LMFDB - Embedded newform 6033.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96725 q^{2} +1.00000 q^{3} +1.87006 q^{4} -1.28401 q^{5} -1.96725 q^{6} +2.13094 q^{7} +0.255618 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.96725 q^{2} +1.00000 q^{3} +1.87006 q^{4} -1.28401 q^{5} -1.96725 q^{6} +2.13094 q^{7} +0.255618 q^{8} +1.00000 q^{9} +2.52597 q^{10} -4.92133 q^{11} +1.87006 q^{12} +5.93739 q^{13} -4.19209 q^{14} -1.28401 q^{15} -4.24299 q^{16} +4.74126 q^{17} -1.96725 q^{18} +5.50171 q^{19} -2.40119 q^{20} +2.13094 q^{21} +9.68147 q^{22} +9.37074 q^{23} +0.255618 q^{24} -3.35131 q^{25} -11.6803 q^{26} +1.00000 q^{27} +3.98499 q^{28} +6.47961 q^{29} +2.52597 q^{30} +5.54915 q^{31} +7.83578 q^{32} -4.92133 q^{33} -9.32723 q^{34} -2.73616 q^{35} +1.87006 q^{36} +5.29454 q^{37} -10.8232 q^{38} +5.93739 q^{39} -0.328217 q^{40} +3.19533 q^{41} -4.19209 q^{42} +5.27370 q^{43} -9.20319 q^{44} -1.28401 q^{45} -18.4346 q^{46} -7.13338 q^{47} -4.24299 q^{48} -2.45910 q^{49} +6.59285 q^{50} +4.74126 q^{51} +11.1033 q^{52} -10.9987 q^{53} -1.96725 q^{54} +6.31905 q^{55} +0.544706 q^{56} +5.50171 q^{57} -12.7470 q^{58} -4.51669 q^{59} -2.40119 q^{60} +4.89792 q^{61} -10.9165 q^{62} +2.13094 q^{63} -6.92893 q^{64} -7.62369 q^{65} +9.68147 q^{66} +14.2719 q^{67} +8.86645 q^{68} +9.37074 q^{69} +5.38270 q^{70} -10.8668 q^{71} +0.255618 q^{72} -4.30253 q^{73} -10.4157 q^{74} -3.35131 q^{75} +10.2885 q^{76} -10.4871 q^{77} -11.6803 q^{78} -2.87862 q^{79} +5.44806 q^{80} +1.00000 q^{81} -6.28600 q^{82} -13.3107 q^{83} +3.98499 q^{84} -6.08784 q^{85} -10.3747 q^{86} +6.47961 q^{87} -1.25798 q^{88} +7.63559 q^{89} +2.52597 q^{90} +12.6522 q^{91} +17.5239 q^{92} +5.54915 q^{93} +14.0331 q^{94} -7.06427 q^{95} +7.83578 q^{96} -14.4642 q^{97} +4.83765 q^{98} -4.92133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−1.96725	−1.39105	−0.695527	−	0.718500i	$-0.744829\pi$
$2$	−1.96725	−1.39105	−0.695527	+	0.718500i	$0.744829\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.87006	0.935032
$5$	−1.28401	−0.574229	−0.287114	−	0.957896i	$-0.592696\pi$
$5$	−1.28401	−0.574229	−0.287114	+	0.957896i	$0.592696\pi$
$6$	−1.96725	−0.803125
$7$	2.13094	0.805419	0.402710	−	0.915328i	$-0.368068\pi$
$7$	2.13094	0.805419	0.402710	+	0.915328i	$0.368068\pi$
$8$	0.255618	0.0903745
$9$	1.00000	0.333333
$10$	2.52597	0.798783
$11$	−4.92133	−1.48384	−0.741918	−	0.670491i	$-0.766084\pi$
$11$	−4.92133	−1.48384	−0.741918	+	0.670491i	$0.766084\pi$
$12$	1.87006	0.539841
$13$	5.93739	1.64674	0.823368	−	0.567508i	$-0.192093\pi$
$13$	5.93739	1.64674	0.823368	+	0.567508i	$0.192093\pi$
$14$	−4.19209	−1.12038
$15$	−1.28401	−0.331531
$16$	−4.24299	−1.06075
$17$	4.74126	1.14992	0.574962	−	0.818180i	$-0.305017\pi$
$17$	4.74126	1.14992	0.574962	+	0.818180i	$0.305017\pi$
$18$	−1.96725	−0.463685
$19$	5.50171	1.26218	0.631089	−	0.775710i	$-0.282608\pi$
$19$	5.50171	1.26218	0.631089	+	0.775710i	$0.282608\pi$
$20$	−2.40119	−0.536922
$21$	2.13094	0.465009
$22$	9.68147	2.06410
$23$	9.37074	1.95394	0.976968	−	0.213387i	$-0.0684496\pi$
$23$	9.37074	1.95394	0.976968	+	0.213387i	$0.0684496\pi$
$24$	0.255618	0.0521777
$25$	−3.35131	−0.670261
$26$	−11.6803	−2.29070
$27$	1.00000	0.192450
$28$	3.98499	0.753093
$29$	6.47961	1.20323	0.601617	−	0.798785i	$-0.294523\pi$
$29$	6.47961	1.20323	0.601617	+	0.798785i	$0.294523\pi$
$30$	2.52597	0.461178
$31$	5.54915	0.996656	0.498328	−	0.866988i	$-0.333947\pi$
$31$	5.54915	0.996656	0.498328	+	0.866988i	$0.333947\pi$
$32$	7.83578	1.38518
$33$	−4.92133	−0.856693
$34$	−9.32723	−1.59961
$35$	−2.73616	−0.462495
$36$	1.87006	0.311677
$37$	5.29454	0.870417	0.435208	−	0.900330i	$-0.356675\pi$
$37$	5.29454	0.870417	0.435208	+	0.900330i	$0.356675\pi$
$38$	−10.8232	−1.75576
$39$	5.93739	0.950743
$40$	−0.328217	−0.0518956
$41$	3.19533	0.499027	0.249513	−	0.968371i	$-0.419729\pi$
$41$	3.19533	0.499027	0.249513	+	0.968371i	$0.419729\pi$
$42$	−4.19209	−0.646853
$43$	5.27370	0.804232	0.402116	−	0.915589i	$-0.368275\pi$
$43$	5.27370	0.804232	0.402116	+	0.915589i	$0.368275\pi$
$44$	−9.20319	−1.38743
$45$	−1.28401	−0.191410
$46$	−18.4346	−2.71803
$47$	−7.13338	−1.04051	−0.520255	−	0.854011i	$-0.674163\pi$
$47$	−7.13338	−1.04051	−0.520255	+	0.854011i	$0.674163\pi$
$48$	−4.24299	−0.612423
$49$	−2.45910	−0.351299
$50$	6.59285	0.932370
$51$	4.74126	0.663909
$52$	11.1033	1.53975
$53$	−10.9987	−1.51079	−0.755393	−	0.655272i	$-0.772554\pi$
$53$	−10.9987	−1.51079	−0.755393	+	0.655272i	$0.772554\pi$
$54$	−1.96725	−0.267708
$55$	6.31905	0.852061
$56$	0.544706	0.0727893
$57$	5.50171	0.728719
$58$	−12.7470	−1.67376
$59$	−4.51669	−0.588023	−0.294011	−	0.955802i	$-0.594990\pi$
$59$	−4.51669	−0.588023	−0.294011	+	0.955802i	$0.594990\pi$
$60$	−2.40119	−0.309992
$61$	4.89792	0.627114	0.313557	−	0.949569i	$-0.398479\pi$
$61$	4.89792	0.627114	0.313557	+	0.949569i	$0.398479\pi$
$62$	−10.9165	−1.38640
$63$	2.13094	0.268473
$64$	−6.92893	−0.866117
$65$	−7.62369	−0.945603
$66$	9.68147	1.19171
$67$	14.2719	1.74359	0.871797	−	0.489867i	$-0.162954\pi$
$67$	14.2719	1.74359	0.871797	+	0.489867i	$0.162954\pi$
$68$	8.86645	1.07522
$69$	9.37074	1.12811
$70$	5.38270	0.643356
$71$	−10.8668	−1.28965	−0.644824	−	0.764331i	$-0.723069\pi$
$71$	−10.8668	−1.28965	−0.644824	+	0.764331i	$0.723069\pi$
$72$	0.255618	0.0301248
$73$	−4.30253	−0.503573	−0.251786	−	0.967783i	$-0.581018\pi$
$73$	−4.30253	−0.503573	−0.251786	+	0.967783i	$0.581018\pi$
$74$	−10.4157	−1.21080
$75$	−3.35131	−0.386976
$76$	10.2885	1.18018
