LMFDB - Embedded newform 177.12.a.a.1.1

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-87.0020 q^{2} -243.000 q^{3} +5521.36 q^{4} -497.667 q^{5} +21141.5 q^{6} +10880.7 q^{7} -302189. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-87.0020 q^{2} -243.000 q^{3} +5521.36 q^{4} -497.667 q^{5} +21141.5 q^{6} +10880.7 q^{7} -302189. q^{8} +59049.0 q^{9} +43298.0 q^{10} +310893. q^{11} -1.34169e6 q^{12} -1.09899e6 q^{13} -946641. q^{14} +120933. q^{15} +1.49833e7 q^{16} +7.19696e6 q^{17} -5.13738e6 q^{18} +6.26538e6 q^{19} -2.74780e6 q^{20} -2.64400e6 q^{21} -2.70483e7 q^{22} +1.54620e7 q^{23} +7.34319e7 q^{24} -4.85805e7 q^{25} +9.56141e7 q^{26} -1.43489e7 q^{27} +6.00761e7 q^{28} -7.10429e6 q^{29} -1.05214e7 q^{30} +4.03274e7 q^{31} -6.84697e8 q^{32} -7.55470e7 q^{33} -6.26150e8 q^{34} -5.41495e6 q^{35} +3.26031e8 q^{36} -7.18924e8 q^{37} -5.45101e8 q^{38} +2.67054e8 q^{39} +1.50390e8 q^{40} +3.85411e8 q^{41} +2.30034e8 q^{42} -6.53643e8 q^{43} +1.71655e9 q^{44} -2.93867e7 q^{45} -1.34522e9 q^{46} +5.83771e8 q^{47} -3.64095e9 q^{48} -1.85894e9 q^{49} +4.22660e9 q^{50} -1.74886e9 q^{51} -6.06790e9 q^{52} -4.97322e9 q^{53} +1.24838e9 q^{54} -1.54721e8 q^{55} -3.28802e9 q^{56} -1.52249e9 q^{57} +6.18088e8 q^{58} +7.14924e8 q^{59} +6.67715e8 q^{60} +4.77228e8 q^{61} -3.50857e9 q^{62} +6.42493e8 q^{63} +2.88842e10 q^{64} +5.46930e8 q^{65} +6.57274e9 q^{66} -2.18049e9 q^{67} +3.97370e10 q^{68} -3.75726e9 q^{69} +4.71112e8 q^{70} +1.54140e10 q^{71} -1.78440e10 q^{72} +2.19704e10 q^{73} +6.25478e10 q^{74} +1.18050e10 q^{75} +3.45934e10 q^{76} +3.38273e9 q^{77} -2.32342e10 q^{78} -4.35217e9 q^{79} -7.45671e9 q^{80} +3.48678e9 q^{81} -3.35315e10 q^{82} +6.40974e10 q^{83} -1.45985e10 q^{84} -3.58169e9 q^{85} +5.68683e10 q^{86} +1.72634e9 q^{87} -9.39485e10 q^{88} -4.53166e10 q^{89} +2.55671e9 q^{90} -1.19577e10 q^{91} +8.53710e10 q^{92} -9.79957e9 q^{93} -5.07892e10 q^{94} -3.11807e9 q^{95} +1.66381e11 q^{96} -1.41445e11 q^{97} +1.61731e11 q^{98} +1.83579e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	−87.0020	−1.92249	−0.961246	−	0.275693i	$-0.911093\pi$
$2$	−87.0020	−1.92249	−0.961246	+	0.275693i	$0.911093\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	5521.36	2.69597
$5$	−497.667	−0.0712203	−0.0356102	−	0.999366i	$-0.511337\pi$
$5$	−497.667	−0.0712203	−0.0356102	+	0.999366i	$0.511337\pi$
$6$	21141.5	1.10995
$7$	10880.7	0.244690	0.122345	−	0.992488i	$-0.460959\pi$
$7$	10880.7	0.244690	0.122345	+	0.992488i	$0.460959\pi$
$8$	−302189.	−3.26050
$9$	59049.0	0.333333
$10$	43298.0	0.136920
$11$	310893.	0.582038	0.291019	−	0.956717i	$-0.406006\pi$
$11$	310893.	0.582038	0.291019	+	0.956717i	$0.406006\pi$
$12$	−1.34169e6	−1.55652
$13$	−1.09899e6	−0.820926	−0.410463	−	0.911877i	$-0.634633\pi$
$13$	−1.09899e6	−0.820926	−0.410463	+	0.911877i	$0.634633\pi$
$14$	−946641.	−0.470415
$15$	120933.	0.0411191
$16$	1.49833e7	3.57230
$17$	7.19696e6	1.22936	0.614681	−	0.788776i	$-0.289285\pi$
$17$	7.19696e6	1.22936	0.614681	+	0.788776i	$0.289285\pi$
$18$	−5.13738e6	−0.640831
$19$	6.26538e6	0.580501	0.290250	−	0.956951i	$-0.406261\pi$
$19$	6.26538e6	0.580501	0.290250	+	0.956951i	$0.406261\pi$
$20$	−2.74780e6	−0.192008
$21$	−2.64400e6	−0.141272
$22$	−2.70483e7	−1.11896
$23$	1.54620e7	0.500912	0.250456	−	0.968128i	$-0.419419\pi$
$23$	1.54620e7	0.500912	0.250456	+	0.968128i	$0.419419\pi$
$24$	7.34319e7	1.88245
$25$	−4.85805e7	−0.994928
$26$	9.56141e7	1.57822
$27$	−1.43489e7	−0.192450
$28$	6.00761e7	0.659679
$29$	−7.10429e6	−0.0643179	−0.0321589	−	0.999483i	$-0.510238\pi$
$29$	−7.10429e6	−0.0643179	−0.0321589	+	0.999483i	$0.510238\pi$
$30$	−1.05214e7	−0.0790511
$31$	4.03274e7	0.252995	0.126497	−	0.991967i	$-0.459626\pi$
$31$	4.03274e7	0.252995	0.126497	+	0.991967i	$0.459626\pi$
$32$	−6.84697e8	−3.60723
$33$	−7.55470e7	−0.336040
$34$	−6.26150e8	−2.36344
$35$	−5.41495e6	−0.0174269
$36$	3.26031e8	0.898658
$37$	−7.18924e8	−1.70441	−0.852204	−	0.523210i	$-0.824734\pi$
$37$	−7.18924e8	−1.70441	−0.852204	+	0.523210i	$0.824734\pi$
$38$	−5.45101e8	−1.11601
$39$	2.67054e8	0.473962
$40$	1.50390e8	0.232214
$41$	3.85411e8	0.519532	0.259766	−	0.965672i	$-0.416355\pi$
$41$	3.85411e8	0.519532	0.259766	+	0.965672i	$0.416355\pi$
$42$	2.30034e8	0.271594
$43$	−6.53643e8	−0.678054	−0.339027	−	0.940777i	$-0.610098\pi$
$43$	−6.53643e8	−0.678054	−0.339027	+	0.940777i	$0.610098\pi$
$44$	1.71655e9	1.56916
$45$	−2.93867e7	−0.0237401
$46$	−1.34522e9	−0.962999
$47$	5.83771e8	0.371282	0.185641	−	0.982618i	$-0.440564\pi$
$47$	5.83771e8	0.371282	0.185641	+	0.982618i	$0.440564\pi$
$48$	−3.64095e9	−2.06247
$49$	−1.85894e9	−0.940127
$50$	4.22660e9	1.91274
$51$	−1.74886e9	−0.709773
$52$	−6.06790e9	−2.21320
$53$	−4.97322e9	−1.63351	−0.816753	−	0.576987i	$-0.804228\pi$
$53$	−4.97322e9	−1.63351	−0.816753	+	0.576987i	$0.804228\pi$
$54$	1.24838e9	0.369984
$55$	−1.54721e8	−0.0414529
$56$	−3.28802e9	−0.797812
$57$	−1.52249e9	−0.335152
$58$	6.18088e8	0.123651
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	6.67715e8	0.110856
$61$	4.77228e8	0.0723456	0.0361728	−	0.999346i	$-0.488483\pi$
$61$	4.77228e8	0.0723456	0.0361728	+	0.999346i	$0.488483\pi$
$62$	−3.50857e9	−0.486380
$63$	6.42493e8	0.0815634
$64$	2.88842e10	3.36256
$65$	5.46930e8	0.0584666
$66$	6.57274e9	0.646033
$67$	−2.18049e9	−0.197307	−0.0986537	−	0.995122i	$-0.531454\pi$
$67$	−2.18049e9	−0.197307	−0.0986537	+	0.995122i	$0.531454\pi$
$68$	3.97370e10	3.31433
$69$	−3.75726e9	−0.289202
$70$	4.71112e8	0.0335031
$71$	1.54140e10	1.01390	0.506950	−	0.861976i	$-0.330773\pi$
$71$	1.54140e10	1.01390	0.506950	+	0.861976i	$0.330773\pi$
$72$	−1.78440e10	−1.08683
$73$	2.19704e10	1.24040	0.620200	−	0.784444i	$-0.287052\pi$
$73$	2.19704e10	1.24040	0.620200	+	0.784444i	$0.287052\pi$
$74$	6.25478e10	3.27671
$75$	1.18050e10	0.574422
$76$	3.45934e10	1.56502
$77$	3.38273e9	0.142419
$78$	−2.32342e10	−0.911188
$79$	−4.35217e9	−0.159132	−0.0795659	−	0.996830i	$-0.525353\pi$
$79$	−4.35217e9	−0.159132	−0.0795659	+	0.996830i	$0.525353\pi$
