Properties

Label 1734.2.f.a.1483.2
Level 17341734
Weight 22
Character 1734.1483
Analytic conductor 13.84613.846
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1734,2,Mod(829,1734)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1734, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1734.829");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1734=23172 1734 = 2 \cdot 3 \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1734.f (of order 44, degree 22, 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: 13.846059710513.8460597105
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
Coefficient field: Q(ζ8)\Q(\zeta_{8})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+1 x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 1483.2
Root 0.707107+0.707107i-0.707107 + 0.707107i of defining polynomial
Character χ\chi == 1734.1483
Dual form 1734.2.f.a.829.2

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) == q1.00000iq2+(0.7071070.707107i)q31.00000q4+(0.707107+0.707107i)q5+(0.7071070.707107i)q6+(2.82843+2.82843i)q7+1.00000iq81.00000iq9+(0.707107+0.707107i)q10+(2.12132+2.12132i)q11+(0.707107+0.707107i)q126.00000q13+(2.828432.82843i)q14+1.00000iq15+1.00000q161.00000q18+4.00000iq19+(0.7071070.707107i)q20+4.00000q21+(2.121322.12132i)q22+(4.242644.24264i)q23+(0.707107+0.707107i)q24+4.00000iq25+6.00000iq26+(0.7071070.707107i)q27+(2.828432.82843i)q28+(4.94975+4.94975i)q29+1.00000q30+(2.121322.12132i)q311.00000iq32+3.00000q334.00000q35+1.00000iq36+(5.65685+5.65685i)q37+4.00000q38+(4.24264+4.24264i)q39+(0.7071070.707107i)q40+(1.41421+1.41421i)q414.00000iq42+4.00000iq43+(2.121322.12132i)q44+(0.707107+0.707107i)q45+(4.24264+4.24264i)q46+2.00000q47+(0.7071070.707107i)q48+9.00000iq49+4.00000q50+6.00000q52+13.0000iq53+(0.707107+0.707107i)q543.00000q55+(2.82843+2.82843i)q56+(2.82843+2.82843i)q57+(4.94975+4.94975i)q589.00000iq591.00000iq60+(7.071077.07107i)q61+(2.121322.12132i)q62+(2.828432.82843i)q631.00000q64+(4.242644.24264i)q653.00000iq666.00000q676.00000q69+4.00000iq70+(8.485288.48528i)q71+1.00000q72+(4.94975+4.94975i)q73+(5.65685+5.65685i)q74+(2.82843+2.82843i)q754.00000iq76+12.0000iq77+(4.24264+4.24264i)q78+(3.53553+3.53553i)q79+(0.707107+0.707107i)q801.00000q81+(1.414211.41421i)q82+12.0000iq834.00000q84+4.00000q86+7.00000iq87+(2.12132+2.12132i)q884.00000q89+(0.7071070.707107i)q90+(16.970616.9706i)q91+(4.24264+4.24264i)q923.00000iq932.00000iq94+(2.828432.82843i)q95+(0.7071070.707107i)q96+(2.121322.12132i)q97+9.00000q98+(2.121322.12132i)q99+O(q100)q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.82843 + 2.82843i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 + 0.707107i) q^{10} +(2.12132 + 2.12132i) q^{11} +(-0.707107 + 0.707107i) q^{12} -6.00000 q^{13} +(2.82843 - 2.82843i) q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.00000i q^{19} +(0.707107 - 0.707107i) q^{20} +4.00000 q^{21} +(2.12132 - 2.12132i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(0.707107 + 0.707107i) q^{24} +4.00000i q^{25} +6.00000i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.82843 - 2.82843i) q^{28} +(-4.94975 + 4.94975i) q^{29} +1.00000 q^{30} +(2.12132 - 2.12132i) q^{31} -1.00000i q^{32} +3.00000 q^{33} -4.00000 q^{35} +1.00000i q^{36} +(-5.65685 + 5.65685i) q^{37} +4.00000 q^{38} +(-4.24264 + 4.24264i) q^{39} +(-0.707107 - 0.707107i) q^{40} +(1.41421 + 1.41421i) q^{41} -4.00000i q^{42} +4.00000i q^{43} +(-2.12132 - 2.12132i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-4.24264 + 4.24264i) q^{46} +2.00000 q^{47} +(0.707107 - 0.707107i) q^{48} +9.00000i q^{49} +4.00000 q^{50} +6.00000 q^{52} +13.0000i q^{53} +(-0.707107 + 0.707107i) q^{54} -3.00000 q^{55} +(-2.82843 + 2.82843i) q^{56} +(2.82843 + 2.82843i) q^{57} +(4.94975 + 4.94975i) q^{58} -9.00000i q^{59} -1.00000i q^{60} +(-7.07107 - 7.07107i) q^{61} +(-2.12132 - 2.12132i) q^{62} +(2.82843 - 2.82843i) q^{63} -1.00000 q^{64} +(4.24264 - 4.24264i) q^{65} -3.00000i q^{66} -6.00000 q^{67} -6.00000 q^{69} +4.00000i q^{70} +(8.48528 - 8.48528i) q^{71} +1.00000 q^{72} +(-4.94975 + 4.94975i) q^{73} +(5.65685 + 5.65685i) q^{74} +(2.82843 + 2.82843i) q^{75} -4.00000i q^{76} +12.0000i q^{77} +(4.24264 + 4.24264i) q^{78} +(3.53553 + 3.53553i) q^{79} +(-0.707107 + 0.707107i) q^{80} -1.00000 q^{81} +(1.41421 - 1.41421i) q^{82} +12.0000i q^{83} -4.00000 q^{84} +4.00000 q^{86} +7.00000i q^{87} +(-2.12132 + 2.12132i) q^{88} -4.00000 q^{89} +(0.707107 - 0.707107i) q^{90} +(-16.9706 - 16.9706i) q^{91} +(4.24264 + 4.24264i) q^{92} -3.00000i q^{93} -2.00000i q^{94} +(-2.82843 - 2.82843i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(2.12132 - 2.12132i) q^{97} +9.00000 q^{98} +(2.12132 - 2.12132i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q424q13+4q164q18+16q21+4q30+12q3316q35+16q38+8q47+16q50+24q5212q554q6424q6724q69+4q724q81++36q98+O(q100) 4 q - 4 q^{4} - 24 q^{13} + 4 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{30} + 12 q^{33} - 16 q^{35} + 16 q^{38} + 8 q^{47} + 16 q^{50} + 24 q^{52} - 12 q^{55} - 4 q^{64} - 24 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81}+ \cdots + 36 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1734Z)×\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times.

nn 11571157 11591159
χ(n)\chi(n) 11 e(34)e\left(\frac{3}{4}\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 1.00000i 0.707107i
33 0.707107 0.707107i 0.408248 0.408248i
44 −1.00000 −0.500000
55 −0.707107 + 0.707107i −0.316228 + 0.316228i −0.847316 0.531089i 0.821783π-0.821783\pi
0.531089 + 0.847316i 0.321783π0.321783\pi
66 −0.707107 0.707107i −0.288675 0.288675i
77 2.82843 + 2.82843i 1.06904 + 1.06904i 0.997433 + 0.0716124i 0.0228145π0.0228145\pi
0.0716124 + 0.997433i 0.477186π0.477186\pi
88 1.00000i 0.353553i
99 1.00000i 0.333333i
1010 0.707107 + 0.707107i 0.223607 + 0.223607i
1111 2.12132 + 2.12132i 0.639602 + 0.639602i 0.950457 0.310855i 0.100615π-0.100615\pi
−0.310855 + 0.950457i 0.600615π0.600615\pi
1212 −0.707107 + 0.707107i −0.204124 + 0.204124i
1313 −6.00000 −1.66410 −0.832050 0.554700i 0.812833π-0.812833\pi
−0.832050 + 0.554700i 0.812833π0.812833\pi
1414 2.82843 2.82843i 0.755929 0.755929i
1515 1.00000i 0.258199i
1616 1.00000 0.250000
1717 0 0
1818 −1.00000 −0.235702
1919 4.00000i 0.917663i 0.888523 + 0.458831i 0.151732π0.151732\pi
−0.888523 + 0.458831i 0.848268π0.848268\pi
2020 0.707107 0.707107i 0.158114 0.158114i
2121 4.00000 0.872872
2222 2.12132 2.12132i 0.452267 0.452267i
2323 −4.24264 4.24264i −0.884652 0.884652i 0.109351 0.994003i 0.465123π-0.465123\pi
−0.994003 + 0.109351i 0.965123π0.965123\pi
2424 0.707107 + 0.707107i 0.144338 + 0.144338i
2525 4.00000i 0.800000i
2626 6.00000i 1.17670i
2727 −0.707107 0.707107i −0.136083 0.136083i
2828 −2.82843 2.82843i −0.534522 0.534522i
