LMFDB - Embedded newform 177.7.c.a.58.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,7,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$40.7195728007$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.6
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.7128i q^{2} -15.5885 q^{3} -124.040 q^{4} +78.2520 q^{5} +213.761i q^{6} +452.461 q^{7} +823.310i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-13.7128i q^{2} -15.5885 q^{3} -124.040 q^{4} +78.2520 q^{5} +213.761i q^{6} +452.461 q^{7} +823.310i q^{8} +243.000 q^{9} -1073.05i q^{10} -259.004i q^{11} +1933.59 q^{12} +652.587i q^{13} -6204.49i q^{14} -1219.83 q^{15} +3351.31 q^{16} -3110.24 q^{17} -3332.20i q^{18} -10605.2 q^{19} -9706.35 q^{20} -7053.17 q^{21} -3551.66 q^{22} -1836.91i q^{23} -12834.1i q^{24} -9501.63 q^{25} +8948.77 q^{26} -3788.00 q^{27} -56123.1 q^{28} -3215.28 q^{29} +16727.2i q^{30} -49794.1i q^{31} +6736.18i q^{32} +4037.48i q^{33} +42650.0i q^{34} +35406.0 q^{35} -30141.6 q^{36} +3989.90i q^{37} +145427. i q^{38} -10172.8i q^{39} +64425.6i q^{40} -48864.4 q^{41} +96718.4i q^{42} +40700.9i q^{43} +32126.8i q^{44} +19015.2 q^{45} -25189.1 q^{46} -14800.9i q^{47} -52241.7 q^{48} +87071.9 q^{49} +130293. i q^{50} +48483.9 q^{51} -80946.7i q^{52} -246352. q^{53} +51943.9i q^{54} -20267.6i q^{55} +372515. i q^{56} +165319. q^{57} +44090.3i q^{58} +(-47272.8 + 199865. i) q^{59} +151307. q^{60} -253372. i q^{61} -682814. q^{62} +109948. q^{63} +306855. q^{64} +51066.3i q^{65} +55365.0 q^{66} -475304. i q^{67} +385793. q^{68} +28634.6i q^{69} -485513. i q^{70} +75588.7 q^{71} +200064. i q^{72} +284785. i q^{73} +54712.6 q^{74} +148116. q^{75} +1.31547e6 q^{76} -117189. i q^{77} -139498. q^{78} -530314. q^{79} +262246. q^{80} +59049.0 q^{81} +670065. i q^{82} +947140. i q^{83} +874873. q^{84} -243383. q^{85} +558121. q^{86} +50121.2 q^{87} +213241. q^{88} -985993. i q^{89} -260751. i q^{90} +295270. i q^{91} +227850. i q^{92} +776213. i q^{93} -202961. q^{94} -829879. q^{95} -105007. i q^{96} +310962. i q^{97} -1.19400e6i q^{98} -62938.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	13.7128i		−	1.71409i	−0.515238	−	0.857047i	$-0.672296\pi$
$2$		−	13.7128i		−	1.71409i	0.515238	−	0.857047i	$-0.327704\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	−124.040			−1.93812
$5$	78.2520			0.626016			0.313008	−	0.949751i	$-0.398663\pi$
$5$	78.2520			0.626016			0.313008	+	0.949751i	$0.398663\pi$
$6$			213.761i			0.989633i
$7$	452.461			1.31913			0.659564	−	0.751648i	$-0.270741\pi$
$7$	452.461			1.31913			0.659564	+	0.751648i	$0.270741\pi$
$8$			823.310i			1.60803i
$9$	243.000			0.333333
$10$		−	1073.05i		−	1.07305i
$11$		−	259.004i		−	0.194594i	−0.995255	−	0.0972969i	$-0.968980\pi$
$11$		−	259.004i		−	0.194594i	0.995255	−	0.0972969i	$-0.0310196\pi$
$12$	1933.59			1.11897
$13$			652.587i			0.297036i	0.988910	+	0.148518i	$0.0474502\pi$
$13$			652.587i			0.297036i	−0.988910	+	0.148518i	$0.952550\pi$
$14$		−	6204.49i		−	2.26111i
$15$	−1219.83			−0.361430
$16$	3351.31			0.818190
$17$	−3110.24			−0.633064			−0.316532	−	0.948582i	$-0.602518\pi$
$17$	−3110.24			−0.633064			−0.316532	+	0.948582i	$0.602518\pi$
$18$		−	3332.20i		−	0.571365i
$19$	−10605.2			−1.54618			−0.773088	−	0.634299i	$-0.781289\pi$
$19$	−10605.2			−1.54618			−0.773088	+	0.634299i	$0.781289\pi$
$20$	−9706.35			−1.21329
$21$	−7053.17			−0.761599
$22$	−3551.66			−0.333552
$23$		−	1836.91i		−	0.150975i	−0.997147	−	0.0754875i	$-0.975949\pi$
$23$		−	1836.91i		−	0.150975i	0.997147	−	0.0754875i	$-0.0240513\pi$
$24$		−	12834.1i		−	0.928395i
$25$	−9501.63			−0.608104
$26$	8948.77			0.509147
$27$	−3788.00			−0.192450
$28$	−56123.1			−2.55663
$29$	−3215.28			−0.131833			−0.0659165	−	0.997825i	$-0.520997\pi$
$29$	−3215.28			−0.131833			−0.0659165	+	0.997825i	$0.520997\pi$
$30$			16727.2i			0.619526i
$31$		−	49794.1i		−	1.67145i	−0.549151	−	0.835723i	$-0.685049\pi$
$31$		−	49794.1i		−	1.67145i	0.549151	−	0.835723i	$-0.314951\pi$
$32$			6736.18i			0.205572i
$33$			4037.48i			0.112349i
$34$			42650.0i			1.08513i
$35$	35406.0			0.825795
$36$	−30141.6			−0.646040
$37$			3989.90i			0.0787693i	0.999224	+	0.0393847i	$0.0125398\pi$
$37$			3989.90i			0.0787693i	−0.999224	+	0.0393847i	$0.987460\pi$
$38$			145427.i			2.65029i
$39$		−	10172.8i		−	0.171494i
$40$			64425.6i			1.00665i
$41$	−48864.4			−0.708991			−0.354495	−	0.935058i	$-0.615347\pi$
$41$	−48864.4			−0.708991			−0.354495	+	0.935058i	$0.615347\pi$
$42$			96718.4i			1.30545i
$43$			40700.9i			0.511916i	0.966688	+	0.255958i	$0.0823909\pi$
$43$			40700.9i			0.511916i	−0.966688	+	0.255958i	$0.917609\pi$
$44$			32126.8i			0.377146i
$45$	19015.2			0.208672
$46$	−25189.1			−0.258785
$47$		−	14800.9i		−	0.142559i	−0.997456	−	0.0712794i	$-0.977292\pi$
$47$		−	14800.9i		−	0.142559i	0.997456	−	0.0712794i	$-0.0227082\pi$
$48$	−52241.7			−0.472382
$49$	87071.9			0.740099
$50$			130293.i			1.04235i
$51$	48483.9			0.365499
$52$		−	80946.7i		−	0.575691i
$53$	−246352.			−1.65474			−0.827368	−	0.561660i	$-0.810163\pi$
$53$	−246352.			−1.65474			−0.827368	+	0.561660i	$0.810163\pi$
$54$			51943.9i			0.329878i
$55$		−	20267.6i		−	0.121819i
$56$			372515.i			2.12119i
$57$	165319.			0.892685
$58$			44090.3i			0.225974i
$59$	−47272.8	+	199865.i	−0.230173	+	0.973150i
$59$	−47272.8	+	199865.i	−0.230173	+	0.973150i
$60$	151307.			0.700496
$61$		−	253372.i		−	1.11627i	−0.829751	−	0.558134i	$-0.811517\pi$
$61$		−	253372.i		−	1.11627i	0.829751	−	0.558134i	$-0.188483\pi$
$62$	−682814.			−2.86502
$63$	109948.			0.439709
$64$	306855.			1.17056
$65$			51066.3i			0.185949i
$66$	55365.0			0.192576
$67$		−	475304.i		−	1.58033i	−0.612895	−	0.790164i	$-0.709995\pi$
$67$		−	475304.i		−	1.58033i	0.612895	−	0.790164i	$-0.290005\pi$
$68$	385793.			1.22695
$69$			28634.6i			0.0871654i
$70$		−	485513.i		−	1.41549i
$71$	75588.7			0.211194			0.105597	−	0.994409i	$-0.466325\pi$
$71$	75588.7			0.211194			0.105597	+	0.994409i	$0.466325\pi$
$72$			200064.i			0.536009i
$73$			284785.i			0.732064i	0.930602	+	0.366032i	$0.119284\pi$
$73$			284785.i			0.732064i	−0.930602	+	0.366032i	$0.880716\pi$
$74$	54712.6			0.135018
$75$	148116.			0.351089
$76$	1.31547e6			2.99667
$77$		−	117189.i		−	0.256694i
$78$	−139498.			−0.293956
$79$	−530314.			−1.07560			−0.537801	−	0.843072i	$-0.680745\pi$
$79$	−530314.			−1.07560			−0.537801	+	0.843072i	$0.680745\pi$
$80$	262246.			0.512200
$81$	59049.0			0.111111
$82$			670065.i			1.21528i
$83$			947140.i			1.65646i	0.560391	+	0.828228i	$0.310651\pi$
