Properties

Label 1785.2.g.f.1429.8
Level 17851785
Weight 22
Character 1785.1429
Analytic conductor 14.25314.253
Analytic rank 00
Dimension 2828
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1785,2,Mod(1429,1785)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1785, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1785.1429");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1785=35717 1785 = 3 \cdot 5 \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1785.g (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 14.253296760814.2532967608
Analytic rank: 00
Dimension: 2828
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1429.8
Character χ\chi == 1785.1429
Dual form 1785.2.g.f.1429.21

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.69985iq21.00000iq30.889490q4+(1.477231.67863i)q51.69985q61.00000iq71.88770iq81.00000q9+(2.853412.51107i)q101.31823q11+0.889490iq124.26284iq131.69985q14+(1.678631.47723i)q154.98779q161.00000iq17+1.69985iq18+5.21905q19+(1.31398+1.49312i)q201.00000q21+2.24079iq22+2.71209iq231.88770q24+(0.6355734.95944i)q257.24619q26+1.00000iq27+0.889490iq28+0.948665q29+(2.51107+2.85341i)q302.19047q31+4.70309iq32+1.31823iq331.69985q34+(1.678631.47723i)q35+0.889490q36+3.64278iq378.87160iq384.26284q39+(3.168742.78857i)q40+10.0648q41+1.69985iq421.43751iq43+1.17255q44+(1.47723+1.67863i)q45+4.61014q46+3.21978iq47+4.98779iq481.00000q49+(8.43031+1.08038i)q501.00000q51+3.79175iq52+14.1176iq53+1.69985q54+(1.94733+2.21282i)q551.88770q565.21905iq571.61259iq5814.0099q59+(1.49312+1.31398i)q60+8.36086q61+3.72347iq62+1.00000iq631.98102q64+(7.155716.29720i)q65+2.24079q6613.6284iq67+0.889490iq68+2.71209q69+(2.51107+2.85341i)q706.66687q71+1.88770iq7213.0816iq73+6.19219q74+(4.95944+0.635573i)q754.64229q76+1.31823iq77+7.24619iq78+9.12564q79+(7.36812+8.37263i)q80+1.00000q8117.1086iq82+6.08519iq83+0.889490q84+(1.678631.47723i)q852.44355q860.948665iq87+2.48842iq880.0400448q89+(2.85341+2.51107i)q904.26284q912.41237iq92+2.19047iq93+5.47315q94+(7.709748.76083i)q95+4.70309q96+7.33549iq97+1.69985iq98+1.31823q99+O(q100)q-1.69985i q^{2} -1.00000i q^{3} -0.889490 q^{4} +(1.47723 - 1.67863i) q^{5} -1.69985 q^{6} -1.00000i q^{7} -1.88770i q^{8} -1.00000 q^{9} +(-2.85341 - 2.51107i) q^{10} -1.31823 q^{11} +0.889490i q^{12} -4.26284i q^{13} -1.69985 q^{14} +(-1.67863 - 1.47723i) q^{15} -4.98779 q^{16} -1.00000i q^{17} +1.69985i q^{18} +5.21905 q^{19} +(-1.31398 + 1.49312i) q^{20} -1.00000 q^{21} +2.24079i q^{22} +2.71209i q^{23} -1.88770 q^{24} +(-0.635573 - 4.95944i) q^{25} -7.24619 q^{26} +1.00000i q^{27} +0.889490i q^{28} +0.948665 q^{29} +(-2.51107 + 2.85341i) q^{30} -2.19047 q^{31} +4.70309i q^{32} +1.31823i q^{33} -1.69985 q^{34} +(-1.67863 - 1.47723i) q^{35} +0.889490 q^{36} +3.64278i q^{37} -8.87160i q^{38} -4.26284 q^{39} +(-3.16874 - 2.78857i) q^{40} +10.0648 q^{41} +1.69985i q^{42} -1.43751i q^{43} +1.17255 q^{44} +(-1.47723 + 1.67863i) q^{45} +4.61014 q^{46} +3.21978i q^{47} +4.98779i q^{48} -1.00000 q^{49} +(-8.43031 + 1.08038i) q^{50} -1.00000 q^{51} +3.79175i q^{52} +14.1176i q^{53} +1.69985 q^{54} +(-1.94733 + 2.21282i) q^{55} -1.88770 q^{56} -5.21905i q^{57} -1.61259i q^{58} -14.0099 q^{59} +(1.49312 + 1.31398i) q^{60} +8.36086 q^{61} +3.72347i q^{62} +1.00000i q^{63} -1.98102 q^{64} +(-7.15571 - 6.29720i) q^{65} +2.24079 q^{66} -13.6284i q^{67} +0.889490i q^{68} +2.71209 q^{69} +(-2.51107 + 2.85341i) q^{70} -6.66687 q^{71} +1.88770i q^{72} -13.0816i q^{73} +6.19219 q^{74} +(-4.95944 + 0.635573i) q^{75} -4.64229 q^{76} +1.31823i q^{77} +7.24619i q^{78} +9.12564 q^{79} +(-7.36812 + 8.37263i) q^{80} +1.00000 q^{81} -17.1086i q^{82} +6.08519i q^{83} +0.889490 q^{84} +(-1.67863 - 1.47723i) q^{85} -2.44355 q^{86} -0.948665i q^{87} +2.48842i q^{88} -0.0400448 q^{89} +(2.85341 + 2.51107i) q^{90} -4.26284 q^{91} -2.41237i q^{92} +2.19047i q^{93} +5.47315 q^{94} +(7.70974 - 8.76083i) q^{95} +4.70309 q^{96} +7.33549i q^{97} +1.69985i q^{98} +1.31823 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 28q34q46q628q9+4q10+8q116q144q15+38q16+12q194q2028q21+30q248q2536q262q30+14q316q344q35+8q99+O(q100) 28 q - 34 q^{4} - 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} - 4 q^{15} + 38 q^{16} + 12 q^{19} - 4 q^{20} - 28 q^{21} + 30 q^{24} - 8 q^{25} - 36 q^{26} - 2 q^{30} + 14 q^{31} - 6 q^{34} - 4 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1785Z)×\left(\mathbb{Z}/1785\mathbb{Z}\right)^\times.

nn 596596 766766 10721072 12611261
χ(n)\chi(n) 11 11 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 1.69985i 1.20198i −0.799258 0.600988i 0.794774π-0.794774\pi
0.799258 0.600988i 0.205226π-0.205226\pi
33 1.00000i 0.577350i
44 −0.889490 −0.444745
55 1.47723 1.67863i 0.660638 0.750705i
66 −1.69985 −0.693961
77 1.00000i 0.377964i
88 1.88770i 0.667403i
99 −1.00000 −0.333333
1010 −2.85341 2.51107i −0.902328 0.794071i
1111 −1.31823 −0.397461 −0.198731 0.980054i 0.563682π-0.563682\pi
−0.198731 + 0.980054i 0.563682π0.563682\pi
1212 0.889490i 0.256774i
1313 4.26284i 1.18230i −0.806562 0.591149i 0.798674π-0.798674\pi
0.806562 0.591149i 0.201326π-0.201326\pi
1414 −1.69985 −0.454304
1515 −1.67863 1.47723i −0.433419 0.381420i
1616 −4.98779 −1.24695
1717 1.00000i 0.242536i
1818 1.69985i 0.400659i
1919 5.21905 1.19733 0.598666 0.800999i 0.295698π-0.295698\pi
0.598666 + 0.800999i 0.295698π0.295698\pi
2020 −1.31398 + 1.49312i −0.293816 + 0.333872i
2121 −1.00000 −0.218218
2222 2.24079i 0.477739i
2323 2.71209i 0.565509i 0.959192 + 0.282754i 0.0912482π0.0912482\pi
−0.959192 + 0.282754i 0.908752π0.908752\pi
2424 −1.88770 −0.385325
2525 −0.635573 4.95944i −0.127115 0.991888i
2626 −7.24619 −1.42109
2727 1.00000i 0.192450i
2828 0.889490i 0.168098i
2929 0.948665 0.176163 0.0880814 0.996113i 0.471926π-0.471926\pi
0.0880814 + 0.996113i 0.471926π0.471926\pi
3030 −2.51107 + 2.85341i −0.458457 + 0.520960i
3131 −2.19047 −0.393420 −0.196710 0.980462i 0.563026π-0.563026\pi
−0.196710 + 0.980462i 0.563026π0.563026\pi
3232 4.70309i 0.831397i
3333 1.31823i 0.229474i
3434 −1.69985 −0.291522
3535 −1.67863 1.47723i −0.283740 0.249698i
