Properties

Label 126.4.g.c.37.1
Level 126126
Weight 44
Character 126.37
Analytic conductor 7.4347.434
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [126,4,Mod(37,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.37"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 126=2327 126 = 2 \cdot 3^{2} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 126.g (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-2,0,-4,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.434240660727.43424066072
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 37.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 126.37
Dual form 126.4.g.c.109.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.00000+1.73205i)q2+(2.000003.46410i)q4+(3.500006.06218i)q5+(10.0000+15.5885i)q7+8.00000q8+(7.00000+12.1244i)q10+(17.5000+30.3109i)q11+66.0000q13+(17.000032.9090i)q14+(8.00000+13.8564i)q16+(29.5000+51.0955i)q17+(68.5000+118.645i)q1928.0000q2070.0000q22+(3.50000+6.06218i)q23+(38.0000+65.8179i)q25+(66.0000+114.315i)q26+(74.0000+3.46410i)q28106.000q29+(37.500064.9519i)q31+(16.000027.7128i)q32118.000q34+(59.5000+115.181i)q35+(5.50000+9.52628i)q37+(137.000237.291i)q38+(28.000048.4974i)q40+498.000q41+260.000q43+(70.0000121.244i)q44+(7.0000012.1244i)q46+(85.5000+148.090i)q47+(143.000311.769i)q49152.000q50+(132.000228.631i)q52+(208.500361.133i)q53+245.000q55+(80.0000+124.708i)q56+(106.000183.597i)q58+(8.5000014.7224i)q59+(25.5000+44.1673i)q61+150.000q62+64.0000q64+(231.000400.104i)q65+(219.500380.185i)q67+(118.000204.382i)q68+(259.00012.1244i)q70+784.000q71+(147.500255.477i)q73+(11.000019.0526i)q74+548.000q76+(647.50030.3109i)q77+(247.500428.683i)q79+(56.0000+96.9948i)q80+(498.000+862.561i)q82932.000q83+413.000q85+(260.000+450.333i)q86+(140.000+242.487i)q88+(436.500+756.040i)q89+(660.000+1028.84i)q91+28.0000q92+(171.000296.181i)q94+(479.500+830.518i)q95290.000q97+(683.000+64.0859i)q98+O(q100)q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.50000 - 6.06218i) q^{5} +(-10.0000 + 15.5885i) q^{7} +8.00000 q^{8} +(7.00000 + 12.1244i) q^{10} +(17.5000 + 30.3109i) q^{11} +66.0000 q^{13} +(-17.0000 - 32.9090i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(29.5000 + 51.0955i) q^{17} +(-68.5000 + 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(38.0000 + 65.8179i) q^{25} +(-66.0000 + 114.315i) q^{26} +(74.0000 + 3.46410i) q^{28} -106.000 q^{29} +(-37.5000 - 64.9519i) q^{31} +(-16.0000 - 27.7128i) q^{32} -118.000 q^{34} +(59.5000 + 115.181i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(-137.000 - 237.291i) q^{38} +(28.0000 - 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(70.0000 - 121.244i) q^{44} +(-7.00000 - 12.1244i) q^{46} +(-85.5000 + 148.090i) q^{47} +(-143.000 - 311.769i) q^{49} -152.000 q^{50} +(-132.000 - 228.631i) q^{52} +(-208.500 - 361.133i) q^{53} +245.000 q^{55} +(-80.0000 + 124.708i) q^{56} +(106.000 - 183.597i) q^{58} +(-8.50000 - 14.7224i) q^{59} +(-25.5000 + 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(231.000 - 400.104i) q^{65} +(-219.500 - 380.185i) q^{67} +(118.000 - 204.382i) q^{68} +(-259.000 - 12.1244i) q^{70} +784.000 q^{71} +(-147.500 - 255.477i) q^{73} +(-11.0000 - 19.0526i) q^{74} +548.000 q^{76} +(-647.500 - 30.3109i) q^{77} +(247.500 - 428.683i) q^{79} +(56.0000 + 96.9948i) q^{80} +(-498.000 + 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(-260.000 + 450.333i) q^{86} +(140.000 + 242.487i) q^{88} +(-436.500 + 756.040i) q^{89} +(-660.000 + 1028.84i) q^{91} +28.0000 q^{92} +(-171.000 - 296.181i) q^{94} +(479.500 + 830.518i) q^{95} -290.000 q^{97} +(683.000 + 64.0859i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q24q4+7q520q7+16q8+14q10+35q11+132q1334q1416q16+59q17137q1956q20140q227q23+76q25132q26++1366q98+O(q100) 2 q - 2 q^{2} - 4 q^{4} + 7 q^{5} - 20 q^{7} + 16 q^{8} + 14 q^{10} + 35 q^{11} + 132 q^{13} - 34 q^{14} - 16 q^{16} + 59 q^{17} - 137 q^{19} - 56 q^{20} - 140 q^{22} - 7 q^{23} + 76 q^{25} - 132 q^{26}+ \cdots + 1366 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/126Z)×\left(\mathbb{Z}/126\mathbb{Z}\right)^\times.

nn 2929 7373
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right)

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 −1.00000 + 1.73205i −0.353553 + 0.612372i
33 0 0
44 −2.00000 3.46410i −0.250000 0.433013i
55 3.50000 6.06218i 0.313050 0.542218i −0.665971 0.745977i 0.731983π-0.731983\pi
0.979021 + 0.203760i 0.0653161π0.0653161\pi
66 0 0
77 −10.0000 + 15.5885i −0.539949 + 0.841698i
88 8.00000 0.353553
99 0 0
1010 7.00000 + 12.1244i 0.221359 + 0.383406i
1111 17.5000 + 30.3109i 0.479677 + 0.830825i 0.999728 0.0233099i 0.00742046π-0.00742046\pi
−0.520051 + 0.854135i 0.674087π0.674087\pi
1212 0 0
1313 66.0000 1.40809 0.704043 0.710158i 0.251376π-0.251376\pi
0.704043 + 0.710158i 0.251376π0.251376\pi
1414 −17.0000 32.9090i −0.324532 0.628235i
1515 0 0
1616 −8.00000 + 13.8564i −0.125000 + 0.216506i
1717 29.5000 + 51.0955i 0.420871 + 0.728969i 0.996025 0.0890757i 0.0283913π-0.0283913\pi
−0.575154 + 0.818045i 0.695058π0.695058\pi
1818 0 0
1919 −68.5000 + 118.645i −0.827104 + 1.43259i 0.0731965 + 0.997318i 0.476680π0.476680\pi
−0.900301 + 0.435269i 0.856653π0.856653\pi
2020 −28.0000 −0.313050
2121 0 0
2222 −70.0000 −0.678366
2323 −3.50000 + 6.06218i −0.0317305 + 0.0549588i −0.881455 0.472269i 0.843435π-0.843435\pi
0.849724 + 0.527228i 0.176768π0.176768\pi
2424 0 0
2525 38.0000 + 65.8179i 0.304000 + 0.526543i
2626 −66.0000 + 114.315i −0.497833 + 0.862273i
2727 0 0
2828 74.0000 + 3.46410i 0.499453 + 0.0233805i
2929 −106.000 −0.678748 −0.339374 0.940651i 0.610215π-0.610215\pi
−0.339374 + 0.940651i 0.610215π0.610215\pi
3030 0 0
3131 −37.5000 64.9519i −0.217264 0.376313i 0.736706 0.676213i 0.236380π-0.236380\pi
−0.953971 + 0.299900i 0.903047π0.903047\pi
3232 −16.0000 27.7128i −0.0883883 0.153093i
3333 0 0
3434 −118.000 −0.595201
3535 59.5000 + 115.181i 0.287352 + 0.556263i
3636 0 0
3737 −5.50000 + 9.52628i −0.0244377 + 0.0423273i −0.877986 0.478687i 0.841113π-0.841113\pi
0.853548 + 0.521014i 0.174446π0.174446\pi
3838 −137.000 237.291i −0.584851 1.01299i
3939 0 0
4040 28.0000 48.4974i 0.110680 0.191703i
4141 498.000 1.89694 0.948470 0.316867i 0.102631π-0.102631\pi
0.948470 + 0.316867i 0.102631π0.102631\pi
4242 0 0
4343 260.000 0.922084 0.461042 0.887378i 0.347476π-0.347476\pi
