LMFDB - Embedded newform 177.12.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-45.9608 q^{2} +243.000 q^{3} +64.3958 q^{4} -11937.5 q^{5} -11168.5 q^{6} -79874.8 q^{7} +91168.1 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-45.9608 q^{2} +243.000 q^{3} +64.3958 q^{4} -11937.5 q^{5} -11168.5 q^{6} -79874.8 q^{7} +91168.1 q^{8} +59049.0 q^{9} +548659. q^{10} +946726. q^{11} +15648.2 q^{12} -1.76618e6 q^{13} +3.67111e6 q^{14} -2.90082e6 q^{15} -4.32204e6 q^{16} -7.18471e6 q^{17} -2.71394e6 q^{18} -1.18388e7 q^{19} -768727. q^{20} -1.94096e7 q^{21} -4.35123e7 q^{22} +1.07020e7 q^{23} +2.21538e7 q^{24} +9.36768e7 q^{25} +8.11749e7 q^{26} +1.43489e7 q^{27} -5.14360e6 q^{28} +1.10825e6 q^{29} +1.33324e8 q^{30} +1.34986e8 q^{31} +1.19323e7 q^{32} +2.30054e8 q^{33} +3.30215e8 q^{34} +9.53509e8 q^{35} +3.80251e6 q^{36} -4.45212e8 q^{37} +5.44120e8 q^{38} -4.29181e8 q^{39} -1.08832e9 q^{40} +1.34475e9 q^{41} +8.92080e8 q^{42} -5.78738e8 q^{43} +6.09651e7 q^{44} -7.04900e8 q^{45} -4.91872e8 q^{46} +2.46985e9 q^{47} -1.05026e9 q^{48} +4.40266e9 q^{49} -4.30546e9 q^{50} -1.74588e9 q^{51} -1.13734e8 q^{52} +3.35994e9 q^{53} -6.59487e8 q^{54} -1.13016e10 q^{55} -7.28203e9 q^{56} -2.87683e9 q^{57} -5.09360e7 q^{58} -7.14924e8 q^{59} -1.86801e8 q^{60} +2.55522e9 q^{61} -6.20407e9 q^{62} -4.71653e9 q^{63} +8.30312e9 q^{64} +2.10838e10 q^{65} -1.05735e10 q^{66} +1.07691e10 q^{67} -4.62665e8 q^{68} +2.60059e9 q^{69} -4.38241e10 q^{70} +1.60386e10 q^{71} +5.38338e9 q^{72} +2.47907e10 q^{73} +2.04623e10 q^{74} +2.27635e10 q^{75} -7.62368e8 q^{76} -7.56196e10 q^{77} +1.97255e10 q^{78} -3.19630e10 q^{79} +5.15945e10 q^{80} +3.48678e9 q^{81} -6.18057e10 q^{82} -3.85068e10 q^{83} -1.24990e9 q^{84} +8.57677e10 q^{85} +2.65992e10 q^{86} +2.69304e8 q^{87} +8.63111e10 q^{88} -7.10593e10 q^{89} +3.23978e10 q^{90} +1.41073e11 q^{91} +6.89164e8 q^{92} +3.28016e10 q^{93} -1.13516e11 q^{94} +1.41326e11 q^{95} +2.89954e9 q^{96} -6.48923e10 q^{97} -2.02350e11 q^{98} +5.59032e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−45.9608	−1.01560	−0.507800	−	0.861475i	$-0.669541\pi$
$2$	−45.9608	−1.01560	−0.507800	+	0.861475i	$0.669541\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	64.3958	0.0314433
$5$	−11937.5	−1.70836	−0.854181	−	0.519976i	$-0.825941\pi$
$5$	−11937.5	−1.70836	−0.854181	+	0.519976i	$0.825941\pi$
$6$	−11168.5	−0.586357
$7$	−79874.8	−1.79627	−0.898133	−	0.439723i	$-0.855077\pi$
$7$	−79874.8	−1.79627	−0.898133	+	0.439723i	$0.855077\pi$
$8$	91168.1	0.983666
$9$	59049.0	0.333333
$10$	548659.	1.73501
$11$	946726.	1.77241	0.886205	−	0.463293i	$-0.153332\pi$
$11$	946726.	1.77241	0.886205	+	0.463293i	$0.153332\pi$
$12$	15648.2	0.0181538
$13$	−1.76618e6	−1.31931	−0.659653	−	0.751570i	$-0.729297\pi$
$13$	−1.76618e6	−1.31931	−0.659653	+	0.751570i	$0.729297\pi$
$14$	3.67111e6	1.82429
$15$	−2.90082e6	−0.986323
$16$	−4.32204e6	−1.03045
$17$	−7.18471e6	−1.22727	−0.613635	−	0.789590i	$-0.710293\pi$
$17$	−7.18471e6	−1.22727	−0.613635	+	0.789590i	$0.710293\pi$
$18$	−2.71394e6	−0.338533
$19$	−1.18388e7	−1.09689	−0.548444	−	0.836187i	$-0.684780\pi$
$19$	−1.18388e7	−1.09689	−0.548444	+	0.836187i	$0.684780\pi$
$20$	−768727.	−0.0537165
$21$	−1.94096e7	−1.03708
$22$	−4.35123e7	−1.80006
$23$	1.07020e7	0.346706	0.173353	−	0.984860i	$-0.444540\pi$
$23$	1.07020e7	0.346706	0.173353	+	0.984860i	$0.444540\pi$
$24$	2.21538e7	0.567920
$25$	9.36768e7	1.91850
$26$	8.11749e7	1.33989
$27$	1.43489e7	0.192450
$28$	−5.14360e6	−0.0564805
$29$	1.10825e6	0.0100334	0.00501670	−	0.999987i	$-0.498403\pi$
$29$	1.10825e6	0.0100334	0.00501670	+	0.999987i	$0.498403\pi$
$30$	1.33324e8	1.00171
$31$	1.34986e8	0.846837	0.423419	−	0.905934i	$-0.360830\pi$
$31$	1.34986e8	0.846837	0.423419	+	0.905934i	$0.360830\pi$
$32$	1.19323e7	0.0628634
$33$	2.30054e8	1.02330
$34$	3.30215e8	1.24642
$35$	9.53509e8	3.06867
$36$	3.80251e6	0.0104811
$37$	−4.45212e8	−1.05550	−0.527749	−	0.849400i	$-0.676964\pi$
$37$	−4.45212e8	−1.05550	−0.527749	+	0.849400i	$0.676964\pi$
$38$	5.44120e8	1.11400
$39$	−4.29181e8	−0.761702
$40$	−1.08832e9	−1.68046
$41$	1.34475e9	1.81271	0.906357	−	0.422512i	$-0.138852\pi$
$41$	1.34475e9	1.81271	0.906357	+	0.422512i	$0.138852\pi$
$42$	8.92080e8	1.05325
$43$	−5.78738e8	−0.600351	−0.300175	−	0.953884i	$-0.597045\pi$
$43$	−5.78738e8	−0.600351	−0.300175	+	0.953884i	$0.597045\pi$
$44$	6.09651e7	0.0557304
$45$	−7.04900e8	−0.569454
$46$	−4.91872e8	−0.352115
$47$	2.46985e9	1.57084	0.785421	−	0.618962i	$-0.212446\pi$
$47$	2.46985e9	1.57084	0.785421	+	0.618962i	$0.212446\pi$
$48$	−1.05026e9	−0.594933
$49$	4.40266e9	2.22657
$50$	−4.30546e9	−1.94843
$51$	−1.74588e9	−0.708565
$52$	−1.13734e8	−0.0414833
$53$	3.35994e9	1.10361	0.551803	−	0.833974i	$-0.313940\pi$
$53$	3.35994e9	1.10361	0.551803	+	0.833974i	$0.313940\pi$
$54$	−6.59487e8	−0.195452
$55$	−1.13016e10	−3.02792
$56$	−7.28203e9	−1.76693
$57$	−2.87683e9	−0.633289
$58$	−5.09360e7	−0.0101899
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−1.86801e8	−0.0310132
$61$	2.55522e9	0.387360	0.193680	−	0.981065i	$-0.437958\pi$
$61$	2.55522e9	0.387360	0.193680	+	0.981065i	$0.437958\pi$
$62$	−6.20407e9	−0.860048
$63$	−4.71653e9	−0.598756
$64$	8.30312e9	0.966610
$65$	2.10838e10	2.25385
$66$	−1.05735e10	−1.03927
$67$	1.07691e10	0.974466	0.487233	−	0.873272i	$-0.338006\pi$
$67$	1.07691e10	0.974466	0.487233	+	0.873272i	$0.338006\pi$
$68$	−4.62665e8	−0.0385894
$69$	2.60059e9	0.200171
$70$	−4.38241e10	−3.11654
$71$	1.60386e10	1.05498	0.527491	−	0.849561i	$-0.323133\pi$
$71$	1.60386e10	1.05498	0.527491	+	0.849561i	$0.323133\pi$
$72$	5.38338e9	0.327889
$73$	2.47907e10	1.39963	0.699814	−	0.714326i	$-0.253266\pi$
$73$	2.47907e10	1.39963	0.699814	+	0.714326i	$0.253266\pi$
$74$	2.04623e10	1.07196
$75$	2.27635e10	1.10765
$76$	−7.62368e8	−0.0344897
$77$	−7.56196e10	−3.18372
$78$	1.97255e10	0.773584
$79$	−3.19630e10	−1.16869	−0.584343	−	0.811507i	$-0.698648\pi$
$79$	−3.19630e10	−1.16869	−0.584343	+	0.811507i	$0.698648\pi$
