LMFDB - Embedded newform 177.12.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-41.5867 q^{2} -243.000 q^{3} -318.543 q^{4} +9657.75 q^{5} +10105.6 q^{6} -11578.9 q^{7} +98416.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-41.5867 q^{2} -243.000 q^{3} -318.543 q^{4} +9657.75 q^{5} +10105.6 q^{6} -11578.9 q^{7} +98416.8 q^{8} +59049.0 q^{9} -401634. q^{10} -521143. q^{11} +77405.9 q^{12} +2.19264e6 q^{13} +481530. q^{14} -2.34683e6 q^{15} -3.44046e6 q^{16} -5.78339e6 q^{17} -2.45566e6 q^{18} +1.37354e7 q^{19} -3.07641e6 q^{20} +2.81368e6 q^{21} +2.16727e7 q^{22} +5.21100e7 q^{23} -2.39153e7 q^{24} +4.44440e7 q^{25} -9.11849e7 q^{26} -1.43489e7 q^{27} +3.68839e6 q^{28} +1.77755e8 q^{29} +9.75971e7 q^{30} -1.22823e8 q^{31} -5.84802e7 q^{32} +1.26638e8 q^{33} +2.40513e8 q^{34} -1.11826e8 q^{35} -1.88096e7 q^{36} +3.62082e8 q^{37} -5.71212e8 q^{38} -5.32812e8 q^{39} +9.50485e8 q^{40} +1.34909e9 q^{41} -1.17012e8 q^{42} +1.17172e9 q^{43} +1.66007e8 q^{44} +5.70280e8 q^{45} -2.16709e9 q^{46} +5.28251e8 q^{47} +8.36031e8 q^{48} -1.84325e9 q^{49} -1.84828e9 q^{50} +1.40536e9 q^{51} -6.98451e8 q^{52} -5.18449e9 q^{53} +5.96724e8 q^{54} -5.03307e9 q^{55} -1.13956e9 q^{56} -3.33771e9 q^{57} -7.39224e9 q^{58} -7.14924e8 q^{59} +7.47567e8 q^{60} -9.00303e9 q^{61} +5.10781e9 q^{62} -6.83725e8 q^{63} +9.47806e9 q^{64} +2.11760e10 q^{65} -5.26646e9 q^{66} +5.11986e9 q^{67} +1.84226e9 q^{68} -1.26627e10 q^{69} +4.65050e9 q^{70} -2.99744e9 q^{71} +5.81141e9 q^{72} -2.74521e10 q^{73} -1.50578e10 q^{74} -1.07999e10 q^{75} -4.37533e9 q^{76} +6.03429e9 q^{77} +2.21579e10 q^{78} +2.06456e10 q^{79} -3.32271e10 q^{80} +3.48678e9 q^{81} -5.61044e10 q^{82} +3.14626e10 q^{83} -8.96278e8 q^{84} -5.58546e10 q^{85} -4.87280e10 q^{86} -4.31944e10 q^{87} -5.12893e10 q^{88} +2.32505e10 q^{89} -2.37161e10 q^{90} -2.53885e10 q^{91} -1.65993e10 q^{92} +2.98460e10 q^{93} -2.19682e10 q^{94} +1.32653e11 q^{95} +1.42107e10 q^{96} -1.39153e11 q^{97} +7.66550e10 q^{98} -3.07730e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * 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 $

$2$	−41.5867	−0.918946	−0.459473	−	0.888192i	$-0.651962\pi$
$2$	−41.5867	−0.918946	−0.459473	+	0.888192i	$0.651962\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−318.543	−0.155539
$5$	9657.75	1.38210	0.691052	−	0.722805i	$-0.257147\pi$
$5$	9657.75	1.38210	0.691052	+	0.722805i	$0.257147\pi$
$6$	10105.6	0.530554
$7$	−11578.9	−0.260393	−0.130197	−	0.991488i	$-0.541561\pi$
$7$	−11578.9	−0.260393	−0.130197	+	0.991488i	$0.541561\pi$
$8$	98416.8	1.06188
$9$	59049.0	0.333333
$10$	−401634.	−1.27008
$11$	−521143.	−0.975658	−0.487829	−	0.872939i	$-0.662211\pi$
$11$	−521143.	−0.975658	−0.487829	+	0.872939i	$0.662211\pi$
$12$	77405.9	0.0898002
$13$	2.19264e6	1.63787	0.818935	−	0.573886i	$-0.194565\pi$
$13$	2.19264e6	1.63787	0.818935	+	0.573886i	$0.194565\pi$
$14$	481530.	0.239287
$15$	−2.34683e6	−0.797958
$16$	−3.44046e6	−0.820269
$17$	−5.78339e6	−0.987902	−0.493951	−	0.869490i	$-0.664448\pi$
$17$	−5.78339e6	−0.987902	−0.493951	+	0.869490i	$0.664448\pi$
$18$	−2.45566e6	−0.306315
$19$	1.37354e7	1.27262	0.636309	−	0.771435i	$-0.280460\pi$
$19$	1.37354e7	1.27262	0.636309	+	0.771435i	$0.280460\pi$
$20$	−3.07641e6	−0.214970
$21$	2.81368e6	0.150338
$22$	2.16727e7	0.896577
$23$	5.21100e7	1.68818	0.844089	−	0.536203i	$-0.180142\pi$
$23$	5.21100e7	1.68818	0.844089	+	0.536203i	$0.180142\pi$
$24$	−2.39153e7	−0.613075
$25$	4.44440e7	0.910213
$26$	−9.11849e7	−1.50511
$27$	−1.43489e7	−0.192450
$28$	3.68839e6	0.0405012
$29$	1.77755e8	1.60928	0.804641	−	0.593761i	$-0.202358\pi$
$29$	1.77755e8	1.60928	0.804641	+	0.593761i	$0.202358\pi$
$30$	9.75971e7	0.733281
$31$	−1.22823e8	−0.770531	−0.385266	−	0.922806i	$-0.625890\pi$
$31$	−1.22823e8	−0.770531	−0.385266	+	0.922806i	$0.625890\pi$
$32$	−5.84802e7	−0.308094
$33$	1.26638e8	0.563296
$34$	2.40513e8	0.907828
$35$	−1.11826e8	−0.359890
$36$	−1.88096e7	−0.0518462
$37$	3.62082e8	0.858414	0.429207	−	0.903206i	$-0.358793\pi$
$37$	3.62082e8	0.858414	0.429207	+	0.903206i	$0.358793\pi$
$38$	−5.71212e8	−1.16947
$39$	−5.32812e8	−0.945625
$40$	9.50485e8	1.46763
$41$	1.34909e9	1.81857	0.909286	−	0.416172i	$-0.136628\pi$
$41$	1.34909e9	1.81857	0.909286	+	0.416172i	$0.136628\pi$
$42$	−1.17012e8	−0.138152
$43$	1.17172e9	1.21548	0.607739	−	0.794136i	$-0.292076\pi$
$43$	1.17172e9	1.21548	0.607739	+	0.794136i	$0.292076\pi$
$44$	1.66007e8	0.151752
$45$	5.70280e8	0.460701
$46$	−2.16709e9	−1.55134
$47$	5.28251e8	0.335971	0.167986	−	0.985789i	$-0.446274\pi$
$47$	5.28251e8	0.335971	0.167986	+	0.985789i	$0.446274\pi$
$48$	8.36031e8	0.473583
$49$	−1.84325e9	−0.932195
$50$	−1.84828e9	−0.836436
$51$	1.40536e9	0.570365
$52$	−6.98451e8	−0.254752
$53$	−5.18449e9	−1.70290	−0.851450	−	0.524436i	$-0.824276\pi$
$53$	−5.18449e9	−1.70290	−0.851450	+	0.524436i	$0.824276\pi$
$54$	5.96724e8	0.176851
$55$	−5.03307e9	−1.34846
$56$	−1.13956e9	−0.276506
$57$	−3.33771e9	−0.734746
$58$	−7.39224e9	−1.47884
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	7.47567e8	0.124113
$61$	−9.00303e9	−1.36482	−0.682409	−	0.730970i	$-0.739068\pi$
$61$	−9.00303e9	−1.36482	−0.682409	+	0.730970i	$0.739068\pi$
$62$	5.10781e9	0.708076
$63$	−6.83725e8	−0.0867977
$64$	9.47806e9	1.10339
$65$	2.11760e10	2.26371
$66$	−5.26646e9	−0.517639
$67$	5.11986e9	0.463284	0.231642	−	0.972801i	$-0.425590\pi$
$67$	5.11986e9	0.463284	0.231642	+	0.972801i	$0.425590\pi$
$68$	1.84226e9	0.153657
$69$	−1.26627e10	−0.974670
$70$	4.65050e9	0.330720
$71$	−2.99744e9	−0.197165	−0.0985823	−	0.995129i	$-0.531431\pi$
$71$	−2.99744e9	−0.197165	−0.0985823	+	0.995129i	$0.531431\pi$
$72$	5.81141e9	0.353959
$73$	−2.74521e10	−1.54989	−0.774943	−	0.632032i	$-0.782221\pi$
$73$	−2.74521e10	−1.54989	−0.774943	+	0.632032i	$0.782221\pi$
$74$	−1.50578e10	−0.788836
$75$	−1.07999e10	−0.525512
$76$	−4.37533e9	−0.197941
$77$	6.03429e9	0.254055
$78$	2.21579e10	0.868978
$79$	2.06456e10	0.754882	0.377441	−	0.926034i	$-0.376804\pi$
