LMFDB - Embedded newform 4030.2.a.h.1.7

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			1.7
Root			$-3.06581$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.06581 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06581 q^{6} -3.10610 q^{7} -1.00000 q^{8} +6.39922 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.06581 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06581 q^{6} -3.10610 q^{7} -1.00000 q^{8} +6.39922 q^{9} -1.00000 q^{10} -3.44378 q^{11} +3.06581 q^{12} -1.00000 q^{13} +3.10610 q^{14} +3.06581 q^{15} +1.00000 q^{16} -3.16590 q^{17} -6.39922 q^{18} -1.99288 q^{19} +1.00000 q^{20} -9.52274 q^{21} +3.44378 q^{22} -4.04579 q^{23} -3.06581 q^{24} +1.00000 q^{25} +1.00000 q^{26} +10.4214 q^{27} -3.10610 q^{28} -3.65125 q^{29} -3.06581 q^{30} +1.00000 q^{31} -1.00000 q^{32} -10.5580 q^{33} +3.16590 q^{34} -3.10610 q^{35} +6.39922 q^{36} -0.111137 q^{37} +1.99288 q^{38} -3.06581 q^{39} -1.00000 q^{40} -7.09504 q^{41} +9.52274 q^{42} -4.15953 q^{43} -3.44378 q^{44} +6.39922 q^{45} +4.04579 q^{46} -4.18331 q^{47} +3.06581 q^{48} +2.64788 q^{49} -1.00000 q^{50} -9.70605 q^{51} -1.00000 q^{52} -0.478049 q^{53} -10.4214 q^{54} -3.44378 q^{55} +3.10610 q^{56} -6.10980 q^{57} +3.65125 q^{58} -6.41502 q^{59} +3.06581 q^{60} +1.74796 q^{61} -1.00000 q^{62} -19.8766 q^{63} +1.00000 q^{64} -1.00000 q^{65} +10.5580 q^{66} +9.25832 q^{67} -3.16590 q^{68} -12.4036 q^{69} +3.10610 q^{70} +11.6309 q^{71} -6.39922 q^{72} -10.6207 q^{73} +0.111137 q^{74} +3.06581 q^{75} -1.99288 q^{76} +10.6967 q^{77} +3.06581 q^{78} +7.38949 q^{79} +1.00000 q^{80} +12.7523 q^{81} +7.09504 q^{82} -16.8359 q^{83} -9.52274 q^{84} -3.16590 q^{85} +4.15953 q^{86} -11.1941 q^{87} +3.44378 q^{88} +3.02890 q^{89} -6.39922 q^{90} +3.10610 q^{91} -4.04579 q^{92} +3.06581 q^{93} +4.18331 q^{94} -1.99288 q^{95} -3.06581 q^{96} +2.17509 q^{97} -2.64788 q^{98} -22.0375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.06581	1.77005	0.885024	−	0.465545i	$-0.154142\pi$
$3$	3.06581	1.77005	0.885024	+	0.465545i	$0.154142\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.06581	−1.25161
$7$	−3.10610	−1.17400	−0.586998	−	0.809588i	$-0.699691\pi$
$7$	−3.10610	−1.17400	−0.586998	+	0.809588i	$0.699691\pi$
$8$	−1.00000	−0.353553
$9$	6.39922	2.13307
$10$	−1.00000	−0.316228
$11$	−3.44378	−1.03834	−0.519170	−	0.854671i	$-0.673759\pi$
$11$	−3.44378	−1.03834	−0.519170	+	0.854671i	$0.673759\pi$
$12$	3.06581	0.885024
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.10610	0.830141
$15$	3.06581	0.791590
$16$	1.00000	0.250000
$17$	−3.16590	−0.767843	−0.383921	−	0.923366i	$-0.625427\pi$
$17$	−3.16590	−0.767843	−0.383921	+	0.923366i	$0.625427\pi$
$18$	−6.39922	−1.50831
$19$	−1.99288	−0.457198	−0.228599	−	0.973521i	$-0.573414\pi$
$19$	−1.99288	−0.457198	−0.228599	+	0.973521i	$0.573414\pi$
$20$	1.00000	0.223607
$21$	−9.52274	−2.07803
$22$	3.44378	0.734217
$23$	−4.04579	−0.843605	−0.421802	−	0.906688i	$-0.638602\pi$
$23$	−4.04579	−0.843605	−0.421802	+	0.906688i	$0.638602\pi$
$24$	−3.06581	−0.625807
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	10.4214	2.00559
$28$	−3.10610	−0.586998
$29$	−3.65125	−0.678021	−0.339010	−	0.940783i	$-0.610092\pi$
$29$	−3.65125	−0.678021	−0.339010	+	0.940783i	$0.610092\pi$
$30$	−3.06581	−0.559739
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−10.5580	−1.83791
$34$	3.16590	0.542947
$35$	−3.10610	−0.525027
$36$	6.39922	1.06654
$37$	−0.111137	−0.0182708	−0.00913540	−	0.999958i	$-0.502908\pi$
$37$	−0.111137	−0.0182708	−0.00913540	+	0.999958i	$0.502908\pi$
$38$	1.99288	0.323288
$39$	−3.06581	−0.490923
$40$	−1.00000	−0.158114
$41$	−7.09504	−1.10806	−0.554029	−	0.832497i	$-0.686910\pi$
$41$	−7.09504	−1.10806	−0.554029	+	0.832497i	$0.686910\pi$
$42$	9.52274	1.46939
$43$	−4.15953	−0.634323	−0.317162	−	0.948372i	$-0.602730\pi$
$43$	−4.15953	−0.634323	−0.317162	+	0.948372i	$0.602730\pi$
$44$	−3.44378	−0.519170
$45$	6.39922	0.953939
$46$	4.04579	0.596519
$47$	−4.18331	−0.610199	−0.305099	−	0.952321i	$-0.598690\pi$
$47$	−4.18331	−0.610199	−0.305099	+	0.952321i	$0.598690\pi$
$48$	3.06581	0.442512
$49$	2.64788	0.378269
$50$	−1.00000	−0.141421
$51$	−9.70605	−1.35912
$52$	−1.00000	−0.138675
$53$	−0.478049	−0.0656651	−0.0328325	−	0.999461i	$-0.510453\pi$
$53$	−0.478049	−0.0656651	−0.0328325	+	0.999461i	$0.510453\pi$
$54$	−10.4214	−1.41817
$55$	−3.44378	−0.464359
$56$	3.10610	0.415071
$57$	−6.10980	−0.809263
$58$	3.65125	0.479433
$59$	−6.41502	−0.835165	−0.417582	−	0.908639i	$-0.637122\pi$
$59$	−6.41502	−0.835165	−0.417582	+	0.908639i	$0.637122\pi$
$60$	3.06581	0.395795
$61$	1.74796	0.223804	0.111902	−	0.993719i	$-0.464306\pi$
$61$	1.74796	0.223804	0.111902	+	0.993719i	$0.464306\pi$
$62$	−1.00000	−0.127000
$63$	−19.8766	−2.50422
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	10.5580	1.29960
$67$	9.25832	1.13108	0.565542	−	0.824720i	$-0.308667\pi$
$67$	9.25832	1.13108	0.565542	+	0.824720i	$0.308667\pi$
$68$	−3.16590	−0.383921
$69$	−12.4036	−1.49322
$70$	3.10610	0.371250
$71$	11.6309	1.38034	0.690169	−	0.723649i	$-0.257536\pi$
$71$	11.6309	1.38034	0.690169	+	0.723649i	$0.257536\pi$
$72$	−6.39922	−0.754155
$73$	−10.6207	−1.24306	−0.621531	−	0.783389i	$-0.713489\pi$
$73$	−10.6207	−1.24306	−0.621531	+	0.783389i	$0.713489\pi$
$74$	0.111137	0.0129194
$75$	3.06581	0.354010
$76$	−1.99288	−0.228599
$77$	10.6967	1.21901
$78$	3.06581	0.347135
$79$	7.38949	0.831382	0.415691	−	0.909506i	$-0.363540\pi$
$79$	7.38949	0.831382	0.415691	+	0.909506i	$0.363540\pi$