2929 −4.94975 + 4.94975i −0.919145 + 0.919145i −0.996967 0.0778222i 0.975203π-0.975203\pi
0.0778222 + 0.996967i 0.475203π0.475203\pi
3030 1.00000 0.182574
3131 2.12132 2.12132i 0.381000 0.381000i −0.490462 0.871463i 0.663172π-0.663172\pi
0.871463 + 0.490462i 0.163172π0.163172\pi
3232 1.00000i 0.176777i
3333 3.00000 0.522233
3434 0 0
3535 −4.00000 −0.676123
3636 1.00000i 0.166667i
3737 −5.65685 + 5.65685i −0.929981 + 0.929981i −0.997704 0.0677230i 0.978427π-0.978427\pi
0.0677230 + 0.997704i 0.478427π0.478427\pi
3838 4.00000 0.648886
3939 −4.24264 + 4.24264i −0.679366 + 0.679366i
4040 −0.707107 0.707107i −0.111803 0.111803i
4141 1.41421 + 1.41421i 0.220863 + 0.220863i 0.808862 0.587999i 0.200084π-0.200084\pi
−0.587999 + 0.808862i 0.700084π0.700084\pi
4242 4.00000i 0.617213i
4343 4.00000i 0.609994i 0.952353 + 0.304997i 0.0986555π0.0986555\pi
−0.952353 + 0.304997i 0.901344π0.901344\pi
4444 −2.12132 2.12132i −0.319801 0.319801i
4545 0.707107 + 0.707107i 0.105409 + 0.105409i
4646 −4.24264 + 4.24264i −0.625543 + 0.625543i
4747 2.00000 0.291730 0.145865 0.989305i 0.453403π-0.453403\pi
0.145865 + 0.989305i 0.453403π0.453403\pi
4848 0.707107 0.707107i 0.102062 0.102062i
4949 9.00000i 1.28571i
5050 4.00000 0.565685
5151 0 0
5252 6.00000 0.832050
5353 13.0000i 1.78569i 0.450367 + 0.892844i 0.351293π0.351293\pi
−0.450367 + 0.892844i 0.648707π0.648707\pi
5454 −0.707107 + 0.707107i −0.0962250 + 0.0962250i
5555 −3.00000 −0.404520
5656 −2.82843 + 2.82843i −0.377964 + 0.377964i
5757 2.82843 + 2.82843i 0.374634 + 0.374634i
5858 4.94975 + 4.94975i 0.649934 + 0.649934i
5959 9.00000i 1.17170i −0.810419 0.585850i 0.800761π-0.800761\pi
0.810419 0.585850i 0.199239π-0.199239\pi
6060 1.00000i 0.129099i
6161 −7.07107 7.07107i −0.905357 0.905357i 0.0905357 0.995893i 0.471142π-0.471142\pi
−0.995893 + 0.0905357i 0.971142π0.971142\pi
6262 −2.12132 2.12132i −0.269408 0.269408i
6363 2.82843 2.82843i 0.356348 0.356348i
6464 −1.00000 −0.125000
6565 4.24264 4.24264i 0.526235 0.526235i
6666 3.00000i 0.369274i
6767 −6.00000 −0.733017 −0.366508 0.930415i 0.619447π-0.619447\pi
−0.366508 + 0.930415i 0.619447π0.619447\pi
6868 0 0
6969 −6.00000 −0.722315
7070 4.00000i 0.478091i
7171 8.48528 8.48528i 1.00702 1.00702i 0.00704243 0.999975i 0.497758π-0.497758\pi
0.999975 0.00704243i 0.00224169π-0.00224169\pi
7272 1.00000 0.117851
7373 −4.94975 + 4.94975i −0.579324 + 0.579324i −0.934717 0.355393i 0.884347π-0.884347\pi
0.355393 + 0.934717i 0.384347π0.384347\pi
7474 5.65685 + 5.65685i 0.657596 + 0.657596i
7575 2.82843 + 2.82843i 0.326599 + 0.326599i
7676 4.00000i 0.458831i
7777 12.0000i 1.36753i
7878 4.24264 + 4.24264i 0.480384 + 0.480384i
7979 3.53553 + 3.53553i 0.397779 + 0.397779i 0.877449 0.479670i 0.159244π-0.159244\pi
−0.479670 + 0.877449i 0.659244π0.659244\pi
8080 −0.707107 + 0.707107i −0.0790569 + 0.0790569i
8181 −1.00000 −0.111111
8282 1.41421 1.41421i 0.156174 0.156174i
8383 12.0000i 1.31717i 0.752506 + 0.658586i 0.228845π0.228845\pi
−0.752506 + 0.658586i 0.771155π0.771155\pi
8484 −4.00000 −0.436436
8585 0 0
8686 4.00000 0.431331
8787 7.00000i 0.750479i
8888 −2.12132 + 2.12132i −0.226134 + 0.226134i
8989 −4.00000 −0.423999 −0.212000 0.977270i 0.567998π-0.567998\pi
−0.212000 + 0.977270i 0.567998π0.567998\pi
9090 0.707107 0.707107i 0.0745356 0.0745356i
9191 −16.9706 16.9706i −1.77900 1.77900i
9292 4.24264 + 4.24264i 0.442326 + 0.442326i
9393 3.00000i 0.311086i
9494 2.00000i 0.206284i
9595 −2.82843 2.82843i −0.290191 0.290191i
9696 −0.707107 0.707107i −0.0721688 0.0721688i
9797 2.12132 2.12132i 0.215387 0.215387i −0.591164 0.806551i 0.701331π-0.701331\pi
0.806551 + 0.591164i 0.201331π0.201331\pi
9898 9.00000 0.909137
9999 2.12132 2.12132i 0.213201 0.213201i
100100 4.00000i 0.400000i
101101 17.0000 1.69156 0.845782 0.533529i 0.179135π-0.179135\pi
0.845782 + 0.533529i 0.179135π0.179135\pi
102102 0 0
103103 13.0000 1.28093 0.640464 0.767988i 0.278742π-0.278742\pi
0.640464 + 0.767988i 0.278742π0.278742\pi
104104 6.00000i 0.588348i
105105 −2.82843 + 2.82843i −0.276026 + 0.276026i
106106 13.0000 1.26267
107107 10.6066 10.6066i 1.02538 1.02538i 0.0257094 0.999669i 0.491816π-0.491816\pi
0.999669 0.0257094i 0.00818447π-0.00818447\pi
108108 0.707107 + 0.707107i 0.0680414 + 0.0680414i
109109 7.07107 + 7.07107i 0.677285 + 0.677285i 0.959385 0.282100i 0.0910309π-0.0910309\pi
−0.282100 + 0.959385i 0.591031π0.591031\pi
110110 3.00000i 0.286039i
111111 8.00000i 0.759326i
112112 2.82843 + 2.82843i 0.267261 + 0.267261i
113113 7.07107 + 7.07107i 0.665190 + 0.665190i 0.956599 0.291409i 0.0941239π-0.0941239\pi
−0.291409 + 0.956599i 0.594124π0.594124\pi
114114 2.82843 2.82843i 0.264906 0.264906i
115115 6.00000 0.559503
116116 4.94975 4.94975i 0.459573 0.459573i
117117 6.00000i 0.554700i
118118 −9.00000 −0.828517
119119 0 0
120120 −1.00000 −0.0912871
121121 2.00000i 0.181818i
122122 −7.07107 + 7.07107i −0.640184 + 0.640184i
123123 2.00000 0.180334
124124 −2.12132 + 2.12132i −0.190500 + 0.190500i
125125 −6.36396 6.36396i −0.569210 0.569210i
126126 −2.82843 2.82843i −0.251976 0.251976i
127127 16.0000i 1.41977i 0.704317 + 0.709885i 0.251253π0.251253\pi
−0.704317 + 0.709885i 0.748747π0.748747\pi
128128 1.00000i 0.0883883i
129129 2.82843 + 2.82843i 0.249029 + 0.249029i
130130 −4.24264 4.24264i −0.372104 0.372104i
131131 14.1421 14.1421i 1.23560 1.23560i 0.273824 0.961780i 0.411711π-0.411711\pi
0.961780 0.273824i 0.0882887π-0.0882887\pi
132132 −3.00000 −0.261116
133133 −11.3137 + 11.3137i −0.981023 + 0.981023i
134134 6.00000i 0.518321i
135135 1.00000 0.0860663
136136 0 0
137137 12.0000 1.02523 0.512615 0.858619i 0.328677π-0.328677\pi
0.512615 + 0.858619i 0.328677π0.328677\pi
138138 6.00000i 0.510754i
139139 −5.65685 + 5.65685i −0.479808 + 0.479808i −0.905070 0.425262i 0.860182π-0.860182\pi
0.425262 + 0.905070i 0.360182π0.360182\pi
140140 4.00000 0.338062
141141 1.41421 1.41421i 0.119098 0.119098i
142142 −8.48528 8.48528i −0.712069 0.712069i
143143 −12.7279 12.7279i −1.06436 1.06436i
144144 1.00000i 0.0833333i
145145 7.00000i 0.581318i
146146 4.94975 + 4.94975i 0.409644 + 0.409644i
147147 6.36396 + 6.36396i 0.524891 + 0.524891i
148148 5.65685 5.65685i 0.464991 0.464991i
149149 −15.0000 −1.22885 −0.614424 0.788976i 0.710612π-0.710612\pi
−0.614424 + 0.788976i 0.710612π0.710612\pi
150150 2.82843 2.82843i 0.230940 0.230940i
151151 9.00000i 0.732410i −0.930534 0.366205i 0.880657π-0.880657\pi
0.930534 0.366205i 0.119343π-0.119343\pi
152152 −4.00000 −0.324443
153153 0 0
154154 12.0000 0.966988
155155 3.00000i 0.240966i
156156 4.24264 4.24264i 0.339683 0.339683i
157157 −12.0000 −0.957704 −0.478852 0.877896i 0.658947π-0.658947\pi
−0.478852 + 0.877896i 0.658947π0.658947\pi
158158 3.53553 3.53553i 0.281272 0.281272i
