Properties

Label 170.2.o.a.7.2
Level 170170
Weight 22
Character 170.7
Analytic conductor 1.3571.357
Analytic rank 00
Dimension 3232
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(3,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([12, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 170=2517 170 = 2 \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 170.o (of order 1616, degree 88, 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: 1.357456834361.35745683436
Analytic rank: 00
Dimension: 3232
Relative dimension: 44 over Q(ζ16)\Q(\zeta_{16})
Twist minimal: yes
Sato-Tate group: SU(2)[C16]\mathrm{SU}(2)[C_{16}]

Embedding invariants

Embedding label 7.2
Character χ\chi == 170.7
Dual form 170.2.o.a.73.2

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+(0.923880+0.382683i)q2+(0.2417381.21530i)q3+(0.7071070.707107i)q4+(1.17123+1.90479i)q5+(0.688411+1.03028i)q6+(0.590918+0.394839i)q7+(0.382683+0.923880i)q8+(1.353120.560483i)q9+(1.811011.31159i)q10+(3.890812.59976i)q11+(1.030280.688411i)q120.327094iq13+(0.3948390.590918i)q14+(2.031761.88385i)q151.00000iq16+(4.06450+0.692689i)q17+(1.03564+1.03564i)q18+(0.4707580.194994i)q19+(2.17507+0.518705i)q20+(0.622694+0.622694i)q21+(2.59976+3.89081i)q22+(0.7291540.145038i)q23+(1.21530+0.241738i)q24+(2.25644+4.46189i)q25+(0.125173+0.302195i)q26+(3.073494.59980i)q27+(0.138649+0.697035i)q28+(1.37720+6.92365i)q29+(1.15618+2.51797i)q30+(2.705601.80782i)q31+(0.382683+0.923880i)q32+(4.100044.10004i)q33+(4.02019+0.915457i)q34+(1.444190.663128i)q35+(0.5604831.35312i)q36+(10.7368+2.13568i)q37+0.509545q38+(0.397517+0.0790710i)q39+(2.20801+0.353144i)q40+(1.396557.02092i)q41+(0.8135900.337000i)q42+(0.3104900.128609i)q43+(0.9129144.58953i)q44+(2.65242+1.92096i)q45+(0.7291540.145038i)q464.22197q47+(1.21530+0.241738i)q48+(2.48550+6.00052i)q49+(0.3771914.98575i)q50+(0.1407215.10703i)q51+(0.2312900.231290i)q52+(1.657754.00217i)q53+(4.59980+3.07349i)q54+(9.50903+4.36627i)q55+(0.1386490.697035i)q56+(0.123176+0.619249i)q57+(3.921935.86959i)q58+(1.52485+3.68132i)q59+(0.1045842.76875i)q60+(6.637831.32035i)q61+(3.19147+0.634823i)q62+(0.578286+0.865466i)q63+(0.7071070.707107i)q64+(0.6230450.383102i)q65+(5.35696+2.21893i)q66+(0.2748160.274816i)q67+(3.363842.38423i)q68+0.921201iq69+(1.58802+0.0599842i)q70+(8.70794+13.0324i)q71+1.46461iq72+(9.94566+6.64548i)q73+(9.102226.08191i)q74+(5.96800+1.66364i)q75+(0.470758+0.194994i)q76+(1.27267+3.07249i)q77+(0.3369980.225175i)q78+(5.348008.00385i)q79+(1.904791.17123i)q80+(1.74024+1.74024i)q81+(1.39655+7.02092i)q82+(11.59724.80373i)q83+0.880623q84+(3.44104+8.55332i)q85+0.336072q86+(8.081383.34742i)q87+(0.912914+4.58953i)q88+(0.374770+0.374770i)q89+(3.185640.759702i)q90+(0.129149+0.193286i)q91+(0.618147+0.413033i)q92+(1.54300+3.72513i)q93+(3.900591.61568i)q94+(0.1799421.12508i)q95+(1.030280.688411i)q96+(8.192715.47419i)q976.49492iq98+(3.807645.69853i)q99+O(q100)q+(-0.923880 + 0.382683i) q^{2} +(-0.241738 - 1.21530i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.17123 + 1.90479i) q^{5} +(0.688411 + 1.03028i) q^{6} +(-0.590918 + 0.394839i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(1.35312 - 0.560483i) q^{9} +(-1.81101 - 1.31159i) q^{10} +(3.89081 - 2.59976i) q^{11} +(-1.03028 - 0.688411i) q^{12} -0.327094i q^{13} +(0.394839 - 0.590918i) q^{14} +(2.03176 - 1.88385i) q^{15} -1.00000i q^{16} +(4.06450 + 0.692689i) q^{17} +(-1.03564 + 1.03564i) q^{18} +(-0.470758 - 0.194994i) q^{19} +(2.17507 + 0.518705i) q^{20} +(0.622694 + 0.622694i) q^{21} +(-2.59976 + 3.89081i) q^{22} +(-0.729154 - 0.145038i) q^{23} +(1.21530 + 0.241738i) q^{24} +(-2.25644 + 4.46189i) q^{25} +(0.125173 + 0.302195i) q^{26} +(-3.07349 - 4.59980i) q^{27} +(-0.138649 + 0.697035i) q^{28} +(1.37720 + 6.92365i) q^{29} +(-1.15618 + 2.51797i) q^{30} +(-2.70560 - 1.80782i) q^{31} +(0.382683 + 0.923880i) q^{32} +(-4.10004 - 4.10004i) q^{33} +(-4.02019 + 0.915457i) q^{34} +(-1.44419 - 0.663128i) q^{35} +(0.560483 - 1.35312i) q^{36} +(-10.7368 + 2.13568i) q^{37} +0.509545 q^{38} +(-0.397517 + 0.0790710i) q^{39} +(-2.20801 + 0.353144i) q^{40} +(1.39655 - 7.02092i) q^{41} +(-0.813590 - 0.337000i) q^{42} +(-0.310490 - 0.128609i) q^{43} +(0.912914 - 4.58953i) q^{44} +(2.65242 + 1.92096i) q^{45} +(0.729154 - 0.145038i) q^{46} -4.22197 q^{47} +(-1.21530 + 0.241738i) q^{48} +(-2.48550 + 6.00052i) q^{49} +(0.377191 - 4.98575i) q^{50} +(-0.140721 - 5.10703i) q^{51} +(-0.231290 - 0.231290i) q^{52} +(-1.65775 - 4.00217i) q^{53} +(4.59980 + 3.07349i) q^{54} +(9.50903 + 4.36627i) q^{55} +(-0.138649 - 0.697035i) q^{56} +(-0.123176 + 0.619249i) q^{57} +(-3.92193 - 5.86959i) q^{58} +(1.52485 + 3.68132i) q^{59} +(0.104584 - 2.76875i) q^{60} +(-6.63783 - 1.32035i) q^{61} +(3.19147 + 0.634823i) q^{62} +(-0.578286 + 0.865466i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(0.623045 - 0.383102i) q^{65} +(5.35696 + 2.21893i) q^{66} +(0.274816 - 0.274816i) q^{67} +(3.36384 - 2.38423i) q^{68} +0.921201i q^{69} +(1.58802 + 0.0599842i) q^{70} +(-8.70794 + 13.0324i) q^{71} +1.46461i q^{72} +(9.94566 + 6.64548i) q^{73} +(9.10222 - 6.08191i) q^{74} +(5.96800 + 1.66364i) q^{75} +(-0.470758 + 0.194994i) q^{76} +(-1.27267 + 3.07249i) q^{77} +(0.336998 - 0.225175i) q^{78} +(-5.34800 - 8.00385i) q^{79} +(1.90479 - 1.17123i) q^{80} +(-1.74024 + 1.74024i) q^{81} +(1.39655 + 7.02092i) q^{82} +(11.5972 - 4.80373i) q^{83} +0.880623 q^{84} +(3.44104 + 8.55332i) q^{85} +0.336072 q^{86} +(8.08138 - 3.34742i) q^{87} +(0.912914 + 4.58953i) q^{88} +(-0.374770 + 0.374770i) q^{89} +(-3.18564 - 0.759702i) q^{90} +(0.129149 + 0.193286i) q^{91} +(-0.618147 + 0.413033i) q^{92} +(-1.54300 + 3.72513i) q^{93} +(3.90059 - 1.61568i) q^{94} +(-0.179942 - 1.12508i) q^{95} +(1.03028 - 0.688411i) q^{96} +(-8.19271 - 5.47419i) q^{97} -6.49492i q^{98} +(3.80764 - 5.69853i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+8q1040q15+16q18+8q208q25+8q2672q27+8q28+8q2916q3164q3324q34+32q35+16q37+32q398q40+16q41++64q99+O(q100) 32 q + 8 q^{10} - 40 q^{15} + 16 q^{18} + 8 q^{20} - 8 q^{25} + 8 q^{26} - 72 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 64 q^{33} - 24 q^{34} + 32 q^{35} + 16 q^{37} + 32 q^{39} - 8 q^{40} + 16 q^{41}+ \cdots + 64 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/170Z)×\left(\mathbb{Z}/170\mathbb{Z}\right)^\times.

