Properties

Label 324.3.d.e.163.4
Level 324324
Weight 33
Character 324.163
Analytic conductor 8.8288.828
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(163,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.163");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 324=2234 324 = 2^{2} \cdot 3^{4}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 324.d (of order 22, degree 11, 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: 8.828360565278.82836056527
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.3636603.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6+8x4+12x2+3 x^{6} + 8x^{4} + 12x^{2} + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 263 2^{6}\cdot 3
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 163.4
Root 2.47367i-2.47367i of defining polynomial
Character χ\chi == 324.163
Dual form 324.3.d.e.163.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.195350+1.99044i)q2+(3.923680.777662i)q47.23805q5+6.88025iq7+(2.314387.65792i)q8+(1.4139514.4069i)q1017.9526iq11+7.67526q13+(13.69471.34405i)q14+(14.7905+6.10259i)q16+1.43720q17+13.8943iq19+(28.3998+5.62876i)q20+(35.7336+3.50704i)q2216.5824iq23+27.3894q25+(1.49936+15.2771i)q26+(5.3505126.9959i)q28+37.5019q2953.9918iq31+(15.0361+28.2474i)q32+(0.280757+2.86066i)q3449.7996iq35+44.4415q37+(27.65582.71425i)q38+(16.7516+55.4284i)q4056.9911q4167.6185iq43+(13.9611+70.4404i)q44+(33.0063+3.23938i)q46+9.43453iq47+1.66212q49+(5.35051+54.5169i)q50+(30.11525.96876i)q52+7.82662q53+129.942iq55+(52.6884+15.9235i)q56+(7.32598+74.6451i)q5822.4125iq5967.1814q61+(107.467+10.5473i)q62+(53.287335.4466i)q6455.5539q6569.2040iq67+(5.639121.11766i)q68+(99.1230+9.72834i)q707.14792iq7180.4410q73+(8.68162+88.4579i)q74+(10.805154.5169i)q76+123.519q77+46.8439iq79+(107.05444.1709i)q80+(11.1332113.437i)q82142.199iq8310.4026q85+(134.590+13.2092i)q86+(137.48041.5492i)q8842.1078q89+52.8077iq91+(12.8955+65.0642i)q92+(18.77881.84303i)q94100.568iq95+62.8955q97+(0.324695+3.30835i)q98+O(q100)q+(-0.195350 + 1.99044i) q^{2} +(-3.92368 - 0.777662i) q^{4} -7.23805 q^{5} +6.88025i q^{7} +(2.31438 - 7.65792i) q^{8} +(1.41395 - 14.4069i) q^{10} -17.9526i q^{11} +7.67526 q^{13} +(-13.6947 - 1.34405i) q^{14} +(14.7905 + 6.10259i) q^{16} +1.43720 q^{17} +13.8943i q^{19} +(28.3998 + 5.62876i) q^{20} +(35.7336 + 3.50704i) q^{22} -16.5824i q^{23} +27.3894 q^{25} +(-1.49936 + 15.2771i) q^{26} +(5.35051 - 26.9959i) q^{28} +37.5019 q^{29} -53.9918i q^{31} +(-15.0361 + 28.2474i) q^{32} +(-0.280757 + 2.86066i) q^{34} -49.7996i q^{35} +44.4415 q^{37} +(-27.6558 - 2.71425i) q^{38} +(-16.7516 + 55.4284i) q^{40} -56.9911 q^{41} -67.6185i q^{43} +(-13.9611 + 70.4404i) q^{44} +(33.0063 + 3.23938i) q^{46} +9.43453i q^{47} +1.66212 q^{49} +(-5.35051 + 54.5169i) q^{50} +(-30.1152 - 5.96876i) q^{52} +7.82662 q^{53} +129.942i q^{55} +(52.6884 + 15.9235i) q^{56} +(-7.32598 + 74.6451i) q^{58} -22.4125i q^{59} -67.1814 q^{61} +(107.467 + 10.5473i) q^{62} +(-53.2873 - 35.4466i) q^{64} -55.5539 q^{65} -69.2040i q^{67} +(-5.63912 - 1.11766i) q^{68} +(99.1230 + 9.72834i) q^{70} -7.14792i q^{71} -80.4410 q^{73} +(-8.68162 + 88.4579i) q^{74} +(10.8051 - 54.5169i) q^{76} +123.519 q^{77} +46.8439i q^{79} +(-107.054 - 44.1709i) q^{80} +(11.1332 - 113.437i) q^{82} -142.199i q^{83} -10.4026 q^{85} +(134.590 + 13.2092i) q^{86} +(-137.480 - 41.5492i) q^{88} -42.1078 q^{89} +52.8077i q^{91} +(-12.8955 + 65.0642i) q^{92} +(-18.7788 - 1.84303i) q^{94} -100.568i q^{95} +62.8955 q^{97} +(-0.324695 + 3.30835i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6qq23q42q57q8+9q10+6q1315q16+10q17+67q20+48q22+73q2648q28+22q2931q32+81q34+54q37168q3881q40++407q98+O(q100) 6 q - q^{2} - 3 q^{4} - 2 q^{5} - 7 q^{8} + 9 q^{10} + 6 q^{13} - 15 q^{16} + 10 q^{17} + 67 q^{20} + 48 q^{22} + 73 q^{26} - 48 q^{28} + 22 q^{29} - 31 q^{32} + 81 q^{34} + 54 q^{37} - 168 q^{38} - 81 q^{40}+ \cdots + 407 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/324Z)×\left(\mathbb{Z}/324\mathbb{Z}\right)^\times.

nn 163163 245245
χ(n)\chi(n) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.195350 + 1.99044i −0.0976748 + 0.995218i
33 0 0
44 −3.92368 0.777662i −0.980919 0.194416i
55 −7.23805 −1.44761 −0.723805 0.690004i 0.757609π-0.757609\pi
−0.723805 + 0.690004i 0.757609π0.757609\pi
66 0 0
77 6.88025i 0.982893i 0.870908 + 0.491447i 0.163532π0.163532\pi
−0.870908 + 0.491447i 0.836468π0.836468\pi
88 2.31438 7.65792i 0.289297 0.957239i
99 0 0
1010 1.41395 14.4069i 0.141395 1.44069i
1111 17.9526i 1.63206i −0.578010 0.816029i 0.696171π-0.696171\pi
0.578010 0.816029i 0.303829π-0.303829\pi
1212 0 0
1313 7.67526 0.590404 0.295202 0.955435i 0.404613π-0.404613\pi
0.295202 + 0.955435i 0.404613π0.404613\pi
1414 −13.6947 1.34405i −0.978193 0.0960039i
1515 0 0
1616 14.7905 + 6.10259i 0.924405 + 0.381412i
1717 1.43720 0.0845413 0.0422707 0.999106i 0.486541π-0.486541\pi
0.0422707 + 0.999106i 0.486541π0.486541\pi
1818 0 0
1919 13.8943i 0.731281i 0.930756 + 0.365641i 0.119150π0.119150\pi
−0.930756 + 0.365641i 0.880850π0.880850\pi
2020 28.3998 + 5.62876i 1.41999 + 0.281438i
2121 0 0
2222 35.7336 + 3.50704i 1.62426 + 0.159411i
2323 16.5824i 0.720976i −0.932764 0.360488i 0.882610π-0.882610\pi
0.932764 0.360488i 0.117390π-0.117390\pi
2424 0 0
2525 27.3894 1.09558
2626 −1.49936 + 15.2771i −0.0576676 + 0.587581i
2727 0 0
2828 5.35051 26.9959i 0.191090 0.964139i
2929 37.5019 1.29317 0.646584 0.762843i 0.276197π-0.276197\pi
0.646584 + 0.762843i 0.276197π0.276197\pi
3030 0 0
3131 53.9918i 1.74167i −0.491575 0.870835i 0.663579π-0.663579\pi
0.491575 0.870835i 0.336421π-0.336421\pi
3232 −15.0361 + 28.2474i −0.469879 + 0.882731i
3333 0 0
3434 −0.280757 + 2.86066i −0.00825756 + 0.0841371i
3535 49.7996i 1.42285i
3636 0 0
3737 44.4415 1.20112 0.600560 0.799580i 0.294944π-0.294944\pi
0.600560 + 0.799580i 0.294944π0.294944\pi
