LMFDB - Embedded newform 31.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(1,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("31.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.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:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} -3.23607 q^{3} +0.618034 q^{4} +1.00000 q^{5} -5.23607 q^{6} +0.236068 q^{7} -2.23607 q^{8} +7.47214 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} -3.23607 q^{3} +0.618034 q^{4} +1.00000 q^{5} -5.23607 q^{6} +0.236068 q^{7} -2.23607 q^{8} +7.47214 q^{9} +1.61803 q^{10} +2.00000 q^{11} -2.00000 q^{12} -3.23607 q^{13} +0.381966 q^{14} -3.23607 q^{15} -4.85410 q^{16} +0.763932 q^{17} +12.0902 q^{18} -2.23607 q^{19} +0.618034 q^{20} -0.763932 q^{21} +3.23607 q^{22} +5.70820 q^{23} +7.23607 q^{24} -4.00000 q^{25} -5.23607 q^{26} -14.4721 q^{27} +0.145898 q^{28} +2.76393 q^{29} -5.23607 q^{30} +1.00000 q^{31} -3.38197 q^{32} -6.47214 q^{33} +1.23607 q^{34} +0.236068 q^{35} +4.61803 q^{36} -2.00000 q^{37} -3.61803 q^{38} +10.4721 q^{39} -2.23607 q^{40} +7.00000 q^{41} -1.23607 q^{42} +1.23607 q^{43} +1.23607 q^{44} +7.47214 q^{45} +9.23607 q^{46} +2.47214 q^{47} +15.7082 q^{48} -6.94427 q^{49} -6.47214 q^{50} -2.47214 q^{51} -2.00000 q^{52} -10.4721 q^{53} -23.4164 q^{54} +2.00000 q^{55} -0.527864 q^{56} +7.23607 q^{57} +4.47214 q^{58} +2.23607 q^{59} -2.00000 q^{60} +8.18034 q^{61} +1.61803 q^{62} +1.76393 q^{63} +4.23607 q^{64} -3.23607 q^{65} -10.4721 q^{66} +8.00000 q^{67} +0.472136 q^{68} -18.4721 q^{69} +0.381966 q^{70} -9.18034 q^{71} -16.7082 q^{72} +8.47214 q^{73} -3.23607 q^{74} +12.9443 q^{75} -1.38197 q^{76} +0.472136 q^{77} +16.9443 q^{78} -11.7082 q^{79} -4.85410 q^{80} +24.4164 q^{81} +11.3262 q^{82} -14.9443 q^{83} -0.472136 q^{84} +0.763932 q^{85} +2.00000 q^{86} -8.94427 q^{87} -4.47214 q^{88} +11.7082 q^{89} +12.0902 q^{90} -0.763932 q^{91} +3.52786 q^{92} -3.23607 q^{93} +4.00000 q^{94} -2.23607 q^{95} +10.9443 q^{96} -15.9443 q^{97} -11.2361 q^{98} +14.9443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 + 2 * q^5 - 6 * q^6 - 4 * q^7 + 6 * q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} - 4 q^{7} + 6 q^{9} + q^{10} + 4 q^{11} - 4 q^{12} - 2 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} + 13 q^{18} - q^{20} - 6 q^{21} + 2 q^{22} - 2 q^{23} + 10 q^{24} - 8 q^{25} - 6 q^{26} - 20 q^{27} + 7 q^{28} + 10 q^{29} - 6 q^{30} + 2 q^{31} - 9 q^{32} - 4 q^{33} - 2 q^{34} - 4 q^{35} + 7 q^{36} - 4 q^{37} - 5 q^{38} + 12 q^{39} + 14 q^{41} + 2 q^{42} - 2 q^{43} - 2 q^{44} + 6 q^{45} + 14 q^{46} - 4 q^{47} + 18 q^{48} + 4 q^{49} - 4 q^{50} + 4 q^{51} - 4 q^{52} - 12 q^{53} - 20 q^{54} + 4 q^{55} - 10 q^{56} + 10 q^{57} - 4 q^{60} - 6 q^{61} + q^{62} + 8 q^{63} + 4 q^{64} - 2 q^{65} - 12 q^{66} + 16 q^{67} - 8 q^{68} - 28 q^{69} + 3 q^{70} + 4 q^{71} - 20 q^{72} + 8 q^{73} - 2 q^{74} + 8 q^{75} - 5 q^{76} - 8 q^{77} + 16 q^{78} - 10 q^{79} - 3 q^{80} + 22 q^{81} + 7 q^{82} - 12 q^{83} + 8 q^{84} + 6 q^{85} + 4 q^{86} + 10 q^{89} + 13 q^{90} - 6 q^{91} + 16 q^{92} - 2 q^{93} + 8 q^{94} + 4 q^{96} - 14 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 + 2 * q^5 - 6 * q^6 - 4 * q^7 + 6 * q^9 + q^10 + 4 * q^11 - 4 * q^12 - 2 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 + 13 * q^18 - q^20 - 6 * q^21 + 2 * q^22 - 2 * q^23 + 10 * q^24 - 8 * q^25 - 6 * q^26 - 20 * q^27 + 7 * q^28 + 10 * q^29 - 6 * q^30 + 2 * q^31 - 9 * q^32 - 4 * q^33 - 2 * q^34 - 4 * q^35 + 7 * q^36 - 4 * q^37 - 5 * q^38 + 12 * q^39 + 14 * q^41 + 2 * q^42 - 2 * q^43 - 2 * q^44 + 6 * q^45 + 14 * q^46 - 4 * q^47 + 18 * q^48 + 4 * q^49 - 4 * q^50 + 4 * q^51 - 4 * q^52 - 12 * q^53 - 20 * q^54 + 4 * q^55 - 10 * q^56 + 10 * q^57 - 4 * q^60 - 6 * q^61 + q^62 + 8 * q^63 + 4 * q^64 - 2 * q^65 - 12 * q^66 + 16 * q^67 - 8 * q^68 - 28 * q^69 + 3 * q^70 + 4 * q^71 - 20 * q^72 + 8 * q^73 - 2 * q^74 + 8 * q^75 - 5 * q^76 - 8 * q^77 + 16 * q^78 - 10 * q^79 - 3 * q^80 + 22 * q^81 + 7 * q^82 - 12 * q^83 + 8 * q^84 + 6 * q^85 + 4 * q^86 + 10 * q^89 + 13 * q^90 - 6 * q^91 + 16 * q^92 - 2 * q^93 + 8 * q^94 + 4 * q^96 - 14 * q^97 - 18 * q^98 + 12 * 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 $

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	−3.23607	−1.86834	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−3.23607	−1.86834	−0.934172	+	0.356822i	$0.883860\pi$
$4$	0.618034	0.309017
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−5.23607	−2.13762
$7$	0.236068	0.0892253	0.0446127	−	0.999004i	$-0.485795\pi$
$7$	0.236068	0.0892253	0.0446127	+	0.999004i	$0.485795\pi$
$8$	−2.23607	−0.790569
$9$	7.47214	2.49071
$10$	1.61803	0.511667
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−2.00000	−0.577350
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	0.381966	0.102085
$15$	−3.23607	−0.835549
$16$	−4.85410	−1.21353
$17$	0.763932	0.185281	0.0926404	−	0.995700i	$-0.470469\pi$
$17$	0.763932	0.185281	0.0926404	+	0.995700i	$0.470469\pi$
$18$	12.0902	2.84968
$19$	−2.23607	−0.512989	−0.256495	−	0.966546i	$-0.582568\pi$
$19$	−2.23607	−0.512989	−0.256495	+	0.966546i	$0.582568\pi$
$20$	0.618034	0.138197
$21$	−0.763932	−0.166704
$22$	3.23607	0.689932
$23$	5.70820	1.19024	0.595121	−	0.803636i	$-0.297104\pi$
$23$	5.70820	1.19024	0.595121	+	0.803636i	$0.297104\pi$
$24$	7.23607	1.47706
$25$	−4.00000	−0.800000
$26$	−5.23607	−1.02688
$27$	−14.4721	−2.78516
$28$	0.145898	0.0275721
$29$	2.76393	0.513249	0.256625	−	0.966511i	$-0.417390\pi$
$29$	2.76393	0.513249	0.256625	+	0.966511i	$0.417390\pi$
$30$	−5.23607	−0.955971
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−3.38197	−0.597853
$33$	−6.47214	−1.12665
$34$	1.23607	0.211984
$35$	0.236068	0.0399028
$36$	4.61803	0.769672
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−3.61803	−0.586923
$39$	10.4721	1.67688
$40$	−2.23607	−0.353553
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	−1.23607	−0.190729
$43$	1.23607	0.188499	0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607	0.188499	0.0942493	+	0.995549i	$0.469955\pi$
$44$	1.23607	0.186344
$45$	7.47214	1.11388
$46$	9.23607	1.36178
$47$	2.47214	0.360598	0.180299	−	0.983612i	$-0.442293\pi$
$47$	2.47214	0.360598	0.180299	+	0.983612i	$0.442293\pi$
$48$	15.7082	2.26728
