LMFDB - Embedded newform 177.8.a.c.1.9

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
Defining polynomial:	$x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + 50741131904 x^{8} - 7480805165760 x^{7} - 10751966150272 x^{6} + 413177144536320 x^{5} + 886760582981376 x^{4} - 10454479722123264 x^{3} - 29180140031461376 x^{2} + 79787300207378432 x + 248723246810300416$
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-3.62331$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-3.62331 q^{2} -27.0000 q^{3} -114.872 q^{4} +300.817 q^{5} +97.8295 q^{6} +1353.78 q^{7} +880.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-3.62331 q^{2} -27.0000 q^{3} -114.872 q^{4} +300.817 q^{5} +97.8295 q^{6} +1353.78 q^{7} +880.000 q^{8} +729.000 q^{9} -1089.96 q^{10} +8127.65 q^{11} +3101.53 q^{12} +1822.67 q^{13} -4905.17 q^{14} -8122.07 q^{15} +11515.0 q^{16} +1656.90 q^{17} -2641.40 q^{18} +18541.4 q^{19} -34555.4 q^{20} -36552.0 q^{21} -29449.0 q^{22} +15601.2 q^{23} -23760.0 q^{24} +12366.0 q^{25} -6604.11 q^{26} -19683.0 q^{27} -155511. q^{28} +150338. q^{29} +29428.8 q^{30} -248513. q^{31} -154363. q^{32} -219447. q^{33} -6003.46 q^{34} +407240. q^{35} -83741.4 q^{36} -170725. q^{37} -67181.2 q^{38} -49212.1 q^{39} +264719. q^{40} +283414. q^{41} +132439. q^{42} +39428.6 q^{43} -933636. q^{44} +219296. q^{45} -56528.0 q^{46} -77426.6 q^{47} -310906. q^{48} +1.00917e6 q^{49} -44805.9 q^{50} -44736.3 q^{51} -209373. q^{52} +1.98028e6 q^{53} +71317.7 q^{54} +2.44494e6 q^{55} +1.19133e6 q^{56} -500617. q^{57} -544721. q^{58} -205379. q^{59} +932995. q^{60} -938894. q^{61} +900440. q^{62} +986905. q^{63} -914622. q^{64} +548291. q^{65} +795124. q^{66} +2.93505e6 q^{67} -190331. q^{68} -421232. q^{69} -1.47556e6 q^{70} -5.87325e6 q^{71} +641520. q^{72} -2.53313e6 q^{73} +618590. q^{74} -333882. q^{75} -2.12988e6 q^{76} +1.10030e7 q^{77} +178311. q^{78} -1.99924e6 q^{79} +3.46392e6 q^{80} +531441. q^{81} -1.02690e6 q^{82} +5.33794e6 q^{83} +4.19879e6 q^{84} +498424. q^{85} -142862. q^{86} -4.05912e6 q^{87} +7.15233e6 q^{88} +2.14988e6 q^{89} -794577. q^{90} +2.46749e6 q^{91} -1.79213e6 q^{92} +6.70985e6 q^{93} +280541. q^{94} +5.57757e6 q^{95} +4.16779e6 q^{96} -3.36902e6 q^{97} -3.65656e6 q^{98} +5.92506e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) $	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

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 $

$2$	−3.62331	−0.320259	−0.160129	−	0.987096i	$-0.551191\pi$
$2$	−3.62331	−0.320259	−0.160129	+	0.987096i	$0.551191\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−114.872	−0.897434
$5$	300.817	1.07624	0.538118	−	0.842869i	$-0.319135\pi$
$5$	300.817	1.07624	0.538118	+	0.842869i	$0.319135\pi$
$6$	97.8295	0.184901
$7$	1353.78	1.49178	0.745890	−	0.666070i	$-0.232025\pi$
$7$	1353.78	1.49178	0.745890	+	0.666070i	$0.232025\pi$
$8$	880.000	0.607670
$9$	729.000	0.333333
$10$	−1089.96	−0.344674
$11$	8127.65	1.84116	0.920578	−	0.390558i	$-0.127718\pi$
$11$	8127.65	1.84116	0.920578	+	0.390558i	$0.127718\pi$
$12$	3101.53	0.518134
$13$	1822.67	0.230095	0.115047	−	0.993360i	$-0.463298\pi$
$13$	1822.67	0.230095	0.115047	+	0.993360i	$0.463298\pi$
$14$	−4905.17	−0.477755
$15$	−8122.07	−0.621365
$16$	11515.0	0.702823
$17$	1656.90	0.0817946	0.0408973	−	0.999163i	$-0.486978\pi$
$17$	1656.90	0.0817946	0.0408973	+	0.999163i	$0.486978\pi$
$18$	−2641.40	−0.106753
$19$	18541.4	0.620161	0.310081	−	0.950710i	$-0.399644\pi$
$19$	18541.4	0.620161	0.310081	+	0.950710i	$0.399644\pi$
$20$	−34555.4	−0.965852
$21$	−36552.0	−0.861279
$22$	−29449.0	−0.589646
$23$	15601.2	0.267369	0.133684	−	0.991024i	$-0.457319\pi$
$23$	15601.2	0.267369	0.133684	+	0.991024i	$0.457319\pi$
$24$	−23760.0	−0.350838
$25$	12366.0	0.158285
$26$	−6604.11	−0.0736899
$27$	−19683.0	−0.192450
$28$	−155511.	−1.33877
$29$	150338.	1.14466	0.572328	−	0.820025i	$-0.306040\pi$
$29$	150338.	1.14466	0.572328	+	0.820025i	$0.306040\pi$
$30$	29428.8	0.198998
$31$	−248513.	−1.49825	−0.749123	−	0.662431i	$-0.769525\pi$
$31$	−248513.	−1.49825	−0.749123	+	0.662431i	$0.769525\pi$
$32$	−154363.	−0.832755
$33$	−219447.	−1.06299
$34$	−6003.46	−0.0261954
$35$	407240.	1.60551
$36$	−83741.4	−0.299145
$37$	−170725.	−0.554104	−0.277052	−	0.960855i	$-0.589357\pi$
$37$	−170725.	−0.554104	−0.277052	+	0.960855i	$0.589357\pi$
$38$	−67181.2	−0.198612
$39$	−49212.1	−0.132845
$40$	264719.	0.653997
$41$	283414.	0.642210	0.321105	−	0.947044i	$-0.395946\pi$
$41$	283414.	0.642210	0.321105	+	0.947044i	$0.395946\pi$
$42$	132439.	0.275832
$43$	39428.6	0.0756261	0.0378130	−	0.999285i	$-0.487961\pi$
$43$	39428.6	0.0756261	0.0378130	+	0.999285i	$0.487961\pi$
$44$	−933636.	−1.65232
$45$	219296.	0.358745
$46$	−56528.0	−0.0856271
$47$	−77426.6	−0.108780	−0.0543898	−	0.998520i	$-0.517321\pi$
$47$	−77426.6	−0.108780	−0.0543898	+	0.998520i	$0.517321\pi$
$48$	−310906.	−0.405775
$49$	1.00917e6	1.22541
$50$	−44805.9	−0.0506921
$51$	−44736.3	−0.0472241
$52$	−209373.	−0.206495
$53$	1.98028e6	1.82709	0.913546	−	0.406735i	$-0.133333\pi$
$53$	1.98028e6	1.82709	0.913546	+	0.406735i	$0.133333\pi$
$54$	71317.7	0.0616338
$55$	2.44494e6	1.98152
$56$	1.19133e6	0.906509
$57$	−500617.	−0.358050
$58$	−544721.	−0.366586
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	932995.	0.557635
$61$	−938894.	−0.529617	−0.264808	−	0.964301i	$-0.585309\pi$
$61$	−938894.	−0.529617	−0.264808	+	0.964301i	$0.585309\pi$
$62$	900440.	0.479826
$63$	986905.	0.497260
$64$	−914622.	−0.436126
$65$	548291.	0.247636
$66$	795124.	0.340433
$67$	2.93505e6	1.19221	0.596107	−	0.802905i	$-0.296714\pi$
$67$	2.93505e6	1.19221	0.596107	+	0.802905i	$0.296714\pi$
$68$	−190331.	−0.0734053
$69$	−421232.	−0.154365
$70$	−1.47556e6	−0.514178
$71$	−5.87325e6	−1.94749	−0.973743	−	0.227650i	$-0.926896\pi$
$71$	−5.87325e6	−1.94749	−0.973743	+	0.227650i	$0.926896\pi$
$72$	641520.	0.202557
$73$	−2.53313e6	−0.762126	−0.381063	−	0.924549i	$-0.624442\pi$
