LMFDB - Embedded newform 8035.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55001 q^{2} +2.17323 q^{3} +4.50255 q^{4} +1.00000 q^{5} -5.54177 q^{6} +4.37483 q^{7} -6.38153 q^{8} +1.72295 q^{9} +O(q^{10})$	\(q-2.55001 q^{2} +2.17323 q^{3} +4.50255 q^{4} +1.00000 q^{5} -5.54177 q^{6} +4.37483 q^{7} -6.38153 q^{8} +1.72295 q^{9} -2.55001 q^{10} +0.414044 q^{11} +9.78509 q^{12} -0.0505392 q^{13} -11.1559 q^{14} +2.17323 q^{15} +7.26785 q^{16} +4.30754 q^{17} -4.39353 q^{18} +2.90038 q^{19} +4.50255 q^{20} +9.50752 q^{21} -1.05582 q^{22} +1.21348 q^{23} -13.8685 q^{24} +1.00000 q^{25} +0.128875 q^{26} -2.77534 q^{27} +19.6979 q^{28} -0.288416 q^{29} -5.54177 q^{30} -9.27330 q^{31} -5.77005 q^{32} +0.899814 q^{33} -10.9843 q^{34} +4.37483 q^{35} +7.75765 q^{36} -8.86161 q^{37} -7.39599 q^{38} -0.109833 q^{39} -6.38153 q^{40} +0.791597 q^{41} -24.2443 q^{42} +8.18713 q^{43} +1.86425 q^{44} +1.72295 q^{45} -3.09438 q^{46} +12.8197 q^{47} +15.7947 q^{48} +12.1391 q^{49} -2.55001 q^{50} +9.36129 q^{51} -0.227555 q^{52} +5.43213 q^{53} +7.07714 q^{54} +0.414044 q^{55} -27.9181 q^{56} +6.30320 q^{57} +0.735463 q^{58} +3.33042 q^{59} +9.78509 q^{60} -9.22386 q^{61} +23.6470 q^{62} +7.53759 q^{63} +0.177967 q^{64} -0.0505392 q^{65} -2.29453 q^{66} +8.47720 q^{67} +19.3949 q^{68} +2.63717 q^{69} -11.1559 q^{70} +13.4144 q^{71} -10.9950 q^{72} -15.2007 q^{73} +22.5972 q^{74} +2.17323 q^{75} +13.0591 q^{76} +1.81137 q^{77} +0.280076 q^{78} +0.578251 q^{79} +7.26785 q^{80} -11.2003 q^{81} -2.01858 q^{82} -13.9339 q^{83} +42.8081 q^{84} +4.30754 q^{85} -20.8773 q^{86} -0.626794 q^{87} -2.64223 q^{88} +16.2546 q^{89} -4.39353 q^{90} -0.221100 q^{91} +5.46374 q^{92} -20.1530 q^{93} -32.6904 q^{94} +2.90038 q^{95} -12.5397 q^{96} -0.156259 q^{97} -30.9549 q^{98} +0.713374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.55001	−1.80313	−0.901565	−	0.432645i	$-0.857581\pi$
$2$	−2.55001	−1.80313	−0.901565	+	0.432645i	$0.857581\pi$
$3$	2.17323	1.25472	0.627359	−	0.778731i	$-0.284136\pi$
$3$	2.17323	1.25472	0.627359	+	0.778731i	$0.284136\pi$
$4$	4.50255	2.25127
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.54177	−2.26242
$7$	4.37483	1.65353	0.826765	−	0.562548i	$-0.190179\pi$
$7$	4.37483	1.65353	0.826765	+	0.562548i	$0.190179\pi$
$8$	−6.38153	−2.25621
$9$	1.72295	0.574315
$10$	−2.55001	−0.806384
$11$	0.414044	0.124839	0.0624194	−	0.998050i	$-0.480118\pi$
$11$	0.414044	0.124839	0.0624194	+	0.998050i	$0.480118\pi$
$12$	9.78509	2.82471
$13$	−0.0505392	−0.0140170	−0.00700852	−	0.999975i	$-0.502231\pi$
$13$	−0.0505392	−0.0140170	−0.00700852	+	0.999975i	$0.502231\pi$
$14$	−11.1559	−2.98153
$15$	2.17323	0.561127
$16$	7.26785	1.81696
$17$	4.30754	1.04473	0.522366	−	0.852722i	$-0.325050\pi$
$17$	4.30754	1.04473	0.522366	+	0.852722i	$0.325050\pi$
$18$	−4.39353	−1.03556
$19$	2.90038	0.665392	0.332696	−	0.943034i	$-0.392042\pi$
$19$	2.90038	0.665392	0.332696	+	0.943034i	$0.392042\pi$
$20$	4.50255	1.00680
$21$	9.50752	2.07471
$22$	−1.05582	−0.225101
$23$	1.21348	0.253028	0.126514	−	0.991965i	$-0.459621\pi$
$23$	1.21348	0.253028	0.126514	+	0.991965i	$0.459621\pi$
$24$	−13.8685	−2.83091
$25$	1.00000	0.200000
$26$	0.128875	0.0252745
$27$	−2.77534	−0.534114
$28$	19.6979	3.72255
$29$	−0.288416	−0.0535574	−0.0267787	−	0.999641i	$-0.508525\pi$
$29$	−0.288416	−0.0535574	−0.0267787	+	0.999641i	$0.508525\pi$
$30$	−5.54177	−1.01178
$31$	−9.27330	−1.66553	−0.832767	−	0.553624i	$-0.813244\pi$
$31$	−9.27330	−1.66553	−0.832767	+	0.553624i	$0.813244\pi$
$32$	−5.77005	−1.02001
$33$	0.899814	0.156637
$34$	−10.9843	−1.88379
$35$	4.37483	0.739481
$36$	7.75765	1.29294
$37$	−8.86161	−1.45684	−0.728420	−	0.685131i	$-0.759745\pi$
$37$	−8.86161	−1.45684	−0.728420	+	0.685131i	$0.759745\pi$
$38$	−7.39599	−1.19979
$39$	−0.109833	−0.0175874
$40$	−6.38153	−1.00901
$41$	0.791597	0.123627	0.0618133	−	0.998088i	$-0.480312\pi$
$41$	0.791597	0.123627	0.0618133	+	0.998088i	$0.480312\pi$
$42$	−24.2443	−3.74097
$43$	8.18713	1.24853	0.624263	−	0.781214i	$-0.285399\pi$
$43$	8.18713	1.24853	0.624263	+	0.781214i	$0.285399\pi$
$44$	1.86425	0.281047
$45$	1.72295	0.256842
$46$	−3.09438	−0.456241
$47$	12.8197	1.86995	0.934974	−	0.354716i	$-0.115422\pi$
$47$	12.8197	1.86995	0.934974	+	0.354716i	$0.115422\pi$
$48$	15.7947	2.27978
$49$	12.1391	1.73416
$50$	−2.55001	−0.360626
$51$	9.36129	1.31084
$52$	−0.227555	−0.0315562
$53$	5.43213	0.746160	0.373080	−	0.927799i	$-0.378302\pi$
$53$	5.43213	0.746160	0.373080	+	0.927799i	$0.378302\pi$
$54$	7.07714	0.963077
$55$	0.414044	0.0558296
$56$	−27.9181	−3.73071
$57$	6.30320	0.834879
$58$	0.735463	0.0965710
$59$	3.33042	0.433583	0.216792	−	0.976218i	$-0.430441\pi$
$59$	3.33042	0.433583	0.216792	+	0.976218i	$0.430441\pi$
$60$	9.78509	1.26325
$61$	−9.22386	−1.18099	−0.590497	−	0.807040i	$-0.701068\pi$
$61$	−9.22386	−1.18099	−0.590497	+	0.807040i	$0.701068\pi$
$62$	23.6470	3.00317
$63$	7.53759	0.949647
$64$	0.177967	0.0222459
$65$	−0.0505392	−0.00626861
$66$	−2.29453	−0.282438
$67$	8.47720	1.03565	0.517827	−	0.855485i	$-0.326741\pi$
$67$	8.47720	1.03565	0.517827	+	0.855485i	$0.326741\pi$
$68$	19.3949	2.35198
$69$	2.63717	0.317478
$70$	−11.1559	−1.33338
$71$	13.4144	1.59199	0.795996	−	0.605302i	$-0.206948\pi$
$71$	13.4144	1.59199	0.795996	+	0.605302i	$0.206948\pi$
$72$	−10.9950	−1.29578
$73$	−15.2007	−1.77911	−0.889555	−	0.456828i	$-0.848985\pi$
$73$	−15.2007	−1.77911	−0.889555	+	0.456828i	$0.848985\pi$
$74$	22.5972	2.62687
$75$	2.17323	0.250943
$76$	13.0591	1.49798