3636 0.889490 0.148248
3737 3.64278i 0.598870i 0.954117 + 0.299435i 0.0967982π0.0967982\pi
−0.954117 + 0.299435i 0.903202π0.903202\pi
3838 8.87160i 1.43916i
3939 −4.26284 −0.682601
4040 −3.16874 2.78857i −0.501022 0.440912i
4141 10.0648 1.57185 0.785925 0.618321i 0.212187π-0.212187\pi
0.785925 + 0.618321i 0.212187π0.212187\pi
4242 1.69985i 0.262293i
4343 1.43751i 0.219218i −0.993975 0.109609i 0.965040π-0.965040\pi
0.993975 0.109609i 0.0349598π-0.0349598\pi
4444 1.17255 0.176769
4545 −1.47723 + 1.67863i −0.220213 + 0.250235i
4646 4.61014 0.679728
4747 3.21978i 0.469654i 0.972037 + 0.234827i 0.0754523π0.0754523\pi
−0.972037 + 0.234827i 0.924548π0.924548\pi
4848 4.98779i 0.719925i
4949 −1.00000 −0.142857
5050 −8.43031 + 1.08038i −1.19223 + 0.152789i
5151 −1.00000 −0.140028
5252 3.79175i 0.525822i
5353 14.1176i 1.93920i 0.244701 + 0.969599i 0.421310π0.421310\pi
−0.244701 + 0.969599i 0.578690π0.578690\pi
5454 1.69985 0.231320
5555 −1.94733 + 2.21282i −0.262578 + 0.298376i
5656 −1.88770 −0.252255
5757 5.21905i 0.691280i
5858 1.61259i 0.211743i
5959 −14.0099 −1.82394 −0.911968 0.410262i 0.865437π-0.865437\pi
−0.911968 + 0.410262i 0.865437π0.865437\pi
6060 1.49312 + 1.31398i 0.192761 + 0.169635i
6161 8.36086 1.07050 0.535249 0.844694i 0.320218π-0.320218\pi
0.535249 + 0.844694i 0.320218π0.320218\pi
6262 3.72347i 0.472881i
6363 1.00000i 0.125988i
6464 −1.98102 −0.247628
6565 −7.15571 6.29720i −0.887557 0.781072i
6666 2.24079 0.275823
6767 13.6284i 1.66497i −0.554049 0.832484i 0.686918π-0.686918\pi
0.554049 0.832484i 0.313082π-0.313082\pi
6868 0.889490i 0.107867i
6969 2.71209 0.326497
7070 −2.51107 + 2.85341i −0.300131 + 0.341048i
7171 −6.66687 −0.791212 −0.395606 0.918420i 0.629465π-0.629465\pi
−0.395606 + 0.918420i 0.629465π0.629465\pi
7272 1.88770i 0.222468i
7373 13.0816i 1.53109i −0.643383 0.765544i 0.722470π-0.722470\pi
0.643383 0.765544i 0.277530π-0.277530\pi
7474 6.19219 0.719827
7575 −4.95944 + 0.635573i −0.572667 + 0.0733896i
7676 −4.64229 −0.532508
7777 1.31823i 0.150226i
7878 7.24619i 0.820469i
7979 9.12564 1.02672 0.513358 0.858175i 0.328401π-0.328401\pi
0.513358 + 0.858175i 0.328401π0.328401\pi
8080 −7.36812 + 8.37263i −0.823781 + 0.936089i
8181 1.00000 0.111111
8282 17.1086i 1.88933i
8383 6.08519i 0.667936i 0.942584 + 0.333968i 0.108388π0.108388\pi
−0.942584 + 0.333968i 0.891612π0.891612\pi
8484 0.889490 0.0970514
8585 −1.67863 1.47723i −0.182073 0.160228i
8686 −2.44355 −0.263494
8787 0.948665i 0.101708i
8888 2.48842i 0.265267i
8989 −0.0400448 −0.00424474 −0.00212237 0.999998i 0.500676π-0.500676\pi
−0.00212237 + 0.999998i 0.500676π0.500676\pi
9090 2.85341 + 2.51107i 0.300776 + 0.264690i
9191 −4.26284 −0.446867
9292 2.41237i 0.251507i
9393 2.19047i 0.227141i
9494 5.47315 0.564512
9595 7.70974 8.76083i 0.791003 0.898842i
9696 4.70309 0.480007
9797 7.33549i 0.744806i 0.928071 + 0.372403i 0.121466π0.121466\pi
−0.928071 + 0.372403i 0.878534π0.878534\pi
9898 1.69985i 0.171711i
9999 1.31823 0.132487
100100 0.565336 + 4.41137i 0.0565336 + 0.441137i
101101 −2.66094 −0.264774 −0.132387 0.991198i 0.542264π-0.542264\pi
−0.132387 + 0.991198i 0.542264π0.542264\pi
102102 1.69985i 0.168310i
103103 8.62526i 0.849872i 0.905223 + 0.424936i 0.139703π0.139703\pi
−0.905223 + 0.424936i 0.860297π0.860297\pi
104104 −8.04696 −0.789069
105105 −1.47723 + 1.67863i −0.144163 + 0.163817i
106106 23.9978 2.33087
107107 19.2943i 1.86525i −0.360852 0.932623i 0.617514π-0.617514\pi
0.360852 0.932623i 0.382486π-0.382486\pi
108108 0.889490i 0.0855913i
109109 −4.03341 −0.386331 −0.193166 0.981166i 0.561875π-0.561875\pi
−0.193166 + 0.981166i 0.561875π0.561875\pi
110110 3.76146 + 3.31017i 0.358641 + 0.315612i
111111 3.64278 0.345758
112112 4.98779i 0.471302i
113113 18.5353i 1.74366i 0.489810 + 0.871829i 0.337066π0.337066\pi
−0.489810 + 0.871829i 0.662934π0.662934\pi
114114 −8.87160 −0.830902
115115 4.55258 + 4.00638i 0.424530 + 0.373597i
116116 −0.843829 −0.0783475
117117 4.26284i 0.394100i
118118 23.8148i 2.19233i
119119 −1.00000 −0.0916698
120120 −2.78857 + 3.16874i −0.254560 + 0.289265i
121121 −9.26227 −0.842024
122122 14.2122i 1.28671i
123123 10.0648i 0.907509i
124124 1.94840 0.174972
125125 −9.26394 6.25935i −0.828592 0.559854i
126126 1.69985 0.151435
127127 7.03516i 0.624269i −0.950038 0.312135i 0.898956π-0.898956\pi
0.950038 0.312135i 0.101044π-0.101044\pi
128128 12.7736i 1.12904i
129129 −1.43751 −0.126565
130130 −10.7043 + 12.1636i −0.938829 + 1.06682i
131131 −2.49412 −0.217913 −0.108956 0.994047i 0.534751π-0.534751\pi
−0.108956 + 0.994047i 0.534751π0.534751\pi
132132 1.17255i 0.102058i
133133 5.21905i 0.452549i
134134 −23.1662 −2.00125
135135 1.67863 + 1.47723i 0.144473 + 0.127140i
136136 −1.88770 −0.161869
137137 4.36841i 0.373218i 0.982434 + 0.186609i 0.0597498π0.0597498\pi
−0.982434 + 0.186609i 0.940250π0.940250\pi
138138 4.61014i 0.392441i
139139 11.3585 0.963413 0.481707 0.876333i 0.340017π-0.340017\pi
0.481707 + 0.876333i 0.340017π0.340017\pi
140140 1.49312 + 1.31398i 0.126192 + 0.111052i
141141 3.21978 0.271155
142142 11.3327i 0.951018i
143143 5.61940i 0.469918i
144144 4.98779 0.415649
145145 1.40140 1.59245i 0.116380 0.132246i
146146 −22.2368 −1.84033
147147 1.00000i 0.0824786i
148148 3.24022i 0.266345i
149149 15.8707 1.30018 0.650090 0.759858i 0.274731π-0.274731\pi
0.650090 + 0.759858i 0.274731π0.274731\pi
150150 1.08038 + 8.43031i 0.0882125 + 0.688332i
151151 10.9078 0.887667 0.443833 0.896109i 0.353618π-0.353618\pi
0.443833 + 0.896109i 0.353618π0.353618\pi
152152 9.85200i 0.799103i
153153 1.00000i 0.0808452i
154154 2.24079 0.180568
155155 −3.23583 + 3.67698i −0.259908 + 0.295342i
156156 3.79175 0.303583
157157 5.06290i 0.404063i 0.979379 + 0.202032i 0.0647544π0.0647544\pi
−0.979379 + 0.202032i 0.935246π0.935246\pi
158158 15.5122i 1.23409i
159159 14.1176 1.11960
160160 7.89473 + 6.94756i 0.624134 + 0.549253i
161161 2.71209 0.213742
162162 1.69985i 0.133553i
163163 13.9637i 1.09372i 0.837224 + 0.546860i 0.184177π0.184177\pi
−0.837224 + 0.546860i 0.815823π0.815823\pi
164164 −8.95250 −0.699073
