LMFDB - Embedded newform 177.12.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q+41.1468 q^{2} -243.000 q^{3} -354.944 q^{4} -4337.67 q^{5} -9998.66 q^{6} +64289.5 q^{7} -98873.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+41.1468 q^{2} -243.000 q^{3} -354.944 q^{4} -4337.67 q^{5} -9998.66 q^{6} +64289.5 q^{7} -98873.4 q^{8} +59049.0 q^{9} -178481. q^{10} -541443. q^{11} +86251.5 q^{12} +289390. q^{13} +2.64531e6 q^{14} +1.05405e6 q^{15} -3.34139e6 q^{16} -5.10994e6 q^{17} +2.42967e6 q^{18} +7.74730e6 q^{19} +1.53963e6 q^{20} -1.56224e7 q^{21} -2.22786e7 q^{22} -1.12741e7 q^{23} +2.40262e7 q^{24} -3.00128e7 q^{25} +1.19075e7 q^{26} -1.43489e7 q^{27} -2.28192e7 q^{28} -1.00038e8 q^{29} +4.33709e7 q^{30} +1.75466e8 q^{31} +6.50052e7 q^{32} +1.31571e8 q^{33} -2.10257e8 q^{34} -2.78867e8 q^{35} -2.09591e7 q^{36} +4.23968e7 q^{37} +3.18776e8 q^{38} -7.03218e7 q^{39} +4.28880e8 q^{40} +9.20980e8 q^{41} -6.42809e8 q^{42} -1.57768e9 q^{43} +1.92182e8 q^{44} -2.56135e8 q^{45} -4.63894e8 q^{46} -3.05940e9 q^{47} +8.11958e8 q^{48} +2.15582e9 q^{49} -1.23493e9 q^{50} +1.24172e9 q^{51} -1.02717e8 q^{52} -2.66837e9 q^{53} -5.90411e8 q^{54} +2.34860e9 q^{55} -6.35652e9 q^{56} -1.88259e9 q^{57} -4.11624e9 q^{58} -7.14924e8 q^{59} -3.74130e8 q^{60} -5.17784e9 q^{61} +7.21984e9 q^{62} +3.79623e9 q^{63} +9.51792e9 q^{64} -1.25528e9 q^{65} +5.41371e9 q^{66} +1.91789e10 q^{67} +1.81374e9 q^{68} +2.73962e9 q^{69} -1.14745e10 q^{70} +1.17361e10 q^{71} -5.83837e9 q^{72} +1.77886e10 q^{73} +1.74449e9 q^{74} +7.29310e9 q^{75} -2.74986e9 q^{76} -3.48091e10 q^{77} -2.89351e9 q^{78} +3.41681e10 q^{79} +1.44939e10 q^{80} +3.48678e9 q^{81} +3.78954e10 q^{82} -1.13758e10 q^{83} +5.54507e9 q^{84} +2.21652e10 q^{85} -6.49162e10 q^{86} +2.43092e10 q^{87} +5.35343e10 q^{88} -5.07069e10 q^{89} -1.05391e10 q^{90} +1.86047e10 q^{91} +4.00169e9 q^{92} -4.26382e10 q^{93} -1.25884e11 q^{94} -3.36052e10 q^{95} -1.57963e10 q^{96} +1.37888e11 q^{97} +8.87049e10 q^{98} -3.19717e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	41.1468	0.909223	0.454612	−	0.890690i	$-0.349778\pi$
$2$	41.1468	0.909223	0.454612	+	0.890690i	$0.349778\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−354.944	−0.173313
$5$	−4337.67	−0.620757	−0.310378	−	0.950613i	$-0.600456\pi$
$5$	−4337.67	−0.620757	−0.310378	+	0.950613i	$0.600456\pi$
$6$	−9998.66	−0.524940
$7$	64289.5	1.44578	0.722888	−	0.690965i	$-0.242814\pi$
$7$	64289.5	1.44578	0.722888	+	0.690965i	$0.242814\pi$
$8$	−98873.4	−1.06680
$9$	59049.0	0.333333
$10$	−178481.	−0.564407
$11$	−541443.	−1.01366	−0.506831	−	0.862046i	$-0.669183\pi$
$11$	−541443.	−1.01366	−0.506831	+	0.862046i	$0.669183\pi$
$12$	86251.5	0.100062
$13$	289390.	0.216170	0.108085	−	0.994142i	$-0.465528\pi$
$13$	289390.	0.216170	0.108085	+	0.994142i	$0.465528\pi$
$14$	2.64531e6	1.31453
$15$	1.05405e6	0.358394
$16$	−3.34139e6	−0.796650
$17$	−5.10994e6	−0.872864	−0.436432	−	0.899737i	$-0.643758\pi$
$17$	−5.10994e6	−0.872864	−0.436432	+	0.899737i	$0.643758\pi$
$18$	2.42967e6	0.303074
$19$	7.74730e6	0.717803	0.358902	−	0.933375i	$-0.383151\pi$
$19$	7.74730e6	0.717803	0.358902	+	0.933375i	$0.383151\pi$
$20$	1.53963e6	0.107585
$21$	−1.56224e7	−0.834719
$22$	−2.22786e7	−0.921645
$23$	−1.12741e7	−0.365242	−0.182621	−	0.983183i	$-0.558458\pi$
$23$	−1.12741e7	−0.365242	−0.182621	+	0.983183i	$0.558458\pi$
$24$	2.40262e7	0.615919
$25$	−3.00128e7	−0.614661
$26$	1.19075e7	0.196547
$27$	−1.43489e7	−0.192450
$28$	−2.28192e7	−0.250571
$29$	−1.00038e8	−0.905683	−0.452842	−	0.891591i	$-0.649590\pi$
$29$	−1.00038e8	−0.905683	−0.452842	+	0.891591i	$0.649590\pi$
$30$	4.33709e7	0.325860
$31$	1.75466e8	1.10079	0.550393	−	0.834906i	$-0.314478\pi$
$31$	1.75466e8	1.10079	0.550393	+	0.834906i	$0.314478\pi$
$32$	6.50052e7	0.342470
$33$	1.31571e8	0.585238
$34$	−2.10257e8	−0.793629
$35$	−2.78867e8	−0.897475
$36$	−2.09591e7	−0.0577709
$37$	4.23968e7	0.100513	0.0502567	−	0.998736i	$-0.483996\pi$
$37$	4.23968e7	0.100513	0.0502567	+	0.998736i	$0.483996\pi$
$38$	3.18776e8	0.652644
$39$	−7.03218e7	−0.124806
$40$	4.28880e8	0.662225
$41$	9.20980e8	1.24148	0.620739	−	0.784017i	$-0.286833\pi$
$41$	9.20980e8	1.24148	0.620739	+	0.784017i	$0.286833\pi$
$42$	−6.42809e8	−0.758946
$43$	−1.57768e9	−1.63659	−0.818297	−	0.574795i	$-0.805082\pi$
$43$	−1.57768e9	−1.63659	−0.818297	+	0.574795i	$0.805082\pi$
$44$	1.92182e8	0.175680
$45$	−2.56135e8	−0.206919
$46$	−4.63894e8	−0.332086
$47$	−3.05940e9	−1.94580	−0.972898	−	0.231234i	$-0.925724\pi$
$47$	−3.05940e9	−1.94580	−0.972898	+	0.231234i	$0.925724\pi$
$48$	8.11958e8	0.459946
$49$	2.15582e9	1.09027
$50$	−1.23493e9	−0.558864
$51$	1.24172e9	0.503948
$52$	−1.02717e8	−0.0374650
$53$	−2.66837e9	−0.876453	−0.438227	−	0.898864i	$-0.644393\pi$
$53$	−2.66837e9	−0.876453	−0.438227	+	0.898864i	$0.644393\pi$
$54$	−5.90411e8	−0.174980
$55$	2.34860e9	0.629237
$56$	−6.35652e9	−1.54236
$57$	−1.88259e9	−0.414424
$58$	−4.11624e9	−0.823468
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−3.74130e8	−0.0621142
$61$	−5.17784e9	−0.784937	−0.392468	−	0.919766i	$-0.628379\pi$
$61$	−5.17784e9	−0.784937	−0.392468	+	0.919766i	$0.628379\pi$
$62$	7.21984e9	1.00086
$63$	3.79623e9	0.481925
$64$	9.51792e9	1.10803
$65$	−1.25528e9	−0.134189
$66$	5.41371e9	0.532112
$67$	1.91789e10	1.73545	0.867726	−	0.497043i	$-0.165581\pi$
$67$	1.91789e10	1.73545	0.867726	+	0.497043i	$0.165581\pi$
$68$	1.81374e9	0.151278
$69$	2.73962e9	0.210872
$70$	−1.14745e10	−0.816005
$71$	1.17361e10	0.771976	0.385988	−	0.922504i	$-0.373861\pi$
$71$	1.17361e10	0.771976	0.385988	+	0.922504i	$0.373861\pi$
$72$	−5.83837e9	−0.355601
$73$	1.77886e10	1.00431	0.502153	−	0.864779i	$-0.332541\pi$
$73$	1.77886e10	1.00431	0.502153	+	0.864779i	$0.332541\pi$
$74$	1.74449e9	0.0913891
$75$	7.29310e9	0.354875
$76$	−2.74986e9	−0.124404
$77$	−3.48091e10	−1.46553
$78$	−2.89351e9	−0.113476
$79$	3.41681e10	1.24932	0.624658	−	0.780898i	$-0.285238\pi$
$79$	3.41681e10	1.24932	0.624658	+	0.780898i	$0.285238\pi$