$77$	1.81137	0.206425
$78$	0.280076	0.0317124
$79$	0.578251	0.0650583	0.0325292	−	0.999471i	$-0.489644\pi$
$79$	0.578251	0.0650583	0.0325292	+	0.999471i	$0.489644\pi$
$80$	7.26785	0.812571
$81$	−11.2003	−1.24448
$82$	−2.01858	−0.222915
$83$	−13.9339	−1.52944	−0.764720	−	0.644362i	$-0.777123\pi$
$83$	−13.9339	−1.52944	−0.764720	+	0.644362i	$0.777123\pi$
$84$	42.8081	4.67075
$85$	4.30754	0.467218
$86$	−20.8773	−2.25125
$87$	−0.626794	−0.0671994
$88$	−2.64223	−0.281663
$89$	16.2546	1.72298	0.861491	−	0.507772i	$-0.169531\pi$
$89$	16.2546	1.72298	0.861491	+	0.507772i	$0.169531\pi$
$90$	−4.39353	−0.463118
$91$	−0.221100	−0.0231776
$92$	5.46374	0.569634
$93$	−20.1530	−2.08977
$94$	−32.6904	−3.37176
$95$	2.90038	0.297572
$96$	−12.5397	−1.27982
$97$	−0.156259	−0.0158657	−0.00793287	−	0.999969i	$-0.502525\pi$
$97$	−0.156259	−0.0158657	−0.00793287	+	0.999969i	$0.502525\pi$
$98$	−30.9549	−3.12691
$99$	0.713374	0.0716968
$100$	4.50255	0.450255
$101$	−14.6880	−1.46151	−0.730757	−	0.682638i	$-0.760833\pi$
$101$	−14.6880	−1.46151	−0.730757	+	0.682638i	$0.760833\pi$
$102$	−23.8714	−2.36362
$103$	13.0272	1.28361	0.641806	−	0.766867i	$-0.278185\pi$
$103$	13.0272	1.28361	0.641806	+	0.766867i	$0.278185\pi$
$104$	0.322517	0.0316254
$105$	9.50752	0.927839
$106$	−13.8520	−1.34542
$107$	9.74404	0.941992	0.470996	−	0.882135i	$-0.343895\pi$
$107$	9.74404	0.941992	0.470996	+	0.882135i	$0.343895\pi$
$108$	−12.4961	−1.20244
$109$	−4.54438	−0.435272	−0.217636	−	0.976030i	$-0.569835\pi$
$109$	−4.54438	−0.435272	−0.217636	+	0.976030i	$0.569835\pi$
$110$	−1.05582	−0.100668
$111$	−19.2584	−1.82792
$112$	31.7956	3.00440
$113$	−3.43480	−0.323119	−0.161559	−	0.986863i	$-0.551652\pi$
$113$	−3.43480	−0.323119	−0.161559	+	0.986863i	$0.551652\pi$
$114$	−16.0732	−1.50539
$115$	1.21348	0.113157
$116$	−1.29861	−0.120572
$117$	−0.0870762	−0.00805020
$118$	−8.49260	−0.781807
$119$	18.8447	1.72749
$120$	−13.8685	−1.26602
$121$	−10.8286	−0.984415
$122$	23.5209	2.12948
$123$	1.72033	0.155117
$124$	−41.7535	−3.74957
$125$	1.00000	0.0894427
$126$	−19.2209	−1.71234
$127$	11.6011	1.02943	0.514716	−	0.857361i	$-0.327897\pi$
$127$	11.6011	1.02943	0.514716	+	0.857361i	$0.327897\pi$
$128$	11.0863	0.979898
$129$	17.7925	1.56655
$130$	0.128875	0.0113031
$131$	4.33058	0.378364	0.189182	−	0.981942i	$-0.439416\pi$
$131$	4.33058	0.378364	0.189182	+	0.981942i	$0.439416\pi$
$132$	4.05146	0.352634
$133$	12.6886	1.10025
$134$	−21.6169	−1.86742
$135$	−2.77534	−0.238863
$136$	−27.4887	−2.35713
$137$	−1.35067	−0.115396	−0.0576980	−	0.998334i	$-0.518376\pi$
$137$	−1.35067	−0.115396	−0.0576980	+	0.998334i	$0.518376\pi$
$138$	−6.72481	−0.572454
$139$	−1.27217	−0.107904	−0.0539522	−	0.998544i	$-0.517182\pi$
$139$	−1.27217	−0.107904	−0.0539522	+	0.998544i	$0.517182\pi$
$140$	19.6979	1.66477
$141$	27.8603	2.34626
$142$	−34.2068	−2.87057
$143$	−0.0209254	−0.00174987
$144$	12.5221	1.04351
$145$	−0.288416	−0.0239516
$146$	38.7620	3.20797
$147$	26.3811	2.17588
$148$	−39.8998	−3.27975
$149$	16.7025	1.36832	0.684160	−	0.729332i	$-0.260169\pi$
$149$	16.7025	1.36832	0.684160	+	0.729332i	$0.260169\pi$
$150$	−5.54177	−0.452483
$151$	−4.82225	−0.392429	−0.196215	−	0.980561i	$-0.562865\pi$
$151$	−4.82225	−0.392429	−0.196215	+	0.980561i	$0.562865\pi$
$152$	−18.5088	−1.50126
$153$	7.42165	0.600005
$154$	−4.61901	−0.372210
$155$	−9.27330	−0.744849
$156$	−0.494530	−0.0395941
$157$	−8.16529	−0.651661	−0.325831	−	0.945428i	$-0.605644\pi$
$157$	−8.16529	−0.651661	−0.325831	+	0.945428i	$0.605644\pi$
$158$	−1.47455	−0.117309
$159$	11.8053	0.936220
$160$	−5.77005	−0.456162
$161$	5.30875	0.418388
$162$	28.5609	2.24395
$163$	12.4823	0.977688	0.488844	−	0.872371i	$-0.337419\pi$
$163$	12.4823	0.977688	0.488844	+	0.872371i	$0.337419\pi$
$164$	3.56421	0.278318
$165$	0.899814	0.0700504
$166$	35.5315	2.75778
$167$	13.5204	1.04624	0.523119	−	0.852259i	$-0.324768\pi$
$167$	13.5204	1.04624	0.523119	+	0.852259i	$0.324768\pi$
$168$	−60.6725	−4.68099
$169$	−12.9974	−0.999804
$170$	−10.9843	−0.842454
$171$	4.99719	0.382145
$172$	36.8630	2.81077
$173$	8.73296	0.663955	0.331977	−	0.943287i	$-0.392284\pi$
$173$	8.73296	0.663955	0.331977	+	0.943287i	$0.392284\pi$
$174$	1.59833	0.121169
$175$	4.37483	0.330706
$176$	3.00921	0.226828
$177$	7.23778	0.544025
$178$	−41.4494	−3.10676
$179$	15.5193	1.15997	0.579984	−	0.814628i	$-0.303059\pi$
$179$	15.5193	1.15997	0.579984	+	0.814628i	$0.303059\pi$
$180$	7.75765	0.578221
$181$	21.3470	1.58671	0.793355	−	0.608760i	$-0.208333\pi$
$181$	21.3470	1.58671	0.793355	+	0.608760i	$0.208333\pi$
$182$	0.563807	0.0417922
$183$	−20.0456	−1.48181
$184$	−7.74384	−0.570883
$185$	−8.86161	−0.651519
$186$	51.3904	3.76813
$187$	1.78351	0.130423
$188$	57.7214	4.20977
$189$	−12.1416	−0.883173
$190$	−7.39599	−0.536561
$191$	6.65046	0.481210	0.240605	−	0.970623i	$-0.422654\pi$
$191$	6.65046	0.481210	0.240605	+	0.970623i	$0.422654\pi$
$192$	0.386764	0.0279123
$193$	21.5266	1.54952	0.774758	−	0.632258i	$-0.217872\pi$
$193$	21.5266	1.54952	0.774758	+	0.632258i	$0.217872\pi$
$194$	0.398463	0.0286080
$195$	−0.109833	−0.00786533
$196$	54.6570	3.90407
$197$	−25.4393	−1.81247	−0.906237	−	0.422769i	$-0.861058\pi$
$197$	−25.4393	−1.81247	−0.906237	+	0.422769i	$0.861058\pi$
$198$	−1.81911	−0.129279
$199$	−8.51895	−0.603892	−0.301946	−	0.953325i	$-0.597636\pi$
$199$	−8.51895	−0.603892	−0.301946	+	0.953325i	$0.597636\pi$
$200$	−6.38153	−0.451242
$201$	18.4229	1.29945
$202$	37.4546	2.63530
$203$	−1.26177	−0.0885588
$204$	42.1497	2.95107
$205$	0.791597	0.0552875
