Properties

Label 891.2.n.g.460.2
Level 891891
Weight 22
Character 891.460
Analytic conductor 7.1157.115
Analytic rank 00
Dimension 3232
Inner twists 88

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 891=3411 891 = 3^{4} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 891.n (of order 1515, degree 88, 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: 7.114670820107.11467082010
Analytic rank: 00
Dimension: 3232
Relative dimension: 44 over Q(ζ15)\Q(\zeta_{15})
Twist minimal: no (minimal twist has level 297)
Sato-Tate group: SU(2)[C15]\mathrm{SU}(2)[C_{15}]

Embedding invariants

Embedding label 460.2
Character χ\chi == 891.460
Dual form 891.2.n.g.676.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.4480850.497649i)q2+(0.1621831.54307i)q4+(1.849932.05455i)q5+(1.379900.614370i)q7+(1.92410+1.39794i)q81.85137q10+(2.651251.99271i)q11+(1.45264+0.308769i)q13+(0.9240520.411414i)q14+(1.477480.314048i)q16+(1.461384.49766i)q17+(2.873282.08756i)q19+(2.870283.18777i)q20+(0.196315+2.21229i)q22+(1.04751+1.81434i)q23+(0.2763132.62894i)q25+(0.804567+0.584552i)q26+(0.7242172.22891i)q28+(7.17542+3.19470i)q29+(8.575931.82287i)q31+(2.88407+4.99535i)q32+(1.58343+2.74259i)q34+(1.290453.97161i)q35+(4.16960+3.02939i)q37+(2.326340.494480i)q38+(0.687303+6.53925i)q40+(6.419242.85803i)q41+(1.45808+2.52546i)q43+(3.50487+3.76786i)q44+(0.4335311.33427i)q46+(0.227425+2.16380i)q47+(3.15725+3.50648i)q49+(1.18448+1.31550i)q50+(0.240857+2.29160i)q52+(4.1341712.7237i)q53+(8.99874+1.76076i)q55+(1.79621+3.11112i)q56+(4.80504+2.13934i)q58+(0.702544+6.68426i)q59+(10.1381+2.15492i)q61+(4.749903.45100i)q62+(0.2600920.800479i)q64+(2.05290+3.55573i)q65+(6.0197010.4264i)q67+(7.17720+1.52556i)q68+(2.55470+1.13743i)q70+(3.3441010.2921i)q71+(3.63900+2.64389i)q73+(0.3607623.43242i)q74+(2.755244.77222i)q76+(4.882711.12089i)q77+(10.322411.4642i)q79+(3.37845+2.45459i)q80+(1.45407+4.47517i)q82+(3.27510+0.696143i)q83+(11.94415.31787i)q85+(1.910140.406012i)q86+(7.88694+0.127887i)q88+10.6583q89+(1.81480+1.31853i)q91+(2.969541.32212i)q92+(0.9749081.08275i)q94+(1.026369.76513i)q95+(1.48572+1.65006i)q97+3.15971q98+O(q100)q+(-0.448085 - 0.497649i) q^{2} +(0.162183 - 1.54307i) q^{4} +(1.84993 - 2.05455i) q^{5} +(1.37990 - 0.614370i) q^{7} +(-1.92410 + 1.39794i) q^{8} -1.85137 q^{10} +(-2.65125 - 1.99271i) q^{11} +(-1.45264 + 0.308769i) q^{13} +(-0.924052 - 0.411414i) q^{14} +(-1.47748 - 0.314048i) q^{16} +(-1.46138 - 4.49766i) q^{17} +(2.87328 - 2.08756i) q^{19} +(-2.87028 - 3.18777i) q^{20} +(0.196315 + 2.21229i) q^{22} +(1.04751 + 1.81434i) q^{23} +(-0.276313 - 2.62894i) q^{25} +(0.804567 + 0.584552i) q^{26} +(-0.724217 - 2.22891i) q^{28} +(-7.17542 + 3.19470i) q^{29} +(8.57593 - 1.82287i) q^{31} +(2.88407 + 4.99535i) q^{32} +(-1.58343 + 2.74259i) q^{34} +(1.29045 - 3.97161i) q^{35} +(4.16960 + 3.02939i) q^{37} +(-2.32634 - 0.494480i) q^{38} +(-0.687303 + 6.53925i) q^{40} +(-6.41924 - 2.85803i) q^{41} +(-1.45808 + 2.52546i) q^{43} +(-3.50487 + 3.76786i) q^{44} +(0.433531 - 1.33427i) q^{46} +(0.227425 + 2.16380i) q^{47} +(-3.15725 + 3.50648i) q^{49} +(-1.18448 + 1.31550i) q^{50} +(0.240857 + 2.29160i) q^{52} +(4.13417 - 12.7237i) q^{53} +(-8.99874 + 1.76076i) q^{55} +(-1.79621 + 3.11112i) q^{56} +(4.80504 + 2.13934i) q^{58} +(-0.702544 + 6.68426i) q^{59} +(10.1381 + 2.15492i) q^{61} +(-4.74990 - 3.45100i) q^{62} +(0.260092 - 0.800479i) q^{64} +(-2.05290 + 3.55573i) q^{65} +(-6.01970 - 10.4264i) q^{67} +(-7.17720 + 1.52556i) q^{68} +(-2.55470 + 1.13743i) q^{70} +(-3.34410 - 10.2921i) q^{71} +(3.63900 + 2.64389i) q^{73} +(-0.360762 - 3.43242i) q^{74} +(-2.75524 - 4.77222i) q^{76} +(-4.88271 - 1.12089i) q^{77} +(-10.3224 - 11.4642i) q^{79} +(-3.37845 + 2.45459i) q^{80} +(1.45407 + 4.47517i) q^{82} +(3.27510 + 0.696143i) q^{83} +(-11.9441 - 5.31787i) q^{85} +(1.91014 - 0.406012i) q^{86} +(7.88694 + 0.127887i) q^{88} +10.6583 q^{89} +(-1.81480 + 1.31853i) q^{91} +(2.96954 - 1.32212i) q^{92} +(0.974908 - 1.08275i) q^{94} +(1.02636 - 9.76513i) q^{95} +(1.48572 + 1.65006i) q^{97} +3.15971 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q2q48q724q108q13+2q16+20q19+24q22+16q2560q28+6q3132q34+24q37+40q40+80q4324q4640q4912q52++46q94+O(q100) 32 q - 2 q^{4} - 8 q^{7} - 24 q^{10} - 8 q^{13} + 2 q^{16} + 20 q^{19} + 24 q^{22} + 16 q^{25} - 60 q^{28} + 6 q^{31} - 32 q^{34} + 24 q^{37} + 40 q^{40} + 80 q^{43} - 24 q^{46} - 40 q^{49} - 12 q^{52}+ \cdots + 46 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/891Z)×\left(\mathbb{Z}/891\mathbb{Z}\right)^\times.

nn 244244 650650
χ(n)\chi(n) e(35)e\left(\frac{3}{5}\right) e(23)e\left(\frac{2}{3}\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 −0.448085 0.497649i −0.316844 0.351891i 0.563594 0.826052i 0.309418π-0.309418\pi
−0.880438 + 0.474161i 0.842752π0.842752\pi
33 0 0
44 0.162183 1.54307i 0.0810914 0.771533i
55 1.84993 2.05455i 0.827313 0.918824i −0.170471 0.985363i 0.554529π-0.554529\pi
0.997784 + 0.0665386i 0.0211955π0.0211955\pi
66 0 0
77 1.37990 0.614370i 0.521552 0.232210i −0.129037 0.991640i 0.541189π-0.541189\pi
0.650589 + 0.759430i 0.274522π0.274522\pi
88 −1.92410 + 1.39794i −0.680271 + 0.494246i
99 0 0
1010 −1.85137 −0.585455
1111 −2.65125 1.99271i −0.799381 0.600824i
1212 0 0
1313 −1.45264 + 0.308769i −0.402891 + 0.0856371i −0.404900 0.914361i 0.632694π-0.632694\pi
0.00200934 + 0.999998i 0.499360π0.499360\pi
1414 −0.924052 0.411414i −0.246963 0.109955i
1515 0 0
1616 −1.47748 0.314048i −0.369369 0.0785119i
1717 −1.46138 4.49766i −0.354436 1.09084i −0.956336 0.292271i 0.905589π-0.905589\pi
0.601899 0.798572i 0.294411π-0.294411\pi
1818 0 0
1919 2.87328 2.08756i 0.659175 0.478919i −0.207209 0.978297i 0.566438π-0.566438\pi
0.866384 + 0.499378i 0.166438π0.166438\pi
2020 −2.87028 3.18777i −0.641815 0.712808i
2121 0 0
2222 0.196315 + 2.21229i 0.0418544 + 0.471663i
2323 1.04751 + 1.81434i 0.218421 + 0.378316i 0.954325 0.298769i 0.0965760π-0.0965760\pi
−0.735904 + 0.677086i 0.763243π0.763243\pi
2424 0 0
2525 −0.276313 2.62894i −0.0552626 0.525788i
2626 0.804567 + 0.584552i 0.157788 + 0.114640i
2727 0 0
2828 −0.724217 2.22891i −0.136864 0.421225i
2929 −7.17542 + 3.19470i −1.33244 + 0.593241i −0.944521 0.328451i 0.893473π-0.893473\pi
−0.387921 + 0.921693i 0.626807π0.626807\pi
3030 0 0
3131 8.57593 1.82287i 1.54028 0.327397i 0.641962 0.766737i 0.278121π-0.278121\pi
0.898321 + 0.439339i 0.144787π0.144787\pi
3232 2.88407 + 4.99535i 0.509836 + 0.883061i
3333 0 0
3434 −1.58343 + 2.74259i −0.271557 + 0.470350i
3535 1.29045 3.97161i 0.218127 0.671325i
3636 0 0
3737 4.16960 + 3.02939i 0.685478 + 0.498029i 0.875170 0.483815i 0.160749π-0.160749\pi
−0.189693 + 0.981844i 0.560749π0.560749\pi
3838 −2.32634 0.494480i −0.377383 0.0802152i