$73$	−2.53313e6	−0.762126	−0.381063	+	0.924549i	$0.624442\pi$
$74$	618590.	0.177457
$75$	−333882.	−0.0913859
$76$	−2.12988e6	−0.556554
$77$	1.10030e7	2.74660
$78$	178311.	0.0425449
$79$	−1.99924e6	−0.456217	−0.228108	−	0.973636i	$-0.573254\pi$
$79$	−1.99924e6	−0.456217	−0.228108	+	0.973636i	$0.573254\pi$
$80$	3.46392e6	0.756403
$81$	531441.	0.111111
$82$	−1.02690e6	−0.205673
$83$	5.33794e6	1.02471	0.512354	−	0.858774i	$-0.328773\pi$
$83$	5.33794e6	1.02471	0.512354	+	0.858774i	$0.328773\pi$
$84$	4.19879e6	0.772942
$85$	498424.	0.0880303
$86$	−142862.	−0.0242199
$87$	−4.05912e6	−0.660867
$88$	7.15233e6	1.11882
$89$	2.14988e6	0.323258	0.161629	−	0.986852i	$-0.448325\pi$
$89$	2.14988e6	0.323258	0.161629	+	0.986852i	$0.448325\pi$
$90$	−794577.	−0.114891
$91$	2.46749e6	0.343251
$92$	−1.79213e6	−0.239946
$93$	6.70985e6	0.865012
$94$	280541.	0.0348376
$95$	5.57757e6	0.667440
$96$	4.16779e6	0.480791
$97$	−3.36902e6	−0.374802	−0.187401	−	0.982283i	$-0.560006\pi$
$97$	−3.36902e6	−0.374802	−0.187401	+	0.982283i	$0.560006\pi$
$98$	−3.65656e6	−0.392447
$99$	5.92506e6	0.613719
$100$	−1.42050e6	−0.142050
$101$	1.18390e6	0.114338	0.0571688	−	0.998365i	$-0.481793\pi$
$101$	1.18390e6	0.114338	0.0571688	+	0.998365i	$0.481793\pi$
$102$	162094.	0.0151239
$103$	−1.00671e7	−0.907764	−0.453882	−	0.891062i	$-0.649961\pi$
$103$	−1.00671e7	−0.907764	−0.453882	+	0.891062i	$0.649961\pi$
$104$	1.60395e6	0.139822
$105$	−1.09955e7	−0.926940
$106$	−7.17517e6	−0.585142
$107$	−5.24702e6	−0.414066	−0.207033	−	0.978334i	$-0.566381\pi$
$107$	−5.24702e6	−0.414066	−0.207033	+	0.978334i	$0.566381\pi$
$108$	2.26102e6	0.172711
$109$	1.31376e7	0.971681	0.485841	−	0.874047i	$-0.338514\pi$
$109$	1.31376e7	0.971681	0.485841	+	0.874047i	$0.338514\pi$
$110$	−8.85878e6	−0.634599
$111$	4.60958e6	0.319912
$112$	1.55888e7	1.04846
$113$	9.32454e6	0.607929	0.303965	−	0.952683i	$-0.401690\pi$
$113$	9.32454e6	0.607929	0.303965	+	0.952683i	$0.401690\pi$
$114$	1.81389e6	0.114669
$115$	4.69311e6	0.287752
$116$	−1.72695e7	−1.02725
$117$	1.32873e6	0.0766983
$118$	744153.	0.0416941
$119$	2.24307e6	0.122020
$120$	−7.14742e6	−0.377585
$121$	4.65715e7	2.38986
$122$	3.40191e6	0.169614
$123$	−7.65217e6	−0.370780
$124$	2.85471e7	1.34458
$125$	−1.97814e7	−0.905884
$126$	−3.57587e6	−0.159252
$127$	1.14096e7	0.494263	0.247131	−	0.968982i	$-0.420512\pi$
$127$	1.14096e7	0.494263	0.247131	+	0.968982i	$0.420512\pi$
$128$	2.30724e7	0.972428
$129$	−1.06457e6	−0.0436627
$130$	−1.98663e6	−0.0793077
$131$	1.68449e7	0.654666	0.327333	−	0.944909i	$-0.393850\pi$
$131$	1.68449e7	0.654666	0.327333	+	0.944909i	$0.393850\pi$
$132$	2.52082e7	0.953966
$133$	2.51009e7	0.925143
$134$	−1.06346e7	−0.381817
$135$	−5.92099e6	−0.207122
$136$	1.45807e6	0.0497041
$137$	−5.53033e7	−1.83751	−0.918754	−	0.394830i	$-0.870804\pi$
$137$	−5.53033e7	−1.83751	−0.918754	+	0.394830i	$0.870804\pi$
$138$	1.52626e6	0.0494368
$139$	−392568.	−0.0123983	−0.00619916	−	0.999981i	$-0.501973\pi$
$139$	−392568.	−0.0123983	−0.00619916	+	0.999981i	$0.501973\pi$
$140$	−4.67803e7	−1.44084
$141$	2.09052e6	0.0628040
$142$	2.12806e7	0.623699
$143$	1.48140e7	0.423640
$144$	8.39447e6	0.234274
$145$	4.52242e7	1.23192
$146$	9.17831e6	0.244078
$147$	−2.72477e7	−0.707488
$148$	1.96115e7	0.497272
$149$	−3.39826e7	−0.841598	−0.420799	−	0.907154i	$-0.638250\pi$
$149$	−3.39826e7	−0.841598	−0.420799	+	0.907154i	$0.638250\pi$
$150$	1.20976e6	0.0292671
$151$	1.86602e7	0.441059	0.220530	−	0.975380i	$-0.429221\pi$
$151$	1.86602e7	0.441059	0.220530	+	0.975380i	$0.429221\pi$
$152$	1.63164e7	0.376853
$153$	1.20788e6	0.0272649
$154$	−3.98675e7	−0.879622
$155$	−7.47570e7	−1.61247
$156$	5.65308e6	0.119220
$157$	3.31311e7	0.683262	0.341631	−	0.939834i	$-0.389021\pi$
$157$	3.31311e7	0.683262	0.341631	+	0.939834i	$0.389021\pi$
$158$	7.24389e6	0.146107
$159$	−5.34675e7	−1.05487
$160$	−4.64349e7	−0.896241
$161$	2.11206e7	0.398855
$162$	−1.92558e6	−0.0355843
$163$	−7.04997e7	−1.27506	−0.637530	−	0.770426i	$-0.720044\pi$
$163$	−7.04997e7	−1.27506	−0.637530	+	0.770426i	$0.720044\pi$
$164$	−3.25562e7	−0.576342
$165$	−6.60133e7	−1.14403
$166$	−1.93410e7	−0.328172
$167$	−5.02367e7	−0.834667	−0.417333	−	0.908753i	$-0.637035\pi$
$167$	−5.02367e7	−0.834667	−0.417333	+	0.908753i	$0.637035\pi$
$168$	−3.21658e7	−0.523373
$169$	−5.94264e7	−0.947056
$170$	−1.80595e6	−0.0281925
$171$	1.35167e7	0.206720
$172$	−4.52922e6	−0.0678694
$173$	3.60070e7	0.528719	0.264360	−	0.964424i	$-0.414839\pi$
$173$	3.60070e7	0.528719	0.264360	+	0.964424i	$0.414839\pi$
$174$	1.47075e7	0.211649
$175$	1.67408e7	0.236126
$176$	9.35903e7	1.29401
$177$	5.54523e6	0.0751646
$178$	−7.78968e6	−0.103526
$179$	−6.95659e7	−0.906589	−0.453295	−	0.891361i	$-0.649751\pi$
$179$	−6.95659e7	−0.906589	−0.453295	+	0.891361i	$0.649751\pi$
$180$	−2.51909e7	−0.321951
$181$	1.45844e8	1.82816	0.914079	−	0.405536i	$-0.132915\pi$
$181$	1.45844e8	1.82816	0.914079	+	0.405536i	$0.132915\pi$
$182$	−8.94051e6	−0.109929
$183$	2.53501e7	0.305775
$184$	1.37291e7	0.162472
$185$	−5.13570e7	−0.596347
$186$	−2.43119e7	−0.277028
$187$	1.34667e7	0.150597
$188$	8.89412e6	0.0976226
$189$	−2.66464e7	−0.287093
$190$	−2.02093e7	−0.213753
$191$	3.79780e7	0.394380	0.197190	−	0.980365i	$-0.436818\pi$
$191$	3.79780e7	0.394380	0.197190	+	0.980365i	$0.436818\pi$
$192$	2.46948e7	0.251797
$193$	−1.18553e8	−1.18704	−0.593518	−	0.804821i	$-0.702261\pi$
$193$	−1.18553e8	−1.18704	−0.593518	+	0.804821i	$0.702261\pi$
$194$	1.22070e7	0.120034
$195$	−1.48039e7	−0.142973
$196$	−1.15925e8	−1.09972
$197$	−1.37665e8	−1.28290	−0.641450	−	0.767165i	$-0.721667\pi$
$197$	−1.37665e8	−1.28290	−0.641450	+	0.767165i	$0.721667\pi$
$198$	−2.14683e7	−0.196549
$199$	−1.00525e8	−0.904248	−0.452124	−	0.891955i	$-0.649334\pi$
$199$	−1.00525e8	−0.904248	−0.452124	+	0.891955i	$0.649334\pi$
$200$	1.08821e7	0.0961850
$201$	−7.92464e7	−0.688325
$202$	−4.28963e6	−0.0366176
