LMFDB - Embedded newform 177.7.c.a.58.19

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			58.19
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.02990i q^{2} -15.5885 q^{3} +14.5805 q^{4} +242.375 q^{5} +109.585i q^{6} +243.138 q^{7} -552.413i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-7.02990i q^{2} -15.5885 q^{3} +14.5805 q^{4} +242.375 q^{5} +109.585i q^{6} +243.138 q^{7} -552.413i q^{8} +243.000 q^{9} -1703.87i q^{10} -1556.52i q^{11} -227.288 q^{12} +1415.05i q^{13} -1709.23i q^{14} -3778.26 q^{15} -2950.26 q^{16} +3197.13 q^{17} -1708.27i q^{18} -454.920 q^{19} +3533.96 q^{20} -3790.14 q^{21} -10942.2 q^{22} +1158.71i q^{23} +8611.27i q^{24} +43120.8 q^{25} +9947.68 q^{26} -3788.00 q^{27} +3545.07 q^{28} +21964.5 q^{29} +26560.8i q^{30} +4418.81i q^{31} -14614.4i q^{32} +24263.8i q^{33} -22475.5i q^{34} +58930.6 q^{35} +3543.06 q^{36} +46436.0i q^{37} +3198.04i q^{38} -22058.5i q^{39} -133891. i q^{40} -132979. q^{41} +26644.3i q^{42} +157011. i q^{43} -22694.9i q^{44} +58897.2 q^{45} +8145.63 q^{46} -163691. i q^{47} +45989.9 q^{48} -58533.1 q^{49} -303135. i q^{50} -49838.3 q^{51} +20632.2i q^{52} +192890. q^{53} +26629.2i q^{54} -377263. i q^{55} -134312. i q^{56} +7091.50 q^{57} -154408. i q^{58} +(14748.1 - 204849. i) q^{59} -55088.9 q^{60} +340178. i q^{61} +31063.8 q^{62} +59082.4 q^{63} -291554. q^{64} +342974. i q^{65} +170572. q^{66} -237657. i q^{67} +46615.8 q^{68} -18062.5i q^{69} -414276. i q^{70} -352597. q^{71} -134236. i q^{72} -456696. i q^{73} +326441. q^{74} -672187. q^{75} -6632.97 q^{76} -378450. i q^{77} -155069. q^{78} +33053.2 q^{79} -715069. q^{80} +59049.0 q^{81} +934832. i q^{82} +40540.7i q^{83} -55262.2 q^{84} +774905. q^{85} +1.10377e6 q^{86} -342393. q^{87} -859844. q^{88} +1.07456e6i q^{89} -414041. i q^{90} +344053. i q^{91} +16894.6i q^{92} -68882.5i q^{93} -1.15073e6 q^{94} -110261. q^{95} +227817. i q^{96} -1.45966e6i q^{97} +411482. i q^{98} -378235. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	7.02990i		−	0.878737i	−0.898307	−	0.439369i	$-0.855202\pi$
$2$		−	7.02990i		−	0.878737i	0.898307	−	0.439369i	$-0.144798\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	14.5805			0.227821
$5$	242.375			1.93900			0.969501	−	0.245086i	$-0.0788163\pi$
$5$	242.375			1.93900			0.969501	+	0.245086i	$0.0788163\pi$
$6$			109.585i			0.507339i
$7$	243.138			0.708856			0.354428	−	0.935083i	$-0.384676\pi$
$7$	243.138			0.708856			0.354428	+	0.935083i	$0.384676\pi$
$8$		−	552.413i		−	1.07893i
$9$	243.000			0.333333
$10$		−	1703.87i		−	1.70387i
$11$		−	1556.52i		−	1.16944i	−0.811235	−	0.584720i	$-0.801204\pi$
$11$		−	1556.52i		−	1.16944i	0.811235	−	0.584720i	$-0.198796\pi$
$12$	−227.288			−0.131532
$13$			1415.05i			0.644084i	0.946725	+	0.322042i	$0.104369\pi$
$13$			1415.05i			0.644084i	−0.946725	+	0.322042i	$0.895631\pi$
$14$		−	1709.23i		−	0.622898i
$15$	−3778.26			−1.11948
$16$	−2950.26			−0.720277
$17$	3197.13			0.650749			0.325374	−	0.945585i	$-0.394510\pi$
$17$	3197.13			0.650749			0.325374	+	0.945585i	$0.394510\pi$
$18$		−	1708.27i		−	0.292912i
$19$	−454.920			−0.0663245			−0.0331623	−	0.999450i	$-0.510558\pi$
$19$	−454.920			−0.0663245			−0.0331623	+	0.999450i	$0.510558\pi$
$20$	3533.96			0.441745
$21$	−3790.14			−0.409258
$22$	−10942.2			−1.02763
$23$			1158.71i			0.0952340i	0.998866	+	0.0476170i	$0.0151627\pi$
$23$			1158.71i			0.0952340i	−0.998866	+	0.0476170i	$0.984837\pi$
$24$			8611.27i			0.622922i
$25$	43120.8			2.75973
$26$	9947.68			0.565981
$27$	−3788.00			−0.192450
$28$	3545.07			0.161492
$29$	21964.5			0.900590			0.450295	−	0.892880i	$-0.351319\pi$
$29$	21964.5			0.900590			0.450295	+	0.892880i	$0.351319\pi$
$30$			26560.8i			0.983732i
$31$			4418.81i			0.148327i	0.997246	+	0.0741636i	$0.0236287\pi$
$31$			4418.81i			0.148327i	−0.997246	+	0.0741636i	$0.976371\pi$
$32$		−	14614.4i		−	0.445997i
$33$			24263.8i			0.675176i
$34$		−	22475.5i		−	0.571837i
$35$	58930.6			1.37447
$36$	3543.06			0.0759402
$37$			46436.0i			0.916748i	0.888760	+	0.458374i	$0.151568\pi$
$37$			46436.0i			0.916748i	−0.888760	+	0.458374i	$0.848432\pi$
$38$			3198.04i			0.0582818i
$39$		−	22058.5i		−	0.371862i
$40$		−	133891.i		−	2.09205i
$41$	−132979.			−1.92945			−0.964724	−	0.263264i	$-0.915201\pi$
$41$	−132979.			−1.92945			−0.964724	+	0.263264i	$0.915201\pi$
$42$			26644.3i			0.359631i
$43$			157011.i			1.97481i	0.158219	+	0.987404i	$0.449425\pi$
$43$			157011.i			1.97481i	−0.158219	+	0.987404i	$0.550575\pi$
$44$		−	22694.9i		−	0.266422i
$45$	58897.2			0.646334
$46$	8145.63			0.0836857
$47$		−	163691.i		−	1.57663i	−0.615271	−	0.788316i	$-0.710953\pi$
$47$		−	163691.i		−	1.57663i	0.615271	−	0.788316i	$-0.289047\pi$
$48$	45989.9			0.415852
$49$	−58533.1			−0.497523
$50$		−	303135.i		−	2.42508i
$51$	−49838.3			−0.375710
$52$			20632.2i			0.146736i
$53$	192890.			1.29563			0.647816	−	0.761797i	$-0.275683\pi$
$53$	192890.			1.29563			0.647816	+	0.761797i	$0.275683\pi$
$54$			26629.2i			0.169113i
$55$		−	377263.i		−	2.26755i
$56$		−	134312.i		−	0.764807i
$57$	7091.50			0.0382925
$58$		−	154408.i		−	0.791382i
$59$	14748.1	−	204849.i	0.0718094	−	0.997418i
$59$	14748.1	−	204849.i	0.0718094	−	0.997418i
$60$	−55088.9			−0.255041
$61$			340178.i			1.49871i	0.662170	+	0.749354i	$0.269636\pi$
$61$			340178.i			1.49871i	−0.662170	+	0.749354i	$0.730364\pi$
$62$	31063.8			0.130341
$63$	59082.4			0.236285
$64$	−291554.			−1.11219
$65$			342974.i			1.24888i
$66$	170572.			0.593303
$67$		−	237657.i		−	0.790180i	−0.918643	−	0.395090i	$-0.870713\pi$
$67$		−	237657.i		−	0.790180i	0.918643	−	0.395090i	$-0.129287\pi$
