LMFDB - Embedded newform 177.10.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q+29.8017 q^{2} -81.0000 q^{3} +376.142 q^{4} +2386.14 q^{5} -2413.94 q^{6} +4536.93 q^{7} -4048.81 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+29.8017 q^{2} -81.0000 q^{3} +376.142 q^{4} +2386.14 q^{5} -2413.94 q^{6} +4536.93 q^{7} -4048.81 q^{8} +6561.00 q^{9} +71111.0 q^{10} -38636.2 q^{11} -30467.5 q^{12} -159530. q^{13} +135208. q^{14} -193277. q^{15} -313246. q^{16} -283077. q^{17} +195529. q^{18} -454290. q^{19} +897527. q^{20} -367491. q^{21} -1.15143e6 q^{22} -2.42107e6 q^{23} +327954. q^{24} +3.74054e6 q^{25} -4.75427e6 q^{26} -531441. q^{27} +1.70653e6 q^{28} +6.69743e6 q^{29} -5.75999e6 q^{30} +4.53852e6 q^{31} -7.26227e6 q^{32} +3.12953e6 q^{33} -8.43617e6 q^{34} +1.08258e7 q^{35} +2.46787e6 q^{36} -1.75422e7 q^{37} -1.35386e7 q^{38} +1.29219e7 q^{39} -9.66103e6 q^{40} -1.25230e7 q^{41} -1.09519e7 q^{42} +23258.2 q^{43} -1.45327e7 q^{44} +1.56555e7 q^{45} -7.21520e7 q^{46} -5.96424e6 q^{47} +2.53729e7 q^{48} -1.97699e7 q^{49} +1.11474e8 q^{50} +2.29292e7 q^{51} -6.00059e7 q^{52} +8.21208e7 q^{53} -1.58378e7 q^{54} -9.21914e7 q^{55} -1.83692e7 q^{56} +3.67975e7 q^{57} +1.99595e8 q^{58} -1.21174e7 q^{59} -7.26997e7 q^{60} -6.81954e7 q^{61} +1.35255e8 q^{62} +2.97668e7 q^{63} -5.60462e7 q^{64} -3.80661e8 q^{65} +9.32654e7 q^{66} -6.03338e7 q^{67} -1.06477e8 q^{68} +1.96107e8 q^{69} +3.22626e8 q^{70} -7.46554e7 q^{71} -2.65642e7 q^{72} +1.87509e8 q^{73} -5.22788e8 q^{74} -3.02984e8 q^{75} -1.70877e8 q^{76} -1.75290e8 q^{77} +3.85096e8 q^{78} -1.18977e8 q^{79} -7.47449e8 q^{80} +4.30467e7 q^{81} -3.73207e8 q^{82} -3.24381e8 q^{83} -1.38229e8 q^{84} -6.75461e8 q^{85} +693134. q^{86} -5.42492e8 q^{87} +1.56431e8 q^{88} -2.07673e7 q^{89} +4.66560e8 q^{90} -7.23777e8 q^{91} -9.10665e8 q^{92} -3.67620e8 q^{93} -1.77745e8 q^{94} -1.08400e9 q^{95} +5.88244e8 q^{96} -6.27270e8 q^{97} -5.89175e8 q^{98} -2.53492e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	29.8017	1.31706	0.658531	−	0.752554i	$-0.271178\pi$
$2$	29.8017	1.31706	0.658531	+	0.752554i	$0.271178\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	376.142	0.734652
$5$	2386.14	1.70738	0.853691	−	0.520779i	$-0.174359\pi$
$5$	2386.14	1.70738	0.853691	+	0.520779i	$0.174359\pi$
$6$	−2413.94	−0.760406
$7$	4536.93	0.714202	0.357101	−	0.934066i	$-0.383765\pi$
$7$	4536.93	0.714202	0.357101	+	0.934066i	$0.383765\pi$
$8$	−4048.81	−0.349480
$9$	6561.00	0.333333
$10$	71111.0	2.24873
$11$	−38636.2	−0.795660	−0.397830	−	0.917459i	$-0.630237\pi$
$11$	−38636.2	−0.795660	−0.397830	+	0.917459i	$0.630237\pi$
$12$	−30467.5	−0.424151
$13$	−159530.	−1.54916	−0.774582	−	0.632473i	$-0.782040\pi$
$13$	−159530.	−1.54916	−0.774582	+	0.632473i	$0.782040\pi$
$14$	135208.	0.940648
$15$	−193277.	−0.985758
$16$	−313246.	−1.19494
$17$	−283077.	−0.822023	−0.411011	−	0.911630i	$-0.634824\pi$
$17$	−283077.	−0.822023	−0.411011	+	0.911630i	$0.634824\pi$
$18$	195529.	0.439021
$19$	−454290.	−0.799727	−0.399863	−	0.916575i	$-0.630942\pi$
$19$	−454290.	−0.799727	−0.399863	+	0.916575i	$0.630942\pi$
$20$	897527.	1.25433
$21$	−367491.	−0.412345
$22$	−1.15143e6	−1.04793
$23$	−2.42107e6	−1.80398	−0.901990	−	0.431757i	$-0.857894\pi$
$23$	−2.42107e6	−1.80398	−0.901990	+	0.431757i	$0.857894\pi$
$24$	327954.	0.201772
$25$	3.74054e6	1.91516
$26$	−4.75427e6	−2.04034
$27$	−531441.	−0.192450
$28$	1.70653e6	0.524690
$29$	6.69743e6	1.75840	0.879199	−	0.476454i	$-0.158078\pi$
$29$	6.69743e6	1.75840	0.879199	+	0.476454i	$0.158078\pi$
$30$	−5.75999e6	−1.29830
$31$	4.53852e6	0.882645	0.441323	−	0.897349i	$-0.354509\pi$
$31$	4.53852e6	0.882645	0.441323	+	0.897349i	$0.354509\pi$
$32$	−7.26227e6	−1.22433
$33$	3.12953e6	0.459374
$34$	−8.43617e6	−1.08266
$35$	1.08258e7	1.21942
$36$	2.46787e6	0.244884
$37$	−1.75422e7	−1.53878	−0.769391	−	0.638779i	$-0.779440\pi$
$37$	−1.75422e7	−1.53878	−0.769391	+	0.638779i	$0.779440\pi$
$38$	−1.35386e7	−1.05329
$39$	1.29219e7	0.894410
$40$	−9.66103e6	−0.596696
$41$	−1.25230e7	−0.692119	−0.346060	−	0.938213i	$-0.612480\pi$
$41$	−1.25230e7	−0.692119	−0.346060	+	0.938213i	$0.612480\pi$
$42$	−1.09519e7	−0.543083
$43$	23258.2	0.00103745	0.000518726	−	1.00000i	$-0.499835\pi$
$43$	23258.2	0.00103745	0.000518726		1.00000i	$0.499835\pi$
$44$	−1.45327e7	−0.584533
$45$	1.56555e7	0.569128
$46$	−7.21520e7	−2.37595
$47$	−5.96424e6	−0.178285	−0.0891425	−	0.996019i	$-0.528413\pi$
$47$	−5.96424e6	−0.178285	−0.0891425	+	0.996019i	$0.528413\pi$
$48$	2.53729e7	0.689898
$49$	−1.97699e7	−0.489916
$50$	1.11474e8	2.52238
$51$	2.29292e7	0.474595
$52$	−6.00059e7	−1.13810
$53$	8.21208e7	1.42959	0.714795	−	0.699334i	$-0.246520\pi$
$53$	8.21208e7	1.42959	0.714795	+	0.699334i	$0.246520\pi$
$54$	−1.58378e7	−0.253469
$55$	−9.21914e7	−1.35850
$56$	−1.83692e7	−0.249599
$57$	3.67975e7	0.461722
$58$	1.99595e8	2.31592
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−7.26997e7	−0.724189
$61$	−6.81954e7	−0.630624	−0.315312	−	0.948988i	$-0.602109\pi$
$61$	−6.81954e7	−0.630624	−0.315312	+	0.948988i	$0.602109\pi$
$62$	1.35255e8	1.16250
$63$	2.97668e7	0.238067
$64$	−5.60462e7	−0.417577
$65$	−3.80661e8	−2.64502
$66$	9.32654e7	0.605025
$67$	−6.03338e7	−0.365784	−0.182892	−	0.983133i	$-0.558546\pi$
$67$	−6.03338e7	−0.365784	−0.182892	+	0.983133i	$0.558546\pi$
$68$	−1.06477e8	−0.603901
$69$	1.96107e8	1.04153
$70$	3.22626e8	1.60605
$71$	−7.46554e7	−0.348657	−0.174328	−	0.984688i	$-0.555775\pi$
$71$	−7.46554e7	−0.348657	−0.174328	+	0.984688i	$0.555775\pi$
$72$	−2.65642e7	−0.116493
$73$	1.87509e8	0.772805	0.386402	−	0.922330i	$-0.373718\pi$
$73$	1.87509e8	0.772805	0.386402	+	0.922330i	$0.373718\pi$
$74$	−5.22788e8	−2.02667
$75$	−3.02984e8	−1.10572
$76$	−1.70877e8	−0.587520
$77$	−1.75290e8	−0.568262
$78$	3.85096e8	1.17799
$79$	−1.18977e8	−0.343670	−0.171835	−	0.985126i	$-0.554970\pi$
$79$	−1.18977e8	−0.343670	−0.171835	+	0.985126i	$0.554970\pi$
$80$	−7.47449e8	−2.04022
