LMFDB - Embedded newform 22.14.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,14,Mod(1,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	22.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$23.5908043694$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{45769}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 11442 $ x^2 - x - 11442
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$107.468$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+64.0000 q^{2} -890.874 q^{3} +4096.00 q^{4} -19080.9 q^{5} -57015.9 q^{6} +408914. q^{7} +262144. q^{8} -800667. q^{9} +O(q^{10})$	\(q+64.0000 q^{2} -890.874 q^{3} +4096.00 q^{4} -19080.9 q^{5} -57015.9 q^{6} +408914. q^{7} +262144. q^{8} -800667. q^{9} -1.22118e6 q^{10} +1.77156e6 q^{11} -3.64902e6 q^{12} -1.51490e7 q^{13} +2.61705e7 q^{14} +1.69987e7 q^{15} +1.67772e7 q^{16} -1.28611e8 q^{17} -5.12427e7 q^{18} -3.68765e8 q^{19} -7.81555e7 q^{20} -3.64291e8 q^{21} +1.13380e8 q^{22} +8.39438e8 q^{23} -2.33537e8 q^{24} -8.56621e8 q^{25} -9.69536e8 q^{26} +2.13363e9 q^{27} +1.67491e9 q^{28} -3.20852e9 q^{29} +1.08792e9 q^{30} -6.16914e9 q^{31} +1.07374e9 q^{32} -1.57824e9 q^{33} -8.23108e9 q^{34} -7.80247e9 q^{35} -3.27953e9 q^{36} -6.11430e9 q^{37} -2.36010e10 q^{38} +1.34958e10 q^{39} -5.00195e9 q^{40} -4.53326e10 q^{41} -2.33146e10 q^{42} +6.02190e10 q^{43} +7.25631e9 q^{44} +1.52775e10 q^{45} +5.37240e10 q^{46} -2.59159e10 q^{47} -1.49464e10 q^{48} +7.03219e10 q^{49} -5.48237e10 q^{50} +1.14576e11 q^{51} -6.20503e10 q^{52} -4.52404e9 q^{53} +1.36553e11 q^{54} -3.38031e10 q^{55} +1.07194e11 q^{56} +3.28523e11 q^{57} -2.05345e11 q^{58} +3.64378e11 q^{59} +6.96267e10 q^{60} +6.03699e11 q^{61} -3.94825e11 q^{62} -3.27404e11 q^{63} +6.87195e10 q^{64} +2.89057e11 q^{65} -1.01007e11 q^{66} +3.03486e11 q^{67} -5.26789e11 q^{68} -7.47833e11 q^{69} -4.99358e11 q^{70} -3.34248e11 q^{71} -2.09890e11 q^{72} +9.59457e11 q^{73} -3.91315e11 q^{74} +7.63141e11 q^{75} -1.51046e12 q^{76} +7.24417e11 q^{77} +8.63734e11 q^{78} -1.25950e12 q^{79} -3.20125e11 q^{80} -6.24277e11 q^{81} -2.90128e12 q^{82} -4.67367e12 q^{83} -1.49214e12 q^{84} +2.45401e12 q^{85} +3.85402e12 q^{86} +2.85838e12 q^{87} +4.64404e11 q^{88} -5.00339e12 q^{89} +9.77759e11 q^{90} -6.19464e12 q^{91} +3.43834e12 q^{92} +5.49592e12 q^{93} -1.65862e12 q^{94} +7.03638e12 q^{95} -9.56568e11 q^{96} +4.72642e12 q^{97} +4.50060e12 q^{98} -1.41843e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9}+O(q^{10}) $ 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9	\( 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9} + 186496 q^{10} + 3543122 q^{11} - 3792896 q^{12} - 6948916 q^{13} - 10915840 q^{14} + 16226114 q^{15} + 33554432 q^{16} - 280144288 q^{17} - 153200384 q^{18} - 349231788 q^{19} + 11935744 q^{20} - 343936280 q^{21} + 226759808 q^{22} - 151278294 q^{23} - 242745344 q^{24} - 1593546344 q^{25} - 444730624 q^{26} + 2245595374 q^{27} - 698613760 q^{28} - 771621928 q^{29} + 1038471296 q^{30} - 8626482070 q^{31} + 2147483648 q^{32} - 1640465486 q^{33} - 17929234432 q^{34} - 20547972800 q^{35} - 9804824576 q^{36} - 26333898490 q^{37} - 22350834432 q^{38} + 13207805428 q^{39} + 763887616 q^{40} - 3560991836 q^{41} - 22011921920 q^{42} - 16329995932 q^{43} + 14512627712 q^{44} - 19762426588 q^{45} - 9681810816 q^{46} + 9513351704 q^{47} - 15535702016 q^{48} + 309223257786 q^{49} - 101986966016 q^{50} + 119898691720 q^{51} - 28462759936 q^{52} + 291363898652 q^{53} + 143718103936 q^{54} + 5162328754 q^{55} - 44711280640 q^{56} + 327836886300 q^{57} - 49383803392 q^{58} + 712019011182 q^{59} + 66462162944 q^{60} + 138918582944 q^{61} - 552094852480 q^{62} + 595750060240 q^{63} + 137438953472 q^{64} + 469417380748 q^{65} - 104989791104 q^{66} + 912599195574 q^{67} - 1147471003648 q^{68} - 713033152350 q^{69} - 1315070259200 q^{70} - 1560848343722 q^{71} - 627508772864 q^{72} + 407382417996 q^{73} - 1685369503360 q^{74} + 789026369816 q^{75} - 1430453403648 q^{76} - 302157444160 q^{77} + 845299547392 q^{78} - 48102676468 q^{79} + 48888807424 q^{80} + 1911689036650 q^{81} - 227903477504 q^{82} - 6313820551012 q^{83} - 1408763002880 q^{84} - 878959681568 q^{85} - 1045119739648 q^{86} + 2772785468872 q^{87} + 928808173568 q^{88} + 977692325462 q^{89} - 1264795301632 q^{90} - 10946374648120 q^{91} - 619635892224 q^{92} + 5582240738434 q^{93} + 608854509056 q^{94} + 7466012570772 q^{95} - 994284929024 q^{96} - 1024977303502 q^{97} + 19790288498304 q^{98} - 4240684773116 q^{99}+O(q^{100}) \) 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9 + 186496 * q^10 + 3543122 * q^11 - 3792896 * q^12 - 6948916 * q^13 - 10915840 * q^14 + 16226114 * q^15 + 33554432 * q^16 - 280144288 * q^17 - 153200384 * q^18 - 349231788 * q^19 + 11935744 * q^20 - 343936280 * q^21 + 226759808 * q^22 - 151278294 * q^23 - 242745344 * q^24 - 1593546344 * q^25 - 444730624 * q^26 + 2245595374 * q^27 - 698613760 * q^28 - 771621928 * q^29 + 1038471296 * q^30 - 8626482070 * q^31 + 2147483648 * q^32 - 1640465486 * q^33 - 17929234432 * q^34 - 20547972800 * q^35 - 9804824576 * q^36 - 26333898490 * q^37 - 22350834432 * q^38 + 13207805428 * q^39 + 763887616 * q^40 - 3560991836 * q^41 - 22011921920 * q^42 - 16329995932 * q^43 + 14512627712 * q^44 - 19762426588 * q^45 - 9681810816 * q^46 + 9513351704 * q^47 - 15535702016 * q^48 + 309223257786 * q^49 - 101986966016 * q^50 + 119898691720 * q^51 - 28462759936 * q^52 + 291363898652 * q^53 + 143718103936 * q^54 + 5162328754 * q^55 - 44711280640 * q^56 + 327836886300 * q^57 - 49383803392 * q^58 + 712019011182 * q^59 + 66462162944 * q^60 + 138918582944 * q^61 - 552094852480 * q^62 + 595750060240 * q^63 + 137438953472 * q^64 + 469417380748 * q^65 - 104989791104 * q^66 + 912599195574 * q^67 - 1147471003648 * q^68 - 713033152350 * q^69 - 1315070259200 * q^70 - 1560848343722 * q^71 - 627508772864 * q^72 + 407382417996 * q^73 - 1685369503360 * q^74 + 789026369816 * q^75 - 1430453403648 * q^76 - 302157444160 * q^77 + 845299547392 * q^78 - 48102676468 * q^79 + 48888807424 * q^80 + 1911689036650 * q^81 - 227903477504 * q^82 - 6313820551012 * q^83 - 1408763002880 * q^84 - 878959681568 * q^85 - 1045119739648 * q^86 + 2772785468872 * q^87 + 928808173568 * q^88 + 977692325462 * q^89 - 1264795301632 * q^90 - 10946374648120 * q^91 - 619635892224 * q^92 + 5582240738434 * q^93 + 608854509056 * q^94 + 7466012570772 * q^95 - 994284929024 * q^96 - 1024977303502 * q^97 + 19790288498304 * q^98 - 4240684773116 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	−890.874	−0.705550	−0.352775	−	0.935708i	$-0.614762\pi$
$3$	−890.874	−0.705550	−0.352775	+	0.935708i	$0.614762\pi$
$4$	4096.00	0.500000
$5$	−19080.9	−0.546128	−0.273064	−	0.961996i	$-0.588037\pi$
$5$	−19080.9	−0.546128	−0.273064	+	0.961996i	$0.588037\pi$
$6$	−57015.9	−0.498899
$7$	408914.	1.31370	0.656848	−	0.754023i	$-0.271889\pi$
$7$	408914.	1.31370	0.656848	+	0.754023i	$0.271889\pi$
$8$	262144.	0.353553
$9$	−800667.	−0.502199
$10$	−1.22118e6	−0.386171
$11$	1.77156e6	0.301511
$11$	1.77156e6	0.301511
