LMFDB - Embedded newform 177.12.a.a.1.16

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			1.16
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)

$f(q)$	$=$	$q+16.4601 q^{2} -243.000 q^{3} -1777.06 q^{4} -11170.6 q^{5} -3999.81 q^{6} -64730.0 q^{7} -62961.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+16.4601 q^{2} -243.000 q^{3} -1777.06 q^{4} -11170.6 q^{5} -3999.81 q^{6} -64730.0 q^{7} -62961.0 q^{8} +59049.0 q^{9} -183870. q^{10} -152927. q^{11} +431827. q^{12} +2.10945e6 q^{13} -1.06546e6 q^{14} +2.71446e6 q^{15} +2.60308e6 q^{16} -1.11407e7 q^{17} +971954. q^{18} -1.27705e7 q^{19} +1.98509e7 q^{20} +1.57294e7 q^{21} -2.51720e6 q^{22} +9.67947e6 q^{23} +1.52995e7 q^{24} +7.59546e7 q^{25} +3.47218e7 q^{26} -1.43489e7 q^{27} +1.15029e8 q^{28} +1.78369e8 q^{29} +4.46803e7 q^{30} +8.93963e7 q^{31} +1.71791e8 q^{32} +3.71614e7 q^{33} -1.83377e8 q^{34} +7.23074e8 q^{35} -1.04934e8 q^{36} -2.78055e8 q^{37} -2.10204e8 q^{38} -5.12596e8 q^{39} +7.03314e8 q^{40} +9.14877e8 q^{41} +2.58908e8 q^{42} -8.43912e7 q^{43} +2.71762e8 q^{44} -6.59614e8 q^{45} +1.59325e8 q^{46} -1.29951e9 q^{47} -6.32549e8 q^{48} +2.21265e9 q^{49} +1.25022e9 q^{50} +2.70719e9 q^{51} -3.74862e9 q^{52} +3.97563e9 q^{53} -2.36185e8 q^{54} +1.70829e9 q^{55} +4.07547e9 q^{56} +3.10324e9 q^{57} +2.93597e9 q^{58} +7.14924e8 q^{59} -4.82377e9 q^{60} -6.12831e9 q^{61} +1.47147e9 q^{62} -3.82224e9 q^{63} -2.50341e9 q^{64} -2.35638e10 q^{65} +6.11680e8 q^{66} +5.63319e9 q^{67} +1.97978e10 q^{68} -2.35211e9 q^{69} +1.19019e10 q^{70} -1.19880e10 q^{71} -3.71779e9 q^{72} -2.52775e10 q^{73} -4.57682e9 q^{74} -1.84570e10 q^{75} +2.26940e10 q^{76} +9.89899e9 q^{77} -8.43739e9 q^{78} +4.83860e10 q^{79} -2.90780e10 q^{80} +3.48678e9 q^{81} +1.50590e10 q^{82} -6.79955e10 q^{83} -2.79521e10 q^{84} +1.24449e11 q^{85} -1.38909e9 q^{86} -4.33436e10 q^{87} +9.62846e9 q^{88} +4.73407e10 q^{89} -1.08573e10 q^{90} -1.36545e11 q^{91} -1.72010e10 q^{92} -2.17233e10 q^{93} -2.13900e10 q^{94} +1.42655e11 q^{95} -4.17453e10 q^{96} -1.10243e11 q^{97} +3.64205e10 q^{98} -9.03021e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	16.4601	0.363721	0.181860	−	0.983324i	$-0.441788\pi$
$2$	16.4601	0.363721	0.181860	+	0.983324i	$0.441788\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1777.06	−0.867707
$5$	−11170.6	−1.59861	−0.799304	−	0.600926i	$-0.794799\pi$
$5$	−11170.6	−1.59861	−0.799304	+	0.600926i	$0.794799\pi$
$6$	−3999.81	−0.209994
$7$	−64730.0	−1.45568	−0.727841	−	0.685746i	$-0.759476\pi$
$7$	−64730.0	−1.45568	−0.727841	+	0.685746i	$0.759476\pi$
$8$	−62961.0	−0.679324
$9$	59049.0	0.333333
$10$	−183870.	−0.581447
$11$	−152927.	−0.286303	−0.143151	−	0.989701i	$-0.545724\pi$
$11$	−152927.	−0.286303	−0.143151	+	0.989701i	$0.545724\pi$
$12$	431827.	0.500971
$13$	2.10945e6	1.57572	0.787862	−	0.615852i	$-0.211188\pi$
$13$	2.10945e6	1.57572	0.787862	+	0.615852i	$0.211188\pi$
$14$	−1.06546e6	−0.529462
$15$	2.71446e6	0.922957
$16$	2.60308e6	0.620623
$17$	−1.11407e7	−1.90302	−0.951511	−	0.307614i	$-0.900469\pi$
$17$	−1.11407e7	−1.90302	−0.951511	+	0.307614i	$0.900469\pi$
$18$	971954.	0.121240
$19$	−1.27705e7	−1.18322	−0.591608	−	0.806226i	$-0.701507\pi$
$19$	−1.27705e7	−1.18322	−0.591608	+	0.806226i	$0.701507\pi$
$20$	1.98509e7	1.38712
$21$	1.57294e7	0.840438
$22$	−2.51720e6	−0.104134
$23$	9.67947e6	0.313580	0.156790	−	0.987632i	$-0.449885\pi$
$23$	9.67947e6	0.313580	0.156790	+	0.987632i	$0.449885\pi$
$24$	1.52995e7	0.392208
$25$	7.59546e7	1.55555
$26$	3.47218e7	0.573124
$27$	−1.43489e7	−0.192450
$28$	1.15029e8	1.26311
$29$	1.78369e8	1.61484	0.807421	−	0.589976i	$-0.200863\pi$
$29$	1.78369e8	1.61484	0.807421	+	0.589976i	$0.200863\pi$
$30$	4.46803e7	0.335699
$31$	8.93963e7	0.560829	0.280414	−	0.959879i	$-0.409528\pi$
$31$	8.93963e7	0.560829	0.280414	+	0.959879i	$0.409528\pi$
$32$	1.71791e8	0.905057
$33$	3.71614e7	0.165297
$34$	−1.83377e8	−0.692169
$35$	7.23074e8	2.32707
$36$	−1.04934e8	−0.289236
$37$	−2.78055e8	−0.659206	−0.329603	−	0.944120i	$-0.606915\pi$
$37$	−2.78055e8	−0.659206	−0.329603	+	0.944120i	$0.606915\pi$
$38$	−2.10204e8	−0.430360
$39$	−5.12596e8	−0.909745
$40$	7.03314e8	1.08597
$41$	9.14877e8	1.23325	0.616625	−	0.787257i	$-0.288499\pi$
$41$	9.14877e8	1.23325	0.616625	+	0.787257i	$0.288499\pi$
$42$	2.58908e8	0.305685
$43$	−8.43912e7	−0.0875428	−0.0437714	−	0.999042i	$-0.513937\pi$
$43$	−8.43912e7	−0.0875428	−0.0437714	+	0.999042i	$0.513937\pi$
$44$	2.71762e8	0.248427
$45$	−6.59614e8	−0.532870
$46$	1.59325e8	0.114056
$47$	−1.29951e9	−0.826495	−0.413247	−	0.910619i	$-0.635606\pi$
$47$	−1.29951e9	−0.826495	−0.413247	+	0.910619i	$0.635606\pi$
$48$	−6.32549e8	−0.358317
$49$	2.21265e9	1.11901
$50$	1.25022e9	0.565786
$51$	2.70719e9	1.09871
$52$	−3.74862e9	−1.36727
$53$	3.97563e9	1.30584	0.652918	−	0.757429i	$-0.273545\pi$
$53$	3.97563e9	1.30584	0.652918	+	0.757429i	$0.273545\pi$
$54$	−2.36185e8	−0.0699981
$55$	1.70829e9	0.457686
$56$	4.07547e9	0.988879
$57$	3.10324e9	0.683130
$58$	2.93597e9	0.587351
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−4.82377e9	−0.800857
$61$	−6.12831e9	−0.929023	−0.464512	−	0.885567i	$-0.653770\pi$
$61$	−6.12831e9	−0.929023	−0.464512	+	0.885567i	$0.653770\pi$
$62$	1.47147e9	0.203985
$63$	−3.82224e9	−0.485227
$64$	−2.50341e9	−0.291435
$65$	−2.35638e10	−2.51897
$66$	6.11680e8	0.0601219
$67$	5.63319e9	0.509733	0.254867	−	0.966976i	$-0.417968\pi$
$67$	5.63319e9	0.509733	0.254867	+	0.966976i	$0.417968\pi$
$68$	1.97978e10	1.65127
$69$	−2.35211e9	−0.181045
$70$	1.19019e10	0.846402
$71$	−1.19880e10	−0.788543	−0.394272	−	0.918994i	$-0.629003\pi$
$71$	−1.19880e10	−0.788543	−0.394272	+	0.918994i	$0.629003\pi$
$72$	−3.71779e9	−0.226441
$73$	−2.52775e10	−1.42711	−0.713555	−	0.700599i	$-0.752916\pi$
$73$	−2.52775e10	−1.42711	−0.713555	+	0.700599i	$0.752916\pi$
$74$	−4.57682e9	−0.239767
$75$	−1.84570e10	−0.898098
$76$	2.26940e10	1.02668
$77$	9.89899e9	0.416766
$78$	−8.43739e9	−0.330893
$79$	4.83860e10	1.76918	0.884588	−	0.466373i	$-0.154440\pi$