$68$	46615.8			0.148254
$69$		−	18062.5i		−	0.0549834i
$70$		−	414276.i		−	1.20780i
$71$	−352597.			−0.985151			−0.492576	−	0.870270i	$-0.663945\pi$
$71$	−352597.			−0.985151			−0.492576	+	0.870270i	$0.663945\pi$
$72$		−	134236.i		−	0.359644i
$73$		−	456696.i		−	1.17398i	−0.809596	−	0.586988i	$-0.800314\pi$
$73$		−	456696.i		−	1.17398i	0.809596	−	0.586988i	$-0.199686\pi$
$74$	326441.			0.805580
$75$	−672187.			−1.59333
$76$	−6632.97			−0.0151101
$77$		−	378450.i		−	0.828964i
$78$	−155069.			−0.326769
$79$	33053.2			0.0670398			0.0335199	−	0.999438i	$-0.489328\pi$
$79$	33053.2			0.0670398			0.0335199	+	0.999438i	$0.489328\pi$
$80$	−715069.			−1.39662
$81$	59049.0			0.111111
$82$			934832.i			1.69548i
$83$			40540.7i			0.0709018i	0.999371	+	0.0354509i	$0.0112867\pi$
$83$			40540.7i			0.0709018i	−0.999371	+	0.0354509i	$0.988713\pi$
$84$	−55262.2			−0.0932374
$85$	774905.			1.26180
$86$	1.10377e6			1.73534
$87$	−342393.			−0.519956
$88$	−859844.			−1.26175
$89$			1.07456e6i			1.52427i	0.647420	+	0.762133i	$0.275848\pi$
$89$			1.07456e6i			1.52427i	−0.647420	+	0.762133i	$0.724152\pi$
$90$		−	414041.i		−	0.567958i
$91$			344053.i			0.456563i
$92$			16894.6i			0.0216963i
$93$		−	68882.5i		−	0.0856367i
$94$	−1.15073e6			−1.38545
$95$	−110261.			−0.128603
$96$			227817.i			0.257497i
$97$		−	1.45966e6i		−	1.59932i	−0.600454	−	0.799660i	$-0.705013\pi$
$97$		−	1.45966e6i		−	1.59932i	0.600454	−	0.799660i	$-0.294987\pi$
$98$			411482.i			0.437192i
$99$		−	378235.i		−	0.389813i
$100$	628723.			0.628723
$101$			264109.i			0.256341i	0.991752	+	0.128171i	$0.0409105\pi$
$101$			264109.i			0.256341i	−0.991752	+	0.128171i	$0.959089\pi$
$102$			350358.i			0.330150i
$103$		−	410416.i		−	0.375589i	−0.982208	−	0.187795i	$-0.939866\pi$
$103$		−	410416.i		−	0.375589i	0.982208	−	0.187795i	$-0.0601339\pi$
$104$	781694.			0.694923
$105$	−918636.			−0.793553
$106$		−	1.35600e6i		−	1.13852i
$107$	1.11097e6			0.906879			0.453439	−	0.891287i	$-0.350197\pi$
$107$	1.11097e6			0.906879			0.453439	+	0.891287i	$0.350197\pi$
$108$	−55230.9			−0.0438441
$109$		−	2.09796e6i		−	1.62001i	−0.586422	−	0.810006i	$-0.699464\pi$
$109$		−	2.09796e6i		−	1.62001i	0.586422	−	0.810006i	$-0.300536\pi$
$110$	−2.65212e6			−1.99258
$111$		−	723866.i		−	0.529284i
$112$	−717318.			−0.510573
$113$			266601.i			0.184768i	0.995723	+	0.0923839i	$0.0294487\pi$
$113$			266601.i			0.184768i	−0.995723	+	0.0923839i	$0.970551\pi$
$114$		−	49852.5i		−	0.0336490i
$115$			280843.i			0.184659i
$116$	320254.			0.205173
$117$			343858.i			0.214695i
$118$	−1.44007e6	−	103678.i	−0.876469	−	0.0631016i
$119$	777342.			0.461287
$120$			2.08716e6i			1.20785i
$121$	−651206.			−0.367589
$122$	2.39142e6			1.31697
$123$	2.07294e6			1.11397
$124$			64428.6i			0.0337920i
$125$	6.66430e6			3.41212
$126$		−	415344.i		−	0.207633i
$127$	−1.74962e6			−0.854148			−0.427074	−	0.904217i	$-0.640456\pi$
$127$	−1.74962e6			−0.854148			−0.427074	+	0.904217i	$0.640456\pi$
$128$			1.11427e6i			0.531327i
$129$		−	2.44756e6i		−	1.14016i
$130$	2.41107e6			1.09744
$131$		−	187240.i		−	0.0832886i	−0.999132	−	0.0416443i	$-0.986740\pi$
$131$		−	187240.i		−	0.0832886i	0.999132	−	0.0416443i	$-0.0132596\pi$
$132$			353779.i			0.153819i
$133$	−110608.			−0.0470145
$134$	−1.67070e6			−0.694360
$135$	−918116.			−0.373161
$136$		−	1.76614e6i		−	0.702114i
$137$	−2.02527e6			−0.787628			−0.393814	−	0.919190i	$-0.628845\pi$
$137$	−2.02527e6			−0.787628			−0.393814	+	0.919190i	$0.628845\pi$
$138$	−126978.			−0.0483159
$139$	−448349.			−0.166944			−0.0834722	−	0.996510i	$-0.526601\pi$
$139$	−448349.			−0.166944			−0.0834722	+	0.996510i	$0.526601\pi$
$140$	859238.			0.313133
$141$			2.55168e6i			0.910269i
$142$			2.47872e6i			0.865689i
$143$	2.20256e6			0.753218
$144$	−716912.			−0.240092
$145$	5.32365e6			1.74625
$146$	−3.21053e6			−1.03162
$147$	912441.			0.287245
$148$			677061.i			0.208854i
$149$			1.99524e6i			0.603166i	0.953440	+	0.301583i	$0.0975150\pi$
$149$			1.99524e6i			0.603166i	−0.953440	+	0.301583i	$0.902485\pi$
$150$			4.72540e6i			1.40012i
$151$			2.13822e6i			0.621042i	0.950567	+	0.310521i	$0.100503\pi$
$151$			2.13822e6i			0.621042i	−0.950567	+	0.310521i	$0.899497\pi$
$152$			251304.i			0.0715596i
$153$	776902.			0.216916
$154$	−2.66046e6			−0.728442
$155$			1.07101e6i			0.287607i
$156$		−	321624.i		−	0.0847178i
$157$			4.26617e6i			1.10240i	0.834373	+	0.551200i	$0.185830\pi$
$157$			4.26617e6i			1.10240i	−0.834373	+	0.551200i	$0.814170\pi$
$158$		−	232361.i		−	0.0589104i
$159$	−3.00685e6			−0.748033
$160$		−	3.54218e6i		−	0.864790i
$161$			281726.i			0.0675072i
$162$		−	415109.i		−	0.0976375i
$163$	−5.52187e6			−1.27504			−0.637519	−	0.770434i	$-0.720039\pi$
$163$	−5.52187e6			−1.27504			−0.637519	+	0.770434i	$0.720039\pi$
$164$	−1.93891e6			−0.439568
$165$			5.88095e6i			1.30917i
$166$	284997.			0.0623041
$167$	−1.59986e6			−0.343505			−0.171753	−	0.985140i	$-0.554943\pi$
$167$	−1.59986e6			−0.343505			−0.171753	+	0.985140i	$0.554943\pi$
$168$			2.09372e6i			0.441562i
$169$	2.82443e6			0.585155
$170$		−	5.44750e6i		−	1.10879i
$171$	−110546.			−0.0221082
$172$			2.28930e6i			0.449902i
$173$			4.65918e6i			0.899852i	0.893066	+	0.449926i	$0.148550\pi$
$173$			4.65918e6i			0.899852i	−0.893066	+	0.449926i	$0.851450\pi$
$174$			2.40699e6i			0.456905i
$175$	1.04843e7			1.95625
$176$			4.59214e6i			0.842321i
$177$	−229901.	+	3.19328e6i	−0.0414592	+	0.575860i
$178$	7.55405e6			1.33943
$179$		−	8.35387e6i		−	1.45656i	−0.685280	−	0.728280i	$-0.740320\pi$
$179$		−	8.35387e6i		−	1.45656i	0.685280	−	0.728280i	$-0.259680\pi$
$180$	858751.			0.147248
