Properties

Label 1305.2.c.j.784.10
Level 13051305
Weight 22
Character 1305.784
Analytic conductor 10.42010.420
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1305,2,Mod(784,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1305.784");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1305=32529 1305 = 3^{2} \cdot 5 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1305.c (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: 10.420477463810.4204774638
Analytic rank: 00
Dimension: 1010
Coefficient field: 10.0.3899266318336.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x102x9+2x8+6x7+19x612x5+4x4+2x3+9x26x+2 x^{10} - 2x^{9} + 2x^{8} + 6x^{7} + 19x^{6} - 12x^{5} + 4x^{4} + 2x^{3} + 9x^{2} - 6x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 435)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 784.10
Root 1.209641.20964i-1.20964 - 1.20964i of defining polynomial
Character χ\chi == 1305.784
Dual form 1305.2.c.j.784.1

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+2.51908iq24.34577q4+(1.274131.83755i)q50.173311iq75.90919iq8+(4.62893+3.20964i)q105.08250q11+1.82669iq13+0.436584q14+6.19418q164.24598iq17+8.62093q19+(5.53709+7.98556i)q2012.8032iq223.16348iq23+(1.753174.68256i)q254.60158q26+0.753170iq28+1.00000q29+3.22185q31+3.78527iq32+10.6960q34+(0.3184670.220821i)q351.97828iq37+21.7168iq38+(10.85847.52909i)q40+9.96541q41+7.91070iq43+22.0874q44+7.96907q468.66893iq47+6.96996q49+(11.79584.41638i)q507.93837iq525.40285iq53+(6.47578+9.33933i)q551.02413q56+2.51908iq58+7.66286q59+2.76215q61+8.11611iq62+2.85296q64+(3.35663+2.32744i)q658.13872iq67+18.4520iq68+(0.5562670.802245i)q70+6.25938q716.74356iq73+4.98345q7437.4646q76+0.880853iq774.54763q79+(7.8922111.3821i)q80+25.1037iq82+11.6224iq83+(7.802195.40994i)q8519.9277q86+30.0334iq8816.4911q89+0.316585q91+13.7478iq92+21.8377q94+(10.984215.8414i)q952.74419iq97+17.5579iq98+O(q100)q+2.51908i q^{2} -4.34577 q^{4} +(1.27413 - 1.83755i) q^{5} -0.173311i q^{7} -5.90919i q^{8} +(4.62893 + 3.20964i) q^{10} -5.08250 q^{11} +1.82669i q^{13} +0.436584 q^{14} +6.19418 q^{16} -4.24598i q^{17} +8.62093 q^{19} +(-5.53709 + 7.98556i) q^{20} -12.8032i q^{22} -3.16348i q^{23} +(-1.75317 - 4.68256i) q^{25} -4.60158 q^{26} +0.753170i q^{28} +1.00000 q^{29} +3.22185 q^{31} +3.78527i q^{32} +10.6960 q^{34} +(-0.318467 - 0.220821i) q^{35} -1.97828i q^{37} +21.7168i q^{38} +(-10.8584 - 7.52909i) q^{40} +9.96541 q^{41} +7.91070i q^{43} +22.0874 q^{44} +7.96907 q^{46} -8.66893i q^{47} +6.96996 q^{49} +(11.7958 - 4.41638i) q^{50} -7.93837i q^{52} -5.40285i q^{53} +(-6.47578 + 9.33933i) q^{55} -1.02413 q^{56} +2.51908i q^{58} +7.66286 q^{59} +2.76215 q^{61} +8.11611i q^{62} +2.85296 q^{64} +(3.35663 + 2.32744i) q^{65} -8.13872i q^{67} +18.4520i q^{68} +(0.556267 - 0.802245i) q^{70} +6.25938 q^{71} -6.74356i q^{73} +4.98345 q^{74} -37.4646 q^{76} +0.880853i q^{77} -4.54763 q^{79} +(7.89221 - 11.3821i) q^{80} +25.1037i q^{82} +11.6224i q^{83} +(-7.80219 - 5.40994i) q^{85} -19.9277 q^{86} +30.0334i q^{88} -16.4911 q^{89} +0.316585 q^{91} +13.7478i q^{92} +21.8377 q^{94} +(10.9842 - 15.8414i) q^{95} -2.74419i q^{97} +17.5579i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q10q4+4q1024q11+12q14+2q16+4q198q20+2q25+10q29+4q318q342q3514q40+28q41+40q4412q46+14q49+12q50++36q95+O(q100) 10 q - 10 q^{4} + 4 q^{10} - 24 q^{11} + 12 q^{14} + 2 q^{16} + 4 q^{19} - 8 q^{20} + 2 q^{25} + 10 q^{29} + 4 q^{31} - 8 q^{34} - 2 q^{35} - 14 q^{40} + 28 q^{41} + 40 q^{44} - 12 q^{46} + 14 q^{49} + 12 q^{50}+ \cdots + 36 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1305Z)×\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times.

nn 146146 262262 901901
χ(n)\chi(n) 11 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 2.51908i 1.78126i 0.454729 + 0.890630i 0.349736π0.349736\pi
−0.454729 + 0.890630i 0.650264π0.650264\pi
33 0 0
44 −4.34577 −2.17289
55 1.27413 1.83755i 0.569810 0.821777i
66 0 0
77 0.173311i 0.0655054i −0.999463 0.0327527i 0.989573π-0.989573\pi
0.999463 0.0327527i 0.0104274π-0.0104274\pi
88 5.90919i 2.08921i
99 0 0
1010 4.62893 + 3.20964i 1.46380 + 1.01498i
1111 −5.08250 −1.53243 −0.766215 0.642584i 0.777862π-0.777862\pi
−0.766215 + 0.642584i 0.777862π0.777862\pi
1212 0 0
1313 1.82669i 0.506632i 0.967384 + 0.253316i 0.0815213π0.0815213\pi
−0.967384 + 0.253316i 0.918479π0.918479\pi
1414 0.436584 0.116682
1515 0 0
1616 6.19418 1.54854
1717 4.24598i 1.02980i −0.857250 0.514901i 0.827829π-0.827829\pi
0.857250 0.514901i 0.172171π-0.172171\pi
1818 0 0
1919 8.62093 1.97778 0.988889 0.148656i 0.0474948π-0.0474948\pi
0.988889 + 0.148656i 0.0474948π0.0474948\pi
2020 −5.53709 + 7.98556i −1.23813 + 1.78563i
2121 0 0
2222 12.8032i 2.72966i
2323 3.16348i 0.659632i −0.944045 0.329816i 0.893013π-0.893013\pi
0.944045 0.329816i 0.106987π-0.106987\pi
2424 0 0
2525 −1.75317 4.68256i −0.350634 0.936513i
2626 −4.60158 −0.902444
2727 0 0
2828 0.753170i 0.142336i
2929 1.00000 0.185695
3030 0 0
3131 3.22185 0.578662 0.289331 0.957229i 0.406567π-0.406567\pi
0.289331 + 0.957229i 0.406567π0.406567\pi
3232 3.78527i 0.669147i
3333 0 0
3434 10.6960 1.83434
3535 −0.318467 0.220821i −0.0538308 0.0373256i
3636 0 0
