Properties

Label 370.2.d.c.221.3
Level 370370
Weight 22
Character 370.221
Analytic conductor 2.9542.954
Analytic rank 00
Dimension 66
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] = [370,2,Mod(221,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) 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("370.221"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 370=2537 370 = 2 \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 370.d (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,-4,-6,0,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.954464874792.95446487479
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.399424.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5+3x46x3+6x28x+8 x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 221.3
Root 0.2646581.38923i0.264658 - 1.38923i of defining polynomial
Character χ\chi == 370.221
Dual form 370.2.d.c.221.6

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) == q1.00000iq2+2.24914q31.00000q4+1.00000iq52.24914iq6+1.52932q7+1.00000iq8+2.05863q9+1.00000q10+2.71982q112.24914q12+0.941367iq131.52932iq14+2.24914iq15+1.00000q164.83709iq172.05863iq180.249141iq191.00000iq20+3.43965q212.71982iq22+0.941367iq23+2.24914iq241.00000q25+0.941367q262.11727q271.52932q28+0.719824iq29+2.24914q30+4.02760iq311.00000iq32+6.11727q334.83709q34+1.52932iq352.05863q36+(4.719823.83709i)q370.249141q38+2.11727iq391.00000q408.27674q413.43965iq42+2.71982iq432.71982q44+2.05863iq45+0.941367q463.30777q47+2.24914q484.66119q49+1.00000iq5010.8793iq510.941367iq52+8.39400q53+2.11727iq54+2.71982iq55+1.52932iq560.560352iq57+0.719824q587.30777iq592.24914iq60+6.83709iq61+4.02760q62+3.14830q631.00000q640.941367q656.11727iq667.68879q67+4.83709iq68+2.11727iq69+1.52932q703.05863q71+2.05863iq72+9.11383q73+(3.83709+4.71982i)q742.24914q75+0.249141iq76+4.15947q77+2.11727q781.75086iq79+1.00000iq8010.9379q81+8.27674iq82+0.131874q833.43965q84+4.83709q85+2.71982q86+1.61899iq87+2.71982iq888.99656iq89+2.05863q90+1.43965iq910.941367iq92+9.05863iq93+3.30777iq94+0.249141q952.24914iq96+16.2767iq97+4.66119iq98+5.59912q99+O(q100)q-1.00000i q^{2} +2.24914 q^{3} -1.00000 q^{4} +1.00000i q^{5} -2.24914i q^{6} +1.52932 q^{7} +1.00000i q^{8} +2.05863 q^{9} +1.00000 q^{10} +2.71982 q^{11} -2.24914 q^{12} +0.941367i q^{13} -1.52932i q^{14} +2.24914i q^{15} +1.00000 q^{16} -4.83709i q^{17} -2.05863i q^{18} -0.249141i q^{19} -1.00000i q^{20} +3.43965 q^{21} -2.71982i q^{22} +0.941367i q^{23} +2.24914i q^{24} -1.00000 q^{25} +0.941367 q^{26} -2.11727 q^{27} -1.52932 q^{28} +0.719824i q^{29} +2.24914 q^{30} +4.02760i q^{31} -1.00000i q^{32} +6.11727 q^{33} -4.83709 q^{34} +1.52932i q^{35} -2.05863 q^{36} +(-4.71982 - 3.83709i) q^{37} -0.249141 q^{38} +2.11727i q^{39} -1.00000 q^{40} -8.27674 q^{41} -3.43965i q^{42} +2.71982i q^{43} -2.71982 q^{44} +2.05863i q^{45} +0.941367 q^{46} -3.30777 q^{47} +2.24914 q^{48} -4.66119 q^{49} +1.00000i q^{50} -10.8793i q^{51} -0.941367i q^{52} +8.39400 q^{53} +2.11727i q^{54} +2.71982i q^{55} +1.52932i q^{56} -0.560352i q^{57} +0.719824 q^{58} -7.30777i q^{59} -2.24914i q^{60} +6.83709i q^{61} +4.02760 q^{62} +3.14830 q^{63} -1.00000 q^{64} -0.941367 q^{65} -6.11727i q^{66} -7.68879 q^{67} +4.83709i q^{68} +2.11727i q^{69} +1.52932 q^{70} -3.05863 q^{71} +2.05863i q^{72} +9.11383 q^{73} +(-3.83709 + 4.71982i) q^{74} -2.24914 q^{75} +0.249141i q^{76} +4.15947 q^{77} +2.11727 q^{78} -1.75086i q^{79} +1.00000i q^{80} -10.9379 q^{81} +8.27674i q^{82} +0.131874 q^{83} -3.43965 q^{84} +4.83709 q^{85} +2.71982 q^{86} +1.61899i q^{87} +2.71982i q^{88} -8.99656i q^{89} +2.05863 q^{90} +1.43965i q^{91} -0.941367i q^{92} +9.05863i q^{93} +3.30777i q^{94} +0.249141 q^{95} -2.24914i q^{96} +16.2767i q^{97} +4.66119i q^{98} +5.59912 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q4q36q4+10q7+14q9+6q102q11+4q12+6q1616q216q25+4q2616q2710q284q30+40q3314q3414q3610q37+58q99+O(q100) 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9} + 6 q^{10} - 2 q^{11} + 4 q^{12} + 6 q^{16} - 16 q^{21} - 6 q^{25} + 4 q^{26} - 16 q^{27} - 10 q^{28} - 4 q^{30} + 40 q^{33} - 14 q^{34} - 14 q^{36} - 10 q^{37}+ \cdots - 58 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/370Z)×\left(\mathbb{Z}/370\mathbb{Z}\right)^\times.

nn 261261 297297
χ(n)\chi(n) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000i 0.707107i
33 2.24914 1.29854 0.649271 0.760557i 0.275074π-0.275074\pi
0.649271 + 0.760557i 0.275074π0.275074\pi
44 −1.00000 −0.500000
55 1.00000i 0.447214i
66 2.24914i 0.918208i
77 1.52932 0.578027 0.289014 0.957325i 0.406673π-0.406673\pi
0.289014 + 0.957325i 0.406673π0.406673\pi
88 1.00000i 0.353553i
99 2.05863 0.686211
1010 1.00000 0.316228
1111 2.71982 0.820058 0.410029 0.912073i 0.365519π-0.365519\pi
0.410029 + 0.912073i 0.365519π0.365519\pi
1212 −2.24914 −0.649271
1313 0.941367i 0.261088i 0.991443 + 0.130544i 0.0416724π0.0416724\pi
−0.991443 + 0.130544i 0.958328π0.958328\pi
1414 1.52932i 0.408727i
1515 2.24914i 0.580726i
1616 1.00000 0.250000
1717 4.83709i 1.17317i −0.809889 0.586583i 0.800473π-0.800473\pi
0.809889 0.586583i 0.199527π-0.199527\pi
1818 2.05863i 0.485224i
1919 0.249141i 0.0571568i −0.999592 0.0285784i 0.990902π-0.990902\pi
0.999592 0.0285784i 0.00909802π-0.00909802\pi
2020 1.00000i 0.223607i
2121 3.43965 0.750593
2222 2.71982i 0.579868i
2323 0.941367i 0.196289i 0.995172 + 0.0981443i 0.0312907π0.0312907\pi
−0.995172 + 0.0981443i 0.968709π0.968709\pi
2424 2.24914i 0.459104i
2525 −1.00000 −0.200000
2626 0.941367 0.184617
2727 −2.11727 −0.407468
2828 −1.52932 −0.289014
2929 0.719824i 0.133668i 0.997764 + 0.0668340i 0.0212898π0.0212898\pi
−0.997764 + 0.0668340i 0.978710π0.978710\pi
