LMFDB - Embedded newform 4030.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 10x^{4} + 26x^{3} - 6x^{2} - 17x - 4 $ x^7 - x^6 - 12x^5 + 10x^4 + 26x^3 - 6x^2 - 17*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.304183$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.304183 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.304183 q^{6} +2.10315 q^{7} -1.00000 q^{8} -2.90747 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.304183 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.304183 q^{6} +2.10315 q^{7} -1.00000 q^{8} -2.90747 q^{9} -1.00000 q^{10} -3.97017 q^{11} +0.304183 q^{12} -1.00000 q^{13} -2.10315 q^{14} +0.304183 q^{15} +1.00000 q^{16} +1.05076 q^{17} +2.90747 q^{18} -6.16589 q^{19} +1.00000 q^{20} +0.639742 q^{21} +3.97017 q^{22} +8.36848 q^{23} -0.304183 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.79695 q^{27} +2.10315 q^{28} -1.02423 q^{29} -0.304183 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.20766 q^{33} -1.05076 q^{34} +2.10315 q^{35} -2.90747 q^{36} +8.35788 q^{37} +6.16589 q^{38} -0.304183 q^{39} -1.00000 q^{40} -4.99441 q^{41} -0.639742 q^{42} +11.4246 q^{43} -3.97017 q^{44} -2.90747 q^{45} -8.36848 q^{46} -4.32012 q^{47} +0.304183 q^{48} -2.57676 q^{49} -1.00000 q^{50} +0.319624 q^{51} -1.00000 q^{52} -2.31105 q^{53} +1.79695 q^{54} -3.97017 q^{55} -2.10315 q^{56} -1.87556 q^{57} +1.02423 q^{58} +0.426462 q^{59} +0.304183 q^{60} -4.93171 q^{61} -1.00000 q^{62} -6.11485 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.20766 q^{66} -15.1971 q^{67} +1.05076 q^{68} +2.54555 q^{69} -2.10315 q^{70} -4.65405 q^{71} +2.90747 q^{72} +0.0835266 q^{73} -8.35788 q^{74} +0.304183 q^{75} -6.16589 q^{76} -8.34987 q^{77} +0.304183 q^{78} -3.04336 q^{79} +1.00000 q^{80} +8.17582 q^{81} +4.99441 q^{82} -12.2286 q^{83} +0.639742 q^{84} +1.05076 q^{85} -11.4246 q^{86} -0.311554 q^{87} +3.97017 q^{88} +5.31251 q^{89} +2.90747 q^{90} -2.10315 q^{91} +8.36848 q^{92} +0.304183 q^{93} +4.32012 q^{94} -6.16589 q^{95} -0.304183 q^{96} -11.0332 q^{97} +2.57676 q^{98} +11.5432 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.304183	0.175620	0.0878100	−	0.996137i	$-0.472013\pi$
$3$	0.304183	0.175620	0.0878100	+	0.996137i	$0.472013\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.304183	−0.124182
$7$	2.10315	0.794916	0.397458	−	0.917620i	$-0.369892\pi$
$7$	2.10315	0.794916	0.397458	+	0.917620i	$0.369892\pi$
$8$	−1.00000	−0.353553
$9$	−2.90747	−0.969158
$10$	−1.00000	−0.316228
$11$	−3.97017	−1.19705	−0.598526	−	0.801103i	$-0.704247\pi$
$11$	−3.97017	−1.19705	−0.598526	+	0.801103i	$0.704247\pi$
$12$	0.304183	0.0878100
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.10315	−0.562090
$15$	0.304183	0.0785397
$16$	1.00000	0.250000
$17$	1.05076	0.254847	0.127424	−	0.991848i	$-0.459329\pi$
$17$	1.05076	0.254847	0.127424	+	0.991848i	$0.459329\pi$
$18$	2.90747	0.685298
$19$	−6.16589	−1.41455	−0.707277	−	0.706937i	$-0.750076\pi$
$19$	−6.16589	−1.41455	−0.707277	+	0.706937i	$0.750076\pi$
$20$	1.00000	0.223607
$21$	0.639742	0.139603
$22$	3.97017	0.846444
$23$	8.36848	1.74495	0.872474	−	0.488661i	$-0.162514\pi$
$23$	8.36848	1.74495	0.872474	+	0.488661i	$0.162514\pi$
$24$	−0.304183	−0.0620911
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−1.79695	−0.345824
$28$	2.10315	0.397458
$29$	−1.02423	−0.190195	−0.0950977	−	0.995468i	$-0.530316\pi$
$29$	−1.02423	−0.190195	−0.0950977	+	0.995468i	$0.530316\pi$
$30$	−0.304183	−0.0555359
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−1.20766	−0.210226
$34$	−1.05076	−0.180204
$35$	2.10315	0.355497
$36$	−2.90747	−0.484579
$37$	8.35788	1.37403	0.687014	−	0.726644i	$-0.258921\pi$
$37$	8.35788	1.37403	0.687014	+	0.726644i	$0.258921\pi$
$38$	6.16589	1.00024
$39$	−0.304183	−0.0487082
$40$	−1.00000	−0.158114
$41$	−4.99441	−0.779995	−0.389998	−	0.920816i	$-0.627524\pi$
$41$	−4.99441	−0.779995	−0.389998	+	0.920816i	$0.627524\pi$
$42$	−0.639742	−0.0987143
$43$	11.4246	1.74223	0.871116	−	0.491077i	$-0.163397\pi$
$43$	11.4246	1.74223	0.871116	+	0.491077i	$0.163397\pi$
$44$	−3.97017	−0.598526
$45$	−2.90747	−0.433420
$46$	−8.36848	−1.23386
$47$	−4.32012	−0.630154	−0.315077	−	0.949066i	$-0.602030\pi$
$47$	−4.32012	−0.630154	−0.315077	+	0.949066i	$0.602030\pi$
$48$	0.304183	0.0439050
$49$	−2.57676	−0.368109
$50$	−1.00000	−0.141421
$51$	0.319624	0.0447563
$52$	−1.00000	−0.138675
$53$	−2.31105	−0.317447	−0.158723	−	0.987323i	$-0.550738\pi$
$53$	−2.31105	−0.317447	−0.158723	+	0.987323i	$0.550738\pi$
$54$	1.79695	0.244534
$55$	−3.97017	−0.535338
$56$	−2.10315	−0.281045
$57$	−1.87556	−0.248424
$58$	1.02423	0.134488
$59$	0.426462	0.0555206	0.0277603	−	0.999615i	$-0.491162\pi$
$59$	0.426462	0.0555206	0.0277603	+	0.999615i	$0.491162\pi$
$60$	0.304183	0.0392698
$61$	−4.93171	−0.631440	−0.315720	−	0.948852i	$-0.602246\pi$
$61$	−4.93171	−0.631440	−0.315720	+	0.948852i	$0.602246\pi$
$62$	−1.00000	−0.127000
$63$	−6.11485	−0.770399
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	1.20766	0.148652
$67$	−15.1971	−1.85662	−0.928308	−	0.371811i	$-0.878737\pi$
$67$	−15.1971	−1.85662	−0.928308	+	0.371811i	$0.878737\pi$
$68$	1.05076	0.127424
$69$	2.54555	0.306448
$70$	−2.10315	−0.251374
$71$	−4.65405	−0.552334	−0.276167	−	0.961110i	$-0.589064\pi$
$71$	−4.65405	−0.552334	−0.276167	+	0.961110i	$0.589064\pi$
$72$	2.90747	0.342649
$73$	0.0835266	0.00977605	0.00488802	−	0.999988i	$-0.498444\pi$
$73$	0.0835266	0.00977605	0.00488802	+	0.999988i	$0.498444\pi$
$74$	−8.35788	−0.971584
$75$	0.304183	0.0351240
$76$	−6.16589	−0.707277
$77$	−8.34987	−0.951556
