LMFDB - Embedded newform 177.12.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-54.1540 q^{2} +243.000 q^{3} +884.652 q^{4} -9497.19 q^{5} -13159.4 q^{6} -21091.6 q^{7} +62999.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-54.1540 q^{2} +243.000 q^{3} +884.652 q^{4} -9497.19 q^{5} -13159.4 q^{6} -21091.6 q^{7} +62999.9 q^{8} +59049.0 q^{9} +514310. q^{10} -843837. q^{11} +214970. q^{12} +2.09397e6 q^{13} +1.14219e6 q^{14} -2.30782e6 q^{15} -5.22346e6 q^{16} -5.90682e6 q^{17} -3.19774e6 q^{18} +4.14828e6 q^{19} -8.40171e6 q^{20} -5.12525e6 q^{21} +4.56971e7 q^{22} -4.05086e7 q^{23} +1.53090e7 q^{24} +4.13685e7 q^{25} -1.13397e8 q^{26} +1.43489e7 q^{27} -1.86587e7 q^{28} +7.14544e7 q^{29} +1.24977e8 q^{30} +2.22524e8 q^{31} +1.53847e8 q^{32} -2.05052e8 q^{33} +3.19878e8 q^{34} +2.00310e8 q^{35} +5.22378e7 q^{36} +5.50364e8 q^{37} -2.24646e8 q^{38} +5.08836e8 q^{39} -5.98322e8 q^{40} -3.58060e8 q^{41} +2.77552e8 q^{42} -8.90997e8 q^{43} -7.46502e8 q^{44} -5.60799e8 q^{45} +2.19370e9 q^{46} +2.37132e9 q^{47} -1.26930e9 q^{48} -1.53247e9 q^{49} -2.24027e9 q^{50} -1.43536e9 q^{51} +1.85244e9 q^{52} +2.90109e9 q^{53} -7.77050e8 q^{54} +8.01408e9 q^{55} -1.32877e9 q^{56} +1.00803e9 q^{57} -3.86954e9 q^{58} -7.14924e8 q^{59} -2.04161e9 q^{60} -7.97897e9 q^{61} -1.20505e10 q^{62} -1.24544e9 q^{63} +2.36620e9 q^{64} -1.98869e10 q^{65} +1.11044e10 q^{66} +9.55219e9 q^{67} -5.22548e9 q^{68} -9.84360e9 q^{69} -1.08476e10 q^{70} -1.49378e9 q^{71} +3.72008e9 q^{72} -4.31992e8 q^{73} -2.98044e10 q^{74} +1.00525e10 q^{75} +3.66979e9 q^{76} +1.77978e10 q^{77} -2.75555e10 q^{78} +4.22383e10 q^{79} +4.96082e10 q^{80} +3.48678e9 q^{81} +1.93904e10 q^{82} +6.44130e9 q^{83} -4.53406e9 q^{84} +5.60982e10 q^{85} +4.82510e10 q^{86} +1.73634e10 q^{87} -5.31617e10 q^{88} +1.02190e11 q^{89} +3.03695e10 q^{90} -4.41651e10 q^{91} -3.58360e10 q^{92} +5.40732e10 q^{93} -1.28416e11 q^{94} -3.93970e10 q^{95} +3.73849e10 q^{96} +1.09002e11 q^{97} +8.29895e10 q^{98} -4.98278e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	−54.1540	−1.19664	−0.598322	−	0.801255i	$-0.704166\pi$
$2$	−54.1540	−1.19664	−0.598322	+	0.801255i	$0.704166\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	884.652	0.431959
$5$	−9497.19	−1.35913	−0.679563	−	0.733617i	$-0.737831\pi$
$5$	−9497.19	−1.35913	−0.679563	+	0.733617i	$0.737831\pi$
$6$	−13159.4	−0.690883
$7$	−21091.6	−0.474318	−0.237159	−	0.971471i	$-0.576216\pi$
$7$	−21091.6	−0.474318	−0.237159	+	0.971471i	$0.576216\pi$
$8$	62999.9	0.679743
$9$	59049.0	0.333333
$10$	514310.	1.62639
$11$	−843837.	−1.57979	−0.789894	−	0.613243i	$-0.789865\pi$
$11$	−843837.	−1.57979	−0.789894	+	0.613243i	$0.789865\pi$
$12$	214970.	0.249392
$13$	2.09397e6	1.56417	0.782083	−	0.623175i	$-0.214157\pi$
$13$	2.09397e6	1.56417	0.782083	+	0.623175i	$0.214157\pi$
$14$	1.14219e6	0.567590
$15$	−2.30782e6	−0.784692
$16$	−5.22346e6	−1.24537
$17$	−5.90682e6	−1.00899	−0.504493	−	0.863416i	$-0.668320\pi$
$17$	−5.90682e6	−1.00899	−0.504493	+	0.863416i	$0.668320\pi$
$18$	−3.19774e6	−0.398882
$19$	4.14828e6	0.384347	0.192173	−	0.981361i	$-0.438446\pi$
$19$	4.14828e6	0.384347	0.192173	+	0.981361i	$0.438446\pi$
$20$	−8.40171e6	−0.587087
$21$	−5.12525e6	−0.273847
$22$	4.56971e7	1.89045
$23$	−4.05086e7	−1.31233	−0.656167	−	0.754616i	$-0.727823\pi$
$23$	−4.05086e7	−1.31233	−0.656167	+	0.754616i	$0.727823\pi$
$24$	1.53090e7	0.392450
$25$	4.13685e7	0.847226
$26$	−1.13397e8	−1.87175
$27$	1.43489e7	0.192450
$28$	−1.86587e7	−0.204886
$29$	7.14544e7	0.646904	0.323452	−	0.946245i	$-0.395157\pi$
$29$	7.14544e7	0.646904	0.323452	+	0.946245i	$0.395157\pi$
$30$	1.24977e8	0.938998
$31$	2.22524e8	1.39600	0.698002	−	0.716096i	$-0.254073\pi$
$31$	2.22524e8	1.39600	0.698002	+	0.716096i	$0.254073\pi$
$32$	1.53847e8	0.810523
$33$	−2.05052e8	−0.912091
$34$	3.19878e8	1.20740
$35$	2.00310e8	0.644658
$36$	5.22378e7	0.143986
$37$	5.50364e8	1.30479	0.652395	−	0.757879i	$-0.273764\pi$
$37$	5.50364e8	1.30479	0.652395	+	0.757879i	$0.273764\pi$
$38$	−2.24646e8	−0.459927
$39$	5.08836e8	0.903071
$40$	−5.98322e8	−0.923858
$41$	−3.58060e8	−0.482664	−0.241332	−	0.970443i	$-0.577584\pi$
$41$	−3.58060e8	−0.482664	−0.241332	+	0.970443i	$0.577584\pi$
$42$	2.77552e8	0.327698
$43$	−8.90997e8	−0.924272	−0.462136	−	0.886809i	$-0.652917\pi$
$43$	−8.90997e8	−0.924272	−0.462136	+	0.886809i	$0.652917\pi$
$44$	−7.46502e8	−0.682404
$45$	−5.60799e8	−0.453042
$46$	2.19370e9	1.57040
$47$	2.37132e9	1.50818	0.754088	−	0.656774i	$-0.228079\pi$
$47$	2.37132e9	1.50818	0.754088	+	0.656774i	$0.228079\pi$
$48$	−1.26930e9	−0.719015
$49$	−1.53247e9	−0.775023
$50$	−2.24027e9	−1.01383
$51$	−1.43536e9	−0.582538
$52$	1.85244e9	0.675655
$53$	2.90109e9	0.952891	0.476446	−	0.879204i	$-0.341925\pi$
$53$	2.90109e9	0.952891	0.476446	+	0.879204i	$0.341925\pi$
$54$	−7.77050e8	−0.230294
$55$	8.01408e9	2.14713
$56$	−1.32877e9	−0.322414
$57$	1.00803e9	0.221903
$58$	−3.86954e9	−0.774114
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−2.04161e9	−0.338955
$61$	−7.97897e9	−1.20958	−0.604788	−	0.796387i	$-0.706742\pi$
$61$	−7.97897e9	−1.20958	−0.604788	+	0.796387i	$0.706742\pi$
$62$	−1.20505e10	−1.67052
$63$	−1.24544e9	−0.158106
$64$	2.36620e9	0.275462
$65$	−1.98869e10	−2.12590
$66$	1.11044e10	1.09145
$67$	9.55219e9	0.864354	0.432177	−	0.901789i	$-0.357746\pi$
$67$	9.55219e9	0.864354	0.432177	+	0.901789i	$0.357746\pi$
$68$	−5.22548e9	−0.435840
$69$	−9.84360e9	−0.757677
$70$	−1.08476e10	−0.771427
$71$	−1.49378e9	−0.0982573	−0.0491287	−	0.998792i	$-0.515644\pi$
$71$	−1.49378e9	−0.0982573	−0.0491287	+	0.998792i	$0.515644\pi$
$72$	3.72008e9	0.226581
$73$	−4.31992e8	−0.0243893	−0.0121947	−	0.999926i	$-0.503882\pi$
$73$	−4.31992e8	−0.0243893	−0.0121947	+	0.999926i	$0.503882\pi$
$74$	−2.98044e10	−1.56137
$75$	1.00525e10	0.489146
$76$	3.66979e9	0.166022
$77$	1.77978e10	0.749322
$78$	−2.75555e10	−1.08066
$79$	4.22383e10	1.54439	0.772196	−	0.635385i	$-0.219159\pi$
$79$	4.22383e10	1.54439	0.772196	+	0.635385i	$0.219159\pi$
