−0.470590	−	0.882352i	$-0.655959\pi$
$541$	−21.8913	−0.941181	−0.470590	+	0.882352i	$0.655959\pi$
$542$	−8.95074	−0.384467
$543$	−3.17626	−0.136306
$544$	2.19123	0.0939481
$545$	−15.8300	−0.678081
$546$	74.8428	3.20298
$547$	2.96232	0.126660	0.0633299	−	0.997993i	$-0.479828\pi$
$547$	2.96232	0.126660	0.0633299	+	0.997993i	$0.479828\pi$
$548$	−7.22627	−0.308691
$549$	−17.8599	−0.762244
$550$	−2.84657	−0.121378
$551$	0	0
$552$	−6.16497	−0.262399
$553$	−75.3388	−3.20373
$554$	7.80141	0.331450
$555$	4.78463	0.203096
$556$	−2.41177	−0.102282
$557$	−30.7697	−1.30376	−0.651878	−	0.758324i	$-0.726018\pi$
$557$	−30.7697	−1.30376	−0.651878	+	0.758324i	$0.726018\pi$
$558$	12.8966	0.545955
$559$	−11.3787	−0.481269
$560$	−4.91674	−0.207770
$561$	14.4697	0.610912
$562$	−18.2982	−0.771865
$563$	−35.5091	−1.49653	−0.748266	−	0.663399i	$-0.769113\pi$
$563$	−35.5091	−1.49653	−0.748266	+	0.663399i	$0.769113\pi$
$564$	6.97098	0.293531
$565$	18.2051	0.765895
$566$	−7.22803	−0.303817
$567$	51.4931	2.16251
$568$	6.16536	0.258693
$569$	33.0813	1.38684	0.693421	−	0.720533i	$-0.256103\pi$
$569$	33.0813	1.38684	0.693421	+	0.720533i	$0.256103\pi$
$570$	0	0
$571$	2.29342	0.0959766	0.0479883	−	0.998848i	$-0.484719\pi$
$571$	2.29342	0.0959766	0.0479883	+	0.998848i	$0.484719\pi$
$572$	−18.6786	−0.780992
$573$	−31.6276	−1.32126
$574$	−46.0074	−1.92031
$575$	−2.65755	−0.110827
$576$	2.38147	0.0992279
$577$	−15.7036	−0.653747	−0.326874	−	0.945068i	$-0.605995\pi$
$577$	−15.7036	−0.653747	−0.326874	+	0.945068i	$0.605995\pi$
$578$	12.1985	0.507391
$579$	12.1081	0.503197
$580$	−7.60179	−0.315647
$581$	6.45109	0.267636
$582$	4.76555	0.197538
$583$	−12.0187	−0.497762
$584$	3.97703	0.164571
$585$	−15.6267	−0.646084
$586$	−11.3866	−0.470376
$587$	−26.5110	−1.09423	−0.547113	−	0.837059i	$-0.684273\pi$
$587$	−26.5110	−1.09423	−0.547113	+	0.837059i	$0.684273\pi$
$588$	−39.8411	−1.64302
$589$	0	0
$590$	0.964592	0.0397116
$591$	−6.62398	−0.272474
$592$	−2.06252	−0.0847691
$593$	−2.92920	−0.120288	−0.0601438	−	0.998190i	$-0.519156\pi$
$593$	−2.92920	−0.120288	−0.0601438	+	0.998190i	$0.519156\pi$
$594$	−4.08446	−0.167587
$595$	10.7737	0.441679
$596$	−6.97873	−0.285860
$597$	3.39764	0.139056
$598$	−17.4383	−0.713103
$599$	37.0535	1.51397	0.756983	−	0.653435i	$-0.226673\pi$
$599$	37.0535	1.51397	0.756983	+	0.653435i	$0.226673\pi$
$600$	2.31980	0.0947054
$601$	−9.69599	−0.395508	−0.197754	−	0.980252i	$-0.563365\pi$
$601$	−9.69599	−0.395508	−0.197754	+	0.980252i	$0.563365\pi$
$602$	8.52607	0.347497
$603$	4.57135	0.186160
$604$	−5.69362	−0.231670
$605$	−2.89703	−0.117781
$606$	−11.6214	−0.472087
$607$	−38.0294	−1.54357	−0.771783	−	0.635886i	$-0.780635\pi$
$607$	−38.0294	−1.54357	−0.771783	+	0.635886i	$0.780635\pi$