3737 1.97828i 0.325227i −0.986690 0.162614i 0.948008π-0.948008\pi
0.986690 0.162614i 0.0519924π-0.0519924\pi
3838 21.7168i 3.52294i
3939 0 0
4040 −10.8584 7.52909i −1.71687 1.19045i
4141 9.96541 1.55634 0.778168 0.628056i 0.216149π-0.216149\pi
0.778168 + 0.628056i 0.216149π0.216149\pi
4242 0 0
4343 7.91070i 1.20637i 0.797601 + 0.603185i 0.206102π0.206102\pi
−0.797601 + 0.603185i 0.793898π0.793898\pi
4444 22.0874 3.32980
4545 0 0
4646 7.96907 1.17497
4747 8.66893i 1.26449i −0.774767 0.632246i 0.782133π-0.782133\pi
0.774767 0.632246i 0.217867π-0.217867\pi
4848 0 0
4949 6.96996 0.995709
5050 11.7958 4.41638i 1.66817 0.624570i
5151 0 0
5252 7.93837i 1.10085i
5353 5.40285i 0.742138i −0.928605 0.371069i 0.878991π-0.878991\pi
0.928605 0.371069i 0.121009π-0.121009\pi
5454 0 0
5555 −6.47578 + 9.33933i −0.873194 + 1.25932i
5656 −1.02413 −0.136855
5757 0 0
5858 2.51908i 0.330772i
5959 7.66286 0.997619 0.498810 0.866712i 0.333771π-0.333771\pi
0.498810 + 0.866712i 0.333771π0.333771\pi
6060 0 0
6161 2.76215 0.353657 0.176828 0.984242i 0.443416π-0.443416\pi
0.176828 + 0.984242i 0.443416π0.443416\pi
6262 8.11611i 1.03075i
6363 0 0
6464 2.85296 0.356620
6565 3.35663 + 2.32744i 0.416339 + 0.288684i
6666 0 0
6767 8.13872i 0.994303i −0.867664 0.497152i 0.834379π-0.834379\pi
0.867664 0.497152i 0.165621π-0.165621\pi
6868 18.4520i 2.23764i
6969 0 0
7070 0.556267 0.802245i 0.0664866 0.0958866i
7171 6.25938 0.742852 0.371426 0.928463i 0.378869π-0.378869\pi
0.371426 + 0.928463i 0.378869π0.378869\pi
7272 0 0
7373 6.74356i 0.789274i −0.918837 0.394637i 0.870870π-0.870870\pi
0.918837 0.394637i 0.129130π-0.129130\pi
7474 4.98345 0.579314
7575 0 0
7676 −37.4646 −4.29748
7777 0.880853i 0.100382i
7878 0 0
7979 −4.54763 −0.511649 −0.255824 0.966723i 0.582347π-0.582347\pi
−0.255824 + 0.966723i 0.582347π0.582347\pi
8080 7.89221 11.3821i 0.882376 1.27256i
8181 0 0
8282 25.1037i 2.77224i
8383 11.6224i 1.27573i 0.770149 + 0.637865i 0.220182π0.220182\pi
−0.770149 + 0.637865i 0.779818π0.779818\pi
8484 0 0
8585 −7.80219 5.40994i −0.846267 0.586791i
8686 −19.9277 −2.14886
8787 0 0
8888 30.0334i 3.20157i
8989 −16.4911 −1.74805 −0.874024 0.485882i 0.838499π-0.838499\pi
−0.874024 + 0.485882i 0.838499π0.838499\pi
9090 0 0
9191 0.316585 0.0331872
9292 13.7478i 1.43330i
9393 0 0
9494 21.8377 2.25239
9595 10.9842 15.8414i 1.12696 1.62529i
9696 0 0
9797 2.74419i 0.278631i −0.990248 0.139315i 0.955510π-0.955510\pi
0.990248 0.139315i 0.0444901π-0.0444901\pi
9898 17.5579i 1.77362i
9999 0 0
100100 7.61887 + 20.3493i 0.761887 + 2.03493i
101101 −6.41474 −0.638290 −0.319145 0.947706i 0.603396π-0.603396\pi
−0.319145 + 0.947706i 0.603396π0.603396\pi
102102 0 0
103103 7.08642i 0.698245i −0.937077 0.349123i 0.886480π-0.886480\pi
0.937077 0.349123i 0.113520π-0.113520\pi
104104 10.7942 1.05846
105105 0 0
106106 13.6102 1.32194
107107 0.925187i 0.0894412i 0.999000 + 0.0447206i 0.0142398π0.0142398\pi
−0.999000 + 0.0447206i 0.985760π0.985760\pi
108108 0 0
109109 −4.11700 −0.394337 −0.197169 0.980370i 0.563175π-0.563175\pi
−0.197169 + 0.980370i 0.563175π0.563175\pi
110110 −23.5265 16.3130i −2.24317 1.55538i
111111 0 0
112112 1.07352i 0.101438i
113113 6.84626i 0.644042i −0.946732 0.322021i 0.895638π-0.895638\pi
0.946732 0.322021i 0.104362π-0.104362\pi
114114 0 0
115115 −5.81305 4.03070i −0.542070 0.375864i
116116 −4.34577 −0.403495
117117 0 0
118118 19.3034i 1.77702i
119119 −0.735875 −0.0674575
120120 0 0
121121 14.8318 1.34834
122122 6.95807i 0.629954i
123123 0 0
124124 −14.0014 −1.25737
125125 −10.8382 2.74467i −0.969399 0.245491i
126126 0 0
127127 5.25850i 0.466617i 0.972403 + 0.233308i 0.0749551π0.0749551\pi
−0.972403 + 0.233308i 0.925045π0.925045\pi
128128 14.7574i 1.30438i
129129 0 0
130130 −5.86302 + 8.45562i −0.514221 + 0.741607i
131131 −17.7157 −1.54783 −0.773913 0.633293i 0.781703π-0.781703\pi
−0.773913 + 0.633293i 0.781703π0.781703\pi
132132 0 0
133133 1.49410i 0.129555i
134134 20.5021 1.77111
135135 0 0
136136 −25.0903 −2.15147
137137 1.14479i 0.0978057i −0.998804 0.0489028i 0.984428π-0.984428\pi
0.998804 0.0489028i 0.0155725π-0.0155725\pi
138138 0 0
139139 −4.08670 −0.346630 −0.173315 0.984866i 0.555448π-0.555448\pi
−0.173315 + 0.984866i 0.555448π0.555448\pi
140140 1.38399 + 0.959639i 0.116968 + 0.0811043i
141141 0 0
142142 15.7679i 1.32321i
143143 9.28414i 0.776379i
144144 0 0
145145 1.27413 1.83755i 0.105811 0.152600i
146146 16.9876 1.40590
147147 0 0
148148 8.59715i 0.706682i
149149 1.50268 0.123105 0.0615523 0.998104i 0.480395π-0.480395\pi
0.0615523 + 0.998104i 0.480395π0.480395\pi
150150 0 0
151151 −21.4897 −1.74881 −0.874404 0.485199i 0.838747π-0.838747\pi
−0.874404 + 0.485199i 0.838747π0.838747\pi
152152 50.9427i 4.13200i
153153 0 0
154154 −2.21894 −0.178807
155155 4.10507 5.92031i 0.329727 0.475531i
156156 0 0
157157 11.1167i 0.887206i −0.896223 0.443603i 0.853700π-0.853700\pi
0.896223 0.443603i 0.146300π-0.146300\pi
158158 11.4559i 0.911379i
159159 0 0
160160 6.95561 + 4.82293i 0.549889 + 0.381286i
161161 −0.548266 −0.0432094
162162 0 0
163163 12.2180i 0.956988i −0.878091 0.478494i 0.841183π-0.841183\pi
0.878091 0.478494i 0.158817π-0.158817\pi
164164 −43.3074 −3.38174
165165 0 0
166166 −29.2779 −2.27240