3838 −27.6558 2.71425i −0.727784 0.0714277i
3939 0 0
4040 −16.7516 + 55.4284i −0.418789 + 1.38571i
4141 −56.9911 −1.39003 −0.695014 0.718997i 0.744602π-0.744602\pi
−0.695014 + 0.718997i 0.744602π0.744602\pi
4242 0 0
4343 67.6185i 1.57252i −0.617894 0.786261i 0.712014π-0.712014\pi
0.617894 0.786261i 0.287986π-0.287986\pi
4444 −13.9611 + 70.4404i −0.317298 + 1.60092i
4545 0 0
4646 33.0063 + 3.23938i 0.717529 + 0.0704212i
4747 9.43453i 0.200735i 0.994950 + 0.100367i 0.0320018π0.0320018\pi
−0.994950 + 0.100367i 0.967998π0.967998\pi
4848 0 0
4949 1.66212 0.0339208
5050 −5.35051 + 54.5169i −0.107010 + 1.09034i
5151 0 0
5252 −30.1152 5.96876i −0.579139 0.114784i
5353 7.82662 0.147672 0.0738360 0.997270i 0.476476π-0.476476\pi
0.0738360 + 0.997270i 0.476476π0.476476\pi
5454 0 0
5555 129.942i 2.36259i
5656 52.6884 + 15.9235i 0.940864 + 0.284348i
5757 0 0
5858 −7.32598 + 74.6451i −0.126310 + 1.28698i
5959 22.4125i 0.379872i −0.981796 0.189936i 0.939172π-0.939172\pi
0.981796 0.189936i 0.0608281π-0.0608281\pi
6060 0 0
6161 −67.1814 −1.10133 −0.550667 0.834725i 0.685627π-0.685627\pi
−0.550667 + 0.834725i 0.685627π0.685627\pi
6262 107.467 + 10.5473i 1.73334 + 0.170117i
6363 0 0
6464 −53.2873 35.4466i −0.832614 0.553853i
6565 −55.5539 −0.854676
6666 0 0
6767 69.2040i 1.03290i −0.856319 0.516448i 0.827254π-0.827254\pi
0.856319 0.516448i 0.172746π-0.172746\pi
6868 −5.63912 1.11766i −0.0829282 0.0164362i
6969 0 0
7070 99.1230 + 9.72834i 1.41604 + 0.138976i
7171 7.14792i 0.100675i −0.998732 0.0503375i 0.983970π-0.983970\pi
0.998732 0.0503375i 0.0160297π-0.0160297\pi
7272 0 0
7373 −80.4410 −1.10193 −0.550965 0.834528i 0.685740π-0.685740\pi
−0.550965 + 0.834528i 0.685740π0.685740\pi
7474 −8.68162 + 88.4579i −0.117319 + 1.19538i
7575 0 0
7676 10.8051 54.5169i 0.142172 0.717328i
7777 123.519 1.60414
7878 0 0
7979 46.8439i 0.592960i 0.955039 + 0.296480i 0.0958129π0.0958129\pi
−0.955039 + 0.296480i 0.904187π0.904187\pi
8080 −107.054 44.1709i −1.33818 0.552136i
8181 0 0
8282 11.1332 113.437i 0.135771 1.38338i
8383 142.199i 1.71324i −0.515950 0.856619i 0.672561π-0.672561\pi
0.515950 0.856619i 0.327439π-0.327439\pi
8484 0 0
8585 −10.4026 −0.122383
8686 134.590 + 13.2092i 1.56500 + 0.153596i
8787 0 0
8888 −137.480 41.5492i −1.56227 0.472150i
8989 −42.1078 −0.473122 −0.236561 0.971617i 0.576020π-0.576020\pi
−0.236561 + 0.971617i 0.576020π0.576020\pi
9090 0 0
9191 52.8077i 0.580304i
9292 −12.8955 + 65.0642i −0.140169 + 0.707219i
9393 0 0
9494 −18.7788 1.84303i −0.199775 0.0196067i
9595 100.568i 1.05861i
9696 0 0
9797 62.8955 0.648408 0.324204 0.945987i 0.394904π-0.394904\pi
0.324204 + 0.945987i 0.394904π0.394904\pi
9898 −0.324695 + 3.30835i −0.00331321 + 0.0337586i
9999 0 0
100100 −107.467 21.2997i −1.07467 0.212997i
101101 −47.6143 −0.471429 −0.235715 0.971822i 0.575743π-0.575743\pi
−0.235715 + 0.971822i 0.575743π0.575743\pi
102102 0 0
103103 53.7241i 0.521593i 0.965394 + 0.260797i 0.0839852π0.0839852\pi
−0.965394 + 0.260797i 0.916015π0.916015\pi
104104 17.7634 58.7765i 0.170802 0.565158i
105105 0 0
106106 −1.52893 + 15.5784i −0.0144238 + 0.146966i
107107 26.4708i 0.247390i 0.992320 + 0.123695i 0.0394745π0.0394745\pi
−0.992320 + 0.123695i 0.960525π0.960525\pi
108108 0 0
109109 83.0647 0.762061 0.381031 0.924562i 0.375569π-0.375569\pi
0.381031 + 0.924562i 0.375569π0.375569\pi
110110 −258.642 25.3842i −2.35129 0.230765i
111111 0 0
112112 −41.9874 + 101.762i −0.374887 + 0.908592i
113113 15.5276 0.137413 0.0687064 0.997637i 0.478113π-0.478113\pi
0.0687064 + 0.997637i 0.478113π0.478113\pi
114114 0 0
115115 120.025i 1.04369i
116116 −147.145 29.1638i −1.26849 0.251412i
117117 0 0
118118 44.6106 + 4.37827i 0.378056 + 0.0371039i
119119 9.88832i 0.0830951i
120120 0 0
121121 −201.298 −1.66362
122122 13.1239 133.720i 0.107573 1.09607i
123123 0 0
124124 −41.9874 + 211.846i −0.338608 + 1.70844i
125125 −17.2947 −0.138358
126126 0 0
127127 157.463i 1.23987i −0.784654 0.619934i 0.787159π-0.787159\pi
0.784654 0.619934i 0.212841π-0.212841\pi
128128 80.9639 99.1406i 0.632530 0.774536i
129129 0 0
130130 10.8524 110.577i 0.0834803 0.850589i
131131 47.0592i 0.359231i 0.983737 + 0.179615i 0.0574853π0.0574853\pi
−0.983737 + 0.179615i 0.942515π0.942515\pi
132132 0 0
133133 −95.5966 −0.718771
134134 137.746 + 13.5190i 1.02796 + 0.100888i
135135 0 0
136136 3.32623 11.0060i 0.0244576 0.0809263i
137137 −117.497 −0.857644 −0.428822 0.903389i 0.641071π-0.641071\pi
−0.428822 + 0.903389i 0.641071π0.641071\pi
138138 0 0
139139 39.6959i 0.285582i −0.989753 0.142791i 0.954392π-0.954392\pi
0.989753 0.142791i 0.0456077π-0.0456077\pi
140140 −38.7273 + 195.398i −0.276624 + 1.39570i
141141 0 0
142142 14.2275 + 1.39634i 0.100194 + 0.00983341i
143143 137.791i 0.963575i
144144 0 0
145145 −271.441 −1.87200
146146 15.7141 160.113i 0.107631 1.09666i
147147 0 0
148148 −174.374 34.5604i −1.17820 0.233516i
149149 114.827 0.770652 0.385326 0.922781i 0.374089π-0.374089\pi
0.385326 + 0.922781i 0.374089π0.374089\pi
150150 0 0
151151 160.122i 1.06041i −0.847869 0.530206i 0.822115π-0.822115\pi
0.847869 0.530206i 0.177885π-0.177885\pi
152152 106.402 + 32.1567i 0.700011 + 0.211557i
153153 0 0
154154 −24.1293 + 245.856i −0.156684 + 1.59647i
155155 390.795i 2.52126i
156156 0 0
157157 225.337 1.43527 0.717634 0.696421i 0.245225π-0.245225\pi
0.717634 + 0.696421i 0.245225π0.245225\pi
158158 −93.2397 9.15093i −0.590125 0.0579173i
159159 0 0
160160 108.832 204.456i 0.680202 1.27785i
161161 114.091 0.708643
162162 0 0
163163 147.165i 0.902850i −0.892309 0.451425i 0.850916π-0.850916\pi
0.892309 0.451425i 0.149084π-0.149084\pi
164164 223.615 + 44.3198i 1.36350 + 0.270243i
165165 0 0
166166 283.038 + 27.7785i 1.70505 + 0.167340i
167167 105.944i 0.634396i 0.948359 + 0.317198i 0.102742π0.102742\pi
−0.948359 + 0.317198i 0.897258π0.897258\pi
