LMFDB - Embedded newform 177.7.c.a.58.11

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			58.11
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3092i q^{2} +15.5885 q^{3} -63.8971 q^{4} -168.463 q^{5} -176.292i q^{6} +92.9299 q^{7} -1.16321i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-11.3092i q^{2} +15.5885 q^{3} -63.8971 q^{4} -168.463 q^{5} -176.292i q^{6} +92.9299 q^{7} -1.16321i q^{8} +243.000 q^{9} +1905.18i q^{10} -2167.83i q^{11} -996.058 q^{12} -1020.13i q^{13} -1050.96i q^{14} -2626.08 q^{15} -4102.57 q^{16} -2220.60 q^{17} -2748.13i q^{18} -5813.42 q^{19} +10764.3 q^{20} +1448.63 q^{21} -24516.3 q^{22} +10077.3i q^{23} -18.1326i q^{24} +12754.9 q^{25} -11536.9 q^{26} +3788.00 q^{27} -5937.96 q^{28} +45564.7 q^{29} +29698.8i q^{30} +32140.9i q^{31} +46322.2i q^{32} -33793.1i q^{33} +25113.1i q^{34} -15655.3 q^{35} -15527.0 q^{36} +30843.3i q^{37} +65745.0i q^{38} -15902.3i q^{39} +195.958i q^{40} -118262. q^{41} -16382.8i q^{42} +58251.0i q^{43} +138518. i q^{44} -40936.6 q^{45} +113966. q^{46} +88089.1i q^{47} -63952.8 q^{48} -109013. q^{49} -144247. i q^{50} -34615.8 q^{51} +65183.7i q^{52} -11175.7 q^{53} -42839.1i q^{54} +365199. i q^{55} -108.097i q^{56} -90622.3 q^{57} -515299. i q^{58} +(98432.3 - 180254. i) q^{59} +167799. q^{60} -318000. i q^{61} +363487. q^{62} +22582.0 q^{63} +261301. q^{64} +171855. i q^{65} -382171. q^{66} +231159. i q^{67} +141890. q^{68} +157090. i q^{69} +177048. i q^{70} +217430. q^{71} -282.659i q^{72} +494177. i q^{73} +348812. q^{74} +198829. q^{75} +371461. q^{76} -201456. i q^{77} -179842. q^{78} -939691. q^{79} +691133. q^{80} +59049.0 q^{81} +1.33745e6i q^{82} -512932. i q^{83} -92563.6 q^{84} +374090. q^{85} +658769. q^{86} +710284. q^{87} -2521.63 q^{88} -336771. i q^{89} +462958. i q^{90} -94801.0i q^{91} -643913. i q^{92} +501028. i q^{93} +996214. q^{94} +979349. q^{95} +722092. i q^{96} +1.00179e6i q^{97} +1.23285e6i q^{98} -526782. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	11.3092i		−	1.41365i	−0.707391	−	0.706823i	$-0.750128\pi$
$2$		−	11.3092i		−	1.41365i	0.707391	−	0.706823i	$-0.249872\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−63.8971			−0.998393
$5$	−168.463			−1.34771			−0.673853	−	0.738865i	$-0.735362\pi$
$5$	−168.463			−1.34771			−0.673853	+	0.738865i	$0.735362\pi$
$6$		−	176.292i		−	0.816168i
$7$	92.9299			0.270933			0.135466	−	0.990782i	$-0.456747\pi$
$7$	92.9299			0.270933			0.135466	+	0.990782i	$0.456747\pi$
$8$		−	1.16321i		−	0.00227189i
$9$	243.000			0.333333
$10$			1905.18i			1.90518i
$11$		−	2167.83i		−	1.62872i	−0.580360	−	0.814360i	$-0.697088\pi$
$11$		−	2167.83i		−	1.62872i	0.580360	−	0.814360i	$-0.302912\pi$
$12$	−996.058			−0.576422
$13$		−	1020.13i		−	0.464331i	−0.972676	−	0.232165i	$-0.925419\pi$
$13$		−	1020.13i		−	0.464331i	0.972676	−	0.232165i	$-0.0745810\pi$
$14$		−	1050.96i		−	0.383003i
$15$	−2626.08			−0.778099
$16$	−4102.57			−1.00160
$17$	−2220.60			−0.451985			−0.225992	−	0.974129i	$-0.572562\pi$
$17$	−2220.60			−0.451985			−0.225992	+	0.974129i	$0.572562\pi$
$18$		−	2748.13i		−	0.471215i
$19$	−5813.42			−0.847561			−0.423781	−	0.905765i	$-0.639297\pi$
$19$	−5813.42			−0.847561			−0.423781	+	0.905765i	$0.639297\pi$
$20$	10764.3			1.34554
$21$	1448.63			0.156423
$22$	−24516.3			−2.30243
$23$			10077.3i			0.828252i	0.910220	+	0.414126i	$0.135913\pi$
$23$			10077.3i			0.828252i	−0.910220	+	0.414126i	$0.864087\pi$
$24$		−	18.1326i		−	0.00131168i
$25$	12754.9			0.816313
$26$	−11536.9			−0.656399
$27$	3788.00			0.192450
$28$	−5937.96			−0.270497
$29$	45564.7			1.86825			0.934124	−	0.356948i	$-0.116183\pi$
$29$	45564.7			1.86825			0.934124	+	0.356948i	$0.116183\pi$
$30$			29698.8i			1.09996i
$31$			32140.9i			1.07888i	0.842024	+	0.539440i	$0.181364\pi$
$31$			32140.9i			1.07888i	−0.842024	+	0.539440i	$0.818636\pi$
$32$			46322.2i			1.41364i
$33$		−	33793.1i		−	0.940342i
$34$			25113.1i			0.638946i
$35$	−15655.3			−0.365138
$36$	−15527.0			−0.332798
$37$			30843.3i			0.608913i	0.952526	+	0.304457i	$0.0984749\pi$
$37$			30843.3i			0.608913i	−0.952526	+	0.304457i	$0.901525\pi$
$38$			65745.0i			1.19815i
$39$		−	15902.3i		−	0.268081i
$40$			195.958i			0.00306184i
$41$	−118262.			−1.71591			−0.857954	−	0.513726i	$-0.828265\pi$
$41$	−118262.			−1.71591			−0.857954	+	0.513726i	$0.828265\pi$
$42$		−	16382.8i		−	0.221127i
$43$			58251.0i			0.732652i	0.930487	+	0.366326i	$0.119384\pi$
$43$			58251.0i			0.732652i	−0.930487	+	0.366326i	$0.880616\pi$
$44$			138518.i			1.62610i
$45$	−40936.6			−0.449236
$46$	113966.			1.17085
$47$			88089.1i			0.848455i	0.905556	+	0.424227i	$0.139454\pi$
$47$			88089.1i			0.848455i	−0.905556	+	0.424227i	$0.860546\pi$
$48$	−63952.8			−0.578277
$49$	−109013.			−0.926595
$50$		−	144247.i		−	1.15398i
$51$	−34615.8			−0.260954
$52$			65183.7i			0.463584i
$53$	−11175.7			−0.0750667			−0.0375334	−	0.999295i	$-0.511950\pi$
$53$	−11175.7			−0.0750667			−0.0375334	+	0.999295i	$0.511950\pi$
$54$		−	42839.1i		−	0.272056i
$55$			365199.i			2.19504i
$56$		−	108.097i		−	0.000615529i
$57$	−90622.3			−0.489340
$58$		−	515299.i		−	2.64104i
$59$	98432.3	−	180254.i	0.479271	−	0.877667i
$59$	98432.3	−	180254.i	0.479271	−	0.877667i
$60$	167799.			0.776848
$61$		−	318000.i		−	1.40100i	−0.713653	−	0.700499i	$-0.752961\pi$
$61$		−	318000.i		−	1.40100i	0.713653	−	0.700499i	$-0.247039\pi$
$62$	363487.			1.52515
$63$	22582.0			0.0903109
$64$	261301.			0.996783
$65$			171855.i			0.625781i
$66$	−382171.			−1.32931
$67$			231159.i			0.768577i	0.923213	+	0.384288i	$0.125553\pi$
$67$			231159.i			0.768577i	−0.923213	+	0.384288i	$0.874447\pi$
$68$	141890.			0.451259
$69$			157090.i			0.478191i
$70$			177048.i			0.516175i
$71$	217430.			0.607499			0.303749	−	0.952752i	$-0.401761\pi$
$71$	217430.			0.607499			0.303749	+	0.952752i	$0.401761\pi$
$72$		−	282.659i		−	0.000757296i
$73$			494177.i			1.27032i	0.772379	+	0.635162i	$0.219067\pi$
$73$			494177.i			1.27032i	−0.772379	+	0.635162i	$0.780933\pi$
$74$	348812.			0.860787
$75$	198829.			0.471298
$76$	371461.			0.846199
$77$		−	201456.i		−	0.441274i
$78$	−179842.			−0.378972
$79$	−939691.			−1.90592			−0.952958	−	0.303101i	$-0.901978\pi$
$79$	−939691.			−1.90592			−0.952958	+	0.303101i	$0.901978\pi$
$80$	691133.			1.34987
$81$	59049.0			0.111111
$82$			1.33745e6i			2.42569i
$83$		−	512932.i		−	0.897068i	−0.893766	−	0.448534i	$-0.851946\pi$
$83$		−	512932.i		−	0.897068i	0.893766	−	0.448534i	$-0.148054\pi$
$84$	−92563.6			−0.156172
