LMFDB - Embedded newform 3467.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3467,2,Mod(1,3467)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3467, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3467.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3467 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3467.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:	$27.6841343808$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	3467.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.59942 q^{2} -0.00337391 q^{3} +4.75700 q^{4} +0.594552 q^{5} +0.00877021 q^{6} -0.0975981 q^{7} -7.16662 q^{8} -2.99999 q^{9} -1.54549 q^{10} +4.55690 q^{11} -0.0160497 q^{12} +3.60741 q^{13} +0.253699 q^{14} -0.00200596 q^{15} +9.11506 q^{16} -3.11202 q^{17} +7.79824 q^{18} -1.74604 q^{19} +2.82828 q^{20} +0.000329287 q^{21} -11.8453 q^{22} +3.14176 q^{23} +0.0241795 q^{24} -4.64651 q^{25} -9.37717 q^{26} +0.0202434 q^{27} -0.464274 q^{28} -5.90318 q^{29} +0.00521435 q^{30} -2.60737 q^{31} -9.36068 q^{32} -0.0153746 q^{33} +8.08947 q^{34} -0.0580272 q^{35} -14.2710 q^{36} -2.47317 q^{37} +4.53870 q^{38} -0.0121710 q^{39} -4.26093 q^{40} +7.21754 q^{41} -0.000855956 q^{42} -2.24710 q^{43} +21.6772 q^{44} -1.78365 q^{45} -8.16675 q^{46} +2.39854 q^{47} -0.0307534 q^{48} -6.99047 q^{49} +12.0782 q^{50} +0.0104997 q^{51} +17.1604 q^{52} +8.95802 q^{53} -0.0526212 q^{54} +2.70931 q^{55} +0.699448 q^{56} +0.00589098 q^{57} +15.3449 q^{58} -9.66529 q^{59} -0.00954237 q^{60} -1.27977 q^{61} +6.77766 q^{62} +0.292793 q^{63} +6.10224 q^{64} +2.14479 q^{65} +0.0399650 q^{66} -5.70467 q^{67} -14.8039 q^{68} -0.0106000 q^{69} +0.150837 q^{70} +3.41814 q^{71} +21.4998 q^{72} -7.75648 q^{73} +6.42882 q^{74} +0.0156769 q^{75} -8.30592 q^{76} -0.444745 q^{77} +0.0316377 q^{78} -6.52354 q^{79} +5.41938 q^{80} +8.99990 q^{81} -18.7614 q^{82} -16.2411 q^{83} +0.00156642 q^{84} -1.85026 q^{85} +5.84116 q^{86} +0.0199168 q^{87} -32.6576 q^{88} +1.79443 q^{89} +4.63646 q^{90} -0.352076 q^{91} +14.9453 q^{92} +0.00879703 q^{93} -6.23482 q^{94} -1.03811 q^{95} +0.0315821 q^{96} -9.50388 q^{97} +18.1712 q^{98} -13.6706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) $ 126 * q - 11 * q^2 - 25 * q^3 + 99 * q^4 - 32 * q^5 - 15 * q^6 - 27 * q^7 - 27 * q^8 + 93 * q^9 - 46 * q^10 - 6 * q^11 - 67 * q^12 - 137 * q^13 - 17 * q^14 - 15 * q^15 + 49 * q^16 - 30 * q^17 - 37 * q^18 - 39 * q^19 - 46 * q^20 - 54 * q^21 - 55 * q^22 - 35 * q^23 - 27 * q^24 + 26 * q^25 - 14 * q^26 - 88 * q^27 - 63 * q^28 - 31 * q^29 - 5 * q^30 - 64 * q^31 - 60 * q^32 - 100 * q^33 - 47 * q^34 - 38 * q^35 + 44 * q^36 - 148 * q^37 - 51 * q^38 + 7 * q^39 - 128 * q^40 - 28 * q^41 - 38 * q^42 - 68 * q^43 - 8 * q^44 - 137 * q^45 - 43 * q^46 - 51 * q^47 - 117 * q^48 + 3 * q^49 - 8 * q^50 - 30 * q^51 - 232 * q^52 - 112 * q^53 - 30 * q^54 - 96 * q^55 - 28 * q^56 - 47 * q^57 - 74 * q^58 - 38 * q^59 - 22 * q^60 - 124 * q^61 - 49 * q^62 - 69 * q^63 - 37 * q^64 - 13 * q^65 - 34 * q^66 - 125 * q^67 - 40 * q^68 - 150 * q^69 - 81 * q^70 - 26 * q^71 - 97 * q^72 - 154 * q^73 + 8 * q^74 - 80 * q^75 - 66 * q^76 - 130 * q^77 - 33 * q^78 - 45 * q^79 - 21 * q^80 + 22 * q^81 - 145 * q^82 - 63 * q^83 - 55 * q^84 - 134 * q^85 - 27 * q^86 - 87 * q^87 - 131 * q^88 - 47 * q^89 - 46 * q^90 - 56 * q^91 - 52 * q^92 - 130 * q^93 - 63 * q^94 + q^95 - 15 * q^96 - 204 * q^97 + 4 * q^98 + 9 * q^99

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 $

$2$	−2.59942	−1.83807	−0.919035	−	0.394176i	$-0.871030\pi$
$2$	−2.59942	−1.83807	−0.919035	+	0.394176i	$0.871030\pi$
$3$	−0.00337391	−0.00194793	−0.000973963	−	1.00000i	$-0.500310\pi$
$3$	−0.00337391	−0.00194793	−0.000973963		1.00000i	$0.500310\pi$
$4$	4.75700	2.37850
$5$	0.594552	0.265892	0.132946	−	0.991123i	$-0.457556\pi$
$5$	0.594552	0.265892	0.132946	+	0.991123i	$0.457556\pi$
$6$	0.00877021	0.00358042
$7$	−0.0975981	−0.0368886	−0.0184443	−	0.999830i	$-0.505871\pi$
$7$	−0.0975981	−0.0368886	−0.0184443	+	0.999830i	$0.505871\pi$
$8$	−7.16662	−2.53378
$9$	−2.99999	−0.999996
$10$	−1.54549	−0.488728
$11$	4.55690	1.37396	0.686979	−	0.726678i	$-0.258937\pi$
$11$	4.55690	1.37396	0.686979	+	0.726678i	$0.258937\pi$
$12$	−0.0160497	−0.00463314
$13$	3.60741	1.00051	0.500257	−	0.865877i	$-0.333239\pi$
$13$	3.60741	1.00051	0.500257	+	0.865877i	$0.333239\pi$
$14$	0.253699	0.0678039
$15$	−0.00200596	−0.000517937 0
$16$	9.11506	2.27877
$17$	−3.11202	−0.754777	−0.377388	−	0.926055i	$-0.623178\pi$
$17$	−3.11202	−0.754777	−0.377388	+	0.926055i	$0.623178\pi$
$18$	7.79824	1.83806
$19$	−1.74604	−0.400569	−0.200285	−	0.979738i	$-0.564187\pi$
$19$	−1.74604	−0.400569	−0.200285	+	0.979738i	$0.564187\pi$
$20$	2.82828	0.632424
$21$	0.000329287 0	7.18563e−5 0
$22$	−11.8453	−2.52543
$23$	3.14176	0.655101	0.327551	−	0.944834i	$-0.393777\pi$
$23$	3.14176	0.655101	0.327551	+	0.944834i	$0.393777\pi$
$24$	0.0241795	0.00493562
$25$	−4.64651	−0.929302
$26$	−9.37717	−1.83901
$27$	0.0202434	0.00389584
$28$	−0.464274	−0.0877396
$29$	−5.90318	−1.09619	−0.548096	−	0.836415i	$-0.684647\pi$
$29$	−5.90318	−1.09619	−0.548096	+	0.836415i	$0.684647\pi$
$30$	0.00521435	0.000952005 0
$31$	−2.60737	−0.468298	−0.234149	−	0.972201i	$-0.575230\pi$
$31$	−2.60737	−0.468298	−0.234149	+	0.972201i	$0.575230\pi$
$32$	−9.36068	−1.65475
$33$	−0.0153746	−0.00267637
$34$	8.08947	1.38733
$35$	−0.0580272	−0.00980838
$36$	−14.2710	−2.37849
$37$	−2.47317	−0.406587	−0.203294	−	0.979118i	$-0.565165\pi$
$37$	−2.47317	−0.406587	−0.203294	+	0.979118i	$0.565165\pi$
$38$	4.53870	0.736274
$39$	−0.0121710	−0.00194893
$40$	−4.26093	−0.673711
$41$	7.21754	1.12719	0.563595	−	0.826051i	$-0.309418\pi$
$41$	7.21754	1.12719	0.563595	+	0.826051i	$0.309418\pi$
$42$	−0.000855956 0	−0.000132077 0
$43$	−2.24710	−0.342679	−0.171340	−	0.985212i	$-0.554810\pi$
$43$	−2.24710	−0.342679	−0.171340	+	0.985212i	$0.554810\pi$
$44$	21.6772	3.26796
$45$	−1.78365	−0.265891
$46$	−8.16675	−1.20412
$47$	2.39854	0.349863	0.174931	−	0.984581i	$-0.444030\pi$
$47$	2.39854	0.349863	0.174931	+	0.984581i	$0.444030\pi$
