LMFDB - Embedded newform 177.12.a.b.1.15

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-2.16187 q^{2} +243.000 q^{3} -2043.33 q^{4} +654.400 q^{5} -525.335 q^{6} +79533.7 q^{7} +8844.92 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-2.16187 q^{2} +243.000 q^{3} -2043.33 q^{4} +654.400 q^{5} -525.335 q^{6} +79533.7 q^{7} +8844.92 q^{8} +59049.0 q^{9} -1414.73 q^{10} -361945. q^{11} -496528. q^{12} -608677. q^{13} -171942. q^{14} +159019. q^{15} +4.16561e6 q^{16} +1.14080e6 q^{17} -127656. q^{18} -6.87969e6 q^{19} -1.33715e6 q^{20} +1.93267e7 q^{21} +782479. q^{22} -2.10594e7 q^{23} +2.14932e6 q^{24} -4.83999e7 q^{25} +1.31588e6 q^{26} +1.43489e7 q^{27} -1.62513e8 q^{28} -1.41194e8 q^{29} -343779. q^{30} +8.71043e7 q^{31} -2.71199e7 q^{32} -8.79527e7 q^{33} -2.46625e6 q^{34} +5.20469e7 q^{35} -1.20656e8 q^{36} +5.08594e8 q^{37} +1.48730e7 q^{38} -1.47909e8 q^{39} +5.78812e6 q^{40} -2.45057e8 q^{41} -4.17818e7 q^{42} +1.63401e8 q^{43} +7.39572e8 q^{44} +3.86417e7 q^{45} +4.55276e7 q^{46} +1.77966e9 q^{47} +1.01224e9 q^{48} +4.34828e9 q^{49} +1.04634e8 q^{50} +2.77213e8 q^{51} +1.24373e9 q^{52} -4.11758e9 q^{53} -3.10205e7 q^{54} -2.36857e8 q^{55} +7.03469e8 q^{56} -1.67176e9 q^{57} +3.05244e8 q^{58} -7.14924e8 q^{59} -3.24928e8 q^{60} -2.50892e9 q^{61} -1.88308e8 q^{62} +4.69639e9 q^{63} -8.47254e9 q^{64} -3.98318e8 q^{65} +1.90142e8 q^{66} -3.37618e9 q^{67} -2.33102e9 q^{68} -5.11743e9 q^{69} -1.12519e8 q^{70} -6.16327e9 q^{71} +5.22284e8 q^{72} +2.20149e9 q^{73} -1.09951e9 q^{74} -1.17612e10 q^{75} +1.40574e10 q^{76} -2.87868e10 q^{77} +3.19759e8 q^{78} +2.69116e10 q^{79} +2.72598e9 q^{80} +3.48678e9 q^{81} +5.29781e8 q^{82} -1.69513e10 q^{83} -3.94907e10 q^{84} +7.46537e8 q^{85} -3.53251e8 q^{86} -3.43102e10 q^{87} -3.20138e9 q^{88} -5.65822e10 q^{89} -8.35384e7 q^{90} -4.84103e10 q^{91} +4.30312e10 q^{92} +2.11663e10 q^{93} -3.84740e9 q^{94} -4.50207e9 q^{95} -6.59014e9 q^{96} -2.14261e9 q^{97} -9.40043e9 q^{98} -2.13725e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) $	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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 $

$2$	−2.16187	−0.0477711	−0.0238855	−	0.999715i	$-0.507604\pi$
$2$	−2.16187	−0.0477711	−0.0238855	+	0.999715i	$0.507604\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−2043.33	−0.997718
$5$	654.400	0.0936502	0.0468251	−	0.998903i	$-0.485090\pi$
$5$	654.400	0.0936502	0.0468251	+	0.998903i	$0.485090\pi$
$6$	−525.335	−0.0275806
$7$	79533.7	1.78859	0.894297	−	0.447473i	$-0.147676\pi$
$7$	79533.7	1.78859	0.894297	+	0.447473i	$0.147676\pi$
$8$	8844.92	0.0954331
$9$	59049.0	0.333333
$10$	−1414.73	−0.00447377
$11$	−361945.	−0.677615	−0.338808	−	0.940856i	$-0.610024\pi$
$11$	−361945.	−0.677615	−0.338808	+	0.940856i	$0.610024\pi$
$12$	−496528.	−0.576033
$13$	−608677.	−0.454672	−0.227336	−	0.973816i	$-0.573002\pi$
$13$	−608677.	−0.454672	−0.227336	+	0.973816i	$0.573002\pi$
$14$	−171942.	−0.0854431
$15$	159019.	0.0540689
$16$	4.16561e6	0.993159
$17$	1.14080e6	0.194867	0.0974336	−	0.995242i	$-0.468937\pi$
$17$	1.14080e6	0.194867	0.0974336	+	0.995242i	$0.468937\pi$
$18$	−127656.	−0.0159237
$19$	−6.87969e6	−0.637418	−0.318709	−	0.947853i	$-0.603249\pi$
$19$	−6.87969e6	−0.637418	−0.318709	+	0.947853i	$0.603249\pi$
$20$	−1.33715e6	−0.0934364
$21$	1.93267e7	1.03265
$22$	782479.	0.0323704
$23$	−2.10594e7	−0.682248	−0.341124	−	0.940018i	$-0.610808\pi$
$23$	−2.10594e7	−0.682248	−0.341124	+	0.940018i	$0.610808\pi$
$24$	2.14932e6	0.0550983
$25$	−4.83999e7	−0.991230
$26$	1.31588e6	0.0217202
$27$	1.43489e7	0.192450
$28$	−1.62513e8	−1.78451
$29$	−1.41194e8	−1.27829	−0.639143	−	0.769088i	$-0.720711\pi$
$29$	−1.41194e8	−1.27829	−0.639143	+	0.769088i	$0.720711\pi$
$30$	−343779.	−0.00258293
$31$	8.71043e7	0.546450	0.273225	−	0.961950i	$-0.411910\pi$
$31$	8.71043e7	0.546450	0.273225	+	0.961950i	$0.411910\pi$
$32$	−2.71199e7	−0.142877
$33$	−8.79527e7	−0.391221
$34$	−2.46625e6	−0.00930901
$35$	5.20469e7	0.167502
$36$	−1.20656e8	−0.332573
$37$	5.08594e8	1.20576	0.602881	−	0.797831i	$-0.294019\pi$
$37$	5.08594e8	1.20576	0.602881	+	0.797831i	$0.294019\pi$
$38$	1.48730e7	0.0304501
$39$	−1.47909e8	−0.262505
$40$	5.78812e6	0.00893733
$41$	−2.45057e8	−0.330336	−0.165168	−	0.986265i	$-0.552817\pi$
$41$	−2.45057e8	−0.330336	−0.165168	+	0.986265i	$0.552817\pi$
$42$	−4.17818e7	−0.0493306
$43$	1.63401e8	0.169503	0.0847514	−	0.996402i	$-0.472990\pi$
$43$	1.63401e8	0.169503	0.0847514	+	0.996402i	$0.472990\pi$
$44$	7.39572e8	0.676069
$45$	3.86417e7	0.0312167
$46$	4.55276e7	0.0325917
$47$	1.77966e9	1.13188	0.565938	−	0.824448i	$-0.308514\pi$
$47$	1.77966e9	1.13188	0.565938	+	0.824448i	$0.308514\pi$
$48$	1.01224e9	0.573401
$49$	4.34828e9	2.19907
$50$	1.04634e8	0.0473521
$51$	2.77213e8	0.112507
$52$	1.24373e9	0.453635
$53$	−4.11758e9	−1.35246	−0.676231	−	0.736690i	$-0.736388\pi$
$53$	−4.11758e9	−1.35246	−0.676231	+	0.736690i	$0.736388\pi$
$54$	−3.10205e7	−0.00919355
$55$	−2.36857e8	−0.0634588
$56$	7.03469e8	0.170691
$57$	−1.67176e9	−0.368013
$58$	3.05244e8	0.0610651
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−3.24928e8	−0.0539456
$61$	−2.50892e9	−0.380340	−0.190170	−	0.981751i	$-0.560904\pi$
$61$	−2.50892e9	−0.380340	−0.190170	+	0.981751i	$0.560904\pi$
$62$	−1.88308e8	−0.0261045
$63$	4.69639e9	0.596198
$64$	−8.47254e9	−0.986334
$65$	−3.98318e8	−0.0425801
$66$	1.90142e8	0.0186891
$67$	−3.37618e9	−0.305502	−0.152751	−	0.988265i	$-0.548813\pi$
$67$	−3.37618e9	−0.305502	−0.152751	+	0.988265i	$0.548813\pi$
$68$	−2.33102e9	−0.194423
$69$	−5.11743e9	−0.393896
$70$	−1.12519e8	−0.00800176
$71$	−6.16327e9	−0.405406	−0.202703	−	0.979240i	$-0.564973\pi$
$71$	−6.16327e9	−0.405406	−0.202703	+	0.979240i	$0.564973\pi$
$72$	5.22284e8	0.0318110
$73$	2.20149e9	0.124292	0.0621458	−	0.998067i	$-0.480206\pi$
$73$	2.20149e9	0.124292	0.0621458	+	0.998067i	$0.480206\pi$
$74$	−1.09951e9	−0.0576005
$75$	−1.17612e10	−0.572287
$76$	1.40574e10	0.635963
$77$	−2.87868e10	−1.21198
$78$	3.19759e8	0.0125402
$79$	2.69116e10	0.983991	0.491995	−	0.870598i	$-0.336268\pi$