$206$	−33.2196	−2.31452
$207$	2.09075	0.145318
$208$	−0.367311	−0.0254684
$209$	1.20088	0.0830668
$210$	−24.2443	−1.67301
$211$	−15.1613	−1.04375	−0.521875	−	0.853022i	$-0.674767\pi$
$211$	−15.1613	−1.04375	−0.521875	+	0.853022i	$0.674767\pi$
$212$	24.4584	1.67981
$213$	29.1525	1.99750
$214$	−24.8474	−1.69853
$215$	8.18713	0.558358
$216$	17.7109	1.20507
$217$	−40.5691	−2.75401
$218$	11.5882	0.784852
$219$	−33.0347	−2.23228
$220$	1.86425	0.125688
$221$	−0.217699	−0.0146440
$222$	49.1090	3.29598
$223$	−22.6066	−1.51385	−0.756923	−	0.653504i	$-0.773298\pi$
$223$	−22.6066	−1.51385	−0.756923	+	0.653504i	$0.773298\pi$
$224$	−25.2430	−1.68662
$225$	1.72295	0.114863
$226$	8.75877	0.582625
$227$	−26.8604	−1.78278	−0.891392	−	0.453233i	$-0.850271\pi$
$227$	−26.8604	−1.78278	−0.891392	+	0.453233i	$0.850271\pi$
$228$	28.3805	1.87954
$229$	−0.108712	−0.00718390	−0.00359195	−	0.999994i	$-0.501143\pi$
$229$	−0.108712	−0.00718390	−0.00359195	+	0.999994i	$0.501143\pi$
$230$	−3.09438	−0.204037
$231$	3.93653	0.259005
$232$	1.84053	0.120837
$233$	15.9636	1.04581	0.522904	−	0.852392i	$-0.324849\pi$
$233$	15.9636	1.04581	0.522904	+	0.852392i	$0.324849\pi$
$234$	0.222045	0.0145155
$235$	12.8197	0.836266
$236$	14.9954	0.976115
$237$	1.25667	0.0816298
$238$	−48.0543	−3.11489
$239$	−2.92586	−0.189258	−0.0946291	−	0.995513i	$-0.530167\pi$
$239$	−2.92586	−0.189258	−0.0946291	+	0.995513i	$0.530167\pi$
$240$	15.7947	1.01955
$241$	16.5688	1.06729	0.533646	−	0.845708i	$-0.320821\pi$
$241$	16.5688	1.06729	0.533646	+	0.845708i	$0.320821\pi$
$242$	27.6130	1.77503
$243$	−16.0148	−1.02735
$244$	−41.5309	−2.65874
$245$	12.1391	0.775540
$246$	−4.38685	−0.279695
$247$	−0.146583	−0.00932682
$248$	59.1778	3.75779
$249$	−30.2816	−1.91902
$250$	−2.55001	−0.161277
$251$	16.6331	1.04987	0.524935	−	0.851142i	$-0.324090\pi$
$251$	16.6331	1.04987	0.524935	+	0.851142i	$0.324090\pi$
$252$	33.9384	2.13792
$253$	0.502432	0.0315877
$254$	−29.5829	−1.85620
$255$	9.36129	0.586226
$256$	−28.6260	−1.78913
$257$	−26.6199	−1.66051	−0.830253	−	0.557386i	$-0.811804\pi$
$257$	−26.6199	−1.66051	−0.830253	+	0.557386i	$0.811804\pi$
$258$	−45.3712	−2.82469
$259$	−38.7680	−2.40893
$260$	−0.227555	−0.0141124
$261$	−0.496924	−0.0307588
$262$	−11.0430	−0.682240
$263$	3.32677	0.205137	0.102569	−	0.994726i	$-0.467294\pi$
$263$	3.32677	0.205137	0.102569	+	0.994726i	$0.467294\pi$
$264$	−5.74218	−0.353407
$265$	5.43213	0.333693
$266$	−32.3562	−1.98388
$267$	35.3250	2.16186
$268$	38.1690	2.33154
$269$	23.0366	1.40456	0.702282	−	0.711899i	$-0.252165\pi$
$269$	23.0366	1.40456	0.702282	+	0.711899i	$0.252165\pi$
$270$	7.07714	0.430701
$271$	7.42421	0.450988	0.225494	−	0.974245i	$-0.427600\pi$
$271$	7.42421	0.450988	0.225494	+	0.974245i	$0.427600\pi$
$272$	31.3066	1.89824
$273$	−0.480502	−0.0290813
$274$	3.44423	0.208074
$275$	0.414044	0.0249678
$276$	11.8740	0.714730
$277$	−7.32500	−0.440117	−0.220058	−	0.975487i	$-0.570625\pi$
$277$	−7.32500	−0.440117	−0.220058	+	0.975487i	$0.570625\pi$
$278$	3.24406	0.194566
$279$	−15.9774	−0.956541
$280$	−27.9181	−1.66842
$281$	29.4827	1.75879	0.879394	−	0.476094i	$-0.157948\pi$
$281$	29.4827	1.75879	0.879394	+	0.476094i	$0.157948\pi$
$282$	−71.0439	−4.23060
$283$	26.3516	1.56644	0.783220	−	0.621744i	$-0.213576\pi$
$283$	26.3516	1.56644	0.783220	+	0.621744i	$0.213576\pi$
$284$	60.3988	3.58401
$285$	6.30320	0.373369
$286$	0.0533600	0.00315524
$287$	3.46310	0.204420
$288$	−9.94147	−0.585807
$289$	1.55488	0.0914635
$290$	0.735463	0.0431878
$291$	−0.339588	−0.0199070
$292$	−68.4420	−4.00527
$293$	−5.57505	−0.325698	−0.162849	−	0.986651i	$-0.552068\pi$
$293$	−5.57505	−0.325698	−0.162849	+	0.986651i	$0.552068\pi$
$294$	−67.2722	−3.92339
$295$	3.33042	0.193904
$296$	56.5506	3.28694
$297$	−1.14911	−0.0666782
$298$	−42.5915	−2.46726
$299$	−0.0613281	−0.00354670
$300$	9.78509	0.564943
$301$	35.8173	2.06447
$302$	12.2968	0.707600
$303$	−31.9205	−1.83379
$304$	21.0795	1.20899
$305$	−9.22386	−0.528156
$306$	−18.9253	−1.08189
$307$	19.4164	1.10815	0.554076	−	0.832466i	$-0.313072\pi$
$307$	19.4164	1.10815	0.554076	+	0.832466i	$0.313072\pi$
$308$	8.15578	0.464719
$309$	28.3112	1.61057
$310$	23.6470	1.34306
$311$	15.8965	0.901406	0.450703	−	0.892674i	$-0.351173\pi$
$311$	15.8965	0.901406	0.450703	+	0.892674i	$0.351173\pi$
$312$	0.700905	0.0396809
$313$	−6.95205	−0.392953	−0.196476	−	0.980509i	$-0.562950\pi$
$313$	−6.95205	−0.392953	−0.196476	+	0.980509i	$0.562950\pi$
$314$	20.8216	1.17503
$315$	7.53759	0.424695
$316$	2.60360	0.146464
$317$	14.2043	0.797792	0.398896	−	0.916996i	$-0.369393\pi$
$317$	14.2043	0.797792	0.398896	+	0.916996i	$0.369393\pi$
$318$	−30.1036	−1.68813
$319$	−0.119417	−0.00668605
$320$	0.177967	0.00994866
$321$	21.1761	1.18193
$322$	−13.5374	−0.754408
$323$	12.4935	0.695156
$324$	−50.4299	−2.80166
$325$	−0.0505392	−0.00280341
$326$	−31.8299	−1.76290
$327$	−9.87599	−0.546144
$328$	−5.05160	−0.278928
$329$	56.0841	3.09201
$330$	−2.29453	−0.126310
$331$	−5.28025	−0.290229	−0.145114	−	0.989415i	$-0.546355\pi$
$331$	−5.28025	−0.290229	−0.145114	+	0.989415i	$0.546355\pi$
$332$	−62.7379	−3.44319
$333$	−15.2681	−0.836685
$334$	−34.4771	−1.88650
$335$	8.47720	0.463159
$336$	69.0993	3.76968
$337$	−9.17471	−0.499778	−0.249889	−	0.968274i	$-0.580394\pi$
$337$	−9.17471	−0.499778	−0.249889	+	0.968274i	$0.580394\pi$
$338$	33.1436	1.80277
$339$	−7.46462	−0.405423
$340$	19.3949	1.05184
$341$	−3.83955	−0.207923
$342$	−12.7429	−0.689056
$343$	22.4828	1.21395
$344$	−52.2464	−2.81694