$83$			947140.i			1.65646i	−0.560391	+	0.828228i	$0.689349\pi$
$84$	874873.			1.47607
$85$	−243383.			−0.396308
$86$	558121.			0.877472
$87$	50121.2			0.0761138
$88$	213241.			0.312912
$89$		−	985993.i		−	1.39863i	−0.714812	−	0.699317i	$-0.753488\pi$
$89$		−	985993.i		−	1.39863i	0.714812	−	0.699317i	$-0.246512\pi$
$90$		−	260751.i		−	0.357684i
$91$			295270.i			0.391828i
$92$			227850.i			0.292608i
$93$			776213.i			0.965010i
$94$	−202961.			−0.244359
$95$	−829879.			−0.967930
$96$		−	105007.i		−	0.118687i
$97$			310962.i			0.340716i	0.985382	+	0.170358i	$0.0544924\pi$
$97$			310962.i			0.340716i	−0.985382	+	0.170358i	$0.945508\pi$
$98$		−	1.19400e6i		−	1.26860i
$99$		−	62938.1i		−	0.0648646i
$100$	1.17858e6			1.17858
$101$			526681.i			0.511191i	0.966784	+	0.255596i	$0.0822716\pi$
$101$			526681.i			0.511191i	−0.966784	+	0.255596i	$0.917728\pi$
$102$		−	664847.i		−	0.626501i
$103$			362144.i			0.331413i	0.986175	+	0.165706i	$0.0529904\pi$
$103$			362144.i			0.331413i	−0.986175	+	0.165706i	$0.947010\pi$
$104$	−537282.			−0.477641
$105$	−551924.			−0.476773
$106$			3.37817e6i			2.83638i
$107$	81885.6			0.0668431			0.0334215	−	0.999441i	$-0.489360\pi$
$107$	81885.6			0.0668431			0.0334215	+	0.999441i	$0.489360\pi$
$108$	469862.			0.372991
$109$			659312.i			0.509110i	0.967058	+	0.254555i	$0.0819290\pi$
$109$			659312.i			0.509110i	−0.967058	+	0.254555i	$0.918071\pi$
$110$	−277925.			−0.208809
$111$		−	62196.4i		−	0.0454775i
$112$	1.51633e6			1.07930
$113$			760603.i			0.527136i	0.964641	+	0.263568i	$0.0848993\pi$
$113$			760603.i			0.527136i	−0.964641	+	0.263568i	$0.915101\pi$
$114$		−	2.26698e6i		−	1.53015i
$115$		−	143742.i		−	0.0945127i
$116$	398822.			0.255508
$117$			158579.i			0.0990119i
$118$	2.74069e6	+	648240.i	1.66807	+	0.394539i
$119$	−1.40726e6			−0.835092
$120$		−	1.00430e6i		−	0.581190i
$121$	1.70448e6			0.962133
$122$	−3.47442e6			−1.91339
$123$	761720.			0.409336
$124$			6.17644e6i			3.23946i
$125$	−1.96621e6			−1.00670
$126$		−	1.50769e6i		−	0.753703i
$127$	609001.			0.297308			0.148654	−	0.988889i	$-0.452506\pi$
$127$	609001.			0.297308			0.148654	+	0.988889i	$0.452506\pi$
$128$		−	3.77672e6i		−	1.80088i
$129$		−	634464.i		−	0.295555i
$130$	700259.			0.318734
$131$		−	354986.i		−	0.157905i	−0.996878	−	0.0789527i	$-0.974842\pi$
$131$		−	354986.i		−	0.157905i	0.996878	−	0.0789527i	$-0.0251576\pi$
$132$		−	500808.i		−	0.217745i
$133$	−4.79845e6			−2.03960
$134$	−6.51773e6			−2.70883
$135$	−296418.			−0.120477
$136$		−	2.56069e6i		−	1.01798i
$137$	−3.51364e6			−1.36646			−0.683229	−	0.730205i	$-0.739425\pi$
$137$	−3.51364e6			−1.36646			−0.683229	+	0.730205i	$0.739425\pi$
$138$	392660.			0.149410
$139$	−3.04917e6			−1.13537			−0.567685	−	0.823246i	$-0.692161\pi$
$139$	−3.04917e6			−1.13537			−0.567685	+	0.823246i	$0.692161\pi$
$140$	−4.39175e6			−1.60049
$141$			230723.i			0.0823064i
$142$		−	1.03653e6i		−	0.362006i
$143$	169023.			0.0578013
$144$	814367.			0.272730
$145$	−251602.			−0.0825296
$146$	3.90519e6			1.25483
$147$	−1.35732e6			−0.427296
$148$		−	494906.i		−	0.152664i
$149$			1.71211e6i			0.517574i	0.965934	+	0.258787i	$0.0833227\pi$
$149$			1.71211e6i			0.517574i	−0.965934	+	0.258787i	$0.916677\pi$
$150$		−	2.03107e6i		−	0.601800i
$151$		−	2.86817e6i		−	0.833057i	−0.909123	−	0.416528i	$-0.863247\pi$
$151$		−	2.86817e6i		−	0.833057i	0.909123	−	0.416528i	$-0.136753\pi$
$152$		−	8.73138e6i		−	2.48629i
$153$	−755789.			−0.211021
$154$	−1.60699e6			−0.439998
$155$		−	3.89648e6i		−	1.04635i
$156$			1.26183e6i			0.332375i
$157$		−	22056.5i		−	0.00569952i	−0.999996	−	0.00284976i	$-0.999093\pi$
$157$		−	22056.5i		−	0.00569952i	0.999996	−	0.00284976i	$-0.000907108\pi$
$158$			7.27206e6i			1.84368i
$159$	3.84025e6			0.955363
$160$			527120.i			0.128691i
$161$		−	831131.i		−	0.199155i
$162$		−	809725.i		−	0.190455i
$163$	−3.33224e6			−0.769438			−0.384719	−	0.923034i	$-0.625702\pi$
$163$	−3.33224e6			−0.769438			−0.384719	+	0.923034i	$0.625702\pi$
$164$	6.06112e6			1.37411
$165$			315941.i			0.0703321i
$166$	1.29879e7			2.83932
$167$	−1.78430e6			−0.383106			−0.191553	−	0.981482i	$-0.561352\pi$
$167$	−1.78430e6			−0.383106			−0.191553	+	0.981482i	$0.561352\pi$
$168$		−	5.80694e6i		−	1.22467i
$169$	4.40094e6			0.911770
$170$			3.33745e6i			0.679309i
$171$	−2.57707e6			−0.515392
$172$		−	5.04853e6i		−	0.992155i
$173$		−	3.85930e6i		−	0.745367i	−0.927959	−	0.372684i	$-0.878438\pi$
$173$		−	3.85930e6i		−	0.745367i	0.927959	−	0.372684i	$-0.121562\pi$
$174$		−	687300.i		−	0.130466i
$175$	−4.29911e6			−0.802167
$176$		−	868003.i		−	0.159215i
$177$	736910.	−	3.11558e6i	0.132891	−	0.561848i
$178$	−1.35207e7			−2.39739
$179$		−	686308.i		−	0.119663i	−0.998208	−	0.0598315i	$-0.980944\pi$
$179$		−	686308.i		−	0.119663i	0.998208	−	0.0598315i	$-0.0190563\pi$
$180$	−2.35864e6			−0.404431
$181$	3.82235e6			0.644606			0.322303	−	0.946637i	$-0.395543\pi$
$181$	3.82235e6			0.644606			0.322303	+	0.946637i	$0.395543\pi$
$182$	4.04897e6			0.671630
$183$			3.94967e6i			0.644478i
$184$	1.51235e6			0.242772
$185$			312218.i			0.0493109i
$186$	1.06440e7			1.65412
$187$			805566.i			0.123190i
$188$			1.83590e6i			0.276296i
$189$	−1.71392e6			−0.253866
$190$			1.13799e7i			1.65912i
$191$			1.30564e6i			0.187380i	0.995601	+	0.0936899i	$0.0298662\pi$
$191$			1.30564e6i			0.187380i	−0.995601	+	0.0936899i	$0.970134\pi$
$192$	−4.78340e6			−0.675823
$193$	2.12355e6			0.295386			0.147693	−	0.989033i	$-0.452815\pi$
$193$	2.12355e6			0.295386			0.147693	+	0.989033i	$0.452815\pi$
$194$	4.26415e6			0.584019
$195$		−	796044.i		−	0.107358i
$196$	−1.08004e7			−1.43440
$197$	−1.97152e6			−0.257872			−0.128936	−	0.991653i	$-0.541156\pi$
$197$	−1.97152e6			−0.257872			−0.128936	+	0.991653i	$0.541156\pi$
$198$	−863054.			−0.111184
$199$	1.10320e7			1.39990			0.699949	−	0.714193i	$-0.253206\pi$
$199$	1.10320e7			1.39990			0.699949	+	0.714193i	$0.253206\pi$
$200$		−	7.82278e6i		−	0.977848i
$201$			7.40926e6i			0.912403i
$202$	7.22225e6			0.876231
$203$	−1.45479e6			−0.173905
$204$	−6.01392e6			−0.708382
$205$	−3.82373e6			−0.443840
$206$	4.96599e6			0.568073
$207$		−	446370.i		−	0.0503250i
$208$			2.18702e6i			0.243032i
$209$			2.74680e6i			0.300876i
$210$			7.56840e6i			0.817234i
$211$		−	1.15651e7i		−	1.23112i	−0.788089	−	0.615561i	$-0.788929\pi$
$211$		−	1.15651e7i		−	1.23112i	0.788089	−	0.615561i	$-0.211071\pi$
$212$	3.05575e7			3.20708
$213$	−1.17831e6			−0.121933
$214$		−	1.12288e6i		−	0.114575i