$77$	−10.4871	−1.19511
$78$	−11.6803	−1.32254
$79$	−2.87862	−0.323870	−0.161935	−	0.986801i	$-0.551774\pi$
$79$	−2.87862	−0.323870	−0.161935	+	0.986801i	$0.551774\pi$
$80$	5.44806	0.609112
$81$	1.00000	0.111111
$82$	−6.28600	−0.694173
$83$	−13.3107	−1.46104	−0.730522	−	0.682889i	$-0.760723\pi$
$83$	−13.3107	−1.46104	−0.730522	+	0.682889i	$0.760723\pi$
$84$	3.98499	0.434798
$85$	−6.08784	−0.660319
$86$	−10.3747	−1.11873
$87$	6.47961	0.694687
$88$	−1.25798	−0.134101
$89$	7.63559	0.809371	0.404686	−	0.914456i	$-0.367381\pi$
$89$	7.63559	0.809371	0.404686	+	0.914456i	$0.367381\pi$
$90$	2.52597	0.266261
$91$	12.6522	1.32631
$92$	17.5239	1.82699
$93$	5.54915	0.575420
$94$	14.0331	1.44741
$95$	−7.06427	−0.724779
$96$	7.83578	0.799736
$97$	−14.4642	−1.46861	−0.734306	−	0.678819i	$-0.762492\pi$
$97$	−14.4642	−1.46861	−0.734306	+	0.678819i	$0.762492\pi$
$98$	4.83765	0.488677
$99$	−4.92133	−0.494612
$100$	−6.26716	−0.626716
$101$	−9.69505	−0.964693	−0.482347	−	0.875980i	$-0.660215\pi$
$101$	−9.69505	−0.964693	−0.482347	+	0.875980i	$0.660215\pi$
$102$	−9.32723	−0.923533
$103$	3.91741	0.385994	0.192997	−	0.981199i	$-0.438179\pi$
$103$	3.91741	0.385994	0.192997	+	0.981199i	$0.438179\pi$
$104$	1.51770	0.148823
$105$	−2.73616	−0.267022
$106$	21.6372	2.10159
$107$	16.8261	1.62664	0.813319	−	0.581818i	$-0.197658\pi$
$107$	16.8261	1.62664	0.813319	+	0.581818i	$0.197658\pi$
$108$	1.87006	0.179947
$109$	17.5506	1.68104	0.840519	−	0.541781i	$-0.182250\pi$
$109$	17.5506	1.68104	0.840519	+	0.541781i	$0.182250\pi$
$110$	−12.4311	−1.18526
$111$	5.29454	0.502535
$112$	−9.04156	−0.854347
$113$	5.64515	0.531051	0.265526	−	0.964104i	$-0.414455\pi$
$113$	5.64515	0.531051	0.265526	+	0.964104i	$0.414455\pi$
$114$	−10.8232	−1.01369
$115$	−12.0322	−1.12201
$116$	12.1173	1.12506
$117$	5.93739	0.548912
$118$	8.88545	0.817972
$119$	10.1033	0.926171
$120$	−0.328217	−0.0299619
$121$	13.2195	1.20177
$122$	−9.63542	−0.872350
$123$	3.19533	0.288113
$124$	10.3773	0.931905
$125$	10.7232	0.959112
$126$	−4.19209	−0.373461
$127$	−13.0842	−1.16104	−0.580519	−	0.814246i	$-0.697150\pi$
$127$	−13.0842	−1.16104	−0.580519	+	0.814246i	$0.697150\pi$
$128$	−2.04062	−0.180367
$129$	5.27370	0.464324
$130$	14.9977	1.31538
$131$	−4.68863	−0.409648	−0.204824	−	0.978799i	$-0.565662\pi$
$131$	−4.68863	−0.409648	−0.204824	+	0.978799i	$0.565662\pi$
$132$	−9.20319	−0.801035
$133$	11.7238	1.01658
$134$	−28.0764	−2.42543
$135$	−1.28401	−0.110510
$136$	1.21195	0.103924
$137$	1.24765	0.106594	0.0532971	−	0.998579i	$-0.483027\pi$
$137$	1.24765	0.106594	0.0532971	+	0.998579i	$0.483027\pi$
$138$	−18.4346	−1.56926
$139$	−18.2254	−1.54586	−0.772929	−	0.634492i	$-0.781209\pi$
$139$	−18.2254	−1.54586	−0.772929	+	0.634492i	$0.781209\pi$
$140$	−5.11679	−0.432447
$141$	−7.13338	−0.600739
$142$	21.3776	1.79397
$143$	−29.2198	−2.44348
$144$	−4.24299	−0.353582
$145$	−8.31991	−0.690931
$146$	8.46413	0.700497
$147$	−2.45910	−0.202823
$148$	9.90112	0.813867
$149$	16.0876	1.31795	0.658974	−	0.752165i	$-0.270991\pi$
$149$	16.0876	1.31795	0.658974	+	0.752165i	$0.270991\pi$
$150$	6.59285	0.538304
$151$	12.8866	1.04869	0.524347	−	0.851505i	$-0.324309\pi$
$151$	12.8866	1.04869	0.524347	+	0.851505i	$0.324309\pi$
$152$	1.40633	0.114069
$153$	4.74126	0.383308
$154$	20.6306	1.66246
$155$	−7.12519	−0.572309
$156$	11.1033	0.888975
$157$	−0.804570	−0.0642117	−0.0321058	−	0.999484i	$-0.510221\pi$
$157$	−0.804570	−0.0642117	−0.0321058	+	0.999484i	$0.510221\pi$
$158$	5.66297	0.450521
$159$	−10.9987	−0.872253
$160$	−10.0612	−0.795412
$161$	19.9685	1.57374
$162$	−1.96725	−0.154562
$163$	12.4238	0.973107	0.486553	−	0.873651i	$-0.338254\pi$
$163$	12.4238	0.973107	0.486553	+	0.873651i	$0.338254\pi$
$164$	5.97547	0.466606
$165$	6.31905	0.491938
$166$	26.1855	2.03239
$167$	−12.3171	−0.953130	−0.476565	−	0.879139i	$-0.658118\pi$
$167$	−12.3171	−0.953130	−0.476565	+	0.879139i	$0.658118\pi$
$168$	0.544706	0.0420249
$169$	22.2526	1.71174
$170$	11.9763	0.918540
$171$	5.50171	0.420726
$172$	9.86216	0.751982
$173$	−22.0132	−1.67363	−0.836816	−	0.547484i	$-0.815586\pi$
$173$	−22.0132	−1.67363	−0.836816	+	0.547484i	$0.815586\pi$
$174$	−12.7470	−0.966348
$175$	−7.14143	−0.539842
$176$	20.8811	1.57398
$177$	−4.51669	−0.339495
$178$	−15.0211	−1.12588
$179$	−23.1025	−1.72676	−0.863379	−	0.504555i	$-0.831656\pi$
$179$	−23.1025	−1.72676	−0.863379	+	0.504555i	$0.831656\pi$
$180$	−2.40119	−0.178974
$181$	4.95235	0.368105	0.184053	−	0.982916i	$-0.441078\pi$
$181$	4.95235	0.368105	0.184053	+	0.982916i	$0.441078\pi$
$182$	−24.8900	−1.84497
$183$	4.89792	0.362065
$184$	2.39533	0.176586
$185$	−6.79826	−0.499818
$186$	−10.9165	−0.800440
$187$	−23.3333	−1.70630
$188$	−13.3399	−0.972910
$189$	2.13094	0.155003
$190$	13.8972	1.00821
$191$	12.1593	0.879817	0.439909	−	0.898043i	$-0.355011\pi$
$191$	12.1593	0.879817	0.439909	+	0.898043i	$0.355011\pi$
$192$	−6.92893	−0.500053
$193$	−10.6535	−0.766858	−0.383429	−	0.923570i	$-0.625257\pi$
$193$	−10.6535	−0.766858	−0.383429	+	0.923570i	$0.625257\pi$
$194$	28.4546	2.04292
$195$	−7.62369	−0.545944
$196$	−4.59867	−0.328476
$197$	−13.9199	−0.991752	−0.495876	−	0.868393i	$-0.665153\pi$
$197$	−13.9199	−0.991752	−0.495876	+	0.868393i	$0.665153\pi$
$198$	9.68147	0.688032
$199$	4.07007	0.288520	0.144260	−	0.989540i	$-0.453920\pi$
$199$	4.07007	0.288520	0.144260	+	0.989540i	$0.453920\pi$
$200$	−0.856653	−0.0605745
$201$	14.2719	1.00666
$202$	19.0726	1.34194
$203$	13.8077	0.969108
$204$	8.86645	0.620776
$205$	−4.10285	−0.286555