$80$	−7.45671e9	−0.254421
$81$	3.48678e9	0.111111
$82$	−3.35315e10	−0.998797
$83$	6.40974e10	1.78612	0.893060	−	0.449938i	$-0.148554\pi$
$83$	6.40974e10	1.78612	0.893060	+	0.449938i	$0.148554\pi$
$84$	−1.45985e10	−0.380866
$85$	−3.58169e9	−0.0875556
$86$	5.68683e10	1.30355
$87$	1.72634e9	0.0371339
$88$	−9.39485e10	−1.89773
$89$	−4.53166e10	−0.860226	−0.430113	−	0.902775i	$-0.641526\pi$
$89$	−4.53166e10	−0.860226	−0.430113	+	0.902775i	$0.641526\pi$
$90$	2.55671e9	0.0456402
$91$	−1.19577e10	−0.200873
$92$	8.53710e10	1.35045
$93$	−9.79957e9	−0.146067
$94$	−5.07892e10	−0.713787
$95$	−3.11807e9	−0.0413434
$96$	1.66381e11	2.08263
$97$	−1.41445e11	−1.67241	−0.836204	−	0.548418i	$-0.815230\pi$
$97$	−1.41445e11	−1.67241	−0.836204	+	0.548418i	$0.815230\pi$
$98$	1.61731e11	1.80739
$99$	1.83579e10	0.194013
$100$	−2.68230e11	−2.68230
$101$	1.59623e11	1.51122	0.755609	−	0.655023i	$-0.227341\pi$
$101$	1.59623e11	1.51122	0.755609	+	0.655023i	$0.227341\pi$
$102$	1.52154e11	1.36453
$103$	1.16182e11	0.987495	0.493748	−	0.869605i	$-0.335627\pi$
$103$	1.16182e11	0.987495	0.493748	+	0.869605i	$0.335627\pi$
$104$	3.32102e11	2.67663
$105$	1.31583e9	0.0100614
$106$	4.32681e11	3.14040
$107$	−1.39522e11	−0.961685	−0.480842	−	0.876807i	$-0.659669\pi$
$107$	−1.39522e11	−0.961685	−0.480842	+	0.876807i	$0.659669\pi$
$108$	−7.92254e10	−0.518841
$109$	4.90855e10	0.305568	0.152784	−	0.988260i	$-0.451176\pi$
$109$	4.90855e10	0.305568	0.152784	+	0.988260i	$0.451176\pi$
$110$	1.34611e10	0.0796929
$111$	1.74698e11	0.984040
$112$	1.63029e11	0.874108
$113$	−5.90391e9	−0.0301445	−0.0150722	−	0.999886i	$-0.504798\pi$
$113$	−5.90391e9	−0.0301445	−0.0150722	+	0.999886i	$0.504798\pi$
$114$	1.32460e11	0.644328
$115$	−7.69491e9	−0.0356751
$116$	−3.92253e10	−0.173399
$117$	−6.48941e10	−0.273642
$118$	−6.21999e10	−0.250287
$119$	7.83078e10	0.300813
$120$	−3.65447e10	−0.134069
$121$	−1.88657e11	−0.661232
$122$	−4.15199e10	−0.139084
$123$	−9.36548e10	−0.299952
$124$	2.22662e11	0.682067
$125$	4.84770e10	0.142079
$126$	−5.58982e10	−0.156805
$127$	1.07144e11	0.287771	0.143886	−	0.989594i	$-0.454040\pi$
$127$	1.07144e11	0.287771	0.143886	+	0.989594i	$0.454040\pi$
$128$	−1.11072e12	−2.85727
$129$	1.58835e11	0.391475
$130$	−4.75840e10	−0.112402
$131$	−1.95333e11	−0.442367	−0.221183	−	0.975232i	$-0.570992\pi$
$131$	−1.95333e11	−0.442367	−0.221183	+	0.975232i	$0.570992\pi$
$132$	−4.17122e11	−0.905954
$133$	6.81716e10	0.142043
$134$	1.89707e11	0.379322
$135$	7.14098e9	0.0137064
$136$	−2.17484e12	−4.00833
$137$	7.38374e10	0.130711	0.0653557	−	0.997862i	$-0.479182\pi$
$137$	7.38374e10	0.130711	0.0653557	+	0.997862i	$0.479182\pi$
$138$	3.26889e11	0.555988
$139$	3.14483e11	0.514062	0.257031	−	0.966403i	$-0.417256\pi$
$139$	3.14483e11	0.514062	0.257031	+	0.966403i	$0.417256\pi$
$140$	−2.98979e10	−0.0469825
$141$	−1.41856e11	−0.214360
$142$	−1.34105e12	−1.94921
$143$	−3.41667e11	−0.477810
$144$	8.84751e11	1.19077
$145$	3.53557e9	0.00458074
$146$	−1.91147e12	−2.38466
$147$	4.51722e11	0.542782
$148$	−3.96943e12	−4.59504
$149$	2.10310e11	0.234604	0.117302	−	0.993096i	$-0.462575\pi$
$149$	2.10310e11	0.234604	0.117302	+	0.993096i	$0.462575\pi$
$150$	−1.02706e12	−1.10432
$151$	1.38807e12	1.43893	0.719463	−	0.694531i	$-0.244388\pi$
$151$	1.38807e12	1.43893	0.719463	+	0.694531i	$0.244388\pi$
$152$	−1.89333e12	−1.89272
$153$	4.24973e11	0.409787
$154$	−2.94304e11	−0.273799
$155$	−2.00696e10	−0.0180184
$156$	1.47450e12	1.27779
$157$	2.74934e11	0.230028	0.115014	−	0.993364i	$-0.463309\pi$
$157$	2.74934e11	0.230028	0.115014	+	0.993364i	$0.463309\pi$
$158$	3.78648e11	0.305930
$159$	1.20849e12	0.943105
$160$	3.40751e11	0.256908
$161$	1.68237e11	0.122568
$162$	−3.03357e11	−0.213610
$163$	−3.64398e11	−0.248053	−0.124027	−	0.992279i	$-0.539581\pi$
$163$	−3.64398e11	−0.248053	−0.124027	+	0.992279i	$0.539581\pi$
$164$	2.12799e12	1.40065
$165$	3.75972e10	0.0239328
$166$	−5.57660e12	−3.43380
$167$	−2.21384e12	−1.31888	−0.659442	−	0.751756i	$-0.729207\pi$
$167$	−2.21384e12	−1.31888	−0.659442	+	0.751756i	$0.729207\pi$
$168$	7.98989e11	0.460617
$169$	−5.84388e11	−0.326080
$170$	3.11614e11	0.168325
$171$	3.69965e11	0.193500
$172$	−3.60900e12	−1.82802
$173$	−8.02401e11	−0.393675	−0.196838	−	0.980436i	$-0.563067\pi$
$173$	−8.02401e11	−0.393675	−0.196838	+	0.980436i	$0.563067\pi$
$174$	−1.50195e11	−0.0713897
$175$	−5.28588e11	−0.243449
$176$	4.65821e12	2.07922
$177$	−1.73727e11	−0.0751646
$178$	3.94264e12	1.65378
$179$	3.13610e12	1.27555	0.637776	−	0.770222i	$-0.279855\pi$
$179$	3.13610e12	1.27555	0.637776	+	0.770222i	$0.279855\pi$
$180$	−1.62255e11	−0.0640027
$181$	5.10220e11	0.195221	0.0976103	−	0.995225i	$-0.468880\pi$
$181$	5.10220e11	0.195221	0.0976103	+	0.995225i	$0.468880\pi$
$182$	1.04035e12	0.386176
$183$	−1.15967e11	−0.0417688
$184$	−4.67243e12	−1.63322
$185$	3.57785e11	0.121388
$186$	8.52582e11	0.280812
$187$	2.23748e12	0.715535
$188$	3.22321e12	1.00097
$189$	−1.56126e11	−0.0470907
$190$	2.71279e11	0.0794824
$191$	−8.22711e11	−0.234187	−0.117094	−	0.993121i	$-0.537358\pi$
$191$	−8.22711e11	−0.234187	−0.117094	+	0.993121i	$0.537358\pi$
$192$	−7.01886e12	−1.94138
$193$	1.70154e12	0.457379	0.228690	−	0.973499i	$-0.426556\pi$
$193$	1.70154e12	0.457379	0.228690	+	0.973499i	$0.426556\pi$
$194$	1.23060e13	3.21519
$195$	−1.32904e11	−0.0337557
$196$	−1.02639e13	−2.53456
$197$	1.95873e12	0.470338	0.235169	−	0.971955i	$-0.424436\pi$
$197$	1.95873e12	0.470338	0.235169	+	0.971955i	$0.424436\pi$
$198$	−1.59718e12	−0.372988
$199$	−4.45516e12	−1.01198	−0.505989	−	0.862540i	$-0.668872\pi$
$199$	−4.45516e12	−1.01198	−0.505989	+	0.862540i	$0.668872\pi$
$200$	1.46805e13	3.24396
$201$	5.29860e11	0.113916
$202$	−1.38875e13	−2.90530
$203$	−7.72995e10	−0.0157380
$204$	−9.65608e12	−1.91353
$205$	−1.91806e11	−0.0370013
$206$	−1.01081e13	−1.89845
$207$	9.13013e11	0.166971
$208$	−1.64665e13	−2.93260
$209$	1.94786e12	0.337873
$210$	−1.14480e11	−0.0193430
