Properties

Label 985.2.a.g.1.14
Level 985985
Weight 22
Character 985.1
Self dual yes
Analytic conductor 7.8657.865
Analytic rank 00
Dimension 1717
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [985,2,Mod(1,985)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(985, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("985.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 985=5197 985 = 5 \cdot 197
Weight: k k == 2 2
Character orbit: [χ][\chi] == 985.a (trivial)

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: yes
Analytic conductor: 7.865264599107.86526459910
Analytic rank: 00
Dimension: 1717
Coefficient field: Q[x]/(x17)\mathbb{Q}[x]/(x^{17} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x176x168x15+106x1460x13698x12+877x11+2076x103556x9++2 x^{17} - 6 x^{16} - 8 x^{15} + 106 x^{14} - 60 x^{13} - 698 x^{12} + 877 x^{11} + 2076 x^{10} - 3556 x^{9} + \cdots + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.14
Root 2.228832.22883 of defining polynomial
Character χ\chi == 985.1

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+2.22883q2+3.02604q3+2.96767q41.00000q5+6.74452q6+1.28446q7+2.15678q8+6.15690q92.22883q104.23897q11+8.98029q120.0326948q13+2.86284q143.02604q151.12826q16+3.18747q17+13.7227q185.69971q192.96767q20+3.88682q219.44795q226.17953q23+6.52650q24+1.00000q250.0728710q26+9.55291q27+3.81186q28+7.19361q296.74452q30+2.81208q316.82825q3212.8273q33+7.10433q341.28446q35+18.2717q3611.8869q3712.7037q380.0989356q392.15678q403.01031q41+8.66306q42+11.6220q4312.5799q446.15690q4513.7731q46+9.37541q473.41415q485.35016q49+2.22883q50+9.64541q510.0970274q52+4.47527q53+21.2918q54+4.23897q55+2.77030q5617.2475q57+16.0333q586.52124q598.98029q60+3.93428q61+6.26764q62+7.90829q6312.9625q64+0.0326948q6528.5898q66+3.36275q67+9.45938q6818.6995q692.86284q70+3.94676q71+13.2791q720.394938q7326.4938q74+3.02604q7516.9149q765.44479q770.220510q78+5.02637q79+1.12826q80+10.4367q816.70945q82+6.36108q83+11.5348q843.18747q85+25.9035q86+21.7681q879.14253q88+8.91236q8913.7227q900.0419951q9118.3388q92+8.50946q93+20.8962q94+5.69971q9520.6625q9615.6077q9711.9246q9826.0990q99+O(q100)q+2.22883 q^{2} +3.02604 q^{3} +2.96767 q^{4} -1.00000 q^{5} +6.74452 q^{6} +1.28446 q^{7} +2.15678 q^{8} +6.15690 q^{9} -2.22883 q^{10} -4.23897 q^{11} +8.98029 q^{12} -0.0326948 q^{13} +2.86284 q^{14} -3.02604 q^{15} -1.12826 q^{16} +3.18747 q^{17} +13.7227 q^{18} -5.69971 q^{19} -2.96767 q^{20} +3.88682 q^{21} -9.44795 q^{22} -6.17953 q^{23} +6.52650 q^{24} +1.00000 q^{25} -0.0728710 q^{26} +9.55291 q^{27} +3.81186 q^{28} +7.19361 q^{29} -6.74452 q^{30} +2.81208 q^{31} -6.82825 q^{32} -12.8273 q^{33} +7.10433 q^{34} -1.28446 q^{35} +18.2717 q^{36} -11.8869 q^{37} -12.7037 q^{38} -0.0989356 q^{39} -2.15678 q^{40} -3.01031 q^{41} +8.66306 q^{42} +11.6220 q^{43} -12.5799 q^{44} -6.15690 q^{45} -13.7731 q^{46} +9.37541 q^{47} -3.41415 q^{48} -5.35016 q^{49} +2.22883 q^{50} +9.64541 q^{51} -0.0970274 q^{52} +4.47527 q^{53} +21.2918 q^{54} +4.23897 q^{55} +2.77030 q^{56} -17.2475 q^{57} +16.0333 q^{58} -6.52124 q^{59} -8.98029 q^{60} +3.93428 q^{61} +6.26764 q^{62} +7.90829 q^{63} -12.9625 q^{64} +0.0326948 q^{65} -28.5898 q^{66} +3.36275 q^{67} +9.45938 q^{68} -18.6995 q^{69} -2.86284 q^{70} +3.94676 q^{71} +13.2791 q^{72} -0.394938 q^{73} -26.4938 q^{74} +3.02604 q^{75} -16.9149 q^{76} -5.44479 q^{77} -0.220510 q^{78} +5.02637 q^{79} +1.12826 q^{80} +10.4367 q^{81} -6.70945 q^{82} +6.36108 q^{83} +11.5348 q^{84} -3.18747 q^{85} +25.9035 q^{86} +21.7681 q^{87} -9.14253 q^{88} +8.91236 q^{89} -13.7227 q^{90} -0.0419951 q^{91} -18.3388 q^{92} +8.50946 q^{93} +20.8962 q^{94} +5.69971 q^{95} -20.6625 q^{96} -15.6077 q^{97} -11.9246 q^{98} -26.0990 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 17q+6q2+5q3+18q417q5+3q6+7q7+18q8+22q96q10+7q11+20q12+3q13+17q145q15+28q16+6q17+13q1823q19+46q99+O(q100) 17 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 17 q^{5} + 3 q^{6} + 7 q^{7} + 18 q^{8} + 22 q^{9} - 6 q^{10} + 7 q^{11} + 20 q^{12} + 3 q^{13} + 17 q^{14} - 5 q^{15} + 28 q^{16} + 6 q^{17} + 13 q^{18} - 23 q^{19}+ \cdots - 46 q^{99}+O(q^{100}) Copy content Toggle raw display

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 2.22883 1.57602 0.788010 0.615663i 0.211112π-0.211112\pi
0.788010 + 0.615663i 0.211112π0.211112\pi
33 3.02604 1.74708 0.873542 0.486749i 0.161817π-0.161817\pi
0.873542 + 0.486749i 0.161817π0.161817\pi
44 2.96767 1.48384
55 −1.00000 −0.447214
66 6.74452 2.75344
77 1.28446 0.485480 0.242740 0.970091i 0.421954π-0.421954\pi
0.242740 + 0.970091i 0.421954π0.421954\pi
88 2.15678 0.762537
99 6.15690 2.05230
1010 −2.22883 −0.704817
1111 −4.23897 −1.27810 −0.639050 0.769166i 0.720672π-0.720672\pi
−0.639050 + 0.769166i 0.720672π0.720672\pi
1212 8.98029 2.59239
1313 −0.0326948 −0.00906790 −0.00453395 0.999990i 0.501443π-0.501443\pi
−0.00453395 + 0.999990i 0.501443π0.501443\pi
1414 2.86284 0.765126
1515 −3.02604 −0.781320
1616 −1.12826 −0.282065
1717 3.18747 0.773076 0.386538 0.922274i 0.373671π-0.373671\pi
0.386538 + 0.922274i 0.373671π0.373671\pi
1818 13.7227 3.23447
1919 −5.69971 −1.30760 −0.653801 0.756666i 0.726827π-0.726827\pi
−0.653801 + 0.756666i 0.726827π0.726827\pi
2020 −2.96767 −0.663592
2121 3.88682 0.848174
2222 −9.44795 −2.01431
2323 −6.17953 −1.28852 −0.644260 0.764806i 0.722835π-0.722835\pi
−0.644260 + 0.764806i 0.722835π0.722835\pi
2424 6.52650 1.33222
2525 1.00000 0.200000
