Properties

Label 637.2.bb.b.227.2
Level 637637
Weight 22
Character 637.227
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [637,2,Mod(227,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.227"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.bb (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 227.2
Character χ\chi == 637.227
Dual form 637.2.bb.b.362.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.65980+1.65980i)q2+(2.390461.38013i)q33.50987iq4+(0.4124301.53921i)q5+(1.67694+6.25841i)q6+(2.50608+2.50608i)q8+(2.309524.00020i)q9+(1.87023+3.23933i)q10+(0.8130803.03446i)q11+(4.844078.39018i)q12+(1.048313.44979i)q13+(1.138414.24862i)q151.29944q160.641590q17+(2.80620+10.4729i)q18+(7.61472+2.04036i)q19+(5.402421.44757i)q20+(3.68704+6.38614i)q22+0.146149iq23+(9.44938+2.53195i)q24+(2.13106+1.23037i)q25+(7.46594+3.98598i)q264.46896iq27+(1.494122.58790i)q29+(8.94139+5.16231i)q30+(6.46586+1.73252i)q31+(2.85535+2.85535i)q32+(2.244318.37589i)q33+(1.064911.06491i)q34+(14.04028.10610i)q36+(2.750502.75050i)q37+(9.2523216.0255i)q38+(7.267096.79977i)q39+(4.890962.82380i)q40+(5.603561.50147i)q41+(2.427131.40130i)q43+(10.65052.85380i)q44+(5.204635.20463i)q45+(0.2425780.242578i)q46+(3.04537+0.816005i)q47+(3.10624+1.79339i)q48+(5.57930+1.49497i)q50+(1.53369+0.885477i)q51+(12.1083+3.67942i)q52+(3.660596.34033i)q53+(7.41757+7.41757i)q54+(4.335332.50300i)q55+(15.3867+15.3867i)q57+(1.81545+6.77534i)q58+(2.932832.93283i)q59+(14.9121+3.99568i)q60+(3.90292+2.25335i)q61+(7.8563913.6077i)q6212.0775iq64+(5.74230+0.190767i)q65+(17.6274+10.1772i)q66+(1.36775+0.366486i)q67+2.25190iq68+(0.201704+0.349362i)q69+(13.8300+3.70574i)q71+(15.81264.23699i)q72+(1.82677+6.81760i)q73+9.13055q74+6.79227q75+(7.16138+26.7267i)q76+(23.34820.775656i)q78+(0.316458+0.548121i)q79+(0.535926+2.00010i)q80+(0.760810+1.31776i)q81+(6.80865+11.7929i)q82+(1.07813+1.07813i)q83+(0.264611+0.987541i)q85+(1.70266+6.35443i)q868.24834iq87+(9.642235.56694i)q88+(9.604719.60471i)q89+17.2773q90+0.512963q92+(13.0652+13.0652i)q93+(6.40911+3.70030i)q94+12.5621iq95+(2.88483+10.7663i)q96+(0.04871600.181811i)q97+(10.260610.2606i)q99+O(q100)q+(-1.65980 + 1.65980i) q^{2} +(2.39046 - 1.38013i) q^{3} -3.50987i q^{4} +(0.412430 - 1.53921i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} +(2.30952 - 4.00020i) q^{9} +(1.87023 + 3.23933i) q^{10} +(0.813080 - 3.03446i) q^{11} +(-4.84407 - 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} -1.29944 q^{16} -0.641590 q^{17} +(2.80620 + 10.4729i) q^{18} +(-7.61472 + 2.04036i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +0.146149i q^{23} +(9.44938 + 2.53195i) q^{24} +(2.13106 + 1.23037i) q^{25} +(7.46594 + 3.98598i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} +(8.94139 + 5.16231i) q^{30} +(-6.46586 + 1.73252i) q^{31} +(-2.85535 + 2.85535i) q^{32} +(-2.24431 - 8.37589i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-2.75050 - 2.75050i) q^{37} +(9.25232 - 16.0255i) q^{38} +(-7.26709 - 6.79977i) q^{39} +(4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(-10.6505 - 2.85380i) q^{44} +(-5.20463 - 5.20463i) q^{45} +(-0.242578 - 0.242578i) q^{46} +(3.04537 + 0.816005i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(-1.53369 + 0.885477i) q^{51} +(-12.1083 + 3.67942i) q^{52} +(3.66059 - 6.34033i) q^{53} +(7.41757 + 7.41757i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(1.81545 + 6.77534i) q^{58} +(2.93283 - 2.93283i) q^{59} +(-14.9121 + 3.99568i) q^{60} +(3.90292 + 2.25335i) q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(-5.74230 + 0.190767i) q^{65} +(17.6274 + 10.1772i) q^{66} +(1.36775 + 0.366486i) q^{67} +2.25190i q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(15.8126 - 4.23699i) q^{72} +(1.82677 + 6.81760i) q^{73} +9.13055 q^{74} +6.79227 q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 + 0.548121i) q^{79} +(-0.535926 + 2.00010i) q^{80} +(0.760810 + 1.31776i) q^{81} +(-6.80865 + 11.7929i) q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(-1.70266 + 6.35443i) q^{86} -8.24834i q^{87} +(9.64223 - 5.56694i) q^{88} +(9.60471 - 9.60471i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(-13.0652 + 13.0652i) q^{93} +(-6.40911 + 3.70030i) q^{94} +12.5621i q^{95} +(-2.88483 + 10.7663i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+4q216q8+8q916q118q1524q16+68q18+4q22+4q2912q3068q328q3748q43+60q44+24q4644q5012q5136q53+60q99+O(q100) 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53}+ \cdots - 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(512)e\left(\frac{5}{12}\right) e(16)e\left(\frac{1}{6}\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 −1.65980 + 1.65980i −1.17366 + 1.17366i −0.192324 + 0.981332i 0.561602π0.561602\pi
−0.981332 + 0.192324i 0.938398π0.938398\pi
33 2.39046 1.38013i 1.38013 0.796818i 0.387956 0.921678i 0.373181π-0.373181\pi
0.992174 + 0.124860i 0.0398481π0.0398481\pi
44 3.50987i 1.75493i
55 0.412430 1.53921i 0.184444 0.688355i −0.810305 0.586009i 0.800698π-0.800698\pi
0.994749 0.102346i 0.0326350π-0.0326350\pi
66 −1.67694 + 6.25841i −0.684607 + 2.55499i
77 0 0
88 2.50608 + 2.50608i 0.886032 + 0.886032i
99 2.30952 4.00020i 0.769839 1.33340i
1010 1.87023 + 3.23933i 0.591418 + 1.02437i
1111 0.813080 3.03446i 0.245153 0.914923i −0.728154 0.685414i 0.759621π-0.759621\pi
0.973306 0.229509i 0.0737121π-0.0737121\pi
1212 −4.84407 8.39018i −1.39836 2.42204i
1313 −1.04831 3.44979i −0.290748 0.956800i
1414 0 0
1515 −1.13841 4.24862i −0.293937 1.09699i
1616 −1.29944 −0.324859
1717 −0.641590 −0.155608 −0.0778042 0.996969i 0.524791π-0.524791\pi
−0.0778042 + 0.996969i 0.524791π0.524791\pi
1818 2.80620 + 10.4729i 0.661427 + 2.46848i
1919 −7.61472 + 2.04036i −1.74694 + 0.468090i −0.983968 0.178346i 0.942925π-0.942925\pi
−0.762968 + 0.646436i 0.776259π0.776259\pi
2020 −5.40242 1.44757i −1.20802 0.323687i
2121 0 0
2222 3.68704 + 6.38614i 0.786080 + 1.36153i
2323 0.146149i 0.0304741i 0.999884 + 0.0152371i 0.00485029π0.00485029\pi
−0.999884 + 0.0152371i 0.995150π0.995150\pi
2424 9.44938 + 2.53195i 1.92885 + 0.516833i
2525 2.13106 + 1.23037i 0.426212 + 0.246074i
2626 7.46594 + 3.98598i 1.46419 + 0.781715i
2727 4.46896i 0.860051i
2828 0 0
2929 1.49412 2.58790i 0.277452 0.480561i −0.693299 0.720650i 0.743843π-0.743843\pi
0.970751 + 0.240089i 0.0771768π0.0771768\pi
3030 8.94139 + 5.16231i 1.63247 + 0.942505i
3131 −6.46586 + 1.73252i −1.16130 + 0.311170i −0.787486 0.616333i 0.788618π-0.788618\pi
−0.373817 + 0.927503i 0.621951π0.621951\pi
3232 −2.85535 + 2.85535i −0.504760 + 0.504760i
3333 −2.24431 8.37589i −0.390685 1.45806i
3434 1.06491 1.06491i 0.182631 0.182631i
3535 0 0
3636 −14.0402 8.10610i −2.34003 1.35102i
3737 −2.75050 2.75050i −0.452179 0.452179i 0.443898 0.896077i 0.353595π-0.353595\pi
−0.896077 + 0.443898i 0.853595π0.853595\pi
3838 9.25232 16.0255i 1.50092 2.59968i
3939 −7.26709 6.79977i −1.16367 1.08883i
4040 4.89096 2.82380i 0.773328 0.446481i
4141 5.60356 1.50147i 0.875129 0.234490i 0.206825 0.978378i 0.433687π-0.433687\pi
0.668305 + 0.743888i 0.267020π0.267020\pi
4242 0 0
4343 2.42713 1.40130i 0.370133 0.213697i −0.303383 0.952869i 0.598116π-0.598116\pi
0.673517 + 0.739172i 0.264783π0.264783\pi
4444 −10.6505 2.85380i −1.60563 0.430227i
4545 −5.20463 5.20463i −0.775861 0.775861i
4646 −0.242578 0.242578i −0.0357661 0.0357661i
