Properties

Label 819.2.j.i.235.4
Level 819819
Weight 22
Character 819.235
Analytic conductor 6.5406.540
Analytic rank 00
Dimension 1212
Inner twists 44

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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] = [819,2,Mod(235,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.235"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 819=32713 819 = 3^{2} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 819.j (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.539747925546.53974792554
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x12+8x10+47x8+122x6+233x4+119x2+49 x^{12} + 8x^{10} + 47x^{8} + 122x^{6} + 233x^{4} + 119x^{2} + 49 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 32 3^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 235.4
Root 0.367252+0.636099i-0.367252 + 0.636099i of defining polynomial
Character χ\chi == 819.235
Dual form 819.2.j.i.352.4

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+(0.367252+0.636099i)q2+(0.7302521.26483i)q4+(1.270882.20122i)q5+(2.257291.38008i)q7+2.54175q8+(0.9334631.61680i)q10+(1.85612+3.21490i)q111.00000q13+(0.04887181.94270i)q14+(0.5270420.912864i)q16+(1.052881.82365i)q17+(2.960505.12774i)q193.71224q202.72665q22+(3.12700+5.41612i)q23+(0.730252+1.26483i)q25+(0.3672520.636099i)q26+(3.39397+1.84730i)q288.83547q29+(2.850874.93786i)q31+(2.928875.07295i)q32+1.54669q34+(0.169121+6.72272i)q35+(3.284345.68864i)q37+(2.174503.76635i)q38+(3.230255.59496i)q4010.3045q4110.6477q43+(2.71087+4.69537i)q44+(2.29679+3.97816i)q46+(0.7345031.27220i)q47+(3.19076+6.23049i)q491.07275q50+(0.730252+1.26483i)q52+(3.22738+5.58999i)q53+9.43560q55+(5.737483.50782i)q56+(3.244845.62023i)q58+(5.717629.90321i)q59+(4.55768+7.89414i)q61+4.18795q62+2.19436q64+(1.27088+2.20122i)q65+(7.0270412.1712i)q67+(1.537742.66345i)q68+(4.33842+2.36135i)q70+14.4527q71+(3.070145.31763i)q73+(2.412364.17832i)q748.64766q76+(8.626634.69537i)q77+(3.98395+6.90040i)q79+(1.33961+2.32027i)q80+(3.784346.55466i)q82+12.1515q835.35234q85+(3.910376.77296i)q86+(4.71780+8.17147i)q88+(5.90660+10.2305i)q89+(2.25729+1.38008i)q91+9.13399q92+(0.5394950.934433i)q94+(7.52487+13.0335i)q95+7.10097q97+(2.79140+4.31780i)q98+O(q100)q+(0.367252 + 0.636099i) q^{2} +(0.730252 - 1.26483i) q^{4} +(-1.27088 - 2.20122i) q^{5} +(-2.25729 - 1.38008i) q^{7} +2.54175 q^{8} +(0.933463 - 1.61680i) q^{10} +(-1.85612 + 3.21490i) q^{11} -1.00000 q^{13} +(0.0488718 - 1.94270i) q^{14} +(-0.527042 - 0.912864i) q^{16} +(1.05288 - 1.82365i) q^{17} +(-2.96050 - 5.12774i) q^{19} -3.71224 q^{20} -2.72665 q^{22} +(3.12700 + 5.41612i) q^{23} +(-0.730252 + 1.26483i) q^{25} +(-0.367252 - 0.636099i) q^{26} +(-3.39397 + 1.84730i) q^{28} -8.83547 q^{29} +(2.85087 - 4.93786i) q^{31} +(2.92887 - 5.07295i) q^{32} +1.54669 q^{34} +(-0.169121 + 6.72272i) q^{35} +(-3.28434 - 5.68864i) q^{37} +(2.17450 - 3.76635i) q^{38} +(-3.23025 - 5.59496i) q^{40} -10.3045 q^{41} -10.6477 q^{43} +(2.71087 + 4.69537i) q^{44} +(-2.29679 + 3.97816i) q^{46} +(-0.734503 - 1.27220i) q^{47} +(3.19076 + 6.23049i) q^{49} -1.07275 q^{50} +(-0.730252 + 1.26483i) q^{52} +(-3.22738 + 5.58999i) q^{53} +9.43560 q^{55} +(-5.73748 - 3.50782i) q^{56} +(-3.24484 - 5.62023i) q^{58} +(5.71762 - 9.90321i) q^{59} +(4.55768 + 7.89414i) q^{61} +4.18795 q^{62} +2.19436 q^{64} +(1.27088 + 2.20122i) q^{65} +(7.02704 - 12.1712i) q^{67} +(-1.53774 - 2.66345i) q^{68} +(-4.33842 + 2.36135i) q^{70} +14.4527 q^{71} +(3.07014 - 5.31763i) q^{73} +(2.41236 - 4.17832i) q^{74} -8.64766 q^{76} +(8.62663 - 4.69537i) q^{77} +(3.98395 + 6.90040i) q^{79} +(-1.33961 + 2.32027i) q^{80} +(-3.78434 - 6.55466i) q^{82} +12.1515 q^{83} -5.35234 q^{85} +(-3.91037 - 6.77296i) q^{86} +(-4.71780 + 8.17147i) q^{88} +(5.90660 + 10.2305i) q^{89} +(2.25729 + 1.38008i) q^{91} +9.13399 q^{92} +(0.539495 - 0.934433i) q^{94} +(-7.52487 + 13.0335i) q^{95} +7.10097 q^{97} +(-2.79140 + 4.31780i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q4q4+4q7+4q1012q13+12q1610q1936q22+4q258q288q31+12q34+10q3726q4080q4322q46+4q52+36q58+2q61++44q97+O(q100) 12 q - 4 q^{4} + 4 q^{7} + 4 q^{10} - 12 q^{13} + 12 q^{16} - 10 q^{19} - 36 q^{22} + 4 q^{25} - 8 q^{28} - 8 q^{31} + 12 q^{34} + 10 q^{37} - 26 q^{40} - 80 q^{43} - 22 q^{46} + 4 q^{52} + 36 q^{58} + 2 q^{61}+ \cdots + 44 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/819Z)×\left(\mathbb{Z}/819\mathbb{Z}\right)^\times.

nn 9292 379379 703703
χ(n)\chi(n) 11 11 e(23)e\left(\frac{2}{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 0.367252 + 0.636099i 0.259686 + 0.449790i 0.966158 0.257952i 0.0830476π-0.0830476\pi
−0.706472 + 0.707741i 0.749714π0.749714\pi
33 0 0
44 0.730252 1.26483i 0.365126 0.632417i
55 −1.27088 2.20122i −0.568353 0.984416i −0.996729 0.0808158i 0.974247π-0.974247\pi
0.428376 0.903601i 0.359086π-0.359086\pi
66 0 0
77 −2.25729 1.38008i −0.853177 0.521621i
88 2.54175 0.898645
99 0 0
1010 0.933463 1.61680i 0.295187 0.511279i
1111 −1.85612 + 3.21490i −0.559641 + 0.969327i 0.437885 + 0.899031i 0.355728π0.355728\pi
−0.997526 + 0.0702963i 0.977606π0.977606\pi
1212 0 0
1313 −1.00000 −0.277350
1414 0.0488718 1.94270i 0.0130615 0.519208i
1515 0 0
1616 −0.527042 0.912864i −0.131761 0.228216i
1717 1.05288 1.82365i 0.255362 0.442299i −0.709632 0.704572i 0.751139π-0.751139\pi
0.964994 + 0.262273i 0.0844721π0.0844721\pi
1818 0 0
1919 −2.96050 5.12774i −0.679186 1.17639i −0.975226 0.221210i 0.928999π-0.928999\pi
0.296040 0.955176i 0.404334π-0.404334\pi
2020 −3.71224 −0.830082
2121 0 0
2222 −2.72665 −0.581325
2323 3.12700 + 5.41612i 0.652024 + 1.12934i 0.982631 + 0.185570i 0.0594132π0.0594132\pi
−0.330607 + 0.943768i 0.607253π0.607253\pi
2424 0 0
2525 −0.730252 + 1.26483i −0.146050 + 0.252967i
2626 −0.367252 0.636099i −0.0720240 0.124749i
2727 0 0
2828 −3.39397 + 1.84730i −0.641400 + 0.349106i
2929 −8.83547 −1.64071 −0.820353 0.571858i 0.806223π-0.806223\pi
−0.820353 + 0.571858i 0.806223π0.806223\pi
3030 0 0
3131 2.85087 4.93786i 0.512032 0.886866i −0.487871 0.872916i 0.662226π-0.662226\pi
0.999903 0.0139496i 0.00444044π-0.00444044\pi
3232 2.92887 5.07295i 0.517755 0.896779i
3333 0 0
3434 1.54669 0.265256
3535 −0.169121 + 6.72272i −0.0285867 + 1.13635i