$12$	−3.64902e6	−0.352775
$13$	−1.51490e7	−0.870466	−0.435233	−	0.900318i	$-0.643334\pi$
$13$	−1.51490e7	−0.870466	−0.435233	+	0.900318i	$0.643334\pi$
$14$	2.61705e7	0.928924
$15$	1.69987e7	0.385321
$16$	1.67772e7	0.250000
$17$	−1.28611e8	−1.29229	−0.646144	−	0.763216i	$-0.723619\pi$
$17$	−1.28611e8	−1.29229	−0.646144	+	0.763216i	$0.723619\pi$
$18$	−5.12427e7	−0.355108
$19$	−3.68765e8	−1.79825	−0.899127	−	0.437687i	$-0.855798\pi$
$19$	−3.68765e8	−1.79825	−0.899127	+	0.437687i	$0.855798\pi$
$20$	−7.81555e7	−0.273064
$21$	−3.64291e8	−0.926879
$22$	1.13380e8	0.213201
$23$	8.39438e8	1.18238	0.591191	−	0.806532i	$-0.298658\pi$
$23$	8.39438e8	1.18238	0.591191	+	0.806532i	$0.298658\pi$
$24$	−2.33537e8	−0.249450
$25$	−8.56621e8	−0.701744
$26$	−9.69536e8	−0.615513
$27$	2.13363e9	1.05988
$28$	1.67491e9	0.656848
$29$	−3.20852e9	−1.00165	−0.500827	−	0.865548i	$-0.666971\pi$
$29$	−3.20852e9	−1.00165	−0.500827	+	0.865548i	$0.666971\pi$
$30$	1.08792e9	0.272463
$31$	−6.16914e9	−1.24846	−0.624228	−	0.781242i	$-0.714587\pi$
$31$	−6.16914e9	−1.24846	−0.624228	+	0.781242i	$0.714587\pi$
$32$	1.07374e9	0.176777
$33$	−1.57824e9	−0.212731
$34$	−8.23108e9	−0.913785
$35$	−7.80247e9	−0.717447
$36$	−3.27953e9	−0.251099
$37$	−6.11430e9	−0.391774	−0.195887	−	0.980626i	$-0.562759\pi$
$37$	−6.11430e9	−0.391774	−0.195887	+	0.980626i	$0.562759\pi$
$38$	−2.36010e10	−1.27156
$39$	1.34958e10	0.614158
$40$	−5.00195e9	−0.193086
$41$	−4.53326e10	−1.49044	−0.745221	−	0.666817i	$-0.767656\pi$
$41$	−4.53326e10	−1.49044	−0.745221	+	0.666817i	$0.767656\pi$
$42$	−2.33146e10	−0.655402
$43$	6.02190e10	1.45274	0.726372	−	0.687302i	$-0.241205\pi$
$43$	6.02190e10	1.45274	0.726372	+	0.687302i	$0.241205\pi$
$44$	7.25631e9	0.150756
$45$	1.52775e10	0.274265
$46$	5.37240e10	0.836070
$47$	−2.59159e10	−0.350696	−0.175348	−	0.984506i	$-0.556105\pi$
$47$	−2.59159e10	−0.350696	−0.175348	+	0.984506i	$0.556105\pi$
$48$	−1.49464e10	−0.176388
$49$	7.03219e10	0.725798
$50$	−5.48237e10	−0.496208
$51$	1.14576e11	0.911774
$52$	−6.20503e10	−0.435233
$53$	−4.52404e9	−0.0280371	−0.0140186	−	0.999902i	$-0.504462\pi$
$53$	−4.52404e9	−0.0280371	−0.0140186	+	0.999902i	$0.504462\pi$
$54$	1.36553e11	0.749446
$55$	−3.38031e10	−0.164664
$56$	1.07194e11	0.464462
$57$	3.28523e11	1.26876
$58$	−2.05345e11	−0.708276
$59$	3.64378e11	1.12464	0.562321	−	0.826919i	$-0.309909\pi$
$59$	3.64378e11	1.12464	0.562321	+	0.826919i	$0.309909\pi$
$60$	6.96267e10	0.192661
$61$	6.03699e11	1.50029	0.750147	−	0.661271i	$-0.229983\pi$
$61$	6.03699e11	1.50029	0.750147	+	0.661271i	$0.229983\pi$
$62$	−3.94825e11	−0.882792
$63$	−3.27404e11	−0.659737
$64$	6.87195e10	0.125000
$65$	2.89057e11	0.475386
$66$	−1.01007e11	−0.150424
$67$	3.03486e11	0.409876	0.204938	−	0.978775i	$-0.434301\pi$
$67$	3.03486e11	0.409876	0.204938	+	0.978775i	$0.434301\pi$
$68$	−5.26789e11	−0.646144
$69$	−7.47833e11	−0.834230
$70$	−4.99358e11	−0.507312
$71$	−3.34248e11	−0.309663	−0.154832	−	0.987941i	$-0.549483\pi$
$71$	−3.34248e11	−0.309663	−0.154832	+	0.987941i	$0.549483\pi$
$72$	−2.09890e11	−0.177554
$73$	9.59457e11	0.742040	0.371020	−	0.928625i	$-0.379008\pi$
$73$	9.59457e11	0.742040	0.371020	+	0.928625i	$0.379008\pi$
$74$	−3.91315e11	−0.277026
$75$	7.63141e11	0.495116
$76$	−1.51046e12	−0.899127
$77$	7.24417e11	0.396094
$78$	8.63734e11	0.434275
$79$	−1.25950e12	−0.582937	−0.291469	−	0.956580i	$-0.594144\pi$
$79$	−1.25950e12	−0.582937	−0.291469	+	0.956580i	$0.594144\pi$
$80$	−3.20125e11	−0.136532
$81$	−6.24277e11	−0.245598
$82$	−2.90128e12	−1.05390
$83$	−4.67367e12	−1.56910	−0.784549	−	0.620066i	$-0.787106\pi$
$83$	−4.67367e12	−1.56910	−0.784549	+	0.620066i	$0.787106\pi$
$84$	−1.49214e12	−0.463439
$85$	2.45401e12	0.705755
$86$	3.85402e12	1.02724
$87$	2.85838e12	0.706717
$88$	4.64404e11	0.106600
$89$	−5.00339e12	−1.06716	−0.533579	−	0.845750i	$-0.679153\pi$
$89$	−5.00339e12	−1.06716	−0.533579	+	0.845750i	$0.679153\pi$
$90$	9.77759e11	0.193935
$91$	−6.19464e12	−1.14353
$92$	3.43834e12	0.591191
$93$	5.49592e12	0.880849
$94$	−1.65862e12	−0.247980
$95$	7.03638e12	0.982078
$96$	−9.56568e11	−0.124725
$97$	4.72642e12	0.576124	0.288062	−	0.957612i	$-0.406989\pi$
$97$	4.72642e12	0.576124	0.288062	+	0.957612i	$0.406989\pi$
$98$	4.50060e12	0.513217
$99$	−1.41843e12	−0.151419
$100$	−3.50872e12	−0.350872
$101$	−1.77951e13	−1.66806	−0.834031	−	0.551717i	$-0.813973\pi$
$101$	−1.77951e13	−1.66806	−0.834031	+	0.551717i	$0.813973\pi$
$102$	7.33286e12	0.644721
$103$	−1.17588e13	−0.970337	−0.485168	−	0.874421i	$-0.661242\pi$
$103$	−1.17588e13	−0.970337	−0.485168	+	0.874421i	$0.661242\pi$
$104$	−3.97122e12	−0.307756
$105$	6.95102e12	0.506195
$106$	−2.89539e11	−0.0198252
$107$	1.32104e13	0.850984	0.425492	−	0.904962i	$-0.360101\pi$
$107$	1.32104e13	0.850984	0.425492	+	0.904962i	$0.360101\pi$
$108$	8.73936e12	0.529938
$109$	1.58826e13	0.907086	0.453543	−	0.891234i	$-0.350160\pi$
$109$	1.58826e13	0.907086	0.453543	+	0.891234i	$0.350160\pi$
$110$	−2.16340e12	−0.116435
$111$	5.44707e12	0.276416
$112$	6.86044e12	0.328424
$113$	5.26193e12	0.237758	0.118879	−	0.992909i	$-0.462070\pi$
$113$	5.26193e12	0.237758	0.118879	+	0.992909i	$0.462070\pi$
$114$	2.10255e13	0.897148
$115$	−1.60173e13	−0.645732
$116$	−1.31421e13	−0.500827
$117$	1.21293e13	0.437147
$118$	2.33202e13	0.795242
$119$	−5.25907e13	−1.69767
$120$	4.45611e12	0.136232
$121$	3.13843e12	0.0909091
$122$	3.86367e13	1.06087
$123$	4.03856e13	1.05158
$124$	−2.52688e13	−0.624228
$125$	3.96373e13	0.929371
$126$	−2.09539e13	−0.466504
$127$	−4.06282e13	−0.859219	−0.429609	−	0.903015i	$-0.641349\pi$
$127$	−4.06282e13	−0.859219	−0.429609	+	0.903015i	$0.641349\pi$
$128$	4.39805e12	0.0883883
$129$	−5.36476e13	−1.02498
$130$	1.84997e13	0.336149
$131$	9.98969e13	1.72698	0.863492	−	0.504362i	$-0.168272\pi$
$131$	9.98969e13	1.72698	0.863492	+	0.504362i	$0.168272\pi$
$132$	−6.46446e12	−0.106366
$133$	−1.50793e14	−2.36236
$134$	1.94231e13	0.289826
$135$	−4.07117e13	−0.578829
$136$	−3.37145e13	−0.456893
$137$	−4.79352e13	−0.619399	−0.309699	−	0.950834i	$-0.600228\pi$
$137$	−4.79352e13	−0.619399	−0.309699	+	0.950834i	$0.600228\pi$
$138$	−4.78613e13	−0.589890
$139$	−8.36426e13	−0.983629	−0.491815	−	0.870700i	$-0.663666\pi$
$139$	−8.36426e13	−0.983629	−0.491815	+	0.870700i	$0.663666\pi$
$140$	−3.19589e13	−0.358723
$141$	2.30878e13	0.247434
$142$	−2.13919e13	−0.218965
$143$	−2.68374e13	−0.262456
$144$	−1.34330e13	−0.125550
$145$	6.12215e13	0.547031
$146$	6.14053e13	0.524701
$147$	−6.26479e13	−0.512087
$148$	−2.50442e13	−0.195887
$149$	−1.26242e14	−0.945135	−0.472567	−	0.881295i	$-0.656673\pi$
$149$	−1.26242e14	−0.945135	−0.472567	+	0.881295i	$0.656673\pi$
$150$	4.88410e13	0.350100
$151$	6.43033e13	0.441451	0.220726	−	0.975336i	$-0.429157\pi$
$151$	6.43033e13	0.441451	0.220726	+	0.975336i	$0.429157\pi$
$152$	−9.66695e13	−0.635779
$153$	1.02974e14	0.648985
$154$	4.63627e13	0.280081
$155$	1.17713e14	0.681818
$156$	5.52790e13	0.307079
$157$	2.18402e14	1.16388	0.581942	−	0.813231i	$-0.302293\pi$
$157$	2.18402e14	1.16388	0.581942	+	0.813231i	$0.302293\pi$
$158$	−8.06080e13	−0.412199
$159$	4.03035e12	0.0197816