$181$	−2.85135e6			−0.480855			−0.240427	−	0.970667i	$-0.577288\pi$
$181$	−2.85135e6			−0.480855			−0.240427	+	0.970667i	$0.577288\pi$
$182$	2.41866e6			0.401199
$183$		−	5.30285e6i		−	0.865279i
$184$	640088.			0.102751
$185$			1.12549e7i			1.77758i
$186$	−484237.			−0.0752522
$187$		−	4.97641e6i		−	0.761011i
$188$		−	2.38669e6i		−	0.359189i
$189$	−921004.			−0.136419
$190$			775126.i			0.113009i
$191$			9.07270e6i			1.30208i	0.759045	+	0.651038i	$0.225666\pi$
$191$			9.07270e6i			1.30208i	−0.759045	+	0.651038i	$0.774334\pi$
$192$	4.54488e6			0.642124
$193$	−7.29522e6			−1.01477			−0.507384	−	0.861720i	$-0.669387\pi$
$193$	−7.29522e6			−1.01477			−0.507384	+	0.861720i	$0.669387\pi$
$194$	−1.02612e7			−1.40538
$195$		−	5.34643e6i		−	0.721042i
$196$	−853443.			−0.113346
$197$	777089.			0.101642			0.0508209	−	0.998708i	$-0.483816\pi$
$197$	777089.			0.101642			0.0508209	+	0.998708i	$0.483816\pi$
$198$	−2.65896e6			−0.342543
$199$	7.75894e6			0.984562			0.492281	−	0.870436i	$-0.336163\pi$
$199$	7.75894e6			0.984562			0.492281	+	0.870436i	$0.336163\pi$
$200$		−	2.38205e7i		−	2.97756i
$201$			3.70470e6i			0.456210i
$202$	1.85666e6			0.225257
$203$	5.34040e6			0.638389
$204$	−726668.			−0.0855944
$205$	−3.22309e7			−3.74120
$206$	−2.88519e6			−0.330044
$207$			281567.i			0.0317447i
$208$		−	4.17477e6i		−	0.463919i
$209$			708094.i			0.0775625i
$210$			6.45792e6i			0.697324i
$211$		−	7.35347e6i		−	0.782789i	−0.920223	−	0.391395i	$-0.871993\pi$
$211$		−	7.35347e6i		−	0.782789i	0.920223	−	0.391395i	$-0.128007\pi$
$212$	2.81243e6			0.295171
$213$	5.49644e6			0.568777
$214$		−	7.80997e6i		−	0.796908i
$215$			3.80556e7i			3.82916i
$216$			2.09254e6i			0.207641i
$217$			1.07438e6i			0.105143i
$218$	−1.47485e7			−1.42356
$219$			7.11919e6i			0.677795i
$220$		−	5.50069e6i		−	0.516594i
$221$			4.52411e6i			0.419137i
$222$	−5.08870e6			−0.465102
$223$	−1.21133e7			−1.09232			−0.546159	−	0.837682i	$-0.683911\pi$
$223$	−1.21133e7			−1.09232			−0.546159	+	0.837682i	$0.683911\pi$
$224$		−	3.55332e6i		−	0.316148i
$225$	1.04784e7			0.919910
$226$	1.87418e6			0.162362
$227$			1.74805e7i			1.49443i	0.664580	+	0.747217i	$0.268610\pi$
$227$			1.74805e7i			1.49443i	−0.664580	+	0.747217i	$0.731390\pi$
$228$	103398.			0.00872381
$229$			1.33528e7i			1.11190i	0.831215	+	0.555952i	$0.187646\pi$
$229$			1.33528e7i			1.11190i	−0.831215	+	0.555952i	$0.812354\pi$
$230$	1.97430e6			0.162267
$231$			5.89944e6i			0.478603i
$232$		−	1.21335e7i		−	0.971676i
$233$			2.01747e6i			0.159492i	0.996815	+	0.0797462i	$0.0254110\pi$
$233$			2.01747e6i			0.159492i	−0.996815	+	0.0797462i	$0.974589\pi$
$234$	2.41729e6			0.188660
$235$		−	3.96746e7i		−	3.05709i
$236$	215035.	−	2.98680e6i	0.0163597	−	0.227232i
$237$	−515249.			−0.0387054
$238$		−	5.46464e6i		−	0.405350i
$239$	1.26466e7			0.926361			0.463180	−	0.886264i	$-0.346708\pi$
$239$	1.26466e7			0.926361			0.463180	+	0.886264i	$0.346708\pi$
$240$	1.11468e7			0.806339
$241$	2.18434e7			1.56052			0.780261	−	0.625454i	$-0.215086\pi$
$241$	2.18434e7			1.56052			0.780261	+	0.625454i	$0.215086\pi$
$242$			4.57791e6i			0.323014i
$243$	−920483.			−0.0641500
$244$			4.95997e6i			0.341436i
$245$	−1.41870e7			−0.964699
$246$		−	1.45726e7i		−	0.978885i
$247$		−	643736.i		−	0.0427186i
$248$	2.44101e6			0.160035
$249$		−	631968.i		−	0.0409352i
$250$		−	4.68494e7i		−	2.99836i
$251$	1.43275e7			0.906042			0.453021	−	0.891500i	$-0.350346\pi$
$251$	1.43275e7			0.906042			0.453021	+	0.891500i	$0.350346\pi$
$252$	861452.			0.0538307
$253$	1.80356e6			0.111370
$254$			1.22997e7i			0.750571i
$255$	−1.20796e7			−0.728503
$256$	−1.08262e7			−0.645295
$257$	−8.65834e6			−0.510076			−0.255038	−	0.966931i	$-0.582088\pi$
$257$	−8.65834e6			−0.510076			−0.255038	+	0.966931i	$0.582088\pi$
$258$	−1.72061e7			−1.00190
$259$			1.12903e7i			0.649842i
$260$			5.00074e6i			0.284521i
$261$	5.33737e6			0.300197
$262$	−1.31628e6			−0.0731888
$263$	−1.37885e7			−0.757965			−0.378982	−	0.925404i	$-0.623726\pi$
$263$	−1.37885e7			−0.757965			−0.378982	+	0.925404i	$0.623726\pi$
$264$	1.34036e7			0.728469
$265$	4.67517e7			2.51223
$266$			777564.i			0.0413134i
$267$		−	1.67507e7i		−	0.880036i
$268$		−	3.46516e6i		−	0.180019i
$269$		−	5.67928e6i		−	0.291767i	−0.989302	−	0.145884i	$-0.953398\pi$
$269$		−	5.67928e6i		−	0.291767i	0.989302	−	0.145884i	$-0.0466025\pi$
$270$			6.45427e6i			0.327911i
$271$	1.92958e7			0.969515			0.484757	−	0.874649i	$-0.338908\pi$
$271$	1.92958e7			0.969515			0.484757	+	0.874649i	$0.338908\pi$
$272$	−9.43235e6			−0.468720
$273$		−	5.36325e6i		−	0.263597i
$274$			1.42374e7i			0.692118i
$275$		−	6.71185e7i		−	3.22734i
$276$		−	263361.i		−	0.0125263i
$277$	−2.29460e6			−0.107961			−0.0539805	−	0.998542i	$-0.517191\pi$
$277$	−2.29460e6			−0.107961			−0.0539805	+	0.998542i	$0.517191\pi$
$278$			3.15185e6i			0.146700i
$279$			1.07377e6i			0.0494424i
$280$		−	3.25540e7i		−	1.48296i
$281$	−5.95760e6			−0.268505			−0.134252	−	0.990947i	$-0.542863\pi$
$281$	−5.95760e6			−0.268505			−0.134252	+	0.990947i	$0.542863\pi$
$282$	1.79381e7			0.799887
$283$		−	4.14139e6i		−	0.182720i	−0.995818	−	0.0913602i	$-0.970879\pi$
$283$		−	4.14139e6i		−	0.182720i	0.995818	−	0.0913602i	$-0.0291214\pi$
$284$	−5.14104e6			−0.224438
$285$	1.71880e6			0.0742492
$286$		−	1.54838e7i		−	0.661880i
$287$	−3.23323e7			−1.36770
$288$		−	3.55131e6i		−	0.148666i
$289$	−1.39159e7			−0.576526
$290$		−	3.74247e7i		−	1.53449i
$291$			2.27538e7i			0.923367i
$292$		−	6.65887e6i		−	0.267456i
$293$	−1.53783e7			−0.611372			−0.305686	−	0.952132i	$-0.598886\pi$
$293$	−1.53783e7			−0.611372			−0.305686	+	0.952132i	$0.598886\pi$