$215$			3.18493e6i			0.320467i
$216$		−	3.11869e6i		−	0.309465i
$217$		−	2.25299e7i		−	2.20485i
$218$	9.04098e6			0.872662
$219$		−	4.43937e6i		−	0.422658i
$220$			2.51399e6i			0.236100i
$221$		−	2.02970e6i		−	0.188042i
$222$	−852885.			−0.0779527
$223$	−966458.			−0.0871502			−0.0435751	−	0.999050i	$-0.513875\pi$
$223$	−966458.			−0.0871502			−0.0435751	+	0.999050i	$0.513875\pi$
$224$			3.04786e6i			0.271176i
$225$	−2.30890e6			−0.202701
$226$	1.04300e7			0.903561
$227$		−	1.11687e6i		−	0.0954824i	−0.998860	−	0.0477412i	$-0.984798\pi$
$227$		−	1.11687e6i		−	0.0954824i	0.998860	−	0.0477412i	$-0.0152023\pi$
$228$	−2.05061e7			−1.73013
$229$			8.34569e6i			0.694953i	0.937689	+	0.347477i	$0.112961\pi$
$229$			8.34569e6i			0.694953i	−0.937689	+	0.347477i	$0.887039\pi$
$230$	−1.97110e6			−0.162004
$231$			1.82680e6i			0.148202i
$232$		−	2.64717e6i		−	0.211991i
$233$		−	1.74749e7i		−	1.38148i	−0.723101	−	0.690742i	$-0.757284\pi$
$233$		−	1.74749e7i		−	1.38148i	0.723101	−	0.690742i	$-0.242716\pi$
$234$	2.17455e6			0.169716
$235$		−	1.15820e6i		−	0.0892441i
$236$	5.86370e6	−	2.47911e7i	0.446104	−	1.88608i
$237$	8.26677e6			0.620999
$238$			1.92974e7i			1.43143i
$239$	−1.75221e7			−1.28349			−0.641744	−	0.766919i	$-0.721789\pi$
$239$	−1.75221e7			−1.28349			−0.641744	+	0.766919i	$0.721789\pi$
$240$	−4.08802e6			−0.295719
$241$	−424356.			−0.0303165			−0.0151583	−	0.999885i	$-0.504825\pi$
$241$	−424356.			−0.0303165			−0.0151583	+	0.999885i	$0.504825\pi$
$242$		−	2.33731e7i		−	1.64919i
$243$	−920483.			−0.0641500
$244$			3.14281e7i			2.16346i
$245$	6.81355e6			0.463313
$246$		−	1.04453e7i		−	0.701641i
$247$		−	6.92083e6i		−	0.459269i
$248$	4.09959e7			2.68773
$249$		−	1.47645e7i		−	0.956355i
$250$			2.69621e7i			1.72558i
$251$	−1.87344e6			−0.118473			−0.0592364	−	0.998244i	$-0.518867\pi$
$251$	−1.87344e6			−0.118473			−0.0592364	+	0.998244i	$0.518867\pi$
$252$	−1.36379e7			−0.852210
$253$	−475768.			−0.0293788
$254$		−	8.35108e6i		−	0.509614i
$255$	3.79396e6			0.228808
$256$	−3.21504e7			−1.91632
$257$	3.56173e6			0.209827			0.104914	−	0.994481i	$-0.466543\pi$
$257$	3.56173e6			0.209827			0.104914	+	0.994481i	$0.466543\pi$
$258$	−8.70025e6			−0.506609
$259$			1.80528e6i			0.103907i
$260$		−	6.33424e6i		−	0.360392i
$261$	−781312.			−0.0439443
$262$	−4.86783e6			−0.270665
$263$	−1.09649e6			−0.0602748			−0.0301374	−	0.999546i	$-0.509594\pi$
$263$	−1.09649e6			−0.0602748			−0.0301374	+	0.999546i	$0.509594\pi$
$264$	−3.32410e6			−0.180660
$265$	−1.92776e7			−1.03589
$266$			6.57999e7i			3.49607i
$267$			1.53701e7i			0.807501i
$268$			5.89566e7i			3.06287i
$269$		−	1.29997e7i		−	0.667848i	−0.942600	−	0.333924i	$-0.891627\pi$
$269$		−	1.29997e7i		−	0.667848i	0.942600	−	0.333924i	$-0.108373\pi$
$270$			4.06471e6i			0.206509i
$271$	4.49647e6			0.225925			0.112962	−	0.993599i	$-0.463966\pi$
$271$	4.49647e6			0.225925			0.112962	+	0.993599i	$0.463966\pi$
$272$	−1.04234e7			−0.517966
$273$		−	4.60281e6i		−	0.226222i
$274$			4.81817e7i			2.34224i
$275$			2.46096e6i			0.118333i
$276$		−	3.55183e6i		−	0.168937i
$277$	9.37091e6			0.440902			0.220451	−	0.975398i	$-0.429247\pi$
$277$	9.37091e6			0.440902			0.220451	+	0.975398i	$0.429247\pi$
$278$			4.18126e7i			1.94613i
$279$		−	1.21000e7i		−	0.557149i
$280$			2.91501e7i			1.32790i
$281$	−2.71429e7			−1.22331			−0.611657	−	0.791123i	$-0.709497\pi$
$281$	−2.71429e7			−1.22331			−0.611657	+	0.791123i	$0.709497\pi$
$282$	3.16385e6			0.141081
$283$			2.60309e7i			1.14850i	0.818681	+	0.574249i	$0.194706\pi$
$283$			2.60309e7i			1.14850i	−0.818681	+	0.574249i	$0.805294\pi$
$284$	−9.37599e6			−0.409319
$285$	1.29365e7			0.558835
$286$		−	2.31777e6i		−	0.0990769i
$287$	−2.21092e7			−0.935250
$288$			1.63689e6i			0.0685240i
$289$	−1.44640e7			−0.599231
$290$			3.45015e6i			0.141464i
$291$		−	4.84742e6i		−	0.196712i
$292$		−	3.53247e7i		−	1.41883i
$293$	−2.55220e7			−1.01464			−0.507319	−	0.861758i	$-0.669363\pi$
$293$	−2.55220e7			−1.01464			−0.507319	+	0.861758i	$0.669363\pi$
$294$			1.86125e7i			0.732426i
$295$	−3.69919e6	+	1.56398e7i	−0.144092	+	0.609207i
$296$	−3.28493e6			−0.126663
$297$			981107.i			0.0374496i
$298$	2.34777e7			0.887170
$299$	1.19875e6			0.0448449
$300$	−1.83722e7			−0.680453
$301$			1.84156e7i			0.675283i
$302$	−3.93306e7			−1.42794
$303$		−	8.21015e6i		−	0.295137i
$304$	−3.55413e7			−1.26506
$305$		−	1.98268e7i		−	0.698802i
$306$			1.03639e7i			0.361710i
$307$	4.11042e7			1.42060			0.710299	−	0.703900i	$-0.248560\pi$
$307$	4.11042e7			1.42060			0.710299	+	0.703900i	$0.248560\pi$
$308$			1.45361e7i			0.497504i
$309$		−	5.64526e6i		−	0.191341i
$310$	−5.34315e7			−1.79355
$311$	4.47374e7			1.48727			0.743634	−	0.668587i	$-0.233101\pi$
$311$	4.47374e7			1.48727			0.743634	+	0.668587i	$0.233101\pi$
$312$	8.37539e6			0.275766
$313$		−	3.06210e7i		−	0.998589i	−0.866432	−	0.499295i	$-0.833593\pi$
$313$		−	3.06210e7i		−	0.998589i	0.866432	−	0.499295i	$-0.166407\pi$
$314$	−302456.			−0.00976952
$315$	8.60365e6			0.275265
$316$	6.57800e7			2.08465
$317$	5.80961e7			1.82377			0.911883	−	0.410450i	$-0.134629\pi$
$317$	5.80961e7			1.82377			0.911883	+	0.410450i	$0.134629\pi$
$318$		−	5.26604e7i		−	1.63758i
$319$			832770.i			0.0256539i
$320$	2.40120e7			0.732789
$321$	−1.27647e6			−0.0385919
$322$	−1.13971e7			−0.341371
$323$	3.29848e7			0.978827
$324$	−7.32442e6			−0.215347
$325$		−	6.20064e6i		−	0.180629i
$326$			4.56942e7i			1.31889i
$327$		−	1.02777e7i		−	0.293935i
$328$		−	4.02305e7i		−	1.14008i
$329$		−	6.69682e6i		−	0.188053i
$330$	4.33242e6			0.120556
$331$	3.32831e7			0.917783			0.458891	−	0.888492i	$-0.348247\pi$
$331$	3.32831e7			0.917783			0.458891	+	0.888492i	$0.348247\pi$
$332$		−	1.17483e8i		−	3.21041i
$333$			969547.i			0.0262564i
$334$			2.44677e7i			0.656680i
$335$		−	3.71935e7i		−	0.989310i
$336$	−2.36373e7			−0.623133
$337$		−	1.87279e7i		−	0.489326i	−0.969608	−	0.244663i	$-0.921323\pi$
$337$		−	1.87279e7i		−	0.489326i	0.969608	−	0.244663i	$-0.0786773\pi$
$338$		−	6.03490e7i		−	1.56286i
$339$		−	1.18566e7i		−	0.304342i
$340$	3.01891e7			0.768092
$341$	−1.28969e7			−0.325253
$342$			3.53387e7i			0.883430i
$343$	−1.38350e7			−0.342843
$344$	−3.35094e7			−0.823174
$345$			2.24072e6i			0.0545669i
$346$	−5.29216e7			−1.27763
$347$			2.98270e7i			0.713874i	0.934128	+	0.356937i	$0.116179\pi$
$347$			2.98270e7i			0.713874i	−0.934128	+	0.356937i	$0.883821\pi$
$348$	−6.21702e6			−0.147518
$349$		−	7.76118e7i		−	1.82579i	−0.408190	−	0.912897i	$-0.633840\pi$
