LMFDB - Embedded newform 4030.2.a.h.1.1

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			1.1
Root			$3.08527$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.08527 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.08527 q^{6} -0.803633 q^{7} -1.00000 q^{8} +6.51887 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.08527 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.08527 q^{6} -0.803633 q^{7} -1.00000 q^{8} +6.51887 q^{9} -1.00000 q^{10} +1.13368 q^{11} -3.08527 q^{12} -1.00000 q^{13} +0.803633 q^{14} -3.08527 q^{15} +1.00000 q^{16} -3.74060 q^{17} -6.51887 q^{18} +5.76176 q^{19} +1.00000 q^{20} +2.47942 q^{21} -1.13368 q^{22} -0.527118 q^{23} +3.08527 q^{24} +1.00000 q^{25} +1.00000 q^{26} -10.8566 q^{27} -0.803633 q^{28} -6.04718 q^{29} +3.08527 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.49771 q^{33} +3.74060 q^{34} -0.803633 q^{35} +6.51887 q^{36} +3.28460 q^{37} -5.76176 q^{38} +3.08527 q^{39} -1.00000 q^{40} -4.91349 q^{41} -2.47942 q^{42} -4.43206 q^{43} +1.13368 q^{44} +6.51887 q^{45} +0.527118 q^{46} +5.06132 q^{47} -3.08527 q^{48} -6.35417 q^{49} -1.00000 q^{50} +11.5407 q^{51} -1.00000 q^{52} -8.77745 q^{53} +10.8566 q^{54} +1.13368 q^{55} +0.803633 q^{56} -17.7766 q^{57} +6.04718 q^{58} +8.40599 q^{59} -3.08527 q^{60} -0.528307 q^{61} -1.00000 q^{62} -5.23878 q^{63} +1.00000 q^{64} -1.00000 q^{65} +3.49771 q^{66} +3.70596 q^{67} -3.74060 q^{68} +1.62630 q^{69} +0.803633 q^{70} +6.17420 q^{71} -6.51887 q^{72} +3.50355 q^{73} -3.28460 q^{74} -3.08527 q^{75} +5.76176 q^{76} -0.911064 q^{77} -3.08527 q^{78} -7.43243 q^{79} +1.00000 q^{80} +13.9390 q^{81} +4.91349 q^{82} -4.62343 q^{83} +2.47942 q^{84} -3.74060 q^{85} +4.43206 q^{86} +18.6571 q^{87} -1.13368 q^{88} +4.42718 q^{89} -6.51887 q^{90} +0.803633 q^{91} -0.527118 q^{92} -3.08527 q^{93} -5.06132 q^{94} +5.76176 q^{95} +3.08527 q^{96} +9.35175 q^{97} +6.35417 q^{98} +7.39032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.08527	−1.78128	−0.890640	−	0.454710i	$-0.849743\pi$
$3$	−3.08527	−1.78128	−0.890640	+	0.454710i	$0.849743\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.08527	1.25955
$7$	−0.803633	−0.303745	−0.151872	−	0.988400i	$-0.548530\pi$
$7$	−0.803633	−0.303745	−0.151872	+	0.988400i	$0.548530\pi$
$8$	−1.00000	−0.353553
$9$	6.51887	2.17296
$10$	−1.00000	−0.316228
$11$	1.13368	0.341818	0.170909	−	0.985287i	$-0.445330\pi$
$11$	1.13368	0.341818	0.170909	+	0.985287i	$0.445330\pi$
$12$	−3.08527	−0.890640
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.803633	0.214780
$15$	−3.08527	−0.796612
$16$	1.00000	0.250000
$17$	−3.74060	−0.907229	−0.453614	−	0.891198i	$-0.649866\pi$
$17$	−3.74060	−0.907229	−0.453614	+	0.891198i	$0.649866\pi$
$18$	−6.51887	−1.53651
$19$	5.76176	1.32184	0.660919	−	0.750457i	$-0.270167\pi$
$19$	5.76176	1.32184	0.660919	+	0.750457i	$0.270167\pi$
$20$	1.00000	0.223607
$21$	2.47942	0.541054
$22$	−1.13368	−0.241702
$23$	−0.527118	−0.109912	−0.0549559	−	0.998489i	$-0.517502\pi$
$23$	−0.527118	−0.109912	−0.0549559	+	0.998489i	$0.517502\pi$
$24$	3.08527	0.629777
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−10.8566	−2.08936
$28$	−0.803633	−0.151872
$29$	−6.04718	−1.12293	−0.561466	−	0.827500i	$-0.689763\pi$
$29$	−6.04718	−1.12293	−0.561466	+	0.827500i	$0.689763\pi$
$30$	3.08527	0.563290
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−3.49771	−0.608873
$34$	3.74060	0.641508
$35$	−0.803633	−0.135839
$36$	6.51887	1.08648
$37$	3.28460	0.539985	0.269992	−	0.962862i	$-0.412979\pi$
$37$	3.28460	0.539985	0.269992	+	0.962862i	$0.412979\pi$
$38$	−5.76176	−0.934681
$39$	3.08527	0.494038
$40$	−1.00000	−0.158114
$41$	−4.91349	−0.767359	−0.383679	−	0.923466i	$-0.625343\pi$
$41$	−4.91349	−0.767359	−0.383679	+	0.923466i	$0.625343\pi$
$42$	−2.47942	−0.382583
$43$	−4.43206	−0.675883	−0.337941	−	0.941167i	$-0.609731\pi$
$43$	−4.43206	−0.675883	−0.337941	+	0.941167i	$0.609731\pi$
$44$	1.13368	0.170909
$45$	6.51887	0.971776
$46$	0.527118	0.0777193
$47$	5.06132	0.738270	0.369135	−	0.929376i	$-0.379654\pi$
$47$	5.06132	0.738270	0.369135	+	0.929376i	$0.379654\pi$
$48$	−3.08527	−0.445320
$49$	−6.35417	−0.907739
$50$	−1.00000	−0.141421
$51$	11.5407	1.61603
$52$	−1.00000	−0.138675
$53$	−8.77745	−1.20568	−0.602838	−	0.797864i	$-0.705963\pi$
$53$	−8.77745	−1.20568	−0.602838	+	0.797864i	$0.705963\pi$
$54$	10.8566	1.47740
$55$	1.13368	0.152866
$56$	0.803633	0.107390
$57$	−17.7766	−2.35456
$58$	6.04718	0.794033
$59$	8.40599	1.09437	0.547183	−	0.837013i	$-0.315700\pi$
$59$	8.40599	1.09437	0.547183	+	0.837013i	$0.315700\pi$
$60$	−3.08527	−0.398306
$61$	−0.528307	−0.0676428	−0.0338214	−	0.999428i	$-0.510768\pi$
$61$	−0.528307	−0.0676428	−0.0338214	+	0.999428i	$0.510768\pi$
$62$	−1.00000	−0.127000
$63$	−5.23878	−0.660024
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	3.49771	0.430538
$67$	3.70596	0.452755	0.226378	−	0.974040i	$-0.427312\pi$
$67$	3.70596	0.452755	0.226378	+	0.974040i	$0.427312\pi$
$68$	−3.74060	−0.453614
$69$	1.62630	0.195783
$70$	0.803633	0.0960525
$71$	6.17420	0.732743	0.366371	−	0.930469i	$-0.380600\pi$
$71$	6.17420	0.732743	0.366371	+	0.930469i	$0.380600\pi$
$72$	−6.51887	−0.768256
$73$	3.50355	0.410059	0.205030	−	0.978756i	$-0.434271\pi$
$73$	3.50355	0.410059	0.205030	+	0.978756i	$0.434271\pi$
$74$	−3.28460	−0.381827
$75$	−3.08527	−0.356256
$76$	5.76176	0.660919
$77$	−0.911064	−0.103825
$78$	−3.08527	−0.349338
$79$	−7.43243	−0.836214	−0.418107	−	0.908398i	$-0.637306\pi$
$79$	−7.43243	−0.836214	−0.418107	+	0.908398i	$0.637306\pi$
