Properties

Label 234.2.h.d.55.2
Level 234234
Weight 22
Character 234.55
Analytic conductor 1.8681.868
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [234,2,Mod(55,234)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(234, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("234.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 234=23213 234 = 2 \cdot 3^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 234.h (of order 33, degree 22, minimal)

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: no
Analytic conductor: 1.868499407301.86849940730
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(3,10)\Q(\sqrt{-3}, \sqrt{10})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+10x2+100 x^{4} + 10x^{2} + 100 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 55.2
Root 1.58114+2.73861i-1.58114 + 2.73861i of defining polynomial
Character χ\chi == 234.55
Dual form 234.2.h.d.217.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5000000.866025i)q2+(0.500000+0.866025i)q4+4.16228q5+(1.58114+2.73861i)q7+1.00000q8+(2.081143.60464i)q10+(0.581139+1.00656i)q11+(0.0811388+3.60464i)q13+3.16228q14+(0.5000000.866025i)q16+(1.500002.59808i)q17+(2.581144.47066i)q19+(2.08114+3.60464i)q20+(0.5811391.00656i)q22+(3.581146.20271i)q23+12.3246q25+(3.081141.87259i)q26+(1.581142.73861i)q28+(0.918861+1.59151i)q296.32456q31+(0.500000+0.866025i)q323.00000q34+(6.58114+11.3989i)q35+(1.918863.32357i)q375.16228q38+4.16228q40+(1.500002.59808i)q41+(4.58114+7.93477i)q431.16228q44+(3.58114+6.20271i)q46+4.83772q47+(1.500002.59808i)q49+(6.1622810.6734i)q50+(3.162281.73205i)q5212.4868q53+(2.41886+4.18959i)q55+(1.58114+2.73861i)q56+(0.9188611.59151i)q58+(1.162282.01312i)q59+(0.0811388+0.140537i)q61+(3.16228+5.47723i)q62+1.00000q64+(0.337722+15.0035i)q65+(1.41886+2.45754i)q67+(1.50000+2.59808i)q68+13.1623q70+(3.581146.20271i)q711.00000q73+(1.91886+3.32357i)q74+(2.58114+4.47066i)q763.67544q774.00000q79+(2.081143.60464i)q80+(1.50000+2.59808i)q823.48683q83+(6.2434210.8139i)q85+9.16228q86+(0.581139+1.00656i)q88+(6.0000010.3923i)q89+(10.00005.47723i)q91+7.16228q92+(2.418864.18959i)q94+(10.743418.6081i)q95+(2.000003.46410i)q97+(1.50000+2.59808i)q98+O(q100)q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +1.00000 q^{8} +(-2.08114 - 3.60464i) q^{10} +(0.581139 + 1.00656i) q^{11} +(0.0811388 + 3.60464i) q^{13} +3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(2.58114 - 4.47066i) q^{19} +(-2.08114 + 3.60464i) q^{20} +(0.581139 - 1.00656i) q^{22} +(-3.58114 - 6.20271i) q^{23} +12.3246 q^{25} +(3.08114 - 1.87259i) q^{26} +(-1.58114 - 2.73861i) q^{28} +(0.918861 + 1.59151i) q^{29} -6.32456 q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-6.58114 + 11.3989i) q^{35} +(-1.91886 - 3.32357i) q^{37} -5.16228 q^{38} +4.16228 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-4.58114 + 7.93477i) q^{43} -1.16228 q^{44} +(-3.58114 + 6.20271i) q^{46} +4.83772 q^{47} +(-1.50000 - 2.59808i) q^{49} +(-6.16228 - 10.6734i) q^{50} +(-3.16228 - 1.73205i) q^{52} -12.4868 q^{53} +(2.41886 + 4.18959i) q^{55} +(-1.58114 + 2.73861i) q^{56} +(0.918861 - 1.59151i) q^{58} +(1.16228 - 2.01312i) q^{59} +(-0.0811388 + 0.140537i) q^{61} +(3.16228 + 5.47723i) q^{62} +1.00000 q^{64} +(0.337722 + 15.0035i) q^{65} +(1.41886 + 2.45754i) q^{67} +(1.50000 + 2.59808i) q^{68} +13.1623 q^{70} +(3.58114 - 6.20271i) q^{71} -1.00000 q^{73} +(-1.91886 + 3.32357i) q^{74} +(2.58114 + 4.47066i) q^{76} -3.67544 q^{77} -4.00000 q^{79} +(-2.08114 - 3.60464i) q^{80} +(-1.50000 + 2.59808i) q^{82} -3.48683 q^{83} +(6.24342 - 10.8139i) q^{85} +9.16228 q^{86} +(0.581139 + 1.00656i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-10.0000 - 5.47723i) q^{91} +7.16228 q^{92} +(-2.41886 - 4.18959i) q^{94} +(10.7434 - 18.6081i) q^{95} +(2.00000 - 3.46410i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q22q4+4q5+4q82q104q116q132q16+6q17+4q192q204q228q23+24q25+6q26+10q292q3212q3420q35+6q98+O(q100) 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{16} + 6 q^{17} + 4 q^{19} - 2 q^{20} - 4 q^{22} - 8 q^{23} + 24 q^{25} + 6 q^{26} + 10 q^{29} - 2 q^{32} - 12 q^{34} - 20 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/234Z)×\left(\mathbb{Z}/234\mathbb{Z}\right)^\times.

nn 145145 209209
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.500000 0.866025i −0.353553 0.612372i
33 0 0
44 −0.500000 + 0.866025i −0.250000 + 0.433013i
55 4.16228 1.86143 0.930714 0.365749i 0.119187π-0.119187\pi
0.930714 + 0.365749i 0.119187π0.119187\pi
66 0 0
77 −1.58114 + 2.73861i −0.597614 + 1.03510i 0.395558 + 0.918441i 0.370551π0.370551\pi
−0.993172 + 0.116657i 0.962782π0.962782\pi
88 1.00000 0.353553
99 0 0
1010 −2.08114 3.60464i −0.658114 1.13989i
1111 0.581139 + 1.00656i 0.175220 + 0.303490i 0.940237 0.340520i 0.110603π-0.110603\pi
−0.765017 + 0.644010i 0.777270π0.777270\pi
1212 0 0
1313 0.0811388 + 3.60464i 0.0225039 + 0.999747i
1414 3.16228 0.845154
1515 0 0
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i 0.714811π-0.714811\pi
0.988583 + 0.150675i 0.0481447π0.0481447\pi
1818 0 0
1919 2.58114 4.47066i 0.592154 1.02564i −0.401788 0.915733i 0.631611π-0.631611\pi
0.993942 0.109908i 0.0350556π-0.0350556\pi
2020 −2.08114 + 3.60464i −0.465357 + 0.806022i
2121 0 0
2222 0.581139 1.00656i 0.123899 0.214600i
2323 −3.58114 6.20271i −0.746719 1.29336i −0.949387 0.314108i 0.898295π-0.898295\pi
0.202668 0.979247i 0.435039π-0.435039\pi
2424 0 0
2525 12.3246 2.46491
2626 3.08114 1.87259i 0.604261 0.367245i
2727 0 0
2828 −1.58114 2.73861i −0.298807 0.517549i
2929 0.918861 + 1.59151i 0.170628 + 0.295537i 0.938640 0.344899i 0.112087π-0.112087\pi
−0.768011 + 0.640436i 0.778754π0.778754\pi
3030 0 0
3131 −6.32456 −1.13592 −0.567962 0.823055i 0.692268π-0.692268\pi
−0.567962 + 0.823055i 0.692268π0.692268\pi
3232 −0.500000 + 0.866025i −0.0883883 + 0.153093i
3333 0 0
3434 −3.00000 −0.514496
3535 −6.58114 + 11.3989i −1.11242 + 1.92676i
3636 0 0
3737 −1.91886 3.32357i −0.315459 0.546391i 0.664076 0.747665i 0.268825π-0.268825\pi
−0.979535 + 0.201274i 0.935492π0.935492\pi
3838 −5.16228 −0.837432
3939 0 0
4040 4.16228 0.658114
4141 −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i 0.241934π-0.241934\pi