$206$	−7.70651	−0.536938
$207$	9.37074	0.651312
$208$	−25.1923	−1.74677
$209$	−27.0757	−1.87287
$210$	5.38270	0.371441
$211$	1.34409	0.0925310	0.0462655	−	0.998929i	$-0.485268\pi$
$211$	1.34409	0.0925310	0.0462655	+	0.998929i	$0.485268\pi$
$212$	−20.5683	−1.41263
$213$	−10.8668	−0.744579
$214$	−33.1011	−2.26274
$215$	−6.77151	−0.461813
$216$	0.255618	0.0173926
$217$	11.8249	0.802727
$218$	−34.5263	−2.33842
$219$	−4.30253	−0.290738
$220$	11.8170	0.796704
$221$	28.1507	1.89362
$222$	−10.4157	−0.699054
$223$	−11.6712	−0.781561	−0.390780	−	0.920484i	$-0.627795\pi$
$223$	−11.6712	−0.781561	−0.390780	+	0.920484i	$0.627795\pi$
$224$	16.6976	1.11565
$225$	−3.35131	−0.223420
$226$	−11.1054	−0.738721
$227$	8.57585	0.569199	0.284599	−	0.958647i	$-0.408139\pi$
$227$	8.57585	0.569199	0.284599	+	0.958647i	$0.408139\pi$
$228$	10.2885	0.681375
$229$	−5.65131	−0.373449	−0.186725	−	0.982412i	$-0.559787\pi$
$229$	−5.65131	−0.373449	−0.186725	+	0.982412i	$0.559787\pi$
$230$	23.6703	1.56077
$231$	−10.4871	−0.689997
$232$	1.65630	0.108742
$233$	8.99454	0.589252	0.294626	−	0.955613i	$-0.404805\pi$
$233$	8.99454	0.589252	0.294626	+	0.955613i	$0.404805\pi$
$234$	−11.6803	−0.763566
$235$	9.15936	0.597491
$236$	−8.44649	−0.549820
$237$	−2.87862	−0.186987
$238$	−19.8758	−1.28835
$239$	−15.4438	−0.998975	−0.499488	−	0.866321i	$-0.666478\pi$
$239$	−15.4438	−0.998975	−0.499488	+	0.866321i	$0.666478\pi$
$240$	5.44806	0.351671
$241$	−10.8764	−0.700609	−0.350305	−	0.936636i	$-0.613922\pi$
$241$	−10.8764	−0.700609	−0.350305	+	0.936636i	$0.613922\pi$
$242$	−26.0059	−1.67173
$243$	1.00000	0.0641500
$244$	9.15942	0.586372
$245$	3.15751	0.201726
$246$	−6.28600	−0.400781
$247$	32.6658	2.07847
$248$	1.41846	0.0900723
$249$	−13.3107	−0.843535
$250$	−21.0952	−1.33418
$251$	14.1205	0.891280	0.445640	−	0.895212i	$-0.352976\pi$
$251$	14.1205	0.891280	0.445640	+	0.895212i	$0.352976\pi$
$252$	3.98499	0.251031
$253$	−46.1165	−2.89932
$254$	25.7399	1.61507
$255$	−6.08784	−0.381235
$256$	17.8723	1.11702
$257$	5.68277	0.354482	0.177241	−	0.984168i	$-0.443283\pi$
$257$	5.68277	0.354482	0.177241	+	0.984168i	$0.443283\pi$
$258$	−10.3747	−0.645899
$259$	11.2823	0.701051
$260$	−14.2568	−0.884168
$261$	6.47961	0.401078
$262$	9.22370	0.569842
$263$	11.6337	0.717365	0.358683	−	0.933460i	$-0.383226\pi$
$263$	11.6337	0.717365	0.358683	+	0.933460i	$0.383226\pi$
$264$	−1.25798	−0.0774232
$265$	14.1225	0.867537
$266$	−23.0636	−1.41412
$267$	7.63559	0.467291
$268$	26.6894	1.63032
$269$	−5.01930	−0.306032	−0.153016	−	0.988224i	$-0.548899\pi$
$269$	−5.01930	−0.306032	−0.153016	+	0.988224i	$0.548899\pi$
$270$	2.52597	0.153726
$271$	−8.92544	−0.542182	−0.271091	−	0.962554i	$-0.587384\pi$
$271$	−8.92544	−0.542182	−0.271091	+	0.962554i	$0.587384\pi$
$272$	−20.1171	−1.21978
$273$	12.6522	0.765747
$274$	−2.45444	−0.148278
$275$	16.4929	0.994558
$276$	17.5239	1.05481
$277$	−29.2039	−1.75469	−0.877347	−	0.479857i	$-0.840688\pi$
$277$	−29.2039	−1.75469	−0.877347	+	0.479857i	$0.840688\pi$
$278$	35.8539	2.15037
$279$	5.54915	0.332219
$280$	−0.699410	−0.0417977
$281$	5.18344	0.309218	0.154609	−	0.987976i	$-0.450588\pi$
$281$	5.18344	0.309218	0.154609	+	0.987976i	$0.450588\pi$
$282$	14.0331	0.835660
$283$	19.2475	1.14415	0.572074	−	0.820202i	$-0.306139\pi$
$283$	19.2475	1.14415	0.572074	+	0.820202i	$0.306139\pi$
$284$	−20.3216	−1.20586
$285$	−7.06427	−0.418451
$286$	57.4826	3.39902
$287$	6.80905	0.401926
$288$	7.83578	0.461728
$289$	5.47952	0.322325
$290$	16.3673	0.961123
$291$	−14.4642	−0.847904
$292$	−8.04600	−0.470856
$293$	19.2823	1.12649	0.563243	−	0.826292i	$-0.309554\pi$
$293$	19.2823	1.12649	0.563243	+	0.826292i	$0.309554\pi$
$294$	4.83765	0.282138
$295$	5.79949	0.337660
$296$	1.35338	0.0786635
$297$	−4.92133	−0.285564
$298$	−31.6483	−1.83334
$299$	55.6377	3.21761
$300$	−6.26716	−0.361834
$301$	11.2379	0.647744
$302$	−25.3511	−1.45879
$303$	−9.69505	−0.556966
$304$	−23.3437	−1.33885
$305$	−6.28900	−0.360107
$306$	−9.32723	−0.533202
$307$	22.8699	1.30525	0.652627	−	0.757679i	$-0.273667\pi$
$307$	22.8699	1.30525	0.652627	+	0.757679i	$0.273667\pi$
$308$	−19.6114	−1.11747
$309$	3.91741	0.222853
$310$	14.0170	0.796112
$311$	28.7331	1.62931	0.814653	−	0.579948i	$-0.196927\pi$
$311$	28.7331	1.62931	0.814653	+	0.579948i	$0.196927\pi$
$312$	1.51770	0.0859229
$313$	−0.114470	−0.00647024	−0.00323512	−	0.999995i	$-0.501030\pi$
$313$	−0.114470	−0.00647024	−0.00323512	+	0.999995i	$0.501030\pi$
$314$	1.58279	0.0893219
$315$	−2.73616	−0.154165
$316$	−5.38321	−0.302829
$317$	−0.0321563	−0.00180608	−0.000903040	−	1.00000i	$-0.500287\pi$
$317$	−0.0321563	−0.00180608	−0.000903040		1.00000i	$0.500287\pi$
$318$	21.6372	1.21335
$319$	−31.8883	−1.78540
$320$	8.89685	0.497349
$321$	16.8261	0.939140
$322$	−39.2830	−2.18915
$323$	26.0850	1.45141
$324$	1.87006	0.103892
$325$	−19.8980	−1.10374
$326$	−24.4407	−1.35364
$327$	17.5506	0.970548
$328$	0.816782	0.0450993
$329$	−15.2008	−0.838047
$330$	−12.4311	−0.684312
$331$	34.2098	1.88034	0.940172	−	0.340701i	$-0.110664\pi$
$331$	34.2098	1.88034	0.940172	+	0.340701i	$0.110664\pi$
$332$	−24.8919	−1.36612
$333$	5.29454	0.290139
$334$	24.2309	1.32585
$335$	−18.3254	−1.00122
$336$	−9.04156	−0.493257
$337$	8.21696	0.447606	0.223803	−	0.974634i	$-0.428153\pi$
$337$	8.21696	0.447606	0.223803	+	0.974634i	$0.428153\pi$
$338$	−43.7763	−2.38112
$339$	5.64515	0.306603
$340$	−11.3847	−0.617419
$341$	−27.3092	−1.47887
$342$	−10.8232	−0.585253
$343$	−20.1568	−1.08836
$344$	1.34805	0.0726820
