LMFDB - Embedded newform 177.10.a.b.1.8

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			1.8
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)

$f(q)$	$=$	$q-12.5454 q^{2} -81.0000 q^{3} -354.612 q^{4} +2378.79 q^{5} +1016.18 q^{6} +4679.29 q^{7} +10872.0 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-12.5454 q^{2} -81.0000 q^{3} -354.612 q^{4} +2378.79 q^{5} +1016.18 q^{6} +4679.29 q^{7} +10872.0 q^{8} +6561.00 q^{9} -29843.0 q^{10} +27377.3 q^{11} +28723.6 q^{12} -94968.3 q^{13} -58703.7 q^{14} -192682. q^{15} +45167.3 q^{16} -363572. q^{17} -82310.6 q^{18} -703094. q^{19} -843549. q^{20} -379022. q^{21} -343460. q^{22} +1.27907e6 q^{23} -880634. q^{24} +3.70553e6 q^{25} +1.19142e6 q^{26} -531441. q^{27} -1.65933e6 q^{28} -6.03733e6 q^{29} +2.41728e6 q^{30} -2.91796e6 q^{31} -6.13312e6 q^{32} -2.21756e6 q^{33} +4.56116e6 q^{34} +1.11311e7 q^{35} -2.32661e6 q^{36} +8.60765e6 q^{37} +8.82061e6 q^{38} +7.69243e6 q^{39} +2.58623e7 q^{40} -1.66287e7 q^{41} +4.75500e6 q^{42} +3.19196e7 q^{43} -9.70831e6 q^{44} +1.56073e7 q^{45} -1.60465e7 q^{46} +4.06112e7 q^{47} -3.65855e6 q^{48} -1.84579e7 q^{49} -4.64875e7 q^{50} +2.94493e7 q^{51} +3.36769e7 q^{52} -6.97055e7 q^{53} +6.66716e6 q^{54} +6.51248e7 q^{55} +5.08733e7 q^{56} +5.69506e7 q^{57} +7.57409e7 q^{58} -1.21174e7 q^{59} +6.83275e7 q^{60} -6.34803e7 q^{61} +3.66070e7 q^{62} +3.07008e7 q^{63} +5.38170e7 q^{64} -2.25910e8 q^{65} +2.78202e7 q^{66} -1.72165e8 q^{67} +1.28927e8 q^{68} -1.03605e8 q^{69} -1.39644e8 q^{70} -1.91685e8 q^{71} +7.13313e7 q^{72} +1.49098e8 q^{73} -1.07987e8 q^{74} -3.00148e8 q^{75} +2.49326e8 q^{76} +1.28106e8 q^{77} -9.65048e7 q^{78} -7.22461e7 q^{79} +1.07444e8 q^{80} +4.30467e7 q^{81} +2.08614e8 q^{82} -1.57839e8 q^{83} +1.34406e8 q^{84} -8.64861e8 q^{85} -4.00445e8 q^{86} +4.89024e8 q^{87} +2.97646e8 q^{88} +5.53997e8 q^{89} -1.95800e8 q^{90} -4.44384e8 q^{91} -4.53574e8 q^{92} +2.36355e8 q^{93} -5.09485e8 q^{94} -1.67251e9 q^{95} +4.96783e8 q^{96} +6.86877e8 q^{97} +2.31562e8 q^{98} +1.79622e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−12.5454	−0.554435	−0.277217	−	0.960807i	$-0.589412\pi$
$2$	−12.5454	−0.554435	−0.277217	+	0.960807i	$0.589412\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−354.612	−0.692602
$5$	2378.79	1.70213	0.851063	−	0.525064i	$-0.175959\pi$
$5$	2378.79	1.70213	0.851063	+	0.525064i	$0.175959\pi$
$6$	1016.18	0.320103
$7$	4679.29	0.736612	0.368306	−	0.929705i	$-0.379938\pi$
$7$	4679.29	0.736612	0.368306	+	0.929705i	$0.379938\pi$
$8$	10872.0	0.938438
$9$	6561.00	0.333333
$10$	−29843.0	−0.943718
$11$	27377.3	0.563797	0.281899	−	0.959444i	$-0.409036\pi$
$11$	27377.3	0.563797	0.281899	+	0.959444i	$0.409036\pi$
$12$	28723.6	0.399874
$13$	−94968.3	−0.922218	−0.461109	−	0.887344i	$-0.652548\pi$
$13$	−94968.3	−0.922218	−0.461109	+	0.887344i	$0.652548\pi$
$14$	−58703.7	−0.408403
$15$	−192682.	−0.982723
$16$	45167.3	0.172299
$17$	−363572.	−1.05577	−0.527886	−	0.849315i	$-0.677015\pi$
$17$	−363572.	−1.05577	−0.527886	+	0.849315i	$0.677015\pi$
$18$	−82310.6	−0.184812
$19$	−703094.	−1.23772	−0.618859	−	0.785502i	$-0.712405\pi$
$19$	−703094.	−1.23772	−0.618859	+	0.785502i	$0.712405\pi$
$20$	−843549.	−1.17890
$21$	−379022.	−0.425283
$22$	−343460.	−0.312589
$23$	1.27907e6	0.953057	0.476529	−	0.879159i	$-0.341895\pi$
$23$	1.27907e6	0.953057	0.476529	+	0.879159i	$0.341895\pi$
$24$	−880634.	−0.541807
$25$	3.70553e6	1.89723
$26$	1.19142e6	0.511310
$27$	−531441.	−0.192450
$28$	−1.65933e6	−0.510179
$29$	−6.03733e6	−1.58509	−0.792545	−	0.609813i	$-0.791245\pi$
$29$	−6.03733e6	−1.58509	−0.792545	+	0.609813i	$0.791245\pi$
$30$	2.41728e6	0.544856
$31$	−2.91796e6	−0.567481	−0.283740	−	0.958901i	$-0.591575\pi$
$31$	−2.91796e6	−0.567481	−0.283740	+	0.958901i	$0.591575\pi$
$32$	−6.13312e6	−1.03397
$33$	−2.21756e6	−0.325508
$34$	4.56116e6	0.585356
$35$	1.11311e7	1.25381
$36$	−2.32661e6	−0.230867
$37$	8.60765e6	0.755052	0.377526	−	0.925999i	$-0.376775\pi$
$37$	8.60765e6	0.755052	0.377526	+	0.925999i	$0.376775\pi$
$38$	8.82061e6	0.686234
$39$	7.69243e6	0.532443
$40$	2.58623e7	1.59734
$41$	−1.66287e7	−0.919033	−0.459516	−	0.888169i	$-0.651977\pi$
$41$	−1.66287e7	−0.919033	−0.459516	+	0.888169i	$0.651977\pi$
$42$	4.75500e6	0.235792
$43$	3.19196e7	1.42380	0.711900	−	0.702281i	$-0.247835\pi$
$43$	3.19196e7	1.42380	0.711900	+	0.702281i	$0.247835\pi$
$44$	−9.70831e6	−0.390487
$45$	1.56073e7	0.567375
$46$	−1.60465e7	−0.528408
$47$	4.06112e7	1.21396	0.606982	−	0.794716i	$-0.292380\pi$
$47$	4.06112e7	1.21396	0.606982	+	0.794716i	$0.292380\pi$
$48$	−3.65855e6	−0.0994771
$49$	−1.84579e7	−0.457403
$50$	−4.64875e7	−1.05189
$51$	2.94493e7	0.609550
$52$	3.36769e7	0.638730
$53$	−6.97055e7	−1.21346	−0.606731	−	0.794907i	$-0.707519\pi$
$53$	−6.97055e7	−1.21346	−0.606731	+	0.794907i	$0.707519\pi$
$54$	6.66716e6	0.106701
$55$	6.51248e7	0.959654
$56$	5.08733e7	0.691264
$57$	5.69506e7	0.714597
$58$	7.57409e7	0.878830
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	6.83275e7	0.680636
$61$	−6.34803e7	−0.587022	−0.293511	−	0.955956i	$-0.594824\pi$
$61$	−6.34803e7	−0.587022	−0.293511	+	0.955956i	$0.594824\pi$
$62$	3.66070e7	0.314631
$63$	3.07008e7	0.245537
$64$	5.38170e7	0.400968
$65$	−2.25910e8	−1.56973
$66$	2.78202e7	0.180473
$67$	−1.72165e8	−1.04378	−0.521888	−	0.853014i	$-0.674772\pi$
$67$	−1.72165e8	−1.04378	−0.521888	+	0.853014i	$0.674772\pi$
$68$	1.28927e8	0.731229
$69$	−1.03605e8	−0.550248
$70$	−1.39644e8	−0.695153
$71$	−1.91685e8	−0.895212	−0.447606	−	0.894231i	$-0.647723\pi$
$71$	−1.91685e8	−0.895212	−0.447606	+	0.894231i	$0.647723\pi$
$72$	7.13313e7	0.312813
$73$	1.49098e8	0.614494	0.307247	−	0.951630i	$-0.400592\pi$
$73$	1.49098e8	0.614494	0.307247	+	0.951630i	$0.400592\pi$
$74$	−1.07987e8	−0.418627
$75$	−3.00148e8	−1.09537
$76$	2.49326e8	0.857246
$77$	1.28106e8	0.415300
$78$	−9.65048e7	−0.295205
$79$	−7.22461e7	−0.208685	−0.104343	−	0.994541i	$-0.533274\pi$
