Properties

Label 495.3.j.a.298.1
Level 495495
Weight 33
Character 495.298
Analytic conductor 13.48813.488
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,3,Mod(298,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.298");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 495=32511 495 = 3^{2} \cdot 5 \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 495.j (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 13.487773085813.4877730858
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x204x19+8x18+4x17+212x16792x15+1480x14+148x13++38416 x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 212 x^{16} - 792 x^{15} + 1480 x^{14} + 148 x^{13} + \cdots + 38416 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 285 2^{8}\cdot 5
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 298.1
Root 2.278682.27868i-2.27868 - 2.27868i of defining polynomial
Character χ\chi == 495.298
Dual form 495.3.j.a.397.1

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+(2.27868+2.27868i)q26.38475iq4+(2.552484.29940i)q5+(3.30878+3.30878i)q7+(5.43407+5.43407i)q8+(15.6132+3.98068i)q103.31662q11+(7.65935+7.65935i)q1315.0793iq14+0.773991q16+(19.813919.8139i)q1717.4895iq19+(27.4506+16.2969i)q20+(7.557527.55752i)q22+(11.7334+11.7334i)q23+(11.9697+21.9483i)q2534.9064q26+(21.1258+21.1258i)q28+14.2026iq2944.6924q31+(23.5000+23.5000i)q32+90.2989iq34+(22.6714+5.78020i)q35+(2.84977+2.84977i)q37+(39.8529+39.8529i)q38+(9.4929137.2336i)q4061.2271q41+(10.248010.2480i)q43+21.1758iq4453.4734q46+(58.6916+58.6916i)q47+27.1039iq49+(22.737977.2881i)q50+(48.903048.9030i)q52+(45.5877+45.5877i)q53+(8.46561+14.2595i)q5535.9603q56+(32.363232.3632i)q58+3.71455iq5915.3228q61+(101.840101.840i)q62104.002iq64+(13.380352.4809i)q65+(23.6682+23.6682i)q67+(126.507126.507i)q68+(64.8320+38.4896i)q7066.4871q71+(93.3093+93.3093i)q7312.9874iq74111.666q76+(10.974010.9740i)q7757.1583iq79+(1.975593.32770i)q80+(139.517139.517i)q82+(45.349045.3490i)q83+(135.76234.6133i)q85+46.7036q86+(18.022818.0228i)q88+114.906iq8950.6863q91+(74.915074.9150i)q92267.479iq94+(75.1944+44.6415i)q95+(31.9248+31.9248i)q97+(61.761061.7610i)q98+O(q100)q+(-2.27868 + 2.27868i) q^{2} -6.38475i q^{4} +(-2.55248 - 4.29940i) q^{5} +(-3.30878 + 3.30878i) q^{7} +(5.43407 + 5.43407i) q^{8} +(15.6132 + 3.98068i) q^{10} -3.31662 q^{11} +(7.65935 + 7.65935i) q^{13} -15.0793i q^{14} +0.773991 q^{16} +(19.8139 - 19.8139i) q^{17} -17.4895i q^{19} +(-27.4506 + 16.2969i) q^{20} +(7.55752 - 7.55752i) q^{22} +(11.7334 + 11.7334i) q^{23} +(-11.9697 + 21.9483i) q^{25} -34.9064 q^{26} +(21.1258 + 21.1258i) q^{28} +14.2026i q^{29} -44.6924 q^{31} +(-23.5000 + 23.5000i) q^{32} +90.2989i q^{34} +(22.6714 + 5.78020i) q^{35} +(-2.84977 + 2.84977i) q^{37} +(39.8529 + 39.8529i) q^{38} +(9.49291 - 37.2336i) q^{40} -61.2271 q^{41} +(-10.2480 - 10.2480i) q^{43} +21.1758i q^{44} -53.4734 q^{46} +(-58.6916 + 58.6916i) q^{47} +27.1039i q^{49} +(-22.7379 - 77.2881i) q^{50} +(48.9030 - 48.9030i) q^{52} +(45.5877 + 45.5877i) q^{53} +(8.46561 + 14.2595i) q^{55} -35.9603 q^{56} +(-32.3632 - 32.3632i) q^{58} +3.71455i q^{59} -15.3228 q^{61} +(101.840 - 101.840i) q^{62} -104.002i q^{64} +(13.3803 - 52.4809i) q^{65} +(-23.6682 + 23.6682i) q^{67} +(-126.507 - 126.507i) q^{68} +(-64.8320 + 38.4896i) q^{70} -66.4871 q^{71} +(93.3093 + 93.3093i) q^{73} -12.9874i q^{74} -111.666 q^{76} +(10.9740 - 10.9740i) q^{77} -57.1583i q^{79} +(-1.97559 - 3.32770i) q^{80} +(139.517 - 139.517i) q^{82} +(-45.3490 - 45.3490i) q^{83} +(-135.762 - 34.6133i) q^{85} +46.7036 q^{86} +(-18.0228 - 18.0228i) q^{88} +114.906i q^{89} -50.6863 q^{91} +(74.9150 - 74.9150i) q^{92} -267.479i q^{94} +(-75.1944 + 44.6415i) q^{95} +(-31.9248 + 31.9248i) q^{97} +(-61.7610 - 61.7610i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q2+8q512q8+12q10+4q1316q1624q17+8q20+86q23+90q2596q26+76q2840q31184q32+60q35126q37184q38+620q98+O(q100) 20 q + 4 q^{2} + 8 q^{5} - 12 q^{8} + 12 q^{10} + 4 q^{13} - 16 q^{16} - 24 q^{17} + 8 q^{20} + 86 q^{23} + 90 q^{25} - 96 q^{26} + 76 q^{28} - 40 q^{31} - 184 q^{32} + 60 q^{35} - 126 q^{37} - 184 q^{38}+ \cdots - 620 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/495Z)×\left(\mathbb{Z}/495\mathbb{Z}\right)^\times.

nn 4646 5656 397397
χ(n)\chi(n) 11 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 −2.27868 + 2.27868i −1.13934 + 1.13934i −0.150770 + 0.988569i 0.548175π0.548175\pi
−0.988569 + 0.150770i 0.951825π0.951825\pi
33 0 0
44 6.38475i 1.59619i
55 −2.55248 4.29940i −0.510496 0.859880i
66 0 0
77 −3.30878 + 3.30878i −0.472684 + 0.472684i −0.902782 0.430098i 0.858479π-0.858479\pi
0.430098 + 0.902782i 0.358479π0.358479\pi
88 5.43407 + 5.43407i 0.679259 + 0.679259i
99 0 0
1010 15.6132 + 3.98068i 1.56132 + 0.398068i
1111 −3.31662 −0.301511
1212 0 0
1313 7.65935 + 7.65935i 0.589180 + 0.589180i 0.937409 0.348229i 0.113217π-0.113217\pi
−0.348229 + 0.937409i 0.613217π0.613217\pi
1414 15.0793i 1.07709i
1515 0 0
1616 0.773991 0.0483744
1717 19.8139 19.8139i 1.16552 1.16552i 0.182274 0.983248i 0.441654π-0.441654\pi
0.983248 0.182274i 0.0583458π-0.0583458\pi
1818 0 0
1919 17.4895i 0.920499i −0.887789 0.460250i 0.847760π-0.847760\pi
0.887789 0.460250i 0.152240π-0.152240\pi
2020 −27.4506 + 16.2969i −1.37253 + 0.814846i
2121 0 0
2222 7.55752 7.55752i 0.343524 0.343524i
2323 11.7334 + 11.7334i 0.510149 + 0.510149i 0.914572 0.404423i 0.132528π-0.132528\pi
−0.404423 + 0.914572i 0.632528π0.632528\pi
2424 0 0
2525 −11.9697 + 21.9483i −0.478789 + 0.877930i
2626 −34.9064 −1.34255
2727 0 0
2828 21.1258 + 21.1258i 0.754491 + 0.754491i
2929 14.2026i 0.489745i 0.969555 + 0.244873i 0.0787461π0.0787461\pi
−0.969555 + 0.244873i 0.921254π0.921254\pi
3030 0 0
3131 −44.6924 −1.44169 −0.720846 0.693096i 0.756246π-0.756246\pi
−0.720846 + 0.693096i 0.756246π0.756246\pi
3232 −23.5000 + 23.5000i −0.734374 + 0.734374i
3333 0 0
3434 90.2989i 2.65585i
3535 22.6714 + 5.78020i 0.647754 + 0.165148i
3636 0 0
