Properties

Label 250.4.e.c.99.7
Level 250250
Weight 44
Character 250.99
Analytic conductor 14.75014.750
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [250,4,Mod(49,250)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(250, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("250.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 250=253 250 = 2 \cdot 5^{3}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 250.e (of order 1010, degree 44, not 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: 14.750477501414.7504775014
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 99.7
Character χ\chi == 250.99
Dual form 250.4.e.c.149.7

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+(1.902110.618034i)q2+(2.58496+3.55790i)q3+(3.236072.35114i)q4+(7.11579+5.16993i)q632.4633iq7+(4.702286.47214i)q8+(2.366877.28447i)q9+(13.675142.0875i)q11+(16.7302+5.43598i)q12+(18.85046.12486i)q13+(20.063461.7488i)q14+(4.9442715.2169i)q16+(48.4207+66.6454i)q1715.3187iq18+(8.36319+6.07621i)q19+(115.50183.9163i)q21+(52.023171.6036i)q22+(184.90860.0803i)q23+35.1824q2439.6409q26+(144.96547.1019i)q27+(76.3257105.053i)q28+(159.317+115.751i)q29+(68.1740+49.5313i)q3132.0000iq32+(114.394157.449i)q33+(50.9126+156.693i)q34+(9.4674729.1379i)q36+(218.389+70.9588i)q37+(19.6630+6.38891i)q38+(26.935982.9003i)q39+(6.39296+19.6755i)q41+(167.833231.002i)q4236.8678iq43+(143.207104.046i)q44+(314.584228.559i)q46+(249.612+343.561i)q47+(66.920921.7439i)q48710.864q49362.283q51+(75.4016+24.4995i)q52+(3.07504+4.23242i)q53+(246.629179.186i)q54+(210.107152.651i)q56+45.4621iq57+(231.502+318.635i)q58+(16.0299+49.3350i)q59+(38.3804118.123i)q61+(160.287+52.0803i)q62+(236.47876.8363i)q63+(19.777160.8676i)q64+(120.280370.185i)q66+(457.984630.360i)q67+329.513iq68+(691.740+502.578i)q69+(496.268+360.560i)q71+(36.016449.5723i)q72+(863.608280.603i)q73+459.255q74+41.3499q76+(1366.30+443.937i)q77+(102.470141.038i)q78+(500.100+363.344i)q79+(375.005+272.457i)q81+41.3761iq82+(265.719+365.730i)q83+(176.470543.118i)q84+(22.785570.1266i)q86+(823.659267.623i)q87+(336.700109.401i)q88+(266.987821.703i)q89+(198.833+611.945i)q91+(457.118629.169i)q92+370.592iq93+(687.123+499.224i)q94+(113.85382.7188i)q96+(384.094+528.660i)q97+(1352.14+439.338i)q98338.953q99+O(q100)q+(1.90211 - 0.618034i) q^{2} +(2.58496 + 3.55790i) q^{3} +(3.23607 - 2.35114i) q^{4} +(7.11579 + 5.16993i) q^{6} -32.4633i q^{7} +(4.70228 - 6.47214i) q^{8} +(2.36687 - 7.28447i) q^{9} +(-13.6751 - 42.0875i) q^{11} +(16.7302 + 5.43598i) q^{12} +(-18.8504 - 6.12486i) q^{13} +(-20.0634 - 61.7488i) q^{14} +(4.94427 - 15.2169i) q^{16} +(-48.4207 + 66.6454i) q^{17} -15.3187i q^{18} +(8.36319 + 6.07621i) q^{19} +(115.501 - 83.9163i) q^{21} +(-52.0231 - 71.6036i) q^{22} +(184.908 - 60.0803i) q^{23} +35.1824 q^{24} -39.6409 q^{26} +(144.965 - 47.1019i) q^{27} +(-76.3257 - 105.053i) q^{28} +(-159.317 + 115.751i) q^{29} +(68.1740 + 49.5313i) q^{31} -32.0000i q^{32} +(114.394 - 157.449i) q^{33} +(-50.9126 + 156.693i) q^{34} +(-9.46747 - 29.1379i) q^{36} +(218.389 + 70.9588i) q^{37} +(19.6630 + 6.38891i) q^{38} +(-26.9359 - 82.9003i) q^{39} +(-6.39296 + 19.6755i) q^{41} +(167.833 - 231.002i) q^{42} -36.8678i q^{43} +(-143.207 - 104.046i) q^{44} +(314.584 - 228.559i) q^{46} +(249.612 + 343.561i) q^{47} +(66.9209 - 21.7439i) q^{48} -710.864 q^{49} -362.283 q^{51} +(-75.4016 + 24.4995i) q^{52} +(3.07504 + 4.23242i) q^{53} +(246.629 - 179.186i) q^{54} +(-210.107 - 152.651i) q^{56} +45.4621i q^{57} +(-231.502 + 318.635i) q^{58} +(-16.0299 + 49.3350i) q^{59} +(-38.3804 - 118.123i) q^{61} +(160.287 + 52.0803i) q^{62} +(-236.478 - 76.8363i) q^{63} +(-19.7771 - 60.8676i) q^{64} +(120.280 - 370.185i) q^{66} +(457.984 - 630.360i) q^{67} +329.513i q^{68} +(691.740 + 502.578i) q^{69} +(-496.268 + 360.560i) q^{71} +(-36.0164 - 49.5723i) q^{72} +(863.608 - 280.603i) q^{73} +459.255 q^{74} +41.3499 q^{76} +(-1366.30 + 443.937i) q^{77} +(-102.470 - 141.038i) q^{78} +(-500.100 + 363.344i) q^{79} +(375.005 + 272.457i) q^{81} +41.3761i q^{82} +(-265.719 + 365.730i) q^{83} +(176.470 - 543.118i) q^{84} +(-22.7855 - 70.1266i) q^{86} +(-823.659 - 267.623i) q^{87} +(-336.700 - 109.401i) q^{88} +(-266.987 - 821.703i) q^{89} +(-198.833 + 611.945i) q^{91} +(457.118 - 629.169i) q^{92} +370.592i q^{93} +(687.123 + 499.224i) q^{94} +(113.853 - 82.7188i) q^{96} +(384.094 + 528.660i) q^{97} +(-1352.14 + 439.338i) q^{98} -338.953 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+32q4+28q6+166q9+304q11104q14128q16+40q19+514q21+128q241432q26210q29+354q31684q34664q36+292q39+924q41++3572q99+O(q100) 32 q + 32 q^{4} + 28 q^{6} + 166 q^{9} + 304 q^{11} - 104 q^{14} - 128 q^{16} + 40 q^{19} + 514 q^{21} + 128 q^{24} - 1432 q^{26} - 210 q^{29} + 354 q^{31} - 684 q^{34} - 664 q^{36} + 292 q^{39} + 924 q^{41}+ \cdots + 3572 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/250Z)×\left(\mathbb{Z}/250\mathbb{Z}\right)^\times.

nn 127127
χ(n)\chi(n) e(910)e\left(\frac{9}{10}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.90211 0.618034i 0.672499 0.218508i
33 2.58496 + 3.55790i 0.497476 + 0.684717i 0.981745 0.190202i 0.0609143π-0.0609143\pi
−0.484269 + 0.874919i 0.660914π0.660914\pi
44 3.23607 2.35114i 0.404508 0.293893i
55 0 0
66 7.11579 + 5.16993i 0.484168 + 0.351769i
77 32.4633i 1.75285i −0.481537 0.876426i 0.659921π-0.659921\pi
0.481537 0.876426i 0.340079π-0.340079\pi
88 4.70228 6.47214i 0.207813 0.286031i
99 2.36687 7.28447i 0.0876618 0.269795i
1010 0 0
1111 −13.6751 42.0875i −0.374835 1.15362i −0.943590 0.331117i 0.892575π-0.892575\pi
0.568754 0.822507i 0.307425π-0.307425\pi
1212 16.7302 + 5.43598i 0.402467 + 0.130769i
1313 −18.8504 6.12486i −0.402166 0.130672i 0.100948 0.994892i 0.467812π-0.467812\pi
−0.503114 + 0.864220i 0.667812π0.667812\pi
1414 −20.0634 61.7488i −0.383012 1.17879i
1515 0 0
1616 4.94427 15.2169i 0.0772542 0.237764i
1717 −48.4207 + 66.6454i −0.690809 + 0.950817i −1.00000 0.000182954i 0.999942π-0.999942\pi
0.309191 + 0.951000i 0.399942π0.399942\pi
1818 15.3187i 0.200592i
1919 8.36319 + 6.07621i 0.100981 + 0.0733673i 0.637130 0.770756i 0.280121π-0.280121\pi
−0.536149 + 0.844124i 0.680121π0.680121\pi
2020 0 0
2121 115.501 83.9163i 1.20021 0.872002i
2222 −52.0231 71.6036i −0.504152 0.693906i
2323 184.908 60.0803i 1.67635 0.544678i 0.692151 0.721753i 0.256663π-0.256663\pi
0.984197 + 0.177075i 0.0566634π0.0566634\pi
2424 35.1824 0.299232
2525 0 0
2626 −39.6409 −0.299009
2727 144.965 47.1019i 1.03328 0.335732i
2828 −76.3257 105.053i −0.515150 0.709043i
2929 −159.317 + 115.751i −1.02016 + 0.741186i −0.966315 0.257363i 0.917146π-0.917146\pi
−0.0538405 + 0.998550i 0.517146π0.517146\pi
3030 0 0
3131 68.1740 + 49.5313i 0.394981 + 0.286970i 0.767493 0.641057i 0.221504π-0.221504\pi
−0.372513 + 0.928027i 0.621504π0.621504\pi
3232 32.0000i 0.176777i
3333 114.394 157.449i 0.603435 0.830557i
3434 −50.9126 + 156.693i −0.256807 + 0.790370i
3535 0 0
3636 −9.46747 29.1379i −0.0438309 0.134898i
