Properties

Label 1000.2.d.c.501.29
Level 10001000
Weight 22
Character 1000.501
Analytic conductor 7.9857.985
Analytic rank 00
Dimension 4040
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1000,2,Mod(501,1000)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1000, 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("1000.501");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1000=2353 1000 = 2^{3} \cdot 5^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1000.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: 7.985040202137.98504020213
Analytic rank: 00
Dimension: 4040
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 501.29
Character χ\chi == 1000.501
Dual form 1000.2.d.c.501.30

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+(0.8001791.16607i)q2+2.62662iq3+(0.7194261.86613i)q4+(3.06282+2.10177i)q6+0.269237q7+(2.751700.654336i)q83.89913q9+4.58163iq11+(4.901601.88966i)q121.55366iq13+(0.2154380.313948i)q14+(2.96485+2.68508i)q16+0.609109q17+(3.12001+4.54665i)q18+6.69309iq19+0.707183iq21+(5.34249+3.66612i)q22+3.52675q23+(1.718697.22767i)q24+(1.811671.24321i)q262.36168iq27+(0.1936960.502430i)q28+7.73304iq293.34096q31+(0.758569+5.60576i)q3212.0342q33+(0.4873960.710262i)q34+(2.80514+7.27627i)q365.32768iq37+(7.80459+5.35567i)q38+4.08087q39+4.38291q41+(0.824623+0.565873i)q42+12.2644iq43+(8.549893.29614i)q44+(2.822034.11243i)q469.54651q47+(7.052687.78754i)q486.92751q49+1.59990iq51+(2.89932+1.11774i)q5210.6574iq53+(2.753881.88977i)q54+(0.7408590.176171i)q5617.5802q57+(9.01725+6.18782i)q5810.2256iq59+13.2628iq61+(2.67337+3.89579i)q621.04979q63+(7.14369+3.60107i)q64+(9.62951+14.0327i)q663.93398iq67+(0.4382091.13667i)q68+9.26343iq69+6.95638q71+(10.7292+2.55134i)q72+5.93156q73+(6.212434.26310i)q74+(12.49014.81518i)q76+1.23354iq77+(3.265434.75857i)q78+10.1382q795.49416q81+(3.507125.11077i)q826.52313iq83+(1.319690.508766i)q84+(14.3012+9.81376i)q8620.3118q87+(2.9979312.6073i)q88+6.69564q890.418302iq91+(2.537246.58136i)q928.77544iq93+(7.63892+11.1319i)q94+(14.7242+1.99247i)q963.99182q97+(5.54325+8.07794i)q9817.8644iq99+O(q100)q+(0.800179 - 1.16607i) q^{2} +2.62662i q^{3} +(-0.719426 - 1.86613i) q^{4} +(3.06282 + 2.10177i) q^{6} +0.269237 q^{7} +(-2.75170 - 0.654336i) q^{8} -3.89913 q^{9} +4.58163i q^{11} +(4.90160 - 1.88966i) q^{12} -1.55366i q^{13} +(0.215438 - 0.313948i) q^{14} +(-2.96485 + 2.68508i) q^{16} +0.609109 q^{17} +(-3.12001 + 4.54665i) q^{18} +6.69309i q^{19} +0.707183i q^{21} +(5.34249 + 3.66612i) q^{22} +3.52675 q^{23} +(1.71869 - 7.22767i) q^{24} +(-1.81167 - 1.24321i) q^{26} -2.36168i q^{27} +(-0.193696 - 0.502430i) q^{28} +7.73304i q^{29} -3.34096 q^{31} +(0.758569 + 5.60576i) q^{32} -12.0342 q^{33} +(0.487396 - 0.710262i) q^{34} +(2.80514 + 7.27627i) q^{36} -5.32768i q^{37} +(7.80459 + 5.35567i) q^{38} +4.08087 q^{39} +4.38291 q^{41} +(0.824623 + 0.565873i) q^{42} +12.2644i q^{43} +(8.54989 - 3.29614i) q^{44} +(2.82203 - 4.11243i) q^{46} -9.54651 q^{47} +(-7.05268 - 7.78754i) q^{48} -6.92751 q^{49} +1.59990i q^{51} +(-2.89932 + 1.11774i) q^{52} -10.6574i q^{53} +(-2.75388 - 1.88977i) q^{54} +(-0.740859 - 0.176171i) q^{56} -17.5802 q^{57} +(9.01725 + 6.18782i) q^{58} -10.2256i q^{59} +13.2628i q^{61} +(-2.67337 + 3.89579i) q^{62} -1.04979 q^{63} +(7.14369 + 3.60107i) q^{64} +(-9.62951 + 14.0327i) q^{66} -3.93398i q^{67} +(-0.438209 - 1.13667i) q^{68} +9.26343i q^{69} +6.95638 q^{71} +(10.7292 + 2.55134i) q^{72} +5.93156 q^{73} +(-6.21243 - 4.26310i) q^{74} +(12.4901 - 4.81518i) q^{76} +1.23354i q^{77} +(3.26543 - 4.75857i) q^{78} +10.1382 q^{79} -5.49416 q^{81} +(3.50712 - 5.11077i) q^{82} -6.52313i q^{83} +(1.31969 - 0.508766i) q^{84} +(14.3012 + 9.81376i) q^{86} -20.3118 q^{87} +(2.99793 - 12.6073i) q^{88} +6.69564 q^{89} -0.418302i q^{91} +(-2.53724 - 6.58136i) q^{92} -8.77544i q^{93} +(-7.63892 + 11.1319i) q^{94} +(-14.7242 + 1.99247i) q^{96} -3.99182 q^{97} +(-5.54325 + 8.07794i) q^{98} -17.8644i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q+6q42q624q9+12q14+18q166q24+20q26+48q316q3440q36+8q39+44q41+8q4430q46+12q492q54+50q56+72q64++12q96+O(q100) 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64}+ \cdots + 12 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1000Z)×\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times.

nn 377377 501501 751751
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 0.800179 1.16607i 0.565812 0.824534i
33 2.62662i 1.51648i 0.651976 + 0.758240i 0.273940π0.273940\pi
−0.651976 + 0.758240i 0.726060π0.726060\pi
44 −0.719426 1.86613i −0.359713 0.933063i
55 0 0
66 3.06282 + 2.10177i 1.25039 + 0.858043i
77 0.269237 0.101762 0.0508810 0.998705i 0.483797π-0.483797\pi
0.0508810 + 0.998705i 0.483797π0.483797\pi
88 −2.75170 0.654336i −0.972872 0.231343i
99 −3.89913 −1.29971
1010 0 0
1111 4.58163i 1.38141i 0.723135 + 0.690706i 0.242700π0.242700\pi
−0.723135 + 0.690706i 0.757300π0.757300\pi
1212 4.90160 1.88966i 1.41497 0.545497i
1313 1.55366i 0.430908i −0.976514 0.215454i 0.930877π-0.930877\pi
0.976514 0.215454i 0.0691231π-0.0691231\pi
1414 0.215438 0.313948i 0.0575782 0.0839062i
1515 0 0
1616 −2.96485 + 2.68508i −0.741213 + 0.671270i
1717 0.609109 0.147731 0.0738653 0.997268i 0.476467π-0.476467\pi
0.0738653 + 0.997268i 0.476467π0.476467\pi
1818 −3.12001 + 4.54665i −0.735392 + 1.07166i
1919 6.69309i 1.53550i 0.640749 + 0.767750i 0.278624π0.278624\pi
−0.640749 + 0.767750i 0.721376π0.721376\pi
2020 0 0
2121 0.707183i 0.154320i
2222 5.34249 + 3.66612i 1.13902 + 0.781620i
2323 3.52675 0.735378 0.367689 0.929949i 0.380149π-0.380149\pi
0.367689 + 0.929949i 0.380149π0.380149\pi
2424 1.71869 7.22767i 0.350827 1.47534i
2525 0 0
2626 −1.81167 1.24321i −0.355298 0.243813i
2727 2.36168i 0.454506i
2828 −0.193696 0.502430i −0.0366051 0.0949503i
2929 7.73304i 1.43599i 0.696048 + 0.717995i 0.254940π0.254940\pi
−0.696048 + 0.717995i 0.745060π0.745060\pi
3030 0 0
3131 −3.34096 −0.600054 −0.300027 0.953931i 0.596996π-0.596996\pi
−0.300027 + 0.953931i 0.596996π0.596996\pi
3232 0.758569 + 5.60576i 0.134097 + 0.990968i
3333 −12.0342 −2.09488
3434 0.487396 0.710262i 0.0835878 0.121809i
3535 0 0
3636 2.80514 + 7.27627i 0.467523 + 1.21271i
3737 5.32768i 0.875865i −0.899008 0.437933i 0.855711π-0.855711\pi
0.899008 0.437933i 0.144289π-0.144289\pi
3838 7.80459 + 5.35567i 1.26607 + 0.868805i