$79$	4.83860e10	1.76918	0.884588	+	0.466373i	$0.154440\pi$
$80$	−2.90780e10	−0.992134
$81$	3.48678e9	0.111111
$82$	1.50590e10	0.448559
$83$	−6.79955e10	−1.89474	−0.947372	−	0.320135i	$-0.896272\pi$
$83$	−6.79955e10	−1.89474	−0.947372	+	0.320135i	$0.896272\pi$
$84$	−2.79521e10	−0.729255
$85$	1.24449e11	3.04219
$86$	−1.38909e9	−0.0318411
$87$	−4.33436e10	−0.932329
$88$	9.62846e9	0.194492
$89$	4.73407e10	0.898648	0.449324	−	0.893369i	$-0.351665\pi$
$89$	4.73407e10	0.898648	0.449324	+	0.893369i	$0.351665\pi$
$90$	−1.08573e10	−0.193816
$91$	−1.36545e11	−2.29375
$92$	−1.72010e10	−0.272096
$93$	−2.17233e10	−0.323795
$94$	−2.13900e10	−0.300613
$95$	1.42655e11	1.89150
$96$	−4.17453e10	−0.522535
$97$	−1.10243e11	−1.30348	−0.651740	−	0.758442i	$-0.725961\pi$
$97$	−1.10243e11	−1.30348	−0.651740	+	0.758442i	$0.725961\pi$
$98$	3.64205e10	0.407007
$99$	−9.03021e9	−0.0954343
$100$	−1.34976e11	−1.34976
$101$	3.27761e10	0.310306	0.155153	−	0.987890i	$-0.450413\pi$
$101$	3.27761e10	0.310306	0.155153	+	0.987890i	$0.450413\pi$
$102$	4.45607e10	0.399624
$103$	−5.94861e10	−0.505604	−0.252802	−	0.967518i	$-0.581352\pi$
$103$	−5.94861e10	−0.505604	−0.252802	+	0.967518i	$0.581352\pi$
$104$	−1.32813e11	−1.07043
$105$	−1.75707e11	−1.34353
$106$	6.54393e10	0.474960
$107$	−1.17653e11	−0.810950	−0.405475	−	0.914106i	$-0.632894\pi$
$107$	−1.17653e11	−0.810950	−0.405475	+	0.914106i	$0.632894\pi$
$108$	2.54989e10	0.166990
$109$	1.58422e11	0.986208	0.493104	−	0.869970i	$-0.335862\pi$
$109$	1.58422e11	0.986208	0.493104	+	0.869970i	$0.335862\pi$
$110$	2.81187e10	0.166470
$111$	6.75673e10	0.380593
$112$	−1.68498e11	−0.903430
$113$	3.71456e11	1.89660	0.948301	−	0.317373i	$-0.102801\pi$
$113$	3.71456e11	1.89660	0.948301	+	0.317373i	$0.102801\pi$
$114$	5.10796e10	0.248468
$115$	−1.08126e11	−0.501292
$116$	−3.16973e11	−1.40121
$117$	1.24561e11	0.525241
$118$	1.17677e10	0.0473524
$119$	7.21139e11	2.77020
$120$	−1.70905e11	−0.626987
$121$	−2.61925e11	−0.918031
$122$	−1.00873e11	−0.337905
$123$	−2.22315e11	−0.712018
$124$	−1.58863e11	−0.486635
$125$	−3.03020e11	−0.888108
$126$	−6.29146e10	−0.176487
$127$	9.64316e10	0.259000	0.129500	−	0.991579i	$-0.458663\pi$
$127$	9.64316e10	0.259000	0.129500	+	0.991579i	$0.458663\pi$
$128$	−3.93035e11	−1.01106
$129$	2.05071e10	0.0505429
$130$	−3.87864e11	−0.916200
$131$	2.77574e11	0.628618	0.314309	−	0.949321i	$-0.398227\pi$
$131$	2.77574e11	0.628618	0.314309	+	0.949321i	$0.398227\pi$
$132$	−6.60381e10	−0.143429
$133$	8.26636e11	1.72239
$134$	9.27230e10	0.185400
$135$	1.60286e11	0.307652
$136$	7.01431e11	1.29277
$137$	1.43914e9	0.00254766	0.00127383	−	0.999999i	$-0.499595\pi$
$137$	1.43914e9	0.00254766	0.00127383	+	0.999999i	$0.499595\pi$
$138$	−3.87160e10	−0.0658500
$139$	3.30415e11	0.540106	0.270053	−	0.962846i	$-0.412959\pi$
$139$	3.30415e11	0.540106	0.270053	+	0.962846i	$0.412959\pi$
$140$	−1.28495e12	−2.01921
$141$	3.15780e11	0.477177
$142$	−1.97324e11	−0.286809
$143$	−3.22592e11	−0.451134
$144$	1.53709e11	0.206874
$145$	−1.99249e12	−2.58150
$146$	−4.16070e11	−0.519070
$147$	−5.37674e11	−0.646061
$148$	4.94121e11	0.571998
$149$	7.88510e11	0.879595	0.439797	−	0.898097i	$-0.355050\pi$
$149$	7.88510e11	0.879595	0.439797	+	0.898097i	$0.355050\pi$
$150$	−3.03804e11	−0.326657
$151$	−3.06791e11	−0.318031	−0.159015	−	0.987276i	$-0.550832\pi$
$151$	−3.06791e11	−0.318031	−0.159015	+	0.987276i	$0.550832\pi$
$152$	8.04045e11	0.803786
$153$	−6.57848e11	−0.634341
$154$	1.62939e11	0.151586
$155$	−9.98612e11	−0.896546
$156$	9.10916e11	0.789392
$157$	1.19299e12	0.998137	0.499069	−	0.866562i	$-0.333676\pi$
$157$	1.19299e12	0.998137	0.499069	+	0.866562i	$0.333676\pi$
$158$	7.96440e11	0.643486
$159$	−9.66078e11	−0.753925
$160$	−1.91901e12	−1.44683
$161$	−6.26552e11	−0.456473
$162$	5.73929e10	0.0404134
$163$	−1.63583e12	−1.11354	−0.556770	−	0.830667i	$-0.687959\pi$
$163$	−1.63583e12	−1.11354	−0.556770	+	0.830667i	$0.687959\pi$
$164$	−1.62579e12	−1.07010
$165$	−4.15115e11	−0.264245
$166$	−1.11921e12	−0.689158
$167$	−6.56904e11	−0.391347	−0.195673	−	0.980669i	$-0.562689\pi$
$167$	−6.56904e11	−0.391347	−0.195673	+	0.980669i	$0.562689\pi$
$168$	−9.90339e11	−0.570930
$169$	2.65761e12	1.48291
$170$	2.04844e12	1.10651
$171$	−7.54086e11	−0.394405
$172$	1.49969e11	0.0759616
$173$	−2.18034e12	−1.06972	−0.534861	−	0.844940i	$-0.679636\pi$
$173$	−2.18034e12	−1.06972	−0.534861	+	0.844940i	$0.679636\pi$
$174$	−7.13441e11	−0.339107
$175$	−4.91654e12	−2.26439
$176$	−3.98083e11	−0.177686
$177$	−1.73727e11	−0.0751646
$178$	7.79234e11	0.326857
$179$	7.00365e11	0.284861	0.142431	−	0.989805i	$-0.454508\pi$
$179$	7.00365e11	0.284861	0.142431	+	0.989805i	$0.454508\pi$
$180$	1.17218e12	0.462375
$181$	2.48114e12	0.949336	0.474668	−	0.880165i	$-0.342568\pi$
$181$	2.48114e12	0.949336	0.474668	+	0.880165i	$0.342568\pi$
$182$	−2.24754e12	−0.834286
$183$	1.48918e12	0.536372
$184$	−6.09429e11	−0.213022
$185$	3.10605e12	1.05381
$186$	−3.57568e11	−0.117771
$187$	1.70372e12	0.544841
$188$	2.30931e12	0.717156
$189$	9.28805e11	0.280146
$190$	2.34811e12	0.687977
$191$	3.13043e12	0.891088	0.445544	−	0.895260i	$-0.353010\pi$
$191$	3.13043e12	0.891088	0.445544	+	0.895260i	$0.353010\pi$
$192$	6.08328e11	0.168260
$193$	6.73197e12	1.80958	0.904788	−	0.425863i	$-0.140029\pi$
$193$	6.73197e12	1.80958	0.904788	+	0.425863i	$0.140029\pi$
$194$	−1.81460e12	−0.474103
$195$	5.72601e12	1.45433
$196$	−3.93202e12	−0.970973
$197$	2.94797e11	0.0707879	0.0353940	−	0.999373i	$-0.488731\pi$
$197$	2.94797e11	0.0707879	0.0353940	+	0.999373i	$0.488731\pi$
$198$	−1.48638e11	−0.0347114
$199$	4.13612e12	0.939509	0.469755	−	0.882797i	$-0.344342\pi$
$199$	4.13612e12	0.939509	0.469755	+	0.882797i	$0.344342\pi$
$200$	−4.78218e12	−1.05672
$201$	−1.36886e12	−0.294295
$202$	5.39499e11	0.112865
$203$	−1.15458e13	−2.35070
$204$	−4.81086e12	−0.953359
$205$	−1.02197e13	−1.97149
$206$	−9.79148e11	−0.183899
$207$	5.71563e11	0.104527
$208$	5.49106e12	0.977931
$209$	1.95296e12	0.338758