nn 7171 137137
χ(n)\chi(n) e(1116)e\left(\frac{11}{16}\right) e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.923880 + 0.382683i −0.653281 + 0.270598i
33 −0.241738 1.21530i −0.139567 0.701653i −0.985677 0.168644i 0.946061π-0.946061\pi
0.846110 0.533009i 0.178939π-0.178939\pi
44 0.707107 0.707107i 0.353553 0.353553i
55 1.17123 + 1.90479i 0.523790 + 0.851848i
66 0.688411 + 1.03028i 0.281043 + 0.420610i
77 −0.590918 + 0.394839i −0.223346 + 0.149235i −0.662210 0.749319i 0.730381π-0.730381\pi
0.438864 + 0.898554i 0.355381π0.355381\pi
88 −0.382683 + 0.923880i −0.135299 + 0.326641i
99 1.35312 0.560483i 0.451042 0.186828i
1010 −1.81101 1.31159i −0.572690 0.414760i
1111 3.89081 2.59976i 1.17312 0.783857i 0.192798 0.981239i 0.438244π-0.438244\pi
0.980327 + 0.197382i 0.0632439π0.0632439\pi
1212 −1.03028 0.688411i −0.297416 0.198727i
1313 0.327094i 0.0907195i −0.998971 0.0453597i 0.985557π-0.985557\pi
0.998971 0.0453597i 0.0144434π-0.0144434\pi
1414 0.394839 0.590918i 0.105525 0.157930i
1515 2.03176 1.88385i 0.524597 0.486409i
1616 1.00000i 0.250000i
1717 4.06450 + 0.692689i 0.985787 + 0.168002i
1818 −1.03564 + 1.03564i −0.244102 + 0.244102i
1919 −0.470758 0.194994i −0.107999 0.0447348i 0.328030 0.944667i 0.393615π-0.393615\pi
−0.436029 + 0.899933i 0.643615π0.643615\pi
2020 2.17507 + 0.518705i 0.486361 + 0.115986i
2121 0.622694 + 0.622694i 0.135883 + 0.135883i
2222 −2.59976 + 3.89081i −0.554270 + 0.829524i
2323 −0.729154 0.145038i −0.152039 0.0302425i 0.118484 0.992956i 0.462197π-0.462197\pi
−0.270523 + 0.962714i 0.587197π0.587197\pi
2424 1.21530 + 0.241738i 0.248072 + 0.0493445i
2525 −2.25644 + 4.46189i −0.451289 + 0.892378i
2626 0.125173 + 0.302195i 0.0245485 + 0.0592654i
2727 −3.07349 4.59980i −0.591493 0.885232i
2828 −0.138649 + 0.697035i −0.0262022 + 0.131727i
2929 1.37720 + 6.92365i 0.255740 + 1.28569i 0.868606 + 0.495503i 0.165016π0.165016\pi
−0.612867 + 0.790186i 0.709984π0.709984\pi
3030 −1.15618 + 2.51797i −0.211089 + 0.459717i
3131 −2.70560 1.80782i −0.485940 0.324695i 0.288351 0.957525i 0.406893π-0.406893\pi
−0.774291 + 0.632830i 0.781893π0.781893\pi
3232 0.382683 + 0.923880i 0.0676495 + 0.163320i
3333 −4.10004 4.10004i −0.713725 0.713725i
3434 −4.02019 + 0.915457i −0.689457 + 0.157000i
3535 −1.44419 0.663128i −0.244112 0.112089i
3636 0.560483 1.35312i 0.0934138 0.225521i
3737 −10.7368 + 2.13568i −1.76512 + 0.351104i −0.967658 0.252265i 0.918824π-0.918824\pi
−0.797462 + 0.603369i 0.793824π0.793824\pi
3838 0.509545 0.0826591
3939 −0.397517 + 0.0790710i −0.0636536 + 0.0126615i
4040 −2.20801 + 0.353144i −0.349116 + 0.0558369i
4141 1.39655 7.02092i 0.218104 1.09648i −0.704195 0.710007i 0.748692π-0.748692\pi
0.922299 0.386477i 0.126308π-0.126308\pi
4242 −0.813590 0.337000i −0.125540 0.0520002i
4343 −0.310490 0.128609i −0.0473492 0.0196127i 0.358883 0.933382i 0.383158π-0.383158\pi
−0.406232 + 0.913770i 0.633158π0.633158\pi
4444 0.912914 4.58953i 0.137627 0.691897i
4545 2.65242 + 1.92096i 0.395400 + 0.286360i
4646 0.729154 0.145038i 0.107508 0.0213847i
4747 −4.22197 −0.615838 −0.307919 0.951413i 0.599632π-0.599632\pi
−0.307919 + 0.951413i 0.599632π0.599632\pi
4848 −1.21530 + 0.241738i −0.175413 + 0.0348919i
4949 −2.48550 + 6.00052i −0.355071 + 0.857217i
5050 0.377191 4.98575i 0.0533428 0.705092i
5151 −0.140721 5.10703i −0.0197049 0.715128i
5252 −0.231290 0.231290i −0.0320742 0.0320742i
5353 −1.65775 4.00217i −0.227710 0.549740i 0.768188 0.640224i 0.221158π-0.221158\pi
−0.995898 + 0.0904843i 0.971158π0.971158\pi
5454 4.59980 + 3.07349i 0.625954 + 0.418249i
5555 9.50903 + 4.36627i 1.28220 + 0.588747i
5656 −0.138649 0.697035i −0.0185277 0.0931453i
5757 −0.123176 + 0.619249i −0.0163151 + 0.0820216i
5858 −3.92193 5.86959i −0.514975 0.770714i
5959 1.52485 + 3.68132i 0.198519 + 0.479267i 0.991520 0.129953i 0.0414826π-0.0414826\pi
−0.793001 + 0.609220i 0.791483π0.791483\pi
6060 0.104584 2.76875i 0.0135017 0.357445i
6161 −6.63783 1.32035i −0.849887 0.169053i −0.249116 0.968474i 0.580140π-0.580140\pi
−0.600772 + 0.799421i 0.705140π0.705140\pi
6262 3.19147 + 0.634823i 0.405317 + 0.0806226i
6363 −0.578286 + 0.865466i −0.0728572 + 0.109038i
6464 −0.707107 0.707107i −0.0883883 0.0883883i
6565 0.623045 0.383102i 0.0772792 0.0475179i
6666 5.35696 + 2.21893i 0.659396 + 0.273131i
6767 0.274816 0.274816i 0.0335741 0.0335741i −0.690120 0.723695i 0.742442π-0.742442\pi
0.723695 + 0.690120i 0.242442π0.242442\pi
6868 3.36384 2.38423i 0.407926 0.289131i
6969 0.921201i 0.110900i
7070 1.58802 + 0.0599842i 0.189805 + 0.00716948i
7171 −8.70794 + 13.0324i −1.03344 + 1.54666i −0.211262 + 0.977429i 0.567757π0.567757\pi
−0.822180 + 0.569227i 0.807243π0.807243\pi
7272 1.46461i 0.172606i
7373 9.94566 + 6.64548i 1.16405 + 0.777795i 0.978784 0.204893i 0.0656848π-0.0656848\pi
0.185268 + 0.982688i 0.440685π0.440685\pi
7474 9.10222 6.08191i 1.05811 0.707008i
7575 5.96800 + 1.66364i 0.689125 + 0.192101i
7676 −0.470758 + 0.194994i −0.0539997 + 0.0223674i
7777 −1.27267 + 3.07249i −0.145034 + 0.350143i
7878 0.336998 0.225175i 0.0381575 0.0254961i
7979 −5.34800 8.00385i −0.601697 0.900504i 0.398161 0.917315i 0.369648π-0.369648\pi
−0.999859 + 0.0168118i 0.994648π0.994648\pi
8080 1.90479 1.17123i 0.212962 0.130947i
8181 −1.74024 + 1.74024i −0.193360 + 0.193360i
8282 1.39655 + 7.02092i 0.154223 + 0.775331i
8383 11.5972 4.80373i 1.27296 0.527278i 0.359098 0.933300i 0.383084π-0.383084\pi
0.913863 + 0.406022i 0.133084π0.133084\pi
8484 0.880623 0.0960838
8585 3.44104 + 8.55332i 0.373233 + 0.927738i
8686 0.336072 0.0362395
8787 8.08138 3.34742i 0.866415 0.358881i
8888 0.912914 + 4.58953i 0.0973169 + 0.489245i
8989 −0.374770 + 0.374770i −0.0397255 + 0.0397255i −0.726691 0.686965i 0.758943π-0.758943\pi
0.686965 + 0.726691i 0.258943π0.258943\pi
9090 −3.18564 0.759702i −0.335796 0.0800796i
9191 0.129149 + 0.193286i 0.0135385 + 0.0202618i
9292 −0.618147 + 0.413033i −0.0644463 + 0.0430616i
9393 −1.54300 + 3.72513i −0.160002 + 0.386278i
9494 3.90059 1.61568i 0.402315 0.166644i
9595 −0.179942 1.12508i −0.0184617 0.115431i
9696 1.03028 0.688411i 0.105153 0.0702607i
9797 −8.19271 5.47419i −0.831844 0.555820i 0.0651439 0.997876i 0.479249π-0.479249\pi
−0.896988 + 0.442056i 0.854249π0.854249\pi
9898 6.49492i 0.656086i
9999 3.80764 5.69853i 0.382682 0.572724i
100100 1.55949 + 4.75058i 0.155949 + 0.475058i
101101 14.4498i 1.43781i −0.695108 0.718906i 0.744643π-0.744643\pi
0.695108 0.718906i 0.255357π-0.255357\pi
102102 2.08439 + 4.66443i 0.206385 + 0.461848i
103103 8.21768 8.21768i 0.809712 0.809712i −0.174878 0.984590i 0.555953π-0.555953\pi
0.984590 + 0.174878i 0.0559531π0.0559531\pi
104104 0.302195 + 0.125173i 0.0296327 + 0.0122743i
105105 −0.456784 + 1.91542i −0.0445775 + 0.186926i
106106 3.06313 + 3.06313i 0.297517 + 0.297517i
107107 5.33929 7.99081i 0.516168 0.772501i −0.478226 0.878237i 0.658720π-0.658720\pi
0.994394 + 0.105736i 0.0337200π0.0337200\pi
108108 −5.42584 1.07927i −0.522101 0.103852i
109109 −4.69116 0.933131i −0.449332 0.0893777i −0.0347631 0.999396i 0.511068π-0.511068\pi
−0.414569 + 0.910018i 0.636068π0.636068\pi
110110 −10.4561 0.394957i −0.996949 0.0376577i
111111 5.19099 + 12.5321i 0.492707 + 1.18950i
112112 0.394839 + 0.590918i 0.0373088 + 0.0558365i
113113 −1.83151 + 9.20761i −0.172294 + 0.866179i 0.793838 + 0.608130i 0.208080π0.208080\pi
−0.966132 + 0.258050i 0.916920π0.916920\pi
114114 −0.123176 0.619249i −0.0115365 0.0579980i
115115 −0.577740 1.55876i −0.0538746 0.145355i
116116 5.86959 + 3.92193i 0.544977 + 0.364142i
117117 −0.183330 0.442599i −0.0169489 0.0409183i
118118 −2.81756 2.81756i −0.259377 0.259377i
119119 −2.67529 + 1.19550i −0.245243 + 0.109591i
120120 0.962934 + 2.59802i 0.0879034 + 0.237166i
121121 4.17017 10.0677i 0.379106 0.915243i
122122 6.63783 1.32035i 0.600961 0.119539i
123123 −8.87012 −0.799792
124124 −3.19147 + 0.634823i −0.286603 + 0.0570088i
125125 −11.1418 + 0.927847i −0.996550 + 0.0829891i
126126 0.203067 1.02089i 0.0180906 0.0909478i
127127 −0.944755 0.391330i −0.0838334 0.0347249i 0.340373 0.940291i 0.389447π-0.389447\pi
−0.424206 + 0.905566i 0.639447π0.639447\pi
128128 0.923880 + 0.382683i 0.0816602 + 0.0338248i
129129 −0.0812413 + 0.408427i −0.00715289 + 0.0359600i
130130 −0.429011 + 0.592369i −0.0376268 + 0.0519542i
131131 −19.6520 + 3.90902i −1.71700 + 0.341532i −0.952835 0.303489i 0.901848π-0.901848\pi
−0.764164 + 0.645022i 0.776848π0.776848\pi
132132 −5.79833 −0.504680
133133 0.355171 0.0706479i 0.0307972 0.00612595i
134134 −0.148729 + 0.359064i −0.0128482 + 0.0310184i
135135 5.16189 11.2418i 0.444265 0.967538i
136136 −2.19538 + 3.49003i −0.188252 + 0.299268i