$80$	1.44939e10	0.494526
$81$	3.48678e9	0.111111
$82$	3.78954e10	1.12878
$83$	−1.13758e10	−0.316995	−0.158498	−	0.987359i	$-0.550665\pi$
$83$	−1.13758e10	−0.316995	−0.158498	+	0.987359i	$0.550665\pi$
$84$	5.54507e9	0.144667
$85$	2.21652e10	0.541836
$86$	−6.49162e10	−1.48803
$87$	2.43092e10	0.522896
$88$	5.35343e10	1.08138
$89$	−5.07069e10	−0.962547	−0.481274	−	0.876570i	$-0.659826\pi$
$89$	−5.07069e10	−0.962547	−0.481274	+	0.876570i	$0.659826\pi$
$90$	−1.05391e10	−0.188136
$91$	1.86047e10	0.312533
$92$	4.00169e9	0.0633010
$93$	−4.26382e10	−0.635539
$94$	−1.25884e11	−1.76916
$95$	−3.36052e10	−0.445581
$96$	−1.57963e10	−0.197725
$97$	1.37888e11	1.63035	0.815175	−	0.579215i	$-0.196641\pi$
$97$	1.37888e11	1.63035	0.815175	+	0.579215i	$0.196641\pi$
$98$	8.87049e10	0.991297
$99$	−3.19717e10	−0.337887
$100$	1.06529e10	0.106529
$101$	9.79204e10	0.927055	0.463528	−	0.886083i	$-0.346584\pi$
$101$	9.79204e10	0.927055	0.463528	+	0.886083i	$0.346584\pi$
$102$	5.10926e10	0.458202
$103$	1.22973e11	1.04522	0.522609	−	0.852573i	$-0.324959\pi$
$103$	1.22973e11	1.04522	0.522609	+	0.852573i	$0.324959\pi$
$104$	−2.86130e10	−0.230611
$105$	6.77646e10	0.518157
$106$	−1.09795e11	−0.796892
$107$	2.87464e11	1.98140	0.990701	−	0.136057i	$-0.0434429\pi$
$107$	2.87464e11	1.98140	0.990701	+	0.136057i	$0.0434429\pi$
$108$	5.09306e9	0.0333540
$109$	2.82590e11	1.75918	0.879591	−	0.475730i	$-0.157816\pi$
$109$	2.82590e11	1.75918	0.879591	+	0.475730i	$0.157816\pi$
$110$	9.66373e10	0.572117
$111$	−1.03024e10	−0.0580314
$112$	−2.14817e11	−1.15178
$113$	3.06089e10	0.156284	0.0781422	−	0.996942i	$-0.475101\pi$
$113$	3.06089e10	0.156284	0.0781422	+	0.996942i	$0.475101\pi$
$114$	−7.74626e10	−0.376804
$115$	4.89035e10	0.226726
$116$	3.55079e10	0.156966
$117$	1.70882e10	0.0720566
$118$	−2.94168e10	−0.118371
$119$	−3.28516e11	−1.26197
$120$	−1.04218e11	−0.382336
$121$	7.84883e9	0.0275097
$122$	−2.13051e11	−0.713683
$123$	−2.23798e11	−0.716768
$124$	−6.22805e10	−0.190780
$125$	3.41986e11	1.00231
$126$	1.56203e11	0.438178
$127$	6.43804e10	0.172915	0.0864576	−	0.996256i	$-0.472445\pi$
$127$	6.43804e10	0.172915	0.0864576	+	0.996256i	$0.472445\pi$
$128$	2.58501e11	0.664979
$129$	3.83375e11	0.944888
$130$	−5.16506e10	−0.122008
$131$	−2.01111e11	−0.455454	−0.227727	−	0.973725i	$-0.573129\pi$
$131$	−2.01111e11	−0.455454	−0.227727	+	0.973725i	$0.573129\pi$
$132$	−4.67002e10	−0.101429
$133$	4.98070e11	1.03778
$134$	7.89150e11	1.57791
$135$	6.22408e10	0.119465
$136$	5.05237e11	0.931175
$137$	1.07444e12	1.90205	0.951023	−	0.309120i	$-0.100035\pi$
$137$	1.07444e12	1.90205	0.951023	+	0.309120i	$0.100035\pi$
$138$	1.12726e11	0.191730
$139$	−7.27147e11	−1.18861	−0.594307	−	0.804238i	$-0.702574\pi$
$139$	−7.27147e11	−1.18861	−0.594307	+	0.804238i	$0.702574\pi$
$140$	9.89821e10	0.155544
$141$	7.43433e11	1.12341
$142$	4.82904e11	0.701899
$143$	−1.56688e11	−0.219123
$144$	−1.97306e11	−0.265550
$145$	4.33932e11	0.562209
$146$	7.31943e11	0.913139
$147$	−5.23863e11	−0.629467
$148$	−1.50485e10	−0.0174202
$149$	−7.09274e11	−0.791206	−0.395603	−	0.918422i	$-0.629464\pi$
$149$	−7.09274e11	−0.791206	−0.395603	+	0.918422i	$0.629464\pi$
$150$	3.00087e11	0.322661
$151$	1.53012e12	1.58618	0.793092	−	0.609102i	$-0.208470\pi$
$151$	1.53012e12	1.58618	0.793092	+	0.609102i	$0.208470\pi$
$152$	−7.66002e11	−0.765755
$153$	−3.01737e11	−0.290955
$154$	−1.43228e12	−1.33249
$155$	−7.61112e11	−0.683320
$156$	2.49603e10	0.0216304
$157$	6.45190e11	0.539809	0.269904	−	0.962887i	$-0.413008\pi$
$157$	6.45190e11	0.539809	0.269904	+	0.962887i	$0.413008\pi$
$158$	1.40591e12	1.13591
$159$	6.48414e11	0.506021
$160$	−2.81971e11	−0.212591
$161$	−7.24809e11	−0.528058
$162$	1.43470e11	0.101025
$163$	−2.28361e12	−1.55450	−0.777248	−	0.629195i	$-0.783385\pi$
$163$	−2.28361e12	−1.55450	−0.777248	+	0.629195i	$0.783385\pi$
$164$	−3.26897e11	−0.215164
$165$	−5.70710e11	−0.363290
$166$	−4.68078e11	−0.288220
$167$	−1.77082e12	−1.05495	−0.527476	−	0.849570i	$-0.676862\pi$
$167$	−1.77082e12	−1.05495	−0.527476	+	0.849570i	$0.676862\pi$
$168$	1.54463e12	0.890481
$169$	−1.70841e12	−0.953271
$170$	9.12027e11	0.492650
$171$	4.57470e11	0.239268
$172$	5.59987e11	0.283642
$173$	−1.00215e11	−0.0491676	−0.0245838	−	0.999698i	$-0.507826\pi$
$173$	−1.00215e11	−0.0491676	−0.0245838	+	0.999698i	$0.507826\pi$
$174$	1.00025e12	0.475430
$175$	−1.92951e12	−0.888662
$176$	1.80917e12	0.807534
$177$	1.73727e11	0.0751646
$178$	−2.08642e12	−0.875171
$179$	−1.89930e11	−0.0772505	−0.0386252	−	0.999254i	$-0.512298\pi$
$179$	−1.89930e11	−0.0772505	−0.0386252	+	0.999254i	$0.512298\pi$
$180$	9.09137e10	0.0358617
$181$	−3.37075e12	−1.28972	−0.644858	−	0.764303i	$-0.723083\pi$
$181$	−3.37075e12	−1.28972	−0.644858	+	0.764303i	$0.723083\pi$
$182$	7.65525e11	0.284163
$183$	1.25822e12	0.453183
$184$	1.11471e12	0.389641
$185$	−1.83903e11	−0.0623944
$186$	−1.75442e12	−0.577847
$187$	2.76674e12	0.884789
$188$	1.08591e12	0.337231
$189$	−9.22484e11	−0.278240
$190$	−1.38275e12	−0.405133
$191$	5.65554e11	0.160987	0.0804934	−	0.996755i	$-0.474350\pi$
$191$	5.65554e11	0.160987	0.0804934	+	0.996755i	$0.474350\pi$
$192$	−2.31286e12	−0.639723
$193$	1.70304e12	0.457782	0.228891	−	0.973452i	$-0.426490\pi$
$193$	1.70304e12	0.457782	0.228891	+	0.973452i	$0.426490\pi$
$194$	5.67363e12	1.48235
$195$	3.05033e11	0.0774740
$196$	−7.65195e11	−0.188957
$197$	4.61776e12	1.10883	0.554417	−	0.832239i	$-0.312941\pi$
$197$	4.61776e12	1.10883	0.554417	+	0.832239i	$0.312941\pi$
$198$	−1.31553e12	−0.307215
$199$	5.51998e12	1.25385	0.626925	−	0.779080i	$-0.284313\pi$
$199$	5.51998e12	1.25385	0.626925	+	0.779080i	$0.284313\pi$
$200$	2.96746e12	0.655723
$201$	−4.66048e12	−1.00196
$202$	4.02911e12	0.842900
$203$	−6.43140e12	−1.30941
$204$	−4.40740e11	−0.0873406
$205$	−3.99491e12	−0.770656
$206$	5.05996e12	0.950336
$207$	−6.65727e11	−0.121747
$208$	−9.66966e11	−0.172212
$209$	−4.19472e12	−0.727610
$210$	2.78829e12	0.471121