$79$	−7.22461e7	−0.208685	−0.104343	+	0.994541i	$0.533274\pi$
$80$	1.07444e8	0.293275
$81$	4.30467e7	0.111111
$82$	2.08614e8	0.509544
$83$	−1.57839e8	−0.365059	−0.182530	−	0.983200i	$-0.558429\pi$
$83$	−1.57839e8	−0.365059	−0.182530	+	0.983200i	$0.558429\pi$
$84$	1.34406e8	0.294552
$85$	−8.64861e8	−1.79706
$86$	−4.00445e8	−0.789405
$87$	4.89024e8	0.915152
$88$	2.97646e8	0.529089
$89$	5.53997e8	0.935949	0.467975	−	0.883742i	$-0.344984\pi$
$89$	5.53997e8	0.935949	0.467975	+	0.883742i	$0.344984\pi$
$90$	−1.95800e8	−0.314573
$91$	−4.44384e8	−0.679316
$92$	−4.53574e8	−0.660089
$93$	2.36355e8	0.327635
$94$	−5.09485e8	−0.673064
$95$	−1.67251e9	−2.10675
$96$	4.96783e8	0.596961
$97$	6.86877e8	0.787783	0.393891	−	0.919157i	$-0.371129\pi$
$97$	6.86877e8	0.787783	0.393891	+	0.919157i	$0.371129\pi$
$98$	2.31562e8	0.253600
$99$	1.79622e8	0.187932
$100$	−1.31403e9	−1.31403
$101$	−1.08954e9	−1.04183	−0.520917	−	0.853608i	$-0.674410\pi$
$101$	−1.08954e9	−1.04183	−0.520917	+	0.853608i	$0.674410\pi$
$102$	−3.69454e8	−0.337956
$103$	4.39108e8	0.384419	0.192209	−	0.981354i	$-0.438435\pi$
$103$	4.39108e8	0.384419	0.192209	+	0.981354i	$0.438435\pi$
$104$	−1.03250e9	−0.865444
$105$	−9.01615e8	−0.723885
$106$	8.74486e8	0.672785
$107$	−5.80854e8	−0.428391	−0.214195	−	0.976791i	$-0.568713\pi$
$107$	−5.80854e8	−0.428391	−0.214195	+	0.976791i	$0.568713\pi$
$108$	1.88455e8	0.133291
$109$	2.45513e9	1.66592	0.832960	−	0.553333i	$-0.186644\pi$
$109$	2.45513e9	1.66592	0.832960	+	0.553333i	$0.186644\pi$
$110$	−8.17019e8	−0.532065
$111$	−6.97220e8	−0.435930
$112$	2.11351e8	0.126918
$113$	−1.05448e9	−0.608396	−0.304198	−	0.952609i	$-0.598388\pi$
$113$	−1.05448e9	−0.608396	−0.304198	+	0.952609i	$0.598388\pi$
$114$	−7.14470e8	−0.396198
$115$	3.04264e9	1.62222
$116$	2.14091e9	1.09784
$117$	−6.23087e8	−0.307406
$118$	1.52017e8	0.0721813
$119$	−1.70126e9	−0.777693
$120$	−2.09485e9	−0.922224
$121$	−1.60843e9	−0.682133
$122$	7.96387e8	0.325466
$123$	1.34692e9	0.530604
$124$	1.03474e9	0.393038
$125$	4.16861e9	1.52720
$126$	−3.85155e8	−0.136134
$127$	−3.43386e9	−1.17129	−0.585646	−	0.810567i	$-0.699159\pi$
$127$	−3.43386e9	−1.17129	−0.585646	+	0.810567i	$0.699159\pi$
$128$	2.46500e9	0.811656
$129$	−2.58549e9	−0.822031
$130$	2.83414e9	0.870313
$131$	−2.83733e9	−0.841760	−0.420880	−	0.907116i	$-0.638279\pi$
$131$	−2.83733e9	−0.841760	−0.420880	+	0.907116i	$0.638279\pi$
$132$	7.86373e8	0.225448
$133$	−3.28998e9	−0.911718
$134$	2.15988e9	0.578706
$135$	−1.26419e9	−0.327574
$136$	−3.95276e9	−0.990775
$137$	−2.92430e9	−0.709217	−0.354608	−	0.935015i	$-0.615386\pi$
$137$	−2.92430e9	−0.709217	−0.354608	+	0.935015i	$0.615386\pi$
$138$	1.29976e9	0.305077
$139$	2.71055e9	0.615873	0.307937	−	0.951407i	$-0.400362\pi$
$139$	2.71055e9	0.615873	0.307937	+	0.951407i	$0.400362\pi$
$140$	−3.94721e9	−0.868388
$141$	−3.28951e9	−0.700882
$142$	2.40477e9	0.496337
$143$	−2.59997e9	−0.519944
$144$	2.96342e8	0.0574331
$145$	−1.43616e10	−2.69802
$146$	−1.87049e9	−0.340697
$147$	1.49509e9	0.264082
$148$	−3.05238e9	−0.522951
$149$	−1.64768e9	−0.273864	−0.136932	−	0.990580i	$-0.543724\pi$
$149$	−1.64768e9	−0.273864	−0.136932	+	0.990580i	$0.543724\pi$
$150$	3.76548e9	0.607310
$151$	−8.11578e9	−1.27038	−0.635191	−	0.772355i	$-0.719078\pi$
$151$	−8.11578e9	−1.27038	−0.635191	+	0.772355i	$0.719078\pi$
$152$	−7.64405e9	−1.16152
$153$	−2.38539e9	−0.351924
$154$	−1.60715e9	−0.230257
$155$	−6.94121e9	−0.965924
$156$	−2.72783e9	−0.368771
$157$	1.60158e9	0.210378	0.105189	−	0.994452i	$-0.466455\pi$
$157$	1.60158e9	0.210378	0.105189	+	0.994452i	$0.466455\pi$
$158$	9.06358e8	0.115703
$159$	5.64615e9	0.700592
$160$	−1.45894e10	−1.75994
$161$	5.98513e9	0.702033
$162$	−5.40040e8	−0.0616039
$163$	−6.76642e9	−0.750783	−0.375392	−	0.926866i	$-0.622492\pi$
$163$	−6.76642e9	−0.750783	−0.375392	+	0.926866i	$0.622492\pi$
$164$	5.89674e9	0.636524
$165$	−5.27511e9	−0.554056
$166$	1.98016e9	0.202401
$167$	−4.09332e9	−0.407241	−0.203621	−	0.979050i	$-0.565271\pi$
$167$	−4.09332e9	−0.407241	−0.203621	+	0.979050i	$0.565271\pi$
$168$	−4.12074e9	−0.399101
$169$	−1.58553e9	−0.149515
$170$	1.08501e10	0.996350
$171$	−4.61300e9	−0.412573
$172$	−1.13191e10	−0.986127
$173$	1.52173e10	1.29160	0.645802	−	0.763505i	$-0.276523\pi$
$173$	1.52173e10	1.29160	0.645802	+	0.763505i	$0.276523\pi$
$174$	−6.13501e9	−0.507392
$175$	1.73392e10	1.39752
$176$	1.23656e9	0.0971419
$177$	9.81506e8	0.0751646
$178$	−6.95013e9	−0.518923
$179$	2.22183e10	1.61761	0.808804	−	0.588079i	$-0.200116\pi$
$179$	2.22183e10	1.61761	0.808804	+	0.588079i	$0.200116\pi$
$180$	−5.53452e9	−0.392965
$181$	−2.47904e10	−1.71684	−0.858420	−	0.512947i	$-0.828554\pi$
$181$	−2.47904e10	−1.71684	−0.858420	+	0.512947i	$0.828554\pi$
$182$	5.57499e9	0.376637
$183$	5.14190e9	0.338917
$184$	1.39061e10	0.894385
$185$	2.04758e10	1.28519
$186$	−2.96517e9	−0.181652
$187$	−9.95360e9	−0.595241
$188$	−1.44012e10	−0.840794
$189$	−2.48677e9	−0.141761
$190$	2.09824e10	1.16806
$191$	−1.94115e10	−1.05538	−0.527691	−	0.849436i	$-0.676942\pi$
$191$	−1.94115e10	−1.05538	−0.527691	+	0.849436i	$0.676942\pi$
$192$	−4.35917e9	−0.231499
$193$	−1.35292e10	−0.701884	−0.350942	−	0.936397i	$-0.614139\pi$
$193$	−1.35292e10	−0.701884	−0.350942	+	0.936397i	$0.614139\pi$
$194$	−8.61717e9	−0.436774
$195$	1.82987e10	0.906284
$196$	6.54539e9	0.316798
$197$	2.17864e10	1.03059	0.515297	−	0.857012i	$-0.327682\pi$
$197$	2.17864e10	1.03059	0.515297	+	0.857012i	$0.327682\pi$
$198$	−2.25344e9	−0.104196
$199$	1.59326e10	0.720190	0.360095	−	0.932916i	$-0.382744\pi$
$199$	1.59326e10	0.720190	0.360095	+	0.932916i	$0.382744\pi$
$200$	4.02866e10	1.78043
$201$	1.39453e10	0.602625
$202$	1.36688e10	0.577629
$203$	−2.82504e10	−1.16760
$204$	−1.04431e10	−0.422175
$205$	−3.95562e10	−1.56431
$206$	−5.50880e9	−0.213135
$207$	8.39198e9	0.317686
$208$	−4.28946e9	−0.158898
$209$	−1.92488e10	−0.697822
$210$	1.13112e10	0.401347
$211$	−2.42054e10	−0.840699	−0.420350	−	0.907362i	$-0.638093\pi$