$79$	2.69116e10	0.983991	0.491995	+	0.870598i	$0.336268\pi$
$80$	2.72598e9	0.0930095
$81$	3.48678e9	0.111111
$82$	5.29781e8	0.0157805
$83$	−1.69513e10	−0.472361	−0.236180	−	0.971709i	$-0.575896\pi$
$83$	−1.69513e10	−0.472361	−0.236180	+	0.971709i	$0.575896\pi$
$84$	−3.94907e10	−1.03029
$85$	7.46537e8	0.0182493
$86$	−3.53251e8	−0.00809733
$87$	−3.43102e10	−0.738019
$88$	−3.20138e9	−0.0646669
$89$	−5.65822e10	−1.07408	−0.537038	−	0.843558i	$-0.680457\pi$
$89$	−5.65822e10	−1.07408	−0.537038	+	0.843558i	$0.680457\pi$
$90$	−8.35384e7	−0.00149126
$91$	−4.84103e10	−0.813224
$92$	4.30312e10	0.680691
$93$	2.11663e10	0.315493
$94$	−3.84740e9	−0.0540710
$95$	−4.50207e9	−0.0596942
$96$	−6.59014e9	−0.0824903
$97$	−2.14261e9	−0.0253336	−0.0126668	−	0.999920i	$-0.504032\pi$
$97$	−2.14261e9	−0.0253336	−0.0126668	+	0.999920i	$0.504032\pi$
$98$	−9.40043e9	−0.105052
$99$	−2.13725e10	−0.225872
$100$	9.88968e10	0.988968
$101$	9.24270e10	0.875047	0.437524	−	0.899207i	$-0.355856\pi$
$101$	9.24270e10	0.875047	0.437524	+	0.899207i	$0.355856\pi$
$102$	−5.99300e8	−0.00537456
$103$	−1.07966e11	−0.917665	−0.458832	−	0.888523i	$-0.651732\pi$
$103$	−1.07966e11	−0.917665	−0.458832	+	0.888523i	$0.651732\pi$
$104$	−5.38370e9	−0.0433908
$105$	1.26474e10	0.0967074
$106$	8.90168e9	0.0646085
$107$	5.38904e10	0.371450	0.185725	−	0.982602i	$-0.440537\pi$
$107$	5.38904e10	0.371450	0.185725	+	0.982602i	$0.440537\pi$
$108$	−2.93195e10	−0.192011
$109$	−8.67119e10	−0.539800	−0.269900	−	0.962888i	$-0.586991\pi$
$109$	−8.67119e10	−0.539800	−0.269900	+	0.962888i	$0.586991\pi$
$110$	5.12055e8	0.00303149
$111$	1.23588e11	0.696147
$112$	3.31306e11	1.77636
$113$	−2.77274e11	−1.41572	−0.707861	−	0.706352i	$-0.750340\pi$
$113$	−2.77274e11	−1.41572	−0.707861	+	0.706352i	$0.750340\pi$
$114$	3.61414e9	0.0175804
$115$	−1.37813e10	−0.0638926
$116$	2.88506e11	1.27537
$117$	−3.59418e10	−0.151557
$118$	1.54557e9	0.00621926
$119$	9.07317e10	0.348538
$120$	1.40651e9	0.00515997
$121$	−1.54307e11	−0.540838
$122$	5.42396e9	0.0181693
$123$	−5.95488e10	−0.190719
$124$	−1.77982e11	−0.545203
$125$	−6.36260e10	−0.186479
$126$	−1.01530e10	−0.0284810
$127$	−2.23170e11	−0.599399	−0.299700	−	0.954034i	$-0.596886\pi$
$127$	−2.23170e11	−0.599399	−0.299700	+	0.954034i	$0.596886\pi$
$128$	7.38581e10	0.189996
$129$	3.97063e10	0.0978625
$130$	8.61113e8	0.00203410
$131$	−8.35848e10	−0.189293	−0.0946467	−	0.995511i	$-0.530172\pi$
$131$	−8.35848e10	−0.189293	−0.0946467	+	0.995511i	$0.530172\pi$
$132$	1.79716e11	0.390329
$133$	−5.47167e11	−1.14008
$134$	7.29887e9	0.0145942
$135$	9.38993e9	0.0180230
$136$	1.00902e10	0.0185968
$137$	4.52915e10	0.0801777	0.0400889	−	0.999196i	$-0.487236\pi$
$137$	4.52915e10	0.0801777	0.0400889	+	0.999196i	$0.487236\pi$
$138$	1.10632e10	0.0188168
$139$	−4.20037e11	−0.686604	−0.343302	−	0.939225i	$-0.611545\pi$
$139$	−4.20037e11	−0.686604	−0.343302	+	0.939225i	$0.611545\pi$
$140$	−1.06349e11	−0.167120
$141$	4.32458e11	0.653489
$142$	1.33242e10	0.0193667
$143$	2.20308e11	0.308093
$144$	2.45975e11	0.331053
$145$	−9.23976e10	−0.119712
$146$	−4.75934e9	−0.00593754
$147$	1.05663e12	1.26963
$148$	−1.03922e12	−1.20301
$149$	3.64336e11	0.406422	0.203211	−	0.979135i	$-0.434862\pi$
$149$	3.64336e11	0.406422	0.203211	+	0.979135i	$0.434862\pi$
$150$	2.54261e10	0.0273387
$151$	−1.39489e12	−1.44599	−0.722996	−	0.690852i	$-0.757236\pi$
$151$	−1.39489e12	−1.44599	−0.722996	+	0.690852i	$0.757236\pi$
$152$	−6.08503e10	−0.0608307
$153$	6.73628e10	0.0649557
$154$	6.22335e10	0.0578975
$155$	5.70011e10	0.0511751
$156$	3.02225e11	0.261906
$157$	4.10340e11	0.343317	0.171659	−	0.985156i	$-0.445087\pi$
$157$	4.10340e11	0.343317	0.171659	+	0.985156i	$0.445087\pi$
$158$	−5.81795e10	−0.0470063
$159$	−1.00057e12	−0.780844
$160$	−1.77473e10	−0.0133805
$161$	−1.67493e12	−1.22027
$162$	−7.53798e9	−0.00530790
$163$	−2.54325e12	−1.73124	−0.865620	−	0.500701i	$-0.833076\pi$
$163$	−2.54325e12	−1.73124	−0.865620	+	0.500701i	$0.833076\pi$
$164$	5.00731e11	0.329582
$165$	−5.75563e10	−0.0366379
$166$	3.66465e10	0.0225652
$167$	−1.38079e11	−0.0822598	−0.0411299	−	0.999154i	$-0.513096\pi$
$167$	−1.38079e11	−0.0822598	−0.0411299	+	0.999154i	$0.513096\pi$
$168$	1.70943e11	0.0985486
$169$	−1.42167e12	−0.793273
$170$	−1.61392e9	−0.000871791 0
$171$	−4.06239e11	−0.212473
$172$	−3.33881e11	−0.169116
$173$	1.91015e11	0.0937159	0.0468580	−	0.998902i	$-0.485079\pi$
$173$	1.91015e11	0.0937159	0.0468580	+	0.998902i	$0.485079\pi$
$174$	7.41743e10	0.0352559
$175$	−3.84942e12	−1.77291
$176$	−1.50772e12	−0.672980
$177$	−1.73727e11	−0.0751646
$178$	1.22323e11	0.0513097
$179$	3.55183e12	1.44464	0.722321	−	0.691558i	$-0.243075\pi$
$179$	3.55183e12	1.44464	0.722321	+	0.691558i	$0.243075\pi$
$180$	−7.89576e10	−0.0311455
$181$	3.50928e12	1.34272	0.671360	−	0.741132i	$-0.265711\pi$
$181$	3.50928e12	1.34272	0.671360	+	0.741132i	$0.265711\pi$
$182$	1.04657e11	0.0388486
$183$	−6.09667e11	−0.219589
$184$	−1.86268e11	−0.0651090
$185$	3.32824e11	0.112920
$186$	−4.57589e10	−0.0150714
$187$	−4.12906e11	−0.132045
$188$	−3.63643e12	−1.12929
$189$	1.14122e12	0.344215
$190$	9.73290e9	0.00285166
$191$	−4.78607e12	−1.36237	−0.681186	−	0.732111i	$-0.738535\pi$
$191$	−4.78607e12	−1.36237	−0.681186	+	0.732111i	$0.738535\pi$
$192$	−2.05883e12	−0.569460
$193$	−2.49448e12	−0.670524	−0.335262	−	0.942125i	$-0.608825\pi$
$193$	−2.49448e12	−0.670524	−0.335262	+	0.942125i	$0.608825\pi$
$194$	4.63204e9	0.00121022
$195$	−9.67914e10	−0.0245836
$196$	−8.88496e12	−2.19405
$197$	−7.83320e12	−1.88094	−0.940470	−	0.339877i	$-0.889615\pi$
$197$	−7.83320e12	−1.88094	−0.940470	+	0.339877i	$0.889615\pi$
$198$	4.62046e10	0.0107901
$199$	1.97236e12	0.448016	0.224008	−	0.974587i	$-0.428086\pi$
$199$	1.97236e12	0.448016	0.224008	+	0.974587i	$0.428086\pi$
$200$	−4.28093e11	−0.0945961
$201$	−8.20412e11	−0.176382
$202$	−1.99815e11	−0.0418019
$203$	−1.12297e13	−2.28634
$204$	−5.66437e11	−0.112250
$205$	−1.60365e11	−0.0309360
$206$	2.33410e11	0.0438378
$207$	−1.24353e12	−0.227416
$208$	−2.53551e12	−0.451562