$81$	4.30467e7	0.111111
$82$	−3.73207e8	−0.911564
$83$	−3.24381e8	−0.750246	−0.375123	−	0.926975i	$-0.622400\pi$
$83$	−3.24381e8	−0.750246	−0.375123	+	0.926975i	$0.622400\pi$
$84$	−1.38229e8	−0.302930
$85$	−6.75461e8	−1.40351
$86$	693134.	0.00136639
$87$	−5.42492e8	−1.01521
$88$	1.56431e8	0.278067
$89$	−2.07673e7	−0.0350852	−0.0175426	−	0.999846i	$-0.505584\pi$
$89$	−2.07673e7	−0.0350852	−0.0175426	+	0.999846i	$0.505584\pi$
$90$	4.66560e8	0.749576
$91$	−7.23777e8	−1.10642
$92$	−9.10665e8	−1.32530
$93$	−3.67620e8	−0.509595
$94$	−1.77745e8	−0.234812
$95$	−1.08400e9	−1.36544
$96$	5.88244e8	0.706866
$97$	−6.27270e8	−0.719419	−0.359709	−	0.933064i	$-0.617124\pi$
$97$	−6.27270e8	−0.719419	−0.359709	+	0.933064i	$0.617124\pi$
$98$	−5.89175e8	−0.645249
$99$	−2.53492e8	−0.265220
$100$	1.40697e9	1.40697
$101$	1.09342e9	1.04554	0.522771	−	0.852473i	$-0.324898\pi$
$101$	1.09342e9	1.04554	0.522771	+	0.852473i	$0.324898\pi$
$102$	6.83330e8	0.625071
$103$	−1.16308e8	−0.101822	−0.0509111	−	0.998703i	$-0.516213\pi$
$103$	−1.16308e8	−0.101822	−0.0509111	+	0.998703i	$0.516213\pi$
$104$	6.45907e8	0.541402
$105$	−8.76886e8	−0.704030
$106$	2.44734e9	1.88286
$107$	−1.88346e9	−1.38908	−0.694542	−	0.719452i	$-0.744393\pi$
$107$	−1.88346e9	−1.38908	−0.694542	+	0.719452i	$0.744393\pi$
$108$	−1.99897e8	−0.141384
$109$	2.51601e9	1.70723	0.853617	−	0.520902i	$-0.174404\pi$
$109$	2.51601e9	1.70723	0.853617	+	0.520902i	$0.174404\pi$
$110$	−2.74746e9	−1.78922
$111$	1.42092e9	0.888416
$112$	−1.42118e9	−0.853428
$113$	−6.06458e8	−0.349903	−0.174952	−	0.984577i	$-0.555977\pi$
$113$	−6.06458e8	−0.349903	−0.174952	+	0.984577i	$0.555977\pi$
$114$	1.09663e9	0.608117
$115$	−5.77701e9	−3.08008
$116$	2.51918e9	1.29181
$117$	−1.04668e9	−0.516388
$118$	−3.61118e8	−0.171467
$119$	−1.28430e9	−0.587090
$120$	7.82543e8	0.344503
$121$	−8.65191e8	−0.366925
$122$	−2.03234e9	−0.830571
$123$	1.01436e9	0.399595
$124$	1.70712e9	0.648437
$125$	4.26502e9	1.56252
$126$	8.87102e8	0.313549
$127$	2.93800e9	1.00216	0.501078	−	0.865402i	$-0.332937\pi$
$127$	2.93800e9	1.00216	0.501078	+	0.865402i	$0.332937\pi$
$128$	2.04801e9	0.674353
$129$	−1.88391e6	−0.000598973 0
$130$	−1.13443e10	−3.48365
$131$	−2.26879e9	−0.673089	−0.336545	−	0.941668i	$-0.609258\pi$
$131$	−2.26879e9	−0.673089	−0.336545	+	0.941668i	$0.609258\pi$
$132$	1.17715e9	0.337480
$133$	−2.06108e9	−0.571166
$134$	−1.79805e9	−0.481760
$135$	−1.26809e9	−0.328586
$136$	1.14612e9	0.287281
$137$	6.51841e9	1.58088	0.790441	−	0.612538i	$-0.209852\pi$
$137$	6.51841e9	1.58088	0.790441	+	0.612538i	$0.209852\pi$
$138$	5.84431e9	1.37176
$139$	5.94315e9	1.35036	0.675181	−	0.737652i	$-0.264066\pi$
$139$	5.94315e9	1.35036	0.675181	+	0.737652i	$0.264066\pi$
$140$	4.07202e9	0.895846
$141$	4.83104e8	0.102933
$142$	−2.22486e9	−0.459203
$143$	6.16364e9	1.23261
$144$	−2.05521e9	−0.398313
$145$	1.59810e10	3.00226
$146$	5.58809e9	1.01783
$147$	1.60136e9	0.282853
$148$	−6.59836e9	−1.13047
$149$	−1.09007e10	−1.81182	−0.905911	−	0.423469i	$-0.860812\pi$
$149$	−1.09007e10	−1.81182	−0.905911	+	0.423469i	$0.860812\pi$
$150$	−9.02943e9	−1.45630
$151$	7.24743e9	1.13446	0.567228	−	0.823561i	$-0.308016\pi$
$151$	7.24743e9	1.13446	0.567228	+	0.823561i	$0.308016\pi$
$152$	1.83933e9	0.279489
$153$	−1.85727e9	−0.274008
$154$	−5.22394e9	−0.748436
$155$	1.08295e10	1.50701
$156$	4.86048e9	0.657080
$157$	−1.21328e10	−1.59372	−0.796861	−	0.604163i	$-0.793507\pi$
$157$	−1.21328e10	−1.59372	−0.796861	+	0.604163i	$0.793507\pi$
$158$	−3.54573e9	−0.452635
$159$	−6.65179e9	−0.825375
$160$	−1.73288e10	−2.09040
$161$	−1.09842e10	−1.28841
$162$	1.28287e9	0.146340
$163$	1.76217e9	0.195525	0.0977626	−	0.995210i	$-0.468831\pi$
$163$	1.76217e9	0.195525	0.0977626	+	0.995210i	$0.468831\pi$
$164$	−4.71042e9	−0.508466
$165$	7.46750e9	0.784328
$166$	−9.66711e9	−0.988121
$167$	−1.15642e10	−1.15051	−0.575254	−	0.817975i	$-0.695097\pi$
$167$	−1.15642e10	−1.15051	−0.575254	+	0.817975i	$0.695097\pi$
$168$	1.48790e9	0.144106
$169$	1.48453e10	1.39991
$170$	−2.01299e10	−1.84851
$171$	−2.98059e9	−0.266576
$172$	8.74837e6	0.000762165 0
$173$	−1.84753e10	−1.56814	−0.784069	−	0.620674i	$-0.786859\pi$
$173$	−1.84753e10	−1.56814	−0.784069	+	0.620674i	$0.786859\pi$
$174$	−1.61672e10	−1.33710
$175$	1.69706e10	1.36781
$176$	1.21026e10	0.950765
$177$	9.81506e8	0.0751646
$178$	−6.18900e8	−0.0462094
$179$	−2.58461e9	−0.188173	−0.0940863	−	0.995564i	$-0.529993\pi$
$179$	−2.58461e9	−0.188173	−0.0940863	+	0.995564i	$0.529993\pi$
$180$	5.88867e9	0.418111
$181$	1.33589e10	0.925162	0.462581	−	0.886577i	$-0.346923\pi$
$181$	1.33589e10	0.925162	0.462581	+	0.886577i	$0.346923\pi$
$182$	−2.15698e10	−1.45722
$183$	5.52382e9	0.364091
$184$	9.80245e9	0.630455
$185$	−4.18582e10	−2.62729
$186$	−1.09557e10	−0.671169
$187$	1.09370e10	0.654051
$188$	−2.24340e9	−0.130977
$189$	−2.41111e9	−0.137448
$190$	−3.23050e10	−1.79837
$191$	2.64984e10	1.44069	0.720343	−	0.693618i	$-0.243984\pi$
$191$	2.64984e10	1.44069	0.720343	+	0.693618i	$0.243984\pi$
$192$	4.53974e9	0.241088
$193$	−1.36817e10	−0.709793	−0.354896	−	0.934906i	$-0.615484\pi$
$193$	−1.36817e10	−0.709793	−0.354896	+	0.934906i	$0.615484\pi$
$194$	−1.86937e10	−0.947519
$195$	3.08335e10	1.52710
$196$	−7.43627e9	−0.359917
$197$	−2.46152e9	−0.116441	−0.0582204	−	0.998304i	$-0.518543\pi$
$197$	−2.46152e9	−0.116441	−0.0582204	+	0.998304i	$0.518543\pi$
$198$	−7.55450e9	−0.349311
$199$	1.05143e10	0.475271	0.237635	−	0.971354i	$-0.423628\pi$
$199$	1.05143e10	0.475271	0.237635	+	0.971354i	$0.423628\pi$
$200$	−1.51447e10	−0.669309
$201$	4.88704e9	0.211185
$202$	3.25858e10	1.37704
$203$	3.03858e10	1.25585
$204$	8.62463e9	0.348662
$205$	−2.98816e10	−1.18171
$206$	−3.46618e9	−0.134106
$207$	−1.58846e10	−0.601327
$208$	4.99721e10	1.85116
$209$	1.75520e10	0.636310
$210$	−2.61327e10	−0.927251
$211$	−1.77059e10	−0.614961	−0.307481	−	0.951554i	$-0.599486\pi$
$211$	−1.77059e10	−0.614961	−0.307481	+	0.951554i	$0.599486\pi$