3737 218.389 + 70.9588i 0.970348 + 0.315285i 0.750956 0.660352i 0.229593π-0.229593\pi
0.219391 + 0.975637i 0.429593π0.429593\pi
3838 19.6630 + 6.38891i 0.0839412 + 0.0272741i
3939 −26.9359 82.9003i −0.110595 0.340376i
4040 0 0
4141 −6.39296 + 19.6755i −0.0243515 + 0.0749463i −0.962494 0.271304i 0.912545π-0.912545\pi
0.938142 + 0.346250i 0.112545π0.112545\pi
4242 167.833 231.002i 0.616599 0.848675i
4343 36.8678i 0.130751i −0.997861 0.0653753i 0.979176π-0.979176\pi
0.997861 0.0653753i 0.0208245π-0.0208245\pi
4444 −143.207 104.046i −0.490666 0.356490i
4545 0 0
4646 314.584 228.559i 1.00832 0.732591i
4747 249.612 + 343.561i 0.774673 + 1.06625i 0.995850 + 0.0910123i 0.0290102π0.0290102\pi
−0.221177 + 0.975234i 0.570990π0.570990\pi
4848 66.9209 21.7439i 0.201233 0.0653847i
4949 −710.864 −2.07249
5050 0 0
5151 −362.283 −0.994702
5252 −75.4016 + 24.4995i −0.201083 + 0.0653358i
5353 3.07504 + 4.23242i 0.00796960 + 0.0109692i 0.812983 0.582287i 0.197842π-0.197842\pi
−0.805014 + 0.593256i 0.797842π0.797842\pi
5454 246.629 179.186i 0.621517 0.451558i
5555 0 0
5656 −210.107 152.651i −0.501369 0.364266i
5757 45.4621i 0.105642i
5858 −231.502 + 318.635i −0.524098 + 0.721359i
5959 −16.0299 + 49.3350i −0.0353715 + 0.108862i −0.967183 0.254079i 0.918228π-0.918228\pi
0.931812 + 0.362942i 0.118228π0.118228\pi
6060 0 0
6161 −38.3804 118.123i −0.0805592 0.247936i 0.902663 0.430348i 0.141609π-0.141609\pi
−0.983222 + 0.182413i 0.941609π0.941609\pi
6262 160.287 + 52.0803i 0.328329 + 0.106681i
6363 −236.478 76.8363i −0.472911 0.153658i
6464 −19.7771 60.8676i −0.0386271 0.118882i
6565 0 0
6666 120.280 370.185i 0.224326 0.690404i
6767 457.984 630.360i 0.835098 1.14941i −0.151854 0.988403i 0.548524π-0.548524\pi
0.986953 0.161011i 0.0514756π-0.0514756\pi
6868 329.513i 0.587637i
6969 691.740 + 502.578i 1.20689 + 0.876860i
7070 0 0
7171 −496.268 + 360.560i −0.829523 + 0.602684i −0.919424 0.393267i 0.871345π-0.871345\pi
0.0899013 + 0.995951i 0.471345π0.471345\pi
7272 −36.0164 49.5723i −0.0589524 0.0811411i
7373 863.608 280.603i 1.38463 0.449892i 0.480439 0.877028i 0.340477π-0.340477\pi
0.904187 + 0.427136i 0.140477π0.140477\pi
7474 459.255 0.721450
7575 0 0
7676 41.3499 0.0624099
7777 −1366.30 + 443.937i −2.02213 + 0.657031i
7878 −102.470 141.038i −0.148750 0.204737i
7979 −500.100 + 363.344i −0.712224 + 0.517461i −0.883890 0.467694i 0.845085π-0.845085\pi
0.171667 + 0.985155i 0.445085π0.445085\pi
8080 0 0
8181 375.005 + 272.457i 0.514411 + 0.373741i
8282 41.3761i 0.0557223i
8383 −265.719 + 365.730i −0.351403 + 0.483664i −0.947728 0.319078i 0.896627π-0.896627\pi
0.596326 + 0.802743i 0.296627π0.296627\pi
8484 176.470 543.118i 0.229219 0.705465i
8585 0 0
8686 −22.7855 70.1266i −0.0285701 0.0879296i
8787 −823.659 267.623i −1.01501 0.329795i
8888 −336.700 109.401i −0.407868 0.132524i
8989 −266.987 821.703i −0.317984 0.978656i −0.974509 0.224350i 0.927974π-0.927974\pi
0.656524 0.754305i 0.272026π-0.272026\pi
9090 0 0
9191 −198.833 + 611.945i −0.229048 + 0.704937i
9292 457.118 629.169i 0.518020 0.712993i
9393 370.592i 0.413211i
9494 687.123 + 499.224i 0.753950 + 0.547777i
9595 0 0
9696 113.853 82.7188i 0.121042 0.0879422i
9797 384.094 + 528.660i 0.402050 + 0.553374i 0.961257 0.275654i 0.0888944π-0.0888944\pi
−0.559207 + 0.829028i 0.688894π0.688894\pi
9898 −1352.14 + 439.338i −1.39375 + 0.452856i
9999 −338.953 −0.344101
100100 0 0
101101 684.563 0.674421 0.337211 0.941429i 0.390517π-0.390517\pi
0.337211 + 0.941429i 0.390517π0.390517\pi
102102 −689.104 + 223.903i −0.668936 + 0.217350i
103103 −2.26783 3.12140i −0.00216948 0.00298603i 0.807931 0.589277i 0.200587π-0.200587\pi
−0.810100 + 0.586291i 0.800587π0.800587\pi
104104 −128.281 + 93.2015i −0.120952 + 0.0878765i
105105 0 0
106106 8.46485 + 6.15007i 0.00775640 + 0.00563536i
107107 1045.89i 0.944951i 0.881344 + 0.472476i 0.156640π0.156640\pi
−0.881344 + 0.472476i 0.843360π0.843360\pi
108108 358.372 493.257i 0.319300 0.439479i
109109 356.163 1096.16i 0.312974 0.963236i −0.663606 0.748082i 0.730975π-0.730975\pi
0.976580 0.215153i 0.0690252π-0.0690252\pi
110110 0 0
111111 312.063 + 960.430i 0.266844 + 0.821261i
112112 −493.990 160.507i −0.416765 0.135415i
113113 129.218 + 41.9853i 0.107573 + 0.0349526i 0.362309 0.932058i 0.381989π-0.381989\pi
−0.254736 + 0.967011i 0.581989π0.581989\pi
114114 28.0971 + 86.4741i 0.0230837 + 0.0710442i
115115 0 0
116116 −243.415 + 749.155i −0.194832 + 0.599632i
117117 −89.2328 + 122.818i −0.0705092 + 0.0970476i
118118 103.748i 0.0809387i
119119 2163.53 + 1571.90i 1.66664 + 1.21089i
120120 0 0
121121 −507.551 + 368.758i −0.381331 + 0.277053i
122122 −146.008 200.963i −0.108352 0.149134i
123123 −86.5290 + 28.1150i −0.0634314 + 0.0206101i
124124 337.071 0.244112
125125 0 0
126126 −497.295 −0.351608
127127 −1556.36 + 505.692i −1.08744 + 0.353330i −0.797256 0.603641i 0.793716π-0.793716\pi
−0.290182 + 0.956971i 0.593716π0.593716\pi
128128 −75.2365 103.554i −0.0519534 0.0715077i
129129 131.172 95.3018i 0.0895273 0.0650454i
130130 0 0
131131 874.934 + 635.677i 0.583537 + 0.423964i 0.839997 0.542590i 0.182556π-0.182556\pi
−0.256461 + 0.966555i 0.582556π0.582556\pi
132132 778.471i 0.513312i
133133 197.254 271.496i 0.128602 0.177005i
134134 481.552 1482.07i 0.310446 0.955455i
135135 0 0
136136 203.650 + 626.771i 0.128403 + 0.395185i
137137 2204.47 + 716.275i 1.37475 + 0.446683i 0.900939 0.433945i 0.142879π-0.142879\pi
0.473809 + 0.880628i 0.342879π0.342879\pi
138138 1626.38 + 528.442i 1.00324 + 0.325971i
139139 327.762 + 1008.75i 0.200003 + 0.615546i 0.999882 + 0.0153844i 0.00489720π0.00489720\pi
−0.799879 + 0.600162i 0.795103π0.795103\pi
140140 0 0
141141 −577.118 + 1776.19i −0.344696 + 1.06086i
142142 −721.119 + 992.535i −0.426162 + 0.586561i
143143 877.124i 0.512929i
144144 −99.1447 72.0328i −0.0573754 0.0416857i
145145 0 0
146146 1469.26 1067.48i 0.832854 0.605104i
147147 −1837.56 2529.18i −1.03101 1.41907i
148148 873.554 283.835i 0.485174 0.157643i
149149 1830.45 1.00642 0.503209 0.864165i 0.332152π-0.332152\pi
0.503209 + 0.864165i 0.332152π0.332152\pi
150150 0 0
151151 −1585.52 −0.854491 −0.427246 0.904136i 0.640516π-0.640516\pi
−0.427246 + 0.904136i 0.640516π0.640516\pi
152152 78.6521 25.5556i 0.0419706 0.0136371i
153153 370.871 + 510.460i 0.195968 + 0.269727i
154154 −2324.49 + 1688.84i −1.21631 + 0.883704i
155155 0 0
156156 −282.077 204.941i −0.144771 0.105182i
157157 1535.51i 0.780554i 0.920698 + 0.390277i 0.127621π0.127621\pi
−0.920698 + 0.390277i 0.872379π0.872379\pi
158158 −726.688 + 1000.20i −0.365900 + 0.503618i
159159 −7.10967 + 21.8813i −0.00354612 + 0.0109138i
160160 0 0
161161 −1950.40 6002.72i −0.954741 2.93839i
162162 881.690 + 286.479i 0.427606 + 0.138938i
163163 −1593.69 517.820i −0.765811 0.248827i −0.100040 0.994983i 0.531897π-0.531897\pi
−0.665771 + 0.746156i 0.731897π0.731897\pi
164164 25.5719 + 78.7021i 0.0121758 + 0.0374732i
165165 0 0
166166 −279.393 + 859.884i −0.130633 + 0.402048i
167167 1209.69 1664.99i 0.560530 0.771503i −0.430864 0.902417i 0.641791π-0.641791\pi