3737 −2.84977 + 2.84977i −0.0770207 + 0.0770207i −0.744568 0.667547i 0.767344π-0.767344\pi
0.667547 + 0.744568i 0.267344π0.267344\pi
3838 39.8529 + 39.8529i 1.04876 + 1.04876i
3939 0 0
4040 9.49291 37.2336i 0.237323 0.930840i
4141 −61.2271 −1.49334 −0.746672 0.665192i 0.768350π-0.768350\pi
−0.746672 + 0.665192i 0.768350π0.768350\pi
4242 0 0
4343 −10.2480 10.2480i −0.238325 0.238325i 0.577832 0.816156i 0.303899π-0.303899\pi
−0.816156 + 0.577832i 0.803899π0.803899\pi
4444 21.1758i 0.481268i
4545 0 0
4646 −53.4734 −1.16247
4747 −58.6916 + 58.6916i −1.24876 + 1.24876i −0.292489 + 0.956269i 0.594484π0.594484\pi
−0.956269 + 0.292489i 0.905516π0.905516\pi
4848 0 0
4949 27.1039i 0.553141i
5050 −22.7379 77.2881i −0.454758 1.54576i
5151 0 0
5252 48.9030 48.9030i 0.940442 0.940442i
5353 45.5877 + 45.5877i 0.860145 + 0.860145i 0.991355 0.131210i 0.0418861π-0.0418861\pi
−0.131210 + 0.991355i 0.541886π0.541886\pi
5454 0 0
5555 8.46561 + 14.2595i 0.153920 + 0.259264i
5656 −35.9603 −0.642149
5757 0 0
5858 −32.3632 32.3632i −0.557986 0.557986i
5959 3.71455i 0.0629584i 0.999504 + 0.0314792i 0.0100218π0.0100218\pi
−0.999504 + 0.0314792i 0.989978π0.989978\pi
6060 0 0
6161 −15.3228 −0.251193 −0.125596 0.992081i 0.540084π-0.540084\pi
−0.125596 + 0.992081i 0.540084π0.540084\pi
6262 101.840 101.840i 1.64258 1.64258i
6363 0 0
6464 104.002i 1.62503i
6565 13.3803 52.4809i 0.205851 0.807399i
6666 0 0
6767 −23.6682 + 23.6682i −0.353257 + 0.353257i −0.861320 0.508063i 0.830362π-0.830362\pi
0.508063 + 0.861320i 0.330362π0.330362\pi
6868 −126.507 126.507i −1.86039 1.86039i
6969 0 0
7070 −64.8320 + 38.4896i −0.926172 + 0.549851i
7171 −66.4871 −0.936438 −0.468219 0.883613i 0.655104π-0.655104\pi
−0.468219 + 0.883613i 0.655104π0.655104\pi
7272 0 0
7373 93.3093 + 93.3093i 1.27821 + 1.27821i 0.941669 + 0.336541i 0.109257π0.109257\pi
0.336541 + 0.941669i 0.390743π0.390743\pi
7474 12.9874i 0.175505i
7575 0 0
7676 −111.666 −1.46929
7777 10.9740 10.9740i 0.142519 0.142519i
7878 0 0
7979 57.1583i 0.723523i −0.932271 0.361762i 0.882175π-0.882175\pi
0.932271 0.361762i 0.117825π-0.117825\pi
8080 −1.97559 3.32770i −0.0246949 0.0415962i
8181 0 0
8282 139.517 139.517i 1.70143 1.70143i
8383 −45.3490 45.3490i −0.546373 0.546373i 0.379017 0.925390i 0.376262π-0.376262\pi
−0.925390 + 0.379017i 0.876262π0.876262\pi
8484 0 0
8585 −135.762 34.6133i −1.59720 0.407216i
8686 46.7036 0.543065
8787 0 0
8888 −18.0228 18.0228i −0.204804 0.204804i
8989 114.906i 1.29107i 0.763729 + 0.645537i 0.223366π0.223366\pi
−0.763729 + 0.645537i 0.776634π0.776634\pi
9090 0 0
9191 −50.6863 −0.556992
9292 74.9150 74.9150i 0.814294 0.814294i
9393 0 0
9494 267.479i 2.84552i
9595 −75.1944 + 44.6415i −0.791519 + 0.469911i
9696 0 0
9797 −31.9248 + 31.9248i −0.329121 + 0.329121i −0.852252 0.523131i 0.824764π-0.824764\pi
0.523131 + 0.852252i 0.324764π0.324764\pi
9898 −61.7610 61.7610i −0.630215 0.630215i
9999 0 0
100100 140.134 + 76.4236i 1.40134 + 0.764236i
101101 −109.388 −1.08305 −0.541523 0.840686i 0.682152π-0.682152\pi
−0.541523 + 0.840686i 0.682152π0.682152\pi
102102 0 0
103103 −28.7421 28.7421i −0.279050 0.279050i 0.553680 0.832730i 0.313223π-0.313223\pi
−0.832730 + 0.553680i 0.813223π0.813223\pi
104104 83.2429i 0.800412i
105105 0 0
106106 −207.759 −1.95999
107107 53.4385 53.4385i 0.499425 0.499425i −0.411834 0.911259i 0.635112π-0.635112\pi
0.911259 + 0.411834i 0.135112π0.135112\pi
108108 0 0
109109 97.4174i 0.893738i 0.894600 + 0.446869i 0.147461π0.147461\pi
−0.894600 + 0.446869i 0.852539π0.852539\pi
110110 −51.7832 13.2024i −0.470757 0.120022i
111111 0 0
112112 −2.56097 + 2.56097i −0.0228658 + 0.0228658i
113113 109.416 + 109.416i 0.968280 + 0.968280i 0.999512 0.0312321i 0.00994311π-0.00994311\pi
−0.0312321 + 0.999512i 0.509943π0.509943\pi
114114 0 0
115115 20.4974 80.3961i 0.178238 0.699096i
116116 90.6801 0.781725
117117 0 0
118118 −8.46425 8.46425i −0.0717310 0.0717310i
119119 131.120i 1.10185i
120120 0 0
121121 11.0000 0.0909091
122122 34.9156 34.9156i 0.286194 0.286194i
123123 0 0
124124 285.350i 2.30121i
125125 124.917 4.55981i 0.999334 0.0364785i
126126 0 0
127127 −3.94652 + 3.94652i −0.0310749 + 0.0310749i −0.722474 0.691399i 0.756995π-0.756995\pi
0.691399 + 0.722474i 0.256995π0.256995\pi
128128 142.987 + 142.987i 1.11708 + 1.11708i
129129 0 0
130130 89.0977 + 150.077i 0.685367 + 1.15443i
131131 165.435 1.26286 0.631430 0.775433i 0.282468π-0.282468\pi
0.631430 + 0.775433i 0.282468π0.282468\pi
132132 0 0
133133 57.8690 + 57.8690i 0.435105 + 0.435105i
134134 107.864i 0.804958i
135135 0 0
136136 215.340 1.58338
137137 −47.3215 + 47.3215i −0.345412 + 0.345412i −0.858397 0.512985i 0.828540π-0.828540\pi
0.512985 + 0.858397i 0.328540π0.328540\pi
138138 0 0
139139 157.241i 1.13123i 0.824670 + 0.565614i 0.191361π0.191361\pi
−0.824670 + 0.565614i 0.808639π0.808639\pi
140140 36.9051 144.751i 0.263608 1.03394i
141141 0 0
142142 151.503 151.503i 1.06692 1.06692i
143143 −25.4032 25.4032i −0.177645 0.177645i
144144 0 0
145145 61.0627 36.2518i 0.421122 0.250013i
146146 −425.244 −2.91263
147147 0 0
148148 18.1950 + 18.1950i 0.122939 + 0.122939i
149149 91.9814i 0.617325i 0.951172 + 0.308663i 0.0998814π0.0998814\pi
−0.951172 + 0.308663i 0.900119π0.900119\pi
150150 0 0
151151 178.745 1.18374 0.591870 0.806034i 0.298390π-0.298390\pi
0.591870 + 0.806034i 0.298390π0.298390\pi
152152 95.0391 95.0391i 0.625257 0.625257i
153153 0 0
154154 50.0124i 0.324756i
155155 114.076 + 192.151i 0.735977 + 1.23968i
156156 0 0
157157 −85.3500 + 85.3500i −0.543631 + 0.543631i −0.924591 0.380961i 0.875593π-0.875593\pi
0.380961 + 0.924591i 0.375593π0.375593\pi
158158 130.245 + 130.245i 0.824338 + 0.824338i
159159 0 0
160160 161.019 + 41.0527i 1.00637 + 0.256579i
161161 −77.6468 −0.482278
162162 0 0
163163 34.8150 + 34.8150i 0.213589 + 0.213589i 0.805790 0.592201i 0.201741π-0.201741\pi
−0.592201 + 0.805790i 0.701741π0.701741\pi
164164 390.920i 2.38366i
165165 0 0
166166 206.671 1.24501