$211$	−2.33831e12	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$211$	−2.33831e12	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$212$	−2.74589e13	−4.40389
$213$	−3.74561e12	−0.585375
$214$	1.21387e13	1.84883
$215$	3.25297e11	0.0482912
$216$	4.33608e12	0.627483
$217$	4.38790e11	0.0619053
$218$	−4.27054e12	−0.587452
$219$	−5.33880e12	−0.716145
$220$	−8.54271e11	−0.111756
$221$	−7.90936e12	−1.00922
$222$	−1.51991e13	−1.89181
$223$	−4.82525e12	−0.585926	−0.292963	−	0.956124i	$-0.594641\pi$
$223$	−4.82525e12	−0.585926	−0.292963	+	0.956124i	$0.594641\pi$
$224$	−7.44997e12	−0.882653
$225$	−2.86863e12	−0.331643
$226$	5.13652e11	0.0579525
$227$	1.20927e13	1.33163	0.665813	−	0.746119i	$-0.268085\pi$
$227$	1.20927e13	1.33163	0.665813	+	0.746119i	$0.268085\pi$
$228$	−8.40620e12	−0.903562
$229$	1.31247e13	1.37719	0.688593	−	0.725148i	$-0.258228\pi$
$229$	1.31247e13	1.37719	0.688593	+	0.725148i	$0.258228\pi$
$230$	6.69473e11	0.0685851
$231$	−8.22002e11	−0.0822256
$232$	2.14684e12	0.209708
$233$	−1.03669e12	−0.0988990	−0.0494495	−	0.998777i	$-0.515747\pi$
$233$	−1.03669e12	−0.0988990	−0.0494495	+	0.998777i	$0.515747\pi$
$234$	5.64592e12	0.526075
$235$	−2.90523e11	−0.0264428
$236$	3.94735e12	0.350986
$237$	1.05758e12	0.0918748
$238$	−6.81294e12	−0.578310
$239$	−1.32504e13	−1.09911	−0.549553	−	0.835459i	$-0.685202\pi$
$239$	−1.32504e13	−1.09911	−0.549553	+	0.835459i	$0.685202\pi$
$240$	1.81198e12	0.146890
$241$	−4.03205e12	−0.319471	−0.159736	−	0.987160i	$-0.551064\pi$
$241$	−4.03205e12	−0.319471	−0.159736	+	0.987160i	$0.551064\pi$
$242$	1.64136e13	1.27121
$243$	−8.47289e11	−0.0641500
$244$	2.63495e12	0.195042
$245$	9.25132e11	0.0669561
$246$	8.14816e12	0.576656
$247$	−6.88558e12	−0.476548
$248$	−1.21865e13	−0.824888
$249$	−1.55757e13	−1.03122
$250$	−4.21760e12	−0.273146
$251$	2.46265e13	1.56026	0.780129	−	0.625619i	$-0.215153\pi$
$251$	2.46265e13	1.56026	0.780129	+	0.625619i	$0.215153\pi$
$252$	3.54743e12	0.219893
$253$	4.80701e12	0.291550
$254$	−9.32175e12	−0.553238
$255$	8.70350e11	0.0505502
$256$	3.74804e13	2.13052
$257$	−2.39787e13	−1.33411	−0.667057	−	0.745007i	$-0.732446\pi$
$257$	−2.39787e13	−1.33411	−0.667057	+	0.745007i	$0.732446\pi$
$258$	−1.38190e13	−0.752607
$259$	−7.82238e12	−0.417052
$260$	3.01979e12	0.157625
$261$	−4.19501e11	−0.0214393
$262$	1.69943e13	0.850447
$263$	5.97421e12	0.292768	0.146384	−	0.989228i	$-0.453236\pi$
$263$	5.97421e12	0.292768	0.146384	+	0.989228i	$0.453236\pi$
$264$	2.28295e13	1.09566
$265$	2.47501e12	0.116339
$266$	−5.93107e12	−0.273076
$267$	1.10119e13	0.496652
$268$	−1.20393e13	−0.531936
$269$	3.10192e12	0.134274	0.0671372	−	0.997744i	$-0.478613\pi$
$269$	3.10192e12	0.134274	0.0671372	+	0.997744i	$0.478613\pi$
$270$	−6.21280e11	−0.0263504
$271$	4.47567e12	0.186006	0.0930030	−	0.995666i	$-0.470353\pi$
$271$	4.47567e12	0.186006	0.0930030	+	0.995666i	$0.470353\pi$
$272$	1.07834e14	4.39166
$273$	2.90573e12	0.115974
$274$	−6.42401e12	−0.251292
$275$	−1.51033e13	−0.579085
$276$	−2.07451e13	−0.779680
$277$	2.20233e13	0.811417	0.405708	−	0.914003i	$-0.367025\pi$
$277$	2.20233e13	0.811417	0.405708	+	0.914003i	$0.367025\pi$
$278$	−2.73606e13	−0.988279
$279$	2.38129e12	0.0843315
$280$	1.63634e12	0.0568204
$281$	−5.04649e13	−1.71832	−0.859162	−	0.511704i	$-0.829014\pi$
$281$	−5.04649e13	−1.71832	−0.859162	+	0.511704i	$0.829014\pi$
$282$	1.23418e13	0.412105
$283$	1.78252e13	0.583725	0.291863	−	0.956460i	$-0.405725\pi$
$283$	1.78252e13	0.583725	0.291863	+	0.956460i	$0.405725\pi$
$284$	8.51063e13	2.73345
$285$	7.57692e11	0.0238696
$286$	2.97258e13	0.918586
$287$	4.19353e12	0.127125
$288$	−4.04307e13	−1.20241
$289$	1.75243e13	0.511332
$290$	−3.07602e11	−0.00880643
$291$	3.43711e13	0.965565
$292$	1.21306e14	3.34409
$293$	4.57165e12	0.123680	0.0618402	−	0.998086i	$-0.480303\pi$
$293$	4.57165e12	0.123680	0.0618402	+	0.998086i	$0.480303\pi$
$294$	−3.93007e13	−1.04349
$295$	−3.55794e11	−0.00927209
$296$	2.17251e14	5.55722
$297$	−4.46097e12	−0.112013
$298$	−1.82974e13	−0.451024
$299$	−1.69925e13	−0.411212
$300$	6.51799e13	1.54863
$301$	−7.11208e12	−0.165913
$302$	−1.20765e14	−2.76632
$303$	−3.87883e13	−0.872502
$304$	9.38763e13	2.07373
$305$	−2.37501e11	−0.00515248
$306$	−3.69735e13	−0.787813
$307$	−2.93239e13	−0.613706	−0.306853	−	0.951757i	$-0.599276\pi$
$307$	−2.93239e13	−0.613706	−0.306853	+	0.951757i	$0.599276\pi$
$308$	1.86772e13	0.383958
$309$	−2.82323e13	−0.570131
$310$	1.74610e12	0.0346401
$311$	2.26927e13	0.442286	0.221143	−	0.975241i	$-0.429021\pi$
$311$	2.26927e13	0.442286	0.221143	+	0.975241i	$0.429021\pi$
$312$	−8.07008e13	−1.54535
$313$	−6.25481e13	−1.17685	−0.588424	−	0.808552i	$-0.700251\pi$
$313$	−6.25481e13	−1.17685	−0.588424	+	0.808552i	$0.700251\pi$
$314$	−2.39199e13	−0.442227
$315$	−3.19748e11	−0.00580897
$316$	−2.40299e13	−0.429015
$317$	3.29402e13	0.577963	0.288981	−	0.957335i	$-0.406683\pi$
$317$	3.29402e13	0.577963	0.288981	+	0.957335i	$0.406683\pi$
$318$	−1.05141e14	−1.81311
$319$	−2.20867e12	−0.0374354
$320$	−1.43747e13	−0.239483
$321$	3.39039e13	0.555229
$322$	−1.46369e13	−0.235636
$323$	4.50917e13	0.713646
$324$	1.92518e13	0.299553
$325$	5.33893e13	0.816762
$326$	3.17034e13	0.476880
$327$	−1.19278e13	−0.176420
$328$	−1.16467e14	−1.69393
$329$	6.35182e12	0.0908491
$330$	−3.27104e12	−0.0460107
$331$	−1.05376e14	−1.45777	−0.728885	−	0.684636i	$-0.759961\pi$
$331$	−1.05376e14	−1.45777	−0.728885	+	0.684636i	$0.759961\pi$
$332$	3.53904e14	4.81533
$333$	−4.24517e13	−0.568136
$334$	1.92609e14	2.53554
$335$	1.08516e12	0.0140523
$336$	−3.96160e13	−0.504666
$337$	−1.28291e14	−1.60780	−0.803900	−	0.594764i	$-0.797245\pi$
$337$	−1.28291e14	−1.60780	−0.803900	+	0.594764i	$0.797245\pi$
$338$	5.08429e13	0.626886
$339$	1.43465e12	0.0174039
$340$	−1.97758e13	−0.236048
$341$	1.25375e13	0.147252
$342$	−3.21877e13	−0.372003
$343$	−4.17411e13	−0.474730
$344$	1.97524e14	2.21079
$345$	1.86986e12	0.0205970
$346$	6.98105e13	0.756837
$347$	−1.02566e14	−1.09444	−0.547219	−	0.836989i	$-0.684314\pi$
$347$	−1.02566e14	−1.09444	−0.547219	+	0.836989i	$0.684314\pi$