0.991394 + 0.130914i 0.0417911π0.0417911\pi
168168 1142.14i 0.524510i
169169 −1459.59 1060.45i −0.664355 0.482682i
170170 0 0
171171 64.0566 46.5398i 0.0286464 0.0208128i
172172 −86.6813 119.307i −0.0384267 0.0528898i
173173 −4099.10 + 1331.88i −1.80144 + 0.585323i −0.999920 0.0126483i 0.995974π-0.995974\pi
−0.801518 + 0.597971i 0.795974π0.795974\pi
174174 −1732.09 −0.754653
175175 0 0
176176 −708.055 −0.303248
177177 −216.966 + 70.4964i −0.0921364 + 0.0299369i
178178 −1015.68 1397.96i −0.427688 0.588662i
179179 −2202.60 + 1600.28i −0.919719 + 0.668215i −0.943454 0.331503i 0.892444π-0.892444\pi
0.0237350 + 0.999718i 0.492444π0.492444\pi
180180 0 0
181181 1056.07 + 767.281i 0.433686 + 0.315091i 0.783121 0.621869i 0.213626π-0.213626\pi
−0.349435 + 0.936961i 0.613626π0.613626\pi
182182 1286.87i 0.524118i
183183 321.057 441.897i 0.129690 0.178502i
184184 480.642 1479.26i 0.192573 0.592679i
185185 0 0
186186 229.039 + 704.909i 0.0902900 + 0.277884i
187187 3467.10 + 1126.53i 1.35583 + 0.440534i
188188 1615.52 + 524.915i 0.626724 + 0.203635i
189189 −1529.08 4706.03i −0.588488 1.81118i
190190 0 0
191191 1225.39 3771.37i 0.464221 1.42872i −0.395739 0.918363i 0.629511π-0.629511\pi
0.859960 0.510362i 0.170489π-0.170489\pi
192192 165.438 227.705i 0.0621845 0.0855897i
193193 1941.18i 0.723986i −0.932181 0.361993i 0.882096π-0.882096\pi
0.932181 0.361993i 0.117904π-0.117904\pi
194194 1057.32 + 768.188i 0.391295 + 0.284292i
195195 0 0
196196 −2300.40 + 1671.34i −0.838340 + 0.609089i
197197 −1186.45 1633.01i −0.429092 0.590595i 0.538652 0.842528i 0.318934π-0.318934\pi
−0.967745 + 0.251933i 0.918934π0.918934\pi
198198 −644.726 + 209.484i −0.231408 + 0.0751889i
199199 −985.509 −0.351060 −0.175530 0.984474i 0.556164π-0.556164\pi
−0.175530 + 0.984474i 0.556164π0.556164\pi
200200 0 0
201201 3426.63 1.20247
202202 1302.12 423.083i 0.453547 0.147366i
203203 3757.65 + 5171.96i 1.29919 + 1.78818i
204204 −1172.37 + 851.779i −0.402365 + 0.292336i
205205 0 0
206206 −6.24281 4.53567i −0.00211144 0.00153405i
207207 1489.16i 0.500018i
208208 −186.403 + 256.562i −0.0621381 + 0.0855257i
209209 141.366 435.079i 0.0467869 0.143995i
210210 0 0
211211 1338.94 + 4120.84i 0.436856 + 1.34450i 0.891173 + 0.453664i 0.149884π0.149884\pi
−0.454317 + 0.890840i 0.650116π0.650116\pi
212212 19.9021 + 6.46657i 0.00644754 + 0.00209493i
213213 −2565.67 833.636i −0.825336 0.268168i
214214 646.394 + 1989.40i 0.206479 + 0.635478i
215215 0 0
216216 376.815 1159.72i 0.118699 0.365318i
217217 1607.95 2213.15i 0.503017 0.692343i
218218 2305.13i 0.716162i
219219 3230.75 + 2347.28i 0.996868 + 0.724267i
220220 0 0
221221 1320.94 959.722i 0.402065 0.292117i
222222 1187.16 + 1633.98i 0.358904 + 0.493989i
223223 4943.88 1606.36i 1.48460 0.482377i 0.549119 0.835744i 0.314963π-0.314963\pi
0.935485 + 0.353367i 0.114963π0.114963\pi
224224 −1038.82 −0.309863
225225 0 0
226226 271.735 0.0799802
227227 3561.42 1157.17i 1.04132 0.338345i 0.262064 0.965051i 0.415597π-0.415597\pi
0.779256 + 0.626705i 0.215597π0.215597\pi
228228 106.888 + 147.119i 0.0310475 + 0.0427332i
229229 −3401.89 + 2471.62i −0.981673 + 0.713227i −0.958082 0.286494i 0.907510π-0.907510\pi
−0.0235912 + 0.999722i 0.507510π0.507510\pi
230230 0 0
231231 −5111.31 3713.59i −1.45584 1.05773i
232232 1575.42i 0.445824i
233233 3653.09 5028.05i 1.02713 1.41373i 0.120055 0.992767i 0.461693π-0.461693\pi
0.907079 0.420961i 0.138307π-0.138307\pi
234234 −93.8249 + 288.763i −0.0262116 + 0.0806712i
235235 0 0
236236 64.1197 + 197.340i 0.0176857 + 0.0544311i
237237 −2585.48 840.073i −0.708629 0.230247i
238238 5086.76 + 1652.79i 1.38540 + 0.450144i
239239 −262.864 809.011i −0.0711432 0.218956i 0.909163 0.416441i 0.136723π-0.136723\pi
−0.980306 + 0.197485i 0.936723π0.936723\pi
240240 0 0
241241 1457.32 4485.16i 0.389518 1.19881i −0.543631 0.839325i 0.682951π-0.682951\pi
0.933149 0.359490i 0.117049π-0.117049\pi
242242 −737.515 + 1015.10i −0.195906 + 0.269642i
243243 2076.95i 0.548298i
244244 −401.925 292.016i −0.105453 0.0766164i
245245 0 0
246246 −147.212 + 106.956i −0.0381540 + 0.0277205i
247247 −120.433 165.762i −0.0310243 0.0427012i
248248 641.146 208.321i 0.164165 0.0533403i
249249 −1988.10 −0.505988
250250 0 0
251251 619.865 0.155879 0.0779393 0.996958i 0.475166π-0.475166\pi
0.0779393 + 0.996958i 0.475166π0.475166\pi
252252 −945.911 + 307.345i −0.236456 + 0.0768291i
253253 −5057.26 6960.72i −1.25671 1.72971i
254254 −2647.84 + 1923.77i −0.654095 + 0.475228i
255255 0 0
256256 −207.108 150.473i −0.0505636 0.0367366i
257257 3006.52i 0.729733i 0.931060 + 0.364867i 0.118885π0.118885\pi
−0.931060 + 0.364867i 0.881115π0.881115\pi
258258 190.604 262.343i 0.0459940 0.0633053i
259259 2303.55 7089.61i 0.552648 1.70088i
260260 0 0
261261 466.101 + 1434.51i 0.110540 + 0.340207i
262262 2057.09 + 668.390i 0.485067 + 0.157608i
263263 458.796 + 149.072i 0.107569 + 0.0349512i 0.362307 0.932059i 0.381989π-0.381989\pi
−0.254738 + 0.967010i 0.581989π0.581989\pi
264264 −481.122 1480.74i −0.112163 0.345202i
265265 0 0
266266 207.405 638.326i 0.0478075 0.147136i
267267 2233.38 3073.99i 0.511913 0.704587i
268268 3116.67i 0.710377i
269269 4209.63 + 3058.48i 0.954148 + 0.693229i 0.951784 0.306768i 0.0992476π-0.0992476\pi
0.00236368 + 0.999997i 0.499248π0.499248\pi
270270 0 0
271271 1750.36 1271.71i 0.392351 0.285059i −0.374067 0.927402i 0.622037π-0.622037\pi
0.766418 + 0.642342i 0.222037π0.222037\pi
272272 774.732 + 1066.33i 0.172702 + 0.237704i
273273 −2691.21 + 874.428i −0.596629 + 0.193856i
274274 4635.83 1.02212
275275 0 0
276276 3420.15 0.745902
277277 −4746.99 + 1542.39i −1.02967 + 0.334561i −0.774660 0.632377i 0.782079π-0.782079\pi
−0.255011 + 0.966938i 0.582079π0.582079\pi
278278 1246.88 + 1716.19i 0.269004 + 0.370252i
279279 522.168 379.377i 0.112048 0.0814076i
280280 0 0
281281 −355.968 258.626i −0.0755704 0.0549051i 0.549359 0.835587i 0.314872π-0.314872\pi
−0.624929 + 0.780682i 0.714872π0.714872\pi
282282 3735.19i 0.788748i
283283 −2136.86 + 2941.14i −0.448845 + 0.617783i −0.972149 0.234364i 0.924699π-0.924699\pi
0.523304 + 0.852146i 0.324699π0.324699\pi
284284 −758.229 + 2333.59i −0.158425 + 0.487581i
285285 0 0
286286 542.093 + 1668.39i 0.112079 + 0.344944i
287287 638.732 + 207.537i 0.131370 + 0.0426846i
288288 −233.103 75.7398i −0.0476935 0.0154966i
289289 −578.844 1781.50i −0.117819 0.362609i
290290 0 0
291291 −888.049 + 2733.13i −0.178895 + 0.550581i
292292 2134.96 2938.52i 0.427873 0.588917i
293293 7040.42i 1.40377i 0.712288 + 0.701887i 0.247659π0.247659\pi
−0.712288 + 0.701887i 0.752341π0.752341\pi
294294 −5058.36 3675.11i −1.00343 0.729037i
295295 0 0
296296 1486.18 1079.77i 0.291833 0.212029i
297297 −3964.80 5457.09i −0.774617 1.06617i
298298 3481.72 1131.28i 0.676815 0.219911i
299299 −3853.57 −0.745344
300300 0 0
301301 −1196.85 −0.229187
302302 −3015.85 + 979.908i −0.574644 + 0.186713i
303303 1769.57 + 2435.60i 0.335509 + 0.461788i
304304 133.811 97.2194i 0.0252454 0.0183418i
305305 0 0
306306 1020.92 + 741.742i 0.190726 + 0.138571i