2626 −0.0728710 −0.0142912
2727 9.55291 1.83846
2828 3.81186 0.720373
2929 7.19361 1.33582 0.667910 0.744242i 0.267189π-0.267189\pi
0.667910 + 0.744242i 0.267189π0.267189\pi
3030 −6.74452 −1.23137
3131 2.81208 0.505064 0.252532 0.967588i 0.418737π-0.418737\pi
0.252532 + 0.967588i 0.418737π0.418737\pi
3232 −6.82825 −1.20708
3333 −12.8273 −2.23295
3434 7.10433 1.21838
3535 −1.28446 −0.217113
3636 18.2717 3.04528
3737 −11.8869 −1.95419 −0.977096 0.212800i 0.931742π-0.931742\pi
−0.977096 + 0.212800i 0.931742π0.931742\pi
3838 −12.7037 −2.06081
3939 −0.0989356 −0.0158424
4040 −2.15678 −0.341017
4141 −3.01031 −0.470131 −0.235065 0.971980i 0.575530π-0.575530\pi
−0.235065 + 0.971980i 0.575530π0.575530\pi
4242 8.66306 1.33674
4343 11.6220 1.77234 0.886172 0.463357i 0.153355π-0.153355\pi
0.886172 + 0.463357i 0.153355π0.153355\pi
4444 −12.5799 −1.89649
4545 −6.15690 −0.917817
4646 −13.7731 −2.03073
4747 9.37541 1.36754 0.683772 0.729695i 0.260338π-0.260338\pi
0.683772 + 0.729695i 0.260338π0.260338\pi
4848 −3.41415 −0.492790
4949 −5.35016 −0.764309
5050 2.22883 0.315204
5151 9.64541 1.35063
5252 −0.0970274 −0.0134553
5353 4.47527 0.614726 0.307363 0.951592i 0.400553π-0.400553\pi
0.307363 + 0.951592i 0.400553π0.400553\pi
5454 21.2918 2.89745
5555 4.23897 0.571583
5656 2.77030 0.370196
5757 −17.2475 −2.28449
5858 16.0333 2.10528
5959 −6.52124 −0.848993 −0.424497 0.905429i 0.639549π-0.639549\pi
−0.424497 + 0.905429i 0.639549π0.639549\pi
6060 −8.98029 −1.15935
6161 3.93428 0.503733 0.251867 0.967762i 0.418956π-0.418956\pi
0.251867 + 0.967762i 0.418956π0.418956\pi
6262 6.26764 0.795991
6363 7.90829 0.996351
6464 −12.9625 −1.62031
6565 0.0326948 0.00405529
6666 −28.5898 −3.51917
6767 3.36275 0.410825 0.205412 0.978675i 0.434146π-0.434146\pi
0.205412 + 0.978675i 0.434146π0.434146\pi
6868 9.45938 1.14712
6969 −18.6995 −2.25115
7070 −2.86284 −0.342175
7171 3.94676 0.468394 0.234197 0.972189i 0.424754π-0.424754\pi
0.234197 + 0.972189i 0.424754π0.424754\pi
7272 13.2791 1.56495
7373 −0.394938 −0.0462240 −0.0231120 0.999733i 0.507357π-0.507357\pi
−0.0231120 + 0.999733i 0.507357π0.507357\pi
7474 −26.4938 −3.07984
7575 3.02604 0.349417
7676 −16.9149 −1.94027
7777 −5.44479 −0.620492
7878 −0.220510 −0.0249679
7979 5.02637 0.565510 0.282755 0.959192i 0.408752π-0.408752\pi
0.282755 + 0.959192i 0.408752π0.408752\pi
8080 1.12826 0.126143
8181 10.4367 1.15964
8282 −6.70945 −0.740935
8383 6.36108 0.698219 0.349110 0.937082i 0.386484π-0.386484\pi
0.349110 + 0.937082i 0.386484π0.386484\pi
8484 11.5348 1.25855
8585 −3.18747 −0.345730
8686 25.9035 2.79325
8787 21.7681 2.33379
8888 −9.14253 −0.974597
8989 8.91236 0.944708 0.472354 0.881409i 0.343404π-0.343404\pi
0.472354 + 0.881409i 0.343404π0.343404\pi
9090 −13.7227 −1.44650
9191 −0.0419951 −0.00440228
9292 −18.3388 −1.91195
9393 8.50946 0.882390
9494 20.8962 2.15528
9595 5.69971 0.584777
9696 −20.6625 −2.10886
9797 −15.6077 −1.58472 −0.792361 0.610052i 0.791148π-0.791148\pi
−0.792361 + 0.610052i 0.791148π0.791148\pi
9898 −11.9246 −1.20457
9999 −26.0990 −2.62304
100100 2.96767 0.296767
101101 16.7632 1.66800 0.834002 0.551762i 0.186044π-0.186044\pi
0.834002 + 0.551762i 0.186044π0.186044\pi
102102 21.4980 2.12862
103103 −2.86345 −0.282144 −0.141072 0.989999i 0.545055π-0.545055\pi
−0.141072 + 0.989999i 0.545055π0.545055\pi
104104 −0.0705154 −0.00691460
105105 −3.88682 −0.379315
106106 9.97461 0.968820
107107 −1.02937 −0.0995130 −0.0497565 0.998761i 0.515845π-0.515845\pi
−0.0497565 + 0.998761i 0.515845π0.515845\pi
108108 28.3499 2.72797
109109 −10.2929 −0.985883 −0.492941 0.870063i 0.664078π-0.664078\pi
−0.492941 + 0.870063i 0.664078π0.664078\pi
110110 9.44795 0.900826
111111 −35.9702 −3.41414
112112 −1.44920 −0.136937
113113 −12.8305 −1.20699 −0.603495 0.797367i 0.706226π-0.706226\pi
−0.603495 + 0.797367i 0.706226π0.706226\pi
114114 −38.4418 −3.60040
115115 6.17953 0.576244
116116 21.3483 1.98214
117117 −0.201298 −0.0186101
118118 −14.5347 −1.33803
119119 4.09418 0.375313
120120 −6.52650 −0.595785
121121 6.96891 0.633537
122122 8.76884 0.793893
123123 −9.10930 −0.821358
124124 8.34534 0.749433
125125 −1.00000 −0.0894427
126126 17.6262 1.57027
127127 −13.2366 −1.17456 −0.587279 0.809385i 0.699801π-0.699801\pi
−0.587279 + 0.809385i 0.699801π0.699801\pi
128128 −15.2346 −1.34656
129129 35.1687 3.09643
130130 0.0728710 0.00639121
131131 10.5920 0.925425 0.462713 0.886508i 0.346876π-0.346876\pi
0.462713 + 0.886508i 0.346876π0.346876\pi
132132 −38.0672 −3.31333
133133 −7.32104 −0.634815
134134 7.49499 0.647468
135135 −9.55291 −0.822183
136136 6.87468 0.589499
137137 −3.82013 −0.326376 −0.163188 0.986595i 0.552178π-0.552178\pi
−0.163188 + 0.986595i 0.552178π0.552178\pi
138138 −41.6779 −3.54786
139139 3.20940 0.272218 0.136109 0.990694i 0.456540π-0.456540\pi
0.136109 + 0.990694i 0.456540π0.456540\pi
140140 −3.81186 −0.322161
141141 28.3704 2.38921
142142 8.79664 0.738198
143143 0.138592 0.0115897
144144 −6.94658 −0.578881
145145 −7.19361 −0.597397
146146 −0.880249 −0.0728499
147147 −16.1898 −1.33531
148148 −35.2764 −2.89970
149149 11.8165 0.968042 0.484021 0.875056i 0.339176π-0.339176\pi
0.484021 + 0.875056i 0.339176π0.339176\pi
150150 6.74452 0.550688
151151 −8.86121 −0.721115 −0.360558 0.932737i 0.617414π-0.617414\pi
−0.360558 + 0.932737i 0.617414π0.617414\pi
152152 −12.2930 −0.997095
153153 19.6250 1.58658
154154 −12.1355 −0.977907
155155 −2.81208 −0.225872
156156 −0.293609 −0.0235075