$80$	1.00000	0.111803
$81$	12.7523	1.41693
$82$	7.09504	0.783516
$83$	−16.8359	−1.84798	−0.923989	−	0.382419i	$-0.875091\pi$
$83$	−16.8359	−1.84798	−0.923989	+	0.382419i	$0.875091\pi$
$84$	−9.52274	−1.03902
$85$	−3.16590	−0.343390
$86$	4.15953	0.448534
$87$	−11.1941	−1.20013
$88$	3.44378	0.367108
$89$	3.02890	0.321063	0.160531	−	0.987031i	$-0.448679\pi$
$89$	3.02890	0.321063	0.160531	+	0.987031i	$0.448679\pi$
$90$	−6.39922	−0.674537
$91$	3.10610	0.325608
$92$	−4.04579	−0.421802
$93$	3.06581	0.317910
$94$	4.18331	0.431476
$95$	−1.99288	−0.204465
$96$	−3.06581	−0.312903
$97$	2.17509	0.220847	0.110423	−	0.993885i	$-0.464779\pi$
$97$	2.17509	0.220847	0.110423	+	0.993885i	$0.464779\pi$
$98$	−2.64788	−0.267476
$99$	−22.0375	−2.21485
$100$	1.00000	0.100000
$101$	5.73021	0.570177	0.285089	−	0.958501i	$-0.407977\pi$
$101$	5.73021	0.570177	0.285089	+	0.958501i	$0.407977\pi$
$102$	9.70605	0.961042
$103$	2.03264	0.200282	0.100141	−	0.994973i	$-0.468071\pi$
$103$	2.03264	0.200282	0.100141	+	0.994973i	$0.468071\pi$
$104$	1.00000	0.0980581
$105$	−9.52274	−0.929324
$106$	0.478049	0.0464322
$107$	17.9475	1.73505	0.867524	−	0.497395i	$-0.165710\pi$
$107$	17.9475	1.73505	0.867524	+	0.497395i	$0.165710\pi$
$108$	10.4214	1.00280
$109$	−8.80666	−0.843525	−0.421762	−	0.906706i	$-0.638588\pi$
$109$	−8.80666	−0.843525	−0.421762	+	0.906706i	$0.638588\pi$
$110$	3.44378	0.328352
$111$	−0.340725	−0.0323402
$112$	−3.10610	−0.293499
$113$	3.02028	0.284124	0.142062	−	0.989858i	$-0.454627\pi$
$113$	3.02028	0.284124	0.142062	+	0.989858i	$0.454627\pi$
$114$	6.10980	0.572235
$115$	−4.04579	−0.377271
$116$	−3.65125	−0.339010
$117$	−6.39922	−0.591608
$118$	6.41502	0.590551
$119$	9.83360	0.901445
$120$	−3.06581	−0.279869
$121$	0.859629	0.0781481
$122$	−1.74796	−0.158253
$123$	−21.7521	−1.96132
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	19.8766	1.77075
$127$	−15.5720	−1.38179	−0.690897	−	0.722953i	$-0.742784\pi$
$127$	−15.5720	−1.38179	−0.690897	+	0.722953i	$0.742784\pi$
$128$	−1.00000	−0.0883883
$129$	−12.7524	−1.12278
$130$	1.00000	0.0877058
$131$	4.22995	0.369572	0.184786	−	0.982779i	$-0.440841\pi$
$131$	4.22995	0.369572	0.184786	+	0.982779i	$0.440841\pi$
$132$	−10.5580	−0.918955
$133$	6.19009	0.536749
$134$	−9.25832	−0.799797
$135$	10.4214	0.896928
$136$	3.16590	0.271473
$137$	−7.66835	−0.655151	−0.327576	−	0.944825i	$-0.606232\pi$
$137$	−7.66835	−0.655151	−0.327576	+	0.944825i	$0.606232\pi$
$138$	12.4036	1.05587
$139$	−8.69334	−0.737360	−0.368680	−	0.929556i	$-0.620190\pi$
$139$	−8.69334	−0.737360	−0.368680	+	0.929556i	$0.620190\pi$
$140$	−3.10610	−0.262514
$141$	−12.8253	−1.08008
$142$	−11.6309	−0.976046
$143$	3.44378	0.287983
$144$	6.39922	0.533268
$145$	−3.65125	−0.303220
$146$	10.6207	0.878978
$147$	8.11791	0.669554
$148$	−0.111137	−0.00913540
$149$	−15.1560	−1.24163	−0.620815	−	0.783957i	$-0.713198\pi$
$149$	−15.1560	−1.24163	−0.620815	+	0.783957i	$0.713198\pi$
$150$	−3.06581	−0.250323
$151$	7.27019	0.591639	0.295820	−	0.955244i	$-0.404407\pi$
$151$	7.27019	0.591639	0.295820	+	0.955244i	$0.404407\pi$
$152$	1.99288	0.161644
$153$	−20.2593	−1.63786
$154$	−10.6967	−0.861968
$155$	1.00000	0.0803219
$156$	−3.06581	−0.245462
$157$	0.666625	0.0532025	0.0266012	−	0.999646i	$-0.491532\pi$
$157$	0.666625	0.0532025	0.0266012	+	0.999646i	$0.491532\pi$
$158$	−7.38949	−0.587876
$159$	−1.46561	−0.116230
$160$	−1.00000	−0.0790569
$161$	12.5666	0.990389
$162$	−12.7523	−1.00192
$163$	−16.9887	−1.33065	−0.665327	−	0.746552i	$-0.731708\pi$
$163$	−16.9887	−1.33065	−0.665327	+	0.746552i	$0.731708\pi$
$164$	−7.09504	−0.554029
$165$	−10.5580	−0.821939
$166$	16.8359	1.30672
$167$	0.229099	0.0177282	0.00886409	−	0.999961i	$-0.497178\pi$
$167$	0.229099	0.0177282	0.00886409	+	0.999961i	$0.497178\pi$
$168$	9.52274	0.734695
$169$	1.00000	0.0769231
$170$	3.16590	0.242813
$171$	−12.7529	−0.975237
$172$	−4.15953	−0.317162
$173$	−5.27366	−0.400949	−0.200474	−	0.979699i	$-0.564248\pi$
$173$	−5.27366	−0.400949	−0.200474	+	0.979699i	$0.564248\pi$
$174$	11.1941	0.848620
$175$	−3.10610	−0.234799
$176$	−3.44378	−0.259585
$177$	−19.6673	−1.47828
$178$	−3.02890	−0.227026
$179$	7.56564	0.565482	0.282741	−	0.959196i	$-0.408756\pi$
$179$	7.56564	0.565482	0.282741	+	0.959196i	$0.408756\pi$
$180$	6.39922	0.476969
$181$	1.20849	0.0898262	0.0449131	−	0.998991i	$-0.485699\pi$
$181$	1.20849	0.0898262	0.0449131	+	0.998991i	$0.485699\pi$
$182$	−3.10610	−0.230240
$183$	5.35893	0.396143
$184$	4.04579	0.298259
$185$	−0.111137	−0.00817095
$186$	−3.06581	−0.224796
$187$	10.9027	0.797281
$188$	−4.18331	−0.305099
$189$	−32.3698	−2.35456
$190$	1.99288	0.144579
$191$	2.71314	0.196316	0.0981580	−	0.995171i	$-0.468705\pi$
$191$	2.71314	0.196316	0.0981580	+	0.995171i	$0.468705\pi$
$192$	3.06581	0.221256
$193$	−18.1392	−1.30569	−0.652844	−	0.757492i	$-0.726424\pi$
$193$	−18.1392	−1.30569	−0.652844	+	0.757492i	$0.726424\pi$
$194$	−2.17509	−0.156162
$195$	−3.06581	−0.219548
$196$	2.64788	0.189134
$197$	−6.06614	−0.432194	−0.216097	−	0.976372i	$-0.569333\pi$
$197$	−6.06614	−0.432194	−0.216097	+	0.976372i	$0.569333\pi$
$198$	22.0375	1.56614
$199$	21.4866	1.52315	0.761573	−	0.648079i	$-0.224427\pi$
$199$	21.4866	1.52315	0.761573	+	0.648079i	$0.224427\pi$
$200$	−1.00000	−0.0707107
$201$	28.3843	2.00207
$202$	−5.73021	−0.403176
$203$	11.3412	0.795994
$204$	−9.70605	−0.679559
$205$	−7.09504	−0.495539
$206$	−2.03264	−0.141621
$207$	−25.8899	−1.79947
$208$	−1.00000	−0.0693375
$209$	6.86304	0.474727
$210$	9.52274	0.657131