159159 9.19239 + 9.19239i 0.729004 + 0.729004i
160160 0.707107 + 0.707107i 0.0559017 + 0.0559017i
161161 24.0000i 1.89146i
162162 1.00000i 0.0785674i
163163 4.24264 + 4.24264i 0.332309 + 0.332309i 0.853463 0.521154i 0.174498π-0.174498\pi
−0.521154 + 0.853463i 0.674498π0.674498\pi
164164 −1.41421 1.41421i −0.110432 0.110432i
165165 −2.12132 + 2.12132i −0.165145 + 0.165145i
166166 12.0000 0.931381
167167 5.65685 5.65685i 0.437741 0.437741i −0.453510 0.891251i 0.649829π-0.649829\pi
0.891251 + 0.453510i 0.149829π0.149829\pi
168168 4.00000i 0.308607i
169169 23.0000 1.76923
170170 0 0
171171 4.00000 0.305888
172172 4.00000i 0.304997i
173173 9.19239 9.19239i 0.698884 0.698884i −0.265286 0.964170i 0.585466π-0.585466\pi
0.964170 + 0.265286i 0.0854662π0.0854662\pi
174174 7.00000 0.530669
175175 −11.3137 + 11.3137i −0.855236 + 0.855236i
176176 2.12132 + 2.12132i 0.159901 + 0.159901i
177177 −6.36396 6.36396i −0.478345 0.478345i
178178 4.00000i 0.299813i
179179 0 0 1.00000 00
−1.00000 π\pi
180180 −0.707107 0.707107i −0.0527046 0.0527046i
181181 −7.07107 7.07107i −0.525588 0.525588i 0.393665 0.919254i 0.371207π-0.371207\pi
−0.919254 + 0.393665i 0.871207π0.871207\pi
182182 −16.9706 + 16.9706i −1.25794 + 1.25794i
183183 −10.0000 −0.739221
184184 4.24264 4.24264i 0.312772 0.312772i
185185 8.00000i 0.588172i
186186 −3.00000 −0.219971
187187 0 0
188188 −2.00000 −0.145865
189189 4.00000i 0.290957i
190190 −2.82843 + 2.82843i −0.205196 + 0.205196i
191191 −14.0000 −1.01300 −0.506502 0.862239i 0.669062π-0.669062\pi
−0.506502 + 0.862239i 0.669062π0.669062\pi
192192 −0.707107 + 0.707107i −0.0510310 + 0.0510310i
193193 −6.36396 6.36396i −0.458088 0.458088i 0.439939 0.898027i 0.355000π-0.355000\pi
−0.898027 + 0.439939i 0.855000π0.855000\pi
194194 −2.12132 2.12132i −0.152302 0.152302i
195195 6.00000i 0.429669i
196196 9.00000i 0.642857i
197197 −7.07107 7.07107i −0.503793 0.503793i 0.408822 0.912614i 0.365940π-0.365940\pi
−0.912614 + 0.408822i 0.865940π0.865940\pi
198198 −2.12132 2.12132i −0.150756 0.150756i
199199 −0.707107 + 0.707107i −0.0501255 + 0.0501255i −0.731725 0.681600i 0.761285π-0.761285\pi
0.681600 + 0.731725i 0.261285π0.261285\pi
200200 −4.00000 −0.282843
201201 −4.24264 + 4.24264i −0.299253 + 0.299253i
202202 17.0000i 1.19612i
203203 −28.0000 −1.96521
204204 0 0
205205 −2.00000 −0.139686
206206 13.0000i 0.905753i
207207 −4.24264 + 4.24264i −0.294884 + 0.294884i
208208 −6.00000 −0.416025
209209 −8.48528 + 8.48528i −0.586939 + 0.586939i
210210 2.82843 + 2.82843i 0.195180 + 0.195180i
211211 5.65685 + 5.65685i 0.389434 + 0.389434i 0.874486 0.485052i 0.161199π-0.161199\pi
−0.485052 + 0.874486i 0.661199π0.661199\pi
212212 13.0000i 0.892844i
213213 12.0000i 0.822226i
214214 −10.6066 10.6066i −0.725052 0.725052i
215215 −2.82843 2.82843i −0.192897 0.192897i
216216 0.707107 0.707107i 0.0481125 0.0481125i
217217 12.0000 0.814613
218218 7.07107 7.07107i 0.478913 0.478913i
219219 7.00000i 0.473016i
220220 3.00000 0.202260
221221 0 0
222222 8.00000 0.536925
223223 17.0000i 1.13840i 0.822198 + 0.569202i 0.192748π0.192748\pi
−0.822198 + 0.569202i 0.807252π0.807252\pi
224224 2.82843 2.82843i 0.188982 0.188982i
225225 4.00000 0.266667
226226 7.07107 7.07107i 0.470360 0.470360i
227227 14.1421 + 14.1421i 0.938647 + 0.938647i 0.998224 0.0595772i 0.0189752π-0.0189752\pi
−0.0595772 + 0.998224i 0.518975π0.518975\pi
228228 −2.82843 2.82843i −0.187317 0.187317i
229229 14.0000i 0.925146i 0.886581 + 0.462573i 0.153074π0.153074\pi
−0.886581 + 0.462573i 0.846926π0.846926\pi
230230 6.00000i 0.395628i
231231 8.48528 + 8.48528i 0.558291 + 0.558291i
232232 −4.94975 4.94975i −0.324967 0.324967i
233233 16.9706 16.9706i 1.11178 1.11178i 0.118869 0.992910i 0.462073π-0.462073\pi
0.992910 0.118869i 0.0379267π-0.0379267\pi
234234 6.00000 0.392232
235235 −1.41421 + 1.41421i −0.0922531 + 0.0922531i
236236 9.00000i 0.585850i
237237 5.00000 0.324785
238238 0 0
239239 −26.0000 −1.68180 −0.840900 0.541190i 0.817974π-0.817974\pi
−0.840900 + 0.541190i 0.817974π0.817974\pi
240240 1.00000i 0.0645497i
241241 −10.6066 + 10.6066i −0.683231 + 0.683231i −0.960727 0.277496i 0.910496π-0.910496\pi
0.277496 + 0.960727i 0.410496π0.410496\pi
242242 −2.00000 −0.128565
243243 −0.707107 + 0.707107i −0.0453609 + 0.0453609i
244244 7.07107 + 7.07107i 0.452679 + 0.452679i
245245 −6.36396 6.36396i −0.406579 0.406579i
246246 2.00000i 0.127515i
247247 24.0000i 1.52708i
248248 2.12132 + 2.12132i 0.134704 + 0.134704i
249249 8.48528 + 8.48528i 0.537733 + 0.537733i
250250 −6.36396 + 6.36396i −0.402492 + 0.402492i
251251 15.0000 0.946792 0.473396 0.880850i 0.343028π-0.343028\pi
0.473396 + 0.880850i 0.343028π0.343028\pi
252252 −2.82843 + 2.82843i −0.178174 + 0.178174i
253253 18.0000i 1.13165i
254254 16.0000 1.00393
255255 0 0
256256 1.00000 0.0625000
257257 0 0 1.00000 00
−1.00000 π\pi
258258 2.82843 2.82843i 0.176090 0.176090i
259259 −32.0000 −1.98838
260260 −4.24264 + 4.24264i −0.263117 + 0.263117i
261261 4.94975 + 4.94975i 0.306382 + 0.306382i
262262 −14.1421 14.1421i −0.873704 0.873704i
263263 18.0000i 1.10993i 0.831875 + 0.554964i 0.187268π0.187268\pi
−0.831875 + 0.554964i 0.812732π0.812732\pi
264264 3.00000i 0.184637i
265265 −9.19239 9.19239i −0.564684 0.564684i
266266 11.3137 + 11.3137i 0.693688 + 0.693688i
267267 −2.82843 + 2.82843i −0.173097 + 0.173097i
268268 6.00000 0.366508
269269 −6.36396 + 6.36396i −0.388018 + 0.388018i −0.873980 0.485962i 0.838469π-0.838469\pi
0.485962 + 0.873980i 0.338469π0.338469\pi
270270 1.00000i 0.0608581i
271271 5.00000 0.303728 0.151864 0.988401i 0.451472π-0.451472\pi
0.151864 + 0.988401i 0.451472π0.451472\pi
272272 0 0
273273 −24.0000 −1.45255
274274 12.0000i 0.724947i
275275 −8.48528 + 8.48528i −0.511682 + 0.511682i
276276 6.00000 0.361158
277277 15.5563 15.5563i 0.934690 0.934690i −0.0633039 0.997994i 0.520164π-0.520164\pi
0.997994 + 0.0633039i 0.0201637π0.0201637\pi
278278 5.65685 + 5.65685i 0.339276 + 0.339276i
279279 −2.12132 2.12132i −0.127000 0.127000i
280280 4.00000i 0.239046i
281281 0 0 1.00000 00
−1.00000 π\pi
282282 −1.41421 1.41421i −0.0842152 0.0842152i
283283 2.82843 + 2.82843i 0.168133 + 0.168133i 0.786158 0.618026i 0.212067π-0.212067\pi
−0.618026 + 0.786158i 0.712067π0.712067\pi
284284 −8.48528 + 8.48528i −0.503509 + 0.503509i
285285 −4.00000 −0.236940
286286 −12.7279 + 12.7279i −0.752618 + 0.752618i
287287 8.00000i 0.472225i
288288 −1.00000 −0.0589256
289289 0 0
290290 −7.00000 −0.411054
291291 3.00000i 0.175863i
292292 4.94975 4.94975i 0.289662 0.289662i
293293 19.0000 1.10999 0.554996 0.831853i 0.312720π-0.312720\pi
0.554996 + 0.831853i 0.312720π0.312720\pi
294294 6.36396 6.36396i 0.371154 0.371154i
295295 6.36396 + 6.36396i 0.370524 + 0.370524i
296296 −5.65685 5.65685i −0.328798 0.328798i
297297 3.00000i 0.174078i
