LMFDB - Embedded newform 177.12.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-4.91496 q^{2} +243.000 q^{3} -2023.84 q^{4} -1117.68 q^{5} -1194.33 q^{6} -21416.7 q^{7} +20012.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-4.91496 q^{2} +243.000 q^{3} -2023.84 q^{4} -1117.68 q^{5} -1194.33 q^{6} -21416.7 q^{7} +20012.9 q^{8} +59049.0 q^{9} +5493.36 q^{10} +110263. q^{11} -491794. q^{12} -34344.1 q^{13} +105262. q^{14} -271597. q^{15} +4.04647e6 q^{16} -8.45888e6 q^{17} -290223. q^{18} +1.50934e7 q^{19} +2.26201e6 q^{20} -5.20426e6 q^{21} -541937. q^{22} +7.31177e6 q^{23} +4.86314e6 q^{24} -4.75789e7 q^{25} +168800. q^{26} +1.43489e7 q^{27} +4.33441e7 q^{28} -3.39103e7 q^{29} +1.33489e6 q^{30} +1.38887e8 q^{31} -6.08747e7 q^{32} +2.67939e7 q^{33} +4.15750e7 q^{34} +2.39371e7 q^{35} -1.19506e8 q^{36} +5.04720e8 q^{37} -7.41832e7 q^{38} -8.34562e6 q^{39} -2.23681e7 q^{40} +6.49327e8 q^{41} +2.55787e7 q^{42} +1.25045e9 q^{43} -2.23155e8 q^{44} -6.59980e7 q^{45} -3.59370e7 q^{46} -1.92452e9 q^{47} +9.83292e8 q^{48} -1.51865e9 q^{49} +2.33848e8 q^{50} -2.05551e9 q^{51} +6.95071e7 q^{52} +5.25997e9 q^{53} -7.05243e7 q^{54} -1.23239e8 q^{55} -4.28611e8 q^{56} +3.66769e9 q^{57} +1.66668e8 q^{58} -7.14924e8 q^{59} +5.49669e8 q^{60} -8.19477e9 q^{61} -6.82622e8 q^{62} -1.26464e9 q^{63} -7.98797e9 q^{64} +3.83858e7 q^{65} -1.31691e8 q^{66} -8.86480e9 q^{67} +1.71194e10 q^{68} +1.77676e9 q^{69} -1.17650e8 q^{70} -3.46434e9 q^{71} +1.18174e9 q^{72} +5.04526e9 q^{73} -2.48068e9 q^{74} -1.15617e10 q^{75} -3.05466e10 q^{76} -2.36147e9 q^{77} +4.10183e7 q^{78} +2.53994e10 q^{79} -4.52266e9 q^{80} +3.48678e9 q^{81} -3.19141e9 q^{82} +2.79697e10 q^{83} +1.05326e10 q^{84} +9.45433e9 q^{85} -6.14593e9 q^{86} -8.24021e9 q^{87} +2.20668e9 q^{88} -9.94834e10 q^{89} +3.24377e8 q^{90} +7.35538e8 q^{91} -1.47979e10 q^{92} +3.37495e10 q^{93} +9.45895e9 q^{94} -1.68696e10 q^{95} -1.47926e10 q^{96} -1.07428e11 q^{97} +7.46410e9 q^{98} +6.51091e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.91496	−0.108606	−0.0543031	−	0.998524i	$-0.517294\pi$
$2$	−4.91496	−0.108606	−0.0543031	+	0.998524i	$0.517294\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−2023.84	−0.988205
$5$	−1117.68	−0.159950	−0.0799748	−	0.996797i	$-0.525484\pi$
$5$	−1117.68	−0.159950	−0.0799748	+	0.996797i	$0.525484\pi$
$6$	−1194.33	−0.0627038
$7$	−21416.7	−0.481630	−0.240815	−	0.970571i	$-0.577415\pi$
$7$	−21416.7	−0.481630	−0.240815	+	0.970571i	$0.577415\pi$
$8$	20012.9	0.215931
$9$	59049.0	0.333333
$10$	5493.36	0.0173715
$11$	110263.	0.206428	0.103214	−	0.994659i	$-0.467087\pi$
$11$	110263.	0.206428	0.103214	+	0.994659i	$0.467087\pi$
$12$	−491794.	−0.570540
$13$	−34344.1	−0.0256545	−0.0128273	−	0.999918i	$-0.504083\pi$
$13$	−34344.1	−0.0256545	−0.0128273	+	0.999918i	$0.504083\pi$
$14$	105262.	0.0523080
$15$	−271597.	−0.0923469
$16$	4.04647e6	0.964753
$17$	−8.45888e6	−1.44492	−0.722460	−	0.691413i	$-0.756989\pi$
$17$	−8.45888e6	−1.44492	−0.722460	+	0.691413i	$0.756989\pi$
$18$	−290223.	−0.0362021
$19$	1.50934e7	1.39843	0.699216	−	0.714911i	$-0.253533\pi$
$19$	1.50934e7	1.39843	0.699216	+	0.714911i	$0.253533\pi$
$20$	2.26201e6	0.158063
$21$	−5.20426e6	−0.278069
$22$	−541937.	−0.0224194
$23$	7.31177e6	0.236875	0.118438	−	0.992961i	$-0.462211\pi$
$23$	7.31177e6	0.236875	0.118438	+	0.992961i	$0.462211\pi$
$24$	4.86314e6	0.124668
$25$	−4.75789e7	−0.974416
$26$	168800.	0.00278624
$27$	1.43489e7	0.192450
$28$	4.33441e7	0.475949
$29$	−3.39103e7	−0.307003	−0.153502	−	0.988148i	$-0.549055\pi$
$29$	−3.39103e7	−0.307003	−0.153502	+	0.988148i	$0.549055\pi$
$30$	1.33489e6	0.0100295
$31$	1.38887e8	0.871307	0.435654	−	0.900114i	$-0.356517\pi$
$31$	1.38887e8	0.871307	0.435654	+	0.900114i	$0.356517\pi$
$32$	−6.08747e7	−0.320710
$33$	2.67939e7	0.119182
$34$	4.15750e7	0.156927
$35$	2.39371e7	0.0770365
$36$	−1.19506e8	−0.329402
$37$	5.04720e8	1.19658	0.598289	−	0.801280i	$-0.295847\pi$
$37$	5.04720e8	1.19658	0.598289	+	0.801280i	$0.295847\pi$
$38$	−7.41832e7	−0.151878
$39$	−8.34562e6	−0.0148116
$40$	−2.23681e7	−0.0345381
$41$	6.49327e8	0.875290	0.437645	−	0.899148i	$-0.355813\pi$
$41$	6.49327e8	0.875290	0.437645	+	0.899148i	$0.355813\pi$
$42$	2.55787e7	0.0302001
$43$	1.25045e9	1.29715	0.648577	−	0.761149i	$-0.275365\pi$
$43$	1.25045e9	1.29715	0.648577	+	0.761149i	$0.275365\pi$
$44$	−2.23155e8	−0.203994
$45$	−6.59980e7	−0.0533165
$46$	−3.59370e7	−0.0257261
$47$	−1.92452e9	−1.22401	−0.612005	−	0.790854i	$-0.709637\pi$
$47$	−1.92452e9	−1.22401	−0.612005	+	0.790854i	$0.709637\pi$
$48$	9.83292e8	0.557001
$49$	−1.51865e9	−0.768032
$50$	2.33848e8	0.105828
$51$	−2.05551e9	−0.834225
$52$	6.95071e7	0.0253519
$53$	5.25997e9	1.72769	0.863846	−	0.503756i	$-0.168049\pi$
$53$	5.25997e9	1.72769	0.863846	+	0.503756i	$0.168049\pi$
$54$	−7.05243e7	−0.0209013
$55$	−1.23239e8	−0.0330181
$56$	−4.28611e8	−0.103999
$57$	3.66769e9	0.807385
$58$	1.66668e8	0.0333425
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	5.49669e8	0.0912576
$61$	−8.19477e9	−1.24229	−0.621145	−	0.783696i	$-0.713332\pi$
$61$	−8.19477e9	−1.24229	−0.621145	+	0.783696i	$0.713332\pi$
$62$	−6.82622e8	−0.0946294
$63$	−1.26464e9	−0.160543
$64$	−7.98797e9	−0.929922
$65$	3.83858e7	0.00410343
$66$	−1.31691e8	−0.0129439
$67$	−8.86480e9	−0.802154	−0.401077	−	0.916044i	$-0.631364\pi$
$67$	−8.86480e9	−0.802154	−0.401077	+	0.916044i	$0.631364\pi$
$68$	1.71194e10	1.42788
$69$	1.77676e9	0.136760
$70$	−1.17650e8	−0.00836665
$71$	−3.46434e9	−0.227877	−0.113938	−	0.993488i	$-0.536347\pi$
$71$	−3.46434e9	−0.227877	−0.113938	+	0.993488i	$0.536347\pi$
$72$	1.18174e9	0.0719771
$73$	5.04526e9	0.284845	0.142422	−	0.989806i	$-0.454511\pi$
$73$	5.04526e9	0.284845	0.142422	+	0.989806i	$0.454511\pi$
$74$	−2.48068e9	−0.129956
$75$	−1.15617e10	−0.562579
$76$	−3.05466e10	−1.38194
$77$	−2.36147e9	−0.0994222
$78$	4.10183e7	0.00160864
$79$	2.53994e10	0.928697	0.464348	−	0.885653i	$-0.346289\pi$
$79$	2.53994e10	0.928697	0.464348	+	0.885653i	$0.346289\pi$
$80$	−4.52266e9	−0.154312