3939 4.08087 0.653463
4040 0 0
4141 4.38291 0.684496 0.342248 0.939610i 0.388812π-0.388812\pi
0.342248 + 0.939610i 0.388812π0.388812\pi
4242 0.824623 + 0.565873i 0.127242 + 0.0873161i
4343 12.2644i 1.87031i 0.354238 + 0.935155i 0.384740π0.384740\pi
−0.354238 + 0.935155i 0.615260π0.615260\pi
4444 8.54989 3.29614i 1.28894 0.496912i
4545 0 0
4646 2.82203 4.11243i 0.416086 0.606345i
4747 −9.54651 −1.39250 −0.696251 0.717798i 0.745150π-0.745150\pi
−0.696251 + 0.717798i 0.745150π0.745150\pi
4848 −7.05268 7.78754i −1.01797 1.12403i
4949 −6.92751 −0.989645
5050 0 0
5151 1.59990i 0.224030i
5252 −2.89932 + 1.11774i −0.402064 + 0.155003i
5353 10.6574i 1.46391i −0.681353 0.731955i 0.738608π-0.738608\pi
0.681353 0.731955i 0.261392π-0.261392\pi
5454 −2.75388 1.88977i −0.374755 0.257165i
5555 0 0
5656 −0.740859 0.176171i −0.0990014 0.0235419i
5757 −17.5802 −2.32855
5858 9.01725 + 6.18782i 1.18402 + 0.812501i
5959 10.2256i 1.33126i −0.746283 0.665629i 0.768163π-0.768163\pi
0.746283 0.665629i 0.231837π-0.231837\pi
6060 0 0
6161 13.2628i 1.69812i 0.528294 + 0.849062i 0.322832π0.322832\pi
−0.528294 + 0.849062i 0.677168π0.677168\pi
6262 −2.67337 + 3.89579i −0.339518 + 0.494765i
6363 −1.04979 −0.132261
6464 7.14369 + 3.60107i 0.892961 + 0.450134i
6565 0 0
6666 −9.62951 + 14.0327i −1.18531 + 1.72730i
6767 3.93398i 0.480613i −0.970697 0.240306i 0.922752π-0.922752\pi
0.970697 0.240306i 0.0772479π-0.0772479\pi
6868 −0.438209 1.13667i −0.0531406 0.137842i
6969 9.26343i 1.11519i
7070 0 0
7171 6.95638 0.825571 0.412785 0.910828i 0.364556π-0.364556\pi
0.412785 + 0.910828i 0.364556π0.364556\pi
7272 10.7292 + 2.55134i 1.26445 + 0.300679i
7373 5.93156 0.694236 0.347118 0.937821i 0.387160π-0.387160\pi
0.347118 + 0.937821i 0.387160π0.387160\pi
7474 −6.21243 4.26310i −0.722181 0.495575i
7575 0 0
7676 12.4901 4.81518i 1.43272 0.552339i
7777 1.23354i 0.140575i
7878 3.26543 4.75857i 0.369737 0.538802i
7979 10.1382 1.14064 0.570321 0.821422i 0.306819π-0.306819\pi
0.570321 + 0.821422i 0.306819π0.306819\pi
8080 0 0
8181 −5.49416 −0.610462
8282 3.50712 5.11077i 0.387296 0.564390i
8383 6.52313i 0.716007i −0.933720 0.358003i 0.883458π-0.883458\pi
0.933720 0.358003i 0.116542π-0.116542\pi
8484 1.31969 0.508766i 0.143990 0.0555109i
8585 0 0
8686 14.3012 + 9.81376i 1.54213 + 1.05824i
8787 −20.3118 −2.17765
8888 2.99793 12.6073i 0.319580 1.34394i
8989 6.69564 0.709736 0.354868 0.934916i 0.384526π-0.384526\pi
0.354868 + 0.934916i 0.384526π0.384526\pi
9090 0 0
9191 0.418302i 0.0438500i
9292 −2.53724 6.58136i −0.264525 0.686154i
9393 8.77544i 0.909970i
9494 −7.63892 + 11.1319i −0.787895 + 1.14817i
9595 0 0
9696 −14.7242 + 1.99247i −1.50278 + 0.203356i
9797 −3.99182 −0.405307 −0.202654 0.979250i 0.564957π-0.564957\pi
−0.202654 + 0.979250i 0.564957π0.564957\pi
9898 −5.54325 + 8.07794i −0.559953 + 0.815996i
9999 17.8644i 1.79544i
100100 0 0
101101 0.361133i 0.0359340i 0.999839 + 0.0179670i 0.00571939π0.00571939\pi
−0.999839 + 0.0179670i 0.994281π0.994281\pi
102102 1.86559 + 1.28020i 0.184721 + 0.126759i
103103 19.0514 1.87719 0.938596 0.345019i 0.112128π-0.112128\pi
0.938596 + 0.345019i 0.112128π0.112128\pi
104104 −1.01662 + 4.27520i −0.0996874 + 0.419218i
105105 0 0
106106 −12.4273 8.52785i −1.20704 0.828298i
107107 7.68019i 0.742472i 0.928539 + 0.371236i 0.121066π0.121066\pi
−0.928539 + 0.371236i 0.878934π0.878934\pi
108108 −4.40719 + 1.69905i −0.424082 + 0.163492i
109109 1.81184i 0.173543i 0.996228 + 0.0867716i 0.0276550π0.0276550\pi
−0.996228 + 0.0867716i 0.972345π0.972345\pi
110110 0 0
111111 13.9938 1.32823
112112 −0.798248 + 0.722922i −0.0754273 + 0.0683097i
113113 1.11278 0.104681 0.0523406 0.998629i 0.483332π-0.483332\pi
0.0523406 + 0.998629i 0.483332π0.483332\pi
114114 −14.0673 + 20.4997i −1.31752 + 1.91997i
115115 0 0
116116 14.4308 5.56335i 1.33987 0.516544i
117117 6.05792i 0.560055i
118118 −11.9237 8.18230i −1.09767 0.753242i
119119 0.163994 0.0150333
120120 0 0
121121 −9.99130 −0.908300
122122 15.4653 + 10.6126i 1.40016 + 0.960819i
123123 11.5122i 1.03802i
124124 2.40357 + 6.23465i 0.215847 + 0.559889i
125125 0 0
126126 −0.840020 + 1.22413i −0.0748350 + 0.109054i
127127 9.81903 0.871298 0.435649 0.900117i 0.356519π-0.356519\pi
0.435649 + 0.900117i 0.356519π0.356519\pi
128128 9.91533 5.44852i 0.876399 0.481585i
129129 −32.2140 −2.83629
130130 0 0
131131 5.00551i 0.437333i 0.975800 + 0.218667i 0.0701708π0.0701708\pi
−0.975800 + 0.218667i 0.929829π0.929829\pi
132132 8.65771 + 22.4573i 0.753557 + 1.95466i
133133 1.80203i 0.156255i
134134 −4.58729 3.14789i −0.396281 0.271936i
135135 0 0
136136 −1.67608 0.398562i −0.143723 0.0341764i
137137 −12.1561 −1.03856 −0.519282 0.854603i 0.673800π-0.673800\pi
−0.519282 + 0.854603i 0.673800π0.673800\pi
138138 10.8018 + 7.41241i 0.919509 + 0.630986i
139139 7.81838i 0.663147i −0.943429 0.331573i 0.892421π-0.892421\pi
0.943429 0.331573i 0.107579π-0.107579\pi
140140 0 0
141141 25.0751i 2.11170i
142142 5.56636 8.11161i 0.467118 0.680711i
143143 7.11829 0.595261
144144 11.5604 10.4695i 0.963363 0.872457i
145145 0 0
146146 4.74631 6.91659i 0.392807 0.572421i
147147 18.1959i 1.50078i
148148 −9.94212 + 3.83287i −0.817237 + 0.315060i
149149 17.0047i 1.39308i −0.717520 0.696538i 0.754723π-0.754723\pi
0.717520 0.696538i 0.245277π-0.245277\pi
150150 0 0
151151 −13.2804 −1.08075 −0.540373 0.841425i 0.681717π-0.681717\pi
−0.540373 + 0.841425i 0.681717π0.681717\pi
152152 4.37953 18.4174i 0.355227 1.49385i
153153 −2.37500 −0.192007
154154 1.43839 + 0.987055i 0.115909 + 0.0795392i
155155 0 0
156156 −2.93589 7.61542i −0.235059 0.609722i
157157 19.0554i 1.52078i −0.649465 0.760391i 0.725007π-0.725007\pi
0.649465 0.760391i 0.274993π-0.274993\pi
158158 8.11241 11.8219i 0.645389 0.940498i
159159 27.9930 2.21999
160160 0 0
161161 0.949531 0.0748335
162162 −4.39632 + 6.40656i −0.345407 + 0.503347i
163163 16.7152i 1.30923i −0.755961 0.654617i 0.772830π-0.772830\pi
0.755961 0.654617i 0.227170π-0.227170\pi
164164 −3.15318 8.17907i −0.246222 0.638678i
165165 0 0
166166 −7.60641 5.21968i −0.590372 0.405125i
167167 12.2045 0.944409 0.472204 0.881489i 0.343458π-0.343458\pi
0.472204 + 0.881489i 0.343458π0.343458\pi
168168 0.462736 1.94595i 0.0357008 0.150134i
169169 10.5861 0.814319
170170 0 0
171171 26.0972i 1.99571i
172172 22.8870 8.82336i 1.74512 0.672775i