$48$	−0.0307534	−0.00443887
$49$	−6.99047	−0.998639
$50$	12.0782	1.70812
$51$	0.0104997	0.00147025
$52$	17.1604	2.37972
$53$	8.95802	1.23048	0.615240	−	0.788340i	$-0.289059\pi$
$53$	8.95802	1.23048	0.615240	+	0.788340i	$0.289059\pi$
$54$	−0.0526212	−0.00716083
$55$	2.70931	0.365324
$56$	0.699448	0.0934677
$57$	0.00589098	0.000780279 0
$58$	15.3449	2.01488
$59$	−9.66529	−1.25831	−0.629157	−	0.777279i	$-0.716600\pi$
$59$	−9.66529	−1.25831	−0.629157	+	0.777279i	$0.716600\pi$
$60$	−0.00954237	−0.00123191
$61$	−1.27977	−0.163857	−0.0819287	−	0.996638i	$-0.526108\pi$
$61$	−1.27977	−0.163857	−0.0819287	+	0.996638i	$0.526108\pi$
$62$	6.77766	0.860764
$63$	0.292793	0.0368885
$64$	6.10224	0.762780
$65$	2.14479	0.266028
$66$	0.0399650	0.00491935
$67$	−5.70467	−0.696937	−0.348468	−	0.937321i	$-0.613298\pi$
$67$	−5.70467	−0.696937	−0.348468	+	0.937321i	$0.613298\pi$
$68$	−14.8039	−1.79524
$69$	−0.0106000	−0.00127609
$70$	0.150837	0.0180285
$71$	3.41814	0.405658	0.202829	−	0.979214i	$-0.434986\pi$
$71$	3.41814	0.405658	0.202829	+	0.979214i	$0.434986\pi$
$72$	21.4998	2.53377
$73$	−7.75648	−0.907828	−0.453914	−	0.891046i	$-0.649973\pi$
$73$	−7.75648	−0.907828	−0.453914	+	0.891046i	$0.649973\pi$
$74$	6.42882	0.747335
$75$	0.0156769	0.00181021
$76$	−8.30592	−0.952754
$77$	−0.444745	−0.0506834
$78$	0.0316377	0.00358226
$79$	−6.52354	−0.733956	−0.366978	−	0.930230i	$-0.619607\pi$
$79$	−6.52354	−0.733956	−0.366978	+	0.930230i	$0.619607\pi$
$80$	5.41938	0.605905
$81$	8.99990	0.999989
$82$	−18.7614	−2.07185
$83$	−16.2411	−1.78269	−0.891347	−	0.453321i	$-0.850239\pi$
$83$	−16.2411	−1.78269	−0.891347	+	0.453321i	$0.850239\pi$
$84$	0.00156642	0.000170910 0
$85$	−1.85026	−0.200689
$86$	5.84116	0.629869
$87$	0.0199168	0.00213530
$88$	−32.6576	−3.48131
$89$	1.79443	0.190209	0.0951047	−	0.995467i	$-0.469681\pi$
$89$	1.79443	0.190209	0.0951047	+	0.995467i	$0.469681\pi$
$90$	4.63646	0.488726
$91$	−0.352076	−0.0369076
$92$	14.9453	1.55816
$93$	0.00879703	0.000912209 0
$94$	−6.23482	−0.643072
$95$	−1.03811	−0.106508
$96$	0.0315821	0.00322333
$97$	−9.50388	−0.964973	−0.482486	−	0.875903i	$-0.660266\pi$
$97$	−9.50388	−0.964973	−0.482486	+	0.875903i	$0.660266\pi$
$98$	18.1712	1.83557
$99$	−13.6706	−1.37395
$100$	−22.1034	−2.21034
$101$	16.6283	1.65458	0.827291	−	0.561774i	$-0.189881\pi$
$101$	16.6283	1.65458	0.827291	+	0.561774i	$0.189881\pi$
$102$	−0.0272931	−0.00270242
$103$	−0.578842	−0.0570350	−0.0285175	−	0.999593i	$-0.509079\pi$
$103$	−0.578842	−0.0570350	−0.0285175	+	0.999593i	$0.509079\pi$
$104$	−25.8529	−2.53508
$105$	0.000195778 0	1.91060e−5 0
$106$	−23.2857	−2.26171
$107$	−9.19023	−0.888454	−0.444227	−	0.895914i	$-0.646522\pi$
$107$	−9.19023	−0.888454	−0.444227	+	0.895914i	$0.646522\pi$
$108$	0.0962979	0.00926627
$109$	6.95353	0.666027	0.333014	−	0.942922i	$-0.391934\pi$
$109$	6.95353	0.666027	0.333014	+	0.942922i	$0.391934\pi$
$110$	−7.04265	−0.671491
$111$	0.00834425	0.000792001 0
$112$	−0.889613	−0.0840605
$113$	4.55475	0.428475	0.214237	−	0.976782i	$-0.431273\pi$
$113$	4.55475	0.428475	0.214237	+	0.976782i	$0.431273\pi$
$114$	−0.0153131	−0.00143421
$115$	1.86794	0.174186
$116$	−28.0814	−2.60730
$117$	−10.8222	−1.00051
$118$	25.1242	2.31287
$119$	0.303728	0.0278427
$120$	0.0143760	0.00131234
$121$	9.76534	0.887758
$122$	3.32666	0.301181
$123$	−0.0243513	−0.00219568
$124$	−12.4033	−1.11385
$125$	−5.73535	−0.512985
$126$	−0.761094	−0.0678036
$127$	−10.6898	−0.948565	−0.474283	−	0.880373i	$-0.657293\pi$
$127$	−10.6898	−0.948565	−0.474283	+	0.880373i	$0.657293\pi$
$128$	2.85905	0.252706
$129$	0.00758150	0.000667514 0
$130$	−5.57522	−0.488979
$131$	−15.6199	−1.36472	−0.682358	−	0.731018i	$-0.739045\pi$
$131$	−15.6199	−1.36472	−0.682358	+	0.731018i	$0.739045\pi$
$132$	−0.0731368	−0.00636574
$133$	0.170410	0.0147764
$134$	14.8289	1.28102
$135$	0.0120358	0.00103587
$136$	22.3027	1.91244
$137$	−9.94478	−0.849640	−0.424820	−	0.905278i	$-0.639663\pi$
$137$	−9.94478	−0.849640	−0.424820	+	0.905278i	$0.639663\pi$
$138$	0.0275539	0.00234554
$139$	18.8168	1.59602	0.798010	−	0.602644i	$-0.205886\pi$
$139$	18.8168	1.59602	0.798010	+	0.602644i	$0.205886\pi$
$140$	−0.276035	−0.0233292
$141$	−0.00809245	−0.000681507 0
$142$	−8.88519	−0.745629
$143$	16.4386	1.37466
$144$	−27.3451	−2.27876
$145$	−3.50975	−0.291469
$146$	20.1624	1.66865
$147$	0.0235852	0.00194528
$148$	−11.7649	−0.967068
$149$	21.7885	1.78498	0.892490	−	0.451067i	$-0.148956\pi$
$149$	21.7885	1.78498	0.892490	+	0.451067i	$0.148956\pi$
$150$	−0.0407509	−0.00332729
$151$	0.356425	0.0290055	0.0145027	−	0.999895i	$-0.495383\pi$
$151$	0.356425	0.0290055	0.0145027	+	0.999895i	$0.495383\pi$
$152$	12.5132	1.01495
$153$	9.33604	0.754774
$154$	1.15608	0.0931596
$155$	−1.55022	−0.124517
$156$	−0.0578977	−0.00463553
$157$	−6.93986	−0.553861	−0.276931	−	0.960890i	$-0.589317\pi$
$157$	−6.93986	−0.553861	−0.276931	+	0.960890i	$0.589317\pi$
$158$	16.9574	1.34906
$159$	−0.0302235	−0.00239688
$160$	−5.56541	−0.439984
$161$	−0.306629	−0.0241658
$162$	−23.3945	−1.83805
$163$	−13.7829	−1.07956	−0.539782	−	0.841805i	$-0.681493\pi$
$163$	−13.7829	−1.07956	−0.539782	+	0.841805i	$0.681493\pi$
$164$	34.3338	2.68102
$165$	−0.00914097	−0.000711624 0
$166$	42.2175	3.27672
$167$	−1.00201	−0.0775382	−0.0387691	−	0.999248i	$-0.512344\pi$
$167$	−1.00201	−0.0775382	−0.0387691	+	0.999248i	$0.512344\pi$
$168$	−0.00235987	−0.000182068 0
$169$	0.0133713	0.00102856
$170$	4.80961	0.368880
$171$	5.23810	0.400568
$172$	−10.6895	−0.815063
$173$	−8.63961	−0.656858	−0.328429	−	0.944529i	$-0.606519\pi$
$173$	−8.63961	−0.656858	−0.328429	+	0.944529i	$0.606519\pi$
$174$	−0.0517721	−0.00392483
$175$	0.453490	0.0342807
$176$	41.5364	3.13093
$177$	0.0326098	0.00245110
$178$	−4.66449	−0.349618
$179$	5.57031	0.416345	0.208172	−	0.978092i	$-0.433248\pi$
$179$	5.57031	0.416345	0.208172	+	0.978092i	$0.433248\pi$
$180$	−8.48482	−0.632421
$181$	24.1935	1.79829	0.899145	−	0.437651i	$-0.144189\pi$
$181$	24.1935	1.79829	0.899145	+	0.437651i	$0.144189\pi$
$182$	0.915195	0.0678387
$183$	0.00431781	0.000319182 0