3636 0 0
3737 −3.28434 5.68864i −0.539942 0.935206i −0.998907 0.0467519i 0.985113π-0.985113\pi
0.458965 0.888454i 0.348220π-0.348220\pi
3838 2.17450 3.76635i 0.352751 0.610982i
3939 0 0
4040 −3.23025 5.59496i −0.510748 0.884641i
4141 −10.3045 −1.60929 −0.804645 0.593757i 0.797644π-0.797644\pi
−0.804645 + 0.593757i 0.797644π0.797644\pi
4242 0 0
4343 −10.6477 −1.62375 −0.811877 0.583829i 0.801554π-0.801554\pi
−0.811877 + 0.583829i 0.801554π0.801554\pi
4444 2.71087 + 4.69537i 0.408680 + 0.707854i
4545 0 0
4646 −2.29679 + 3.97816i −0.338643 + 0.586547i
4747 −0.734503 1.27220i −0.107138 0.185569i 0.807472 0.589907i 0.200835π-0.200835\pi
−0.914610 + 0.404338i 0.867502π0.867502\pi
4848 0 0
4949 3.19076 + 6.23049i 0.455822 + 0.890071i
5050 −1.07275 −0.151709
5151 0 0
5252 −0.730252 + 1.26483i −0.101268 + 0.175401i
5353 −3.22738 + 5.58999i −0.443315 + 0.767845i −0.997933 0.0642606i 0.979531π-0.979531\pi
0.554618 + 0.832105i 0.312864π0.312864\pi
5454 0 0
5555 9.43560 1.27230
5656 −5.73748 3.50782i −0.766704 0.468752i
5757 0 0
5858 −3.24484 5.62023i −0.426069 0.737972i
5959 5.71762 9.90321i 0.744371 1.28929i −0.206117 0.978527i 0.566083π-0.566083\pi
0.950488 0.310761i 0.100584π-0.100584\pi
6060 0 0
6161 4.55768 + 7.89414i 0.583551 + 1.01074i 0.995054 + 0.0993323i 0.0316707π0.0316707\pi
−0.411503 + 0.911408i 0.634996π0.634996\pi
6262 4.18795 0.531871
6363 0 0
6464 2.19436 0.274294
6565 1.27088 + 2.20122i 0.157633 + 0.273028i
6666 0 0
6767 7.02704 12.1712i 0.858490 1.48695i −0.0148794 0.999889i 0.504736π-0.504736\pi
0.873369 0.487059i 0.161930π-0.161930\pi
6868 −1.53774 2.66345i −0.186478 0.322990i
6969 0 0
7070 −4.33842 + 2.36135i −0.518540 + 0.282235i
7171 14.4527 1.71522 0.857610 0.514300i 0.171948π-0.171948\pi
0.857610 + 0.514300i 0.171948π0.171948\pi
7272 0 0
7373 3.07014 5.31763i 0.359332 0.622382i −0.628517 0.777796i 0.716338π-0.716338\pi
0.987849 + 0.155414i 0.0496712π0.0496712\pi
7474 2.41236 4.17832i 0.280431 0.485720i
7575 0 0
7676 −8.64766 −0.991955
7777 8.62663 4.69537i 0.983095 0.535087i
7878 0 0
7979 3.98395 + 6.90040i 0.448229 + 0.776356i 0.998271 0.0587814i 0.0187215π-0.0187215\pi
−0.550042 + 0.835137i 0.685388π0.685388\pi
8080 −1.33961 + 2.32027i −0.149773 + 0.259414i
8181 0 0
8282 −3.78434 6.55466i −0.417910 0.723841i
8383 12.1515 1.33380 0.666898 0.745149i 0.267622π-0.267622\pi
0.666898 + 0.745149i 0.267622π0.267622\pi
8484 0 0
8585 −5.35234 −0.580542
8686 −3.91037 6.77296i −0.421666 0.730347i
8787 0 0
8888 −4.71780 + 8.17147i −0.502919 + 0.871081i
8989 5.90660 + 10.2305i 0.626099 + 1.08444i 0.988327 + 0.152346i 0.0486827π0.0486827\pi
−0.362228 + 0.932089i 0.617984π0.617984\pi
9090 0 0
9191 2.25729 + 1.38008i 0.236629 + 0.144672i
9292 9.13399 0.952284
9393 0 0
9494 0.539495 0.934433i 0.0556447 0.0963794i
9595 −7.52487 + 13.0335i −0.772035 + 1.33720i
9696 0 0
9797 7.10097 0.720994 0.360497 0.932760i 0.382607π-0.382607\pi
0.360497 + 0.932760i 0.382607π0.382607\pi
9898 −2.79140 + 4.31780i −0.281974 + 0.436163i
9999 0 0
100100 1.06654 + 1.84730i 0.106654 + 0.184730i
101101 4.24861 7.35882i 0.422753 0.732230i −0.573455 0.819237i 0.694397π-0.694397\pi
0.996208 + 0.0870077i 0.0277305π0.0277305\pi
102102 0 0
103103 −1.09358 1.89413i −0.107754 0.186635i 0.807106 0.590406i 0.201032π-0.201032\pi
−0.914860 + 0.403771i 0.867699π0.867699\pi
104104 −2.54175 −0.249239
105105 0 0
106106 −4.74105 −0.460491
107107 −3.76376 6.51902i −0.363856 0.630217i 0.624736 0.780836i 0.285207π-0.285207\pi
−0.988592 + 0.150619i 0.951873π0.951873\pi
108108 0 0
109109 −0.0270421 + 0.0468383i −0.00259016 + 0.00448630i −0.867318 0.497755i 0.834158π-0.834158\pi
0.864727 + 0.502241i 0.167491π0.167491\pi
110110 3.46524 + 6.00197i 0.330398 + 0.572265i
111111 0 0
112112 −0.0701359 + 2.78796i −0.00662722 + 0.263438i
113113 6.25399 0.588326 0.294163 0.955755i 0.404959π-0.404959\pi
0.294163 + 0.955755i 0.404959π0.404959\pi
114114 0 0
115115 7.94805 13.7664i 0.741160 1.28373i
116116 −6.45212 + 11.1754i −0.599065 + 1.03761i
117117 0 0
118118 8.39922 0.773211
119119 −4.89345 + 2.66345i −0.448582 + 0.244158i
120120 0 0
121121 −1.39037 2.40819i −0.126397 0.218926i
122122 −3.34763 + 5.79827i −0.303080 + 0.524951i
123123 0 0
124124 −4.16372 7.21177i −0.373913 0.647636i
125125 −8.99652 −0.804673
126126 0 0
127127 −2.49261 −0.221183 −0.110592 0.993866i 0.535275π-0.535275\pi
−0.110592 + 0.993866i 0.535275π0.535275\pi
128128 −5.05185 8.75006i −0.446525 0.773404i
129129 0 0
130130 −0.933463 + 1.61680i −0.0818701 + 0.141803i
131131 −4.42688 7.66759i −0.386779 0.669920i 0.605236 0.796046i 0.293079π-0.293079\pi
−0.992014 + 0.126126i 0.959746π0.959746\pi
132132 0 0
133133 −0.393968 + 15.6606i −0.0341613 + 1.35794i
134134 10.3228 0.891752
135135 0 0
136136 2.67617 4.63526i 0.229480 0.397470i
137137 1.35947 2.35468i 0.116148 0.201174i −0.802090 0.597203i 0.796279π-0.796279\pi
0.918238 + 0.396029i 0.129612π0.129612\pi
138138 0 0
139139 13.1694 1.11702 0.558509 0.829498i 0.311374π-0.311374\pi
0.558509 + 0.829498i 0.311374π0.311374\pi
140140 8.37962 + 5.12319i 0.708207 + 0.432989i
141141 0 0
142142 5.30778 + 9.19334i 0.445419 + 0.771488i
143143 1.85612 3.21490i 0.155217 0.268843i
144144 0 0
145145 11.2288 + 19.4488i 0.932500 + 1.61514i
146146 4.51005 0.373254
147147 0 0
148148 −9.59358 −0.788587
149149 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
150150 0 0
151151 3.64766 6.31794i 0.296843 0.514147i −0.678569 0.734536i 0.737400π-0.737400\pi
0.975412 + 0.220390i 0.0707330π0.0707330\pi
152152 −7.52487 13.0335i −0.610348 1.05715i
153153 0 0
154154 6.15486 + 3.76300i 0.495973 + 0.303231i
155155 −14.4924 −1.16406
156156 0 0
157157 2.83628 4.91259i 0.226360 0.392067i −0.730366 0.683055i 0.760651π-0.760651\pi
0.956727 + 0.290988i 0.0939840π0.0939840\pi
158158 −2.92622 + 5.06837i −0.232798 + 0.403218i
159159 0 0
160160 −14.8889 −1.17707
161161 0.416123 16.5413i 0.0327951 1.30364i
162162 0 0
163163 10.3581 + 17.9407i 0.811307 + 1.40522i 0.911950 + 0.410302i 0.134577π0.134577\pi
−0.100643 + 0.994923i 0.532090π0.532090\pi
164164 −7.52487 + 13.0335i −0.587594 + 1.01774i
165165 0 0
166166 4.46264 + 7.72952i 0.346368 + 0.599927i
167167 −14.3152 −1.10775 −0.553873 0.832601i 0.686851π-0.686851\pi