$81$	3.48678e9	0.111111
$82$	−3.19141e9	−0.0950620
$83$	2.79697e10	0.779398	0.389699	−	0.920942i	$-0.372579\pi$
$83$	2.79697e10	0.779398	0.389699	+	0.920942i	$0.372579\pi$
$84$	1.05326e10	0.274789
$85$	9.45433e9	0.231114
$86$	−6.14593e9	−0.140879
$87$	−8.24021e9	−0.177248
$88$	2.20668e9	0.0445744
$89$	−9.94834e10	−1.88845	−0.944226	−	0.329299i	$-0.893188\pi$
$89$	−9.94834e10	−1.88845	−0.944226	+	0.329299i	$0.893188\pi$
$90$	3.24377e8	0.00579051
$91$	7.35538e8	0.0123560
$92$	−1.47979e10	−0.234081
$93$	3.37495e10	0.503049
$94$	9.45895e9	0.132935
$95$	−1.68696e10	−0.223679
$96$	−1.47926e10	−0.185162
$97$	−1.07428e11	−1.27020	−0.635100	−	0.772430i	$-0.719041\pi$
$97$	−1.07428e11	−1.27020	−0.635100	+	0.772430i	$0.719041\pi$
$98$	7.46410e9	0.0834131
$99$	6.51091e9	0.0688095
$100$	9.62923e10	0.962923
$101$	−1.77126e11	−1.67693	−0.838466	−	0.544955i	$-0.816547\pi$
$101$	−1.77126e11	−1.67693	−0.838466	+	0.544955i	$0.816547\pi$
$102$	1.01027e10	0.0906020
$103$	−8.41645e10	−0.715359	−0.357679	−	0.933844i	$-0.616432\pi$
$103$	−8.41645e10	−0.715359	−0.357679	+	0.933844i	$0.616432\pi$
$104$	−6.87326e8	−0.00553961
$105$	5.81671e9	0.0444771
$106$	−2.58525e10	−0.187638
$107$	1.83896e11	1.26754	0.633771	−	0.773521i	$-0.281506\pi$
$107$	1.83896e11	1.26754	0.633771	+	0.773521i	$0.281506\pi$
$108$	−2.90399e10	−0.190180
$109$	−3.45814e10	−0.215277	−0.107638	−	0.994190i	$-0.534329\pi$
$109$	−3.45814e10	−0.215277	−0.107638	+	0.994190i	$0.534329\pi$
$110$	6.05713e8	0.00358598
$111$	1.22647e11	0.690845
$112$	−8.66621e10	−0.464654
$113$	1.64949e11	0.842206	0.421103	−	0.907013i	$-0.361643\pi$
$113$	1.64949e11	0.842206	0.421103	+	0.907013i	$0.361643\pi$
$114$	−1.80265e10	−0.0876870
$115$	−8.17223e9	−0.0378881
$116$	6.86292e10	0.303382
$117$	−2.02798e9	−0.00855150
$118$	3.51382e9	0.0141393
$119$	1.81161e11	0.695917
$120$	−5.43544e9	−0.0199406
$121$	−2.73154e11	−0.957387
$122$	4.02770e10	0.134920
$123$	1.57786e11	0.505349
$124$	−2.81085e11	−0.861030
$125$	1.07752e11	0.315807
$126$	6.21563e9	0.0174360
$127$	4.41527e11	1.18587	0.592934	−	0.805251i	$-0.297969\pi$
$127$	4.41527e11	1.18587	0.592934	+	0.805251i	$0.297969\pi$
$128$	1.63932e11	0.421705
$129$	3.03860e11	0.748912
$130$	−1.88664e8	−0.000445658 0
$131$	−1.61559e11	−0.365880	−0.182940	−	0.983124i	$-0.558561\pi$
$131$	−1.61559e11	−0.365880	−0.182940	+	0.983124i	$0.558561\pi$
$132$	−5.42266e10	−0.117776
$133$	−3.23250e11	−0.673527
$134$	4.35701e10	0.0871189
$135$	−1.60375e10	−0.0307823
$136$	−1.69287e11	−0.312004
$137$	−4.86495e11	−0.861223	−0.430611	−	0.902538i	$-0.641702\pi$
$137$	−4.86495e11	−0.861223	−0.430611	+	0.902538i	$0.641702\pi$
$138$	−8.73270e9	−0.0148530
$139$	4.81449e11	0.786989	0.393495	−	0.919327i	$-0.371266\pi$
$139$	4.81449e11	0.786989	0.393495	+	0.919327i	$0.371266\pi$
$140$	−4.84449e10	−0.0761279
$141$	−4.67659e11	−0.706683
$142$	1.70271e10	0.0247488
$143$	−3.78688e9	−0.00529582
$144$	2.38940e11	0.321584
$145$	3.79009e10	0.0491050
$146$	−2.47973e10	−0.0309359
$147$	−3.69032e11	−0.443424
$148$	−1.02147e12	−1.18246
$149$	3.55211e10	0.0396243	0.0198121	−	0.999804i	$-0.493693\pi$
$149$	3.55211e10	0.0396243	0.0198121	+	0.999804i	$0.493693\pi$
$150$	5.68251e10	0.0610996
$151$	9.14071e11	0.947560	0.473780	−	0.880643i	$-0.342889\pi$
$151$	9.14071e11	0.947560	0.473780	+	0.880643i	$0.342889\pi$
$152$	3.02063e11	0.301965
$153$	−4.99488e11	−0.481640
$154$	1.16065e10	0.0107979
$155$	−1.55231e11	−0.139365
$156$	1.68902e10	0.0146369
$157$	−1.23688e12	−1.03485	−0.517426	−	0.855728i	$-0.673110\pi$
$157$	−1.23688e12	−1.03485	−0.517426	+	0.855728i	$0.673110\pi$
$158$	−1.24837e11	−0.100862
$159$	1.27817e12	0.997483
$160$	6.80385e10	0.0512974
$161$	−1.56594e11	−0.114086
$162$	−1.71374e10	−0.0120674
$163$	−7.79907e11	−0.530898	−0.265449	−	0.964125i	$-0.585520\pi$
$163$	−7.79907e11	−0.530898	−0.265449	+	0.964125i	$0.585520\pi$
$164$	−1.31414e12	−0.864966
$165$	−2.99470e10	−0.0190630
$166$	−1.37470e11	−0.0846474
$167$	−2.22097e12	−1.32313	−0.661564	−	0.749889i	$-0.730107\pi$
$167$	−2.22097e12	−1.32313	−0.661564	+	0.749889i	$0.730107\pi$
$168$	−1.04153e11	−0.0600439
$169$	−1.79098e12	−0.999342
$170$	−4.64676e10	−0.0251004
$171$	8.91248e11	0.466144
$172$	−2.53072e12	−1.28185
$173$	−2.39491e12	−1.17500	−0.587498	−	0.809226i	$-0.699887\pi$
$173$	−2.39491e12	−1.17500	−0.587498	+	0.809226i	$0.699887\pi$
$174$	4.05003e10	0.0192503
$175$	1.01898e12	0.469308
$176$	4.46175e11	0.199153
$177$	−1.73727e11	−0.0751646
$178$	4.88957e11	0.205098
$179$	−4.47136e12	−1.81865	−0.909323	−	0.416092i	$-0.863400\pi$
$179$	−4.47136e12	−1.81865	−0.909323	+	0.416092i	$0.863400\pi$
$180$	1.33570e11	0.0526876
$181$	−4.87250e12	−1.86432	−0.932158	−	0.362052i	$-0.882076\pi$
$181$	−4.87250e12	−1.86432	−0.932158	+	0.362052i	$0.882076\pi$
$182$	−3.61514e9	−0.00134194
$183$	−1.99133e12	−0.717236
$184$	1.46330e11	0.0511488
$185$	−5.64117e11	−0.191392
$186$	−1.65877e11	−0.0546343
$187$	−9.32700e11	−0.298272
$188$	3.89493e12	1.20957
$189$	−3.07306e11	−0.0926898
$190$	8.29132e10	0.0242929
$191$	−1.25233e12	−0.356480	−0.178240	−	0.983987i	$-0.557040\pi$
$191$	−1.25233e12	−0.356480	−0.178240	+	0.983987i	$0.557040\pi$
$192$	−1.94108e12	−0.536891
$193$	−6.09566e12	−1.63853	−0.819267	−	0.573412i	$-0.805620\pi$
$193$	−6.09566e12	−1.63853	−0.819267	+	0.573412i	$0.805620\pi$
$194$	5.28003e11	0.137952
$195$	9.32774e9	0.00236911
$196$	3.07351e12	0.758973
$197$	4.02584e12	0.966700	0.483350	−	0.875427i	$-0.339420\pi$
$197$	4.02584e12	0.966700	0.483350	+	0.875427i	$0.339420\pi$
$198$	−3.20009e10	−0.00747314
$199$	−4.07863e12	−0.926450	−0.463225	−	0.886241i	$-0.653308\pi$
$199$	−4.07863e12	−0.926450	−0.463225	+	0.886241i	$0.653308\pi$
$200$	−9.52194e11	−0.210407
$201$	−2.15415e12	−0.463124
$202$	8.70568e11	0.182125
$203$	7.26248e11	0.147862
$204$	4.16002e12	0.824385
$205$	−7.25740e11	−0.140002
$206$	4.13665e11	0.0776924
$207$	4.31753e11	0.0789584
$208$	−1.38972e11	−0.0247503
$209$	1.66424e12	0.288676
$210$	−2.85889e10	−0.00483049
$211$	3.79950e12	0.625421	0.312710	−	0.949848i	$-0.398763\pi$