$80$	4.96082e10	1.69262
$81$	3.48678e9	0.111111
$82$	1.93904e10	0.577577
$83$	6.44130e9	0.179492	0.0897458	−	0.995965i	$-0.471395\pi$
$83$	6.44130e9	0.179492	0.0897458	+	0.995965i	$0.471395\pi$
$84$	−4.53406e9	−0.118291
$85$	5.60982e10	1.37134
$86$	4.82510e10	1.10603
$87$	1.73634e10	0.373490
$88$	−5.31617e10	−1.07385
$89$	1.02190e11	1.93983	0.969913	−	0.243451i	$-0.0782795\pi$
$89$	1.02190e11	1.93983	0.969913	+	0.243451i	$0.0782795\pi$
$90$	3.03695e10	0.542131
$91$	−4.41651e10	−0.741911
$92$	−3.58360e10	−0.566875
$93$	5.40732e10	0.805983
$94$	−1.28416e11	−1.80475
$95$	−3.93970e10	−0.522376
$96$	3.73849e10	0.467956
$97$	1.09002e11	1.28881	0.644407	−	0.764683i	$-0.277104\pi$
$97$	1.09002e11	1.28881	0.644407	+	0.764683i	$0.277104\pi$
$98$	8.29895e10	0.927427
$99$	−4.98278e10	−0.526596
$100$	3.65967e10	0.365967
$101$	1.45203e11	1.37470	0.687350	−	0.726326i	$-0.258774\pi$
$101$	1.45203e11	1.37470	0.687350	+	0.726326i	$0.258774\pi$
$102$	7.77303e10	0.697091
$103$	−2.78583e10	−0.236783	−0.118391	−	0.992967i	$-0.537774\pi$
$103$	−2.78583e10	−0.236783	−0.118391	+	0.992967i	$0.537774\pi$
$104$	1.31920e11	1.06323
$105$	4.86754e10	0.372193
$106$	−1.57105e11	−1.14027
$107$	2.33740e10	0.161110	0.0805549	−	0.996750i	$-0.474331\pi$
$107$	2.33740e10	0.161110	0.0805549	+	0.996750i	$0.474331\pi$
$108$	1.26938e10	0.0831305
$109$	−2.25343e11	−1.40281	−0.701404	−	0.712764i	$-0.747443\pi$
$109$	−2.25343e11	−1.40281	−0.701404	+	0.712764i	$0.747443\pi$
$110$	−4.33994e11	−2.56936
$111$	1.33739e11	0.753321
$112$	1.10171e11	0.590701
$113$	−3.49445e11	−1.78422	−0.892109	−	0.451820i	$-0.850775\pi$
$113$	−3.49445e11	−1.78422	−0.892109	+	0.451820i	$0.850775\pi$
$114$	−5.45889e10	−0.265539
$115$	3.84718e11	1.78363
$116$	6.32123e10	0.279436
$117$	1.23647e11	0.521389
$118$	3.87160e10	0.155790
$119$	1.24584e11	0.478580
$120$	−1.45392e11	−0.533389
$121$	4.26750e11	1.49573
$122$	4.32093e11	1.44743
$123$	−8.70086e10	−0.278666
$124$	1.96856e11	0.603016
$125$	7.08458e10	0.207639
$126$	6.74452e10	0.189197
$127$	3.87569e11	1.04095	0.520473	−	0.853878i	$-0.325756\pi$
$127$	3.87569e11	1.04095	0.520473	+	0.853878i	$0.325756\pi$
$128$	−4.43219e11	−1.14015
$129$	−2.16512e11	−0.533629
$130$	1.07695e12	2.54395
$131$	−6.16968e10	−0.139724	−0.0698619	−	0.997557i	$-0.522256\pi$
$131$	−6.16968e10	−0.139724	−0.0698619	+	0.997557i	$0.522256\pi$
$132$	−1.81400e11	−0.393986
$133$	−8.74937e10	−0.182303
$134$	−5.17289e11	−1.03432
$135$	−1.36274e11	−0.261564
$136$	−3.72129e11	−0.685851
$137$	−8.92149e11	−1.57934	−0.789668	−	0.613534i	$-0.789747\pi$
$137$	−8.92149e11	−1.57934	−0.789668	+	0.613534i	$0.789747\pi$
$138$	5.33070e11	0.906670
$139$	−7.61455e11	−1.24469	−0.622347	−	0.782741i	$-0.713821\pi$
$139$	−7.61455e11	−1.24469	−0.622347	+	0.782741i	$0.713821\pi$
$140$	1.77205e11	0.278466
$141$	5.76231e11	0.870745
$142$	8.08940e10	0.117579
$143$	−1.76697e12	−2.47105
$144$	−3.08440e11	−0.415123
$145$	−6.78616e11	−0.879225
$146$	2.33941e10	0.0291854
$147$	−3.72391e11	−0.447460
$148$	4.86881e11	0.563616
$149$	−1.13242e12	−1.26323	−0.631614	−	0.775283i	$-0.717607\pi$
$149$	−1.13242e12	−1.26323	−0.631614	+	0.775283i	$0.717607\pi$
$150$	−5.44385e11	−0.585334
$151$	2.38730e11	0.247477	0.123738	−	0.992315i	$-0.460512\pi$
$151$	2.38730e11	0.247477	0.123738	+	0.992315i	$0.460512\pi$
$152$	2.61341e11	0.261257
$153$	−3.48792e11	−0.336328
$154$	−9.63824e11	−0.896672
$155$	−2.11335e12	−1.89735
$156$	4.50142e11	0.390090
$157$	4.59169e11	0.384171	0.192086	−	0.981378i	$-0.438475\pi$
$157$	4.59169e11	0.384171	0.192086	+	0.981378i	$0.438475\pi$
$158$	−2.28737e12	−1.84809
$159$	7.04964e11	0.550152
$160$	−1.46112e12	−1.10160
$161$	8.54390e11	0.622463
$162$	−1.88823e11	−0.132961
$163$	8.33481e11	0.567367	0.283683	−	0.958918i	$-0.408444\pi$
$163$	8.33481e11	0.567367	0.283683	+	0.958918i	$0.408444\pi$
$164$	−3.16759e11	−0.208491
$165$	1.94742e12	1.23965
$166$	−3.48822e11	−0.214788
$167$	−2.27175e12	−1.35338	−0.676689	−	0.736269i	$-0.736586\pi$
$167$	−2.27175e12	−1.35338	−0.676689	+	0.736269i	$0.736586\pi$
$168$	−3.22890e11	−0.186146
$169$	2.59256e12	1.44661
$170$	−3.03794e12	−1.64101
$171$	2.44952e11	0.128116
$172$	−7.88223e11	−0.399248
$173$	3.69756e12	1.81410	0.907050	−	0.421022i	$-0.138329\pi$
$173$	3.69756e12	1.81410	0.907050	+	0.421022i	$0.138329\pi$
$174$	−9.40298e11	−0.446935
$175$	−8.72525e11	−0.401854
$176$	4.40775e12	1.96742
$177$	−1.73727e11	−0.0751646
$178$	−5.53399e12	−2.32128
$179$	−3.41963e12	−1.39087	−0.695436	−	0.718588i	$-0.744789\pi$
$179$	−3.41963e12	−1.39087	−0.695436	+	0.718588i	$0.744789\pi$
$180$	−4.96112e11	−0.195696
$181$	8.98229e11	0.343680	0.171840	−	0.985125i	$-0.445029\pi$
$181$	8.98229e11	0.343680	0.171840	+	0.985125i	$0.445029\pi$
$182$	2.39172e12	0.887805
$183$	−1.93889e12	−0.698349
$184$	−2.55204e12	−0.892051
$185$	−5.22692e12	−1.77338
$186$	−2.92828e12	−0.964476
$187$	4.98440e12	1.59398
$188$	2.09779e12	0.651470
$189$	−3.02641e11	−0.0912825
$190$	2.13350e12	0.625099
$191$	4.05225e12	1.15349	0.576743	−	0.816926i	$-0.304323\pi$
$191$	4.05225e12	1.15349	0.576743	+	0.816926i	$0.304323\pi$
$192$	5.74988e11	0.159038
$193$	−3.96024e12	−1.06453	−0.532264	−	0.846579i	$-0.678659\pi$
$193$	−3.96024e12	−1.06453	−0.532264	+	0.846579i	$0.678659\pi$
$194$	−5.90289e12	−1.54225
$195$	−4.83251e12	−1.22739
$196$	−1.35571e12	−0.334778
$197$	−4.64358e12	−1.11504	−0.557518	−	0.830165i	$-0.688246\pi$
$197$	−4.64358e12	−1.11504	−0.557518	+	0.830165i	$0.688246\pi$
$198$	2.69837e12	0.630149
$199$	−4.70935e12	−1.06972	−0.534859	−	0.844942i	$-0.679635\pi$
$199$	−4.70935e12	−1.06972	−0.534859	+	0.844942i	$0.679635\pi$
$200$	2.60621e12	0.575896
$201$	2.32118e12	0.499035
$202$	−7.86332e12	−1.64503
$203$	−1.50708e12	−0.306838
$204$	−1.26979e12	−0.251632
$205$	3.40057e12	0.656002
$206$	1.50864e12	0.283345
$207$	−2.39199e12	−0.437445
$208$	−1.09378e13	−1.94797
$209$	−3.50047e12	−0.607187
$210$	−2.63597e12	−0.445383
$211$	−1.17839e13	−1.93971	−0.969853	−	0.243692i	$-0.921642\pi$