$211$	1.41210e12	0.232441	0.116221	−	0.993223i	$-0.462922\pi$
$211$	1.41210e12	0.232441	0.116221	+	0.993223i	$0.462922\pi$
$212$	9.47123e11	0.151900
$213$	−2.85188e12	−0.445701
$214$	1.18282e13	1.80154
$215$	6.84343e12	1.01593
$216$	1.41872e12	0.205306
$217$	1.12806e13	1.59149
$218$	1.16277e13	1.59949
$219$	−4.32263e12	−0.579837
$220$	−8.33622e11	−0.109055
$221$	−1.47877e12	−0.188687
$222$	−4.23912e11	−0.0527635
$223$	8.59996e11	0.104429	0.0522143	−	0.998636i	$-0.483372\pi$
$223$	8.59996e11	0.104429	0.0522143	+	0.998636i	$0.483372\pi$
$224$	4.17915e12	0.495136
$225$	−1.77222e12	−0.204887
$226$	1.25946e12	0.142098
$227$	−1.38605e13	−1.52629	−0.763145	−	0.646228i	$-0.776346\pi$
$227$	−1.38605e13	−1.52629	−0.763145	+	0.646228i	$0.776346\pi$
$228$	6.68216e11	0.0718249
$229$	5.84705e12	0.613538	0.306769	−	0.951784i	$-0.400752\pi$
$229$	5.84705e12	0.613538	0.306769	+	0.951784i	$0.400752\pi$
$230$	2.01222e12	0.206145
$231$	8.45861e12	0.846123
$232$	9.89110e12	0.966186
$233$	9.79197e12	0.934142	0.467071	−	0.884220i	$-0.345309\pi$
$233$	9.79197e12	0.934142	0.467071	+	0.884220i	$0.345309\pi$
$234$	7.03124e11	0.0655156
$235$	1.32706e13	1.20787
$236$	2.53758e11	0.0225634
$237$	−8.30286e12	−0.721293
$238$	−1.35174e13	−1.14741
$239$	1.78247e13	1.47855	0.739273	−	0.673406i	$-0.235170\pi$
$239$	1.78247e13	1.47855	0.739273	+	0.673406i	$0.235170\pi$
$240$	−3.52201e12	−0.285515
$241$	−1.59589e13	−1.26447	−0.632234	−	0.774777i	$-0.717862\pi$
$241$	−1.59589e13	−1.26447	−0.632234	+	0.774777i	$0.717862\pi$
$242$	3.22954e11	0.0250124
$243$	−8.47289e11	−0.0641500
$244$	1.83784e12	0.136039
$245$	−9.35122e12	−0.676791
$246$	−9.20857e12	−0.651702
$247$	2.24199e12	0.155167
$248$	−1.73489e13	−1.17432
$249$	2.76432e12	0.183017
$250$	1.40716e13	0.911325
$251$	−1.37229e13	−0.869444	−0.434722	−	0.900565i	$-0.643153\pi$
$251$	−1.37229e13	−0.869444	−0.434722	+	0.900565i	$0.643153\pi$
$252$	−1.34745e12	−0.0835237
$253$	6.10431e12	0.370232
$254$	2.64904e12	0.157219
$255$	−5.38615e12	−0.312829
$256$	−8.85623e12	−0.503418
$257$	3.00076e13	1.66955	0.834775	−	0.550591i	$-0.185598\pi$
$257$	3.00076e13	1.66955	0.834775	+	0.550591i	$0.185598\pi$
$258$	1.57746e13	0.859115
$259$	2.72567e12	0.145320
$260$	4.45554e11	0.0232566
$261$	−5.90715e12	−0.301894
$262$	−8.27508e12	−0.414109
$263$	4.69654e12	0.230155	0.115078	−	0.993356i	$-0.463288\pi$
$263$	4.69654e12	0.230155	0.115078	+	0.993356i	$0.463288\pi$
$264$	−1.30088e13	−0.624334
$265$	1.15745e13	0.544064
$266$	2.04940e13	0.943577
$267$	1.23218e13	0.555727
$268$	−6.80745e12	−0.300776
$269$	1.25814e13	0.544618	0.272309	−	0.962210i	$-0.412213\pi$
$269$	1.25814e13	0.544618	0.272309	+	0.962210i	$0.412213\pi$
$270$	2.56101e12	0.108620
$271$	−3.84736e13	−1.59894	−0.799469	−	0.600707i	$-0.794886\pi$
$271$	−3.84736e13	−1.59894	−0.799469	+	0.600707i	$0.794886\pi$
$272$	1.70743e13	0.695367
$273$	−4.52095e12	−0.180441
$274$	4.42099e13	1.72938
$275$	1.62502e13	0.623058
$276$	−9.72411e11	−0.0365469
$277$	3.08447e13	1.13643	0.568213	−	0.822881i	$-0.307635\pi$
$277$	3.08447e13	1.13643	0.568213	+	0.822881i	$0.307635\pi$
$278$	−2.99198e13	−1.08072
$279$	1.03611e13	0.366929
$280$	2.75725e13	0.957429
$281$	−8.58731e12	−0.292397	−0.146198	−	0.989255i	$-0.546704\pi$
$281$	−8.58731e12	−0.292397	−0.146198	+	0.989255i	$0.546704\pi$
$282$	3.05899e13	1.02143
$283$	−3.69092e13	−1.20868	−0.604338	−	0.796728i	$-0.706562\pi$
$283$	−3.69092e13	−1.20868	−0.604338	+	0.796728i	$0.706562\pi$
$284$	−4.16567e12	−0.133793
$285$	8.16607e12	0.257256
$286$	−6.44721e12	−0.199232
$287$	5.92094e13	1.79490
$288$	3.83849e12	0.114157
$289$	−8.16041e12	−0.238108
$290$	1.78549e13	0.511173
$291$	−3.35067e13	−0.941283
$292$	−6.31396e12	−0.174059
$293$	5.18707e13	1.40330	0.701649	−	0.712523i	$-0.252447\pi$
$293$	5.18707e13	1.40330	0.701649	+	0.712523i	$0.252447\pi$
$294$	−2.15553e13	−0.572326
$295$	3.10110e12	0.0808156
$296$	−4.19192e12	−0.107228
$297$	7.76911e12	0.195079
$298$	−2.91843e13	−0.719383
$299$	−3.26262e12	−0.0789543
$300$	−2.58864e12	−0.0615043
$301$	−1.01428e14	−2.36615
$302$	6.29597e13	1.44220
$303$	−2.37947e13	−0.535236
$304$	−2.58868e13	−0.571838
$305$	2.24598e13	0.487255
$306$	−1.24155e13	−0.264543
$307$	4.44715e13	0.930724	0.465362	−	0.885120i	$-0.345924\pi$
$307$	4.44715e13	0.930724	0.465362	+	0.885120i	$0.345924\pi$
$308$	1.23553e13	0.253994
$309$	−2.98825e13	−0.603456
$310$	−3.13173e13	−0.621291
$311$	1.94368e13	0.378828	0.189414	−	0.981897i	$-0.439341\pi$
$311$	1.94368e13	0.378828	0.189414	+	0.981897i	$0.439341\pi$
$312$	6.95295e12	0.133143
$313$	−2.32955e13	−0.438307	−0.219153	−	0.975690i	$-0.570329\pi$
$313$	−2.32955e13	−0.438307	−0.219153	+	0.975690i	$0.570329\pi$
$314$	2.65475e13	0.490807
$315$	−1.64668e13	−0.299158
$316$	−1.21278e13	−0.216522
$317$	−1.33535e13	−0.234298	−0.117149	−	0.993114i	$-0.537376\pi$
$317$	−1.33535e13	−0.234298	−0.117149	+	0.993114i	$0.537376\pi$
$318$	2.66801e13	0.460086
$319$	5.41649e13	0.918056
$320$	−4.12856e13	−0.687818
$321$	−6.98537e13	−1.14396
$322$	−2.98236e13	−0.480123
$323$	−3.95882e13	−0.626545
$324$	−1.23761e12	−0.0192570
$325$	−8.68539e12	−0.132871
$326$	−9.39630e13	−1.41338
$327$	−6.86694e13	−1.01566
$328$	−9.10604e13	−1.32441
$329$	−1.96687e14	−2.81319
$330$	−2.34829e13	−0.330312
$331$	9.72625e13	1.34552	0.672762	−	0.739859i	$-0.265108\pi$
$331$	9.72625e13	1.34552	0.672762	+	0.739859i	$0.265108\pi$
$332$	4.03778e12	0.0549393
$333$	2.50349e12	0.0335045
$334$	−7.28634e13	−0.959188
$335$	−8.31918e13	−1.07729
$336$	5.22004e13	0.664979
$337$	−2.39917e12	−0.0300674	−0.0150337	−	0.999887i	$-0.504786\pi$
$337$	−2.39917e12	−0.0300674	−0.0150337	+	0.999887i	$0.504786\pi$
$338$	−7.02957e13	−0.866736
$339$	−7.43796e12	−0.0902309
$340$	−7.86742e12	−0.0939071
$341$	−9.50046e13	−1.11582
$342$	1.88234e13	0.217548
$343$	1.14750e13	0.130507
$344$	1.55990e14	1.74592
$345$	−1.18836e13	−0.130900
$346$	−4.12352e12	−0.0447043
$347$	−1.29189e14	−1.37852	−0.689261	−	0.724513i	$-0.742065\pi$
$347$	−1.29189e14	−1.37852	−0.689261	+	0.724513i	$0.742065\pi$