$211$	22.1091	1.52205	0.761027	−	0.648721i	$-0.224696\pi$
$211$	22.1091	1.52205	0.761027	+	0.648721i	$0.224696\pi$
$212$	−0.478049	−0.0328325
$213$	35.6583	2.44326
$214$	−17.9475	−1.22686
$215$	−4.15953	−0.283678
$216$	−10.4214	−0.709084
$217$	−3.10610	−0.210856
$218$	8.80666	0.596462
$219$	−32.5612	−2.20028
$220$	−3.44378	−0.232180
$221$	3.16590	0.212961
$222$	0.340725	0.0228680
$223$	10.7230	0.718068	0.359034	−	0.933324i	$-0.383106\pi$
$223$	10.7230	0.718068	0.359034	+	0.933324i	$0.383106\pi$
$224$	3.10610	0.207535
$225$	6.39922	0.426614
$226$	−3.02028	−0.200906
$227$	13.1126	0.870313	0.435156	−	0.900355i	$-0.356693\pi$
$227$	13.1126	0.870313	0.435156	+	0.900355i	$0.356693\pi$
$228$	−6.10980	−0.404631
$229$	−16.6472	−1.10008	−0.550039	−	0.835139i	$-0.685387\pi$
$229$	−16.6472	−1.10008	−0.550039	+	0.835139i	$0.685387\pi$
$230$	4.04579	0.266771
$231$	32.7942	2.15770
$232$	3.65125	0.239717
$233$	−13.7018	−0.897637	−0.448818	−	0.893623i	$-0.648155\pi$
$233$	−13.7018	−0.897637	−0.448818	+	0.893623i	$0.648155\pi$
$234$	6.39922	0.418330
$235$	−4.18331	−0.272889
$236$	−6.41502	−0.417582
$237$	22.6548	1.47159
$238$	−9.83360	−0.637418
$239$	8.12924	0.525837	0.262918	−	0.964818i	$-0.415315\pi$
$239$	8.12924	0.525837	0.262918	+	0.964818i	$0.415315\pi$
$240$	3.06581	0.197897
$241$	7.85430	0.505940	0.252970	−	0.967474i	$-0.418593\pi$
$241$	7.85430	0.505940	0.252970	+	0.967474i	$0.418593\pi$
$242$	−0.859629	−0.0552590
$243$	7.83216	0.502433
$244$	1.74796	0.111902
$245$	2.64788	0.169167
$246$	21.7521	1.38686
$247$	1.99288	0.126804
$248$	−1.00000	−0.0635001
$249$	−51.6157	−3.27101
$250$	−1.00000	−0.0632456
$251$	3.85464	0.243303	0.121651	−	0.992573i	$-0.461181\pi$
$251$	3.85464	0.243303	0.121651	+	0.992573i	$0.461181\pi$
$252$	−19.8766	−1.25211
$253$	13.9328	0.875948
$254$	15.5720	0.977076
$255$	−9.70605	−0.607816
$256$	1.00000	0.0625000
$257$	−12.8381	−0.800816	−0.400408	−	0.916337i	$-0.631132\pi$
$257$	−12.8381	−0.800816	−0.400408	+	0.916337i	$0.631132\pi$
$258$	12.7524	0.793927
$259$	0.345203	0.0214499
$260$	−1.00000	−0.0620174
$261$	−23.3652	−1.44627
$262$	−4.22995	−0.261327
$263$	15.0184	0.926074	0.463037	−	0.886339i	$-0.346760\pi$
$263$	15.0184	0.926074	0.463037	+	0.886339i	$0.346760\pi$
$264$	10.5580	0.649800
$265$	−0.478049	−0.0293663
$266$	−6.19009	−0.379539
$267$	9.28604	0.568297
$268$	9.25832	0.565542
$269$	−17.5507	−1.07009	−0.535043	−	0.844825i	$-0.679705\pi$
$269$	−17.5507	−1.07009	−0.535043	+	0.844825i	$0.679705\pi$
$270$	−10.4214	−0.634224
$271$	9.38978	0.570388	0.285194	−	0.958470i	$-0.407942\pi$
$271$	9.38978	0.570388	0.285194	+	0.958470i	$0.407942\pi$
$272$	−3.16590	−0.191961
$273$	9.52274	0.576342
$274$	7.66835	0.463262
$275$	−3.44378	−0.207668
$276$	−12.4036	−0.746611
$277$	20.2268	1.21531	0.607655	−	0.794201i	$-0.292110\pi$
$277$	20.2268	1.21531	0.607655	+	0.794201i	$0.292110\pi$
$278$	8.69334	0.521392
$279$	6.39922	0.383111
$280$	3.10610	0.185625
$281$	−21.8015	−1.30057	−0.650286	−	0.759690i	$-0.725351\pi$
$281$	−21.8015	−1.30057	−0.650286	+	0.759690i	$0.725351\pi$
$282$	12.8253	0.763733
$283$	11.7331	0.697463	0.348732	−	0.937223i	$-0.386612\pi$
$283$	11.7331	0.697463	0.348732	+	0.937223i	$0.386612\pi$
$284$	11.6309	0.690169
$285$	−6.10980	−0.361913
$286$	−3.44378	−0.203635
$287$	22.0379	1.30086
$288$	−6.39922	−0.377077
$289$	−6.97710	−0.410418
$290$	3.65125	0.214409
$291$	6.66842	0.390910
$292$	−10.6207	−0.621531
$293$	−1.82769	−0.106775	−0.0533875	−	0.998574i	$-0.517002\pi$
$293$	−1.82769	−0.106775	−0.0533875	+	0.998574i	$0.517002\pi$
$294$	−8.11791	−0.473446
$295$	−6.41502	−0.373497
$296$	0.111137	0.00645970
$297$	−35.8889	−2.08249
$298$	15.1560	0.877965
$299$	4.04579	0.233974
$300$	3.06581	0.177005
$301$	12.9199	0.744693
$302$	−7.27019	−0.418352
$303$	17.5678	1.00924
$304$	−1.99288	−0.114300
$305$	1.74796	0.100088
$306$	20.2593	1.15814
$307$	17.6760	1.00882	0.504412	−	0.863463i	$-0.331709\pi$
$307$	17.6760	1.00882	0.504412	+	0.863463i	$0.331709\pi$
$308$	10.6967	0.609503
$309$	6.23170	0.354509
$310$	−1.00000	−0.0567962
$311$	−1.53132	−0.0868331	−0.0434165	−	0.999057i	$-0.513824\pi$
$311$	−1.53132	−0.0868331	−0.0434165	+	0.999057i	$0.513824\pi$
$312$	3.06581	0.173568
$313$	6.07525	0.343393	0.171697	−	0.985150i	$-0.445075\pi$
$313$	6.07525	0.343393	0.171697	+	0.985150i	$0.445075\pi$
$314$	−0.666625	−0.0376198
$315$	−19.8766	−1.11992
$316$	7.38949	0.415691
$317$	18.8272	1.05744	0.528721	−	0.848796i	$-0.322672\pi$
$317$	18.8272	1.05744	0.528721	+	0.848796i	$0.322672\pi$
$318$	1.46561	0.0821873
$319$	12.5741	0.704016
$320$	1.00000	0.0559017
$321$	55.0236	3.07112
$322$	−12.5666	−0.700311
$323$	6.30925	0.351056
$324$	12.7523	0.708463
$325$	−1.00000	−0.0554700
$326$	16.9887	0.940915
$327$	−26.9996	−1.49308
$328$	7.09504	0.391758
$329$	12.9938	0.716372
$330$	10.5580	0.581198
$331$	−18.9741	−1.04291	−0.521455	−	0.853279i	$-0.674611\pi$
$331$	−18.9741	−1.04291	−0.521455	+	0.853279i	$0.674611\pi$
$332$	−16.8359	−0.923989
$333$	−0.711189	−0.0389729
$334$	−0.229099	−0.0125357
$335$	9.25832	0.505836
$336$	−9.52274	−0.519508
$337$	30.0970	1.63949	0.819744	−	0.572730i	$-0.194116\pi$
$337$	30.0970	1.63949	0.819744	+	0.572730i	$0.194116\pi$
$338$	−1.00000	−0.0543928
$339$	9.25963	0.502914
$340$	−3.16590	−0.171695
$341$	−3.44378	−0.186491
$342$	12.7529	0.689596
$343$	13.5181	0.729911
$344$	4.15953	0.224267
$345$	−12.4036	−0.667789
$346$	5.27366	0.283514
$347$	−15.3804	−0.825662	−0.412831	−	0.910808i	$-0.635460\pi$
$347$	−15.3804	−0.825662	−0.412831	+	0.910808i	$0.635460\pi$