−0.959058 + 0.283211i 0.908600π0.908600\pi
4242 0 0
4343 −4.58114 + 7.93477i −0.698617 + 1.21004i 0.270329 + 0.962768i 0.412868π0.412868\pi
−0.968946 + 0.247272i 0.920466π0.920466\pi
4444 −1.16228 −0.175220
4545 0 0
4646 −3.58114 + 6.20271i −0.528010 + 0.914540i
4747 4.83772 0.705654 0.352827 0.935689i 0.385220π-0.385220\pi
0.352827 + 0.935689i 0.385220π0.385220\pi
4848 0 0
4949 −1.50000 2.59808i −0.214286 0.371154i
5050 −6.16228 10.6734i −0.871478 1.50944i
5151 0 0
5252 −3.16228 1.73205i −0.438529 0.240192i
5353 −12.4868 −1.71520 −0.857599 0.514319i 0.828045π-0.828045\pi
−0.857599 + 0.514319i 0.828045π0.828045\pi
5454 0 0
5555 2.41886 + 4.18959i 0.326159 + 0.564924i
5656 −1.58114 + 2.73861i −0.211289 + 0.365963i
5757 0 0
5858 0.918861 1.59151i 0.120652 0.208976i
5959 1.16228 2.01312i 0.151316 0.262086i −0.780396 0.625286i 0.784982π-0.784982\pi
0.931711 + 0.363200i 0.118316π0.118316\pi
6060 0 0
6161 −0.0811388 + 0.140537i −0.0103888 + 0.0179939i −0.871173 0.490976i 0.836640π-0.836640\pi
0.860784 + 0.508970i 0.169974π0.169974\pi
6262 3.16228 + 5.47723i 0.401610 + 0.695608i
6363 0 0
6464 1.00000 0.125000
6565 0.337722 + 15.0035i 0.0418893 + 1.86096i
6666 0 0
6767 1.41886 + 2.45754i 0.173341 + 0.300236i 0.939586 0.342313i 0.111210π-0.111210\pi
−0.766245 + 0.642549i 0.777877π0.777877\pi
6868 1.50000 + 2.59808i 0.181902 + 0.315063i
6969 0 0
7070 13.1623 1.57319
7171 3.58114 6.20271i 0.425003 0.736127i −0.571418 0.820659i 0.693606π-0.693606\pi
0.996421 + 0.0845326i 0.0269397π0.0269397\pi
7272 0 0
7373 −1.00000 −0.117041 −0.0585206 0.998286i 0.518638π-0.518638\pi
−0.0585206 + 0.998286i 0.518638π0.518638\pi
7474 −1.91886 + 3.32357i −0.223063 + 0.386357i
7575 0 0
7676 2.58114 + 4.47066i 0.296077 + 0.512820i
7777 −3.67544 −0.418856
7878 0 0
7979 −4.00000 −0.450035 −0.225018 0.974355i 0.572244π-0.572244\pi
−0.225018 + 0.974355i 0.572244π0.572244\pi
8080 −2.08114 3.60464i −0.232678 0.403011i
8181 0 0
8282 −1.50000 + 2.59808i −0.165647 + 0.286910i
8383 −3.48683 −0.382730 −0.191365 0.981519i 0.561291π-0.561291\pi
−0.191365 + 0.981519i 0.561291π0.561291\pi
8484 0 0
8585 6.24342 10.8139i 0.677194 1.17293i
8686 9.16228 0.987994
8787 0 0
8888 0.581139 + 1.00656i 0.0619496 + 0.107300i
8989 −6.00000 10.3923i −0.635999 1.10158i −0.986303 0.164946i 0.947255π-0.947255\pi
0.350304 0.936636i 0.386078π-0.386078\pi
9090 0 0
9191 −10.0000 5.47723i −1.04828 0.574169i
9292 7.16228 0.746719
9393 0 0
9494 −2.41886 4.18959i −0.249486 0.432123i
9595 10.7434 18.6081i 1.10225 1.90916i
9696 0 0
9797 2.00000 3.46410i 0.203069 0.351726i −0.746447 0.665445i 0.768242π-0.768242\pi
0.949516 + 0.313719i 0.101575π0.101575\pi
9898 −1.50000 + 2.59808i −0.151523 + 0.262445i
9999 0 0
100100 −6.16228 + 10.6734i −0.616228 + 1.06734i
101101 −3.91886 6.78767i −0.389941 0.675398i 0.602500 0.798119i 0.294171π-0.294171\pi
−0.992441 + 0.122721i 0.960838π0.960838\pi
102102 0 0
103103 −15.8114 −1.55794 −0.778971 0.627060i 0.784258π-0.784258\pi
−0.778971 + 0.627060i 0.784258π0.784258\pi
104104 0.0811388 + 3.60464i 0.00795632 + 0.353464i
105105 0 0
106106 6.24342 + 10.8139i 0.606414 + 1.05034i
107107 8.90569 + 15.4251i 0.860946 + 1.49120i 0.871017 + 0.491253i 0.163461π0.163461\pi
−0.0100711 + 0.999949i 0.503206π0.503206\pi
108108 0 0
109109 6.64911 0.636869 0.318435 0.947945i 0.396843π-0.396843\pi
0.318435 + 0.947945i 0.396843π0.396843\pi
110110 2.41886 4.18959i 0.230629 0.399462i
111111 0 0
112112 3.16228 0.298807
113113 −3.33772 + 5.78110i −0.313987 + 0.543841i −0.979222 0.202793i 0.934998π-0.934998\pi
0.665235 + 0.746634i 0.268331π0.268331\pi
114114 0 0
115115 −14.9057 25.8174i −1.38996 2.40749i
116116 −1.83772 −0.170628
117117 0 0
118118 −2.32456 −0.213993
119119 4.74342 + 8.21584i 0.434828 + 0.753145i
120120 0 0
121121 4.82456 8.35637i 0.438596 0.759670i
122122 0.162278 0.0146919
123123 0 0
124124 3.16228 5.47723i 0.283981 0.491869i
125125 30.4868 2.72683
126126 0 0
127127 9.16228 + 15.8695i 0.813021 + 1.40819i 0.910740 + 0.412979i 0.135512π0.135512\pi
−0.0977198 + 0.995214i 0.531155π0.531155\pi
128128 −0.500000 0.866025i −0.0441942 0.0765466i
129129 0 0
130130 12.8246 7.79423i 1.12479 0.683599i
131131 16.6491 1.45464 0.727320 0.686299i 0.240766π-0.240766\pi
0.727320 + 0.686299i 0.240766π0.240766\pi
132132 0 0
133133 8.16228 + 14.1375i 0.707759 + 1.22587i
134134 1.41886 2.45754i 0.122571 0.212299i
135135 0 0
136136 1.50000 2.59808i 0.128624 0.222783i
137137 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i 0.792428π-0.792428\pi
0.922961 + 0.384893i 0.125762π0.125762\pi
138138 0 0
139139 3.16228 5.47723i 0.268221 0.464572i −0.700182 0.713965i 0.746898π-0.746898\pi
0.968402 + 0.249393i 0.0802310π0.0802310\pi
140140 −6.58114 11.3989i −0.556208 0.963380i
141141 0 0
142142 −7.16228 −0.601045
143143 −3.58114 + 2.17647i −0.299470 + 0.182005i
144144 0 0
145145 3.82456 + 6.62432i 0.317612 + 0.550120i
146146 0.500000 + 0.866025i 0.0413803 + 0.0716728i
147147 0 0
148148 3.83772 0.315459
149149 −0.243416 + 0.421610i −0.0199415 + 0.0345396i −0.875824 0.482631i 0.839681π-0.839681\pi
0.855882 + 0.517170i 0.173015π0.173015\pi
150150 0 0
151151 0.837722 0.0681729 0.0340864 0.999419i 0.489148π-0.489148\pi
0.0340864 + 0.999419i 0.489148π0.489148\pi
152152 2.58114 4.47066i 0.209358 0.362619i
153153 0 0
154154 1.83772 + 3.18303i 0.148088 + 0.256496i
155155 −26.3246 −2.11444
156156 0 0
157157 −10.4868 −0.836940 −0.418470 0.908231i 0.637434π-0.637434\pi
−0.418470 + 0.908231i 0.637434π0.637434\pi
158158 2.00000 + 3.46410i 0.159111 + 0.275589i
159159 0 0
160160 −2.08114 + 3.60464i −0.164528 + 0.284972i
161161 22.6491 1.78500
162162 0 0
163163 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i 0.617776π-0.617776\pi
0.988227 0.152992i 0.0488907π-0.0488907\pi
164164 3.00000 0.234261
165165 0 0
166166 1.74342 + 3.01969i 0.135315 + 0.234373i
167167 −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i 0.320359π-0.320359\pi
−0.999169 + 0.0407502i 0.987025π0.987025\pi
168168 0 0
169169 −12.9868 + 0.584952i −0.998987 + 0.0449963i
170170 −12.4868 −0.957696
171171 0 0
172172 −4.58114 7.93477i −0.349309 0.605020i
173173 −11.3246 + 19.6147i −0.860990 + 1.49128i 0.00998448 + 0.999950i 0.496822π0.496822\pi