$211$	3.79950e12	0.625421	0.312710	+	0.949848i	$0.398763\pi$
$212$	−1.06454e13	−1.70731
$213$	−8.41835e11	−0.131565
$214$	−9.03843e11	−0.137663
$215$	−1.39761e12	−0.207479
$216$	2.87164e11	0.0415560
$217$	−2.97450e12	−0.419648
$218$	1.69966e11	0.0233804
$219$	1.22600e12	0.164455
$220$	2.49416e11	0.0326287
$221$	2.90513e11	0.0370687
$222$	−6.02805e11	−0.0750301
$223$	1.60866e12	0.195339	0.0976695	−	0.995219i	$-0.468861\pi$
$223$	1.60866e12	0.195339	0.0976695	+	0.995219i	$0.468861\pi$
$224$	1.30374e12	0.154463
$225$	−2.80949e12	−0.324805
$226$	−8.10718e11	−0.0914688
$227$	−1.20558e13	−1.32755	−0.663777	−	0.747931i	$-0.731048\pi$
$227$	−1.20558e13	−1.32755	−0.663777	+	0.747931i	$0.731048\pi$
$228$	−7.42282e12	−0.797862
$229$	−6.53920e12	−0.686167	−0.343083	−	0.939305i	$-0.611471\pi$
$229$	−6.53920e12	−0.686167	−0.343083	+	0.939305i	$0.611471\pi$
$230$	4.01662e10	0.00411488
$231$	−5.73837e11	−0.0574014
$232$	−6.78645e11	−0.0662917
$233$	9.39440e12	0.896214	0.448107	−	0.893980i	$-0.352098\pi$
$233$	9.39440e12	0.896214	0.448107	+	0.893980i	$0.352098\pi$
$234$	9.96746e9	0.000928747 0
$235$	2.15100e12	0.195780
$236$	1.44689e12	0.128653
$237$	6.17205e12	0.536183
$238$	−8.90400e11	−0.0755809
$239$	1.81396e12	0.150466	0.0752330	−	0.997166i	$-0.476030\pi$
$239$	1.81396e12	0.150466	0.0752330	+	0.997166i	$0.476030\pi$
$240$	−1.09901e12	−0.0890920
$241$	1.38604e12	0.109820	0.0549102	−	0.998491i	$-0.482513\pi$
$241$	1.38604e12	0.109820	0.0549102	+	0.998491i	$0.482513\pi$
$242$	1.34254e12	0.103978
$243$	8.47289e11	0.0641500
$244$	1.65849e13	1.22764
$245$	1.69737e12	0.122846
$246$	−7.75513e11	−0.0548841
$247$	−5.18368e11	−0.0358761
$248$	2.77953e12	0.188143
$249$	6.79665e12	0.449985
$250$	−5.29598e11	−0.0342986
$251$	5.62633e12	0.356467	0.178234	−	0.983988i	$-0.442962\pi$
$251$	5.62633e12	0.356467	0.178234	+	0.983988i	$0.442962\pi$
$252$	2.55942e12	0.158650
$253$	8.06217e11	0.0488978
$254$	−2.17008e12	−0.128793
$255$	2.29740e12	0.133434
$256$	1.55536e13	0.884122
$257$	−2.81452e13	−1.56593	−0.782964	−	0.622067i	$-0.786293\pi$
$257$	−2.81452e13	−1.56593	−0.782964	+	0.622067i	$0.786293\pi$
$258$	−1.49346e12	−0.0813365
$259$	−1.08095e13	−0.576309
$260$	−7.76868e10	−0.00405503
$261$	−2.00237e12	−0.102334
$262$	7.94056e11	0.0397369
$263$	−8.05576e12	−0.394775	−0.197388	−	0.980326i	$-0.563246\pi$
$263$	−8.05576e12	−0.394775	−0.197388	+	0.980326i	$0.563246\pi$
$264$	5.36224e11	0.0257350
$265$	−5.87897e12	−0.276343
$266$	1.58876e12	0.0731492
$267$	−2.41745e13	−1.09030
$268$	1.79410e13	0.792692
$269$	−1.30424e13	−0.564571	−0.282286	−	0.959330i	$-0.591093\pi$
$269$	−1.30424e13	−0.564571	−0.282286	+	0.959330i	$0.591093\pi$
$270$	7.88237e10	0.00334315
$271$	−2.56349e13	−1.06537	−0.532686	−	0.846313i	$-0.678817\pi$
$271$	−2.56349e13	−1.06537	−0.532686	+	0.846313i	$0.678817\pi$
$272$	−3.42286e13	−1.39399
$273$	1.78736e11	0.00713373
$274$	2.39110e12	0.0935341
$275$	−5.24619e12	−0.201147
$276$	−3.59588e12	−0.135147
$277$	2.17695e13	0.802066	0.401033	−	0.916064i	$-0.368651\pi$
$277$	2.17695e13	0.802066	0.401033	+	0.916064i	$0.368651\pi$
$278$	−2.36630e12	−0.0854719
$279$	8.20112e12	0.290436
$280$	4.79051e11	0.0166346
$281$	2.32643e13	0.792147	0.396073	−	0.918219i	$-0.370373\pi$
$281$	2.32643e13	0.792147	0.396073	+	0.918219i	$0.370373\pi$
$282$	2.29853e12	0.0767501
$283$	4.41058e13	1.44434	0.722171	−	0.691715i	$-0.243144\pi$
$283$	4.41058e13	1.44434	0.722171	+	0.691715i	$0.243144\pi$
$284$	7.01128e12	0.225189
$285$	−4.09931e12	−0.129141
$286$	1.86124e10	0.000575159 0
$287$	−1.39064e13	−0.421566
$288$	−3.59459e12	−0.106903
$289$	3.72807e13	1.08779
$290$	−1.86282e11	−0.00533311
$291$	−2.61050e13	−0.733350
$292$	−1.02108e13	−0.281485
$293$	9.13485e12	0.247132	0.123566	−	0.992336i	$-0.460567\pi$
$293$	9.13485e12	0.247132	0.123566	+	0.992336i	$0.460567\pi$
$294$	1.81378e12	0.0481586
$295$	7.99058e11	0.0208237
$296$	1.01009e13	0.258379
$297$	1.58215e12	0.0397272
$298$	−1.74585e11	−0.00430345
$299$	−2.51116e11	−0.00607692
$300$	2.33990e13	0.555944
$301$	−2.67806e13	−0.624748
$302$	−4.49262e12	−0.102911
$303$	−4.30417e13	−0.968177
$304$	6.10748e13	1.34914
$305$	9.15915e12	0.198704
$306$	2.45496e12	0.0523091
$307$	−5.62621e13	−1.17748	−0.588742	−	0.808321i	$-0.700377\pi$
$307$	−5.62621e13	−1.17748	−0.588742	+	0.808321i	$0.700377\pi$
$308$	4.77924e12	0.0982495
$309$	−2.04520e13	−0.413013
$310$	7.62954e11	0.0151359
$311$	7.74516e13	1.50955	0.754776	−	0.655983i	$-0.227746\pi$
$311$	7.74516e13	1.50955	0.754776	+	0.655983i	$0.227746\pi$
$312$	−1.67020e11	−0.00319830
$313$	1.66025e13	0.312378	0.156189	−	0.987727i	$-0.450079\pi$
$313$	1.66025e13	0.312378	0.156189	+	0.987727i	$0.450079\pi$
$314$	6.07920e12	0.112391
$315$	1.41346e12	0.0256788
$316$	−5.14043e13	−0.917743
$317$	−1.01258e14	−1.77666	−0.888330	−	0.459206i	$-0.848134\pi$
$317$	−1.01258e14	−1.77666	−0.888330	+	0.459206i	$0.848134\pi$
$318$	−6.28217e12	−0.108333
$319$	−3.73905e12	−0.0633742
$320$	8.92801e12	0.148741
$321$	4.46868e13	0.731816
$322$	7.69654e11	0.0123905
$323$	−1.27673e14	−2.02062
$324$	−7.05670e12	−0.109801
$325$	1.63405e12	0.0249982
$326$	3.83321e12	0.0576588
$327$	−8.40329e12	−0.124290
$328$	1.29949e13	0.189003
$329$	4.12170e13	0.589520
$330$	1.47188e11	0.00207036
$331$	7.41087e13	1.02522	0.512608	−	0.858623i	$-0.328679\pi$
$331$	7.41087e13	1.02522	0.512608	+	0.858623i	$0.328679\pi$
$332$	−5.66064e13	−0.770204
$333$	2.98032e13	0.398860
$334$	1.09160e13	0.143700
$335$	9.90802e12	0.128304
$336$	−2.10589e13	−0.268268
$337$	5.34310e13	0.669621	0.334811	−	0.942285i	$-0.391328\pi$
$337$	5.34310e13	0.669621	0.334811	+	0.942285i	$0.391328\pi$
$338$	8.80259e12	0.108535
$339$	4.00826e13	0.486248
$340$	−1.91341e13	−0.228388
$341$	1.53140e13	0.179863
$342$	−4.38045e12	−0.0506261
$343$	7.48724e13	0.851538
$344$	2.50253e13	0.280096
$345$	−1.98585e12	−0.0218747
$346$	1.17709e13	0.127612
$347$	1.17978e14	1.25889	0.629446	−	0.777044i	$-0.283282\pi$
$347$	1.17978e14	1.25889	0.629446	+	0.777044i	$0.283282\pi$
$348$	1.66769e13	0.175158