$184$	−22.5158	−1.65988
$185$	−1.47043	−0.108108
$186$	−0.0228672	−0.00167670
$187$	−14.1812	−1.03703
$188$	11.4099	0.832149
$189$	−0.00197572	−0.000143712 0
$190$	2.69849	0.195769
$191$	26.8851	1.94534	0.972670	−	0.232192i	$-0.0745896\pi$
$191$	26.8851	1.94534	0.972670	+	0.232192i	$0.0745896\pi$
$192$	−0.0205884	−0.00148584
$193$	10.6855	0.769156	0.384578	−	0.923092i	$-0.374347\pi$
$193$	10.6855	0.769156	0.384578	+	0.923092i	$0.374347\pi$
$194$	24.7046	1.77369
$195$	−0.00723632	−0.000518204 0
$196$	−33.2537	−2.37526
$197$	−18.6151	−1.32627	−0.663136	−	0.748499i	$-0.730775\pi$
$197$	−18.6151	−1.32627	−0.663136	+	0.748499i	$0.730775\pi$
$198$	35.5358	2.52542
$199$	−2.33027	−0.165189	−0.0825943	−	0.996583i	$-0.526321\pi$
$199$	−2.33027	−0.165189	−0.0825943	+	0.996583i	$0.526321\pi$
$200$	33.2997	2.35465
$201$	0.0192470	0.00135758
$202$	−43.2241	−3.04124
$203$	0.576139	0.0404370
$204$	0.0499470	0.00349699
$205$	4.29120	0.299710
$206$	1.50466	0.104834
$207$	−9.42523	−0.655099
$208$	32.8817	2.27994
$209$	−7.95653	−0.550365
$210$	−0.000508910 0	−3.51182e−5 0
$211$	2.67107	0.183884	0.0919419	−	0.995764i	$-0.470693\pi$
$211$	2.67107	0.183884	0.0919419	+	0.995764i	$0.470693\pi$
$212$	42.6133	2.92670
$213$	−0.0115325	−0.000790193 0
$214$	23.8893	1.63304
$215$	−1.33602	−0.0911156
$216$	−0.145077	−0.00987122
$217$	0.254475	0.0172749
$218$	−18.0752	−1.22420
$219$	0.0261697	0.00176838
$220$	12.8882	0.868923
$221$	−11.2263	−0.755165
$222$	−0.0216902	−0.00145575
$223$	−20.0392	−1.34192	−0.670962	−	0.741492i	$-0.734118\pi$
$223$	−20.0392	−1.34192	−0.670962	+	0.741492i	$0.734118\pi$
$224$	0.913585	0.0610415
$225$	13.9395	0.929298
$226$	−11.8397	−0.787566
$227$	1.76167	0.116926	0.0584629	−	0.998290i	$-0.481380\pi$
$227$	1.76167	0.116926	0.0584629	+	0.998290i	$0.481380\pi$
$228$	0.0280234	0.00185589
$229$	3.08910	0.204134	0.102067	−	0.994778i	$-0.467454\pi$
$229$	3.08910	0.204134	0.102067	+	0.994778i	$0.467454\pi$
$230$	−4.85556	−0.320166
$231$	0.00150053	9.87275e−5 0
$232$	42.3058	2.77751
$233$	18.4145	1.20637	0.603187	−	0.797600i	$-0.293897\pi$
$233$	18.4145	1.20637	0.603187	+	0.797600i	$0.293897\pi$
$234$	28.1314	1.83901
$235$	1.42606	0.0930256
$236$	−45.9778	−2.99290
$237$	0.0220098	0.00142969
$238$	−0.789517	−0.0511768
$239$	3.14369	0.203348	0.101674	−	0.994818i	$-0.467580\pi$
$239$	3.14369	0.203348	0.101674	+	0.994818i	$0.467580\pi$
$240$	−0.0182845	−0.00118026
$241$	−20.6320	−1.32903	−0.664513	−	0.747276i	$-0.731361\pi$
$241$	−20.6320	−1.32903	−0.664513	+	0.747276i	$0.731361\pi$
$242$	−25.3843	−1.63176
$243$	−0.0910950	−0.00584375
$244$	−6.08785	−0.389735
$245$	−4.15620	−0.265530
$246$	0.0632993	0.00403582
$247$	−6.29868	−0.400775
$248$	18.6860	1.18656
$249$	0.0547960	0.00347256
$250$	14.9086	0.942903
$251$	−21.2346	−1.34032	−0.670159	−	0.742218i	$-0.733774\pi$
$251$	−21.2346	−1.34032	−0.670159	+	0.742218i	$0.733774\pi$
$252$	1.39282	0.0877393
$253$	14.3167	0.900081
$254$	27.7873	1.74353
$255$	0.00624260	0.000390927 0
$256$	−19.6364	−1.22727
$257$	−9.15601	−0.571137	−0.285568	−	0.958358i	$-0.592182\pi$
$257$	−9.15601	−0.571137	−0.285568	+	0.958358i	$0.592182\pi$
$258$	−0.0197075	−0.00122694
$259$	0.241377	0.0149984
$260$	10.2028	0.632749
$261$	17.7095	1.09619
$262$	40.6027	2.50844
$263$	−18.2169	−1.12330	−0.561652	−	0.827373i	$-0.689834\pi$
$263$	−18.2169	−1.12330	−0.561652	+	0.827373i	$0.689834\pi$
$264$	0.110184	0.00678133
$265$	5.32601	0.327174
$266$	−0.442969	−0.0271601
$267$	−0.00605425	−0.000370514 0
$268$	−27.1371	−1.65766
$269$	9.87796	0.602270	0.301135	−	0.953582i	$-0.402635\pi$
$269$	9.87796	0.602270	0.301135	+	0.953582i	$0.402635\pi$
$270$	−0.0312860	−0.00190401
$271$	−8.09704	−0.491860	−0.245930	−	0.969288i	$-0.579093\pi$
$271$	−8.09704	−0.491860	−0.245930	+	0.969288i	$0.579093\pi$
$272$	−28.3663	−1.71996
$273$	0.00118787	7.18932e−5 0
$274$	25.8507	1.56170
$275$	−21.1737	−1.27682
$276$	−0.0504242	−0.00303518
$277$	−0.0749800	−0.00450511	−0.00225256	−	0.999997i	$-0.500717\pi$
$277$	−0.0749800	−0.00450511	−0.00225256	+	0.999997i	$0.500717\pi$
$278$	−48.9128	−2.93360
$279$	7.82209	0.468296
$280$	0.415858	0.0248523
$281$	−21.1108	−1.25936	−0.629681	−	0.776854i	$-0.716814\pi$
$281$	−21.1108	−1.25936	−0.629681	+	0.776854i	$0.716814\pi$
$282$	0.0210357	0.00125266
$283$	18.0289	1.07171	0.535854	−	0.844311i	$-0.319990\pi$
$283$	18.0289	1.07171	0.535854	+	0.844311i	$0.319990\pi$
$284$	16.2601	0.964859
$285$	0.00350249	0.000207470 0
$286$	−42.7308	−2.52673
$287$	−0.704418	−0.0415805
$288$	28.0819	1.65474
$289$	−7.31531	−0.430312
$290$	9.12332	0.535740
$291$	0.0320652	0.00187970
$292$	−36.8976	−2.15927
$293$	−1.70230	−0.0994493	−0.0497247	−	0.998763i	$-0.515834\pi$
$293$	−1.70230	−0.0994493	−0.0497247	+	0.998763i	$0.515834\pi$
$294$	−0.0613079	−0.00357555
$295$	−5.74652	−0.334575
$296$	17.7243	1.03020
$297$	0.0922472	0.00535272
$298$	−56.6374	−3.28092
$299$	11.3336	0.655438
$300$	0.0745750	0.00430559
$301$	0.219313	0.0126410
$302$	−0.926500	−0.0533141
$303$	−0.0561024	−0.00322300
$304$	−15.9153	−0.912804
$305$	−0.760888	−0.0435683
$306$	−24.2683	−1.38733
$307$	−1.70918	−0.0975479	−0.0487740	−	0.998810i	$-0.515531\pi$
$307$	−1.70918	−0.0975479	−0.0487740	+	0.998810i	$0.515531\pi$
$308$	−2.11565	−0.120550
$309$	0.00195296	0.000111100 0
$310$	4.02967	0.228870
$311$	23.8812	1.35418	0.677089	−	0.735901i	$-0.263241\pi$
$311$	23.8812	1.35418	0.677089	+	0.735901i	$0.263241\pi$
$312$	0.0872252	0.00493816
$313$	−18.9816	−1.07290	−0.536451	−	0.843932i	$-0.680235\pi$
$313$	−18.9816	−1.07290	−0.536451	+	0.843932i	$0.680235\pi$
$314$	18.0396	1.01804
$315$	0.174081	0.00980834
$316$	−31.0325	−1.74571
$317$	−22.1688	−1.24512	−0.622562	−	0.782571i	$-0.713908\pi$
$317$	−22.1688	−1.24512	−0.622562	+	0.782571i	$0.713908\pi$
$318$	0.0785638	0.00440564
$319$	−26.9002	−1.50612
$320$	3.62810	0.202817
$321$	0.0310070	0.00173064
$322$	0.797060	0.0444184
$323$	5.43372	0.302340
$324$	42.8125	2.37847
$325$	−16.7618	−0.929779
$326$	35.8277	1.98431
$327$	−0.0234606	−0.00129737
$328$	−51.7253	−2.85605
$329$	−0.234093	−0.0129060