3939 0 0
4040 −0.687303 + 6.53925i −0.108672 + 1.03395i
4141 −6.41924 2.85803i −1.00252 0.446350i −0.161218 0.986919i 0.551542π-0.551542\pi
−0.841299 + 0.540569i 0.818209π0.818209\pi
4242 0 0
4343 −1.45808 + 2.52546i −0.222355 + 0.385129i −0.955522 0.294918i 0.904708π-0.904708\pi
0.733168 + 0.680048i 0.238041π0.238041\pi
4444 −3.50487 + 3.76786i −0.528379 + 0.568027i
4545 0 0
4646 0.433531 1.33427i 0.0639207 0.196728i
4747 0.227425 + 2.16380i 0.0331733 + 0.315623i 0.998508 + 0.0546074i 0.0173907π0.0173907\pi
−0.965335 + 0.261016i 0.915943π0.915943\pi
4848 0 0
4949 −3.15725 + 3.50648i −0.451036 + 0.500926i
5050 −1.18448 + 1.31550i −0.167511 + 0.186039i
5151 0 0
5252 0.240857 + 2.29160i 0.0334009 + 0.317788i
5353 4.13417 12.7237i 0.567872 1.74773i −0.0913880 0.995815i 0.529130π-0.529130\pi
0.659260 0.751915i 0.270870π-0.270870\pi
5454 0 0
5555 −8.99874 + 1.76076i −1.21339 + 0.237421i
5656 −1.79621 + 3.11112i −0.240028 + 0.415741i
5757 0 0
5858 4.80504 + 2.13934i 0.630932 + 0.280909i
5959 −0.702544 + 6.68426i −0.0914634 + 0.870216i 0.848558 + 0.529102i 0.177471π0.177471\pi
−0.940022 + 0.341115i 0.889196π0.889196\pi
6060 0 0
6161 10.1381 + 2.15492i 1.29805 + 0.275909i 0.804575 0.593851i 0.202393π-0.202393\pi
0.493475 + 0.869760i 0.335726π0.335726\pi
6262 −4.74990 3.45100i −0.603238 0.438278i
6363 0 0
6464 0.260092 0.800479i 0.0325114 0.100060i
6565 −2.05290 + 3.55573i −0.254631 + 0.441035i
6666 0 0
6767 −6.01970 10.4264i −0.735423 1.27379i −0.954538 0.298091i 0.903650π-0.903650\pi
0.219115 0.975699i 0.429683π-0.429683\pi
6868 −7.17720 + 1.52556i −0.870363 + 0.185001i
6969 0 0
7070 −2.55470 + 1.13743i −0.305345 + 0.135948i
7171 −3.34410 10.2921i −0.396872 1.22145i −0.927494 0.373838i 0.878042π-0.878042\pi
0.530622 0.847608i 0.321958π-0.321958\pi
7272 0 0
7373 3.63900 + 2.64389i 0.425913 + 0.309444i 0.780013 0.625764i 0.215213π-0.215213\pi
−0.354099 + 0.935208i 0.615213π0.615213\pi
7474 −0.360762 3.43242i −0.0419377 0.399011i
7575 0 0
7676 −2.75524 4.77222i −0.316048 0.547411i
7777 −4.88271 1.12089i −0.556436 0.127737i
7878 0 0
7979 −10.3224 11.4642i −1.16136 1.28983i −0.949940 0.312432i 0.898856π-0.898856\pi
−0.211425 0.977394i 0.567810π-0.567810\pi
8080 −3.37845 + 2.45459i −0.377723 + 0.274432i
8181 0 0
8282 1.45407 + 4.47517i 0.160575 + 0.494200i
8383 3.27510 + 0.696143i 0.359488 + 0.0764116i 0.384115 0.923285i 0.374506π-0.374506\pi
−0.0246270 + 0.999697i 0.507840π0.507840\pi
8484 0 0
8585 −11.9441 5.31787i −1.29552 0.576804i
8686 1.91014 0.406012i 0.205975 0.0437814i
8787 0 0
8888 7.88694 + 0.127887i 0.840751 + 0.0136328i
8989 10.6583 1.12978 0.564888 0.825167i 0.308919π-0.308919\pi
0.564888 + 0.825167i 0.308919π0.308919\pi
9090 0 0
9191 −1.81480 + 1.31853i −0.190243 + 0.138219i
9292 2.96954 1.32212i 0.309596 0.137841i
9393 0 0
9494 0.974908 1.08275i 0.100554 0.111677i
9595 1.02636 9.76513i 0.105302 1.00188i
9696 0 0
9797 1.48572 + 1.65006i 0.150852 + 0.167538i 0.813835 0.581097i 0.197376π-0.197376\pi
−0.662982 + 0.748635i 0.730710π0.730710\pi
9898 3.15971 0.319179
9999 0 0
100100 −4.10144 −0.410144
101101 0.325123 + 0.361085i 0.0323509 + 0.0359293i 0.759103 0.650970i 0.225638π-0.225638\pi
−0.726752 + 0.686900i 0.758971π0.758971\pi
102102 0 0
103103 0.668220 6.35769i 0.0658417 0.626441i −0.910989 0.412430i 0.864680π-0.864680\pi
0.976831 0.214012i 0.0686531π-0.0686531\pi
104104 2.36339 2.62481i 0.231749 0.257384i
105105 0 0
106106 −8.18438 + 3.64392i −0.794937 + 0.353929i
107107 −9.78725 + 7.11085i −0.946169 + 0.687432i −0.949898 0.312561i 0.898813π-0.898813\pi
0.00372856 + 0.999993i 0.498813π0.498813\pi
108108 0 0
109109 −4.73854 −0.453870 −0.226935 0.973910i 0.572871π-0.572871\pi
−0.226935 + 0.973910i 0.572871π0.572871\pi
110110 4.90844 + 3.68925i 0.468002 + 0.351756i
111111 0 0
112112 −2.23171 + 0.474364i −0.210877 + 0.0448232i
113113 16.7903 + 7.47551i 1.57950 + 0.703237i 0.994196 0.107581i 0.0343104π-0.0343104\pi
0.585299 + 0.810817i 0.300977π0.300977\pi
114114 0 0
115115 5.66548 + 1.20424i 0.528309 + 0.112296i
116116 3.76591 + 11.5903i 0.349656 + 1.07613i
117117 0 0
118118 3.64121 2.64550i 0.335201 0.243538i
119119 −4.77978 5.30848i −0.438162 0.486628i
120120 0 0
121121 3.05822 + 10.5663i 0.278020 + 0.960575i
122122 −3.47034 6.01080i −0.314190 0.544192i
123123 0 0
124124 −1.42194 13.5289i −0.127694 1.21493i
125125 5.27088 + 3.82952i 0.471442 + 0.342523i
126126 0 0
127127 −6.90430 21.2493i −0.612658 1.88557i −0.431501 0.902112i 0.642016π-0.642016\pi
−0.181156 0.983454i 0.557984π-0.557984\pi
128128 10.0240 4.46297i 0.886005 0.394475i
129129 0 0
130130 2.68938 0.571646i 0.235874 0.0501367i
131131 −1.98522 3.43851i −0.173450 0.300424i 0.766174 0.642633i 0.222158π-0.222158\pi
−0.939624 + 0.342209i 0.888825π0.888825\pi
132132 0 0
133133 2.68229 4.64587i 0.232584 0.402848i
134134 −2.49136 + 7.66762i −0.215221 + 0.662381i
135135 0 0
136136 9.09929 + 6.61102i 0.780258 + 0.566890i
137137 5.86012 + 1.24561i 0.500664 + 0.106419i 0.451320 0.892362i 0.350953π-0.350953\pi
0.0493445 + 0.998782i 0.484287π0.484287\pi
138138 0 0
139139 −1.79667 + 17.0942i −0.152392 + 1.44991i 0.604623 + 0.796512i 0.293324π0.293324\pi
−0.757014 + 0.653398i 0.773343π0.773343\pi
140140 −5.91917 2.63538i −0.500261 0.222731i
141141 0 0
142142 −3.62340 + 6.27592i −0.304069 + 0.526664i
143143 4.46660 + 2.07607i 0.373516 + 0.173610i
144144 0 0
145145 −6.71032 + 20.6522i −0.557262 + 1.71508i
146146 −0.314854 2.99564i −0.0260575 0.247921i
147147 0 0
148148 5.35079 5.94265i 0.439832 0.488483i
149149 8.61520 9.56815i 0.705784 0.783853i −0.278501 0.960436i 0.589838π-0.589838\pi
0.984286 + 0.176583i 0.0565043π0.0565043\pi
150150 0 0
151151 0.878973 + 8.36287i 0.0715298 + 0.680560i 0.970261 + 0.242061i 0.0778233π0.0778233\pi
−0.898731 + 0.438500i 0.855510π0.855510\pi
152152 −2.61019 + 8.03333i −0.211714 + 0.651589i
153153 0 0
154154 1.63006 + 2.93213i 0.131354 + 0.236278i
155155 12.1197 20.9919i 0.973476 1.68611i
156156 0 0
157157 10.7910 + 4.80445i 0.861214 + 0.383437i 0.789325 0.613976i 0.210431π-0.210431\pi
0.0718888 + 0.997413i 0.477097π0.477097\pi
158158 −1.07983 + 10.2739i −0.0859067 + 0.817347i
159159 0 0
160160 15.5985 + 3.31557i 1.23317 + 0.262119i
161161 2.56013 + 1.86005i 0.201767 + 0.146592i
162162 0 0
163163 1.42569 4.38781i 0.111668 0.343680i −0.879569 0.475771i 0.842169π-0.842169\pi
0.991238 + 0.132091i 0.0421691π0.0421691\pi
164164 −5.45122 + 9.44179i −0.425669 + 0.737280i
165165 0 0
166166 −1.12109 1.94178i −0.0870132 0.150711i
167167 9.63126 2.04719i 0.745289 0.158416i 0.180412 0.983591i 0.442257π-0.442257\pi
0.564877 + 0.825175i 0.308924π0.308924\pi
168168 0 0
169169 −9.86126 + 4.39051i −0.758558 + 0.337732i
170170 2.70556 + 8.32684i 0.207507 + 0.638640i