0.461042 + 0.887378i 0.347476π0.347476\pi
4444 70.0000 121.244i 0.239839 0.415413i
4545 0 0
4646 −7.00000 12.1244i −0.0224368 0.0388617i
4747 −85.5000 + 148.090i −0.265350 + 0.459600i −0.967655 0.252276i 0.918821π-0.918821\pi
0.702305 + 0.711876i 0.252154π0.252154\pi
4848 0 0
4949 −143.000 311.769i −0.416910 0.908948i
5050 −152.000 −0.429921
5151 0 0
5252 −132.000 228.631i −0.352021 0.609719i
5353 −208.500 361.133i −0.540371 0.935951i −0.998883 0.0472619i 0.984950π-0.984950\pi
0.458511 0.888689i 0.348383π-0.348383\pi
5454 0 0
5555 245.000 0.600651
5656 −80.0000 + 124.708i −0.190901 + 0.297585i
5757 0 0
5858 106.000 183.597i 0.239974 0.415647i
5959 −8.50000 14.7224i −0.0187560 0.0324864i 0.856495 0.516155i 0.172637π-0.172637\pi
−0.875251 + 0.483669i 0.839304π0.839304\pi
6060 0 0
6161 −25.5000 + 44.1673i −0.0535236 + 0.0927056i −0.891546 0.452930i 0.850379π-0.850379\pi
0.838022 + 0.545636i 0.183712π0.183712\pi
6262 150.000 0.307258
6363 0 0
6464 64.0000 0.125000
6565 231.000 400.104i 0.440800 0.763489i
6666 0 0
6767 −219.500 380.185i −0.400242 0.693239i 0.593513 0.804824i 0.297740π-0.297740\pi
−0.993755 + 0.111585i 0.964407π0.964407\pi
6868 118.000 204.382i 0.210435 0.364485i
6969 0 0
7070 −259.000 12.1244i −0.442235 0.0207020i
7171 784.000 1.31047 0.655237 0.755423i 0.272569π-0.272569\pi
0.655237 + 0.755423i 0.272569π0.272569\pi
7272 0 0
7373 −147.500 255.477i −0.236487 0.409608i 0.723217 0.690621i 0.242663π-0.242663\pi
−0.959704 + 0.281013i 0.909329π0.909329\pi
7474 −11.0000 19.0526i −0.0172801 0.0299299i
7575 0 0
7676 548.000 0.827104
7777 −647.500 30.3109i −0.958305 0.0448603i
7878 0 0
7979 247.500 428.683i 0.352480 0.610513i −0.634203 0.773166i 0.718672π-0.718672\pi
0.986683 + 0.162653i 0.0520051π0.0520051\pi
8080 56.0000 + 96.9948i 0.0782624 + 0.135554i
8181 0 0
8282 −498.000 + 862.561i −0.670670 + 1.16163i
8383 −932.000 −1.23253 −0.616267 0.787537i 0.711356π-0.711356\pi
−0.616267 + 0.787537i 0.711356π0.711356\pi
8484 0 0
8585 413.000 0.527013
8686 −260.000 + 450.333i −0.326006 + 0.564659i
8787 0 0
8888 140.000 + 242.487i 0.169591 + 0.293741i
8989 −436.500 + 756.040i −0.519875 + 0.900451i 0.479858 + 0.877346i 0.340688π0.340688\pi
−0.999733 + 0.0231042i 0.992645π0.992645\pi
9090 0 0
9191 −660.000 + 1028.84i −0.760294 + 1.18518i
9292 28.0000 0.0317305
9393 0 0
9494 −171.000 296.181i −0.187631 0.324986i
9595 479.500 + 830.518i 0.517849 + 0.896941i
9696 0 0
9797 −290.000 −0.303557 −0.151779 0.988415i 0.548500π-0.548500\pi
−0.151779 + 0.988415i 0.548500π0.548500\pi
9898 683.000 + 64.0859i 0.704014 + 0.0660577i
9999 0 0
100100 152.000 263.272i 0.152000 0.263272i
101101 −542.500 939.638i −0.534463 0.925717i −0.999189 0.0402627i 0.987181π-0.987181\pi
0.464726 0.885454i 0.346153π-0.346153\pi
102102 0 0
103103 −776.500 + 1344.94i −0.742823 + 1.28661i 0.208381 + 0.978048i 0.433181π0.433181\pi
−0.951205 + 0.308560i 0.900153π0.900153\pi
104104 528.000 0.497833
105105 0 0
106106 834.000 0.764200
107107 64.5000 111.717i 0.0582752 0.100936i −0.835416 0.549618i 0.814773π-0.814773\pi
0.893691 + 0.448682i 0.148107π0.148107\pi
108108 0 0
109109 482.500 + 835.715i 0.423992 + 0.734376i 0.996326 0.0856452i 0.0272952π-0.0272952\pi
−0.572334 + 0.820021i 0.693962π0.693962\pi
110110 −245.000 + 424.352i −0.212362 + 0.367822i
111111 0 0
112112 −136.000 263.272i −0.114739 0.222115i
113113 50.0000 0.0416248 0.0208124 0.999783i 0.493375π-0.493375\pi
0.0208124 + 0.999783i 0.493375π0.493375\pi
114114 0 0
115115 24.5000 + 42.4352i 0.0198664 + 0.0344096i
116116 212.000 + 367.195i 0.169687 + 0.293907i
117117 0 0
118118 34.0000 0.0265250
119119 −1091.50 51.0955i −0.840821 0.0393606i
120120 0 0
121121 53.0000 91.7987i 0.0398197 0.0689697i
122122 −51.0000 88.3346i −0.0378469 0.0655528i
123123 0 0
124124 −150.000 + 259.808i −0.108632 + 0.188157i
125125 1407.00 1.00677
126126 0 0
127127 936.000 0.653989 0.326994 0.945026i 0.393964π-0.393964\pi
0.326994 + 0.945026i 0.393964π0.393964\pi
128128 −64.0000 + 110.851i −0.0441942 + 0.0765466i
129129 0 0
130130 462.000 + 800.207i 0.311693 + 0.539868i
131131 −377.500 + 653.849i −0.251773 + 0.436084i −0.964014 0.265851i 0.914347π-0.914347\pi
0.712241 + 0.701935i 0.247680π0.247680\pi
132132 0 0
133133 −1164.50 2254.26i −0.759210 1.46970i
134134 878.000 0.566027
135135 0 0
136136 236.000 + 408.764i 0.148800 + 0.257730i
137137 −1178.50 2041.22i −0.734935 1.27294i −0.954752 0.297403i 0.903879π-0.903879\pi
0.219817 0.975541i 0.429454π-0.429454\pi
138138 0 0
139139 28.0000 0.0170858 0.00854291 0.999964i 0.497281π-0.497281\pi
0.00854291 + 0.999964i 0.497281π0.497281\pi
140140 280.000 436.477i 0.169031 0.263493i
141141 0 0
142142 −784.000 + 1357.93i −0.463323 + 0.802498i
143143 1155.00 + 2000.52i 0.675426 + 1.16987i
144144 0 0
145145 −371.000 + 642.591i −0.212482 + 0.368029i
146146 590.000 0.334443
147147 0 0
148148 44.0000 0.0244377
149149 1147.50 1987.53i 0.630919 1.09278i −0.356446 0.934316i 0.616012π-0.616012\pi
0.987364 0.158467i 0.0506551π-0.0506551\pi
150150 0 0
151151 554.500 + 960.422i 0.298838 + 0.517603i 0.975870 0.218350i 0.0700676π-0.0700676\pi
−0.677032 + 0.735953i 0.736734π0.736734\pi
152152 −548.000 + 949.164i −0.292425 + 0.506496i
153153 0 0
154154 700.000 1091.19i 0.366283 0.570979i
155155 −525.000 −0.272058
156156 0 0
157157 −779.500 1350.13i −0.396248 0.686321i 0.597012 0.802232i 0.296354π-0.296354\pi
−0.993260 + 0.115911i 0.963021π0.963021\pi
158158 495.000 + 857.365i 0.249241 + 0.431698i
159159 0 0
160160 −224.000 −0.110680
161161 −59.5000 115.181i −0.0291258 0.0563824i
162162 0 0
163163 1125.50 1949.42i 0.540834 0.936752i −0.458022 0.888941i 0.651442π-0.651442\pi
0.998856 0.0478115i 0.0152247π-0.0152247\pi
164164 −996.000 1725.12i −0.474235 0.821399i
165165 0 0
166166 932.000 1614.27i 0.435766 0.754770i
167167 −2788.00 −1.29187 −0.645934 0.763393i 0.723532π-0.723532\pi
−0.645934 + 0.763393i 0.723532π0.723532\pi
168168 0 0
169169 2159.00 0.982704
170170 −413.000 + 715.337i −0.186327 + 0.322728i
171171 0 0
172172 −520.000 900.666i −0.230521 0.399274i
173173 789.500 1367.45i 0.346963 0.600957i −0.638746 0.769418i 0.720546π-0.720546\pi
0.985708 + 0.168461i 0.0538797π0.0538797\pi
174174 0 0
175175 −1406.00 65.8179i −0.607335 0.0284307i
176176 −560.000 −0.239839
177177 0 0
178178 −873.000 1512.08i −0.367607 0.636715i