$294$		−	6.41437e6i		−	0.252413i
$295$	3.57459e6	−	4.96503e7i	0.139239	−	1.93400i
$296$	2.56519e7			0.989108
$297$			5.89611e6i			0.225059i
$298$	1.40264e7			0.530025
$299$	−1.63964e6			−0.0613387
$300$	−9.80083e6			−0.362994
$301$			3.81753e7i			1.39985i
$302$	1.50314e7			0.545733
$303$		−	4.11705e6i		−	0.147999i
$304$	1.34213e6			0.0477721
$305$			8.24508e7i			2.90600i
$306$		−	5.46154e6i		−	0.190612i
$307$	1.16956e7			0.404210			0.202105	−	0.979364i	$-0.435222\pi$
$307$	1.16956e7			0.404210			0.202105	+	0.979364i	$0.435222\pi$
$308$		−	5.51799e6i		−	0.188855i
$309$			6.39776e6i			0.216846i
$310$	7.52910e6			0.252731
$311$	4.23584e7			1.40818			0.704090	−	0.710110i	$-0.251355\pi$
$311$	4.23584e7			1.40818			0.704090	+	0.710110i	$0.251355\pi$
$312$	−1.21854e7			−0.401214
$313$		−	1.68961e7i		−	0.551002i	−0.961301	−	0.275501i	$-0.911156\pi$
$313$		−	1.68961e7i		−	0.551002i	0.961301	−	0.275501i	$-0.0888437\pi$
$314$	2.99908e7			0.968721
$315$	1.43201e7			0.458158
$316$	481933.			0.0152730
$317$	−1.41974e7			−0.445688			−0.222844	−	0.974854i	$-0.571534\pi$
$317$	−1.41974e7			−0.445688			−0.222844	+	0.974854i	$0.571534\pi$
$318$			2.11379e7i			0.657325i
$319$		−	3.41883e7i		−	1.05319i
$320$	−7.06656e7			−2.15654
$321$	−1.73182e7			−0.523587
$322$	1.98051e6			0.0593211
$323$	−1.45444e6			−0.0431606
$324$	860965.			0.0253134
$325$			6.10182e7i			1.77750i
$326$			3.88182e7i			1.12042i
$327$			3.27040e7i			0.935314i
$328$			7.34596e7i			2.08174i
$329$		−	3.97993e7i		−	1.11760i
$330$	4.13425e7			1.15042
$331$	−5.51311e7			−1.52024			−0.760121	−	0.649781i	$-0.774860\pi$
$331$	−5.51311e7			−1.52024			−0.760121	+	0.649781i	$0.774860\pi$
$332$			591105.i			0.0161529i
$333$			1.12840e7i			0.305583i
$334$			1.12469e7i			0.301851i
$335$		−	5.76021e7i		−	1.53216i
$336$	1.11819e7			0.294779
$337$			6.03833e7i			1.57771i	0.614580	+	0.788855i	$0.289326\pi$
$337$			6.03833e7i			1.57771i	−0.614580	+	0.788855i	$0.710674\pi$
$338$		−	1.98555e7i		−	0.514198i
$339$		−	4.15589e6i		−	0.106676i
$340$	1.12985e7			0.287465
$341$	6.87799e6			0.173460
$342$			777124.i			0.0194273i
$343$	−4.28365e7			−1.06153
$344$	8.67350e7			2.13068
$345$		−	4.37791e6i		−	0.106613i
$346$	3.27536e7			0.790734
$347$			8.76068e6i			0.209676i	0.994489	+	0.104838i	$0.0334325\pi$
$347$			8.76068e6i			0.209676i	−0.994489	+	0.104838i	$0.966568\pi$
$348$	−4.99226e6			−0.118457
$349$			4.14009e7i			0.973943i	0.873418	+	0.486971i	$0.161898\pi$
$349$			4.14009e7i			0.973943i	−0.873418	+	0.486971i	$0.838102\pi$
$350$		−	7.37035e7i		−	1.71903i
$351$		−	5.36021e6i		−	0.123954i
$352$	−2.27477e7			−0.521567
$353$			3.12584e7i			0.710629i	0.934747	+	0.355315i	$0.115626\pi$
$353$			3.12584e7i			0.710629i	−0.934747	+	0.355315i	$0.884374\pi$
$354$	2.24484e7	+	1.61618e6i	0.506030	+	0.0364317i
$355$	−8.54607e7			−1.91021
$356$			1.56676e7i			0.347259i
$357$	−1.21176e7			−0.266324
$358$	−5.87268e7			−1.27993
$359$	−2.79538e7			−0.604168			−0.302084	−	0.953281i	$-0.597682\pi$
$359$	−2.79538e7			−0.604168			−0.302084	+	0.953281i	$0.597682\pi$
$360$		−	3.25356e7i		−	0.697351i
$361$	−4.68389e7			−0.995601
$362$			2.00447e7i			0.422545i
$363$	1.01513e7			0.212227
$364$			5.01646e6i			0.104014i
$365$		−	1.10692e8i		−	2.27634i
$366$	−3.72785e7			−0.760353
$367$		−	1.31779e7i		−	0.266592i	−0.991076	−	0.133296i	$-0.957444\pi$
$367$		−	1.31779e7i		−	0.266592i	0.991076	−	0.133296i	$-0.0425562\pi$
$368$		−	3.41850e6i		−	0.0685949i
$369$	−3.23140e7			−0.643149
$370$	7.91211e7			1.56202
$371$	4.68987e7			0.918416
$372$		−	1.00434e6i		−	0.0195098i
$373$	4.74124e7			0.913619			0.456810	−	0.889564i	$-0.348992\pi$
$373$	4.74124e7			0.913619			0.456810	+	0.889564i	$0.348992\pi$
$374$	−3.49836e7			−0.668729
$375$	−1.03886e8			−1.96999
$376$	−9.04248e7			−1.70108
$377$			3.10809e7i			0.580056i
$378$			6.47457e6i			0.119877i
$379$	8.30070e7			1.52475			0.762373	−	0.647138i	$-0.224034\pi$
$379$	8.30070e7			1.52475			0.762373	+	0.647138i	$0.224034\pi$
$380$	−1.60767e6			−0.0292985
$381$	2.72739e7			0.493142
$382$	6.37801e7			1.14418
$383$	−5.00229e7			−0.890375			−0.445187	−	0.895437i	$-0.646863\pi$
$383$	−5.00229e7			−0.890375			−0.445187	+	0.895437i	$0.646863\pi$
$384$		−	1.73698e7i		−	0.306762i
$385$		−	9.17268e7i		−	1.60736i
$386$			5.12847e7i			0.891715i
$387$			3.81537e7i			0.658269i
$388$		−	2.12825e7i		−	0.364358i
$389$	5.23965e7			0.890131			0.445065	−	0.895498i	$-0.353180\pi$
$389$	5.23965e7			0.890131			0.445065	+	0.895498i	$0.353180\pi$
$390$	−3.75849e7			−0.633606
$391$			3.70455e6i			0.0619734i
$392$			3.23344e7i			0.536794i
$393$			2.91879e6i			0.0480867i
$394$		−	5.46286e6i		−	0.0893164i
$395$	8.01129e6			0.129990
$396$		−	5.51487e6i		−	0.0888074i
$397$			3.41681e6i			0.0546072i	0.999627	+	0.0273036i	$0.00869209\pi$
$397$			3.41681e6i			0.0546072i	−0.999627	+	0.0273036i	$0.991308\pi$
$398$		−	5.45446e7i		−	0.865172i
$399$	1.72421e6			0.0271439
$400$	−1.27217e8			−1.98777
$401$			1.60966e7i			0.249633i	0.992180	+	0.124817i	$0.0398342\pi$
$401$			1.60966e7i			0.249633i	−0.992180	+	0.124817i	$0.960166\pi$
$402$	2.60437e7			0.400889
$403$	−6.25286e6			−0.0955352
$404$			3.85084e6i			0.0583998i
$405$	1.43120e7			0.215445
$406$		−	3.75424e7i		−	0.560976i
$407$	7.22788e7			1.07208
$408$			2.75313e7i			0.405365i
$409$			6.15574e7i			0.899726i	0.893097	+	0.449863i	$0.148527\pi$
$409$			6.15574e7i			0.899726i	−0.893097	+	0.449863i	$0.851473\pi$
$410$			2.26580e8i			3.28754i
$411$	3.15708e7			0.454737
$412$		−	5.98408e6i		−	0.0855669i
$413$	3.58583e6	−	4.98064e7i	0.0509025	−	0.707026i
$414$	1.97939e6			0.0278952
$415$			9.82607e6i			0.137479i