137137 12.6973 + 12.6973i 1.08480 + 1.08480i 0.996054 + 0.0887476i 0.0282864π0.0282864\pi
0.0887476 + 0.996054i 0.471714π0.471714\pi
138138 −0.352528 0.851079i −0.0300092 0.0724486i
139139 −13.6528 9.12249i −1.15801 0.773759i −0.180280 0.983615i 0.557700π-0.557700\pi
−0.977732 + 0.209856i 0.932700π0.932700\pi
140140 −1.49010 + 0.552291i −0.125936 + 0.0466771i
141141 1.02061 + 5.13095i 0.0859509 + 0.432104i
142142 3.05782 15.3727i 0.256607 1.29005i
143143 −0.850365 1.27266i −0.0711111 0.106425i
144144 −0.560483 1.35312i −0.0467069 0.112760i
145145 −11.5751 + 10.7325i −0.961258 + 0.891282i
146146 −11.7317 2.33358i −0.970923 0.193129i
147147 7.89327 + 1.57007i 0.651026 + 0.129497i
148148 −6.08191 + 9.10222i −0.499930 + 0.748198i
149149 4.02675 + 4.02675i 0.329884 + 0.329884i 0.852542 0.522658i 0.175060π-0.175060\pi
−0.522658 + 0.852542i 0.675060π0.675060\pi
150150 −6.15036 + 0.746846i −0.502175 + 0.0609797i
151151 9.87709 + 4.09122i 0.803786 + 0.332939i 0.746472 0.665417i 0.231746π-0.231746\pi
0.0573142 + 0.998356i 0.481746π0.481746\pi
152152 0.360303 0.360303i 0.0292244 0.0292244i
153153 5.88802 1.34079i 0.476018 0.108396i
154154 3.32564i 0.267987i
155155 0.274646 7.27097i 0.0220601 0.584018i
156156 −0.225175 + 0.336998i −0.0180284 + 0.0269815i
157157 16.1039i 1.28523i −0.766189 0.642616i 0.777849π-0.777849\pi
0.766189 0.642616i 0.222151π-0.222151\pi
158158 8.00385 + 5.34800i 0.636752 + 0.425464i
159159 −4.46309 + 2.98214i −0.353946 + 0.236499i
160160 −1.31159 + 1.81101i −0.103690 + 0.143173i
161161 0.488137 0.202193i 0.0384706 0.0159350i
162162 0.941813 2.27374i 0.0739958 0.178642i
163163 −18.2797 + 12.2141i −1.43178 + 0.956684i −0.433317 + 0.901242i 0.642657π0.642657\pi
−0.998462 + 0.0554422i 0.982343π0.982343\pi
164164 −3.97703 5.95205i −0.310554 0.464777i
165165 3.00762 12.6118i 0.234143 0.981827i
166166 −8.87613 + 8.87613i −0.688922 + 0.688922i
167167 3.23562 + 16.2666i 0.250380 + 1.25875i 0.877406 + 0.479748i 0.159272π0.159272\pi
−0.627026 + 0.778998i 0.715728π0.715728\pi
168168 −0.813590 + 0.337000i −0.0627698 + 0.0260001i
169169 12.8930 0.991770
170170 −6.45232 6.58541i −0.494870 0.505078i
171171 −0.746286 −0.0570699
172172 −0.310490 + 0.128609i −0.0236746 + 0.00980635i
173173 1.67213 + 8.40635i 0.127129 + 0.639123i 0.990830 + 0.135117i 0.0431410π0.0431410\pi
−0.863700 + 0.504006i 0.831859π0.831859\pi
174174 −6.18522 + 6.18522i −0.468900 + 0.468900i
175175 −0.428354 3.52754i −0.0323805 0.266657i
176176 −2.59976 3.89081i −0.195964 0.293281i
177177 4.10529 2.74307i 0.308572 0.206181i
178178 0.202824 0.489660i 0.0152023 0.0367016i
179179 −18.8787 + 7.81980i −1.41106 + 0.584479i −0.952597 0.304235i 0.901599π-0.901599\pi
−0.458461 + 0.888715i 0.651599π0.651599\pi
180180 3.23387 0.517218i 0.241039 0.0385512i
181181 3.58349 2.39441i 0.266359 0.177975i −0.415218 0.909722i 0.636295π-0.636295\pi
0.681577 + 0.731747i 0.261295π0.261295\pi
182182 −0.193286 0.129149i −0.0143273 0.00957318i
183183 8.38613i 0.619920i
184184 0.413033 0.618147i 0.0304492 0.0455704i
185185 −16.6433 17.9500i −1.22364 1.31971i
186186 4.03205i 0.295644i
187187 17.6150 7.87160i 1.28814 0.575629i
188188 −2.98538 + 2.98538i −0.217731 + 0.217731i
189189 3.63236 + 1.50457i 0.264215 + 0.109442i
190190 0.596794 + 0.970576i 0.0432960 + 0.0704130i
191191 11.4696 + 11.4696i 0.829911 + 0.829911i 0.987504 0.157593i 0.0503733π-0.0503733\pi
−0.157593 + 0.987504i 0.550373π0.550373\pi
192192 −0.688411 + 1.03028i −0.0496818 + 0.0743541i
193193 0.0549621 + 0.0109326i 0.00395626 + 0.000786949i 0.197068 0.980390i 0.436858π-0.436858\pi
−0.193112 + 0.981177i 0.561858π0.561858\pi
194194 9.66396 + 1.92228i 0.693832 + 0.138012i
195195 −0.616197 0.664575i −0.0441267 0.0475912i
196196 2.48550 + 6.00052i 0.177536 + 0.428609i
197197 −2.06071 3.08408i −0.146820 0.219731i 0.750769 0.660565i 0.229683π-0.229683\pi
−0.897589 + 0.440833i 0.854683π0.854683\pi
198198 −1.33706 + 6.72188i −0.0950210 + 0.477703i
199199 1.29609 + 6.51587i 0.0918771 + 0.461898i 0.999145 + 0.0413442i 0.0131640π0.0131640\pi
−0.907268 + 0.420553i 0.861836π0.861836\pi
200200 −3.25875 3.79217i −0.230428 0.268147i
201201 −0.400417 0.267550i −0.0282432 0.0188715i
202202 5.52971 + 13.3499i 0.389069 + 0.939295i
203203 −3.54754 3.54754i −0.248988 0.248988i
204204 −3.71072 3.51171i −0.259803 0.245869i
205205 15.0091 5.56298i 1.04828 0.388535i
206206 −4.44738 + 10.7369i −0.309863 + 0.748077i
207207 −1.06793 + 0.212424i −0.0742261 + 0.0147645i
208208 −0.327094 −0.0226799
209209 −2.33857 + 0.465170i −0.161762 + 0.0321765i
210210 −0.310986 1.94442i −0.0214601 0.134178i
211211 3.42608 17.2241i 0.235861 1.18575i −0.663373 0.748289i 0.730876π-0.730876\pi
0.899235 0.437466i 0.144124π-0.144124\pi
212212 −4.00217 1.65775i −0.274870 0.113855i
213213 17.9432 + 7.43234i 1.22945 + 0.509255i
214214 −1.87491 + 9.42580i −0.128166 + 0.644334i
215215 −0.118682 0.742048i −0.00809401 0.0506073i
216216 5.42584 1.07927i 0.369181 0.0734348i
217217 2.31259 0.156989
218218 4.69116 0.933131i 0.317726 0.0631996i
219219 5.67200 13.6934i 0.383278 0.925315i
220220 9.81131 3.63648i 0.661479 0.245171i
221221 0.226574 1.32947i 0.0152410 0.0894300i
222222 −9.59169 9.59169i −0.643752 0.643752i
223223 3.99002 + 9.63276i 0.267192 + 0.645058i 0.999349 0.0360779i 0.0114864π-0.0114864\pi
−0.732157 + 0.681136i 0.761486π0.761486\pi
224224 −0.590918 0.394839i −0.0394824 0.0263813i
225225 −0.552438 + 7.30219i −0.0368292 + 0.486813i
226226 −1.83151 9.20761i −0.121830 0.612481i
227227 2.39499 12.0404i 0.158961 0.799152i −0.816220 0.577742i 0.803934π-0.803934\pi
0.975181 0.221410i 0.0710659π-0.0710659\pi
228228 0.350776 + 0.524974i 0.0232307 + 0.0347673i
229229 −1.03397 2.49621i −0.0683263 0.164954i 0.886028 0.463633i 0.153454π-0.153454\pi
−0.954354 + 0.298678i 0.903454π0.903454\pi
230230 1.13027 + 1.21901i 0.0745280 + 0.0803793i
231231 4.04164 + 0.803933i 0.265921 + 0.0528949i
232232 −6.92365 1.37720i −0.454560 0.0904176i
233233 10.8532 16.2429i 0.711014 1.06411i −0.283446 0.958988i 0.591478π-0.591478\pi
0.994460 0.105119i 0.0335224π-0.0335224\pi
234234 0.338750 + 0.338750i 0.0221448 + 0.0221448i
235235 −4.94489 8.04196i −0.322569 0.524600i
236236 3.68132 + 1.52485i 0.239633 + 0.0992594i
237237 −8.43425 + 8.43425i −0.547864 + 0.547864i
238238 2.01415 2.12829i 0.130558 0.137956i
239239 25.3901i 1.64235i 0.570679 + 0.821173i 0.306680π0.306680\pi
−0.570679 + 0.821173i 0.693320π0.693320\pi
240240 −1.88385 2.03176i −0.121602 0.131149i
241241 4.45194 6.66280i 0.286775 0.429189i −0.659913 0.751342i 0.729407π-0.729407\pi
0.946687 + 0.322154i 0.104407π0.104407\pi
242242 10.8972i 0.700497i
243243 −11.2638 7.52624i −0.722574 0.482808i
244244 −5.62728 + 3.76003i −0.360250 + 0.240711i
245245 −14.3408 + 2.29364i −0.916201 + 0.146535i
246246 8.19492 3.39445i 0.522489 0.216422i
247247 −0.0637814 + 0.153982i −0.00405832 + 0.00979764i
248248 2.70560 1.80782i 0.171806 0.114797i
249249 −8.64145 12.9329i −0.547630 0.819586i
250250 9.93858 5.12099i 0.628571 0.323880i
251251 −14.7371 + 14.7371i −0.930197 + 0.930197i −0.997718 0.0675209i 0.978491π-0.978491\pi
0.0675209 + 0.997718i 0.478491π0.478491\pi
252252 0.203067 + 1.02089i 0.0127920 + 0.0643098i
253253 −3.21407 + 1.33131i −0.202067 + 0.0836987i
254254 1.02260 0.0641633
255255 9.56301 6.24955i 0.598859 0.391362i
256256 −1.00000 −0.0625000
257257 −7.87318 + 3.26118i −0.491115 + 0.203427i −0.614476 0.788935i 0.710633π-0.710633\pi
0.123361 + 0.992362i 0.460633π0.460633\pi
258258 −0.0812413 0.408427i −0.00505786 0.0254276i
259259 5.50132 5.50132i 0.341836 0.341836i
260260 0.169665 0.711453i 0.0105222 0.0441224i
261261 5.74411 + 8.59667i 0.355551 + 0.532120i
262262 16.6601 11.1319i 1.02927 0.687733i
263263 8.47208 20.4534i 0.522411 1.26121i −0.413991 0.910281i 0.635865π-0.635865\pi
0.936402 0.350930i 0.114135π-0.114135\pi
264264 5.35696 2.21893i 0.329698 0.136565i
265265 5.68168 7.84512i 0.349023 0.481922i
266266 −0.301099 + 0.201188i −0.0184616 + 0.0123356i
267267 0.546053 + 0.364861i 0.0334179 + 0.0223291i
268268 0.388648i 0.0237405i
269269 13.2164 19.7798i 0.805819 1.20599i −0.169573 0.985518i 0.554239π-0.554239\pi
0.975392 0.220476i 0.0707611π-0.0707611\pi
270270 −0.466926 + 12.3614i −0.0284162 + 0.752292i
271271 20.8191i 1.26467i 0.774694 + 0.632336i 0.217904π0.217904\pi
−0.774694 + 0.632336i 0.782096π0.782096\pi
272272 0.692689 4.06450i 0.0420004 0.246447i
273273 0.203679 0.203679i 0.0123272 0.0123272i
274274 −16.5898 6.87172i −1.00223 0.415136i
275275 2.82043 + 23.2266i 0.170079 + 1.40062i
276276 0.651388 + 0.651388i 0.0392089 + 0.0392089i