165165 2.21282 + 1.94733i 0.172267 + 0.151600i
166166 10.3439 0.802843
167167 20.0975i 1.55519i 0.628766 + 0.777595i 0.283560π0.283560\pi
−0.628766 + 0.777595i 0.716440π0.716440\pi
168168 1.88770i 0.145639i
169169 −5.17180 −0.397830
170170 −2.51107 + 2.85341i −0.192590 + 0.218847i
171171 −5.21905 −0.399111
172172 1.27865i 0.0974960i
173173 9.66834i 0.735071i −0.930010 0.367535i 0.880202π-0.880202\pi
0.930010 0.367535i 0.119798π-0.119798\pi
174174 −1.61259 −0.122250
175175 −4.95944 + 0.635573i −0.374898 + 0.0480448i
176176 6.57505 0.495613
177177 14.0099i 1.05305i
178178 0.0680701i 0.00510207i
179179 −2.03325 −0.151972 −0.0759859 0.997109i 0.524210π-0.524210\pi
−0.0759859 + 0.997109i 0.524210π0.524210\pi
180180 1.31398 1.49312i 0.0979385 0.111291i
181181 22.0739 1.64074 0.820369 0.571835i 0.193768π-0.193768\pi
0.820369 + 0.571835i 0.193768π0.193768\pi
182182 7.24619i 0.537123i
183183 8.36086i 0.618052i
184184 5.11960 0.377422
185185 6.11487 + 5.38124i 0.449574 + 0.395636i
186186 3.72347 0.273018
187187 1.31823i 0.0963985i
188188 2.86397i 0.208876i
189189 1.00000 0.0727393
190190 −14.8921 13.1054i −1.08039 0.950766i
191191 18.4256 1.33323 0.666614 0.745403i 0.267743π-0.267743\pi
0.666614 + 0.745403i 0.267743π0.267743\pi
192192 1.98102i 0.142968i
193193 20.9313i 1.50666i −0.657640 0.753332i 0.728445π-0.728445\pi
0.657640 0.753332i 0.271555π-0.271555\pi
194194 12.4692 0.895239
195195 −6.29720 + 7.15571i −0.450952 + 0.512431i
196196 0.889490 0.0635350
197197 16.7970i 1.19674i −0.801221 0.598368i 0.795816π-0.795816\pi
0.801221 0.598368i 0.204184π-0.204184\pi
198198 2.24079i 0.159246i
199199 −17.0325 −1.20740 −0.603700 0.797211i 0.706308π-0.706308\pi
−0.603700 + 0.797211i 0.706308π0.706308\pi
200200 −9.36193 + 1.19977i −0.661989 + 0.0848366i
201201 −13.6284 −0.961270
202202 4.52320i 0.318252i
203203 0.948665i 0.0665832i
204204 0.889490 0.0622768
205205 14.8680 16.8950i 1.03842 1.18000i
206206 14.6616 1.02152
207207 2.71209i 0.188503i
208208 21.2621i 1.47426i
209209 −6.87991 −0.475893
210210 2.85341 + 2.51107i 0.196904 + 0.173280i
211211 −10.1723 −0.700293 −0.350147 0.936695i 0.613868π-0.613868\pi
−0.350147 + 0.936695i 0.613868π0.613868\pi
212212 12.5574i 0.862449i
213213 6.66687i 0.456807i
214214 −32.7974 −2.24198
215215 −2.41304 2.12353i −0.164568 0.144824i
216216 1.88770 0.128442
217217 2.19047i 0.148699i
218218 6.85620i 0.464361i
219219 −13.0816 −0.883974
220220 1.73213 1.96828i 0.116780 0.132701i
221221 −4.26284 −0.286750
222222 6.19219i 0.415592i
223223 2.54258i 0.170264i 0.996370 + 0.0851320i 0.0271312π0.0271312\pi
−0.996370 + 0.0851320i 0.972869π0.972869\pi
224224 4.70309 0.314239
225225 0.635573 + 4.95944i 0.0423715 + 0.330629i
226226 31.5073 2.09583
227227 10.5749i 0.701883i −0.936397 0.350942i 0.885862π-0.885862\pi
0.936397 0.350942i 0.114138π-0.114138\pi
228228 4.64229i 0.307443i
229229 16.7374 1.10604 0.553020 0.833168i 0.313475π-0.313475\pi
0.553020 + 0.833168i 0.313475π0.313475\pi
230230 6.81024 7.73870i 0.449054 0.510275i
231231 1.31823 0.0867332
232232 1.79080i 0.117571i
233233 5.57246i 0.365064i −0.983200 0.182532i 0.941571π-0.941571\pi
0.983200 0.182532i 0.0584293π-0.0584293\pi
234234 7.24619 0.473698
235235 5.40481 + 4.75637i 0.352571 + 0.310271i
236236 12.4617 0.811187
237237 9.12564i 0.592774i
238238 1.69985i 0.110185i
239239 −12.4766 −0.807041 −0.403521 0.914971i 0.632214π-0.632214\pi
−0.403521 + 0.914971i 0.632214π0.632214\pi
240240 8.37263 + 7.36812i 0.540451 + 0.475610i
241241 10.1786 0.655659 0.327829 0.944737i 0.393683π-0.393683\pi
0.327829 + 0.944737i 0.393683π0.393683\pi
242242 15.7445i 1.01209i
243243 1.00000i 0.0641500i
244244 −7.43690 −0.476099
245245 −1.47723 + 1.67863i −0.0943769 + 0.107244i
246246 −17.1086 −1.09080
247247 22.2480i 1.41560i
248248 4.13495i 0.262569i
249249 6.08519 0.385633
250250 −10.6400 + 15.7473i −0.672930 + 0.995947i
251251 −5.67410 −0.358146 −0.179073 0.983836i 0.557310π-0.557310\pi
−0.179073 + 0.983836i 0.557310π0.557310\pi
252252 0.889490i 0.0560326i
253253 3.57515i 0.224768i
254254 −11.9587 −0.750356
255255 −1.47723 + 1.67863i −0.0925078 + 0.105120i
256256 17.7512 1.10945
257257 18.9299i 1.18082i −0.807105 0.590408i 0.798967π-0.798967\pi
0.807105 0.590408i 0.201033π-0.201033\pi
258258 2.44355i 0.152129i
259259 3.64278 0.226352
260260 6.36494 + 5.60130i 0.394737 + 0.347378i
261261 −0.948665 −0.0587209
262262 4.23963i 0.261926i
263263 4.50632i 0.277872i 0.990301 + 0.138936i 0.0443682π0.0443682\pi
−0.990301 + 0.138936i 0.955632π0.955632\pi
264264 2.48842 0.153152
265265 23.6981 + 20.8549i 1.45576 + 1.28111i
266266 −8.87160 −0.543953
267267 0.0400448i 0.00245070i
268268 12.1223i 0.740487i
269269 6.65868 0.405987 0.202993 0.979180i 0.434933π-0.434933\pi
0.202993 + 0.979180i 0.434933π0.434933\pi
270270 2.51107 2.85341i 0.152819 0.173653i
271271 6.91612 0.420124 0.210062 0.977688i 0.432633π-0.432633\pi
0.210062 + 0.977688i 0.432633π0.432633\pi
272272 4.98779i 0.302429i
273273 4.26284i 0.257999i
274274 7.42564 0.448599
275275 0.837831 + 6.53768i 0.0505231 + 0.394237i
276276 −2.41237 −0.145208
277277 8.39750i 0.504557i −0.967655 0.252278i 0.918820π-0.918820\pi
0.967655 0.252278i 0.0811799π-0.0811799\pi
278278 19.3077i 1.15800i
279279 2.19047 0.131140
280280 −2.78857 + 3.16874i −0.166649 + 0.189369i
281281 5.79215 0.345531 0.172765 0.984963i 0.444730π-0.444730\pi
0.172765 + 0.984963i 0.444730π0.444730\pi
282282 5.47315i 0.325921i
283283 25.7255i 1.52922i 0.644493 + 0.764610i 0.277068π0.277068\pi
−0.644493 + 0.764610i 0.722932π0.722932\pi
284284 5.93012 0.351888
285285 −8.76083 7.70974i −0.518947 0.456686i
286286 9.55214 0.564830
287287 10.0648i 0.594104i
288288 4.70309i 0.277132i
289289 −1.00000 −0.0588235
290290 −2.70693 2.38217i −0.158957 0.139886i
291291 7.33549 0.430014
292292 11.6360i 0.680944i
293293 3.51413i 0.205298i −0.994718 0.102649i 0.967268π-0.967268\pi
0.994718 0.102649i 0.0327318π-0.0327318\pi
294294 1.69985 0.0991373
295295 −20.6959 + 23.5174i −1.20496 + 1.36924i
296296 6.87648 0.399687
297297 1.31823i 0.0764915i
298298 26.9778i 1.56278i
299299 11.5612 0.668600