157157 −0.0926825 −0.00739687 −0.00369843 0.999993i 0.501177π-0.501177\pi
−0.00369843 + 0.999993i 0.501177π0.501177\pi
158158 11.2029 0.891255
159159 13.5423 1.07398
160160 6.82825 0.539821
161161 −7.93735 −0.625551
162162 23.2617 1.82761
163163 5.54121 0.434021 0.217010 0.976169i 0.430369π-0.430369\pi
0.217010 + 0.976169i 0.430369π0.430369\pi
164164 −8.93361 −0.697598
165165 12.8273 0.998604
166166 14.1778 1.10041
167167 −22.8426 −1.76761 −0.883806 0.467854i 0.845027π-0.845027\pi
−0.883806 + 0.467854i 0.845027π0.845027\pi
168168 8.38302 0.646764
169169 −12.9989 −0.999918
170170 −7.10433 −0.544877
171171 −35.0925 −2.68359
172172 34.4904 2.62987
173173 19.4621 1.47968 0.739840 0.672783i 0.234901π-0.234901\pi
0.739840 + 0.672783i 0.234901π0.234901\pi
174174 48.5174 3.67810
175175 1.28446 0.0970960
176176 4.78266 0.360506
177177 −19.7335 −1.48326
178178 19.8641 1.48888
179179 1.50622 0.112580 0.0562902 0.998414i 0.482073π-0.482073\pi
0.0562902 + 0.998414i 0.482073π0.482073\pi
180180 −18.2717 −1.36189
181181 −13.5177 −1.00476 −0.502380 0.864647i 0.667542π-0.667542\pi
−0.502380 + 0.864647i 0.667542π0.667542\pi
182182 −0.0935998 −0.00693808
183183 11.9053 0.880064
184184 −13.3279 −0.982544
185185 11.8869 0.873941
186186 18.9661 1.39066
187187 −13.5116 −0.988067
188188 27.8232 2.02921
189189 12.2703 0.892535
190190 12.7037 0.921621
191191 26.7463 1.93529 0.967646 0.252310i 0.0811904π-0.0811904\pi
0.967646 + 0.252310i 0.0811904π0.0811904\pi
192192 −39.2250 −2.83082
193193 19.6630 1.41538 0.707688 0.706525i 0.249738π-0.249738\pi
0.707688 + 0.706525i 0.249738π0.249738\pi
194194 −34.7869 −2.49755
195195 0.0989356 0.00708492
196196 −15.8775 −1.13411
197197 1.00000 0.0712470
198198 −58.1701 −4.13397
199199 19.4206 1.37669 0.688345 0.725383i 0.258338π-0.258338\pi
0.688345 + 0.725383i 0.258338π0.258338\pi
200200 2.15678 0.152507
201201 10.1758 0.717746
202202 37.3624 2.62881
203203 9.23990 0.648514
204204 28.6244 2.00411
205205 3.01031 0.210249
206206 −6.38214 −0.444665
207207 −38.0468 −2.64443
208208 0.0368881 0.00255773
209209 24.1609 1.67124
210210 −8.66306 −0.597808
211211 9.62672 0.662731 0.331365 0.943502i 0.392491π-0.392491\pi
0.331365 + 0.943502i 0.392491π0.392491\pi
212212 13.2812 0.912153
213213 11.9430 0.818323
214214 −2.29429 −0.156834
215215 −11.6220 −0.792616
216216 20.6035 1.40189
217217 3.61200 0.245199
218218 −22.9411 −1.55377
219219 −1.19510 −0.0807572
220220 12.5799 0.848136
221221 −0.104214 −0.00701017
222222 −80.1713 −5.38074
223223 27.1858 1.82050 0.910249 0.414061i 0.135890π-0.135890\pi
0.910249 + 0.414061i 0.135890π0.135890\pi
224224 −8.77061 −0.586011
225225 6.15690 0.410460
226226 −28.5969 −1.90224
227227 −20.7178 −1.37509 −0.687543 0.726144i 0.741311π-0.741311\pi
−0.687543 + 0.726144i 0.741311π0.741311\pi
228228 −51.1850 −3.38981
229229 −16.6170 −1.09808 −0.549042 0.835795i 0.685007π-0.685007\pi
−0.549042 + 0.835795i 0.685007π0.685007\pi
230230 13.7731 0.908172
231231 −16.4761 −1.08405
232232 15.5150 1.01861
233233 −0.693861 −0.0454563 −0.0227282 0.999742i 0.507235π-0.507235\pi
−0.0227282 + 0.999742i 0.507235π0.507235\pi
234234 −0.448660 −0.0293298
235235 −9.37541 −0.611585
236236 −19.3529 −1.25977
237237 15.2100 0.987994
238238 9.12522 0.591500
239239 29.2959 1.89500 0.947498 0.319763i 0.103603π-0.103603\pi
0.947498 + 0.319763i 0.103603π0.103603\pi
240240 3.41415 0.220383
241241 −2.16835 −0.139676 −0.0698378 0.997558i 0.522248π-0.522248\pi
−0.0698378 + 0.997558i 0.522248π0.522248\pi
242242 15.5325 0.998467
243243 2.92326 0.187528
244244 11.6757 0.747458
245245 5.35016 0.341809
246246 −20.3031 −1.29448
247247 0.186351 0.0118572
248248 6.06504 0.385130
249249 19.2489 1.21985
250250 −2.22883 −0.140963
251251 −14.5046 −0.915521 −0.457760 0.889076i 0.651348π-0.651348\pi
−0.457760 + 0.889076i 0.651348π0.651348\pi
252252 23.4692 1.47842
253253 26.1949 1.64686
254254 −29.5021 −1.85113
255255 −9.64541 −0.604019
256256 −8.03043 −0.501902
257257 9.76616 0.609196 0.304598 0.952481i 0.401478π-0.401478\pi
0.304598 + 0.952481i 0.401478π0.401478\pi
258258 78.3850 4.88004
259259 −15.2682 −0.948721
260260 0.0970274 0.00601738
261261 44.2903 2.74150
262262 23.6077 1.45849
263263 6.64141 0.409527 0.204764 0.978811i 0.434357π-0.434357\pi
0.204764 + 0.978811i 0.434357π0.434357\pi
264264 −27.6656 −1.70270
265265 −4.47527 −0.274914
266266 −16.3173 −1.00048
267267 26.9691 1.65048
268268 9.97954 0.609597
269269 5.15503 0.314308 0.157154 0.987574i 0.449768π-0.449768\pi
0.157154 + 0.987574i 0.449768π0.449768\pi
270270 −21.2918 −1.29578
271271 −1.63478 −0.0993061 −0.0496530 0.998767i 0.515812π-0.515812\pi
−0.0496530 + 0.998767i 0.515812π0.515812\pi
272272 −3.59629 −0.218057
273273 −0.127079 −0.00769115
274274 −8.51442 −0.514375
275275 −4.23897 −0.255620
276276 −55.4940 −3.34034
277277 −10.2128 −0.613629 −0.306814 0.951769i 0.599263π-0.599263\pi
−0.306814 + 0.951769i 0.599263π0.599263\pi
278278 7.15320 0.429020
279279 17.3137 1.03654
280280 −2.77030 −0.165557
281281 −15.4518 −0.921779 −0.460890 0.887457i 0.652470π-0.652470\pi
−0.460890 + 0.887457i 0.652470π0.652470\pi
282282 63.2326 3.76545
283283 −12.8317 −0.762765 −0.381383 0.924417i 0.624552π-0.624552\pi
−0.381383 + 0.924417i 0.624552π0.624552\pi
284284 11.7127 0.695020
285285 17.2475 1.02166
286286 0.308898 0.0182655
287287 −3.86662 −0.228239
288288 −42.0409 −2.47728
289289 −6.84001 −0.402354
290290 −16.0333 −0.941509