$416$	2.06802e7			0.287260
$417$	6.98907e6			0.0963854
$418$	4.97783e6			0.0681571
$419$			8.43328e7i			1.14645i	0.819399	+	0.573224i	$0.194308\pi$
$419$			8.43328e7i			1.14645i	−0.819399	+	0.573224i	$0.805692\pi$
$420$	−1.33942e7			−0.180788
$421$			1.10031e8i			1.47458i	0.675578	+	0.737288i	$0.263894\pi$
$421$			1.10031e8i			1.47458i	−0.675578	+	0.737288i	$0.736106\pi$
$422$	−5.16941e7			−0.687866
$423$		−	3.97768e7i		−	0.525544i
$424$		−	1.06555e8i		−	1.39790i
$425$	1.37863e8			1.79589
$426$		−	3.86394e7i		−	0.499806i
$427$			8.27101e7i			1.06237i
$428$	1.61984e7			0.206606
$429$	−3.43346e7			−0.434870
$430$	2.67527e8			3.36482
$431$		−	7.18805e7i		−	0.897799i	−0.893582	−	0.448900i	$-0.851816\pi$
$431$		−	7.18805e7i		−	0.897799i	0.893582	−	0.448900i	$-0.148184\pi$
$432$	1.11756e7			0.138617
$433$	−7.25464e7			−0.893618			−0.446809	−	0.894629i	$-0.647440\pi$
$433$	−7.25464e7			−0.893618			−0.446809	+	0.894629i	$0.647440\pi$
$434$	7.55278e6			0.0923927
$435$	−8.29875e7			−1.00820
$436$		−	3.05894e7i		−	0.369072i
$437$		−	527121.i		−	0.00631635i
$438$	5.00472e7			0.595604
$439$	1.41616e7			0.167386			0.0836930	−	0.996492i	$-0.473328\pi$
$439$	1.41616e7			0.167386			0.0836930	+	0.996492i	$0.473328\pi$
$440$	−2.08405e8			−2.44653
$441$	−1.42235e7			−0.165841
$442$	3.18040e7			0.368311
$443$			1.02675e8i			1.18101i	0.807034	+	0.590504i	$0.201071\pi$
$443$			1.02675e8i			1.18101i	−0.807034	+	0.590504i	$0.798929\pi$
$444$		−	1.05543e7i		−	0.120582i
$445$			2.60447e8i			2.95556i
$446$			8.51555e7i			0.959861i
$447$		−	3.11028e7i		−	0.348238i
$448$	−7.08878e7			−0.788384
$449$	2.43759e7			0.269290			0.134645	−	0.990894i	$-0.457011\pi$
$449$	2.43759e7			0.269290			0.134645	+	0.990894i	$0.457011\pi$
$450$		−	7.36618e7i		−	0.808360i
$451$			2.06986e8i			2.25637i
$452$			3.88718e6i			0.0420939i
$453$		−	3.33315e7i		−	0.358559i
$454$	1.22886e8			1.31322
$455$			8.33899e7i			0.885277i
$456$		−	3.91744e6i		−	0.0413150i
$457$		−	5.10616e7i		−	0.534990i	−0.963559	−	0.267495i	$-0.913804\pi$
$457$		−	5.10616e7i		−	0.534990i	0.963559	−	0.267495i	$-0.0861959\pi$
$458$	9.38691e7			0.977071
$459$	−1.21107e7			−0.125237
$460$			4.09484e6i			0.0420691i
$461$	−1.05217e8			−1.07395			−0.536976	−	0.843598i	$-0.680433\pi$
$461$	−1.05217e8			−1.07395			−0.536976	+	0.843598i	$0.680433\pi$
$462$	4.14725e7			0.420566
$463$			9.27594e7i			0.934577i	0.884105	+	0.467288i	$0.154769\pi$
$463$			9.27594e7i			0.934577i	−0.884105	+	0.467288i	$0.845231\pi$
$464$	−6.48009e7			−0.648675
$465$		−	1.66954e7i		−	0.166050i
$466$	1.41826e7			0.140152
$467$			9.12870e7i			0.896310i	0.893956	+	0.448155i	$0.147919\pi$
$467$			9.12870e7i			0.896310i	−0.893956	+	0.448155i	$0.852081\pi$
$468$			5.01362e6i			0.0489119i
$469$		−	5.77833e7i		−	0.560124i
$470$	−2.78908e8			−2.68638
$471$		−	6.65031e7i		−	0.636471i
$472$	−1.13161e8	−	8.14707e6i	−1.07615	−	0.0774774i
$473$	2.44391e8			2.30942
$474$			3.62215e6i			0.0340119i
$475$	−1.96165e7			−0.183038
$476$	1.13340e7			0.105091
$477$	4.68722e7			0.431877
$478$		−	8.89044e7i		−	0.814028i
$479$	1.64950e8			1.50088			0.750441	−	0.660938i	$-0.229841\pi$
$479$	1.64950e8			1.50088			0.750441	+	0.660938i	$0.229841\pi$
$480$			5.52171e7i			0.499287i
$481$	−6.57094e7			−0.590463
$482$		−	1.53557e8i		−	1.37129i
$483$		−	4.39168e6i		−	0.0389753i
$484$	−9.49492e6			−0.0837443
$485$		−	3.53784e8i		−	3.10108i
$486$			6.47090e6i			0.0563710i
$487$	−1.45605e8			−1.26063			−0.630315	−	0.776339i	$-0.717074\pi$
$487$	−1.45605e8			−1.26063			−0.630315	+	0.776339i	$0.717074\pi$
$488$	1.87919e8			1.61700
$489$	8.60775e7			0.736144
$490$			9.97330e7i			0.847717i
$491$	1.50309e8			1.26981			0.634907	−	0.772589i	$-0.281038\pi$
$491$	1.50309e8			1.26981			0.634907	+	0.772589i	$0.281038\pi$
$492$	3.02246e7			0.253785
$493$	7.02233e7			0.586058
$494$	−4.52540e6			−0.0375384
$495$		−	9.16749e7i		−	0.755849i
$496$		−	1.30366e7i		−	0.106837i
$497$	−8.57295e7			−0.698331
$498$	−4.44267e6			−0.0359713
$499$	7.21471e7			0.580654			0.290327	−	0.956927i	$-0.406236\pi$
$499$	7.21471e7			0.580654			0.290327	+	0.956927i	$0.406236\pi$
$500$	9.71689e7			0.777351
$501$	2.49394e7			0.198323
$502$		−	1.00721e8i		−	0.796173i
$503$		−	1.37613e8i		−	1.08132i	−0.841240	−	0.540662i	$-0.818174\pi$
$503$		−	1.37613e8i		−	1.08132i	0.841240	−	0.540662i	$-0.181826\pi$
$504$		−	3.26379e7i		−	0.254936i
$505$			6.40134e7i			0.497046i
$506$		−	1.26789e7i		−	0.0978653i
$507$	−4.40286e7			−0.337840
$508$	−2.55104e7			−0.194592
$509$			9.86537e7i			0.748101i	0.927408	+	0.374050i	$0.122031\pi$
$509$			9.86537e7i			0.748101i	−0.927408	+	0.374050i	$0.877969\pi$
$510$			8.49182e7i			0.640162i
$511$		−	1.11040e8i		−	0.832180i
$512$			1.47421e8i			1.09837i
$513$	1.72323e6			0.0127642
$514$			6.08672e7i			0.448223i
$515$		−	9.94748e7i		−	0.728268i
$516$		−	3.56867e7i		−	0.259751i
$517$	−2.54788e8			−1.84378
$518$	7.93700e7			0.571041
$519$		−	7.26294e7i		−	0.519530i
$520$	1.89463e8			1.34746
$521$	−1.22686e8			−0.867524			−0.433762	−	0.901028i	$-0.642814\pi$
$521$	−1.22686e8			−0.867524			−0.433762	+	0.901028i	$0.642814\pi$
$522$		−	3.75212e7i		−	0.263794i
$523$	1.06812e8			0.746645			0.373323	−	0.927702i	$-0.378218\pi$
$523$	1.06812e8			0.746645			0.373323	+	0.927702i	$0.378218\pi$
$524$		−	2.73006e6i		−	0.0189749i
$525$	−1.63434e8			−1.12944
$526$			9.69316e7i			0.666052i
$527$			1.41275e7i			0.0965237i
$528$		−	7.15844e7i		−	0.486314i
$529$	1.46693e8			0.990930
$530$		−	3.28660e8i		−	2.20759i
$531$	3.58380e6	−	4.97783e7i	0.0239365	−	0.332473i
$532$	−1.61272e6			−0.0107109
$533$		−	1.88173e8i		−	1.24273i