$80$	1.00000	0.111803
$81$	13.9390	1.54878
$82$	4.91349	0.542605
$83$	−4.62343	−0.507487	−0.253744	−	0.967272i	$-0.581662\pi$
$83$	−4.62343	−0.507487	−0.253744	+	0.967272i	$0.581662\pi$
$84$	2.47942	0.270527
$85$	−3.74060	−0.405725
$86$	4.43206	0.477921
$87$	18.6571	2.00026
$88$	−1.13368	−0.120851
$89$	4.42718	0.469281	0.234640	−	0.972082i	$-0.424609\pi$
$89$	4.42718	0.469281	0.234640	+	0.972082i	$0.424609\pi$
$90$	−6.51887	−0.687149
$91$	0.803633	0.0842437
$92$	−0.527118	−0.0549559
$93$	−3.08527	−0.319927
$94$	−5.06132	−0.522036
$95$	5.76176	0.591144
$96$	3.08527	0.314889
$97$	9.35175	0.949526	0.474763	−	0.880114i	$-0.342534\pi$
$97$	9.35175	0.949526	0.474763	+	0.880114i	$0.342534\pi$
$98$	6.35417	0.641868
$99$	7.39032	0.742755
$100$	1.00000	0.100000
$101$	0.701435	0.0697954	0.0348977	−	0.999391i	$-0.488889\pi$
$101$	0.701435	0.0697954	0.0348977	+	0.999391i	$0.488889\pi$
$102$	−11.5407	−1.14270
$103$	3.02900	0.298456	0.149228	−	0.988803i	$-0.452321\pi$
$103$	3.02900	0.298456	0.149228	+	0.988803i	$0.452321\pi$
$104$	1.00000	0.0980581
$105$	2.47942	0.241967
$106$	8.77745	0.852541
$107$	−3.93472	−0.380384	−0.190192	−	0.981747i	$-0.560911\pi$
$107$	−3.93472	−0.380384	−0.190192	+	0.981747i	$0.560911\pi$
$108$	−10.8566	−1.04468
$109$	7.37533	0.706429	0.353214	−	0.935542i	$-0.385089\pi$
$109$	7.37533	0.706429	0.353214	+	0.935542i	$0.385089\pi$
$110$	−1.13368	−0.108092
$111$	−10.1339	−0.961864
$112$	−0.803633	−0.0759362
$113$	1.58750	0.149340	0.0746698	−	0.997208i	$-0.476210\pi$
$113$	1.58750	0.149340	0.0746698	+	0.997208i	$0.476210\pi$
$114$	17.7766	1.66493
$115$	−0.527118	−0.0491540
$116$	−6.04718	−0.561466
$117$	−6.51887	−0.602670
$118$	−8.40599	−0.773834
$119$	3.00607	0.275566
$120$	3.08527	0.281645
$121$	−9.71477	−0.883161
$122$	0.528307	0.0478307
$123$	15.1594	1.36688
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	5.23878	0.466708
$127$	12.7056	1.12744	0.563718	−	0.825967i	$-0.309370\pi$
$127$	12.7056	1.12744	0.563718	+	0.825967i	$0.309370\pi$
$128$	−1.00000	−0.0883883
$129$	13.6741	1.20394
$130$	1.00000	0.0877058
$131$	−7.62308	−0.666032	−0.333016	−	0.942921i	$-0.608066\pi$
$131$	−7.62308	−0.666032	−0.333016	+	0.942921i	$0.608066\pi$
$132$	−3.49771	−0.304437
$133$	−4.63034	−0.401501
$134$	−3.70596	−0.320146
$135$	−10.8566	−0.934391
$136$	3.74060	0.320754
$137$	2.32633	0.198751	0.0993757	−	0.995050i	$-0.468315\pi$
$137$	2.32633	0.198751	0.0993757	+	0.995050i	$0.468315\pi$
$138$	−1.62630	−0.138440
$139$	6.39863	0.542725	0.271362	−	0.962477i	$-0.412526\pi$
$139$	6.39863	0.542725	0.271362	+	0.962477i	$0.412526\pi$
$140$	−0.803633	−0.0679194
$141$	−15.6155	−1.31507
$142$	−6.17420	−0.518128
$143$	−1.13368	−0.0948032
$144$	6.51887	0.543239
$145$	−6.04718	−0.502191
$146$	−3.50355	−0.289956
$147$	19.6043	1.61694
$148$	3.28460	0.269992
$149$	−3.68443	−0.301840	−0.150920	−	0.988546i	$-0.548224\pi$
$149$	−3.68443	−0.301840	−0.150920	+	0.988546i	$0.548224\pi$
$150$	3.08527	0.251911
$151$	16.8783	1.37354	0.686770	−	0.726875i	$-0.259028\pi$
$151$	16.8783	1.37354	0.686770	+	0.726875i	$0.259028\pi$
$152$	−5.76176	−0.467340
$153$	−24.3845	−1.97137
$154$	0.911064	0.0734156
$155$	1.00000	0.0803219
$156$	3.08527	0.247019
$157$	−16.7593	−1.33754	−0.668770	−	0.743470i	$-0.733179\pi$
$157$	−16.7593	−1.33754	−0.668770	+	0.743470i	$0.733179\pi$
$158$	7.43243	0.591292
$159$	27.0808	2.14765
$160$	−1.00000	−0.0790569
$161$	0.423610	0.0333851
$162$	−13.9390	−1.09515
$163$	17.7472	1.39007	0.695034	−	0.718976i	$-0.255389\pi$
$163$	17.7472	1.39007	0.695034	+	0.718976i	$0.255389\pi$
$164$	−4.91349	−0.383679
$165$	−3.49771	−0.272296
$166$	4.62343	0.358848
$167$	−12.5342	−0.969926	−0.484963	−	0.874535i	$-0.661167\pi$
$167$	−12.5342	−0.969926	−0.484963	+	0.874535i	$0.661167\pi$
$168$	−2.47942	−0.191292
$169$	1.00000	0.0769231
$170$	3.74060	0.286891
$171$	37.5601	2.87230
$172$	−4.43206	−0.337941
$173$	8.94535	0.680102	0.340051	−	0.940407i	$-0.389556\pi$
$173$	8.94535	0.680102	0.340051	+	0.940407i	$0.389556\pi$
$174$	−18.6571	−1.41439
$175$	−0.803633	−0.0607490
$176$	1.13368	0.0854545
$177$	−25.9347	−1.94937
$178$	−4.42718	−0.331831
$179$	6.59902	0.493234	0.246617	−	0.969113i	$-0.420681\pi$
$179$	6.59902	0.493234	0.246617	+	0.969113i	$0.420681\pi$
$180$	6.51887	0.485888
$181$	−9.45188	−0.702553	−0.351276	−	0.936272i	$-0.614252\pi$
$181$	−9.45188	−0.702553	−0.351276	+	0.936272i	$0.614252\pi$
$182$	−0.803633	−0.0595693
$183$	1.62997	0.120491
$184$	0.527118	0.0388597
$185$	3.28460	0.241489
$186$	3.08527	0.226223
$187$	−4.24065	−0.310107
$188$	5.06132	0.369135
$189$	8.72476	0.634633
$190$	−5.76176	−0.418002
$191$	0.376200	0.0272209	0.0136104	−	0.999907i	$-0.495668\pi$
$191$	0.376200	0.0272209	0.0136104	+	0.999907i	$0.495668\pi$
$192$	−3.08527	−0.222660
$193$	−0.558480	−0.0402002	−0.0201001	−	0.999798i	$-0.506398\pi$
$193$	−0.558480	−0.0402002	−0.0201001	+	0.999798i	$0.506398\pi$
$194$	−9.35175	−0.671416
$195$	3.08527	0.220941
$196$	−6.35417	−0.453870
$197$	−2.48631	−0.177142	−0.0885711	−	0.996070i	$-0.528230\pi$
$197$	−2.48631	−0.177142	−0.0885711	+	0.996070i	$0.528230\pi$
$198$	−7.39032	−0.525207
$199$	5.41727	0.384020	0.192010	−	0.981393i	$-0.438499\pi$
$199$	5.41727	0.384020	0.192010	+	0.981393i	$0.438499\pi$
$200$	−1.00000	−0.0707107
$201$	−11.4339	−0.806484
$202$	−0.701435	−0.0493528
$203$	4.85971	0.341085
$204$	11.5407	0.808014
$205$	−4.91349	−0.343173
$206$	−3.02900	−0.211040
$207$	−3.43621	−0.238833
$208$	−1.00000	−0.0693375
$209$	6.53200	0.451828