179179 1225.50 + 2122.63i 0.511722 + 0.886328i 0.999908 + 0.0135883i 0.00432541π0.00432541\pi
−0.488186 + 0.872740i 0.662341π0.662341\pi
180180 0 0
181181 −1170.00 −0.480472 −0.240236 0.970715i 0.577225π-0.577225\pi
−0.240236 + 0.970715i 0.577225π0.577225\pi
182182 −1122.00 2171.99i −0.456968 0.884608i
183183 0 0
184184 −28.0000 + 48.4974i −0.0112184 + 0.0194309i
185185 38.5000 + 66.6840i 0.0153004 + 0.0265011i
186186 0 0
187187 −1032.50 + 1788.34i −0.403764 + 0.699340i
188188 684.000 0.265350
189189 0 0
190190 −1918.00 −0.732349
191191 −637.500 + 1104.18i −0.241507 + 0.418303i −0.961144 0.276048i 0.910975π-0.910975\pi
0.719637 + 0.694351i 0.244308π0.244308\pi
192192 0 0
193193 −17.5000 30.3109i −0.00652683 0.0113048i 0.862744 0.505642i 0.168744π-0.168744\pi
−0.869270 + 0.494337i 0.835411π0.835411\pi
194194 290.000 502.295i 0.107324 0.185890i
195195 0 0
196196 −794.000 + 1118.90i −0.289359 + 0.407764i
197197 2734.00 0.988779 0.494389 0.869241i 0.335392π-0.335392\pi
0.494389 + 0.869241i 0.335392π0.335392\pi
198198 0 0
199199 −1121.50 1942.49i −0.399503 0.691959i 0.594162 0.804345i 0.297484π-0.297484\pi
−0.993665 + 0.112387i 0.964151π0.964151\pi
200200 304.000 + 526.543i 0.107480 + 0.186161i
201201 0 0
202202 2170.00 0.755845
203203 1060.00 1652.38i 0.366490 0.571301i
204204 0 0
205205 1743.00 3018.96i 0.593836 1.02855i
206206 −1553.00 2689.87i −0.525256 0.909769i
207207 0 0
208208 −528.000 + 914.523i −0.176011 + 0.304859i
209209 −4795.00 −1.58697
210210 0 0
211211 1172.00 0.382388 0.191194 0.981552i 0.438764π-0.438764\pi
0.191194 + 0.981552i 0.438764π0.438764\pi
212212 −834.000 + 1444.53i −0.270186 + 0.467975i
213213 0 0
214214 129.000 + 223.435i 0.0412068 + 0.0713723i
215215 910.000 1576.17i 0.288658 0.499970i
216216 0 0
217217 1387.50 + 64.9519i 0.434054 + 0.0203190i
218218 −1930.00 −0.599615
219219 0 0
220220 −490.000 848.705i −0.150163 0.260089i
221221 1947.00 + 3372.30i 0.592622 + 1.02645i
222222 0 0
223223 2024.00 0.607790 0.303895 0.952706i 0.401713π-0.401713\pi
0.303895 + 0.952706i 0.401713π0.401713\pi
224224 592.000 + 27.7128i 0.176583 + 0.00826625i
225225 0 0
226226 −50.0000 + 86.6025i −0.0147166 + 0.0254899i
227227 1285.50 + 2226.55i 0.375866 + 0.651019i 0.990456 0.137827i 0.0440119π-0.0440119\pi
−0.614590 + 0.788847i 0.710679π0.710679\pi
228228 0 0
229229 −447.500 + 775.093i −0.129134 + 0.223666i −0.923341 0.383980i 0.874553π-0.874553\pi
0.794207 + 0.607647i 0.207886π0.207886\pi
230230 −98.0000 −0.0280953
231231 0 0
232232 −848.000 −0.239974
233233 893.500 1547.59i 0.251224 0.435132i −0.712639 0.701531i 0.752500π-0.752500\pi
0.963863 + 0.266398i 0.0858337π0.0858337\pi
234234 0 0
235235 598.500 + 1036.63i 0.166135 + 0.287755i
236236 −34.0000 + 58.8897i −0.00937801 + 0.0162432i
237237 0 0
238238 1180.00 1839.44i 0.321378 0.500979i
239239 5100.00 1.38030 0.690150 0.723667i 0.257545π-0.257545\pi
0.690150 + 0.723667i 0.257545π0.257545\pi
240240 0 0
241241 2088.50 + 3617.39i 0.558225 + 0.966873i 0.997645 + 0.0685917i 0.0218506π0.0218506\pi
−0.439420 + 0.898282i 0.644816π0.644816\pi
242242 106.000 + 183.597i 0.0281568 + 0.0487690i
243243 0 0
244244 204.000 0.0535236
245245 −2390.50 224.301i −0.623361 0.0584900i
246246 0 0
247247 −4521.00 + 7830.60i −1.16463 + 2.01720i
248248 −300.000 519.615i −0.0768146 0.133047i
249249 0 0
250250 −1407.00 + 2437.00i −0.355946 + 0.616517i
251251 4680.00 1.17689 0.588444 0.808538i 0.299741π-0.299741\pi
0.588444 + 0.808538i 0.299741π0.299741\pi
252252 0 0
253253 −245.000 −0.0608815
254254 −936.000 + 1621.20i −0.231220 + 0.400485i
255255 0 0
256256 −128.000 221.703i −0.0312500 0.0541266i
257257 −874.500 + 1514.68i −0.212256 + 0.367638i −0.952420 0.304788i 0.901414π-0.901414\pi
0.740164 + 0.672426i 0.234748π0.234748\pi
258258 0 0
259259 −93.5000 180.999i −0.0224317 0.0434237i
260260 −1848.00 −0.440800
261261 0 0
262262 −755.000 1307.70i −0.178031 0.308358i
263263 −2236.50 3873.73i −0.524367 0.908230i −0.999598 0.0283689i 0.990969π-0.990969\pi
0.475231 0.879861i 0.342365π-0.342365\pi
264264 0 0
265265 −2919.00 −0.676652
266266 5069.00 + 237.291i 1.16842 + 0.0546964i
267267 0 0
268268 −878.000 + 1520.74i −0.200121 + 0.346619i
269269 987.500 + 1710.40i 0.223825 + 0.387676i 0.955966 0.293476i 0.0948122π-0.0948122\pi
−0.732141 + 0.681153i 0.761479π0.761479\pi
270270 0 0
271271 4219.50 7308.39i 0.945817 1.63820i 0.191710 0.981452i 0.438597π-0.438597\pi
0.754107 0.656751i 0.228070π-0.228070\pi
272272 −944.000 −0.210435
273273 0 0
274274 4714.00 1.03935
275275 −1330.00 + 2303.63i −0.291644 + 0.505142i
276276 0 0
277277 −263.500 456.395i −0.0571559 0.0989969i 0.836032 0.548681i 0.184870π-0.184870\pi
−0.893188 + 0.449684i 0.851537π0.851537\pi
278278 −28.0000 + 48.4974i −0.00604075 + 0.0104629i
279279 0 0
280280 476.000 + 921.451i 0.101594 + 0.196669i
281281 202.000 0.0428837 0.0214418 0.999770i 0.493174π-0.493174\pi
0.0214418 + 0.999770i 0.493174π0.493174\pi
282282 0 0
283283 3974.50 + 6884.04i 0.834839 + 1.44598i 0.894161 + 0.447745i 0.147773π0.147773\pi
−0.0593220 + 0.998239i 0.518894π0.518894\pi
284284 −1568.00 2715.86i −0.327619 0.567452i
285285 0 0
286286 −4620.00 −0.955197
287287 −4980.00 + 7763.05i −1.02425 + 1.59665i
288288 0 0
289289 716.000 1240.15i 0.145736 0.252422i
290290 −742.000 1285.18i −0.150247 0.260236i
291291 0 0
292292 −590.000 + 1021.91i −0.118244 + 0.204804i
293293 −318.000 −0.0634053 −0.0317027 0.999497i 0.510093π-0.510093\pi
−0.0317027 + 0.999497i 0.510093π0.510093\pi
294294 0 0
295295 −119.000 −0.0234863
296296 −44.0000 + 76.2102i −0.00864003 + 0.0149650i
297297 0 0
298298 2295.00 + 3975.06i 0.446127 + 0.772714i
299299 −231.000 + 400.104i −0.0446792 + 0.0773866i
300300 0 0
301301 −2600.00 + 4053.00i −0.497879 + 0.776116i
302302 −2218.00 −0.422621
303303 0 0
304304 −1096.00 1898.33i −0.206776 0.358147i
305305 178.500 + 309.171i 0.0335111 + 0.0580429i
306306 0 0
307307 −8132.00 −1.51178 −0.755892 0.654696i 0.772797π-0.772797\pi
−0.755892 + 0.654696i 0.772797π0.772797\pi
308308 1190.00 + 2303.63i 0.220151 + 0.426173i
309309 0 0
310310 525.000 909.327i 0.0961871 0.166601i
311311 −464.500 804.538i −0.0846925 0.146692i 0.820568 0.571549i 0.193657π-0.193657\pi
−0.905260 + 0.424858i 0.860324π0.860324\pi
312312 0 0
313313 104.500 180.999i 0.0188712 0.0326859i −0.856436 0.516254i 0.827326π-0.827326\pi
0.875307 + 0.483568i 0.160659π0.160659\pi