$534$	−1.17756e8			−0.773320
$535$	2.69271e8			1.75844
$536$	−1.31285e8			−0.852550
$537$			1.30224e8i			0.840945i
$538$	−3.99248e7			−0.256387
$539$			9.11082e7i			0.581823i
$540$	−1.33866e7			−0.0850138
$541$			8.06570e7i			0.509390i	0.967021	+	0.254695i	$0.0819750\pi$
$541$			8.06570e7i			0.509390i	−0.967021	+	0.254695i	$0.918025\pi$
$542$		−	1.35647e8i		−	0.851949i
$543$	4.44481e7			0.277622
$544$		−	4.67242e7i		−	0.290232i
$545$		−	5.08494e8i		−	3.14121i
$546$	−3.77031e7			−0.231632
$547$	−8.28546e7			−0.506238			−0.253119	−	0.967435i	$-0.581456\pi$
$547$	−8.28546e7			−0.506238			−0.253119	+	0.967435i	$0.581456\pi$
$548$	−2.95295e7			−0.179438
$549$			8.26633e7i			0.499569i
$550$	−4.71837e8			−2.83598
$551$	−9.99209e6			−0.0597312
$552$	−9.97798e6			−0.0593233
$553$	8.03648e6			0.0475216
$554$			1.61308e7i			0.0948694i
$555$		−	1.75447e8i		−	1.02628i
$556$	−6.53716e6			−0.0380334
$557$	−1.37517e8			−0.795774			−0.397887	−	0.917434i	$-0.630256\pi$
$557$	−1.37517e8			−0.795774			−0.397887	+	0.917434i	$0.630256\pi$
$558$	7.54851e6			0.0434469
$559$	−2.22179e8			−1.27194
$560$	−1.73860e8			−0.990002
$561$			7.75745e7i			0.439370i
$562$			4.18813e7i			0.235945i
$563$			6.42052e6i			0.0359786i	0.999838	+	0.0179893i	$0.00572649\pi$
$563$			6.42052e6i			0.0359786i	−0.999838	+	0.0179893i	$0.994274\pi$
$564$			3.72049e7i			0.207378i
$565$			6.46174e7i			0.358265i
$566$	−2.91136e7			−0.160563
$567$	1.43570e7			0.0787618
$568$			1.94779e8i			1.06291i
$569$			9.06946e7i			0.492317i	0.969230	+	0.246158i	$0.0791684\pi$
$569$			9.06946e7i			0.492317i	−0.969230	+	0.246158i	$0.920832\pi$
$570$		−	1.20830e7i		−	0.0652456i
$571$		−	5.56109e7i		−	0.298711i	−0.988784	−	0.149356i	$-0.952280\pi$
$571$		−	5.56109e7i		−	0.298711i	0.988784	−	0.149356i	$-0.0477199\pi$
$572$	3.21145e7			0.171598
$573$		−	1.41429e8i		−	0.751754i
$574$			2.27293e8i			1.20185i
$575$			4.99646e7i			0.262820i
$576$	−7.08477e7			−0.370731
$577$	1.05665e8			0.550050			0.275025	−	0.961437i	$-0.411314\pi$
$577$	1.05665e8			0.550050			0.275025	+	0.961437i	$0.411314\pi$
$578$			9.78277e7i			0.506615i
$579$	1.13721e8			0.585877
$580$	7.76216e7			0.397831
$581$			9.85698e6i			0.0502592i
$582$	1.59957e8			0.811397
$583$		−	3.00237e8i		−	1.51516i
$584$	−2.52285e8			−1.26664
$585$			8.33427e7i			0.416294i
$586$			1.08108e8i			0.537236i
$587$		−	3.43340e8i		−	1.69750i	−0.528792	−	0.848752i	$-0.677355\pi$
$587$		−	3.43340e8i		−	1.69750i	0.528792	−	0.848752i	$-0.322645\pi$
$588$	1.33039e7			0.0654403
$589$		−	2.01021e6i		−	0.00983773i
$590$	−3.49037e8	−	2.51290e7i	−1.69948	−	0.122354i
$591$	−1.21136e7			−0.0586829
$592$		−	1.36998e8i		−	0.660312i
$593$	2.14834e8			1.03024			0.515121	−	0.857118i	$-0.327747\pi$
$593$	2.14834e8			1.03024			0.515121	+	0.857118i	$0.327747\pi$
$594$	4.14490e7			0.197768
$595$	1.88409e8			0.894437
$596$			2.90917e7i			0.137414i
$597$	−1.20950e8			−0.568437
$598$			1.15265e7i			0.0539006i
$599$	−3.49377e8			−1.62560			−0.812800	−	0.582543i	$-0.802058\pi$
$599$	−3.49377e8			−1.62560			−0.812800	+	0.582543i	$0.802058\pi$
$600$			3.71325e8i			1.71910i
$601$			1.07047e8i			0.493117i	0.969128	+	0.246558i	$0.0792997\pi$
$601$			1.07047e8i			0.493117i	−0.969128	+	0.246558i	$0.920700\pi$
$602$	2.68369e8			1.23010
$603$		−	5.77506e7i		−	0.263393i
$604$			3.11763e7i			0.141486i
$605$	−1.57836e8			−0.712755
$606$	−2.89424e7			−0.130052
$607$	1.14105e8			0.510197			0.255098	−	0.966915i	$-0.417892\pi$
$607$	1.14105e8			0.510197			0.255098	+	0.966915i	$0.417892\pi$
$608$			6.64840e6i			0.0295806i
$609$	−8.32485e7			−0.368574
$610$	5.79621e8			2.55361
$611$	2.31631e8			1.01548
$612$	1.13276e7			0.0494180
$613$		−	2.88932e8i		−	1.25434i	−0.778884	−	0.627169i	$-0.784214\pi$
$613$		−	2.88932e8i		−	1.25434i	0.778884	−	0.627169i	$-0.215786\pi$
$614$		−	8.22189e7i		−	0.355195i
$615$	5.02431e8			2.15998
$616$	−2.09060e8			−0.894396
$617$	−2.75011e8			−1.17083			−0.585415	−	0.810734i	$-0.699068\pi$
$617$	−2.75011e8			−1.17083			−0.585415	+	0.810734i	$0.699068\pi$
$618$	4.49756e7			0.190551
$619$	−3.55949e8			−1.50078			−0.750388	−	0.660998i	$-0.770133\pi$
$619$	−3.55949e8			−1.50078			−0.750388	+	0.660998i	$0.770133\pi$
$620$			1.56159e7i			0.0655227i
$621$		−	4.38919e6i		−	0.0183278i
$622$		−	2.97775e8i		−	1.23742i
$623$			2.61266e8i			1.08049i
$624$			6.50782e7i			0.267844i
$625$	9.41500e8			3.85638
$626$	−1.18778e8			−0.484186
$627$		−	1.10381e7i		−	0.0447807i
$628$			6.22030e7i			0.251150i
$629$			1.48462e8i			0.596572i
$630$		−	1.00669e8i		−	0.402600i
$631$	−1.67383e8			−0.666228			−0.333114	−	0.942887i	$-0.608099\pi$
$631$	−1.67383e8			−0.666228			−0.333114	+	0.942887i	$0.608099\pi$
$632$		−	1.82590e7i		−	0.0723314i
$633$			1.14629e8i			0.451944i
$634$			9.98063e7i			0.391643i
$635$	−4.24065e8			−1.65619
$636$	−4.38415e7			−0.170417
$637$		−	8.28274e7i		−	0.320447i
$638$	−2.40340e8			−0.925474
$639$	−8.56810e7			−0.328384
$640$			2.70073e8i			1.03024i
$641$	−2.37255e8			−0.900826			−0.450413	−	0.892820i	$-0.648723\pi$
$641$	−2.37255e8			−0.900826			−0.450413	+	0.892820i	$0.648723\pi$
$642$			1.21745e8i			0.460095i
$643$	6.55653e7			0.246627			0.123314	−	0.992368i	$-0.460648\pi$
$643$	6.55653e7			0.246627			0.123314	+	0.992368i	$0.460648\pi$
$644$			4.10772e6i			0.0153795i
$645$		−	5.93228e8i		−	2.21077i
$646$			1.02245e7i			0.0379268i
$647$	−3.23977e8			−1.19619			−0.598096	−	0.801425i	$-0.704076\pi$
$647$	−3.23977e8			−1.19619			−0.598096	+	0.801425i	$0.704076\pi$
$648$		−	3.26194e7i		−	0.119881i
$649$	−3.18852e8	−	2.29558e7i	−1.16642	−	0.0839767i
$650$	4.28952e8			1.56195
$651$		−	1.67479e7i		−	0.0607041i