−0.870974 + 0.491328i 0.836512π0.836512\pi
174174 0 0
175175 −19.4868 + 33.7522i −1.47307 + 2.55143i
176176 0.581139 1.00656i 0.0438050 0.0758725i
177177 0 0
178178 −6.00000 + 10.3923i −0.449719 + 0.778936i
179179 −7.74342 13.4120i −0.578770 1.00246i −0.995621 0.0934843i 0.970200π-0.970200\pi
0.416851 0.908975i 0.363134π-0.363134\pi
180180 0 0
181181 3.83772 0.285256 0.142628 0.989776i 0.454445π-0.454445\pi
0.142628 + 0.989776i 0.454445π0.454445\pi
182182 0.256584 + 11.3989i 0.0190192 + 0.844940i
183183 0 0
184184 −3.58114 6.20271i −0.264005 0.457270i
185185 −7.98683 13.8336i −0.587204 1.01707i
186186 0 0
187187 3.48683 0.254982
188188 −2.41886 + 4.18959i −0.176414 + 0.305557i
189189 0 0
190190 −21.4868 −1.55882
191191 −7.16228 + 12.4054i −0.518244 + 0.897625i 0.481531 + 0.876429i 0.340081π0.340081\pi
−0.999775 + 0.0211963i 0.993252π0.993252\pi
192192 0 0
193193 9.98683 + 17.2977i 0.718868 + 1.24512i 0.961449 + 0.274985i 0.0886728π0.0886728\pi
−0.242581 + 0.970131i 0.577994π0.577994\pi
194194 −4.00000 −0.287183
195195 0 0
196196 3.00000 0.214286
197197 −9.48683 16.4317i −0.675909 1.17071i −0.976202 0.216862i 0.930418π-0.930418\pi
0.300293 0.953847i 0.402915π-0.402915\pi
198198 0 0
199199 3.25658 5.64057i 0.230853 0.399849i −0.727206 0.686419i 0.759182π-0.759182\pi
0.958059 + 0.286570i 0.0925150π0.0925150\pi
200200 12.3246 0.871478
201201 0 0
202202 −3.91886 + 6.78767i −0.275730 + 0.477579i
203203 −5.81139 −0.407879
204204 0 0
205205 −6.24342 10.8139i −0.436059 0.755277i
206206 7.90569 + 13.6931i 0.550816 + 0.954041i
207207 0 0
208208 3.08114 1.87259i 0.213639 0.129841i
209209 6.00000 0.415029
210210 0 0
211211 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i 0.122700π-0.122700\pi
−0.788935 + 0.614477i 0.789367π0.789367\pi
212212 6.24342 10.8139i 0.428800 0.742703i
213213 0 0
214214 8.90569 15.4251i 0.608781 1.05444i
215215 −19.0680 + 33.0267i −1.30042 + 2.25240i
216216 0 0
217217 10.0000 17.3205i 0.678844 1.17579i
218218 −3.32456 5.75830i −0.225167 0.390001i
219219 0 0
220220 −4.83772 −0.326159
221221 9.48683 + 5.19615i 0.638153 + 0.349531i
222222 0 0
223223 0.837722 + 1.45098i 0.0560980 + 0.0971647i 0.892711 0.450630i 0.148801π-0.148801\pi
−0.836613 + 0.547795i 0.815467π0.815467\pi
224224 −1.58114 2.73861i −0.105644 0.182981i
225225 0 0
226226 6.67544 0.444044
227227 7.74342 13.4120i 0.513949 0.890185i −0.485920 0.874003i 0.661516π-0.661516\pi
0.999869 0.0161821i 0.00515113π-0.00515113\pi
228228 0 0
229229 22.3246 1.47525 0.737624 0.675212i 0.235948π-0.235948\pi
0.737624 + 0.675212i 0.235948π0.235948\pi
230230 −14.9057 + 25.8174i −0.982852 + 1.70235i
231231 0 0
232232 0.918861 + 1.59151i 0.0603262 + 0.104488i
233233 −16.6491 −1.09072 −0.545360 0.838202i 0.683607π-0.683607\pi
−0.545360 + 0.838202i 0.683607π0.683607\pi
234234 0 0
235235 20.1359 1.31352
236236 1.16228 + 2.01312i 0.0756578 + 0.131043i
237237 0 0
238238 4.74342 8.21584i 0.307470 0.532554i
239239 −21.4868 −1.38987 −0.694934 0.719074i 0.744566π-0.744566\pi
−0.694934 + 0.719074i 0.744566π0.744566\pi
240240 0 0
241241 −6.66228 + 11.5394i −0.429155 + 0.743318i −0.996798 0.0799563i 0.974522π-0.974522\pi
0.567643 + 0.823275i 0.307855π0.307855\pi
242242 −9.64911 −0.620268
243243 0 0
244244 −0.0811388 0.140537i −0.00519438 0.00899693i
245245 −6.24342 10.8139i −0.398877 0.690876i
246246 0 0
247247 16.3246 + 8.94133i 1.03871 + 0.568923i
248248 −6.32456 −0.401610
249249 0 0
250250 −15.2434 26.4024i −0.964078 1.66983i
251251 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i 0.709699π-0.709699\pi
0.990876 + 0.134778i 0.0430322π0.0430322\pi
252252 0 0
253253 4.16228 7.20928i 0.261680 0.453243i
254254 9.16228 15.8695i 0.574892 0.995743i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 10.9868 + 19.0298i 0.685340 + 1.18704i 0.973330 + 0.229410i 0.0736797π0.0736797\pi
−0.287990 + 0.957633i 0.592987π0.592987\pi
258258 0 0
259259 12.1359 0.754091
260260 −13.1623 7.20928i −0.816290 0.447100i
261261 0 0
262262 −8.32456 14.4186i −0.514293 0.890781i
263263 1.25658 + 2.17647i 0.0774843 + 0.134207i 0.902164 0.431393i 0.141978π-0.141978\pi
−0.824680 + 0.565600i 0.808645π0.808645\pi
264264 0 0
265265 −51.9737 −3.19272
266266 8.16228 14.1375i 0.500461 0.866824i
267267 0 0
268268 −2.83772 −0.173341
269269 −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i 0.891886π-0.891886\pi
0.759958 + 0.649972i 0.225219π0.225219\pi
270270 0 0
271271 3.16228 + 5.47723i 0.192095 + 0.332718i 0.945944 0.324329i 0.105139π-0.105139\pi
−0.753850 + 0.657047i 0.771805π0.771805\pi
272272 −3.00000 −0.181902
273273 0 0
274274 −3.00000 −0.181237
275275 7.16228 + 12.4054i 0.431902 + 0.748076i
276276 0 0
277277 −5.40569 + 9.36294i −0.324797 + 0.562564i −0.981471 0.191610i 0.938629π-0.938629\pi
0.656675 + 0.754174i 0.271963π0.271963\pi
278278 −6.32456 −0.379322
279279 0 0
280280 −6.58114 + 11.3989i −0.393298 + 0.681213i
281281 −0.675445 −0.0402937 −0.0201468 0.999797i 0.506413π-0.506413\pi
−0.0201468 + 0.999797i 0.506413π0.506413\pi
282282 0 0
283283 1.41886 + 2.45754i 0.0843425 + 0.146086i 0.905111 0.425176i 0.139788π-0.139788\pi
−0.820768 + 0.571261i 0.806454π0.806454\pi
284284 3.58114 + 6.20271i 0.212501 + 0.368063i
285285 0 0
286286 3.67544 + 2.01312i 0.217334 + 0.119039i
287287 9.48683 0.559990
288288 0 0
289289 4.00000 + 6.92820i 0.235294 + 0.407541i
290290 3.82456 6.62432i 0.224586 0.388994i
291291 0 0
292292 0.500000 0.866025i 0.0292603 0.0506803i
293293 −0.918861 + 1.59151i −0.0536804 + 0.0929773i −0.891617 0.452790i 0.850429π-0.850429\pi
0.837937 + 0.545768i 0.183762π0.183762\pi
294294 0 0
295295 4.83772 8.37918i 0.281663 0.487855i
296296 −1.91886 3.32357i −0.111532 0.193178i
297297 0 0
298298 0.486833 0.0282015
299299 22.0680 13.4120i 1.27622 0.775635i
300300 0 0
301301 −14.4868 25.0919i −0.835007 1.44627i
302302 −0.418861 0.725489i −0.0241028 0.0417472i
303303 0 0
304304 −5.16228 −0.296077
305305 −0.337722 + 0.584952i −0.0193379 + 0.0334943i
306306 0 0
307307 11.4868 0.655588 0.327794 0.944749i 0.393695π-0.393695\pi
0.327794 + 0.944749i 0.393695π0.393695\pi
308308 1.83772 3.18303i 0.104714 0.181370i
309309 0 0
310310 13.1623 + 22.7977i 0.747567 + 1.29482i