167167 8.73842 8.73842i 0.0523259 0.0523259i −0.680460 0.732786i 0.738220π-0.738220\pi
0.732786 + 0.680460i 0.238220π0.238220\pi
168168 0 0
169169 51.6688i 0.305733i
170170 388.231 230.486i 2.28371 1.35580i
171171 0 0
172172 −65.4306 + 65.4306i −0.380411 + 0.380411i
173173 −40.7527 40.7527i −0.235565 0.235565i 0.579446 0.815011i 0.303269π-0.303269\pi
−0.815011 + 0.579446i 0.803269π0.803269\pi
174174 0 0
175175 −33.0168 112.227i −0.188668 0.641299i
176176 −2.56704 −0.0145854
177177 0 0
178178 −261.833 261.833i −1.47097 1.47097i
179179 299.550i 1.67346i −0.547613 0.836732i 0.684463π-0.684463\pi
0.547613 0.836732i 0.315537π-0.315537\pi
180180 0 0
181181 −204.042 −1.12730 −0.563651 0.826013i 0.690604π-0.690604\pi
−0.563651 + 0.826013i 0.690604π0.690604\pi
182182 115.498 115.498i 0.634602 0.634602i
183183 0 0
184184 127.521i 0.693047i
185185 19.5263 + 4.97833i 0.105547 + 0.0269099i
186186 0 0
187187 −65.7152 + 65.7152i −0.351418 + 0.351418i
188188 374.731 + 374.731i 1.99325 + 1.99325i
189189 0 0
190190 69.6200 273.067i 0.366421 1.43720i
191191 −68.1555 −0.356835 −0.178418 0.983955i 0.557098π-0.557098\pi
−0.178418 + 0.983955i 0.557098π0.557098\pi
192192 0 0
193193 56.3440 + 56.3440i 0.291938 + 0.291938i 0.837845 0.545908i 0.183815π-0.183815\pi
−0.545908 + 0.837845i 0.683815π0.683815\pi
194194 145.493i 0.749962i
195195 0 0
196196 173.051 0.882916
197197 −61.2935 + 61.2935i −0.311134 + 0.311134i −0.845349 0.534215i 0.820607π-0.820607\pi
0.534215 + 0.845349i 0.320607π0.320607\pi
198198 0 0
199199 291.772i 1.46619i 0.680125 + 0.733096i 0.261925π0.261925\pi
−0.680125 + 0.733096i 0.738075π0.738075\pi
200200 −184.313 + 54.2241i −0.921563 + 0.271120i
201201 0 0
202202 249.259 249.259i 1.23396 1.23396i
203203 −46.9934 46.9934i −0.231494 0.231494i
204204 0 0
205205 156.281 + 263.240i 0.762346 + 1.28410i
206206 130.988 0.635864
207207 0 0
208208 5.92826 + 5.92826i 0.0285013 + 0.0285013i
209209 58.0061i 0.277541i
210210 0 0
211211 −93.8771 −0.444915 −0.222458 0.974942i 0.571408π-0.571408\pi
−0.222458 + 0.974942i 0.571408π0.571408\pi
212212 291.066 291.066i 1.37295 1.37295i
213213 0 0
214214 243.538i 1.13803i
215215 −17.9024 + 70.2178i −0.0832670 + 0.326594i
216216 0 0
217217 147.878 147.878i 0.681464 0.681464i
218218 −221.983 221.983i −1.01827 1.01827i
219219 0 0
220220 91.0433 54.0508i 0.413833 0.245685i
221221 303.523 1.37341
222222 0 0
223223 −158.088 158.088i −0.708915 0.708915i 0.257392 0.966307i 0.417137π-0.417137\pi
−0.966307 + 0.257392i 0.917137π0.917137\pi
224224 155.513i 0.694253i
225225 0 0
226226 −498.646 −2.20640
227227 −158.917 + 158.917i −0.700076 + 0.700076i −0.964427 0.264351i 0.914842π-0.914842\pi
0.264351 + 0.964427i 0.414842π0.414842\pi
228228 0 0
229229 43.6426i 0.190579i 0.995450 + 0.0952895i 0.0303777π0.0303777\pi
−0.995450 + 0.0952895i 0.969622π0.969622\pi
230230 136.490 + 229.904i 0.593434 + 0.999582i
231231 0 0
232232 −77.1780 + 77.1780i −0.332664 + 0.332664i
233233 −231.736 231.736i −0.994574 0.994574i 0.00541090 0.999985i 0.498278π-0.498278\pi
−0.999985 + 0.00541090i 0.998278π0.998278\pi
234234 0 0
235235 402.148 + 102.530i 1.71127 + 0.436297i
236236 23.7164 0.100493
237237 0 0
238238 −298.780 298.780i −1.25538 1.25538i
239239 203.850i 0.852930i −0.904504 0.426465i 0.859759π-0.859759\pi
0.904504 0.426465i 0.140241π-0.140241\pi
240240 0 0
241241 96.8670 0.401938 0.200969 0.979598i 0.435591π-0.435591\pi
0.200969 + 0.979598i 0.435591π0.435591\pi
242242 −25.0655 + 25.0655i −0.103576 + 0.103576i
243243 0 0
244244 97.8320i 0.400951i
245245 116.531 69.1821i 0.475635 0.282376i
246246 0 0
247247 133.958 133.958i 0.542340 0.542340i
248248 −242.862 242.862i −0.979282 0.979282i
249249 0 0
250250 −274.255 + 295.036i −1.09702 + 1.18014i
251251 165.654 0.659978 0.329989 0.943985i 0.392955π-0.392955\pi
0.329989 + 0.943985i 0.392955π0.392955\pi
252252 0 0
253253 −38.9154 38.9154i −0.153816 0.153816i
254254 17.9857i 0.0708098i
255255 0 0
256256 −235.634 −0.920445
257257 −168.525 + 168.525i −0.655740 + 0.655740i −0.954369 0.298629i 0.903471π-0.903471\pi
0.298629 + 0.954369i 0.403471π0.403471\pi
258258 0 0
259259 18.8585i 0.0728128i
260260 −335.077 85.4298i −1.28876 0.328576i
261261 0 0
262262 −376.972 + 376.972i −1.43883 + 1.43883i
263263 50.7899 + 50.7899i 0.193117 + 0.193117i 0.797042 0.603924i 0.206397π-0.206397\pi
−0.603924 + 0.797042i 0.706397π0.706397\pi
264264 0 0
265265 79.6382 312.361i 0.300522 1.17872i
266266 −263.729 −0.991464
267267 0 0
268268 151.115 + 151.115i 0.563864 + 0.563864i
269269 256.648i 0.954081i 0.878881 + 0.477041i 0.158291π0.158291\pi
−0.878881 + 0.477041i 0.841709π0.841709\pi
270270 0 0
271271 −215.163 −0.793958 −0.396979 0.917828i 0.629941π-0.629941\pi
−0.396979 + 0.917828i 0.629941π0.629941\pi
272272 15.3358 15.3358i 0.0563815 0.0563815i
273273 0 0
274274 215.661i 0.787083i
275275 39.6991 72.7941i 0.144360 0.264706i
276276 0 0
277277 73.9418 73.9418i 0.266938 0.266938i −0.560927 0.827865i 0.689555π-0.689555\pi
0.827865 + 0.560927i 0.189555π0.189555\pi
278278 −358.301 358.301i −1.28885 1.28885i
279279 0 0
280280 91.7880 + 154.608i 0.327814 + 0.552171i
281281 −190.836 −0.679133 −0.339566 0.940582i 0.610280π-0.610280\pi
−0.339566 + 0.940582i 0.610280π0.610280\pi
282282 0 0
283283 −87.1090 87.1090i −0.307806 0.307806i 0.536252 0.844058i 0.319840π-0.319840\pi
−0.844058 + 0.536252i 0.819840π0.819840\pi
284284 424.503i 1.49473i
285285 0 0
286286 115.771 0.404795
287287 202.587 202.587i 0.705879 0.705879i
288288 0 0
289289 496.179i 1.71688i
290290 −56.5360 + 221.749i −0.194952 + 0.764650i
291291 0 0
292292 595.756 595.756i 2.04026 2.04026i
293293 317.484 + 317.484i 1.08356 + 1.08356i 0.996174 + 0.0873871i 0.0278517π0.0278517\pi
0.0873871 + 0.996174i 0.472148π0.472148\pi
294294 0 0
295295 15.9703 9.48129i 0.0541367 0.0321400i
296296 −30.9717 −0.104634
297297 0 0
298298 −209.596 209.596i −0.703343 0.703343i
299299 179.741i 0.601140i
300300 0 0
301301 67.8166 0.225304
302302 −407.302 + 407.302i −1.34868 + 1.34868i