$160$	−2.04880e13	−0.0965428
$161$	3.43258e14	1.55329
$162$	−3.99537e13	−0.173664
$163$	4.33670e14	1.81109	0.905544	−	0.424251i	$-0.139463\pi$
$163$	4.33670e14	1.81109	0.905544	+	0.424251i	$0.139463\pi$
$164$	−1.85682e14	−0.745221
$165$	3.01143e13	0.116179
$166$	−2.99115e14	−1.10952
$167$	2.41832e14	0.862694	0.431347	−	0.902186i	$-0.358039\pi$
$167$	2.41832e14	0.862694	0.431347	+	0.902186i	$0.358039\pi$
$168$	−9.54967e13	−0.327701
$169$	−7.33831e13	−0.242288
$170$	1.57057e14	0.499044
$171$	2.95258e14	0.903081
$172$	2.46657e14	0.726372
$173$	−6.01148e12	−0.0170483	−0.00852416	−	0.999964i	$-0.502713\pi$
$173$	−6.01148e12	−0.0170483	−0.00852416	+	0.999964i	$0.502713\pi$
$174$	1.82937e14	0.499724
$175$	−3.50284e14	−0.921878
$176$	2.97219e13	0.0753778
$177$	−3.24615e14	−0.793492
$178$	−3.20217e14	−0.754595
$179$	−1.98246e14	−0.450463	−0.225232	−	0.974305i	$-0.572314\pi$
$179$	−1.98246e14	−0.450463	−0.225232	+	0.974305i	$0.572314\pi$
$180$	6.25766e13	0.137132
$181$	1.63759e14	0.346173	0.173087	−	0.984907i	$-0.444626\pi$
$181$	1.63759e14	0.346173	0.173087	+	0.984907i	$0.444626\pi$
$182$	−3.96457e14	−0.808597
$183$	−5.37820e14	−1.05853
$184$	2.20054e14	0.418035
$185$	1.16667e14	0.213959
$186$	3.51739e14	0.622854
$187$	−2.27842e14	−0.389639
$188$	−1.06152e14	−0.175348
$189$	8.72473e14	1.39236
$190$	4.50328e14	0.694434
$191$	−8.97668e14	−1.33782	−0.668911	−	0.743342i	$-0.733239\pi$
$191$	−8.97668e14	−1.33782	−0.668911	+	0.743342i	$0.733239\pi$
$192$	−6.12204e13	−0.0881938
$193$	1.69830e13	0.0236533	0.0118267	−	0.999930i	$-0.496235\pi$
$193$	1.69830e13	0.0236533	0.0118267	+	0.999930i	$0.496235\pi$
$194$	3.02491e14	0.407381
$195$	−2.57513e14	−0.335409
$196$	2.88038e14	0.362899
$197$	5.00048e14	0.609511	0.304756	−	0.952431i	$-0.401425\pi$
$197$	5.00048e14	0.609511	0.304756	+	0.952431i	$0.401425\pi$
$198$	−9.07795e13	−0.107069
$199$	−6.84572e13	−0.0781401	−0.0390701	−	0.999236i	$-0.512440\pi$
$199$	−6.84572e13	−0.0781401	−0.0390701	+	0.999236i	$0.512440\pi$
$200$	−2.24558e14	−0.248104
$201$	−2.70368e14	−0.289188
$202$	−1.13889e15	−1.17950
$203$	−1.31201e15	−1.31587
$204$	4.69303e14	0.455887
$205$	8.64988e14	0.813973
$206$	−7.52566e14	−0.686132
$207$	−6.72110e14	−0.593790
$208$	−2.54158e14	−0.217617
$209$	−6.53290e14	−0.542194
$210$	4.44865e14	0.357934
$211$	−2.62383e14	−0.204691	−0.102346	−	0.994749i	$-0.532635\pi$
$211$	−2.62383e14	−0.204691	−0.102346	+	0.994749i	$0.532635\pi$
$212$	−1.85305e13	−0.0140186
$213$	2.97773e14	0.218483
$214$	8.45466e14	0.601737
$215$	−1.14904e15	−0.793385
$216$	5.59319e14	0.374723
$217$	−2.52265e15	−1.64009
$218$	1.01648e15	0.641407
$219$	−8.54755e14	−0.523546
$220$	−1.38457e14	−0.0823320
$221$	1.94832e15	1.12489
$222$	3.48613e14	0.195456
$223$	2.44598e15	1.33190	0.665948	−	0.745998i	$-0.268027\pi$
$223$	2.44598e15	1.33190	0.665948	+	0.745998i	$0.268027\pi$
$224$	4.39068e14	0.232231
$225$	6.85868e14	0.352415
$226$	3.36763e14	0.168120
$227$	6.33176e14	0.307154	0.153577	−	0.988137i	$-0.450921\pi$
$227$	6.33176e14	0.307154	0.153577	+	0.988137i	$0.450921\pi$
$228$	1.34563e15	0.634380
$229$	1.51480e14	0.0694106	0.0347053	−	0.999398i	$-0.488951\pi$
$229$	1.51480e14	0.0694106	0.0347053	+	0.999398i	$0.488951\pi$
$230$	−1.02511e15	−0.456602
$231$	−6.45364e14	−0.279465
$232$	−8.41094e14	−0.354138
$233$	−1.10144e15	−0.450968	−0.225484	−	0.974247i	$-0.572396\pi$
$233$	−1.10144e15	−0.450968	−0.225484	+	0.974247i	$0.572396\pi$
$234$	7.76275e14	0.309110
$235$	4.94501e14	0.191525
$236$	1.49249e15	0.562321
$237$	1.12206e15	0.411292
$238$	−3.36581e15	−1.20044
$239$	−4.51154e15	−1.56581	−0.782903	−	0.622144i	$-0.786262\pi$
$239$	−4.51154e15	−1.56581	−0.782903	+	0.622144i	$0.786262\pi$
$240$	2.85191e14	0.0963303
$241$	4.89841e15	1.61044	0.805220	−	0.592976i	$-0.202047\pi$
$241$	4.89841e15	1.61044	0.805220	+	0.592976i	$0.202047\pi$
$242$	2.00859e14	0.0642824
$243$	−2.84555e15	−0.886595
$244$	2.47275e15	0.750147
$245$	−1.34181e15	−0.396379
$246$	2.58468e15	0.743581
$247$	5.58642e15	1.56532
$248$	−1.61720e15	−0.441396
$249$	4.16365e15	1.10708
$250$	2.53679e15	0.657164
$251$	−2.16451e15	−0.546361	−0.273181	−	0.961963i	$-0.588076\pi$
$251$	−2.16451e15	−0.546361	−0.273181	+	0.961963i	$0.588076\pi$
$252$	−1.34105e15	−0.329868
$253$	1.48712e15	0.356501
$254$	−2.60021e15	−0.607559
$255$	−2.18622e15	−0.497946
$256$	2.81475e14	0.0625000
$257$	3.74322e15	0.810364	0.405182	−	0.914236i	$-0.367208\pi$
$257$	3.74322e15	0.810364	0.405182	+	0.914236i	$0.367208\pi$
$258$	−3.43344e15	−0.724773
$259$	−2.50023e15	−0.514672
$260$	1.18398e15	0.237693
$261$	2.56895e15	0.503029
$262$	6.39340e15	1.22116
$263$	−4.34637e15	−0.809867	−0.404934	−	0.914346i	$-0.632705\pi$
$263$	−4.34637e15	−0.809867	−0.404934	+	0.914346i	$0.632705\pi$
$264$	−4.13725e14	−0.0752119
$265$	8.63230e13	0.0153119
$266$	−9.65077e15	−1.67044
$267$	4.45739e15	0.752934
$268$	1.24308e15	0.204938
$269$	−4.49858e15	−0.723911	−0.361956	−	0.932195i	$-0.617891\pi$
$269$	−4.49858e15	−0.723911	−0.361956	+	0.932195i	$0.617891\pi$
$270$	−2.60555e15	−0.409294
$271$	4.22189e15	0.647450	0.323725	−	0.946151i	$-0.395065\pi$
$271$	4.22189e15	0.647450	0.323725	+	0.946151i	$0.395065\pi$
$272$	−2.15773e15	−0.323072
$273$	5.51864e15	0.806817
$274$	−3.06785e15	−0.437981
$275$	−1.51756e15	−0.211584
$276$	−3.06312e15	−0.417115
$277$	2.79516e15	0.371781	0.185891	−	0.982570i	$-0.440483\pi$
$277$	2.79516e15	0.371781	0.185891	+	0.982570i	$0.440483\pi$
$278$	−5.35313e15	−0.695531
$279$	4.93942e15	0.626973
$280$	−2.04537e15	−0.253656
$281$	5.56550e15	0.674393	0.337196	−	0.941434i	$-0.390521\pi$
$281$	5.56550e15	0.674393	0.337196	+	0.941434i	$0.390521\pi$
$282$	1.47762e15	0.174962
$283$	−1.17337e16	−1.35776	−0.678880	−	0.734249i	$-0.737535\pi$
$283$	−1.17337e16	−1.35776	−0.678880	+	0.734249i	$0.737535\pi$
$284$	−1.36908e15	−0.154832
$285$	−6.26853e15	−0.692906
$286$	−1.71759e15	−0.185584
$287$	−1.85371e16	−1.95799
$288$	−8.59709e14	−0.0887770
$289$	6.63613e15	0.670006
$290$	3.91818e15	0.386810
$291$	−4.21064e15	−0.406484
$292$	3.92994e15	0.371020
$293$	−8.12856e15	−0.750540	−0.375270	−	0.926916i	$-0.622450\pi$
$293$	−8.12856e15	−0.750540	−0.375270	+	0.926916i	$0.622450\pi$
$294$	−4.00947e15	−0.362100
$295$	−6.95268e15	−0.614199
$296$	−1.60283e15	−0.138513
$297$	3.77986e15	0.319565
$298$	−8.07950e15	−0.668311
$299$	−1.27166e16	−1.02922
$300$	3.12583e15	0.247558
$301$	2.46244e16	1.90846
$302$	4.11541e15	0.312153
$303$	1.58532e16	1.17690
$304$	−6.18685e15	−0.449564
$305$	−1.15191e16	−0.819353
$306$	6.59036e15	0.458902
$307$	2.41487e16	1.64624	0.823121	−	0.567866i	$-0.192231\pi$
$307$	2.41487e16	1.64624	0.823121	+	0.567866i	$0.192231\pi$
$308$	2.96721e15	0.198047
$309$	1.04756e16	0.684621
$310$	7.53363e15	0.482118
$311$	−5.30719e15	−0.332600	−0.166300	−	0.986075i	$-0.553182\pi$
$311$	−5.30719e15	−0.332600	−0.166300	+	0.986075i	$0.553182\pi$
$312$	3.53785e15	0.217138
$313$	−2.41876e16	−1.45397	−0.726983	−	0.686655i	$-0.759078\pi$
$313$	−2.41876e16	−1.45397	−0.726983	+	0.686655i	$0.759078\pi$
$314$	1.39777e16	0.822990
$315$	6.24718e15	0.360301