314314 3118.00 0.560379
315315 0 0
316316 −1980.00 −0.352480
317317 3565.50 6175.63i 0.631730 1.09419i −0.355468 0.934689i 0.615678π-0.615678\pi
0.987198 0.159500i 0.0509882π-0.0509882\pi
318318 0 0
319319 −1855.00 3212.95i −0.325580 0.563921i
320320 224.000 387.979i 0.0391312 0.0677772i
321321 0 0
322322 259.000 + 12.1244i 0.0448246 + 0.00209834i
323323 −8083.00 −1.39242
324324 0 0
325325 2508.00 + 4343.98i 0.428058 + 0.741418i
326326 2251.00 + 3898.85i 0.382427 + 0.662384i
327327 0 0
328328 3984.00 0.670670
329329 −1453.50 2813.72i −0.243569 0.471505i
330330 0 0
331331 3285.50 5690.65i 0.545581 0.944975i −0.452989 0.891516i 0.649642π-0.649642\pi
0.998570 0.0534583i 0.0170244π-0.0170244\pi
332332 1864.00 + 3228.54i 0.308133 + 0.533703i
333333 0 0
334334 2788.00 4828.96i 0.456744 0.791104i
335335 −3073.00 −0.501182
336336 0 0
337337 −11466.0 −1.85339 −0.926696 0.375813i 0.877364π-0.877364\pi
−0.926696 + 0.375813i 0.877364π0.877364\pi
338338 −2159.00 + 3739.50i −0.347438 + 0.601781i
339339 0 0
340340 −826.000 1430.67i −0.131753 0.228203i
341341 1312.50 2273.32i 0.208434 0.361018i
342342 0 0
343343 6290.00 + 888.542i 0.990169 + 0.139874i
344344 2080.00 0.326006
345345 0 0
346346 1579.00 + 2734.91i 0.245340 + 0.424941i
347347 −4888.50 8467.13i −0.756278 1.30991i −0.944737 0.327831i 0.893682π-0.893682\pi
0.188459 0.982081i 0.439651π-0.439651\pi
348348 0 0
349349 11914.0 1.82734 0.913670 0.406456i 0.133236π-0.133236\pi
0.913670 + 0.406456i 0.133236π0.133236\pi
350350 1520.00 2369.45i 0.232135 0.361863i
351351 0 0
352352 560.000 969.948i 0.0847957 0.146871i
353353 4561.50 + 7900.75i 0.687774 + 1.19126i 0.972556 + 0.232667i 0.0747452π0.0747452\pi
−0.284783 + 0.958592i 0.591921π0.591921\pi
354354 0 0
355355 2744.00 4752.75i 0.410243 0.710562i
356356 3492.00 0.519875
357357 0 0
358358 −4902.00 −0.723684
359359 4074.50 7057.24i 0.599008 1.03751i −0.393960 0.919128i 0.628895π-0.628895\pi
0.992968 0.118385i 0.0377716π-0.0377716\pi
360360 0 0
361361 −5955.00 10314.4i −0.868202 1.50377i
362362 1170.00 2026.50i 0.169872 0.294228i
363363 0 0
364364 4884.00 + 228.631i 0.703272 + 0.0329217i
365365 −2065.00 −0.296129
366366 0 0
367367 −4835.50 8375.33i −0.687769 1.19125i −0.972558 0.232660i 0.925257π-0.925257\pi
0.284790 0.958590i 0.408076π-0.408076\pi
368368 −56.0000 96.9948i −0.00793261 0.0137397i
369369 0 0
370370 −154.000 −0.0216381
371371 7714.50 + 361.133i 1.07956 + 0.0505366i
372372 0 0
373373 2054.50 3558.50i 0.285196 0.493973i −0.687461 0.726221i 0.741275π-0.741275\pi
0.972657 + 0.232248i 0.0746081π0.0746081\pi
374374 −2065.00 3576.68i −0.285504 0.494508i
375375 0 0
376376 −684.000 + 1184.72i −0.0938154 + 0.162493i
377377 −6996.00 −0.955736
378378 0 0
379379 −3488.00 −0.472735 −0.236367 0.971664i 0.575957π-0.575957\pi
−0.236367 + 0.971664i 0.575957π0.575957\pi
380380 1918.00 3322.07i 0.258925 0.448470i
381381 0 0
382382 −1275.00 2208.36i −0.170771 0.295785i
383383 4358.50 7549.14i 0.581485 1.00716i −0.413818 0.910360i 0.635805π-0.635805\pi
0.995304 0.0968028i 0.0308616π-0.0308616\pi
384384 0 0
385385 −2450.00 + 3819.17i −0.324321 + 0.505566i
386386 70.0000 0.00923033
387387 0 0
388388 580.000 + 1004.59i 0.0758893 + 0.131444i
389389 81.5000 + 141.162i 0.0106227 + 0.0183990i 0.871288 0.490772i 0.163285π-0.163285\pi
−0.860665 + 0.509171i 0.829952π0.829952\pi
390390 0 0
391391 −413.000 −0.0534177
392392 −1144.00 2494.15i −0.147400 0.321362i
393393 0 0
394394 −2734.00 + 4735.43i −0.349586 + 0.605501i
395395 −1732.50 3000.78i −0.220687 0.382242i
396396 0 0
397397 −499.500 + 865.159i −0.0631466 + 0.109373i −0.895870 0.444316i 0.853447π-0.853447\pi
0.832724 + 0.553689i 0.186780π0.186780\pi
398398 4486.00 0.564982
399399 0 0
400400 −1216.00 −0.152000
401401 −7378.50 + 12779.9i −0.918865 + 1.59152i −0.117722 + 0.993047i 0.537559π0.537559\pi
−0.801143 + 0.598474i 0.795774π0.795774\pi
402402 0 0
403403 −2475.00 4286.83i −0.305927 0.529881i
404404 −2170.00 + 3758.55i −0.267232 + 0.462859i
405405 0 0
406406 1802.00 + 3488.35i 0.220275 + 0.426414i
407407 −385.000 −0.0468888
408408 0 0
409409 66.5000 + 115.181i 0.00803964 + 0.0139251i 0.870017 0.493021i 0.164108π-0.164108\pi
−0.861978 + 0.506946i 0.830774π0.830774\pi
410410 3486.00 + 6037.93i 0.419906 + 0.727298i
411411 0 0
412412 6212.00 0.742823
413413 314.500 + 14.7224i 0.0374710 + 0.00175410i
414414 0 0
415415 −3262.00 + 5649.95i −0.385844 + 0.668302i
416416 −1056.00 1829.05i −0.124458 0.215568i
417417 0 0
418418 4795.00 8305.18i 0.561079 0.971818i
419419 6420.00 0.748538 0.374269 0.927320i 0.377894π-0.377894\pi
0.374269 + 0.927320i 0.377894π0.377894\pi
420420 0 0
421421 10266.0 1.18844 0.594221 0.804302i 0.297460π-0.297460\pi
0.594221 + 0.804302i 0.297460π0.297460\pi
422422 −1172.00 + 2029.96i −0.135194 + 0.234164i
423423 0 0
424424 −1668.00 2889.06i −0.191050 0.330908i
425425 −2242.00 + 3883.26i −0.255889 + 0.443213i
426426 0 0
427427 −433.500 839.179i −0.0491301 0.0951070i
428428 −516.000 −0.0582752
429429 0 0
430430 1820.00 + 3152.33i 0.204112 + 0.353532i
431431 −7606.50 13174.8i −0.850098 1.47241i −0.881119 0.472894i 0.843209π-0.843209\pi
0.0310213 0.999519i 0.490124π-0.490124\pi
432432 0 0
433433 −1378.00 −0.152939 −0.0764693 0.997072i 0.524365π-0.524365\pi
−0.0764693 + 0.997072i 0.524365π0.524365\pi
434434 −1500.00 + 2338.27i −0.165904 + 0.258619i
435435 0 0
436436 1930.00 3342.86i 0.211996 0.367188i
437437 −479.500 830.518i −0.0524888 0.0909132i
438438 0 0
439439 1381.50 2392.83i 0.150195 0.260145i −0.781104 0.624401i 0.785343π-0.785343\pi
0.931299 + 0.364256i 0.118677π0.118677\pi
440440 1960.00 0.212362
441441 0 0
442442 −7788.00 −0.838094
443443 2924.50 5065.38i 0.313651 0.543259i −0.665499 0.746399i 0.731781π-0.731781\pi
0.979150 + 0.203140i 0.0651146π0.0651146\pi
444444 0 0
445445 3055.50 + 5292.28i 0.325493 + 0.563771i
446446 −2024.00 + 3505.67i −0.214886 + 0.372194i
447447 0 0
448448 −640.000 + 997.661i −0.0674937 + 0.105212i
449449 −4582.00 −0.481599 −0.240799 0.970575i 0.577410π-0.577410\pi
−0.240799 + 0.970575i 0.577410π0.577410\pi
450450 0 0
451451 8715.00 + 15094.8i 0.909919 + 1.57603i
452452 −100.000 173.205i −0.0104062 0.0180241i
453453 0 0
454454 −5142.00 −0.531555
455455 3927.00 + 7601.97i 0.404617 + 0.783266i
456456 0 0
457457 −5775.50 + 10003.5i −0.591174 + 1.02394i 0.402901 + 0.915244i 0.368002π0.368002\pi