$78$	0.304183	0.0344419
$79$	−3.04336	−0.342405	−0.171202	−	0.985236i	$-0.554765\pi$
$79$	−3.04336	−0.342405	−0.171202	+	0.985236i	$0.554765\pi$
$80$	1.00000	0.111803
$81$	8.17582	0.908424
$82$	4.99441	0.551540
$83$	−12.2286	−1.34226	−0.671131	−	0.741338i	$-0.734191\pi$
$83$	−12.2286	−1.34226	−0.671131	+	0.741338i	$0.734191\pi$
$84$	0.639742	0.0698016
$85$	1.05076	0.113971
$86$	−11.4246	−1.23194
$87$	−0.311554	−0.0334021
$88$	3.97017	0.423222
$89$	5.31251	0.563125	0.281562	−	0.959543i	$-0.409147\pi$
$89$	5.31251	0.563125	0.281562	+	0.959543i	$0.409147\pi$
$90$	2.90747	0.306475
$91$	−2.10315	−0.220470
$92$	8.36848	0.872474
$93$	0.304183	0.0315423
$94$	4.32012	0.445586
$95$	−6.16589	−0.632607
$96$	−0.304183	−0.0310455
$97$	−11.0332	−1.12025	−0.560126	−	0.828408i	$-0.689247\pi$
$97$	−11.0332	−1.12025	−0.560126	+	0.828408i	$0.689247\pi$
$98$	2.57676	0.260292
$99$	11.5432	1.16013
$100$	1.00000	0.100000
$101$	−7.58568	−0.754804	−0.377402	−	0.926050i	$-0.623182\pi$
$101$	−7.58568	−0.754804	−0.377402	+	0.926050i	$0.623182\pi$
$102$	−0.319624	−0.0316475
$103$	−15.2933	−1.50689	−0.753447	−	0.657509i	$-0.771610\pi$
$103$	−15.2933	−1.50689	−0.753447	+	0.657509i	$0.771610\pi$
$104$	1.00000	0.0980581
$105$	0.639742	0.0624324
$106$	2.31105	0.224469
$107$	−1.83570	−0.177464	−0.0887319	−	0.996056i	$-0.528281\pi$
$107$	−1.83570	−0.177464	−0.0887319	+	0.996056i	$0.528281\pi$
$108$	−1.79695	−0.172912
$109$	−3.53837	−0.338914	−0.169457	−	0.985538i	$-0.554201\pi$
$109$	−3.53837	−0.338914	−0.169457	+	0.985538i	$0.554201\pi$
$110$	3.97017	0.378541
$111$	2.54232	0.241307
$112$	2.10315	0.198729
$113$	−14.7079	−1.38360	−0.691802	−	0.722088i	$-0.743183\pi$
$113$	−14.7079	−1.38360	−0.691802	+	0.722088i	$0.743183\pi$
$114$	1.87556	0.175662
$115$	8.36848	0.780364
$116$	−1.02423	−0.0950977
$117$	2.90747	0.268796
$118$	−0.426462	−0.0392590
$119$	2.20991	0.202582
$120$	−0.304183	−0.0277680
$121$	4.76228	0.432934
$122$	4.93171	0.446496
$123$	−1.51921	−0.136983
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	6.11485	0.544754
$127$	−7.97754	−0.707893	−0.353946	−	0.935266i	$-0.615160\pi$
$127$	−7.97754	−0.707893	−0.353946	+	0.935266i	$0.615160\pi$
$128$	−1.00000	−0.0883883
$129$	3.47516	0.305971
$130$	1.00000	0.0877058
$131$	−3.45770	−0.302101	−0.151051	−	0.988526i	$-0.548266\pi$
$131$	−3.45770	−0.302101	−0.151051	+	0.988526i	$0.548266\pi$
$132$	−1.20766	−0.105113
$133$	−12.9678	−1.12445
$134$	15.1971	1.31283
$135$	−1.79695	−0.154657
$136$	−1.05076	−0.0901021
$137$	−11.0174	−0.941280	−0.470640	−	0.882325i	$-0.655977\pi$
$137$	−11.0174	−0.941280	−0.470640	+	0.882325i	$0.655977\pi$
$138$	−2.54555	−0.216691
$139$	7.32295	0.621125	0.310562	−	0.950553i	$-0.399483\pi$
$139$	7.32295	0.621125	0.310562	+	0.950553i	$0.399483\pi$
$140$	2.10315	0.177749
$141$	−1.31411	−0.110668
$142$	4.65405	0.390559
$143$	3.97017	0.332003
$144$	−2.90747	−0.242289
$145$	−1.02423	−0.0850580
$146$	−0.0835266	−0.00691271
$147$	−0.783806	−0.0646473
$148$	8.35788	0.687014
$149$	−21.3885	−1.75222	−0.876109	−	0.482113i	$-0.839869\pi$
$149$	−21.3885	−1.75222	−0.876109	+	0.482113i	$0.839869\pi$
$150$	−0.304183	−0.0248364
$151$	4.88056	0.397174	0.198587	−	0.980083i	$-0.436365\pi$
$151$	4.88056	0.397174	0.198587	+	0.980083i	$0.436365\pi$
$152$	6.16589	0.500120
$153$	−3.05506	−0.246987
$154$	8.34987	0.672852
$155$	1.00000	0.0803219
$156$	−0.304183	−0.0243541
$157$	14.4227	1.15105	0.575527	−	0.817783i	$-0.304797\pi$
$157$	14.4227	1.15105	0.575527	+	0.817783i	$0.304797\pi$
$158$	3.04336	0.242117
$159$	−0.702980	−0.0557500
$160$	−1.00000	−0.0790569
$161$	17.6002	1.38709
$162$	−8.17582	−0.642353
$163$	8.39797	0.657780	0.328890	−	0.944368i	$-0.393325\pi$
$163$	8.39797	0.657780	0.328890	+	0.944368i	$0.393325\pi$
$164$	−4.99441	−0.389998
$165$	−1.20766	−0.0940161
$166$	12.2286	0.949123
$167$	−12.0484	−0.932330	−0.466165	−	0.884698i	$-0.654365\pi$
$167$	−12.0484	−0.932330	−0.466165	+	0.884698i	$0.654365\pi$
$168$	−0.639742	−0.0493572
$169$	1.00000	0.0769231
$170$	−1.05076	−0.0805898
$171$	17.9272	1.37092
$172$	11.4246	0.871116
$173$	10.0096	0.761019	0.380509	−	0.924777i	$-0.375749\pi$
$173$	10.0096	0.761019	0.380509	+	0.924777i	$0.375749\pi$
$174$	0.311554	0.0236189
$175$	2.10315	0.158983
$176$	−3.97017	−0.299263
$177$	0.129722	0.00975052
$178$	−5.31251	−0.398189
$179$	0.254704	0.0190375	0.00951875	−	0.999955i	$-0.496970\pi$
$179$	0.254704	0.0190375	0.00951875	+	0.999955i	$0.496970\pi$
$180$	−2.90747	−0.216710
$181$	−4.55710	−0.338726	−0.169363	−	0.985554i	$-0.554171\pi$
$181$	−4.55710	−0.338726	−0.169363	+	0.985554i	$0.554171\pi$
$182$	2.10315	0.155896
$183$	−1.50014	−0.110894
$184$	−8.36848	−0.616932
$185$	8.35788	0.614484
$186$	−0.304183	−0.0223038
$187$	−4.17171	−0.305066
$188$	−4.32012	−0.315077
$189$	−3.77926	−0.274901
$190$	6.16589	0.447321
$191$	−18.6965	−1.35283	−0.676417	−	0.736519i	$-0.736468\pi$
$191$	−18.6965	−1.35283	−0.676417	+	0.736519i	$0.736468\pi$
$192$	0.304183	0.0219525
$193$	15.0082	1.08032	0.540159	−	0.841563i	$-0.318364\pi$
$193$	15.0082	1.08032	0.540159	+	0.841563i	$0.318364\pi$
$194$	11.0332	0.792137
$195$	−0.304183	−0.0217830
$196$	−2.57676	−0.184054
$197$	−1.68190	−0.119830	−0.0599151	−	0.998203i	$-0.519083\pi$
$197$	−1.68190	−0.119830	−0.0599151	+	0.998203i	$0.519083\pi$
$198$	−11.5432	−0.820337
$199$	2.41198	0.170980	0.0854902	−	0.996339i	$-0.472754\pi$
$199$	2.41198	0.170980	0.0854902	+	0.996339i	$0.472754\pi$
$200$	−1.00000	−0.0707107
$201$	−4.62268	−0.326059
$202$	7.58568	0.533727
$203$	−2.15412	−0.151189
$204$	0.319624	0.0223781
$205$	−4.99441	−0.348825