4747 3.04537 + 0.816005i 0.444213 + 0.119027i 0.473990 0.880530i 0.342813π-0.342813\pi
−0.0297773 + 0.999557i 0.509480π0.509480\pi
4848 −3.10624 + 1.79339i −0.448348 + 0.258854i
4949 0 0
5050 −5.57930 + 1.49497i −0.789032 + 0.211420i
5151 −1.53369 + 0.885477i −0.214760 + 0.123992i
5252 −12.1083 + 3.67942i −1.67912 + 0.510243i
5353 3.66059 6.34033i 0.502821 0.870912i −0.497173 0.867651i 0.665629π-0.665629\pi
0.999995 0.00326078i 0.00103794π-0.00103794\pi
5454 7.41757 + 7.41757i 1.00940 + 1.00940i
5555 −4.33533 2.50300i −0.584575 0.337505i
5656 0 0
5757 −15.3867 + 15.3867i −2.03802 + 2.03802i
5858 1.81545 + 6.77534i 0.238380 + 0.889646i
5959 2.93283 2.93283i 0.381821 0.381821i −0.489937 0.871758i 0.662980π-0.662980\pi
0.871758 + 0.489937i 0.162980π0.162980\pi
6060 −14.9121 + 3.99568i −1.92514 + 0.515840i
6161 3.90292 + 2.25335i 0.499718 + 0.288512i 0.728597 0.684942i 0.240173π-0.240173\pi
−0.228879 + 0.973455i 0.573506π0.573506\pi
6262 7.85639 13.6077i 0.997763 1.72818i
6363 0 0
6464 12.0775i 1.50969i
6565 −5.74230 + 0.190767i −0.712245 + 0.0236617i
6666 17.6274 + 10.1772i 2.16978 + 1.25273i
6767 1.36775 + 0.366486i 0.167097 + 0.0447734i 0.341397 0.939919i 0.389100π-0.389100\pi
−0.174301 + 0.984692i 0.555766π0.555766\pi
6868 2.25190i 0.273082i
6969 0.201704 + 0.349362i 0.0242823 + 0.0420582i
7070 0 0
7171 13.8300 + 3.70574i 1.64132 + 0.439791i 0.957165 0.289544i 0.0935038π-0.0935038\pi
0.684157 + 0.729335i 0.260170π0.260170\pi
7272 15.8126 4.23699i 1.86354 0.499334i
7373 1.82677 + 6.81760i 0.213807 + 0.797940i 0.986583 + 0.163261i 0.0522011π0.0522011\pi
−0.772776 + 0.634679i 0.781132π0.781132\pi
7474 9.13055 1.06140
7575 6.79227 0.784304
7676 7.16138 + 26.7267i 0.821467 + 3.06576i
7777 0 0
7878 23.3482 0.775656i 2.64366 0.0878258i
7979 0.316458 + 0.548121i 0.0356043 + 0.0616685i 0.883278 0.468849i 0.155331π-0.155331\pi
−0.847674 + 0.530517i 0.821998π0.821998\pi
8080 −0.535926 + 2.00010i −0.0599184 + 0.223618i
8181 0.760810 + 1.31776i 0.0845344 + 0.146418i
8282 −6.80865 + 11.7929i −0.751890 + 1.30231i
8383 1.07813 + 1.07813i 0.118340 + 0.118340i 0.763797 0.645457i 0.223333π-0.223333\pi
−0.645457 + 0.763797i 0.723333π0.723333\pi
8484 0 0
8585 −0.264611 + 0.987541i −0.0287011 + 0.107114i
8686 −1.70266 + 6.35443i −0.183603 + 0.685215i
8787 8.24834i 0.884315i
8888 9.64223 5.56694i 1.02786 0.593438i
8989 9.60471 9.60471i 1.01810 1.01810i 0.0182641 0.999833i 0.494186π-0.494186\pi
0.999833 0.0182641i 0.00581396π-0.00581396\pi
9090 17.2773 1.82119
9191 0 0
9292 0.512963 0.0534801
9393 −13.0652 + 13.0652i −1.35480 + 1.35480i
9494 −6.40911 + 3.70030i −0.661049 + 0.381657i
9595 12.5621i 1.28885i
9696 −2.88483 + 10.7663i −0.294432 + 1.09884i
9797 0.0487160 0.181811i 0.00494637 0.0184601i −0.963409 0.268037i 0.913625π-0.913625\pi
0.968355 + 0.249577i 0.0802916π0.0802916\pi
9898 0 0
9999 −10.2606 10.2606i −1.03123 1.03123i
100100 4.31843 7.47974i 0.431843 0.747974i
101101 −0.596904 1.03387i −0.0593942 0.102874i 0.834799 0.550554i 0.185584π-0.185584\pi
−0.894194 + 0.447680i 0.852250π0.852250\pi
102102 1.07591 4.01534i 0.106531 0.397577i
103103 −2.39792 4.15331i −0.236274 0.409238i 0.723368 0.690462i 0.242593π-0.242593\pi
−0.959642 + 0.281224i 0.909260π0.909260\pi
104104 6.01830 11.2726i 0.590143 1.10537i
105105 0 0
106106 4.44783 + 16.5995i 0.432012 + 1.61229i
107107 15.2964 1.47876 0.739378 0.673290i 0.235120π-0.235120\pi
0.739378 + 0.673290i 0.235120π0.235120\pi
108108 −15.6855 −1.50933
109109 3.33967 + 12.4638i 0.319883 + 1.19382i 0.919357 + 0.393424i 0.128710π0.128710\pi
−0.599475 + 0.800394i 0.704624π0.704624\pi
110110 11.3503 3.04129i 1.08220 0.289976i
111111 −10.3710 2.77890i −0.984370 0.263761i
112112 0 0
113113 −0.770731 1.33494i −0.0725042 0.125581i 0.827494 0.561475i 0.189766π-0.189766\pi
−0.899998 + 0.435894i 0.856432π0.856432\pi
114114 51.0776i 4.78386i
115115 0.224953 + 0.0602761i 0.0209770 + 0.00562078i
116116 −9.08318 5.24418i −0.843352 0.486910i
117117 −16.2209 3.77391i −1.49963 0.348898i
118118 9.73580i 0.896253i
119119 0 0
120120 7.79441 13.5003i 0.711529 1.23240i
121121 0.979449 + 0.565485i 0.0890408 + 0.0514077i
122122 −10.2182 + 2.73796i −0.925111 + 0.247883i
123123 11.3228 11.3228i 1.02095 1.02095i
124124 6.08092 + 22.6943i 0.546083 + 2.03801i
125125 8.40660 8.40660i 0.751910 0.751910i
126126 0 0
127127 2.81842 + 1.62722i 0.250095 + 0.144392i 0.619808 0.784754i 0.287211π-0.287211\pi
−0.369713 + 0.929146i 0.620544π0.620544\pi
128128 14.3355 + 14.3355i 1.26709 + 1.26709i
129129 3.86796 6.69950i 0.340555 0.589858i
130130 9.21443 9.84770i 0.808159 0.863701i
131131 −14.2615 + 8.23390i −1.24604 + 0.719400i −0.970317 0.241838i 0.922250π-0.922250\pi
−0.275720 + 0.961238i 0.588916π0.588916\pi
132132 −29.3983 + 7.87724i −2.55879 + 0.685626i
133133 0 0
134134 −2.87848 + 1.66189i −0.248663 + 0.143565i
135135 −6.87866 1.84313i −0.592021 0.158632i
136136 −1.60787 1.60787i −0.137874 0.137874i
137137 −0.267239 0.267239i −0.0228318 0.0228318i 0.695599 0.718431i 0.255139π-0.255139\pi
−0.718431 + 0.695599i 0.755139π0.755139\pi
138138 −0.914659 0.245082i −0.0778610 0.0208628i
139139 −8.52132 + 4.91978i −0.722769 + 0.417291i −0.815771 0.578375i 0.803687π-0.803687\pi
0.0930022 + 0.995666i 0.470354π0.470354\pi
140140 0 0
141141 8.40602 2.25239i 0.707914 0.189685i
142142 −29.1058 + 16.8043i −2.44251 + 1.41018i
143143 −11.3206 + 0.376085i −0.946676 + 0.0314498i
144144 −3.00107 + 5.19801i −0.250089 + 0.433167i
145145 −3.36710 3.36710i −0.279622 0.279622i
146146 −14.3479 8.28378i −1.18744 0.685570i
147147 0 0
148148 −9.65388 + 9.65388i −0.793544 + 0.793544i
149149 1.43738 + 5.36436i 0.117754 + 0.439465i 0.999478 0.0323006i 0.0102834π-0.0102834\pi
−0.881724 + 0.471766i 0.843617π0.843617\pi
150150 −11.2738 + 11.2738i −0.920503 + 0.920503i
151151 −4.58330 + 1.22809i −0.372983 + 0.0999406i −0.440441 0.897782i 0.645178π-0.645178\pi
0.0674576 + 0.997722i 0.478511π0.478511\pi
152152 −24.1964 13.9698i −1.96258 1.13310i
153153 −1.48176 + 2.56649i −0.119793 + 0.207488i
154154 0 0
155155 10.6669i 0.856782i
156156 −23.8663 + 25.5065i −1.91083 + 2.04216i
157157 −10.9293 6.31006i −0.872257 0.503598i −0.00415919 0.999991i 0.501324π-0.501324\pi
−0.868098 + 0.496394i 0.834657π0.834657\pi
158158 −1.43503 0.384515i −0.114165 0.0305904i
159159 20.2084i 1.60263i
160160 3.21735 + 5.57262i 0.254354 + 0.440554i
161161 0 0
162162 −3.45001 0.924428i −0.271058 0.0726299i
163163 12.6085 3.37843i 0.987571 0.264619i 0.271341 0.962483i 0.412533π-0.412533\pi
0.716230 + 0.697864i 0.245866π0.245866\pi
164164 −5.26996 19.6678i −0.411515 1.53579i
165165 −13.8179 −1.07572
166166 −3.57897 −0.277782
167167 −4.79697 17.9025i −0.371201 1.38534i −0.858817 0.512282i 0.828800π-0.828800\pi
0.487616 0.873058i 0.337867π-0.337867\pi
168168 0 0
169169 −10.8021 + 7.23288i −0.830931 + 0.556375i
170170 −1.19992 2.07832i −0.0920296 0.159400i
171171 −9.42448 + 35.1726i −0.720708 + 2.68972i
172172 −4.91839 8.51890i −0.375024 0.649560i
173173 −2.79684 + 4.84427i −0.212640 + 0.368303i −0.952540 0.304414i 0.901540π-0.901540\pi
0.739900 + 0.672717i 0.234873π0.234873\pi
174174 13.6906 + 13.6906i 1.03788 + 1.03788i
175175 0 0
176176 −1.05655 + 3.94308i −0.0796402 + 0.297221i
177177 2.96311 11.0585i 0.222721 0.831205i
178178 31.8838i 2.38979i