167167 21.3634i 1.65315i 0.562826 + 0.826576i 0.309714π0.309714\pi
−0.562826 + 0.826576i 0.690286π0.690286\pi
168168 0 0
169169 9.66321 0.743324
170170 13.6281 19.6544i 1.04523 1.50742i
171171 0 0
172172 34.3781i 2.62130i
173173 13.1686i 1.00119i −0.865682 0.500594i 0.833115π-0.833115\pi
0.865682 0.500594i 0.166885π-0.166885\pi
174174 0 0
175175 −0.811540 + 0.303844i −0.0613466 + 0.0229684i
176176 −31.4819 −2.37304
177177 0 0
178178 41.5423i 3.11373i
179179 10.6947 0.799357 0.399679 0.916655i 0.369122π-0.369122\pi
0.399679 + 0.916655i 0.369122π0.369122\pi
180180 0 0
181181 −15.2511 −1.13361 −0.566804 0.823852i 0.691820π-0.691820\pi
−0.566804 + 0.823852i 0.691820π0.691820\pi
182182 0.797504i 0.0591149i
183183 0 0
184184 −18.6936 −1.37811
185185 −3.63519 2.52059i −0.267264 0.185318i
186186 0 0
187187 21.5802i 1.57810i
188188 37.6732i 2.74760i
189189 0 0
190190 39.9057 + 27.6701i 2.89507 + 2.00740i
191191 25.7131 1.86053 0.930266 0.366885i 0.119576π-0.119576\pi
0.930266 + 0.366885i 0.119576π0.119576\pi
192192 0 0
193193 22.8935i 1.64791i −0.566658 0.823953i 0.691764π-0.691764\pi
0.566658 0.823953i 0.308236π-0.308236\pi
194194 6.91284 0.496313
195195 0 0
196196 −30.2899 −2.16356
197197 0.840810i 0.0599052i 0.999551 + 0.0299526i 0.00953564π0.00953564\pi
−0.999551 + 0.0299526i 0.990464π0.990464\pi
198198 0 0
199199 26.5996 1.88560 0.942799 0.333361i 0.108183π-0.108183\pi
0.942799 + 0.333361i 0.108183π0.108183\pi
200200 −27.6701 + 10.3598i −1.95657 + 0.732549i
201201 0 0
202202 16.1592i 1.13696i
203203 0.173311i 0.0121640i
204204 0 0
205205 12.6973 18.3119i 0.886815 1.27896i
206206 17.8513 1.24376
207207 0 0
208208 11.3148i 0.784543i
209209 −43.8159 −3.03081
210210 0 0
211211 1.86360 0.128296 0.0641478 0.997940i 0.479567π-0.479567\pi
0.0641478 + 0.997940i 0.479567π0.479567\pi
212212 23.4795i 1.61258i
213213 0 0
214214 −2.33062 −0.159318
215215 14.5363 + 10.0793i 0.991367 + 0.687401i
216216 0 0
217217 0.558382i 0.0379055i
218218 10.3711i 0.702417i
219219 0 0
220220 28.1422 40.5866i 1.89735 2.73635i
221221 7.75608 0.521731
222222 0 0
223223 25.0759i 1.67920i 0.543202 + 0.839602i 0.317212π0.317212\pi
−0.543202 + 0.839602i 0.682788π0.682788\pi
224224 0.656028 0.0438327
225225 0 0
226226 17.2463 1.14721
227227 20.3877i 1.35318i 0.736360 + 0.676590i 0.236543π0.236543\pi
−0.736360 + 0.676590i 0.763457π0.763457\pi
228228 0 0
229229 5.84179 0.386037 0.193018 0.981195i 0.438172π-0.438172\pi
0.193018 + 0.981195i 0.438172π0.438172\pi
230230 10.1537 14.6435i 0.669512 0.965567i
231231 0 0
232232 5.90919i 0.387957i
233233 14.1216i 0.925134i −0.886584 0.462567i 0.846928π-0.846928\pi
0.886584 0.462567i 0.153072π-0.153072\pi
234234 0 0
235235 −15.9296 11.0454i −1.03913 0.720520i
236236 −33.3010 −2.16771
237237 0 0
238238 1.85373i 0.120159i
239239 −6.39059 −0.413373 −0.206686 0.978407i 0.566268π-0.566268\pi
−0.206686 + 0.978407i 0.566268π0.566268\pi
240240 0 0
241241 −10.1713 −0.655188 −0.327594 0.944819i 0.606238π-0.606238\pi
−0.327594 + 0.944819i 0.606238π0.606238\pi
242242 37.3624i 2.40175i
243243 0 0
244244 −12.0037 −0.768455
245245 8.88066 12.8076i 0.567365 0.818251i
246246 0 0
247247 15.7478i 1.00201i
248248 19.0385i 1.20895i
249249 0 0
250250 6.91406 27.3023i 0.437283 1.72675i
251251 15.7587 0.994678 0.497339 0.867556i 0.334310π-0.334310\pi
0.497339 + 0.867556i 0.334310π0.334310\pi
252252 0 0
253253 16.0784i 1.01084i
254254 −13.2466 −0.831165
255255 0 0
256256 −31.4691 −1.96682
257257 12.3486i 0.770283i 0.922858 + 0.385142i 0.125847π0.125847\pi
−0.922858 + 0.385142i 0.874153π0.874153\pi
258258 0 0
259259 −0.342858 −0.0213041
260260 −14.5871 10.1145i −0.904656 0.627277i
261261 0 0
262262 44.6272i 2.75708i
263263 4.16928i 0.257089i 0.991704 + 0.128545i 0.0410305π0.0410305\pi
−0.991704 + 0.128545i 0.958969π0.958969\pi
264264 0 0
265265 −9.92799 6.88395i −0.609872 0.422877i
266266 3.76377 0.230771
267267 0 0
268268 35.3690i 2.16051i
269269 −1.36011 −0.0829273 −0.0414636 0.999140i 0.513202π-0.513202\pi
−0.0414636 + 0.999140i 0.513202π0.513202\pi
270270 0 0
271271 11.1448 0.676998 0.338499 0.940967i 0.390081π-0.390081\pi
0.338499 + 0.940967i 0.390081π0.390081\pi
272272 26.3003i 1.59469i
273273 0 0
274274 2.88381 0.174217
275275 8.91048 + 23.7991i 0.537322 + 1.43514i
276276 0 0
277277 0.704673i 0.0423397i −0.999776 0.0211699i 0.993261π-0.993261\pi
0.999776 0.0211699i 0.00673908π-0.00673908\pi
278278 10.2947i 0.617437i
279279 0 0
280280 −1.30487 + 1.88188i −0.0779811 + 0.112464i
281281 13.8119 0.823950 0.411975 0.911195i 0.364839π-0.364839\pi
0.411975 + 0.911195i 0.364839π0.364839\pi
282282 0 0
283283 8.92142i 0.530324i 0.964204 + 0.265162i 0.0854254π0.0854254\pi
−0.964204 + 0.265162i 0.914575π0.914575\pi
284284 −27.2018 −1.61413
285285 0 0
286286 23.3875 1.38293
287287 1.72712i 0.101948i
288288 0 0
289289 −1.02833 −0.0604902
290290 4.62893 + 3.20964i 0.271820 + 0.188477i
291291 0 0
292292 29.3060i 1.71500i
293293 31.2817i 1.82750i 0.406278 + 0.913749i 0.366826π0.366826\pi
−0.406278 + 0.913749i 0.633174π0.633174\pi
294294 0 0
295295 9.76350 14.0809i 0.568453 0.819820i
296296 −11.6900 −0.679469
297297 0 0
298298 3.78538i 0.219281i
299299 5.77870 0.334191
300300 0 0
301301 1.37101 0.0790238