303303 0 0
304304 13.5367i 0.0445286i
305305 39.1110 + 65.8787i 0.128233 + 0.215996i
306306 0 0
307307 −263.140 + 263.140i −0.857132 + 0.857132i −0.990999 0.133867i 0.957261π-0.957261\pi
0.133867 + 0.990999i 0.457261π0.457261\pi
308308 −70.0662 70.0662i −0.227488 0.227488i
309309 0 0
310310 −697.793 177.906i −2.25095 0.573891i
311311 −301.613 −0.969816 −0.484908 0.874565i 0.661147π-0.661147\pi
−0.484908 + 0.874565i 0.661147π0.661147\pi
312312 0 0
313313 98.0189 + 98.0189i 0.313159 + 0.313159i 0.846132 0.532973i 0.178925π-0.178925\pi
−0.532973 + 0.846132i 0.678925π0.678925\pi
314314 388.971i 1.23876i
315315 0 0
316316 −364.941 −1.15488
317317 −232.617 + 232.617i −0.733806 + 0.733806i −0.971372 0.237565i 0.923651π-0.923651\pi
0.237565 + 0.971372i 0.423651π0.423651\pi
318318 0 0
319319 47.1047i 0.147664i
320320 −447.145 + 265.462i −1.39733 + 0.829569i
321321 0 0
322322 176.932 176.932i 0.549479 0.549479i
323323 −346.535 346.535i −1.07286 1.07286i
324324 0 0
325325 −259.789 + 76.4291i −0.799352 + 0.235166i
326326 −158.664 −0.486701
327327 0 0
328328 −332.713 332.713i −1.01437 1.01437i
329329 388.396i 1.18053i
330330 0 0
331331 124.210 0.375256 0.187628 0.982240i 0.439920π-0.439920\pi
0.187628 + 0.982240i 0.439920π0.439920\pi
332332 −289.542 + 289.542i −0.872113 + 0.872113i
333333 0 0
334334 39.8241i 0.119234i
335335 162.172 + 41.3466i 0.484095 + 0.123423i
336336 0 0
337337 248.427 248.427i 0.737171 0.737171i −0.234858 0.972030i 0.575463π-0.575463\pi
0.972030 + 0.234858i 0.0754626π0.0754626\pi
338338 117.737 + 117.737i 0.348333 + 0.348333i
339339 0 0
340340 −220.997 + 866.808i −0.649992 + 2.54943i
341341 148.228 0.434686
342342 0 0
343343 −251.811 251.811i −0.734144 0.734144i
344344 111.376i 0.323768i
345345 0 0
346346 185.724 0.536776
347347 −194.711 + 194.711i −0.561127 + 0.561127i −0.929628 0.368501i 0.879871π-0.879871\pi
0.368501 + 0.929628i 0.379871π0.379871\pi
348348 0 0
349349 23.5545i 0.0674914i −0.999430 0.0337457i 0.989256π-0.989256\pi
0.999430 0.0337457i 0.0107436π-0.0107436\pi
350350 330.965 + 180.495i 0.945613 + 0.515700i
351351 0 0
352352 77.9406 77.9406i 0.221422 0.221422i
353353 60.4688 + 60.4688i 0.171300 + 0.171300i 0.787550 0.616251i 0.211349π-0.211349\pi
−0.616251 + 0.787550i 0.711349π0.711349\pi
354354 0 0
355355 169.707 + 285.855i 0.478047 + 0.805224i
356356 733.643 2.06080
357357 0 0
358358 682.578 + 682.578i 1.90664 + 1.90664i
359359 502.684i 1.40024i −0.714028 0.700118i 0.753131π-0.753131\pi
0.714028 0.700118i 0.246869π-0.246869\pi
360360 0 0
361361 55.1177 0.152681
362362 464.945 464.945i 1.28438 1.28438i
363363 0 0
364364 323.619i 0.889063i
365365 163.004 639.344i 0.446587 1.75163i
366366 0 0
367367 −402.334 + 402.334i −1.09628 + 1.09628i −0.101437 + 0.994842i 0.532344π0.532344\pi
−0.994842 + 0.101437i 0.967656π0.967656\pi
368368 9.08157 + 9.08157i 0.0246782 + 0.0246782i
369369 0 0
370370 −55.8381 + 33.1500i −0.150914 + 0.0895947i
371371 −301.680 −0.813153
372372 0 0
373373 −129.594 129.594i −0.347437 0.347437i 0.511717 0.859154i 0.329010π-0.329010\pi
−0.859154 + 0.511717i 0.829010π0.829010\pi
374374 299.487i 0.800769i
375375 0 0
376376 −637.869 −1.69646
377377 −108.783 + 108.783i −0.288548 + 0.288548i
378378 0 0
379379 308.983i 0.815260i −0.913147 0.407630i 0.866355π-0.866355\pi
0.913147 0.407630i 0.133645π-0.133645\pi
380380 285.025 + 480.097i 0.750066 + 1.26341i
381381 0 0
382382 155.305 155.305i 0.406556 0.406556i
383383 137.024 + 137.024i 0.357765 + 0.357765i 0.862989 0.505223i 0.168590π-0.168590\pi
−0.505223 + 0.862989i 0.668590π0.668590\pi
384384 0 0
385385 −75.1925 19.1707i −0.195305 0.0497941i
386386 −256.780 −0.665232
387387 0 0
388388 203.832 + 203.832i 0.525339 + 0.525339i
389389 219.114i 0.563275i 0.959521 + 0.281637i 0.0908775π0.0908775\pi
−0.959521 + 0.281637i 0.909122π0.909122\pi
390390 0 0
391391 464.970 1.18918
392392 −147.284 + 147.284i −0.375726 + 0.375726i
393393 0 0
394394 279.336i 0.708975i
395395 −245.747 + 145.895i −0.622143 + 0.369355i
396396 0 0
397397 447.147 447.147i 1.12631 1.12631i 0.135542 0.990772i 0.456722π-0.456722\pi
0.990772 0.135542i 0.0432777π-0.0432777\pi
398398 −664.855 664.855i −1.67049 1.67049i
399399 0 0
400400 −9.26445 + 16.9878i −0.0231611 + 0.0424694i
401401 697.196 1.73864 0.869321 0.494247i 0.164556π-0.164556\pi
0.869321 + 0.494247i 0.164556π0.164556\pi
402402 0 0
403403 −342.315 342.315i −0.849416 0.849416i
404404 698.412i 1.72874i
405405 0 0
406406 214.166 0.527501
407407 9.45161 9.45161i 0.0232226 0.0232226i
408408 0 0
409409 37.7115i 0.0922043i 0.998937 + 0.0461021i 0.0146800π0.0146800\pi
−0.998937 + 0.0461021i 0.985320π0.985320\pi
410410 −955.953 243.725i −2.33159 0.594452i
411411 0 0
412412 −183.511 + 183.511i −0.445415 + 0.445415i
413413 −12.2906 12.2906i −0.0297594 0.0297594i
414414 0 0
415415 −79.2212 + 310.726i −0.190894 + 0.748736i
416416 −359.989 −0.865357
417417 0 0
418418 −132.177 132.177i −0.316213 0.316213i
419419 486.001i 1.15991i −0.814650 0.579953i 0.803071π-0.803071\pi
0.814650 0.579953i 0.196929π-0.196929\pi
420420 0 0
421421 −388.904 −0.923762 −0.461881 0.886942i 0.652825π-0.652825\pi
−0.461881 + 0.886942i 0.652825π0.652825\pi
422422 213.916 213.916i 0.506909 0.506909i
423423 0 0
424424 495.453i 1.16852i
425425 197.714 + 672.046i 0.465208 + 1.58129i
426426 0 0
427427 50.6997 50.6997i 0.118735 0.118735i
428428 −341.191 341.191i −0.797175 0.797175i
429429 0 0
430430 −119.210 200.797i −0.277232 0.466971i
431431 −504.929 −1.17153 −0.585764 0.810482i 0.699205π-0.699205\pi
−0.585764 + 0.810482i 0.699205π0.699205\pi
432432 0 0
433433 150.370 + 150.370i 0.347274 + 0.347274i 0.859093 0.511819i 0.171028π-0.171028\pi
−0.511819 + 0.859093i 0.671028π0.671028\pi
434434 673.931i 1.55284i
435435 0 0
436436 621.985 1.42657
437437 205.212 205.212i 0.469592 0.469592i
438438 0 0
439439 210.919i 0.480454i 0.970717 + 0.240227i 0.0772219π0.0772219\pi
−0.970717 + 0.240227i 0.922778π0.922778\pi
440440 −31.4844 + 123.490i −0.0715555 + 0.280659i
