Properties

Label 63.6.e.d.37.2
Level 6363
Weight 66
Character 63.37
Analytic conductor 10.10410.104
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,6,Mod(37,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 63=327 63 = 3^{2} \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 63.e (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 10.104180648210.1041806482
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(3,37)\Q(\sqrt{-3}, \sqrt{37})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x3+10x2+9x+81 x^{4} - x^{3} + 10x^{2} + 9x + 81 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 37.2
Root 1.770693.06693i1.77069 - 3.06693i of defining polynomial
Character χ\chi == 63.37
Dual form 63.6.e.d.46.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(3.541386.13385i)q2+(9.0827615.7318i)q4+(39.9138+69.1328i)q5+(43.1587+122.247i)q7+97.9863q8+(282.700+489.651i)q10+(175.952+304.757i)q11291.683q13+(902.686+168.194i)q14+(637.6551104.45i)q16+(185.038320.495i)q17+(752.463+1303.30i)q19+1450.11q20+2492.45q22+(212.855+368.676i)q23+(1623.722812.37i)q25+(1032.96+1789.14i)q26+(1531.171789.30i)q28+7783.93q29+(1287.59+2230.17i)q31+(2948.585107.09i)q322621.16q34+(10173.91895.67i)q35+(369.809+640.528i)q37+(5329.51+9230.99i)q38+(3911.01+6774.06i)q407029.84q41+1835.23q43+(3196.265536.08i)q44+(1507.60+2611.25i)q46+(766.342+1327.34i)q47+(13081.7+10552.0i)q4923000.9q50+(2649.28+4588.69i)q52+(4768.738259.68i)q5328091.6q55+(4228.96+11978.5i)q56+(27565.947745.5i)q58+(14837.025698.5i)q59+(23255.440279.5i)q61+18239.4q62958.246q64+(11642.220164.8i)q65+(13373.023162.8i)q67+(3361.31+5821.95i)q68+(47657.4+55691.9i)q70+14388.8q71+(35047.6+60704.2i)q73+(2619.27+4536.71i)q74+27337.8q76+(29661.8+34662.5i)q77+(13542.923457.0i)q79+(50902.5+88165.7i)q80+(24895.3+43120.0i)q82+79755.4q83+29542.2q85+(6499.2611257.0i)q86+(17240.9+29862.1i)q88+(21788.737739.1i)q89+(12588.635657.3i)q91+7733.26q92+(5427.82+9401.25i)q94+(60067.3104040.i)q95+103374.q97+(18397.5+117610.i)q98+O(q100)q+(3.54138 - 6.13385i) q^{2} +(-9.08276 - 15.7318i) q^{4} +(-39.9138 + 69.1328i) q^{5} +(43.1587 + 122.247i) q^{7} +97.9863 q^{8} +(282.700 + 489.651i) q^{10} +(175.952 + 304.757i) q^{11} -291.683 q^{13} +(902.686 + 168.194i) q^{14} +(637.655 - 1104.45i) q^{16} +(-185.038 - 320.495i) q^{17} +(-752.463 + 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(-212.855 + 368.676i) q^{23} +(-1623.72 - 2812.37i) q^{25} +(-1032.96 + 1789.14i) q^{26} +(1531.17 - 1789.30i) q^{28} +7783.93 q^{29} +(1287.59 + 2230.17i) q^{31} +(-2948.58 - 5107.09i) q^{32} -2621.16 q^{34} +(-10173.9 - 1895.67i) q^{35} +(-369.809 + 640.528i) q^{37} +(5329.51 + 9230.99i) q^{38} +(-3911.01 + 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(3196.26 - 5536.08i) q^{44} +(1507.60 + 2611.25i) q^{46} +(-766.342 + 1327.34i) q^{47} +(-13081.7 + 10552.0i) q^{49} -23000.9 q^{50} +(2649.28 + 4588.69i) q^{52} +(-4768.73 - 8259.68i) q^{53} -28091.6 q^{55} +(4228.96 + 11978.5i) q^{56} +(27565.9 - 47745.5i) q^{58} +(-14837.0 - 25698.5i) q^{59} +(23255.4 - 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(11642.2 - 20164.8i) q^{65} +(-13373.0 - 23162.8i) q^{67} +(-3361.31 + 5821.95i) q^{68} +(-47657.4 + 55691.9i) q^{70} +14388.8 q^{71} +(35047.6 + 60704.2i) q^{73} +(2619.27 + 4536.71i) q^{74} +27337.8 q^{76} +(-29661.8 + 34662.5i) q^{77} +(13542.9 - 23457.0i) q^{79} +(50902.5 + 88165.7i) q^{80} +(-24895.3 + 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(6499.26 - 11257.0i) q^{86} +(17240.9 + 29862.1i) q^{88} +(21788.7 - 37739.1i) q^{89} +(-12588.6 - 35657.3i) q^{91} +7733.26 q^{92} +(5427.82 + 9401.25i) q^{94} +(-60067.3 - 104040. i) q^{95} +103374. q^{97} +(18397.5 + 117610. i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q212q438q5168q7192q8+778q10+424q111848q13+2674q14+2064q162346q17+360q19+3416q20+4252q2212q231872q25+98686q98+O(q100) 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25}+ \cdots - 98686 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/63Z)×\left(\mathbb{Z}/63\mathbb{Z}\right)^\times.

nn 1010 2929
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 3.54138 6.13385i 0.626034 1.08432i −0.362306 0.932059i 0.618011π-0.618011\pi
0.988340 0.152263i 0.0486561π-0.0486561\pi
33 0 0
44 −9.08276 15.7318i −0.283836 0.491619i
55 −39.9138 + 69.1328i −0.714000 + 1.23668i 0.249344 + 0.968415i 0.419785π0.419785\pi
−0.963344 + 0.268269i 0.913548π0.913548\pi
66 0 0
77 43.1587 + 122.247i 0.332907 + 0.942960i
88 97.9863 0.541303
99 0 0
1010 282.700 + 489.651i 0.893976 + 1.54841i
1111 175.952 + 304.757i 0.438442 + 0.759403i 0.997570 0.0696781i 0.0221972π-0.0221972\pi
−0.559128 + 0.829082i 0.688864π0.688864\pi
1212 0 0
1313 −291.683 −0.478688 −0.239344 0.970935i 0.576932π-0.576932\pi
−0.239344 + 0.970935i 0.576932π0.576932\pi
1414 902.686 + 168.194i 1.23088 + 0.229346i
1515 0 0
1616 637.655 1104.45i 0.622710 1.07857i
1717 −185.038 320.495i −0.155288 0.268967i 0.777876 0.628418i 0.216297π-0.216297\pi
−0.933164 + 0.359451i 0.882964π0.882964\pi
1818 0 0
1919 −752.463 + 1303.30i −0.478190 + 0.828250i −0.999687 0.0250030i 0.992040π-0.992040\pi
0.521497 + 0.853253i 0.325374π0.325374\pi
2020 1450.11 0.810637
2121 0 0
2222 2492.45 1.09792
2323 −212.855 + 368.676i −0.0839006 + 0.145320i −0.904922 0.425577i 0.860071π-0.860071\pi
0.821022 + 0.570897i 0.193404π0.193404\pi
2424 0 0
2525 −1623.72 2812.37i −0.519592 0.899960i
2626 −1032.96 + 1789.14i −0.299675 + 0.519052i
2727 0 0
2828 1531.17 1789.30i 0.369086 0.431310i
2929 7783.93 1.71872 0.859358 0.511374i 0.170863π-0.170863\pi
0.859358 + 0.511374i 0.170863π0.170863\pi
3030 0 0
3131 1287.59 + 2230.17i 0.240643 + 0.416805i 0.960898 0.276904i 0.0893085π-0.0893085\pi
−0.720255 + 0.693710i 0.755975π0.755975\pi
3232 −2948.58 5107.09i −0.509024 0.881655i
3333 0 0
3434 −2621.16 −0.388862
3535 −10173.9 1895.67i −1.40384 0.261572i
3636 0 0
3737 −369.809 + 640.528i −0.0444092 + 0.0769190i −0.887376 0.461047i 0.847474π-0.847474\pi
0.842966 + 0.537966i 0.180807π0.180807\pi
3838 5329.51 + 9230.99i 0.598727 + 1.03703i
3939 0 0
4040 −3911.01 + 6774.06i −0.386490 + 0.669421i
4141 −7029.84 −0.653109 −0.326554 0.945178i 0.605888π-0.605888\pi
−0.326554 + 0.945178i 0.605888π0.605888\pi
4242 0 0
4343 1835.23 0.151363 0.0756816 0.997132i 0.475887π-0.475887\pi
0.0756816 + 0.997132i 0.475887π0.475887\pi
4444 3196.26 5536.08i 0.248891 0.431093i