3030 2.24914 0.410635
3131 4.02760i 0.723378i 0.932299 + 0.361689i 0.117800π0.117800\pi
−0.932299 + 0.361689i 0.882200π0.882200\pi
3232 1.00000i 0.176777i
3333 6.11727 1.06488
3434 −4.83709 −0.829554
3535 1.52932i 0.258502i
3636 −2.05863 −0.343106
3737 −4.71982 3.83709i −0.775934 0.630814i
3838 −0.249141 −0.0404159
3939 2.11727i 0.339034i
4040 −1.00000 −0.158114
4141 −8.27674 −1.29261 −0.646305 0.763079i 0.723686π-0.723686\pi
−0.646305 + 0.763079i 0.723686π0.723686\pi
4242 3.43965i 0.530749i
4343 2.71982i 0.414769i 0.978259 + 0.207385i 0.0664952π0.0664952\pi
−0.978259 + 0.207385i 0.933505π0.933505\pi
4444 −2.71982 −0.410029
4545 2.05863i 0.306883i
4646 0.941367 0.138797
4747 −3.30777 −0.482488 −0.241244 0.970464i 0.577555π-0.577555\pi
−0.241244 + 0.970464i 0.577555π0.577555\pi
4848 2.24914 0.324635
4949 −4.66119 −0.665884
5050 1.00000i 0.141421i
5151 10.8793i 1.52341i
5252 0.941367i 0.130544i
5353 8.39400 1.15301 0.576503 0.817095i 0.304417π-0.304417\pi
0.576503 + 0.817095i 0.304417π0.304417\pi
5454 2.11727i 0.288123i
5555 2.71982i 0.366741i
5656 1.52932i 0.204364i
5757 0.560352i 0.0742204i
5858 0.719824 0.0945175
5959 7.30777i 0.951391i −0.879610 0.475696i 0.842196π-0.842196\pi
0.879610 0.475696i 0.157804π-0.157804\pi
6060 2.24914i 0.290363i
6161 6.83709i 0.875400i 0.899121 + 0.437700i 0.144207π0.144207\pi
−0.899121 + 0.437700i 0.855793π0.855793\pi
6262 4.02760 0.511505
6363 3.14830 0.396649
6464 −1.00000 −0.125000
6565 −0.941367 −0.116762
6666 6.11727i 0.752983i
6767 −7.68879 −0.939335 −0.469668 0.882843i 0.655626π-0.655626\pi
−0.469668 + 0.882843i 0.655626π0.655626\pi
6868 4.83709i 0.586583i
6969 2.11727i 0.254889i
7070 1.52932 0.182788
7171 −3.05863 −0.362993 −0.181496 0.983392i 0.558094π-0.558094\pi
−0.181496 + 0.983392i 0.558094π0.558094\pi
7272 2.05863i 0.242612i
7373 9.11383 1.06669 0.533346 0.845897i 0.320934π-0.320934\pi
0.533346 + 0.845897i 0.320934π0.320934\pi
7474 −3.83709 + 4.71982i −0.446053 + 0.548668i
7575 −2.24914 −0.259708
7676 0.249141i 0.0285784i
7777 4.15947 0.474016
7878 2.11727 0.239733
7979 1.75086i 0.196987i −0.995138 0.0984935i 0.968598π-0.968598\pi
0.995138 0.0984935i 0.0314024π-0.0314024\pi
8080 1.00000i 0.111803i
8181 −10.9379 −1.21533
8282 8.27674i 0.914013i
8383 0.131874 0.0144751 0.00723754 0.999974i 0.497696π-0.497696\pi
0.00723754 + 0.999974i 0.497696π0.497696\pi
8484 −3.43965 −0.375296
8585 4.83709 0.524656
8686 2.71982 0.293286
8787 1.61899i 0.173573i
8888 2.71982i 0.289934i
8989 8.99656i 0.953634i −0.879003 0.476817i 0.841790π-0.841790\pi
0.879003 0.476817i 0.158210π-0.158210\pi
9090 2.05863 0.216999
9191 1.43965i 0.150916i
9292 0.941367i 0.0981443i
9393 9.05863i 0.939337i
9494 3.30777i 0.341171i
9595 0.249141 0.0255613
9696 2.24914i 0.229552i
9797 16.2767i 1.65265i 0.563192 + 0.826326i 0.309573π0.309573\pi
−0.563192 + 0.826326i 0.690427π0.690427\pi
9898 4.66119i 0.470851i
9999 5.59912 0.562733
100100 1.00000 0.100000
101101 −11.1138 −1.10587 −0.552934 0.833225i 0.686492π-0.686492\pi
−0.552934 + 0.833225i 0.686492π0.686492\pi
102102 −10.8793 −1.07721
103103 14.1725i 1.39645i 0.715876 + 0.698227i 0.246027π0.246027\pi
−0.715876 + 0.698227i 0.753973π0.753973\pi
104104 −0.941367 −0.0923086
105105 3.43965i 0.335675i
106106 8.39400i 0.815298i
107107 10.6922 1.03366 0.516828 0.856089i 0.327113π-0.327113\pi
0.516828 + 0.856089i 0.327113π0.327113\pi
108108 2.11727 0.203734
109109 12.2767i 1.17590i 0.808898 + 0.587949i 0.200064π0.200064\pi
−0.808898 + 0.587949i 0.799936π0.799936\pi
110110 2.71982 0.259325
111111 −10.6155 8.63016i −1.00758 0.819138i
112112 1.52932 0.144507
113113 2.95436i 0.277922i −0.990298 0.138961i 0.955624π-0.955624\pi
0.990298 0.138961i 0.0443763π-0.0443763\pi
114114 −0.560352 −0.0524818
115115 −0.941367 −0.0877829
116116 0.719824i 0.0668340i
117117 1.93793i 0.179162i
118118 −7.30777 −0.672735
119119 7.39744i 0.678122i
120120 −2.24914 −0.205318
121121 −3.60256 −0.327505
122122 6.83709 0.619001
123123 −18.6155 −1.67851
124124 4.02760i 0.361689i
125125 1.00000i 0.0894427i
126126 3.14830i 0.280473i
127127 8.30434 0.736891 0.368445 0.929649i 0.379890π-0.379890\pi
0.368445 + 0.929649i 0.379890π0.379890\pi
128128 1.00000i 0.0883883i
129129 6.11727i 0.538595i
130130 0.941367i 0.0825633i
131131 11.0732i 0.967474i −0.875214 0.483737i 0.839279π-0.839279\pi
0.875214 0.483737i 0.160721π-0.160721\pi
132132 −6.11727 −0.532440
133133 0.381015i 0.0330382i
134134 7.68879i 0.664210i
135135 2.11727i 0.182225i
136136 4.83709 0.414777
137137 0.325819 0.0278366 0.0139183 0.999903i 0.495570π-0.495570\pi
0.0139183 + 0.999903i 0.495570π0.495570\pi
138138 2.11727 0.180234
139139 −13.3906 −1.13577 −0.567887 0.823107i 0.692239π-0.692239\pi
−0.567887 + 0.823107i 0.692239π0.692239\pi
140140 1.52932i 0.129251i
141141 −7.43965 −0.626531
142142 3.05863i 0.256675i
143143 2.56035i 0.214107i
144144 2.05863 0.171553
145145 −0.719824 −0.0597781
146146 9.11383i 0.754266i
147147 −10.4837 −0.864679
148148 4.71982 + 3.83709i 0.387967 + 0.315407i
149149 8.44309 0.691685 0.345842 0.938293i 0.387593π-0.387593\pi
0.345842 + 0.938293i 0.387593π0.387593\pi
150150 2.24914i 0.183642i
151151 −4.94137 −0.402123 −0.201061 0.979579i 0.564439π-0.564439\pi
−0.201061 + 0.979579i 0.564439π0.564439\pi
152152 0.249141 0.0202080
153153 9.95779i 0.805040i
154154 4.15947i 0.335180i
155155 −4.02760 −0.323504
156156 2.11727i 0.169517i
157157 19.2733 1.53818 0.769088 0.639142i 0.220711π-0.220711\pi
0.769088 + 0.639142i 0.220711π0.220711\pi
158158 −1.75086 −0.139291
159159 18.8793 1.49723
160160 1.00000 0.0790569
161161 1.43965i 0.113460i
162162 10.9379i 0.859365i
163163 17.3354i 1.35781i −0.734226 0.678906i 0.762455π-0.762455\pi
0.734226 0.678906i 0.237545π-0.237545\pi