168168 0 0
169169 −110.090 −0.651423
170170 2.03213 20.7056i 0.0119537 0.121798i
171171 0 0
172172 −52.5843 + 265.313i −0.305723 + 1.54252i
173173 186.424 1.07759 0.538797 0.842436i 0.318879π-0.318879\pi
0.538797 + 0.842436i 0.318879π0.318879\pi
174174 0 0
175175 188.446i 1.07683i
176176 109.558 265.528i 0.622487 1.50868i
177177 0 0
178178 8.22575 83.8130i 0.0462121 0.470859i
179179 191.597i 1.07037i 0.844734 + 0.535187i 0.179759π0.179759\pi
−0.844734 + 0.535187i 0.820241π0.820241\pi
180180 0 0
181181 204.960 1.13237 0.566187 0.824277i 0.308418π-0.308418\pi
0.566187 + 0.824277i 0.308418π0.308418\pi
182182 −105.110 10.3160i −0.577530 0.0566811i
183183 0 0
184184 −126.987 38.3780i −0.690147 0.208576i
185185 −321.670 −1.73875
186186 0 0
187187 25.8016i 0.137976i
188188 7.33688 37.0180i 0.0390259 0.196904i
189189 0 0
190190 200.174 + 19.6459i 1.05355 + 0.103400i
191191 89.8155i 0.470238i −0.971967 0.235119i 0.924452π-0.924452\pi
0.971967 0.235119i 0.0755480π-0.0755480\pi
192192 0 0
193193 167.596 0.868374 0.434187 0.900823i 0.357036π-0.357036\pi
0.434187 + 0.900823i 0.357036π0.357036\pi
194194 −12.2866 + 125.190i −0.0633331 + 0.645307i
195195 0 0
196196 −6.52163 1.29257i −0.0332736 0.00659474i
197197 −185.277 −0.940492 −0.470246 0.882535i 0.655835π-0.655835\pi
−0.470246 + 0.882535i 0.655835π0.655835\pi
198198 0 0
199199 137.625i 0.691585i −0.938311 0.345793i 0.887610π-0.887610\pi
0.938311 0.345793i 0.112390π-0.112390\pi
200200 63.3894 209.746i 0.316947 1.04873i
201201 0 0
202202 9.30144 94.7733i 0.0460467 0.469175i
203203 258.022i 1.27105i
204204 0 0
205205 412.505 2.01222
206206 −106.934 10.4950i −0.519099 0.0509465i
207207 0 0
208208 113.521 + 46.8389i 0.545773 + 0.225187i
209209 249.440 1.19349
210210 0 0
211211 305.254i 1.44670i 0.690482 + 0.723350i 0.257398π0.257398\pi
−0.690482 + 0.723350i 0.742602π0.742602\pi
212212 −30.7091 6.08647i −0.144854 0.0287097i
213213 0 0
214214 −52.6884 5.17106i −0.246207 0.0241638i
215215 489.426i 2.27640i
216216 0 0
217217 371.477 1.71188
218218 −16.2267 + 165.335i −0.0744342 + 0.758417i
219219 0 0
220220 101.051 509.851i 0.459323 2.31751i
221221 11.0309 0.0499136
222222 0 0
223223 17.2224i 0.0772303i 0.999254 + 0.0386152i 0.0122946π0.0122946\pi
−0.999254 + 0.0386152i 0.987705π0.987705\pi
224224 −194.349 103.452i −0.867630 0.461841i
225225 0 0
226226 −3.03332 + 30.9068i −0.0134218 + 0.136756i
227227 40.9846i 0.180549i −0.995917 0.0902744i 0.971226π-0.971226\pi
0.995917 0.0902744i 0.0287744π-0.0287744\pi
228228 0 0
229229 −133.453 −0.582763 −0.291381 0.956607i 0.594115π-0.594115\pi
−0.291381 + 0.956607i 0.594115π0.594115\pi
230230 −238.901 23.4468i −1.03870 0.101942i
231231 0 0
232232 86.7935 287.186i 0.374110 1.23787i
233233 368.345 1.58088 0.790441 0.612539i 0.209852π-0.209852\pi
0.790441 + 0.612539i 0.209852π0.209852\pi
234234 0 0
235235 68.2876i 0.290586i
236236 −17.4293 + 87.9393i −0.0738531 + 0.372624i
237237 0 0
238238 −19.6821 1.93168i −0.0826978 0.00811630i
239239 288.560i 1.20737i 0.797225 + 0.603683i 0.206301π0.206301\pi
−0.797225 + 0.603683i 0.793699π0.793699\pi
240240 0 0
241241 −102.987 −0.427333 −0.213667 0.976907i 0.568541π-0.568541\pi
−0.213667 + 0.976907i 0.568541π0.568541\pi
242242 39.3234 400.670i 0.162493 1.65566i
243243 0 0
244244 263.598 + 52.2444i 1.08032 + 0.214116i
245245 −12.0305 −0.0491042
246246 0 0
247247 106.643i 0.431751i
248248 −413.464 124.957i −1.66720 0.503860i
249249 0 0
250250 3.37852 34.4241i 0.0135141 0.137696i
251251 69.9866i 0.278831i −0.990234 0.139416i 0.955478π-0.955478\pi
0.990234 0.139416i 0.0445224π-0.0445224\pi
252252 0 0
253253 −297.699 −1.17668
254254 313.421 + 30.7604i 1.23394 + 0.121104i
255255 0 0
256256 181.517 + 180.521i 0.709050 + 0.705158i
257257 −97.0819 −0.377751 −0.188875 0.982001i 0.560484π-0.560484\pi
−0.188875 + 0.982001i 0.560484π0.560484\pi
258258 0 0
259259 305.768i 1.18057i
260260 217.976 + 43.2022i 0.838368 + 0.166162i
261261 0 0
262262 −93.6684 9.19301i −0.357513 0.0350878i
263263 8.40472i 0.0319571i 0.999872 + 0.0159785i 0.00508635π0.00508635\pi
−0.999872 + 0.0159785i 0.994914π0.994914\pi
264264 0 0
265265 −56.6495 −0.213772
266266 18.6748 190.279i 0.0702058 0.715334i
267267 0 0
268268 −53.8174 + 271.534i −0.200811 + 1.01319i
269269 −281.198 −1.04535 −0.522673 0.852533i 0.675065π-0.675065\pi
−0.522673 + 0.852533i 0.675065π0.675065\pi
270270 0 0
271271 369.456i 1.36331i −0.731675 0.681654i 0.761261π-0.761261\pi
0.731675 0.681654i 0.238739π-0.238739\pi
272272 21.2569 + 8.77066i 0.0781505 + 0.0322451i
273273 0 0
274274 22.9530 233.871i 0.0837702 0.853543i
275275 491.713i 1.78805i
276276 0 0
277277 132.909 0.479817 0.239908 0.970796i 0.422883π-0.422883\pi
0.239908 + 0.970796i 0.422883π0.422883\pi
278278 79.0123 + 7.75459i 0.284217 + 0.0278942i
279279 0 0
280280 −381.361 115.255i −1.36200 0.411625i
281281 −37.3154 −0.132795 −0.0663974 0.997793i 0.521151π-0.521151\pi
−0.0663974 + 0.997793i 0.521151π0.521151\pi
282282 0 0
283283 156.168i 0.551832i 0.961182 + 0.275916i 0.0889811π0.0889811\pi
−0.961182 + 0.275916i 0.911019π0.911019\pi
284284 −5.55867 + 28.0461i −0.0195728 + 0.0987540i
285285 0 0
286286 274.265 + 26.9175i 0.958967 + 0.0941170i
287287 392.113i 1.36625i
288288 0 0
289289 −286.934 −0.992853
290290 53.0258 540.285i 0.182848 1.86305i
291291 0 0
292292 315.624 + 62.5559i 1.08091 + 0.214232i
293293 −25.9762 −0.0886561 −0.0443280 0.999017i 0.514115π-0.514115\pi
−0.0443280 + 0.999017i 0.514115π0.514115\pi
294294 0 0
295295 162.223i 0.549907i
296296 102.854 340.329i 0.347481 1.14976i
297297 0 0
298298 −22.4314 + 228.556i −0.0752733 + 0.766967i
299299 127.275i 0.425667i
300300 0 0
301301 465.232 1.54562
302302 318.713 + 31.2798i 1.05534 + 0.103575i
303303 0 0
304304 −84.7915 + 205.504i −0.278919 + 0.676000i
305305 486.262 1.59430
306306 0 0