$345$	−12.0322	−0.647790
$346$	43.3054	2.32811
$347$	11.3547	0.609554	0.304777	−	0.952424i	$-0.401418\pi$
$347$	11.3547	0.609554	0.304777	+	0.952424i	$0.401418\pi$
$348$	12.1173	0.649555
$349$	−24.1323	−1.29177	−0.645887	−	0.763433i	$-0.723512\pi$
$349$	−24.1323	−1.29177	−0.645887	+	0.763433i	$0.723512\pi$
$350$	14.0490	0.750949
$351$	5.93739	0.316914
$352$	−38.5624	−2.05538
$353$	−24.4909	−1.30352	−0.651759	−	0.758426i	$-0.725969\pi$
$353$	−24.4909	−1.30352	−0.651759	+	0.758426i	$0.725969\pi$
$354$	8.88545	0.472256
$355$	13.9531	0.740553
$356$	14.2790	0.756788
$357$	10.1033	0.534725
$358$	45.4483	2.40201
$359$	−10.1909	−0.537853	−0.268926	−	0.963161i	$-0.586669\pi$
$359$	−10.1909	−0.537853	−0.268926	+	0.963161i	$0.586669\pi$
$360$	−0.328217	−0.0172985
$361$	11.2688	0.593094
$362$	−9.74250	−0.512054
$363$	13.2195	0.693841
$364$	23.6604	1.24014
$365$	5.52451	0.289166
$366$	−9.63542	−0.503651
$367$	18.7643	0.979490	0.489745	−	0.871866i	$-0.337090\pi$
$367$	18.7643	0.979490	0.489745	+	0.871866i	$0.337090\pi$
$368$	−39.7600	−2.07263
$369$	3.19533	0.166342
$370$	13.3739	0.695274
$371$	−23.4376	−1.21682
$372$	10.3773	0.538036
$373$	−31.9360	−1.65358	−0.826792	−	0.562507i	$-0.809837\pi$
$373$	−31.9360	−1.65358	−0.826792	+	0.562507i	$0.809837\pi$
$374$	45.9023	2.37355
$375$	10.7232	0.553744
$376$	−1.82342	−0.0940356
$377$	38.4720	1.98141
$378$	−4.19209	−0.215618
$379$	10.3671	0.532523	0.266261	−	0.963901i	$-0.414212\pi$
$379$	10.3671	0.532523	0.266261	+	0.963901i	$0.414212\pi$
$380$	−13.2106	−0.677691
$381$	−13.0842	−0.670326
$382$	−23.9204	−1.22387
$383$	−19.6525	−1.00420	−0.502098	−	0.864811i	$-0.667438\pi$
$383$	−19.6525	−1.00420	−0.502098	+	0.864811i	$0.667438\pi$
$384$	−2.04062	−0.104135
$385$	13.4655	0.686267
$386$	20.9581	1.06674
$387$	5.27370	0.268077
$388$	−27.0489	−1.37320
$389$	29.7647	1.50913	0.754565	−	0.656225i	$-0.227848\pi$
$389$	29.7647	1.50913	0.754565	+	0.656225i	$0.227848\pi$
$390$	14.9977	0.759438
$391$	44.4291	2.24688
$392$	−0.628588	−0.0317485
$393$	−4.68863	−0.236510
$394$	27.3839	1.37958
$395$	3.69619	0.185976
$396$	−9.20319	−0.462478
$397$	−30.1934	−1.51536	−0.757681	−	0.652626i	$-0.773668\pi$
$397$	−30.1934	−1.51536	−0.757681	+	0.652626i	$0.773668\pi$
$398$	−8.00684	−0.401346
$399$	11.7238	0.586924
$400$	14.2196	0.710978
$401$	34.0603	1.70089	0.850444	−	0.526065i	$-0.176333\pi$
$401$	34.0603	1.70089	0.850444	+	0.526065i	$0.176333\pi$
$402$	−28.0764	−1.40033
$403$	32.9474	1.64123
$404$	−18.1304	−0.902019
$405$	−1.28401	−0.0638032
$406$	−27.1631	−1.34808
$407$	−26.0562	−1.29156
$408$	1.21195	0.0600004
$409$	−22.2409	−1.09974	−0.549872	−	0.835249i	$-0.685324\pi$
$409$	−22.2409	−1.09974	−0.549872	+	0.835249i	$0.685324\pi$
$410$	8.07132	0.398614
$411$	1.24765	0.0615422
$412$	7.32580	0.360916
$413$	−9.62479	−0.473605
$414$	−18.4346	−0.906010
$415$	17.0912	0.838974
$416$	46.5240	2.28103
$417$	−18.2254	−0.892502
$418$	53.2646	2.60526
$419$	−37.6854	−1.84105	−0.920527	−	0.390679i	$-0.872240\pi$
$419$	−37.6854	−1.84105	−0.920527	+	0.390679i	$0.872240\pi$
$420$	−5.11679	−0.249674
$421$	−13.9296	−0.678887	−0.339443	−	0.940627i	$-0.610239\pi$
$421$	−13.9296	−0.678887	−0.339443	+	0.940627i	$0.610239\pi$
$422$	−2.64416	−0.128716
$423$	−7.13338	−0.346837
$424$	−2.81146	−0.136537
$425$	−15.8894	−0.770750
$426$	21.3776	1.03575
$427$	10.4372	0.505090
$428$	31.4658	1.52096
$429$	−29.2198	−1.41075
$430$	13.3212	0.642407
$431$	−17.7896	−0.856897	−0.428448	−	0.903566i	$-0.640940\pi$
$431$	−17.7896	−0.856897	−0.428448	+	0.903566i	$0.640940\pi$
$432$	−4.24299	−0.204141
$433$	1.75231	0.0842106	0.0421053	−	0.999113i	$-0.486594\pi$
$433$	1.75231	0.0842106	0.0421053	+	0.999113i	$0.486594\pi$
$434$	−23.2625	−1.11664
$435$	−8.31991	−0.398909
$436$	32.8207	1.57182
$437$	51.5551	2.46621
$438$	8.46413	0.404432
$439$	0.336466	0.0160587	0.00802933	−	0.999968i	$-0.497444\pi$
$439$	0.336466	0.0160587	0.00802933	+	0.999968i	$0.497444\pi$
$440$	1.61526	0.0770046
$441$	−2.45910	−0.117100
$442$	−55.3794	−2.63413
$443$	−14.5731	−0.692390	−0.346195	−	0.938163i	$-0.612526\pi$
$443$	−14.5731	−0.692390	−0.346195	+	0.938163i	$0.612526\pi$
$444$	9.90112	0.469887
$445$	−9.80421	−0.464764
$446$	22.9601	1.08719
$447$	16.0876	0.760918
$448$	−14.7651	−0.697587
$449$	7.27330	0.343248	0.171624	−	0.985163i	$-0.445099\pi$
$449$	7.27330	0.343248	0.171624	+	0.985163i	$0.445099\pi$
$450$	6.59285	0.310790
$451$	−15.7253	−0.740473
$452$	10.5568	0.496550
$453$	12.8866	0.605464
$454$	−16.8708	−0.791787
$455$	−16.2456	−0.761607
$456$	1.40633	0.0658576
$457$	8.98115	0.420121	0.210060	−	0.977688i	$-0.432634\pi$
$457$	8.98115	0.420121	0.210060	+	0.977688i	$0.432634\pi$
$458$	11.1175	0.519488
$459$	4.74126	0.221303
$460$	−22.5009	−1.04911
$461$	−24.3020	−1.13186	−0.565928	−	0.824455i	$-0.691482\pi$
$461$	−24.3020	−1.13186	−0.565928	+	0.824455i	$0.691482\pi$
$462$	20.6306	0.959824
$463$	−6.35005	−0.295112	−0.147556	−	0.989054i	$-0.547141\pi$
$463$	−6.35005	−0.295112	−0.147556	+	0.989054i	$0.547141\pi$
$464$	−27.4929	−1.27633
$465$	−7.12519	−0.330423
$466$	−17.6945	−0.819681
$467$	−4.47445	−0.207053	−0.103526	−	0.994627i	$-0.533013\pi$
$467$	−4.47445	−0.207053	−0.103526	+	0.994627i	$0.533013\pi$
$468$	11.1033	0.513250
$469$	30.4126	1.40433
$470$	−18.0187	−0.831142
$471$	−0.804570	−0.0370726
$472$	−1.15454	−0.0531422
$473$	−25.9536	−1.19335
$474$	5.66297	0.260109
$475$	−18.4379	−0.845989
$476$	18.8939	0.865999
$477$	−10.9987	−0.503596
$478$	30.3818	1.38963