$203$	2.03524e8	1.70757
$204$	5.13893e6	0.0423806
$205$	8.52557e7	0.691170
$206$	3.64762e7	0.290719
$207$	1.13733e7	0.0891229
$208$	2.09882e7	0.161716
$209$	1.50698e8	1.14181
$210$	3.98401e7	0.296861
$211$	2.62670e8	1.92496	0.962480	−	0.271354i	$-0.0874714\pi$
$211$	2.62670e8	1.92496	0.962480	+	0.271354i	$0.0874714\pi$
$212$	−2.27478e8	−1.63970
$213$	1.58578e8	1.12438
$214$	1.90116e7	0.132608
$215$	1.18608e7	0.0813915
$216$	−1.73210e7	−0.116946
$217$	−3.36432e8	−2.23505
$218$	−4.76017e7	−0.311189
$219$	6.83944e7	0.440014
$220$	−2.80854e8	−1.77828
$221$	3.01998e6	0.0188205
$222$	−1.67019e7	−0.102455
$223$	2.67872e8	1.61756	0.808781	−	0.588110i	$-0.200128\pi$
$223$	2.67872e8	1.61756	0.808781	+	0.588110i	$0.200128\pi$
$224$	−2.08973e8	−1.24229
$225$	9.01482e6	0.0527616
$226$	−3.37857e7	−0.194695
$227$	−9.46663e7	−0.537161	−0.268581	−	0.963257i	$-0.586555\pi$
$227$	−9.46663e7	−0.537161	−0.268581	+	0.963257i	$0.586555\pi$
$228$	5.75067e7	0.321326
$229$	2.26035e8	1.24380	0.621900	−	0.783096i	$-0.286361\pi$
$229$	2.26035e8	1.24380	0.621900	+	0.783096i	$0.286361\pi$
$230$	−1.70046e7	−0.0921550
$231$	−2.97082e8	−1.58575
$232$	1.32297e8	0.695573
$233$	−6.28293e7	−0.325399	−0.162700	−	0.986676i	$-0.552020\pi$
$233$	−6.28293e7	−0.325399	−0.162700	+	0.986676i	$0.552020\pi$
$234$	−4.81440e6	−0.0245633
$235$	−2.32913e7	−0.117073
$236$	2.35922e7	0.116836
$237$	5.39796e7	0.263397
$238$	−8.12736e6	−0.0390778
$239$	−1.86677e7	−0.0884499	−0.0442250	−	0.999022i	$-0.514082\pi$
$239$	−1.86677e7	−0.0884499	−0.0442250	+	0.999022i	$0.514082\pi$
$240$	−9.35260e7	−0.436710
$241$	−2.43058e7	−0.111854	−0.0559268	−	0.998435i	$-0.517811\pi$
$241$	−2.43058e7	−0.111854	−0.0559268	+	0.998435i	$0.517811\pi$
$242$	−1.68743e8	−0.765372
$243$	−1.43489e7	−0.0641500
$244$	1.07852e8	0.475296
$245$	3.03577e8	1.31883
$246$	2.77262e7	0.118746
$247$	3.37949e7	0.142696
$248$	−2.18691e8	−0.910439
$249$	−1.44124e8	−0.591616
$250$	7.16744e7	0.290117
$251$	−1.85068e8	−0.738708	−0.369354	−	0.929289i	$-0.620421\pi$
$251$	−1.85068e8	−0.738708	−0.369354	+	0.929289i	$0.620421\pi$
$252$	−1.13367e8	−0.446258
$253$	1.26801e8	0.492267
$254$	−4.13406e7	−0.158292
$255$	−1.34574e7	−0.0508243
$256$	3.34731e7	0.124697
$257$	7.99627e7	0.293847	0.146924	−	0.989148i	$-0.453063\pi$
$257$	7.99627e7	0.293847	0.146924	+	0.989148i	$0.453063\pi$
$258$	3.85728e6	0.0139834
$259$	−2.31124e8	−0.826601
$260$	−6.29831e7	−0.222237
$261$	1.09596e8	0.381552
$262$	−6.10345e7	−0.209663
$263$	−4.27501e7	−0.144908	−0.0724539	−	0.997372i	$-0.523083\pi$
$263$	−4.27501e7	−0.144908	−0.0724539	+	0.997372i	$0.523083\pi$
$264$	−1.93113e8	−0.645948
$265$	5.95702e8	1.96638
$266$	−9.09486e7	−0.296285
$267$	−5.80467e7	−0.186633
$268$	−3.37154e8	−1.06993
$269$	−2.49600e8	−0.781830	−0.390915	−	0.920427i	$-0.627841\pi$
$269$	−2.49600e8	−0.781830	−0.390915	+	0.920427i	$0.627841\pi$
$270$	2.14536e7	0.0663326
$271$	−6.59051e7	−0.201153	−0.100577	−	0.994929i	$-0.532069\pi$
$271$	−6.59051e7	−0.201153	−0.100577	+	0.994929i	$0.532069\pi$
$272$	1.90793e7	0.0574871
$273$	−6.66224e7	−0.198176
$274$	2.00381e8	0.588478
$275$	1.00507e8	0.291427
$276$	4.83876e7	0.138533
$277$	9.39872e7	0.265699	0.132849	−	0.991136i	$-0.457587\pi$
$277$	9.39872e7	0.265699	0.132849	+	0.991136i	$0.457587\pi$
$278$	1.42240e6	0.00397067
$279$	−1.81166e8	−0.499415
$280$	3.58371e8	0.975619
$281$	1.08507e8	0.291733	0.145867	−	0.989304i	$-0.453403\pi$
$281$	1.08507e8	0.291733	0.145867	+	0.989304i	$0.453403\pi$
$282$	−7.57460e6	−0.0201135
$283$	6.20243e8	1.62671	0.813353	−	0.581770i	$-0.197640\pi$
$283$	6.20243e8	1.62671	0.813353	+	0.581770i	$0.197640\pi$
$284$	6.74670e8	1.74774
$285$	−1.50594e8	−0.385347
$286$	−5.36759e7	−0.135675
$287$	3.83679e8	0.958036
$288$	−1.12530e8	−0.277585
$289$	−4.07593e8	−0.993310
$290$	−1.63861e8	−0.394533
$291$	9.09634e7	0.216392
$292$	2.90984e8	0.683958
$293$	6.28432e8	1.45956	0.729779	−	0.683683i	$-0.239623\pi$
$293$	6.28432e8	1.45956	0.729779	+	0.683683i	$0.239623\pi$
$294$	9.87270e7	0.226579
$295$	−6.17815e7	−0.140114
$296$	−1.50238e8	−0.336712
$297$	−1.59977e8	−0.354331
$298$	1.23130e8	0.269529
$299$	2.84359e7	0.0615201
$300$	3.83536e7	0.0820128
$301$	5.33776e7	0.112817
$302$	−6.76117e7	−0.141253
$303$	−3.19652e7	−0.0660129
$304$	2.13505e8	0.435863
$305$	−2.82435e8	−0.569993
$306$	−4.37653e6	−0.00873181
$307$	7.45356e8	1.47021	0.735105	−	0.677953i	$-0.237133\pi$
$307$	7.45356e8	1.47021	0.735105	+	0.677953i	$0.237133\pi$
$308$	−1.26394e9	−2.46489
$309$	2.71811e8	0.524098
$310$	2.70868e8	0.516407
$311$	7.31974e8	1.37986	0.689929	−	0.723877i	$-0.257642\pi$
$311$	7.31974e8	1.37986	0.689929	+	0.723877i	$0.257642\pi$
$312$	−4.33067e7	−0.0807261
$313$	3.03184e8	0.558857	0.279429	−	0.960166i	$-0.409855\pi$
$313$	3.03184e8	0.558857	0.279429	+	0.960166i	$0.409855\pi$
$314$	−1.20044e8	−0.218821
$315$	2.96878e8	0.535169
$316$	2.29656e8	0.409425
$317$	2.79655e8	0.493077	0.246539	−	0.969133i	$-0.420707\pi$
$317$	2.79655e8	0.493077	0.246539	+	0.969133i	$0.420707\pi$
$318$	1.93730e8	0.337832
$319$	1.22189e9	2.10749
$320$	−2.75134e8	−0.469374
$321$	1.41670e8	0.239061
$322$	−7.65264e7	−0.127737
$323$	3.07212e7	0.0507258
$324$	−6.10475e7	−0.0997149
$325$	2.25392e7	0.0364205
$326$	2.55443e8	0.408349
$327$	−3.54716e8	−0.561000
$328$	2.49404e8	0.390252
$329$	−1.04818e8	−0.162275
$330$	2.39187e8	0.366386
$331$	1.20182e9	1.82156	0.910778	−	0.412897i	$-0.135483\pi$
$331$	1.20182e9	1.82156	0.910778	+	0.412897i	$0.135483\pi$
$332$	−6.13178e8	−0.919609
$333$	−1.24459e8	−0.184701
$334$	1.82023e8	0.267309
$335$	8.82914e8	1.28310
$336$	−4.20898e8	−0.605327
$337$	−1.16073e9	−1.65206	−0.826031	−	0.563624i	$-0.809407\pi$
$337$	−1.16073e9	−1.65206	−0.826031	+	0.563624i	$0.809407\pi$
$338$	2.15320e8	0.303303
$339$	−2.51763e8	−0.350988
$340$	−5.72547e7	−0.0790015
$341$	−2.01983e9	−2.75850
$342$	−4.89751e7	−0.0662040
$343$	2.51304e8	0.336255
$344$	3.46971e7	0.0459557