$80$	5.15945e10	1.76039
$81$	3.48678e9	0.111111
$82$	−6.18057e10	−1.84099
$83$	−3.85068e10	−1.07302	−0.536509	−	0.843894i	$-0.680257\pi$
$83$	−3.85068e10	−1.07302	−0.536509	+	0.843894i	$0.680257\pi$
$84$	−1.24990e9	−0.0326090
$85$	8.57677e10	2.09662
$86$	2.65992e10	0.609716
$87$	2.69304e8	0.00579279
$88$	8.63111e10	1.74346
$89$	−7.10593e10	−1.34889	−0.674444	−	0.738326i	$-0.735617\pi$
$89$	−7.10593e10	−1.34889	−0.674444	+	0.738326i	$0.735617\pi$
$90$	3.23978e10	0.578337
$91$	1.41073e11	2.36983
$92$	6.89164e8	0.0109016
$93$	3.28016e10	0.488922
$94$	−1.13516e11	−1.59535
$95$	1.41326e11	1.87388
$96$	2.89954e9	0.0362942
$97$	−6.48923e10	−0.767271	−0.383636	−	0.923485i	$-0.625328\pi$
$97$	−6.48923e10	−0.767271	−0.383636	+	0.923485i	$0.625328\pi$
$98$	−2.02350e11	−2.26131
$99$	5.59032e10	0.590804
$100$	6.03239e9	0.0603239
$101$	−8.28856e10	−0.784714	−0.392357	−	0.919813i	$-0.628340\pi$
$101$	−8.28856e10	−0.784714	−0.392357	+	0.919813i	$0.628340\pi$
$102$	8.02422e10	0.719618
$103$	−3.80678e10	−0.323558	−0.161779	−	0.986827i	$-0.551723\pi$
$103$	−3.80678e10	−0.323558	−0.161779	+	0.986827i	$0.551723\pi$
$104$	−1.61019e11	−1.29776
$105$	2.31703e11	1.77170
$106$	−1.54426e11	−1.12082
$107$	1.14863e11	0.791716	0.395858	−	0.918312i	$-0.370447\pi$
$107$	1.14863e11	0.791716	0.395858	+	0.918312i	$0.370447\pi$
$108$	9.24009e8	0.00605126
$109$	−1.45645e11	−0.906674	−0.453337	−	0.891339i	$-0.649767\pi$
$109$	−1.45645e11	−0.906674	−0.453337	+	0.891339i	$0.649767\pi$
$110$	5.19430e11	3.07515
$111$	−1.08187e11	−0.609392
$112$	3.45222e11	1.85097
$113$	−5.69768e10	−0.290915	−0.145458	−	0.989364i	$-0.546465\pi$
$113$	−5.69768e10	−0.290915	−0.145458	+	0.989364i	$0.546465\pi$
$114$	1.32221e11	0.643168
$115$	−1.27756e11	−0.592300
$116$	7.13665e7	0.000315483 0
$117$	−1.04291e11	−0.439769
$118$	3.28585e10	0.132220
$119$	5.73877e11	2.20450
$120$	−2.64462e11	−0.970213
$121$	6.10978e11	2.14144
$122$	−1.17440e11	−0.393403
$123$	3.26774e11	1.04657
$124$	8.69254e9	0.0266273
$125$	−5.35382e11	−1.56913
$126$	2.16776e11	0.608096
$127$	2.48672e11	0.667892	0.333946	−	0.942592i	$-0.391620\pi$
$127$	2.48672e11	0.667892	0.333946	+	0.942592i	$0.391620\pi$
$128$	−4.06055e11	−1.04455
$129$	−1.40633e11	−0.346613
$130$	−9.69029e11	−2.28901
$131$	5.44777e10	0.123375	0.0616874	−	0.998096i	$-0.480352\pi$
$131$	5.44777e10	0.123375	0.0616874	+	0.998096i	$0.480352\pi$
$132$	1.48145e10	0.0321759
$133$	9.45621e11	1.97030
$134$	−4.94955e11	−0.989668
$135$	−1.71291e11	−0.328774
$136$	−6.55016e11	−1.20722
$137$	−2.41952e11	−0.428318	−0.214159	−	0.976799i	$-0.568701\pi$
$137$	−2.41952e11	−0.428318	−0.214159	+	0.976799i	$0.568701\pi$
$138$	−1.19525e11	−0.203294
$139$	1.34844e11	0.220419	0.110210	−	0.993908i	$-0.464848\pi$
$139$	1.34844e11	0.220419	0.110210	+	0.993908i	$0.464848\pi$
$140$	6.14020e10	0.0964891
$141$	6.00174e11	0.906926
$142$	−7.37146e11	−1.07144
$143$	−1.67208e12	−2.33835
$144$	−2.55212e11	−0.343485
$145$	−1.32298e10	−0.0171407
$146$	−1.13940e12	−1.42146
$147$	1.06985e12	1.28551
$148$	−2.86698e10	−0.0331883
$149$	8.73681e11	0.974604	0.487302	−	0.873233i	$-0.337981\pi$
$149$	8.73681e11	0.974604	0.487302	+	0.873233i	$0.337981\pi$
$150$	−1.04623e12	−1.12493
$151$	−9.24165e11	−0.958024	−0.479012	−	0.877808i	$-0.659005\pi$
$151$	−9.24165e11	−0.958024	−0.479012	+	0.877808i	$0.659005\pi$
$152$	−1.07932e12	−1.07897
$153$	−4.24250e11	−0.409090
$154$	3.47554e12	3.23339
$155$	−1.61140e12	−1.44670
$156$	−2.76374e10	−0.0239504
$157$	−1.06220e10	−0.00888706	−0.00444353	−	0.999990i	$-0.501414\pi$
$157$	−1.06220e10	−0.00888706	−0.00444353	+	0.999990i	$0.501414\pi$
$158$	1.46904e12	1.18692
$159$	8.16466e11	0.637168
$160$	−1.42442e11	−0.107393
$161$	−8.54820e11	−0.622777
$162$	−1.60255e11	−0.112844
$163$	1.82975e12	1.24555	0.622774	−	0.782402i	$-0.286006\pi$
$163$	1.82975e12	1.24555	0.622774	+	0.782402i	$0.286006\pi$
$164$	8.65960e10	0.0569976
$165$	−2.74628e12	−1.74817
$166$	1.76980e12	1.08976
$167$	−1.88729e12	−1.12434	−0.562170	−	0.827022i	$-0.690033\pi$
$167$	−1.88729e12	−1.12434	−0.562170	+	0.827022i	$0.690033\pi$
$168$	−1.76953e12	−1.02014
$169$	1.32722e12	0.740570
$170$	−3.94195e12	−2.12933
$171$	−6.99069e11	−0.365629
$172$	−3.72683e10	−0.0188770
$173$	−2.29470e12	−1.12583	−0.562915	−	0.826515i	$-0.690320\pi$
$173$	−2.29470e12	−1.12583	−0.562915	+	0.826515i	$0.690320\pi$
$174$	−1.23774e10	−0.00588315
$175$	−7.48242e12	−3.44614
$176$	−4.09179e12	−1.82639
$177$	−1.73727e11	−0.0751646
$178$	3.26594e12	1.36993
$179$	2.87738e12	1.17032	0.585162	−	0.810917i	$-0.301031\pi$
$179$	2.87738e12	1.17032	0.585162	+	0.810917i	$0.301031\pi$
$180$	−4.53926e10	−0.0179055
$181$	−6.19841e11	−0.237164	−0.118582	−	0.992944i	$-0.537835\pi$
$181$	−6.19841e11	−0.237164	−0.118582	+	0.992944i	$0.537835\pi$
$182$	−6.48383e12	−2.40680
$183$	6.20919e11	0.223642
$184$	9.75680e11	0.341043
$185$	5.31474e12	1.80317
$186$	−1.50759e12	−0.496549
$187$	−6.80195e12	−2.17523
$188$	1.59048e11	0.0493924
$189$	−1.14612e12	−0.345692
$190$	−6.49546e12	−1.90311
$191$	2.40903e12	0.685739	0.342870	−	0.939383i	$-0.388601\pi$
$191$	2.40903e12	0.685739	0.342870	+	0.939383i	$0.388601\pi$
$192$	2.01766e12	0.558073
$193$	−1.78608e12	−0.480105	−0.240052	−	0.970760i	$-0.577165\pi$
$193$	−1.78608e12	−0.480105	−0.240052	+	0.970760i	$0.577165\pi$
$194$	2.98250e12	0.779241
$195$	5.12336e12	1.30126
$196$	2.83513e11	0.0700107
$197$	−5.74904e12	−1.38048	−0.690241	−	0.723579i	$-0.742496\pi$
$197$	−5.74904e12	−1.38048	−0.690241	+	0.723579i	$0.742496\pi$
$198$	−2.56936e12	−0.600020
$199$	−1.16531e12	−0.264698	−0.132349	−	0.991203i	$-0.542252\pi$
$199$	−1.16531e12	−0.264698	−0.132349	+	0.991203i	$0.542252\pi$
$200$	8.54033e12	1.88716
$201$	2.61688e12	0.562608
$202$	3.80949e12	0.796955
$203$	−8.85212e10	−0.0180227
$204$	−1.12428e11	−0.0222796
$205$	−1.60530e13	−3.09677
$206$	1.74963e12	0.328606
$207$	6.31942e11	0.115569
$208$	7.63349e12	1.35949
$209$	−1.12081e13	−1.94414
$210$	−1.06492e13	−1.79934
$211$	5.68606e12	0.935961	0.467980	−	0.883739i	$-0.344982\pi$