4545 0 0
4646 1507.60 + 2611.25i 0.105049 + 0.181950i
4747 −766.342 + 1327.34i −0.0506032 + 0.0876473i −0.890217 0.455536i 0.849448π-0.849448\pi
0.839614 + 0.543183i 0.182781π0.182781\pi
4848 0 0
4949 −13081.7 + 10552.0i −0.778346 + 0.627836i
5050 −23000.9 −1.30113
5151 0 0
5252 2649.28 + 4588.69i 0.135869 + 0.235332i
5353 −4768.73 8259.68i −0.233192 0.403900i 0.725554 0.688165i 0.241584π-0.241584\pi
−0.958746 + 0.284265i 0.908250π0.908250\pi
5454 0 0
5555 −28091.6 −1.25219
5656 4228.96 + 11978.5i 0.180204 + 0.510427i
5757 0 0
5858 27565.9 47745.5i 1.07597 1.86364i
5959 −14837.0 25698.5i −0.554903 0.961120i −0.997911 0.0646022i 0.979422π-0.979422\pi
0.443008 0.896517i 0.353911π-0.353911\pi
6060 0 0
6161 23255.4 40279.5i 0.800201 1.38599i −0.119282 0.992860i 0.538059π-0.538059\pi
0.919483 0.393129i 0.128607π-0.128607\pi
6262 18239.4 0.602602
6363 0 0
6464 −958.246 −0.0292434
6565 11642.2 20164.8i 0.341783 0.591985i
6666 0 0
6767 −13373.0 23162.8i −0.363951 0.630381i 0.624656 0.780900i 0.285239π-0.285239\pi
−0.988607 + 0.150518i 0.951906π0.951906\pi
6868 −3361.31 + 5821.95i −0.0881527 + 0.152685i
6969 0 0
7070 −47657.4 + 55691.9i −1.16248 + 1.35846i
7171 14388.8 0.338748 0.169374 0.985552i 0.445825π-0.445825\pi
0.169374 + 0.985552i 0.445825π0.445825\pi
7272 0 0
7373 35047.6 + 60704.2i 0.769752 + 1.33325i 0.937697 + 0.347453i 0.112953π0.112953\pi
−0.167946 + 0.985796i 0.553713π0.553713\pi
7474 2619.27 + 4536.71i 0.0556033 + 0.0963078i
7575 0 0
7676 27337.8 0.542911
7777 −29661.8 + 34662.5i −0.570126 + 0.666244i
7878 0 0
7979 13542.9 23457.0i 0.244143 0.422868i −0.717748 0.696303i 0.754827π-0.754827\pi
0.961890 + 0.273436i 0.0881601π0.0881601\pi
8080 50902.5 + 88165.7i 0.889230 + 1.54019i
8181 0 0
8282 −24895.3 + 43120.0i −0.408868 + 0.708181i
8383 79755.4 1.27076 0.635382 0.772198i 0.280843π-0.280843\pi
0.635382 + 0.772198i 0.280843π0.280843\pi
8484 0 0
8585 29542.2 0.443502
8686 6499.26 11257.0i 0.0947584 0.164126i
8787 0 0
8888 17240.9 + 29862.1i 0.237330 + 0.411067i
8989 21788.7 37739.1i 0.291579 0.505029i −0.682605 0.730788i 0.739153π-0.739153\pi
0.974183 + 0.225759i 0.0724862π0.0724862\pi
9090 0 0
9191 −12588.6 35657.3i −0.159358 0.451383i
9292 7733.26 0.0952561
9393 0 0
9494 5427.82 + 9401.25i 0.0633586 + 0.109740i
9595 −60067.3 104040.i −0.682856 1.18274i
9696 0 0
9797 103374. 1.11553 0.557765 0.829999i 0.311659π-0.311659\pi
0.557765 + 0.829999i 0.311659π0.311659\pi
9898 18397.5 + 117610.i 0.193506 + 1.23702i
9999 0 0
100100 −29495.8 + 51088.3i −0.294958 + 0.510883i
101101 14350.1 + 24855.1i 0.139975 + 0.242444i 0.927487 0.373855i 0.121964π-0.121964\pi
−0.787512 + 0.616300i 0.788631π0.788631\pi
102102 0 0
103103 −14614.0 + 25312.1i −0.135730 + 0.235091i −0.925876 0.377828i 0.876671π-0.876671\pi
0.790146 + 0.612918i 0.210005π0.210005\pi
104104 −28580.9 −0.259115
105105 0 0
106106 −67551.6 −0.583944
107107 43929.2 76087.6i 0.370932 0.642472i −0.618778 0.785566i 0.712372π-0.712372\pi
0.989709 + 0.143094i 0.0457051π0.0457051\pi
108108 0 0
109109 −110314. 191069.i −0.889333 1.54037i −0.840665 0.541555i 0.817836π-0.817836\pi
−0.0486678 0.998815i 0.515498π-0.515498\pi
110110 −99483.2 + 172310.i −0.783913 + 1.35778i
111111 0 0
112112 162536. + 30284.8i 1.22435 + 0.228128i
113113 −39665.6 −0.292225 −0.146113 0.989268i 0.546676π-0.546676\pi
−0.146113 + 0.989268i 0.546676π0.546676\pi
114114 0 0
115115 −16991.7 29430.5i −0.119810 0.207517i
116116 −70699.6 122455.i −0.487834 0.844953i
117117 0 0
118118 −210174. −1.38955
119119 31193.5 36452.4i 0.201928 0.235971i
120120 0 0
121121 18607.4 32229.0i 0.115538 0.200117i
122122 −164712. 285290.i −1.00191 1.73535i
123123 0 0
124124 23389.7 40512.2i 0.136606 0.236609i
125125 9774.87 0.0559546
126126 0 0
127127 51740.3 0.284655 0.142328 0.989820i 0.454541π-0.454541\pi
0.142328 + 0.989820i 0.454541π0.454541\pi
128128 90961.0 157549.i 0.490716 0.849946i
129129 0 0
130130 −82458.7 142823.i −0.427935 0.741206i
131131 −83336.9 + 144344.i −0.424286 + 0.734885i −0.996353 0.0853215i 0.972808π-0.972808\pi
0.572067 + 0.820207i 0.306142π0.306142\pi
132132 0 0
133133 −191800. 35737.4i −0.940200 0.175184i
134134 −189436. −0.911382
135135 0 0
136136 −18131.2 31404.1i −0.0840578 0.145592i
137137 14129.7 + 24473.4i 0.0643178 + 0.111402i 0.896391 0.443264i 0.146180π-0.146180\pi
−0.832073 + 0.554666i 0.812846π0.812846\pi
138138 0 0
139139 336393. 1.47676 0.738380 0.674384i 0.235591π-0.235591\pi
0.738380 + 0.674384i 0.235591π0.235591\pi
140140 62584.9 + 177272.i 0.269867 + 0.764398i
141141 0 0
142142 50956.1 88258.5i 0.212068 0.367312i
143143 −51322.1 88892.4i −0.209877 0.363517i
144144 0 0
145145 −310686. + 538125.i −1.22716 + 2.12551i
146146 496467. 1.92756
147147 0 0
148148 13435.5 0.0504198
149149 −177691. + 307769.i −0.655691 + 1.13569i 0.326030 + 0.945360i 0.394289π0.394289\pi
−0.981720 + 0.190330i 0.939044π0.939044\pi
150150 0 0
151151 179399. + 310727.i 0.640290 + 1.10901i 0.985368 + 0.170441i 0.0545191π0.0545191\pi
−0.345078 + 0.938574i 0.612148π0.612148\pi
152152 −73731.0 + 127706.i −0.258846 + 0.448334i
153153 0 0
154154 107571. + 304694.i 0.365504 + 1.03529i
155155 −205570. −0.687275
156156 0 0
157157 −229455. 397428.i −0.742932 1.28680i −0.951155 0.308714i 0.900101π-0.900101\pi
0.208223 0.978081i 0.433232π-0.433232\pi
158158 −95921.1 166140.i −0.305683 0.529459i
159159 0 0
160160 470756. 1.45377
161161 −54256.1 10109.3i −0.164962 0.0307368i
162162 0 0
163163 −251220. + 435126.i −0.740603 + 1.28276i 0.211618 + 0.977353i 0.432127π0.432127\pi
−0.952221 + 0.305410i 0.901206π0.901206\pi
164164 63850.3 + 110592.i 0.185376 + 0.321081i
165165 0 0
166166 282444. 489208.i 0.795541 1.37792i
167167 676652. 1.87748 0.938738 0.344632i 0.111996π-0.111996\pi
0.938738 + 0.344632i 0.111996π0.111996\pi
168168 0 0
169169 −286214. −0.770858
170170 104620. 181208.i 0.277647 0.480900i
171171 0 0
172172 −16669.0 28871.5i −0.0429623 0.0744130i
173173 −124580. + 215779.i −0.316470 + 0.548143i −0.979749 0.200230i 0.935831π-0.935831\pi
0.663279 + 0.748373i 0.269164π0.269164\pi
174174 0 0
175175 273726. 319874.i 0.675650 0.789557i
176176 448786. 1.09209
177177 0 0
178178 −154324. 267297.i −0.365076 0.632330i
179179 69628.9 + 120601.i 0.162427 + 0.281331i 0.935738 0.352695i 0.114735π-0.114735\pi
−0.773312 + 0.634026i 0.781401π0.781401\pi
180180 0 0