179179 −8.21928 + 4.74540i −0.614338 + 0.354688i −0.774661 0.632377i 0.782080π-0.782080\pi
0.160324 + 0.987065i 0.448746π0.448746\pi
180180 −18.2676 + 18.2676i −1.36158 + 1.36158i
181181 6.91516 0.514000 0.257000 0.966411i 0.417266π-0.417266\pi
0.257000 + 0.966411i 0.417266π0.417266\pi
182182 0 0
183183 12.4397 0.919568
184184 −0.366260 + 0.366260i −0.0270011 + 0.0270011i
185185 −5.36798 + 3.09920i −0.394662 + 0.227858i
186186 43.3714i 3.18014i
187187 −0.521664 + 1.94688i −0.0381479 + 0.142370i
188188 2.86407 10.6889i 0.208884 0.779565i
189189 0 0
190190 −20.8506 20.8506i −1.51266 1.51266i
191191 1.25251 2.16942i 0.0906287 0.156974i −0.817147 0.576429i 0.804446π-0.804446\pi
0.907776 + 0.419456i 0.137779π0.137779\pi
192192 −16.6685 28.8707i −1.20295 2.08356i
193193 −5.83813 + 21.7882i −0.420238 + 1.56835i 0.353870 + 0.935295i 0.384866π0.384866\pi
−0.774108 + 0.633054i 0.781801π0.781801\pi
194194 0.220911 + 0.382628i 0.0158605 + 0.0274711i
195195 −13.4634 + 8.38114i −0.964136 + 0.600186i
196196 0 0
197197 −4.63560 17.3003i −0.330273 1.23259i −0.908904 0.417005i 0.863080π-0.863080\pi
0.578631 0.815589i 0.303587π-0.303587\pi
198198 34.0611 2.42062
199199 16.4123 1.16344 0.581720 0.813389i 0.302380π-0.302380\pi
0.581720 + 0.813389i 0.302380π0.302380\pi
200200 2.25720 + 8.42400i 0.159608 + 0.595667i
201201 3.77533 1.01160i 0.266291 0.0713526i
202202 2.70675 + 0.725273i 0.190447 + 0.0510300i
203203 0 0
204204 3.10791 + 5.38306i 0.217597 + 0.376889i
205205 9.24430i 0.645650i
206206 10.8737 + 2.91361i 0.757609 + 0.203001i
207207 0.584624 + 0.337533i 0.0406342 + 0.0234602i
208208 1.36221 + 4.48278i 0.0944521 + 0.310825i
209209 24.7655i 1.71307i
210210 0 0
211211 4.93176 8.54207i 0.339517 0.588060i −0.644825 0.764330i 0.723070π-0.723070\pi
0.984342 + 0.176270i 0.0564032π0.0564032\pi
212212 −22.2537 12.8482i −1.52839 0.882418i
213213 38.1744 10.2288i 2.61567 0.700867i
214214 −25.3889 + 25.3889i −1.73555 + 1.73555i
215215 −1.15588 4.31380i −0.0788302 0.294198i
216216 11.1996 11.1996i 0.762033 0.762033i
217217 0 0
218218 −26.2306 15.1443i −1.77656 1.02570i
219219 13.7760 + 13.7760i 0.930895 + 0.930895i
220220 −8.78520 + 15.2164i −0.592298 + 1.02589i
221221 0.672583 + 2.21335i 0.0452428 + 0.148886i
222222 21.8262 12.6013i 1.46488 0.845747i
223223 −8.41926 + 2.25594i −0.563796 + 0.151069i −0.529450 0.848341i 0.677602π-0.677602\pi
−0.0343461 + 0.999410i 0.510935π0.510935\pi
224224 0 0
225225 9.84344 5.68312i 0.656230 0.378874i
226226 3.49500 + 0.936482i 0.232484 + 0.0622939i
227227 11.9452 + 11.9452i 0.792834 + 0.792834i 0.981954 0.189120i 0.0605636π-0.0605636\pi
−0.189120 + 0.981954i 0.560564π0.560564\pi
228228 54.0052 + 54.0052i 3.57658 + 3.57658i
229229 −2.36198 0.632892i −0.156084 0.0418227i 0.179931 0.983679i 0.442413π-0.442413\pi
−0.336015 + 0.941857i 0.609079π0.609079\pi
230230 −0.473424 + 0.273331i −0.0312166 + 0.0180229i
231231 0 0
232232 10.2299 2.74108i 0.671624 0.179961i
233233 4.65474 2.68741i 0.304942 0.176058i −0.339719 0.940527i 0.610332π-0.610332\pi
0.644661 + 0.764469i 0.276999π0.276999\pi
234234 33.1874 20.6596i 2.16953 1.35056i
235235 2.51200 4.35092i 0.163865 0.283823i
236236 −10.2938 10.2938i −0.670071 0.670071i
237237 1.51296 + 0.873507i 0.0982772 + 0.0567404i
238238 0 0
239239 −11.9572 + 11.9572i −0.773448 + 0.773448i −0.978708 0.205260i 0.934196π-0.934196\pi
0.205260 + 0.978708i 0.434196π0.434196\pi
240240 1.47930 + 5.52081i 0.0954882 + 0.356367i
241241 −9.50881 + 9.50881i −0.612516 + 0.612516i −0.943601 0.331085i 0.892585π-0.892585\pi
0.331085 + 0.943601i 0.392585π0.392585\pi
242242 −2.56428 + 0.687097i −0.164838 + 0.0441682i
243243 15.2481 + 8.80347i 0.978163 + 0.564743i
244244 7.90898 13.6987i 0.506320 0.876972i
245245 0 0
246246 37.5873i 2.39648i
247247 15.0214 + 24.1303i 0.955786 + 1.53537i
248248 −20.5458 11.8621i −1.30466 0.753245i
249249 4.06519 + 1.08926i 0.257621 + 0.0690293i
250250 27.9066i 1.76497i
251251 6.40248 + 11.0894i 0.404121 + 0.699958i 0.994219 0.107374i 0.0342441π-0.0342441\pi
−0.590098 + 0.807332i 0.700911π0.700911\pi
252252 0 0
253253 0.443482 + 0.118831i 0.0278815 + 0.00747082i
254254 −7.37887 + 1.97716i −0.462992 + 0.124058i
255255 0.730395 + 2.72587i 0.0457391 + 0.170701i
256256 −23.4332 −1.46457
257257 −10.3807 −0.647532 −0.323766 0.946137i 0.604949π-0.604949\pi
−0.323766 + 0.946137i 0.604949π0.604949\pi
258258 4.69979 + 17.5399i 0.292596 + 1.09198i
259259 0 0
260260 0.669566 + 20.1547i 0.0415247 + 1.24994i
261261 −6.90141 11.9536i −0.427187 0.739909i
262262 10.0047 37.3379i 0.618090 2.30674i
263263 2.18977 + 3.79279i 0.135027 + 0.233873i 0.925608 0.378484i 0.123555π-0.123555\pi
−0.790581 + 0.612358i 0.790221π0.790221\pi
264264 15.3662 26.6151i 0.945725 1.63804i
265265 −8.24936 8.24936i −0.506754 0.506754i
266266 0 0
267267 9.70388 36.2154i 0.593868 2.21635i
268268 1.28632 4.80061i 0.0785744 0.293244i
269269 11.6847i 0.712427i −0.934405 0.356213i 0.884068π-0.884068\pi
0.934405 0.356213i 0.115932π-0.115932\pi
270270 14.4764 8.35797i 0.881007 0.508650i
271271 21.7031 21.7031i 1.31837 1.31837i 0.403303 0.915066i 0.367862π-0.367862\pi
0.915066 0.403303i 0.132138π-0.132138\pi
272272 0.833705 0.0505508
273273 0 0
274274 0.887127 0.0535933
275275 5.46622 5.46622i 0.329626 0.329626i
276276 1.22621 0.707955i 0.0738094 0.0426139i
277277 19.0652i 1.14552i −0.819724 0.572758i 0.805873π-0.805873\pi
0.819724 0.572758i 0.194127π-0.194127\pi
278278 5.97782 22.3095i 0.358526 1.33804i
279279 −8.00258 + 29.8660i −0.479102 + 1.78803i
280280 0 0
281281 11.8671 + 11.8671i 0.707931 + 0.707931i 0.966100 0.258169i 0.0831190π-0.0831190\pi
−0.258169 + 0.966100i 0.583119π0.583119\pi
282282 −10.2138 + 17.6908i −0.608223 + 1.05347i
283283 4.21864 + 7.30690i 0.250772 + 0.434350i 0.963739 0.266848i 0.0859821π-0.0859821\pi
−0.712966 + 0.701198i 0.752649π0.752649\pi
284284 13.0067 48.5415i 0.771804 2.88041i
285285 17.3374 + 30.0292i 1.02698 + 1.77878i
286286 18.1657 19.4141i 1.07416 1.14798i
287287 0 0
288288 4.82750 + 18.0165i 0.284463 + 1.06163i
289289 −16.5884 −0.975786
290290 11.1774 0.656360
291291 −0.134469 0.501845i −0.00788271 0.0294187i
292292 23.9289 6.41172i 1.40033 0.375218i
293293 −8.00676 2.14541i −0.467760 0.125336i 0.0172376 0.999851i 0.494513π-0.494513\pi
−0.484998 + 0.874516i 0.661180π0.661180\pi
294294 0 0
295295 −3.30465 5.72382i −0.192404 0.333253i
296296 13.7859i 0.801290i
297297 −13.5609 3.63362i −0.786881 0.210844i
298298 −11.2895 6.51800i −0.653984 0.377578i
299299 0.504183 0.153209i 0.0291576 0.00886029i
300300 23.8400i 1.37640i
301301 0 0
302302 5.56897 9.64574i 0.320458 0.555050i
303303 −2.85375 1.64761i −0.163943 0.0946528i
304304 9.89484 2.65131i 0.567508 0.152063i
305305 5.07807 5.07807i 0.290769 0.290769i
306306 −1.80043 6.71929i −0.102924 0.384116i
307307 −17.3438 + 17.3438i −0.989863 + 0.989863i −0.999949 0.0100865i 0.996789π-0.996789\pi
0.0100865 + 0.999949i 0.496789π0.496789\pi
308308 0 0
309309 −11.4642 6.61887i −0.652177 0.376535i
310310 −17.7048 17.7048i −1.00557 1.00557i
311311 −11.8560 + 20.5353i −0.672294 + 1.16445i 0.304958 + 0.952366i 0.401358π0.401358\pi
−0.977252 + 0.212082i 0.931976π0.931976\pi
312312 −1.17114 35.2526i −0.0663026 1.99579i
313313 −12.1862 + 7.03573i −0.688808 + 0.397683i −0.803165 0.595756i 0.796852π-0.796852\pi
0.114358 + 0.993440i 0.463519π0.463519\pi