$79$	2.06456e10	0.754882	0.377441	+	0.926034i	$0.376804\pi$
$80$	−3.32271e10	−1.13370
$81$	3.48678e9	0.111111
$82$	−5.61044e10	−1.67117
$83$	3.14626e10	0.876729	0.438365	−	0.898797i	$-0.355558\pi$
$83$	3.14626e10	0.876729	0.438365	+	0.898797i	$0.355558\pi$
$84$	−8.96278e8	−0.0233834
$85$	−5.58546e10	−1.36538
$86$	−4.87280e10	−1.11696
$87$	−4.31944e10	−0.929120
$88$	−5.12893e10	−1.03603
$89$	2.32505e10	0.441355	0.220678	−	0.975347i	$-0.429173\pi$
$89$	2.32505e10	0.441355	0.220678	+	0.975347i	$0.429173\pi$
$90$	−2.37161e10	−0.423360
$91$	−2.53885e10	−0.426490
$92$	−1.65993e10	−0.262577
$93$	2.98460e10	0.444866
$94$	−2.19682e10	−0.308739
$95$	1.32653e11	1.75889
$96$	1.42107e10	0.177878
$97$	−1.39153e11	−1.64531	−0.822656	−	0.568539i	$-0.807509\pi$
$97$	−1.39153e11	−1.64531	−0.822656	+	0.568539i	$0.807509\pi$
$98$	7.66550e10	0.856637
$99$	−3.07730e10	−0.325219
$100$	−1.41573e10	−0.141573
$101$	−4.73242e10	−0.448039	−0.224020	−	0.974585i	$-0.571918\pi$
$101$	−4.73242e10	−0.448039	−0.224020	+	0.974585i	$0.571918\pi$
$102$	−5.84446e10	−0.524135
$103$	1.63494e11	1.38962	0.694812	−	0.719192i	$-0.255488\pi$
$103$	1.63494e11	1.38962	0.694812	+	0.719192i	$0.255488\pi$
$104$	2.15793e11	1.73922
$105$	2.71738e10	0.207783
$106$	2.15606e11	1.56487
$107$	−4.94181e10	−0.340624	−0.170312	−	0.985390i	$-0.554478\pi$
$107$	−4.94181e10	−0.340624	−0.170312	+	0.985390i	$0.554478\pi$
$108$	4.57074e9	0.0299334
$109$	−6.78251e10	−0.422226	−0.211113	−	0.977462i	$-0.567709\pi$
$109$	−6.78251e10	−0.422226	−0.211113	+	0.977462i	$0.567709\pi$
$110$	2.09309e11	1.23916
$111$	−8.79858e10	−0.495606
$112$	3.98369e10	0.213592
$113$	−1.69239e11	−0.864110	−0.432055	−	0.901847i	$-0.642211\pi$
$113$	−1.69239e11	−0.864110	−0.432055	+	0.901847i	$0.642211\pi$
$114$	1.38805e11	0.675192
$115$	5.03266e11	2.33324
$116$	−5.66225e10	−0.250305
$117$	1.29473e11	0.545957
$118$	2.97314e10	0.119637
$119$	6.69656e10	0.257243
$120$	−2.30968e11	−0.847334
$121$	−1.37211e10	−0.0480917
$122$	3.74407e11	1.25419
$123$	−3.27829e11	−1.04995
$124$	3.91244e10	0.119847
$125$	−4.23410e10	−0.124095
$126$	2.84339e10	0.0797624
$127$	8.54400e10	0.229478	0.114739	−	0.993396i	$-0.463397\pi$
$127$	8.54400e10	0.229478	0.114739	+	0.993396i	$0.463397\pi$
$128$	−2.74394e11	−0.705863
$129$	−2.84728e11	−0.701757
$130$	−8.80641e11	−2.08023
$131$	−2.76029e11	−0.625118	−0.312559	−	0.949898i	$-0.601186\pi$
$131$	−2.76029e11	−0.625118	−0.312559	+	0.949898i	$0.601186\pi$
$132$	−4.03396e10	−0.0876143
$133$	−1.59042e11	−0.331381
$134$	−2.12918e11	−0.425733
$135$	−1.38578e11	−0.265986
$136$	−5.69183e11	−1.04903
$137$	4.55733e11	0.806765	0.403383	−	0.915031i	$-0.367834\pi$
$137$	4.55733e11	0.806765	0.403383	+	0.915031i	$0.367834\pi$
$138$	5.26602e11	0.895669
$139$	−2.37619e11	−0.388418	−0.194209	−	0.980960i	$-0.562214\pi$
$139$	−2.37619e11	−0.388418	−0.194209	+	0.980960i	$0.562214\pi$
$140$	3.56215e10	0.0559768
$141$	−1.28365e11	−0.193973
$142$	1.24654e11	0.181184
$143$	−1.14268e12	−1.59800
$144$	−2.03156e11	−0.273423
$145$	1.71671e12	2.22420
$146$	1.14164e12	1.42426
$147$	4.47911e11	0.538203
$148$	−1.15339e11	−0.133516
$149$	4.93394e11	0.550388	0.275194	−	0.961389i	$-0.411258\pi$
$149$	4.93394e11	0.550388	0.275194	+	0.961389i	$0.411258\pi$
$150$	4.49132e11	0.482917
$151$	1.58009e12	1.63798	0.818991	−	0.573806i	$-0.194534\pi$
$151$	1.58009e12	1.63798	0.818991	+	0.573806i	$0.194534\pi$
$152$	1.35180e12	1.35136
$153$	−3.41504e11	−0.329301
$154$	−2.50946e11	−0.233462
$155$	−1.18619e12	−1.06495
$156$	1.69724e11	0.147081
$157$	5.92635e11	0.495837	0.247919	−	0.968781i	$-0.420253\pi$
$157$	5.92635e11	0.495837	0.247919	+	0.968781i	$0.420253\pi$
$158$	−8.58585e11	−0.693696
$159$	1.25983e12	0.983170
$160$	−5.64787e11	−0.425818
$161$	−6.03379e11	−0.439590
$162$	−1.45004e11	−0.102105
$163$	−5.95948e11	−0.405674	−0.202837	−	0.979213i	$-0.565016\pi$
$163$	−5.95948e11	−0.405674	−0.202837	+	0.979213i	$0.565016\pi$
$164$	−4.29744e11	−0.282858
$165$	1.22304e12	0.778534
$166$	−1.30843e12	−0.805667
$167$	−3.42070e11	−0.203786	−0.101893	−	0.994795i	$-0.532490\pi$
$167$	−3.42070e11	−0.203786	−0.101893	+	0.994795i	$0.532490\pi$
$168$	2.76914e11	0.159641
$169$	3.01552e12	1.68262
$170$	2.32281e12	1.25471
$171$	8.11064e11	0.424206
$172$	−3.73243e11	−0.189054
$173$	2.76695e12	1.35753	0.678763	−	0.734357i	$-0.262516\pi$
$173$	2.76695e12	1.35753	0.678763	+	0.734357i	$0.262516\pi$
$174$	1.79631e12	0.853811
$175$	−5.14614e11	−0.237013
$176$	1.79297e12	0.800302
$177$	1.73727e11	0.0751646
$178$	−9.66915e11	−0.405581
$179$	8.79091e11	0.357555	0.178777	−	0.983890i	$-0.442786\pi$
$179$	8.79091e11	0.357555	0.178777	+	0.983890i	$0.442786\pi$
$180$	−1.81659e11	−0.0716568
$181$	1.33882e12	0.512258	0.256129	−	0.966643i	$-0.417553\pi$
$181$	1.33882e12	0.512258	0.256129	+	0.966643i	$0.417553\pi$
$182$	1.05582e12	0.391921
$183$	2.18774e12	0.787978
$184$	5.12850e12	1.79264
$185$	3.49689e12	1.18642
$186$	−1.24120e12	−0.408808
$187$	3.01398e12	0.963854
$188$	−1.68271e11	−0.0522565
$189$	1.66145e11	0.0501127
$190$	−5.51662e12	−1.61632
$191$	−2.43082e12	−0.691941	−0.345971	−	0.938245i	$-0.612450\pi$
$191$	−2.43082e12	−0.691941	−0.345971	+	0.938245i	$0.612450\pi$
$192$	−2.30317e12	−0.637043
$193$	−4.51748e12	−1.21431	−0.607157	−	0.794582i	$-0.707690\pi$
$193$	−4.51748e12	−1.21431	−0.607157	+	0.794582i	$0.707690\pi$
$194$	5.78692e12	1.51195
$195$	−5.14577e12	−1.30695
$196$	5.87156e11	0.144992
$197$	1.97497e12	0.474238	0.237119	−	0.971481i	$-0.423797\pi$
$197$	1.97497e12	0.474238	0.237119	+	0.971481i	$0.423797\pi$
$198$	1.27975e12	0.298859
$199$	5.67332e12	1.28868	0.644340	−	0.764739i	$-0.277132\pi$
$199$	5.67332e12	1.28868	0.644340	+	0.764739i	$0.277132\pi$
$200$	4.37403e12	0.966534
$201$	−1.24413e12	−0.267477
$202$	1.96806e12	0.411724
$203$	−2.05821e12	−0.419046
$204$	−4.47669e11	−0.0887138
$205$	1.30292e13	2.51346
$206$	−6.79918e12	−1.27699
$207$	3.07705e12	0.562726
$208$	−7.54370e12	−1.34349
$209$	−7.15814e12	−1.24164