$206$	15.2933	1.06554
$207$	−24.3311	−1.69113
$208$	−1.00000	−0.0693375
$209$	24.4797	1.69329
$210$	−0.639742	−0.0441464
$211$	16.1364	1.11087	0.555437	−	0.831559i	$-0.312551\pi$
$211$	16.1364	1.11087	0.555437	+	0.831559i	$0.312551\pi$
$212$	−2.31105	−0.158723
$213$	−1.41568	−0.0970010
$214$	1.83570	0.125486
$215$	11.4246	0.779150
$216$	1.79695	0.122267
$217$	2.10315	0.142771
$218$	3.53837	0.239649
$219$	0.0254074	0.00171687
$220$	−3.97017	−0.267669
$221$	−1.05076	−0.0706819
$222$	−2.54232	−0.170630
$223$	22.8741	1.53176	0.765880	−	0.642983i	$-0.222303\pi$
$223$	22.8741	1.53176	0.765880	+	0.642983i	$0.222303\pi$
$224$	−2.10315	−0.140523
$225$	−2.90747	−0.193832
$226$	14.7079	0.978355
$227$	16.3042	1.08215	0.541075	−	0.840974i	$-0.318018\pi$
$227$	16.3042	1.08215	0.541075	+	0.840974i	$0.318018\pi$
$228$	−1.87556	−0.124212
$229$	−16.7855	−1.10922	−0.554608	−	0.832112i	$-0.687132\pi$
$229$	−16.7855	−1.10922	−0.554608	+	0.832112i	$0.687132\pi$
$230$	−8.36848	−0.551801
$231$	−2.53989	−0.167112
$232$	1.02423	0.0672442
$233$	−23.1767	−1.51836	−0.759179	−	0.650881i	$-0.774399\pi$
$233$	−23.1767	−1.51836	−0.759179	+	0.650881i	$0.774399\pi$
$234$	−2.90747	−0.190067
$235$	−4.32012	−0.281813
$236$	0.426462	0.0277603
$237$	−0.925737	−0.0601331
$238$	−2.20991	−0.143247
$239$	−0.486100	−0.0314432	−0.0157216	−	0.999876i	$-0.505005\pi$
$239$	−0.486100	−0.0314432	−0.0157216	+	0.999876i	$0.505005\pi$
$240$	0.304183	0.0196349
$241$	−7.85061	−0.505702	−0.252851	−	0.967505i	$-0.581368\pi$
$241$	−7.85061	−0.505702	−0.252851	+	0.967505i	$0.581368\pi$
$242$	−4.76228	−0.306131
$243$	7.87780	0.505361
$244$	−4.93171	−0.315720
$245$	−2.57676	−0.164623
$246$	1.51921	0.0968615
$247$	6.16589	0.392326
$248$	−1.00000	−0.0635001
$249$	−3.71973	−0.235728
$250$	−1.00000	−0.0632456
$251$	3.27141	0.206490	0.103245	−	0.994656i	$-0.467077\pi$
$251$	3.27141	0.206490	0.103245	+	0.994656i	$0.467077\pi$
$252$	−6.11485	−0.385199
$253$	−33.2243	−2.08879
$254$	7.97754	0.500556
$255$	0.319624	0.0200156
$256$	1.00000	0.0625000
$257$	−3.48783	−0.217565	−0.108783	−	0.994066i	$-0.534695\pi$
$257$	−3.48783	−0.217565	−0.108783	+	0.994066i	$0.534695\pi$
$258$	−3.47516	−0.216354
$259$	17.5779	1.09224
$260$	−1.00000	−0.0620174
$261$	2.97793	0.184329
$262$	3.45770	0.213618
$263$	−24.2693	−1.49651	−0.748256	−	0.663410i	$-0.769108\pi$
$263$	−24.2693	−1.49651	−0.748256	+	0.663410i	$0.769108\pi$
$264$	1.20766	0.0743262
$265$	−2.31105	−0.141966
$266$	12.9678	0.795107
$267$	1.61597	0.0988960
$268$	−15.1971	−0.928308
$269$	3.20727	0.195551	0.0977753	−	0.995209i	$-0.468827\pi$
$269$	3.20727	0.195551	0.0977753	+	0.995209i	$0.468827\pi$
$270$	1.79695	0.109359
$271$	10.1627	0.617338	0.308669	−	0.951170i	$-0.400116\pi$
$271$	10.1627	0.617338	0.308669	+	0.951170i	$0.400116\pi$
$272$	1.05076	0.0637118
$273$	−0.639742	−0.0387189
$274$	11.0174	0.665585
$275$	−3.97017	−0.239410
$276$	2.54555	0.153224
$277$	−9.22566	−0.554316	−0.277158	−	0.960824i	$-0.589393\pi$
$277$	−9.22566	−0.554316	−0.277158	+	0.960824i	$0.589393\pi$
$278$	−7.32295	−0.439201
$279$	−2.90747	−0.174066
$280$	−2.10315	−0.125687
$281$	−20.4373	−1.21919	−0.609593	−	0.792715i	$-0.708667\pi$
$281$	−20.4373	−1.21919	−0.609593	+	0.792715i	$0.708667\pi$
$282$	1.31411	0.0782539
$283$	14.9327	0.887659	0.443830	−	0.896111i	$-0.353620\pi$
$283$	14.9327	0.887659	0.443830	+	0.896111i	$0.353620\pi$
$284$	−4.65405	−0.276167
$285$	−1.87556	−0.111099
$286$	−3.97017	−0.234761
$287$	−10.5040	−0.620031
$288$	2.90747	0.171324
$289$	−15.8959	−0.935053
$290$	1.02423	0.0601451
$291$	−3.35611	−0.196739
$292$	0.0835266	0.00488802
$293$	14.3370	0.837578	0.418789	−	0.908084i	$-0.362455\pi$
$293$	14.3370	0.837578	0.418789	+	0.908084i	$0.362455\pi$
$294$	0.783806	0.0457125
$295$	0.426462	0.0248296
$296$	−8.35788	−0.485792
$297$	7.13421	0.413969
$298$	21.3885	1.23901
$299$	−8.36848	−0.483962
$300$	0.304183	0.0175620
$301$	24.0276	1.38493
$302$	−4.88056	−0.280845
$303$	−2.30743	−0.132559
$304$	−6.16589	−0.353638
$305$	−4.93171	−0.282389
$306$	3.05506	0.174646
$307$	−12.7617	−0.728349	−0.364175	−	0.931331i	$-0.618649\pi$
$307$	−12.7617	−0.728349	−0.364175	+	0.931331i	$0.618649\pi$
$308$	−8.34987	−0.475778
$309$	−4.65196	−0.264641
$310$	−1.00000	−0.0567962
$311$	−13.0304	−0.738883	−0.369442	−	0.929254i	$-0.620451\pi$
$311$	−13.0304	−0.738883	−0.369442	+	0.929254i	$0.620451\pi$
$312$	0.304183	0.0172210
$313$	0.434442	0.0245561	0.0122780	−	0.999925i	$-0.496092\pi$
$313$	0.434442	0.0245561	0.0122780	+	0.999925i	$0.496092\pi$
$314$	−14.4227	−0.813918
$315$	−6.11485	−0.344533
$316$	−3.04336	−0.171202
$317$	2.42178	0.136021	0.0680104	−	0.997685i	$-0.478335\pi$
$317$	2.42178	0.136021	0.0680104	+	0.997685i	$0.478335\pi$
$318$	0.702980	0.0394212
$319$	4.06638	0.227674
$320$	1.00000	0.0559017
$321$	−0.558388	−0.0311662
$322$	−17.6002	−0.980819
$323$	−6.47889	−0.360495
$324$	8.17582	0.454212
$325$	−1.00000	−0.0554700
$326$	−8.39797	−0.465121
$327$	−1.07631	−0.0595202
$328$	4.99441	0.275770
$329$	−9.08586	−0.500919
$330$	1.20766	0.0664794
$331$	14.3808	0.790440	0.395220	−	0.918586i	$-0.370668\pi$
$331$	14.3808	0.790440	0.395220	+	0.918586i	$0.370668\pi$
$332$	−12.2286	−0.671131
$333$	−24.3003	−1.33165
$334$	12.0484	0.659257
$335$	−15.1971	−0.830304
$336$	0.639742	0.0349008
$337$	−3.19078	−0.173813	−0.0869063	−	0.996216i	$-0.527698\pi$
$337$	−3.19078	−0.173813	−0.0869063	+	0.996216i	$0.527698\pi$
$338$	−1.00000	−0.0543928
$339$	−4.47389	−0.242988
$340$	1.05076	0.0569856
$341$	−3.97017	−0.214997
$342$	−17.9272	−0.969390
$343$	−20.1414	−1.08753