311311 21.4868 1.21841 0.609203 0.793014i 0.291489π-0.291489\pi
0.609203 + 0.793014i 0.291489π0.291489\pi
312312 0 0
313313 −4.00000 −0.226093 −0.113047 0.993590i 0.536061π-0.536061\pi
−0.113047 + 0.993590i 0.536061π0.536061\pi
314314 5.24342 + 9.08186i 0.295903 + 0.512519i
315315 0 0
316316 2.00000 3.46410i 0.112509 0.194871i
317317 12.4868 0.701330 0.350665 0.936501i 0.385956π-0.385956\pi
0.350665 + 0.936501i 0.385956π0.385956\pi
318318 0 0
319319 −1.06797 + 1.84978i −0.0597949 + 0.103568i
320320 4.16228 0.232678
321321 0 0
322322 −11.3246 19.6147i −0.631093 1.09308i
323323 −7.74342 13.4120i −0.430855 0.746263i
324324 0 0
325325 1.00000 + 44.4256i 0.0554700 + 2.46429i
326326 −16.0000 −0.886158
327327 0 0
328328 −1.50000 2.59808i −0.0828236 0.143455i
329329 −7.64911 + 13.2486i −0.421709 + 0.730422i
330330 0 0
331331 5.48683 9.50347i 0.301584 0.522358i −0.674911 0.737899i 0.735818π-0.735818\pi
0.976495 + 0.215541i 0.0691514π0.0691514\pi
332332 1.74342 3.01969i 0.0956824 0.165727i
333333 0 0
334334 −6.00000 + 10.3923i −0.328305 + 0.568642i
335335 5.90569 + 10.2290i 0.322663 + 0.558868i
336336 0 0
337337 11.0000 0.599208 0.299604 0.954064i 0.403145π-0.403145\pi
0.299604 + 0.954064i 0.403145π0.403145\pi
338338 7.00000 + 10.9545i 0.380750 + 0.595844i
339339 0 0
340340 6.24342 + 10.8139i 0.338597 + 0.586467i
341341 −3.67544 6.36606i −0.199036 0.344741i
342342 0 0
343343 −12.6491 −0.682988
344344 −4.58114 + 7.93477i −0.246998 + 0.427814i
345345 0 0
346346 22.6491 1.21762
347347 7.74342 13.4120i 0.415688 0.719993i −0.579812 0.814750i 0.696874π-0.696874\pi
0.995500 + 0.0947569i 0.0302074π0.0302074\pi
348348 0 0
349349 2.67544 + 4.63401i 0.143213 + 0.248053i 0.928705 0.370820i 0.120923π-0.120923\pi
−0.785492 + 0.618872i 0.787590π0.787590\pi
350350 38.9737 2.08323
351351 0 0
352352 −1.16228 −0.0619496
353353 −14.6623 25.3958i −0.780394 1.35168i −0.931712 0.363197i 0.881685π-0.881685\pi
0.151318 0.988485i 0.451648π-0.451648\pi
354354 0 0
355355 14.9057 25.8174i 0.791112 1.37025i
356356 12.0000 0.635999
357357 0 0
358358 −7.74342 + 13.4120i −0.409252 + 0.708846i
359359 28.4605 1.50209 0.751044 0.660252i 0.229551π-0.229551\pi
0.751044 + 0.660252i 0.229551π0.229551\pi
360360 0 0
361361 −3.82456 6.62432i −0.201292 0.348649i
362362 −1.91886 3.32357i −0.100853 0.174683i
363363 0 0
364364 9.74342 5.92164i 0.510694 0.310378i
365365 −4.16228 −0.217864
366366 0 0
367367 12.7434 + 22.0722i 0.665201 + 1.15216i 0.979231 + 0.202749i 0.0649875π0.0649875\pi
−0.314030 + 0.949413i 0.601679π0.601679\pi
368368 −3.58114 + 6.20271i −0.186680 + 0.323339i
369369 0 0
370370 −7.98683 + 13.8336i −0.415216 + 0.719175i
371371 19.7434 34.1966i 1.02503 1.77540i
372372 0 0
373373 8.24342 14.2780i 0.426828 0.739288i −0.569761 0.821810i 0.692964π-0.692964\pi
0.996589 + 0.0825226i 0.0262977π0.0262977\pi
374374 −1.74342 3.01969i −0.0901499 0.156144i
375375 0 0
376376 4.83772 0.249486
377377 −5.66228 + 3.44130i −0.291622 + 0.177236i
378378 0 0
379379 −8.83772 15.3074i −0.453963 0.786288i 0.544665 0.838654i 0.316657π-0.316657\pi
−0.998628 + 0.0523664i 0.983324π0.983324\pi
380380 10.7434 + 18.6081i 0.551126 + 0.954578i
381381 0 0
382382 14.3246 0.732908
383383 −15.4868 + 26.8240i −0.791340 + 1.37064i 0.133797 + 0.991009i 0.457283π0.457283\pi
−0.925137 + 0.379633i 0.876050π0.876050\pi
384384 0 0
385385 −15.2982 −0.779670
386386 9.98683 17.2977i 0.508316 0.880430i
387387 0 0
388388 2.00000 + 3.46410i 0.101535 + 0.175863i
389389 12.4868 0.633108 0.316554 0.948575i 0.397474π-0.397474\pi
0.316554 + 0.948575i 0.397474π0.397474\pi
390390 0 0
391391 −21.4868 −1.08664
392392 −1.50000 2.59808i −0.0757614 0.131223i
393393 0 0
394394 −9.48683 + 16.4317i −0.477940 + 0.827816i
395395 −16.6491 −0.837708
396396 0 0
397397 −13.0000 + 22.5167i −0.652451 + 1.13008i 0.330075 + 0.943955i 0.392926π0.392926\pi
−0.982526 + 0.186124i 0.940407π0.940407\pi
398398 −6.51317 −0.326476
399399 0 0
400400 −6.16228 10.6734i −0.308114 0.533669i
401401 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i 0.0444700π-0.0444700\pi
−0.615725 + 0.787961i 0.711137π0.711137\pi
402402 0 0
403403 −0.513167 22.7977i −0.0255627 1.13564i
404404 7.83772 0.389941
405405 0 0
406406 2.90569 + 5.03281i 0.144207 + 0.249774i
407407 2.23025 3.86291i 0.110549 0.191477i
408408 0 0
409409 −7.33772 + 12.7093i −0.362827 + 0.628435i −0.988425 0.151711i 0.951522π-0.951522\pi
0.625598 + 0.780146i 0.284855π0.284855\pi
410410 −6.24342 + 10.8139i −0.308340 + 0.534061i
411411 0 0
412412 7.90569 13.6931i 0.389486 0.674609i
413413 3.67544 + 6.36606i 0.180857 + 0.313253i
414414 0 0
415415 −14.5132 −0.712423
416416 −3.16228 1.73205i −0.155043 0.0849208i
417417 0 0
418418 −3.00000 5.19615i −0.146735 0.254152i
419419 15.4868 + 26.8240i 0.756581 + 1.31044i 0.944584 + 0.328269i 0.106465π0.106465\pi
−0.188003 + 0.982168i 0.560201π0.560201\pi
420420 0 0
421421 −23.8377 −1.16178 −0.580890 0.813982i 0.697295π-0.697295\pi
−0.580890 + 0.813982i 0.697295π0.697295\pi
422422 2.00000 3.46410i 0.0973585 0.168630i
423423 0 0
424424 −12.4868 −0.606414
425425 18.4868 32.0201i 0.896743 1.55320i
426426 0 0
427427 −0.256584 0.444416i −0.0124169 0.0215068i
428428 −17.8114 −0.860946
429429 0 0
430430 38.1359 1.83908
431431 4.74342 + 8.21584i 0.228482 + 0.395743i 0.957359 0.288903i 0.0932904π-0.0932904\pi
−0.728876 + 0.684646i 0.759957π0.759957\pi
432432 0 0
433433 4.66228 8.07530i 0.224055 0.388074i −0.731981 0.681325i 0.761404π-0.761404\pi
0.956035 + 0.293251i 0.0947372π0.0947372\pi
434434 −20.0000 −0.960031
435435 0 0
436436 −3.32456 + 5.75830i −0.159217 + 0.275772i
437437 −36.9737 −1.76869
438438 0 0
439439 12.7434 + 22.0722i 0.608210 + 1.05345i 0.991535 + 0.129837i 0.0414455π0.0414455\pi
−0.383325 + 0.923613i 0.625221π0.625221\pi
440440 2.41886 + 4.18959i 0.115315 + 0.199731i
441441 0 0
442442 −0.243416 10.8139i −0.0115781 0.514365i
443443 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
444444 0 0
445445 −24.9737 43.2557i −1.18387 2.05051i
446446 0.837722 1.45098i 0.0396673 0.0687058i
447447 0 0
448448 −1.58114 + 2.73861i −0.0747018 + 0.129387i
449449 −3.67544 + 6.36606i −0.173455 + 0.300433i −0.939625 0.342205i 0.888826π-0.888826\pi
