LMFDB - Embedded newform 31.2.a.a.1.1

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			1.1
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.618034 q^{2} +1.23607 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.763932 q^{6} -4.23607 q^{7} +2.23607 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +1.23607 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.763932 q^{6} -4.23607 q^{7} +2.23607 q^{8} -1.47214 q^{9} -0.618034 q^{10} +2.00000 q^{11} -2.00000 q^{12} +1.23607 q^{13} +2.61803 q^{14} +1.23607 q^{15} +1.85410 q^{16} +5.23607 q^{17} +0.909830 q^{18} +2.23607 q^{19} -1.61803 q^{20} -5.23607 q^{21} -1.23607 q^{22} -7.70820 q^{23} +2.76393 q^{24} -4.00000 q^{25} -0.763932 q^{26} -5.52786 q^{27} +6.85410 q^{28} +7.23607 q^{29} -0.763932 q^{30} +1.00000 q^{31} -5.61803 q^{32} +2.47214 q^{33} -3.23607 q^{34} -4.23607 q^{35} +2.38197 q^{36} -2.00000 q^{37} -1.38197 q^{38} +1.52786 q^{39} +2.23607 q^{40} +7.00000 q^{41} +3.23607 q^{42} -3.23607 q^{43} -3.23607 q^{44} -1.47214 q^{45} +4.76393 q^{46} -6.47214 q^{47} +2.29180 q^{48} +10.9443 q^{49} +2.47214 q^{50} +6.47214 q^{51} -2.00000 q^{52} -1.52786 q^{53} +3.41641 q^{54} +2.00000 q^{55} -9.47214 q^{56} +2.76393 q^{57} -4.47214 q^{58} -2.23607 q^{59} -2.00000 q^{60} -14.1803 q^{61} -0.618034 q^{62} +6.23607 q^{63} -0.236068 q^{64} +1.23607 q^{65} -1.52786 q^{66} +8.00000 q^{67} -8.47214 q^{68} -9.52786 q^{69} +2.61803 q^{70} +13.1803 q^{71} -3.29180 q^{72} -0.472136 q^{73} +1.23607 q^{74} -4.94427 q^{75} -3.61803 q^{76} -8.47214 q^{77} -0.944272 q^{78} +1.70820 q^{79} +1.85410 q^{80} -2.41641 q^{81} -4.32624 q^{82} +2.94427 q^{83} +8.47214 q^{84} +5.23607 q^{85} +2.00000 q^{86} +8.94427 q^{87} +4.47214 q^{88} -1.70820 q^{89} +0.909830 q^{90} -5.23607 q^{91} +12.4721 q^{92} +1.23607 q^{93} +4.00000 q^{94} +2.23607 q^{95} -6.94427 q^{96} +1.94427 q^{97} -6.76393 q^{98} -2.94427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	1.23607	0.713644	0.356822	−	0.934172i	$-0.383860\pi$
$3$	1.23607	0.713644	0.356822	+	0.934172i	$0.383860\pi$
$4$	−1.61803	−0.809017
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.763932	−0.311874
$7$	−4.23607	−1.60108	−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607	−1.60108	−0.800542	+	0.599277i	$0.795455\pi$
$8$	2.23607	0.790569
$9$	−1.47214	−0.490712
$10$	−0.618034	−0.195440
$11$	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
$13$	1.23607	0.342824	0.171412	−	0.985199i	$-0.445167\pi$
$13$	1.23607	0.342824	0.171412	+	0.985199i	$0.445167\pi$
$14$	2.61803	0.699699
$15$	1.23607	0.319151
$16$	1.85410	0.463525
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	0.909830	0.214449
$19$	2.23607	0.512989	0.256495	−	0.966546i	$-0.417432\pi$
$19$	2.23607	0.512989	0.256495	+	0.966546i	$0.417432\pi$
$20$	−1.61803	−0.361803
$21$	−5.23607	−1.14260
$22$	−1.23607	−0.263531
$23$	−7.70820	−1.60727	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−7.70820	−1.60727	−0.803636	+	0.595121i	$0.797104\pi$
$24$	2.76393	0.564185
$25$	−4.00000	−0.800000
$26$	−0.763932	−0.149819
$27$	−5.52786	−1.06384
$28$	6.85410	1.29530
$29$	7.23607	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$29$	7.23607	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$30$	−0.763932	−0.139474
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−5.61803	−0.993137
$33$	2.47214	0.430344
$34$	−3.23607	−0.554981
$35$	−4.23607	−0.716026
$36$	2.38197	0.396994
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−1.38197	−0.224184
$39$	1.52786	0.244654
$40$	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	$0.315919\pi$
$42$	3.23607	0.499336
$43$	−3.23607	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$44$	−3.23607	−0.487856
$45$	−1.47214	−0.219453
$46$	4.76393	0.702403
$47$	−6.47214	−0.944058	−0.472029	−	0.881583i	$-0.656478\pi$
$47$	−6.47214	−0.944058	−0.472029	+	0.881583i	$0.656478\pi$
$48$	2.29180	0.330792
$49$	10.9443	1.56347
$50$	2.47214	0.349613
$51$	6.47214	0.906280
$52$	−2.00000	−0.277350
$53$	−1.52786	−0.209868	−0.104934	−	0.994479i	$-0.533463\pi$
$53$	−1.52786	−0.209868	−0.104934	+	0.994479i	$0.533463\pi$
$54$	3.41641	0.464914
$55$	2.00000	0.269680
$56$	−9.47214	−1.26577
$57$	2.76393	0.366092
$58$	−4.47214	−0.587220
$59$	−2.23607	−0.291111	−0.145556	−	0.989350i	$-0.546497\pi$
$59$	−2.23607	−0.291111	−0.145556	+	0.989350i	$0.546497\pi$
$60$	−2.00000	−0.258199
$61$	−14.1803	−1.81561	−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803	−1.81561	−0.907803	+	0.419396i	$0.862242\pi$
$62$	−0.618034	−0.0784904
$63$	6.23607	0.785671
$64$	−0.236068	−0.0295085
$65$	1.23607	0.153315
$66$	−1.52786	−0.188067
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−8.47214	−1.02740
$69$	−9.52786	−1.14702
$70$	2.61803	0.312915
$71$	13.1803	1.56422	0.782109	−	0.623141i	$-0.214144\pi$
$71$	13.1803	1.56422	0.782109	+	0.623141i	$0.214144\pi$
$72$	−3.29180	−0.387942
$73$	−0.472136	−0.0552593	−0.0276297	−	0.999618i	$-0.508796\pi$
$73$	−0.472136	−0.0552593	−0.0276297	+	0.999618i	$0.508796\pi$
$74$	1.23607	0.143690
$75$	−4.94427	−0.570915
$76$	−3.61803	−0.415017
$77$	−8.47214	−0.965489
$78$	−0.944272	−0.106918
$79$	1.70820	0.192188	0.0960940	−	0.995372i	$-0.469365\pi$
$79$	1.70820	0.192188	0.0960940	+	0.995372i	$0.469365\pi$
$80$	1.85410	0.207295
$81$	−2.41641	−0.268490
$82$	−4.32624	−0.477753
$83$	2.94427	0.323176	0.161588	−	0.986858i	$-0.448338\pi$
$83$	2.94427	0.323176	0.161588	+	0.986858i	$0.448338\pi$
$84$	8.47214	0.924386
$85$	5.23607	0.567931
$86$	2.00000	0.215666
$87$	8.94427	0.958927
$88$	4.47214	0.476731
$89$	−1.70820	−0.181069	−0.0905346	−	0.995893i	$-0.528858\pi$
$89$	−1.70820	−0.181069	−0.0905346	+	0.995893i	$0.528858\pi$
$90$	0.909830	0.0959045