$85$	374090.			0.609143
$86$	658769.			1.03571
$87$	710284.			1.07863
$88$	−2521.63			−0.00370027
$89$		−	336771.i		−	0.477710i	−0.971055	−	0.238855i	$-0.923228\pi$
$89$		−	336771.i		−	0.477710i	0.971055	−	0.238855i	$-0.0767721\pi$
$90$			462958.i			0.635060i
$91$		−	94801.0i		−	0.125802i
$92$		−	643913.i		−	0.826921i
$93$			501028.i			0.622892i
$94$	996214.			1.19941
$95$	979349.			1.14226
$96$			722092.i			0.816166i
$97$			1.00179e6i			1.09764i	0.835939	+	0.548822i	$0.184923\pi$
$97$			1.00179e6i			1.09764i	−0.835939	+	0.548822i	$0.815077\pi$
$98$			1.23285e6i			1.30988i
$99$		−	526782.i		−	0.542907i
$100$	−815001.			−0.815001
$101$			455641.i			0.442240i	0.975247	+	0.221120i	$0.0709713\pi$
$101$			455641.i			0.442240i	−0.975247	+	0.221120i	$0.929029\pi$
$102$			391475.i			0.368896i
$103$		−	1.35184e6i		−	1.23712i	−0.785737	−	0.618561i	$-0.787716\pi$
$103$		−	1.35184e6i		−	1.23712i	0.785737	−	0.618561i	$-0.212284\pi$
$104$	−1186.63			−0.00105491
$105$	−244042.			−0.210812
$106$			126388.i			0.106118i
$107$	−420968.			−0.343635			−0.171818	−	0.985129i	$-0.554964\pi$
$107$	−420968.			−0.343635			−0.171818	+	0.985129i	$0.554964\pi$
$108$	−242042.			−0.192141
$109$		−	342130.i		−	0.264187i	−0.991237	−	0.132093i	$-0.957830\pi$
$109$		−	342130.i		−	0.264187i	0.991237	−	0.132093i	$-0.0421699\pi$
$110$	4.13010e6			3.10300
$111$			480799.i			0.351556i
$112$	−381252.			−0.271367
$113$		−	350125.i		−	0.242654i	−0.992613	−	0.121327i	$-0.961285\pi$
$113$		−	350125.i		−	0.242654i	0.992613	−	0.121327i	$-0.0387150\pi$
$114$			1.02486e6i			0.691753i
$115$		−	1.69766e6i		−	1.11624i
$116$	−2.91146e6			−1.86525
$117$		−	247893.i		−	0.154777i
$118$	−2.03853e6	−	1.11319e6i	−1.24071	−	0.677520i
$119$	−206360.			−0.122458
$120$			3054.68i			0.00176775i
$121$	−2.92791e6			−1.65273
$122$	−3.59631e6			−1.98052
$123$	−1.84352e6			−0.990680
$124$		−	2.05371e6i		−	1.07715i
$125$	483509.			0.247556
$126$		−	255383.i		−	0.127668i
$127$	2.73008e6			1.33280			0.666399	−	0.745596i	$-0.267835\pi$
$127$	2.73008e6			1.33280			0.666399	+	0.745596i	$0.267835\pi$
$128$			9528.98i			0.00454377i
$129$			908042.i			0.422997i
$130$	1.94354e6			0.884633
$131$		−	1.24107e6i		−	0.552055i	−0.961150	−	0.276028i	$-0.910982\pi$
$131$		−	1.24107e6i		−	0.552055i	0.961150	−	0.276028i	$-0.0890181\pi$
$132$			2.15928e6i			0.938830i
$133$	−540241.			−0.229632
$134$	2.61422e6			1.08649
$135$	−638138.			−0.259366
$136$			2583.02i			0.00102686i
$137$	−935575.			−0.363846			−0.181923	−	0.983313i	$-0.558232\pi$
$137$	−935575.			−0.363846			−0.181923	+	0.983313i	$0.558232\pi$
$138$	1.77656e6			0.675993
$139$	−4.06182e6			−1.51243			−0.756217	−	0.654321i	$-0.772954\pi$
$139$	−4.06182e6			−1.51243			−0.756217	+	0.654321i	$0.772954\pi$
$140$	1.00033e6			0.364551
$141$			1.37317e6i			0.489856i
$142$		−	2.45896e6i		−	0.858788i
$143$	−2.21147e6			−0.756264
$144$	−996925.			−0.333868
$145$	−7.67598e6			−2.51785
$146$	5.58873e6			1.79579
$147$	−1.69934e6			−0.534970
$148$		−	1.97080e6i		−	0.607935i
$149$		−	2.93990e6i		−	0.888738i	−0.895844	−	0.444369i	$-0.853428\pi$
$149$		−	2.93990e6i		−	0.888738i	0.895844	−	0.444369i	$-0.146572\pi$
$150$		−	2.24859e6i		−	0.666249i
$151$			4.14191e6i			1.20301i	0.798869	+	0.601506i	$0.205432\pi$
$151$			4.14191e6i			1.20301i	−0.798869	+	0.601506i	$0.794568\pi$
$152$			6762.21i			0.00192556i
$153$	−539606.			−0.150662
$154$	−2.27830e6			−0.623804
$155$		−	5.41457e6i		−	1.45401i
$156$			1.01611e6i			0.267651i
$157$		−	2.10154e6i		−	0.543050i	−0.962431	−	0.271525i	$-0.912472\pi$
$157$		−	2.10154e6i		−	0.543050i	0.962431	−	0.271525i	$-0.0875279\pi$
$158$			1.06271e7i			2.69429i
$159$	−174212.			−0.0433398
$160$		−	7.80359e6i		−	1.90517i
$161$			936487.i			0.224401i
$162$		−	667795.i		−	0.157072i
$163$	−6.16709e6			−1.42403			−0.712013	−	0.702167i	$-0.752216\pi$
$163$	−6.16709e6			−1.42403			−0.712013	+	0.702167i	$0.752216\pi$
$164$	7.55661e6			1.71315
$165$			5.69289e6i			1.26730i
$166$	−5.80083e6			−1.26814
$167$	−4.27307e6			−0.917466			−0.458733	−	0.888574i	$-0.651697\pi$
$167$	−4.27307e6			−0.917466			−0.458733	+	0.888574i	$0.651697\pi$
$168$		−	1685.06i		−	0.000355376i
$169$	3.78614e6			0.784397
$170$		−	4.23064e6i		−	0.861112i
$171$	−1.41266e6			−0.282520
$172$		−	3.72207e6i		−	0.731474i
$173$			3.88594e6i			0.750512i	0.926921	+	0.375256i	$0.122445\pi$
$173$			3.88594e6i			0.750512i	−0.926921	+	0.375256i	$0.877555\pi$
$174$		−	8.03271e6i		−	1.52481i
$175$	1.18531e6			0.221166
$176$			8.89366e6i			1.63133i
$177$	1.53441e6	−	2.80989e6i	0.276707	−	0.506721i
$178$	−3.80860e6			−0.675313
$179$			5.75429e6i			1.00330i	0.865070	+	0.501652i	$0.167274\pi$
$179$			5.75429e6i			1.00330i	−0.865070	+	0.501652i	$0.832726\pi$
$180$	2.61573e6			0.448514
$181$	−4.25879e6			−0.718209			−0.359105	−	0.933297i	$-0.616918\pi$
$181$	−4.25879e6			−0.718209			−0.359105	+	0.933297i	$0.616918\pi$
$182$	−1.07212e6			−0.177840
$183$		−	4.95713e6i		−	0.808867i
$184$	11722.0			0.00188170
$185$		−	5.19596e6i		−	0.820636i
$186$	5.66620e6			0.880549
$187$			4.81388e6i			0.736157i
$188$		−	5.62864e6i		−	0.847091i
$189$	352018.			0.0521410
$190$		−	1.10756e7i		−	1.61476i
$191$		−	1.21863e7i		−	1.74893i	−0.485090	−	0.874464i	$-0.661213\pi$
$191$		−	1.21863e7i		−	1.74893i	0.485090	−	0.874464i	$-0.338787\pi$
$192$	4.07328e6			0.575493
$193$	9.12282e6			1.26899			0.634494	−	0.772928i	$-0.281209\pi$
$193$	9.12282e6			1.26899			0.634494	+	0.772928i	$0.281209\pi$
$194$	1.13294e7			1.55168
$195$			2.67896e6i			0.361295i
$196$	6.96562e6			0.925106
$197$	−6.85796e6			−0.897008			−0.448504	−	0.893781i	$-0.648043\pi$
$197$	−6.85796e6			−0.897008			−0.448504	+	0.893781i	$0.648043\pi$
$198$	−5.95746e6			−0.767477
$199$	8.47472e6			1.07539			0.537695	−	0.843139i	$-0.319295\pi$
$199$	8.47472e6			1.07539			0.537695	+	0.843139i	$0.319295\pi$
$200$		−	14836.6i		−	0.00185457i
$201$			3.60342e6i			0.443738i
$202$	5.15291e6			0.625171
$203$	4.23433e6			0.506170
$204$	2.21185e6			0.260534
$205$	1.99228e7			2.31254
$206$	−1.52881e7			−1.74885
$207$			2.44879e6i			0.276084i
$208$			4.18517e6i			0.465076i
$209$			1.26025e7i			1.38044i
$210$			2.75991e6i			0.298014i
$211$		−	1.57833e7i		−	1.68016i	−0.542459	−	0.840082i	$-0.682507\pi$
$211$		−	1.57833e7i		−	1.68016i	0.542459	−	0.840082i	$-0.317493\pi$
$212$	714096.			0.0749461
$213$	3.38941e6			0.350740
$214$			4.76079e6i			0.485778i
$215$		−	9.81315e6i		−	0.987400i
$216$		−	4406.22i		−	0.000437225i