307307 111.670i 0.363745i −0.983322 0.181872i 0.941784π-0.941784\pi
0.983322 0.181872i 0.0582158π-0.0582158\pi
308308 −484.648 96.0559i −1.57353 0.311870i
309309 0 0
310310 −777.854 76.3417i −2.50920 0.246264i
311311 323.742i 1.04097i 0.853871 + 0.520485i 0.174249π0.174249\pi
−0.853871 + 0.520485i 0.825751π0.825751\pi
312312 0 0
313313 −366.181 −1.16991 −0.584953 0.811067i 0.698887π-0.698887\pi
−0.584953 + 0.811067i 0.698887π0.698887\pi
314314 −44.0195 + 448.519i −0.140189 + 1.42840i
315315 0 0
316316 36.4287 183.800i 0.115281 0.581646i
317317 −65.0029 −0.205056 −0.102528 0.994730i 0.532693π-0.532693\pi
−0.102528 + 0.994730i 0.532693π0.532693\pi
318318 0 0
319319 673.258i 2.11053i
320320 385.696 + 256.564i 1.20530 + 0.801764i
321321 0 0
322322 −22.2877 + 227.092i −0.0692165 + 0.705254i
323323 19.9690i 0.0618235i
324324 0 0
325325 210.221 0.646833
326326 292.922 + 28.7485i 0.898533 + 0.0881857i
327327 0 0
328328 −131.899 + 436.433i −0.402131 + 1.33059i
329329 −64.9119 −0.197301
330330 0 0
331331 439.440i 1.32761i −0.747904 0.663807i 0.768940π-0.768940\pi
0.747904 0.663807i 0.231060π-0.231060\pi
332332 −110.583 + 557.942i −0.333080 + 1.68055i
333333 0 0
334334 −210.875 20.6962i −0.631363 0.0619645i
335335 500.902i 1.49523i
336336 0 0
337337 −374.818 −1.11222 −0.556109 0.831109i 0.687706π-0.687706\pi
−0.556109 + 0.831109i 0.687706π0.687706\pi
338338 21.5061 219.128i 0.0636276 0.648308i
339339 0 0
340340 40.8163 + 8.08967i 0.120048 + 0.0237931i
341341 −969.295 −2.84251
342342 0 0
343343 348.568i 1.01623i
344344 −517.816 156.495i −1.50528 0.454926i
345345 0 0
346346 −36.4178 + 371.065i −0.105254 + 1.07244i
347347 329.030i 0.948213i −0.880467 0.474107i 0.842771π-0.842771\pi
0.880467 0.474107i 0.157229π-0.157229\pi
348348 0 0
349349 372.506 1.06735 0.533676 0.845689i 0.320810π-0.320810\pi
0.533676 + 0.845689i 0.320810π0.320810\pi
350350 −375.090 36.8129i −1.07169 0.105180i
351351 0 0
352352 507.115 + 269.938i 1.44067 + 0.766871i
353353 −217.758 −0.616879 −0.308440 0.951244i 0.599807π-0.599807\pi
−0.308440 + 0.951244i 0.599807π0.599807\pi
354354 0 0
355355 51.7370i 0.145738i
356356 165.218 + 32.7457i 0.464094 + 0.0919822i
357357 0 0
358358 −381.361 37.4284i −1.06526 0.104549i
359359 145.576i 0.405505i −0.979230 0.202753i 0.935011π-0.935011\pi
0.979230 0.202753i 0.0649887π-0.0649887\pi
360360 0 0
361361 167.947 0.465228
362362 −40.0388 + 407.959i −0.110604 + 1.12696i
363363 0 0
364364 41.0666 207.200i 0.112820 0.569232i
365365 582.236 1.59517
366366 0 0
367367 53.4769i 0.145714i 0.997342 + 0.0728568i 0.0232116π0.0232116\pi
−0.997342 + 0.0728568i 0.976788π0.976788\pi
368368 101.196 245.262i 0.274989 0.666474i
369369 0 0
370370 62.8380 640.263i 0.169833 1.73044i
371371 53.8491i 0.145146i
372372 0 0
373373 −341.504 −0.915561 −0.457781 0.889065i 0.651355π-0.651355\pi
−0.457781 + 0.889065i 0.651355π0.651355\pi
374374 51.3565 + 5.04033i 0.137317 + 0.0134768i
375375 0 0
376376 72.2488 + 21.8350i 0.192151 + 0.0580719i
377377 287.837 0.763492
378378 0 0
379379 220.189i 0.580972i 0.956879 + 0.290486i 0.0938170π0.0938170\pi
−0.956879 + 0.290486i 0.906183π0.906183\pi
380380 −78.2079 + 394.596i −0.205810 + 1.03841i
381381 0 0
382382 178.772 + 17.5454i 0.467990 + 0.0459304i
383383 671.073i 1.75215i −0.482175 0.876075i 0.660153π-0.660153\pi
0.482175 0.876075i 0.339847π-0.339847\pi
384384 0 0
385385 −894.035 −2.32217
386386 −32.7399 + 333.590i −0.0848183 + 0.864222i
387387 0 0
388388 −246.782 48.9115i −0.636036 0.126061i
389389 −484.924 −1.24659 −0.623296 0.781986i 0.714207π-0.714207\pi
−0.623296 + 0.781986i 0.714207π0.714207\pi
390390 0 0
391391 23.8323i 0.0609523i
392392 3.84677 12.7284i 0.00981320 0.0324704i
393393 0 0
394394 36.1938 368.782i 0.0918624 0.935995i
395395 339.058i 0.858376i
396396 0 0
397397 −279.373 −0.703711 −0.351855 0.936054i 0.614449π-0.614449\pi
−0.351855 + 0.936054i 0.614449π0.614449\pi
398398 273.935 + 26.8851i 0.688278 + 0.0675505i
399399 0 0
400400 405.103 + 167.146i 1.01276 + 0.417866i
401401 582.199 1.45187 0.725934 0.687765i 0.241408π-0.241408\pi
0.725934 + 0.687765i 0.241408π0.241408\pi
402402 0 0
403403 414.401i 1.02829i
404404 186.823 + 37.0279i 0.462434 + 0.0916531i
405405 0 0
406406 −513.577 50.4046i −1.26497 0.124149i
407407 797.842i 1.96030i
408408 0 0
409409 −436.661 −1.06763 −0.533815 0.845601i 0.679242π-0.679242\pi
−0.533815 + 0.845601i 0.679242π0.679242\pi
410410 −80.5827 + 821.065i −0.196543 + 2.00260i
411411 0 0
412412 41.7792 210.796i 0.101406 0.511641i
413413 154.203 0.373374
414414 0 0
415415 1029.24i 2.48010i
416416 −115.406 + 216.806i −0.277419 + 0.521168i
417417 0 0
418418 −48.7281 + 496.495i −0.116574 + 1.18779i
419419 758.271i 1.80972i 0.425714 + 0.904858i 0.360023π0.360023\pi
−0.425714 + 0.904858i 0.639977π0.639977\pi
420420 0 0
421421 523.348 1.24311 0.621553 0.783372i 0.286502π-0.286502\pi
0.621553 + 0.783372i 0.286502π0.286502\pi
422422 −607.588 59.6312i −1.43978 0.141306i
423423 0 0
424424 18.1137 59.9356i 0.0427211 0.141358i
425425 39.3641 0.0926215
426426 0 0
427427 462.225i 1.08249i
428428 20.5853 103.863i 0.0480965 0.242670i
429429 0 0
430430 −974.171 95.6092i −2.26551 0.222347i
431431 729.146i 1.69176i 0.533377 + 0.845878i 0.320923π0.320923\pi
−0.533377 + 0.845878i 0.679077π0.679077\pi
432432 0 0
433433 −491.219 −1.13445 −0.567227 0.823561i 0.691984π-0.691984\pi
−0.567227 + 0.823561i 0.691984π0.691984\pi
434434 −72.5679 + 739.402i −0.167207 + 1.70369i
435435 0 0
436436 −325.919 64.5963i −0.747521 0.148157i
437437 230.402 0.527236
438438 0 0
439439 188.693i 0.429825i 0.976633 + 0.214913i 0.0689467π0.0689467\pi
−0.976633 + 0.214913i 0.931053π0.931053\pi
440440 995.087 + 300.735i 2.26156 + 0.683489i
441441 0 0
442442 −2.15488 + 21.9563i −0.00487530 + 0.0496749i
443443 413.208i 0.932749i −0.884587 0.466375i 0.845560π-0.845560\pi