$91$	−5.23607	−0.548889
$92$	12.4721	1.30031
$93$	1.23607	0.128174
$94$	4.00000	0.412568
$95$	2.23607	0.229416
$96$	−6.94427	−0.708747
$97$	1.94427	0.197411	0.0987055	−	0.995117i	$-0.468530\pi$
$97$	1.94427	0.197411	0.0987055	+	0.995117i	$0.468530\pi$
$98$	−6.76393	−0.683260
$99$	−2.94427	−0.295910
$100$	6.47214	0.647214
$101$	−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
$103$	1.76393	0.173805	0.0869027	−	0.996217i	$-0.472303\pi$
$103$	1.76393	0.173805	0.0869027	+	0.996217i	$0.472303\pi$
$104$	2.76393	0.271026
$105$	−5.23607	−0.510988
$106$	0.944272	0.0917158
$107$	10.2361	0.989558	0.494779	−	0.869019i	$-0.335249\pi$
$107$	10.2361	0.989558	0.494779	+	0.869019i	$0.335249\pi$
$108$	8.94427	0.860663
$109$	3.94427	0.377793	0.188896	−	0.981997i	$-0.439509\pi$
$109$	3.94427	0.377793	0.188896	+	0.981997i	$0.439509\pi$
$110$	−1.23607	−0.117854
$111$	−2.47214	−0.234645
$112$	−7.85410	−0.742143
$113$	−5.47214	−0.514775	−0.257388	−	0.966308i	$-0.582862\pi$
$113$	−5.47214	−0.514775	−0.257388	+	0.966308i	$0.582862\pi$
$114$	−1.70820	−0.159988
$115$	−7.70820	−0.718794
$116$	−11.7082	−1.08708
$117$	−1.81966	−0.168228
$118$	1.38197	0.127220
$119$	−22.1803	−2.03327
$120$	2.76393	0.252311
$121$	−7.00000	−0.636364
$122$	8.76393	0.793449
$123$	8.65248	0.780167
$124$	−1.61803	−0.145304
$125$	−9.00000	−0.804984
$126$	−3.85410	−0.343351
$127$	3.52786	0.313047	0.156524	−	0.987674i	$-0.449971\pi$
$127$	3.52786	0.313047	0.156524	+	0.987674i	$0.449971\pi$
$128$	11.3820	1.00603
$129$	−4.00000	−0.352180
$130$	−0.763932	−0.0670013
$131$	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
$133$	−9.47214	−0.821338
$134$	−4.94427	−0.427120
$135$	−5.52786	−0.475763
$136$	11.7082	1.00397
$137$	19.7082	1.68379	0.841893	−	0.539645i	$-0.181441\pi$
$137$	19.7082	1.68379	0.841893	+	0.539645i	$0.181441\pi$
$138$	5.88854	0.501266
$139$	−13.4164	−1.13796	−0.568982	−	0.822350i	$-0.692663\pi$
$139$	−13.4164	−1.13796	−0.568982	+	0.822350i	$0.692663\pi$
$140$	6.85410	0.579277
$141$	−8.00000	−0.673722
$142$	−8.14590	−0.683589
$143$	2.47214	0.206730
$144$	−2.72949	−0.227458
$145$	7.23607	0.600923
$146$	0.291796	0.0241492
$147$	13.5279	1.11576
$148$	3.23607	0.266003
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	3.05573	0.249499
$151$	8.18034	0.665707	0.332853	−	0.942979i	$-0.391989\pi$
$151$	8.18034	0.665707	0.332853	+	0.942979i	$0.391989\pi$
$152$	5.00000	0.405554
$153$	−7.70820	−0.623171
$154$	5.23607	0.421934
$155$	1.00000	0.0803219
$156$	−2.47214	−0.197929
$157$	−14.8885	−1.18824	−0.594118	−	0.804378i	$-0.702499\pi$
$157$	−14.8885	−1.18824	−0.594118	+	0.804378i	$0.702499\pi$
$158$	−1.05573	−0.0839892
$159$	−1.88854	−0.149771
$160$	−5.61803	−0.444145
$161$	32.6525	2.57338
$162$	1.49342	0.117334
$163$	−2.70820	−0.212123	−0.106061	−	0.994360i	$-0.533824\pi$
$163$	−2.70820	−0.212123	−0.106061	+	0.994360i	$0.533824\pi$
$164$	−11.3262	−0.884431
$165$	2.47214	0.192456
$166$	−1.81966	−0.141233
$167$	2.47214	0.191300	0.0956498	−	0.995415i	$-0.469507\pi$
$167$	2.47214	0.191300	0.0956498	+	0.995415i	$0.469507\pi$
$168$	−11.7082	−0.903308
$169$	−11.4721	−0.882472
$170$	−3.23607	−0.248195
$171$	−3.29180	−0.251730
$172$	5.23607	0.399246
$173$	−14.9443	−1.13619	−0.568096	−	0.822962i	$-0.692320\pi$
$173$	−14.9443	−1.13619	−0.568096	+	0.822962i	$0.692320\pi$
$174$	−5.52786	−0.419066
$175$	16.9443	1.28087
$176$	3.70820	0.279516
$177$	−2.76393	−0.207750
$178$	1.05573	0.0791302
$179$	−11.7082	−0.875112	−0.437556	−	0.899191i	$-0.644156\pi$
$179$	−11.7082	−0.875112	−0.437556	+	0.899191i	$0.644156\pi$
$180$	2.38197	0.177541
$181$	18.1803	1.35133	0.675667	−	0.737207i	$-0.263856\pi$
$181$	18.1803	1.35133	0.675667	+	0.737207i	$0.263856\pi$
$182$	3.23607	0.239873
$183$	−17.5279	−1.29570
$184$	−17.2361	−1.27066
$185$	−2.00000	−0.147043
$186$	−0.763932	−0.0560142
$187$	10.4721	0.765798
$188$	10.4721	0.763759
$189$	23.4164	1.70329
$190$	−1.38197	−0.100258
$191$	3.18034	0.230121	0.115061	−	0.993358i	$-0.463294\pi$
$191$	3.18034	0.230121	0.115061	+	0.993358i	$0.463294\pi$
$192$	−0.291796	−0.0210586
$193$	−5.47214	−0.393893	−0.196946	−	0.980414i	$-0.563103\pi$
$193$	−5.47214	−0.393893	−0.196946	+	0.980414i	$0.563103\pi$
$194$	−1.20163	−0.0862717
$195$	1.52786	0.109413
$196$	−17.7082	−1.26487
$197$	−15.4164	−1.09837	−0.549187	−	0.835700i	$-0.685062\pi$
$197$	−15.4164	−1.09837	−0.549187	+	0.835700i	$0.685062\pi$
$198$	1.81966	0.129318
$199$	−1.05573	−0.0748386	−0.0374193	−	0.999300i	$-0.511914\pi$
$199$	−1.05573	−0.0748386	−0.0374193	+	0.999300i	$0.511914\pi$
$200$	−8.94427	−0.632456
$201$	9.88854	0.697484
$202$	1.85410	0.130454
$203$	−30.6525	−2.15138
$204$	−10.4721	−0.733196
$205$	7.00000	0.488901
$206$	−1.09017	−0.0759557
$207$	11.3475	0.788707
$208$	2.29180	0.158907
$209$	4.47214	0.309344
$210$	3.23607	0.223310
$211$	0.819660	0.0564277	0.0282139	−	0.999602i	$-0.491018\pi$
$211$	0.819660	0.0564277	0.0282139	+	0.999602i	$0.491018\pi$
$212$	2.47214	0.169787
$213$	16.2918	1.11630
$214$	−6.32624	−0.432453
$215$	−3.23607	−0.220698
$216$	−12.3607	−0.841038
$217$	−4.23607	−0.287563
$218$	−2.43769	−0.165101
$219$	−0.583592	−0.0394355
$220$	−3.23607	−0.218176
$221$	6.47214	0.435363
$222$	1.52786	0.102544
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	23.7984	1.59010
$225$	5.88854	0.392570
$226$	3.38197	0.224965
$227$	2.47214	0.164081	0.0820407	−	0.996629i	$-0.473856\pi$
$227$	2.47214	0.164081	0.0820407	+	0.996629i	$0.473856\pi$
$228$	−4.47214	−0.296174
$229$	13.4164	0.886581	0.443291	−	0.896378i	$-0.353811\pi$
$229$	13.4164	0.886581	0.443291	+	0.896378i	$0.353811\pi$
$230$	4.76393	0.314124
$231$	−10.4721	−0.689016
$232$	16.1803	1.06229
$233$	0.0557281	0.00365087	0.00182543	−	0.999998i	$-0.499419\pi$