$345$	2.63717	0.141980
$346$	−22.2691	−1.19720
$347$	−9.71647	−0.521607	−0.260804	−	0.965392i	$-0.583988\pi$
$347$	−9.71647	−0.521607	−0.260804	+	0.965392i	$0.583988\pi$
$348$	−2.82217	−0.151284
$349$	12.4856	0.668338	0.334169	−	0.942513i	$-0.391544\pi$
$349$	12.4856	0.668338	0.334169	+	0.942513i	$0.391544\pi$
$350$	−11.1559	−0.596305
$351$	0.140263	0.00748670
$352$	−2.38905	−0.127337
$353$	−32.3163	−1.72002	−0.860012	−	0.510274i	$-0.829544\pi$
$353$	−32.3163	−1.72002	−0.860012	+	0.510274i	$0.829544\pi$
$354$	−18.4564	−0.980946
$355$	13.4144	0.711960
$356$	73.1871	3.87891
$357$	40.9540	2.16752
$358$	−39.5744	−2.09157
$359$	−6.29624	−0.332303	−0.166151	−	0.986100i	$-0.553134\pi$
$359$	−6.29624	−0.332303	−0.166151	+	0.986100i	$0.553134\pi$
$360$	−10.9950	−0.579488
$361$	−10.5878	−0.557254
$362$	−54.4350	−2.86104
$363$	−23.5330	−1.23516
$364$	−0.995514	−0.0521791
$365$	−15.2007	−0.795642
$366$	51.1165	2.67190
$367$	0.738646	0.0385570	0.0192785	−	0.999814i	$-0.493863\pi$
$367$	0.738646	0.0385570	0.0192785	+	0.999814i	$0.493863\pi$
$368$	8.81938	0.459742
$369$	1.36388	0.0710007
$370$	22.5972	1.17477
$371$	23.7646	1.23380
$372$	−90.7401	−4.70465
$373$	8.66408	0.448609	0.224305	−	0.974519i	$-0.427989\pi$
$373$	8.66408	0.448609	0.224305	+	0.974519i	$0.427989\pi$
$374$	−4.54796	−0.235170
$375$	2.17323	0.112225
$376$	−81.8094	−4.21900
$377$	0.0145763	0.000750717 0
$378$	30.9613	1.59248
$379$	−11.4394	−0.587601	−0.293800	−	0.955867i	$-0.594920\pi$
$379$	−11.4394	−0.587601	−0.293800	+	0.955867i	$0.594920\pi$
$380$	13.0591	0.669917
$381$	25.2119	1.29165
$382$	−16.9587	−0.867684
$383$	−34.4900	−1.76236	−0.881179	−	0.472783i	$-0.843249\pi$
$383$	−34.4900	−1.76236	−0.881179	+	0.472783i	$0.843249\pi$
$384$	24.0931	1.22949
$385$	1.81137	0.0923159
$386$	−54.8929	−2.79398
$387$	14.1060	0.717047
$388$	−0.703566	−0.0357181
$389$	−14.8790	−0.754395	−0.377197	−	0.926133i	$-0.623112\pi$
$389$	−14.8790	−0.754395	−0.377197	+	0.926133i	$0.623112\pi$
$390$	0.280076	0.0141822
$391$	5.22710	0.264346
$392$	−77.4661	−3.91263
$393$	9.41136	0.474740
$394$	64.8705	3.26813
$395$	0.578251	0.0290950
$396$	3.21200	0.161409
$397$	24.3266	1.22092	0.610460	−	0.792047i	$-0.290985\pi$
$397$	24.3266	1.22092	0.610460	+	0.792047i	$0.290985\pi$
$398$	21.7234	1.08890
$399$	27.5754	1.38050
$400$	7.26785	0.363393
$401$	−21.3460	−1.06597	−0.532985	−	0.846125i	$-0.678930\pi$
$401$	−21.3460	−1.06597	−0.532985	+	0.846125i	$0.678930\pi$
$402$	−46.9787	−2.34308
$403$	0.468665	0.0233458
$404$	−66.1336	−3.29027
$405$	−11.2003	−0.556547
$406$	3.21752	0.159683
$407$	−3.66909	−0.181870
$408$	−59.7393	−2.95754
$409$	−37.1465	−1.83678	−0.918389	−	0.395679i	$-0.870509\pi$
$409$	−37.1465	−1.83678	−0.918389	+	0.395679i	$0.870509\pi$
$410$	−2.01858	−0.0996906
$411$	−2.93533	−0.144789
$412$	58.6558	2.88976
$413$	14.5700	0.716943
$414$	−5.33145	−0.262026
$415$	−13.9339	−0.683987
$416$	0.291613	0.0142975
$417$	−2.76473	−0.135390
$418$	−3.06226	−0.149780
$419$	−28.3950	−1.38718	−0.693592	−	0.720368i	$-0.743973\pi$
$419$	−28.3950	−1.38718	−0.693592	+	0.720368i	$0.743973\pi$
$420$	42.8081	2.08882
$421$	24.4208	1.19020	0.595098	−	0.803653i	$-0.297113\pi$
$421$	24.4208	1.19020	0.595098	+	0.803653i	$0.297113\pi$
$422$	38.6615	1.88201
$423$	22.0877	1.07394
$424$	−34.6653	−1.68349
$425$	4.30754	0.208946
$426$	−74.3393	−3.60175
$427$	−40.3528	−1.95281
$428$	43.8730	2.12068
$429$	−0.0454758	−0.00219559
$430$	−20.8773	−1.00679
$431$	16.4191	0.790879	0.395439	−	0.918492i	$-0.370592\pi$
$431$	16.4191	0.790879	0.395439	+	0.918492i	$0.370592\pi$
$432$	−20.1708	−0.970466
$433$	−12.6521	−0.608021	−0.304010	−	0.952669i	$-0.598326\pi$
$433$	−12.6521	−0.608021	−0.304010	+	0.952669i	$0.598326\pi$
$434$	103.452	4.96583
$435$	−0.626794	−0.0300525
$436$	−20.4613	−0.979918
$437$	3.51954	0.168362
$438$	84.2389	4.02509
$439$	3.27648	0.156378	0.0781889	−	0.996939i	$-0.475086\pi$
$439$	3.27648	0.156378	0.0781889	+	0.996939i	$0.475086\pi$
$440$	−2.64223	−0.125963
$441$	20.9150	0.995954
$442$	0.555135	0.0264051
$443$	29.4985	1.40152	0.700758	−	0.713399i	$-0.252845\pi$
$443$	29.4985	1.40152	0.700758	+	0.713399i	$0.252845\pi$
$444$	−86.7117	−4.11515
$445$	16.2546	0.770541
$446$	57.6469	2.72966
$447$	36.2984	1.71685
$448$	0.778575	0.0367842
$449$	−35.2532	−1.66370	−0.831851	−	0.555000i	$-0.812718\pi$
$449$	−35.2532	−1.66370	−0.831851	+	0.555000i	$0.812718\pi$
$450$	−4.39353	−0.207113
$451$	0.327756	0.0154334
$452$	−15.4654	−0.727429
$453$	−10.4799	−0.492387
$454$	68.4942	3.21459
$455$	−0.221100	−0.0103653
$456$	−40.2240	−1.88366
$457$	−33.4765	−1.56597	−0.782983	−	0.622043i	$-0.786303\pi$
$457$	−33.4765	−1.56597	−0.782983	+	0.622043i	$0.786303\pi$
$458$	0.277217	0.0129535
$459$	−11.9549	−0.558006
$460$	5.46374	0.254748
$461$	−9.29039	−0.432697	−0.216348	−	0.976316i	$-0.569415\pi$
$461$	−9.29039	−0.432697	−0.216348	+	0.976316i	$0.569415\pi$
$462$	−10.0382	−0.467019
$463$	6.87329	0.319429	0.159714	−	0.987163i	$-0.448943\pi$
$463$	6.87329	0.319429	0.159714	+	0.987163i	$0.448943\pi$
$464$	−2.09616	−0.0973119
$465$	−20.1530	−0.934575
$466$	−40.7073	−1.88573
$467$	−40.9205	−1.89358	−0.946788	−	0.321857i	$-0.895693\pi$
$467$	−40.9205	−1.89358	−0.946788	+	0.321857i	$0.895693\pi$
$468$	−0.392065	−0.0181232
$469$	37.0863	1.71249
$470$	−32.6904	−1.50790
$471$	−17.7451	−0.817651
$472$	−21.2531	−0.978255
$473$	3.38983	0.155864
$474$	−3.20453	−0.147189
$475$	2.90038	0.133078
$476$	84.8494	3.88906
$477$	9.35926	0.428531
$478$	7.46097	0.341257