$349$	1.24768e14	1.28992	0.644962	−	0.764214i	$-0.276873\pi$
$349$	1.24768e14	1.28992	0.644962	+	0.764214i	$0.276873\pi$
$350$	−5.00826e12	−0.0509698
$351$	−4.92800e11	−0.00493721
$352$	−6.71222e12	−0.0662036
$353$	−2.43773e13	−0.236715	−0.118357	−	0.992971i	$-0.537763\pi$
$353$	−2.43773e13	−0.236715	−0.118357	+	0.992971i	$0.537763\pi$
$354$	8.53859e11	0.00816334
$355$	3.87203e12	0.0364488
$356$	2.01339e14	1.86618
$357$	4.40222e13	0.401788
$358$	2.19765e13	0.197516
$359$	9.88821e12	0.0875182	0.0437591	−	0.999042i	$-0.486067\pi$
$359$	9.88821e12	0.0875182	0.0437591	+	0.999042i	$0.486067\pi$
$360$	−1.32081e12	−0.0115127
$361$	1.11319e14	0.955611
$362$	2.39481e13	0.202476
$363$	−6.63764e13	−0.552748
$364$	−1.48861e12	−0.0122102
$365$	−5.63900e12	−0.0455608
$366$	9.78730e12	0.0778963
$367$	1.72600e14	1.35325	0.676624	−	0.736328i	$-0.263442\pi$
$367$	1.72600e14	1.35325	0.676624	+	0.736328i	$0.263442\pi$
$368$	2.95869e13	0.228526
$369$	3.83421e13	0.291763
$370$	2.77261e12	0.0207864
$371$	−1.12651e14	−0.832108
$372$	−6.83036e13	−0.497116
$373$	−9.71366e13	−0.696601	−0.348301	−	0.937383i	$-0.613241\pi$
$373$	−9.71366e13	−0.696601	−0.348301	+	0.937383i	$0.613241\pi$
$374$	4.58418e12	0.0323943
$375$	2.61838e13	0.182331
$376$	−3.85154e13	−0.264302
$377$	1.16462e12	0.00787602
$378$	1.51040e12	0.0100667
$379$	−9.40338e13	−0.617687	−0.308843	−	0.951113i	$-0.599942\pi$
$379$	−9.40338e13	−0.617687	−0.308843	+	0.951113i	$0.599942\pi$
$380$	3.41414e13	0.221040
$381$	1.07291e14	0.684661
$382$	6.15514e12	0.0387159
$383$	1.42485e14	0.883438	0.441719	−	0.897153i	$-0.354369\pi$
$383$	1.42485e14	0.883438	0.441719	+	0.897153i	$0.354369\pi$
$384$	3.98355e13	0.243471
$385$	2.63937e12	0.0159025
$386$	2.99599e13	0.177955
$387$	7.38381e13	0.432384
$388$	2.17417e14	1.25522
$389$	1.74109e14	0.991054	0.495527	−	0.868593i	$-0.334975\pi$
$389$	1.74109e14	0.991054	0.495527	+	0.868593i	$0.334975\pi$
$390$	−4.58454e10	−0.000257301 0
$391$	−6.18494e13	−0.342266
$392$	−3.03927e13	−0.165842
$393$	−3.92588e13	−0.211241
$394$	−1.97868e13	−0.104990
$395$	−2.83884e13	−0.148545
$396$	−1.31771e13	−0.0679979
$397$	−3.15493e14	−1.60562	−0.802808	−	0.596238i	$-0.796662\pi$
$397$	−3.15493e14	−1.60562	−0.802808	+	0.596238i	$0.796662\pi$
$398$	2.00463e13	0.100618
$399$	−7.85498e13	−0.388861
$400$	−1.92527e14	−0.940071
$401$	−2.81606e14	−1.35628	−0.678138	−	0.734935i	$-0.737213\pi$
$401$	−2.81606e14	−1.35628	−0.678138	+	0.734935i	$0.737213\pi$
$402$	1.05875e13	0.0502981
$403$	−4.76994e12	−0.0223530
$404$	3.58476e14	1.65715
$405$	−3.89711e12	−0.0177722
$406$	−3.56948e12	−0.0160587
$407$	5.56519e13	0.247008
$408$	−4.11367e13	−0.180135
$409$	4.50963e14	1.94833	0.974166	−	0.225831i	$-0.0725097\pi$
$409$	4.50963e14	1.94833	0.974166	+	0.225831i	$0.0725097\pi$
$410$	3.56698e12	0.0152051
$411$	−1.18218e14	−0.497227
$412$	1.70336e14	0.706921
$413$	1.53113e13	0.0627029
$414$	−2.12205e12	−0.00857537
$415$	−3.12613e13	−0.124664
$416$	2.09069e12	0.00822765
$417$	1.16992e14	0.454368
$418$	−8.17966e12	−0.0313520
$419$	−2.40157e14	−0.908485	−0.454242	−	0.890878i	$-0.650090\pi$
$419$	−2.40157e14	−0.908485	−0.454242	+	0.890878i	$0.650090\pi$
$420$	−1.17721e13	−0.0439524
$421$	2.25985e14	0.832776	0.416388	−	0.909187i	$-0.363296\pi$
$421$	2.25985e14	0.832776	0.416388	+	0.909187i	$0.363296\pi$
$422$	−1.86744e13	−0.0679246
$423$	−1.13641e14	−0.408003
$424$	1.05267e14	0.373063
$425$	4.02464e14	1.40795
$426$	4.13758e12	0.0142887
$427$	1.75505e14	0.598324
$428$	−3.72177e14	−1.25259
$429$	−9.20212e11	−0.00305754
$430$	6.86919e12	0.0225335
$431$	2.23695e13	0.0724487	0.0362244	−	0.999344i	$-0.488467\pi$
$431$	2.23695e13	0.0724487	0.0362244	+	0.999344i	$0.488467\pi$
$432$	5.80624e13	0.185667
$433$	−5.15388e14	−1.62724	−0.813618	−	0.581400i	$-0.802505\pi$
$433$	−5.15388e14	−1.62724	−0.813618	+	0.581400i	$0.802505\pi$
$434$	1.46195e13	0.0455764
$435$	9.20993e12	0.0283508
$436$	6.99874e13	0.212737
$437$	1.10359e14	0.331254
$438$	−6.02573e12	−0.0178609
$439$	−4.93570e14	−1.44475	−0.722377	−	0.691499i	$-0.756951\pi$
$439$	−4.93570e14	−1.44475	−0.722377	+	0.691499i	$0.756951\pi$
$440$	−2.46637e12	−0.00712965
$441$	−8.96748e13	−0.256011
$442$	−1.42786e12	−0.00402589
$443$	1.66783e14	0.464442	0.232221	−	0.972663i	$-0.425401\pi$
$443$	1.66783e14	0.464442	0.232221	+	0.972663i	$0.425401\pi$
$444$	−2.48218e14	−0.682696
$445$	1.11191e14	0.302057
$446$	−7.90652e12	−0.0212150
$447$	8.63162e12	0.0228771
$448$	1.71076e14	0.447879
$449$	−2.74518e14	−0.709932	−0.354966	−	0.934879i	$-0.615508\pi$
$449$	−2.74518e14	−0.709932	−0.354966	+	0.934879i	$0.615508\pi$
$450$	1.38085e13	0.0352759
$451$	7.15966e13	0.180685
$452$	−3.33831e14	−0.832272
$453$	2.22119e14	0.547074
$454$	5.92535e13	0.144181
$455$	−8.22097e11	−0.00197633
$456$	7.34012e13	0.174340
$457$	−5.18597e14	−1.21700	−0.608501	−	0.793553i	$-0.708229\pi$
$457$	−5.18597e14	−1.21700	−0.608501	+	0.793553i	$0.708229\pi$
$458$	3.21399e13	0.0745220
$459$	−1.21376e14	−0.278075
$460$	1.65393e13	0.0374412
$461$	−7.27089e14	−1.62642	−0.813209	−	0.581971i	$-0.802282\pi$
$461$	−7.27089e14	−1.62642	−0.813209	+	0.581971i	$0.802282\pi$
$462$	2.82038e12	0.00623415
$463$	6.19864e14	1.35395	0.676973	−	0.736008i	$-0.263291\pi$
$463$	6.19864e14	1.35395	0.676973	+	0.736008i	$0.263291\pi$
$464$	−1.37217e14	−0.296182
$465$	−3.77211e13	−0.0804625
$466$	−4.61731e13	−0.0973344
$467$	−7.39953e14	−1.54156	−0.770782	−	0.637099i	$-0.780134\pi$
$467$	−7.39953e14	−1.54156	−0.770782	+	0.637099i	$0.780134\pi$
$468$	4.10432e12	0.00845064
$469$	1.89855e14	0.386341
$470$	−1.05721e13	−0.0212629
$471$	−3.00561e14	−0.597473
$472$	−1.43077e13	−0.0281119
$473$	1.37879e14	0.267769
$474$	−3.03354e13	−0.0582329
$475$	−7.18126e14	−1.36265
$476$	−3.66642e14	−0.687708
$477$	3.10596e14	0.575897
$478$	−8.91551e12	−0.0163415
$479$	3.46919e14	0.628611	0.314306	−	0.949322i	$-0.398228\pi$
$479$	3.46919e14	0.628611	0.314306	+	0.949322i	$0.398228\pi$
$480$	1.65334e13	0.0296165
$481$	−1.73342e13	−0.0306976
$482$	−6.81234e12	−0.0119272
$483$	−3.80524e13	−0.0658677