$49$	−6.94427	−0.992039
$50$	−6.47214	−0.915298
$51$	−2.47214	−0.346168
$52$	−2.00000	−0.277350
$53$	−10.4721	−1.43846	−0.719229	−	0.694773i	$-0.755505\pi$
$53$	−10.4721	−1.43846	−0.719229	+	0.694773i	$0.755505\pi$
$54$	−23.4164	−3.18657
$55$	2.00000	0.269680
$56$	−0.527864	−0.0705388
$57$	7.23607	0.958441
$58$	4.47214	0.587220
$59$	2.23607	0.291111	0.145556	−	0.989350i	$-0.453503\pi$
$59$	2.23607	0.291111	0.145556	+	0.989350i	$0.453503\pi$
$60$	−2.00000	−0.258199
$61$	8.18034	1.04739	0.523693	−	0.851907i	$-0.324554\pi$
$61$	8.18034	1.04739	0.523693	+	0.851907i	$0.324554\pi$
$62$	1.61803	0.205491
$63$	1.76393	0.222235
$64$	4.23607	0.529508
$65$	−3.23607	−0.401385
$66$	−10.4721	−1.28903
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0.472136	0.0572549
$69$	−18.4721	−2.22378
$70$	0.381966	0.0456537
$71$	−9.18034	−1.08951	−0.544753	−	0.838597i	$-0.683377\pi$
$71$	−9.18034	−1.08951	−0.544753	+	0.838597i	$0.683377\pi$
$72$	−16.7082	−1.96908
$73$	8.47214	0.991589	0.495794	−	0.868440i	$-0.334877\pi$
$73$	8.47214	0.991589	0.495794	+	0.868440i	$0.334877\pi$
$74$	−3.23607	−0.376185
$75$	12.9443	1.49468
$76$	−1.38197	−0.158522
$77$	0.472136	0.0538049
$78$	16.9443	1.91856
$79$	−11.7082	−1.31728	−0.658638	−	0.752460i	$-0.728867\pi$
$79$	−11.7082	−1.31728	−0.658638	+	0.752460i	$0.728867\pi$
$80$	−4.85410	−0.542705
$81$	24.4164	2.71293
$82$	11.3262	1.25077
$83$	−14.9443	−1.64035	−0.820173	−	0.572115i	$-0.806123\pi$
$83$	−14.9443	−1.64035	−0.820173	+	0.572115i	$0.806123\pi$
$84$	−0.472136	−0.0515143
$85$	0.763932	0.0828601
$86$	2.00000	0.215666
$87$	−8.94427	−0.958927
$88$	−4.47214	−0.476731
$89$	11.7082	1.24107	0.620534	−	0.784180i	$-0.286916\pi$
$89$	11.7082	1.24107	0.620534	+	0.784180i	$0.286916\pi$
$90$	12.0902	1.27442
$91$	−0.763932	−0.0800818
$92$	3.52786	0.367805
$93$	−3.23607	−0.335565
$94$	4.00000	0.412568
$95$	−2.23607	−0.229416
$96$	10.9443	1.11700
$97$	−15.9443	−1.61890	−0.809448	−	0.587192i	$-0.800233\pi$
$97$	−15.9443	−1.61890	−0.809448	+	0.587192i	$0.800233\pi$
$98$	−11.2361	−1.13501
$99$	14.9443	1.50196
$100$	−2.47214	−0.247214
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	−4.00000	−0.396059
$103$	6.23607	0.614458	0.307229	−	0.951636i	$-0.400598\pi$
$103$	6.23607	0.614458	0.307229	+	0.951636i	$0.400598\pi$
$104$	7.23607	0.709555
$105$	−0.763932	−0.0745521
$106$	−16.9443	−1.64577
$107$	5.76393	0.557220	0.278610	−	0.960404i	$-0.410126\pi$
$107$	5.76393	0.557220	0.278610	+	0.960404i	$0.410126\pi$
$108$	−8.94427	−0.860663
$109$	−13.9443	−1.33562	−0.667810	−	0.744332i	$-0.732768\pi$
$109$	−13.9443	−1.33562	−0.667810	+	0.744332i	$0.732768\pi$
$110$	3.23607	0.308547
$111$	6.47214	0.614308
$112$	−1.14590	−0.108277
$113$	3.47214	0.326631	0.163316	−	0.986574i	$-0.447781\pi$
$113$	3.47214	0.326631	0.163316	+	0.986574i	$0.447781\pi$
$114$	11.7082	1.09657
$115$	5.70820	0.532293
$116$	1.70820	0.158603
$117$	−24.1803	−2.23547
$118$	3.61803	0.333067
$119$	0.180340	0.0165317
$120$	7.23607	0.660560
$121$	−7.00000	−0.636364
$122$	13.2361	1.19834
$123$	−22.6525	−2.04250
$124$	0.618034	0.0555011
$125$	−9.00000	−0.804984
$126$	2.85410	0.254264
$127$	12.4721	1.10672	0.553362	−	0.832941i	$-0.313345\pi$
$127$	12.4721	1.10672	0.553362	+	0.832941i	$0.313345\pi$
$128$	13.6180	1.20368
$129$	−4.00000	−0.352180
$130$	−5.23607	−0.459234
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−4.00000	−0.348155
$133$	−0.527864	−0.0457716
$134$	12.9443	1.11821
$135$	−14.4721	−1.24556
$136$	−1.70820	−0.146477
$137$	6.29180	0.537544	0.268772	−	0.963204i	$-0.413382\pi$
$137$	6.29180	0.537544	0.268772	+	0.963204i	$0.413382\pi$
$138$	−29.8885	−2.54428
$139$	13.4164	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$140$	0.145898	0.0123306
$141$	−8.00000	−0.673722
$142$	−14.8541	−1.24653
$143$	−6.47214	−0.541227
$144$	−36.2705	−3.02254
$145$	2.76393	0.229532
$146$	13.7082	1.13450
$147$	22.4721	1.85347
$148$	−1.23607	−0.101604
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	20.9443	1.71009
$151$	−14.1803	−1.15398	−0.576990	−	0.816751i	$-0.695773\pi$
$151$	−14.1803	−1.15398	−0.576990	+	0.816751i	$0.695773\pi$
$152$	5.00000	0.405554
$153$	5.70820	0.461481
$154$	0.763932	0.0615594
$155$	1.00000	0.0803219
$156$	6.47214	0.518186
$157$	20.8885	1.66709	0.833544	−	0.552454i	$-0.186308\pi$
$157$	20.8885	1.66709	0.833544	+	0.552454i	$0.186308\pi$
$158$	−18.9443	−1.50713
$159$	33.8885	2.68754
$160$	−3.38197	−0.267368
$161$	1.34752	0.106200
$162$	39.5066	3.10393
$163$	10.7082	0.838731	0.419366	−	0.907817i	$-0.362253\pi$
$163$	10.7082	0.838731	0.419366	+	0.907817i	$0.362253\pi$
$164$	4.32624	0.337822
$165$	−6.47214	−0.503855
$166$	−24.1803	−1.87676
$167$	−6.47214	−0.500829	−0.250414	−	0.968139i	$-0.580567\pi$
$167$	−6.47214	−0.500829	−0.250414	+	0.968139i	$0.580567\pi$
$168$	1.70820	0.131791
$169$	−2.52786	−0.194451
$170$	1.23607	0.0948021
$171$	−16.7082	−1.27771
$172$	0.763932	0.0582493
$173$	2.94427	0.223849	0.111924	−	0.993717i	$-0.464299\pi$
$173$	2.94427	0.223849	0.111924	+	0.993717i	$0.464299\pi$
$174$	−14.4721	−1.09713
$175$	−0.944272	−0.0713802
$176$	−9.70820	−0.731783
$177$	−7.23607	−0.543896
$178$	18.9443	1.41993
$179$	1.70820	0.127677	0.0638386	−	0.997960i	$-0.479666\pi$
$179$	1.70820	0.127677	0.0638386	+	0.997960i	$0.479666\pi$
$180$	4.61803	0.344208
$181$	−4.18034	−0.310722	−0.155361	−	0.987858i	$-0.549654\pi$
$181$	−4.18034	−0.310722	−0.155361	+	0.987858i	$0.549654\pi$
$182$	−1.23607	−0.0916235
$183$	−26.4721	−1.95688
$184$	−12.7639	−0.940970
$185$	−2.00000	−0.147043
$186$	−5.23607	−0.383927
$187$	1.52786	0.111728
$188$	1.52786	0.111431
$189$	−3.41641	−0.248507
$190$	−3.61803	−0.262480
$191$	−19.1803	−1.38784	−0.693920	−	0.720052i	$-0.744118\pi$
$191$	−19.1803	−1.38784	−0.693920	+	0.720052i	$0.744118\pi$
$192$	−13.7082	−0.989304
$193$	3.47214	0.249930	0.124965	−	0.992161i	$-0.460118\pi$
$193$	3.47214	0.249930	0.124965	+	0.992161i	$0.460118\pi$
$194$	−25.7984	−1.85222
$195$	10.4721	0.749925
$196$	−4.29180	−0.306557
$197$	11.4164	0.813385	0.406693	−	0.913565i	$-0.366682\pi$
$197$	11.4164	0.813385	0.406693	+	0.913565i	$0.366682\pi$
$198$	24.1803	1.71842
$199$	−18.9443	−1.34292	−0.671462	−	0.741039i	$-0.734333\pi$
$199$	−18.9443	−1.34292	−0.671462	+	0.741039i	$0.734333\pi$
$200$	8.94427	0.632456