$348$	9.53175e12	0.100112
$349$	−7.67112e12	−0.0793083	−0.0396542	−	0.999213i	$-0.512626\pi$
$349$	−7.67112e12	−0.0793083	−0.0396542	+	0.999213i	$0.512626\pi$
$350$	4.59882e13	0.468029
$351$	1.57693e13	0.157987
$352$	−2.12868e14	−2.09954
$353$	−8.27561e13	−0.803598	−0.401799	−	0.915728i	$-0.631615\pi$
$353$	−8.27561e13	−0.803598	−0.401799	+	0.915728i	$0.631615\pi$
$354$	1.51146e13	0.144503
$355$	−7.67105e12	−0.0722102
$356$	−2.50209e14	−2.31915
$357$	−1.90288e13	−0.173674
$358$	−2.72847e14	−2.45224
$359$	5.25379e13	0.465000	0.232500	−	0.972596i	$-0.425309\pi$
$359$	5.25379e13	0.465000	0.232500	+	0.972596i	$0.425309\pi$
$360$	8.88035e12	0.0774045
$361$	−7.72352e13	−0.663019
$362$	−4.43902e13	−0.375310
$363$	4.58437e13	0.381762
$364$	−6.60228e13	−0.541548
$365$	−1.09339e13	−0.0883416
$366$	1.00893e13	0.0803001
$367$	−8.76316e13	−0.687064	−0.343532	−	0.939141i	$-0.611623\pi$
$367$	−8.76316e13	−0.687064	−0.343532	+	0.939141i	$0.611623\pi$
$368$	2.31672e14	1.78941
$369$	2.27581e13	0.173177
$370$	−3.11280e13	−0.233368
$371$	−5.41120e13	−0.399703
$372$	−5.41069e13	−0.393792
$373$	−2.72590e14	−1.95484	−0.977419	−	0.211310i	$-0.932227\pi$
$373$	−2.72590e14	−1.95484	−0.977419	+	0.211310i	$0.932227\pi$
$374$	−1.94666e14	−1.37561
$375$	−1.17799e13	−0.0820296
$376$	−1.76409e14	−1.21056
$377$	7.80752e12	0.0528002
$378$	1.35833e13	0.0905314
$379$	−6.18379e13	−0.406199	−0.203100	−	0.979158i	$-0.565101\pi$
$379$	−6.18379e13	−0.406199	−0.203100	+	0.979158i	$0.565101\pi$
$380$	−1.72160e13	−0.111461
$381$	−2.60360e13	−0.166145
$382$	7.15775e13	0.450223
$383$	1.20075e14	0.744491	0.372245	−	0.928134i	$-0.378588\pi$
$383$	1.20075e14	0.744491	0.372245	+	0.928134i	$0.378588\pi$
$384$	2.69906e14	1.64965
$385$	−1.68347e12	−0.0101431
$386$	−1.48037e14	−0.879308
$387$	−3.85970e13	−0.226018
$388$	−7.80967e14	−4.50877
$389$	−1.68458e14	−0.958888	−0.479444	−	0.877573i	$-0.659162\pi$
$389$	−1.68458e14	−0.958888	−0.479444	+	0.877573i	$0.659162\pi$
$390$	1.15629e13	0.0648951
$391$	1.11279e14	0.615802
$392$	5.61751e14	3.06528
$393$	4.74658e13	0.255401
$394$	−1.70413e14	−0.904220
$395$	2.16593e12	0.0113334
$396$	1.01361e14	0.523053
$397$	5.51988e13	0.280919	0.140460	−	0.990086i	$-0.455142\pi$
$397$	5.51988e13	0.280919	0.140460	+	0.990086i	$0.455142\pi$
$398$	3.87608e14	1.94552
$399$	−1.65657e13	−0.0820085
$400$	−7.27897e14	−3.55418
$401$	−7.47170e13	−0.359853	−0.179927	−	0.983680i	$-0.557586\pi$
$401$	−7.47170e13	−0.359853	−0.179927	+	0.983680i	$0.557586\pi$
$402$	−4.60989e13	−0.219002
$403$	−4.43193e13	−0.207690
$404$	8.81334e14	4.07421
$405$	−1.73526e12	−0.00791337
$406$	6.72521e12	0.0302561
$407$	−2.23508e14	−0.992029
$408$	5.28487e14	2.31421
$409$	3.86108e14	1.66813	0.834066	−	0.551664i	$-0.186007\pi$
$409$	3.86108e14	1.66813	0.834066	+	0.551664i	$0.186007\pi$
$410$	1.66875e13	0.0711346
$411$	−1.79425e13	−0.0754663
$412$	6.41484e14	2.66226
$413$	7.77886e12	0.0318560
$414$	−7.94340e13	−0.321000
$415$	−3.18991e13	−0.127208
$416$	7.52473e14	2.96127
$417$	−7.64193e13	−0.296794
$418$	−1.69468e14	−0.649559
$419$	2.76663e14	1.04658	0.523291	−	0.852154i	$-0.324704\pi$
$419$	2.76663e14	1.04658	0.523291	+	0.852154i	$0.324704\pi$
$420$	7.26519e12	0.0271254
$421$	5.22220e13	0.192443	0.0962214	−	0.995360i	$-0.469324\pi$
$421$	5.22220e13	0.192443	0.0962214	+	0.995360i	$0.469324\pi$
$422$	2.03437e14	0.739967
$423$	3.44711e13	0.123761
$424$	1.50285e15	5.32604
$425$	−3.49631e14	−1.22313
$426$	3.25875e14	1.12538
$427$	5.19257e12	0.0177023
$428$	−7.70352e14	−2.59268
$429$	8.30252e13	0.275864
$430$	−2.83015e13	−0.0928395
$431$	−4.64077e14	−1.50302	−0.751511	−	0.659720i	$-0.770675\pi$
$431$	−4.64077e14	−1.50302	−0.751511	+	0.659720i	$0.770675\pi$
$432$	−2.14994e14	−0.687490
$433$	7.89752e13	0.249349	0.124674	−	0.992198i	$-0.460211\pi$
$433$	7.89752e13	0.249349	0.124674	+	0.992198i	$0.460211\pi$
$434$	−3.81756e13	−0.119012
$435$	−8.59144e11	−0.00264469
$436$	2.71019e14	0.823803
$437$	9.68751e13	0.290780
$438$	4.64486e14	1.37678
$439$	−1.27763e14	−0.373982	−0.186991	−	0.982362i	$-0.559873\pi$
$439$	−1.27763e14	−0.373982	−0.186991	+	0.982362i	$0.559873\pi$
$440$	4.67551e13	0.135157
$441$	−1.09768e14	−0.313376
$442$	6.88131e14	1.94021
$443$	3.11261e14	0.866772	0.433386	−	0.901208i	$-0.357319\pi$
$443$	3.11261e14	0.866772	0.433386	+	0.901208i	$0.357319\pi$
$444$	9.64573e14	2.65295
$445$	2.25526e13	0.0612656
$446$	4.19806e14	1.12644
$447$	−5.11053e13	−0.135449
$448$	3.14279e14	0.822786
$449$	−7.05942e13	−0.182563	−0.0912817	−	0.995825i	$-0.529096\pi$
$449$	−7.05942e13	−0.182563	−0.0912817	+	0.995825i	$0.529096\pi$
$450$	2.49576e14	0.637580
$451$	1.19822e14	0.302387
$452$	−3.25976e13	−0.0812688
$453$	−3.37301e14	−0.830765
$454$	−1.05209e15	−2.56004
$455$	5.95096e12	0.0143062
$456$	4.60079e14	1.09276
$457$	−3.60614e14	−0.846259	−0.423130	−	0.906069i	$-0.639069\pi$
$457$	−3.60614e14	−0.846259	−0.423130	+	0.906069i	$0.639069\pi$
$458$	−1.14187e15	−2.64763
$459$	−1.03268e14	−0.236591
$460$	−4.24863e13	−0.0961792
$461$	−7.46336e14	−1.66947	−0.834736	−	0.550650i	$-0.814380\pi$
$461$	−7.46336e14	−1.66947	−0.834736	+	0.550650i	$0.814380\pi$
$462$	7.15159e13	0.158078
$463$	−7.54481e14	−1.64798	−0.823991	−	0.566602i	$-0.808258\pi$
$463$	−7.54481e14	−1.64798	−0.823991	+	0.566602i	$0.808258\pi$
$464$	−1.06446e14	−0.229763
$465$	4.87692e12	0.0104029
$466$	9.01942e13	0.190132
$467$	−2.58798e14	−0.539161	−0.269581	−	0.962978i	$-0.586885\pi$
$467$	−2.58798e14	−0.539161	−0.269581	+	0.962978i	$0.586885\pi$
$468$	−3.58303e14	−0.737732
$469$	−2.37253e13	−0.0482792
$470$	2.52761e13	0.0508361
$471$	−6.68091e13	−0.132807
$472$	−2.16042e14	−0.424481
$473$	−2.03213e14	−0.394653
$474$	−9.20114e13	−0.176629
$475$	−3.04375e14	−0.577556
$476$	4.32365e14	0.810984
$477$	−2.93664e14	−0.544502
$478$	1.15281e15	2.11302
$479$	9.95737e13	0.180426	0.0902130	−	0.995922i	$-0.471245\pi$
$479$	9.95737e13	0.180426	0.0902130	+	0.995922i	$0.471245\pi$
$480$	−8.28025e13	−0.148326
$481$	7.90088e14	1.39919