$348$	−11.1941	−0.600065
$349$	26.3176	1.40875	0.704374	−	0.709829i	$-0.251228\pi$
$349$	26.3176	1.40875	0.704374	+	0.709829i	$0.251228\pi$
$350$	3.10610	0.166028
$351$	−10.4214	−0.556251
$352$	3.44378	0.183554
$353$	10.3955	0.553297	0.276648	−	0.960971i	$-0.410776\pi$
$353$	10.3955	0.553297	0.276648	+	0.960971i	$0.410776\pi$
$354$	19.6673	1.04530
$355$	11.6309	0.617306
$356$	3.02890	0.160531
$357$	30.1480	1.59560
$358$	−7.56564	−0.399856
$359$	6.76535	0.357061	0.178531	−	0.983934i	$-0.442866\pi$
$359$	6.76535	0.357061	0.178531	+	0.983934i	$0.442866\pi$
$360$	−6.39922	−0.337268
$361$	−15.0284	−0.790970
$362$	−1.20849	−0.0635167
$363$	2.63546	0.138326
$364$	3.10610	0.162804
$365$	−10.6207	−0.555915
$366$	−5.35893	−0.280116
$367$	12.4265	0.648656	0.324328	−	0.945945i	$-0.394862\pi$
$367$	12.4265	0.648656	0.324328	+	0.945945i	$0.394862\pi$
$368$	−4.04579	−0.210901
$369$	−45.4027	−2.36357
$370$	0.111137	0.00577773
$371$	1.48487	0.0770906
$372$	3.06581	0.158955
$373$	0.863573	0.0447141	0.0223571	−	0.999750i	$-0.492883\pi$
$373$	0.863573	0.0447141	0.0223571	+	0.999750i	$0.492883\pi$
$374$	−10.9027	−0.563763
$375$	3.06581	0.158318
$376$	4.18331	0.215738
$377$	3.65125	0.188049
$378$	32.3698	1.66493
$379$	14.2270	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$379$	14.2270	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$380$	−1.99288	−0.102233
$381$	−47.7410	−2.44584
$382$	−2.71314	−0.138816
$383$	−11.7683	−0.601332	−0.300666	−	0.953729i	$-0.597209\pi$
$383$	−11.7683	−0.601332	−0.300666	+	0.953729i	$0.597209\pi$
$384$	−3.06581	−0.156452
$385$	10.6967	0.545156
$386$	18.1392	0.923261
$387$	−26.6178	−1.35306
$388$	2.17509	0.110423
$389$	−0.229830	−0.0116528	−0.00582641	−	0.999983i	$-0.501855\pi$
$389$	−0.229830	−0.0116528	−0.00582641	+	0.999983i	$0.501855\pi$
$390$	3.06581	0.155244
$391$	12.8085	0.647756
$392$	−2.64788	−0.133738
$393$	12.9682	0.654161
$394$	6.06614	0.305608
$395$	7.38949	0.371805
$396$	−22.0375	−1.10743
$397$	−37.0422	−1.85909	−0.929546	−	0.368705i	$-0.879801\pi$
$397$	−37.0422	−1.85909	−0.929546	+	0.368705i	$0.879801\pi$
$398$	−21.4866	−1.07703
$399$	18.9777	0.950072
$400$	1.00000	0.0500000
$401$	−27.5633	−1.37644	−0.688222	−	0.725500i	$-0.741609\pi$
$401$	−27.5633	−1.37644	−0.688222	+	0.725500i	$0.741609\pi$
$402$	−28.3843	−1.41568
$403$	−1.00000	−0.0498135
$404$	5.73021	0.285089
$405$	12.7523	0.633668
$406$	−11.3412	−0.562853
$407$	0.382731	0.0189713
$408$	9.70605	0.480521
$409$	0.466887	0.0230861	0.0115430	−	0.999933i	$-0.496326\pi$
$409$	0.466887	0.0230861	0.0115430	+	0.999933i	$0.496326\pi$
$410$	7.09504	0.350399
$411$	−23.5097	−1.15965
$412$	2.03264	0.100141
$413$	19.9257	0.980481
$414$	25.8899	1.27242
$415$	−16.8359	−0.826441
$416$	1.00000	0.0490290
$417$	−26.6522	−1.30516
$418$	−6.86304	−0.335682
$419$	15.9281	0.778138	0.389069	−	0.921209i	$-0.372797\pi$
$419$	15.9281	0.778138	0.389069	+	0.921209i	$0.372797\pi$
$420$	−9.52274	−0.464662
$421$	24.7607	1.20676	0.603382	−	0.797452i	$-0.293819\pi$
$421$	24.7607	1.20676	0.603382	+	0.797452i	$0.293819\pi$
$422$	−22.1091	−1.07625
$423$	−26.7699	−1.30160
$424$	0.478049	0.0232161
$425$	−3.16590	−0.153569
$426$	−35.6583	−1.72765
$427$	−5.42935	−0.262745
$428$	17.9475	0.867524
$429$	10.5580	0.509745
$430$	4.15953	0.200591
$431$	−18.8436	−0.907665	−0.453832	−	0.891087i	$-0.649943\pi$
$431$	−18.8436	−0.907665	−0.453832	+	0.891087i	$0.649943\pi$
$432$	10.4214	0.501398
$433$	−40.3197	−1.93764	−0.968820	−	0.247767i	$-0.920303\pi$
$433$	−40.3197	−1.93764	−0.968820	+	0.247767i	$0.920303\pi$
$434$	3.10610	0.149098
$435$	−11.1941	−0.536714
$436$	−8.80666	−0.421762
$437$	8.06277	0.385694
$438$	32.5612	1.55583
$439$	23.5447	1.12373	0.561864	−	0.827229i	$-0.310084\pi$
$439$	23.5447	1.12373	0.561864	+	0.827229i	$0.310084\pi$
$440$	3.44378	0.164176
$441$	16.9444	0.806874
$442$	−3.16590	−0.150586
$443$	−7.02105	−0.333580	−0.166790	−	0.985992i	$-0.553340\pi$
$443$	−7.02105	−0.333580	−0.166790	+	0.985992i	$0.553340\pi$
$444$	−0.340725	−0.0161701
$445$	3.02890	0.143584
$446$	−10.7230	−0.507751
$447$	−46.4655	−2.19774
$448$	−3.10610	−0.146750
$449$	−7.73680	−0.365122	−0.182561	−	0.983195i	$-0.558439\pi$
$449$	−7.73680	−0.365122	−0.182561	+	0.983195i	$0.558439\pi$
$450$	−6.39922	−0.301662
$451$	24.4338	1.15054
$452$	3.02028	0.142062
$453$	22.2890	1.04723
$454$	−13.1126	−0.615404
$455$	3.10610	0.145616
$456$	6.10980	0.286118
$457$	−10.7496	−0.502843	−0.251422	−	0.967878i	$-0.580898\pi$
$457$	−10.7496	−0.502843	−0.251422	+	0.967878i	$0.580898\pi$
$458$	16.6472	0.777873
$459$	−32.9930	−1.53998
$460$	−4.04579	−0.188636
$461$	−27.4833	−1.28002	−0.640011	−	0.768366i	$-0.721070\pi$
$461$	−27.4833	−1.28002	−0.640011	+	0.768366i	$0.721070\pi$
$462$	−32.7942	−1.52573
$463$	15.3609	0.713882	0.356941	−	0.934127i	$-0.383820\pi$
$463$	15.3609	0.713882	0.356941	+	0.934127i	$0.383820\pi$
$464$	−3.65125	−0.169505
$465$	3.06581	0.142174
$466$	13.7018	0.634725
$467$	−12.3125	−0.569755	−0.284878	−	0.958564i	$-0.591953\pi$
$467$	−12.3125	−0.569755	−0.284878	+	0.958564i	$0.591953\pi$
$468$	−6.39922	−0.295804
$469$	−28.7573	−1.32789
$470$	4.18331	0.192962
$471$	2.04375	0.0941709
$472$	6.41502	0.295275
$473$	14.3245	0.658642
$474$	−22.6548	−1.04057
$475$	−1.99288	−0.0914396
$476$	9.83360	0.450722
$477$	−3.05914	−0.140068
$478$	−8.12924	−0.371823
$479$	26.8218	1.22552	0.612759	−	0.790270i	$-0.290060\pi$
$479$	26.8218	1.22552	0.612759	+	0.790270i	$0.290060\pi$
$480$	−3.06581	−0.139935
$481$	0.111137	0.00506741