277277 2.22543 3.33059i 0.133713 0.200116i −0.758571 0.651591i 0.774102π-0.774102\pi
0.892284 + 0.451475i 0.149102π0.149102\pi
278278 16.1045 + 3.20339i 0.965886 + 0.192127i
279279 −4.67427 0.929769i −0.279841 0.0556638i
280280 1.16532 1.08049i 0.0696409 0.0645714i
281281 5.55980 + 13.4226i 0.331670 + 0.800722i 0.998460 + 0.0554766i 0.0176678π0.0176678\pi
−0.666790 + 0.745246i 0.732332π0.732332\pi
282282 −2.90645 4.34981i −0.173077 0.259028i
283283 −2.47657 + 12.4506i −0.147217 + 0.740110i 0.834686 + 0.550726i 0.185649π0.185649\pi
−0.981903 + 0.189384i 0.939351π0.939351\pi
284284 3.05782 + 15.3727i 0.181448 + 0.912203i
285285 −1.32381 + 0.490658i −0.0784156 + 0.0290641i
286286 1.27266 + 0.850365i 0.0752540 + 0.0502831i
287287 1.94689 + 4.70020i 0.114921 + 0.277444i
288288 1.03564 + 1.03564i 0.0610255 + 0.0610255i
289289 16.0404 + 5.63087i 0.943551 + 0.331228i
290290 6.58684 14.3451i 0.386793 0.842372i
291291 −4.67229 + 11.2799i −0.273895 + 0.661240i
292292 11.7317 2.33358i 0.686546 0.136563i
293293 −8.34021 −0.487240 −0.243620 0.969871i 0.578335π-0.578335\pi
−0.243620 + 0.969871i 0.578335π0.578335\pi
294294 −7.89327 + 1.57007i −0.460345 + 0.0915682i
295295 −5.22619 + 7.21619i −0.304280 + 0.420143i
296296 2.13568 10.7368i 0.124134 0.624064i
297297 −23.9167 9.90664i −1.38779 0.574842i
298298 −5.26121 2.17926i −0.304773 0.126241i
299299 −0.0474409 + 0.238502i −0.00274358 + 0.0137929i
300300 5.39639 3.04364i 0.311560 0.175724i
301301 0.234254 0.0465960i 0.0135022 0.00268575i
302302 −10.6909 −0.615191
303303 −17.5608 + 3.49307i −1.00884 + 0.200672i
304304 −0.194994 + 0.470758i −0.0111837 + 0.0269998i
305305 −5.25944 14.1901i −0.301155 0.812523i
306306 −4.92672 + 3.49198i −0.281642 + 0.199623i
307307 0.0891571 + 0.0891571i 0.00508847 + 0.00508847i 0.709646 0.704558i 0.248855π-0.248855\pi
−0.704558 + 0.709646i 0.748855π0.748855\pi
308308 1.27267 + 3.07249i 0.0725169 + 0.175071i
309309 −11.9735 8.00041i −0.681146 0.455128i
310310 2.52874 + 6.82260i 0.143623 + 0.387498i
311311 −1.86727 9.38742i −0.105883 0.532312i −0.996923 0.0783864i 0.975023π-0.975023\pi
0.891040 0.453926i 0.149977π-0.149977\pi
312312 0.0790710 0.397517i 0.00447651 0.0225049i
313313 9.66650 + 14.4669i 0.546383 + 0.817719i 0.997191 0.0749013i 0.0238642π-0.0238642\pi
−0.450808 + 0.892621i 0.648864π0.648864\pi
314314 6.16270 + 14.8781i 0.347781 + 0.839618i
315315 −2.32583 0.0878535i −0.131046 0.00494999i
316316 −9.44119 1.87797i −0.531108 0.105644i
317317 19.6461 + 3.90786i 1.10344 + 0.219487i 0.713015 0.701149i 0.247329π-0.247329\pi
0.390422 + 0.920636i 0.372329π0.372329\pi
318318 2.98214 4.46309i 0.167230 0.250277i
319319 23.3582 + 23.3582i 1.30781 + 1.30781i
320320 0.518705 2.17507i 0.0289965 0.121590i
321321 −11.0019 4.55715i −0.614068 0.254355i
322322 −0.373604 + 0.373604i −0.0208201 + 0.0208201i
323323 −1.77833 1.11864i −0.0989488 0.0622430i
324324 2.46108i 0.136726i
325325 1.45946 + 0.738069i 0.0809561 + 0.0409407i
326326 12.2141 18.2797i 0.676478 1.01242i
327327 5.92674i 0.327749i
328328 5.95205 + 3.97703i 0.328647 + 0.219595i
329329 2.49484 1.66700i 0.137545 0.0919045i
330330 2.04764 + 12.8028i 0.112719 + 0.704768i
331331 13.3662 5.53646i 0.734673 0.304312i 0.0162023 0.999869i 0.494842π-0.494842\pi
0.718471 + 0.695557i 0.244842π0.244842\pi
332332 4.80373 11.5972i 0.263639 0.636480i
333333 −13.3312 + 8.90764i −0.730547 + 0.488136i
334334 −9.21428 13.7901i −0.504183 0.754563i
335335 0.845338 + 0.201594i 0.0461858 + 0.0110142i
336336 0.622694 0.622694i 0.0339708 0.0339708i
337337 1.57543 + 7.92021i 0.0858190 + 0.431441i 0.999677 + 0.0254078i 0.00808841π0.00808841\pi
−0.913858 + 0.406034i 0.866912π0.866912\pi
338338 −11.9116 + 4.93394i −0.647905 + 0.268371i
339339 11.6327 0.631804
340340 8.48129 + 3.61493i 0.459963 + 0.196047i
341341 −15.2269 −0.824582
342342 0.689478 0.285591i 0.0372827 0.0154430i
343343 −1.87106 9.40644i −0.101028 0.507900i
344344 0.237639 0.237639i 0.0128126 0.0128126i
345345 −1.75469 + 1.07894i −0.0944695 + 0.0580881i
346346 −4.76181 7.12656i −0.255997 0.383126i
347347 −14.2098 + 9.49472i −0.762825 + 0.509703i −0.875081 0.483976i 0.839192π-0.839192\pi
0.112257 + 0.993679i 0.464192π0.464192\pi
348348 3.34742 8.08138i 0.179440 0.433207i
349349 24.1690 10.0111i 1.29374 0.535884i 0.373641 0.927573i 0.378109π-0.378109\pi
0.920098 + 0.391689i 0.128109π0.128109\pi
350350 1.74568 + 3.09510i 0.0933105 + 0.165440i
351351 −1.50457 + 1.00532i −0.0803078 + 0.0536600i
352352 3.89081 + 2.59976i 0.207381 + 0.138568i
353353 34.0507i 1.81234i −0.422919 0.906168i 0.638994π-0.638994\pi
0.422919 0.906168i 0.361006π-0.361006\pi
354354 −2.74307 + 4.10529i −0.145792 + 0.218194i
355355 −35.0229 1.32292i −1.85882 0.0702131i
356356 0.530005i 0.0280902i
357357 2.09961 + 2.96228i 0.111123 + 0.156780i
358358 14.4491 14.4491i 0.763659 0.763659i
359359 1.81224 + 0.750656i 0.0956465 + 0.0396181i 0.429994 0.902832i 0.358516π-0.358516\pi
−0.334347 + 0.942450i 0.608516π0.608516\pi
360360 −2.78978 + 1.71540i −0.147034 + 0.0904093i
361361 −13.2514 13.2514i −0.697444 0.697444i
362362 −2.39441 + 3.58349i −0.125847 + 0.188344i
363363 −13.2433 2.63426i −0.695094 0.138263i
364364 0.227996 + 0.0453512i 0.0119502 + 0.00237705i
365365 −1.00959 + 26.7278i −0.0528441 + 1.39900i
366366 −3.20923 7.74777i −0.167749 0.404983i
367367 −9.32545 13.9565i −0.486785 0.728525i 0.504040 0.863681i 0.331847π-0.331847\pi
−0.990824 + 0.135156i 0.956847π0.956847\pi
368368 −0.145038 + 0.729154i −0.00756062 + 0.0380098i
369369 −2.04540 10.2829i −0.106479 0.535308i
370370 22.2456 + 10.2145i 1.15649 + 0.531027i
371371 2.55981 + 1.71041i 0.132898 + 0.0887999i
372372 1.54300 + 3.72513i 0.0800008 + 0.193139i
373373 −5.16638 5.16638i −0.267505 0.267505i 0.560589 0.828094i 0.310575π-0.310575\pi
−0.828094 + 0.560589i 0.810575π0.810575\pi
374374 −13.2618 + 14.0134i −0.685754 + 0.724616i
375375 3.82100 + 13.3163i 0.197316 + 0.687650i
376376 1.61568 3.90059i 0.0833222 0.201158i
377377 2.26468 0.450473i 0.116637 0.0232006i
378378 −3.93164 −0.202222
379379 −35.1483 + 6.99144i −1.80545 + 0.359126i −0.978996 0.203879i 0.934645π-0.934645\pi
−0.826453 + 0.563005i 0.809645π0.809645\pi
380380 −0.922789 0.668312i −0.0473381 0.0342837i
381381 −0.247200 + 1.24276i −0.0126644 + 0.0636685i
382382 −14.9858 6.20731i −0.766738 0.317593i
383383 −15.2856 6.33151i −0.781058 0.323525i −0.0437158 0.999044i 0.513920π-0.513920\pi
−0.737343 + 0.675519i 0.763920π0.763920\pi
384384 0.241738 1.21530i 0.0123361 0.0620179i
385385 −7.34303 + 1.17443i −0.374235 + 0.0598544i
386386 −0.0549621 + 0.0109326i −0.00279750 + 0.000556457i
387387 −0.492215 −0.0250207
388388 −9.66396 + 1.92228i −0.490613 + 0.0975890i
389389 7.18782 17.3529i 0.364437 0.879829i −0.630203 0.776430i 0.717028π-0.717028\pi
0.994640 0.103398i 0.0329717π-0.0329717\pi
390390 0.823613 + 0.378179i 0.0417053 + 0.0191498i
391391 −2.86318 1.09458i −0.144797 0.0553554i
392392 −4.59260 4.59260i −0.231961 0.231961i
393393 9.50125 + 22.9380i 0.479274 + 1.15707i
394394 3.08408 + 2.06071i 0.155373 + 0.103817i
395395 8.98191 19.5612i 0.451929 0.984229i
396396 −1.33706 6.72188i −0.0671900 0.337787i
397397 −1.60682 + 8.07804i −0.0806440 + 0.405425i 0.919286 + 0.393590i 0.128767π0.128767\pi
−0.999930 + 0.0118346i 0.996233π0.996233\pi
398398 −3.69094 5.52389i −0.185010 0.276887i
399399 −0.171717 0.414560i −0.00859658 0.0207540i
400400 4.46189 + 2.25644i 0.223094 + 0.112822i
401401 −7.93345 1.57806i −0.396178 0.0788046i −0.00701892 0.999975i 0.502234π-0.502234\pi
−0.389159 + 0.921171i 0.627234π0.627234\pi
402402 0.472324 + 0.0939510i 0.0235574 + 0.00468585i
403403 −0.591328 + 0.884984i −0.0294561 + 0.0440842i
404404 −10.2176 10.2176i −0.508343 0.508343i
405405 −5.35302 1.27657i −0.265994 0.0634334i
406406 4.63508 + 1.91991i 0.230035 + 0.0952837i
407407 −36.2226 + 36.2226i −1.79549 + 1.79549i
408408 4.77214 + 1.82437i 0.236256 + 0.0903197i
409409 6.01170i 0.297259i 0.988893 + 0.148630i 0.0474863π0.0474863\pi
−0.988893 + 0.148630i 0.952514π0.952514\pi
410410 −11.7377 + 10.8832i −0.579684 + 0.537485i
411411 12.3616 18.5004i 0.609751 0.912557i
412412 11.6216i 0.572553i
413413 −2.35459 1.57329i −0.115862 0.0774164i
414414 0.905345 0.604932i 0.0444953 0.0297308i
415415 22.7331 + 16.4640i 1.11592 + 0.808186i
416416 0.302195 0.125173i 0.0148163 0.00613713i
417417 −7.78616 + 18.7974i −0.381290 + 0.920515i
418418 1.98254 1.32469i 0.0969694 0.0647929i
419419 3.45852 + 5.17603i 0.168960 + 0.252866i 0.906280 0.422677i 0.138909π-0.138909\pi
−0.737321 + 0.675543i 0.763909π0.763909\pi
420420 1.03141 + 1.67740i 0.0503277 + 0.0818488i