$482$	3.50796e14	0.614181
$483$	−4.08815e13	−0.0707648
$484$	−1.04164e15	−1.78266
$485$	7.03924e13	0.119109
$486$	7.37158e13	0.123328
$487$	−4.77882e14	−0.790517	−0.395258	−	0.918570i	$-0.629345\pi$
$487$	−4.77882e14	−0.790517	−0.395258	+	0.918570i	$0.629345\pi$
$488$	−1.44213e14	−0.235883
$489$	8.85488e13	0.143214
$490$	−8.04884e13	−0.128723
$491$	−1.03256e15	−1.63293	−0.816465	−	0.577395i	$-0.804069\pi$
$491$	−1.03256e15	−1.63293	−0.816465	+	0.577395i	$0.804069\pi$
$492$	−5.17102e14	−0.808663
$493$	−5.11293e13	−0.0790700
$494$	5.99059e14	0.916160
$495$	−9.13613e12	−0.0138176
$496$	6.04239e14	0.903774
$497$	1.67715e14	0.248091
$498$	1.35511e15	1.98251
$499$	−4.81188e13	−0.0696245	−0.0348122	−	0.999394i	$-0.511083\pi$
$499$	−4.81188e13	−0.0696245	−0.0348122	+	0.999394i	$0.511083\pi$
$500$	2.67659e14	0.383042
$501$	5.37964e14	0.761458
$502$	−2.14255e15	−2.99958
$503$	−1.16003e15	−1.60637	−0.803184	−	0.595731i	$-0.796862\pi$
$503$	−1.16003e15	−1.60637	−0.803184	+	0.595731i	$0.796862\pi$
$504$	−1.94154e14	−0.265937
$505$	−7.94390e13	−0.107629
$506$	−4.18220e14	−0.560502
$507$	1.42006e14	0.188262
$508$	5.91580e14	0.775824
$509$	3.15698e14	0.409566	0.204783	−	0.978807i	$-0.434351\pi$
$509$	3.15698e14	0.409566	0.204783	+	0.978807i	$0.434351\pi$
$510$	−7.57223e13	−0.0971824
$511$	2.39052e14	0.303514
$512$	−9.86111e14	−1.23863
$513$	−8.99014e13	−0.111717
$514$	2.08619e15	2.56482
$515$	−5.78201e13	−0.0703297
$516$	8.76987e14	1.05541
$517$	1.81490e14	0.216100
$518$	6.80563e14	0.801779
$519$	1.94983e14	0.227288
$520$	−1.65276e14	−0.190630
$521$	1.24006e15	1.41525	0.707626	−	0.706587i	$-0.249766\pi$
$521$	1.24006e15	1.41525	0.707626	+	0.706587i	$0.249766\pi$
$522$	3.64975e13	0.0412169
$523$	−1.64034e15	−1.83305	−0.916526	−	0.399975i	$-0.869019\pi$
$523$	−1.64034e15	−1.83305	−0.916526	+	0.399975i	$0.869019\pi$
$524$	−1.07850e15	−1.19261
$525$	1.28447e14	0.140555
$526$	−5.19769e14	−0.562845
$527$	2.90235e14	0.311022
$528$	−1.13195e15	−1.20044
$529$	−7.13738e14	−0.749087
$530$	−2.15331e14	−0.223660
$531$	4.22156e13	0.0433963
$532$	3.76400e14	0.382944
$533$	−4.23561e14	−0.426498
$534$	−9.58062e14	−0.954809
$535$	6.94356e13	0.0684915
$536$	6.58922e14	0.643320
$537$	−7.62072e14	−0.736440
$538$	−2.69874e14	−0.258142
$539$	−5.77931e14	−0.547189
$540$	3.94279e13	0.0369520
$541$	1.20176e15	1.11489	0.557444	−	0.830215i	$-0.311782\pi$
$541$	1.20176e15	1.11489	0.557444	+	0.830215i	$0.311782\pi$
$542$	−3.89392e14	−0.357595
$543$	−1.23984e14	−0.112711
$544$	−4.92774e15	−4.43459
$545$	−2.44282e13	−0.0217626
$546$	−2.52804e14	−0.222959
$547$	6.94610e14	0.606472	0.303236	−	0.952915i	$-0.401933\pi$
$547$	6.94610e14	0.606472	0.303236	+	0.952915i	$0.401933\pi$
$548$	4.07683e14	0.352395
$549$	2.81799e13	0.0241152
$550$	1.31402e15	1.11329
$551$	−4.45111e13	−0.0373366
$552$	1.13540e15	0.942941
$553$	−4.73546e13	−0.0389380
$554$	−1.91607e15	−1.55994
$555$	−8.69417e13	−0.0700836
$556$	1.73637e15	1.38590
$557$	−4.88417e14	−0.386000	−0.193000	−	0.981199i	$-0.561822\pi$
$557$	−4.88417e14	−0.386000	−0.193000	+	0.981199i	$0.561822\pi$
$558$	−2.07178e14	−0.162127
$559$	7.18346e14	0.556633
$560$	−8.11340e13	−0.0622542
$561$	−5.43709e14	−0.413114
$562$	4.39055e15	3.30346
$563$	−2.37293e14	−0.176803	−0.0884013	−	0.996085i	$-0.528176\pi$
$563$	−2.37293e14	−0.176803	−0.0884013	+	0.996085i	$0.528176\pi$
$564$	−7.83239e14	−0.577909
$565$	2.93818e12	0.00214690
$566$	−1.55083e15	−1.12221
$567$	3.79386e13	0.0271878
$568$	−4.65795e15	−3.30582
$569$	1.01923e15	0.716399	0.358199	−	0.933645i	$-0.383391\pi$
$569$	1.01923e15	0.716399	0.358199	+	0.933645i	$0.383391\pi$
$570$	−6.59208e13	−0.0458892
$571$	2.20057e15	1.51718	0.758589	−	0.651569i	$-0.225889\pi$
$571$	2.20057e15	1.51718	0.758589	+	0.651569i	$0.225889\pi$
$572$	−1.88647e15	−1.28816
$573$	1.99919e14	0.135208
$574$	−3.64846e14	−0.244396
$575$	−7.51149e14	−0.498371
$576$	1.70558e15	1.12085
$577$	1.03069e15	0.670908	0.335454	−	0.942057i	$-0.391110\pi$
$577$	1.03069e15	0.670908	0.335454	+	0.942057i	$0.391110\pi$
$578$	−1.52465e15	−0.983031
$579$	−4.13474e14	−0.264068
$580$	1.95211e13	0.0123496
$581$	6.97422e14	0.437046
$582$	−2.99035e15	−1.85629
$583$	−1.54614e15	−0.950762
$584$	−6.63920e15	−4.04432
$585$	3.22957e13	0.0194889
$586$	−3.97743e14	−0.237775
$587$	9.95367e14	0.589486	0.294743	−	0.955577i	$-0.404766\pi$
$587$	9.95367e14	0.589486	0.294743	+	0.955577i	$0.404766\pi$
$588$	2.49412e15	1.46333
$589$	2.52667e14	0.146864
$590$	3.09548e13	0.0178255
$591$	−4.75971e14	−0.271550
$592$	−1.07719e16	−6.08866
$593$	−3.14138e15	−1.75922	−0.879610	−	0.475695i	$-0.842197\pi$
$593$	−3.14138e15	−1.75922	−0.879610	+	0.475695i	$0.842197\pi$
$594$	3.88114e14	0.215344
$595$	−3.89712e13	−0.0214240
$596$	1.16120e15	0.632486
$597$	1.08260e15	0.584266
$598$	1.47838e15	0.790551
$599$	1.13720e15	0.602547	0.301274	−	0.953538i	$-0.402588\pi$
$599$	1.13720e15	0.602547	0.301274	+	0.953538i	$0.402588\pi$
$600$	−3.56736e15	−1.87290
$601$	−1.10569e15	−0.575208	−0.287604	−	0.957749i	$-0.592859\pi$
$601$	−1.10569e15	−0.575208	−0.287604	+	0.957749i	$0.592859\pi$
$602$	6.18766e14	0.318967
$603$	−1.28756e14	−0.0657692
$604$	7.66404e15	3.87931
$605$	9.38885e13	0.0470931
$606$	3.37466e15	1.67738
$607$	3.39894e15	1.67420	0.837098	−	0.547053i	$-0.184250\pi$
$607$	3.39894e15	1.67420	0.837098	+	0.547053i	$0.184250\pi$
$608$	−4.28989e15	−2.09400
$609$	1.87838e13	0.00908631
$610$	2.06631e13	0.00990560
$611$	−6.41557e14	−0.304795
$612$	2.34643e15	1.10478
$613$	−2.72226e15	−1.27027	−0.635137	−	0.772400i	$-0.719056\pi$
$613$	−2.72226e15	−1.27027	−0.635137	+	0.772400i	$0.719056\pi$
$614$	2.55124e15	1.17984
$615$	4.66089e13	0.0213627
$616$	−1.02222e15	−0.464357
$617$	−3.28617e15	−1.47952	−0.739761	−	0.672870i	$-0.765061\pi$
$617$	−3.28617e15	−1.47952	−0.739761	+	0.672870i	$0.765061\pi$
$618$	2.45627e15	1.09607
$619$	−2.92121e15	−1.29200	−0.646002	−	0.763336i	$-0.723560\pi$
$619$	−2.92121e15	−1.29200	−0.646002	+	0.763336i	$0.723560\pi$