$211$	−2.42054e10	−0.840699	−0.420350	+	0.907362i	$0.638093\pi$
$212$	2.47184e10	0.840446
$213$	1.55265e10	0.516851
$214$	7.28707e9	0.237515
$215$	7.59301e10	2.42349
$216$	−5.77784e9	−0.180602
$217$	−1.36540e10	−0.418013
$218$	−3.08006e10	−0.923645
$219$	−1.20769e10	−0.354778
$220$	−2.30941e10	−0.664658
$221$	3.45278e10	0.973651
$222$	8.74692e9	0.241695
$223$	−1.04006e10	−0.281636	−0.140818	−	0.990036i	$-0.544973\pi$
$223$	−1.04006e10	−0.281636	−0.140818	+	0.990036i	$0.544973\pi$
$224$	−2.86986e10	−0.761632
$225$	2.43120e10	0.632410
$226$	1.32289e10	0.337316
$227$	1.85297e10	0.463182	0.231591	−	0.972813i	$-0.425607\pi$
$227$	1.85297e10	0.463182	0.231591	+	0.972813i	$0.425607\pi$
$228$	−2.01954e10	−0.494931
$229$	−4.59022e10	−1.10300	−0.551498	−	0.834176i	$-0.685944\pi$
$229$	−4.59022e10	−1.10300	−0.551498	+	0.834176i	$0.685944\pi$
$230$	−3.81712e10	−0.899417
$231$	−1.03766e10	−0.239773
$232$	−6.56380e10	−1.48751
$233$	7.97085e10	1.77175	0.885876	−	0.463922i	$-0.153558\pi$
$233$	7.97085e10	1.77175	0.885876	+	0.463922i	$0.153558\pi$
$234$	7.81689e9	0.170437
$235$	9.66057e10	2.06632
$236$	4.29696e9	0.0901691
$237$	5.85193e9	0.120485
$238$	2.13430e10	0.431180
$239$	−2.10848e10	−0.418002	−0.209001	−	0.977915i	$-0.567021\pi$
$239$	−2.10848e10	−0.418002	−0.209001	+	0.977915i	$0.567021\pi$
$240$	−8.70293e9	−0.169323
$241$	8.05924e10	1.53892	0.769462	−	0.638693i	$-0.220524\pi$
$241$	8.05924e10	1.53892	0.769462	+	0.638693i	$0.220524\pi$
$242$	2.01785e10	0.378198
$243$	−3.48678e9	−0.0641500
$244$	2.25109e10	0.406573
$245$	−4.39075e10	−0.778558
$246$	−1.68977e10	−0.294185
$247$	6.67716e10	1.14145
$248$	−3.17241e10	−0.532545
$249$	1.27850e10	0.210767
$250$	−5.22970e10	−0.846733
$251$	−7.67172e10	−1.22000	−0.610002	−	0.792400i	$-0.708831\pi$
$251$	−7.67172e10	−1.22000	−0.610002	+	0.792400i	$0.708831\pi$
$252$	−1.08869e10	−0.170060
$253$	3.50174e10	0.537331
$254$	4.30792e10	0.649405
$255$	7.00538e10	1.03753
$256$	−5.84788e10	−0.850978
$257$	−1.42887e10	−0.204312	−0.102156	−	0.994768i	$-0.532574\pi$
$257$	−1.42887e10	−0.204312	−0.102156	+	0.994768i	$0.532574\pi$
$258$	3.24360e10	0.455763
$259$	4.02777e10	0.556180
$260$	8.01104e10	1.08720
$261$	−3.96109e10	−0.528364
$262$	3.55955e10	0.466701
$263$	−1.53883e11	−1.98331	−0.991655	−	0.128923i	$-0.958848\pi$
$263$	−1.53883e11	−1.98331	−0.991655	+	0.128923i	$0.958848\pi$
$264$	−2.41093e10	−0.305469
$265$	−1.65815e11	−2.06546
$266$	4.12742e10	0.505488
$267$	−4.48738e10	−0.540371
$268$	6.10517e10	0.722922
$269$	1.59562e10	0.185800	0.0928998	−	0.995675i	$-0.470386\pi$
$269$	1.59562e10	0.185800	0.0928998	+	0.995675i	$0.470386\pi$
$270$	1.58598e10	0.181619
$271$	−4.94957e10	−0.557450	−0.278725	−	0.960371i	$-0.589912\pi$
$271$	−4.94957e10	−0.557450	−0.278725	+	0.960371i	$0.589912\pi$
$272$	−1.64215e10	−0.181909
$273$	3.59951e10	0.392203
$274$	3.66866e10	0.393214
$275$	1.01447e11	1.06965
$276$	3.67395e10	0.381103
$277$	−4.78501e10	−0.488342	−0.244171	−	0.969732i	$-0.578516\pi$
$277$	−4.78501e10	−0.488342	−0.244171	+	0.969732i	$0.578516\pi$
$278$	−3.40051e10	−0.341462
$279$	−1.91447e10	−0.189160
$280$	1.21017e11	1.17662
$281$	1.87649e11	1.79543	0.897716	−	0.440575i	$-0.145225\pi$
$281$	1.87649e11	1.79543	0.897716	+	0.440575i	$0.145225\pi$
$282$	4.12683e10	0.388594
$283$	9.35083e10	0.866585	0.433292	−	0.901253i	$-0.357352\pi$
$283$	9.35083e10	0.866585	0.433292	+	0.901253i	$0.357352\pi$
$284$	6.79739e10	0.620026
$285$	1.35474e11	1.21633
$286$	3.26178e10	0.288275
$287$	−7.78105e10	−0.676970
$288$	−4.02394e10	−0.344655
$289$	1.35964e10	0.114653
$290$	1.80172e11	1.49588
$291$	−5.56371e10	−0.454826
$292$	−5.28718e10	−0.425600
$293$	−6.02379e10	−0.477491	−0.238746	−	0.971082i	$-0.576736\pi$
$293$	−6.02379e10	−0.477491	−0.238746	+	0.971082i	$0.576736\pi$
$294$	−1.87565e10	−0.146416
$295$	−2.88247e10	−0.221598
$296$	9.35826e10	0.708570
$297$	−1.45494e10	−0.108503
$298$	2.06709e10	0.151840
$299$	−1.21471e11	−0.878926
$300$	1.06436e11	0.758653
$301$	1.49361e11	1.04879
$302$	1.01816e11	0.704344
$303$	8.82530e10	0.601503
$304$	−3.17568e10	−0.213258
$305$	−1.51006e11	−0.999185
$306$	2.99258e10	0.195119
$307$	−2.53708e10	−0.163009	−0.0815044	−	0.996673i	$-0.525972\pi$
$307$	−2.53708e10	−0.163009	−0.0815044	+	0.996673i	$0.525972\pi$
$308$	−4.54280e10	−0.287637
$309$	−3.55678e10	−0.221944
$310$	8.70805e10	0.535542
$311$	−1.97030e11	−1.19429	−0.597147	−	0.802132i	$-0.703699\pi$
$311$	−1.97030e11	−1.19429	−0.597147	+	0.802132i	$0.703699\pi$
$312$	8.36323e10	0.499664
$313$	1.03704e10	0.0610728	0.0305364	−	0.999534i	$-0.490278\pi$
$313$	1.03704e10	0.0610728	0.0305364	+	0.999534i	$0.490278\pi$
$314$	−2.00925e10	−0.116641
$315$	7.30309e10	0.417935
$316$	2.56193e10	0.144536
$317$	2.39312e11	1.33106	0.665530	−	0.746371i	$-0.268206\pi$
$317$	2.39312e11	1.33106	0.665530	+	0.746371i	$0.268206\pi$
$318$	−7.08334e10	−0.388433
$319$	−1.65286e11	−0.893670
$320$	1.28019e11	0.682497
$321$	4.70492e10	0.247332
$322$	−7.50861e10	−0.389232
$323$	2.55625e11	1.30675
$324$	−1.52649e10	−0.0769558
$325$	−3.51908e11	−1.74966
$326$	8.48876e10	0.416260
$327$	−1.98865e11	−0.961820
$328$	−1.80788e11	−0.862455
$329$	1.90032e11	0.894220
$330$	6.61785e10	0.307188
$331$	1.79055e11	0.819901	0.409951	−	0.912108i	$-0.365546\pi$
$331$	1.79055e11	0.819901	0.409951	+	0.912108i	$0.365546\pi$
$332$	5.59717e10	0.252841
$333$	5.64748e10	0.251684
$334$	5.13525e10	0.225789
$335$	−4.09544e11	−1.77664
$336$	−1.71194e10	−0.0732760
$337$	−3.60414e11	−1.52218	−0.761091	−	0.648645i	$-0.775336\pi$
$337$	−3.60414e11	−1.52218	−0.761091	+	0.648645i	$0.775336\pi$
$338$	1.98911e10	0.0828962
$339$	8.54131e10	0.351258
$340$	3.06690e11	1.24464
$341$	−7.98857e10	−0.319944
$342$	5.78720e10	0.228745
$343$	−2.75196e11	−1.07354
$344$	3.47030e11	1.33615
$345$	−2.46454e11	−0.936591
$346$	−1.90907e11	−0.716111
$347$	−6.49091e10	−0.240338	−0.120169	−	0.992753i	$-0.538344\pi$
$347$	−6.49091e10	−0.240338	−0.120169	+	0.992753i	$0.538344\pi$