$209$	2.49007e12	0.431924
$210$	−2.73420e10	−0.00461982
$211$	−1.10288e12	−0.181540	−0.0907702	−	0.995872i	$-0.528933\pi$
$211$	−1.10288e12	−0.181540	−0.0907702	+	0.995872i	$0.528933\pi$
$212$	8.41356e12	1.34937
$213$	−1.49768e12	−0.234061
$214$	−1.16504e11	−0.0177446
$215$	1.06929e11	0.0158740
$216$	1.26915e11	0.0183661
$217$	6.92773e12	0.977377
$218$	1.87460e11	0.0257868
$219$	5.34963e11	0.0717597
$220$	4.83976e11	0.0633139
$221$	−6.94376e11	−0.0886007
$222$	−2.67182e11	−0.0332557
$223$	−6.53558e12	−0.793610	−0.396805	−	0.917903i	$-0.629881\pi$
$223$	−6.53558e12	−0.793610	−0.396805	+	0.917903i	$0.629881\pi$
$224$	−2.15695e12	−0.255550
$225$	−2.85796e12	−0.330410
$226$	5.99431e11	0.0676305
$227$	1.24917e13	1.37556	0.687778	−	0.725921i	$-0.258586\pi$
$227$	1.24917e13	1.37556	0.687778	+	0.725921i	$0.258586\pi$
$228$	3.41596e12	0.367173
$229$	6.05763e12	0.635635	0.317817	−	0.948152i	$-0.397050\pi$
$229$	6.05763e12	0.635635	0.317817	+	0.948152i	$0.397050\pi$
$230$	2.97933e10	0.00305222
$231$	−6.99520e12	−0.699736
$232$	−1.24885e12	−0.121991
$233$	−8.58130e12	−0.818644	−0.409322	−	0.912390i	$-0.634235\pi$
$233$	−8.58130e12	−0.818644	−0.409322	+	0.912390i	$0.634235\pi$
$234$	7.77015e10	0.00724006
$235$	1.16461e12	0.106000
$236$	1.46082e12	0.129892
$237$	6.53953e12	0.568107
$238$	−1.96150e11	−0.0166501
$239$	−1.96699e12	−0.163160	−0.0815799	−	0.996667i	$-0.525997\pi$
$239$	−1.96699e12	−0.163160	−0.0815799	+	0.996667i	$0.525997\pi$
$240$	6.62412e11	0.0536991
$241$	1.96077e13	1.55358	0.776789	−	0.629761i	$-0.216847\pi$
$241$	1.96077e13	1.55358	0.776789	+	0.629761i	$0.216847\pi$
$242$	3.33593e11	0.0258364
$243$	8.47289e11	0.0641500
$244$	5.12654e12	0.379472
$245$	2.84552e12	0.205943
$246$	1.28737e11	0.00911087
$247$	4.18751e12	0.289816
$248$	7.70431e11	0.0521494
$249$	−4.11917e12	−0.272718
$250$	1.37551e11	0.00890830
$251$	−4.19882e12	−0.266025	−0.133012	−	0.991114i	$-0.542465\pi$
$251$	−4.19882e12	−0.266025	−0.133012	+	0.991114i	$0.542465\pi$
$252$	−9.59625e12	−0.594838
$253$	7.62234e12	0.462302
$254$	4.82466e11	0.0286339
$255$	1.81409e11	0.0105363
$256$	1.71921e13	0.977257
$257$	−2.94651e13	−1.63937	−0.819684	−	0.572816i	$-0.805851\pi$
$257$	−2.94651e13	−1.63937	−0.819684	+	0.572816i	$0.805851\pi$
$258$	−8.58400e10	−0.00467500
$259$	4.04503e13	2.15662
$260$	8.13895e11	0.0424830
$261$	−8.33738e12	−0.426095
$262$	1.80700e11	0.00904274
$263$	−1.13059e13	−0.554049	−0.277024	−	0.960863i	$-0.589348\pi$
$263$	−1.13059e13	−0.554049	−0.277024	+	0.960863i	$0.589348\pi$
$264$	−7.77935e11	−0.0373355
$265$	−2.69455e12	−0.126658
$266$	1.18290e12	0.0544629
$267$	−1.37495e13	−0.620118
$268$	6.89864e12	0.304805
$269$	−3.82578e13	−1.65608	−0.828042	−	0.560665i	$-0.810545\pi$
$269$	−3.82578e13	−1.65608	−0.828042	+	0.560665i	$0.810545\pi$
$270$	−2.02998e10	−0.000860977 0
$271$	−9.60782e12	−0.399295	−0.199647	−	0.979868i	$-0.563980\pi$
$271$	−9.60782e12	−0.399295	−0.199647	+	0.979868i	$0.563980\pi$
$272$	4.75211e12	0.193534
$273$	−1.17637e13	−0.469515
$274$	−9.79144e10	−0.00383017
$275$	1.75181e13	0.671672
$276$	1.04566e13	0.392997
$277$	−2.31076e13	−0.851366	−0.425683	−	0.904872i	$-0.639966\pi$
$277$	−2.31076e13	−0.851366	−0.425683	+	0.904872i	$0.639966\pi$
$278$	9.08066e11	0.0327998
$279$	5.14342e12	0.182150
$280$	4.60351e11	0.0159853
$281$	−3.08669e13	−1.05101	−0.525506	−	0.850790i	$-0.676124\pi$
$281$	−3.08669e13	−1.05101	−0.525506	+	0.850790i	$0.676124\pi$
$282$	−9.34918e11	−0.0312179
$283$	−2.49874e13	−0.818268	−0.409134	−	0.912474i	$-0.634169\pi$
$283$	−2.49874e13	−0.818268	−0.409134	+	0.912474i	$0.634169\pi$
$284$	1.25936e13	0.404481
$285$	−1.09400e12	−0.0344645
$286$	−4.76277e11	−0.0147179
$287$	−1.94903e13	−0.590837
$288$	−1.60140e12	−0.0476258
$289$	−3.29705e13	−0.962027
$290$	1.99752e11	0.00571875
$291$	−5.20653e11	−0.0146264
$292$	−4.49837e12	−0.124008
$293$	−2.28908e13	−0.619283	−0.309642	−	0.950853i	$-0.600209\pi$
$293$	−2.28908e13	−0.619283	−0.309642	+	0.950853i	$0.600209\pi$
$294$	−2.28430e12	−0.0606518
$295$	−4.67847e11	−0.0121922
$296$	4.49847e12	0.115070
$297$	−5.19352e12	−0.130407
$298$	−7.87647e11	−0.0194152
$299$	1.28184e13	0.310199
$300$	2.40319e13	0.570981
$301$	1.29958e13	0.303172
$302$	3.01557e12	0.0690766
$303$	2.24598e13	0.505209
$304$	−2.86581e13	−0.633057
$305$	−1.64184e12	−0.0356189
$306$	−1.45630e11	−0.00310300
$307$	9.03824e12	0.189157	0.0945786	−	0.995517i	$-0.469850\pi$
$307$	9.03824e12	0.189157	0.0945786	+	0.995517i	$0.469850\pi$
$308$	5.88209e13	1.20921
$309$	−2.62358e13	−0.529814
$310$	−1.23229e11	−0.00244469
$311$	2.75466e13	0.536891	0.268445	−	0.963295i	$-0.413490\pi$
$311$	2.75466e13	0.536891	0.268445	+	0.963295i	$0.413490\pi$
$312$	−1.30824e12	−0.0250517
$313$	−5.33653e13	−1.00407	−0.502036	−	0.864847i	$-0.667415\pi$
$313$	−5.33653e13	−1.00407	−0.502036	+	0.864847i	$0.667415\pi$
$314$	−8.87103e11	−0.0164006
$315$	3.07332e12	0.0558341
$316$	−5.49892e13	−0.981745
$317$	2.18062e13	0.382607	0.191304	−	0.981531i	$-0.438728\pi$
$317$	2.18062e13	0.382607	0.191304	+	0.981531i	$0.438728\pi$
$318$	2.16311e12	0.0373017
$319$	5.11046e13	0.866186
$320$	−5.54443e12	−0.0923703
$321$	1.30954e13	0.214457
$322$	3.62098e12	0.0582934
$323$	−7.84832e12	−0.124212
$324$	−7.12464e12	−0.110858
$325$	2.94599e13	0.450685
$326$	5.49818e12	0.0827032
$327$	−2.10710e13	−0.311654
$328$	−2.16751e12	−0.0315250
$329$	1.41543e14	2.02447
$330$	1.24429e11	0.00175023
$331$	5.38836e13	0.745423	0.372712	−	0.927947i	$-0.378428\pi$
$331$	5.38836e13	0.745423	0.372712	+	0.927947i	$0.378428\pi$
$332$	3.46371e13	0.471283
$333$	3.00320e13	0.401921
$334$	2.98509e11	0.00392964
$335$	−2.20937e12	−0.0286103
$336$	8.05075e13	1.02558
$337$	6.64623e13	0.832935	0.416467	−	0.909151i	$-0.363268\pi$
$337$	6.64623e13	0.832935	0.416467	+	0.909151i	$0.363268\pi$
$338$	3.07347e12	0.0378955
$339$	−6.73776e13	−0.817367
$340$	−1.52542e12	−0.0182077
$341$	−3.15270e13	−0.370283
$342$	8.78236e11	0.0101500
$343$	1.88571e14	2.14465
$344$	1.44527e12	0.0161762
$345$	−3.34885e12	−0.0368884
$346$	−4.12949e11	−0.00447691