$479$	−7.23032	−0.330362	−0.165181	−	0.986263i	$-0.552821\pi$
$479$	−7.23032	−0.330362	−0.165181	+	0.986263i	$0.552821\pi$
$480$	−12.5397	−0.572355
$481$	0.447858	0.0204206
$482$	−42.2507	−1.92447
$483$	11.5372	0.524959
$484$	−48.7562	−2.21619
$485$	−0.156259	−0.00709537
$486$	40.8380	1.85245
$487$	−3.55416	−0.161054	−0.0805272	−	0.996752i	$-0.525660\pi$
$487$	−3.55416	−0.161054	−0.0805272	+	0.996752i	$0.525660\pi$
$488$	58.8623	2.66457
$489$	27.1269	1.22672
$490$	−30.9549	−1.39840
$491$	33.9028	1.53001	0.765005	−	0.644024i	$-0.222736\pi$
$491$	33.9028	1.53001	0.765005	+	0.644024i	$0.222736\pi$
$492$	7.74585	0.349210
$493$	−1.24236	−0.0559531
$494$	0.373787	0.0168175
$495$	0.713374	0.0320638
$496$	−67.3970	−3.02621
$497$	58.6855	2.63241
$498$	77.2183	3.46023
$499$	−39.5980	−1.77265	−0.886325	−	0.463063i	$-0.846750\pi$
$499$	−39.5980	−1.77265	−0.886325	+	0.463063i	$0.846750\pi$
$500$	4.50255	0.201360
$501$	29.3830	1.31273
$502$	−42.4145	−1.89305
$503$	−7.77178	−0.346527	−0.173263	−	0.984876i	$-0.555431\pi$
$503$	−7.77178	−0.346527	−0.173263	+	0.984876i	$0.555431\pi$
$504$	−48.1013	−2.14260
$505$	−14.6880	−0.653609
$506$	−1.28121	−0.0569566
$507$	−28.2465	−1.25447
$508$	52.2346	2.31753
$509$	−8.80931	−0.390466	−0.195233	−	0.980757i	$-0.562546\pi$
$509$	−8.80931	−0.390466	−0.195233	+	0.980757i	$0.562546\pi$
$510$	−23.8714	−1.05704
$511$	−66.5005	−2.94181
$512$	50.8241	2.24613
$513$	−8.04953	−0.355395
$514$	67.8811	2.99411
$515$	13.0272	0.574049
$516$	80.1118	3.52673
$517$	5.30792	0.233442
$518$	98.8588	4.34361
$519$	18.9788	0.833076
$520$	0.322517	0.0141433
$521$	−42.7272	−1.87191	−0.935957	−	0.352114i	$-0.885463\pi$
$521$	−42.7272	−1.87191	−0.935957	+	0.352114i	$0.885463\pi$
$522$	1.26716	0.0554622
$523$	15.8307	0.692228	0.346114	−	0.938193i	$-0.387501\pi$
$523$	15.8307	0.692228	0.346114	+	0.938193i	$0.387501\pi$
$524$	19.4986	0.851802
$525$	9.50752	0.414942
$526$	−8.48329	−0.369889
$527$	−39.9451	−1.74003
$528$	6.53971	0.284604
$529$	−21.5275	−0.935977
$530$	−13.8520	−0.601692
$531$	5.73813	0.249013
$532$	57.1313	2.47695
$533$	−0.0400066	−0.00173288
$534$	−90.0791	−3.89811
$535$	9.74404	0.421271
$536$	−54.0975	−2.33665
$537$	33.7271	1.45543
$538$	−58.7434	−2.53261
$539$	5.02612	0.216490
$540$	−12.4961	−0.537747
$541$	−5.53313	−0.237888	−0.118944	−	0.992901i	$-0.537951\pi$
$541$	−5.53313	−0.237888	−0.118944	+	0.992901i	$0.537951\pi$
$542$	−18.9318	−0.813190
$543$	46.3920	1.99087
$544$	−24.8547	−1.06564
$545$	−4.54438	−0.194660
$546$	1.22529	0.0524374
$547$	17.0406	0.728604	0.364302	−	0.931281i	$-0.381308\pi$
$547$	17.0406	0.728604	0.364302	+	0.931281i	$0.381308\pi$
$548$	−6.08148	−0.259788
$549$	−15.8922	−0.678262
$550$	−1.05582	−0.0450201
$551$	−0.836514	−0.0356367
$552$	−16.8292	−0.716297
$553$	2.52975	0.107576
$554$	18.6788	0.793587
$555$	−19.2584	−0.817471
$556$	−5.72803	−0.242922
$557$	−23.9518	−1.01487	−0.507435	−	0.861690i	$-0.669406\pi$
$557$	−23.9518	−1.01487	−0.507435	+	0.861690i	$0.669406\pi$
$558$	40.7425	1.72477
$559$	−0.413771	−0.0175006
$560$	31.7956	1.34361
$561$	3.87598	0.163644
$562$	−75.1811	−3.17132
$563$	−18.9168	−0.797247	−0.398623	−	0.917115i	$-0.630512\pi$
$563$	−18.9168	−0.797247	−0.398623	+	0.917115i	$0.630512\pi$
$564$	125.442	5.28207
$565$	−3.43480	−0.144503
$566$	−67.1969	−2.82449
$567$	−48.9994	−2.05778
$568$	−85.6041	−3.59187
$569$	22.4139	0.939641	0.469821	−	0.882762i	$-0.344319\pi$
$569$	22.4139	0.939641	0.469821	+	0.882762i	$0.344319\pi$
$570$	−16.0732	−0.673233
$571$	41.4043	1.73272	0.866359	−	0.499422i	$-0.166454\pi$
$571$	41.4043	1.73272	0.866359	+	0.499422i	$0.166454\pi$
$572$	−0.0942177	−0.00393944
$573$	14.4530	0.603783
$574$	−8.83094	−0.368596
$575$	1.21348	0.0506055
$576$	0.306627	0.0127761
$577$	7.12121	0.296460	0.148230	−	0.988953i	$-0.452642\pi$
$577$	7.12121	0.296460	0.148230	+	0.988953i	$0.452642\pi$
$578$	−3.96496	−0.164921
$579$	46.7822	1.94420
$580$	−1.29861	−0.0539217
$581$	−60.9583	−2.52898
$582$	0.865953	0.0358949
$583$	2.24914	0.0931498
$584$	97.0038	4.01405
$585$	−0.0870762	−0.00360016
$586$	14.2164	0.587276
$587$	−30.5229	−1.25982	−0.629908	−	0.776669i	$-0.716908\pi$
$587$	−30.5229	−1.25982	−0.629908	+	0.776669i	$0.716908\pi$
$588$	118.782	4.89850
$589$	−26.8960	−1.10823
$590$	−8.49260	−0.349635
$591$	−55.2855	−2.27414
$592$	−64.4049	−2.64702
$593$	21.4282	0.879950	0.439975	−	0.898010i	$-0.354987\pi$
$593$	21.4282	0.879950	0.439975	+	0.898010i	$0.354987\pi$
$594$	2.93024	0.120229
$595$	18.8447	0.772559
$596$	75.2037	3.08046
$597$	−18.5137	−0.757714
$598$	0.156387	0.00639515
$599$	29.2315	1.19437	0.597184	−	0.802104i	$-0.296286\pi$
$599$	29.2315	1.19437	0.597184	+	0.802104i	$0.296286\pi$
$600$	−13.8685	−0.566181
$601$	−4.25710	−0.173651	−0.0868253	−	0.996224i	$-0.527672\pi$
$601$	−4.25710	−0.173651	−0.0868253	+	0.996224i	$0.527672\pi$
$602$	−91.3344	−3.72251
$603$	14.6057	0.594792
$604$	−21.7124	−0.883466
$605$	−10.8286	−0.440244
$606$	81.3976	3.30655
$607$	−17.2926	−0.701886	−0.350943	−	0.936397i	$-0.614139\pi$
$607$	−17.2926	−0.701886	−0.350943	+	0.936397i	$0.614139\pi$
$608$	−16.7353	−0.678706
$609$	−2.74212	−0.111116
$610$	23.5209	0.952334
$611$	−0.647898	−0.0262111
$612$	33.4164	1.35078
$613$	−43.6486	−1.76295	−0.881475	−	0.472231i	$-0.843449\pi$
$613$	−43.6486	−1.76295	−0.881475	+	0.472231i	$0.843449\pi$
$614$	−49.5120	−1.99814
$615$	1.72033	0.0693702
$616$	−11.5593	−0.465737
$617$	4.57134	0.184035	0.0920176	−	0.995757i	$-0.470668\pi$
$617$	4.57134	0.184035	0.0920176	+	0.995757i	$0.470668\pi$
