LMFDB - Embedded newform 177.10.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-4.11702 q^{2} -81.0000 q^{3} -495.050 q^{4} -2185.60 q^{5} +333.479 q^{6} -4537.74 q^{7} +4146.05 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-4.11702 q^{2} -81.0000 q^{3} -495.050 q^{4} -2185.60 q^{5} +333.479 q^{6} -4537.74 q^{7} +4146.05 q^{8} +6561.00 q^{9} +8998.14 q^{10} -28540.1 q^{11} +40099.1 q^{12} -102441. q^{13} +18681.9 q^{14} +177033. q^{15} +236396. q^{16} +121059. q^{17} -27011.8 q^{18} -212496. q^{19} +1.08198e6 q^{20} +367557. q^{21} +117500. q^{22} -1.13375e6 q^{23} -335830. q^{24} +2.82370e6 q^{25} +421753. q^{26} -531441. q^{27} +2.24641e6 q^{28} +4.92713e6 q^{29} -728849. q^{30} +8.24073e6 q^{31} -3.09602e6 q^{32} +2.31174e6 q^{33} -498400. q^{34} +9.91765e6 q^{35} -3.24802e6 q^{36} +2.14954e7 q^{37} +874852. q^{38} +8.29775e6 q^{39} -9.06158e6 q^{40} +1.27066e7 q^{41} -1.51324e6 q^{42} -4.07034e7 q^{43} +1.41288e7 q^{44} -1.43397e7 q^{45} +4.66765e6 q^{46} +1.82085e7 q^{47} -1.91481e7 q^{48} -1.97626e7 q^{49} -1.16252e7 q^{50} -9.80574e6 q^{51} +5.07136e7 q^{52} -6.37339e7 q^{53} +2.18795e6 q^{54} +6.23770e7 q^{55} -1.88137e7 q^{56} +1.72122e7 q^{57} -2.02851e7 q^{58} -1.21174e7 q^{59} -8.76403e7 q^{60} +2.27505e7 q^{61} -3.39272e7 q^{62} -2.97721e7 q^{63} -1.08289e8 q^{64} +2.23895e8 q^{65} -9.51750e6 q^{66} -3.95243e7 q^{67} -5.99301e7 q^{68} +9.18334e7 q^{69} -4.08312e7 q^{70} -1.08585e7 q^{71} +2.72022e7 q^{72} +1.10383e8 q^{73} -8.84968e7 q^{74} -2.28720e8 q^{75} +1.05196e8 q^{76} +1.29507e8 q^{77} -3.41620e7 q^{78} -2.80040e7 q^{79} -5.16667e8 q^{80} +4.30467e7 q^{81} -5.23132e7 q^{82} -2.16977e8 q^{83} -1.81959e8 q^{84} -2.64585e8 q^{85} +1.67577e8 q^{86} -3.99098e8 q^{87} -1.18328e8 q^{88} +4.03240e8 q^{89} +5.90368e7 q^{90} +4.64852e8 q^{91} +5.61261e8 q^{92} -6.67499e8 q^{93} -7.49647e7 q^{94} +4.64431e8 q^{95} +2.50778e8 q^{96} +7.17322e8 q^{97} +8.13629e7 q^{98} -1.87251e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	−4.11702	−0.181948	−0.0909741	−	0.995853i	$-0.528998\pi$
$2$	−4.11702	−0.181948	−0.0909741	+	0.995853i	$0.528998\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−495.050	−0.966895
$5$	−2185.60	−1.56388	−0.781942	−	0.623351i	$-0.785771\pi$
$5$	−2185.60	−1.56388	−0.781942	+	0.623351i	$0.785771\pi$
$6$	333.479	0.105048
$7$	−4537.74	−0.714329	−0.357164	−	0.934042i	$-0.616256\pi$
$7$	−4537.74	−0.714329	−0.357164	+	0.934042i	$0.616256\pi$
$8$	4146.05	0.357873
$9$	6561.00	0.333333
$10$	8998.14	0.284546
$11$	−28540.1	−0.587743	−0.293872	−	0.955845i	$-0.594944\pi$
$11$	−28540.1	−0.587743	−0.293872	+	0.955845i	$0.594944\pi$
$12$	40099.1	0.558237
$13$	−102441.	−0.994787	−0.497394	−	0.867525i	$-0.665709\pi$
$13$	−102441.	−0.994787	−0.497394	+	0.867525i	$0.665709\pi$
$14$	18681.9	0.129971
$15$	177033.	0.902909
$16$	236396.	0.901780
$17$	121059.	0.351540	0.175770	−	0.984431i	$-0.443758\pi$
$17$	121059.	0.351540	0.175770	+	0.984431i	$0.443758\pi$
$18$	−27011.8	−0.0606494
$19$	−212496.	−0.374076	−0.187038	−	0.982353i	$-0.559889\pi$
$19$	−212496.	−0.374076	−0.187038	+	0.982353i	$0.559889\pi$
$20$	1.08198e6	1.51211
$21$	367557.	0.412418
$22$	117500.	0.106939
$23$	−1.13375e6	−0.844773	−0.422387	−	0.906416i	$-0.638808\pi$
$23$	−1.13375e6	−0.844773	−0.422387	+	0.906416i	$0.638808\pi$
$24$	−335830.	−0.206618
$25$	2.82370e6	1.44573
$26$	421753.	0.181000
$27$	−531441.	−0.192450
$28$	2.24641e6	0.690681
$29$	4.92713e6	1.29361	0.646805	−	0.762656i	$-0.276105\pi$
$29$	4.92713e6	1.29361	0.646805	+	0.762656i	$0.276105\pi$
$30$	−728849.	−0.164283
$31$	8.24073e6	1.60265	0.801324	−	0.598231i	$-0.204130\pi$
$31$	8.24073e6	1.60265	0.801324	+	0.598231i	$0.204130\pi$
$32$	−3.09602e6	−0.521951
$33$	2.31174e6	0.339334
$34$	−498400.	−0.0639622
$35$	9.91765e6	1.11713
$36$	−3.24802e6	−0.322298
$37$	2.14954e7	1.88555	0.942773	−	0.333436i	$-0.108208\pi$
$37$	2.14954e7	1.88555	0.942773	+	0.333436i	$0.108208\pi$
$38$	874852.	0.0680626
$39$	8.29775e6	0.574341
$40$	−9.06158e6	−0.559672
$41$	1.27066e7	0.702265	0.351132	−	0.936326i	$-0.385797\pi$
$41$	1.27066e7	0.702265	0.351132	+	0.936326i	$0.385797\pi$
$42$	−1.51324e6	−0.0750387
$43$	−4.07034e7	−1.81561	−0.907806	−	0.419391i	$-0.862244\pi$
$43$	−4.07034e7	−1.81561	−0.907806	+	0.419391i	$0.862244\pi$
$44$	1.41288e7	0.568286
$45$	−1.43397e7	−0.521295
$46$	4.66765e6	0.153705
$47$	1.82085e7	0.544294	0.272147	−	0.962256i	$-0.412266\pi$
$47$	1.82085e7	0.544294	0.272147	+	0.962256i	$0.412266\pi$
$48$	−1.91481e7	−0.520643
$49$	−1.97626e7	−0.489735
$50$	−1.16252e7	−0.263049
$51$	−9.80574e6	−0.202962
$52$	5.07136e7	0.961854
$53$	−6.37339e7	−1.10950	−0.554752	−	0.832016i	$-0.687187\pi$
$53$	−6.37339e7	−1.10950	−0.554752	+	0.832016i	$0.687187\pi$
$54$	2.18795e6	0.0350160
$55$	6.23770e7	0.919163
$56$	−1.88137e7	−0.255639
$57$	1.72122e7	0.215973
$58$	−2.02851e7	−0.235370
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−8.76403e7	−0.873018
$61$	2.27505e7	0.210382	0.105191	−	0.994452i	$-0.466455\pi$
$61$	2.27505e7	0.210382	0.105191	+	0.994452i	$0.466455\pi$
$62$	−3.39272e7	−0.291599
$63$	−2.97721e7	−0.238110
$64$	−1.08289e8	−0.806812
$65$	2.23895e8	1.55573
$66$	−9.51750e6	−0.0617412
$67$	−3.95243e7	−0.239623	−0.119811	−	0.992797i	$-0.538229\pi$
$67$	−3.95243e7	−0.239623	−0.119811	+	0.992797i	$0.538229\pi$
$68$	−5.99301e7	−0.339903
$69$	9.18334e7	0.487730
$70$	−4.08312e7	−0.203259
$71$	−1.08585e7	−0.0507114	−0.0253557	−	0.999678i	$-0.508072\pi$
$71$	−1.08585e7	−0.0507114	−0.0253557	+	0.999678i	$0.508072\pi$
$72$	2.72022e7	0.119291
$73$	1.10383e8	0.454935	0.227467	−	0.973786i	$-0.426955\pi$
$73$	1.10383e8	0.454935	0.227467	+	0.973786i	$0.426955\pi$
$74$	−8.84968e7	−0.343072
$75$	−2.28720e8	−0.834695
$76$	1.05196e8	0.361693
$77$	1.29507e8	0.419842
$78$	−3.41620e7	−0.104500
$79$	−2.80040e7	−0.0808906	−0.0404453	−	0.999182i	$-0.512878\pi$
$79$	−2.80040e7	−0.0808906	−0.0404453	+	0.999182i	$0.512878\pi$
$80$	−5.16667e8	−1.41028