$217$			2.98686e6i			0.292304i
$218$	−3.86920e6			−0.373467
$219$			7.70346e6i			0.733422i
$220$		−	2.33352e7i		−	2.19151i
$221$			2.26531e6i			0.209870i
$222$	5.43744e6			0.496976
$223$	−1.74562e7			−1.57411			−0.787055	−	0.616882i	$-0.788395\pi$
$223$	−1.74562e7			−1.57411			−0.787055	+	0.616882i	$0.788395\pi$
$224$			4.30472e6i			0.383002i
$225$	3.09944e6			0.272104
$226$	−3.95962e6			−0.343027
$227$		−	6.98819e6i		−	0.597430i	−0.954342	−	0.298715i	$-0.903442\pi$
$227$		−	6.98819e6i		−	0.597430i	0.954342	−	0.298715i	$-0.0965581\pi$
$228$	5.79051e6			0.488553
$229$		−	4.63019e6i		−	0.385560i	−0.981242	−	0.192780i	$-0.938250\pi$
$229$		−	4.63019e6i		−	0.385560i	0.981242	−	0.192780i	$-0.0617504\pi$
$230$	−1.91991e7			−1.57797
$231$		−	3.14039e6i		−	0.254769i
$232$		−	53001.2i		−	0.00424445i
$233$			2.02015e7i			1.59704i	0.601968	+	0.798520i	$0.294383\pi$
$233$			2.02015e7i			1.59704i	−0.601968	+	0.798520i	$0.705617\pi$
$234$	−2.80346e6			−0.218800
$235$		−	1.48398e7i		−	1.14347i
$236$	−6.28954e6	+	1.15177e7i	−0.478501	+	0.876256i
$237$	−1.46483e7			−1.10038
$238$			2.33376e6i			0.173112i
$239$	−2.80006e6			−0.205104			−0.102552	−	0.994728i	$-0.532701\pi$
$239$	−2.80006e6			−0.205104			−0.102552	+	0.994728i	$0.532701\pi$
$240$	1.07737e7			0.779347
$241$	−9.86332e6			−0.704648			−0.352324	−	0.935878i	$-0.614608\pi$
$241$	−9.86332e6			−0.704648			−0.352324	+	0.935878i	$0.614608\pi$
$242$			3.31122e7i			2.33637i
$243$	920483.			0.0641500
$244$			2.03193e7i			1.39875i
$245$	1.83647e7			1.24878
$246$			2.08487e7i			1.40047i
$247$			5.93047e6i			0.393549i
$248$	37386.6			0.00245110
$249$		−	7.99582e6i		−	0.517923i
$250$		−	5.46808e6i		−	0.349957i
$251$	1.88216e6			0.119024			0.0595121	−	0.998228i	$-0.481046\pi$
$251$	1.88216e6			0.119024			0.0595121	+	0.998228i	$0.481046\pi$
$252$	−1.44292e6			−0.0901658
$253$	2.18459e7			1.34899
$254$		−	3.08749e7i		−	1.88410i
$255$	5.83149e6			0.351689
$256$	1.68310e7			1.00321
$257$	−1.37476e7			−0.809891			−0.404945	−	0.914341i	$-0.632709\pi$
$257$	−1.37476e7			−0.809891			−0.404945	+	0.914341i	$0.632709\pi$
$258$	1.02692e7			0.597967
$259$			2.86626e6i			0.164975i
$260$		−	1.09811e7i		−	0.624776i
$261$	1.10722e7			0.622750
$262$	−1.40355e7			−0.780410
$263$	−1.68338e7			−0.925370			−0.462685	−	0.886523i	$-0.653114\pi$
$263$	−1.68338e7			−0.925370			−0.462685	+	0.886523i	$0.653114\pi$
$264$	−39308.3			−0.00213635
$265$	1.88270e6			0.101168
$266$			6.10967e6i			0.324618i
$267$		−	5.24974e6i		−	0.275806i
$268$		−	1.47704e7i		−	0.767342i
$269$		−	1.72737e7i		−	0.887418i	−0.896171	−	0.443709i	$-0.853662\pi$
$269$		−	1.72737e7i		−	0.887418i	0.896171	−	0.443709i	$-0.146338\pi$
$270$			7.21681e6i			0.366652i
$271$	−3.26972e7			−1.64287			−0.821435	−	0.570302i	$-0.806826\pi$
$271$	−3.26972e7			−1.64287			−0.821435	+	0.570302i	$0.806826\pi$
$272$	9.11018e6			0.452710
$273$		−	1.47780e6i		−	0.0726320i
$274$			1.05806e7i			0.514349i
$275$		−	2.76504e7i		−	1.32954i
$276$		−	1.00376e7i		−	0.477423i
$277$	−533431.			−0.0250980			−0.0125490	−	0.999921i	$-0.503995\pi$
$277$	−533431.			−0.0250980			−0.0125490	+	0.999921i	$0.503995\pi$
$278$			4.59358e7i			2.13804i
$279$			7.81025e6i			0.359627i
$280$			18210.3i			0.000829552i
$281$	2.06979e7			0.932839			0.466419	−	0.884564i	$-0.345544\pi$
$281$	2.06979e7			0.932839			0.466419	+	0.884564i	$0.345544\pi$
$282$	1.55294e7			0.692482
$283$			1.73488e7i			0.765437i	0.923865	+	0.382718i	$0.125012\pi$
$283$			1.73488e7i			0.765437i	−0.923865	+	0.382718i	$0.874988\pi$
$284$	−1.38932e7			−0.606522
$285$	1.52665e7			0.659486
$286$			2.50099e7i			1.06909i
$287$	−1.09901e7			−0.464896
$288$			1.12563e7i			0.471214i
$289$	−1.92065e7			−0.795710
$290$			8.68089e7i			3.55935i
$291$			1.56164e7i			0.633725i
$292$		−	3.15765e7i		−	1.26828i
$293$	−3.04473e7			−1.21045			−0.605224	−	0.796055i	$-0.706917\pi$
$293$	−3.04473e7			−1.21045			−0.605224	+	0.796055i	$0.706917\pi$
$294$			1.92182e7i			0.756258i
$295$	−1.65822e7	+	3.03662e7i	−0.645917	+	1.18284i
$296$	35877.1			0.00138338
$297$		−	8.21171e6i		−	0.313447i
$298$	−3.32478e7			−1.25636
$299$	1.02802e7			0.384583
$300$	−1.27046e7			−0.470541
$301$			5.41326e6i			0.198499i
$302$	4.68415e7			1.70063
$303$			7.10273e6i			0.255328i
$304$	2.38500e7			0.848921
$305$			5.35713e7i			1.88814i
$306$			6.10249e6i			0.212982i
$307$	2.60536e7			0.900434			0.450217	−	0.892919i	$-0.351347\pi$
$307$	2.60536e7			0.900434			0.450217	+	0.892919i	$0.351347\pi$
$308$			1.28725e7i			0.440564i
$309$		−	2.10731e7i		−	0.714253i
$310$	−6.12342e7			−2.05546
$311$	2.88151e6			0.0957943			0.0478971	−	0.998852i	$-0.484748\pi$
$311$	2.88151e6			0.0957943			0.0478971	+	0.998852i	$0.484748\pi$
$312$	−18497.7			−0.000609051
$313$		−	2.54062e7i		−	0.828527i	−0.910157	−	0.414263i	$-0.864039\pi$
$313$		−	2.54062e7i		−	0.828527i	0.910157	−	0.414263i	$-0.135961\pi$
$314$	−2.37667e7			−0.767680
$315$	−3.80423e6			−0.121713
$316$	6.00436e7			1.90285
$317$	1.01318e7			0.318061			0.159031	−	0.987274i	$-0.449163\pi$
$317$	1.01318e7			0.318061			0.159031	+	0.987274i	$0.449163\pi$
$318$			1.97019e6i			0.0612671i
$319$		−	9.87764e7i		−	3.04285i
$320$	−4.40196e7			−1.34337
$321$	−6.56224e6			−0.198398
$322$	1.05909e7			0.317223
$323$	1.29093e7			0.383085
$324$	−3.77306e6			−0.110933
$325$		−	1.30117e7i		−	0.379039i
$326$			6.97447e7i			2.01307i
$327$		−	5.33328e6i		−	0.152528i
$328$			137563.i			0.00389835i
$329$			8.18612e6i			0.229874i
$330$	6.43818e7			1.79152
$331$	1.79208e7			0.494165			0.247083	−	0.968994i	$-0.420528\pi$
$331$	1.79208e7			0.494165			0.247083	+	0.968994i	$0.420528\pi$
$332$			3.27749e7i			0.895627i
$333$			7.49492e6i			0.202971i
$334$			4.83248e7i			1.29697i
$335$		−	3.89419e7i		−	1.03582i
$336$	−5.94313e6			−0.156674
$337$		−	4.02550e7i		−	1.05179i	−0.850549	−	0.525896i	$-0.823730\pi$
$337$		−	4.02550e7i		−	1.05179i	0.850549	−	0.525896i	$-0.176270\pi$
$338$		−	4.28180e7i		−	1.10886i
$339$		−	5.45791e6i		−	0.140096i
$340$	−2.39033e7			−0.608164
$341$	6.96760e7			1.75719
$342$			1.59760e7i			0.399384i
$343$	−2.10637e7			−0.521978
$344$	67757.9			0.00166450
$345$		−	2.64639e7i		−	0.644462i
$346$	4.39467e7			1.06096
$347$		−	7.99654e7i		−	1.91388i	−0.290293	−	0.956938i	$-0.593753\pi$
$347$		−	7.99654e7i		−	1.91388i	0.290293	−	0.956938i	$-0.406247\pi$
$348$	−4.53851e7			−1.07690
$349$			2.89196e7i			0.680324i	0.940367	+	0.340162i	$0.110482\pi$
$349$			2.89196e7i			0.680324i	−0.940367	+	0.340162i	$0.889518\pi$