$201$	−25.8885	−1.82604
$202$	−4.85410	−0.341533
$203$	0.652476	0.0457948
$204$	−1.52786	−0.106972
$205$	7.00000	0.488901
$206$	10.0902	0.703015
$207$	42.6525	2.96455
$208$	15.7082	1.08917
$209$	−4.47214	−0.309344
$210$	−1.23607	−0.0852968
$211$	23.1803	1.59580	0.797900	−	0.602790i	$-0.205944\pi$
$211$	23.1803	1.59580	0.797900	+	0.602790i	$0.205944\pi$
$212$	−6.47214	−0.444508
$213$	29.7082	2.03557
$214$	9.32624	0.637528
$215$	1.23607	0.0842991
$216$	32.3607	2.20187
$217$	0.236068	0.0160253
$218$	−22.5623	−1.52811
$219$	−27.4164	−1.85263
$220$	1.23607	0.0833357
$221$	−2.47214	−0.166294
$222$	10.4721	0.702844
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−0.798374	−0.0533436
$225$	−29.8885	−1.99257
$226$	5.61803	0.373706
$227$	−6.47214	−0.429571	−0.214785	−	0.976661i	$-0.568905\pi$
$227$	−6.47214	−0.429571	−0.214785	+	0.976661i	$0.568905\pi$
$228$	4.47214	0.296174
$229$	−13.4164	−0.886581	−0.443291	−	0.896378i	$-0.646189\pi$
$229$	−13.4164	−0.886581	−0.443291	+	0.896378i	$0.646189\pi$
$230$	9.23607	0.609008
$231$	−1.52786	−0.100526
$232$	−6.18034	−0.405759
$233$	17.9443	1.17557	0.587784	−	0.809018i	$-0.300000\pi$
$233$	17.9443	1.17557	0.587784	+	0.809018i	$0.300000\pi$
$234$	−39.1246	−2.55766
$235$	2.47214	0.161264
$236$	1.38197	0.0899583
$237$	37.8885	2.46113
$238$	0.291796	0.0189143
$239$	−11.7082	−0.757341	−0.378670	−	0.925532i	$-0.623619\pi$
$239$	−11.7082	−0.757341	−0.378670	+	0.925532i	$0.623619\pi$
$240$	15.7082	1.01396
$241$	14.3607	0.925053	0.462526	−	0.886606i	$-0.346943\pi$
$241$	14.3607	0.925053	0.462526	+	0.886606i	$0.346943\pi$
$242$	−11.3262	−0.728078
$243$	−35.5967	−2.28353
$244$	5.05573	0.323660
$245$	−6.94427	−0.443653
$246$	−36.6525	−2.33688
$247$	7.23607	0.460420
$248$	−2.23607	−0.141990
$249$	48.3607	3.06473
$250$	−14.5623	−0.921001
$251$	−1.81966	−0.114856	−0.0574280	−	0.998350i	$-0.518290\pi$
$251$	−1.81966	−0.114856	−0.0574280	+	0.998350i	$0.518290\pi$
$252$	1.09017	0.0686743
$253$	11.4164	0.717743
$254$	20.1803	1.26623
$255$	−2.47214	−0.154811
$256$	13.5623	0.847644
$257$	1.94427	0.121280	0.0606402	−	0.998160i	$-0.480686\pi$
$257$	1.94427	0.121280	0.0606402	+	0.998160i	$0.480686\pi$
$258$	−6.47214	−0.402938
$259$	−0.472136	−0.0293371
$260$	−2.00000	−0.124035
$261$	20.6525	1.27836
$262$	19.4164	1.19955
$263$	−23.2361	−1.43280	−0.716399	−	0.697691i	$-0.754211\pi$
$263$	−23.2361	−1.43280	−0.716399	+	0.697691i	$0.754211\pi$
$264$	14.4721	0.890698
$265$	−10.4721	−0.643298
$266$	−0.854102	−0.0523684
$267$	−37.8885	−2.31874
$268$	4.94427	0.302019
$269$	−11.0557	−0.674080	−0.337040	−	0.941490i	$-0.609426\pi$
$269$	−11.0557	−0.674080	−0.337040	+	0.941490i	$0.609426\pi$
$270$	−23.4164	−1.42508
$271$	−14.1803	−0.861394	−0.430697	−	0.902497i	$-0.641732\pi$
$271$	−14.1803	−0.861394	−0.430697	+	0.902497i	$0.641732\pi$
$272$	−3.70820	−0.224843
$273$	2.47214	0.149620
$274$	10.1803	0.615017
$275$	−8.00000	−0.482418
$276$	−11.4164	−0.687187
$277$	−12.6525	−0.760214	−0.380107	−	0.924943i	$-0.624113\pi$
$277$	−12.6525	−0.760214	−0.380107	+	0.924943i	$0.624113\pi$
$278$	21.7082	1.30197
$279$	7.47214	0.447345
$280$	−0.527864	−0.0315459
$281$	17.0000	1.01413	0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000	1.01413	0.507067	+	0.861906i	$0.330729\pi$
$282$	−12.9443	−0.770820
$283$	−13.8885	−0.825588	−0.412794	−	0.910824i	$-0.635447\pi$
$283$	−13.8885	−0.825588	−0.412794	+	0.910824i	$0.635447\pi$
$284$	−5.67376	−0.336676
$285$	7.23607	0.428628
$286$	−10.4721	−0.619230
$287$	1.65248	0.0975426
$288$	−25.2705	−1.48908
$289$	−16.4164	−0.965671
$290$	4.47214	0.262613
$291$	51.5967	3.02465
$292$	5.23607	0.306418
$293$	−0.472136	−0.0275825	−0.0137912	−	0.999905i	$-0.504390\pi$
$293$	−0.472136	−0.0275825	−0.0137912	+	0.999905i	$0.504390\pi$
$294$	36.3607	2.12060
$295$	2.23607	0.130189
$296$	4.47214	0.259938
$297$	−28.9443	−1.67952
$298$	16.1803	0.937302
$299$	−18.4721	−1.06827
$300$	8.00000	0.461880
$301$	0.291796	0.0168188
$302$	−22.9443	−1.32029
$303$	9.70820	0.557722
$304$	10.8541	0.622525
$305$	8.18034	0.468405
$306$	9.23607	0.527991
$307$	−28.7082	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$307$	−28.7082	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$308$	0.291796	0.0166266
$309$	−20.1803	−1.14802
$310$	1.61803	0.0918982
$311$	−29.1803	−1.65467	−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803	−1.65467	−0.827333	+	0.561712i	$0.810143\pi$
$312$	−23.4164	−1.32569
$313$	16.7639	0.947553	0.473777	−	0.880645i	$-0.342890\pi$
$313$	16.7639	0.947553	0.473777	+	0.880645i	$0.342890\pi$
$314$	33.7984	1.90735
$315$	1.76393	0.0993863
$316$	−7.23607	−0.407061
$317$	4.05573	0.227792	0.113896	−	0.993493i	$-0.463667\pi$
$317$	4.05573	0.227792	0.113896	+	0.993493i	$0.463667\pi$
$318$	54.8328	3.07487
$319$	5.52786	0.309501
$320$	4.23607	0.236803
$321$	−18.6525	−1.04108
$322$	2.18034	0.121506
$323$	−1.70820	−0.0950470
$324$	15.0902	0.838343
$325$	12.9443	0.718019
$326$	17.3262	0.959612
$327$	45.1246	2.49540
$328$	−15.6525	−0.864263
$329$	0.583592	0.0321745
$330$	−10.4721	−0.576472
$331$	2.00000	0.109930	0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000	0.109930	0.0549650	+	0.998488i	$0.482495\pi$
$332$	−9.23607	−0.506895
$333$	−14.9443	−0.818941
$334$	−10.4721	−0.573010
$335$	8.00000	0.437087
$336$	3.70820	0.202299
$337$	−14.7639	−0.804243	−0.402121	−	0.915586i	$-0.631727\pi$
$337$	−14.7639	−0.804243	−0.402121	+	0.915586i	$0.631727\pi$
$338$	−4.09017	−0.222476
$339$	−11.2361	−0.610259
$340$	0.472136	0.0256052
$341$	2.00000	0.108306
$342$	−27.0344	−1.46186
$343$	−3.29180	−0.177740
$344$	−2.76393	−0.149021
$345$	−18.4721	−0.994506
$346$	4.76393	0.256111
$347$	24.1803	1.29807	0.649034	−	0.760759i	$-0.275173\pi$
$347$	24.1803	1.29807	0.649034	+	0.760759i	$0.275173\pi$
$348$	−5.52786	−0.296325
$349$	−7.88854	−0.422264	−0.211132	−	0.977458i	$-0.567715\pi$
$349$	−7.88854	−0.422264	−0.211132	+	0.977458i	$0.567715\pi$
$350$	−1.52786	−0.0816678
$351$	46.8328	2.49975
$352$	−6.76393	−0.360519
$353$	7.41641	0.394736	0.197368	−	0.980330i	$-0.436761\pi$
$353$	7.41641	0.394736	0.197368	+	0.980330i	$0.436761\pi$
$354$	−11.7082	−0.622284
$355$	−9.18034	−0.487242
$356$	7.23607	0.383511
$357$	−0.583592	−0.0308870
$358$	2.76393	0.146078
$359$	22.2361	1.17357	0.586787	−	0.809741i	$-0.300392\pi$