$233$	0.0557281	0.00365087	0.00182543	+	0.999998i	$0.499419\pi$
$234$	1.12461	0.0735182
$235$	−6.47214	−0.422196
$236$	3.61803	0.235514
$237$	2.11146	0.137154
$238$	13.7082	0.888571
$239$	1.70820	0.110495	0.0552473	−	0.998473i	$-0.482405\pi$
$239$	1.70820	0.110495	0.0552473	+	0.998473i	$0.482405\pi$
$240$	2.29180	0.147935
$241$	−30.3607	−1.95570	−0.977852	−	0.209299i	$-0.932882\pi$
$241$	−30.3607	−1.95570	−0.977852	+	0.209299i	$0.932882\pi$
$242$	4.32624	0.278101
$243$	13.5967	0.872232
$244$	22.9443	1.46886
$245$	10.9443	0.699204
$246$	−5.34752	−0.340946
$247$	2.76393	0.175865
$248$	2.23607	0.141990
$249$	3.63932	0.230633
$250$	5.56231	0.351791
$251$	−24.1803	−1.52625	−0.763125	−	0.646251i	$-0.776336\pi$
$251$	−24.1803	−1.52625	−0.763125	+	0.646251i	$0.776336\pi$
$252$	−10.0902	−0.635621
$253$	−15.4164	−0.969221
$254$	−2.18034	−0.136807
$255$	6.47214	0.405301
$256$	−6.56231	−0.410144
$257$	−15.9443	−0.994576	−0.497288	−	0.867585i	$-0.665671\pi$
$257$	−15.9443	−0.994576	−0.497288	+	0.867585i	$0.665671\pi$
$258$	2.47214	0.153908
$259$	8.47214	0.526433
$260$	−2.00000	−0.124035
$261$	−10.6525	−0.659372
$262$	−7.41641	−0.458187
$263$	−18.7639	−1.15703	−0.578517	−	0.815670i	$-0.696368\pi$
$263$	−18.7639	−1.15703	−0.578517	+	0.815670i	$0.696368\pi$
$264$	5.52786	0.340217
$265$	−1.52786	−0.0938559
$266$	5.85410	0.358938
$267$	−2.11146	−0.129219
$268$	−12.9443	−0.790697
$269$	−28.9443	−1.76476	−0.882382	−	0.470534i	$-0.844061\pi$
$269$	−28.9443	−1.76476	−0.882382	+	0.470534i	$0.844061\pi$
$270$	3.41641	0.207916
$271$	8.18034	0.496920	0.248460	−	0.968642i	$-0.420076\pi$
$271$	8.18034	0.496920	0.248460	+	0.968642i	$0.420076\pi$
$272$	9.70820	0.588646
$273$	−6.47214	−0.391711
$274$	−12.1803	−0.735841
$275$	−8.00000	−0.482418
$276$	15.4164	0.927959
$277$	18.6525	1.12072	0.560359	−	0.828250i	$-0.310663\pi$
$277$	18.6525	1.12072	0.560359	+	0.828250i	$0.310663\pi$
$278$	8.29180	0.497309
$279$	−1.47214	−0.0881345
$280$	−9.47214	−0.566068
$281$	17.0000	1.01413	0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000	1.01413	0.507067	+	0.861906i	$0.330729\pi$
$282$	4.94427	0.294427
$283$	21.8885	1.30114	0.650569	−	0.759447i	$-0.274530\pi$
$283$	21.8885	1.30114	0.650569	+	0.759447i	$0.274530\pi$
$284$	−21.3262	−1.26548
$285$	2.76393	0.163721
$286$	−1.52786	−0.0903445
$287$	−29.6525	−1.75033
$288$	8.27051	0.487344
$289$	10.4164	0.612730
$290$	−4.47214	−0.262613
$291$	2.40325	0.140881
$292$	0.763932	0.0447057
$293$	8.47214	0.494947	0.247474	−	0.968895i	$-0.420400\pi$
$293$	8.47214	0.494947	0.247474	+	0.968895i	$0.420400\pi$
$294$	−8.36068	−0.487605
$295$	−2.23607	−0.130189
$296$	−4.47214	−0.259938
$297$	−11.0557	−0.641518
$298$	−6.18034	−0.358017
$299$	−9.52786	−0.551011
$300$	8.00000	0.461880
$301$	13.7082	0.790128
$302$	−5.05573	−0.290924
$303$	−3.70820	−0.213031
$304$	4.14590	0.237784
$305$	−14.1803	−0.811964
$306$	4.76393	0.272336
$307$	−15.2918	−0.872749	−0.436374	−	0.899765i	$-0.643738\pi$
$307$	−15.2918	−0.872749	−0.436374	+	0.899765i	$0.643738\pi$
$308$	13.7082	0.781097
$309$	2.18034	0.124035
$310$	−0.618034	−0.0351020
$311$	−6.81966	−0.386707	−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966	−0.386707	−0.193354	+	0.981129i	$0.561936\pi$
$312$	3.41641	0.193416
$313$	21.2361	1.20033	0.600167	−	0.799875i	$-0.295101\pi$
$313$	21.2361	1.20033	0.600167	+	0.799875i	$0.295101\pi$
$314$	9.20163	0.519278
$315$	6.23607	0.351363
$316$	−2.76393	−0.155483
$317$	21.9443	1.23251	0.616257	−	0.787545i	$-0.288648\pi$
$317$	21.9443	1.23251	0.616257	+	0.787545i	$0.288648\pi$
$318$	1.16718	0.0654524
$319$	14.4721	0.810284
$320$	−0.236068	−0.0131966
$321$	12.6525	0.706192
$322$	−20.1803	−1.12461
$323$	11.7082	0.651462
$324$	3.90983	0.217213
$325$	−4.94427	−0.274259
$326$	1.67376	0.0927011
$327$	4.87539	0.269610
$328$	15.6525	0.864263
$329$	27.4164	1.51152
$330$	−1.52786	−0.0841061
$331$	2.00000	0.109930	0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000	0.109930	0.0549650	+	0.998488i	$0.482495\pi$
$332$	−4.76393	−0.261455
$333$	2.94427	0.161345
$334$	−1.52786	−0.0836010
$335$	8.00000	0.437087
$336$	−9.70820	−0.529626
$337$	−19.2361	−1.04786	−0.523928	−	0.851763i	$-0.675534\pi$
$337$	−19.2361	−1.04786	−0.523928	+	0.851763i	$0.675534\pi$
$338$	7.09017	0.385654
$339$	−6.76393	−0.367366
$340$	−8.47214	−0.459466
$341$	2.00000	0.108306
$342$	2.03444	0.110010
$343$	−16.7082	−0.902158
$344$	−7.23607	−0.390143
$345$	−9.52786	−0.512963
$346$	9.23607	0.496534
$347$	1.81966	0.0976845	0.0488422	−	0.998807i	$-0.484447\pi$
$347$	1.81966	0.0976845	0.0488422	+	0.998807i	$0.484447\pi$
$348$	−14.4721	−0.775788
$349$	27.8885	1.49284	0.746420	−	0.665475i	$-0.231771\pi$
$349$	27.8885	1.49284	0.746420	+	0.665475i	$0.231771\pi$
$350$	−10.4721	−0.559759
$351$	−6.83282	−0.364709
$352$	−11.2361	−0.598884
$353$	−19.4164	−1.03343	−0.516716	−	0.856157i	$-0.672846\pi$
$353$	−19.4164	−1.03343	−0.516716	+	0.856157i	$0.672846\pi$
$354$	1.70820	0.0907900
$355$	13.1803	0.699540
$356$	2.76393	0.146488
$357$	−27.4164	−1.45103
$358$	7.23607	0.382438
$359$	17.7639	0.937544	0.468772	−	0.883319i	$-0.344697\pi$
$359$	17.7639	0.937544	0.468772	+	0.883319i	$0.344697\pi$
$360$	−3.29180	−0.173493
$361$	−14.0000	−0.736842
$362$	−11.2361	−0.590555
$363$	−8.65248	−0.454137
$364$	8.47214	0.444061
$365$	−0.472136	−0.0247127
$366$	10.8328	0.566240
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	−14.2918	−0.745011
$369$	−10.3050	−0.536454
$370$	1.23607	0.0642601
$371$	6.47214	0.336017
$372$	−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	$0.336306\pi$
$374$	−6.47214	−0.334666
$375$	−11.1246	−0.574472
$376$	−14.4721	−0.746343
$377$	8.94427	0.460653
$378$	−14.4721	−0.744366