307307 3985.50i 0.740927i −0.928847 0.370463i 0.879199π-0.879199\pi
0.928847 0.370463i 0.120801π-0.120801\pi
308308 −3377.68 + 4648.97i −0.624873 + 0.860064i
309309 5.24337 16.1374i 0.000965323 0.00297096i
310310 0 0
311311 1984.51 + 6107.70i 0.361837 + 1.11362i 0.951938 + 0.306290i 0.0990878π0.0990878\pi
−0.590101 + 0.807329i 0.700912π0.700912\pi
312312 −663.202 215.487i −0.120341 0.0391012i
313313 −6592.67 2142.09i −1.19054 0.386831i −0.354269 0.935143i 0.615270π-0.615270\pi
−0.836273 + 0.548313i 0.815270π0.815270\pi
314314 948.996 + 2920.71i 0.170557 + 0.524921i
315315 0 0
316316 −764.085 + 2351.61i −0.136023 + 0.418634i
317317 −3884.35 + 5346.35i −0.688223 + 0.947258i −0.999996 0.00289895i 0.999077π-0.999077\pi
0.311773 + 0.950157i 0.399077π0.399077\pi
318318 46.0148i 0.00811440i
319319 7050.35 + 5122.38i 1.23744 + 0.899053i
320320 0 0
321321 −3721.16 + 2703.58i −0.647024 + 0.470091i
322322 −7419.77 10212.4i −1.28412 1.76744i
323323 −809.903 + 263.154i −0.139518 + 0.0453321i
324324 1854.13 0.317923
325325 0 0
326326 −3351.40 −0.569378
327327 4820.68 1566.33i 0.815241 0.264888i
328328 97.2811 + 133.896i 0.0163764 + 0.0225401i
329329 11153.1 8103.22i 1.86897 1.35789i
330330 0 0
331331 3033.15 + 2203.71i 0.503676 + 0.365942i 0.810420 0.585850i 0.199239π-0.199239\pi
−0.306743 + 0.951792i 0.599239π0.599239\pi
332332 1808.27i 0.298921i
333333 1033.79 1422.90i 0.170125 0.234157i
334334 1271.94 3914.63i 0.208376 0.641315i
335335 0 0
336336 −705.879 2172.47i −0.114610 0.352732i
337337 −300.782 97.7299i −0.0486191 0.0157973i 0.284606 0.958644i 0.408137π-0.408137\pi
−0.333226 + 0.942847i 0.608137π0.608137\pi
338338 −3431.70 1115.03i −0.552247 0.179436i
339339 184.643 + 568.273i 0.0295824 + 0.0910453i
340340 0 0
341341 1152.37 3546.62i 0.183003 0.563226i
342342 93.0796 128.113i 0.0147169 0.0202560i
343343 11942.1i 1.87992i
344344 −238.613 173.363i −0.0373987 0.0271718i
345345 0 0
346346 −6973.80 + 5066.77i −1.08357 + 0.787257i
347347 3486.20 + 4798.35i 0.539335 + 0.742331i 0.988517 0.151109i 0.0482845π-0.0482845\pi
−0.449182 + 0.893440i 0.648285π0.648285\pi
348348 −3294.64 + 1070.49i −0.507503 + 0.164898i
349349 −8313.16 −1.27505 −0.637526 0.770429i 0.720042π-0.720042\pi
−0.637526 + 0.770429i 0.720042π0.720042\pi
350350 0 0
351351 −3021.13 −0.459419
352352 −1346.80 + 437.602i −0.203934 + 0.0662621i
353353 2118.46 + 2915.82i 0.319418 + 0.439641i 0.938289 0.345851i 0.112410π-0.112410\pi
−0.618872 + 0.785492i 0.712410π0.712410\pi
354354 −369.124 + 268.184i −0.0554201 + 0.0402651i
355355 0 0
356356 −2795.93 2031.36i −0.416247 0.302421i
357357 11760.9i 1.74357i
358358 −3200.56 + 4405.19i −0.472499 + 0.650340i
359359 −2483.37 + 7643.04i −0.365090 + 1.12363i 0.584834 + 0.811153i 0.301160π0.301160\pi
−0.949924 + 0.312480i 0.898840π0.898840\pi
360360 0 0
361361 −2086.53 6421.66i −0.304203 0.936239i
362362 2482.97 + 806.767i 0.360503 + 0.117135i
363363 −2624.00 852.590i −0.379406 0.123277i
364364 795.332 + 2447.78i 0.114524 + 0.352469i
365365 0 0
366366 337.579 1038.96i 0.0482119 0.148381i
367367 −7641.29 + 10517.3i −1.08684 + 1.49591i −0.235090 + 0.971974i 0.575538π0.575538\pi
−0.851755 + 0.523940i 0.824462π0.824462\pi
368368 3110.78i 0.440654i
369369 128.194 + 93.1387i 0.0180855 + 0.0131399i
370370 0 0
371371 137.398 99.8257i 0.0192274 0.0139695i
372372 871.315 + 1199.26i 0.121440 + 0.167147i
373373 6641.04 2157.81i 0.921877 0.299536i 0.190641 0.981660i 0.438944π-0.438944\pi
0.731237 + 0.682124i 0.238944π0.238944\pi
374374 7291.05 1.00805
375375 0 0
376376 3397.32 0.465967
377377 3712.15 1206.15i 0.507124 0.164774i
378378 −5816.97 8006.37i −0.791515 1.08943i
379379 −741.524 + 538.749i −0.100500 + 0.0730176i −0.636900 0.770946i 0.719784π-0.719784\pi
0.536400 + 0.843964i 0.319784π0.319784\pi
380380 0 0
381381 −5822.33 4230.17i −0.782906 0.568814i
382382 7930.90i 1.06225i
383383 329.322 453.273i 0.0439362 0.0604730i −0.786484 0.617611i 0.788101π-0.788101\pi
0.830420 + 0.557138i 0.188101π0.188101\pi
384384 173.951 535.367i 0.0231170 0.0711467i
385385 0 0
386386 −1199.72 3692.35i −0.158197 0.486880i
387387 −268.562 87.2611i −0.0352759 0.0114618i
388388 2485.91 + 807.721i 0.325265 + 0.105685i
389389 917.355 + 2823.33i 0.119567 + 0.367991i 0.992872 0.119183i 0.0380277π-0.0380277\pi
−0.873305 + 0.487174i 0.838028π0.838028\pi
390390 0 0
391391 −4949.31 + 15232.4i −0.640147 + 1.97017i
392392 −3342.68 + 4600.81i −0.430691 + 0.592796i
393393 4756.12i 0.610470i
394394 −3266.02 2372.90i −0.417613 0.303414i
395395 0 0
396396 −1096.87 + 796.925i −0.139192 + 0.101129i
397397 −3716.55 5115.40i −0.469845 0.646686i 0.506669 0.862141i 0.330877π-0.330877\pi
−0.976514 + 0.215455i 0.930877π0.930877\pi
398398 −1874.55 + 609.078i −0.236087 + 0.0767094i
399399 1475.85 0.185175
400400 0 0
401401 −3008.68 −0.374679 −0.187339 0.982295i 0.559986π-0.559986\pi
−0.187339 + 0.982295i 0.559986π0.559986\pi
402402 6517.83 2117.77i 0.808656 0.262748i
403403 −981.734 1351.24i −0.121349 0.167023i
404404 2215.29 1609.50i 0.272809 0.198207i
405405 0 0
406406 10343.9 + 7515.30i 1.26443 + 0.918666i
407407 10161.8i 1.23760i
408408 −1703.56 + 2344.75i −0.206712 + 0.284515i
409409 −3472.20 + 10686.3i −0.419778 + 1.29194i 0.488129 + 0.872771i 0.337680π0.337680\pi
−0.907907 + 0.419172i 0.862320π0.862320\pi
410410 0 0
411411 3150.04 + 9694.82i 0.378053 + 1.16353i
412412 −14.6777 4.76908i −0.00175514 0.000570281i
413413 1601.58 + 520.384i 0.190819 + 0.0620010i
414414 −920.352 2832.55i −0.109258 0.336262i
415415 0 0
416416 −195.996 + 603.212i −0.0230997 + 0.0710936i
417417 −2741.77 + 3773.72i −0.321978 + 0.443165i
418418 914.937i 0.107060i
419419 3609.66 + 2622.57i 0.420867 + 0.305778i 0.777987 0.628281i 0.216241π-0.216241\pi
−0.357119 + 0.934059i 0.616241π0.616241\pi
420420 0 0
421421 4617.41 3354.74i 0.534534 0.388361i −0.287517 0.957775i 0.592830π-0.592830\pi
0.822051 + 0.569414i 0.192830π0.192830\pi
422422 5093.64 + 7010.80i 0.587570 + 0.808721i
423423 3093.46 1005.13i 0.355577 0.115534i
424424 41.8525 0.00479372
425425 0 0
426426 −5395.40 −0.613634
427427 −3834.65 + 1245.95i −0.434595 + 0.141208i
428428 2459.03 + 3384.56i 0.277714 + 0.382241i
429429 −3120.72 + 2267.33i −0.351211 + 0.255170i
430430 0 0
431431 6487.97 + 4713.79i 0.725092 + 0.526810i 0.888007 0.459830i 0.152090π-0.152090\pi
−0.162915 + 0.986640i 0.552090π0.552090\pi
432432 2438.80i 0.271613i
433433 3399.31 4678.75i 0.377276 0.519276i −0.577584 0.816331i 0.696005π-0.696005\pi
0.954860 + 0.297055i 0.0960046π0.0960046\pi
434434 1690.70 5203.43i 0.186995 0.575513i
435435 0 0
436436 −1424.65 4384.62i −0.156487 0.481618i
437437 1911.48 + 621.078i 0.209242 + 0.0679867i
438438 7595.95 + 2468.08i 0.828650 + 0.269245i
439439 −3630.68 11174.1i −0.394721 1.21483i −0.929178 0.369632i 0.879484π-0.879484\pi
0.534457 0.845196i 0.320516π-0.320516\pi
440440 0 0
441441 −1682.52 + 5178.27i −0.181678 + 0.559148i
442442 1919.44 2641.89i 0.206558 0.284303i
443443 3568.50i 0.382719i 0.981520 + 0.191360i 0.0612897π0.0612897\pi