291291 −47.2295 −2.76864
292292 −1.17205 −0.0685889
293293 −13.1558 −0.768571 −0.384285 0.923214i 0.625552π-0.625552\pi
−0.384285 + 0.923214i 0.625552π0.625552\pi
294294 −36.0843 −2.10448
295295 6.52124 0.379681
296296 −25.6374 −1.49014
297297 −40.4945 −2.34973
298298 26.3369 1.52565
299299 0.202038 0.0116842
300300 8.98029 0.518477
301301 14.9280 0.860437
302302 −19.7501 −1.13649
303303 50.7262 2.91414
304304 6.43074 0.368828
305305 −3.93428 −0.225276
306306 43.7407 2.50049
307307 −5.07199 −0.289474 −0.144737 0.989470i 0.546234π-0.546234\pi
−0.144737 + 0.989470i 0.546234π0.546234\pi
308308 −16.1584 −0.920708
309309 −8.66491 −0.492929
310310 −6.26764 −0.355978
311311 5.96977 0.338515 0.169257 0.985572i 0.445863π-0.445863\pi
0.169257 + 0.985572i 0.445863π0.445863\pi
312312 −0.213382 −0.0120804
313313 −14.9712 −0.846224 −0.423112 0.906077i 0.639062π-0.639062\pi
−0.423112 + 0.906077i 0.639062π0.639062\pi
314314 −0.206573 −0.0116576
315315 −7.90829 −0.445582
316316 14.9166 0.839125
317317 −10.8677 −0.610388 −0.305194 0.952290i 0.598721π-0.598721\pi
−0.305194 + 0.952290i 0.598721π0.598721\pi
318318 30.1836 1.69261
319319 −30.4935 −1.70731
320320 12.9625 0.724625
321321 −3.11491 −0.173857
322322 −17.6910 −0.985880
323323 −18.1677 −1.01088
324324 30.9729 1.72071
325325 −0.0326948 −0.00181358
326326 12.3504 0.684025
327327 −31.1468 −1.72242
328328 −6.49257 −0.358492
329329 12.0423 0.663916
330330 28.5898 1.57382
331331 25.5182 1.40261 0.701304 0.712862i 0.252602π-0.252602\pi
0.701304 + 0.712862i 0.252602π0.252602\pi
332332 18.8776 1.03604
333333 −73.1864 −4.01059
334334 −50.9122 −2.78579
335335 −3.36275 −0.183727
336336 −4.38534 −0.239240
337337 −26.3413 −1.43490 −0.717450 0.696610i 0.754691π-0.754691\pi
−0.717450 + 0.696610i 0.754691π0.754691\pi
338338 −28.9724 −1.57589
339339 −38.8255 −2.10871
340340 −9.45938 −0.513007
341341 −11.9203 −0.645522
342342 −78.2152 −4.22939
343343 −15.8633 −0.856537
344344 25.0662 1.35148
345345 18.6995 1.00675
346346 43.3778 2.33200
347347 −11.8578 −0.636562 −0.318281 0.947996i 0.603106π-0.603106\pi
−0.318281 + 0.947996i 0.603106π0.603106\pi
348348 64.6007 3.46296
349349 −8.47396 −0.453601 −0.226800 0.973941i 0.572826π-0.572826\pi
−0.226800 + 0.973941i 0.572826π0.572826\pi
350350 2.86284 0.153025
351351 −0.312330 −0.0166709
352352 28.9448 1.54276
353353 17.4148 0.926894 0.463447 0.886125i 0.346612π-0.346612\pi
0.463447 + 0.886125i 0.346612π0.346612\pi
354354 −43.9826 −2.33765
355355 −3.94676 −0.209472
356356 26.4490 1.40179
357357 12.3891 0.655703
358358 3.35711 0.177429
359359 10.3720 0.547413 0.273706 0.961813i 0.411750π-0.411750\pi
0.273706 + 0.961813i 0.411750π0.411750\pi
360360 −13.2791 −0.699869
361361 13.4866 0.709823
362362 −30.1286 −1.58352
363363 21.0882 1.10684
364364 −0.124628 −0.00653227
365365 0.394938 0.0206720
366366 26.5348 1.38700
367367 33.3869 1.74278 0.871392 0.490588i 0.163218π-0.163218\pi
0.871392 + 0.490588i 0.163218π0.163218\pi
368368 6.97210 0.363446
369369 −18.5342 −0.964850
370370 26.4938 1.37735
371371 5.74831 0.298437
372372 25.2533 1.30932
373373 −22.5229 −1.16619 −0.583096 0.812403i 0.698159π-0.698159\pi
−0.583096 + 0.812403i 0.698159π0.698159\pi
374374 −30.1151 −1.55721
375375 −3.02604 −0.156264
376376 20.2207 1.04280
377377 −0.235193 −0.0121131
378378 27.3484 1.40665
379379 −9.58707 −0.492455 −0.246227 0.969212i 0.579191π-0.579191\pi
−0.246227 + 0.969212i 0.579191π0.579191\pi
380380 16.9149 0.867714
381381 −40.0544 −2.05205
382382 59.6129 3.05006
383383 −3.52599 −0.180170 −0.0900848 0.995934i 0.528714π-0.528714\pi
−0.0900848 + 0.995934i 0.528714π0.528714\pi
384384 −46.1006 −2.35256
385385 5.44479 0.277492
386386 43.8255 2.23066
387387 71.5557 3.63738
388388 −46.3186 −2.35147
389389 −9.44773 −0.479019 −0.239509 0.970894i 0.576987π-0.576987\pi
−0.239509 + 0.970894i 0.576987π0.576987\pi
390390 0.220510 0.0111660
391391 −19.6971 −0.996124
392392 −11.5391 −0.582814
393393 32.0517 1.61680
394394 2.22883 0.112287
395395 −5.02637 −0.252904
396396 −77.4532 −3.89217
397397 21.3370 1.07087 0.535437 0.844575i 0.320147π-0.320147\pi
0.535437 + 0.844575i 0.320147π0.320147\pi
398398 43.2852 2.16969
399399 −22.1537 −1.10907
400400 −1.12826 −0.0564129
401401 35.9093 1.79322 0.896611 0.442819i 0.146021π-0.146021\pi
0.896611 + 0.442819i 0.146021π0.146021\pi
402402 22.6801 1.13118
403403 −0.0919403 −0.00457987
404404 49.7478 2.47505
405405 −10.4367 −0.518606
406406 20.5941 1.02207
407407 50.3882 2.49765
408408 20.8030 1.02990
409409 −8.75900 −0.433105 −0.216552 0.976271i 0.569481π-0.569481\pi
−0.216552 + 0.976271i 0.569481π0.569481\pi
410410 6.70945 0.331356
411411 −11.5599 −0.570206
412412 −8.49779 −0.418656
413413 −8.37627 −0.412169
414414 −84.7997 −4.16768
415415 −6.36108 −0.312253
416416 0.223248 0.0109456
417417 9.71176 0.475587
418418 53.8505 2.63391
419419 −39.8981 −1.94915 −0.974575 0.224063i 0.928068π-0.928068\pi
−0.974575 + 0.224063i 0.928068π0.928068\pi
420420 −11.5348 −0.562842
421421 −1.39340 −0.0679103 −0.0339552 0.999423i 0.510810π-0.510810\pi
−0.0339552 + 0.999423i 0.510810π0.510810\pi
422422 21.4563 1.04448
423423 57.7235 2.80661
424424 9.65218 0.468751
425425 3.18747 0.154615
426426 26.6190 1.28969
427427 5.05342 0.244552
428428 −3.05484 −0.147661
429429 0.419385 0.0202481
430430 −25.9035 −1.24918
431431 28.4874 1.37219 0.686094 0.727513i 0.259324π-0.259324\pi
0.686094 + 0.727513i 0.259324π0.259324\pi
432432 −10.7781 −0.518564