314314 28.6140 7.66709i 1.61478 0.432679i
315315 0 0
316316 1.92383 1.11073i 0.108224 0.0624832i
317317 −16.1695 4.33262i −0.908172 0.243344i −0.225649 0.974209i 0.572450π-0.572450\pi
−0.682522 + 0.730865i 0.739117π0.739117\pi
318318 33.5419 + 33.5419i 1.88093 + 1.88093i
319319 −6.63803 6.63803i −0.371658 0.371658i
320320 −18.5898 4.98112i −1.03920 0.278453i
321321 36.5653 21.1110i 2.04088 1.17830i
322322 0 0
323323 4.88553 1.30907i 0.271838 0.0728388i
324324 4.62517 2.67034i 0.256954 0.148352i
325325 2.01051 8.64152i 0.111523 0.479345i
326326 −15.3200 + 26.5350i −0.848497 + 1.46964i
327327 25.1850 + 25.1850i 1.39274 + 1.39274i
328328 17.8058 + 10.2802i 0.983159 + 0.567627i
329329 0 0
330330 22.9349 22.9349i 1.26252 1.26252i
331331 −2.50489 9.34837i −0.137681 0.513833i −0.999972 0.00742049i 0.997638π-0.997638\pi
0.862291 0.506413i 0.169029π-0.169029\pi
332332 3.78410 3.78410i 0.207680 0.207680i
333333 −17.3549 + 4.65022i −0.951041 + 0.254831i
334334 37.6766 + 21.7526i 2.06157 + 1.19025i
335335 1.12820 1.95410i 0.0616401 0.106764i
336336 0 0
337337 20.0838i 1.09403i 0.837122 + 0.547016i 0.184236π0.184236\pi
−0.837122 + 0.547016i 0.815764π0.815764\pi
338338 5.92421 29.9345i 0.322234 1.62822i
339339 −3.68479 2.12742i −0.200131 0.115545i
340340 3.46614 + 0.928749i 0.187978 + 0.0503685i
341341 21.0291i 1.13879i
342342 −42.7368 74.0223i −2.31094 4.00267i
343343 0 0
344344 9.59434 + 2.57080i 0.517292 + 0.138608i
345345 0.620930 0.166378i 0.0334298 0.00895748i
346346 −3.39833 12.6827i −0.182695 0.681827i
347347 −22.2015 −1.19184 −0.595920 0.803044i 0.703212π-0.703212\pi
−0.595920 + 0.803044i 0.703212π0.703212\pi
348348 −28.9506 −1.55191
349349 −1.38593 5.17235i −0.0741869 0.276869i 0.918861 0.394582i 0.129111π-0.129111\pi
−0.993048 + 0.117713i 0.962444π0.962444\pi
350350 0 0
351351 −15.4170 + 4.68484i −0.822897 + 0.250058i
352352 6.34281 + 10.9861i 0.338073 + 0.585560i
353353 6.75514 25.2105i 0.359540 1.34182i −0.515134 0.857110i 0.672258π-0.672258\pi
0.874674 0.484712i 0.161075π-0.161075\pi
354354 13.4367 + 23.2730i 0.714151 + 1.23695i
355355 11.4078 19.7589i 0.605465 1.04870i
356356 −33.7113 33.7113i −1.78669 1.78669i
357357 0 0
358358 5.76594 21.5188i 0.304739 1.13730i
359359 −5.86066 + 21.8723i −0.309314 + 1.15437i 0.619854 + 0.784717i 0.287192π0.287192\pi
−0.929168 + 0.369658i 0.879475π0.879475\pi
360360 26.0864i 1.37488i
361361 37.3664 21.5735i 1.96665 1.13545i
362362 −11.4778 + 11.4778i −0.603258 + 0.603258i
363363 3.12177 0.163850
364364 0 0
365365 11.2471 0.588702
366366 −20.6474 + 20.6474i −1.07926 + 1.07926i
367367 −12.2942 + 7.09806i −0.641752 + 0.370516i −0.785289 0.619129i 0.787486π-0.787486\pi
0.143537 + 0.989645i 0.454152π0.454152\pi
368368 0.189911i 0.00989980i
369369 6.93534 25.8831i 0.361040 1.34742i
370370 3.76571 14.0538i 0.195770 0.730624i
371371 0 0
372372 45.8573 + 45.8573i 2.37759 + 2.37759i
373373 −1.75321 + 3.03665i −0.0907778 + 0.157232i −0.907839 0.419320i 0.862269π-0.862269\pi
0.817061 + 0.576551i 0.195602π0.195602\pi
374374 −2.36557 4.09728i −0.122321 0.211865i
375375 8.49340 31.6978i 0.438598 1.63687i
376376 5.58697 + 9.67691i 0.288126 + 0.499048i
377377 −10.4940 2.44150i −0.540469 0.125744i
378378 0 0
379379 6.94797 + 25.9302i 0.356893 + 1.33194i 0.878085 + 0.478504i 0.158821π0.158821\pi
−0.521192 + 0.853439i 0.674513π0.674513\pi
380380 44.0915 2.26184
381381 8.98309 0.460217
382382 1.52188 + 5.67972i 0.0778660 + 0.290600i
383383 −32.9891 + 8.83941i −1.68567 + 0.451673i −0.969266 0.246017i 0.920878π-0.920878\pi
−0.716400 + 0.697690i 0.754211π0.754211\pi
384384 54.0533 + 14.4835i 2.75839 + 0.739110i
385385 0 0
386386 −26.4739 45.8542i −1.34749 2.33392i
387387 12.9453i 0.658048i
388388 −0.638132 0.170987i −0.0323962 0.00868054i
389389 23.7849 + 13.7322i 1.20594 + 0.696251i 0.961870 0.273506i 0.0881834π-0.0881834\pi
0.244072 + 0.969757i 0.421517π0.421517\pi
390390 8.43558 36.2576i 0.427152 1.83598i
391391 0.0937676i 0.00474203i
392392 0 0
393393 −22.7277 + 39.3656i −1.14646 + 1.98573i
394394 36.4092 + 21.0208i 1.83427 + 1.05901i
395395 0.974190 0.261034i 0.0490168 0.0131340i
396396 −36.0134 + 36.0134i −1.80974 + 1.80974i
397397 −9.59343 35.8032i −0.481480 1.79691i −0.595412 0.803420i 0.703011π-0.703011\pi
0.113932 0.993489i 0.463655π-0.463655\pi
398398 −27.2412 + 27.2412i −1.36548 + 1.36548i
399399 0 0
400400 −2.76918 1.59879i −0.138459 0.0799393i
401401 12.2868 + 12.2868i 0.613574 + 0.613574i 0.943876 0.330301i 0.107150π-0.107150\pi
−0.330301 + 0.943876i 0.607150π0.607150\pi
402402 −4.58725 + 7.94535i −0.228791 + 0.396278i
403403 12.7550 + 20.4896i 0.635374 + 1.02066i
404404 −3.62874 + 2.09505i −0.180537 + 0.104233i
405405 2.34209 0.627561i 0.116379 0.0311838i
406406 0 0
407407 −10.5826 + 6.10989i −0.524562 + 0.302856i
408408 −6.06263 1.62448i −0.300145 0.0804235i
409409 7.97850 + 7.97850i 0.394512 + 0.394512i 0.876292 0.481780i 0.160010π-0.160010\pi
−0.481780 + 0.876292i 0.660010π0.660010\pi
410410 15.3437 + 15.3437i 0.757771 + 0.757771i
411411 −1.00765 0.269999i −0.0497036 0.0133180i
412412 −14.5776 + 8.41637i −0.718186 + 0.414645i
413413 0 0
414414 −1.53060 + 0.410122i −0.0752247 + 0.0201564i
415415 2.10413 1.21482i 0.103287 0.0596330i
416416 12.8436 + 6.85708i 0.629712 + 0.336196i
417417 −13.5799 + 23.5211i −0.665010 + 1.15183i
418418 −41.1058 41.1058i −2.01055 2.01055i
419419 16.1248 + 9.30964i 0.787747 + 0.454806i 0.839169 0.543871i 0.183042π-0.183042\pi
−0.0514220 + 0.998677i 0.516375π0.516375\pi
420420 0 0
421421 18.9024 18.9024i 0.921247 0.921247i −0.0758709 0.997118i 0.524174π-0.524174\pi
0.997118 + 0.0758709i 0.0241737π0.0241737\pi
422422 5.99238 + 22.3639i 0.291704 + 1.08866i
423423 10.2975 10.2975i 0.500683 0.500683i
424424 25.0631 6.71564i 1.21717 0.326140i
425425 −1.36727 0.789392i −0.0663222 0.0382911i
426426 −46.3841 + 80.3397i −2.24732 + 3.89247i
427427 0 0
428428 53.6883i 2.59512i
429429 −26.5423 + 16.5229i −1.28148 + 0.797734i
430430 9.07856 + 5.24151i 0.437807 + 0.252768i
431431 28.5158 + 7.64079i 1.37356 + 0.368044i 0.868777 0.495203i 0.164906π-0.164906\pi
0.504782 + 0.863247i 0.331573π0.331573\pi
432432 5.80713i 0.279396i
433433 17.9660 + 31.1180i 0.863390 + 1.49543i 0.868637 + 0.495449i 0.164996π0.164996\pi
−0.00524758 + 0.999986i 0.501670π0.501670\pi
434434 0 0
435435 −12.6959 3.40186i −0.608723 0.163107i
436436 43.7464 11.7218i 2.09507 0.561373i
437437 −0.298196 1.11288i −0.0142646 0.0532363i
438438 −45.7308 −2.18510
439439 9.75982 0.465811 0.232906 0.972499i 0.425177π-0.425177\pi
0.232906 + 0.972499i 0.425177π0.425177\pi
440440 −4.59195 17.1374i −0.218912 0.816992i
441441 0 0
442442 −4.79007 2.55737i −0.227840 0.121641i
443443 −19.3899 33.5843i −0.921241 1.59564i −0.797497 0.603323i 0.793843π-0.793843\pi
−0.123744 0.992314i 0.539490π-0.539490\pi
444444 −9.75356 + 36.4008i −0.462884 + 1.72751i
445445 −10.8224 18.7449i −0.513030 0.888595i
446446 10.2299 17.7187i 0.484399 0.839004i
447447 10.8395 + 10.8395i 0.512690 + 0.512690i
448448 0 0
449449 −2.42216 + 9.03963i −0.114309 + 0.426606i −0.999234 0.0391263i 0.987543π-0.987543\pi
0.884925 + 0.465733i 0.154209π0.154209\pi
450450 −6.90531 + 25.7710i −0.325520 + 1.21486i
451451 18.2246i 0.858162i
452452 −4.68548 + 2.70516i −0.220386 + 0.127240i
453453 −9.26124 + 9.26124i −0.435131 + 0.435131i