$211$	−1.17839e13	−1.93971	−0.969853	+	0.243692i	$0.921642\pi$
$212$	2.56645e12	0.411610
$213$	−3.62988e11	−0.0567289
$214$	−1.26579e12	−0.192791
$215$	8.46197e12	1.25620
$216$	9.03980e11	0.130817
$217$	−4.69337e12	−0.662149
$218$	1.22032e13	1.67866
$219$	−1.04974e11	−0.0140812
$220$	7.08967e12	0.927474
$221$	−1.23687e13	−1.57822
$222$	−7.24247e12	−0.901458
$223$	8.78662e12	1.06695	0.533476	−	0.845815i	$-0.320885\pi$
$223$	8.78662e12	1.06695	0.533476	+	0.845815i	$0.320885\pi$
$224$	−3.24488e12	−0.384445
$225$	2.44277e12	0.282409
$226$	1.89239e13	2.13508
$227$	−9.68408e11	−0.106639	−0.0533195	−	0.998578i	$-0.516980\pi$
$227$	−9.68408e11	−0.106639	−0.0533195	+	0.998578i	$0.516980\pi$
$228$	8.91758e11	0.0958529
$229$	8.09890e12	0.849827	0.424914	−	0.905234i	$-0.360304\pi$
$229$	8.09890e12	0.849827	0.424914	+	0.905234i	$0.360304\pi$
$230$	−2.08340e13	−2.13437
$231$	4.32488e12	0.432621
$232$	4.50162e12	0.439729
$233$	1.38783e13	1.32397	0.661986	−	0.749516i	$-0.269714\pi$
$233$	1.38783e13	1.32397	0.661986	+	0.749516i	$0.269714\pi$
$234$	−6.69598e12	−0.623917
$235$	−2.25209e13	−2.04980
$236$	−6.32459e11	−0.0562363
$237$	1.02639e13	0.891655
$238$	−6.74672e12	−0.572690
$239$	−1.24484e13	−1.03258	−0.516290	−	0.856414i	$-0.672687\pi$
$239$	−1.24484e13	−1.03258	−0.516290	+	0.856414i	$0.672687\pi$
$240$	1.20548e13	0.977233
$241$	−1.18378e13	−0.937943	−0.468972	−	0.883213i	$-0.655375\pi$
$241$	−1.18378e13	−0.937943	−0.468972	+	0.883213i	$0.655375\pi$
$242$	−2.31102e13	−1.78986
$243$	8.47289e11	0.0641500
$244$	−7.05861e12	−0.522487
$245$	1.45542e13	1.05335
$246$	4.71186e12	0.333464
$247$	8.68639e12	0.601182
$248$	1.40190e13	0.948924
$249$	1.56524e12	0.103629
$250$	−3.83658e12	−0.248470
$251$	−2.56906e12	−0.162768	−0.0813840	−	0.996683i	$-0.525934\pi$
$251$	−2.56906e12	−0.162768	−0.0813840	+	0.996683i	$0.525934\pi$
$252$	−1.10178e12	−0.0682953
$253$	3.41827e13	2.07321
$254$	−2.09884e13	−1.24564
$255$	1.36319e13	0.791743
$256$	1.91561e13	1.08890
$257$	−7.66562e10	−0.00426496	−0.00213248	−	0.999998i	$-0.500679\pi$
$257$	−7.66562e10	−0.00426496	−0.00213248	+	0.999998i	$0.500679\pi$
$258$	1.17250e13	0.638564
$259$	−1.16080e13	−0.618885
$260$	−1.75930e13	−0.918302
$261$	4.21931e12	0.215635
$262$	3.34113e12	0.167200
$263$	−2.94684e13	−1.44411	−0.722054	−	0.691837i	$-0.756802\pi$
$263$	−2.94684e13	−1.44411	−0.722054	+	0.691837i	$0.756802\pi$
$264$	−1.29183e13	−0.619988
$265$	−2.75522e13	−1.29510
$266$	4.73813e12	0.218151
$267$	2.48321e13	1.11996
$268$	8.45037e12	0.373366
$269$	6.96896e12	0.301669	0.150834	−	0.988559i	$-0.451804\pi$
$269$	6.96896e12	0.301669	0.150834	+	0.988559i	$0.451804\pi$
$270$	7.37979e12	0.312999
$271$	−4.26561e13	−1.77276	−0.886381	−	0.462956i	$-0.846789\pi$
$271$	−4.26561e13	−1.77276	−0.886381	+	0.462956i	$0.846789\pi$
$272$	3.08541e13	1.25656
$273$	−1.07321e13	−0.428343
$274$	4.83134e13	1.88990
$275$	−3.49083e13	−1.33844
$276$	−8.70816e12	−0.327285
$277$	2.39786e13	0.883455	0.441728	−	0.897149i	$-0.354366\pi$
$277$	2.39786e13	0.883455	0.441728	+	0.897149i	$0.354366\pi$
$278$	4.12358e13	1.48946
$279$	1.31398e13	0.465335
$280$	1.26195e13	0.438202
$281$	−5.17816e13	−1.76316	−0.881578	−	0.472039i	$-0.843518\pi$
$281$	−5.17816e13	−1.76316	−0.881578	+	0.472039i	$0.843518\pi$
$282$	−3.12052e13	−1.04197
$283$	−7.35010e11	−0.0240695	−0.0120348	−	0.999928i	$-0.503831\pi$
$283$	−7.35010e11	−0.0240695	−0.0120348	+	0.999928i	$0.503831\pi$
$284$	−1.32147e12	−0.0424431
$285$	−9.57347e12	−0.301594
$286$	9.56886e13	2.95697
$287$	7.55205e12	0.228936
$288$	9.08453e12	0.270174
$289$	6.18651e11	0.0180513
$290$	3.67497e13	1.05212
$291$	2.64875e13	0.744097
$292$	−3.82162e11	−0.0105352
$293$	−4.01628e13	−1.08656	−0.543278	−	0.839553i	$-0.682817\pi$
$293$	−4.01628e13	−1.08656	−0.543278	+	0.839553i	$0.682817\pi$
$294$	2.01664e13	0.535450
$295$	6.78977e12	0.176943
$296$	3.46729e13	0.886923
$297$	−1.21081e13	−0.304030
$298$	6.13248e13	1.51164
$299$	−8.48240e13	−2.05271
$300$	8.89300e12	0.211291
$301$	1.87925e13	0.438399
$302$	−1.29282e13	−0.296142
$303$	3.52843e13	0.793684
$304$	−2.16684e13	−0.478654
$305$	7.57778e13	1.64397
$306$	1.88885e13	0.402466
$307$	−5.24893e13	−1.09852	−0.549262	−	0.835650i	$-0.685091\pi$
$307$	−5.24893e13	−1.09852	−0.549262	+	0.835650i	$0.685091\pi$
$308$	1.57449e13	0.323676
$309$	−6.76957e12	−0.136707
$310$	1.14446e14	2.27045
$311$	−2.53969e13	−0.494992	−0.247496	−	0.968889i	$-0.579608\pi$
$311$	−2.53969e13	−0.494992	−0.247496	+	0.968889i	$0.579608\pi$
$312$	3.20566e13	0.613857
$313$	−1.99353e13	−0.375085	−0.187542	−	0.982256i	$-0.560052\pi$
$313$	−1.99353e13	−0.375085	−0.187542	+	0.982256i	$0.560052\pi$
$314$	−2.48658e13	−0.459716
$315$	1.18281e13	0.214886
$316$	3.73662e13	0.667114
$317$	6.84447e13	1.20092	0.600460	−	0.799655i	$-0.294984\pi$
$317$	6.84447e13	1.20092	0.600460	+	0.799655i	$0.294984\pi$
$318$	−3.81766e13	−0.658337
$319$	−6.02959e13	−1.02197
$320$	−2.24723e13	−0.374388
$321$	5.67987e12	0.0930167
$322$	−4.62686e13	−0.744868
$323$	−2.45032e13	−0.387800
$324$	3.08459e12	0.0479954
$325$	8.66245e13	1.32520
$326$	−4.51363e13	−0.678937
$327$	−5.47583e13	−0.809911
$328$	−2.25578e13	−0.328088
$329$	−5.00148e13	−0.715354
$330$	−1.05461e14	−1.48342
$331$	−9.22756e13	−1.27653	−0.638267	−	0.769815i	$-0.720349\pi$
$331$	−9.22756e13	−1.27653	−0.638267	+	0.769815i	$0.720349\pi$
$332$	5.69831e12	0.0775330
$333$	3.24985e13	0.434930
$334$	1.23024e14	1.61951
$335$	−9.07190e13	−1.17477
$336$	2.67715e13	0.341042
$337$	5.13142e13	0.643092	0.321546	−	0.946894i	$-0.395797\pi$
$337$	5.13142e13	0.643092	0.321546	+	0.946894i	$0.395797\pi$
$338$	−1.40398e14	−1.73108
$339$	−8.49152e13	−1.03012
$340$	4.96274e13	0.592362
$341$	−1.87774e14	−2.20539
$342$	−1.32651e13	−0.153309
$343$	7.40271e13	0.841925
$344$	−5.61327e13	−0.628268
$345$	9.34865e13	1.02978
$346$	−2.00237e14	−2.17083
$347$	−8.79861e13	−0.938862	−0.469431	−	0.882969i	$-0.655541\pi$
$347$	−8.79861e13	−0.938862	−0.469431	+	0.882969i	$0.655541\pi$