173173 2.55690i 0.194397i 0.995265 + 0.0971986i 0.0309882π0.0309882\pi
−0.995265 + 0.0971986i 0.969012π0.969012\pi
174174 −16.2531 + 23.6849i −1.23214 + 1.79555i
175175 0 0
176176 −12.3020 13.5838i −0.927300 1.02392i
177177 26.8587 2.01883
178178 5.35771 7.80756i 0.401577 0.585202i
179179 18.3566i 1.37204i −0.727584 0.686019i 0.759357π-0.759357\pi
0.727584 0.686019i 0.240643π-0.240643\pi
180180 0 0
181181 8.74009i 0.649646i 0.945775 + 0.324823i 0.105305π0.105305\pi
−0.945775 + 0.324823i 0.894695π0.894695\pi
182182 −0.487769 0.334717i −0.0361558 0.0248109i
183183 −34.8362 −2.57517
184184 −9.70455 2.30768i −0.715429 0.170125i
185185 0 0
186186 −10.2327 7.02192i −0.750302 0.514872i
187187 2.79071i 0.204077i
188188 6.86801 + 17.8150i 0.500901 + 1.29929i
189189 0.635851i 0.0462514i
190190 0 0
191191 −21.5766 −1.56123 −0.780614 0.625013i 0.785094π-0.785094\pi
−0.780614 + 0.625013i 0.785094π0.785094\pi
192192 −9.45865 + 18.7638i −0.682619 + 1.35416i
193193 9.90462 0.712950 0.356475 0.934305i 0.383978π-0.383978\pi
0.356475 + 0.934305i 0.383978π0.383978\pi
194194 −3.19417 + 4.65473i −0.229328 + 0.334190i
195195 0 0
196196 4.98383 + 12.9276i 0.355988 + 0.923401i
197197 9.37856i 0.668195i −0.942539 0.334097i 0.891569π-0.891569\pi
0.942539 0.334097i 0.108431π-0.108431\pi
198198 −20.8311 14.2947i −1.48040 1.01588i
199199 16.8855 1.19698 0.598491 0.801130i 0.295767π-0.295767\pi
0.598491 + 0.801130i 0.295767π0.295767\pi
200200 0 0
201201 10.3331 0.728839
202202 0.421105 + 0.288971i 0.0296288 + 0.0203319i
203203 2.08202i 0.146129i
204204 2.98561 1.15101i 0.209034 0.0805866i
205205 0 0
206206 15.2445 22.2152i 1.06214 1.54781i
207207 −13.7513 −0.955779
208208 4.17170 + 4.60637i 0.289255 + 0.319394i
209209 −30.6652 −2.12116
210210 0 0
211211 14.0265i 0.965623i −0.875724 0.482811i 0.839616π-0.839616\pi
0.875724 0.482811i 0.160384π-0.160384\pi
212212 −19.8881 + 7.66723i −1.36592 + 0.526587i
213213 18.2718i 1.25196i
214214 8.95561 + 6.14553i 0.612193 + 0.420100i
215215 0 0
216216 −1.54533 + 6.49863i −0.105147 + 0.442176i
217217 −0.899510 −0.0610627
218218 2.11273 + 1.44980i 0.143092 + 0.0981928i
219219 15.5799i 1.05280i
220220 0 0
221221 0.946347i 0.0636582i
222222 11.1975 16.3177i 0.751530 1.09517i
223223 −2.06137 −0.138039 −0.0690197 0.997615i 0.521987π-0.521987\pi
−0.0690197 + 0.997615i 0.521987π0.521987\pi
224224 0.204235 + 1.50928i 0.0136460 + 0.100843i
225225 0 0
226226 0.890421 1.29757i 0.0592299 0.0863133i
227227 3.13275i 0.207928i −0.994581 0.103964i 0.966847π-0.966847\pi
0.994581 0.103964i 0.0331526π-0.0331526\pi
228228 12.6477 + 32.8069i 0.837611 + 2.17269i
229229 17.0738i 1.12827i 0.825682 + 0.564136i 0.190791π0.190791\pi
−0.825682 + 0.564136i 0.809209π0.809209\pi
230230 0 0
231231 −3.24005 −0.213179
232232 5.06001 21.2790i 0.332206 1.39704i
233233 −7.63474 −0.500169 −0.250084 0.968224i 0.580458π-0.580458\pi
−0.250084 + 0.968224i 0.580458π0.580458\pi
234234 7.06395 + 4.84743i 0.461785 + 0.316886i
235235 0 0
236236 −19.0822 + 7.35655i −1.24215 + 0.478871i
237237 26.6293i 1.72976i
238238 0.131225 0.191229i 0.00850605 0.0123955i
239239 4.92104 0.318315 0.159158 0.987253i 0.449122π-0.449122\pi
0.159158 + 0.987253i 0.449122π0.449122\pi
240240 0 0
241241 19.1214 1.23172 0.615860 0.787855i 0.288809π-0.288809\pi
0.615860 + 0.787855i 0.288809π0.288809\pi
242242 −7.99484 + 11.6505i −0.513927 + 0.748925i
243243 21.5161i 1.38026i
244244 24.7500 9.54158i 1.58446 0.610837i
245245 0 0
246246 13.4241 + 9.21186i 0.855887 + 0.587327i
247247 10.3988 0.661659
248248 9.19332 + 2.18611i 0.583776 + 0.138818i
249249 17.1338 1.08581
250250 0 0
251251 29.7004i 1.87467i 0.348423 + 0.937337i 0.386717π0.386717\pi
−0.348423 + 0.937337i 0.613283π0.613283\pi
252252 0.755246 + 1.95904i 0.0475760 + 0.123408i
253253 16.1583i 1.01586i
254254 7.85699 11.4497i 0.492991 0.718415i
255255 0 0
256256 1.58070 15.9217i 0.0987939 0.995108i
257257 −13.1697 −0.821501 −0.410750 0.911748i 0.634733π-0.634733\pi
−0.410750 + 0.911748i 0.634733π0.634733\pi
258258 −25.7770 + 37.5637i −1.60481 + 2.33862i
259259 1.43441i 0.0891297i
260260 0 0
261261 30.1522i 1.86637i
262262 5.83676 + 4.00531i 0.360596 + 0.247449i
263263 −17.7204 −1.09269 −0.546345 0.837560i 0.683981π-0.683981\pi
−0.546345 + 0.837560i 0.683981π0.683981\pi
264264 33.1145 + 7.87441i 2.03805 + 0.484636i
265265 0 0
266266 2.10128 + 1.44194i 0.128838 + 0.0884113i
267267 17.5869i 1.07630i
268268 −7.34131 + 2.83021i −0.448442 + 0.172883i
269269 1.52445i 0.0929474i −0.998920 0.0464737i 0.985202π-0.985202\pi
0.998920 0.0464737i 0.0147984π-0.0147984\pi
270270 0 0
271271 16.1497 0.981024 0.490512 0.871435i 0.336810π-0.336810\pi
0.490512 + 0.871435i 0.336810π0.336810\pi
272272 −1.80592 + 1.63550i −0.109500 + 0.0991670i
273273 1.09872 0.0664976
274274 −9.72704 + 14.1748i −0.587632 + 0.856331i
275275 0 0
276276 17.2867 6.66436i 1.04054 0.401147i
277277 12.3707i 0.743283i 0.928376 + 0.371642i 0.121205π0.121205\pi
−0.928376 + 0.371642i 0.878795π0.878795\pi
278278 −9.11676 6.25611i −0.546787 0.375217i
279279 13.0269 0.779897
280280 0 0
281281 −4.03820 −0.240899 −0.120450 0.992719i 0.538434π-0.538434\pi
−0.120450 + 0.992719i 0.538434π0.538434\pi
282282 −29.2392 20.0645i −1.74117 1.19483i
283283 4.13989i 0.246091i −0.992401 0.123046i 0.960734π-0.960734\pi
0.992401 0.123046i 0.0392661π-0.0392661\pi
284284 −5.00460 12.9815i −0.296969 0.770310i
285285 0 0
286286 5.69591 8.30040i 0.336806 0.490813i
287287 1.18004 0.0696557
288288 −2.95776 21.8576i −0.174288 1.28797i
289289 −16.6290 −0.978176
290290 0 0
291291 10.4850i 0.614641i
292292 −4.26732 11.0690i −0.249726 0.647766i
293293 25.2638i 1.47593i 0.674840 + 0.737964i 0.264213π0.264213\pi
−0.674840 + 0.737964i 0.735787π0.735787\pi
294294 −21.2177 14.5600i −1.23744 0.849157i
295295 0 0
296296 −3.48609 + 14.6602i −0.202625 + 0.852105i
297297 10.8203 0.627860
298298 −19.8286 13.6068i −1.14864 0.788219i
299299 5.47937i 0.316880i
300300 0 0
301301 3.30204i 0.190326i
302302 −10.6267 + 15.4859i −0.611500 + 0.891112i
303303 −0.948558 −0.0544933
304304 −17.9715 19.8440i −1.03073 1.13813i
305305 0 0
306306 −1.90042 + 2.76940i −0.108640 + 0.158316i
307307 10.6692i 0.608922i 0.952525 + 0.304461i 0.0984764π0.0984764\pi
−0.952525 + 0.304461i 0.901524π0.901524\pi
308308 2.30195 0.887443i 0.131166 0.0505667i
309309 50.0408i 2.84672i