−0.994075 + 0.108700i 0.965331π0.965331\pi
458458 −895.000 1550.19i −0.0913114 0.158156i
459459 0 0
460460 98.0000 169.741i 0.00993320 0.0172048i
461461 9494.00 0.959175 0.479587 0.877494i 0.340786π-0.340786\pi
0.479587 + 0.877494i 0.340786π0.340786\pi
462462 0 0
463463 −10160.0 −1.01982 −0.509908 0.860229i 0.670321π-0.670321\pi
−0.509908 + 0.860229i 0.670321π0.670321\pi
464464 848.000 1468.78i 0.0848436 0.146953i
465465 0 0
466466 1787.00 + 3095.17i 0.177642 + 0.307685i
467467 −653.500 + 1131.90i −0.0647545 + 0.112158i −0.896585 0.442872i 0.853960π-0.853960\pi
0.831831 + 0.555030i 0.187293π0.187293\pi
468468 0 0
469469 8121.50 + 380.185i 0.799608 + 0.0374314i
470470 −2394.00 −0.234951
471471 0 0
472472 −68.0000 117.779i −0.00663126 0.0114857i
473473 4550.00 + 7880.83i 0.442303 + 0.766091i
474474 0 0
475475 −10412.0 −1.00576
476476 2006.00 + 3883.26i 0.193161 + 0.373926i
477477 0 0
478478 −5100.00 + 8833.46i −0.488010 + 0.845257i
479479 9143.50 + 15837.0i 0.872186 + 1.51067i 0.859730 + 0.510748i 0.170632π0.170632\pi
0.0124559 + 0.999922i 0.496035π0.496035\pi
480480 0 0
481481 −363.000 + 628.734i −0.0344103 + 0.0596005i
482482 −8354.00 −0.789449
483483 0 0
484484 −424.000 −0.0398197
485485 −1015.00 + 1758.03i −0.0950284 + 0.164594i
486486 0 0
487487 7476.50 + 12949.7i 0.695673 + 1.20494i 0.969953 + 0.243291i 0.0782269π0.0782269\pi
−0.274281 + 0.961650i 0.588440π0.588440\pi
488488 −204.000 + 353.338i −0.0189235 + 0.0327764i
489489 0 0
490490 2779.00 3916.17i 0.256209 0.361050i
491491 −14352.0 −1.31914 −0.659569 0.751644i 0.729261π-0.729261\pi
−0.659569 + 0.751644i 0.729261π0.729261\pi
492492 0 0
493493 −3127.00 5416.12i −0.285665 0.494787i
494494 −9042.00 15661.2i −0.823520 1.42638i
495495 0 0
496496 1200.00 0.108632
497497 −7840.00 + 12221.4i −0.707590 + 1.10302i
498498 0 0
499499 2765.50 4789.99i 0.248098 0.429718i −0.714900 0.699226i 0.753528π-0.753528\pi
0.962998 + 0.269509i 0.0868612π0.0868612\pi
500500 −2814.00 4873.99i −0.251692 0.435943i
501501 0 0
502502 −4680.00 + 8106.00i −0.416093 + 0.720694i
503503 −8400.00 −0.744607 −0.372304 0.928111i 0.621432π-0.621432\pi
−0.372304 + 0.928111i 0.621432π0.621432\pi
504504 0 0
505505 −7595.00 −0.669254
506506 245.000 424.352i 0.0215249 0.0372821i
507507 0 0
508508 −1872.00 3242.40i −0.163497 0.283185i
509509 −1192.50 + 2065.47i −0.103844 + 0.179863i −0.913265 0.407365i 0.866448π-0.866448\pi
0.809421 + 0.587228i 0.199781π0.199781\pi
510510 0 0
511511 5457.50 + 255.477i 0.472457 + 0.0221167i
512512 512.000 0.0441942
513513 0 0
514514 −1749.00 3029.36i −0.150088 0.259960i
515515 5435.50 + 9414.56i 0.465081 + 0.805544i
516516 0 0
517517 −5985.00 −0.509130
518518 407.000 + 19.0526i 0.0345223 + 0.00161606i
519519 0 0
520520 1848.00 3200.83i 0.155846 0.269934i
521521 −4576.50 7926.73i −0.384837 0.666557i 0.606910 0.794771i 0.292409π-0.292409\pi
−0.991747 + 0.128214i 0.959076π0.959076\pi
522522 0 0
523523 6903.50 11957.2i 0.577187 0.999718i −0.418613 0.908165i 0.637484π-0.637484\pi
0.995800 0.0915530i 0.0291831π-0.0291831\pi
524524 3020.00 0.251773
525525 0 0
526526 8946.00 0.741567
527527 2212.50 3832.16i 0.182880 0.316758i
528528 0 0
529529 6059.00 + 10494.5i 0.497986 + 0.862538i
530530 2919.00 5055.86i 0.239233 0.414363i
531531 0 0
532532 −5480.00 + 8542.47i −0.446594 + 0.696172i
533533 32868.0 2.67105
534534 0 0
535535 −451.500 782.021i −0.0364861 0.0631957i
536536 −1756.00 3041.48i −0.141507 0.245097i
537537 0 0
538538 −3950.00 −0.316536
539539 6947.50 9790.42i 0.555195 0.782381i
540540 0 0
541541 −4087.50 + 7079.76i −0.324834 + 0.562629i −0.981479 0.191571i 0.938642π-0.938642\pi
0.656645 + 0.754200i 0.271975π0.271975\pi
542542 8439.00 + 14616.8i 0.668794 + 1.15838i
543543 0 0
544544 944.000 1635.06i 0.0744001 0.128865i
545545 6755.00 0.530922
546546 0 0
547547 4656.00 0.363942 0.181971 0.983304i 0.441752π-0.441752\pi
0.181971 + 0.983304i 0.441752π0.441752\pi
548548 −4714.00 + 8164.89i −0.367467 + 0.636472i
549549 0 0
550550 −2660.00 4607.26i −0.206223 0.357189i
551551 7261.00 12576.4i 0.561396 0.972366i
552552 0 0
553553 4207.50 + 8144.97i 0.323546 + 0.626328i
554554 1054.00 0.0808306
555555 0 0
556556 −56.0000 96.9948i −0.00427146 0.00739838i
557557 3501.50 + 6064.78i 0.266361 + 0.461352i 0.967919 0.251261i 0.0808452π-0.0808452\pi
−0.701558 + 0.712612i 0.747512π0.747512\pi
558558 0 0
559559 17160.0 1.29837
560560 −2072.00 96.9948i −0.156354 0.00731925i
561561 0 0
562562 −202.000 + 349.874i −0.0151617 + 0.0262608i
563563 −9876.50 17106.6i −0.739334 1.28056i −0.952796 0.303612i 0.901807π-0.901807\pi
0.213462 0.976951i 0.431526π-0.431526\pi
564564 0 0
565565 175.000 303.109i 0.0130306 0.0225697i
566566 −15898.0 −1.18064
567567 0 0
568568 6272.00 0.463323
569569 −3448.50 + 5972.98i −0.254075 + 0.440071i −0.964644 0.263557i 0.915104π-0.915104\pi
0.710569 + 0.703628i 0.248438π0.248438\pi
570570 0 0
571571 −12457.5 21577.0i −0.913013 1.58138i −0.809785 0.586726i 0.800416π-0.800416\pi
−0.103227 0.994658i 0.532917π-0.532917\pi
572572 4620.00 8002.07i 0.337713 0.584936i
573573 0 0
574574 −8466.00 16388.7i −0.615617 1.19172i
575575 −532.000 −0.0385842
576576 0 0
577577 −63.5000 109.985i −0.00458152 0.00793543i 0.863726 0.503962i 0.168125π-0.168125\pi
−0.868307 + 0.496027i 0.834792π0.834792\pi
578578 1432.00 + 2480.30i 0.103051 + 0.178489i
579579 0 0
580580 2968.00 0.212482
581581 9320.00 14528.4i 0.665506 1.03742i
582582 0 0
583583 7297.50 12639.6i 0.518407 0.897908i
584584 −1180.00 2043.82i −0.0836109 0.144818i
585585 0 0
586586 318.000 550.792i 0.0224172 0.0388277i
587587 −9044.00 −0.635921 −0.317961 0.948104i 0.602998π-0.602998\pi
−0.317961 + 0.948104i 0.602998π0.602998\pi
588588 0 0
589589 10275.0 0.718801
590590 119.000 206.114i 0.00830365 0.0143823i
591591 0 0
592592 −88.0000 152.420i −0.00610942 0.0105818i
593593 −5350.50 + 9267.34i −0.370521 + 0.641760i −0.989646 0.143532i 0.954154π-0.954154\pi
0.619125 + 0.785292i 0.287487π0.287487\pi
594594 0 0
595595 −4130.00 + 6438.03i −0.284560 + 0.443586i
596596 −9180.00 −0.630919
597597 0 0
598598 −462.000 800.207i −0.0315930 0.0547206i
599599 10399.5 + 18012.5i 0.709369 + 1.22866i 0.965091 + 0.261913i 0.0843533π0.0843533\pi
−0.255722 + 0.966750i 0.582313π0.582313\pi
600600 0 0
601601 −1402.00 −0.0951560 −0.0475780 0.998868i 0.515150π-0.515150\pi