441441 0 0
442442 −691.630 + 691.630i −1.56477 + 1.56477i
443443 442.849 + 442.849i 0.999660 + 0.999660i 1.00000 0.000339697i 0.000108129π-0.000108129\pi
−0.000339697 1.00000i 0.500108π0.500108\pi
444444 0 0
445445 494.026 293.294i 1.11017 0.659088i
446446 720.463 1.61539
447447 0 0
448448 344.119 + 344.119i 0.768123 + 0.768123i
449449 641.685i 1.42914i −0.699563 0.714571i 0.746622π-0.746622\pi
0.699563 0.714571i 0.253378π-0.253378\pi
450450 0 0
451451 203.067 0.450260
452452 698.591 698.591i 1.54556 1.54556i
453453 0 0
454454 724.243i 1.59525i
455455 129.376 + 217.921i 0.284342 + 0.478946i
456456 0 0
457457 −103.709 + 103.709i −0.226934 + 0.226934i −0.811411 0.584477i 0.801300π-0.801300\pi
0.584477 + 0.811411i 0.301300π0.301300\pi
458458 −99.4474 99.4474i −0.217134 0.217134i
459459 0 0
460460 −513.309 130.871i −1.11589 0.284502i
461461 800.040 1.73544 0.867722 0.497050i 0.165583π-0.165583\pi
0.867722 + 0.497050i 0.165583π0.165583\pi
462462 0 0
463463 252.447 + 252.447i 0.545242 + 0.545242i 0.925061 0.379819i 0.124014π-0.124014\pi
−0.379819 + 0.925061i 0.624014π0.624014\pi
464464 10.9927i 0.0236911i
465465 0 0
466466 1056.10 2.26631
467467 −80.1036 + 80.1036i −0.171528 + 0.171528i −0.787650 0.616122i 0.788703π-0.788703\pi
0.616122 + 0.787650i 0.288703π0.288703\pi
468468 0 0
469469 156.626i 0.333957i
470470 −1150.00 + 682.733i −2.44680 + 1.45262i
471471 0 0
472472 −20.1851 + 20.1851i −0.0427651 + 0.0427651i
473473 33.9886 + 33.9886i 0.0718576 + 0.0718576i
474474 0 0
475475 383.864 + 209.344i 0.808134 + 0.440725i
476476 837.166 1.75875
477477 0 0
478478 464.509 + 464.509i 0.971776 + 0.971776i
479479 411.116i 0.858280i −0.903238 0.429140i 0.858817π-0.858817\pi
0.903238 0.429140i 0.141183π-0.141183\pi
480480 0 0
481481 −43.6547 −0.0907582
482482 −220.729 + 220.729i −0.457944 + 0.457944i
483483 0 0
484484 70.2322i 0.145108i
485485 218.745 + 55.7702i 0.451020 + 0.114990i
486486 0 0
487487 −212.163 + 212.163i −0.435652 + 0.435652i −0.890546 0.454894i 0.849677π-0.849677\pi
0.454894 + 0.890546i 0.349677π0.349677\pi
488488 −83.2650 83.2650i −0.170625 0.170625i
489489 0 0
490490 −107.892 + 423.179i −0.220187 + 0.863631i
491491 −113.699 −0.231566 −0.115783 0.993275i 0.536938π-0.536938\pi
−0.115783 + 0.993275i 0.536938π0.536938\pi
492492 0 0
493493 281.409 + 281.409i 0.570809 + 0.570809i
494494 610.495i 1.23582i
495495 0 0
496496 −34.5915 −0.0697410
497497 219.991 219.991i 0.442639 0.442639i
498498 0 0
499499 343.023i 0.687421i −0.939076 0.343711i 0.888316π-0.888316\pi
0.939076 0.343711i 0.111684π-0.111684\pi
500500 −29.1133 797.562i −0.0582265 1.59512i
501501 0 0
502502 −377.473 + 377.473i −0.751939 + 0.751939i
503503 625.342 + 625.342i 1.24323 + 1.24323i 0.958655 + 0.284571i 0.0918510π0.0918510\pi
0.284571 + 0.958655i 0.408149π0.408149\pi
504504 0 0
505505 279.209 + 470.301i 0.552890 + 0.931290i
506506 177.351 0.350497
507507 0 0
508508 25.1975 + 25.1975i 0.0496014 + 0.0496014i
509509 106.269i 0.208780i 0.994536 + 0.104390i 0.0332890π0.0332890\pi
−0.994536 + 0.104390i 0.966711π0.966711\pi
510510 0 0
511511 −617.481 −1.20838
512512 −35.0124 + 35.0124i −0.0683837 + 0.0683837i
513513 0 0
514514 768.029i 1.49422i
515515 −50.2103 + 196.937i −0.0974957 + 0.382403i
516516 0 0
517517 194.658 194.658i 0.376515 0.376515i
518518 42.9725 + 42.9725i 0.0829585 + 0.0829585i
519519 0 0
520520 357.895 212.476i 0.688259 0.408607i
521521 −483.272 −0.927586 −0.463793 0.885944i 0.653512π-0.653512\pi
−0.463793 + 0.885944i 0.653512π0.653512\pi
522522 0 0
523523 −224.917 224.917i −0.430052 0.430052i 0.458594 0.888646i 0.348353π-0.348353\pi
−0.888646 + 0.458594i 0.848353π0.848353\pi
524524 1056.26i 2.01576i
525525 0 0
526526 −231.468 −0.440052
527527 −885.530 + 885.530i −1.68032 + 1.68032i
528528 0 0
529529 253.653i 0.479495i
530530 530.301 + 893.241i 1.00057 + 1.68536i
531531 0 0
532532 369.479 369.479i 0.694509 0.694509i
533533 −468.960 468.960i −0.879849 0.879849i
534534 0 0
535535 −366.154 93.3530i −0.684400 0.174492i
536536 −257.229 −0.479906
537537 0 0
538538 −584.818 584.818i −1.08702 1.08702i
539539 89.8934i 0.166778i
540540 0 0
541541 507.591 0.938246 0.469123 0.883133i 0.344570π-0.344570\pi
0.469123 + 0.883133i 0.344570π0.344570\pi
542542 490.286 490.286i 0.904587 0.904587i
543543 0 0
544544 931.251i 1.71186i
545545 418.837 248.656i 0.768507 0.456249i
546546 0 0
547547 −224.439 + 224.439i −0.410309 + 0.410309i −0.881846 0.471537i 0.843699π-0.843699\pi
0.471537 + 0.881846i 0.343699π0.343699\pi
548548 302.136 + 302.136i 0.551342 + 0.551342i
549549 0 0
550550 75.4130 + 256.336i 0.137115 + 0.466065i
551551 248.396 0.450810
552552 0 0
553553 189.125 + 189.125i 0.341997 + 0.341997i
554554 336.979i 0.608265i
555555 0 0
556556 1003.94 1.80565
557557 −40.3442 + 40.3442i −0.0724312 + 0.0724312i −0.742394 0.669963i 0.766310π-0.766310\pi
0.669963 + 0.742394i 0.266310π0.266310\pi
558558 0 0
559559 156.985i 0.280832i
560560 17.5475 + 4.47382i 0.0313347 + 0.00798896i
561561 0 0
562562 434.854 434.854i 0.773762 0.773762i
563563 75.8838 + 75.8838i 0.134785 + 0.134785i 0.771280 0.636496i 0.219617π-0.219617\pi
−0.636496 + 0.771280i 0.719617π0.719617\pi
564564 0 0
565565 191.141 749.703i 0.338302 1.32691i
566566 396.987 0.701390
567567 0 0
568568 −361.295 361.295i −0.636084 0.636084i
569569 940.148i 1.65228i −0.563464 0.826141i 0.690532π-0.690532\pi
0.563464 0.826141i 0.309468π-0.309468\pi
570570 0 0
571571 −77.9393 −0.136496 −0.0682481 0.997668i 0.521741π-0.521741\pi
−0.0682481 + 0.997668i 0.521741π0.521741\pi
572572 −162.193 + 162.193i −0.283554 + 0.283554i
573573 0 0
574574 923.263i 1.60847i
575575 −397.974 + 117.083i −0.692129 + 0.203622i
576576 0 0
577577 −500.861 + 500.861i −0.868043 + 0.868043i −0.992256 0.124213i 0.960359π-0.960359\pi
0.124213 + 0.992256i 0.460359π0.460359\pi
578578 1130.63 + 1130.63i 1.95611 + 1.95611i
579579 0 0
580580 −231.459 389.870i −0.399067 0.672190i
581581 300.100 0.516523
582582 0 0