$482$	−7.85430	−0.357754
$483$	38.5270	1.75304
$484$	0.859629	0.0390740
$485$	2.17509	0.0987657
$486$	−7.83216	−0.355274
$487$	−18.8674	−0.854966	−0.427483	−	0.904023i	$-0.640600\pi$
$487$	−18.8674	−0.854966	−0.427483	+	0.904023i	$0.640600\pi$
$488$	−1.74796	−0.0791265
$489$	−52.0841	−2.35532
$490$	−2.64788	−0.119619
$491$	−5.04918	−0.227866	−0.113933	−	0.993488i	$-0.536345\pi$
$491$	−5.04918	−0.227866	−0.113933	+	0.993488i	$0.536345\pi$
$492$	−21.7521	−0.980659
$493$	11.5595	0.520613
$494$	−1.99288	−0.0896639
$495$	−22.0375	−0.990512
$496$	1.00000	0.0449013
$497$	−36.1269	−1.62051
$498$	51.6157	2.31295
$499$	−10.9834	−0.491684	−0.245842	−	0.969310i	$-0.579065\pi$
$499$	−10.9834	−0.491684	−0.245842	+	0.969310i	$0.579065\pi$
$500$	1.00000	0.0447214
$501$	0.702374	0.0313797
$502$	−3.85464	−0.172041
$503$	−35.9761	−1.60409	−0.802047	−	0.597261i	$-0.796256\pi$
$503$	−35.9761	−1.60409	−0.802047	+	0.597261i	$0.796256\pi$
$504$	19.8766	0.885376
$505$	5.73021	0.254991
$506$	−13.9328	−0.619389
$507$	3.06581	0.136158
$508$	−15.5720	−0.690897
$509$	24.2566	1.07515	0.537576	−	0.843215i	$-0.319340\pi$
$509$	24.2566	1.07515	0.537576	+	0.843215i	$0.319340\pi$
$510$	9.70605	0.429791
$511$	32.9891	1.45935
$512$	−1.00000	−0.0441942
$513$	−20.7685	−0.916953
$514$	12.8381	0.566263
$515$	2.03264	0.0895688
$516$	−12.7524	−0.561391
$517$	14.4064	0.633593
$518$	−0.345203	−0.0151673
$519$	−16.1681	−0.709699
$520$	1.00000	0.0438529
$521$	−28.9269	−1.26731	−0.633655	−	0.773616i	$-0.718446\pi$
$521$	−28.9269	−1.26731	−0.633655	+	0.773616i	$0.718446\pi$
$522$	23.3652	1.02267
$523$	−38.9930	−1.70505	−0.852523	−	0.522689i	$-0.824929\pi$
$523$	−38.9930	−1.70505	−0.852523	+	0.522689i	$0.824929\pi$
$524$	4.22995	0.184786
$525$	−9.52274	−0.415606
$526$	−15.0184	−0.654833
$527$	−3.16590	−0.137909
$528$	−10.5580	−0.459478
$529$	−6.63162	−0.288331
$530$	0.478049	0.0207651
$531$	−41.0511	−1.78147
$532$	6.19009	0.268375
$533$	7.09504	0.307320
$534$	−9.28604	−0.401846
$535$	17.9475	0.775937
$536$	−9.25832	−0.399898
$537$	23.1948	1.00093
$538$	17.5507	0.756665
$539$	−9.11872	−0.392771
$540$	10.4214	0.448464
$541$	44.4989	1.91316	0.956579	−	0.291472i	$-0.0941451\pi$
$541$	44.4989	1.91316	0.956579	+	0.291472i	$0.0941451\pi$
$542$	−9.38978	−0.403325
$543$	3.70500	0.158997
$544$	3.16590	0.135737
$545$	−8.80666	−0.377236
$546$	−9.52274	−0.407536
$547$	8.83962	0.377955	0.188977	−	0.981981i	$-0.439483\pi$
$547$	8.83962	0.377955	0.188977	+	0.981981i	$0.439483\pi$
$548$	−7.66835	−0.327576
$549$	11.1856	0.477389
$550$	3.44378	0.146843
$551$	7.27651	0.309990
$552$	12.4036	0.527933
$553$	−22.9525	−0.976040
$554$	−20.2268	−0.859354
$555$	−0.340725	−0.0144630
$556$	−8.69334	−0.368680
$557$	−9.76997	−0.413967	−0.206984	−	0.978344i	$-0.566365\pi$
$557$	−9.76997	−0.413967	−0.206984	+	0.978344i	$0.566365\pi$
$558$	−6.39922	−0.270900
$559$	4.15953	0.175930
$560$	−3.10610	−0.131257
$561$	33.4255	1.41123
$562$	21.8015	0.919643
$563$	12.4351	0.524077	0.262038	−	0.965057i	$-0.415605\pi$
$563$	12.4351	0.524077	0.262038	+	0.965057i	$0.415605\pi$
$564$	−12.8253	−0.540041
$565$	3.02028	0.127064
$566$	−11.7331	−0.493181
$567$	−39.6100	−1.66347
$568$	−11.6309	−0.488023
$569$	−15.4905	−0.649397	−0.324698	−	0.945818i	$-0.605263\pi$
$569$	−15.4905	−0.649397	−0.324698	+	0.945818i	$0.605263\pi$
$570$	6.10980	0.255911
$571$	2.92711	0.122496	0.0612480	−	0.998123i	$-0.480492\pi$
$571$	2.92711	0.122496	0.0612480	+	0.998123i	$0.480492\pi$
$572$	3.44378	0.143992
$573$	8.31799	0.347489
$574$	−22.0379	−0.919845
$575$	−4.04579	−0.168721
$576$	6.39922	0.266634
$577$	29.3091	1.22015	0.610077	−	0.792342i	$-0.291138\pi$
$577$	29.3091	1.22015	0.610077	+	0.792342i	$0.291138\pi$
$578$	6.97710	0.290209
$579$	−55.6114	−2.31113
$580$	−3.65125	−0.151610
$581$	52.2940	2.16952
$582$	−6.66842	−0.276415
$583$	1.64630	0.0681826
$584$	10.6207	0.439489
$585$	−6.39922	−0.264575
$586$	1.82769	0.0755013
$587$	−6.46755	−0.266944	−0.133472	−	0.991053i	$-0.542613\pi$
$587$	−6.46755	−0.266944	−0.133472	+	0.991053i	$0.542613\pi$
$588$	8.11791	0.334777
$589$	−1.99288	−0.0821152
$590$	6.41502	0.264102
$591$	−18.5976	−0.765005
$592$	−0.111137	−0.00456770
$593$	39.6440	1.62798	0.813992	−	0.580876i	$-0.197290\pi$
$593$	39.6440	1.62798	0.813992	+	0.580876i	$0.197290\pi$
$594$	35.8889	1.47254
$595$	9.83360	0.403138
$596$	−15.1560	−0.620815
$597$	65.8740	2.69604
$598$	−4.04579	−0.165444
$599$	−34.3545	−1.40369	−0.701844	−	0.712331i	$-0.747640\pi$
$599$	−34.3545	−1.40369	−0.701844	+	0.712331i	$0.747640\pi$
$600$	−3.06581	−0.125161
$601$	2.91649	0.118966	0.0594830	−	0.998229i	$-0.481055\pi$
$601$	2.91649	0.118966	0.0594830	+	0.998229i	$0.481055\pi$
$602$	−12.9199	−0.526578
$603$	59.2460	2.41268
$604$	7.27019	0.295820
$605$	0.859629	0.0349489
$606$	−17.5678	−0.713641
$607$	−25.6992	−1.04310	−0.521550	−	0.853221i	$-0.674646\pi$
$607$	−25.6992	−1.04310	−0.521550	+	0.853221i	$0.674646\pi$
$608$	1.99288	0.0808220
$609$	34.7699	1.40895
$610$	−1.74796	−0.0707729
$611$	4.18331	0.169239
$612$	−20.2593	−0.818932
$613$	27.0969	1.09443	0.547217	−	0.836990i	$-0.315687\pi$
$613$	27.0969	1.09443	0.547217	+	0.836990i	$0.315687\pi$
$614$	−17.6760	−0.713346
$615$	−21.7521	−0.877128
$616$	−10.6967	−0.430984
$617$	28.5716	1.15025	0.575125	−	0.818066i	$-0.304953\pi$
$617$	28.5716	1.15025	0.575125	+	0.818066i	$0.304953\pi$
$618$	−6.23170	−0.250676
$619$	−10.3474	−0.415895	−0.207948	−	0.978140i	$-0.566678\pi$
$619$	−10.3474	−0.415895	−0.207948	+	0.978140i	$0.566678\pi$