181181 306246. 0.694823 0.347412 0.937713i 0.387061π-0.387061\pi
0.347412 + 0.937713i 0.387061π0.387061\pi
182182 −263298. 49059.4i −0.589209 0.109785i
183183 0 0
184184 −20856.9 + 36125.2i −0.0454156 + 0.0786622i
185185 −29521.0 51131.8i −0.0634163 0.109840i
186186 0 0
187187 65115.4 112783.i 0.136169 0.235852i
188188 27842.0 0.0574521
189189 0 0
190190 −850885. −1.70996
191191 113747. 197015.i 0.225609 0.390766i −0.730893 0.682492i 0.760896π-0.760896\pi
0.956502 + 0.291726i 0.0942295π0.0942295\pi
192192 0 0
193193 336187. + 582293.i 0.649663 + 1.12525i 0.983203 + 0.182513i 0.0584231π0.0584231\pi
−0.333541 + 0.942736i 0.608244π0.608244\pi
194194 366086. 634079.i 0.698359 1.20959i
195195 0 0
196196 284820. + 109956.i 0.529579 + 0.204447i
197197 1282.76 0.00235493 0.00117747 0.999999i 0.499625π-0.499625\pi
0.00117747 + 0.999999i 0.499625π0.499625\pi
198198 0 0
199199 −184449. 319475.i −0.330175 0.571879i 0.652371 0.757900i 0.273774π-0.273774\pi
−0.982546 + 0.186020i 0.940441π0.940441\pi
200200 −159103. 275574.i −0.281257 0.487151i
201201 0 0
202202 203277. 0.350517
203203 335944. + 951563.i 0.572173 + 1.62068i
204204 0 0
205205 280588. 485992.i 0.466320 0.807690i
206206 103507. + 179280.i 0.169943 + 0.294349i
207207 0 0
208208 −185993. + 322149.i −0.298084 + 0.516296i
209209 −529589. −0.838635
210210 0 0
211211 502168. 0.776503 0.388251 0.921553i 0.373079π-0.373079\pi
0.388251 + 0.921553i 0.373079π0.373079\pi
212212 −86626.5 + 150042.i −0.132377 + 0.229283i
213213 0 0
214214 −311140. 538910.i −0.464431 0.804419i
215215 −73251.1 + 126875.i −0.108073 + 0.187188i
216216 0 0
217217 −217061. + 253655.i −0.312919 + 0.365674i
218218 −1.56266e6 −2.22701
219219 0 0
220220 255150. + 441932.i 0.355417 + 0.615600i
221221 53972.3 + 93482.7i 0.0743344 + 0.128751i
222222 0 0
223223 −1.17328e6 −1.57993 −0.789967 0.613149i 0.789902π-0.789902\pi
−0.789967 + 0.613149i 0.789902π0.789902\pi
224224 497070. 580870.i 0.661907 0.773498i
225225 0 0
226226 −140471. + 243303.i −0.182943 + 0.316867i
227227 −455079. 788220.i −0.586168 1.01527i −0.994729 0.102542i 0.967302π-0.967302\pi
0.408560 0.912731i 0.366031π-0.366031\pi
228228 0 0
229229 −260962. + 452000.i −0.328843 + 0.569573i −0.982283 0.187406i 0.939992π-0.939992\pi
0.653439 + 0.756979i 0.273325π0.273325\pi
230230 −240697. −0.300020
231231 0 0
232232 762719. 0.930346
233233 −521394. + 903081.i −0.629182 + 1.08977i 0.358535 + 0.933516i 0.383277π0.383277\pi
−0.987716 + 0.156258i 0.950057π0.950057\pi
234234 0 0
235235 −61175.2 105959.i −0.0722613 0.125160i
236236 −269522. + 466826.i −0.315003 + 0.545601i
237237 0 0
238238 −113126. 320428.i −0.129455 0.366681i
239239 1.53447e6 1.73766 0.868830 0.495110i 0.164872π-0.164872\pi
0.868830 + 0.495110i 0.164872π0.164872\pi
240240 0 0
241241 503789. + 872588.i 0.558735 + 0.967758i 0.997602 + 0.0692059i 0.0220465π0.0220465\pi
−0.438867 + 0.898552i 0.644620π0.644620\pi
242242 −131792. 228271.i −0.144661 0.250560i
243243 0 0
244244 −844893. −0.908505
245245 −207353. 1.32554e6i −0.220696 1.41084i
246246 0 0
247247 219480. 380151.i 0.228904 0.396473i
248248 126166. + 218526.i 0.130261 + 0.225618i
249249 0 0
250250 34616.6 59957.6i 0.0350295 0.0606729i
251251 −8511.89 −0.00852789 −0.00426394 0.999991i 0.501357π-0.501357\pi
−0.00426394 + 0.999991i 0.501357π0.501357\pi
252252 0 0
253253 −149809. −0.147142
254254 183232. 317367.i 0.178204 0.308658i
255255 0 0
256256 −659587. 1.14244e6i −0.629032 1.08951i
257257 −263766. + 456856.i −0.249107 + 0.431466i −0.963278 0.268505i 0.913470π-0.913470\pi
0.714171 + 0.699971i 0.246804π0.246804\pi
258258 0 0
259259 −94263.0 17563.7i −0.0873156 0.0162692i
260260 −422972. −0.388042
261261 0 0
262262 590255. + 1.02235e6i 0.531235 + 0.920126i
263263 −176042. 304914.i −0.156938 0.271824i 0.776825 0.629716i 0.216829π-0.216829\pi
−0.933763 + 0.357892i 0.883496π0.883496\pi
264264 0 0
265265 761353. 0.665996
266266 −898446. + 1.04991e6i −0.778552 + 0.909808i
267267 0 0
268268 −242928. + 420764.i −0.206605 + 0.357850i
269269 239770. + 415294.i 0.202029 + 0.349925i 0.949182 0.314727i 0.101913π-0.101913\pi
−0.747153 + 0.664652i 0.768580π0.768580\pi
270270 0 0
271271 488805. 846636.i 0.404308 0.700283i −0.589932 0.807453i 0.700846π-0.700846\pi
0.994241 + 0.107170i 0.0341789π0.0341789\pi
272272 −471961. −0.386798
273273 0 0
274274 200155. 0.161061
275275 571395. 989684.i 0.455622 0.789160i
276276 0 0
277277 −484362. 838939.i −0.379289 0.656948i 0.611670 0.791113i 0.290498π-0.290498\pi
−0.990959 + 0.134165i 0.957165π0.957165\pi
278278 1.19130e6 2.06339e6i 0.924502 1.60128i
279279 0 0
280280 −996903. 185749.i −0.759902 0.141590i
281281 318333. 0.240501 0.120250 0.992744i 0.461630π-0.461630\pi
0.120250 + 0.992744i 0.461630π0.461630\pi
282282 0 0
283283 −886051. 1.53468e6i −0.657646 1.13908i −0.981223 0.192875i 0.938219π-0.938219\pi
0.323577 0.946202i 0.395115π-0.395115\pi
284284 −130690. 226361.i −0.0961491 0.166535i
285285 0 0
286286 −727004. −0.525559
287287 −303398. 859377.i −0.217425 0.615855i
288288 0 0
289289 641451. 1.11103e6i 0.451771 0.782491i
290290 2.20052e6 + 3.81141e6i 1.53649 + 2.66128i
291291 0 0
292292 636657. 1.10272e6i 0.436967 0.756849i
293293 −1.64148e6 −1.11703 −0.558516 0.829494i 0.688629π-0.688629\pi
−0.558516 + 0.829494i 0.688629π0.688629\pi
294294 0 0
295295 2.36881e6 1.58480
296296 −36236.2 + 62762.9i −0.0240388 + 0.0416365i
297297 0 0
298298 1.25854e6 + 2.17986e6i 0.820969 + 1.42196i
299299 62086.2 107536.i 0.0401622 0.0695629i
300300 0 0
301301 79206.2 + 224352.i 0.0503898 + 0.142729i
302302 2.54128e6 1.60337
303303 0 0
304304 959623. + 1.66212e6i 0.595548 + 1.03152i
305305 1.85642e6 + 3.21542e6i 1.14269 + 1.97919i
306306 0 0
307307 −466930. −0.282752 −0.141376 0.989956i 0.545153π-0.545153\pi
−0.141376 + 0.989956i 0.545153π0.545153\pi
308308 814715. + 151803.i 0.489361 + 0.0911808i
309309 0 0
310310 −728002. + 1.26094e6i −0.430257 + 0.745228i
311311 −1.21898e6 2.11134e6i −0.714654 1.23782i −0.963093 0.269169i 0.913251π-0.913251\pi
0.248439 0.968647i 0.420082π-0.420082\pi
312312 0 0
313313 −1.21047e6 + 2.09659e6i −0.698381 + 1.20963i 0.270646 + 0.962679i 0.412763π0.412763\pi
−0.969028 + 0.246953i 0.920571π0.920571\pi
314314 −3.25035e6 −1.86040
315315 0 0
316316 −492028. −0.277186
317317 938057. 1.62476e6i 0.524301 0.908116i −0.475298 0.879825i 0.657660π-0.657660\pi
0.999600 0.0282918i 0.00900675π-0.00900675\pi