$344$	−11.4246	−0.615972
$345$	2.54555	0.137048
$346$	−10.0096	−0.538122
$347$	−16.6005	−0.891164	−0.445582	−	0.895241i	$-0.647003\pi$
$347$	−16.6005	−0.891164	−0.445582	+	0.895241i	$0.647003\pi$
$348$	−0.311554	−0.0167011
$349$	−25.2618	−1.35223	−0.676117	−	0.736794i	$-0.736339\pi$
$349$	−25.2618	−1.35223	−0.676117	+	0.736794i	$0.736339\pi$
$350$	−2.10315	−0.112418
$351$	1.79695	0.0959142
$352$	3.97017	0.211611
$353$	15.0704	0.802118	0.401059	−	0.916052i	$-0.368642\pi$
$353$	15.0704	0.802118	0.401059	+	0.916052i	$0.368642\pi$
$354$	−0.129722	−0.00689466
$355$	−4.65405	−0.247011
$356$	5.31251	0.281562
$357$	0.672217	0.0355775
$358$	−0.254704	−0.0134615
$359$	−32.9701	−1.74009	−0.870047	−	0.492968i	$-0.835912\pi$
$359$	−32.9701	−1.74009	−0.870047	+	0.492968i	$0.835912\pi$
$360$	2.90747	0.153237
$361$	19.0182	1.00096
$362$	4.55710	0.239516
$363$	1.44860	0.0760319
$364$	−2.10315	−0.110235
$365$	0.0835266	0.00437198
$366$	1.50014	0.0784136
$367$	−20.4402	−1.06697	−0.533484	−	0.845810i	$-0.679117\pi$
$367$	−20.4402	−1.06697	−0.533484	+	0.845810i	$0.679117\pi$
$368$	8.36848	0.436237
$369$	14.5211	0.755938
$370$	−8.35788	−0.434506
$371$	−4.86047	−0.252343
$372$	0.304183	0.0157711
$373$	37.5315	1.94331	0.971655	−	0.236405i	$-0.0759692\pi$
$373$	37.5315	1.94331	0.971655	+	0.236405i	$0.0759692\pi$
$374$	4.17171	0.215714
$375$	0.304183	0.0157079
$376$	4.32012	0.222793
$377$	1.02423	0.0527507
$378$	3.77926	0.194384
$379$	36.7618	1.88833	0.944164	−	0.329475i	$-0.106872\pi$
$379$	36.7618	1.88833	0.944164	+	0.329475i	$0.106872\pi$
$380$	−6.16589	−0.316304
$381$	−2.42663	−0.124320
$382$	18.6965	0.956598
$383$	−5.29265	−0.270442	−0.135221	−	0.990815i	$-0.543174\pi$
$383$	−5.29265	−0.270442	−0.135221	+	0.990815i	$0.543174\pi$
$384$	−0.304183	−0.0155228
$385$	−8.34987	−0.425549
$386$	−15.0082	−0.763900
$387$	−33.2167	−1.68850
$388$	−11.0332	−0.560126
$389$	34.7991	1.76438	0.882192	−	0.470890i	$-0.156067\pi$
$389$	34.7991	1.76438	0.882192	+	0.470890i	$0.156067\pi$
$390$	0.304183	0.0154029
$391$	8.79328	0.444695
$392$	2.57676	0.130146
$393$	−1.05177	−0.0530550
$394$	1.68190	0.0847328
$395$	−3.04336	−0.153128
$396$	11.5432	0.580066
$397$	33.4672	1.67967	0.839835	−	0.542842i	$-0.182652\pi$
$397$	33.4672	1.67967	0.839835	+	0.542842i	$0.182652\pi$
$398$	−2.41198	−0.120901
$399$	−3.94458	−0.197476
$400$	1.00000	0.0500000
$401$	12.4276	0.620607	0.310303	−	0.950638i	$-0.399569\pi$
$401$	12.4276	0.620607	0.310303	+	0.950638i	$0.399569\pi$
$402$	4.62268	0.230559
$403$	−1.00000	−0.0498135
$404$	−7.58568	−0.377402
$405$	8.17582	0.406260
$406$	2.15412	0.106907
$407$	−33.1822	−1.64478
$408$	−0.319624	−0.0158237
$409$	−27.5607	−1.36279	−0.681394	−	0.731917i	$-0.738626\pi$
$409$	−27.5607	−1.36279	−0.681394	+	0.731917i	$0.738626\pi$
$410$	4.99441	0.246656
$411$	−3.35130	−0.165308
$412$	−15.2933	−0.753447
$413$	0.896913	0.0441342
$414$	24.3311	1.19581
$415$	−12.2286	−0.600278
$416$	1.00000	0.0490290
$417$	2.22752	0.109082
$418$	−24.4797	−1.19734
$419$	33.4846	1.63583	0.817916	−	0.575338i	$-0.195129\pi$
$419$	33.4846	1.63583	0.817916	+	0.575338i	$0.195129\pi$
$420$	0.639742	0.0312162
$421$	6.08340	0.296487	0.148243	−	0.988951i	$-0.452638\pi$
$421$	6.08340	0.296487	0.148243	+	0.988951i	$0.452638\pi$
$422$	−16.1364	−0.785507
$423$	12.5606	0.610719
$424$	2.31105	0.112234
$425$	1.05076	0.0509695
$426$	1.41568	0.0685901
$427$	−10.3721	−0.501942
$428$	−1.83570	−0.0887319
$429$	1.20766	0.0583063
$430$	−11.4246	−0.550942
$431$	6.74074	0.324690	0.162345	−	0.986734i	$-0.448094\pi$
$431$	6.74074	0.324690	0.162345	+	0.986734i	$0.448094\pi$
$432$	−1.79695	−0.0864559
$433$	28.9173	1.38968	0.694838	−	0.719166i	$-0.255476\pi$
$433$	28.9173	1.38968	0.694838	+	0.719166i	$0.255476\pi$
$434$	−2.10315	−0.100954
$435$	−0.311554	−0.0149379
$436$	−3.53837	−0.169457
$437$	−51.5991	−2.46832
$438$	−0.0254074	−0.00121401
$439$	4.10908	0.196115	0.0980577	−	0.995181i	$-0.468737\pi$
$439$	4.10908	0.196115	0.0980577	+	0.995181i	$0.468737\pi$
$440$	3.97017	0.189271
$441$	7.49186	0.356755
$442$	1.05076	0.0499797
$443$	13.4087	0.637066	0.318533	−	0.947912i	$-0.396810\pi$
$443$	13.4087	0.637066	0.318533	+	0.947912i	$0.396810\pi$
$444$	2.54232	0.120653
$445$	5.31251	0.251837
$446$	−22.8741	−1.08312
$447$	−6.50603	−0.307725
$448$	2.10315	0.0993645
$449$	−11.5057	−0.542986	−0.271493	−	0.962440i	$-0.587517\pi$
$449$	−11.5057	−0.542986	−0.271493	+	0.962440i	$0.587517\pi$
$450$	2.90747	0.137060
$451$	19.8287	0.933695
$452$	−14.7079	−0.691802
$453$	1.48458	0.0697518
$454$	−16.3042	−0.765195
$455$	−2.10315	−0.0985972
$456$	1.87556	0.0878311
$457$	−11.9812	−0.560458	−0.280229	−	0.959933i	$-0.590410\pi$
$457$	−11.9812	−0.560458	−0.280229	+	0.959933i	$0.590410\pi$
$458$	16.7855	0.784335
$459$	−1.88817	−0.0881322
$460$	8.36848	0.390182
$461$	−2.97335	−0.138483	−0.0692414	−	0.997600i	$-0.522058\pi$
$461$	−2.97335	−0.138483	−0.0692414	+	0.997600i	$0.522058\pi$
$462$	2.53989	0.118166
$463$	11.4183	0.530653	0.265327	−	0.964159i	$-0.414520\pi$
$463$	11.4183	0.530653	0.265327	+	0.964159i	$0.414520\pi$
$464$	−1.02423	−0.0475488
$465$	0.304183	0.0141061
$466$	23.1767	1.07364
$467$	−2.64607	−0.122445	−0.0612227	−	0.998124i	$-0.519500\pi$
$467$	−2.64607	−0.122445	−0.0612227	+	0.998124i	$0.519500\pi$
$468$	2.90747	0.134398
$469$	−31.9617	−1.47585
$470$	4.32012	0.199272
$471$	4.38713	0.202148
$472$	−0.426462	−0.0196295
$473$	−45.3576	−2.08554
$474$	0.925737	0.0425205
$475$	−6.16589	−0.282911
$476$	2.20991	0.101291
$477$	6.71930	0.307656
$478$	0.486100	0.0222337
$479$	25.4763	1.16404	0.582020	−	0.813175i	$-0.302263\pi$