$211$	5.68606e12	0.935961	0.467980	+	0.883739i	$0.344982\pi$
$212$	2.16366e11	0.0347010
$213$	3.89738e12	0.609094
$214$	−5.27919e12	−0.804066
$215$	6.90870e12	1.02562
$216$	1.30816e12	0.189307
$217$	−1.07820e13	−1.52115
$218$	6.69398e12	0.920818
$219$	6.02413e12	0.808075
$220$	−7.27774e11	−0.0952076
$221$	1.26895e13	1.61914
$222$	4.97234e12	0.618899
$223$	−7.10973e12	−0.863329	−0.431665	−	0.902034i	$-0.642074\pi$
$223$	−7.10973e12	−0.863329	−0.431665	+	0.902034i	$0.642074\pi$
$224$	−9.53088e11	−0.112920
$225$	5.53152e12	0.639500
$226$	2.61870e12	0.295453
$227$	1.49744e13	1.64895	0.824474	−	0.565900i	$-0.191471\pi$
$227$	1.49744e13	1.64895	0.824474	+	0.565900i	$0.191471\pi$
$228$	−1.85255e11	−0.0199127
$229$	−1.02108e13	−1.07143	−0.535715	−	0.844399i	$-0.679958\pi$
$229$	−1.02108e13	−1.07143	−0.535715	+	0.844399i	$0.679958\pi$
$230$	5.87175e12	0.601540
$231$	−1.83756e13	−1.83812
$232$	1.01037e11	0.00986951
$233$	−6.44340e12	−0.614692	−0.307346	−	0.951598i	$-0.599441\pi$
$233$	−6.44340e12	−0.614692	−0.307346	+	0.951598i	$0.599441\pi$
$234$	4.79330e12	0.446629
$235$	−2.94840e13	−2.68357
$236$	−4.60381e10	−0.00409356
$237$	−7.76700e12	−0.674741
$238$	−2.63759e13	−2.23889
$239$	−2.10460e13	−1.74575	−0.872873	−	0.487948i	$-0.837746\pi$
$239$	−2.10460e13	−1.74575	−0.872873	+	0.487948i	$0.837746\pi$
$240$	1.25375e13	1.01636
$241$	2.15329e13	1.70612	0.853059	−	0.521815i	$-0.174745\pi$
$241$	2.15329e13	1.70612	0.853059	+	0.521815i	$0.174745\pi$
$242$	−2.80810e13	−2.17485
$243$	8.47289e11	0.0641500
$244$	1.64546e11	0.0121799
$245$	−5.25570e13	−3.80379
$246$	−1.50188e13	−1.06290
$247$	2.09094e13	1.44713
$248$	1.23064e13	0.833005
$249$	−9.35714e12	−0.619508
$250$	2.46066e13	1.59361
$251$	2.15058e13	1.36254	0.681270	−	0.732032i	$-0.261428\pi$
$251$	2.15058e13	1.36254	0.681270	+	0.732032i	$0.261428\pi$
$252$	−3.03725e11	−0.0188268
$253$	1.01319e13	0.614506
$254$	−1.14292e13	−0.678311
$255$	2.08416e13	1.21048
$256$	1.65784e12	0.0942375
$257$	−1.16136e13	−0.646154	−0.323077	−	0.946373i	$-0.604717\pi$
$257$	−1.16136e13	−0.646154	−0.323077	+	0.946373i	$0.604717\pi$
$258$	6.46362e12	0.352020
$259$	3.55613e13	1.89596
$260$	1.35771e12	0.0708685
$261$	6.54410e10	0.00334447
$262$	−2.50384e12	−0.125299
$263$	1.27802e12	0.0626297	0.0313148	−	0.999510i	$-0.490031\pi$
$263$	1.27802e12	0.0626297	0.0313148	+	0.999510i	$0.490031\pi$
$264$	2.09736e13	1.00659
$265$	−4.01094e13	−1.88536
$266$	−4.34615e13	−2.00104
$267$	−1.72674e13	−0.778781
$268$	6.93483e11	0.0306404
$269$	1.33643e13	0.578505	0.289253	−	0.957253i	$-0.406593\pi$
$269$	1.33643e13	0.578505	0.289253	+	0.957253i	$0.406593\pi$
$270$	7.87266e12	0.333903
$271$	8.16318e12	0.339257	0.169628	−	0.985508i	$-0.445743\pi$
$271$	8.16318e12	0.339257	0.169628	+	0.985508i	$0.445743\pi$
$272$	3.10526e13	1.26465
$273$	3.42808e13	1.36822
$274$	1.11203e13	0.434999
$275$	8.86862e13	3.40037
$276$	1.67467e11	0.00629403
$277$	2.11796e13	0.780331	0.390166	−	0.920745i	$-0.372418\pi$
$277$	2.11796e13	0.780331	0.390166	+	0.920745i	$0.372418\pi$
$278$	−6.19753e12	−0.223858
$279$	7.97080e12	0.282279
$280$	8.69296e13	3.01855
$281$	2.20969e13	0.752396	0.376198	−	0.926539i	$-0.377231\pi$
$281$	2.20969e13	0.752396	0.376198	+	0.926539i	$0.377231\pi$
$282$	−2.75845e13	−0.921074
$283$	−2.65237e13	−0.868578	−0.434289	−	0.900774i	$-0.643000\pi$
$283$	−2.65237e13	−0.868578	−0.434289	+	0.900774i	$0.643000\pi$
$284$	1.03282e12	0.0331721
$285$	3.43422e13	1.08189
$286$	7.68504e13	2.37483
$287$	−1.07411e14	−3.25612
$288$	7.04589e11	0.0209545
$289$	1.73481e13	0.506191
$290$	6.08050e11	0.0174081
$291$	−1.57688e13	−0.442984
$292$	1.59641e12	0.0440088
$293$	6.41386e12	0.173519	0.0867596	−	0.996229i	$-0.472349\pi$
$293$	6.41386e12	0.173519	0.0867596	+	0.996229i	$0.472349\pi$
$294$	−4.91711e13	−1.30557
$295$	8.53444e12	0.222410
$296$	−4.05891e13	−1.03826
$297$	1.35845e13	0.341101
$298$	−4.01551e13	−0.989808
$299$	−1.89016e13	−0.457412
$300$	1.46587e12	0.0348280
$301$	4.62266e13	1.07839
$302$	4.24754e13	0.972969
$303$	−2.01412e13	−0.453055
$304$	5.11677e13	1.13029
$305$	−3.05031e13	−0.661751
$306$	1.94989e13	0.415472
$307$	1.23817e13	0.259132	0.129566	−	0.991571i	$-0.458642\pi$
$307$	1.23817e13	0.259132	0.129566	+	0.991571i	$0.458642\pi$
$308$	−4.86958e12	−0.100107
$309$	−9.25047e12	−0.186807
$310$	7.40614e13	1.46927
$311$	−3.10921e13	−0.605994	−0.302997	−	0.952991i	$-0.597987\pi$
$311$	−3.10921e13	−0.605994	−0.302997	+	0.952991i	$0.597987\pi$
$312$	−3.91276e13	−0.749260
$313$	−2.14700e13	−0.403960	−0.201980	−	0.979390i	$-0.564738\pi$
$313$	−2.14700e13	−0.403960	−0.201980	+	0.979390i	$0.564738\pi$
$314$	4.88196e11	0.00902570
$315$	5.63038e13	1.02289
$316$	−2.05828e12	−0.0367473
$317$	−8.12504e13	−1.42561	−0.712803	−	0.701364i	$-0.752575\pi$
$317$	−8.12504e13	−1.42561	−0.712803	+	0.701364i	$0.752575\pi$
$318$	−3.75254e13	−0.647107
$319$	1.04921e12	0.0177833
$320$	−9.91188e13	−1.65132
$321$	2.79117e13	0.457097
$322$	3.92882e13	0.632492
$323$	8.50582e13	1.34618
$324$	2.24534e11	0.00349370
$325$	−1.65450e14	−2.53109
$326$	−8.40968e13	−1.26498
$327$	−3.53918e13	−0.523468
$328$	1.22598e14	1.78311
$329$	−1.97279e14	−2.82165
$330$	1.26221e14	1.77544
$331$	5.57980e13	0.771907	0.385953	−	0.922518i	$-0.373873\pi$
$331$	5.57980e13	0.771907	0.385953	+	0.922518i	$0.373873\pi$
$332$	−2.47967e12	−0.0337392
$333$	−2.62893e13	−0.351833
$334$	8.67413e13	1.14188
$335$	−1.28556e14	−1.66474
$336$	8.38890e13	1.06866
$337$	4.36993e12	0.0547659	0.0273830	−	0.999625i	$-0.491283\pi$
$337$	4.36993e12	0.0547659	0.0273830	+	0.999625i	$0.491283\pi$
$338$	−6.10001e13	−0.752122
$339$	−1.38454e13	−0.167960
$340$	5.52308e12	0.0659246
$341$	1.27795e14	1.50094
$342$	3.21298e13	0.371333
$343$	−1.93723e14	−2.20325
$344$	−5.27624e13	−0.590545
$345$	−3.10446e13	−0.341964
$346$	1.05466e14	1.14339
$347$	−1.11128e13	−0.118580	−0.0592900	−	0.998241i	$-0.518884\pi$
$347$	−1.11128e13	−0.118580	−0.0592900	+	0.998241i	$0.518884\pi$