$330$	0.0237613	0.00130801
$331$	30.3310	1.66714	0.833570	−	0.552413i	$-0.186293\pi$
$331$	30.3310	1.66714	0.833570	+	0.552413i	$0.186293\pi$
$332$	−77.2590	−4.24014
$333$	7.41949	0.406585
$334$	2.60466	0.142521
$335$	−3.39172	−0.185310
$336$	0.00300147	0.000163744 0
$337$	−31.9713	−1.74159	−0.870793	−	0.491649i	$-0.836394\pi$
$337$	−31.9713	−1.74159	−0.870793	+	0.491649i	$0.836394\pi$
$338$	−0.0347576	−0.00189057
$339$	−0.0153673	−0.000834637 0
$340$	−8.80169	−0.477339
$341$	−11.8815	−0.643421
$342$	−13.6160	−0.736271
$343$	1.36544	0.0737270
$344$	16.1041	0.868275
$345$	−0.00630224	−0.000339301 0
$346$	22.4580	1.20735
$347$	19.5498	1.04949	0.524744	−	0.851260i	$-0.324161\pi$
$347$	19.5498	1.04949	0.524744	+	0.851260i	$0.324161\pi$
$348$	0.0947441	0.00507882
$349$	−32.7279	−1.75188	−0.875942	−	0.482417i	$-0.839759\pi$
$349$	−32.7279	−1.75188	−0.875942	+	0.482417i	$0.839759\pi$
$350$	−1.17881	−0.0630102
$351$	0.0730261	0.00389785
$352$	−42.6557	−2.27356
$353$	−36.7941	−1.95835	−0.979175	−	0.203017i	$-0.934925\pi$
$353$	−36.7941	−1.95835	−0.979175	+	0.203017i	$0.934925\pi$
$354$	−0.0847666	−0.00450529
$355$	2.03226	0.107861
$356$	8.53612	0.452413
$357$	−0.00102475	−5.42355e−5 0
$358$	−14.4796	−0.765271
$359$	11.8696	0.626452	0.313226	−	0.949679i	$-0.398590\pi$
$359$	11.8696	0.626452	0.313226	+	0.949679i	$0.398590\pi$
$360$	12.7827	0.673709
$361$	−15.9513	−0.839544
$362$	−62.8892	−3.30538
$363$	−0.0329473	−0.00172929
$364$	−1.67483	−0.0877847
$365$	−4.61163	−0.241384
$366$	−0.0112238	−0.000586679 0
$367$	−12.0078	−0.626800	−0.313400	−	0.949621i	$-0.601468\pi$
$367$	−12.0078	−0.626800	−0.313400	+	0.949621i	$0.601468\pi$
$368$	28.6373	1.49282
$369$	−21.6525	−1.12719
$370$	3.82227	0.198710
$371$	−0.874286	−0.0453907
$372$	0.0418475	0.00216969
$373$	−1.25304	−0.0648800	−0.0324400	−	0.999474i	$-0.510328\pi$
$373$	−1.25304	−0.0648800	−0.0324400	+	0.999474i	$0.510328\pi$
$374$	36.8629	1.90614
$375$	0.0193505	0.000999257 0
$376$	−17.1894	−0.886476
$377$	−21.2952	−1.09676
$378$	0.00513573	0.000264153 0
$379$	−8.79057	−0.451541	−0.225771	−	0.974180i	$-0.572490\pi$
$379$	−8.79057	−0.451541	−0.225771	+	0.974180i	$0.572490\pi$
$380$	−4.93830	−0.253329
$381$	0.0360663	0.00184773
$382$	−69.8859	−3.57567
$383$	18.9606	0.968839	0.484420	−	0.874836i	$-0.339031\pi$
$383$	18.9606	0.968839	0.484420	+	0.874836i	$0.339031\pi$
$384$	−0.00964615	−0.000492253 0
$385$	−0.264424	−0.0134763
$386$	−27.7760	−1.41376
$387$	6.74127	0.342678
$388$	−45.2100	−2.29519
$389$	7.98679	0.404947	0.202473	−	0.979288i	$-0.435102\pi$
$389$	7.98679	0.404947	0.202473	+	0.979288i	$0.435102\pi$
$390$	0.0188103	0.000952494 0
$391$	−9.77722	−0.494455
$392$	50.0980	2.53033
$393$	0.0527000	0.00265836
$394$	48.3886	2.43778
$395$	−3.87858	−0.195153
$396$	−65.0313	−3.26795
$397$	−1.65075	−0.0828490	−0.0414245	−	0.999142i	$-0.513190\pi$
$397$	−1.65075	−0.0828490	−0.0414245	+	0.999142i	$0.513190\pi$
$398$	6.05737	0.303628
$399$	−0.000574948 0	−2.87834e−5 0
$400$	−42.3532	−2.11766
$401$	14.7174	0.734954	0.367477	−	0.930033i	$-0.380222\pi$
$401$	14.7174	0.734954	0.367477	+	0.930033i	$0.380222\pi$
$402$	−0.0500312	−0.00249533
$403$	−9.40585	−0.468539
$404$	79.1010	3.93542
$405$	5.35091	0.265889
$406$	−1.49763	−0.0743261
$407$	−11.2700	−0.558633
$408$	−0.0752472	−0.00372529
$409$	20.4796	1.01265	0.506325	−	0.862343i	$-0.331004\pi$
$409$	20.4796	1.01265	0.506325	+	0.862343i	$0.331004\pi$
$410$	−11.1546	−0.550889
$411$	0.0335528	0.00165504
$412$	−2.75355	−0.135658
$413$	0.943314	0.0464174
$414$	24.5002	1.20412
$415$	−9.65619	−0.474004
$416$	−33.7678	−1.65560
$417$	−0.0634861	−0.00310893
$418$	20.6824	1.01161
$419$	−26.9833	−1.31822	−0.659111	−	0.752046i	$-0.729067\pi$
$419$	−26.9833	−1.31822	−0.659111	+	0.752046i	$0.729067\pi$
$420$	0.000931317 0	4.54436e−5 0
$421$	−13.3818	−0.652188	−0.326094	−	0.945337i	$-0.605733\pi$
$421$	−13.3818	−0.652188	−0.326094	+	0.945337i	$0.605733\pi$
$422$	−6.94323	−0.337991
$423$	−7.19559	−0.349862
$424$	−64.1987	−3.11776
$425$	14.4600	0.701415
$426$	0.0299778	0.00145243
$427$	0.124903	0.00604447
$428$	−43.7180	−2.11319
$429$	−0.0554622	−0.00267774
$430$	3.47287	0.167477
$431$	2.04708	0.0986042	0.0493021	−	0.998784i	$-0.484300\pi$
$431$	2.04708	0.0986042	0.0493021	+	0.998784i	$0.484300\pi$
$432$	0.184520	0.00887772
$433$	−2.04669	−0.0983576	−0.0491788	−	0.998790i	$-0.515660\pi$
$433$	−2.04669	−0.0983576	−0.0491788	+	0.998790i	$0.515660\pi$
$434$	−0.661487	−0.0317524
$435$	0.0118416	0.000567759 0
$436$	33.0779	1.58415
$437$	−5.48563	−0.262413
$438$	−0.0680260	−0.00325041
$439$	−2.67226	−0.127540	−0.0637699	−	0.997965i	$-0.520312\pi$
$439$	−2.67226	−0.127540	−0.0637699	+	0.997965i	$0.520312\pi$
$440$	−19.4166	−0.925651
$441$	20.9713	0.998635
$442$	29.1820	1.38805
$443$	−35.7597	−1.69899	−0.849496	−	0.527595i	$-0.823094\pi$
$443$	−35.7597	−1.69899	−0.849496	+	0.527595i	$0.823094\pi$
$444$	0.0396936	0.00188378
$445$	1.06688	0.0505751
$446$	52.0903	2.46655
$447$	−0.0735122	−0.00347701
$448$	−0.595568	−0.0281379
$449$	−15.7928	−0.745306	−0.372653	−	0.927971i	$-0.621552\pi$
$449$	−15.7928	−0.745306	−0.372653	+	0.927971i	$0.621552\pi$
$450$	−36.2346	−1.70811
$451$	32.8896	1.54871
$452$	21.6669	1.01913
$453$	−0.00120254	−5.65005e−5 0
$454$	−4.57932	−0.214918
$455$	−0.209327	−0.00981342
$456$	−0.0422184	−0.00197706
$457$	19.6235	0.917946	0.458973	−	0.888450i	$-0.348217\pi$
$457$	19.6235	0.917946	0.458973	+	0.888450i	$0.348217\pi$
$458$	−8.02988	−0.375212
$459$	−0.0629980	−0.00294049
$460$	8.88578	0.414302
$461$	−3.78192	−0.176141	−0.0880707	−	0.996114i	$-0.528070\pi$
$461$	−3.78192	−0.176141	−0.0880707	+	0.996114i	$0.528070\pi$
$462$	−0.00390051	−0.000181468 0
$463$	−21.3665	−0.992986	−0.496493	−	0.868041i	$-0.665379\pi$
$463$	−21.3665	−0.992986	−0.496493	+	0.868041i	$0.665379\pi$
$464$	−53.8078	−2.49797
$465$	0.00523029	0.000242549 0
$466$	−47.8671	−2.21740
$467$	24.3214	1.12546	0.562730	−	0.826641i	$-0.309751\pi$
$467$	24.3214	1.12546	0.562730	+	0.826641i	$0.309751\pi$
$468$	−51.4811	−2.37971
$469$	0.556765	0.0257090