310310 0 0
311311 1.78111 0.100998 0.0504988 0.998724i 0.483919π-0.483919\pi
0.0504988 + 0.998724i 0.483919π0.483919\pi
312312 −11.2293 2.67026i −0.635736 0.151174i
313313 26.6250 1.50494 0.752468 0.658629i 0.228863π-0.228863\pi
0.752468 + 0.658629i 0.228863π0.228863\pi
314314 −22.2198 15.2477i −1.25394 0.860478i
315315 0 0
316316 −7.29371 18.9192i −0.410303 1.06429i
317317 9.16369i 0.514684i −0.966320 0.257342i 0.917153π-0.917153\pi
0.966320 0.257342i 0.0828467π-0.0828467\pi
318318 22.3994 32.6417i 1.25610 1.83046i
319319 −35.4299 −1.98369
320320 0 0
321321 −20.1729 −1.12594
322322 0.759795 1.10722i 0.0423417 0.0617028i
323323 4.07682i 0.226840i
324324 3.95264 + 10.2528i 0.219591 + 0.569600i
325325 0 0
326326 −19.4910 13.3751i −1.07951 0.740781i
327327 −4.75903 −0.263175
328328 −12.0605 2.86790i −0.665927 0.158353i
329329 −2.57027 −0.141704
330330 0 0
331331 7.83419i 0.430606i 0.976547 + 0.215303i 0.0690739π0.0690739\pi
−0.976547 + 0.215303i 0.930926π0.930926\pi
332332 −12.1730 + 4.69291i −0.668079 + 0.257557i
333333 20.7733i 1.13837i
334334 9.76575 14.2312i 0.534358 0.778697i
335335 0 0
336336 −1.89884 2.09669i −0.103590 0.114384i
337337 −0.636306 −0.0346618 −0.0173309 0.999850i 0.505517π-0.505517\pi
−0.0173309 + 0.999850i 0.505517π0.505517\pi
338338 8.47081 12.3442i 0.460752 0.671434i
339339 2.92284i 0.158747i
340340 0 0
341341 15.3070i 0.828923i
342342 −30.4311 20.8825i −1.64553 1.12920i
343343 −3.74980 −0.202470
344344 8.02508 33.7481i 0.432683 1.81957i
345345 0 0
346346 2.98151 + 2.04598i 0.160287 + 0.109992i
347347 23.5999i 1.26691i 0.773780 + 0.633455i 0.218364π0.218364\pi
−0.773780 + 0.633455i 0.781636π0.781636\pi
348348 14.6128 + 37.9043i 0.783329 + 2.03188i
349349 19.1542i 1.02530i 0.858597 + 0.512651i 0.171336π0.171336\pi
−0.858597 + 0.512651i 0.828664π0.828664\pi
350350 0 0
351351 −3.66925 −0.195850
352352 −25.6835 + 3.47548i −1.36894 + 0.185244i
353353 21.9765 1.16969 0.584845 0.811145i 0.301155π-0.301155\pi
0.584845 + 0.811145i 0.301155π0.301155\pi
354354 21.4918 31.3191i 1.14228 1.66459i
355355 0 0
356356 −4.81702 12.4949i −0.255301 0.662229i
357357 0.430751i 0.0227978i
358358 −21.4050 14.6886i −1.13129 0.776316i
359359 −5.63031 −0.297156 −0.148578 0.988901i 0.547470π-0.547470\pi
−0.148578 + 0.988901i 0.547470π0.547470\pi
360360 0 0
361361 −25.7974 −1.35776
362362 10.1915 + 6.99364i 0.535655 + 0.367578i
363363 26.2434i 1.37742i
364364 −0.780605 + 0.300938i −0.0409148 + 0.0157734i
365365 0 0
366366 −27.8752 + 40.6214i −1.45706 + 2.12332i
367367 5.21463 0.272201 0.136101 0.990695i 0.456543π-0.456543\pi
0.136101 + 0.990695i 0.456543π0.456543\pi
368368 −10.4563 + 9.46960i −0.545072 + 0.493637i
369369 −17.0896 −0.889647
370370 0 0
371371 2.86937i 0.148970i
372372 −16.3761 + 6.31328i −0.849060 + 0.327328i
373373 12.6000i 0.652405i −0.945300 0.326202i 0.894231π-0.894231\pi
0.945300 0.326202i 0.105769π-0.105769\pi
374374 3.25415 + 2.23307i 0.168268 + 0.115469i
375375 0 0
376376 26.2691 + 6.24663i 1.35473 + 0.322145i
377377 12.0145 0.618779
378378 −0.741445 0.508795i −0.0381358 0.0261696i
379379 1.28403i 0.0659562i 0.999456 + 0.0329781i 0.0104992π0.0104992\pi
−0.999456 + 0.0329781i 0.989501π0.989501\pi
380380 0 0
381381 25.7909i 1.32131i
382382 −17.2652 + 25.1598i −0.883362 + 1.28729i
383383 −18.3642 −0.938369 −0.469185 0.883100i 0.655452π-0.655452\pi
−0.469185 + 0.883100i 0.655452π0.655452\pi
384384 14.3112 + 26.0438i 0.730314 + 1.32904i
385385 0 0
386386 7.92547 11.5495i 0.403396 0.587852i
387387 47.8207i 2.43086i
388388 2.87182 + 7.44923i 0.145794 + 0.378177i
389389 20.5311i 1.04097i −0.853871 0.520485i 0.825751π-0.825751\pi
0.853871 0.520485i 0.174249π-0.174249\pi
390390 0 0
391391 2.14817 0.108638
392392 19.0624 + 4.53292i 0.962798 + 0.228947i
393393 −13.1476 −0.663207
394394 −10.9360 7.50453i −0.550949 0.378073i
395395 0 0
396396 −33.3372 + 12.8521i −1.67526 + 0.645842i
397397 17.0191i 0.854164i −0.904213 0.427082i 0.859542π-0.859542\pi
0.904213 0.427082i 0.140458π-0.140458\pi
398398 13.5114 19.6896i 0.677267 0.986952i
399399 −4.73324 −0.236958
400400 0 0
401401 7.62575 0.380812 0.190406 0.981705i 0.439020π-0.439020\pi
0.190406 + 0.981705i 0.439020π0.439020\pi
402402 8.26832 12.0491i 0.412386 0.600953i
403403 5.19072i 0.258568i
404404 0.673919 0.259808i 0.0335287 0.0129259i
405405 0 0
406406 2.42778 + 1.66599i 0.120488 + 0.0826817i
407407 24.4094 1.20993
408408 1.04687 4.40243i 0.0518278 0.217953i
409409 7.37530 0.364685 0.182342 0.983235i 0.441632π-0.441632\pi
0.182342 + 0.983235i 0.441632π0.441632\pi
410410 0 0
411411 31.9294i 1.57496i
412412 −13.7061 35.5523i −0.675250 1.75154i
413413 2.75310i 0.135471i
414414 −11.0035 + 16.0349i −0.540792 + 0.788073i
415415 0 0
416416 8.70944 1.17856i 0.427016 0.0577835i
417417 20.5359 1.00565
418418 −24.5377 + 35.7577i −1.20018 + 1.74897i
419419 22.0835i 1.07885i 0.842034 + 0.539425i 0.181358π0.181358\pi
−0.842034 + 0.539425i 0.818642π0.818642\pi
420420 0 0
421421 29.2485i 1.42549i 0.701425 + 0.712743i 0.252547π0.252547\pi
−0.701425 + 0.712743i 0.747453π0.747453\pi
422422 −16.3558 11.2237i −0.796189 0.546361i
423423 37.2231 1.80985
424424 −6.97354 + 29.3260i −0.338665 + 1.42420i
425425 0 0
426426 21.3061 + 14.6207i 1.03229 + 0.708375i
427427 3.57083i 0.172804i
428428 14.3322 5.52532i 0.692773 0.267077i
429429 18.6970i 0.902701i
430430 0 0
431431 −6.99018 −0.336705 −0.168353 0.985727i 0.553845π-0.553845\pi
−0.168353 + 0.985727i 0.553845π0.553845\pi
432432 6.34130 + 7.00203i 0.305096 + 0.336885i
433433 19.1288 0.919271 0.459636 0.888108i 0.347980π-0.347980\pi
0.459636 + 0.888108i 0.347980π0.347980\pi
434434 −0.719769 + 1.04889i −0.0345500 + 0.0503483i
435435 0 0
436436 3.38113 1.30349i 0.161927 0.0624257i
437437 23.6049i 1.12917i
438438 18.1673 + 12.4667i 0.868065 + 0.595684i
439439 −2.78856 −0.133091 −0.0665453 0.997783i 0.521198π-0.521198\pi
−0.0665453 + 0.997783i 0.521198π0.521198\pi
440440 0 0
441441 27.0113 1.28625
442442 −1.10350 0.757248i −0.0524884 0.0360186i
443443 16.8836i 0.802164i −0.916042 0.401082i 0.868634π-0.868634\pi
0.916042 0.401082i 0.131366π-0.131366\pi
444444 −10.0675 26.1142i −0.477782 1.23932i
445445 0 0
446446 −1.64946 + 2.40369i −0.0781043 + 0.113818i
447447 44.6648 2.11257
448448 1.92334 + 0.969542i 0.0908695 + 0.0458065i
449449 −13.1404 −0.620135 −0.310068 0.950714i 0.600352π-0.600352\pi