$359$	22.2361	1.17357	0.586787	+	0.809741i	$0.300392\pi$
$360$	−16.7082	−0.880600
$361$	−14.0000	−0.736842
$362$	−6.76393	−0.355504
$363$	22.6525	1.18895
$364$	−0.472136	−0.0247466
$365$	8.47214	0.443452
$366$	−42.8328	−2.23891
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	−27.7082	−1.44439
$369$	52.3050	2.72289
$370$	−3.23607	−0.168235
$371$	−2.47214	−0.128347
$372$	−2.00000	−0.103695
$373$	19.0000	0.983783	0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000	0.983783	0.491891	+	0.870657i	$0.336306\pi$
$374$	2.47214	0.127831
$375$	29.1246	1.50399
$376$	−5.52786	−0.285078
$377$	−8.94427	−0.460653
$378$	−5.52786	−0.284323
$379$	−2.11146	−0.108458	−0.0542291	−	0.998529i	$-0.517270\pi$
$379$	−2.11146	−0.108458	−0.0542291	+	0.998529i	$0.517270\pi$
$380$	−1.38197	−0.0708934
$381$	−40.3607	−2.06774
$382$	−31.0344	−1.58786
$383$	−23.8885	−1.22065	−0.610324	−	0.792152i	$-0.708961\pi$
$383$	−23.8885	−1.22065	−0.610324	+	0.792152i	$0.708961\pi$
$384$	−44.0689	−2.24888
$385$	0.472136	0.0240623
$386$	5.61803	0.285950
$387$	9.23607	0.469496
$388$	−9.85410	−0.500266
$389$	−17.8885	−0.906985	−0.453493	−	0.891260i	$-0.649822\pi$
$389$	−17.8885	−0.906985	−0.453493	+	0.891260i	$0.649822\pi$
$390$	16.9443	0.858007
$391$	4.36068	0.220529
$392$	15.5279	0.784276
$393$	−38.8328	−1.95886
$394$	18.4721	0.930613
$395$	−11.7082	−0.589104
$396$	9.23607	0.464130
$397$	−7.00000	−0.351320	−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000	−0.351320	−0.175660	+	0.984451i	$0.556206\pi$
$398$	−30.6525	−1.53647
$399$	1.70820	0.0855172
$400$	19.4164	0.970820
$401$	38.1803	1.90664	0.953318	−	0.301969i	$-0.0976441\pi$
$401$	38.1803	1.90664	0.953318	+	0.301969i	$0.0976441\pi$
$402$	−41.8885	−2.08921
$403$	−3.23607	−0.161200
$404$	−1.85410	−0.0922450
$405$	24.4164	1.21326
$406$	1.05573	0.0523949
$407$	−4.00000	−0.198273
$408$	5.52786	0.273670
$409$	−3.81966	−0.188870	−0.0944350	−	0.995531i	$-0.530104\pi$
$409$	−3.81966	−0.188870	−0.0944350	+	0.995531i	$0.530104\pi$
$410$	11.3262	0.559363
$411$	−20.3607	−1.00432
$412$	3.85410	0.189878
$413$	0.527864	0.0259745
$414$	69.0132	3.39181
$415$	−14.9443	−0.733585
$416$	10.9443	0.536587
$417$	−43.4164	−2.12611
$418$	−7.23607	−0.353928
$419$	−10.1246	−0.494620	−0.247310	−	0.968936i	$-0.579547\pi$
$419$	−10.1246	−0.494620	−0.247310	+	0.968936i	$0.579547\pi$
$420$	−0.472136	−0.0230379
$421$	29.3607	1.43095	0.715476	−	0.698637i	$-0.246210\pi$
$421$	29.3607	1.43095	0.715476	+	0.698637i	$0.246210\pi$
$422$	37.5066	1.82579
$423$	18.4721	0.898146
$424$	23.4164	1.13720
$425$	−3.05573	−0.148225
$426$	48.0689	2.32895
$427$	1.93112	0.0934533
$428$	3.56231	0.172191
$429$	20.9443	1.01120
$430$	2.00000	0.0964486
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	70.2492	3.37987
$433$	10.1803	0.489236	0.244618	−	0.969620i	$-0.421337\pi$
$433$	10.1803	0.489236	0.244618	+	0.969620i	$0.421337\pi$
$434$	0.381966	0.0183350
$435$	−8.94427	−0.428845
$436$	−8.61803	−0.412729
$437$	−12.7639	−0.610582
$438$	−44.3607	−2.11964
$439$	−1.18034	−0.0563345	−0.0281673	−	0.999603i	$-0.508967\pi$
$439$	−1.18034	−0.0563345	−0.0281673	+	0.999603i	$0.508967\pi$
$440$	−4.47214	−0.213201
$441$	−51.8885	−2.47088
$442$	−4.00000	−0.190261
$443$	30.7082	1.45899	0.729495	−	0.683986i	$-0.239755\pi$
$443$	30.7082	1.45899	0.729495	+	0.683986i	$0.239755\pi$
$444$	4.00000	0.189832
$445$	11.7082	0.555022
$446$	6.47214	0.306465
$447$	−32.3607	−1.53061
$448$	1.00000	0.0472456
$449$	−31.3050	−1.47737	−0.738686	−	0.674050i	$-0.764553\pi$
$449$	−31.3050	−1.47737	−0.738686	+	0.674050i	$0.764553\pi$
$450$	−48.3607	−2.27974
$451$	14.0000	0.659234
$452$	2.14590	0.100935
$453$	45.8885	2.15603
$454$	−10.4721	−0.491482
$455$	−0.763932	−0.0358137
$456$	−16.1803	−0.757714
$457$	−3.05573	−0.142941	−0.0714705	−	0.997443i	$-0.522769\pi$
$457$	−3.05573	−0.142941	−0.0714705	+	0.997443i	$0.522769\pi$
$458$	−21.7082	−1.01436
$459$	−11.0557	−0.516037
$460$	3.52786	0.164488
$461$	34.3607	1.60034	0.800168	−	0.599776i	$-0.204744\pi$
$461$	34.3607	1.60034	0.800168	+	0.599776i	$0.204744\pi$
$462$	−2.47214	−0.115014
$463$	−2.58359	−0.120070	−0.0600349	−	0.998196i	$-0.519121\pi$
$463$	−2.58359	−0.120070	−0.0600349	+	0.998196i	$0.519121\pi$
$464$	−13.4164	−0.622841
$465$	−3.23607	−0.150069
$466$	29.0344	1.34499
$467$	4.70820	0.217870	0.108935	−	0.994049i	$-0.465256\pi$
$467$	4.70820	0.217870	0.108935	+	0.994049i	$0.465256\pi$
$468$	−14.9443	−0.690799
$469$	1.88854	0.0872049
$470$	4.00000	0.184506
$471$	−67.5967	−3.11469
$472$	−5.00000	−0.230144
$473$	2.47214	0.113669
$474$	61.3050	2.81583
$475$	8.94427	0.410391
$476$	0.111456	0.00510859
$477$	−78.2492	−3.58279
$478$	−18.9443	−0.866491
$479$	23.2918	1.06423	0.532115	−	0.846672i	$-0.321398\pi$
$479$	23.2918	1.06423	0.532115	+	0.846672i	$0.321398\pi$
$480$	10.9443	0.499535
$481$	6.47214	0.295104
$482$	23.2361	1.05837
$483$	−4.36068	−0.198418
$484$	−4.32624	−0.196647
$485$	−15.9443	−0.723992
$486$	−57.5967	−2.61264
$487$	−19.2361	−0.871669	−0.435835	−	0.900027i	$-0.643547\pi$
$487$	−19.2361	−0.871669	−0.435835	+	0.900027i	$0.643547\pi$
$488$	−18.2918	−0.828031
$489$	−34.6525	−1.56704
$490$	−11.2361	−0.507594
$491$	4.36068	0.196795	0.0983974	−	0.995147i	$-0.468628\pi$
$491$	4.36068	0.196795	0.0983974	+	0.995147i	$0.468628\pi$
$492$	−14.0000	−0.631169
$493$	2.11146	0.0950952
$494$	11.7082	0.526777
$495$	14.9443	0.671695
$496$	−4.85410	−0.217956
$497$	−2.16718	−0.0972115
$498$	78.2492	3.50643
$499$	−6.58359	−0.294722	−0.147361	−	0.989083i	$-0.547078\pi$
$499$	−6.58359	−0.294722	−0.147361	+	0.989083i	$0.547078\pi$
$500$	−5.56231	−0.248754
$501$	20.9443	0.935721
$502$	−2.94427	−0.131409
$503$	29.6525	1.32214	0.661069	−	0.750325i	$-0.270103\pi$
$503$	29.6525	1.32214	0.661069	+	0.750325i	$0.270103\pi$
$504$	−3.94427	−0.175692
$505$	−3.00000	−0.133498
$506$	18.4721	0.821187
$507$	8.18034	0.363302
$508$	7.70820	0.341996
$509$	29.5967	1.31185	0.655926	−	0.754825i	$-0.272278\pi$
$509$	29.5967	1.31185	0.655926	+	0.754825i	$0.272278\pi$
$510$	−4.00000	−0.177123
$511$	2.00000	0.0884748
$512$	−5.29180	−0.233867
$513$	32.3607	1.42876
$514$	3.14590	0.138760
$515$	6.23607	0.274794
$516$	−2.47214	−0.108830
$517$	4.94427	0.217449
$518$	−0.763932	−0.0335652
$519$	−9.52786	−0.418227