$348$	1.73421e10	0.000182144 0
$349$	−1.11101e13	−0.114863	−0.0574313	−	0.998349i	$-0.518291\pi$
$349$	−1.11101e13	−0.114863	−0.0574313	+	0.998349i	$0.518291\pi$
$350$	3.43898e14	3.49990
$351$	−2.53427e13	−0.253901
$352$	1.12966e13	0.111420
$353$	−6.20785e13	−0.602810	−0.301405	−	0.953496i	$-0.597456\pi$
$353$	−6.20785e13	−0.602810	−0.301405	+	0.953496i	$0.597456\pi$
$354$	7.98461e12	0.0763372
$355$	−1.91461e14	−1.80229
$356$	−4.57592e12	−0.0424134
$357$	1.39452e14	1.27277
$358$	−1.32247e14	−1.18858
$359$	5.26471e13	0.465967	0.232983	−	0.972481i	$-0.425151\pi$
$359$	5.26471e13	0.465967	0.232983	+	0.972481i	$0.425151\pi$
$360$	−6.42643e13	−0.560153
$361$	2.36666e13	0.203164
$362$	2.84884e13	0.240863
$363$	1.48468e14	1.23636
$364$	9.08451e12	0.0745151
$365$	−2.95940e14	−2.39107
$366$	−2.85380e13	−0.227131
$367$	−7.12029e12	−0.0558257	−0.0279129	−	0.999610i	$-0.508886\pi$
$367$	−7.12029e12	−0.0558257	−0.0279129	+	0.999610i	$0.508886\pi$
$368$	−4.62545e13	−0.357265
$369$	7.94060e13	0.604238
$370$	−2.44270e14	−1.83130
$371$	−2.68375e14	−1.98237
$372$	2.11229e12	0.0153733
$373$	1.28958e14	0.924801	0.462401	−	0.886671i	$-0.346988\pi$
$373$	1.28958e14	0.924801	0.462401	+	0.886671i	$0.346988\pi$
$374$	3.12623e14	2.20916
$375$	−1.30098e14	−0.905938
$376$	2.25172e14	1.54518
$377$	−1.95736e12	−0.0132371
$378$	5.26764e13	0.351084
$379$	1.49484e14	0.981928	0.490964	−	0.871180i	$-0.336645\pi$
$379$	1.49484e14	0.981928	0.490964	+	0.871180i	$0.336645\pi$
$380$	9.10080e12	0.0589210
$381$	6.04272e13	0.385607
$382$	−1.10721e14	−0.696437
$383$	1.40469e14	0.870940	0.435470	−	0.900203i	$-0.356582\pi$
$383$	1.40469e14	0.870940	0.435470	+	0.900203i	$0.356582\pi$
$384$	−9.86715e13	−0.603073
$385$	9.02712e14	5.43895
$386$	8.20897e13	0.487594
$387$	−3.41739e13	−0.200117
$388$	−4.17879e12	−0.0241255
$389$	1.27503e14	0.725767	0.362884	−	0.931834i	$-0.381792\pi$
$389$	1.27503e14	0.725767	0.362884	+	0.931834i	$0.381792\pi$
$390$	−2.35474e14	−1.32156
$391$	−7.68907e13	−0.425502
$392$	4.01382e14	2.19021
$393$	1.32381e13	0.0712305
$394$	2.64230e14	1.40202
$395$	3.81559e14	1.99654
$396$	3.59993e12	0.0185768
$397$	−1.77885e14	−0.905299	−0.452650	−	0.891688i	$-0.649521\pi$
$397$	−1.77885e14	−0.905299	−0.452650	+	0.891688i	$0.649521\pi$
$398$	5.35587e13	0.268827
$399$	2.29786e14	1.13756
$400$	−4.04875e14	−1.97693
$401$	8.12140e13	0.391144	0.195572	−	0.980689i	$-0.437344\pi$
$401$	8.12140e13	0.391144	0.195572	+	0.980689i	$0.437344\pi$
$402$	−1.20274e14	−0.571385
$403$	−2.38409e14	−1.11724
$404$	−5.33748e12	−0.0246740
$405$	−4.16236e13	−0.189818
$406$	4.06850e12	0.0183038
$407$	−4.21494e14	−1.87078
$408$	−1.59169e14	−0.696991
$409$	−2.01695e14	−0.871398	−0.435699	−	0.900093i	$-0.643499\pi$
$409$	−2.01695e14	−0.871398	−0.435699	+	0.900093i	$0.643499\pi$
$410$	7.37808e14	3.14508
$411$	−5.87943e13	−0.247289
$412$	−2.45140e12	−0.0101737
$413$	5.71045e13	0.233854
$414$	−2.90446e13	−0.117372
$415$	4.59676e14	1.83310
$416$	−2.10745e13	−0.0829361
$417$	3.27671e13	0.127259
$418$	5.15133e14	1.97446
$419$	−2.81412e14	−1.06455	−0.532274	−	0.846572i	$-0.678663\pi$
$419$	−2.81412e14	−1.06455	−0.532274	+	0.846572i	$0.678663\pi$
$420$	1.49207e13	0.0557080
$421$	1.37748e14	0.507615	0.253808	−	0.967255i	$-0.418317\pi$
$421$	1.37748e14	0.507615	0.253808	+	0.967255i	$0.418317\pi$
$422$	−2.61336e14	−0.950562
$423$	1.45842e14	0.523614
$424$	3.06319e14	1.08558
$425$	−6.73040e14	−2.35452
$426$	−1.79127e14	−0.618596
$427$	−2.04098e14	−0.695802
$428$	7.39669e12	0.0248941
$429$	−4.06317e14	−1.35005
$430$	−3.17530e14	−1.04162
$431$	1.15761e14	0.374919	0.187460	−	0.982272i	$-0.439975\pi$
$431$	1.15761e14	0.374919	0.187460	+	0.982272i	$0.439975\pi$
$432$	−6.20165e13	−0.198311
$433$	−3.86740e14	−1.22106	−0.610528	−	0.791995i	$-0.709043\pi$
$433$	−3.86740e14	−1.22106	−0.610528	+	0.791995i	$0.709043\pi$
$434$	4.95549e14	1.54488
$435$	−3.21483e12	−0.00989617
$436$	−9.37895e12	−0.0285088
$437$	−1.26699e14	−0.380298
$438$	−2.76874e14	−0.820681
$439$	3.30433e14	0.967228	0.483614	−	0.875281i	$-0.339324\pi$
$439$	3.30433e14	0.967228	0.483614	+	0.875281i	$0.339324\pi$
$440$	−1.03034e15	−2.97846
$441$	2.59973e14	0.742191
$442$	−5.83218e14	−1.64440
$443$	5.19386e14	1.44634	0.723169	−	0.690672i	$-0.242685\pi$
$443$	5.19386e14	1.44634	0.723169	+	0.690672i	$0.242685\pi$
$444$	−6.96676e12	−0.0191613
$445$	8.48273e14	2.30439
$446$	3.26769e14	0.876797
$447$	2.12304e14	0.562688
$448$	−6.63210e14	−1.73629
$449$	7.61057e14	1.96817	0.984085	−	0.177699i	$-0.0568654\pi$
$449$	7.61057e14	1.96817	0.984085	+	0.177699i	$0.0568654\pi$
$450$	−2.54233e14	−0.649476
$451$	1.27311e15	3.21287
$452$	−3.66906e12	−0.00914732
$453$	−2.24572e14	−0.553115
$454$	−6.88235e14	−1.67467
$455$	−1.68407e15	−4.04852
$456$	−2.62275e14	−0.622945
$457$	−7.47629e13	−0.175448	−0.0877238	−	0.996145i	$-0.527959\pi$
$457$	−7.47629e13	−0.175448	−0.0877238	+	0.996145i	$0.527959\pi$
$458$	4.69296e14	1.08814
$459$	−1.03093e14	−0.236188
$460$	−8.22692e12	−0.0186238
$461$	−3.26176e14	−0.729621	−0.364810	−	0.931082i	$-0.618866\pi$
$461$	−3.26176e14	−0.729621	−0.364810	+	0.931082i	$0.618866\pi$
$462$	8.44555e14	1.86680
$463$	−2.70438e14	−0.590707	−0.295353	−	0.955388i	$-0.595437\pi$
$463$	−2.70438e14	−0.590707	−0.295353	+	0.955388i	$0.595437\pi$
$464$	−4.78989e12	−0.0103390
$465$	−3.91571e14	−0.835255
$466$	2.96144e14	0.624281
$467$	5.44006e14	1.13334	0.566671	−	0.823944i	$-0.308231\pi$
$467$	5.44006e14	1.13334	0.566671	+	0.823944i	$0.308231\pi$
$468$	−6.71590e12	−0.0138278
$469$	−8.60178e14	−1.75040
$470$	1.35511e15	2.72543
$471$	−2.58115e12	−0.00513095
$472$	−6.51783e13	−0.128062
$473$	−5.47906e14	−1.06407
$474$	3.56977e14	0.685267
$475$	−1.10902e15	−2.10438
$476$	3.69553e13	0.0693168
$477$	1.98401e14	0.367869
$478$	9.67291e14	1.77298
$479$	−1.44509e14	−0.261847	−0.130924	−	0.991392i	$-0.541794\pi$
$479$	−1.44509e14	−0.261847	−0.130924	+	0.991392i	$0.541794\pi$
$480$	−3.46134e13	−0.0620037
$481$	7.86323e14	1.39253
$482$	−9.89670e14	−1.73273