$620$	1.00000	0.0401610
$621$	−42.1626	−1.69193
$622$	1.53132	0.0614003
$623$	−9.40807	−0.376927
$624$	−3.06581	−0.122731
$625$	1.00000	0.0400000
$626$	−6.07525	−0.242816
$627$	21.0408	0.840289
$628$	0.666625	0.0266012
$629$	0.351848	0.0140291
$630$	19.8766	0.791904
$631$	4.63908	0.184679	0.0923394	−	0.995728i	$-0.470566\pi$
$631$	4.63908	0.184679	0.0923394	+	0.995728i	$0.470566\pi$
$632$	−7.38949	−0.293938
$633$	67.7824	2.69411
$634$	−18.8272	−0.747725
$635$	−15.5720	−0.617957
$636$	−1.46561	−0.0581152
$637$	−2.64788	−0.104913
$638$	−12.5741	−0.497814
$639$	74.4288	2.94436
$640$	−1.00000	−0.0395285
$641$	−6.10309	−0.241058	−0.120529	−	0.992710i	$-0.538459\pi$
$641$	−6.10309	−0.241058	−0.120529	+	0.992710i	$0.538459\pi$
$642$	−55.0236	−2.17161
$643$	−35.0110	−1.38070	−0.690350	−	0.723476i	$-0.742543\pi$
$643$	−35.0110	−1.38070	−0.690350	+	0.723476i	$0.742543\pi$
$644$	12.5666	0.495195
$645$	−12.7524	−0.502124
$646$	−6.30925	−0.248234
$647$	−35.9543	−1.41351	−0.706755	−	0.707458i	$-0.749842\pi$
$647$	−35.9543	−1.41351	−0.706755	+	0.707458i	$0.749842\pi$
$648$	−12.7523	−0.500959
$649$	22.0919	0.867184
$650$	1.00000	0.0392232
$651$	−9.52274	−0.373225
$652$	−16.9887	−0.665327
$653$	−28.6339	−1.12053	−0.560266	−	0.828313i	$-0.689301\pi$
$653$	−28.6339	−1.12053	−0.560266	+	0.828313i	$0.689301\pi$
$654$	26.9996	1.05577
$655$	4.22995	0.165278
$656$	−7.09504	−0.277015
$657$	−67.9644	−2.65154
$658$	−12.9938	−0.506551
$659$	−15.0240	−0.585251	−0.292626	−	0.956227i	$-0.594529\pi$
$659$	−15.0240	−0.585251	−0.292626	+	0.956227i	$0.594529\pi$
$660$	−10.5580	−0.410969
$661$	29.1766	1.13484	0.567420	−	0.823429i	$-0.307942\pi$
$661$	29.1766	1.13484	0.567420	+	0.823429i	$0.307942\pi$
$662$	18.9741	0.737449
$663$	9.70605	0.376952
$664$	16.8359	0.653359
$665$	6.19009	0.240041
$666$	0.711189	0.0275580
$667$	14.7722	0.571982
$668$	0.229099	0.00886409
$669$	32.8749	1.27102
$670$	−9.25832	−0.357680
$671$	−6.01960	−0.232384
$672$	9.52274	0.367348
$673$	−26.5397	−1.02303	−0.511515	−	0.859274i	$-0.670916\pi$
$673$	−26.5397	−1.02303	−0.511515	+	0.859274i	$0.670916\pi$
$674$	−30.0970	−1.15929
$675$	10.4214	0.401119
$676$	1.00000	0.0384615
$677$	−14.1223	−0.542763	−0.271382	−	0.962472i	$-0.587481\pi$
$677$	−14.1223	−0.542763	−0.271382	+	0.962472i	$0.587481\pi$
$678$	−9.25963	−0.355614
$679$	−6.75605	−0.259274
$680$	3.16590	0.121407
$681$	40.2007	1.54050
$682$	3.44378	0.131869
$683$	−31.9648	−1.22310	−0.611549	−	0.791206i	$-0.709453\pi$
$683$	−31.9648	−1.22310	−0.611549	+	0.791206i	$0.709453\pi$
$684$	−12.7529	−0.487618
$685$	−7.66835	−0.292993
$686$	−13.5181	−0.516125
$687$	−51.0373	−1.94719
$688$	−4.15953	−0.158581
$689$	0.478049	0.0182122
$690$	12.4036	0.472198
$691$	−5.57784	−0.212191	−0.106095	−	0.994356i	$-0.533835\pi$
$691$	−5.57784	−0.212191	−0.106095	+	0.994356i	$0.533835\pi$
$692$	−5.27366	−0.200474
$693$	68.4508	2.60023
$694$	15.3804	0.583831
$695$	−8.69334	−0.329757
$696$	11.1941	0.424310
$697$	22.4621	0.850814
$698$	−26.3176	−0.996136
$699$	−42.0073	−1.58886
$700$	−3.10610	−0.117400
$701$	35.7026	1.34847	0.674234	−	0.738518i	$-0.264474\pi$
$701$	35.7026	1.34847	0.674234	+	0.738518i	$0.264474\pi$
$702$	10.4214	0.393329
$703$	0.221483	0.00835337
$704$	−3.44378	−0.129792
$705$	−12.8253	−0.483027
$706$	−10.3955	−0.391240
$707$	−17.7986	−0.669386
$708$	−19.6673	−0.739141
$709$	16.3876	0.615450	0.307725	−	0.951475i	$-0.400432\pi$
$709$	16.3876	0.615450	0.307725	+	0.951475i	$0.400432\pi$
$710$	−11.6309	−0.436501
$711$	47.2869	1.77340
$712$	−3.02890	−0.113513
$713$	−4.04579	−0.151516
$714$	−30.1480	−1.12826
$715$	3.44378	0.128790
$716$	7.56564	0.282741
$717$	24.9227	0.930757
$718$	−6.76535	−0.252481
$719$	−26.0265	−0.970625	−0.485313	−	0.874341i	$-0.661294\pi$
$719$	−26.0265	−0.970625	−0.485313	+	0.874341i	$0.661294\pi$
$720$	6.39922	0.238485
$721$	−6.31359	−0.235130
$722$	15.0284	0.559300
$723$	24.0798	0.895539
$724$	1.20849	0.0449131
$725$	−3.65125	−0.135604
$726$	−2.63546	−0.0978111
$727$	46.4383	1.72230	0.861151	−	0.508349i	$-0.169744\pi$
$727$	46.4383	1.72230	0.861151	+	0.508349i	$0.169744\pi$
$728$	−3.10610	−0.115120
$729$	−14.2450	−0.527594
$730$	10.6207	0.393091
$731$	13.1687	0.487060
$732$	5.35893	0.198072
$733$	6.90489	0.255038	0.127519	−	0.991836i	$-0.459299\pi$
$733$	6.90489	0.255038	0.127519	+	0.991836i	$0.459299\pi$
$734$	−12.4265	−0.458669
$735$	8.11791	0.299434
$736$	4.04579	0.149130
$737$	−31.8836	−1.17445
$738$	45.4027	1.67130
$739$	40.9759	1.50732	0.753662	−	0.657263i	$-0.228286\pi$
$739$	40.9759	1.50732	0.753662	+	0.657263i	$0.228286\pi$
$740$	−0.111137	−0.00408547
$741$	6.10980	0.224449
$742$	−1.48487	−0.0545113
$743$	0.336697	0.0123522	0.00617611	−	0.999981i	$-0.498034\pi$
$743$	0.336697	0.0123522	0.00617611	+	0.999981i	$0.498034\pi$
$744$	−3.06581	−0.112398
$745$	−15.1560	−0.555274
$746$	−0.863573	−0.0316176
$747$	−107.736	−3.94187
$748$	10.9027	0.398640
$749$	−55.7467	−2.03694
$750$	−3.06581	−0.111948
$751$	−20.0320	−0.730980	−0.365490	−	0.930815i	$-0.619098\pi$
$751$	−20.0320	−0.730980	−0.365490	+	0.930815i	$0.619098\pi$
$752$	−4.18331	−0.152550
$753$	11.8176	0.430658
$754$	−3.65125	−0.132971
$755$	7.27019	0.264589
$756$	−32.3698	−1.17728
$757$	−31.1597	−1.13252	−0.566259	−	0.824228i	$-0.691610\pi$
$757$	−31.1597	−1.13252	−0.566259	+	0.824228i	$0.691610\pi$
$758$	−14.2270	−0.516749
$759$	42.7154	1.55047
$760$	1.99288	0.0722894
$761$	28.7488	1.04214	0.521072	−	0.853512i	$-0.325532\pi$
$761$	28.7488	1.04214	0.521072	+	0.853512i	$0.325532\pi$
$762$	47.7410	1.72947