$347$	−7.03218e12	−0.0750374	−0.0375187	−	0.999296i	$-0.511945\pi$
$347$	−7.03218e12	−0.0750374	−0.0375187	+	0.999296i	$0.511945\pi$
$348$	7.01069e13	0.736335
$349$	−8.02464e13	−0.829632	−0.414816	−	0.909905i	$-0.636154\pi$
$349$	−8.02464e13	−0.829632	−0.414816	+	0.909905i	$0.636154\pi$
$350$	8.32195e12	0.0846937
$351$	−8.73385e12	−0.0875017
$352$	9.81592e12	0.0968159
$353$	4.65152e13	0.451683	0.225842	−	0.974164i	$-0.427487\pi$
$353$	4.65152e13	0.451683	0.225842	+	0.974164i	$0.427487\pi$
$354$	3.75575e11	0.00359069
$355$	−4.03325e12	−0.0379664
$356$	1.15616e14	1.07162
$357$	2.20478e13	0.201229
$358$	−7.67860e12	−0.0690121
$359$	3.18415e13	0.281822	0.140911	−	0.990022i	$-0.454997\pi$
$359$	3.18415e13	0.281822	0.140911	+	0.990022i	$0.454997\pi$
$360$	3.41783e11	0.00297911
$361$	−6.91601e13	−0.593699
$362$	−7.58660e12	−0.0641431
$363$	−3.74967e13	−0.312253
$364$	9.89181e13	0.811369
$365$	1.44066e12	0.0116399
$366$	1.31802e12	0.0104900
$367$	1.63532e14	1.28215	0.641074	−	0.767479i	$-0.278489\pi$
$367$	1.63532e14	1.28215	0.641074	+	0.767479i	$0.278489\pi$
$368$	−8.77251e13	−0.677581
$369$	−1.44704e13	−0.110112
$370$	−7.19523e11	−0.00539430
$371$	−3.27486e14	−2.41900
$372$	−4.32497e13	−0.314773
$373$	1.16018e14	0.832010	0.416005	−	0.909362i	$-0.363430\pi$
$373$	1.16018e14	0.832010	0.416005	+	0.909362i	$0.363430\pi$
$374$	8.92649e11	0.00630793
$375$	−1.54611e13	−0.107664
$376$	1.57410e13	0.108019
$377$	8.59417e13	0.581201
$378$	−2.46717e12	−0.0164435
$379$	2.33930e14	1.53664	0.768318	−	0.640069i	$-0.221094\pi$
$379$	2.33930e14	1.53664	0.768318	+	0.640069i	$0.221094\pi$
$380$	9.19920e12	0.0595580
$381$	−5.42304e13	−0.346063
$382$	1.03469e13	0.0650819
$383$	3.07371e14	1.90577	0.952884	−	0.303336i	$-0.0981005\pi$
$383$	3.07371e14	1.90577	0.952884	+	0.303336i	$0.0981005\pi$
$384$	1.79475e13	0.109694
$385$	−1.88381e13	−0.113502
$386$	5.39274e12	0.0320316
$387$	9.64864e12	0.0565010
$388$	4.37804e12	0.0252758
$389$	−1.43081e14	−0.814442	−0.407221	−	0.913330i	$-0.633502\pi$
$389$	−1.43081e14	−0.814442	−0.407221	+	0.913330i	$0.633502\pi$
$390$	2.09251e11	0.00117439
$391$	−2.40244e13	−0.132948
$392$	3.84602e13	0.209864
$393$	−2.03111e13	−0.109289
$394$	1.69344e13	0.0898545
$395$	1.76110e13	0.0921509
$396$	4.36710e13	0.225356
$397$	1.73602e14	0.883502	0.441751	−	0.897138i	$-0.354358\pi$
$397$	1.73602e14	0.883502	0.441751	+	0.897138i	$0.354358\pi$
$398$	−4.26398e12	−0.0214022
$399$	−1.32962e14	−0.658226
$400$	−2.01615e14	−0.984449
$401$	2.06844e14	0.996206	0.498103	−	0.867118i	$-0.334030\pi$
$401$	2.06844e14	0.996206	0.498103	+	0.867118i	$0.334030\pi$
$402$	1.77362e12	0.00842594
$403$	−5.30184e13	−0.248456
$404$	−1.88859e14	−0.873050
$405$	2.28175e12	0.0104056
$406$	2.42772e13	0.109221
$407$	−1.84083e14	−0.817043
$408$	2.45193e12	0.0107369
$409$	4.82766e13	0.208573	0.104287	−	0.994547i	$-0.466744\pi$
$409$	4.82766e13	0.208573	0.104287	+	0.994547i	$0.466744\pi$
$410$	3.46689e11	0.00147784
$411$	1.10058e13	0.0462906
$412$	2.20611e14	0.915570
$413$	−5.68606e13	−0.232855
$414$	2.68836e12	0.0108639
$415$	−1.10929e13	−0.0442366
$416$	1.65073e13	0.0649624
$417$	−1.02069e14	−0.396411
$418$	−5.38321e12	−0.0206335
$419$	9.62691e13	0.364175	0.182087	−	0.983282i	$-0.441715\pi$
$419$	9.62691e13	0.364175	0.182087	+	0.983282i	$0.441715\pi$
$420$	−2.58427e13	−0.0964867
$421$	3.57648e14	1.31797	0.658984	−	0.752157i	$-0.270987\pi$
$421$	3.57648e14	1.31797	0.658984	+	0.752157i	$0.270987\pi$
$422$	2.38428e12	0.00867238
$423$	1.05087e14	0.377292
$424$	−3.64197e13	−0.129070
$425$	−5.52144e13	−0.193158
$426$	3.23778e12	0.0111814
$427$	−1.99543e14	−0.680274
$428$	−1.10116e14	−0.370603
$429$	5.35348e13	0.177877
$430$	−2.31168e11	−0.000758316 0
$431$	−1.62300e14	−0.525648	−0.262824	−	0.964844i	$-0.584654\pi$
$431$	−1.62300e14	−0.525648	−0.262824	+	0.964844i	$0.584654\pi$
$432$	5.97720e13	0.191134
$433$	1.89586e14	0.598581	0.299290	−	0.954162i	$-0.403250\pi$
$433$	1.89586e14	0.598581	0.299290	+	0.954162i	$0.403250\pi$
$434$	−1.49769e13	−0.0466903
$435$	−2.24526e13	−0.0691156
$436$	1.77181e14	0.538569
$437$	1.44882e14	0.434877
$438$	−1.15652e12	−0.00342804
$439$	5.87391e14	1.71938	0.859691	−	0.510815i	$-0.170656\pi$
$439$	5.87391e14	1.71938	0.859691	+	0.510815i	$0.170656\pi$
$440$	−2.09498e12	−0.00605607
$441$	2.56762e14	0.733024
$442$	1.50115e12	0.00423255
$443$	9.54123e13	0.265695	0.132848	−	0.991136i	$-0.457588\pi$
$443$	9.54123e13	0.265695	0.132848	+	0.991136i	$0.457588\pi$
$444$	−2.52531e14	−0.694558
$445$	−3.70274e13	−0.100587
$446$	1.41291e13	0.0379116
$447$	8.85335e13	0.234648
$448$	−6.73852e14	−1.76415
$449$	−2.82045e14	−0.729396	−0.364698	−	0.931126i	$-0.618828\pi$
$449$	−2.82045e14	−0.729396	−0.364698	+	0.931126i	$0.618828\pi$
$450$	6.17855e12	0.0157840
$451$	8.86971e13	0.223840
$452$	5.66562e14	1.41249
$453$	−3.38958e14	−0.834844
$454$	−2.70054e13	−0.0657117
$455$	−3.16797e13	−0.0761586
$456$	−1.47866e13	−0.0351206
$457$	−5.40931e14	−1.26941	−0.634706	−	0.772754i	$-0.718879\pi$
$457$	−5.40931e14	−1.26941	−0.634706	+	0.772754i	$0.718879\pi$
$458$	−1.30958e13	−0.0303649
$459$	1.63692e13	0.0375022
$460$	2.81596e13	0.0637468
$461$	3.87690e14	0.867221	0.433610	−	0.901100i	$-0.357239\pi$
$461$	3.87690e14	0.867221	0.433610	+	0.901100i	$0.357239\pi$
$462$	1.51227e13	0.0334271
$463$	−6.36506e14	−1.39029	−0.695147	−	0.718867i	$-0.744661\pi$
$463$	−6.36506e14	−1.39029	−0.695147	+	0.718867i	$0.744661\pi$
$464$	−5.88160e14	−1.26954
$465$	1.38513e13	0.0295460
$466$	1.85517e13	0.0391075
$467$	−5.78961e14	−1.20616	−0.603082	−	0.797679i	$-0.706061\pi$
$467$	−5.78961e14	−1.20616	−0.603082	+	0.797679i	$0.706061\pi$
$468$	7.34408e13	0.151212
$469$	−2.68520e14	−0.546419
$470$	−2.51774e12	−0.00506375
$471$	9.97126e13	0.198214
$472$	−6.32345e12	−0.0124243
$473$	−5.91421e13	−0.114858
$474$	−1.41376e13	−0.0271391
$475$	3.32976e14	0.631827
$476$	−1.85394e14	−0.347743
$477$	−2.43139e14	−0.450820
$478$	4.25237e12	0.00779432
$479$	−3.77517e14	−0.684055	−0.342027	−	0.939690i	$-0.611114\pi$
$479$	−3.77517e14	−0.684055	−0.342027	+	0.939690i	$0.611114\pi$