421421 18.1423 18.1423i 0.884200 0.884200i −0.109759 0.993958i 0.535008π-0.535008\pi
0.993958 + 0.109759i 0.0350078π0.0350078\pi
422422 3.42608 + 17.2241i 0.166779 + 0.838455i
423423 −5.71285 + 2.36634i −0.277768 + 0.115055i
424424 4.33191 0.210376
425425 −12.2620 + 16.5724i −0.594795 + 0.803877i
426426 −19.4216 −0.940981
427427 4.44374 1.84066i 0.215048 0.0890757i
428428 −1.87491 9.42580i −0.0906271 0.455613i
429429 −1.34110 + 1.34110i −0.0647488 + 0.0647488i
430430 0.393617 + 0.640146i 0.0189819 + 0.0308706i
431431 20.5669 + 30.7805i 0.990671 + 1.48264i 0.871877 + 0.489725i 0.162903π0.162903\pi
0.118795 + 0.992919i 0.462097π0.462097\pi
432432 −4.59980 + 3.07349i −0.221308 + 0.147873i
433433 2.79464 6.74685i 0.134302 0.324233i −0.842394 0.538862i 0.818854π-0.818854\pi
0.976696 + 0.214629i 0.0688543π0.0688543\pi
434434 −2.13655 + 0.884988i −0.102558 + 0.0424808i
435435 15.8413 + 11.4727i 0.759531 + 0.550075i
436436 −3.97698 + 2.65733i −0.190463 + 0.127263i
437437 0.314974 + 0.210459i 0.0150672 + 0.0100676i
438438 14.8216i 0.708206i
439439 17.4852 26.1685i 0.834523 1.24895i −0.131711 0.991288i 0.542047π-0.542047\pi
0.966235 0.257664i 0.0829528π-0.0829528\pi
440440 −7.67285 + 7.11430i −0.365789 + 0.339161i
441441 9.51253i 0.452978i
442442 0.299440 + 1.31498i 0.0142429 + 0.0625472i
443443 11.7784 11.7784i 0.559607 0.559607i −0.369589 0.929195i 0.620501π-0.620501\pi
0.929195 + 0.369589i 0.120501π0.120501\pi
444444 12.5321 + 5.19099i 0.594749 + 0.246353i
445445 −1.15280 0.274916i −0.0546479 0.0130323i
446446 −7.37260 7.37260i −0.349103 0.349103i
447447 3.92029 5.86713i 0.185423 0.277506i
448448 0.697035 + 0.138649i 0.0329318 + 0.00655055i
449449 −15.7553 3.13392i −0.743537 0.147899i −0.191237 0.981544i 0.561250π-0.561250\pi
−0.552300 + 0.833645i 0.686250π0.686250\pi
450450 −2.28404 6.95776i −0.107671 0.327992i
451451 −12.8190 30.9478i −0.603623 1.45727i
452452 5.21569 + 7.80584i 0.245326 + 0.367156i
453453 2.58439 12.9926i 0.121425 0.610446i
454454 2.39499 + 12.0404i 0.112403 + 0.565086i
455455 −0.216905 + 0.472384i −0.0101687 + 0.0221457i
456456 −0.524974 0.350776i −0.0245842 0.0164266i
457457 3.23943 + 7.82067i 0.151534 + 0.365835i 0.981358 0.192190i 0.0615591π-0.0615591\pi
−0.829824 + 0.558026i 0.811559π0.811559\pi
458458 1.91052 + 1.91052i 0.0892727 + 0.0892727i
459459 −9.30598 20.8249i −0.434366 0.972022i
460460 −1.51073 0.693684i −0.0704382 0.0323432i
461461 12.8444 31.0091i 0.598223 1.44424i −0.277168 0.960822i 0.589396π-0.589396\pi
0.875391 0.483416i 0.160604π-0.160604\pi
462462 −4.04164 + 0.803933i −0.188034 + 0.0374023i
463463 5.72199 0.265924 0.132962 0.991121i 0.457551π-0.457551\pi
0.132962 + 0.991121i 0.457551π0.457551\pi
464464 6.92365 1.37720i 0.321422 0.0639349i
465465 −8.90279 + 1.42389i −0.412857 + 0.0660314i
466466 −3.81112 + 19.1598i −0.176547 + 0.887561i
467467 34.3166 + 14.2144i 1.58798 + 0.657764i 0.989652 0.143485i 0.0458310π-0.0458310\pi
0.598330 + 0.801249i 0.295831π0.295831\pi
468468 −0.442599 0.183330i −0.0204591 0.00847445i
469469 −0.0538857 + 0.270902i −0.00248821 + 0.0125091i
470470 7.64601 + 5.53747i 0.352684 + 0.255425i
471471 −19.5711 + 3.89292i −0.901787 + 0.179377i
472472 −3.98463 −0.183408
473473 −1.54241 + 0.306804i −0.0709201 + 0.0141069i
474474 4.56459 11.0199i 0.209658 0.506160i
475475 1.93228 1.66048i 0.0886592 0.0761879i
476476 −1.04637 + 2.73706i −0.0479602 + 0.125453i
477477 −4.48629 4.48629i −0.205413 0.205413i
478478 −9.71636 23.4574i −0.444416 1.07291i
479479 −16.0975 10.7560i −0.735513 0.491454i 0.130517 0.991446i 0.458336π-0.458336\pi
−0.866030 + 0.499992i 0.833336π0.833336\pi
480480 2.51797 + 1.15618i 0.114929 + 0.0527721i
481481 0.698569 + 3.51194i 0.0318520 + 0.160131i
482482 −1.56331 + 7.85931i −0.0712070 + 0.357982i
483483 −0.363726 0.544354i −0.0165501 0.0247690i
484484 −4.17017 10.0677i −0.189553 0.457621i
485485 0.831643 22.0169i 0.0377630 0.999737i
486486 13.2866 + 2.64286i 0.602691 + 0.119883i
487487 −1.95796 0.389463i −0.0887238 0.0176483i 0.150529 0.988606i 0.451902π-0.451902\pi
−0.239253 + 0.970957i 0.576902π0.576902\pi
488488 3.76003 5.62728i 0.170209 0.254735i
489489 19.2627 + 19.2627i 0.871090 + 0.871090i
490490 12.3714 7.60704i 0.558885 0.343651i
491491 18.8235 + 7.79693i 0.849491 + 0.351871i 0.764589 0.644519i 0.222942π-0.222942\pi
0.0849021 + 0.996389i 0.472942π0.472942\pi
492492 −6.27212 + 6.27212i −0.282769 + 0.282769i
493493 0.801699 + 29.0952i 0.0361067 + 1.31038i
494494 0.166669i 0.00749879i
495495 15.3141 + 0.578459i 0.688318 + 0.0259998i
496496 −1.80782 + 2.70560i −0.0811737 + 0.121485i
497497 11.1393i 0.499665i
498498 12.9329 + 8.64145i 0.579535 + 0.387233i
499499 12.9080 8.62482i 0.577840 0.386100i −0.232031 0.972708i 0.574537π-0.574537\pi
0.809871 + 0.586608i 0.199537π0.199537\pi
500500 −7.22234 + 8.53451i −0.322993 + 0.381675i
501501 18.9866 7.86450i 0.848258 0.351360i
502502 7.97566 19.2549i 0.355971 0.859390i
503503 35.9136 23.9967i 1.60131 1.06996i 0.650808 0.759242i 0.274430π-0.274430\pi
0.950502 0.310719i 0.100570π-0.100570\pi
504504 −0.578286 0.865466i −0.0257589 0.0385509i
505505 27.5239 16.9241i 1.22480 0.753111i
506506 2.45994 2.45994i 0.109358 0.109358i
507507 −3.11673 15.6689i −0.138419 0.695878i
508508 −0.944755 + 0.391330i −0.0419167 + 0.0173625i
509509 35.6718 1.58113 0.790563 0.612381i 0.209788π-0.209788\pi
0.790563 + 0.612381i 0.209788π0.209788\pi
510510 −6.44347 + 9.43344i −0.285321 + 0.417720i
511511 −8.50097 −0.376061
512512 0.923880 0.382683i 0.0408301 0.0169124i
513513 0.549934 + 2.76471i 0.0242802 + 0.122065i
514514 6.02587 6.02587i 0.265790 0.265790i
515515 25.2777 + 6.02816i 1.11387 + 0.265633i
516516 0.231356 + 0.346248i 0.0101849 + 0.0152427i
517517 −16.4269 + 10.9761i −0.722454 + 0.482728i
518518 −2.97729 + 7.18782i −0.130815 + 0.315815i
519519 9.81200 4.06426i 0.430699 0.178401i
520520 0.115511 + 0.722225i 0.00506549 + 0.0316717i
521521 6.25857 4.18185i 0.274193 0.183210i −0.410870 0.911694i 0.634775π-0.634775\pi
0.685063 + 0.728484i 0.259775π0.259775\pi
522522 −8.59667 5.74411i −0.376266 0.251413i
523523 17.7492i 0.776116i −0.921635 0.388058i 0.873146π-0.873146\pi
0.921635 0.388058i 0.126854π-0.126854\pi
524524 −11.1319 + 16.6601i −0.486301 + 0.727801i
525525 −4.18347 + 1.37332i −0.182582 + 0.0599366i
526526 22.1386i 0.965289i
527527 −9.74465 9.22204i −0.424484 0.401718i
528528 −4.10004 + 4.10004i −0.178431 + 0.178431i
529529 −20.7386 8.59021i −0.901678 0.373487i
530530 −2.24699 + 9.42223i −0.0976028 + 0.409275i
531531 4.12663 + 4.12663i 0.179081 + 0.179081i
532532 0.201188 0.301099i 0.00872261 0.0130543i
533533 −2.29650 0.456802i −0.0994725 0.0197863i
534534 −0.644114 0.128122i −0.0278735 0.00554439i
535535 21.4743 + 0.811148i 0.928416 + 0.0350690i
536536 0.148729 + 0.359064i 0.00642412 + 0.0155092i
537537 14.0671 + 21.0529i 0.607039 + 0.908499i
538538 −4.64099 + 23.3318i −0.200087 + 1.00591i
539539 5.92930 + 29.8086i 0.255393 + 1.28395i
540540 −4.29912 11.5991i −0.185005 0.499148i
541541 8.89263 + 5.94187i 0.382324 + 0.255461i 0.731850 0.681466i 0.238657π-0.238657\pi
−0.349526 + 0.936927i 0.613657π0.613657\pi
542542 −7.96714 19.2344i −0.342218 0.826187i
543543 −3.77619 3.77619i −0.162052 0.162052i
544544 0.915457 + 4.02019i 0.0392499 + 0.172364i
545545 −3.71701 10.0286i −0.159219 0.429578i
546546 −0.110231 + 0.266120i −0.00471743 + 0.0113889i
547547 −13.3586 + 2.65720i −0.571174 + 0.113614i −0.472224 0.881479i 0.656548π-0.656548\pi
−0.0989503 + 0.995092i 0.531548π0.531548\pi
548548 17.9567 0.767071
549549 −9.72185 + 1.93380i −0.414918 + 0.0825324i
550550 −11.4942 20.3792i −0.490113 0.868974i
551551 0.701745 3.52791i 0.0298953 0.150294i
552552 −0.851079 0.352528i −0.0362243 0.0150046i
553553 6.32046 + 2.61802i 0.268773 + 0.111330i
554554 −0.781467 + 3.92870i −0.0332013 + 0.166914i
555555 −17.7913 + 24.5658i −0.755197 + 1.04276i
556556 −16.1045 + 3.20339i −0.682985 + 0.135854i
557557 −1.23472 −0.0523168 −0.0261584 0.999658i 0.508327π-0.508327\pi
−0.0261584 + 0.999658i 0.508327π0.508327\pi
558558 4.67427 0.929769i 0.197877 0.0393603i
559559 −0.0420672 + 0.101559i −0.00177925 + 0.00429550i
560560 −0.663128 + 1.44419i −0.0280223 + 0.0610280i
561561 −13.8246 19.5047i −0.583674 0.823488i
562562 −10.2732 10.2732i −0.433348 0.433348i
563563 8.16721 + 19.7174i 0.344207 + 0.830989i 0.997281 + 0.0736946i 0.0234790π0.0234790\pi
−0.653074 + 0.757294i 0.726521π0.726521\pi
564564 4.34981 + 2.90645i 0.183160 + 0.122384i
565565 −19.6837 + 7.29559i −0.828099 + 0.306928i
566566 −2.47657 12.4506i −0.104098 0.523337i
567567 0.341226 1.71546i 0.0143301 0.0720424i
568568 −8.70794 13.0324i −0.365377 0.546826i