171171 0 0
172172 3.66048 + 2.65949i 0.279109 + 0.202785i
173173 1.53520 + 14.6065i 0.116719 + 1.11051i 0.883445 + 0.468535i 0.155218π0.155218\pi
−0.766726 + 0.641975i 0.778115π0.778115\pi
174174 0 0
175175 −1.99643 3.45791i −0.150916 0.261393i
176176 3.29135 + 3.77680i 0.248095 + 0.284687i
177177 0 0
178178 −4.77582 5.30409i −0.357963 0.397558i
179179 −9.16182 + 6.65645i −0.684787 + 0.497527i −0.874942 0.484227i 0.839101π-0.839101\pi
0.190156 + 0.981754i 0.439101π0.439101\pi
180180 0 0
181181 −1.94459 5.98485i −0.144541 0.444850i 0.852411 0.522872i 0.175140π-0.175140\pi
−0.996952 + 0.0780221i 0.975140π0.975140\pi
182182 1.46935 + 0.312320i 0.108915 + 0.0231507i
183183 0 0
184184 −4.55185 2.02661i −0.335567 0.149404i
185185 13.9375 2.96251i 1.02471 0.217808i
186186 0 0
187187 −5.08806 + 14.8365i −0.372076 + 1.08495i
188188 3.37577 0.246204
189189 0 0
190190 −5.31950 + 3.86484i −0.385917 + 0.280385i
191191 3.35252 1.49264i 0.242580 0.108004i −0.281846 0.959460i 0.590947π-0.590947\pi
0.524426 + 0.851456i 0.324280π0.324280\pi
192192 0 0
193193 0.940575 1.04461i 0.0677041 0.0751930i −0.708341 0.705870i 0.750556π-0.750556\pi
0.776045 + 0.630677i 0.217223π0.217223\pi
194194 0.155421 1.47874i 0.0111586 0.106167i
195195 0 0
196196 4.89868 + 5.44053i 0.349906 + 0.388609i
197197 3.38982 0.241514 0.120757 0.992682i 0.461468π-0.461468\pi
0.120757 + 0.992682i 0.461468π0.461468\pi
198198 0 0
199199 7.38470 0.523487 0.261744 0.965137i 0.415703π-0.415703\pi
0.261744 + 0.965137i 0.415703π0.415703\pi
200200 4.20675 + 4.67207i 0.297462 + 0.330365i
201201 0 0
202202 0.0340111 0.323594i 0.00239301 0.0227680i
203203 −7.93861 + 8.81672i −0.557181 + 0.618812i
204204 0 0
205205 −17.7471 + 7.90153i −1.23951 + 0.551866i
206206 −3.46332 + 2.51625i −0.241301 + 0.175315i
207207 0 0
208208 2.24322 0.155539
209209 −11.7777 0.190975i −0.814678 0.0132100i
210210 0 0
211211 1.90178 0.404237i 0.130924 0.0278288i −0.141983 0.989869i 0.545348π-0.545348\pi
0.272908 + 0.962040i 0.412015π0.412015\pi
212212 −18.9630 8.44286i −1.30238 0.579858i
213213 0 0
214214 7.92423 + 1.68435i 0.541689 + 0.115140i
215215 2.49136 + 7.66762i 0.169909 + 0.522927i
216216 0 0
217217 10.7140 7.78417i 0.727313 0.528424i
218218 2.12327 + 2.35813i 0.143806 + 0.159713i
219219 0 0
220220 1.25753 + 14.1712i 0.0847824 + 0.955423i
221221 3.51160 + 6.08227i 0.236216 + 0.409138i
222222 0 0
223223 −1.77476 16.8857i −0.118847 1.13075i −0.877607 0.479381i 0.840861π-0.840861\pi
0.758760 0.651370i 0.225806π-0.225806\pi
224224 7.04870 + 5.12118i 0.470961 + 0.342173i
225225 0 0
226226 −3.80329 11.7053i −0.252991 0.778626i
227227 14.8946 6.63150i 0.988590 0.440148i 0.152239 0.988344i 0.451352π-0.451352\pi
0.836350 + 0.548195i 0.184685π0.184685\pi
228228 0 0
229229 19.8772 4.22503i 1.31352 0.279198i 0.502686 0.864469i 0.332345π-0.332345\pi
0.810838 + 0.585271i 0.199012π0.199012\pi
230230 −1.93933 3.35902i −0.127876 0.221487i
231231 0 0
232232 9.34021 16.1777i 0.613215 1.06212i
233233 0.139989 0.430843i 0.00917101 0.0282255i −0.946366 0.323096i 0.895276π-0.895276\pi
0.955537 + 0.294870i 0.0952764π0.0952764\pi
234234 0 0
235235 4.86637 + 3.53562i 0.317447 + 0.230639i
236236 10.2003 + 2.16814i 0.663984 + 0.141134i
237237 0 0
238238 −0.500013 + 4.75730i −0.0324110 + 0.308370i
239239 17.3973 + 7.74579i 1.12534 + 0.501033i 0.883101 0.469183i 0.155452π-0.155452\pi
0.242239 + 0.970217i 0.422118π0.422118\pi
240240 0 0
241241 8.93559 15.4769i 0.575592 0.996955i −0.420385 0.907346i 0.638105π-0.638105\pi
0.995977 0.0896090i 0.0285617π-0.0285617\pi
242242 3.88798 6.25653i 0.249929 0.402185i
243243 0 0
244244 4.96941 15.2943i 0.318134 0.979114i
245245 1.36357 + 12.9735i 0.0871151 + 0.828845i
246246 0 0
247247 −3.52927 + 3.91966i −0.224562 + 0.249402i
248248 −13.9527 + 15.4960i −0.885995 + 0.983998i
249249 0 0
250250 −0.456047 4.33900i −0.0288430 0.274422i
251251 3.85401 11.8614i 0.243263 0.748687i −0.752654 0.658416i 0.771227π-0.771227\pi
0.995917 0.0902709i 0.0287733π-0.0287733\pi
252252 0 0
253253 0.838246 6.89765i 0.0527001 0.433652i
254254 −7.48095 + 12.9574i −0.469397 + 0.813019i
255255 0 0
256256 −8.25041 3.67332i −0.515651 0.229583i
257257 2.51918 23.9684i 0.157142 1.49511i −0.577353 0.816495i 0.695914π-0.695914\pi
0.734495 0.678614i 0.237419π-0.237419\pi
258258 0 0
259259 7.61478 + 1.61857i 0.473160 + 0.100573i
260260 5.15379 + 3.74444i 0.319624 + 0.232221i
261261 0 0
262262 −0.821621 + 2.52869i −0.0507599 + 0.156223i
263263 9.07714 15.7221i 0.559720 0.969464i −0.437799 0.899073i 0.644242π-0.644242\pi
0.997519 0.0703912i 0.0224247π-0.0224247\pi
264264 0 0
265265 −18.4935 32.0317i −1.13605 1.96769i
266266 −3.51391 + 0.746904i −0.215451 + 0.0457956i
267267 0 0
268268 −17.0649 + 7.59780i −1.04241 + 0.464110i
269269 4.12310 + 12.6896i 0.251390 + 0.773698i 0.994520 + 0.104551i 0.0333405π0.0333405\pi
−0.743130 + 0.669147i 0.766660π0.766660\pi
270270 0 0
271271 5.26488 + 3.82516i 0.319819 + 0.232362i 0.736098 0.676875i 0.236666π-0.236666\pi
−0.416279 + 0.909237i 0.636666π0.636666\pi
272272 0.746675 + 7.10414i 0.0452738 + 0.430752i
273273 0 0
274274 −2.00596 3.47442i −0.121184 0.209898i
275275 −4.50614 + 7.52058i −0.271731 + 0.453508i
276276 0 0
277277 −9.07255 10.0761i −0.545117 0.605413i 0.406141 0.913810i 0.366874π-0.366874\pi
−0.951258 + 0.308397i 0.900208π0.900208\pi
278278 9.31197 6.76554i 0.558495 0.405770i
279279 0 0
280280 3.06911 + 9.44574i 0.183414 + 0.564491i
281281 29.9118 + 6.35794i 1.78439 + 0.379283i 0.977418 0.211313i 0.0677739π-0.0677739\pi
0.806968 + 0.590596i 0.201107π0.201107\pi
282282 0 0
283283 −0.686047 0.305448i −0.0407812 0.0181570i 0.386245 0.922396i 0.373772π-0.373772\pi
−0.427026 + 0.904239i 0.640439π0.640439\pi
284284 −16.4237 + 3.49097i −0.974569 + 0.207151i
285285 0 0
286286 −0.968263 3.15306i −0.0572546 0.186444i
287287 −10.6138 −0.626512
288288 0 0
289289 −4.34004 + 3.15323i −0.255297 + 0.185484i
290290 13.2844 5.91458i 0.780085 0.347316i
291291 0 0
292292 4.66988 5.18643i 0.273284 0.303513i
293293 −1.59034 + 15.1310i −0.0929084 + 0.883964i 0.844459 + 0.535621i 0.179922π0.179922\pi
−0.937367 + 0.348343i 0.886744π0.886744\pi
294294 0 0
295295 12.4335 + 13.8088i 0.723907 + 0.803980i
296296 −12.2576 −0.712460
297297 0 0
298298 −8.62192 −0.499454
299299 −2.08187 2.31215i −0.120398 0.133715i
300300 0 0
301301 −0.460428 + 4.38068i −0.0265386 + 0.252498i
302302 3.76792 4.18470i 0.216819 0.240802i
303303 0 0
304304 −4.90079 + 2.18197i −0.281080 + 0.125145i
305305 23.1821 16.8428i 1.32741 0.964417i
306306 0 0
307307 2.79291 0.159400 0.0797000 0.996819i 0.474604π-0.474604\pi
0.0797000 + 0.996819i 0.474604π0.474604\pi
308308 −2.52149 + 7.35255i −0.143675 + 0.418950i
309309 0 0