$210$	−1.13007e12	−0.190941
$211$	5.87075e12	0.966363	0.483181	−	0.875520i	$-0.339481\pi$
$211$	5.87075e12	0.966363	0.483181	+	0.875520i	$0.339481\pi$
$212$	1.65148e12	0.264867
$213$	7.28377e11	0.113833
$214$	2.05514e12	0.313015
$215$	1.13162e13	1.67992
$216$	−1.41217e12	−0.204358
$217$	1.42216e12	0.200641
$218$	2.82063e12	0.388003
$219$	6.67086e12	0.894827
$220$	1.60325e12	0.209738
$221$	−1.26809e13	−1.61806
$222$	3.65904e12	0.455435
$223$	5.76894e12	0.700518	0.350259	−	0.936653i	$-0.386094\pi$
$223$	5.76894e12	0.700518	0.350259	+	0.936653i	$0.386094\pi$
$224$	6.77138e11	0.0802256
$225$	2.62437e12	0.303404
$226$	7.03810e12	0.794070
$227$	−1.03297e13	−1.13749	−0.568744	−	0.822515i	$-0.692570\pi$
$227$	−1.03297e13	−1.13749	−0.568744	+	0.822515i	$0.692570\pi$
$228$	1.06320e12	0.114281
$229$	7.46366e12	0.783171	0.391586	−	0.920142i	$-0.371927\pi$
$229$	7.46366e12	0.783171	0.391586	+	0.920142i	$0.371927\pi$
$230$	−2.09292e13	−2.14412
$231$	−1.46633e12	−0.146678
$232$	1.74941e13	1.70886
$233$	−1.19773e13	−1.14262	−0.571309	−	0.820735i	$-0.693564\pi$
$233$	−1.19773e13	−1.14262	−0.571309	+	0.820735i	$0.693564\pi$
$234$	−5.38438e12	−0.501705
$235$	5.10171e12	0.464347
$236$	2.27734e11	0.0202494
$237$	−5.01689e12	−0.435832
$238$	−2.78488e12	−0.236392
$239$	1.09656e13	0.909585	0.454792	−	0.890598i	$-0.349713\pi$
$239$	1.09656e13	0.909585	0.454792	+	0.890598i	$0.349713\pi$
$240$	8.07418e12	0.654541
$241$	−5.17342e12	−0.409906	−0.204953	−	0.978772i	$-0.565704\pi$
$241$	−5.17342e12	−0.409906	−0.204953	+	0.978772i	$0.565704\pi$
$242$	5.70617e11	0.0441937
$243$	−8.47289e11	−0.0641500
$244$	2.86785e12	0.212282
$245$	−1.78017e13	−1.28839
$246$	1.36334e13	0.964850
$247$	3.01169e13	2.08438
$248$	−1.20878e13	−0.818209
$249$	−7.64542e12	−0.506180
$250$	1.76082e12	0.114037
$251$	1.53032e13	0.969567	0.484784	−	0.874634i	$-0.338898\pi$
$251$	1.53032e13	0.969567	0.484784	+	0.874634i	$0.338898\pi$
$252$	2.17796e11	0.0135004
$253$	−2.71568e13	−1.64708
$254$	−3.55317e12	−0.210878
$255$	1.35727e13	0.788305
$256$	−7.99990e12	−0.454742
$257$	−1.06963e13	−0.595116	−0.297558	−	0.954704i	$-0.596172\pi$
$257$	−1.06963e13	−0.595116	−0.297558	+	0.954704i	$0.596172\pi$
$258$	1.18409e13	0.644877
$259$	−4.19252e12	−0.223525
$260$	−6.74546e12	−0.352094
$261$	1.04962e13	0.536427
$262$	1.14791e13	0.574450
$263$	7.37052e12	0.361195	0.180597	−	0.983557i	$-0.442197\pi$
$263$	7.37052e12	0.361195	0.180597	+	0.983557i	$0.442197\pi$
$264$	1.24633e13	0.598152
$265$	−5.00705e13	−2.35359
$266$	6.61403e12	0.304521
$267$	−5.64988e12	−0.254816
$268$	−1.63090e12	−0.0720585
$269$	3.47705e13	1.50513	0.752564	−	0.658519i	$-0.228817\pi$
$269$	3.47705e13	1.50513	0.752564	+	0.658519i	$0.228817\pi$
$270$	5.76301e12	0.244427
$271$	−6.38370e12	−0.265303	−0.132651	−	0.991163i	$-0.542349\pi$
$271$	−6.38370e12	−0.265303	−0.132651	+	0.991163i	$0.542349\pi$
$272$	1.98975e13	0.810345
$273$	6.16940e12	0.246234
$274$	−1.89524e13	−0.741374
$275$	−2.31617e13	−0.888056
$276$	4.03362e12	0.151599
$277$	2.57063e13	0.947112	0.473556	−	0.880764i	$-0.342970\pi$
$277$	2.57063e13	0.947112	0.473556	+	0.880764i	$0.342970\pi$
$278$	9.88179e12	0.356935
$279$	−7.25257e12	−0.256844
$280$	−1.10056e13	−0.382159
$281$	−3.20177e13	−1.09020	−0.545098	−	0.838372i	$-0.683508\pi$
$281$	−3.20177e13	−1.09020	−0.545098	+	0.838372i	$0.683508\pi$
$282$	5.33828e12	0.178251
$283$	−1.70757e13	−0.559182	−0.279591	−	0.960119i	$-0.590199\pi$
$283$	−1.70757e13	−0.559182	−0.279591	+	0.960119i	$0.590199\pi$
$284$	9.54812e11	0.0306667
$285$	−3.22348e13	−1.01550
$286$	4.75204e13	1.46848
$287$	−1.56211e13	−0.473544
$288$	−3.45319e12	−0.102698
$289$	−8.24239e11	−0.0240500
$290$	−7.13924e13	−2.04392
$291$	3.38142e13	0.949922
$292$	8.74466e12	0.241067
$293$	−4.38934e13	−1.18748	−0.593742	−	0.804656i	$-0.702350\pi$
$293$	−4.38934e13	−1.18748	−0.593742	+	0.804656i	$0.702350\pi$
$294$	−1.86272e13	−0.494580
$295$	−6.90456e12	−0.179935
$296$	3.56349e13	0.911531
$297$	7.47784e12	0.187765
$298$	−2.05186e13	−0.505777
$299$	1.14259e14	2.76502
$300$	3.44023e12	0.0817373
$301$	−1.35673e13	−0.316502
$302$	−6.57109e13	−1.50522
$303$	1.14998e13	0.258676
$304$	−4.72562e13	−1.04389
$305$	−8.69490e13	−1.88632
$306$	1.42020e13	0.302609
$307$	6.67684e13	1.39737	0.698683	−	0.715432i	$-0.253770\pi$
$307$	6.67684e13	1.39737	0.698683	+	0.715432i	$0.253770\pi$
$308$	−1.92218e12	−0.0395153
$309$	−3.97291e13	−0.802300
$310$	4.93299e13	0.978635
$311$	−3.26129e13	−0.635634	−0.317817	−	0.948152i	$-0.602950\pi$
$311$	−3.26129e13	−0.635634	−0.317817	+	0.948152i	$0.602950\pi$
$312$	−5.24377e13	−1.00414
$313$	2.01566e13	0.379247	0.189624	−	0.981857i	$-0.439273\pi$
$313$	2.01566e13	0.379247	0.189624	+	0.981857i	$0.439273\pi$
$314$	−2.46458e13	−0.455648
$315$	−6.60324e12	−0.119963
$316$	−6.57652e12	−0.117413
$317$	8.99054e12	0.157746	0.0788732	−	0.996885i	$-0.474868\pi$
$317$	8.99054e12	0.157746	0.0788732	+	0.996885i	$0.474868\pi$
$318$	−5.23923e13	−0.903480
$319$	−9.26357e13	−1.57011
$320$	9.15367e13	1.52500
$321$	1.20086e13	0.196660
$322$	2.50926e13	0.403959
$323$	−7.94375e13	−1.25722
$324$	−1.11069e12	−0.0172821
$325$	9.74498e13	1.49081
$326$	2.47836e13	0.372792
$327$	1.64815e13	0.243772
$328$	1.32773e14	1.93110
$329$	−6.11658e12	−0.0874846
$330$	−5.08621e13	−0.715431
$331$	1.91983e13	0.265588	0.132794	−	0.991144i	$-0.457605\pi$
$331$	1.91983e13	0.265588	0.132794	+	0.991144i	$0.457605\pi$
$332$	−1.00222e13	−0.136365
$333$	2.13806e13	0.286138
$334$	1.42256e13	0.187268
$335$	4.94464e13	0.640306
$336$	−9.68035e12	−0.123318
$337$	−1.52067e14	−1.90577	−0.952884	−	0.303334i	$-0.901900\pi$
$337$	−1.52067e14	−1.90577	−0.952884	+	0.303334i	$0.901900\pi$
$338$	−1.25406e14	−1.54624
$339$	4.11251e13	0.498894
$340$	1.77921e13	0.212370
$341$	6.40084e13	0.751775
$342$	−3.37295e13	−0.389822
$343$	4.42383e13	0.503130
$344$	1.15317e14	1.29069
$345$	−1.22294e14	−1.34710
$346$	−1.15069e14	−1.24749
$347$	−2.53920e13	−0.270948	−0.135474	−	0.990781i	$-0.543256\pi$