433433 4.19554 0.201625 0.100812 0.994905i 0.467856π-0.467856\pi
0.100812 + 0.994905i 0.467856π0.467856\pi
434434 8.05053 0.386438
435435 −21.7681 −1.04370
436436 −30.5460 −1.46289
437437 35.2215 1.68487
438438 −2.66367 −0.127275
439439 −0.288756 −0.0137816 −0.00689079 0.999976i 0.502193π-0.502193\pi
−0.00689079 + 0.999976i 0.502193π0.502193\pi
440440 9.14253 0.435853
441441 −32.9404 −1.56859
442442 −0.232274 −0.0110482
443443 2.51971 0.119715 0.0598576 0.998207i 0.480935π-0.480935\pi
0.0598576 + 0.998207i 0.480935π0.480935\pi
444444 −106.748 −5.06602
445445 −8.91236 −0.422486
446446 60.5926 2.86914
447447 35.7571 1.69125
448448 −16.6498 −0.786628
449449 11.0944 0.523579 0.261790 0.965125i 0.415687π-0.415687\pi
0.261790 + 0.965125i 0.415687π0.415687\pi
450450 13.7227 0.646893
451451 12.7606 0.600874
452452 −38.0767 −1.79098
453453 −26.8144 −1.25985
454454 −46.1763 −2.16716
455455 0.0419951 0.00196876
456456 −37.1991 −1.74201
457457 11.7408 0.549211 0.274606 0.961557i 0.411453π-0.411453\pi
0.274606 + 0.961557i 0.411453π0.411453\pi
458458 −37.0365 −1.73060
459459 30.4496 1.42127
460460 18.3388 0.855052
461461 −22.3702 −1.04188 −0.520941 0.853593i 0.674419π-0.674419\pi
−0.520941 + 0.853593i 0.674419π0.674419\pi
462462 −36.7225 −1.70848
463463 33.4077 1.55259 0.776294 0.630371i 0.217097π-0.217097\pi
0.776294 + 0.630371i 0.217097π0.217097\pi
464464 −8.11625 −0.376787
465465 −8.50946 −0.394617
466466 −1.54650 −0.0716400
467467 −19.6617 −0.909837 −0.454919 0.890533i 0.650332π-0.650332\pi
−0.454919 + 0.890533i 0.650332π0.650332\pi
468468 −0.597388 −0.0276143
469469 4.31931 0.199447
470470 −20.8962 −0.963869
471471 −0.280461 −0.0129229
472472 −14.0649 −0.647389
473473 −49.2655 −2.26523
474474 33.9004 1.55710
475475 −5.69971 −0.261520
476476 12.1502 0.556903
477477 27.5538 1.26160
478478 65.2956 2.98655
479479 −39.2770 −1.79461 −0.897306 0.441410i 0.854479π-0.854479\pi
−0.897306 + 0.441410i 0.854479π0.854479\pi
480480 20.6625 0.943112
481481 0.388639 0.0177204
482482 −4.83288 −0.220131
483483 −24.0187 −1.09289
484484 20.6814 0.940066
485485 15.6077 0.708709
486486 6.51545 0.295547
487487 7.76387 0.351815 0.175907 0.984407i 0.443714π-0.443714\pi
0.175907 + 0.984407i 0.443714π0.443714\pi
488488 8.48538 0.384115
489489 16.7679 0.758271
490490 11.9246 0.538698
491491 −35.9660 −1.62312 −0.811562 0.584267i 0.801382π-0.801382\pi
−0.811562 + 0.584267i 0.801382π0.801382\pi
492492 −27.0334 −1.21876
493493 22.9294 1.03269
494494 0.415343 0.0186872
495495 26.0990 1.17306
496496 −3.17275 −0.142461
497497 5.06945 0.227396
498498 42.9024 1.92250
499499 −12.6195 −0.564926 −0.282463 0.959278i 0.591151π-0.591151\pi
−0.282463 + 0.959278i 0.591151π0.591151\pi
500500 −2.96767 −0.132718
501501 −69.1225 −3.08816
502502 −32.3282 −1.44288
503503 41.7449 1.86131 0.930656 0.365895i 0.119237π-0.119237\pi
0.930656 + 0.365895i 0.119237π0.119237\pi
504504 17.0564 0.759754
505505 −16.7632 −0.745954
506506 58.3838 2.59548
507507 −39.3353 −1.74694
508508 −39.2819 −1.74285
509509 −9.54868 −0.423238 −0.211619 0.977352i 0.567874π-0.567874\pi
−0.211619 + 0.977352i 0.567874π0.567874\pi
510510 −21.4980 −0.951946
511511 −0.507282 −0.0224408
512512 12.5708 0.555558
513513 −54.4488 −2.40397
514514 21.7671 0.960105
515515 2.86345 0.126179
516516 104.369 4.59460
517517 −39.7421 −1.74786
518518 −34.0302 −1.49520
519519 58.8932 2.58512
520520 0.0705154 0.00309230
521521 9.48197 0.415412 0.207706 0.978191i 0.433400π-0.433400\pi
0.207706 + 0.978191i 0.433400π0.433400\pi
522522 98.7156 4.32066
523523 21.5237 0.941164 0.470582 0.882356i 0.344044π-0.344044\pi
0.470582 + 0.882356i 0.344044π0.344044\pi
524524 31.4335 1.37318
525525 3.88682 0.169635
526526 14.8026 0.645423
527527 8.96343 0.390453
528528 14.4725 0.629835
529529 15.1866 0.660285
530530 −9.97461 −0.433270
531531 −40.1507 −1.74239
532532 −21.7265 −0.941962
533533 0.0984212 0.00426310
534534 60.1096 2.60120
535535 1.02937 0.0445036
536536 7.25270 0.313269
537537 4.55788 0.196687
538538 11.4897 0.495355
539539 22.6792 0.976863
540540 −28.3499 −1.21999
541541 5.18867 0.223078 0.111539 0.993760i 0.464422π-0.464422\pi
0.111539 + 0.993760i 0.464422π0.464422\pi
542542 −3.64365 −0.156508
543543 −40.9050 −1.75540
544544 −21.7649 −0.933161
545545 10.2929 0.440900
546546 −0.283237 −0.0121214
547547 5.82831 0.249201 0.124600 0.992207i 0.460235π-0.460235\pi
0.124600 + 0.992207i 0.460235π0.460235\pi
548548 −11.3369 −0.484289
549549 24.2230 1.03381
550550 −9.44795 −0.402862
551551 −41.0014 −1.74672
552552 −40.3307 −1.71659
553553 6.45616 0.274544
554554 −22.7626 −0.967090
555555 35.9702 1.52685
556556 9.52445 0.403927
557557 −7.89296 −0.334435 −0.167218 0.985920i 0.553478π-0.553478\pi
−0.167218 + 0.985920i 0.553478π0.553478\pi
558558 38.5893 1.63361
559559 −0.379980 −0.0160714
560560 1.44920 0.0612400
561561 −40.8867 −1.72624
562562 −34.4395 −1.45274
563563 −30.1329 −1.26995 −0.634974 0.772533i 0.718989π-0.718989\pi
−0.634974 + 0.772533i 0.718989π0.718989\pi
564564 84.1940 3.54521
565565 12.8305 0.539782
566566 −28.5997 −1.20213
567567 13.4056 0.562981
568568 8.51228 0.357167
569569 −0.652674 −0.0273615 −0.0136808 0.999906i 0.504355π-0.504355\pi
−0.0136808 + 0.999906i 0.504355π0.504355\pi
570570 38.4418 1.61015
571571 8.64196 0.361655 0.180827 0.983515i 0.442122π-0.442122\pi
0.180827 + 0.983515i 0.442122π0.442122\pi
572572 0.411297 0.0171972
573573 80.9352 3.38112
574574 −8.61802 −0.359709
575575 −6.17953 −0.257704