$345$	−1.26714e8	−0.166134
$346$	−1.30465e8	−0.169327
$347$	−1.18359e8	−0.152071	−0.0760356	−	0.997105i	$-0.524226\pi$
$347$	−1.18359e8	−0.152071	−0.0760356	+	0.997105i	$0.524226\pi$
$348$	4.66277e8	0.593085
$349$	2.87181e8	0.361632	0.180816	−	0.983517i	$-0.442126\pi$
$349$	2.87181e8	0.361632	0.180816	+	0.983517i	$0.442126\pi$
$350$	−6.06573e7	−0.0756215
$351$	−3.58757e7	−0.0442818
$352$	−1.25461e9	−1.53323
$353$	−4.86525e8	−0.588700	−0.294350	−	0.955698i	$-0.595103\pi$
$353$	−4.86525e8	−0.588700	−0.294350	+	0.955698i	$0.595103\pi$
$354$	−2.00921e7	−0.0240721
$355$	−1.76678e9	−2.09596
$356$	−2.46960e8	−0.290102
$357$	−6.05630e7	−0.0704480
$358$	2.52059e8	0.290343
$359$	1.52624e9	1.74098	0.870488	−	0.492189i	$-0.163803\pi$
$359$	1.52624e9	1.74098	0.870488	+	0.492189i	$0.163803\pi$
$360$	1.92980e8	0.217999
$361$	−5.50089e8	−0.615400
$362$	−5.28439e8	−0.585484
$363$	−1.25743e9	−1.37978
$364$	−2.83445e8	−0.308045
$365$	−7.62008e8	−0.820228
$366$	−9.18515e7	−0.0979270
$367$	−1.48262e8	−0.156566	−0.0782832	−	0.996931i	$-0.524944\pi$
$367$	−1.48262e8	−0.156566	−0.0782832	+	0.996931i	$0.524944\pi$
$368$	1.79648e8	0.187913
$369$	2.06609e8	0.214070
$370$	1.86083e8	0.190985
$371$	2.68086e9	2.72562
$372$	−7.70771e8	−0.776292
$373$	−1.55988e9	−1.55636	−0.778180	−	0.628041i	$-0.783857\pi$
$373$	−1.55988e9	−1.55636	−0.778180	+	0.628041i	$0.783857\pi$
$374$	−4.87941e7	−0.0482299
$375$	5.34099e8	0.523013
$376$	−6.81354e7	−0.0661021
$377$	2.74016e8	0.263379
$378$	9.65484e7	0.0919441
$379$	1.77311e9	1.67301	0.836504	−	0.547961i	$-0.184596\pi$
$379$	1.77311e9	1.67301	0.836504	+	0.547961i	$0.184596\pi$
$380$	−6.40704e8	−0.598983
$381$	−3.08059e8	−0.285363
$382$	−1.37606e8	−0.126304
$383$	1.71331e9	1.55826	0.779129	−	0.626863i	$-0.215662\pi$
$383$	1.71331e9	1.55826	0.779129	+	0.626863i	$0.215662\pi$
$384$	−6.22954e8	−0.561432
$385$	3.30990e9	2.95599
$386$	4.29557e8	0.380159
$387$	2.87434e7	0.0252087
$388$	3.87004e8	0.336360
$389$	−9.34250e8	−0.804711	−0.402355	−	0.915484i	$-0.631808\pi$
$389$	−9.34250e8	−0.804711	−0.402355	+	0.915484i	$0.631808\pi$
$390$	5.36390e7	0.0457883
$391$	2.58496e7	0.0218693
$392$	8.88073e8	0.744642
$393$	−4.54814e8	−0.377972
$394$	4.98805e8	0.410860
$395$	−6.01407e8	−0.490997
$396$	−6.80621e8	−0.550772
$397$	7.43414e8	0.596299	0.298150	−	0.954519i	$-0.403631\pi$
$397$	7.43414e8	0.596299	0.298150	+	0.954519i	$0.403631\pi$
$398$	3.64233e8	0.289593
$399$	−6.77725e8	−0.534132
$400$	1.42395e8	0.111246
$401$	2.43334e9	1.88450	0.942252	−	0.334905i	$-0.108704\pi$
$401$	2.43334e9	1.88450	0.942252	+	0.334905i	$0.108704\pi$
$402$	2.87135e8	0.220442
$403$	−4.52957e8	−0.344739
$404$	−1.35996e8	−0.102611
$405$	1.59867e8	0.119582
$406$	−7.37432e8	−0.546866
$407$	−1.38759e9	−1.02019
$408$	−3.93679e7	−0.0286967
$409$	−2.52851e9	−1.82740	−0.913701	−	0.406388i	$-0.866788\pi$
$409$	−2.52851e9	−1.82740	−0.913701	+	0.406388i	$0.866788\pi$
$410$	−3.08908e8	−0.221353
$411$	1.49319e9	1.06089
$412$	1.15642e9	0.814659
$413$	−2.78038e8	−0.194213
$414$	−4.12089e7	−0.0285424
$415$	1.60574e9	1.10283
$416$	−2.81352e8	−0.191613
$417$	1.05993e7	0.00715818
$418$	−5.46026e8	−0.365676
$419$	−1.34539e9	−0.893507	−0.446753	−	0.894657i	$-0.647420\pi$
$419$	−1.34539e9	−0.893507	−0.446753	+	0.894657i	$0.647420\pi$
$420$	1.26307e9	0.831868
$421$	1.01782e9	0.664790	0.332395	−	0.943140i	$-0.392143\pi$
$421$	1.01782e9	0.664790	0.332395	+	0.943140i	$0.392143\pi$
$422$	−9.51735e8	−0.616485
$423$	−5.64440e7	−0.0362599
$424$	1.74264e9	1.11027
$425$	2.04892e7	0.0129469
$426$	−5.74577e8	−0.360093
$427$	−1.27105e9	−0.790072
$428$	6.02734e8	0.371597
$429$	−3.99979e8	−0.244589
$430$	−4.29754e7	−0.0260663
$431$	−2.08550e9	−1.25470	−0.627349	−	0.778738i	$-0.715860\pi$
$431$	−2.08550e9	−1.25470	−0.627349	+	0.778738i	$0.715860\pi$
$432$	−2.26651e8	−0.135258
$433$	−1.27758e9	−0.756277	−0.378139	−	0.925749i	$-0.623436\pi$
$433$	−1.27758e9	−0.756277	−0.378139	+	0.925749i	$0.623436\pi$
$434$	1.21900e9	0.715795
$435$	−1.22105e9	−0.711250
$436$	−1.50914e9	−0.872020
$437$	2.89268e8	0.165812
$438$	−2.47814e8	−0.140918
$439$	−3.72523e8	−0.210149	−0.105074	−	0.994464i	$-0.533508\pi$
$439$	−3.72523e8	−0.210149	−0.105074	+	0.994464i	$0.533508\pi$
$440$	2.15155e9	1.20411
$441$	7.35688e8	0.408469
$442$	−1.09423e7	−0.00602743
$443$	2.51167e8	0.137262	0.0686309	−	0.997642i	$-0.478137\pi$
$443$	2.51167e8	0.137262	0.0686309	+	0.997642i	$0.478137\pi$
$444$	−5.29509e8	−0.287100
$445$	6.46720e8	0.347902
$446$	−9.70586e8	−0.518038
$447$	9.17531e8	0.485897
$448$	−1.23820e9	−0.650603
$449$	−7.22359e8	−0.376609	−0.188304	−	0.982111i	$-0.560299\pi$
$449$	−7.22359e8	−0.376609	−0.188304	+	0.982111i	$0.560299\pi$
$450$	−3.26635e7	−0.0168974
$451$	2.30349e9	1.18241
$452$	−1.07113e9	−0.545577
$453$	−5.03825e8	−0.254646
$454$	3.43006e8	0.172031
$455$	7.42265e8	0.369419
$456$	−4.40543e8	−0.217576
$457$	−3.81278e9	−1.86868	−0.934341	−	0.356380i	$-0.884011\pi$
$457$	−3.81278e9	−1.86868	−0.934341	+	0.356380i	$0.884011\pi$
$458$	−8.18995e8	−0.398338
$459$	−3.26127e7	−0.0157414
$460$	−5.39105e8	−0.258238
$461$	−2.43626e9	−1.15817	−0.579083	−	0.815269i	$-0.696589\pi$
$461$	−2.43626e9	−1.15817	−0.579083	+	0.815269i	$0.696589\pi$
$462$	1.07642e9	0.507850
$463$	−2.87487e9	−1.34612	−0.673061	−	0.739587i	$-0.735021\pi$
$463$	−2.87487e9	−1.34612	−0.673061	+	0.739587i	$0.735021\pi$
$464$	1.73115e9	0.804490
$465$	2.01844e9	0.930958
$466$	2.27650e8	0.104212
$467$	−1.80431e9	−0.819787	−0.409894	−	0.912133i	$-0.634434\pi$
$467$	−1.80431e9	−0.819787	−0.409894	+	0.912133i	$0.634434\pi$
$468$	−1.52633e8	−0.0688317
$469$	3.97341e9	1.77852
$470$	8.43915e7	0.0374935
$471$	−8.94541e8	−0.394482
$472$	−1.80734e8	−0.0791119
$473$	3.20462e8	0.139239
$474$	−1.95585e8	−0.0843551
$475$	2.29283e8	0.0981621
$476$	−2.57666e8	−0.109504
$477$	1.44362e9	0.609031
$478$	6.76388e7	0.0283269
$479$	−2.36338e9	−0.982558	−0.491279	−	0.871002i	$-0.663471\pi$