454454 −39.6534 −1.86103
455455 0 0
456456 −77.1204 −3.61150
457457 13.5913 13.5913i 0.635775 0.635775i −0.313735 0.949511i 0.601580π-0.601580\pi
0.949511 + 0.313735i 0.101580π0.101580\pi
458458 4.97089 2.86995i 0.232275 0.134104i
459459 2.86724i 0.133831i
460460 0.211561 0.789557i 0.00986409 0.0368133i
461461 3.50466 13.0796i 0.163228 0.609175i −0.835031 0.550202i 0.814551π-0.814551\pi
0.998260 0.0589733i 0.0187827π-0.0187827\pi
462462 0 0
463463 −14.6336 14.6336i −0.680081 0.680081i 0.279937 0.960018i 0.409686π-0.409686\pi
−0.960018 + 0.279937i 0.909686π0.909686\pi
464464 −1.94152 + 3.36281i −0.0901328 + 0.156115i
465465 14.7216 + 25.4986i 0.682700 + 1.18247i
466466 −3.26536 + 12.1865i −0.151265 + 0.564529i
467467 15.4866 + 26.8236i 0.716634 + 1.24125i 0.962326 + 0.271899i 0.0876515π0.0876515\pi
−0.245692 + 0.969348i 0.579015π0.579015\pi
468468 −13.2459 + 56.9334i −0.612294 + 2.63175i
469469 0 0
470470 3.05223 + 11.3911i 0.140789 + 0.525431i
471471 −34.8348 −1.60510
472472 14.6998 0.676612
473473 −2.27874 8.50439i −0.104777 0.391032i
474474 −3.96105 + 1.06136i −0.181937 + 0.0487499i
475475 −18.7378 5.02078i −0.859750 0.230369i
476476 0 0
477477 −16.9084 29.2862i −0.774183 1.34092i
478478 39.6932i 1.81552i
479479 7.09483 + 1.90105i 0.324171 + 0.0868613i 0.417235 0.908799i 0.362999π-0.362999\pi
−0.0930636 + 0.995660i 0.529666π0.529666\pi
480480 15.3819 + 8.88072i 0.702083 + 0.405348i
481481 −6.60528 + 12.3720i −0.301175 + 0.564115i
482482 31.5654i 1.43777i
483483 0 0
484484 1.98478 3.43773i 0.0902171 0.156261i
485485 −0.259753 0.149968i −0.0117948 0.00680971i
486486 −39.9207 + 10.6967i −1.81084 + 0.485213i
487487 −6.97359 + 6.97359i −0.316004 + 0.316004i −0.847230 0.531226i 0.821731π-0.821731\pi
0.531226 + 0.847230i 0.321731π0.321731\pi
488488 4.13395 + 15.4281i 0.187135 + 0.698398i
489489 25.4773 25.4773i 1.15212 1.15212i
490490 0 0
491491 33.1372 + 19.1318i 1.49546 + 0.863404i 0.999986 0.00521946i 0.00166141π-0.00166141\pi
0.495473 + 0.868623i 0.334995π0.334995\pi
492492 −39.7417 39.7417i −1.79169 1.79169i
493493 −0.958615 + 1.66037i −0.0431738 + 0.0747793i
494494 −64.9838 15.1189i −2.92376 0.680233i
495495 −20.0250 + 11.5615i −0.900058 + 0.519649i
496496 8.40197 2.25130i 0.377260 0.101086i
497497 0 0
498498 −8.55536 + 4.93944i −0.383375 + 0.221342i
499499 −0.00140307 0.000375951i −6.28100e−5 1.68299e-5i 0.258788 0.965934i 0.416677π-0.416677\pi
−0.258850 + 0.965917i 0.583344π0.583344\pi
500500 −29.5061 29.5061i −1.31955 1.31955i
501501 −36.1748 36.1748i −1.61617 1.61617i
502502 −29.0331 7.77938i −1.29581 0.347211i
503503 −21.6205 + 12.4826i −0.964012 + 0.556573i −0.897406 0.441206i 0.854551π-0.854551\pi
−0.0666068 + 0.997779i 0.521217π0.521217\pi
504504 0 0
505505 −1.83752 + 0.492362i −0.0817686 + 0.0219098i
506506 −0.933326 + 0.538856i −0.0414914 + 0.0239551i
507507 −15.8396 + 32.1982i −0.703463 + 1.42997i
508508 5.71132 9.89229i 0.253399 0.438900i
509509 −1.85338 1.85338i −0.0821495 0.0821495i 0.664838 0.746988i 0.268501π-0.268501\pi
−0.746988 + 0.664838i 0.768501π0.768501\pi
510510 −5.73671 3.31209i −0.254026 0.146662i
511511 0 0
512512 10.2233 10.2233i 0.451811 0.451811i
513513 9.11827 + 34.0299i 0.402582 + 1.50245i
514514 17.2299 17.2299i 0.759979 0.759979i
515515 −7.38179 + 1.97795i −0.325281 + 0.0871587i
516516 −23.5144 13.5760i −1.03516 0.597651i
517517 4.95226 8.57757i 0.217800 0.377241i
518518 0 0
519519 15.4400i 0.677742i
520520 −14.8687 13.9126i −0.652037 0.610107i
521521 −25.8598 14.9302i −1.13294 0.654102i −0.188266 0.982118i 0.560287π-0.560287\pi
−0.944672 + 0.328016i 0.893620π0.893620\pi
522522 31.2955 + 8.38561i 1.36977 + 0.367028i
523523 16.0812i 0.703184i −0.936153 0.351592i 0.885640π-0.885640\pi
0.936153 0.351592i 0.114360π-0.114360\pi
524524 28.8999 + 50.0561i 1.26250 + 2.18671i
525525 0 0
526526 −9.92985 2.66069i −0.432962 0.116012i
527527 4.14843 1.11157i 0.180708 0.0484207i
528528 2.91634 + 10.8839i 0.126918 + 0.473663i
529529 22.9786 0.999071
530530 27.3846 1.18951
531531 −4.95848 18.5053i −0.215180 0.803062i
532532 0 0
533533 −11.0540 17.7571i −0.478802 0.769146i
534534 44.0038 + 76.2168i 1.90423 + 3.29822i
535535 6.30868 23.5443i 0.272748 1.01791i
536536 2.50923 + 4.34612i 0.108382 + 0.187724i
537537 −13.0985 + 22.6873i −0.565244 + 0.979031i
538538 19.3942 + 19.3942i 0.836143 + 0.836143i
539539 0 0
540540 −6.46915 + 24.1432i −0.278388 + 1.03896i
541541 4.55572 17.0022i 0.195866 0.730980i −0.796176 0.605066i 0.793147π-0.793147\pi
0.992041 0.125915i 0.0401865π-0.0401865\pi
542542 72.0456i 3.09462i
543543 16.5304 9.54381i 0.709386 0.409564i
544544 1.83196 1.83196i 0.0785448 0.0785448i
545545 20.5618 0.880771
546546 0 0
547547 −15.8734 −0.678698 −0.339349 0.940661i 0.610207π-0.610207\pi
−0.339349 + 0.940661i 0.610207π0.610207\pi
548548 −0.937974 + 0.937974i −0.0400683 + 0.0400683i
549549 18.0277 10.4083i 0.769405 0.444216i
550550 18.1457i 0.773734i
551551 −6.09709 + 22.7547i −0.259745 + 0.969381i
552552 −0.370042 + 1.38101i −0.0157500 + 0.0587799i
553553 0 0
554554 31.6444 + 31.6444i 1.34444 + 1.34444i
555555 −8.55461 + 14.8170i −0.363123 + 0.628947i
556556 17.2678 + 29.9087i 0.732318 + 1.26841i
557557 0.655582 2.44666i 0.0277779 0.103668i −0.950645 0.310280i 0.899577π-0.899577\pi
0.978423 + 0.206612i 0.0662437π0.0662437\pi
558558 −36.2889 62.8543i −1.53623 2.66083i
559559 −7.37857 6.90409i −0.312080 0.292012i
560560 0 0
561561 1.43993 + 5.37389i 0.0607938 + 0.226886i
562562 −39.3940 −1.66173
563563 −20.2319 −0.852673 −0.426336 0.904565i 0.640196π-0.640196\pi
−0.426336 + 0.904565i 0.640196π0.640196\pi
564564 −7.90558 29.5040i −0.332885 1.24234i
565565 −2.37263 + 0.635745i −0.0998174 + 0.0267460i
566566 −19.1301 5.12589i −0.804098 0.215457i
567567 0 0
568568 25.3722 + 43.9460i 1.06459 + 1.84393i
569569 14.8726i 0.623493i 0.950165 + 0.311747i 0.100914π0.100914\pi
−0.950165 + 0.311747i 0.899086π0.899086\pi
570570 −78.6191 21.0659i −3.29299 0.882355i
571571 −31.9767 18.4617i −1.33818 0.772600i −0.351645 0.936133i 0.614378π-0.614378\pi
−0.986538 + 0.163533i 0.947711π0.947711\pi
572572 1.32001 + 39.7338i 0.0551923 + 1.66135i
573573 6.91453i 0.288859i
574574 0 0
575575 −0.179817 + 0.311452i −0.00749888 + 0.0129884i
576576 −48.3124 27.8932i −2.01302 1.16222i
577577 19.8217 5.31122i 0.825189 0.221109i 0.178575 0.983926i 0.442851π-0.442851\pi
0.646614 + 0.762817i 0.276184π0.276184\pi
578578 27.5334 27.5334i 1.14524 1.14524i
579579 16.1148 + 60.1411i 0.669706 + 2.49938i
580580 −11.8181 + 11.8181i −0.490718 + 0.490718i
581581 0 0
582582 1.05615 + 0.609771i 0.0437790 + 0.0252758i
583583 −16.2631 16.2631i −0.673550 0.673550i
584584 −12.5074 + 21.6635i −0.517560 + 0.896441i
585585 −12.4988 + 23.4109i −0.516764 + 0.967923i
586586 16.8506 9.72867i 0.696090 0.401888i
587587 19.8321 5.31399i 0.818557 0.219332i 0.174842 0.984597i 0.444059π-0.444059\pi
0.643715 + 0.765265i 0.277392π0.277392\pi
588588 0 0
589589 45.7007 26.3853i 1.88307 1.08719i
590590 14.9854 + 4.01534i 0.616941 + 0.165309i
591591 −34.9578 34.9578i −1.43797 1.43797i
592592 3.57410 + 3.57410i 0.146894 + 0.146894i
593593 40.1793 + 10.7660i 1.64997 + 0.442107i 0.959603 0.281357i 0.0907844π-0.0907844\pi
0.690362 + 0.723464i 0.257451π0.257451\pi
594594 28.5394 16.4772i 1.17099 0.676069i
595595 0 0
596596 18.8282 5.04500i 0.771233 0.206651i