$349$		−	7.76118e7i		−	1.82579i	0.408190	−	0.912897i	$-0.366160\pi$
$350$			5.89527e7i			1.37499i
$351$		−	2.47200e6i		−	0.0571645i
$352$	1.74470e6			0.0400030
$353$		−	6.61940e7i		−	1.50485i	−0.658676	−	0.752427i	$-0.728883\pi$
$353$		−	6.61940e7i		−	1.50485i	0.658676	−	0.752427i	$-0.271117\pi$
$354$	−4.27232e7	−	1.01051e7i	−0.963061	−	0.227787i
$355$	5.91496e6			0.132211
$356$			1.22302e8i			2.71072i
$357$	2.19371e7			0.482140
$358$	−9.41118e6			−0.205114
$359$	5.98796e7			1.29418			0.647091	−	0.762413i	$-0.275985\pi$
$359$	5.98796e7			1.29418			0.647091	+	0.762413i	$0.275985\pi$
$360$			1.56554e7i			0.335550i
$361$	6.54247e7			1.39066
$362$		−	5.24149e7i		−	1.10492i
$363$	−2.65702e7			−0.555488
$364$		−	3.66252e7i		−	0.759410i
$365$			2.22850e7i			0.458284i
$366$	5.41609e7			1.10470
$367$			6.54533e7i			1.32414i	0.749443	+	0.662069i	$0.230322\pi$
$367$			6.54533e7i			1.32414i	−0.749443	+	0.662069i	$0.769678\pi$
$368$		−	6.15605e6i		−	0.123526i
$369$	−1.18740e7			−0.236330
$370$	4.28137e6			0.0845235
$371$	−1.11465e8			−2.18281
$372$		−	9.62812e7i		−	1.87031i
$373$	6.29630e7			1.21327			0.606637	−	0.794979i	$-0.292518\pi$
$373$	6.29630e7			1.21327			0.606637	+	0.794979i	$0.292518\pi$
$374$	1.10465e7			0.211160
$375$	3.06502e7			0.581218
$376$	1.21857e7			0.229238
$377$		−	2.09825e6i		−	0.0391591i
$378$			2.35026e7i			0.435151i
$379$	−2.82722e7			−0.519328			−0.259664	−	0.965699i	$-0.583612\pi$
$379$	−2.82722e7			−0.519328			−0.259664	+	0.965699i	$0.583612\pi$
$380$	1.02938e8			1.87597
$381$	−9.49338e6			−0.171651
$382$	1.79039e7			0.321187
$383$	−1.86237e7			−0.331489			−0.165744	−	0.986169i	$-0.553003\pi$
$383$	−1.86237e7			−0.331489			−0.165744	+	0.986169i	$0.553003\pi$
$384$			5.88732e7i			1.03974i
$385$		−	9.17030e6i		−	0.160695i
$386$		−	2.91197e7i		−	0.506320i
$387$			9.89032e6i			0.170639i
$388$		−	3.85716e7i		−	0.660348i
$389$	−4.03075e7			−0.684758			−0.342379	−	0.939562i	$-0.611233\pi$
$389$	−4.03075e7			−0.684758			−0.342379	+	0.939562i	$0.611233\pi$
$390$	−1.09160e7			−0.184021
$391$			5.71324e6i			0.0955767i
$392$			7.16871e7i			1.19010i
$393$			5.53368e6i			0.0911667i
$394$			2.70350e7i			0.442016i
$395$	−4.14981e7			−0.673344
$396$			7.80682e6i			0.125715i
$397$		−	6.55839e7i		−	1.04816i	−0.851671	−	0.524078i	$-0.824410\pi$
$397$		−	6.55839e7i		−	1.04816i	0.851671	−	0.524078i	$-0.175590\pi$
$398$		−	1.51280e8i		−	2.39956i
$399$	7.48004e7			1.17757
$400$	−3.18429e7			−0.497545
$401$			1.24598e8i			1.93232i	0.257950	+	0.966158i	$0.416953\pi$
$401$			1.24598e8i			1.93232i	−0.257950	+	0.966158i	$0.583047\pi$
$402$	1.01601e8			1.56394
$403$	3.24950e7			0.496479
$404$		−	6.53294e7i		−	0.990751i
$405$	4.62070e6			0.0695573
$406$			1.99491e7i			0.298089i
$407$	1.03340e6			0.0153280
$408$			3.99172e7i			0.587733i
$409$		−	1.03807e8i		−	1.51725i	−0.651526	−	0.758626i	$-0.725871\pi$
$409$		−	1.03807e8i		−	1.51725i	0.651526	−	0.758626i	$-0.274129\pi$
$410$			5.24339e7i			0.760783i
$411$	5.47723e7			0.788924
$412$		−	4.49202e7i		−	0.642318i
$413$	−2.13891e7	+	9.04309e7i	−0.303628	+	1.28371i
$414$	−6.12096e6			−0.0862618
$415$			7.41156e7i			1.03697i
$416$	−4.39595e6			−0.0610622
$417$	4.75319e7			0.655507
$418$	3.76662e7			0.515730
$419$			9.05965e7i			1.23160i	0.787903	+	0.615799i	$0.211167\pi$
$419$			9.05965e7i			1.23160i	−0.787903	+	0.615799i	$0.788833\pi$
$420$	6.84605e7			0.924043
$421$			2.63419e7i			0.353022i	0.984299	+	0.176511i	$0.0564811\pi$
$421$			2.63419e7i			0.353022i	−0.984299	+	0.176511i	$0.943519\pi$
$422$	−1.58589e8			−2.11026
$423$		−	3.59662e6i		−	0.0475196i
$424$		−	2.02824e8i		−	2.66086i
$425$	2.95523e7			0.384968
$426$			1.61579e7i			0.209005i
$427$		−	1.14641e8i		−	1.47250i
$428$	−1.01571e7			−0.129550
$429$	−2.63481e6			−0.0333716
$430$	4.36741e7			0.549312
$431$		−	4.56261e7i		−	0.569877i	−0.958546	−	0.284939i	$-0.908027\pi$
$431$		−	4.56261e7i		−	0.569877i	0.958546	−	0.284939i	$-0.0919732\pi$
$432$	−1.26947e7			−0.157461
$433$	−1.22197e8			−1.50521			−0.752604	−	0.658473i	$-0.771202\pi$
$433$	−1.22197e8			−1.50521			−0.752604	+	0.658473i	$0.771202\pi$
$434$	−3.08947e8			−3.77932
$435$	3.92208e6			0.0476485
$436$		−	8.17808e7i		−	0.986716i
$437$			1.94808e7i			0.233434i
$438$	−6.08760e7			−0.724475
$439$	5.78606e7			0.683895			0.341947	−	0.939719i	$-0.388914\pi$
$439$	5.78606e7			0.683895			0.341947	+	0.939719i	$0.388914\pi$
$440$	1.66865e7			0.195888
$441$	2.11585e7			0.246700
$442$	−2.78328e7			−0.322323
$443$			1.17033e8i			1.34616i	0.739570	+	0.673079i	$0.235029\pi$
$443$			1.17033e8i			1.34616i	−0.739570	+	0.673079i	$0.764971\pi$
$444$			7.71483e6i			0.0881409i
$445$		−	7.71559e7i		−	0.875567i
$446$			1.32528e7i			0.149384i
$447$		−	2.66891e7i		−	0.298821i
$448$	1.38840e8			1.54412
$449$	−1.21901e8			−1.34669			−0.673344	−	0.739329i	$-0.735143\pi$
$449$	−1.21901e8			−1.34669			−0.673344	+	0.739329i	$0.735143\pi$
$450$			3.16613e7i			0.347449i
$451$			1.26561e7i			0.137965i
$452$		−	9.43450e7i		−	1.02165i
$453$			4.47104e7i			0.480966i
$454$	−1.53153e7			−0.163666
$455$			2.31055e7i			0.245291i
$456$			1.36109e8i			1.43546i
$457$		−	1.76454e8i		−	1.84877i	−0.381462	−	0.924385i	$-0.624579\pi$
$457$		−	1.76454e8i		−	1.84877i	0.381462	−	0.924385i	$-0.375421\pi$
$458$	1.14442e8			1.19122
$459$	1.17816e7			0.121833
$460$			1.78297e7i			0.183177i
$461$	−1.42578e8			−1.45530			−0.727648	−	0.685951i	$-0.759386\pi$
$461$	−1.42578e8			−1.45530			−0.727648	+	0.685951i	$0.759386\pi$
$462$	2.50505e7			0.254033
$463$			1.45074e8i			1.46166i	0.682558	+	0.730832i	$0.260868\pi$
$463$			1.45074e8i			1.46166i	−0.682558	+	0.730832i	$0.739132\pi$
$464$	−1.07754e7			−0.107864
$465$			6.07402e7i			0.604112i
$466$	−2.39628e8			−2.36799
$467$		−	1.48028e8i		−	1.45342i	−0.686942	−	0.726712i	$-0.741048\pi$
$467$		−	1.48028e8i		−	1.45342i	0.686942	−	0.726712i	$-0.258952\pi$
$468$		−	1.96701e7i		−	0.191897i
$469$		−	2.15057e8i		−	2.08465i
$470$	−1.58821e7			−0.152973
$471$			343827.i			0.00329062i
$472$	−1.64550e8	−	3.89201e7i	−1.56485	−	0.370125i
$473$	1.05417e7			0.0996157
$474$		−	1.13360e8i		−	1.06445i
$475$	1.00767e8			0.940235
$476$	1.74556e8			1.61851
$477$	−5.98636e7			−0.551579
$478$			2.40276e8i			2.20002i
$479$	−1.49506e8			−1.36036			−0.680178	−	0.733047i	$-0.738098\pi$
$479$	−1.49506e8			−1.36036			−0.680178	+	0.733047i	$0.738098\pi$
$480$		−	8.21698e6i		−	0.0743000i
$481$	−2.60376e6			−0.0233973
$482$			5.81910e6i			0.0519654i
$483$			1.29560e7i			0.114982i