−0.981520 + 0.191360i 0.938710π0.938710\pi
444444 3267.96 + 2374.31i 0.349303 + 0.253784i
445445 0 0
446446 8411.03 6110.97i 0.892990 0.648795i
447447 4731.65 + 6512.55i 0.500669 + 0.689112i
448448 −1975.96 + 642.029i −0.208383 + 0.0677076i
449449 14369.1 1.51029 0.755145 0.655558i 0.227566π-0.227566\pi
0.755145 + 0.655558i 0.227566π0.227566\pi
450450 0 0
451451 915.518 0.0955878
452452 516.870 167.941i 0.0537866 0.0174763i
453453 −4098.52 5641.13i −0.425089 0.585085i
454454 6059.05 4402.15i 0.626355 0.455073i
455455 0 0
456456 294.237 + 213.776i 0.0302169 + 0.0219539i
457457 402.073i 0.0411558i 0.999788 + 0.0205779i 0.00655061π0.00655061\pi
−0.999788 + 0.0205779i 0.993449π0.993449\pi
458458 −4943.23 + 6803.78i −0.504328 + 0.694148i
459459 −3880.17 + 11941.9i −0.394577 + 1.21438i
460460 0 0
461461 2232.00 + 6869.38i 0.225498 + 0.694010i 0.998241 + 0.0592914i 0.0188841π0.0188841\pi
−0.772743 + 0.634719i 0.781116π0.781116\pi
462462 −12017.4 3904.70i −1.21018 0.393210i
463463 −3116.67 1012.67i −0.312838 0.101647i 0.148390 0.988929i 0.452591π-0.452591\pi
−0.461228 + 0.887282i 0.652591π0.652591\pi
464464 973.661 + 2996.62i 0.0974162 + 0.299816i
465465 0 0
466466 3841.09 11821.7i 0.381835 1.17517i
467467 3399.75 4679.36i 0.336877 0.463672i −0.606649 0.794970i 0.707487π-0.707487\pi
0.943526 + 0.331298i 0.107487π0.107487\pi
468468 607.248i 0.0599787i
469469 −20463.6 14867.6i −2.01475 1.46380i
470470 0 0
471471 −5463.18 + 3969.23i −0.534459 + 0.388307i
472472 243.926 + 335.735i 0.0237873 + 0.0327404i
473473 −1551.67 + 504.169i −0.150837 + 0.0490100i
474474 −5437.07 −0.526863
475475 0 0
476476 10697.1 1.03004
477477 38.1092 12.3824i 0.00365807 0.00118858i
478478 −999.992 1376.37i −0.0956874 0.131702i
479479 1896.17 1377.64i 0.180873 0.131412i −0.493665 0.869652i 0.664343π-0.664343\pi
0.674538 + 0.738241i 0.264343π0.264343\pi
480480 0 0
481481 −3682.10 2675.20i −0.349042 0.253594i
482482 9431.94i 0.891314i
483483 16315.3 22456.1i 1.53701 2.11551i
484484 −775.469 + 2386.65i −0.0728277 + 0.224141i
485485 0 0
486486 −1283.63 3950.60i −0.119808 0.368730i
487487 −11188.2 3635.26i −1.04104 0.338253i −0.261892 0.965097i 0.584346π-0.584346\pi
−0.779145 + 0.626844i 0.784346π0.784346\pi
488488 −944.983 307.044i −0.0876585 0.0284820i
489489 −2277.27 7008.72i −0.210597 0.648150i
490490 0 0
491491 3398.57 10459.7i 0.312374 0.961387i −0.664448 0.747334i 0.731333π-0.731333\pi
0.976822 0.214053i 0.0686666π-0.0686666\pi
492492 −213.912 + 294.424i −0.0196014 + 0.0269790i
493493 16222.5i 1.48200i
494494 −331.525 240.867i −0.0301943 0.0219375i
495495 0 0
496496 1090.78 792.501i 0.0987452 0.0717426i
497497 11704.9 + 16110.5i 1.05642 + 1.45403i
498498 −3781.60 + 1228.72i −0.340276 + 0.110562i
499499 −12608.1 −1.13109 −0.565545 0.824717i 0.691334π-0.691334\pi
−0.565545 + 0.824717i 0.691334π0.691334\pi
500500 0 0
501501 9050.87 0.807112
502502 1179.05 383.098i 0.104828 0.0340607i
503503 1904.41 + 2621.20i 0.168814 + 0.232353i 0.885039 0.465517i 0.154131π-0.154131\pi
−0.716225 + 0.697870i 0.754131π0.754131\pi
504504 −1609.28 + 1169.21i −0.142228 + 0.103335i
505505 0 0
506506 −13921.4 10114.5i −1.22309 0.888627i
507507 7934.29i 0.695018i
508508 −3847.53 + 5295.68i −0.336037 + 0.462515i
509509 −1458.15 + 4487.74i −0.126977 + 0.390797i −0.994256 0.107026i 0.965867π-0.965867\pi
0.867279 + 0.497823i 0.165867π0.165867\pi
510510 0 0
511511 −9109.30 28035.6i −0.788595 2.42704i
512512 −486.941 158.217i −0.0420312 0.0136568i
513513 1498.57 + 486.914i 0.128973 + 0.0419060i
514514 1858.13 + 5718.74i 0.159453 + 0.490744i
515515 0 0
516516 200.412 616.806i 0.0170982 0.0526228i
517517 11046.2 15203.8i 0.939673 1.29335i
518518 14908.9i 1.26459i
519519 −15334.7 11141.3i −1.29695 0.942292i
520520 0 0
521521 7016.16 5097.54i 0.589987 0.428651i −0.252324 0.967643i 0.581195π-0.581195\pi
0.842311 + 0.538992i 0.181195π0.181195\pi
522522 1773.15 + 2440.53i 0.148676 + 0.204635i
523523 −4454.00 + 1447.19i −0.372390 + 0.120997i −0.489232 0.872154i 0.662723π-0.662723\pi
0.116842 + 0.993150i 0.462723π0.462723\pi
524524 4325.91 0.360646
525525 0 0
526526 964.814 0.0799769
527527 −6602.07 + 2145.14i −0.545713 + 0.177313i
528528 −1830.30 2519.19i −0.150859 0.207639i
529529 20738.1 15067.1i 1.70445 1.23836i
530530 0 0
531531 321.439 + 233.539i 0.0262698 + 0.0190861i
532532 1342.35i 0.109395i
533533 241.020 331.735i 0.0195867 0.0269588i
534534 2348.32 7227.37i 0.190303 0.585691i
535535 0 0
536536 −1926.21 5928.26i −0.155223 0.477728i
537537 −11387.3 3699.94i −0.915077 0.297327i
538538 9897.44 + 3215.87i 0.793139 + 0.257707i
539539 9721.11 + 29918.5i 0.776842 + 2.39087i
540540 0 0
541541 1143.80 3520.25i 0.0908980 0.279755i −0.895265 0.445534i 0.853014π-0.853014\pi
0.986163 + 0.165779i 0.0530138π0.0530138\pi
542542 2543.43 3500.73i 0.201567 0.277434i
543543 5740.78i 0.453703i
544544 2132.65 + 1549.46i 0.168082 + 0.122119i
545545 0 0
546546 −4578.57 + 3326.52i −0.358873 + 0.260736i
547547 11392.7 + 15680.7i 0.890524 + 1.22570i 0.973393 + 0.229141i 0.0735917π0.0735917\pi
−0.0828689 + 0.996560i 0.526408π0.526408\pi
548548 8817.88 2865.10i 0.687374 0.223341i
549549 −951.304 −0.0739539
550550 0 0
551551 −2035.73 −0.157396
552552 6505.51 2113.77i 0.501618 0.162985i
553553 11795.3 + 16234.9i 0.907032 + 1.24842i
554554 −8076.06 + 5867.60i −0.619348 + 0.449983i
555555 0 0
556556 3432.37 + 2493.76i 0.261807 + 0.190214i
557557 4428.74i 0.336897i 0.985710 + 0.168448i 0.0538757π0.0538757\pi
−0.985710 + 0.168448i 0.946124π0.946124\pi
558558 758.755 1044.34i 0.0575639 0.0792299i
559559 −225.810 + 694.972i −0.0170854 + 0.0525835i
560560 0 0
561561 4954.25 + 15247.6i 0.372849 + 1.14751i
562562 −836.932 271.936i −0.0628182 0.0204109i
563563 10531.5 + 3421.90i 0.788367 + 0.256156i 0.675409 0.737444i 0.263967π-0.263967\pi
0.112959 + 0.993600i 0.463967π0.463967\pi
564564 2308.47 + 7104.74i 0.172348 + 0.530432i
565565 0 0
566566 −2246.83 + 6915.03i −0.166857 + 0.513534i
567567 8844.85 12173.9i 0.655113 0.901685i
568568 4907.36i 0.362515i
569569 −21829.5 15860.1i −1.60833 1.16852i −0.868432 0.495809i 0.834872π-0.834872\pi
−0.739903 0.672714i 0.765128π-0.765128\pi
570570 0 0
571571 −10821.3 + 7862.17i −0.793099 + 0.576220i −0.908881 0.417055i 0.863062π-0.863062\pi
0.115783 + 0.993275i 0.463062π0.463062\pi
572572 2062.24 + 2838.43i 0.150746 + 0.207484i
573573 16585.7 5389.03i 1.20921 0.392897i
574574 1343.20 0.0976730
575575 0 0
576576 −490.198 −0.0354599
577577 9915.34 3221.69i 0.715391 0.232445i 0.0713674 0.997450i 0.477264π-0.477264\pi
0.644024 + 0.765005i 0.277264π0.277264\pi
578578 −2202.05 3030.87i −0.158466 0.218110i
579579 6906.52 5017.88i 0.495726 0.360166i
580580 0 0
581581 11872.8 + 8626.10i 0.847792 + 0.615957i
582582 5747.57i 0.409355i
583583 136.081 187.299i 0.00966706 0.0133056i
584584 2244.83 6908.87i 0.159061 0.489539i
585585 0 0
586586 4351.22 + 13391.7i 0.306736 + 0.944036i
587587 12717.0 + 4132.00i 0.894184 + 0.290538i 0.719835 0.694146i 0.244218π-0.244218\pi