0.766171 + 0.642637i 0.222160π0.222160\pi
450450 0 0
451451 1.74342 3.01969i 0.0820943 0.142191i
452452 −3.33772 5.78110i −0.156993 0.271920i
453453 0 0
454454 −15.4868 −0.726833
455455 −41.6228 22.7977i −1.95131 1.06877i
456456 0 0
457457 1.66228 + 2.87915i 0.0777581 + 0.134681i 0.902282 0.431146i 0.141890π-0.141890\pi
−0.824524 + 0.565827i 0.808557π0.808557\pi
458458 −11.1623 19.3336i −0.521579 0.903401i
459459 0 0
460460 29.8114 1.38996
461461 −9.24342 + 16.0101i −0.430509 + 0.745663i −0.996917 0.0784616i 0.974999π-0.974999\pi
0.566408 + 0.824125i 0.308333π0.308333\pi
462462 0 0
463463 15.1623 0.704651 0.352325 0.935878i 0.385391π-0.385391\pi
0.352325 + 0.935878i 0.385391π0.385391\pi
464464 0.918861 1.59151i 0.0426571 0.0738842i
465465 0 0
466466 8.32456 + 14.4186i 0.385628 + 0.667927i
467467 6.18861 0.286375 0.143187 0.989696i 0.454265π-0.454265\pi
0.143187 + 0.989696i 0.454265π0.454265\pi
468468 0 0
469469 −8.97367 −0.414365
470470 −10.0680 17.4382i −0.464401 0.804366i
471471 0 0
472472 1.16228 2.01312i 0.0534982 0.0926615i
473473 −10.6491 −0.489647
474474 0 0
475475 31.8114 55.0989i 1.45961 2.52811i
476476 −9.48683 −0.434828
477477 0 0
478478 10.7434 + 18.6081i 0.491392 + 0.851117i
479479 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i 0.0180558π0.0180558\pi
−0.450098 + 0.892979i 0.648611π0.648611\pi
480480 0 0
481481 11.8246 7.18647i 0.539153 0.327675i
482482 13.3246 0.606917
483483 0 0
484484 4.82456 + 8.35637i 0.219298 + 0.379835i
485485 8.32456 14.4186i 0.377999 0.654713i
486486 0 0
487487 6.74342 11.6799i 0.305573 0.529269i −0.671815 0.740719i 0.734485π-0.734485\pi
0.977389 + 0.211450i 0.0678185π0.0678185\pi
488488 −0.0811388 + 0.140537i −0.00367298 + 0.00636179i
489489 0 0
490490 −6.24342 + 10.8139i −0.282049 + 0.488523i
491491 −2.90569 5.03281i −0.131132 0.227128i 0.792981 0.609246i 0.208528π-0.208528\pi
−0.924113 + 0.382119i 0.875195π0.875195\pi
492492 0 0
493493 5.51317 0.248301
494494 −0.418861 18.6081i −0.0188455 0.837220i
495495 0 0
496496 3.16228 + 5.47723i 0.141990 + 0.245935i
497497 11.3246 + 19.6147i 0.507976 + 0.879840i
498498 0 0
499499 12.6491 0.566252 0.283126 0.959083i 0.408629π-0.408629\pi
0.283126 + 0.959083i 0.408629π0.408629\pi
500500 −15.2434 + 26.4024i −0.681706 + 1.18075i
501501 0 0
502502 −12.0000 −0.535586
503503 0.0943058 0.163343i 0.00420489 0.00728308i −0.863915 0.503637i 0.831995π-0.831995\pi
0.868120 + 0.496354i 0.165328π0.165328\pi
504504 0 0
505505 −16.3114 28.2522i −0.725847 1.25720i
506506 −8.32456 −0.370072
507507 0 0
508508 −18.3246 −0.813021
509509 14.0811 + 24.3892i 0.624136 + 1.08103i 0.988707 + 0.149859i 0.0478820π0.0478820\pi
−0.364572 + 0.931175i 0.618785π0.618785\pi
510510 0 0
511511 1.58114 2.73861i 0.0699455 0.121149i
512512 1.00000 0.0441942
513513 0 0
514514 10.9868 19.0298i 0.484608 0.839366i
515515 −65.8114 −2.90000
516516 0 0
517517 2.81139 + 4.86947i 0.123645 + 0.214159i
518518 −6.06797 10.5100i −0.266611 0.461784i
519519 0 0
520520 0.337722 + 15.0035i 0.0148101 + 0.657947i
521521 −27.0000 −1.18289 −0.591446 0.806345i 0.701443π-0.701443\pi
−0.591446 + 0.806345i 0.701443π0.701443\pi
522522 0 0
523523 2.58114 + 4.47066i 0.112865 + 0.195488i 0.916924 0.399061i 0.130664π-0.130664\pi
−0.804059 + 0.594549i 0.797330π0.797330\pi
524524 −8.32456 + 14.4186i −0.363660 + 0.629877i
525525 0 0
526526 1.25658 2.17647i 0.0547896 0.0948984i
527527 −9.48683 + 16.4317i −0.413253 + 0.715775i
528528 0 0
529529 −14.1491 + 24.5070i −0.615179 + 1.06552i
530530 25.9868 + 45.0105i 1.12880 + 1.95513i
531531 0 0
532532 −16.3246 −0.707759
533533 9.24342 5.61776i 0.400377 0.243332i
534534 0 0
535535 37.0680 + 64.2036i 1.60259 + 2.77576i
536536 1.41886 + 2.45754i 0.0612855 + 0.106150i
537537 0 0
538538 6.00000 0.258678
539539 1.74342 3.01969i 0.0750943 0.130067i
540540 0 0
541541 −15.5132 −0.666963 −0.333482 0.942757i 0.608223π-0.608223\pi
−0.333482 + 0.942757i 0.608223π0.608223\pi
542542 3.16228 5.47723i 0.135831 0.235267i
543543 0 0
544544 1.50000 + 2.59808i 0.0643120 + 0.111392i
545545 27.6754 1.18549
546546 0 0
547547 −33.8114 −1.44567 −0.722835 0.691020i 0.757161π-0.757161\pi
−0.722835 + 0.691020i 0.757161π0.757161\pi
548548 1.50000 + 2.59808i 0.0640768 + 0.110984i
549549 0 0
550550 7.16228 12.4054i 0.305401 0.528969i
551551 9.48683 0.404153
552552 0 0
553553 6.32456 10.9545i 0.268947 0.465831i
554554 10.8114 0.459332
555555 0 0
556556 3.16228 + 5.47723i 0.134110 + 0.232286i
557557 9.24342 + 16.0101i 0.391656 + 0.678368i 0.992668 0.120872i 0.0385690π-0.0385690\pi
−0.601012 + 0.799240i 0.705236π0.705236\pi
558558 0 0
559559 −28.9737 15.8695i −1.22546 0.671210i
560560 13.1623 0.556208
561561 0 0
562562 0.337722 + 0.584952i 0.0142460 + 0.0246747i
563563 −20.3246 + 35.2032i −0.856578 + 1.48364i 0.0185956 + 0.999827i 0.494081π0.494081\pi
−0.875173 + 0.483809i 0.839253π0.839253\pi
564564 0 0
565565 −13.8925 + 24.0626i −0.584463 + 1.01232i
566566 1.41886 2.45754i 0.0596392 0.103298i
567567 0 0
568568 3.58114 6.20271i 0.150261 0.260260i
569569 −13.6491 23.6410i −0.572200 0.991080i −0.996340 0.0854833i 0.972757π-0.972757\pi
0.424139 0.905597i 0.360577π-0.360577\pi
570570 0 0
571571 −36.1359 −1.51224 −0.756121 0.654432i 0.772908π-0.772908\pi
−0.756121 + 0.654432i 0.772908π0.772908\pi
572572 −0.0943058 4.18959i −0.00394313 0.175176i
573573 0 0
574574 −4.74342 8.21584i −0.197986 0.342922i
575575 −44.1359 76.4457i −1.84060 3.18801i
576576 0 0
577577 0.350889 0.0146077 0.00730386 0.999973i 0.497675π-0.497675\pi
0.00730386 + 0.999973i 0.497675π0.497675\pi
578578 4.00000 6.92820i 0.166378 0.288175i
579579 0 0
580580 −7.64911 −0.317612
581581 5.51317 9.54909i 0.228725 0.396163i
582582 0 0
583583 −7.25658 12.5688i −0.300537 0.520545i
584584 −1.00000 −0.0413803
585585 0 0
586586 1.83772 0.0759156
587587 −14.3246 24.8109i −0.591238 1.02405i −0.994066 0.108778i 0.965306π-0.965306\pi
0.402828 0.915276i 0.368027π-0.368027\pi
588588 0 0
589589 −16.3246 + 28.2750i −0.672642 + 1.16505i
590590 −9.67544 −0.398332
591591 0 0
592592 −1.91886 + 3.32357i −0.0788647 + 0.136598i
593593 0.675445 0.0277372 0.0138686 0.999904i 0.495585π-0.495585\pi
0.0138686 + 0.999904i 0.495585π0.495585\pi