$484$	−2.11423e8			−1.86473
$485$			2.43334e7i			0.213293i
$486$			1.26224e7i			0.109959i
$487$	−1.09033e8			−0.943996			−0.471998	−	0.881600i	$-0.656467\pi$
$487$	−1.09033e8			−0.943996			−0.471998	+	0.881600i	$0.656467\pi$
$488$	2.08603e8			1.79499
$489$	5.19445e7			0.444235
$490$		−	9.34325e7i		−	0.794163i
$491$	−1.57201e8			−1.32804			−0.664019	−	0.747715i	$-0.731151\pi$
$491$	−1.57201e8			−1.32804			−0.664019	+	0.747715i	$0.731151\pi$
$492$	−9.44835e7			−0.793343
$493$	1.00003e7			0.0834587
$494$	−9.49037e7			−0.787231
$495$		−	4.92503e6i		−	0.0406063i
$496$		−	1.66875e8i		−	1.36756i
$497$	3.42009e7			0.278592
$498$	−2.02461e8			−1.63928
$499$	6.89738e7			0.555114			0.277557	−	0.960709i	$-0.410475\pi$
$499$	6.89738e7			0.555114			0.277557	+	0.960709i	$0.410475\pi$
$500$	2.43888e8			1.95110
$501$	2.78145e7			0.221186
$502$			2.56900e7i			0.203073i
$503$		−	1.36368e8i		−	1.07154i	−0.844363	−	0.535771i	$-0.820021\pi$
$503$		−	1.36368e8i		−	1.07154i	0.844363	−	0.535771i	$-0.179979\pi$
$504$			9.05213e7i			0.707064i
$505$			4.12138e7i			0.320014i
$506$			6.52409e6i			0.0503580i
$507$	−6.86038e7			−0.526411
$508$	−7.55402e7			−0.576219
$509$			2.13696e7i			0.162047i	0.996712	+	0.0810237i	$0.0258190\pi$
$509$			2.13696e7i			0.162047i	−0.996712	+	0.0810237i	$0.974181\pi$
$510$		−	5.20256e7i		−	0.392199i
$511$			1.28854e8i			0.965687i
$512$			1.99161e8i			1.48387i
$513$	4.01725e7			0.297562
$514$		−	4.88412e7i		−	0.359664i
$515$			2.83385e7i			0.207470i
$516$			7.86987e7i			0.572821i
$517$	−3.83349e6			−0.0277411
$518$	2.47553e7			0.178106
$519$			6.01605e7i			0.430338i
$520$	−4.20434e7			−0.299011
$521$	−2.25805e8			−1.59669			−0.798345	−	0.602200i	$-0.794291\pi$
$521$	−2.25805e8			−1.59669			−0.798345	+	0.602200i	$0.794291\pi$
$522$			1.07139e7i			0.0753248i
$523$	3.75262e7			0.262319			0.131160	−	0.991361i	$-0.458130\pi$
$523$	3.75262e7			0.262319			0.131160	+	0.991361i	$0.458130\pi$
$524$			4.40323e7i			0.306040i
$525$	6.70166e7			0.463131
$526$			1.50358e7i			0.103317i
$527$			1.54872e8i			1.05813i
$528$			1.35308e7i			0.0919227i
$529$	1.44662e8			0.977207
$530$			2.64348e8i			1.77562i
$531$	−1.14873e7	+	4.85671e7i	−0.0767244	+	0.324383i
$532$	5.95198e8			3.95300
$533$		−	3.18883e7i		−	0.210596i
$534$	2.10767e8			1.38413
$535$	6.40771e6			0.0418448
$536$	3.91323e8			2.54121
$537$			1.06985e7i			0.0690875i
$538$	−1.78262e8			−1.14476
$539$		−	2.25520e7i		−	0.144019i
$540$	3.67676e7			0.233499
$541$		−	1.13661e8i		−	0.717825i	−0.933371	−	0.358913i	$-0.883148\pi$
$541$		−	1.13661e8i		−	0.717825i	0.933371	−	0.358913i	$-0.116852\pi$
$542$		−	6.16590e7i		−	0.387257i
$543$	−5.95845e7			−0.372163
$544$		−	2.09511e7i		−	0.130140i
$545$			5.15925e7i			0.318711i
$546$	−6.31172e7			−0.387766
$547$	−1.35059e8			−0.825203			−0.412601	−	0.910912i	$-0.635380\pi$
$547$	−1.35059e8			−0.825203			−0.412601	+	0.910912i	$0.635380\pi$
$548$	4.35831e8			2.64836
$549$		−	6.15693e7i		−	0.372089i
$550$	3.37466e7			0.202834
$551$	3.40987e7			0.203837
$552$	−2.35752e7			−0.140164
$553$	−2.39946e8			−1.41886
$554$		−	1.28501e8i		−	0.755748i
$555$		−	4.86700e6i		−	0.0284696i
$556$	3.78218e8			2.20048
$557$	8.63421e7			0.499640			0.249820	−	0.968292i	$-0.419629\pi$
$557$	8.63421e7			0.499640			0.249820	+	0.968292i	$0.419629\pi$
$558$	−1.65924e8			−0.955006
$559$	−2.65609e7			−0.152057
$560$	1.18656e8			0.675657
$561$		−	1.25575e7i		−	0.0711239i
$562$			3.72204e8i			2.09687i
$563$			1.55337e8i			0.870461i	0.900319	+	0.435231i	$0.143333\pi$
$563$			1.55337e8i			0.870461i	−0.900319	+	0.435231i	$0.856667\pi$
$564$		−	2.86188e7i		−	0.159520i
$565$			5.95187e7i			0.329996i
$566$	3.56956e8			1.96864
$567$	2.67174e7			0.146570
$568$			6.22329e7i			0.339606i
$569$		−	3.58071e7i		−	0.194371i	−0.995266	−	0.0971856i	$-0.969016\pi$
$569$		−	3.58071e7i		−	0.194371i	0.995266	−	0.0971856i	$-0.0309840\pi$
$570$		−	1.77396e8i		−	0.957896i
$571$		−	4.23278e7i		−	0.227362i	−0.993517	−	0.113681i	$-0.963736\pi$
$571$		−	4.23278e7i		−	0.227362i	0.993517	−	0.113681i	$-0.0362642\pi$
$572$	−2.09656e7			−0.112026
$573$		−	2.03529e7i		−	0.108184i
$574$			3.03178e8i			1.60311i
$575$			1.74537e7i			0.0918085i
$576$	7.45658e7			0.390187
$577$	−1.16324e8			−0.605541			−0.302770	−	0.953064i	$-0.597912\pi$
$577$	−1.16324e8			−0.605541			−0.302770	+	0.953064i	$0.597912\pi$
$578$			1.98341e8i			1.02714i
$579$	−3.31029e7			−0.170541
$580$	3.12086e7			0.159952
$581$			4.28544e8i			2.18508i
$582$	−6.64715e7			−0.337183
$583$			6.38063e7i			0.322002i
$584$	−2.34467e8			−1.17718
$585$			1.24091e7i			0.0619830i
$586$			3.49977e8i			1.73919i
$587$		−	2.56920e8i		−	1.27024i	−0.772415	−	0.635118i	$-0.780951\pi$
$587$		−	2.56920e8i		−	1.27024i	0.772415	−	0.635118i	$-0.219049\pi$
$588$	1.68361e8			0.828151
$589$			5.28077e8i			2.58435i
$590$	2.14465e8	+	5.07261e7i	1.04424	+	0.246988i
$591$	3.07330e7			0.148882
$592$			1.33714e7i			0.0644483i
$593$	2.20865e7			0.105916			0.0529581	−	0.998597i	$-0.483135\pi$
$593$	2.20865e7			0.105916			0.0529581	+	0.998597i	$0.483135\pi$
$594$	1.34537e7			0.0641922
$595$	−1.10121e8			−0.522781
$596$		−	2.12369e8i		−	1.00312i
$597$	−1.71972e8			−0.808231
$598$		−	1.64381e7i		−	0.0768685i
$599$	−3.37760e8			−1.57155			−0.785773	−	0.618515i	$-0.787735\pi$
$599$	−3.37760e8			−1.57155			−0.785773	+	0.618515i	$0.787735\pi$
$600$			1.21945e8i			0.564561i
$601$		−	1.94838e8i		−	0.897533i	−0.893649	−	0.448766i	$-0.851864\pi$
$601$		−	1.94838e8i		−	0.897533i	0.893649	−	0.448766i	$-0.148136\pi$
$602$	2.52528e8			1.15750
$603$		−	1.15499e8i		−	0.526776i
$604$			3.55767e8i			1.61456i
$605$	1.33379e8			0.602311
$606$	−1.12584e8			−0.505892
$607$	1.31760e7			0.0589138			0.0294569	−	0.999566i	$-0.490622\pi$
$607$	1.31760e7			0.0589138			0.0294569	+	0.999566i	$0.490622\pi$
$608$		−	7.14387e7i		−	0.317850i
$609$	2.26779e7			0.100404
$610$	−2.71881e8			−1.19781
$611$	9.65887e6			0.0423451
$612$	9.37478e7			0.408984
$613$			9.33914e7i			0.405439i	0.979237	+	0.202719i	$0.0649779\pi$
$613$			9.33914e7i			0.405439i	−0.979237	+	0.202719i	$0.935022\pi$
$614$		−	5.63652e8i		−	2.43504i
$615$	5.96061e7			0.256251
$616$	9.64831e7			0.412771
$617$	2.34906e8			1.00009			0.500045	−	0.866000i	$-0.333317\pi$
$617$	2.34906e8			1.00009			0.500045	+	0.866000i	$0.333317\pi$
$618$	−7.74121e7			−0.327977
$619$	3.69057e8			1.55604			0.778020	−	0.628239i	$-0.216224\pi$
$619$	3.69057e8			1.55604			0.778020	+	0.628239i	$0.216224\pi$
$620$			4.83319e8i			2.02796i
$621$			6.95821e6i			0.0290551i