$608$	0	0
$609$	−86.7049	−3.51346
$610$	7.49955	0.303648
$611$	19.7181	0.797710
$612$	−5.21834	−0.210939
$613$	−22.8475	−0.922800	−0.461400	−	0.887192i	$-0.652653\pi$
$613$	−22.8475	−0.922800	−0.461400	+	0.887192i	$0.652653\pi$
$614$	−4.94292	−0.199480
$615$	21.7070	0.875312
$616$	13.9959	0.563909
$617$	−25.4472	−1.02447	−0.512233	−	0.858847i	$-0.671181\pi$
$617$	−25.4472	−1.02447	−0.512233	+	0.858847i	$0.671181\pi$
$618$	−20.9591	−0.843100
$619$	15.9156	0.639701	0.319850	−	0.947468i	$-0.396367\pi$
$619$	15.9156	0.639701	0.319850	+	0.947468i	$0.396367\pi$
$620$	−5.41539	−0.217487
$621$	−3.81323	−0.153020
$622$	−24.1172	−0.967013
$623$	52.9843	2.12277
$624$	15.2220	0.609369
$625$	1.00000	0.0400000
$626$	30.9756	1.23803
$627$	0	0
$628$	−5.31383	−0.212045
$629$	4.51945	0.180202
$630$	11.7091	0.466500
$631$	−19.9368	−0.793673	−0.396836	−	0.917889i	$-0.629892\pi$
$631$	−19.9368	−0.793673	−0.396836	+	0.917889i	$0.629892\pi$
$632$	−15.3229	−0.609513
$633$	−3.04011	−0.120833
$634$	6.91053	0.274452
$635$	7.64954	0.303563
$636$	9.79454	0.388379
$637$	−112.695	−4.46512
$638$	21.6390	0.856697
$639$	−14.6826	−0.580835
$640$	−1.00000	−0.0395285
$641$	2.42799	0.0958998	0.0479499	−	0.998850i	$-0.484731\pi$
$641$	2.42799	0.0958998	0.0479499	+	0.998850i	$0.484731\pi$
$642$	13.8442	0.546385
$643$	−6.69448	−0.264005	−0.132002	−	0.991249i	$-0.542141\pi$
$643$	−6.69448	−0.264005	−0.132002	+	0.991249i	$0.542141\pi$
$644$	13.0665	0.514891
$645$	−4.02274	−0.158395
$646$	0	0
$647$	28.2280	1.10976	0.554878	−	0.831932i	$-0.312765\pi$
$647$	28.2280	1.10976	0.554878	+	0.831932i	$0.312765\pi$
$648$	10.4730	0.411419
$649$	−2.74578	−0.107781
$650$	6.56179	0.257375
$651$	−61.7671	−2.42084
$652$	−4.47359	−0.175199
$653$	16.9827	0.664585	0.332293	−	0.943176i	$-0.392178\pi$
$653$	16.9827	0.664585	0.332293	+	0.943176i	$0.392178\pi$
$654$	−36.7223	−1.43596
$655$	−13.3148	−0.520251
$656$	−9.35729	−0.365341
$657$	−9.47118	−0.369506
$658$	−14.7748	−0.575981
$659$	−18.3003	−0.712877	−0.356438	−	0.934319i	$-0.616009\pi$
$659$	−18.3003	−0.712877	−0.356438	+	0.934319i	$0.616009\pi$
$660$	−6.60347	−0.257040
$661$	5.43955	0.211574	0.105787	−	0.994389i	$-0.466264\pi$
$661$	5.43955	0.211574	0.105787	+	0.994389i	$0.466264\pi$
$662$	−4.17886	−0.162416
$663$	−33.3550	−1.29540
$664$	1.31206	0.0509180
$665$	0	0
$666$	4.91183	0.190329
$667$	20.2021	0.782228
$668$	3.64877	0.141175
$669$	−65.2568	−2.52297
$670$	−1.91955	−0.0741587
$671$	−21.3480	−0.824131
$672$	−11.4059	−0.439990
$673$	−29.9144	−1.15311	−0.576557	−	0.817057i	$-0.695604\pi$
$673$	−29.9144	−1.15311	−0.576557	+	0.817057i	$0.695604\pi$
$674$	−17.2012	−0.662565
$675$	1.43487	0.0552281
$676$	30.0571	1.15604