$347$	−2.53920e13	−0.270948	−0.135474	+	0.990781i	$0.543256\pi$
$348$	1.37593e13	0.144514
$349$	−1.71683e14	−1.77495	−0.887477	−	0.460851i	$-0.847544\pi$
$349$	−1.71683e14	−1.77495	−0.887477	+	0.460851i	$0.847544\pi$
$350$	2.14011e13	0.217802
$351$	−3.14620e13	−0.315208
$352$	3.04766e13	0.300595
$353$	1.59851e13	0.155223	0.0776114	−	0.996984i	$-0.475271\pi$
$353$	1.59851e13	0.155223	0.0776114	+	0.996984i	$0.475271\pi$
$354$	−7.22472e12	−0.0690722
$355$	−2.89485e13	−0.272502
$356$	−7.40630e12	−0.0686477
$357$	−1.62726e13	−0.148519
$358$	−3.65586e13	−0.328573
$359$	−9.11753e13	−0.806970	−0.403485	−	0.914986i	$-0.632201\pi$
$359$	−9.11753e13	−0.806970	−0.403485	+	0.914986i	$0.632201\pi$
$360$	5.61252e13	0.489208
$361$	7.21721e13	0.619555
$362$	−5.56770e13	−0.470737
$363$	3.33423e12	0.0277658
$364$	8.08732e12	0.0663356
$365$	−2.65125e14	−2.14210
$366$	−9.09809e13	−0.724109
$367$	2.08132e14	1.63184	0.815918	−	0.578168i	$-0.196232\pi$
$367$	2.08132e14	1.63184	0.815918	+	0.578168i	$0.196232\pi$
$368$	−1.79282e14	−1.38476
$369$	7.96626e13	0.606191
$370$	−1.45424e14	−1.09025
$371$	6.00309e13	0.443423
$372$	−9.50722e12	−0.0691938
$373$	−7.64019e13	−0.547905	−0.273953	−	0.961743i	$-0.588331\pi$
$373$	−7.64019e13	−0.547905	−0.273953	+	0.961743i	$0.588331\pi$
$374$	−1.25342e14	−0.885730
$375$	1.02889e13	0.0716466
$376$	5.19888e13	0.356760
$377$	3.89753e14	2.63580
$378$	−6.90943e12	−0.0460508
$379$	2.62872e14	1.72675	0.863373	−	0.504566i	$-0.168348\pi$
$379$	2.62872e14	1.72675	0.863373	+	0.504566i	$0.168348\pi$
$380$	−4.22558e13	−0.273575
$381$	−2.07619e13	−0.132489
$382$	1.01090e14	0.635857
$383$	8.49676e12	0.0526817	0.0263409	−	0.999653i	$-0.491614\pi$
$383$	8.49676e12	0.0526817	0.0263409	+	0.999653i	$0.491614\pi$
$384$	6.66778e13	0.407530
$385$	5.82776e13	0.351130
$386$	1.87867e14	1.11589
$387$	6.91889e13	0.405160
$388$	4.43262e13	0.255909
$389$	1.44073e14	0.820085	0.410042	−	0.912066i	$-0.365514\pi$
$389$	1.44073e14	0.820085	0.410042	+	0.912066i	$0.365514\pi$
$390$	2.13996e14	1.20102
$391$	−3.01373e14	−1.66775
$392$	−1.81407e14	−0.989877
$393$	6.70750e13	0.360912
$394$	−8.21326e13	−0.435799
$395$	1.99390e14	1.04333
$396$	9.80252e12	0.0505841
$397$	2.01462e14	1.02529	0.512643	−	0.858602i	$-0.328666\pi$
$397$	2.01462e14	1.02529	0.512643	+	0.858602i	$0.328666\pi$
$398$	−2.35935e14	−1.18423
$399$	3.86472e13	0.191323
$400$	−1.52908e14	−0.746619
$401$	−3.32883e14	−1.60323	−0.801617	−	0.597838i	$-0.796027\pi$
$401$	−3.32883e14	−1.60323	−0.801617	+	0.597838i	$0.796027\pi$
$402$	5.17392e13	0.245797
$403$	−2.69307e14	−1.26203
$404$	1.50748e13	0.0696874
$405$	3.36745e13	0.153567
$406$	8.55943e13	0.385081
$407$	−1.88696e14	−0.837519
$408$	1.38312e14	0.605658
$409$	4.12130e14	1.78056	0.890280	−	0.455414i	$-0.150509\pi$
$409$	4.12130e14	1.78056	0.890280	+	0.455414i	$0.150509\pi$
$410$	−5.41842e14	−2.30973
$411$	−1.10743e14	−0.465786
$412$	−5.20799e13	−0.216140
$413$	8.27806e12	0.0339003
$414$	−1.27964e14	−0.517115
$415$	3.03858e14	1.21173
$416$	−1.28226e14	−0.504619
$417$	5.77413e13	0.224253
$418$	2.97684e14	1.14100
$419$	4.57021e14	1.72886	0.864429	−	0.502755i	$-0.167680\pi$
$419$	4.57021e14	1.72886	0.864429	+	0.502755i	$0.167680\pi$
$420$	−8.65603e12	−0.0323182
$421$	2.48837e13	0.0916987	0.0458494	−	0.998948i	$-0.485401\pi$
$421$	2.48837e13	0.0916987	0.0458494	+	0.998948i	$0.485401\pi$
$422$	−2.44145e14	−0.888035
$423$	3.11927e13	0.111990
$424$	−5.10241e14	−1.80827
$425$	−2.57037e14	−0.899201
$426$	−3.02908e13	−0.104606
$427$	1.04246e14	0.355389
$428$	1.57418e13	0.0529802
$429$	2.77672e14	0.922606
$430$	−4.70603e14	−1.54375
$431$	4.08017e14	1.32146	0.660729	−	0.750625i	$-0.270247\pi$
$431$	4.08017e14	1.32146	0.660729	+	0.750625i	$0.270247\pi$
$432$	4.93668e13	0.157861
$433$	5.62181e14	1.77498	0.887489	−	0.460829i	$-0.152448\pi$
$433$	5.62181e14	1.77498	0.887489	+	0.460829i	$0.152448\pi$
$434$	−5.91430e13	−0.184378
$435$	−4.17161e14	−1.28414
$436$	2.16052e13	0.0656724
$437$	7.15754e14	2.14840
$438$	−2.77419e14	−0.822297
$439$	−1.79597e14	−0.525708	−0.262854	−	0.964836i	$-0.584664\pi$
$439$	−1.79597e14	−0.525708	−0.262854	+	0.964836i	$0.584664\pi$
$440$	−4.95339e14	−1.43190
$441$	−1.08842e14	−0.310732
$442$	5.27358e14	1.48691
$443$	2.18111e14	0.607376	0.303688	−	0.952771i	$-0.401782\pi$
$443$	2.18111e14	0.607376	0.303688	+	0.952771i	$0.401782\pi$
$444$	2.80273e13	0.0770858
$445$	2.24548e14	0.609999
$446$	−2.39911e14	−0.643738
$447$	−1.19895e14	−0.317767
$448$	−1.09746e14	−0.287315
$449$	−6.26011e12	−0.0161893	−0.00809463	−	0.999967i	$-0.502577\pi$
$449$	−6.26011e12	−0.0161893	−0.00809463	+	0.999967i	$0.502577\pi$
$450$	−1.09139e14	−0.278812
$451$	−7.03071e14	−1.77430
$452$	5.39099e13	0.134402
$453$	−3.83962e14	−0.945689
$454$	4.29580e14	1.04529
$455$	−2.45196e14	−0.589454
$456$	−3.28487e14	−0.780210
$457$	−1.30469e13	−0.0306173	−0.0153087	−	0.999883i	$-0.504873\pi$
$457$	−1.30469e13	−0.0306173	−0.0153087	+	0.999883i	$0.504873\pi$
$458$	−3.10389e14	−0.719692
$459$	8.29854e13	0.190122
$460$	−1.60312e14	−0.362908
$461$	5.92125e14	1.32452	0.662259	−	0.749275i	$-0.269598\pi$
$461$	5.92125e14	1.32452	0.662259	+	0.749275i	$0.269598\pi$
$462$	6.09800e13	0.134790
$463$	−6.22058e14	−1.35874	−0.679368	−	0.733798i	$-0.737746\pi$
$463$	−6.22058e14	−1.35874	−0.679368	+	0.733798i	$0.737746\pi$
$464$	−6.11558e14	−1.32004
$465$	2.88245e14	0.614852
$466$	4.98097e14	1.05000
$467$	−4.68824e14	−0.976712	−0.488356	−	0.872644i	$-0.662403\pi$
$467$	−4.68824e14	−0.976712	−0.488356	+	0.872644i	$0.662403\pi$
$468$	−4.12428e13	−0.0849173
$469$	−5.92826e13	−0.120636
$470$	−2.12164e14	−0.426710
$471$	−1.44010e14	−0.286272
$472$	−7.03606e13	−0.138245
$473$	−6.10634e14	−1.18589
$474$	2.08636e14	0.400506
$475$	6.10458e14	1.15835
$476$	−2.13314e13	−0.0400112
$477$	−3.06139e14	−0.567633
$478$	−4.56023e14	−0.835859
$479$	6.74900e14	1.22291	0.611454	−	0.791280i	$-0.290585\pi$
$479$	6.74900e14	1.22291	0.611454	+	0.791280i	$0.290585\pi$