310310 −15.8772 + 3.37481i −0.901766 + 0.191676i
311311 −21.2421 9.45760i −1.20453 0.536291i −0.296434 0.955053i 0.595798π-0.595798\pi
−0.908096 + 0.418762i 0.862464π0.862464\pi
312312 0 0
313313 13.6182 + 2.89465i 0.769748 + 0.163615i 0.576015 0.817439i 0.304607π-0.304607\pi
0.193733 + 0.981054i 0.437940π0.437940\pi
314314 −2.44435 7.52292i −0.137942 0.424543i
315315 0 0
316316 −19.3642 + 14.0689i −1.08932 + 0.791437i
317317 4.35049 + 4.83171i 0.244348 + 0.271376i 0.852826 0.522195i 0.174887π-0.174887\pi
−0.608479 + 0.793570i 0.708220π0.708220\pi
318318 0 0
319319 25.3899 + 5.82858i 1.42156 + 0.326338i
320320 −1.16348 2.01520i −0.0650403 0.112653i
321321 0 0
322322 −0.221508 2.10751i −0.0123442 0.117447i
323323 −13.5881 9.87231i −0.756061 0.549310i
324324 0 0
325325 1.21312 + 3.73360i 0.0672918 + 0.207103i
326326 −2.82242 + 1.25662i −0.156319 + 0.0695978i
327327 0 0
328328 16.3466 3.47458i 0.902590 0.191851i
329329 1.64320 + 2.84610i 0.0905924 + 0.156911i
330330 0 0
331331 6.50427 11.2657i 0.357507 0.619220i −0.630037 0.776565i 0.716960π-0.716960\pi
0.987544 + 0.157345i 0.0502935π0.0502935\pi
332332 1.60536 4.94079i 0.0881055 0.271161i
333333 0 0
334334 −5.33441 3.87567i −0.291886 0.212067i
335335 −32.5576 6.92034i −1.77881 0.378099i
336336 0 0
337337 −3.04908 + 29.0100i −0.166094 + 1.58028i 0.520903 + 0.853616i 0.325595π0.325595\pi
−0.686997 + 0.726661i 0.741071π0.741071\pi
338338 6.60362 + 2.94012i 0.359189 + 0.159921i
339339 0 0
340340 −10.1430 + 17.5681i −0.550079 + 0.952765i
341341 −26.3694 12.2565i −1.42798 0.663725i
342342 0 0
343343 −5.46976 + 16.8342i −0.295339 + 0.908961i
344344 −0.724960 6.89754i −0.0390872 0.371890i
345345 0 0
346346 6.58100 7.30894i 0.353797 0.392931i
347347 15.4911 17.2046i 0.831604 0.923590i −0.166443 0.986051i 0.553228π-0.553228\pi
0.998047 + 0.0624611i 0.0198949π0.0198949\pi
348348 0 0
349349 0.887486 + 8.44386i 0.0475060 + 0.451990i 0.992257 + 0.124201i 0.0396368π0.0396368\pi
−0.944751 + 0.327789i 0.893697π0.893697\pi
350350 −0.826257 + 2.54296i −0.0441653 + 0.135927i
351351 0 0
352352 2.30791 18.9910i 0.123012 1.01222i
353353 0.687569 1.19090i 0.0365956 0.0633854i −0.847148 0.531358i 0.821682π-0.821682\pi
0.883743 + 0.467972i 0.155015π0.155015\pi
354354 0 0
355355 −27.3320 12.1690i −1.45063 0.645863i
356356 1.72859 16.4464i 0.0916152 0.871660i
357357 0 0
358358 7.41785 + 1.57671i 0.392046 + 0.0833319i
359359 16.8945 + 12.2746i 0.891658 + 0.647827i 0.936310 0.351175i 0.114218π-0.114218\pi
−0.0446518 + 0.999003i 0.514218π0.514218\pi
360360 0 0
361361 −1.97350 + 6.07381i −0.103868 + 0.319674i
362362 −2.10701 + 3.64945i −0.110742 + 0.191811i
363363 0 0
364364 1.74025 + 3.01420i 0.0912138 + 0.157987i
365365 12.1639 2.58552i 0.636688 0.135332i
366366 0 0
367367 11.3730 5.06358i 0.593666 0.264317i −0.0878343 0.996135i 0.527995π-0.527995\pi
0.681500 + 0.731818i 0.261328π0.261328\pi
368368 −0.977884 3.00962i −0.0509757 0.156887i
369369 0 0
370370 −7.71948 5.60853i −0.401316 0.291574i
371371 −2.11231 20.0973i −0.109666 1.04340i
372372 0 0
373373 14.2488 + 24.6796i 0.737774 + 1.27786i 0.953496 + 0.301407i 0.0974563π0.0974563\pi
−0.215722 + 0.976455i 0.569210π0.569210\pi
374374 9.66326 4.11596i 0.499675 0.212831i
375375 0 0
376376 −3.46245 3.84544i −0.178562 0.198313i
377377 9.43690 6.85631i 0.486025 0.353118i
378378 0 0
379379 −1.33092 4.09616i −0.0683649 0.210405i 0.911038 0.412323i 0.135283π-0.135283\pi
−0.979402 + 0.201918i 0.935283π0.935283\pi
380380 −14.9018 3.16747i −0.764445 0.162488i
381381 0 0
382382 −2.24503 0.999550i −0.114866 0.0511414i
383383 −17.5964 + 3.74024i −0.899136 + 0.191117i −0.634219 0.773154i 0.718678π-0.718678\pi
−0.264918 + 0.964271i 0.585345π0.585345\pi
384384 0 0
385385 −11.3356 + 7.95822i −0.577715 + 0.405589i
386386 −0.941309 −0.0479114
387387 0 0
388388 2.78711 2.02496i 0.141494 0.102802i
389389 −32.7940 + 14.6008i −1.66272 + 0.740291i −0.999964 0.00854185i 0.997281π-0.997281\pi
−0.662758 + 0.748833i 0.730614π0.730614\pi
390390 0 0
391391 6.62949 7.36279i 0.335267 0.372352i
392392 1.17301 11.1604i 0.0592460 0.563688i
393393 0 0
394394 −1.51893 1.68694i −0.0765224 0.0849867i
395395 −42.6496 −2.14594
396396 0 0
397397 19.8332 0.995398 0.497699 0.867350i 0.334178π-0.334178\pi
0.497699 + 0.867350i 0.334178π0.334178\pi
398398 −3.30897 3.67499i −0.165864 0.184210i
399399 0 0
400400 −0.417367 + 3.97098i −0.0208683 + 0.198549i
401401 −9.22764 + 10.2483i −0.460807 + 0.511778i −0.928103 0.372323i 0.878561π-0.878561\pi
0.467297 + 0.884101i 0.345228π0.345228\pi
402402 0 0
403403 −11.8949 + 5.29596i −0.592529 + 0.263811i
404404 0.609908 0.443124i 0.0303440 0.0220462i
405405 0 0
406406 7.94480 0.394294
407407 −5.01794 16.3405i −0.248730 0.809967i
408408 0 0
409409 −36.1043 + 7.67421i −1.78524 + 0.379465i −0.977644 0.210266i 0.932567π-0.932567\pi
−0.807599 + 0.589731i 0.799234π0.799234\pi
410410 11.8844 + 5.29128i 0.586929 + 0.261318i
411411 0 0
412412 −9.70195 2.06221i −0.477981 0.101598i
413413 3.13717 + 9.65521i 0.154370 + 0.475102i
414414 0 0
415415 7.48895 5.44104i 0.367618 0.267090i
416416 −5.73193 6.36595i −0.281031 0.312116i
417417 0 0
418418 5.18236 + 5.94671i 0.253477 + 0.290863i
419419 −1.16856 2.02400i −0.0570879 0.0988791i 0.836069 0.548624i 0.184848π-0.184848\pi
−0.893157 + 0.449745i 0.851515π0.851515\pi
420420 0 0
421421 1.60297 + 15.2513i 0.0781242 + 0.743302i 0.961531 + 0.274696i 0.0885771π0.0885771\pi
−0.883407 + 0.468606i 0.844756π0.844756\pi
422422 −1.05333 0.765289i −0.0512753 0.0372537i
423423 0 0
424424 9.83236 + 30.2609i 0.477502 + 1.46960i
425425 −11.4203 + 5.08464i −0.553966 + 0.246641i
426426 0 0
427427 15.3134 3.25497i 0.741070 0.157519i
428428 9.38519 + 16.2556i 0.453650 + 0.785745i
429429 0 0
430430 2.69944 4.67557i 0.130179 0.225476i
431431 2.41444 7.43087i 0.116299 0.357932i −0.875917 0.482463i 0.839742π-0.839742\pi
0.992216 + 0.124530i 0.0397424π0.0397424\pi
432432 0 0
433433 −20.3571 14.7903i −0.978301 0.710777i −0.0209724 0.999780i 0.506676π-0.506676\pi
−0.957328 + 0.289003i 0.906676π0.906676\pi
434434 −8.67456 1.84383i −0.416392 0.0885069i
435435 0 0
436436 −0.768510 + 7.31188i −0.0368049 + 0.350176i
437437 6.79733 + 3.02637i 0.325160 + 0.144771i
438438 0 0
439439 −0.492942 + 0.853801i −0.0235268 + 0.0407497i −0.877549 0.479487i 0.840823π-0.840823\pi
0.854022 + 0.520236i 0.174156π0.174156\pi
440440 14.8530 15.9676i 0.708090 0.761224i
441441 0 0
442442 1.45334 4.47292i 0.0691283 0.212755i
443443 1.12634 + 10.7164i 0.0535139 + 0.509150i 0.988144 + 0.153529i 0.0490639π0.0490639\pi
−0.934630 + 0.355621i 0.884269π0.884269\pi
444444 0 0
445445 19.7171 21.8980i 0.934679 1.03807i
446446 −7.60792 + 8.44945i −0.360245 + 0.400093i
447447 0 0
448448 −0.132891 1.26437i −0.00627850 0.0597359i