$622$		−	6.13472e8i		−	2.54932i
$623$		−	4.46123e8i		−	1.84498i
$624$		−	3.40923e7i		−	0.140314i
$625$	−5.39683e6			−0.0221054
$626$	−4.19899e8			−1.71168
$627$		−	4.28183e7i		−	0.173711i
$628$			2.73589e6i			0.0110464i
$629$		−	1.24096e7i		−	0.0498660i
$630$		−	1.17980e8i		−	0.471830i
$631$	−2.90620e7			−0.115675			−0.0578373	−	0.998326i	$-0.518420\pi$
$631$	−2.90620e7			−0.115675			−0.0578373	+	0.998326i	$0.518420\pi$
$632$		−	4.36613e8i		−	1.72960i
$633$			1.80282e8i			0.710789i
$634$		−	7.96657e8i		−	3.12611i
$635$	4.76555e7			0.186120
$636$	−4.76344e8			−1.85161
$637$			5.68220e7i			0.219836i
$638$	1.14196e7			0.0439732
$639$	1.83680e7			0.0703980
$640$		−	2.95535e8i		−	1.12738i
$641$	5.18494e8			1.96865			0.984327	−	0.176353i	$-0.0564301\pi$
$641$	5.18494e8			1.96865			0.984327	+	0.176353i	$0.0564301\pi$
$642$			1.75039e7i			0.0661501i
$643$	−1.94176e8			−0.730403			−0.365202	−	0.930928i	$-0.619000\pi$
$643$	−1.94176e8			−0.730403			−0.365202	+	0.930928i	$0.619000\pi$
$644$			1.03093e8i			0.385987i
$645$		−	4.96481e7i		−	0.185022i
$646$		−	4.52312e8i		−	1.67780i
$647$	5.09645e8			1.88172			0.940859	−	0.338798i	$-0.110020\pi$
$647$	5.09645e8			1.88172			0.940859	+	0.338798i	$0.110020\pi$
$648$			4.86156e7i			0.178670i
$649$	5.17658e7	+	1.22439e7i	0.189369	+	0.0447903i
$650$	−8.50279e7			−0.309614
$651$			3.51206e8i			1.27297i
$652$	4.13330e8			1.49126
$653$	1.15463e8			0.414672			0.207336	−	0.978270i	$-0.433521\pi$
$653$	1.15463e8			0.414672			0.207336	+	0.978270i	$0.433521\pi$
$654$	−1.40935e8			−0.503832
$655$		−	2.77783e7i		−	0.0988513i
$656$	−1.63759e8			−0.580089
$657$			6.92029e7i			0.244021i
$658$	−9.18319e7			−0.322341
$659$			2.63375e8i			0.920277i	0.887847	+	0.460139i	$0.152200\pi$
$659$			2.63375e8i			0.920277i	−0.887847	+	0.460139i	$0.847800\pi$
$660$		−	3.91892e7i		−	0.136312i
$661$	−3.64442e7			−0.126190			−0.0630948	−	0.998008i	$-0.520097\pi$
$661$	−3.64442e7			−0.126190			−0.0630948	+	0.998008i	$0.520097\pi$
$662$		−	4.56403e8i		−	1.57317i
$663$			3.16400e7i			0.108566i
$664$	−7.79790e8			−2.66363
$665$	−3.75488e8			−1.27682
$666$	1.32952e7			0.0450060
$667$			5.90618e6i			0.0199035i
$668$	2.21324e8			0.742505
$669$	1.50656e7			0.0503162
$670$	−5.10025e8			−1.69577
$671$	−6.56244e7			−0.217219
$672$		−	4.75114e7i		−	0.156563i
$673$		−	3.87285e8i		−	1.27053i	−0.772293	−	0.635266i	$-0.780890\pi$
$673$		−	3.87285e8i		−	1.27053i	0.772293	−	0.635266i	$-0.219110\pi$
$674$	−2.56811e8			−0.838751
$675$	3.59921e7			0.117030
$676$	−5.45891e8			−1.76712
$677$	−6.45220e7			−0.207942			−0.103971	−	0.994580i	$-0.533155\pi$
$677$	−6.45220e7			−0.207942			−0.103971	+	0.994580i	$0.533155\pi$
$678$	−1.62587e8			−0.521671
$679$			1.40698e8i			0.449448i
$680$		−	2.00379e8i		−	0.637274i
$681$			1.74102e7i			0.0551268i
$682$			1.76852e8i			0.557515i
$683$			2.66210e8i			0.835531i	0.908555	+	0.417765i	$0.137187\pi$
$683$			2.66210e8i			0.835531i	−0.908555	+	0.417765i	$0.862813\pi$
$684$	3.19659e8			0.998891
$685$	−2.74950e8			−0.855424
$686$			1.89715e8i			0.587666i
$687$		−	1.30096e8i		−	0.401231i
$688$			1.36401e8i			0.418844i
$689$		−	1.60766e8i		−	0.491516i
$690$	3.07264e7			0.0935329
$691$		−	2.91925e6i		−	0.00884785i	−0.999990	−	0.00442392i	$-0.998592\pi$
$691$		−	2.91925e6i		−	0.00884785i	0.999990	−	0.00442392i	$-0.00140818\pi$
$692$			4.78706e8i			1.44461i
$693$		−	2.84770e7i		−	0.0855647i
$694$	4.09011e8			1.22365
$695$	−2.38604e8			−0.710760
$696$			4.12653e7i			0.122393i
$697$	1.51980e8			0.448836
$698$	−1.06427e9			−3.12958
$699$			2.72406e8i			0.797600i
$700$	5.33261e8			1.55470
$701$			5.60034e8i			1.62577i	0.582421	+	0.812887i	$0.302105\pi$
$701$			5.60034e8i			1.62577i	−0.582421	+	0.812887i	$0.697895\pi$
$702$	−3.38979e7			−0.0979854
$703$		−	4.23138e7i		−	0.121791i
$704$		−	7.94768e7i		−	0.227784i
$705$			1.80545e7i			0.0515251i
$706$	−9.07702e8			−2.57946
$707$			2.38303e8i			0.674327i
$708$	−9.14060e7	+	3.86456e8i	−0.257558	+	1.08893i
$709$	−1.51717e7			−0.0425692			−0.0212846	−	0.999773i	$-0.506776\pi$
$709$	−1.51717e7			−0.0425692			−0.0212846	+	0.999773i	$0.506776\pi$
$710$		−	8.11104e7i		−	0.226622i
$711$	−1.28866e8			−0.358534
$712$	8.11778e8			2.24904
$713$	−9.14673e7			−0.252347
$714$		−	3.00817e8i		−	0.826434i
$715$	1.32264e7			0.0361845
$716$			8.51294e7i			0.231921i
$717$	2.73142e8			0.741023
$718$		−	8.21114e8i		−	2.21835i
$719$			3.86036e8i			1.03858i	0.854597	+	0.519292i	$0.173804\pi$
$719$			3.86036e8i			1.03858i	−0.854597	+	0.519292i	$0.826196\pi$
$720$	6.37259e7			0.170733
$721$			1.63856e8i			0.437176i
$722$		−	8.97153e8i		−	2.38372i
$723$	6.61506e6			0.0175033
$724$	−4.74123e8			−1.24932
$725$	3.05503e7			0.0801682
$726$			3.64350e8i			0.952159i
$727$	3.33880e8			0.868935			0.434468	−	0.900687i	$-0.356937\pi$
$727$	3.33880e8			0.868935			0.434468	+	0.900687i	$0.356937\pi$
$728$	−2.43099e8			−0.630070
$729$	1.43489e7			0.0370370
$730$	3.05589e8			0.785542
$731$		−	1.26590e8i		−	0.324075i
$732$		−	4.89916e8i		−	1.24908i
$733$	−7.33257e8			−1.86185			−0.930924	−	0.365214i	$-0.880996\pi$
$733$	−7.33257e8			−1.86185			−0.930924	+	0.365214i	$0.880996\pi$
$734$	8.97545e8			2.26970
$735$	−1.06213e8			−0.267494
$736$	1.23738e7			0.0310362
$737$	−1.23106e8			−0.307522
$738$			1.62826e8i			0.405092i
$739$		−	8.14134e7i		−	0.201726i	−0.994900	−	0.100863i	$-0.967840\pi$
$739$		−	8.14134e7i		−	0.201726i	0.994900	−	0.100863i	$-0.0321604\pi$
$740$		−	3.87274e7i		−	0.0955704i
$741$			1.07885e8i			0.265159i
$742$			1.52849e9i			3.74154i
$743$	3.99055e8			0.972895			0.486448	−	0.873710i	$-0.338292\pi$
$743$	3.99055e8			0.972895			0.486448	+	0.873710i	$0.338292\pi$
$744$	−6.39063e8			−1.55176
$745$			1.33976e8i			0.324009i
$746$		−	8.63397e8i		−	2.07967i
$747$			2.30155e8i			0.552152i
$748$		−	9.99222e7i		−	0.238758i
$749$	3.70500e7			0.0881746
$750$		−	4.20298e8i		−	0.996262i
$751$		−	6.73928e8i		−	1.59109i	−0.605897	−	0.795543i	$-0.707186\pi$
$751$		−	6.73928e8i		−	1.59109i	0.605897	−	0.795543i	$-0.292814\pi$
$752$		−	4.96023e7i		−	0.116640i
$753$	2.92040e7			0.0684003
$754$	−2.87728e7			−0.0671224
$755$		−	2.24440e8i		−	0.521507i
$756$	2.12594e8			0.492023
$757$	6.32443e8			1.45792			0.728960	−	0.684556i	$-0.240004\pi$
$757$	6.32443e8			1.45792			0.728960	+	0.684556i	$0.240004\pi$
$758$			3.87689e8i			0.890177i
$759$	7.41649e6			0.0169619
$760$		−	6.83248e8i		−	1.55646i
$761$	−3.07136e8			−0.696909			−0.348454	−	0.937326i	$-0.613293\pi$