$479$	−2.36338e9	−0.982558	−0.491279	+	0.871002i	$0.663471\pi$
$480$	1.25374e9	0.517445
$481$	−3.11176e8	−0.127496
$482$	8.80674e7	0.0358221
$483$	−5.70255e8	−0.230279
$484$	−5.34975e9	−2.14474
$485$	−1.01346e9	−0.403376
$486$	5.19906e7	0.0205446
$487$	3.50576e9	1.37541	0.687703	−	0.725993i	$-0.258619\pi$
$487$	3.50576e9	1.37541	0.687703	+	0.725993i	$0.258619\pi$
$488$	−8.26226e8	−0.321832
$489$	1.90349e9	0.736156
$490$	−1.09995e9	−0.422366
$491$	−3.92494e9	−1.49640	−0.748199	−	0.663474i	$-0.769081\pi$
$491$	−3.92494e9	−1.49640	−0.748199	+	0.663474i	$0.769081\pi$
$492$	8.79017e8	0.332751
$493$	2.49094e8	0.0936267
$494$	−1.22449e8	−0.0456996
$495$	1.78236e9	0.660506
$496$	−2.86164e9	−1.05300
$497$	−7.95108e9	−2.90522
$498$	5.22208e8	0.189470
$499$	−3.58721e9	−1.29242	−0.646212	−	0.763158i	$-0.723648\pi$
$499$	−3.58721e9	−1.29242	−0.646212	+	0.763158i	$0.723648\pi$
$500$	2.27233e9	0.812972
$501$	1.35639e9	0.481895
$502$	6.70559e8	0.236578
$503$	2.48168e9	0.869475	0.434737	−	0.900557i	$-0.356841\pi$
$503$	2.48168e9	0.869475	0.434737	+	0.900557i	$0.356841\pi$
$504$	8.68476e8	0.302170
$505$	3.56137e8	0.123054
$506$	−4.59440e8	−0.157653
$507$	1.60451e9	0.546783
$508$	−1.31064e9	−0.443568
$509$	3.73752e9	1.25624	0.628118	−	0.778118i	$-0.283826\pi$
$509$	3.73752e9	1.25624	0.628118	+	0.778118i	$0.283826\pi$
$510$	4.87605e7	0.0162769
$511$	−3.42929e9	−1.13692
$512$	−3.07455e9	−1.01236
$513$	−3.64950e8	−0.119350
$514$	−2.89730e8	−0.0941071
$515$	−3.02835e9	−0.976969
$516$	1.22289e8	0.0391844
$517$	−6.29296e8	−0.200280
$518$	8.37435e8	0.264726
$519$	−9.72188e8	−0.305256
$520$	4.82496e8	0.150481
$521$	−3.12643e9	−0.968539	−0.484270	−	0.874919i	$-0.660915\pi$
$521$	−3.12643e9	−0.968539	−0.484270	+	0.874919i	$0.660915\pi$
$522$	−3.97101e8	−0.122195
$523$	3.47385e9	1.06183	0.530915	−	0.847425i	$-0.321848\pi$
$523$	3.47385e9	1.06183	0.530915	+	0.847425i	$0.321848\pi$
$524$	−1.93501e9	−0.587520
$525$	−4.52003e8	−0.136328
$526$	1.54897e8	0.0464080
$527$	−4.11761e8	−0.122548
$528$	−2.52694e9	−0.747095
$529$	−3.16143e9	−0.928514
$530$	−2.15841e9	−0.629752
$531$	−1.49721e8	−0.0433963
$532$	−2.88338e9	−0.830255
$533$	5.16570e8	0.147769
$534$	2.10321e8	0.0597708
$535$	−1.57839e9	−0.445633
$536$	2.58285e9	0.724472
$537$	1.87828e9	0.523419
$538$	9.04381e8	0.250388
$539$	8.20222e9	2.25616
$540$	6.80153e8	0.185878
$541$	6.14788e8	0.166930	0.0834651	−	0.996511i	$-0.473401\pi$
$541$	6.14788e8	0.166930	0.0834651	+	0.996511i	$0.473401\pi$
$542$	2.38795e8	0.0644210
$543$	−3.93779e9	−1.05549
$544$	−2.55763e8	−0.0681149
$545$	3.95202e9	1.04576
$546$	2.41394e8	0.0634676
$547$	−3.36033e9	−0.877863	−0.438931	−	0.898521i	$-0.644643\pi$
$547$	−3.36033e9	−0.877863	−0.438931	+	0.898521i	$0.644643\pi$
$548$	6.35278e9	1.64904
$549$	−6.84453e8	−0.176539
$550$	−3.64167e8	−0.0933321
$551$	2.78747e9	0.709871
$552$	−3.70684e8	−0.0938032
$553$	−2.70654e9	−0.680575
$554$	−3.40545e8	−0.0850923
$555$	1.38664e9	0.344301
$556$	4.50949e7	0.0111267
$557$	−2.92483e8	−0.0717145	−0.0358572	−	0.999357i	$-0.511416\pi$
$557$	−2.92483e8	−0.0717145	−0.0358572	+	0.999357i	$0.511416\pi$
$558$	6.56421e8	0.159942
$559$	7.18654e7	0.0174012
$560$	4.68939e9	1.12839
$561$	−3.63601e8	−0.0869470
$562$	−3.93156e8	−0.0934302
$563$	5.83190e9	1.37731	0.688653	−	0.725091i	$-0.258202\pi$
$563$	5.83190e9	1.37731	0.688653	+	0.725091i	$0.258202\pi$
$564$	−2.40141e8	−0.0563624
$565$	2.80498e9	0.654276
$566$	−2.24733e9	−0.520967
$567$	7.19454e8	0.165753
$568$	−5.16846e9	−1.18343
$569$	−1.28209e9	−0.291760	−0.145880	−	0.989302i	$-0.546601\pi$
$569$	−1.28209e9	−0.291760	−0.145880	+	0.989302i	$0.546601\pi$
$570$	5.45650e8	0.123411
$571$	2.52700e9	0.568041	0.284020	−	0.958818i	$-0.408332\pi$
$571$	2.52700e9	0.568041	0.284020	+	0.958818i	$0.408332\pi$
$572$	−1.70171e9	−0.380189
$573$	−1.02541e9	−0.227696
$574$	−1.39019e9	−0.306819
$575$	1.92925e8	0.0423204
$576$	−6.66759e8	−0.145375
$577$	−3.17996e9	−0.689139	−0.344570	−	0.938761i	$-0.611975\pi$
$577$	−3.17996e9	−0.689139	−0.344570	+	0.938761i	$0.611975\pi$
$578$	1.47684e9	0.318116
$579$	3.20094e9	0.685335
$580$	−5.19497e9	−1.10557
$581$	7.22639e9	1.52864
$582$	−3.29589e8	−0.0693015
$583$	1.60950e10	3.36396
$584$	−2.22915e9	−0.463121
$585$	3.99704e8	0.0825455
$586$	−2.27701e9	−0.467437
$587$	3.74135e9	0.763474	0.381737	−	0.924271i	$-0.375326\pi$
$587$	3.74135e9	0.763474	0.381737	+	0.924271i	$0.375326\pi$
$588$	3.12999e9	0.634924
$589$	−4.60777e9	−0.929154
$590$	2.23854e8	0.0448728
$591$	3.71696e9	0.740683
$592$	−1.96591e9	−0.389437
$593$	−1.49511e8	−0.0294430	−0.0147215	−	0.999892i	$-0.504686\pi$
$593$	−1.49511e8	−0.0294430	−0.0147215	+	0.999892i	$0.504686\pi$
$594$	5.79645e8	0.113478
$595$	6.74755e8	0.131322
$596$	3.90364e9	0.755279
$597$	2.71417e9	0.522068
$598$	−1.03032e8	−0.0197024
$599$	−4.90943e9	−0.933335	−0.466668	−	0.884433i	$-0.654546\pi$
$599$	−4.90943e9	−0.933335	−0.466668	+	0.884433i	$0.654546\pi$
$600$	−2.93816e8	−0.0555324
$601$	9.51517e9	1.78795	0.893976	−	0.448114i	$-0.147904\pi$
$601$	9.51517e9	1.78795	0.893976	+	0.448114i	$0.147904\pi$
$602$	−1.93404e8	−0.0361308
$603$	2.13965e9	0.397404
$604$	−2.14353e9	−0.395822
$605$	1.40095e10	2.57205
$606$	1.15820e8	0.0211412
$607$	6.23277e9	1.13115	0.565576	−	0.824696i	$-0.308654\pi$
$607$	6.23277e9	1.13115	0.565576	+	0.824696i	$0.308654\pi$
$608$	−2.86210e9	−0.516442
$609$	−5.49515e9	−0.985868
$610$	1.02335e9	0.182545
$611$	−1.41123e8	−0.0250296
$612$	−1.38751e8	−0.0244684
$613$	−2.97929e9	−0.522397	−0.261198	−	0.965285i	$-0.584118\pi$
$613$	−2.97929e9	−0.522397	−0.261198	+	0.965285i	$0.584118\pi$
$614$	−2.70066e9	−0.470848
$615$	−2.30190e9	−0.399047
$616$	9.68268e9	1.66903
$617$	3.18056e9	0.545137	0.272569	−	0.962136i	$-0.412127\pi$
$617$	3.18056e9	0.545137	0.272569	+	0.962136i	$0.412127\pi$
$618$	−9.84857e8	−0.167847
$619$	1.21436e8	0.0205793	0.0102896	−	0.999947i	$-0.496725\pi$
$619$	1.21436e8	0.0205793	0.0102896	+	0.999947i	$0.496725\pi$