$212$	3.08891e10	1.05025
$213$	6.04708e9	0.201297
$214$	−5.61302e10	−1.82951
$215$	5.54973e7	0.00177133
$216$	2.15170e9	0.0672575
$217$	2.05909e10	0.630387
$218$	7.49813e10	2.24853
$219$	−1.51882e10	−0.446179
$220$	−3.46770e10	−0.998021
$221$	4.51592e10	1.27345
$222$	4.23458e10	1.17010
$223$	−4.47265e10	−1.21114	−0.605568	−	0.795794i	$-0.707054\pi$
$223$	−4.47265e10	−1.21114	−0.605568	+	0.795794i	$0.707054\pi$
$224$	−3.29484e10	−0.874417
$225$	2.45417e10	0.638385
$226$	−1.80735e10	−0.460844
$227$	−7.40431e10	−1.85084	−0.925419	−	0.378946i	$-0.876287\pi$
$227$	−7.40431e10	−1.85084	−0.925419	+	0.378946i	$0.876287\pi$
$228$	1.38411e10	0.339205
$229$	4.82154e10	1.15858	0.579290	−	0.815121i	$-0.303330\pi$
$229$	4.82154e10	1.15858	0.579290	+	0.815121i	$0.303330\pi$
$230$	−1.72165e11	−4.05666
$231$	1.41985e10	0.328086
$232$	−2.71166e10	−0.614525
$233$	−1.60111e10	−0.355894	−0.177947	−	0.984040i	$-0.556946\pi$
$233$	−1.60111e10	−0.355894	−0.177947	+	0.984040i	$0.556946\pi$
$234$	−3.11927e10	−0.680115
$235$	−1.42315e10	−0.304401
$236$	−4.55784e9	−0.0956435
$237$	9.63716e9	0.198418
$238$	−3.82743e10	−0.773234
$239$	−1.89080e10	−0.374848	−0.187424	−	0.982279i	$-0.560014\pi$
$239$	−1.89080e10	−0.374848	−0.187424	+	0.982279i	$0.560014\pi$
$240$	6.05433e10	1.17792
$241$	2.01485e10	0.384740	0.192370	−	0.981323i	$-0.438383\pi$
$241$	2.01485e10	0.384740	0.192370	+	0.981323i	$0.438383\pi$
$242$	−2.57842e10	−0.483263
$243$	−3.48678e9	−0.0641500
$244$	−2.56511e10	−0.463289
$245$	−4.71736e10	−0.836473
$246$	3.02297e10	0.526291
$247$	7.24728e10	1.23891
$248$	−1.83756e10	−0.308467
$249$	2.62749e10	0.433155
$250$	1.27105e11	2.05794
$251$	3.70895e10	0.589819	0.294909	−	0.955525i	$-0.404711\pi$
$251$	3.70895e10	0.589819	0.294909	+	0.955525i	$0.404711\pi$
$252$	1.11965e10	0.174897
$253$	9.35409e10	1.43535
$254$	8.75574e10	1.31990
$255$	5.47123e10	0.810316
$256$	8.97299e10	1.30574
$257$	2.31046e10	0.330370	0.165185	−	0.986263i	$-0.447178\pi$
$257$	2.31046e10	0.330370	0.165185	+	0.986263i	$0.447178\pi$
$258$	−5.61438e7	−0.000788884 0
$259$	−7.95879e10	−1.09900
$260$	−1.43182e11	−1.94317
$261$	4.39419e10	0.586133
$262$	−6.76137e10	−0.886500
$263$	−1.11735e11	−1.44009	−0.720043	−	0.693930i	$-0.755878\pi$
$263$	−1.11735e11	−1.44009	−0.720043	+	0.693930i	$0.755878\pi$
$264$	−1.26709e10	−0.160542
$265$	1.95952e11	2.44086
$266$	−6.14237e10	−0.752261
$267$	1.68215e9	0.0202565
$268$	−2.26941e10	−0.268724
$269$	2.85710e10	0.332691	0.166345	−	0.986068i	$-0.446803\pi$
$269$	2.85710e10	0.332691	0.166345	+	0.986068i	$0.446803\pi$
$270$	−3.77913e10	−0.432768
$271$	4.59693e10	0.517733	0.258866	−	0.965913i	$-0.416651\pi$
$271$	4.59693e10	0.517733	0.258866	+	0.965913i	$0.416651\pi$
$272$	8.86726e10	0.982267
$273$	5.86259e10	0.638790
$274$	1.94260e11	2.08212
$275$	−1.44520e11	−1.52381
$276$	7.37638e10	0.765161
$277$	−3.17922e10	−0.324460	−0.162230	−	0.986753i	$-0.551869\pi$
$277$	−3.17922e10	−0.324460	−0.162230	+	0.986753i	$0.551869\pi$
$278$	1.77116e11	1.77851
$279$	2.97772e10	0.294215
$280$	−4.38314e10	−0.426162
$281$	4.11361e9	0.0393590	0.0196795	−	0.999806i	$-0.493735\pi$
$281$	4.11361e9	0.0393590	0.0196795	+	0.999806i	$0.493735\pi$
$282$	1.43973e10	0.135569
$283$	−6.70679e10	−0.621550	−0.310775	−	0.950484i	$-0.600588\pi$
$283$	−6.70679e10	−0.621550	−0.310775	+	0.950484i	$0.600588\pi$
$284$	−2.80810e10	−0.256141
$285$	8.78039e10	0.788337
$286$	1.83687e11	1.62342
$287$	−5.68160e10	−0.494313
$288$	−4.76478e10	−0.408109
$289$	−3.84555e10	−0.324278
$290$	4.76261e11	3.95416
$291$	5.08089e10	0.415357
$292$	7.05300e10	0.567742
$293$	2.36249e11	1.87269	0.936344	−	0.351084i	$-0.114187\pi$
$293$	2.36249e11	1.87269	0.936344	+	0.351084i	$0.114187\pi$
$294$	4.77232e10	0.372535
$295$	−2.89137e10	−0.222282
$296$	7.10251e10	0.537773
$297$	2.05329e10	0.153125
$298$	−3.24859e11	−2.38628
$299$	3.86233e11	2.79466
$300$	−1.13965e11	−0.812316
$301$	1.05521e8	0.000740950 0
$302$	2.15986e11	1.49415
$303$	−8.85671e10	−0.603644
$304$	1.42304e11	0.955624
$305$	−1.62724e11	−1.07672
$306$	−5.53497e10	−0.360885
$307$	2.97016e11	1.90835	0.954174	−	0.299252i	$-0.0967371\pi$
$307$	2.97016e11	1.90835	0.954174	+	0.299252i	$0.0967371\pi$
$308$	−6.59338e10	−0.417475
$309$	9.42095e9	0.0587870
$310$	3.22739e11	1.98483
$311$	5.87677e10	0.356219	0.178109	−	0.984011i	$-0.443002\pi$
$311$	5.87677e10	0.356219	0.178109	+	0.984011i	$0.443002\pi$
$312$	−5.23185e10	−0.312579
$313$	−6.36206e10	−0.374670	−0.187335	−	0.982296i	$-0.559985\pi$
$313$	−6.36206e10	−0.374670	−0.187335	+	0.982296i	$0.559985\pi$
$314$	−3.61578e11	−2.09903
$315$	7.10278e10	0.406472
$316$	−4.47523e10	−0.252478
$317$	4.71059e10	0.262004	0.131002	−	0.991382i	$-0.458181\pi$
$317$	4.71059e10	0.262004	0.131002	+	0.991382i	$0.458181\pi$
$318$	−1.98235e11	−1.08707
$319$	−2.58763e11	−1.39909
$320$	−1.33734e11	−0.712963
$321$	1.52560e11	0.801988
$322$	−3.27349e11	−1.69691
$323$	1.28599e11	0.657394
$324$	1.61917e10	0.0816280
$325$	−5.96728e11	−2.96689
$326$	5.25156e10	0.257519
$327$	−2.03797e11	−0.985671
$328$	5.07032e10	0.241882
$329$	−2.70594e10	−0.127332
$330$	2.22544e11	1.03301
$331$	2.06454e11	0.945362	0.472681	−	0.881234i	$-0.343286\pi$
$331$	2.06454e11	0.945362	0.472681	+	0.881234i	$0.343286\pi$
$332$	−1.22013e11	−0.551170
$333$	−1.15095e11	−0.512927
$334$	−3.44631e11	−1.51529
$335$	−1.43965e11	−0.624533
$336$	1.15115e11	0.492727
$337$	−1.31797e11	−0.556636	−0.278318	−	0.960489i	$-0.589777\pi$
$337$	−1.31797e11	−0.556636	−0.278318	+	0.960489i	$0.589777\pi$
$338$	4.42416e11	1.84377
$339$	4.91231e10	0.202017
$340$	−2.54069e11	−1.03109
$341$	−1.75351e11	−0.702285
$342$	−8.88268e10	−0.351096
$343$	−2.72776e11	−1.06410
$344$	−9.41680e7	−0.000362569 0
$345$	4.67938e11	1.77829
$346$	−5.50596e11	−2.06533
$347$	−9.11544e10	−0.337517	−0.168758	−	0.985657i	$-0.553976\pi$
$347$	−9.11544e10	−0.337517	−0.168758	+	0.985657i	$0.553976\pi$
$348$	−2.04054e11	−0.745827
$349$	1.77044e10	0.0638804	0.0319402	−	0.999490i	$-0.489831\pi$