$520$	7.23607	0.317323
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	33.4164	1.46260
$523$	−17.7082	−0.774326	−0.387163	−	0.922011i	$-0.626545\pi$
$523$	−17.7082	−0.774326	−0.387163	+	0.922011i	$0.626545\pi$
$524$	7.41641	0.323987
$525$	3.05573	0.133363
$526$	−37.5967	−1.63930
$527$	0.763932	0.0332774
$528$	31.4164	1.36722
$529$	9.58359	0.416678
$530$	−16.9443	−0.736012
$531$	16.7082	0.725074
$532$	−0.326238	−0.0141442
$533$	−22.6525	−0.981188
$534$	−61.3050	−2.65292
$535$	5.76393	0.249197
$536$	−17.8885	−0.772667
$537$	−5.52786	−0.238545
$538$	−17.8885	−0.771230
$539$	−13.8885	−0.598222
$540$	−8.94427	−0.384900
$541$	−25.3607	−1.09034	−0.545170	−	0.838325i	$-0.683535\pi$
$541$	−25.3607	−1.09034	−0.545170	+	0.838325i	$0.683535\pi$
$542$	−22.9443	−0.985541
$543$	13.5279	0.580536
$544$	−2.58359	−0.110771
$545$	−13.9443	−0.597307
$546$	4.00000	0.171184
$547$	−12.1246	−0.518411	−0.259205	−	0.965822i	$-0.583461\pi$
$547$	−12.1246	−0.518411	−0.259205	+	0.965822i	$0.583461\pi$
$548$	3.88854	0.166110
$549$	61.1246	2.60873
$550$	−12.9443	−0.551946
$551$	−6.18034	−0.263291
$552$	41.3050	1.75806
$553$	−2.76393	−0.117534
$554$	−20.4721	−0.869778
$555$	6.47214	0.274727
$556$	8.29180	0.351650
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	12.0902	0.511818
$559$	−4.00000	−0.169182
$560$	−1.14590	−0.0484230
$561$	−4.94427	−0.208747
$562$	27.5066	1.16029
$563$	27.5410	1.16072	0.580358	−	0.814362i	$-0.302913\pi$
$563$	27.5410	1.16072	0.580358	+	0.814362i	$0.302913\pi$
$564$	−4.94427	−0.208191
$565$	3.47214	0.146074
$566$	−22.4721	−0.944574
$567$	5.76393	0.242062
$568$	20.5279	0.861330
$569$	5.52786	0.231740	0.115870	−	0.993264i	$-0.463034\pi$
$569$	5.52786	0.231740	0.115870	+	0.993264i	$0.463034\pi$
$570$	11.7082	0.490403
$571$	28.1803	1.17931	0.589655	−	0.807655i	$-0.299264\pi$
$571$	28.1803	1.17931	0.589655	+	0.807655i	$0.299264\pi$
$572$	−4.00000	−0.167248
$573$	62.0689	2.59296
$574$	2.67376	0.111601
$575$	−22.8328	−0.952194
$576$	31.6525	1.31885
$577$	−28.8328	−1.20033	−0.600163	−	0.799878i	$-0.704898\pi$
$577$	−28.8328	−1.20033	−0.600163	+	0.799878i	$0.704898\pi$
$578$	−26.5623	−1.10485
$579$	−11.2361	−0.466955
$580$	1.70820	0.0709293
$581$	−3.52786	−0.146360
$582$	83.4853	3.46058
$583$	−20.9443	−0.867423
$584$	−18.9443	−0.783920
$585$	−24.1803	−0.999734
$586$	−0.763932	−0.0315577
$587$	−6.47214	−0.267134	−0.133567	−	0.991040i	$-0.542643\pi$
$587$	−6.47214	−0.267134	−0.133567	+	0.991040i	$0.542643\pi$
$588$	13.8885	0.572754
$589$	−2.23607	−0.0921356
$590$	3.61803	0.148952
$591$	−36.9443	−1.51968
$592$	9.70820	0.399005
$593$	−6.52786	−0.268067	−0.134034	−	0.990977i	$-0.542793\pi$
$593$	−6.52786	−0.268067	−0.134034	+	0.990977i	$0.542793\pi$
$594$	−46.8328	−1.92157
$595$	0.180340	0.00739321
$596$	6.18034	0.253157
$597$	61.3050	2.50904
$598$	−29.8885	−1.22223
$599$	−14.5967	−0.596407	−0.298203	−	0.954502i	$-0.596387\pi$
$599$	−14.5967	−0.596407	−0.298203	+	0.954502i	$0.596387\pi$
$600$	−28.9443	−1.18164
$601$	30.5410	1.24579	0.622897	−	0.782304i	$-0.285956\pi$
$601$	30.5410	1.24579	0.622897	+	0.782304i	$0.285956\pi$
$602$	0.472136	0.0192428
$603$	59.7771	2.43431
$604$	−8.76393	−0.356599
$605$	−7.00000	−0.284590
$606$	15.7082	0.638102
$607$	22.4721	0.912116	0.456058	−	0.889950i	$-0.349261\pi$
$607$	22.4721	0.912116	0.456058	+	0.889950i	$0.349261\pi$
$608$	7.56231	0.306692
$609$	−2.11146	−0.0855605
$610$	13.2361	0.535913
$611$	−8.00000	−0.323645
$612$	3.52786	0.142605
$613$	−43.8885	−1.77264	−0.886321	−	0.463072i	$-0.846747\pi$
$613$	−43.8885	−1.77264	−0.886321	+	0.463072i	$0.846747\pi$
$614$	−46.4508	−1.87460
$615$	−22.6525	−0.913436
$616$	−1.05573	−0.0425365
$617$	32.4721	1.30728	0.653639	−	0.756806i	$-0.273241\pi$
$617$	32.4721	1.30728	0.653639	+	0.756806i	$0.273241\pi$
$618$	−32.6525	−1.31348
$619$	6.18034	0.248409	0.124204	−	0.992257i	$-0.460362\pi$
$619$	6.18034	0.248409	0.124204	+	0.992257i	$0.460362\pi$
$620$	0.618034	0.0248208
$621$	−82.6099	−3.31502
$622$	−47.2148	−1.89314
$623$	2.76393	0.110735
$624$	−50.8328	−2.03494
$625$	11.0000	0.440000
$626$	27.1246	1.08412
$627$	14.4721	0.577961
$628$	12.9098	0.515158
$629$	−1.52786	−0.0609199
$630$	2.85410	0.113710
$631$	34.3607	1.36788	0.683939	−	0.729540i	$-0.260266\pi$
$631$	34.3607	1.36788	0.683939	+	0.729540i	$0.260266\pi$
$632$	26.1803	1.04140
$633$	−75.0132	−2.98151
$634$	6.56231	0.260622
$635$	12.4721	0.494942
$636$	20.9443	0.830494
$637$	22.4721	0.890378
$638$	8.94427	0.354107
$639$	−68.5967	−2.71365
$640$	13.6180	0.538300
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	−30.1803	−1.19112
$643$	19.5279	0.770104	0.385052	−	0.922895i	$-0.374184\pi$
$643$	19.5279	0.770104	0.385052	+	0.922895i	$0.374184\pi$
$644$	0.832816	0.0328175
$645$	−4.00000	−0.157500
$646$	−2.76393	−0.108745
$647$	−0.944272	−0.0371232	−0.0185616	−	0.999828i	$-0.505909\pi$
$647$	−0.944272	−0.0371232	−0.0185616	+	0.999828i	$0.505909\pi$
$648$	−54.5967	−2.14476
$649$	4.47214	0.175547
$650$	20.9443	0.821502
$651$	−0.763932	−0.0299409
$652$	6.61803	0.259182
$653$	−47.3050	−1.85119	−0.925593	−	0.378521i	$-0.876433\pi$
$653$	−47.3050	−1.85119	−0.925593	+	0.378521i	$0.876433\pi$
$654$	73.0132	2.85504
$655$	12.0000	0.468879
$656$	−33.9787	−1.32665
$657$	63.3050	2.46976
$658$	0.944272	0.0368116
$659$	25.6525	0.999279	0.499639	−	0.866234i	$-0.333466\pi$
$659$	25.6525	0.999279	0.499639	+	0.866234i	$0.333466\pi$
$660$	−4.00000	−0.155700
$661$	−0.639320	−0.0248667	−0.0124333	−	0.999923i	$-0.503958\pi$
$661$	−0.639320	−0.0248667	−0.0124333	+	0.999923i	$0.503958\pi$
$662$	3.23607	0.125773
$663$	8.00000	0.310694
$664$	33.4164	1.29681
$665$	−0.527864	−0.0204697
$666$	−24.1803	−0.936969
$667$	15.7771	0.610891
$668$	−4.00000	−0.154765
$669$	−12.9443	−0.500454
$670$	12.9443	0.500081
$671$	16.3607	0.631597
$672$	2.58359	0.0996642
$673$	−29.0132	−1.11837	−0.559187	−	0.829041i	$-0.688887\pi$
$673$	−29.0132	−1.11837	−0.559187	+	0.829041i	$0.688887\pi$
$674$	−23.8885	−0.920152
$675$	57.8885	2.22813
$676$	−1.56231	−0.0600887
$677$	−46.7214	−1.79565	−0.897824	−	0.440355i	$-0.854853\pi$
$677$	−46.7214	−1.79565	−0.897824	+	0.440355i	$0.854853\pi$
$678$	−18.1803	−0.698212
$679$	−3.76393	−0.144446
$680$	−1.70820	−0.0655066
$681$	20.9443	0.802586
$682$	3.23607	0.123915