$316$	−5.15891e15	−0.291469
$317$	3.84291e15	0.212703	0.106352	−	0.994329i	$-0.466083\pi$
$317$	3.84291e15	0.212703	0.106352	+	0.994329i	$0.466083\pi$
$318$	2.57942e14	0.0139877
$319$	−5.68408e15	−0.302010
$320$	−1.31123e15	−0.0682661
$321$	−1.17688e16	−0.600412
$322$	2.19685e16	1.09834
$323$	4.74271e16	2.32386
$324$	−2.55704e15	−0.122799
$325$	1.29769e16	0.610844
$326$	2.77549e16	1.28063
$327$	−1.41494e16	−0.639995
$328$	−1.18837e16	−0.526951
$329$	−1.05974e16	−0.460708
$330$	1.92731e15	0.0821507
$331$	−1.04252e16	−0.435714	−0.217857	−	0.975981i	$-0.569907\pi$
$331$	−1.04252e16	−0.435714	−0.217857	+	0.975981i	$0.569907\pi$
$332$	−1.91433e16	−0.784549
$333$	4.89552e15	0.196748
$334$	1.54772e16	0.610017
$335$	−5.79080e15	−0.223845
$336$	−6.11179e15	−0.231720
$337$	4.10811e16	1.52773	0.763866	−	0.645375i	$-0.223299\pi$
$337$	4.10811e16	1.52773	0.763866	+	0.645375i	$0.223299\pi$
$338$	−4.69652e15	−0.171324
$339$	−4.68771e15	−0.167750
$340$	1.00516e16	0.352877
$341$	−1.09290e16	−0.376424
$342$	1.88965e16	0.638575
$343$	−1.08637e16	−0.360218
$344$	1.57861e16	0.513622
$345$	1.42694e16	0.455597
$346$	−3.84734e14	−0.0120550
$347$	−2.65623e16	−0.816817	−0.408409	−	0.912799i	$-0.633916\pi$
$347$	−2.65623e16	−0.816817	−0.408409	+	0.912799i	$0.633916\pi$
$348$	1.17079e16	0.353358
$349$	−6.51017e16	−1.92853	−0.964267	−	0.264934i	$-0.914650\pi$
$349$	−6.51017e16	−1.92853	−0.964267	+	0.264934i	$0.914650\pi$
$350$	−2.24182e16	−0.651866
$351$	−3.23224e16	−0.922587
$352$	1.90220e15	0.0533002
$353$	−6.38707e16	−1.75698	−0.878489	−	0.477763i	$-0.841448\pi$
$353$	−6.38707e16	−1.75698	−0.878489	+	0.477763i	$0.841448\pi$
$354$	−2.07754e16	−0.561083
$355$	6.37776e15	0.169116
$356$	−2.04939e16	−0.533579
$357$	4.68517e16	1.19779
$358$	−1.26877e16	−0.318526
$359$	−7.75328e16	−1.91149	−0.955744	−	0.294198i	$-0.904947\pi$
$359$	−7.75328e16	−1.91149	−0.955744	+	0.294198i	$0.904947\pi$
$360$	4.00490e15	0.0969673
$361$	9.39346e16	2.23372
$362$	1.04806e16	0.244782
$363$	−2.79594e15	−0.0641409
$364$	−2.53732e16	−0.571764
$365$	−1.83074e16	−0.405249
$366$	−3.44204e16	−0.748496
$367$	5.87459e15	0.125501	0.0627506	−	0.998029i	$-0.480013\pi$
$367$	5.87459e15	0.125501	0.0627506	+	0.998029i	$0.480013\pi$
$368$	1.40834e16	0.295595
$369$	3.62963e16	0.748498
$370$	7.46667e15	0.151292
$371$	−1.84994e15	−0.0368323
$372$	2.25113e16	0.440425
$373$	−8.52297e16	−1.63864	−0.819320	−	0.573336i	$-0.805649\pi$
$373$	−8.52297e16	−1.63864	−0.819320	+	0.573336i	$0.805649\pi$
$374$	−1.45819e16	−0.275517
$375$	−3.53118e16	−0.655718
$376$	−6.79371e15	−0.123990
$377$	4.86058e16	0.871906
$378$	5.58383e16	0.984545
$379$	9.79727e16	1.69805	0.849024	−	0.528354i	$-0.177190\pi$
$379$	9.79727e16	1.69805	0.849024	+	0.528354i	$0.177190\pi$
$380$	2.88210e16	0.491039
$381$	3.61946e16	0.606222
$382$	−5.74507e16	−0.945984
$383$	1.15630e16	0.187188	0.0935940	−	0.995610i	$-0.470164\pi$
$383$	1.15630e16	0.187188	0.0935940	+	0.995610i	$0.470164\pi$
$384$	−3.91810e15	−0.0623624
$385$	−1.38226e16	−0.216318
$386$	1.08691e15	0.0167254
$387$	−4.82154e16	−0.729566
$388$	1.93594e16	0.288062
$389$	7.43337e16	1.08771	0.543855	−	0.839179i	$-0.316964\pi$
$389$	7.43337e16	1.08771	0.543855	+	0.839179i	$0.316964\pi$
$390$	−1.64809e16	−0.237170
$391$	−1.07961e17	−1.52798
$392$	1.84345e16	0.256608
$393$	−8.89955e16	−1.21847
$394$	3.20031e16	0.430989
$395$	2.40324e16	0.318359
$396$	−5.80989e15	−0.0757093
$397$	−4.07628e16	−0.522548	−0.261274	−	0.965265i	$-0.584143\pi$
$397$	−4.07628e16	−0.522548	−0.261274	+	0.965265i	$0.584143\pi$
$398$	−4.38126e15	−0.0552534
$399$	1.34338e17	1.66676
$400$	−1.43717e16	−0.175436
$401$	−2.84853e16	−0.342123	−0.171061	−	0.985260i	$-0.554720\pi$
$401$	−2.84853e16	−0.342123	−0.171061	+	0.985260i	$0.554720\pi$
$402$	−1.73035e16	−0.204487
$403$	9.34562e16	1.08674
$404$	−7.28889e16	−0.834031
$405$	1.19118e16	0.134128
$406$	−8.39685e16	−0.930459
$407$	−1.08319e16	−0.118124
$408$	3.00354e16	0.322361
$409$	−3.73463e16	−0.394499	−0.197250	−	0.980353i	$-0.563201\pi$
$409$	−3.73463e16	−0.394499	−0.197250	+	0.980353i	$0.563201\pi$
$410$	5.53592e16	0.575566
$411$	4.27042e16	0.437017
$412$	−4.81642e16	−0.485168
$413$	1.48999e17	1.47744
$414$	−4.30150e16	−0.419873
$415$	8.91780e16	0.856929
$416$	−1.62661e16	−0.153878
$417$	7.45150e16	0.694000
$418$	−4.18105e16	−0.383389
$419$	2.15455e15	0.0194520	0.00972602	−	0.999953i	$-0.496904\pi$
$419$	2.15455e15	0.0194520	0.00972602	+	0.999953i	$0.496904\pi$
$420$	2.84714e16	0.253097
$421$	−1.37056e17	−1.19968	−0.599841	−	0.800119i	$-0.704769\pi$
$421$	−1.37056e17	−1.19968	−0.599841	+	0.800119i	$0.704769\pi$
$422$	−1.67925e16	−0.144739
$423$	2.07500e16	0.176119
$424$	−1.18595e15	−0.00991262
$425$	1.10171e17	0.906854
$426$	1.90574e16	0.154491
$427$	2.46861e17	1.97093
$428$	5.41098e16	0.425492
$429$	2.39087e16	0.185176
$430$	−7.35383e16	−0.561008
$431$	1.30171e17	0.978165	0.489083	−	0.872237i	$-0.337332\pi$
$431$	1.30171e17	0.978165	0.489083	+	0.872237i	$0.337332\pi$
$432$	3.57964e16	0.264969
$433$	−2.33719e17	−1.70421	−0.852105	−	0.523371i	$-0.824674\pi$
$433$	−2.33719e17	−1.70421	−0.852105	+	0.523371i	$0.824674\pi$
$434$	−1.61450e17	−1.15972
$435$	−5.45407e16	−0.385958
$436$	6.50550e16	0.453543
$437$	−3.09555e17	−2.12622
$438$	−5.47044e16	−0.370203
$439$	1.35595e17	0.904117	0.452059	−	0.891988i	$-0.350690\pi$
$439$	1.35595e17	0.904117	0.452059	+	0.891988i	$0.350690\pi$
$440$	−8.86127e15	−0.0582175
$441$	−5.63044e16	−0.364495
$442$	1.24693e17	0.795419
$443$	1.72941e17	1.08711	0.543555	−	0.839374i	$-0.317078\pi$
$443$	1.72941e17	1.08711	0.543555	+	0.839374i	$0.317078\pi$
$444$	2.23112e16	0.138208
$445$	9.54693e16	0.582806
$446$	1.56542e17	0.941793
$447$	1.12466e17	0.666840
$448$	2.81004e16	0.164212
$449$	−1.36132e17	−0.784078	−0.392039	−	0.919949i	$-0.628230\pi$
$449$	−1.36132e17	−0.784078	−0.392039	+	0.919949i	$0.628230\pi$
$450$	4.38955e16	0.249195
$451$	−8.03094e16	−0.449385
$452$	2.15529e16	0.118879
$453$	−5.72861e16	−0.311466
$454$	4.05232e16	0.217191
$455$	1.18200e17	0.624513
$456$	8.61203e16	0.448574
$457$	−1.25869e17	−0.646345	−0.323172	−	0.946340i	$-0.604749\pi$
$457$	−1.25869e17	−0.646345	−0.323172	+	0.946340i	$0.604749\pi$
$458$	9.69475e15	0.0490807
$459$	−2.74408e17	−1.36967
$460$	−6.56067e16	−0.322866
$461$	−2.54842e17	−1.23656	−0.618280	−	0.785958i	$-0.712170\pi$
$461$	−2.54842e17	−1.23656	−0.618280	+	0.785958i	$0.712170\pi$
$462$	−4.13033e16	−0.197611
$463$	−3.90892e17	−1.84408	−0.922042	−	0.387089i	$-0.873481\pi$
$463$	−3.90892e17	−1.84408	−0.922042	+	0.387089i	$0.873481\pi$
$464$	−5.38300e16	−0.250413
$465$	−1.04867e17	−0.481057
$466$	−7.04919e16	−0.318883
$467$	−9.99967e16	−0.446093	−0.223047	−	0.974808i	$-0.571600\pi$
$467$	−9.99967e16	−0.446093	−0.223047	+	0.974808i	$0.571600\pi$
$468$	4.96816e16	0.218574
$469$	1.24100e17	0.538452
$470$	3.16480e16	0.135429
$471$	−1.94569e17	−0.821178
$472$	9.55196e16	0.397621
$473$	1.06682e17	0.438019
$474$	7.18115e16	0.290827
$475$	3.15892e17	1.26191
$476$	−2.15412e17	−0.848837
$477$	3.62225e15	0.0140802
$478$	−2.88738e17	−1.10719