$761$	−3.07136e8			−0.696909			−0.348454	+	0.937326i	$0.613293\pi$
$762$			1.30180e8i			0.294226i
$763$			2.98313e8i			0.671581i
$764$		−	1.61951e8i		−	0.363164i
$765$	−5.91420e7			−0.132103
$766$			2.55382e8i			0.568203i
$767$	−1.30429e8	−	3.08496e7i	−0.289060	−	0.0683697i
$768$	5.01176e8			1.10639
$769$		−	4.77329e8i		−	1.04964i	−0.851214	−	0.524818i	$-0.824133\pi$
$769$		−	4.77329e8i		−	1.04964i	0.851214	−	0.524818i	$-0.175867\pi$
$770$	−1.25750e8			−0.275446
$771$	−5.55219e7			−0.121144
$772$	−2.63404e8			−0.572494
$773$			2.57272e8i			0.556999i	0.960436	+	0.278500i	$0.0898371\pi$
$773$			2.57272e8i			0.556999i	−0.960436	+	0.278500i	$0.910163\pi$
$774$	1.35624e8			0.292491
$775$			4.73125e8i			1.01641i
$776$	−2.56018e8			−0.547880
$777$		−	2.81415e7i		−	0.0599906i
$778$			5.52727e8i			1.17374i
$779$	5.18217e8			1.09622
$780$			9.87411e7i			0.208072i
$781$		−	1.95778e7i		−	0.0410970i
$782$	7.83443e7			0.163828
$783$	1.21794e7			0.0253713
$784$	2.91804e8			0.605541
$785$		−	1.72597e6i		−	0.00356799i
$786$	7.58820e7			0.156268
$787$	−3.50470e8			−0.718996			−0.359498	−	0.933146i	$-0.617052\pi$
$787$	−3.50470e8			−0.718996			−0.359498	+	0.933146i	$0.617052\pi$
$788$	2.44547e8			0.499786
$789$	1.70925e7			0.0347997
$790$			5.69054e8i			1.15418i
$791$			3.44143e8i			0.695360i
$792$	5.18175e7			0.104304
$793$	1.65347e8			0.331572
$794$	−8.99336e8			−1.79664
$795$	3.00507e8			0.598072
$796$	−1.36841e9			−2.71317
$797$		−	2.47372e8i		−	0.488626i	−0.969696	−	0.244313i	$-0.921438\pi$
$797$		−	2.47372e8i		−	0.488626i	0.969696	−	0.244313i	$-0.0785624\pi$
$798$		−	1.02572e9i		−	2.01846i
$799$			4.60343e7i			0.0902488i
$800$		−	6.40047e7i		−	0.125009i
$801$		−	2.39596e8i		−	0.466211i
$802$	1.70858e9			3.31217
$803$	7.37607e7			0.142455
$804$		−	9.19042e8i		−	1.76835i
$805$		−	6.50376e7i		−	0.124674i
$806$		−	4.45596e8i		−	0.851012i
$807$			2.02646e8i			0.385582i
$808$	−4.33622e8			−0.822010
$809$		−	9.95238e8i		−	1.87967i	−0.341629	−	0.939835i	$-0.610979\pi$
$809$		−	9.95238e8i		−	1.87967i	0.341629	−	0.939835i	$-0.389021\pi$
$810$		−	6.33626e7i		−	0.119228i
$811$		−	9.52402e8i		−	1.78549i	−0.450560	−	0.892746i	$-0.648776\pi$
$811$		−	9.52402e8i		−	1.78549i	0.450560	−	0.892746i	$-0.351224\pi$
$812$	1.80451e8			0.337048
$813$	−7.00931e7			−0.130438
$814$		−	1.41708e7i		−	0.0262737i
$815$	−2.60754e8			−0.481680
$816$	1.62484e8			0.299048
$817$		−	4.31642e8i		−	0.791512i
$818$	−1.42348e9			−2.60071
$819$			7.17507e7i			0.130609i
$820$	4.74295e8			0.860214
$821$		−	5.46045e7i		−	0.0986731i	−0.998782	−	0.0493366i	$-0.984289\pi$
$821$		−	5.46045e7i		−	0.0986731i	0.998782	−	0.0493366i	$-0.0157107\pi$
$822$		−	7.51079e8i		−	1.35229i
$823$			9.80986e8i			1.75980i	0.475159	+	0.879900i	$0.342391\pi$
$823$			9.80986e8i			1.75980i	−0.475159	+	0.879900i	$0.657609\pi$
$824$	−2.98156e8			−0.532921
$825$		−	3.83626e7i		−	0.0683198i
$826$	1.24006e9	+	2.93303e8i	2.20040	+	0.520447i
$827$	9.25388e8			1.63609			0.818045	−	0.575154i	$-0.195058\pi$
$827$	9.25388e8			1.63609			0.818045	+	0.575154i	$0.195058\pi$
$828$			5.53676e7i			0.0975359i
$829$	7.87859e8			1.38288			0.691440	−	0.722433i	$-0.256976\pi$
$829$	7.87859e8			1.38288			0.691440	+	0.722433i	$0.256976\pi$
$830$	1.01633e9			1.77746
$831$	−1.46078e8			−0.254555
$832$			2.00250e8i			0.347698i
$833$	−2.70814e8			−0.468529
$834$		−	6.51793e8i		−	1.12360i
$835$	−1.39625e8			−0.239830
$836$		−	3.40712e8i		−	0.583134i
$837$			1.88620e8i			0.321670i
$838$	1.24233e9			2.11108
$839$		−	6.31753e7i		−	0.106970i	−0.998569	−	0.0534849i	$-0.982967\pi$
$839$		−	6.31753e7i		−	0.106970i	0.998569	−	0.0534849i	$-0.0170329\pi$
$840$		−	4.54405e8i		−	0.766664i
$841$	−5.84485e8			−0.982620
$842$	3.61221e8			0.605113
$843$	4.23116e8			0.706280
$844$			1.43453e9i			2.38606i
$845$	3.44382e8			0.570782
$846$	−4.93195e7			−0.0814531
$847$	7.71210e8			1.26918
$848$	−8.25602e8			−1.35389
$849$		−	4.05782e8i		−	0.663086i
$850$		−	4.05244e8i		−	0.659872i
$851$	7.32910e6			0.0118922
$852$	1.46157e8			0.236321
$853$	6.77396e8			1.09143			0.545714	−	0.837971i	$-0.316258\pi$
$853$	6.77396e8			1.09143			0.545714	+	0.837971i	$0.316258\pi$
$854$	−1.57204e9			−2.52401
$855$	−2.01661e8			−0.322643
$856$			6.74172e7i			0.107485i
$857$		−	3.55653e8i		−	0.565046i	−0.959261	−	0.282523i	$-0.908829\pi$
$857$		−	3.55653e8i		−	0.565046i	0.959261	−	0.282523i	$-0.0911713\pi$
$858$			3.61305e7i			0.0572021i
$859$		−	6.92963e8i		−	1.09328i	−0.837368	−	0.546639i	$-0.815907\pi$
$859$		−	6.92963e8i		−	1.09328i	0.837368	−	0.546639i	$-0.184093\pi$
$860$		−	3.95057e8i		−	0.621105i
$861$	3.44648e8			0.539967
$862$	−6.25659e8			−0.976824
$863$			7.24024e8i			1.12647i	0.826296	+	0.563236i	$0.190444\pi$
$863$			7.24024e8i			1.12647i	−0.826296	+	0.563236i	$0.809556\pi$
$864$		−	2.55166e7i		−	0.0395623i
$865$		−	3.01998e8i		−	0.466612i
$866$			1.67566e9i			2.58007i
$867$	2.25471e8			0.345966
$868$			2.79460e9i			4.27327i
$869$			1.37354e8i			0.209306i
$870$		−	5.37826e7i		−	0.0816740i
$871$	3.10178e8			0.469414
$872$	−5.42818e8			−0.818662
$873$			7.55638e7i			0.113572i
$874$	2.67136e8			0.400127
$875$	−8.89632e8			−1.32796
$876$			5.50658e8i			0.819161i
$877$	3.22550e8			0.478187			0.239094	−	0.970997i	$-0.423150\pi$
$877$	3.22550e8			0.478187			0.239094	+	0.970997i	$0.423150\pi$
$878$		−	7.93428e8i		−	1.17226i
$879$	3.97848e8			0.585802
$880$		−	6.79230e7i		−	0.0996709i
$881$		−	1.25113e9i		−	1.82967i	−0.403825	−	0.914836i	$-0.632319\pi$
$881$		−	1.25113e9i		−	1.82967i	0.403825	−	0.914836i	$-0.367681\pi$
$882$		−	2.90141e8i		−	0.422866i
$883$	8.60311e6			0.0124961			0.00624803	−	0.999980i	$-0.498011\pi$
$883$	8.60311e6			0.0124961			0.00624803	+	0.999980i	$0.498011\pi$
$884$			2.51764e8i			0.364449i
$885$	5.76646e7	−	2.43800e8i	0.0831917	−	0.351726i
$886$	1.60484e9			2.30744
$887$			1.02492e9i			1.46865i	0.678798	+	0.734325i	$0.262501\pi$
$887$			1.02492e9i			1.46865i	−0.678798	+	0.734325i	$0.737499\pi$
$888$	5.12069e7			0.0731290
$889$	2.75549e8			0.392187
$890$	−1.05802e9			−1.50080
$891$		−	1.52939e7i		−	0.0216215i
$892$	1.19879e8			0.168908
$893$			1.56967e8i			0.220421i
$894$	−3.65981e8			−0.512208
$895$		−	5.37050e7i		−	0.0749110i
$896$		−	1.70882e9i		−	2.37559i
$897$	−1.86866e7			−0.0258912
$898$			1.67159e9i			2.30835i
$899$			1.60102e8i			0.220352i
$900$	2.86395e8			0.392860
$901$	7.66215e8			1.04755
$902$	1.73550e8			0.236485
$903$		−	2.87070e8i		−	0.389875i
$904$	−6.26212e8			−0.847649
$905$	2.99106e8			0.403534
$906$	6.13103e8			0.824420