302302 54.1343i 3.11508i
303303 0 0
304304 53.3996 3.06268
305305 3.51934 5.07558i 0.201517 0.290627i
306306 0 0
307307 21.8533i 1.24723i 0.781730 + 0.623617i 0.214338π0.214338\pi
−0.781730 + 0.623617i 0.785662π0.785662\pi
308308 3.82798i 0.218120i
309309 0 0
310310 14.9137 + 10.3410i 0.847043 + 0.587329i
311311 −28.8838 −1.63785 −0.818925 0.573901i 0.805430π-0.805430\pi
−0.818925 + 0.573901i 0.805430π0.805430\pi
312312 0 0
313313 8.24232i 0.465884i 0.972491 + 0.232942i 0.0748352π0.0748352\pi
−0.972491 + 0.232942i 0.925165π0.925165\pi
314314 28.0038 1.58034
315315 0 0
316316 19.7630 1.11175
317317 7.15829i 0.402050i −0.979586 0.201025i 0.935573π-0.935573\pi
0.979586 0.201025i 0.0644272π-0.0644272\pi
318318 0 0
319319 −5.08250 −0.284565
320320 3.63505 5.24246i 0.203206 0.293062i
321321 0 0
322322 1.38113i 0.0769672i
323323 36.6043i 2.03672i
324324 0 0
325325 8.55359 3.20250i 0.474468 0.177643i
326326 30.7781 1.70464
327327 0 0
328328 58.8875i 3.25152i
329329 −1.50242 −0.0828311
330330 0 0
331331 −24.6936 −1.35728 −0.678642 0.734470i 0.737431π-0.737431\pi
−0.678642 + 0.734470i 0.737431π0.737431\pi
332332 50.5085i 2.77201i
333333 0 0
334334 −53.8162 −2.94469
335335 −14.9553 10.3698i −0.817095 0.566563i
336336 0 0
337337 11.7142i 0.638116i −0.947735 0.319058i 0.896634π-0.896634\pi
0.947735 0.319058i 0.103366π-0.103366\pi
338338 24.3424i 1.32405i
339339 0 0
340340 33.9065 + 23.5104i 1.83884 + 1.27503i
341341 −16.3751 −0.886759
342342 0 0
343343 2.42115i 0.130730i
344344 46.7458 2.52036
345345 0 0
346346 33.1727 1.78337
347347 0.828990i 0.0445025i 0.999752 + 0.0222513i 0.00708338π0.00708338\pi
−0.999752 + 0.0222513i 0.992917π0.992917\pi
348348 0 0
349349 8.44370 0.451981 0.225991 0.974129i 0.427438π-0.427438\pi
0.225991 + 0.974129i 0.427438π0.427438\pi
350350 −0.765407 2.04433i −0.0409127 0.109274i
351351 0 0
352352 19.2386i 1.02542i
353353 4.90553i 0.261095i 0.991442 + 0.130547i 0.0416735π0.0416735\pi
−0.991442 + 0.130547i 0.958327π0.958327\pi
354354 0 0
355355 7.97528 11.5019i 0.423284 0.610458i
356356 71.6664 3.79831
357357 0 0
358358 26.9407i 1.42386i
359359 4.69044 0.247552 0.123776 0.992310i 0.460500π-0.460500\pi
0.123776 + 0.992310i 0.460500π0.460500\pi
360360 0 0
361361 55.3205 2.91161
362362 38.4189i 2.01925i
363363 0 0
364364 −1.37581 −0.0721119
365365 −12.3916 8.59219i −0.648607 0.449736i
366366 0 0
367367 29.2460i 1.52663i −0.646028 0.763314i 0.723571π-0.723571\pi
0.646028 0.763314i 0.276429π-0.276429\pi
368368 19.5952i 1.02147i
369369 0 0
370370 6.34958 9.15733i 0.330099 0.476067i
371371 −0.936373 −0.0486140
372372 0 0
373373 34.5171i 1.78723i 0.448839 + 0.893613i 0.351838π0.351838\pi
−0.448839 + 0.893613i 0.648162π0.648162\pi
374374 −54.3622 −2.81100
375375 0 0
376376 −51.2263 −2.64179
377377 1.82669i 0.0940793i
378378 0 0
379379 3.20131 0.164440 0.0822201 0.996614i 0.473799π-0.473799\pi
0.0822201 + 0.996614i 0.473799π0.473799\pi
380380 −47.7349 + 68.8430i −2.44875 + 3.53157i
381381 0 0
382382 64.7733i 3.31409i
383383 19.4424i 0.993458i −0.867906 0.496729i 0.834534π-0.834534\pi
0.867906 0.496729i 0.165466π-0.165466\pi
384384 0 0
385385 1.61861 + 1.12232i 0.0824920 + 0.0571989i
386386 57.6705 2.93535
387387 0 0
388388 11.9256i 0.605432i
389389 2.55875 0.129734 0.0648669 0.997894i 0.479338π-0.479338\pi
0.0648669 + 0.997894i 0.479338π0.479338\pi
390390 0 0
391391 −13.4321 −0.679289
392392 41.1868i 2.08025i
393393 0 0
394394 −2.11807 −0.106707
395395 −5.79429 + 8.35650i −0.291542 + 0.420461i
396396 0 0
397397 30.6583i 1.53869i −0.638831 0.769347i 0.720582π-0.720582\pi
0.638831 0.769347i 0.279418π-0.279418\pi
398398 67.0067i 3.35874i
399399 0 0
400400 −10.8594 29.0046i −0.542972 1.45023i
401401 −11.1628 −0.557446 −0.278723 0.960372i 0.589911π-0.589911\pi
−0.278723 + 0.960372i 0.589911π0.589911\pi
402402 0 0
403403 5.88532i 0.293169i
404404 27.8770 1.38693
405405 0 0
406406 0.436584 0.0216673
407407 10.0546i 0.498388i
408408 0 0
409409 −13.3880 −0.661994 −0.330997 0.943632i 0.607385π-0.607385\pi
−0.330997 + 0.943632i 0.607385π0.607385\pi
410410 46.1292 + 31.9854i 2.27816 + 1.57965i
411411 0 0
412412 30.7959i 1.51721i
413413 1.32806i 0.0653495i
414414 0 0
415415 21.3568 + 14.8085i 1.04836 + 0.726923i
416416 −6.91451 −0.339012
417417 0 0
418418 110.376i 5.39865i
419419 29.2982 1.43131 0.715655 0.698454i 0.246128π-0.246128\pi
0.715655 + 0.698454i 0.246128π0.246128\pi
420420 0 0
421421 10.1098 0.492724 0.246362 0.969178i 0.420765π-0.420765\pi
0.246362 + 0.969178i 0.420765π0.420765\pi
422422 4.69456i 0.228528i
423423 0 0
424424 −31.9264 −1.55048
425425 −19.8821 + 7.44392i −0.964422 + 0.361083i
426426 0 0
427427 0.478710i 0.0231664i
428428 4.02065i 0.194345i
429429 0 0
430430 −25.3905 + 36.6181i −1.22444 + 1.76588i
431431 −30.3330 −1.46109 −0.730545 0.682865i 0.760734π-0.760734\pi
−0.730545 + 0.682865i 0.760734π0.760734\pi
432432 0 0
433433 6.50520i 0.312620i −0.987708 0.156310i 0.950040π-0.950040\pi
0.987708 0.156310i 0.0499599π-0.0499599\pi
434434 1.40661 0.0675195
435435 0 0
436436 17.8915 0.856850
437437 27.2722i 1.30460i
438438 0 0
439439 9.40248 0.448756 0.224378 0.974502i 0.427965π-0.427965\pi
0.224378 + 0.974502i 0.427965π0.427965\pi
440440 55.1879 + 38.2666i 2.63098 + 1.82429i