$677$	−31.4564	−1.20897	−0.604483	−	0.796618i	$-0.706620\pi$
$677$	−31.4564	−1.20897	−0.604483	+	0.796618i	$0.706620\pi$
$678$	42.2322	1.62192
$679$	−10.1004	−0.387619
$680$	2.19123	0.0840298
$681$	−29.3375	−1.12421
$682$	15.4153	0.590282
$683$	−49.8920	−1.90906	−0.954532	−	0.298109i	$-0.903644\pi$
$683$	−49.8920	−1.90906	−0.954532	+	0.298109i	$0.903644\pi$
$684$	0	0
$685$	−7.22627	−0.276101
$686$	50.0247	1.90995
$687$	−31.8832	−1.21642
$688$	1.73409	0.0661115
$689$	27.7049	1.05547
$690$	−6.16497	−0.234697
$691$	18.7274	0.712424	0.356212	−	0.934405i	$-0.384068\pi$
$691$	18.7274	0.712424	0.356212	+	0.934405i	$0.384068\pi$
$692$	−1.17631	−0.0447167
$693$	−33.3307	−1.26613
$694$	−18.4628	−0.700839
$695$	−2.41177	−0.0914837
$696$	−17.6346	−0.668438
$697$	20.5040	0.776643
$698$	−24.7409	−0.936455
$699$	−57.1091	−2.16007
$700$	−4.91674	−0.185835
$701$	−17.9049	−0.676258	−0.338129	−	0.941100i	$-0.609794\pi$
$701$	−17.9049	−0.676258	−0.338129	+	0.941100i	$0.609794\pi$
$702$	9.41531	0.355358
$703$	0	0
$704$	2.84657	0.107284
$705$	6.97098	0.262542
$706$	6.40992	0.241240
$707$	24.6312	0.926352
$708$	2.23766	0.0840964
$709$	26.9792	1.01323	0.506613	−	0.862173i	$-0.330897\pi$
$709$	26.9792	1.01323	0.506613	+	0.862173i	$0.330897\pi$
$710$	6.16536	0.231382
$711$	36.4910	1.36852
$712$	10.7763	0.403859
$713$	14.3916	0.538971
$714$	24.9928	0.935333
$715$	−18.6786	−0.698540
$716$	4.33057	0.161841
$717$	37.7987	1.41162
$718$	36.8154	1.37394
$719$	42.4173	1.58190	0.790950	−	0.611881i	$-0.209587\pi$
$719$	42.4173	1.58190	0.790950	+	0.611881i	$0.209587\pi$
$720$	2.38147	0.0887521
$721$	44.4222	1.65437
$722$	0	0
$723$	44.6672	1.66119
$724$	1.36920	0.0508857
$725$	−7.60179	−0.282323
$726$	−6.72053	−0.249422
$727$	−43.0435	−1.59639	−0.798197	−	0.602396i	$-0.794213\pi$
$727$	−43.0435	−1.59639	−0.798197	+	0.602396i	$0.794213\pi$
$728$	−32.2626	−1.19573
$729$	−14.9553	−0.553901
$730$	3.97703	0.147197
$731$	−3.79978	−0.140540
$732$	17.3974	0.643028
$733$	−30.3958	−1.12269	−0.561347	−	0.827580i	$-0.689717\pi$
$733$	−30.3958	−1.12269	−0.561347	+	0.827580i	$0.689717\pi$
$734$	−14.6238	−0.539774
$735$	−39.8411	−1.46956
$736$	2.65755	0.0979584
$737$	5.46414	0.201274
$738$	22.2841	0.820289
$739$	−36.8924	−1.35711	−0.678554	−	0.734550i	$-0.737393\pi$
$739$	−36.8924	−1.35711	−0.678554	+	0.734550i	$0.737393\pi$
$740$	−2.06252	−0.0758198
$741$	0	0
$742$	−20.7592	−0.762095
$743$	24.5709	0.901420	0.450710	−	0.892670i	$-0.351171\pi$
$743$	24.5709	0.901420	0.450710	+	0.892670i	$0.351171\pi$
$744$	−12.5626	−0.460568
$745$	−6.97873	−0.255681
$746$	13.5574	0.496373
$747$	−3.12464	−0.114325
$748$	−6.23749	−0.228065
$749$	−29.3423	−1.07214
$750$	2.31980	0.0847071
$751$	9.47401	0.345712	0.172856	−	0.984947i	$-0.444701\pi$