576576 −79.8088 −3.32536
577577 39.1576 1.63015 0.815076 0.579354i 0.196695π-0.196695\pi
0.815076 + 0.579354i 0.196695π0.196695\pi
578578 −15.2452 −0.634117
579579 59.5011 2.47278
580580 −21.3483 −0.886439
581581 8.17055 0.338972
582582 −105.266 −4.36343
583583 −18.9706 −0.785681
584584 −0.851794 −0.0352475
585585 0.201298 0.00832267
586586 −29.3220 −1.21128
587587 −19.2485 −0.794472 −0.397236 0.917716i 0.630031π-0.630031\pi
−0.397236 + 0.917716i 0.630031π0.630031\pi
588588 −48.0460 −1.98139
589589 −16.0280 −0.660423
590590 14.5347 0.598385
591591 3.02604 0.124475
592592 13.4115 0.551208
593593 −44.9942 −1.84769 −0.923845 0.382768i 0.874971π-0.874971\pi
−0.923845 + 0.382768i 0.874971π0.874971\pi
594594 −90.2554 −3.70322
595595 −4.09418 −0.167845
596596 35.0674 1.43642
597597 58.7675 2.40519
598598 0.450308 0.0184145
599599 36.4837 1.49068 0.745342 0.666682i 0.232286π-0.232286\pi
0.745342 + 0.666682i 0.232286π0.232286\pi
600600 6.52650 0.266443
601601 36.7049 1.49722 0.748612 0.663008i 0.230720π-0.230720\pi
0.748612 + 0.663008i 0.230720π0.230720\pi
602602 33.2720 1.35607
603603 20.7041 0.843137
604604 −26.2972 −1.07002
605605 −6.96891 −0.283326
606606 113.060 4.59274
607607 5.22622 0.212126 0.106063 0.994359i 0.466176π-0.466176\pi
0.106063 + 0.994359i 0.466176π0.466176\pi
608608 38.9190 1.57837
609609 27.9603 1.13301
610610 −8.76884 −0.355040
611611 −0.306527 −0.0124008
612612 58.2405 2.35423
613613 2.54201 0.102671 0.0513353 0.998681i 0.483652π-0.483652\pi
0.0513353 + 0.998681i 0.483652π0.483652\pi
614614 −11.3046 −0.456216
615615 9.10930 0.367322
616616 −11.7432 −0.473148
617617 −22.4800 −0.905011 −0.452506 0.891762i 0.649470π-0.649470\pi
−0.452506 + 0.891762i 0.649470π0.649470\pi
618618 −19.3126 −0.776866
619619 13.4275 0.539696 0.269848 0.962903i 0.413026π-0.413026\pi
0.269848 + 0.962903i 0.413026π0.413026\pi
620620 −8.34534 −0.335157
621621 −59.0325 −2.36889
622622 13.3056 0.533506
623623 11.4476 0.458637
624624 0.111625 0.00446857
625625 1.00000 0.0400000
626626 −33.3683 −1.33367
627627 73.1118 2.91980
628628 −0.275051 −0.0109757
629629 −37.8891 −1.51074
630630 −17.6262 −0.702245
631631 −32.2619 −1.28433 −0.642163 0.766568i 0.721963π-0.721963\pi
−0.642163 + 0.766568i 0.721963π0.721963\pi
632632 10.8408 0.431222
633633 29.1308 1.15785
634634 −24.2221 −0.961984
635635 13.2366 0.525278
636636 40.1893 1.59361
637637 0.174922 0.00693068
638638 −67.9648 −2.69075
639639 24.2998 0.961285
640640 15.2346 0.602202
641641 9.71139 0.383577 0.191788 0.981436i 0.438571π-0.438571\pi
0.191788 + 0.981436i 0.438571π0.438571\pi
642642 −6.94260 −0.274003
643643 −11.3068 −0.445897 −0.222949 0.974830i 0.571568π-0.571568\pi
−0.222949 + 0.974830i 0.571568π0.571568\pi
644644 −23.5555 −0.928216
645645 −35.1687 −1.38477
646646 −40.4926 −1.59316
647647 33.4004 1.31311 0.656553 0.754280i 0.272014π-0.272014\pi
0.656553 + 0.754280i 0.272014π0.272014\pi
648648 22.5098 0.884267
649649 27.6434 1.08510
650650 −0.0728710 −0.00285824
651651 10.9301 0.428383
652652 16.4445 0.644016
653653 39.2091 1.53437 0.767185 0.641426i 0.221657π-0.221657\pi
0.767185 + 0.641426i 0.221657π0.221657\pi
654654 −69.4208 −2.71457
655655 −10.5920 −0.413863
656656 3.39640 0.132607
657657 −2.43159 −0.0948655
658658 26.8403 1.04634
659659 13.5095 0.526254 0.263127 0.964761i 0.415246π-0.415246\pi
0.263127 + 0.964761i 0.415246π0.415246\pi
660660 38.0672 1.48177
661661 −33.2439 −1.29304 −0.646519 0.762898i 0.723776π-0.723776\pi
−0.646519 + 0.762898i 0.723776π0.723776\pi
662662 56.8757 2.21054
663663 −0.315355 −0.0122474
664664 13.7194 0.532418
665665 7.32104 0.283898
666666 −163.120 −6.32077
667667 −44.4531 −1.72123
668668 −67.7893 −2.62285
669669 82.2654 3.18056
670670 −7.49499 −0.289557
671671 −16.6773 −0.643821
672672 −26.5402 −1.02381
673673 17.3913 0.670386 0.335193 0.942149i 0.391198π-0.391198\pi
0.335193 + 0.942149i 0.391198π0.391198\pi
674674 −58.7102 −2.26143
675675 9.55291 0.367692
676676 −38.5766 −1.48372
677677 −1.49868 −0.0575991 −0.0287995 0.999585i 0.509168π-0.509168\pi
−0.0287995 + 0.999585i 0.509168π0.509168\pi
678678 −86.5354 −3.32337
679679 −20.0475 −0.769351
680680 −6.87468 −0.263632
681681 −62.6927 −2.40239
682682 −26.5684 −1.01736
683683 38.8528 1.48666 0.743331 0.668924i 0.233245π-0.233245\pi
0.743331 + 0.668924i 0.233245π0.233245\pi
684684 −104.143 −3.98202
685685 3.82013 0.145960
686686 −35.3565 −1.34992
687687 −50.2837 −1.91844
688688 −13.1127 −0.499915
689689 −0.146318 −0.00557427
690690 41.6779 1.58665
691691 −31.4387 −1.19598 −0.597992 0.801502i 0.704035π-0.704035\pi
−0.597992 + 0.801502i 0.704035π0.704035\pi
692692 57.7573 2.19560
693693 −33.5231 −1.27344
694694 −26.4291 −1.00323
695695 −3.20940 −0.121739
696696 46.9490 1.77960
697697 −9.59527 −0.363447
698698 −18.8870 −0.714883
699699 −2.09965 −0.0794160
700700 3.81186 0.144075
701701 −14.6371 −0.552835 −0.276418 0.961038i 0.589147π-0.589147\pi
−0.276418 + 0.961038i 0.589147π0.589147\pi
702702 −0.696130 −0.0262737
703703 67.7517 2.55530
704704 54.9476 2.07092
705705 −28.3704 −1.06849
706706 38.8145 1.46080
707707 21.5317 0.809783
708708 −58.5627 −2.20092
709709 3.84602 0.144440 0.0722201 0.997389i 0.476992π-0.476992\pi
0.0722201 + 0.997389i 0.476992π0.476992\pi
710710 −8.79664 −0.330132
711711 30.9468 1.16060
712712 19.2220 0.720375
713713 −17.3773 −0.650786
714714 27.6133 1.03340
715715 −0.138592 −0.00518306
716716 4.46998 0.167051
717717 88.6505 3.31072