594594 0 0
595595 19.7434 + 34.1966i 0.809401 + 1.40192i
596596 −0.243416 0.421610i −0.00997073 0.0172698i
597597 0 0
598598 −22.6491 12.4054i −0.926191 0.507296i
599599 −23.6228 −0.965200 −0.482600 0.875841i 0.660308π-0.660308\pi
−0.482600 + 0.875841i 0.660308π0.660308\pi
600600 0 0
601601 17.1491 + 29.7031i 0.699527 + 1.21162i 0.968631 + 0.248505i 0.0799392π0.0799392\pi
−0.269104 + 0.963111i 0.586727π0.586727\pi
602602 −14.4868 + 25.0919i −0.590439 + 1.02267i
603603 0 0
604604 −0.418861 + 0.725489i −0.0170432 + 0.0295197i
605605 20.0811 34.7816i 0.816414 1.41407i
606606 0 0
607607 −8.64911 + 14.9807i −0.351057 + 0.608048i −0.986435 0.164153i 0.947511π-0.947511\pi
0.635378 + 0.772201i 0.280844π0.280844\pi
608608 2.58114 + 4.47066i 0.104679 + 0.181309i
609609 0 0
610610 0.675445 0.0273480
611611 0.392527 + 17.4382i 0.0158799 + 0.705476i
612612 0 0
613613 −10.2434 17.7421i −0.413728 0.716597i 0.581566 0.813499i 0.302440π-0.302440\pi
−0.995294 + 0.0969016i 0.969107π0.969107\pi
614614 −5.74342 9.94789i −0.231785 0.401464i
615615 0 0
616616 −3.67544 −0.148088
617617 13.3114 23.0560i 0.535896 0.928200i −0.463223 0.886242i 0.653307π-0.653307\pi
0.999119 0.0419579i 0.0133595π-0.0133595\pi
618618 0 0
619619 24.6491 0.990731 0.495366 0.868685i 0.335034π-0.335034\pi
0.495366 + 0.868685i 0.335034π0.335034\pi
620620 13.1623 22.7977i 0.528610 0.915579i
621621 0 0
622622 −10.7434 18.6081i −0.430772 0.746119i
623623 37.9473 1.52033
624624 0 0
625625 65.2719 2.61088
626626 2.00000 + 3.46410i 0.0799361 + 0.138453i
627627 0 0
628628 5.24342 9.08186i 0.209235 0.362406i
629629 −11.5132 −0.459060
630630 0 0
631631 12.6491 21.9089i 0.503553 0.872180i −0.496438 0.868072i 0.665359π-0.665359\pi
0.999992 0.00410769i 0.00130752π-0.00130752\pi
632632 −4.00000 −0.159111
633633 0 0
634634 −6.24342 10.8139i −0.247958 0.429475i
635635 38.1359 + 66.0534i 1.51338 + 2.62125i
636636 0 0
637637 9.24342 5.61776i 0.366237 0.222584i
638638 2.13594 0.0845628
639639 0 0
640640 −2.08114 3.60464i −0.0822642 0.142486i
641641 −8.17544 + 14.1603i −0.322911 + 0.559298i −0.981087 0.193566i 0.937995π-0.937995\pi
0.658177 + 0.752864i 0.271328π0.271328\pi
642642 0 0
643643 −10.0000 + 17.3205i −0.394362 + 0.683054i −0.993019 0.117951i 0.962368π-0.962368\pi
0.598658 + 0.801005i 0.295701π0.295701\pi
644644 −11.3246 + 19.6147i −0.446250 + 0.772928i
645645 0 0
646646 −7.74342 + 13.4120i −0.304661 + 0.527688i
647647 20.3246 + 35.2032i 0.799041 + 1.38398i 0.920241 + 0.391351i 0.127992π0.127992\pi
−0.121201 + 0.992628i 0.538674π0.538674\pi
648648 0 0
649649 2.70178 0.106054
650650 37.9737 23.0788i 1.48945 0.905225i
651651 0 0
652652 8.00000 + 13.8564i 0.313304 + 0.542659i
653653 −15.0000 25.9808i −0.586995 1.01671i −0.994623 0.103558i 0.966977π-0.966977\pi
0.407628 0.913148i 0.366356π-0.366356\pi
654654 0 0
655655 69.2982 2.70771
656656 −1.50000 + 2.59808i −0.0585652 + 0.101438i
657657 0 0
658658 15.2982 0.596387
659659 2.51317 4.35293i 0.0978991 0.169566i −0.812916 0.582381i 0.802121π-0.802121\pi
0.910815 + 0.412815i 0.135454π0.135454\pi
660660 0 0
661661 −13.2434 22.9383i −0.515109 0.892195i −0.999846 0.0175354i 0.994418π-0.994418\pi
0.484737 0.874660i 0.338915π-0.338915\pi
662662 −10.9737 −0.426504
663663 0 0
664664 −3.48683 −0.135315
665665 33.9737 + 58.8441i 1.31744 + 2.28188i
666666 0 0
667667 6.58114 11.3989i 0.254823 0.441366i
668668 12.0000 0.464294
669669 0 0
670670 5.90569 10.2290i 0.228157 0.395179i
671671 −0.188612 −0.00728127
672672 0 0
673673 −7.33772 12.7093i −0.282848 0.489908i 0.689237 0.724536i 0.257946π-0.257946\pi
−0.972085 + 0.234628i 0.924613π0.924613\pi
674674 −5.50000 9.52628i −0.211852 0.366939i
675675 0 0
676676 5.98683 11.5394i 0.230263 0.443823i
677677 18.0000 0.691796 0.345898 0.938272i 0.387574π-0.387574\pi
0.345898 + 0.938272i 0.387574π0.387574\pi
678678 0 0
679679 6.32456 + 10.9545i 0.242714 + 0.420393i
680680 6.24342 10.8139i 0.239424 0.414695i
681681 0 0
682682 −3.67544 + 6.36606i −0.140740 + 0.243769i
683683 17.8114 30.8502i 0.681534 1.18045i −0.292979 0.956119i 0.594647π-0.594647\pi
0.974513 0.224332i 0.0720201π-0.0720201\pi
684684 0 0
685685 6.24342 10.8139i 0.238549 0.413178i
686686 6.32456 + 10.9545i 0.241473 + 0.418243i
687687 0 0
688688 9.16228 0.349309
689689 −1.01317 45.0105i −0.0385986 1.71476i
690690 0 0
691691 −4.58114 7.93477i −0.174275 0.301853i 0.765635 0.643275i 0.222425π-0.222425\pi
−0.939910 + 0.341422i 0.889091π0.889091\pi
692692 −11.3246 19.6147i −0.430495 0.745639i
693693 0 0
694694 −15.4868 −0.587872
695695 13.1623 22.7977i 0.499274 0.864767i
696696 0 0
697697 −9.00000 −0.340899
698698 2.67544 4.63401i 0.101267 0.175400i
699699 0 0
700700 −19.4868 33.7522i −0.736533 1.27571i
701701 18.0000 0.679851 0.339925 0.940452i 0.389598π-0.389598\pi
0.339925 + 0.940452i 0.389598π0.389598\pi
702702 0 0
703703 −19.8114 −0.747201
704704 0.581139 + 1.00656i 0.0219025 + 0.0379362i
705705 0 0
706706 −14.6623 + 25.3958i −0.551822 + 0.955784i
707707 24.7851 0.932138
708708 0 0
709709 −22.7302 + 39.3699i −0.853652 + 1.47857i 0.0242371 + 0.999706i 0.492284π0.492284\pi
−0.877890 + 0.478863i 0.841049π0.841049\pi
710710 −29.8114 −1.11880
711711 0 0
712712 −6.00000 10.3923i −0.224860 0.389468i
713713 22.6491 + 39.2294i 0.848216 + 1.46915i
714714 0 0
715715 −14.9057 + 9.05906i −0.557441 + 0.338790i
716716 15.4868 0.578770
717717 0 0
718718 −14.2302 24.6475i −0.531068 0.919837i
719719 19.1623 33.1900i 0.714632 1.23778i −0.248469 0.968640i 0.579927π-0.579927\pi
0.963101 0.269140i 0.0867393π-0.0867393\pi
720720 0 0
721721 25.0000 43.3013i 0.931049 1.61262i
722722 −3.82456 + 6.62432i −0.142335 + 0.246532i
723723 0 0
724724 −1.91886 + 3.32357i −0.0713139 + 0.123519i
725725 11.3246 + 19.6147i 0.420583 + 0.728472i
726726 0 0
727727 −8.83772 −0.327773 −0.163886 0.986479i 0.552403π-0.552403\pi
−0.163886 + 0.986479i 0.552403π0.552403\pi
728728 −10.0000 5.47723i −0.370625 0.202999i
729729 0 0
730730 2.08114 + 3.60464i 0.0770264 + 0.133414i
731731 13.7434 + 23.8043i 0.508319 + 0.880434i
732732 0 0
733733 21.4605 0.792662 0.396331 0.918108i 0.370283π-0.370283\pi
0.396331 + 0.918108i 0.370283π0.370283\pi
734734 12.7434 22.0722i 0.470368 0.814701i