$210$	−2.47942	−0.171096
$211$	−9.20356	−0.633599	−0.316800	−	0.948492i	$-0.602608\pi$
$211$	−9.20356	−0.633599	−0.316800	+	0.948492i	$0.602608\pi$
$212$	−8.77745	−0.602838
$213$	−19.0491	−1.30522
$214$	3.93472	0.268972
$215$	−4.43206	−0.302264
$216$	10.8566	0.738701
$217$	−0.803633	−0.0545542
$218$	−7.37533	−0.499521
$219$	−10.8094	−0.730430
$220$	1.13368	0.0764328
$221$	3.74060	0.251620
$222$	10.1339	0.680140
$223$	−15.2237	−1.01945	−0.509727	−	0.860336i	$-0.670254\pi$
$223$	−15.2237	−1.01945	−0.509727	+	0.860336i	$0.670254\pi$
$224$	0.803633	0.0536950
$225$	6.51887	0.434591
$226$	−1.58750	−0.105599
$227$	11.9658	0.794197	0.397099	−	0.917776i	$-0.370017\pi$
$227$	11.9658	0.794197	0.397099	+	0.917776i	$0.370017\pi$
$228$	−17.7766	−1.17728
$229$	−12.2014	−0.806292	−0.403146	−	0.915136i	$-0.632083\pi$
$229$	−12.2014	−0.806292	−0.403146	+	0.915136i	$0.632083\pi$
$230$	0.527118	0.0347571
$231$	2.81088	0.184942
$232$	6.04718	0.397017
$233$	−22.0717	−1.44597	−0.722984	−	0.690865i	$-0.757230\pi$
$233$	−22.0717	−1.44597	−0.722984	+	0.690865i	$0.757230\pi$
$234$	6.51887	0.426152
$235$	5.06132	0.330164
$236$	8.40599	0.547183
$237$	22.9310	1.48953
$238$	−3.00607	−0.194855
$239$	−23.5059	−1.52047	−0.760235	−	0.649649i	$-0.774916\pi$
$239$	−23.5059	−1.52047	−0.760235	+	0.649649i	$0.774916\pi$
$240$	−3.08527	−0.199153
$241$	−28.5698	−1.84034	−0.920172	−	0.391514i	$-0.871951\pi$
$241$	−28.5698	−1.84034	−0.920172	+	0.391514i	$0.871951\pi$
$242$	9.71477	0.624489
$243$	−10.4357	−0.669452
$244$	−0.528307	−0.0338214
$245$	−6.35417	−0.405953
$246$	−15.1594	−0.966531
$247$	−5.76176	−0.366612
$248$	−1.00000	−0.0635001
$249$	14.2645	0.903976
$250$	−1.00000	−0.0632456
$251$	−23.2391	−1.46684	−0.733418	−	0.679778i	$-0.762076\pi$
$251$	−23.2391	−1.46684	−0.733418	+	0.679778i	$0.762076\pi$
$252$	−5.23878	−0.330012
$253$	−0.597584	−0.0375698
$254$	−12.7056	−0.797218
$255$	11.5407	0.722710
$256$	1.00000	0.0625000
$257$	−24.1908	−1.50898	−0.754491	−	0.656311i	$-0.772116\pi$
$257$	−24.1908	−1.50898	−0.754491	+	0.656311i	$0.772116\pi$
$258$	−13.6741	−0.851311
$259$	−2.63961	−0.164018
$260$	−1.00000	−0.0620174
$261$	−39.4207	−2.44008
$262$	7.62308	0.470956
$263$	19.0564	1.17507	0.587533	−	0.809200i	$-0.300099\pi$
$263$	19.0564	1.17507	0.587533	+	0.809200i	$0.300099\pi$
$264$	3.49771	0.215269
$265$	−8.77745	−0.539195
$266$	4.63034	0.283904
$267$	−13.6590	−0.835920
$268$	3.70596	0.226378
$269$	10.6445	0.649009	0.324504	−	0.945884i	$-0.394802\pi$
$269$	10.6445	0.649009	0.324504	+	0.945884i	$0.394802\pi$
$270$	10.8566	0.660714
$271$	−28.4316	−1.72709	−0.863547	−	0.504268i	$-0.831762\pi$
$271$	−28.4316	−1.72709	−0.863547	+	0.504268i	$0.831762\pi$
$272$	−3.74060	−0.226807
$273$	−2.47942	−0.150061
$274$	−2.32633	−0.140538
$275$	1.13368	0.0683636
$276$	1.62630	0.0978917
$277$	−9.86136	−0.592512	−0.296256	−	0.955109i	$-0.595738\pi$
$277$	−9.86136	−0.592512	−0.296256	+	0.955109i	$0.595738\pi$
$278$	−6.39863	−0.383764
$279$	6.51887	0.390274
$280$	0.803633	0.0480263
$281$	23.2103	1.38461	0.692305	−	0.721605i	$-0.256595\pi$
$281$	23.2103	1.38461	0.692305	+	0.721605i	$0.256595\pi$
$282$	15.6155	0.929892
$283$	13.2211	0.785915	0.392958	−	0.919557i	$-0.371452\pi$
$283$	13.2211	0.785915	0.392958	+	0.919557i	$0.371452\pi$
$284$	6.17420	0.366371
$285$	−17.7766	−1.05299
$286$	1.13368	0.0670360
$287$	3.94865	0.233081
$288$	−6.51887	−0.384128
$289$	−3.00791	−0.176936
$290$	6.04718	0.355102
$291$	−28.8526	−1.69137
$292$	3.50355	0.205030
$293$	−6.33837	−0.370291	−0.185146	−	0.982711i	$-0.559276\pi$
$293$	−6.33837	−0.370291	−0.185146	+	0.982711i	$0.559276\pi$
$294$	−19.6043	−1.14335
$295$	8.40599	0.489416
$296$	−3.28460	−0.190913
$297$	−12.3080	−0.714182
$298$	3.68443	0.213433
$299$	0.527118	0.0304840
$300$	−3.08527	−0.178128
$301$	3.56175	0.205296
$302$	−16.8783	−0.971239
$303$	−2.16411	−0.124325
$304$	5.76176	0.330460
$305$	−0.528307	−0.0302508
$306$	24.3845	1.39397
$307$	−34.2788	−1.95639	−0.978197	−	0.207678i	$-0.933409\pi$
$307$	−34.2788	−1.95639	−0.978197	+	0.207678i	$0.933409\pi$
$308$	−0.911064	−0.0519127
$309$	−9.34527	−0.531634
$310$	−1.00000	−0.0567962
$311$	−27.7083	−1.57120	−0.785598	−	0.618738i	$-0.787644\pi$
$311$	−27.7083	−1.57120	−0.785598	+	0.618738i	$0.787644\pi$
$312$	−3.08527	−0.174669
$313$	4.38067	0.247610	0.123805	−	0.992307i	$-0.460490\pi$
$313$	4.38067	0.247610	0.123805	+	0.992307i	$0.460490\pi$
$314$	16.7593	0.945783
$315$	−5.23878	−0.295172
$316$	−7.43243	−0.418107
$317$	−4.25307	−0.238876	−0.119438	−	0.992842i	$-0.538109\pi$
$317$	−4.25307	−0.238876	−0.119438	+	0.992842i	$0.538109\pi$
$318$	−27.0808	−1.51861
$319$	−6.85557	−0.383838
$320$	1.00000	0.0559017
$321$	12.1397	0.677570
$322$	−0.423610	−0.0236068
$323$	−21.5524	−1.19921
$324$	13.9390	0.774391
$325$	−1.00000	−0.0554700
$326$	−17.7472	−0.982927
$327$	−22.7549	−1.25835
$328$	4.91349	0.271302
$329$	−4.06745	−0.224246
$330$	3.49771	0.192543
$331$	−7.11651	−0.391159	−0.195579	−	0.980688i	$-0.562659\pi$
$331$	−7.11651	−0.391159	−0.195579	+	0.980688i	$0.562659\pi$
$332$	−4.62343	−0.253744
$333$	21.4119	1.17336
$334$	12.5342	0.685841
$335$	3.70596	0.202478
$336$	2.47942	0.135264
$337$	−28.0945	−1.53041	−0.765203	−	0.643789i	$-0.777361\pi$
$337$	−28.0945	−1.53041	−0.765203	+	0.643789i	$0.777361\pi$
$338$	−1.00000	−0.0543928
$339$	−4.89787	−0.266016
$340$	−3.74060	−0.202863
$341$	1.13368	0.0613923
$342$	−37.5601	−2.03102
$343$	10.7319	0.579466
$344$	4.43206	0.238961
$345$	1.62630	0.0875570
$346$	−8.94535	−0.480905