583583 −151.197 151.197i −0.259343 0.259343i
584584 1014.10i 1.73647i
585585 0 0
586586 −1446.89 −2.46909
587587 101.416 101.416i 0.172771 0.172771i −0.615425 0.788196i 0.711016π-0.711016\pi
0.788196 + 0.615425i 0.211016π0.211016\pi
588588 0 0
589589 781.648i 1.32708i
590590 −14.7864 + 57.9960i −0.0250617 + 0.0982984i
591591 0 0
592592 −2.20569 + 2.20569i −0.00372583 + 0.00372583i
593593 −597.297 597.297i −1.00725 1.00725i −0.999974 0.00727231i 0.997685π-0.997685\pi
−0.00727231 0.999974i 0.502315π-0.502315\pi
594594 0 0
595595 563.736 334.680i 0.947456 0.562487i
596596 587.278 0.985366
597597 0 0
598598 −409.572 409.572i −0.684902 0.684902i
599599 347.771i 0.580585i 0.956938 + 0.290293i 0.0937527π0.0937527\pi
−0.956938 + 0.290293i 0.906247π0.906247\pi
600600 0 0
601601 −192.174 −0.319757 −0.159878 0.987137i 0.551110π-0.551110\pi
−0.159878 + 0.987137i 0.551110π0.551110\pi
602602 −154.532 + 154.532i −0.256698 + 0.256698i
603603 0 0
604604 1141.24i 1.88947i
605605 −28.0773 47.2934i −0.0464087 0.0781709i
606606 0 0
607607 −74.3868 + 74.3868i −0.122548 + 0.122548i −0.765721 0.643173i 0.777618π-0.777618\pi
0.643173 + 0.765721i 0.277618π0.277618\pi
608608 411.002 + 411.002i 0.675991 + 0.675991i
609609 0 0
610610 −239.238 60.9950i −0.392193 0.0999918i
611611 −899.079 −1.47149
612612 0 0
613613 599.202 + 599.202i 0.977491 + 0.977491i 0.999752 0.0222612i 0.00708655π-0.00708655\pi
−0.0222612 + 0.999752i 0.507087π0.507087\pi
614614 1199.22i 1.95313i
615615 0 0
616616 119.267 0.193615
617617 95.9908 95.9908i 0.155577 0.155577i −0.625027 0.780603i 0.714912π-0.714912\pi
0.780603 + 0.625027i 0.214912π0.214912\pi
618618 0 0
619619 349.611i 0.564800i 0.959297 + 0.282400i 0.0911305π0.0911305\pi
−0.959297 + 0.282400i 0.908869π0.908869\pi
620620 1226.83 728.349i 1.97876 1.17476i
621621 0 0
622622 687.279 687.279i 1.10495 1.10495i
623623 −380.198 380.198i −0.610270 0.610270i
624624 0 0
625625 −338.452 525.429i −0.541523 0.840686i
626626 −446.707 −0.713590
627627 0 0
628628 544.938 + 544.938i 0.867736 + 0.867736i
629629 112.930i 0.179539i
630630 0 0
631631 249.068 0.394720 0.197360 0.980331i 0.436763π-0.436763\pi
0.197360 + 0.980331i 0.436763π0.436763\pi
632632 310.602 310.602i 0.491460 0.491460i
633633 0 0
634634 1060.12i 1.67211i
635635 27.0411 + 6.89426i 0.0425843 + 0.0108571i
636636 0 0
637637 −207.598 + 207.598i −0.325900 + 0.325900i
638638 107.337 + 107.337i 0.168239 + 0.168239i
639639 0 0
640640 249.787 979.727i 0.390292 1.53082i
641641 −1112.98 −1.73632 −0.868159 0.496287i 0.834696π-0.834696\pi
−0.868159 + 0.496287i 0.834696π0.834696\pi
642642 0 0
643643 −396.093 396.093i −0.616008 0.616008i 0.328497 0.944505i 0.393458π-0.393458\pi
−0.944505 + 0.328497i 0.893458π0.893458\pi
644644 495.755i 0.769806i
645645 0 0
646646 1579.28 2.44471
647647 −190.770 + 190.770i −0.294854 + 0.294854i −0.838994 0.544140i 0.816856π-0.816856\pi
0.544140 + 0.838994i 0.316856π0.316856\pi
648648 0 0
649649 12.3198i 0.0189827i
650650 417.819 766.134i 0.642799 1.17867i
651651 0 0
652652 222.285 222.285i 0.340928 0.340928i
653653 −41.7823 41.7823i −0.0639851 0.0639851i 0.674390 0.738375i 0.264407π-0.264407\pi
−0.738375 + 0.674390i 0.764407π0.764407\pi
654654 0 0
655655 −422.268 711.270i −0.644684 1.08591i
656656 −47.3892 −0.0722397
657657 0 0
658658 885.029 + 885.029i 1.34503 + 1.34503i
659659 690.184i 1.04732i −0.851927 0.523660i 0.824566π-0.824566\pi
0.851927 0.523660i 0.175434π-0.175434\pi
660660 0 0
661661 −658.583 −0.996344 −0.498172 0.867078i 0.665995π-0.665995\pi
−0.498172 + 0.867078i 0.665995π0.665995\pi
662662 −283.034 + 283.034i −0.427544 + 0.427544i
663663 0 0
664664 492.859i 0.742258i
665665 101.093 396.511i 0.152019 0.596257i
666666 0 0
667667 −166.645 + 166.645i −0.249843 + 0.249843i
668668 −55.7926 55.7926i −0.0835219 0.0835219i
669669 0 0
670670 −463.753 + 275.322i −0.692168 + 0.410928i
671671 50.8198 0.0757375
672672 0 0
673673 −901.911 901.911i −1.34014 1.34014i −0.895920 0.444216i 0.853482π-0.853482\pi
−0.444216 0.895920i 0.646518π-0.646518\pi
674674 1132.17i 1.67978i
675675 0 0
676676 −329.893 −0.488007
677677 485.397 485.397i 0.716982 0.716982i −0.251004 0.967986i 0.580761π-0.580761\pi
0.967986 + 0.251004i 0.0807608π0.0807608\pi
678678 0 0
679679 211.264i 0.311141i
680680 −549.651 925.833i −0.808310 1.36152i
681681 0 0
682682 −337.764 + 337.764i −0.495255 + 0.495255i
683683 −713.724 713.724i −1.04498 1.04498i −0.998939 0.0460448i 0.985338π-0.985338\pi
−0.0460448 0.998939i 0.514662π-0.514662\pi
684684 0 0
685685 324.241 + 82.6670i 0.473345 + 0.120682i
686686 1147.59 1.67288
687687 0 0
688688 −7.93183 7.93183i −0.0115288 0.0115288i
689689 698.344i 1.01356i
690690 0 0
691691 −1319.75 −1.90991 −0.954954 0.296754i 0.904096π-0.904096\pi
−0.954954 + 0.296754i 0.904096π0.904096\pi
692692 −260.195 + 260.195i −0.376005 + 0.376005i
693693 0 0
694694 887.368i 1.27863i
695695 676.041 401.353i 0.972721 0.577487i
696696 0 0
697697 −1213.15 + 1213.15i −1.74053 + 1.74053i
698698 53.6731 + 53.6731i 0.0768955 + 0.0768955i
699699 0 0
700700 −716.543 + 210.804i −1.02363 + 0.301149i
701701 1276.93 1.82159 0.910795 0.412859i 0.135470π-0.135470\pi
0.910795 + 0.412859i 0.135470π0.135470\pi
702702 0 0
703703 49.8410 + 49.8410i 0.0708975 + 0.0708975i
704704 344.935i 0.489964i
705705 0 0
706706 −275.578 −0.390337
707707 361.940 361.940i 0.511938 0.511938i
708708 0 0
709709 746.781i 1.05329i 0.850086 + 0.526644i 0.176550π0.176550\pi
−0.850086 + 0.526644i 0.823450π0.823450\pi
710710 −1038.08 264.664i −1.46208 0.372766i
711711 0 0
712712 −624.405 + 624.405i −0.876974 + 0.876974i
713713 −524.396 524.396i −0.735478 0.735478i
714714 0 0
715715 −44.3774 + 174.060i −0.0620663 + 0.243440i
716716 −1912.55 −2.67116
717717 0 0
718718 1145.46 + 1145.46i 1.59534 + 1.59534i
719719 135.949i 0.189080i 0.995521 + 0.0945402i 0.0301381π0.0301381\pi
−0.995521 + 0.0945402i 0.969862π0.969862\pi
720720 0 0
721721 190.203 0.263804
722722 −125.596 + 125.596i −0.173955 + 0.173955i