318318 0 0
319319 1.36960e6 + 2.37221e6i 0.753557 + 1.30520i
320320 38247.3 66246.2i 0.0208798 0.0361648i
321321 0 0
322322 −254151. + 296998.i −0.136600 + 0.159630i
323323 556936. 0.297029
324324 0 0
325325 473612. + 820321.i 0.248722 + 0.430800i
326326 1.77933e6 + 3.08190e6i 0.927285 + 1.60611i
327327 0 0
328328 −688828. −0.353530
329329 −195338. 36396.6i −0.0994940 0.0185384i
330330 0 0
331331 541549. 937990.i 0.271686 0.470575i −0.697607 0.716480i 0.745752π-0.745752\pi
0.969294 + 0.245906i 0.0790853π0.0790853\pi
332332 −724399. 1.25470e6i −0.360689 0.624732i
333333 0 0
334334 2.39628e6 4.15048e6i 1.17536 2.03579i
335335 2.13507e6 1.03944
336336 0 0
337337 −2.59465e6 −1.24453 −0.622263 0.782809i 0.713786π-0.713786\pi
−0.622263 + 0.782809i 0.713786π0.713786\pi
338338 −1.01359e6 + 1.75560e6i −0.482583 + 0.835859i
339339 0 0
340340 −268325. 464753.i −0.125882 0.218034i
341341 −453107. + 784804.i −0.211016 + 0.365490i
342342 0 0
343343 −1.85454e6 1.14378e6i −0.851141 0.524938i
344344 179828. 0.0819333
345345 0 0
346346 882371. + 1.52831e6i 0.396242 + 0.686312i
347347 −935255. 1.61991e6i −0.416972 0.722216i 0.578662 0.815568i 0.303575π-0.303575\pi
−0.995633 + 0.0933518i 0.970242π0.970242\pi
348348 0 0
349349 −1.61685e6 −0.710568 −0.355284 0.934758i 0.615616π-0.615616\pi
−0.355284 + 0.934758i 0.615616π0.615616\pi
350350 −992689. 2.81179e6i −0.433155 1.22691i
351351 0 0
352352 1.03762e6 1.79720e6i 0.446354 0.773109i
353353 −289153. 500827.i −0.123507 0.213920i 0.797642 0.603132i 0.206081π-0.206081\pi
−0.921148 + 0.389212i 0.872747π0.872747\pi
354354 0 0
355355 −574310. + 994734.i −0.241866 + 0.418925i
356356 −791605. −0.331042
357357 0 0
358358 986330. 0.406738
359359 −984090. + 1.70449e6i −0.402994 + 0.698006i −0.994086 0.108598i 0.965364π-0.965364\pi
0.591092 + 0.806604i 0.298697π0.298697\pi
360360 0 0
361361 105650. + 182990.i 0.0426677 + 0.0739027i
362362 1.08453e6 1.87847e6i 0.434983 0.753412i
363363 0 0
364364 −446615. + 521909.i −0.176677 + 0.206463i
365365 −5.59553e6 −2.19841
366366 0 0
367367 −1.08726e6 1.88319e6i −0.421375 0.729842i 0.574700 0.818364i 0.305119π-0.305119\pi
−0.996074 + 0.0885223i 0.971786π0.971786\pi
368368 271457. + 470177.i 0.104491 + 0.180985i
369369 0 0
370370 −418180. −0.158803
371371 803910. 939440.i 0.303230 0.354352i
372372 0 0
373373 −692379. + 1.19924e6i −0.257675 + 0.446306i −0.965619 0.259963i 0.916290π-0.916290\pi
0.707944 + 0.706269i 0.249623π0.249623\pi
374374 −461197. 798817.i −0.170493 0.295303i
375375 0 0
376376 −75091.0 + 130061.i −0.0273916 + 0.0474437i
377377 −2.27044e6 −0.822728
378378 0 0
379379 3.37190e6 1.20580 0.602902 0.797815i 0.294011π-0.294011\pi
0.602902 + 0.797815i 0.294011π0.294011\pi
380380 −1.09115e6 + 1.88993e6i −0.387639 + 0.671410i
381381 0 0
382382 −805642. 1.39541e6i −0.282478 0.489265i
383383 1.64030e6 2.84108e6i 0.571382 0.989662i −0.425043 0.905173i 0.639741π-0.639741\pi
0.996424 0.0844886i 0.0269257π-0.0269257\pi
384384 0 0
385385 −1.21240e6 3.43412e6i −0.416863 1.18076i
386386 4.76227e6 1.62684
387387 0 0
388388 −938919. 1.62626e6i −0.316628 0.548415i
389389 −1.47405e6 2.55313e6i −0.493899 0.855457i 0.506077 0.862488i 0.331095π-0.331095\pi
−0.999975 + 0.00703108i 0.997762π0.997762\pi
390390 0 0
391391 157545. 0.0521150
392392 −1.28182e6 + 1.03396e6i −0.421321 + 0.339849i
393393 0 0
394394 4542.73 7868.24i 0.00147427 0.00255351i
395395 1.08110e6 + 1.87251e6i 0.348636 + 0.603855i
396396 0 0
397397 34635.1 59989.7i 0.0110291 0.0191030i −0.860458 0.509521i 0.829823π-0.829823\pi
0.871487 + 0.490418i 0.163156π0.163156\pi
398398 −2.61282e6 −0.826802
399399 0 0
400400 −4.14151e6 −1.29422
401401 −1.67393e6 + 2.89933e6i −0.519848 + 0.900404i 0.479886 + 0.877331i 0.340678π0.340678\pi
−0.999734 + 0.0230725i 0.992655π0.992655\pi
402402 0 0
403403 −375567. 650501.i −0.115193 0.199520i
404404 260677. 451506.i 0.0794602 0.137629i
405405 0 0
406406 7.02645e6 + 1.30921e6i 2.11554 + 0.394181i
407407 −260274. −0.0778834
408408 0 0
409409 −1.45608e6 2.52201e6i −0.430406 0.745485i 0.566502 0.824060i 0.308296π-0.308296\pi
−0.996908 + 0.0785754i 0.974963π0.974963\pi
410410 −1.98734e6 3.44217e6i −0.583864 1.01128i
411411 0 0
412412 530940. 0.154100
413413 2.50122e6 2.92289e6i 0.721566 0.843214i
414414 0 0
415415 −3.18334e6 + 5.51371e6i −0.907326 + 1.57153i
416416 860050. + 1.48965e6i 0.243663 + 0.422037i
417417 0 0
418418 −1.87547e6 + 3.24842e6i −0.525014 + 0.909350i
419419 4.62361e6 1.28661 0.643304 0.765611i 0.277563π-0.277563\pi
0.643304 + 0.765611i 0.277563π0.277563\pi
420420 0 0
421421 −2.63042e6 −0.723303 −0.361652 0.932313i 0.617787π-0.617787\pi
−0.361652 + 0.932313i 0.617787π0.617787\pi
422422 1.77837e6 3.08023e6i 0.486117 0.841979i
423423 0 0
424424 −467270. 809336.i −0.126227 0.218632i
425425 −600901. + 1.04079e6i −0.161373 + 0.279506i
426426 0 0
427427 5.92772e6 + 1.10449e6i 1.57332 + 0.293152i
428428 −1.59599e6 −0.421135
429429 0 0
430430 518820. + 898623.i 0.135315 + 0.234372i
431431 3.77064e6 + 6.53094e6i 0.977736 + 1.69349i 0.670592 + 0.741826i 0.266040π0.266040\pi
0.307144 + 0.951663i 0.400627π0.400627\pi
432432 0 0
433433 5.83558e6 1.49577 0.747883 0.663830i 0.231070π-0.231070\pi
0.747883 + 0.663830i 0.231070π0.231070\pi
434434 787186. + 2.22971e6i 0.200610 + 0.568229i
435435 0 0
436436 −2.00391e6 + 3.47088e6i −0.504850 + 0.874426i
437437 −320331. 554830.i −0.0802409 0.138981i
438438 0 0
439439 −84051.9 + 145582.i −0.0208155 + 0.0360535i −0.876246 0.481865i 0.839960π-0.839960\pi
0.855430 + 0.517918i 0.173293π0.173293\pi
440440 −2.75259e6 −0.677814
441441 0 0
442442 764546. 0.186143
443443 −1.42076e6 + 2.46082e6i −0.343962 + 0.595760i −0.985165 0.171612i 0.945102π-0.945102\pi
0.641203 + 0.767372i 0.278436π0.278436\pi
444444 0 0
445445 1.73934e6 + 3.01262e6i 0.416374 + 0.721181i
446446 −4.15503e6 + 7.19672e6i −0.989092 + 1.71316i
447447 0 0
448448 −41356.6 117143.i −0.00973532 0.0275753i
449449 1.41567e6 0.331396 0.165698 0.986177i 0.447012π-0.447012\pi
0.165698 + 0.986177i 0.447012π0.447012\pi
450450 0 0
451451 −1.23691e6 2.14240e6i −0.286350 0.495973i
452452 360273. + 624012.i 0.0829442 + 0.143664i
453453 0 0
454454 −6.44644e6 −1.46784
455455 2.96755e6 + 552933.i 0.672000 + 0.125211i
456456 0 0
457457 −778637. + 1.34864e6i −0.174399 + 0.302068i −0.939953 0.341303i 0.889132π-0.889132\pi