300300 4.41137 0.565336i 0.254691 0.0326397i
301301 −1.43751 −0.0828565
302302 18.5417i 1.06695i
303303 2.66094i 0.152867i
304304 −26.0315 −1.49301
305305 12.3509 14.0348i 0.707212 0.803628i
306306 1.69985 0.0971740
307307 15.6901i 0.895481i 0.894163 + 0.447741i 0.147771π0.147771\pi
−0.894163 + 0.447741i 0.852229π0.852229\pi
308308 1.17255i 0.0668124i
309309 8.62526 0.490674
310310 6.25031 + 5.50043i 0.354994 + 0.312403i
311311 −33.0126 −1.87197 −0.935987 0.352035i 0.885490π-0.885490\pi
−0.935987 + 0.352035i 0.885490π0.885490\pi
312312 8.04696i 0.455569i
313313 1.96627i 0.111140i 0.998455 + 0.0555702i 0.0176977π0.0176977\pi
−0.998455 + 0.0555702i 0.982302π0.982302\pi
314314 8.60617 0.485674
315315 1.67863 + 1.47723i 0.0945799 + 0.0832326i
316316 −8.11717 −0.456627
317317 29.0692i 1.63269i −0.577564 0.816345i 0.695997π-0.695997\pi
0.577564 0.816345i 0.304003π-0.304003\pi
318318 23.9978i 1.34573i
319319 −1.25056 −0.0700179
320320 −2.92643 + 3.32540i −0.163593 + 0.185895i
321321 −19.2943 −1.07690
322322 4.61014i 0.256913i
323323 5.21905i 0.290396i
324324 −0.889490 −0.0494161
325325 −21.1413 + 2.70934i −1.17271 + 0.150287i
326326 23.7362 1.31462
327327 4.03341i 0.223048i
328328 18.9992i 1.04906i
329329 3.21978 0.177512
330330 3.31017 3.76146i 0.182219 0.207061i
331331 29.7790 1.63680 0.818401 0.574647i 0.194861π-0.194861\pi
0.818401 + 0.574647i 0.194861π0.194861\pi
332332 5.41272i 0.297061i
333333 3.64278i 0.199623i
334334 34.1627 1.86930
335335 −22.8769 20.1322i −1.24990 1.09994i
336336 4.98779 0.272106
337337 31.8660i 1.73585i −0.496694 0.867925i 0.665453π-0.665453\pi
0.496694 0.867925i 0.334547π-0.334547\pi
338338 8.79128i 0.478182i
339339 18.5353 1.00670
340340 1.49312 + 1.31398i 0.0809759 + 0.0712608i
341341 2.88754 0.156369
342342 8.87160i 0.479721i
343343 1.00000i 0.0539949i
344344 −2.71358 −0.146306
345345 4.00638 4.55258i 0.215696 0.245103i
346346 −16.4347 −0.883537
347347 1.62114i 0.0870273i −0.999053 0.0435136i 0.986145π-0.986145\pi
0.999053 0.0435136i 0.0138552π-0.0138552\pi
348348 0.843829i 0.0452340i
349349 −24.2326 −1.29714 −0.648572 0.761153i 0.724633π-0.724633\pi
−0.648572 + 0.761153i 0.724633π0.724633\pi
350350 1.08038 + 8.43031i 0.0577487 + 0.450619i
351351 4.26284 0.227534
352352 6.19976i 0.330448i
353353 13.1172i 0.698159i −0.937093 0.349080i 0.886494π-0.886494\pi
0.937093 0.349080i 0.113506π-0.113506\pi
354354 23.8148 1.26574
355355 −9.84851 + 11.1912i −0.522705 + 0.593967i
356356 0.0356195 0.00188783
357357 1.00000i 0.0529256i
358358 3.45621i 0.182666i
359359 0.584856 0.0308675 0.0154338 0.999881i 0.495087π-0.495087\pi
0.0154338 + 0.999881i 0.495087π0.495087\pi
360360 3.16874 + 2.78857i 0.167007 + 0.146971i
361361 8.23847 0.433604
362362 37.5223i 1.97213i
363363 9.26227i 0.486143i
364364 3.79175 0.198742
365365 −21.9592 19.3246i −1.14940 1.01150i
366366 −14.2122 −0.742884
367367 20.0167i 1.04486i −0.852682 0.522431i 0.825025π-0.825025\pi
0.852682 0.522431i 0.174975π-0.174975\pi
368368 13.5273i 0.705160i
369369 −10.0648 −0.523950
370370 9.14730 10.3944i 0.475545 0.540377i
371371 14.1176 0.732948
372372 1.94840i 0.101020i
373373 18.8646i 0.976774i −0.872627 0.488387i 0.837585π-0.837585\pi
0.872627 0.488387i 0.162415π-0.162415\pi
374374 2.24079 0.115869
375375 −6.25935 + 9.26394i −0.323232 + 0.478388i
376376 6.07798 0.313448
377377 4.04401i 0.208277i
378378 1.69985i 0.0874309i
379379 20.4953 1.05277 0.526385 0.850246i 0.323547π-0.323547\pi
0.526385 + 0.850246i 0.323547π0.323547\pi
380380 −6.85774 + 7.79268i −0.351795 + 0.399756i
381381 −7.03516 −0.360422
382382 31.3207i 1.60251i
383383 13.8741i 0.708935i 0.935068 + 0.354468i 0.115338π0.115338\pi
−0.935068 + 0.354468i 0.884662π0.884662\pi
384384 12.7736 0.651851
385385 2.21282 + 1.94733i 0.112776 + 0.0992452i
386386 −35.5800 −1.81097
387387 1.43751i 0.0730726i
388388 6.52485i 0.331249i
389389 35.8144 1.81586 0.907931 0.419120i 0.137661π-0.137661\pi
0.907931 + 0.419120i 0.137661π0.137661\pi
390390 12.1636 + 10.7043i 0.615930 + 0.542033i
391391 2.71209 0.137156
392392 1.88770i 0.0953432i
393393 2.49412i 0.125812i
394394 −28.5524 −1.43845
395395 13.4807 15.3185i 0.678287 0.770760i
396396 −1.17255 −0.0589230
397397 16.1355i 0.809820i −0.914357 0.404910i 0.867303π-0.867303\pi
0.914357 0.404910i 0.132697π-0.132697\pi
398398 28.9527i 1.45127i
399399 −5.21905 −0.261279
400400 3.17010 + 24.7366i 0.158505 + 1.23683i
401401 −10.5679 −0.527736 −0.263868 0.964559i 0.584998π-0.584998\pi
−0.263868 + 0.964559i 0.584998π0.584998\pi
402402 23.1662i 1.15542i
403403 9.33761i 0.465140i
404404 2.36688 0.117757
405405 1.47723 1.67863i 0.0734042 0.0834116i
406406 −1.61259 −0.0800314
407407 4.80203i 0.238028i
408408 1.88770i 0.0934551i
409409 −16.7929 −0.830353 −0.415177 0.909741i 0.636280π-0.636280\pi
−0.415177 + 0.909741i 0.636280π0.636280\pi
410410 −28.7189 25.2733i −1.41833 1.24816i
411411 4.36841 0.215478
412412 7.67208i 0.377976i
413413 14.0099i 0.689383i
414414 −4.61014 −0.226576
415415 10.2148 + 8.98923i 0.501423 + 0.441264i
416416 20.0485 0.982960
417417 11.3585i 0.556227i
418418 11.6948i 0.572012i
419419 −15.1395 −0.739612 −0.369806 0.929109i 0.620576π-0.620576\pi
−0.369806 + 0.929109i 0.620576π0.620576\pi
420420 1.31398 1.49312i 0.0641158 0.0728569i
421421 17.1786 0.837236 0.418618 0.908162i 0.362515π-0.362515\pi
0.418618 + 0.908162i 0.362515π0.362515\pi
422422 17.2915i 0.841735i
423423 3.21978i 0.156551i
424424 26.6497 1.29423
425425 −4.95944 + 0.635573i −0.240568 + 0.0308298i
426426 11.3327 0.549070
427427 8.36086i 0.404610i
428428 17.1621i 0.829559i
429429 5.61940 0.271307
430430 −3.60968 + 4.10180i −0.174074 + 0.197806i
431431 −34.0312 −1.63922 −0.819612 0.572919i 0.805811π-0.805811\pi
−0.819612 + 0.572919i 0.805811π0.805811\pi
432432 4.98779i 0.239975i
433433 16.0610i 0.771842i −0.922532 0.385921i 0.873884π-0.873884\pi
0.922532 0.385921i 0.126116π-0.126116\pi
434434 3.72347 0.178732
435435 −1.59245 1.40140i −0.0763523 0.0671919i
436436 3.58768 0.171819
437437 14.1545i 0.677102i
438438 22.2368i 1.06252i
439439 −10.1471 −0.484293 −0.242147 0.970240i 0.577852π-0.577852\pi