−0.553873 + 0.832601i 0.686851π0.686851\pi
168168 0 0
169169 1.00000 0.0769231
170170 −1.96565 3.40461i −0.150759 0.261122i
171171 0 0
172172 −7.77548 + 13.4675i −0.592875 + 1.02689i
173173 −11.2081 19.4130i −0.852136 1.47594i −0.879277 0.476312i 0.841973π-0.841973\pi
0.0271403 0.999632i 0.491360π-0.491360\pi
174174 0 0
175175 3.39397 1.84730i 0.256560 0.139643i
176176 3.91302 0.294955
177177 0 0
178178 −4.33842 + 7.51437i −0.325178 + 0.563225i
179179 4.13101 7.15512i 0.308766 0.534799i −0.669327 0.742968i 0.733417π-0.733417\pi
0.978093 + 0.208170i 0.0667506π0.0667506\pi
180180 0 0
181181 −0.787935 −0.0585668 −0.0292834 0.999571i 0.509323π-0.509323\pi
−0.0292834 + 0.999571i 0.509323π0.509323\pi
182182 −0.0488718 + 1.94270i −0.00362262 + 0.144002i
183183 0 0
184184 7.94805 + 13.7664i 0.585938 + 1.01487i
185185 −8.34797 + 14.4591i −0.613755 + 1.06305i
186186 0 0
187187 3.90856 + 6.76982i 0.285822 + 0.495058i
188188 −2.14549 −0.156476
189189 0 0
190190 −11.0541 −0.801948
191191 0.198130 + 0.343172i 0.0143362 + 0.0248311i 0.873105 0.487533i 0.162103π-0.162103\pi
−0.858768 + 0.512364i 0.828770π0.828770\pi
192192 0 0
193193 −1.89397 + 3.28045i −0.136331 + 0.236132i −0.926105 0.377266i 0.876864π-0.876864\pi
0.789774 + 0.613398i 0.210198π0.210198\pi
194194 2.60784 + 4.51692i 0.187232 + 0.324296i
195195 0 0
196196 10.2106 + 0.514055i 0.729329 + 0.0367182i
197197 −12.0484 −0.858415 −0.429207 0.903206i 0.641207π-0.641207\pi
−0.429207 + 0.903206i 0.641207π0.641207\pi
198198 0 0
199199 2.58113 4.47064i 0.182971 0.316915i −0.759920 0.650017i 0.774762π-0.774762\pi
0.942891 + 0.333101i 0.108095π0.108095\pi
200200 −1.85612 + 3.21490i −0.131248 + 0.227327i
201201 0 0
202202 6.24124 0.439132
203203 19.9443 + 12.1937i 1.39981 + 0.855827i
204204 0 0
205205 13.0957 + 22.6824i 0.914644 + 1.58421i
206206 0.803238 1.39125i 0.0559642 0.0969329i
207207 0 0
208208 0.527042 + 0.912864i 0.0365438 + 0.0632957i
209209 21.9802 1.52040
210210 0 0
211211 17.9794 1.23775 0.618875 0.785489i 0.287589π-0.287589\pi
0.618875 + 0.785489i 0.287589π0.287589\pi
212212 4.71361 + 8.16421i 0.323732 + 0.560720i
213213 0 0
214214 2.76449 4.78824i 0.188977 0.327317i
215215 13.5319 + 23.4379i 0.922865 + 1.59845i
216216 0 0
217217 −13.2499 + 7.21177i −0.899462 + 0.489567i
218218 −0.0397250 −0.00269052
219219 0 0
220220 6.89037 11.9345i 0.464549 0.804622i
221221 −1.05288 + 1.82365i −0.0708246 + 0.122672i
222222 0 0
223223 1.96790 0.131780 0.0658901 0.997827i 0.479011π-0.479011\pi
0.0658901 + 0.997827i 0.479011π0.479011\pi
224224 −13.6124 + 7.40906i −0.909516 + 0.495039i
225225 0 0
226226 2.29679 + 3.97816i 0.152780 + 0.264623i
227227 −6.21427 + 10.7634i −0.412456 + 0.714394i −0.995158 0.0982919i 0.968662π-0.968662\pi
0.582702 + 0.812686i 0.301995π0.301995\pi
228228 0 0
229229 −10.5292 18.2371i −0.695788 1.20514i −0.969914 0.243446i 0.921722π-0.921722\pi
0.274127 0.961694i 0.411611π-0.411611\pi
230230 11.6757 0.769876
231231 0 0
232232 −22.4576 −1.47441
233233 −3.63436 6.29490i −0.238095 0.412392i 0.722073 0.691817i 0.243190π-0.243190\pi
−0.960168 + 0.279425i 0.909856π0.909856\pi
234234 0 0
235235 −1.86693 + 3.23361i −0.121785 + 0.210937i
236236 −8.35061 14.4637i −0.543579 0.941506i
237237 0 0
238238 −3.49134 2.13456i −0.226310 0.138363i
239239 −12.8698 −0.832479 −0.416239 0.909255i 0.636652π-0.636652\pi
−0.416239 + 0.909255i 0.636652π0.636652\pi
240240 0 0
241241 −6.59931 + 11.4303i −0.425099 + 0.736293i −0.996430 0.0844267i 0.973094π-0.973094\pi
0.571331 + 0.820720i 0.306427π0.306427\pi
242242 1.02123 1.76882i 0.0656472 0.113704i
243243 0 0
244244 13.3130 0.852280
245245 9.65965 14.9418i 0.617132 0.954594i
246246 0 0
247247 2.96050 + 5.12774i 0.188372 + 0.326271i
248248 7.24622 12.5508i 0.460135 0.796977i
249249 0 0
250250 −3.30399 5.72267i −0.208962 0.361934i
251251 −10.1617 −0.641402 −0.320701 0.947180i 0.603919π-0.603919\pi
−0.320701 + 0.947180i 0.603919π0.603919\pi
252252 0 0
253253 −23.2163 −1.45960
254254 −0.915414 1.58554i −0.0574382 0.0994859i
255255 0 0
256256 5.90496 10.2277i 0.369060 0.639230i
257257 0.120249 + 0.208278i 0.00750095 + 0.0129920i 0.869752 0.493490i 0.164279π-0.164279\pi
−0.862251 + 0.506482i 0.830946π0.830946\pi
258258 0 0
259259 −0.437061 + 17.3736i −0.0271577 + 1.07954i
260260 3.71224 0.230223
261261 0 0
262262 3.25156 5.63187i 0.200882 0.347938i
263263 8.37962 14.5139i 0.516710 0.894967i −0.483102 0.875564i 0.660490π-0.660490\pi
0.999812 0.0194034i 0.00617667π-0.00617667\pi
264264 0 0
265265 16.4064 1.00784
266266 −10.1063 + 5.50077i −0.619660 + 0.337274i
267267 0 0
268268 −10.2630 17.7761i −0.626914 1.08585i
269269 −7.41534 + 12.8437i −0.452121 + 0.783097i −0.998518 0.0544300i 0.982666π-0.982666\pi
0.546397 + 0.837527i 0.315999π0.315999\pi
270270 0 0
271271 −13.6352 23.6169i −0.828280 1.43462i −0.899386 0.437154i 0.855986π-0.855986\pi
0.0711064 0.997469i 0.477347π-0.477347\pi
272272 −2.21966 −0.134586
273273 0 0
274274 1.99707 0.120648
275275 −2.71087 4.69537i −0.163472 0.283142i
276276 0 0
277277 13.8456 23.9813i 0.831903 1.44090i −0.0646250 0.997910i 0.520585π-0.520585\pi
0.896528 0.442988i 0.146082π-0.146082\pi
278278 4.83650 + 8.37707i 0.290074 + 0.502423i
279279 0 0
280280 −0.429864 + 17.0875i −0.0256893 + 1.02117i
281281 16.6959 0.995996 0.497998 0.867178i 0.334069π-0.334069\pi
0.497998 + 0.867178i 0.334069π0.334069\pi
282282 0 0
283283 0.160117 0.277330i 0.00951794 0.0164856i −0.861227 0.508220i 0.830304π-0.830304\pi
0.870745 + 0.491735i 0.163637π0.163637\pi
284284 10.5541 18.2803i 0.626272 1.08473i
285285 0 0
286286 2.72665 0.161230
287287 23.2602 + 14.2210i 1.37301 + 0.839439i
288288 0 0
289289 6.28287 + 10.8823i 0.369581 + 0.640133i
290290 −8.24758 + 14.2852i −0.484315 + 0.838858i
291291 0 0
292292 −4.48395 7.76643i −0.262403 0.454496i
293293 −8.07954 −0.472012 −0.236006 0.971752i 0.575838π-0.575838\pi
−0.236006 + 0.971752i 0.575838π0.575838\pi
294294 0 0
295295 −29.0656 −1.69226
296296 −8.34797 14.4591i −0.485216 0.840419i
297297 0 0
298298 0 0
299299 −3.12700 5.41612i −0.180839 0.313222i
300300 0 0
301301 24.0349 + 14.6946i 1.38535 + 0.846984i
302302 5.35844 0.308344
303303 0 0
304304 −3.12062 + 5.40507i −0.178980 + 0.310002i