298298 15.0000i 0.868927i
299299 25.4558 + 25.4558i 1.47215 + 1.47215i
300300 −2.82843 2.82843i −0.163299 0.163299i
301301 −11.3137 + 11.3137i −0.652111 + 0.652111i
302302 −9.00000 −0.517892
303303 12.0208 12.0208i 0.690578 0.690578i
304304 4.00000i 0.229416i
305305 10.0000 0.572598
306306 0 0
307307 −12.0000 −0.684876 −0.342438 0.939540i 0.611253π-0.611253\pi
−0.342438 + 0.939540i 0.611253π0.611253\pi
308308 12.0000i 0.683763i
309309 9.19239 9.19239i 0.522937 0.522937i
310310 3.00000 0.170389
311311 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
312312 −4.24264 4.24264i −0.240192 0.240192i
313313 −9.89949 9.89949i −0.559553 0.559553i 0.369627 0.929180i 0.379485π-0.379485\pi
−0.929180 + 0.369627i 0.879485π0.879485\pi
314314 12.0000i 0.677199i
315315 4.00000i 0.225374i
316316 −3.53553 3.53553i −0.198889 0.198889i
317317 −1.41421 1.41421i −0.0794301 0.0794301i 0.666276 0.745706i 0.267887π-0.267887\pi
−0.745706 + 0.666276i 0.767887π0.767887\pi
318318 9.19239 9.19239i 0.515484 0.515484i
319319 −21.0000 −1.17577
320320 0.707107 0.707107i 0.0395285 0.0395285i
321321 15.0000i 0.837218i
322322 −24.0000 −1.33747
323323 0 0
324324 1.00000 0.0555556
325325 24.0000i 1.33128i
326326 4.24264 4.24264i 0.234978 0.234978i
327327 10.0000 0.553001
328328 −1.41421 + 1.41421i −0.0780869 + 0.0780869i
329329 5.65685 + 5.65685i 0.311872 + 0.311872i
330330 2.12132 + 2.12132i 0.116775 + 0.116775i
331331 22.0000i 1.20923i 0.796518 + 0.604615i 0.206673π0.206673\pi
−0.796518 + 0.604615i 0.793327π0.793327\pi
332332 12.0000i 0.658586i
333333 5.65685 + 5.65685i 0.309994 + 0.309994i
334334 −5.65685 5.65685i −0.309529 0.309529i
335335 4.24264 4.24264i 0.231800 0.231800i
336336 4.00000 0.218218
337337 −21.2132 + 21.2132i −1.15556 + 1.15556i −0.170136 + 0.985421i 0.554421π0.554421\pi
−0.985421 + 0.170136i 0.945579π0.945579\pi
338338 23.0000i 1.25104i
339339 10.0000 0.543125
340340 0 0
341341 9.00000 0.487377
342342 4.00000i 0.216295i
343343 −5.65685 + 5.65685i −0.305441 + 0.305441i
344344 −4.00000 −0.215666
345345 4.24264 4.24264i 0.228416 0.228416i
346346 −9.19239 9.19239i −0.494186 0.494186i
347347 12.0208 + 12.0208i 0.645311 + 0.645311i 0.951856 0.306545i 0.0991730π-0.0991730\pi
−0.306545 + 0.951856i 0.599173π0.599173\pi
348348 7.00000i 0.375239i
349349 12.0000i 0.642345i −0.947021 0.321173i 0.895923π-0.895923\pi
0.947021 0.321173i 0.104077π-0.104077\pi
350350 11.3137 + 11.3137i 0.604743 + 0.604743i
351351 4.24264 + 4.24264i 0.226455 + 0.226455i
352352 2.12132 2.12132i 0.113067 0.113067i
353353 4.00000 0.212899 0.106449 0.994318i 0.466052π-0.466052\pi
0.106449 + 0.994318i 0.466052π0.466052\pi
354354 −6.36396 + 6.36396i −0.338241 + 0.338241i
355355 12.0000i 0.636894i
356356 4.00000 0.212000
357357 0 0
358358 0 0
359359 30.0000i 1.58334i −0.610949 0.791670i 0.709212π-0.709212\pi
0.610949 0.791670i 0.290788π-0.290788\pi
360360 −0.707107 + 0.707107i −0.0372678 + 0.0372678i
361361 3.00000 0.157895
362362 −7.07107 + 7.07107i −0.371647 + 0.371647i
363363 −1.41421 1.41421i −0.0742270 0.0742270i
364364 16.9706 + 16.9706i 0.889499 + 0.889499i
365365 7.00000i 0.366397i
366366 10.0000i 0.522708i
367367 −12.0208 12.0208i −0.627481 0.627481i 0.319952 0.947434i 0.396333π-0.396333\pi
−0.947434 + 0.319952i 0.896333π0.896333\pi
368368 −4.24264 4.24264i −0.221163 0.221163i
369369 1.41421 1.41421i 0.0736210 0.0736210i
370370 −8.00000 −0.415900
371371 −36.7696 + 36.7696i −1.90898 + 1.90898i
372372 3.00000i 0.155543i
373373 −32.0000 −1.65690 −0.828449 0.560065i 0.810776π-0.810776\pi
−0.828449 + 0.560065i 0.810776π0.810776\pi
374374 0 0
375375 −9.00000 −0.464758
376376 2.00000i 0.103142i
377377 29.6985 29.6985i 1.52955 1.52955i
378378 −4.00000 −0.205738
379379 −7.07107 + 7.07107i −0.363216 + 0.363216i −0.864996 0.501779i 0.832679π-0.832679\pi
0.501779 + 0.864996i 0.332679π0.332679\pi
380380 2.82843 + 2.82843i 0.145095 + 0.145095i
381381 11.3137 + 11.3137i 0.579619 + 0.579619i
382382 14.0000i 0.716302i
383383 2.00000i 0.102195i 0.998694 + 0.0510976i 0.0162720π0.0162720\pi
−0.998694 + 0.0510976i 0.983728π0.983728\pi
384384 0.707107 + 0.707107i 0.0360844 + 0.0360844i
385385 −8.48528 8.48528i −0.432450 0.432450i
386386 −6.36396 + 6.36396i −0.323917 + 0.323917i
387387 4.00000 0.203331
388388 −2.12132 + 2.12132i −0.107694 + 0.107694i
389389 5.00000i 0.253510i −0.991934 0.126755i 0.959544π-0.959544\pi
0.991934 0.126755i 0.0404562π-0.0404562\pi
390390 −6.00000 −0.303822
391391 0 0
392392 −9.00000 −0.454569
393393 20.0000i 1.00887i
394394 −7.07107 + 7.07107i −0.356235 + 0.356235i
395395 −5.00000 −0.251577
396396 −2.12132 + 2.12132i −0.106600 + 0.106600i
397397 15.5563 + 15.5563i 0.780751 + 0.780751i 0.979957 0.199207i 0.0638365π-0.0638365\pi
−0.199207 + 0.979957i 0.563837π0.563837\pi
398398 0.707107 + 0.707107i 0.0354441 + 0.0354441i
399399 16.0000i 0.801002i
400400 4.00000i 0.200000i
401401 −8.48528 8.48528i −0.423735 0.423735i 0.462753 0.886487i 0.346862π-0.346862\pi
−0.886487 + 0.462753i 0.846862π0.846862\pi
402402 4.24264 + 4.24264i 0.211604 + 0.211604i
403403 −12.7279 + 12.7279i −0.634023 + 0.634023i
404404 −17.0000 −0.845782
405405 0.707107 0.707107i 0.0351364 0.0351364i
406406 28.0000i 1.38962i
407407 −24.0000 −1.18964
408408 0 0
409409 19.0000 0.939490 0.469745 0.882802i 0.344346π-0.344346\pi
0.469745 + 0.882802i 0.344346π0.344346\pi
410410 2.00000i 0.0987730i
411411 8.48528 8.48528i 0.418548 0.418548i
412412 −13.0000 −0.640464
413413 25.4558 25.4558i 1.25260 1.25260i
414414 4.24264 + 4.24264i 0.208514 + 0.208514i
415415 −8.48528 8.48528i −0.416526 0.416526i
416416 6.00000i 0.294174i
417417 8.00000i 0.391762i
418418 8.48528 + 8.48528i 0.415029 + 0.415029i
419419 2.12132 + 2.12132i 0.103633 + 0.103633i 0.757022 0.653389i 0.226653π-0.226653\pi
−0.653389 + 0.757022i 0.726653π0.726653\pi
420420 2.82843 2.82843i 0.138013 0.138013i
421421 −22.0000 −1.07221 −0.536107 0.844150i 0.680106π-0.680106\pi
−0.536107 + 0.844150i 0.680106π0.680106\pi
422422 5.65685 5.65685i 0.275371 0.275371i
423423 2.00000i 0.0972433i
424424 −13.0000 −0.631336
425425 0 0
426426 −12.0000 −0.581402
427427 40.0000i 1.93574i
428428 −10.6066 + 10.6066i −0.512689 + 0.512689i
429429 −18.0000 −0.869048
430430 −2.82843 + 2.82843i −0.136399 + 0.136399i
431431 7.07107 + 7.07107i 0.340601 + 0.340601i 0.856593 0.515992i 0.172577π-0.172577\pi
−0.515992 + 0.856593i 0.672577π0.672577\pi
432432 −0.707107 0.707107i −0.0340207 0.0340207i
433433 3.00000i 0.144171i 0.997398 + 0.0720854i 0.0229654π0.0229654\pi
−0.997398 + 0.0720854i 0.977035π0.977035\pi
434434 12.0000i 0.576018i
435435 −4.94975 4.94975i −0.237322 0.237322i
436436 −7.07107 7.07107i −0.338643 0.338643i
437437 16.9706 16.9706i 0.811812 0.811812i
438438 7.00000 0.334473