$479$	−2.35451e17	−0.890675	−0.445337	−	0.895363i	$-0.646916\pi$
$479$	−2.35451e17	−0.890675	−0.445337	+	0.895363i	$0.646916\pi$
$480$	1.82522e16	0.0681158
$481$	9.26255e16	0.341026
$482$	3.13498e17	1.13875
$483$	−3.05800e17	−1.09592
$484$	1.28550e16	0.0454545
$485$	−9.01845e16	−0.314638
$486$	−1.82115e17	−0.626917
$487$	2.30352e17	0.782446	0.391223	−	0.920296i	$-0.372052\pi$
$487$	2.30352e17	0.782446	0.391223	+	0.920296i	$0.372052\pi$
$488$	1.58256e17	0.530434
$489$	−3.86345e17	−1.27781
$490$	−8.58757e16	−0.280282
$491$	5.51154e16	0.177518	0.0887591	−	0.996053i	$-0.471710\pi$
$491$	5.51154e16	0.177518	0.0887591	+	0.996053i	$0.471710\pi$
$492$	1.65419e17	0.525791
$493$	4.12650e17	1.29442
$494$	3.57531e17	1.10685
$495$	2.70650e16	0.0826940
$496$	−1.03501e17	−0.312114
$497$	−1.36679e17	−0.406803
$498$	2.66474e17	0.782823
$499$	1.14451e17	0.331868	0.165934	−	0.986137i	$-0.446936\pi$
$499$	1.14451e17	0.331868	0.165934	+	0.986137i	$0.446936\pi$
$500$	1.62354e17	0.464685
$501$	−2.15442e17	−0.608674
$502$	−1.38528e17	−0.386336
$503$	4.24342e17	1.16822	0.584110	−	0.811675i	$-0.301444\pi$
$503$	4.24342e17	1.16822	0.584110	+	0.811675i	$0.301444\pi$
$504$	−8.58270e16	−0.233252
$505$	3.39548e17	0.910977
$506$	9.51754e16	0.252085
$507$	6.53750e16	0.170947
$508$	−1.66413e17	−0.429609
$509$	−4.51945e17	−1.15191	−0.575957	−	0.817480i	$-0.695370\pi$
$509$	−4.51945e17	−1.15191	−0.575957	+	0.817480i	$0.695370\pi$
$510$	−1.39918e17	−0.352101
$511$	3.92336e17	0.974815
$512$	1.80144e16	0.0441942
$513$	−7.86809e17	−1.90593
$514$	2.39566e17	0.573014
$515$	2.24370e17	0.529928
$516$	−2.19740e17	−0.512492
$517$	−4.59117e16	−0.105739
$518$	−1.60014e17	−0.363928
$519$	5.35547e15	0.0120284
$520$	7.57746e16	0.168075
$521$	5.89411e17	1.29114	0.645570	−	0.763701i	$-0.276620\pi$
$521$	5.89411e17	1.29114	0.645570	+	0.763701i	$0.276620\pi$
$522$	1.64413e17	0.355695
$523$	−1.25520e17	−0.268196	−0.134098	−	0.990968i	$-0.542814\pi$
$523$	−1.25520e17	−0.268196	−0.134098	+	0.990968i	$0.542814\pi$
$524$	4.09178e17	0.863492
$525$	3.12059e17	0.650431
$526$	−2.78167e17	−0.572663
$527$	7.93417e17	1.61336
$528$	−2.64784e16	−0.0531829
$529$	2.00620e17	0.398026
$530$	5.52467e15	0.0108271
$531$	−2.91746e17	−0.564794
$532$	−6.17649e17	−1.18118
$533$	6.86743e17	1.29738
$534$	2.85273e17	0.532405
$535$	−2.52067e17	−0.464747
$536$	7.95570e16	0.144913
$537$	1.76612e17	0.317825
$538$	−2.87909e17	−0.511882
$539$	1.24579e17	0.218836
$540$	−1.66755e17	−0.289414
$541$	1.09147e18	1.87166	0.935832	−	0.352446i	$-0.114650\pi$
$541$	1.09147e18	1.87166	0.935832	+	0.352446i	$0.114650\pi$
$542$	2.70201e17	0.457816
$543$	−1.45888e17	−0.244243
$544$	−1.38095e17	−0.228446
$545$	−3.03054e17	−0.495386
$546$	3.53193e17	0.570506
$547$	−8.38667e17	−1.33867	−0.669333	−	0.742963i	$-0.733420\pi$
$547$	−8.38667e17	−1.33867	−0.669333	+	0.742963i	$0.733420\pi$
$548$	−1.96342e17	−0.309699
$549$	−4.83362e17	−0.753446
$550$	−9.71236e16	−0.149612
$551$	1.18319e18	1.80123
$552$	−1.96040e17	−0.294945
$553$	−5.15027e17	−0.765803
$554$	1.78890e17	0.262889
$555$	−1.03935e17	−0.150959
$556$	−3.42600e17	−0.491815
$557$	−3.94275e17	−0.559423	−0.279711	−	0.960084i	$-0.590239\pi$
$557$	−3.94275e17	−0.559423	−0.279711	+	0.960084i	$0.590239\pi$
$558$	3.16123e17	0.443337
$559$	−9.12258e17	−1.26456
$560$	−1.30904e17	−0.179362
$561$	2.02978e17	0.274910
$562$	3.56192e17	0.476868
$563$	−5.37163e17	−0.710889	−0.355444	−	0.934697i	$-0.615670\pi$
$563$	−5.37163e17	−0.710889	−0.355444	+	0.934697i	$0.615670\pi$
$564$	9.45678e16	0.123717
$565$	−1.00403e17	−0.129846
$566$	−7.50957e17	−0.960082
$567$	−2.55276e17	−0.322641
$568$	−8.76211e16	−0.109482
$569$	7.97334e17	0.984942	0.492471	−	0.870329i	$-0.336094\pi$
$569$	7.97334e17	0.984942	0.492471	+	0.870329i	$0.336094\pi$
$570$	−4.01186e17	−0.489958
$571$	−5.26828e16	−0.0636113	−0.0318056	−	0.999494i	$-0.510126\pi$
$571$	−5.26828e16	−0.0636113	−0.0318056	+	0.999494i	$0.510126\pi$
$572$	−1.09926e17	−0.131228
$573$	7.99709e17	0.943902
$574$	−1.18638e18	−1.38451
$575$	−7.19080e17	−0.829729
$576$	−5.50214e16	−0.0627748
$577$	−6.96269e17	−0.785479	−0.392739	−	0.919650i	$-0.628473\pi$
$577$	−6.96269e17	−0.785479	−0.392739	+	0.919650i	$0.628473\pi$
$578$	4.24712e17	0.473766
$579$	−1.51297e16	−0.0166886
$580$	2.50763e17	0.273516
$581$	−1.91113e18	−2.06132
$582$	−2.69481e17	−0.287428
$583$	−8.01461e15	−0.00845351
$584$	2.51516e17	0.262351
$585$	−2.31438e17	−0.238738
$586$	−5.20228e17	−0.530712
$587$	−1.09371e18	−1.10346	−0.551729	−	0.834023i	$-0.686032\pi$
$587$	−1.09371e18	−1.10346	−0.551729	+	0.834023i	$0.686032\pi$
$588$	−2.56606e17	−0.256044
$589$	2.27496e18	2.24504
$590$	−4.44971e17	−0.434304
$591$	−4.45480e17	−0.430041
$592$	−1.02581e17	−0.0979435
$593$	1.01813e18	0.961492	0.480746	−	0.876860i	$-0.340366\pi$
$593$	1.01813e18	0.961492	0.480746	+	0.876860i	$0.340366\pi$
$594$	2.41911e17	0.225967
$595$	1.00348e18	0.927148
$596$	−5.17088e17	−0.472567
$597$	6.09867e16	0.0551318
$598$	−8.13865e17	−0.727771
$599$	1.76214e18	1.55871	0.779354	−	0.626583i	$-0.215547\pi$
$599$	1.76214e18	1.55871	0.779354	+	0.626583i	$0.215547\pi$
$600$	2.00053e17	0.175050
$601$	−1.34738e18	−1.16628	−0.583142	−	0.812370i	$-0.698177\pi$
$601$	−1.34738e18	−1.16628	−0.583142	+	0.812370i	$0.698177\pi$
$602$	1.57596e18	1.34949
$603$	−2.42991e17	−0.205839
$604$	2.63386e17	0.220726
$605$	−5.98842e16	−0.0496480
$606$	1.01461e18	0.832196
$607$	1.24831e18	1.01297	0.506485	−	0.862249i	$-0.330945\pi$
$607$	1.24831e18	1.01297	0.506485	+	0.862249i	$0.330945\pi$
$608$	−3.95958e17	−0.317890
$609$	1.16883e18	0.928411
$610$	−7.37225e17	−0.579370
$611$	3.92601e17	0.305269
$612$	4.21783e17	0.324492
$613$	−5.51788e16	−0.0420029	−0.0210015	−	0.999779i	$-0.506685\pi$
$613$	−5.51788e16	−0.0420029	−0.0210015	+	0.999779i	$0.506685\pi$
$614$	1.54551e18	1.16407
$615$	−7.70595e17	−0.574299
$616$	1.89901e17	0.140041
$617$	−7.99015e17	−0.583044	−0.291522	−	0.956564i	$-0.594162\pi$
$617$	−7.99015e17	−0.583044	−0.291522	+	0.956564i	$0.594162\pi$
$618$	6.70441e17	0.484100
$619$	−7.56330e16	−0.0540409	−0.0270204	−	0.999635i	$-0.508602\pi$
$619$	−7.56330e16	−0.0540409	−0.0270204	+	0.999635i	$0.508602\pi$
$620$	4.82152e17	0.340909
$621$	1.79105e18	1.25318
$622$	−3.39660e17	−0.235184
$623$	−2.04596e18	−1.40192
$624$	2.26423e17	0.153539
$625$	2.89363e17	0.194188
$626$	−1.54801e18	−1.02811
$627$	5.81999e17	0.382545
$628$	8.94576e17	0.581942
$629$	7.86365e17	0.506285
$630$	3.99819e17	0.254771
$631$	−2.70211e18	−1.70417	−0.852084	−	0.523404i	$-0.824662\pi$
$631$	−2.70211e18	−1.70417	−0.852084	+	0.523404i	$0.824662\pi$
$632$	−3.30170e17	−0.206100
$633$	2.33750e17	0.144420
$634$	2.45946e17	0.150404
$635$	7.75225e17	0.469244
$636$	1.65083e16	0.00989080
$637$	−1.06531e18	−0.631783
$638$	−3.63781e17	−0.213553
$639$	2.67621e17	0.155512
$640$	−8.39189e16	−0.0482714
$641$	−2.14427e18	−1.22096	−0.610481	−	0.792031i	$-0.709024\pi$
$641$	−2.14427e18	−1.22096	−0.610481	+	0.792031i	$0.709024\pi$
$642$	−7.53203e17	−0.424556
$643$	−5.55483e16	−0.0309955	−0.0154978	−	0.999880i	$-0.504933\pi$
$643$	−5.55483e16	−0.0309955	−0.0154978	+	0.999880i	$0.504933\pi$