$620$	8.58745e9	1.44708
$621$	−3.07078e8	−0.0514551
$622$	−2.65217e9	−0.441912
$623$	2.91046e9	0.482229
$624$	−5.66680e8	−0.0933667
$625$	−6.91669e9	−1.13323
$626$	−1.09853e9	−0.178979
$627$	−4.06884e9	−0.659226
$628$	−3.80583e9	−0.613183
$629$	−2.82874e8	−0.0453227
$630$	−1.07568e9	−0.171393
$631$	−5.92643e9	−0.939053	−0.469527	−	0.882918i	$-0.655575\pi$
$631$	−5.92643e9	−0.939053	−0.469527	+	0.882918i	$0.655575\pi$
$632$	−1.75934e9	−0.277229
$633$	−7.09208e9	−1.11138
$634$	−1.01328e9	−0.157912
$635$	3.43221e9	0.531943
$636$	6.14190e9	0.946679
$637$	1.83939e9	0.281959
$638$	−4.42730e9	−0.674942
$639$	−4.28160e9	−0.649162
$640$	6.94057e9	1.04656
$641$	−7.39788e8	−0.110944	−0.0554721	−	0.998460i	$-0.517666\pi$
$641$	−7.39788e8	−0.110944	−0.0554721	+	0.998460i	$0.517666\pi$
$642$	−5.13313e8	−0.0765614
$643$	5.85977e9	0.869245	0.434622	−	0.900613i	$-0.356882\pi$
$643$	5.85977e9	0.869245	0.434622	+	0.900613i	$0.356882\pi$
$644$	−2.42615e9	−0.357946
$645$	−3.20241e8	−0.0469914
$646$	−1.11313e8	−0.0162454
$647$	−7.09749e9	−1.03024	−0.515122	−	0.857117i	$-0.672253\pi$
$647$	−7.09749e9	−1.03024	−0.515122	+	0.857117i	$0.672253\pi$
$648$	4.67668e8	0.0675189
$649$	−1.66925e9	−0.239698
$650$	−8.16665e7	−0.0116640
$651$	9.08365e9	1.29041
$652$	8.09841e9	1.14428
$653$	3.83880e9	0.539510	0.269755	−	0.962929i	$-0.413057\pi$
$653$	3.83880e9	0.539510	0.269755	+	0.962929i	$0.413057\pi$
$654$	1.28525e9	0.179665
$655$	5.06725e9	0.704576
$656$	3.26352e9	0.451360
$657$	−1.84665e9	−0.254042
$658$	3.79790e8	0.0519701
$659$	−4.88094e9	−0.664361	−0.332181	−	0.943216i	$-0.607784\pi$
$659$	−4.88094e9	−0.664361	−0.332181	+	0.943216i	$0.607784\pi$
$660$	7.58305e9	1.02669
$661$	−5.63851e9	−0.759381	−0.379690	−	0.925114i	$-0.623969\pi$
$661$	−5.63851e9	−0.759381	−0.379690	+	0.925114i	$0.623969\pi$
$662$	−4.35458e9	−0.583369
$663$	−8.15395e7	−0.0108660
$664$	4.69739e9	0.622685
$665$	7.55079e9	0.995673
$666$	4.50952e8	0.0591522
$667$	2.34545e9	0.306045
$668$	5.77076e9	0.749059
$669$	−7.23255e9	−0.933900
$670$	−3.19907e9	−0.410925
$671$	−7.63100e9	−0.975108
$672$	5.64227e9	0.717235
$673$	1.34178e10	1.69680	0.848399	−	0.529358i	$-0.177567\pi$
$673$	1.34178e10	1.69680	0.848399	+	0.529358i	$0.177567\pi$
$674$	4.20569e9	0.529088
$675$	−2.43400e8	−0.0304620
$676$	6.82640e9	0.849921
$677$	−1.49956e10	−1.85740	−0.928699	−	0.370835i	$-0.879072\pi$
$677$	−1.49956e10	−1.85740	−0.928699	+	0.370835i	$0.879072\pi$
$678$	9.12215e8	0.112407
$679$	−4.56090e9	−0.559122
$680$	4.38613e8	0.0534934
$681$	2.55599e9	0.310130
$682$	7.31846e9	0.883435
$683$	−6.32321e9	−0.759391	−0.379695	−	0.925112i	$-0.623971\pi$
$683$	−6.32321e9	−0.759391	−0.379695	+	0.925112i	$0.623971\pi$
$684$	−1.55268e9	−0.185518
$685$	−1.66362e10	−1.97759
$686$	−9.10552e8	−0.107689
$687$	−6.10294e9	−0.718109
$688$	4.54022e8	0.0531517
$689$	3.60940e9	0.420404
$690$	4.59124e8	0.0532057
$691$	−1.51402e10	−1.74565	−0.872826	−	0.488031i	$-0.837715\pi$
$691$	−1.51402e10	−1.74565	−0.872826	+	0.488031i	$0.837715\pi$
$692$	−4.13618e9	−0.474491
$693$	8.02122e9	0.915533
$694$	4.28850e8	0.0487021
$695$	−1.18091e8	−0.0133435
$696$	−3.57202e9	−0.401589
$697$	4.69588e8	0.0525293
$698$	−1.04055e9	−0.115816
$699$	1.69639e9	0.187869
$700$	−1.92305e9	−0.211908
$701$	1.32383e10	1.45151	0.725755	−	0.687953i	$-0.241491\pi$
$701$	1.32383e10	1.45151	0.725755	+	0.687953i	$0.241491\pi$
$702$	1.29989e8	0.0141816
$703$	−3.16548e9	−0.343634
$704$	−7.43373e9	−0.802975
$705$	6.28864e8	0.0675919
$706$	1.76283e9	0.188536
$707$	1.60274e9	0.170567
$708$	−6.36990e8	−0.0674553
$709$	−6.66730e9	−0.702568	−0.351284	−	0.936269i	$-0.614255\pi$
$709$	−6.66730e9	−0.702568	−0.351284	+	0.936269i	$0.614255\pi$
$710$	6.40158e9	0.671248
$711$	−1.45745e9	−0.152072
$712$	1.89189e9	0.196434
$713$	−3.87710e9	−0.400584
$714$	2.19439e8	0.0225616
$715$	4.45632e9	0.455937
$716$	7.99114e9	0.813604
$717$	5.04027e8	0.0510666
$718$	−5.53005e9	−0.557563
$719$	−5.24566e9	−0.526319	−0.263159	−	0.964752i	$-0.584765\pi$
$719$	−5.24566e9	−0.526319	−0.263159	+	0.964752i	$0.584765\pi$
$720$	2.52520e9	0.252134
$721$	−1.36286e10	−1.35418
$722$	1.99315e9	0.197087
$723$	6.56256e8	0.0645787
$724$	−1.67533e10	−1.64065
$725$	1.85908e9	0.181182
$726$	4.55607e9	0.441888
$727$	4.33721e9	0.418639	0.209320	−	0.977847i	$-0.432875\pi$
$727$	4.33721e9	0.418639	0.209320	+	0.977847i	$0.432875\pi$
$728$	2.17140e9	0.208583
$729$	3.87420e8	0.0370370
$730$	2.76099e9	0.262685
$731$	6.53291e7	0.00618580
$732$	−2.91201e9	−0.274413
$733$	−1.14178e10	−1.07083	−0.535413	−	0.844590i	$-0.679844\pi$
$733$	−1.14178e10	−1.07083	−0.535413	+	0.844590i	$0.679844\pi$
$734$	5.37200e8	0.0501417
$735$	−8.19658e9	−0.761425
$736$	−2.40824e9	−0.222653
$737$	2.38551e10	2.19505
$738$	−7.48608e8	−0.0685578
$739$	−1.87923e9	−0.171287	−0.0856433	−	0.996326i	$-0.527295\pi$
$739$	−1.87923e9	−0.171287	−0.0856433	+	0.996326i	$0.527295\pi$
$740$	5.89946e9	0.535182
$741$	−9.12461e8	−0.0823855
$742$	−9.71359e9	−0.872903
$743$	−9.66780e9	−0.864703	−0.432351	−	0.901705i	$-0.642316\pi$
$743$	−9.66780e9	−0.864703	−0.432351	+	0.901705i	$0.642316\pi$
$744$	5.90467e9	0.525642
$745$	−1.02226e10	−0.905759
$746$	5.65193e9	0.498438
$747$	3.89136e9	0.341570
$748$	−1.54694e9	−0.135151
$749$	−7.10331e9	−0.617695
$750$	−1.93521e9	−0.167499
$751$	−1.07300e10	−0.924403	−0.462202	−	0.886775i	$-0.652940\pi$
$751$	−1.07300e10	−0.924403	−0.462202	+	0.886775i	$0.652940\pi$
$752$	−8.91571e8	−0.0764528
$753$	4.99683e9	0.426493
$754$	−9.92847e8	−0.0843496
$755$	5.61331e9	0.474684
$756$	3.06092e9	0.257647
$757$	1.90038e10	1.59223	0.796115	−	0.605145i	$-0.206885\pi$
$757$	1.90038e10	1.59223	0.796115	+	0.605145i	$0.206885\pi$
$758$	−6.42453e9	−0.535796
$759$	−3.42363e9	−0.284211
$760$	4.90826e9	0.405583
$761$	8.07062e9	0.663836	0.331918	−	0.943308i	$-0.392304\pi$
$761$	8.07062e9	0.663836	0.331918	+	0.943308i	$0.392304\pi$
$762$	1.11620e9	0.0913899