439439 19.7990 19.7990i 0.944954 0.944954i −0.0536078 0.998562i 0.517072π-0.517072\pi
0.998562 + 0.0536078i 0.0170721π0.0170721\pi
440440 3.00000i 0.143019i
441441 9.00000 0.428571
442442 0 0
443443 −12.0000 −0.570137 −0.285069 0.958507i 0.592016π-0.592016\pi
−0.285069 + 0.958507i 0.592016π0.592016\pi
444444 8.00000i 0.379663i
445445 2.82843 2.82843i 0.134080 0.134080i
446446 17.0000 0.804973
447447 −10.6066 + 10.6066i −0.501675 + 0.501675i
448448 −2.82843 2.82843i −0.133631 0.133631i
449449 2.82843 + 2.82843i 0.133482 + 0.133482i 0.770691 0.637209i 0.219911π-0.219911\pi
−0.637209 + 0.770691i 0.719911π0.719911\pi
450450 4.00000i 0.188562i
451451 6.00000i 0.282529i
452452 −7.07107 7.07107i −0.332595 0.332595i
453453 −6.36396 6.36396i −0.299005 0.299005i
454454 14.1421 14.1421i 0.663723 0.663723i
455455 24.0000 1.12514
456456 −2.82843 + 2.82843i −0.132453 + 0.132453i
457457 17.0000i 0.795226i −0.917553 0.397613i 0.869839π-0.869839\pi
0.917553 0.397613i 0.130161π-0.130161\pi
458458 14.0000 0.654177
459459 0 0
460460 −6.00000 −0.279751
461461 35.0000i 1.63011i 0.579382 + 0.815056i 0.303294π0.303294\pi
−0.579382 + 0.815056i 0.696706π0.696706\pi
462462 8.48528 8.48528i 0.394771 0.394771i
463463 −5.00000 −0.232370 −0.116185 0.993228i 0.537067π-0.537067\pi
−0.116185 + 0.993228i 0.537067π0.537067\pi
464464 −4.94975 + 4.94975i −0.229786 + 0.229786i
465465 2.12132 + 2.12132i 0.0983739 + 0.0983739i
466466 −16.9706 16.9706i −0.786146 0.786146i
467467 3.00000i 0.138823i 0.997588 + 0.0694117i 0.0221122π0.0221122\pi
−0.997588 + 0.0694117i 0.977888π0.977888\pi
468468 6.00000i 0.277350i
469469 −16.9706 16.9706i −0.783628 0.783628i
470470 1.41421 + 1.41421i 0.0652328 + 0.0652328i
471471 −8.48528 + 8.48528i −0.390981 + 0.390981i
472472 9.00000 0.414259
473473 −8.48528 + 8.48528i −0.390154 + 0.390154i
474474 5.00000i 0.229658i
475475 −16.0000 −0.734130
476476 0 0
477477 13.0000 0.595229
478478 26.0000i 1.18921i
479479 9.89949 9.89949i 0.452319 0.452319i −0.443804 0.896124i 0.646371π-0.646371\pi
0.896124 + 0.443804i 0.146371π0.146371\pi
480480 1.00000 0.0456435
481481 33.9411 33.9411i 1.54758 1.54758i
482482 10.6066 + 10.6066i 0.483117 + 0.483117i
483483 −16.9706 16.9706i −0.772187 0.772187i
484484 2.00000i 0.0909091i
485485 3.00000i 0.136223i
486486 0.707107 + 0.707107i 0.0320750 + 0.0320750i
487487 −17.6777 17.6777i −0.801052 0.801052i 0.182208 0.983260i 0.441675π-0.441675\pi
−0.983260 + 0.182208i 0.941675π0.941675\pi
488488 7.07107 7.07107i 0.320092 0.320092i
489489 6.00000 0.271329
490490 −6.36396 + 6.36396i −0.287494 + 0.287494i
491491 23.0000i 1.03798i −0.854782 0.518988i 0.826309π-0.826309\pi
0.854782 0.518988i 0.173691π-0.173691\pi
492492 −2.00000 −0.0901670
493493 0 0
494494 −24.0000 −1.07981
495495 3.00000i 0.134840i
496496 2.12132 2.12132i 0.0952501 0.0952501i
497497 48.0000 2.15309
498498 8.48528 8.48528i 0.380235 0.380235i
499499 −5.65685 5.65685i −0.253236 0.253236i 0.569060 0.822296i 0.307307π-0.307307\pi
−0.822296 + 0.569060i 0.807307π0.807307\pi
500500 6.36396 + 6.36396i 0.284605 + 0.284605i
501501 8.00000i 0.357414i
502502 15.0000i 0.669483i
503503 −1.41421 1.41421i −0.0630567 0.0630567i 0.674875 0.737932i 0.264197π-0.264197\pi
−0.737932 + 0.674875i 0.764197π0.764197\pi
504504 2.82843 + 2.82843i 0.125988 + 0.125988i
505505 −12.0208 + 12.0208i −0.534919 + 0.534919i
506506 −18.0000 −0.800198
507507 16.2635 16.2635i 0.722285 0.722285i
508508 16.0000i 0.709885i
509509 −31.0000 −1.37405 −0.687025 0.726633i 0.741084π-0.741084\pi
−0.687025 + 0.726633i 0.741084π0.741084\pi
510510 0 0
511511 −28.0000 −1.23865
512512 1.00000i 0.0441942i
513513 2.82843 2.82843i 0.124878 0.124878i
514514 0 0
515515 −9.19239 + 9.19239i −0.405065 + 0.405065i
516516 −2.82843 2.82843i −0.124515 0.124515i
517517 4.24264 + 4.24264i 0.186591 + 0.186591i
518518 32.0000i 1.40600i
519519 13.0000i 0.570637i
520520 4.24264 + 4.24264i 0.186052 + 0.186052i
521521 −14.1421 14.1421i −0.619578 0.619578i 0.325845 0.945423i 0.394351π-0.394351\pi
−0.945423 + 0.325845i 0.894351π0.894351\pi
522522 4.94975 4.94975i 0.216645 0.216645i
523523 26.0000 1.13690 0.568450 0.822718i 0.307543π-0.307543\pi
0.568450 + 0.822718i 0.307543π0.307543\pi
524524 −14.1421 + 14.1421i −0.617802 + 0.617802i
525525 16.0000i 0.698297i
526526 18.0000 0.784837
527527 0 0
528528 3.00000 0.130558
529529 13.0000i 0.565217i
530530 −9.19239 + 9.19239i −0.399292 + 0.399292i
531531 −9.00000 −0.390567
532532 11.3137 11.3137i 0.490511 0.490511i
533533 −8.48528 8.48528i −0.367538 0.367538i
534534 2.82843 + 2.82843i 0.122398 + 0.122398i
535535 15.0000i 0.648507i
536536 6.00000i 0.259161i
537537 0 0
538538 6.36396 + 6.36396i 0.274370 + 0.274370i
539539 −19.0919 + 19.0919i −0.822346 + 0.822346i
540540 −1.00000 −0.0430331
541541 −12.7279 + 12.7279i −0.547216 + 0.547216i −0.925635 0.378419i 0.876468π-0.876468\pi
0.378419 + 0.925635i 0.376468π0.376468\pi
542542 5.00000i 0.214768i
543543 −10.0000 −0.429141
544544 0 0
545545 −10.0000 −0.428353
546546 24.0000i 1.02711i
547547 18.3848 18.3848i 0.786076 0.786076i −0.194772 0.980848i 0.562397π-0.562397\pi
0.980848 + 0.194772i 0.0623968π0.0623968\pi
548548 −12.0000 −0.512615
549549 −7.07107 + 7.07107i −0.301786 + 0.301786i
550550 8.48528 + 8.48528i 0.361814 + 0.361814i
551551 −19.7990 19.7990i −0.843465 0.843465i
552552 6.00000i 0.255377i
553553 20.0000i 0.850487i
554554 −15.5563 15.5563i −0.660926 0.660926i
555555 −5.65685 5.65685i −0.240120 0.240120i
556556 5.65685 5.65685i 0.239904 0.239904i
557557 −14.0000 −0.593199 −0.296600 0.955002i 0.595853π-0.595853\pi
−0.296600 + 0.955002i 0.595853π0.595853\pi
558558 −2.12132 + 2.12132i −0.0898027 + 0.0898027i
559559 24.0000i 1.01509i
560560 −4.00000 −0.169031
561561 0 0
562562 0 0
563563 23.0000i 0.969334i 0.874699 + 0.484667i 0.161059π0.161059\pi
−0.874699 + 0.484667i 0.838941π0.838941\pi
564564 −1.41421 + 1.41421i −0.0595491 + 0.0595491i
565565 −10.0000 −0.420703
566566 2.82843 2.82843i 0.118888 0.118888i
567567 −2.82843 2.82843i −0.118783 0.118783i
568568 8.48528 + 8.48528i 0.356034 + 0.356034i
569569 18.0000i 0.754599i −0.926091 0.377300i 0.876853π-0.876853\pi
0.926091 0.377300i 0.123147π-0.123147\pi
570570 4.00000i 0.167542i
571571 14.1421 + 14.1421i 0.591830 + 0.591830i 0.938125 0.346296i 0.112561π-0.112561\pi
−0.346296 + 0.938125i 0.612561π0.612561\pi
572572 12.7279 + 12.7279i 0.532181 + 0.532181i
573573 −9.89949 + 9.89949i −0.413557 + 0.413557i
574574 8.00000 0.333914
575575 16.9706 16.9706i 0.707721 0.707721i
576576 1.00000i 0.0416667i
577577 30.0000 1.24892 0.624458 0.781058i 0.285320π-0.285320\pi
0.624458 + 0.781058i 0.285320π0.285320\pi
578578 0 0
579579 −9.00000 −0.374027
580580 7.00000i 0.290659i
581581 −33.9411 + 33.9411i −1.40812 + 1.40812i
582582 −3.00000 −0.124354
583583 −27.5772 + 27.5772i −1.14213 + 1.14213i