$479$	17.2657	0.788891	0.394446	−	0.918919i	$-0.370937\pi$
$479$	17.2657	0.788891	0.394446	+	0.918919i	$0.370937\pi$
$480$	−10.0612	−0.459231
$481$	31.4357	1.43335
$482$	21.3965	0.974585
$483$	19.9685	0.908598
$484$	24.7212	1.12369
$485$	18.5722	0.843319
$486$	−1.96725	−0.0892362
$487$	−16.9240	−0.766898	−0.383449	−	0.923562i	$-0.625264\pi$
$487$	−16.9240	−0.766898	−0.383449	+	0.923562i	$0.625264\pi$
$488$	1.25199	0.0566751
$489$	12.4238	0.561823
$490$	−6.21161	−0.280612
$491$	−31.2926	−1.41222	−0.706108	−	0.708104i	$-0.749551\pi$
$491$	−31.2926	−1.41222	−0.706108	+	0.708104i	$0.749551\pi$
$492$	5.97547	0.269395
$493$	30.7215	1.38363
$494$	−64.2617	−2.89127
$495$	6.31905	0.284020
$496$	−23.5450	−1.05720
$497$	−23.1564	−1.03871
$498$	26.1855	1.17340
$499$	24.0906	1.07844	0.539221	−	0.842164i	$-0.318719\pi$
$499$	24.0906	1.07844	0.539221	+	0.842164i	$0.318719\pi$
$500$	20.0531	0.896800
$501$	−12.3171	−0.550290
$502$	−27.7786	−1.23982
$503$	1.83122	0.0816501	0.0408250	−	0.999166i	$-0.487001\pi$
$503$	1.83122	0.0816501	0.0408250	+	0.999166i	$0.487001\pi$
$504$	0.544706	0.0242631
$505$	12.4486	0.553955
$506$	90.7226	4.03311
$507$	22.2526	0.988272
$508$	−24.4684	−1.08561
$509$	−1.37213	−0.0608188	−0.0304094	−	0.999538i	$-0.509681\pi$
$509$	−1.37213	−0.0608188	−0.0304094	+	0.999538i	$0.509681\pi$
$510$	11.9763	0.530319
$511$	−9.16842	−0.405587
$512$	−31.0780	−1.37346
$513$	5.50171	0.242906
$514$	−11.1794	−0.493103
$515$	−5.03001	−0.221649
$516$	9.86216	0.434157
$517$	35.1057	1.54395
$518$	−22.1952	−0.975200
$519$	−22.0132	−0.966272
$520$	−1.94875	−0.0854583
$521$	32.2186	1.41152	0.705760	−	0.708451i	$-0.250606\pi$
$521$	32.2186	1.41152	0.705760	+	0.708451i	$0.250606\pi$
$522$	−12.7470	−0.557921
$523$	6.36066	0.278132	0.139066	−	0.990283i	$-0.455590\pi$
$523$	6.36066	0.278132	0.139066	+	0.990283i	$0.455590\pi$
$524$	−8.76804	−0.383033
$525$	−7.14143	−0.311678
$526$	−22.8864	−0.997894
$527$	26.3099	1.14608
$528$	20.8811	0.908735
$529$	64.8109	2.81786
$530$	−27.7824	−1.20679
$531$	−4.51669	−0.196008
$532$	21.9243	0.950537
$533$	18.9719	0.821765
$534$	−15.0211	−0.650027
$535$	−21.6049	−0.934062
$536$	3.64816	0.157576
$537$	−23.1025	−0.996945
$538$	9.87420	0.425707
$539$	12.1020	0.521271
$540$	−2.40119	−0.103331
$541$	14.1584	0.608717	0.304359	−	0.952557i	$-0.401558\pi$
$541$	14.1584	0.608717	0.304359	+	0.952557i	$0.401558\pi$
$542$	17.5586	0.754204
$543$	4.95235	0.212526
$544$	37.1514	1.59285
$545$	−22.5352	−0.965301
$546$	−24.8900	−1.06520
$547$	5.32556	0.227705	0.113852	−	0.993498i	$-0.463681\pi$
$547$	5.32556	0.227705	0.113852	+	0.993498i	$0.463681\pi$
$548$	2.33319	0.0996689
$549$	4.89792	0.209038
$550$	−32.4456	−1.38348
$551$	35.6489	1.51870
$552$	2.39533	0.101952
$553$	−6.13417	−0.260852
$554$	57.4513	2.44087
$555$	−6.79826	−0.288570
$556$	−34.0827	−1.44543
$557$	9.92164	0.420393	0.210197	−	0.977659i	$-0.432590\pi$
$557$	9.92164	0.420393	0.210197	+	0.977659i	$0.432590\pi$
$558$	−10.9165	−0.462134
$559$	31.3120	1.32436
$560$	11.6095	0.490590
$561$	−23.3333	−0.985132
$562$	−10.1971	−0.430139
$563$	3.84171	0.161909	0.0809544	−	0.996718i	$-0.474203\pi$
$563$	3.84171	0.161909	0.0809544	+	0.996718i	$0.474203\pi$
$564$	−13.3399	−0.561710
$565$	−7.24846	−0.304945
$566$	−37.8647	−1.59157
$567$	2.13094	0.0894911
$568$	−2.77774	−0.116551
$569$	−12.9327	−0.542166	−0.271083	−	0.962556i	$-0.587382\pi$
$569$	−12.9327	−0.542166	−0.271083	+	0.962556i	$0.587382\pi$
$570$	13.8972	0.582088
$571$	23.0878	0.966196	0.483098	−	0.875566i	$-0.339512\pi$
$571$	23.0878	0.966196	0.483098	+	0.875566i	$0.339512\pi$
$572$	−54.6429	−2.28474
$573$	12.1593	0.507963
$574$	−13.3951	−0.559100
$575$	−31.4042	−1.30965
$576$	−6.92893	−0.288706
$577$	−11.5637	−0.481402	−0.240701	−	0.970599i	$-0.577377\pi$
$577$	−11.5637	−0.481402	−0.240701	+	0.970599i	$0.577377\pi$
$578$	−10.7796	−0.448371
$579$	−10.6535	−0.442746
$580$	−15.5588	−0.646043
$581$	−28.3644	−1.17675
$582$	28.4546	1.17948
$583$	54.1282	2.24176
$584$	−1.09980	−0.0455101
$585$	−7.62369	−0.315201
$586$	−37.9331	−1.56700
$587$	−46.2900	−1.91059	−0.955297	−	0.295649i	$-0.904464\pi$
$587$	−46.2900	−1.91059	−0.955297	+	0.295649i	$0.904464\pi$
$588$	−4.59867	−0.189646
$589$	30.5298	1.25796
$590$	−11.4090	−0.469703
$591$	−13.9199	−0.572588
$592$	−22.4647	−0.923293
$593$	2.67965	0.110040	0.0550200	−	0.998485i	$-0.482478\pi$
$593$	2.67965	0.110040	0.0550200	+	0.998485i	$0.482478\pi$
$594$	9.68147	0.397235
$595$	−12.9728	−0.531834
$596$	30.0849	1.23232
$597$	4.07007	0.166577
$598$	−109.453	−4.47588
$599$	21.0791	0.861268	0.430634	−	0.902527i	$-0.358290\pi$
$599$	21.0791	0.861268	0.430634	+	0.902527i	$0.358290\pi$
$600$	−0.856653	−0.0349727
$601$	20.8399	0.850076	0.425038	−	0.905175i	$-0.360261\pi$
$601$	20.8399	0.850076	0.425038	+	0.905175i	$0.360261\pi$
$602$	−22.1078	−0.901047
$603$	14.2719	0.581198
$604$	24.0987	0.980563
$605$	−16.9740	−0.690090
$606$	19.0726	0.774770
$607$	49.0011	1.98889	0.994446	−	0.105244i	$-0.0335623\pi$
$607$	49.0011	1.98889	0.994446	+	0.105244i	$0.0335623\pi$
$608$	43.1101	1.74835
$609$	13.8077	0.559515
$610$	12.3720	0.500928
$611$	−42.3536	−1.71344
$612$	8.86645	0.358405
$613$	−12.3929	−0.500546	−0.250273	−	0.968175i	$-0.580520\pi$
$613$	−12.3929	−0.500546	−0.250273	+	0.968175i	$0.580520\pi$
$614$	−44.9908	−1.81568
$615$	−4.10285	−0.165443
$616$	−2.68067	−0.108007
$617$	−13.7306	−0.552774	−0.276387	−	0.961046i	$-0.589137\pi$
$617$	−13.7306	−0.552774	−0.276387	+	0.961046i	$0.589137\pi$
$618$	−7.70651	−0.310001