$618$	−72.1940	−2.90407
$619$	34.2670	1.37731	0.688653	−	0.725091i	$-0.258202\pi$
$619$	34.2670	1.37731	0.688653	+	0.725091i	$0.258202\pi$
$620$	−41.7535	−1.67686
$621$	−3.36781	−0.135146
$622$	−40.5361	−1.62535
$623$	71.1110	2.84900
$624$	−0.798253	−0.0319557
$625$	1.00000	0.0400000
$626$	17.7278	0.708545
$627$	2.60980	0.104225
$628$	−36.7646	−1.46707
$629$	−38.1717	−1.52201
$630$	−19.2209	−0.765780
$631$	19.9184	0.792938	0.396469	−	0.918048i	$-0.370235\pi$
$631$	19.9184	0.792938	0.396469	+	0.918048i	$0.370235\pi$
$632$	−3.69012	−0.146785
$633$	−32.9491	−1.30961
$634$	−36.2211	−1.43852
$635$	11.6011	0.460376
$636$	53.1539	2.10769
$637$	−0.613501	−0.0243078
$638$	0.304514	0.0120558
$639$	23.1122	0.914305
$640$	11.0863	0.438224
$641$	9.02357	0.356409	0.178205	−	0.983993i	$-0.442971\pi$
$641$	9.02357	0.356409	0.178205	+	0.983993i	$0.442971\pi$
$642$	−53.9992	−2.13118
$643$	−46.4429	−1.83153	−0.915764	−	0.401716i	$-0.868414\pi$
$643$	−46.4429	−1.83153	−0.915764	+	0.401716i	$0.868414\pi$
$644$	23.9029	0.941907
$645$	17.7925	0.700581
$646$	−31.8585	−1.25346
$647$	−48.0151	−1.88767	−0.943833	−	0.330422i	$-0.892809\pi$
$647$	−48.0151	−1.88767	−0.943833	+	0.330422i	$0.892809\pi$
$648$	71.4750	2.80780
$649$	1.37894	0.0541280
$650$	0.128875	0.00505491
$651$	−88.1661	−3.45550
$652$	56.2021	2.20104
$653$	−27.4828	−1.07549	−0.537743	−	0.843109i	$-0.680723\pi$
$653$	−27.4828	−1.07549	−0.537743	+	0.843109i	$0.680723\pi$
$654$	25.1839	0.984768
$655$	4.33058	0.169210
$656$	5.75321	0.224625
$657$	−26.1900	−1.02177
$658$	−143.015	−5.57530
$659$	27.5644	1.07376	0.536878	−	0.843660i	$-0.319604\pi$
$659$	27.5644	1.07376	0.536878	+	0.843660i	$0.319604\pi$
$660$	4.05146	0.157703
$661$	22.5049	0.875340	0.437670	−	0.899136i	$-0.355804\pi$
$661$	22.5049	0.875340	0.437670	+	0.899136i	$0.355804\pi$
$662$	13.4647	0.523320
$663$	−0.473112	−0.0183741
$664$	88.9194	3.45074
$665$	12.6886	0.492045
$666$	38.9337	1.50865
$667$	−0.349986	−0.0135515
$668$	60.8762	2.35537
$669$	−49.1293	−1.89945
$670$	−21.6169	−0.835135
$671$	−3.81908	−0.147434
$672$	−54.8589	−2.11623
$673$	−37.2790	−1.43700	−0.718501	−	0.695526i	$-0.755171\pi$
$673$	−37.2790	−1.43700	−0.718501	+	0.695526i	$0.755171\pi$
$674$	23.3956	0.901165
$675$	−2.77534	−0.106823
$676$	−58.5216	−2.25083
$677$	−23.5654	−0.905691	−0.452845	−	0.891589i	$-0.649591\pi$
$677$	−23.5654	−0.905691	−0.452845	+	0.891589i	$0.649591\pi$
$678$	19.0349	0.731030
$679$	−0.683608	−0.0262345
$680$	−27.4887	−1.05414
$681$	−58.3738	−2.23689
$682$	9.79089	0.374912
$683$	−15.4091	−0.589612	−0.294806	−	0.955557i	$-0.595255\pi$
$683$	−15.4091	−0.589612	−0.294806	+	0.955557i	$0.595255\pi$
$684$	22.5001	0.860313
$685$	−1.35067	−0.0516066
$686$	−57.3312	−2.18892
$687$	−0.236257	−0.00901377
$688$	59.5029	2.26853
$689$	−0.274535	−0.0104590
$690$	−6.72481	−0.256009
$691$	15.8108	0.601471	0.300735	−	0.953708i	$-0.402768\pi$
$691$	15.8108	0.601471	0.300735	+	0.953708i	$0.402768\pi$
$692$	39.3206	1.49474
$693$	3.12089	0.118553
$694$	24.7771	0.940525
$695$	−1.27217	−0.0482563
$696$	3.99991	0.151616
$697$	3.40983	0.129157
$698$	−31.8384	−1.20510
$699$	34.6926	1.31219
$700$	19.6979	0.744510
$701$	37.1097	1.40162	0.700808	−	0.713350i	$-0.252823\pi$
$701$	37.1097	1.40162	0.700808	+	0.713350i	$0.252823\pi$
$702$	−0.357673	−0.0134995
$703$	−25.7020	−0.969369
$704$	0.0736861	0.00277715
$705$	27.8603	1.04928
$706$	82.4069	3.10142
$707$	−64.2576	−2.41665
$708$	32.5884	1.22475
$709$	32.3882	1.21636	0.608182	−	0.793798i	$-0.291899\pi$
$709$	32.3882	1.21636	0.608182	+	0.793798i	$0.291899\pi$
$710$	−34.2068	−1.28376
$711$	0.996295	0.0373640
$712$	−103.729	−3.88741
$713$	−11.2529	−0.421426
$714$	−104.433	−3.90831
$715$	−0.0209254	−0.000782566 0
$716$	69.8765	2.61141
$717$	−6.35858	−0.237465
$718$	16.0555	0.599185
$719$	−10.1842	−0.379808	−0.189904	−	0.981803i	$-0.560818\pi$
$719$	−10.1842	−0.379808	−0.189904	+	0.981803i	$0.560818\pi$
$720$	12.5221	0.466672
$721$	56.9919	2.12249
$722$	26.9990	1.00480
$723$	36.0079	1.33915
$724$	96.1159	3.57212
$725$	−0.288416	−0.0107115
$726$	60.0094	2.22716
$727$	−5.22717	−0.193865	−0.0969325	−	0.995291i	$-0.530903\pi$
$727$	−5.22717	−0.193865	−0.0969325	+	0.995291i	$0.530903\pi$
$728$	1.41096	0.0522935
$729$	−1.20312	−0.0445599
$730$	38.7620	1.43465
$731$	35.2664	1.30437
$732$	−90.2563	−3.33597
$733$	27.8809	1.02980	0.514902	−	0.857249i	$-0.327828\pi$
$733$	27.8809	1.02980	0.514902	+	0.857249i	$0.327828\pi$
$734$	−1.88355	−0.0695232
$735$	26.3811	0.973083
$736$	−7.00182	−0.258091
$737$	3.50993	0.129290
$738$	−3.47790	−0.128023
$739$	0.328447	0.0120821	0.00604106	−	0.999982i	$-0.498077\pi$
$739$	0.328447	0.0120821	0.00604106	+	0.999982i	$0.498077\pi$
$740$	−39.8998	−1.46675
$741$	−0.318558	−0.0117025
$742$	−60.6000	−2.22470
$743$	43.8201	1.60760	0.803802	−	0.594897i	$-0.202807\pi$
$743$	43.8201	1.60760	0.803802	+	0.594897i	$0.202807\pi$
$744$	128.607	4.71497
$745$	16.7025	0.611931
$746$	−22.0935	−0.808900
$747$	−24.0073	−0.878381
$748$	8.03033	0.293618
$749$	42.6285	1.55761
$750$	−5.54177	−0.202357
$751$	18.7334	0.683590	0.341795	−	0.939775i	$-0.388965\pi$
$751$	18.7334	0.683590	0.341795	+	0.939775i	$0.388965\pi$
$752$	93.1719	3.39763
$753$	36.1476	1.31729
$754$	−0.0371697	−0.00135364
$755$	−4.82225	−0.175500
$756$	−54.6683	−1.98827
$757$	6.86717	0.249592	0.124796	−	0.992182i	$-0.460172\pi$
$757$	6.86717	0.249592	0.124796	+	0.992182i	$0.460172\pi$
$758$	29.1705	1.05952
$759$	1.09190	0.0396336
$760$	−18.5088	−0.671386