$479$	25.4763	1.16404	0.582020	+	0.813175i	$0.302263\pi$
$480$	−0.304183	−0.0138840
$481$	−8.35788	−0.381087
$482$	7.85061	0.357585
$483$	5.35367	0.243600
$484$	4.76228	0.216467
$485$	−11.0332	−0.500992
$486$	−7.87780	−0.357344
$487$	−39.7751	−1.80238	−0.901192	−	0.433420i	$-0.857307\pi$
$487$	−39.7751	−1.80238	−0.901192	+	0.433420i	$0.857307\pi$
$488$	4.93171	0.223248
$489$	2.55452	0.115519
$490$	2.57676	0.116406
$491$	23.2343	1.04855	0.524275	−	0.851549i	$-0.324336\pi$
$491$	23.2343	1.04855	0.524275	+	0.851549i	$0.324336\pi$
$492$	−1.51921	−0.0684914
$493$	−1.07623	−0.0484708
$494$	−6.16589	−0.277417
$495$	11.5432	0.518827
$496$	1.00000	0.0449013
$497$	−9.78817	−0.439059
$498$	3.71973	0.166685
$499$	−35.8193	−1.60349	−0.801745	−	0.597666i	$-0.796095\pi$
$499$	−35.8193	−1.60349	−0.801745	+	0.597666i	$0.796095\pi$
$500$	1.00000	0.0447214
$501$	−3.66490	−0.163736
$502$	−3.27141	−0.146010
$503$	−37.2386	−1.66039	−0.830193	−	0.557477i	$-0.811770\pi$
$503$	−37.2386	−1.66039	−0.830193	+	0.557477i	$0.811770\pi$
$504$	6.11485	0.272377
$505$	−7.58568	−0.337558
$506$	33.2243	1.47700
$507$	0.304183	0.0135092
$508$	−7.97754	−0.353946
$509$	−21.8873	−0.970138	−0.485069	−	0.874476i	$-0.661205\pi$
$509$	−21.8873	−0.970138	−0.485069	+	0.874476i	$0.661205\pi$
$510$	−0.319624	−0.0141532
$511$	0.175669	0.00777114
$512$	−1.00000	−0.0441942
$513$	11.0798	0.489186
$514$	3.48783	0.153842
$515$	−15.2933	−0.673904
$516$	3.47516	0.152985
$517$	17.1516	0.754327
$518$	−17.5779	−0.772328
$519$	3.04476	0.133650
$520$	1.00000	0.0438529
$521$	−28.8896	−1.26568	−0.632839	−	0.774283i	$-0.718111\pi$
$521$	−28.8896	−1.26568	−0.632839	+	0.774283i	$0.718111\pi$
$522$	−2.97793	−0.130340
$523$	11.2926	0.493793	0.246896	−	0.969042i	$-0.420589\pi$
$523$	11.2926	0.493793	0.246896	+	0.969042i	$0.420589\pi$
$524$	−3.45770	−0.151051
$525$	0.639742	0.0279206
$526$	24.2693	1.05819
$527$	1.05076	0.0457719
$528$	−1.20766	−0.0525566
$529$	47.0314	2.04484
$530$	2.31105	0.100385
$531$	−1.23993	−0.0538082
$532$	−12.9678	−0.562225
$533$	4.99441	0.216332
$534$	−1.61597	−0.0699300
$535$	−1.83570	−0.0793642
$536$	15.1971	0.656413
$537$	0.0774767	0.00334337
$538$	−3.20727	−0.138275
$539$	10.2302	0.440645
$540$	−1.79695	−0.0773285
$541$	3.37393	0.145057	0.0725283	−	0.997366i	$-0.476893\pi$
$541$	3.37393	0.145057	0.0725283	+	0.997366i	$0.476893\pi$
$542$	−10.1627	−0.436524
$543$	−1.38619	−0.0594871
$544$	−1.05076	−0.0450511
$545$	−3.53837	−0.151567
$546$	0.639742	0.0273784
$547$	−25.3057	−1.08199	−0.540996	−	0.841025i	$-0.681953\pi$
$547$	−25.3057	−1.08199	−0.540996	+	0.841025i	$0.681953\pi$
$548$	−11.0174	−0.470640
$549$	14.3388	0.611965
$550$	3.97017	0.169289
$551$	6.31531	0.269041
$552$	−2.54555	−0.108346
$553$	−6.40064	−0.272183
$554$	9.22566	0.391961
$555$	2.54232	0.107916
$556$	7.32295	0.310562
$557$	−38.0316	−1.61145	−0.805726	−	0.592289i	$-0.798224\pi$
$557$	−38.0316	−1.61145	−0.805726	+	0.592289i	$0.798224\pi$
$558$	2.90747	0.123083
$559$	−11.4246	−0.483208
$560$	2.10315	0.0888743
$561$	−1.26896	−0.0535756
$562$	20.4373	0.862094
$563$	26.3626	1.11105	0.555525	−	0.831500i	$-0.312517\pi$
$563$	26.3626	1.11105	0.555525	+	0.831500i	$0.312517\pi$
$564$	−1.31411	−0.0553338
$565$	−14.7079	−0.618766
$566$	−14.9327	−0.627670
$567$	17.1950	0.722121
$568$	4.65405	0.195280
$569$	31.5730	1.32361	0.661804	−	0.749677i	$-0.269791\pi$
$569$	31.5730	1.32361	0.661804	+	0.749677i	$0.269791\pi$
$570$	1.87556	0.0785585
$571$	18.8757	0.789923	0.394961	−	0.918698i	$-0.370758\pi$
$571$	18.8757	0.789923	0.394961	+	0.918698i	$0.370758\pi$
$572$	3.97017	0.166001
$573$	−5.68716	−0.237585
$574$	10.5040	0.438428
$575$	8.36848	0.348990
$576$	−2.90747	−0.121145
$577$	−19.8962	−0.828289	−0.414144	−	0.910211i	$-0.635919\pi$
$577$	−19.8962	−0.828289	−0.414144	+	0.910211i	$0.635919\pi$
$578$	15.8959	0.661182
$579$	4.56525	0.189725
$580$	−1.02423	−0.0425290
$581$	−25.7186	−1.06699
$582$	3.35611	0.139115
$583$	9.17525	0.380000
$584$	−0.0835266	−0.00345636
$585$	2.90747	0.120209
$586$	−14.3370	−0.592257
$587$	33.2708	1.37323	0.686617	−	0.727020i	$-0.259095\pi$
$587$	33.2708	1.37323	0.686617	+	0.727020i	$0.259095\pi$
$588$	−0.783806	−0.0323236
$589$	−6.16589	−0.254061
$590$	−0.426462	−0.0175571
$591$	−0.511604	−0.0210446
$592$	8.35788	0.343507
$593$	−4.90311	−0.201347	−0.100673	−	0.994920i	$-0.532100\pi$
$593$	−4.90311	−0.201347	−0.100673	+	0.994920i	$0.532100\pi$
$594$	−7.13421	−0.292720
$595$	2.20991	0.0905975
$596$	−21.3885	−0.876109
$597$	0.733682	0.0300276
$598$	8.36848	0.342212
$599$	−34.0011	−1.38925	−0.694623	−	0.719373i	$-0.744429\pi$
$599$	−34.0011	−1.38925	−0.694623	+	0.719373i	$0.744429\pi$
$600$	−0.304183	−0.0124182
$601$	30.8232	1.25730	0.628652	−	0.777687i	$-0.283607\pi$
$601$	30.8232	1.25730	0.628652	+	0.777687i	$0.283607\pi$
$602$	−24.0276	−0.979292
$603$	44.1850	1.79935
$604$	4.88056	0.198587
$605$	4.76228	0.193614
$606$	2.30743	0.0937331
$607$	2.42570	0.0984563	0.0492282	−	0.998788i	$-0.484324\pi$
$607$	2.42570	0.0984563	0.0492282	+	0.998788i	$0.484324\pi$
$608$	6.16589	0.250060
$609$	−0.655245	−0.0265519
$610$	4.93171	0.199679
$611$	4.32012	0.174773
$612$	−3.05506	−0.123494
$613$	−2.14597	−0.0866748	−0.0433374	−	0.999060i	$-0.513799\pi$
$613$	−2.14597	−0.0866748	−0.0433374	+	0.999060i	$0.513799\pi$
$614$	12.7617	0.515021
$615$	−1.51921	−0.0612606
$616$	8.34987	0.336426
$617$	−17.3171	−0.697159	−0.348579	−	0.937279i	$-0.613336\pi$
$617$	−17.3171	−0.697159	−0.348579	+	0.937279i	$0.613336\pi$
$618$	4.65196	0.187129
$619$	−5.46719	−0.219745	−0.109872	−	0.993946i	$-0.535044\pi$