$619$	−39.0933	−1.57129	−0.785646	−	0.618677i	$-0.787669\pi$
$619$	−39.0933	−1.57129	−0.785646	+	0.618677i	$0.787669\pi$
$620$	−13.3245	−0.535127
$621$	9.37074	0.376035
$622$	−56.5252	−2.26645
$623$	16.2710	0.651883
$624$	−25.1923	−1.00850
$625$	2.98780	0.119512
$626$	0.225191	0.00900046
$627$	−27.0757	−1.08130
$628$	−1.50460	−0.0600399
$629$	25.1028	1.00091
$630$	5.38270	0.214452
$631$	6.69116	0.266371	0.133185	−	0.991091i	$-0.457479\pi$
$631$	6.69116	0.266371	0.133185	+	0.991091i	$0.457479\pi$
$632$	−0.735827	−0.0292696
$633$	1.34409	0.0534228
$634$	0.0632595	0.00251235
$635$	16.8004	0.666702
$636$	−20.5683	−0.815584
$637$	−14.6006	−0.578497
$638$	62.7322	2.48359
$639$	−10.8668	−0.429883
$640$	2.62019	0.103572
$641$	−21.0644	−0.831995	−0.415997	−	0.909366i	$-0.636567\pi$
$641$	−21.0644	−0.831995	−0.415997	+	0.909366i	$0.636567\pi$
$642$	−33.1011	−1.30639
$643$	−2.12112	−0.0836489	−0.0418244	−	0.999125i	$-0.513317\pi$
$643$	−2.12112	−0.0836489	−0.0418244	+	0.999125i	$0.513317\pi$
$644$	37.3423	1.47149
$645$	−6.77151	−0.266628
$646$	−51.3157	−2.01899
$647$	45.1917	1.77667	0.888335	−	0.459195i	$-0.151862\pi$
$647$	45.1917	1.77667	0.888335	+	0.459195i	$0.151862\pi$
$648$	0.255618	0.0100416
$649$	22.2281	0.872529
$650$	39.1443	1.53537
$651$	11.8249	0.463454
$652$	23.2333	0.909886
$653$	−0.422187	−0.0165214	−0.00826072	−	0.999966i	$-0.502630\pi$
$653$	−0.422187	−0.0165214	−0.00826072	+	0.999966i	$0.502630\pi$
$654$	−34.5263	−1.35009
$655$	6.02027	0.235231
$656$	−13.5577	−0.529341
$657$	−4.30253	−0.167858
$658$	29.9037	1.16577
$659$	35.1068	1.36757	0.683783	−	0.729686i	$-0.260334\pi$
$659$	35.1068	1.36757	0.683783	+	0.729686i	$0.260334\pi$
$660$	11.8170	0.459977
$661$	25.4403	0.989513	0.494757	−	0.869032i	$-0.335257\pi$
$661$	25.4403	0.989513	0.494757	+	0.869032i	$0.335257\pi$
$662$	−67.2992	−2.61566
$663$	28.1507	1.09328
$664$	−3.40246	−0.132041
$665$	−15.0535	−0.583751
$666$	−10.4157	−0.403599
$667$	60.7188	2.35104
$668$	−23.0338	−0.891206
$669$	−11.6712	−0.451234
$670$	36.0506	1.39275
$671$	−24.1043	−0.930535
$672$	16.6976	0.644123
$673$	39.8819	1.53733	0.768667	−	0.639649i	$-0.220920\pi$
$673$	39.8819	1.53733	0.768667	+	0.639649i	$0.220920\pi$
$674$	−16.1648	−0.622645
$675$	−3.35131	−0.128992
$676$	41.6137	1.60053
$677$	51.0508	1.96204	0.981021	−	0.193903i	$-0.0621148\pi$
$677$	51.0508	1.96204	0.981021	+	0.193903i	$0.0621148\pi$
$678$	−11.1054	−0.426501
$679$	−30.8222	−1.18285
$680$	−1.55616	−0.0596760
$681$	8.57585	0.328627
$682$	53.7239	2.05719
$683$	−7.26487	−0.277982	−0.138991	−	0.990294i	$-0.544386\pi$
$683$	−7.26487	−0.277982	−0.138991	+	0.990294i	$0.544386\pi$
$684$	10.2885	0.393392
$685$	−1.60200	−0.0612094
$686$	39.6533	1.51397
$687$	−5.65131	−0.215611
$688$	−22.3763	−0.853087
$689$	−65.3035	−2.48787
$690$	23.6703	0.901111
$691$	−28.8402	−1.09713	−0.548566	−	0.836107i	$-0.684826\pi$
$691$	−28.8402	−1.09713	−0.548566	+	0.836107i	$0.684826\pi$
$692$	−41.1661	−1.56490
$693$	−10.4871	−0.398370
$694$	−22.3376	−0.847922
$695$	23.4017	0.887676
$696$	1.65630	0.0627820
$697$	15.1499	0.573842
$698$	47.4743	1.79693
$699$	8.99454	0.340205
$700$	−13.3549	−0.504769
$701$	5.46960	0.206584	0.103292	−	0.994651i	$-0.467062\pi$
$701$	5.46960	0.206584	0.103292	+	0.994651i	$0.467062\pi$
$702$	−11.6803	−0.440845
$703$	29.1290	1.09862
$704$	34.0995	1.28517
$705$	9.15936	0.344962
$706$	48.1796	1.81326
$707$	−20.6596	−0.776983
$708$	−8.44649	−0.317439
$709$	33.8897	1.27275	0.636377	−	0.771378i	$-0.280432\pi$
$709$	33.8897	1.27275	0.636377	+	0.771378i	$0.280432\pi$
$710$	−27.4492	−1.03015
$711$	−2.87862	−0.107957
$712$	1.95179	0.0731465
$713$	51.9997	1.94740
$714$	−19.8758	−0.743832
$715$	37.5187	1.40312
$716$	−43.2031	−1.61457
$717$	−15.4438	−0.576759
$718$	20.0479	0.748182
$719$	−14.7380	−0.549634	−0.274817	−	0.961497i	$-0.588617\pi$
$719$	−14.7380	−0.549634	−0.274817	+	0.961497i	$0.588617\pi$
$720$	5.44806	0.203037
$721$	8.34776	0.310887
$722$	−22.1685	−0.825025
$723$	−10.8764	−0.404497
$724$	9.26121	0.344190
$725$	−21.7152	−0.806481
$726$	−26.0059	−0.965171
$727$	−17.6455	−0.654435	−0.327218	−	0.944949i	$-0.606111\pi$
$727$	−17.6455	−0.654435	−0.327218	+	0.944949i	$0.606111\pi$
$728$	3.23413	0.119865
$729$	1.00000	0.0370370
$730$	−10.8681	−0.402245
$731$	25.0040	0.924806
$732$	9.15942	0.338542
$733$	−13.4862	−0.498122	−0.249061	−	0.968488i	$-0.580122\pi$
$733$	−13.4862	−0.498122	−0.249061	+	0.968488i	$0.580122\pi$
$734$	−36.9141	−1.36252
$735$	3.15751	0.116467
$736$	73.4271	2.70656
$737$	−70.2369	−2.58721
$738$	−6.28600	−0.231391
$739$	−10.7085	−0.393918	−0.196959	−	0.980412i	$-0.563107\pi$
$739$	−10.7085	−0.393918	−0.196959	+	0.980412i	$0.563107\pi$
$740$	−12.7132	−0.467346
$741$	32.6658	1.20001
$742$	46.1075	1.69266
$743$	2.72768	0.100069	0.0500344	−	0.998747i	$-0.484067\pi$
$743$	2.72768	0.100069	0.0500344	+	0.998747i	$0.484067\pi$
$744$	1.41846	0.0520033
$745$	−20.6567	−0.756804
$746$	62.8261	2.30023
$747$	−13.3107	−0.487015
$748$	−43.6347	−1.59544
$749$	35.8554	1.31013
$750$	−21.0952	−0.770287
$751$	−42.3073	−1.54381	−0.771907	−	0.635735i	$-0.780697\pi$
$751$	−42.3073	−1.54381	−0.771907	+	0.635735i	$0.780697\pi$
$752$	30.2669	1.10372
$753$	14.1205	0.514581
$754$	−75.6839	−2.75624
$755$	−16.5465	−0.602190
$756$	3.98499	0.144933
$757$	−11.6123	−0.422055	−0.211028	−	0.977480i	$-0.567681\pi$
$757$	−11.6123	−0.422055	−0.211028	+	0.977480i	$0.567681\pi$
$758$	−20.3947	−0.740768
$759$	−46.1165	−1.67392
$760$	−1.80575	−0.0655015