−0.310068 + 0.950714i 0.600352π0.600352\pi
450450 0 0
451451 20.0809i 0.945571i
452452 −0.800561 2.07658i −0.0376552 0.0976742i
453453 34.8827i 1.63893i
454454 −3.65299 2.50676i −0.171443 0.117648i
455455 0 0
456456 48.3754 + 11.5034i 2.26539 + 0.538695i
457457 33.4760 1.56594 0.782971 0.622058i 0.213703π-0.213703\pi
0.782971 + 0.622058i 0.213703π0.213703\pi
458458 19.9093 + 13.6621i 0.930298 + 0.638390i
459459 1.43852i 0.0671444i
460460 0 0
461461 27.6037i 1.28563i 0.766021 + 0.642816i 0.222234π0.222234\pi
−0.766021 + 0.642816i 0.777766π0.777766\pi
462462 −2.59262 + 3.77811i −0.120620 + 0.175774i
463463 14.9227 0.693517 0.346758 0.937955i 0.387282π-0.387282\pi
0.346758 + 0.937955i 0.387282π0.387282\pi
464464 −20.7638 22.9273i −0.963937 1.06437i
465465 0 0
466466 −6.10916 + 8.90262i −0.283002 + 0.412406i
467467 11.8685i 0.549210i 0.961557 + 0.274605i 0.0885472π0.0885472\pi
−0.961557 + 0.274605i 0.911453π0.911453\pi
468468 11.3048 4.35823i 0.522567 0.201459i
469469 1.05917i 0.0489081i
470470 0 0
471471 50.0512 2.30624
472472 −6.69097 + 28.1377i −0.307977 + 1.29514i
473473 −56.1911 −2.58367
474474 31.0516 + 21.3082i 1.42625 + 0.978719i
475475 0 0
476476 −0.117982 0.306034i −0.00540769 0.0140271i
477477 41.5547i 1.90266i
478478 3.93771 5.73826i 0.180107 0.262462i
479479 15.4425 0.705586 0.352793 0.935701i 0.385232π-0.385232\pi
0.352793 + 0.935701i 0.385232π0.385232\pi
480480 0 0
481481 −8.27740 −0.377417
482482 15.3006 22.2969i 0.696923 1.01560i
483483 2.49406i 0.113484i
484484 7.18800 + 18.6450i 0.326727 + 0.847501i
485485 0 0
486486 −25.0892 17.2168i −1.13807 0.780968i
487487 7.58171 0.343560 0.171780 0.985135i 0.445048π-0.445048\pi
0.171780 + 0.985135i 0.445048π0.445048\pi
488488 8.67831 36.4951i 0.392849 1.65206i
489489 43.9044 1.98543
490490 0 0
491491 5.55509i 0.250698i 0.992113 + 0.125349i 0.0400050π0.0400050\pi
−0.992113 + 0.125349i 0.959995π0.959995\pi
492492 21.4833 8.28221i 0.968542 0.373391i
493493 4.71026i 0.212140i
494494 8.32089 12.1257i 0.374375 0.545560i
495495 0 0
496496 9.90546 8.97074i 0.444768 0.402798i
497497 1.87291 0.0840117
498498 13.7101 19.9792i 0.614364 0.895287i
499499 14.1201i 0.632102i 0.948742 + 0.316051i 0.102357π0.102357\pi
−0.948742 + 0.316051i 0.897643π0.897643\pi
500500 0 0
501501 32.0565i 1.43218i
502502 34.6327 + 23.7657i 1.54573 + 1.06071i
503503 −14.3503 −0.639847 −0.319924 0.947443i 0.603657π-0.603657\pi
−0.319924 + 0.947443i 0.603657π0.603657\pi
504504 2.88871 + 0.686916i 0.128673 + 0.0305977i
505505 0 0
506506 18.8416 + 12.9295i 0.837612 + 0.574787i
507507 27.8058i 1.23490i
508508 −7.06407 18.3236i −0.313417 0.812976i
509509 42.9057i 1.90176i −0.309557 0.950881i 0.600181π-0.600181\pi
0.309557 0.950881i 0.399819π-0.399819\pi
510510 0 0
511511 1.59699 0.0706468
512512 −17.3010 14.5834i −0.764602 0.644503i
513513 15.8069 0.697893
514514 −10.5381 + 15.3567i −0.464815 + 0.677356i
515515 0 0
516516 23.1756 + 60.1155i 1.02025 + 2.64644i
517517 43.7386i 1.92362i
518518 −1.67262 1.14778i −0.0734905 0.0504307i
519519 −6.71600 −0.294800
520520 0 0
521521 11.4542 0.501817 0.250909 0.968011i 0.419271π-0.419271\pi
0.250909 + 0.968011i 0.419271π0.419271\pi
522522 −35.1595 24.1271i −1.53889 1.05602i
523523 21.7522i 0.951156i 0.879674 + 0.475578i 0.157761π0.157761\pi
−0.879674 + 0.475578i 0.842239π0.842239\pi
524524 9.34091 3.60109i 0.408060 0.157315i
525525 0 0
526526 −14.1795 + 20.6632i −0.618257 + 0.900960i
527527 −2.03501 −0.0886464
528528 35.6796 32.3128i 1.55276 1.40623i
529529 −10.5620 −0.459219
530530 0 0
531531 39.8709i 1.73025i
532532 3.36281 1.29642i 0.145796 0.0562071i
533533 6.80955i 0.294955i
534534 20.5075 + 14.0727i 0.887446 + 0.608984i
535535 0 0
536536 −2.57415 + 10.8251i −0.111186 + 0.467575i
537537 48.2158 2.08067
538538 −1.77761 1.21983i −0.0766383 0.0525908i
539539 31.7393i 1.36711i
540540 0 0
541541 36.5960i 1.57339i −0.617344 0.786693i 0.711791π-0.711791\pi
0.617344 0.786693i 0.288209π-0.288209\pi
542542 12.9226 18.8316i 0.555075 0.808887i
543543 −22.9569 −0.985175
544544 0.462051 + 3.41452i 0.0198103 + 0.146396i
545545 0 0
546546 0.879174 1.28118i 0.0376252 0.0548296i
547547 15.8078i 0.675893i 0.941165 + 0.337946i 0.109732π0.109732\pi
−0.941165 + 0.337946i 0.890268π0.890268\pi
548548 8.74539 + 22.6848i 0.373585 + 0.969045i
549549 51.7133i 2.20707i
550550 0 0
551551 −51.7580 −2.20496
552552 6.06140 25.4902i 0.257990 1.08493i
553553 2.72959 0.116074
554554 14.4251 + 9.89878i 0.612863 + 0.420559i
555555 0 0
556556 −14.5901 + 5.62475i −0.618758 + 0.238542i
557557 12.7121i 0.538629i −0.963052 0.269315i 0.913203π-0.913203\pi
0.963052 0.269315i 0.0867971π-0.0867971\pi
558558 10.4238 15.1902i 0.441275 0.643052i
559559 19.0548 0.805931
560560 0 0
561561 −7.33013 −0.309478
562562 −3.23129 + 4.70882i −0.136304 + 0.198630i
563563 14.3700i 0.605624i 0.953050 + 0.302812i 0.0979255π0.0979255\pi
−0.953050 + 0.302812i 0.902075π0.902075\pi
564564 −46.7932 + 18.0396i −1.97035 + 0.759606i
565565 0 0
566566 −4.82740 3.31266i −0.202911 0.139241i
567567 −1.47923 −0.0621219
568568 −19.1419 4.55182i −0.803175 0.190990i
569569 32.5495 1.36455 0.682274 0.731097i 0.260991π-0.260991\pi
0.682274 + 0.731097i 0.260991π0.260991\pi
570570 0 0
571571 16.2274i 0.679097i 0.940589 + 0.339548i 0.110274π0.110274\pi
−0.940589 + 0.339548i 0.889726π0.889726\pi
572572 −5.12108 13.2836i −0.214123 0.555416i
573573 56.6736i 2.36757i
574574 0.944245 1.37601i 0.0394120 0.0574335i
575575 0 0
576576 −27.8542 14.0411i −1.16059 0.585044i
577577 −30.1137 −1.25365 −0.626825 0.779160i 0.715646π-0.715646\pi
−0.626825 + 0.779160i 0.715646π0.715646\pi
578578 −13.3062 + 19.3905i −0.553464 + 0.806539i
579579 26.0157i 1.08117i
580580 0 0
581581 1.75627i 0.0728622i
582582 −12.2262 8.38987i −0.506792 0.347771i
583583 48.8283 2.02226
584584 −16.3219 3.88123i −0.675403 0.160607i
585585 0 0
586586 29.4593 + 20.2156i 1.21695 + 0.835098i
587587 14.1963i 0.585943i 0.956121 + 0.292971i 0.0946440π0.0946440\pi
−0.956121 + 0.292971i 0.905356π0.905356\pi
588588 −33.9559 + 13.0906i −1.40032 + 0.539849i
589589 22.3614i 0.921384i
590590 0 0
591591 24.6339 1.01330
592592 14.3052 + 15.7958i 0.587942 + 0.649203i
593593 −12.2025 −0.501098 −0.250549 0.968104i 0.580611π-0.580611\pi
−0.250549 + 0.968104i 0.580611π0.580611\pi
594594 8.65821 12.6172i 0.355251 0.517692i