$619$	−5.46719	−0.219745	−0.109872	+	0.993946i	$0.535044\pi$
$620$	1.00000	0.0401610
$621$	−15.0377	−0.603444
$622$	13.0304	0.522470
$623$	11.1730	0.447637
$624$	−0.304183	−0.0121771
$625$	1.00000	0.0400000
$626$	−0.434442	−0.0173638
$627$	7.44629	0.297376
$628$	14.4227	0.575527
$629$	8.78215	0.350167
$630$	6.11485	0.243621
$631$	28.6210	1.13939	0.569693	−	0.821858i	$-0.307062\pi$
$631$	28.6210	1.13939	0.569693	+	0.821858i	$0.307062\pi$
$632$	3.04336	0.121058
$633$	4.90841	0.195092
$634$	−2.42178	−0.0961812
$635$	−7.97754	−0.316579
$636$	−0.702980	−0.0278750
$637$	2.57676	0.102095
$638$	−4.06638	−0.160990
$639$	13.5315	0.535299
$640$	−1.00000	−0.0395285
$641$	−19.4516	−0.768290	−0.384145	−	0.923273i	$-0.625504\pi$
$641$	−19.4516	−0.768290	−0.384145	+	0.923273i	$0.625504\pi$
$642$	0.558388	0.0220378
$643$	30.3913	1.19852	0.599258	−	0.800556i	$-0.295462\pi$
$643$	30.3913	1.19852	0.599258	+	0.800556i	$0.295462\pi$
$644$	17.6002	0.693543
$645$	3.47516	0.136834
$646$	6.47889	0.254909
$647$	3.65820	0.143819	0.0719093	−	0.997411i	$-0.477091\pi$
$647$	3.65820	0.143819	0.0719093	+	0.997411i	$0.477091\pi$
$648$	−8.17582	−0.321176
$649$	−1.69313	−0.0664610
$650$	1.00000	0.0392232
$651$	0.639742	0.0250735
$652$	8.39797	0.328890
$653$	15.4167	0.603302	0.301651	−	0.953418i	$-0.402462\pi$
$653$	15.4167	0.603302	0.301651	+	0.953418i	$0.402462\pi$
$654$	1.07631	0.0420871
$655$	−3.45770	−0.135104
$656$	−4.99441	−0.194999
$657$	−0.242851	−0.00947453
$658$	9.08586	0.354204
$659$	−11.1097	−0.432774	−0.216387	−	0.976308i	$-0.569427\pi$
$659$	−11.1097	−0.432774	−0.216387	+	0.976308i	$0.569427\pi$
$660$	−1.20766	−0.0470080
$661$	16.0584	0.624598	0.312299	−	0.949984i	$-0.398901\pi$
$661$	16.0584	0.624598	0.312299	+	0.949984i	$0.398901\pi$
$662$	−14.3808	−0.558926
$663$	−0.319624	−0.0124132
$664$	12.2286	0.474562
$665$	−12.9678	−0.502870
$666$	24.3003	0.941618
$667$	−8.57127	−0.331881
$668$	−12.0484	−0.466165
$669$	6.95790	0.269008
$670$	15.1971	0.587114
$671$	19.5797	0.755867
$672$	−0.639742	−0.0246786
$673$	5.91250	0.227910	0.113955	−	0.993486i	$-0.463648\pi$
$673$	5.91250	0.227910	0.113955	+	0.993486i	$0.463648\pi$
$674$	3.19078	0.122904
$675$	−1.79695	−0.0691647
$676$	1.00000	0.0384615
$677$	38.2263	1.46916	0.734578	−	0.678524i	$-0.237380\pi$
$677$	38.2263	1.46916	0.734578	+	0.678524i	$0.237380\pi$
$678$	4.47389	0.171819
$679$	−23.2045	−0.890506
$680$	−1.05076	−0.0402949
$681$	4.95947	0.190047
$682$	3.97017	0.152026
$683$	22.7820	0.871728	0.435864	−	0.900013i	$-0.356443\pi$
$683$	22.7820	0.871728	0.435864	+	0.900013i	$0.356443\pi$
$684$	17.9272	0.685462
$685$	−11.0174	−0.420953
$686$	20.1414	0.769001
$687$	−5.10586	−0.194801
$688$	11.4246	0.435558
$689$	2.31105	0.0880438
$690$	−2.54555	−0.0969073
$691$	30.3502	1.15458	0.577288	−	0.816541i	$-0.304111\pi$
$691$	30.3502	1.15458	0.577288	+	0.816541i	$0.304111\pi$
$692$	10.0096	0.380509
$693$	24.2770	0.922208
$694$	16.6005	0.630148
$695$	7.32295	0.277775
$696$	0.311554	0.0118094
$697$	−5.24794	−0.198780
$698$	25.2618	0.956174
$699$	−7.04997	−0.266654
$700$	2.10315	0.0794916
$701$	−12.9321	−0.488440	−0.244220	−	0.969720i	$-0.578532\pi$
$701$	−12.9321	−0.488440	−0.244220	+	0.969720i	$0.578532\pi$
$702$	−1.79695	−0.0678216
$703$	−51.5338	−1.94363
$704$	−3.97017	−0.149632
$705$	−1.31411	−0.0494921
$706$	−15.0704	−0.567183
$707$	−15.9538	−0.600005
$708$	0.129722	0.00487526
$709$	−21.7007	−0.814987	−0.407494	−	0.913208i	$-0.633597\pi$
$709$	−21.7007	−0.814987	−0.407494	+	0.913208i	$0.633597\pi$
$710$	4.65405	0.174663
$711$	8.84848	0.331844
$712$	−5.31251	−0.199095
$713$	8.36848	0.313402
$714$	−0.672217	−0.0251571
$715$	3.97017	0.148476
$716$	0.254704	0.00951875
$717$	−0.147863	−0.00552205
$718$	32.9701	1.23043
$719$	−2.84582	−0.106131	−0.0530657	−	0.998591i	$-0.516899\pi$
$719$	−2.84582	−0.106131	−0.0530657	+	0.998591i	$0.516899\pi$
$720$	−2.90747	−0.108355
$721$	−32.1641	−1.19785
$722$	−19.0182	−0.707786
$723$	−2.38802	−0.0888114
$724$	−4.55710	−0.169363
$725$	−1.02423	−0.0380391
$726$	−1.44860	−0.0537627
$727$	24.7692	0.918640	0.459320	−	0.888271i	$-0.348093\pi$
$727$	24.7692	0.918640	0.459320	+	0.888271i	$0.348093\pi$
$728$	2.10315	0.0779479
$729$	−22.1312	−0.819673
$730$	−0.0835266	−0.00309146
$731$	12.0045	0.444003
$732$	−1.50014	−0.0554468
$733$	14.9482	0.552126	0.276063	−	0.961140i	$-0.410970\pi$
$733$	14.9482	0.552126	0.276063	+	0.961140i	$0.410970\pi$
$734$	20.4402	0.754460
$735$	−0.783806	−0.0289111
$736$	−8.36848	−0.308466
$737$	60.3350	2.22247
$738$	−14.5211	−0.534529
$739$	−24.6251	−0.905850	−0.452925	−	0.891549i	$-0.649619\pi$
$739$	−24.6251	−0.905850	−0.452925	+	0.891549i	$0.649619\pi$
$740$	8.35788	0.307242
$741$	1.87556	0.0689004
$742$	4.86047	0.178434
$743$	−12.2952	−0.451067	−0.225534	−	0.974235i	$-0.572413\pi$
$743$	−12.2952	−0.451067	−0.225534	+	0.974235i	$0.572413\pi$
$744$	−0.304183	−0.0111519
$745$	−21.3885	−0.783616
$746$	−37.5315	−1.37413
$747$	35.5543	1.30086
$748$	−4.17171	−0.152533
$749$	−3.86075	−0.141069
$750$	−0.304183	−0.0111072
$751$	36.2121	1.32140	0.660700	−	0.750650i	$-0.270260\pi$
$751$	36.2121	1.32140	0.660700	+	0.750650i	$0.270260\pi$
$752$	−4.32012	−0.157538
$753$	0.995108	0.0362638
$754$	−1.02423	−0.0373004
$755$	4.88056	0.177622
$756$	−3.77926	−0.137450
$757$	−46.2224	−1.67998	−0.839991	−	0.542600i	$-0.817440\pi$
$757$	−46.2224	−1.67998	−0.839991	+	0.542600i	$0.817440\pi$
$758$	−36.7618	−1.33525
$759$	−10.1063	−0.366834
$760$	6.16589	0.223660
$761$	−35.1016	−1.27243	−0.636217	−	0.771510i	$-0.719502\pi$
$761$	−35.1016	−1.27243	−0.636217	+	0.771510i	$0.719502\pi$