441441 0 0
442442 19.5382i 0.929337i
443443 28.1657i 1.33819i −0.743175 0.669097i 0.766681π-0.766681\pi
0.743175 0.669097i 0.233319π-0.233319\pi
444444 0 0
445445 −21.0118 + 30.3031i −0.996055 + 1.43651i
446446 −63.1682 −2.99110
447447 0 0
448448 0.494450i 0.0233605i
449449 −32.2625 −1.52256 −0.761281 0.648422i 0.775429π-0.775429\pi
−0.761281 + 0.648422i 0.775429π0.775429\pi
450450 0 0
451451 −50.6492 −2.38498
452452 29.7523i 1.39943i
453453 0 0
454454 −51.3583 −2.41037
455455 0.403372 0.581741i 0.0189104 0.0272724i
456456 0 0
457457 27.1466i 1.26986i −0.772568 0.634932i 0.781028π-0.781028\pi
0.772568 0.634932i 0.218972π-0.218972\pi
458458 14.7160i 0.687631i
459459 0 0
460460 25.2622 + 17.5165i 1.17786 + 0.816710i
461461 −7.00940 −0.326460 −0.163230 0.986588i 0.552191π-0.552191\pi
−0.163230 + 0.986588i 0.552191π0.552191\pi
462462 0 0
463463 21.7590i 1.01123i −0.862760 0.505613i 0.831266π-0.831266\pi
0.862760 0.505613i 0.168734π-0.168734\pi
464464 6.19418 0.287558
465465 0 0
466466 35.5733 1.64790
467467 30.7825i 1.42445i 0.701953 + 0.712223i 0.252312π0.252312\pi
−0.701953 + 0.712223i 0.747688π0.747688\pi
468468 0 0
469469 −1.41053 −0.0651322
470470 27.8242 40.1279i 1.28343 1.85096i
471471 0 0
472472 45.2813i 2.08424i
473473 40.2061i 1.84868i
474474 0 0
475475 −15.1140 40.3681i −0.693476 1.85221i
476476 3.19794 0.146577
477477 0 0
478478 16.0984i 0.736324i
479479 −6.29237 −0.287506 −0.143753 0.989614i 0.545917π-0.545917\pi
−0.143753 + 0.989614i 0.545917π0.545917\pi
480480 0 0
481481 3.61370 0.164771
482482 25.6222i 1.16706i
483483 0 0
484484 −64.4555 −2.92979
485485 −5.04259 3.49647i −0.228972 0.158766i
486486 0 0
487487 30.3406i 1.37487i 0.726248 + 0.687433i 0.241262π0.241262\pi
−0.726248 + 0.687433i 0.758738π0.758738\pi
488488 16.3220i 0.738864i
489489 0 0
490490 32.2635 + 22.3711i 1.45752 + 1.01062i
491491 −17.7822 −0.802502 −0.401251 0.915968i 0.631424π-0.631424\pi
−0.401251 + 0.915968i 0.631424π0.631424\pi
492492 0 0
493493 4.24598i 0.191229i
494494 −39.6699 −1.78483
495495 0 0
496496 19.9567 0.896083
497497 1.08482i 0.0486608i
498498 0 0
499499 −0.262248 −0.0117399 −0.00586993 0.999983i 0.501868π-0.501868\pi
−0.00586993 + 0.999983i 0.501868π0.501868\pi
500500 47.1004 + 11.9277i 2.10639 + 0.533424i
501501 0 0
502502 39.6974i 1.77178i
503503 15.0486i 0.670986i 0.942043 + 0.335493i 0.108903π0.108903\pi
−0.942043 + 0.335493i 0.891097π0.891097\pi
504504 0 0
505505 −8.17323 + 11.7874i −0.363704 + 0.524532i
506506 −40.5028 −1.80057
507507 0 0
508508 22.8522i 1.01390i
509509 39.8752 1.76744 0.883719 0.468019i 0.155032π-0.155032\pi
0.883719 + 0.468019i 0.155032π0.155032\pi
510510 0 0
511511 −1.16873 −0.0517017
512512 49.7585i 2.19904i
513513 0 0
514514 −31.1071 −1.37207
515515 −13.0216 9.02904i −0.573802 0.397867i
516516 0 0
517517 44.0598i 1.93775i
518518 0.863687i 0.0379482i
519519 0 0
520520 13.7533 19.8349i 0.603122 0.869820i
521521 −18.3187 −0.802557 −0.401279 0.915956i 0.631434π-0.631434\pi
−0.401279 + 0.915956i 0.631434π0.631434\pi
522522 0 0
523523 6.04576i 0.264363i −0.991226 0.132181i 0.957802π-0.957802\pi
0.991226 0.132181i 0.0421981π-0.0421981\pi
524524 76.9882 3.36325
525525 0 0
526526 −10.5028 −0.457942
527527 13.6799i 0.595906i
528528 0 0
529529 12.9924 0.564886
530530 17.3412 25.0094i 0.753254 1.08634i
531531 0 0
532532 6.49303i 0.281508i
533533 18.2037i 0.788490i
534534 0 0
535535 1.70008 + 1.17881i 0.0735007 + 0.0509645i
536536 −48.0932 −2.07731
537537 0 0
538538 3.42622i 0.147715i
539539 −35.4248 −1.52585
540540 0 0
541541 −35.6643 −1.53333 −0.766664 0.642049i 0.778085π-0.778085\pi
−0.766664 + 0.642049i 0.778085π0.778085\pi
542542 28.0746i 1.20591i
543543 0 0
544544 16.0722 0.689088
545545 −5.24561 + 7.56519i −0.224697 + 0.324057i
546546 0 0
547547 5.23087i 0.223656i 0.993728 + 0.111828i 0.0356706π0.0356706\pi
−0.993728 + 0.111828i 0.964329π0.964329\pi
548548 4.97498i 0.212520i
549549 0 0
550550 −59.9519 + 22.4462i −2.55636 + 0.957110i
551551 8.62093 0.367264
552552 0 0
553553 0.788155i 0.0335157i
554554 1.77513 0.0754180
555555 0 0
556556 17.7599 0.753186
557557 32.9893i 1.39780i 0.715219 + 0.698900i 0.246327π0.246327\pi
−0.715219 + 0.698900i 0.753673π0.753673\pi
558558 0 0
559559 −14.4504 −0.611186
560560 −1.97264 1.36781i −0.0833594 0.0578004i
561561 0 0
562562 34.7933i 1.46767i
563563 5.94931i 0.250734i −0.992110 0.125367i 0.959989π-0.959989\pi
0.992110 0.125367i 0.0400108π-0.0400108\pi
564564 0 0
565565 −12.5803 8.72305i −0.529259 0.366981i
566566 −22.4738 −0.944644
567567 0 0
568568 36.9878i 1.55198i
569569 −14.6940 −0.616003 −0.308002 0.951386i 0.599660π-0.599660\pi
−0.308002 + 0.951386i 0.599660π0.599660\pi
570570 0 0
571571 7.86509 0.329144 0.164572 0.986365i 0.447376π-0.447376\pi
0.164572 + 0.986365i 0.447376π0.447376\pi
572572 40.3467i 1.68698i
573573 0 0
574574 4.35074 0.181597
575575 −14.8132 + 5.54612i −0.617753 + 0.231289i
576576 0 0
577577 29.7454i 1.23832i −0.785265 0.619159i 0.787474π-0.787474\pi
0.785265 0.619159i 0.212526π-0.212526\pi
578578 2.59045i 0.107749i
579579 0 0
580580 −5.53709 + 7.98556i −0.229915 + 0.331582i
581581 2.01430 0.0835671
582582 0 0
583583 27.4599i 1.13727i
584584 −39.8489 −1.64896