$644$	1.40599e18	0.776645
$645$	1.02365e18	0.559773
$646$	3.03534e18	1.64322
$647$	−1.20663e17	−0.0646693	−0.0323346	−	0.999477i	$-0.510294\pi$
$647$	−1.20663e17	−0.0646693	−0.0323346	+	0.999477i	$0.510294\pi$
$648$	−1.63650e17	−0.0868320
$649$	6.45518e17	0.339092
$650$	8.30524e17	0.431932
$651$	2.24736e18	1.15717
$652$	1.77631e18	0.905544
$653$	−1.16372e18	−0.587372	−0.293686	−	0.955902i	$-0.594882\pi$
$653$	−1.16372e18	−0.587372	−0.293686	+	0.955902i	$0.594882\pi$
$654$	−9.05559e17	−0.452545
$655$	−1.90613e18	−0.943155
$656$	−7.60554e17	−0.372611
$657$	−7.68206e17	−0.372651
$658$	−6.78234e17	−0.325770
$659$	−4.59728e16	−0.0218648	−0.0109324	−	0.999940i	$-0.503480\pi$
$659$	−4.59728e16	−0.0218648	−0.0109324	+	0.999940i	$0.503480\pi$
$660$	1.23348e17	0.0580893
$661$	3.20380e18	1.49402	0.747010	−	0.664813i	$-0.231489\pi$
$661$	3.20380e18	1.49402	0.747010	+	0.664813i	$0.231489\pi$
$662$	−6.67212e17	−0.308097
$663$	−1.73571e18	−0.793668
$664$	−1.22517e18	−0.554760
$665$	2.87728e18	1.29015
$666$	3.13313e17	0.139122
$667$	−2.69335e18	−1.18434
$668$	9.90544e17	0.431347
$669$	−2.17906e18	−0.939720
$670$	−3.70611e17	−0.158282
$671$	1.06949e18	0.452356
$672$	−3.91154e17	−0.163851
$673$	−6.62013e17	−0.274643	−0.137321	−	0.990527i	$-0.543849\pi$
$673$	−6.62013e17	−0.274643	−0.137321	+	0.990527i	$0.543849\pi$
$674$	2.62919e18	1.08027
$675$	−1.82771e18	−0.743762
$676$	−3.00577e17	−0.121144
$677$	−3.41465e18	−1.36308	−0.681538	−	0.731783i	$-0.738688\pi$
$677$	−3.41465e18	−1.36308	−0.681538	+	0.731783i	$0.738688\pi$
$678$	−3.00014e17	−0.118617
$679$	1.93270e18	0.756852
$680$	6.43305e17	0.249522
$681$	−5.64080e17	−0.216713
$682$	−6.99456e17	−0.266172
$683$	−3.22490e18	−1.21557	−0.607787	−	0.794100i	$-0.707942\pi$
$683$	−3.22490e18	−1.21557	−0.607787	+	0.794100i	$0.707942\pi$
$684$	1.20938e18	0.451541
$685$	9.14648e17	0.338271
$686$	−6.95276e17	−0.254713
$687$	−1.34950e17	−0.0489727
$688$	1.01031e18	0.363186
$689$	6.85347e16	0.0244054
$690$	9.13239e17	0.322155
$691$	1.76193e18	0.615718	0.307859	−	0.951432i	$-0.400388\pi$
$691$	1.76193e18	0.615718	0.307859	+	0.951432i	$0.400388\pi$
$692$	−2.46230e16	−0.00852416
$693$	−5.80016e17	−0.198918
$694$	−1.69999e18	−0.577577
$695$	1.59598e18	0.537188
$696$	7.49308e17	0.249862
$697$	5.83025e18	1.92608
$698$	−4.16651e18	−1.36368
$699$	9.81241e17	0.318181
$700$	−1.43477e18	−0.460939
$701$	1.49504e18	0.475867	0.237933	−	0.971281i	$-0.423530\pi$
$701$	1.49504e18	0.475867	0.237933	+	0.971281i	$0.423530\pi$
$702$	−2.06863e18	−0.652368
$703$	2.25474e18	0.704510
$704$	1.21741e17	0.0376889
$705$	−4.40538e17	−0.135131
$706$	−4.08773e18	−1.24237
$707$	−7.27669e18	−2.19133
$708$	−1.32962e18	−0.396746
$709$	4.36588e18	1.29084	0.645418	−	0.763830i	$-0.276683\pi$
$709$	4.36588e18	1.29084	0.645418	+	0.763830i	$0.276683\pi$
$710$	4.08177e17	0.119583
$711$	1.00844e18	0.292750
$712$	−1.31161e18	−0.377298
$713$	−5.17861e18	−1.47615
$714$	2.99851e18	0.846968
$715$	5.12082e17	0.143334
$716$	−8.12015e17	−0.225232
$717$	4.01921e18	1.10476
$718$	−4.96210e18	−1.35163
$719$	−1.08446e18	−0.292737	−0.146368	−	0.989230i	$-0.546758\pi$
$719$	−1.08446e18	−0.292737	−0.146368	+	0.989230i	$0.546758\pi$
$720$	2.56314e17	0.0685662
$721$	−4.80836e18	−1.27473
$722$	6.01181e18	1.57948
$723$	−4.36387e18	−1.13625
$724$	6.70756e17	0.173087
$725$	2.74848e18	0.702904
$726$	−1.78940e17	−0.0453545
$727$	2.78867e18	0.700525	0.350262	−	0.936652i	$-0.386092\pi$
$727$	2.78867e18	0.700525	0.350262	+	0.936652i	$0.386092\pi$
$728$	−1.62389e18	−0.404298
$729$	3.53032e18	0.871135
$730$	−1.17167e18	−0.286554
$731$	−7.74481e18	−1.87736
$732$	−2.20291e18	−0.529267
$733$	−2.43955e18	−0.580943	−0.290472	−	0.956884i	$-0.593812\pi$
$733$	−2.43955e18	−0.580943	−0.290472	+	0.956884i	$0.593812\pi$
$734$	3.75974e17	0.0887428
$735$	1.19538e18	0.279665
$736$	9.01340e17	0.209017
$737$	5.37644e17	0.123582
$738$	2.32296e18	0.529268
$739$	6.60898e18	1.49261	0.746304	−	0.665605i	$-0.231827\pi$
$739$	6.60898e18	1.49261	0.746304	+	0.665605i	$0.231827\pi$
$740$	4.77867e17	0.106979
$741$	−4.97679e18	−1.10441
$742$	−1.18396e17	−0.0260443
$743$	−4.64117e18	−1.01204	−0.506022	−	0.862520i	$-0.668885\pi$
$743$	−4.64117e18	−1.01204	−0.506022	+	0.862520i	$0.668885\pi$
$744$	1.44072e18	0.311427
$745$	2.40882e18	0.516165
$746$	−5.45470e18	−1.15869
$747$	3.74205e18	0.787999
$748$	−9.33240e17	−0.194820
$749$	5.40192e18	1.11794
$750$	−2.25996e18	−0.463663
$751$	4.82668e18	0.981724	0.490862	−	0.871237i	$-0.336682\pi$
$751$	4.82668e18	0.981724	0.490862	+	0.871237i	$0.336682\pi$
$752$	−4.34797e17	−0.0876740
$753$	1.92830e18	0.385485
$754$	3.11077e18	0.616530
$755$	−1.22697e18	−0.241089
$756$	3.57365e18	0.696178
$757$	6.06453e18	1.17132	0.585658	−	0.810558i	$-0.300836\pi$
$757$	6.06453e18	1.17132	0.585658	+	0.810558i	$0.300836\pi$
$758$	6.27025e18	1.20070
$759$	−1.32483e18	−0.251530
$760$	1.84455e18	0.347217
$761$	5.49710e18	1.02597	0.512984	−	0.858398i	$-0.328540\pi$
$761$	5.49710e18	1.02597	0.512984	+	0.858398i	$0.328540\pi$
$762$	2.31646e18	0.428664
$763$	6.49461e18	1.19164
$764$	−3.67685e18	−0.668911
$765$	−1.96485e18	−0.354429
$766$	7.40031e17	0.132362
$767$	−5.51996e18	−0.978963
$768$	−2.50759e17	−0.0440969
$769$	−3.37929e18	−0.589256	−0.294628	−	0.955612i	$-0.595196\pi$
$769$	−3.37929e18	−0.589256	−0.294628	+	0.955612i	$0.595196\pi$
$770$	−8.84643e17	−0.152960
$771$	−3.33474e18	−0.571753
$772$	6.95624e16	0.0118267
$773$	−1.34462e18	−0.226690	−0.113345	−	0.993556i	$-0.536157\pi$
$773$	−1.34462e18	−0.226690	−0.113345	+	0.993556i	$0.536157\pi$
$774$	−3.08579e18	−0.515881
$775$	5.28461e18	0.876097
$776$	1.23900e18	0.203690
$777$	2.22739e18	0.363127
$778$	4.75735e18	0.769127
$779$	1.67171e19	2.68020
$780$	−1.05477e18	−0.167705
$781$	−5.92140e17	−0.0933669
$782$	−6.90948e18	−1.08044
$783$	−6.84580e18	−1.06163
$784$	1.17980e18	0.181450
$785$	−4.16732e18	−0.635630
$786$	−5.69571e18	−0.861592
$787$	5.34448e18	0.801806	0.400903	−	0.916120i	$-0.368696\pi$
$787$	5.34448e18	0.801806	0.400903	+	0.916120i	$0.368696\pi$
$788$	2.04820e18	0.304756
$789$	3.87206e18	0.571402
$790$	1.53808e18	0.225114
$791$	2.15168e18	0.312342
$792$	−3.71833e17	−0.0535346
$793$	−9.14543e18	−1.30596
$794$	−2.60882e18	−0.369497
$795$	−7.69029e16	−0.0108033
$796$	−2.80401e17	−0.0390701
$797$	1.11778e18	0.154482	0.0772409	−	0.997012i	$-0.475389\pi$
$797$	1.11778e18	0.154482	0.0772409	+	0.997012i	$0.475389\pi$
$798$	8.59762e18	1.17858
$799$	3.33307e18	0.453200
$800$	−9.19790e17	−0.124052
$801$	4.00605e18	0.535926
$802$	−1.82306e18	−0.241917
$803$	1.69974e18	0.223733
$804$	−1.10743e18	−0.144594
$805$	−6.54969e18	−0.848296
$806$	5.98120e18	0.768441
$807$	4.00766e18	0.510756
$808$	−4.66489e18	−0.589749
$809$	−1.47598e19	−1.85104	−0.925521	−	0.378697i	$-0.876372\pi$
$809$	−1.47598e19	−1.85104	−0.925521	+	0.378697i	$0.876372\pi$
$810$	7.62355e17	0.0948428
$811$	−1.40141e19	−1.72953	−0.864767	−	0.502173i	$-0.832534\pi$
$811$	−1.40141e19	−1.72953	−0.864767	+	0.502173i	$0.832534\pi$
$812$	−5.37399e18	−0.657934
$813$	−3.76117e18	−0.456809
$814$	−6.93239e17	−0.0835265