$470$	−3.70692	−0.170988
$471$	0.0234144	0.00107888
$472$	69.2674	3.18829
$473$	−10.2398	−0.470827
$474$	−0.0572128	−0.00262787
$475$	8.11299	0.372250
$476$	1.44483	0.0662238
$477$	−26.8740	−1.23047
$478$	−8.17178	−0.373769
$479$	−23.5372	−1.07544	−0.537722	−	0.843123i	$-0.680715\pi$
$479$	−23.5372	−1.07544	−0.537722	+	0.843123i	$0.680715\pi$
$480$	0.0187772	0.000857057 0
$481$	−8.92173	−0.406796
$482$	53.6314	2.44284
$483$	0.00103454	4.70732e−5 0
$484$	46.4537	2.11153
$485$	−5.65055	−0.256578
$486$	0.236795	0.0107412
$487$	−37.4391	−1.69653	−0.848264	−	0.529574i	$-0.822352\pi$
$487$	−37.4391	−1.69653	−0.848264	+	0.529574i	$0.822352\pi$
$488$	9.17160	0.415179
$489$	0.0465024	0.00210291
$490$	10.8037	0.488063
$491$	13.6906	0.617850	0.308925	−	0.951086i	$-0.400031\pi$
$491$	13.6906	0.617850	0.308925	+	0.951086i	$0.400031\pi$
$492$	−0.115839	−0.00522243
$493$	18.3708	0.827381
$494$	16.3729	0.736653
$495$	−8.12791	−0.365322
$496$	−23.7664	−1.06714
$497$	−0.333604	−0.0149642
$498$	−0.142438	−0.00638280
$499$	−29.2075	−1.30751	−0.653754	−	0.756707i	$-0.726807\pi$
$499$	−29.2075	−1.30751	−0.653754	+	0.756707i	$0.726807\pi$
$500$	−27.2831	−1.22014
$501$	0.00338070	0.000151039 0
$502$	55.1978	2.46360
$503$	12.2304	0.545325	0.272663	−	0.962110i	$-0.412096\pi$
$503$	12.2304	0.545325	0.272663	+	0.962110i	$0.412096\pi$
$504$	−2.09834	−0.0934673
$505$	9.88641	0.439939
$506$	−37.2151	−1.65441
$507$	−4.51135e−5 0	−2.00356e−6 0
$508$	−50.8513	−2.25616
$509$	−2.58517	−0.114586	−0.0572929	−	0.998357i	$-0.518247\pi$
$509$	−2.58517	−0.114586	−0.0572929	+	0.998357i	$0.518247\pi$
$510$	−0.0162272	−0.000718551 0
$511$	0.757018	0.0334885
$512$	45.3251	2.00311
$513$	−0.0353458	−0.00156056
$514$	23.8004	1.04979
$515$	−0.344152	−0.0151651
$516$	0.0360652	0.00158768
$517$	10.9299	0.480697
$518$	−0.627441	−0.0275682
$519$	0.0291492	0.00127951
$520$	−15.3709	−0.674058
$521$	−37.0958	−1.62520	−0.812598	−	0.582825i	$-0.801947\pi$
$521$	−37.0958	−1.62520	−0.812598	+	0.582825i	$0.801947\pi$
$522$	−46.0344	−2.01487
$523$	−17.0542	−0.745729	−0.372864	−	0.927886i	$-0.621624\pi$
$523$	−17.0542	−0.745729	−0.372864	+	0.927886i	$0.621624\pi$
$524$	−74.3038	−3.24598
$525$	−0.00153003	−6.67762e−5 0
$526$	47.3535	2.06471
$527$	8.11420	0.353460
$528$	−0.140140	−0.00609881
$529$	−13.1294	−0.570842
$530$	−13.8446	−0.601369
$531$	28.9958	1.25831
$532$	0.810642	0.0351458
$533$	26.0366	1.12777
$534$	0.0157376	0.000681030 0
$535$	−5.46407	−0.236232
$536$	40.8832	1.76588
$537$	−0.0187937	−0.000811009 0
$538$	−25.6770	−1.10701
$539$	−31.8549	−1.37209
$540$	0.0572541	0.00246382
$541$	1.90887	0.0820687	0.0410344	−	0.999158i	$-0.486935\pi$
$541$	1.90887	0.0820687	0.0410344	+	0.999158i	$0.486935\pi$
$542$	21.0476	0.904073
$543$	−0.0816267	−0.00350293
$544$	29.1307	1.24897
$545$	4.13423	0.177091
$546$	−0.00308778	−0.000132145 0
$547$	10.6285	0.454442	0.227221	−	0.973843i	$-0.427036\pi$
$547$	10.6285	0.454442	0.227221	+	0.973843i	$0.427036\pi$
$548$	−47.3073	−2.02087
$549$	3.83929	0.163857
$550$	55.0393	2.34689
$551$	10.3072	0.439101
$552$	0.0759660	0.00323333
$553$	0.636685	0.0270746
$554$	0.194905	0.00828071
$555$	0.00496109	0.000210587 0
$556$	89.5115	3.79613
$557$	11.6690	0.494430	0.247215	−	0.968961i	$-0.420485\pi$
$557$	11.6690	0.494430	0.247215	+	0.968961i	$0.420485\pi$
$558$	−20.3329	−0.860761
$559$	−8.10620	−0.342856
$560$	−0.528921	−0.0223510
$561$	0.0478460	0.00202006
$562$	54.8758	2.31480
$563$	24.2388	1.02154	0.510771	−	0.859717i	$-0.329360\pi$
$563$	24.2388	1.02154	0.510771	+	0.859717i	$0.329360\pi$
$564$	−0.0384958	−0.00162096
$565$	2.70803	0.113928
$566$	−46.8648	−1.96987
$567$	−0.878373	−0.0368882
$568$	−24.4965	−1.02785
$569$	−18.6664	−0.782538	−0.391269	−	0.920276i	$-0.627964\pi$
$569$	−18.6664	−0.782538	−0.391269	+	0.920276i	$0.627964\pi$
$570$	−0.00910446	−0.000381344 0
$571$	−6.80786	−0.284900	−0.142450	−	0.989802i	$-0.545498\pi$
$571$	−6.80786	−0.284900	−0.142450	+	0.989802i	$0.545498\pi$
$572$	78.1984	3.26964
$573$	−0.0907079	−0.00378938
$574$	1.83108	0.0764278
$575$	−14.5982	−0.608787
$576$	−18.3067	−0.762778
$577$	−2.81089	−0.117019	−0.0585095	−	0.998287i	$-0.518635\pi$
$577$	−2.81089	−0.117019	−0.0585095	+	0.998287i	$0.518635\pi$
$578$	19.0156	0.790944
$579$	−0.0360518	−0.00149826
$580$	−16.6959	−0.693258
$581$	1.58510	0.0657611
$582$	−0.0833511	−0.00345501
$583$	40.8208	1.69063
$584$	55.5877	2.30024
$585$	−6.43434	−0.266027
$586$	4.42499	0.182795
$587$	7.55722	0.311920	0.155960	−	0.987763i	$-0.450153\pi$
$587$	7.55722	0.311920	0.155960	+	0.987763i	$0.450153\pi$
$588$	0.112195	0.00462684
$589$	4.55258	0.187586
$590$	14.9376	0.614972
$591$	0.0628057	0.00258348
$592$	−22.5431	−0.926517
$593$	−9.15299	−0.375868	−0.187934	−	0.982182i	$-0.560179\pi$
$593$	−9.15299	−0.375868	−0.187934	+	0.982182i	$0.560179\pi$
$594$	−0.239789	−0.00983868
$595$	0.180582	0.00740314
$596$	103.648	4.24558
$597$	0.00786212	0.000321775 0
$598$	−29.4608	−1.20474
$599$	−36.5296	−1.49256	−0.746279	−	0.665634i	$-0.768161\pi$
$599$	−36.5296	−1.49256	−0.746279	+	0.665634i	$0.768161\pi$
$600$	−0.112350	−0.00458668
$601$	−31.4479	−1.28279	−0.641394	−	0.767212i	$-0.721644\pi$
$601$	−31.4479	−1.28279	−0.641394	+	0.767212i	$0.721644\pi$
$602$	−0.570086	−0.0232350
$603$	17.1139	0.696934
$604$	1.69551	0.0689895
$605$	5.80600	0.236048
$606$	0.145834	0.00592410
$607$	4.40403	0.178754	0.0893771	−	0.995998i	$-0.471512\pi$
$607$	4.40403	0.178754	0.0893771	+	0.995998i	$0.471512\pi$
$608$	16.3441	0.662842
$609$	−0.00194384	−7.87683e−5 0
$610$	1.97787	0.0800816
$611$	8.65250	0.350043
$612$	44.4115	1.79523
$613$	−19.2007	−0.775508	−0.387754	−	0.921763i	$-0.626749\pi$
$613$	−19.2007	−0.775508	−0.387754	+	0.921763i	$0.626749\pi$
$614$	4.44288	0.179300
$615$	−0.0144781	−0.000583814 0
$616$	3.18732	0.128421
$617$	10.8097	0.435181	0.217590	−	0.976040i	$-0.430180\pi$
$617$	10.8097	0.435181	0.217590	+	0.976040i	$0.430180\pi$
$618$	−0.00507657	−0.000204210 0
$619$	10.5278	0.423147	0.211574	−	0.977362i	$-0.432141\pi$
$619$	10.5278	0.423147	0.211574	+	0.977362i	$0.432141\pi$