$620$	−1.10812e14	−0.0485770
$621$	−2.21862e14	−0.0964005
$622$	−1.97431e15	−0.850292
$623$	−4.93076e14	−0.210489
$624$	4.00136e15	1.69314
$625$	2.34797e15	0.984809
$626$	5.44182e15	2.26248
$627$	−4.73331e14	−0.195071
$628$	1.51801e15	0.620150
$629$	−5.17406e15	−2.09533
$630$	2.78187e13	0.0111677
$631$	2.34220e15	0.932098	0.466049	−	0.884759i	$-0.345677\pi$
$631$	2.34220e15	0.932098	0.466049	+	0.884759i	$0.345677\pi$
$632$	1.31518e15	0.518849
$633$	5.68208e14	0.222222
$634$	−2.86586e15	−1.11113
$635$	−5.33221e13	−0.0204952
$636$	6.67252e15	2.54259
$637$	2.04295e15	0.771775
$638$	1.92159e14	0.0719693
$639$	9.10182e14	0.337966
$640$	5.52771e14	0.203496
$641$	−2.51161e14	−0.0916712	−0.0458356	−	0.998949i	$-0.514595\pi$
$641$	−2.51161e14	−0.0916712	−0.0458356	+	0.998949i	$0.514595\pi$
$642$	−2.94971e15	−1.06742
$643$	2.37034e15	0.850452	0.425226	−	0.905087i	$-0.360195\pi$
$643$	2.37034e15	0.850452	0.425226	+	0.905087i	$0.360195\pi$
$644$	9.28894e14	0.330441
$645$	−7.90471e13	−0.0278810
$646$	−3.92307e15	−1.37198
$647$	3.65947e15	1.26895	0.634476	−	0.772943i	$-0.281216\pi$
$647$	3.65947e15	1.26895	0.634476	+	0.772943i	$0.281216\pi$
$648$	−1.05367e15	−0.362277
$649$	2.22265e14	0.0757749
$650$	−4.64498e15	−1.57022
$651$	−1.06626e14	−0.0357410
$652$	−2.01197e15	−0.668745
$653$	3.28323e15	1.08213	0.541063	−	0.840982i	$-0.318022\pi$
$653$	3.28323e15	1.08213	0.541063	+	0.840982i	$0.318022\pi$
$654$	1.03774e15	0.339165
$655$	9.72106e13	0.0315055
$656$	5.77474e15	1.85593
$657$	1.29733e15	0.413466
$658$	−5.52621e14	−0.174657
$659$	5.06314e15	1.58690	0.793451	−	0.608634i	$-0.208282\pi$
$659$	5.06314e15	1.58690	0.793451	+	0.608634i	$0.208282\pi$
$660$	2.07588e14	0.0645223
$661$	1.00841e15	0.310834	0.155417	−	0.987849i	$-0.450328\pi$
$661$	1.00841e15	0.310834	0.155417	+	0.987849i	$0.450328\pi$
$662$	9.16795e15	2.80255
$663$	1.92198e15	0.582671
$664$	−1.93695e16	−5.82364
$665$	−3.39268e13	−0.0101163
$666$	3.69339e15	1.09224
$667$	−1.09846e14	−0.0322176
$668$	−1.22234e16	−3.55568
$669$	1.17253e15	0.338284
$670$	−9.44112e13	−0.0270154
$671$	1.48367e14	0.0421079
$672$	1.81034e15	0.509600
$673$	3.76567e15	1.05138	0.525690	−	0.850676i	$-0.323807\pi$
$673$	3.76567e15	1.05138	0.525690	+	0.850676i	$0.323807\pi$
$674$	1.11616e16	3.09098
$675$	6.97076e14	0.191474
$676$	−3.22661e15	−0.879103
$677$	−6.19641e15	−1.67457	−0.837283	−	0.546769i	$-0.815858\pi$
$677$	−6.19641e15	−1.67457	−0.837283	+	0.546769i	$0.815858\pi$
$678$	−1.24817e14	−0.0334589
$679$	−1.53901e15	−0.409222
$680$	1.08235e15	0.285475
$681$	−2.93853e15	−0.768815
$682$	−1.09079e15	−0.283092
$683$	3.26788e15	0.841301	0.420651	−	0.907223i	$-0.361802\pi$
$683$	3.26788e15	0.841301	0.420651	+	0.907223i	$0.361802\pi$
$684$	2.04271e15	0.521672
$685$	−3.67465e13	−0.00930931
$686$	3.63157e15	0.912665
$687$	−3.18929e15	−0.795119
$688$	−9.79376e15	−2.42222
$689$	5.46551e15	1.34099
$690$	−1.62682e14	−0.0395976
$691$	−2.65936e15	−0.642167	−0.321084	−	0.947051i	$-0.604047\pi$
$691$	−2.65936e15	−0.642167	−0.321084	+	0.947051i	$0.604047\pi$
$692$	−4.43034e15	−1.06134
$693$	1.99747e14	0.0474730
$694$	8.92345e15	2.10405
$695$	−1.56508e14	−0.0366116
$696$	−5.21682e14	−0.121075
$697$	2.77379e15	0.638694
$698$	6.67403e14	0.152470
$699$	2.51916e14	0.0570993
$700$	−2.91852e15	−0.656333
$701$	−8.34269e15	−1.86147	−0.930737	−	0.365689i	$-0.880833\pi$
$701$	−8.34269e15	−1.86147	−0.930737	+	0.365689i	$0.880833\pi$
$702$	−1.37196e15	−0.303729
$703$	−4.50433e15	−0.989410
$704$	8.97989e15	1.95714
$705$	7.05972e13	0.0152668
$706$	7.19995e15	1.54491
$707$	1.73680e15	0.369780
$708$	−9.59206e14	−0.202642
$709$	−5.12010e15	−1.07331	−0.536653	−	0.843803i	$-0.680312\pi$
$709$	−5.12010e15	−1.07331	−0.536653	+	0.843803i	$0.680312\pi$
$710$	6.67397e14	0.138824
$711$	−2.56991e14	−0.0530439
$712$	1.36942e16	2.80477
$713$	6.23541e14	0.126728
$714$	1.65554e15	0.333888
$715$	1.70037e14	0.0340298
$716$	1.73155e16	3.43885
$717$	3.21984e15	0.634569
$718$	−4.57090e15	−0.893959
$719$	−2.63545e14	−0.0511500	−0.0255750	−	0.999673i	$-0.508142\pi$
$719$	−2.63545e14	−0.0511500	−0.0255750	+	0.999673i	$0.508142\pi$
$720$	−4.40311e14	−0.0848069
$721$	1.26414e15	0.241630
$722$	6.71962e15	1.27465
$723$	9.79787e14	0.184447
$724$	2.81711e15	0.526310
$725$	3.45130e14	0.0639916
$726$	−3.98850e15	−0.733935
$727$	2.19833e15	0.401471	0.200735	−	0.979646i	$-0.435667\pi$
$727$	2.19833e15	0.401471	0.200735	+	0.979646i	$0.435667\pi$
$728$	3.61349e15	0.654945
$729$	2.05891e14	0.0370370
$730$	9.51274e14	0.169836
$731$	−4.70424e15	−0.833574
$732$	−6.40292e14	−0.112608
$733$	−2.95864e15	−0.516440	−0.258220	−	0.966086i	$-0.583136\pi$
$733$	−2.95864e15	−0.516440	−0.258220	+	0.966086i	$0.583136\pi$
$734$	7.62413e15	1.32088
$735$	−2.24807e14	−0.0386571
$736$	−1.05868e16	−1.80690
$737$	−6.77900e14	−0.114840
$738$	−1.98000e15	−0.332932
$739$	2.61427e15	0.436321	0.218161	−	0.975913i	$-0.429994\pi$
$739$	2.61427e15	0.436321	0.218161	+	0.975913i	$0.429994\pi$
$740$	1.97546e15	0.327260
$741$	1.67319e15	0.275135
$742$	4.70786e15	0.768426
$743$	−7.87753e15	−1.27630	−0.638148	−	0.769913i	$-0.720299\pi$
$743$	−7.87753e15	−1.27630	−0.638148	+	0.769913i	$0.720299\pi$
$744$	2.96132e15	0.476249
$745$	−1.04664e14	−0.0167086
$746$	2.37159e16	3.75816
$747$	3.78488e15	0.595373
$748$	1.23539e16	1.92906
$749$	−1.51810e15	−0.235315
$750$	1.02488e15	0.157701
$751$	−9.92797e15	−1.51649	−0.758247	−	0.651967i	$-0.773944\pi$
$751$	−9.92797e15	−1.51649	−0.758247	+	0.651967i	$0.773944\pi$
$752$	8.74683e15	1.32633
$753$	−5.98423e15	−0.900815
$754$	−6.79270e14	−0.101508
$755$	−6.90797e14	−0.102481
$756$	−8.62026e14	−0.126955
$757$	8.71053e15	1.27355	0.636777	−	0.771048i	$-0.280267\pi$
$757$	8.71053e15	1.27355	0.636777	+	0.771048i	$0.280267\pi$
$758$	5.38002e15	0.780914
$759$	−1.16810e15	−0.168326
$760$	9.42248e14	0.134800
$761$	1.30399e16	1.85207	0.926037	−	0.377432i	$-0.123193\pi$
$761$	1.30399e16	1.85207	0.926037	+	0.377432i	$0.123193\pi$
$762$	2.26519e15	0.319412
$763$	5.34084e14	0.0747695