$350$		−	1.34049e7i		−	0.312650i
$351$		−	3.86426e6i		−	0.0893605i
$352$	1.00418e8			2.30243
$353$			5.02325e6i			0.114199i	0.998369	+	0.0570993i	$0.0181852\pi$
$353$			5.02325e6i			0.114199i	−0.998369	+	0.0570993i	$0.981815\pi$
$354$	−3.17775e7	−	1.73529e7i	−0.716324	−	0.391166i
$355$	−3.66291e7			−0.818730
$356$			2.15187e7i			0.476943i
$357$	−3.21684e6			−0.0707009
$358$	6.50762e7			1.41832
$359$	6.63944e7			1.43499			0.717494	−	0.696565i	$-0.245289\pi$
$359$	6.63944e7			1.43499			0.717494	+	0.696565i	$0.245289\pi$
$360$			47617.7i			0.00102061i
$361$	−1.32500e7			−0.281640
$362$			4.81634e7i			1.01529i
$363$	−4.56416e7			−0.954203
$364$			6.05751e6i			0.125600i
$365$		−	8.32508e7i		−	1.71202i
$366$	−5.60610e7			−1.14345
$367$		−	5.35677e7i		−	1.08369i	−0.840479	−	0.541845i	$-0.817726\pi$
$367$		−	5.35677e7i		−	1.08369i	0.840479	−	0.541845i	$-0.182274\pi$
$368$		−	4.13430e7i		−	0.829581i
$369$	−2.87377e7			−0.571969
$370$	−5.87620e7			−1.16009
$371$	−1.03856e6			−0.0203380
$372$		−	3.20142e7i		−	0.621891i
$373$	−1.04211e7			−0.200811			−0.100406	−	0.994947i	$-0.532014\pi$
$373$	−1.04211e7			−0.200811			−0.100406	+	0.994947i	$0.532014\pi$
$374$	5.44409e7			1.04066
$375$	7.53715e6			0.142927
$376$	102466.			0.00192759
$377$		−	4.64821e7i		−	0.867485i
$378$		−	3.98103e6i		−	0.0737089i
$379$	−2.74387e6			−0.0504017			−0.0252009	−	0.999682i	$-0.508023\pi$
$379$	−2.74387e6			−0.0504017			−0.0252009	+	0.999682i	$0.508023\pi$
$380$	−6.25776e7			−1.14043
$381$	4.25577e7			0.769491
$382$	−1.37817e8			−2.47236
$383$	−1.28382e7			−0.228511			−0.114256	−	0.993451i	$-0.536448\pi$
$383$	−1.28382e7			−0.228511			−0.114256	+	0.993451i	$0.536448\pi$
$384$			148542.i			0.00262335i
$385$			3.39379e7i			0.594707i
$386$		−	1.03171e8i		−	1.79390i
$387$			1.41550e7i			0.244217i
$388$		−	6.40115e7i		−	1.09588i
$389$	−2.90971e7			−0.494312			−0.247156	−	0.968976i	$-0.579496\pi$
$389$	−2.90971e7			−0.494312			−0.247156	+	0.968976i	$0.579496\pi$
$390$	3.02968e7			0.510743
$391$		−	2.23778e7i		−	0.374357i
$392$			126805.i			0.00210512i
$393$		−	1.93464e7i		−	0.318729i
$394$			7.75578e7i			1.26805i
$395$	1.58304e8			2.56862
$396$			3.36598e7i			0.542034i
$397$		−	7.44147e7i		−	1.18929i	−0.803989	−	0.594645i	$-0.797293\pi$
$397$		−	7.44147e7i		−	1.18929i	0.803989	−	0.594645i	$-0.202707\pi$
$398$		−	9.58420e7i		−	1.52022i
$399$	−8.42153e6			−0.132578
$400$	−5.23278e7			−0.817623
$401$			9.10030e7i			1.41131i	0.708555	+	0.705656i	$0.249347\pi$
$401$			9.10030e7i			1.41131i	−0.708555	+	0.705656i	$0.750653\pi$
$402$	4.07516e7			0.627288
$403$	3.27881e7			0.500957
$404$		−	2.91141e7i		−	0.441530i
$405$	−9.94759e6			−0.149745
$406$		−	4.78867e7i		−	0.715545i
$407$	6.68629e7			0.991749
$408$			40265.3i			0.000592857i
$409$			3.42520e7i			0.500629i	0.968165	+	0.250315i	$0.0805341\pi$
$409$			3.42520e7i			0.500629i	−0.968165	+	0.250315i	$0.919466\pi$
$410$		−	2.25311e8i		−	3.26911i
$411$	−1.45842e7			−0.210066
$412$			8.63785e7i			1.23513i
$413$	9.14730e6	−	1.67510e7i	0.129850	−	0.237789i
$414$	2.76938e7			0.390285
$415$			8.64102e7i			1.20899i
$416$	4.72549e7			0.656397
$417$	−6.33175e7			−0.873204
$418$	1.42524e8			1.95145
$419$		−	5.34154e7i		−	0.726147i	−0.931761	−	0.363073i	$-0.881727\pi$
$419$		−	5.34154e7i		−	0.726147i	0.931761	−	0.363073i	$-0.118273\pi$
$420$	1.55936e7			0.210474
$421$			1.18306e8i			1.58549i	0.609557	+	0.792743i	$0.291348\pi$
$421$			1.18306e8i			1.58549i	−0.609557	+	0.792743i	$0.708652\pi$
$422$	−1.78496e8			−2.37516
$423$			2.14057e7i			0.282818i
$424$			12999.7i			0.000170543i
$425$	−2.83235e7			−0.368961
$426$		−	3.83313e7i		−	0.495821i
$427$		−	2.95517e7i		−	0.379576i
$428$	2.68986e7			0.343083
$429$	−3.44735e7			−0.436629
$430$	−1.10978e8			−1.39583
$431$		−	5.76869e6i		−	0.0720519i	−0.999351	−	0.0360260i	$-0.988530\pi$
$431$		−	5.76869e6i		−	0.0720519i	0.999351	−	0.0360260i	$-0.0114699\pi$
$432$	−1.55405e7			−0.192759
$433$	2.45928e7			0.302931			0.151465	−	0.988463i	$-0.451601\pi$
$433$	2.45928e7			0.302931			0.151465	+	0.988463i	$0.451601\pi$
$434$	3.37788e7			0.413214
$435$	−1.19657e8			−1.45368
$436$			2.18611e7i			0.263762i
$437$		−	5.85839e7i		−	0.701994i
$438$	8.71197e7			1.03680
$439$	−1.40058e8			−1.65545			−0.827725	−	0.561134i	$-0.810365\pi$
$439$	−1.40058e8			−1.65545			−0.827725	+	0.561134i	$0.810365\pi$
$440$	424802.			0.00498688
$441$	−2.64902e7			−0.308865
$442$	2.56188e7			0.296682
$443$		−	4.00366e7i		−	0.460517i	−0.973129	−	0.230259i	$-0.926043\pi$
$443$		−	4.00366e7i		−	0.460517i	0.973129	−	0.230259i	$-0.0739572\pi$
$444$		−	3.07217e7i		−	0.350991i
$445$			5.67336e7i			0.643813i
$446$			1.97415e8i			2.22523i
$447$		−	4.58285e7i		−	0.513113i
$448$	2.42827e7			0.270061
$449$	−3.40721e7			−0.376409			−0.188205	−	0.982130i	$-0.560267\pi$
$449$	−3.40721e7			−0.376409			−0.188205	+	0.982130i	$0.560267\pi$
$450$		−	3.50520e7i		−	0.384659i
$451$			2.56372e8i			2.79473i
$452$			2.23720e7i			0.242264i
$453$			6.45660e7i			0.694559i
$454$	−7.90306e7			−0.844555
$455$			1.59705e7i			0.169545i
$456$			105412.i			0.00111173i
$457$		−	1.04927e6i		−	0.0109936i	−0.999985	−	0.00549681i	$-0.998250\pi$
$457$		−	1.04927e6i		−	0.0109936i	0.999985	−	0.00549681i	$-0.00174970\pi$
$458$	−5.23636e7			−0.545045
$459$	−8.41163e6			−0.0869845
$460$			1.08476e8i			1.11445i
$461$	−1.56607e8			−1.59848			−0.799242	−	0.601009i	$-0.794765\pi$
$461$	−1.56607e8			−1.59848			−0.799242	+	0.601009i	$0.794765\pi$
$462$	−3.55151e7			−0.360154
$463$			6.06662e7i			0.611228i	0.952155	+	0.305614i	$0.0988618\pi$
$463$			6.06662e7i			0.611228i	−0.952155	+	0.305614i	$0.901138\pi$
$464$	−1.86933e8			−1.87125
$465$		−	8.44048e7i		−	0.839476i
$466$	2.28462e8			2.25765
$467$			3.79040e7i			0.372164i	0.982534	+	0.186082i	$0.0595790\pi$
$467$			3.79040e7i			0.372164i	−0.982534	+	0.186082i	$0.940421\pi$
$468$			1.58396e7i			0.154528i
$469$			2.14816e7i			0.208233i
$470$	−1.67826e8			−1.61646
$471$		−	3.27598e7i		−	0.313530i
$472$	−209673.	−	114497.i	−0.00199396	−	0.00108885i
$473$	1.26278e8			1.19328
$474$			1.65660e8i			1.55555i
$475$	−7.41496e7			−0.691875
$476$	1.31858e7			0.122261
$477$	−2.71570e6			−0.0250222
$478$			3.16664e7i			0.289944i
$479$	9.92174e7			0.902779			0.451389	−	0.892327i	$-0.350929\pi$
$479$	9.92174e7			0.902779			0.451389	+	0.892327i	$0.350929\pi$
$480$		−	1.21646e8i		−	1.09995i
$481$	3.14643e7			0.282737
$482$			1.11546e8i			0.996122i
$483$			1.45984e7i			0.129558i
$484$	1.87085e8			1.65007