$348$	−1.73414e11	−0.633836
$349$	−3.82648e11	−1.38066	−0.690328	−	0.723497i	$-0.742534\pi$
$349$	−3.82648e11	−1.38066	−0.690328	+	0.723497i	$0.742534\pi$
$350$	−2.17528e11	−0.774835
$351$	5.04700e10	0.177481
$352$	−1.67908e11	−0.582947
$353$	−3.78040e11	−1.29584	−0.647919	−	0.761709i	$-0.724361\pi$
$353$	−3.78040e11	−1.29584	−0.647919	+	0.761709i	$0.724361\pi$
$354$	−1.23134e10	−0.0416739
$355$	−4.55979e11	−1.52376
$356$	−1.96454e11	−0.648240
$357$	1.37802e11	0.449001
$358$	−2.78739e11	−0.896858
$359$	1.86227e11	0.591723	0.295861	−	0.955231i	$-0.404393\pi$
$359$	1.86227e11	0.591723	0.295861	+	0.955231i	$0.404393\pi$
$360$	1.69682e11	0.532446
$361$	1.71653e11	0.531948
$362$	3.11006e11	0.951876
$363$	1.30283e11	0.393829
$364$	1.57584e11	0.470496
$365$	3.54672e11	1.04595
$366$	−6.45074e10	−0.187908
$367$	3.89606e11	1.12106	0.560529	−	0.828135i	$-0.310598\pi$
$367$	3.89606e11	1.12106	0.560529	+	0.828135i	$0.310598\pi$
$368$	5.77721e10	0.164211
$369$	−1.09101e11	−0.306344
$370$	−2.56878e11	−0.712556
$371$	−3.26172e11	−0.893850
$372$	−8.38142e10	−0.226921
$373$	−2.61650e11	−0.699893	−0.349946	−	0.936770i	$-0.613800\pi$
$373$	−2.61650e11	−0.699893	−0.349946	+	0.936770i	$0.613800\pi$
$374$	1.24872e11	0.330022
$375$	−3.37657e11	−0.881729
$376$	4.41526e11	1.13923
$377$	5.73355e11	1.46180
$378$	3.11975e10	0.0785972
$379$	−5.94167e11	−1.47922	−0.739608	−	0.673037i	$-0.764989\pi$
$379$	−5.94167e11	−1.47922	−0.739608	+	0.673037i	$0.764989\pi$
$380$	5.93094e11	1.45914
$381$	2.78142e11	0.676246
$382$	2.43526e11	0.585141
$383$	−7.50953e11	−1.78327	−0.891637	−	0.452750i	$-0.850443\pi$
$383$	−7.50953e11	−1.78327	−0.891637	+	0.452750i	$0.850443\pi$
$384$	−1.99665e11	−0.468610
$385$	3.04738e11	0.706892
$386$	1.69730e11	0.389149
$387$	2.09424e11	0.474600
$388$	−2.43575e11	−0.545620
$389$	6.24639e11	1.38311	0.691554	−	0.722325i	$-0.256926\pi$
$389$	6.24639e11	1.38311	0.691554	+	0.722325i	$0.256926\pi$
$390$	−2.29565e11	−0.502476
$391$	−4.65033e11	−1.00621
$392$	−2.00674e11	−0.429244
$393$	2.29823e11	0.485991
$394$	−2.73320e11	−0.571398
$395$	−1.71858e11	−0.355209
$396$	−6.36962e10	−0.130162
$397$	5.02778e11	1.01583	0.507913	−	0.861408i	$-0.330417\pi$
$397$	5.02778e11	1.01583	0.507913	+	0.861408i	$0.330417\pi$
$398$	−1.99881e11	−0.399298
$399$	2.66488e11	0.526381
$400$	1.67369e11	0.326892
$401$	−8.79008e11	−1.69763	−0.848815	−	0.528690i	$-0.822683\pi$
$401$	−8.79008e11	−1.69763	−0.848815	+	0.528690i	$0.822683\pi$
$402$	−1.74950e11	−0.334116
$403$	2.77113e11	0.523341
$404$	3.86365e11	0.721576
$405$	1.02399e11	0.189125
$406$	3.54414e11	0.647356
$407$	2.35654e11	0.425696
$408$	3.20173e11	0.572024
$409$	3.67932e11	0.650150	0.325075	−	0.945688i	$-0.394611\pi$
$409$	3.67932e11	0.650150	0.325075	+	0.945688i	$0.394611\pi$
$410$	4.96250e11	0.867307
$411$	2.36868e11	0.409466
$412$	−1.55713e11	−0.266249
$413$	−5.67006e10	−0.0958987
$414$	−1.05281e11	−0.176136
$415$	−3.75466e11	−0.621376
$416$	5.82452e11	0.953542
$417$	−2.19555e11	−0.355575
$418$	2.41484e11	0.386897
$419$	−1.62115e11	−0.256957	−0.128478	−	0.991712i	$-0.541009\pi$
$419$	−1.62115e11	−0.256957	−0.128478	+	0.991712i	$0.541009\pi$
$420$	3.19724e11	0.501364
$421$	−6.72976e11	−1.04407	−0.522035	−	0.852924i	$-0.674827\pi$
$421$	−6.72976e11	−1.04407	−0.522035	+	0.852924i	$0.674827\pi$
$422$	3.03667e11	0.466113
$423$	2.66450e11	0.404655
$424$	−7.57840e11	−1.13876
$425$	−1.34723e12	−2.00304
$426$	−1.94787e11	−0.286560
$427$	−2.97042e11	−0.432407
$428$	2.05978e11	0.296704
$429$	2.10598e11	0.300190
$430$	−9.52575e11	−1.34367
$431$	−5.75800e11	−0.803755	−0.401877	−	0.915693i	$-0.631642\pi$
$431$	−5.75800e11	−0.803755	−0.401877	+	0.915693i	$0.631642\pi$
$432$	−2.40037e10	−0.0331590
$433$	1.04209e12	1.42465	0.712326	−	0.701849i	$-0.247642\pi$
$433$	1.04209e12	1.42465	0.712326	+	0.701849i	$0.247642\pi$
$434$	1.71295e11	0.231761
$435$	1.16329e12	1.55770
$436$	−8.70617e11	−1.15382
$437$	−8.99306e11	−1.17962
$438$	1.51510e11	0.196702
$439$	−7.00416e11	−0.900048	−0.450024	−	0.893017i	$-0.648584\pi$
$439$	−7.00416e11	−0.900048	−0.450024	+	0.893017i	$0.648584\pi$
$440$	7.08039e11	0.900575
$441$	−1.21102e11	−0.152468
$442$	−4.33166e11	−0.539826
$443$	−2.07557e11	−0.256048	−0.128024	−	0.991771i	$-0.540863\pi$
$443$	−2.07557e11	−0.256048	−0.128024	+	0.991771i	$0.540863\pi$
$444$	2.47243e11	0.301926
$445$	1.31784e12	1.59310
$446$	1.30480e11	0.156149
$447$	1.33462e11	0.158115
$448$	2.51825e11	0.295357
$449$	−7.72881e11	−0.897437	−0.448718	−	0.893673i	$-0.648119\pi$
$449$	−7.72881e11	−0.897437	−0.448718	+	0.893673i	$0.648119\pi$
$450$	−3.05004e11	−0.350630
$451$	−4.55248e11	−0.518148
$452$	3.73932e11	0.421376
$453$	6.57378e11	0.733455
$454$	−2.32463e11	−0.256805
$455$	−1.05710e12	−1.15628
$456$	6.19168e11	0.670605
$457$	1.64560e11	0.176482	0.0882412	−	0.996099i	$-0.471875\pi$
$457$	1.64560e11	0.176482	0.0882412	+	0.996099i	$0.471875\pi$
$458$	5.75863e11	0.611540
$459$	1.93217e11	0.203183
$460$	−1.07896e12	−1.12355
$461$	−1.67596e12	−1.72827	−0.864133	−	0.503264i	$-0.832132\pi$
$461$	−1.67596e12	−1.72827	−0.864133	+	0.503264i	$0.832132\pi$
$462$	1.30179e11	0.132939
$463$	1.94865e11	0.197070	0.0985348	−	0.995134i	$-0.468584\pi$
$463$	1.94865e11	0.197070	0.0985348	+	0.995134i	$0.468584\pi$
$464$	−2.72690e11	−0.273110
$465$	5.62238e11	0.557676
$466$	−9.99977e11	−0.982321
$467$	1.16272e12	1.13122	0.565611	−	0.824672i	$-0.308641\pi$
$467$	1.16272e12	1.13122	0.565611	+	0.824672i	$0.308641\pi$
$468$	2.20954e11	0.212910
$469$	−8.05608e11	−0.768858
$470$	−1.21196e12	−1.14564
$471$	−1.29728e11	−0.121462
$472$	−1.31740e11	−0.122174
$473$	8.73871e11	0.802735
$474$	−7.34150e10	−0.0668009
$475$	−2.60533e12	−2.34824
$476$	6.03286e11	0.538632
$477$	−4.57338e11	−0.404487
$478$	2.64517e11	0.231755
$479$	−2.02118e12	−1.75427	−0.877133	−	0.480247i	$-0.840547\pi$
$479$	−2.02118e12	−1.75427	−0.877133	+	0.480247i	$0.840547\pi$
$480$	1.18174e12	1.01610
$481$	−8.17454e11	−0.696323