597597 39.2330 22.6512i 1.60570 0.927050i
598598 −0.582546 + 1.09114i −0.0238221 + 0.0446199i
599599 2.16999 3.75853i 0.0886634 0.153569i −0.818283 0.574816i 0.805074π-0.805074\pi
0.906946 + 0.421246i 0.138407π0.138407\pi
600600 17.0220 + 17.0220i 0.694919 + 0.694919i
601601 −5.72067 3.30283i −0.233351 0.134725i 0.378766 0.925492i 0.376348π-0.376348\pi
−0.612117 + 0.790767i 0.709682π0.709682\pi
602602 0 0
603603 4.62485 4.62485i 0.188339 0.188339i
604604 4.31044 + 16.0868i 0.175389 + 0.654561i
605605 1.27435 1.27435i 0.0518098 0.0518098i
606606 7.47135 2.00194i 0.303503 0.0813233i
607607 −39.8777 23.0234i −1.61859 0.934492i −0.987286 0.158954i 0.949188π-0.949188\pi
−0.631301 0.775538i 0.717479π-0.717479\pi
608608 15.9168 27.5686i 0.645510 1.11806i
609609 0 0
610610 16.8571i 0.682526i
611611 −0.377438 11.3613i −0.0152695 0.459630i
612612 9.00804 + 5.20079i 0.364128 + 0.210230i
613613 −27.7207 7.42773i −1.11963 0.300003i −0.348895 0.937162i 0.613443π-0.613443\pi
−0.770733 + 0.637159i 0.780110π0.780110\pi
614614 57.5744i 2.32352i
615615 −12.7583 22.0981i −0.514466 0.891081i
616616 0 0
617617 0.0947548 + 0.0253895i 0.00381469 + 0.00102214i 0.260726 0.965413i 0.416038π-0.416038\pi
−0.256911 + 0.966435i 0.582705π0.582705\pi
618618 30.0143 8.04231i 1.20735 0.323509i
619619 10.9468 + 40.8542i 0.439991 + 1.64207i 0.728834 + 0.684691i 0.240063π0.240063\pi
−0.288843 + 0.957376i 0.593271π0.593271\pi
620620 37.4392 1.50360
621621 0.653133 0.0262093
622622 −14.4058 53.7630i −0.577619 2.15570i
623623 0 0
624624 9.44312 + 8.83587i 0.378027 + 0.353718i
625625 −3.32054 5.75135i −0.132822 0.230054i
626626 8.54882 31.9046i 0.341680 1.27517i
627627 34.1796 + 59.2008i 1.36500 + 2.36425i
628628 −22.1475 + 38.3606i −0.883781 + 1.53075i
629629 1.76469 + 1.76469i 0.0703629 + 0.0703629i
630630 0 0
631631 2.02584 7.56053i 0.0806473 0.300980i −0.913807 0.406148i 0.866872π-0.866872\pi
0.994454 + 0.105169i 0.0335383π0.0335383\pi
632632 −0.580566 + 2.16670i −0.0230937 + 0.0861868i
633633 27.2259i 1.08213i
634634 34.0295 19.6469i 1.35148 0.780279i
635635 3.66703 3.66703i 0.145522 0.145522i
636636 −70.9288 −2.81251
637637 0 0
638638 22.0356 0.872397
639639 46.7644 46.7644i 1.84997 1.84997i
640640 27.9777 16.1530i 1.10592 0.638502i
641641 33.4026i 1.31932i −0.751563 0.659661i 0.770700π-0.770700\pi
0.751563 0.659661i 0.229300π-0.229300\pi
642642 −25.6511 + 95.7311i −1.01237 + 3.77820i
643643 4.94009 18.4367i 0.194818 0.727071i −0.797496 0.603324i 0.793842π-0.793842\pi
0.992314 0.123746i 0.0394909π-0.0394909\pi
644644 0 0
645645 −8.71667 8.71667i −0.343219 0.343219i
646646 −5.93619 + 10.2818i −0.233556 + 0.404532i
647647 −16.4522 28.4961i −0.646804 1.12030i −0.983882 0.178821i 0.942772π-0.942772\pi
0.337078 0.941477i 0.390561π-0.390561\pi
648648 −1.39576 + 5.20906i −0.0548308 + 0.204631i
649649 −6.51491 11.2842i −0.255733 0.442942i
650650 11.0061 + 17.6802i 0.431696 + 0.693475i
651651 0 0
652652 −11.8578 44.2541i −0.464389 1.73312i
653653 27.9965 1.09559 0.547793 0.836614i 0.315468π-0.315468\pi
0.547793 + 0.836614i 0.315468π0.315468\pi
654654 −83.6042 −3.26918
655655 6.79182 + 25.3474i 0.265378 + 0.990405i
656656 −7.28147 + 1.95106i −0.284294 + 0.0761763i
657657 31.4907 + 8.43792i 1.22857 + 0.329195i
658658 0 0
659659 −5.35203 9.27000i −0.208486 0.361108i 0.742752 0.669567i 0.233520π-0.233520\pi
−0.951238 + 0.308459i 0.900187π0.900187\pi
660660 48.4989i 1.88782i
661661 23.2066 + 6.21818i 0.902631 + 0.241859i 0.680146 0.733077i 0.261916π-0.261916\pi
0.222485 + 0.974936i 0.428583π0.428583\pi
662662 19.6740 + 11.3588i 0.764653 + 0.441473i
663663 4.66249 + 4.36266i 0.181076 + 0.169432i
664664 5.40377i 0.209707i
665665 0 0
666666 21.0872 36.5240i 0.817111 1.41528i
667667 0.378218 + 0.218364i 0.0146447 + 0.00845510i
668668 −62.8356 + 16.8367i −2.43118 + 0.651433i
669669 −17.0124 + 17.0124i −0.657737 + 0.657737i
670670 1.37083 + 5.11599i 0.0529596 + 0.197648i
671671 10.0111 10.0111i 0.386474 0.386474i
672672 0 0
673673 4.79792 + 2.77008i 0.184946 + 0.106779i 0.589615 0.807685i 0.299280π-0.299280\pi
−0.404668 + 0.914464i 0.632613π0.632613\pi
674674 −33.3350 33.3350i −1.28402 1.28402i
675675 5.49846 9.52362i 0.211636 0.366564i
676676 25.3864 + 37.9140i 0.976402 + 1.45823i
677677 38.1640 22.0340i 1.46676 0.846835i 0.467454 0.884018i 0.345172π-0.345172\pi
0.999309 + 0.0371822i 0.0118382π0.0118382\pi
678678 9.64710 2.58493i 0.370495 0.0992738i
679679 0 0
680680 −3.13799 + 1.81172i −0.120336 + 0.0694763i
681681 45.0406 + 12.0686i 1.72596 + 0.462469i
682682 −34.9040 34.9040i −1.33654 1.33654i
683683 3.64259 + 3.64259i 0.139380 + 0.139380i 0.773354 0.633974i 0.218578π-0.218578\pi
−0.633974 + 0.773354i 0.718578π0.718578\pi
684684 123.451 + 33.0787i 4.72028 + 1.26480i
685685 −0.521554 + 0.301120i −0.0199276 + 0.0115052i
686686 0 0
687687 −6.51969 + 1.74695i −0.248742 + 0.0666501i
688688 −3.15390 + 1.82090i −0.120241 + 0.0694213i
689689 −25.7103 5.98167i −0.979483 0.227883i
690690 −0.754466 + 1.30677i −0.0287220 + 0.0497480i
691691 2.16091 + 2.16091i 0.0822048 + 0.0822048i 0.747014 0.664809i 0.231487π-0.231487\pi
−0.664809 + 0.747014i 0.731487π0.731487\pi
692692 17.0028 + 9.81655i 0.646348 + 0.373169i
693693 0 0
694694 36.8501 36.8501i 1.39881 1.39881i
695695 4.05813 + 15.1452i 0.153934 + 0.574489i
696696 20.6710 20.6710i 0.783532 0.783532i
697697 −3.59519 + 0.963328i −0.136177 + 0.0364886i
698698 10.8854 + 6.28470i 0.412019 + 0.237879i
699699 7.41796 12.8483i 0.280573 0.485967i
700700 0 0
701701 11.0158i 0.416061i −0.978122 0.208031i 0.933295π-0.933295\pi
0.978122 0.208031i 0.0667054π-0.0667054\pi
702702 17.8132 33.3650i 0.672315 1.25928i
703703 26.5563 + 15.3323i 1.00159 + 0.578267i
704704 −36.6486 9.81997i −1.38125 0.370104i
705705 13.8676i 0.522283i
706706 30.6322 + 53.0566i 1.15286 + 1.99681i
707707 0 0
708708 −38.8138 10.4001i −1.45871 0.390860i
709709 −27.2109 + 7.29113i −1.02192 + 0.273824i −0.730604 0.682801i 0.760761π-0.760761\pi
−0.291321 + 0.956625i 0.594095π0.594095\pi
710710 13.8612 + 51.7306i 0.520200 + 1.94141i
711711 2.92346 0.109638
712712 48.1403 1.80413
713713 −0.253206 0.944977i −0.00948263 0.0353897i
714714 0 0
715715 −4.09008 + 17.5799i −0.152960 + 0.657450i
716716 16.6557 + 28.8486i 0.622454 + 1.07812i
717717 −12.0807 + 45.0857i −0.451161 + 1.68376i
718718 −26.5761 46.0311i −0.991811 1.71787i
719719 −21.0559 + 36.4699i −0.785252 + 1.36010i 0.143596 + 0.989636i 0.454133π0.454133\pi
−0.928848 + 0.370460i 0.879200π0.879200\pi
720720 6.76309 + 6.76309i 0.252045 + 0.252045i
721721 0 0
722722 −26.2130 + 97.8284i −0.975548 + 3.64079i
723723 −9.60699 + 35.8538i −0.357288 + 1.33342i
724724 24.2713i 0.902035i
725725 6.36814 3.67665i 0.236507 0.136547i
726726 −5.18151 + 5.18151i −0.192304 + 0.192304i
727727 −10.0901 −0.374223 −0.187111 0.982339i 0.559913π-0.559913\pi
−0.187111 + 0.982339i 0.559913π0.559913\pi
728728 0 0
729729 44.0349 1.63092
730730 −18.6680 + 18.6680i −0.690933 + 0.690933i
731731 −1.55722 + 0.899062i −0.0575959 + 0.0332530i
732732 43.6617i 1.61378i
733733 6.87790 25.6687i 0.254041 0.948093i −0.714581 0.699553i 0.753382π-0.753382\pi
0.968622 0.248540i 0.0799509π-0.0799509\pi
734734 8.62455 32.1873i 0.318338 1.18805i
735735 0 0
736736 −0.417306 0.417306i −0.0153821 0.0153821i
737737 2.22417 3.85238i 0.0819285 0.141904i