164164 8.27674 0.646305
165165 6.11727i 0.476229i
166166 0.131874i 0.0102354i
167167 17.0518i 1.31950i −0.751483 0.659752i 0.770661π-0.770661\pi
0.751483 0.659752i 0.229339π-0.229339\pi
168168 3.43965i 0.265375i
169169 12.1138 0.931833
170170 4.83709i 0.370988i
171171 0.512889i 0.0392216i
172172 2.71982i 0.207385i
173173 10.7198 0.815013 0.407507 0.913202i 0.366398π-0.366398\pi
0.407507 + 0.913202i 0.366398π0.366398\pi
174174 1.61899 0.122735
175175 −1.52932 −0.115605
176176 2.71982 0.205014
177177 16.4362i 1.23542i
178178 −8.99656 −0.674321
179179 9.48024i 0.708586i −0.935134 0.354293i 0.884722π-0.884722\pi
0.935134 0.354293i 0.115278π-0.115278\pi
180180 2.05863i 0.153441i
181181 20.9966 1.56066 0.780331 0.625367i 0.215051π-0.215051\pi
0.780331 + 0.625367i 0.215051π0.215051\pi
182182 1.43965 0.106714
183183 15.3776i 1.13674i
184184 −0.941367 −0.0693985
185185 3.83709 4.71982i 0.282108 0.347008i
186186 9.05863 0.664211
187187 13.1560i 0.962064i
188188 3.30777 0.241244
189189 −3.23797 −0.235528
190190 0.249141i 0.0180746i
191191 11.0862i 0.802172i −0.916041 0.401086i 0.868633π-0.868633\pi
0.916041 0.401086i 0.131367π-0.131367\pi
192192 −2.24914 −0.162318
193193 2.23453i 0.160845i 0.996761 + 0.0804226i 0.0256270π0.0256270\pi
−0.996761 + 0.0804226i 0.974373π0.974373\pi
194194 16.2767 1.16860
195195 −2.11727 −0.151621
196196 4.66119 0.332942
197197 13.4396 0.957535 0.478768 0.877942i 0.341084π-0.341084\pi
0.478768 + 0.877942i 0.341084π0.341084\pi
198198 5.59912i 0.397912i
199199 23.4802i 1.66447i −0.554423 0.832235i 0.687061π-0.687061\pi
0.554423 0.832235i 0.312939π-0.312939\pi
200200 1.00000i 0.0707107i
201201 −17.2932 −1.21977
202202 11.1138i 0.781966i
203203 1.10084i 0.0772637i
204204 10.8793i 0.761703i
205205 8.27674i 0.578072i
206206 14.1725 0.987442
207207 1.93793i 0.134695i
208208 0.941367i 0.0652720i
209209 0.677618i 0.0468718i
210210 3.43965 0.237358
211211 −19.7716 −1.36113 −0.680566 0.732687i 0.738266π-0.738266\pi
−0.680566 + 0.732687i 0.738266π0.738266\pi
212212 −8.39400 −0.576503
213213 −6.87930 −0.471362
214214 10.6922i 0.730906i
215215 −2.71982 −0.185490
216216 2.11727i 0.144062i
217217 6.15947i 0.418132i
218218 12.2767 0.831486
219219 20.4983 1.38515
220220 2.71982i 0.183370i
221221 4.55348 0.306300
222222 −8.63016 + 10.6155i −0.579218 + 0.712469i
223223 −9.14143 −0.612155 −0.306078 0.952007i 0.599017π-0.599017\pi
−0.306078 + 0.952007i 0.599017π0.599017\pi
224224 1.52932i 0.102182i
225225 −2.05863 −0.137242
226226 −2.95436 −0.196521
227227 18.7198i 1.24248i −0.783621 0.621239i 0.786630π-0.786630\pi
0.783621 0.621239i 0.213370π-0.213370\pi
228228 0.560352i 0.0371102i
229229 −25.1138 −1.65957 −0.829784 0.558084i 0.811537π-0.811537\pi
−0.829784 + 0.558084i 0.811537π0.811537\pi
230230 0.941367i 0.0620719i
231231 9.35524 0.615529
232232 −0.719824 −0.0472588
233233 20.4362 1.33882 0.669410 0.742893i 0.266547π-0.266547\pi
0.669410 + 0.742893i 0.266547π0.266547\pi
234234 1.93793 0.126686
235235 3.30777i 0.215775i
236236 7.30777i 0.475696i
237237 3.93793i 0.255796i
238238 −7.39744 −0.479505
239239 8.91377i 0.576584i 0.957543 + 0.288292i 0.0930873π0.0930873\pi
−0.957543 + 0.288292i 0.906913π0.906913\pi
240240 2.24914i 0.145181i
241241 13.8827i 0.894265i 0.894468 + 0.447133i 0.147555π0.147555\pi
−0.894468 + 0.447133i 0.852445π0.852445\pi
242242 3.60256i 0.231581i
243243 −18.2491 −1.17068
244244 6.83709i 0.437700i
245245 4.66119i 0.297793i
246246 18.6155i 1.18688i
247247 0.234533 0.0149230
248248 −4.02760 −0.255753
249249 0.296604 0.0187965
250250 −1.00000 −0.0632456
251251 3.80605i 0.240236i 0.992760 + 0.120118i 0.0383273π0.0383273\pi
−0.992760 + 0.120118i 0.961673π0.961673\pi
252252 −3.14830 −0.198324
253253 2.56035i 0.160968i
254254 8.30434i 0.521060i
255255 10.8793 0.681288
256256 1.00000 0.0625000
257257 8.78801i 0.548181i −0.961704 0.274090i 0.911623π-0.911623\pi
0.961704 0.274090i 0.0883768π-0.0883768\pi
258258 6.11727 0.380844
259259 −7.21811 5.86813i −0.448511 0.364628i
260260 0.941367 0.0583811
261261 1.48185i 0.0917244i
262262 −11.0732 −0.684107
263263 −10.4707 −0.645650 −0.322825 0.946459i 0.604633π-0.604633\pi
−0.322825 + 0.946459i 0.604633π0.604633\pi
264264 6.11727i 0.376492i
265265 8.39400i 0.515640i
266266 −0.381015 −0.0233615
267267 20.2345i 1.23833i
268268 7.68879 0.469668
269269 −5.88273 −0.358677 −0.179338 0.983787i 0.557396π-0.557396\pi
−0.179338 + 0.983787i 0.557396π0.557396\pi
270270 −2.11727 −0.128853
271271 7.61211 0.462403 0.231201 0.972906i 0.425734π-0.425734\pi
0.231201 + 0.972906i 0.425734π0.425734\pi
272272 4.83709i 0.293292i
273273 3.23797i 0.195971i
274274 0.325819i 0.0196835i
275275 −2.71982 −0.164012
276276 2.11727i 0.127444i
277277 26.4914i 1.59171i 0.605484 + 0.795857i 0.292979π0.292979\pi
−0.605484 + 0.795857i 0.707021π0.707021\pi
278278 13.3906i 0.803113i
279279 8.29135i 0.496390i
280280 −1.52932 −0.0913941
281281 26.6707i 1.59104i 0.605925 + 0.795522i 0.292803π0.292803\pi
−0.605925 + 0.795522i 0.707197π0.707197\pi
282282 7.43965i 0.443025i
283283 8.73281i 0.519112i 0.965728 + 0.259556i 0.0835762π0.0835762\pi
−0.965728 + 0.259556i 0.916424π0.916424\pi
284284 3.05863 0.181496
285285 0.560352 0.0331924
286286 2.56035 0.151397
287287 −12.6578 −0.747164
288288 2.05863i 0.121306i
289289 −6.39744 −0.376320
290290 0.719824i 0.0422695i
291291 36.6087i 2.14604i
292292 −9.11383 −0.533346
293293 23.4819 1.37182 0.685912 0.727684i 0.259403π-0.259403\pi
0.685912 + 0.727684i 0.259403π0.259403\pi
294294 10.4837i 0.611420i
295295 7.30777 0.425475
296296 3.83709 4.71982i 0.223026 0.274334i
297297 −5.75859 −0.334147
298298 8.44309i 0.489095i
299299 −0.886172 −0.0512486
300300 2.24914 0.129854