$482$	−1.01107e12	−0.853233
$483$	−4.84796e11	−0.405319
$484$	5.70370e11	0.472446
$485$	1.63394e12	1.34090
$486$	4.37432e10	0.0355670
$487$	−1.82880e12	−1.47328	−0.736642	−	0.676283i	$-0.763590\pi$
$487$	−1.82880e12	−1.47328	−0.736642	+	0.676283i	$0.763590\pi$
$488$	−6.90159e11	−0.550884
$489$	5.48080e11	0.433465
$490$	5.50838e11	0.431660
$491$	−3.89531e11	−0.302465	−0.151232	−	0.988498i	$-0.548324\pi$
$491$	−3.89531e11	−0.302465	−0.151232	+	0.988498i	$0.548324\pi$
$492$	−4.77636e11	−0.367497
$493$	2.19500e12	1.67349
$494$	−8.37678e11	−0.632857
$495$	4.27284e11	0.319885
$496$	−1.31796e11	−0.0977766
$497$	−8.96950e11	−0.659424
$498$	−1.60393e11	−0.116857
$499$	−7.68705e11	−0.555019	−0.277509	−	0.960723i	$-0.589509\pi$
$499$	−7.68705e11	−0.555019	−0.277509	+	0.960723i	$0.589509\pi$
$500$	−1.47824e12	−1.05774
$501$	3.31559e11	0.235121
$502$	9.62450e11	0.676412
$503$	−1.59173e12	−1.10870	−0.554349	−	0.832285i	$-0.687033\pi$
$503$	−1.59173e12	−1.10870	−0.554349	+	0.832285i	$0.687033\pi$
$504$	3.33780e11	0.230421
$505$	−2.59180e12	−1.77333
$506$	−4.39309e11	−0.297915
$507$	1.28428e11	0.0863224
$508$	1.21769e12	0.811239
$509$	1.48575e12	0.981105	0.490552	−	0.871412i	$-0.336795\pi$
$509$	1.48575e12	0.981105	0.490552	+	0.871412i	$0.336795\pi$
$510$	−8.78855e11	−0.575243
$511$	6.97671e11	0.452644
$512$	−5.28439e11	−0.339844
$513$	3.73653e11	0.238199
$514$	1.79258e11	0.113277
$515$	1.04455e12	0.654329
$516$	9.16845e11	0.569341
$517$	1.11182e12	0.684429
$518$	−5.05301e11	−0.308366
$519$	−1.23260e12	−0.745708
$520$	−2.45610e12	−1.47309
$521$	2.56479e11	0.152505	0.0762523	−	0.997089i	$-0.475705\pi$
$521$	2.56479e11	0.152505	0.0762523	+	0.997089i	$0.475705\pi$
$522$	4.96936e11	0.292943
$523$	−4.08961e10	−0.0239015	−0.0119507	−	0.999929i	$-0.503804\pi$
$523$	−4.08961e10	−0.0239015	−0.0119507	+	0.999929i	$0.503804\pi$
$524$	1.00615e12	0.583005
$525$	−1.40448e12	−0.806860
$526$	1.93053e12	1.09962
$527$	1.06089e12	0.599130
$528$	−1.00161e11	−0.0560849
$529$	−1.65134e11	−0.0916822
$530$	2.08022e12	1.14516
$531$	−7.95020e10	−0.0433963
$532$	1.16667e12	0.631458
$533$	1.57920e12	0.847548
$534$	5.62960e11	0.299600
$535$	−1.38173e12	−0.729175
$536$	−1.87178e12	−0.979519
$537$	−1.79969e12	−0.933926
$538$	−2.00178e11	−0.103014
$539$	−5.05326e11	−0.257883
$540$	4.48296e11	0.226879
$541$	1.22129e12	0.612957	0.306478	−	0.951878i	$-0.400849\pi$
$541$	1.22129e12	0.612957	0.306478	+	0.951878i	$0.400849\pi$
$542$	6.20945e11	0.309070
$543$	2.00802e12	0.991218
$544$	2.22983e12	1.09163
$545$	5.84023e12	2.83561
$546$	−4.51574e11	−0.217451
$547$	2.08681e12	0.996645	0.498323	−	0.866992i	$-0.333949\pi$
$547$	2.08681e12	0.996645	0.498323	+	0.866992i	$0.333949\pi$
$548$	1.03699e12	0.491205
$549$	−4.16494e11	−0.195674
$550$	−1.27270e12	−0.593053
$551$	4.24481e12	1.96190
$552$	−1.12639e12	−0.516373
$553$	−3.38060e11	−0.153720
$554$	6.00300e11	0.270754
$555$	−1.65854e12	−0.742007
$556$	−9.61195e11	−0.426555
$557$	3.43626e12	1.51265	0.756323	−	0.654199i	$-0.226994\pi$
$557$	3.43626e12	1.51265	0.756323	+	0.654199i	$0.226994\pi$
$558$	2.40179e11	0.104877
$559$	−3.03135e12	−1.31305
$560$	5.02759e11	0.216030
$561$	8.06241e11	0.343662
$562$	−2.35414e12	−0.995450
$563$	−5.32352e11	−0.223311	−0.111656	−	0.993747i	$-0.535615\pi$
$563$	−5.32352e11	−0.223311	−0.111656	+	0.993747i	$0.535615\pi$
$564$	1.16650e12	0.485432
$565$	−2.50840e12	−1.03557
$566$	−1.17310e12	−0.480465
$567$	2.01428e11	0.0818457
$568$	−2.08401e12	−0.840101
$569$	4.30475e11	0.172164	0.0860820	−	0.996288i	$-0.472565\pi$
$569$	4.30475e11	0.172164	0.0860820	+	0.996288i	$0.472565\pi$
$570$	−1.69957e12	−0.674378
$571$	4.07772e12	1.60530	0.802649	−	0.596452i	$-0.203423\pi$
$571$	4.07772e12	1.60530	0.802649	+	0.596452i	$0.203423\pi$
$572$	9.21981e11	0.360114
$573$	1.57234e12	0.609325
$574$	9.76166e11	0.375336
$575$	4.73963e12	1.80817
$576$	3.53093e11	0.133656
$577$	2.87140e12	1.07845	0.539227	−	0.842160i	$-0.318716\pi$
$577$	2.87140e12	1.07845	0.539227	+	0.842160i	$0.318716\pi$
$578$	−1.70573e11	−0.0635675
$579$	1.09587e12	0.405233
$580$	5.09278e12	1.86866
$581$	−7.38574e11	−0.268907
$582$	6.97991e11	0.252172
$583$	−1.90835e12	−0.684146
$584$	1.62099e12	0.576665
$585$	−1.48219e12	−0.523243
$586$	7.55710e11	0.264738
$587$	1.97794e12	0.687609	0.343804	−	0.939041i	$-0.388284\pi$
$587$	1.97794e12	0.687609	0.343804	+	0.939041i	$0.388284\pi$
$588$	−5.30176e11	−0.182904
$589$	2.05160e12	0.702382
$590$	3.61618e11	0.122862
$591$	−1.76470e12	−0.595014
$592$	3.88784e11	0.130095
$593$	−1.12402e12	−0.373275	−0.186637	−	0.982429i	$-0.559759\pi$
$593$	−1.12402e12	−0.373275	−0.186637	+	0.982429i	$0.559759\pi$
$594$	1.82528e11	0.0601578
$595$	−4.04694e12	−1.32373
$596$	5.84287e11	0.189679
$597$	−1.29054e12	−0.415802
$598$	1.52391e12	0.487307
$599$	4.59815e12	1.45936	0.729680	−	0.683789i	$-0.239669\pi$
$599$	4.59815e12	1.45936	0.729680	+	0.683789i	$0.239669\pi$
$600$	−3.26321e12	−1.02793
$601$	−3.40227e12	−1.06374	−0.531868	−	0.846827i	$-0.678510\pi$
$601$	−3.40227e12	−1.06374	−0.531868	+	0.846827i	$0.678510\pi$
$602$	−1.87380e12	−0.581485
$603$	−1.12957e12	−0.347925
$604$	2.87795e12	0.879868
$605$	−3.82613e12	−1.16108
$606$	−1.10717e12	−0.333494
$607$	−4.76313e12	−1.42411	−0.712055	−	0.702124i	$-0.752235\pi$
$607$	−4.76313e12	−1.42411	−0.712055	+	0.702124i	$0.752235\pi$
$608$	4.31216e12	1.27976
$609$	2.28828e12	0.674112
$610$	1.89444e12	0.553983
$611$	−3.85678e12	−1.11954
$612$	8.45890e11	0.243743
$613$	−1.30004e12	−0.371863	−0.185932	−	0.982563i	$-0.559530\pi$
$613$	−1.30004e12	−0.371863	−0.185932	+	0.982563i	$0.559530\pi$
$614$	3.18287e11	0.0903777
$615$	3.20405e12	0.903154
$616$	1.39277e12	0.389733
$617$	6.20428e12	1.72349	0.861744	−	0.507343i	$-0.169372\pi$
$617$	6.20428e12	1.72349	0.861744	+	0.507343i	$0.169372\pi$
$618$	4.46213e11	0.123054
$619$	4.36576e12	1.19523	0.597615	−	0.801783i	$-0.296115\pi$
$619$	4.36576e12	1.19523	0.597615	+	0.801783i	$0.296115\pi$