723723 0 0
724724 1302.75i 1.79938i
725725 −311.723 170.001i −0.429962 0.234484i
726726 0 0
727727 192.127 192.127i 0.264273 0.264273i −0.562514 0.826788i 0.690166π-0.690166\pi
0.826788 + 0.562514i 0.190166π0.190166\pi
728728 −275.433 275.433i −0.378342 0.378342i
729729 0 0
730730 1085.43 + 1828.29i 1.48688 + 2.50451i
731731 −406.103 −0.555545
732732 0 0
733733 −288.677 288.677i −0.393830 0.393830i 0.482220 0.876050i 0.339830π-0.339830\pi
−0.876050 + 0.482220i 0.839830π0.839830\pi
734734 1833.58i 2.49807i
735735 0 0
736736 −551.471 −0.749281
737737 78.4985 78.4985i 0.106511 0.106511i
738738 0 0
739739 135.495i 0.183349i −0.995789 0.0916746i 0.970778π-0.970778\pi
0.995789 0.0916746i 0.0292220π-0.0292220\pi
740740 31.7854 124.670i 0.0429532 0.168473i
741741 0 0
742742 687.431 687.431i 0.926457 0.926457i
743743 350.021 + 350.021i 0.471091 + 0.471091i 0.902268 0.431177i 0.141901π-0.141901\pi
−0.431177 + 0.902268i 0.641901π0.641901\pi
744744 0 0
745745 395.465 234.781i 0.530826 0.315142i
746746 590.605 0.791696
747747 0 0
748748 419.575 + 419.575i 0.560929 + 0.560929i
749749 353.633i 0.472140i
750750 0 0
751751 1143.86 1.52311 0.761556 0.648099i 0.224436π-0.224436\pi
0.761556 + 0.648099i 0.224436π0.224436\pi
752752 −45.4268 + 45.4268i −0.0604080 + 0.0604080i
753753 0 0
754754 495.761i 0.657509i
755755 −456.242 768.495i −0.604294 1.01787i
756756 0 0
757757 −99.4207 + 99.4207i −0.131335 + 0.131335i −0.769719 0.638383i 0.779603π-0.779603\pi
0.638383 + 0.769719i 0.279603π0.279603\pi
758758 704.074 + 704.074i 0.928857 + 0.928857i
759759 0 0
760760 −651.197 166.026i −0.856838 0.218456i
761761 782.950 1.02884 0.514421 0.857537i 0.328007π-0.328007\pi
0.514421 + 0.857537i 0.328007π0.328007\pi
762762 0 0
763763 −322.333 322.333i −0.422455 0.422455i
764764 435.156i 0.569576i
765765 0 0
766766 −624.467 −0.815231
767767 −28.4510 + 28.4510i −0.0370939 + 0.0370939i
768768 0 0
769769 1060.55i 1.37913i −0.724224 0.689565i 0.757802π-0.757802\pi
0.724224 0.689565i 0.242198π-0.242198\pi
770770 215.023 127.656i 0.279251 0.165786i
771771 0 0
772772 359.742 359.742i 0.465987 0.465987i
773773 599.585 + 599.585i 0.775660 + 0.775660i 0.979090 0.203429i 0.0652087π-0.0652087\pi
−0.203429 + 0.979090i 0.565209π0.565209\pi
774774 0 0
775775 534.956 980.921i 0.690265 1.26570i
776776 −346.963 −0.447117
777777 0 0
778778 −499.290 499.290i −0.641761 0.641761i
779779 1070.83i 1.37462i
780780 0 0
781781 220.513 0.282347
782782 −1059.52 + 1059.52i −1.35488 + 1.35488i
783783 0 0
784784 20.9782i 0.0267579i
785785 584.808 + 149.100i 0.744979 + 0.189936i
786786 0 0
787787 −10.9757 + 10.9757i −0.0139462 + 0.0139462i −0.714046 0.700099i 0.753139π-0.753139\pi
0.700099 + 0.714046i 0.253139π0.253139\pi
788788 391.343 + 391.343i 0.496628 + 0.496628i
789789 0 0
790790 227.529 892.426i 0.288011 1.12965i
791791 −724.066 −0.915380
792792 0 0
793793 −117.362 117.362i −0.147998 0.147998i
794794 2037.81i 2.56651i
795795 0 0
796796 1862.89 2.34032
797797 −291.068 + 291.068i −0.365205 + 0.365205i −0.865725 0.500520i 0.833142π-0.833142\pi
0.500520 + 0.865725i 0.333142π0.333142\pi
798798 0 0
799799 2325.82i 2.91091i
800800 −234.495 797.071i −0.293119 0.996339i
801801 0 0
802802 −1588.68 + 1588.68i −1.98090 + 1.98090i
803803 −309.472 309.472i −0.385395 0.385395i
804804 0 0
805805 198.192 + 333.835i 0.246201 + 0.414702i
806806 1560.05 1.93555
807807 0 0
808808 −594.420 594.420i −0.735669 0.735669i
809809 934.080i 1.15461i 0.816528 + 0.577305i 0.195896π0.195896\pi
−0.816528 + 0.577305i 0.804104π0.804104\pi
810810 0 0
811811 247.443 0.305109 0.152554 0.988295i 0.451250π-0.451250\pi
0.152554 + 0.988295i 0.451250π0.451250\pi
812812 −300.041 + 300.041i −0.369508 + 0.369508i
813813 0 0
814814 43.0743i 0.0529169i
815815 60.8192 238.548i 0.0746248 0.292697i
816816 0 0
817817 −179.232 + 179.232i −0.219378 + 0.219378i
818818 −85.9325 85.9325i −0.105052 0.105052i
819819 0 0
820820 1680.72 997.814i 2.04966 1.21685i
821821 958.912 1.16798 0.583990 0.811761i 0.301491π-0.301491\pi
0.583990 + 0.811761i 0.301491π0.301491\pi
822822 0 0
823823 −841.533 841.533i −1.02252 1.02252i −0.999741 0.0227782i 0.992749π-0.992749\pi
−0.0227782 0.999741i 0.507251π-0.507251\pi
824824 312.373i 0.379094i
825825 0 0
826826 56.0128 0.0678121
827827 −501.948 + 501.948i −0.606951 + 0.606951i −0.942148 0.335197i 0.891197π-0.891197\pi
0.335197 + 0.942148i 0.391197π0.391197\pi
828828 0 0
829829 219.411i 0.264670i −0.991205 0.132335i 0.957753π-0.957753\pi
0.991205 0.132335i 0.0422474π-0.0422474\pi
830830 −527.524 888.563i −0.635571 1.07056i
831831 0 0
832832 796.585 796.585i 0.957434 0.957434i
833833 537.033 + 537.033i 0.644697 + 0.644697i
834834 0 0
835835 −59.8746 15.2654i −0.0717061 0.0182819i
836836 370.354 0.443007
837837 0 0
838838 1107.44 + 1107.44i 1.32153 + 1.32153i
839839 1101.77i 1.31320i 0.754241 + 0.656598i 0.228005π0.228005\pi
−0.754241 + 0.656598i 0.771995π0.771995\pi
840840 0 0
841841 639.286 0.760150
842842 886.187 886.187i 1.05248 1.05248i
843843 0 0
844844 599.381i 0.710168i
845845 −222.145 + 131.884i −0.262894 + 0.156075i
846846 0 0
847847 −36.3966 + 36.3966i −0.0429712 + 0.0429712i
848848 35.2845 + 35.2845i 0.0416090 + 0.0416090i
849849 0 0
850850 −1981.90 1080.85i −2.33165 1.27159i
851851 −66.8751 −0.0785841
852852 0 0
853853 1045.69 + 1045.69i 1.22589 + 1.22589i 0.965504 + 0.260387i 0.0838501π0.0838501\pi
0.260387 + 0.965504i 0.416150π0.416150\pi
854854 231.057i 0.270558i
855855 0 0
856856 580.777 0.678478
857857 1006.72 1006.72i 1.17471 1.17471i 0.193632 0.981074i 0.437973π-0.437973\pi
0.981074 0.193632i 0.0620268π-0.0620268\pi
858858 0 0
859859 1366.58i 1.59090i 0.606021 + 0.795448i 0.292765π0.292765\pi
−0.606021 + 0.795448i 0.707235π0.707235\pi
860860 448.323 + 114.302i 0.521305 + 0.132910i
861861 0 0
862862 1150.57 1150.57i 1.33477 1.33477i
863863 −947.174 947.174i −1.09754 1.09754i −0.994698 0.102838i 0.967208π-0.967208\pi
−0.102838 0.994698i 0.532792π-0.532792\pi