584584 −4.94975 4.94975i −0.204822 0.204822i
585585 −4.24264 4.24264i −0.175412 0.175412i
586586 19.0000i 0.784883i
587587 3.00000i 0.123823i 0.998082 + 0.0619116i 0.0197197π0.0197197\pi
−0.998082 + 0.0619116i 0.980280π0.980280\pi
588588 −6.36396 6.36396i −0.262445 0.262445i
589589 8.48528 + 8.48528i 0.349630 + 0.349630i
590590 6.36396 6.36396i 0.262000 0.262000i
591591 −10.0000 −0.411345
592592 −5.65685 + 5.65685i −0.232495 + 0.232495i
593593 6.00000i 0.246390i 0.992382 + 0.123195i 0.0393141π0.0393141\pi
−0.992382 + 0.123195i 0.960686π0.960686\pi
594594 −3.00000 −0.123091
595595 0 0
596596 15.0000 0.614424
597597 1.00000i 0.0409273i
598598 25.4558 25.4558i 1.04097 1.04097i
599599 4.00000 0.163436 0.0817178 0.996656i 0.473959π-0.473959\pi
0.0817178 + 0.996656i 0.473959π0.473959\pi
600600 −2.82843 + 2.82843i −0.115470 + 0.115470i
601601 3.53553 + 3.53553i 0.144217 + 0.144217i 0.775529 0.631312i 0.217483π-0.217483\pi
−0.631312 + 0.775529i 0.717483π0.717483\pi
602602 11.3137 + 11.3137i 0.461112 + 0.461112i
603603 6.00000i 0.244339i
604604 9.00000i 0.366205i
605605 1.41421 + 1.41421i 0.0574960 + 0.0574960i
606606 −12.0208 12.0208i −0.488312 0.488312i
607607 9.19239 9.19239i 0.373108 0.373108i −0.495500 0.868608i 0.665015π-0.665015\pi
0.868608 + 0.495500i 0.165015π0.165015\pi
608608 4.00000 0.162221
609609 −19.7990 + 19.7990i −0.802296 + 0.802296i
610610 10.0000i 0.404888i
611611 −12.0000 −0.485468
612612 0 0
613613 24.0000 0.969351 0.484675 0.874694i 0.338938π-0.338938\pi
0.484675 + 0.874694i 0.338938π0.338938\pi
614614 12.0000i 0.484281i
615615 −1.41421 + 1.41421i −0.0570266 + 0.0570266i
616616 −12.0000 −0.483494
617617 −8.48528 + 8.48528i −0.341605 + 0.341605i −0.856970 0.515366i 0.827656π-0.827656\pi
0.515366 + 0.856970i 0.327656π0.327656\pi
618618 −9.19239 9.19239i −0.369772 0.369772i
619619 7.07107 + 7.07107i 0.284210 + 0.284210i 0.834786 0.550575i 0.185592π-0.185592\pi
−0.550575 + 0.834786i 0.685592π0.685592\pi
620620 3.00000i 0.120483i
621621 6.00000i 0.240772i
622622 0 0
623623 −11.3137 11.3137i −0.453274 0.453274i
624624 −4.24264 + 4.24264i −0.169842 + 0.169842i
625625 −11.0000 −0.440000
626626 −9.89949 + 9.89949i −0.395663 + 0.395663i
627627 12.0000i 0.479234i
628628 12.0000 0.478852
629629 0 0
630630 4.00000 0.159364
631631 25.0000i 0.995234i −0.867397 0.497617i 0.834208π-0.834208\pi
0.867397 0.497617i 0.165792π-0.165792\pi
632632 −3.53553 + 3.53553i −0.140636 + 0.140636i
633633 8.00000 0.317971
634634 −1.41421 + 1.41421i −0.0561656 + 0.0561656i
635635 −11.3137 11.3137i −0.448971 0.448971i
636636 −9.19239 9.19239i −0.364502 0.364502i
637637 54.0000i 2.13956i
638638 21.0000i 0.831398i
639639 −8.48528 8.48528i −0.335673 0.335673i
640640 −0.707107 0.707107i −0.0279508 0.0279508i
641641 11.3137 11.3137i 0.446865 0.446865i −0.447446 0.894311i 0.647666π-0.647666\pi
0.894311 + 0.447446i 0.147666π0.147666\pi
642642 −15.0000 −0.592003
643643 26.8701 26.8701i 1.05965 1.05965i 0.0615475 0.998104i 0.480396π-0.480396\pi
0.998104 0.0615475i 0.0196036π-0.0196036\pi
644644 24.0000i 0.945732i
645645 −4.00000 −0.157500
646646 0 0
647647 4.00000 0.157256 0.0786281 0.996904i 0.474946π-0.474946\pi
0.0786281 + 0.996904i 0.474946π0.474946\pi
648648 1.00000i 0.0392837i
649649 19.0919 19.0919i 0.749422 0.749422i
650650 −24.0000 −0.941357
651651 8.48528 8.48528i 0.332564 0.332564i
652652 −4.24264 4.24264i −0.166155 0.166155i
653653 −15.5563 15.5563i −0.608767 0.608767i 0.333857 0.942624i 0.391650π-0.391650\pi
−0.942624 + 0.333857i 0.891650π0.891650\pi
654654 10.0000i 0.391031i
655655 20.0000i 0.781465i
656656 1.41421 + 1.41421i 0.0552158 + 0.0552158i
657657 4.94975 + 4.94975i 0.193108 + 0.193108i
658658 5.65685 5.65685i 0.220527 0.220527i
659659 3.00000 0.116863 0.0584317 0.998291i 0.481390π-0.481390\pi
0.0584317 + 0.998291i 0.481390π0.481390\pi
660660 2.12132 2.12132i 0.0825723 0.0825723i
661661 22.0000i 0.855701i 0.903850 + 0.427850i 0.140729π0.140729\pi
−0.903850 + 0.427850i 0.859271π0.859271\pi
662662 22.0000 0.855054
663663 0 0
664664 −12.0000 −0.465690
665665 16.0000i 0.620453i
666666 5.65685 5.65685i 0.219199 0.219199i
667667 42.0000 1.62625
668668 −5.65685 + 5.65685i −0.218870 + 0.218870i
669669 12.0208 + 12.0208i 0.464752 + 0.464752i
670670 −4.24264 4.24264i −0.163908 0.163908i
671671 30.0000i 1.15814i
672672 4.00000i 0.154303i
673673 24.0416 + 24.0416i 0.926737 + 0.926737i 0.997494 0.0707568i 0.0225414π-0.0225414\pi
−0.0707568 + 0.997494i 0.522541π0.522541\pi
674674 21.2132 + 21.2132i 0.817102 + 0.817102i
675675 2.82843 2.82843i 0.108866 0.108866i
676676 −23.0000 −0.884615
677677 15.5563 15.5563i 0.597879 0.597879i −0.341869 0.939748i 0.611060π-0.611060\pi
0.939748 + 0.341869i 0.111060π0.111060\pi
678678 10.0000i 0.384048i
679679 12.0000 0.460518
680680 0 0
681681 20.0000 0.766402
682682 9.00000i 0.344628i
683683 −19.0919 + 19.0919i −0.730531 + 0.730531i −0.970725 0.240194i 0.922789π-0.922789\pi
0.240194 + 0.970725i 0.422789π0.422789\pi
684684 −4.00000 −0.152944
685685 −8.48528 + 8.48528i −0.324206 + 0.324206i
686686 5.65685 + 5.65685i 0.215980 + 0.215980i
687687 9.89949 + 9.89949i 0.377689 + 0.377689i
688688 4.00000i 0.152499i
689689 78.0000i 2.97156i
690690 −4.24264 4.24264i −0.161515 0.161515i
691691 5.65685 + 5.65685i 0.215197 + 0.215197i 0.806471 0.591274i 0.201375π-0.201375\pi
−0.591274 + 0.806471i 0.701375π0.701375\pi
692692 −9.19239 + 9.19239i −0.349442 + 0.349442i
693693 12.0000 0.455842
694694 12.0208 12.0208i 0.456304 0.456304i
695695 8.00000i 0.303457i
696696 −7.00000 −0.265334
697697 0 0
698698 −12.0000 −0.454207
699699 24.0000i 0.907763i
700700 11.3137 11.3137i 0.427618 0.427618i
701701 15.0000 0.566542 0.283271 0.959040i 0.408580π-0.408580\pi
0.283271 + 0.959040i 0.408580π0.408580\pi
702702 4.24264 4.24264i 0.160128 0.160128i
703703 −22.6274 22.6274i −0.853409 0.853409i
704704 −2.12132 2.12132i −0.0799503 0.0799503i
705705 2.00000i 0.0753244i
706706 4.00000i 0.150542i
707707 48.0833 + 48.0833i 1.80836 + 1.80836i
708708 6.36396 + 6.36396i 0.239172 + 0.239172i
709709 5.65685 5.65685i 0.212448 0.212448i −0.592859 0.805306i 0.702001π-0.702001\pi
0.805306 + 0.592859i 0.202001π0.202001\pi
710710 12.0000 0.450352
711711 3.53553 3.53553i 0.132593 0.132593i
712712 4.00000i 0.149906i
713713 −18.0000 −0.674105
714714 0 0
715715 18.0000 0.673162
716716 0 0
717717 −18.3848 + 18.3848i −0.686592 + 0.686592i
718718 −30.0000 −1.11959
719719 8.48528 8.48528i 0.316448 0.316448i −0.530953 0.847401i 0.678166π-0.678166\pi
0.847401 + 0.530953i 0.178166π0.178166\pi
720720 0.707107 + 0.707107i 0.0263523 + 0.0263523i
721721 36.7696 + 36.7696i 1.36937 + 1.36937i
722722 3.00000i 0.111648i
723723 15.0000i 0.557856i
724724 7.07107 + 7.07107i 0.262794 + 0.262794i