$751$	9.47401	0.345712	0.172856	+	0.984947i	$0.444701\pi$
$752$	−3.00499	−0.109581
$753$	64.4210	2.34763
$754$	−49.8813	−1.81657
$755$	−5.69362	−0.207212
$756$	−7.05488	−0.256584
$757$	−7.07511	−0.257149	−0.128575	−	0.991700i	$-0.541040\pi$
$757$	−7.07511	−0.257149	−0.128575	+	0.991700i	$0.541040\pi$
$758$	−30.2899	−1.10018
$759$	17.5490	0.636990
$760$	0	0
$761$	−45.9880	−1.66706	−0.833531	−	0.552472i	$-0.813684\pi$
$761$	−45.9880	−1.66706	−0.833531	+	0.552472i	$0.813684\pi$
$762$	17.7454	0.642848
$763$	77.8319	2.81770
$764$	13.6338	0.493252
$765$	−5.21834	−0.188670
$766$	28.6630	1.03564
$767$	6.32945	0.228543
$768$	−2.31980	−0.0837085
$769$	−45.1430	−1.62790	−0.813948	−	0.580937i	$-0.802686\pi$
$769$	−45.1430	−1.62790	−0.813948	+	0.580937i	$0.802686\pi$
$770$	13.9959	0.504376
$771$	−30.3204	−1.09196
$772$	−5.21947	−0.187853
$773$	−0.771491	−0.0277486	−0.0138743	−	0.999904i	$-0.504416\pi$
$773$	−0.771491	−0.0277486	−0.0138743	+	0.999904i	$0.504416\pi$
$774$	−4.12968	−0.148438
$775$	−5.41539	−0.194526
$776$	−2.05429	−0.0737448
$777$	−23.5248	−0.843948
$778$	−17.1263	−0.614007
$779$	0	0
$780$	15.2220	0.545036
$781$	−17.5501	−0.627993
$782$	−5.82329	−0.208240
$783$	−10.9076	−0.389805
$784$	17.1744	0.613370
$785$	−5.31383	−0.189659
$786$	−30.8876	−1.10172
$787$	−13.5272	−0.482191	−0.241095	−	0.970501i	$-0.577507\pi$
$787$	−13.5272	−0.482191	−0.241095	+	0.970501i	$0.577507\pi$
$788$	2.85541	0.101720
$789$	−34.9269	−1.24343
$790$	−15.3229	−0.545165
$791$	−89.5098	−3.18260
$792$	−6.77902	−0.240882
$793$	49.2105	1.74751
$794$	−26.1050	−0.926430
$795$	9.79454	0.347377
$796$	−1.46463	−0.0519123
$797$	−33.8026	−1.19735	−0.598674	−	0.800992i	$-0.704306\pi$
$797$	−33.8026	−1.19735	−0.598674	+	0.800992i	$0.704306\pi$
$798$	0	0
$799$	6.58463	0.232947
$800$	−1.00000	−0.0353553
$801$	−25.6634	−0.906772
$802$	9.31093	0.328781
$803$	−11.3209	−0.399506
$804$	−4.45297	−0.157044
$805$	13.0665	0.460533
$806$	−35.5346	−1.25165
$807$	−56.7314	−1.99704
$808$	5.00966	0.176239
$809$	−12.9095	−0.453875	−0.226938	−	0.973909i	$-0.572871\pi$
$809$	−12.9095	−0.453875	−0.226938	+	0.973909i	$0.572871\pi$
$810$	10.4730	0.367984
$811$	55.2362	1.93961	0.969803	−	0.243889i	$-0.0784234\pi$
$811$	55.2362	1.93961	0.969803	+	0.243889i	$0.0784234\pi$
$812$	37.3760	1.31164
$813$	−20.7639	−0.728222
$814$	5.87111	0.205782
$815$	−4.47359	−0.156703
$816$	5.08321	0.177948
$817$	0	0
$818$	−14.5798	−0.509771
$819$	76.8324	2.68474
$820$	−9.35729	−0.326771
$821$	51.5462	1.79897	0.899487	−	0.436948i	$-0.143941\pi$
$821$	51.5462	1.79897	0.899487	+	0.436948i	$0.143941\pi$
$822$	−16.7635	−0.584694
$823$	−26.7834	−0.933609	−0.466805	−	0.884360i	$-0.654595\pi$