864864 0 0
865865 −71.1918 + 279.232i −0.0823027 + 0.322812i
866866 −685.288 −0.791325
867867 0 0
868868 −944.161 944.161i −1.08774 1.08774i
869869 189.573i 0.218150i
870870 0 0
871871 −362.566 −0.416264
872872 −529.373 + 529.373i −0.607079 + 0.607079i
873873 0 0
874874 935.223i 1.07005i
875875 −398.235 + 428.410i −0.455126 + 0.489612i
876876 0 0
877877 −87.0484 + 87.0484i −0.0992570 + 0.0992570i −0.754992 0.655735i 0.772359π-0.772359\pi
0.655735 + 0.754992i 0.272359π0.272359\pi
878878 −480.617 480.617i −0.547400 0.547400i
879879 0 0
880880 6.55231 + 11.0367i 0.00744580 + 0.0125417i
881881 −868.490 −0.985800 −0.492900 0.870086i 0.664063π-0.664063\pi
−0.492900 + 0.870086i 0.664063π0.664063\pi
882882 0 0
883883 608.328 + 608.328i 0.688934 + 0.688934i 0.961996 0.273063i 0.0880366π-0.0880366\pi
−0.273063 + 0.961996i 0.588037π0.588037\pi
884884 1937.92i 2.19221i
885885 0 0
886886 −2018.22 −2.27790
887887 −495.738 + 495.738i −0.558892 + 0.558892i −0.928992 0.370100i 0.879324π-0.879324\pi
0.370100 + 0.928992i 0.379324π0.379324\pi
888888 0 0
889889 26.1163i 0.0293772i
890890 −457.402 + 1794.05i −0.513935 + 2.01578i
891891 0 0
892892 −1009.35 + 1009.35i −1.13156 + 1.13156i
893893 1026.49 + 1026.49i 1.14948 + 1.14948i
894894 0 0
895895 −1287.89 + 764.595i −1.43898 + 0.854296i
896896 −946.224 −1.05605
897897 0 0
898898 1462.19 + 1462.19i 1.62828 + 1.62828i
899899 634.749i 0.706061i
900900 0 0
901901 1806.54 2.00504
902902 −462.725 + 462.725i −0.512999 + 0.512999i
903903 0 0
904904 1189.14i 1.31543i
905905 520.812 + 877.257i 0.575483 + 0.969345i
906906 0 0
907907 163.744 163.744i 0.180534 0.180534i −0.611055 0.791588i 0.709254π-0.709254\pi
0.791588 + 0.611055i 0.209254π0.209254\pi
908908 1014.65 + 1014.65i 1.11745 + 1.11745i
909909 0 0
910910 −791.376 201.766i −0.869644 0.221720i
911911 −1750.93 −1.92199 −0.960995 0.276566i 0.910804π-0.910804\pi
−0.960995 + 0.276566i 0.910804π0.910804\pi
912912 0 0
913913 150.405 + 150.405i 0.164738 + 0.164738i
914914 472.638i 0.517109i
915915 0 0
916916 278.647 0.304200
917917 −547.388 + 547.388i −0.596933 + 0.596933i
918918 0 0
919919 1637.39i 1.78170i −0.454293 0.890852i 0.650108π-0.650108\pi
0.454293 0.890852i 0.349892π-0.349892\pi
920920 548.263 325.494i 0.595938 0.353797i
921921 0 0
922922 −1823.03 + 1823.03i −1.97726 + 1.97726i
923923 −509.247 509.247i −0.551731 0.551731i
924924 0 0
925925 −28.4365 96.6583i −0.0307422 0.104495i
926926 −1150.49 −1.24243
927927 0 0
928928 −333.761 333.761i −0.359656 0.359656i
929929 1639.43i 1.76473i −0.470568 0.882364i 0.655951π-0.655951\pi
0.470568 0.882364i 0.344049π-0.344049\pi
930930 0 0
931931 474.033 0.509166
932932 −1479.57 + 1479.57i −1.58753 + 1.58753i
933933 0 0
934934 365.061i 0.390857i
935935 450.273 + 114.799i 0.481575 + 0.122780i
936936 0 0
937937 −141.600 + 141.600i −0.151121 + 0.151121i −0.778618 0.627498i 0.784079π-0.784079\pi
0.627498 + 0.778618i 0.284079π0.284079\pi
938938 356.900 + 356.900i 0.380491 + 0.380491i
939939 0 0
940940 654.627 2567.61i 0.696412 2.73150i
941941 −1074.74 −1.14212 −0.571062 0.820907i 0.693469π-0.693469\pi
−0.571062 + 0.820907i 0.693469π0.693469\pi
942942 0 0
943943 −718.405 718.405i −0.761829 0.761829i
944944 2.87502i 0.00304558i
945945 0 0
946946 −154.898 −0.163740
947947 1127.43 1127.43i 1.19053 1.19053i 0.213609 0.976919i 0.431478π-0.431478\pi
0.976919 0.213609i 0.0685217π-0.0685217\pi
948948 0 0
949949 1429.38i 1.50619i
950950 −1351.73 + 397.674i −1.42287 + 0.418604i
951951 0 0
952952 −712.514 + 712.514i −0.748439 + 0.748439i
953953 −99.4706 99.4706i −0.104376 0.104376i 0.652990 0.757366i 0.273514π-0.273514\pi
−0.757366 + 0.652990i 0.773514π0.773514\pi
954954 0 0
955955 173.965 + 293.028i 0.182163 + 0.306836i
956956 −1301.53 −1.36144
957957 0 0
958958 936.801 + 936.801i 0.977871 + 0.977871i
959959 313.153i 0.326541i
960960 0 0
961961 1036.41 1.07847
962962 99.4750 99.4750i 0.103404 0.103404i
963963 0 0
964964 618.472i 0.641568i
965965 98.4287 386.062i 0.101999 0.400065i
966966 0 0
967967 1260.15 1260.15i 1.30315 1.30315i 0.376896 0.926256i 0.376992π-0.376992\pi
0.926256 0.376896i 0.123008π-0.123008\pi
968968 59.7748 + 59.7748i 0.0617508 + 0.0617508i
969969 0 0
970970 −625.531 + 371.367i −0.644878 + 0.382852i
971971 −1148.23 −1.18252 −0.591261 0.806481i 0.701370π-0.701370\pi
−0.591261 + 0.806481i 0.701370π0.701370\pi
972972 0 0
973973 −520.275 520.275i −0.534713 0.534713i
974974 966.900i 0.992711i
975975 0 0
976976 −11.8597 −0.0121513
977977 −145.709 + 145.709i −0.149139 + 0.149139i −0.777733 0.628594i 0.783631π-0.783631\pi
0.628594 + 0.777733i 0.283631π0.283631\pi
978978 0 0
979979 381.099i 0.389274i
980980 −441.710 744.018i −0.450725 0.759202i
981981 0 0
982982 259.083 259.083i 0.263832 0.263832i
983983 562.675 + 562.675i 0.572406 + 0.572406i 0.932800 0.360394i 0.117358π-0.117358\pi
−0.360394 + 0.932800i 0.617358π0.617358\pi
984984 0 0
985985 419.975 + 107.075i 0.426371 + 0.108706i
986986 −1282.48 −1.30069
987987 0 0
988988 −855.288 855.288i −0.865676 0.865676i
989989 240.487i 0.243162i
990990 0 0
991991 −1445.80 −1.45893 −0.729464 0.684019i 0.760231π-0.760231\pi
−0.729464 + 0.684019i 0.760231π0.760231\pi
992992 1050.27 1050.27i 1.05874 1.05874i
993993 0 0
994994 1002.58i 1.00863i
995995 1254.45 744.742i 1.26075 0.748484i
996996 0 0
997997 273.932 273.932i 0.274757 0.274757i −0.556255 0.831012i 0.687762π-0.687762\pi
0.831012 + 0.556255i 0.187762π0.187762\pi
998998 781.639 + 781.639i 0.783206 + 0.783206i
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 495.3.j.a.298.1 20
3.2 odd 2 55.3.f.a.23.10 yes 20
5.2 odd 4 inner 495.3.j.a.397.1 20
15.2 even 4 55.3.f.a.12.10 20
15.8 even 4 275.3.f.b.232.1 20
15.14 odd 2 275.3.f.b.243.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.3.f.a.12.10 20 15.2 even 4
55.3.f.a.23.10 yes 20 3.2 odd 2
275.3.f.b.232.1 20 15.8 even 4
275.3.f.b.243.1 20 15.14 odd 2
495.3.j.a.298.1 20 1.1 even 1 trivial
495.3.j.a.397.1 20 5.2 odd 4 inner