595595 0 0
596596 −31.7328 + 12.2336i −1.29983 + 0.501107i
597597 44.3518i 1.81520i
598598 −6.38931 4.38448i −0.261278 0.179295i
599599 −2.44106 −0.0997391 −0.0498695 0.998756i 0.515881π-0.515881\pi
−0.0498695 + 0.998756i 0.515881π0.515881\pi
600600 0 0
601601 −13.7234 −0.559789 −0.279895 0.960031i 0.590300π-0.590300\pi
−0.279895 + 0.960031i 0.590300π0.590300\pi
602602 3.85040 + 2.64223i 0.156931 + 0.107689i
603603 15.3391i 0.624657i
604604 9.55429 + 24.7830i 0.388759 + 1.00840i
605605 0 0
606606 −0.759017 + 1.10608i −0.0308330 + 0.0449315i
607607 25.0502 1.01676 0.508378 0.861134i 0.330245π-0.330245\pi
0.508378 + 0.861134i 0.330245π0.330245\pi
608608 −37.5199 + 5.07717i −1.52163 + 0.205906i
609609 −5.46868 −0.221602
610610 0 0
611611 14.8320i 0.600040i
612612 1.70863 + 4.43204i 0.0690674 + 0.179155i
613613 26.4690i 1.06907i 0.845146 + 0.534536i 0.179514π0.179514\pi
−0.845146 + 0.534536i 0.820486π0.820486\pi
614614 12.4410 + 8.53726i 0.502077 + 0.344536i
615615 0 0
616616 0.807152 3.39434i 0.0325211 0.136762i
617617 −20.2771 −0.816324 −0.408162 0.912909i 0.633830π-0.633830\pi
−0.408162 + 0.912909i 0.633830π0.633830\pi
618618 58.3510 + 40.0416i 2.34722 + 1.61071i
619619 13.1584i 0.528880i 0.964402 + 0.264440i 0.0851871π0.0851871\pi
−0.964402 + 0.264440i 0.914813π0.914813\pi
620620 0 0
621621 8.32906i 0.334234i
622622 1.42521 2.07690i 0.0571457 0.0832760i
623623 1.80271 0.0722241
624624 −12.0992 + 10.9575i −0.484355 + 0.438650i
625625 0 0
626626 21.3048 31.0466i 0.851511 1.24087i
627627 80.5459i 3.21669i
628628 −35.5597 + 13.7089i −1.41899 + 0.547045i
629629 3.24514i 0.129392i
630630 0 0
631631 30.4366 1.21166 0.605830 0.795594i 0.292841π-0.292841\pi
0.605830 + 0.795594i 0.292841π0.292841\pi
632632 −27.8974 6.63382i −1.10970 0.263879i
633633 36.8422 1.46435
634634 −10.6855 7.33260i −0.424375 0.291215i
635635 0 0
636636 −20.1389 52.2385i −0.798559 2.07139i
637637 10.7630i 0.426445i
638638 −28.3503 + 41.3137i −1.12240 + 1.63562i
639639 −27.1239 −1.07300
640640 0 0
641641 22.4237 0.885683 0.442841 0.896600i 0.353971π-0.353971\pi
0.442841 + 0.896600i 0.353971π0.353971\pi
642642 −16.1420 + 23.5230i −0.637072 + 0.928379i
643643 36.0640i 1.42222i 0.703078 + 0.711112i 0.251808π0.251808\pi
−0.703078 + 0.711112i 0.748192π0.748192\pi
644644 −0.683117 1.77194i −0.0269186 0.0698244i
645645 0 0
646646 4.75385 + 3.26219i 0.187038 + 0.128349i
647647 2.35270 0.0924942 0.0462471 0.998930i 0.485274π-0.485274\pi
0.0462471 + 0.998930i 0.485274π0.485274\pi
648648 15.1183 + 3.59503i 0.593902 + 0.141226i
649649 46.8498 1.83902
650650 0 0
651651 2.36267i 0.0926004i
652652 −31.1926 + 12.0253i −1.22160 + 0.470949i
653653 13.9239i 0.544886i −0.962172 0.272443i 0.912168π-0.912168\pi
0.962172 0.272443i 0.0878317π-0.0878317\pi
654654 −3.80807 + 5.54934i −0.148907 + 0.216997i
655655 0 0
656656 −12.9947 + 11.7685i −0.507357 + 0.459481i
657657 −23.1279 −0.902306
658658 −2.05668 + 2.99711i −0.0801777 + 0.116840i
659659 20.8197i 0.811022i −0.914090 0.405511i 0.867094π-0.867094\pi
0.914090 0.405511i 0.132906π-0.132906\pi
660660 0 0
661661 9.83003i 0.382344i −0.981557 0.191172i 0.938771π-0.938771\pi
0.981557 0.191172i 0.0612288π-0.0612288\pi
662662 9.13519 + 6.26876i 0.355049 + 0.243642i
663663 2.48569 0.0965364
664664 −4.26832 + 17.9497i −0.165643 + 0.696583i
665665 0 0
666666 24.2231 + 16.6224i 0.938626 + 0.644105i
667667 27.2725i 1.05600i
668668 −8.78020 22.7750i −0.339716 0.881193i
669669 5.41443i 0.209334i
670670 0 0
671671 −60.7650 −2.34581
672672 −3.96430 + 0.536447i −0.152926 + 0.0206939i
673673 −45.7820 −1.76476 −0.882382 0.470533i 0.844062π-0.844062\pi
−0.882382 + 0.470533i 0.844062π0.844062\pi
674674 −0.509159 + 0.741975i −0.0196121 + 0.0285798i
675675 0 0
676676 −7.61595 19.7551i −0.292921 0.759811i
677677 49.9162i 1.91844i −0.282669 0.959218i 0.591220π-0.591220\pi
0.282669 0.959218i 0.408780π-0.408780\pi
678678 3.40823 + 2.33880i 0.130892 + 0.0898210i
679679 −1.07474 −0.0412449
680680 0 0
681681 8.22853 0.315318
682682 −17.8490 12.2484i −0.683475 0.469015i
683683 14.4414i 0.552584i −0.961074 0.276292i 0.910894π-0.910894\pi
0.961074 0.276292i 0.0891056π-0.0891056\pi
684684 −48.7007 + 18.7750i −1.86212 + 0.717881i
685685 0 0
686686 −3.00051 + 4.37252i −0.114560 + 0.166944i
687687 −44.8465 −1.71100
688688 −32.9310 36.3623i −1.25548 1.38630i
689689 −16.5580 −0.630810
690690 0 0
691691 20.6371i 0.785072i −0.919737 0.392536i 0.871598π-0.871598\pi
0.919737 0.392536i 0.128402π-0.128402\pi
692692 4.77149 1.83950i 0.181385 0.0699272i
693693 4.80975i 0.182707i
694694 27.5191 + 18.8842i 1.04461 + 0.716833i
695695 0 0
696696 55.8919 + 13.2907i 2.11858 + 0.503784i
697697 2.66967 0.101121
698698 22.3351 + 15.3268i 0.845396 + 0.580128i
699699 20.0536i 0.758496i
700700 0 0
701701 30.0040i 1.13323i −0.823981 0.566617i 0.808252π-0.808252\pi
0.823981 0.566617i 0.191748π-0.191748\pi
702702 −2.93605 + 4.27859i −0.110814 + 0.161485i
703703 35.6586 1.34489
704704 −16.4988 + 32.7297i −0.621821 + 1.23355i
705705 0 0
706706 17.5851 25.6261i 0.661825 0.964450i
707707 0.0972302i 0.00365672i
708708 −19.3229 50.1218i −0.726198 1.88369i
709709 8.10493i 0.304387i −0.988351 0.152194i 0.951366π-0.951366\pi
0.988351 0.152194i 0.0486337π-0.0486337\pi
710710 0 0
711711 −39.5303 −1.48250
712712 −18.4244 4.38120i −0.690483 0.164192i
713713 −11.7827 −0.441267
714714 0.502285 + 0.344678i 0.0187975 + 0.0128993i
715715 0 0
716716 −34.2557 + 13.2062i −1.28020 + 0.493540i
717717 12.9257i 0.482719i
718718 −4.50526 + 6.56532i −0.168135 + 0.245015i
719719 −38.0224 −1.41800 −0.708998 0.705210i 0.750852π-0.750852\pi
−0.708998 + 0.705210i 0.750852π0.750852\pi
720720 0 0
721721 5.12934 0.191027
722722 −20.6426 + 30.0816i −0.768237 + 1.11952i
723723 50.2248i 1.86788i
724724 16.3101 6.28785i 0.606161 0.233686i
725725 0 0
726726 −30.6015 20.9994i −1.13573 0.779361i
727727 −33.5323 −1.24364 −0.621821 0.783159i 0.713607π-0.713607\pi
−0.621821 + 0.783159i 0.713607π0.713607\pi
728728 −0.273710 + 1.15104i −0.0101444 + 0.0426604i
729729 40.0322 1.48267
730730 0 0
731731 7.47038i 0.276302i
732732 25.0621 + 65.0088i 0.926322 + 2.40280i
733733 8.77824i 0.324232i 0.986772 + 0.162116i 0.0518318π0.0518318\pi
−0.986772 + 0.162116i 0.948168π0.948168\pi
734734 4.17264 6.08061i 0.154015 0.224439i
735735 0 0