585585 0 0
586586 −78.8013 −3.25525
587587 46.1639i 1.90539i −0.303929 0.952695i 0.598299π-0.598299\pi
0.303929 0.952695i 0.401701π-0.401701\pi
588588 0 0
589589 27.7754 1.14446
590590 35.4709 + 24.5951i 1.46031 + 1.01256i
591591 0 0
592592 12.2538i 0.503629i
593593 22.6806i 0.931382i 0.884948 + 0.465691i 0.154194π0.154194\pi
−0.884948 + 0.465691i 0.845806π0.845806\pi
594594 0 0
595595 −0.937602 + 1.35221i −0.0384379 + 0.0554350i
596596 −6.53031 −0.267492
597597 0 0
598598 14.5570i 0.595280i
599599 22.8764 0.934704 0.467352 0.884071i 0.345208π-0.345208\pi
0.467352 + 0.884071i 0.345208π0.345208\pi
600600 0 0
601601 14.6918 0.599291 0.299646 0.954051i 0.403132π-0.403132\pi
0.299646 + 0.954051i 0.403132π0.403132\pi
602602 3.45369i 0.140762i
603603 0 0
604604 93.3893 3.79996
605605 18.8977 27.2541i 0.768299 1.10804i
606606 0 0
607607 20.9484i 0.850270i 0.905130 + 0.425135i 0.139773π0.139773\pi
−0.905130 + 0.425135i 0.860227π0.860227\pi
608608 32.6325i 1.32342i
609609 0 0
610610 12.7858 + 8.86551i 0.517682 + 0.358954i
611611 15.8354 0.640633
612612 0 0
613613 42.0373i 1.69787i −0.528496 0.848936i 0.677244π-0.677244\pi
0.528496 0.848936i 0.322756π-0.322756\pi
614614 −55.0503 −2.22165
615615 0 0
616616 5.20512 0.209720
617617 44.6853i 1.79896i 0.436958 + 0.899482i 0.356056π0.356056\pi
−0.436958 + 0.899482i 0.643944π0.643944\pi
618618 0 0
619619 22.1966 0.892157 0.446079 0.894994i 0.352820π-0.352820\pi
0.446079 + 0.894994i 0.352820π0.352820\pi
620620 −17.8397 + 25.7283i −0.716459 + 1.03327i
621621 0 0
622622 72.7606i 2.91744i
623623 2.85808i 0.114507i
624624 0 0
625625 −18.8528 + 16.4187i −0.754112 + 0.656746i
626626 −20.7631 −0.829859
627627 0 0
628628 48.3104i 1.92780i
629629 −8.39974 −0.334919
630630 0 0
631631 −5.29765 −0.210896 −0.105448 0.994425i 0.533628π-0.533628\pi
−0.105448 + 0.994425i 0.533628π0.533628\pi
632632 26.8728i 1.06894i
633633 0 0
634634 18.0323 0.716155
635635 9.66275 + 6.70003i 0.383455 + 0.265883i
636636 0 0
637637 12.7320i 0.504458i
638638 12.8032i 0.506884i
639639 0 0
640640 27.1174 + 18.8029i 1.07191 + 0.743248i
641641 −3.21592 −0.127021 −0.0635107 0.997981i 0.520230π-0.520230\pi
−0.0635107 + 0.997981i 0.520230π0.520230\pi
642642 0 0
643643 32.0630i 1.26444i 0.774788 + 0.632221i 0.217857π0.217857\pi
−0.774788 + 0.632221i 0.782143π0.782143\pi
644644 2.38264 0.0938891
645645 0 0
646646 92.2092 3.62792
647647 9.26571i 0.364273i 0.983273 + 0.182136i 0.0583012π0.0583012\pi
−0.983273 + 0.182136i 0.941699π0.941699\pi
648648 0 0
649649 −38.9465 −1.52878
650650 8.06735 + 21.5472i 0.316427 + 0.845150i
651651 0 0
652652 53.0966i 2.07942i
653653 22.2362i 0.870171i −0.900389 0.435085i 0.856718π-0.856718\pi
0.900389 0.435085i 0.143282π-0.143282\pi
654654 0 0
655655 −22.5721 + 32.5534i −0.881966 + 1.27197i
656656 61.7275 2.41006
657657 0 0
658658 3.78472i 0.147544i
659659 34.6708 1.35058 0.675291 0.737552i 0.264018π-0.264018\pi
0.675291 + 0.737552i 0.264018π0.264018\pi
660660 0 0
661661 −9.67217 −0.376204 −0.188102 0.982150i 0.560234π-0.560234\pi
−0.188102 + 0.982150i 0.560234π0.560234\pi
662662 62.2052i 2.41767i
663663 0 0
664664 68.6792 2.66527
665665 −2.74549 1.90369i −0.106465 0.0738218i
666666 0 0
667667 3.16348i 0.122491i
668668 92.8405i 3.59211i
669669 0 0
670670 26.1224 37.6736i 1.00920 1.45546i
671671 −14.0386 −0.541954
672672 0 0
673673 24.7689i 0.954770i 0.878694 + 0.477385i 0.158415π0.158415\pi
−0.878694 + 0.477385i 0.841585π0.841585\pi
674674 29.5091 1.13665
675675 0 0
676676 −41.9941 −1.61516
677677 33.3636i 1.28227i 0.767430 + 0.641133i 0.221535π0.221535\pi
−0.767430 + 0.641133i 0.778465π0.778465\pi
678678 0 0
679679 −0.475599 −0.0182518
680680 −31.9684 + 46.1046i −1.22593 + 1.76803i
681681 0 0
682682 41.2501i 1.57955i
683683 13.9516i 0.533842i 0.963718 + 0.266921i 0.0860063π0.0860063\pi
−0.963718 + 0.266921i 0.913994π0.913994\pi
684684 0 0
685685 −2.10360 1.45861i −0.0803744 0.0557306i
686686 6.09907 0.232864
687687 0 0
688688 49.0003i 1.86812i
689689 9.86932 0.375991
690690 0 0
691691 50.5611 1.92344 0.961718 0.274042i 0.0883607π-0.0883607\pi
0.961718 + 0.274042i 0.0883607π0.0883607\pi
692692 57.2276i 2.17547i
693693 0 0
694694 −2.08829 −0.0792705
695695 −5.20700 + 7.50952i −0.197513 + 0.284852i
696696 0 0
697697 42.3129i 1.60272i
698698 21.2704i 0.805096i
699699 0 0
700700 3.52676 1.32043i 0.133299 0.0499077i
701701 24.0803 0.909499 0.454749 0.890620i 0.349729π-0.349729\pi
0.454749 + 0.890620i 0.349729π0.349729\pi
702702 0 0
703703 17.0546i 0.643227i
704704 −14.5002 −0.546496
705705 0 0
706706 −12.3574 −0.465078
707707 1.11174i 0.0418114i
708708 0 0
709709 −0.769569 −0.0289018 −0.0144509 0.999896i 0.504600π-0.504600\pi
−0.0144509 + 0.999896i 0.504600π0.504600\pi
710710 28.9743 + 20.0904i 1.08738 + 0.753979i
711711 0 0
712712 97.4487i 3.65205i
713713 10.1923i 0.381703i
714714 0 0
715715 −17.0601 11.8292i −0.638010 0.442388i
716716 −46.4766 −1.73691
717717 0 0
718718 11.8156i 0.440955i
719719 4.92456 0.183655 0.0918275 0.995775i 0.470729π-0.470729\pi
0.0918275 + 0.995775i 0.470729π0.470729\pi
720720 0 0
721721 −1.22815 −0.0457388
722722 139.357i 5.18632i
723723 0 0
724724 66.2780 2.46320
725725 −1.75317 4.68256i −0.0651111 0.173906i