449449 −7.13830 + 21.9694i −0.336877 + 1.03680i 0.628913 + 0.777476i 0.283500π0.283500\pi
−0.965790 + 0.259326i 0.916500π0.916500\pi
450450 0 0
451451 11.3238 + 20.3690i 0.533216 + 0.959140i
452452 14.2583 24.6961i 0.670654 1.16161i
453453 0 0
454454 −9.97421 4.44081i −0.468113 0.208417i
455455 −0.648261 + 6.16779i −0.0303909 + 0.289150i
456456 0 0
457457 −26.7704 5.69023i −1.25227 0.266178i −0.466401 0.884573i 0.654450π-0.654450\pi
−0.785867 + 0.618395i 0.787783π0.787783\pi
458458 −11.0093 7.99870i −0.514429 0.373755i
459459 0 0
460460 2.77706 8.54690i 0.129481 0.398501i
461461 −9.76471 + 16.9130i −0.454788 + 0.787715i −0.998676 0.0514422i 0.983618π-0.983618\pi
0.543888 + 0.839158i 0.316952π0.316952\pi
462462 0 0
463463 −7.29658 12.6380i −0.339101 0.587340i 0.645163 0.764045i 0.276789π-0.276789\pi
−0.984264 + 0.176705i 0.943456π0.943456\pi
464464 11.6048 2.46668i 0.538740 0.114513i
465465 0 0
466466 −0.277136 + 0.123389i −0.0128381 + 0.00571587i
467467 −1.87684 5.77631i −0.0868496 0.267296i 0.898194 0.439598i 0.144879π-0.144879\pi
−0.985044 + 0.172303i 0.944879π0.944879\pi
468468 0 0
469469 −14.7122 10.6891i −0.679348 0.493575i
470470 −0.421048 4.00600i −0.0194215 0.184783i
471471 0 0
472472 −7.99242 13.8433i −0.367881 0.637189i
473473 8.89823 3.79010i 0.409141 0.174269i
474474 0 0
475475 −6.28199 6.97686i −0.288238 0.320120i
476476 −8.96654 + 6.51457i −0.410980 + 0.298595i
477477 0 0
478478 −3.94080 12.1285i −0.180248 0.554746i
479479 −39.7307 8.44502i −1.81534 0.385863i −0.830181 0.557495i 0.811763π-0.811763\pi
−0.985161 + 0.171632i 0.945096π0.945096\pi
480480 0 0
481481 −6.99232 3.11318i −0.318823 0.141949i
482482 −11.7060 + 2.48818i −0.533192 + 0.113334i
483483 0 0
484484 16.8005 3.00536i 0.763660 0.136607i
485485 6.13862 0.278740
486486 0 0
487487 −11.9767 + 8.70158i −0.542716 + 0.394306i −0.825093 0.564998i 0.808877π-0.808877\pi
0.282377 + 0.959304i 0.408877π0.408877\pi
488488 −22.5191 + 10.0262i −1.01939 + 0.453863i
489489 0 0
490490 5.84524 6.49180i 0.264061 0.293269i
491491 −4.12695 + 39.2653i −0.186247 + 1.77202i 0.358608 + 0.933488i 0.383251π0.383251\pi
−0.544855 + 0.838530i 0.683415π0.683415\pi
492492 0 0
493493 24.8547 + 27.6039i 1.11940 + 1.24322i
494494 3.53203 0.158913
495495 0 0
496496 −13.2432 −0.594638
497497 −10.9377 12.1475i −0.490621 0.544890i
498498 0 0
499499 0.332064 3.15938i 0.0148652 0.141433i −0.984572 0.174981i 0.944014π-0.944014\pi
0.999437 + 0.0335472i 0.0106804π0.0106804\pi
500500 6.76405 7.51223i 0.302497 0.335957i
501501 0 0
502502 −7.62976 + 3.39699i −0.340533 + 0.151615i
503503 14.8735 10.8062i 0.663174 0.481824i −0.204559 0.978854i 0.565576π-0.565576\pi
0.867733 + 0.497030i 0.165576π0.165576\pi
504504 0 0
505505 1.34332 0.0597771
506506 −3.80821 + 2.67358i −0.169296 + 0.118855i
507507 0 0
508508 −33.9088 + 7.20753i −1.50446 + 0.319782i
509509 14.3026 + 6.36791i 0.633950 + 0.282253i 0.698443 0.715665i 0.253876π-0.253876\pi
−0.0644931 + 0.997918i 0.520543π0.520543\pi
510510 0 0
511511 6.64578 + 1.41260i 0.293992 + 0.0624899i
512512 −4.91260 15.1194i −0.217108 0.668190i
513513 0 0
514514 −13.0567 + 9.48623i −0.575905 + 0.418419i
515515 −11.8260 13.1342i −0.521118 0.578760i
516516 0 0
517517 3.70887 6.18996i 0.163116 0.272234i
518518 −2.60659 4.51475i −0.114527 0.198367i
519519 0 0
520520 −1.02071 9.71141i −0.0447611 0.425874i
521521 −14.6674 10.6565i −0.642592 0.466870i 0.218148 0.975916i 0.429999π-0.429999\pi
−0.860740 + 0.509045i 0.829999π0.829999\pi
522522 0 0
523523 5.24113 + 16.1305i 0.229178 + 0.705339i 0.997840 + 0.0656837i 0.0209228π0.0209228\pi
−0.768662 + 0.639655i 0.779077π0.779077\pi
524524 −5.62781 + 2.50566i −0.245852 + 0.109460i
525525 0 0
526526 −11.8914 + 2.52759i −0.518490 + 0.110208i
527527 −20.7313 35.9077i −0.903071 1.56417i
528528 0 0
529529 9.30544 16.1175i 0.404584 0.700761i
530530 −7.65389 + 23.5562i −0.332464 + 1.02322i
531531 0 0
532532 −6.73386 4.89243i −0.291950 0.212114i
533533 10.2073 + 2.16964i 0.442129 + 0.0939775i
534534 0 0
535535 −3.49608 + 33.2630i −0.151149 + 1.43808i
536536 26.1580 + 11.6463i 1.12985 + 0.503043i
537537 0 0
538538 4.46746 7.73787i 0.192606 0.333603i
539539 15.3580 3.00506i 0.661518 0.129437i
540540 0 0
541541 −2.07721 + 6.39299i −0.0893062 + 0.274856i −0.985728 0.168346i 0.946158π-0.946158\pi
0.896422 + 0.443202i 0.146158π0.146158\pi
542542 −0.455528 4.33406i −0.0195666 0.186164i
543543 0 0
544544 18.2527 20.2716i 0.782577 0.869140i
545545 −8.76596 + 9.73559i −0.375493 + 0.417027i
546546 0 0
547547 −4.78907 45.5650i −0.204766 1.94822i −0.302846 0.953040i 0.597937π-0.597937\pi
0.0980800 0.995179i 0.468730π-0.468730\pi
548548 2.87247 8.84054i 0.122706 0.377649i
549549 0 0
550550 5.76175 1.12738i 0.245682 0.0480719i
551551 −13.9478 + 24.1584i −0.594198 + 1.02918i
552552 0 0
553553 −21.2872 9.47766i −0.905223 0.403031i
554554 −0.949080 + 9.02989i −0.0403225 + 0.383643i
555555 0 0
556556 26.0861 + 5.54477i 1.10630 + 0.235150i
557557 −9.67054 7.02606i −0.409754 0.297704i 0.363748 0.931497i 0.381497π-0.381497\pi
−0.773502 + 0.633794i 0.781497π0.781497\pi
558558 0 0
559559 1.33828 4.11881i 0.0566033 0.174207i
560560 −3.15389 + 5.46270i −0.133276 + 0.230841i
561561 0 0
562562 −10.2390 17.7345i −0.431906 0.748083i
563563 −33.6515 + 7.15285i −1.41824 + 0.301457i −0.852328 0.523008i 0.824810π-0.824810\pi
−0.565914 + 0.824464i 0.691476π0.691476\pi
564564 0 0
565565 46.4196 20.6673i 1.95289 0.869482i
566566 0.155402 + 0.478277i 0.00653202 + 0.0201035i
567567 0 0
568568 20.8221 + 15.1281i 0.873675 + 0.634762i
569569 1.20274 + 11.4433i 0.0504215 + 0.479729i 0.990373 + 0.138422i 0.0442029π0.0442029\pi
−0.939952 + 0.341307i 0.889130π0.889130\pi
570570 0 0
571571 18.2755 + 31.6542i 0.764807 + 1.32469i 0.940348 + 0.340213i 0.110499π0.110499\pi
−0.175541 + 0.984472i 0.556167π0.556167\pi
572572 3.92792 6.55556i 0.164235 0.274102i
573573 0 0
574574 4.75588 + 5.28194i 0.198507 + 0.220464i
575575 4.48036 3.25517i 0.186844 0.135750i
576576 0 0
577577 −6.88976 21.2045i −0.286824 0.882754i −0.985846 0.167654i 0.946381π-0.946381\pi
0.699022 0.715101i 0.253619π-0.253619\pi
578578 3.51391 + 0.746904i 0.146159 + 0.0310671i
579579 0 0
580580 30.7795 + 13.7039i 1.27805 + 0.569024i
581581 4.94698 1.05151i 0.205235 0.0436242i
582582 0 0
583583 −36.3153 + 25.4954i −1.50403 + 1.05591i
584584 −10.6978 −0.442678
585585 0 0
586586 8.24255 5.98856i 0.340497 0.247385i
587587 21.4946 9.56999i 0.887175 0.394996i 0.0880187 0.996119i 0.471946π-0.471946\pi
0.799157 + 0.601123i 0.205280π0.205280\pi
588588 0 0
589589 20.8357 23.1404i 0.858519 0.953482i
590590 1.30067 12.3750i 0.0535477 0.509473i
591591 0 0
592592 −5.20912 5.78531i −0.214093 0.237775i