$480$	1.37243e14	0.245846
$481$	7.93916e14	1.40597
$482$	2.15146e14	0.376681
$483$	1.46621e14	0.253797
$484$	4.37077e12	0.00748012
$485$	−1.34391e15	−2.27399
$486$	3.52360e13	0.0589504
$487$	4.12963e14	0.683127	0.341564	−	0.939859i	$-0.389044\pi$
$487$	4.12963e14	0.683127	0.341564	+	0.939859i	$0.389044\pi$
$488$	−8.86050e14	−1.44927
$489$	1.44815e14	0.234216
$490$	7.40314e14	1.18396
$491$	9.20913e14	1.45636	0.728182	−	0.685383i	$-0.240365\pi$
$491$	9.20913e14	1.45636	0.728182	+	0.685383i	$0.240365\pi$
$492$	1.04428e14	0.163308
$493$	−1.02803e15	−1.58981
$494$	−1.25246e15	−1.91543
$495$	−2.97198e14	−0.449487
$496$	4.22567e14	0.632043
$497$	3.47071e13	0.0513403
$498$	3.17948e14	0.465152
$499$	6.50653e14	0.941449	0.470724	−	0.882280i	$-0.343993\pi$
$499$	6.50653e14	0.941449	0.470724	+	0.882280i	$0.343993\pi$
$500$	1.34874e13	0.0193016
$501$	8.31230e13	0.117656
$502$	−6.36412e14	−0.890980
$503$	−7.61481e14	−1.05447	−0.527236	−	0.849719i	$-0.676772\pi$
$503$	−7.61481e14	−1.05447	−0.527236	+	0.849719i	$0.676772\pi$
$504$	−6.72900e13	−0.0921685
$505$	−4.57046e14	−0.619237
$506$	1.12936e15	1.51358
$507$	−7.32772e14	−0.971461
$508$	−2.72163e13	−0.0356926
$509$	3.56627e14	0.462665	0.231332	−	0.972875i	$-0.425692\pi$
$509$	3.56627e14	0.462665	0.231332	+	0.972875i	$0.425692\pi$
$510$	−5.64443e14	−0.724409
$511$	3.17866e14	0.403579
$512$	8.94649e14	1.12375
$513$	−1.97089e14	−0.244915
$514$	4.44825e14	0.546879
$515$	1.57898e15	1.92060
$516$	9.06981e13	0.109150
$517$	−2.75295e14	−0.327793
$518$	1.74353e14	0.205408
$519$	−6.72370e14	−0.783768
$520$	2.08407e15	2.40378
$521$	−8.99603e14	−1.02670	−0.513350	−	0.858179i	$-0.671596\pi$
$521$	−8.99603e14	−1.02670	−0.513350	+	0.858179i	$0.671596\pi$
$522$	−4.36504e14	−0.492948
$523$	−5.90284e14	−0.659632	−0.329816	−	0.944045i	$-0.606987\pi$
$523$	−5.90284e14	−0.659632	−0.329816	+	0.944045i	$0.606987\pi$
$524$	8.79270e13	0.0972300
$525$	1.25051e14	0.136840
$526$	−3.06516e14	−0.331919
$527$	7.10334e14	0.761209
$528$	−4.35692e14	−0.462055
$529$	1.76265e15	1.84995
$530$	2.08227e15	2.16282
$531$	−4.22156e13	−0.0433963
$532$	5.06616e13	0.0515425
$533$	2.95808e15	2.97859
$534$	2.34960e14	0.234163
$535$	−4.77268e14	−0.470778
$536$	5.03881e14	0.491950
$537$	−2.13619e14	−0.206434
$538$	−1.44599e15	−1.38313
$539$	9.60600e14	0.909504
$540$	4.41431e13	0.0413711
$541$	1.22095e15	1.13270	0.566350	−	0.824165i	$-0.308355\pi$
$541$	1.22095e15	1.13270	0.566350	+	0.824165i	$0.308355\pi$
$542$	2.65477e14	0.243799
$543$	−3.25332e14	−0.295752
$544$	3.38214e14	0.304367
$545$	−6.55038e14	−0.583560
$546$	−2.56565e14	−0.226276
$547$	6.79223e12	0.00593037	0.00296519	−	0.999996i	$-0.499056\pi$
$547$	6.79223e12	0.00593037	0.00296519	+	0.999996i	$0.499056\pi$
$548$	−1.45170e14	−0.125483
$549$	−5.31620e14	−0.454939
$550$	9.63219e14	0.816076
$551$	2.44154e15	2.04800
$552$	−1.24623e15	−1.03498
$553$	−2.39054e14	−0.196566
$554$	−1.06904e15	−0.870345
$555$	−8.49745e14	−0.684979
$556$	7.56917e13	0.0604139
$557$	−1.01178e15	−0.799619	−0.399810	−	0.916598i	$-0.630924\pi$
$557$	−1.01178e15	−0.799619	−0.399810	+	0.916598i	$0.630924\pi$
$558$	3.01611e14	0.236025
$559$	2.56916e15	1.99080
$560$	3.84734e14	0.295207
$561$	−7.32397e14	−0.556481
$562$	1.33151e15	1.00183
$563$	2.02865e15	1.51151	0.755755	−	0.654854i	$-0.227270\pi$
$563$	2.02865e15	1.51151	0.755755	+	0.654854i	$0.227270\pi$
$564$	4.08897e13	0.0301703
$565$	−1.63447e15	−1.19429
$566$	7.10123e14	0.513858
$567$	−4.03733e13	−0.0289326
$568$	−2.94998e14	−0.209365
$569$	1.08182e15	0.760395	0.380198	−	0.924905i	$-0.375856\pi$
$569$	1.08182e15	0.760395	0.380198	+	0.924905i	$0.375856\pi$
$570$	1.34054e15	0.933186
$571$	7.81982e14	0.539136	0.269568	−	0.962981i	$-0.413119\pi$
$571$	7.81982e14	0.539136	0.269568	+	0.962981i	$0.413119\pi$
$572$	3.63993e14	0.248551
$573$	5.90689e14	0.399493
$574$	6.49629e14	0.435161
$575$	2.31598e15	1.53660
$576$	5.59670e14	0.367797
$577$	2.29077e15	1.49113	0.745564	−	0.666434i	$-0.232180\pi$
$577$	2.29077e15	1.49113	0.745564	+	0.666434i	$0.232180\pi$
$578$	3.42774e13	0.0221006
$579$	1.09775e15	0.701084
$580$	−5.46846e14	−0.345948
$581$	−3.64304e14	−0.228294
$582$	−1.40622e15	−0.872926
$583$	2.70187e15	1.66145
$584$	−2.70175e15	−1.64579
$585$	1.25042e15	0.754569
$586$	1.82538e15	1.09123
$587$	−1.00599e15	−0.595780	−0.297890	−	0.954600i	$-0.596283\pi$
$587$	−1.00599e15	−0.595780	−0.297890	+	0.954600i	$0.596283\pi$
$588$	−1.42679e14	−0.0837113
$589$	−1.68703e15	−0.980591
$590$	2.87138e14	0.165350
$591$	−4.79918e14	−0.273801
$592$	−1.24573e15	−0.704131
$593$	−1.68886e15	−0.945787	−0.472894	−	0.881119i	$-0.656791\pi$
$593$	−1.68886e15	−0.945787	−0.472894	+	0.881119i	$0.656791\pi$
$594$	−3.10979e14	−0.172546
$595$	6.46737e14	0.355536
$596$	−1.57167e14	−0.0856065
$597$	−1.37862e15	−0.744020
$598$	−4.75165e15	−2.54090
$599$	−2.30225e15	−1.21985	−0.609924	−	0.792460i	$-0.708800\pi$
$599$	−2.30225e15	−1.21985	−0.609924	+	0.792460i	$0.708800\pi$
$600$	−1.06289e15	−0.558029
$601$	−2.09855e15	−1.09172	−0.545859	−	0.837877i	$-0.683796\pi$
$601$	−2.09855e15	−1.09172	−0.545859	+	0.837877i	$0.683796\pi$
$602$	5.64219e14	0.290848
$603$	3.02323e14	0.154428
$604$	−5.03327e14	−0.254769
$605$	−1.32515e14	−0.0664678
$606$	−4.78239e14	−0.237709
$607$	1.77589e15	0.874739	0.437370	−	0.899282i	$-0.355910\pi$
$607$	1.77589e15	0.874739	0.437370	+	0.899282i	$0.355910\pi$
$608$	−8.03251e14	−0.392086
$609$	5.00145e14	0.241936
$610$	3.61593e15	1.73343
$611$	1.15827e15	0.550277
$612$	1.08784e14	0.0512189
$613$	2.69677e15	1.25838	0.629190	−	0.777251i	$-0.283387\pi$
$613$	2.69677e15	1.25838	0.629190	+	0.777251i	$0.283387\pi$
$614$	−2.77668e15	−1.28410
$615$	−3.16609e15	−1.45114
$616$	5.93875e14	0.269775
$617$	5.08744e14	0.229050	0.114525	−	0.993420i	$-0.463465\pi$
$617$	5.08744e14	0.229050	0.114525	+	0.993420i	$0.463465\pi$
$618$	1.65220e15	0.737270
$619$	−3.61935e14	−0.160078	−0.0800391	−	0.996792i	$-0.525505\pi$
$619$	−3.61935e14	−0.160078	−0.0800391	+	0.996792i	$0.525505\pi$