0.884587 0.466375i 0.154440π-0.154440\pi
444444 0 0
445445 304.779 0.684896
446446 −34.2800 3.36438i −0.0768610 0.00754346i
447447 0 0
448448 243.882 366.630i 0.544378 0.818371i
449449 638.253 1.42150 0.710749 0.703446i 0.248356π-0.248356\pi
0.710749 + 0.703446i 0.248356π0.248356\pi
450450 0 0
451451 1023.14i 2.26861i
452452 −60.9255 12.0753i −0.134791 0.0267152i
453453 0 0
454454 81.5772 + 8.00633i 0.179686 + 0.0176351i
455455 382.225i 0.840055i
456456 0 0
457457 −230.687 −0.504786 −0.252393 0.967625i 0.581218π-0.581218\pi
−0.252393 + 0.967625i 0.581218π0.581218\pi
458458 26.0699 265.629i 0.0569213 0.579976i
459459 0 0
460460 93.3386 470.938i 0.202910 1.02378i
461461 400.188 0.868088 0.434044 0.900892i 0.357086π-0.357086\pi
0.434044 + 0.900892i 0.357086π0.357086\pi
462462 0 0
463463 296.656i 0.640727i 0.947295 + 0.320363i 0.103805π0.103805\pi
−0.947295 + 0.320363i 0.896195π0.896195\pi
464464 554.671 + 228.859i 1.19541 + 0.493230i
465465 0 0
466466 −71.9561 + 733.168i −0.154412 + 1.57332i
467467 127.057i 0.272070i −0.990704 0.136035i 0.956564π-0.956564\pi
0.990704 0.136035i 0.0434359π-0.0434359\pi
468468 0 0
469469 476.141 1.01523
470470 135.922 + 13.3400i 0.289196 + 0.0283829i
471471 0 0
472472 −171.633 51.8709i −0.363629 0.109896i
473473 −1213.93 −2.56645
474474 0 0
475475 380.558i 0.801174i
476476 7.68977 38.7986i 0.0161550 0.0815096i
477477 0 0
478478 −574.361 56.3701i −1.20159 0.117929i
479479 12.3150i 0.0257098i 0.999917 + 0.0128549i 0.00409195π0.00409195\pi
−0.999917 + 0.0128549i 0.995908π0.995908\pi
480480 0 0
481481 341.100 0.709147
482482 20.1185 204.990i 0.0417397 0.425290i
483483 0 0
484484 789.827 + 156.542i 1.63187 + 0.323433i
485485 −455.241 −0.938642
486486 0 0
487487 181.054i 0.371773i −0.982571 0.185887i 0.940484π-0.940484\pi
0.982571 0.185887i 0.0595157π-0.0595157\pi
488488 −155.483 + 514.469i −0.318613 + 1.05424i
489489 0 0
490490 2.35016 23.9460i 0.00479624 0.0488694i
491491 497.080i 1.01238i −0.862421 0.506191i 0.831053π-0.831053\pi
0.862421 0.506191i 0.168947π-0.168947\pi
492492 0 0
493493 53.8978 0.109326
494494 −212.265 20.8326i −0.429687 0.0421712i
495495 0 0
496496 329.490 798.565i 0.664294 1.61001i
497497 49.1795 0.0989527
498498 0 0
499499 762.567i 1.52819i −0.645103 0.764096i 0.723186π-0.723186\pi
0.645103 0.764096i 0.276814π-0.276814\pi
500500 67.8589 + 13.4495i 0.135718 + 0.0268989i
501501 0 0
502502 139.304 + 13.6719i 0.277498 + 0.0272348i
503503 994.596i 1.97733i −0.150146 0.988664i 0.547974π-0.547974\pi
0.150146 0.988664i 0.452026π-0.452026\pi
504504 0 0
505505 344.635 0.682446
506506 58.1554 592.551i 0.114932 1.17105i
507507 0 0
508508 −122.453 + 617.835i −0.241050 + 1.21621i
509509 −53.7310 −0.105562 −0.0527810 0.998606i 0.516809π-0.516809\pi
−0.0527810 + 0.998606i 0.516809π0.516809\pi
510510 0 0
511511 553.454i 1.08308i
512512 −394.774 + 326.033i −0.771043 + 0.636783i
513513 0 0
514514 18.9649 193.235i 0.0368967 0.375944i
515515 388.858i 0.755064i
516516 0 0
517517 169.375 0.327611
518518 −608.613 59.7318i −1.17493 0.115312i
519519 0 0
520520 −128.573 + 425.427i −0.247255 + 0.818129i
521521 −616.206 −1.18274 −0.591369 0.806401i 0.701412π-0.701412\pi
−0.591369 + 0.806401i 0.701412π0.701412\pi
522522 0 0
523523 683.938i 1.30772i −0.756615 0.653860i 0.773148π-0.773148\pi
0.756615 0.653860i 0.226852π-0.226852\pi
524524 36.5962 184.645i 0.0698401 0.352376i
525525 0 0
526526 −16.7291 1.64186i −0.0318043 0.00312140i
527527 77.5971i 0.147243i
528528 0 0
529529 254.022 0.480194
530530 11.0665 112.757i 0.0208801 0.212749i
531531 0 0
532532 375.090 + 74.3418i 0.705057 + 0.139740i
533533 −437.421 −0.820678
534534 0 0
535535 191.597i 0.358125i
536536 −529.959 160.164i −0.988729 0.298814i
537537 0 0
538538 54.9320 559.707i 0.102104 1.04035i
539539 29.8395i 0.0553608i
540540 0 0
541541 518.000 0.957486 0.478743 0.877955i 0.341093π-0.341093\pi
0.478743 + 0.877955i 0.341093π0.341093\pi
542542 735.379 + 72.1731i 1.35679 + 0.133161i
543543 0 0
544544 −21.6100 + 40.5972i −0.0397242 + 0.0746272i
545545 −601.227 −1.10317
546546 0 0
547547 294.263i 0.537957i 0.963146 + 0.268979i 0.0866861π0.0866861\pi
−0.963146 + 0.268979i 0.913314π0.913314\pi
548548 461.021 + 91.3732i 0.841280 + 0.166739i
549549 0 0
550550 978.723 + 96.0559i 1.77950 + 0.174647i
551551 521.064i 0.945669i
552552 0 0
553553 −322.298 −0.582817
554554 −25.9638 + 264.547i −0.0468660 + 0.477522i
555555 0 0
556556 −30.8700 + 155.754i −0.0555216 + 0.280133i
557557 −395.706 −0.710424 −0.355212 0.934786i 0.615591π-0.615591\pi
−0.355212 + 0.934786i 0.615591π0.615591\pi
558558 0 0
559559 518.989i 0.928424i
560560 303.907 736.561i 0.542691 1.31529i
561561 0 0
562562 7.28954 74.2739i 0.0129707 0.132160i
563563 259.253i 0.460484i 0.973133 + 0.230242i 0.0739518π0.0739518\pi
−0.973133 + 0.230242i 0.926048π0.926048\pi
564564 0 0
565565 −112.390 −0.198920
566566 −310.843 30.5074i −0.549193 0.0539001i
567567 0 0
568568 −54.7382 16.5430i −0.0963700 0.0291250i
569569 247.188 0.434426 0.217213 0.976124i 0.430303π-0.430303\pi
0.217213 + 0.976124i 0.430303π0.430303\pi
570570 0 0
571571 601.307i 1.05308i −0.850151 0.526539i 0.823489π-0.823489\pi
0.850151 0.526539i 0.176511π-0.176511\pi
572572 −107.155 + 540.648i −0.187334 + 0.945189i
573573 0 0
574574 780.477 + 76.5992i 1.35972 + 0.133448i
575575 454.184i 0.789885i
576576 0 0
577577 −754.648 −1.30788 −0.653941 0.756545i 0.726886π-0.726886\pi
−0.653941 + 0.756545i 0.726886π0.726886\pi
578578 56.0525 571.125i 0.0969767 0.988105i
579579 0 0
580580 1065.05 + 211.089i 1.83628 + 0.363947i
581581 978.363 1.68393
582582 0 0
583583 140.509i 0.241010i
584584 −186.171 + 616.010i −0.318785 + 1.05481i
585585 0 0
586586 5.07445 51.7040i 0.00865946 0.0882321i
587587 243.805i 0.415342i 0.978199 + 0.207671i 0.0665883π0.0665883\pi
−0.978199 + 0.207671i 0.933412π0.933412\pi
588588 0 0