$480$	−4.31259e12	−0.00772523
$481$	−3.09569e14	−0.548227
$482$	−4.23894e13	−0.0742161
$483$	−4.07008e14	−0.704520
$484$	3.15300e14	0.539603
$485$	−1.40212e12	−0.00237250
$486$	−1.83173e12	−0.00306452
$487$	5.88866e14	0.974109	0.487054	−	0.873372i	$-0.338071\pi$
$487$	5.88866e14	0.974109	0.487054	+	0.873372i	$0.338071\pi$
$488$	−2.21912e13	−0.0362970
$489$	−6.18010e14	−0.999532
$490$	−6.15164e12	−0.00983813
$491$	7.81722e14	1.23624	0.618122	−	0.786082i	$-0.287894\pi$
$491$	7.81722e14	1.23624	0.618122	+	0.786082i	$0.287894\pi$
$492$	1.21678e14	0.190284
$493$	−1.61074e14	−0.249096
$494$	−9.05286e12	−0.0138448
$495$	−1.39862e13	−0.0211529
$496$	3.62843e14	0.542711
$497$	−4.90188e14	−0.725108
$498$	8.90511e12	0.0130280
$499$	3.04135e14	0.440062	0.220031	−	0.975493i	$-0.429384\pi$
$499$	3.04135e14	0.440062	0.220031	+	0.975493i	$0.429384\pi$
$500$	1.30009e14	0.186053
$501$	−3.35532e13	−0.0474927
$502$	9.07731e12	0.0127083
$503$	5.32879e14	0.737912	0.368956	−	0.929447i	$-0.379715\pi$
$503$	5.32879e14	0.737912	0.368956	+	0.929447i	$0.379715\pi$
$504$	4.15392e13	0.0568970
$505$	6.04843e13	0.0819483
$506$	−1.64785e13	−0.0220846
$507$	−3.45466e14	−0.457996
$508$	4.56010e14	0.598031
$509$	−1.28977e15	−1.67326	−0.836631	−	0.547767i	$-0.815478\pi$
$509$	−1.28977e15	−1.67326	−0.836631	+	0.547767i	$0.815478\pi$
$510$	−3.92182e11	−0.000503329 0
$511$	1.75093e14	0.222307
$512$	−1.88429e14	−0.236680
$513$	−9.87160e13	−0.122671
$514$	6.36998e13	0.0783143
$515$	−7.06533e13	−0.0859394
$516$	−8.11330e13	−0.0976392
$517$	−6.44140e14	−0.766977
$518$	−8.74485e13	−0.103024
$519$	4.64166e13	0.0541069
$520$	−3.52310e12	−0.00406355
$521$	−1.32247e15	−1.50930	−0.754652	−	0.656125i	$-0.772194\pi$
$521$	−1.32247e15	−1.50930	−0.754652	+	0.656125i	$0.772194\pi$
$522$	1.80243e13	0.0203550
$523$	4.00732e14	0.447811	0.223906	−	0.974611i	$-0.428119\pi$
$523$	4.00732e14	0.447811	0.223906	+	0.974611i	$0.428119\pi$
$524$	1.70791e14	0.188861
$525$	−9.35409e14	−1.02359
$526$	2.44419e13	0.0264675
$527$	9.93682e13	0.106485
$528$	−3.66377e14	−0.388545
$529$	−5.09313e14	−0.534538
$530$	5.82526e12	0.00605060
$531$	−4.22156e13	−0.0433963
$532$	1.11804e15	1.13748
$533$	1.49160e14	0.150194
$534$	2.97246e13	0.0296237
$535$	3.52659e13	0.0347864
$536$	−2.98621e13	−0.0291550
$537$	8.63094e14	0.834065
$538$	8.27085e13	0.0791129
$539$	−1.57384e15	−1.49012
$540$	−1.91867e13	−0.0179819
$541$	−7.68108e14	−0.712586	−0.356293	−	0.934374i	$-0.615959\pi$
$541$	−7.68108e14	−0.712586	−0.356293	+	0.934374i	$0.615959\pi$
$542$	2.07709e13	0.0190747
$543$	8.52754e14	0.775219
$544$	−3.09383e13	−0.0278421
$545$	−5.67443e13	−0.0505524
$546$	2.54316e13	0.0224292
$547$	1.79943e14	0.157111	0.0785553	−	0.996910i	$-0.474969\pi$
$547$	1.79943e14	0.157111	0.0785553	+	0.996910i	$0.474969\pi$
$548$	−9.25453e13	−0.0799947
$549$	−1.48149e14	−0.126780
$550$	−3.78719e13	−0.0320865
$551$	9.71373e14	0.814802
$552$	−4.52632e13	−0.0375907
$553$	2.14038e15	1.75996
$554$	4.99557e13	0.0406707
$555$	8.08762e13	0.0651943
$556$	8.58273e14	0.685037
$557$	−2.08144e14	−0.164498	−0.0822491	−	0.996612i	$-0.526210\pi$
$557$	−2.08144e14	−0.164498	−0.0822491	+	0.996612i	$0.526210\pi$
$558$	−1.11194e13	−0.00870150
$559$	−9.94582e13	−0.0770682
$560$	2.16807e14	0.166356
$561$	−1.00336e14	−0.0762362
$562$	6.67302e13	0.0502080
$563$	−1.07254e14	−0.0799131	−0.0399566	−	0.999201i	$-0.512722\pi$
$563$	−1.07254e14	−0.0799131	−0.0399566	+	0.999201i	$0.512722\pi$
$564$	−8.83652e14	−0.651998
$565$	−1.81448e14	−0.132583
$566$	5.40196e13	0.0390895
$567$	2.77317e14	0.198733
$568$	−5.45137e13	−0.0386892
$569$	−2.74553e15	−1.92978	−0.964892	−	0.262648i	$-0.915404\pi$
$569$	−2.74553e15	−1.92978	−0.964892	+	0.262648i	$0.915404\pi$
$570$	2.36509e12	0.00164641
$571$	2.88426e14	0.198855	0.0994275	−	0.995045i	$-0.468299\pi$
$571$	2.88426e14	0.198855	0.0994275	+	0.995045i	$0.468299\pi$
$572$	−4.50161e14	−0.307390
$573$	−1.16301e15	−0.786565
$574$	4.21355e13	0.0282249
$575$	1.01927e15	0.676264
$576$	−5.00295e14	−0.328778
$577$	−7.87983e13	−0.0512920	−0.0256460	−	0.999671i	$-0.508164\pi$
$577$	−7.87983e13	−0.0512920	−0.0256460	+	0.999671i	$0.508164\pi$
$578$	7.12779e13	0.0459570
$579$	−6.06158e14	−0.387127
$580$	1.88798e14	0.119438
$581$	−1.34820e15	−0.844862
$582$	1.12559e12	0.000698718 0
$583$	1.49034e15	0.916448
$584$	1.94720e13	0.0118615
$585$	−2.35203e13	−0.0141934
$586$	4.94870e13	0.0295838
$587$	4.26298e14	0.252466	0.126233	−	0.992001i	$-0.459711\pi$
$587$	4.26298e14	0.252466	0.126233	+	0.992001i	$0.459711\pi$
$588$	−2.15904e15	−1.26674
$589$	−5.99250e14	−0.348317
$590$	1.01142e12	0.000582435 0
$591$	−1.90347e15	−1.08596
$592$	2.11860e15	1.19751
$593$	−2.68295e15	−1.50249	−0.751245	−	0.660023i	$-0.770546\pi$
$593$	−2.68295e15	−1.50249	−0.751245	+	0.660023i	$0.770546\pi$
$594$	1.12277e13	0.00622969
$595$	5.93748e13	0.0326407
$596$	−7.44456e14	−0.405494
$597$	4.79283e14	0.258662
$598$	−2.77116e13	−0.0148185
$599$	−1.34478e15	−0.712533	−0.356266	−	0.934384i	$-0.615950\pi$
$599$	−1.34478e15	−0.712533	−0.356266	+	0.934384i	$0.615950\pi$
$600$	−1.04027e14	−0.0546151
$601$	−1.99759e15	−1.03919	−0.519597	−	0.854412i	$-0.673918\pi$
$601$	−1.99759e15	−1.03919	−0.519597	+	0.854412i	$0.673918\pi$
$602$	−2.80954e13	−0.0144828
$603$	−1.99360e14	−0.101834
$604$	2.85021e15	1.44269
$605$	−1.00979e14	−0.0506495
$606$	−4.85551e13	−0.0241344
$607$	−1.08277e15	−0.533331	−0.266666	−	0.963789i	$-0.585922\pi$
$607$	−1.08277e15	−0.533331	−0.266666	+	0.963789i	$0.585922\pi$
$608$	1.86577e14	0.0910725
$609$	−2.72882e15	−1.32002
$610$	3.54944e12	0.00170155
$611$	−1.08324e15	−0.514633
$612$	−1.37644e14	−0.0648075
$613$	2.68608e15	1.25339	0.626694	−	0.779265i	$-0.284407\pi$
$613$	2.68608e15	1.25339	0.626694	+	0.779265i	$0.284407\pi$
$614$	−1.95395e13	−0.00903624
$615$	−3.89687e13	−0.0178609
$616$	−2.54617e14	−0.115663
$617$	1.09022e15	0.490847	0.245423	−	0.969416i	$-0.421073\pi$
$617$	1.09022e15	0.490847	0.245423	+	0.969416i	$0.421073\pi$
$618$	5.67185e13	0.0253098
$619$	1.99913e15	0.884182	0.442091	−	0.896970i	$-0.354237\pi$