$620$	3.77853e14	0.165641
$621$	−7.47722e14	−0.324890
$622$	1.35626e15	0.584113
$623$	−2.69217e14	−0.114926
$624$	1.83312e15	0.775667
$625$	−2.57903e15	−1.08173
$626$	−8.38246e14	−0.348508
$627$	1.73943e15	0.716861
$628$	−1.88780e14	−0.0771218
$629$	−2.09406e15	−0.848029
$630$	2.74607e14	0.110240
$631$	−1.96859e15	−0.783418	−0.391709	−	0.920089i	$-0.628116\pi$
$631$	−1.96859e15	−0.783418	−0.391709	+	0.920089i	$0.628116\pi$
$632$	2.03188e15	0.801592
$633$	−1.42659e15	−0.557930
$634$	−3.73887e14	−0.144960
$635$	8.25158e14	0.317162
$636$	−4.01311e14	−0.152921
$637$	−4.04160e15	−1.52682
$638$	3.85242e15	1.44285
$639$	−1.76996e14	−0.0657216
$640$	−2.65003e15	−0.975576
$641$	5.42899e15	1.98153	0.990764	−	0.135600i	$-0.0432962\pi$
$641$	5.42899e15	1.98153	0.990764	+	0.135600i	$0.0432962\pi$
$642$	−4.99399e14	−0.180719
$643$	5.23242e15	1.87734	0.938669	−	0.344820i	$-0.112060\pi$
$643$	5.23242e15	1.87734	0.938669	+	0.344820i	$0.112060\pi$
$644$	1.92202e14	0.0683732
$645$	−2.74983e15	−0.969902
$646$	3.30355e15	1.15532
$647$	−4.57841e15	−1.58760	−0.793799	−	0.608180i	$-0.791900\pi$
$647$	−4.57841e15	−1.58760	−0.793799	+	0.608180i	$0.791900\pi$
$648$	3.43158e14	0.117986
$649$	3.72578e14	0.127020
$650$	−4.05262e15	−1.36997
$651$	−3.45585e14	−0.115840
$652$	1.89835e14	0.0630979
$653$	−4.77225e14	−0.157290	−0.0786449	−	0.996903i	$-0.525059\pi$
$653$	−4.77225e14	−0.157290	−0.0786449	+	0.996903i	$0.525059\pi$
$654$	−6.85412e14	−0.224014
$655$	−2.66582e15	−0.863979
$656$	−4.64150e15	−1.49172
$657$	−1.62102e15	−0.516628
$658$	2.54369e14	0.0803936
$659$	−6.04420e15	−1.89439	−0.947195	−	0.320659i	$-0.896096\pi$
$659$	−6.04420e15	−1.89439	−0.947195	+	0.320659i	$0.896096\pi$
$660$	−3.89590e14	−0.121092
$661$	−1.66802e15	−0.514153	−0.257077	−	0.966391i	$-0.582759\pi$
$661$	−1.66802e15	−0.514153	−0.257077	+	0.966391i	$0.582759\pi$
$662$	−7.98394e14	−0.244061
$663$	3.08146e15	0.934185
$664$	3.09645e15	0.930979
$665$	−1.53599e15	−0.458003
$666$	−8.89148e14	−0.262945
$667$	9.26281e15	2.71676
$668$	1.08964e14	0.0316966
$669$	−1.40185e15	−0.404444
$670$	−2.05631e15	−0.588407
$671$	4.69187e15	1.33160
$672$	−1.64545e14	−0.0463183
$673$	3.51506e15	0.981409	0.490704	−	0.871326i	$-0.336739\pi$
$673$	3.51506e15	0.981409	0.490704	+	0.871326i	$0.336739\pi$
$674$	6.32397e15	1.75130
$675$	−6.37722e14	−0.175171
$676$	−9.60574e14	−0.261712
$677$	6.05494e15	1.63633	0.818167	−	0.574980i	$-0.194990\pi$
$677$	6.05494e15	1.63633	0.818167	+	0.574980i	$0.194990\pi$
$678$	−1.71026e15	−0.458457
$679$	1.61124e15	0.428428
$680$	−5.49703e15	−1.44987
$681$	2.51012e15	0.656729
$682$	−2.66190e15	−0.690840
$683$	−3.36699e15	−0.866817	−0.433409	−	0.901198i	$-0.642689\pi$
$683$	−3.36699e15	−0.866817	−0.433409	+	0.901198i	$0.642689\pi$
$684$	−2.58359e14	−0.0659803
$685$	4.40135e15	1.11503
$686$	−1.83973e15	−0.462350
$687$	−1.81367e15	−0.452164
$688$	−4.03126e15	−0.997020
$689$	−1.13677e16	−2.78913
$690$	5.08579e15	1.23791
$691$	3.69145e14	0.0891389	0.0445695	−	0.999006i	$-0.485808\pi$
$691$	3.69145e14	0.0891389	0.0445695	+	0.999006i	$0.485808\pi$
$692$	−8.81393e14	−0.211148
$693$	3.56319e14	0.0846849
$694$	1.05597e15	0.248986
$695$	−2.29486e15	−0.536834
$696$	−4.25106e15	−0.986611
$697$	−7.80234e15	−1.79657
$698$	7.13973e15	1.63109
$699$	2.91048e15	0.659691
$700$	1.63927e14	0.0368647
$701$	−7.45701e15	−1.66386	−0.831928	−	0.554884i	$-0.812763\pi$
$701$	−7.45701e15	−1.66386	−0.831928	+	0.554884i	$0.812763\pi$
$702$	1.30840e15	0.289659
$703$	4.97335e15	1.09243
$704$	−4.93943e15	−1.07653
$705$	−1.23972e15	−0.268091
$706$	−6.64770e14	−0.142641
$707$	5.47964e14	0.116666
$708$	−5.53394e13	−0.0116910
$709$	1.02668e15	0.215220	0.107610	−	0.994193i	$-0.465680\pi$
$709$	1.02668e15	0.215220	0.107610	+	0.994193i	$0.465680\pi$
$710$	1.20387e15	0.250415
$711$	1.21910e15	0.251627
$712$	2.28824e15	0.468665
$713$	−6.40031e15	−1.30079
$714$	6.76726e14	0.136481
$715$	−1.10357e16	−2.20860
$716$	−2.80028e14	−0.0556135
$717$	−2.66464e15	−0.525149
$718$	3.79168e15	0.741562
$719$	−8.42355e15	−1.63488	−0.817441	−	0.576013i	$-0.804608\pi$
$719$	−8.42355e15	−1.63488	−0.817441	+	0.576013i	$0.804608\pi$
$720$	−1.96203e15	−0.377899
$721$	−1.89309e15	−0.361848
$722$	−3.00140e15	−0.569337
$723$	1.25714e15	0.236659
$724$	−4.26470e14	−0.0796758
$725$	7.90013e15	1.46479
$726$	−1.38660e14	−0.0255152
$727$	−2.08220e15	−0.380262	−0.190131	−	0.981759i	$-0.560891\pi$
$727$	−2.08220e15	−0.380262	−0.190131	+	0.981759i	$0.560891\pi$
$728$	−2.49865e15	−0.452880
$729$	2.05891e14	0.0370370
$730$	1.10257e16	1.96848
$731$	−6.77652e15	−1.20077
$732$	−6.96888e14	−0.122561
$733$	4.41378e15	0.770439	0.385220	−	0.922825i	$-0.374126\pi$
$733$	4.41378e15	0.770439	0.385220	+	0.922825i	$0.374126\pi$
$734$	−8.65555e15	−1.49957
$735$	4.32581e15	0.743853
$736$	−3.04740e15	−0.520118
$737$	−2.66818e15	−0.452006
$738$	−3.31291e15	−0.557056
$739$	−3.08125e15	−0.514259	−0.257130	−	0.966377i	$-0.582777\pi$
$739$	−3.08125e15	−0.514259	−0.257130	+	0.966377i	$0.582777\pi$
$740$	−1.11391e15	−0.184534
$741$	−7.31841e15	−1.20342
$742$	−2.49649e15	−0.407482
$743$	−4.93087e15	−0.798887	−0.399443	−	0.916758i	$-0.630797\pi$
$743$	−4.93087e15	−0.798887	−0.399443	+	0.916758i	$0.630797\pi$
$744$	2.93735e15	0.472393
$745$	4.76507e15	0.760694
$746$	3.17730e15	0.503495
$747$	1.85784e15	0.292243
$748$	−9.60081e14	−0.149916
$749$	5.72210e14	0.0886962
$750$	−4.27880e14	−0.0658393
$751$	8.61170e12	0.00131543	0.000657717	−	1.00000i	$-0.499791\pi$
$751$	8.61170e12	0.00131543	0.000657717		1.00000i	$0.499791\pi$
$752$	−1.81743e15	−0.275587
$753$	−3.71869e15	−0.559780
$754$	−1.62085e16	−2.42215
$755$	1.52601e16	2.26386
$756$	−5.29243e13	−0.00779445
$757$	2.83321e15	0.414240	0.207120	−	0.978316i	$-0.433591\pi$
$757$	2.83321e15	0.414240	0.207120	+	0.978316i	$0.433591\pi$
$758$	−1.09320e16	−1.58679
$759$	6.59910e15	0.950944
$760$	1.30553e16	1.86773
$761$	−1.10169e16	−1.56475	−0.782373	−	0.622810i	$-0.785991\pi$