569569 12.6066 + 30.4351i 0.528498 + 1.27591i 0.932507 + 0.361152i 0.117616π0.117616\pi
−0.404009 + 0.914755i 0.632384π0.632384\pi
570570 1.03527 0.959908i 0.0433628 0.0402061i
571571 42.1343 + 8.38102i 1.76326 + 0.350735i 0.967110 0.254359i 0.0818646π-0.0818646\pi
0.796154 + 0.605094i 0.206865π0.206865\pi
572572 −1.50121 0.298608i −0.0627685 0.0124854i
573573 11.1664 16.7116i 0.466481 0.698138i
574574 −3.59738 3.59738i −0.150152 0.150152i
575575 2.29244 2.92614i 0.0956013 0.122028i
576576 −1.35312 0.560483i −0.0563802 0.0233534i
577577 −32.4025 + 32.4025i −1.34893 + 1.34893i −0.462109 + 0.886823i 0.652907π0.652907\pi
−0.886823 + 0.462109i 0.847093π0.847093\pi
578578 −16.9742 + 0.936137i −0.706034 + 0.0389382i
579579 0.0694382i 0.00288575i
580580 −0.595822 + 15.7738i −0.0247402 + 0.654972i
581581 −4.95631 + 7.41765i −0.205622 + 0.307736i
582582 12.2093i 0.506091i
583583 −16.8547 11.2619i −0.698049 0.466421i
584584 −9.94566 + 6.64548i −0.411554 + 0.274992i
585585 0.628335 0.867590i 0.0259785 0.0358704i
586586 7.70535 3.19166i 0.318305 0.131846i
587587 5.23957 12.6495i 0.216260 0.522099i −0.778101 0.628139i 0.783817π-0.783817\pi
0.994362 + 0.106040i 0.0338171π0.0338171\pi
588588 6.69159 4.47118i 0.275956 0.184388i
589589 0.921167 + 1.37862i 0.0379560 + 0.0568052i
590590 2.06685 8.66687i 0.0850908 0.356809i
591591 −3.24992 + 3.24992i −0.133684 + 0.133684i
592592 2.13568 + 10.7368i 0.0877760 + 0.441280i
593593 9.66064 4.00157i 0.396715 0.164325i −0.175402 0.984497i 0.556122π-0.556122\pi
0.572117 + 0.820172i 0.306122π0.306122\pi
594594 25.8873 1.06217
595595 −5.41055 3.69565i −0.221811 0.151507i
596596 5.69469 0.233264
597597 7.60541 3.15026i 0.311269 0.128932i
598598 −0.0474409 0.238502i −0.00194000 0.00975306i
599599 −9.67035 + 9.67035i −0.395120 + 0.395120i −0.876508 0.481388i 0.840133π-0.840133\pi
0.481388 + 0.876508i 0.340133π0.340133\pi
600600 −3.82086 + 4.87706i −0.155986 + 0.199105i
601601 9.25488 + 13.8509i 0.377514 + 0.564990i 0.970766 0.240027i 0.0771562π-0.0771562\pi
−0.593252 + 0.805017i 0.702156π0.702156\pi
602602 −0.198591 + 0.132694i −0.00809396 + 0.00540821i
603603 0.217831 0.525890i 0.00887075 0.0214159i
604604 9.87709 4.09122i 0.401893 0.166470i
605605 24.0610 3.84826i 0.978219 0.156454i
606606 14.8874 9.94742i 0.604758 0.404086i
607607 −8.81933 5.89289i −0.357966 0.239185i 0.363563 0.931570i 0.381560π-0.381560\pi
−0.721529 + 0.692385i 0.756560π0.756560\pi
608608 0.509545i 0.0206648i
609609 −3.45374 + 5.16889i −0.139953 + 0.209454i
610610 10.2894 + 11.0972i 0.416606 + 0.449314i
611611 1.38098i 0.0558685i
612612 3.21538 5.11154i 0.129974 0.206622i
613613 −29.6325 + 29.6325i −1.19685 + 1.19685i −0.221742 + 0.975105i 0.571174π0.571174\pi
−0.975105 + 0.221742i 0.928826π0.928826\pi
614614 −0.116489 0.0482515i −0.00470113 0.00194727i
615615 −10.3889 16.8957i −0.418923 0.681301i
616616 −2.35158 2.35158i −0.0947479 0.0947479i
617617 21.3342 31.9289i 0.858882 1.28541i −0.0980747 0.995179i 0.531268π-0.531268\pi
0.956957 0.290229i 0.0937316π-0.0937316\pi
618618 14.1237 + 2.80937i 0.568137 + 0.113009i
619619 −2.57153 0.511509i −0.103358 0.0205593i 0.143140 0.989702i 0.454280π-0.454280\pi
−0.246499 + 0.969143i 0.579280π0.579280\pi
620620 −4.94715 5.33556i −0.198682 0.214281i
621621 1.57390 + 3.79974i 0.0631585 + 0.152478i
622622 5.31755 + 7.95827i 0.213214 + 0.319098i
623623 0.0734846 0.369432i 0.00294410 0.0148010i
624624 0.0790710 + 0.397517i 0.00316537 + 0.0159134i
625625 −14.8169 20.1360i −0.592677 0.805440i
626626 −14.4669 9.66650i −0.578215 0.386351i
627627 1.13064 + 2.72961i 0.0451535 + 0.109010i
628628 −11.3872 11.3872i −0.454398 0.454398i
629629 −45.1191 + 1.24323i −1.79902 + 0.0495708i
630630 2.18241 0.808892i 0.0869493 0.0322270i
631631 −3.04583 + 7.35329i −0.121253 + 0.292730i −0.972838 0.231486i 0.925641π-0.925641\pi
0.851586 + 0.524216i 0.175641π0.175641\pi
632632 9.44119 1.87797i 0.375550 0.0747016i
633633 −21.7606 −0.864907
634634 −19.6461 + 3.90786i −0.780247 + 0.155201i
635635 −0.361123 2.25790i −0.0143307 0.0896019i
636636 −1.04719 + 5.26457i −0.0415237 + 0.208754i
637637 1.96273 + 0.812991i 0.0777663 + 0.0322119i
638638 −30.5190 12.6414i −1.20826 0.500477i
639639 −4.47852 + 22.5151i −0.177168 + 0.890682i
640640 0.353144 + 2.20801i 0.0139592 + 0.0872791i
641641 −20.1899 + 4.01602i −0.797453 + 0.158623i −0.576968 0.816767i 0.695764π-0.695764\pi
−0.220485 + 0.975390i 0.570764π0.570764\pi
642642 11.9084 0.469987
643643 −29.8237 + 5.93231i −1.17613 + 0.233947i −0.744199 0.667958i 0.767169π-0.767169\pi
−0.431934 + 0.901905i 0.642169π0.642169\pi
644644 0.202193 0.488137i 0.00796752 0.0192353i
645645 −0.873120 + 0.323615i −0.0343791 + 0.0127423i
646646 2.07105 + 0.352956i 0.0814842 + 0.0138869i
647647 −34.7745 34.7745i −1.36712 1.36712i −0.864511 0.502614i 0.832372π-0.832372\pi
−0.502614 0.864511i 0.667628π-0.667628\pi
648648 −0.941813 2.27374i −0.0369979 0.0893209i
649649 15.5035 + 10.3591i 0.608564 + 0.406629i
650650 −1.63081 0.123377i −0.0639656 0.00483923i
651651 −0.559040 2.81048i −0.0219105 0.110151i
652652 −4.28903 + 21.5624i −0.167971 + 0.844449i
653653 3.53808 + 5.29511i 0.138456 + 0.207214i 0.894217 0.447633i 0.147733π-0.147733\pi
−0.755761 + 0.654847i 0.772733π0.772733\pi
654654 −2.26806 5.47559i −0.0886884 0.214113i
655655 −30.4628 32.8545i −1.19028 1.28373i
656656 −7.02092 1.39655i −0.274121 0.0545261i
657657 17.1824 + 3.41779i 0.670349 + 0.133341i
658658 −1.66700 + 2.49484i −0.0649863 + 0.0972589i
659659 −19.7490 19.7490i −0.769313 0.769313i 0.208672 0.977986i 0.433086π-0.433086\pi
−0.977986 + 0.208672i 0.933086π0.933086\pi
660660 −6.79118 11.0446i −0.264346 0.429910i
661661 −2.39578 0.992363i −0.0931849 0.0385984i 0.335604 0.942003i 0.391060π-0.391060\pi
−0.428789 + 0.903405i 0.641060π0.641060\pi
662662 −10.2301 + 10.2301i −0.397602 + 0.397602i
663663 −1.67048 + 0.0460290i −0.0648760 + 0.00178762i
664664 12.5527i 0.487141i
665665 0.550556 + 0.593781i 0.0213496 + 0.0230258i
666666 8.90764 13.3312i 0.345164 0.516575i
667667 5.24815i 0.203209i
668668 13.7901 + 9.21428i 0.533557 + 0.356511i
669669 10.7421 7.17767i 0.415315 0.277505i
670670 −0.858138 + 0.137249i −0.0331527 + 0.00530238i
671671 −29.2592 + 12.1195i −1.12954 + 0.467870i
672672 −0.337000 + 0.813590i −0.0130000 + 0.0313849i
673673 −9.14587 + 6.11108i −0.352548 + 0.235565i −0.719215 0.694787i 0.755499π-0.755499\pi
0.366668 + 0.930352i 0.380499π0.380499\pi
674674 −4.48644 6.71443i −0.172811 0.258630i
675675 27.4590 3.33438i 1.05690 0.128340i
676676 9.11673 9.11673i 0.350644 0.350644i
677677 −1.15687 5.81600i −0.0444623 0.223527i 0.952165 0.305583i 0.0988514π-0.0988514\pi
−0.996628 + 0.0820560i 0.973851π0.973851\pi
678678 −10.7473 + 4.45166i −0.412746 + 0.170965i
679679 7.00265 0.268737
680680 −9.21906 0.0941074i −0.353535 0.00360885i
681681 −15.2117 −0.582913
682682 14.0678 5.82707i 0.538684 0.223130i
683683 4.12555 + 20.7405i 0.157860 + 0.793615i 0.975860 + 0.218397i 0.0700828π0.0700828\pi
−0.818000 + 0.575218i 0.804917π0.804917\pi
684684 −0.527704 + 0.527704i −0.0201772 + 0.0201772i
685685 −9.31421 + 39.0571i −0.355878 + 1.49229i
686686 5.32832 + 7.97439i 0.203436 + 0.304464i
687687 −2.78370 + 1.86001i −0.106205 + 0.0709637i
688688 −0.128609 + 0.310490i −0.00490317 + 0.0118373i
689689 −1.30908 + 0.542240i −0.0498721 + 0.0206577i
690690 1.20823 1.66830i 0.0459967 0.0635111i
691691 −11.6317 + 7.77206i −0.442491 + 0.295663i −0.756787 0.653662i 0.773232π-0.773232\pi
0.314295 + 0.949325i 0.398232π0.398232\pi
692692 7.12656 + 4.76181i 0.270911 + 0.181017i
693693 4.87077i 0.185025i
694694 9.49472 14.2098i 0.360415 0.539398i
695695 1.38589 36.6902i 0.0525700 1.39174i
696696 8.74722i 0.331563i
697697 10.5396 27.5692i 0.399215 1.04426i
698698 −18.4982 + 18.4982i −0.700167 + 0.700167i
699699 −22.3636 9.26330i −0.845868 0.350370i
700700 −2.79724 2.19146i −0.105726 0.0828293i
701701 −29.0853 29.0853i −1.09853 1.09853i −0.994582 0.103953i 0.966851π-0.966851\pi
−0.103953 0.994582i 0.533149π-0.533149\pi
702702 1.00532 1.50457i 0.0379433 0.0567862i
703703 5.47088 + 1.08823i 0.206338 + 0.0410432i
704704 −4.58953 0.912914i −0.172974 0.0344067i
705705 −8.57802 + 7.95357i −0.323067 + 0.299549i
706706 13.0306 + 31.4587i 0.490414 + 1.18397i
707707 5.70535 + 8.53866i 0.214572 + 0.321129i
708708 0.963237 4.84252i 0.0362006 0.181993i
709709 5.86964 + 29.5087i 0.220439 + 1.10822i 0.919479 + 0.393139i 0.128611π0.128611\pi
−0.699040 + 0.715082i 0.746389π0.746389\pi
710710 32.8632 12.1805i 1.23333 0.457125i
711711 −11.7225 7.83275i −0.439629 0.293751i