−0.242147 + 0.970240i 0.577852π0.577852\pi
440440 4.17713 + 3.67598i 0.199137 + 0.175245i
441441 1.00000 0.0476190
442442 7.24619i 0.344666i
443443 20.6208i 0.979726i 0.871799 + 0.489863i 0.162953π0.162953\pi
−0.871799 + 0.489863i 0.837047π0.837047\pi
444444 −3.24022 −0.153774
445445 −0.0591554 + 0.0672202i −0.00280424 + 0.00318654i
446446 4.32201 0.204653
447447 15.8707i 0.750659i
448448 1.98102i 0.0935946i
449449 −16.1240 −0.760940 −0.380470 0.924793i 0.624238π-0.624238\pi
−0.380470 + 0.924793i 0.624238π0.624238\pi
450450 8.43031 1.08038i 0.397408 0.0509295i
451451 −13.2677 −0.624750
452452 16.4870i 0.775484i
453453 10.9078i 0.512495i
454454 −17.9758 −0.843646
455455 −6.29720 + 7.15571i −0.295217 + 0.335465i
456456 −9.85200 −0.461362
457457 8.92593i 0.417538i −0.977965 0.208769i 0.933054π-0.933054\pi
0.977965 0.208769i 0.0669456π-0.0669456\pi
458458 28.4511i 1.32943i
459459 1.00000 0.0466760
460460 −4.04947 3.56364i −0.188808 0.166155i
461461 −15.6712 −0.729881 −0.364941 0.931031i 0.618911π-0.618911\pi
−0.364941 + 0.931031i 0.618911π0.618911\pi
462462 2.24079i 0.104251i
463463 20.0753i 0.932980i −0.884526 0.466490i 0.845518π-0.845518\pi
0.884526 0.466490i 0.154482π-0.154482\pi
464464 −4.73174 −0.219666
465465 3.67698 + 3.23583i 0.170516 + 0.150058i
466466 −9.47234 −0.438798
467467 20.2971i 0.939239i 0.882869 + 0.469619i 0.155609π0.155609\pi
−0.882869 + 0.469619i 0.844391π0.844391\pi
468468 3.79175i 0.175274i
469469 −13.6284 −0.629299
470470 8.08511 9.18737i 0.372938 0.423782i
471471 5.06290 0.233286
472472 26.4465i 1.21730i
473473 1.89496i 0.0871306i
474474 −15.5122 −0.712500
475475 −3.31709 25.8836i −0.152198 1.18762i
476476 0.889490 0.0407697
477477 14.1176i 0.646399i
478478 21.2083i 0.970044i
479479 40.7298 1.86099 0.930496 0.366301i 0.119376π-0.119376\pi
0.930496 + 0.366301i 0.119376π0.119376\pi
480480 6.94756 7.89473i 0.317111 0.360344i
481481 15.5286 0.708043
482482 17.3020i 0.788086i
483483 2.71209i 0.123404i
484484 8.23870 0.374486
485485 12.3135 + 10.8362i 0.559129 + 0.492047i
486486 −1.69985 −0.0771068
487487 28.7836i 1.30431i −0.758085 0.652156i 0.773865π-0.773865\pi
0.758085 0.652156i 0.226135π-0.226135\pi
488488 15.7828i 0.714453i
489489 13.9637 0.631459
490490 2.85341 + 2.51107i 0.128904 + 0.113439i
491491 −5.30798 −0.239546 −0.119773 0.992801i 0.538217π-0.538217\pi
−0.119773 + 0.992801i 0.538217π0.538217\pi
492492 8.95250i 0.403610i
493493 0.948665i 0.0427257i
494494 −37.8182 −1.70152
495495 1.94733 2.21282i 0.0875260 0.0994587i
496496 10.9256 0.490574
497497 6.66687i 0.299050i
498498 10.3439i 0.463522i
499499 −11.5574 −0.517378 −0.258689 0.965961i 0.583291π-0.583291\pi
−0.258689 + 0.965961i 0.583291π0.583291\pi
500500 8.24018 + 5.56763i 0.368512 + 0.248992i
501501 20.0975 0.897889
502502 9.64512i 0.430483i
503503 9.99769i 0.445775i −0.974844 0.222888i 0.928452π-0.928452\pi
0.974844 0.222888i 0.0715483π-0.0715483\pi
504504 1.88770 0.0840848
505505 −3.93083 + 4.46673i −0.174920 + 0.198767i
506506 −6.07722 −0.270166
507507 5.17180i 0.229688i
508508 6.25770i 0.277641i
509509 31.2809 1.38650 0.693250 0.720697i 0.256178π-0.256178\pi
0.693250 + 0.720697i 0.256178π0.256178\pi
510510 2.85341 + 2.51107i 0.126351 + 0.111192i
511511 −13.0816 −0.578697
512512 4.62713i 0.204492i
513513 5.21905i 0.230427i
514514 −32.1780 −1.41931
515515 14.4786 + 12.7415i 0.638002 + 0.561458i
516516 1.27865 0.0562894
517517 4.24442i 0.186669i
518518 6.19219i 0.272069i
519519 −9.66834 −0.424393
520520 −11.8872 + 13.5078i −0.521289 + 0.592358i
521521 −5.52167 −0.241909 −0.120954 0.992658i 0.538595π-0.538595\pi
−0.120954 + 0.992658i 0.538595π0.538595\pi
522522 1.61259i 0.0705811i
523523 32.7457i 1.43187i 0.698167 + 0.715935i 0.253999π0.253999\pi
−0.698167 + 0.715935i 0.746001π0.746001\pi
524524 2.21850 0.0969155
525525 0.635573 + 4.95944i 0.0277387 + 0.216448i
526526 7.66007 0.333995
527527 2.19047i 0.0954183i
528528 6.57505i 0.286142i
529529 15.6446 0.680200
530530 35.4502 40.2833i 1.53986 1.74979i
531531 14.0099 0.607978
532532 4.64229i 0.201269i
533533 42.9044i 1.85840i
534534 0.0680701 0.00294568
535535 −32.3879 28.5021i −1.40025 1.23225i
536536 −25.7262 −1.11120
537537 2.03325i 0.0877410i
538538 11.3187i 0.487986i
539539 1.31823 0.0567802
540540 −1.49312 1.31398i −0.0642537 0.0565448i
541541 10.3254 0.443923 0.221961 0.975055i 0.428754π-0.428754\pi
0.221961 + 0.975055i 0.428754π0.428754\pi
542542 11.7564i 0.504979i
543543 22.0739i 0.947280i
544544 4.70309 0.201643
545545 −5.95829 + 6.77060i −0.255225 + 0.290020i
546546 7.24619 0.310108
547547 14.0894i 0.602417i −0.953558 0.301209i 0.902610π-0.902610\pi
0.953558 0.301209i 0.0973901π-0.0973901\pi
548548 3.88566i 0.165987i
549549 −8.36086 −0.356833
550550 11.1131 1.42419i 0.473863 0.0607276i
551551 4.95113 0.210925
552552 5.11960i 0.217905i
553553 9.12564i 0.388062i
554554 −14.2745 −0.606465
555555 5.38124 6.11487i 0.228421 0.259562i
556556 −10.1033 −0.428473
557557 11.2428i 0.476374i −0.971219 0.238187i 0.923447π-0.923447\pi
0.971219 0.238187i 0.0765531π-0.0765531\pi
558558 3.72347i 0.157627i
559559 −6.12786 −0.259181
560560 8.37263 + 7.36812i 0.353808 + 0.311360i
561561 1.31823 0.0556557
562562 9.84579i 0.415320i
563563 22.1961i 0.935455i 0.883873 + 0.467727i 0.154927π0.154927\pi
−0.883873 + 0.467727i 0.845073π0.845073\pi
564564 −2.86397 −0.120595
565565 31.1139 + 27.3810i 1.30897 + 1.15193i
566566 43.7294 1.83808
567567 1.00000i 0.0419961i
568568 12.5851i 0.528057i
569569 −12.0342 −0.504500 −0.252250 0.967662i 0.581170π-0.581170\pi
−0.252250 + 0.967662i 0.581170π0.581170\pi
570570 −13.1054 + 14.8921i −0.548925 + 0.623762i
571571 −0.950397 −0.0397729 −0.0198864 0.999802i 0.506330π-0.506330\pi
−0.0198864 + 0.999802i 0.506330π0.506330\pi
572572 4.99841i 0.208994i
573573 18.4256i 0.769739i
574574 −17.1086 −0.714098
575575 13.4504 1.72373i 0.560921 0.0718844i
576576 1.98102 0.0825427
577577 11.5643i 0.481430i 0.970596 + 0.240715i 0.0773819π0.0773819\pi
−0.970596 + 0.240715i 0.922618π0.922618\pi
578578 1.69985i 0.0707044i
579579 −20.9313 −0.869873