301301 4.15947i 0.239748i
302302 4.94137i 0.284344i
303303 −24.9966 −1.43601
304304 0.249141i 0.0142892i
305305 −6.83709 −0.391491
306306 −9.95779 −0.569249
307307 27.2457 1.55499 0.777497 0.628886i 0.216489π-0.216489\pi
0.777497 + 0.628886i 0.216489π0.216489\pi
308308 −4.15947 −0.237008
309309 31.8759i 1.81335i
310310 4.02760i 0.228752i
311311 17.7018i 1.00378i 0.864933 + 0.501888i 0.167361π0.167361\pi
−0.864933 + 0.501888i 0.832639π0.832639\pi
312312 −2.11727 −0.119867
313313 23.9931i 1.35617i −0.734983 0.678086i 0.762810π-0.762810\pi
0.734983 0.678086i 0.237190π-0.237190\pi
314314 19.2733i 1.08766i
315315 3.14830i 0.177387i
316316 1.75086i 0.0984935i
317317 −3.16291 −0.177647 −0.0888234 0.996047i 0.528311π-0.528311\pi
−0.0888234 + 0.996047i 0.528311π0.528311\pi
318318 18.8793i 1.05870i
319319 1.95779i 0.109615i
320320 1.00000i 0.0559017i
321321 24.0483 1.34225
322322 1.43965 0.0802284
323323 −1.20512 −0.0670544
324324 10.9379 0.607663
325325 0.941367i 0.0522176i
326326 −17.3354 −0.960117
327327 27.6121i 1.52695i
328328 8.27674i 0.457006i
329329 −5.05863 −0.278891
330330 6.11727 0.336744
331331 4.48367i 0.246445i 0.992379 + 0.123222i 0.0393229π0.0393229\pi
−0.992379 + 0.123222i 0.960677π0.960677\pi
332332 −0.131874 −0.00723754
333333 −9.71639 7.89916i −0.532455 0.432871i
334334 −17.0518 −0.933031
335335 7.68879i 0.420083i
336336 3.43965 0.187648
337337 −11.2051 −0.610382 −0.305191 0.952291i 0.598720π-0.598720\pi
−0.305191 + 0.952291i 0.598720π0.598720\pi
338338 12.1138i 0.658905i
339339 6.64476i 0.360894i
340340 −4.83709 −0.262328
341341 10.9544i 0.593212i
342342 −0.512889 −0.0277339
343343 −17.8337 −0.962927
344344 −2.71982 −0.146643
345345 −2.11727 −0.113990
346346 10.7198i 0.576301i
347347 13.9931i 0.751190i 0.926784 + 0.375595i 0.122562π0.122562\pi
−0.926784 + 0.375595i 0.877438π0.877438\pi
348348 1.61899i 0.0867867i
349349 −6.56035 −0.351168 −0.175584 0.984464i 0.556181π-0.556181\pi
−0.175584 + 0.984464i 0.556181π0.556181\pi
350350 1.52932i 0.0817454i
351351 1.99312i 0.106385i
352352 2.71982i 0.144967i
353353 36.5957i 1.94779i −0.226995 0.973896i 0.572890π-0.572890\pi
0.226995 0.973896i 0.427110π-0.427110\pi
354354 −16.4362 −0.873575
355355 3.05863i 0.162335i
356356 8.99656i 0.476817i
357357 16.6379i 0.880570i
358358 −9.48024 −0.501046
359359 21.2311 1.12053 0.560267 0.828312i 0.310698π-0.310698\pi
0.560267 + 0.828312i 0.310698π0.310698\pi
360360 −2.05863 −0.108499
361361 18.9379 0.996733
362362 20.9966i 1.10355i
363363 −8.10266 −0.425279
364364 1.43965i 0.0754581i
365365 9.11383i 0.477040i
366366 15.3776 0.803799
367367 23.4932 1.22634 0.613168 0.789952i 0.289895π-0.289895\pi
0.613168 + 0.789952i 0.289895π0.289895\pi
368368 0.941367i 0.0490721i
369369 −17.0388 −0.887003
370370 −4.71982 3.83709i −0.245372 0.199481i
371371 12.8371 0.666469
372372 9.05863i 0.469668i
373373 −7.55691 −0.391282 −0.195641 0.980676i 0.562679π-0.562679\pi
−0.195641 + 0.980676i 0.562679π0.562679\pi
374374 −13.1560 −0.680282
375375 2.24914i 0.116145i
376376 3.30777i 0.170585i
377377 −0.677618 −0.0348991
378378 3.23797i 0.166543i
379379 12.2637 0.629946 0.314973 0.949101i 0.398004π-0.398004\pi
0.314973 + 0.949101i 0.398004π0.398004\pi
380380 −0.249141 −0.0127806
381381 18.6776 0.956883
382382 −11.0862 −0.567221
383383 33.5208i 1.71283i 0.516285 + 0.856417i 0.327315π0.327315\pi
−0.516285 + 0.856417i 0.672685π0.672685\pi
384384 2.24914i 0.114776i
385385 4.15947i 0.211986i
386386 2.23453 0.113735
387387 5.59912i 0.284619i
388388 16.2767i 0.826326i
389389 9.95092i 0.504532i 0.967658 + 0.252266i 0.0811757π0.0811757\pi
−0.967658 + 0.252266i 0.918824π0.918824\pi
390390 2.11727i 0.107212i
391391 4.55348 0.230279
392392 4.66119i 0.235426i
393393 24.9053i 1.25630i
394394 13.4396i 0.677080i
395395 1.75086 0.0880953
396396 −5.59912 −0.281366
397397 8.67762 0.435517 0.217759 0.976003i 0.430125π-0.430125\pi
0.217759 + 0.976003i 0.430125π0.430125\pi
398398 −23.4802 −1.17696
399399 0.856956i 0.0429014i
400400 −1.00000 −0.0500000
401401 11.5569i 0.577125i −0.957461 0.288562i 0.906823π-0.906823\pi
0.957461 0.288562i 0.0931773π-0.0931773\pi
402402 17.2932i 0.862505i
403403 −3.79145 −0.188865
404404 11.1138 0.552934
405405 10.9379i 0.543510i
406406 1.10084 0.0546337
407407 −12.8371 10.4362i −0.636311 0.517304i
408408 10.8793 0.538605
409409 3.34836i 0.165566i 0.996568 + 0.0827829i 0.0263808π0.0263808\pi
−0.996568 + 0.0827829i 0.973619π0.973619\pi
410410 −8.27674 −0.408759
411411 0.732814 0.0361470
412412 14.1725i 0.698227i
413413 11.1759i 0.549930i
414414 1.93793 0.0952440
415415 0.131874i 0.00647345i
416416 0.941367 0.0461543
417417 −30.1173 −1.47485
418418 −0.677618 −0.0331434
419419 −11.3776 −0.555831 −0.277916 0.960606i 0.589644π-0.589644\pi
−0.277916 + 0.960606i 0.589644π0.589644\pi
420420 3.43965i 0.167838i
421421 3.23109i 0.157474i −0.996895 0.0787370i 0.974911π-0.974911\pi
0.996895 0.0787370i 0.0250887π-0.0250887\pi
422422 19.7716i 0.962466i
423423 −6.80949 −0.331089
424424 8.39400i 0.407649i
425425 4.83709i 0.234633i
426426 6.87930i 0.333303i
427427 10.4561i 0.506005i
428428 −10.6922 −0.516828
429429 5.75859i 0.278027i
430430 2.71982i 0.131162i
431431 29.2327i 1.40809i 0.710155 + 0.704045i 0.248625π0.248625\pi
−0.710155 + 0.704045i 0.751375π0.751375\pi
432432 −2.11727 −0.101867
433433 17.7655 0.853754 0.426877 0.904310i 0.359614π-0.359614\pi
0.426877 + 0.904310i 0.359614π0.359614\pi
434434 6.15947 0.295664
435435 −1.61899 −0.0776244
436436 12.2767i 0.587949i
437437 0.234533 0.0112192
438438 20.4983i 0.979446i
439439 32.7604i 1.56357i −0.623549 0.781785i 0.714310π-0.714310\pi
0.623549 0.781785i 0.285690π-0.285690\pi
440440 −2.71982 −0.129663
441441 −9.59568 −0.456937