$347$	−2.72382	−0.146222	−0.0731111	−	0.997324i	$-0.523293\pi$
$347$	−2.72382	−0.146222	−0.0731111	+	0.997324i	$0.523293\pi$
$348$	18.6571	1.00013
$349$	−15.0189	−0.803945	−0.401973	−	0.915652i	$-0.631675\pi$
$349$	−15.0189	−0.803945	−0.401973	+	0.915652i	$0.631675\pi$
$350$	0.803633	0.0429560
$351$	10.8566	0.579485
$352$	−1.13368	−0.0604254
$353$	3.00327	0.159848	0.0799240	−	0.996801i	$-0.474532\pi$
$353$	3.00327	0.159848	0.0799240	+	0.996801i	$0.474532\pi$
$354$	25.9347	1.37841
$355$	6.17420	0.327693
$356$	4.42718	0.234640
$357$	−9.27453	−0.490860
$358$	−6.59902	−0.348769
$359$	−34.3150	−1.81108	−0.905539	−	0.424262i	$-0.860533\pi$
$359$	−34.3150	−1.81108	−0.905539	+	0.424262i	$0.860533\pi$
$360$	−6.51887	−0.343575
$361$	14.1979	0.747256
$362$	9.45188	0.496780
$363$	29.9726	1.57316
$364$	0.803633	0.0421218
$365$	3.50355	0.183384
$366$	−1.62997	−0.0851998
$367$	13.2191	0.690032	0.345016	−	0.938597i	$-0.387874\pi$
$367$	13.2191	0.690032	0.345016	+	0.938597i	$0.387874\pi$
$368$	−0.527118	−0.0274779
$369$	−32.0304	−1.66744
$370$	−3.28460	−0.170758
$371$	7.05385	0.366218
$372$	−3.08527	−0.159964
$373$	−4.36986	−0.226263	−0.113131	−	0.993580i	$-0.536088\pi$
$373$	−4.36986	−0.226263	−0.113131	+	0.993580i	$0.536088\pi$
$374$	4.24065	0.219279
$375$	−3.08527	−0.159322
$376$	−5.06132	−0.261018
$377$	6.04718	0.311445
$378$	−8.72476	−0.448753
$379$	23.3856	1.20124	0.600618	−	0.799536i	$-0.294921\pi$
$379$	23.3856	1.20124	0.600618	+	0.799536i	$0.294921\pi$
$380$	5.76176	0.295572
$381$	−39.2000	−2.00828
$382$	−0.376200	−0.0192481
$383$	16.0361	0.819408	0.409704	−	0.912218i	$-0.365632\pi$
$383$	16.0361	0.819408	0.409704	+	0.912218i	$0.365632\pi$
$384$	3.08527	0.157444
$385$	−0.911064	−0.0464321
$386$	0.558480	0.0284259
$387$	−28.8920	−1.46866
$388$	9.35175	0.474763
$389$	−6.07420	−0.307974	−0.153987	−	0.988073i	$-0.549211\pi$
$389$	−6.07420	−0.307974	−0.153987	+	0.988073i	$0.549211\pi$
$390$	−3.08527	−0.156229
$391$	1.97174	0.0997151
$392$	6.35417	0.320934
$393$	23.5192	1.18639
$394$	2.48631	0.125259
$395$	−7.43243	−0.373966
$396$	7.39032	0.371378
$397$	15.3362	0.769702	0.384851	−	0.922979i	$-0.374253\pi$
$397$	15.3362	0.769702	0.384851	+	0.922979i	$0.374253\pi$
$398$	−5.41727	−0.271543
$399$	14.2858	0.715186
$400$	1.00000	0.0500000
$401$	−20.6094	−1.02918	−0.514591	−	0.857436i	$-0.672056\pi$
$401$	−20.6094	−1.02918	−0.514591	+	0.857436i	$0.672056\pi$
$402$	11.4339	0.570270
$403$	−1.00000	−0.0498135
$404$	0.701435	0.0348977
$405$	13.9390	0.692637
$406$	−4.85971	−0.241183
$407$	3.72369	0.184576
$408$	−11.5407	−0.571352
$409$	18.6708	0.923212	0.461606	−	0.887085i	$-0.347273\pi$
$409$	18.6708	0.923212	0.461606	+	0.887085i	$0.347273\pi$
$410$	4.91349	0.242660
$411$	−7.17733	−0.354032
$412$	3.02900	0.149228
$413$	−6.75533	−0.332408
$414$	3.43621	0.168881
$415$	−4.62343	−0.226955
$416$	1.00000	0.0490290
$417$	−19.7415	−0.966745
$418$	−6.53200	−0.319491
$419$	5.23492	0.255743	0.127871	−	0.991791i	$-0.459186\pi$
$419$	5.23492	0.255743	0.127871	+	0.991791i	$0.459186\pi$
$420$	2.47942	0.120983
$421$	8.33717	0.406329	0.203164	−	0.979145i	$-0.434877\pi$
$421$	8.33717	0.406329	0.203164	+	0.979145i	$0.434877\pi$
$422$	9.20356	0.448022
$423$	32.9941	1.60423
$424$	8.77745	0.426271
$425$	−3.74060	−0.181446
$426$	19.0491	0.922930
$427$	0.424565	0.0205462
$428$	−3.93472	−0.190192
$429$	3.49771	0.168871
$430$	4.43206	0.213733
$431$	−27.9749	−1.34751	−0.673753	−	0.738957i	$-0.735319\pi$
$431$	−27.9749	−1.34751	−0.673753	+	0.738957i	$0.735319\pi$
$432$	−10.8566	−0.522341
$433$	−1.07186	−0.0515102	−0.0257551	−	0.999668i	$-0.508199\pi$
$433$	−1.07186	−0.0515102	−0.0257551	+	0.999668i	$0.508199\pi$
$434$	0.803633	0.0385756
$435$	18.6571	0.894542
$436$	7.37533	0.353214
$437$	−3.03713	−0.145285
$438$	10.8094	0.516492
$439$	33.9990	1.62268	0.811342	−	0.584572i	$-0.198737\pi$
$439$	33.9990	1.62268	0.811342	+	0.584572i	$0.198737\pi$
$440$	−1.13368	−0.0540462
$441$	−41.4220	−1.97248
$442$	−3.74060	−0.177922
$443$	−9.79931	−0.465579	−0.232790	−	0.972527i	$-0.574785\pi$
$443$	−9.79931	−0.465579	−0.232790	+	0.972527i	$0.574785\pi$
$444$	−10.1339	−0.480932
$445$	4.42718	0.209869
$446$	15.2237	0.720863
$447$	11.3675	0.537662
$448$	−0.803633	−0.0379681
$449$	10.9208	0.515384	0.257692	−	0.966227i	$-0.417038\pi$
$449$	10.9208	0.515384	0.257692	+	0.966227i	$0.417038\pi$
$450$	−6.51887	−0.307302
$451$	−5.57034	−0.262297
$452$	1.58750	0.0746698
$453$	−52.0742	−2.44666
$454$	−11.9658	−0.561582
$455$	0.803633	0.0376749
$456$	17.7766	0.832464
$457$	−33.2940	−1.55743	−0.778713	−	0.627380i	$-0.784127\pi$
$457$	−33.2940	−1.55743	−0.778713	+	0.627380i	$0.784127\pi$
$458$	12.2014	0.570134
$459$	40.6104	1.89553
$460$	−0.527118	−0.0245770
$461$	4.47762	0.208543	0.104272	−	0.994549i	$-0.466749\pi$
$461$	4.47762	0.208543	0.104272	+	0.994549i	$0.466749\pi$
$462$	−2.81088	−0.130774
$463$	5.76257	0.267810	0.133905	−	0.990994i	$-0.457248\pi$
$463$	5.76257	0.267810	0.133905	+	0.990994i	$0.457248\pi$
$464$	−6.04718	−0.280733
$465$	−3.08527	−0.143076
$466$	22.0717	1.02245
$467$	−2.28732	−0.105845	−0.0529223	−	0.998599i	$-0.516854\pi$
$467$	−2.28732	−0.105845	−0.0529223	+	0.998599i	$0.516854\pi$
$468$	−6.51887	−0.301335
$469$	−2.97823	−0.137522
$470$	−5.06132	−0.233461
$471$	51.7070	2.38253
$472$	−8.40599	−0.386917
$473$	−5.02454	−0.231029
$474$	−22.9310	−1.05326
$475$	5.76176	0.264368
$476$	3.00607	0.137783
$477$	−57.2190	−2.61988
$478$	23.5059	1.07513
$479$	−9.74521	−0.445270	−0.222635	−	0.974902i	$-0.571466\pi$