589589 750.180 1.27365
590590 −322.894 31.6901i −0.547278 0.0537121i
591591 0 0
592592 657.311 + 271.208i 1.11032 + 0.458122i
593593 1091.73 1.84103 0.920516 0.390704i 0.127768π-0.127768\pi
0.920516 + 0.390704i 0.127768π0.127768\pi
594594 0 0
595595 71.5722i 0.120289i
596596 −450.545 89.2967i −0.755947 0.149827i
597597 0 0
598598 253.332 + 24.8630i 0.423632 + 0.0415770i
599599 940.721i 1.57049i −0.619188 0.785243i 0.712538π-0.712538\pi
0.619188 0.785243i 0.287462π-0.287462\pi
600600 0 0
601601 1052.23 1.75079 0.875396 0.483406i 0.160600π-0.160600\pi
0.875396 + 0.483406i 0.160600π0.160600\pi
602602 −90.8829 + 926.015i −0.150968 + 1.53823i
603603 0 0
604604 −124.521 + 628.267i −0.206160 + 1.04018i
605605 1457.00 2.40827
606606 0 0
607607 439.798i 0.724544i 0.932072 + 0.362272i 0.117999π0.117999\pi
−0.932072 + 0.362272i 0.882001π0.882001\pi
608608 −392.479 208.917i −0.645524 0.343614i
609609 0 0
610610 −94.9912 + 967.875i −0.155723 + 1.58668i
611611 72.4124i 0.118515i
612612 0 0
613613 449.866 0.733876 0.366938 0.930245i 0.380406π-0.380406\pi
0.366938 + 0.930245i 0.380406π0.380406\pi
614614 222.271 + 21.8146i 0.362005 + 0.0355287i
615615 0 0
616616 285.869 945.896i 0.464073 1.53555i
617617 −848.536 −1.37526 −0.687630 0.726061i 0.741349π-0.741349\pi
−0.687630 + 0.726061i 0.741349π0.741349\pi
618618 0 0
619619 539.918i 0.872242i 0.899888 + 0.436121i 0.143648π0.143648\pi
−0.899888 + 0.436121i 0.856352π0.856352\pi
620620 303.907 1533.35i 0.490172 2.47315i
621621 0 0
622622 −644.387 63.2428i −1.03599 0.101677i
623623 289.713i 0.465028i
624624 0 0
625625 −559.555 −0.895288
626626 71.5332 728.859i 0.114270 1.16431i
627627 0 0
628628 −884.150 175.236i −1.40788 0.279038i
629629 63.8714 0.101544
630630 0 0
631631 43.6036i 0.0691024i 0.999403 + 0.0345512i 0.0110002π0.0110002\pi
−0.999403 + 0.0345512i 0.989000π0.989000\pi
632632 358.726 + 108.414i 0.567605 + 0.171542i
633633 0 0
634634 12.6983 129.384i 0.0200288 0.204076i
635635 1139.73i 1.79485i
636636 0 0
637637 12.7572 0.0200270
638638 1340.08 + 131.521i 2.10043 + 0.206145i
639639 0 0
640640 −586.021 + 717.585i −0.915657 + 1.12123i
641641 −167.263 −0.260940 −0.130470 0.991452i 0.541649π-0.541649\pi
−0.130470 + 0.991452i 0.541649π0.541649\pi
642642 0 0
643643 745.770i 1.15983i 0.814678 + 0.579914i 0.196914π0.196914\pi
−0.814678 + 0.579914i 0.803086π0.803086\pi
644644 −447.658 88.7246i −0.695121 0.137771i
645645 0 0
646646 −39.7470 3.90093i −0.0615279 0.00603860i
647647 596.836i 0.922467i 0.887279 + 0.461233i 0.152593π0.152593\pi
−0.887279 + 0.461233i 0.847407π0.847407\pi
648648 0 0
649649 −402.363 −0.619974
650650 −41.0666 + 418.431i −0.0631793 + 0.643740i
651651 0 0
652652 −114.444 + 577.426i −0.175528 + 0.885623i
653653 −790.871 −1.21113 −0.605567 0.795794i 0.707054π-0.707054\pi
−0.605567 + 0.795794i 0.707054π0.707054\pi
654654 0 0
655655 340.617i 0.520026i
656656 −842.926 347.793i −1.28495 0.530173i
657657 0 0
658658 12.6805 129.203i 0.0192713 0.196357i
659659 402.569i 0.610878i 0.952212 + 0.305439i 0.0988033π0.0988033\pi
−0.952212 + 0.305439i 0.901197π0.901197\pi
660660 0 0
661661 486.544 0.736072 0.368036 0.929811i 0.380030π-0.380030\pi
0.368036 + 0.929811i 0.380030π0.380030\pi
662662 874.678 + 85.8445i 1.32127 + 0.129674i
663663 0 0
664664 −1088.95 329.101i −1.63998 0.495634i
665665 691.933 1.04050
666666 0 0
667667 621.873i 0.932343i
668668 82.3888 415.691i 0.123337 0.622292i
669669 0 0
670670 −997.015 97.8511i −1.48808 0.146046i
671671 1206.08i 1.79744i
672672 0 0
673673 −171.727 −0.255167 −0.127583 0.991828i 0.540722π-0.540722\pi
−0.127583 + 0.991828i 0.540722π0.540722\pi
674674 73.2205 746.051i 0.108636 1.10690i
675675 0 0
676676 431.959 + 85.6132i 0.638993 + 0.126647i
677677 213.095 0.314763 0.157382 0.987538i 0.449695π-0.449695\pi
0.157382 + 0.987538i 0.449695π0.449695\pi
678678 0 0
679679 432.737i 0.637316i
680680 −24.0754 + 79.6619i −0.0354050 + 0.117150i
681681 0 0
682682 189.352 1929.32i 0.277642 2.82892i
683683 602.265i 0.881794i 0.897558 + 0.440897i 0.145340π0.145340\pi
−0.897558 + 0.440897i 0.854660π0.854660\pi
684684 0 0
685685 850.451 1.24153
686686 −693.803 68.0927i −1.01137 0.0992605i
687687 0 0
688688 412.648 1000.11i 0.599779 1.45365i
689689 60.0713 0.0871862
690690 0 0
691691 1227.31i 1.77614i −0.459705 0.888071i 0.652045π-0.652045\pi
0.459705 0.888071i 0.347955π-0.347955\pi
692692 −731.466 144.975i −1.05703 0.209501i
693693 0 0
694694 654.913 + 64.2759i 0.943679 + 0.0926166i
695695 287.321i 0.413412i
696696 0 0
697697 −81.9078 −0.117515
698698 −72.7689 + 741.449i −0.104253 + 1.06225i
699699 0 0
700700 146.547 739.402i 0.209353 1.05629i
701701 −133.314 −0.190176 −0.0950882 0.995469i 0.530313π-0.530313\pi
−0.0950882 + 0.995469i 0.530313π0.530313\pi
702702 0 0
703703 617.485i 0.878357i
704704 −636.360 + 956.649i −0.903921 + 1.35888i
705705 0 0
706706 42.5390 433.434i 0.0602536 0.613929i
707707 327.599i 0.463364i
708708 0 0
709709 −610.256 −0.860728 −0.430364 0.902655i 0.641615π-0.641615\pi
−0.430364 + 0.902655i 0.641615π0.641615\pi
710710 −102.979 10.1068i −0.145041 0.0142349i
711711 0 0
712712 −97.4534 + 322.458i −0.136873 + 0.452891i
713713 −895.316 −1.25570
714714 0 0
715715 997.340i 1.39488i
716716 148.998 751.764i 0.208097 1.04995i
717717 0 0
718718 289.761 + 28.4383i 0.403566 + 0.0396077i
719719 967.279i 1.34531i 0.739956 + 0.672656i 0.234846π0.234846\pi
−0.739956 + 0.672656i 0.765154π0.765154\pi
720720 0 0
721721 −369.635 −0.512671
722722 −32.8084 + 334.289i −0.0454411 + 0.463004i
723723 0 0
724724 −804.196 159.389i −1.11077 0.220151i
725725 1027.15 1.41676
726726 0 0
727727 1396.59i 1.92103i 0.278220 + 0.960517i 0.410256π0.410256\pi
−0.278220 + 0.960517i 0.589744π0.589744\pi
728728 404.397 + 122.217i 0.555490 + 0.167880i
729729 0 0
730730 −113.740 + 1158.90i −0.155808 + 1.58754i