442442 4.55348i 0.216587i
443443 −0.600939 −0.0285515 −0.0142757 0.999898i 0.504544π-0.504544\pi
−0.0142757 + 0.999898i 0.504544π0.504544\pi
444444 10.6155 + 8.63016i 0.503792 + 0.409569i
445445 8.99656 0.426478
446446 9.14143i 0.432859i
447447 18.9897 0.898181
448448 −1.52932 −0.0722534
449449 34.0191i 1.60546i 0.596342 + 0.802730i 0.296620π0.296620\pi
−0.596342 + 0.802730i 0.703380π0.703380\pi
450450 2.05863i 0.0970449i
451451 −22.5113 −1.06001
452452 2.95436i 0.138961i
453453 −11.1138 −0.522173
454454 −18.7198 −0.878565
455455 −1.43965 −0.0674917
456456 0.560352 0.0262409
457457 30.9215i 1.44645i 0.690614 + 0.723223i 0.257340π0.257340\pi
−0.690614 + 0.723223i 0.742660π0.742660\pi
458458 25.1138i 1.17349i
459459 10.2414i 0.478028i
460460 0.941367 0.0438915
461461 1.27330i 0.0593035i −0.999560 0.0296518i 0.990560π-0.990560\pi
0.999560 0.0296518i 0.00943983π-0.00943983\pi
462462 9.35524i 0.435245i
463463 2.61555i 0.121555i −0.998151 0.0607774i 0.980642π-0.980642\pi
0.998151 0.0607774i 0.0193580π-0.0193580\pi
464464 0.719824i 0.0334170i
465465 −9.05863 −0.420084
466466 20.4362i 0.946689i
467467 19.0096i 0.879657i −0.898082 0.439829i 0.855039π-0.855039\pi
0.898082 0.439829i 0.144961π-0.144961\pi
468468 1.93793i 0.0895808i
469469 −11.7586 −0.542961
470470 −3.30777 −0.152576
471471 43.3484 1.99739
472472 7.30777 0.336368
473473 7.39744i 0.340135i
474474 −3.93793 −0.180875
475475 0.249141i 0.0114314i
476476 7.39744i 0.339061i
477477 17.2802 0.791205
478478 8.91377 0.407706
479479 38.8578i 1.77546i 0.460366 + 0.887729i 0.347718π0.347718\pi
−0.460366 + 0.887729i 0.652282π0.652282\pi
480480 2.24914 0.102659
481481 3.61211 4.44309i 0.164698 0.202587i
482482 13.8827 0.632341
483483 3.23797i 0.147333i
484484 3.60256 0.163753
485485 −16.2767 −0.739089
486486 18.2491i 0.827798i
487487 38.4914i 1.74421i 0.489317 + 0.872106i 0.337246π0.337246\pi
−0.489317 + 0.872106i 0.662754π0.662754\pi
488488 −6.83709 −0.309501
489489 38.9897i 1.76317i
490490 −4.66119 −0.210571
491491 −11.2672 −0.508481 −0.254240 0.967141i 0.581825π-0.581825\pi
−0.254240 + 0.967141i 0.581825π0.581825\pi
492492 18.6155 0.839254
493493 3.48185 0.156815
494494 0.234533i 0.0105521i
495495 5.59912i 0.251662i
496496 4.02760i 0.180844i
497497 −4.67762 −0.209820
498498 0.296604i 0.0132911i
499499 20.8578i 0.933724i −0.884330 0.466862i 0.845384π-0.845384\pi
0.884330 0.466862i 0.154616π-0.154616\pi
500500 1.00000i 0.0447214i
501501 38.3518i 1.71343i
502502 3.80605 0.169873
503503 6.64476i 0.296275i 0.988967 + 0.148138i 0.0473279π0.0473279\pi
−0.988967 + 0.148138i 0.952672π0.952672\pi
504504 3.14830i 0.140237i
505505 11.1138i 0.494559i
506506 2.56035 0.113822
507507 27.2457 1.21002
508508 −8.30434 −0.368445
509509 −18.5535 −0.822368 −0.411184 0.911552i 0.634885π-0.634885\pi
−0.411184 + 0.911552i 0.634885π0.634885\pi
510510 10.8793i 0.481743i
511511 13.9379 0.616578
512512 1.00000i 0.0441942i
513513 0.527497i 0.0232896i
514514 −8.78801 −0.387622
515515 −14.1725 −0.624513
516516 6.11727i 0.269298i
517517 −8.99656 −0.395668
518518 −5.86813 + 7.21811i −0.257831 + 0.317145i
519519 24.1104 1.05833
520520 0.941367i 0.0412817i
521521 −42.6509 −1.86857 −0.934284 0.356529i 0.883960π-0.883960\pi
−0.934284 + 0.356529i 0.883960π0.883960\pi
522522 1.48185 0.0648590
523523 12.3879i 0.541685i −0.962624 0.270842i 0.912698π-0.912698\pi
0.962624 0.270842i 0.0873022π-0.0873022\pi
524524 11.0732i 0.483737i
525525 −3.43965 −0.150119
526526 10.4707i 0.456543i
527527 19.4819 0.848643
528528 6.11727 0.266220
529529 22.1138 0.961471
530530 8.39400 0.364612
531531 15.0440i 0.652855i
532532 0.381015i 0.0165191i
533533 7.79145i 0.337485i
534534 −20.2345 −0.875634
535535 10.6922i 0.462265i
536536 7.68879i 0.332105i
537537 21.3224i 0.920129i
538538 5.88273i 0.253623i
539539 −12.6776 −0.546064
540540 2.11727i 0.0911126i
541541 7.64820i 0.328822i 0.986392 + 0.164411i 0.0525723π0.0525723\pi
−0.986392 + 0.164411i 0.947428π0.947428\pi
542542 7.61211i 0.326968i
543543 47.2242 2.02659
544544 −4.83709 −0.207389
545545 −12.2767 −0.525878
546546 3.23797 0.138572
547547 12.6837i 0.542317i −0.962535 0.271159i 0.912593π-0.912593\pi
0.962535 0.271159i 0.0874068π-0.0874068\pi
548548 −0.325819 −0.0139183
549549 14.0751i 0.600709i
550550 2.71982i 0.115974i
551551 0.179337 0.00764003
552552 −2.11727 −0.0901168
553553 2.67762i 0.113864i
554554 26.4914 1.12551
555555 8.63016 10.6155i 0.366330 0.450605i
556556 13.3906 0.567887
557557 2.61555i 0.110824i −0.998464 0.0554121i 0.982353π-0.982353\pi
0.998464 0.0554121i 0.0176473π-0.0176473\pi
558558 8.29135 0.351001
559559 −2.56035 −0.108291
560560 1.52932i 0.0646254i
561561 29.5898i 1.24928i
562562 26.6707 1.12504
563563 35.3285i 1.48892i −0.667668 0.744459i 0.732707π-0.732707\pi
0.667668 0.744459i 0.267293π-0.267293\pi
564564 7.43965 0.313266
565565 2.95436 0.124291
566566 8.73281 0.367068
567567 −16.7276 −0.702491
568568 3.05863i 0.128337i
569569 28.8724i 1.21039i −0.796075 0.605197i 0.793094π-0.793094\pi
0.796075 0.605197i 0.206906π-0.206906\pi
570570 0.560352i 0.0234706i
571571 −8.15947 −0.341463 −0.170732 0.985318i 0.554613π-0.554613\pi
−0.170732 + 0.985318i 0.554613π0.554613\pi
572572 2.56035i 0.107054i
573573 24.9345i 1.04165i
574574 12.6578i 0.528324i
575575 0.941367i 0.0392577i
576576 −2.05863 −0.0857764
577577 37.5500i 1.56323i 0.623762 + 0.781614i 0.285603π0.285603\pi
−0.623762 + 0.781614i 0.714397π0.714397\pi
578578 6.39744i 0.266099i
579579 5.02578i 0.208864i
580580 0.719824 0.0298891
581581 0.201677 0.00836699
582582 36.6087 1.51748
583583 22.8302 0.945531
584584 9.11383i 0.377133i
585585 −1.93793 −0.0801235
586586 23.4819i 0.970026i
587587 19.5078i 0.805174i 0.915382 + 0.402587i 0.131889π0.131889\pi