$485$		−	1.68765e8i		−	1.47930i
$486$		−	1.04099e7i		−	0.0906854i
$487$	6.99901e7			0.605968			0.302984	−	0.952996i	$-0.402017\pi$
$487$	6.99901e7			0.605968			0.302984	+	0.952996i	$0.402017\pi$
$488$	−369900.			−0.00318291
$489$	−9.61355e7			−0.822161
$490$		−	2.07689e8i		−	1.76533i
$491$	3.01568e7			0.254766			0.127383	−	0.991854i	$-0.459342\pi$
$491$	3.01568e7			0.254766			0.127383	+	0.991854i	$0.459342\pi$
$492$	1.17796e8			0.989088
$493$	−1.01181e8			−0.844420
$494$	6.70687e7			0.556338
$495$			8.87434e7i			0.731679i
$496$		−	1.31861e8i		−	1.08061i
$497$	2.02058e7			0.164591
$498$	−9.04260e7			−0.732159
$499$	1.43575e7			0.115552			0.0577759	−	0.998330i	$-0.481599\pi$
$499$	1.43575e7			0.115552			0.0577759	+	0.998330i	$0.481599\pi$
$500$	−3.08948e7			−0.247159
$501$	−6.66105e7			−0.529699
$502$		−	2.12856e7i		−	0.168258i
$503$		−	1.00141e8i		−	0.786883i	−0.919350	−	0.393441i	$-0.871284\pi$
$503$		−	1.00141e8i		−	0.786883i	0.919350	−	0.393441i	$-0.128716\pi$
$504$		−	26267.5i		−	0.000205176i
$505$		−	7.67587e7i		−	0.596010i
$506$		−	2.47059e8i		−	1.90699i
$507$	5.90200e7			0.452872
$508$	−1.74444e8			−1.33066
$509$		−	1.08822e8i		−	0.825211i	−0.910910	−	0.412606i	$-0.864619\pi$
$509$		−	1.08822e8i		−	0.825211i	0.910910	−	0.412606i	$-0.135381\pi$
$510$		−	6.59492e7i		−	0.497163i
$511$			4.59239e7i			0.344172i
$512$		−	1.89735e8i		−	1.41363i
$513$	−2.20212e7			−0.163113
$514$			1.55473e8i			1.14490i
$515$			2.27735e8i			1.66728i
$516$		−	5.80213e7i		−	0.422317i
$517$	1.90962e8			1.38189
$518$	3.24151e7			0.233216
$519$			6.05758e7i			0.433308i
$520$	199903.			0.00142171
$521$	7.68972e7			0.543748			0.271874	−	0.962333i	$-0.412357\pi$
$521$	7.68972e7			0.543748			0.271874	+	0.962333i	$0.412357\pi$
$522$		−	1.25218e8i		−	0.880347i
$523$	−1.09922e7			−0.0768389			−0.0384194	−	0.999262i	$-0.512232\pi$
$523$	−1.09922e7			−0.0768389			−0.0384194	+	0.999262i	$0.512232\pi$
$524$			7.93008e7i			0.551168i
$525$	1.84772e7			0.127690
$526$			1.90376e8i			1.30815i
$527$		−	7.13722e7i		−	0.487638i
$528$			1.38638e8i			0.941850i
$529$	4.64831e7			0.313999
$530$		−	2.12917e7i		−	0.143016i
$531$	2.39190e7	−	4.38018e7i	0.159757	−	0.292556i
$532$	3.45199e7			0.229263
$533$			1.20643e8i			0.796749i
$534$	−5.93702e7			−0.389892
$535$	7.09176e7			0.463119
$536$	268886.			0.00174612
$537$			8.97005e7i			0.579258i
$538$	−1.95351e8			−1.25449
$539$			2.36321e8i			1.50916i
$540$	4.07752e7			0.258949
$541$			8.42068e7i			0.531808i	0.963999	+	0.265904i	$0.0856705\pi$
$541$			8.42068e7i			0.531808i	−0.963999	+	0.265904i	$0.914330\pi$
$542$			3.69778e8i			2.32244i
$543$	−6.63880e7			−0.414658
$544$		−	1.02863e8i		−	0.638945i
$545$			5.76363e7i			0.356046i
$546$	−1.67127e7			−0.102676
$547$	2.79154e8			1.70562			0.852808	−	0.522225i	$-0.174898\pi$
$547$	2.79154e8			1.70562			0.852808	+	0.522225i	$0.174898\pi$
$548$	5.97806e7			0.363261
$549$		−	7.72740e7i		−	0.467000i
$550$	−3.12703e8			−1.87950
$551$	−2.64887e8			−1.58346
$552$	182728.			0.00108640
$553$	−8.73255e7			−0.516375
$554$			6.03266e6i			0.0354797i
$555$		−	8.09970e7i		−	0.473795i
$556$	2.59539e8			1.51000
$557$	−1.47415e7			−0.0853055			−0.0426528	−	0.999090i	$-0.513581\pi$
$557$	−1.47415e7			−0.0853055			−0.0426528	+	0.999090i	$0.513581\pi$
$558$	8.83274e7			0.508385
$559$	5.94238e7			0.340193
$560$	6.42269e7			0.365724
$561$			7.50409e7i			0.425020i
$562$		−	2.34075e8i		−	1.31870i
$563$		−	6.53827e7i		−	0.366385i	−0.983077	−	0.183192i	$-0.941357\pi$
$563$		−	6.53827e7i		−	0.366385i	0.983077	−	0.183192i	$-0.0586432\pi$
$564$		−	8.77419e7i		−	0.489068i
$565$			5.89832e7i			0.327027i
$566$	1.96200e8			1.08206
$567$	5.48742e6			0.0301036
$568$		−	252917.i		−	0.00138017i
$569$			1.66059e8i			0.901415i	0.892672	+	0.450707i	$0.148828\pi$
$569$			1.66059e8i			0.901415i	−0.892672	+	0.450707i	$0.851172\pi$
$570$		−	1.72652e8i		−	0.932280i
$571$			2.76472e8i			1.48506i	0.669815	+	0.742528i	$0.266374\pi$
$571$			2.76472e8i			1.48506i	−0.669815	+	0.742528i	$0.733626\pi$
$572$	1.41307e8			0.755049
$573$		−	1.89966e8i		−	1.00974i
$574$			1.24289e8i			0.657198i
$575$			1.28535e8i			0.676113i
$576$	6.34961e7			0.332261
$577$	−3.22502e8			−1.67883			−0.839413	−	0.543494i	$-0.817101\pi$
$577$	−3.22502e8			−1.67883			−0.839413	+	0.543494i	$0.817101\pi$
$578$			2.17209e8i			1.12485i
$579$	1.42211e8			0.732650
$580$	4.90473e8			2.51380
$581$		−	4.76667e7i		−	0.243045i
$582$	1.76608e8			0.895862
$583$			2.42270e7i			0.122263i
$584$	574831.			0.00288603
$585$			4.17608e7i			0.208594i
$586$			3.44334e8i			1.71114i
$587$		−	1.21510e7i		−	0.0600754i	−0.999549	−	0.0300377i	$-0.990437\pi$
$587$		−	1.21510e7i		−	0.0600754i	0.999549	−	0.0300377i	$-0.00956274\pi$
$588$	1.08583e8			0.534110
$589$		−	1.86849e8i		−	0.914418i
$590$	3.43417e8	+	1.87531e8i	1.67211	+	0.913098i
$591$	−1.06905e8			−0.517888
$592$		−	1.26537e8i		−	0.609890i
$593$	4.17858e6			0.0200385			0.0100192	−	0.999950i	$-0.496811\pi$
$593$	4.17858e6			0.0200385			0.0100192	+	0.999950i	$0.496811\pi$
$594$	−9.28676e7			−0.443103
$595$	3.47642e7			0.165037
$596$			1.87851e8i			0.887310i
$597$	1.32108e8			0.620877
$598$		−	1.16261e8i		−	0.543663i
$599$	−2.48158e8			−1.15464			−0.577322	−	0.816517i	$-0.695902\pi$
$599$	−2.48158e8			−1.15464			−0.577322	+	0.816517i	$0.695902\pi$
$600$		−	231279.i		−	0.00107074i
$601$		−	1.92847e8i		−	0.888361i	−0.895937	−	0.444180i	$-0.853495\pi$
$601$		−	1.92847e8i		−	0.888361i	0.895937	−	0.444180i	$-0.146505\pi$
$602$	6.12194e7			0.280608
$603$			5.61717e7i			0.256192i
$604$		−	2.64656e8i		−	1.20108i
$605$	4.93245e8			2.22739
$606$	8.03260e7			0.360943
$607$	3.24748e8			1.45205			0.726023	−	0.687671i	$-0.241367\pi$
$607$	3.24748e8			1.45205			0.726023	+	0.687671i	$0.241367\pi$
$608$		−	2.69291e8i		−	1.19815i
$609$	6.60066e7			0.292237
$610$	6.05847e8			2.66915
$611$	8.98627e7			0.393963
$612$	3.44793e7			0.150420
$613$			1.14218e8i			0.495851i	0.968779	+	0.247926i	$0.0797489\pi$
$613$			1.14218e8i			0.495851i	−0.968779	+	0.247926i	$0.920251\pi$
$614$		−	2.94644e8i		−	1.27289i
$615$	3.10566e8			1.33515
$616$	−234335.			−0.00100252
$617$	−1.75757e8			−0.748266			−0.374133	−	0.927375i	$-0.622060\pi$
$617$	−1.75757e8			−0.748266			−0.374133	+	0.927375i	$0.622060\pi$
$618$	−2.38319e8			−1.00970
$619$	−3.06354e8			−1.29167			−0.645835	−	0.763477i	$-0.723491\pi$
$619$	−3.06354e8			−1.29167			−0.645835	+	0.763477i	$0.723491\pi$
$620$			3.45976e8i			1.45168i
$621$			3.81729e7i			0.159397i