$907$	−5.61846e8			−0.753001			−0.376500	−	0.926416i	$-0.622873\pi$
$907$	−5.61846e8			−0.753001			−0.376500	+	0.926416i	$0.622873\pi$
$908$			1.38536e8i			0.185056i
$909$			1.27984e8i			0.170397i
$910$	3.16840e8			0.420451
$911$	1.18732e9			1.57041			0.785206	−	0.619234i	$-0.212557\pi$
$911$	1.18732e9			1.57041			0.785206	+	0.619234i	$0.212557\pi$
$912$	5.54034e8			0.730386
$913$	2.45313e8			0.322336
$914$	−2.41967e9			−3.16896
$915$			3.09070e8i			0.403453i
$916$		−	1.03520e9i		−	1.34690i
$917$		−	1.60617e8i		−	0.208297i
$918$		−	1.61558e8i		−	0.208834i
$919$			1.48969e9i			1.91932i	0.281156	+	0.959662i	$0.409282\pi$
$919$			1.48969e9i			1.91932i	−0.281156	+	0.959662i	$0.590718\pi$
$920$	1.18344e8			0.151979
$921$	−6.40751e8			−0.820183
$922$			1.95514e9i			2.49451i
$923$			4.93282e7i			0.0627321i
$924$		−	2.26596e8i		−	0.287234i
$925$		−	3.79106e7i		−	0.0479000i
$926$	1.98937e9			2.50543
$927$			8.80009e7i			0.110471i
$928$		−	2.16587e7i		−	0.0271012i
$929$			1.12410e9i			1.40203i	0.713146	+	0.701015i	$0.247270\pi$
$929$			1.12410e9i			1.40203i	−0.713146	+	0.701015i	$0.752730\pi$
$930$	8.32915e8			1.03550
$931$	−9.23416e8			−1.14432
$932$			2.16758e9i			2.67748i
$933$	−6.97386e8			−0.858674
$934$	−2.02987e9			−2.49131
$935$			6.30371e7i			0.0771191i
$936$	−1.30559e8			−0.159214
$937$		−	1.12266e9i		−	1.36468i	−0.731037	−	0.682338i	$-0.760963\pi$
$937$		−	1.12266e9i		−	1.36468i	0.731037	−	0.682338i	$-0.239037\pi$
$938$	−2.94902e9			−3.57330
$939$			4.77335e8i			0.576536i
$940$			1.43663e8i			0.172966i
$941$			8.62986e7i			0.103570i	0.998658	+	0.0517851i	$0.0164911\pi$
$941$			8.62986e7i			0.103570i	−0.998658	+	0.0517851i	$0.983509\pi$
$942$	4.71482e6			0.00564043
$943$			8.97595e7i			0.107040i
$944$	−1.58426e8	+	6.69807e8i	−0.188326	+	0.796221i
$945$	−1.34118e8			−0.158924
$946$		−	1.44556e8i		−	0.170751i
$947$	1.15823e9			1.36378			0.681889	−	0.731456i	$-0.261159\pi$
$947$	1.15823e9			1.36378			0.681889	+	0.731456i	$0.261159\pi$
$948$	−1.02541e9			−1.20357
$949$	−1.85847e8			−0.217449
$950$		−	1.38179e9i		−	1.61165i
$951$	−9.05628e8			−1.05295
$952$		−	1.15861e9i		−	1.34285i
$953$	1.05961e9			1.22424			0.612120	−	0.790765i	$-0.290317\pi$
$953$	1.05961e9			1.22424			0.612120	+	0.790765i	$0.290317\pi$
$954$			8.20895e8i			0.945458i
$955$			1.02169e8i			0.117303i
$956$	2.17343e9			2.48756
$957$		−	1.29816e7i		−	0.0148113i
$958$			2.05014e9i			2.33178i
$959$	−1.58979e9			−1.80253
$960$	−3.74311e8			−0.423076
$961$	−1.59194e9			−1.79373
$962$			3.57047e7i			0.0401052i
$963$	1.98982e7			0.0222810
$964$	5.26370e7			0.0587571
$965$	1.66172e8			0.184917
$966$	1.77663e8			0.197091
$967$			2.94496e7i			0.0325687i	0.999867	+	0.0162843i	$0.00518370\pi$
$967$			2.94496e7i			0.0325687i	−0.999867	+	0.0162843i	$0.994816\pi$
$968$			1.40331e9i			1.54714i
$969$	−5.14182e8			−0.565126
$970$	3.33678e8			0.365605
$971$	1.96774e8			0.214936			0.107468	−	0.994209i	$-0.465726\pi$
$971$	1.96774e8			0.214936			0.107468	+	0.994209i	$0.465726\pi$
$972$	1.14176e8			0.124330
$973$	−1.37963e9			−1.49770
$974$			1.49514e9i			1.61810i
$975$			9.66584e7i			0.104286i
$976$		−	8.49126e8i		−	0.913319i
$977$		−	3.80962e8i		−	0.408506i	−0.978918	−	0.204253i	$-0.934524\pi$
$977$		−	3.80962e8i		−	0.408506i	0.978918	−	0.204253i	$-0.0654765\pi$
$978$		−	7.12302e8i		−	0.761461i
$979$	−2.55377e8			−0.272165
$980$	−8.45150e8			−0.897957
$981$			1.60213e8i			0.169703i
$982$			2.15566e9i			2.27638i
$983$		−	3.93998e8i		−	0.414795i	−0.978257	−	0.207398i	$-0.933501\pi$
$983$		−	3.93998e8i		−	0.414795i	0.978257	−	0.207398i	$-0.0664994\pi$
$984$			6.27131e8i			0.658223i
$985$	−1.54276e8			−0.161432
$986$		−	1.37131e8i		−	0.143056i
$987$			1.04393e8i			0.108573i
$988$			8.58458e8i			0.890119i
$989$	7.47640e7			0.0772865
$990$	−6.75357e7			−0.0696030
$991$		−	1.18032e9i		−	1.21277i	−0.795172	−	0.606384i	$-0.792619\pi$
$991$		−	1.18032e9i		−	1.21277i	0.795172	−	0.606384i	$-0.207381\pi$
$992$	3.35422e8			0.343602
$993$	−5.18832e8			−0.529882
$994$		−	4.68989e8i		−	0.477533i
$995$	8.63278e8			0.876358
$996$			1.83138e9i			1.85353i
$997$	−1.14829e9			−1.15868			−0.579342	−	0.815085i	$-0.696690\pi$
$997$	−1.14829e9			−1.15868			−0.579342	+	0.815085i	$0.696690\pi$
$998$		−	9.45821e8i		−	0.951518i
$999$		−	1.51137e7i		−	0.0151592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.6	✓	60
59.58	odd	2	inner	177.7.c.a.58.55	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.6	✓	60	1.1	even	1	trivial
177.7.c.a.58.55	yes	60	59.58	odd	2	inner

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-13.7128i q^{2} -15.5885 q^{3} -124.040 q^{4} +78.2520 q^{5} +213.761i q^{6} +452.461 q^{7} +823.310i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-13.7128i q^{2} -15.5885 q^{3} -124.040 q^{4} +78.2520 q^{5} +213.761i q^{6} +452.461 q^{7} +823.310i q^{8} +243.000 q^{9} -1073.05i q^{10} -259.004i q^{11} +1933.59 q^{12} +652.587i q^{13} -6204.49i q^{14} -1219.83 q^{15} +3351.31 q^{16} -3110.24 q^{17} -3332.20i q^{18} -10605.2 q^{19} -9706.35 q^{20} -7053.17 q^{21} -3551.66 q^{22} -1836.91i q^{23} -12834.1i q^{24} -9501.63 q^{25} +8948.77 q^{26} -3788.00 q^{27} -56123.1 q^{28} -3215.28 q^{29} +16727.2i q^{30} -49794.1i q^{31} +6736.18i q^{32} +4037.48i q^{33} +42650.0i q^{34} +35406.0 q^{35} -30141.6 q^{36} +3989.90i q^{37} +145427. i q^{38} -10172.8i q^{39} +64425.6i q^{40} -48864.4 q^{41} +96718.4i q^{42} +40700.9i q^{43} +32126.8i q^{44} +19015.2 q^{45} -25189.1 q^{46} -14800.9i q^{47} -52241.7 q^{48} +87071.9 q^{49} +130293. i q^{50} +48483.9 q^{51} -80946.7i q^{52} -246352. q^{53} +51943.9i q^{54} -20267.6i q^{55} +372515. i q^{56} +165319. q^{57} +44090.3i q^{58} +(-47272.8 + 199865. i) q^{59} +151307. q^{60} -253372. i q^{61} -682814. q^{62} +109948. q^{63} +306855. q^{64} +51066.3i q^{65} +55365.0 q^{66} -475304. i q^{67} +385793. q^{68} +28634.6i q^{69} -485513. i q^{70} +75588.7 q^{71} +200064. i q^{72} +284785. i q^{73} +54712.6 q^{74} +148116. q^{75} +1.31547e6 q^{76} -117189. i q^{77} -139498. q^{78} -530314. q^{79} +262246. q^{80} +59049.0 q^{81} +670065. i q^{82} +947140. i q^{83} +874873. q^{84} -243383. q^{85} +558121. q^{86} +50121.2 q^{87} +213241. q^{88} -985993. i q^{89} -260751. i q^{90} +295270. i q^{91} +227850. i q^{92} +776213. i q^{93} -202961. q^{94} -829879. q^{95} -105007. i q^{96} +310962. i q^{97} -1.19400e6i q^{98} -62938.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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