718718 23.1174 0.862733
719719 −43.8516 −1.63539 −0.817693 0.575654i 0.804748π-0.804748\pi
−0.817693 + 0.575654i 0.804748π0.804748\pi
720720 6.94658 0.258884
721721 −3.67798 −0.136975
722722 30.0594 1.11870
723723 −6.56150 −0.244025
724724 −40.1160 −1.49090
725725 7.19361 0.267164
726726 47.0019 1.74440
727727 −35.0618 −1.30037 −0.650186 0.759775i 0.725309π-0.725309\pi
−0.650186 + 0.759775i 0.725309π0.725309\pi
728728 −0.0905741 −0.00335690
729729 −22.4643 −0.832012
730730 0.880249 0.0325795
731731 37.0449 1.37016
732732 35.3310 1.30587
733733 −17.3916 −0.642375 −0.321187 0.947016i 0.604082π-0.604082\pi
−0.321187 + 0.947016i 0.604082π0.604082\pi
734734 74.4137 2.74666
735735 16.1898 0.597170
736736 42.1954 1.55534
737737 −14.2546 −0.525075
738738 −41.3095 −1.52062
739739 −35.9634 −1.32293 −0.661467 0.749974i 0.730066π-0.730066\pi
−0.661467 + 0.749974i 0.730066π0.730066\pi
740740 35.2764 1.29679
741741 0.563904 0.0207155
742742 12.8120 0.470343
743743 7.32782 0.268832 0.134416 0.990925i 0.457084π-0.457084\pi
0.134416 + 0.990925i 0.457084π0.457084\pi
744744 18.3530 0.672855
745745 −11.8165 −0.432922
746746 −50.1997 −1.83794
747747 39.1646 1.43296
748748 −40.0981 −1.46613
749749 −1.32218 −0.0483116
750750 −6.74452 −0.246275
751751 −4.38020 −0.159836 −0.0799179 0.996801i 0.525466π-0.525466\pi
−0.0799179 + 0.996801i 0.525466π0.525466\pi
752752 −10.5779 −0.385736
753753 −43.8914 −1.59949
754754 −0.524205 −0.0190904
755755 8.86121 0.322493
756756 36.4143 1.32438
757757 14.6109 0.531042 0.265521 0.964105i 0.414456π-0.414456\pi
0.265521 + 0.964105i 0.414456π0.414456\pi
758758 −21.3679 −0.776118
759759 79.2666 2.87720
760760 12.2930 0.445914
761761 25.1421 0.911401 0.455700 0.890133i 0.349389π-0.349389\pi
0.455700 + 0.890133i 0.349389π0.349389\pi
762762 −89.2745 −3.23407
763763 −13.2208 −0.478626
764764 79.3742 2.87166
765765 −19.6250 −0.709542
766766 −7.85883 −0.283951
767767 0.213210 0.00769858
768768 −24.3004 −0.876864
769769 −8.07722 −0.291272 −0.145636 0.989338i 0.546523π-0.546523\pi
−0.145636 + 0.989338i 0.546523π0.546523\pi
770770 12.1355 0.437333
771771 29.5528 1.06432
772772 58.3535 2.10019
773773 35.4654 1.27560 0.637802 0.770201i 0.279844π-0.279844\pi
0.637802 + 0.770201i 0.279844π0.279844\pi
774774 159.485 5.73258
775775 2.81208 0.101013
776776 −33.6624 −1.20841
777777 −46.2022 −1.65749
778778 −21.0574 −0.754943
779779 17.1579 0.614744
780780 0.293609 0.0105129
781781 −16.7302 −0.598654
782782 −43.9014 −1.56991
783783 68.7199 2.45585
784784 6.03637 0.215585
785785 0.0926825 0.00330798
786786 71.4378 2.54810
787787 36.2547 1.29234 0.646171 0.763193i 0.276369π-0.276369\pi
0.646171 + 0.763193i 0.276369π0.276369\pi
788788 2.96767 0.105719
789789 20.0972 0.715478
790790 −11.2029 −0.398581
791791 −16.4802 −0.585969
792792 −56.2897 −2.00017
793793 −0.128630 −0.00456780
794794 47.5566 1.68772
795795 −13.5423 −0.480297
796796 57.6340 2.04278
797797 37.6915 1.33510 0.667551 0.744565i 0.267343π-0.267343\pi
0.667551 + 0.744565i 0.267343π0.267343\pi
798798 −49.3769 −1.74792
799799 29.8839 1.05722
800800 −6.82825 −0.241415
801801 54.8725 1.93883
802802 80.0355 2.82615
803803 1.67413 0.0590788
804804 30.1985 1.06502
805805 7.93735 0.279755
806806 −0.204919 −0.00721797
807807 15.5993 0.549122
808808 36.1546 1.27191
809809 −40.7120 −1.43136 −0.715678 0.698430i 0.753882π-0.753882\pi
−0.715678 + 0.698430i 0.753882π0.753882\pi
810810 −23.2617 −0.817333
811811 −50.3877 −1.76935 −0.884676 0.466207i 0.845620π-0.845620\pi
−0.884676 + 0.466207i 0.845620π0.845620\pi
812812 27.4210 0.962289
813813 −4.94692 −0.173496
814814 112.307 3.93634
815815 −5.54121 −0.194100
816816 −10.8825 −0.380964
817817 −66.2421 −2.31752
818818 −19.5223 −0.682581
819819 −0.258560 −0.00903481
820820 8.93361 0.311975
821821 27.4410 0.957697 0.478849 0.877897i 0.341054π-0.341054\pi
0.478849 + 0.877897i 0.341054π0.341054\pi
822822 −25.7650 −0.898656
823823 −35.1356 −1.22475 −0.612375 0.790567i 0.709786π-0.709786\pi
−0.612375 + 0.790567i 0.709786π0.709786\pi
824824 −6.17583 −0.215145
825825 −12.8273 −0.446589
826826 −18.6693 −0.649587
827827 6.76979 0.235409 0.117704 0.993049i 0.462447π-0.462447\pi
0.117704 + 0.993049i 0.462447π0.462447\pi
828828 −112.910 −3.92391
829829 −37.4923 −1.30216 −0.651080 0.759009i 0.725684π-0.725684\pi
−0.651080 + 0.759009i 0.725684π0.725684\pi
830830 −14.1778 −0.492117
831831 −30.9044 −1.07206
832832 0.423805 0.0146928
833833 −17.0535 −0.590869
834834 21.6458 0.749534
835835 22.8426 0.790500
836836 71.7017 2.47986
837837 26.8635 0.928540
838838 −88.9260 −3.07190
839839 39.5332 1.36484 0.682419 0.730961i 0.260928π-0.260928\pi
0.682419 + 0.730961i 0.260928π0.260928\pi
840840 −8.38302 −0.289242
841841 22.7480 0.784413
842842 −3.10566 −0.107028
843843 −46.7578 −1.61043
844844 28.5690 0.983385
845845 12.9989 0.447177
846846 128.656 4.42328
847847 8.95128 0.307570
848848 −5.04926 −0.173392
849849 −38.8292 −1.33261
850850 7.10433 0.243677
851851 73.4553 2.51802
852852 35.4430 1.21426
853853 −48.5066 −1.66084 −0.830418 0.557141i 0.811898π-0.811898\pi
−0.830418 + 0.557141i 0.811898π0.811898\pi
854854 11.2632 0.385419
855855 35.0925 1.20014
856856 −2.22012 −0.0758823
857857 −23.5135 −0.803205 −0.401602 0.915814i 0.631547π-0.631547\pi
−0.401602 + 0.915814i 0.631547π0.631547\pi
858858 0.934738 0.0319114
859859 −53.5959 −1.82867 −0.914335 0.404959i 0.867286π-0.867286\pi
−0.914335 + 0.404959i 0.867286π0.867286\pi