$763$	1.77854e10	1.44953
$764$	−4.36259e9	−0.353930
$765$	3.63351e8	0.0293434
$766$	−6.20785e9	−0.499046
$767$	−3.74339e8	−0.0299558
$768$	−9.03773e8	−0.0719938
$769$	−4.19821e9	−0.332906	−0.166453	−	0.986049i	$-0.553231\pi$
$769$	−4.19821e9	−0.332906	−0.166453	+	0.986049i	$0.553231\pi$
$770$	−1.19928e10	−0.946682
$771$	−2.15899e9	−0.169653
$772$	1.36184e10	1.06529
$773$	−1.26866e10	−0.987910	−0.493955	−	0.869487i	$-0.664449\pi$
$773$	−1.26866e10	−0.987910	−0.493955	+	0.869487i	$0.664449\pi$
$774$	−1.04146e8	−0.00807330
$775$	−3.07311e9	−0.237150
$776$	−2.96473e9	−0.227756
$777$	6.24035e9	0.477238
$778$	3.38508e9	0.257716
$779$	5.25488e9	0.398274
$780$	1.70054e9	0.128309
$781$	−4.77357e10	−3.58563
$782$	−9.36612e7	−0.00700384
$783$	−2.95910e9	−0.220289
$784$	1.16207e10	0.861243
$785$	9.96642e9	0.735352
$786$	1.64793e9	0.121049
$787$	1.93383e10	1.41419	0.707093	−	0.707121i	$-0.250006\pi$
$787$	1.93383e10	1.41419	0.707093	+	0.707121i	$0.250006\pi$
$788$	1.58138e10	1.15132
$789$	1.15425e9	0.0836625
$790$	2.17909e9	0.157246
$791$	1.26234e10	0.906896
$792$	5.21405e9	0.372938
$793$	−1.71129e9	−0.121862
$794$	−2.69362e9	−0.190970
$795$	−1.60839e10	−1.13529
$796$	1.15474e10	0.811503
$797$	−2.47116e10	−1.72901	−0.864505	−	0.502624i	$-0.832368\pi$
$797$	−2.47116e10	−1.72901	−0.864505	+	0.502624i	$0.832368\pi$
$798$	2.45561e9	0.171060
$799$	−1.28288e8	−0.00889759
$800$	−1.90885e9	−0.131813
$801$	1.56726e9	0.107753
$802$	−8.81675e9	−0.603529
$803$	−2.05884e10	−1.40319
$804$	9.10316e9	0.617726
$805$	6.35343e9	0.429262
$806$	1.64121e9	0.110406
$807$	6.73921e9	0.451390
$808$	1.04183e9	0.0694796
$809$	2.28215e10	1.51539	0.757695	−	0.652609i	$-0.226326\pi$
$809$	2.28215e10	1.51539	0.757695	+	0.652609i	$0.226326\pi$
$810$	−5.79247e8	−0.0382971
$811$	−2.67364e10	−1.76007	−0.880037	−	0.474906i	$-0.842482\pi$
$811$	−2.67364e10	−1.76007	−0.880037	+	0.474906i	$0.842482\pi$
$812$	−2.33791e10	−1.53244
$813$	1.77944e9	0.116136
$814$	5.02769e9	0.326725
$815$	−2.12075e10	−1.37227
$816$	−5.15140e8	−0.0331902
$817$	7.31060e8	0.0469003
$818$	9.16160e9	0.585241
$819$	1.79880e9	0.114417
$820$	−9.79346e9	−0.620280
$821$	1.71127e10	1.07924	0.539618	−	0.841910i	$-0.318569\pi$
$821$	1.71127e10	1.07924	0.539618	+	0.841910i	$0.318569\pi$
$822$	−5.41030e9	−0.339758
$823$	−2.37659e10	−1.48612	−0.743061	−	0.669224i	$-0.766627\pi$
$823$	−2.37659e10	−1.48612	−0.743061	+	0.669224i	$0.766627\pi$
$824$	−8.85903e9	−0.551621
$825$	−2.71368e9	−0.168256
$826$	1.00742e9	0.0621985
$827$	−6.09517e9	−0.374728	−0.187364	−	0.982291i	$-0.559994\pi$
$827$	−6.09517e9	−0.374728	−0.187364	+	0.982291i	$0.559994\pi$
$828$	−1.30647e9	−0.0799819
$829$	−5.59971e9	−0.341370	−0.170685	−	0.985326i	$-0.554598\pi$
$829$	−5.59971e9	−0.341370	−0.170685	+	0.985326i	$0.554598\pi$
$830$	−5.81812e9	−0.353191
$831$	−2.53765e9	−0.153401
$832$	−1.66706e9	−0.100350
$833$	1.67210e9	0.100232
$834$	−3.84047e7	−0.00229247
$835$	−1.51121e10	−0.898299
$836$	−1.73109e10	−1.02470
$837$	4.89148e9	0.288337
$838$	4.87476e9	0.286153
$839$	−1.48782e10	−0.869730	−0.434865	−	0.900496i	$-0.643204\pi$
$839$	−1.48782e10	−0.869730	−0.434865	+	0.900496i	$0.643204\pi$
$840$	−9.67602e9	−0.563274
$841$	5.35156e9	0.310237
$842$	−3.68789e9	−0.212905
$843$	−2.92969e9	−0.168432
$844$	−3.01733e10	−1.72752
$845$	−1.78765e10	−1.01926
$846$	2.04514e8	0.0116125
$847$	6.30476e10	3.56514
$848$	2.28030e10	1.28412
$849$	−1.67466e10	−0.939179
$850$	−7.42389e7	−0.00414634
$851$	−2.66351e9	−0.148150
$852$	−1.82161e10	−1.00906
$853$	3.87811e9	0.213943	0.106972	−	0.994262i	$-0.465885\pi$
$853$	3.87811e9	0.213943	0.106972	+	0.994262i	$0.465885\pi$
$854$	4.60543e9	0.253027
$855$	4.06605e9	0.222480
$856$	−4.61738e9	−0.251616
$857$	−1.92983e10	−1.04733	−0.523667	−	0.851923i	$-0.675436\pi$
$857$	−1.92983e10	−1.04733	−0.523667	+	0.851923i	$0.675436\pi$
$858$	1.44925e9	0.0783317
$859$	2.34053e10	1.25990	0.629952	−	0.776634i	$-0.283074\pi$
$859$	2.34053e10	1.25990	0.629952	+	0.776634i	$0.283074\pi$
$860$	−1.36247e9	−0.0730435
$861$	−1.03593e10	−0.553122
$862$	7.55642e9	0.401828
$863$	2.15437e10	1.14099	0.570495	−	0.821301i	$-0.306751\pi$
$863$	2.15437e10	1.14099	0.570495	+	0.821301i	$0.306751\pi$
$864$	3.03832e9	0.160264
$865$	1.08315e10	0.569027
$866$	4.62908e9	0.242204
$867$	1.10050e10	0.573488
$868$	3.86464e10	2.00581
$869$	−1.62492e10	−0.839966
$870$	4.42426e9	0.227784
$871$	5.34964e9	0.274322
$872$	1.15611e10	0.590462
$873$	−2.45601e9	−0.124934
$874$	−1.04811e9	−0.0531026
$875$	−2.67797e10	−1.35138
$876$	−7.85657e9	−0.394883
$877$	−1.77005e10	−0.886108	−0.443054	−	0.896495i	$-0.646105\pi$
$877$	−1.77005e10	−0.886108	−0.443054	+	0.896495i	$0.646105\pi$
$878$	1.34977e9	0.0673021
$879$	−1.69677e10	−0.842677
$880$	2.81536e10	1.39266
$881$	−2.35041e10	−1.15805	−0.579027	−	0.815308i	$-0.696567\pi$
$881$	−2.35041e10	−1.15805	−0.579027	+	0.815308i	$0.696567\pi$
$882$	−2.66563e9	−0.130816
$883$	6.99377e9	0.341860	0.170930	−	0.985283i	$-0.445323\pi$
$883$	6.99377e9	0.341860	0.170930	+	0.985283i	$0.445323\pi$
$884$	−3.46910e8	−0.0168902
$885$	1.66810e9	0.0808949
$886$	−9.10057e8	−0.0439593
$887$	−1.04556e10	−0.503056	−0.251528	−	0.967850i	$-0.580933\pi$
$887$	−1.04556e10	−0.503056	−0.251528	+	0.967850i	$0.580933\pi$
$888$	4.05643e9	0.194401
$889$	1.54461e10	0.737331
$890$	−2.34327e9	−0.111419
$891$	4.31937e9	0.204573
$892$	−3.07709e10	−1.45166
$893$	−1.43560e9	−0.0674609
$894$	−3.32450e9	−0.155613
$895$	−2.09266e10	−0.975704
$896$	3.12349e10	1.45065
$897$	−7.67768e8	−0.0355187
$898$	2.61733e9	0.120612
$899$	−3.73609e10	−1.71498
$900$	−1.03555e9	−0.0473501
$901$	3.28112e9	0.149446
$902$	−8.34626e9	−0.378677
$903$	−1.44119e9	−0.0651352
$904$	8.20560e9	0.369420
$905$	4.38724e10	1.96753
$906$	1.82552e9	0.0815525
$907$	2.84631e10	1.26665	0.633325	−	0.773886i	$-0.281690\pi$
$907$	2.84631e10	1.26665	0.633325	+	0.773886i	$0.281690\pi$
$908$	1.08745e10	0.482067