731731 97.1814i 0.132943i
732732 0 0
733733 −306.229 −0.417775 −0.208888 0.977940i 0.566984π-0.566984\pi
−0.208888 + 0.977940i 0.566984π0.566984\pi
734734 −106.442 10.4467i −0.145017 0.0142325i
735735 0 0
736736 468.411 + 249.336i 0.636428 + 0.338772i
737737 −1242.40 −1.68575
738738 0 0
739739 463.182i 0.626769i −0.949626 0.313384i 0.898537π-0.898537\pi
0.949626 0.313384i 0.101463π-0.101463\pi
740740 1262.13 + 250.150i 1.70558 + 0.338041i
741741 0 0
742742 −107.183 10.5194i −0.144452 0.0141771i
743743 810.697i 1.09111i 0.838074 + 0.545557i 0.183682π0.183682\pi
−0.838074 + 0.545557i 0.816318π0.816318\pi
744744 0 0
745745 −831.125 −1.11560
746746 66.7128 679.743i 0.0894273 0.911183i
747747 0 0
748748 −20.0649 + 101.237i −0.0268248 + 0.135344i
749749 −182.126 −0.243158
750750 0 0
751751 990.928i 1.31948i 0.751495 + 0.659739i 0.229333π0.229333\pi
−0.751495 + 0.659739i 0.770667π0.770667\pi
752752 −57.5751 + 139.541i −0.0765626 + 0.185560i
753753 0 0
754754 −56.2288 + 572.920i −0.0745739 + 0.759841i
755755 1158.97i 1.53506i
756756 0 0
757757 −320.001 −0.422723 −0.211361 0.977408i 0.567790π-0.567790\pi
−0.211361 + 0.977408i 0.567790π0.567790\pi
758758 −438.271 43.0137i −0.578194 0.0567464i
759759 0 0
760760 −770.141 232.752i −1.01334 0.306253i
761761 635.976 0.835710 0.417855 0.908514i 0.362782π-0.362782\pi
0.417855 + 0.908514i 0.362782π0.362782\pi
762762 0 0
763763 571.506i 0.749025i
764764 −69.8461 + 352.407i −0.0914217 + 0.461266i
765765 0 0
766766 1335.73 + 131.094i 1.74377 + 0.171141i
767767 172.021i 0.224278i
768768 0 0
769769 305.852 0.397727 0.198864 0.980027i 0.436275π-0.436275\pi
0.198864 + 0.980027i 0.436275π0.436275\pi
770770 174.649 1779.52i 0.226818 2.31107i
771771 0 0
772772 −657.593 130.333i −0.851805 0.168825i
773773 −187.263 −0.242255 −0.121128 0.992637i 0.538651π-0.538651\pi
−0.121128 + 0.992637i 0.538651π0.538651\pi
774774 0 0
775775 1478.80i 1.90813i
776776 145.564 481.649i 0.187582 0.620681i
777777 0 0
778778 94.7298 965.211i 0.121761 1.24063i
779779 791.854i 1.01650i
780780 0 0
781781 −128.324 −0.164307
782782 47.4368 + 4.65564i 0.0606608 + 0.00595350i
783783 0 0
784784 24.5836 + 10.1432i 0.0313566 + 0.0129378i
785785 −1631.00 −2.07771
786786 0 0
787787 185.475i 0.235674i 0.993033 + 0.117837i 0.0375960π0.0375960\pi
−0.993033 + 0.117837i 0.962404π0.962404\pi
788788 726.967 + 144.083i 0.922547 + 0.182846i
789789 0 0
790790 674.874 + 66.2349i 0.854271 + 0.0838417i
791791 106.834i 0.135062i
792792 0 0
793793 −515.634 −0.650232
794794 54.5754 556.075i 0.0687348 0.700346i
795795 0 0
796796 −107.026 + 539.998i −0.134455 + 0.678389i
797797 1092.40 1.37064 0.685322 0.728240i 0.259662π-0.259662\pi
0.685322 + 0.728240i 0.259662π0.259662\pi
798798 0 0
799799 13.5593i 0.0169704i
800800 −411.831 + 773.679i −0.514789 + 0.967099i
801801 0 0
802802 −113.732 + 1158.83i −0.141811 + 1.44493i
803803 1444.13i 1.79842i
804804 0 0
805805 −825.800 −1.02584
806806 824.838 + 80.9530i 1.02337 + 0.100438i
807807 0 0
808808 −110.197 + 364.627i −0.136383 + 0.451270i
809809 51.1143 0.0631821 0.0315911 0.999501i 0.489943π-0.489943\pi
0.0315911 + 0.999501i 0.489943π0.489943\pi
810810 0 0
811811 680.159i 0.838667i 0.907832 + 0.419333i 0.137736π0.137736\pi
−0.907832 + 0.419333i 0.862264π0.862264\pi
812812 200.654 1012.40i 0.247111 1.24679i
813813 0 0
814814 1588.05 + 155.858i 1.95093 + 0.191472i
815815 1065.19i 1.30698i
816816 0 0
817817 939.514 1.14996
818818 85.3016 869.146i 0.104281 1.06253i
819819 0 0
820820 −1618.54 320.789i −1.97382 0.391207i
821821 124.267 0.151361 0.0756805 0.997132i 0.475887π-0.475887\pi
0.0756805 + 0.997132i 0.475887π0.475887\pi
822822 0 0
823823 1107.83i 1.34609i −0.739602 0.673044i 0.764986π-0.764986\pi
0.739602 0.673044i 0.235014π-0.235014\pi
824824 411.415 + 124.338i 0.499290 + 0.150895i
825825 0 0
826826 −30.1236 + 306.932i −0.0364692 + 0.371588i
827827 856.831i 1.03607i −0.855359 0.518036i 0.826663π-0.826663\pi
0.855359 0.518036i 0.173337π-0.173337\pi
828828 0 0
829829 −59.5071 −0.0717818 −0.0358909 0.999356i 0.511427π-0.511427\pi
−0.0358909 + 0.999356i 0.511427π0.511427\pi
830830 −2048.64 201.062i −2.46824 0.242243i
831831 0 0
832832 −408.994 272.062i −0.491579 0.326997i
833833 2.38881 0.00286771
834834 0 0
835835 766.830i 0.918359i
836836 −978.723 193.980i −1.17072 0.232034i
837837 0 0
838838 −1509.29 148.128i −1.80106 0.176764i
839839 464.691i 0.553863i 0.960890 + 0.276932i 0.0893176π0.0893176\pi
−0.960890 + 0.276932i 0.910682π0.910682\pi
840840 0 0
841841 565.391 0.672284
842842 −102.236 + 1041.69i −0.121420 + 1.23716i
843843 0 0
844844 237.384 1197.72i 0.281261 1.41910i
845845 796.840 0.943006
846846 0 0
847847 1384.98i 1.63516i
848848 115.759 + 47.7627i 0.136509 + 0.0563239i
849849 0 0
850850 −7.68977 + 78.3518i −0.00904679 + 0.0921786i
851851 736.948i 0.865979i
852852 0 0
853853 −1366.33 −1.60179 −0.800896 0.598803i 0.795643π-0.795643\pi
−0.800896 + 0.598803i 0.795643π0.795643\pi
854854 920.029 + 90.2955i 1.07732 + 0.105732i
855855 0 0
856856 202.711 + 61.2633i 0.236812 + 0.0715693i
857857 1677.60 1.95752 0.978762 0.205000i 0.0657193π-0.0657193\pi
0.978762 + 0.205000i 0.0657193π0.0657193\pi
858858 0 0
859859 1645.03i 1.91505i 0.288355 + 0.957524i 0.406892π0.406892\pi
−0.288355 + 0.957524i 0.593108π0.593108\pi
860860 380.608 1920.35i 0.442568 2.23296i
861861 0 0
862862 −1451.32 142.439i −1.68367 0.165242i
863863 294.311i 0.341033i −0.985355 0.170516i 0.945456π-0.945456\pi
0.985355 0.170516i 0.0545436π-0.0545436\pi
864864 0 0
865865 −1349.34 −1.55994
866866 95.9594 977.740i 0.110808 1.12903i
867867 0 0
868868 −1457.56 288.884i −1.67921 0.332815i
869869 840.971 0.967746
870870 0 0
871871 531.159i 0.609826i
872872 192.243 636.102i 0.220462 0.729475i
873873 0 0
874874 −45.0090 + 458.601i −0.0514977 + 0.524715i
875875 118.992i 0.135991i
876876 0 0