860860 −34.4904 −1.17611
861861 −11.7005 −0.398753
862862 63.4935 2.16260
863863 21.5279 0.732819 0.366409 0.930454i 0.380587π-0.380587\pi
0.366409 + 0.930454i 0.380587π0.380587\pi
864864 −65.2297 −2.21916
865865 −19.4621 −0.661733
866866 9.35113 0.317764
867867 −20.6981 −0.702946
868868 10.7192 0.363835
869869 −21.3066 −0.722778
870870 −48.5174 −1.64489
871871 −0.109944 −0.00372532
872872 −22.1996 −0.751772
873873 −96.0951 −3.25233
874874 78.5026 2.65539
875875 −1.28446 −0.0434227
876876 −3.54666 −0.119830
877877 7.08676 0.239303 0.119651 0.992816i 0.461822π-0.461822\pi
0.119651 + 0.992816i 0.461822π0.461822\pi
878878 −0.643588 −0.0217200
879879 −39.8100 −1.34276
880880 −4.78266 −0.161223
881881 −38.2223 −1.28774 −0.643871 0.765134i 0.722673π-0.722673\pi
−0.643871 + 0.765134i 0.722673π0.722673\pi
882882 −73.4186 −2.47213
883883 58.3397 1.96329 0.981644 0.190723i 0.0610832π-0.0610832\pi
0.981644 + 0.190723i 0.0610832π0.0610832\pi
884884 −0.309272 −0.0104020
885885 19.7335 0.663335
886886 5.61601 0.188673
887887 25.8682 0.868570 0.434285 0.900776i 0.357001π-0.357001\pi
0.434285 + 0.900776i 0.357001π0.357001\pi
888888 −77.5797 −2.60340
889889 −17.0019 −0.570224
890890 −19.8641 −0.665847
891891 −44.2411 −1.48213
892892 80.6787 2.70132
893893 −53.4371 −1.78820
894894 79.6963 2.66544
895895 −1.50622 −0.0503475
896896 −19.5683 −0.653730
897897 0.611375 0.0204132
898898 24.7276 0.825171
899899 20.2290 0.674675
900900 18.2717 0.609056
901901 14.2648 0.475230
902902 28.4412 0.946989
903903 45.1728 1.50326
904904 −27.6725 −0.920374
905905 13.5177 0.449342
906906 −59.7646 −1.98555
907907 −34.0342 −1.13009 −0.565043 0.825061i 0.691140π-0.691140\pi
−0.565043 + 0.825061i 0.691140π0.691140\pi
908908 −61.4835 −2.04040
909909 103.210 3.42325
910910 0.0935998 0.00310280
911911 −38.9474 −1.29039 −0.645193 0.764020i 0.723223π-0.723223\pi
−0.645193 + 0.764020i 0.723223π0.723223\pi
912912 19.4597 0.644374
913913 −26.9645 −0.892394
914914 26.1682 0.865568
915915 −11.9053 −0.393576
916916 −49.3139 −1.62938
917917 13.6050 0.449276
918918 67.8670 2.23994
919919 5.14400 0.169685 0.0848424 0.996394i 0.472961π-0.472961\pi
0.0848424 + 0.996394i 0.472961π0.472961\pi
920920 13.3279 0.439407
921921 −15.3480 −0.505735
922922 −49.8592 −1.64203
923923 −0.129038 −0.00424735
924924 −48.8958 −1.60855
925925 −11.8869 −0.390838
926926 74.4601 2.44691
927927 −17.6300 −0.579045
928928 −49.1198 −1.61244
929929 44.9253 1.47395 0.736976 0.675919i 0.236253π-0.236253\pi
0.736976 + 0.675919i 0.236253π0.236253\pi
930930 −18.9661 −0.621924
931931 30.4944 0.999412
932932 −2.05915 −0.0674498
933933 18.0647 0.591413
934934 −43.8227 −1.43392
935935 13.5116 0.441877
936936 −0.434156 −0.0141908
937937 −32.4004 −1.05848 −0.529238 0.848473i 0.677522π-0.677522\pi
−0.529238 + 0.848473i 0.677522π0.677522\pi
938938 9.62700 0.314333
939939 −45.3035 −1.47842
940940 −27.8232 −0.907492
941941 −14.0427 −0.457777 −0.228889 0.973453i 0.573509π-0.573509\pi
−0.228889 + 0.973453i 0.573509π0.573509\pi
942942 −0.625098 −0.0203668
943943 18.6023 0.605773
944944 7.35765 0.239471
945945 −12.2703 −0.399154
946946 −109.804 −3.57005
947947 15.7483 0.511751 0.255876 0.966710i 0.417636π-0.417636\pi
0.255876 + 0.966710i 0.417636π0.417636\pi
948948 45.1382 1.46602
949949 0.0129124 0.000419154 0
950950 −12.7037 −0.412161
951951 −32.8859 −1.06640
952952 8.83024 0.286190
953953 7.73667 0.250615 0.125308 0.992118i 0.460008π-0.460008\pi
0.125308 + 0.992118i 0.460008π0.460008\pi
954954 61.4127 1.98831
955955 −26.7463 −0.865489
956956 86.9407 2.81186
957957 −92.2745 −2.98281
958958 −87.5417 −2.82834
959959 −4.90681 −0.158449
960960 39.2250 1.26598
961961 −23.0922 −0.744910
962962 0.866209 0.0279277
963963 −6.33773 −0.204231
964964 −6.43495 −0.207256
965965 −19.6630 −0.632975
966966 −53.5336 −1.72242
967967 −31.6140 −1.01664 −0.508319 0.861169i 0.669733π-0.669733\pi
−0.508319 + 0.861169i 0.669733π0.669733\pi
968968 15.0304 0.483095
969969 −54.9760 −1.76608
970970 34.7869 1.11694
971971 −35.4323 −1.13708 −0.568539 0.822657i 0.692491π-0.692491\pi
−0.568539 + 0.822657i 0.692491π0.692491\pi
972972 8.67530 0.278260
973973 4.12234 0.132156
974974 17.3043 0.554467
975975 −0.0989356 −0.00316847
976976 −4.43889 −0.142085
977977 55.8056 1.78538 0.892690 0.450671i 0.148815π-0.148815\pi
0.892690 + 0.450671i 0.148815π0.148815\pi
978978 37.3728 1.19505
979979 −37.7793 −1.20743
980980 15.8775 0.507190
981981 −63.3725 −2.02333
982982 −80.1620 −2.55807
983983 −29.2455 −0.932787 −0.466393 0.884577i 0.654447π-0.654447\pi
−0.466393 + 0.884577i 0.654447π0.654447\pi
984984 −19.6467 −0.626315
985985 −1.00000 −0.0318626
986986 51.1058 1.62754
987987 36.4406 1.15992
988988 0.553028 0.0175942
989989 −71.8187 −2.28370
990990 58.1701 1.84877
991991 −15.9250 −0.505875 −0.252937 0.967483i 0.581397π-0.581397\pi
−0.252937 + 0.967483i 0.581397π0.581397\pi
992992 −19.2016 −0.609651
993993 77.2191 2.45047
994994 11.2989 0.358380
995995 −19.4206 −0.615674
996996 57.1244 1.81006
997997 7.45247 0.236022 0.118011 0.993012i 0.462348π-0.462348\pi
0.118011 + 0.993012i 0.462348π0.462348\pi
998998 −28.1267 −0.890334
999999 −113.554 −3.59270
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 985.2.a.g.1.14 17
3.2 odd 2 8865.2.a.z.1.4 17
5.4 even 2 4925.2.a.l.1.4 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
985.2.a.g.1.14 17 1.1 even 1 trivial
4925.2.a.l.1.4 17 5.4 even 2
8865.2.a.z.1.4 17 3.2 odd 2