$210$	−2.89216e12	−0.488671
$211$	−4.91072e12	−0.808336	−0.404168	−	0.914685i	$-0.632439\pi$
$211$	−4.91072e12	−0.808336	−0.404168	+	0.914685i	$0.632439\pi$
$212$	−7.06495e12	−1.13308
$213$	2.91308e12	0.455266
$214$	−1.93659e12	−0.294959
$215$	9.42702e11	0.139947
$216$	9.03422e11	0.130736
$217$	−5.78663e12	−0.816389
$218$	2.60764e12	0.358704
$219$	6.14242e12	0.823943
$220$	−3.03575e12	−0.397138
$221$	−2.35007e13	−2.99864
$222$	1.11217e12	0.138429
$223$	6.81556e12	0.827608	0.413804	−	0.910366i	$-0.364200\pi$
$223$	6.81556e12	0.827608	0.413804	+	0.910366i	$0.364200\pi$
$224$	−1.11200e13	−1.31748
$225$	4.48504e12	0.518517
$226$	6.11421e12	0.689833
$227$	1.77863e12	0.195859	0.0979297	−	0.995193i	$-0.468778\pi$
$227$	1.77863e12	0.195859	0.0979297	+	0.995193i	$0.468778\pi$
$228$	−5.51465e12	−0.592757
$229$	−9.79549e12	−1.02785	−0.513927	−	0.857834i	$-0.671810\pi$
$229$	−9.79549e12	−1.02785	−0.513927	+	0.857834i	$0.671810\pi$
$230$	−1.77976e12	−0.182330
$231$	−2.40546e12	−0.240620
$232$	−1.12303e13	−1.09700
$233$	7.07640e11	0.0675079	0.0337540	−	0.999430i	$-0.489254\pi$
$233$	7.07640e11	0.0675079	0.0337540	+	0.999430i	$0.489254\pi$
$234$	2.05028e12	0.191041
$235$	1.45163e13	1.32124
$236$	−1.27047e12	−0.112966
$237$	−1.17578e13	−1.02143
$238$	1.18700e13	1.00758
$239$	1.37934e13	1.14415	0.572074	−	0.820202i	$-0.306139\pi$
$239$	1.37934e13	1.14415	0.572074	+	0.820202i	$0.306139\pi$
$240$	7.06596e12	0.572809
$241$	−1.47934e13	−1.17213	−0.586064	−	0.810264i	$-0.699323\pi$
$241$	−1.47934e13	−1.17213	−0.586064	+	0.810264i	$0.699323\pi$
$242$	−4.31131e12	−0.333907
$243$	−8.47289e11	−0.0641500
$244$	1.08904e13	0.806120
$245$	−2.47167e13	−1.78886
$246$	−3.65933e12	−0.258976
$247$	−2.69387e13	−1.86442
$248$	−5.62848e12	−0.380984
$249$	1.65229e13	1.09393
$250$	−4.98774e12	−0.323023
$251$	−2.11426e13	−1.33953	−0.669766	−	0.742573i	$-0.733605\pi$
$251$	−2.11426e13	−1.33953	−0.669766	+	0.742573i	$0.733605\pi$
$252$	6.79237e12	0.421035
$253$	−1.48026e12	−0.0897788
$254$	1.58728e12	0.0942035
$255$	−3.02410e13	−1.75641
$256$	−1.34242e12	−0.0763077
$257$	1.68358e13	0.936704	0.468352	−	0.883542i	$-0.344848\pi$
$257$	1.68358e13	0.936704	0.468352	+	0.883542i	$0.344848\pi$
$258$	3.37549e11	0.0183835
$259$	1.79985e13	0.959594
$260$	4.18745e13	2.18573
$261$	1.05325e13	0.538280
$262$	4.56891e12	0.228642
$263$	−9.58815e12	−0.469870	−0.234935	−	0.972011i	$-0.575488\pi$
$263$	−9.58815e12	−0.469870	−0.234935	+	0.972011i	$0.575488\pi$
$264$	−2.33972e12	−0.112290
$265$	−4.44102e13	−2.08752
$266$	1.36065e13	0.626467
$267$	−1.15038e13	−0.518835
$268$	−1.00105e13	−0.442299
$269$	7.58983e12	0.328545	0.164272	−	0.986415i	$-0.447472\pi$
$269$	7.58983e12	0.328545	0.164272	+	0.986415i	$0.447472\pi$
$270$	2.63833e12	0.111900
$271$	6.24707e12	0.259624	0.129812	−	0.991539i	$-0.458563\pi$
$271$	6.24707e12	0.259624	0.129812	+	0.991539i	$0.458563\pi$
$272$	−2.90002e13	−1.18106
$273$	3.31803e13	1.32430
$274$	2.36885e10	0.000926635 0
$275$	−1.16155e13	−0.445358
$276$	4.17985e12	0.157094
$277$	1.30447e13	0.480611	0.240306	−	0.970697i	$-0.422752\pi$
$277$	1.30447e13	0.480611	0.240306	+	0.970697i	$0.422752\pi$
$278$	5.43867e12	0.196448
$279$	5.27876e12	0.186943
$280$	−4.55255e13	−1.58083
$281$	2.02178e13	0.688413	0.344207	−	0.938894i	$-0.388148\pi$
$281$	2.02178e13	0.688413	0.344207	+	0.938894i	$0.388148\pi$
$282$	5.19778e12	0.173559
$283$	5.92770e11	0.0194116	0.00970578	−	0.999953i	$-0.496911\pi$
$283$	5.92770e11	0.0194116	0.00970578	+	0.999953i	$0.496911\pi$
$284$	2.13034e13	0.684225
$285$	−3.46651e13	−1.09206
$286$	−5.30991e12	−0.164087
$287$	−5.92200e13	−1.79522
$288$	1.01441e13	0.301686
$289$	8.98436e13	2.62149
$290$	−3.27966e13	−0.938945
$291$	2.67889e13	0.752565
$292$	4.49197e13	1.23831
$293$	1.59170e12	0.0430615	0.0215308	−	0.999768i	$-0.493146\pi$
$293$	1.59170e12	0.0430615	0.0215308	+	0.999768i	$0.493146\pi$
$294$	−8.85017e12	−0.234986
$295$	−7.98615e12	−0.208121
$296$	1.75066e13	0.447814
$297$	2.19434e12	0.0550990
$298$	1.29790e13	0.319927
$299$	2.04183e13	0.494116
$300$	3.27992e13	0.779286
$301$	5.46264e12	0.127435
$302$	−5.04982e12	−0.115674
$303$	−7.96460e12	−0.179155
$304$	−3.32427e13	−0.734331
$305$	6.84570e13	1.48515
$306$	−1.08283e13	−0.230723
$307$	6.83866e12	0.143123	0.0715616	−	0.997436i	$-0.477202\pi$
$307$	6.83866e12	0.143123	0.0715616	+	0.997436i	$0.477202\pi$
$308$	−1.75912e13	−0.361631
$309$	1.44551e13	0.291911
$310$	−1.64373e13	−0.326092
$311$	−1.84837e13	−0.360253	−0.180126	−	0.983643i	$-0.557651\pi$
$311$	−1.84837e13	−0.360253	−0.180126	+	0.983643i	$0.557651\pi$
$312$	3.22735e13	0.618011
$313$	−8.66400e13	−1.63014	−0.815069	−	0.579364i	$-0.803301\pi$
$313$	−8.66400e13	−1.63014	−0.815069	+	0.579364i	$0.803301\pi$
$314$	1.96368e13	0.363043
$315$	4.26968e13	0.775689
$316$	−8.59851e13	−1.53513
$317$	1.39730e13	0.245169	0.122584	−	0.992458i	$-0.460882\pi$
$317$	1.39730e13	0.245169	0.122584	+	0.992458i	$0.460882\pi$
$318$	−1.59018e13	−0.274218
$319$	−2.72775e13	−0.462334
$320$	2.79646e13	0.465891
$321$	2.85898e13	0.468202
$322$	−1.03131e13	−0.166029
$323$	1.42273e14	2.25169
$324$	−6.19624e12	−0.0964119
$325$	1.60222e14	2.45112
$326$	−2.69259e13	−0.405017
$327$	−3.84964e13	−0.569388
$328$	−5.76016e13	−0.837776
$329$	8.41171e13	1.20311
$330$	−6.83285e12	−0.0961115
$331$	−8.87012e13	−1.22709	−0.613544	−	0.789661i	$-0.710257\pi$
$331$	−8.87012e13	−1.22709	−0.613544	+	0.789661i	$0.710257\pi$
$332$	1.20832e14	1.64408
$333$	−1.64189e13	−0.219735
$334$	−1.08127e13	−0.142341
$335$	−6.29262e13	−0.814864
$336$	4.09449e13	0.521596
$337$	−1.90009e13	−0.238128	−0.119064	−	0.992887i	$-0.537989\pi$
$337$	−1.90009e13	−0.238128	−0.119064	+	0.992887i	$0.537989\pi$
$338$	4.37445e13	0.539364
$339$	−9.02638e13	−1.09500
$340$	−2.21153e14	−2.63973
$341$	−1.36711e13	−0.160567
$342$	−1.24124e13	−0.143453
$343$	−1.52324e13	−0.173241
$344$	5.31336e12	0.0594699
$345$	2.62745e13	0.289421
$346$	−3.58887e13	−0.389080
$347$	1.24628e14	1.32985	0.664926	−	0.746910i	$-0.268463\pi$