$349$	1.77044e10	0.0638804	0.0319402	+	0.999490i	$0.489831\pi$
$350$	5.05752e11	1.80149
$351$	8.47808e10	0.298137
$352$	2.80587e11	0.974148
$353$	5.36706e11	1.83972	0.919858	−	0.392253i	$-0.128304\pi$
$353$	5.36706e11	1.83972	0.919858	+	0.392253i	$0.128304\pi$
$354$	2.92506e10	0.0989964
$355$	−1.78138e11	−0.595291
$356$	−7.81143e9	−0.0257754
$357$	1.04028e11	0.338957
$358$	−7.70258e10	−0.247835
$359$	−2.70489e11	−0.859457	−0.429728	−	0.902958i	$-0.641391\pi$
$359$	−2.70489e11	−0.859457	−0.429728	+	0.902958i	$0.641391\pi$
$360$	−6.33860e10	−0.198899
$361$	−1.16309e11	−0.360437
$362$	3.98119e11	1.21850
$363$	7.00805e10	0.211844
$364$	−2.72243e11	−0.812830
$365$	4.47423e11	1.31947
$366$	1.64619e11	0.479530
$367$	−5.34031e11	−1.53663	−0.768315	−	0.640072i	$-0.778905\pi$
$367$	−5.34031e11	−1.53663	−0.768315	+	0.640072i	$0.778905\pi$
$368$	7.58390e11	2.15565
$369$	−8.21634e10	−0.230706
$370$	−1.24745e12	−3.46030
$371$	3.72576e11	1.02102
$372$	−1.38277e11	−0.374375
$373$	−2.50709e11	−0.670625	−0.335313	−	0.942107i	$-0.608842\pi$
$373$	−2.50709e11	−0.670625	−0.335313	+	0.942107i	$0.608842\pi$
$374$	3.25942e11	0.861425
$375$	−3.45467e11	−0.902122
$376$	2.41481e10	0.0623071
$377$	−1.06844e12	−2.72405
$378$	−7.18552e10	−0.181028
$379$	−9.62945e10	−0.239731	−0.119866	−	0.992790i	$-0.538246\pi$
$379$	−9.62945e10	−0.239731	−0.119866	+	0.992790i	$0.538246\pi$
$380$	−4.07737e11	−1.00312
$381$	−2.37978e11	−0.578595
$382$	7.89697e11	1.89747
$383$	−2.04722e11	−0.486150	−0.243075	−	0.970007i	$-0.578156\pi$
$383$	−2.04722e11	−0.486150	−0.243075	+	0.970007i	$0.578156\pi$
$384$	−1.65889e11	−0.389338
$385$	−4.18266e11	−0.970240
$386$	−4.07737e11	−0.934841
$387$	1.52597e8	0.000345817 0
$388$	−2.35942e11	−0.528522
$389$	−2.39385e11	−0.530059	−0.265030	−	0.964240i	$-0.585382\pi$
$389$	−2.39385e11	−0.530059	−0.265030	+	0.964240i	$0.585382\pi$
$390$	9.18892e11	2.01129
$391$	6.85348e11	1.48291
$392$	8.00444e10	0.171216
$393$	1.83772e11	0.388608
$394$	−7.33574e10	−0.153360
$395$	−2.83896e11	−0.586777
$396$	−9.53490e10	−0.194844
$397$	7.87958e11	1.59201	0.796005	−	0.605290i	$-0.206943\pi$
$397$	7.87958e11	1.59201	0.796005	+	0.605290i	$0.206943\pi$
$398$	3.13344e11	0.625961
$399$	1.66948e11	0.329763
$400$	−1.17171e12	−2.28849
$401$	2.39918e11	0.463355	0.231678	−	0.972793i	$-0.425579\pi$
$401$	2.39918e11	0.463355	0.231678	+	0.972793i	$0.425579\pi$
$402$	1.45642e11	0.278144
$403$	−7.24030e11	−1.36736
$404$	4.11281e11	0.768109
$405$	1.02715e11	0.189709
$406$	9.05548e11	1.65403
$407$	6.77765e11	1.22435
$408$	−9.28360e10	−0.165862
$409$	6.11043e11	1.07973	0.539867	−	0.841750i	$-0.318474\pi$
$409$	6.11043e11	1.07973	0.539867	+	0.841750i	$0.318474\pi$
$410$	−8.90523e11	−1.55639
$411$	−5.27992e11	−0.912722
$412$	−4.37483e10	−0.0748038
$413$	−5.49756e10	−0.0929812
$414$	−4.73389e11	−0.791984
$415$	−7.74018e11	−1.28096
$416$	1.15855e12	1.89668
$417$	−4.81395e11	−0.779632
$418$	5.23080e11	0.838060
$419$	−6.22265e11	−0.986308	−0.493154	−	0.869942i	$-0.664156\pi$
$419$	−6.22265e11	−0.986308	−0.493154	+	0.869942i	$0.664156\pi$
$420$	−3.29833e11	−0.517217
$421$	−7.96680e11	−1.23599	−0.617994	−	0.786183i	$-0.712054\pi$
$421$	−7.96680e11	−1.23599	−0.617994	+	0.786183i	$0.712054\pi$
$422$	−5.27667e11	−0.809942
$423$	−3.91314e10	−0.0594284
$424$	−3.32492e11	−0.499614
$425$	−1.05886e12	−1.57430
$426$	1.80213e11	0.265121
$427$	−3.09398e11	−0.450393
$428$	−7.08446e11	−1.02049
$429$	−4.99255e11	−0.711646
$430$	1.65391e9	0.00233295
$431$	1.12004e12	1.56346	0.781729	−	0.623619i	$-0.214338\pi$
$431$	1.12004e12	1.56346	0.781729	+	0.623619i	$0.214338\pi$
$432$	1.66472e11	0.229966
$433$	9.65636e11	1.32013	0.660067	−	0.751207i	$-0.270528\pi$
$433$	9.65636e11	1.32013	0.660067	+	0.751207i	$0.270528\pi$
$434$	6.13645e11	0.830259
$435$	−1.29446e12	−1.73336
$436$	9.46375e11	1.25422
$437$	1.09987e12	1.44269
$438$	−4.52636e11	−0.587645
$439$	−6.43221e11	−0.826552	−0.413276	−	0.910606i	$-0.635615\pi$
$439$	−6.43221e11	−0.826552	−0.413276	+	0.910606i	$0.635615\pi$
$440$	3.73266e11	0.474767
$441$	−1.29710e11	−0.163305
$442$	1.34582e12	1.67721
$443$	5.95044e11	0.734061	0.367030	−	0.930209i	$-0.380374\pi$
$443$	5.95044e11	0.734061	0.367030	+	0.930209i	$0.380374\pi$
$444$	5.34467e11	0.652676
$445$	−4.95536e10	−0.0599039
$446$	−1.33293e12	−1.59514
$447$	8.82955e11	1.04606
$448$	−2.54278e11	−0.298234
$449$	−7.83154e10	−0.0909366	−0.0454683	−	0.998966i	$-0.514478\pi$
$449$	−7.83154e10	−0.0909366	−0.0454683	+	0.998966i	$0.514478\pi$
$450$	7.31384e11	0.840793
$451$	4.83841e11	0.550691
$452$	−2.28114e11	−0.257057
$453$	−5.87042e11	−0.654979
$454$	−2.20661e12	−2.43767
$455$	−1.72703e12	−1.88908
$456$	−1.48986e11	−0.161363
$457$	−1.38358e11	−0.148382	−0.0741909	−	0.997244i	$-0.523637\pi$
$457$	−1.38358e11	−0.148382	−0.0741909	+	0.997244i	$0.523637\pi$
$458$	1.43690e12	1.52592
$459$	1.50439e11	0.158198
$460$	−2.17297e12	−2.26279
$461$	1.35849e12	1.40088	0.700442	−	0.713710i	$-0.252986\pi$
$461$	1.35849e12	1.40088	0.700442	+	0.713710i	$0.252986\pi$
$462$	4.23139e11	0.432110
$463$	−1.12512e12	−1.13785	−0.568924	−	0.822390i	$-0.692640\pi$
$463$	−1.12512e12	−1.13785	−0.568924	+	0.822390i	$0.692640\pi$
$464$	−2.09794e12	−2.10118
$465$	−8.77192e11	−0.870074
$466$	−4.77159e11	−0.468734
$467$	−2.51270e11	−0.244464	−0.122232	−	0.992502i	$-0.539005\pi$
$467$	−2.51270e11	−0.244464	−0.122232	+	0.992502i	$0.539005\pi$
$468$	−3.93699e11	−0.379365
$469$	−2.73730e11	−0.261243
$470$	−4.24124e11	−0.400915
$471$	9.82756e11	0.920135
$472$	4.90609e10	0.0454984
$473$	−8.98608e8	−0.000825458 0
$474$	2.87204e11	0.261329
$475$	−1.69929e12	−1.53160
$476$	−4.83079e11	−0.431307
$477$	5.38795e11	0.476530
$478$	−5.63491e11	−0.493698
$479$	−9.84792e11	−0.854742	−0.427371	−	0.904076i	$-0.640560\pi$
$479$	−9.84792e11	−0.854742	−0.427371	+	0.904076i	$0.640560\pi$
$480$	1.40363e12	1.20689
$481$	2.79851e12	2.38382
$482$	6.00461e11	0.506726