$622$		−	3.25875e7i		−	0.135419i
$623$		−	3.12961e7i		−	0.129427i
$624$			6.52404e7i			0.268512i
$625$	−2.80749e8			−1.14995
$626$	−2.87323e8			−1.17124
$627$			1.96453e8i			0.796997i
$628$			1.34283e8i			0.542177i
$629$		−	6.84907e7i		−	0.275220i
$630$			4.30227e7i			0.172058i
$631$	8.45835e7			0.336665			0.168332	−	0.985730i	$-0.446162\pi$
$631$	8.45835e7			0.336665			0.168332	+	0.985730i	$0.446162\pi$
$632$			1.09306e6i			0.00433003i
$633$		−	2.46038e8i		−	0.970043i
$634$		−	1.14583e8i		−	0.449625i
$635$	−4.59918e8			−1.79622
$636$	1.11317e7			0.0432701
$637$			1.11208e8i			0.430247i
$638$	−1.11708e9			−4.30152
$639$	5.28356e7			0.202500
$640$		−	1.60528e6i		−	0.00612367i
$641$	2.62531e8			0.996796			0.498398	−	0.866948i	$-0.333922\pi$
$641$	2.62531e8			0.996796			0.498398	+	0.866948i	$0.333922\pi$
$642$			7.42134e7i			0.280464i
$643$	2.91322e8			1.09582			0.547911	−	0.836537i	$-0.315423\pi$
$643$	2.91322e8			1.09582			0.547911	+	0.836537i	$0.315423\pi$
$644$		−	5.98388e7i		−	0.224040i
$645$		−	1.52972e8i		−	0.570075i
$646$		−	1.45993e8i		−	0.541546i
$647$	−5.24571e8			−1.93683			−0.968415	−	0.249345i	$-0.919785\pi$
$647$	−5.24571e8			−1.93683			−0.968415	+	0.249345i	$0.919785\pi$
$648$		−	68686.2i		−	0.000252432i
$649$	−3.90760e8	−	2.13384e8i	−1.42947	−	0.780599i
$650$	−1.47151e8			−0.535827
$651$			4.65605e7i			0.168762i
$652$	3.94060e8			1.42174
$653$	−4.08780e8			−1.46808			−0.734040	−	0.679106i	$-0.762368\pi$
$653$	−4.08780e8			−1.46808			−0.734040	+	0.679106i	$0.762368\pi$
$654$	−6.03149e7			−0.215621
$655$			2.09075e8i			0.744008i
$656$	4.85179e8			1.71866
$657$			1.20085e8i			0.423441i
$658$	9.25781e7			0.324961
$659$		−	3.23254e8i		−	1.12950i	−0.825261	−	0.564751i	$-0.808972\pi$
$659$		−	3.23254e8i		−	1.12950i	0.825261	−	0.564751i	$-0.191028\pi$
$660$		−	3.63759e8i		−	1.26527i
$661$	1.67484e8			0.579922			0.289961	−	0.957039i	$-0.406358\pi$
$661$	1.67484e8			0.579922			0.289961	+	0.957039i	$0.406358\pi$
$662$		−	2.02669e8i		−	0.698574i
$663$			3.53127e7i			0.121169i
$664$	−596646.			−0.00203804
$665$	9.10108e7			0.309477
$666$	8.47612e7			0.286929
$667$			4.59171e8i			1.54738i
$668$	2.73037e8			0.915992
$669$	−2.72115e8			−0.908813
$670$	−4.40400e8			−1.46428
$671$	−6.89369e8			−2.28183
$672$			6.71039e7i			0.221126i
$673$			4.37433e8i			1.43505i	0.696534	+	0.717523i	$0.254724\pi$
$673$			4.37433e8i			1.43505i	−0.696534	+	0.717523i	$0.745276\pi$
$674$	−4.55250e8			−1.48686
$675$	4.83155e7			0.157099
$676$	−2.41923e8			−0.783137
$677$	1.68879e8			0.544263			0.272131	−	0.962260i	$-0.412271\pi$
$677$	1.68879e8			0.544263			0.272131	+	0.962260i	$0.412271\pi$
$678$	−6.17244e7			−0.198047
$679$			9.30963e7i			0.297388i
$680$		−	435144.i		−	0.00138390i
$681$		−	1.08935e8i		−	0.344927i
$682$		−	7.87977e8i		−	2.48405i
$683$			3.53781e8i			1.11038i	0.831723	+	0.555191i	$0.187355\pi$
$683$			3.53781e8i			1.11038i	−0.831723	+	0.555191i	$0.812645\pi$
$684$	9.02651e7			0.282066
$685$	1.57610e8			0.490357
$686$			2.38213e8i			0.737892i
$687$		−	7.21775e7i		−	0.222603i
$688$		−	2.38979e8i		−	0.733827i
$689$			1.14007e7i			0.0348558i
$690$	−2.99285e8			−0.911040
$691$			4.68094e8i			1.41873i	0.704843	+	0.709364i	$0.251018\pi$
$691$			4.68094e8i			1.41873i	−0.704843	+	0.709364i	$0.748982\pi$
$692$		−	2.48300e8i		−	0.749305i
$693$		−	4.89538e7i		−	0.147091i
$694$	−9.04342e8			−2.70554
$695$	6.84268e8			2.03832
$696$		−	826207.i		−	0.00245054i
$697$	2.62613e8			0.775565
$698$	3.27056e8			0.961737
$699$			3.14910e8i			0.922052i
$700$	−7.57380e7			−0.220810
$701$			1.00783e8i			0.292572i	0.989242	+	0.146286i	$0.0467319\pi$
$701$			1.00783e8i			0.292572i	−0.989242	+	0.146286i	$0.953268\pi$
$702$	−4.37016e7			−0.126324
$703$		−	1.79305e8i		−	0.516091i
$704$		−	5.66454e8i		−	1.62348i
$705$		−	2.31329e8i		−	0.660182i
$706$	5.68087e7			0.161436
$707$			4.23427e7i			0.119817i
$708$	−9.80442e7	+	1.79544e8i	−0.276263	+	0.505907i
$709$	−5.94810e7			−0.166893			−0.0834467	−	0.996512i	$-0.526593\pi$
$709$	−5.94810e7			−0.166893			−0.0834467	+	0.996512i	$0.526593\pi$
$710$			4.14244e8i			1.15739i
$711$	−2.28345e8			−0.635306
$712$	−391734.			−0.00108530
$713$	−3.23895e8			−0.893585
$714$			3.63798e7i			0.0999460i
$715$	3.72552e8			1.01922
$716$		−	3.67683e8i		−	1.00169i
$717$	−4.36487e7			−0.118417
$718$		−	7.50865e8i		−	2.02856i
$719$		−	5.99700e8i		−	1.61342i	−0.590948	−	0.806709i	$-0.701246\pi$
$719$		−	5.99700e8i		−	1.61342i	0.590948	−	0.806709i	$-0.298754\pi$
$720$	1.67945e8			0.449956
$721$		−	1.25626e8i		−	0.335177i
$722$			1.49846e8i			0.398138i
$723$	−1.53754e8			−0.406828
$724$	2.72125e8			0.717055
$725$	5.81173e8			1.52508
$726$			5.16168e8i			1.34890i
$727$	7.48401e7			0.194774			0.0973870	−	0.995247i	$-0.468952\pi$
$727$	7.48401e7			0.194774			0.0973870	+	0.995247i	$0.468952\pi$
$728$	−110273.			−0.000285809
$729$	1.43489e7			0.0370370
$730$	−9.41496e8			−2.42019
$731$		−	1.29352e8i		−	0.331148i
$732$			3.16746e8i			0.807567i
$733$	4.96276e8			1.26012			0.630059	−	0.776547i	$-0.283031\pi$
$733$	4.96276e8			1.26012			0.630059	+	0.776547i	$0.283031\pi$
$734$	−6.05806e8			−1.53195
$735$	2.86277e8			0.720983
$736$	−4.66805e8			−1.17085
$737$	5.01113e8			1.25180
$738$			3.24999e8i			0.808562i
$739$			7.85026e8i			1.94514i	0.232613	+	0.972569i	$0.425273\pi$
$739$			7.85026e8i			1.94514i	−0.232613	+	0.972569i	$0.574727\pi$
$740$			3.32007e8i			0.819318i
$741$			9.24469e7i			0.227215i
$742$			1.17452e7i			0.0287508i
$743$	−3.78436e8			−0.922626			−0.461313	−	0.887237i	$-0.652621\pi$
$743$	−3.78436e8			−0.922626			−0.461313	+	0.887237i	$0.652621\pi$
$744$	582799.			0.00141514
$745$			4.95265e8i			1.19776i
$746$			1.17854e8i			0.283876i
$747$		−	1.24642e8i		−	0.299023i
$748$		−	3.07593e8i		−	0.734974i
$749$	−3.91205e7			−0.0931020
$750$		−	8.52389e7i		−	0.202048i
$751$		−	1.08582e8i		−	0.256354i	−0.991751	−	0.128177i	$-0.959087\pi$
$751$		−	1.08582e8i		−	0.256354i	0.991751	−	0.128177i	$-0.0409125\pi$
$752$		−	3.61392e8i		−	0.849816i
$753$	2.93400e7			0.0687187
$754$	−5.25674e8			−1.22632
$755$		−	6.97760e8i		−	1.62131i
$756$	−2.24930e7			−0.0520572
$757$	−2.72312e8			−0.627739			−0.313870	−	0.949466i	$-0.601625\pi$
$757$	−2.72312e8			−0.627739			−0.313870	+	0.949466i	$0.601625\pi$
$758$			3.10308e7i			0.0712501i
$759$	3.40544e8			0.778840
$760$		−	1.13919e6i		−	0.00259510i
$761$	−3.11053e8			−0.705798			−0.352899	−	0.935661i	$-0.614804\pi$
$761$	−3.11053e8			−0.705798			−0.352899	+	0.935661i	$0.614804\pi$