$764$	−4.54248e15	−0.631363
$765$	−2.11495e14	−0.0291852
$766$	−1.04468e16	−1.43128
$767$	−7.85693e14	−0.106876
$768$	−9.10774e15	−1.23005
$769$	−6.96474e15	−0.933921	−0.466961	−	0.884278i	$-0.654651\pi$
$769$	−6.96474e15	−0.933921	−0.466961	+	0.884278i	$0.654651\pi$
$770$	1.46465e14	0.0195001
$771$	5.82682e15	0.770251
$772$	9.39479e15	1.23308
$773$	3.66907e15	0.478155	0.239077	−	0.971001i	$-0.423155\pi$
$773$	3.66907e15	0.478155	0.239077	+	0.971001i	$0.423155\pi$
$774$	3.35802e15	0.434518
$775$	−1.95913e15	−0.251711
$776$	4.27431e16	5.45288
$777$	1.90084e15	0.240785
$778$	1.46562e16	1.84345
$779$	2.41475e15	0.301589
$780$	−7.33810e14	−0.0910046
$781$	4.79211e15	0.590128
$782$	−9.68151e15	−1.18387
$783$	1.01939e14	0.0123780
$784$	−2.78531e16	−3.35842
$785$	−1.36826e14	−0.0163827
$786$	−4.12962e15	−0.491006
$787$	1.29771e15	0.153221	0.0766105	−	0.997061i	$-0.475590\pi$
$787$	1.29771e15	0.153221	0.0766105	+	0.997061i	$0.475590\pi$
$788$	1.08148e16	1.26802
$789$	−1.45173e15	−0.169030
$790$	−1.88441e14	−0.0217884
$791$	−6.42385e13	−0.00737606
$792$	−5.54756e15	−0.632577
$793$	−5.24468e14	−0.0593904
$794$	−4.80241e15	−0.540065
$795$	−6.01427e14	−0.0671682
$796$	−2.45985e16	−2.72827
$797$	2.62688e15	0.289347	0.144674	−	0.989479i	$-0.453787\pi$
$797$	2.62688e15	0.289347	0.144674	+	0.989479i	$0.453787\pi$
$798$	1.44125e15	0.157661
$799$	4.20137e15	0.456440
$800$	3.32629e16	3.58893
$801$	−2.67590e15	−0.286742
$802$	6.50053e15	0.691815
$803$	6.83043e15	0.721959
$804$	2.92555e15	0.307113
$805$	−8.37258e13	−0.00872935
$806$	3.85587e15	0.399282
$807$	−7.53767e14	−0.0775234
$808$	−4.82362e16	−4.92732
$809$	7.36382e15	0.747113	0.373556	−	0.927607i	$-0.378138\pi$
$809$	7.36382e15	0.747113	0.373556	+	0.927607i	$0.378138\pi$
$810$	1.50971e14	0.0152134
$811$	1.11764e16	1.11863	0.559314	−	0.828956i	$-0.311065\pi$
$811$	1.11764e16	1.11863	0.559314	+	0.828956i	$0.311065\pi$
$812$	−4.26798e14	−0.0424291
$813$	−1.08759e15	−0.107391
$814$	1.94457e16	1.90717
$815$	1.81349e14	0.0176664
$816$	−2.62038e16	−2.53552
$817$	−4.09533e15	−0.393611
$818$	−3.35922e16	−3.20697
$819$	−7.06092e14	−0.0669575
$820$	−1.05903e15	−0.0997544
$821$	−8.65540e15	−0.809841	−0.404921	−	0.914352i	$-0.632701\pi$
$821$	−8.65540e15	−0.809841	−0.404921	+	0.914352i	$0.632701\pi$
$822$	1.56103e15	0.145083
$823$	−1.76556e16	−1.62999	−0.814994	−	0.579469i	$-0.803260\pi$
$823$	−1.76556e16	−1.62999	−0.814994	+	0.579469i	$0.803260\pi$
$824$	−3.51090e16	−3.21973
$825$	3.67011e15	0.334335
$826$	−6.76777e14	−0.0612428
$827$	−1.25112e16	−1.12465	−0.562325	−	0.826916i	$-0.690093\pi$
$827$	−1.25112e16	−1.12465	−0.562325	+	0.826916i	$0.690093\pi$
$828$	5.04107e15	0.450149
$829$	1.85690e16	1.64717	0.823586	−	0.567192i	$-0.191970\pi$
$829$	1.85690e16	1.64717	0.823586	+	0.567192i	$0.191970\pi$
$830$	2.77529e15	0.244556
$831$	−5.35166e15	−0.468472
$832$	−3.17434e16	−2.76042
$833$	−1.33787e16	−1.15576
$834$	6.64863e15	0.570583
$835$	1.10176e15	0.0939313
$836$	1.07548e16	0.910898
$837$	−5.78655e14	−0.0486888
$838$	−2.40702e16	−2.01205
$839$	−1.68722e16	−1.40114	−0.700569	−	0.713584i	$-0.747071\pi$
$839$	−1.68722e16	−1.40114	−0.700569	+	0.713584i	$0.747071\pi$
$840$	−3.97631e14	−0.0328053
$841$	−1.21500e16	−0.995863
$842$	−4.54342e15	−0.369970
$843$	1.22630e16	0.992075
$844$	−1.29106e16	−1.03768
$845$	2.90830e14	0.0232235
$846$	−2.99905e15	−0.237929
$847$	−2.05272e15	−0.161797
$848$	−7.45155e16	−5.83538
$849$	−4.33152e15	−0.337014
$850$	3.04187e16	2.35145
$851$	−1.11160e16	−0.853758
$852$	−2.06808e16	−1.57816
$853$	3.17535e15	0.240753	0.120377	−	0.992728i	$-0.461590\pi$
$853$	3.17535e15	0.240753	0.120377	+	0.992728i	$0.461590\pi$
$854$	−4.51764e14	−0.0340325
$855$	−1.84119e14	−0.0137811
$856$	4.21621e16	3.13557
$857$	−3.21870e15	−0.237841	−0.118920	−	0.992904i	$-0.537943\pi$
$857$	−3.21870e15	−0.237841	−0.118920	+	0.992904i	$0.537943\pi$
$858$	−7.22336e15	−0.530346
$859$	1.77583e16	1.29550	0.647751	−	0.761852i	$-0.275710\pi$
$859$	1.77583e16	1.29550	0.647751	+	0.761852i	$0.275710\pi$
$860$	1.79608e15	0.130192
$861$	−1.01903e15	−0.0733954
$862$	4.03757e16	2.88955
$863$	−1.16475e16	−0.828274	−0.414137	−	0.910215i	$-0.635917\pi$
$863$	−1.16475e16	−0.828274	−0.414137	+	0.910215i	$0.635917\pi$
$864$	9.82465e15	0.694211
$865$	3.99329e14	0.0280377
$866$	−6.87100e15	−0.479371
$867$	−4.25841e15	−0.295217
$868$	2.42271e15	0.166895
$869$	−1.35306e15	−0.0926207
$870$	7.47472e13	0.00508440
$871$	2.39634e15	0.161975
$872$	−1.48331e16	−0.996303
$873$	−8.35217e15	−0.557469
$874$	−8.42833e15	−0.559022
$875$	5.27463e14	0.0347654
$876$	−2.94774e16	−1.93071
$877$	3.25080e15	0.211589	0.105795	−	0.994388i	$-0.466261\pi$
$877$	3.25080e15	0.211589	0.105795	+	0.994388i	$0.466261\pi$
$878$	1.11156e16	0.718976
$879$	−1.11091e15	−0.0714069
$880$	−2.31824e15	−0.148082
$881$	6.06655e15	0.385101	0.192550	−	0.981287i	$-0.438324\pi$
$881$	6.06655e15	0.385101	0.192550	+	0.981287i	$0.438324\pi$
$882$	9.55008e15	0.602462
$883$	2.27045e15	0.142340	0.0711701	−	0.997464i	$-0.477327\pi$
$883$	2.27045e15	0.142340	0.0711701	+	0.997464i	$0.477327\pi$
$884$	−4.36704e16	−2.72082
$885$	8.64580e13	0.00535325
$886$	−2.70804e16	−1.66636
$887$	−2.68480e16	−1.64185	−0.820924	−	0.571038i	$-0.806541\pi$
$887$	−2.68480e16	−1.64185	−0.820924	+	0.571038i	$0.806541\pi$
$888$	−5.27920e16	−3.20846
$889$	1.16580e15	0.0704148
$890$	−1.96212e15	−0.117783
$891$	1.08402e15	0.0646709
$892$	−2.66419e16	−1.57964
$893$	3.65755e15	0.215530
$894$	4.44627e15	0.260399
$895$	−1.56073e15	−0.0908451
$896$	−1.20854e16	−0.699146
$897$	4.12918e15	0.237413
$898$	6.14184e15	0.350977
$899$	−2.86498e14	−0.0162721
$900$	−1.58387e16	−0.894100
$901$	−3.57921e16	−2.00817
$902$	−1.04247e16	−0.581337
$903$	1.72824e15	0.0957901
$904$	1.78410e15	0.0982860
$905$	−2.53920e14	−0.0139037
$906$	2.93459e16	1.59714
$907$	5.46793e14	0.0295789	0.0147895	−	0.999891i	$-0.495292\pi$
$907$	5.46793e14	0.0295789	0.0147895	+	0.999891i	$0.495292\pi$
$908$	6.67683e16	3.59003
$909$	9.42556e15	0.503739