$619$	1.99913e15	0.884182	0.442091	+	0.896970i	$0.354237\pi$
$620$	−1.16472e14	−0.0510583
$621$	−3.02179e14	−0.131299
$622$	−5.95522e13	−0.0256479
$623$	−4.50019e15	−1.92109
$624$	−6.16129e14	−0.260709
$625$	2.32164e15	0.973766
$626$	1.15369e14	0.0479656
$627$	6.05087e14	0.249371
$628$	−8.38459e14	−0.342534
$629$	5.80202e14	0.234964
$630$	−6.64411e12	−0.00266725
$631$	−1.60230e14	−0.0637650	−0.0318825	−	0.999492i	$-0.510150\pi$
$631$	−1.60230e14	−0.0637650	−0.0318825	+	0.999492i	$0.510150\pi$
$632$	2.38031e14	0.0939053
$633$	−2.67999e14	−0.104812
$634$	−4.71421e13	−0.0182776
$635$	−1.46043e14	−0.0561338
$636$	2.04450e15	0.779062
$637$	−2.64670e15	−0.999857
$638$	−1.10482e14	−0.0413786
$639$	−3.63935e14	−0.135135
$640$	4.83328e13	0.0177931
$641$	3.08509e15	1.12603	0.563013	−	0.826448i	$-0.309642\pi$
$641$	3.08509e15	1.12603	0.563013	+	0.826448i	$0.309642\pi$
$642$	−2.83105e13	−0.0102448
$643$	1.17294e15	0.420837	0.210419	−	0.977611i	$-0.432517\pi$
$643$	1.17294e15	0.420837	0.210419	+	0.977611i	$0.432517\pi$
$644$	3.42243e15	1.21748
$645$	2.59838e13	0.00916484
$646$	1.69671e13	0.00593373
$647$	1.06206e15	0.368277	0.184139	−	0.982900i	$-0.441050\pi$
$647$	1.06206e15	0.368277	0.184139	+	0.982900i	$0.441050\pi$
$648$	3.08403e13	0.0106037
$649$	2.58763e14	0.0882180
$650$	−6.36885e13	−0.0215297
$651$	1.68344e15	0.564289
$652$	5.19669e15	1.72729
$653$	5.17742e15	1.70644	0.853219	−	0.521552i	$-0.174647\pi$
$653$	5.17742e15	1.70644	0.853219	+	0.521552i	$0.174647\pi$
$654$	4.55528e13	0.0148880
$655$	−5.46979e13	−0.0177273
$656$	−1.02081e15	−0.328076
$657$	1.29996e14	0.0414305
$658$	−3.05998e14	−0.0967110
$659$	−5.76292e15	−1.80623	−0.903114	−	0.429400i	$-0.858725\pi$
$659$	−5.76292e15	−1.80623	−0.903114	+	0.429400i	$0.858725\pi$
$660$	1.17606e14	0.0365543
$661$	1.35104e15	0.416447	0.208224	−	0.978081i	$-0.433232\pi$
$661$	1.35104e15	0.416447	0.208224	+	0.978081i	$0.433232\pi$
$662$	−1.16489e14	−0.0356097
$663$	−1.68733e14	−0.0511537
$664$	−1.49933e14	−0.0450788
$665$	−3.58066e14	−0.106769
$666$	−6.49252e13	−0.0192002
$667$	2.97346e15	0.872108
$668$	2.82141e14	0.0820720
$669$	−1.58815e15	−0.458191
$670$	4.77638e12	0.00136675
$671$	9.08091e14	0.257724
$672$	−5.24138e14	−0.147542
$673$	−3.33582e14	−0.0931364	−0.0465682	−	0.998915i	$-0.514828\pi$
$673$	−3.33582e14	−0.0931364	−0.0465682	+	0.998915i	$0.514828\pi$
$674$	−1.43683e14	−0.0397902
$675$	−6.94485e14	−0.190762
$676$	2.90494e15	0.791463
$677$	1.21173e15	0.327469	0.163734	−	0.986504i	$-0.447646\pi$
$677$	1.21173e15	0.327469	0.163734	+	0.986504i	$0.447646\pi$
$678$	1.45662e14	0.0390465
$679$	−1.70409e14	−0.0453116
$680$	6.60306e12	0.00174159
$681$	3.03547e15	0.794177
$682$	6.81573e13	0.0176888
$683$	3.59538e15	0.925617	0.462808	−	0.886458i	$-0.346842\pi$
$683$	3.59538e15	0.925617	0.462808	+	0.886458i	$0.346842\pi$
$684$	8.30078e14	0.211988
$685$	2.96388e13	0.00750866
$686$	−4.07666e14	−0.102452
$687$	1.47200e15	0.366984
$688$	6.80663e14	0.168343
$689$	2.50628e15	0.614927
$690$	7.23977e12	0.00176220
$691$	−1.63600e15	−0.395051	−0.197525	−	0.980298i	$-0.563290\pi$
$691$	−1.63600e15	−0.395051	−0.197525	+	0.980298i	$0.563290\pi$
$692$	−3.90305e14	−0.0935020
$693$	−1.69983e15	−0.403993
$694$	1.52027e13	0.00358462
$695$	−2.74872e14	−0.0643005
$696$	−3.03471e14	−0.0704314
$697$	−2.79560e14	−0.0643716
$698$	1.73482e14	0.0396324
$699$	−2.08525e15	−0.472645
$700$	7.86562e15	1.76886
$701$	−3.60539e15	−0.804458	−0.402229	−	0.915539i	$-0.631764\pi$
$701$	−3.60539e15	−0.804458	−0.402229	+	0.915539i	$0.631764\pi$
$702$	1.88815e13	0.00418005
$703$	−3.49897e15	−0.768574
$704$	3.06660e15	0.668355
$705$	2.83000e14	0.0611994
$706$	−1.00560e14	−0.0215774
$707$	7.35106e15	1.56510
$708$	3.54980e14	0.0749931
$709$	3.80021e15	0.796624	0.398312	−	0.917250i	$-0.369596\pi$
$709$	3.80021e15	0.796624	0.398312	+	0.917250i	$0.369596\pi$
$710$	8.71937e12	0.00181369
$711$	1.58910e15	0.327997
$712$	−5.00465e14	−0.102502
$713$	−1.83436e15	−0.372814
$714$	−4.76645e13	−0.00961291
$715$	1.44169e14	0.0288529
$716$	−7.25755e15	−1.44135
$717$	−4.77978e14	−0.0942003
$718$	−6.88373e13	−0.0134629
$719$	−3.94798e15	−0.766243	−0.383121	−	0.923698i	$-0.625151\pi$
$719$	−3.94798e15	−0.766243	−0.383121	+	0.923698i	$0.625151\pi$
$720$	1.60966e14	0.0310032
$721$	−8.58697e15	−1.64133
$722$	1.49515e14	0.0283616
$723$	4.76467e15	0.896959
$724$	−7.17059e15	−1.33966
$725$	6.83379e15	1.26708
$726$	8.10630e13	0.0149166
$727$	3.22833e15	0.589574	0.294787	−	0.955563i	$-0.404751\pi$
$727$	3.22833e15	0.589574	0.294787	+	0.955563i	$0.404751\pi$
$728$	−4.28186e14	−0.0776085
$729$	2.05891e14	0.0370370
$730$	−3.11452e12	−0.000556051 0
$731$	1.86407e14	0.0330306
$732$	1.24575e15	0.219088
$733$	−3.11347e14	−0.0543466	−0.0271733	−	0.999631i	$-0.508651\pi$
$733$	−3.11347e14	−0.0543466	−0.0271733	+	0.999631i	$0.508651\pi$
$734$	−3.53534e14	−0.0612496
$735$	6.91461e14	0.118901
$736$	5.71128e14	0.0974778
$737$	1.22199e15	0.207013
$738$	3.12830e13	0.00526016
$739$	−8.06786e15	−1.34652	−0.673262	−	0.739404i	$-0.735107\pi$
$739$	−8.06786e15	−1.34652	−0.673262	+	0.739404i	$0.735107\pi$
$740$	−6.80068e14	−0.112662
$741$	1.01756e15	0.167325
$742$	7.07983e14	0.115558
$743$	−5.25372e15	−0.851194	−0.425597	−	0.904913i	$-0.639936\pi$
$743$	−5.25372e15	−0.851194	−0.425597	+	0.904913i	$0.639936\pi$
$744$	1.87215e14	0.0301085
$745$	2.38421e14	0.0380615
$746$	−2.50817e14	−0.0397460
$747$	−1.00096e15	−0.157454
$748$	8.43701e14	0.131744
$749$	4.28610e15	0.664374
$750$	3.34250e13	0.00514321
$751$	9.17937e15	1.40215	0.701073	−	0.713090i	$-0.252705\pi$
$751$	9.17937e15	1.40215	0.701073	+	0.713090i	$0.252705\pi$
$752$	7.41338e15	1.12413
$753$	−1.02031e15	−0.153589
$754$	−1.85795e14	−0.0277646
$755$	−9.12815e14	−0.135417
$756$	−2.33189e15	−0.343430
$757$	4.74779e15	0.694168	0.347084	−	0.937834i	$-0.387172\pi$
$757$	4.74779e15	0.694168	0.347084	+	0.937834i	$0.387172\pi$
$758$	−5.05727e14	−0.0734067
$759$	1.85223e15	0.266910
$760$	−3.98205e13	−0.00569681
$761$	−1.64969e14	−0.0234307	−0.0117154	−	0.999931i	$-0.503729\pi$