0.765554 + 0.643372i 0.222465π0.222465\pi
458458 1.84833e6 + 3.20141e6i 0.411734 + 0.713144i
459459 0 0
460460 −308664. + 534621.i −0.0680129 + 0.117802i
461461 4.45345e6 0.975987 0.487994 0.872847i 0.337729π-0.337729\pi
0.487994 + 0.872847i 0.337729π0.337729\pi
462462 0 0
463463 4.92263e6 1.06720 0.533599 0.845738i 0.320839π-0.320839\pi
0.533599 + 0.845738i 0.320839π0.320839\pi
464464 4.96347e6 8.59698e6i 1.07026 1.85375i
465465 0 0
466466 3.69291e6 + 6.39631e6i 0.787778 + 1.36447i
467467 2.54545e6 4.40885e6i 0.540098 0.935477i −0.458800 0.888540i 0.651720π-0.651720\pi
0.998898 0.0469376i 0.0149462π-0.0149462\pi
468468 0 0
469469 2.25442e6 2.63449e6i 0.473262 0.553049i
470470 −866579. −0.180952
471471 0 0
472472 −1.45383e6 2.51810e6i −0.300370 0.520257i
473473 322912. + 559301.i 0.0663639 + 0.114946i
474474 0 0
475475 4.88717e6 0.993856
476476 −856786. 159642.i −0.173322 0.0322946i
477477 0 0
478478 5.43416e6 9.41224e6i 1.08783 1.88418i
479479 −4.15042e6 7.18874e6i −0.826521 1.43158i −0.900752 0.434334i 0.856984π-0.856984\pi
0.0742312 0.997241i 0.476350π-0.476350\pi
480480 0 0
481481 107867. 186831.i 0.0212581 0.0368202i
482482 7.13644e6 1.39915
483483 0 0
484484 −676028. −0.131175
485485 −4.12604e6 + 7.14651e6i −0.796488 + 1.37956i
486486 0 0
487487 −4.31701e6 7.47727e6i −0.824822 1.42863i −0.902055 0.431621i 0.857942π-0.857942\pi
0.0772330 0.997013i 0.475391π-0.475391\pi
488488 2.27871e6 3.94684e6i 0.433151 0.750240i
489489 0 0
490490 −8.86500e6 3.42238e6i −1.66797 0.643930i
491491 −95039.5 −0.0177910 −0.00889550 0.999960i 0.502832π-0.502832\pi
−0.00889550 + 0.999960i 0.502832π0.502832\pi
492492 0 0
493493 −1.44032e6 2.49471e6i −0.266896 0.462277i
494494 −1.55453e6 2.69252e6i −0.286603 0.496411i
495495 0 0
496496 3.28415e6 0.599402
497497 621000. + 1.75898e6i 0.112772 + 0.319426i
498498 0 0
499499 −1.07102e6 + 1.85506e6i −0.192551 + 0.333507i −0.946095 0.323890i 0.895009π-0.895009\pi
0.753544 + 0.657397i 0.228343π0.228343\pi
500500 −88782.9 153776.i −0.0158820 0.0275084i
501501 0 0
502502 −30143.8 + 52210.7i −0.00533875 + 0.00924698i
503503 −5.24794e6 −0.924844 −0.462422 0.886660i 0.653019π-0.653019\pi
−0.462422 + 0.886660i 0.653019π0.653019\pi
504504 0 0
505505 −2.29107e6 −0.399769
506506 −530531. + 918907.i −0.0921159 + 0.159549i
507507 0 0
508508 −469945. 813968.i −0.0807956 0.139942i
509509 −5.29453e6 + 9.17040e6i −0.905802 + 1.56889i −0.0859643 + 0.996298i 0.527397π0.527397\pi
−0.819837 + 0.572596i 0.805936π0.805936\pi
510510 0 0
511511 −5.90829e6 + 6.90437e6i −1.00094 + 1.16969i
512512 −3.52190e6 −0.593747
513513 0 0
514514 1.86819e6 + 3.23580e6i 0.311899 + 0.540225i
515515 −1.16660e6 2.02061e6i −0.193822 0.335709i
516516 0 0
517517 −539357. −0.0887462
518518 −441554. + 515996.i −0.0723036 + 0.0844932i
519519 0 0
520520 1.14077e6 1.97588e6i 0.185008 0.320443i
521521 −2.27232e6 3.93578e6i −0.366755 0.635238i 0.622301 0.782778i 0.286198π-0.286198\pi
−0.989056 + 0.147540i 0.952865π0.952865\pi
522522 0 0
523523 2.63599e6 4.56566e6i 0.421394 0.729877i −0.574682 0.818377i 0.694874π-0.694874\pi
0.996076 + 0.0885004i 0.0282075π0.0282075\pi
524524 3.02772e6 0.481711
525525 0 0
526526 −2.49373e6 −0.392993
527527 476504. 825330.i 0.0747378 0.129450i
528528 0 0
529529 3.12756e6 + 5.41709e6i 0.485921 + 0.841641i
530530 2.69624e6 4.67003e6i 0.416936 0.722154i
531531 0 0
532532 1.17986e6 + 3.34196e6i 0.180739 + 0.511943i
533533 2.05048e6 0.312635
534534 0 0
535535 3.50676e6 + 6.07389e6i 0.529690 + 0.917451i
536536 −1.31037e6 2.26963e6i −0.197008 0.341227i
537537 0 0
538538 3.39647e6 0.505908
539539 −5.51755e6 2.13008e6i −0.818040 0.315809i
540540 0 0
541541 −2.96723e6 + 5.13939e6i −0.435871 + 0.754950i −0.997366 0.0725298i 0.976893π-0.976893\pi
0.561496 + 0.827480i 0.310226π0.310226\pi
542542 −3.46209e6 5.99652e6i −0.506221 0.876801i
543543 0 0
544544 −1.09120e6 + 1.89001e6i −0.158091 + 0.273821i
545545 1.76122e7 2.53994
546546 0 0
547547 −8.82017e6 −1.26040 −0.630200 0.776433i 0.717027π-0.717027\pi
−0.630200 + 0.776433i 0.717027π0.717027\pi
548548 256673. 444571.i 0.0365115 0.0632397i
549549 0 0
550550 −4.04705e6 7.00970e6i −0.570469 0.988081i
551551 −5.85712e6 + 1.01448e7i −0.821874 + 1.42353i
552552 0 0
553553 3.45204e6 + 643206.i 0.480024 + 0.0894411i
554554 −6.86124e6 −0.949791
555555 0 0
556556 −3.05538e6 5.29207e6i −0.419158 0.726004i
557557 −591120. 1.02385e6i −0.0807304 0.139829i 0.822833 0.568283i 0.192392π-0.192392\pi
−0.903564 + 0.428453i 0.859059π0.859059\pi
558558 0 0
559559 −535306. −0.0724556
560560 −8.58111e6 + 1.00278e7i −1.15631 + 1.35125i
561561 0 0
562562 1.12734e6 1.95261e6i 0.150561 0.260780i
563563 2.03870e6 + 3.53114e6i 0.271071 + 0.469509i 0.969136 0.246525i 0.0792888π-0.0792888\pi
−0.698065 + 0.716034i 0.745955π0.745955\pi
564564 0 0
565565 1.58321e6 2.74219e6i 0.208649 0.361391i
566566 −1.25514e7 −1.64684
567567 0 0
568568 1.40990e6 0.183366
569569 4.08807e6 7.08075e6i 0.529344 0.916851i −0.470070 0.882629i 0.655771π-0.655771\pi
0.999414 0.0342216i 0.0108952π-0.0108952\pi
570570 0 0
571571 −1.65307e6 2.86321e6i −0.212179 0.367504i 0.740217 0.672368i 0.234723π-0.234723\pi
−0.952396 + 0.304863i 0.901389π0.901389\pi
572572 −932292. + 1.61478e6i −0.119141 + 0.206359i
573573 0 0
574574 −6.34574e6 1.18238e6i −0.803901 0.149788i
575575 1.38247e6 0.174376
576576 0 0
577577 3.57497e6 + 6.19203e6i 0.447026 + 0.774272i 0.998191 0.0601245i 0.0191498π-0.0191498\pi
−0.551165 + 0.834396i 0.685816π0.685816\pi
578578 −4.54324e6 7.86913e6i −0.565648 0.979731i
579579 0 0
580580 1.12876e7 1.39325
581581 3.44214e6 + 9.74986e6i 0.423046 + 1.19828i
582582 0 0
583583 1.67813e6 2.90661e6i 0.204482 0.354173i
584584 3.43418e6 + 5.94818e6i 0.416669 + 0.721692i
585585 0 0
586586 −5.81309e6 + 1.00686e7i −0.699300 + 1.21122i
587587 −9.69191e6 −1.16095 −0.580476 0.814277i 0.697133π-0.697133\pi
−0.580476 + 0.814277i 0.697133π0.697133\pi
588588 0 0
589589 −3.87545e6 −0.460292
590590 8.38886e6 1.45299e7i 0.992139 1.71844i
591591 0 0
592592 471621. + 816872.i 0.0553081 + 0.0957965i
593593 3.31980e6 5.75006e6i 0.387682 0.671484i −0.604456 0.796639i 0.706609π-0.706609\pi
0.992137 + 0.125154i 0.0399426π0.0399426\pi
594594 0 0
595595 1.27500e6 + 3.61145e6i 0.147645 + 0.418205i
596596 6.45569e6 0.744435
597597 0 0
598598 −439742. 761655.i −0.0502857 0.0870974i
599599 −1.62096e6 2.80758e6i −0.184588 0.319716i 0.758849 0.651266i 0.225762π-0.225762\pi