$620$	−7.37439	−0.296163
$621$	0.0635998	0.00255217
$622$	−62.0773	−2.48907
$623$	−0.175133	−0.00701657
$624$	−0.110940	−0.00444115
$625$	19.8226	0.792903
$626$	49.3411	1.97207
$627$	0.0268446	0.00107207
$628$	−33.0129	−1.31736
$629$	7.69657	0.306882
$630$	−0.452510	−0.0180284
$631$	9.90341	0.394249	0.197124	−	0.980379i	$-0.436840\pi$
$631$	9.90341	0.394249	0.197124	+	0.980379i	$0.436840\pi$
$632$	46.7517	1.85968
$633$	−0.00901193	−0.000358192 0
$634$	57.6261	2.28862
$635$	−6.35563	−0.252216
$636$	−0.143773	−0.00570099
$637$	−25.2175	−0.999153
$638$	69.9250	2.76836
$639$	−10.2544	−0.405657
$640$	1.69985	0.0671925
$641$	1.01904	0.0402498	0.0201249	−	0.999797i	$-0.493594\pi$
$641$	1.01904	0.0402498	0.0201249	+	0.999797i	$0.493594\pi$
$642$	−0.0806003	−0.00318104
$643$	8.08554	0.318863	0.159431	−	0.987209i	$-0.449034\pi$
$643$	8.08554	0.318863	0.159431	+	0.987209i	$0.449034\pi$
$644$	−1.45864	−0.0574783
$645$	0.00450760	0.000177486 0
$646$	−14.1245	−0.555723
$647$	34.0661	1.33928	0.669639	−	0.742687i	$-0.266449\pi$
$647$	34.0661	1.33928	0.669639	+	0.742687i	$0.266449\pi$
$648$	−64.4988	−2.53375
$649$	−44.0437	−1.72887
$650$	43.5711	1.70900
$651$	−0.000858573 0	−3.36501e−5 0
$652$	−65.5655	−2.56774
$653$	−29.9821	−1.17329	−0.586644	−	0.809845i	$-0.699551\pi$
$653$	−29.9821	−1.17329	−0.586644	+	0.809845i	$0.699551\pi$
$654$	0.0609839	0.00238466
$655$	−9.28683	−0.362867
$656$	65.7883	2.56860
$657$	23.2694	0.907824
$658$	0.608507	0.0237221
$659$	−46.2245	−1.80065	−0.900326	−	0.435217i	$-0.856672\pi$
$659$	−46.2245	−1.80065	−0.900326	+	0.435217i	$0.856672\pi$
$660$	−0.0434836	−0.00169260
$661$	−17.1271	−0.666167	−0.333084	−	0.942897i	$-0.608089\pi$
$661$	−17.1271	−0.666167	−0.333084	+	0.942897i	$0.608089\pi$
$662$	−78.8430	−3.06432
$663$	0.0378766	0.00147100
$664$	116.394	4.51696
$665$	0.101318	0.00392893
$666$	−19.2864	−0.747333
$667$	−18.5463	−0.718117
$668$	−4.76659	−0.184425
$669$	0.0676103	0.00261397
$670$	8.81653	0.340612
$671$	−5.83177	−0.225133
$672$	−0.00308235	−0.000118904 0
$673$	−35.8342	−1.38131	−0.690653	−	0.723186i	$-0.742677\pi$
$673$	−35.8342	−1.38131	−0.690653	+	0.723186i	$0.742677\pi$
$674$	83.1069	3.20116
$675$	−0.0940611	−0.00362041
$676$	0.0636072	0.00244643
$677$	−1.95792	−0.0752490	−0.0376245	−	0.999292i	$-0.511979\pi$
$677$	−1.95792	−0.0752490	−0.0376245	+	0.999292i	$0.511979\pi$
$678$	0.0399461	0.00153412
$679$	0.927561	0.0355965
$680$	13.2601	0.508502
$681$	−0.00594370	−0.000227763 0
$682$	30.8851	1.18265
$683$	42.5099	1.62660	0.813298	−	0.581847i	$-0.197670\pi$
$683$	42.5099	1.62660	0.813298	+	0.581847i	$0.197670\pi$
$684$	24.9177	0.952751
$685$	−5.91269	−0.225912
$686$	−3.54937	−0.135515
$687$	−0.0104223	−0.000397637 0
$688$	−20.4825	−0.780886
$689$	32.3152	1.23111
$690$	0.0163822	0.000623660 0
$691$	40.5428	1.54232	0.771161	−	0.636641i	$-0.219677\pi$
$691$	40.5428	1.54232	0.771161	+	0.636641i	$0.219677\pi$
$692$	−41.0987	−1.56234
$693$	1.33423	0.0506832
$694$	−50.8182	−1.92903
$695$	11.1876	0.424368
$696$	−0.142736	−0.00541039
$697$	−22.4611	−0.850777
$698$	85.0736	3.22009
$699$	−0.0621288	−0.00234993
$700$	2.15726	0.0815366
$701$	−9.72840	−0.367437	−0.183718	−	0.982979i	$-0.558813\pi$
$701$	−9.72840	−0.367437	−0.183718	+	0.982979i	$0.558813\pi$
$702$	−0.189826	−0.00716452
$703$	4.31826	0.162866
$704$	27.8073	1.04803
$705$	−0.00481138	−0.000181207 0
$706$	95.6433	3.59958
$707$	−1.62289	−0.0610352
$708$	0.155125	0.00582995
$709$	10.2256	0.384031	0.192016	−	0.981392i	$-0.438498\pi$
$709$	10.2256	0.384031	0.192016	+	0.981392i	$0.438498\pi$
$710$	−5.28271	−0.198256
$711$	19.5705	0.733953
$712$	−12.8600	−0.481949
$713$	−8.19172	−0.306782
$714$	0.00266376	9.96886e−5 0
$715$	9.77359	0.365512
$716$	26.4980	0.990277
$717$	−0.0106065	−0.000396108 0
$718$	−30.8541	−1.15146
$719$	19.6013	0.731005	0.365502	−	0.930810i	$-0.380897\pi$
$719$	19.6013	0.731005	0.365502	+	0.930810i	$0.380897\pi$
$720$	−16.2581	−0.605903
$721$	0.0564939	0.00210394
$722$	41.4643	1.54314
$723$	0.0696106	0.00258885
$724$	115.089	4.27723
$725$	27.4292	1.01869
$726$	0.0856441	0.00317855
$727$	−22.8302	−0.846726	−0.423363	−	0.905960i	$-0.639150\pi$
$727$	−22.8302	−0.846726	−0.423363	+	0.905960i	$0.639150\pi$
$728$	2.52319	0.0935158
$729$	−26.9994	−0.999977
$730$	11.9876	0.443680
$731$	6.99303	0.258646
$732$	0.0205398	0.000759175 0
$733$	−5.30960	−0.196115	−0.0980573	−	0.995181i	$-0.531263\pi$
$733$	−5.30960	−0.196115	−0.0980573	+	0.995181i	$0.531263\pi$
$734$	31.2132	1.15210
$735$	0.0140226	0.000517233 0
$736$	−29.4090	−1.08403
$737$	−25.9956	−0.957561
$738$	56.2841	2.07185
$739$	14.3102	0.526408	0.263204	−	0.964740i	$-0.415221\pi$
$739$	14.3102	0.526408	0.263204	+	0.964740i	$0.415221\pi$
$740$	−6.99484	−0.257135
$741$	0.0212511	0.000780680 0
$742$	2.27264	0.0834312
$743$	42.0472	1.54256	0.771282	−	0.636494i	$-0.219616\pi$
$743$	42.0472	1.54256	0.771282	+	0.636494i	$0.219616\pi$
$744$	−0.0630449	−0.00231134
$745$	12.9544	0.474612
$746$	3.25718	0.119254
$747$	48.7232	1.78269
$748$	−67.4599	−2.46658
$749$	0.896950	0.0327738
$750$	−0.0503002	−0.00183670
$751$	−18.3173	−0.668407	−0.334203	−	0.942501i	$-0.608467\pi$
$751$	−18.3173	−0.668407	−0.334203	+	0.942501i	$0.608467\pi$
$752$	21.8628	0.797256
$753$	0.0716436	0.00261084
$754$	55.3551	2.01591
$755$	0.211913	0.00771231
$756$	−0.00939849	−0.000341820 0
$757$	17.0316	0.619025	0.309513	−	0.950895i	$-0.399834\pi$
$757$	17.0316	0.619025	0.309513	+	0.950895i	$0.399834\pi$
$758$	22.8504	0.829964
$759$	−0.0483031	−0.00175329
$760$	7.43975	0.269868
$761$	49.9088	1.80919	0.904595	−	0.426271i	$-0.140173\pi$
$761$	49.9088	1.80919	0.904595	+	0.426271i	$0.140173\pi$
$762$	−0.0937517	−0.00339627
$763$	−0.678651	−0.0245688
$764$	127.893	4.62699
$765$	5.55076	0.200688
$766$	−49.2865	−1.78079
$767$	−34.8666	−1.25896
$768$	0.0662512	0.00239064
$769$	26.2141	0.945306	0.472653	−	0.881249i	$-0.343296\pi$
$769$	26.2141	0.945306	0.472653	+	0.881249i	$0.343296\pi$
$770$	0.687350	0.0247704
$771$	0.0308915	0.00111253
$772$	50.8308	1.82944