$763$	27.3544	0.990295
$764$	2.71314	0.0981580
$765$	−20.2593	−0.732475
$766$	11.7683	0.425206
$767$	6.41502	0.231633
$768$	3.06581	0.110628
$769$	−39.1484	−1.41173	−0.705864	−	0.708347i	$-0.749441\pi$
$769$	−39.1484	−1.41173	−0.705864	+	0.708347i	$0.749441\pi$
$770$	−10.6967	−0.385484
$771$	−39.3591	−1.41748
$772$	−18.1392	−0.652844
$773$	−29.5141	−1.06155	−0.530773	−	0.847514i	$-0.678098\pi$
$773$	−29.5141	−1.06155	−0.530773	+	0.847514i	$0.678098\pi$
$774$	26.6178	0.956756
$775$	1.00000	0.0359211
$776$	−2.17509	−0.0780812
$777$	1.05833	0.0379673
$778$	0.229830	0.00823979
$779$	14.1396	0.506602
$780$	−3.06581	−0.109774
$781$	−40.0544	−1.43326
$782$	−12.8085	−0.458032
$783$	−38.0511	−1.35983
$784$	2.64788	0.0945672
$785$	0.666625	0.0237929
$786$	−12.9682	−0.462561
$787$	−52.0480	−1.85531	−0.927655	−	0.373438i	$-0.878179\pi$
$787$	−52.0480	−1.85531	−0.927655	+	0.373438i	$0.878179\pi$
$788$	−6.06614	−0.216097
$789$	46.0436	1.63920
$790$	−7.38949	−0.262906
$791$	−9.38132	−0.333561
$792$	22.0375	0.783069
$793$	−1.74796	−0.0620720
$794$	37.0422	1.31458
$795$	−1.46561	−0.0519798
$796$	21.4866	0.761573
$797$	11.8868	0.421053	0.210527	−	0.977588i	$-0.432482\pi$
$797$	11.8868	0.421053	0.210527	+	0.977588i	$0.432482\pi$
$798$	−18.9777	−0.671802
$799$	13.2439	0.468537
$800$	−1.00000	−0.0353553
$801$	19.3826	0.684850
$802$	27.5633	0.973293
$803$	36.5755	1.29072
$804$	28.3843	1.00104
$805$	12.5666	0.442916
$806$	1.00000	0.0352235
$807$	−53.8072	−1.89410
$808$	−5.73021	−0.201588
$809$	23.8146	0.837278	0.418639	−	0.908153i	$-0.362507\pi$
$809$	23.8146	0.837278	0.418639	+	0.908153i	$0.362507\pi$
$810$	−12.7523	−0.448071
$811$	40.8102	1.43304	0.716520	−	0.697567i	$-0.245734\pi$
$811$	40.8102	1.43304	0.716520	+	0.697567i	$0.245734\pi$
$812$	11.3412	0.397997
$813$	28.7873	1.00962
$814$	−0.382731	−0.0134147
$815$	−16.9887	−0.595087
$816$	−9.70605	−0.339780
$817$	8.28945	0.290011
$818$	−0.466887	−0.0163243
$819$	19.8766	0.694546
$820$	−7.09504	−0.247769
$821$	19.9792	0.697277	0.348639	−	0.937257i	$-0.386644\pi$
$821$	19.9792	0.697277	0.348639	+	0.937257i	$0.386644\pi$
$822$	23.5097	0.819996
$823$	−35.6651	−1.24321	−0.621604	−	0.783332i	$-0.713519\pi$
$823$	−35.6651	−1.24321	−0.621604	+	0.783332i	$0.713519\pi$
$824$	−2.03264	−0.0708104
$825$	−10.5580	−0.367582
$826$	−19.9257	−0.693305
$827$	−7.51549	−0.261339	−0.130670	−	0.991426i	$-0.541713\pi$
$827$	−7.51549	−0.261339	−0.130670	+	0.991426i	$0.541713\pi$
$828$	−25.8899	−0.899735
$829$	1.62875	0.0565688	0.0282844	−	0.999600i	$-0.490996\pi$
$829$	1.62875	0.0565688	0.0282844	+	0.999600i	$0.490996\pi$
$830$	16.8359	0.584382
$831$	62.0116	2.15116
$832$	−1.00000	−0.0346688
$833$	−8.38291	−0.290451
$834$	26.6522	0.922889
$835$	0.229099	0.00792828
$836$	6.86304	0.237363
$837$	10.4214	0.360215
$838$	−15.9281	−0.550227
$839$	41.5367	1.43401	0.717003	−	0.697071i	$-0.245514\pi$
$839$	41.5367	1.43401	0.717003	+	0.697071i	$0.245514\pi$
$840$	9.52274	0.328566
$841$	−15.6683	−0.540288
$842$	−24.7607	−0.853311
$843$	−66.8395	−2.30207
$844$	22.1091	0.761027
$845$	1.00000	0.0344010
$846$	26.7699	0.920369
$847$	−2.67010	−0.0917456
$848$	−0.478049	−0.0164163
$849$	35.9717	1.23454
$850$	3.16590	0.108589
$851$	0.449636	0.0154133
$852$	35.6583	1.22163
$853$	−35.6509	−1.22067	−0.610333	−	0.792145i	$-0.708964\pi$
$853$	−35.6509	−1.22067	−0.610333	+	0.792145i	$0.708964\pi$
$854$	5.42935	0.185789
$855$	−12.7529	−0.436139
$856$	−17.9475	−0.613432
$857$	8.16891	0.279045	0.139522	−	0.990219i	$-0.455443\pi$
$857$	8.16891	0.279045	0.139522	+	0.990219i	$0.455443\pi$
$858$	−10.5580	−0.360444
$859$	45.1221	1.53955	0.769774	−	0.638317i	$-0.220369\pi$
$859$	45.1221	1.53955	0.769774	+	0.638317i	$0.220369\pi$
$860$	−4.15953	−0.141839
$861$	67.5642	2.30258
$862$	18.8436	0.641816
$863$	−34.9938	−1.19120	−0.595601	−	0.803280i	$-0.703086\pi$
$863$	−34.9938	−1.19120	−0.595601	+	0.803280i	$0.703086\pi$
$864$	−10.4214	−0.354542
$865$	−5.27366	−0.179310
$866$	40.3197	1.37012
$867$	−21.3905	−0.726459
$868$	−3.10610	−0.105428
$869$	−25.4478	−0.863256
$870$	11.1941	0.379514
$871$	−9.25832	−0.313706
$872$	8.80666	0.298231
$873$	13.9189	0.471082
$874$	−8.06277	−0.272727
$875$	−3.10610	−0.105005
$876$	−32.5612	−1.10014
$877$	−3.83930	−0.129644	−0.0648220	−	0.997897i	$-0.520648\pi$
$877$	−3.83930	−0.129644	−0.0648220	+	0.997897i	$0.520648\pi$
$878$	−23.5447	−0.794596
$879$	−5.60337	−0.188997
$880$	−3.44378	−0.116090
$881$	−9.70100	−0.326835	−0.163418	−	0.986557i	$-0.552252\pi$
$881$	−9.70100	−0.326835	−0.163418	+	0.986557i	$0.552252\pi$
$882$	−16.9444	−0.570546
$883$	3.93777	0.132516	0.0662582	−	0.997803i	$-0.478894\pi$
$883$	3.93777	0.132516	0.0662582	+	0.997803i	$0.478894\pi$
$884$	3.16590	0.106481
$885$	−19.6673	−0.661108
$886$	7.02105	0.235877
$887$	−4.82157	−0.161893	−0.0809463	−	0.996718i	$-0.525794\pi$
$887$	−4.82157	−0.161893	−0.0809463	+	0.996718i	$0.525794\pi$
$888$	0.340725	0.0114340
$889$	48.3684	1.62222
$890$	−3.02890	−0.101529
$891$	−43.9162	−1.47125
$892$	10.7230	0.359034
$893$	8.33684	0.278982
$894$	46.4655	1.55404
$895$	7.56564	0.252891
$896$	3.10610	0.103768
$897$	12.4036	0.414145
$898$	7.73680	0.258180
$899$	−3.65125	−0.121776
$900$	6.39922	0.213307
$901$	1.51345	0.0504204
$902$	−24.4338	−0.813555
$903$	39.6102	1.31814
$904$	−3.02028	−0.100453
$905$	1.20849	0.0401715
$906$	−22.2890	−0.740504
$907$	−7.37790	−0.244979	−0.122490	−	0.992470i	$-0.539088\pi$
$907$	−7.37790	−0.244979	−0.122490	+	0.992470i	$0.539088\pi$
$908$	13.1126	0.435156