$379$	−37.8885	−1.94620	−0.973102	−	0.230375i	$-0.926005\pi$
$379$	−37.8885	−1.94620	−0.973102	+	0.230375i	$0.926005\pi$
$380$	−3.61803	−0.185601
$381$	4.36068	0.223404
$382$	−1.96556	−0.100567
$383$	11.8885	0.607476	0.303738	−	0.952756i	$-0.401765\pi$
$383$	11.8885	0.607476	0.303738	+	0.952756i	$0.401765\pi$
$384$	14.0689	0.717950
$385$	−8.47214	−0.431780
$386$	3.38197	0.172138
$387$	4.76393	0.242164
$388$	−3.14590	−0.159709
$389$	17.8885	0.906985	0.453493	−	0.891260i	$-0.350178\pi$
$389$	17.8885	0.906985	0.453493	+	0.891260i	$0.350178\pi$
$390$	−0.944272	−0.0478151
$391$	−40.3607	−2.04113
$392$	24.4721	1.23603
$393$	14.8328	0.748217
$394$	9.52786	0.480007
$395$	1.70820	0.0859491
$396$	4.76393	0.239397
$397$	−7.00000	−0.351320	−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000	−0.351320	−0.175660	+	0.984451i	$0.556206\pi$
$398$	0.652476	0.0327057
$399$	−11.7082	−0.586143
$400$	−7.41641	−0.370820
$401$	15.8197	0.789996	0.394998	−	0.918682i	$-0.370745\pi$
$401$	15.8197	0.789996	0.394998	+	0.918682i	$0.370745\pi$
$402$	−6.11146	−0.304812
$403$	1.23607	0.0615729
$404$	4.85410	0.241501
$405$	−2.41641	−0.120072
$406$	18.9443	0.940188
$407$	−4.00000	−0.198273
$408$	14.4721	0.716477
$409$	−26.1803	−1.29453	−0.647267	−	0.762263i	$-0.724088\pi$
$409$	−26.1803	−1.29453	−0.647267	+	0.762263i	$0.724088\pi$
$410$	−4.32624	−0.213658
$411$	24.3607	1.20162
$412$	−2.85410	−0.140612
$413$	9.47214	0.466093
$414$	−7.01316	−0.344678
$415$	2.94427	0.144529
$416$	−6.94427	−0.340471
$417$	−16.5836	−0.812102
$418$	−2.76393	−0.135188
$419$	30.1246	1.47168	0.735842	−	0.677153i	$-0.236787\pi$
$419$	30.1246	1.47168	0.735842	+	0.677153i	$0.236787\pi$
$420$	8.47214	0.413398
$421$	−15.3607	−0.748634	−0.374317	−	0.927301i	$-0.622123\pi$
$421$	−15.3607	−0.748634	−0.374317	+	0.927301i	$0.622123\pi$
$422$	−0.506578	−0.0246598
$423$	9.52786	0.463261
$424$	−3.41641	−0.165915
$425$	−20.9443	−1.01595
$426$	−10.0689	−0.487839
$427$	60.0689	2.90694
$428$	−16.5623	−0.800569
$429$	3.05573	0.147532
$430$	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	$0.406674\pi$
$432$	−10.2492	−0.493116
$433$	−12.1803	−0.585350	−0.292675	−	0.956212i	$-0.594545\pi$
$433$	−12.1803	−0.585350	−0.292675	+	0.956212i	$0.594545\pi$
$434$	2.61803	0.125670
$435$	8.94427	0.428845
$436$	−6.38197	−0.305641
$437$	−17.2361	−0.824513
$438$	0.360680	0.0172339
$439$	21.1803	1.01088	0.505441	−	0.862861i	$-0.331330\pi$
$439$	21.1803	1.01088	0.505441	+	0.862861i	$0.331330\pi$
$440$	4.47214	0.213201
$441$	−16.1115	−0.767212
$442$	−4.00000	−0.190261
$443$	17.2918	0.821558	0.410779	−	0.911735i	$-0.365257\pi$
$443$	17.2918	0.821558	0.410779	+	0.911735i	$0.365257\pi$
$444$	4.00000	0.189832
$445$	−1.70820	−0.0809766
$446$	−2.47214	−0.117059
$447$	12.3607	0.584640
$448$	1.00000	0.0472456
$449$	31.3050	1.47737	0.738686	−	0.674050i	$-0.235447\pi$
$449$	31.3050	1.47737	0.738686	+	0.674050i	$0.235447\pi$
$450$	−3.63932	−0.171559
$451$	14.0000	0.659234
$452$	8.85410	0.416462
$453$	10.1115	0.475078
$454$	−1.52786	−0.0717062
$455$	−5.23607	−0.245471
$456$	6.18034	0.289421
$457$	−20.9443	−0.979732	−0.489866	−	0.871798i	$-0.662954\pi$
$457$	−20.9443	−0.979732	−0.489866	+	0.871798i	$0.662954\pi$
$458$	−8.29180	−0.387450
$459$	−28.9443	−1.35100
$460$	12.4721	0.581516
$461$	−10.3607	−0.482545	−0.241272	−	0.970457i	$-0.577565\pi$
$461$	−10.3607	−0.482545	−0.241272	+	0.970457i	$0.577565\pi$
$462$	6.47214	0.301111
$463$	−29.4164	−1.36710	−0.683548	−	0.729905i	$-0.739564\pi$
$463$	−29.4164	−1.36710	−0.683548	+	0.729905i	$0.739564\pi$
$464$	13.4164	0.622841
$465$	1.23607	0.0573213
$466$	−0.0344419	−0.00159549
$467$	−8.70820	−0.402968	−0.201484	−	0.979492i	$-0.564576\pi$
$467$	−8.70820	−0.402968	−0.201484	+	0.979492i	$0.564576\pi$
$468$	2.94427	0.136099
$469$	−33.8885	−1.56483
$470$	4.00000	0.184506
$471$	−18.4033	−0.847977
$472$	−5.00000	−0.230144
$473$	−6.47214	−0.297589
$474$	−1.30495	−0.0599384
$475$	−8.94427	−0.410391
$476$	35.8885	1.64495
$477$	2.24922	0.102985
$478$	−1.05573	−0.0482879
$479$	36.7082	1.67724	0.838620	−	0.544716i	$-0.183363\pi$
$479$	36.7082	1.67724	0.838620	+	0.544716i	$0.183363\pi$
$480$	−6.94427	−0.316961
$481$	−2.47214	−0.112720
$482$	18.7639	0.854674
$483$	40.3607	1.83647
$484$	11.3262	0.514829
$485$	1.94427	0.0882848
$486$	−8.40325	−0.381179
$487$	−14.7639	−0.669018	−0.334509	−	0.942393i	$-0.608570\pi$
$487$	−14.7639	−0.669018	−0.334509	+	0.942393i	$0.608570\pi$
$488$	−31.7082	−1.43536
$489$	−3.34752	−0.151380
$490$	−6.76393	−0.305563
$491$	−40.3607	−1.82145	−0.910726	−	0.413011i	$-0.864477\pi$
$491$	−40.3607	−1.82145	−0.910726	+	0.413011i	$0.864477\pi$
$492$	−14.0000	−0.631169
$493$	37.8885	1.70641
$494$	−1.70820	−0.0768557
$495$	−2.94427	−0.132335
$496$	1.85410	0.0832516
$497$	−55.8328	−2.50444
$498$	−2.24922	−0.100790
$499$	−33.4164	−1.49592	−0.747962	−	0.663742i	$-0.768967\pi$
$499$	−33.4164	−1.49592	−0.747962	+	0.663742i	$0.768967\pi$
$500$	14.5623	0.651246
$501$	3.05573	0.136520
$502$	14.9443	0.666995
$503$	−1.65248	−0.0736803	−0.0368401	−	0.999321i	$-0.511729\pi$
$503$	−1.65248	−0.0736803	−0.0368401	+	0.999321i	$0.511729\pi$
$504$	13.9443	0.621127
$505$	−3.00000	−0.133498
$506$	9.52786	0.423565
$507$	−14.1803	−0.629771
$508$	−5.70820	−0.253261
$509$	−19.5967	−0.868611	−0.434305	−	0.900766i	$-0.643006\pi$
$509$	−19.5967	−0.868611	−0.434305	+	0.900766i	$0.643006\pi$
$510$	−4.00000	−0.177123
$511$	2.00000	0.0884748
$512$	−18.7082	−0.826794
$513$	−12.3607	−0.545737
$514$	9.85410	0.434646
$515$	1.76393	0.0777281
$516$	6.47214	0.284920
$517$	−12.9443	−0.569288
$518$	−5.23607	−0.230060
$519$	−18.4721	−0.810837
$520$	2.76393	0.121206
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	6.58359	0.288156