$652$	−8.05117e7			−0.290480
$653$	3.44498e8			1.23722			0.618611	−	0.785697i	$-0.287696\pi$
$653$	3.44498e8			1.23722			0.618611	+	0.785697i	$0.287696\pi$
$654$	2.29906e8			0.821896
$655$		−	4.53824e7i		−	0.161497i
$656$	3.92323e8			1.38974
$657$		−	1.10977e8i		−	0.391325i
$658$	−2.79785e8			−0.982081
$659$			9.99031e7i			0.349078i	0.984650	+	0.174539i	$0.0558436\pi$
$659$			9.99031e7i			0.349078i	−0.984650	+	0.174539i	$0.944156\pi$
$660$			8.57472e7i			0.298255i
$661$	2.49357e8			0.863409			0.431705	−	0.902015i	$-0.357912\pi$
$661$	2.49357e8			0.863409			0.431705	+	0.902015i	$0.357912\pi$
$662$			3.87566e8i			1.33589i
$663$		−	7.05238e7i		−	0.241989i
$664$	2.23952e7			0.0764982
$665$	−2.68087e7			−0.0911613
$666$	7.93250e7			0.268527
$667$			2.54505e7i			0.0857668i
$668$	−2.33268e7			−0.0782575
$669$	1.88828e8			0.630650
$670$	−4.04937e8			−1.34637
$671$	5.29495e8			1.75265
$672$			5.53908e7i			0.182528i
$673$			9.58193e6i			0.0314346i	0.999876	+	0.0157173i	$0.00500317\pi$
$673$			9.58193e6i			0.0314346i	−0.999876	+	0.0157173i	$0.994997\pi$
$674$	4.24488e8			1.38639
$675$	−1.63341e8			−0.531110
$676$	4.11817e7			0.133310
$677$	−4.60108e8			−1.48284			−0.741420	−	0.671042i	$-0.765847\pi$
$677$	−4.60108e8			−1.48284			−0.741420	+	0.671042i	$0.765847\pi$
$678$	−2.92155e7			−0.0937399
$679$		−	3.54897e8i		−	1.13369i
$680$		−	4.28068e8i		−	1.36140i
$681$		−	2.72494e8i		−	0.862812i
$682$		−	4.83516e7i		−	0.152425i
$683$			3.83112e8i			1.20244i	0.799083	+	0.601221i	$0.205319\pi$
$683$			3.83112e8i			1.20244i	−0.799083	+	0.601221i	$0.794681\pi$
$684$	−1.61181e6			−0.00503670
$685$	−4.90875e8			−1.52721
$686$			3.01136e8i			0.932805i
$687$		−	2.08150e8i		−	0.641958i
$688$		−	4.63223e8i		−	1.42241i
$689$			2.72949e8i			0.834496i
$690$	−3.07763e7			−0.0936847
$691$			3.91705e8i			1.18720i	0.804759	+	0.593602i	$0.202294\pi$
$691$			3.91705e8i			1.18720i	−0.804759	+	0.593602i	$0.797706\pi$
$692$			6.79332e7i			0.205005i
$693$		−	9.19632e7i		−	0.276321i
$694$	6.15867e7			0.184250
$695$	−1.08669e8			−0.323706
$696$			1.89142e8i			0.560997i
$697$	−4.25152e8			−1.25559
$698$	2.91044e8			0.855840
$699$		−	3.14493e7i		−	0.0920829i
$700$	1.52866e8			0.445674
$701$		−	5.84516e8i		−	1.69685i	−0.529318	−	0.848423i	$-0.677552\pi$
$701$		−	5.84516e8i		−	1.69685i	0.529318	−	0.848423i	$-0.322448\pi$
$702$	−3.76818e7			−0.108923
$703$		−	2.11247e7i		−	0.0608029i
$704$			4.53811e8i			1.30064i
$705$			6.18465e8i			1.76501i
$706$	2.19744e8			0.624456
$707$			6.42148e7i			0.181709i
$708$	−3.35207e6	+	4.65596e7i	−0.00944525	+	0.131193i
$709$	1.79681e8			0.504154			0.252077	−	0.967707i	$-0.418886\pi$
$709$	1.79681e8			0.504154			0.252077	+	0.967707i	$0.418886\pi$
$710$			6.00780e8i			1.67857i
$711$	8.03193e6			0.0223466
$712$	5.93601e8			1.64458
$713$	−5.12013e6			−0.0141258
$714$			8.51853e7i			0.234029i
$715$	5.33847e8			1.46049
$716$		−	1.21804e8i		−	0.331834i
$717$	−1.97141e8			−0.534835
$718$			1.96512e8i			0.530905i
$719$			4.43984e7i			0.119448i	0.998215	+	0.0597242i	$0.0190221\pi$
$719$			4.43984e7i			0.119448i	−0.998215	+	0.0597242i	$0.980978\pi$
$720$	−1.73762e8			−0.465540
$721$		−	9.97877e7i		−	0.266239i
$722$			3.29273e8i			0.874872i
$723$	−3.40505e8			−0.900968
$724$	−4.15741e7			−0.109549
$725$	9.47127e8			2.48539
$726$		−	7.13626e7i		−	0.186492i
$727$	−1.40640e8			−0.366021			−0.183011	−	0.983111i	$-0.558584\pi$
$727$	−1.40640e8			−0.366021			−0.183011	+	0.983111i	$0.558584\pi$
$728$	1.90059e8			0.492600
$729$	1.43489e7			0.0370370
$730$	−7.78153e8			−2.00031
$731$			5.01985e8i			1.28510i
$732$		−	7.73183e7i		−	0.197128i
$733$	3.63182e8			0.922173			0.461087	−	0.887355i	$-0.347460\pi$
$733$	3.63182e8			0.922173			0.461087	+	0.887355i	$0.347460\pi$
$734$	−9.26393e7			−0.234265
$735$	2.21153e8			0.556969
$736$	1.69339e7			0.0424741
$737$	−3.69918e8			−0.924067
$738$			2.27164e8i			0.565159i
$739$		−	5.57713e6i		−	0.0138190i	−0.999976	−	0.00690951i	$-0.997801\pi$
$739$		−	5.57713e6i		−	0.0138190i	0.999976	−	0.00690951i	$-0.00219938\pi$
$740$			1.64103e8i			0.404968i
$741$			1.00348e7i			0.0246636i
$742$		−	3.29693e8i		−	0.807047i
$743$	3.32916e8			0.811648			0.405824	−	0.913951i	$-0.366985\pi$
$743$	3.32916e8			0.811648			0.405824	+	0.913951i	$0.366985\pi$
$744$	−3.80516e7			−0.0923962
$745$			4.83597e8i			1.16954i
$746$		−	3.33304e8i		−	0.802832i
$747$			9.85140e6i			0.0236339i
$748$		−	7.25586e7i		−	0.173374i
$749$	2.70117e8			0.642846
$750$			7.30309e8i			1.73110i
$751$		−	3.17334e8i		−	0.749199i	−0.927187	−	0.374599i	$-0.877780\pi$
$751$		−	3.17334e8i		−	0.749199i	0.927187	−	0.374599i	$-0.122220\pi$
$752$			4.82929e8i			1.13561i
$753$	−2.23343e8			−0.523104
$754$	2.18496e8			0.509717
$755$			5.18251e8i			1.20420i
$756$	−1.34287e7			−0.0310791
$757$	−4.60544e8			−1.06165			−0.530827	−	0.847480i	$-0.678119\pi$
$757$	−4.60544e8			−1.06165			−0.530827	+	0.847480i	$0.678119\pi$
$758$		−	5.83531e8i		−	1.33985i
$759$	−2.81148e7			−0.0642997
$760$			6.09098e7i			0.138754i
$761$	6.75942e8			1.53375			0.766877	−	0.641795i	$-0.221810\pi$
$761$	6.75942e8			1.53375			0.766877	+	0.641795i	$0.221810\pi$
$762$		−	1.91733e8i		−	0.433343i
$763$		−	5.10094e8i		−	1.14836i
$764$			1.32285e8i			0.296640i
$765$	1.88302e8			0.420601
$766$			3.51656e8i			0.782405i
$767$	2.89872e8	+	2.08694e7i	0.642421	+	0.0462513i
$768$	1.68764e8			0.372561
$769$			6.34399e8i			1.39503i	0.716571	+	0.697514i	$0.245711\pi$
$769$			6.34399e8i			1.39503i	−0.716571	+	0.697514i	$0.754289\pi$
$770$	−6.44830e8			−1.41245
$771$	1.34970e8			0.294493
$772$	−1.06368e8			−0.231185