$483$	8.89722e11	0.743862
$484$	−3.25434e11	−0.269562
$485$	−1.49675e12	−1.22832
$486$	−1.03912e11	−0.0844896
$487$	6.52730e11	0.525839	0.262920	−	0.964818i	$-0.415315\pi$
$487$	6.52730e11	0.525839	0.262920	+	0.964818i	$0.415315\pi$
$488$	2.76110e11	0.220391
$489$	−1.42736e11	−0.112887
$490$	−1.40586e12	−1.10169
$491$	−1.94676e12	−1.51163	−0.755816	−	0.654784i	$-0.772760\pi$
$491$	−1.94676e12	−1.51163	−0.755816	+	0.654784i	$0.772760\pi$
$492$	3.81544e11	0.293563
$493$	−1.89589e12	−1.44544
$494$	2.15981e12	1.63172
$495$	−6.04868e11	−0.452832
$496$	−1.42167e12	−1.05471
$497$	−3.38706e11	−0.249012
$498$	7.83036e11	0.570492
$499$	1.39758e12	1.00908	0.504540	−	0.863388i	$-0.331662\pi$
$499$	1.39758e12	1.00908	0.504540	+	0.863388i	$0.331662\pi$
$500$	1.60425e12	1.14791
$501$	9.36696e11	0.664246
$502$	1.10533e12	0.776828
$503$	1.86980e12	1.30238	0.651191	−	0.758914i	$-0.274270\pi$
$503$	1.86980e12	1.30238	0.651191	+	0.758914i	$0.274270\pi$
$504$	−1.20520e11	−0.0831998
$505$	2.60906e12	1.78514
$506$	2.78768e12	1.89045
$507$	−1.20247e12	−0.808238
$508$	1.10510e12	0.736235
$509$	2.58542e12	1.70726	0.853632	−	0.520876i	$-0.174395\pi$
$509$	2.58542e12	1.70726	0.853632	+	0.520876i	$0.174395\pi$
$510$	1.63052e12	1.06724
$511$	8.50716e11	0.551939
$512$	1.62552e12	1.04539
$513$	2.41428e11	0.153907
$514$	6.88558e11	0.435117
$515$	−2.77527e11	−0.173849
$516$	−7.08618e8	−0.000440036 0
$517$	2.30436e11	0.141854
$518$	−2.37185e12	−1.44745
$519$	1.49650e12	0.905365
$520$	1.54122e12	0.924381
$521$	−6.28243e11	−0.373558	−0.186779	−	0.982402i	$-0.559805\pi$
$521$	−6.28243e11	−0.373558	−0.186779	+	0.982402i	$0.559805\pi$
$522$	1.30954e12	0.771973
$523$	9.72209e10	0.0568201	0.0284101	−	0.999596i	$-0.490956\pi$
$523$	9.72209e10	0.0568201	0.0284101	+	0.999596i	$0.490956\pi$
$524$	−8.53385e11	−0.494486
$525$	−1.37462e12	−0.789704
$526$	−3.32989e12	−1.89668
$527$	−1.28475e12	−0.725555
$528$	−9.80314e11	−0.548924
$529$	4.06042e12	2.25434
$530$	5.83970e12	3.21476
$531$	−7.95020e10	−0.0433963
$532$	−7.75258e11	−0.419608
$533$	1.99779e12	1.07221
$534$	5.01309e10	0.0266790
$535$	−4.49419e12	−2.37170
$536$	2.44280e11	0.127834
$537$	2.09353e11	0.108642
$538$	8.51465e11	0.438174
$539$	7.63832e11	0.389806
$540$	−4.76982e11	−0.241396
$541$	−2.95963e12	−1.48542	−0.742710	−	0.669613i	$-0.766460\pi$
$541$	−2.95963e12	−1.48542	−0.742710	+	0.669613i	$0.766460\pi$
$542$	1.36996e12	0.681886
$543$	−1.08207e12	−0.534142
$544$	2.05578e12	1.00643
$545$	6.00355e12	2.91490
$546$	1.74715e12	0.841325
$547$	−7.61194e10	−0.0363540	−0.0181770	−	0.999835i	$-0.505786\pi$
$547$	−7.61194e10	−0.0363540	−0.0181770	+	0.999835i	$0.505786\pi$
$548$	2.45185e12	1.16140
$549$	−4.47430e11	−0.210208
$550$	−4.30695e12	−2.00696
$551$	−3.04257e12	−1.40624
$552$	−7.93998e11	−0.363994
$553$	−5.39792e11	−0.245450
$554$	−9.47461e11	−0.427334
$555$	3.39051e12	1.51687
$556$	2.23547e12	0.992046
$557$	−2.53535e11	−0.111607	−0.0558034	−	0.998442i	$-0.517772\pi$
$557$	−2.53535e11	−0.111607	−0.0558034	+	0.998442i	$0.517772\pi$
$558$	8.87411e11	0.387499
$559$	−3.71038e9	−0.00160718
$560$	−3.39112e12	−1.45713
$561$	−8.85898e11	−0.377616
$562$	1.22592e11	0.0518383
$563$	3.97944e12	1.66930	0.834650	−	0.550781i	$-0.185670\pi$
$563$	3.97944e12	1.66930	0.834650	+	0.550781i	$0.185670\pi$
$564$	1.81715e11	0.0756199
$565$	−1.44709e12	−0.597419
$566$	−1.99874e12	−0.818619
$567$	1.95300e11	0.0793558
$568$	3.02265e11	0.121849
$569$	−4.78419e12	−1.91339	−0.956695	−	0.291093i	$-0.905981\pi$
$569$	−4.78419e12	−1.91339	−0.956695	+	0.291093i	$0.905981\pi$
$570$	2.61671e12	1.03829
$571$	−3.60842e12	−1.42054	−0.710272	−	0.703927i	$-0.751428\pi$
$571$	−3.60842e12	−1.42054	−0.710272	+	0.703927i	$0.751428\pi$
$572$	2.31840e12	0.905537
$573$	−2.14637e12	−0.831780
$574$	−1.69321e12	−0.651040
$575$	−9.05610e12	−3.45490
$576$	−3.67719e11	−0.139192
$577$	−2.72207e12	−1.02237	−0.511185	−	0.859471i	$-0.670793\pi$
$577$	−2.72207e12	−1.02237	−0.511185	+	0.859471i	$0.670793\pi$
$578$	−1.14604e12	−0.427094
$579$	1.10822e12	0.409799
$580$	6.01112e12	2.20561
$581$	−1.47169e12	−0.535827
$582$	1.51419e12	0.547050
$583$	−3.17284e12	−1.13747
$584$	−7.59189e11	−0.270080
$585$	−2.49752e12	−0.881672
$586$	7.04062e12	2.46645
$587$	−1.09398e12	−0.380311	−0.190155	−	0.981754i	$-0.560899\pi$
$587$	−1.09398e12	−0.380311	−0.190155	+	0.981754i	$0.560899\pi$
$588$	6.02338e11	0.207798
$589$	−2.06180e12	−0.705875
$590$	−8.61678e11	−0.292760
$591$	1.99383e11	0.0672271
$592$	5.49503e12	1.83875
$593$	−3.44381e12	−1.14365	−0.571825	−	0.820376i	$-0.693764\pi$
$593$	−3.44381e12	−1.14365	−0.571825	+	0.820376i	$0.693764\pi$
$594$	6.11914e11	0.201675
$595$	−3.06452e12	−1.00239
$596$	−4.10020e12	−1.33106
$597$	−8.51657e11	−0.274398
$598$	1.15104e13	3.68074
$599$	5.37863e12	1.70707	0.853535	−	0.521036i	$-0.174454\pi$
$599$	5.37863e12	1.70707	0.853535	+	0.521036i	$0.174454\pi$
$600$	1.22672e12	0.386426
$601$	−3.41951e12	−1.06912	−0.534562	−	0.845129i	$-0.679524\pi$
$601$	−3.41951e12	−1.06912	−0.534562	+	0.845129i	$0.679524\pi$
$602$	3.14470e9	0.000975877 0
$603$	−3.95850e11	−0.121928
$604$	2.72606e12	0.833431
$605$	−2.06447e12	−0.626482
$606$	−2.63945e12	−0.795036
$607$	−4.54496e12	−1.35888	−0.679440	−	0.733731i	$-0.737777\pi$
$607$	−4.54496e12	−1.35888	−0.679440	+	0.733731i	$0.737777\pi$
$608$	3.29917e12	0.979127
$609$	−2.46125e12	−0.725066
$610$	−4.84944e12	−1.41810
$611$	9.51476e11	0.276193
$612$	−6.98595e11	−0.201300
$613$	4.16258e12	1.19067	0.595334	−	0.803478i	$-0.297020\pi$
$613$	4.16258e12	1.19067	0.595334	+	0.803478i	$0.297020\pi$
$614$	8.85159e12	2.51341
$615$	2.42041e12	0.682262
$616$	7.09715e11	0.198596
$617$	−3.97173e12	−1.10331	−0.551653	−	0.834074i	$-0.686003\pi$
$617$	−3.97173e12	−1.10331	−0.551653	+	0.834074i	$0.686003\pi$
$618$	2.80760e11	0.0774261
$619$	−5.61410e12	−1.53700	−0.768498	−	0.639853i	$-0.778995\pi$
$619$	−5.61410e12	−1.53700	−0.768498	+	0.639853i	$0.778995\pi$
$620$	4.07344e12	1.10713