$761$	−10.0459	−0.364162	−0.182081	−	0.983283i	$-0.558283\pi$
$761$	−10.0459	−0.364162	−0.182081	+	0.983283i	$0.558283\pi$
$762$	25.7399	0.932460
$763$	37.3992	1.35394
$764$	22.7387	0.822657
$765$	−6.08784	−0.220106
$766$	38.6613	1.39689
$767$	−26.8173	−0.968318
$768$	17.8723	0.644910
$769$	−35.5303	−1.28126	−0.640628	−	0.767851i	$-0.721326\pi$
$769$	−35.5303	−1.28126	−0.640628	+	0.767851i	$0.721326\pi$
$770$	−26.4900	−0.954634
$771$	5.68277	0.204660
$772$	−19.9228	−0.717037
$773$	19.9449	0.717369	0.358685	−	0.933459i	$-0.383225\pi$
$773$	19.9449	0.717369	0.358685	+	0.933459i	$0.383225\pi$
$774$	−10.3747	−0.372910
$775$	−18.5969	−0.668020
$776$	−3.69729	−0.132725
$777$	11.2823	0.404752
$778$	−58.5546	−2.09928
$779$	17.5798	0.629860
$780$	−14.2568	−0.510475
$781$	53.4789	1.91363
$782$	−87.4031	−3.12553
$783$	6.47961	0.231562
$784$	10.4339	0.372640
$785$	1.03308	0.0368722
$786$	9.22370	0.328998
$787$	−21.4752	−0.765510	−0.382755	−	0.923850i	$-0.625025\pi$
$787$	−21.4752	−0.765510	−0.382755	+	0.923850i	$0.625025\pi$
$788$	−26.0311	−0.927320
$789$	11.6337	0.414171
$790$	−7.27133	−0.258702
$791$	12.0295	0.427719
$792$	−1.25798	−0.0447003
$793$	29.0808	1.03269
$794$	59.3978	2.10795
$795$	14.1225	0.500873
$796$	7.61129	0.269775
$797$	−8.49310	−0.300841	−0.150421	−	0.988622i	$-0.548063\pi$
$797$	−8.49310	−0.300841	−0.150421	+	0.988622i	$0.548063\pi$
$798$	−23.0636	−0.816444
$799$	−33.8212	−1.19651
$800$	−26.2601	−0.928435
$801$	7.63559	0.269790
$802$	−67.0050	−2.36603
$803$	21.1741	0.747219
$804$	26.6894	0.941264
$805$	−25.6398	−0.903685
$806$	−64.8158	−2.28304
$807$	−5.01930	−0.176688
$808$	−2.47822	−0.0871836
$809$	28.7267	1.00998	0.504988	−	0.863127i	$-0.331497\pi$
$809$	28.7267	1.00998	0.504988	+	0.863127i	$0.331497\pi$
$810$	2.52597	0.0887537
$811$	−0.830741	−0.0291713	−0.0145856	−	0.999894i	$-0.504643\pi$
$811$	−0.830741	−0.0291713	−0.0145856	+	0.999894i	$0.504643\pi$
$812$	25.8212	0.906147
$813$	−8.92544	−0.313029
$814$	51.2589	1.79662
$815$	−15.9523	−0.558786
$816$	−20.1171	−0.704240
$817$	29.0144	1.01508
$818$	43.7534	1.52980
$819$	12.6522	0.442104
$820$	−7.67259	−0.267938
$821$	55.6790	1.94321	0.971606	−	0.236604i	$-0.0760345\pi$
$821$	55.6790	1.94321	0.971606	+	0.236604i	$0.0760345\pi$
$822$	−2.45444	−0.0856085
$823$	25.1602	0.877030	0.438515	−	0.898724i	$-0.355505\pi$
$823$	25.1602	0.877030	0.438515	+	0.898724i	$0.355505\pi$
$824$	1.00136	0.0348840
$825$	16.4929	0.574208
$826$	18.9343	0.658810
$827$	−2.99675	−0.104207	−0.0521036	−	0.998642i	$-0.516593\pi$
$827$	−2.99675	−0.104207	−0.0521036	+	0.998642i	$0.516593\pi$
$828$	17.5239	0.608997
$829$	23.3708	0.811701	0.405851	−	0.913939i	$-0.366975\pi$
$829$	23.3708	0.811701	0.405851	+	0.913939i	$0.366975\pi$
$830$	−33.6226	−1.16706
$831$	−29.2039	−1.01307
$832$	−41.1398	−1.42626
$833$	−11.6592	−0.403968
$834$	35.8539	1.24152
$835$	15.8154	0.547314
$836$	−50.6333	−1.75119
$837$	5.54915	0.191807
$838$	74.1366	2.56101
$839$	44.0991	1.52247	0.761235	−	0.648476i	$-0.224593\pi$
$839$	44.0991	1.52247	0.761235	+	0.648476i	$0.224593\pi$
$840$	−0.699410	−0.0241319
$841$	12.9854	0.447771
$842$	27.4030	0.944368
$843$	5.18344	0.178527
$844$	2.51354	0.0865195
$845$	−28.5726	−0.982928
$846$	14.0331	0.482469
$847$	28.1699	0.967928
$848$	46.6673	1.60256
$849$	19.2475	0.660574
$850$	31.2584	1.07215
$851$	49.6138	1.70074
$852$	−20.3216	−0.696205
$853$	−44.3036	−1.51693	−0.758463	−	0.651716i	$-0.774049\pi$
$853$	−44.3036	−1.51693	−0.758463	+	0.651716i	$0.774049\pi$
$854$	−20.5325	−0.702608
$855$	−7.06427	−0.241593
$856$	4.30104	0.147007
$857$	22.8691	0.781192	0.390596	−	0.920562i	$-0.372269\pi$
$857$	22.8691	0.781192	0.390596	+	0.920562i	$0.372269\pi$
$858$	57.4826	1.96242
$859$	4.05424	0.138329	0.0691644	−	0.997605i	$-0.477967\pi$
$859$	4.05424	0.138329	0.0691644	+	0.997605i	$0.477967\pi$
$860$	−12.6632	−0.431810
$861$	6.80905	0.232052
$862$	34.9966	1.19199
$863$	15.2791	0.520105	0.260052	−	0.965594i	$-0.416260\pi$
$863$	15.2791	0.520105	0.260052	+	0.965594i	$0.416260\pi$
$864$	7.83578	0.266579
$865$	28.2653	0.961048
$866$	−3.44723	−0.117141
$867$	5.47952	0.186094
$868$	22.1133	0.750575
$869$	14.1666	0.480571
$870$	16.3673	0.554905
$871$	84.7380	2.87124
$872$	4.48623	0.151923
$873$	−14.4642	−0.489537
$874$	−101.422	−3.43064
$875$	22.8505	0.772488
$876$	−8.04600	−0.271849
$877$	3.12162	0.105410	0.0527048	−	0.998610i	$-0.483216\pi$
$877$	3.12162	0.105410	0.0527048	+	0.998610i	$0.483216\pi$
$878$	−0.661913	−0.0223385
$879$	19.2823	0.650377
$880$	−26.8117	−0.903822
$881$	−12.1240	−0.408470	−0.204235	−	0.978922i	$-0.565471\pi$
$881$	−12.1240	−0.408470	−0.204235	+	0.978922i	$0.565471\pi$
$882$	4.83765	0.162892
$883$	11.2849	0.379766	0.189883	−	0.981807i	$-0.439189\pi$
$883$	11.2849	0.379766	0.189883	+	0.981807i	$0.439189\pi$
$884$	52.6436	1.77059
$885$	5.79949	0.194948
$886$	28.6689	0.963152
$887$	−56.6764	−1.90301	−0.951503	−	0.307638i	$-0.900461\pi$
$887$	−56.6764	−1.90301	−0.951503	+	0.307638i	$0.900461\pi$
$888$	1.35338	0.0454164
$889$	−27.8817	−0.935123
$890$	19.2873	0.646512
$891$	−4.92133	−0.164871
$892$	−21.8259	−0.730784
$893$	−39.2458	−1.31331
$894$	−31.6483	−1.05848
$895$	29.6639	0.991554
$896$	−4.34845	−0.145271
$897$	55.6377	1.85769
$898$	−14.3084	−0.477477
$899$	35.9563	1.19921
$900$	−6.26716	−0.208905
$901$	−52.1476	−1.73729
$902$	30.9355	1.03004
$903$	11.2379	0.373975
$904$	1.44300	0.0479935
$905$	−6.35889	−0.211377
$906$	−25.3511	−0.842233
$907$	−3.65642	−0.121410	−0.0607048	−	0.998156i	$-0.519335\pi$