$347$	1.24628e14	1.32985	0.664926	+	0.746910i	$0.268463\pi$
$348$	7.70244e13	0.808989
$349$	1.32777e14	1.37272	0.686360	−	0.727262i	$-0.259207\pi$
$349$	1.32777e14	1.37272	0.686360	+	0.727262i	$0.259207\pi$
$350$	−8.09269e13	−0.823605
$351$	−3.02683e13	−0.303248
$352$	−2.62716e13	−0.259120
$353$	1.02923e14	0.999425	0.499712	−	0.866191i	$-0.333439\pi$
$353$	1.02923e14	0.999425	0.499712	+	0.866191i	$0.333439\pi$
$354$	−2.85956e12	−0.0273389
$355$	1.33913e14	1.26057
$356$	−8.41275e13	−0.779763
$357$	−1.75237e14	−1.59937
$358$	1.15281e13	0.103610
$359$	−3.37199e13	−0.298446	−0.149223	−	0.988804i	$-0.547677\pi$
$359$	−3.37199e13	−0.298446	−0.149223	+	0.988804i	$0.547677\pi$
$360$	4.15300e13	0.361991
$361$	4.65959e13	0.399998
$362$	4.08399e13	0.345293
$363$	6.36477e13	0.530025
$364$	2.42649e14	1.99031
$365$	2.82365e14	2.28139
$366$	2.45121e13	0.195090
$367$	1.19637e14	0.938002	0.469001	−	0.883198i	$-0.344614\pi$
$367$	1.19637e14	0.938002	0.469001	+	0.883198i	$0.344614\pi$
$368$	2.51964e13	0.194615
$369$	5.40226e13	0.411084
$370$	5.11259e13	0.383293
$371$	−2.57343e14	−1.90088
$372$	3.86037e13	0.280959
$373$	1.00137e14	0.718115	0.359058	−	0.933315i	$-0.383098\pi$
$373$	1.00137e14	0.718115	0.359058	+	0.933315i	$0.383098\pi$
$374$	2.80434e13	0.198170
$375$	7.36338e13	0.512750
$376$	8.18182e13	0.561458
$377$	3.76260e14	2.54455
$378$	1.52882e13	0.101895
$379$	−1.71675e14	−1.12770	−0.563848	−	0.825879i	$-0.690680\pi$
$379$	−1.71675e14	−1.12770	−0.563848	+	0.825879i	$0.690680\pi$
$380$	−2.53506e14	−1.64127
$381$	−2.34329e13	−0.149533
$382$	5.15273e13	0.324107
$383$	1.39642e14	0.865811	0.432906	−	0.901439i	$-0.357488\pi$
$383$	1.39642e14	0.865811	0.432906	+	0.901439i	$0.357488\pi$
$384$	9.55075e13	0.583735
$385$	−1.10578e14	−0.666246
$386$	1.10809e14	0.658180
$387$	−4.98322e12	−0.0291809
$388$	1.95908e14	1.13104
$389$	−9.70423e13	−0.552381	−0.276190	−	0.961103i	$-0.589072\pi$
$389$	−9.70423e13	−0.552381	−0.276190	+	0.961103i	$0.589072\pi$
$390$	9.42508e13	0.528969
$391$	−1.07836e14	−0.596750
$392$	−1.39311e14	−0.760170
$393$	−6.74506e13	−0.362933
$394$	4.85240e12	0.0257470
$395$	−5.40502e14	−2.82822
$396$	1.60473e13	0.0828090
$397$	−9.02498e13	−0.459302	−0.229651	−	0.973273i	$-0.573758\pi$
$397$	−9.02498e13	−0.459302	−0.229651	+	0.973273i	$0.573758\pi$
$398$	6.80810e13	0.341719
$399$	−2.00873e14	−0.994420
$400$	1.97716e14	0.965411
$401$	2.30178e14	1.10859	0.554294	−	0.832321i	$-0.312988\pi$
$401$	2.30178e14	1.10859	0.554294	+	0.832321i	$0.312988\pi$
$402$	−2.25317e13	−0.107041
$403$	1.88577e14	0.883712
$404$	−5.82453e13	−0.269255
$405$	−3.89495e13	−0.177623
$406$	−1.90046e14	−0.854997
$407$	4.25222e13	0.188732
$408$	−1.70448e14	−0.746380
$409$	−9.68498e13	−0.418428	−0.209214	−	0.977870i	$-0.567090\pi$
$409$	−9.68498e13	−0.418428	−0.209214	+	0.977870i	$0.567090\pi$
$410$	−1.68218e14	−0.717070
$411$	−3.49712e11	−0.00147089
$412$	1.05711e14	0.438716
$413$	−4.62771e13	−0.189514
$414$	9.40799e12	0.0380185
$415$	7.59552e14	3.02895
$416$	3.62385e14	1.42612
$417$	−8.02909e13	−0.311830
$418$	3.21460e13	0.123213
$419$	−3.76267e14	−1.42337	−0.711687	−	0.702496i	$-0.752069\pi$
$419$	−3.76267e14	−1.42337	−0.711687	+	0.702496i	$0.752069\pi$
$420$	3.12243e14	1.16579
$421$	4.89674e14	1.80449	0.902246	−	0.431221i	$-0.141917\pi$
$421$	4.89674e14	1.80449	0.902246	+	0.431221i	$0.141917\pi$
$422$	−8.08310e13	−0.294008
$423$	−7.67346e13	−0.275498
$424$	−2.50310e14	−0.887085
$425$	−8.46189e14	−2.96025
$426$	4.79497e13	0.165590
$427$	3.96686e14	1.35236
$428$	2.09078e14	0.703667
$429$	7.83899e13	0.260462
$430$	1.55170e13	0.0509015
$431$	−1.98756e14	−0.643717	−0.321858	−	0.946788i	$-0.604308\pi$
$431$	−1.98756e14	−0.643717	−0.321858	+	0.946788i	$0.604308\pi$
$432$	−3.73514e13	−0.119439
$433$	−3.45187e14	−1.08986	−0.544931	−	0.838481i	$-0.683444\pi$
$433$	−3.45187e14	−1.08986	−0.544931	+	0.838481i	$0.683444\pi$
$434$	−9.52486e13	−0.296937
$435$	4.84175e14	1.49043
$436$	−2.81525e14	−0.855740
$437$	−1.23612e14	−0.371033
$438$	1.01105e14	0.299685
$439$	2.91082e14	0.852041	0.426021	−	0.904714i	$-0.359915\pi$
$439$	2.91082e14	0.852041	0.426021	+	0.904714i	$0.359915\pi$
$440$	−1.07556e14	−0.310917
$441$	1.30655e14	0.373003
$442$	−3.86825e14	−1.09067
$443$	2.93730e14	0.817951	0.408976	−	0.912545i	$-0.365886\pi$
$443$	2.93730e14	0.817951	0.408976	+	0.912545i	$0.365886\pi$
$444$	−1.20072e14	−0.330243
$445$	−5.28825e14	−1.43659
$446$	1.12185e14	0.301018
$447$	−1.91608e14	−0.507834
$448$	1.62046e14	0.424237
$449$	−2.68378e14	−0.694053	−0.347026	−	0.937855i	$-0.612809\pi$
$449$	−2.68378e14	−0.694053	−0.347026	+	0.937855i	$0.612809\pi$
$450$	7.38244e13	0.188595
$451$	−1.39910e14	−0.353083
$452$	−6.60102e14	−1.64569
$453$	7.45502e13	0.183615
$454$	2.92765e13	0.0712381
$455$	1.52529e15	3.66682
$456$	−1.95383e14	−0.464066
$457$	−8.00988e14	−1.87969	−0.939847	−	0.341596i	$-0.889032\pi$
$457$	−8.00988e14	−1.87969	−0.939847	+	0.341596i	$0.889032\pi$
$458$	−1.61235e14	−0.373851
$459$	1.59857e14	0.366237
$460$	1.92146e14	0.434974
$461$	5.13483e14	1.14861	0.574303	−	0.818643i	$-0.305273\pi$
$461$	5.13483e14	1.14861	0.574303	+	0.818643i	$0.305273\pi$
$462$	−3.95941e13	−0.0875184
$463$	−8.22013e14	−1.79549	−0.897746	−	0.440514i	$-0.854796\pi$
$463$	−8.22013e14	−1.79549	−0.897746	+	0.440514i	$0.854796\pi$
$464$	4.64309e14	1.00221
$465$	2.42663e14	0.517621
$466$	1.16478e13	0.0245540
$467$	−8.62251e14	−1.79635	−0.898175	−	0.439638i	$-0.855107\pi$
$467$	−8.62251e14	−1.79635	−0.898175	+	0.439638i	$0.855107\pi$
$468$	−2.21352e14	−0.455756
$469$	−3.64636e14	−0.742009
$470$	2.38940e14	0.480563
$471$	−2.89898e14	−0.576275
$472$	−4.50124e13	−0.0884404
$473$	1.29057e13	0.0250638
$474$	−1.93535e14	−0.371517
$475$	−9.69980e14	−1.84055
$476$	−1.28151e15	−2.40372
$477$	2.34757e14	0.435279
$478$	2.27041e14	0.416150
$479$	−3.18332e14	−0.576813	−0.288406	−	0.957508i	$-0.593125\pi$
$479$	−3.18332e14	−0.576813	−0.288406	+	0.957508i	$0.593125\pi$
$480$	4.66320e14	0.835329