$479$	−9.74521	−0.445270	−0.222635	+	0.974902i	$0.571466\pi$
$480$	3.08527	0.140822
$481$	−3.28460	−0.149765
$482$	28.5698	1.30132
$483$	−1.30695	−0.0594682
$484$	−9.71477	−0.441580
$485$	9.35175	0.424641
$486$	10.4357	0.473374
$487$	8.85518	0.401267	0.200633	−	0.979666i	$-0.435700\pi$
$487$	8.85518	0.401267	0.200633	+	0.979666i	$0.435700\pi$
$488$	0.528307	0.0239154
$489$	−54.7549	−2.47610
$490$	6.35417	0.287052
$491$	−8.25609	−0.372592	−0.186296	−	0.982494i	$-0.559648\pi$
$491$	−8.25609	−0.372592	−0.186296	+	0.982494i	$0.559648\pi$
$492$	15.1594	0.683440
$493$	22.6201	1.01876
$494$	5.76176	0.259234
$495$	7.39032	0.332170
$496$	1.00000	0.0449013
$497$	−4.96179	−0.222567
$498$	−14.2645	−0.639208
$499$	12.6061	0.564328	0.282164	−	0.959366i	$-0.408948\pi$
$499$	12.6061	0.564328	0.282164	+	0.959366i	$0.408948\pi$
$500$	1.00000	0.0447214
$501$	38.6714	1.72771
$502$	23.2391	1.03721
$503$	−31.4656	−1.40298	−0.701492	−	0.712677i	$-0.747482\pi$
$503$	−31.4656	−1.40298	−0.701492	+	0.712677i	$0.747482\pi$
$504$	5.23878	0.233354
$505$	0.701435	0.0312135
$506$	0.597584	0.0265659
$507$	−3.08527	−0.137021
$508$	12.7056	0.563718
$509$	29.5220	1.30854	0.654270	−	0.756261i	$-0.272976\pi$
$509$	29.5220	1.30854	0.654270	+	0.756261i	$0.272976\pi$
$510$	−11.5407	−0.511033
$511$	−2.81557	−0.124553
$512$	−1.00000	−0.0441942
$513$	−62.5534	−2.76180
$514$	24.1908	1.06701
$515$	3.02900	0.133474
$516$	13.6741	0.601968
$517$	5.73793	0.252354
$518$	2.63961	0.115978
$519$	−27.5988	−1.21145
$520$	1.00000	0.0438529
$521$	−17.6918	−0.775090	−0.387545	−	0.921851i	$-0.626677\pi$
$521$	−17.6918	−0.775090	−0.387545	+	0.921851i	$0.626677\pi$
$522$	39.4207	1.72540
$523$	−5.11523	−0.223674	−0.111837	−	0.993727i	$-0.535673\pi$
$523$	−5.11523	−0.223674	−0.111837	+	0.993727i	$0.535673\pi$
$524$	−7.62308	−0.333016
$525$	2.47942	0.108211
$526$	−19.0564	−0.830897
$527$	−3.74060	−0.162943
$528$	−3.49771	−0.152218
$529$	−22.7221	−0.987919
$530$	8.77745	0.381268
$531$	54.7976	2.37801
$532$	−4.63034	−0.200751
$533$	4.91349	0.212827
$534$	13.6590	0.591085
$535$	−3.93472	−0.170113
$536$	−3.70596	−0.160073
$537$	−20.3597	−0.878587
$538$	−10.6445	−0.458919
$539$	−7.20361	−0.310281
$540$	−10.8566	−0.467196
$541$	8.33129	0.358190	0.179095	−	0.983832i	$-0.442683\pi$
$541$	8.33129	0.358190	0.179095	+	0.983832i	$0.442683\pi$
$542$	28.4316	1.22124
$543$	29.1616	1.25144
$544$	3.74060	0.160377
$545$	7.37533	0.315925
$546$	2.47942	0.106109
$547$	−33.4747	−1.43127	−0.715637	−	0.698472i	$-0.753864\pi$
$547$	−33.4747	−1.43127	−0.715637	+	0.698472i	$0.753864\pi$
$548$	2.32633	0.0993757
$549$	−3.44397	−0.146985
$550$	−1.13368	−0.0483403
$551$	−34.8424	−1.48433
$552$	−1.62630	−0.0692199
$553$	5.97295	0.253996
$554$	9.86136	0.418969
$555$	−10.1339	−0.430159
$556$	6.39863	0.271362
$557$	−13.6649	−0.579000	−0.289500	−	0.957178i	$-0.593489\pi$
$557$	−13.6649	−0.579000	−0.289500	+	0.957178i	$0.593489\pi$
$558$	−6.51887	−0.275966
$559$	4.43206	0.187456
$560$	−0.803633	−0.0339597
$561$	13.0835	0.552387
$562$	−23.2103	−0.979067
$563$	−6.17296	−0.260159	−0.130080	−	0.991504i	$-0.541523\pi$
$563$	−6.17296	−0.260159	−0.130080	+	0.991504i	$0.541523\pi$
$564$	−15.6155	−0.657533
$565$	1.58750	0.0667867
$566$	−13.2211	−0.555726
$567$	−11.2019	−0.470435
$568$	−6.17420	−0.259064
$569$	−33.6591	−1.41106	−0.705531	−	0.708679i	$-0.749291\pi$
$569$	−33.6591	−1.41106	−0.705531	+	0.708679i	$0.749291\pi$
$570$	17.7766	0.744578
$571$	−4.06400	−0.170073	−0.0850366	−	0.996378i	$-0.527101\pi$
$571$	−4.06400	−0.170073	−0.0850366	+	0.996378i	$0.527101\pi$
$572$	−1.13368	−0.0474016
$573$	−1.16068	−0.0484880
$574$	−3.94865	−0.164813
$575$	−0.527118	−0.0219823
$576$	6.51887	0.271620
$577$	−46.7482	−1.94615	−0.973076	−	0.230484i	$-0.925969\pi$
$577$	−46.7482	−1.94615	−0.973076	+	0.230484i	$0.925969\pi$
$578$	3.00791	0.125113
$579$	1.72306	0.0716079
$580$	−6.04718	−0.251095
$581$	3.71554	0.154147
$582$	28.8526	1.19598
$583$	−9.95084	−0.412121
$584$	−3.50355	−0.144978
$585$	−6.51887	−0.269522
$586$	6.33837	0.261835
$587$	−17.4066	−0.718449	−0.359224	−	0.933251i	$-0.616959\pi$
$587$	−17.4066	−0.718449	−0.359224	+	0.933251i	$0.616959\pi$
$588$	19.6043	0.808468
$589$	5.76176	0.237409
$590$	−8.40599	−0.346069
$591$	7.67093	0.315540
$592$	3.28460	0.134996
$593$	20.0850	0.824791	0.412396	−	0.911005i	$-0.364692\pi$
$593$	20.0850	0.824791	0.412396	+	0.911005i	$0.364692\pi$
$594$	12.3080	0.505003
$595$	3.00607	0.123237
$596$	−3.68443	−0.150920
$597$	−16.7137	−0.684048
$598$	−0.527118	−0.0215555
$599$	−30.9114	−1.26300	−0.631502	−	0.775374i	$-0.717561\pi$
$599$	−30.9114	−1.26300	−0.631502	+	0.775374i	$0.717561\pi$
$600$	3.08527	0.125955
$601$	27.3860	1.11710	0.558550	−	0.829471i	$-0.311358\pi$
$601$	27.3860	1.11710	0.558550	+	0.829471i	$0.311358\pi$
$602$	−3.56175	−0.145166
$603$	24.1587	0.983817
$604$	16.8783	0.686770
$605$	−9.71477	−0.394961
$606$	2.16411	0.0879111
$607$	17.4907	0.709927	0.354963	−	0.934880i	$-0.384493\pi$
$607$	17.4907	0.709927	0.354963	+	0.934880i	$0.384493\pi$
$608$	−5.76176	−0.233670
$609$	−14.9935	−0.607567
$610$	0.528307	0.0213905
$611$	−5.06132	−0.204759
$612$	−24.3845	−0.985684
$613$	−4.11176	−0.166072	−0.0830361	−	0.996547i	$-0.526462\pi$
$613$	−4.11176	−0.166072	−0.0830361	+	0.996547i	$0.526462\pi$
$614$	34.2788	1.38338
$615$	15.1594	0.611288
$616$	0.911064	0.0367078
$617$	−26.3586	−1.06116	−0.530579	−	0.847635i	$-0.678026\pi$
$617$	−26.3586	−1.06116	−0.530579	+	0.847635i	$0.678026\pi$
$618$	9.34527	0.375922
$619$	34.7829	1.39804	0.699022	−	0.715100i	$-0.253619\pi$