$773$	−15.4280	−0.554906	−0.277453	−	0.960739i	$-0.589490\pi$
$773$	−15.4280	−0.554906	−0.277453	+	0.960739i	$0.589490\pi$
$774$	−17.5234	−0.629866
$775$	12.1152	0.435190
$776$	68.1107	2.44503
$777$	−0.000814383 0	−2.92158e−5 0
$778$	−20.7611	−0.744320
$779$	−12.6021	−0.451518
$780$	−0.0344232	−0.00123255
$781$	15.5761	0.557357
$782$	25.4151	0.908843
$783$	−0.119500	−0.00427060
$784$	−63.7186	−2.27567
$785$	−4.12611	−0.147267
$786$	−0.136990	−0.00488626
$787$	15.0905	0.537917	0.268959	−	0.963152i	$-0.413321\pi$
$787$	15.0905	0.537917	0.268959	+	0.963152i	$0.413321\pi$
$788$	−88.5522	−3.15454
$789$	0.0614623	0.00218811
$790$	10.0821	0.358704
$791$	−0.444535	−0.0158058
$792$	97.9723	3.48129
$793$	−4.61664	−0.163942
$794$	4.29101	0.152282
$795$	−0.0179695	−0.000637311 0
$796$	−11.0851	−0.392901
$797$	−27.6386	−0.979009	−0.489505	−	0.872001i	$-0.662822\pi$
$797$	−27.6386	−0.979009	−0.489505	+	0.872001i	$0.662822\pi$
$798$	0.00149453	5.29059e−5 0
$799$	−7.46431	−0.264068
$800$	43.4945	1.53776
$801$	−5.38328	−0.190209
$802$	−38.2569	−1.35090
$803$	−35.3455	−1.24732
$804$	0.0915581	0.00322901
$805$	−0.182307	−0.00642548
$806$	24.4498	0.861207
$807$	−0.0333273	−0.00117318
$808$	−119.169	−4.19235
$809$	16.1486	0.567754	0.283877	−	0.958861i	$-0.408379\pi$
$809$	16.1486	0.567754	0.283877	+	0.958861i	$0.408379\pi$
$810$	−13.9093	−0.488722
$811$	−10.4318	−0.366309	−0.183155	−	0.983084i	$-0.558631\pi$
$811$	−10.4318	−0.366309	−0.183155	+	0.983084i	$0.558631\pi$
$812$	2.74069	0.0961795
$813$	0.0273186	0.000958107 0
$814$	29.2955	1.02681
$815$	−8.19468	−0.287047
$816$	0.0957052	0.00335035
$817$	3.92353	0.137267
$818$	−53.2351	−1.86132
$819$	1.05622	0.0369074
$820$	20.4132	0.712862
$821$	17.4476	0.608924	0.304462	−	0.952525i	$-0.401523\pi$
$821$	17.4476	0.608924	0.304462	+	0.952525i	$0.401523\pi$
$822$	−0.0872178	−0.00304207
$823$	−36.4490	−1.27053	−0.635266	−	0.772293i	$-0.719110\pi$
$823$	−36.4490	−1.27053	−0.635266	+	0.772293i	$0.719110\pi$
$824$	4.14834	0.144514
$825$	0.0714380	0.00248715
$826$	−2.45207	−0.0853185
$827$	−13.9293	−0.484368	−0.242184	−	0.970230i	$-0.577864\pi$
$827$	−13.9293	−0.484368	−0.242184	+	0.970230i	$0.577864\pi$
$828$	−44.8358	−1.55815
$829$	−40.4902	−1.40628	−0.703142	−	0.711049i	$-0.748220\pi$
$829$	−40.4902	−1.40628	−0.703142	+	0.711049i	$0.748220\pi$
$830$	25.1005	0.871252
$831$	0.000252976 0	8.77563e−6 0
$832$	22.0133	0.763173
$833$	21.7545	0.753750
$834$	0.165027	0.00571443
$835$	−0.595750	−0.0206168
$836$	−37.8492	−1.30904
$837$	−0.0527821	−0.00182442
$838$	70.1411	2.42298
$839$	−29.5202	−1.01915	−0.509575	−	0.860426i	$-0.670198\pi$
$839$	−29.5202	−1.01915	−0.509575	+	0.860426i	$0.670198\pi$
$840$	−0.00140307	−4.84104e−5 0
$841$	5.84751	0.201638
$842$	34.7849	1.19877
$843$	0.0712257	0.00245314
$844$	12.7063	0.437368
$845$	0.00794992	0.000273486 0
$846$	18.7044	0.643070
$847$	−0.953079	−0.0327482
$848$	81.6530	2.80397
$849$	−0.0608279	−0.00208761
$850$	−37.5878	−1.28925
$851$	−7.77010	−0.266356
$852$	−0.0548600	−0.00187947
$853$	43.9395	1.50446	0.752230	−	0.658901i	$-0.228978\pi$
$853$	43.9395	1.50446	0.752230	+	0.658901i	$0.228978\pi$
$854$	−0.324675	−0.0111102
$855$	3.11432	0.106508
$856$	65.8629	2.25115
$857$	−32.9429	−1.12531	−0.562655	−	0.826692i	$-0.690220\pi$
$857$	−32.9429	−1.12531	−0.562655	+	0.826692i	$0.690220\pi$
$858$	0.144170	0.00492188
$859$	−14.9390	−0.509711	−0.254855	−	0.966979i	$-0.582028\pi$
$859$	−14.9390	−0.509711	−0.254855	+	0.966979i	$0.582028\pi$
$860$	−6.35544	−0.216719
$861$	0.00237664	8.09957e−5 0
$862$	−5.32122	−0.181241
$863$	−2.52654	−0.0860044	−0.0430022	−	0.999075i	$-0.513692\pi$
$863$	−2.52654	−0.0860044	−0.0430022	+	0.999075i	$0.513692\pi$
$864$	−0.189492	−0.00644665
$865$	−5.13670	−0.174653
$866$	5.32021	0.180788
$867$	0.0246812	0.000838216 0
$868$	1.21054	0.0410883
$869$	−29.7271	−1.00842
$870$	−0.0307812	−0.00104358
$871$	−20.5791	−0.697295
$872$	−49.8333	−1.68757
$873$	28.5115	0.964969
$874$	14.2595	0.482334
$875$	0.559759	0.0189233
$876$	0.124489	0.00420610
$877$	51.1104	1.72588	0.862938	−	0.505309i	$-0.168622\pi$
$877$	51.1104	1.72588	0.862938	+	0.505309i	$0.168622\pi$
$878$	6.94633	0.234427
$879$	0.00574340	0.000193720 0
$880$	24.6956	0.832488
$881$	8.53838	0.287665	0.143833	−	0.989602i	$-0.454057\pi$
$881$	8.53838	0.287665	0.143833	+	0.989602i	$0.454057\pi$
$882$	−54.5134	−1.83556
$883$	−32.2224	−1.08437	−0.542185	−	0.840259i	$-0.682403\pi$
$883$	−32.2224	−1.08437	−0.542185	+	0.840259i	$0.682403\pi$
$884$	−53.4037	−1.79616
$885$	0.0193882	0.000651727 0
$886$	92.9545	3.12287
$887$	5.45199	0.183060	0.0915299	−	0.995802i	$-0.470824\pi$
$887$	5.45199	0.183060	0.0915299	+	0.995802i	$0.470824\pi$
$888$	−0.0598000	−0.00200676
$889$	1.04330	0.0349913
$890$	−2.77328	−0.0929606
$891$	41.0116	1.37394
$892$	−95.3265	−3.19177
$893$	−4.18795	−0.140144
$894$	0.191089	0.00639099
$895$	3.31184	0.110703
$896$	−0.279038	−0.00932199
$897$	−0.0382385	−0.00127674
$898$	41.0521	1.36993
$899$	15.3918	0.513345
$900$	66.3101	2.21034
$901$	−27.8776	−0.928737
$902$	−85.4940	−2.84664
$903$	−0.000739940 0	−2.46237e−5 0
$904$	−32.6421	−1.08566
$905$	14.3843	0.478150
$906$	0.00312592	0.000103852 0
$907$	28.9496	0.961256	0.480628	−	0.876924i	$-0.340409\pi$
$907$	28.9496	0.961256	0.480628	+	0.876924i	$0.340409\pi$
$908$	8.38025	0.278108
$909$	−49.8848	−1.65458
$910$	0.544131	0.0180378
$911$	16.5234	0.547443	0.273722	−	0.961809i	$-0.411745\pi$
$911$	16.5234	0.547443	0.273722	+	0.961809i	$0.411745\pi$
$912$	0.0536966	0.00177807
$913$	−74.0092	−2.44935
$914$	−51.0097	−1.68725
$915$	0.00256716	8.48678e−5 0
$916$	14.6949	0.485532
$917$	1.52447	0.0503425
$918$	0.163758	0.00540483
$919$	36.9864	1.22007	0.610034	−	0.792375i	$-0.291156\pi$
$919$	36.9864	1.22007	0.610034	+	0.792375i	$0.291156\pi$
$920$	−13.3868	−0.441349
$921$	0.00576661	0.000190016 0
$922$	9.83081	0.323760
$923$	12.3306	0.405867
$924$	0.00713801	0.000234823 0
$925$	11.4916	0.377842
$926$	55.5406	1.82518
$927$	1.73652	0.0570348
$928$	55.2578	1.81392
$929$	51.7731	1.69862	0.849309	−	0.527895i	$-0.177019\pi$