$81$	4.30467e7	0.111111
$82$	−5.23132e7	−0.127776
$83$	−2.16977e8	−0.501836	−0.250918	−	0.968008i	$-0.580732\pi$
$83$	−2.16977e8	−0.501836	−0.250918	+	0.968008i	$0.580732\pi$
$84$	−1.81959e8	−0.398765
$85$	−2.64585e8	−0.549769
$86$	1.67577e8	0.330347
$87$	−3.99098e8	−0.746866
$88$	−1.18328e8	−0.210338
$89$	4.03240e8	0.681253	0.340627	−	0.940199i	$-0.389361\pi$
$89$	4.03240e8	0.681253	0.340627	+	0.940199i	$0.389361\pi$
$90$	5.90368e7	0.0948487
$91$	4.64852e8	0.710605
$92$	5.61261e8	0.816807
$93$	−6.67499e8	−0.925289
$94$	−7.49647e7	−0.0990334
$95$	4.64431e8	0.585012
$96$	2.50778e8	0.301348
$97$	7.17322e8	0.822699	0.411350	−	0.911478i	$-0.365058\pi$
$97$	7.17322e8	0.822699	0.411350	+	0.911478i	$0.365058\pi$
$98$	8.13629e7	0.0891064
$99$	−1.87251e8	−0.195914
$100$	−1.39787e9	−1.39787
$101$	1.28611e9	1.22980	0.614898	−	0.788607i	$-0.289197\pi$
$101$	1.28611e9	1.22980	0.614898	+	0.788607i	$0.289197\pi$
$102$	4.03704e7	0.0369286
$103$	−1.87942e9	−1.64534	−0.822672	−	0.568517i	$-0.807517\pi$
$103$	−1.87942e9	−1.64534	−0.822672	+	0.568517i	$0.807517\pi$
$104$	−4.24726e8	−0.356008
$105$	−8.03330e8	−0.644974
$106$	2.62394e8	0.201872
$107$	−5.07856e6	−0.00374553	−0.00187277	−	0.999998i	$-0.500596\pi$
$107$	−5.07856e6	−0.00374553	−0.00187277	+	0.999998i	$0.500596\pi$
$108$	2.63090e8	0.186079
$109$	2.03800e9	1.38288	0.691442	−	0.722432i	$-0.256976\pi$
$109$	2.03800e9	1.38288	0.691442	+	0.722432i	$0.256976\pi$
$110$	−2.56807e8	−0.167240
$111$	−1.74112e9	−1.08862
$112$	−1.07270e9	−0.644168
$113$	−2.04814e9	−1.18170	−0.590848	−	0.806783i	$-0.701207\pi$
$113$	−2.04814e9	−1.18170	−0.590848	+	0.806783i	$0.701207\pi$
$114$	−7.08630e7	−0.0392959
$115$	2.47791e9	1.32113
$116$	−2.43918e9	−1.25078
$117$	−6.72118e8	−0.331596
$118$	4.98874e7	0.0236876
$119$	−5.49332e8	−0.251115
$120$	7.33988e8	0.323127
$121$	−1.54341e9	−0.654558
$122$	−9.36645e7	−0.0382786
$123$	−1.02923e9	−0.405453
$124$	−4.07957e9	−1.54959
$125$	−1.90273e9	−0.697078
$126$	1.22572e8	0.0433236
$127$	−1.67854e9	−0.572553	−0.286276	−	0.958147i	$-0.592418\pi$
$127$	−1.67854e9	−0.572553	−0.286276	+	0.958147i	$0.592418\pi$
$128$	2.03099e9	0.668749
$129$	3.29698e9	1.04824
$130$	−9.21781e8	−0.283063
$131$	1.04403e9	0.309736	0.154868	−	0.987935i	$-0.450505\pi$
$131$	1.04403e9	0.309736	0.154868	+	0.987935i	$0.450505\pi$
$132$	−1.14443e9	−0.328100
$133$	9.64253e8	0.267214
$134$	1.62722e8	0.0435989
$135$	1.16151e9	0.300970
$136$	5.01914e8	0.125807
$137$	−5.73514e9	−1.39092	−0.695458	−	0.718566i	$-0.744799\pi$
$137$	−5.73514e9	−1.39092	−0.695458	+	0.718566i	$0.744799\pi$
$138$	−3.78080e8	−0.0887417
$139$	3.09481e9	0.703182	0.351591	−	0.936154i	$-0.385641\pi$
$139$	3.09481e9	0.703182	0.351591	+	0.936154i	$0.385641\pi$
$140$	−4.90974e9	−1.08014
$141$	−1.47489e9	−0.314248
$142$	4.47045e7	0.00922686
$143$	2.92368e9	0.584680
$144$	1.55100e9	0.300593
$145$	−1.07687e10	−2.02306
$146$	−4.54449e8	−0.0827746
$147$	1.60077e9	0.282748
$148$	−1.06413e10	−1.82312
$149$	4.59376e9	0.763538	0.381769	−	0.924258i	$-0.375315\pi$
$149$	4.59376e9	0.763538	0.381769	+	0.924258i	$0.375315\pi$
$150$	9.41644e8	0.151871
$151$	−1.25131e9	−0.195871	−0.0979356	−	0.995193i	$-0.531224\pi$
$151$	−1.25131e9	−0.195871	−0.0979356	+	0.995193i	$0.531224\pi$
$152$	−8.81020e8	−0.133872
$153$	7.94265e8	0.117180
$154$	−5.33184e8	−0.0763895
$155$	−1.80109e10	−2.50636
$156$	−4.10780e9	−0.555327
$157$	−5.24043e8	−0.0688364	−0.0344182	−	0.999408i	$-0.510958\pi$
$157$	−5.24043e8	−0.0688364	−0.0344182	+	0.999408i	$0.510958\pi$
$158$	1.15293e8	0.0147179
$159$	5.16245e9	0.640573
$160$	6.76665e9	0.816270
$161$	5.14464e9	0.603446
$162$	−1.77224e8	−0.0202165
$163$	1.58599e10	1.75978	0.879888	−	0.475182i	$-0.157618\pi$
$163$	1.58599e10	1.75978	0.879888	+	0.475182i	$0.157618\pi$
$164$	−6.29039e9	−0.679016
$165$	−5.05254e9	−0.530679
$166$	8.93298e8	0.0913082
$167$	−2.20185e9	−0.219060	−0.109530	−	0.993983i	$-0.534935\pi$
$167$	−2.20185e9	−0.219060	−0.109530	+	0.993983i	$0.534935\pi$
$168$	1.52391e9	0.147593
$169$	−1.10273e8	−0.0103987
$170$	1.08930e9	0.100029
$171$	−1.39419e9	−0.124692
$172$	2.01502e10	1.75551
$173$	1.23180e10	1.04552	0.522759	−	0.852481i	$-0.324903\pi$
$173$	1.23180e10	1.04552	0.522759	+	0.852481i	$0.324903\pi$
$174$	1.64309e9	0.135891
$175$	−1.28132e10	−1.03273
$176$	−6.74677e9	−0.530016
$177$	9.81506e8	0.0751646
$178$	−1.66015e9	−0.123953
$179$	3.98351e9	0.290020	0.145010	−	0.989430i	$-0.453679\pi$
$179$	3.98351e9	0.290020	0.145010	+	0.989430i	$0.453679\pi$
$180$	7.09887e9	0.504037
$181$	1.22416e10	0.847781	0.423890	−	0.905713i	$-0.360664\pi$
$181$	1.22416e10	0.847781	0.423890	+	0.905713i	$0.360664\pi$
$182$	−1.91380e9	−0.129293
$183$	−1.84279e9	−0.121464
$184$	−4.70056e9	−0.302322
$185$	−4.69802e10	−2.94878
$186$	2.74811e9	0.168355
$187$	−3.45502e9	−0.206616
$188$	−9.01412e9	−0.526275
$189$	2.41154e9	0.137473
$190$	−1.91207e9	−0.106442
$191$	−1.74290e10	−0.947592	−0.473796	−	0.880635i	$-0.657117\pi$
$191$	−1.74290e10	−0.947592	−0.473796	+	0.880635i	$0.657117\pi$
$192$	8.77137e9	0.465813
$193$	−3.72667e10	−1.93336	−0.966682	−	0.255982i	$-0.917601\pi$
$193$	−3.72667e10	−1.93336	−0.966682	+	0.255982i	$0.917601\pi$
$194$	−2.95323e9	−0.149689
$195$	−1.81355e10	−0.898202
$196$	9.78346e9	0.473522
$197$	2.23776e10	1.05856	0.529280	−	0.848447i	$-0.322462\pi$
$197$	2.23776e10	1.05856	0.529280	+	0.848447i	$0.322462\pi$
$198$	7.70917e8	0.0356463
$199$	−4.17052e8	−0.0188517	−0.00942587	−	0.999956i	$-0.503000\pi$
$199$	−4.17052e8	−0.0188517	−0.00942587	+	0.999956i	$0.503000\pi$
$200$	1.17072e10	0.517390
$201$	3.20147e9	0.138346
$202$	−5.29495e9	−0.223759
$203$	−2.23580e10	−0.924062
$204$	4.85433e9	0.196243
$205$	−2.77714e10	−1.09826
$206$	7.73761e9	0.299367
$207$	−7.43850e9	−0.281591
$208$	−2.42168e10	−0.897079
$209$	6.06466e9	0.219861
$210$	3.30733e9	0.117352
$211$	4.42985e10	1.53857	0.769286	−	0.638904i	$-0.220612\pi$
$211$	4.42985e10	1.53857	0.769286	+	0.638904i	$0.220612\pi$
$212$	3.15515e10	1.07277