712712 −0.202824 0.489660i −0.00760115 0.0183508i
713713 1.71060 + 1.71060i 0.0640623 + 0.0640623i
714714 −3.07340 1.93330i −0.115019 0.0723520i
715715 1.42818 3.11034i 0.0534108 0.116320i
716716 −7.81980 + 18.8787i −0.292240 + 0.705529i
717717 30.8565 6.13774i 1.15236 0.229218i
718718 −1.96156 −0.0732047
719719 42.2633 8.40669i 1.57616 0.313517i 0.671944 0.740602i 0.265460π-0.265460\pi
0.904211 + 0.427085i 0.140460π0.140460\pi
720720 1.92096 2.65242i 0.0715901 0.0988499i
721721 −1.61132 + 8.10064i −0.0600086 + 0.301683i
722722 17.3138 + 7.17163i 0.644354 + 0.266900i
723723 −9.17350 3.79979i −0.341166 0.141316i
724724 0.840805 4.22701i 0.0312483 0.157096i
725725 −34.0001 9.47791i −1.26273 0.352001i
726726 13.2433 2.63426i 0.491505 0.0977665i
727727 22.7691 0.844459 0.422230 0.906489i 0.361248π-0.361248\pi
0.422230 + 0.906489i 0.361248π0.361248\pi
728728 −0.227996 + 0.0453512i −0.00845009 + 0.00168083i
729729 −9.24917 + 22.3295i −0.342562 + 0.827018i
730730 −9.29554 25.0796i −0.344043 0.928237i
731731 −1.17290 0.737804i −0.0433813 0.0272887i
732732 5.92989 + 5.92989i 0.219175 + 0.219175i
733733 2.78355 + 6.72010i 0.102813 + 0.248212i 0.966912 0.255109i 0.0821113π-0.0821113\pi
−0.864099 + 0.503321i 0.832111π0.832111\pi
734734 13.9565 + 9.32545i 0.515145 + 0.344209i
735735 6.25418 + 16.8739i 0.230689 + 0.622404i
736736 −0.145038 0.729154i −0.00534616 0.0268770i
737737 0.354802 1.78371i 0.0130693 0.0657039i
738738 5.82481 + 8.71745i 0.214414 + 0.320894i
739739 −19.3452 46.7035i −0.711626 1.71802i −0.695898 0.718140i 0.744994π-0.744994\pi
−0.0157273 0.999876i 0.505006π-0.505006\pi
740740 −24.4611 0.923968i −0.899209 0.0339657i
741741 0.202553 + 0.0402902i 0.00744095 + 0.00148010i
742742 −3.01950 0.600615i −0.110849 0.0220493i
743743 −13.1834 + 19.7303i −0.483651 + 0.723835i −0.990396 0.138261i 0.955849π-0.955849\pi
0.506745 + 0.862096i 0.330849π0.330849\pi
744744 −2.85109 2.85109i −0.104526 0.104526i
745745 −2.95386 + 12.3864i −0.108221 + 0.453801i
746746 6.75020 + 2.79603i 0.247143 + 0.102370i
747747 13.0001 13.0001i 0.475648 0.475648i
748748 6.88965 18.0218i 0.251911 0.658942i
749749 6.83007i 0.249565i
750750 −8.62607 10.8404i −0.314979 0.395836i
751751 15.9309 23.8422i 0.581326 0.870016i −0.417934 0.908477i 0.637246π-0.637246\pi
0.999260 + 0.0384614i 0.0122457π0.0122457\pi
752752 4.22197i 0.153959i
753753 21.4725 + 14.3475i 0.782501 + 0.522850i
754754 −1.91990 + 1.28284i −0.0699188 + 0.0467183i
755755 3.77542 + 23.6055i 0.137401 + 0.859093i
756756 3.63236 1.50457i 0.132108 0.0547208i
757757 −4.12913 + 9.96860i −0.150076 + 0.362315i −0.980982 0.194097i 0.937822π-0.937822\pi
0.830907 + 0.556412i 0.187822π0.187822\pi
758758 29.7973 19.9099i 1.08229 0.723162i
759759 2.39490 + 3.58422i 0.0869294 + 0.130099i
760760 1.10830 + 0.264304i 0.0402022 + 0.00958730i
761761 16.8074 16.8074i 0.609267 0.609267i −0.333487 0.942755i 0.608225π-0.608225\pi
0.942755 + 0.333487i 0.108225π0.108225\pi
762762 −0.247200 1.24276i −0.00895511 0.0450204i
763763 3.14053 1.30085i 0.113695 0.0470939i
764764 16.2205 0.586836
765765 9.45014 + 9.64507i 0.341671 + 0.348718i
766766 16.5450 0.597796
767767 1.20414 0.498770i 0.0434788 0.0180095i
768768 0.241738 + 1.21530i 0.00872297 + 0.0438533i
769769 −11.7131 + 11.7131i −0.422384 + 0.422384i −0.886024 0.463640i 0.846543π-0.846543\pi
0.463640 + 0.886024i 0.346543π0.346543\pi
770770 6.33464 3.89508i 0.228285 0.140369i
771771 5.86655 + 8.77991i 0.211279 + 0.316201i
772772 0.0465946 0.0311335i 0.00167698 0.00112052i
773773 −8.01916 + 19.3600i −0.288429 + 0.696329i −0.999980 0.00630500i 0.997993π-0.997993\pi
0.711551 + 0.702634i 0.247993π0.247993\pi
774774 0.454747 0.188362i 0.0163455 0.00677054i
775775 14.1713 7.99283i 0.509050 0.287111i
776776 8.19271 5.47419i 0.294101 0.196512i
777777 −8.01563 5.35587i −0.287559 0.192141i
778778 18.7827i 0.673392i
779779 −2.02648 + 3.03284i −0.0726061 + 0.108663i
780780 −0.905642 0.0342087i −0.0324272 0.00122487i
781781 73.3450i 2.62449i
782782 3.06411 0.0844297i 0.109573 0.00301920i
783783 27.6146 27.6146i 0.986866 0.986866i
784784 6.00052 + 2.48550i 0.214304 + 0.0887678i
785785 30.6745 18.8614i 1.09482 0.673191i
786786 −17.5560 17.5560i −0.626202 0.626202i
787787 −7.31354 + 10.9455i −0.260700 + 0.390164i −0.938610 0.344980i 0.887886π-0.887886\pi
0.677910 + 0.735144i 0.262886π0.262886\pi
788788 −3.63792 0.723626i −0.129595 0.0257781i
789789 −26.9050 5.35174i −0.957844 0.190527i
790790 −0.812472 + 21.5094i −0.0289065 + 0.765270i
791791 −2.55325 6.16410i −0.0907832 0.219170i
792792 3.80764 + 5.69853i 0.135298 + 0.202488i
793793 −0.431877 + 2.17119i −0.0153364 + 0.0771013i
794794 −1.60682 8.07804i −0.0570240 0.286679i
795795 −10.9076 5.00847i −0.386854 0.177632i
796796 5.52389 + 3.69094i 0.195789 + 0.130822i
797797 −6.38819 15.4224i −0.226281 0.546291i 0.769438 0.638722i 0.220536π-0.220536\pi
−0.995719 + 0.0924305i 0.970536π0.970536\pi
798798 0.317291 + 0.317291i 0.0112320 + 0.0112320i
799799 −17.1602 2.92451i −0.607084 0.103462i
800800 −4.98575 0.377191i −0.176273 0.0133357i
801801 −0.297058 + 0.717163i −0.0104960 + 0.0253397i
802802 7.93345 1.57806i 0.280140 0.0557233i
803803 55.9734 1.97526
804804 −0.472324 + 0.0939510i −0.0166576 + 0.00331340i
805805 0.956855 + 0.692984i 0.0337247 + 0.0244245i
806806 0.207647 1.04391i 0.00731404 0.0367702i
807807 −27.2332 11.2804i −0.958655 0.397088i
808808 13.3499 + 5.52971i 0.469648 + 0.194534i
809809 1.40383 7.05754i 0.0493561 0.248130i −0.948229 0.317588i 0.897127π-0.897127\pi
0.997585 + 0.0694582i 0.0221271π0.0221271\pi
810810 5.43407 0.869113i 0.190934 0.0305375i
811811 −10.1395 + 2.01688i −0.356048 + 0.0708223i −0.369873 0.929082i 0.620599π-0.620599\pi
0.0138259 + 0.999904i 0.495599π0.495599\pi
812812 −5.01698 −0.176061
813813 25.3015 5.03278i 0.887362 0.176507i
814814 19.6036 47.3272i 0.687104 1.65882i
815815 −44.6751 20.5135i −1.56490 0.718556i
816816 −5.10703 + 0.140721i −0.178782 + 0.00492622i
817817 0.121087 + 0.121087i 0.00423632 + 0.00423632i
818818 −2.30058 5.55409i −0.0804378 0.194194i
819819 0.283088 + 0.189154i 0.00989191 + 0.00660956i
820820 6.67939 14.5466i 0.233254 0.507990i
821821 7.89804 + 39.7061i 0.275643 + 1.38575i 0.831984 + 0.554799i 0.187205π0.187205\pi
−0.556341 + 0.830954i 0.687795π0.687795\pi
822822 −4.34081 + 21.8227i −0.151403 + 0.761154i
823823 22.4842 + 33.6500i 0.783751 + 1.17297i 0.981264 + 0.192666i 0.0617133π0.0617133\pi
−0.197514 + 0.980300i 0.563287π0.563287\pi
824824 4.44738 + 10.7369i 0.154932 + 0.374038i
825825 27.5454 9.04242i 0.959009 0.314817i
826826 2.77743 + 0.552465i 0.0966391 + 0.0192227i
827827 44.2399 + 8.79987i 1.53837 + 0.306001i 0.890228 0.455515i 0.150545π-0.150545\pi
0.648145 + 0.761517i 0.275545π0.275545\pi
828828 −0.604932 + 0.905345i −0.0210229 + 0.0314629i
829829 3.20565 + 3.20565i 0.111337 + 0.111337i 0.760580 0.649244i 0.224914π-0.224914\pi
−0.649244 + 0.760580i 0.724914π0.724914\pi
830830 −27.3031 6.51117i −0.947706 0.226006i
831831 −4.58563 1.89943i −0.159074 0.0658905i
832832 −0.231290 + 0.231290i −0.00801854 + 0.00801854i
833833 −14.2588 + 22.6675i −0.494038 + 0.785381i
834834 20.3462i 0.704531i
835835 −27.1948 + 25.2151i −0.941113 + 0.872604i
836836 −1.32469 + 1.98254i −0.0458155 + 0.0685677i
837837 18.0015i 0.622224i
838838 −5.17603 3.45852i −0.178803 0.119472i
839839 5.29222 3.53615i 0.182708 0.122081i −0.460853 0.887477i 0.652456π-0.652456\pi
0.643561 + 0.765395i 0.277456π0.277456\pi
840840 −1.59481 1.15501i −0.0550263 0.0398517i
841841 −19.2477 + 7.97267i −0.663715 + 0.274920i
842842 −9.81852 + 23.7040i −0.338369 + 0.816894i
843843 14.9684 10.0016i 0.515539 0.344472i
844844 −9.75666 14.6019i −0.335838 0.502617i
845845 15.1007 + 24.5585i 0.519479 + 0.844837i
846846 4.37243 4.37243i 0.150327 0.150327i
847847 1.51088 + 7.59571i 0.0519145 + 0.260992i
848848 −4.00217 + 1.65775i −0.137435 + 0.0569274i
849849 15.7299 0.539847
850850 4.98667 20.0033i 0.171041 0.686109i
851851 8.13854 0.278986
852852 17.9432 7.43234i 0.614726 0.254628i
853853 −4.89959 24.6319i −0.167759 0.843381i −0.969383 0.245553i 0.921031π-0.921031\pi
0.801624 0.597828i 0.203969π-0.203969\pi
854854 −3.40109 + 3.40109i −0.116383 + 0.116383i
855855 −0.874071 1.42152i −0.0298926 0.0486148i
856856 5.33929 + 7.99081i 0.182493 + 0.273120i
857857 29.5811 19.7655i 1.01047 0.675175i 0.0639953 0.997950i 0.479616π-0.479616\pi
0.946476 + 0.322775i 0.104616π0.104616\pi
858858 0.725797 1.75223i 0.0247783 0.0598201i
859859 −21.0814 + 8.73222i −0.719289 + 0.297939i −0.712142 0.702035i 0.752275π-0.752275\pi
−0.00714690 + 0.999974i 0.502275π0.502275\pi