$523$	−4.29180	−0.187667	−0.0938336	−	0.995588i	$-0.529912\pi$
$523$	−4.29180	−0.187667	−0.0938336	+	0.995588i	$0.529912\pi$
$524$	−19.4164	−0.848210
$525$	20.9443	0.914083
$526$	11.5967	0.505642
$527$	5.23607	0.228087
$528$	4.58359	0.199475
$529$	36.4164	1.58332
$530$	0.944272	0.0410166
$531$	3.29180	0.142852
$532$	15.3262	0.664477
$533$	8.65248	0.374780
$534$	1.30495	0.0564708
$535$	10.2361	0.442544
$536$	17.8885	0.772667
$537$	−14.4721	−0.624519
$538$	17.8885	0.771230
$539$	21.8885	0.942806
$540$	8.94427	0.384900
$541$	19.3607	0.832381	0.416190	−	0.909278i	$-0.363365\pi$
$541$	19.3607	0.832381	0.416190	+	0.909278i	$0.363365\pi$
$542$	−5.05573	−0.217162
$543$	22.4721	0.964372
$544$	−29.4164	−1.26122
$545$	3.94427	0.168954
$546$	4.00000	0.171184
$547$	28.1246	1.20252	0.601261	−	0.799053i	$-0.294665\pi$
$547$	28.1246	1.20252	0.601261	+	0.799053i	$0.294665\pi$
$548$	−31.8885	−1.36221
$549$	20.8754	0.890940
$550$	4.94427	0.210824
$551$	16.1803	0.689306
$552$	−21.3050	−0.906799
$553$	−7.23607	−0.307709
$554$	−11.5279	−0.489772
$555$	−2.47214	−0.104936
$556$	21.7082	0.920633
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0.909830	0.0385162
$559$	−4.00000	−0.169182
$560$	−7.85410	−0.331896
$561$	12.9443	0.546508
$562$	−10.5066	−0.443193
$563$	−39.5410	−1.66646	−0.833228	−	0.552930i	$-0.813510\pi$
$563$	−39.5410	−1.66646	−0.833228	+	0.552930i	$0.813510\pi$
$564$	12.9443	0.545052
$565$	−5.47214	−0.230214
$566$	−13.5279	−0.568619
$567$	10.2361	0.429874
$568$	29.4721	1.23662
$569$	14.4721	0.606704	0.303352	−	0.952879i	$-0.401894\pi$
$569$	14.4721	0.606704	0.303352	+	0.952879i	$0.401894\pi$
$570$	−1.70820	−0.0715488
$571$	5.81966	0.243545	0.121773	−	0.992558i	$-0.461142\pi$
$571$	5.81966	0.243545	0.121773	+	0.992558i	$0.461142\pi$
$572$	−4.00000	−0.167248
$573$	3.93112	0.164225
$574$	18.3262	0.764922
$575$	30.8328	1.28582
$576$	0.347524	0.0144802
$577$	24.8328	1.03380	0.516902	−	0.856045i	$-0.327085\pi$
$577$	24.8328	1.03380	0.516902	+	0.856045i	$0.327085\pi$
$578$	−6.43769	−0.267773
$579$	−6.76393	−0.281099
$580$	−11.7082	−0.486157
$581$	−12.4721	−0.517431
$582$	−1.48529	−0.0615673
$583$	−3.05573	−0.126555
$584$	−1.05573	−0.0436863
$585$	−1.81966	−0.0752337
$586$	−5.23607	−0.216300
$587$	2.47214	0.102036	0.0510180	−	0.998698i	$-0.483753\pi$
$587$	2.47214	0.102036	0.0510180	+	0.998698i	$0.483753\pi$
$588$	−21.8885	−0.902668
$589$	2.23607	0.0921356
$590$	1.38197	0.0568946
$591$	−19.0557	−0.783848
$592$	−3.70820	−0.152406
$593$	−15.4721	−0.635364	−0.317682	−	0.948197i	$-0.602905\pi$
$593$	−15.4721	−0.635364	−0.317682	+	0.948197i	$0.602905\pi$
$594$	6.83282	0.280354
$595$	−22.1803	−0.909305
$596$	−16.1803	−0.662773
$597$	−1.30495	−0.0534081
$598$	5.88854	0.240800
$599$	34.5967	1.41358	0.706792	−	0.707421i	$-0.250141\pi$
$599$	34.5967	1.41358	0.706792	+	0.707421i	$0.250141\pi$
$600$	−11.0557	−0.451348
$601$	−36.5410	−1.49054	−0.745270	−	0.666763i	$-0.767679\pi$
$601$	−36.5410	−1.49054	−0.745270	+	0.666763i	$0.767679\pi$
$602$	−8.47214	−0.345298
$603$	−11.7771	−0.479600
$604$	−13.2361	−0.538568
$605$	−7.00000	−0.284590
$606$	2.29180	0.0930979
$607$	13.5279	0.549079	0.274540	−	0.961576i	$-0.411475\pi$
$607$	13.5279	0.549079	0.274540	+	0.961576i	$0.411475\pi$
$608$	−12.5623	−0.509469
$609$	−37.8885	−1.53532
$610$	8.76393	0.354841
$611$	−8.00000	−0.323645
$612$	12.4721	0.504156
$613$	−8.11146	−0.327619	−0.163809	−	0.986492i	$-0.552378\pi$
$613$	−8.11146	−0.327619	−0.163809	+	0.986492i	$0.552378\pi$
$614$	9.45085	0.381405
$615$	8.65248	0.348902
$616$	−18.9443	−0.763286
$617$	23.5279	0.947196	0.473598	−	0.880741i	$-0.342955\pi$
$617$	23.5279	0.947196	0.473598	+	0.880741i	$0.342955\pi$
$618$	−1.34752	−0.0542054
$619$	−16.1803	−0.650343	−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803	−0.650343	−0.325171	+	0.945655i	$0.605422\pi$
$620$	−1.61803	−0.0649818
$621$	42.6099	1.70988
$622$	4.21478	0.168997
$623$	7.23607	0.289907
$624$	2.83282	0.113403
$625$	11.0000	0.440000
$626$	−13.1246	−0.524565
$627$	5.52786	0.220762
$628$	24.0902	0.961302
$629$	−10.4721	−0.417551
$630$	−3.85410	−0.153551
$631$	−10.3607	−0.412452	−0.206226	−	0.978504i	$-0.566118\pi$
$631$	−10.3607	−0.412452	−0.206226	+	0.978504i	$0.566118\pi$
$632$	3.81966	0.151938
$633$	1.01316	0.0402693
$634$	−13.5623	−0.538628
$635$	3.52786	0.139999
$636$	3.05573	0.121168
$637$	13.5279	0.535993
$638$	−8.94427	−0.354107
$639$	−19.4033	−0.767581
$640$	11.3820	0.449912
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	−7.81966	−0.308617
$643$	28.4721	1.12283	0.561416	−	0.827534i	$-0.310257\pi$
$643$	28.4721	1.12283	0.561416	+	0.827534i	$0.310257\pi$
$644$	−52.8328	−2.08190
$645$	−4.00000	−0.157500
$646$	−7.23607	−0.284699
$647$	16.9443	0.666148	0.333074	−	0.942901i	$-0.391914\pi$
$647$	16.9443	0.666148	0.333074	+	0.942901i	$0.391914\pi$
$648$	−5.40325	−0.212260
$649$	−4.47214	−0.175547
$650$	3.05573	0.119856
$651$	−5.23607	−0.205218
$652$	4.38197	0.171611
$653$	15.3050	0.598929	0.299465	−	0.954107i	$-0.403192\pi$
$653$	15.3050	0.598929	0.299465	+	0.954107i	$0.403192\pi$
$654$	−3.01316	−0.117824
$655$	12.0000	0.468879
$656$	12.9787	0.506734
$657$	0.695048	0.0271164
$658$	−16.9443	−0.660556
$659$	−5.65248	−0.220189	−0.110095	−	0.993921i	$-0.535115\pi$
$659$	−5.65248	−0.220189	−0.110095	+	0.993921i	$0.535115\pi$
$660$	−4.00000	−0.155700
$661$	−45.3607	−1.76433	−0.882163	−	0.470944i	$-0.843913\pi$
$661$	−45.3607	−1.76433	−0.882163	+	0.470944i	$0.843913\pi$
$662$	−1.23607	−0.0480411
$663$	8.00000	0.310694
$664$	6.58359	0.255493
$665$	−9.47214	−0.367314
$666$	−1.81966	−0.0705104
$667$	−55.7771	−2.15970
$668$	−4.00000	−0.154765
$669$	4.94427	0.191157
$670$	−4.94427	−0.191014
$671$	−28.3607	−1.09485