−0.0475780 + 0.998868i 0.515150π0.515150\pi
602602 −4420.00 8556.33i −0.299245 0.579286i
603603 0 0
604604 2218.00 3841.69i 0.149419 0.258801i
605605 −371.000 642.591i −0.0249311 0.0431819i
606606 0 0
607607 −3262.50 + 5650.82i −0.218156 + 0.377858i −0.954244 0.299028i 0.903338π-0.903338\pi
0.736088 + 0.676886i 0.236671π0.236671\pi
608608 4384.00 0.292425
609609 0 0
610610 −714.000 −0.0473918
611611 −5643.00 + 9773.96i −0.373636 + 0.647156i
612612 0 0
613613 −7525.50 13034.5i −0.495844 0.858826i 0.504145 0.863619i 0.331808π-0.331808\pi
−0.999989 + 0.00479285i 0.998474π0.998474\pi
614614 8132.00 14085.0i 0.534496 0.925775i
615615 0 0
616616 −5180.00 242.487i −0.338812 0.0158605i
617617 −11150.0 −0.727524 −0.363762 0.931492i 0.618508π-0.618508\pi
−0.363762 + 0.931492i 0.618508π0.618508\pi
618618 0 0
619619 −1707.50 2957.48i −0.110873 0.192037i 0.805250 0.592936i 0.202031π-0.202031\pi
−0.916122 + 0.400899i 0.868698π0.868698\pi
620620 1050.00 + 1818.65i 0.0680145 + 0.117805i
621621 0 0
622622 1858.00 0.119773
623623 −7420.50 14364.8i −0.477201 0.923775i
624624 0 0
625625 174.500 302.243i 0.0111680 0.0193435i
626626 209.000 + 361.999i 0.0133440 + 0.0231124i
627627 0 0
628628 −3118.00 + 5400.53i −0.198124 + 0.343160i
629629 −649.000 −0.0411404
630630 0 0
631631 −21184.0 −1.33648 −0.668242 0.743944i 0.732953π-0.732953\pi
−0.668242 + 0.743944i 0.732953π0.732953\pi
632632 1980.00 3429.46i 0.124621 0.215849i
633633 0 0
634634 7131.00 + 12351.3i 0.446701 + 0.773708i
635635 3276.00 5674.20i 0.204731 0.354604i
636636 0 0
637637 −9438.00 20576.8i −0.587044 1.27988i
638638 7420.00 0.460440
639639 0 0
640640 448.000 + 775.959i 0.0276699 + 0.0479257i
641641 −5352.50 9270.80i −0.329814 0.571255i 0.652660 0.757651i 0.273653π-0.273653\pi
−0.982475 + 0.186395i 0.940320π0.940320\pi
642642 0 0
643643 6860.00 0.420734 0.210367 0.977622i 0.432534π-0.432534\pi
0.210367 + 0.977622i 0.432534π0.432534\pi
644644 −280.000 + 436.477i −0.0171328 + 0.0267074i
645645 0 0
646646 8083.00 14000.2i 0.492293 0.852677i
647647 7231.50 + 12525.3i 0.439412 + 0.761084i 0.997644 0.0686008i 0.0218535π-0.0218535\pi
−0.558232 + 0.829685i 0.688520π0.688520\pi
648648 0 0
649649 297.500 515.285i 0.0179937 0.0311660i
650650 −10032.0 −0.605365
651651 0 0
652652 −9004.00 −0.540834
653653 2989.50 5177.97i 0.179155 0.310305i −0.762436 0.647063i 0.775997π-0.775997\pi
0.941591 + 0.336758i 0.109330π0.109330\pi
654654 0 0
655655 2642.50 + 4576.94i 0.157635 + 0.273032i
656656 −3984.00 + 6900.49i −0.237117 + 0.410700i
657657 0 0
658658 6327.00 + 296.181i 0.374851 + 0.0175476i
659659 6940.00 0.410234 0.205117 0.978737i 0.434243π-0.434243\pi
0.205117 + 0.978737i 0.434243π0.434243\pi
660660 0 0
661661 −6699.50 11603.9i −0.394221 0.682812i 0.598780 0.800914i 0.295652π-0.295652\pi
−0.993001 + 0.118102i 0.962319π0.962319\pi
662662 6571.00 + 11381.3i 0.385784 + 0.668198i
663663 0 0
664664 −7456.00 −0.435766
665665 −17741.5 830.518i −1.03457 0.0484303i
666666 0 0
667667 371.000 642.591i 0.0215370 0.0373032i
668668 5576.00 + 9657.92i 0.322967 + 0.559395i
669669 0 0
670670 3073.00 5322.59i 0.177195 0.306910i
671671 −1785.00 −0.102696
672672 0 0
673673 29510.0 1.69023 0.845117 0.534582i 0.179531π-0.179531\pi
0.845117 + 0.534582i 0.179531π0.179531\pi
674674 11466.0 19859.7i 0.655273 1.13497i
675675 0 0
676676 −4318.00 7479.00i −0.245676 0.425523i
677677 −13000.5 + 22517.5i −0.738035 + 1.27831i 0.215344 + 0.976538i 0.430913π0.430913\pi
−0.953379 + 0.301776i 0.902421π0.902421\pi
678678 0 0
679679 2900.00 4520.65i 0.163905 0.255503i
680680 3304.00 0.186327
681681 0 0
682682 2625.00 + 4546.63i 0.147385 + 0.255278i
683683 −4402.50 7625.35i −0.246643 0.427198i 0.715949 0.698152i 0.245994π-0.245994\pi
−0.962592 + 0.270954i 0.912661π0.912661\pi
684684 0 0
685685 −16499.0 −0.920284
686686 −7829.00 + 10006.1i −0.435733 + 0.556899i
687687 0 0
688688 −2080.00 + 3602.67i −0.115261 + 0.199637i
689689 −13761.0 23834.8i −0.760889 1.31790i
690690 0 0
691691 −14342.5 + 24841.9i −0.789601 + 1.36763i 0.136610 + 0.990625i 0.456379π0.456379\pi
−0.926211 + 0.377004i 0.876954π0.876954\pi
692692 −6316.00 −0.346963
693693 0 0
694694 19554.0 1.06954
695695 98.0000 169.741i 0.00534871 0.00926423i
696696 0 0
697697 14691.0 + 25445.6i 0.798366 + 1.38281i
698698 −11914.0 + 20635.7i −0.646062 + 1.11901i
699699 0 0
700700 2584.00 + 5002.16i 0.139523 + 0.270091i
701701 3146.00 0.169505 0.0847523 0.996402i 0.472990π-0.472990\pi
0.0847523 + 0.996402i 0.472990π0.472990\pi
702702 0 0
703703 −753.500 1305.10i −0.0404250 0.0700182i
704704 1120.00 + 1939.90i 0.0599596 + 0.103853i
705705 0 0
706706 −18246.0 −0.972659
707707 20072.5 + 939.638i 1.06776 + 0.0499840i
708708 0 0
709709 −629.500 + 1090.33i −0.0333447 + 0.0577547i −0.882216 0.470845i 0.843949π-0.843949\pi
0.848871 + 0.528599i 0.177283π0.177283\pi
710710 5488.00 + 9505.49i 0.290086 + 0.502443i
711711 0 0
712712 −3492.00 + 6048.32i −0.183804 + 0.318357i
713713 525.000 0.0275756
714714 0 0
715715 16170.0 0.845767
716716 4902.00 8490.51i 0.255861 0.443164i
717717 0 0
718718 8149.00 + 14114.5i 0.423563 + 0.733632i
719719 8212.50 14224.5i 0.425973 0.737807i −0.570538 0.821271i 0.693265π-0.693265\pi
0.996511 + 0.0834645i 0.0265985π0.0265985\pi
720720 0 0
721721 −13200.5 25553.8i −0.681848 1.31994i
722722 23820.0 1.22782
723723 0 0
724724 2340.00 + 4053.00i 0.120118 + 0.208050i
725725 −4028.00 6976.70i −0.206340 0.357391i
726726 0 0
727727 −6032.00 −0.307723 −0.153861 0.988092i 0.549171π-0.549171\pi
−0.153861 + 0.988092i 0.549171π0.549171\pi
728728 −5280.00 + 8230.71i −0.268805 + 0.419025i
729729 0 0
730730 2065.00 3576.68i 0.104697 0.181341i
731731 7670.00 + 13284.8i 0.388078 + 0.672171i
732732 0 0
733733 −7621.50 + 13200.8i −0.384047 + 0.665189i −0.991636 0.129062i 0.958803π-0.958803\pi
0.607589 + 0.794251i 0.292137π0.292137\pi
734734 19342.0 0.972652
735735 0 0
736736 224.000 0.0112184
737737 7682.50 13306.5i 0.383974 0.665062i
738738 0 0
739739 5026.50 + 8706.15i 0.250207 + 0.433371i 0.963583 0.267411i 0.0861681π-0.0861681\pi
−0.713376 + 0.700782i 0.752835π0.752835\pi
740740 154.000 266.736i 0.00765021 0.0132505i
741741 0 0
742742 −8340.00 + 13000.8i −0.412629 + 0.643226i
743743 −24384.0 −1.20399 −0.601993 0.798501i 0.705627π-0.705627\pi
−0.601993 + 0.798501i 0.705627π0.705627\pi
744744 0 0