$761$	−1.64969e14	−0.0234307	−0.0117154	+	0.999931i	$0.503729\pi$
$762$	1.17239e14	0.0165318
$763$	−6.89652e15	−0.965484
$764$	9.77950e15	1.35926
$765$	4.40823e13	0.00608311
$766$	−6.64497e14	−0.0910405
$767$	4.35158e14	0.0591933
$768$	4.17768e15	0.564220
$769$	−7.50627e15	−1.00654	−0.503268	−	0.864130i	$-0.667869\pi$
$769$	−7.50627e15	−1.00654	−0.503268	+	0.864130i	$0.667869\pi$
$770$	4.07256e13	0.00542211
$771$	−7.16003e15	−0.946489
$772$	5.09703e15	0.668993
$773$	−9.39637e15	−1.22454	−0.612270	−	0.790649i	$-0.709743\pi$
$773$	−9.39637e15	−1.22454	−0.612270	+	0.790649i	$0.709743\pi$
$774$	−2.08591e13	−0.00269911
$775$	−4.21584e15	−0.541657
$776$	−1.89512e13	−0.00241767
$777$	9.82943e15	1.24512
$778$	3.09324e14	0.0389068
$779$	1.68591e15	0.210562
$780$	1.97776e14	0.0245275
$781$	2.23077e15	0.274710
$782$	5.19377e13	0.00635106
$783$	−2.02598e15	−0.246006
$784$	1.81132e16	2.18403
$785$	2.68527e14	0.0321517
$786$	4.39100e13	0.00522083
$787$	9.95129e15	1.17495	0.587474	−	0.809243i	$-0.300123\pi$
$787$	9.95129e15	1.17495	0.587474	+	0.809243i	$0.300123\pi$
$788$	1.60058e16	1.87665
$789$	−2.74733e15	−0.319880
$790$	−3.80727e13	−0.00440214
$791$	−2.20526e16	−2.53215
$792$	−1.89038e14	−0.0215556
$793$	1.52712e15	0.172930
$794$	−3.75306e14	−0.0422058
$795$	−6.54775e14	−0.0731261
$796$	−4.03017e15	−0.446994
$797$	1.29552e15	0.142700	0.0713498	−	0.997451i	$-0.477269\pi$
$797$	1.29552e15	0.142700	0.0713498	+	0.997451i	$0.477269\pi$
$798$	2.87446e14	0.0314442
$799$	2.03023e15	0.220566
$800$	1.31260e15	0.141624
$801$	−3.34112e15	−0.358025
$802$	−4.47171e14	−0.0475898
$803$	−7.96820e14	−0.0842218
$804$	1.67637e15	0.175979
$805$	−1.09607e15	−0.114278
$806$	1.14619e14	0.0118690
$807$	−9.29665e15	−0.956141
$808$	8.17510e14	0.0835085
$809$	−1.76699e16	−1.79274	−0.896372	−	0.443303i	$-0.853807\pi$
$809$	−1.76699e16	−1.79274	−0.896372	+	0.443303i	$0.853807\pi$
$810$	−4.93286e12	−0.000497085 0
$811$	5.13792e15	0.514248	0.257124	−	0.966378i	$-0.417225\pi$
$811$	5.13792e15	0.514248	0.257124	+	0.966378i	$0.417225\pi$
$812$	2.29459e16	2.28112
$813$	−2.33470e15	−0.230533
$814$	3.97964e14	0.0390310
$815$	−1.66430e15	−0.162131
$816$	1.15476e15	0.111737
$817$	−1.12415e15	−0.108044
$818$	−1.04368e14	−0.00996377
$819$	−2.85858e15	−0.271075
$820$	3.27678e14	0.0308654
$821$	1.65798e16	1.55128	0.775641	−	0.631174i	$-0.217427\pi$
$821$	1.65798e16	1.55128	0.775641	+	0.631174i	$0.217427\pi$
$822$	−2.37932e13	−0.00221135
$823$	8.54594e15	0.788970	0.394485	−	0.918902i	$-0.370923\pi$
$823$	8.54594e15	0.788970	0.394485	+	0.918902i	$0.370923\pi$
$824$	−9.54955e14	−0.0875756
$825$	4.25690e15	0.387790
$826$	1.22925e14	0.0111237
$827$	−9.25100e15	−0.831588	−0.415794	−	0.909459i	$-0.636496\pi$
$827$	−9.25100e15	−0.831588	−0.415794	+	0.909459i	$0.636496\pi$
$828$	2.54095e15	0.226897
$829$	1.22466e16	1.08634	0.543168	−	0.839624i	$-0.317225\pi$
$829$	1.22466e16	1.08634	0.543168	+	0.839624i	$0.317225\pi$
$830$	2.39815e13	0.00211323
$831$	−5.61515e15	−0.491536
$832$	5.15704e15	0.448459
$833$	4.96050e15	0.428527
$834$	2.20660e14	0.0189370
$835$	−9.03590e13	−0.00770364
$836$	−5.08803e15	−0.430938
$837$	1.24985e15	0.105164
$838$	−2.08121e14	−0.0173970
$839$	1.38137e16	1.14715	0.573575	−	0.819153i	$-0.305556\pi$
$839$	1.38137e16	1.14715	0.573575	+	0.819153i	$0.305556\pi$
$840$	1.11865e14	0.00922909
$841$	7.73531e15	0.634015
$842$	−7.73190e14	−0.0629607
$843$	−7.50065e15	−0.606802
$844$	2.25354e15	0.181126
$845$	−9.30343e14	−0.0742901
$846$	−2.27185e14	−0.0180237
$847$	−1.22726e16	−0.967339
$848$	−1.71522e16	−1.34321
$849$	−6.07194e15	−0.472427
$850$	1.19366e14	0.00922737
$851$	−1.07107e16	−0.822629
$852$	3.06024e15	0.233527
$853$	1.29744e16	0.983712	0.491856	−	0.870677i	$-0.336319\pi$
$853$	1.29744e16	0.983712	0.491856	+	0.870677i	$0.336319\pi$
$854$	4.31387e14	0.0324974
$855$	−2.65843e14	−0.0198981
$856$	4.76657e14	0.0354487
$857$	6.64958e15	0.491360	0.245680	−	0.969351i	$-0.420989\pi$
$857$	6.64958e15	0.491360	0.245680	+	0.969351i	$0.420989\pi$
$858$	−1.15735e14	−0.00849740
$859$	1.88846e15	0.137767	0.0688836	−	0.997625i	$-0.478056\pi$
$859$	1.88846e15	0.137767	0.0688836	+	0.997625i	$0.478056\pi$
$860$	−2.18492e14	−0.0158377
$861$	−4.73613e15	−0.341120
$862$	3.50873e14	0.0251108
$863$	−1.84854e16	−1.31453	−0.657264	−	0.753661i	$-0.728286\pi$
$863$	−1.84854e16	−1.31453	−0.657264	+	0.753661i	$0.728286\pi$
$864$	−3.89141e14	−0.0274968
$865$	1.25000e14	0.00877651
$866$	−4.09860e14	−0.0285948
$867$	−8.01183e15	−0.555426
$868$	−1.41556e16	−0.975147
$869$	−9.74054e15	−0.666767
$870$	4.85397e13	0.00330172
$871$	2.05500e15	0.138903
$872$	−7.66960e14	−0.0515148
$873$	−1.26519e14	−0.00844455
$874$	−3.13216e14	−0.0207745
$875$	−5.06041e15	−0.333535
$876$	−1.09310e15	−0.0715960
$877$	−1.83116e16	−1.19187	−0.595934	−	0.803033i	$-0.703218\pi$
$877$	−1.83116e16	−1.19187	−0.595934	+	0.803033i	$0.703218\pi$
$878$	−1.26986e15	−0.0821367
$879$	−5.56247e15	−0.357543
$880$	−9.86654e14	−0.0630246
$881$	−2.42101e16	−1.53684	−0.768419	−	0.639947i	$-0.778956\pi$
$881$	−2.42101e16	−1.53684	−0.768419	+	0.639947i	$0.778956\pi$
$882$	−5.55086e14	−0.0350173
$883$	−8.16078e14	−0.0511620	−0.0255810	−	0.999673i	$-0.508144\pi$
$883$	−8.16078e14	−0.0511620	−0.0255810	+	0.999673i	$0.508144\pi$
$884$	1.41884e15	0.0883985
$885$	−1.13687e14	−0.00703918
$886$	−2.06269e14	−0.0126925
$887$	3.04467e16	1.86192	0.930959	−	0.365124i	$-0.118974\pi$
$887$	3.04467e16	1.86192	0.930959	+	0.365124i	$0.118974\pi$
$888$	1.09313e15	0.0664355
$889$	−1.77496e16	−1.07208
$890$	8.00485e13	0.00480516
$891$	−1.26203e15	−0.0752906
$892$	1.33543e16	0.791799
$893$	−1.22435e16	−0.721478
$894$	−1.91398e14	−0.0112094
$895$	2.32432e15	0.135291
$896$	5.87421e15	0.339825
$897$	3.11486e15	0.179094
$898$	6.09745e14	0.0348440
$899$	−1.22986e16	−0.698519
$900$	5.83975e15	0.329656
$901$	−4.69732e15	−0.263550
$902$	−1.91752e14	−0.0106931
$903$	3.15799e15	0.175036
$904$	−2.45247e15	−0.135107
$905$	2.29647e15	0.125746
$906$	7.32783e14	0.0398814
$907$	−6.06387e15	−0.328027	−0.164013	−	0.986458i	$-0.552444\pi$