$348$	−8.62843e12	−0.0906246
$349$	6.60836e13	0.683210	0.341605	−	0.939844i	$-0.389030\pi$
$349$	6.60836e13	0.683210	0.341605	+	0.939844i	$0.389030\pi$
$350$	−7.93929e13	−0.807993
$351$	−4.15243e12	−0.0416019
$352$	−3.51966e13	−0.347149
$353$	9.77591e13	0.949285	0.474642	−	0.880179i	$-0.342577\pi$
$353$	9.77591e13	0.949285	0.474642	+	0.880179i	$0.342577\pi$
$354$	7.14829e12	0.0683414
$355$	−5.09074e13	−0.479209
$356$	1.79981e13	0.166822
$357$	7.98293e13	0.728596
$358$	−7.81499e12	−0.0702379
$359$	1.93981e14	1.71688	0.858441	−	0.512913i	$-0.171434\pi$
$359$	1.93981e14	1.71688	0.858441	+	0.512913i	$0.171434\pi$
$360$	2.53249e13	0.220742
$361$	−5.64696e13	−0.484758
$362$	−1.38695e14	−1.17264
$363$	−1.90727e12	−0.0158827
$364$	−6.60365e12	−0.0541660
$365$	−7.71611e13	−0.623430
$366$	5.17715e13	0.412045
$367$	−8.64895e13	−0.678110	−0.339055	−	0.940767i	$-0.610107\pi$
$367$	−8.64895e13	−0.678110	−0.339055	+	0.940767i	$0.610107\pi$
$368$	3.76713e13	0.290970
$369$	5.43830e13	0.413826
$370$	−7.56703e12	−0.0567304
$371$	−1.71548e14	−1.26716
$372$	1.51342e13	0.110147
$373$	−2.14662e14	−1.53942	−0.769708	−	0.638396i	$-0.779598\pi$
$373$	−2.14662e14	−1.53942	−0.769708	+	0.638396i	$0.779598\pi$
$374$	1.13842e14	0.804471
$375$	−8.31025e13	−0.578685
$376$	3.02493e14	2.07578
$377$	−2.89500e13	−0.195781
$378$	−3.79572e13	−0.252982
$379$	1.65130e14	1.08470	0.542352	−	0.840151i	$-0.317534\pi$
$379$	1.65130e14	1.08470	0.542352	+	0.840151i	$0.317534\pi$
$380$	1.19280e13	0.0772249
$381$	−1.56444e13	−0.0998326
$382$	2.32707e13	0.146373
$383$	−6.64821e13	−0.412203	−0.206102	−	0.978531i	$-0.566078\pi$
$383$	−6.64821e13	−0.412203	−0.206102	+	0.978531i	$0.566078\pi$
$384$	−6.28158e13	−0.383926
$385$	1.50990e14	0.909736
$386$	7.00745e13	0.416227
$387$	−9.31601e13	−0.545531
$388$	−4.89424e13	−0.282560
$389$	−1.50018e14	−0.853927	−0.426964	−	0.904269i	$-0.640417\pi$
$389$	−1.50018e14	−0.853927	−0.426964	+	0.904269i	$0.640417\pi$
$390$	1.25511e13	0.0704412
$391$	5.76102e13	0.318806
$392$	−2.13153e14	−1.16310
$393$	4.88701e13	0.262956
$394$	1.90006e14	1.00818
$395$	−1.48210e14	−0.775521
$396$	1.13482e13	0.0585601
$397$	−1.82934e14	−0.930994	−0.465497	−	0.885050i	$-0.654124\pi$
$397$	−1.82934e14	−0.930994	−0.465497	+	0.885050i	$0.654124\pi$
$398$	2.27129e14	1.14003
$399$	−1.21031e14	−0.599164
$400$	1.00284e14	0.489670
$401$	2.93556e14	1.41383	0.706914	−	0.707299i	$-0.250087\pi$
$401$	2.93556e14	1.41383	0.706914	+	0.707299i	$0.250087\pi$
$402$	−1.91763e14	−0.911009
$403$	5.07780e13	0.237957
$404$	−3.47563e13	−0.160670
$405$	−1.51245e13	−0.0689730
$406$	−2.64631e14	−1.19055
$407$	−2.29555e13	−0.101887
$408$	−1.22773e14	−0.537614
$409$	2.59552e13	0.112136	0.0560682	−	0.998427i	$-0.482144\pi$
$409$	2.59552e13	0.112136	0.0560682	+	0.998427i	$0.482144\pi$
$410$	−1.64378e14	−0.700699
$411$	−2.61090e14	−1.09815
$412$	−4.36487e13	−0.181149
$413$	−4.59621e13	−0.188224
$414$	−2.73925e13	−0.110695
$415$	4.93445e13	0.196777
$416$	1.88119e13	0.0740318
$417$	1.76697e14	0.686247
$418$	−1.72599e14	−0.661560
$419$	1.79032e14	0.677257	0.338629	−	0.940920i	$-0.390037\pi$
$419$	1.79032e14	0.677257	0.338629	+	0.940920i	$0.390037\pi$
$420$	−2.40527e13	−0.0898032
$421$	−2.82305e14	−1.04032	−0.520160	−	0.854069i	$-0.674128\pi$
$421$	−2.82305e14	−1.04032	−0.520160	+	0.854069i	$0.674128\pi$
$422$	5.81035e13	0.211341
$423$	−1.80654e14	−0.648599
$424$	2.63831e14	0.935004
$425$	1.53363e14	0.536516
$426$	−1.17346e14	−0.405241
$427$	−3.32881e14	−1.13484
$428$	−1.02034e14	−0.343402
$429$	3.80752e13	0.126511
$430$	2.81585e14	0.923705
$431$	−1.29967e14	−0.420929	−0.210464	−	0.977602i	$-0.567498\pi$
$431$	−1.29967e14	−0.420929	−0.210464	+	0.977602i	$0.567498\pi$
$432$	4.79453e13	0.153315
$433$	4.10611e14	1.29642	0.648212	−	0.761460i	$-0.275517\pi$
$433$	4.10611e14	1.29642	0.648212	+	0.761460i	$0.275517\pi$
$434$	4.64160e14	1.44702
$435$	−1.05445e14	−0.324591
$436$	−1.00304e14	−0.304889
$437$	−8.73442e13	−0.262172
$438$	−1.77862e14	−0.527201
$439$	7.71968e13	0.225967	0.112983	−	0.993597i	$-0.463959\pi$
$439$	7.71968e13	0.225967	0.112983	+	0.993597i	$0.463959\pi$
$440$	−2.32214e14	−0.671272
$441$	1.27299e14	0.363423
$442$	−6.08464e13	−0.171559
$443$	−2.80872e14	−0.782147	−0.391073	−	0.920359i	$-0.627896\pi$
$443$	−2.80872e14	−0.782147	−0.391073	+	0.920359i	$0.627896\pi$
$444$	3.65679e12	0.0100576
$445$	2.19950e14	0.597508
$446$	3.53860e13	0.0949490
$447$	1.72354e14	0.456803
$448$	6.11903e14	1.60197
$449$	−6.51039e14	−1.68365	−0.841825	−	0.539750i	$-0.818519\pi$
$449$	−6.51039e14	−1.68365	−0.841825	+	0.539750i	$0.818519\pi$
$450$	−7.29212e13	−0.186288
$451$	−4.98658e14	−1.25844
$452$	−1.08644e13	−0.0270861
$453$	−3.71820e14	−0.915784
$454$	−5.70315e14	−1.38774
$455$	−8.07012e13	−0.194007
$456$	1.86138e14	0.442109
$457$	1.31023e14	0.307474	0.153737	−	0.988112i	$-0.450869\pi$
$457$	1.31023e14	0.307474	0.153737	+	0.988112i	$0.450869\pi$
$458$	2.40587e14	0.557844
$459$	7.33220e13	0.167983
$460$	−1.73580e13	−0.0392945
$461$	4.27698e14	0.956713	0.478357	−	0.878166i	$-0.341233\pi$
$461$	4.27698e14	0.956713	0.478357	+	0.878166i	$0.341233\pi$
$462$	3.48045e14	0.769315
$463$	−2.53709e13	−0.0554167	−0.0277084	−	0.999616i	$-0.508821\pi$
$463$	−2.53709e13	−0.0554167	−0.0277084	+	0.999616i	$0.508821\pi$
$464$	3.34266e14	0.721513
$465$	1.84950e14	0.394515
$466$	4.02908e14	0.849344
$467$	5.75188e14	1.19830	0.599152	−	0.800635i	$-0.295504\pi$
$467$	5.75188e14	1.19830	0.599152	+	0.800635i	$0.295504\pi$
$468$	−6.06536e12	−0.0124883
$469$	1.23300e15	2.50907
$470$	5.46044e14	1.09822
$471$	−1.56781e14	−0.311659
$472$	7.06870e13	0.138886
$473$	8.54221e14	1.65895
$474$	−3.41636e14	−0.655817
$475$	−2.32518e14	−0.441206
$476$	1.16605e14	0.218715
$477$	−1.57565e14	−0.292151
$478$	7.33430e14	1.34433
$479$	−5.96075e14	−1.08008	−0.540039	−	0.841640i	$-0.681591\pi$
$479$	−5.96075e14	−1.08008	−0.540039	+	0.841640i	$0.681591\pi$
$480$	6.85189e13	0.122739