736736 2.67528 + 19.7701i 0.0986123 + 0.728737i
737737 18.0240 0.663924
738738 −13.6747 + 19.9276i −0.503373 + 0.733544i
739739 10.4760i 0.385365i −0.981261 0.192683i 0.938281π-0.938281\pi
0.981261 0.192683i 0.0617187π-0.0617187\pi
740740 0 0
741741 27.3136i 1.00339i
742742 −3.34588 2.29601i −0.122831 0.0842892i
743743 4.29242 0.157474 0.0787368 0.996895i 0.474911π-0.474911\pi
0.0787368 + 0.996895i 0.474911π0.474911\pi
744744 −5.74209 + 24.1474i −0.210515 + 0.885285i
745745 0 0
746746 −14.6925 10.0823i −0.537930 0.369139i
747747 25.4346i 0.930602i
748748 5.20781 2.00771i 0.190417 0.0734091i
749749 2.06779i 0.0755554i
750750 0 0
751751 54.2895 1.98105 0.990526 0.137324i 0.0438500π-0.0438500\pi
0.990526 + 0.137324i 0.0438500π0.0438500\pi
752752 28.3040 25.6331i 1.03214 0.934744i
753753 −78.0118 −2.84291
754754 9.61377 14.0097i 0.350113 0.510204i
755755 0 0
756756 −1.18658 + 0.457448i −0.0431554 + 0.0166372i
757757 15.6468i 0.568691i 0.958722 + 0.284345i 0.0917763π0.0917763\pi
−0.958722 + 0.284345i 0.908224π0.908224\pi
758758 1.49727 + 1.02745i 0.0543832 + 0.0373188i
759759 −42.4416 −1.54053
760760 0 0
761761 33.5439 1.21597 0.607983 0.793950i 0.291979π-0.291979\pi
0.607983 + 0.793950i 0.291979π0.291979\pi
762762 30.0739 + 20.6373i 1.08946 + 0.747611i
763763 0.487815i 0.0176601i
764764 15.5228 + 40.2647i 0.561594 + 1.45673i
765765 0 0
766766 −14.6947 + 21.4139i −0.530941 + 0.773717i
767767 −15.8871 −0.573649
768768 41.8203 + 4.15190i 1.50906 + 0.149819i
769769 −12.1137 −0.436832 −0.218416 0.975856i 0.570089π-0.570089\pi
−0.218416 + 0.975856i 0.570089π0.570089\pi
770770 0 0
771771 34.5917i 1.24579i
772772 −7.12564 18.4833i −0.256457 0.665227i
773773 29.0451i 1.04468i −0.852737 0.522340i 0.825059π-0.825059\pi
0.852737 0.522340i 0.174941π-0.174941\pi
774774 −55.7622 38.2651i −2.00433 1.37541i
775775 0 0
776776 10.9843 + 2.61199i 0.394312 + 0.0937650i
777777 3.76764 0.135163
778778 −23.9407 16.4286i −0.858315 0.588993i
779779 29.3352i 1.05104i
780780 0 0
781781 31.8716i 1.14045i
782782 1.71892 2.50492i 0.0614686 0.0895756i
783783 18.2630 0.652665
784784 20.5391 18.6009i 0.733538 0.664318i
785785 0 0
786786 −10.5204 + 15.3310i −0.375251 + 0.546837i
787787 29.0437i 1.03530i −0.855593 0.517649i 0.826807π-0.826807\pi
0.855593 0.517649i 0.173193π-0.173193\pi
788788 −17.5016 + 6.74718i −0.623468 + 0.240358i
789789 46.5449i 1.65704i
790790 0 0
791791 0.299601 0.0106526
792792 −11.6893 + 49.1574i −0.415362 + 1.74673i
793793 20.6058 0.731734
794794 −19.8454 13.6183i −0.704287 0.483296i
795795 0 0
796796 −12.1479 31.5105i −0.430570 1.11686i
797797 40.5313i 1.43569i −0.696201 0.717847i 0.745128π-0.745128\pi
0.696201 0.717847i 0.254872π-0.254872\pi
798798 −3.78744 + 5.51927i −0.134074 + 0.195380i
799799 −5.81486 −0.205715
800800 0 0
801801 −26.1072 −0.922452
802802 6.10197 8.89213i 0.215468 0.313992i
803803 27.1762i 0.959026i
804804 −7.43389 19.2828i −0.262173 0.680053i
805805 0 0
806806 6.05272 + 4.15350i 0.213198 + 0.146301i
807807 4.00415 0.140953
808808 0.236302 0.993728i 0.00831309 0.0349592i
809809 52.0674 1.83059 0.915297 0.402781i 0.131956π-0.131956\pi
0.915297 + 0.402781i 0.131956π0.131956\pi
810810 0 0
811811 27.5707i 0.968138i 0.875030 + 0.484069i 0.160842π0.160842\pi
−0.875030 + 0.484069i 0.839158π0.839158\pi
812812 3.88531 1.49786i 0.136348 0.0525646i
813813 42.4191i 1.48770i
814814 19.5319 28.4630i 0.684594 0.997629i
815815 0 0
816816 −4.29585 4.74346i −0.150385 0.166054i
817817 −82.0870 −2.87186
818818 5.90156 8.60009i 0.206343 0.300695i
819819 1.63102i 0.0569923i
820820 0 0
821821 51.8915i 1.81103i −0.424318 0.905513i 0.639486π-0.639486\pi
0.424318 0.905513i 0.360514π-0.360514\pi
822822 −37.2318 25.5492i −1.29861 0.891132i
823823 −42.8229 −1.49271 −0.746356 0.665547i 0.768198π-0.768198\pi
−0.746356 + 0.665547i 0.768198π0.768198\pi
824824 −52.4237 12.4660i −1.82627 0.434275i
825825 0 0
826826 −3.21030 2.20298i −0.111701 0.0766514i
827827 24.7187i 0.859554i 0.902935 + 0.429777i 0.141408π0.141408\pi
−0.902935 + 0.429777i 0.858592π0.858592\pi
828828 9.89302 + 25.6616i 0.343806 + 0.891802i
829829 9.70912i 0.337212i 0.985684 + 0.168606i 0.0539265π0.0539265\pi
−0.985684 + 0.168606i 0.946073π0.946073\pi
830830 0 0
831831 −32.4931 −1.12717
832832 5.59484 11.0989i 0.193966 0.384784i
833833 −4.21961 −0.146201
834834 16.4324 23.9463i 0.569008 0.829192i
835835 0 0
836836 22.0614 + 57.2252i 0.763008 + 1.97917i
837837 7.89028i 0.272728i
838838 25.7509 + 17.6708i 0.889549 + 0.610427i
839839 −15.1090 −0.521620 −0.260810 0.965390i 0.583990π-0.583990\pi
−0.260810 + 0.965390i 0.583990π0.583990\pi
840840 0 0
841841 −30.8000 −1.06207
842842 34.1057 + 23.4041i 1.17536 + 0.806557i
843843 10.6068i 0.365319i
844844 −26.1752 + 10.0910i −0.900987 + 0.347347i
845845 0 0
846846 29.7852 43.4047i 1.02404 1.49228i
847847 −2.69003 −0.0924304
848848 28.6160 + 31.5977i 0.982678 + 1.08507i
849849 10.8739 0.373192
850850 0 0
851851 18.7894i 0.644092i
852852 34.0974 13.1452i 1.16816 0.450347i
853853 15.5755i 0.533295i −0.963794 0.266647i 0.914084π-0.914084\pi
0.963794 0.266647i 0.0859159π-0.0859159\pi
854854 4.16382 + 2.85730i 0.142483 + 0.0977748i
855855 0 0
856856 5.02543 21.1336i 0.171766 0.722330i
857857 −24.5547 −0.838773 −0.419386 0.907808i 0.637755π-0.637755\pi
−0.419386 + 0.907808i 0.637755π0.637755\pi
858858 21.8020 + 14.9610i 0.744308 + 0.510759i
859859 38.2985i 1.30673i 0.757044 + 0.653363i 0.226643π0.226643\pi
−0.757044 + 0.653363i 0.773357π0.773357\pi
860860 0 0
861861 3.09952i 0.105631i
862862 −5.59340 + 8.15102i −0.190512 + 0.277625i
863863 −45.7916 −1.55876 −0.779382 0.626549i 0.784467π-0.784467\pi
−0.779382 + 0.626549i 0.784467π0.784467\pi
864864 13.2390 1.79150i 0.450401 0.0609480i
865865 0 0
866866 15.3065 22.3055i 0.520135 0.757970i
867867 43.6780i 1.48338i
868868 0.647131 + 1.67860i 0.0219650 + 0.0569754i
869869 46.4496i 1.57570i
870870 0 0
871871 −6.11207 −0.207100
872872 1.18556 4.98565i 0.0401480 0.168835i
873873 15.5646 0.526783
874874 27.5249 + 18.8881i 0.931042 + 0.638900i
875875 0 0
876876 29.0741 11.2086i 0.982324 0.378704i
877877 42.8419i 1.44667i 0.690499 + 0.723334i 0.257391π0.257391\pi
−0.690499 + 0.723334i 0.742609π0.742609\pi
878878 −2.23135 + 3.25165i −0.0753043 + 0.109738i
879879 −66.3585 −2.23822
880880 0 0
881881 26.0361 0.877180 0.438590 0.898687i 0.355478π-0.355478\pi