726726 0 0
727727 41.8838i 1.55339i 0.629880 + 0.776693i 0.283104π0.283104\pi
−0.629880 + 0.776693i 0.716896π0.716896\pi
728728 1.87076i 0.0693350i
729729 0 0
730730 21.6444 31.2155i 0.801096 1.15534i
731731 33.5887 1.24232
732732 0 0
733733 27.1372i 1.00234i 0.865350 + 0.501168i 0.167096π0.167096\pi
−0.865350 + 0.501168i 0.832904π0.832904\pi
734734 73.6730 2.71932
735735 0 0
736736 11.9746 0.441390
737737 41.3650i 1.52370i
738738 0 0
739739 3.41445 0.125603 0.0628013 0.998026i 0.479997π-0.479997\pi
0.0628013 + 0.998026i 0.479997π0.479997\pi
740740 15.7977 + 10.9539i 0.580735 + 0.402674i
741741 0 0
742742 2.35880i 0.0865942i
743743 3.73961i 0.137193i 0.997644 + 0.0685966i 0.0218521π0.0218521\pi
−0.997644 + 0.0685966i 0.978148π0.978148\pi
744744 0 0
745745 1.91462 2.76125i 0.0701461 0.101164i
746746 −86.9513 −3.18351
747747 0 0
748748 93.7825i 3.42903i
749749 0.160345 0.00585888
750750 0 0
751751 −24.1900 −0.882707 −0.441354 0.897333i 0.645502π-0.645502\pi
−0.441354 + 0.897333i 0.645502π0.645502\pi
752752 53.6969i 1.95812i
753753 0 0
754754 −4.60158 −0.167580
755755 −27.3807 + 39.4884i −0.996487 + 1.43713i
756756 0 0
757757 3.55451i 0.129191i −0.997912 0.0645953i 0.979424π-0.979424\pi
0.997912 0.0645953i 0.0205757π-0.0205757\pi
758758 8.06436i 0.292911i
759759 0 0
760760 −93.6097 64.9078i −3.39558 2.35445i
761761 44.2390 1.60366 0.801832 0.597550i 0.203859π-0.203859\pi
0.801832 + 0.597550i 0.203859π0.203859\pi
762762 0 0
763763 0.713522i 0.0258312i
764764 −111.743 −4.04272
765765 0 0
766766 48.9769 1.76961
767767 13.9977i 0.505426i
768768 0 0
769769 −6.30558 −0.227385 −0.113692 0.993516i 0.536268π-0.536268\pi
−0.113692 + 0.993516i 0.536268π0.536268\pi
770770 −2.82722 + 4.07741i −0.101886 + 0.146940i
771771 0 0
772772 99.4897i 3.58071i
773773 24.2649i 0.872747i −0.899766 0.436374i 0.856263π-0.856263\pi
0.899766 0.436374i 0.143737π-0.143737\pi
774774 0 0
775775 −5.64845 15.0865i −0.202898 0.541924i
776776 −16.2159 −0.582118
777777 0 0
778778 6.44570i 0.231090i
779779 85.9111 3.07809
780780 0 0
781781 −31.8133 −1.13837
782782 33.8365i 1.20999i
783783 0 0
784784 43.1732 1.54190
785785 −20.4274 14.1641i −0.729085 0.505538i
786786 0 0
787787 39.1338i 1.39497i 0.716600 + 0.697484i 0.245697π0.245697\pi
−0.716600 + 0.697484i 0.754303π0.754303\pi
788788 3.65397i 0.130167i
789789 0 0
790790 −21.0507 14.5963i −0.748950 0.519312i
791791 −1.18653 −0.0421882
792792 0 0
793793 5.04558i 0.179174i
794794 77.2307 2.74081
795795 0 0
796796 −115.596 −4.09719
797797 29.3166i 1.03845i 0.854638 + 0.519224i 0.173779π0.173779\pi
−0.854638 + 0.519224i 0.826221π0.826221\pi
798798 0 0
799799 −36.8081 −1.30218
800800 17.7248 6.63622i 0.626665 0.234626i
801801 0 0
802802 28.1201i 0.992956i
803803 34.2741i 1.20951i
804804 0 0
805805 −0.698564 + 1.00747i −0.0246211 + 0.0355085i
806806 −14.8256 −0.522210
807807 0 0
808808 37.9059i 1.33352i
809809 −28.7412 −1.01049 −0.505244 0.862977i 0.668597π-0.668597\pi
−0.505244 + 0.862977i 0.668597π0.668597\pi
810810 0 0
811811 4.04326 0.141978 0.0709891 0.997477i 0.477384π-0.477384\pi
0.0709891 + 0.997477i 0.477384π0.477384\pi
812812 0.753170i 0.0264311i
813813 0 0
814814 −25.3284 −0.887759
815815 −22.4512 15.5674i −0.786430 0.545301i
816816 0 0
817817 68.1976i 2.38593i
818818 33.7255i 1.17918i
819819 0 0
820820 −55.1794 + 79.5794i −1.92695 + 2.77903i
821821 −1.38325 −0.0482758 −0.0241379 0.999709i 0.507684π-0.507684\pi
−0.0241379 + 0.999709i 0.507684π0.507684\pi
822822 0 0
823823 11.7734i 0.410395i −0.978721 0.205197i 0.934216π-0.934216\pi
0.978721 0.205197i 0.0657836π-0.0657836\pi
824824 −41.8749 −1.45878
825825 0 0
826826 3.34549 0.116404
827827 19.4700i 0.677040i 0.940959 + 0.338520i 0.109926π0.109926\pi
−0.940959 + 0.338520i 0.890074π0.890074\pi
828828 0 0
829829 −16.9194 −0.587634 −0.293817 0.955862i 0.594926π-0.594926\pi
−0.293817 + 0.955862i 0.594926π0.594926\pi
830830 −37.3039 + 53.7995i −1.29484 + 1.86741i
831831 0 0
832832 5.21147i 0.180675i
833833 29.5943i 1.02538i
834834 0 0
835835 39.2563 + 27.2198i 1.35852 + 0.941982i
836836 190.414 6.58560
837837 0 0
838838 73.8045i 2.54953i
839839 17.9764 0.620615 0.310308 0.950636i 0.399568π-0.399568\pi
0.310308 + 0.950636i 0.399568π0.399568\pi
840840 0 0
841841 1.00000 0.0344828
842842 25.4675i 0.877669i
843843 0 0
844844 −8.09878 −0.278772
845845 12.3122 17.7566i 0.423553 0.610846i
846846 0 0
847847 2.57051i 0.0883237i
848848 33.4662i 1.14923i
849849 0 0
850850 −18.7518 50.0845i −0.643183 1.71789i
851851 −6.25826 −0.214530
852852 0 0
853853 25.1608i 0.861489i −0.902474 0.430744i 0.858251π-0.858251\pi
0.902474 0.430744i 0.141749π-0.141749\pi
854854 1.20591 0.0412654
855855 0 0
856856 5.46710 0.186862
857857 27.8748i 0.952184i 0.879395 + 0.476092i 0.157947π0.157947\pi
−0.879395 + 0.476092i 0.842053π0.842053\pi
858858 0 0
859859 −21.0421 −0.717947 −0.358973 0.933348i 0.616873π-0.616873\pi
−0.358973 + 0.933348i 0.616873π0.616873\pi
860860 −63.1714 43.8022i −2.15413 1.49364i
861861 0 0
862862 76.4113i 2.60258i
863863 29.1647i 0.992779i 0.868100 + 0.496390i 0.165341π0.165341\pi
−0.868100 + 0.496390i 0.834659π0.834659\pi
864864 0 0
865865 −24.1979 16.7785i −0.822753 0.570486i
866866 16.3871 0.556858