305305 11.5845 20.0649i 0.663327 1.14892i
306306 0 0
307307 −4.94299 −0.282111 −0.141056 0.990002i 0.545050π-0.545050\pi
−0.141056 + 0.990002i 0.545050π0.545050\pi
308308 0.360748 14.3401i 0.0205555 0.817101i
309309 0 0
310310 −5.32237 9.21861i −0.302290 0.523582i
311311 −2.02524 + 3.50782i −0.114841 + 0.198910i −0.917716 0.397237i 0.869969π-0.869969\pi
0.802875 + 0.596147i 0.203303π0.203303\pi
312312 0 0
313313 5.18356 + 8.97819i 0.292992 + 0.507477i 0.974516 0.224319i 0.0720157π-0.0720157\pi
−0.681524 + 0.731796i 0.738682π0.738682\pi
314314 4.16652 0.235130
315315 0 0
316316 11.6372 0.654641
317317 6.03864 + 10.4592i 0.339164 + 0.587449i 0.984276 0.176639i 0.0565225π-0.0565225\pi
−0.645112 + 0.764088i 0.723189π0.723189\pi
318318 0 0
319319 16.3997 28.4051i 0.918207 1.59038i
320320 −2.78875 4.83026i −0.155896 0.270020i
321321 0 0
322322 10.6747 5.81012i 0.594878 0.323785i
323323 −12.4683 −0.693753
324324 0 0
325325 0.730252 1.26483i 0.0405071 0.0701604i
326326 −7.60804 + 13.1775i −0.421370 + 0.729835i
327327 0 0
328328 −26.1914 −1.44618
329329 −0.0977436 + 3.88540i −0.00538878 + 0.214209i
330330 0 0
331331 11.0883 + 19.2055i 0.609469 + 1.05563i 0.991328 + 0.131411i 0.0419508π0.0419508\pi
−0.381859 + 0.924221i 0.624716π0.624716\pi
332332 8.87363 15.3696i 0.487004 0.843515i
333333 0 0
334334 −5.25729 9.10590i −0.287666 0.498253i
335335 −35.7220 −1.95170
336336 0 0
337337 −5.95311 −0.324287 −0.162143 0.986767i 0.551841π-0.551841\pi
−0.162143 + 0.986767i 0.551841π0.551841\pi
338338 0.367252 + 0.636099i 0.0199759 + 0.0345992i
339339 0 0
340340 −3.90856 + 6.76982i −0.211971 + 0.367145i
341341 10.5831 + 18.3305i 0.573109 + 0.992654i
342342 0 0
343343 1.39610 18.4676i 0.0753825 0.997155i
344344 −27.0637 −1.45918
345345 0 0
346346 8.23239 14.2589i 0.442576 0.766564i
347347 −9.52110 + 16.4910i −0.511120 + 0.885285i 0.488797 + 0.872397i 0.337436π0.337436\pi
−0.999917 + 0.0128877i 0.995898π0.995898\pi
348348 0 0
349349 −3.61556 −0.193537 −0.0967683 0.995307i 0.530851π-0.530851\pi
−0.0967683 + 0.995307i 0.530851π0.530851\pi
350350 2.42150 + 1.48048i 0.129435 + 0.0791347i
351351 0 0
352352 10.8727 + 18.8320i 0.579515 + 1.00375i
353353 2.98845 5.17615i 0.159059 0.275499i −0.775470 0.631384i 0.782487π-0.782487\pi
0.934530 + 0.355885i 0.115821π0.115821\pi
354354 0 0
355355 −18.3676 31.8136i −0.974851 1.68849i
356356 17.2533 0.914420
357357 0 0
358358 6.06848 0.320729
359359 −7.57639 13.1227i −0.399866 0.692589i 0.593843 0.804581i 0.297610π-0.297610\pi
−0.993709 + 0.111992i 0.964277π0.964277\pi
360360 0 0
361361 −8.02918 + 13.9069i −0.422588 + 0.731944i
362362 −0.289371 0.501204i −0.0152090 0.0263427i
363363 0 0
364364 3.39397 1.84730i 0.177892 0.0968247i
365365 −15.6070 −0.816910
366366 0 0
367367 3.37578 5.84702i 0.176214 0.305212i −0.764367 0.644782i 0.776948π-0.776948\pi
0.940581 + 0.339570i 0.110282π0.110282\pi
368368 3.29612 5.70904i 0.171822 0.297604i
369369 0 0
370370 −12.2632 −0.637535
371371 14.9998 8.16421i 0.778751 0.423865i
372372 0 0
373373 −3.15486 5.46438i −0.163352 0.282935i 0.772716 0.634751i 0.218897π-0.218897\pi
−0.936069 + 0.351816i 0.885564π0.885564\pi
374374 −2.87085 + 4.97245i −0.148448 + 0.257119i
375375 0 0
376376 −1.86693 3.23361i −0.0962793 0.166761i
377377 8.83547 0.455050
378378 0 0
379379 0.0861875 0.00442715 0.00221358 0.999998i 0.499295π-0.499295\pi
0.00221358 + 0.999998i 0.499295π0.499295\pi
380380 10.9901 + 19.0354i 0.563781 + 0.976497i
381381 0 0
382382 −0.145527 + 0.252061i −0.00744583 + 0.0128966i
383383 −10.6889 18.5138i −0.546180 0.946011i −0.998532 0.0541716i 0.982748π-0.982748\pi
0.452352 0.891840i 0.350585π-0.350585\pi
384384 0 0
385385 −21.2989 13.0219i −1.08549 0.663657i
386386 −2.78225 −0.141613
387387 0 0
388388 5.18550 8.98155i 0.263254 0.455969i
389389 −16.0420 + 27.7855i −0.813360 + 1.40878i 0.0971400 + 0.995271i 0.469031π0.469031\pi
−0.910500 + 0.413510i 0.864303π0.864303\pi
390390 0 0
391391 13.1694 0.666008
392392 8.11011 + 15.8364i 0.409623 + 0.799858i
393393 0 0
394394 −4.42480 7.66398i −0.222918 0.386106i
395395 10.1262 17.5391i 0.509505 0.882488i
396396 0 0
397397 −6.05982 10.4959i −0.304134 0.526775i 0.672934 0.739702i 0.265034π-0.265034\pi
−0.977068 + 0.212927i 0.931700π0.931700\pi
398398 3.79169 0.190060
399399 0 0
400400 1.53950 0.0769748
401401 13.3139 + 23.0603i 0.664863 + 1.15158i 0.979322 + 0.202305i 0.0648434π0.0648434\pi
−0.314460 + 0.949271i 0.601823π0.601823\pi
402402 0 0
403403 −2.85087 + 4.93786i −0.142012 + 0.245972i
404404 −6.20512 10.7476i −0.308716 0.534712i
405405 0 0
406406 −0.431806 + 17.1647i −0.0214302 + 0.851868i
407407 24.3845 1.20869
408408 0 0
409409 3.24484 5.62023i 0.160447 0.277903i −0.774582 0.632473i 0.782040π-0.782040\pi
0.935029 + 0.354571i 0.115373π0.115373\pi
410410 −9.61885 + 16.6603i −0.475041 + 0.822795i
411411 0 0
412412 −3.19436 −0.157375
413413 −26.5736 + 14.4637i −1.30760 + 0.711712i
414414 0 0
415415 −15.4430 26.7480i −0.758067 1.31301i
416416 −2.92887 + 5.07295i −0.143599 + 0.248722i
417417 0 0
418418 8.07227 + 13.9816i 0.394828 + 0.683862i
419419 31.3097 1.52958 0.764789 0.644280i 0.222843π-0.222843\pi
0.764789 + 0.644280i 0.222843π0.222843\pi
420420 0 0
421421 −24.3097 −1.18478 −0.592392 0.805650i 0.701816π-0.701816\pi
−0.592392 + 0.805650i 0.701816π0.701816\pi
422422 6.60295 + 11.4366i 0.321427 + 0.556727i
423423 0 0
424424 −8.20321 + 14.2084i −0.398383 + 0.690020i
425425 1.53774 + 2.66345i 0.0745914 + 0.129196i
426426 0 0
427427 0.606511 24.1094i 0.0293511 1.16673i
428428 −10.9940 −0.531414
429429 0 0
430430 −9.93920 + 17.2152i −0.479311 + 0.830190i
431431 9.89750 17.1430i 0.476746 0.825748i −0.522899 0.852395i 0.675150π-0.675150\pi
0.999645 + 0.0266466i 0.00848287π0.00848287\pi
432432 0 0
433433 −31.8932 −1.53269 −0.766344 0.642430i 0.777926π-0.777926\pi
−0.766344 + 0.642430i 0.777926π0.777926\pi
434434 −9.45344 5.77971i −0.453780 0.277435i
435435 0 0
436436 0.0394951 + 0.0684076i 0.00189147 + 0.00327613i
437437 18.5150 32.0689i 0.885692 1.53406i
438438 0 0
439439 14.4231 + 24.9816i 0.688379 + 1.19231i 0.972362 + 0.233478i 0.0750108π0.0750108\pi
−0.283983 + 0.958829i 0.591656π0.591656\pi
440440 23.9830 1.14334
441441 0 0
442442 −1.54669 −0.0735687