−0.943438 + 0.331550i 0.892428π0.892428\pi
600600 0 0
601601 −5.65076e6 −0.638147 −0.319074 0.947730i 0.603372π-0.603372\pi
−0.319074 + 0.947730i 0.603372π0.603372\pi
602602 1.65664e6 + 308676.i 0.186310 + 0.0347145i
603603 0 0
604604 3.25887e6 5.64453e6i 0.363475 0.629557i
605605 1.48539e6 + 2.57277e6i 0.164988 + 0.285767i
606606 0 0
607607 −117837. + 204100.i −0.0129811 + 0.0224839i −0.872443 0.488716i 0.837465π-0.837465\pi
0.859462 + 0.511200i 0.170799π0.170799\pi
608608 8.87478e6 0.973641
609609 0 0
610610 2.62972e7 2.86144
611611 223529. 387163.i 0.0242231 0.0419557i
612612 0 0
613613 −394438. 683187.i −0.0423963 0.0734325i 0.844049 0.536267i 0.180166π-0.180166\pi
−0.886445 + 0.462834i 0.846833π0.846833\pi
614614 −1.65358e6 + 2.86408e6i −0.177012 + 0.306595i
615615 0 0
616616 −2.90645e6 + 3.39645e6i −0.308611 + 0.360640i
617617 −1.67739e7 −1.77387 −0.886935 0.461894i 0.847170π-0.847170\pi
−0.886935 + 0.461894i 0.847170π0.847170\pi
618618 0 0
619619 −4.11150e6 7.12132e6i −0.431294 0.747023i 0.565691 0.824617i 0.308610π-0.308610\pi
−0.996985 + 0.0775941i 0.975276π0.975276\pi
620620 1.86714e6 + 3.23399e6i 0.195074 + 0.337878i
621621 0 0
622622 −1.72675e7 −1.78959
623623 5.55386e6 + 1.03483e6i 0.573290 + 0.106819i
624624 0 0
625625 4.68399e6 8.11290e6i 0.479640 0.830761i
626626 8.57346e6 + 1.48497e7i 0.874420 + 1.51454i
627627 0 0
628628 −4.16818e6 + 7.21949e6i −0.421742 + 0.730479i
629629 273714. 0.0275849
630630 0 0
631631 −5.94507e6 −0.594406 −0.297203 0.954814i 0.596054π-0.596054\pi
−0.297203 + 0.954814i 0.596054π0.596054\pi
632632 1.32702e6 2.29846e6i 0.132155 0.228899i
633633 0 0
634634 −6.64403e6 1.15078e7i −0.656460 1.13702i
635635 −2.06515e6 + 3.57695e6i −0.203244 + 0.352029i
636636 0 0
637637 3.81569e6 3.07785e6i 0.372585 0.300537i
638638 1.94011e7 1.88701
639639 0 0
640640 7.26120e6 + 1.25768e7i 0.700743 + 1.21372i
641641 −5.33804e6 9.24576e6i −0.513141 0.888786i −0.999884 0.0152411i 0.995148π-0.995148\pi
0.486743 0.873545i 0.338185π-0.338185\pi
642642 0 0
643643 −3.13159e6 −0.298701 −0.149351 0.988784i 0.547718π-0.547718\pi
−0.149351 + 0.988784i 0.547718π0.547718\pi
644644 333757. + 945367.i 0.0317114 + 0.0898227i
645645 0 0
646646 1.97232e6 3.41616e6i 0.185950 0.322075i
647647 −2.46728e6 4.27346e6i −0.231717 0.401346i 0.726596 0.687065i 0.241101π-0.241101\pi
−0.958314 + 0.285719i 0.907768π0.907768\pi
648648 0 0
649649 5.22120e6 9.04339e6i 0.486585 0.842790i
650650 6.70897e6 0.622834
651651 0 0
652652 9.12710e6 0.840841
653653 2.86112e6 4.95561e6i 0.262575 0.454793i −0.704351 0.709852i 0.748762π-0.748762\pi
0.966925 + 0.255059i 0.0820950π0.0820950\pi
654654 0 0
655655 −6.65258e6 1.15226e7i −0.605881 1.04942i
656656 −4.48261e6 + 7.76411e6i −0.406698 + 0.704421i
657657 0 0
658658 −915018. + 1.06928e6i −0.0823881 + 0.0962779i
659659 −362477. −0.0325137 −0.0162569 0.999868i 0.505175π-0.505175\pi
−0.0162569 + 0.999868i 0.505175π0.505175\pi
660660 0 0
661661 9.56053e6 + 1.65593e7i 0.851096 + 1.47414i 0.880220 + 0.474565i 0.157395π0.157395\pi
−0.0291249 + 0.999576i 0.509272π0.509272\pi
662662 −3.83566e6 6.64356e6i −0.340170 0.589191i
663663 0 0
664664 7.81494e6 0.687868
665665 1.01261e7 1.18333e7i 0.887950 1.03765i
666666 0 0
667667 −1.65685e6 + 2.86975e6i −0.144201 + 0.249764i
668668 −6.14587e6 1.06450e7i −0.532896 0.923003i
669669 0 0
670670 7.56111e6 1.30962e7i 0.650727 1.12709i
671671 1.63673e7 1.40337
672672 0 0
673673 −573374. −0.0487978 −0.0243989 0.999702i 0.507767π-0.507767\pi
−0.0243989 + 0.999702i 0.507767π0.507767\pi
674674 −9.18864e6 + 1.59152e7i −0.779115 + 1.34947i
675675 0 0
676676 2.59962e6 + 4.50267e6i 0.218798 + 0.378968i
677677 5.84516e6 1.01241e7i 0.490146 0.848957i −0.509790 0.860299i 0.670277π-0.670277\pi
0.999936 + 0.0113419i 0.00361030π0.00361030\pi
678678 0 0
679679 4.46148e6 + 1.26371e7i 0.371368 + 1.05190i
680680 2.89473e6 0.240069
681681 0 0
682682 3.20925e6 + 5.55858e6i 0.264206 + 0.457618i
683683 9.18370e6 + 1.59066e7i 0.753297 + 1.30475i 0.946217 + 0.323534i 0.104871π0.104871\pi
−0.192920 + 0.981214i 0.561796π0.561796\pi
684684 0 0
685685 −2.25588e6 −0.183692
686686 −1.35834e7 + 7.32492e6i −1.10204 + 0.594282i
687687 0 0
688688 1.17025e6 2.02693e6i 0.0942554 0.163255i
689689 1.39096e6 + 2.40921e6i 0.111626 + 0.193342i
690690 0 0
691691 −1.17806e7 + 2.04045e7i −0.938579 + 1.62567i −0.170454 + 0.985366i 0.554523π0.554523\pi
−0.768125 + 0.640300i 0.778810π0.778810\pi
692692 4.52612e6 0.359303
693693 0 0
694694 −1.32484e7 −1.04415
695695 −1.34267e7 + 2.32558e7i −1.05441 + 1.82629i
696696 0 0
697697 1.30078e6 + 2.25303e6i 0.101420 + 0.175665i
698698 −5.72587e6 + 9.91750e6i −0.444839 + 0.770484i
699699 0 0
700700 −7.51839e6 1.40087e6i −0.579935 0.108057i
701701 −1.32980e7 −1.02210 −0.511048 0.859552i 0.670743π-0.670743\pi
−0.511048 + 0.859552i 0.670743π0.670743\pi
702702 0 0
703703 −556535. 963946.i −0.0424721 0.0735639i
704704 −168605. 292033.i −0.0128215 0.0222075i
705705 0 0
706706 −4.09600e6 −0.309277
707707 −2.41913e6 + 2.82697e6i −0.182016 + 0.212703i
708708 0 0
709709 3.42677e6 5.93533e6i 0.256017 0.443434i −0.709154 0.705053i 0.750923π-0.750923\pi
0.965171 + 0.261619i 0.0842564π0.0842564\pi
710710 4.06770e6 + 7.04547e6i 0.302833 + 0.524522i
711711 0 0
712712 2.13499e6 3.69791e6i 0.157832 0.273374i
713713 −1.09628e6 −0.0807602
714714 0 0
715715 8.19384e6 0.599408
716716 1.26485e6 2.19078e6i 0.0922051 0.159704i
717717 0 0
718718 6.97008e6 + 1.20725e7i 0.504576 + 0.873951i
719719 1.32865e7 2.30128e7i 0.958490 1.66015i 0.232318 0.972640i 0.425369π-0.425369\pi
0.726172 0.687513i 0.241298π-0.241298\pi
720720 0 0
721721 −3.72505e6 694075.i −0.266866 0.0497242i
722722 1.49658e6 0.106846
723723 0 0
724724 −2.78156e6 4.81781e6i −0.197216 0.341588i
725725 −1.26390e7 2.18913e7i −0.893031 1.54678i
726726 0 0
727727 2.16991e6 0.152267 0.0761335 0.997098i 0.475742π-0.475742\pi
0.0761335 + 0.997098i 0.475742π0.475742\pi
728728 −1.23351e6 3.49393e6i −0.0862612 0.244335i
729729 0 0
730730 −1.98159e7 + 3.43221e7i −1.37628 + 2.38379i
731731 −339587. 588182.i −0.0235049 0.0407116i
732732 0 0
733733 8.73265e6 1.51254e7i 0.600324 1.03979i −0.392447 0.919774i 0.628372π-0.628372\pi
0.992772 0.120018i 0.0382951π-0.0382951\pi
734734 −1.54016e7 −1.05518
735735 0 0
736736 2.51048e6 0.170829
737737 4.70602e6 8.15106e6i 0.319143 0.552771i