$481$	1.22692e13	0.0217280
$482$	−6.56655e14	−1.14968
$483$	1.76129e14	0.304874
$484$	−2.78590e12	−0.00476777
$485$	−5.98111e14	−1.01205
$486$	−3.48632e13	−0.0583267
$487$	2.82223e14	0.466857	0.233428	−	0.972374i	$-0.425006\pi$
$487$	2.82223e14	0.466857	0.233428	+	0.972374i	$0.425006\pi$
$488$	5.11950e14	0.837373
$489$	5.54916e14	0.897488
$490$	−3.84772e14	−0.615354
$491$	−1.58749e14	−0.251051	−0.125526	−	0.992090i	$-0.540062\pi$
$491$	−1.58749e14	−0.251051	−0.125526	+	0.992090i	$0.540062\pi$
$492$	7.94359e13	0.124225
$493$	5.11188e14	0.790538
$494$	9.22507e13	0.141082
$495$	1.38683e14	0.209746
$496$	−5.86300e14	−0.876941
$497$	7.54510e14	1.11610
$498$	1.13743e14	0.166404
$499$	6.43076e14	0.930484	0.465242	−	0.885183i	$-0.345967\pi$
$499$	6.43076e14	0.930484	0.465242	+	0.885183i	$0.345967\pi$
$500$	−1.21386e14	−0.173713
$501$	4.30309e14	0.609077
$502$	−5.64654e14	−0.790519
$503$	−9.67165e14	−1.33930	−0.669648	−	0.742679i	$-0.733555\pi$
$503$	−9.67165e14	−1.33930	−0.669648	+	0.742679i	$0.733555\pi$
$504$	−3.75346e14	−0.514120
$505$	−4.24746e14	−0.575476
$506$	2.51172e14	0.336623
$507$	4.15145e14	0.550371
$508$	−2.28515e13	−0.0299684
$509$	5.42613e14	0.703951	0.351975	−	0.936009i	$-0.385510\pi$
$509$	5.42613e14	0.703951	0.351975	+	0.936009i	$0.385510\pi$
$510$	−2.21623e14	−0.284432
$511$	1.14362e15	1.45200
$512$	−8.93815e14	−1.12270
$513$	−1.11165e14	−0.138141
$514$	1.23472e15	1.51799
$515$	−5.33418e14	−0.648826
$516$	−1.36077e14	−0.163761
$517$	1.65649e15	1.97238
$518$	1.12153e14	0.132128
$519$	2.43522e13	0.0283869
$520$	1.24114e14	0.143153
$521$	−6.72659e14	−0.767693	−0.383846	−	0.923397i	$-0.625401\pi$
$521$	−6.72659e14	−0.767693	−0.383846	+	0.923397i	$0.625401\pi$
$522$	−2.43060e14	−0.274489
$523$	1.57267e15	1.75743	0.878717	−	0.477343i	$-0.158400\pi$
$523$	1.57267e15	1.75743	0.878717	+	0.477343i	$0.158400\pi$
$524$	7.13833e13	0.0789359
$525$	4.68870e14	0.513069
$526$	1.93247e14	0.209263
$527$	−8.96619e14	−0.960836
$528$	−4.39629e14	−0.466230
$529$	−8.25703e14	−0.866598
$530$	4.76253e14	0.494676
$531$	−4.22156e13	−0.0433963
$532$	−1.76787e14	−0.179861
$533$	2.66523e14	0.268370
$534$	5.07001e14	0.505280
$535$	−1.24692e15	−1.22997
$536$	−1.89628e15	−1.85139
$537$	4.61529e13	0.0446006
$538$	5.17684e14	0.495179
$539$	−1.16725e15	−1.10516
$540$	−2.20920e13	−0.0207047
$541$	1.82845e15	1.69628	0.848141	−	0.529770i	$-0.177722\pi$
$541$	1.82845e15	1.69628	0.848141	+	0.529770i	$0.177722\pi$
$542$	−1.58306e15	−1.45379
$543$	8.19091e14	0.744618
$544$	−3.32173e14	−0.298930
$545$	−1.22578e15	−1.09202
$546$	−1.86023e14	−0.164061
$547$	−1.38114e15	−1.20589	−0.602946	−	0.797782i	$-0.706007\pi$
$547$	−1.38114e15	−1.20589	−0.602946	+	0.797782i	$0.706007\pi$
$548$	−3.81368e14	−0.329649
$549$	−3.05746e14	−0.261646
$550$	6.68643e14	0.566499
$551$	−7.75025e14	−0.650102
$552$	−2.70875e14	−0.224959
$553$	2.19665e15	1.80623
$554$	1.26916e15	1.03327
$555$	4.46885e13	0.0360234
$556$	2.58097e14	0.206002
$557$	6.87300e13	0.0543179	0.0271589	−	0.999631i	$-0.491354\pi$
$557$	6.87300e13	0.0543179	0.0271589	+	0.999631i	$0.491354\pi$
$558$	4.26324e14	0.333620
$559$	−4.56563e14	−0.353782
$560$	9.31803e14	0.714974
$561$	−6.72318e14	−0.510833
$562$	−3.53340e14	−0.265854
$563$	−4.13813e14	−0.308324	−0.154162	−	0.988046i	$-0.549268\pi$
$563$	−4.13813e14	−0.308324	−0.154162	+	0.988046i	$0.549268\pi$
$564$	−2.63877e14	−0.194700
$565$	−1.32771e14	−0.0970146
$566$	−1.51870e15	−1.09896
$567$	2.24164e14	0.160642
$568$	−1.16039e15	−0.823547
$569$	1.44956e15	1.01887	0.509433	−	0.860510i	$-0.329855\pi$
$569$	1.44956e15	1.01887	0.509433	+	0.860510i	$0.329855\pi$
$570$	3.36007e14	0.233904
$571$	1.93283e14	0.133258	0.0666291	−	0.997778i	$-0.478776\pi$
$571$	1.93283e14	0.133258	0.0666291	+	0.997778i	$0.478776\pi$
$572$	5.56156e13	0.0379768
$573$	−1.37430e14	−0.0929458
$574$	2.43627e15	1.63196
$575$	3.38368e14	0.224500
$576$	5.62024e14	0.369344
$577$	1.92752e15	1.25468	0.627339	−	0.778746i	$-0.284144\pi$
$577$	1.92752e15	1.25468	0.627339	+	0.778746i	$0.284144\pi$
$578$	−3.35775e14	−0.216493
$579$	−4.13838e14	−0.264301
$580$	−1.54022e14	−0.0974379
$581$	−7.31346e14	−0.458304
$582$	−1.37869e15	−0.855836
$583$	1.44477e15	0.888427
$584$	−1.75882e15	−1.07140
$585$	−7.41229e13	−0.0447296
$586$	2.13431e15	1.27591
$587$	2.27708e15	1.34856	0.674278	−	0.738478i	$-0.264455\pi$
$587$	2.27708e15	1.34856	0.674278	+	0.738478i	$0.264455\pi$
$588$	1.85942e14	0.109095
$589$	1.35938e15	0.790148
$590$	1.27600e14	0.0734795
$591$	−1.12211e15	−0.640186
$592$	−1.41664e14	−0.0800740
$593$	9.08968e14	0.509035	0.254518	−	0.967068i	$-0.418083\pi$
$593$	9.08968e14	0.509035	0.254518	+	0.967068i	$0.418083\pi$
$594$	3.19674e14	0.177371
$595$	1.42499e15	0.783374
$596$	2.51753e14	0.137126
$597$	−1.34135e15	−0.723910
$598$	−1.34246e14	−0.0717871
$599$	3.31252e15	1.75514	0.877569	−	0.479450i	$-0.159164\pi$
$599$	3.31252e15	1.75514	0.877569	+	0.479450i	$0.159164\pi$
$600$	−7.21093e14	−0.378582
$601$	−4.32128e14	−0.224803	−0.112402	−	0.993663i	$-0.535854\pi$
$601$	−4.32128e14	−0.224803	−0.112402	+	0.993663i	$0.535854\pi$
$602$	−4.17343e15	−2.15136
$603$	1.13250e15	0.578484
$604$	−5.43109e14	−0.274906
$605$	−3.40456e13	−0.0170768
$606$	−9.79073e14	−0.486649
$607$	−1.58856e15	−0.782464	−0.391232	−	0.920292i	$-0.627951\pi$
$607$	−1.58856e15	−0.782464	−0.391232	+	0.920292i	$0.627951\pi$
$608$	5.03615e14	0.245826
$609$	1.56283e15	0.755991
$610$	9.24146e14	0.443023
$611$	−8.85359e14	−0.420623
$612$	1.07100e14	0.0504261
$613$	1.44900e15	0.676138	0.338069	−	0.941121i	$-0.390226\pi$
$613$	1.44900e15	0.676138	0.338069	+	0.941121i	$0.390226\pi$
$614$	1.82986e15	0.846236
$615$	9.70763e14	0.444938
$616$	3.44169e15	1.56343
$617$	7.43149e14	0.334586	0.167293	−	0.985907i	$-0.446497\pi$
$617$	7.43149e14	0.334586	0.167293	+	0.985907i	$0.446497\pi$
$618$	−1.22957e15	−0.548677
$619$	2.27293e15	1.00528	0.502641	−	0.864495i	$-0.332362\pi$
$619$	2.27293e15	1.00528	0.502641	+	0.864495i	$0.332362\pi$