$762$		−	4.81292e8i		−	1.08779i
$763$		−	3.17941e7i		−	0.0715769i
$764$			7.78670e8i			1.74612i
$765$	9.09039e7			0.203048
$766$			1.45189e8i			0.323034i
$767$	−1.83884e8	−	1.00414e8i	−0.407528	−	0.222540i
$768$	2.62370e8			0.579202
$769$		−	2.21410e8i		−	0.486876i	−0.969916	−	0.243438i	$-0.921725\pi$
$769$		−	2.21410e8i		−	0.486876i	0.969916	−	0.243438i	$-0.0782753\pi$
$770$	3.83810e8			0.840705
$771$	−2.14303e8			−0.467591
$772$	−5.82922e8			−1.26695
$773$		−	1.59034e8i		−	0.344311i	−0.985070	−	0.172155i	$-0.944927\pi$
$773$		−	1.59034e8i		−	0.344311i	0.985070	−	0.172155i	$-0.0550731\pi$
$774$	1.60081e8			0.345237
$775$			4.09954e8i			0.880704i
$776$	1.16529e6			0.00249372
$777$			4.46806e7i			0.0952481i
$778$			3.29064e8i			0.698782i
$779$	6.87508e8			1.45434
$780$		−	1.71178e8i		−	0.360714i
$781$		−	4.71351e8i		−	0.989445i
$782$	−2.53074e8			−0.529208
$783$	1.72599e8			0.359545
$784$	4.47234e8			0.928082
$785$			3.54033e8i			0.731872i
$786$	−2.18791e8			−0.450570
$787$	4.14281e8			0.849906			0.424953	−	0.905215i	$-0.360291\pi$
$787$	4.14281e8			0.849906			0.424953	+	0.905215i	$0.360291\pi$
$788$	4.38204e8			0.895567
$789$	−2.62413e8			−0.534263
$790$		−	1.79028e9i		−	3.63111i
$791$		−	3.25371e7i		−	0.0657430i
$792$	−612756.			−0.00123342
$793$	−3.24403e8			−0.650526
$794$	−8.41568e8			−1.68123
$795$	2.93483e7			0.0584093
$796$	−5.41510e8			−1.07366
$797$		−	6.89771e8i		−	1.36248i	−0.732060	−	0.681240i	$-0.761441\pi$
$797$		−	6.89771e8i		−	1.36248i	0.732060	−	0.681240i	$-0.238559\pi$
$798$			9.52404e7i			0.187419i
$799$		−	1.95611e8i		−	0.383489i
$800$			5.90835e8i			1.15397i
$801$		−	8.18353e7i		−	0.159237i
$802$	1.02917e9			1.99509
$803$	1.07129e9			2.06900
$804$		−	2.30248e8i		−	0.443025i
$805$		−	1.57764e8i		−	0.302426i
$806$		−	3.70806e8i		−	0.708176i
$807$		−	2.69270e8i		−	0.512351i
$808$	530004.			0.00100472
$809$		−	2.65613e8i		−	0.501654i	−0.968032	−	0.250827i	$-0.919297\pi$
$809$		−	2.65613e8i		−	0.501654i	0.968032	−	0.250827i	$-0.0807026\pi$
$810$			1.12499e8i			0.211687i
$811$		−	2.75450e8i		−	0.516393i	−0.966092	−	0.258196i	$-0.916872\pi$
$811$		−	2.75450e8i		−	0.516393i	0.966092	−	0.258196i	$-0.0831282\pi$
$812$	−2.70561e8			−0.505356
$813$	−5.09699e8			−0.948511
$814$		−	7.56163e8i		−	1.40198i
$815$	1.03893e9			1.91917
$816$	1.42014e8			0.261372
$817$		−	3.38637e8i		−	0.620967i
$818$	3.87362e8			0.707712
$819$		−	2.30366e7i		−	0.0419341i
$820$	−1.27301e9			−2.30882
$821$			5.97003e8i			1.07881i	0.842045	+	0.539407i	$0.181352\pi$
$821$			5.97003e8i			1.07881i	−0.842045	+	0.539407i	$0.818648\pi$
$822$			1.64935e8i			0.296959i
$823$		−	9.15895e8i		−	1.64303i	−0.570184	−	0.821517i	$-0.693128\pi$
$823$		−	9.15895e8i		−	1.64303i	0.570184	−	0.821517i	$-0.306872\pi$
$824$	−1.57247e6			−0.00281060
$825$		−	4.31027e8i		−	0.767613i
$826$	−1.89440e8	−	1.03448e8i	−0.336149	−	0.183562i
$827$	3.36650e8			0.595199			0.297599	−	0.954691i	$-0.403814\pi$
$827$	3.36650e8			0.595199			0.297599	+	0.954691i	$0.403814\pi$
$828$		−	1.56471e8i		−	0.275640i
$829$	−8.40810e8			−1.47582			−0.737912	−	0.674897i	$-0.764188\pi$
$829$	−8.40810e8			−1.47582			−0.737912	+	0.674897i	$0.764188\pi$
$830$	9.77227e8			1.70908
$831$	−8.31537e6			−0.0144903
$832$		−	2.66562e8i		−	0.462837i
$833$	2.42075e8			0.418807
$834$			7.16068e8i			1.23440i
$835$	7.19855e8			1.23648
$836$		−	8.05263e8i		−	1.37822i
$837$			1.21750e8i			0.207631i
$838$	−6.04083e8			−1.02651
$839$			7.10141e8i			1.20243i	0.799088	+	0.601214i	$0.205316\pi$
$839$			7.10141e8i			1.20243i	−0.799088	+	0.601214i	$0.794684\pi$
$840$			283871.i			0.000478942i
$841$	1.48132e9			2.49035
$842$	1.33795e9			2.24131
$843$	3.22648e8			0.538575
$844$			1.00851e9i			1.67746i
$845$	−6.37825e8			−1.05714
$846$	2.42080e8			0.399805
$847$	−2.72090e8			−0.447778
$848$	4.58491e7			0.0751872
$849$			2.70441e8i			0.441925i
$850$			3.20315e8i			0.521580i
$851$	−3.10818e8			−0.504334
$852$	−2.16573e8			−0.350176
$853$	−6.29926e8			−1.01494			−0.507472	−	0.861668i	$-0.669420\pi$
$853$	−6.29926e8			−1.01494			−0.507472	+	0.861668i	$0.669420\pi$
$854$	−3.34205e8			−0.536586
$855$	2.37982e8			0.380755
$856$			489673.i			0.000780701i
$857$		−	7.98551e8i		−	1.26870i	−0.773045	−	0.634352i	$-0.781267\pi$
$857$		−	7.98551e8i		−	1.26870i	0.773045	−	0.634352i	$-0.218733\pi$
$858$			3.89866e8i			0.617239i
$859$			2.77310e8i			0.437508i	0.975780	+	0.218754i	$0.0701992\pi$
$859$			2.77310e8i			0.437508i	−0.975780	+	0.218754i	$0.929801\pi$
$860$			6.27032e8i			0.985813i
$861$	−1.71319e8			−0.268408
$862$	−6.52391e7			−0.101856
$863$		−	6.15639e8i		−	0.957841i	−0.877858	−	0.478921i	$-0.841028\pi$
$863$		−	6.15639e8i		−	0.957841i	0.877858	−	0.478921i	$-0.158972\pi$
$864$			1.75468e8i			0.272055i
$865$		−	6.54638e8i		−	1.01147i
$866$		−	2.78124e8i		−	0.428237i
$867$	−2.99400e8			−0.459403
$868$		−	1.90852e8i		−	0.291834i
$869$			2.03709e9i			3.10420i
$870$			1.35322e9i			2.05499i
$871$	2.35814e8			0.356874
$872$	−397968.			−0.000600203
$873$			2.43435e8i			0.365881i
$874$	−6.62534e8			−0.992371
$875$	4.49324e7			0.0670711
$876$		−	4.92229e8i		−	0.732243i
$877$	−8.99394e7			−0.133337			−0.0666686	−	0.997775i	$-0.521237\pi$
$877$	−8.99394e7			−0.133337			−0.0666686	+	0.997775i	$0.521237\pi$
$878$			1.58394e9i			2.34022i
$879$	−4.74627e8			−0.698853
$880$		−	1.49826e9i		−	2.19856i
$881$		−	5.93854e8i		−	0.868465i	−0.900801	−	0.434232i	$-0.857020\pi$
$881$		−	5.93854e8i		−	0.868465i	0.900801	−	0.434232i	$-0.142980\pi$
$882$			2.99582e8i			0.436626i
$883$	−9.44698e8			−1.37218			−0.686089	−	0.727517i	$-0.740674\pi$
$883$	−9.44698e8			−1.37218			−0.686089	+	0.727517i	$0.740674\pi$
$884$		−	1.44747e8i		−	0.209533i
$885$	−2.58491e8	+	4.73363e8i	−0.372920	+	0.682911i
$886$	−4.52780e8			−0.651008
$887$			9.99176e8i			1.43176i	0.698222	+	0.715882i	$0.253975\pi$
$887$			9.99176e8i			1.43176i	−0.698222	+	0.715882i	$0.746025\pi$
$888$	559269.			0.000798696
$889$	2.53706e8			0.361098
$890$	6.41609e8			0.910124
$891$		−	1.28008e8i		−	0.180969i
$892$	1.11540e9			1.57158
$893$		−	5.12099e8i		−	0.719118i
$894$	−5.18282e8			−0.725360
$895$		−	9.69386e8i		−	1.35216i
$896$			885527.i			0.00123106i
$897$	1.60253e8			0.222039
$898$			3.85327e8i			0.532109i
$899$			1.46449e9i			2.01562i
$900$	−1.98045e8			−0.271667
$901$	2.48168e7			0.0339290
$902$	2.89935e9			3.95076
$903$			8.43843e7i			0.114604i
$904$	−407268.			−0.000551283
$905$	7.17451e8			0.967935
$906$	7.30187e8			0.981860