$484$	5.52820e14	0.946095
$485$	1.20070e14	0.203168
$486$	−4.16439e12	−0.00696709
$487$	9.31866e14	1.54150	0.770751	−	0.637136i	$-0.219881\pi$
$487$	9.31866e14	1.54150	0.770751	+	0.637136i	$0.219881\pi$
$488$	−1.64001e14	−0.268249
$489$	−1.89517e14	−0.306514
$490$	−8.34249e12	−0.0133419
$491$	7.29686e14	1.15395	0.576976	−	0.816761i	$-0.304232\pi$
$491$	7.29686e14	1.15395	0.576976	+	0.816761i	$0.304232\pi$
$492$	−3.19335e14	−0.499388
$493$	2.86843e14	0.443595
$494$	2.54776e12	0.00389637
$495$	−7.27713e12	−0.0110060
$496$	5.62000e14	0.840596
$497$	7.41948e13	0.109752
$498$	−3.34052e13	−0.0488712
$499$	1.14051e15	1.65023	0.825117	−	0.564962i	$-0.191109\pi$
$499$	1.14051e15	1.65023	0.825117	+	0.564962i	$0.191109\pi$
$500$	−2.18074e14	−0.312082
$501$	−5.39695e14	−0.763908
$502$	−2.76532e13	−0.0387146
$503$	1.51279e14	0.209486	0.104743	−	0.994499i	$-0.466598\pi$
$503$	1.51279e14	0.209486	0.104743	+	0.994499i	$0.466598\pi$
$504$	−2.53091e13	−0.0346664
$505$	1.97971e14	0.268224
$506$	−3.96252e12	−0.00531060
$507$	−4.35208e14	−0.576970
$508$	−8.93581e14	−1.17188
$509$	−1.04534e15	−1.35616	−0.678079	−	0.734989i	$-0.737187\pi$
$509$	−1.04534e15	−1.35616	−0.678079	+	0.734989i	$0.737187\pi$
$510$	−1.12916e13	−0.0144917
$511$	−1.08053e14	−0.137190
$512$	−4.12178e14	−0.517726
$513$	2.16573e14	0.269128
$514$	1.38332e14	0.170070
$515$	9.40690e13	0.114421
$516$	−6.14966e14	−0.740078
$517$	−2.12204e14	−0.252671
$518$	5.31280e13	0.0625907
$519$	−5.81964e14	−0.678384
$520$	7.68212e11	0.000886059 0
$521$	−9.86353e14	−1.12571	−0.562853	−	0.826557i	$-0.690296\pi$
$521$	−9.86353e14	−1.12571	−0.562853	+	0.826557i	$0.690296\pi$
$522$	9.84157e12	0.0111142
$523$	1.59830e15	1.78607	0.893033	−	0.449990i	$-0.148573\pi$
$523$	1.59830e15	1.78607	0.893033	+	0.449990i	$0.148573\pi$
$524$	3.26970e14	0.361565
$525$	2.47613e14	0.270955
$526$	3.95937e13	0.0428750
$527$	−1.17483e15	−1.25897
$528$	1.08421e14	0.114981
$529$	−8.99348e14	−0.943890
$530$	2.88949e13	0.0300126
$531$	−4.22156e13	−0.0433963
$532$	6.54208e14	0.665582
$533$	−2.23005e13	−0.0224551
$534$	1.18817e14	0.118413
$535$	−2.05538e14	−0.202743
$536$	−1.77411e14	−0.173210
$537$	−1.08654e15	−1.05000
$538$	6.41027e13	0.0613160
$539$	−1.67451e14	−0.158544
$540$	3.24574e13	0.0304192
$541$	−5.76950e14	−0.535246	−0.267623	−	0.963524i	$-0.586238\pi$
$541$	−5.76950e14	−0.535246	−0.267623	+	0.963524i	$0.586238\pi$
$542$	1.25995e14	0.115706
$543$	−1.18402e15	−1.07636
$544$	5.14932e14	0.463400
$545$	3.86510e13	0.0344334
$546$	−8.78478e11	−0.000774768 0
$547$	1.07123e15	0.935300	0.467650	−	0.883914i	$-0.345101\pi$
$547$	1.07123e15	0.935300	0.467650	+	0.883914i	$0.345101\pi$
$548$	9.84590e14	0.851064
$549$	−4.83893e14	−0.414097
$550$	2.57848e13	0.0218458
$551$	−5.11821e14	−0.429323
$552$	3.55582e13	0.0295308
$553$	−5.43971e14	−0.447288
$554$	−1.06996e14	−0.0871094
$555$	−1.37080e14	−0.110500
$556$	−9.74377e14	−0.777706
$557$	1.18124e15	0.933546	0.466773	−	0.884377i	$-0.345417\pi$
$557$	1.18124e15	0.933546	0.466773	+	0.884377i	$0.345417\pi$
$558$	−4.03082e13	−0.0315431
$559$	−4.29457e13	−0.0332778
$560$	9.68606e13	0.0743212
$561$	−2.26646e14	−0.172208
$562$	−1.14343e14	−0.0860321
$563$	−1.70145e15	−1.26772	−0.633858	−	0.773449i	$-0.718530\pi$
$563$	−1.70145e15	−1.26772	−0.633858	+	0.773449i	$0.718530\pi$
$564$	9.46469e14	0.698347
$565$	−1.84361e14	−0.134710
$566$	−2.16778e14	−0.156865
$567$	−7.46755e13	−0.0535145
$568$	−6.93316e13	−0.0492057
$569$	−1.64736e15	−1.15790	−0.578951	−	0.815363i	$-0.696538\pi$
$569$	−1.64736e15	−1.15790	−0.578951	+	0.815363i	$0.696538\pi$
$570$	2.01479e13	0.0140255
$571$	1.91521e14	0.132044	0.0660219	−	0.997818i	$-0.478969\pi$
$571$	1.91521e14	0.132044	0.0660219	+	0.997818i	$0.478969\pi$
$572$	7.66405e12	0.00523336
$573$	−3.04316e14	−0.205814
$574$	6.83496e13	0.0457847
$575$	−3.47886e14	−0.230815
$576$	−4.71682e14	−0.309974
$577$	1.78676e15	1.16305	0.581526	−	0.813528i	$-0.302456\pi$
$577$	1.78676e15	1.16305	0.581526	+	0.813528i	$0.302456\pi$
$578$	−1.83233e14	−0.118141
$579$	−1.48125e15	−0.946008
$580$	−7.67056e13	−0.0485258
$581$	−5.99020e14	−0.375381
$582$	1.28305e14	0.0796464
$583$	5.79980e14	0.356645
$584$	1.00971e14	0.0615069
$585$	2.26664e12	0.00136781
$586$	−4.48974e13	−0.0268401
$587$	−2.87784e15	−1.70434	−0.852170	−	0.523264i	$-0.824714\pi$
$587$	−2.87784e15	−1.70434	−0.852170	+	0.523264i	$0.824714\pi$
$588$	7.46863e14	0.438193
$589$	2.09627e15	1.21846
$590$	−3.92733e12	−0.00226158
$591$	9.78278e14	0.558125
$592$	2.04233e15	1.15440
$593$	−8.09682e14	−0.453434	−0.226717	−	0.973961i	$-0.572799\pi$
$593$	−8.09682e14	−0.453434	−0.226717	+	0.973961i	$0.572799\pi$
$594$	−7.77621e12	−0.00431462
$595$	−2.02481e14	−0.111312
$596$	−7.18891e13	−0.0391569
$597$	−9.91107e14	−0.534886
$598$	1.23423e12	0.000659991 0
$599$	−6.86915e14	−0.363961	−0.181981	−	0.983302i	$-0.558251\pi$
$599$	−6.86915e14	−0.363961	−0.181981	+	0.983302i	$0.558251\pi$
$600$	−2.31383e14	−0.121479
$601$	2.86881e15	1.49243	0.746213	−	0.665707i	$-0.231870\pi$
$601$	2.86881e15	1.49243	0.746213	+	0.665707i	$0.231870\pi$
$602$	1.31626e14	0.0678516
$603$	−5.23458e14	−0.267385
$604$	−1.84994e15	−0.936383
$605$	3.05299e14	0.153134
$606$	2.11548e14	0.105150
$607$	−3.35448e15	−1.65229	−0.826147	−	0.563454i	$-0.809472\pi$
$607$	−3.35448e15	−1.65229	−0.826147	+	0.563454i	$0.809472\pi$
$608$	−9.18804e14	−0.448491
$609$	1.76478e14	0.0853682
$610$	−4.50168e13	−0.0215805
$611$	6.60960e13	0.0314014
$612$	1.01089e15	0.475959
$613$	−1.76110e15	−0.821771	−0.410886	−	0.911687i	$-0.634780\pi$
$613$	−1.76110e15	−0.821771	−0.410886	+	0.911687i	$0.634780\pi$
$614$	2.76526e14	0.127882
$615$	−1.76355e14	−0.0808303
$616$	−4.72599e13	−0.0214684
$617$	2.20526e15	0.992868	0.496434	−	0.868074i	$-0.334642\pi$
$617$	2.20526e15	0.992868	0.496434	+	0.868074i	$0.334642\pi$
$618$	1.00521e14	0.0448557
$619$	−3.35617e15	−1.48438	−0.742190	−	0.670189i	$-0.766213\pi$
$619$	−3.35617e15	−1.48438	−0.742190	+	0.670189i	$0.766213\pi$
$620$	3.14163e14	0.137721
$621$	1.04916e14	0.0455866