738738 31.4494 + 54.4719i 1.15767 + 2.00514i
739739 6.51146 24.3011i 0.239528 0.893930i −0.736528 0.676407i 0.763536π-0.763536\pi
0.976055 0.217522i 0.0697975π-0.0697975\pi
740740 10.8778 + 18.8409i 0.399876 + 0.692605i
741741 69.2108 + 36.9509i 2.54252 + 1.35742i
742742 0 0
743743 −2.81817 10.5175i −0.103388 0.385851i 0.894769 0.446530i 0.147340π-0.147340\pi
−0.998157 + 0.0606785i 0.980674π0.980674\pi
744744 −65.4850 −2.40080
745745 8.84969 0.324227
746746 −2.13025 7.95021i −0.0779941 0.291078i
747747 6.80271 1.82278i 0.248898 0.0666921i
748748 6.83328 + 1.83097i 0.249850 + 0.0669470i
749749 0 0
750750 38.5147 + 66.7094i 1.40636 + 2.43588i
751751 32.2340i 1.17623i 0.808776 + 0.588117i 0.200131π0.200131\pi
−0.808776 + 0.588117i 0.799869π0.799869\pi
752752 −3.95727 1.06035i −0.144307 0.0386669i
753753 30.6097 + 17.6725i 1.11548 + 0.644022i
754754 21.4704 13.3655i 0.781904 0.486744i
755755 7.56115i 0.275179i
756756 0 0
757757 −16.9609 + 29.3771i −0.616453 + 1.06773i 0.373675 + 0.927560i 0.378098π0.378098\pi
−0.990128 + 0.140168i 0.955236π0.955236\pi
758758 −54.5711 31.5066i −1.98211 1.14437i
759759 1.22413 0.328004i 0.0444330 0.0119058i
760760 −31.4817 + 31.4817i −1.14196 + 1.14196i
761761 2.50812 + 9.36045i 0.0909194 + 0.339316i 0.996369 0.0851375i 0.0271329π-0.0271329\pi
−0.905450 + 0.424453i 0.860466π0.860466\pi
762762 −14.9101 + 14.9101i −0.540137 + 0.540137i
763763 0 0
764764 −7.61437 4.39616i −0.275478 0.159047i
765765 3.33924 + 3.33924i 0.120730 + 0.120730i
766766 40.0837 69.4270i 1.44828 2.50850i
767767 −13.1921 7.04313i −0.476340 0.254313i
768768 −56.0159 + 32.3408i −2.02130 + 1.16700i
769769 14.6001 3.91210i 0.526495 0.141074i 0.0142256 0.999899i 0.495472π-0.495472\pi
0.512269 + 0.858825i 0.328805π0.328805\pi
770770 0 0
771771 −24.8147 + 14.3268i −0.893678 + 0.515965i
772772 76.4737 + 20.4911i 2.75235 + 0.737490i
773773 −27.6552 27.6552i −0.994687 0.994687i 0.00529914 0.999986i 0.498313π-0.498313\pi
−0.999986 + 0.00529914i 0.998313π0.998313\pi
774774 21.4867 + 21.4867i 0.772322 + 0.772322i
775775 −15.9108 4.26328i −0.571532 0.153142i
776776 0.577718 0.333546i 0.0207389 0.0119736i
777777 0 0
778778 −62.2709 + 16.6854i −2.23252 + 0.598202i
779779 −39.6060 + 22.8665i −1.41903 + 0.819279i
780780 29.4167 + 47.2549i 1.05329 + 1.69200i
781781 22.4898 38.9535i 0.804750 1.39387i
782782 0.155635 + 0.155635i 0.00556551 + 0.00556551i
783783 −11.5652 6.67718i −0.413307 0.238623i
784784 0 0
785785 −14.2201 + 14.2201i −0.507537 + 0.507537i
786786 −27.6155 103.062i −0.985012 3.67611i
787787 1.23354 1.23354i 0.0439711 0.0439711i −0.684779 0.728750i 0.740101π-0.740101\pi
0.728750 + 0.684779i 0.240101π0.240101\pi
788788 −60.7217 + 16.2703i −2.16312 + 0.579607i
789789 10.4691 + 6.04433i 0.372709 + 0.215184i
790790 −1.18370 + 2.05022i −0.0421141 + 0.0729437i
791791 0 0
792792 51.4278i 1.82741i
793793 3.68214 15.8265i 0.130757 0.562015i
794794 75.3492 + 43.5029i 2.67404 + 1.54386i
795795 −31.1049 8.33454i −1.10318 0.295596i
796796 57.6051i 2.04176i
797797 −12.2921 21.2905i −0.435407 0.754148i 0.561921 0.827191i 0.310062π-0.310062\pi
−0.997329 + 0.0730430i 0.976729π0.976729\pi
798798 0 0
799799 −1.95388 0.523540i −0.0691233 0.0185215i
800800 −9.59806 + 2.57179i −0.339343 + 0.0909266i
801801 −16.2385 60.6030i −0.573760 2.14130i
802802 −40.7873 −1.44025
803803 22.1730 0.782469
804804 −3.55057 13.2509i −0.125219 0.467324i
805805 0 0
806806 −55.1795 12.8379i −1.94362 0.452195i
807807 −16.1264 27.9317i −0.567675 0.983241i
808808 1.09507 4.08684i 0.0385243 0.143775i
809809 1.41467 + 2.45029i 0.0497373 + 0.0861475i 0.889822 0.456307i 0.150828π-0.150828\pi
−0.840085 + 0.542455i 0.817495π0.817495\pi
810810 −2.84577 + 4.92903i −0.0999903 + 0.173188i
811811 −6.39483 6.39483i −0.224553 0.224553i 0.585860 0.810412i 0.300757π-0.300757\pi
−0.810412 + 0.585860i 0.800757π0.800757\pi
812812 0 0
813813 21.9272 81.8334i 0.769020 2.87002i
814814 7.42387 27.7063i 0.260207 0.971104i
815815 20.8004i 0.728607i
816816 1.99294 1.15062i 0.0697667 0.0402798i
817817 −15.6227 + 15.6227i −0.546570 + 0.546570i
818818 −26.4854 −0.926041
819819 0 0
820820 −32.4463 −1.13307
821821 26.3858 26.3858i 0.920872 0.920872i −0.0762190 0.997091i 0.524285π-0.524285\pi
0.997091 + 0.0762190i 0.0242848π0.0242848\pi
822822 2.12064 1.22435i 0.0739657 0.0427041i
823823 39.4868i 1.37642i 0.725510 + 0.688212i 0.241604π0.241604\pi
−0.725510 + 0.688212i 0.758396π0.758396\pi
824824 4.39916 16.4179i 0.153252 0.571944i
825825 5.52266 20.6109i 0.192274 0.717578i
826826 0 0
827827 −24.4804 24.4804i −0.851267 0.851267i 0.139022 0.990289i 0.455604π-0.455604\pi
−0.990289 + 0.139022i 0.955604π0.955604\pi
828828 1.18470 2.05195i 0.0411711 0.0713104i
829829 −6.73903 11.6723i −0.234056 0.405397i 0.724942 0.688810i 0.241867π-0.241867\pi
−0.958998 + 0.283413i 0.908533π0.908533\pi
830830 −1.47607 + 5.50878i −0.0512352 + 0.191212i
831831 −26.3125 45.5745i −0.912769 1.58096i
832832 −41.6648 + 12.6609i −1.44447 + 0.438938i
833833 0 0
834834 −16.5003 61.5801i −0.571360 2.13234i
835835 −29.5342 −1.02207
836836 86.9237 3.00632
837837 7.74257 + 28.8957i 0.267622 + 0.998780i
838838 −42.2160 + 11.3118i −1.45833 + 0.390758i
839839 48.1190 + 12.8935i 1.66125 + 0.445132i 0.962732 0.270457i 0.0871749π-0.0871749\pi
0.698522 + 0.715589i 0.253842π0.253842\pi
840840 0 0
841841 10.0352 + 17.3815i 0.346041 + 0.599360i
842842 62.7484i 2.16245i
843843 44.7459 + 11.9896i 1.54113 + 0.412944i
844844 −29.9815 17.3098i −1.03201 0.595829i
845845 6.67780 + 19.6098i 0.229723 + 0.674596i
846846 34.1836i 1.17526i
847847 0 0
848848 −4.75671 + 8.23886i −0.163346 + 0.282924i
849849 20.1690 + 11.6445i 0.692197 + 0.399640i
850850 3.57962 0.959157i 0.122780 0.0328988i
851851 0.401982 0.401982i 0.0137798 0.0137798i
852852 −35.9018 133.987i −1.22997 4.59033i
853853 −15.4604 + 15.4604i −0.529355 + 0.529355i −0.920380 0.391025i 0.872121π-0.872121\pi
0.391025 + 0.920380i 0.372121π0.372121\pi
854854 0 0
855855 50.2511 + 29.0125i 1.71855 + 0.992207i
856856 38.3339 + 38.3339i 1.31023 + 1.31023i
857857 −12.5050 + 21.6594i −0.427164 + 0.739869i −0.996620 0.0821525i 0.973821π-0.973821\pi
0.569456 + 0.822022i 0.307154π0.307154\pi
858858 16.6302 71.4797i 0.567747 2.44028i
859859 30.9754 17.8837i 1.05687 0.610183i 0.132304 0.991209i 0.457762π-0.457762\pi
0.924564 + 0.381026i 0.124429π0.124429\pi
860860 −15.1409 + 4.05698i −0.516299 + 0.138342i
861861 0 0
862862 −60.0127 + 34.6484i −2.04404 + 1.18013i
863863 −39.9815 10.7130i −1.36099 0.364675i −0.496807 0.867861i 0.665494π-0.665494\pi
−0.864178 + 0.503186i 0.832161π0.832161\pi
864864 12.7604 + 12.7604i 0.434119 + 0.434119i
865865 6.30285 + 6.30285i 0.214303 + 0.214303i
866866 −81.4695 21.8297i −2.76845 0.741803i
867867 −39.6537 + 22.8941i −1.34671 + 0.777524i
868868 0 0
869869 1.92056 0.514612i 0.0651504 0.0174570i
870870 26.7191 15.4263i 0.905862 0.523000i
871871 −0.169516 5.10263i −0.00574382 0.172896i
872872 −22.8658 + 39.6048i −0.774335 + 1.34119i
873873 −0.614769 0.614769i −0.0208068 0.0208068i
874874 2.34210 + 1.35221i 0.0792229 + 0.0457393i
875875 0 0
876876 48.3519 48.3519i 1.63366 1.63366i
877877 6.49432 + 24.2371i 0.219298 + 0.818430i 0.984609 + 0.174770i 0.0559183π0.0559183\pi
−0.765312 + 0.643660i 0.777415π0.777415\pi
878878 −16.1994 + 16.1994i −0.546702 + 0.546702i