$213$	8.79536e8	0.0292783
$214$	2.09085e7	0.000681493 0
$215$	8.89612e10	2.83941
$216$	−2.20338e9	−0.0688727
$217$	−3.73942e10	−1.14482
$218$	−8.39050e9	−0.251613
$219$	−8.94102e9	−0.262657
$220$	−3.08798e10	−0.888734
$221$	−1.24014e10	−0.349708
$222$	7.16824e9	0.198073
$223$	−4.23952e10	−1.14801	−0.574004	−	0.818852i	$-0.694611\pi$
$223$	−4.23952e10	−1.14801	−0.574004	+	0.818852i	$0.694611\pi$
$224$	1.40489e10	0.372844
$225$	1.85263e10	0.481912
$226$	8.43221e9	0.215008
$227$	6.90422e10	1.72583	0.862916	−	0.505347i	$-0.168636\pi$
$227$	6.90422e10	1.72583	0.862916	+	0.505347i	$0.168636\pi$
$228$	−8.52091e9	−0.208823
$229$	−3.84678e10	−0.924352	−0.462176	−	0.886788i	$-0.652931\pi$
$229$	−3.84678e10	−0.924352	−0.462176	+	0.886788i	$0.652931\pi$
$230$	−1.02016e10	−0.240377
$231$	−1.04901e10	−0.242396
$232$	2.04281e10	0.462948
$233$	4.93231e10	1.09635	0.548174	−	0.836364i	$-0.315323\pi$
$233$	4.93231e10	1.09635	0.548174	+	0.836364i	$0.315323\pi$
$234$	2.76712e9	0.0603333
$235$	−3.97964e10	−0.851213
$236$	5.99870e9	0.125879
$237$	2.26832e9	0.0467022
$238$	2.26161e9	0.0456900
$239$	6.71458e10	1.33115	0.665577	−	0.746329i	$-0.268185\pi$
$239$	6.71458e10	1.33115	0.665577	+	0.746329i	$0.268185\pi$
$240$	4.18500e10	0.814226
$241$	4.26510e8	0.00814428	0.00407214	−	0.999992i	$-0.498704\pi$
$241$	4.26510e8	0.00814428	0.00407214	+	0.999992i	$0.498704\pi$
$242$	6.35426e9	0.119096
$243$	−3.48678e9	−0.0641500
$244$	−1.12627e10	−0.203417
$245$	4.31930e10	0.765888
$246$	4.23737e9	0.0737714
$247$	2.17684e10	0.372126
$248$	3.41664e10	0.573544
$249$	1.75751e10	0.289735
$250$	7.83356e9	0.126832
$251$	2.84787e10	0.452886	0.226443	−	0.974024i	$-0.427290\pi$
$251$	2.84787e10	0.452886	0.226443	+	0.974024i	$0.427290\pi$
$252$	1.47387e10	0.230227
$253$	3.23572e10	0.496510
$254$	6.91059e9	0.104175
$255$	2.14314e10	0.317409
$256$	4.70821e10	0.685135
$257$	8.11981e9	0.116104	0.0580520	−	0.998314i	$-0.481511\pi$
$257$	8.11981e9	0.116104	0.0580520	+	0.998314i	$0.481511\pi$
$258$	−1.35737e10	−0.190726
$259$	−9.75403e10	−1.34690
$260$	−1.10839e11	−1.50423
$261$	3.23269e10	0.431203
$262$	−4.29829e9	−0.0563560
$263$	8.00335e10	1.03150	0.515752	−	0.856738i	$-0.327513\pi$
$263$	8.00335e10	1.03150	0.515752	+	0.856738i	$0.327513\pi$
$264$	9.58460e9	0.121438
$265$	1.39296e11	1.73514
$266$	−3.96985e9	−0.0486190
$267$	−3.26624e10	−0.393322
$268$	1.95665e10	0.231690
$269$	−5.89366e10	−0.686277	−0.343139	−	0.939285i	$-0.611490\pi$
$269$	−5.89366e10	−0.686277	−0.343139	+	0.939285i	$0.611490\pi$
$270$	−4.78198e9	−0.0547609
$271$	−4.77297e10	−0.537560	−0.268780	−	0.963202i	$-0.586620\pi$
$271$	−4.77297e10	−0.537560	−0.268780	+	0.963202i	$0.586620\pi$
$272$	2.86178e10	0.317012
$273$	−3.76530e10	−0.410268
$274$	2.36117e10	0.253075
$275$	−8.05886e10	−0.849721
$276$	−4.54621e10	−0.471584
$277$	1.52146e11	1.55275	0.776374	−	0.630273i	$-0.217057\pi$
$277$	1.52146e11	1.55275	0.776374	+	0.630273i	$0.217057\pi$
$278$	−1.27414e10	−0.127943
$279$	5.40674e10	0.534216
$280$	4.11190e10	0.399790
$281$	1.46537e11	1.40207	0.701036	−	0.713126i	$-0.252721\pi$
$281$	1.46537e11	1.40207	0.701036	+	0.713126i	$0.252721\pi$
$282$	6.07214e9	0.0571769
$283$	−8.94439e10	−0.828918	−0.414459	−	0.910068i	$-0.636029\pi$
$283$	−8.94439e10	−0.828918	−0.414459	+	0.910068i	$0.636029\pi$
$284$	5.37548e9	0.0490326
$285$	−3.76189e10	−0.337757
$286$	−1.20369e10	−0.106381
$287$	−5.76590e10	−0.501648
$288$	−2.03130e10	−0.173984
$289$	−1.03933e11	−0.876419
$290$	4.43350e10	0.368092
$291$	−5.81031e10	−0.474986
$292$	−5.46451e10	−0.439874
$293$	1.36928e11	1.08540	0.542699	−	0.839928i	$-0.317403\pi$
$293$	1.36928e11	1.08540	0.542699	+	0.839928i	$0.317403\pi$
$294$	−6.59039e9	−0.0514456
$295$	2.64836e10	0.203600
$296$	8.91208e10	0.674786
$297$	1.51674e10	0.113111
$298$	−1.89126e10	−0.138924
$299$	1.16142e11	0.840370
$300$	1.13228e11	0.807063
$301$	1.84701e11	1.29694
$302$	5.15169e9	0.0356384
$303$	−1.04175e11	−0.710023
$304$	−5.02334e10	−0.337335
$305$	−4.97235e10	−0.329012
$306$	−3.27001e9	−0.0213207
$307$	−1.57622e11	−1.01273	−0.506364	−	0.862320i	$-0.669011\pi$
$307$	−1.57622e11	−1.01273	−0.506364	+	0.862320i	$0.669011\pi$
$308$	−6.41126e10	−0.405943
$309$	1.52233e11	0.949939
$310$	7.41512e10	0.456027
$311$	−2.48195e11	−1.50443	−0.752214	−	0.658919i	$-0.771014\pi$
$311$	−2.48195e11	−1.50443	−0.752214	+	0.658919i	$0.771014\pi$
$312$	3.44028e10	0.205541
$313$	3.42026e10	0.201423	0.100712	−	0.994916i	$-0.467888\pi$
$313$	3.42026e10	0.201423	0.100712	+	0.994916i	$0.467888\pi$
$314$	2.15749e9	0.0125247
$315$	6.50697e10	0.372376
$316$	1.38634e10	0.0782127
$317$	−8.90724e10	−0.495423	−0.247712	−	0.968834i	$-0.579679\pi$
$317$	−8.90724e10	−0.495423	−0.247712	+	0.968834i	$0.579679\pi$
$318$	−2.12539e10	−0.116551
$319$	−1.40621e11	−0.760310
$320$	2.36675e11	1.26176
$321$	4.11363e8	0.00216248
$322$	−2.11806e10	−0.109796
$323$	−2.57245e10	−0.131503
$324$	−2.13103e10	−0.107433
$325$	−2.89264e11	−1.43820
$326$	−6.52957e10	−0.320188
$327$	−1.65078e11	−0.798409
$328$	5.26820e10	0.251322
$329$	−8.26253e10	−0.388805
$330$	2.08014e10	0.0965561
$331$	2.22269e11	1.01778	0.508889	−	0.860832i	$-0.330056\pi$
$331$	2.22269e11	1.01778	0.508889	+	0.860832i	$0.330056\pi$
$332$	1.07414e11	0.485223
$333$	1.41031e11	0.628515
$334$	9.06507e9	0.0398577
$335$	8.63842e10	0.374742
$336$	8.68890e10	0.371910
$337$	5.95001e10	0.251295	0.125647	−	0.992075i	$-0.459899\pi$
$337$	5.95001e10	0.251295	0.125647	+	0.992075i	$0.459899\pi$
$338$	4.53998e8	0.00189203
$339$	1.65899e11	0.682252
$340$	1.30983e11	0.531568
$341$	−2.35191e11	−0.941945
$342$	5.73990e9	0.0226875
$343$	2.72791e11	1.06416
$344$	−1.68758e11	−0.649759
$345$	−2.00711e11	−0.762754
$346$	−5.07133e10	−0.190230
$347$	7.30117e10	0.270340	0.135170	−	0.990822i	$-0.456842\pi$
$347$	7.30117e10	0.270340	0.135170	+	0.990822i	$0.456842\pi$
$348$	1.97573e11	0.722141
$349$	2.73470e11	0.986722	0.493361	−	0.869825i	$-0.335768\pi$