$823$	−26.7834	−0.933609	−0.466805	+	0.884360i	$0.654595\pi$
$824$	9.03489	0.314745
$825$	−6.60347	−0.229903
$826$	−4.74265	−0.165018
$827$	−4.52302	−0.157281	−0.0786404	−	0.996903i	$-0.525058\pi$
$827$	−4.52302	−0.157281	−0.0786404	+	0.996903i	$0.525058\pi$
$828$	−6.32886	−0.219943
$829$	−13.1174	−0.455584	−0.227792	−	0.973710i	$-0.573151\pi$
$829$	−13.1174	−0.455584	−0.227792	+	0.973710i	$0.573151\pi$
$830$	1.31206	0.0455424
$831$	18.0977	0.627802
$832$	−6.56179	−0.227489
$833$	−37.6329	−1.30390
$834$	−5.59483	−0.193733
$835$	3.64877	0.126271
$836$	0	0
$837$	−7.77037	−0.268583
$838$	−14.5969	−0.504240
$839$	−25.1910	−0.869688	−0.434844	−	0.900506i	$-0.643197\pi$
$839$	−25.1910	−0.869688	−0.434844	+	0.900506i	$0.643197\pi$
$840$	−11.4059	−0.393539
$841$	28.7871	0.992660
$842$	39.2412	1.35234
$843$	−42.4483	−1.46200
$844$	1.31050	0.0451094
$845$	30.0571	1.03399
$846$	7.15630	0.246039
$847$	14.2439	0.489428
$848$	−4.22215	−0.144989
$849$	−16.7676	−0.575462
$850$	2.19123	0.0751585
$851$	5.48124	0.187895
$852$	14.3024	0.489992
$853$	−34.0294	−1.16514	−0.582572	−	0.812779i	$-0.697953\pi$
$853$	−34.0294	−1.16514	−0.582572	+	0.812779i	$0.697953\pi$
$854$	−36.8734	−1.26178
$855$	0	0
$856$	−5.96783	−0.203976
$857$	−1.08201	−0.0369609	−0.0184804	−	0.999829i	$-0.505883\pi$
$857$	−1.08201	−0.0369609	−0.0184804	+	0.999829i	$0.505883\pi$
$858$	−43.3306	−1.47928
$859$	34.1318	1.16456	0.582280	−	0.812988i	$-0.302161\pi$
$859$	34.1318	1.16456	0.582280	+	0.812988i	$0.302161\pi$
$860$	1.73409	0.0591319
$861$	−106.728	−3.63728
$862$	−21.8767	−0.745122
$863$	−34.3216	−1.16832	−0.584160	−	0.811639i	$-0.698576\pi$
$863$	−34.3216	−1.16832	−0.584160	+	0.811639i	$0.698576\pi$
$864$	−1.43487	−0.0488152
$865$	−1.17631	−0.0399958
$866$	1.10168	0.0374368
$867$	28.2981	0.961054
$868$	26.6261	0.903747
$869$	43.6178	1.47963
$870$	−17.6346	−0.597870
$871$	−12.5957	−0.426789
$872$	15.8300	0.536070
$873$	4.89223	0.165577
$874$	0	0
$875$	−4.91674	−0.166216
$876$	9.22592	0.311715
$877$	1.58533	0.0535327	0.0267664	−	0.999642i	$-0.491479\pi$
$877$	1.58533	0.0535327	0.0267664	+	0.999642i	$0.491479\pi$
$878$	4.21717	0.142323
$879$	−26.4146	−0.890943
$880$	2.84657	0.0959579
$881$	−16.8300	−0.567018	−0.283509	−	0.958970i	$-0.591499\pi$
$881$	−16.8300	−0.567018	−0.283509	+	0.958970i	$0.591499\pi$
$882$	−40.9002	−1.37718
$883$	−47.8406	−1.60996	−0.804982	−	0.593300i	$-0.797825\pi$
$883$	−47.8406	−1.60996	−0.804982	+	0.593300i	$0.797825\pi$
$884$	14.3784	0.483597
$885$	2.23766	0.0752181
$886$	−7.58310	−0.254759
$887$	30.8712	1.03655	0.518276	−	0.855213i	$-0.326574\pi$
$887$	30.8712	1.03655	0.518276	+	0.855213i	$0.326574\pi$
$888$	−4.78463	−0.160562
$889$	−37.6108	−1.26143
$890$	10.7763	0.361222