593593 26.7811 1.09977 0.549884 0.835241i 0.314672π-0.314672\pi
0.549884 + 0.835241i 0.314672π0.314672\pi
594594 0 0
595595 −19.7488 −0.809622
596596 −13.3670 14.8456i −0.547535 0.608100i
597597 0 0
598598 −0.217785 + 2.07208i −0.00890588 + 0.0847338i
599599 −7.09422 + 7.87893i −0.289862 + 0.321924i −0.870435 0.492284i 0.836162π-0.836162\pi
0.580573 + 0.814209i 0.302829π0.302829\pi
600600 0 0
601601 −35.7548 + 15.9190i −1.45847 + 0.649352i −0.974224 0.225582i 0.927572π-0.927572\pi
−0.484243 + 0.874933i 0.660905π0.660905\pi
602602 2.38635 1.73378i 0.0972603 0.0706638i
603603 0 0
604604 13.0470 0.530875
605605 27.3666 + 13.2637i 1.11261 + 0.539245i
606606 0 0
607607 −8.40273 + 1.78605i −0.341056 + 0.0724937i −0.375256 0.926921i 0.622445π-0.622445\pi
0.0341997 + 0.999415i 0.489112π0.489112\pi
608608 18.7148 + 8.33236i 0.758985 + 0.337922i
609609 0 0
610610 −18.7694 3.98956i −0.759950 0.161532i
611611 −0.998482 3.07301i −0.0403943 0.124321i
612612 0 0
613613 8.05694 5.85371i 0.325417 0.236429i −0.413067 0.910701i 0.635542π-0.635542\pi
0.738483 + 0.674272i 0.235542π0.235542\pi
614614 −1.25146 1.38989i −0.0505049 0.0560914i
615615 0 0
616616 10.9617 4.66903i 0.441661 0.188121i
617617 −3.64515 6.31358i −0.146748 0.254175i 0.783276 0.621674i 0.213547π-0.213547\pi
−0.930024 + 0.367499i 0.880214π0.880214\pi
618618 0 0
619619 3.44301 + 32.7581i 0.138386 + 1.31666i 0.814631 + 0.579980i 0.196940π0.196940\pi
−0.676244 + 0.736677i 0.736394π0.736394\pi
620620 −30.4263 22.1060i −1.22195 0.887797i
621621 0 0
622622 4.81171 + 14.8089i 0.192932 + 0.593784i
623623 14.7073 6.54813i 0.589237 0.262345i
624624 0 0
625625 30.5470 6.49296i 1.22188 0.259719i
626626 −4.66161 8.07415i −0.186315 0.322708i
627627 0 0
628628 9.16370 15.8720i 0.365671 0.633361i
629629 7.53181 23.1805i 0.300313 0.924268i
630630 0 0
631631 6.31372 + 4.58719i 0.251345 + 0.182613i 0.706323 0.707890i 0.250353π-0.250353\pi
−0.454978 + 0.890503i 0.650353π0.650353\pi
632632 35.8877 + 7.62816i 1.42753 + 0.303432i
633633 0 0
634634 0.455105 4.33003i 0.0180745 0.171968i
635635 −56.4302 25.1243i −2.23936 0.997029i
636636 0 0
637637 3.50367 6.06853i 0.138820 0.240444i
638638 −8.47626 15.2470i −0.335578 0.603633i
639639 0 0
640640 9.37426 28.8510i 0.370550 1.14044i
641641 1.25810 + 11.9700i 0.0496920 + 0.472788i 0.990864 + 0.134861i 0.0430589π0.0430589\pi
−0.941172 + 0.337927i 0.890274π0.890274\pi
642642 0 0
643643 −22.6305 + 25.1337i −0.892459 + 0.991177i −0.999995 0.00302455i 0.999037π-0.999037\pi
0.107536 + 0.994201i 0.465704π0.465704\pi
644644 3.28538 3.64879i 0.129462 0.143782i
645645 0 0
646646 1.17567 + 11.1857i 0.0462560 + 0.440097i
647647 −5.98134 + 18.4087i −0.235151 + 0.723719i 0.761951 + 0.647635i 0.224242π0.224242\pi
−0.997101 + 0.0760844i 0.975758π0.975758\pi
648648 0 0
649649 15.1824 16.3217i 0.595961 0.640681i
650650 1.31444 2.27668i 0.0515566 0.0892986i
651651 0 0
652652 −6.53946 2.91155i −0.256105 0.114025i
653653 0.277176 2.63715i 0.0108467 0.103200i −0.987759 0.155988i 0.950144π-0.950144\pi
0.998606 + 0.0527878i 0.0168107π0.0168107\pi
654654 0 0
655655 −10.7371 2.28224i −0.419534 0.0891747i
656656 8.58673 + 6.23863i 0.335256 + 0.243577i
657657 0 0
658658 0.680067 2.09303i 0.0265118 0.0815948i
659659 1.34963 2.33764i 0.0525743 0.0910614i −0.838541 0.544839i 0.816591π-0.816591\pi
0.891115 + 0.453778i 0.149924π0.149924\pi
660660 0 0
661661 6.28133 + 10.8796i 0.244315 + 0.423167i 0.961939 0.273265i 0.0881035π-0.0881035\pi
−0.717624 + 0.696431i 0.754770π0.754770\pi
662662 −8.52084 + 1.81116i −0.331172 + 0.0703928i
663663 0 0
664664 −7.27477 + 3.23894i −0.282316 + 0.125695i
665665 −4.58313 14.1054i −0.177726 0.546985i
666666 0 0
667667 −13.3126 9.67218i −0.515466 0.374508i
668668 −1.59692 15.1937i −0.0617867 0.587861i
669669 0 0
670670 11.1447 + 19.3032i 0.430557 + 0.745747i
671671 −22.5845 25.9155i −0.871864 1.00046i
672672 0 0
673673 −15.1664 16.8440i −0.584621 0.649287i 0.376174 0.926549i 0.377240π-0.377240\pi
−0.960794 + 0.277262i 0.910573π0.910573\pi
674674 15.8031 11.4816i 0.608711 0.442254i
675675 0 0
676676 5.17553 + 15.9286i 0.199059 + 0.612640i
677677 28.8786 + 6.13834i 1.10990 + 0.235915i 0.726159 0.687527i 0.241304π-0.241304\pi
0.383736 + 0.923443i 0.374637π0.374637\pi
678678 0 0
679679 3.06389 + 1.36413i 0.117581 + 0.0523506i
680680 30.4157 6.46506i 1.16639 0.247924i
681681 0 0
682682 5.71631 + 18.6146i 0.218889 + 0.712791i
683683 −16.5916 −0.634859 −0.317430 0.948282i 0.602820π-0.602820\pi
−0.317430 + 0.948282i 0.602820π0.602820\pi
684684 0 0
685685 13.4000 9.73565i 0.511987 0.371980i
686686 10.8284 4.82113i 0.413432 0.184072i
687687 0 0
688688 2.94739 3.27341i 0.112368 0.124798i
689689 −2.07680 + 19.7595i −0.0791199 + 0.752775i
690690 0 0
691691 15.7421 + 17.4833i 0.598857 + 0.665098i 0.964015 0.265848i 0.0856519π-0.0856519\pi
−0.365158 + 0.930945i 0.618985π0.618985\pi
692692 22.7877 0.866260
693693 0 0
694694 −15.5032 −0.588492
695695 31.7972 + 35.3144i 1.20614 + 1.33955i
696696 0 0
697697 −3.47351 + 33.0483i −0.131569 + 1.25179i
698698 3.80441 4.22523i 0.143999 0.159927i
699699 0 0
700700 −5.65957 + 2.51980i −0.213912 + 0.0952396i
701701 −18.3698 + 13.3465i −0.693819 + 0.504089i −0.877913 0.478820i 0.841065π-0.841065\pi
0.184095 + 0.982909i 0.441065π0.441065\pi
702702 0 0
703703 18.3044 0.690365
704704 −2.28469 + 1.60398i −0.0861075 + 0.0604523i
705705 0 0
706706 −0.900741 + 0.191458i −0.0338998 + 0.00720563i
707707 0.670476 + 0.298515i 0.0252158 + 0.0112268i
708708 0 0
709709 11.2512 + 2.39151i 0.422546 + 0.0898149i 0.414277 0.910151i 0.364035π-0.364035\pi
0.00826904 + 0.999966i 0.497368π0.497368\pi
710710 6.19118 + 19.0545i 0.232351 + 0.715102i
711711 0 0
712712 −20.5076 + 14.8996i −0.768555 + 0.558388i
713713 12.2907 + 13.6502i 0.460290 + 0.511204i
714714 0 0
715715 12.5283 5.33629i 0.468532 0.199566i
716716 8.78545 + 15.2169i 0.328328 + 0.568680i
717717 0 0
718718 −1.46175 13.9076i −0.0545519 0.519027i
719719 37.1445 + 26.9870i 1.38526 + 1.00645i 0.996367 + 0.0851620i 0.0271408π0.0271408\pi
0.388888 + 0.921285i 0.372859π0.372859\pi
720720 0 0
721721 −2.98390 9.18349i −0.111126 0.342011i
722722 3.90692 1.73947i 0.145401 0.0647365i
723723 0 0
724724 −9.55039 + 2.03000i −0.354937 + 0.0754443i
725725 10.3813 + 17.9810i 0.385554 + 0.667798i
726726 0 0
727727 0.417822 0.723690i 0.0154962 0.0268402i −0.858173 0.513360i 0.828401π-0.828401\pi
0.873670 + 0.486520i 0.161734π0.161734\pi
728728 1.64863 5.07396i 0.0611023 0.188053i
729729 0 0
730730 −6.73715 4.89483i −0.249353 0.181166i
731731 13.4895 + 2.86728i 0.498926 + 0.106050i
732732 0 0
733733 3.34101 31.7876i 0.123403 1.17410i −0.741072 0.671426i 0.765682π-0.765682\pi
0.864475 0.502676i 0.167651π-0.167651\pi