738738 0 0
739739 6.82304e6 + 1.18178e7i 0.459586 + 0.796026i 0.998939 0.0460536i 0.0146645π-0.0146645\pi
−0.539353 + 0.842080i 0.681331π0.681331\pi
740740 −536264. + 928836.i −0.0359997 + 0.0623533i
741741 0 0
742742 −2.91544e6 8.25798e6i −0.194399 0.550635i
743743 −1.48965e7 −0.989944 −0.494972 0.868909i 0.664822π-0.664822\pi
−0.494972 + 0.868909i 0.664822π0.664822\pi
744744 0 0
745745 −1.41846e7 2.45685e7i −0.936326 1.62176i
746746 4.90396e6 + 8.49390e6i 0.322626 + 0.558805i
747747 0 0
748748 −2.36571e6 −0.154599
749749 1.11974e7 + 2.08637e6i 0.729311 + 0.135890i
750750 0 0
751751 1.26731e7 2.19505e7i 0.819944 1.42019i −0.0857783 0.996314i 0.527338π-0.527338\pi
0.905723 0.423871i 0.139329π-0.139329\pi
752752 977324. + 1.69277e6i 0.0630222 + 0.109158i
753753 0 0
754754 −8.04049e6 + 1.39265e7i −0.515056 + 0.892102i
755755 −2.86419e7 −1.82867
756756 0 0
757757 −2.66725e7 −1.69170 −0.845852 0.533417i 0.820908π-0.820908\pi
−0.845852 + 0.533417i 0.820908π0.820908\pi
758758 1.19412e7 2.06828e7i 0.754875 1.30748i
759759 0 0
760760 −5.88577e6 1.01945e7i −0.369632 0.640221i
761761 289914. 502146.i 0.0181471 0.0314318i −0.856809 0.515634i 0.827557π-0.827557\pi
0.874956 + 0.484202i 0.160890π0.160890\pi
762762 0 0
763763 1.85967e7 2.17319e7i 1.15644 1.35141i
764764 −4.13255e6 −0.256144
765765 0 0
766766 −1.16179e7 2.01227e7i −0.715408 1.23912i
767767 4.32770e6 + 7.49580e6i 0.265625 + 0.460076i
768768 0 0
769769 1.52438e7 0.929562 0.464781 0.885426i 0.346133π-0.346133\pi
0.464781 + 0.885426i 0.346133π0.346133\pi
770770 −2.53579e7 4.72485e6i −1.54130 0.287185i
771771 0 0
772772 6.10702e6 1.05777e7i 0.368796 0.638773i
773773 −9.74628e6 1.68810e7i −0.586665 1.01613i −0.994666 0.103152i 0.967107π-0.967107\pi
0.408001 0.912982i 0.366226π-0.366226\pi
774774 0 0
775775 4.18138e6 7.24236e6i 0.250072 0.433137i
776776 1.01292e7 0.603839
777777 0 0
778778 −2.08807e7 −1.23679
779779 5.28969e6 9.16201e6i 0.312311 0.540938i
780780 0 0
781781 2.53173e6 + 4.38508e6i 0.148521 + 0.257247i
782782 557927. 966358.i 0.0326257 0.0565094i
783783 0 0
784784 3.31262e6 + 2.11766e7i 0.192478 + 1.23046i
785785 3.66337e7 2.12181
786786 0 0
787787 −6.81384e6 1.18019e7i −0.392153 0.679228i 0.600580 0.799564i 0.294936π-0.294936\pi
−0.992733 + 0.120336i 0.961603π0.961603\pi
788788 −11651.0 20180.1i −0.000668416 0.00115773i
789789 0 0
790790 1.53143e7 0.873031
791791 −1.71192e6 4.84900e6i −0.0972839 0.275557i
792792 0 0
793793 −6.78320e6 + 1.17488e7i −0.383046 + 0.663456i
794794 −245312. 424893.i −0.0138092 0.0239182i
795795 0 0
796796 −3.35061e6 + 5.80343e6i −0.187431 + 0.324640i
797797 −3.62853e6 −0.202341 −0.101171 0.994869i 0.532259π-0.532259\pi
−0.101171 + 0.994869i 0.532259π0.532259\pi
798798 0 0
799799 567208. 0.0314323
800800 −9.57537e6 + 1.65850e7i −0.528969 + 0.916202i
801801 0 0
802802 1.18561e7 + 2.05353e7i 0.650885 + 1.12737i
803803 −1.23334e7 + 2.13620e7i −0.674983 + 1.16910i
804804 0 0
805805 2.86446e6 3.34737e6i 0.155795 0.182060i
806806 −5.32010e6 −0.288458
807807 0 0
808808 1.40611e6 + 2.43546e6i 0.0757691 + 0.131236i
809809 1.49390e7 + 2.58751e7i 0.802509 + 1.38999i 0.917960 + 0.396673i 0.129835π0.129835\pi
−0.115451 + 0.993313i 0.536831π0.536831\pi
810810 0 0
811811 −1.02643e6 −0.0547995 −0.0273998 0.999625i 0.508723π-0.508723\pi
−0.0273998 + 0.999625i 0.508723π0.508723\pi
812812 1.19185e7 1.39278e7i 0.634354 0.741299i
813813 0 0
814814 −921730. + 1.59648e6i −0.0487576 + 0.0844507i
815815 −2.00543e7 3.47351e7i −1.05758 1.83178i
816816 0 0
817817 −1.38094e6 + 2.39187e6i −0.0723804 + 0.125367i
818818 −2.06262e7 −1.07779
819819 0 0
820820 −1.01940e7 −0.529434
821821 −5.75312e6 + 9.96470e6i −0.297883 + 0.515948i −0.975651 0.219327i 0.929614π-0.929614\pi
0.677768 + 0.735275i 0.262947π0.262947\pi
822822 0 0
823823 1.25605e7 + 2.17554e7i 0.646408 + 1.11961i 0.983974 + 0.178310i 0.0570630π0.0570630\pi
−0.337566 + 0.941302i 0.609604π0.609604\pi
824824 −1.43197e6 + 2.48024e6i −0.0734708 + 0.127255i
825825 0 0
826826 −9.07084e6 2.56932e7i −0.462591 1.31029i
827827 2.14447e6 0.109032 0.0545162 0.998513i 0.482638π-0.482638\pi
0.0545162 + 0.998513i 0.482638π0.482638\pi
828828 0 0
829829 −409033. 708465.i −0.0206715 0.0358041i 0.855505 0.517795i 0.173247π-0.173247\pi
−0.876176 + 0.481991i 0.839914π0.839914\pi
830830 2.25469e7 + 3.90523e7i 1.13603 + 1.96767i
831831 0 0
832832 279504. 0.0139984
833833 5.80247e6 + 2.24008e6i 0.289735 + 0.111854i
834834 0 0
835835 −2.70078e7 + 4.67788e7i −1.34052 + 2.32184i
836836 4.81013e6 + 8.33138e6i 0.238035 + 0.412289i
837837 0 0
838838 1.63740e7 2.83606e7i 0.805460 1.39510i
839839 2.11279e7 1.03622 0.518110 0.855314i 0.326636π-0.326636\pi
0.518110 + 0.855314i 0.326636π0.326636\pi
840840 0 0
841841 4.00785e7 1.95398
842842 −9.31533e6 + 1.61346e7i −0.452812 + 0.784294i
843843 0 0
844844 −4.56107e6 7.90001e6i −0.220400 0.381743i
845845 1.14239e7 1.97868e7i 0.550393 0.953308i
846846 0 0
847847 4.74298e6 + 883742.i 0.227166 + 0.0423269i
848848 −1.21632e7 −0.580844
849849 0 0
850850 4.25604e6 + 7.37167e6i 0.202050 + 0.349960i
851851 −157432. 272679.i −0.00745191 0.0129071i
852852 0 0
853853 −1.89000e7 −0.889386 −0.444693 0.895683i 0.646687π-0.646687\pi
−0.444693 + 0.895683i 0.646687π0.646687\pi
854854 2.77671e7 3.24484e7i 1.30283 1.52247i
855855 0 0
856856 4.30446e6 7.45554e6i 0.200786 0.347772i
857857 1.86143e7 + 3.22409e7i 0.865753 + 1.49953i 0.866297 + 0.499529i 0.166493π0.166493\pi
−0.000544054 1.00000i 0.500173π0.500173\pi
858858 0 0
859859 −1.51032e6 + 2.61595e6i −0.0698371 + 0.120961i −0.898829 0.438298i 0.855581π-0.855581\pi
0.828992 + 0.559260i 0.188915π0.188915\pi
860860 2.66129e6 0.122700
861861 0 0
862862 5.34131e7 2.44838
863863 −1.35921e7 + 2.35423e7i −0.621242 + 1.07602i 0.368013 + 0.929821i 0.380038π0.380038\pi
−0.989255 + 0.146202i 0.953295π0.953295\pi
864864 0 0
865865 −9.94493e6 1.72251e7i −0.451920 0.782748i
866866 2.06660e7 3.57946e7i 0.936400 1.62189i
867867 0 0
868868 5.96196e6 + 1.11087e6i 0.268590 + 0.0500454i
869869 9.53158e6 0.428169
870870 0 0
871871 3.90068e6 + 6.75618e6i 0.174219 + 0.301756i
872872 −1.08093e7 1.87222e7i −0.481399 0.833807i
873873 0 0
874874 −4.53766e6 −0.200934
875875 421871. + 1.19495e6i 0.0186277 + 0.0527630i
876876 0 0
877877 −8.69339e6 + 1.50574e7i −0.381672 + 0.661075i −0.991301 0.131611i 0.957985π-0.957985\pi
0.609629 + 0.792687i 0.291318π0.291318\pi