735735 0 0
736736 7.16228 0.264005
737737 −1.64911 + 2.85634i −0.0607458 + 0.105215i
738738 0 0
739739 19.8114 + 34.3143i 0.728774 + 1.26227i 0.957402 + 0.288759i 0.0932427π0.0932427\pi
−0.228628 + 0.973514i 0.573424π0.573424\pi
740740 15.9737 0.587204
741741 0 0
742742 −39.4868 −1.44961
743743 −1.16228 2.01312i −0.0426398 0.0738544i 0.843918 0.536472i 0.180243π-0.180243\pi
−0.886558 + 0.462618i 0.846910π0.846910\pi
744744 0 0
745745 −1.01317 + 1.75486i −0.0371196 + 0.0642930i
746746 −16.4868 −0.603626
747747 0 0
748748 −1.74342 + 3.01969i −0.0637456 + 0.110411i
749749 −56.3246 −2.05805
750750 0 0
751751 −19.3925 33.5888i −0.707643 1.22567i −0.965729 0.259552i 0.916425π-0.916425\pi
0.258086 0.966122i 0.416908π-0.416908\pi
752752 −2.41886 4.18959i −0.0882068 0.152779i
753753 0 0
754754 5.81139 + 3.18303i 0.211638 + 0.115919i
755755 3.48683 0.126899
756756 0 0
757757 13.3246 + 23.0788i 0.484289 + 0.838814i 0.999837 0.0180472i 0.00574493π-0.00574493\pi
−0.515548 + 0.856861i 0.672412π0.672412\pi
758758 −8.83772 + 15.3074i −0.321001 + 0.555989i
759759 0 0
760760 10.7434 18.6081i 0.389705 0.674988i
761761 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i 0.763543π-0.763543\pi
0.954043 + 0.299670i 0.0968765π0.0968765\pi
762762 0 0
763763 −10.5132 + 18.2093i −0.380602 + 0.659222i
764764 −7.16228 12.4054i −0.259122 0.448813i
765765 0 0
766766 30.9737 1.11912
767767 7.35089 + 4.02625i 0.265425 + 0.145379i
768768 0 0
769769 −1.67544 2.90196i −0.0604181 0.104647i 0.834234 0.551410i 0.185910π-0.185910\pi
−0.894652 + 0.446763i 0.852577π0.852577\pi
770770 7.64911 + 13.2486i 0.275655 + 0.477448i
771771 0 0
772772 −19.9737 −0.718868
773773 −11.3246 + 19.6147i −0.407316 + 0.705492i −0.994588 0.103898i 0.966869π-0.966869\pi
0.587272 + 0.809390i 0.300202π0.300202\pi
774774 0 0
775775 −77.9473 −2.79995
776776 2.00000 3.46410i 0.0717958 0.124354i
777777 0 0
778778 −6.24342 10.8139i −0.223837 0.387698i
779779 −15.4868 −0.554873
780780 0 0
781781 8.32456 0.297876
782782 10.7434 + 18.6081i 0.384184 + 0.665426i
783783 0 0
784784 −1.50000 + 2.59808i −0.0535714 + 0.0927884i
785785 −43.6491 −1.55790
786786 0 0
787787 4.51317 7.81703i 0.160877 0.278647i −0.774306 0.632811i 0.781901π-0.781901\pi
0.935183 + 0.354164i 0.115234π0.115234\pi
788788 18.9737 0.675909
789789 0 0
790790 8.32456 + 14.4186i 0.296174 + 0.512989i
791791 −10.5548 18.2815i −0.375286 0.650014i
792792 0 0
793793 −0.513167 0.281073i −0.0182231 0.00998120i
794794 26.0000 0.922705
795795 0 0
796796 3.25658 + 5.64057i 0.115427 + 0.199925i
797797 9.48683 16.4317i 0.336041 0.582040i −0.647643 0.761944i 0.724245π-0.724245\pi
0.983684 + 0.179904i 0.0575786π0.0575786\pi
798798 0 0
799799 7.25658 12.5688i 0.256719 0.444651i
800800 −6.16228 + 10.6734i −0.217869 + 0.377361i
801801 0 0
802802 7.50000 12.9904i 0.264834 0.458706i
803803 −0.581139 1.00656i −0.0205079 0.0355208i
804804 0 0
805805 94.2719 3.32265
806806 −19.4868 + 11.8433i −0.686394 + 0.417162i
807807 0 0
808808 −3.91886 6.78767i −0.137865 0.238789i
809809 −1.50000 2.59808i −0.0527372 0.0913435i 0.838452 0.544976i 0.183461π-0.183461\pi
−0.891189 + 0.453632i 0.850128π0.850128\pi
810810 0 0
811811 1.02633 0.0360395 0.0180197 0.999838i 0.494264π-0.494264\pi
0.0180197 + 0.999838i 0.494264π0.494264\pi
812812 2.90569 5.03281i 0.101970 0.176617i
813813 0 0
814814 −4.46050 −0.156340
815815 33.2982 57.6742i 1.16639 2.02024i
816816 0 0
817817 23.6491 + 40.9615i 0.827378 + 1.43306i
818818 14.6754 0.513115
819819 0 0
820820 12.4868 0.436059
821821 −5.32456 9.22240i −0.185828 0.321864i 0.758027 0.652223i 0.226163π-0.226163\pi
−0.943855 + 0.330359i 0.892830π0.892830\pi
822822 0 0
823823 −26.6491 + 46.1576i −0.928930 + 1.60895i −0.143813 + 0.989605i 0.545936π0.545936\pi
−0.785116 + 0.619348i 0.787397π0.787397\pi
824824 −15.8114 −0.550816
825825 0 0
826826 3.67544 6.36606i 0.127885 0.221503i
827827 −6.97367 −0.242498 −0.121249 0.992622i 0.538690π-0.538690\pi
−0.121249 + 0.992622i 0.538690π0.538690\pi
828828 0 0
829829 −6.08114 10.5328i −0.211207 0.365821i 0.740886 0.671631i 0.234406π-0.234406\pi
−0.952092 + 0.305810i 0.901073π0.901073\pi
830830 7.25658 + 12.5688i 0.251880 + 0.436268i
831831 0 0
832832 0.0811388 + 3.60464i 0.00281298 + 0.124968i
833833 −9.00000 −0.311832
834834 0 0
835835 −24.9737 43.2557i −0.864249 1.49692i
836836 −3.00000 + 5.19615i −0.103757 + 0.179713i
837837 0 0
838838 15.4868 26.8240i 0.534984 0.926619i
839839 −2.32456 + 4.02625i −0.0802526 + 0.139002i −0.903358 0.428887i 0.858906π-0.858906\pi
0.823106 + 0.567888i 0.192239π0.192239\pi
840840 0 0
841841 12.8114 22.1900i 0.441772 0.765172i
842842 11.9189 + 20.6441i 0.410751 + 0.711442i
843843 0 0
844844 −4.00000 −0.137686
845845 −54.0548 + 2.43473i −1.85954 + 0.0837574i
846846 0 0
847847 15.2566 + 26.4252i 0.524222 + 0.907980i
848848 6.24342 + 10.8139i 0.214400 + 0.371351i
849849 0 0
850850 −36.9737 −1.26819
851851 −13.7434 + 23.8043i −0.471118 + 0.816001i
852852 0 0
853853 55.1359 1.88782 0.943909 0.330205i 0.107118π-0.107118\pi
0.943909 + 0.330205i 0.107118π0.107118\pi
854854 −0.256584 + 0.444416i −0.00878011 + 0.0152076i
855855 0 0
856856 8.90569 + 15.4251i 0.304390 + 0.527220i
857857 −25.6491 −0.876157 −0.438078 0.898937i 0.644341π-0.644341\pi
−0.438078 + 0.898937i 0.644341π0.644341\pi
858858 0 0
859859 28.5132 0.972857 0.486428 0.873720i 0.338299π-0.338299\pi
0.486428 + 0.873720i 0.338299π0.338299\pi
860860 −19.0680 33.0267i −0.650212 1.12620i
861861 0 0
862862 4.74342 8.21584i 0.161561 0.279833i
863863 47.8114 1.62752 0.813759 0.581202i 0.197417π-0.197417\pi
0.813759 + 0.581202i 0.197417π0.197417\pi
864864 0 0
865865 −47.1359 + 81.6418i −1.60267 + 2.77591i
866866 −9.32456 −0.316861
867867 0 0
868868 10.0000 + 17.3205i 0.339422 + 0.587896i
869869 −2.32456 4.02625i −0.0788551 0.136581i
870870 0 0
871871 −8.74342 + 5.31388i −0.296259 + 0.180054i
872872 6.64911 0.225167
873873 0 0
874874 18.4868 + 32.0201i 0.625326 + 1.08310i
875875 −48.2039 + 83.4916i −1.62959 + 2.82253i
876876 0 0
877877 22.5680 39.0889i 0.762066 1.31994i −0.179717 0.983718i 0.557518π-0.557518\pi
0.941784 0.336219i 0.109148π-0.109148\pi
878878 12.7434 22.0722i 0.430069 0.744902i