$762$	2.42663	0.0879076
$763$	−7.44172	−0.269408
$764$	−18.6965	−0.676417
$765$	−3.05506	−0.110456
$766$	5.29265	0.191231
$767$	−0.426462	−0.0153986
$768$	0.304183	0.0109763
$769$	38.3488	1.38289	0.691447	−	0.722427i	$-0.256974\pi$
$769$	38.3488	1.38289	0.691447	+	0.722427i	$0.256974\pi$
$770$	8.34987	0.300908
$771$	−1.06094	−0.0382088
$772$	15.0082	0.540159
$773$	27.1278	0.975718	0.487859	−	0.872923i	$-0.337778\pi$
$773$	27.1278	0.975718	0.487859	+	0.872923i	$0.337778\pi$
$774$	33.2167	1.19395
$775$	1.00000	0.0359211
$776$	11.0332	0.396069
$777$	5.34689	0.191819
$778$	−34.7991	−1.24761
$779$	30.7950	1.10334
$780$	−0.304183	−0.0108915
$781$	18.4774	0.661173
$782$	−8.79328	−0.314447
$783$	1.84050	0.0657740
$784$	−2.57676	−0.0920272
$785$	14.4227	0.514767
$786$	1.05177	0.0375155
$787$	−19.5872	−0.698208	−0.349104	−	0.937084i	$-0.613514\pi$
$787$	−19.5872	−0.698208	−0.349104	+	0.937084i	$0.613514\pi$
$788$	−1.68190	−0.0599151
$789$	−7.38232	−0.262817
$790$	3.04336	0.108278
$791$	−30.9329	−1.09985
$792$	−11.5432	−0.410169
$793$	4.93171	0.175130
$794$	−33.4672	−1.18771
$795$	−0.702980	−0.0249321
$796$	2.41198	0.0854902
$797$	−13.5883	−0.481323	−0.240662	−	0.970609i	$-0.577364\pi$
$797$	−13.5883	−0.481323	−0.240662	+	0.970609i	$0.577364\pi$
$798$	3.94458	0.139637
$799$	−4.53942	−0.160593
$800$	−1.00000	−0.0353553
$801$	−15.4460	−0.545757
$802$	−12.4276	−0.438835
$803$	−0.331615	−0.0117024
$804$	−4.62268	−0.163030
$805$	17.6002	0.620324
$806$	1.00000	0.0352235
$807$	0.975596	0.0343426
$808$	7.58568	0.266863
$809$	−43.6606	−1.53503	−0.767513	−	0.641034i	$-0.778506\pi$
$809$	−43.6606	−1.53503	−0.767513	+	0.641034i	$0.778506\pi$
$810$	−8.17582	−0.287269
$811$	18.4240	0.646953	0.323477	−	0.946236i	$-0.395148\pi$
$811$	18.4240	0.646953	0.323477	+	0.946236i	$0.395148\pi$
$812$	−2.15412	−0.0755947
$813$	3.09131	0.108417
$814$	33.1822	1.16304
$815$	8.39797	0.294168
$816$	0.319624	0.0111891
$817$	−70.4428	−2.46448
$818$	27.5607	0.963637
$819$	6.11485	0.213670
$820$	−4.99441	−0.174412
$821$	0.576779	0.0201297	0.0100649	−	0.999949i	$-0.496796\pi$
$821$	0.576779	0.0201297	0.0100649	+	0.999949i	$0.496796\pi$
$822$	3.35130	0.116890
$823$	3.55352	0.123868	0.0619340	−	0.998080i	$-0.480273\pi$
$823$	3.55352	0.123868	0.0619340	+	0.998080i	$0.480273\pi$
$824$	15.2933	0.532768
$825$	−1.20766	−0.0420453
$826$	−0.896913	−0.0312076
$827$	−1.18696	−0.0412746	−0.0206373	−	0.999787i	$-0.506570\pi$
$827$	−1.18696	−0.0412746	−0.0206373	+	0.999787i	$0.506570\pi$
$828$	−24.3311	−0.845565
$829$	−16.5139	−0.573553	−0.286777	−	0.957998i	$-0.592584\pi$
$829$	−16.5139	−0.573553	−0.286777	+	0.957998i	$0.592584\pi$
$830$	12.2286	0.424461
$831$	−2.80629	−0.0973490
$832$	−1.00000	−0.0346688
$833$	−2.70756	−0.0938115
$834$	−2.22752	−0.0771326
$835$	−12.0484	−0.416951
$836$	24.4797	0.846647
$837$	−1.79695	−0.0621117
$838$	−33.4846	−1.15671
$839$	27.9564	0.965162	0.482581	−	0.875851i	$-0.339699\pi$
$839$	27.9564	0.965162	0.482581	+	0.875851i	$0.339699\pi$
$840$	−0.639742	−0.0220732
$841$	−27.9509	−0.963826
$842$	−6.08340	−0.209648
$843$	−6.21667	−0.214113
$844$	16.1364	0.555437
$845$	1.00000	0.0344010
$846$	−12.5606	−0.431843
$847$	10.0158	0.344146
$848$	−2.31105	−0.0793616
$849$	4.54228	0.155891
$850$	−1.05076	−0.0360409
$851$	69.9427	2.39761
$852$	−1.41568	−0.0485005
$853$	−49.5412	−1.69626	−0.848129	−	0.529790i	$-0.822271\pi$
$853$	−49.5412	−1.69626	−0.848129	+	0.529790i	$0.822271\pi$
$854$	10.3721	0.354927
$855$	17.9272	0.613096
$856$	1.83570	0.0627429
$857$	50.2409	1.71620	0.858098	−	0.513486i	$-0.171646\pi$
$857$	50.2409	1.71620	0.858098	+	0.513486i	$0.171646\pi$
$858$	−1.20766	−0.0412288
$859$	41.1478	1.40394	0.701972	−	0.712204i	$-0.252303\pi$
$859$	41.1478	1.40394	0.701972	+	0.712204i	$0.252303\pi$
$860$	11.4246	0.389575
$861$	−3.19513	−0.108890
$862$	−6.74074	−0.229591
$863$	31.3004	1.06548	0.532738	−	0.846280i	$-0.321163\pi$
$863$	31.3004	1.06548	0.532738	+	0.846280i	$0.321163\pi$
$864$	1.79695	0.0611335
$865$	10.0096	0.340338
$866$	−28.9173	−0.982650
$867$	−4.83526	−0.164214
$868$	2.10315	0.0713856
$869$	12.0827	0.409876
$870$	0.311554	0.0105627
$871$	15.1971	0.514933
$872$	3.53837	0.119824
$873$	32.0787	1.08570
$874$	51.5991	1.74537
$875$	2.10315	0.0710994
$876$	0.0254074	0.000858435 0
$877$	−36.0534	−1.21744	−0.608719	−	0.793386i	$-0.708316\pi$
$877$	−36.0534	−1.21744	−0.608719	+	0.793386i	$0.708316\pi$
$878$	−4.10908	−0.138675
$879$	4.36108	0.147095
$880$	−3.97017	−0.133835
$881$	−44.1693	−1.48810	−0.744051	−	0.668123i	$-0.767098\pi$
$881$	−44.1693	−1.48810	−0.744051	+	0.668123i	$0.767098\pi$
$882$	−7.49186	−0.252264
$883$	−37.0262	−1.24603	−0.623015	−	0.782210i	$-0.714092\pi$
$883$	−37.0262	−1.24603	−0.623015	+	0.782210i	$0.714092\pi$
$884$	−1.05076	−0.0353410
$885$	0.129722	0.00436057
$886$	−13.4087	−0.450474
$887$	−27.9417	−0.938190	−0.469095	−	0.883148i	$-0.655420\pi$
$887$	−27.9417	−0.938190	−0.469095	+	0.883148i	$0.655420\pi$
$888$	−2.54232	−0.0853148
$889$	−16.7780	−0.562715
$890$	−5.31251	−0.178076
$891$	−32.4594	−1.08743
$892$	22.8741	0.765880
$893$	26.6374	0.891386
$894$	6.50603	0.217594
$895$	0.254704	0.00851383
$896$	−2.10315	−0.0702613
$897$	−2.54555	−0.0849933
$898$	11.5057	0.383949
$899$	−1.02423	−0.0341601
$900$	−2.90747	−0.0969158
$901$	−2.42836	−0.0809004
$902$	−19.8287	−0.660222
$903$	7.30878	0.243221
$904$	14.7079	0.489178
$905$	−4.55710	−0.151483
$906$	−1.48458	−0.0493219
$907$	50.4130	1.67394	0.836968	−	0.547251i	$-0.184326\pi$
$907$	50.4130	1.67394	0.836968	+	0.547251i	$0.184326\pi$
$908$	16.3042	0.541075