725725 −19.7990 19.7990i −0.735316 0.735316i
726726 −1.41421 + 1.41421i −0.0524864 + 0.0524864i
727727 41.0000 1.52061 0.760303 0.649569i 0.225051π-0.225051\pi
0.760303 + 0.649569i 0.225051π0.225051\pi
728728 16.9706 16.9706i 0.628971 0.628971i
729729 1.00000i 0.0370370i
730730 −7.00000 −0.259082
731731 0 0
732732 10.0000 0.369611
733733 12.0000i 0.443230i −0.975134 0.221615i 0.928867π-0.928867\pi
0.975134 0.221615i 0.0711328π-0.0711328\pi
734734 −12.0208 + 12.0208i −0.443696 + 0.443696i
735735 −9.00000 −0.331970
736736 −4.24264 + 4.24264i −0.156386 + 0.156386i
737737 −12.7279 12.7279i −0.468839 0.468839i
738738 −1.41421 1.41421i −0.0520579 0.0520579i
739739 6.00000i 0.220714i −0.993892 0.110357i 0.964801π-0.964801\pi
0.993892 0.110357i 0.0351994π-0.0351994\pi
740740 8.00000i 0.294086i
741741 −16.9706 16.9706i −0.623429 0.623429i
742742 36.7696 + 36.7696i 1.34985 + 1.34985i
743743 −7.07107 + 7.07107i −0.259412 + 0.259412i −0.824815 0.565403i 0.808721π-0.808721\pi
0.565403 + 0.824815i 0.308721π0.308721\pi
744744 3.00000 0.109985
745745 10.6066 10.6066i 0.388596 0.388596i
746746 32.0000i 1.17160i
747747 12.0000 0.439057
748748 0 0
749749 60.0000 2.19235
750750 9.00000i 0.328634i
751751 −24.7487 + 24.7487i −0.903094 + 0.903094i −0.995703 0.0926084i 0.970480π-0.970480\pi
0.0926084 + 0.995703i 0.470480π0.470480\pi
752752 2.00000 0.0729325
753753 10.6066 10.6066i 0.386526 0.386526i
754754 −29.6985 29.6985i −1.08156 1.08156i
755755 6.36396 + 6.36396i 0.231608 + 0.231608i
756756 4.00000i 0.145479i
757757 38.0000i 1.38113i −0.723269 0.690567i 0.757361π-0.757361\pi
0.723269 0.690567i 0.242639π-0.242639\pi
758758 7.07107 + 7.07107i 0.256833 + 0.256833i
759759 −12.7279 12.7279i −0.461994 0.461994i
760760 2.82843 2.82843i 0.102598 0.102598i
761761 −34.0000 −1.23250 −0.616250 0.787551i 0.711349π-0.711349\pi
−0.616250 + 0.787551i 0.711349π0.711349\pi
762762 11.3137 11.3137i 0.409852 0.409852i
763763 40.0000i 1.44810i
764764 14.0000 0.506502
765765 0 0
766766 2.00000 0.0722629
767767 54.0000i 1.94983i
768768 0.707107 0.707107i 0.0255155 0.0255155i
769769 55.0000 1.98335 0.991675 0.128763i 0.0411007π-0.0411007\pi
0.991675 + 0.128763i 0.0411007π0.0411007\pi
770770 −8.48528 + 8.48528i −0.305788 + 0.305788i
771771 0 0
772772 6.36396 + 6.36396i 0.229044 + 0.229044i
773773 51.0000i 1.83434i 0.398493 + 0.917171i 0.369533π0.369533\pi
−0.398493 + 0.917171i 0.630467π0.630467\pi
774774 4.00000i 0.143777i
775775 8.48528 + 8.48528i 0.304800 + 0.304800i
776776 2.12132 + 2.12132i 0.0761510 + 0.0761510i
777777 −22.6274 + 22.6274i −0.811754 + 0.811754i
778778 −5.00000 −0.179259
779779 −5.65685 + 5.65685i −0.202678 + 0.202678i
780780 6.00000i 0.214834i
781781 36.0000 1.28818
782782 0 0
783783 7.00000 0.250160
784784 9.00000i 0.321429i
785785 8.48528 8.48528i 0.302853 0.302853i
786786 −20.0000 −0.713376
787787 16.9706 16.9706i 0.604935 0.604935i −0.336683 0.941618i 0.609305π-0.609305\pi
0.941618 + 0.336683i 0.109305π0.109305\pi
788788 7.07107 + 7.07107i 0.251896 + 0.251896i
789789 12.7279 + 12.7279i 0.453126 + 0.453126i
790790 5.00000i 0.177892i
791791 40.0000i 1.42224i
792792 2.12132 + 2.12132i 0.0753778 + 0.0753778i
793793 42.4264 + 42.4264i 1.50661 + 1.50661i
794794 15.5563 15.5563i 0.552074 0.552074i
795795 −13.0000 −0.461062
796796 0.707107 0.707107i 0.0250627 0.0250627i
797797 14.0000i 0.495905i −0.968772 0.247953i 0.920242π-0.920242\pi
0.968772 0.247953i 0.0797578π-0.0797578\pi
798798 16.0000 0.566394
799799 0 0
800800 4.00000 0.141421
801801 4.00000i 0.141333i
802802 −8.48528 + 8.48528i −0.299626 + 0.299626i
803803 −21.0000 −0.741074
804804 4.24264 4.24264i 0.149626 0.149626i
805805 16.9706 + 16.9706i 0.598134 + 0.598134i
806806 12.7279 + 12.7279i 0.448322 + 0.448322i
807807 9.00000i 0.316815i
808808 17.0000i 0.598058i
809809 −31.1127 31.1127i −1.09386 1.09386i −0.995112 0.0987522i 0.968515π-0.968515\pi
−0.0987522 0.995112i 0.531485π-0.531485\pi
810810 −0.707107 0.707107i −0.0248452 0.0248452i
811811 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
812812 28.0000 0.982607
813813 3.53553 3.53553i 0.123997 0.123997i
814814 24.0000i 0.841200i
815815 −6.00000 −0.210171
816816 0 0
817817 −16.0000 −0.559769
818818 19.0000i 0.664319i
819819 −16.9706 + 16.9706i −0.592999 + 0.592999i
820820 2.00000 0.0698430
821821 21.2132 21.2132i 0.740346 0.740346i −0.232299 0.972645i 0.574625π-0.574625\pi
0.972645 + 0.232299i 0.0746247π0.0746247\pi
822822 −8.48528 8.48528i −0.295958 0.295958i
823823 −27.5772 27.5772i −0.961280 0.961280i 0.0379983 0.999278i 0.487902π-0.487902\pi
−0.999278 + 0.0379983i 0.987902π0.987902\pi
824824 13.0000i 0.452876i
825825 12.0000i 0.417786i
826826 −25.4558 25.4558i −0.885722 0.885722i
827827 3.53553 + 3.53553i 0.122943 + 0.122943i 0.765901 0.642958i 0.222293π-0.222293\pi
−0.642958 + 0.765901i 0.722293π0.722293\pi
828828 4.24264 4.24264i 0.147442 0.147442i
829829 12.0000 0.416777 0.208389 0.978046i 0.433178π-0.433178\pi
0.208389 + 0.978046i 0.433178π0.433178\pi
830830 −8.48528 + 8.48528i −0.294528 + 0.294528i
831831 22.0000i 0.763172i
832832 6.00000 0.208013
833833 0 0
834834 8.00000 0.277017
835835 8.00000i 0.276851i
836836 8.48528 8.48528i 0.293470 0.293470i
837837 −3.00000 −0.103695
838838 2.12132 2.12132i 0.0732798 0.0732798i
839839 −21.2132 21.2132i −0.732361 0.732361i 0.238726 0.971087i 0.423270π-0.423270\pi
−0.971087 + 0.238726i 0.923270π0.923270\pi
840840 −2.82843 2.82843i −0.0975900 0.0975900i
841841 20.0000i 0.689655i
842842 22.0000i 0.758170i
843843 0 0
844844 −5.65685 5.65685i −0.194717 0.194717i
845845 −16.2635 + 16.2635i −0.559480 + 0.559480i
846846 −2.00000 −0.0687614
847847 5.65685 5.65685i 0.194372 0.194372i
848848 13.0000i 0.446422i
849849 4.00000 0.137280
850850 0 0
851851 48.0000 1.64542
852852 12.0000i 0.411113i
853853 −22.6274 + 22.6274i −0.774748 + 0.774748i −0.978932 0.204184i 0.934546π-0.934546\pi
0.204184 + 0.978932i 0.434546π0.434546\pi
854854 −40.0000 −1.36877
855855 −2.82843 + 2.82843i −0.0967302 + 0.0967302i
856856 10.6066 + 10.6066i 0.362526 + 0.362526i
857857 35.3553 + 35.3553i 1.20772 + 1.20772i 0.971765 + 0.235950i 0.0758202π0.0758202\pi
0.235950 + 0.971765i 0.424180π0.424180\pi
858858 18.0000i 0.614510i
859859 40.0000i 1.36478i 0.730987 + 0.682391i 0.239060π0.239060\pi
−0.730987 + 0.682391i 0.760940π0.760940\pi
860860 2.82843 + 2.82843i 0.0964486 + 0.0964486i
861861 5.65685 + 5.65685i 0.192785 + 0.192785i
862862 7.07107 7.07107i 0.240842 0.240842i
863863 30.0000 1.02121 0.510606 0.859815i 0.329421π-0.329421\pi
0.510606 + 0.859815i 0.329421π0.329421\pi
864864 −0.707107 + 0.707107i −0.0240563 + 0.0240563i
865865 13.0000i 0.442013i
866866 3.00000 0.101944
867867 0 0
868868 −12.0000 −0.407307
869869 15.0000i 0.508840i
870870 −4.94975 + 4.94975i −0.167812 + 0.167812i