$891$	−29.8122	−0.998746
$892$	28.1303	0.941874
$893$	0	0
$894$	−16.1893	−0.541450
$895$	4.33057	0.144755
$896$	4.91674	0.164257
$897$	−40.4533	−1.35069
$898$	−29.6975	−0.991018
$899$	41.1666	1.37298
$900$	2.38147	0.0793823
$901$	9.25170	0.308219
$902$	26.6362	0.886889
$903$	19.7788	0.658196
$904$	−18.2051	−0.605493
$905$	1.36920	0.0455136
$906$	−13.2080	−0.438808
$907$	−22.7276	−0.754656	−0.377328	−	0.926080i	$-0.623157\pi$
$907$	−22.7276	−0.754656	−0.377328	+	0.926080i	$0.623157\pi$
$908$	12.6466	0.419691
$909$	−11.9303	−0.395704
$910$	−32.2626	−1.06950
$911$	−58.5516	−1.93990	−0.969950	−	0.243305i	$-0.921768\pi$
$911$	−58.5516	−1.93990	−0.969950	+	0.243305i	$0.921768\pi$
$912$	0	0
$913$	−3.73489	−0.123607
$914$	−9.12576	−0.301853
$915$	17.3974	0.575142
$916$	13.7440	0.454113
$917$	65.4653	2.16186
$918$	3.14413	0.103772
$919$	9.12200	0.300907	0.150454	−	0.988617i	$-0.451927\pi$
$919$	9.12200	0.300907	0.150454	+	0.988617i	$0.451927\pi$
$920$	2.65755	0.0876167
$921$	−11.4666	−0.377836
$922$	26.3855	0.868962
$923$	40.4558	1.33162
$924$	32.4676	1.06811
$925$	−2.06252	−0.0678153
$926$	15.7219	0.516653
$927$	−21.5163	−0.706688
$928$	7.60179	0.249541
$929$	55.1704	1.81008	0.905041	−	0.425323i	$-0.139840\pi$
$929$	55.1704	1.81008	0.905041	+	0.425323i	$0.139840\pi$
$930$	−12.5626	−0.411944
$931$	0	0
$932$	24.6181	0.806394
$933$	−55.9472	−1.83163
$934$	6.89932	0.225753
$935$	−6.23749	−0.203988
$936$	15.6267	0.510774
$937$	46.3056	1.51274	0.756370	−	0.654144i	$-0.226971\pi$
$937$	46.3056	1.51274	0.756370	+	0.654144i	$0.226971\pi$
$938$	9.43794	0.308160
$939$	71.8572	2.34497
$940$	−3.00499	−0.0980121
$941$	−21.9322	−0.714969	−0.357485	−	0.933919i	$-0.616366\pi$
$941$	−21.9322	−0.714969	−0.357485	+	0.933919i	$0.616366\pi$
$942$	−12.3270	−0.401636
$943$	24.8674	0.809795
$944$	−0.964592	−0.0313948
$945$	−7.05488	−0.229495
$946$	−4.93621	−0.160490
$947$	14.6270	0.475315	0.237657	−	0.971349i	$-0.423620\pi$
$947$	14.6270	0.475315	0.237657	+	0.971349i	$0.423620\pi$
$948$	−35.5461	−1.15448
$949$	26.0965	0.847127
$950$	0	0
$951$	16.0310	0.519842
$952$	−10.7737	−0.349178
$953$	7.15456	0.231759	0.115879	−	0.993263i	$-0.463031\pi$
$953$	7.15456	0.231759	0.115879	+	0.993263i	$0.463031\pi$
$954$	10.0549	0.325540
$955$	13.6338	0.441178
$956$	−16.2940	−0.526984
$957$	50.1982	1.62268
$958$	3.64861	0.117881
$959$	35.5297	1.14731
$960$	−2.31980	−0.0748712
$961$	−1.67359	−0.0539869
$962$	−13.5338	−0.436348
$963$	14.2122	0.457981
$964$	−19.2548	−0.620155
$965$	−5.21947	−0.168021
$966$	30.3116	0.975259
$967$	−10.7856	−0.346841	−0.173420	−	0.984848i	$-0.555482\pi$
$967$	−10.7856	−0.346841	−0.173420	+	0.984848i	$0.555482\pi$
$968$	2.89703	0.0931141
$969$	0	0