−0.915382 + 0.402587i 0.868111π0.868111\pi
588588 10.4837 0.432339
589589 1.00344 0.0413459
590590 7.30777i 0.300856i
591591 30.2277 1.24340
592592 −4.71982 3.83709i −0.193984 0.157703i
593593 41.5569 1.70654 0.853269 0.521471i 0.174617π-0.174617\pi
0.853269 + 0.521471i 0.174617π0.174617\pi
594594 5.75859i 0.236278i
595595 7.39744 0.303266
596596 −8.44309 −0.345842
597597 52.8103i 2.16138i
598598 0.886172i 0.0362382i
599599 27.6381 1.12926 0.564631 0.825344i 0.309019π-0.309019\pi
0.564631 + 0.825344i 0.309019π0.309019\pi
600600 2.24914i 0.0918208i
601601 14.4301 0.588616 0.294308 0.955711i 0.404911π-0.404911\pi
0.294308 + 0.955711i 0.404911π0.404911\pi
602602 4.15947 0.169527
603603 −15.8284 −0.644582
604604 4.94137 0.201061
605605 3.60256i 0.146465i
606606 24.9966i 1.01542i
607607 47.4880i 1.92748i 0.266848 + 0.963739i 0.414018π0.414018\pi
−0.266848 + 0.963739i 0.585982π0.585982\pi
608608 −0.249141 −0.0101040
609609 2.47594i 0.100330i
610610 6.83709i 0.276826i
611611 3.11383i 0.125972i
612612 9.95779i 0.402520i
613613 −18.7198 −0.756087 −0.378043 0.925788i 0.623403π-0.623403\pi
−0.378043 + 0.925788i 0.623403π0.623403\pi
614614 27.2457i 1.09955i
615615 18.6155i 0.750651i
616616 4.15947i 0.167590i
617617 −15.0225 −0.604785 −0.302392 0.953184i 0.597785π-0.597785\pi
−0.302392 + 0.953184i 0.597785π0.597785\pi
618618 31.8759 1.28224
619619 16.6318 0.668487 0.334244 0.942487i 0.391519π-0.391519\pi
0.334244 + 0.942487i 0.391519π0.391519\pi
620620 4.02760 0.161752
621621 1.99312i 0.0799813i
622622 17.7018 0.709777
623623 13.7586i 0.551226i
624624 2.11727i 0.0847585i
625625 1.00000 0.0400000
626626 −23.9931 −0.958958
627627 1.52406i 0.0608651i
628628 −19.2733 −0.769088
629629 −18.5604 + 22.8302i −0.740050 + 0.910300i
630630 3.14830 0.125431
631631 35.9294i 1.43033i −0.698957 0.715164i 0.746352π-0.746352\pi
0.698957 0.715164i 0.253648π-0.253648\pi
632632 1.75086 0.0696454
633633 −44.4691 −1.76749
634634 3.16291i 0.125615i
635635 8.30434i 0.329548i
636636 −18.8793 −0.748613
637637 4.38789i 0.173855i
638638 1.95779 0.0775098
639639 −6.29660 −0.249090
640640 −1.00000 −0.0395285
641641 29.3354 1.15868 0.579339 0.815087i 0.303311π-0.303311\pi
0.579339 + 0.815087i 0.303311π0.303311\pi
642642 24.0483i 0.949111i
643643 0.368025i 0.0145135i −0.999974 0.00725674i 0.997690π-0.997690\pi
0.999974 0.00725674i 0.00230991π-0.00230991\pi
644644 1.43965i 0.0567301i
645645 −6.11727 −0.240867
646646 1.20512i 0.0474146i
647647 26.7811i 1.05287i 0.850214 + 0.526437i 0.176473π0.176473\pi
−0.850214 + 0.526437i 0.823527π0.823527\pi
648648 10.9379i 0.429682i
649649 19.8759i 0.780196i
650650 −0.941367 −0.0369234
651651 13.8535i 0.542962i
652652 17.3354i 0.678906i
653653 2.00000i 0.0782660i 0.999234 + 0.0391330i 0.0124596π0.0124596\pi
−0.999234 + 0.0391330i 0.987540π0.987540\pi
654654 27.6121 1.07972
655655 11.0732 0.432667
656656 −8.27674 −0.323152
657657 18.7620 0.731976
658658 5.05863i 0.197206i
659659 −12.9966 −0.506274 −0.253137 0.967430i 0.581462π-0.581462\pi
−0.253137 + 0.967430i 0.581462π0.581462\pi
660660 6.11727i 0.238114i
661661 18.6026i 0.723556i −0.932264 0.361778i 0.882170π-0.882170\pi
0.932264 0.361778i 0.117830π-0.117830\pi
662662 4.48367 0.174263
663663 10.2414 0.397743
664664 0.131874i 0.00511771i
665665 0.381015 0.0147751
666666 −7.89916 + 9.71639i −0.306086 + 0.376502i
667667 −0.677618 −0.0262375
668668 17.0518i 0.659752i
669669 −20.5604 −0.794909
670670 −7.68879 −0.297044
671671 18.5957i 0.717878i
672672 3.43965i 0.132687i
673673 20.4622 0.788759 0.394380 0.918948i 0.370959π-0.370959\pi
0.394380 + 0.918948i 0.370959π0.370959\pi
674674 11.2051i 0.431605i
675675 2.11727 0.0814936
676676 −12.1138 −0.465916
677677 −39.9018 −1.53355 −0.766776 0.641915i 0.778140π-0.778140\pi
−0.766776 + 0.641915i 0.778140π0.778140\pi
678678 −6.64476 −0.255191
679679 24.8923i 0.955278i
680680 4.83709i 0.185494i
681681 42.1035i 1.61341i
682682 10.9544 0.419464
683683 12.3940i 0.474243i 0.971480 + 0.237122i 0.0762040π0.0762040\pi
−0.971480 + 0.237122i 0.923796π0.923796\pi
684684 0.512889i 0.0196108i
685685 0.325819i 0.0124489i
686686 17.8337i 0.680892i
687687 −56.4845 −2.15502
688688 2.71982i 0.103692i
689689 7.90184i 0.301036i
690690 2.11727i 0.0806030i
691691 −51.5630 −1.96155 −0.980775 0.195142i 0.937483π-0.937483\pi
−0.980775 + 0.195142i 0.937483π0.937483\pi
692692 −10.7198 −0.407507
693693 8.56283 0.325275
694694 13.9931 0.531172
695695 13.3906i 0.507933i
696696 −1.61899 −0.0613675
697697 40.0353i 1.51645i
698698 6.56035i 0.248313i
699699 45.9639 1.73851
700700 1.52932 0.0578027
701701 9.76547i 0.368837i −0.982848 0.184418i 0.940960π-0.940960\pi
0.982848 0.184418i 0.0590401π-0.0590401\pi
702702 −1.99312 −0.0752256
703703 −0.955975 + 1.17590i −0.0360553 + 0.0443499i
704704 −2.71982 −0.102507
705705 7.43965i 0.280193i
706706 −36.5957 −1.37730
707707 −16.9966 −0.639222
708708 16.4362i 0.617711i
709709 49.8268i 1.87128i −0.352951 0.935642i 0.614822π-0.614822\pi
0.352951 0.935642i 0.385178π-0.385178\pi
710710 −3.05863 −0.114788
711711 3.60438i 0.135175i
712712 8.99656 0.337160
713713 −3.79145 −0.141991
714714 −16.6379 −0.622657
715715 −2.56035 −0.0957517
716716 9.48024i 0.354293i
717717 20.0483i 0.748718i
718718 21.2311i 0.792337i
719719 −4.26375 −0.159011 −0.0795055 0.996834i 0.525334π-0.525334\pi
−0.0795055 + 0.996834i 0.525334π0.525334\pi
720720 2.05863i 0.0767207i
721721 21.6742i 0.807189i
722722 18.9379i 0.704797i
723723 31.2242i 1.16124i
724724 −20.9966 −0.780331
725725 0.719824i 0.0267336i
726726 8.10266i 0.300718i
727727 13.1759i 0.488667i −0.969691 0.244334i 0.921431π-0.921431\pi
0.969691 0.244334i 0.0785692π-0.0785692\pi
728728 −1.43965 −0.0533569