443443 1.62898 + 2.82148i 0.0773952 + 0.134052i 0.902125 0.431474i 0.142006π-0.142006\pi
−0.824730 + 0.565526i 0.808673π0.808673\pi
444444 0 0
445445 15.0131 26.0035i 0.711690 1.23268i
446446 0.722713 + 1.25178i 0.0342215 + 0.0592733i
447447 0 0
448448 −4.95331 3.02839i −0.234022 0.143078i
449449 −1.03302 −0.0487513 −0.0243756 0.999703i 0.507760π-0.507760\pi
−0.0243756 + 0.999703i 0.507760π0.507760\pi
450450 0 0
451451 19.1264 33.1278i 0.900625 1.55993i
452452 4.56699 7.91027i 0.214813 0.372068i
453453 0 0
454454 −9.12880 −0.428436
455455 0.169121 6.72272i 0.00792852 0.315166i
456456 0 0
457457 8.73239 + 15.1249i 0.408484 + 0.707515i 0.994720 0.102625i 0.0327243π-0.0327243\pi
−0.586236 + 0.810140i 0.699391π0.699391\pi
458458 7.73372 13.3952i 0.361373 0.625916i
459459 0 0
460460 −11.6082 20.1059i −0.541234 0.937444i
461461 32.4060 1.50930 0.754649 0.656128i 0.227807π-0.227807\pi
0.754649 + 0.656128i 0.227807π0.227807\pi
462462 0 0
463463 −34.8788 −1.62095 −0.810477 0.585770i 0.800792π-0.800792\pi
−0.810477 + 0.585770i 0.800792π0.800792\pi
464464 4.65667 + 8.06558i 0.216180 + 0.374435i
465465 0 0
466466 2.66945 4.62362i 0.123660 0.214185i
467467 −16.2626 28.1676i −0.752543 1.30344i −0.946586 0.322450i 0.895494π-0.895494\pi
0.194043 0.980993i 0.437840π-0.437840\pi
468468 0 0
469469 −32.6593 + 17.7761i −1.50807 + 0.820823i
470470 −2.74253 −0.126503
471471 0 0
472472 14.5328 25.1715i 0.668925 1.15861i
473473 19.7634 34.2311i 0.908720 1.57395i
474474 0 0
475475 8.64766 0.396782
476476 −0.204634 + 8.13439i −0.00937939 + 0.372839i
477477 0 0
478478 −4.72646 8.18647i −0.216183 0.374440i
479479 −2.52189 + 4.36804i −0.115228 + 0.199581i −0.917871 0.396879i 0.870093π-0.870093\pi
0.802643 + 0.596460i 0.203427π0.203427\pi
480480 0 0
481481 3.28434 + 5.68864i 0.149753 + 0.259380i
482482 −9.69444 −0.441569
483483 0 0
484484 −4.06128 −0.184604
485485 −9.02446 15.6308i −0.409779 0.709759i
486486 0 0
487487 5.60097 9.70117i 0.253804 0.439602i −0.710766 0.703429i 0.751651π-0.751651\pi
0.964570 + 0.263827i 0.0849848π0.0849848\pi
488488 11.5845 + 20.0649i 0.524406 + 0.908297i
489489 0 0
490490 13.0519 + 0.657103i 0.589627 + 0.0296849i
491491 21.6420 0.976689 0.488344 0.872651i 0.337601π-0.337601\pi
0.488344 + 0.872651i 0.337601π0.337601\pi
492492 0 0
493493 −9.30272 + 16.1128i −0.418973 + 0.725683i
494494 −2.17450 + 3.76635i −0.0978354 + 0.169456i
495495 0 0
496496 −6.01012 −0.269862
497497 −32.6240 19.9459i −1.46339 0.894696i
498498 0 0
499499 6.40642 + 11.0962i 0.286791 + 0.496736i 0.973042 0.230629i 0.0740782π-0.0740782\pi
−0.686251 + 0.727365i 0.740745π0.740745\pi
500500 −6.56973 + 11.3791i −0.293807 + 0.508889i
501501 0 0
502502 −3.73191 6.46386i −0.166563 0.288496i
503503 −24.9763 −1.11364 −0.556818 0.830635i 0.687978π-0.687978\pi
−0.556818 + 0.830635i 0.687978π0.687978\pi
504504 0 0
505505 −21.5979 −0.961092
506506 −8.52624 14.7679i −0.379038 0.656512i
507507 0 0
508508 −1.82023 + 3.15274i −0.0807598 + 0.139880i
509509 17.8003 + 30.8311i 0.788986 + 1.36656i 0.926589 + 0.376077i 0.122727π0.122727\pi
−0.137602 + 0.990488i 0.543940π0.543940\pi
510510 0 0
511511 −14.2690 + 7.76643i −0.631222 + 0.343566i
512512 −11.5330 −0.509691
513513 0 0
514514 −0.0883236 + 0.152981i −0.00389578 + 0.00674770i
515515 −2.77961 + 4.81442i −0.122484 + 0.212149i
516516 0 0
517517 5.45331 0.239836
518518 −11.2118 + 6.10246i −0.492619 + 0.268127i
519519 0 0
520520 3.23025 + 5.59496i 0.141656 + 0.245355i
521521 −18.4039 + 31.8765i −0.806288 + 1.39653i 0.109129 + 0.994028i 0.465194π0.465194\pi
−0.915418 + 0.402505i 0.868140π0.868140\pi
522522 0 0
523523 7.75876 + 13.4386i 0.339267 + 0.587627i 0.984295 0.176531i 0.0564877π-0.0564877\pi
−0.645028 + 0.764159i 0.723154π0.723154\pi
524524 −12.9310 −0.564892
525525 0 0
526526 12.3097 0.536729
527527 −6.00327 10.3980i −0.261507 0.452943i
528528 0 0
529529 −8.05622 + 13.9538i −0.350270 + 0.606686i
530530 6.02529 + 10.4361i 0.261722 + 0.453315i
531531 0 0
532532 19.5203 + 11.9345i 0.846313 + 0.517425i
533533 10.3045 0.446336
534534 0 0
535535 −9.56654 + 16.5697i −0.413597 + 0.716372i
536536 17.8610 30.9362i 0.771478 1.33624i
537537 0 0
538538 −10.8932 −0.469638
539539 −25.9528 1.30660i −1.11787 0.0562792i
540540 0 0
541541 −11.2630 19.5081i −0.484235 0.838720i 0.515601 0.856829i 0.327569π-0.327569\pi
−0.999836 + 0.0181087i 0.994236π0.994236\pi
542542 10.0151 17.3467i 0.430186 0.745103i
543543 0 0
544544 −6.16751 10.6824i −0.264430 0.458006i
545545 0.137469 0.00588851
546546 0 0
547547 1.73812 0.0743168 0.0371584 0.999309i 0.488169π-0.488169\pi
0.0371584 + 0.999309i 0.488169π0.488169\pi
548548 −1.98552 3.43902i −0.0848171 0.146907i
549549 0 0
550550 1.99115 3.44877i 0.0849027 0.147056i
551551 26.1575 + 45.3060i 1.11435 + 1.93010i
552552 0 0
553553 0.530162 21.0744i 0.0225448 0.896175i
554554 20.3393 0.864134
555555 0 0
556556 9.61702 16.6572i 0.407853 0.706421i
557557 −13.1528 + 22.7814i −0.557303 + 0.965277i 0.440417 + 0.897793i 0.354830π0.354830\pi
−0.997720 + 0.0674838i 0.978503π0.978503\pi
558558 0 0
559559 10.6477 0.450348
560560 6.22606 3.38877i 0.263099 0.143202i
561561 0 0
562562 6.13161 + 10.6203i 0.258646 + 0.447989i
563563 6.86825 11.8962i 0.289462 0.501363i −0.684219 0.729276i 0.739857π-0.739857\pi
0.973681 + 0.227913i 0.0731902π0.0731902\pi
564564 0 0
565565 −7.94805 13.7664i −0.334377 0.579158i
566566 0.235212 0.00988671
567567 0 0
568568 36.7352 1.54137
569569 9.82612 + 17.0193i 0.411933 + 0.713488i 0.995101 0.0988631i 0.0315206π-0.0315206\pi
−0.583169 + 0.812351i 0.698187π0.698187\pi
570570 0 0
571571 8.37578 14.5073i 0.350515 0.607111i −0.635824 0.771834i 0.719340π-0.719340\pi
0.986340 + 0.164723i 0.0526731π0.0526731\pi
572572 −2.71087 4.69537i −0.113347 0.196323i
573573 0 0
574574 −0.503599 + 20.0185i −0.0210198 + 0.835556i
575575 −9.13399 −0.380914
576576 0 0
577577 11.6965 20.2589i 0.486931 0.843390i −0.512956 0.858415i 0.671450π-0.671450\pi
0.999887 + 0.0150252i 0.00478286π0.00478286\pi
578578 −4.61479 + 7.99305i −0.191950 + 0.332467i
579579 0 0
580580 32.7994 1.36192
581581 −27.4294 16.7700i −1.13796 0.695736i
582582 0 0
583583 −11.9808 20.7514i −0.496195 0.859435i
584584 7.80352 13.5161i 0.322912 0.559300i
585585 0 0