860860 −0.608628 0.440787i −0.0207540 0.0150307i
861861 5.24151 3.50227i 0.178630 0.119357i
862862 −30.7805 20.5669i −1.04839 0.700510i
863863 25.2963i 0.861095i −0.902568 0.430548i 0.858320π-0.858320\pi
0.902568 0.430548i 0.141680π-0.141680\pi
864864 3.07349 4.59980i 0.104562 0.156488i
865865 −14.0539 + 13.0308i −0.477846 + 0.443061i
866866 7.30274i 0.248157i
867867 2.96562 20.8550i 0.100718 0.708274i
868868 1.63525 1.63525i 0.0555038 0.0555038i
869869 −41.6162 17.2380i −1.41173 0.584758i
870870 −19.0259 4.53723i −0.645037 0.153826i
871871 −0.0898905 0.0898905i −0.00304582 0.00304582i
872872 2.65733 3.97698i 0.0899886 0.134677i
873873 −14.1540 2.81540i −0.479039 0.0952867i
874874 −0.371537 0.0739032i −0.0125674 0.00249981i
875875 6.21753 4.94749i 0.210191 0.167256i
876876 −5.67200 13.6934i −0.191639 0.462658i
877877 7.20665 + 10.7855i 0.243351 + 0.364201i 0.932959 0.359982i 0.117217π-0.117217\pi
−0.689608 + 0.724183i 0.742217π0.742217\pi
878878 −6.13999 + 30.8678i −0.207214 + 1.04174i
879879 2.01615 + 10.1358i 0.0680029 + 0.341874i
880880 4.36627 9.50903i 0.147187 0.320549i
881881 11.7274 + 7.83599i 0.395106 + 0.264001i 0.737214 0.675659i 0.236141π-0.236141\pi
−0.342108 + 0.939661i 0.611141π0.611141\pi
882882 −3.64029 8.78844i −0.122575 0.295922i
883883 2.99147 + 2.99147i 0.100671 + 0.100671i 0.755648 0.654977i 0.227322π-0.227322\pi
−0.654977 + 0.755648i 0.727322π0.727322\pi
884884 −0.779867 1.10029i −0.0262298 0.0370068i
885885 10.0332 + 4.60695i 0.337262 + 0.154861i
886886 −6.37440 + 15.3892i −0.214152 + 0.517009i
887887 39.1177 7.78099i 1.31344 0.261260i 0.511822 0.859092i 0.328971π-0.328971\pi
0.801622 + 0.597831i 0.203971π0.203971\pi
888888 −13.5647 −0.455202
889889 0.712785 0.141782i 0.0239060 0.00475521i
890890 1.17025 0.187168i 0.0392270 0.00627388i
891891 −2.24675 + 11.2952i −0.0752690 + 0.378403i
892892 9.63276 + 3.99002i 0.322529 + 0.133596i
893893 1.98753 + 0.823260i 0.0665100 + 0.0275494i
894894 −1.37662 + 6.92075i −0.0460411 + 0.231464i
895895 −37.0063 26.8011i −1.23698 0.895862i
896896 −0.697035 + 0.138649i −0.0232863 + 0.00463194i
897897 0.301319 0.0100608
898898 15.7553 3.13392i 0.525760 0.104580i
899899 8.79058 21.2223i 0.293182 0.707805i
900900 4.77280 + 5.55406i 0.159093 + 0.185135i
901901 −3.96568 17.4151i −0.132116 0.580182i
902902 23.6864 + 23.6864i 0.788671 + 0.788671i
903903 −0.113256 0.273424i −0.00376893 0.00909899i
904904 −7.80584 5.21569i −0.259618 0.173471i
905905 8.75794 + 4.02139i 0.291124 + 0.133675i
906906 2.58439 + 12.9926i 0.0858607 + 0.431651i
907907 −0.756884 + 3.80511i −0.0251319 + 0.126347i −0.991315 0.131512i 0.958017π-0.958017\pi
0.966183 + 0.257859i 0.0830169π0.0830169\pi
908908 −6.82036 10.2074i −0.226342 0.338744i
909909 −8.09888 19.5524i −0.268623 0.648513i
910910 0.0196204 0.519432i 0.000650411 0.0172190i
911911 −21.2127 4.21946i −0.702807 0.139797i −0.169265 0.985571i 0.554139π-0.554139\pi
−0.533542 + 0.845773i 0.679139π0.679139\pi
912912 0.619249 + 0.123176i 0.0205054 + 0.00407878i
913913 32.6341 48.8404i 1.08003 1.61638i
914914 −5.98568 5.98568i −0.197989 0.197989i
915915 −15.9738 + 9.82208i −0.528078 + 0.324708i
916916 −2.49621 1.03397i −0.0824772 0.0341632i
917917 10.0693 10.0693i 0.332516 0.332516i
918918 16.5669 + 15.6784i 0.546790 + 0.517466i
919919 21.0567i 0.694597i 0.937755 + 0.347298i 0.112901π0.112901\pi
−0.937755 + 0.347298i 0.887099π0.887099\pi
920920 1.66120 + 0.0627482i 0.0547680 + 0.00206875i
921921 0.0867999 0.129905i 0.00286015 0.00428052i
922922 33.5640i 1.10537i
923923 4.26280 + 2.84831i 0.140312 + 0.0937534i
924924 3.42634 2.28941i 0.112718 0.0753159i
925925 14.6978 52.7255i 0.483261 1.73360i
926926 −5.28643 + 2.18971i −0.173723 + 0.0719584i
927927 6.51368 15.7254i 0.213937 0.516491i
928928 −5.86959 + 3.92193i −0.192679 + 0.128744i
929929 −15.1360 22.6526i −0.496595 0.743207i 0.495512 0.868601i 0.334980π-0.334980\pi
−0.992107 + 0.125394i 0.959980π0.959980\pi
930930 7.68021 4.72246i 0.251844 0.154855i
931931 2.34014 2.34014i 0.0766949 0.0766949i
932932 −3.81112 19.1598i −0.124837 0.627600i
933933 −10.9571 + 4.53859i −0.358720 + 0.148587i
934934 −37.1440 −1.21539
935935 35.6250 + 24.3335i 1.16506 + 0.795790i
936936 0.479065 0.0156587
937937 −15.7890 + 6.54003i −0.515805 + 0.213653i −0.625373 0.780326i 0.715053π-0.715053\pi
0.109568 + 0.993979i 0.465053π0.465053\pi
938938 −0.0538857 0.270902i −0.00175943 0.00884525i
939939 15.2449 15.2449i 0.497498 0.497498i
940940 −9.18309 2.18996i −0.299519 0.0714285i
941941 −3.01100 4.50628i −0.0981558 0.146900i 0.779141 0.626849i 0.215656π-0.215656\pi
−0.877297 + 0.479948i 0.840656π0.840656\pi
942942 16.5915 11.0861i 0.540582 0.361205i
943943 −2.03660 + 4.91678i −0.0663208 + 0.160112i
944944 3.68132 1.52485i 0.119817 0.0496297i
945945 1.38843 + 8.68108i 0.0451657 + 0.282396i
946946 1.30759 0.873705i 0.0425135 0.0284066i
947947 4.92140 + 3.28837i 0.159924 + 0.106858i 0.632957 0.774187i 0.281841π-0.281841\pi
−0.473033 + 0.881045i 0.656841π0.656841\pi
948948 11.9278i 0.387398i
949949 2.17369 3.25316i 0.0705611 0.105602i
950950 −1.14976 + 2.27353i −0.0373031 + 0.0737632i
951951 24.8206i 0.804863i
952952 −0.0807107 2.92914i −0.00261585 0.0949341i
953953 −15.4098 + 15.4098i −0.499172 + 0.499172i −0.911180 0.412008i 0.864827π-0.864827\pi
0.412008 + 0.911180i 0.364827π0.364827\pi
954954 5.86162 + 2.42796i 0.189777 + 0.0786082i
955955 −8.41364 + 35.2807i −0.272259 + 1.14166i
956956 17.9535 + 17.9535i 0.580657 + 0.580657i
957957 22.7407 34.0338i 0.735101 1.10016i
958958 18.9883 + 3.77700i 0.613484 + 0.122029i
959959 −12.5164 2.48967i −0.404177 0.0803957i
960960 −2.76875 0.104584i −0.0893612 0.00337543i
961961 −7.81115 18.8578i −0.251973 0.608315i
962962 −1.98935 2.97728i −0.0641394 0.0959914i
963963 2.74601 13.8051i 0.0884890 0.444864i
964964 −1.56331 7.85931i −0.0503510 0.253131i
965965 0.0435488 + 0.117496i 0.00140189 + 0.00378233i
966966 0.544354 + 0.363726i 0.0175143 + 0.0117027i
967967 17.7739 + 42.9099i 0.571569 + 1.37989i 0.900219 + 0.435438i 0.143407π0.143407\pi
−0.328649 + 0.944452i 0.606593π0.606593\pi
968968 7.70546 + 7.70546i 0.247663 + 0.247663i
969969 −0.929597 + 2.43162i −0.0298630 + 0.0781148i
970970 7.65717 + 20.6592i 0.245857 + 0.663328i
971971 −6.91456 + 16.6932i −0.221899 + 0.535711i −0.995148 0.0983915i 0.968630π-0.968630\pi
0.773249 + 0.634102i 0.218630π0.218630\pi
972972 −13.2866 + 2.64286i −0.426167 + 0.0847699i
973973 11.6696 0.374110
974974 1.95796 0.389463i 0.0627372 0.0124792i
975975 0.544168 1.95209i 0.0174273 0.0625170i
976976 −1.32035 + 6.63783i −0.0422633 + 0.212472i
977977 11.5625 + 4.78935i 0.369917 + 0.153225i 0.559895 0.828564i 0.310842π-0.310842\pi
−0.189978 + 0.981788i 0.560842π0.560842\pi
978978 −25.1679 10.4249i −0.804782 0.333352i
979979 −0.483849 + 2.43247i −0.0154639 + 0.0777421i
980980 −8.51864 + 11.7623i −0.272118 + 0.375734i
981981 −6.87074 + 1.36667i −0.219366 + 0.0436346i
982982 −20.3744 −0.650172
983983 −52.3512 + 10.4133i −1.66974 + 0.332132i −0.937254 0.348647i 0.886641π-0.886641\pi
−0.732489 + 0.680779i 0.761641π0.761641\pi
984984 3.39445 8.19492i 0.108211 0.261245i
985985 3.46095 7.53738i 0.110275 0.240161i
986986 −11.8749 26.5736i −0.378174 0.846277i
987987 −2.62900 2.62900i −0.0836819 0.0836819i
988988 0.0637814 + 0.153982i 0.00202916 + 0.00489882i
989989 0.207742 + 0.138809i 0.00660580 + 0.00441385i
990990 −14.3698 + 5.32603i −0.456701 + 0.169272i
991991 −5.61025 28.2046i −0.178216 0.895950i −0.961609 0.274424i 0.911513π-0.911513\pi
0.783393 0.621526i 0.213487π-0.213487\pi
992992 0.634823 3.19147i 0.0201557 0.101329i
993993 −9.95958 14.9056i −0.316058 0.473014i
994994 4.26282 + 10.2914i 0.135209 + 0.326422i
995995 −10.8933 + 10.1003i −0.345342 + 0.320202i
996996 −15.2553 3.03448i −0.483384 0.0961510i
997997 −20.8465 4.14662i −0.660215 0.131325i −0.146399 0.989226i 0.546768π-0.546768\pi
−0.513815 + 0.857901i 0.671768π0.671768\pi
998998 −8.62482 + 12.9080i −0.273014 + 0.408594i
999999 42.8232 + 42.8232i 1.35487 + 1.35487i
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 170.2.o.a.7.2 32
5.2 odd 4 850.2.v.c.143.2 32
5.3 odd 4 170.2.r.a.143.3 yes 32
5.4 even 2 850.2.s.c.7.3 32
17.5 odd 16 170.2.r.a.107.3 yes 32
85.22 even 16 850.2.s.c.243.3 32
85.39 odd 16 850.2.v.c.107.2 32
85.73 even 16 inner 170.2.o.a.73.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.o.a.7.2 32 1.1 even 1 trivial
170.2.o.a.73.2 yes 32 85.73 even 16 inner
170.2.r.a.107.3 yes 32 17.5 odd 16
170.2.r.a.143.3 yes 32 5.3 odd 4
850.2.s.c.7.3 32 5.4 even 2
850.2.s.c.243.3 32 85.22 even 16
850.2.v.c.107.2 32 85.39 odd 16
850.2.v.c.143.2 32 5.2 odd 4