$970$	−2.05429	−0.0659594
$971$	−56.3934	−1.80975	−0.904874	−	0.425679i	$-0.860035\pi$
$971$	−56.3934	−1.80975	−0.904874	+	0.425679i	$0.860035\pi$
$972$	19.9907	0.641201
$973$	11.8581	0.380152
$974$	22.5151	0.721430
$975$	15.2220	0.487495
$976$	−7.49955	−0.240055
$977$	17.7247	0.567063	0.283532	−	0.958963i	$-0.408494\pi$
$977$	17.7247	0.567063	0.283532	+	0.958963i	$0.408494\pi$
$978$	−10.3778	−0.331846
$979$	−30.6755	−0.980393
$980$	17.1744	0.548615
$981$	−37.6986	−1.20362
$982$	−25.1612	−0.802925
$983$	−28.4112	−0.906178	−0.453089	−	0.891465i	$-0.649678\pi$
$983$	−28.4112	−0.906178	−0.453089	+	0.891465i	$0.649678\pi$
$984$	−21.7070	−0.691995
$985$	2.85541	0.0909810
$986$	−16.6573	−0.530475
$987$	−34.2745	−1.09097
$988$	0	0
$989$	−4.60842	−0.146539
$990$	−6.77902	−0.215451
$991$	−23.1887	−0.736614	−0.368307	−	0.929704i	$-0.620063\pi$
$991$	−23.1887	−0.736614	−0.368307	+	0.929704i	$0.620063\pi$
$992$	5.41539	0.171939
$993$	−9.69411	−0.307633
$994$	−30.3135	−0.961485
$995$	−1.46463	−0.0464318
$996$	3.04373	0.0964442
$997$	30.4921	0.965694	0.482847	−	0.875705i	$-0.339603\pi$
$997$	30.4921	0.965694	0.482847	+	0.875705i	$0.339603\pi$
$998$	−31.7722	−1.00573
$999$	−2.95945	−0.0936328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bi.1.3		9
19.6	even	9		190.2.k.d.131.1	✓	18
19.16	even	9		190.2.k.d.161.1	yes	18
19.18	odd	2		3610.2.a.bj.1.7		9
95.44	even	18		950.2.l.i.701.3		18
95.54	even	18		950.2.l.i.351.3		18
95.63	odd	36		950.2.u.g.549.6		36
95.73	odd	36		950.2.u.g.199.1		36
95.82	odd	36		950.2.u.g.549.1		36
95.92	odd	36		950.2.u.g.199.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.1	✓	18	19.6	even	9
190.2.k.d.161.1	yes	18	19.16	even	9
950.2.l.i.351.3		18	95.54	even	18
950.2.l.i.701.3		18	95.44	even	18
950.2.u.g.199.1		36	95.73	odd	36
950.2.u.g.199.6		36	95.92	odd	36
950.2.u.g.549.1		36	95.82	odd	36
950.2.u.g.549.6		36	95.63	odd	36
3610.2.a.bi.1.3		9	1.1	even	1	trivial
3610.2.a.bj.1.7		9	19.18	odd	2

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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} -1.00000 q^{8} +2.38147 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} -1.00000 q^{8} +2.38147 q^{9} -1.00000 q^{10} +2.84657 q^{11} -2.31980 q^{12} -6.56179 q^{13} +4.91674 q^{14} -2.31980 q^{15} +1.00000 q^{16} -2.19123 q^{17} -2.38147 q^{18} +1.00000 q^{20} +11.4059 q^{21} -2.84657 q^{22} -2.65755 q^{23} +2.31980 q^{24} +1.00000 q^{25} +6.56179 q^{26} +1.43487 q^{27} -4.91674 q^{28} -7.60179 q^{29} +2.31980 q^{30} -5.41539 q^{31} -1.00000 q^{32} -6.60347 q^{33} +2.19123 q^{34} -4.91674 q^{35} +2.38147 q^{36} -2.06252 q^{37} +15.2220 q^{39} -1.00000 q^{40} -9.35729 q^{41} -11.4059 q^{42} +1.73409 q^{43} +2.84657 q^{44} +2.38147 