$620$	2.70152e14	0.118428
$621$	1.61772e14	0.0702908
$622$	7.99761e14	0.344440
$623$	−3.25992e15	−1.39163
$624$	2.34973e14	0.0994265
$625$	−1.79540e13	−0.00753046
$626$	−9.58534e14	−0.398519
$627$	1.01932e15	0.420086
$628$	−2.29007e14	−0.0935557
$629$	−2.16645e14	−0.0877345
$630$	−6.77555e14	−0.272002
$631$	−3.65257e15	−1.45357	−0.726786	−	0.686864i	$-0.758987\pi$
$631$	−3.65257e15	−1.45357	−0.726786	+	0.686864i	$0.758987\pi$
$632$	−3.37832e15	−1.33277
$633$	−3.43141e14	−0.134200
$634$	−5.49454e14	−0.213030
$635$	−2.79261e14	−0.107338
$636$	−2.30151e14	−0.0876998
$637$	6.23872e14	0.235683
$638$	2.22871e15	0.834718
$639$	6.93007e14	0.257325
$640$	−1.12129e15	−0.412790
$641$	−4.59570e15	−1.67738	−0.838691	−	0.544607i	$-0.816679\pi$
$641$	−4.59570e15	−1.67738	−0.838691	+	0.544607i	$0.816679\pi$
$642$	−2.87426e15	−1.04012
$643$	1.49893e15	0.537801	0.268900	−	0.963168i	$-0.413340\pi$
$643$	1.49893e15	0.537801	0.268900	+	0.963168i	$0.413340\pi$
$644$	2.57267e14	0.0915191
$645$	−1.66295e15	−0.586546
$646$	−1.62893e15	−0.569669
$647$	−1.85166e15	−0.642077	−0.321039	−	0.947066i	$-0.604032\pi$
$647$	−1.85166e15	−0.642077	−0.321039	+	0.947066i	$0.604032\pi$
$648$	−3.44750e14	−0.118534
$649$	3.87091e14	0.131967
$650$	−3.57376e14	−0.120810
$651$	−2.74119e15	−0.918847
$652$	8.10553e14	0.269414
$653$	4.48071e15	1.47681	0.738404	−	0.674358i	$-0.235580\pi$
$653$	4.48071e15	1.47681	0.738404	+	0.674358i	$0.235580\pi$
$654$	−2.82552e15	−0.923466
$655$	8.72355e14	0.282726
$656$	−3.07736e15	−0.989024
$657$	1.05040e15	0.334769
$658$	−8.09304e15	−2.55781
$659$	−2.57359e15	−0.806623	−0.403311	−	0.915063i	$-0.632141\pi$
$659$	−2.57359e15	−0.806623	−0.403311	+	0.915063i	$0.632141\pi$
$660$	2.02570e14	0.0629628
$661$	2.69950e15	0.832100	0.416050	−	0.909342i	$-0.363414\pi$
$661$	2.69950e15	0.832100	0.416050	+	0.909342i	$0.363414\pi$
$662$	4.00204e15	1.22338
$663$	3.59340e14	0.108938
$664$	1.12477e15	0.338172
$665$	−2.16046e15	−0.644211
$666$	1.03011e14	0.0304630
$667$	1.12784e15	0.330793
$668$	6.28541e14	0.182837
$669$	−2.08979e14	−0.0602919
$670$	−3.42307e15	−0.979500
$671$	2.80351e15	0.795660
$672$	−1.01553e15	−0.285867
$673$	−4.85570e15	−1.35572	−0.677858	−	0.735193i	$-0.737091\pi$
$673$	−4.85570e15	−1.35572	−0.677858	+	0.735193i	$0.737091\pi$
$674$	−9.87179e13	−0.0273380
$675$	4.30650e14	0.118292
$676$	6.06392e14	0.165214
$677$	−2.83566e15	−0.766332	−0.383166	−	0.923680i	$-0.625166\pi$
$677$	−2.83566e15	−0.766332	−0.383166	+	0.923680i	$0.625166\pi$
$678$	−3.06048e14	−0.0820400
$679$	8.86473e15	2.35712
$680$	−2.19155e15	−0.578033
$681$	3.36810e15	0.881204
$682$	−3.90913e15	−1.01453
$683$	−4.40038e15	−1.13286	−0.566430	−	0.824110i	$-0.691676\pi$
$683$	−4.40038e15	−1.13286	−0.566430	+	0.824110i	$0.691676\pi$
$684$	−1.62376e14	−0.0414681
$685$	−4.66059e15	−1.18071
$686$	4.72159e14	0.118660
$687$	−1.42083e15	−0.354227
$688$	5.27163e15	1.30379
$689$	−7.72200e14	−0.189463
$690$	−4.88970e14	−0.119018
$691$	2.97282e15	0.717859	0.358930	−	0.933365i	$-0.383142\pi$
$691$	2.97282e15	0.717859	0.358930	+	0.933365i	$0.383142\pi$
$692$	3.55707e13	0.00852137
$693$	−2.05544e15	−0.488509
$694$	−5.31571e15	−1.25338
$695$	3.15413e15	0.737840
$696$	−2.40354e15	−0.557828
$697$	−4.70615e15	−1.08364
$698$	2.71913e15	0.621190
$699$	−2.37945e15	−0.539327
$700$	6.84867e14	0.154016
$701$	6.40626e15	1.42940	0.714702	−	0.699429i	$-0.246562\pi$
$701$	6.40626e15	1.42940	0.714702	+	0.699429i	$0.246562\pi$
$702$	−1.70859e14	−0.0378254
$703$	3.28461e14	0.0721489
$704$	−5.15341e15	−1.12317
$705$	−3.22477e15	−0.697362
$706$	4.02247e15	0.863112
$707$	6.29525e15	1.34031
$708$	−6.16633e13	−0.0130270
$709$	−4.50543e15	−0.944457	−0.472228	−	0.881476i	$-0.656550\pi$
$709$	−4.50543e15	−0.944457	−0.472228	+	0.881476i	$0.656550\pi$
$710$	−2.09468e15	−0.435708
$711$	2.01759e15	0.416439
$712$	5.01356e15	1.02685
$713$	−1.97822e15	−0.402053
$714$	3.28472e15	0.662457
$715$	6.79662e14	0.136022
$716$	6.74144e13	0.0133885
$717$	−4.33141e15	−0.853638
$718$	7.98170e15	1.56103
$719$	2.98746e15	0.579821	0.289910	−	0.957054i	$-0.406374\pi$
$719$	2.98746e15	0.579821	0.289910	+	0.957054i	$0.406374\pi$
$720$	8.55848e14	0.164842
$721$	7.90590e15	1.51115
$722$	−2.32354e15	−0.440754
$723$	3.87800e15	0.730041
$724$	1.19643e15	0.223524
$725$	3.00242e15	0.556688
$726$	−7.84778e13	−0.0144409
$727$	−1.50136e15	−0.274185	−0.137093	−	0.990558i	$-0.543776\pi$
$727$	−1.50136e15	−0.274185	−0.137093	+	0.990558i	$0.543776\pi$
$728$	−1.83951e15	−0.333411
$729$	2.05891e14	0.0370370
$730$	−3.17493e15	−0.566837
$731$	8.06182e15	1.42852
$732$	−4.46596e14	−0.0785424
$733$	2.64632e15	0.461923	0.230962	−	0.972963i	$-0.425813\pi$
$733$	2.64632e15	0.461923	0.230962	+	0.972963i	$0.425813\pi$
$734$	−3.55876e15	−0.616553
$735$	2.27235e15	0.390746
$736$	−7.32878e14	−0.125085
$737$	−1.03843e16	−1.75916
$738$	2.23768e15	0.376260
$739$	−1.18888e16	−1.98423	−0.992117	−	0.125313i	$-0.960006\pi$
$739$	−1.18888e16	−1.98423	−0.992117	+	0.125313i	$0.960006\pi$
$740$	6.52755e13	0.0108137
$741$	−5.44804e14	−0.0895860
$742$	−7.05866e15	−1.15213
$743$	−8.52748e15	−1.38160	−0.690800	−	0.723046i	$-0.742741\pi$
$743$	−8.52748e15	−1.38160	−0.690800	+	0.723046i	$0.742741\pi$
$744$	4.21578e15	0.677995
$745$	3.07659e15	0.491146
$746$	−8.83263e15	−1.39967
$747$	−6.71730e14	−0.105665
$748$	−9.82039e14	−0.153345
$749$	1.84809e16	2.86466
$750$	−3.41940e15	−0.526154
$751$	−5.33920e15	−0.815561	−0.407781	−	0.913080i	$-0.633697\pi$
$751$	−5.33920e15	−0.815561	−0.407781	+	0.913080i	$0.633697\pi$
$752$	1.02226e16	1.55012
$753$	3.33467e15	0.501974
$754$	−1.19120e15	−0.178009
$755$	−6.63717e15	−0.984634
$756$	3.27431e14	0.0482225
$757$	−9.52636e15	−1.39283	−0.696417	−	0.717637i	$-0.745224\pi$
$757$	−9.52636e15	−1.39283	−0.696417	+	0.717637i	$0.745224\pi$
$758$	6.79458e15	0.986238
$759$	−1.48335e15	−0.213753
$760$	3.32266e15	0.475348
$761$	2.96485e15	0.421102	0.210551	−	0.977583i	$-0.432474\pi$
$761$	2.96485e15	0.421102	0.210551	+	0.977583i	$0.432474\pi$