$620$	2.46144e12	0.669001
$621$	−6.79750e11	−0.183416
$622$	2.47183e12	0.662158
$623$	2.59231e12	0.689431
$624$	3.47446e11	0.0917395
$625$	2.67889e12	0.702255
$626$	−1.30102e11	−0.0338609
$627$	1.55915e12	0.402888
$628$	−5.67939e11	−0.145708
$629$	−3.12950e12	−0.797163
$630$	−9.16203e11	−0.231718
$631$	4.38403e12	1.10088	0.550441	−	0.834874i	$-0.314459\pi$
$631$	4.38403e12	1.10088	0.550441	+	0.834874i	$0.314459\pi$
$632$	−7.85461e11	−0.195838
$633$	1.96063e12	0.485378
$634$	−3.00227e12	−0.737986
$635$	−8.16843e12	−1.99369
$636$	−2.00219e12	−0.485232
$637$	1.75291e12	0.421825
$638$	2.07358e12	0.495482
$639$	−1.25765e12	−0.298404
$640$	5.86372e12	1.38154
$641$	−2.65746e12	−0.621734	−0.310867	−	0.950453i	$-0.600619\pi$
$641$	−2.65746e12	−0.621734	−0.310867	+	0.950453i	$0.600619\pi$
$642$	−5.90252e11	−0.137129
$643$	−4.60843e12	−1.06317	−0.531586	−	0.847004i	$-0.678404\pi$
$643$	−4.60843e12	−1.06317	−0.531586	+	0.847004i	$0.678404\pi$
$644$	−2.12240e12	−0.486229
$645$	−6.15033e12	−1.39920
$646$	−3.20692e12	−0.724507
$647$	−1.13960e12	−0.255672	−0.127836	−	0.991795i	$-0.540803\pi$
$647$	−1.13960e12	−0.255672	−0.127836	+	0.991795i	$0.540803\pi$
$648$	4.68005e11	0.104271
$649$	−3.31740e11	−0.0734001
$650$	4.41483e12	0.970072
$651$	1.10597e12	0.241340
$652$	2.39945e12	0.519994
$653$	−1.92790e12	−0.414929	−0.207465	−	0.978243i	$-0.566521\pi$
$653$	−1.92790e12	−0.414929	−0.207465	+	0.978243i	$0.566521\pi$
$654$	2.49485e12	0.533267
$655$	−6.74941e12	−1.43278
$656$	−7.51073e11	−0.158349
$657$	9.78229e11	0.204831
$658$	−2.38403e12	−0.495787
$659$	−6.04821e12	−1.24923	−0.624615	−	0.780933i	$-0.714744\pi$
$659$	−6.04821e12	−1.24923	−0.624615	+	0.780933i	$0.714744\pi$
$660$	1.87062e12	0.383740
$661$	8.21417e12	1.67362	0.836810	−	0.547493i	$-0.184418\pi$
$661$	8.21417e12	1.67362	0.836810	+	0.547493i	$0.184418\pi$
$662$	−2.24633e12	−0.454582
$663$	−2.79675e12	−0.562138
$664$	−1.71603e12	−0.342585
$665$	−7.82617e12	−1.55186
$666$	−7.08501e11	−0.139542
$667$	−7.72217e12	−1.51068
$668$	1.45154e12	0.282056
$669$	8.42451e11	0.162602
$670$	5.13791e12	0.985030
$671$	−1.73792e12	−0.330961
$672$	2.32459e12	0.439728
$673$	3.76497e12	0.707447	0.353724	−	0.935350i	$-0.384915\pi$
$673$	3.76497e12	0.707447	0.353724	+	0.935350i	$0.384915\pi$
$674$	4.52155e12	0.843951
$675$	−1.96927e12	−0.365122
$676$	5.62248e11	0.103554
$677$	6.21117e12	1.13638	0.568191	−	0.822897i	$-0.307644\pi$
$677$	6.21117e12	1.13638	0.568191	+	0.822897i	$0.307644\pi$
$678$	−1.07154e12	−0.194749
$679$	3.21410e12	0.580290
$680$	−9.40279e12	−1.68642
$681$	−1.50091e12	−0.267419
$682$	1.00220e12	0.177388
$683$	8.19423e12	1.44084	0.720419	−	0.693539i	$-0.243950\pi$
$683$	8.19423e12	1.44084	0.720419	+	0.693539i	$0.243950\pi$
$684$	1.63583e12	0.285749
$685$	−6.95630e12	−1.20718
$686$	3.45245e12	0.595208
$687$	3.71808e12	0.636816
$688$	1.44172e12	0.245320
$689$	6.61981e12	1.11908
$690$	3.09187e12	0.519279
$691$	−3.72136e12	−0.620942	−0.310471	−	0.950583i	$-0.600487\pi$
$691$	−3.72136e12	−0.620942	−0.310471	+	0.950583i	$0.600487\pi$
$692$	−5.39623e12	−0.894568
$693$	8.40504e11	0.138433
$694$	8.14312e11	0.133252
$695$	6.44784e12	1.04829
$696$	5.31668e12	0.858813
$697$	6.04572e12	0.970288
$698$	4.80049e12	0.765483
$699$	−6.45639e12	−1.02292
$700$	−6.14871e12	−0.967927
$701$	3.58404e12	0.560585	0.280293	−	0.959915i	$-0.409568\pi$
$701$	3.58404e12	0.560585	0.280293	+	0.959915i	$0.409568\pi$
$702$	−6.33168e11	−0.0984016
$703$	−6.05199e12	−0.934542
$704$	1.47336e12	0.226064
$705$	−7.82506e12	−1.19299
$706$	4.74267e12	0.718458
$707$	−5.09828e12	−0.767426
$708$	−3.48054e11	−0.0520592
$709$	−1.86082e12	−0.276565	−0.138282	−	0.990393i	$-0.544158\pi$
$709$	−1.86082e12	−0.276565	−0.138282	+	0.990393i	$0.544158\pi$
$710$	5.72046e12	0.844828
$711$	−4.74006e11	−0.0695618
$712$	6.02307e12	0.878330
$713$	−3.73227e12	−0.540842
$714$	−1.72878e12	−0.248942
$715$	−6.18479e12	−0.885009
$716$	−7.87890e12	−1.12036
$717$	1.70787e12	0.241334
$718$	−2.33630e12	−0.328072
$719$	8.32527e12	1.16176	0.580882	−	0.813988i	$-0.302708\pi$
$719$	8.32527e12	1.16176	0.580882	+	0.813988i	$0.302708\pi$
$720$	7.04937e11	0.0977584
$721$	2.05471e12	0.283167
$722$	−2.15346e12	−0.294930
$723$	−6.52798e12	−0.888498
$724$	8.79098e12	1.18909
$725$	−2.23715e13	−3.00728
$726$	−1.63446e12	−0.218353
$727$	1.05496e13	1.40066	0.700329	−	0.713821i	$-0.253037\pi$
$727$	1.05496e13	1.40066	0.700329	+	0.713821i	$0.253037\pi$
$728$	−4.83135e12	−0.637496
$729$	2.82430e11	0.0370370
$730$	−4.44952e12	−0.579909
$731$	−1.16051e13	−1.50321
$732$	−1.82338e12	−0.234735
$733$	−3.93351e12	−0.503283	−0.251641	−	0.967821i	$-0.580970\pi$
$733$	−3.93351e12	−0.503283	−0.251641	+	0.967821i	$0.580970\pi$
$734$	−4.88777e12	−0.621554
$735$	3.55650e12	0.449501
$736$	−7.84468e12	−0.985429
$737$	−4.71340e12	−0.588478
$738$	1.36872e12	0.169848
$739$	−6.24664e12	−0.770454	−0.385227	−	0.922822i	$-0.625877\pi$
$739$	−6.24664e12	−0.770454	−0.385227	+	0.922822i	$0.625877\pi$
$740$	−7.26098e12	−0.890128
$741$	−5.40850e12	−0.659014
$742$	4.09197e12	0.495581
$743$	−8.32453e12	−1.00210	−0.501049	−	0.865419i	$-0.667052\pi$
$743$	−8.32453e12	−1.00210	−0.501049	+	0.865419i	$0.667052\pi$
$744$	2.56965e12	0.307465
$745$	−3.91949e12	−0.466151
$746$	3.28251e12	0.388045
$747$	−1.03558e12	−0.121686
$748$	3.52967e12	0.412265
$749$	−2.71798e12	−0.315558
$750$	4.23605e12	0.488861
$751$	9.51081e12	1.09103	0.545516	−	0.838100i	$-0.316334\pi$
$751$	9.51081e12	1.09103	0.545516	+	0.838100i	$0.316334\pi$
$752$	1.83430e12	0.209165
$753$	6.21409e12	0.704369
$754$	−7.19298e12	−0.810472
$755$	−1.93058e13	−2.16235
$756$	8.81837e11	0.0981839
$757$	4.64714e12	0.514345	0.257172	−	0.966366i	$-0.417209\pi$
$757$	4.64714e12	0.514345	0.257172	+	0.966366i	$0.417209\pi$
$758$	7.45408e12	0.820129
$759$	−2.83641e12	−0.310228
$760$	−1.81836e13	−1.97706
$761$	8.45553e12	0.913924	0.456962	−	0.889486i	$-0.348938\pi$
$761$	8.45553e12	0.913924	0.456962	+	0.889486i	$0.348938\pi$