$348$	1.53606e13	0.161332
$349$	6.86479e13	0.709720	0.354860	−	0.934919i	$-0.384528\pi$
$349$	6.86479e13	0.709720	0.354860	+	0.934919i	$0.384528\pi$
$350$	4.72507e13	0.480877
$351$	3.00462e13	0.301024
$352$	−1.29822e14	−1.28045
$353$	3.14822e13	0.305706	0.152853	−	0.988249i	$-0.451154\pi$
$353$	3.14822e13	0.305706	0.152853	+	0.988249i	$0.451154\pi$
$354$	9.40798e12	0.0899453
$355$	1.41867e13	0.133544
$356$	9.04025e13	0.837926
$357$	3.02739e13	0.276308
$358$	1.85186e14	1.66438
$359$	1.59050e14	1.40772	0.703858	−	0.710340i	$-0.251459\pi$
$359$	1.59050e14	1.40772	0.703858	+	0.710340i	$0.251459\pi$
$360$	−3.53303e13	−0.307953
$361$	−9.92820e13	−0.852277
$362$	−4.86426e13	−0.411263
$363$	1.03700e14	0.863561
$364$	−3.90708e13	−0.320475
$365$	4.10271e12	0.0331482
$366$	1.04999e14	0.835675
$367$	−2.18228e14	−1.71099	−0.855495	−	0.517811i	$-0.826747\pi$
$367$	−2.18228e14	−1.71099	−0.855495	+	0.517811i	$0.826747\pi$
$368$	2.11595e14	1.63434
$369$	−2.11431e13	−0.160888
$370$	2.83058e14	2.12210
$371$	−6.11884e13	−0.451973
$372$	4.78360e13	0.348152
$373$	−1.49568e13	−0.107261	−0.0536303	−	0.998561i	$-0.517079\pi$
$373$	−1.49568e13	−0.107261	−0.0536303	+	0.998561i	$0.517079\pi$
$374$	−2.69925e14	−1.90743
$375$	1.72155e13	0.119880
$376$	1.49393e14	1.02517
$377$	1.49624e14	1.01186
$378$	1.63892e13	0.109233
$379$	1.40600e14	0.923568	0.461784	−	0.886992i	$-0.347210\pi$
$379$	1.40600e14	0.923568	0.461784	+	0.886992i	$0.347210\pi$
$380$	−3.48526e13	−0.225645
$381$	9.41792e13	0.600990
$382$	−2.19445e14	−1.38031
$383$	1.75255e14	1.08662	0.543310	−	0.839532i	$-0.317171\pi$
$383$	1.75255e14	1.08662	0.543310	+	0.839532i	$0.317171\pi$
$384$	−1.07702e14	−0.658268
$385$	−1.69029e14	−1.01842
$386$	2.14463e14	1.27386
$387$	−5.26125e13	−0.308091
$388$	9.64289e13	0.556715
$389$	−6.98850e13	−0.397797	−0.198898	−	0.980020i	$-0.563736\pi$
$389$	−6.98850e13	−0.397797	−0.198898	+	0.980020i	$0.563736\pi$
$390$	2.61699e14	1.46875
$391$	2.39277e14	1.32413
$392$	−9.65457e13	−0.526817
$393$	−1.49923e13	−0.0806696
$394$	2.51468e14	1.33430
$395$	−4.01145e14	−2.09902
$396$	−4.40802e13	−0.227468
$397$	1.34492e14	0.684463	0.342231	−	0.939616i	$-0.388817\pi$
$397$	1.34492e14	0.684463	0.342231	+	0.939616i	$0.388817\pi$
$398$	2.55030e14	1.28007
$399$	−2.12610e13	−0.105252
$400$	−2.16087e14	−1.05511
$401$	1.81027e14	0.871863	0.435932	−	0.899980i	$-0.356419\pi$
$401$	1.81027e14	0.871863	0.435932	+	0.899980i	$0.356419\pi$
$402$	−1.25701e14	−0.597168
$403$	4.65958e14	2.18358
$404$	1.28454e14	0.593814
$405$	−3.31146e13	−0.151014
$406$	8.16146e13	0.367176
$407$	−4.64418e14	−2.06129
$408$	−9.04274e13	−0.395976
$409$	−1.82091e14	−0.786704	−0.393352	−	0.919388i	$-0.628685\pi$
$409$	−1.82091e14	−0.786704	−0.393352	+	0.919388i	$0.628685\pi$
$410$	−1.84154e14	−0.785001
$411$	−2.16792e14	−0.911830
$412$	−2.46449e13	−0.102280
$413$	1.50789e13	0.0617509
$414$	1.29536e14	0.523466
$415$	−6.11742e13	−0.243952
$416$	3.22152e14	1.26779
$417$	−1.85034e14	−0.718625
$418$	1.89565e14	0.726587
$419$	5.36966e13	0.203128	0.101564	−	0.994829i	$-0.467615\pi$
$419$	5.36966e13	0.203128	0.101564	+	0.994829i	$0.467615\pi$
$420$	4.30608e13	0.160772
$421$	1.97113e14	0.726380	0.363190	−	0.931715i	$-0.381688\pi$
$421$	1.97113e14	0.726380	0.363190	+	0.931715i	$0.381688\pi$
$422$	6.38145e14	2.32114
$423$	1.40024e14	0.502725
$424$	1.82768e14	0.647722
$425$	−2.44356e14	−0.854839
$426$	1.96572e13	0.0678843
$427$	1.68289e14	0.573723
$428$	2.06778e13	0.0695928
$429$	−4.29374e14	−1.42666
$430$	−4.58249e14	−1.50323
$431$	1.11050e14	0.359660	0.179830	−	0.983698i	$-0.442445\pi$
$431$	1.11050e14	0.359660	0.179830	+	0.983698i	$0.442445\pi$
$432$	−7.49510e13	−0.239672
$433$	3.97259e14	1.25427	0.627133	−	0.778912i	$-0.284228\pi$
$433$	3.97259e14	1.25427	0.627133	+	0.778912i	$0.284228\pi$
$434$	2.54164e14	0.792358
$435$	−1.64904e14	−0.507621
$436$	−1.99350e14	−0.605955
$437$	−1.68041e14	−0.504392
$438$	5.68476e12	0.0168502
$439$	2.43660e14	0.713229	0.356615	−	0.934252i	$-0.383931\pi$
$439$	2.43660e14	0.713229	0.356615	+	0.934252i	$0.383931\pi$
$440$	5.04886e14	1.45950
$441$	−9.04910e13	−0.258341
$442$	6.69816e14	1.88857
$443$	−2.28088e14	−0.635159	−0.317580	−	0.948232i	$-0.602870\pi$
$443$	−2.28088e14	−0.635159	−0.317580	+	0.948232i	$0.602870\pi$
$444$	1.18312e14	0.325404
$445$	−9.70517e14	−2.63647
$446$	−4.75830e14	−1.27676
$447$	−2.75177e14	−0.729325
$448$	−4.99069e13	−0.130657
$449$	−4.97053e14	−1.28543	−0.642714	−	0.766107i	$-0.722191\pi$
$449$	−4.97053e14	−1.28543	−0.642714	+	0.766107i	$0.722191\pi$
$450$	−1.32285e14	−0.337943
$451$	3.02145e14	0.762507
$452$	−3.09138e14	−0.770709
$453$	5.80114e13	0.142881
$454$	5.24431e13	0.127609
$455$	4.19445e14	1.00835
$456$	6.35059e13	0.150837
$457$	−5.40036e13	−0.126731	−0.0633656	−	0.997990i	$-0.520183\pi$
$457$	−5.40036e13	−0.126731	−0.0633656	+	0.997990i	$0.520183\pi$
$458$	−4.38587e14	−1.01694
$459$	−8.47564e13	−0.194179
$460$	3.40342e14	0.770455
$461$	−1.30960e14	−0.292943	−0.146472	−	0.989215i	$-0.546792\pi$
$461$	−1.30960e14	−0.292943	−0.146472	+	0.989215i	$0.546792\pi$
$462$	−2.34209e14	−0.517694
$463$	7.29383e14	1.59316	0.796581	−	0.604532i	$-0.206640\pi$
$463$	7.29383e14	1.59316	0.796581	+	0.604532i	$0.206640\pi$
$464$	−3.73239e14	−0.805635
$465$	−5.13544e14	−1.09543
$466$	−7.51565e14	−1.58432
$467$	6.78306e14	1.41313	0.706566	−	0.707647i	$-0.250243\pi$
$467$	6.78306e14	1.41313	0.706566	+	0.707647i	$0.250243\pi$
$468$	1.09385e14	0.225218
$469$	−2.01471e14	−0.409978
$470$	1.21959e15	2.45288
$471$	1.11578e14	0.221801
$472$	−4.50402e13	−0.0884950
$473$	7.51857e14	1.46015
$474$	−5.55831e14	−1.06699
$475$	1.71608e14	0.325629
$476$	1.10214e14	0.206727
$477$	1.71306e14	0.317630
$478$	6.74128e14	1.23563
$479$	5.16339e14	0.935599	0.467800	−	0.883835i	$-0.345047\pi$
$479$	5.16339e14	0.935599	0.467800	+	0.883835i	$0.345047\pi$
$480$	−3.55052e14	−0.636011
$481$	1.15245e15	2.04091
$482$	6.41063e14	1.12239
$483$	2.07617e14	0.359379