$483$	−2.07721e14	−0.359560
$484$	3.93444e13	0.0673338
$485$	7.74655e14	1.31078
$486$	−3.89421e13	−0.0651508
$487$	4.92506e14	0.814709	0.407354	−	0.913270i	$-0.366451\pi$
$487$	4.92506e14	0.814709	0.407354	+	0.913270i	$0.366451\pi$
$488$	2.32955e14	0.381033
$489$	4.44630e14	0.719117
$490$	2.41556e15	3.86313
$491$	3.57330e14	0.565095	0.282548	−	0.959253i	$-0.408820\pi$
$491$	3.57330e14	0.565095	0.282548	+	0.959253i	$0.408820\pi$
$492$	2.10428e13	0.0329076
$493$	−7.96244e12	−0.0123137
$494$	−9.61012e14	−1.46971
$495$	−6.67347e14	−1.00931
$496$	−5.83416e14	−0.872627
$497$	−1.28108e15	−1.89503
$498$	4.30062e14	0.629172
$499$	1.02704e14	0.148606	0.0743029	−	0.997236i	$-0.476327\pi$
$499$	1.02704e14	0.148606	0.0743029	+	0.997236i	$0.476327\pi$
$500$	−3.44764e13	−0.0493386
$501$	−4.58611e14	−0.649138
$502$	−9.88422e14	−1.38380
$503$	−1.08451e15	−1.50179	−0.750893	−	0.660424i	$-0.770376\pi$
$503$	−1.08451e15	−1.50179	−0.750893	+	0.660424i	$0.770376\pi$
$504$	−4.29997e14	−0.588976
$505$	9.89450e14	1.34058
$506$	−4.65668e14	−0.624092
$507$	3.22514e14	0.427568
$508$	1.60134e13	0.0210007
$509$	1.09362e15	1.41879	0.709395	−	0.704811i	$-0.248968\pi$
$509$	1.09362e15	1.41879	0.709395	+	0.704811i	$0.248968\pi$
$510$	−9.57895e14	−1.22937
$511$	−1.98015e15	−2.51410
$512$	7.55406e14	0.948845
$513$	−1.69874e14	−0.211096
$514$	5.33772e14	0.656234
$515$	4.54436e14	0.552755
$516$	−9.05619e12	−0.0108986
$517$	2.33827e15	2.78418
$518$	−1.63442e15	−1.92553
$519$	−5.57613e14	−0.649999
$520$	1.92217e15	2.21704
$521$	−5.41160e14	−0.617616	−0.308808	−	0.951124i	$-0.599930\pi$
$521$	−5.41160e14	−0.617616	−0.308808	+	0.951124i	$0.599930\pi$
$522$	−3.00772e12	−0.00339664
$523$	−1.71054e15	−1.91150	−0.955748	−	0.294185i	$-0.904952\pi$
$523$	−1.71054e15	−1.91150	−0.955748	+	0.294185i	$0.904952\pi$
$524$	3.50813e12	0.00387931
$525$	−1.81823e15	−1.98963
$526$	−5.87387e13	−0.0636067
$527$	−9.69836e14	−1.03930
$528$	−9.94304e14	−1.05447
$529$	−8.38277e14	−0.879795
$530$	1.84346e15	1.91477
$531$	−4.22156e13	−0.0433963
$532$	6.08940e13	0.0619528
$533$	−2.37506e15	−2.39153
$534$	7.93624e14	0.790930
$535$	−1.37118e15	−1.35254
$536$	9.81795e14	0.958549
$537$	6.99204e14	0.675687
$538$	−6.14232e14	−0.587530
$539$	4.16811e15	3.94640
$540$	−1.10304e13	−0.0103377
$541$	7.76317e14	0.720202	0.360101	−	0.932913i	$-0.382742\pi$
$541$	7.76317e14	0.720202	0.360101	+	0.932913i	$0.382742\pi$
$542$	−3.75186e14	−0.344549
$543$	−1.50621e14	−0.136927
$544$	−8.57299e13	−0.0771504
$545$	1.73865e15	1.54893
$546$	−1.57557e15	−1.38956
$547$	−2.24867e15	−1.96334	−0.981668	−	0.190598i	$-0.938957\pi$
$547$	−2.24867e15	−1.96334	−0.981668	+	0.190598i	$0.938957\pi$
$548$	−1.55807e13	−0.0134677
$549$	1.50883e14	0.129120
$550$	−4.07609e15	−3.45342
$551$	−1.31203e13	−0.0110055
$552$	2.37090e14	0.196901
$553$	2.55304e15	2.09927
$554$	−9.73431e14	−0.792504
$555$	1.29148e15	1.04106
$556$	8.68338e12	0.00693070
$557$	−9.31655e14	−0.736295	−0.368147	−	0.929767i	$-0.620008\pi$
$557$	−9.31655e14	−0.736295	−0.368147	+	0.929767i	$0.620008\pi$
$558$	−3.66344e14	−0.286683
$559$	1.02215e15	0.792047
$560$	−4.12110e15	−3.16213
$561$	−1.65287e15	−1.25587
$562$	−1.01559e15	−0.764133
$563$	8.93930e14	0.666051	0.333025	−	0.942918i	$-0.391930\pi$
$563$	8.93930e14	0.666051	0.333025	+	0.942918i	$0.391930\pi$
$564$	3.86487e13	0.0285167
$565$	6.80163e14	0.496988
$566$	1.21905e15	0.882127
$567$	−2.78506e14	−0.199585
$568$	1.46221e15	1.03775
$569$	−2.06733e15	−1.45309	−0.726544	−	0.687120i	$-0.758875\pi$
$569$	−2.06733e15	−1.45309	−0.726544	+	0.687120i	$0.758875\pi$
$570$	−1.57840e15	−1.09876
$571$	−2.02285e14	−0.139465	−0.0697326	−	0.997566i	$-0.522215\pi$
$571$	−2.02285e14	−0.139465	−0.0697326	+	0.997566i	$0.522215\pi$
$572$	−1.07675e14	−0.0735254
$573$	5.85395e14	0.395912
$574$	4.93672e15	3.30691
$575$	1.00253e15	0.665156
$576$	4.90291e14	0.322203
$577$	−1.99205e14	−0.129668	−0.0648341	−	0.997896i	$-0.520652\pi$
$577$	−1.99205e14	−0.129668	−0.0648341	+	0.997896i	$0.520652\pi$
$578$	−7.97334e14	−0.514088
$579$	−4.34018e14	−0.277189
$580$	−8.51941e11	−0.000538959 0
$581$	3.07572e15	1.92743
$582$	7.24748e14	0.449895
$583$	3.18094e15	1.95604
$584$	2.26012e15	1.37677
$585$	1.24498e15	0.751284
$586$	−2.94786e14	−0.176226
$587$	−1.43802e15	−0.851639	−0.425819	−	0.904808i	$-0.640014\pi$
$587$	−1.43802e15	−0.851639	−0.425819	+	0.904808i	$0.640014\pi$
$588$	6.88937e13	0.0404207
$589$	−1.59807e15	−0.928886
$590$	−3.92250e14	−0.225879
$591$	−1.39702e15	−0.797022
$592$	1.92422e15	1.08764
$593$	3.94642e14	0.221005	0.110503	−	0.993876i	$-0.464754\pi$
$593$	3.94642e14	0.221005	0.110503	+	0.993876i	$0.464754\pi$
$594$	−6.24354e14	−0.346422
$595$	−6.85069e15	−3.76609
$596$	5.62614e13	0.0306447
$597$	−2.83171e14	−0.152823
$598$	8.68734e14	0.464547
$599$	−1.61368e15	−0.855008	−0.427504	−	0.904013i	$-0.640607\pi$
$599$	−1.61368e15	−0.855008	−0.427504	+	0.904013i	$0.640607\pi$
$600$	2.07530e15	1.08955
$601$	−3.82239e15	−1.98850	−0.994248	−	0.107099i	$-0.965844\pi$
$601$	−3.82239e15	−1.98850	−0.994248	+	0.107099i	$0.965844\pi$
$602$	−2.12461e15	−1.09521
$603$	6.35903e14	0.324822
$604$	−5.95123e13	−0.0301234
$605$	−7.29357e15	−3.65835
$606$	9.25705e14	0.460122
$607$	3.49037e15	1.71923	0.859613	−	0.510945i	$-0.170705\pi$
$607$	3.49037e15	1.71923	0.859613	+	0.510945i	$0.170705\pi$
$608$	−1.41264e14	−0.0689542
$609$	−2.15106e13	−0.0104054
$610$	1.40195e15	0.672074
$611$	−4.36219e15	−2.07242
$612$	−2.73199e13	−0.0128631
$613$	−3.05426e14	−0.142519	−0.0712596	−	0.997458i	$-0.522702\pi$
$613$	−3.05426e14	−0.142519	−0.0712596	+	0.997458i	$0.522702\pi$
$614$	−5.69075e14	−0.263174
$615$	−3.90087e15	−1.78792
$616$	−6.89409e15	−3.13172
$617$	−1.80306e15	−0.811786	−0.405893	−	0.913921i	$-0.633039\pi$
$617$	−1.80306e15	−0.811786	−0.405893	+	0.913921i	$0.633039\pi$
$618$	4.25159e14	0.189721
$619$	2.65088e15	1.17244	0.586222	−	0.810151i	$-0.300615\pi$
$619$	2.65088e15	1.17244	0.586222	+	0.810151i	$0.300615\pi$
$620$	−1.03768e14	−0.0454891