$815$	−8.27483e18	−0.989087
$816$	1.92226e18	0.227943
$817$	−2.22067e19	−2.61240
$818$	−2.39017e18	−0.278953
$819$	4.95984e18	0.574279
$820$	3.54299e18	0.406987
$821$	3.74661e17	0.0426981	0.0213490	−	0.999772i	$-0.493204\pi$
$821$	3.74661e17	0.0426981	0.0213490	+	0.999772i	$0.493204\pi$
$822$	2.73307e18	0.309018
$823$	−1.42852e18	−0.160246	−0.0801232	−	0.996785i	$-0.525531\pi$
$823$	−1.42852e18	−0.160246	−0.0801232	+	0.996785i	$0.525531\pi$
$824$	−3.08251e18	−0.343066
$825$	1.35195e18	0.149283
$826$	9.53596e18	1.04471
$827$	−6.43302e18	−0.699245	−0.349622	−	0.936891i	$-0.613690\pi$
$827$	−6.43302e18	−0.699245	−0.349622	+	0.936891i	$0.613690\pi$
$828$	−2.75296e18	−0.296895
$829$	1.65255e19	1.76828	0.884140	−	0.467223i	$-0.154745\pi$
$829$	1.65255e19	1.76828	0.884140	+	0.467223i	$0.154745\pi$
$830$	5.70739e18	0.605941
$831$	−2.49013e18	−0.262310
$832$	−1.04103e18	−0.108808
$833$	−9.04414e18	−0.937940
$834$	4.76896e18	0.490732
$835$	−4.61438e18	−0.471142
$836$	−2.67587e18	−0.271097
$837$	−1.31627e19	−1.32321
$838$	1.37891e17	0.0137547
$839$	8.31033e18	0.822557	0.411278	−	0.911510i	$-0.365082\pi$
$839$	8.31033e18	0.822557	0.411278	+	0.911510i	$0.365082\pi$
$840$	1.82217e18	0.178967
$841$	3.39566e16	0.00330940
$842$	−8.77161e18	−0.848303
$843$	−4.95816e18	−0.475818
$844$	−1.07472e18	−0.102346
$845$	1.40022e18	0.132320
$846$	1.32800e18	0.124535
$847$	1.28335e18	0.119427
$848$	−7.59008e16	−0.00700928
$849$	1.04532e19	0.957969
$850$	7.05092e18	0.641243
$851$	−5.13258e18	−0.463226
$852$	1.21968e18	0.109241
$853$	4.65134e18	0.413437	0.206718	−	0.978400i	$-0.433722\pi$
$853$	4.65134e18	0.413437	0.206718	+	0.978400i	$0.433722\pi$
$854$	1.57991e19	1.39366
$855$	−5.63380e18	−0.493198
$856$	3.46303e18	0.300868
$857$	−1.85183e19	−1.59671	−0.798353	−	0.602189i	$-0.794295\pi$
$857$	−1.85183e19	−1.59671	−0.798353	+	0.602189i	$0.794295\pi$
$858$	1.53016e18	0.130939
$859$	6.46518e18	0.549067	0.274533	−	0.961578i	$-0.411477\pi$
$859$	6.46518e18	0.549067	0.274533	+	0.961578i	$0.411477\pi$
$860$	−4.70645e18	−0.396692
$861$	1.65142e19	1.38146
$862$	8.33095e18	0.691667
$863$	1.68337e19	1.38711	0.693554	−	0.720405i	$-0.256044\pi$
$863$	1.68337e19	1.38711	0.693554	+	0.720405i	$0.256044\pi$
$864$	2.29097e18	0.187362
$865$	1.14705e17	0.00931057
$866$	−1.49580e19	−1.20506
$867$	−5.91196e18	−0.472723
$868$	−1.03328e19	−0.820046
$869$	−2.23128e18	−0.175762
$870$	−3.49060e18	−0.272914
$871$	−4.59751e18	−0.356783
$872$	4.16352e18	0.320703
$873$	−3.78428e18	−0.289329
$874$	−1.98115e19	−1.50347
$875$	1.62083e19	1.22091
$876$	−3.50108e18	−0.261773
$877$	−2.58967e19	−1.92197	−0.960987	−	0.276593i	$-0.910795\pi$
$877$	−2.58967e19	−1.92197	−0.960987	+	0.276593i	$0.910795\pi$
$878$	8.67809e18	0.639308
$879$	7.24152e18	0.529544
$880$	−5.67121e17	−0.0411660
$881$	−2.16077e18	−0.155692	−0.0778458	−	0.996965i	$-0.524804\pi$
$881$	−2.16077e18	−0.155692	−0.0778458	+	0.996965i	$0.524804\pi$
$882$	−3.60348e18	−0.257737
$883$	1.86376e19	1.32326	0.661632	−	0.749829i	$-0.269864\pi$
$883$	1.86376e19	1.32326	0.661632	+	0.749829i	$0.269864\pi$
$884$	7.98033e18	0.562446
$885$	6.19396e18	0.433348
$886$	1.10682e19	0.768703
$887$	1.09599e19	0.755616	0.377808	−	0.925884i	$-0.376678\pi$
$887$	1.09599e19	0.755616	0.377808	+	0.925884i	$0.376678\pi$
$888$	1.42792e18	0.0977279
$889$	−1.66135e19	−1.12875
$890$	6.11004e18	0.412106
$891$	−1.10594e18	−0.0740505
$892$	1.00187e19	0.665948
$893$	9.55689e18	0.630641
$894$	7.19781e18	0.471527
$895$	3.78272e18	0.246011
$896$	1.79842e18	0.116115
$897$	1.13289e19	0.726169
$898$	−8.71245e18	−0.554427
$899$	1.97938e19	1.25052
$900$	2.80931e18	0.176207
$901$	5.81840e17	0.0362320
$902$	−5.13980e18	−0.317763
$903$	−2.19373e19	−1.34652
$904$	1.37938e18	0.0840601
$905$	−3.12467e18	−0.189055
$906$	−3.66631e18	−0.220240
$907$	2.17959e19	1.29995	0.649977	−	0.759954i	$-0.274778\pi$
$907$	2.17959e19	1.29995	0.649977	+	0.759954i	$0.274778\pi$
$908$	2.59349e18	0.153577
$909$	1.42480e19	0.837699
$910$	7.56477e18	0.441598
$911$	−4.15235e18	−0.240672	−0.120336	−	0.992733i	$-0.538397\pi$
$911$	−4.15235e18	−0.240672	−0.120336	+	0.992733i	$0.538397\pi$
$912$	5.51170e18	0.317190
$913$	−8.27969e18	−0.473101
$914$	−8.05563e18	−0.457035
$915$	1.02621e19	0.578095
$916$	6.20464e17	0.0347053
$917$	4.08493e19	2.26873
$918$	−1.75621e19	−0.968500
$919$	1.53057e18	0.0838110	0.0419055	−	0.999122i	$-0.486657\pi$
$919$	1.53057e18	0.0838110	0.0419055	+	0.999122i	$0.486657\pi$
$920$	−4.19883e18	−0.228301
$921$	−2.15134e19	−1.16151
$922$	−1.63099e19	−0.874380
$923$	5.06352e18	0.269551
$924$	−2.64341e18	−0.139732
$925$	5.23764e18	0.274925
$926$	−2.50171e19	−1.30396
$927$	9.41491e18	0.487302
$928$	−3.44512e18	−0.177069
$929$	−6.73168e18	−0.343575	−0.171787	−	0.985134i	$-0.554954\pi$
$929$	−6.73168e18	−0.343575	−0.171787	+	0.985134i	$0.554954\pi$
$930$	−6.71151e18	−0.340159
$931$	−2.59322e19	−1.30517
$932$	−4.51148e18	−0.225484
$933$	4.72804e18	0.234666
$934$	−6.39979e18	−0.315436
$935$	4.34743e18	0.212793
$936$	3.17962e18	0.154555
$937$	−2.39113e19	−1.15424	−0.577120	−	0.816659i	$-0.695824\pi$
$937$	−2.39113e19	−1.15424	−0.577120	+	0.816659i	$0.695824\pi$
$938$	7.94238e18	0.380743
$939$	2.15481e19	1.02585
$940$	2.02548e18	0.0957626
$941$	1.71543e19	0.805455	0.402728	−	0.915320i	$-0.368062\pi$
$941$	1.71543e19	0.805455	0.402728	+	0.915320i	$0.368062\pi$
$942$	−1.24524e19	−0.580661
$943$	−3.80539e19	−1.76227
$944$	6.11325e18	0.281160
$945$	−1.66476e19	−0.760405
$946$	6.82763e18	0.309726
$947$	3.55165e19	1.60013	0.800064	−	0.599914i	$-0.204799\pi$
$947$	3.55165e19	1.60013	0.800064	+	0.599914i	$0.204799\pi$
$948$	4.59594e18	0.205646
$949$	−1.45348e19	−0.645921
$950$	2.02171e19	0.892308
$951$	−3.42354e18	−0.150073
$952$	−1.37863e19	−0.600218
$953$	1.17913e19	0.509868	0.254934	−	0.966959i	$-0.417946\pi$
$953$	1.17913e19	0.509868	0.254934	+	0.966959i	$0.417946\pi$
$954$	2.31824e17	0.00995621
$955$	1.71283e19	0.730623
$956$	−1.84792e19	−0.782903
$957$	5.06380e18	0.213083
$958$	−1.50688e19	−0.629802
$959$	−1.96014e19	−0.813702
$960$	1.16814e18	0.0481651
$961$	1.36407e19	0.558644
$962$	5.92803e18	0.241142
$963$	−1.05771e19	−0.427363
$964$	2.00639e19	0.805220
$965$	−3.24052e17	−0.0129178
$966$	−1.95712e19	−0.774936
$967$	3.44703e18	0.135573	0.0677866	−	0.997700i	$-0.478406\pi$
$967$	3.44703e18	0.135573	0.0677866	+	0.997700i	$0.478406\pi$
$968$	8.22720e17	0.0321412
$969$	−4.22516e19	−1.63960
$970$	−5.77181e18	−0.222482
$971$	−1.00588e19	−0.385143	−0.192571	−	0.981283i	$-0.561683\pi$
$971$	−1.00588e19	−0.385143	−0.192571	+	0.981283i	$0.561683\pi$
$972$	−1.16554e19	−0.443298
$973$	−3.42027e19	−1.29219
$974$	1.47426e19	0.553273
$975$	−1.15608e19	−0.430981
$976$	1.01284e19	0.375074
$977$	1.62882e19	0.599182	0.299591	−	0.954068i	$-0.403150\pi$
$977$	1.62882e19	0.599182	0.299591	+	0.954068i	$0.403150\pi$
$978$	−2.47261e19	−0.903551
$979$	−8.86380e18	−0.321760
$980$	−5.49604e18	−0.198189
$981$	−1.27166e19	−0.455537
$982$	3.52738e18	0.125524
$983$	1.40217e18	0.0495683	0.0247841	−	0.999693i	$-0.492110\pi$