$484$	3.77525e14	0.646095
$485$	−1.03521e15	−1.75166
$486$	−4.58840e13	−0.0767648
$487$	3.93458e14	0.650862	0.325431	−	0.945566i	$-0.394491\pi$
$487$	3.93458e14	0.650862	0.325431	+	0.945566i	$0.394491\pi$
$488$	−5.02675e14	−0.822201
$489$	2.02536e14	0.327569
$490$	−7.88167e14	−1.26049
$491$	−3.95822e14	−0.625968	−0.312984	−	0.949758i	$-0.601329\pi$
$491$	−3.95822e14	−0.625968	−0.312984	+	0.949758i	$0.601329\pi$
$492$	−7.69724e13	−0.120372
$493$	−4.22068e14	−0.652717
$494$	−4.70402e14	−0.719402
$495$	4.73224e14	0.715711
$496$	−1.16234e15	−1.73854
$497$	3.15061e13	0.0466052
$498$	−8.47637e13	−0.124008
$499$	−4.03104e14	−0.583262	−0.291631	−	0.956531i	$-0.594198\pi$
$499$	−4.03104e14	−0.583262	−0.291631	+	0.956531i	$0.594198\pi$
$500$	6.26739e13	0.0896916
$501$	−5.52034e14	−0.781373
$502$	1.39125e14	0.194776
$503$	5.09614e14	0.705695	0.352848	−	0.935681i	$-0.385213\pi$
$503$	5.09614e14	0.705695	0.352848	+	0.935681i	$0.385213\pi$
$504$	−7.84623e13	−0.107471
$505$	−1.37902e15	−1.86839
$506$	−1.85113e15	−2.48090
$507$	6.29993e14	0.835203
$508$	3.42863e14	0.449646
$509$	−9.09009e14	−1.17929	−0.589645	−	0.807663i	$-0.700732\pi$
$509$	−9.09009e14	−1.17929	−0.589645	+	0.807663i	$0.700732\pi$
$510$	−7.38219e14	−0.947435
$511$	9.11138e12	0.0115683
$512$	−1.29665e14	−0.162869
$513$	5.95233e13	0.0739676
$514$	4.15123e12	0.00510364
$515$	2.64576e14	0.321818
$516$	−1.91538e14	−0.230506
$517$	−2.00101e15	−2.38260
$518$	6.28621e14	0.740586
$519$	8.98507e14	1.04737
$520$	−1.25287e15	−1.44507
$521$	−4.16939e14	−0.475844	−0.237922	−	0.971284i	$-0.576466\pi$
$521$	−4.16939e14	−0.475844	−0.237922	+	0.971284i	$0.576466\pi$
$522$	−2.28492e14	−0.258038
$523$	7.53757e12	0.00842310	0.00421155	−	0.999991i	$-0.498659\pi$
$523$	7.53757e12	0.00842310	0.00421155	+	0.999991i	$0.498659\pi$
$524$	−5.45802e13	−0.0603550
$525$	−2.12024e14	−0.232011
$526$	1.59583e15	1.72808
$527$	−1.31441e15	−1.40855
$528$	1.07108e15	1.13589
$529$	6.88140e14	0.722221
$530$	1.49206e15	1.54978
$531$	−4.22156e13	−0.0433963
$532$	−7.74015e13	−0.0787472
$533$	−7.49769e14	−0.754966
$534$	−1.34476e15	−1.34019
$535$	−2.21987e14	−0.218969
$536$	6.01787e14	0.587539
$537$	−8.30970e14	−0.803021
$538$	−3.77397e14	−0.360990
$539$	1.29316e15	1.22437
$540$	−1.20555e14	−0.112985
$541$	−5.57911e14	−0.517583	−0.258791	−	0.965933i	$-0.583324\pi$
$541$	−5.57911e14	−0.517583	−0.258791	+	0.965933i	$0.583324\pi$
$542$	2.31000e15	2.12137
$543$	2.18270e14	0.198424
$544$	−9.08749e14	−0.817806
$545$	2.14012e15	1.90659
$546$	5.81187e14	0.512574
$547$	9.47126e14	0.826947	0.413473	−	0.910516i	$-0.364315\pi$
$547$	9.47126e14	0.826947	0.413473	+	0.910516i	$0.364315\pi$
$548$	−7.89242e14	−0.682208
$549$	−4.71150e14	−0.403192
$550$	1.89042e15	1.60164
$551$	2.96413e14	0.248636
$552$	−6.20146e14	−0.515026
$553$	−8.90871e14	−0.732532
$554$	−1.29853e15	−1.05718
$555$	−1.27014e15	−1.02386
$556$	−6.73623e14	−0.537657
$557$	−1.55868e14	−0.123184	−0.0615919	−	0.998101i	$-0.519618\pi$
$557$	−1.55868e14	−0.123184	−0.0615919	+	0.998101i	$0.519618\pi$
$558$	−7.11572e14	−0.556840
$559$	−1.86572e15	−1.44571
$560$	−1.04631e15	−0.802838
$561$	1.21121e15	0.920287
$562$	2.80418e15	2.10987
$563$	−1.20905e15	−0.900837	−0.450419	−	0.892817i	$-0.648725\pi$
$563$	−1.20905e15	−0.900837	−0.450419	+	0.892817i	$0.648725\pi$
$564$	5.09764e14	0.376126
$565$	3.31875e15	2.42498
$566$	3.98037e13	0.0288027
$567$	−7.35417e13	−0.0527020
$568$	−9.41078e13	−0.0667898
$569$	−2.21496e15	−1.55686	−0.778428	−	0.627734i	$-0.783983\pi$
$569$	−2.21496e15	−1.55686	−0.778428	+	0.627734i	$0.783983\pi$
$570$	5.18441e14	0.360901
$571$	1.13013e14	0.0779164	0.0389582	−	0.999241i	$-0.487596\pi$
$571$	1.13013e14	0.0779164	0.0389582	+	0.999241i	$0.487596\pi$
$572$	−1.56316e15	−1.06739
$573$	9.84696e14	0.665966
$574$	−4.08973e14	−0.273955
$575$	−1.67578e15	−1.11184
$576$	1.39722e14	0.0918208
$577$	2.63239e15	1.71350	0.856750	−	0.515732i	$-0.172480\pi$
$577$	2.63239e15	1.71350	0.856750	+	0.515732i	$0.172480\pi$
$578$	−3.35024e13	−0.0216009
$579$	−9.62340e14	−0.614605
$580$	−6.00339e14	−0.379789
$581$	−1.35857e14	−0.0851360
$582$	−1.43440e15	−0.890420
$583$	−2.44805e15	−1.50537
$584$	−2.72154e13	−0.0165785
$585$	−1.17430e15	−0.708633
$586$	2.17498e15	1.30022
$587$	−7.18576e14	−0.425563	−0.212781	−	0.977100i	$-0.568252\pi$
$587$	−7.18576e14	−0.425563	−0.212781	+	0.977100i	$0.568252\pi$
$588$	−3.29436e14	−0.193284
$589$	9.23090e14	0.536550
$590$	−3.67693e14	−0.211738
$591$	−1.12839e15	−0.643766
$592$	−2.87481e15	−1.62495
$593$	−7.56098e13	−0.0423426	−0.0211713	−	0.999776i	$-0.506740\pi$
$593$	−7.56098e13	−0.0423426	−0.0211713	+	0.999776i	$0.506740\pi$
$594$	6.55704e14	0.363817
$595$	−1.18320e15	−0.650450
$596$	−1.00179e15	−0.545663
$597$	−1.14437e15	−0.617602
$598$	4.59356e15	2.45636
$599$	1.94727e14	0.103176	0.0515879	−	0.998668i	$-0.483572\pi$
$599$	1.94727e14	0.103176	0.0515879	+	0.998668i	$0.483572\pi$
$600$	6.33309e14	0.332494
$601$	1.51012e15	0.785603	0.392802	−	0.919623i	$-0.371506\pi$
$601$	1.51012e15	0.785603	0.392802	+	0.919623i	$0.371506\pi$
$602$	−1.01769e15	−0.524608
$603$	5.64048e14	0.288118
$604$	2.11193e14	0.106900
$605$	−4.05292e15	−2.03289
$606$	−1.91079e15	−0.949758
$607$	2.27582e15	1.12099	0.560493	−	0.828159i	$-0.310612\pi$
$607$	2.27582e15	1.12099	0.560493	+	0.828159i	$0.310612\pi$
$608$	6.38202e14	0.311522
$609$	−3.66221e14	−0.177153
$610$	−4.10367e15	−1.96724
$611$	4.96548e15	2.35904
$612$	−3.08560e14	−0.145280
$613$	7.28934e14	0.340138	0.170069	−	0.985432i	$-0.445601\pi$
$613$	7.28934e14	0.340138	0.170069	+	0.985432i	$0.445601\pi$
$614$	2.84250e15	1.31454
$615$	8.26337e14	0.378743
$616$	1.12126e15	0.509346
$617$	−3.28279e15	−1.47800	−0.739001	−	0.673704i	$-0.764702\pi$
$617$	−3.28279e15	−1.47800	−0.739001	+	0.673704i	$0.764702\pi$
$618$	3.66599e14	0.163589
$619$	3.79250e14	0.167736	0.0838682	−	0.996477i	$-0.473273\pi$
$619$	3.79250e14	0.167736	0.0838682	+	0.996477i	$0.473273\pi$
$620$	−1.86958e15	−0.819576