580580 −1.24653 + 1.41647i −0.0517594 + 0.0588158i
581581 6.08519 0.252456
582582 12.4692i 0.516866i
583583 18.6102i 0.770756i
584584 −24.6942 −1.02185
585585 7.15571 + 6.29720i 0.295852 + 0.260357i
586586 −5.97350 −0.246763
587587 5.90911i 0.243895i −0.992537 0.121947i 0.961086π-0.961086\pi
0.992537 0.121947i 0.0389139π-0.0389139\pi
588588 0.889490i 0.0366820i
589589 −11.4322 −0.471054
590590 39.9761 + 35.1799i 1.64579 + 1.44833i
591591 −16.7970 −0.690936
592592 18.1694i 0.746759i
593593 42.4543i 1.74339i 0.490051 + 0.871694i 0.336978π0.336978\pi
−0.490051 + 0.871694i 0.663022π0.663022\pi
594594 −2.24079 −0.0919409
595595 −1.47723 + 1.67863i −0.0605606 + 0.0688170i
596596 −14.1168 −0.578249
597597 17.0325i 0.697093i
598598 19.6523i 0.803641i
599599 27.1576 1.10963 0.554815 0.831974i 0.312789π-0.312789\pi
0.554815 + 0.831974i 0.312789π0.312789\pi
600600 1.19977 + 9.36193i 0.0489804 + 0.382199i
601601 25.5859 1.04367 0.521836 0.853046i 0.325247π-0.325247\pi
0.521836 + 0.853046i 0.325247π0.325247\pi
602602 2.44355i 0.0995915i
603603 13.6284i 0.554990i
604604 −9.70241 −0.394786
605605 −13.6825 + 15.5479i −0.556273 + 0.632112i
606606 4.52320 0.183743
607607 23.6758i 0.960970i 0.877003 + 0.480485i 0.159539π0.159539\pi
−0.877003 + 0.480485i 0.840461π0.840461\pi
608608 24.5457i 0.995458i
609609 −0.948665 −0.0384419
610610 −23.8570 20.9947i −0.965941 0.850052i
611611 13.7254 0.555271
612612 0.889490i 0.0359555i
613613 34.1771i 1.38040i −0.723619 0.690199i 0.757523π-0.757523\pi
0.723619 0.690199i 0.242477π-0.242477\pi
614614 26.6708 1.07635
615615 −16.8950 14.8680i −0.681271 0.599535i
616616 2.48842 0.100261
617617 39.7875i 1.60178i −0.598810 0.800891i 0.704359π-0.704359\pi
0.598810 0.800891i 0.295641π-0.295641\pi
618618 14.6616i 0.589778i
619619 41.5801 1.67125 0.835623 0.549303i 0.185107π-0.185107\pi
0.835623 + 0.549303i 0.185107π0.185107\pi
620620 2.87824 3.27064i 0.115593 0.131352i
621621 −2.71209 −0.108832
622622 56.1165i 2.25007i
623623 0.0400448i 0.00160436i
624624 21.2621 0.851167
625625 −24.1921 + 6.30417i −0.967684 + 0.252167i
626626 3.34237 0.133588
627627 6.87991i 0.274757i
628628 4.50340i 0.179705i
629629 3.64278 0.145247
630630 2.51107 2.85341i 0.100044 0.113683i
631631 −28.5787 −1.13770 −0.568849 0.822442i 0.692611π-0.692611\pi
−0.568849 + 0.822442i 0.692611π0.692611\pi
632632 17.2265i 0.685232i
633633 10.1723i 0.404315i
634634 −49.4133 −1.96245
635635 −11.8094 10.3926i −0.468642 0.412416i
636636 −12.5574 −0.497935
637637 4.26284i 0.168900i
638638 2.12576i 0.0841598i
639639 6.66687 0.263737
640640 21.4421 + 18.8696i 0.847575 + 0.745887i
641641 13.0074 0.513760 0.256880 0.966443i 0.417306π-0.417306\pi
0.256880 + 0.966443i 0.417306π0.417306\pi
642642 32.7974i 1.29441i
643643 0.285527i 0.0112601i −0.999984 0.00563003i 0.998208π-0.998208\pi
0.999984 0.00563003i 0.00179211π-0.00179211\pi
644644 −2.41237 −0.0950608
645645 −2.12353 + 2.41304i −0.0836139 + 0.0950132i
646646 −8.87160 −0.349048
647647 14.0337i 0.551722i −0.961198 0.275861i 0.911037π-0.911037\pi
0.961198 0.275861i 0.0889629π-0.0889629\pi
648648 1.88770i 0.0741559i
649649 18.4683 0.724944
650650 4.60548 + 35.9370i 0.180642 + 1.40957i
651651 2.19047 0.0858512
652652 12.4206i 0.486427i
653653 23.1312i 0.905193i 0.891715 + 0.452597i 0.149502π0.149502\pi
−0.891715 + 0.452597i 0.850498π0.850498\pi
654654 6.85620 0.268099
655655 −3.68440 + 4.18670i −0.143961 + 0.163588i
656656 −50.2009 −1.96001
657657 13.0816i 0.510363i
658658 5.47315i 0.213366i
659659 20.8210 0.811072 0.405536 0.914079i 0.367085π-0.367085\pi
0.405536 + 0.914079i 0.367085π0.367085\pi
660660 −1.96828 1.73213i −0.0766151 0.0674232i
661661 −20.3681 −0.792229 −0.396114 0.918201i 0.629642π-0.629642\pi
−0.396114 + 0.918201i 0.629642π0.629642\pi
662662 50.6198i 1.96740i
663663 4.26284i 0.165555i
664664 11.4870 0.445782
665665 −8.76083 7.70974i −0.339731 0.298971i
666666 −6.19219 −0.239942
667667 2.57286i 0.0996216i
668668 17.8765i 0.691663i
669669 2.54258 0.0983019
670670 −34.2218 + 38.8873i −1.32210 + 1.50235i
671671 −11.0215 −0.425482
672672 4.70309i 0.181426i
673673 11.0671i 0.426604i 0.976986 + 0.213302i 0.0684219π0.0684219\pi
−0.976986 + 0.213302i 0.931578π0.931578\pi
674674 −54.1674 −2.08645
675675 4.95944 0.635573i 0.190889 0.0244632i
676676 4.60026 0.176933
677677 1.98385i 0.0762456i −0.999273 0.0381228i 0.987862π-0.987862\pi
0.999273 0.0381228i 0.0121378π-0.0121378\pi
678678 31.5073i 1.21003i
679679 7.33549 0.281510
680680 −2.78857 + 3.16874i −0.106937 + 0.121516i
681681 −10.5749 −0.405232
682682 4.90839i 0.187952i
683683 45.6910i 1.74832i 0.485641 + 0.874158i 0.338586π0.338586\pi
−0.485641 + 0.874158i 0.661414π0.661414\pi
684684 4.64229 0.177503
685685 7.33293 + 6.45315i 0.280177 + 0.246562i
686686 1.69985 0.0649006
687687 16.7374i 0.638573i
688688 7.16998i 0.273353i
689689 60.1809 2.29271
690690 −7.73870 6.81024i −0.294607 0.259262i
691691 0.629981 0.0239656 0.0119828 0.999928i 0.496186π-0.496186\pi
0.0119828 + 0.999928i 0.496186π0.496186\pi
692692 8.59990i 0.326919i
693693 1.31823i 0.0500754i
694694 −2.75569 −0.104605
695695 16.7791 19.0666i 0.636467 0.723239i
696696 −1.79080 −0.0678799
697697 10.0648i 0.381230i
698698 41.1919i 1.55913i
699699 −5.57246 −0.210770
700700 4.41137 0.565336i 0.166734 0.0213677i
701701 10.2343 0.386545 0.193272 0.981145i 0.438090π-0.438090\pi
0.193272 + 0.981145i 0.438090π0.438090\pi
702702 7.24619i 0.273490i
703703 19.0119i 0.717046i
704704 2.61145 0.0984226
705705 4.75637 5.40481i 0.179135 0.203557i
706706 −22.2973 −0.839170
707707 2.66094i 0.100075i
708708 12.4617i 0.468339i
709709 −7.85615 −0.295044 −0.147522 0.989059i 0.547130π-0.547130\pi
−0.147522 + 0.989059i 0.547130π0.547130\pi
710710 19.0233 + 16.7410i 0.713933 + 0.628278i
711711 −9.12564 −0.342238
712712 0.0755925i 0.00283295i
713713 5.94074i 0.222482i
714714 1.69985 0.0636153
715715 9.43288 + 8.30116i 0.352770 + 0.310446i
716716 1.80855 0.0675888
717717 12.4766i 0.465945i
718718 0.994168i 0.0371020i
719719 −0.739304 −0.0275714 −0.0137857 0.999905i 0.504388π-0.504388\pi
−0.0137857 + 0.999905i 0.504388π0.504388\pi