745745 −8032.50 13912.7i −0.395017 0.684190i
746746 4109.00 + 7117.00i 0.201664 + 0.349292i
747747 0 0
748748 8260.00 0.403764
749749 1096.50 + 2122.63i 0.0534916 + 0.103550i
750750 0 0
751751 −5794.50 + 10036.4i −0.281550 + 0.487660i −0.971767 0.235943i 0.924182π-0.924182\pi
0.690216 + 0.723603i 0.257515π0.257515\pi
752752 −1368.00 2369.45i −0.0663375 0.114900i
753753 0 0
754754 6996.00 12117.4i 0.337904 0.585266i
755755 7763.00 0.374205
756756 0 0
757757 14562.0 0.699161 0.349581 0.936906i 0.386324π-0.386324\pi
0.349581 + 0.936906i 0.386324π0.386324\pi
758758 3488.00 6041.39i 0.167137 0.289490i
759759 0 0
760760 3836.00 + 6644.15i 0.183087 + 0.317116i
761761 −11382.5 + 19715.1i −0.542201 + 0.939120i 0.456576 + 0.889684i 0.349076π0.349076\pi
−0.998777 + 0.0494360i 0.984258π0.984258\pi
762762 0 0
763763 −17852.5 835.715i −0.847056 0.0396526i
764764 5100.00 0.241507
765765 0 0
766766 8717.00 + 15098.3i 0.411172 + 0.712171i
767767 −561.000 971.681i −0.0264101 0.0457436i
768768 0 0
769769 3766.00 0.176600 0.0883000 0.996094i 0.471857π-0.471857\pi
0.0883000 + 0.996094i 0.471857π0.471857\pi
770770 −4165.00 8062.70i −0.194930 0.377350i
771771 0 0
772772 −70.0000 + 121.244i −0.00326341 + 0.00565240i
773773 −13430.5 23262.3i −0.624918 1.08239i −0.988557 0.150849i 0.951799π-0.951799\pi
0.363639 0.931540i 0.381534π-0.381534\pi
774774 0 0
775775 2850.00 4936.34i 0.132097 0.228798i
776776 −2320.00 −0.107324
777777 0 0
778778 −326.000 −0.0150227
779779 −34113.0 + 59085.4i −1.56897 + 2.71753i
780780 0 0
781781 13720.0 + 23763.7i 0.628605 + 1.08878i
782782 413.000 715.337i 0.0188860 0.0327115i
783783 0 0
784784 5464.00 + 512.687i 0.248907 + 0.0233549i
785785 −10913.0 −0.496180
786786 0 0
787787 1048.50 + 1816.06i 0.0474905 + 0.0822559i 0.888793 0.458308i 0.151544π-0.151544\pi
−0.841303 + 0.540564i 0.818211π0.818211\pi
788788 −5468.00 9470.85i −0.247195 0.428154i
789789 0 0
790790 6930.00 0.312099
791791 −500.000 + 779.423i −0.0224753 + 0.0350355i
792792 0 0
793793 −1683.00 + 2915.04i −0.0753658 + 0.130537i
794794 −999.000 1730.32i −0.0446514 0.0773384i
795795 0 0
796796 −4486.00 + 7769.98i −0.199751 + 0.345979i
797797 35334.0 1.57038 0.785191 0.619254i 0.212565π-0.212565\pi
0.785191 + 0.619254i 0.212565π0.212565\pi
798798 0 0
799799 −10089.0 −0.446712
800800 1216.00 2106.17i 0.0537401 0.0930806i
801801 0 0
802802 −14757.0 25559.9i −0.649735 1.12537i
803803 5162.50 8941.71i 0.226875 0.392959i
804804 0 0
805805 −906.500 42.4352i −0.0396894 0.00185795i
806806 9900.00 0.432646
807807 0 0
808808 −4340.00 7517.10i −0.188961 0.327290i
809809 21267.5 + 36836.4i 0.924259 + 1.60086i 0.792749 + 0.609549i 0.208649π0.208649\pi
0.131510 + 0.991315i 0.458017π0.458017\pi
810810 0 0
811811 30676.0 1.32821 0.664106 0.747638i 0.268812π-0.268812\pi
0.664106 + 0.747638i 0.268812π0.268812\pi
812812 −7844.00 367.195i −0.339003 0.0158695i
813813 0 0
814814 385.000 666.840i 0.0165777 0.0287134i
815815 −7878.50 13646.0i −0.338616 0.586500i
816816 0 0
817817 −17810.0 + 30847.8i −0.762660 + 1.32097i
818818 −266.000 −0.0113698
819819 0 0
820820 −13944.0 −0.593836
821821 18671.5 32340.0i 0.793715 1.37475i −0.129937 0.991522i 0.541478π-0.541478\pi
0.923652 0.383232i 0.125189π-0.125189\pi
822822 0 0
823823 −1407.50 2437.86i −0.0596141 0.103255i 0.834678 0.550738i 0.185654π-0.185654\pi
−0.894292 + 0.447483i 0.852320π0.852320\pi
824824 −6212.00 + 10759.5i −0.262628 + 0.454885i
825825 0 0
826826 −340.000 + 530.008i −0.0143222 + 0.0223261i
827827 9276.00 0.390034 0.195017 0.980800i 0.437524π-0.437524\pi
0.195017 + 0.980800i 0.437524π0.437524\pi
828828 0 0
829829 −9285.50 16083.0i −0.389021 0.673805i 0.603297 0.797517i 0.293853π-0.293853\pi
−0.992318 + 0.123712i 0.960520π0.960520\pi
830830 −6524.00 11299.9i −0.272833 0.472561i
831831 0 0
832832 4224.00 0.176011
833833 11711.5 16503.8i 0.487130 0.686464i
834834 0 0
835835 −9758.00 + 16901.4i −0.404419 + 0.700474i
836836 9590.00 + 16610.4i 0.396743 + 0.687179i
837837 0 0
838838 −6420.00 + 11119.8i −0.264648 + 0.458384i
839839 −29048.0 −1.19529 −0.597645 0.801761i 0.703897π-0.703897\pi
−0.597645 + 0.801761i 0.703897π0.703897\pi
840840 0 0
841841 −13153.0 −0.539301
842842 −10266.0 + 17781.2i −0.420178 + 0.727769i
843843 0 0
844844 −2344.00 4059.93i −0.0955969 0.165579i
845845 7556.50 13088.2i 0.307635 0.532839i
846846 0 0
847847 901.000 + 1744.18i 0.0365510 + 0.0707563i
848848 6672.00 0.270186
849849 0 0
850850 −4484.00 7766.52i −0.180941 0.313399i
851851 −38.5000 66.6840i −0.00155084 0.00268613i
852852 0 0
853853 32090.0 1.28809 0.644045 0.764988i 0.277255π-0.277255\pi
0.644045 + 0.764988i 0.277255π0.277255\pi
854854 1887.00 + 88.3346i 0.0756110 + 0.00353952i
855855 0 0
856856 516.000 893.738i 0.0206034 0.0356861i
857857 −12268.5 21249.7i −0.489013 0.846995i 0.510907 0.859636i 0.329310π-0.329310\pi
−0.999920 + 0.0126408i 0.995976π0.995976\pi
858858 0 0
859859 −10412.5 + 18035.0i −0.413585 + 0.716351i −0.995279 0.0970571i 0.969057π-0.969057\pi
0.581693 + 0.813408i 0.302390π0.302390\pi
860860 −7280.00 −0.288658
861861 0 0
862862 30426.0 1.20222
863863 −11423.5 + 19786.1i −0.450591 + 0.780447i −0.998423 0.0561414i 0.982120π-0.982120\pi
0.547831 + 0.836589i 0.315454π0.315454\pi
864864 0 0
865865 −5526.50 9572.18i −0.217233 0.376259i
866866 1378.00 2386.77i 0.0540720 0.0936554i
867867 0 0
868868 −2550.00 4936.34i −0.0997150 0.193030i
869869 17325.0 0.676307
870870 0 0
871871 −14487.0 25092.2i −0.563574 0.976139i
872872 3860.00 + 6685.72i 0.149904 + 0.259641i
873873 0 0
874874 1918.00 0.0742303
875875 −14070.0 + 21933.0i −0.543603 + 0.847394i
876876 0 0
877877 21368.5 37011.3i 0.822763 1.42507i −0.0808543 0.996726i 0.525765π-0.525765\pi
0.903617 0.428341i 0.140902π-0.140902\pi
878878 2763.00 + 4785.66i 0.106204 + 0.183950i
879879 0 0
880880 −1960.00 + 3394.82i −0.0750813 + 0.130045i
881881 −6162.00 −0.235645 −0.117822 0.993035i 0.537591π-0.537591\pi
−0.117822 + 0.993035i 0.537591π0.537591\pi
882882 0 0
883883 7748.00 0.295290 0.147645 0.989040i 0.452831π-0.452831\pi
0.147645 + 0.989040i 0.452831π0.452831\pi
884884 7788.00 13489.2i 0.296311 0.513225i
885885 0 0
886886 5849.00 + 10130.8i 0.221784 + 0.384142i
887887 −12961.5 + 22450.0i −0.490648 + 0.849827i −0.999942 0.0107656i 0.996573π-0.996573\pi
0.509294 + 0.860592i 0.329906π0.329906\pi
888888 0 0
889889 −9360.00 + 14590.8i −0.353121 + 0.550461i