$481$	−5.86542e14	−1.03873
$482$	−2.43502e14	−0.426328
$483$	1.52252e14	0.263545
$484$	4.65457e14	0.796582
$485$	1.23148e15	2.08376
$486$	−1.39465e13	−0.0233327
$487$	−4.48030e13	−0.0741136	−0.0370568	−	0.999313i	$-0.511798\pi$
$487$	−4.48030e13	−0.0741136	−0.0370568	+	0.999313i	$0.511798\pi$
$488$	3.85845e14	0.631108
$489$	3.97506e14	0.642903
$490$	−4.06839e14	−0.650645
$491$	8.28198e14	1.30974	0.654871	−	0.755740i	$-0.272723\pi$
$491$	8.28198e14	1.30974	0.654871	+	0.755740i	$0.272723\pi$
$492$	3.95068e14	0.617823
$493$	−1.98716e15	−3.07308
$494$	−4.43415e14	−0.678129
$495$	1.00873e14	0.152562
$496$	2.32706e14	0.348063
$497$	7.75983e14	1.14787
$498$	2.71969e14	0.397885
$499$	−6.53023e14	−0.944877	−0.472438	−	0.881364i	$-0.656626\pi$
$499$	−6.53023e14	−0.944877	−0.472438	+	0.881364i	$0.656626\pi$
$500$	5.38486e14	0.770618
$501$	1.59628e14	0.225944
$502$	−3.48010e14	−0.487215
$503$	7.51686e14	1.04091	0.520455	−	0.853889i	$-0.325763\pi$
$503$	7.51686e14	1.04091	0.520455	+	0.853889i	$0.325763\pi$
$504$	2.40652e14	0.329626
$505$	−3.66130e14	−0.496058
$506$	−2.43652e13	−0.0326544
$507$	−6.45799e14	−0.856157
$508$	−1.71365e14	−0.224736
$509$	−1.01096e15	−1.31156	−0.655780	−	0.754952i	$-0.727660\pi$
$509$	−1.01096e15	−1.31156	−0.655780	+	0.754952i	$0.727660\pi$
$510$	−4.97771e14	−0.638842
$511$	1.63621e15	2.07742
$512$	7.82839e14	0.983304
$513$	1.83243e14	0.227710
$514$	2.77120e14	0.340698
$515$	6.64496e14	0.808263
$516$	−3.64424e13	−0.0438564
$517$	1.98730e14	0.236628
$518$	2.96257e14	0.349024
$519$	5.29823e14	0.617604
$520$	1.48360e15	1.71119
$521$	1.53933e15	1.75681	0.878406	−	0.477915i	$-0.158607\pi$
$521$	1.53933e15	1.75681	0.878406	+	0.477915i	$0.158607\pi$
$522$	1.73366e14	0.195784
$523$	−1.22582e15	−1.36983	−0.684914	−	0.728624i	$-0.740160\pi$
$523$	−1.22582e15	−1.36983	−0.684914	+	0.728624i	$0.740160\pi$
$524$	−4.93267e14	−0.545457
$525$	1.19472e15	1.30734
$526$	−1.57822e14	−0.170902
$527$	−9.95939e14	−1.06727
$528$	9.67341e13	0.102587
$529$	−8.59118e14	−0.901668
$530$	−7.30998e14	−0.759275
$531$	4.22156e13	0.0433963
$532$	−1.46899e15	−1.49453
$533$	1.92988e15	1.94326
$534$	−1.89354e14	−0.188711
$535$	1.31426e15	1.29639
$536$	−3.54671e14	−0.346274
$537$	−1.70189e14	−0.164465
$538$	1.24929e14	0.119498
$539$	−3.38375e14	−0.320376
$540$	−2.84839e14	−0.266952
$541$	−1.25060e15	−1.16020	−0.580101	−	0.814544i	$-0.696987\pi$
$541$	−1.25060e15	−1.16020	−0.580101	+	0.814544i	$0.696987\pi$
$542$	1.02827e14	0.0944307
$543$	−6.02918e14	−0.548099
$544$	−1.91388e15	−1.72234
$545$	−1.76967e15	−1.57656
$546$	5.46152e14	0.481675
$547$	1.43464e14	0.125260	0.0626302	−	0.998037i	$-0.480051\pi$
$547$	1.43464e14	0.125260	0.0626302	+	0.998037i	$0.480051\pi$
$548$	−2.55745e12	−0.00221062
$549$	−3.61871e14	−0.309674
$550$	−1.91193e14	−0.161986
$551$	−2.27786e15	−1.91070
$552$	1.48091e14	0.122988
$553$	−3.13203e15	−2.57536
$554$	2.14717e14	0.174808
$555$	−7.54769e14	−0.608419
$556$	−5.87169e14	−0.468654
$557$	−6.32352e14	−0.499753	−0.249877	−	0.968278i	$-0.580390\pi$
$557$	−6.32352e14	−0.499753	−0.249877	+	0.968278i	$0.580390\pi$
$558$	8.68891e13	0.0679950
$559$	−1.78019e14	−0.137943
$560$	1.88222e15	1.44423
$561$	−4.14004e14	−0.314564
$562$	3.32787e14	0.250390
$563$	1.54714e15	1.15275	0.576373	−	0.817187i	$-0.304468\pi$
$563$	1.54714e15	1.15275	0.576373	+	0.817187i	$0.304468\pi$
$564$	−5.61161e14	−0.414050
$565$	−4.14940e15	−3.03192
$566$	9.75706e12	0.00706039
$567$	−2.25700e14	−0.161742
$568$	7.54776e14	0.535676
$569$	−1.14138e15	−0.802257	−0.401128	−	0.916022i	$-0.631382\pi$
$569$	−1.14138e15	−0.802257	−0.401128	+	0.916022i	$0.631382\pi$
$570$	−5.70591e14	−0.397204
$571$	1.47138e15	1.01444	0.507218	−	0.861818i	$-0.330674\pi$
$571$	1.47138e15	1.01444	0.507218	+	0.861818i	$0.330674\pi$
$572$	5.73267e14	0.391452
$573$	−7.60695e14	−0.514470
$574$	−9.74768e14	−0.652959
$575$	7.35200e14	0.487790
$576$	−1.47824e14	−0.0971450
$577$	4.32743e14	0.281684	0.140842	−	0.990032i	$-0.455019\pi$
$577$	4.32743e14	0.281684	0.140842	+	0.990032i	$0.455019\pi$
$578$	1.47884e15	0.953492
$579$	−1.63587e15	−1.04476
$580$	3.54078e15	2.23999
$581$	4.40135e15	2.75814
$582$	4.40949e14	0.273723
$583$	−6.07983e14	−0.373864
$584$	1.59149e15	0.969470
$585$	−1.39142e15	−0.839656
$586$	2.61996e13	0.0156624
$587$	5.38665e14	0.319014	0.159507	−	0.987197i	$-0.449010\pi$
$587$	5.38665e14	0.319014	0.159507	+	0.987197i	$0.449010\pi$
$588$	9.55481e14	0.560592
$589$	−1.14164e15	−0.663581
$590$	−1.31453e14	−0.0756980
$591$	−7.16357e13	−0.0408694
$592$	−7.23800e14	−0.409118
$593$	−2.95891e15	−1.65703	−0.828517	−	0.559965i	$-0.810815\pi$
$593$	−2.95891e15	−1.65703	−0.828517	+	0.559965i	$0.810815\pi$
$594$	3.61191e13	0.0200406
$595$	−8.05556e15	−4.42846
$596$	−1.40123e15	−0.763231
$597$	−1.00508e15	−0.542426
$598$	3.36088e14	0.179720
$599$	3.63909e15	1.92817	0.964084	−	0.265598i	$-0.0855694\pi$
$599$	3.63909e15	1.92817	0.964084	+	0.265598i	$0.0855694\pi$
$600$	1.16207e15	0.610099
$601$	−8.03333e13	−0.0417913	−0.0208957	−	0.999782i	$-0.506652\pi$
$601$	−8.03333e13	−0.0417913	−0.0208957	+	0.999782i	$0.506652\pi$
$602$	8.99158e13	0.0463506
$603$	3.32634e14	0.169911
$604$	5.45187e14	0.275958
$605$	2.92586e15	1.46757
$606$	−1.31098e14	−0.0651624
$607$	−1.24715e15	−0.614302	−0.307151	−	0.951661i	$-0.599376\pi$
$607$	−1.24715e15	−0.614302	−0.307151	+	0.951661i	$0.599376\pi$
$608$	−2.19386e15	−1.07088
$609$	2.80563e15	1.35717
$610$	1.12681e15	0.540178
$611$	−2.74124e15	−1.30233
$612$	1.16904e15	0.550422
$613$	−2.30183e15	−1.07409	−0.537045	−	0.843553i	$-0.680460\pi$
$613$	−2.30183e15	−1.07409	−0.537045	+	0.843553i	$0.680460\pi$
$614$	1.12565e14	0.0520569
$615$	2.48340e15	1.13824
$616$	−6.23251e14	−0.283119
$617$	−1.60231e15	−0.721405	−0.360702	−	0.932681i	$-0.617463\pi$
$617$	−1.60231e15	−0.721405	−0.360702	+	0.932681i	$0.617463\pi$
$618$	2.37933e14	0.106174
$619$	7.65945e14	0.338765	0.169383	−	0.985550i	$-0.445823\pi$
$619$	7.65945e14	0.338765	0.169383	+	0.985550i	$0.445823\pi$