586586 −2.96722 5.13938i −0.122575 0.212306i
587587 −6.05322 −0.249843 −0.124922 0.992167i 0.539868π-0.539868\pi
−0.124922 + 0.992167i 0.539868π0.539868\pi
588588 0 0
589589 −33.7601 −1.39106
590590 −10.6744 18.4886i −0.439457 0.761162i
591591 0 0
592592 −3.46197 + 5.99630i −0.142286 + 0.246447i
593593 3.27361 + 5.67006i 0.134431 + 0.232842i 0.925380 0.379041i 0.123746π-0.123746\pi
−0.790949 + 0.611882i 0.790413π0.790413\pi
594594 0 0
595595 12.0818 + 7.38665i 0.495306 + 0.302823i
596596 0 0
597597 0 0
598598 2.29679 3.97816i 0.0939227 0.162679i
599599 −1.18121 + 2.04591i −0.0482627 + 0.0835935i −0.889148 0.457621i 0.848702π-0.848702\pi
0.840885 + 0.541214i 0.182035π0.182035\pi
600600 0 0
601601 40.5408 1.65370 0.826848 0.562426i 0.190132π-0.190132\pi
0.826848 + 0.562426i 0.190132π0.190132\pi
602602 −0.520371 + 20.6852i −0.0212087 + 0.843066i
603603 0 0
604604 −5.32743 9.22738i −0.216770 0.375457i
605605 −3.53397 + 6.12102i −0.143676 + 0.248855i
606606 0 0
607607 5.72306 + 9.91262i 0.232292 + 0.402341i 0.958482 0.285153i 0.0920443π-0.0920443\pi
−0.726190 + 0.687494i 0.758711π0.758711\pi
608608 −34.6837 −1.40661
609609 0 0
610610 17.0177 0.689027
611611 0.734503 + 1.27220i 0.0297148 + 0.0514676i
612612 0 0
613613 −6.35301 + 11.0037i −0.256596 + 0.444437i −0.965328 0.261041i 0.915934π-0.915934\pi
0.708732 + 0.705478i 0.249268π0.249268\pi
614614 −1.81532 3.14423i −0.0732604 0.126891i
615615 0 0
616616 21.9267 11.9345i 0.883454 0.480853i
617617 −30.9500 −1.24600 −0.623000 0.782221i 0.714087π-0.714087\pi
−0.623000 + 0.782221i 0.714087π0.714087\pi
618618 0 0
619619 −2.28220 + 3.95289i −0.0917294 + 0.158880i −0.908239 0.418452i 0.862573π-0.862573\pi
0.816510 + 0.577332i 0.195906π0.195906\pi
620620 −10.5831 + 18.3305i −0.425029 + 0.736172i
621621 0 0
622622 −2.97509 −0.119290
623623 0.786018 31.2449i 0.0314912 1.25180i
624624 0 0
625625 15.0847 + 26.1275i 0.603389 + 1.04510i
626626 −3.80734 + 6.59451i −0.152172 + 0.263570i
627627 0 0
628628 −4.14241 7.17486i −0.165300 0.286308i
629629 −13.8321 −0.551522
630630 0 0
631631 15.0803 0.600339 0.300169 0.953886i 0.402957π-0.402957\pi
0.300169 + 0.953886i 0.402957π0.402957\pi
632632 10.1262 + 17.5391i 0.402799 + 0.697668i
633633 0 0
634634 −4.43540 + 7.68235i −0.176152 + 0.305105i
635635 3.16780 + 5.48678i 0.125710 + 0.217736i
636636 0 0
637637 −3.19076 6.23049i −0.126422 0.246861i
638638 24.0913 0.953783
639639 0 0
640640 −12.8406 + 22.2405i −0.507568 + 0.879133i
641641 −3.02118 + 5.23284i −0.119329 + 0.206685i −0.919502 0.393085i 0.871408π-0.871408\pi
0.800173 + 0.599770i 0.204741π0.204741\pi
642642 0 0
643643 −16.2881 −0.642341 −0.321171 0.947021i 0.604076π-0.604076\pi
−0.321171 + 0.947021i 0.604076π0.604076\pi
644644 −20.6181 12.6056i −0.812467 0.496732i
645645 0 0
646646 −4.57899 7.93104i −0.180158 0.312043i
647647 −3.58020 + 6.20109i −0.140752 + 0.243790i −0.927780 0.373127i 0.878285π-0.878285\pi
0.787028 + 0.616917i 0.211619π0.211619\pi
648648 0 0
649649 21.2252 + 36.7631i 0.833162 + 1.44308i
650650 1.07275 0.0420765
651651 0 0
652652 30.2560 1.18492
653653 11.7628 + 20.3737i 0.460313 + 0.797285i 0.998976 0.0452359i 0.0144040π-0.0144040\pi
−0.538664 + 0.842521i 0.681071π0.681071\pi
654654 0 0
655655 −11.2520 + 19.4891i −0.439654 + 0.761502i
656656 5.43089 + 9.40658i 0.212041 + 0.367265i
657657 0 0
658658 −2.50739 + 1.36474i −0.0977483 + 0.0532033i
659659 8.73459 0.340251 0.170126 0.985422i 0.445583π-0.445583\pi
0.170126 + 0.985422i 0.445583π0.445583\pi
660660 0 0
661661 −5.60078 + 9.70083i −0.217845 + 0.377319i −0.954149 0.299332i 0.903236π-0.903236\pi
0.736304 + 0.676651i 0.236569π0.236569\pi
662662 −8.14441 + 14.1065i −0.316542 + 0.548266i
663663 0 0
664664 30.8860 1.19861
665665 34.9731 19.0354i 1.35620 0.738162i
666666 0 0
667667 −27.6285 47.8540i −1.06978 1.85291i
668668 −10.4537 + 18.1064i −0.404467 + 0.700558i
669669 0 0
670670 −13.1190 22.7227i −0.506830 0.877855i
671671 −33.8384 −1.30632
672672 0 0
673673 −11.0728 −0.426823 −0.213412 0.976962i 0.568458π-0.568458\pi
−0.213412 + 0.976962i 0.568458π0.568458\pi
674674 −2.18629 3.78677i −0.0842128 0.145861i
675675 0 0
676676 0.730252 1.26483i 0.0280866 0.0486475i
677677 −18.0419 31.2495i −0.693407 1.20102i −0.970715 0.240235i 0.922775π-0.922775\pi
0.277308 0.960781i 0.410558π-0.410558\pi
678678 0 0
679679 −16.0290 9.79991i −0.615136 0.376086i
680680 −13.6043 −0.521702
681681 0 0
682682 −7.77335 + 13.4638i −0.297657 + 0.515557i
683683 24.4624 42.3701i 0.936027 1.62125i 0.163235 0.986587i 0.447807π-0.447807\pi
0.772792 0.634659i 0.218860π-0.218860\pi
684684 0 0
685685 −6.91089 −0.264051
686686 12.2599 5.89418i 0.468086 0.225041i
687687 0 0
688688 5.61177 + 9.71987i 0.213947 + 0.370566i
689689 3.22738 5.58999i 0.122954 0.212962i
690690 0 0
691691 18.8353 + 32.6237i 0.716529 + 1.24106i 0.962367 + 0.271753i 0.0876034π0.0876034\pi
−0.245838 + 0.969311i 0.579063π0.579063\pi
692692 −32.7390 −1.24455
693693 0 0
694694 −13.9866 −0.530923
695695 −16.7367 28.9889i −0.634861 1.09961i
696696 0 0
697697 −10.8494 + 18.7917i −0.410951 + 0.711788i
698698 −1.32782 2.29985i −0.0502587 0.0870507i
699699 0 0
700700 0.141929 5.64180i 0.00536441 0.213240i
701701 19.9325 0.752839 0.376420 0.926449i 0.377155π-0.377155\pi
0.376420 + 0.926449i 0.377155π0.377155\pi
702702 0 0
703703 −19.4466 + 33.6825i −0.733442 + 1.27036i
704704 −4.07299 + 7.05463i −0.153507 + 0.265881i
705705 0 0
706706 4.39006 0.165222
707707 −19.7461 + 10.7476i −0.742630 + 0.404205i
708708 0 0
709709 2.03803 + 3.52998i 0.0765399 + 0.132571i 0.901755 0.432248i 0.142279π-0.142279\pi
−0.825215 + 0.564819i 0.808946π0.808946\pi
710710 13.4911 23.3672i 0.506311 0.876956i
711711 0 0
712712 15.0131 + 26.0035i 0.562641 + 0.974522i
713713 35.6587 1.33543
714714 0 0
715715 −9.43560 −0.352871
716716 −6.03336 10.4501i −0.225477 0.390538i
717717 0 0
718718 5.56488 9.63865i 0.207679 0.359711i
719719 −2.06232 3.57205i −0.0769117 0.133215i 0.825004 0.565126i 0.191173π-0.191173\pi
−0.901916 + 0.431911i 0.857839π0.857839\pi
720720 0 0
721721 −0.145527 + 5.78485i −0.00541973 + 0.215439i
722722 −11.7949 −0.438961
723723 0 0
724724 −0.575392 + 0.996608i −0.0213843 + 0.0370386i
725725 6.45212 11.1754i 0.239626 0.415044i
726726 0 0