0.174350 + 0.984684i 0.444218π0.444218\pi
588588 −11892.9 3864.24i −0.834108 0.271018i
589589 269.189 + 828.479i 0.0188315 + 0.0579573i
590590 0 0
591591 2743.15 8442.54i 0.190927 0.587614i
592592 2159.55 2972.36i 0.149927 0.206357i
593593 2768.13i 0.191693i −0.995396 0.0958463i 0.969444π-0.969444\pi
0.995396 0.0958463i 0.0305557π-0.0305557\pi
594594 −10914.2 7929.61i −0.753895 0.547737i
595595 0 0
596596 5923.46 4303.65i 0.407105 0.295779i
597597 −2547.50 3506.34i −0.174644 0.240377i
598598 −7329.93 + 2381.64i −0.501243 + 0.162864i
599599 −4098.71 −0.279580 −0.139790 0.990181i 0.544643π-0.544643\pi
−0.139790 + 0.990181i 0.544643π0.544643\pi
600600 0 0
601601 −17523.5 −1.18935 −0.594673 0.803968i 0.702718π-0.702718\pi
−0.594673 + 0.803968i 0.702718π0.702718\pi
602602 −2276.54 + 739.693i −0.154128 + 0.0500791i
603603 −3507.85 4828.15i −0.236900 0.326065i
604604 −5130.87 + 3727.79i −0.345649 + 0.251129i
605605 0 0
606606 4871.21 + 3539.14i 0.326533 + 0.237240i
607607 14982.0i 1.00182i −0.865501 0.500908i 0.833000π-0.833000\pi
0.865501 0.500908i 0.167000π-0.167000\pi
608608 194.439 267.622i 0.0129696 0.0178512i
609609 −8687.92 + 26738.7i −0.578083 + 1.77916i
610610 0 0
611611 −2601.02 8005.10i −0.172219 0.530036i
612612 2400.33 + 779.914i 0.158542 + 0.0515133i
613613 −28387.1 9223.52i −1.87038 0.607723i −0.991400 0.130864i 0.958225π-0.958225\pi
−0.878980 0.476859i 0.841775π-0.841775\pi
614614 −2463.17 7580.87i −0.161898 0.498272i
615615 0 0
616616 −3551.50 + 10930.4i −0.232295 + 0.714932i
617617 −11272.8 + 15515.7i −0.735538 + 1.01238i 0.263325 + 0.964707i 0.415181π0.415181\pi
−0.998863 + 0.0476742i 0.984819π0.984819\pi
618618 33.9358i 0.00220890i
619619 12120.6 + 8806.12i 0.787023 + 0.571806i 0.907079 0.420961i 0.138307π-0.138307\pi
−0.120055 + 0.992767i 0.538307π0.538307\pi
620620 0 0
621621 23975.3 17419.0i 1.54927 1.12561i
622622 7549.53 + 10391.0i 0.486670 + 0.669843i
623623 −26675.2 + 8667.29i −1.71544 + 0.557380i
624624 −1394.66 −0.0894731
625625 0 0
626626 −13863.9 −0.885164
627627 1913.39 621.698i 0.121871 0.0395984i
628628 3610.20 + 4969.01i 0.229399 + 0.315741i
629629 −15303.6 + 11118.7i −0.970103 + 0.704821i
630630 0 0
631631 −15151.7 11008.3i −0.955908 0.694508i −0.00371118 0.999993i 0.501181π-0.501181\pi
−0.952197 + 0.305485i 0.901181π0.901181\pi
632632 4945.26i 0.311253i
633633 −11200.4 + 15416.0i −0.703280 + 0.967982i
634634 −4084.24 + 12570.0i −0.255846 + 0.787412i
635635 0 0
636636 28.4387 + 87.5253i 0.00177306 + 0.00545692i
637637 13400.1 + 4353.94i 0.833485 + 0.270816i
638638 16576.4 + 5385.98i 1.02863 + 0.334221i
639639 1451.89 + 4468.44i 0.0898837 + 0.276634i
640640 0 0
641641 −5889.14 + 18124.9i −0.362881 + 1.11683i 0.588416 + 0.808558i 0.299752π0.299752\pi
−0.951297 + 0.308275i 0.900248π0.900248\pi
642642 −5407.16 + 7442.32i −0.332404 + 0.457515i
643643 10953.1i 0.671768i −0.941903 0.335884i 0.890965π-0.890965\pi
0.941903 0.335884i 0.109035π-0.109035\pi
644644 −20424.9 14839.5i −1.24977 0.908012i
645645 0 0
646646 −1377.89 + 1001.10i −0.0839201 + 0.0609715i
647647 −6308.42 8682.80i −0.383323 0.527598i 0.573138 0.819459i 0.305726π-0.305726\pi
−0.956461 + 0.291860i 0.905726π0.905726\pi
648648 3526.76 1145.91i 0.213803 0.0694688i
649649 2295.60 0.138845
650650 0 0
651651 12030.6 0.724298
652652 −6374.75 + 2071.28i −0.382906 + 0.124414i
653653 4644.00 + 6391.92i 0.278306 + 0.383055i 0.925172 0.379548i 0.123921π-0.123921\pi
−0.646866 + 0.762604i 0.723921π0.723921\pi
654654 8201.42 5958.68i 0.490368 0.356274i
655655 0 0
656656 267.792 + 194.562i 0.0159383 + 0.0115798i
657657 6955.08i 0.413004i
658658 16206.4 22306.2i 0.960171 1.32156i
659659 4537.13 13963.8i 0.268196 0.825423i −0.722743 0.691116i 0.757119π-0.757119\pi
0.990940 0.134307i 0.0428808π-0.0428808\pi
660660 0 0
661661 −3412.01 10501.1i −0.200774 0.617919i −0.999860 0.0167028i 0.994683π-0.994683\pi
0.799086 0.601216i 0.205317π-0.205317\pi
662662 7131.36 + 2317.12i 0.418683 + 0.136038i
663663 6829.18 + 2218.94i 0.400035 + 0.129979i
664664 1117.57 + 3439.54i 0.0653166 + 0.201024i
665665 0 0
666666 1087.00 3345.43i 0.0632436 0.194644i
667667 −22504.7 + 30975.1i −1.30643 + 1.79814i
668668 8232.18i 0.476815i
669669 18495.0 + 13437.4i 1.06885 + 0.776563i
670670 0 0
671671 −4446.64 + 3230.68i −0.255828 + 0.185870i
672672 −2685.32 3696.03i −0.154150 0.212169i
673673 −13104.2 + 4257.81i −0.750564 + 0.243873i −0.659224 0.751947i 0.729115π-0.729115\pi
−0.0913399 + 0.995820i 0.529115π0.529115\pi
674674 −632.521 −0.0361481
675675 0 0
676676 −7216.60 −0.410594
677677 6144.11 1996.34i 0.348799 0.113332i −0.129377 0.991595i 0.541298π-0.541298\pi
0.478177 + 0.878264i 0.341298π0.341298\pi
678678 702.424 + 966.804i 0.0397882 + 0.0547638i
679679 17162.0 12468.9i 0.969983 0.704734i
680680 0 0
681681 13323.2 + 9679.90i 0.749703 + 0.544691i
682682 7458.27i 0.418756i
683683 −6638.66 + 9137.33i −0.371920 + 0.511904i −0.953421 0.301641i 0.902465π-0.902465\pi
0.581501 + 0.813545i 0.302465π0.302465\pi
684684 97.8697 301.212i 0.00547097 0.0168379i
685685 0 0
686686 7380.60 + 22715.2i 0.410777 + 1.26424i
687687 −17587.5 5714.53i −0.976718 0.317355i
688688 −561.013 182.284i −0.0310878 0.0101010i
689689 −32.0426 98.6170i −0.00177174 0.00545284i
690690 0 0
691691 828.470 2549.77i 0.0456100 0.140373i −0.925658 0.378361i 0.876488π-0.876488\pi
0.971268 + 0.237988i 0.0764878π0.0764878\pi
692692 −10133.5 + 13947.6i −0.556675 + 0.766197i
693693 11003.5i 0.603158i
694694 9596.70 + 6972.41i 0.524907 + 0.381367i
695695 0 0
696696 −5605.17 + 4072.39i −0.305264 + 0.221787i
697697 −1001.73 1378.76i −0.0544380 0.0749275i
698698 −15812.6 + 5137.82i −0.857471 + 0.278609i
699699 27332.4 1.47898
700700 0 0
701701 −34520.6 −1.85995 −0.929976 0.367620i 0.880173π-0.880173\pi
−0.929976 + 0.367620i 0.880173π0.880173\pi
702702 −5746.54 + 1867.16i −0.308959 + 0.100387i
703703 1395.26 + 1920.42i 0.0748555 + 0.103030i
704704 −2291.31 + 1664.74i −0.122666 + 0.0891224i
705705 0 0
706706 5831.63 + 4236.93i 0.310873 + 0.225862i
707707 22223.1i 1.18216i
708708 −536.369 + 738.248i −0.0284717 + 0.0391879i
709709 6361.25 19577.9i 0.336956 1.03704i −0.628794 0.777572i 0.716451π-0.716451\pi
0.965751 0.259472i 0.0835487π-0.0835487\pi
710710 0 0
711711 1463.10 + 4502.95i 0.0771736 + 0.237516i
712712 −6573.62 2135.90i −0.346007 0.112424i
713713 15581.8 + 5062.82i 0.818432 + 0.265925i
714714 7268.64 + 22370.6i 0.380983 + 1.17255i
715715 0 0
716716 −3365.27 + 10357.2i −0.175651 + 0.540597i
717717 2198.88 3026.50i 0.114531 0.157639i
718718 16072.7i 0.835417i
719719 −8049.33 5848.18i −0.417510 0.303339i 0.359125 0.933289i 0.383075π-0.383075\pi
−0.776635 + 0.629951i 0.783075π0.783075\pi
720720 0 0
721721 −101.331 + 73.6213i −0.00523407 + 0.00380277i
722722 −7937.61 10925.2i −0.409151 0.563149i
723723 19724.8 6408.98i 1.01463 0.329672i
724724 5221.50 0.268033
725725 0 0
726726 −5518.08 −0.282087
727727 −9111.21 + 2960.41i −0.464809 + 0.151026i −0.532053 0.846711i 0.678579π-0.678579\pi