$349$	2.73470e11	0.986722	0.493361	+	0.869825i	$0.335768\pi$
$350$	5.27522e10	0.187903
$351$	5.44415e10	0.191447
$352$	8.83607e10	0.306773
$353$	3.47728e11	1.19194	0.595969	−	0.803008i	$-0.296768\pi$
$353$	3.47728e11	1.19194	0.595969	+	0.803008i	$0.296768\pi$
$354$	−4.04088e9	−0.0136761
$355$	2.37322e10	0.0793068
$356$	−1.99624e11	−0.658700
$357$	4.44959e10	0.144982
$358$	−1.64002e10	−0.0527686
$359$	1.13271e11	0.359908	0.179954	−	0.983675i	$-0.442405\pi$
$359$	1.13271e11	0.359908	0.179954	+	0.983675i	$0.442405\pi$
$360$	−5.94530e10	−0.186557
$361$	−2.77533e11	−0.860067
$362$	−5.03988e10	−0.154252
$363$	1.25016e11	0.377909
$364$	−2.30125e11	−0.687080
$365$	−2.41252e11	−0.711465
$366$	7.58682e9	0.0221001
$367$	−6.24382e11	−1.79661	−0.898303	−	0.439376i	$-0.855200\pi$
$367$	−6.24382e11	−1.79661	−0.898303	+	0.439376i	$0.855200\pi$
$368$	−2.68013e11	−0.761800
$369$	8.33678e10	0.234088
$370$	1.93418e11	0.536525
$371$	2.89208e11	0.792551
$372$	3.30445e11	0.894657
$373$	−4.41064e11	−1.17981	−0.589905	−	0.807473i	$-0.700835\pi$
$373$	−4.41064e11	−1.17981	−0.589905	+	0.807473i	$0.700835\pi$
$374$	1.42244e10	0.0375934
$375$	1.54121e11	0.402458
$376$	7.54932e10	0.194788
$377$	−5.04742e11	−1.28687
$378$	−9.92835e9	−0.0250129
$379$	−4.38615e11	−1.09196	−0.545981	−	0.837798i	$-0.683843\pi$
$379$	−4.38615e11	−1.09196	−0.545981	+	0.837798i	$0.683843\pi$
$380$	−2.29917e11	−0.565645
$381$	1.35962e11	0.330564
$382$	7.17554e10	0.172413
$383$	6.07210e11	1.44193	0.720965	−	0.692971i	$-0.243699\pi$
$383$	6.07210e11	1.44193	0.720965	+	0.692971i	$0.243699\pi$
$384$	−1.64510e11	−0.386102
$385$	−2.83050e11	−0.656584
$386$	1.53428e11	0.351772
$387$	−2.67055e11	−0.605204
$388$	−3.55110e11	−0.795464
$389$	−8.77368e10	−0.194271	−0.0971356	−	0.995271i	$-0.530968\pi$
$389$	−8.77368e10	−0.194271	−0.0971356	+	0.995271i	$0.530968\pi$
$390$	7.46643e10	0.163426
$391$	−1.37250e11	−0.296972
$392$	−8.19365e10	−0.175263
$393$	−8.45664e10	−0.178826
$394$	−9.21291e10	−0.192603
$395$	6.12054e10	0.126504
$396$	9.26988e10	0.189429
$397$	−9.23550e11	−1.86596	−0.932982	−	0.359923i	$-0.882803\pi$
$397$	−9.23550e11	−1.86596	−0.932982	+	0.359923i	$0.882803\pi$
$398$	1.71701e9	0.00343004
$399$	−7.81045e10	−0.154276
$400$	6.67512e11	1.30374
$401$	−6.29706e11	−1.21615	−0.608076	−	0.793879i	$-0.708059\pi$
$401$	−6.29706e11	−1.21615	−0.608076	+	0.793879i	$0.708059\pi$
$402$	−1.31805e10	−0.0251719
$403$	−8.44191e11	−1.59429
$404$	−6.36690e11	−1.18908
$405$	−9.40827e10	−0.173765
$406$	9.20484e10	0.168132
$407$	−6.13479e11	−1.10822
$408$	−4.06551e10	−0.0726346
$409$	−2.55790e11	−0.451990	−0.225995	−	0.974129i	$-0.572563\pi$
$409$	−2.55790e11	−0.451990	−0.225995	+	0.974129i	$0.572563\pi$
$410$	1.14335e11	0.199827
$411$	4.64546e11	0.803046
$412$	9.30407e11	1.59087
$413$	5.49854e10	0.0929977
$414$	3.06245e10	0.0512350
$415$	4.74223e11	0.784814
$416$	3.17161e11	0.519230
$417$	−2.50680e11	−0.405982
$418$	−2.49683e10	−0.0400033
$419$	3.00606e11	0.476468	0.238234	−	0.971208i	$-0.423431\pi$
$419$	3.00606e11	0.476468	0.238234	+	0.971208i	$0.423431\pi$
$420$	3.97689e11	0.623622
$421$	−5.34648e11	−0.829465	−0.414733	−	0.909943i	$-0.636125\pi$
$421$	−5.34648e11	−0.829465	−0.414733	+	0.909943i	$0.636125\pi$
$422$	−1.82378e11	−0.279941
$423$	1.19466e11	0.181431
$424$	−2.64244e11	−0.397062
$425$	3.41833e11	0.508234
$426$	−3.62107e9	−0.00532713
$427$	−1.03236e11	−0.150282
$428$	2.51414e9	0.00362153
$429$	−2.36818e11	−0.337565
$430$	−3.66255e11	−0.516625
$431$	1.04001e12	1.45174	0.725872	−	0.687830i	$-0.241436\pi$
$431$	1.04001e12	1.45174	0.725872	+	0.687830i	$0.241436\pi$
$432$	−1.25631e11	−0.173548
$433$	−6.20670e11	−0.848526	−0.424263	−	0.905539i	$-0.639467\pi$
$433$	−6.20670e11	−0.848526	−0.424263	+	0.905539i	$0.639467\pi$
$434$	1.53953e11	0.208297
$435$	8.72266e11	1.16801
$436$	−1.00891e12	−1.33710
$437$	2.40917e11	0.316010
$438$	3.68104e10	0.0477899
$439$	−1.54852e10	−0.0198987	−0.00994937	−	0.999951i	$-0.503167\pi$
$439$	−1.54852e10	−0.0198987	−0.00994937	+	0.999951i	$0.503167\pi$
$440$	2.58618e11	0.328944
$441$	−1.29662e11	−0.163245
$442$	5.10568e10	0.0636288
$443$	1.29678e12	1.59974	0.799870	−	0.600174i	$-0.204902\pi$
$443$	1.29678e12	1.59974	0.799870	+	0.600174i	$0.204902\pi$
$444$	8.61944e11	1.05258
$445$	−8.81319e11	−1.06540
$446$	1.74542e11	0.208878
$447$	−3.72095e11	−0.440829
$448$	4.91385e11	0.576329
$449$	1.20779e12	1.40244	0.701220	−	0.712945i	$-0.252639\pi$
$449$	1.20779e12	1.40244	0.701220	+	0.712945i	$0.252639\pi$
$450$	−7.62731e10	−0.0876830
$451$	−3.62646e11	−0.412751
$452$	1.01393e12	1.14258
$453$	1.01357e11	0.113086
$454$	−2.84248e11	−0.314012
$455$	−1.01598e12	−1.11130
$456$	7.13626e10	0.0772910
$457$	−4.64846e11	−0.498524	−0.249262	−	0.968436i	$-0.580188\pi$
$457$	−4.64846e11	−0.498524	−0.249262	+	0.968436i	$0.580188\pi$
$458$	1.58373e11	0.168184
$459$	−6.43355e10	−0.0676540
$460$	−1.22669e12	−1.27739
$461$	−6.03462e11	−0.622294	−0.311147	−	0.950362i	$-0.600713\pi$
$461$	−6.03462e11	−0.622294	−0.311147	+	0.950362i	$0.600713\pi$
$462$	4.31879e10	0.0441035
$463$	−1.84771e12	−1.86861	−0.934306	−	0.356473i	$-0.883979\pi$
$463$	−1.84771e12	−1.86861	−0.934306	+	0.356473i	$0.883979\pi$
$464$	1.16476e12	1.16655
$465$	1.45888e12	1.44704
$466$	−2.03064e11	−0.199479
$467$	−1.07799e12	−1.04879	−0.524394	−	0.851475i	$-0.675708\pi$
$467$	−1.07799e12	−1.04879	−0.524394	+	0.851475i	$0.675708\pi$
$468$	3.32732e11	0.320618
$469$	1.79351e11	0.171169
$470$	1.63843e11	0.154877
$471$	4.24475e10	0.0397427
$472$	−5.02391e10	−0.0465911
$473$	1.16168e12	1.06711
$474$	−9.33874e9	−0.00849739
$475$	−6.00026e11	−0.540815
$476$	2.71947e11	0.242802
$477$	−4.18158e11	−0.369835
$478$	−2.76441e11	−0.242201
$479$	−2.02790e12	−1.76010	−0.880050	−	0.474881i	$-0.842491\pi$
$479$	−2.02790e12	−1.76010	−0.880050	+	0.474881i	$0.842491\pi$
$480$	−5.48099e11	−0.471274
$481$	−2.20201e12	−1.87572
$482$	−1.75595e9	−0.00148184
$483$	−4.16716e11	−0.348400
$484$	7.64067e11	0.632888
$485$	−1.56777e12	−1.28661