$619$	34.7829	1.39804	0.699022	+	0.715100i	$0.253619\pi$
$620$	1.00000	0.0401610
$621$	5.72273	0.229645
$622$	27.7083	1.11100
$623$	−3.55783	−0.142542
$624$	3.08527	0.123510
$625$	1.00000	0.0400000
$626$	−4.38067	−0.175087
$627$	−20.1530	−0.804832
$628$	−16.7593	−0.668770
$629$	−12.2864	−0.489890
$630$	5.23878	0.208718
$631$	−22.4885	−0.895252	−0.447626	−	0.894221i	$-0.647730\pi$
$631$	−22.4885	−0.895252	−0.447626	+	0.894221i	$0.647730\pi$
$632$	7.43243	0.295646
$633$	28.3954	1.12862
$634$	4.25307	0.168911
$635$	12.7056	0.504205
$636$	27.0808	1.07382
$637$	6.35417	0.251762
$638$	6.85557	0.271415
$639$	40.2488	1.59222
$640$	−1.00000	−0.0395285
$641$	−43.7617	−1.72848	−0.864242	−	0.503077i	$-0.832201\pi$
$641$	−43.7617	−1.72848	−0.864242	+	0.503077i	$0.832201\pi$
$642$	−12.1397	−0.479114
$643$	−12.9992	−0.512637	−0.256318	−	0.966592i	$-0.582510\pi$
$643$	−12.9992	−0.512637	−0.256318	+	0.966592i	$0.582510\pi$
$644$	0.423610	0.0166926
$645$	13.6741	0.538416
$646$	21.5524	0.847969
$647$	16.2714	0.639696	0.319848	−	0.947469i	$-0.396368\pi$
$647$	16.2714	0.639696	0.319848	+	0.947469i	$0.396368\pi$
$648$	−13.9390	−0.547577
$649$	9.52972	0.374074
$650$	1.00000	0.0392232
$651$	2.47942	0.0971762
$652$	17.7472	0.695034
$653$	8.43789	0.330200	0.165100	−	0.986277i	$-0.447205\pi$
$653$	8.43789	0.330200	0.165100	+	0.986277i	$0.447205\pi$
$654$	22.7549	0.889786
$655$	−7.62308	−0.297858
$656$	−4.91349	−0.191840
$657$	22.8392	0.891041
$658$	4.06745	0.158566
$659$	−24.3190	−0.947335	−0.473667	−	0.880704i	$-0.657070\pi$
$659$	−24.3190	−0.947335	−0.473667	+	0.880704i	$0.657070\pi$
$660$	−3.49771	−0.136148
$661$	18.8435	0.732928	0.366464	−	0.930432i	$-0.380568\pi$
$661$	18.8435	0.732928	0.366464	+	0.930432i	$0.380568\pi$
$662$	7.11651	0.276591
$663$	−11.5407	−0.448205
$664$	4.62343	0.179424
$665$	−4.63034	−0.179557
$666$	−21.4119	−0.829693
$667$	3.18758	0.123423
$668$	−12.5342	−0.484963
$669$	46.9692	1.81593
$670$	−3.70596	−0.143174
$671$	−0.598932	−0.0231215
$672$	−2.47942	−0.0956458
$673$	−5.67871	−0.218898	−0.109449	−	0.993992i	$-0.534909\pi$
$673$	−5.67871	−0.218898	−0.109449	+	0.993992i	$0.534909\pi$
$674$	28.0945	1.08216
$675$	−10.8566	−0.417873
$676$	1.00000	0.0384615
$677$	29.3112	1.12652	0.563261	−	0.826279i	$-0.309547\pi$
$677$	29.3112	1.12652	0.563261	+	0.826279i	$0.309547\pi$
$678$	4.89787	0.188102
$679$	−7.51537	−0.288414
$680$	3.74060	0.143445
$681$	−36.9176	−1.41469
$682$	−1.13368	−0.0434109
$683$	−7.33827	−0.280791	−0.140395	−	0.990096i	$-0.544837\pi$
$683$	−7.33827	−0.280791	−0.140395	+	0.990096i	$0.544837\pi$
$684$	37.5601	1.43615
$685$	2.32633	0.0888843
$686$	−10.7319	−0.409744
$687$	37.6446	1.43623
$688$	−4.43206	−0.168971
$689$	8.77745	0.334394
$690$	−1.62630	−0.0619122
$691$	34.2550	1.30312	0.651560	−	0.758597i	$-0.274115\pi$
$691$	34.2550	1.30312	0.651560	+	0.758597i	$0.274115\pi$
$692$	8.94535	0.340051
$693$	−5.93911	−0.225608
$694$	2.72382	0.103395
$695$	6.39863	0.242714
$696$	−18.6571	−0.707197
$697$	18.3794	0.696170
$698$	15.0189	0.568475
$699$	68.0972	2.57567
$700$	−0.803633	−0.0303745
$701$	−11.0230	−0.416332	−0.208166	−	0.978093i	$-0.566749\pi$
$701$	−11.0230	−0.416332	−0.208166	+	0.978093i	$0.566749\pi$
$702$	−10.8566	−0.409758
$703$	18.9251	0.713773
$704$	1.13368	0.0427272
$705$	−15.6155	−0.588115
$706$	−3.00327	−0.113030
$707$	−0.563697	−0.0212000
$708$	−25.9347	−0.974687
$709$	24.7720	0.930332	0.465166	−	0.885224i	$-0.345995\pi$
$709$	24.7720	0.930332	0.465166	+	0.885224i	$0.345995\pi$
$710$	−6.17420	−0.231714
$711$	−48.4510	−1.81706
$712$	−4.42718	−0.165916
$713$	−0.527118	−0.0197407
$714$	9.27453	0.347090
$715$	−1.13368	−0.0423973
$716$	6.59902	0.246617
$717$	72.5219	2.70838
$718$	34.3150	1.28063
$719$	6.58114	0.245435	0.122718	−	0.992442i	$-0.460839\pi$
$719$	6.58114	0.245435	0.122718	+	0.992442i	$0.460839\pi$
$720$	6.51887	0.242944
$721$	−2.43420	−0.0906545
$722$	−14.1979	−0.528390
$723$	88.1455	3.27817
$724$	−9.45188	−0.351276
$725$	−6.04718	−0.224586
$726$	−29.9726	−1.11239
$727$	13.0601	0.484372	0.242186	−	0.970230i	$-0.422136\pi$
$727$	13.0601	0.484372	0.242186	+	0.970230i	$0.422136\pi$
$728$	−0.803633	−0.0297846
$729$	−9.62016	−0.356302
$730$	−3.50355	−0.129672
$731$	16.5786	0.613180
$732$	1.62997	0.0602454
$733$	20.9313	0.773117	0.386558	−	0.922265i	$-0.373664\pi$
$733$	20.9313	0.773117	0.386558	+	0.922265i	$0.373664\pi$
$734$	−13.2191	−0.487926
$735$	19.6043	0.723116
$736$	0.527118	0.0194298
$737$	4.20138	0.154760
$738$	32.0304	1.17906
$739$	−1.38411	−0.0509154	−0.0254577	−	0.999676i	$-0.508104\pi$
$739$	−1.38411	−0.0509154	−0.0254577	+	0.999676i	$0.508104\pi$
$740$	3.28460	0.120744
$741$	17.7766	0.653038
$742$	−7.05385	−0.258955
$743$	−10.4612	−0.383786	−0.191893	−	0.981416i	$-0.561463\pi$
$743$	−10.4612	−0.383786	−0.191893	+	0.981416i	$0.561463\pi$
$744$	3.08527	0.113111
$745$	−3.68443	−0.134987
$746$	4.36986	0.159992
$747$	−30.1395	−1.10275
$748$	−4.24065	−0.155054
$749$	3.16207	0.115540
$750$	3.08527	0.112658
$751$	12.5472	0.457855	0.228927	−	0.973444i	$-0.426478\pi$
$751$	12.5472	0.457855	0.228927	+	0.973444i	$0.426478\pi$
$752$	5.06132	0.184568
$753$	71.6987	2.61284
$754$	−6.04718	−0.220225
$755$	16.8783	0.614266
$756$	8.72476	0.317317
$757$	7.42102	0.269721	0.134861	−	0.990865i	$-0.456941\pi$
$757$	7.42102	0.269721	0.134861	+	0.990865i	$0.456941\pi$
$758$	−23.3856	−0.849402
$759$	1.84371	0.0669223
$760$	−5.76176	−0.209001
$761$	−17.7688	−0.644119	−0.322059	−	0.946719i	$-0.604375\pi$
$761$	−17.7688	−0.644119	−0.322059	+	0.946719i	$0.604375\pi$