$621$	1.28665e12	0.347176
$622$	1.75138e12	0.469162
$623$	−9.42196e10	−0.0250579
$624$	−4.04774e12	−1.06877
$625$	2.87119e12	0.752666
$626$	−1.89600e12	−0.493463
$627$	−1.42171e12	−0.367374
$628$	−4.56365e12	−1.17083
$629$	4.96579e12	1.26491
$630$	2.11675e12	0.535349
$631$	−1.35635e12	−0.340596	−0.170298	−	0.985393i	$-0.554473\pi$
$631$	−1.35635e12	−0.340596	−0.170298	+	0.985393i	$0.554473\pi$
$632$	4.81717e11	0.120106
$633$	1.43418e12	0.355048
$634$	1.40384e12	0.345076
$635$	7.01048e12	1.71106
$636$	−2.50201e12	−0.606363
$637$	3.15389e12	0.758959
$638$	−7.71159e12	−1.84268
$639$	−4.89814e11	−0.116219
$640$	4.88684e12	1.15138
$641$	7.66190e12	1.79257	0.896283	−	0.443482i	$-0.146257\pi$
$641$	7.66190e12	1.79257	0.896283	+	0.443482i	$0.146257\pi$
$642$	4.54654e12	1.05627
$643$	−2.08161e10	−0.00480231	−0.00240115	−	0.999997i	$-0.500764\pi$
$643$	−2.08161e10	−0.00480231	−0.00240115	+	0.999997i	$0.500764\pi$
$644$	−4.13162e12	−0.946530
$645$	−4.49528e9	−0.00102268
$646$	3.83246e12	0.865828
$647$	3.70962e12	0.832262	0.416131	−	0.909305i	$-0.363386\pi$
$647$	3.70962e12	0.832262	0.416131	+	0.909305i	$0.363386\pi$
$648$	−1.74288e11	−0.0388311
$649$	4.68169e11	0.103586
$650$	−1.77835e13	−3.90758
$651$	−1.66787e12	−0.363954
$652$	6.62825e11	0.143643
$653$	1.71707e12	0.369555	0.184777	−	0.982780i	$-0.440844\pi$
$653$	1.71707e12	0.369555	0.184777	+	0.982780i	$0.440844\pi$
$654$	−6.07349e12	−1.29819
$655$	−5.41364e12	−1.14922
$656$	3.92278e12	0.827040
$657$	1.23025e12	0.257602
$658$	−8.06415e11	−0.167704
$659$	−8.75824e12	−1.80897	−0.904487	−	0.426502i	$-0.859746\pi$
$659$	−8.75824e12	−1.80897	−0.904487	+	0.426502i	$0.859746\pi$
$660$	2.80884e12	0.576208
$661$	−1.83195e12	−0.373256	−0.186628	−	0.982431i	$-0.559756\pi$
$661$	−1.83195e12	−0.373256	−0.186628	+	0.982431i	$0.559756\pi$
$662$	6.15269e12	1.24510
$663$	−3.65790e12	−0.735226
$664$	1.31336e12	0.262196
$665$	−4.91803e12	−0.975200
$666$	−3.43001e12	−0.675557
$667$	−1.62149e13	−3.17212
$668$	−4.34976e12	−0.845223
$669$	3.62285e12	0.699250
$670$	−4.29040e12	−0.822548
$671$	2.63481e12	0.501762
$672$	2.66882e12	0.504845
$673$	8.48178e12	1.59375	0.796873	−	0.604147i	$-0.206486\pi$
$673$	8.48178e12	1.59375	0.796873	+	0.604147i	$0.206486\pi$
$674$	−3.92778e12	−0.733124
$675$	−1.98788e12	−0.368572
$676$	5.58395e12	1.02845
$677$	−3.79185e12	−0.693748	−0.346874	−	0.937912i	$-0.612757\pi$
$677$	−3.79185e12	−0.693748	−0.346874	+	0.937912i	$0.612757\pi$
$678$	1.46395e12	0.266068
$679$	−2.84588e12	−0.513810
$680$	2.73481e12	0.490498
$681$	5.99749e12	1.06858
$682$	−5.22576e12	−0.924953
$683$	6.53274e12	1.14869	0.574344	−	0.818614i	$-0.305257\pi$
$683$	6.53274e12	1.14869	0.574344	+	0.818614i	$0.305257\pi$
$684$	−1.12113e12	−0.195840
$685$	1.55538e13	2.69917
$686$	−8.12919e12	−1.40149
$687$	−3.90545e12	−0.668907
$688$	−7.28553e9	−0.00123969
$689$	−1.31007e13	−2.21467
$690$	1.39453e13	2.34211
$691$	1.88280e12	0.314162	0.157081	−	0.987586i	$-0.449792\pi$
$691$	1.88280e12	0.314162	0.157081	+	0.987586i	$0.449792\pi$
$692$	−6.94933e12	−1.15204
$693$	−1.15008e12	−0.189421
$694$	−2.71656e12	−0.444530
$695$	1.41812e13	2.30558
$696$	2.19645e12	0.354796
$697$	3.54497e12	0.568938
$698$	5.27622e11	0.0841344
$699$	1.29690e12	0.205475
$700$	6.38334e12	1.00486
$701$	3.95934e12	0.619287	0.309643	−	0.950853i	$-0.399790\pi$
$701$	3.95934e12	0.619287	0.309643	+	0.950853i	$0.399790\pi$
$702$	2.52661e12	0.392665
$703$	7.96925e12	1.23060
$704$	2.16541e12	0.332249
$705$	1.15275e12	0.175746
$706$	1.59948e13	2.42302
$707$	4.96078e12	0.746728
$708$	3.69185e11	0.0552198
$709$	−4.42959e12	−0.658347	−0.329174	−	0.944269i	$-0.606770\pi$
$709$	−4.42959e12	−0.658347	−0.329174	+	0.944269i	$0.606770\pi$
$710$	−5.30882e12	−0.784035
$711$	−7.80610e11	−0.114557
$712$	8.40827e10	0.0122616
$713$	−1.09881e13	−1.59227
$714$	3.10022e12	0.446427
$715$	1.47073e13	2.10453
$716$	−9.72180e11	−0.138241
$717$	1.53155e12	0.216419
$718$	−8.06103e12	−1.13196
$719$	−1.03766e13	−1.44803	−0.724014	−	0.689786i	$-0.757705\pi$
$719$	−1.03766e13	−1.44803	−0.724014	+	0.689786i	$0.757705\pi$
$720$	−4.90401e12	−0.680073
$721$	−5.27681e11	−0.0727216
$722$	−3.46620e12	−0.474718
$723$	−1.63203e12	−0.222129
$724$	5.02485e12	0.679672
$725$	2.50520e13	3.36761
$726$	2.08852e12	0.279012
$727$	−1.05595e13	−1.40197	−0.700985	−	0.713176i	$-0.747256\pi$
$727$	−1.05595e13	−1.40197	−0.700985	+	0.713176i	$0.747256\pi$
$728$	2.93044e12	0.386670
$729$	2.82430e11	0.0370370
$730$	1.33340e13	1.73783
$731$	−6.58385e9	−0.000852809 0
$732$	2.07774e12	0.267480
$733$	7.65386e12	0.979292	0.489646	−	0.871921i	$-0.337126\pi$
$733$	7.65386e12	0.979292	0.489646	+	0.871921i	$0.337126\pi$
$734$	−1.59150e13	−2.02384
$735$	3.82107e12	0.482938
$736$	1.75825e13	2.20866
$737$	2.33107e12	0.291039
$738$	−2.44861e12	−0.303855
$739$	−1.13401e13	−1.39867	−0.699335	−	0.714794i	$-0.746520\pi$
$739$	−1.13401e13	−1.39867	−0.699335	+	0.714794i	$0.746520\pi$
$740$	−1.57446e13	−1.93014
$741$	−5.87030e12	−0.715284
$742$	1.11034e13	1.34474
$743$	−1.41428e13	−1.70249	−0.851245	−	0.524768i	$-0.824152\pi$
$743$	−1.41428e13	−1.70249	−0.851245	+	0.524768i	$0.824152\pi$
$744$	1.48842e12	0.178093
$745$	−2.60105e13	−3.09347
$746$	−7.47155e12	−0.883255
$747$	−2.12826e12	−0.250082
$748$	4.11387e12	0.480499
$749$	−8.54511e12	−0.992086
$750$	−1.02955e13	−1.18815
$751$	2.00665e12	0.230193	0.115097	−	0.993354i	$-0.463282\pi$
$751$	2.00665e12	0.230193	0.115097	+	0.993354i	$0.463282\pi$
$752$	1.86828e12	0.213040
$753$	−3.00425e12	−0.340532
$754$	−3.18414e13	−3.58774
$755$	1.72934e13	1.93695
$756$	−9.06919e11	−0.100977
$757$	−2.68492e12	−0.297166	−0.148583	−	0.988900i	$-0.547471\pi$
$757$	−2.68492e12	−0.297166	−0.148583	+	0.988900i	$0.547471\pi$
$758$	−2.86974e12	−0.315741
$759$	−7.57681e12	−0.828702
$760$	4.38890e12	0.477194
$761$	1.32884e13	1.43629	0.718145	−	0.695894i	$-0.244992\pi$
$761$	1.32884e13	1.43629	0.718145	+	0.695894i	$0.244992\pi$
$762$	−7.09215e12	−0.762045