$486$	1.43552e10	0.0116720
$487$	1.07277e12	0.864226	0.432113	−	0.901820i	$-0.357768\pi$
$487$	1.07277e12	0.864226	0.432113	+	0.901820i	$0.357768\pi$
$488$	9.43248e10	0.0752899
$489$	−1.28465e12	−1.01601
$490$	−1.77826e11	−0.139352
$491$	3.65166e11	0.283546	0.141773	−	0.989899i	$-0.454720\pi$
$491$	3.65166e11	0.283546	0.141773	+	0.989899i	$0.454720\pi$
$492$	5.09521e11	0.392030
$493$	5.96471e11	0.454756
$494$	−8.96210e10	−0.0677078
$495$	4.09256e11	0.306388
$496$	1.94808e12	1.44524
$497$	4.92728e10	0.0362246
$498$	−7.23571e10	−0.0527168
$499$	3.12250e11	0.225450	0.112725	−	0.993626i	$-0.464042\pi$
$499$	3.12250e11	0.225450	0.112725	+	0.993626i	$0.464042\pi$
$500$	9.41945e11	0.674001
$501$	1.78350e11	0.126475
$502$	−1.17247e11	−0.0824018
$503$	−8.92839e11	−0.621895	−0.310948	−	0.950427i	$-0.600646\pi$
$503$	−8.92839e11	−0.621895	−0.310948	+	0.950427i	$0.600646\pi$
$504$	−1.23436e11	−0.0852130
$505$	−2.81092e12	−1.92326
$506$	−1.33215e11	−0.0903392
$507$	8.93214e9	0.00600371
$508$	8.30963e11	0.553598
$509$	3.33406e11	0.220162	0.110081	−	0.993923i	$-0.464889\pi$
$509$	3.33406e11	0.220162	0.110081	+	0.993923i	$0.464889\pi$
$510$	−8.82334e10	−0.0577520
$511$	−5.00889e11	−0.324973
$512$	−1.23370e12	−0.793408
$513$	1.12929e11	0.0719911
$514$	−3.34294e10	−0.0211249
$515$	4.10765e12	2.57313
$516$	−1.63217e12	−1.01354
$517$	−5.19671e11	−0.319905
$518$	4.01575e11	0.245066
$519$	−9.97755e11	−0.603630
$520$	9.28280e11	0.556755
$521$	5.42475e10	0.0322559	0.0161280	−	0.999870i	$-0.494866\pi$
$521$	5.42475e10	0.0322559	0.0161280	+	0.999870i	$0.494866\pi$
$522$	−1.33091e11	−0.0784567
$523$	−1.01037e12	−0.590502	−0.295251	−	0.955420i	$-0.595403\pi$
$523$	−1.01037e12	−0.590502	−0.295251	+	0.955420i	$0.595403\pi$
$524$	−5.16847e11	−0.299482
$525$	1.03787e12	0.596247
$526$	−3.29499e11	−0.187680
$527$	9.97610e11	0.563395
$528$	5.46488e11	0.306005
$529$	−5.15774e11	−0.286358
$530$	−5.73486e11	−0.315705
$531$	−7.95020e10	−0.0433963
$532$	−4.77353e11	−0.258367
$533$	−1.30168e12	−0.698604
$534$	1.34472e11	0.0715642
$535$	1.10997e10	0.00585758
$536$	−1.63870e11	−0.0857545
$537$	−3.22664e11	−0.167443
$538$	2.42643e11	0.124867
$539$	5.64025e11	0.287838
$540$	−5.75008e11	−0.291006
$541$	5.44947e11	0.273506	0.136753	−	0.990605i	$-0.456333\pi$
$541$	5.44947e11	0.273506	0.136753	+	0.990605i	$0.456333\pi$
$542$	1.96504e11	0.0978081
$543$	−9.91567e11	−0.489467
$544$	−3.74800e11	−0.183487
$545$	−4.45425e12	−2.16267
$546$	1.55018e11	0.0746475
$547$	2.16389e12	1.03346	0.516728	−	0.856150i	$-0.327150\pi$
$547$	2.16389e12	1.03346	0.516728	+	0.856150i	$0.327150\pi$
$548$	2.83918e12	1.34487
$549$	1.49266e11	0.0701272
$550$	3.31785e11	0.154605
$551$	−1.04700e12	−0.483909
$552$	3.80745e11	0.174546
$553$	1.27075e11	0.0577825
$554$	−6.26387e11	−0.282520
$555$	3.80539e12	1.70248
$556$	−1.53209e12	−0.679903
$557$	−1.07781e12	−0.474455	−0.237227	−	0.971454i	$-0.576239\pi$
$557$	−1.07781e12	−0.474455	−0.237227	+	0.971454i	$0.576239\pi$
$558$	−2.22597e11	−0.0971996
$559$	4.16971e12	1.80615
$560$	2.34450e12	1.00740
$561$	2.79856e11	0.119290
$562$	−6.03298e11	−0.255105
$563$	2.44892e12	1.02727	0.513637	−	0.858008i	$-0.328298\pi$
$563$	2.44892e12	1.02727	0.513637	+	0.858008i	$0.328298\pi$
$564$	7.30143e11	0.303845
$565$	4.47639e12	1.84804
$566$	3.68242e11	0.150820
$567$	−1.95335e11	−0.0793698
$568$	−4.50197e10	−0.0181483
$569$	1.30612e12	0.522368	0.261184	−	0.965289i	$-0.415887\pi$
$569$	1.30612e12	0.522368	0.261184	+	0.965289i	$0.415887\pi$
$570$	1.54878e11	0.0614543
$571$	−3.54701e12	−1.39637	−0.698185	−	0.715918i	$-0.746009\pi$
$571$	−3.54701e12	−1.39637	−0.698185	+	0.715918i	$0.746009\pi$
$572$	−1.44737e12	−0.565324
$573$	1.41175e12	0.547092
$574$	2.37383e11	0.0912739
$575$	−3.20136e12	−1.22132
$576$	−7.10481e11	−0.268937
$577$	−3.18837e11	−0.119751	−0.0598753	−	0.998206i	$-0.519070\pi$
$577$	−3.18837e11	−0.119751	−0.0598753	+	0.998206i	$0.519070\pi$
$578$	4.27893e11	0.159463
$579$	3.01861e12	1.11623
$580$	5.33105e12	1.95608
$581$	9.84583e11	0.358476
$582$	2.39211e11	0.0864228
$583$	1.81897e12	0.652104
$584$	4.57653e11	0.162809
$585$	1.46898e12	0.518577
$586$	−5.63736e11	−0.197486
$587$	−4.42811e11	−0.153938	−0.0769692	−	0.997033i	$-0.524524\pi$
$587$	−4.42811e11	−0.153938	−0.0769692	+	0.997033i	$0.524524\pi$
$588$	−7.92460e11	−0.273388
$589$	−1.75112e12	−0.599513
$590$	−1.09034e11	−0.0370447
$591$	−1.81259e12	−0.611160
$592$	5.08143e12	1.70035
$593$	−3.09210e12	−1.02685	−0.513426	−	0.858134i	$-0.671624\pi$
$593$	−3.09210e12	−1.02685	−0.513426	+	0.858134i	$0.671624\pi$
$594$	−6.24443e10	−0.0205804
$595$	1.20062e12	0.392715
$596$	−2.27414e12	−0.738261
$597$	3.37812e10	0.0108841
$598$	−4.78160e11	−0.152904
$599$	3.17880e12	1.00889	0.504444	−	0.863445i	$-0.331698\pi$
$599$	3.17880e12	1.00889	0.504444	+	0.863445i	$0.331698\pi$
$600$	−9.48283e11	−0.298715
$601$	1.03443e12	0.323420	0.161710	−	0.986838i	$-0.448299\pi$
$601$	1.03443e12	0.323420	0.161710	+	0.986838i	$0.448299\pi$
$602$	−7.60419e11	−0.235977
$603$	−2.59319e11	−0.0798742
$604$	6.19464e11	0.189387
$605$	3.37328e12	1.02365
$606$	4.28891e11	0.129187
$607$	−1.05095e10	−0.00314220	−0.00157110	−	0.999999i	$-0.500500\pi$
$607$	−1.05095e10	−0.00314220	−0.00157110	+	0.999999i	$0.500500\pi$
$608$	6.57894e11	0.195249
$609$	1.81100e12	0.533508
$610$	2.04713e11	0.0598632
$611$	−1.86530e12	−0.541457
$612$	−3.93201e11	−0.113301
$613$	6.62484e12	1.89498	0.947488	−	0.319792i	$-0.103613\pi$
$613$	6.62484e12	1.89498	0.947488	+	0.319792i	$0.103613\pi$
$614$	6.48931e11	0.184264
$615$	2.24948e12	0.634081
$616$	5.36943e11	0.150250
$617$	6.32056e12	1.75579	0.877895	−	0.478854i	$-0.158948\pi$
$617$	6.32056e12	1.75579	0.877895	+	0.478854i	$0.158948\pi$
$618$	−6.26747e11	−0.172840
$619$	9.68111e10	0.0265044	0.0132522	−	0.999912i	$-0.495782\pi$
$619$	9.68111e10	0.0265044	0.0132522	+	0.999912i	$0.495782\pi$
$620$	8.91630e12	2.42338
$621$	6.02519e11	0.162577
$622$	1.02182e12	0.273728