$621$	1.53562e14	0.0667237
$622$	1.42902e15	0.615448
$623$	5.67585e15	2.42296
$624$	1.85494e15	0.784899
$625$	1.81709e15	0.762143
$626$	9.86779e14	0.410262
$627$	−2.72356e15	−1.12245
$628$	−6.84012e11	−0.000279438 0
$629$	3.19872e15	1.29538
$630$	−2.58777e15	−1.03885
$631$	3.66420e15	1.45820	0.729102	−	0.684405i	$-0.239938\pi$
$631$	3.66420e15	1.45820	0.729102	+	0.684405i	$0.239938\pi$
$632$	−2.91400e15	−1.14960
$633$	1.38171e15	0.540377
$634$	3.73434e15	1.44785
$635$	−2.96853e15	−1.14100
$636$	5.25769e13	0.0200346
$637$	−7.77588e15	−2.93753
$638$	−4.82224e13	−0.0180607
$639$	9.47063e14	0.351661
$640$	4.84730e15	1.78447
$641$	−1.21408e15	−0.443129	−0.221564	−	0.975146i	$-0.571116\pi$
$641$	−1.21408e15	−0.443129	−0.221564	+	0.975146i	$0.571116\pi$
$642$	−1.28284e15	−0.464228
$643$	3.44096e15	1.23458	0.617290	−	0.786736i	$-0.288231\pi$
$643$	3.44096e15	1.23458	0.617290	+	0.786736i	$0.288231\pi$
$644$	−5.50468e13	−0.0195821
$645$	1.67881e15	0.592140
$646$	−3.90934e15	−1.36718
$647$	2.32690e15	0.806873	0.403436	−	0.915008i	$-0.367816\pi$
$647$	2.32690e15	0.806873	0.403436	+	0.915008i	$0.367816\pi$
$648$	3.17883e14	0.109296
$649$	−6.76837e14	−0.230748
$650$	7.60420e15	2.57057
$651$	−2.62003e15	−0.878234
$652$	1.17828e14	0.0391641
$653$	5.76213e15	1.89916	0.949578	−	0.313531i	$-0.101512\pi$
$653$	5.76213e15	1.89916	0.949578	+	0.313531i	$0.101512\pi$
$654$	1.62664e15	0.531634
$655$	−6.50330e14	−0.210769
$656$	−5.81205e15	−1.86792
$657$	1.46386e15	0.466542
$658$	9.06710e15	2.86567
$659$	−5.53554e15	−1.73496	−0.867481	−	0.497470i	$-0.834263\pi$
$659$	−5.53554e15	−1.73496	−0.867481	+	0.497470i	$0.834263\pi$
$660$	−1.76849e14	−0.0549681
$661$	−6.17895e14	−0.190461	−0.0952307	−	0.995455i	$-0.530359\pi$
$661$	−6.17895e14	−0.190461	−0.0952307	+	0.995455i	$0.530359\pi$
$662$	−2.56452e15	−0.783948
$663$	3.08354e15	0.934814
$664$	−3.51059e15	−1.05549
$665$	−1.12884e16	−3.36599
$666$	1.20828e15	0.357321
$667$	1.18605e13	0.00347864
$668$	−1.21533e14	−0.0353529
$669$	−1.72766e15	−0.498443
$670$	5.90855e15	1.69071
$671$	2.41910e15	0.686561
$672$	−2.31600e14	−0.0651941
$673$	−2.86734e15	−0.800565	−0.400283	−	0.916392i	$-0.631088\pi$
$673$	−2.86734e15	−0.800565	−0.400283	+	0.916392i	$0.631088\pi$
$674$	−2.00846e14	−0.0556203
$675$	1.34416e15	0.369216
$676$	8.54674e13	0.0232859
$677$	1.79243e15	0.484400	0.242200	−	0.970226i	$-0.422131\pi$
$677$	1.79243e15	0.484400	0.242200	+	0.970226i	$0.422131\pi$
$678$	6.36344e14	0.170580
$679$	5.18327e15	1.37822
$680$	7.81928e15	2.06237
$681$	3.63878e15	0.952021
$682$	−5.87355e15	−1.52436
$683$	7.45091e15	1.91821	0.959104	−	0.283055i	$-0.0913478\pi$
$683$	7.45091e15	1.91821	0.959104	+	0.283055i	$0.0913478\pi$
$684$	−4.50171e13	−0.0114966
$685$	2.88831e15	0.731721
$686$	8.90369e15	2.23762
$687$	−2.48122e15	−0.618591
$688$	2.50133e15	0.618634
$689$	−5.93425e15	−1.45600
$690$	1.42683e15	0.347299
$691$	2.90089e15	0.700491	0.350246	−	0.936658i	$-0.386098\pi$
$691$	2.90089e15	0.700491	0.350246	+	0.936658i	$0.386098\pi$
$692$	−1.47769e14	−0.0353998
$693$	−4.46526e15	−1.06124
$694$	5.10754e14	0.120430
$695$	−1.60970e15	−0.376556
$696$	2.45520e13	0.00569817
$697$	−9.66161e15	−2.22469
$698$	5.10630e14	0.116655
$699$	−1.56575e15	−0.354893
$700$	−4.81836e14	−0.108358
$701$	−4.72763e15	−1.05486	−0.527430	−	0.849599i	$-0.676844\pi$
$701$	−4.72763e15	−1.05486	−0.527430	+	0.849599i	$0.676844\pi$
$702$	1.16477e15	0.257861
$703$	5.27077e15	1.15776
$704$	7.86078e15	1.71323
$705$	−7.16460e15	−1.54936
$706$	2.85318e15	0.612213
$707$	6.62047e15	1.40956
$708$	−1.11873e13	−0.00236342
$709$	−6.66263e15	−1.39666	−0.698331	−	0.715775i	$-0.746074\pi$
$709$	−6.66263e15	−1.39666	−0.698331	+	0.715775i	$0.746074\pi$
$710$	8.79972e15	1.83041
$711$	−1.88738e15	−0.389562
$712$	−6.47834e15	−1.32686
$713$	1.44462e15	0.293604
$714$	−6.40934e15	−1.29263
$715$	1.99606e16	3.99475
$716$	1.85291e14	0.0367988
$717$	−5.11418e15	−1.00791
$718$	−2.41970e15	−0.473236
$719$	9.90807e15	1.92300	0.961502	−	0.274798i	$-0.0886110\pi$
$719$	9.90807e15	1.92300	0.961502	+	0.274798i	$0.0886110\pi$
$720$	3.04661e15	0.586796
$721$	3.04066e15	0.581197
$722$	−1.08774e15	−0.206333
$723$	5.23250e15	0.985027
$724$	−3.99152e13	−0.00745720
$725$	1.03817e14	0.0192491
$726$	−6.82369e15	−1.25565
$727$	2.85309e15	0.521047	0.260523	−	0.965468i	$-0.416105\pi$
$727$	2.85309e15	0.521047	0.260523	+	0.965468i	$0.416105\pi$
$728$	1.28614e16	2.33112
$729$	2.05891e14	0.0370370
$730$	1.36016e16	2.42837
$731$	4.15806e15	0.736792
$732$	3.99846e13	0.00703205
$733$	1.97703e15	0.345097	0.172548	−	0.985001i	$-0.444800\pi$
$733$	1.97703e15	0.345097	0.172548	+	0.985001i	$0.444800\pi$
$734$	3.27254e14	0.0566966
$735$	−1.27713e16	−2.19612
$736$	1.27699e14	0.0217951
$737$	1.01954e16	1.72715
$738$	−3.64956e15	−0.613664
$739$	4.92807e15	0.822493	0.411247	−	0.911524i	$-0.365093\pi$
$739$	4.92807e15	0.822493	0.411247	+	0.911524i	$0.365093\pi$
$740$	3.42247e14	0.0566976
$741$	5.08098e15	0.835502
$742$	1.23347e16	2.01330
$743$	−3.34590e14	−0.0542094	−0.0271047	−	0.999633i	$-0.508629\pi$
$743$	−3.34590e14	−0.0542094	−0.0271047	+	0.999633i	$0.508629\pi$
$744$	2.99046e15	0.480936
$745$	−1.04296e16	−1.66498
$746$	−5.92700e15	−0.939228
$747$	−2.27379e15	−0.357673
$748$	−4.38017e14	−0.0683962
$749$	−9.17466e15	−1.42213
$750$	5.97941e15	0.920071
$751$	1.47597e15	0.225454	0.112727	−	0.993626i	$-0.464041\pi$
$751$	1.47597e15	0.225454	0.112727	+	0.993626i	$0.464041\pi$
$752$	−1.06748e16	−1.61868
$753$	5.22590e15	0.786663
$754$	8.99619e13	0.0134436
$755$	1.10323e16	1.63665
$756$	−7.38051e13	−0.0108697
$757$	1.34026e16	1.95958	0.979789	−	0.200036i	$-0.0641059\pi$
$757$	1.34026e16	1.95958	0.979789	+	0.200036i	$0.0641059\pi$
$758$	−6.87042e15	−0.997246
$759$	2.46204e15	0.354785
$760$	1.28844e16	1.84327
$761$	−3.37274e15	−0.479035	−0.239517	−	0.970892i	$-0.576989\pi$
$761$	−3.37274e15	−0.479035	−0.239517	+	0.970892i	$0.576989\pi$
$762$	−2.77728e15	−0.391623
$763$	1.16334e16	1.62863