890890 −12222.0 −0.460317
891891 0 0
892892 −4048.00 7011.34i −0.151947 0.263181i
893893 −11713.5 20288.4i −0.438944 0.760274i
894894 0 0
895895 17157.0 0.640777
896896 −1088.00 2106.17i −0.0405664 0.0785294i
897897 0 0
898898 4582.00 7936.26i 0.170271 0.294918i
899899 3975.00 + 6884.90i 0.147468 + 0.255422i
900900 0 0
901901 12301.5 21306.8i 0.454853 0.787828i
902902 −34860.0 −1.28682
903903 0 0
904904 400.000 0.0147166
905905 −4095.00 + 7092.75i −0.150411 + 0.260520i
906906 0 0
907907 −15967.5 27656.5i −0.584556 1.01248i −0.994931 0.100563i 0.967935π-0.967935\pi
0.410375 0.911917i 0.365398π-0.365398\pi
908908 5142.00 8906.21i 0.187933 0.325510i
909909 0 0
910910 −17094.0 800.207i −0.622704 0.0291501i
911911 −3408.00 −0.123943 −0.0619715 0.998078i 0.519739π-0.519739\pi
−0.0619715 + 0.998078i 0.519739π0.519739\pi
912912 0 0
913913 −16310.0 28249.7i −0.591218 1.02402i
914914 −11551.0 20006.9i −0.418023 0.724037i
915915 0 0
916916 3580.00 0.129134
917917 −6417.50 12423.1i −0.231106 0.447381i
918918 0 0
919919 −6954.50 + 12045.5i −0.249628 + 0.432368i −0.963423 0.267987i 0.913642π-0.913642\pi
0.713795 + 0.700355i 0.246975π0.246975\pi
920920 196.000 + 339.482i 0.00702384 + 0.0121656i
921921 0 0
922922 −9494.00 + 16444.1i −0.339120 + 0.587372i
923923 51744.0 1.84526
924924 0 0
925925 −836.000 −0.0297162
926926 10160.0 17597.6i 0.360560 0.624508i
927927 0 0
928928 1696.00 + 2937.56i 0.0599935 + 0.103912i
929929 −12268.5 + 21249.7i −0.433279 + 0.750462i −0.997153 0.0753990i 0.975977π-0.975977\pi
0.563874 + 0.825861i 0.309310π0.309310\pi
930930 0 0
931931 46785.5 + 4389.88i 1.64697 + 0.154536i
932932 −7148.00 −0.251224
933933 0 0
934934 −1307.00 2263.79i −0.0457884 0.0793078i
935935 7227.50 + 12518.4i 0.252796 + 0.437856i
936936 0 0
937937 −32758.0 −1.14211 −0.571055 0.820912i 0.693466π-0.693466\pi
−0.571055 + 0.820912i 0.693466π0.693466\pi
938938 −8780.00 + 13686.7i −0.305626 + 0.476424i
939939 0 0
940940 2394.00 4146.53i 0.0830677 0.143878i
941941 −19280.5 33394.8i −0.667934 1.15690i −0.978481 0.206338i 0.933845π-0.933845\pi
0.310546 0.950558i 0.399488π-0.399488\pi
942942 0 0
943943 −1743.00 + 3018.96i −0.0601908 + 0.104253i
944944 272.000 0.00937801
945945 0 0
946946 −18200.0 −0.625511
947947 19830.5 34347.4i 0.680470 1.17861i −0.294368 0.955692i 0.595109π-0.595109\pi
0.974838 0.222916i 0.0715575π-0.0715575\pi
948948 0 0
949949 −9735.00 16861.5i −0.332994 0.576763i
950950 10412.0 18034.1i 0.355589 0.615899i
951951 0 0
952952 −8732.00 408.764i −0.297275 0.0139161i
953953 46618.0 1.58458 0.792290 0.610144i 0.208889π-0.208889\pi
0.792290 + 0.610144i 0.208889π0.208889\pi
954954 0 0
955955 4462.50 + 7729.28i 0.151207 + 0.261899i
956956 −10200.0 17666.9i −0.345075 0.597687i
957957 0 0
958958 −36574.0 −1.23346
959959 43604.5 + 2041.22i 1.46826 + 0.0687325i
960960 0 0
961961 12083.0 20928.4i 0.405592 0.702506i
962962 −726.000 1257.47i −0.0243318 0.0421439i
963963 0 0
964964 8354.00 14469.6i 0.279112 0.483437i
965965 −245.000 −0.00817288
966966 0 0
967967 14816.0 0.492710 0.246355 0.969180i 0.420767π-0.420767\pi
0.246355 + 0.969180i 0.420767π0.420767\pi
968968 424.000 734.390i 0.0140784 0.0243845i
969969 0 0
970970 −2030.00 3516.06i −0.0671952 0.116386i
971971 −8437.50 + 14614.2i −0.278859 + 0.482998i −0.971102 0.238667i 0.923290π-0.923290\pi
0.692242 + 0.721665i 0.256623π0.256623\pi
972972 0 0
973973 −280.000 + 436.477i −0.00922548 + 0.0143811i
974974 −29906.0 −0.983830
975975 0 0
976976 −408.000 706.677i −0.0133809 0.0231764i
977977 −7918.50 13715.2i −0.259299 0.449119i 0.706755 0.707458i 0.250158π-0.250158\pi
−0.966054 + 0.258339i 0.916825π0.916825\pi
978978 0 0
979979 −30555.0 −0.997489
980980 4004.00 + 8729.54i 0.130513 + 0.284546i
981981 0 0
982982 14352.0 24858.4i 0.466386 0.807804i
983983 4957.50 + 8586.64i 0.160854 + 0.278608i 0.935175 0.354185i 0.115242π-0.115242\pi
−0.774321 + 0.632793i 0.781908π0.781908\pi
984984 0 0
985985 9569.00 16574.0i 0.309537 0.536133i
986986 12508.0 0.403992
987987 0 0
988988 36168.0 1.16463
989989 −910.000 + 1576.17i −0.0292582 + 0.0506766i
990990 0 0
991991 21840.5 + 37828.9i 0.700087 + 1.21259i 0.968435 + 0.249265i 0.0801889π0.0801889\pi
−0.268348 + 0.963322i 0.586478π0.586478\pi
992992 −1200.00 + 2078.46i −0.0384073 + 0.0665234i
993993 0 0
994994 −13328.0 25800.6i −0.425290 0.823286i
995995 −15701.0 −0.500256
996996 0 0
997997 23556.5 + 40801.1i 0.748287 + 1.29607i 0.948643 + 0.316348i 0.102457π0.102457\pi
−0.200357 + 0.979723i 0.564210π0.564210\pi
998998 5531.00 + 9579.97i 0.175432 + 0.303856i
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 126.4.g.c.37.1 2
3.2 odd 2 14.4.c.b.9.1 2
7.2 even 3 882.4.a.k.1.1 1
7.3 odd 6 882.4.g.d.361.1 2
7.4 even 3 inner 126.4.g.c.109.1 2
7.5 odd 6 882.4.a.p.1.1 1
7.6 odd 2 882.4.g.d.667.1 2
12.11 even 2 112.4.i.b.65.1 2
15.2 even 4 350.4.j.d.149.2 4
15.8 even 4 350.4.j.d.149.1 4
15.14 odd 2 350.4.e.b.51.1 2
21.2 odd 6 98.4.a.b.1.1 1
21.5 even 6 98.4.a.c.1.1 1
21.11 odd 6 14.4.c.b.11.1 yes 2
21.17 even 6 98.4.c.e.67.1 2
21.20 even 2 98.4.c.e.79.1 2
24.5 odd 2 448.4.i.c.65.1 2
24.11 even 2 448.4.i.d.65.1 2
84.11 even 6 112.4.i.b.81.1 2
84.23 even 6 784.4.a.l.1.1 1
84.47 odd 6 784.4.a.j.1.1 1
105.32 even 12 350.4.j.d.249.1 4
105.44 odd 6 2450.4.a.bh.1.1 1
105.53 even 12 350.4.j.d.249.2 4
105.74 odd 6 350.4.e.b.151.1 2
105.89 even 6 2450.4.a.bf.1.1 1
168.11 even 6 448.4.i.d.193.1 2
168.53 odd 6 448.4.i.c.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.b.9.1 2 3.2 odd 2
14.4.c.b.11.1 yes 2 21.11 odd 6
98.4.a.b.1.1 1 21.2 odd 6
98.4.a.c.1.1 1 21.5 even 6
98.4.c.e.67.1 2 21.17 even 6
98.4.c.e.79.1 2 21.20 even 2
112.4.i.b.65.1 2 12.11 even 2
112.4.i.b.81.1 2 84.11 even 6
126.4.g.c.37.1 2 1.1 even 1 trivial
126.4.g.c.109.1 2 7.4 even 3 inner
350.4.e.b.51.1 2 15.14 odd 2
350.4.e.b.151.1 2 105.74 odd 6
350.4.j.d.149.1 4 15.8 even 4
350.4.j.d.149.2 4 15.2 even 4
350.4.j.d.249.1 4 105.32 even 12
350.4.j.d.249.2 4 105.53 even 12
448.4.i.c.65.1 2 24.5 odd 2
448.4.i.c.193.1 2 168.53 odd 6
448.4.i.d.65.1 2 24.11 even 2
448.4.i.d.193.1 2 168.11 even 6
784.4.a.j.1.1 1 84.47 odd 6
784.4.a.l.1.1 1 84.23 even 6
882.4.a.k.1.1 1 7.2 even 3
882.4.a.p.1.1 1 7.5 odd 6
882.4.g.d.361.1 2 7.3 odd 6
882.4.g.d.667.1 2 7.6 odd 2
2450.4.a.bf.1.1 1 105.89 even 6
2450.4.a.bh.1.1 1 105.44 odd 6