727727 −7.39203 −0.274155 −0.137078 0.990560i 0.543771π-0.543771\pi
−0.137078 + 0.990560i 0.543771π0.543771\pi
728728 5.73748 + 3.50782i 0.212645 + 0.130009i
729729 0 0
730730 −5.73171 9.92762i −0.212140 0.367438i
731731 −11.2107 + 19.4176i −0.414644 + 0.718185i
732732 0 0
733733 3.52918 + 6.11272i 0.130353 + 0.225778i 0.923813 0.382845i 0.125056π-0.125056\pi
−0.793460 + 0.608623i 0.791722π0.791722\pi
734734 4.95904 0.183042
735735 0 0
736736 36.6342 1.35036
737737 26.0861 + 45.1824i 0.960893 + 1.66432i
738738 0 0
739739 16.9517 29.3611i 0.623577 1.08007i −0.365238 0.930914i 0.619012π-0.619012\pi
0.988814 0.149152i 0.0476544π-0.0476544\pi
740740 12.1923 + 21.1176i 0.448196 + 0.776298i
741741 0 0
742742 10.7019 + 6.54303i 0.392881 + 0.240202i
743743 16.3211 0.598763 0.299382 0.954133i 0.403220π-0.403220\pi
0.299382 + 0.954133i 0.403220π0.403220\pi
744744 0 0
745745 0 0
746746 2.31726 4.01360i 0.0848408 0.146949i
747747 0 0
748748 11.4169 0.417444
749749 −0.500860 + 19.9096i −0.0183010 + 0.727482i
750750 0 0
751751 11.7733 + 20.3920i 0.429616 + 0.744116i 0.996839 0.0794480i 0.0253158π-0.0253158\pi
−0.567224 + 0.823564i 0.691982π0.691982\pi
752752 −0.774228 + 1.34100i −0.0282332 + 0.0489013i
753753 0 0
754754 3.24484 + 5.62023i 0.118170 + 0.204677i
755755 −18.5429 −0.674846
756756 0 0
757757 35.1019 1.27580 0.637901 0.770119i 0.279803π-0.279803\pi
0.637901 + 0.770119i 0.279803π0.279803\pi
758758 0.0316525 + 0.0548237i 0.00114967 + 0.00199129i
759759 0 0
760760 −19.1264 + 33.1278i −0.693786 + 1.20167i
761761 −22.7346 39.3775i −0.824128 1.42743i −0.902584 0.430514i 0.858332π-0.858332\pi
0.0784558 0.996918i 0.475001π-0.475001\pi
762762 0 0
763763 0.125683 0.0684076i 0.00455002 0.00247652i
764764 0.578741 0.0209381
765765 0 0
766766 7.85107 13.5984i 0.283671 0.491332i
767767 −5.71762 + 9.90321i −0.206451 + 0.357584i
768768 0 0
769769 −42.4543 −1.53094 −0.765470 0.643472i 0.777493π-0.777493\pi
−0.765470 + 0.643472i 0.777493π0.777493\pi
770770 0.461135 18.3305i 0.0166181 0.660586i
771771 0 0
772772 2.76615 + 4.79111i 0.0995559 + 0.172436i
773773 −23.3010 + 40.3586i −0.838080 + 1.45160i 0.0534175 + 0.998572i 0.482989π0.482989\pi
−0.891498 + 0.453025i 0.850345π0.850345\pi
774774 0 0
775775 4.16372 + 7.21177i 0.149565 + 0.259054i
776776 18.0489 0.647918
777777 0 0
778778 −23.5657 −0.844873
779779 30.5065 + 52.8387i 1.09301 + 1.89314i
780780 0 0
781781 −26.8260 + 46.4639i −0.959909 + 1.66261i
782782 4.83650 + 8.37707i 0.172953 + 0.299563i
783783 0 0
784784 4.00593 6.19646i 0.143069 0.221302i
785785 −14.4183 −0.514610
786786 0 0
787787 −13.1908 + 22.8471i −0.470200 + 0.814410i −0.999419 0.0340751i 0.989151π-0.989151\pi
0.529220 + 0.848485i 0.322485π0.322485\pi
788788 −8.79839 + 15.2393i −0.313430 + 0.542876i
789789 0 0
790790 14.8755 0.529245
791791 −14.1171 8.63101i −0.501947 0.306884i
792792 0 0
793793 −4.55768 7.89414i −0.161848 0.280329i
794794 4.45096 7.70928i 0.157959 0.273592i
795795 0 0
796796 −3.76975 6.52939i −0.133615 0.231428i
797797 17.6474 0.625102 0.312551 0.949901i 0.398817π-0.398817\pi
0.312551 + 0.949901i 0.398817π0.398817\pi
798798 0 0
799799 −3.09338 −0.109436
800800 4.27762 + 7.40906i 0.151237 + 0.261950i
801801 0 0
802802 −9.77908 + 16.9379i −0.345311 + 0.598097i
803803 11.3971 + 19.7403i 0.402194 + 0.696621i
804804 0 0
805805 −36.9399 + 20.1059i −1.30196 + 0.708641i
806806 −4.18795 −0.147514
807807 0 0
808808 10.7989 18.7043i 0.379905 0.658015i
809809 8.98580 15.5639i 0.315924 0.547197i −0.663709 0.747990i 0.731019π-0.731019\pi
0.979633 + 0.200794i 0.0643522π0.0643522\pi
810810 0 0
811811 43.5159 1.52805 0.764026 0.645186i 0.223220π-0.223220\pi
0.764026 + 0.645186i 0.223220π0.223220\pi
812812 29.9873 16.3217i 1.05235 0.572781i
813813 0 0
814814 8.95525 + 15.5109i 0.313881 + 0.543658i
815815 26.3277 45.6008i 0.922217 1.59733i
816816 0 0
817817 31.5225 + 54.5985i 1.10283 + 1.91016i
818818 4.76669 0.166664
819819 0 0
820820 38.2527 1.33584
821821 −18.3642 31.8076i −0.640913 1.11009i −0.985229 0.171241i 0.945222π-0.945222\pi
0.344316 0.938854i 0.388111π-0.388111\pi
822822 0 0
823823 20.6118 35.7006i 0.718481 1.24445i −0.243120 0.969996i 0.578171π-0.578171\pi
0.961601 0.274450i 0.0884956π-0.0884956\pi
824824 −2.77961 4.81442i −0.0968322 0.167718i
825825 0 0
826826 −18.9595 11.5916i −0.659686 0.403323i
827827 −10.0060 −0.347941 −0.173971 0.984751i 0.555660π-0.555660\pi
−0.173971 + 0.984751i 0.555660π0.555660\pi
828828 0 0
829829 −7.48035 + 12.9563i −0.259803 + 0.449992i −0.966189 0.257835i 0.916991π-0.916991\pi
0.706386 + 0.707827i 0.250324π0.250324\pi
830830 11.3429 19.6465i 0.393719 0.681941i
831831 0 0
832832 −2.19436 −0.0760756
833833 14.7217 + 0.741168i 0.510077 + 0.0256799i
834834 0 0
835835 18.1929 + 31.5110i 0.629591 + 1.09048i
836836 16.0511 27.8013i 0.555139 0.961529i
837837 0 0
838838 11.4985 + 19.9161i 0.397210 + 0.687989i
839839 −27.0026 −0.932232 −0.466116 0.884724i 0.654347π-0.654347\pi
−0.466116 + 0.884724i 0.654347π0.654347\pi
840840 0 0
841841 49.0656 1.69192
842842 −8.92779 15.4634i −0.307672 0.532903i
843843 0 0
844844 13.1295 22.7409i 0.451935 0.782775i
845845 −1.27088 2.20122i −0.0437195 0.0757243i
846846 0 0
847847 −0.185023 + 7.35481i −0.00635745 + 0.252714i
848848 6.80387 0.233646
849849 0 0
850850 −1.12948 + 1.95631i −0.0387407 + 0.0671009i
851851 20.5402 35.5767i 0.704110 1.21955i
852852 0 0
853853 −10.5438 −0.361012 −0.180506 0.983574i 0.557773π-0.557773\pi
−0.180506 + 0.983574i 0.557773π0.557773\pi
854854 15.5587 8.46840i 0.532407 0.289783i
855855 0 0
856856 −9.56654 16.5697i −0.326978 0.566342i
857857 3.74018 6.47818i 0.127762 0.221290i −0.795047 0.606548i 0.792554π-0.792554\pi
0.922809 + 0.385257i 0.125887π0.125887\pi
858858 0 0
859859 −21.6862 37.5616i −0.739923 1.28158i −0.952530 0.304446i 0.901529π-0.901529\pi
0.212607 0.977138i 0.431805π-0.431805\pi
860860 39.5267 1.34785
861861 0 0
862862 14.5395 0.495217
863863 16.0114 + 27.7325i 0.545034 + 0.944026i 0.998605 + 0.0528061i 0.0168165π0.0168165\pi
−0.453571 + 0.891220i 0.649850π0.649850\pi
864864 0 0
865865 −28.4882 + 49.3430i −0.968629 + 1.67771i
866866 −11.7128 20.2872i −0.398018 0.689387i
867867 0 0
868868 −0.554084 + 22.0253i −0.0188068 + 0.747589i