$672$	29.4164	1.13476
$673$	47.0132	1.81222	0.906112	−	0.423038i	$-0.139036\pi$
$673$	47.0132	1.81222	0.906112	+	0.423038i	$0.139036\pi$
$674$	11.8885	0.457930
$675$	22.1115	0.851070
$676$	18.5623	0.713935
$677$	42.7214	1.64192	0.820958	−	0.570989i	$-0.193440\pi$
$677$	42.7214	1.64192	0.820958	+	0.570989i	$0.193440\pi$
$678$	4.18034	0.160545
$679$	−8.23607	−0.316071
$680$	11.7082	0.448989
$681$	3.05573	0.117096
$682$	−1.23607	−0.0473315
$683$	−17.1803	−0.657387	−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803	−0.657387	−0.328694	+	0.944437i	$0.606608\pi$
$684$	5.32624	0.203654
$685$	19.7082	0.753012
$686$	10.3262	0.394258
$687$	16.5836	0.632704
$688$	−6.00000	−0.228748
$689$	−1.88854	−0.0719478
$690$	5.88854	0.224173
$691$	−19.1803	−0.729655	−0.364827	−	0.931075i	$-0.618872\pi$
$691$	−19.1803	−0.729655	−0.364827	+	0.931075i	$0.618872\pi$
$692$	24.1803	0.919199
$693$	12.4721	0.473777
$694$	−1.12461	−0.0426897
$695$	−13.4164	−0.508913
$696$	20.0000	0.758098
$697$	36.6525	1.38831
$698$	−17.2361	−0.652395
$699$	0.0688837	0.00260542
$700$	−27.4164	−1.03624
$701$	7.00000	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$701$	7.00000	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$702$	4.22291	0.159384
$703$	−4.47214	−0.168670
$704$	−0.472136	−0.0177943
$705$	−8.00000	−0.301297
$706$	12.0000	0.451626
$707$	12.7082	0.477941
$708$	4.47214	0.168073
$709$	34.4721	1.29463	0.647314	−	0.762223i	$-0.275892\pi$
$709$	34.4721	1.29463	0.647314	+	0.762223i	$0.275892\pi$
$710$	−8.14590	−0.305710
$711$	−2.51471	−0.0943089
$712$	−3.81966	−0.143148
$713$	−7.70820	−0.288675
$714$	16.9443	0.634123
$715$	2.47214	0.0924526
$716$	18.9443	0.707981
$717$	2.11146	0.0788538
$718$	−10.9787	−0.409722
$719$	−36.1803	−1.34930	−0.674649	−	0.738138i	$-0.735705\pi$
$719$	−36.1803	−1.34930	−0.674649	+	0.738138i	$0.735705\pi$
$720$	−2.72949	−0.101722
$721$	−7.47214	−0.278277
$722$	8.65248	0.322012
$723$	−37.5279	−1.39568
$724$	−29.4164	−1.09325
$725$	−28.9443	−1.07496
$726$	5.34752	0.198465
$727$	−39.7639	−1.47476	−0.737381	−	0.675477i	$-0.763938\pi$
$727$	−39.7639	−1.47476	−0.737381	+	0.675477i	$0.763938\pi$
$728$	−11.7082	−0.433935
$729$	24.0557	0.890953
$730$	0.291796	0.0107999
$731$	−16.9443	−0.626707
$732$	28.3607	1.04824
$733$	−5.47214	−0.202118	−0.101059	−	0.994880i	$-0.532223\pi$
$733$	−5.47214	−0.202118	−0.101059	+	0.994880i	$0.532223\pi$
$734$	−11.1246	−0.410617
$735$	13.5279	0.498983
$736$	43.3050	1.59624
$737$	16.0000	0.589368
$738$	6.36881	0.234439
$739$	−16.1803	−0.595203	−0.297602	−	0.954690i	$-0.596187\pi$
$739$	−16.1803	−0.595203	−0.297602	+	0.954690i	$0.596187\pi$
$740$	3.23607	0.118960
$741$	3.41641	0.125505
$742$	−4.00000	−0.146845
$743$	27.8197	1.02060	0.510302	−	0.859995i	$-0.329534\pi$
$743$	27.8197	1.02060	0.510302	+	0.859995i	$0.329534\pi$
$744$	2.76393	0.101331
$745$	10.0000	0.366372
$746$	−11.7426	−0.429929
$747$	−4.33437	−0.158586
$748$	−16.9443	−0.619544
$749$	−43.3607	−1.58436
$750$	6.87539	0.251054
$751$	45.5410	1.66182	0.830908	−	0.556410i	$-0.187822\pi$
$751$	45.5410	1.66182	0.830908	+	0.556410i	$0.187822\pi$
$752$	−12.0000	−0.437595
$753$	−29.8885	−1.08920
$754$	−5.52786	−0.201313
$755$	8.18034	0.297713
$756$	−37.8885	−1.37799
$757$	−22.6525	−0.823318	−0.411659	−	0.911338i	$-0.635051\pi$
$757$	−22.6525	−0.823318	−0.411659	+	0.911338i	$0.635051\pi$
$758$	23.4164	0.850522
$759$	−19.0557	−0.691679
$760$	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	$0.488459\pi$
$762$	−2.69505	−0.0976313
$763$	−16.7082	−0.604878
$764$	−5.14590	−0.186172
$765$	−7.70820	−0.278691
$766$	−7.34752	−0.265477
$767$	−2.76393	−0.0997998
$768$	−8.11146	−0.292697
$769$	−2.63932	−0.0951763	−0.0475882	−	0.998867i	$-0.515154\pi$
$769$	−2.63932	−0.0951763	−0.0475882	+	0.998867i	$0.515154\pi$
$770$	5.23607	0.188695
$771$	−19.7082	−0.709774
$772$	8.85410	0.318666
$773$	29.1246	1.04754	0.523770	−	0.851860i	$-0.324525\pi$
$773$	29.1246	1.04754	0.523770	+	0.851860i	$0.324525\pi$
$774$	−2.94427	−0.105830
$775$	−4.00000	−0.143684
$776$	4.34752	0.156067
$777$	10.4721	0.375686
$778$	−11.0557	−0.396367
$779$	15.6525	0.560808
$780$	−2.47214	−0.0885167
$781$	26.3607	0.943259
$782$	24.9443	0.892005
$783$	−40.0000	−1.42948
$784$	20.2918	0.724707
$785$	−14.8885	−0.531395
$786$	−9.16718	−0.326983
$787$	38.6525	1.37781	0.688906	−	0.724851i	$-0.258091\pi$
$787$	38.6525	1.37781	0.688906	+	0.724851i	$0.258091\pi$
$788$	24.9443	0.888603
$789$	−23.1935	−0.825710
$790$	−1.05573	−0.0375611
$791$	23.1803	0.824198
$792$	−6.58359	−0.233938
$793$	−17.5279	−0.622433
$794$	4.32624	0.153532
$795$	−1.88854	−0.0669797
$796$	1.70820	0.0605457
$797$	−28.5836	−1.01248	−0.506241	−	0.862392i	$-0.668966\pi$
$797$	−28.5836	−1.01248	−0.506241	+	0.862392i	$0.668966\pi$
$798$	7.23607	0.256154
$799$	−33.8885	−1.19889
$800$	22.4721	0.794510
$801$	2.51471	0.0888529
$802$	−9.77709	−0.345241
$803$	−0.944272	−0.0333226
$804$	−16.0000	−0.564276
$805$	32.6525	1.15085
$806$	−0.763932	−0.0269084
$807$	−35.7771	−1.25941
$808$	−6.70820	−0.235994
$809$	−3.41641	−0.120115	−0.0600573	−	0.998195i	$-0.519128\pi$
$809$	−3.41641	−0.120115	−0.0600573	+	0.998195i	$0.519128\pi$
$810$	1.49342	0.0524735
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	49.5967	1.74050
$813$	10.1115	0.354624
$814$	2.47214	0.0866483
$815$	−2.70820	−0.0948642
$816$	12.0000	0.420084
$817$	−7.23607	−0.253158
$818$	16.1803	0.565732
$819$	7.70820	0.269346
$820$	−11.3262	−0.395529
$821$	−36.5410	−1.27529	−0.637645	−	0.770330i	$-0.720091\pi$
$821$	−36.5410	−1.27529	−0.637645	+	0.770330i	$0.720091\pi$
$822$	−15.0557	−0.525129
$823$	−27.7082	−0.965847	−0.482924	−	0.875662i	$-0.660425\pi$
$823$	−27.7082	−0.965847	−0.482924	+	0.875662i	$0.660425\pi$