$683$	5.18034	0.198220	0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034	0.198220	0.0991101	+	0.995076i	$0.468400\pi$
$684$	−10.3262	−0.394834
$685$	6.29180	0.240397
$686$	−5.32624	−0.203357
$687$	43.4164	1.65644
$688$	−6.00000	−0.228748
$689$	33.8885	1.29105
$690$	−29.8885	−1.13784
$691$	3.18034	0.120986	0.0604929	−	0.998169i	$-0.480733\pi$
$691$	3.18034	0.120986	0.0604929	+	0.998169i	$0.480733\pi$
$692$	1.81966	0.0691731
$693$	3.52786	0.134012
$694$	39.1246	1.48515
$695$	13.4164	0.508913
$696$	20.0000	0.758098
$697$	5.34752	0.202552
$698$	−12.7639	−0.483122
$699$	−58.0689	−2.19637
$700$	−0.583592	−0.0220577
$701$	7.00000	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$701$	7.00000	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$702$	75.7771	2.86002
$703$	4.47214	0.168670
$704$	8.47214	0.319306
$705$	−8.00000	−0.301297
$706$	12.0000	0.451626
$707$	−0.708204	−0.0266348
$708$	−4.47214	−0.168073
$709$	25.5279	0.958719	0.479360	−	0.877619i	$-0.340869\pi$
$709$	25.5279	0.958719	0.479360	+	0.877619i	$0.340869\pi$
$710$	−14.8541	−0.557465
$711$	−87.4853	−3.28095
$712$	−26.1803	−0.981150
$713$	5.70820	0.213774
$714$	−0.944272	−0.0353385
$715$	−6.47214	−0.242044
$716$	1.05573	0.0394544
$717$	37.8885	1.41497
$718$	35.9787	1.34271
$719$	−13.8197	−0.515386	−0.257693	−	0.966227i	$-0.582962\pi$
$719$	−13.8197	−0.515386	−0.257693	+	0.966227i	$0.582962\pi$
$720$	−36.2705	−1.35172
$721$	1.47214	0.0548252
$722$	−22.6525	−0.843038
$723$	−46.4721	−1.72832
$724$	−2.58359	−0.0960184
$725$	−11.0557	−0.410599
$726$	36.6525	1.36030
$727$	−44.2361	−1.64062	−0.820312	−	0.571916i	$-0.806200\pi$
$727$	−44.2361	−1.64062	−0.820312	+	0.571916i	$0.806200\pi$
$728$	1.70820	0.0633102
$729$	41.9443	1.55349
$730$	13.7082	0.507363
$731$	0.944272	0.0349252
$732$	−16.3607	−0.604708
$733$	3.47214	0.128246	0.0641231	−	0.997942i	$-0.479575\pi$
$733$	3.47214	0.128246	0.0641231	+	0.997942i	$0.479575\pi$
$734$	29.1246	1.07501
$735$	22.4721	0.828897
$736$	−19.3050	−0.711590
$737$	16.0000	0.589368
$738$	84.6312	3.11532
$739$	6.18034	0.227347	0.113674	−	0.993518i	$-0.463738\pi$
$739$	6.18034	0.227347	0.113674	+	0.993518i	$0.463738\pi$
$740$	−1.23607	−0.0454388
$741$	−23.4164	−0.860223
$742$	−4.00000	−0.146845
$743$	50.1803	1.84094	0.920469	−	0.390815i	$-0.127807\pi$
$743$	50.1803	1.84094	0.920469	+	0.390815i	$0.127807\pi$
$744$	7.23607	0.265287
$745$	10.0000	0.366372
$746$	30.7426	1.12557
$747$	−111.666	−4.08563
$748$	0.944272	0.0345260
$749$	1.36068	0.0497182
$750$	47.1246	1.72075
$751$	−21.5410	−0.786043	−0.393021	−	0.919529i	$-0.628570\pi$
$751$	−21.5410	−0.786043	−0.393021	+	0.919529i	$0.628570\pi$
$752$	−12.0000	−0.437595
$753$	5.88854	0.214590
$754$	−14.4721	−0.527044
$755$	−14.1803	−0.516075
$756$	−2.11146	−0.0767929
$757$	8.65248	0.314480	0.157240	−	0.987560i	$-0.449740\pi$
$757$	8.65248	0.314480	0.157240	+	0.987560i	$0.449740\pi$
$758$	−3.41641	−0.124090
$759$	−36.9443	−1.34099
$760$	5.00000	0.181369
$761$	2.00000	0.0724999	0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000	0.0724999	0.0362500	+	0.999343i	$0.488459\pi$
$762$	−65.3050	−2.36575
$763$	−3.29180	−0.119171
$764$	−11.8541	−0.428866
$765$	5.70820	0.206381
$766$	−38.6525	−1.39657
$767$	−7.23607	−0.261279
$768$	−43.8885	−1.58369
$769$	−47.3607	−1.70787	−0.853935	−	0.520380i	$-0.825790\pi$
$769$	−47.3607	−1.70787	−0.853935	+	0.520380i	$0.825790\pi$
$770$	0.763932	0.0275302
$771$	−6.29180	−0.226594
$772$	2.14590	0.0772326
$773$	−11.1246	−0.400124	−0.200062	−	0.979783i	$-0.564114\pi$
$773$	−11.1246	−0.400124	−0.200062	+	0.979783i	$0.564114\pi$
$774$	14.9443	0.537161
$775$	−4.00000	−0.143684
$776$	35.6525	1.27985
$777$	1.52786	0.0548118
$778$	−28.9443	−1.03770
$779$	−15.6525	−0.560808
$780$	6.47214	0.231740
$781$	−18.3607	−0.656997
$782$	7.05573	0.252312
$783$	−40.0000	−1.42948
$784$	33.7082	1.20386
$785$	20.8885	0.745544
$786$	−62.8328	−2.24117
$787$	7.34752	0.261911	0.130955	−	0.991388i	$-0.458196\pi$
$787$	7.34752	0.261911	0.130955	+	0.991388i	$0.458196\pi$
$788$	7.05573	0.251350
$789$	75.1935	2.67696
$790$	−18.9443	−0.674007
$791$	0.819660	0.0291438
$792$	−33.4164	−1.18740
$793$	−26.4721	−0.940053
$794$	−11.3262	−0.401953
$795$	33.8885	1.20190
$796$	−11.7082	−0.414986
$797$	−55.4164	−1.96295	−0.981475	−	0.191591i	$-0.938635\pi$
$797$	−55.4164	−1.96295	−0.981475	+	0.191591i	$0.938635\pi$
$798$	2.76393	0.0978421
$799$	1.88854	0.0668119
$800$	13.5279	0.478282
$801$	87.4853	3.09114
$802$	61.7771	2.18142
$803$	16.9443	0.597950
$804$	−16.0000	−0.564276
$805$	1.34752	0.0474940
$806$	−5.23607	−0.184433
$807$	35.7771	1.25941
$808$	6.70820	0.235994
$809$	23.4164	0.823277	0.411639	−	0.911347i	$-0.364957\pi$
$809$	23.4164	0.823277	0.411639	+	0.911347i	$0.364957\pi$
$810$	39.5066	1.38812
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0.403252	0.0141514
$813$	45.8885	1.60938
$814$	−6.47214	−0.226848
$815$	10.7082	0.375092
$816$	12.0000	0.420084
$817$	−2.76393	−0.0966977
$818$	−6.18034	−0.216091
$819$	−5.70820	−0.199461
$820$	4.32624	0.151079
$821$	30.5410	1.06589	0.532944	−	0.846150i	$-0.321085\pi$
$821$	30.5410	1.06589	0.532944	+	0.846150i	$0.321085\pi$
$822$	−32.9443	−1.14906
$823$	−14.2918	−0.498181	−0.249090	−	0.968480i	$-0.580132\pi$
$823$	−14.2918	−0.498181	−0.249090	+	0.968480i	$0.580132\pi$
$824$	−13.9443	−0.485772
$825$	25.8885	0.901323
$826$	0.854102	0.0297180
$827$	17.3475	0.603233	0.301616	−	0.953429i	$-0.402474\pi$
$827$	17.3475	0.603233	0.301616	+	0.953429i	$0.402474\pi$
$828$	26.3607	0.916097
$829$	16.8328	0.584628	0.292314	−	0.956322i	$-0.405575\pi$
$829$	16.8328	0.584628	0.292314	+	0.956322i	$0.405575\pi$
$830$	−24.1803	−0.839312
$831$	40.9443	1.42034
$832$	−13.7082	−0.475246
$833$	−5.30495	−0.183806
$834$	−70.2492	−2.43253
$835$	−6.47214	−0.223978
$836$	−2.76393	−0.0955926
$837$	−14.4721	−0.500230
$838$	−16.3820	−0.565906
$839$	28.9443	0.999267	0.499634	−	0.866237i	$-0.333468\pi$
$839$	28.9443	0.999267	0.499634	+	0.866237i	$0.333468\pi$
$840$	1.70820	0.0589386
$841$	−21.3607	−0.736575
$842$	47.5066	1.63718
$843$	−55.0132	−1.89475
$844$	14.3262	0.493129
$845$	−2.52786	−0.0869612
$846$	29.8885	1.02759
$847$	−1.65248	−0.0567797
$848$	50.8328	1.74561
$849$	44.9443	1.54248
$850$	−4.94427	−0.169587
$851$	−11.4164	−0.391349