$622$	−3.80671e14	−0.163947
$623$	2.13061e15	0.909535
$624$	−3.37703e13	−0.0142896
$625$	2.20276e15	0.923903
$626$	−8.16008e13	−0.0339262
$627$	4.04410e14	0.166667
$628$	2.50325e15	1.02265
$629$	−4.26937e15	−1.72896
$630$	−6.94709e12	−0.00278888
$631$	3.89824e15	1.55134	0.775669	−	0.631140i	$-0.217412\pi$
$631$	3.89824e15	1.55134	0.775669	+	0.631140i	$0.217412\pi$
$632$	5.08316e14	0.200535
$633$	9.23277e14	0.361087
$634$	4.97680e14	0.192956
$635$	−4.93486e14	−0.189679
$636$	−2.58682e15	−0.985718
$637$	5.21567e13	0.0197035
$638$	1.83773e13	0.00688284
$639$	−2.04566e14	−0.0759589
$640$	−1.83224e14	−0.0674515
$641$	2.92809e15	1.06872	0.534362	−	0.845256i	$-0.320552\pi$
$641$	2.92809e15	1.06872	0.534362	+	0.845256i	$0.320552\pi$
$642$	−2.19634e14	−0.0794798
$643$	−8.03768e14	−0.288384	−0.144192	−	0.989550i	$-0.546058\pi$
$643$	−8.03768e14	−0.288384	−0.144192	+	0.989550i	$0.546058\pi$
$644$	3.16922e14	0.112741
$645$	−3.39619e14	−0.119788
$646$	6.27507e14	0.219452
$647$	3.77555e15	1.30920	0.654601	−	0.755975i	$-0.272837\pi$
$647$	3.77555e15	1.30920	0.654601	+	0.755975i	$0.272837\pi$
$648$	6.97808e13	0.0239924
$649$	−7.88296e13	−0.0268747
$650$	−8.03131e12	−0.00271496
$651$	−7.22803e14	−0.242284
$652$	1.57841e15	0.524636
$653$	−4.89684e15	−1.61396	−0.806982	−	0.590576i	$-0.798900\pi$
$653$	−4.89684e15	−1.61396	−0.806982	+	0.590576i	$0.798900\pi$
$654$	4.13018e13	0.0134987
$655$	1.80571e14	0.0585224
$656$	2.62748e15	0.844439
$657$	2.97918e14	0.0949482
$658$	−2.02580e14	−0.0640256
$659$	−4.06346e15	−1.27358	−0.636789	−	0.771038i	$-0.719738\pi$
$659$	−4.06346e15	−1.27358	−0.636789	+	0.771038i	$0.719738\pi$
$660$	6.06081e13	0.0188382
$661$	6.20815e15	1.91361	0.956807	−	0.290724i	$-0.0938961\pi$
$661$	6.20815e15	1.91361	0.956807	+	0.290724i	$0.0938961\pi$
$662$	−3.64241e14	−0.111345
$663$	7.05945e13	0.0214016
$664$	5.59757e14	0.168296
$665$	3.61291e14	0.107730
$666$	−1.46482e14	−0.0433186
$667$	−2.47945e14	−0.0727215
$668$	4.49489e15	1.30752
$669$	3.90906e14	0.112779
$670$	−4.86975e13	−0.0139346
$671$	−9.03579e14	−0.256444
$672$	3.16808e14	0.0891795
$673$	−1.49379e15	−0.417068	−0.208534	−	0.978015i	$-0.566869\pi$
$673$	−1.49379e15	−0.417068	−0.208534	+	0.978015i	$0.566869\pi$
$674$	−2.62611e14	−0.0727250
$675$	−6.82705e14	−0.187526
$676$	3.62466e15	0.987554
$677$	−7.20599e15	−1.94740	−0.973702	−	0.227824i	$-0.926839\pi$
$677$	−7.20599e15	−1.94740	−0.973702	+	0.227824i	$0.926839\pi$
$678$	−1.97004e14	−0.0528096
$679$	2.30075e15	0.611767
$680$	1.89209e14	0.0499048
$681$	−2.92955e15	−0.766463
$682$	−7.52679e13	−0.0195342
$683$	5.08063e15	1.30799	0.653993	−	0.756500i	$-0.273092\pi$
$683$	5.08063e15	1.30799	0.653993	+	0.756500i	$0.273092\pi$
$684$	−1.80375e15	−0.460646
$685$	5.43747e14	0.137752
$686$	−3.67994e14	−0.0924823
$687$	−1.58903e15	−0.396158
$688$	5.05992e15	1.25143
$689$	−1.80649e14	−0.0443231
$690$	9.76038e12	0.00237573
$691$	−5.57864e15	−1.34710	−0.673549	−	0.739143i	$-0.735231\pi$
$691$	−5.57864e15	−1.34710	−0.673549	+	0.739143i	$0.735231\pi$
$692$	4.84693e15	1.16114
$693$	−1.39442e14	−0.0331407
$694$	−5.79856e14	−0.136723
$695$	−5.38106e14	−0.125879
$696$	−1.64911e14	−0.0382735
$697$	−5.49257e15	−1.26472
$698$	−6.13231e14	−0.140094
$699$	2.28284e15	0.517429
$700$	−2.06226e15	−0.463773
$701$	−1.09283e15	−0.243839	−0.121920	−	0.992540i	$-0.538905\pi$
$701$	−1.09283e15	−0.243839	−0.121920	+	0.992540i	$0.538905\pi$
$702$	2.42209e12	0.000536212 0
$703$	7.61793e15	1.67333
$704$	−8.80777e14	−0.191962
$705$	5.22694e14	0.113034
$706$	1.19813e14	0.0257087
$707$	3.79346e15	0.807661
$708$	3.51595e14	0.0742780
$709$	4.80995e15	1.00829	0.504146	−	0.863618i	$-0.331807\pi$
$709$	4.80995e15	1.00829	0.504146	+	0.863618i	$0.331807\pi$
$710$	−1.90309e13	−0.00395856
$711$	1.49981e15	0.309566
$712$	−1.99096e15	−0.407776
$713$	1.01551e15	0.206391
$714$	−2.16367e14	−0.0436367
$715$	4.23252e12	0.000847064 0
$716$	9.04933e15	1.79719
$717$	4.40791e14	0.0868716
$718$	−4.86001e13	−0.00950502
$719$	6.79376e15	1.31856	0.659282	−	0.751895i	$-0.270860\pi$
$719$	6.79376e15	1.31856	0.659282	+	0.751895i	$0.270860\pi$
$720$	−2.67059e14	−0.0514373
$721$	1.80253e15	0.344538
$722$	−5.47130e14	−0.103785
$723$	3.36808e14	0.0634048
$724$	9.86117e15	1.84233
$725$	1.61342e15	0.299149
$726$	3.26237e14	0.0600319
$727$	−6.19146e15	−1.13072	−0.565359	−	0.824845i	$-0.691262\pi$
$727$	−6.19146e15	−1.13072	−0.565359	+	0.824845i	$0.691262\pi$
$728$	1.47203e13	0.00266805
$729$	2.05891e14	0.0370370
$730$	2.77154e13	0.00494819
$731$	−1.05774e16	−1.87428
$732$	4.03014e15	0.708776
$733$	−9.15432e15	−1.59792	−0.798958	−	0.601387i	$-0.794615\pi$
$733$	−9.15432e15	−1.59792	−0.798958	+	0.601387i	$0.794615\pi$
$734$	−8.48322e14	−0.146971
$735$	4.12460e14	0.0709254
$736$	−4.45102e14	−0.0759682
$737$	−9.77459e14	−0.165587
$738$	−1.88450e14	−0.0316873
$739$	8.83935e15	1.47529	0.737643	−	0.675191i	$-0.235939\pi$
$739$	8.83935e15	1.47529	0.737643	+	0.675191i	$0.235939\pi$
$740$	1.14168e15	0.189135
$741$	−1.25963e14	−0.0207131
$742$	5.53677e14	0.0903722
$743$	8.60916e15	1.39483	0.697417	−	0.716666i	$-0.254333\pi$
$743$	8.60916e15	1.39483	0.697417	+	0.716666i	$0.254333\pi$
$744$	6.75426e14	0.108624
$745$	−3.97012e13	−0.00633789
$746$	4.77422e14	0.0756553
$747$	1.65159e15	0.259799
$748$	1.88764e15	0.294754
$749$	−3.93846e15	−0.610487
$750$	−1.28692e14	−0.0198023
$751$	−3.67452e15	−0.561281	−0.280641	−	0.959813i	$-0.590547\pi$
$751$	−3.67452e15	−0.561281	−0.280641	+	0.959813i	$0.590547\pi$
$752$	−7.78752e15	−1.18087
$753$	1.36720e15	0.205806
$754$	−5.72406e12	−0.000855385 0
$755$	−1.02164e15	−0.151562
$756$	6.21940e14	0.0915965
$757$	−5.82737e15	−0.852011	−0.426006	−	0.904721i	$-0.640080\pi$
$757$	−5.82737e15	−0.852011	−0.426006	+	0.904721i	$0.640080\pi$
$758$	4.62172e14	0.0670846
$759$	1.95911e14	0.0282311
$760$	−3.37610e14	−0.0482992
$761$	8.24910e14	0.117163	0.0585816	−	0.998283i	$-0.481342\pi$
$761$	8.24910e14	0.117163	0.0585816	+	0.998283i	$0.481342\pi$
$762$	−5.27330e14	−0.0743585
$763$	7.40621e14	0.103684