$824$	3.94427	0.137405
$825$	−9.88854	−0.344275
$826$	−5.85410	−0.203690
$827$	48.6525	1.69181	0.845906	−	0.533332i	$-0.179060\pi$
$827$	48.6525	1.69181	0.845906	+	0.533332i	$0.179060\pi$
$828$	−18.3607	−0.638078
$829$	−36.8328	−1.27926	−0.639628	−	0.768684i	$-0.720912\pi$
$829$	−36.8328	−1.27926	−0.639628	+	0.768684i	$0.720912\pi$
$830$	−1.81966	−0.0631613
$831$	23.0557	0.799794
$832$	−0.291796	−0.0101162
$833$	57.3050	1.98550
$834$	10.2492	0.354902
$835$	2.47214	0.0855518
$836$	−7.23607	−0.250265
$837$	−5.52786	−0.191071
$838$	−18.6180	−0.643149
$839$	11.0557	0.381686	0.190843	−	0.981621i	$-0.438878\pi$
$839$	11.0557	0.381686	0.190843	+	0.981621i	$0.438878\pi$
$840$	−11.7082	−0.403971
$841$	23.3607	0.805541
$842$	9.49342	0.327165
$843$	21.0132	0.723732
$844$	−1.32624	−0.0456510
$845$	−11.4721	−0.394653
$846$	−5.88854	−0.202452
$847$	29.6525	1.01887
$848$	−2.83282	−0.0972793
$849$	27.0557	0.928550
$850$	12.9443	0.443985
$851$	15.4164	0.528468
$852$	−26.3607	−0.903102
$853$	37.4164	1.28111	0.640557	−	0.767911i	$-0.278704\pi$
$853$	37.4164	1.28111	0.640557	+	0.767911i	$0.278704\pi$
$854$	−37.1246	−1.27038
$855$	−3.29180	−0.112577
$856$	22.8885	0.782314
$857$	51.6656	1.76486	0.882432	−	0.470440i	$-0.155905\pi$
$857$	51.6656	1.76486	0.882432	+	0.470440i	$0.155905\pi$
$858$	−1.88854	−0.0644738
$859$	37.8885	1.29274	0.646370	−	0.763024i	$-0.276286\pi$
$859$	37.8885	1.29274	0.646370	+	0.763024i	$0.276286\pi$
$860$	5.23607	0.178548
$861$	−36.6525	−1.24911
$862$	−7.41641	−0.252604
$863$	−32.1803	−1.09543	−0.547716	−	0.836664i	$-0.684502\pi$
$863$	−32.1803	−1.09543	−0.547716	+	0.836664i	$0.684502\pi$
$864$	31.0557	1.05654
$865$	−14.9443	−0.508120
$866$	7.52786	0.255807
$867$	12.8754	0.437271
$868$	6.85410	0.232643
$869$	3.41641	0.115894
$870$	−5.52786	−0.187412
$871$	9.88854	0.335061
$872$	8.81966	0.298671
$873$	−2.86223	−0.0968719
$874$	10.6525	0.360325
$875$	38.1246	1.28885
$876$	0.944272	0.0319040
$877$	−35.9443	−1.21375	−0.606876	−	0.794797i	$-0.707578\pi$
$877$	−35.9443	−1.21375	−0.606876	+	0.794797i	$0.707578\pi$
$878$	−13.0902	−0.441772
$879$	10.4721	0.353216
$880$	3.70820	0.125004
$881$	24.3607	0.820732	0.410366	−	0.911921i	$-0.365401\pi$
$881$	24.3607	0.820732	0.410366	+	0.911921i	$0.365401\pi$
$882$	9.95743	0.335284
$883$	39.7771	1.33861	0.669303	−	0.742990i	$-0.266593\pi$
$883$	39.7771	1.33861	0.669303	+	0.742990i	$0.266593\pi$
$884$	−10.4721	−0.352216
$885$	−2.76393	−0.0929086
$886$	−10.6869	−0.359034
$887$	−31.0689	−1.04319	−0.521596	−	0.853193i	$-0.674663\pi$
$887$	−31.0689	−1.04319	−0.521596	+	0.853193i	$0.674663\pi$
$888$	−5.52786	−0.185503
$889$	−14.9443	−0.501215
$890$	1.05573	0.0353881
$891$	−4.83282	−0.161905
$892$	−6.47214	−0.216703
$893$	−14.4721	−0.484292
$894$	−7.63932	−0.255497
$895$	−11.7082	−0.391362
$896$	−48.2148	−1.61074
$897$	−11.7771	−0.393226
$898$	−19.3475	−0.645635
$899$	7.23607	0.241336
$900$	−9.52786	−0.317595
$901$	−8.00000	−0.266519
$902$	−8.65248	−0.288096
$903$	16.9443	0.563870
$904$	−12.2361	−0.406966
$905$	18.1803	0.604335
$906$	−6.24922	−0.207617
$907$	−19.7639	−0.656251	−0.328125	−	0.944634i	$-0.606417\pi$
$907$	−19.7639	−0.656251	−0.328125	+	0.944634i	$0.606417\pi$
$908$	−4.00000	−0.132745
$909$	4.41641	0.146483
$910$	3.23607	0.107275
$911$	−4.18034	−0.138501	−0.0692504	−	0.997599i	$-0.522061\pi$
$911$	−4.18034	−0.138501	−0.0692504	+	0.997599i	$0.522061\pi$
$912$	5.12461	0.169693
$913$	5.88854	0.194882
$914$	12.9443	0.428158
$915$	−17.5279	−0.579453
$916$	−21.7082	−0.717259
$917$	−50.8328	−1.67865
$918$	17.8885	0.590410
$919$	−5.52786	−0.182347	−0.0911737	−	0.995835i	$-0.529062\pi$
$919$	−5.52786	−0.182347	−0.0911737	+	0.995835i	$0.529062\pi$
$920$	−17.2361	−0.568256
$921$	−18.9017	−0.622832
$922$	6.40325	0.210880
$923$	16.2918	0.536251
$924$	16.9443	0.557426
$925$	8.00000	0.263038
$926$	18.1803	0.597443
$927$	−2.59675	−0.0852884
$928$	−40.6525	−1.33448
$929$	−20.0000	−0.656179	−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000	−0.656179	−0.328089	+	0.944647i	$0.606405\pi$
$930$	−0.763932	−0.0250503
$931$	24.4721	0.802042
$932$	−0.0901699	−0.00295361
$933$	−8.42956	−0.275972
$934$	5.38197	0.176103
$935$	10.4721	0.342475
$936$	−4.06888	−0.132996
$937$	26.9443	0.880231	0.440115	−	0.897941i	$-0.354937\pi$
$937$	26.9443	0.880231	0.440115	+	0.897941i	$0.354937\pi$
$938$	20.9443	0.683855
$939$	26.2492	0.856611
$940$	10.4721	0.341563
$941$	−38.0000	−1.23876	−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000	−1.23876	−0.619382	+	0.785090i	$0.712617\pi$
$942$	11.3738	0.370580
$943$	−53.9574	−1.75710
$944$	−4.14590	−0.134937
$945$	23.4164	0.761736
$946$	4.00000	0.130051
$947$	−30.9443	−1.00555	−0.502777	−	0.864416i	$-0.667688\pi$
$947$	−30.9443	−1.00555	−0.502777	+	0.864416i	$0.667688\pi$
$948$	−3.41641	−0.110960
$949$	−0.583592	−0.0189442
$950$	5.52786	0.179348
$951$	27.1246	0.879576
$952$	−49.5967	−1.60744
$953$	32.2918	1.04603	0.523017	−	0.852322i	$-0.324806\pi$
$953$	32.2918	1.04603	0.523017	+	0.852322i	$0.324806\pi$
$954$	−1.39010	−0.0450060
$955$	3.18034	0.102913
$956$	−2.76393	−0.0893920
$957$	17.8885	0.578254
$958$	−22.6869	−0.732981
$959$	−83.4853	−2.69588
$960$	−0.291796	−0.00941768
$961$	1.00000	0.0322581
$962$	1.52786	0.0492603
$963$	−15.0689	−0.485588
$964$	49.1246	1.58220
$965$	−5.47214	−0.176154
$966$	−24.9443	−0.802569
$967$	15.6393	0.502927	0.251463	−	0.967867i	$-0.419088\pi$
$967$	15.6393	0.502927	0.251463	+	0.967867i	$0.419088\pi$
$968$	−15.6525	−0.503090
$969$	14.4721	0.464912
$970$	−1.20163	−0.0385819
$971$	−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
$973$	56.8328	1.82198
$974$	9.12461	0.292371
$975$	−6.11146	−0.195723
$976$	−26.2918	−0.841580