$762$	−3.48941e12	−0.374934
$763$	1.14882e13	1.22714
$764$	6.88357e12	0.730960
$765$	−5.67436e12	−0.599018
$766$	9.42103e12	0.988710
$767$	1.15076e12	0.120063
$768$	4.73678e12	0.491312
$769$	1.48631e13	1.53264	0.766321	−	0.642457i	$-0.222085\pi$
$769$	1.48631e13	1.53264	0.766321	+	0.642457i	$0.222085\pi$
$770$	−3.82307e12	−0.391926
$771$	1.15738e12	0.117959
$772$	4.79763e12	0.486126
$773$	−1.81427e13	−1.82765	−0.913827	−	0.406103i	$-0.866887\pi$
$773$	−1.81427e13	−1.82765	−0.913827	+	0.406103i	$0.866887\pi$
$774$	−2.62732e12	−0.263135
$775$	−1.08126e13	−1.07664
$776$	7.46775e12	0.739285
$777$	−3.26249e12	−0.321111
$778$	−7.83637e12	−0.766843
$779$	1.16915e13	1.13750
$780$	−6.48894e12	−0.627694
$781$	−5.24782e12	−0.504718
$782$	5.83404e12	0.557878
$783$	3.20849e12	0.305051
$784$	−8.33691e11	−0.0788103
$785$	3.80982e12	0.358089
$786$	−2.88323e12	−0.269450
$787$	1.05260e13	0.978087	0.489044	−	0.872259i	$-0.337346\pi$
$787$	1.05260e13	0.978087	0.489044	+	0.872259i	$0.337346\pi$
$788$	−7.72573e12	−0.713792
$789$	1.24645e13	1.14506
$790$	2.15604e12	0.196940
$791$	−4.93423e12	−0.448152
$792$	1.95286e12	0.176363
$793$	6.02861e12	0.541362
$794$	−6.30757e12	−0.563209
$795$	1.34310e13	1.19250
$796$	−5.64988e12	−0.498805
$797$	5.90203e12	0.518131	0.259065	−	0.965860i	$-0.416586\pi$
$797$	5.90203e12	0.518131	0.259065	+	0.965860i	$0.416586\pi$
$798$	−3.34321e12	−0.291844
$799$	−1.47651e13	−1.28167
$800$	−2.27264e13	−1.96167
$801$	3.63477e12	0.311983
$802$	1.10275e13	0.941225
$803$	4.08188e12	0.346450
$804$	−4.94519e12	−0.417379
$805$	1.42374e13	1.19495
$806$	−3.47651e12	−0.290158
$807$	−1.29245e12	−0.107271
$808$	−1.18455e13	−0.977695
$809$	1.36585e13	1.12107	0.560536	−	0.828130i	$-0.310595\pi$
$809$	1.36585e13	1.12107	0.560536	+	0.828130i	$0.310595\pi$
$810$	−1.28464e12	−0.104858
$811$	−1.76828e13	−1.43535	−0.717675	−	0.696379i	$-0.754793\pi$
$811$	−1.76828e13	−1.43535	−0.717675	+	0.696379i	$0.754793\pi$
$812$	1.00179e13	0.808679
$813$	4.00915e12	0.321844
$814$	−2.95638e12	−0.236021
$815$	−1.60959e13	−1.27793
$816$	1.33014e12	0.105025
$817$	−2.24425e13	−1.76226
$818$	−4.61587e12	−0.360466
$819$	−2.91560e12	−0.226439
$820$	1.40271e13	1.08344
$821$	2.37038e12	0.182085	0.0910423	−	0.995847i	$-0.470980\pi$
$821$	2.37038e12	0.182085	0.0910423	+	0.995847i	$0.470980\pi$
$822$	−2.97161e12	−0.227022
$823$	−4.92072e12	−0.373878	−0.186939	−	0.982372i	$-0.559857\pi$
$823$	−4.92072e12	−0.373878	−0.186939	+	0.982372i	$0.559857\pi$
$824$	4.77400e12	0.360753
$825$	−8.21723e12	−0.617565
$826$	7.11334e11	0.0531696
$827$	1.33372e13	0.991496	0.495748	−	0.868466i	$-0.334894\pi$
$827$	1.33372e13	0.991496	0.495748	+	0.868466i	$0.334894\pi$
$828$	−2.97590e12	−0.220030
$829$	−1.21354e13	−0.892395	−0.446198	−	0.894934i	$-0.647222\pi$
$829$	−1.21354e13	−0.892395	−0.446198	+	0.894934i	$0.647222\pi$
$830$	4.71039e12	0.344513
$831$	3.87586e12	0.281944
$832$	−5.11090e12	−0.369779
$833$	6.71076e12	0.482913
$834$	2.75441e12	0.197143
$835$	−9.73716e12	−0.693175
$836$	6.82585e12	0.483313
$837$	1.55072e12	0.109212
$838$	2.03380e12	0.142466
$839$	1.56293e12	0.108896	0.0544479	−	0.998517i	$-0.482660\pi$
$839$	1.56293e12	0.108896	0.0544479	+	0.998517i	$0.482660\pi$
$840$	−9.80238e12	−0.679321
$841$	2.19422e13	1.51251
$842$	8.44277e12	0.578869
$843$	−1.51996e13	−1.03659
$844$	8.58352e12	0.582270
$845$	−3.77164e12	−0.254493
$846$	−3.34273e12	−0.224355
$847$	−7.52632e12	−0.502467
$848$	−3.14841e12	−0.209079
$849$	−7.57417e12	−0.500323
$850$	1.69015e13	1.11056
$851$	1.10098e13	0.719608
$852$	−5.50589e12	−0.357972
$853$	−1.21011e13	−0.782624	−0.391312	−	0.920258i	$-0.627979\pi$
$853$	−1.21011e13	−0.782624	−0.391312	+	0.920258i	$0.627979\pi$
$854$	3.72652e12	0.239742
$855$	−1.09734e13	−0.702251
$856$	−6.31506e12	−0.402018
$857$	−4.10860e12	−0.260184	−0.130092	−	0.991502i	$-0.541527\pi$
$857$	−4.10860e12	−0.260184	−0.130092	+	0.991502i	$0.541527\pi$
$858$	−2.64204e12	−0.166436
$859$	2.13660e13	1.33892	0.669460	−	0.742848i	$-0.266526\pi$
$859$	2.13660e13	1.33892	0.669460	+	0.742848i	$0.266526\pi$
$860$	−2.69257e13	−1.67851
$861$	6.30265e12	0.390849
$862$	7.22365e12	0.445630
$863$	−2.75466e13	−1.69052	−0.845259	−	0.534356i	$-0.820554\pi$
$863$	−2.75466e13	−1.69052	−0.845259	+	0.534356i	$0.820554\pi$
$864$	3.25939e12	0.198987
$865$	3.61988e13	2.19847
$866$	−1.30734e13	−0.789876
$867$	−1.10131e12	−0.0661948
$868$	4.84186e12	0.289517
$869$	−1.97790e12	−0.117656
$870$	−1.45939e13	−0.863646
$871$	1.63502e13	0.962589
$872$	2.66922e13	1.56336
$873$	4.50660e12	0.262594
$874$	1.12822e13	0.654021
$875$	1.95061e13	1.12495
$876$	4.28262e12	0.245720
$877$	−2.30078e13	−1.31334	−0.656670	−	0.754178i	$-0.728035\pi$
$877$	−2.30078e13	−1.31334	−0.656670	+	0.754178i	$0.728035\pi$
$878$	8.78701e12	0.499018
$879$	4.87927e12	0.275680
$880$	2.94151e12	0.165348
$881$	−8.63759e12	−0.483060	−0.241530	−	0.970393i	$-0.577649\pi$
$881$	−8.63759e12	−0.483060	−0.241530	+	0.970393i	$0.577649\pi$
$882$	1.51928e12	0.0845335
$883$	2.79887e13	1.54938	0.774692	−	0.632338i	$-0.217905\pi$
$883$	2.79887e13	1.54938	0.774692	+	0.632338i	$0.217905\pi$
$884$	−1.22440e13	−0.674352
$885$	2.33480e12	0.127940
$886$	2.60390e12	0.141962
$887$	−2.43474e13	−1.32068	−0.660338	−	0.750968i	$-0.729587\pi$
$887$	−2.43474e13	−1.32068	−0.660338	+	0.750968i	$0.729587\pi$
$888$	−7.58019e12	−0.409093
$889$	−1.60680e13	−0.862787
$890$	−1.65329e13	−0.883272
$891$	1.17850e12	0.0626441
$892$	3.68819e12	0.195061
$893$	−2.85535e13	−1.50255
$894$	−1.67434e12	−0.0876647
$895$	5.28528e13	2.75337
$896$	1.15344e13	0.597875
$897$	9.83915e12	0.507448
$898$	9.69612e12	0.497570
$899$	1.76167e13	0.899509
$900$	−8.62132e12	−0.438009
$901$	2.53430e13	1.28114
$902$	5.71129e12	0.287279
$903$	−1.20982e13	−0.605518
$904$	−1.14644e13	−0.570942
$905$	−5.89712e13	−2.92228
$906$	−8.24709e12	−0.406653
$907$	2.29403e13	1.12556	0.562778	−	0.826608i	$-0.309733\pi$
$907$	2.29403e13	1.12556	0.562778	+	0.826608i	$0.309733\pi$