$761$	−1.10169e16	−1.56475	−0.782373	+	0.622810i	$0.785991\pi$
$762$	8.63421e14	0.121750
$763$	7.85343e14	0.109945
$764$	7.74321e14	0.107624
$765$	−3.29816e15	−0.455128
$766$	−3.53352e14	−0.0484116
$767$	−1.56757e15	−0.213233
$768$	1.94398e15	0.262545
$769$	7.47818e15	1.00277	0.501385	−	0.865224i	$-0.332824\pi$
$769$	7.47818e15	1.00277	0.501385	+	0.865224i	$0.332824\pi$
$770$	−2.42358e15	−0.322669
$771$	2.59920e15	0.343590
$772$	1.43901e15	0.188873
$773$	−2.78492e15	−0.362932	−0.181466	−	0.983397i	$-0.558084\pi$
$773$	−2.78492e15	−0.362932	−0.181466	+	0.983397i	$0.558084\pi$
$774$	−2.87734e15	−0.372320
$775$	−5.45874e15	−0.701347
$776$	−1.36950e16	−1.74712
$777$	1.01878e15	0.129052
$778$	−5.99151e15	−0.753614
$779$	1.85304e16	2.31435
$780$	1.63915e15	0.203281
$781$	1.56209e15	0.192365
$782$	1.25331e16	1.53258
$783$	−2.55059e15	−0.309707
$784$	6.34164e15	0.764651
$785$	5.72352e15	0.685299
$786$	−2.78943e15	−0.331659
$787$	1.00576e16	1.18750	0.593752	−	0.804648i	$-0.297646\pi$
$787$	1.00576e16	1.18750	0.593752	+	0.804648i	$0.297646\pi$
$788$	−6.29113e14	−0.0737623
$789$	−1.79104e15	−0.208536
$790$	−8.29199e15	−0.958760
$791$	1.95961e15	0.225008
$792$	−3.02858e15	−0.345343
$793$	−1.97404e16	−2.23540
$794$	−8.37815e15	−0.942183
$795$	1.21671e16	1.35884
$796$	−1.80720e15	−0.200439
$797$	6.39013e15	0.703864	0.351932	−	0.936026i	$-0.385525\pi$
$797$	6.39013e15	0.703864	0.351932	+	0.936026i	$0.385525\pi$
$798$	−1.60721e15	−0.175815
$799$	−3.05508e15	−0.331907
$800$	−2.59909e15	−0.280431
$801$	1.37292e15	0.147118
$802$	1.38435e16	1.47329
$803$	1.43065e16	1.51216
$804$	3.96308e14	0.0416030
$805$	−5.82728e15	−0.607559
$806$	1.11996e16	1.15974
$807$	−8.44923e15	−0.868986
$808$	−4.65750e15	−0.475763
$809$	−7.95064e15	−0.806650	−0.403325	−	0.915057i	$-0.632146\pi$
$809$	−7.95064e15	−0.806650	−0.403325	+	0.915057i	$0.632146\pi$
$810$	−1.40041e15	−0.141120
$811$	−1.46618e16	−1.46748	−0.733742	−	0.679428i	$-0.762228\pi$
$811$	−1.46618e16	−1.46748	−0.733742	+	0.679428i	$0.762228\pi$
$812$	6.55628e14	0.0651778
$813$	1.55124e15	0.153173
$814$	7.84727e15	0.769634
$815$	−5.75552e15	−0.560683
$816$	−4.83510e15	−0.467853
$817$	1.60941e16	1.54684
$818$	−1.71392e16	−1.63624
$819$	−1.49916e15	−0.142163
$820$	−4.15036e15	−0.390939
$821$	4.75644e15	0.445036	0.222518	−	0.974929i	$-0.428572\pi$
$821$	4.75644e15	0.445036	0.222518	+	0.974929i	$0.428572\pi$
$822$	4.60544e15	0.428032
$823$	2.04699e16	1.88980	0.944901	−	0.327357i	$-0.106158\pi$
$823$	2.04699e16	1.88980	0.944901	+	0.327357i	$0.106158\pi$
$824$	1.60906e16	1.47561
$825$	5.62829e15	0.512719
$826$	−3.44258e14	−0.0311525
$827$	1.10892e16	0.996832	0.498416	−	0.866938i	$-0.333915\pi$
$827$	1.10892e16	0.996832	0.498416	+	0.866938i	$0.333915\pi$
$828$	−9.80171e14	−0.0875256
$829$	−1.63458e16	−1.44996	−0.724980	−	0.688770i	$-0.758151\pi$
$829$	−1.63458e16	−1.44996	−0.724980	+	0.688770i	$0.758151\pi$
$830$	−1.26365e16	−1.11352
$831$	−6.24664e15	−0.546816
$832$	2.07820e16	1.80721
$833$	1.06603e16	0.920918
$834$	−2.40127e15	−0.206077
$835$	−3.30362e15	−0.281653
$836$	2.28017e15	0.193123
$837$	1.76237e15	0.148289
$838$	−1.90060e16	−1.58873
$839$	−1.76209e16	−1.46331	−0.731656	−	0.681674i	$-0.761252\pi$
$839$	−1.76209e16	−1.46331	−0.731656	+	0.681674i	$0.761252\pi$
$840$	2.67436e15	0.220640
$841$	1.93962e16	1.58979
$842$	−1.03483e15	−0.0842662
$843$	7.78029e15	0.629425
$844$	−1.87009e15	−0.150307
$845$	2.91232e16	2.32556
$846$	−1.29720e15	−0.102913
$847$	1.58876e14	0.0125228
$848$	1.78370e16	1.39684
$849$	4.14940e15	0.322844
$850$	1.06893e16	0.826317
$851$	1.88681e16	1.44916
$852$	−2.32019e14	−0.0177054
$853$	1.75870e16	1.33344	0.666719	−	0.745309i	$-0.267698\pi$
$853$	1.75870e16	1.33344	0.666719	+	0.745309i	$0.267698\pi$
$854$	−4.33523e15	−0.326583
$855$	7.83305e15	0.586297
$856$	−4.86358e15	−0.361701
$857$	−2.59257e16	−1.91574	−0.957868	−	0.287209i	$-0.907272\pi$
$857$	−2.59257e16	−1.91574	−0.957868	+	0.287209i	$0.907272\pi$
$858$	−1.15475e16	−0.847825
$859$	−6.63970e15	−0.484380	−0.242190	−	0.970229i	$-0.577866\pi$
$859$	−6.63970e15	−0.484380	−0.242190	+	0.970229i	$0.577866\pi$
$860$	−3.60469e15	−0.261292
$861$	3.79592e15	0.273401
$862$	−1.69681e16	−1.21435
$863$	1.81587e16	1.29129	0.645646	−	0.763637i	$-0.276588\pi$
$863$	1.81587e16	1.29129	0.645646	+	0.763637i	$0.276588\pi$
$864$	8.39126e14	0.0592928
$865$	2.67225e16	1.87624
$866$	−2.33793e16	−1.63111
$867$	2.00290e14	0.0138853
$868$	−4.53019e14	−0.0312074
$869$	−1.07593e16	−0.736507
$870$	1.73484e16	1.18006
$871$	1.12260e16	0.758799
$872$	−6.67513e15	−0.448352
$873$	−8.21685e15	−0.548437
$874$	−2.97659e16	−1.97427
$875$	4.90264e14	0.0323136
$876$	−2.12495e15	−0.139180
$877$	−7.62216e14	−0.0496113	−0.0248056	−	0.999692i	$-0.507897\pi$
$877$	−7.62216e14	−0.0496113	−0.0248056	+	0.999692i	$0.507897\pi$
$878$	7.46886e15	0.483097
$879$	1.06661e16	0.685594
$880$	1.73161e16	1.10610
$881$	9.89653e15	0.628225	0.314113	−	0.949386i	$-0.398293\pi$
$881$	9.89653e15	0.628225	0.314113	+	0.949386i	$0.398293\pi$
$882$	4.52640e15	0.285546
$883$	1.41170e16	0.885034	0.442517	−	0.896760i	$-0.354086\pi$
$883$	1.41170e16	0.885034	0.442517	+	0.896760i	$0.354086\pi$
$884$	4.03942e15	0.251670
$885$	1.67781e15	0.103885
$886$	−9.07054e15	−0.558146
$887$	−2.86512e16	−1.75211	−0.876057	−	0.482207i	$-0.839835\pi$
$887$	−2.86512e16	−1.75211	−0.876057	+	0.482207i	$0.839835\pi$
$888$	−8.65928e15	−0.526273
$889$	−9.89304e14	−0.0597545
$890$	−9.33822e15	−0.560556
$891$	−1.81711e15	−0.108406
$892$	−1.83765e15	−0.108957
$893$	7.25576e15	0.427563
$894$	4.98603e15	0.292010
$895$	8.49004e15	0.494178
$896$	3.17719e15	0.183802
$897$	−2.77649e16	−1.59638
$898$	2.60337e14	0.0148770
$899$	−2.18324e16	−1.24000
$900$	−8.35975e14	−0.0471910
$901$	2.99840e16	1.68230
$902$	2.92384e16	1.63049
$903$	3.29685e15	0.182733
$904$	−1.66560e16	−0.917579
$905$	1.29299e16	0.707994
$906$	1.59677e16	0.869037
$907$	−1.59018e16	−0.860213	−0.430106	−	0.902778i	$-0.641524\pi$