0.0672442 + 0.997737i 0.478579π0.478579\pi
728728 3025.62 + 4164.41i 0.154034 + 0.212010i
729729 17514.7 12725.2i 0.889840 0.646506i
730730 0 0
731731 2457.07 + 1785.16i 0.124320 + 0.0903238i
732732 2184.86i 0.110321i
733733 −18669.8 + 25696.8i −0.940772 + 1.29486i 0.0147351 + 0.999891i 0.495310π0.495310\pi
−0.955507 + 0.294970i 0.904690π0.904690\pi
734734 −8034.53 + 24727.7i −0.404032 + 1.24348i
735735 0 0
736736 −1922.57 5917.06i −0.0962865 0.296339i
737737 −32793.3 10655.2i −1.63902 0.532549i
738738 301.403 + 97.9319i 0.0150336 + 0.00488472i
739739 −4249.28 13077.9i −0.211519 0.650987i −0.999382 0.0351378i 0.988813π-0.988813\pi
0.787864 0.615849i 0.211187π-0.211187\pi
740740 0 0
741741 278.449 856.979i 0.0138044 0.0424857i
742742 199.651 274.797i 0.00987795 0.0135958i
743743 6312.16i 0.311670i −0.987783 0.155835i 0.950193π-0.950193\pi
0.987783 0.155835i 0.0498068π-0.0498068\pi
744744 2398.52 + 1742.63i 0.118191 + 0.0858708i
745745 0 0
746746 11298.4 8208.78i 0.554510 0.402875i
747747 2035.23 + 2801.26i 0.0996857 + 0.137206i
748748 13868.4 4506.11i 0.677913 0.220267i
749749 33952.9 1.65636
750750 0 0
751751 40114.6 1.94914 0.974569 0.224087i 0.0719400π-0.0719400\pi
0.974569 + 0.224087i 0.0719400π0.0719400\pi
752752 6462.09 2099.66i 0.313362 0.101817i
753753 1602.33 + 2205.42i 0.0775459 + 0.106733i
754754 6315.49 4588.47i 0.305035 0.221621i
755755 0 0
756756 −16012.7 11633.9i −0.770341 0.559686i
757757 8151.37i 0.391369i 0.980667 + 0.195685i 0.0626929π0.0626929\pi
−0.980667 + 0.195685i 0.937307π0.937307\pi
758758 −1077.50 + 1483.05i −0.0516312 + 0.0710643i
759759 11692.7 35986.4i 0.559181 1.72098i
760760 0 0
761761 −1730.96 5327.36i −0.0824538 0.253767i 0.901328 0.433138i 0.142594π-0.142594\pi
−0.983781 + 0.179371i 0.942594π0.942594\pi
762762 −13689.1 4447.87i −0.650793 0.211456i
763763 −35584.8 11562.2i −1.68841 0.548597i
764764 −4901.56 15085.5i −0.232110 0.714362i
765765 0 0
766766 346.270 1065.71i 0.0163332 0.0502684i
767767 604.341 831.804i 0.0284504 0.0391587i
768768 1125.84i 0.0528973i
769769 2973.61 + 2160.45i 0.139442 + 0.101311i 0.655320 0.755352i 0.272534π-0.272534\pi
−0.515877 + 0.856662i 0.672534π0.672534\pi
770770 0 0
771771 −10696.9 + 7771.73i −0.499661 + 0.363025i
772772 −4563.99 6281.80i −0.212774 0.292859i
773773 6444.75 2094.03i 0.299873 0.0974345i −0.155216 0.987881i 0.549607π-0.549607\pi
0.455089 + 0.890446i 0.349607π0.349607\pi
774774 −564.766 −0.0262275
775775 0 0
776776 5227.68 0.241833
777777 31178.7 10130.6i 1.43955 0.467738i
778778 3489.83 + 4803.33i 0.160818 + 0.221347i
779779 −173.018 + 125.705i −0.00795766 + 0.00578158i
780780 0 0
781781 21961.6 + 15956.0i 1.00621 + 0.731051i
782782 32032.6i 1.46481i
783783 −17643.3 + 24283.9i −0.805263 + 1.10835i
784784 −3514.70 + 10817.1i −0.160109 + 0.492764i
785785 0 0
786786 2939.45 + 9046.69i 0.133393 + 0.410540i
787787 −4951.65 1608.89i −0.224278 0.0728725i 0.194722 0.980858i 0.437619π-0.437619\pi
−0.419001 + 0.907986i 0.637619π0.637619\pi
788788 −7678.87 2495.02i −0.347143 0.112794i
789789 655.588 + 2017.69i 0.0295812 + 0.0910416i
790790 0 0
791791 1362.98 4194.82i 0.0612668 0.188560i
792792 −1593.85 + 2193.75i −0.0715089 + 0.0984235i
793793 2461.74i 0.110238i
794794 −10230.8 7433.11i −0.457276 0.332231i
795795 0 0
796796 −3189.17 + 2317.07i −0.142007 + 0.103174i
797797 −19082.9 26265.4i −0.848121 1.16734i −0.984274 0.176650i 0.943474π-0.943474\pi
0.136153 0.990688i 0.456526π-0.456526\pi
798798 2807.23 912.125i 0.124530 0.0404623i
799799 −34983.2 −1.54896
800800 0 0
801801 −6617.60 −0.291912
802802 −5722.85 + 1859.47i −0.251971 + 0.0818703i
803803 −23619.8 32509.9i −1.03801 1.42870i
804804 11088.8 8056.48i 0.486408 0.353396i
805805 0 0
806806 −2702.48 1963.47i −0.118103 0.0858067i
807807 22883.5i 0.998187i
808808 3219.01 4430.58i 0.140154 0.192905i
809809 −4880.74 + 15021.4i −0.212111 + 0.652811i 0.787235 + 0.616653i 0.211512π0.211512\pi
−0.999346 + 0.0361575i 0.988488π0.988488\pi
810810 0 0
811811 1468.40 + 4519.27i 0.0635789 + 0.195676i 0.977800 0.209540i 0.0671965π-0.0671965\pi
−0.914221 + 0.405215i 0.867197π0.867197\pi
812812 24320.0 + 7902.06i 1.05107 + 0.341512i
813813 9049.25 + 2940.28i 0.390370 + 0.126839i
814814 −6280.34 19328.9i −0.270425 0.832282i
815815 0 0
816816 −1791.23 + 5512.83i −0.0768450 + 0.236504i
817817 224.016 308.332i 0.00959282 0.0132034i
818818 22472.5i 0.960555i
819819 3987.09 + 2896.79i 0.170110 + 0.123592i
820820 0 0
821821 −33068.5 + 24025.6i −1.40572 + 1.02132i −0.411794 + 0.911277i 0.635098π0.635098\pi
−0.993927 + 0.110039i 0.964902π0.964902\pi
822822 11983.5 + 16493.8i 0.508480 + 0.699863i
823823 −14439.2 + 4691.60i −0.611568 + 0.198710i −0.598393 0.801203i 0.704194π-0.704194\pi
−0.0131750 + 0.999913i 0.504194π0.504194\pi
824824 −30.8661 −0.00130494
825825 0 0
826826 3367.99 0.141874
827827 −15044.7 + 4888.31i −0.632593 + 0.205542i −0.607723 0.794149i 0.707917π-0.707917\pi
−0.0248693 + 0.999691i 0.507917π0.507917\pi
828828 −3501.23 4819.02i −0.146952 0.202262i
829829 1.67554 1.21735i 7.01976e−5 5.10015e-5i −0.587750 0.809042i 0.699986π-0.699986\pi
0.587820 + 0.808991i 0.299986π0.299986\pi
830830 0 0
831831 −17758.5 12902.3i −0.741317 0.538598i
832832 1268.51i 0.0528578i
833833 34420.6 47375.8i 1.43169 1.97056i
834834 −2882.87 + 8872.55i −0.119695 + 0.368383i
835835 0 0
836836 −565.462 1740.31i −0.0233935 0.0719976i
837837 12215.8 + 3969.17i 0.504470 + 0.163912i
838838 8486.82 + 2757.53i 0.349848 + 0.113672i
839839 −5938.00 18275.3i −0.244341 0.752005i −0.995744 0.0921615i 0.970622π-0.970622\pi
0.751403 0.659844i 0.229378π-0.229378\pi
840840 0 0
841841 4447.16 13686.9i 0.182343 0.561193i
842842 6709.49 9234.81i 0.274613 0.377972i
843843 1935.04i 0.0790584i
844844 14021.6 + 10187.3i 0.571852 + 0.415475i
845845 0 0
846846 5262.91 3823.73i 0.213880 0.155393i
847847 11971.1 + 16476.8i 0.485633 + 0.668416i
848848 79.6082 25.8663i 0.00322377 0.00104747i
849849 −15988.0 −0.646296
850850 0 0
851851 44645.0 1.79837
852852 −10262.7 + 3334.54i −0.412668 + 0.134084i
853853 14792.5 + 20360.1i 0.593769 + 0.817253i 0.995120 0.0986714i 0.0314593π-0.0314593\pi
−0.401351 + 0.915924i 0.631459π0.631459\pi
854854 −6523.90 + 4739.89i −0.261409 + 0.189925i
855855 0 0
856856 6769.13 + 4918.06i 0.270285 + 0.196374i
857857 32539.4i 1.29699i −0.761217 0.648497i 0.775398π-0.775398\pi
0.761217 0.648497i 0.224602π-0.224602\pi
858858 −4534.67 + 6241.43i −0.180432 + 0.248344i
859859 −14076.7 + 43323.7i −0.559129 + 1.72082i 0.125654 + 0.992074i 0.459897π0.459897\pi
−0.684783 + 0.728747i 0.740103π0.740103\pi
860860 0 0
861861 912.704 + 2809.02i 0.0361265 + 0.111186i
862862 15254.1 + 4956.37i 0.602735 + 0.195841i
863863 3800.08 + 1234.72i 0.149892 + 0.0487027i 0.383002 0.923748i 0.374890π-0.374890\pi
−0.233110 + 0.972450i 0.574890π0.574890\pi
864864 −1507.26 4638.87i −0.0593496 0.182659i
865865 0 0
866866 3574.25 11000.4i 0.140252 0.431650i
867867 4842.10 6664.58i 0.189673 0.261062i
868868 10942.4i 0.427891i
869869 22131.2 + 16079.2i 0.863922 + 0.627676i