$908$	−6.57086e12	−0.320801
$909$	−7.14849e12	−0.347278
$910$	1.32617e13	0.641083
$911$	3.68575e13	1.77293	0.886467	−	0.462792i	$-0.153152\pi$
$911$	3.68575e13	1.77293	0.886467	+	0.462792i	$0.153152\pi$
$912$	2.57230e12	0.123125
$913$	−4.32120e12	−0.205819
$914$	−2.06448e12	−0.0978480
$915$	1.22315e13	0.576880
$916$	1.62775e13	0.763938
$917$	−1.32767e13	−0.620050
$918$	−2.42399e12	−0.112652
$919$	1.18969e12	0.0550192	0.0275096	−	0.999622i	$-0.491242\pi$
$919$	1.18969e12	0.0550192	0.0275096	+	0.999622i	$0.491242\pi$
$920$	3.30797e13	1.52235
$921$	2.05503e12	0.0941131
$922$	2.10257e13	0.958210
$923$	1.82040e13	0.825581
$924$	3.67967e12	0.166067
$925$	3.18959e13	1.43251
$926$	−2.44467e12	−0.109262
$927$	2.88099e12	0.128140
$928$	3.70277e13	1.63893
$929$	3.55367e13	1.56533	0.782667	−	0.622441i	$-0.213859\pi$
$929$	3.55367e13	1.56533	0.782667	+	0.622441i	$0.213859\pi$
$930$	−7.05352e12	−0.309195
$931$	1.29776e13	0.566137
$932$	−2.82656e13	−1.22712
$933$	1.59595e13	0.689526
$934$	−1.45868e13	−0.627189
$935$	−2.36775e13	−1.01317
$936$	−6.77421e12	−0.288481
$937$	−3.70448e13	−1.57000	−0.784999	−	0.619498i	$-0.787336\pi$
$937$	−3.70448e13	−1.57000	−0.784999	+	0.619498i	$0.787336\pi$
$938$	1.01067e13	0.426282
$939$	−8.40005e11	−0.0352604
$940$	−3.42575e13	−1.43114
$941$	−4.72046e13	−1.96260	−0.981298	−	0.192496i	$-0.938342\pi$
$941$	−4.72046e13	−1.96260	−0.981298	+	0.192496i	$0.938342\pi$
$942$	1.62749e12	0.0673426
$943$	−2.12693e13	−0.875891
$944$	−5.47308e11	−0.0224315
$945$	−5.91550e12	−0.241295
$946$	−1.09631e13	−0.445064
$947$	3.75098e13	1.51555	0.757774	−	0.652517i	$-0.226287\pi$
$947$	3.75098e13	1.51555	0.757774	+	0.652517i	$0.226287\pi$
$948$	−2.07517e12	−0.0834479
$949$	−1.41595e13	−0.566697
$950$	3.26850e13	1.30195
$951$	−1.93843e13	−0.768488
$952$	−1.84961e13	−0.729817
$953$	−1.68178e13	−0.660467	−0.330233	−	0.943899i	$-0.607127\pi$
$953$	−1.68178e13	−0.660467	−0.330233	+	0.943899i	$0.607127\pi$
$954$	5.73750e12	0.224262
$955$	−4.61760e13	−1.79639
$956$	7.47692e12	0.289509
$957$	1.33881e13	0.515960
$958$	2.53566e13	0.972626
$959$	−1.36836e13	−0.522417
$960$	−1.03696e13	−0.394040
$961$	−1.79251e13	−0.677965
$962$	1.02553e13	0.386066
$963$	−3.81099e12	−0.142797
$964$	−2.85790e13	−1.06586
$965$	−3.21832e13	−1.19469
$966$	6.08197e12	0.224723
$967$	1.43412e13	0.527430	0.263715	−	0.964601i	$-0.415052\pi$
$967$	1.43412e13	0.527430	0.263715	+	0.964601i	$0.415052\pi$
$968$	−1.74869e13	−0.640139
$969$	−2.07056e13	−0.754451
$970$	−2.04985e13	−0.743444
$971$	−1.95428e13	−0.705504	−0.352752	−	0.935717i	$-0.614754\pi$
$971$	−1.95428e13	−0.705504	−0.352752	+	0.935717i	$0.614754\pi$
$972$	1.23646e12	0.0444304
$973$	1.26835e13	0.453659
$974$	2.29431e13	0.816840
$975$	2.85045e13	1.01017
$976$	−2.86723e12	−0.101144
$977$	1.37309e13	0.482140	0.241070	−	0.970508i	$-0.422502\pi$
$977$	1.37309e13	0.482140	0.241070	+	0.970508i	$0.422502\pi$
$978$	−6.87590e12	−0.240328
$979$	1.51669e13	0.527686
$980$	1.55701e13	0.539231
$981$	1.61081e13	0.555307
$982$	4.88683e12	0.167697
$983$	−3.86404e12	−0.131993	−0.0659965	−	0.997820i	$-0.521023\pi$
$983$	−3.86404e12	−0.131993	−0.0659965	+	0.997820i	$0.521023\pi$
$984$	1.46438e13	0.497938
$985$	5.18254e13	1.75420
$986$	−2.75372e13	−0.927843
$987$	−1.53926e13	−0.516278
$988$	−2.36780e13	−0.790568
$989$	4.08274e13	1.35696
$990$	−5.36046e12	−0.177355
$991$	−3.55386e13	−1.17049	−0.585246	−	0.810855i	$-0.699002\pi$
$991$	−3.55386e13	−1.17049	−0.585246	+	0.810855i	$0.699002\pi$
$992$	1.78962e13	0.586756
$993$	−1.45035e13	−0.473370
$994$	1.12526e13	0.365608
$995$	3.79003e13	1.22585
$996$	−4.53370e12	−0.145978
$997$	−4.68278e12	−0.150098	−0.0750491	−	0.997180i	$-0.523911\pi$
$997$	−4.68278e12	−0.150098	−0.0750491	+	0.997180i	$0.523911\pi$
$998$	9.64374e12	0.307722
$999$	−4.57446e12	−0.145310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.8	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-12.5454 q^{2} -81.0000 q^{3} -354.612 q^{4} +2378.79 q^{5} +1016.18 q^{6} +4679.29 q^{7} +10872.0 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-12.5454 q^{2} -81.0000 q^{3} -354.612 q^{4} +2378.79 q^{5} +1016.18 q^{6} +4679.29 q^{7} +10872.0 q^{8} +6561.00 q^{9} -29843.0 q^{10} +27377.3 q^{11} +28723.6 q^{12} -94968.3 q^{13} -58703.7 q^{14} -192682. q^{15} +45167.3 q^{16} -363572. q^{17} -82310.6 q^{18} -703094. q^{19} -843549. q^{20} -379022. q^{21} -343460. q^{22} +1.27907e6 q^{23} -880634. q^{24} +3.70553e6 q^{25} +1.19142e6 q^{26} -531441. q^{27} -1.65933e6 q^{28} -6.03733e6 q^{29} +2.41728e6 q^{30} -2.91796e6 q^{31} -6.13312e6 q^{32} -2.21756e6 q^{33} +4.56116e6 q^{34} +1.11311e7 q^{35} -2.32661e6 q^{36} +8.60765e6 q^{37} +8.82061e6 q^{38} +7.69243e6 q^{39} +2.58623e7 q^{40} -1.66287e7 q^{41} +4.75500e6 q^{42} +3.19196e7 q^{43} -9.70831e6 q^{44} +1.56073e7 q^{45} -1.60465e7 q^{46} +4.06112e7 q^{47} -3.65855e6 q^{48} -1.84579e7 q^{49} -4.64875e7 q^{50} +2.94493e7 q^{51} +3.36769e7 q^{52} -6.97055e7 q^{53} +6.66716e6 q^{54} +6.51248e7 q^{55} +5.08733e7 q^{56} +5.69506e7 q^{57} +7.57409e7 q^{58} -1.21174e7 q^{59} +6.83275e7 q^{60} -6.34803e7 q^{61} +3.66070e7 q^{62} +3.07008e7 q^{63} +5.38170e7 q^{64} -2.25910e8 q^{65} +2.78202e7 q^{66} -1.72165e8 q^{67} +1.28927e8 q^{68} -1.03605e8 q^{69} -1.39644e8 q^{70} -1.91685e8 q^{71} +7.13313e7 q^{72} +1.49098e8 q^{73} -1.07987e8 q^{74} -3.00148e8 q^{75} +2.49326e8 q^{76} +1.28106e8 q^{77} -9.65048e7 q^{78} -7.22461e7 q^{79} +1.07444e8 q^{80} +4.30467e7 q^{81} +2.08614e8 q^{82} -1.57839e8 q^{83} +1.34406e8 q^{84} -8.64861e8 q^{85} -4.00445e8 q^{86} +4.89024e8 q^{87} +2.97646e8 q^{88} +5.53997e8 q^{89} -1.95800e8 q^{90} -4.44384e8 q^{91} -4.53574e8 q^{92} +2.36355e8 q^{93} -5.09485e8 q^{94} -1.67251e9 q^{95} +4.96783e8 q^{96} +6.86877e8 q^{97} +2.31562e8 q^{98} +1.79622e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

L-functions

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