869869 −29.5788 −1.00339
870870 0 0
871871 −7.02704 + 12.1712i −0.238102 + 0.412405i
872872 −0.0687343 + 0.119051i −0.00232764 + 0.00403159i
873873 0 0
874874 27.1986 0.920007
875875 20.3078 + 12.4159i 0.686529 + 0.419735i
876876 0 0
877877 −16.3078 28.2459i −0.550675 0.953796i −0.998226 0.0595382i 0.981037π-0.981037\pi
0.447551 0.894258i 0.352296π-0.352296\pi
878878 −10.5938 + 18.3491i −0.357525 + 0.619252i
879879 0 0
880880 −4.97296 8.61342i −0.167638 0.290358i
881881 34.6890 1.16870 0.584351 0.811501i 0.301349π-0.301349\pi
0.584351 + 0.811501i 0.301349π0.301349\pi
882882 0 0
883883 7.36381 0.247812 0.123906 0.992294i 0.460458π-0.460458\pi
0.123906 + 0.992294i 0.460458π0.460458\pi
884884 1.53774 + 2.66345i 0.0517198 + 0.0895814i
885885 0 0
886886 −1.19649 + 2.07238i −0.0401969 + 0.0696231i
887887 15.6258 + 27.0647i 0.524664 + 0.908745i 0.999588 + 0.0287180i 0.00914248π0.00914248\pi
−0.474923 + 0.880027i 0.657524π0.657524\pi
888888 0 0
889889 5.62655 + 3.44000i 0.188708 + 0.115374i
890890 22.0544 0.739265
891891 0 0
892892 1.43706 2.48906i 0.0481164 0.0833400i
893893 −4.34900 + 7.53269i −0.145534 + 0.252072i
894894 0 0
895895 −21.0000 −0.701953
896896 −0.672273 + 26.7234i −0.0224591 + 0.892767i
897897 0 0
898898 −0.379379 0.657103i −0.0126600 0.0219278i
899899 −25.1888 + 43.6283i −0.840094 + 1.45509i
900900 0 0
901901 6.79612 + 11.7712i 0.226411 + 0.392156i
902902 28.0967 0.935519
903903 0 0
904904 15.8961 0.528697
905905 1.00137 + 1.73442i 0.0332866 + 0.0576541i
906906 0 0
907907 28.3602 49.1213i 0.941685 1.63105i 0.179429 0.983771i 0.442575π-0.442575\pi
0.762256 0.647276i 0.224092π-0.224092\pi
908908 9.07597 + 15.7200i 0.301197 + 0.521688i
909909 0 0
910910 4.33842 2.36135i 0.143817 0.0782780i
911911 22.4742 0.744604 0.372302 0.928112i 0.378569π-0.378569\pi
0.372302 + 0.928112i 0.378569π0.378569\pi
912912 0 0
913913 −22.5546 + 39.0656i −0.746447 + 1.29288i
914914 −6.41397 + 11.1093i −0.212155 + 0.367464i
915915 0 0
916916 −30.7558 −1.01620
917917 −0.589105 + 23.4175i −0.0194540 + 0.773312i
918918 0 0
919919 −1.24271 2.15243i −0.0409931 0.0710021i 0.844801 0.535081i 0.179719π-0.179719\pi
−0.885794 + 0.464079i 0.846385π0.846385\pi
920920 20.2020 34.9909i 0.666040 1.15361i
921921 0 0
922922 11.9012 + 20.6134i 0.391944 + 0.678867i
923923 −14.4527 −0.475717
924924 0 0
925925 9.59358 0.315435
926926 −12.8093 22.1863i −0.420939 0.729088i
927927 0 0
928928 −25.8779 + 44.8219i −0.849484 + 1.47135i
929929 17.5996 + 30.4833i 0.577423 + 1.00013i 0.995774 + 0.0918404i 0.0292750π0.0292750\pi
−0.418351 + 0.908286i 0.637392π0.637392\pi
930930 0 0
931931 22.5021 34.8068i 0.737478 1.14075i
932932 −10.6160 −0.347739
933933 0 0
934934 11.9449 20.6892i 0.390850 0.676972i
935935 9.93458 17.2072i 0.324896 0.562736i
936936 0 0
937937 40.0613 1.30875 0.654373 0.756172i 0.272933π-0.272933\pi
0.654373 + 0.756172i 0.272933π0.272933\pi
938938 −23.3015 14.2463i −0.760822 0.465157i
939939 0 0
940940 2.72665 + 4.72270i 0.0889336 + 0.154038i
941941 −16.0038 + 27.7194i −0.521709 + 0.903627i 0.477972 + 0.878375i 0.341372π0.341372\pi
−0.999681 + 0.0252517i 0.991961π0.991961\pi
942942 0 0
943943 −32.2221 55.8103i −1.04930 1.81743i
944944 −12.0537 −0.392315
945945 0 0
946946 29.0325 0.943928
947947 −11.3692 19.6919i −0.369448 0.639902i 0.620032 0.784577i 0.287120π-0.287120\pi
−0.989479 + 0.144675i 0.953786π0.953786\pi
948948 0 0
949949 −3.07014 + 5.31763i −0.0996608 + 0.172618i
950950 3.17587 + 5.50077i 0.103039 + 0.178468i
951951 0 0
952952 −12.4379 + 6.76982i −0.403116 + 0.219411i
953953 −16.7884 −0.543830 −0.271915 0.962321i 0.587657π-0.587657\pi
−0.271915 + 0.962321i 0.587657π0.587657\pi
954954 0 0
955955 0.503599 0.872258i 0.0162961 0.0282256i
956956 −9.39821 + 16.2782i −0.303960 + 0.526474i
957957 0 0
958958 −3.70467 −0.119693
959959 −6.31837 + 3.43902i −0.204031 + 0.111052i
960960 0 0
961961 −0.754964 1.30764i −0.0243537 0.0421818i
962962 −2.41236 + 4.17832i −0.0777775 + 0.134715i
963963 0 0
964964 9.63833 + 16.6941i 0.310430 + 0.537680i
965965 9.62799 0.309936
966966 0 0
967967 44.3533 1.42631 0.713153 0.701009i 0.247267π-0.247267\pi
0.713153 + 0.701009i 0.247267π0.247267\pi
968968 −3.53397 6.12102i −0.113586 0.196737i
969969 0 0
970970 6.62849 11.4809i 0.212828 0.368629i
971971 −2.03968 3.53282i −0.0654563 0.113374i 0.831440 0.555615i 0.187517π-0.187517\pi
−0.896896 + 0.442241i 0.854184π0.854184\pi
972972 0 0
973973 −29.7273 18.1749i −0.953014 0.582660i
974974 8.22786 0.263638
975975 0 0
976976 4.80418 8.32109i 0.153778 0.266351i
977977 4.88009 8.45256i 0.156128 0.270421i −0.777341 0.629079i 0.783432π-0.783432\pi
0.933469 + 0.358658i 0.116765π0.116765\pi
978978 0 0
979979 −43.8535 −1.40156
980980 −11.8449 23.1291i −0.378370 0.738832i
981981 0 0
982982 7.94805 + 13.7664i 0.253633 + 0.439304i
983983 −25.6582 + 44.4412i −0.818368 + 1.41746i 0.0885154 + 0.996075i 0.471788π0.471788\pi
−0.906884 + 0.421381i 0.861546π0.861546\pi
984984 0 0
985985 15.3121 + 26.5213i 0.487883 + 0.845037i
986986 −13.6658 −0.435206
987987 0 0
988988 8.64766 0.275119
989989 −33.2952 57.6690i −1.05873 1.83377i
990990 0 0
991991 0.352336 0.610265i 0.0111923 0.0193857i −0.860375 0.509662i 0.829771π-0.829771\pi
0.871567 + 0.490276i 0.163104π0.163104\pi
992992 −16.6997 28.9247i −0.530215 0.918359i
993993 0 0
994994 0.706330 28.0772i 0.0224034 0.890556i
995995 −13.1212 −0.415969
996996 0 0
997997 −17.0129 + 29.4673i −0.538805 + 0.933238i 0.460164 + 0.887834i 0.347791π0.347791\pi
−0.998969 + 0.0454035i 0.985543π0.985543\pi
998998 −4.70554 + 8.15023i −0.148951 + 0.257991i
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 819.2.j.i.235.4 yes 12
3.2 odd 2 inner 819.2.j.i.235.3 12
7.2 even 3 inner 819.2.j.i.352.4 yes 12
7.3 odd 6 5733.2.a.bt.1.3 6
7.4 even 3 5733.2.a.bs.1.3 6
21.2 odd 6 inner 819.2.j.i.352.3 yes 12
21.11 odd 6 5733.2.a.bs.1.4 6
21.17 even 6 5733.2.a.bt.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.j.i.235.3 12 3.2 odd 2 inner
819.2.j.i.235.4 yes 12 1.1 even 1 trivial
819.2.j.i.352.3 yes 12 21.2 odd 6 inner
819.2.j.i.352.4 yes 12 7.2 even 3 inner
5733.2.a.bs.1.3 6 7.4 even 3
5733.2.a.bs.1.4 6 21.11 odd 6
5733.2.a.bt.1.3 6 7.3 odd 6
5733.2.a.bt.1.4 6 21.17 even 6