871871 36.0000 1.21981
872872 −7.07107 + 7.07107i −0.239457 + 0.239457i
873873 −2.12132 2.12132i −0.0717958 0.0717958i
874874 −16.9706 16.9706i −0.574038 0.574038i
875875 36.0000i 1.21702i
876876 7.00000i 0.236508i
877877 12.7279 + 12.7279i 0.429791 + 0.429791i 0.888557 0.458766i 0.151708π-0.151708\pi
−0.458766 + 0.888557i 0.651708π0.651708\pi
878878 −19.7990 19.7990i −0.668184 0.668184i
879879 13.4350 13.4350i 0.453152 0.453152i
880880 −3.00000 −0.101130
881881 32.5269 32.5269i 1.09586 1.09586i 0.100970 0.994889i 0.467805π-0.467805\pi
0.994889 0.100970i 0.0321946π-0.0321946\pi
882882 9.00000i 0.303046i
883883 2.00000 0.0673054 0.0336527 0.999434i 0.489286π-0.489286\pi
0.0336527 + 0.999434i 0.489286π0.489286\pi
884884 0 0
885885 9.00000 0.302532
886886 12.0000i 0.403148i
887887 −25.4558 + 25.4558i −0.854724 + 0.854724i −0.990711 0.135987i 0.956579π-0.956579\pi
0.135987 + 0.990711i 0.456579π0.456579\pi
888888 −8.00000 −0.268462
889889 −45.2548 + 45.2548i −1.51780 + 1.51780i
890890 −2.82843 2.82843i −0.0948091 0.0948091i
891891 −2.12132 2.12132i −0.0710669 0.0710669i
892892 17.0000i 0.569202i
893893 8.00000i 0.267710i
894894 10.6066 + 10.6066i 0.354738 + 0.354738i
895895 0 0
896896 −2.82843 + 2.82843i −0.0944911 + 0.0944911i
897897 36.0000 1.20201
898898 2.82843 2.82843i 0.0943858 0.0943858i
899899 21.0000i 0.700389i
900900 −4.00000 −0.133333
901901 0 0
902902 6.00000 0.199778
903903 16.0000i 0.532447i
904904 −7.07107 + 7.07107i −0.235180 + 0.235180i
905905 10.0000 0.332411
906906 −6.36396 + 6.36396i −0.211428 + 0.211428i
907907 38.1838 + 38.1838i 1.26787 + 1.26787i 0.947186 + 0.320685i 0.103913π0.103913\pi
0.320685 + 0.947186i 0.396087π0.396087\pi
908908 −14.1421 14.1421i −0.469323 0.469323i
909909 17.0000i 0.563854i
910910 24.0000i 0.795592i
911911 −15.5563 15.5563i −0.515405 0.515405i 0.400773 0.916178i 0.368742π-0.368742\pi
−0.916178 + 0.400773i 0.868742π0.868742\pi
912912 2.82843 + 2.82843i 0.0936586 + 0.0936586i
913913 −25.4558 + 25.4558i −0.842465 + 0.842465i
914914 −17.0000 −0.562310
915915 7.07107 7.07107i 0.233762 0.233762i
916916 14.0000i 0.462573i
917917 80.0000 2.64183
918918 0 0
919919 16.0000 0.527791 0.263896 0.964551i 0.414993π-0.414993\pi
0.263896 + 0.964551i 0.414993π0.414993\pi
920920 6.00000i 0.197814i
921921 −8.48528 + 8.48528i −0.279600 + 0.279600i
922922 35.0000 1.15266
923923 −50.9117 + 50.9117i −1.67578 + 1.67578i
924924 −8.48528 8.48528i −0.279145 0.279145i
925925 −22.6274 22.6274i −0.743985 0.743985i
926926 5.00000i 0.164310i
927927 13.0000i 0.426976i
928928 4.94975 + 4.94975i 0.162483 + 0.162483i
929929 −5.65685 5.65685i −0.185595 0.185595i 0.608193 0.793789i 0.291894π-0.291894\pi
−0.793789 + 0.608193i 0.791894π0.791894\pi
930930 2.12132 2.12132i 0.0695608 0.0695608i
931931 −36.0000 −1.17985
932932 −16.9706 + 16.9706i −0.555889 + 0.555889i
933933 0 0
934934 3.00000 0.0981630
935935 0 0
936936 −6.00000 −0.196116
937937 19.0000i 0.620703i 0.950622 + 0.310351i 0.100447π0.100447\pi
−0.950622 + 0.310351i 0.899553π0.899553\pi
938938 −16.9706 + 16.9706i −0.554109 + 0.554109i
939939 −14.0000 −0.456873
940940 1.41421 1.41421i 0.0461266 0.0461266i
941941 21.2132 + 21.2132i 0.691531 + 0.691531i 0.962569 0.271038i 0.0873669π-0.0873669\pi
−0.271038 + 0.962569i 0.587367π0.587367\pi
942942 8.48528 + 8.48528i 0.276465 + 0.276465i
943943 12.0000i 0.390774i
944944 9.00000i 0.292925i
945945 2.82843 + 2.82843i 0.0920087 + 0.0920087i
946946 8.48528 + 8.48528i 0.275880 + 0.275880i
947947 −2.12132 + 2.12132i −0.0689336 + 0.0689336i −0.740733 0.671799i 0.765522π-0.765522\pi
0.671799 + 0.740733i 0.265522π0.265522\pi
948948 −5.00000 −0.162392
949949 29.6985 29.6985i 0.964054 0.964054i
950950 16.0000i 0.519109i
951951 −2.00000 −0.0648544
952952 0 0
953953 4.00000 0.129573 0.0647864 0.997899i 0.479363π-0.479363\pi
0.0647864 + 0.997899i 0.479363π0.479363\pi
954954 13.0000i 0.420891i
955955 9.89949 9.89949i 0.320340 0.320340i
956956 26.0000 0.840900
957957 −14.8492 + 14.8492i −0.480008 + 0.480008i
958958 −9.89949 9.89949i −0.319838 0.319838i
959959 33.9411 + 33.9411i 1.09602 + 1.09602i
960960 1.00000i 0.0322749i
961961 22.0000i 0.709677i
962962 −33.9411 33.9411i −1.09431 1.09431i
963963 −10.6066 10.6066i −0.341793 0.341793i
964964 10.6066 10.6066i 0.341616 0.341616i
965965 9.00000 0.289720
966966 −16.9706 + 16.9706i −0.546019 + 0.546019i
967967 13.0000i 0.418052i 0.977910 + 0.209026i 0.0670293π0.0670293\pi
−0.977910 + 0.209026i 0.932971π0.932971\pi
968968 2.00000 0.0642824
969969 0 0
970970 3.00000 0.0963242
971971 19.0000i 0.609739i −0.952394 0.304870i 0.901387π-0.901387\pi
0.952394 0.304870i 0.0986129π-0.0986129\pi
972972 0.707107 0.707107i 0.0226805 0.0226805i
973973 −32.0000 −1.02587
974974 −17.6777 + 17.6777i −0.566429 + 0.566429i
975975 −16.9706 16.9706i −0.543493 0.543493i
976976 −7.07107 7.07107i −0.226339 0.226339i
977977 16.0000i 0.511885i 0.966692 + 0.255943i 0.0823858π0.0823858\pi
−0.966692 + 0.255943i 0.917614π0.917614\pi
978978 6.00000i 0.191859i
979979 −8.48528 8.48528i −0.271191 0.271191i
980980 6.36396 + 6.36396i 0.203289 + 0.203289i
981981 7.07107 7.07107i 0.225762 0.225762i
982982 −23.0000 −0.733959
983983 9.89949 9.89949i 0.315745 0.315745i −0.531385 0.847130i 0.678328π-0.678328\pi
0.847130 + 0.531385i 0.178328π0.178328\pi
984984 2.00000i 0.0637577i
985985 10.0000 0.318626
986986 0 0
987987 8.00000 0.254643
988988 24.0000i 0.763542i
989989 16.9706 16.9706i 0.539633 0.539633i
990990 3.00000 0.0953463
991991 −2.82843 + 2.82843i −0.0898479 + 0.0898479i −0.750602 0.660754i 0.770237π-0.770237\pi
0.660754 + 0.750602i 0.270237π0.270237\pi
992992 −2.12132 2.12132i −0.0673520 0.0673520i
993993 15.5563 + 15.5563i 0.493666 + 0.493666i
994994 48.0000i 1.52247i
995995 1.00000i 0.0317021i
996996 −8.48528 8.48528i −0.268866 0.268866i
997997 −15.5563 15.5563i −0.492675 0.492675i 0.416473 0.909148i 0.363266π-0.363266\pi
−0.909148 + 0.416473i 0.863266π0.863266\pi
998998 −5.65685 + 5.65685i −0.179065 + 0.179065i
999999 8.00000 0.253109
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 1734.2.f.a.1483.2 4
17.2 even 8 1734.2.b.g.577.1 2
17.4 even 4 inner 1734.2.f.a.829.1 4
17.8 even 8 1734.2.a.a.1.1 1
17.9 even 8 1734.2.a.g.1.1 yes 1
17.13 even 4 inner 1734.2.f.a.829.2 4
17.15 even 8 1734.2.b.g.577.2 2
17.16 even 2 inner 1734.2.f.a.1483.1 4
51.8 odd 8 5202.2.a.m.1.1 1
51.26 odd 8 5202.2.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1734.2.a.a.1.1 1 17.8 even 8
1734.2.a.g.1.1 yes 1 17.9 even 8
1734.2.b.g.577.1 2 17.2 even 8
1734.2.b.g.577.2 2 17.15 even 8
1734.2.f.a.829.1 4 17.4 even 4 inner
1734.2.f.a.829.2 4 17.13 even 4 inner
1734.2.f.a.1483.1 4 17.16 even 2 inner
1734.2.f.a.1483.2 4 1.1 even 1 trivial
5202.2.a.i.1.1 1 51.26 odd 8
5202.2.a.m.1.1 1 51.8 odd 8