$763$	1.14150e13	1.21931
$764$	9.96715e12	1.05840
$765$	−4.43170e12	−0.467836
$766$	−6.10107e12	−0.640290
$767$	1.93308e12	0.201684
$768$	−7.26812e12	−0.753870
$769$	9.49050e12	0.978635	0.489317	−	0.872106i	$-0.337246\pi$
$769$	9.49050e12	0.978635	0.489317	+	0.872106i	$0.337246\pi$
$770$	−1.24650e13	−1.27787
$771$	−1.87148e12	−0.190739
$772$	−5.14625e12	−0.521450
$773$	−1.65964e13	−1.67188	−0.835940	−	0.548821i	$-0.815077\pi$
$773$	−1.65964e13	−1.67188	−0.835940	+	0.548821i	$0.815077\pi$
$774$	4.54765e9	0.000455463 0
$775$	1.69765e13	1.69040
$776$	2.53970e12	0.251423
$777$	6.44662e12	0.634508
$778$	−7.13409e12	−0.698121
$779$	5.68906e12	0.553506
$780$	1.15978e13	1.12189
$781$	2.88440e12	0.277412
$782$	2.04245e13	1.95309
$783$	−3.55929e12	−0.338404
$784$	6.19283e12	0.585419
$785$	−2.89505e13	−2.72109
$786$	5.47671e12	0.511821
$787$	−1.57061e13	−1.45943	−0.729715	−	0.683752i	$-0.760347\pi$
$787$	−1.57061e13	−1.45943	−0.729715	+	0.683752i	$0.760347\pi$
$788$	−9.25879e11	−0.0855434
$789$	9.05053e12	0.831434
$790$	−8.46060e12	−0.772822
$791$	−2.75146e12	−0.249902
$792$	1.02634e12	0.0926891
$793$	1.08792e13	0.976940
$794$	2.34825e13	2.09678
$795$	−1.58721e13	−1.40923
$796$	3.95486e12	0.349158
$797$	−9.19907e12	−0.807572	−0.403786	−	0.914853i	$-0.632306\pi$
$797$	−9.19907e12	−0.807572	−0.403786	+	0.914853i	$0.632306\pi$
$798$	4.97532e12	0.434318
$799$	1.68834e12	0.146554
$800$	−2.71648e13	−2.34478
$801$	−1.36254e11	−0.0116951
$802$	7.14998e12	0.610267
$803$	−7.24465e12	−0.614890
$804$	1.83822e12	0.155148
$805$	−2.62099e13	−2.19980
$806$	−2.15773e13	−1.80090
$807$	−2.31425e12	−0.192079
$808$	−4.42705e12	−0.365396
$809$	−4.51270e12	−0.370397	−0.185199	−	0.982701i	$-0.559293\pi$
$809$	−4.51270e12	−0.370397	−0.185199	+	0.982701i	$0.559293\pi$
$810$	3.06110e12	0.249859
$811$	1.23066e13	0.998954	0.499477	−	0.866327i	$-0.333526\pi$
$811$	1.23066e13	0.998954	0.499477	+	0.866327i	$0.333526\pi$
$812$	1.14294e13	0.922614
$813$	−3.72351e12	−0.298913
$814$	2.01986e13	1.61254
$815$	4.20478e12	0.333836
$816$	−7.18248e12	−0.567112
$817$	−1.05660e10	−0.000829677 0
$818$	1.82101e13	1.42208
$819$	−4.74870e12	−0.368805
$820$	−1.12397e13	−0.868147
$821$	1.38659e13	1.06513	0.532566	−	0.846389i	$-0.321228\pi$
$821$	1.38659e13	1.06513	0.532566	+	0.846389i	$0.321228\pi$
$822$	−1.57350e13	−1.20211
$823$	1.32295e13	1.00518	0.502591	−	0.864525i	$-0.332380\pi$
$823$	1.32295e13	1.00518	0.502591	+	0.864525i	$0.332380\pi$
$824$	4.70909e11	0.0355848
$825$	1.17061e13	0.879774
$826$	−1.63837e12	−0.122462
$827$	5.96201e12	0.443218	0.221609	−	0.975136i	$-0.428869\pi$
$827$	5.96201e12	0.443218	0.221609	+	0.975136i	$0.428869\pi$
$828$	−5.97487e12	−0.441766
$829$	1.03751e13	0.762954	0.381477	−	0.924378i	$-0.375415\pi$
$829$	1.03751e13	0.762954	0.381477	+	0.924378i	$0.375415\pi$
$830$	−2.30671e13	−1.68710
$831$	2.57517e12	0.187327
$832$	8.94105e12	0.646895
$833$	5.59639e12	0.402722
$834$	−1.43464e13	−1.02682
$835$	−2.75937e13	−1.96436
$836$	6.60205e12	0.467466
$837$	−2.41195e12	−0.169865
$838$	−1.85446e13	−1.29903
$839$	9.79768e12	0.682644	0.341322	−	0.939946i	$-0.389125\pi$
$839$	9.79768e12	0.682644	0.341322	+	0.939946i	$0.389125\pi$
$840$	3.55035e12	0.246045
$841$	3.03485e13	2.09197
$842$	−2.37424e13	−1.62787
$843$	−3.33202e11	−0.0227239
$844$	−6.65994e12	−0.451782
$845$	3.54230e13	2.39018
$846$	−1.16618e12	−0.0782708
$847$	−3.92531e12	−0.262059
$848$	−2.57240e13	−1.70827
$849$	5.43250e12	0.358852
$850$	−3.15558e13	−2.07345
$851$	4.24709e13	2.77593
$852$	2.27456e12	0.147883
$853$	−2.47801e12	−0.160263	−0.0801313	−	0.996784i	$-0.525534\pi$
$853$	−2.47801e12	−0.160263	−0.0801313	+	0.996784i	$0.525534\pi$
$854$	−9.22058e12	−0.593195
$855$	−7.11211e12	−0.455146
$856$	7.62575e12	0.485457
$857$	−1.95528e12	−0.123821	−0.0619105	−	0.998082i	$-0.519719\pi$
$857$	−1.95528e12	−0.123821	−0.0619105	+	0.998082i	$0.519719\pi$
$858$	−1.48786e13	−0.937282
$859$	−2.05939e13	−1.29054	−0.645268	−	0.763956i	$-0.723254\pi$
$859$	−2.05939e13	−1.29054	−0.645268	+	0.763956i	$0.723254\pi$
$860$	2.08748e10	0.00130131
$861$	4.60209e12	0.285392
$862$	3.33791e13	2.05917
$863$	2.06141e13	1.26507	0.632537	−	0.774530i	$-0.282014\pi$
$863$	2.06141e13	1.26507	0.632537	+	0.774530i	$0.282014\pi$
$864$	3.85947e12	0.235622
$865$	−4.40847e13	−2.67741
$866$	2.87776e13	1.73870
$867$	3.11489e12	0.187222
$868$	7.74511e12	0.463115
$869$	4.59683e12	0.273445
$870$	−3.85772e13	−2.28294
$871$	9.62506e12	0.566659
$872$	−1.01868e13	−0.596644
$873$	−4.11552e12	−0.239806
$874$	3.27779e13	1.90011
$875$	1.93501e13	1.11596
$876$	−5.71293e12	−0.327786
$877$	2.61353e13	1.49186	0.745931	−	0.666023i	$-0.232005\pi$
$877$	2.61353e13	1.49186	0.745931	+	0.666023i	$0.232005\pi$
$878$	−1.91691e13	−1.08862
$879$	−1.91362e13	−1.08120
$880$	2.88786e13	1.62332
$881$	−1.51843e13	−0.849188	−0.424594	−	0.905384i	$-0.639583\pi$
$881$	−1.51843e13	−0.849188	−0.424594	+	0.905384i	$0.639583\pi$
$882$	−3.86558e12	−0.215083
$883$	−2.16816e13	−1.20024	−0.600119	−	0.799911i	$-0.704880\pi$
$883$	−2.16816e13	−1.20024	−0.600119	+	0.799911i	$0.704880\pi$
$884$	1.69863e13	0.935541
$885$	2.34201e12	0.128335
$886$	1.77333e13	0.966804
$887$	−2.05352e13	−1.11389	−0.556945	−	0.830550i	$-0.688026\pi$
$887$	−2.05352e13	−1.11389	−0.556945	+	0.830550i	$0.688026\pi$
$888$	−5.75304e12	−0.310484
$889$	1.33295e13	0.715741
$890$	−1.47678e12	−0.0788971
$891$	−1.66316e12	−0.0884067
$892$	−1.68235e13	−0.889763
$893$	2.70949e12	0.142579
$894$	2.63136e13	1.37772
$895$	−6.16724e12	−0.321283
$896$	9.29169e12	0.481625
$897$	−3.12849e13	−1.61350
$898$	−2.33393e12	−0.119769
$899$	3.03964e13	1.55204
$900$	9.23115e12	0.468991
$901$	−2.32465e13	−1.17516
$902$	1.44193e13	0.725295
$903$	−8.54718e9	−0.000427788 0
$904$	2.45543e12	0.122284
$905$	3.18762e13	1.57961
$906$	−1.74949e13	−0.862648
$907$	−7.71988e12	−0.378772	−0.189386	−	0.981903i	$-0.560650\pi$
$907$	−7.71988e12	−0.378772	−0.189386	+	0.981903i	$0.560650\pi$