$929$	51.7731	1.69862	0.849309	+	0.527895i	$0.177019\pi$
$930$	−0.0135957	−0.000445822 0
$931$	12.2057	0.400024
$932$	87.5978	2.86936
$933$	−0.0805729	−0.00263784
$934$	−63.2216	−2.06867
$935$	−8.43145	−0.275738
$936$	77.5584	2.53507
$937$	−34.3503	−1.12218	−0.561088	−	0.827756i	$-0.689617\pi$
$937$	−34.3503	−1.12218	−0.561088	+	0.827756i	$0.689617\pi$
$938$	−1.44727	−0.0472550
$939$	0.0640420	0.00208993
$940$	6.78375	0.221262
$941$	−21.9208	−0.714597	−0.357298	−	0.933990i	$-0.616302\pi$
$941$	−21.9208	−0.714597	−0.357298	+	0.933990i	$0.616302\pi$
$942$	−0.0608640	−0.00198306
$943$	22.6757	0.738423
$944$	−88.0997	−2.86740
$945$	−0.00117467	−3.82119e−5 0
$946$	26.6176	0.865412
$947$	13.6329	0.443009	0.221504	−	0.975159i	$-0.428903\pi$
$947$	13.6329	0.443009	0.221504	+	0.975159i	$0.428903\pi$
$948$	0.104701	0.00340052
$949$	−27.9808	−0.908295
$950$	−21.0891	−0.684221
$951$	0.0747955	0.00242541
$952$	−2.17670	−0.0705472
$953$	−52.4620	−1.69941	−0.849706	−	0.527257i	$-0.823220\pi$
$953$	−52.4620	−1.69941	−0.849706	+	0.527257i	$0.823220\pi$
$954$	69.8568	2.26170
$955$	15.9846	0.517250
$956$	14.9545	0.483665
$957$	0.0907587	0.00293381
$958$	61.1832	1.97674
$959$	0.970592	0.0313420
$960$	−0.0122409	−0.000395072 0
$961$	−24.2016	−0.780697
$962$	23.1914	0.747720
$963$	27.5706	0.888450
$964$	−98.1467	−3.16109
$965$	6.35306	0.204512
$966$	−0.00268920	−8.65237e−5 0
$967$	27.2886	0.877544	0.438772	−	0.898599i	$-0.355414\pi$
$967$	27.2886	0.877544	0.438772	+	0.898599i	$0.355414\pi$
$968$	−69.9844	−2.24938
$969$	−0.0183329	−0.000588937 0
$970$	14.6882	0.471609
$971$	−29.3255	−0.941099	−0.470550	−	0.882374i	$-0.655944\pi$
$971$	−29.3255	−0.941099	−0.470550	+	0.882374i	$0.655944\pi$
$972$	−0.433339	−0.0138994
$973$	−1.83648	−0.0588750
$974$	97.3201	3.11834
$975$	0.0565529	0.00181114
$976$	−11.6652	−0.373393
$977$	−19.2756	−0.616680	−0.308340	−	0.951276i	$-0.599774\pi$
$977$	−19.2756	−0.616680	−0.308340	+	0.951276i	$0.599774\pi$
$978$	−0.120879	−0.00386530
$979$	8.17705	0.261340
$980$	−19.7711	−0.631563
$981$	−20.8605	−0.666025
$982$	−35.5878	−1.13565
$983$	−32.5670	−1.03873	−0.519363	−	0.854554i	$-0.673831\pi$
$983$	−32.5670	−1.03873	−0.519363	+	0.854554i	$0.673831\pi$
$984$	0.174516	0.00556338
$985$	−11.0677	−0.352645
$986$	−47.7536	−1.52078
$987$	0.000789808 0	2.51399e−5 0
$988$	−29.9628	−0.953244
$989$	−7.05983	−0.224490
$990$	21.1279	0.671488
$991$	32.9676	1.04725	0.523625	−	0.851949i	$-0.324579\pi$
$991$	32.9676	1.04725	0.523625	+	0.851949i	$0.324579\pi$
$992$	24.4068	0.774916
$993$	−0.102334	−0.00324747
$994$	0.867178	0.0275052
$995$	−1.38547	−0.0439223
$996$	0.260665	0.00825948
$997$	−18.3017	−0.579621	−0.289810	−	0.957084i	$-0.593592\pi$
$997$	−18.3017	−0.579621	−0.289810	+	0.957084i	$0.593592\pi$
$998$	75.9227	2.40329
$999$	−0.0500654	−0.00158400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3467.2.a.b.1.4	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3467.2.a.b.1.4	✓	126	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3467 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3467.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59942 q^{2} -0.00337391 q^{3} +4.75700 q^{4} +0.594552 q^{5} +0.00877021 q^{6} -0.0975981 q^{7} -7.16662 q^{8} -2.99999 q^{9} -1.54549 q^{10} +4.55690 q^{11} -0.0160497 q^{12} +3.60741 q^{13} +0.253699 q^{14} -0.00200596 q^{15} +9.11506 q^{16} -3.11202 q^{17} +7.79824 q^{18} -1.74604 q^{19} +2.82828 q^{20} +0.000329287 q^{21} -11.8453 q^{22} +3.14176 q^{23} +0.0241795 q^{24} -4.64651 q^{25} -9.37717 q^{26} +0.0202434 q^{27} -0.464274 q^{28} -5.90318 q^{29} +0.00521435 q^{30} -2.60737 q^{31} -9.36068 q^{32} -0.0153746 q^{33} +8.08947 q^{34} -0.0580272 q^{35} -14.2710 q^{36} -2.47317 q^{37} +4.53870 q^{38} -0.0121710 q^{39} -4.26093 q^{40} +7.21754 q^{41} -0.000855956 q^{42} -2.24710 q^{43} +21.6772 q^{44} -1.78365 q^{45} -8.16675 q^{46} +2.39854 q^{47} -0.0307534 q^{48} -6.99047 q^{49} +12.0782 q^{50} +0.0104997 q^{51} +17.1604 q^{52} +8.95802 q^{53} -0.0526212 q^{54} +2.70931 q^{55} +0.699448 q^{56} +0.00589098 q^{57} +15.3449 q^{58} -9.66529 q^{59} -0.00954237 q^{60} -1.27977 q^{61} +6.77766 q^{62} +0.292793 q^{63} +6.10224 q^{64} +2.14479 q^{65} +0.0399650 q^{66} -5.70467 q^{67} -14.8039 q^{68} -0.0106000 q^{69} +0.150837 q^{70} +3.41814 q^{71} +21.4998 q^{72} -7.75648 q^{73} +6.42882 q^{74} +0.0156769 q^{75} -8.30592 q^{76} -0.444745 q^{77} +0.0316377 q^{78} -6.52354 q^{79} +5.41938 q^{80} +8.99990 q^{81} -18.7614 q^{82} -16.2411 q^{83} +0.00156642 q^{84} -1.85026 q^{85} +5.84116 q^{86} +0.0199168 q^{87} -32.6576 q^{88} +1.79443 q^{89} +4.63646 q^{90} -0.352076 q^{91} +14.9453 q^{92} +0.00879703 q^{93} -6.23482 q^{94} -1.03811 q^{95} +0.0315821 q^{96} -9.50388 q^{97} +18.1712 q^{98} -13.6706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) \) 126 * q - 11 * q^2 - 25 * q^3 + 99 * q^4 - 32 * q^5 - 15 * q^6 - 27 * q^7 - 27 * q^8 + 93 * q^9 - 46 * q^10 - 6 * q^11 - 67 * q^12 - 137 * q^13 - 17 * q^14 - 15 * q^15 + 49 * q^16 - 30 * q^17 - 37 * q^18 - 39 * q^19 - 46 * q^20 - 54 * q^21 - 55 * q^22 - 35 * q^23 - 27 * q^24 + 26 * q^25 - 14 * q^26 - 88 * q^27 - 63 * q^28 - 31 * q^29 - 5 * q^30 - 64 * q^31 - 60 * q^32 - 100 * q^33 - 47 * q^34 - 38 * q^35 + 44 * q^36 - 148 * q^37 - 51 * q^38 + 7 * q^39 - 128 * q^40 - 28 * q^41 - 38 * q^42 - 68 * q^43 - 8 * q^44 - 137 * q^45 - 43 * q^46 - 51 * q^47 - 117 * q^48 + 3 * q^49 - 8 * q^50 - 30 * q^51 - 232 * q^52 - 112 * q^53 - 30 * q^54 - 96 * q^55 - 28 * q^56 - 47 * q^57 - 74 * q^58 - 38 * q^59 - 22 * q^60 - 124 * q^61 - 49 * q^62 - 69 * q^63 - 37 * q^64 - 13 * q^65 - 34 * q^66 - 125 * q^67 - 40 * q^68 - 150 * q^69 - 81 * q^70 - 26 * q^71 - 97 * q^72 - 154 * q^73 + 8 * q^74 - 80 * q^75 - 66 * q^76 - 130 * q^77 - 33 * q^78 - 45 * q^79 - 21 * q^80 + 22 * q^81 - 145 * q^82 - 63 * q^83 - 55 * q^84 - 134 * q^85 - 27 * q^86 - 87 * q^87 - 131 * q^88 - 47 * q^89 - 46 * q^90 - 56 * q^91 - 52 * q^92 - 130 * q^93 - 63 * q^94 + q^95 - 15 * q^96 - 204 * q^97 + 4 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more