$909$	8.63061e8	0.0381126
$910$	−2.68946e9	−0.118310
$911$	−8.69725e9	−0.381125	−0.190562	−	0.981675i	$-0.561031\pi$
$911$	−8.69725e9	−0.381125	−0.190562	+	0.981675i	$0.561031\pi$
$912$	−5.76463e9	−0.251646
$913$	4.33849e10	1.88665
$914$	1.38149e10	0.598462
$915$	7.62575e9	0.329086
$916$	−2.59650e10	−1.11623
$917$	2.28043e10	0.976618
$918$	1.18166e8	0.00504131
$919$	1.81679e10	0.772148	0.386074	−	0.922468i	$-0.373831\pi$
$919$	1.81679e10	0.772148	0.386074	+	0.922468i	$0.373831\pi$
$920$	4.12993e9	0.174858
$921$	−2.01246e10	−0.848826
$922$	8.82735e9	0.370913
$923$	−1.07050e10	−0.448106
$924$	3.41263e10	1.42311
$925$	−2.11119e9	−0.0877063
$926$	1.04166e10	0.431107
$927$	−7.33890e9	−0.302588
$928$	−2.32065e10	−0.953218
$929$	2.23626e10	0.915098	0.457549	−	0.889184i	$-0.348727\pi$
$929$	2.23626e10	0.915098	0.457549	+	0.889184i	$0.348727\pi$
$930$	−7.31344e9	−0.298147
$931$	1.87115e10	0.759949
$932$	7.21731e9	0.292025
$933$	−1.97633e10	−0.796661
$934$	6.53757e9	0.262544
$935$	4.05101e9	0.162078
$936$	1.16928e9	0.0466072
$937$	−4.79626e8	−0.0190465	−0.00952323	−	0.999955i	$-0.503031\pi$
$937$	−4.79626e8	−0.0190465	−0.00952323	+	0.999955i	$0.503031\pi$
$938$	−1.43969e10	−0.569586
$939$	−8.18596e9	−0.322656
$940$	2.67550e9	0.105065
$941$	−3.41566e10	−1.33632	−0.668161	−	0.744017i	$-0.732918\pi$
$941$	−3.41566e10	−1.33632	−0.668161	+	0.744017i	$0.732918\pi$
$942$	3.24120e9	0.126336
$943$	4.42159e9	0.171707
$944$	−2.36495e9	−0.0914997
$945$	−8.01571e9	−0.308980
$946$	−1.16113e9	−0.0445926
$947$	−1.00641e10	−0.385079	−0.192539	−	0.981289i	$-0.561672\pi$
$947$	−1.00641e10	−0.385079	−0.192539	+	0.981289i	$0.561672\pi$
$948$	−6.20072e9	−0.236381
$949$	−4.61706e9	−0.175361
$950$	−8.30764e8	−0.0314373
$951$	−7.55068e9	−0.284678
$952$	1.97391e9	0.0741476
$953$	−2.94200e10	−1.10108	−0.550539	−	0.834810i	$-0.685578\pi$
$953$	−2.94200e10	−1.10108	−0.550539	+	0.834810i	$0.685578\pi$
$954$	−5.23070e9	−0.195047
$955$	1.14244e10	0.424446
$956$	2.14438e9	0.0793780
$957$	−3.29911e10	−1.21676
$958$	8.56325e9	0.314673
$959$	−7.48685e10	−2.74116
$960$	7.42862e9	0.270993
$961$	3.42460e10	1.24474
$962$	1.12749e9	0.0408318
$963$	−3.82508e9	−0.138022
$964$	2.79204e9	0.100381
$965$	−3.56629e10	−1.27753
$966$	2.06621e9	0.0737489
$967$	9.18664e9	0.326711	0.163356	−	0.986567i	$-0.447768\pi$
$967$	9.18664e9	0.326711	0.163356	+	0.986567i	$0.447768\pi$
$968$	4.09830e10	1.45224
$969$	−8.29472e8	−0.0292866
$970$	3.67208e9	0.129185
$971$	2.46294e10	0.863348	0.431674	−	0.902030i	$-0.357923\pi$
$971$	2.46294e10	0.863348	0.431674	+	0.902030i	$0.357923\pi$
$972$	1.64828e9	0.0575704
$973$	−5.31450e8	−0.0184956
$974$	−1.27025e10	−0.440486
$975$	−6.08558e8	−0.0210274
$976$	−1.08114e10	−0.372227
$977$	3.26473e10	1.12000	0.559998	−	0.828494i	$-0.310802\pi$
$977$	3.26473e10	1.12000	0.559998	+	0.828494i	$0.310802\pi$
$978$	−6.89695e9	−0.235760
$979$	1.74735e10	0.595168
$980$	−3.48724e10	−1.18356
$981$	9.57732e9	0.323894
$982$	1.42213e10	0.479235
$983$	4.98914e9	0.167528	0.0837641	−	0.996486i	$-0.473306\pi$
$983$	4.98914e9	0.167528	0.0837641	+	0.996486i	$0.473306\pi$
$984$	−6.73391e9	−0.225312
$985$	−4.14121e10	−1.38070
$986$	−9.02547e8	−0.0299848
$987$	2.83010e9	0.0936897
$988$	−3.88207e9	−0.128060
$989$	6.15133e8	0.0202200
$990$	−6.45805e9	−0.211533
$991$	−1.15183e10	−0.375950	−0.187975	−	0.982174i	$-0.560192\pi$
$991$	−1.15183e10	−0.375950	−0.187975	+	0.982174i	$0.560192\pi$
$992$	3.83611e10	1.24767
$993$	−3.24492e10	−1.05168
$994$	2.88093e10	0.930422
$995$	−3.02396e10	−0.973185
$996$	1.65558e10	0.530936
$997$	2.00277e10	0.640026	0.320013	−	0.947413i	$-0.396313\pi$
$997$	2.00277e10	0.640026	0.320013	+	0.947413i	$0.396313\pi$
$998$	1.29976e10	0.413910
$999$	3.36038e9	0.106637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.9	✓	17
3.2	odd	2		531.8.a.c.1.9		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.9	✓	17	1.1	even	1	trivial
531.8.a.c.1.9		17	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-3.62331 q^{2} -27.0000 q^{3} -114.872 q^{4} +300.817 q^{5} +97.8295 q^{6} +1353.78 q^{7} +880.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-3.62331 q^{2} -27.0000 q^{3} -114.872 q^{4} +300.817 q^{5} +97.8295 q^{6} +1353.78 q^{7} +880.000 q^{8} +729.000 q^{9} -1089.96 q^{10} +8127.65 q^{11} +3101.53 q^{12} +1822.67 q^{13} -4905.17 q^{14} -8122.07 q^{15} +11515.0 q^{16} +1656.90 q^{17} -2641.40 q^{18} +18541.4 q^{19} -34555.4 q^{20} -36552.0 q^{21} -29449.0 q^{22} +15601.2 q^{23} -23760.0 q^{24} +12366.0 q^{25} -6604.11 q^{26} -19683.0 q^{27} -155511. q^{28} +150338. q^{29} +29428.8 q^{30} -248513. q^{31} -154363. q^{32} -219447. q^{33} -6003.46 q^{34} +407240. q^{35} -83741.4 q^{36} -170725. q^{37} -67181.2 q^{38} -49212.1 q^{39} +264719. q^{40} +283414. q^{41} +132439. q^{42} +39428.6 q^{43} -933636. q^{44} +219296. q^{45} -56528.0 q^{46} -77426.6 q^{47} -310906. q^{48} +1.00917e6 q^{49} -44805.9 q^{50} -44736.3 q^{51} -209373. q^{52} +1.98028e6 q^{53} +71317.7 q^{54} +2.44494e6 q^{55} +1.19133e6 q^{56} -500617. q^{57} -544721. q^{58} -205379. q^{59} +932995. q^{60} -938894. q^{61} +900440. q^{62} +986905. q^{63} -914622. q^{64} +548291. q^{65} +795124. q^{66} +2.93505e6 q^{67} -190331. q^{68} -421232. q^{69} -1.47556e6 q^{70} -5.87325e6 q^{71} +641520. q^{72} -2.53313e6 q^{73} +618590. q^{74} -333882. q^{75} -2.12988e6 q^{76} +1.10030e7 q^{77} +178311. q^{78} -1.99924e6 q^{79} +3.46392e6 q^{80} +531441. q^{81} -1.02690e6 q^{82} +5.33794e6 q^{83} +4.19879e6 q^{84} +498424. q^{85} -142862. q^{86} -4.05912e6 q^{87} +7.15233e6 q^{88} +2.14988e6 q^{89} -794577. q^{90} +2.46749e6 q^{91} -1.79213e6 q^{92} +6.70985e6 q^{93} +280541. q^{94} +5.57757e6 q^{95} +4.16779e6 q^{96} -3.36902e6 q^{97} -3.65656e6 q^{98} +5.92506e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) \)	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

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