720720 7.36812 8.37263i 0.274594 0.312030i
721721 8.62526 0.321221
722722 14.0042i 0.521181i
723723 10.1786i 0.378545i
724724 −19.6345 −0.729710
725725 −0.602946 4.70485i −0.0223928 0.174734i
726726 15.7445 0.584332
727727 34.2680i 1.27093i 0.772129 + 0.635465i 0.219192π0.219192\pi
−0.772129 + 0.635465i 0.780808π0.780808\pi
728728 8.04696i 0.298240i
729729 −1.00000 −0.0370370
730730 −32.8489 + 37.3273i −1.21579 + 1.38154i
731731 −1.43751 −0.0531681
732732 7.43690i 0.274876i
733733 32.0094i 1.18229i 0.806564 + 0.591147i 0.201325π0.201325\pi
−0.806564 + 0.591147i 0.798675π0.798675\pi
734734 −34.0253 −1.25590
735735 1.67863 + 1.47723i 0.0619171 + 0.0544885i
736736 −12.7552 −0.470162
737737 17.9653i 0.661761i
738738 17.1086i 0.629775i
739739 −37.4413 −1.37730 −0.688650 0.725094i 0.741796π-0.741796\pi
−0.688650 + 0.725094i 0.741796π0.741796\pi
740740 −5.43912 4.78656i −0.199946 0.175957i
741741 −22.2480 −0.817299
742742 23.9978i 0.880985i
743743 49.8815i 1.82997i 0.403484 + 0.914987i 0.367799π0.367799\pi
−0.403484 + 0.914987i 0.632201π0.632201\pi
744744 4.13495 0.151595
745745 23.4447 26.6410i 0.858948 0.976050i
746746 −32.0671 −1.17406
747747 6.08519i 0.222645i
748748 1.17255i 0.0428728i
749749 −19.2943 −0.704997
750750 15.7473 + 10.6400i 0.575010 + 0.388516i
751751 27.9959 1.02158 0.510792 0.859704i 0.329352π-0.329352\pi
0.510792 + 0.859704i 0.329352π0.329352\pi
752752 16.0596i 0.585633i
753753 5.67410i 0.206776i
754754 −6.87421 −0.250344
755755 16.1134 18.3102i 0.586427 0.666376i
756756 −0.889490 −0.0323505
757757 39.6490i 1.44107i 0.693419 + 0.720534i 0.256103π0.256103\pi
−0.693419 + 0.720534i 0.743897π0.743897\pi
758758 34.8389i 1.26540i
759759 −3.57515 −0.129770
760760 −16.5378 14.5537i −0.599890 0.527918i
761761 25.0189 0.906933 0.453467 0.891273i 0.350187π-0.350187\pi
0.453467 + 0.891273i 0.350187π0.350187\pi
762762 11.9587i 0.433218i
763763 4.03341i 0.146019i
764764 −16.3894 −0.592947
765765 1.67863 + 1.47723i 0.0606909 + 0.0534094i
766766 23.5840 0.852123
767767 59.7220i 2.15644i
768768 17.7512i 0.640541i
769769 39.9051 1.43901 0.719507 0.694486i 0.244368π-0.244368\pi
0.719507 + 0.694486i 0.244368π0.244368\pi
770770 3.31017 3.76146i 0.119290 0.135553i
771771 −18.9299 −0.681744
772772 18.6182i 0.670082i
773773 31.4649i 1.13171i 0.824503 + 0.565857i 0.191455π0.191455\pi
−0.824503 + 0.565857i 0.808545π0.808545\pi
774774 2.44355 0.0878314
775775 1.39220 + 10.8635i 0.0500094 + 0.390228i
776776 13.8472 0.497086
777777 3.64278i 0.130684i
778778 60.8791i 2.18262i
779779 52.5285 1.88203
780780 5.60130 6.36494i 0.200559 0.227901i
781781 8.78847 0.314476
782782 4.61014i 0.164858i
783783 0.948665i 0.0339025i
784784 4.98779 0.178135
785785 8.49872 + 7.47908i 0.303332 + 0.266940i
786786 4.23963 0.151223
787787 3.16406i 0.112787i 0.998409 + 0.0563933i 0.0179601π0.0179601\pi
−0.998409 + 0.0563933i 0.982040π0.982040\pi
788788 14.9408i 0.532243i
789789 4.50632 0.160429
790790 −26.0392 22.9152i −0.926434 0.815284i
791791 18.5353 0.659041
792792 2.48842i 0.0884223i
793793 35.6410i 1.26565i
794794 −27.4280 −0.973384
795795 20.8549 23.6981i 0.739648 0.840486i
796796 15.1502 0.536986
797797 53.2495i 1.88619i 0.332519 + 0.943097i 0.392102π0.392102\pi
−0.332519 + 0.943097i 0.607898π0.607898\pi
798798 8.87160i 0.314051i
799799 3.21978 0.113908
800800 23.3247 2.98916i 0.824653 0.105683i
801801 0.0400448 0.00141491
802802 17.9639i 0.634326i
803803 17.2446i 0.608549i
804804 12.1223 0.427520
805805 4.00638 4.55258i 0.141206 0.160457i
806806 15.8725 0.559087
807807 6.65868i 0.234396i
808808 5.02306i 0.176711i
809809 −44.4117 −1.56143 −0.780716 0.624886i 0.785145π-0.785145\pi
−0.780716 + 0.624886i 0.785145π0.785145\pi
810810 −2.85341 2.51107i −0.100259 0.0882301i
811811 12.0589 0.423445 0.211723 0.977330i 0.432093π-0.432093\pi
0.211723 + 0.977330i 0.432093π0.432093\pi
812812 0.843829i 0.0296126i
813813 6.91612i 0.242559i
814814 −8.16273 −0.286103
815815 23.4398 + 20.6276i 0.821060 + 0.722553i
816816 4.98779 0.174607
817817 7.50242i 0.262476i
818818 28.5453i 0.998064i
819819 4.26284 0.148956
820820 −13.2249 + 15.0279i −0.461834 + 0.524797i
821821 34.5235 1.20488 0.602440 0.798165i 0.294195π-0.294195\pi
0.602440 + 0.798165i 0.294195π0.294195\pi
822822 7.42564i 0.258999i
823823 7.07375i 0.246576i 0.992371 + 0.123288i 0.0393438π0.0393438\pi
−0.992371 + 0.123288i 0.960656π0.960656\pi
824824 16.2819 0.567207
825825 6.53768 0.837831i 0.227613 0.0291695i
826826 23.8148 0.828621
827827 26.2151i 0.911589i −0.890085 0.455795i 0.849355π-0.849355\pi
0.890085 0.455795i 0.150645π-0.150645\pi
828828 2.41237i 0.0838358i
829829 −21.0062 −0.729577 −0.364788 0.931090i 0.618859π-0.618859\pi
−0.364788 + 0.931090i 0.618859π0.618859\pi
830830 15.2803 17.3636i 0.530389 0.602698i
831831 −8.39750 −0.291306
832832 8.44479i 0.292770i
833833 1.00000i 0.0346479i
834834 −19.3077 −0.668571
835835 33.7362 + 29.6886i 1.16749 + 1.02742i
836836 6.11961 0.211651
837837 2.19047i 0.0757137i
838838 25.7348i 0.888995i
839839 33.1058 1.14294 0.571469 0.820624i 0.306374π-0.306374\pi
0.571469 + 0.820624i 0.306374π0.306374\pi
840840 3.16874 + 2.78857i 0.109332 + 0.0962148i
841841 −28.1000 −0.968967
842842 29.2011i 1.00634i
843843 5.79215i 0.199492i
844844 9.04821 0.311452
845845 −7.63994 + 8.68151i −0.262822 + 0.298653i
846846 −5.47315 −0.188171
847847 9.26227i 0.318255i
848848 70.4154i 2.41808i
849849 25.7255 0.882895
850850 1.08038 + 8.43031i 0.0370567 + 0.289157i
851851 −9.87954 −0.338666
852852 5.93012i 0.203163i
853853 30.3394i 1.03880i −0.854531 0.519401i 0.826155π-0.826155\pi
0.854531 0.519401i 0.173845π-0.173845\pi
854854 −14.2122 −0.486332
855855 −7.70974 + 8.76083i −0.263668 + 0.299614i
856856 −36.4218 −1.24487
857857 21.2155i 0.724708i 0.932041 + 0.362354i 0.118027π0.118027\pi
−0.932041 + 0.362354i 0.881973π0.881973\pi
858858 9.55214i 0.326105i
859859 9.64903 0.329221 0.164610 0.986359i 0.447363π-0.447363\pi
0.164610 + 0.986359i 0.447363π0.447363\pi
860860 2.14637 + 1.88886i 0.0731907 + 0.0644096i
861861 −10.0648 −0.343006
862862 57.8479i 1.97031i