$620$	1.77460e15	0.777940
$621$	−1.38890e14	−0.0603485
$622$	−3.04244e14	−0.131031
$623$	−3.06436e15	−1.30815
$624$	−1.33433e15	−0.564609
$625$	−3.23803e14	−0.135813
$626$	−1.42610e15	−0.592915
$627$	−4.74570e14	−0.195582
$628$	−2.12003e15	−0.866091
$629$	3.09773e15	1.25448
$630$	7.02795e14	0.282134
$631$	4.62791e15	1.84172	0.920860	−	0.389894i	$-0.127488\pi$
$631$	4.62791e15	1.84172	0.920860	+	0.389894i	$0.127488\pi$
$632$	−3.04643e15	−1.20184
$633$	1.19331e15	0.466693
$634$	2.29998e14	0.0891729
$635$	−1.07720e15	−0.414039
$636$	1.71678e15	0.654186
$637$	4.66747e15	1.76325
$638$	−4.48991e14	−0.168160
$639$	−7.07879e14	−0.262848
$640$	4.39044e15	1.61629
$641$	−2.60535e15	−0.950926	−0.475463	−	0.879736i	$-0.657719\pi$
$641$	−2.60535e15	−0.950926	−0.475463	+	0.879736i	$0.657719\pi$
$642$	4.70591e14	0.170295
$643$	−4.08506e15	−1.46568	−0.732839	−	0.680402i	$-0.761805\pi$
$643$	−4.08506e15	−1.46568	−0.732839	+	0.680402i	$0.761805\pi$
$644$	1.11342e15	0.396085
$645$	−2.29077e14	−0.0807983
$646$	2.34183e15	0.818984
$647$	3.60941e15	1.25159	0.625797	−	0.779986i	$-0.284774\pi$
$647$	3.60941e15	1.25159	0.625797	+	0.779986i	$0.284774\pi$
$648$	−2.19531e14	−0.0754804
$649$	−1.09332e14	−0.0372734
$650$	2.63728e15	0.891523
$651$	1.40615e15	0.471342
$652$	2.90697e15	0.966227
$653$	6.85186e14	0.225832	0.112916	−	0.993605i	$-0.463981\pi$
$653$	6.85186e14	0.225832	0.112916	+	0.993605i	$0.463981\pi$
$654$	−6.33656e14	−0.207098
$655$	−3.10068e15	−1.00492
$656$	2.38150e15	0.765384
$657$	−1.49261e15	−0.475704
$658$	1.38458e15	0.437597
$659$	6.08725e15	1.90788	0.953941	−	0.299995i	$-0.0969850\pi$
$659$	6.08725e15	1.90788	0.953941	+	0.299995i	$0.0969850\pi$
$660$	7.37687e14	0.229288
$661$	−2.77767e15	−0.856193	−0.428097	−	0.903733i	$-0.640816\pi$
$661$	−2.77767e15	−0.856193	−0.428097	+	0.903733i	$0.640816\pi$
$662$	−1.46003e15	−0.446317
$663$	5.71068e15	1.73126
$664$	4.28106e15	1.28714
$665$	−9.23404e15	−2.75342
$666$	−2.70256e14	−0.0799223
$667$	1.72651e15	0.506382
$668$	1.16736e15	0.339574
$669$	−1.65618e15	−0.477820
$670$	−1.03577e15	−0.296383
$671$	9.37187e14	0.265982
$672$	2.70217e15	0.760645
$673$	1.00569e15	0.280789	0.140395	−	0.990096i	$-0.455163\pi$
$673$	1.00569e15	0.280789	0.140395	+	0.990096i	$0.455163\pi$
$674$	−3.12758e14	−0.0866121
$675$	−1.08987e15	−0.299366
$676$	−4.72274e15	−1.28673
$677$	3.18500e15	0.860740	0.430370	−	0.902652i	$-0.358383\pi$
$677$	3.18500e15	0.860740	0.430370	+	0.902652i	$0.358383\pi$
$678$	−1.48575e15	−0.398275
$679$	7.13600e15	1.89745
$680$	−7.83541e15	−2.06663
$681$	−4.32208e14	−0.113079
$682$	−2.25029e14	−0.0584015
$683$	−3.93928e15	−1.01415	−0.507076	−	0.861901i	$-0.669274\pi$
$683$	−3.93928e15	−1.01415	−0.507076	+	0.861901i	$0.669274\pi$
$684$	1.34006e15	0.342228
$685$	−1.60761e13	−0.00407271
$686$	−2.50727e14	−0.0630114
$687$	2.38030e15	0.593431
$688$	−2.19677e14	−0.0543311
$689$	8.38638e15	2.05764
$690$	4.32482e14	0.105268
$691$	4.91573e15	1.18702	0.593511	−	0.804826i	$-0.297741\pi$
$691$	4.91573e15	1.18702	0.593511	+	0.804826i	$0.297741\pi$
$692$	3.87461e15	0.928206
$693$	5.84526e14	0.138922
$694$	2.05139e15	0.483694
$695$	−3.69094e15	−0.863418
$696$	2.72896e15	0.633353
$697$	−1.01924e16	−2.34690
$698$	2.18552e15	0.499287
$699$	−1.71956e14	−0.0389757
$700$	8.73702e15	1.96483
$701$	−7.69250e14	−0.171640	−0.0858200	−	0.996311i	$-0.527351\pi$
$701$	−7.69250e14	−0.171640	−0.0858200	+	0.996311i	$0.527351\pi$
$702$	−4.98219e14	−0.110298
$703$	3.55091e15	0.779982
$704$	3.82840e14	0.0834387
$705$	−3.52746e15	−0.762820
$706$	1.69412e15	0.363511
$707$	−2.12160e15	−0.451707
$708$	3.08723e14	0.0652209
$709$	−6.83725e15	−1.43327	−0.716633	−	0.697450i	$-0.754318\pi$
$709$	−6.83725e15	−1.43327	−0.716633	+	0.697450i	$0.754318\pi$
$710$	2.20423e15	0.458496
$711$	2.85715e15	0.589725
$712$	−2.98062e15	−0.610473
$713$	8.65309e14	0.175865
$714$	−2.88442e15	−0.581725
$715$	3.60356e15	0.721187
$716$	−1.24459e15	−0.247176
$717$	−3.35179e15	−0.660574
$718$	−5.55033e14	−0.108551
$719$	−9.95468e15	−1.93205	−0.966025	−	0.258450i	$-0.916788\pi$
$719$	−9.95468e15	−1.93205	−0.966025	+	0.258450i	$0.916788\pi$
$720$	−1.71703e15	−0.330711
$721$	3.85054e15	0.735999
$722$	7.66974e14	0.145488
$723$	3.59481e15	0.676729
$724$	−4.40915e15	−0.823746
$725$	1.35479e16	2.51197
$726$	1.04765e15	0.192781
$727$	−5.39737e15	−0.985696	−0.492848	−	0.870115i	$-0.664044\pi$
$727$	−5.39737e15	−0.985696	−0.492848	+	0.870115i	$0.664044\pi$
$728$	8.59699e15	1.55820
$729$	2.05891e14	0.0370370
$730$	4.64776e15	0.829789
$731$	9.40178e14	0.166596
$732$	−2.64637e15	−0.465414
$733$	7.52773e14	0.131399	0.0656995	−	0.997839i	$-0.479072\pi$
$733$	7.52773e14	0.131399	0.0656995	+	0.997839i	$0.479072\pi$
$734$	1.96925e15	0.341171
$735$	6.00615e15	1.03280
$736$	1.66285e15	0.283808
$737$	−8.61469e14	−0.145938
$738$	8.89218e14	0.149520
$739$	1.89513e15	0.316297	0.158149	−	0.987415i	$-0.449447\pi$
$739$	1.89513e15	0.316297	0.158149	+	0.987415i	$0.449447\pi$
$740$	−5.51964e15	−0.914401
$741$	6.54611e15	1.07642
$742$	−4.23589e15	−0.691390
$743$	−4.47283e15	−0.724675	−0.362338	−	0.932047i	$-0.618021\pi$
$743$	−4.47283e15	−0.724675	−0.362338	+	0.932047i	$0.618021\pi$
$744$	1.36772e15	0.219961
$745$	−8.80814e15	−1.40613
$746$	1.64826e15	0.261193
$747$	−4.01506e15	−0.631581
$748$	−3.02762e15	−0.472762
$749$	7.61571e15	1.18048
$750$	1.21202e15	0.186498
$751$	−9.55724e15	−1.45987	−0.729933	−	0.683519i	$-0.760449\pi$
$751$	−9.55724e15	−1.45987	−0.729933	+	0.683519i	$0.760449\pi$
$752$	−3.38272e15	−0.512942
$753$	5.13765e15	0.773379
$754$	6.19328e15	0.925504
$755$	3.42704e15	0.508407
$756$	−1.65055e15	−0.243085
$757$	−3.34017e15	−0.488361	−0.244181	−	0.969730i	$-0.578519\pi$
$757$	−3.34017e15	−0.488361	−0.244181	+	0.969730i	$0.578519\pi$
$758$	−2.82580e15	−0.410166
$759$	3.59702e14	0.0518338
$760$	−8.98168e15	−1.28494
$761$	1.20740e16	1.71489	0.857446	−	0.514574i	$-0.172050\pi$
$761$	1.20740e16	1.71489	0.857446	+	0.514574i	$0.172050\pi$
$762$	−3.85708e14	−0.0543884