878878 595320. + 1.03112e6i 0.0260624 + 0.0451414i
879879 0 0
880880 −1.79128e7 + 3.10258e7i −0.779751 + 1.35057i
881881 8.14472e6 0.353538 0.176769 0.984252i 0.443435π-0.443435\pi
0.176769 + 0.984252i 0.443435π0.443435\pi
882882 0 0
883883 −3.10298e7 −1.33930 −0.669649 0.742678i 0.733555π-0.733555\pi
−0.669649 + 0.742678i 0.733555π0.733555\pi
884884 980435. 1.69816e6i 0.0421976 0.0730884i
885885 0 0
886886 1.00629e7 + 1.74294e7i 0.430664 + 0.745931i
887887 −7.35138e6 + 1.27330e7i −0.313733 + 0.543401i −0.979167 0.203055i 0.934913π-0.934913\pi
0.665435 + 0.746456i 0.268246π0.268246\pi
888888 0 0
889889 2.23304e6 + 6.32509e6i 0.0947638 + 0.268419i
890890 2.46386e7 1.04266
891891 0 0
892892 1.06566e7 + 1.84578e7i 0.448443 + 0.776726i
893893 −1.15329e6 1.99755e6i −0.0483959 0.0838242i
894894 0 0
895895 −1.11166e7 −0.463890
896896 2.31857e7 + 4.32010e6i 0.964827 + 0.179773i
897897 0 0
898898 5.01344e6 8.68354e6i 0.207465 0.359340i
899899 1.00225e7 + 1.73595e7i 0.413596 + 0.716370i
900900 0 0
901901 −1.76479e6 + 3.05671e6i −0.0724238 + 0.125442i
902902 −1.75215e7 −0.717060
903903 0 0
904904 −3.88669e6 −0.158183
905905 −1.22235e7 + 2.11716e7i −0.496104 + 0.859277i
906906 0 0
907907 −6.54701e6 1.13398e7i −0.264256 0.457705i 0.703112 0.711079i 0.251793π-0.251793\pi
−0.967368 + 0.253374i 0.918460π0.918460\pi
908908 −8.26675e6 + 1.43184e7i −0.332752 + 0.576343i
909909 0 0
910910 1.39008e7 1.62444e7i 0.556464 0.650278i
911911 −2.68695e7 −1.07266 −0.536332 0.844007i 0.680191π-0.680191\pi
−0.536332 + 0.844007i 0.680191π0.680191\pi
912912 0 0
913913 1.40331e7 + 2.43061e7i 0.557156 + 0.965023i
914914 5.51490e6 + 9.55209e6i 0.218360 + 0.378210i
915915 0 0
916916 9.48103e6 0.373351
917917 −2.12423e7 3.95800e6i −0.834215 0.155436i
918918 0 0
919919 −636586. + 1.10260e6i −0.0248638 + 0.0430654i −0.878190 0.478313i 0.841249π-0.841249\pi
0.853326 + 0.521378i 0.174582π0.174582\pi
920920 −1.66496e6 2.88379e6i −0.0648535 0.112330i
921921 0 0
922922 1.57714e7 2.73168e7i 0.611001 1.05828i
923923 −4.19695e6 −0.162155
924924 0 0
925925 2.40187e6 0.0922986
926926 1.74329e7 3.01947e7i 0.668102 1.15719i
927927 0 0
928928 −2.29516e7 3.97533e7i −0.874867 1.51531i
929929 −4.65852e6 + 8.06880e6i −0.177096 + 0.306740i −0.940885 0.338727i 0.890004π-0.890004\pi
0.763789 + 0.645467i 0.223337π0.223337\pi
930930 0 0
931931 −3.90905e6 2.49894e7i −0.147808 0.944890i
932932 1.89428e7 0.714338
933933 0 0
934934 −1.80288e7 3.12268e7i −0.676239 1.17128i
935935 5.19801e6 + 9.00322e6i 0.194450 + 0.336797i
936936 0 0
937937 1.18158e7 0.439657 0.219829 0.975539i 0.429450π-0.429450\pi
0.219829 + 0.975539i 0.429450π0.429450\pi
938938 −8.17581e6 2.31580e7i −0.303406 0.859397i
939939 0 0
940940 −1.11128e6 + 1.92479e6i −0.0410208 + 0.0710501i
941941 −1.26765e7 2.19563e7i −0.466685 0.808323i 0.532591 0.846373i 0.321219π-0.321219\pi
−0.999276 + 0.0380504i 0.987885π0.987885\pi
942942 0 0
943943 1.49634e6 2.59173e6i 0.0547962 0.0949098i
944944 −3.78436e7 −1.38217
945945 0 0
946946 4.57422e6 0.166184
947947 1.32471e7 2.29446e7i 0.480004 0.831391i −0.519733 0.854329i 0.673969π-0.673969\pi
0.999737 + 0.0229375i 0.00730187π0.00730187\pi
948948 0 0
949949 −1.02228e7 1.77063e7i −0.368471 0.638210i
950950 1.73073e7 2.99772e7i 0.622187 1.07766i
951951 0 0
952952 3.05654e6 3.57184e6i 0.109304 0.127732i
953953 1.88335e7 0.671735 0.335868 0.941909i 0.390970π-0.390970\pi
0.335868 + 0.941909i 0.390970π0.390970\pi
954954 0 0
955955 9.08015e6 + 1.57273e7i 0.322170 + 0.558014i
956956 −1.39373e7 2.41401e7i −0.493211 0.854267i
957957 0 0
958958 −5.87929e7 −2.06972
959959 −2.38198e6 + 2.78355e6i −0.0836355 + 0.0977356i
960960 0 0
961961 1.09988e7 1.90505e7i 0.384182 0.665423i
962962 −763995. 1.32328e6i −0.0266166 0.0461013i
963963 0 0
964964 9.15159e6 1.58510e7i 0.317179 0.549370i
965965 −5.36740e7 −1.85544
966966 0 0
967967 −3.14956e7 −1.08314 −0.541569 0.840656i 0.682169π-0.682169\pi
−0.541569 + 0.840656i 0.682169π0.682169\pi
968968 1.82328e6 3.15801e6i 0.0625409 0.108324i
969969 0 0
970970 2.92238e7 + 5.06171e7i 0.997257 + 1.72730i
971971 −3.42834e6 + 5.93806e6i −0.116691 + 0.202114i −0.918454 0.395527i 0.870562π-0.870562\pi
0.801764 + 0.597641i 0.203895π0.203895\pi
972972 0 0
973973 1.45183e7 + 4.11231e7i 0.491624 + 1.39253i
974974 −6.11527e7 −2.06547
975975 0 0
976976 −2.96579e7 5.13689e7i −0.996587 1.72614i
977977 1.40735e7 + 2.43761e7i 0.471701 + 0.817010i 0.999476 0.0323741i 0.0103068π-0.0103068\pi
−0.527775 + 0.849384i 0.676973π0.676973\pi
978978 0 0
979979 1.53350e7 0.511361
980980 −1.89699e7 + 1.53016e7i −0.630956 + 0.508947i
981981 0 0
982982 −336571. + 582958.i −0.0111378 + 0.0192912i
983983 1.17458e7 + 2.03443e7i 0.387703 + 0.671521i 0.992140 0.125132i 0.0399354π-0.0399354\pi
−0.604437 + 0.796653i 0.706602π0.706602\pi
984984 0 0
985985 −51199.7 + 88680.5i −0.00168142 + 0.00291231i
986986 −2.04029e7 −0.668343
987987 0 0
988988 −7.97395e6 −0.259885
989989 −390639. + 676607.i −0.0126995 + 0.0219961i
990990 0 0
991991 1.07206e6 + 1.85686e6i 0.0346765 + 0.0600615i 0.882843 0.469669i 0.155627π-0.155627\pi
−0.848166 + 0.529730i 0.822293π0.822293\pi
992992 7.59311e6 1.31517e7i 0.244986 0.424327i
993993 0 0
994994 1.29885e7 + 2.42011e6i 0.416960 + 0.0776906i
995995 2.94483e7 0.942979
996996 0 0
997997 −1.25436e7 2.17261e7i −0.399654 0.692220i 0.594029 0.804443i 0.297536π-0.297536\pi
−0.993683 + 0.112223i 0.964203π0.964203\pi
998998 7.58576e6 + 1.31389e7i 0.241086 + 0.417574i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 63.6.e.d.37.2 4
3.2 odd 2 7.6.c.a.2.1 4
7.2 even 3 441.6.a.n.1.1 2
7.4 even 3 inner 63.6.e.d.46.2 4
7.5 odd 6 441.6.a.m.1.1 2
12.11 even 2 112.6.i.c.65.1 4
21.2 odd 6 49.6.a.d.1.2 2
21.5 even 6 49.6.a.e.1.2 2
21.11 odd 6 7.6.c.a.4.1 yes 4
21.17 even 6 49.6.c.f.18.1 4
21.20 even 2 49.6.c.f.30.1 4
84.11 even 6 112.6.i.c.81.1 4
84.23 even 6 784.6.a.ba.1.2 2
84.47 odd 6 784.6.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.6.c.a.2.1 4 3.2 odd 2
7.6.c.a.4.1 yes 4 21.11 odd 6
49.6.a.d.1.2 2 21.2 odd 6
49.6.a.e.1.2 2 21.5 even 6
49.6.c.f.18.1 4 21.17 even 6
49.6.c.f.30.1 4 21.20 even 2
63.6.e.d.37.2 4 1.1 even 1 trivial
63.6.e.d.46.2 4 7.4 even 3 inner
112.6.i.c.65.1 4 12.11 even 2
112.6.i.c.81.1 4 84.11 even 6
441.6.a.m.1.1 2 7.5 odd 6
441.6.a.n.1.1 2 7.2 even 3
784.6.a.t.1.1 2 84.47 odd 6
784.6.a.ba.1.2 2 84.23 even 6