$852$	18.3607	0.629027
$853$	10.5836	0.362375	0.181188	−	0.983449i	$-0.442006\pi$
$853$	10.5836	0.362375	0.181188	+	0.983449i	$0.442006\pi$
$854$	3.12461	0.106922
$855$	−16.7082	−0.571409
$856$	−12.8885	−0.440521
$857$	−55.6656	−1.90150	−0.950751	−	0.309956i	$-0.899686\pi$
$857$	−55.6656	−1.90150	−0.950751	+	0.309956i	$0.899686\pi$
$858$	33.8885	1.15694
$859$	2.11146	0.0720420	0.0360210	−	0.999351i	$-0.488532\pi$
$859$	2.11146	0.0720420	0.0360210	+	0.999351i	$0.488532\pi$
$860$	0.763932	0.0260499
$861$	−5.34752	−0.182243
$862$	19.4164	0.661325
$863$	−9.81966	−0.334265	−0.167133	−	0.985934i	$-0.553451\pi$
$863$	−9.81966	−0.334265	−0.167133	+	0.985934i	$0.553451\pi$
$864$	48.9443	1.66512
$865$	2.94427	0.100108
$866$	16.4721	0.559746
$867$	53.1246	1.80421
$868$	0.145898	0.00495210
$869$	−23.4164	−0.794347
$870$	−14.4721	−0.490651
$871$	−25.8885	−0.877200
$872$	31.1803	1.05590
$873$	−119.138	−4.03220
$874$	−20.6525	−0.698580
$875$	−2.12461	−0.0718250
$876$	−16.9443	−0.572494
$877$	−18.0557	−0.609699	−0.304849	−	0.952401i	$-0.598606\pi$
$877$	−18.0557	−0.609699	−0.304849	+	0.952401i	$0.598606\pi$
$878$	−1.90983	−0.0644536
$879$	1.52786	0.0515336
$880$	−9.70820	−0.327263
$881$	−20.3607	−0.685969	−0.342984	−	0.939341i	$-0.611438\pi$
$881$	−20.3607	−0.685969	−0.342984	+	0.939341i	$0.611438\pi$
$882$	−83.9574	−2.82699
$883$	−31.7771	−1.06938	−0.534692	−	0.845047i	$-0.679572\pi$
$883$	−31.7771	−1.06938	−0.534692	+	0.845047i	$0.679572\pi$
$884$	−1.52786	−0.0513876
$885$	−7.23607	−0.243238
$886$	49.6869	1.66926
$887$	27.0689	0.908884	0.454442	−	0.890776i	$-0.349839\pi$
$887$	27.0689	0.908884	0.454442	+	0.890776i	$0.349839\pi$
$888$	−14.4721	−0.485653
$889$	2.94427	0.0987477
$890$	18.9443	0.635013
$891$	48.8328	1.63596
$892$	2.47214	0.0827732
$893$	−5.52786	−0.184983
$894$	−52.3607	−1.75120
$895$	1.70820	0.0570990
$896$	3.21478	0.107398
$897$	59.7771	1.99590
$898$	−50.6525	−1.69030
$899$	2.76393	0.0921823
$900$	−18.4721	−0.615738
$901$	−8.00000	−0.266519
$902$	22.6525	0.754245
$903$	−0.944272	−0.0314234
$904$	−7.76393	−0.258225
$905$	−4.18034	−0.138959
$906$	74.2492	2.46677
$907$	−24.2361	−0.804745	−0.402373	−	0.915476i	$-0.631814\pi$
$907$	−24.2361	−0.804745	−0.402373	+	0.915476i	$0.631814\pi$
$908$	−4.00000	−0.132745
$909$	−22.4164	−0.743505
$910$	−1.23607	−0.0409753
$911$	18.1803	0.602342	0.301171	−	0.953570i	$-0.402623\pi$
$911$	18.1803	0.602342	0.301171	+	0.953570i	$0.402623\pi$
$912$	−35.1246	−1.16309
$913$	−29.8885	−0.989166
$914$	−4.94427	−0.163542
$915$	−26.4721	−0.875142
$916$	−8.29180	−0.273969
$917$	2.83282	0.0935478
$918$	−17.8885	−0.590410
$919$	−14.4721	−0.477392	−0.238696	−	0.971094i	$-0.576720\pi$
$919$	−14.4721	−0.477392	−0.238696	+	0.971094i	$0.576720\pi$
$920$	−12.7639	−0.420814
$921$	92.9017	3.06122
$922$	55.5967	1.83098
$923$	29.7082	0.977857
$924$	−0.944272	−0.0310643
$925$	8.00000	0.263038
$926$	−4.18034	−0.137374
$927$	46.5967	1.53044
$928$	−9.34752	−0.306848
$929$	−20.0000	−0.656179	−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000	−0.656179	−0.328089	+	0.944647i	$0.606405\pi$
$930$	−5.23607	−0.171697
$931$	15.5279	0.508905
$932$	11.0902	0.363271
$933$	94.4296	3.09149
$934$	7.61803	0.249270
$935$	1.52786	0.0499665
$936$	54.0689	1.76730
$937$	9.05573	0.295838	0.147919	−	0.988999i	$-0.452743\pi$
$937$	9.05573	0.295838	0.147919	+	0.988999i	$0.452743\pi$
$938$	3.05573	0.0997731
$939$	−54.2492	−1.77036
$940$	1.52786	0.0498334
$941$	−38.0000	−1.23876	−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000	−1.23876	−0.619382	+	0.785090i	$0.712617\pi$
$942$	−109.374	−3.56359
$943$	39.9574	1.30119
$944$	−10.8541	−0.353271
$945$	−3.41641	−0.111136
$946$	4.00000	0.130051
$947$	−13.0557	−0.424254	−0.212127	−	0.977242i	$-0.568039\pi$
$947$	−13.0557	−0.424254	−0.212127	+	0.977242i	$0.568039\pi$
$948$	23.4164	0.760530
$949$	−27.4164	−0.889974
$950$	14.4721	0.469538
$951$	−13.1246	−0.425595
$952$	−0.403252	−0.0130695
$953$	45.7082	1.48063	0.740317	−	0.672258i	$-0.234675\pi$
$953$	45.7082	1.48063	0.740317	+	0.672258i	$0.234675\pi$
$954$	−126.610	−4.09915
$955$	−19.1803	−0.620661
$956$	−7.23607	−0.234031
$957$	−17.8885	−0.578254
$958$	37.6869	1.21761
$959$	1.48529	0.0479626
$960$	−13.7082	−0.442430
$961$	1.00000	0.0322581
$962$	10.4721	0.337635
$963$	43.0689	1.38788
$964$	8.87539	0.285857
$965$	3.47214	0.111772
$966$	−7.05573	−0.227014
$967$	60.3607	1.94107	0.970534	−	0.240963i	$-0.0774632\pi$
$967$	60.3607	1.94107	0.970534	+	0.240963i	$0.0774632\pi$
$968$	15.6525	0.503090
$969$	5.52786	0.177581
$970$	−25.7984	−0.828336
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	−22.0000	−0.705650
$973$	3.16718	0.101535
$974$	−31.1246	−0.997297
$975$	−41.8885	−1.34151
$976$	−39.7082	−1.27103
$977$	−47.2492	−1.51164	−0.755818	−	0.654781i	$-0.772761\pi$
$977$	−47.2492	−1.51164	−0.755818	+	0.654781i	$0.772761\pi$
$978$	−56.0689	−1.79289
$979$	23.4164	0.748392
$980$	−4.29180	−0.137096
$981$	−104.193	−3.32664
$982$	7.05573	0.225157
$983$	39.5279	1.26074	0.630372	−	0.776294i	$-0.282903\pi$
$983$	39.5279	1.26074	0.630372	+	0.776294i	$0.282903\pi$
$984$	50.6525	1.61474
$985$	11.4164	0.363757
$986$	3.41641	0.108801
$987$	−1.88854	−0.0601130
$988$	4.47214	0.142278
$989$	7.05573	0.224359
$990$	24.1803	0.768502
$991$	−16.5410	−0.525443	−0.262721	−	0.964872i	$-0.584620\pi$
$991$	−16.5410	−0.525443	−0.262721	+	0.964872i	$0.584620\pi$
$992$	−3.38197	−0.107378
$993$	−6.47214	−0.205387
$994$	−3.50658	−0.111222
$995$	−18.9443	−0.600574
$996$	29.8885	0.947055
$997$	−29.3607	−0.929862	−0.464931	−	0.885347i	$-0.653921\pi$
$997$	−29.3607	−0.929862	−0.464931	+	0.885347i	$0.653921\pi$
$998$	−10.6525	−0.337198
$999$	28.9443	0.915756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.a.a.1.2	✓	2
3.2	odd	2		279.2.a.a.1.1		2
4.3	odd	2		496.2.a.i.1.2		2
5.2	odd	4		775.2.b.d.249.4		4
5.3	odd	4		775.2.b.d.249.1		4
5.4	even	2		775.2.a.d.1.1		2
7.6	odd	2		1519.2.a.a.1.2		2
8.3	odd	2		1984.2.a.n.1.1		2
8.5	even	2		1984.2.a.r.1.2		2
11.10	odd	2		3751.2.a.b.1.1		2
12.11	even	2		4464.2.a.bf.1.1		2
13.12	even	2		5239.2.a.f.1.1		2
15.14	odd	2		6975.2.a.y.1.2		2
17.16	even	2		8959.2.a.b.1.2		2
31.2	even	5		961.2.d.d.531.1		4
31.3	odd	30		961.2.g.e.846.1		8
31.4	even	5		961.2.d.c.388.1		4
31.5	even	3		961.2.c.e.521.2		4