$909$	22.0552	0.731524
$910$	2.10315	0.0697187
$911$	36.7808	1.21860	0.609302	−	0.792938i	$-0.291450\pi$
$911$	36.7808	1.21860	0.609302	+	0.792938i	$0.291450\pi$
$912$	−1.87556	−0.0621060
$913$	48.5496	1.60676
$914$	11.9812	0.396304
$915$	−1.50014	−0.0495931
$916$	−16.7855	−0.554608
$917$	−7.27207	−0.240145
$918$	1.88817	0.0623189
$919$	−0.583811	−0.0192581	−0.00962907	−	0.999954i	$-0.503065\pi$
$919$	−0.583811	−0.0192581	−0.00962907	+	0.999954i	$0.503065\pi$
$920$	−8.36848	−0.275901
$921$	−3.88189	−0.127913
$922$	2.97335	0.0979221
$923$	4.65405	0.153190
$924$	−2.53989	−0.0835561
$925$	8.35788	0.274805
$926$	−11.4183	−0.375229
$927$	44.4649	1.46042
$928$	1.02423	0.0336221
$929$	−11.6659	−0.382745	−0.191372	−	0.981518i	$-0.561294\pi$
$929$	−11.6659	−0.382745	−0.191372	+	0.981518i	$0.561294\pi$
$930$	−0.304183	−0.00997455
$931$	15.8880	0.520709
$932$	−23.1767	−0.759179
$933$	−3.96361	−0.129763
$934$	2.64607	0.0865820
$935$	−4.17171	−0.136429
$936$	−2.90747	−0.0950337
$937$	−24.4429	−0.798514	−0.399257	−	0.916839i	$-0.630732\pi$
$937$	−24.4429	−0.798514	−0.399257	+	0.916839i	$0.630732\pi$
$938$	31.9617	1.04359
$939$	0.132150	0.00431254
$940$	−4.32012	−0.140907
$941$	−2.71505	−0.0885080	−0.0442540	−	0.999020i	$-0.514091\pi$
$941$	−2.71505	−0.0885080	−0.0442540	+	0.999020i	$0.514091\pi$
$942$	−4.38713	−0.142940
$943$	−41.7956	−1.36105
$944$	0.426462	0.0138801
$945$	−3.77926	−0.122939
$946$	45.3576	1.47470
$947$	−28.7987	−0.935831	−0.467916	−	0.883773i	$-0.654995\pi$
$947$	−28.7987	−0.935831	−0.467916	+	0.883773i	$0.654995\pi$
$948$	−0.925737	−0.0300665
$949$	−0.0835266	−0.00271139
$950$	6.16589	0.200048
$951$	0.736664	0.0238880
$952$	−2.20991	−0.0716236
$953$	41.6565	1.34939	0.674693	−	0.738099i	$-0.264276\pi$
$953$	41.6565	1.34939	0.674693	+	0.738099i	$0.264276\pi$
$954$	−6.71930	−0.217545
$955$	−18.6965	−0.605006
$956$	−0.486100	−0.0157216
$957$	1.23692	0.0399841
$958$	−25.4763	−0.823100
$959$	−23.1712	−0.748238
$960$	0.304183	0.00981746
$961$	1.00000	0.0322581
$962$	8.35788	0.269469
$963$	5.33725	0.171990
$964$	−7.85061	−0.252851
$965$	15.0082	0.483133
$966$	−5.35367	−0.172251
$967$	−16.2282	−0.521864	−0.260932	−	0.965357i	$-0.584030\pi$
$967$	−16.2282	−0.521864	−0.260932	+	0.965357i	$0.584030\pi$
$968$	−4.76228	−0.153065
$969$	−1.97077	−0.0633102
$970$	11.0332	0.354255
$971$	35.4199	1.13668	0.568340	−	0.822794i	$-0.307586\pi$
$971$	35.4199	1.13668	0.568340	+	0.822794i	$0.307586\pi$
$972$	7.87780	0.252680
$973$	15.4013	0.493742
$974$	39.7751	1.27448
$975$	−0.304183	−0.00974165
$976$	−4.93171	−0.157860
$977$	10.3958	0.332590	0.166295	−	0.986076i	$-0.446820\pi$
$977$	10.3958	0.332590	0.166295	+	0.986076i	$0.446820\pi$
$978$	−2.55452	−0.0816845
$979$	−21.0916	−0.674090
$980$	−2.57676	−0.0823116
$981$	10.2877	0.328461
$982$	−23.2343	−0.741437
$983$	−0.100023	−0.00319023	−0.00159512	−	0.999999i	$-0.500508\pi$
$983$	−0.100023	−0.00319023	−0.00159512	+	0.999999i	$0.500508\pi$
$984$	1.51921	0.0484307
$985$	−1.68190	−0.0535897
$986$	1.07623	0.0342740
$987$	−2.76376	−0.0879715
$988$	6.16589	0.196163
$989$	95.6063	3.04010
$990$	−11.5432	−0.366866
$991$	−17.4939	−0.555711	−0.277855	−	0.960623i	$-0.589624\pi$
$991$	−17.4939	−0.555711	−0.277855	+	0.960623i	$0.589624\pi$
$992$	−1.00000	−0.0317500
$993$	4.37439	0.138817
$994$	9.78817	0.310462
$995$	2.41198	0.0764648
$996$	−3.71973	−0.117864
$997$	7.16784	0.227008	0.113504	−	0.993538i	$-0.463793\pi$
$997$	7.16784	0.227008	0.113504	+	0.993538i	$0.463793\pi$
$998$	35.8193	1.13384
$999$	−15.0187	−0.475171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.h.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.h.1.4	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.304183 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.304183 q^{6} +2.10315 q^{7} -1.00000 q^{8} -2.90747 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.304183 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.304183 q^{6} +2.10315 q^{7} -1.00000 q^{8} -2.90747 q^{9} -1.00000 q^{10} -3.97017 q^{11} +0.304183 q^{12} -1.00000 q^{13} -2.10315 q^{14} +0.304183 q^{15} +1.00000 q^{16} +1.05076 q^{17} +2.90747 q^{18} -6.16589 q^{19} +1.00000 q^{20} +0.639742 q^{21} +3.97017 q^{22} +8.36848 q^{23} -0.304183 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.79695 q^{27} +2.10315 q^{28} -1.02423 q^{29} -0.304183 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.20766 q^{33} -1.05076 q^{34} +2.10315 q^{35} -2.90747 q^{36} +8.35788 q^{37} +6.16589 q^{38} -0.304183 q^{39} -1.00000 q^{40} -4.99441 q^{41} -0.639742 q^{42} +11.4246 q^{43} -3.97017 q^{44} -2.90747 q^{45} -8.36848 q^{46} -4.32012 q^{47} +0.304183 q^{48} -2.57676 q^{49} -1.00000 q^{50} +0.319624 q^{51} -1.00000 q^{52} -2.31105 q^{53} +1.79695 q^{54} -3.97017 q^{55} -2.10315 q^{56} -1.87556 q^{57} +1.02423 q^{58} +0.426462 q^{59} +0.304183 q^{60} -4.93171 q^{61} -1.00000 q^{62} -6.11485 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.20766 q^{66} -15.1971 q^{67} +1.05076 q^{68} +2.54555 q^{69} -2.10315 q^{70} -4.65405 q^{71} +2.90747 q^{72} +0.0835266 q^{73} -8.35788 q^{74} +0.304183 q^{75} -6.16589 q^{76} -8.34987 q^{77} +0.304183 q^{78} -3.04336 q^{79} +1.00000 q^{80} +8.17582 q^{81} +4.99441 q^{82} -12.2286 q^{83} +0.639742 q^{84} +1.05076 q^{85} -11.4246 q^{86} -0.311554 q^{87} +3.97017 q^{88} +5.31251 q^{89} +2.90747 q^{90} -2.10315 q^{91} +8.36848 q^{92} +0.304183 q^{93} +4.32012 q^{94} -6.16589 q^{95} -0.304183 q^{96} -11.0332 q^{97} +2.57676 q^{98} +11.5432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more