$623$	−1.82980e12	−0.486639
$624$	1.96156e12	0.517929
$625$	−1.35645e12	−0.355586
$626$	−1.40813e11	−0.0366486
$627$	−4.91237e11	−0.126937
$628$	2.59427e11	0.0665576
$629$	2.60220e12	0.662846
$630$	−2.67893e11	−0.0677531
$631$	1.23445e12	0.309986	0.154993	−	0.987916i	$-0.450464\pi$
$631$	1.23445e12	0.309986	0.154993	+	0.987916i	$0.450464\pi$
$632$	−1.16106e11	−0.0289486
$633$	−3.58818e12	−0.888295
$634$	3.66713e11	0.0901415
$635$	3.66861e12	0.895407
$636$	−2.55567e12	−0.619366
$637$	2.02450e12	0.487182
$638$	5.78938e11	0.138337
$639$	−7.12424e10	−0.0169038
$640$	−4.43892e12	−1.04585
$641$	−6.56416e11	−0.153574	−0.0767870	−	0.997048i	$-0.524466\pi$
$641$	−6.56416e11	−0.153574	−0.0767870	+	0.997048i	$0.524466\pi$
$642$	−1.69359e9	−0.000393460 0
$643$	1.17626e12	0.271366	0.135683	−	0.990752i	$-0.456677\pi$
$643$	1.17626e12	0.271366	0.135683	+	0.990752i	$0.456677\pi$
$644$	−2.54685e12	−0.583469
$645$	−7.20586e12	−1.63933
$646$	1.05908e11	0.0239267
$647$	−4.97075e12	−1.11520	−0.557599	−	0.830110i	$-0.688277\pi$
$647$	−4.97075e12	−1.11520	−0.557599	+	0.830110i	$0.688277\pi$
$648$	1.78474e11	0.0397637
$649$	3.45830e11	0.0765177
$650$	1.19090e12	0.261678
$651$	3.02893e12	0.660960
$652$	−7.85146e12	−1.70152
$653$	−7.55691e12	−1.62643	−0.813214	−	0.581964i	$-0.802284\pi$
$653$	−7.55691e12	−1.62643	−0.813214	+	0.581964i	$0.802284\pi$
$654$	6.79631e11	0.145269
$655$	−2.28183e12	−0.484392
$656$	3.00379e12	0.633289
$657$	7.24223e11	0.151645
$658$	3.40170e11	0.0707424
$659$	1.16657e12	0.240949	0.120475	−	0.992716i	$-0.461558\pi$
$659$	1.16657e12	0.240949	0.120475	+	0.992716i	$0.461558\pi$
$660$	2.50126e12	0.513111
$661$	−4.45159e12	−0.907003	−0.453502	−	0.891255i	$-0.649825\pi$
$661$	−4.45159e12	−0.907003	−0.453502	+	0.891255i	$0.649825\pi$
$662$	−9.15086e11	−0.185183
$663$	1.00451e12	0.201904
$664$	−8.99596e11	−0.179594
$665$	−2.10747e12	−0.417891
$666$	−5.80628e11	−0.114357
$667$	−5.58611e12	−1.09281
$668$	1.09003e12	0.211808
$669$	3.43401e12	0.662803
$670$	−3.55645e11	−0.0681837
$671$	−6.49302e11	−0.123650
$672$	−1.13796e12	−0.215262
$673$	−8.24006e11	−0.154833	−0.0774163	−	0.996999i	$-0.524667\pi$
$673$	−8.24006e11	−0.154833	−0.0774163	+	0.996999i	$0.524667\pi$
$674$	−2.44963e11	−0.0457226
$675$	−1.50063e12	−0.278232
$676$	5.45908e10	0.0100545
$677$	−8.90116e12	−1.62854	−0.814268	−	0.580489i	$-0.802862\pi$
$677$	−8.90116e12	−1.62854	−0.814268	+	0.580489i	$0.802862\pi$
$678$	−6.83009e11	−0.124135
$679$	−3.25502e12	−0.587678
$680$	−1.09698e12	−0.196747
$681$	−5.59242e12	−0.996409
$682$	9.68285e11	0.171385
$683$	1.83731e12	0.323065	0.161533	−	0.986867i	$-0.448356\pi$
$683$	1.83731e12	0.323065	0.161533	+	0.986867i	$0.448356\pi$
$684$	6.90193e11	0.120564
$685$	1.25347e13	2.17523
$686$	−1.12309e12	−0.193622
$687$	3.11589e12	0.533675
$688$	−9.62214e12	−1.63728
$689$	6.52899e12	1.10372
$690$	8.26329e11	0.138782
$691$	−1.19065e12	−0.198670	−0.0993351	−	0.995054i	$-0.531672\pi$
$691$	−1.19065e12	−0.198670	−0.0993351	+	0.995054i	$0.531672\pi$
$692$	−6.09801e12	−1.01091
$693$	8.49697e11	0.139947
$694$	−3.00591e11	−0.0491878
$695$	−6.76401e12	−1.09970
$696$	−1.65468e12	−0.267283
$697$	1.53824e12	0.246874
$698$	−1.12588e12	−0.179532
$699$	−3.99517e12	−0.632977
$700$	6.34318e12	0.998541
$701$	1.69029e12	0.264381	0.132191	−	0.991224i	$-0.457799\pi$
$701$	1.69029e12	0.264381	0.132191	+	0.991224i	$0.457799\pi$
$702$	−2.24137e11	−0.0348334
$703$	−4.56769e12	−0.705338
$704$	3.09056e12	0.474199
$705$	3.22351e12	0.491448
$706$	−1.43160e12	−0.216871
$707$	−5.83604e12	−0.878478
$708$	−4.85895e11	−0.0726763
$709$	8.69883e12	1.29286	0.646432	−	0.762971i	$-0.276260\pi$
$709$	8.69883e12	1.29286	0.646432	+	0.762971i	$0.276260\pi$
$710$	−9.77060e10	−0.0144297
$711$	−1.83734e11	−0.0269635
$712$	1.67185e12	0.243802
$713$	−9.34289e12	−1.35387
$714$	−1.83190e11	−0.0263791
$715$	−6.38998e12	−0.914371
$716$	−1.97204e12	−0.280418
$717$	−5.43881e12	−0.768543
$718$	−4.66337e11	−0.0654847
$719$	−2.71206e12	−0.378460	−0.189230	−	0.981933i	$-0.560599\pi$
$719$	−2.71206e12	−0.378460	−0.189230	+	0.981933i	$0.560599\pi$
$720$	−3.38985e12	−0.470093
$721$	8.52831e12	1.17532
$722$	1.14261e12	0.156488
$723$	−3.45473e10	−0.00470210
$724$	−6.06019e12	−0.819715
$725$	1.39127e13	1.87022
$726$	−5.14695e11	−0.0687599
$727$	1.96997e11	0.0261550	0.0130775	−	0.999914i	$-0.495837\pi$
$727$	1.96997e11	0.0261550	0.0130775	+	0.999914i	$0.495837\pi$
$728$	1.92730e12	0.254306
$729$	2.82430e11	0.0370370
$730$	9.93241e11	0.129450
$731$	−4.92750e12	−0.638261
$732$	9.12276e11	0.117443
$733$	4.11357e12	0.526321	0.263161	−	0.964752i	$-0.415235\pi$
$733$	4.11357e12	0.526321	0.263161	+	0.964752i	$0.415235\pi$
$734$	2.57059e12	0.326889
$735$	−3.49863e12	−0.442186
$736$	3.51010e12	0.440930
$737$	1.12803e12	0.140837
$738$	−3.43227e11	−0.0425920
$739$	−1.45772e13	−1.79794	−0.898968	−	0.438015i	$-0.855682\pi$
$739$	−1.45772e13	−1.79794	−0.898968	+	0.438015i	$0.855682\pi$
$740$	2.32575e13	2.85116
$741$	−1.76324e12	−0.214847
$742$	−1.19067e12	−0.144203
$743$	−1.04103e13	−1.25318	−0.626591	−	0.779349i	$-0.715550\pi$
$743$	−1.04103e13	−1.25318	−0.626591	+	0.779349i	$0.715550\pi$
$744$	−2.76748e12	−0.331136
$745$	−1.00401e13	−1.19408
$746$	1.81587e12	0.214664
$747$	−1.42358e12	−0.167279
$748$	1.71041e12	0.199776
$749$	2.30451e10	0.00267554
$750$	−6.34518e11	−0.0732265
$751$	−9.98578e12	−1.14552	−0.572760	−	0.819723i	$-0.694127\pi$
$751$	−9.98578e12	−1.14552	−0.572760	+	0.819723i	$0.694127\pi$
$752$	4.30442e12	0.490834
$753$	−2.30678e12	−0.261474
$754$	2.07803e12	0.234143
$755$	2.73487e12	0.306320
$756$	−1.19383e12	−0.132922
$757$	−5.63871e12	−0.624091	−0.312046	−	0.950067i	$-0.601014\pi$
$757$	−5.63871e12	−0.624091	−0.312046	+	0.950067i	$0.601014\pi$
$758$	1.80579e12	0.198681
$759$	−2.62093e12	−0.286660
$760$	1.92555e12	0.209360
$761$	−1.70348e13	−1.84122	−0.920611	−	0.390481i	$-0.872309\pi$
$761$	−1.70348e13	−1.84122	−0.920611	+	0.390481i	$0.872309\pi$