734734 −7.61596 3.39084i −0.281110 0.125158i
735735 0 0
736736 −6.04218 + 10.4654i −0.222718 + 0.385758i
737737 −4.81712 + 39.6385i −0.177441 + 1.46010i
738738 0 0
739739 2.00537 6.17190i 0.0737687 0.227037i −0.907373 0.420326i 0.861916π-0.861916\pi
0.981142 + 0.193289i 0.0619156π0.0619156\pi
740740 −2.31092 21.9870i −0.0849512 0.808256i
741741 0 0
742742 −9.05489 + 10.0565i −0.332415 + 0.369185i
743743 7.45493 8.27954i 0.273495 0.303747i −0.590713 0.806882i 0.701153π-0.701153\pi
0.864208 + 0.503135i 0.167820π0.167820\pi
744744 0 0
745745 −3.72077 35.4008i −0.136318 1.29698i
746746 5.89712 18.1495i 0.215909 0.664499i
747747 0 0
748748 22.0685 + 10.2574i 0.806905 + 0.375049i
749749 −9.13670 + 15.8252i −0.333848 + 0.578242i
750750 0 0
751751 −32.6141 14.5207i −1.19010 0.529869i −0.286435 0.958100i 0.592470π-0.592470\pi
−0.903669 + 0.428231i 0.859137π0.859137\pi
752752 0.343522 3.26839i 0.0125269 0.119186i
753753 0 0
754754 −7.64057 1.62405i −0.278253 0.0591445i
755755 18.8080 + 13.6648i 0.684493 + 0.497313i
756756 0 0
757757 −1.57431 + 4.84524i −0.0572194 + 0.176103i −0.975581 0.219638i 0.929512π-0.929512\pi
0.918362 + 0.395741i 0.129512π0.129512\pi
758758 −1.44208 + 2.49776i −0.0523788 + 0.0907227i
759759 0 0
760760 11.6762 + 20.2238i 0.423542 + 0.733596i
761761 12.2197 2.59739i 0.442966 0.0941552i 0.0189711 0.999820i 0.493961π-0.493961\pi
0.423994 + 0.905665i 0.360628π0.360628\pi
762762 0 0
763763 −6.53870 + 2.91122i −0.236717 + 0.105393i
764764 −1.75952 5.41525i −0.0636572 0.195917i
765765 0 0
766766 9.74603 + 7.08091i 0.352138 + 0.255844i
767767 −1.04335 9.92677i −0.0376730 0.358435i
768768 0 0
769769 −2.74929 4.76192i −0.0991421 0.171719i 0.812188 0.583396i 0.198277π-0.198277\pi
−0.911330 + 0.411677i 0.864943π0.864943\pi
770770 9.03971 + 2.07518i 0.325768 + 0.0747843i
771771 0 0
772772 −1.45936 1.62079i −0.0525236 0.0583334i
773773 −39.4097 + 28.6328i −1.41747 + 1.02985i −0.425284 + 0.905060i 0.639826π0.639826\pi
−0.992183 + 0.124790i 0.960174π0.960174\pi
774774 0 0
775775 −7.16186 22.0419i −0.257262 0.791770i
776776 −5.16536 1.09793i −0.185426 0.0394134i
777777 0 0
778778 21.9606 + 9.77749i 0.787325 + 0.350540i
779779 −24.4106 + 5.18863i −0.874599 + 0.185902i
780780 0 0
781781 −11.6431 + 33.9507i −0.416623 + 1.21485i
782782 −6.63466 −0.237255
783783 0 0
784784 5.76597 4.18922i 0.205927 0.149615i
785785 29.8335 13.2827i 1.06480 0.474082i
786786 0 0
787787 13.6091 15.1145i 0.485114 0.538773i −0.450043 0.893007i 0.648591π-0.648591\pi
0.935157 + 0.354233i 0.115258π0.115258\pi
788788 0.549770 5.23071i 0.0195847 0.186336i
789789 0 0
790790 19.1107 + 21.2245i 0.679927 + 0.755135i
791791 27.7616 0.987088
792792 0 0
793793 −15.3924 −0.546601
794794 −8.88695 9.86995i −0.315386 0.350272i
795795 0 0
796796 1.19767 11.3951i 0.0424503 0.403888i
797797 11.5649 12.8441i 0.409650 0.454963i −0.502647 0.864492i 0.667640π-0.667640\pi
0.912297 + 0.409529i 0.134307π0.134307\pi
798798 0 0
799799 9.39969 4.18501i 0.332537 0.148055i
800800 12.3356 8.96232i 0.436128 0.316866i
801801 0 0
802802 9.23484 0.326094
803803 −4.37939 14.2611i −0.154545 0.503263i
804804 0 0
805805 8.55763 1.81898i 0.301617 0.0641106i
806806 7.96547 + 3.54646i 0.280572 + 0.124919i
807807 0 0
808808 −1.13034 0.240262i −0.0397653 0.00845238i
809809 3.94755 + 12.1493i 0.138789 + 0.427147i 0.996160 0.0875508i 0.0279040π-0.0279040\pi
−0.857371 + 0.514698i 0.827904π0.827904\pi
810810 0 0
811811 −14.3899 + 10.4549i −0.505298 + 0.367121i −0.811037 0.584995i 0.801097π-0.801097\pi
0.305739 + 0.952115i 0.401097π0.401097\pi
812812 12.3173 + 13.6797i 0.432252 + 0.480064i
813813 0 0
814814 −5.88335 + 9.81909i −0.206211 + 0.344159i
815815 −6.37757 11.0463i −0.223397 0.386934i
816816 0 0
817817 1.08259 + 10.3002i 0.0378751 + 0.360357i
818818 19.9969 + 14.5286i 0.699174 + 0.507980i
819819 0 0
820820 9.31430 + 28.6665i 0.325269 + 1.00108i
821821 −27.7585 + 12.3589i −0.968780 + 0.431329i −0.829243 0.558888i 0.811228π-0.811228\pi
−0.139537 + 0.990217i 0.544561π0.544561\pi
822822 0 0
823823 −25.0774 + 5.33037i −0.874143 + 0.185805i −0.623073 0.782164i 0.714116π-0.714116\pi
−0.251071 + 0.967969i 0.580783π0.580783\pi
824824 7.60194 + 13.1669i 0.264826 + 0.458692i
825825 0 0
826826 3.39919 5.88756i 0.118273 0.204855i
827827 −3.14133 + 9.66803i −0.109235 + 0.336190i −0.990701 0.136057i 0.956557π-0.956557\pi
0.881466 + 0.472247i 0.156557π0.156557\pi
828828 0 0
829829 −2.17360 1.57922i −0.0754924 0.0548484i 0.549399 0.835560i 0.314857π-0.314857\pi
−0.624891 + 0.780712i 0.714857π0.714857\pi
830830 −6.06342 1.28882i −0.210464 0.0447356i
831831 0 0
832832 −0.130657 + 1.24312i −0.00452972 + 0.0430974i
833833 20.3849 + 9.07594i 0.706295 + 0.314463i
834834 0 0
835835 13.6111 23.5751i 0.471031 0.815850i
836836 −2.20482 + 18.1427i −0.0762553 + 0.627479i
837837 0 0
838838 −0.483630 + 1.48846i −0.0167067 + 0.0514180i
839839 −1.36910 13.0262i −0.0472667 0.449713i −0.992402 0.123035i 0.960737π-0.960737\pi
0.945136 0.326678i 0.105929π-0.105929\pi
840840 0 0
841841 21.8757 24.2954i 0.754335 0.837774i
842842 6.87152 7.63159i 0.236808 0.263002i
843843 0 0
844844 −0.315327 3.00014i −0.0108540 0.103269i
845845 −9.22207 + 28.3826i −0.317249 + 0.976391i
846846 0 0
847847 10.7117 + 12.7016i 0.368057 + 0.436431i
848848 −10.1040 + 17.5006i −0.346972 + 0.600973i
849849 0 0
850850 7.64763 + 3.40494i 0.262312 + 0.116789i
851851 −1.12865 + 10.7384i −0.0386897 + 0.368108i
852852 0 0
853853 −1.57801 0.335417i −0.0540301 0.0114844i 0.180817 0.983517i 0.442126π-0.442126\pi
−0.234847 + 0.972032i 0.575459π0.575459\pi
854854 −8.48156 6.16221i −0.290233 0.210867i
855855 0 0
856856 8.89109 27.3639i 0.303891 0.935281i
857857 20.7735 35.9807i 0.709608 1.22908i −0.255395 0.966837i 0.582205π-0.582205\pi
0.965003 0.262240i 0.0844612π-0.0844612\pi
858858 0 0
859859 −19.0349 32.9695i −0.649463 1.12490i −0.983251 0.182255i 0.941660π-0.941660\pi
0.333788 0.942648i 0.391673π-0.391673\pi
860860 12.2357 2.60078i 0.417234 0.0886858i
861861 0 0
862862 −4.77984 + 2.12812i −0.162802 + 0.0724841i
863863 13.1442 + 40.4536i 0.447433 + 1.37706i 0.879793 + 0.475357i 0.157681π0.157681\pi
−0.432360 + 0.901701i 0.642319π0.642319\pi
864864 0 0
865865 32.8498 + 23.8668i 1.11693 + 0.811495i
866866 1.76134 + 16.7580i 0.0598527 + 0.569461i
867867 0 0
868868 −10.2739 17.7948i −0.348717 0.603996i
869869 4.52245 + 50.9641i 0.153414 + 1.72884i
870870 0 0
871871 11.9638 + 13.2872i 0.405379 + 0.450219i
872872 9.11742 6.62419i 0.308755 0.224323i
873873 0 0
874874 −1.53971 4.73875i −0.0520816 0.160291i
875875 9.62601 + 2.04607i 0.325419 + 0.0691699i
876876 0 0
877877 −7.22380 3.21624i −0.243930 0.108605i 0.281130 0.959670i 0.409291π-0.409291\pi
−0.525061 + 0.851065i 0.675957π0.675957\pi