$764$	1.55131e14	0.0215619
$765$	5.06450e15	0.698874
$766$	−6.45609e15	−0.884527
$767$	1.26268e15	0.171759
$768$	4.02856e14	0.0544080
$769$	−9.79858e15	−1.31392	−0.656959	−	0.753926i	$-0.728158\pi$
$769$	−9.79858e15	−1.31392	−0.656959	+	0.753926i	$0.728158\pi$
$770$	−4.14894e16	−5.52380
$771$	−2.82211e15	−0.373057
$772$	−1.15016e14	−0.0150961
$773$	−1.36395e16	−1.77751	−0.888754	−	0.458384i	$-0.848429\pi$
$773$	−1.36395e16	−1.77751	−0.888754	+	0.458384i	$0.848429\pi$
$774$	1.57066e15	0.203239
$775$	1.26451e16	1.62466
$776$	−5.91611e15	−0.754739
$777$	8.64138e15	1.09463
$778$	−5.86014e15	−0.737089
$779$	−1.59202e16	−1.98835
$780$	3.29923e14	0.0409159
$781$	1.51841e16	1.86986
$782$	3.53396e15	0.432140
$783$	1.59022e13	0.00193093
$784$	−1.90285e16	−2.29438
$785$	1.26801e14	0.0151823
$786$	−6.08433e14	−0.0723417
$787$	−3.22872e15	−0.381214	−0.190607	−	0.981666i	$-0.561046\pi$
$787$	−3.22872e15	−0.381214	−0.190607	+	0.981666i	$0.561046\pi$
$788$	−3.70214e14	−0.0434069
$789$	3.10558e14	0.0361593
$790$	−1.75368e16	−2.02768
$791$	4.55101e15	0.522561
$792$	5.09659e15	0.581153
$793$	−4.51298e15	−0.511047
$794$	8.17575e15	0.919422
$795$	−9.74659e15	−1.08851
$796$	−7.50412e13	−0.00832296
$797$	−8.17049e15	−0.899968	−0.449984	−	0.893037i	$-0.648570\pi$
$797$	−8.17049e15	−0.899968	−0.449984	+	0.893037i	$0.648570\pi$
$798$	−1.05611e16	−1.15530
$799$	−1.77452e16	−1.92785
$800$	1.11778e15	0.120604
$801$	−4.19598e15	−0.449629
$802$	−3.73266e15	−0.397246
$803$	2.34700e16	2.48071
$804$	1.68516e14	0.0176902
$805$	1.02045e16	1.06393
$806$	1.09575e16	1.13467
$807$	3.24751e15	0.334000
$808$	−7.55652e15	−0.771896
$809$	1.38353e16	1.40369	0.701846	−	0.712329i	$-0.252360\pi$
$809$	1.38353e16	1.40369	0.701846	+	0.712329i	$0.252360\pi$
$810$	1.91306e15	0.192779
$811$	−9.02019e15	−0.902820	−0.451410	−	0.892317i	$-0.649079\pi$
$811$	−9.02019e15	−0.902820	−0.451410	+	0.892317i	$0.649079\pi$
$812$	−5.70039e12	−0.000566691 0
$813$	1.98365e15	0.195870
$814$	1.93722e16	1.89996
$815$	−2.18427e16	−2.12785
$816$	7.54578e15	0.730144
$817$	6.85155e15	0.658518
$818$	9.27005e15	0.884991
$819$	8.33022e15	0.789942
$820$	−1.03374e15	−0.0973726
$821$	1.23694e15	0.115734	0.0578670	−	0.998324i	$-0.481570\pi$
$821$	1.23694e15	0.115734	0.0578670	+	0.998324i	$0.481570\pi$
$822$	2.70223e15	0.251147
$823$	9.81837e15	0.906442	0.453221	−	0.891398i	$-0.350275\pi$
$823$	9.81837e15	0.906442	0.453221	+	0.891398i	$0.350275\pi$
$824$	−3.47056e15	−0.318274
$825$	2.15507e16	1.96320
$826$	−2.62457e15	−0.237502
$827$	−7.96875e15	−0.716325	−0.358162	−	0.933659i	$-0.616597\pi$
$827$	−7.96875e15	−0.716325	−0.358162	+	0.933659i	$0.616597\pi$
$828$	4.06944e13	0.00363386
$829$	−1.14116e16	−1.01227	−0.506134	−	0.862455i	$-0.668926\pi$
$829$	−1.14116e16	−1.01227	−0.506134	+	0.862455i	$0.668926\pi$
$830$	−2.11271e16	−1.86170
$831$	5.14664e15	0.450524
$832$	−1.46648e16	−1.27526
$833$	−3.16319e16	−2.73261
$834$	−1.50600e15	−0.129244
$835$	2.25296e16	1.92078
$836$	−7.21753e14	−0.0611300
$837$	1.93690e15	0.162974
$838$	1.29339e16	1.08116
$839$	2.51139e15	0.208556	0.104278	−	0.994548i	$-0.466747\pi$
$839$	2.51139e15	0.208556	0.104278	+	0.994548i	$0.466747\pi$
$840$	2.11239e16	1.74276
$841$	−1.21993e16	−0.999899
$842$	−6.33102e15	−0.515534
$843$	5.36955e15	0.434396
$844$	3.66158e14	0.0294297
$845$	−1.58437e16	−1.26516
$846$	−6.70303e15	−0.531783
$847$	−4.88017e16	−3.84660
$848$	−1.45218e16	−1.13722
$849$	−6.44526e15	−0.501474
$850$	3.09335e16	2.39125
$851$	−4.76466e15	−0.365948
$852$	2.50975e14	0.0191519
$853$	1.25539e16	0.951828	0.475914	−	0.879492i	$-0.342117\pi$
$853$	1.25539e16	0.951828	0.475914	+	0.879492i	$0.342117\pi$
$854$	9.38051e15	0.706656
$855$	8.34516e15	0.624627
$856$	1.04718e16	0.778784
$857$	1.60910e16	1.18902	0.594508	−	0.804090i	$-0.297347\pi$
$857$	1.60910e16	1.18902	0.594508	+	0.804090i	$0.297347\pi$
$858$	1.86746e16	1.37111
$859$	1.83850e16	1.34122	0.670610	−	0.741810i	$-0.266032\pi$
$859$	1.83850e16	1.34122	0.670610	+	0.741810i	$0.266032\pi$
$860$	4.44891e14	0.0322487
$861$	−2.61010e16	−1.87992
$862$	−5.32047e15	−0.380768
$863$	1.15024e16	0.817956	0.408978	−	0.912544i	$-0.365885\pi$
$863$	1.15024e16	0.817956	0.408978	+	0.912544i	$0.365885\pi$
$864$	1.71215e14	0.0120981
$865$	2.73931e16	1.92333
$866$	1.77749e16	1.24010
$867$	4.21559e15	0.292249
$868$	−6.94315e14	−0.0478298
$869$	−3.02601e16	−2.07139
$870$	1.47756e14	0.0100506
$871$	−1.90201e16	−1.28562
$872$	−1.32782e16	−0.891864
$873$	−3.83183e15	−0.255757
$874$	5.82317e15	0.386231
$875$	4.27636e16	2.81858
$876$	3.87929e14	0.0254085
$877$	−1.34056e16	−0.872549	−0.436274	−	0.899814i	$-0.643702\pi$
$877$	−1.34056e16	−0.872549	−0.436274	+	0.899814i	$0.643702\pi$
$878$	−1.51870e16	−0.982317
$879$	1.55857e15	0.100181
$880$	4.88459e16	3.12013
$881$	−7.65716e14	−0.0486072	−0.0243036	−	0.999705i	$-0.507737\pi$
$881$	−7.65716e14	−0.0486072	−0.0243036	+	0.999705i	$0.507737\pi$
$882$	−1.19486e16	−0.753769
$883$	−5.83349e15	−0.365717	−0.182858	−	0.983139i	$-0.558535\pi$
$883$	−5.83349e15	−0.365717	−0.182858	+	0.983139i	$0.558535\pi$
$884$	8.17148e14	0.0509112
$885$	2.07387e15	0.128408
$886$	−2.38714e16	−1.46890
$887$	−7.79861e15	−0.476911	−0.238455	−	0.971153i	$-0.576641\pi$
$887$	−7.79861e15	−0.476911	−0.238455	+	0.971153i	$0.576641\pi$
$888$	−9.86316e15	−0.599439
$889$	−1.98626e16	−1.19971
$890$	−3.89873e16	−2.34034
$891$	3.30103e15	0.196935
$892$	−4.57837e14	−0.0271459
$893$	−2.92401e16	−1.72304
$894$	−9.75769e15	−0.571466
$895$	−3.43489e16	−1.99934
$896$	3.24336e16	1.87630
$897$	−4.59309e15	−0.264087
$898$	−3.49788e16	−1.99887
$899$	1.49598e14	0.00849665
$900$	3.56207e14	0.0201080
$901$	−2.41402e16	−1.35442
$902$	−5.85130e16	−3.26299
$903$	1.12331e16	0.622609
$904$	−5.19446e15	−0.286163
$905$	7.39938e15	0.405161
$906$	1.03215e16	0.561744
$907$	1.16614e15	0.0630828	0.0315414	−	0.999502i	$-0.489958\pi$
$907$	1.16614e15	0.0630828	0.0315414	+	0.999502i	$0.489958\pi$
$908$	9.64288e14	0.0518483
$909$	−4.89431e15	−0.261571