$977$	33.2492	1.06374	0.531868	−	0.846827i	$-0.321490\pi$
$977$	33.2492	1.06374	0.531868	+	0.846827i	$0.321490\pi$
$978$	2.06888	0.0661556
$979$	−3.41641	−0.109189
$980$	−17.7082	−0.565668
$981$	−5.80650	−0.185387
$982$	24.9443	0.796004
$983$	48.4721	1.54602	0.773011	−	0.634393i	$-0.218750\pi$
$983$	48.4721	1.54602	0.773011	+	0.634393i	$0.218750\pi$
$984$	19.3475	0.616777
$985$	−15.4164	−0.491208
$986$	−23.4164	−0.745730
$987$	33.8885	1.07868
$988$	−4.47214	−0.142278
$989$	24.9443	0.793182
$990$	1.81966	0.0578326
$991$	50.5410	1.60549	0.802744	−	0.596324i	$-0.203372\pi$
$991$	50.5410	1.60549	0.802744	+	0.596324i	$0.203372\pi$
$992$	−5.61803	−0.178373
$993$	2.47214	0.0784509
$994$	34.5066	1.09448
$995$	−1.05573	−0.0334688
$996$	−5.88854	−0.186586
$997$	15.3607	0.486478	0.243239	−	0.969966i	$-0.421790\pi$
$997$	15.3607	0.486478	0.243239	+	0.969966i	$0.421790\pi$
$998$	20.6525	0.653743
$999$	11.0557	0.349788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.a.a.1.1	✓	2
3.2	odd	2		279.2.a.a.1.2		2
4.3	odd	2		496.2.a.i.1.1		2
5.2	odd	4		775.2.b.d.249.2		4
5.3	odd	4		775.2.b.d.249.3		4
5.4	even	2		775.2.a.d.1.2		2
7.6	odd	2		1519.2.a.a.1.1		2
8.3	odd	2		1984.2.a.n.1.2		2
8.5	even	2		1984.2.a.r.1.1		2
11.10	odd	2		3751.2.a.b.1.2		2
12.11	even	2		4464.2.a.bf.1.2		2
13.12	even	2		5239.2.a.f.1.2		2
15.14	odd	2		6975.2.a.y.1.1		2
17.16	even	2		8959.2.a.b.1.1		2
31.2	even	5		961.2.d.c.531.1		4
31.3	odd	30		961.2.g.d.846.1		8
31.4	even	5		961.2.d.d.388.1		4
31.5	even	3		961.2.c.e.521.1		4
31.6	odd	6		961.2.c.c.439.1		4
31.7	even	15		961.2.g.h.235.1		8
31.8	even	5		961.2.d.d.374.1		4
31.9	even	15		961.2.g.h.732.1		8
31.10	even	15		961.2.g.a.844.1		8
31.11	odd	30		961.2.g.e.338.1		8
31.12	odd	30		961.2.g.d.547.1		8
31.13	odd	30		961.2.g.d.448.1		8
31.14	even	15		961.2.g.h.816.1		8
31.15	odd	10		961.2.d.a.628.1		4
31.16	even	5		961.2.d.c.628.1		4
31.17	odd	30		961.2.g.e.816.1		8
31.18	even	15		961.2.g.a.448.1		8
31.19	even	15		961.2.g.a.547.1		8
31.20	even	15		961.2.g.h.338.1		8
31.21	odd	30		961.2.g.d.844.1		8
31.22	odd	30		961.2.g.e.732.1		8
31.23	odd	10		961.2.d.g.374.1		4
31.24	odd	30		961.2.g.e.235.1		8
31.25	even	3		961.2.c.e.439.1		4
31.26	odd	6		961.2.c.c.521.1		4
31.27	odd	10		961.2.d.g.388.1		4
31.28	even	15		961.2.g.a.846.1		8
31.29	odd	10		961.2.d.a.531.1		4
31.30	odd	2		961.2.a.f.1.1		2
93.92	even	2		8649.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	1.1	even	1	trivial
279.2.a.a.1.2		2	3.2	odd	2
496.2.a.i.1.1		2	4.3	odd	2
775.2.a.d.1.2		2	5.4	even	2
775.2.b.d.249.2		4	5.2	odd	4
775.2.b.d.249.3		4	5.3	odd	4
961.2.a.f.1.1		2	31.30	odd	2
961.2.c.c.439.1		4	31.6	odd	6
961.2.c.c.521.1		4	31.26	odd	6
961.2.c.e.439.1		4	31.25	even	3
961.2.c.e.521.1		4	31.5	even	3
961.2.d.a.531.1		4	31.29	odd	10
961.2.d.a.628.1		4	31.15	odd	10
961.2.d.c.531.1		4	31.2	even	5
961.2.d.c.628.1		4	31.16	even	5
961.2.d.d.374.1		4	31.8	even	5
961.2.d.d.388.1		4	31.4	even	5
961.2.d.g.374.1		4	31.23	odd	10
961.2.d.g.388.1		4	31.27	odd	10
961.2.g.a.448.1		8	31.18	even	15
961.2.g.a.547.1		8	31.19	even	15
961.2.g.a.844.1		8	31.10	even	15
961.2.g.a.846.1		8	31.28	even	15
961.2.g.d.448.1		8	31.13	odd	30
961.2.g.d.547.1		8	31.12	odd	30
961.2.g.d.844.1		8	31.21	odd	30
961.2.g.d.846.1		8	31.3	odd	30
961.2.g.e.235.1		8	31.24	odd	30
961.2.g.e.338.1		8	31.11	odd	30
961.2.g.e.732.1		8	31.22	odd	30
961.2.g.e.816.1		8	31.17	odd	30
961.2.g.h.235.1		8	31.7	even	15
961.2.g.h.338.1		8	31.20	even	15
961.2.g.h.732.1		8	31.9	even	15
961.2.g.h.816.1		8	31.14	even	15
1519.2.a.a.1.1		2	7.6	odd	2
1984.2.a.n.1.2		2	8.3	odd	2
1984.2.a.r.1.1		2	8.5	even	2
3751.2.a.b.1.2		2	11.10	odd	2
4464.2.a.bf.1.2		2	12.11	even	2
5239.2.a.f.1.2		2	13.12	even	2
6975.2.a.y.1.1		2	15.14	odd	2
8649.2.a.c.1.2		2	93.92	even	2
8959.2.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +1.23607 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.763932 q^{6} -4.23607 q^{7} +2.23607 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +1.23607 q^{3} -1.61803 q^{4} +1.00000 q^{5} -0.763932 q^{6} -4.23607 q^{7} +2.23607 q^{8} -1.47214 q^{9} -0.618034 q^{10} +2.00000 q^{11} -2.00000 q^{12} +1.23607 q^{13} +2.61803 q^{14} +1.23607 q^{15} +1.85410 q^{16} +5.23607 q^{17} +0.909830 q^{18} +2.23607 q^{19} -1.61803 q^{20} -5.23607 q^{21} -1.23607 q^{22} -7.70820 q^{23} +2.76393 q^{24} -4.00000 q^{25} -0.763932 q^{26} -5.52786 q^{27} +6.85410 q^{28} +7.23607 q^{29} -0.763932 q^{30} +1.00000 q^{31} -5.61803 q^{32} +2.47214 q^{33} -3.23607 q^{34} -4.23607 q^{35} +2.38197 q^{36} -2.00000 q^{37} -1.38197 q^{38} +1.52786 q^{39} +2.23607 q^{40} +7.00000 q^{41} +3.23607 q^{42} -3.23607 q^{43} -3.23607 q^{44} -1.47214 q^{45} +4.76393 q^{46} -6.47214 q^{47} +2.29180 q^{48} +10.9443 q^{49} +2.47214 q^{50} +6.47214 q^{51} -2.00000 q^{52} -1.52786 q^{53} +3.41641 q^{54} +2.00000 q^{55} -9.47214 q^{56} +2.76393 q^{57} -4.47214 q^{58} -2.23607 q^{59} -2.00000 q^{60} -14.1803 q^{61} -0.618034 q^{62} +6.23607 q^{63} -0.236068 q^{64} +1.23607 q^{65} -1.52786 q^{66} +8.00000 q^{67} -8.47214 q^{68} -9.52786 q^{69} +2.61803 q^{70} +13.1803 q^{71} -3.29180 q^{72} -0.472136 q^{73} +1.23607 q^{74} -4.94427 q^{75} -3.61803 q^{76} -8.47214 q^{77} -0.944272 q^{78} +1.70820 q^{79} +1.85410 q^{80} -2.41641 q^{81} -4.32624 q^{82} +2.94427 q^{83} +8.47214 q^{84} +5.23607 q^{85} +2.00000 q^{86} +8.94427 q^{87} +4.47214 q^{88} -1.70820 q^{89} +0.909830 q^{90} -5.23607 q^{91} +12.4721 q^{92} +1.23607 q^{93} +4.00000 q^{94} +2.23607 q^{95} -6.94427 q^{96} +1.94427 q^{97} -6.76393 q^{98} -2.94427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 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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