$907$	−1.59018e16	−0.860213	−0.430106	+	0.902778i	$0.641524\pi$
$908$	3.29046e15	0.176923
$909$	−2.79445e15	−0.149346
$910$	1.01969e16	0.541676
$911$	−2.43582e16	−1.28616	−0.643080	−	0.765799i	$-0.722344\pi$
$911$	−2.43582e16	−1.28616	−0.643080	+	0.765799i	$0.722344\pi$
$912$	1.14833e16	0.602690
$913$	−1.63965e16	−0.855388
$914$	5.42577e14	0.0281357
$915$	2.11286e16	1.08907
$916$	−2.37750e15	−0.121813
$917$	3.19612e15	0.162777
$918$	−3.45109e15	−0.174712
$919$	−1.12252e16	−0.564885	−0.282442	−	0.959284i	$-0.591145\pi$
$919$	−1.12252e16	−0.564885	−0.282442	+	0.959284i	$0.591145\pi$
$920$	4.95298e16	2.47761
$921$	−1.62247e16	−0.806769
$922$	−2.46245e16	−1.21716
$923$	−6.57231e15	−0.322930
$924$	4.67090e14	0.0228142
$925$	1.60923e16	0.781340
$926$	2.58694e16	1.24861
$927$	9.65416e15	0.463208
$928$	−1.03951e16	−0.495811
$929$	2.38103e16	1.12896	0.564480	−	0.825447i	$-0.309077\pi$
$929$	2.38103e16	1.12896	0.564480	+	0.825447i	$0.309077\pi$
$930$	−1.19872e16	−0.565015
$931$	−2.53179e16	−1.18633
$932$	3.81528e15	0.177721
$933$	7.92493e15	0.366984
$934$	1.94968e16	0.897546
$935$	2.91082e16	1.33215
$936$	1.27424e16	0.579739
$937$	8.95352e15	0.404973	0.202486	−	0.979285i	$-0.435098\pi$
$937$	8.95352e15	0.404973	0.202486	+	0.979285i	$0.435098\pi$
$938$	2.46537e15	0.110858
$939$	−4.89805e15	−0.218959
$940$	−1.62511e15	−0.0722239
$941$	−1.50764e16	−0.666126	−0.333063	−	0.942905i	$-0.608082\pi$
$941$	−1.50764e16	−0.666126	−0.333063	+	0.942905i	$0.608082\pi$
$942$	5.98892e15	0.263068
$943$	7.03013e16	3.07007
$944$	2.45967e15	0.106790
$945$	1.60459e15	0.0692609
$946$	2.53943e16	1.08977
$947$	−3.25117e16	−1.38712	−0.693562	−	0.720397i	$-0.743960\pi$
$947$	−3.25117e16	−1.38712	−0.693562	+	0.720397i	$0.743960\pi$
$948$	1.59809e15	0.0677886
$949$	−6.01926e16	−2.53851
$950$	−2.53869e16	−1.06446
$951$	−2.18470e15	−0.0910750
$952$	6.59054e15	0.273160
$953$	−3.67755e15	−0.151547	−0.0757735	−	0.997125i	$-0.524143\pi$
$953$	−3.67755e15	−0.151547	−0.0757735	+	0.997125i	$0.524143\pi$
$954$	1.27313e16	0.521624
$955$	−2.34763e16	−0.956335
$956$	−3.49301e15	−0.141475
$957$	2.25105e16	0.906503
$958$	−2.80669e16	−1.12379
$959$	−5.27690e15	−0.210076
$960$	−2.22434e16	−0.880460
$961$	−1.03230e16	−0.406282
$962$	−3.30164e16	−1.29201
$963$	−2.91809e15	−0.113541
$964$	1.64796e15	0.0637561
$965$	−4.36287e16	−1.67831
$966$	−6.09749e15	−0.233226
$967$	−4.22043e16	−1.60513	−0.802567	−	0.596562i	$-0.796533\pi$
$967$	−4.22043e16	−1.60513	−0.802567	+	0.596562i	$0.796533\pi$
$968$	−1.35039e15	−0.0510675
$969$	1.93033e16	0.725857
$970$	5.58887e16	2.08968
$971$	2.20791e16	0.820871	0.410435	−	0.911890i	$-0.365377\pi$
$971$	2.20791e16	0.820871	0.410435	+	0.911890i	$0.365377\pi$
$972$	2.69898e14	0.00997780
$973$	2.75137e15	0.101141
$974$	−1.71738e16	−0.627757
$975$	−2.36803e16	−0.860720
$976$	3.09746e16	1.11952
$977$	−3.75496e16	−1.34954	−0.674770	−	0.738028i	$-0.735757\pi$
$977$	−3.75496e16	−1.34954	−0.674770	+	0.738028i	$0.735757\pi$
$978$	−6.02240e15	−0.215232
$979$	−1.21169e16	−0.430612
$980$	5.67060e15	0.200394
$981$	−4.00501e15	−0.140742
$982$	−3.82978e16	−1.33832
$983$	4.99505e15	0.173578	0.0867892	−	0.996227i	$-0.472339\pi$
$983$	4.99505e15	0.173578	0.0867892	+	0.996227i	$0.472339\pi$
$984$	−3.22639e16	−1.11492
$985$	1.90738e16	0.655446
$986$	4.27523e16	1.46095
$987$	1.48633e15	0.0505092
$988$	−9.59353e15	−0.324202
$989$	6.10584e16	2.05194
$990$	1.23595e16	0.413054
$991$	−1.30791e16	−0.434684	−0.217342	−	0.976096i	$-0.569739\pi$
$991$	−1.30791e16	−0.434684	−0.217342	+	0.976096i	$0.569739\pi$
$992$	7.18270e15	0.237396
$993$	−4.66518e15	−0.153337
$994$	−1.44336e15	−0.0471790
$995$	5.47915e16	1.78109
$996$	2.43539e15	0.0787305
$997$	3.07717e16	0.989301	0.494651	−	0.869092i	$-0.335296\pi$
$997$	3.07717e16	0.989301	0.494651	+	0.869092i	$0.335296\pi$
$998$	−2.70586e16	−0.865140
$999$	−5.19548e15	−0.165202

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-41.5867 q^{2} -243.000 q^{3} -318.543 q^{4} +9657.75 q^{5} +10105.6 q^{6} -11578.9 q^{7} +98416.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-41.5867 q^{2} -243.000 q^{3} -318.543 q^{4} +9657.75 q^{5} +10105.6 q^{6} -11578.9 q^{7} +98416.8 q^{8} +59049.0 q^{9} -401634. q^{10} -521143. q^{11} +77405.9 q^{12} +2.19264e6 q^{13} +481530. q^{14} -2.34683e6 q^{15} -3.44046e6 q^{16} -5.78339e6 q^{17} -2.45566e6 q^{18} +1.37354e7 q^{19} -3.07641e6 q^{20} +2.81368e6 q^{21} +2.16727e7 q^{22} +5.21100e7 q^{23} -2.39153e7 q^{24} +4.44440e7 q^{25} -9.11849e7 q^{26} -1.43489e7 q^{27} +3.68839e6 q^{28} +1.77755e8 q^{29} +9.75971e7 q^{30} -1.22823e8 q^{31} -5.84802e7 q^{32} +1.26638e8 q^{33} +2.40513e8 q^{34} -1.11826e8 q^{35} -1.88096e7 q^{36} +3.62082e8 q^{37} -5.71212e8 q^{38} -5.32812e8 q^{39} +9.50485e8 q^{40} +1.34909e9 q^{41} -1.17012e8 q^{42} +1.17172e9 q^{43} +1.66007e8 q^{44} +5.70280e8 q^{45} -2.16709e9 q^{46} +5.28251e8 q^{47} +8.36031e8 q^{48} -1.84325e9 q^{49} -1.84828e9 q^{50} +1.40536e9 q^{51} -6.98451e8 q^{52} -5.18449e9 q^{53} +5.96724e8 q^{54} -5.03307e9 q^{55} -1.13956e9 q^{56} -3.33771e9 q^{57} -7.39224e9 q^{58} -7.14924e8 q^{59} +7.47567e8 q^{60} -9.00303e9 q^{61} +5.10781e9 q^{62} -6.83725e8 q^{63} +9.47806e9 q^{64} +2.11760e10 q^{65} -5.26646e9 q^{66} +5.11986e9 q^{67} +1.84226e9 q^{68} -1.26627e10 q^{69} +4.65050e9 q^{70} -2.99744e9 q^{71} +5.81141e9 q^{72} -2.74521e10 q^{73} -1.50578e10 q^{74} -1.07999e10 q^{75} -4.37533e9 q^{76} +6.03429e9 q^{77} +2.21579e10 q^{78} +2.06456e10 q^{79} -3.32271e10 q^{80} +3.48678e9 q^{81} -5.61044e10 q^{82} +3.14626e10 q^{83} -8.96278e8 q^{84} -5.58546e10 q^{85} -4.87280e10 q^{86} -4.31944e10 q^{87} -5.12893e10 q^{88} +2.32505e10 q^{89} -2.37161e10 q^{90} -2.53885e10 q^{91} -1.65993e10 q^{92} +2.98460e10 q^{93} -2.19682e10 q^{94} +1.32653e11 q^{95} +1.42107e10 q^{96} -1.39153e11 q^{97} +7.66550e10 q^{98} -3.07730e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * q^99

Introduction

L-functions

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