$909$	36.6689	1.21623
$910$	−3.10610	−0.102966
$911$	−36.5275	−1.21021	−0.605105	−	0.796146i	$-0.706869\pi$
$911$	−36.5275	−1.21021	−0.605105	+	0.796146i	$0.706869\pi$
$912$	−6.10980	−0.202316
$913$	57.9791	1.91883
$914$	10.7496	0.355564
$915$	5.35893	0.177161
$916$	−16.6472	−0.550039
$917$	−13.1387	−0.433877
$918$	32.9930	1.08893
$919$	12.6963	0.418813	0.209406	−	0.977829i	$-0.432847\pi$
$919$	12.6963	0.418813	0.209406	+	0.977829i	$0.432847\pi$
$920$	4.04579	0.133386
$921$	54.1914	1.78567
$922$	27.4833	0.905113
$923$	−11.6309	−0.382837
$924$	32.7942	1.07885
$925$	−0.111137	−0.00365416
$926$	−15.3609	−0.504791
$927$	13.0073	0.427216
$928$	3.65125	0.119858
$929$	20.6463	0.677383	0.338692	−	0.940897i	$-0.390016\pi$
$929$	20.6463	0.677383	0.338692	+	0.940897i	$0.390016\pi$
$930$	−3.06581	−0.100532
$931$	−5.27691	−0.172944
$932$	−13.7018	−0.448818
$933$	−4.69474	−0.153699
$934$	12.3125	0.402878
$935$	10.9027	0.356555
$936$	6.39922	0.209165
$937$	−10.9317	−0.357124	−0.178562	−	0.983929i	$-0.557145\pi$
$937$	−10.9317	−0.357124	−0.178562	+	0.983929i	$0.557145\pi$
$938$	28.7573	0.938959
$939$	18.6256	0.607823
$940$	−4.18331	−0.136445
$941$	33.5993	1.09531	0.547653	−	0.836705i	$-0.315521\pi$
$941$	33.5993	1.09531	0.547653	+	0.836705i	$0.315521\pi$
$942$	−2.04375	−0.0665889
$943$	28.7050	0.934763
$944$	−6.41502	−0.208791
$945$	−32.3698	−1.05299
$946$	−14.3245	−0.465731
$947$	−37.8687	−1.23057	−0.615284	−	0.788306i	$-0.710959\pi$
$947$	−37.8687	−1.23057	−0.615284	+	0.788306i	$0.710959\pi$
$948$	22.6548	0.735793
$949$	10.6207	0.344764
$950$	1.99288	0.0646576
$951$	57.7208	1.87172
$952$	−9.83360	−0.318709
$953$	−28.7862	−0.932476	−0.466238	−	0.884659i	$-0.654391\pi$
$953$	−28.7862	−0.932476	−0.466238	+	0.884659i	$0.654391\pi$
$954$	3.05914	0.0990433
$955$	2.71314	0.0877952
$956$	8.12924	0.262918
$957$	38.5499	1.24614
$958$	−26.8218	−0.866572
$959$	23.8187	0.769145
$960$	3.06581	0.0989487
$961$	1.00000	0.0322581
$962$	−0.111137	−0.00358320
$963$	114.850	3.70098
$964$	7.85430	0.252970
$965$	−18.1392	−0.583921
$966$	−38.5270	−1.23958
$967$	41.7930	1.34397	0.671985	−	0.740564i	$-0.265442\pi$
$967$	41.7930	1.34397	0.671985	+	0.740564i	$0.265442\pi$
$968$	−0.859629	−0.0276295
$969$	19.3430	0.621386
$970$	−2.17509	−0.0698379
$971$	−20.3146	−0.651927	−0.325964	−	0.945382i	$-0.605689\pi$
$971$	−20.3146	−0.651927	−0.325964	+	0.945382i	$0.605689\pi$
$972$	7.83216	0.251217
$973$	27.0024	0.865658
$974$	18.8674	0.604552
$975$	−3.06581	−0.0981846
$976$	1.74796	0.0559509
$977$	−9.90144	−0.316775	−0.158388	−	0.987377i	$-0.550630\pi$
$977$	−9.90144	−0.316775	−0.158388	+	0.987377i	$0.550630\pi$
$978$	52.0841	1.66547
$979$	−10.4309	−0.333372
$980$	2.64788	0.0845834
$981$	−56.3557	−1.79930
$982$	5.04918	0.161126
$983$	40.9389	1.30575	0.652875	−	0.757466i	$-0.273563\pi$
$983$	40.9389	1.30575	0.652875	+	0.757466i	$0.273563\pi$
$984$	21.7521	0.693430
$985$	−6.06614	−0.193283
$986$	−11.5595	−0.368129
$987$	39.8366	1.26801
$988$	1.99288	0.0634020
$989$	16.8286	0.535118
$990$	22.0375	0.700398
$991$	7.58943	0.241086	0.120543	−	0.992708i	$-0.461536\pi$
$991$	7.58943	0.241086	0.120543	+	0.992708i	$0.461536\pi$
$992$	−1.00000	−0.0317500
$993$	−58.1711	−1.84600
$994$	36.1269	1.14587
$995$	21.4866	0.681172
$996$	−51.6157	−1.63551
$997$	46.3618	1.46829	0.734146	−	0.678992i	$-0.237583\pi$
$997$	46.3618	1.46829	0.734146	+	0.678992i	$0.237583\pi$
$998$	10.9834	0.347673
$999$	−1.15820	−0.0366438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.h.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.h.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.06581 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06581 q^{6} -3.10610 q^{7} -1.00000 q^{8} +6.39922 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.06581 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.06581 q^{6} -3.10610 q^{7} -1.00000 q^{8} +6.39922 q^{9} -1.00000 q^{10} -3.44378 q^{11} +3.06581 q^{12} -1.00000 q^{13} +3.10610 q^{14} +3.06581 q^{15} +1.00000 q^{16} -3.16590 q^{17} -6.39922 q^{18} -1.99288 q^{19} +1.00000 q^{20} -9.52274 q^{21} +3.44378 q^{22} -4.04579 q^{23} -3.06581 q^{24} +1.00000 q^{25} +1.00000 q^{26} +10.4214 q^{27} -3.10610 q^{28} -3.65125 q^{29} -3.06581 q^{30} +1.00000 q^{31} -1.00000 q^{32} -10.5580 q^{33} +3.16590 q^{34} -3.10610 q^{35} +6.39922 q^{36} -0.111137 q^{37} +1.99288 q^{38} -3.06581 q^{39} -1.00000 q^{40} -7.09504 q^{41} +9.52274 q^{42} -4.15953 q^{43} -3.44378 q^{44} +6.39922 q^{45} +4.04579 q^{46} -4.18331 q^{47} +3.06581 q^{48} +2.64788 q^{49} -1.00000 q^{50} -9.70605 q^{51} -1.00000 q^{52} -0.478049 q^{53} -10.4214 q^{54} -3.44378 q^{55} +3.10610 q^{56} -6.10980 q^{57} +3.65125 q^{58} -6.41502 q^{59} +3.06581 q^{60} +1.74796 q^{61} -1.00000 q^{62} -19.8766 q^{63} +1.00000 q^{64} -1.00000 q^{65} +10.5580 q^{66} +9.25832 q^{67} -3.16590 q^{68} -12.4036 q^{69} +3.10610 q^{70} +11.6309 q^{71} -6.39922 q^{72} -10.6207 q^{73} +0.111137 q^{74} +3.06581 q^{75} -1.99288 q^{76} +10.6967 q^{77} +3.06581 q^{78} +7.38949 q^{79} +1.00000 q^{80} +12.7523 q^{81} +7.09504 q^{82} -16.8359 q^{83} -9.52274 q^{84} -3.16590 q^{85} +4.15953 q^{86} -11.1941 q^{87} +3.44378 q^{88} +3.02890 q^{89} -6.39922 q^{90} +3.10610 q^{91} -4.04579 q^{92} +3.06581 q^{93} +4.18331 q^{94} -1.99288 q^{95} -3.06581 q^{96} +2.17509 q^{97} -2.64788 q^{98} -22.0375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 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

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