729729 −8.23109 −0.304855
730730 9.11383 0.337318
731731 13.1560 0.486593
732732 15.3776i 0.568372i
733733 9.39057 0.346848 0.173424 0.984847i 0.444517π-0.444517\pi
0.173424 + 0.984847i 0.444517π0.444517\pi
734734 23.4932i 0.867151i
735735 10.4837i 0.386696i
736736 0.941367 0.0346992
737737 −20.9122 −0.770309
738738 17.0388i 0.627206i
739739 −9.62510 −0.354065 −0.177033 0.984205i 0.556650π-0.556650\pi
−0.177033 + 0.984205i 0.556650π0.556650\pi
740740 −3.83709 + 4.71982i −0.141054 + 0.173504i
741741 0.527497 0.0193781
742742 12.8371i 0.471264i
743743 −25.6137 −0.939677 −0.469838 0.882753i 0.655688π-0.655688\pi
−0.469838 + 0.882753i 0.655688π0.655688\pi
744744 −9.05863 −0.332106
745745 8.44309i 0.309331i
746746 7.55691i 0.276678i
747747 0.271481 0.00993296
748748 13.1560i 0.481032i
749749 16.3518 0.597482
750750 −2.24914 −0.0821270
751751 11.9740 0.436938 0.218469 0.975844i 0.429894π-0.429894\pi
0.218469 + 0.975844i 0.429894π0.429894\pi
752752 −3.30777 −0.120622
753753 8.56035i 0.311957i
754754 0.677618i 0.0246774i
755755 4.94137i 0.179835i
756756 3.23797 0.117764
757757 19.2051i 0.698022i −0.937119 0.349011i 0.886518π-0.886518\pi
0.937119 0.349011i 0.113482π-0.113482\pi
758758 12.2637i 0.445439i
759759 5.75859i 0.209024i
760760 0.249141i 0.00903728i
761761 −31.8596 −1.15491 −0.577455 0.816422i 0.695954π-0.695954\pi
−0.577455 + 0.816422i 0.695954π0.695954\pi
762762 18.6776i 0.676619i
763763 18.7750i 0.679701i
764764 11.0862i 0.401086i
765765 9.95779 0.360025
766766 33.5208 1.21116
767767 6.87930 0.248397
768768 2.24914 0.0811589
769769 35.2242i 1.27022i 0.772423 + 0.635109i 0.219045π0.219045\pi
−0.772423 + 0.635109i 0.780955π0.780955\pi
770770 4.15947 0.149897
771771 19.7655i 0.711836i
772772 2.23453i 0.0804226i
773773 −50.2630 −1.80783 −0.903917 0.427708i 0.859321π-0.859321\pi
−0.903917 + 0.427708i 0.859321π0.859321\pi
774774 5.59912 0.201256
775775 4.02760i 0.144676i
776776 −16.2767 −0.584301
777777 −16.2345 13.1982i −0.582411 0.473484i
778778 9.95092 0.356758
779779 2.06207i 0.0738814i
780780 2.11727 0.0758103
781781 −8.31894 −0.297675
782782 4.55348i 0.162832i
783783 1.52406i 0.0544654i
784784 −4.66119 −0.166471
785785 19.2733i 0.687894i
786786 −24.9053 −0.888342
787787 −51.9525 −1.85191 −0.925954 0.377636i 0.876737π-0.876737\pi
−0.925954 + 0.377636i 0.876737π0.876737\pi
788788 −13.4396 −0.478768
789789 −23.5500 −0.838404
790790 1.75086i 0.0622928i
791791 4.51815i 0.160647i
792792 5.59912i 0.198956i
793793 −6.43621 −0.228557
794794 8.67762i 0.307957i
795795 18.8793i 0.669580i
796796 23.4802i 0.832235i
797797 35.4880i 1.25705i −0.777790 0.628524i 0.783659π-0.783659\pi
0.777790 0.628524i 0.216341π-0.216341\pi
798798 −0.856956 −0.0303359
799799 16.0000i 0.566039i
800800 1.00000i 0.0353553i
801801 18.5206i 0.654394i
802802 −11.5569 −0.408089
803803 24.7880 0.874750
804804 17.2932 0.609883
805805 −1.43965 −0.0507409
806806 3.79145i 0.133548i
807807 −13.2311 −0.465757
808808 11.1138i 0.390983i
809809 13.2051i 0.464267i −0.972684 0.232134i 0.925429π-0.925429\pi
0.972684 0.232134i 0.0745706π-0.0745706\pi
810810 −10.9379 −0.384320
811811 −10.1173 −0.355265 −0.177633 0.984097i 0.556844π-0.556844\pi
−0.177633 + 0.984097i 0.556844π0.556844\pi
812812 1.10084i 0.0386319i
813813 17.1207 0.600449
814814 −10.4362 + 12.8371i −0.365789 + 0.449940i
815815 17.3354 0.607232
816816 10.8793i 0.380852i
817817 0.677618 0.0237069
818818 3.34836 0.117073
819819 2.96371i 0.103560i
820820 8.27674i 0.289036i
821821 5.68106 0.198270 0.0991351 0.995074i 0.468392π-0.468392\pi
0.0991351 + 0.995074i 0.468392π0.468392\pi
822822 0.732814i 0.0255598i
823823 −22.3404 −0.778738 −0.389369 0.921082i 0.627307π-0.627307\pi
−0.389369 + 0.921082i 0.627307π0.627307\pi
824824 −14.1725 −0.493721
825825 −6.11727 −0.212976
826826 −11.1759 −0.388859
827827 3.71639i 0.129231i −0.997910 0.0646157i 0.979418π-0.979418\pi
0.997910 0.0646157i 0.0205822π-0.0205822\pi
828828 1.93793i 0.0673477i
829829 15.8596i 0.550828i −0.961326 0.275414i 0.911185π-0.911185\pi
0.961326 0.275414i 0.0888149π-0.0888149\pi
830830 0.131874 0.00457742
831831 59.5829i 2.06691i
832832 0.941367i 0.0326360i
833833 22.5466i 0.781193i
834834 30.1173i 1.04288i
835835 17.0518 0.590100
836836 0.677618i 0.0234359i
837837 8.52750i 0.294753i
838838 11.3776i 0.393032i
839839 −33.8950 −1.17018 −0.585092 0.810967i 0.698942π-0.698942\pi
−0.585092 + 0.810967i 0.698942π0.698942\pi
840840 −3.43965 −0.118679
841841 28.4819 0.982133
842842 −3.23109 −0.111351
843843 59.9862i 2.06604i
844844 19.7716 0.680566
845845 12.1138i 0.416728i
846846 6.80949i 0.234115i
847847 −5.50945 −0.189307
848848 8.39400 0.288251
849849 19.6413i 0.674089i
850850 4.83709 0.165911
851851 3.61211 4.44309i 0.123822 0.152307i
852852 6.87930 0.235681
853853 35.7586i 1.22435i 0.790722 + 0.612175i 0.209705π0.209705\pi
−0.790722 + 0.612175i 0.790295π0.790295\pi
854854 10.4561 0.357800
855855 0.512889 0.0175404
856856 10.6922i 0.365453i
857857 17.3837i 0.593816i 0.954906 + 0.296908i 0.0959554π0.0959554\pi
−0.954906 + 0.296908i 0.904045π0.904045\pi
858858 5.75859 0.196595
859859 43.3922i 1.48052i −0.672319 0.740261i 0.734702π-0.734702\pi
0.672319 0.740261i 0.265298π-0.265298\pi
860860 2.71982 0.0927452
861861 −28.4691 −0.970223
862862 29.2327 0.995670
863863 34.8708 1.18702 0.593508 0.804828i 0.297743π-0.297743\pi
0.593508 + 0.804828i 0.297743π0.297743\pi
864864 2.11727i 0.0720309i
865865 10.7198i 0.364485i
866866 17.7655i 0.603695i
867867 −14.3887 −0.488667
868868 6.15947i 0.209066i
869869 4.76203i 0.161541i
870870 1.61899i 0.0548887i
871871 7.23797i 0.245249i
872872 −12.2767 −0.415743
873873 33.5078i 1.13407i
874874 0.234533i 0.00793318i
875875 1.52932i 0.0517003i