$762$	39.2000	1.42007
$763$	−5.92706	−0.214574
$764$	0.376200	0.0136104
$765$	−24.3845	−0.881623
$766$	−16.0361	−0.579409
$767$	−8.40599	−0.303523
$768$	−3.08527	−0.111330
$769$	45.5335	1.64198	0.820990	−	0.570943i	$-0.193422\pi$
$769$	45.5335	1.64198	0.820990	+	0.570943i	$0.193422\pi$
$770$	0.911064	0.0328325
$771$	74.6351	2.68792
$772$	−0.558480	−0.0201001
$773$	−40.8437	−1.46905	−0.734523	−	0.678584i	$-0.762594\pi$
$773$	−40.8437	−1.46905	−0.734523	+	0.678584i	$0.762594\pi$
$774$	28.8920	1.03850
$775$	1.00000	0.0359211
$776$	−9.35175	−0.335708
$777$	8.14391	0.292161
$778$	6.07420	0.217771
$779$	−28.3104	−1.01432
$780$	3.08527	0.110470
$781$	6.99958	0.250465
$782$	−1.97174	−0.0705092
$783$	65.6521	2.34621
$784$	−6.35417	−0.226935
$785$	−16.7593	−0.598166
$786$	−23.5192	−0.838903
$787$	32.8687	1.17164	0.585821	−	0.810440i	$-0.300772\pi$
$787$	32.8687	1.17164	0.585821	+	0.810440i	$0.300772\pi$
$788$	−2.48631	−0.0885711
$789$	−58.7940	−2.09312
$790$	7.43243	0.264434
$791$	−1.27577	−0.0453612
$792$	−7.39032	−0.262604
$793$	0.528307	0.0187607
$794$	−15.3362	−0.544262
$795$	27.0808	0.960456
$796$	5.41727	0.192010
$797$	44.9081	1.59073	0.795363	−	0.606134i	$-0.207280\pi$
$797$	44.9081	1.59073	0.795363	+	0.606134i	$0.207280\pi$
$798$	−14.2858	−0.505713
$799$	−18.9324	−0.669780
$800$	−1.00000	−0.0353553
$801$	28.8602	1.01973
$802$	20.6094	0.727742
$803$	3.97191	0.140166
$804$	−11.4339	−0.403242
$805$	0.423610	0.0149303
$806$	1.00000	0.0352235
$807$	−32.8412	−1.15607
$808$	−0.701435	−0.0246764
$809$	−14.9903	−0.527031	−0.263515	−	0.964655i	$-0.584882\pi$
$809$	−14.9903	−0.527031	−0.263515	+	0.964655i	$0.584882\pi$
$810$	−13.9390	−0.489768
$811$	46.9839	1.64983	0.824914	−	0.565258i	$-0.191223\pi$
$811$	46.9839	1.64983	0.824914	+	0.565258i	$0.191223\pi$
$812$	4.85971	0.170542
$813$	87.7189	3.07644
$814$	−3.72369	−0.130515
$815$	17.7472	0.621658
$816$	11.5407	0.404007
$817$	−25.5364	−0.893407
$818$	−18.6708	−0.652810
$819$	5.23878	0.183058
$820$	−4.91349	−0.171587
$821$	−11.8619	−0.413982	−0.206991	−	0.978343i	$-0.566367\pi$
$821$	−11.8619	−0.413982	−0.206991	+	0.978343i	$0.566367\pi$
$822$	7.17733	0.250338
$823$	−20.2560	−0.706079	−0.353040	−	0.935608i	$-0.614852\pi$
$823$	−20.2560	−0.706079	−0.353040	+	0.935608i	$0.614852\pi$
$824$	−3.02900	−0.105520
$825$	−3.49771	−0.121775
$826$	6.75533	0.235048
$827$	−8.06100	−0.280308	−0.140154	−	0.990130i	$-0.544760\pi$
$827$	−8.06100	−0.280308	−0.140154	+	0.990130i	$0.544760\pi$
$828$	−3.43621	−0.119417
$829$	37.2477	1.29367	0.646833	−	0.762631i	$-0.276093\pi$
$829$	37.2477	1.29367	0.646833	+	0.762631i	$0.276093\pi$
$830$	4.62343	0.160482
$831$	30.4249	1.05543
$832$	−1.00000	−0.0346688
$833$	23.7684	0.823527
$834$	19.7415	0.683592
$835$	−12.5342	−0.433764
$836$	6.53200	0.225914
$837$	−10.8566	−0.375261
$838$	−5.23492	−0.180837
$839$	21.3167	0.735935	0.367968	−	0.929839i	$-0.380054\pi$
$839$	21.3167	0.735935	0.367968	+	0.929839i	$0.380054\pi$
$840$	−2.47942	−0.0855482
$841$	7.56834	0.260977
$842$	−8.33717	−0.287318
$843$	−71.6099	−2.46638
$844$	−9.20356	−0.316800
$845$	1.00000	0.0344010
$846$	−32.9941	−1.13436
$847$	7.80711	0.268255
$848$	−8.77745	−0.301419
$849$	−40.7908	−1.39994
$850$	3.74060	0.128302
$851$	−1.73137	−0.0593507
$852$	−19.0491	−0.652610
$853$	29.3476	1.00484	0.502421	−	0.864623i	$-0.332443\pi$
$853$	29.3476	1.00484	0.502421	+	0.864623i	$0.332443\pi$
$854$	−0.424565	−0.0145283
$855$	37.5601	1.28453
$856$	3.93472	0.134486
$857$	−32.0583	−1.09509	−0.547545	−	0.836776i	$-0.684438\pi$
$857$	−32.0583	−1.09509	−0.547545	+	0.836776i	$0.684438\pi$
$858$	−3.49771	−0.119410
$859$	−19.9170	−0.679558	−0.339779	−	0.940505i	$-0.610352\pi$
$859$	−19.9170	−0.679558	−0.339779	+	0.940505i	$0.610352\pi$
$860$	−4.43206	−0.151132
$861$	−12.1826	−0.415183
$862$	27.9749	0.952830
$863$	−34.2178	−1.16479	−0.582394	−	0.812907i	$-0.697884\pi$
$863$	−34.2178	−1.16479	−0.582394	+	0.812907i	$0.697884\pi$
$864$	10.8566	0.369351
$865$	8.94535	0.304151
$866$	1.07186	0.0364232
$867$	9.28021	0.315172
$868$	−0.803633	−0.0272771
$869$	−8.42601	−0.285833
$870$	−18.6571	−0.632537
$871$	−3.70596	−0.125572
$872$	−7.37533	−0.249760
$873$	60.9628	2.06328
$874$	3.03713	0.102732
$875$	−0.803633	−0.0271678
$876$	−10.8094	−0.365215
$877$	−16.8038	−0.567424	−0.283712	−	0.958910i	$-0.591566\pi$
$877$	−16.8038	−0.567424	−0.283712	+	0.958910i	$0.591566\pi$
$878$	−33.9990	−1.14741
$879$	19.5555	0.659592
$880$	1.13368	0.0382164
$881$	−20.6784	−0.696673	−0.348336	−	0.937370i	$-0.613253\pi$
$881$	−20.6784	−0.696673	−0.348336	+	0.937370i	$0.613253\pi$
$882$	41.4220	1.39475
$883$	−1.62594	−0.0547171	−0.0273585	−	0.999626i	$-0.508710\pi$
$883$	−1.62594	−0.0547171	−0.0273585	+	0.999626i	$0.508710\pi$
$884$	3.74060	0.125810
$885$	−25.9347	−0.871786
$886$	9.79931	0.329214
$887$	−16.8597	−0.566095	−0.283047	−	0.959106i	$-0.591345\pi$
$887$	−16.8597	−0.566095	−0.283047	+	0.959106i	$0.591345\pi$
$888$	10.1339	0.340070
$889$	−10.2106	−0.342453
$890$	−4.42718	−0.148400
$891$	15.8024	0.529402
$892$	−15.2237	−0.509727
$893$	29.1621	0.975873
$894$	−11.3675	−0.380185
$895$	6.59902	0.220581
$896$	0.803633	0.0268475
$897$	−1.62630	−0.0543006
$898$	−10.9208	−0.364431
$899$	−6.04718	−0.201685
$900$	6.51887	0.217296
$901$	32.8329	1.09382
$902$	5.57034	0.185472
$903$	−10.9889	−0.365689
$904$	−1.58750	−0.0527996
$905$	−9.45188	−0.314191
$906$	52.0742	1.73005
$907$	−54.8392	−1.82091	−0.910453	−	0.413612i	$-0.864267\pi$
$907$	−54.8392	−1.82091	−0.910453	+	0.413612i	$0.864267\pi$