$762$	−6.43718e14	−0.0907702
$763$	1.81676e16	2.54338
$764$	−2.00740e14	−0.0279010
$765$	1.30883e15	0.180612
$766$	−2.73552e15	−0.374785
$767$	−2.06892e14	−0.0281429
$768$	2.15206e15	0.290649
$769$	9.49392e15	1.27307	0.636533	−	0.771250i	$-0.280368\pi$
$769$	9.49392e15	1.27307	0.636533	+	0.771250i	$0.280368\pi$
$770$	6.21277e15	0.827153
$771$	−7.29185e15	−0.963915
$772$	−6.04484e14	−0.0793395
$773$	−2.48526e15	−0.323880	−0.161940	−	0.986801i	$-0.551775\pi$
$773$	−2.48526e15	−0.323880	−0.161940	+	0.986801i	$0.551775\pi$
$774$	−3.83324e15	−0.496010
$775$	−5.26621e15	−0.676610
$776$	−1.36334e16	−1.73926
$777$	−6.62338e14	−0.0839004
$778$	−6.17276e15	−0.776411
$779$	7.13511e15	0.891137
$780$	−1.08270e14	−0.0134272
$781$	−6.35444e15	−0.782522
$782$	2.37047e15	0.289866
$783$	1.43544e15	0.174299
$784$	−7.20343e15	−0.868562
$785$	−2.79862e15	−0.335090
$786$	2.01084e15	0.239086
$787$	6.76231e15	0.798425	0.399212	−	0.916859i	$-0.369284\pi$
$787$	6.76231e15	0.798425	0.399212	+	0.916859i	$0.369284\pi$
$788$	−1.63905e15	−0.192175
$789$	−1.14126e15	−0.132880
$790$	−6.09837e15	−0.705122
$791$	1.96783e15	0.225952
$792$	3.16115e15	0.360459
$793$	−1.49842e15	−0.169680
$794$	−7.52714e15	−0.846481
$795$	−2.81261e15	−0.314116
$796$	−1.95928e15	−0.217308
$797$	−7.96991e15	−0.877875	−0.438937	−	0.898518i	$-0.644645\pi$
$797$	−7.96991e15	−0.877875	−0.438937	+	0.898518i	$0.644645\pi$
$798$	−4.98004e15	−0.544774
$799$	1.56333e16	1.69842
$800$	−1.95098e15	−0.210503
$801$	−2.99419e15	−0.320849
$802$	1.20789e16	1.28549
$803$	−9.63152e15	−1.01803
$804$	1.65421e15	0.173653
$805$	3.14398e15	0.327795
$806$	2.08935e15	0.216356
$807$	−3.05728e15	−0.314435
$808$	−9.68172e15	−0.988986
$809$	1.52337e16	1.54557	0.772787	−	0.634665i	$-0.218862\pi$
$809$	1.52337e16	1.54557	0.772787	+	0.634665i	$0.218862\pi$
$810$	−6.22325e14	−0.0627118
$811$	6.78720e15	0.679323	0.339661	−	0.940548i	$-0.389688\pi$
$811$	6.78720e15	0.679323	0.339661	+	0.940548i	$0.389688\pi$
$812$	2.28279e15	0.226938
$813$	9.34908e15	0.923148
$814$	−9.44543e14	−0.0926376
$815$	9.90553e15	0.964963
$816$	−4.14906e15	−0.401471
$817$	−1.22227e16	−1.17475
$818$	1.06797e15	0.101957
$819$	1.09859e15	0.104178
$820$	1.41797e15	0.133564
$821$	9.39770e15	0.879294	0.439647	−	0.898171i	$-0.355104\pi$
$821$	9.39770e15	0.879294	0.439647	+	0.898171i	$0.355104\pi$
$822$	−1.07430e16	−0.998461
$823$	−5.61268e15	−0.518169	−0.259084	−	0.965855i	$-0.583421\pi$
$823$	−5.61268e15	−0.518169	−0.259084	+	0.965855i	$0.583421\pi$
$824$	−1.21588e16	−1.11504
$825$	−3.94880e15	−0.359723
$826$	−1.89119e15	−0.171138
$827$	2.83293e15	0.254657	0.127328	−	0.991861i	$-0.459360\pi$
$827$	2.83293e15	0.254657	0.127328	+	0.991861i	$0.459360\pi$
$828$	2.36296e14	0.0211003
$829$	−7.31651e15	−0.649014	−0.324507	−	0.945883i	$-0.605198\pi$
$829$	−7.31651e15	−0.649014	−0.324507	+	0.945883i	$0.605198\pi$
$830$	2.03037e15	0.178914
$831$	−7.49525e15	−0.656116
$832$	2.75439e15	0.239523
$833$	−1.10161e16	−0.951656
$834$	7.27050e15	0.623952
$835$	7.68122e15	0.654869
$836$	1.48889e15	0.126104
$837$	−2.51774e15	−0.211846
$838$	7.36659e15	0.615778
$839$	−1.05461e15	−0.0875793	−0.0437896	−	0.999041i	$-0.513943\pi$
$839$	−1.05461e15	−0.0875793	−0.0437896	+	0.999041i	$0.513943\pi$
$840$	−6.70011e15	−0.552772
$841$	−2.19290e15	−0.179738
$842$	−1.16159e16	−0.945883
$843$	2.08672e15	0.168815
$844$	−5.01218e14	−0.0402850
$845$	7.41053e15	0.591749
$846$	−7.43334e15	−0.589721
$847$	5.04597e14	0.0397728
$848$	8.91607e15	0.698227
$849$	8.96894e15	0.697829
$850$	6.31040e15	0.487813
$851$	−4.77988e14	−0.0367117
$852$	1.01226e15	0.0772455
$853$	6.21804e15	0.471448	0.235724	−	0.971820i	$-0.424254\pi$
$853$	6.21804e15	0.471448	0.235724	+	0.971820i	$0.424254\pi$
$854$	−1.36970e16	−1.03183
$855$	−1.98435e15	−0.148527
$856$	−2.84225e16	−2.11377
$857$	−1.23315e16	−0.911213	−0.455606	−	0.890181i	$-0.650578\pi$
$857$	−1.23315e16	−0.911213	−0.455606	+	0.890181i	$0.650578\pi$
$858$	1.56667e15	0.115027
$859$	−5.58613e15	−0.407520	−0.203760	−	0.979021i	$-0.565316\pi$
$859$	−5.58613e15	−0.407520	−0.203760	+	0.979021i	$0.565316\pi$
$860$	−2.42904e15	−0.176073
$861$	−1.43879e16	−1.03629
$862$	−5.34773e15	−0.382718
$863$	1.14764e16	0.816106	0.408053	−	0.912958i	$-0.366208\pi$
$863$	1.14764e16	0.816106	0.408053	+	0.912958i	$0.366208\pi$
$864$	−9.32753e14	−0.0659085
$865$	4.34699e14	0.0305211
$866$	1.68953e16	1.17874
$867$	1.98298e15	0.137472
$868$	−4.00399e15	−0.275825
$869$	−1.85001e16	−1.26638
$870$	−4.33874e15	−0.295126
$871$	5.55019e15	0.375152
$872$	−2.79406e16	−1.87670
$873$	8.14213e15	0.543450
$874$	−3.59393e15	−0.238373
$875$	2.19861e16	1.44912
$876$	1.53429e15	0.100493
$877$	8.06301e15	0.524807	0.262403	−	0.964958i	$-0.415485\pi$
$877$	8.06301e15	0.524807	0.262403	+	0.964958i	$0.415485\pi$
$878$	3.17640e15	0.205454
$879$	−1.26046e16	−0.810195
$880$	−7.84760e15	−0.501282
$881$	2.43541e16	1.54598	0.772991	−	0.634417i	$-0.218760\pi$
$881$	2.43541e16	1.54598	0.772991	+	0.634417i	$0.218760\pi$
$882$	5.23793e15	0.330432
$883$	2.72747e16	1.70992	0.854960	−	0.518694i	$-0.173581\pi$
$883$	2.72747e16	1.70992	0.854960	+	0.518694i	$0.173581\pi$
$884$	5.24879e14	0.0327018
$885$	−7.53569e14	−0.0466589
$886$	−1.15570e16	−0.711146
$887$	2.52449e16	1.54381	0.771904	−	0.635739i	$-0.219305\pi$
$887$	2.52449e16	1.54381	0.771904	+	0.635739i	$0.219305\pi$
$888$	1.01864e15	0.0619081
$889$	4.13899e15	0.249997
$890$	9.05022e15	0.543268
$891$	−1.88789e15	−0.112629
$892$	−3.05251e14	−0.0180988
$893$	−2.37021e16	−1.39670
$894$	7.09179e15	0.415336
$895$	8.23852e14	0.0479537
$896$	1.66189e16	0.961410
$897$	7.92818e14	0.0455843
$898$	−2.67881e16	−1.53081
$899$	−1.75532e16	−0.996963
$900$	6.29040e14	0.0355095
$901$	1.36352e16	0.765025
$902$	−2.05182e16	−1.14420
$903$	2.46470e16	1.36610
$904$	−3.02640e15	−0.166725
$905$	1.46212e16	0.800600
$906$	−1.52992e16	−0.832652
$907$	1.39982e16	0.757235	0.378618	−	0.925553i	$-0.376400\pi$