$621$	−5.81255e14	−0.252559
$622$	1.37534e15	0.592330
$623$	−2.15534e15	−0.920094
$624$	−2.65788e15	−1.12466
$625$	−2.69278e15	−1.12943
$626$	1.07958e15	0.448843
$627$	−8.50615e14	−0.350559
$628$	4.06205e14	0.165946
$629$	−3.25090e15	−1.31651
$630$	−6.40540e14	−0.257142
$631$	−3.80252e15	−1.51325	−0.756623	−	0.653851i	$-0.773152\pi$
$631$	−3.80252e15	−1.51325	−0.756623	+	0.653851i	$0.773152\pi$
$632$	2.66101e15	1.04979
$633$	−2.86349e15	−1.11989
$634$	−3.70655e15	−1.43708
$635$	−3.68081e15	−1.41478
$636$	6.23648e14	0.237643
$637$	−3.20896e15	−1.21226
$638$	3.26526e15	1.22294
$639$	−8.82061e13	−0.0327524
$640$	4.20933e15	1.54961
$641$	3.00206e15	1.09572	0.547861	−	0.836570i	$-0.315442\pi$
$641$	3.00206e15	1.09572	0.547861	+	0.836570i	$0.315442\pi$
$642$	−3.07588e14	−0.111308
$643$	−1.62443e15	−0.582829	−0.291414	−	0.956597i	$-0.594126\pi$
$643$	−1.62443e15	−0.582829	−0.291414	+	0.956597i	$0.594126\pi$
$644$	7.55838e14	0.268879
$645$	2.05626e15	0.725269
$646$	1.32694e15	0.464059
$647$	1.51869e15	0.526618	0.263309	−	0.964712i	$-0.415186\pi$
$647$	1.51869e15	0.526618	0.263309	+	0.964712i	$0.415186\pi$
$648$	2.19667e14	0.0755270
$649$	6.03280e14	0.205671
$650$	−4.69106e15	−1.58580
$651$	−1.14049e15	−0.382292
$652$	7.37341e14	0.245079
$653$	2.96946e14	0.0978711	0.0489356	−	0.998802i	$-0.484417\pi$
$653$	2.96946e14	0.0978711	0.0489356	+	0.998802i	$0.484417\pi$
$654$	2.96538e15	0.969176
$655$	5.85946e14	0.189902
$656$	1.87031e15	0.601095
$657$	−2.55087e13	−0.00812977
$658$	2.70850e15	0.856025
$659$	9.64420e13	0.0302271	0.0151136	−	0.999886i	$-0.495189\pi$
$659$	9.64420e13	0.0302271	0.0151136	+	0.999886i	$0.495189\pi$
$660$	1.72279e15	0.535477
$661$	−2.32501e15	−0.716665	−0.358333	−	0.933594i	$-0.616655\pi$
$661$	−2.32501e15	−0.716665	−0.358333	+	0.933594i	$0.616655\pi$
$662$	4.99709e15	1.52756
$663$	−3.00560e15	−0.911186
$664$	4.05801e14	0.122008
$665$	8.30944e14	0.247772
$666$	−1.75992e15	−0.520457
$667$	−2.89452e15	−0.848954
$668$	−2.00970e15	−0.584604
$669$	2.13515e15	0.616005
$670$	4.91279e15	1.40578
$671$	6.73296e15	1.91087
$672$	−7.88506e14	−0.221960
$673$	−8.70992e14	−0.243182	−0.121591	−	0.992580i	$-0.538800\pi$
$673$	−8.70992e14	−0.243182	−0.121591	+	0.992580i	$0.538800\pi$
$674$	−2.77887e15	−0.769553
$675$	5.93592e14	0.163049
$676$	2.29352e15	0.624878
$677$	−6.51500e14	−0.176067	−0.0880333	−	0.996118i	$-0.528058\pi$
$677$	−6.51500e14	−0.176067	−0.0880333	+	0.996118i	$0.528058\pi$
$678$	4.59850e15	1.23269
$679$	−2.29902e15	−0.611307
$680$	3.53418e15	0.932159
$681$	−2.35323e14	−0.0615681
$682$	1.01687e16	2.63907
$683$	1.63952e15	0.422087	0.211043	−	0.977477i	$-0.432314\pi$
$683$	1.63952e15	0.422087	0.211043	+	0.977477i	$0.432314\pi$
$684$	2.16697e14	0.0553407
$685$	8.47291e15	2.14652
$686$	−4.00886e15	−1.00748
$687$	1.96803e15	0.490648
$688$	4.65409e15	1.15106
$689$	6.07480e15	1.49048
$690$	−5.06266e15	−1.23228
$691$	−7.87017e15	−1.90044	−0.950221	−	0.311576i	$-0.899143\pi$
$691$	−7.87017e15	−1.90044	−0.950221	+	0.311576i	$0.899143\pi$
$692$	3.27105e15	0.783617
$693$	1.05094e15	0.249774
$694$	4.76480e15	1.12348
$695$	7.23168e15	1.69170
$696$	1.09389e15	0.253877
$697$	2.11500e15	0.487001
$698$	−3.71755e15	−0.849283
$699$	3.37243e15	0.764396
$700$	−7.71881e14	−0.173585
$701$	1.03894e15	0.231816	0.115908	−	0.993260i	$-0.463022\pi$
$701$	1.03894e15	0.231816	0.115908	+	0.993260i	$0.463022\pi$
$702$	−1.62712e15	−0.360219
$703$	2.28307e15	0.501492
$704$	−1.99669e15	−0.435172
$705$	−5.47257e15	−1.18345
$706$	−1.70488e15	−0.365821
$707$	−3.06256e15	−0.652045
$708$	−1.53688e14	−0.0324680
$709$	−5.34928e15	−1.12135	−0.560675	−	0.828036i	$-0.689458\pi$
$709$	−5.34928e15	−1.12135	−0.560675	+	0.828036i	$0.689458\pi$
$710$	−7.68265e14	−0.159805
$711$	2.49413e15	0.514797
$712$	6.43795e15	1.31858
$713$	−9.01412e15	−1.83202
$714$	−1.63945e15	−0.330643
$715$	1.67813e16	3.35847
$716$	−3.02518e15	−0.600800
$717$	−3.02495e15	−0.596161
$718$	−8.61321e15	−1.68454
$719$	5.92269e15	1.14950	0.574751	−	0.818328i	$-0.305099\pi$
$719$	5.92269e15	1.14950	0.574751	+	0.818328i	$0.305099\pi$
$720$	2.92931e15	0.564206
$721$	5.87575e14	0.112310
$722$	5.37652e15	1.01987
$723$	−2.87658e15	−0.541522
$724$	7.94620e14	0.148456
$725$	2.95596e15	0.548074
$726$	−5.61578e15	−1.03338
$727$	−3.27751e15	−0.598556	−0.299278	−	0.954166i	$-0.596746\pi$
$727$	−3.27751e15	−0.598556	−0.299278	+	0.954166i	$0.596746\pi$
$728$	−2.78240e15	−0.504309
$729$	2.05891e14	0.0370370
$730$	−2.22178e14	−0.0396666
$731$	5.26296e15	0.932577
$732$	−1.71524e15	−0.301658
$733$	8.20340e15	1.43193	0.715966	−	0.698135i	$-0.245987\pi$
$733$	8.20340e15	1.43193	0.715966	+	0.698135i	$0.245987\pi$
$734$	1.18179e16	2.04745
$735$	3.53667e15	0.608154
$736$	−6.23215e15	−1.06368
$737$	−8.06050e15	−1.36550
$738$	1.14498e15	0.192526
$739$	1.02218e16	1.70601	0.853006	−	0.521900i	$-0.174777\pi$
$739$	1.02218e16	1.70601	0.853006	+	0.521900i	$0.174777\pi$
$740$	−4.62400e15	−0.766026
$741$	2.11079e15	0.347093
$742$	3.31360e15	0.540852
$743$	−4.91377e15	−0.796116	−0.398058	−	0.917360i	$-0.630316\pi$
$743$	−4.91377e15	−0.796116	−0.398058	+	0.917360i	$0.630316\pi$
$744$	3.40661e15	0.547862
$745$	1.07548e16	1.71689
$746$	8.09970e14	0.128353
$747$	3.80352e14	0.0598305
$748$	4.40946e15	0.688536
$749$	−4.92993e14	−0.0764172
$750$	−9.32289e14	−0.143454
$751$	3.36651e15	0.514234	0.257117	−	0.966380i	$-0.417227\pi$
$751$	3.36651e15	0.514234	0.257117	+	0.966380i	$0.417227\pi$
$752$	−1.23865e16	−1.87824
$753$	−6.24282e14	−0.0939742
$754$	−8.10271e15	−1.21084
$755$	−2.26727e15	−0.336352
$756$	−2.67732e14	−0.0394303
$757$	−9.37741e14	−0.137106	−0.0685529	−	0.997647i	$-0.521838\pi$
$757$	−9.37741e14	−0.137106	−0.0685529	+	0.997647i	$0.521838\pi$
$758$	−7.61403e15	−1.10518
$759$	8.30640e15	1.19697
$760$	−2.48201e15	−0.355082
$761$	1.09329e16	1.55281	0.776407	−	0.630232i	$-0.217040\pi$
$761$	1.09329e16	1.55281	0.776407	+	0.630232i	$0.217040\pi$
$762$	−5.10018e15	−0.719172
$763$	4.75283e15	0.665376