0.438590 + 0.898687i 0.355478π0.355478\pi
882882 21.6139 31.4970i 0.727777 1.06056i
883883 19.3468i 0.651072i 0.945530 + 0.325536i 0.105545π0.105545\pi
−0.945530 + 0.325536i 0.894455π0.894455\pi
884884 −1.76600 + 0.680827i −0.0593971 + 0.0228987i
885885 0 0
886886 −19.6874 13.5099i −0.661411 0.453874i
887887 26.1028 0.876445 0.438222 0.898867i 0.355608π-0.355608\pi
0.438222 + 0.898867i 0.355608π0.355608\pi
888888 −38.5067 9.15665i −1.29220 0.307277i
889889 2.64365 0.0886650
890890 0 0
891891 25.1722i 0.843300i
892892 1.48300 + 3.84677i 0.0496545 + 0.128799i
893893 63.8957i 2.13819i
894894 35.7398 52.0821i 1.19532 1.74189i
895895 0 0
896896 2.66957 1.46694i 0.0891841 0.0490071i
897897 14.3922 0.480542
898898 −10.5147 + 15.3226i −0.350880 + 0.511323i
899899 25.8358i 0.861672i
900900 0 0
901901 6.49153i 0.216264i
902902 23.4156 + 16.0683i 0.779656 + 0.535016i
903903 −8.67321 −0.288626
904904 −3.06203 0.728130i −0.101841 0.0242173i
905905 0 0
906906 −40.6755 27.9124i −1.35135 0.927327i
907907 47.0568i 1.56249i 0.624222 + 0.781247i 0.285416π0.285416\pi
−0.624222 + 0.781247i 0.714584π0.714584\pi
908908 −5.84610 + 2.25378i −0.194010 + 0.0747943i
909909 1.40810i 0.0467039i
910910 0 0
911911 57.6189 1.90900 0.954499 0.298214i 0.0963909π-0.0963909\pi
0.954499 + 0.298214i 0.0963909π0.0963909\pi
912912 52.1227 47.2042i 1.72596 1.56309i
913913 29.8866 0.989101
914914 26.7868 39.0353i 0.886029 1.29117i
915915 0 0
916916 31.8620 12.2834i 1.05275 0.405854i
917917 1.34767i 0.0445039i
918918 −1.67741 1.15107i −0.0553628 0.0379911i
919919 22.6047 0.745661 0.372830 0.927900i 0.378387π-0.378387\pi
0.372830 + 0.927900i 0.378387π0.378387\pi
920920 0 0
921921 −28.0239 −0.923418
922922 32.1878 + 22.0879i 1.06005 + 0.727426i
923923 10.8079i 0.355745i
924924 2.33097 + 6.04634i 0.0766834 + 0.198910i
925925 0 0
926926 11.9408 17.4009i 0.392400 0.571828i
927927 −74.2840 −2.43981
928928 −43.3496 + 5.86605i −1.42302 + 0.192562i
929929 22.2533 0.730108 0.365054 0.930986i 0.381050π-0.381050\pi
0.365054 + 0.930986i 0.381050π0.381050\pi
930930 0 0
931931 46.3665i 1.51960i
932932 5.49263 + 14.2474i 0.179917 + 0.466689i
933933 4.67831i 0.153161i
934934 13.8395 + 9.49696i 0.452843 + 0.310750i
935935 0 0
936936 3.96392 16.6696i 0.129565 0.544862i
937937 20.8873 0.682358 0.341179 0.939998i 0.389174π-0.389174\pi
0.341179 + 0.939998i 0.389174π0.389174\pi
938938 −1.23507 0.847529i −0.0403264 0.0276728i
939939 69.9339i 2.28221i
940940 0 0
941941 13.7530i 0.448335i 0.974551 + 0.224168i 0.0719664π0.0719664\pi
−0.974551 + 0.224168i 0.928034π0.928034\pi
942942 40.0499 58.3630i 1.30490 1.90157i
943943 15.4574 0.503364
944944 27.4565 + 30.3174i 0.893633 + 0.986746i
945945 0 0
946946 −44.9630 + 65.5226i −1.46187 + 2.13032i
947947 31.2715i 1.01619i −0.861302 0.508094i 0.830350π-0.830350\pi
0.861302 0.508094i 0.169650π-0.169650\pi
948948 49.6936 19.1578i 1.61397 0.622217i
949949 9.21562i 0.299152i
950950 0 0
951951 24.0695 0.780508
952952 −0.451263 0.107308i −0.0146255 0.00347786i
953953 −26.2447 −0.850150 −0.425075 0.905158i 0.639752π-0.639752\pi
−0.425075 + 0.905158i 0.639752π0.639752\pi
954954 48.4556 + 33.2512i 1.56881 + 1.07655i
955955 0 0
956956 −3.54032 9.18327i −0.114502 0.297008i
957957 93.0609i 3.00823i
958958 12.3568 18.0070i 0.399229 0.581780i
959959 −3.27286 −0.105686
960960 0 0
961961 −19.8380 −0.639935
962962 −6.62340 + 9.65200i −0.213547 + 0.311193i
963963 29.9461i 0.964998i
964964 −13.7565 35.6830i −0.443066 1.14927i
965965 0 0
966966 2.90824 + 1.99569i 0.0935711 + 0.0642104i
967967 −18.5089 −0.595208 −0.297604 0.954689i 0.596187π-0.596187\pi
−0.297604 + 0.954689i 0.596187π0.596187\pi
968968 27.4931 + 6.53767i 0.883660 + 0.210129i
969969 −10.7083 −0.343999
970970 0 0
971971 16.7762i 0.538373i −0.963088 0.269187i 0.913245π-0.913245\pi
0.963088 0.269187i 0.0867548π-0.0867548\pi
972972 −40.1518 + 15.4793i −1.28787 + 0.496497i
973973 2.10500i 0.0674831i
974974 6.06673 8.84078i 0.194390 0.283277i
975975 0 0
976976 −35.6116 39.3221i −1.13990 1.25867i
977977 11.2815 0.360926 0.180463 0.983582i 0.442240π-0.442240\pi
0.180463 + 0.983582i 0.442240π0.442240\pi
978978 35.1314 51.1955i 1.12338 1.63705i
979979 30.6769i 0.980438i
980980 0 0
981981 7.06462i 0.225556i
982982 6.47761 + 4.44507i 0.206709 + 0.141848i
983983 28.6404 0.913488 0.456744 0.889598i 0.349016π-0.349016\pi
0.456744 + 0.889598i 0.349016π0.349016\pi
984984 7.53288 31.6782i 0.240140 1.00987i
985985 0 0
986986 5.49248 + 3.76906i 0.174916 + 0.120031i
987987 6.75113i 0.214891i
988988 −7.48115 19.4054i −0.238007 0.617369i
989989 43.2537i 1.37539i
990990 0 0
991991 −17.4805 −0.555287 −0.277643 0.960684i 0.589553π-0.589553\pi
−0.277643 + 0.960684i 0.589553π0.589553\pi
992992 −2.53435 18.7286i −0.0804657 0.594635i
993993 −20.5774 −0.653005
994994 1.49867 2.18394i 0.0475349 0.0692705i
995995 0 0
996996 −12.3265 31.9738i −0.390580 1.01313i
997997 17.6990i 0.560533i 0.959922 + 0.280266i 0.0904228π0.0904228\pi
−0.959922 + 0.280266i 0.909577π0.909577\pi
998998 16.4650 + 11.2986i 0.521190 + 0.357651i
999999 −12.5823 −0.398086
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 1000.2.d.c.501.29 yes 40
4.3 odd 2 4000.2.d.c.2001.13 40
5.2 odd 4 1000.2.f.d.749.16 20
5.3 odd 4 1000.2.f.c.749.5 20
5.4 even 2 inner 1000.2.d.c.501.12 yes 40
8.3 odd 2 4000.2.d.c.2001.14 40
8.5 even 2 inner 1000.2.d.c.501.30 yes 40
20.3 even 4 4000.2.f.c.3249.20 20
20.7 even 4 4000.2.f.d.3249.1 20
20.19 odd 2 4000.2.d.c.2001.28 40
40.3 even 4 4000.2.f.d.3249.2 20
40.13 odd 4 1000.2.f.d.749.15 20
40.19 odd 2 4000.2.d.c.2001.27 40
40.27 even 4 4000.2.f.c.3249.19 20
40.29 even 2 inner 1000.2.d.c.501.11 40
40.37 odd 4 1000.2.f.c.749.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1000.2.d.c.501.11 40 40.29 even 2 inner
1000.2.d.c.501.12 yes 40 5.4 even 2 inner
1000.2.d.c.501.29 yes 40 1.1 even 1 trivial
1000.2.d.c.501.30 yes 40 8.5 even 2 inner
1000.2.f.c.749.5 20 5.3 odd 4
1000.2.f.c.749.6 20 40.37 odd 4
1000.2.f.d.749.15 20 40.13 odd 4
1000.2.f.d.749.16 20 5.2 odd 4
4000.2.d.c.2001.13 40 4.3 odd 2
4000.2.d.c.2001.14 40 8.3 odd 2
4000.2.d.c.2001.27 40 40.19 odd 2
4000.2.d.c.2001.28 40 20.19 odd 2
4000.2.f.c.3249.19 20 40.27 even 4
4000.2.f.c.3249.20 20 20.3 even 4
4000.2.f.d.3249.1 20 20.7 even 4
4000.2.f.d.3249.2 20 40.3 even 4