$907$	1.39982e16	0.757235	0.378618	+	0.925553i	$0.376400\pi$
$908$	4.91971e15	0.264525
$909$	5.78210e15	0.309018
$910$	−3.32059e15	−0.176396
$911$	2.63670e16	1.39223	0.696113	−	0.717933i	$-0.254911\pi$
$911$	2.63670e16	1.39223	0.696113	+	0.717933i	$0.254911\pi$
$912$	6.29048e15	0.330151
$913$	6.15936e15	0.321326
$914$	5.39117e15	0.279563
$915$	−5.45772e15	−0.281317
$916$	−2.07538e15	−0.106334
$917$	−1.29294e16	−0.658484
$918$	3.01696e15	0.152734
$919$	−1.07900e16	−0.542982	−0.271491	−	0.962441i	$-0.587517\pi$
$919$	−1.07900e16	−0.542982	−0.271491	+	0.962441i	$0.587517\pi$
$920$	−4.83525e15	−0.241872
$921$	−1.08066e16	−0.537354
$922$	1.75984e16	0.869866
$923$	3.39632e15	0.166878
$924$	−3.00234e15	−0.146644
$925$	−1.27245e15	−0.0617817
$926$	−1.04393e15	−0.0503862
$927$	7.26146e15	0.348406
$928$	−6.50299e15	−0.310170
$929$	1.47613e16	0.699903	0.349952	−	0.936768i	$-0.386198\pi$
$929$	1.47613e16	0.699903	0.349952	+	0.936768i	$0.386198\pi$
$930$	7.61010e15	0.358702
$931$	1.67018e16	0.782598
$932$	−3.47561e15	−0.161899
$933$	−4.72314e15	−0.218717
$934$	2.36671e16	1.08953
$935$	−1.20012e16	−0.549239
$936$	−1.68957e15	−0.0768703
$937$	1.11966e15	0.0506428	0.0253214	−	0.999679i	$-0.491939\pi$
$937$	1.11966e15	0.0506428	0.0253214	+	0.999679i	$0.491939\pi$
$938$	5.07341e16	2.28131
$939$	5.66081e15	0.253056
$940$	−4.71034e15	−0.209338
$941$	−2.41753e16	−1.06814	−0.534072	−	0.845439i	$-0.679339\pi$
$941$	−2.41753e16	−1.06814	−0.534072	+	0.845439i	$0.679339\pi$
$942$	−6.45104e15	−0.283367
$943$	−1.03833e16	−0.453440
$944$	2.38884e15	0.103715
$945$	4.00143e15	0.172719
$946$	3.51484e16	1.50836
$947$	−3.69952e16	−1.57841	−0.789206	−	0.614129i	$-0.789508\pi$
$947$	−3.69952e16	−1.57841	−0.789206	+	0.614129i	$0.789508\pi$
$948$	2.94705e15	0.125009
$949$	5.14785e15	0.217101
$950$	−9.56735e15	−0.401155
$951$	3.24490e15	0.135272
$952$	3.24814e16	1.34627
$953$	4.76843e15	0.196501	0.0982505	−	0.995162i	$-0.468675\pi$
$953$	4.76843e15	0.196501	0.0982505	+	0.995162i	$0.468675\pi$
$954$	−6.48327e15	−0.265631
$955$	−2.45318e15	−0.0999336
$956$	−6.32679e15	−0.256251
$957$	−1.31621e16	−0.530040
$958$	−2.45265e16	−0.982033
$959$	6.90756e16	2.74993
$960$	1.00324e16	0.397112
$961$	5.37972e15	0.211729
$962$	5.04839e14	0.0197556
$963$	1.69745e16	0.660467
$964$	5.66451e15	0.219148
$965$	−7.38722e15	−0.284172
$966$	7.24712e15	0.277199
$967$	1.44949e16	0.551276	0.275638	−	0.961261i	$-0.411111\pi$
$967$	1.44949e16	0.551276	0.275638	+	0.961261i	$0.411111\pi$
$968$	−7.76040e14	−0.0293474
$969$	9.61994e15	0.361736
$970$	−2.46103e16	−0.920180
$971$	2.89022e16	1.07455	0.537273	−	0.843409i	$-0.319455\pi$
$971$	2.89022e16	1.07455	0.537273	+	0.843409i	$0.319455\pi$
$972$	3.00740e14	0.0111180
$973$	−4.67480e16	−1.71847
$974$	1.16126e16	0.424477
$975$	2.11055e15	0.0767132
$976$	1.73012e16	0.625320
$977$	3.86502e16	1.38909	0.694546	−	0.719448i	$-0.255605\pi$
$977$	3.86502e16	1.38909	0.694546	+	0.719448i	$0.255605\pi$
$978$	2.28330e16	0.816017
$979$	2.74549e16	0.975697
$980$	3.31916e15	0.117296
$981$	1.66867e16	0.586394
$982$	−6.53200e15	−0.228262
$983$	−5.15943e16	−1.79290	−0.896452	−	0.443140i	$-0.853864\pi$
$983$	−5.15943e16	−1.79290	−0.896452	+	0.443140i	$0.853864\pi$
$984$	2.21277e16	0.764650
$985$	−2.00303e16	−0.688316
$986$	2.10337e16	0.718776
$987$	4.77950e16	1.62419
$988$	−7.95782e14	−0.0268925
$989$	1.77869e16	0.597753
$990$	5.70634e15	0.190706
$991$	−3.25115e16	−1.08052	−0.540259	−	0.841499i	$-0.681674\pi$
$991$	−3.25115e16	−1.08052	−0.540259	+	0.841499i	$0.681674\pi$
$992$	1.14062e16	0.376987
$993$	−2.36348e16	−0.776839
$994$	3.10456e16	1.01479
$995$	−2.39438e16	−0.778335
$996$	−9.81181e14	−0.0317192
$997$	−1.73387e16	−0.557434	−0.278717	−	0.960373i	$-0.589909\pi$
$997$	−1.73387e16	−0.557434	−0.278717	+	0.960373i	$0.589909\pi$
$998$	2.64605e16	0.846018
$999$	−6.08348e14	−0.0193438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.19	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+41.1468 q^{2} -243.000 q^{3} -354.944 q^{4} -4337.67 q^{5} -9998.66 q^{6} +64289.5 q^{7} -98873.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+41.1468 q^{2} -243.000 q^{3} -354.944 q^{4} -4337.67 q^{5} -9998.66 q^{6} +64289.5 q^{7} -98873.4 q^{8} +59049.0 q^{9} -178481. q^{10} -541443. q^{11} +86251.5 q^{12} +289390. q^{13} +2.64531e6 q^{14} +1.05405e6 q^{15} -3.34139e6 q^{16} -5.10994e6 q^{17} +2.42967e6 q^{18} +7.74730e6 q^{19} +1.53963e6 q^{20} -1.56224e7 q^{21} -2.22786e7 q^{22} -1.12741e7 q^{23} +2.40262e7 q^{24} -3.00128e7 q^{25} +1.19075e7 q^{26} -1.43489e7 q^{27} -2.28192e7 q^{28} -1.00038e8 q^{29} +4.33709e7 q^{30} +1.75466e8 q^{31} +6.50052e7 q^{32} +1.31571e8 q^{33} -2.10257e8 q^{34} -2.78867e8 q^{35} -2.09591e7 q^{36} +4.23968e7 q^{37} +3.18776e8 q^{38} -7.03218e7 q^{39} +4.28880e8 q^{40} +9.20980e8 q^{41} -6.42809e8 q^{42} -1.57768e9 q^{43} +1.92182e8 q^{44} -2.56135e8 q^{45} -4.63894e8 q^{46} -3.05940e9 q^{47} +8.11958e8 q^{48} +2.15582e9 q^{49} -1.23493e9 q^{50} +1.24172e9 q^{51} -1.02717e8 q^{52} -2.66837e9 q^{53} -5.90411e8 q^{54} +2.34860e9 q^{55} -6.35652e9 q^{56} -1.88259e9 q^{57} -4.11624e9 q^{58} -7.14924e8 q^{59} -3.74130e8 q^{60} -5.17784e9 q^{61} +7.21984e9 q^{62} +3.79623e9 q^{63} +9.51792e9 q^{64} -1.25528e9 q^{65} +5.41371e9 q^{66} +1.91789e10 q^{67} +1.81374e9 q^{68} +2.73962e9 q^{69} -1.14745e10 q^{70} +1.17361e10 q^{71} -5.83837e9 q^{72} +1.77886e10 q^{73} +1.74449e9 q^{74} +7.29310e9 q^{75} -2.74986e9 q^{76} -3.48091e10 q^{77} -2.89351e9 q^{78} +3.41681e10 q^{79} +1.44939e10 q^{80} +3.48678e9 q^{81} +3.78954e10 q^{82} -1.13758e10 q^{83} +5.54507e9 q^{84} +2.21652e10 q^{85} -6.49162e10 q^{86} +2.43092e10 q^{87} +5.35343e10 q^{88} -5.07069e10 q^{89} -1.05391e10 q^{90} +1.86047e10 q^{91} +4.00169e9 q^{92} -4.26382e10 q^{93} -1.25884e11 q^{94} -3.36052e10 q^{95} -1.57963e10 q^{96} +1.37888e11 q^{97} +8.87049e10 q^{98} -3.19717e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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