q^{45} +2.65755 q^{46} -3.00499 q^{47} -2.31980 q^{48} +17.1744 q^{49} -1.00000 q^{50} +5.08321 q^{51} -6.56179 q^{52} -4.22215 q^{53} -1.43487 q^{54} +2.84657 q^{55} +4.91674 q^{56} +7.60179 q^{58} -0.964592 q^{59} -2.31980 q^{60} -7.49955 q^{61} +5.41539 q^{62} -11.7091 q^{63} +1.00000 q^{64} -6.56179 q^{65} +6.60347 q^{66} +1.91955 q^{67} -2.19123 q^{68} +6.16497 q^{69} +4.91674 q^{70} -6.16536 q^{71} -2.38147 q^{72} -3.97703 q^{73} +2.06252 q^{74} -2.31980 q^{75} -13.9959 q^{77} -15.2220 q^{78} +15.3229 q^{79} +1.00000 q^{80} -10.4730 q^{81} +9.35729 q^{82} -1.31206 q^{83} +11.4059 q^{84} -2.19123 q^{85} -1.73409 q^{86} +17.6346 q^{87} -2.84657 q^{88} -10.7763 q^{89} -2.38147 q^{90} +32.2626 q^{91} -2.65755 q^{92} +12.5626 q^{93} +3.00499 q^{94} +2.31980 q^{96} +2.05429 q^{97} -17.1744 q^{98} +6.77902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9	\( 9 q - 9 q^{2} + 9 q^{4} + 9 q^{5} - 9 q^{8} + 21 q^{9} - 9 q^{10} + 12 q^{11} - 9 q^{13} + 9 q^{16} + 6 q^{17} - 21 q^{18} + 9 q^{20} - 6 q^{21} - 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} + 18 q^{27} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 6 q^{34} + 21 q^{36} - 6 q^{37} + 24 q^{39} - 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} - 18 q^{46} - 3 q^{47} + 39 q^{49} - 9 q^{50} + 48 q^{51} - 9 q^{52} - 18 q^{54} + 12 q^{55} - 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} - 9 q^{65} + 6 q^{66} + 6 q^{68} + 30 q^{69} - 18 q^{71} - 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} - 24 q^{78} + 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} - 6 q^{84} + 6 q^{85} - 18 q^{86} - 24 q^{87} - 12 q^{88} + 18 q^{89} - 21 q^{90} + 60 q^{91} + 18 q^{92} + 3 q^{94} - 18 q^{97} - 39 q^{98} + 54 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^4 + 9 * q^5 - 9 * q^8 + 21 * q^9 - 9 * q^10 + 12 * q^11 - 9 * q^13 + 9 * q^16 + 6 * q^17 - 21 * q^18 + 9 * q^20 - 6 * q^21 - 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 + 18 * q^27 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 6 * q^34 + 21 * q^36 - 6 * q^37 + 24 * q^39 - 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 - 18 * q^46 - 3 * q^47 + 39 * q^49 - 9 * q^50 + 48 * q^51 - 9 * q^52 - 18 * q^54 + 12 * q^55 - 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 - 9 * q^65 + 6 * q^66 + 6 * q^68 + 30 * q^69 - 18 * q^71 - 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 - 24 * q^78 + 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 - 6 * q^84 + 6 * q^85 - 18 * q^86 - 24 * q^87 - 12 * q^88 + 18 * q^89 - 21 * q^90 + 60 * q^91 + 18 * q^92 + 3 * q^94 - 18 * q^97 - 39 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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