$910$	−5.17746e14	−0.0275036
$911$	8.84768e15	0.467174	0.233587	−	0.972336i	$-0.424954\pi$
$911$	8.84768e15	0.467174	0.233587	+	0.972336i	$0.424954\pi$
$912$	−2.28119e16	−1.19727
$913$	1.99274e16	1.03959
$914$	3.13742e16	1.62693
$915$	5.77127e13	0.00297478
$916$	7.24659e16	3.71286
$917$	−2.12535e15	−0.108243
$918$	8.98457e15	0.454844
$919$	−2.50273e16	−1.25944	−0.629722	−	0.776821i	$-0.716831\pi$
$919$	−2.50273e16	−1.25944	−0.629722	+	0.776821i	$0.716831\pi$
$920$	2.32532e15	0.116319
$921$	7.12570e15	0.354323
$922$	6.49327e16	3.20955
$923$	−1.69398e16	−0.832337
$924$	−4.53857e15	−0.221678
$925$	3.49256e16	1.69576
$926$	6.56414e16	3.16823
$927$	6.86045e15	0.329165
$928$	4.86429e15	0.232009
$929$	3.42467e16	1.62380	0.811901	−	0.583796i	$-0.198433\pi$
$929$	3.42467e16	1.62380	0.811901	+	0.583796i	$0.198433\pi$
$930$	−4.24302e14	−0.0199995
$931$	−1.16470e16	−0.545744
$932$	−5.72394e15	−0.266629
$933$	−5.51432e15	−0.255354
$934$	2.25160e16	1.03653
$935$	−1.11352e15	−0.0509606
$936$	1.96103e16	0.892209
$937$	3.20191e16	1.44824	0.724121	−	0.689673i	$-0.242246\pi$
$937$	3.20191e16	1.44824	0.724121	+	0.689673i	$0.242246\pi$
$938$	2.06415e15	0.0928164
$939$	1.51992e16	0.679454
$940$	−1.60408e15	−0.0712892
$941$	−2.01964e16	−0.892343	−0.446171	−	0.894948i	$-0.647213\pi$
$941$	−2.01964e16	−0.892343	−0.446171	+	0.894948i	$0.647213\pi$
$942$	5.81253e15	0.255320
$943$	5.95920e15	0.260240
$944$	1.07119e16	0.465074
$945$	7.76987e13	0.00335381
$946$	1.76800e16	0.758717
$947$	−2.12489e16	−0.906592	−0.453296	−	0.891360i	$-0.649752\pi$
$947$	−2.12489e16	−0.906592	−0.453296	+	0.891360i	$0.649752\pi$
$948$	5.83926e15	0.247692
$949$	−2.41452e16	−1.01828
$950$	2.64813e16	1.11035
$951$	−8.00446e15	−0.333687
$952$	−2.36637e16	−0.980800
$953$	2.57898e16	1.06276	0.531382	−	0.847132i	$-0.321673\pi$
$953$	2.57898e16	1.06276	0.531382	+	0.847132i	$0.321673\pi$
$954$	2.55494e16	1.04680
$955$	4.09436e14	0.0166789
$956$	−7.31600e16	−2.96316
$957$	5.36708e14	0.0216134
$958$	−8.66312e15	−0.346868
$959$	8.03401e14	0.0319838
$960$	3.49305e15	0.138265
$961$	−2.37822e16	−0.935994
$962$	−6.87393e16	−2.68994
$963$	−8.23865e15	−0.320562
$964$	−2.22624e16	−0.861286
$965$	−8.46799e14	−0.0325747
$966$	3.55677e15	0.136045
$967$	−6.39376e15	−0.243170	−0.121585	−	0.992581i	$-0.538798\pi$
$967$	−6.39376e15	−0.243170	−0.121585	+	0.992581i	$0.538798\pi$
$968$	5.70101e16	2.15595
$969$	−1.09573e16	−0.412024
$970$	−6.12428e15	−0.228987
$971$	1.52562e16	0.567205	0.283602	−	0.958942i	$-0.408470\pi$
$971$	1.52562e16	0.567205	0.283602	+	0.958942i	$0.408470\pi$
$972$	−4.67818e15	−0.172947
$973$	3.42178e15	0.125786
$974$	4.15767e16	1.51976
$975$	−1.29736e16	−0.471558
$976$	7.15047e15	0.258441
$977$	−3.95039e16	−1.41978	−0.709889	−	0.704314i	$-0.751255\pi$
$977$	−3.95039e16	−1.41978	−0.709889	+	0.704314i	$0.751255\pi$
$978$	−7.70393e15	−0.275327
$979$	−1.40886e16	−0.500684
$980$	5.10798e15	0.180512
$981$	2.89845e15	0.101856
$982$	8.98349e16	3.13929
$983$	−3.17929e16	−1.10480	−0.552402	−	0.833578i	$-0.686289\pi$
$983$	−3.17929e16	−1.10480	−0.552402	+	0.833578i	$0.686289\pi$
$984$	2.83015e16	0.977993
$985$	−9.74794e14	−0.0334976
$986$	4.44835e15	0.152011
$987$	−1.54349e15	−0.0524518
$988$	−3.80177e16	−1.28476
$989$	−1.01066e16	−0.339645
$990$	7.94862e14	0.0265643
$991$	−3.94441e16	−1.31092	−0.655461	−	0.755229i	$-0.727525\pi$
$991$	−3.94441e16	−1.31092	−0.655461	+	0.755229i	$0.727525\pi$
$992$	−2.76121e16	−0.912609
$993$	2.56064e16	0.841644
$994$	−1.45915e16	−0.476953
$995$	2.21718e15	0.0720734
$996$	−8.59987e16	−2.78013
$997$	−4.52291e16	−1.45410	−0.727050	−	0.686584i	$-0.759109\pi$
$997$	−4.52291e16	−1.45410	−0.727050	+	0.686584i	$0.759109\pi$
$998$	4.18644e15	0.133853
$999$	1.03158e16	0.328013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.1	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.1	✓	26	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)

\(f(q)\)	\(=\)	\(q-87.0020 q^{2} -243.000 q^{3} +5521.36 q^{4} -497.667 q^{5} +21141.5 q^{6} +10880.7 q^{7} -302189. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-87.0020 q^{2} -243.000 q^{3} +5521.36 q^{4} -497.667 q^{5} +21141.5 q^{6} +10880.7 q^{7} -302189. q^{8} +59049.0 q^{9} +43298.0 q^{10} +310893. q^{11} -1.34169e6 q^{12} -1.09899e6 q^{13} -946641. q^{14} +120933. q^{15} +1.49833e7 q^{16} +7.19696e6 q^{17} -5.13738e6 q^{18} +6.26538e6 q^{19} -2.74780e6 q^{20} -2.64400e6 q^{21} -2.70483e7 q^{22} +1.54620e7 q^{23} +7.34319e7 q^{24} -4.85805e7 q^{25} +9.56141e7 q^{26} -1.43489e7 q^{27} +6.00761e7 q^{28} -7.10429e6 q^{29} -1.05214e7 q^{30} +4.03274e7 q^{31} -6.84697e8 q^{32} -7.55470e7 q^{33} -6.26150e8 q^{34} -5.41495e6 q^{35} +3.26031e8 q^{36} -7.18924e8 q^{37} -5.45101e8 q^{38} +2.67054e8 q^{39} +1.50390e8 q^{40} +3.85411e8 q^{41} +2.30034e8 q^{42} -6.53643e8 q^{43} +1.71655e9 q^{44} -2.93867e7 q^{45} -1.34522e9 q^{46} +5.83771e8 q^{47} -3.64095e9 q^{48} -1.85894e9 q^{49} +4.22660e9 q^{50} -1.74886e9 q^{51} -6.06790e9 q^{52} -4.97322e9 q^{53} +1.24838e9 q^{54} -1.54721e8 q^{55} -3.28802e9 q^{56} -1.52249e9 q^{57} +6.18088e8 q^{58} +7.14924e8 q^{59} +6.67715e8 q^{60} +4.77228e8 q^{61} -3.50857e9 q^{62} +6.42493e8 q^{63} +2.88842e10 q^{64} +5.46930e8 q^{65} +6.57274e9 q^{66} -2.18049e9 q^{67} +3.97370e10 q^{68} -3.75726e9 q^{69} +4.71112e8 q^{70} +1.54140e10 q^{71} -1.78440e10 q^{72} +2.19704e10 q^{73} +6.25478e10 q^{74} +1.18050e10 q^{75} +3.45934e10 q^{76} +3.38273e9 q^{77} -2.32342e10 q^{78} -4.35217e9 q^{79} -7.45671e9 q^{80} +3.48678e9 q^{81} -3.35315e10 q^{82} +6.40974e10 q^{83} -1.45985e10 q^{84} -3.58169e9 q^{85} +5.68683e10 q^{86} +1.72634e9 q^{87} -9.39485e10 q^{88} -4.53166e10 q^{89} +2.55671e9 q^{90} -1.19577e10 q^{91} +8.53710e10 q^{92} -9.79957e9 q^{93} -5.07892e10 q^{94} -3.11807e9 q^{95} +1.66381e11 q^{96} -1.41445e11 q^{97} +1.61731e11 q^{98} +1.83579e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

Modular forms

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