$761$	22.4599	0.814169	0.407085	−	0.913390i	$-0.366545\pi$
$761$	22.4599	0.814169	0.407085	+	0.913390i	$0.366545\pi$
$762$	−64.2906	−2.32900
$763$	−19.8809	−0.719736
$764$	29.9440	1.08334
$765$	7.42165	0.268330
$766$	87.9499	3.17776
$767$	−0.168316	−0.00607756
$768$	−62.2111	−2.24485
$769$	−10.6842	−0.385282	−0.192641	−	0.981269i	$-0.561705\pi$
$769$	−10.6842	−0.385282	−0.192641	+	0.981269i	$0.561705\pi$
$770$	−4.61901	−0.166458
$771$	−57.8514	−2.08347
$772$	96.9244	3.48838
$773$	−25.7258	−0.925292	−0.462646	−	0.886543i	$-0.653100\pi$
$773$	−25.7258	−0.925292	−0.462646	+	0.886543i	$0.653100\pi$
$774$	−35.9704	−1.29293
$775$	−9.27330	−0.333107
$776$	0.997174	0.0357964
$777$	−84.2520	−3.02252
$778$	37.9416	1.36027
$779$	2.29593	0.0822602
$780$	−0.494530	−0.0177070
$781$	5.55413	0.198742
$782$	−13.3292	−0.476650
$783$	0.800451	0.0286058
$784$	88.2253	3.15090
$785$	−8.16529	−0.291432
$786$	−23.9991	−0.856018
$787$	14.8966	0.531006	0.265503	−	0.964110i	$-0.414462\pi$
$787$	14.8966	0.531006	0.265503	+	0.964110i	$0.414462\pi$
$788$	−114.542	−4.08038
$789$	7.22985	0.257389
$790$	−1.47455	−0.0524620
$791$	−15.0267	−0.534287
$792$	−4.55242	−0.161763
$793$	0.466166	0.0165540
$794$	−62.0332	−2.20148
$795$	11.8053	0.418690
$796$	−38.3570	−1.35953
$797$	−43.5697	−1.54332	−0.771658	−	0.636037i	$-0.780572\pi$
$797$	−43.5697	−1.54332	−0.771658	+	0.636037i	$0.780572\pi$
$798$	−70.3175	−2.48921
$799$	55.2214	1.95359
$800$	−5.77005	−0.204002
$801$	28.0058	0.989535
$802$	54.4326	1.92208
$803$	−6.29376	−0.222102
$804$	82.9502	2.92543
$805$	5.30875	0.187109
$806$	−1.19510	−0.0420956
$807$	50.0638	1.76233
$808$	93.7320	3.29748
$809$	−21.0067	−0.738555	−0.369277	−	0.929319i	$-0.620395\pi$
$809$	−21.0067	−0.738555	−0.369277	+	0.929319i	$0.620395\pi$
$810$	28.5609	1.00353
$811$	−13.7041	−0.481216	−0.240608	−	0.970622i	$-0.577347\pi$
$811$	−13.7041	−0.481216	−0.240608	+	0.970622i	$0.577347\pi$
$812$	−5.68117	−0.199370
$813$	16.1345	0.565863
$814$	9.35622	0.327935
$815$	12.4823	0.437235
$816$	68.0365	2.38175
$817$	23.7458	0.830759
$818$	94.7240	3.31195
$819$	−0.380943	−0.0133112
$820$	3.56421	0.124467
$821$	−27.1989	−0.949248	−0.474624	−	0.880189i	$-0.657416\pi$
$821$	−27.1989	−0.949248	−0.474624	+	0.880189i	$0.657416\pi$
$822$	7.48513	0.261074
$823$	24.1011	0.840113	0.420056	−	0.907498i	$-0.362010\pi$
$823$	24.1011	0.840113	0.420056	+	0.907498i	$0.362010\pi$
$824$	−83.1337	−2.89610
$825$	0.899814	0.0313275
$826$	−37.1536	−1.29274
$827$	24.2855	0.844489	0.422244	−	0.906482i	$-0.361242\pi$
$827$	24.2855	0.844489	0.422244	+	0.906482i	$0.361242\pi$
$828$	9.41373	0.327150
$829$	5.94891	0.206614	0.103307	−	0.994650i	$-0.467058\pi$
$829$	5.94891	0.206614	0.103307	+	0.994650i	$0.467058\pi$
$830$	35.5315	1.23332
$831$	−15.9189	−0.552222
$832$	−0.00899430	−0.000311821 0
$833$	52.2897	1.81173
$834$	7.05009	0.244125
$835$	13.5204	0.467892
$836$	5.40703	0.187006
$837$	25.7365	0.889585
$838$	72.4074	2.50127
$839$	12.5564	0.433496	0.216748	−	0.976228i	$-0.430455\pi$
$839$	12.5564	0.433496	0.216748	+	0.976228i	$0.430455\pi$
$840$	−60.6725	−2.09340
$841$	−28.9168	−0.997132
$842$	−62.2732	−2.14608
$843$	64.0727	2.20678
$844$	−68.2646	−2.34977
$845$	−12.9974	−0.447126
$846$	−56.3238	−1.93645
$847$	−47.3731	−1.62776
$848$	39.4799	1.35575
$849$	57.2682	1.96544
$850$	−10.9843	−0.376757
$851$	−10.7534	−0.368621
$852$	131.261	4.49692
$853$	−40.1927	−1.37617	−0.688086	−	0.725629i	$-0.741549\pi$
$853$	−40.1927	−1.37617	−0.688086	+	0.725629i	$0.741549\pi$
$854$	102.900	3.52116
$855$	4.99719	0.170900
$856$	−62.1818	−2.12533
$857$	16.3040	0.556935	0.278468	−	0.960446i	$-0.410174\pi$
$857$	16.3040	0.556935	0.278468	+	0.960446i	$0.410174\pi$
$858$	0.115964	0.00395894
$859$	24.4070	0.832756	0.416378	−	0.909192i	$-0.363299\pi$
$859$	24.4070	0.832756	0.416378	+	0.909192i	$0.363299\pi$
$860$	36.8630	1.25702
$861$	7.52613	0.256490
$862$	−41.8688	−1.42606
$863$	−45.7326	−1.55676	−0.778379	−	0.627795i	$-0.783958\pi$
$863$	−45.7326	−1.55676	−0.778379	+	0.627795i	$0.783958\pi$
$864$	16.0138	0.544802
$865$	8.73296	0.296930
$866$	32.2630	1.09634
$867$	3.37912	0.114761
$868$	−182.664	−6.20003
$869$	0.239421	0.00812181
$870$	1.59833	0.0541885
$871$	−0.428430	−0.0145168
$872$	29.0001	0.982066
$873$	−0.269226	−0.00911193
$874$	−8.97486	−0.303579
$875$	4.37483	0.147896
$876$	−148.740	−5.02548
$877$	−40.5333	−1.36871	−0.684356	−	0.729148i	$-0.739917\pi$
$877$	−40.5333	−1.36871	−0.684356	+	0.729148i	$0.739917\pi$
$878$	−8.35505	−0.281969
$879$	−12.1159	−0.408659
$880$	3.00921	0.101440
$881$	−45.2063	−1.52304	−0.761520	−	0.648142i	$-0.775547\pi$
$881$	−45.2063	−1.52304	−0.761520	+	0.648142i	$0.775547\pi$
$882$	−53.3335	−1.79583
$883$	51.8961	1.74644	0.873222	−	0.487322i	$-0.162026\pi$
$883$	51.8961	1.74644	0.873222	+	0.487322i	$0.162026\pi$
$884$	−0.980202	−0.0329678
$885$	7.23778	0.243295
$886$	−75.2215	−2.52712
$887$	43.9301	1.47503	0.737514	−	0.675332i	$-0.236000\pi$
$887$	43.9301	1.47503	0.737514	+	0.675332i	$0.236000\pi$
$888$	122.898	4.12418
$889$	50.7528	1.70220
$890$	−41.4494	−1.38939
$891$	−4.63741	−0.155359
$892$	−101.787	−3.40809
$893$	37.1820	1.24425
$894$	−92.5612	−3.09571
$895$	15.5193	0.518754
$896$	48.5005	1.62029
$897$	−0.133280	−0.00445010
$898$	89.8960	2.99987
$899$	2.67456	0.0892017
$900$	7.75765	0.258588
$901$	23.3991	0.779537
$902$	−0.835780	−0.0278284
$903$	77.8393	2.59033
$904$	21.9193	0.729024
$905$	21.3470	0.709598
$906$	26.7238	0.887838
$907$	−39.8261	−1.32240	−0.661201	−	0.750208i	$-0.729953\pi$