$908$	−2.78507e13	−1.35972
$909$	7.17394e12	0.348514
$910$	−5.14685e13	−2.48803
$911$	−4.01977e13	−1.93361	−0.966805	−	0.255516i	$-0.917755\pi$
$911$	−4.01977e13	−1.93361	−0.966805	+	0.255516i	$0.917755\pi$
$912$	−1.15267e13	−0.551730
$913$	1.25329e13	0.596941
$914$	−4.12330e12	−0.195428
$915$	1.31806e13	0.621643
$916$	1.81358e13	0.851153
$917$	−1.02933e13	−0.480722
$918$	4.48333e12	0.208357
$919$	−1.82906e13	−0.845879	−0.422939	−	0.906158i	$-0.639002\pi$
$919$	−1.82906e13	−0.845879	−0.422939	+	0.906158i	$0.639002\pi$
$920$	2.33900e13	1.07643
$921$	−2.40583e13	−1.10179
$922$	4.04853e13	1.84505
$923$	1.19098e13	0.540127
$924$	5.34064e12	0.241029
$925$	−6.56174e13	−2.94701
$926$	−3.35305e13	−1.49862
$927$	−7.63097e11	−0.0339407
$928$	−4.86386e13	−2.15286
$929$	−7.48341e12	−0.329631	−0.164816	−	0.986324i	$-0.552703\pi$
$929$	−7.48341e12	−0.329631	−0.164816	+	0.986324i	$0.552703\pi$
$930$	−2.61418e13	−1.14594
$931$	8.98124e12	0.391798
$932$	−6.02245e12	−0.261458
$933$	−4.76018e12	−0.205663
$934$	−7.48827e12	−0.321974
$935$	2.60972e13	1.11671
$936$	4.23780e12	0.180467
$937$	2.83293e12	0.120063	0.0600313	−	0.998196i	$-0.480880\pi$
$937$	2.83293e12	0.120063	0.0600313	+	0.998196i	$0.480880\pi$
$938$	−8.15763e12	−0.344074
$939$	5.15327e12	0.216316
$940$	−5.35307e12	−0.223629
$941$	2.67700e13	1.11300	0.556500	−	0.830848i	$-0.312144\pi$
$941$	2.67700e13	1.11300	0.556500	+	0.830848i	$0.312144\pi$
$942$	2.92878e13	1.21187
$943$	3.03190e13	1.24857
$944$	3.79571e12	0.155568
$945$	−5.75325e12	−0.234677
$946$	−2.67801e10	−0.00108718
$947$	3.96311e13	1.60126	0.800628	−	0.599161i	$-0.204499\pi$
$947$	3.96311e13	1.60126	0.800628	+	0.599161i	$0.204499\pi$
$948$	3.62494e12	0.145768
$949$	−2.99134e13	−1.19720
$950$	−5.06417e13	−2.01721
$951$	−3.81558e12	−0.151268
$952$	5.19989e12	0.205176
$953$	3.16563e13	1.24320	0.621601	−	0.783334i	$-0.286483\pi$
$953$	3.16563e13	1.24320	0.621601	+	0.783334i	$0.286483\pi$
$954$	1.60570e13	0.627620
$955$	6.32289e13	2.45980
$956$	−7.11209e12	−0.275383
$957$	2.09598e13	0.807763
$958$	−2.93485e13	−1.12575
$959$	2.95736e13	1.12907
$960$	1.08325e13	0.411630
$961$	−5.84150e12	−0.220937
$962$	8.34004e13	3.13964
$963$	−1.23574e13	−0.463028
$964$	7.57870e12	0.282650
$965$	−3.26464e13	−1.21189
$966$	2.65152e13	0.979712
$967$	2.31023e13	0.849642	0.424821	−	0.905277i	$-0.360337\pi$
$967$	2.31023e13	0.849642	0.424821	+	0.905277i	$0.360337\pi$
$968$	3.50299e12	0.128233
$969$	−1.04165e13	−0.379546
$970$	−4.46058e13	−1.61778
$971$	−2.14504e13	−0.774369	−0.387185	−	0.922002i	$-0.626552\pi$
$971$	−2.14504e13	−0.774369	−0.387185	+	0.922002i	$0.626552\pi$
$972$	−1.31152e12	−0.0471279
$973$	2.69637e13	0.964431
$974$	1.94525e13	0.692563
$975$	4.83350e13	1.71293
$976$	2.13619e13	0.753557
$977$	−4.35915e13	−1.53065	−0.765325	−	0.643644i	$-0.777422\pi$
$977$	−4.35915e13	−1.53065	−0.765325	+	0.643644i	$0.777422\pi$
$978$	−4.25376e12	−0.148679
$979$	8.02368e11	0.0279159
$980$	−1.77440e13	−0.614516
$981$	1.65075e13	0.569078
$982$	−5.80168e13	−1.99091
$983$	2.79176e13	0.953647	0.476824	−	0.878999i	$-0.341788\pi$
$983$	2.79176e13	0.953647	0.476824	+	0.878999i	$0.341788\pi$
$984$	−4.10696e12	−0.139651
$985$	−5.87352e12	−0.198809
$986$	−5.65007e13	−1.90374
$987$	2.19181e12	0.0735149
$988$	2.72601e13	0.910166
$989$	−5.63097e10	−0.00187154
$990$	−1.80261e13	−0.596408
$991$	1.63625e13	0.538913	0.269456	−	0.963013i	$-0.413156\pi$
$991$	1.63625e13	0.538913	0.269456	+	0.963013i	$0.413156\pi$
$992$	−3.29599e13	−1.08065
$993$	−1.67228e13	−0.545805
$994$	−1.00940e13	−0.327964
$995$	2.50886e13	0.811469
$996$	9.88307e12	0.318218
$997$	1.67058e13	0.535476	0.267738	−	0.963492i	$-0.413724\pi$
$997$	1.67058e13	0.535476	0.267738	+	0.963492i	$0.413724\pi$
$998$	4.16504e13	1.32902
$999$	9.32266e12	0.296139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.17	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+29.8017 q^{2} -81.0000 q^{3} +376.142 q^{4} +2386.14 q^{5} -2413.94 q^{6} +4536.93 q^{7} -4048.81 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+29.8017 q^{2} -81.0000 q^{3} +376.142 q^{4} +2386.14 q^{5} -2413.94 q^{6} +4536.93 q^{7} -4048.81 q^{8} +6561.00 q^{9} +71111.0 q^{10} -38636.2 q^{11} -30467.5 q^{12} -159530. q^{13} +135208. q^{14} -193277. q^{15} -313246. q^{16} -283077. q^{17} +195529. q^{18} -454290. q^{19} +897527. q^{20} -367491. q^{21} -1.15143e6 q^{22} -2.42107e6 q^{23} +327954. q^{24} +3.74054e6 q^{25} -4.75427e6 q^{26} -531441. q^{27} +1.70653e6 q^{28} +6.69743e6 q^{29} -5.75999e6 q^{30} +4.53852e6 q^{31} -7.26227e6 q^{32} +3.12953e6 q^{33} -8.43617e6 q^{34} +1.08258e7 q^{35} +2.46787e6 q^{36} -1.75422e7 q^{37} -1.35386e7 q^{38} +1.29219e7 q^{39} -9.66103e6 q^{40} -1.25230e7 q^{41} -1.09519e7 q^{42} +23258.2 q^{43} -1.45327e7 q^{44} +1.56555e7 q^{45} -7.21520e7 q^{46} -5.96424e6 q^{47} +2.53729e7 q^{48} -1.97699e7 q^{49} +1.11474e8 q^{50} +2.29292e7 q^{51} -6.00059e7 q^{52} +8.21208e7 q^{53} -1.58378e7 q^{54} -9.21914e7 q^{55} -1.83692e7 q^{56} +3.67975e7 q^{57} +1.99595e8 q^{58} -1.21174e7 q^{59} -7.26997e7 q^{60} -6.81954e7 q^{61} +1.35255e8 q^{62} +2.97668e7 q^{63} -5.60462e7 q^{64} -3.80661e8 q^{65} +9.32654e7 q^{66} -6.03338e7 q^{67} -1.06477e8 q^{68} +1.96107e8 q^{69} +3.22626e8 q^{70} -7.46554e7 q^{71} -2.65642e7 q^{72} +1.87509e8 q^{73} -5.22788e8 q^{74} -3.02984e8 q^{75} -1.70877e8 q^{76} -1.75290e8 q^{77} +3.85096e8 q^{78} -1.18977e8 q^{79} -7.47449e8 q^{80} +4.30467e7 q^{81} -3.73207e8 q^{82} -3.24381e8 q^{83} -1.38229e8 q^{84} -6.75461e8 q^{85} +693134. q^{86} -5.42492e8 q^{87} +1.56431e8 q^{88} -2.07673e7 q^{89} +4.66560e8 q^{90} -7.23777e8 q^{91} -9.10665e8 q^{92} -3.67620e8 q^{93} -1.77745e8 q^{94} -1.08400e9 q^{95} +5.88244e8 q^{96} -6.27270e8 q^{97} -5.89175e8 q^{98} -2.53492e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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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