$763$	−1.02546e16	−1.43561
$764$	−5.56298e15	−0.773204
$765$	7.34857e15	1.01406
$766$	2.29853e15	0.314914
$767$	1.50810e15	0.205142
$768$	3.26208e14	0.0440563
$769$	9.51994e15	1.27655	0.638277	−	0.769807i	$-0.279647\pi$
$769$	9.51994e15	1.27655	0.638277	+	0.769807i	$0.279647\pi$
$770$	−1.82013e15	−0.242327
$771$	−4.09111e15	−0.540806
$772$	−1.19631e16	−1.57018
$773$	4.88498e15	0.636614	0.318307	−	0.947988i	$-0.396886\pi$
$773$	4.88498e15	0.636614	0.318307	+	0.947988i	$0.396886\pi$
$774$	−8.20243e13	−0.0106137
$775$	6.79006e15	0.872398
$776$	6.94098e15	0.885485
$777$	−4.37364e15	−0.554022
$778$	−1.59733e15	−0.200912
$779$	−1.16835e16	−1.45920
$780$	−1.01755e16	−1.26193
$781$	1.83329e15	0.225762
$782$	−1.77500e15	−0.217050
$783$	−2.55940e15	−0.310776
$784$	5.75971e15	0.694484
$785$	−1.33265e16	−1.59563
$786$	−1.11024e15	−0.132006
$787$	−5.43878e14	−0.0642156	−0.0321078	−	0.999484i	$-0.510222\pi$
$787$	−5.43878e14	−0.0642156	−0.0321078	+	0.999484i	$0.510222\pi$
$788$	−5.23874e14	−0.0614232
$789$	2.32992e15	0.271280
$790$	−8.89673e15	−1.02868
$791$	−2.40444e16	−2.76085
$792$	5.68551e14	0.0648308
$793$	−1.29273e16	−1.46388
$794$	−1.48552e15	−0.167058
$795$	1.07917e16	1.20523
$796$	−7.35015e15	−0.815219
$797$	7.21945e14	0.0795212	0.0397606	−	0.999209i	$-0.487340\pi$
$797$	7.21945e14	0.0795212	0.0397606	+	0.999209i	$0.487340\pi$
$798$	−3.30639e15	−0.361691
$799$	1.44774e16	1.57284
$800$	1.30483e16	1.40786
$801$	2.79542e15	0.299549
$802$	3.78876e15	0.403217
$803$	3.86562e15	0.408586
$804$	2.43256e15	0.255362
$805$	6.99897e15	0.729721
$806$	3.10400e15	0.321424
$807$	−1.84433e15	−0.189685
$808$	−2.06362e15	−0.210798
$809$	−5.35902e15	−0.543711	−0.271856	−	0.962338i	$-0.587637\pi$
$809$	−5.35902e15	−0.543711	−0.271856	+	0.962338i	$0.587637\pi$
$810$	−6.41114e14	−0.0646052
$811$	−8.07892e15	−0.808609	−0.404305	−	0.914624i	$-0.632486\pi$
$811$	−8.07892e15	−0.808609	−0.404305	+	0.914624i	$0.632486\pi$
$812$	2.05177e16	2.03972
$813$	−1.51804e15	−0.149894
$814$	6.99921e14	0.0686459
$815$	1.82732e16	1.78011
$816$	7.04705e15	0.681885
$817$	1.07772e15	0.103582
$818$	−1.59416e15	−0.152191
$819$	−8.06282e15	−0.764585
$820$	1.81611e16	1.71067
$821$	−1.54990e16	−1.45017	−0.725083	−	0.688662i	$-0.758198\pi$
$821$	−1.54990e16	−1.45017	−0.725083	+	0.688662i	$0.758198\pi$
$822$	−5.75630e12	−0.000534993 0
$823$	9.28888e15	0.857559	0.428780	−	0.903409i	$-0.358944\pi$
$823$	9.28888e15	0.857559	0.428780	+	0.903409i	$0.358944\pi$
$824$	3.74530e15	0.343469
$825$	2.82258e15	0.257128
$826$	−7.61726e14	−0.0689300
$827$	−2.77458e15	−0.249412	−0.124706	−	0.992194i	$-0.539799\pi$
$827$	−2.77458e15	−0.249412	−0.124706	+	0.992194i	$0.539799\pi$
$828$	−1.01570e15	−0.0906985
$829$	6.35935e15	0.564108	0.282054	−	0.959398i	$-0.408984\pi$
$829$	6.35935e15	0.564108	0.282054	+	0.959398i	$0.408984\pi$
$830$	1.25023e16	1.10169
$831$	−3.16985e15	−0.277481
$832$	−5.28081e15	−0.459221
$833$	−2.46505e16	−2.12950
$834$	−1.32160e15	−0.113419
$835$	7.33803e15	0.625610
$836$	−3.47054e15	−0.293943
$837$	−1.28274e15	−0.107932
$838$	−6.19340e15	−0.517711
$839$	1.15571e16	0.959748	0.479874	−	0.877337i	$-0.340682\pi$
$839$	1.15571e16	0.959748	0.479874	+	0.877337i	$0.340682\pi$
$840$	1.10627e16	0.912694
$841$	1.96149e16	1.60771
$842$	8.06009e15	0.656331
$843$	−4.91293e15	−0.397456
$844$	8.72667e15	0.701399
$845$	−2.96871e16	−2.37059
$846$	−1.26306e15	−0.100204
$847$	1.69544e16	1.33636
$848$	1.03489e16	0.810432
$849$	−1.44043e14	−0.0112073
$850$	−1.39284e16	−1.07670
$851$	−2.69142e15	−0.206714
$852$	−5.17673e15	−0.395037
$853$	−1.56446e16	−1.18617	−0.593083	−	0.805141i	$-0.702089\pi$
$853$	−1.56446e16	−1.18617	−0.593083	+	0.805141i	$0.702089\pi$
$854$	6.52949e15	0.491882
$855$	8.42361e15	0.630499
$856$	7.40758e15	0.550897
$857$	−2.08939e16	−1.54392	−0.771960	−	0.635671i	$-0.780724\pi$
$857$	−2.08939e16	−1.54392	−0.771960	+	0.635671i	$0.780724\pi$
$858$	1.29031e15	0.0947356
$859$	−1.69176e16	−1.23417	−0.617086	−	0.786896i	$-0.711687\pi$
$859$	−1.69176e16	−1.23417	−0.617086	+	0.786896i	$0.711687\pi$
$860$	−1.67524e15	−0.121433
$861$	1.43905e16	1.03647
$862$	−3.27154e15	−0.234133
$863$	1.88111e16	1.33769	0.668843	−	0.743404i	$-0.266790\pi$
$863$	1.88111e16	1.33769	0.668843	+	0.743404i	$0.266790\pi$
$864$	−2.46502e15	−0.174178
$865$	2.43558e16	1.71007
$866$	−5.68183e15	−0.396405
$867$	−2.18320e16	−1.51352
$868$	1.02832e16	0.708386
$869$	−7.39955e15	−0.506520
$870$	7.96958e15	0.542100
$871$	1.18829e16	0.803199
$872$	−9.97438e15	−0.669955
$873$	−6.50971e15	−0.434494
$874$	−2.03467e15	−0.134952
$875$	1.96145e16	1.29280
$876$	−1.09155e16	−0.714941
$877$	−1.19995e16	−0.781029	−0.390514	−	0.920597i	$-0.627703\pi$
$877$	−1.19995e16	−0.781029	−0.390514	+	0.920597i	$0.627703\pi$
$878$	4.79124e15	0.309905
$879$	−3.86783e14	−0.0248616
$880$	4.44683e15	0.284051
$881$	1.22001e16	0.774457	0.387229	−	0.921984i	$-0.373432\pi$
$881$	1.22001e16	0.774457	0.387229	+	0.921984i	$0.373432\pi$
$882$	2.15059e15	0.135669
$883$	1.42018e16	0.890349	0.445174	−	0.895444i	$-0.353142\pi$
$883$	1.42018e16	0.890349	0.445174	+	0.895444i	$0.353142\pi$
$884$	4.17623e16	2.60194
$885$	1.94063e15	0.120159
$886$	4.83483e15	0.297506
$887$	2.18442e16	1.33584	0.667921	−	0.744232i	$-0.267184\pi$
$887$	2.18442e16	1.33584	0.667921	+	0.744232i	$0.267184\pi$
$888$	−4.25411e15	−0.258546
$889$	−6.24202e15	−0.377021
$890$	−8.70452e15	−0.522516
$891$	−5.33225e14	−0.0318114
$892$	−1.21117e16	−0.718122
$893$	1.65954e16	0.977921
$894$	−3.15389e15	−0.184710
$895$	−7.82352e15	−0.455381
$896$	2.54412e16	1.47178
$897$	−4.96165e15	−0.285278
$898$	−4.41754e15	−0.252441
$899$	1.59455e16	0.905650
$900$	−7.97021e15	−0.449921
$901$	−4.42913e16	−2.48504
$902$	−2.30293e15	−0.128424
$903$	−1.32742e15	−0.0735744
$904$	−2.33873e16	−1.28841
$905$	−2.77159e16	−1.51762
$906$	1.22711e15	0.0667847
$907$	−3.97869e15	−0.215229	−0.107614	−	0.994193i	$-0.534321\pi$
$907$	−3.97869e15	−0.215229	−0.107614	+	0.994193i	$0.534321\pi$
$908$	−3.16075e15	−0.169949