$907$	−3.65642	−0.121410	−0.0607048	+	0.998156i	$0.519335\pi$
$908$	16.0374	0.532219
$909$	−9.69505	−0.321564
$910$	31.9592	1.05944
$911$	40.5240	1.34262	0.671310	−	0.741176i	$-0.265732\pi$
$911$	40.5240	1.34262	0.671310	+	0.741176i	$0.265732\pi$
$912$	−23.3437	−0.772987
$913$	65.5065	2.16795
$914$	−17.6681	−0.584410
$915$	−6.28900	−0.207908
$916$	−10.5683	−0.349187
$917$	−9.99119	−0.329938
$918$	−9.32723	−0.307844
$919$	−40.4142	−1.33314	−0.666571	−	0.745442i	$-0.732239\pi$
$919$	−40.4142	−1.33314	−0.666571	+	0.745442i	$0.732239\pi$
$920$	−3.07563	−0.101401
$921$	22.8699	0.753589
$922$	47.8080	1.57447
$923$	−64.5202	−2.12371
$924$	−19.6114	−0.645169
$925$	−17.7436	−0.583407
$926$	12.4921	0.410517
$927$	3.91741	0.128665
$928$	50.7728	1.66670
$929$	−14.0892	−0.462253	−0.231126	−	0.972924i	$-0.574241\pi$
$929$	−14.0892	−0.462253	−0.231126	+	0.972924i	$0.574241\pi$
$930$	14.0170	0.459636
$931$	−13.5292	−0.443402
$932$	16.8204	0.550969
$933$	28.7331	0.940681
$934$	8.80235	0.288022
$935$	29.9603	0.979805
$936$	1.51770	0.0496076
$937$	−20.3602	−0.665139	−0.332570	−	0.943079i	$-0.607916\pi$
$937$	−20.3602	−0.665139	−0.332570	+	0.943079i	$0.607916\pi$
$938$	−59.8292	−1.95349
$939$	−0.114470	−0.00373560
$940$	17.1286	0.558673
$941$	−30.2046	−0.984640	−0.492320	−	0.870414i	$-0.663851\pi$
$941$	−30.2046	−0.984640	−0.492320	+	0.870414i	$0.663851\pi$
$942$	1.58279	0.0515700
$943$	29.9426	0.975066
$944$	19.1643	0.623744
$945$	−2.73616	−0.0890072
$946$	51.0572	1.66001
$947$	41.8823	1.36099	0.680496	−	0.732752i	$-0.261764\pi$
$947$	41.8823	1.36099	0.680496	+	0.732752i	$0.261764\pi$
$948$	−5.38321	−0.174838
$949$	−25.5458	−0.829251
$950$	36.2719	1.17682
$951$	−0.0321563	−0.00104274
$952$	2.58259	0.0837022
$953$	−45.9346	−1.48797	−0.743984	−	0.668198i	$-0.767066\pi$
$953$	−45.9346	−1.48797	−0.743984	+	0.668198i	$0.767066\pi$
$954$	21.6372	0.700529
$955$	−15.6127	−0.505216
$956$	−28.8809	−0.934074
$957$	−31.8883	−1.03080
$958$	−33.9660	−1.09739
$959$	2.65867	0.0858530
$960$	8.89685	0.287145
$961$	−0.206951	−0.00667582
$962$	−61.8419	−1.99386
$963$	16.8261	0.542213
$964$	−20.3395	−0.655092
$965$	13.6793	0.440352
$966$	−39.2830	−1.26391
$967$	43.5168	1.39941	0.699703	−	0.714433i	$-0.253316\pi$
$967$	43.5168	1.39941	0.699703	+	0.714433i	$0.253316\pi$
$968$	3.37912	0.108609
$969$	26.0850	0.837971
$970$	−36.5361	−1.17310
$971$	18.5448	0.595132	0.297566	−	0.954701i	$-0.403825\pi$
$971$	18.5448	0.595132	0.297566	+	0.954701i	$0.403825\pi$
$972$	1.87006	0.0599823
$973$	−38.8372	−1.24506
$974$	33.2936	1.06680
$975$	−19.8980	−0.637246
$976$	−20.7818	−0.665210
$977$	48.5874	1.55445	0.777224	−	0.629224i	$-0.216627\pi$
$977$	48.5874	1.55445	0.777224	+	0.629224i	$0.216627\pi$
$978$	−24.4407	−0.781527
$979$	−37.5773	−1.20097
$980$	5.90475	0.188620
$981$	17.5506	0.560346
$982$	61.5603	1.96447
$983$	23.0124	0.733982	0.366991	−	0.930225i	$-0.380388\pi$
$983$	23.0124	0.733982	0.366991	+	0.930225i	$0.380388\pi$
$984$	0.816782	0.0260381
$985$	17.8734	0.569493
$986$	−60.4368	−1.92470
$987$	−15.2008	−0.483847
$988$	61.0871	1.94344
$989$	49.4185	1.57142
$990$	−12.4311	−0.395088
$991$	49.4324	1.57027	0.785135	−	0.619324i	$-0.212593\pi$
$991$	49.4324	1.57027	0.785135	+	0.619324i	$0.212593\pi$
$992$	43.4819	1.38055
$993$	34.2098	1.08562
$994$	45.5544	1.44490
$995$	−5.22603	−0.165676
$996$	−24.8919	−0.788731
$997$	−44.8817	−1.42142	−0.710708	−	0.703487i	$-0.751625\pi$
$997$	−44.8817	−1.42142	−0.710708	+	0.703487i	$0.751625\pi$
$998$	−47.3921	−1.50017
$999$	5.29454	0.167512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.17	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.17	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96725 q^{2} +1.00000 q^{3} +1.87006 q^{4} -1.28401 q^{5} -1.96725 q^{6} +2.13094 q^{7} +0.255618 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.96725 q^{2} +1.00000 q^{3} +1.87006 q^{4} -1.28401 q^{5} -1.96725 q^{6} +2.13094 q^{7} +0.255618 q^{8} +1.00000 q^{9} +2.52597 q^{10} -4.92133 q^{11} +1.87006 q^{12} +5.93739 q^{13} -4.19209 q^{14} -1.28401 q^{15} -4.24299 q^{16} +4.74126 q^{17} -1.96725 q^{18} +5.50171 q^{19} -2.40119 q^{20} +2.13094 q^{21} +9.68147 q^{22} +9.37074 q^{23} +0.255618 q^{24} -3.35131 q^{25} -11.6803 q^{26} +1.00000 q^{27} +3.98499 q^{28} +6.47961 q^{29} +2.52597 q^{30} +5.54915 q^{31} +7.83578 q^{32} -4.92133 q^{33} -9.32723 q^{34} -2.73616 q^{35} +1.87006 q^{36} +5.29454 q^{37} -10.8232 q^{38} +5.93739 q^{39} -0.328217 q^{40} +3.19533 q^{41} -4.19209 q^{42} +5.27370 q^{43} -9.20319 q^{44} -1.28401 q^{45} -18.4346 q^{46} -7.13338 q^{47} -4.24299 q^{48} -2.45910 q^{49} +6.59285 q^{50} +4.74126 q^{51} +11.1033 q^{52} -10.9987 q^{53} -1.96725 q^{54} +6.31905 q^{55} +0.544706 q^{56} +5.50171 q^{57} -12.7470 q^{58} -4.51669 q^{59} -2.40119 q^{60} +4.89792 q^{61} -10.9165 q^{62} +2.13094 q^{63} -6.92893 q^{64} -7.62369 q^{65} +9.68147 q^{66} +14.2719 q^{67} +8.86645 q^{68} +9.37074 q^{69} +5.38270 q^{70} -10.8668 q^{71} +0.255618 q^{72} -4.30253 q^{73} -10.4157 q^{74} -3.35131 q^{75} +10.2885 q^{76} -10.4871 q^{77} -11.6803 q^{78} -2.87862 q^{79} +5.44806 q^{80} +1.00000 q^{81} -6.28600 q^{82} -13.3107 q^{83} +3.98499 q^{84} -6.08784 q^{85} -10.3747 q^{86} +6.47961 q^{87} -1.25798 q^{88} +7.63559 q^{89} +2.52597 q^{90} +12.6522 q^{91} +17.5239 q^{92} +5.54915 q^{93} +14.0331 q^{94} -7.06427 q^{95} +7.83578 q^{96} -14.4642 q^{97} +4.83765 q^{98} -4.92133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more