879879 0 0
880880 2.41886 4.18959i 0.0815398 0.141231i
881881 −4.98683 8.63745i −0.168011 0.291003i 0.769710 0.638394i 0.220401π-0.220401\pi
−0.937720 + 0.347391i 0.887068π0.887068\pi
882882 0 0
883883 −11.3509 −0.381988 −0.190994 0.981591i 0.561171π-0.561171\pi
−0.190994 + 0.981591i 0.561171π0.561171\pi
884884 −9.24342 + 5.61776i −0.310890 + 0.188946i
885885 0 0
886886 0 0
887887 −19.1623 33.1900i −0.643406 1.11441i −0.984667 0.174444i 0.944187π-0.944187\pi
0.341261 0.939969i 0.389146π-0.389146\pi
888888 0 0
889889 −57.9473 −1.94349
890890 −24.9737 + 43.2557i −0.837119 + 1.44993i
891891 0 0
892892 −1.67544 −0.0560980
893893 12.4868 21.6278i 0.417856 0.723748i
894894 0 0
895895 −32.2302 55.8244i −1.07734 1.86600i
896896 3.16228 0.105644
897897 0 0
898898 7.35089 0.245302
899899 −5.81139 10.0656i −0.193821 0.335707i
900900 0 0
901901 −18.7302 + 32.4417i −0.623995 + 1.08079i
902902 −3.48683 −0.116099
903903 0 0
904904 −3.33772 + 5.78110i −0.111011 + 0.192277i
905905 15.9737 0.530983
906906 0 0
907907 −18.1359 31.4124i −0.602194 1.04303i −0.992488 0.122341i 0.960960π-0.960960\pi
0.390294 0.920690i 0.372373π-0.372373\pi
908908 7.74342 + 13.4120i 0.256974 + 0.445093i
909909 0 0
910910 1.06797 + 47.4452i 0.0354029 + 1.57279i
911911 −49.9473 −1.65483 −0.827414 0.561592i 0.810189π-0.810189\pi
−0.827414 + 0.561592i 0.810189π0.810189\pi
912912 0 0
913913 −2.02633 3.50971i −0.0670619 0.116155i
914914 1.66228 2.87915i 0.0549833 0.0952338i
915915 0 0
916916 −11.1623 + 19.3336i −0.368812 + 0.638801i
917917 −26.3246 + 45.5955i −0.869313 + 1.50569i
918918 0 0
919919 −1.67544 + 2.90196i −0.0552678 + 0.0957267i −0.892336 0.451372i 0.850935π-0.850935\pi
0.837068 + 0.547099i 0.184268π0.184268\pi
920920 −14.9057 25.8174i −0.491426 0.851175i
921921 0 0
922922 18.4868 0.608831
923923 22.6491 + 12.4054i 0.745505 + 0.408330i
924924 0 0
925925 −23.6491 40.9615i −0.777578 1.34680i
926926 −7.58114 13.1309i −0.249132 0.431509i
927927 0 0
928928 −1.83772 −0.0603262
929929 −14.4737 + 25.0691i −0.474866 + 0.822491i −0.999586 0.0287835i 0.990837π-0.990837\pi
0.524720 + 0.851275i 0.324170π0.324170\pi
930930 0 0
931931 −15.4868 −0.507560
932932 8.32456 14.4186i 0.272680 0.472295i
933933 0 0
934934 −3.09431 5.35949i −0.101249 0.175368i
935935 14.5132 0.474631
936936 0 0
937937 14.2982 0.467103 0.233551 0.972344i 0.424965π-0.424965\pi
0.233551 + 0.972344i 0.424965π0.424965\pi
938938 4.48683 + 7.77142i 0.146500 + 0.253746i
939939 0 0
940940 −10.0680 + 17.4382i −0.328381 + 0.568773i
941941 −48.5964 −1.58420 −0.792099 0.610392i 0.791012π-0.791012\pi
−0.792099 + 0.610392i 0.791012π0.791012\pi
942942 0 0
943943 −10.7434 + 18.6081i −0.349854 + 0.605965i
944944 −2.32456 −0.0756578
945945 0 0
946946 5.32456 + 9.22240i 0.173116 + 0.299846i
947947 −9.48683 16.4317i −0.308281 0.533958i 0.669706 0.742627i 0.266420π-0.266420\pi
−0.977986 + 0.208669i 0.933087π0.933087\pi
948948 0 0
949949 −0.0811388 3.60464i −0.00263388 0.117012i
950950 −63.6228 −2.06420
951951 0 0
952952 4.74342 + 8.21584i 0.153735 + 0.266277i
953953 13.6491 23.6410i 0.442138 0.765806i −0.555710 0.831376i 0.687553π-0.687553\pi
0.997848 + 0.0655707i 0.0208868π0.0208868\pi
954954 0 0
955955 −29.8114 + 51.6348i −0.964674 + 1.67086i
956956 10.7434 18.6081i 0.347467 0.601830i
957957 0 0
958958 12.0000 20.7846i 0.387702 0.671520i
959959 4.74342 + 8.21584i 0.153173 + 0.265303i
960960 0 0
961961 9.00000 0.290323
962962 −12.1359 6.64713i −0.391279 0.214312i
963963 0 0
964964 −6.66228 11.5394i −0.214578 0.371659i
965965 41.5680 + 71.9978i 1.33812 + 2.31769i
966966 0 0
967967 34.5132 1.10987 0.554934 0.831894i 0.312743π-0.312743\pi
0.554934 + 0.831894i 0.312743π0.312743\pi
968968 4.82456 8.35637i 0.155067 0.268584i
969969 0 0
970970 −16.6491 −0.534571
971971 9.48683 16.4317i 0.304447 0.527318i −0.672691 0.739923i 0.734862π-0.734862\pi
0.977138 + 0.212606i 0.0681950π0.0681950\pi
972972 0 0
973973 10.0000 + 17.3205i 0.320585 + 0.555270i
974974 −13.4868 −0.432146
975975 0 0
976976 0.162278 0.00519438
977977 −10.5000 18.1865i −0.335925 0.581839i 0.647737 0.761864i 0.275715π-0.275715\pi
−0.983662 + 0.180025i 0.942382π0.942382\pi
978978 0 0
979979 6.97367 12.0787i 0.222879 0.386038i
980980 12.4868 0.398877
981981 0 0
982982 −2.90569 + 5.03281i −0.0927244 + 0.160603i
983983 23.6228 0.753450 0.376725 0.926325i 0.377050π-0.377050\pi
0.376725 + 0.926325i 0.377050π0.377050\pi
984984 0 0
985985 −39.4868 68.3932i −1.25816 2.17919i
986986 −2.75658 4.77454i −0.0877875 0.152052i
987987 0 0
988988 −15.9057 + 9.66682i −0.506028 + 0.307542i
989989 65.6228 2.08668
990990 0 0
991991 −13.3925 23.1965i −0.425428 0.736862i 0.571033 0.820927i 0.306543π-0.306543\pi
−0.996460 + 0.0840651i 0.973210π0.973210\pi
992992 3.16228 5.47723i 0.100402 0.173902i
993993 0 0
994994 11.3246 19.6147i 0.359193 0.622141i
995995 13.5548 23.4776i 0.429716 0.744290i
996996 0 0
997997 29.7302 51.4943i 0.941566 1.63084i 0.179082 0.983834i 0.442687π-0.442687\pi
0.762484 0.647007i 0.223979π-0.223979\pi
998998 −6.32456 10.9545i −0.200200 0.346757i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 234.2.h.d.55.2 4
3.2 odd 2 234.2.h.e.55.1 yes 4
4.3 odd 2 1872.2.t.p.289.2 4
12.11 even 2 1872.2.t.n.289.1 4
13.2 odd 12 3042.2.b.k.1351.1 4
13.3 even 3 3042.2.a.w.1.2 2
13.9 even 3 inner 234.2.h.d.217.2 yes 4
13.10 even 6 3042.2.a.q.1.1 2
13.11 odd 12 3042.2.b.k.1351.4 4
39.2 even 12 3042.2.b.j.1351.4 4
39.11 even 12 3042.2.b.j.1351.1 4
39.23 odd 6 3042.2.a.x.1.2 2
39.29 odd 6 3042.2.a.r.1.1 2
39.35 odd 6 234.2.h.e.217.1 yes 4
52.35 odd 6 1872.2.t.p.1153.2 4
156.35 even 6 1872.2.t.n.1153.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
234.2.h.d.55.2 4 1.1 even 1 trivial
234.2.h.d.217.2 yes 4 13.9 even 3 inner
234.2.h.e.55.1 yes 4 3.2 odd 2
234.2.h.e.217.1 yes 4 39.35 odd 6
1872.2.t.n.289.1 4 12.11 even 2
1872.2.t.n.1153.1 4 156.35 even 6
1872.2.t.p.289.2 4 4.3 odd 2
1872.2.t.p.1153.2 4 52.35 odd 6
3042.2.a.q.1.1 2 13.10 even 6
3042.2.a.r.1.1 2 39.29 odd 6
3042.2.a.w.1.2 2 13.3 even 3
3042.2.a.x.1.2 2 39.23 odd 6
3042.2.b.j.1351.1 4 39.11 even 12
3042.2.b.j.1351.4 4 39.2 even 12
3042.2.b.k.1351.1 4 13.2 odd 12
3042.2.b.k.1351.4 4 13.11 odd 12