$909$	1.93540e15	0.103435
$910$	2.51064e16	1.33370
$911$	−1.74764e16	−0.922785	−0.461393	−	0.887196i	$-0.652650\pi$
$911$	−1.74764e16	−0.922785	−0.461393	+	0.887196i	$0.652650\pi$
$912$	8.07798e15	0.423966
$913$	1.03984e16	0.542470
$914$	−1.31844e16	−0.683683
$915$	−1.66351e16	−0.857449
$916$	1.74072e16	0.891876
$917$	−1.79674e16	−0.915069
$918$	2.63127e15	0.133208
$919$	6.80581e15	0.342487	0.171244	−	0.985229i	$-0.445221\pi$
$919$	6.80581e15	0.342487	0.171244	+	0.985229i	$0.445221\pi$
$920$	6.80770e15	0.340539
$921$	−1.66179e15	−0.0826322
$922$	8.45199e15	0.417772
$923$	−2.52880e16	−1.24253
$924$	4.27465e15	0.208788
$925$	−2.11196e16	−1.02543
$926$	−1.35304e16	−0.653058
$927$	−3.51259e15	−0.168535
$928$	3.06422e16	1.46152
$929$	8.16106e15	0.386955	0.193477	−	0.981105i	$-0.438023\pi$
$929$	8.16106e15	0.386955	0.193477	+	0.981105i	$0.438023\pi$
$930$	3.99426e15	0.188270
$931$	−2.82567e16	−1.32403
$932$	−1.25752e15	−0.0585771
$933$	4.49155e15	0.207992
$934$	−1.41928e16	−0.653370
$935$	−1.90316e16	−0.870987
$936$	−7.84247e15	−0.356809
$937$	2.62034e16	1.18520	0.592598	−	0.805499i	$-0.298102\pi$
$937$	2.62034e16	1.18520	0.592598	+	0.805499i	$0.298102\pi$
$938$	−6.00196e15	−0.269884
$939$	2.10535e16	0.941161
$940$	−2.57964e16	−1.14645
$941$	−3.62454e16	−1.60144	−0.800718	−	0.599042i	$-0.795548\pi$
$941$	−3.62454e16	−1.60144	−0.800718	+	0.599042i	$0.795548\pi$
$942$	−4.77175e15	−0.209603
$943$	8.85552e15	0.386723
$944$	1.86101e15	0.0807983
$945$	−1.03753e16	−0.447844
$946$	2.12430e14	0.00911621
$947$	2.14057e16	0.913282	0.456641	−	0.889651i	$-0.349052\pi$
$947$	2.14057e16	0.913282	0.456641	+	0.889651i	$0.349052\pi$
$948$	2.08944e16	0.886306
$949$	−5.33215e16	−2.24873
$950$	−1.59660e16	−0.669447
$951$	−3.39545e15	−0.141548
$952$	−4.54036e16	−1.88186
$953$	−1.55330e16	−0.640096	−0.320048	−	0.947401i	$-0.603699\pi$
$953$	−1.55330e16	−0.640096	−0.320048	+	0.947401i	$0.603699\pi$
$954$	3.86413e15	0.158320
$955$	−3.49689e16	−1.42450
$956$	−2.45117e16	−0.992785
$957$	6.62843e15	0.266928
$958$	−5.23978e15	−0.209799
$959$	−9.31558e13	−0.00370858
$960$	−6.79540e15	−0.268982
$961$	−1.74168e16	−0.685471
$962$	−9.65455e15	−0.377806
$963$	−6.94732e15	−0.270317
$964$	2.62889e16	1.01706
$965$	−7.52002e16	−2.89280
$966$	2.50609e15	0.0958566
$967$	−4.38978e16	−1.66954	−0.834771	−	0.550597i	$-0.814400\pi$
$967$	−4.38978e16	−1.66954	−0.834771	+	0.550597i	$0.814400\pi$
$968$	1.64911e16	0.623640
$969$	−3.45723e16	−1.30001
$970$	2.02703e16	0.757905
$971$	−2.75018e16	−1.02248	−0.511241	−	0.859437i	$-0.670814\pi$
$971$	−2.75018e16	−1.02248	−0.511241	+	0.859437i	$0.670814\pi$
$972$	1.50569e15	0.0556634
$973$	−2.13878e16	−0.786222
$974$	−7.37463e14	−0.0269566
$975$	−3.89340e16	−1.41515
$976$	−1.59525e16	−0.576573
$977$	−1.21036e16	−0.435004	−0.217502	−	0.976060i	$-0.569791\pi$
$977$	−1.21036e16	−0.435004	−0.217502	+	0.976060i	$0.569791\pi$
$978$	6.54300e15	0.233837
$979$	−7.23969e15	−0.257285
$980$	4.39231e16	1.55221
$981$	9.35464e15	0.328736
$982$	1.36322e16	0.476380
$983$	3.98310e15	0.138413	0.0692065	−	0.997602i	$-0.477953\pi$
$983$	3.98310e15	0.138413	0.0692065	+	0.997602i	$0.477953\pi$
$984$	1.39972e16	0.483690
$985$	−3.29307e15	−0.113162
$986$	−3.27088e16	−1.11774
$987$	−2.04404e16	−0.694618
$988$	4.78719e16	1.61777
$989$	−8.16862e14	−0.0274517
$990$	1.66038e15	0.0554900
$991$	−3.26106e16	−1.08381	−0.541906	−	0.840439i	$-0.682297\pi$
$991$	−3.26106e16	−1.08381	−0.541906	+	0.840439i	$0.682297\pi$
$992$	1.53575e16	0.507582
$993$	2.15544e16	0.708460
$994$	1.27728e16	0.417503
$995$	−4.62030e16	−1.50191
$996$	−2.93623e16	−0.949212
$997$	3.71945e16	1.19579	0.597895	−	0.801574i	$-0.296004\pi$
$997$	3.71945e16	1.19579	0.597895	+	0.801574i	$0.296004\pi$
$998$	−1.07488e16	−0.343671
$999$	3.98978e15	0.126864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.16	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+16.4601 q^{2} -243.000 q^{3} -1777.06 q^{4} -11170.6 q^{5} -3999.81 q^{6} -64730.0 q^{7} -62961.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+16.4601 q^{2} -243.000 q^{3} -1777.06 q^{4} -11170.6 q^{5} -3999.81 q^{6} -64730.0 q^{7} -62961.0 q^{8} +59049.0 q^{9} -183870. q^{10} -152927. q^{11} +431827. q^{12} +2.10945e6 q^{13} -1.06546e6 q^{14} +2.71446e6 q^{15} +2.60308e6 q^{16} -1.11407e7 q^{17} +971954. q^{18} -1.27705e7 q^{19} +1.98509e7 q^{20} +1.57294e7 q^{21} -2.51720e6 q^{22} +9.67947e6 q^{23} +1.52995e7 q^{24} +7.59546e7 q^{25} +3.47218e7 q^{26} -1.43489e7 q^{27} +1.15029e8 q^{28} +1.78369e8 q^{29} +4.46803e7 q^{30} +8.93963e7 q^{31} +1.71791e8 q^{32} +3.71614e7 q^{33} -1.83377e8 q^{34} +7.23074e8 q^{35} -1.04934e8 q^{36} -2.78055e8 q^{37} -2.10204e8 q^{38} -5.12596e8 q^{39} +7.03314e8 q^{40} +9.14877e8 q^{41} +2.58908e8 q^{42} -8.43912e7 q^{43} +2.71762e8 q^{44} -6.59614e8 q^{45} +1.59325e8 q^{46} -1.29951e9 q^{47} -6.32549e8 q^{48} +2.21265e9 q^{49} +1.25022e9 q^{50} +2.70719e9 q^{51} -3.74862e9 q^{52} +3.97563e9 q^{53} -2.36185e8 q^{54} +1.70829e9 q^{55} +4.07547e9 q^{56} +3.10324e9 q^{57} +2.93597e9 q^{58} +7.14924e8 q^{59} -4.82377e9 q^{60} -6.12831e9 q^{61} +1.47147e9 q^{62} -3.82224e9 q^{63} -2.50341e9 q^{64} -2.35638e10 q^{65} +6.11680e8 q^{66} +5.63319e9 q^{67} +1.97978e10 q^{68} -2.35211e9 q^{69} +1.19019e10 q^{70} -1.19880e10 q^{71} -3.71779e9 q^{72} -2.52775e10 q^{73} -4.57682e9 q^{74} -1.84570e10 q^{75} +2.26940e10 q^{76} +9.89899e9 q^{77} -8.43739e9 q^{78} +4.83860e10 q^{79} -2.90780e10 q^{80} +3.48678e9 q^{81} +1.50590e10 q^{82} -6.79955e10 q^{83} -2.79521e10 q^{84} +1.24449e11 q^{85} -1.38909e9 q^{86} -4.33436e10 q^{87} +9.62846e9 q^{88} +4.73407e10 q^{89} -1.08573e10 q^{90} -1.36545e11 q^{91} -1.72010e10 q^{92} -2.17233e10 q^{93} -2.13900e10 q^{94} +1.42655e11 q^{95} -4.17453e10 q^{96} -1.10243e11 q^{97} +3.64205e10 q^{98} -9.03021e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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

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