877877 719.169 0.820033 0.410016 0.912078i 0.365523π-0.365523\pi
0.410016 + 0.912078i 0.365523π0.365523\pi
878878 −375.582 36.8612i −0.427770 0.0419831i
879879 0 0
880880 −792.984 + 1921.91i −0.901118 + 2.18399i
881881 16.3083 0.0185112 0.00925559 0.999957i 0.497054π-0.497054\pi
0.00925559 + 0.999957i 0.497054π0.497054\pi
882882 0 0
883883 1190.35i 1.34807i −0.738698 0.674036i 0.764559π-0.764559\pi
0.738698 0.674036i 0.235441π-0.235441\pi
884884 −43.2817 8.57831i −0.0489612 0.00970398i
885885 0 0
886886 822.464 + 80.7200i 0.928289 + 0.0911061i
887887 400.666i 0.451709i −0.974161 0.225855i 0.927483π-0.927483\pi
0.974161 0.225855i 0.0725174π-0.0725174\pi
888888 0 0
889889 1083.39 1.21866
890890 −59.5384 + 606.643i −0.0668971 + 0.681621i
891891 0 0
892892 13.3932 67.5750i 0.0150148 0.0757567i
893893 −131.087 −0.146793
894894 0 0
895895 1386.79i 1.54948i
896896 682.112 + 557.052i 0.761286 + 0.621710i
897897 0 0
898898 −124.682 + 1270.40i −0.138845 + 1.41470i
899899 2024.79i 2.25227i
900900 0 0
901901 11.2484 0.0124844
902902 −2036.50 199.870i −2.25776 0.221586i
903903 0 0
904904 35.9368 118.909i 0.0397531 0.131537i
905905 −1483.51 −1.63924
906906 0 0
907907 1260.24i 1.38946i 0.719270 + 0.694731i 0.244476π0.244476\pi
−0.719270 + 0.694731i 0.755524π0.755524\pi
908908 −31.8722 + 160.810i −0.0351015 + 0.177104i
909909 0 0
910910 760.795 + 74.6675i 0.836038 + 0.0820522i
911911 964.398i 1.05862i 0.848430 + 0.529308i 0.177548π0.177548\pi
−0.848430 + 0.529308i 0.822452π0.822452\pi
912912 0 0
913913 −2552.84 −2.79610
914914 45.0646 459.168i 0.0493048 0.502372i
915915 0 0
916916 523.625 + 103.781i 0.571643 + 0.113298i
917917 −323.779 −0.353086
918918 0 0
919919 424.406i 0.461813i −0.972976 0.230906i 0.925831π-0.925831\pi
0.972976 0.230906i 0.0741691π-0.0741691\pi
920920 919.139 + 277.782i 0.999064 + 0.301937i
921921 0 0
922922 −78.1767 + 796.550i −0.0847903 + 0.863937i
923923 54.8621i 0.0594389i
924924 0 0
925925 1217.23 1.31592
926926 −590.476 57.9517i −0.637663 0.0625829i
927927 0 0
928928 −563.883 + 1059.33i −0.607633 + 1.14152i
929929 −858.458 −0.924067 −0.462033 0.886862i 0.652880π-0.652880\pi
−0.462033 + 0.886862i 0.652880π0.652880\pi
930930 0 0
931931 23.0941i 0.0248057i
932932 −1445.27 286.448i −1.55072 0.307348i
933933 0 0
934934 252.898 + 24.8205i 0.270769 + 0.0265744i
935935 186.753i 0.199736i
936936 0 0
937937 858.258 0.915964 0.457982 0.888962i 0.348572π-0.348572\pi
0.457982 + 0.888962i 0.348572π0.348572\pi
938938 −93.0140 + 947.729i −0.0991621 + 1.01037i
939939 0 0
940940 −53.1047 + 267.939i −0.0564944 + 0.285041i
941941 −937.106 −0.995862 −0.497931 0.867217i 0.665907π-0.665907\pi
−0.497931 + 0.867217i 0.665907π0.665907\pi
942942 0 0
943943 945.052i 1.00218i
944944 136.774 331.491i 0.144888 0.351156i
945945 0 0
946946 237.141 2416.25i 0.250677 2.55418i
947947 887.159i 0.936810i −0.883514 0.468405i 0.844829π-0.844829\pi
0.883514 0.468405i 0.155171π-0.155171\pi
948948 0 0
949949 −617.405 −0.650585
950950 −757.476 74.3418i −0.797344 0.0782546i
951951 0 0
952952 75.7239 + 22.8853i 0.0795419 + 0.0240392i
953953 1078.46 1.13164 0.565821 0.824528i 0.308559π-0.308559\pi
0.565821 + 0.824528i 0.308559π0.308559\pi
954954 0 0
955955 650.090i 0.680722i
956956 224.402 1132.22i 0.234731 1.18433i
957957 0 0
958958 −24.5122 2.40573i −0.0255868 0.00251120i
959959 808.411i 0.842973i
960960 0 0
961961 −1954.11 −2.03342
962962 −66.6337 + 678.937i −0.0692658 + 0.705756i
963963 0 0
964964 404.089 + 80.0894i 0.419180 + 0.0830803i
965965 −1213.07 −1.25707
966966 0 0
967967 119.065i 0.123128i −0.998103 0.0615640i 0.980391π-0.980391\pi
0.998103 0.0615640i 0.0196088π-0.0196088\pi
968968 −465.878 + 1541.52i −0.481279 + 1.59248i
969969 0 0
970970 88.9312 906.129i 0.0916817 0.934154i
971971 1516.56i 1.56185i 0.624624 + 0.780926i 0.285252π0.285252\pi
−0.624624 + 0.780926i 0.714748π0.714748\pi
972972 0 0
973973 273.118 0.280697
974974 360.376 + 35.3687i 0.369996 + 0.0363129i
975975 0 0
976976 −993.645 409.980i −1.01808 0.420062i
977977 1578.30 1.61546 0.807729 0.589555i 0.200697π-0.200697\pi
0.807729 + 0.589555i 0.200697π0.200697\pi
978978 0 0
979979 755.947i 0.772162i
980980 47.2039 + 9.35568i 0.0481672 + 0.00954661i
981981 0 0
982982 989.406 + 97.1044i 1.00754 + 0.0988843i
983983 592.742i 0.602993i −0.953467 0.301497i 0.902514π-0.902514\pi
0.953467 0.301497i 0.0974862π-0.0974862\pi
984984 0 0
985985 1341.04 1.36147
986986 −10.5289 + 107.280i −0.0106784 + 0.108803i
987987 0 0
988988 82.9319 418.431i 0.0839392 0.423513i
989989 −1121.28 −1.13375
990990 0 0
991991 1896.17i 1.91339i 0.291098 + 0.956693i 0.405980π0.405980\pi
−0.291098 + 0.956693i 0.594020π0.594020\pi
992992 1525.13 + 811.828i 1.53743 + 0.818375i
993993 0 0
994994 −9.60720 + 97.8887i −0.00966519 + 0.0984796i
995995 996.141i 1.00115i
996996 0 0
997997 69.7126 0.0699224 0.0349612 0.999389i 0.488869π-0.488869\pi
0.0349612 + 0.999389i 0.488869π0.488869\pi
998998 1517.84 + 148.967i 1.52088 + 0.149266i
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 324.3.d.e.163.4 yes 6
3.2 odd 2 324.3.d.f.163.3 yes 6
4.3 odd 2 inner 324.3.d.e.163.3 6
9.2 odd 6 324.3.f.q.271.1 12
9.4 even 3 324.3.f.r.55.2 12
9.5 odd 6 324.3.f.q.55.5 12
9.7 even 3 324.3.f.r.271.6 12
12.11 even 2 324.3.d.f.163.4 yes 6
36.7 odd 6 324.3.f.r.271.2 12
36.11 even 6 324.3.f.q.271.5 12
36.23 even 6 324.3.f.q.55.1 12
36.31 odd 6 324.3.f.r.55.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
324.3.d.e.163.3 6 4.3 odd 2 inner
324.3.d.e.163.4 yes 6 1.1 even 1 trivial
324.3.d.f.163.3 yes 6 3.2 odd 2
324.3.d.f.163.4 yes 6 12.11 even 2
324.3.f.q.55.1 12 36.23 even 6
324.3.f.q.55.5 12 9.5 odd 6
324.3.f.q.271.1 12 9.2 odd 6
324.3.f.q.271.5 12 36.11 even 6
324.3.f.r.55.2 12 9.4 even 3
324.3.f.r.55.6 12 36.31 odd 6
324.3.f.r.271.2 12 36.7 odd 6
324.3.f.r.271.6 12 9.7 even 3