$907$	−6.06387e15	−0.328027	−0.164013	+	0.986458i	$0.552444\pi$
$908$	−2.55245e16	−1.37242
$909$	5.45772e15	0.291682
$910$	6.84875e13	0.00363818
$911$	−2.44461e16	−1.29080	−0.645400	−	0.763845i	$-0.723309\pi$
$911$	−2.44461e16	−1.29080	−0.645400	+	0.763845i	$0.723309\pi$
$912$	−6.96392e15	−0.365496
$913$	6.13545e15	0.320079
$914$	1.16942e15	0.0606412
$915$	−3.98966e14	−0.0205646
$916$	−1.23777e16	−0.634184
$917$	−6.64781e15	−0.338569
$918$	−3.53880e13	−0.00179152
$919$	−4.61347e15	−0.232162	−0.116081	−	0.993240i	$-0.537033\pi$
$919$	−4.61347e15	−0.232162	−0.116081	+	0.993240i	$0.537033\pi$
$920$	−1.21894e14	−0.00609747
$921$	2.19629e15	0.109210
$922$	−8.38136e14	−0.0414281
$923$	3.75144e15	0.184327
$924$	1.42935e16	0.698139
$925$	−2.46159e16	−1.19519
$926$	1.37604e15	0.0664159
$927$	−6.37531e15	−0.305888
$928$	3.82918e15	0.182638
$929$	−1.59191e16	−0.754802	−0.377401	−	0.926050i	$-0.623182\pi$
$929$	−1.59191e16	−0.754802	−0.377401	+	0.926050i	$0.623182\pi$
$930$	−2.99446e13	−0.00141144
$931$	−2.99148e16	−1.40173
$932$	1.75344e16	0.816776
$933$	6.69383e15	0.309974
$934$	1.25164e15	0.0576197
$935$	−2.70206e14	−0.0123660
$936$	−3.17902e14	−0.0144636
$937$	9.86284e15	0.446102	0.223051	−	0.974807i	$-0.428398\pi$
$937$	9.86284e15	0.446102	0.223051	+	0.974807i	$0.428398\pi$
$938$	5.80506e14	0.0261030
$939$	−1.29678e16	−0.579701
$940$	−2.37968e15	−0.105759
$941$	4.42260e16	1.95404	0.977022	−	0.213138i	$-0.0683685\pi$
$941$	4.42260e16	1.95404	0.977022	+	0.213138i	$0.0683685\pi$
$942$	−2.15566e14	−0.00946891
$943$	5.16074e15	0.225371
$944$	−2.97810e15	−0.129298
$945$	7.46816e14	0.0322358
$946$	1.27858e14	0.00548687
$947$	−1.88298e16	−0.803381	−0.401690	−	0.915776i	$-0.631577\pi$
$947$	−1.88298e16	−0.803381	−0.401690	+	0.915776i	$0.631577\pi$
$948$	−1.33624e16	−0.566811
$949$	−1.34000e15	−0.0565119
$950$	−7.19852e14	−0.0301831
$951$	5.29890e15	0.220898
$952$	8.02515e14	0.0332621
$953$	−1.95109e15	−0.0804018	−0.0402009	−	0.999192i	$-0.512800\pi$
$953$	−1.95109e15	−0.0804018	−0.0402009	+	0.999192i	$0.512800\pi$
$954$	5.25635e14	0.0215362
$955$	−3.13200e15	−0.127586
$956$	4.01920e15	0.162787
$957$	1.24184e16	0.500093
$958$	8.16142e14	0.0326780
$959$	3.60220e15	0.143405
$960$	−1.34730e15	−0.0533300
$961$	−1.78213e16	−0.701393
$962$	6.69249e14	0.0261894
$963$	3.18218e15	0.123817
$964$	−4.00650e16	−1.55003
$965$	−1.63239e15	−0.0627946
$966$	8.79899e14	0.0336557
$967$	3.19445e16	1.21493	0.607464	−	0.794347i	$-0.292187\pi$
$967$	3.19445e16	1.21493	0.607464	+	0.794347i	$0.292187\pi$
$968$	−1.36484e15	−0.0516138
$969$	−1.90714e15	−0.0717137
$970$	3.03121e12	0.000113337 0
$971$	1.80781e16	0.672120	0.336060	−	0.941841i	$-0.390905\pi$
$971$	1.80781e16	0.672120	0.336060	+	0.941841i	$0.390905\pi$
$972$	−1.73129e15	−0.0640036
$973$	−3.34071e16	−1.22806
$974$	−1.27305e15	−0.0465342
$975$	7.15876e15	0.260203
$976$	−1.04512e16	−0.377738
$977$	1.30976e16	0.470731	0.235366	−	0.971907i	$-0.424371\pi$
$977$	1.30976e16	0.470731	0.235366	+	0.971907i	$0.424371\pi$
$978$	1.33606e15	0.0477487
$979$	2.04797e16	0.727810
$980$	−5.81432e15	−0.205473
$981$	−5.12025e15	−0.179933
$982$	−1.68998e15	−0.0590567
$983$	−4.30264e16	−1.49517	−0.747586	−	0.664165i	$-0.768787\pi$
$983$	−4.30264e16	−1.49517	−0.747586	+	0.664165i	$0.768787\pi$
$984$	−5.26704e14	−0.0182009
$985$	−5.12605e15	−0.176150
$986$	3.48221e14	0.0118996
$987$	3.43950e16	1.16883
$988$	−8.55645e15	−0.289155
$989$	−3.44111e15	−0.115643
$990$	3.02363e13	0.00101050
$991$	−1.77981e16	−0.591520	−0.295760	−	0.955262i	$-0.595573\pi$
$991$	−1.77981e16	−0.591520	−0.295760	+	0.955262i	$0.595573\pi$
$992$	−2.36226e15	−0.0780753
$993$	1.30937e16	0.430370
$994$	1.05972e15	0.0346392
$995$	1.29071e15	0.0419568
$996$	8.41680e15	0.272095
$997$	−2.02344e16	−0.650529	−0.325264	−	0.945623i	$-0.605453\pi$
$997$	−2.02344e16	−0.650529	−0.325264	+	0.945623i	$0.605453\pi$
$998$	−6.57501e14	−0.0210222
$999$	7.29777e15	0.232049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.15	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.16187 q^{2} +243.000 q^{3} -2043.33 q^{4} +654.400 q^{5} -525.335 q^{6} +79533.7 q^{7} +8844.92 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-2.16187 q^{2} +243.000 q^{3} -2043.33 q^{4} +654.400 q^{5} -525.335 q^{6} +79533.7 q^{7} +8844.92 q^{8} +59049.0 q^{9} -1414.73 q^{10} -361945. q^{11} -496528. q^{12} -608677. q^{13} -171942. q^{14} +159019. q^{15} +4.16561e6 q^{16} +1.14080e6 q^{17} -127656. q^{18} -6.87969e6 q^{19} -1.33715e6 q^{20} +1.93267e7 q^{21} +782479. q^{22} -2.10594e7 q^{23} +2.14932e6 q^{24} -4.83999e7 q^{25} +1.31588e6 q^{26} +1.43489e7 q^{27} -1.62513e8 q^{28} -1.41194e8 q^{29} -343779. q^{30} +8.71043e7 q^{31} -2.71199e7 q^{32} -8.79527e7 q^{33} -2.46625e6 q^{34} +5.20469e7 q^{35} -1.20656e8 q^{36} +5.08594e8 q^{37} +1.48730e7 q^{38} -1.47909e8 q^{39} +5.78812e6 q^{40} -2.45057e8 q^{41} -4.17818e7 q^{42} +1.63401e8 q^{43} +7.39572e8 q^{44} +3.86417e7 q^{45} +4.55276e7 q^{46} +1.77966e9 q^{47} +1.01224e9 q^{48} +4.34828e9 q^{49} +1.04634e8 q^{50} +2.77213e8 q^{51} +1.24373e9 q^{52} -4.11758e9 q^{53} -3.10205e7 q^{54} -2.36857e8 q^{55} +7.03469e8 q^{56} -1.67176e9 q^{57} +3.05244e8 q^{58} -7.14924e8 q^{59} -3.24928e8 q^{60} -2.50892e9 q^{61} -1.88308e8 q^{62} +4.69639e9 q^{63} -8.47254e9 q^{64} -3.98318e8 q^{65} +1.90142e8 q^{66} -3.37618e9 q^{67} -2.33102e9 q^{68} -5.11743e9 q^{69} -1.12519e8 q^{70} -6.16327e9 q^{71} +5.22284e8 q^{72} +2.20149e9 q^{73} -1.09951e9 q^{74} -1.17612e10 q^{75} +1.40574e10 q^{76} -2.87868e10 q^{77} +3.19759e8 q^{78} +2.69116e10 q^{79} +2.72598e9 q^{80} +3.48678e9 q^{81} +5.29781e8 q^{82} -1.69513e10 q^{83} -3.94907e10 q^{84} +7.46537e8 q^{85} -3.53251e8 q^{86} -3.43102e10 q^{87} -3.20138e9 q^{88} -5.65822e10 q^{89} -8.35384e7 q^{90} -4.84103e10 q^{91} +4.30312e10 q^{92} +2.11663e10 q^{93} -3.84740e9 q^{94} -4.50207e9 q^{95} -6.59014e9 q^{96} -2.14261e9 q^{97} -9.40043e9 q^{98} -2.13725e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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