$762$	−5.59758e11	−0.0601455
$763$	−9.24793e12	−0.987834
$764$	8.62821e12	0.916222
$765$	−1.73594e12	−0.183256
$766$	−2.49989e12	−0.262357
$767$	1.24132e12	0.129510
$768$	−3.81365e12	−0.395563
$769$	3.87246e12	0.399317	0.199659	−	0.979866i	$-0.436017\pi$
$769$	3.87246e12	0.399317	0.199659	+	0.979866i	$0.436017\pi$
$770$	1.16532e12	0.119464
$771$	−6.57705e11	−0.0670326
$772$	1.84489e13	1.86936
$773$	−4.36357e12	−0.439576	−0.219788	−	0.975548i	$-0.570537\pi$
$773$	−4.36357e12	−0.439576	−0.219788	+	0.975548i	$0.570537\pi$
$774$	1.09947e12	0.110116
$775$	2.32693e13	2.31700
$776$	2.97405e12	0.294422
$777$	7.90076e12	0.777633
$778$	3.61214e11	0.0353473
$779$	−2.70010e12	−0.262701
$780$	8.97799e12	0.868467
$781$	3.09901e11	0.0298053
$782$	5.65059e11	0.0540336
$783$	−2.61848e12	−0.248955
$784$	−4.67180e12	−0.441633
$785$	1.14535e12	0.107652
$786$	3.48161e11	0.0325371
$787$	1.26301e13	1.17360	0.586800	−	0.809732i	$-0.300388\pi$
$787$	1.26301e13	1.17360	0.586800	+	0.809732i	$0.300388\pi$
$788$	−1.10780e13	−1.02352
$789$	−6.48271e12	−0.595539
$790$	−2.51984e11	−0.0230171
$791$	9.29390e12	0.844119
$792$	−7.76353e11	−0.0701125
$793$	−2.33060e12	−0.209285
$794$	3.80227e12	0.339509
$795$	−1.12830e13	−1.00178
$796$	2.06462e11	0.0182276
$797$	1.04796e13	0.919988	0.459994	−	0.887922i	$-0.347852\pi$
$797$	1.04796e13	0.919988	0.459994	+	0.887922i	$0.347852\pi$
$798$	3.21558e11	0.0280702
$799$	2.20429e12	0.191341
$800$	−8.74224e12	−0.754602
$801$	2.64566e12	0.227084
$802$	2.59251e12	0.221277
$803$	−3.15034e12	−0.267385
$804$	−1.58489e12	−0.133766
$805$	−1.12441e13	−0.943720
$806$	3.47555e12	0.290079
$807$	4.77386e12	0.396222
$808$	5.33228e12	0.440111
$809$	−5.80061e12	−0.476108	−0.238054	−	0.971252i	$-0.576509\pi$
$809$	−5.80061e12	−0.476108	−0.238054	+	0.971252i	$0.576509\pi$
$810$	3.87340e11	0.0316162
$811$	−3.93373e11	−0.0319309	−0.0159654	−	0.999873i	$-0.505082\pi$
$811$	−3.93373e11	−0.0319309	−0.0159654	+	0.999873i	$0.505082\pi$
$812$	1.10683e13	0.893471
$813$	3.86610e12	0.310360
$814$	2.52571e12	0.201638
$815$	−3.46634e13	−2.75209
$816$	−2.31804e12	−0.183027
$817$	8.64933e12	0.679178
$818$	1.05309e12	0.0822387
$819$	3.04989e12	0.236868
$820$	1.37482e13	1.06190
$821$	2.02203e13	1.55326	0.776629	−	0.629958i	$-0.216928\pi$
$821$	2.02203e13	1.55326	0.776629	+	0.629958i	$0.216928\pi$
$822$	−1.91255e12	−0.146113
$823$	1.11306e13	0.845704	0.422852	−	0.906199i	$-0.361029\pi$
$823$	1.11306e13	0.845704	0.422852	+	0.906199i	$0.361029\pi$
$824$	−7.79216e12	−0.588824
$825$	6.52768e12	0.490587
$826$	−2.26376e11	−0.0169208
$827$	−5.16551e12	−0.384007	−0.192003	−	0.981394i	$-0.561498\pi$
$827$	−5.16551e12	−0.384007	−0.192003	+	0.981394i	$0.561498\pi$
$828$	3.68243e12	0.272269
$829$	−2.28015e13	−1.67675	−0.838373	−	0.545097i	$-0.816493\pi$
$829$	−2.28015e13	−1.67675	−0.838373	+	0.545097i	$0.816493\pi$
$830$	−1.95239e12	−0.142795
$831$	−1.23238e13	−0.896479
$832$	1.10932e13	0.802607
$833$	−2.39243e12	−0.172162
$834$	1.03205e12	0.0738678
$835$	4.81236e12	0.342585
$836$	−3.00231e12	−0.212582
$837$	−4.37946e12	−0.308430
$838$	−1.23760e12	−0.0866926
$839$	−2.67338e13	−1.86265	−0.931326	−	0.364187i	$-0.881347\pi$
$839$	−2.67338e13	−1.86265	−0.931326	+	0.364187i	$0.881347\pi$
$840$	−3.33064e12	−0.230819
$841$	9.76948e12	0.673425
$842$	2.20115e12	0.150920
$843$	−1.18695e13	−0.809486
$844$	−2.19300e13	−1.48764
$845$	2.41013e11	0.0162624
$846$	−4.91844e11	−0.0330111
$847$	7.00360e12	0.467569
$848$	−1.50665e13	−1.00053
$849$	7.24495e12	0.478576
$850$	−1.40733e12	−0.0924724
$851$	−2.43703e13	−1.59286
$852$	−4.35414e11	−0.0283090
$853$	−4.21472e11	−0.0272583	−0.0136291	−	0.999907i	$-0.504338\pi$
$853$	−4.21472e11	−0.0272583	−0.0136291	+	0.999907i	$0.504338\pi$
$854$	4.25025e11	0.0273435
$855$	3.04713e12	0.195004
$856$	−2.10559e10	−0.00134042
$857$	1.66883e13	1.05682	0.528408	−	0.848991i	$-0.322789\pi$
$857$	1.66883e13	1.05682	0.528408	+	0.848991i	$0.322789\pi$
$858$	9.74985e11	0.0614194
$859$	−6.34553e12	−0.397648	−0.198824	−	0.980035i	$-0.563712\pi$
$859$	−6.34553e12	−0.397648	−0.198824	+	0.980035i	$0.563712\pi$
$860$	−4.40403e13	−2.74541
$861$	4.67038e12	0.289626
$862$	−4.28175e12	−0.264142
$863$	−1.35407e13	−0.830982	−0.415491	−	0.909597i	$-0.636390\pi$
$863$	−1.35407e13	−0.830982	−0.415491	+	0.909597i	$0.636390\pi$
$864$	1.64535e12	0.100449
$865$	−2.69221e13	−1.63507
$866$	2.55531e12	0.154388
$867$	8.41855e12	0.506001
$868$	1.85120e13	1.10692
$869$	7.99236e11	0.0475429
$870$	−3.59114e12	−0.212518
$871$	4.04893e12	0.238374
$872$	8.44966e12	0.494897
$873$	4.70635e12	0.274233
$874$	−9.91859e11	−0.0574975
$875$	8.63407e12	0.497943
$876$	4.42625e12	0.253961
$877$	−1.99340e13	−1.13788	−0.568940	−	0.822379i	$-0.692646\pi$
$877$	−1.99340e13	−1.13788	−0.568940	+	0.822379i	$0.692646\pi$
$878$	6.37528e10	0.00362054
$879$	−1.10912e13	−0.626654
$880$	1.47457e13	0.828883
$881$	−1.87654e13	−1.04946	−0.524731	−	0.851268i	$-0.675834\pi$
$881$	−1.87654e13	−1.04946	−0.524731	+	0.851268i	$0.675834\pi$
$882$	5.33822e11	0.0297021
$883$	2.61652e13	1.44844	0.724222	−	0.689567i	$-0.242199\pi$
$883$	2.61652e13	1.44844	0.724222	+	0.689567i	$0.242199\pi$
$884$	6.13931e12	0.338131
$885$	−2.14518e12	−0.117549
$886$	−5.33886e12	−0.291070
$887$	−2.15861e13	−1.17089	−0.585446	−	0.810711i	$-0.699081\pi$
$887$	−2.15861e13	−1.17089	−0.585446	+	0.810711i	$0.699081\pi$
$888$	−7.21878e12	−0.389588
$889$	7.61678e12	0.408991
$890$	3.62841e12	0.193848
$891$	−1.22856e12	−0.0653048
$892$	2.09878e13	1.11000
$893$	−3.86924e12	−0.203608
$894$	1.53192e12	0.0802080
$895$	−8.70634e12	−0.453557
$896$	−9.21610e12	−0.477706
$897$	−9.40753e12	−0.485188
$898$	−4.97251e12	−0.255172
$899$	4.06031e13	2.07320
$900$	−9.17145e12	−0.465958
$901$	−7.71553e12	−0.390036
$902$	1.49302e12	0.0750994
$903$	−1.49608e13	−0.748791
$904$	−8.49166e12	−0.422897
$905$	−2.67551e13	−1.32583
$906$	−4.17287e11	−0.0205758
$907$	3.13055e13	1.53599	0.767993	−	0.640458i	$-0.221255\pi$