878878 0.645773 0.137263i 0.0217938 0.00463241i
879879 0 0
880880 13.8484 + 0.224552i 0.466830 + 0.00756963i
881881 41.5877 1.40113 0.700563 0.713591i 0.252932π-0.252932\pi
0.700563 + 0.713591i 0.252932π0.252932\pi
882882 0 0
883883 −9.71314 + 7.05701i −0.326873 + 0.237487i −0.739103 0.673593i 0.764750π-0.764750\pi
0.412229 + 0.911080i 0.364750π0.364750\pi
884884 9.95486 4.43219i 0.334818 0.149071i
885885 0 0
886886 4.82830 5.36237i 0.162210 0.180152i
887887 4.98779 47.4557i 0.167474 1.59341i −0.511527 0.859267i 0.670920π-0.670920\pi
0.679000 0.734138i 0.262413π-0.262413\pi
888888 0 0
889889 −22.5821 25.0800i −0.757380 0.841156i
890890 −19.7325 −0.661434
891891 0 0
892892 −26.3436 −0.882050
893893 5.17052 + 5.74244i 0.173025 + 0.192163i
894894 0 0
895895 −3.27267 + 31.1374i −0.109393 + 1.04081i
896896 11.0902 12.3169i 0.370497 0.411478i
897897 0 0
898898 14.1316 6.29181i 0.471579 0.209960i
899899 −55.7124 + 40.4774i −1.85811 + 1.35000i
900900 0 0
901901 −63.2683 −2.10777
902902 5.06261 14.7623i 0.168567 0.491532i
903903 0 0
904904 −42.7564 + 9.08816i −1.42206 + 0.302268i
905905 −15.8935 7.07626i −0.528319 0.235223i
906906 0 0
907907 2.19782 + 0.467161i 0.0729774 + 0.0155118i 0.244256 0.969711i 0.421456π-0.421456\pi
−0.171278 + 0.985223i 0.554790π0.554790\pi
908908 −7.81720 24.0589i −0.259423 0.798422i
909909 0 0
910910 3.35987 2.44109i 0.111379 0.0809213i
911911 8.56488 + 9.51226i 0.283767 + 0.315155i 0.868130 0.496337i 0.165322π-0.165322\pi
−0.584363 + 0.811493i 0.698655π0.698655\pi
912912 0 0
913913 −7.29588 8.37196i −0.241458 0.277071i
914914 9.16370 + 15.8720i 0.303108 + 0.524999i
915915 0 0
916916 −3.29576 31.3571i −0.108895 1.03607i
917917 −4.85192 3.52513i −0.160224 0.116410i
918918 0 0
919919 3.53256 + 10.8721i 0.116528 + 0.358637i 0.992263 0.124156i 0.0396223π-0.0396223\pi
−0.875734 + 0.482793i 0.839622π0.839622\pi
920920 −12.5844 + 5.60293i −0.414895 + 0.184723i
921921 0 0
922922 12.7921 2.71905i 0.421287 0.0895472i
923923 8.03567 + 13.9182i 0.264497 + 0.458123i
924924 0 0
925925 6.81198 11.7987i 0.223976 0.387939i
926926 −3.01982 + 9.29405i −0.0992375 + 0.305422i
927927 0 0
928928 −36.6530 26.6300i −1.20319 0.874172i
929929 9.03552 + 1.92056i 0.296446 + 0.0630115i 0.353734 0.935346i 0.384912π-0.384912\pi
−0.0572878 + 0.998358i 0.518245π0.518245\pi
930930 0 0
931931 −1.75167 + 16.6660i −0.0574087 + 0.546207i
932932 −0.642115 0.285888i −0.0210332 0.00936457i
933933 0 0
934934 −2.03359 + 3.52228i −0.0665411 + 0.115253i
935935 21.0699 + 37.9002i 0.689058 + 1.23947i
936936 0 0
937937 −10.4711 + 32.2266i −0.342075 + 1.05280i 0.621056 + 0.783766i 0.286704π0.286704\pi
−0.963131 + 0.269032i 0.913296π0.913296\pi
938938 1.27293 + 12.1111i 0.0415627 + 0.395443i
939939 0 0
940940 6.24494 6.93570i 0.203687 0.226218i
941941 −7.07680 + 7.85958i −0.230697 + 0.256215i −0.847368 0.531006i 0.821814π-0.821814\pi
0.616671 + 0.787221i 0.288481π0.288481\pi
942942 0 0
943943 −1.53878 14.6405i −0.0501096 0.476761i
944944 3.13717 9.65521i 0.102106 0.314250i
945945 0 0
946946 −5.87331 2.72991i −0.190958 0.0887570i
947947 −1.82612 + 3.16292i −0.0593408 + 0.102781i −0.894170 0.447728i 0.852233π-0.852233\pi
0.834829 + 0.550510i 0.185567π0.185567\pi
948948 0 0
949949 −6.10253 2.71702i −0.198096 0.0881982i
950950 −0.657159 + 6.25245i −0.0213211 + 0.202856i
951951 0 0
952952 16.6177 + 3.53220i 0.538583 + 0.114479i
953953 −11.6292 8.44909i −0.376706 0.273693i 0.383280 0.923632i 0.374794π-0.374794\pi
−0.759986 + 0.649939i 0.774794π0.774794\pi
954954 0 0
955955 3.13522 9.64922i 0.101453 0.312241i
956956 14.7738 25.5890i 0.477819 0.827607i
957957 0 0
958958 13.6001 + 23.5560i 0.439399 + 0.761061i
959959 8.85163 1.88147i 0.285834 0.0607559i
960960 0 0
961961 41.9039 18.6568i 1.35174 0.601832i
962962 1.58388 + 4.87469i 0.0510665 + 0.157166i
963963 0 0
964964 −22.4327 16.2983i −0.722508 0.524933i
965965 −0.406220 3.86492i −0.0130767 0.124416i
966966 0 0
967967 −17.6955 30.6496i −0.569050 0.985623i −0.996660 0.0816600i 0.973978π-0.973978\pi
0.427610 0.903963i 0.359356π-0.359356\pi
968968 −20.6554 16.0554i −0.663889 0.516041i
969969 0 0
970970 −2.75062 3.05488i −0.0883172 0.0980862i
971971 0.118477 0.0860787i 0.00380211 0.00276240i −0.585883 0.810396i 0.699252π-0.699252\pi
0.589685 + 0.807634i 0.299252π0.299252\pi
972972 0 0
973973 8.02293 + 24.6920i 0.257203 + 0.791591i
974974 9.69691 + 2.06114i 0.310709 + 0.0660432i
975975 0 0
976976 −14.3021 6.36769i −0.457798 0.203825i
977977 39.1373 8.31889i 1.25211 0.266145i 0.466310 0.884622i 0.345583π-0.345583\pi
0.785803 + 0.618477i 0.212250π0.212250\pi
978978 0 0
979979 −28.2578 21.2389i −0.903122 0.678798i
980980 20.2401 0.646545
981981 0 0
982982 21.3896 15.5404i 0.682568 0.495915i
983983 −13.9510 + 6.21137i −0.444967 + 0.198112i −0.616974 0.786984i 0.711641π-0.711641\pi
0.172007 + 0.985096i 0.444975π0.444975\pi
984984 0 0
985985 6.27092 6.96456i 0.199808 0.221909i
986986 2.60005 24.7378i 0.0828025 0.787813i
987987 0 0
988988 5.47590 + 6.08160i 0.174212 + 0.193482i
989989 −6.10940 −0.194268
990990 0 0
991991 21.5067 0.683184 0.341592 0.939848i 0.389034π-0.389034\pi
0.341592 + 0.939848i 0.389034π0.389034\pi
992992 33.8394 + 37.5825i 1.07440 + 1.19325i
993993 0 0
994994 −1.14419 + 10.8862i −0.0362915 + 0.345290i
995995 13.6612 15.1723i 0.433088 0.480993i
996996 0 0
997997 −20.1502 + 8.97143i −0.638162 + 0.284128i −0.700201 0.713946i 0.746906π-0.746906\pi
0.0620390 + 0.998074i 0.480240π0.480240\pi
998998 −1.72106 + 1.25042i −0.0544791 + 0.0395814i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 891.2.n.g.460.2 32
3.2 odd 2 inner 891.2.n.g.460.3 32
9.2 odd 6 297.2.f.c.163.3 yes 16
9.4 even 3 inner 891.2.n.g.757.3 32
9.5 odd 6 inner 891.2.n.g.757.2 32
9.7 even 3 297.2.f.c.163.2 yes 16
11.5 even 5 inner 891.2.n.g.379.3 32
33.5 odd 10 inner 891.2.n.g.379.2 32
99.5 odd 30 inner 891.2.n.g.676.3 32
99.7 odd 30 3267.2.a.bh.1.5 8
99.16 even 15 297.2.f.c.82.2 16
99.29 even 30 3267.2.a.bh.1.4 8
99.38 odd 30 297.2.f.c.82.3 yes 16
99.49 even 15 inner 891.2.n.g.676.2 32
99.70 even 15 3267.2.a.bg.1.4 8
99.92 odd 30 3267.2.a.bg.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
297.2.f.c.82.2 16 99.16 even 15
297.2.f.c.82.3 yes 16 99.38 odd 30
297.2.f.c.163.2 yes 16 9.7 even 3
297.2.f.c.163.3 yes 16 9.2 odd 6
891.2.n.g.379.2 32 33.5 odd 10 inner
891.2.n.g.379.3 32 11.5 even 5 inner
891.2.n.g.460.2 32 1.1 even 1 trivial
891.2.n.g.460.3 32 3.2 odd 2 inner
891.2.n.g.676.2 32 99.49 even 15 inner
891.2.n.g.676.3 32 99.5 odd 30 inner
891.2.n.g.757.2 32 9.5 odd 6 inner
891.2.n.g.757.3 32 9.4 even 3 inner
3267.2.a.bg.1.4 8 99.70 even 15
3267.2.a.bg.1.5 8 99.92 odd 30
3267.2.a.bh.1.4 8 99.29 even 30
3267.2.a.bh.1.5 8 99.7 odd 30