$910$	7.74010e16	4.11168
$911$	1.68621e16	0.890349	0.445174	−	0.895444i	$-0.353142\pi$
$911$	1.68621e16	0.890349	0.445174	+	0.895444i	$0.353142\pi$
$912$	1.24338e16	0.652575
$913$	−3.64553e16	−1.90183
$914$	3.43617e15	0.178185
$915$	−7.41225e15	−0.382062
$916$	−6.57532e14	−0.0336893
$917$	−4.35140e15	−0.221614
$918$	4.73822e15	0.239873
$919$	−1.31495e16	−0.661717	−0.330859	−	0.943680i	$-0.607338\pi$
$919$	−1.31495e16	−0.661717	−0.330859	+	0.943680i	$0.607338\pi$
$920$	−1.16472e16	−0.582625
$921$	3.00876e15	0.149610
$922$	1.49913e16	0.741003
$923$	−2.83270e16	−1.39185
$924$	−1.18331e15	−0.0577966
$925$	−4.17060e16	−2.02497
$926$	1.24295e16	0.599922
$927$	−2.24786e15	−0.107853
$928$	1.32239e13	0.000630734 0
$929$	−1.08228e16	−0.513162	−0.256581	−	0.966523i	$-0.582596\pi$
$929$	−1.08228e16	−0.513162	−0.256581	+	0.966523i	$0.582596\pi$
$930$	1.79969e16	0.848285
$931$	−5.21222e16	−2.44230
$932$	−4.14928e14	−0.0193279
$933$	−7.55539e15	−0.349871
$934$	−2.50029e16	−1.15102
$935$	8.11985e16	3.71607
$936$	−9.50800e15	−0.432586
$937$	−6.72798e15	−0.304311	−0.152155	−	0.988357i	$-0.548621\pi$
$937$	−6.72798e15	−0.304311	−0.152155	+	0.988357i	$0.548621\pi$
$938$	3.95345e16	1.77771
$939$	−5.21721e15	−0.233226
$940$	−1.89864e15	−0.0843801
$941$	−3.78738e16	−1.67338	−0.836692	−	0.547674i	$-0.815513\pi$
$941$	−3.78738e16	−1.67338	−0.836692	+	0.547674i	$0.815513\pi$
$942$	1.18632e14	0.00521099
$943$	1.43915e16	0.628479
$944$	3.08993e15	0.134154
$945$	1.36818e16	0.590566
$946$	2.51822e16	1.08067
$947$	−3.31537e16	−1.41451	−0.707257	−	0.706957i	$-0.750068\pi$
$947$	−3.31537e16	−1.41451	−0.707257	+	0.706957i	$0.750068\pi$
$948$	−5.00162e14	−0.0212161
$949$	−4.37847e16	−1.84654
$950$	5.09714e16	2.13721
$951$	−1.97439e16	−0.823075
$952$	5.23193e16	2.16850
$953$	3.02516e16	1.24663	0.623314	−	0.781971i	$-0.285786\pi$
$953$	3.02516e16	1.24663	0.623314	+	0.781971i	$0.285786\pi$
$954$	−9.11868e15	−0.373608
$955$	−2.87579e16	−1.17149
$956$	−1.35527e15	−0.0548919
$957$	2.54957e14	0.0102672
$958$	6.64173e15	0.265932
$959$	1.93259e16	0.769373
$960$	−2.40859e16	−0.953390
$961$	−7.18722e15	−0.282867
$962$	−3.61401e16	−1.41425
$963$	6.78254e15	0.263905
$964$	1.38663e15	0.0536459
$965$	2.13214e16	0.820192
$966$	9.54704e15	0.365170
$967$	−3.09551e16	−1.17730	−0.588649	−	0.808389i	$-0.700340\pi$
$967$	−3.09551e16	−1.17730	−0.588649	+	0.808389i	$0.700340\pi$
$968$	5.57016e16	2.10646
$969$	2.06691e16	0.777216
$970$	−3.56038e16	−1.33122
$971$	−1.20450e16	−0.447819	−0.223910	−	0.974610i	$-0.571882\pi$
$971$	−1.20450e16	−0.447819	−0.223910	+	0.974610i	$0.571882\pi$
$972$	5.45618e13	0.00201709
$973$	−1.07706e16	−0.395932
$974$	−2.26360e16	−0.827418
$975$	−4.02043e16	−1.46133
$976$	−1.10438e16	−0.399157
$977$	−4.83305e15	−0.173701	−0.0868504	−	0.996221i	$-0.527680\pi$
$977$	−4.83305e15	−0.173701	−0.0868504	+	0.996221i	$0.527680\pi$
$978$	−2.04355e16	−0.730335
$979$	−6.72737e16	−2.39078
$980$	−3.38445e15	−0.119604
$981$	−8.60021e15	−0.302225
$982$	−1.64232e16	−0.573911
$983$	3.08059e15	0.107051	0.0535254	−	0.998566i	$-0.482954\pi$
$983$	3.08059e15	0.107051	0.0535254	+	0.998566i	$0.482954\pi$
$984$	2.97913e16	1.02948
$985$	6.86294e16	2.35836
$986$	3.65960e14	0.0125058
$987$	−4.79388e16	−1.62908
$988$	1.34648e15	0.0455025
$989$	−6.19365e15	−0.208145
$990$	3.06718e16	1.02505
$991$	−2.17402e15	−0.0722535	−0.0361268	−	0.999347i	$-0.511502\pi$
$991$	−2.17402e15	−0.0722535	−0.0361268	+	0.999347i	$0.511502\pi$
$992$	1.61069e15	0.0532351
$993$	1.35589e16	0.445661
$994$	5.88795e16	1.92459
$995$	1.39110e16	0.452200
$996$	−6.02560e14	−0.0194793
$997$	9.08856e15	0.292194	0.146097	−	0.989270i	$-0.453329\pi$
$997$	9.08856e15	0.292194	0.146097	+	0.989270i	$0.453329\pi$
$998$	−4.72037e15	−0.150924
$999$	−6.38831e15	−0.203131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.9	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.9	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-45.9608 q^{2} +243.000 q^{3} +64.3958 q^{4} -11937.5 q^{5} -11168.5 q^{6} -79874.8 q^{7} +91168.1 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-45.9608 q^{2} +243.000 q^{3} +64.3958 q^{4} -11937.5 q^{5} -11168.5 q^{6} -79874.8 q^{7} +91168.1 q^{8} +59049.0 q^{9} +548659. q^{10} +946726. q^{11} +15648.2 q^{12} -1.76618e6 q^{13} +3.67111e6 q^{14} -2.90082e6 q^{15} -4.32204e6 q^{16} -7.18471e6 q^{17} -2.71394e6 q^{18} -1.18388e7 q^{19} -768727. q^{20} -1.94096e7 q^{21} -4.35123e7 q^{22} +1.07020e7 q^{23} +2.21538e7 q^{24} +9.36768e7 q^{25} +8.11749e7 q^{26} +1.43489e7 q^{27} -5.14360e6 q^{28} +1.10825e6 q^{29} +1.33324e8 q^{30} +1.34986e8 q^{31} +1.19323e7 q^{32} +2.30054e8 q^{33} +3.30215e8 q^{34} +9.53509e8 q^{35} +3.80251e6 q^{36} -4.45212e8 q^{37} +5.44120e8 q^{38} -4.29181e8 q^{39} -1.08832e9 q^{40} +1.34475e9 q^{41} +8.92080e8 q^{42} -5.78738e8 q^{43} +6.09651e7 q^{44} -7.04900e8 q^{45} -4.91872e8 q^{46} +2.46985e9 q^{47} -1.05026e9 q^{48} +4.40266e9 q^{49} -4.30546e9 q^{50} -1.74588e9 q^{51} -1.13734e8 q^{52} +3.35994e9 q^{53} -6.59487e8 q^{54} -1.13016e10 q^{55} -7.28203e9 q^{56} -2.87683e9 q^{57} -5.09360e7 q^{58} -7.14924e8 q^{59} -1.86801e8 q^{60} +2.55522e9 q^{61} -6.20407e9 q^{62} -4.71653e9 q^{63} +8.30312e9 q^{64} +2.10838e10 q^{65} -1.05735e10 q^{66} +1.07691e10 q^{67} -4.62665e8 q^{68} +2.60059e9 q^{69} -4.38241e10 q^{70} +1.60386e10 q^{71} +5.38338e9 q^{72} +2.47907e10 q^{73} +2.04623e10 q^{74} +2.27635e10 q^{75} -7.62368e8 q^{76} -7.56196e10 q^{77} +1.97255e10 q^{78} -3.19630e10 q^{79} +5.15945e10 q^{80} +3.48678e9 q^{81} -6.18057e10 q^{82} -3.85068e10 q^{83} -1.24990e9 q^{84} +8.57677e10 q^{85} +2.65992e10 q^{86} +2.69304e8 q^{87} +8.63111e10 q^{88} -7.10593e10 q^{89} +3.23978e10 q^{90} +1.41073e11 q^{91} +6.89164e8 q^{92} +3.28016e10 q^{93} -1.13516e11 q^{94} +1.41326e11 q^{95} +2.89954e9 q^{96} -6.48923e10 q^{97} -2.02350e11 q^{98} +5.59032e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

Modular forms

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