$983$	1.40217e18	0.0495683	0.0247841	+	0.999693i	$0.492110\pi$
$984$	1.05868e19	0.371791
$985$	−9.54139e18	−0.332871
$986$	2.64096e19	0.915296
$987$	9.44095e18	0.325053
$988$	2.28820e19	0.782660
$989$	5.05501e19	1.71770
$990$	1.73216e18	0.0584735
$991$	−2.38767e19	−0.800747	−0.400373	−	0.916352i	$-0.631120\pi$
$991$	−2.38767e19	−0.800747	−0.400373	+	0.916352i	$0.631120\pi$
$992$	−6.62406e18	−0.220698
$993$	9.28752e18	0.307418
$994$	−8.74744e18	−0.287653
$995$	1.30623e18	0.0426745
$996$	1.70543e19	0.553539
$997$	1.79348e19	0.578332	0.289166	−	0.957279i	$-0.406622\pi$
$997$	1.79348e19	0.578332	0.289166	+	0.957279i	$0.406622\pi$
$998$	7.32484e18	0.234666
$999$	−1.30457e19	−0.415232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.a.c.1.1	✓	2
3.2	odd	2		198.14.a.a.1.2		2
4.3	odd	2		176.14.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.a.c.1.1	✓	2	1.1	even	1	trivial
176.14.a.c.1.2		2	4.3	odd	2
198.14.a.a.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} -890.874 q^{3} +4096.00 q^{4} -19080.9 q^{5} -57015.9 q^{6} +408914. q^{7} +262144. q^{8} -800667. q^{9} +O(q^{10})\)	\(q+64.0000 q^{2} -890.874 q^{3} +4096.00 q^{4} -19080.9 q^{5} -57015.9 q^{6} +408914. q^{7} +262144. q^{8} -800667. q^{9} -1.22118e6 q^{10} +1.77156e6 q^{11} -3.64902e6 q^{12} -1.51490e7 q^{13} +2.61705e7 q^{14} +1.69987e7 q^{15} +1.67772e7 q^{16} -1.28611e8 q^{17} -5.12427e7 q^{18} -3.68765e8 q^{19} -7.81555e7 q^{20} -3.64291e8 q^{21} +1.13380e8 q^{22} +8.39438e8 q^{23} -2.33537e8 q^{24} -8.56621e8 q^{25} -9.69536e8 q^{26} +2.13363e9 q^{27} +1.67491e9 q^{28} -3.20852e9 q^{29} +1.08792e9 q^{30} -6.16914e9 q^{31} +1.07374e9 q^{32} -1.57824e9 q^{33} -8.23108e9 q^{34} -7.80247e9 q^{35} -3.27953e9 q^{36} -6.11430e9 q^{37} -2.36010e10 q^{38} +1.34958e10 q^{39} -5.00195e9 q^{40} -4.53326e10 q^{41} -2.33146e10 q^{42} +6.02190e10 q^{43} +7.25631e9 q^{44} +1.52775e10 q^{45} +5.37240e10 q^{46} -2.59159e10 q^{47} -1.49464e10 q^{48} +7.03219e10 q^{49} -5.48237e10 q^{50} +1.14576e11 q^{51} -6.20503e10 q^{52} -4.52404e9 q^{53} +1.36553e11 q^{54} -3.38031e10 q^{55} +1.07194e11 q^{56} +3.28523e11 q^{57} -2.05345e11 q^{58} +3.64378e11 q^{59} +6.96267e10 q^{60} +6.03699e11 q^{61} -3.94825e11 q^{62} -3.27404e11 q^{63} +6.87195e10 q^{64} +2.89057e11 q^{65} -1.01007e11 q^{66} +3.03486e11 q^{67} -5.26789e11 q^{68} -7.47833e11 q^{69} -4.99358e11 q^{70} -3.34248e11 q^{71} -2.09890e11 q^{72} +9.59457e11 q^{73} -3.91315e11 q^{74} +7.63141e11 q^{75} -1.51046e12 q^{76} +7.24417e11 q^{77} +8.63734e11 q^{78} -1.25950e12 q^{79} -3.20125e11 q^{80} -6.24277e11 q^{81} -2.90128e12 q^{82} -4.67367e12 q^{83} -1.49214e12 q^{84} +2.45401e12 q^{85} +3.85402e12 q^{86} +2.85838e12 q^{87} +4.64404e11 q^{88} -5.00339e12 q^{89} +9.77759e11 q^{90} -6.19464e12 q^{91} +3.43834e12 q^{92} +5.49592e12 q^{93} -1.65862e12 q^{94} +7.03638e12 q^{95} -9.56568e11 q^{96} +4.72642e12 q^{97} +4.50060e12 q^{98} -1.41843e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9}+O(q^{10}) \) 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9	\( 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9} + 186496 q^{10} + 3543122 q^{11} - 3792896 q^{12} - 6948916 q^{13} - 10915840 q^{14} + 16226114 q^{15} + 33554432 q^{16} - 280144288 q^{17} - 153200384 q^{18} - 349231788 q^{19} + 11935744 q^{20} - 343936280 q^{21} + 226759808 q^{22} - 151278294 q^{23} - 242745344 q^{24} - 1593546344 q^{25} - 444730624 q^{26} + 2245595374 q^{27} - 698613760 q^{28} - 771621928 q^{29} + 1038471296 q^{30} - 8626482070 q^{31} + 2147483648 q^{32} - 1640465486 q^{33} - 17929234432 q^{34} - 20547972800 q^{35} - 9804824576 q^{36} - 26333898490 q^{37} - 22350834432 q^{38} + 13207805428 q^{39} + 763887616 q^{40} - 3560991836 q^{41} - 22011921920 q^{42} - 16329995932 q^{43} + 14512627712 q^{44} - 19762426588 q^{45} - 9681810816 q^{46} + 9513351704 q^{47} - 15535702016 q^{48} + 309223257786 q^{49} - 101986966016 q^{50} + 119898691720 q^{51} - 28462759936 q^{52} + 291363898652 q^{53} + 143718103936 q^{54} + 5162328754 q^{55} - 44711280640 q^{56} + 327836886300 q^{57} - 49383803392 q^{58} + 712019011182 q^{59} + 66462162944 q^{60} + 138918582944 q^{61} - 552094852480 q^{62} + 595750060240 q^{63} + 137438953472 q^{64} + 469417380748 q^{65} - 104989791104 q^{66} + 912599195574 q^{67} - 1147471003648 q^{68} - 713033152350 q^{69} - 1315070259200 q^{70} - 1560848343722 q^{71} - 627508772864 q^{72} + 407382417996 q^{73} - 1685369503360 q^{74} + 789026369816 q^{75} - 1430453403648 q^{76} - 302157444160 q^{77} + 845299547392 q^{78} - 48102676468 q^{79} + 48888807424 q^{80} + 1911689036650 q^{81} - 227903477504 q^{82} - 6313820551012 q^{83} - 1408763002880 q^{84} - 878959681568 q^{85} - 1045119739648 q^{86} + 2772785468872 q^{87} + 928808173568 q^{88} + 977692325462 q^{89} - 1264795301632 q^{90} - 10946374648120 q^{91} - 619635892224 q^{92} + 5582240738434 q^{93} + 608854509056 q^{94} + 7466012570772 q^{95} - 994284929024 q^{96} - 1024977303502 q^{97} + 19790288498304 q^{98} - 4240684773116 q^{99}+O(q^{100}) \) 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9 + 186496 * q^10 + 3543122 * q^11 - 3792896 * q^12 - 6948916 * q^13 - 10915840 * q^14 + 16226114 * q^15 + 33554432 * q^16 - 280144288 * q^17 - 153200384 * q^18 - 349231788 * q^19 + 11935744 * q^20 - 343936280 * q^21 + 226759808 * q^22 - 151278294 * q^23 - 242745344 * q^24 - 1593546344 * q^25 - 444730624 * q^26 + 2245595374 * q^27 - 698613760 * q^28 - 771621928 * q^29 + 1038471296 * q^30 - 8626482070 * q^31 + 2147483648 * q^32 - 1640465486 * q^33 - 17929234432 * q^34 - 20547972800 * q^35 - 9804824576 * q^36 - 26333898490 * q^37 - 22350834432 * q^38 + 13207805428 * q^39 + 763887616 * q^40 - 3560991836 * q^41 - 22011921920 * q^42 - 16329995932 * q^43 + 14512627712 * q^44 - 19762426588 * q^45 - 9681810816 * q^46 + 9513351704 * q^47 - 15535702016 * q^48 + 309223257786 * q^49 - 101986966016 * q^50 + 119898691720 * q^51 - 28462759936 * q^52 + 291363898652 * q^53 + 143718103936 * q^54 + 5162328754 * q^55 - 44711280640 * q^56 + 327836886300 * q^57 - 49383803392 * q^58 + 712019011182 * q^59 + 66462162944 * q^60 + 138918582944 * q^61 - 552094852480 * q^62 + 595750060240 * q^63 + 137438953472 * q^64 + 469417380748 * q^65 - 104989791104 * q^66 + 912599195574 * q^67 - 1147471003648 * q^68 - 713033152350 * q^69 - 1315070259200 * q^70 - 1560848343722 * q^71 - 627508772864 * q^72 + 407382417996 * q^73 - 1685369503360 * q^74 + 789026369816 * q^75 - 1430453403648 * q^76 - 302157444160 * q^77 + 845299547392 * q^78 - 48102676468 * q^79 + 48888807424 * q^80 + 1911689036650 * q^81 - 227903477504 * q^82 - 6313820551012 * q^83 - 1408763002880 * q^84 - 878959681568 * q^85 - 1045119739648 * q^86 + 2772785468872 * q^87 + 928808173568 * q^88 + 977692325462 * q^89 - 1264795301632 * q^90 - 10946374648120 * q^91 - 619635892224 * q^92 + 5582240738434 * q^93 + 608854509056 * q^94 + 7466012570772 * q^95 - 994284929024 * q^96 - 1024977303502 * q^97 + 19790288498304 * q^98 - 4240684773116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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