863863 15.2145i 0.517906i −0.965890 0.258953i 0.916622π-0.916622\pi
0.965890 0.258953i 0.0833776π-0.0833776\pi
864864 −4.70309 −0.160002
865865 −16.2295 14.2824i −0.551821 0.485616i
866866 −27.3013 −0.927735
867867 1.00000i 0.0339618i
868868 1.94840i 0.0661330i
869869 −12.0297 −0.408080
870870 −2.38217 + 2.70693i −0.0807630 + 0.0917737i
871871 −58.0955 −1.96849
872872 7.61388i 0.257838i
873873 7.33549i 0.248269i
874874 24.0605 0.813860
875875 −6.25935 + 9.26394i −0.211605 + 0.313178i
876876 11.6360 0.393143
877877 53.5867i 1.80949i −0.425949 0.904747i 0.640060π-0.640060\pi
0.425949 0.904747i 0.359940π-0.359940\pi
878878 17.2485i 0.582109i
879879 −3.51413 −0.118529
880880 9.71288 11.0371i 0.327421 0.372059i
881881 −24.1273 −0.812870 −0.406435 0.913680i 0.633228π-0.633228\pi
−0.406435 + 0.913680i 0.633228π0.633228\pi
882882 1.69985i 0.0572369i
883883 41.1894i 1.38614i −0.720873 0.693068i 0.756259π-0.756259\pi
0.720873 0.693068i 0.243741π-0.243741\pi
884884 3.79175 0.127531
885885 23.5174 + 20.6959i 0.790529 + 0.695685i
886886 35.0523 1.17761
887887 13.5093i 0.453599i 0.973942 + 0.226799i 0.0728261π0.0728261\pi
−0.973942 + 0.226799i 0.927174π0.927174\pi
888888 6.87648i 0.230760i
889889 −7.03516 −0.235952
890890 0.114264 + 0.100555i 0.00383015 + 0.00337062i
891891 −1.31823 −0.0441624
892892 2.26160i 0.0757241i
893893 16.8042i 0.562331i
894894 −26.9778 −0.902274
895895 −3.00357 + 3.41306i −0.100398 + 0.114086i
896896 12.7736 0.426737
897897 11.5612i 0.386017i
898898 27.4084i 0.914631i
899899 −2.07802 −0.0693059
900900 −0.565336 4.41137i −0.0188445 0.147046i
901901 14.1176 0.470324
902902 22.5530i 0.750934i
903903 1.43751i 0.0478372i
904904 34.9892 1.16372
905905 32.6082 37.0538i 1.08393 1.23171i
906906 −18.5417 −0.616006
907907 47.6075i 1.58078i 0.612603 + 0.790391i 0.290123π0.290123\pi
−0.612603 + 0.790391i 0.709877π0.709877\pi
908908 9.40630i 0.312159i
909909 2.66094 0.0882579
910910 12.1636 + 10.7043i 0.403221 + 0.354844i
911911 22.5367 0.746674 0.373337 0.927696i 0.378214π-0.378214\pi
0.373337 + 0.927696i 0.378214π0.378214\pi
912912 26.0315i 0.861989i
913913 8.02168i 0.265479i
914914 −15.1727 −0.501870
915915 −14.0348 12.3509i −0.463975 0.408309i
916916 −14.8878 −0.491906
917917 2.49412i 0.0823632i
918918 1.69985i 0.0561034i
919919 −21.8566 −0.720982 −0.360491 0.932763i 0.617391π-0.617391\pi
−0.360491 + 0.932763i 0.617391π0.617391\pi
920920 7.56284 8.59390i 0.249339 0.283333i
921921 15.6901 0.517006
922922 26.6387i 0.877299i
923923 28.4198i 0.935449i
924924 −1.17255 −0.0385742
925925 18.0662 2.31525i 0.594012 0.0761251i
926926 −34.1251 −1.12142
927927 8.62526i 0.283291i
928928 4.46166i 0.146461i
929929 34.2174 1.12264 0.561318 0.827600i 0.310294π-0.310294\pi
0.561318 + 0.827600i 0.310294π0.310294\pi
930930 5.50043 6.25031i 0.180366 0.204956i
931931 −5.21905 −0.171047
932932 4.95665i 0.162360i
933933 33.0126i 1.08078i
934934 34.5021 1.12894
935935 2.21282 + 1.94733i 0.0723668 + 0.0636846i
936936 8.04696 0.263023
937937 31.9632i 1.04419i 0.852887 + 0.522095i 0.174849π0.174849\pi
−0.852887 + 0.522095i 0.825151π0.825151\pi
938938 23.1662i 0.756402i
939939 1.96627 0.0641669
940940 −4.80753 4.23074i −0.156804 0.137992i
941941 −7.31089 −0.238328 −0.119164 0.992875i 0.538021π-0.538021\pi
−0.119164 + 0.992875i 0.538021π0.538021\pi
942942 8.60617i 0.280404i
943943 27.2965i 0.888896i
944944 69.8785 2.27435
945945 1.47723 1.67863i 0.0480544 0.0546057i
946946 3.22116 0.104729
947947 19.7154i 0.640664i −0.947305 0.320332i 0.896205π-0.896205\pi
0.947305 0.320332i 0.103795π-0.103795\pi
948948 8.11717i 0.263633i
949949 −55.7649 −1.81020
950950 −43.9982 + 5.63855i −1.42749 + 0.182939i
951951 −29.0692 −0.942635
952952 1.88770i 0.0611807i
953953 36.8324i 1.19312i 0.802569 + 0.596560i 0.203466π0.203466\pi
−0.802569 + 0.596560i 0.796534π0.796534\pi
954954 −23.9978 −0.776956
955955 27.2188 30.9297i 0.880781 1.00086i
956956 11.0978 0.358928
957957 1.25056i 0.0404248i
958958 69.2346i 2.23687i
959959 4.36841 0.141063
960960 3.32540 + 2.92643i 0.107327 + 0.0944502i
961961 −26.2018 −0.845221
962962 26.3963i 0.851051i
963963 19.2943i 0.621749i
964964 −9.05373 −0.291601
965965 −35.1358 30.9203i −1.13106 0.995360i
966966 −4.61014 −0.148329
967967 24.8807i 0.800109i −0.916491 0.400054i 0.868991π-0.868991\pi
0.916491 0.400054i 0.131009π-0.131009\pi
968968 17.4844i 0.561969i
969969 −5.21905 −0.167660
970970 18.4199 20.9312i 0.591429 0.672060i
971971 −37.8289 −1.21399 −0.606993 0.794707i 0.707625π-0.707625\pi
−0.606993 + 0.794707i 0.707625π0.707625\pi
972972 0.889490i 0.0285304i
973973 11.3585i 0.364136i
974974 −48.9279 −1.56775
975975 2.70934 + 21.1413i 0.0867685 + 0.677063i
976976 −41.7022 −1.33485
977977 59.8958i 1.91624i 0.286374 + 0.958118i 0.407550π0.407550\pi
−0.286374 + 0.958118i 0.592450π0.592450\pi
978978 23.7362i 0.758999i
979979 0.0527883 0.00168712
980980 1.31398 1.49312i 0.0419737 0.0476960i
981981 4.03341 0.128777
982982 9.02276i 0.287928i
983983 40.5495i 1.29333i −0.762775 0.646664i 0.776164π-0.776164\pi
0.762775 0.646664i 0.223836π-0.223836\pi
984984 −18.9992 −0.605674
985985 −28.1959 24.8131i −0.898396 0.790610i
986986 −1.61259 −0.0513553
987987 3.21978i 0.102487i
988988 19.7894i 0.629583i
989989 3.89864 0.123970
990990 −3.76146 3.31017i −0.119547 0.105204i
991991 −38.2772 −1.21591 −0.607957 0.793970i 0.708011π-0.708011\pi
−0.607957 + 0.793970i 0.708011π0.708011\pi
992992 10.3020i 0.327088i
993993 29.7790i 0.945008i
994994 11.3327 0.359451
995995 −25.1609 + 28.5912i −0.797655 + 0.906401i
996996 −5.41272 −0.171508
997997 27.4621i 0.869732i −0.900495 0.434866i 0.856796π-0.856796\pi
0.900495 0.434866i 0.143204π-0.143204\pi
998998 19.6458i 0.621876i
999999 −3.64278 −0.115253
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 1785.2.g.f.1429.8 28
5.2 odd 4 8925.2.a.cw.1.10 14
5.3 odd 4 8925.2.a.cv.1.5 14
5.4 even 2 inner 1785.2.g.f.1429.21 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1785.2.g.f.1429.8 28 1.1 even 1 trivial
1785.2.g.f.1429.21 yes 28 5.4 even 2 inner
8925.2.a.cv.1.5 14 5.3 odd 4
8925.2.a.cw.1.10 14 5.2 odd 4