$907$	3.13055e13	1.53599	0.767993	+	0.640458i	$0.221255\pi$
$908$	−3.41794e13	−1.66870
$909$	8.43818e12	0.409932
$910$	4.18280e12	0.202200
$911$	−2.87721e12	−0.138401	−0.0692003	−	0.997603i	$-0.522045\pi$
$911$	−2.87721e12	−0.138401	−0.0692003	+	0.997603i	$0.522045\pi$
$912$	4.06890e12	0.194760
$913$	6.19253e12	0.294951
$914$	1.91378e12	0.0907056
$915$	4.02760e12	0.189955
$916$	1.90435e13	0.893751
$917$	−4.73753e12	−0.221253
$918$	2.64870e11	0.0123095
$919$	2.26769e12	0.104873	0.0524365	−	0.998624i	$-0.483301\pi$
$919$	2.26769e12	0.104873	0.0524365	+	0.998624i	$0.483301\pi$
$920$	1.02735e13	0.472796
$921$	1.27673e13	0.584699
$922$	2.48446e12	0.113225
$923$	1.11236e12	0.0504471
$924$	5.19312e12	0.234371
$925$	6.06965e13	2.72600
$926$	7.60705e12	0.339991
$927$	−1.23309e13	−0.548448
$928$	−1.52545e13	−0.675200
$929$	2.30174e13	1.01388	0.506939	−	0.861982i	$-0.330777\pi$
$929$	2.30174e13	1.01388	0.506939	+	0.861982i	$0.330777\pi$
$930$	−6.00625e12	−0.263287
$931$	4.19947e12	0.183198
$932$	−2.44174e13	−1.06005
$933$	2.01038e13	0.868582
$934$	4.43810e12	0.190825
$935$	7.55127e12	0.323123
$936$	−2.78663e12	−0.118669
$937$	4.32512e13	1.83303	0.916515	−	0.399999i	$-0.130990\pi$
$937$	4.32512e13	1.83303	0.916515	+	0.399999i	$0.130990\pi$
$938$	−7.38392e11	−0.0311440
$939$	−2.77041e12	−0.116292
$940$	1.97012e13	0.823033
$941$	−3.10490e12	−0.129091	−0.0645453	−	0.997915i	$-0.520560\pi$
$941$	−3.10490e12	−0.129091	−0.0645453	+	0.997915i	$0.520560\pi$
$942$	−1.74757e11	−0.00723112
$943$	−1.44060e13	−0.593255
$944$	−2.86450e12	−0.117402
$945$	−5.27065e12	−0.214991
$946$	−4.78265e12	−0.194160
$947$	3.07748e13	1.24343	0.621713	−	0.783245i	$-0.286437\pi$
$947$	3.07748e13	1.24343	0.621713	+	0.783245i	$0.286437\pi$
$948$	−1.12293e12	−0.0451561
$949$	−1.13078e13	−0.452563
$950$	2.47032e12	0.0984004
$951$	7.21487e12	0.286033
$952$	−2.27755e12	−0.0898675
$953$	3.98634e13	1.56551	0.782756	−	0.622328i	$-0.213813\pi$
$953$	3.98634e13	1.56551	0.782756	+	0.622328i	$0.213813\pi$
$954$	1.72157e12	0.0672908
$955$	3.80926e13	1.48192
$956$	−3.32406e13	−1.28709
$957$	1.13903e13	0.438965
$958$	8.34892e12	0.320247
$959$	2.60245e13	0.993572
$960$	−1.91707e13	−0.728478
$961$	4.14700e13	1.56848
$962$	9.06573e12	0.341283
$963$	−3.33204e10	−0.00124851
$964$	−2.11144e11	−0.00787466
$965$	8.14500e13	3.02356
$966$	1.71563e12	0.0633907
$967$	1.25763e13	0.462522	0.231261	−	0.972892i	$-0.425715\pi$
$967$	1.25763e13	0.462522	0.231261	+	0.972892i	$0.425715\pi$
$968$	−6.39906e12	−0.234249
$969$	2.08369e12	0.0759233
$970$	6.45456e12	0.234096
$971$	−2.35665e13	−0.850763	−0.425381	−	0.905014i	$-0.639860\pi$
$971$	−2.35665e13	−0.850763	−0.425381	+	0.905014i	$0.639860\pi$
$972$	1.72613e12	0.0620263
$973$	−1.40434e13	−0.502303
$974$	−4.41662e12	−0.157244
$975$	2.34304e13	0.830344
$976$	5.37815e12	0.189718
$977$	3.13588e13	1.10112	0.550559	−	0.834796i	$-0.314415\pi$
$977$	3.13588e13	1.10112	0.550559	+	0.834796i	$0.314415\pi$
$978$	5.28895e12	0.184861
$979$	−1.15085e13	−0.400402
$980$	−2.13827e13	−0.740534
$981$	1.33713e13	0.460961
$982$	−1.50340e12	−0.0515908
$983$	7.07864e12	0.241802	0.120901	−	0.992665i	$-0.461422\pi$
$983$	7.07864e12	0.241802	0.120901	+	0.992665i	$0.461422\pi$
$984$	−4.26724e12	−0.145101
$985$	−4.89084e13	−1.65547
$986$	−2.45568e12	−0.0827421
$987$	6.69265e12	0.224477
$988$	−1.07765e13	−0.359807
$989$	4.61473e13	1.53378
$990$	−1.68491e12	−0.0557467
$991$	−1.23331e13	−0.406201	−0.203100	−	0.979158i	$-0.565102\pi$
$991$	−1.23331e13	−0.406201	−0.203100	+	0.979158i	$0.565102\pi$
$992$	−2.55135e13	−0.836503
$993$	−1.80038e13	−0.587614
$994$	−2.02857e11	−0.00659101
$995$	9.11507e11	0.0294819
$996$	−8.70056e12	−0.280143
$997$	8.76998e12	0.281106	0.140553	−	0.990073i	$-0.455112\pi$
$997$	8.76998e12	0.281106	0.140553	+	0.990073i	$0.455112\pi$
$998$	−1.28554e12	−0.0410202
$999$	−1.14235e13	−0.362873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.10	✓	21	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-4.11702 q^{2} -81.0000 q^{3} -495.050 q^{4} -2185.60 q^{5} +333.479 q^{6} -4537.74 q^{7} +4146.05 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-4.11702 q^{2} -81.0000 q^{3} -495.050 q^{4} -2185.60 q^{5} +333.479 q^{6} -4537.74 q^{7} +4146.05 q^{8} +6561.00 q^{9} +8998.14 q^{10} -28540.1 q^{11} +40099.1 q^{12} -102441. q^{13} +18681.9 q^{14} +177033. q^{15} +236396. q^{16} +121059. q^{17} -27011.8 q^{18} -212496. q^{19} +1.08198e6 q^{20} +367557. q^{21} +117500. q^{22} -1.13375e6 q^{23} -335830. q^{24} +2.82370e6 q^{25} +421753. q^{26} -531441. q^{27} +2.24641e6 q^{28} +4.92713e6 q^{29} -728849. q^{30} +8.24073e6 q^{31} -3.09602e6 q^{32} +2.31174e6 q^{33} -498400. q^{34} +9.91765e6 q^{35} -3.24802e6 q^{36} +2.14954e7 q^{37} +874852. q^{38} +8.29775e6 q^{39} -9.06158e6 q^{40} +1.27066e7 q^{41} -1.51324e6 q^{42} -4.07034e7 q^{43} +1.41288e7 q^{44} -1.43397e7 q^{45} +4.66765e6 q^{46} +1.82085e7 q^{47} -1.91481e7 q^{48} -1.97626e7 q^{49} -1.16252e7 q^{50} -9.80574e6 q^{51} +5.07136e7 q^{52} -6.37339e7 q^{53} +2.18795e6 q^{54} +6.23770e7 q^{55} -1.88137e7 q^{56} +1.72122e7 q^{57} -2.02851e7 q^{58} -1.21174e7 q^{59} -8.76403e7 q^{60} +2.27505e7 q^{61} -3.39272e7 q^{62} -2.97721e7 q^{63} -1.08289e8 q^{64} +2.23895e8 q^{65} -9.51750e6 q^{66} -3.95243e7 q^{67} -5.99301e7 q^{68} +9.18334e7 q^{69} -4.08312e7 q^{70} -1.08585e7 q^{71} +2.72022e7 q^{72} +1.10383e8 q^{73} -8.84968e7 q^{74} -2.28720e8 q^{75} +1.05196e8 q^{76} +1.29507e8 q^{77} -3.41620e7 q^{78} -2.80040e7 q^{79} -5.16667e8 q^{80} +4.30467e7 q^{81} -5.23132e7 q^{82} -2.16977e8 q^{83} -1.81959e8 q^{84} -2.64585e8 q^{85} +1.67577e8 q^{86} -3.99098e8 q^{87} -1.18328e8 q^{88} +4.03240e8 q^{89} +5.90368e7 q^{90} +4.64852e8 q^{91} +5.61261e8 q^{92} -6.67499e8 q^{93} -7.49647e7 q^{94} +4.64431e8 q^{95} +2.50778e8 q^{96} +7.17322e8 q^{97} +8.13629e7 q^{98} -1.87251e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

Introduction

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