$907$	1.11742e9			1.49759			0.748796	−	0.662800i	$-0.230632\pi$
$907$	1.11742e9			1.49759			0.748796	+	0.662800i	$0.230632\pi$
$908$			4.46526e8i			0.596470i
$909$			1.10721e8i			0.147413i
$910$	1.80613e8			0.239676
$911$	−1.01971e9			−1.34871			−0.674357	−	0.738406i	$-0.735579\pi$
$911$	−1.01971e9			−1.34871			−0.674357	+	0.738406i	$0.735579\pi$
$912$	3.71785e8			0.490125
$913$	−1.11195e9			−1.46107
$914$	−1.18664e7			−0.0155411
$915$			8.35095e8i			1.09012i
$916$			2.95856e8i			0.384941i
$917$		−	1.15333e8i		−	0.149570i
$918$			9.51285e7i			0.122965i
$919$			1.79264e8i			0.230966i	0.993309	+	0.115483i	$0.0368415\pi$
$919$			1.79264e8i			0.230966i	−0.993309	+	0.115483i	$0.963158\pi$
$920$	−1.97473e6			−0.00253597
$921$	4.06135e8			0.519866
$922$			1.77109e9i			2.25969i
$923$		−	2.21808e8i		−	0.282080i
$924$			2.00662e8i			0.254360i
$925$			3.93403e8i			0.497064i
$926$	6.86083e8			0.864060
$927$		−	3.28496e8i		−	0.412374i
$928$			2.11066e9i			2.64103i
$929$		−	5.45373e8i		−	0.680215i	−0.940387	−	0.340108i	$-0.889537\pi$
$929$		−	5.45373e8i		−	0.680215i	0.940387	−	0.340108i	$-0.110463\pi$
$930$	−9.54547e8			−1.18672
$931$	6.33739e8			0.785347
$932$		−	1.29082e9i		−	1.59447i
$933$	4.49184e7			0.0553068
$934$	4.28662e8			0.526108
$935$		−	8.10962e8i		−	0.992123i
$936$	−288350.			−0.000351636
$937$			3.42476e8i			0.416305i	0.978096	+	0.208152i	$0.0667450\pi$
$937$			3.42476e8i			0.416305i	−0.978096	+	0.208152i	$0.933255\pi$
$938$	2.42939e8			0.294367
$939$		−	3.96043e8i		−	0.478350i
$940$			9.48220e8i			1.14163i
$941$			9.95723e8i			1.19501i	0.801867	+	0.597503i	$0.203840\pi$
$941$			9.95723e8i			1.19501i	−0.801867	+	0.597503i	$0.796160\pi$
$942$	−3.70486e8			−0.443220
$943$		−	1.19177e9i		−	1.42120i
$944$	−4.03825e8	+	7.39506e8i	−0.480040	+	0.879075i
$945$	−5.93021e7			−0.0702708
$946$		−	1.42810e9i		−	1.68688i
$947$	−1.36505e9			−1.60731			−0.803654	−	0.595097i	$-0.797113\pi$
$947$	−1.36505e9			−1.60731			−0.803654	+	0.595097i	$0.797113\pi$
$948$	9.35987e8			1.09861
$949$	5.04127e8			0.589850
$950$			8.38570e8i			0.978066i
$951$	1.57940e8			0.183633
$952$			240040.i			0.000278210i
$953$	6.82798e7			0.0788885			0.0394442	−	0.999222i	$-0.487441\pi$
$953$	6.82798e7			0.0788885			0.0394442	+	0.999222i	$0.487441\pi$
$954$			3.07123e7i			0.0353726i
$955$			2.05295e9i			2.35704i
$956$	1.78916e8			0.204774
$957$		−	1.53977e9i		−	1.75679i
$958$		−	1.12207e9i		−	1.27621i
$959$	−8.69430e7			−0.0985777
$960$	−6.86197e8			−0.775596
$961$	−1.45536e8			−0.163984
$962$		−	3.55835e8i		−	0.399690i
$963$	−1.02295e8			−0.114545
$964$	6.30238e8			0.703515
$965$	−1.53686e9			−1.71022
$966$	1.65095e8			0.183149
$967$			1.76113e9i			1.94765i	0.227294	+	0.973826i	$0.427012\pi$
$967$			1.76113e9i			1.94765i	−0.227294	+	0.973826i	$0.572988\pi$
$968$			3.40576e6i			0.00375481i
$969$	2.01236e8			0.221174
$970$	−1.90859e9			−2.09121
$971$	6.70688e8			0.732594			0.366297	−	0.930498i	$-0.380625\pi$
$971$	6.70688e8			0.732594			0.366297	+	0.930498i	$0.380625\pi$
$972$	−5.88162e7			−0.0640469
$973$	−3.77465e8			−0.409768
$974$		−	7.91529e8i		−	0.856624i
$975$		−	2.02832e8i		−	0.218838i
$976$			1.30462e9i			1.40325i
$977$		−	1.75799e9i		−	1.88509i	−0.334074	−	0.942547i	$-0.608424\pi$
$977$		−	1.75799e9i		−	1.88509i	0.334074	−	0.942547i	$-0.391576\pi$
$978$			1.08721e9i			1.16224i
$979$	−7.30061e8			−0.778056
$980$	−1.17345e9			−1.24677
$981$		−	8.31375e7i		−	0.0880623i
$982$		−	3.41048e8i		−	0.360148i
$983$			5.59701e8i			0.589244i	0.955614	+	0.294622i	$0.0951938\pi$
$983$			5.59701e8i			0.589244i	−0.955614	+	0.294622i	$0.904806\pi$
$984$			2.14440e6i			0.00225071i
$985$	1.15532e9			1.20890
$986$			1.14427e9i			1.19371i
$987$			1.27609e8i			0.132718i
$988$		−	3.78940e8i		−	0.392916i
$989$	−5.87015e8			−0.606820
$990$	1.00361e9			1.03433
$991$		−	2.37943e8i		−	0.244485i	−0.992500	−	0.122243i	$-0.960991\pi$
$991$		−	2.37943e8i		−	0.244485i	0.992500	−	0.122243i	$-0.0390086\pi$
$992$	−1.48884e9			−1.52515
$993$	2.79357e8			0.285306
$994$		−	2.28511e8i		−	0.232674i
$995$	−1.42768e9			−1.44931
$996$			5.10910e8i			0.517090i
$997$	1.33444e9			1.34652			0.673260	−	0.739406i	$-0.264893\pi$
$997$	1.33444e9			1.34652			0.673260	+	0.739406i	$0.264893\pi$
$998$		−	1.62371e8i		−	0.163349i
$999$			1.16834e8i			0.117185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.11	✓	60
59.58	odd	2	inner	177.7.c.a.58.50	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.11	✓	60	1.1	even	1	trivial
177.7.c.a.58.50	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)

\(f(q)\)	\(=\)	\(q-11.3092i q^{2} +15.5885 q^{3} -63.8971 q^{4} -168.463 q^{5} -176.292i q^{6} +92.9299 q^{7} -1.16321i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-11.3092i q^{2} +15.5885 q^{3} -63.8971 q^{4} -168.463 q^{5} -176.292i q^{6} +92.9299 q^{7} -1.16321i q^{8} +243.000 q^{9} +1905.18i q^{10} -2167.83i q^{11} -996.058 q^{12} -1020.13i q^{13} -1050.96i q^{14} -2626.08 q^{15} -4102.57 q^{16} -2220.60 q^{17} -2748.13i q^{18} -5813.42 q^{19} +10764.3 q^{20} +1448.63 q^{21} -24516.3 q^{22} +10077.3i q^{23} -18.1326i q^{24} +12754.9 q^{25} -11536.9 q^{26} +3788.00 q^{27} -5937.96 q^{28} +45564.7 q^{29} +29698.8i q^{30} +32140.9i q^{31} +46322.2i q^{32} -33793.1i q^{33} +25113.1i q^{34} -15655.3 q^{35} -15527.0 q^{36} +30843.3i q^{37} +65745.0i q^{38} -15902.3i q^{39} +195.958i q^{40} -118262. q^{41} -16382.8i q^{42} +58251.0i q^{43} +138518. i q^{44} -40936.6 q^{45} +113966. q^{46} +88089.1i q^{47} -63952.8 q^{48} -109013. q^{49} -144247. i q^{50} -34615.8 q^{51} +65183.7i q^{52} -11175.7 q^{53} -42839.1i q^{54} +365199. i q^{55} -108.097i q^{56} -90622.3 q^{57} -515299. i q^{58} +(98432.3 - 180254. i) q^{59} +167799. q^{60} -318000. i q^{61} +363487. q^{62} +22582.0 q^{63} +261301. q^{64} +171855. i q^{65} -382171. q^{66} +231159. i q^{67} +141890. q^{68} +157090. i q^{69} +177048. i q^{70} +217430. q^{71} -282.659i q^{72} +494177. i q^{73} +348812. q^{74} +198829. q^{75} +371461. q^{76} -201456. i q^{77} -179842. q^{78} -939691. q^{79} +691133. q^{80} +59049.0 q^{81} +1.33745e6i q^{82} -512932. i q^{83} -92563.6 q^{84} +374090. q^{85} +658769. q^{86} +710284. q^{87} -2521.63 q^{88} -336771. i q^{89} +462958. i q^{90} -94801.0i q^{91} -643913. i q^{92} +501028. i q^{93} +996214. q^{94} +979349. q^{95} +722092. i q^{96} +1.00179e6i q^{97} +1.23285e6i q^{98} -526782. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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