$764$	2.53452e15	0.352275
$765$	5.58269e14	0.0770381
$766$	−7.00308e14	−0.0959469
$767$	2.45534e13	0.00333993
$768$	3.77954e15	0.510448
$769$	1.40962e16	1.89020	0.945099	−	0.326783i	$-0.105965\pi$
$769$	1.40962e16	1.89020	0.945099	+	0.326783i	$0.105965\pi$
$770$	−1.29724e13	−0.00172711
$771$	−6.83928e15	−0.904089
$772$	1.23367e16	1.61921
$773$	−7.51145e14	−0.0978896	−0.0489448	−	0.998801i	$-0.515586\pi$
$773$	−7.51145e14	−0.0978896	−0.0489448	+	0.998801i	$0.515586\pi$
$774$	−3.62911e14	−0.0469596
$775$	−6.60808e15	−0.849016
$776$	−2.14995e15	−0.274276
$777$	−2.62670e15	−0.332732
$778$	−8.55736e14	−0.107635
$779$	9.80052e15	1.22403
$780$	−1.88779e13	−0.00234117
$781$	−3.81988e14	−0.0470402
$782$	3.03987e14	0.0371722
$783$	−4.86576e14	−0.0590828
$784$	−6.14517e15	−0.740962
$785$	1.38244e15	0.165524
$786$	1.92955e14	0.0229421
$787$	−4.03518e15	−0.476433	−0.238216	−	0.971212i	$-0.576563\pi$
$787$	−4.03518e15	−0.476433	−0.238216	+	0.971212i	$0.576563\pi$
$788$	−8.14766e15	−0.955298
$789$	−1.95755e15	−0.227923
$790$	1.39528e14	0.0161329
$791$	−3.53267e15	−0.405632
$792$	1.30302e14	0.0148581
$793$	2.81442e14	0.0318703
$794$	1.55063e15	0.174380
$795$	−1.42859e15	−0.159547
$796$	8.25450e15	0.915523
$797$	−1.52361e16	−1.67824	−0.839119	−	0.543949i	$-0.816929\pi$
$797$	−1.52361e16	−1.67824	−0.839119	+	0.543949i	$0.816929\pi$
$798$	3.86069e14	0.0422327
$799$	1.62793e16	1.76860
$800$	2.89635e15	0.312505
$801$	−5.87440e15	−0.629484
$802$	1.38408e15	0.147300
$803$	5.56305e14	0.0588001
$804$	4.35966e15	0.457661
$805$	1.75022e14	0.0182480
$806$	2.34440e13	0.00242767
$807$	−3.16929e15	−0.325955
$808$	−3.54481e15	−0.362102
$809$	−1.31662e16	−1.33581	−0.667905	−	0.744246i	$-0.732809\pi$
$809$	−1.31662e16	−1.33581	−0.667905	+	0.744246i	$0.732809\pi$
$810$	1.91541e13	0.00193017
$811$	2.59337e15	0.259567	0.129783	−	0.991542i	$-0.458572\pi$
$811$	2.59337e15	0.259567	0.129783	+	0.991542i	$0.458572\pi$
$812$	−1.46981e15	−0.146118
$813$	−6.22929e15	−0.615093
$814$	−2.73527e14	−0.0268266
$815$	8.71687e14	0.0849168
$816$	−8.31754e15	−0.804821
$817$	1.88736e16	1.81398
$818$	−2.21647e15	−0.211601
$819$	4.34328e13	0.00411866
$820$	1.46878e15	0.138351
$821$	1.40402e16	1.31366	0.656832	−	0.754037i	$-0.271896\pi$
$821$	1.40402e16	1.31366	0.656832	+	0.754037i	$0.271896\pi$
$822$	5.81038e14	0.0540020
$823$	−1.93117e15	−0.178287	−0.0891437	−	0.996019i	$-0.528413\pi$
$823$	−1.93117e15	−0.178287	−0.0891437	+	0.996019i	$0.528413\pi$
$824$	−1.68438e15	−0.154468
$825$	−1.27482e15	−0.116132
$826$	−7.52545e13	−0.00680993
$827$	7.18683e15	0.646037	0.323018	−	0.946393i	$-0.395302\pi$
$827$	7.18683e15	0.646037	0.323018	+	0.946393i	$0.395302\pi$
$828$	−8.73800e14	−0.0780270
$829$	−2.90585e15	−0.257765	−0.128882	−	0.991660i	$-0.541139\pi$
$829$	−2.90585e15	−0.257765	−0.128882	+	0.991660i	$0.541139\pi$
$830$	1.53648e14	0.0135393
$831$	5.29000e15	0.463073
$832$	2.74340e14	0.0238567
$833$	1.28461e16	1.10974
$834$	−5.75011e14	−0.0493472
$835$	2.48233e15	0.211634
$836$	−3.36816e15	−0.285271
$837$	1.99287e15	0.167683
$838$	1.18036e15	0.0986671
$839$	3.48645e15	0.289530	0.144765	−	0.989466i	$-0.453757\pi$
$839$	3.48645e15	0.289530	0.144765	+	0.989466i	$0.453757\pi$
$840$	1.16409e14	0.00960400
$841$	−1.10506e16	−0.905749
$842$	−1.11071e15	−0.0904446
$843$	5.65323e15	0.457346
$844$	−7.68958e15	−0.618044
$845$	2.00175e15	0.159844
$846$	5.58542e14	0.0443117
$847$	5.85006e15	0.461107
$848$	2.12843e16	1.66680
$849$	1.07177e16	0.833891
$850$	−1.97809e15	−0.152912
$851$	3.69040e15	0.283440
$852$	1.70374e15	0.130013
$853$	−1.56899e16	−1.18960	−0.594798	−	0.803875i	$-0.702768\pi$
$853$	−1.56899e16	−1.18960	−0.594798	+	0.803875i	$0.702768\pi$
$854$	−8.62600e14	−0.0649817
$855$	−9.96131e14	−0.0745595
$856$	3.68031e15	0.273702
$857$	−2.24133e16	−1.65619	−0.828096	−	0.560586i	$-0.810576\pi$
$857$	−2.24133e16	−1.65619	−0.828096	+	0.560586i	$0.810576\pi$
$858$	4.52280e12	0.000332068 0
$859$	−1.61591e16	−1.17884	−0.589419	−	0.807827i	$-0.700643\pi$
$859$	−1.61591e16	−1.17884	−0.589419	+	0.807827i	$0.700643\pi$
$860$	2.82854e15	0.205032
$861$	−3.37927e15	−0.243391
$862$	−1.09945e14	−0.00786839
$863$	−2.44408e16	−1.73802	−0.869012	−	0.494791i	$-0.835245\pi$
$863$	−2.44408e16	−1.73802	−0.869012	+	0.494791i	$0.835245\pi$
$864$	−8.73486e14	−0.0617206
$865$	2.67675e15	0.187940
$866$	2.53311e15	0.176728
$867$	9.05921e15	0.628037
$868$	6.01992e15	0.414698
$869$	2.80061e15	0.191709
$870$	−4.52664e13	−0.00307907
$871$	3.04454e14	0.0205789
$872$	−6.92076e14	−0.0464850
$873$	−6.34350e15	−0.423400
$874$	−5.42411e14	−0.0359762
$875$	−2.30770e15	−0.152102
$876$	−2.48123e15	−0.162515
$877$	6.14296e15	0.399835	0.199917	−	0.979813i	$-0.435933\pi$
$877$	6.14296e15	0.399835	0.199917	+	0.979813i	$0.435933\pi$
$878$	2.42588e15	0.156909
$879$	2.21977e15	0.142682
$880$	−4.98682e14	−0.0318544
$881$	−7.46371e15	−0.473791	−0.236896	−	0.971535i	$-0.576130\pi$
$881$	−7.46371e15	−0.473791	−0.236896	+	0.971535i	$0.576130\pi$
$882$	4.40748e14	0.0278044
$883$	−4.58663e15	−0.287548	−0.143774	−	0.989611i	$-0.545924\pi$
$883$	−4.58663e15	−0.287548	−0.143774	+	0.989611i	$0.545924\pi$
$884$	−5.87952e14	−0.0366315
$885$	1.94171e14	0.0120225
$886$	−8.19731e14	−0.0504413
$887$	−9.08615e15	−0.555649	−0.277824	−	0.960632i	$-0.589613\pi$
$887$	−9.08615e15	−0.555649	−0.277824	+	0.960632i	$0.589613\pi$
$888$	2.45453e15	0.149175
$889$	−9.45605e15	−0.571150
$890$	−5.46498e14	−0.0328053
$891$	3.84463e14	0.0229365
$892$	−3.25569e15	−0.193035
$893$	−2.90475e16	−1.71169
$894$	−4.24240e13	−0.00248460
$895$	4.99756e15	0.290891
$896$	−3.51088e15	−0.203106
$897$	−6.10212e13	−0.00350851
$898$	1.34925e15	0.0771030
$899$	−4.70969e15	−0.267494
$900$	5.68596e15	0.320974
$901$	−4.44935e16	−2.49637
$902$	−3.51894e14	−0.0196235
$903$	−6.50769e15	−0.360699
$904$	3.30112e15	0.181859
$905$	5.44590e15	0.298196
$906$	−1.09171e15	−0.0594156
$907$	5.09917e14	0.0275842	0.0137921	−	0.999905i	$-0.495610\pi$
$907$	5.09917e14	0.0275842	0.0137921	+	0.999905i	$0.495610\pi$
$908$	2.43990e16	1.31189