867867 0 0
868868 2.42660i 0.0823642i
869869 23.1133 0.784066
870870 0 0
871871 14.8669 0.503746
872872 24.3281i 0.823854i
873873 0 0
874874 68.7008 2.32384
875875 −0.475682 + 1.87838i −0.0160810 + 0.0635009i
876876 0 0
877877 11.5743i 0.390836i −0.980720 0.195418i 0.937394π-0.937394\pi
0.980720 0.195418i 0.0626064π-0.0626064\pi
878878 23.6856i 0.799350i
879879 0 0
880880 −40.1121 + 57.8495i −1.35218 + 1.95011i
881881 −21.8843 −0.737299 −0.368650 0.929568i 0.620180π-0.620180\pi
−0.368650 + 0.929568i 0.620180π0.620180\pi
882882 0 0
883883 20.2591i 0.681773i −0.940104 0.340887i 0.889273π-0.889273\pi
0.940104 0.340887i 0.110727π-0.110727\pi
884884 −33.7062 −1.13366
885885 0 0
886886 70.9517 2.38367
887887 37.5330i 1.26023i −0.776500 0.630117i 0.783007π-0.783007\pi
0.776500 0.630117i 0.216993π-0.216993\pi
888888 0 0
889889 0.911356 0.0305659
890890 −76.3360 52.9304i −2.55879 1.77423i
891891 0 0
892892 108.974i 3.64872i
893893 74.7342i 2.50089i
894894 0 0
895895 13.6264 19.6520i 0.455481 0.656893i
896896 2.55762 0.0854439
897897 0 0
898898 81.2719i 2.71208i
899899 3.22185 0.107455
900900 0 0
901901 −22.9404 −0.764254
902902 127.589i 4.24826i
903903 0 0
904904 −40.4558 −1.34554
905905 −19.4320 + 28.0247i −0.645941 + 0.931573i
906906 0 0
907907 17.7096i 0.588037i −0.955800 0.294018i 0.905007π-0.905007\pi
0.955800 0.294018i 0.0949927π-0.0949927\pi
908908 88.6004i 2.94031i
909909 0 0
910910 1.46545 + 1.01613i 0.0485793 + 0.0336843i
911911 6.63407 0.219796 0.109898 0.993943i 0.464948π-0.464948\pi
0.109898 + 0.993943i 0.464948π0.464948\pi
912912 0 0
913913 59.0710i 1.95497i
914914 68.3845 2.26196
915915 0 0
916916 −25.3871 −0.838813
917917 3.07032i 0.101391i
918918 0 0
919919 −4.71782 −0.155626 −0.0778132 0.996968i 0.524794π-0.524794\pi
−0.0778132 + 0.996968i 0.524794π0.524794\pi
920920 −23.8181 + 34.3504i −0.785261 + 1.13250i
921921 0 0
922922 17.6572i 0.581510i
923923 11.4339i 0.376353i
924924 0 0
925925 −9.26342 + 3.46826i −0.304580 + 0.114036i
926926 54.8127 1.80126
927927 0 0
928928 3.78527i 0.124257i
929929 43.4668 1.42610 0.713049 0.701114i 0.247314π-0.247314\pi
0.713049 + 0.701114i 0.247314π0.247314\pi
930930 0 0
931931 60.0876 1.96929
932932 61.3690i 2.01021i
933933 0 0
934934 −77.5437 −2.53731
935935 39.6546 + 27.4960i 1.29684 + 0.899216i
936936 0 0
937937 50.9680i 1.66505i −0.553986 0.832526i 0.686894π-0.686894\pi
0.553986 0.832526i 0.313106π-0.313106\pi
938938 3.55324i 0.116017i
939939 0 0
940940 69.2263 + 48.0006i 2.25791 + 1.56561i
941941 −11.0790 −0.361165 −0.180583 0.983560i 0.557798π-0.557798\pi
−0.180583 + 0.983560i 0.557798π0.557798\pi
942942 0 0
943943 31.5254i 1.02661i
944944 47.4651 1.54486
945945 0 0
946946 101.282 3.29298
947947 58.5923i 1.90399i 0.306107 + 0.951997i 0.400974π0.400974\pi
−0.306107 + 0.951997i 0.599026π0.599026\pi
948948 0 0
949949 12.3184 0.399872
950950 101.690 38.0733i 3.29927 1.23526i
951951 0 0
952952 4.34842i 0.140933i
953953 22.9017i 0.741859i −0.928661 0.370929i 0.879039π-0.879039\pi
0.928661 0.370929i 0.120961π-0.120961\pi
954954 0 0
955955 32.7619 47.2490i 1.06015 1.52894i
956956 27.7720 0.898211
957957 0 0
958958 15.8510i 0.512123i
959959 −0.198404 −0.00640680
960960 0 0
961961 −20.6197 −0.665151
962962 9.10321i 0.293499i
963963 0 0
964964 44.2019 1.42365
965965 −42.0678 29.1693i −1.35421 0.938993i
966966 0 0
967967 49.6623i 1.59703i 0.601973 + 0.798516i 0.294381π0.294381\pi
−0.601973 + 0.798516i 0.705619π0.705619\pi
968968 87.6437i 2.81698i
969969 0 0
970970 8.80788 12.7027i 0.282804 0.407859i
971971 6.90899 0.221720 0.110860 0.993836i 0.464639π-0.464639\pi
0.110860 + 0.993836i 0.464639π0.464639\pi
972972 0 0
973973 0.708271i 0.0227061i
974974 −76.4305 −2.44899
975975 0 0
976976 17.1092 0.547653
977977 8.17310i 0.261481i −0.991417 0.130740i 0.958265π-0.958265\pi
0.991417 0.130740i 0.0417354π-0.0417354\pi
978978 0 0
979979 83.8158 2.67876
980980 −38.5933 + 55.6591i −1.23282 + 1.77796i
981981 0 0
982982 44.7949i 1.42946i
983983 24.1451i 0.770108i 0.922894 + 0.385054i 0.125817π0.125817\pi
−0.922894 + 0.385054i 0.874183π0.874183\pi
984984 0 0
985985 1.54503 + 1.07130i 0.0492287 + 0.0341346i
986986 10.6960 0.340629
987987 0 0
988988 68.4362i 2.17724i
989989 25.0253 0.795760
990990 0 0
991991 −51.7396 −1.64356 −0.821781 0.569803i 0.807020π-0.807020\pi
−0.821781 + 0.569803i 0.807020π0.807020\pi
992992 12.1956i 0.387210i
993993 0 0
994994 2.73275 0.0866775
995995 33.8915 48.8781i 1.07443 1.54954i
996996 0 0
997997 9.07880i 0.287528i 0.989612 + 0.143764i 0.0459207π0.0459207\pi
−0.989612 + 0.143764i 0.954079π0.954079\pi
998998 0.660625i 0.0209117i
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 1305.2.c.j.784.10 10
3.2 odd 2 435.2.c.e.349.1 10
5.2 odd 4 6525.2.a.bl.1.1 5
5.3 odd 4 6525.2.a.bs.1.5 5
5.4 even 2 inner 1305.2.c.j.784.1 10
15.2 even 4 2175.2.a.z.1.5 5
15.8 even 4 2175.2.a.w.1.1 5
15.14 odd 2 435.2.c.e.349.10 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.2.c.e.349.1 10 3.2 odd 2
435.2.c.e.349.10 yes 10 15.14 odd 2
1305.2.c.j.784.1 10 5.4 even 2 inner
1305.2.c.j.784.10 10 1.1 even 1 trivial
2175.2.a.w.1.1 5 15.8 even 4
2175.2.a.z.1.5 5 15.2 even 4
6525.2.a.bl.1.1 5 5.2 odd 4
6525.2.a.bs.1.5 5 5.3 odd 4