$764$	3.58483e15	0.498259
$765$	3.31254e15	0.457113
$766$	−9.49076e15	−1.30030
$767$	−1.49703e15	−0.203637
$768$	4.65492e15	0.628675
$769$	7.90499e15	1.06000	0.530001	−	0.847997i	$-0.322192\pi$
$769$	7.90499e15	1.06000	0.530001	+	0.847997i	$0.322192\pi$
$770$	9.15361e15	1.21869
$771$	−1.86274e13	−0.00246238
$772$	−3.50344e15	−0.459832
$773$	5.18761e15	0.676051	0.338026	−	0.941137i	$-0.390241\pi$
$773$	5.18761e15	0.676051	0.338026	+	0.941137i	$0.390241\pi$
$774$	2.84918e15	0.368675
$775$	9.20546e15	1.18273
$776$	6.86712e15	0.876062
$777$	−2.82075e15	−0.357314
$778$	3.78455e15	0.476021
$779$	−1.48533e15	−0.185510
$780$	−4.27509e15	−0.530182
$781$	1.26051e15	0.155226
$782$	−1.29578e16	−1.58451
$783$	1.02529e15	0.124497
$784$	8.00482e15	0.965190
$785$	−4.36082e15	−0.522137
$786$	8.11894e14	0.0965329
$787$	−3.95929e15	−0.467473	−0.233736	−	0.972300i	$-0.575095\pi$
$787$	−3.95929e15	−0.467473	−0.233736	+	0.972300i	$0.575095\pi$
$788$	−4.10795e15	−0.481650
$789$	−7.16082e15	−0.833756
$790$	2.17236e16	2.51179
$791$	7.37035e15	0.846286
$792$	−3.13914e15	−0.357950
$793$	−1.67078e16	−1.89198
$794$	−7.28329e15	−0.819059
$795$	−6.69518e15	−0.747727
$796$	−4.16614e15	−0.462074
$797$	−5.07604e15	−0.559119	−0.279560	−	0.960128i	$-0.590188\pi$
$797$	−5.07604e15	−0.559119	−0.279560	+	0.960128i	$0.590188\pi$
$798$	1.15137e15	0.125950
$799$	−1.40070e16	−1.52173
$800$	6.36443e15	0.686696
$801$	6.03421e15	0.646609
$802$	−9.80331e15	−1.04331
$803$	3.64531e14	0.0385300
$804$	2.05344e15	0.215563
$805$	−8.11430e15	−0.846007
$806$	−2.52335e16	−2.61297
$807$	1.69346e15	0.174168
$808$	9.14778e15	0.934444
$809$	−7.66663e15	−0.777836	−0.388918	−	0.921272i	$-0.627151\pi$
$809$	−7.66663e15	−0.777836	−0.388918	+	0.921272i	$0.627151\pi$
$810$	1.79329e15	0.180710
$811$	4.76464e14	0.0476886	0.0238443	−	0.999716i	$-0.492409\pi$
$811$	4.76464e14	0.0476886	0.0238443	+	0.999716i	$0.492409\pi$
$812$	−1.33324e15	−0.132541
$813$	−1.03654e16	−1.02350
$814$	2.51501e16	2.46664
$815$	−7.91573e15	−0.771124
$816$	7.49754e15	0.725475
$817$	−3.69611e15	−0.355241
$818$	9.86097e15	0.941405
$819$	−2.60791e15	−0.247304
$820$	3.00832e15	0.283366
$821$	1.12022e16	1.04814	0.524068	−	0.851676i	$-0.324414\pi$
$821$	1.12022e16	1.04814	0.524068	+	0.851676i	$0.324414\pi$
$822$	1.17402e16	1.09114
$823$	6.54641e14	0.0604372	0.0302186	−	0.999543i	$-0.490380\pi$
$823$	6.54641e14	0.0604372	0.0302186	+	0.999543i	$0.490380\pi$
$824$	−1.75507e15	−0.160952
$825$	−8.48271e15	−0.772748
$826$	−8.16580e14	−0.0738939
$827$	−1.97462e16	−1.77502	−0.887508	−	0.460792i	$-0.847565\pi$
$827$	−1.97462e16	−1.77502	−0.887508	+	0.460792i	$0.847565\pi$
$828$	−2.11608e15	−0.188958
$829$	−8.65393e15	−0.767650	−0.383825	−	0.923406i	$-0.625393\pi$
$829$	−8.65393e15	−0.767650	−0.383825	+	0.923406i	$0.625393\pi$
$830$	3.31283e15	0.291924
$831$	5.82679e15	0.510063
$832$	4.95477e15	0.430869
$833$	9.05205e15	0.781987
$834$	1.00203e16	0.859939
$835$	2.15752e16	1.83941
$836$	−3.09670e15	−0.262280
$837$	3.19297e15	0.268661
$838$	−2.90788e15	−0.243072
$839$	3.61570e15	0.300263	0.150131	−	0.988666i	$-0.452030\pi$
$839$	3.61570e15	0.300263	0.150131	+	0.988666i	$0.452030\pi$
$840$	3.06655e15	0.252996
$841$	−7.09478e15	−0.581515
$842$	−1.06745e16	−0.869219
$843$	−1.25829e16	−1.01796
$844$	−1.04247e16	−0.837873
$845$	−2.46221e16	−1.96613
$846$	−7.58286e15	−0.601583
$847$	−9.00082e15	−0.709452
$848$	−1.51537e16	−1.18670
$849$	−1.78607e14	−0.0138966
$850$	1.32329e16	1.02294
$851$	−2.22945e16	−1.71232
$852$	−3.21118e14	−0.0245046
$853$	5.30884e15	0.402513	0.201257	−	0.979539i	$-0.435498\pi$
$853$	5.30884e15	0.402513	0.201257	+	0.979539i	$0.435498\pi$
$854$	−9.11351e15	−0.686543
$855$	−2.32635e15	−0.174125
$856$	1.47256e15	0.109513
$857$	2.14371e16	1.58406	0.792028	−	0.610484i	$-0.209025\pi$
$857$	2.14371e16	1.58406	0.792028	+	0.610484i	$0.209025\pi$
$858$	2.32523e16	1.70721
$859$	−6.17747e15	−0.450659	−0.225330	−	0.974283i	$-0.572346\pi$
$859$	−6.17747e15	−0.450659	−0.225330	+	0.974283i	$0.572346\pi$
$860$	7.48590e15	0.542628
$861$	1.83515e15	0.132176
$862$	−6.01378e15	−0.430385
$863$	2.52467e16	1.79534	0.897668	−	0.440673i	$-0.145260\pi$
$863$	2.52467e16	1.79534	0.897668	+	0.440673i	$0.145260\pi$
$864$	2.20754e15	0.155985
$865$	−3.51164e16	−2.46559
$866$	−2.15131e16	−1.50091
$867$	1.50332e14	0.0104219
$868$	−4.15200e15	−0.286021
$869$	−3.56422e16	−2.43981
$870$	8.93018e15	0.607442
$871$	2.00020e16	1.35199
$872$	−1.41966e16	−0.953549
$873$	6.43646e15	0.429605
$874$	9.10010e15	0.603578
$875$	−1.49425e15	−0.0984869
$876$	−9.28655e13	−0.00608249
$877$	−2.49885e16	−1.62646	−0.813228	−	0.581945i	$-0.802292\pi$
$877$	−2.49885e16	−1.62646	−0.813228	+	0.581945i	$0.802292\pi$
$878$	−1.31951e16	−0.853482
$879$	−9.75957e15	−0.627324
$880$	−4.18613e16	−2.67398
$881$	2.60473e16	1.65346	0.826731	−	0.562597i	$-0.190198\pi$
$881$	2.60473e16	1.65346	0.826731	+	0.562597i	$0.190198\pi$
$882$	4.90045e15	0.309142
$883$	−2.06710e16	−1.29592	−0.647961	−	0.761674i	$-0.724378\pi$
$883$	−2.06710e16	−1.29592	−0.647961	+	0.761674i	$0.724378\pi$
$884$	−1.09420e16	−0.681726
$885$	1.64991e15	0.102158
$886$	1.23519e16	0.760060
$887$	1.33866e16	0.818637	0.409319	−	0.912392i	$-0.365766\pi$
$887$	1.33866e16	0.818637	0.409319	+	0.912392i	$0.365766\pi$
$888$	8.42552e15	0.512065
$889$	−8.17442e15	−0.493739
$890$	5.25573e16	3.15492
$891$	−2.94228e15	−0.175532
$892$	7.77310e15	0.460880
$893$	9.83690e15	0.579662
$894$	1.49019e16	0.872743
$895$	3.24769e16	1.89037
$896$	9.34817e15	0.540795
$897$	−2.06122e16	−1.18513
$898$	2.69174e16	1.53820
$899$	1.59003e16	0.903080
$900$	2.16100e15	0.121989
$901$	−1.71362e16	−0.961453
$902$	−1.63623e16	−0.912450
$903$	4.56658e15	0.253110
$904$	−2.20150e16	−1.21281
$905$	−8.53065e15	−0.467105
$906$	−3.14155e15	−0.170977
$907$	−2.11356e16	−1.14334	−0.571668	−	0.820485i	$-0.693704\pi$
$907$	−2.11356e16	−1.14334	−0.571668	+	0.820485i	$0.693704\pi$
$908$	−8.56704e14	−0.0460637
$909$	8.57409e15	0.458234