$909$	−1.04591e16	−0.558977
$910$	4.04057e12	0.000214642 0
$911$	−2.44976e16	−1.29352	−0.646759	−	0.762695i	$-0.723876\pi$
$911$	−2.44976e16	−1.29352	−0.646759	+	0.762695i	$0.723876\pi$
$912$	1.48412e16	0.778927
$913$	3.08402e15	0.160890
$914$	2.54888e15	0.132174
$915$	2.22567e15	0.114722
$916$	1.32343e16	0.678073
$917$	3.46006e15	0.176219
$918$	5.96556e14	0.0302007
$919$	−6.89140e15	−0.346795	−0.173397	−	0.984852i	$-0.555474\pi$
$919$	−6.89140e15	−0.346795	−0.173397	+	0.984852i	$0.555474\pi$
$920$	−1.63550e14	−0.00818123
$921$	−1.36717e16	−0.679821
$922$	3.57361e15	0.176639
$923$	1.18980e14	0.00584606
$924$	1.16136e15	0.0567244
$925$	−2.40140e16	−1.16597
$926$	−3.04661e15	−0.147047
$927$	−4.96983e15	−0.238453
$928$	2.06428e15	0.0984589
$929$	3.98005e15	0.188713	0.0943566	−	0.995538i	$-0.469921\pi$
$929$	3.98005e15	0.188713	0.0943566	+	0.995538i	$0.469921\pi$
$930$	1.85398e14	0.00873873
$931$	−2.29216e16	−1.07404
$932$	−1.90128e16	−0.885642
$933$	1.88207e16	0.871540
$934$	3.63684e15	0.167423
$935$	1.04246e15	0.0477085
$936$	−4.05859e13	−0.00184654
$937$	1.17505e16	0.531483	0.265741	−	0.964044i	$-0.414383\pi$
$937$	1.17505e16	0.531483	0.265741	+	0.964044i	$0.414383\pi$
$938$	−9.33129e14	−0.0419591
$939$	4.03442e15	0.180352
$940$	−4.35330e15	−0.193471
$941$	4.44968e15	0.196601	0.0983005	−	0.995157i	$-0.468659\pi$
$941$	4.44968e15	0.196601	0.0983005	+	0.995157i	$0.468659\pi$
$942$	1.47725e15	0.0648893
$943$	4.74773e15	0.207334
$944$	−2.89292e15	−0.125600
$945$	3.43471e14	0.0148257
$946$	−6.77668e14	−0.0290814
$947$	7.19250e15	0.306870	0.153435	−	0.988159i	$-0.450966\pi$
$947$	7.19250e15	0.306870	0.153435	+	0.988159i	$0.450966\pi$
$948$	−1.24913e16	−0.529859
$949$	−1.73275e14	−0.00730755
$950$	3.52956e15	0.147993
$951$	−2.46057e16	−1.02575
$952$	3.62557e15	0.150270
$953$	−4.08844e16	−1.68479	−0.842397	−	0.538858i	$-0.818856\pi$
$953$	−4.08844e16	−1.68479	−0.842397	+	0.538858i	$0.818856\pi$
$954$	−1.52657e15	−0.0625460
$955$	1.39970e15	0.0570187
$956$	−3.67116e15	−0.148691
$957$	−9.08589e14	−0.0365891
$958$	−1.70509e15	−0.0682711
$959$	1.04191e16	0.414791
$960$	2.16951e15	0.0858754
$961$	−6.11897e15	−0.240824
$962$	8.51967e13	0.00333396
$963$	1.08589e16	0.422514
$964$	−2.80513e15	−0.108525
$965$	6.81301e15	0.262083
$966$	1.87026e14	0.00715364
$967$	−1.05658e16	−0.401842	−0.200921	−	0.979607i	$-0.564393\pi$
$967$	−1.05658e16	−0.401842	−0.200921	+	0.979607i	$0.564393\pi$
$968$	−5.46661e15	−0.206730
$969$	−3.10245e16	−1.16661
$970$	−5.90139e14	−0.0220653
$971$	−3.89633e15	−0.144860	−0.0724302	−	0.997373i	$-0.523075\pi$
$971$	−3.89633e15	−0.144860	−0.0724302	+	0.997373i	$0.523075\pi$
$972$	−1.71478e15	−0.0633934
$973$	−1.03111e16	−0.379038
$974$	−4.58008e15	−0.167417
$975$	3.97075e14	0.0144327
$976$	−3.31599e16	−1.19850
$977$	1.92641e16	0.692355	0.346177	−	0.938169i	$-0.387480\pi$
$977$	1.92641e16	0.692355	0.346177	+	0.938169i	$0.387480\pi$
$978$	9.31470e14	0.0332893
$979$	−1.09693e16	−0.389830
$980$	−3.43521e15	−0.121397
$981$	−2.04200e15	−0.0717589
$982$	−3.58638e15	−0.125326
$983$	−1.44449e16	−0.501961	−0.250981	−	0.967992i	$-0.580753\pi$
$983$	−1.44449e16	−0.501961	−0.250981	+	0.967992i	$0.580753\pi$
$984$	3.15777e15	0.109121
$985$	−4.49960e15	−0.154623
$986$	−1.40982e15	−0.0481772
$987$	1.00157e16	0.340360
$988$	1.04910e15	0.0354529
$989$	9.14304e15	0.307263
$990$	3.57668e13	0.00119533
$991$	−1.69598e16	−0.563659	−0.281830	−	0.959464i	$-0.590941\pi$
$991$	−1.69598e16	−0.563659	−0.281830	+	0.959464i	$0.590941\pi$
$992$	−8.45469e15	−0.279437
$993$	1.80084e16	0.591909
$994$	−3.64664e14	−0.0119198
$995$	4.55861e15	0.148185
$996$	−1.37554e16	−0.444678
$997$	−1.62198e16	−0.521461	−0.260731	−	0.965412i	$-0.583963\pi$
$997$	−1.62198e16	−0.521461	−0.260731	+	0.965412i	$0.583963\pi$
$998$	−5.60555e15	−0.179226
$999$	7.24219e15	0.230282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.14	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.14	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.91496 q^{2} +243.000 q^{3} -2023.84 q^{4} -1117.68 q^{5} -1194.33 q^{6} -21416.7 q^{7} +20012.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-4.91496 q^{2} +243.000 q^{3} -2023.84 q^{4} -1117.68 q^{5} -1194.33 q^{6} -21416.7 q^{7} +20012.9 q^{8} +59049.0 q^{9} +5493.36 q^{10} +110263. q^{11} -491794. q^{12} -34344.1 q^{13} +105262. q^{14} -271597. q^{15} +4.04647e6 q^{16} -8.45888e6 q^{17} -290223. q^{18} +1.50934e7 q^{19} +2.26201e6 q^{20} -5.20426e6 q^{21} -541937. q^{22} +7.31177e6 q^{23} +4.86314e6 q^{24} -4.75789e7 q^{25} +168800. q^{26} +1.43489e7 q^{27} +4.33441e7 q^{28} -3.39103e7 q^{29} +1.33489e6 q^{30} +1.38887e8 q^{31} -6.08747e7 q^{32} +2.67939e7 q^{33} +4.15750e7 q^{34} +2.39371e7 q^{35} -1.19506e8 q^{36} +5.04720e8 q^{37} -7.41832e7 q^{38} -8.34562e6 q^{39} -2.23681e7 q^{40} +6.49327e8 q^{41} +2.55787e7 q^{42} +1.25045e9 q^{43} -2.23155e8 q^{44} -6.59980e7 q^{45} -3.59370e7 q^{46} -1.92452e9 q^{47} +9.83292e8 q^{48} -1.51865e9 q^{49} +2.33848e8 q^{50} -2.05551e9 q^{51} +6.95071e7 q^{52} +5.25997e9 q^{53} -7.05243e7 q^{54} -1.23239e8 q^{55} -4.28611e8 q^{56} +3.66769e9 q^{57} +1.66668e8 q^{58} -7.14924e8 q^{59} +5.49669e8 q^{60} -8.19477e9 q^{61} -6.82622e8 q^{62} -1.26464e9 q^{63} -7.98797e9 q^{64} +3.83858e7 q^{65} -1.31691e8 q^{66} -8.86480e9 q^{67} +1.71194e10 q^{68} +1.77676e9 q^{69} -1.17650e8 q^{70} -3.46434e9 q^{71} +1.18174e9 q^{72} +5.04526e9 q^{73} -2.48068e9 q^{74} -1.15617e10 q^{75} -3.05466e10 q^{76} -2.36147e9 q^{77} +4.10183e7 q^{78} +2.53994e10 q^{79} -4.52266e9 q^{80} +3.48678e9 q^{81} -3.19141e9 q^{82} +2.79697e10 q^{83} +1.05326e10 q^{84} +9.45433e9 q^{85} -6.14593e9 q^{86} -8.24021e9 q^{87} +2.20668e9 q^{88} -9.94834e10 q^{89} +3.24377e8 q^{90} +7.35538e8 q^{91} -1.47979e10 q^{92} +3.37495e10 q^{93} +9.45895e9 q^{94} -1.68696e10 q^{95} -1.47926e10 q^{96} -1.07428e11 q^{97} +7.46410e9 q^{98} +6.51091e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

Modular forms

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