31.6	odd	6		961.2.c.c.439.2		4
31.7	even	15		961.2.g.a.235.1		8
31.8	even	5		961.2.d.c.374.1		4
31.9	even	15		961.2.g.a.732.1		8
31.10	even	15		961.2.g.h.844.1		8
31.11	odd	30		961.2.g.d.338.1		8
31.12	odd	30		961.2.g.e.547.1		8
31.13	odd	30		961.2.g.e.448.1		8
31.14	even	15		961.2.g.a.816.1		8
31.15	odd	10		961.2.d.g.628.1		4
31.16	even	5		961.2.d.d.628.1		4
31.17	odd	30		961.2.g.d.816.1		8
31.18	even	15		961.2.g.h.448.1		8
31.19	even	15		961.2.g.h.547.1		8
31.20	even	15		961.2.g.a.338.1		8
31.21	odd	30		961.2.g.e.844.1		8
31.22	odd	30		961.2.g.d.732.1		8
31.23	odd	10		961.2.d.a.374.1		4
31.24	odd	30		961.2.g.d.235.1		8
31.25	even	3		961.2.c.e.439.2		4
31.26	odd	6		961.2.c.c.521.2		4
31.27	odd	10		961.2.d.a.388.1		4
31.28	even	15		961.2.g.h.846.1		8
31.29	odd	10		961.2.d.g.531.1		4
31.30	odd	2		961.2.a.f.1.2		2
93.92	even	2		8649.2.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	1.1	even	1	trivial
279.2.a.a.1.1		2	3.2	odd	2
496.2.a.i.1.2		2	4.3	odd	2
775.2.a.d.1.1		2	5.4	even	2
775.2.b.d.249.1		4	5.3	odd	4
775.2.b.d.249.4		4	5.2	odd	4
961.2.a.f.1.2		2	31.30	odd	2
961.2.c.c.439.2		4	31.6	odd	6
961.2.c.c.521.2		4	31.26	odd	6
961.2.c.e.439.2		4	31.25	even	3
961.2.c.e.521.2		4	31.5	even	3
961.2.d.a.374.1		4	31.23	odd	10
961.2.d.a.388.1		4	31.27	odd	10
961.2.d.c.374.1		4	31.8	even	5
961.2.d.c.388.1		4	31.4	even	5
961.2.d.d.531.1		4	31.2	even	5
961.2.d.d.628.1		4	31.16	even	5
961.2.d.g.531.1		4	31.29	odd	10
961.2.d.g.628.1		4	31.15	odd	10
961.2.g.a.235.1		8	31.7	even	15
961.2.g.a.338.1		8	31.20	even	15
961.2.g.a.732.1		8	31.9	even	15
961.2.g.a.816.1		8	31.14	even	15
961.2.g.d.235.1		8	31.24	odd	30
961.2.g.d.338.1		8	31.11	odd	30
961.2.g.d.732.1		8	31.22	odd	30
961.2.g.d.816.1		8	31.17	odd	30
961.2.g.e.448.1		8	31.13	odd	30
961.2.g.e.547.1		8	31.12	odd	30
961.2.g.e.844.1		8	31.21	odd	30
961.2.g.e.846.1		8	31.3	odd	30
961.2.g.h.448.1		8	31.18	even	15
961.2.g.h.547.1		8	31.19	even	15
961.2.g.h.844.1		8	31.10	even	15
961.2.g.h.846.1		8	31.28	even	15
1519.2.a.a.1.2		2	7.6	odd	2
1984.2.a.n.1.1		2	8.3	odd	2
1984.2.a.r.1.2		2	8.5	even	2
3751.2.a.b.1.1		2	11.10	odd	2
4464.2.a.bf.1.1		2	12.11	even	2
5239.2.a.f.1.1		2	13.12	even	2
6975.2.a.y.1.2		2	15.14	odd	2
8649.2.a.c.1.1		2	93.92	even	2
8959.2.a.b.1.2		2	17.16	even	2

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} -3.23607 q^{3} +0.618034 q^{4} +1.00000 q^{5} -5.23607 q^{6} +0.236068 q^{7} -2.23607 q^{8} +7.47214 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} -3.23607 q^{3} +0.618034 q^{4} +1.00000 q^{5} -5.23607 q^{6} +0.236068 q^{7} -2.23607 q^{8} +7.47214 q^{9} +1.61803 q^{10} +2.00000 q^{11} -2.00000 q^{12} -3.23607 q^{13} +0.381966 q^{14} -3.23607 q^{15} -4.85410 q^{16} +0.763932 q^{17} +12.0902 q^{18} -2.23607 q^{19} +0.618034 q^{20} -0.763932 q^{21} +3.23607 q^{22} +5.70820 q^{23} +7.23607 q^{24} -4.00000 q^{25} -5.23607 q^{26} -14.4721 q^{27} +0.145898 q^{28} +2.76393 q^{29} -5.23607 q^{30} +1.00000 q^{31} -3.38197 q^{32} -6.47214 q^{33} +1.23607 q^{34} +0.236068 q^{35} +4.61803 q^{36} -2.00000 q^{37} -3.61803 q^{38} +10.4721 q^{39} -2.23607 q^{40} +7.00000 q^{41} -1.23607 q^{42} +1.23607 q^{43} +1.23607 q^{44} +7.47214 q^{45} +9.23607 q^{46} +2.47214 q^{47} +15.7082 q^{48} -6.94427 q^{49} -6.47214 q^{50} -2.47214 q^{51} -2.00000 q^{52} -10.4721 q^{53} -23.4164 q^{54} +2.00000 q^{55} -0.527864 q^{56} +7.23607 q^{57} +4.47214 q^{58} +2.23607 q^{59} -2.00000 q^{60} +8.18034 q^{61} +1.61803 q^{62} +1.76393 q^{63} +4.23607 q^{64} -3.23607 q^{65} -10.4721 q^{66} +8.00000 q^{67} +0.472136 q^{68} -18.4721 q^{69} +0.381966 q^{70} -9.18034 q^{71} -16.7082 q^{72} +8.47214 q^{73} -3.23607 q^{74} +12.9443 q^{75} -1.38197 q^{76} +0.472136 q^{77} +16.9443 q^{78} -11.7082 q^{79} -4.85410 q^{80} +24.4164 q^{81} +11.3262 q^{82} -14.9443 q^{83} -0.472136 q^{84} +0.763932 q^{85} +2.00000 q^{86} -8.94427 q^{87} -4.47214 q^{88} +11.7082 q^{89} +12.0902 q^{90} -0.763932 q^{91} +3.52786 q^{92} -3.23607 q^{93} +4.00000 q^{94} -2.23607 q^{95} +10.9443 q^{96} -15.9443 q^{97} -11.2361 q^{98} +14.9443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 + 2 * q^5 - 6 * q^6 - 4 * q^7 + 6 * q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} - 4 q^{7} + 6 q^{9} + q^{10} + 4 q^{11} - 4 q^{12} - 2 q^{13} + 3 q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} + 13 q^{18} - q^{20} - 6 q^{21} + 2 q^{22} - 2 q^{23} + 10 q^{24} - 8 q^{25} - 6 q^{26} - 20 q^{27} + 7 q^{28} + 10 q^{29} - 6 q^{30} + 2 q^{31} - 9 q^{32} - 4 q^{33} - 2 q^{34} - 4 q^{35} + 7 q^{36} - 4 q^{37} - 5 q^{38} + 12 q^{39} + 14 q^{41} + 2 q^{42} - 2 q^{43} - 2 q^{44} + 6 q^{45} + 14 q^{46} - 4 q^{47} + 18 q^{48} + 4 q^{49} - 4 q^{50} + 4 q^{51} - 4 q^{52} - 12 q^{53} - 20 q^{54} + 4 q^{55} - 10 q^{56} + 10 q^{57} - 4 q^{60} - 6 q^{61} + q^{62} + 8 q^{63} + 4 q^{64} - 2 q^{65} - 12 q^{66} + 16 q^{67} - 8 q^{68} - 28 q^{69} + 3 q^{70} + 4 q^{71} - 20 q^{72} + 8 q^{73} - 2 q^{74} + 8 q^{75} - 5 q^{76} - 8 q^{77} + 16 q^{78} - 10 q^{79} - 3 q^{80} + 22 q^{81} + 7 q^{82} - 12 q^{83} + 8 q^{84} + 6 q^{85} + 4 q^{86} + 10 q^{89} + 13 q^{90} - 6 q^{91} + 16 q^{92} - 2 q^{93} + 8 q^{94} + 4 q^{96} - 14 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 + 2 * q^5 - 6 * q^6 - 4 * q^7 + 6 * q^9 + q^10 + 4 * q^11 - 4 * q^12 - 2 * q^13 + 3 * q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 + 13 * q^18 - q^20 - 6 * q^21 + 2 * q^22 - 2 * q^23 + 10 * q^24 - 8 * q^25 - 6 * q^26 - 20 * q^27 + 7 * q^28 + 10 * q^29 - 6 * q^30 + 2 * q^31 - 9 * q^32 - 4 * q^33 - 2 * q^34 - 4 * q^35 + 7 * q^36 - 4 * q^37 - 5 * q^38 + 12 * q^39 + 14 * q^41 + 2 * q^42 - 2 * q^43 - 2 * q^44 + 6 * q^45 + 14 * q^46 - 4 * q^47 + 18 * q^48 + 4 * q^49 - 4 * q^50 + 4 * q^51 - 4 * q^52 - 12 * q^53 - 20 * q^54 + 4 * q^55 - 10 * q^56 + 10 * q^57 - 4 * q^60 - 6 * q^61 + q^62 + 8 * q^63 + 4 * q^64 - 2 * q^65 - 12 * q^66 + 16 * q^67 - 8 * q^68 - 28 * q^69 + 3 * q^70 + 4 * q^71 - 20 * q^72 + 8 * q^73 - 2 * q^74 + 8 * q^75 - 5 * q^76 - 8 * q^77 + 16 * q^78 - 10 * q^79 - 3 * q^80 + 22 * q^81 + 7 * q^82 - 12 * q^83 + 8 * q^84 + 6 * q^85 + 4 * q^86 + 10 * q^89 + 13 * q^90 - 6 * q^91 + 16 * q^92 - 2 * q^93 + 8 * q^94 + 4 * q^96 - 14 * q^97 - 18 * q^98 + 12 * q^99

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