876876 −20.4983 −0.692573
877877 47.0907 1.59014 0.795070 0.606517i 0.207434π-0.207434\pi
0.795070 + 0.606517i 0.207434π0.207434\pi
878878 −32.7604 −1.10561
879879 52.8140 1.78137
880880 2.71982i 0.0916852i
881881 29.0027 0.977125 0.488562 0.872529i 0.337521π-0.337521\pi
0.488562 + 0.872529i 0.337521π0.337521\pi
882882 9.59568i 0.323103i
883883 11.0388i 0.371484i −0.982599 0.185742i 0.940531π-0.940531\pi
0.982599 0.185742i 0.0594689π-0.0594689\pi
884884 −4.55348 −0.153150
885885 16.4362 0.552497
886886 0.600939i 0.0201890i
887887 −5.76709 −0.193640 −0.0968199 0.995302i 0.530867π-0.530867\pi
−0.0968199 + 0.995302i 0.530867π0.530867\pi
888888 8.63016 10.6155i 0.289609 0.356234i
889889 12.7000 0.425943
890890 8.99656i 0.301565i
891891 −29.7492 −0.996637
892892 9.14143 0.306078
893893 0.824101i 0.0275775i
894894 18.9897i 0.635110i
895895 9.48024 0.316889
896896 1.52932i 0.0510909i
897897 −1.99312 −0.0665485
898898 34.0191 1.13523
899899 −2.89916 −0.0966924
900900 2.05863 0.0686211
901901 40.6026i 1.35267i
902902 22.5113i 0.749543i
903903 9.35524i 0.311323i
904904 2.95436 0.0982604
905905 20.9966i 0.697949i
906906 11.1138i 0.369232i
907907 54.2139i 1.80014i −0.435742 0.900072i 0.643514π-0.643514\pi
0.435742 0.900072i 0.356486π-0.356486\pi
908908 18.7198i 0.621239i
909909 −22.8793 −0.758858
910910 1.43965i 0.0477239i
911911 37.1284i 1.23012i −0.788480 0.615060i 0.789132π-0.789132\pi
0.788480 0.615060i 0.210868π-0.210868\pi
912912 0.560352i 0.0185551i
913913 0.358675 0.0118704
914914 30.9215 1.02279
915915 −15.3776 −0.508367
916916 25.1138 0.829784
917917 16.9345i 0.559226i
918918 10.2414 0.338017
919919 20.0889i 0.662672i −0.943513 0.331336i 0.892501π-0.892501\pi
0.943513 0.331336i 0.107499π-0.107499\pi
920920 0.941367i 0.0310359i
921921 61.2794 2.01923
922922 −1.27330 −0.0419339
923923 2.87930i 0.0947732i
924924 −9.35524 −0.307765
925925 4.71982 + 3.83709i 0.155187 + 0.126163i
926926 −2.61555 −0.0859522
927927 29.1759i 0.958262i
928928 0.719824 0.0236294
929929 12.9803 0.425871 0.212936 0.977066i 0.431698π-0.431698\pi
0.212936 + 0.977066i 0.431698π0.431698\pi
930930 9.05863i 0.297044i
931931 1.16129i 0.0380598i
932932 −20.4362 −0.669410
933933 39.8138i 1.30344i
934934 −19.0096 −0.622012
935935 13.1560 0.430248
936936 −1.93793 −0.0633432
937937 −9.32238 −0.304549 −0.152274 0.988338i 0.548660π-0.548660\pi
−0.152274 + 0.988338i 0.548660π0.548660\pi
938938 11.7586i 0.383932i
939939 53.9639i 1.76105i
940940 3.30777i 0.107888i
941941 −17.7586 −0.578914 −0.289457 0.957191i 0.593475π-0.593475\pi
−0.289457 + 0.957191i 0.593475π0.593475\pi
942942 43.3484i 1.41237i
943943 7.79145i 0.253724i
944944 7.30777i 0.237848i
945945 3.23797i 0.105331i
946946 7.39744 0.240512
947947 17.3354i 0.563324i −0.959514 0.281662i 0.909114π-0.909114\pi
0.959514 0.281662i 0.0908857π-0.0908857\pi
948948 3.93793i 0.127898i
949949 8.57946i 0.278501i
950950 0.249141 0.00808319
951951 −7.11383 −0.230682
952952 7.39744 0.239752
953953 −5.88961 −0.190783 −0.0953916 0.995440i 0.530410π-0.530410\pi
−0.0953916 + 0.995440i 0.530410π0.530410\pi
954954 17.2802i 0.559466i
955955 11.0862 0.358742
956956 8.91377i 0.288292i
957957 4.40335i 0.142340i
958958 38.8578 1.25544
959959 0.498281 0.0160903
960960 2.24914i 0.0725907i
961961 14.7785 0.476724
962962 −4.44309 3.61211i −0.143251 0.116459i
963963 22.0114 0.709307
964964 13.8827i 0.447133i
965965 −2.23453 −0.0719322
966966 3.23797 0.104180
967967 32.3189i 1.03931i −0.854377 0.519654i 0.826061π-0.826061\pi
0.854377 0.519654i 0.173939π-0.173939\pi
968968 3.60256i 0.115791i
969969 −2.71047 −0.0870730
970970 16.2767i 0.522615i
971971 6.11115 0.196116 0.0980581 0.995181i 0.468737π-0.468737\pi
0.0980581 + 0.995181i 0.468737π0.468737\pi
972972 18.2491 0.585341
973973 −20.4784 −0.656508
974974 38.4914 1.23334
975975 2.11727i 0.0678068i
976976 6.83709i 0.218850i
977977 47.3906i 1.51616i 0.652162 + 0.758079i 0.273862π0.273862\pi
−0.652162 + 0.758079i 0.726138π0.726138\pi
978978 −38.9897 −1.24675
979979 24.4691i 0.782035i
980980 4.66119i 0.148896i
981981 25.2733i 0.806914i
982982 11.2672i 0.359550i
983983 −55.7862 −1.77930 −0.889652 0.456640i 0.849053π-0.849053\pi
−0.889652 + 0.456640i 0.849053π0.849053\pi
984984 18.6155i 0.593442i
985985 13.4396i 0.428223i
986986 3.48185i 0.110885i
987987 −11.3776 −0.362152
988988 −0.234533 −0.00746148
989989 −2.56035 −0.0814145
990990 5.59912 0.177952
991991 29.9655i 0.951886i 0.879476 + 0.475943i 0.157893π0.157893\pi
−0.879476 + 0.475943i 0.842107π0.842107\pi
992992 4.02760 0.127876
993993 10.0844i 0.320019i
994994 4.67762i 0.148365i
995995 23.4802 0.744374
996996 −0.296604 −0.00939825
997997 20.7811i 0.658145i −0.944305 0.329073i 0.893264π-0.893264\pi
0.944305 0.329073i 0.106736π-0.106736\pi
998998 −20.8578 −0.660243
999999 9.99312 + 8.12414i 0.316168 + 0.257036i
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 370.2.d.c.221.3 6
3.2 odd 2 3330.2.h.n.2071.5 6
4.3 odd 2 2960.2.p.g.961.2 6
5.2 odd 4 1850.2.c.j.1849.2 6
5.3 odd 4 1850.2.c.i.1849.5 6
5.4 even 2 1850.2.d.f.1701.4 6
37.36 even 2 inner 370.2.d.c.221.6 yes 6
111.110 odd 2 3330.2.h.n.2071.2 6
148.147 odd 2 2960.2.p.g.961.1 6
185.73 odd 4 1850.2.c.j.1849.5 6
185.147 odd 4 1850.2.c.i.1849.2 6
185.184 even 2 1850.2.d.f.1701.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.d.c.221.3 6 1.1 even 1 trivial
370.2.d.c.221.6 yes 6 37.36 even 2 inner
1850.2.c.i.1849.2 6 185.147 odd 4
1850.2.c.i.1849.5 6 5.3 odd 4
1850.2.c.j.1849.2 6 5.2 odd 4
1850.2.c.j.1849.5 6 185.73 odd 4
1850.2.d.f.1701.1 6 185.184 even 2
1850.2.d.f.1701.4 6 5.4 even 2
2960.2.p.g.961.1 6 148.147 odd 2
2960.2.p.g.961.2 6 4.3 odd 2
3330.2.h.n.2071.2 6 111.110 odd 2
3330.2.h.n.2071.5 6 3.2 odd 2