879879 −22.1007 + 5.92188i −0.745440 + 0.199740i
880880 5.63348 + 3.25249i 0.189905 + 0.109641i
881881 −18.7477 + 32.4719i −0.631624 + 1.09401i 0.355595 + 0.934640i 0.384278π0.384278\pi
−0.987220 + 0.159365i 0.949055π0.949055\pi
882882 0 0
883883 19.9652i 0.671881i 0.941883 + 0.335941i 0.109054π0.109054\pi
−0.941883 + 0.335941i 0.890946π0.890946\pi
884884 7.76857 2.36068i 0.261285 0.0793982i
885885 −15.7992 9.12168i −0.531085 0.306622i
886886 87.9265 + 23.5598i 2.95395 + 0.791508i
887887 51.4854i 1.72871i 0.502882 + 0.864355i 0.332273π0.332273\pi
−0.502882 + 0.864355i 0.667727π0.667727\pi
888888 −19.0264 32.9546i −0.638483 1.10588i
889889 0 0
890890 49.0758 + 13.1498i 1.64502 + 0.440783i
891891 4.61729 1.23720i 0.154685 0.0414477i
892892 7.91803 + 29.5505i 0.265115 + 0.989424i
893893 −24.8546 −0.831727
894894 −35.9828 −1.20344
895895 3.91429 + 14.6083i 0.130840 + 0.488303i
896896 0 0
897897 0.993778 1.06208i 0.0331813 0.0354617i
898898 −10.9837 19.0243i −0.366530 0.634848i
899899 −5.17720 + 19.3216i −0.172669 + 0.644411i
900900 −19.9470 34.5492i −0.664899 1.15164i
901901 −2.34860 + 4.06789i −0.0782432 + 0.135521i
902902 30.2492 + 30.2492i 1.00719 + 1.00719i
903903 0 0
904904 1.41396 5.27699i 0.0470277 0.175510i
905905 2.85202 10.6439i 0.0948042 0.353814i
906906 30.7436i 1.02139i
907907 −25.0770 + 14.4782i −0.832669 + 0.480742i −0.854766 0.519014i 0.826299π-0.826299\pi
0.0220968 + 0.999756i 0.492966π0.492966\pi
908908 41.9262 41.9262i 1.39137 1.39137i
909909 −5.51424 −0.182896
910910 0 0
911911 3.65299 0.121029 0.0605144 0.998167i 0.480726π-0.480726\pi
0.0605144 + 0.998167i 0.480726π0.480726\pi
912912 19.9940 19.9940i 0.662068 0.662068i
913913 4.14815 2.39494i 0.137284 0.0792609i
914914 45.1178i 1.49236i
915915 5.13050 19.1473i 0.169609 0.632990i
916916 −2.22137 + 8.29025i −0.0733960 + 0.273918i
917917 0 0
918918 −4.75904 4.75904i −0.157072 0.157072i
919919 −21.3670 + 37.0087i −0.704831 + 1.22080i 0.261922 + 0.965089i 0.415644π0.415644\pi
−0.966753 + 0.255714i 0.917690π0.917690\pi
920920 0.412694 + 0.714807i 0.0136061 + 0.0235665i
921921 −17.5229 + 65.3963i −0.577398 + 2.15488i
922922 15.8924 + 27.5265i 0.523389 + 0.906536i
923923 −1.71407 51.5954i −0.0564192 1.69828i
924924 0 0
925925 −2.47735 9.24560i −0.0814548 0.303994i
926926 48.5777 1.59636
927927 −22.1521 −0.727571
928928 3.12311 + 11.6556i 0.102521 + 0.382614i
929929 16.3504 4.38107i 0.536438 0.143738i 0.0195786 0.999808i 0.493768π-0.493768\pi
0.516860 + 0.856070i 0.327101π0.327101\pi
930930 −66.7576 17.8876i −2.18907 0.586559i
931931 0 0
932932 −9.43247 16.3375i −0.308971 0.535153i
933933 65.4515i 2.14279i
934934 −70.2264 18.8171i −2.29788 0.615714i
935935 2.78150 + 1.60590i 0.0909648 + 0.0525186i
936936 −31.1932 50.1087i −1.01958 1.63785i
937937 46.5686i 1.52133i −0.649145 0.760665i 0.724873π-0.724873\pi
0.649145 0.760665i 0.275127π-0.275127\pi
938938 0 0
939939 −19.4205 + 33.6372i −0.633763 + 1.09771i
940940 −15.2712 8.81680i −0.498090 0.287572i
941941 −11.4955 + 3.08022i −0.374744 + 0.100412i −0.441275 0.897372i 0.645474π-0.645474\pi
0.0665310 + 0.997784i 0.478807π0.478807\pi
942942 57.8188 57.8188i 1.88384 1.88384i
943943 0.219438 + 0.818954i 0.00714588 + 0.0266688i
944944 −3.81102 + 3.81102i −0.124038 + 0.124038i
945945 0 0
946946 17.8978 + 10.3333i 0.581909 + 0.335965i
947947 30.5491 + 30.5491i 0.992714 + 0.992714i 0.999974 0.00726000i 0.00231095π-0.00231095\pi
−0.00726000 + 0.999974i 0.502311π0.502311\pi
948948 3.06589 5.31028i 0.0995756 0.172470i
949949 21.6043 13.4489i 0.701305 0.436570i
950950 39.4345 22.7675i 1.27942 0.738676i
951951 −44.6321 + 11.9591i −1.44730 + 0.387802i
952952 0 0
953953 −50.8066 + 29.3332i −1.64579 + 0.950195i −0.667066 + 0.744999i 0.732450π0.732450\pi
−0.978721 + 0.205196i 0.934217π0.934217\pi
954954 76.6738 + 20.5447i 2.48241 + 0.665159i
955955 −2.82261 2.82261i −0.0913376 0.0913376i
956956 41.9682 + 41.9682i 1.35735 + 1.35735i
957957 −25.0292 6.70657i −0.809080 0.216792i
958958 −14.9314 + 8.62062i −0.482410 + 0.278520i
959959 0 0
960960 −51.3127 + 13.7492i −1.65611 + 0.443753i
961961 11.9589 6.90448i 0.385771 0.222725i
962962 −9.57161 31.4985i −0.308601 1.01555i
963963 35.3273 61.1886i 1.13840 1.97178i
964964 33.3747 + 33.3747i 1.07493 + 1.07493i
965965 31.1288 + 17.9722i 1.00207 + 0.578546i
966966 0 0
967967 −7.53769 + 7.53769i −0.242396 + 0.242396i −0.817841 0.575445i 0.804829π-0.804829\pi
0.575445 + 0.817841i 0.304829π0.304829\pi
968968 1.03743 + 3.87172i 0.0333441 + 0.124442i
969969 9.87194 9.87194i 0.317132 0.317132i
970970 0.680055 0.182220i 0.0218353 0.00585074i
971971 −27.3314 15.7798i −0.877107 0.506398i −0.00740334 0.999973i 0.502357π-0.502357\pi
−0.869703 + 0.493575i 0.835690π0.835690\pi
972972 30.8990 53.5187i 0.991086 1.71661i
973973 0 0
974974 23.1495i 0.741759i
975975 −7.12039 23.4319i −0.228035 0.750422i
976976 −5.07160 2.92809i −0.162338 0.0937259i
977977 1.10312 + 0.295580i 0.0352919 + 0.00945644i 0.276422 0.961036i 0.410851π-0.410851\pi
−0.241130 + 0.970493i 0.577518π0.577518\pi
978978 84.5744i 2.70439i
979979 −21.3357 36.9545i −0.681891 1.18107i
980980 0 0
981981 57.5708 + 15.4261i 1.83810 + 0.492516i
982982 −86.7559 + 23.2462i −2.76849 + 0.741815i
983983 7.63569 + 28.4968i 0.243541 + 0.908907i 0.974111 + 0.226069i 0.0725876π0.0725876\pi
−0.730570 + 0.682837i 0.760746π0.760746\pi
984984 56.7518 1.80918
985985 −28.5406 −0.909380
986986 −1.16477 4.34699i −0.0370939 0.138436i
987987 0 0
988988 84.6940 52.7230i 2.69448 1.67734i
989989 0.204799 + 0.354722i 0.00651222 + 0.0112795i
990990 14.0478 52.4272i 0.446469 1.66625i
991991 22.8046 + 39.4987i 0.724412 + 1.25472i 0.959216 + 0.282675i 0.0912219π0.0912219\pi
−0.234804 + 0.972043i 0.575445π0.575445\pi
992992 13.5153 23.4093i 0.429113 0.743245i
993993 −18.8898 18.8898i −0.599450 0.599450i
994994 0 0
995995 6.76894 25.2620i 0.214590 0.800860i
996996 3.82317 14.2683i 0.121142 0.452108i
997997 26.0713i 0.825686i 0.910802 + 0.412843i 0.135464π0.135464\pi
−0.910802 + 0.412843i 0.864536π0.864536\pi
998998 0.00295282 0.00170481i 9.34698e−5 5.39648e-5i
999999 −12.2919 + 12.2919i −0.388897 + 0.388897i
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 637.2.bb.b.227.2 32
7.2 even 3 637.2.x.b.19.8 32
7.3 odd 6 91.2.bc.a.6.2 yes 32
7.4 even 3 91.2.bc.a.6.1 32
7.5 odd 6 637.2.x.b.19.7 32
7.6 odd 2 inner 637.2.bb.b.227.1 32
13.11 odd 12 637.2.x.b.570.8 32
21.11 odd 6 819.2.fm.g.370.7 32
21.17 even 6 819.2.fm.g.370.8 32
91.11 odd 12 91.2.bc.a.76.2 yes 32
91.24 even 12 91.2.bc.a.76.1 yes 32
91.37 odd 12 inner 637.2.bb.b.362.1 32
91.76 even 12 637.2.x.b.570.7 32
91.89 even 12 inner 637.2.bb.b.362.2 32
273.11 even 12 819.2.fm.g.622.8 32
273.206 odd 12 819.2.fm.g.622.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.bc.a.6.1 32 7.4 even 3
91.2.bc.a.6.2 yes 32 7.3 odd 6
91.2.bc.a.76.1 yes 32 91.24 even 12
91.2.bc.a.76.2 yes 32 91.11 odd 12
637.2.x.b.19.7 32 7.5 odd 6
637.2.x.b.19.8 32 7.2 even 3
637.2.x.b.570.7 32 91.76 even 12
637.2.x.b.570.8 32 13.11 odd 12
637.2.bb.b.227.1 32 7.6 odd 2 inner
637.2.bb.b.227.2 32 1.1 even 1 trivial
637.2.bb.b.362.1 32 91.37 odd 12 inner
637.2.bb.b.362.2 32 91.89 even 12 inner
819.2.fm.g.370.7 32 21.11 odd 6
819.2.fm.g.370.8 32 21.17 even 6
819.2.fm.g.622.7 32 273.206 odd 12
819.2.fm.g.622.8 32 273.11 even 12