870870 0 0
871871 −12494.0 + 9077.45i −0.486044 + 0.353132i
872872 −5419.69 7459.57i −0.210475 0.289694i
873873 4760.11 1546.65i 0.184542 0.0599614i
874874 4019.70 0.155570
875875 0 0
876876 15973.7 0.616098
877877 −2331.16 + 757.438i −0.0897577 + 0.0291641i −0.353552 0.935415i 0.615026π-0.615026\pi
0.263794 + 0.964579i 0.415026π0.415026\pi
878878 −13811.9 19010.5i −0.530899 0.730720i
879879 −25049.1 + 18199.2i −0.961189 + 0.698345i
880880 0 0
881881 −28818.0 20937.5i −1.10205 0.800684i −0.120654 0.992695i 0.538499π-0.538499\pi
−0.981393 + 0.192011i 0.938499π0.938499\pi
882882 10889.5i 0.415724i
883883 12345.8 16992.6i 0.470521 0.647617i −0.506128 0.862459i 0.668924π-0.668924\pi
0.976649 + 0.214842i 0.0689236π0.0689236\pi
884884 2018.22 6211.45i 0.0767875 0.236328i
885885 0 0
886886 2205.45 + 6787.69i 0.0836272 + 0.257378i
887887 −11581.2 3762.96i −0.438398 0.142444i 0.0814984 0.996673i 0.474029π-0.474029\pi
−0.519896 + 0.854229i 0.674029π0.674029\pi
888888 7683.44 + 2496.50i 0.290360 + 0.0943435i
889889 16416.4 + 50524.5i 0.619335 + 1.90612i
890890 0 0
891891 6338.83 19508.9i 0.238338 0.733528i
892892 12221.9 16822.1i 0.458768 0.631440i
893893 4389.96i 0.164507i
894894 13025.1 + 9463.29i 0.487276 + 0.354027i
895895 0 0
896896 −3361.71 + 2442.42i −0.125342 + 0.0910666i
897897 −9961.34 13710.6i −0.370791 0.510350i
898898 27331.7 8880.60i 1.01567 0.330011i
899899 −16594.6 −0.615640
900900 0 0
901901 −430.967 −0.0159352
902902 1741.42 565.821i 0.0642826 0.0208867i
903903 −3093.81 4258.26i −0.114015 0.156928i
904904 879.352 638.887i 0.0323527 0.0235056i
905905 0 0
906906 −11282.3 8197.04i −0.413718 0.300583i
907907 33352.4i 1.22100i 0.792015 + 0.610501i 0.209032π0.209032\pi
−0.792015 + 0.610501i 0.790968π0.790968\pi
908908 8804.31 12118.1i 0.321786 0.442900i
909909 1620.27 4986.68i 0.0591210 0.181956i
910910 0 0
911911 5604.85 + 17249.9i 0.203839 + 0.627350i 0.999759 + 0.0219494i 0.00698727π0.00698727\pi
−0.795921 + 0.605401i 0.793013π0.793013\pi
912912 691.793 + 224.777i 0.0251179 + 0.00816131i
913913 19026.4 + 6182.06i 0.689685 + 0.224092i
914914 248.495 + 764.789i 0.00899287 + 0.0276772i
915915 0 0
916916 −5197.62 + 15996.6i −0.187483 + 0.577013i
917917 20636.1 28403.2i 0.743147 1.02285i
918918 25113.0i 0.902889i
919919 −25633.4 18623.8i −0.920096 0.668489i 0.0234522 0.999725i 0.492534π-0.492534\pi
−0.943548 + 0.331236i 0.892534π0.892534\pi
920920 0 0
921921 14180.0 10302.4i 0.507325 0.368593i
922922 8491.02 + 11686.9i 0.303294 + 0.417448i
923923 11563.2 3757.12i 0.412360 0.133984i
924924 −25271.7 −0.899761
925925 0 0
926926 −6554.13 −0.232594
927927 −28.1054 + 9.13201i −0.000995797 + 0.000323554i
928928 3704.03 + 5098.16i 0.131024 + 0.180340i
929929 −22563.0 + 16393.0i −0.796844 + 0.578941i −0.909987 0.414638i 0.863908π-0.863908\pi
0.113143 + 0.993579i 0.463908π0.463908\pi
930930 0 0
931931 −5945.09 4319.36i −0.209283 0.152053i
932932 24860.1i 0.873732i
933933 −16600.7 + 22848.8i −0.582509 + 0.801755i
934934 3574.71 11001.8i 0.125234 0.385429i
935935 0 0
936936 375.300 + 1155.05i 0.0131058 + 0.0403356i
937937 38777.9 + 12599.7i 1.35200 + 0.439290i 0.893363 0.449336i 0.148339π-0.148339\pi
0.458633 + 0.888626i 0.348339π0.348339\pi
938938 −48112.7 15632.8i −1.67477 0.544166i
939939 −9420.48 28993.3i −0.327397 1.00762i
940940 0 0
941941 −7635.56 + 23499.8i −0.264519 + 0.814105i 0.727285 + 0.686335i 0.240782π0.240782\pi
−0.991804 + 0.127769i 0.959218π0.959218\pi
942942 −7938.46 + 10926.4i −0.274574 + 0.377919i
943943 4022.25i 0.138900i
944944 671.470 + 487.852i 0.0231509 + 0.0168201i
945945 0 0
946946 −2639.86 + 1917.97i −0.0907287 + 0.0659183i
947947 19473.6 + 26803.1i 0.668223 + 0.919730i 0.999718 0.0237270i 0.00755325π-0.00755325\pi
−0.331496 + 0.943457i 0.607553π0.607553\pi
948948 −10341.9 + 3360.29i −0.354314 + 0.115124i
949949 −17998.0 −0.615638
950950 0 0
951951 −29062.6 −0.990978
952952 20347.0 6611.15i 0.692701 0.225072i
953953 −18998.2 26148.8i −0.645763 0.888816i 0.353144 0.935569i 0.385113π-0.385113\pi
−0.998906 + 0.0467529i 0.985113π0.985113\pi
954954 64.8352 47.1055i 0.00220033 0.00159864i
955955 0 0
956956 −2752.74 1999.98i −0.0931277 0.0676612i
957957 38325.5i 1.29455i
958958 2755.29 3792.33i 0.0929221 0.127896i
959959 23252.6 71564.3i 0.782969 2.40973i
960960 0 0
961961 −7011.58 21579.4i −0.235359 0.724361i
962962 −8657.13 2812.87i −0.290143 0.0942730i
963963 7618.74 + 2475.48i 0.254943 + 0.0828361i
964964 −5829.26 17940.6i −0.194759 0.599407i
965965 0 0
966966 17155.0 52797.6i 0.571379 1.75852i
967967 −7523.54 + 10355.3i −0.250197 + 0.344367i −0.915580 0.402135i 0.868268π-0.868268\pi
0.665383 + 0.746502i 0.268268π0.268268\pi
968968 5018.94i 0.166648i
969969 −3029.84 2201.31i −0.100446 0.0729786i
970970 0 0
971971 30611.3 22240.4i 1.01170 0.735046i 0.0471385 0.998888i 0.484990π-0.484990\pi
0.964566 + 0.263842i 0.0849898π0.0849898\pi
972972 −4883.20 6721.15i −0.161141 0.221791i
973973 32747.3 10640.2i 1.07896 0.350576i
974974 −23527.9 −0.774006
975975 0 0
976976 −1987.23 −0.0651738
977977 28089.5 9126.82i 0.919817 0.298867i 0.189425 0.981895i 0.439337π-0.439337\pi
0.730392 + 0.683028i 0.239337π0.239337\pi
978978 −8663.25 11923.9i −0.283252 0.389863i
979979 −30932.4 + 22473.7i −1.00981 + 0.733669i
980980 0 0
981981 −7141.93 5188.91i −0.232441 0.168878i
982982 21996.0i 0.714788i
983983 −624.445 + 859.475i −0.0202611 + 0.0278871i −0.819027 0.573754i 0.805486π-0.805486\pi
0.798766 + 0.601641i 0.205486π0.205486\pi
984984 −224.920 + 692.232i −0.00728677 + 0.0224264i
985985 0 0
986986 −10026.1 30857.1i −0.323829 0.996642i
987987 57660.8 + 18735.1i 1.85954 + 0.604200i
988988 −779.461 253.262i −0.0250992 0.00815521i
989989 −2215.03 6817.15i −0.0712171 0.219184i
990990 0 0
991991 15803.1 48637.0i 0.506561 1.55904i −0.291568 0.956550i 0.594177π-0.594177\pi
0.798130 0.602486i 0.205823π-0.205823\pi
992992 1585.00 2181.57i 0.0507297 0.0698234i
993993 16488.1i 0.526924i
994994 32220.9 + 23409.9i 1.02816 + 0.746998i
995995 0 0
996996 −6433.64 + 4674.31i −0.204676 + 0.148706i
997997 −27686.5 38107.1i −0.879477 1.21050i −0.976565 0.215221i 0.930953π-0.930953\pi
0.0970879 0.995276i 0.469047π-0.469047\pi
998998 −23982.0 + 7792.21i −0.760657 + 0.247152i
999999 35000.9 1.10849
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 250.4.e.c.99.7 32
5.2 odd 4 50.4.d.b.31.3 yes 16
5.3 odd 4 250.4.d.b.151.2 16
5.4 even 2 inner 250.4.e.c.99.2 32
25.2 odd 20 1250.4.a.j.1.3 8
25.3 odd 20 250.4.d.b.101.2 16
25.4 even 10 inner 250.4.e.c.149.7 32
25.21 even 5 inner 250.4.e.c.149.2 32
25.22 odd 20 50.4.d.b.21.3 16
25.23 odd 20 1250.4.a.g.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.4.d.b.21.3 16 25.22 odd 20
50.4.d.b.31.3 yes 16 5.2 odd 4
250.4.d.b.101.2 16 25.3 odd 20
250.4.d.b.151.2 16 5.3 odd 4
250.4.e.c.99.2 32 5.4 even 2 inner
250.4.e.c.99.7 32 1.1 even 1 trivial
250.4.e.c.149.2 32 25.21 even 5 inner
250.4.e.c.149.7 32 25.4 even 10 inner
1250.4.a.g.1.6 8 25.23 odd 20
1250.4.a.j.1.3 8 25.2 odd 20