$908$	11.9658	0.397099
$909$	4.57256	0.151662
$910$	−0.803633	−0.0266402
$911$	3.84671	0.127447	0.0637236	−	0.997968i	$-0.479702\pi$
$911$	3.84671	0.127447	0.0637236	+	0.997968i	$0.479702\pi$
$912$	−17.7766	−0.588641
$913$	−5.24150	−0.173468
$914$	33.2940	1.10127
$915$	1.62997	0.0538851
$916$	−12.2014	−0.403146
$917$	6.12616	0.202304
$918$	−40.6104	−1.34034
$919$	−55.5201	−1.83144	−0.915719	−	0.401819i	$-0.868378\pi$
$919$	−55.5201	−1.83144	−0.915719	+	0.401819i	$0.868378\pi$
$920$	0.527118	0.0173786
$921$	105.759	3.48489
$922$	−4.47762	−0.147462
$923$	−6.17420	−0.203226
$924$	2.81088	0.0924710
$925$	3.28460	0.107997
$926$	−5.76257	−0.189370
$927$	19.7457	0.648532
$928$	6.04718	0.198508
$929$	9.68567	0.317777	0.158888	−	0.987297i	$-0.449209\pi$
$929$	9.68567	0.317777	0.158888	+	0.987297i	$0.449209\pi$
$930$	3.08527	0.101170
$931$	−36.6112	−1.19988
$932$	−22.0717	−0.722984
$933$	85.4876	2.79874
$934$	2.28732	0.0748435
$935$	−4.24065	−0.138684
$936$	6.51887	0.213076
$937$	2.37312	0.0775265	0.0387632	−	0.999248i	$-0.487658\pi$
$937$	2.37312	0.0775265	0.0387632	+	0.999248i	$0.487658\pi$
$938$	2.97823	0.0972428
$939$	−13.5155	−0.441063
$940$	5.06132	0.165082
$941$	−27.5684	−0.898706	−0.449353	−	0.893354i	$-0.648345\pi$
$941$	−27.5684	−0.898706	−0.449353	+	0.893354i	$0.648345\pi$
$942$	−51.7070	−1.68470
$943$	2.58999	0.0843417
$944$	8.40599	0.273592
$945$	8.72476	0.283817
$946$	5.02454	0.163362
$947$	0.822217	0.0267185	0.0133592	−	0.999911i	$-0.495747\pi$
$947$	0.822217	0.0267185	0.0133592	+	0.999911i	$0.495747\pi$
$948$	22.9310	0.744765
$949$	−3.50355	−0.113730
$950$	−5.76176	−0.186936
$951$	13.1219	0.425505
$952$	−3.00607	−0.0974273
$953$	−2.00831	−0.0650557	−0.0325278	−	0.999471i	$-0.510356\pi$
$953$	−2.00831	−0.0650557	−0.0325278	+	0.999471i	$0.510356\pi$
$954$	57.2190	1.85254
$955$	0.376200	0.0121735
$956$	−23.5059	−0.760235
$957$	21.1513	0.683723
$958$	9.74521	0.314854
$959$	−1.86951	−0.0603697
$960$	−3.08527	−0.0995765
$961$	1.00000	0.0322581
$962$	3.28460	0.105900
$963$	−25.6499	−0.826557
$964$	−28.5698	−0.920172
$965$	−0.558480	−0.0179781
$966$	1.30695	0.0420504
$967$	32.1216	1.03296	0.516481	−	0.856299i	$-0.327242\pi$
$967$	32.1216	1.03296	0.516481	+	0.856299i	$0.327242\pi$
$968$	9.71477	0.312244
$969$	66.4950	2.13613
$970$	−9.35175	−0.300266
$971$	27.4600	0.881234	0.440617	−	0.897695i	$-0.354760\pi$
$971$	27.4600	0.881234	0.440617	+	0.897695i	$0.354760\pi$
$972$	−10.4357	−0.334726
$973$	−5.14215	−0.164850
$974$	−8.85518	−0.283738
$975$	3.08527	0.0988076
$976$	−0.528307	−0.0169107
$977$	−16.6241	−0.531853	−0.265926	−	0.963993i	$-0.585678\pi$
$977$	−16.6241	−0.531853	−0.265926	+	0.963993i	$0.585678\pi$
$978$	54.7549	1.75087
$979$	5.01902	0.160408
$980$	−6.35417	−0.202977
$981$	48.0788	1.53504
$982$	8.25609	0.263463
$983$	14.9924	0.478183	0.239091	−	0.970997i	$-0.423150\pi$
$983$	14.9924	0.478183	0.239091	+	0.970997i	$0.423150\pi$
$984$	−15.1594	−0.483265
$985$	−2.48631	−0.0792204
$986$	−22.6201	−0.720370
$987$	12.5492	0.399444
$988$	−5.76176	−0.183306
$989$	2.33622	0.0742874
$990$	−7.39032	−0.234880
$991$	0.450726	0.0143178	0.00715890	−	0.999974i	$-0.497721\pi$
$991$	0.450726	0.0143178	0.00715890	+	0.999974i	$0.497721\pi$
$992$	−1.00000	−0.0317500
$993$	21.9563	0.696763
$994$	4.96179	0.157379
$995$	5.41727	0.171739
$996$	14.2645	0.451988
$997$	38.3102	1.21330	0.606648	−	0.794970i	$-0.292514\pi$
$997$	38.3102	1.21330	0.606648	+	0.794970i	$0.292514\pi$
$998$	−12.6061	−0.399040
$999$	−35.6597	−1.12822

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.h.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.08527 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.08527 q^{6} -0.803633 q^{7} -1.00000 q^{8} +6.51887 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.08527 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.08527 q^{6} -0.803633 q^{7} -1.00000 q^{8} +6.51887 q^{9} -1.00000 q^{10} +1.13368 q^{11} -3.08527 q^{12} -1.00000 q^{13} +0.803633 q^{14} -3.08527 q^{15} +1.00000 q^{16} -3.74060 q^{17} -6.51887 q^{18} +5.76176 q^{19} +1.00000 q^{20} +2.47942 q^{21} -1.13368 q^{22} -0.527118 q^{23} +3.08527 q^{24} +1.00000 q^{25} +1.00000 q^{26} -10.8566 q^{27} -0.803633 q^{28} -6.04718 q^{29} +3.08527 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.49771 q^{33} +3.74060 q^{34} -0.803633 q^{35} +6.51887 q^{36} +3.28460 q^{37} -5.76176 q^{38} +3.08527 q^{39} -1.00000 q^{40} -4.91349 q^{41} -2.47942 q^{42} -4.43206 q^{43} +1.13368 q^{44} +6.51887 q^{45} +0.527118 q^{46} +5.06132 q^{47} -3.08527 q^{48} -6.35417 q^{49} -1.00000 q^{50} +11.5407 q^{51} -1.00000 q^{52} -8.77745 q^{53} +10.8566 q^{54} +1.13368 q^{55} +0.803633 q^{56} -17.7766 q^{57} +6.04718 q^{58} +8.40599 q^{59} -3.08527 q^{60} -0.528307 q^{61} -1.00000 q^{62} -5.23878 q^{63} +1.00000 q^{64} -1.00000 q^{65} +3.49771 q^{66} +3.70596 q^{67} -3.74060 q^{68} +1.62630 q^{69} +0.803633 q^{70} +6.17420 q^{71} -6.51887 q^{72} +3.50355 q^{73} -3.28460 q^{74} -3.08527 q^{75} +5.76176 q^{76} -0.911064 q^{77} -3.08527 q^{78} -7.43243 q^{79} +1.00000 q^{80} +13.9390 q^{81} +4.91349 q^{82} -4.62343 q^{83} +2.47942 q^{84} -3.74060 q^{85} +4.43206 q^{86} +18.6571 q^{87} -1.13368 q^{88} +4.42718 q^{89} -6.51887 q^{90} +0.803633 q^{91} -0.527118 q^{92} -3.08527 q^{93} -5.06132 q^{94} +5.76176 q^{95} +3.08527 q^{96} +9.35175 q^{97} +6.35417 q^{98} +7.39032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 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