$907$	−39.8261	−1.32240	−0.661201	+	0.750208i	$0.729953\pi$
$908$	−120.940	−4.01354
$909$	−25.3067	−0.839369
$910$	0.563807	0.0186900
$911$	0.284598	0.00942917	0.00471458	−	0.999989i	$-0.498499\pi$
$911$	0.284598	0.00942917	0.00471458	+	0.999989i	$0.498499\pi$
$912$	45.8107	1.51694
$913$	−5.76923	−0.190934
$914$	85.3655	2.82364
$915$	−20.0456	−0.662687
$916$	−0.489482	−0.0161729
$917$	18.9455	0.625637
$918$	30.4850	1.00616
$919$	−0.329286	−0.0108621	−0.00543107	−	0.999985i	$-0.501729\pi$
$919$	−0.329286	−0.0108621	−0.00543107	+	0.999985i	$0.501729\pi$
$920$	−7.74384	−0.255307
$921$	42.1964	1.39042
$922$	23.6906	0.780208
$923$	−0.677951	−0.0223150
$924$	17.7244	0.583091
$925$	−8.86161	−0.291368
$926$	−17.5269	−0.575971
$927$	22.4452	0.737198
$928$	1.66417	0.0546291
$929$	−28.0272	−0.919541	−0.459771	−	0.888038i	$-0.652068\pi$
$929$	−28.0272	−0.919541	−0.459771	+	0.888038i	$0.652068\pi$
$930$	51.3904	1.68516
$931$	35.2080	1.15390
$932$	71.8768	2.35440
$933$	34.5467	1.13101
$934$	104.348	3.41436
$935$	1.78351	0.0583270
$936$	0.555679	0.0181629
$937$	−35.5755	−1.16220	−0.581101	−	0.813832i	$-0.697378\pi$
$937$	−35.5755	−1.16220	−0.581101	+	0.813832i	$0.697378\pi$
$938$	−94.5704	−3.08783
$939$	−15.1084	−0.493045
$940$	57.7214	1.88267
$941$	26.3928	0.860380	0.430190	−	0.902738i	$-0.358446\pi$
$941$	26.3928	0.860380	0.430190	+	0.902738i	$0.358446\pi$
$942$	45.2502	1.47433
$943$	0.960585	0.0312810
$944$	24.2050	0.787805
$945$	−12.1416	−0.394967
$946$	−8.64410	−0.281044
$947$	10.0450	0.326417	0.163209	−	0.986592i	$-0.447816\pi$
$947$	10.0450	0.326417	0.163209	+	0.986592i	$0.447816\pi$
$948$	5.65824	0.183771
$949$	0.768232	0.0249379
$950$	−7.39599	−0.239958
$951$	30.8692	1.00100
$952$	−120.258	−3.89759
$953$	−49.3773	−1.59949	−0.799745	−	0.600340i	$-0.795032\pi$
$953$	−49.3773	−1.59949	−0.799745	+	0.600340i	$0.795032\pi$
$954$	−23.8662	−0.772697
$955$	6.65046	0.215204
$956$	−13.1738	−0.426072
$957$	−0.259520	−0.00838910
$958$	18.4374	0.595685
$959$	−5.90897	−0.190811
$960$	0.386764	0.0124828
$961$	54.9940	1.77400
$962$	−1.14204	−0.0368209
$963$	16.7884	0.541000
$964$	74.6020	2.40277
$965$	21.5266	0.692964
$966$	−29.4199	−0.946569
$967$	−25.0855	−0.806696	−0.403348	−	0.915047i	$-0.632154\pi$
$967$	−25.0855	−0.806696	−0.403348	+	0.915047i	$0.632154\pi$
$968$	69.1028	2.22105
$969$	27.1513	0.872224
$970$	0.398463	0.0127939
$971$	19.8577	0.637265	0.318633	−	0.947878i	$-0.396776\pi$
$971$	19.8577	0.637265	0.318633	+	0.947878i	$0.396776\pi$
$972$	−72.1076	−2.31285
$973$	−5.56554	−0.178423
$974$	9.06314	0.290402
$975$	−0.109833	−0.00351748
$976$	−67.0376	−2.14582
$977$	35.7493	1.14372	0.571861	−	0.820351i	$-0.306222\pi$
$977$	35.7493	1.14372	0.571861	+	0.820351i	$0.306222\pi$
$978$	−69.1739	−2.21194
$979$	6.73011	0.215095
$980$	54.6570	1.74595
$981$	−7.82971	−0.249984
$982$	−86.4524	−2.75881
$983$	34.6952	1.10661	0.553303	−	0.832980i	$-0.313367\pi$
$983$	34.6952	1.10661	0.553303	+	0.832980i	$0.313367\pi$
$984$	−10.9783	−0.349975
$985$	−25.4393	−0.810563
$986$	3.16803	0.100891
$987$	121.884	3.87960
$988$	−0.659995	−0.0209972
$989$	9.93490	0.315911
$990$	−1.81911	−0.0578152
$991$	24.0117	0.762758	0.381379	−	0.924419i	$-0.375449\pi$
$991$	24.0117	0.762758	0.381379	+	0.924419i	$0.375449\pi$
$992$	53.5073	1.69886
$993$	−11.4752	−0.364155
$994$	−149.649	−4.74657
$995$	−8.51895	−0.270069
$996$	−136.344	−4.32023
$997$	−14.7271	−0.466413	−0.233207	−	0.972427i	$-0.574922\pi$
$997$	−14.7271	−0.466413	−0.233207	+	0.972427i	$0.574922\pi$
$998$	100.975	3.19632
$999$	24.5940	0.778119

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.9	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.9	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55001 q^{2} +2.17323 q^{3} +4.50255 q^{4} +1.00000 q^{5} -5.54177 q^{6} +4.37483 q^{7} -6.38153 q^{8} +1.72295 q^{9} +O(q^{10})\)	\(q-2.55001 q^{2} +2.17323 q^{3} +4.50255 q^{4} +1.00000 q^{5} -5.54177 q^{6} +4.37483 q^{7} -6.38153 q^{8} +1.72295 q^{9} -2.55001 q^{10} +0.414044 q^{11} +9.78509 q^{12} -0.0505392 q^{13} -11.1559 q^{14} +2.17323 q^{15} +7.26785 q^{16} +4.30754 q^{17} -4.39353 q^{18} +2.90038 q^{19} +4.50255 q^{20} +9.50752 q^{21} -1.05582 q^{22} +1.21348 q^{23} -13.8685 q^{24} +1.00000 q^{25} +0.128875 q^{26} -2.77534 q^{27} +19.6979 q^{28} -0.288416 q^{29} -5.54177 q^{30} -9.27330 q^{31} -5.77005 q^{32} +0.899814 q^{33} -10.9843 q^{34} +4.37483 q^{35} +7.75765 q^{36} -8.86161 q^{37} -7.39599 q^{38} -0.109833 q^{39} -6.38153 q^{40} +0.791597 q^{41} -24.2443 q^{42} +8.18713 q^{43} +1.86425 q^{44} +1.72295 q^{45} -3.09438 q^{46} +12.8197 q^{47} +15.7947 q^{48} +12.1391 q^{49} -2.55001 q^{50} +9.36129 q^{51} -0.227555 q^{52} +5.43213 q^{53} +7.07714 q^{54} +0.414044 q^{55} -27.9181 q^{56} +6.30320 q^{57} +0.735463 q^{58} +3.33042 q^{59} +9.78509 q^{60} -9.22386 q^{61} +23.6470 q^{62} +7.53759 q^{63} +0.177967 q^{64} -0.0505392 q^{65} -2.29453 q^{66} +8.47720 q^{67} +19.3949 q^{68} +2.63717 q^{69} -11.1559 q^{70} +13.4144 q^{71} -10.9950 q^{72} -15.2007 q^{73} +22.5972 q^{74} +2.17323 q^{75} +13.0591 q^{76} +1.81137 q^{77} +0.280076 q^{78} +0.578251 q^{79} +7.26785 q^{80} -11.2003 q^{81} -2.01858 q^{82} -13.9339 q^{83} +42.8081 q^{84} +4.30754 q^{85} -20.8773 q^{86} -0.626794 q^{87} -2.64223 q^{88} +16.2546 q^{89} -4.39353 q^{90} -0.221100 q^{91} +5.46374 q^{92} -20.1530 q^{93} -32.6904 q^{94} +2.90038 q^{95} -12.5397 q^{96} -0.156259 q^{97} -30.9549 q^{98} +0.713374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more