$910$	−2.27146e16	−1.20664
$911$	−2.91385e16	−1.53857	−0.769283	−	0.638908i	$-0.779387\pi$
$911$	−2.91385e16	−1.53857	−0.769283	+	0.638908i	$0.779387\pi$
$912$	−5.26542e15	−0.276351
$913$	−5.43541e15	−0.283559
$914$	2.92451e15	0.151652
$915$	1.84140e16	0.949144
$916$	7.16471e15	0.367091
$917$	1.30128e15	0.0662735
$918$	4.58990e15	0.232364
$919$	−2.56566e16	−1.29111	−0.645557	−	0.763712i	$-0.723375\pi$
$919$	−2.56566e16	−1.29111	−0.645557	+	0.763712i	$0.723375\pi$
$920$	2.42372e16	1.21241
$921$	−1.27549e16	−0.634233
$922$	7.09200e15	0.350549
$923$	−3.12793e15	−0.153691
$924$	3.82601e15	0.186875
$925$	2.27677e16	1.10545
$926$	−3.94990e16	−1.90645
$927$	−1.64501e15	−0.0789276
$928$	1.09931e16	0.524330
$929$	−9.20273e15	−0.436345	−0.218173	−	0.975910i	$-0.570010\pi$
$929$	−9.20273e15	−0.436345	−0.218173	+	0.975910i	$0.570010\pi$
$930$	2.78104e16	1.31084
$931$	−6.35713e15	−0.297878
$932$	1.22775e16	0.571902
$933$	−6.17144e15	−0.285784
$934$	−3.67330e16	−1.69102
$935$	−4.73378e16	−2.16643
$936$	7.78975e15	0.354410
$937$	−2.05016e16	−0.927299	−0.463650	−	0.886019i	$-0.653460\pi$
$937$	−2.05016e16	−0.927299	−0.463650	+	0.886019i	$0.653460\pi$
$938$	1.09104e16	0.490599
$939$	−4.84429e15	−0.216555
$940$	−1.99231e16	−0.885430
$941$	−1.85084e16	−0.817762	−0.408881	−	0.912588i	$-0.634081\pi$
$941$	−1.85084e16	−0.817762	−0.408881	+	0.912588i	$0.634081\pi$
$942$	−6.04240e15	−0.265417
$943$	1.45045e16	0.633416
$944$	3.73438e15	0.162133
$945$	2.87424e15	0.124064
$946$	−4.07160e16	−1.74729
$947$	−5.79326e15	−0.247171	−0.123586	−	0.992334i	$-0.539439\pi$
$947$	−5.79326e15	−0.247171	−0.123586	+	0.992334i	$0.539439\pi$
$948$	9.07998e15	0.385158
$949$	−9.04579e14	−0.0381489
$950$	−9.29325e15	−0.389662
$951$	1.66321e16	0.693352
$952$	7.84878e15	0.325311
$953$	−2.10008e16	−0.865418	−0.432709	−	0.901534i	$-0.642442\pi$
$953$	−2.10008e16	−0.865418	−0.432709	+	0.901534i	$0.642442\pi$
$954$	−9.27691e15	−0.380091
$955$	−3.84850e16	−1.56773
$956$	−1.10125e16	−0.446032
$957$	−1.46519e16	−0.590036
$958$	−2.79618e16	−1.11958
$959$	1.88168e16	0.749107
$960$	−5.46077e15	−0.216153
$961$	2.41082e16	0.948827
$962$	−6.24097e16	−2.44224
$963$	1.38021e15	0.0537032
$964$	−1.04723e16	−0.405153
$965$	3.76112e16	1.44683
$966$	−1.12433e16	−0.430050
$967$	3.25364e16	1.23744	0.618720	−	0.785612i	$-0.287652\pi$
$967$	3.25364e16	1.23744	0.618720	+	0.785612i	$0.287652\pi$
$968$	2.68852e16	1.01671
$969$	−5.95427e15	−0.223897
$970$	5.60609e16	2.09612
$971$	8.82887e14	0.0328246	0.0164123	−	0.999865i	$-0.494776\pi$
$971$	8.82887e14	0.0328246	0.0164123	+	0.999865i	$0.494776\pi$
$972$	7.49556e14	0.0277102
$973$	1.60603e16	0.590381
$974$	−2.13073e16	−0.778851
$975$	2.10497e16	0.765106
$976$	4.16779e16	1.50637
$977$	2.39526e16	0.860859	0.430429	−	0.902624i	$-0.358362\pi$
$977$	2.39526e16	0.860859	0.430429	+	0.902624i	$0.358362\pi$
$978$	−1.09681e16	−0.391984
$979$	−8.62316e16	−3.06452
$980$	1.28754e16	0.455006
$981$	−1.33063e16	−0.467602
$982$	2.14353e16	0.749061
$983$	−9.42036e15	−0.327358	−0.163679	−	0.986514i	$-0.552336\pi$
$983$	−9.42036e15	−0.327358	−0.163679	+	0.986514i	$0.552336\pi$
$984$	−5.48154e15	−0.189421
$985$	4.41010e16	1.51548
$986$	2.28567e16	0.781070
$987$	−1.21536e16	−0.413010
$988$	7.68443e15	0.259686
$989$	3.60931e16	1.21295
$990$	−2.56269e16	−0.856452
$991$	−1.26830e16	−0.421520	−0.210760	−	0.977538i	$-0.567594\pi$
$991$	−1.26830e16	−0.421520	−0.210760	+	0.977538i	$0.567594\pi$
$992$	3.42347e16	1.13149
$993$	−2.24230e16	−0.737008
$994$	−1.70618e15	−0.0557699
$995$	4.47256e16	1.45388
$996$	1.38469e15	0.0447637
$997$	−3.73904e16	−1.20209	−0.601045	−	0.799215i	$-0.705249\pi$
$997$	−3.73904e16	−1.20209	−0.601045	+	0.799215i	$0.705249\pi$
$998$	2.18297e16	0.697958
$999$	7.89713e15	0.251107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.7	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.7	✓	27	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-54.1540 q^{2} +243.000 q^{3} +884.652 q^{4} -9497.19 q^{5} -13159.4 q^{6} -21091.6 q^{7} +62999.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-54.1540 q^{2} +243.000 q^{3} +884.652 q^{4} -9497.19 q^{5} -13159.4 q^{6} -21091.6 q^{7} +62999.9 q^{8} +59049.0 q^{9} +514310. q^{10} -843837. q^{11} +214970. q^{12} +2.09397e6 q^{13} +1.14219e6 q^{14} -2.30782e6 q^{15} -5.22346e6 q^{16} -5.90682e6 q^{17} -3.19774e6 q^{18} +4.14828e6 q^{19} -8.40171e6 q^{20} -5.12525e6 q^{21} +4.56971e7 q^{22} -4.05086e7 q^{23} +1.53090e7 q^{24} +4.13685e7 q^{25} -1.13397e8 q^{26} +1.43489e7 q^{27} -1.86587e7 q^{28} +7.14544e7 q^{29} +1.24977e8 q^{30} +2.22524e8 q^{31} +1.53847e8 q^{32} -2.05052e8 q^{33} +3.19878e8 q^{34} +2.00310e8 q^{35} +5.22378e7 q^{36} +5.50364e8 q^{37} -2.24646e8 q^{38} +5.08836e8 q^{39} -5.98322e8 q^{40} -3.58060e8 q^{41} +2.77552e8 q^{42} -8.90997e8 q^{43} -7.46502e8 q^{44} -5.60799e8 q^{45} +2.19370e9 q^{46} +2.37132e9 q^{47} -1.26930e9 q^{48} -1.53247e9 q^{49} -2.24027e9 q^{50} -1.43536e9 q^{51} +1.85244e9 q^{52} +2.90109e9 q^{53} -7.77050e8 q^{54} +8.01408e9 q^{55} -1.32877e9 q^{56} +1.00803e9 q^{57} -3.86954e9 q^{58} -7.14924e8 q^{59} -2.04161e9 q^{60} -7.97897e9 q^{61} -1.20505e10 q^{62} -1.24544e9 q^{63} +2.36620e9 q^{64} -1.98869e10 q^{65} +1.11044e10 q^{66} +9.55219e9 q^{67} -5.22548e9 q^{68} -9.84360e9 q^{69} -1.08476e10 q^{70} -1.49378e9 q^{71} +3.72008e9 q^{72} -4.31992e8 q^{73} -2.98044e10 q^{74} +1.00525e10 q^{75} +3.66979e9 q^{76} +1.77978e10 q^{77} -2.75555e10 q^{78} +4.22383e10 q^{79} +4.96082e10 q^{80} +3.48678e9 q^{81} +1.93904e10 q^{82} +6.44130e9 q^{83} -4.53406e9 q^{84} +5.60982e10 q^{85} +4.82510e10 q^{86} +1.73634e10 q^{87} -5.31617e10 q^{88} +1.02190e11 q^{89} +3.03695e10 q^{90} -4.41651e10 q^{91} -3.58360e10 q^{92} +5.40732e10 q^{93} -1.28416e11 q^{94} -3.93970e10 q^{95} +3.73849e10 q^{96} +1.09002e11 q^{97} +8.29895e10 q^{98} -4.98278e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

Modular forms

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