$773$		−	8.78120e8i		−	1.90115i	−0.310501	−	0.950573i	$-0.600497\pi$
$773$		−	8.78120e8i		−	1.90115i	0.310501	−	0.950573i	$-0.399503\pi$
$774$	2.68217e8			0.578446
$775$			1.90543e8i			0.409343i
$776$	−8.06333e8			−1.72556
$777$		−	1.75999e8i		−	0.375186i
$778$		−	3.68342e8i		−	0.782191i
$779$	6.04950e7			0.127970
$780$		−	7.79538e7i		−	0.164268i
$781$			5.48825e8i			1.15207i
$782$	2.60426e7			0.0544583
$783$	−8.32014e7			−0.173319
$784$	1.72688e8			0.358355
$785$			1.03402e9i			2.13756i
$786$	2.05188e7			0.0422556
$787$	4.50279e8			0.923757			0.461878	−	0.886943i	$-0.347176\pi$
$787$	4.50279e8			0.923757			0.461878	+	0.886943i	$0.347176\pi$
$788$	1.13304e7			0.0231561
$789$	2.14941e8			0.437611
$790$		−	5.63185e7i		−	0.114227i
$791$			6.48207e7i			0.130974i
$792$	−2.08942e8			−0.420582
$793$	−4.81370e8			−0.965294
$794$	2.40199e7			0.0479854
$795$	−7.28787e8			−1.45044
$796$	1.13129e8			0.224303
$797$			7.09594e8i			1.40164i	0.713340	+	0.700818i	$0.247181\pi$
$797$			7.09594e8i			1.40164i	−0.713340	+	0.700818i	$0.752819\pi$
$798$		−	1.21210e7i		−	0.0238523i
$799$		−	5.23340e8i		−	1.02599i
$800$		−	6.30186e8i		−	1.23083i
$801$			2.61118e8i			0.508089i
$802$	1.13158e8			0.219362
$803$	−7.10859e8			−1.37289
$804$			5.40165e7i			0.103934i
$805$			6.82835e7i			0.130897i
$806$			4.39570e7i			0.0839503i
$807$			8.85312e7i			0.168452i
$808$	1.45897e8			0.276575
$809$		−	9.28962e8i		−	1.75450i	−0.480038	−	0.877248i	$-0.659377\pi$
$809$		−	9.28962e8i		−	1.75450i	0.480038	−	0.877248i	$-0.340623\pi$
$810$		−	1.00612e8i		−	0.189319i
$811$		−	5.31263e8i		−	0.995972i	−0.867185	−	0.497986i	$-0.834073\pi$
$811$		−	5.31263e8i		−	0.995972i	0.867185	−	0.497986i	$-0.165927\pi$
$812$	7.78657e7			0.145438
$813$	−3.00791e8			−0.559750
$814$		−	5.08112e8i		−	0.942078i
$815$	−1.33837e9			−2.47230
$816$	1.47036e8			0.270615
$817$		−	7.14275e7i		−	0.130978i
$818$	4.32742e8			0.790623
$819$			8.36048e7i			0.152188i
$820$	−4.69944e8			−0.852323
$821$		−	5.91335e8i		−	1.06857i	−0.845303	−	0.534287i	$-0.820580\pi$
$821$		−	5.91335e8i		−	1.06857i	0.845303	−	0.534287i	$-0.179420\pi$
$822$		−	2.21940e8i		−	0.399595i
$823$			3.62827e8i			0.650879i	0.945563	+	0.325439i	$0.105512\pi$
$823$			3.62827e8i			0.650879i	−0.945563	+	0.325439i	$0.894488\pi$
$824$	−2.26719e8			−0.405235
$825$			1.04627e9i			1.86330i
$826$	−3.50134e8	−	2.52080e7i	−0.621290	−	0.0447300i
$827$	−4.48415e8			−0.792799			−0.396400	−	0.918078i	$-0.629741\pi$
$827$	−4.48415e8			−0.792799			−0.396400	+	0.918078i	$0.629741\pi$
$828$			4.10539e6i			0.00723208i
$829$	2.31653e8			0.406606			0.203303	−	0.979116i	$-0.434832\pi$
$829$	2.31653e8			0.406606			0.203303	+	0.979116i	$0.434832\pi$
$830$	6.90763e7			0.120808
$831$	3.57692e7			0.0623313
$832$		−	4.12565e8i		−	0.716345i
$833$	−1.87138e8			−0.323763
$834$		−	4.91325e7i		−	0.0846975i
$835$	−3.87767e8			−0.666057
$836$			1.03244e7i			0.0176703i
$837$		−	1.67384e7i		−	0.0285456i
$838$	5.92851e8			1.00743
$839$		−	1.10355e9i		−	1.86856i	−0.356543	−	0.934279i	$-0.616045\pi$
$839$		−	1.10355e9i		−	1.86856i	0.356543	−	0.934279i	$-0.383955\pi$
$840$			5.07467e8i			0.856189i
$841$	−1.12384e8			−0.188937
$842$	7.73504e8			1.29577
$843$	9.28697e7			0.155021
$844$		−	1.07217e8i		−	0.178335i
$845$	6.84573e8			1.13462
$846$	−2.79627e8			−0.461815
$847$	−1.58333e8			−0.260568
$848$	−5.69074e8			−0.933214
$849$			6.45579e7i			0.105494i
$850$		−	9.69161e8i		−	1.57812i
$851$	−5.38060e7			−0.0873055
$852$	8.01409e7			0.129579
$853$	−5.49608e8			−0.885535			−0.442768	−	0.896636i	$-0.646003\pi$
$853$	−5.49608e8			−0.885535			−0.442768	+	0.896636i	$0.646003\pi$
$854$	5.81444e8			0.933543
$855$	−2.67935e7			−0.0428678
$856$		−	6.13712e8i		−	0.978460i
$857$		−	1.68235e8i		−	0.267285i	−0.991030	−	0.133642i	$-0.957333\pi$
$857$		−	1.68235e8i		−	0.267285i	0.991030	−	0.133642i	$-0.0426673\pi$
$858$			2.41369e8i			0.382137i
$859$		−	1.19293e9i		−	1.88207i	−0.338304	−	0.941037i	$-0.609853\pi$
$859$		−	1.19293e9i		−	1.88207i	0.338304	−	0.941037i	$-0.390147\pi$
$860$			5.54870e8i			0.872361i
$861$	5.04011e8			0.789642
$862$	−5.05313e8			−0.788930
$863$		−	1.86737e8i		−	0.290535i	−0.989392	−	0.145267i	$-0.953596\pi$
$863$		−	1.86737e8i		−	0.290535i	0.989392	−	0.145267i	$-0.0464043\pi$
$864$			5.53594e7i			0.0858322i
$865$			1.12927e9i			1.74482i
$866$			5.09994e8i			0.785256i
$867$	2.16928e8			0.332858
$868$			1.56650e7i			0.0239536i
$869$		−	5.14481e7i		−	0.0783990i
$870$			5.83394e8i			0.885940i
$871$	3.36297e8			0.508942
$872$	−1.15894e9			−1.74788
$873$		−	3.54696e8i		−	0.533106i
$874$	−3.70561e6			−0.00555041
$875$	1.62034e9			2.41870
$876$			1.03801e8i			0.154416i
$877$	−6.25541e8			−0.927379			−0.463689	−	0.885998i	$-0.653475\pi$
$877$	−6.25541e8			−0.927379			−0.463689	+	0.885998i	$0.653475\pi$
$878$		−	9.95547e7i		−	0.147088i
$879$	2.39724e8			0.352976
$880$			1.11302e9i			1.63326i
$881$			2.10650e6i			0.00308059i	0.999999	+	0.00154029i	$0.000490291\pi$
$881$			2.10650e6i			0.00308059i	−0.999999	+	0.00154029i	$0.999510\pi$
$882$			9.99901e7i			0.145731i
$883$	−1.36927e9			−1.98888			−0.994438	−	0.105325i	$-0.966412\pi$
$883$	−1.36927e9			−1.98888			−0.994438	+	0.105325i	$0.966412\pi$
$884$			6.59638e7i			0.0954880i
$885$	−5.57223e7	+	7.73971e8i	−0.0803894	+	1.11659i
$886$	7.21794e8			1.03780
$887$		−	3.56428e8i		−	0.510742i	−0.966843	−	0.255371i	$-0.917802\pi$
$887$		−	3.56428e8i		−	0.510742i	0.966843	−	0.255371i	$-0.0821976\pi$
$888$	−3.99873e8			−0.571062
$889$	−4.25399e8			−0.605468
$890$	1.83092e9			2.59716
$891$		−	9.19112e7i		−	0.129938i
$892$	−1.76619e8			−0.248852
$893$			7.44661e7i			0.104569i
$894$	−2.18649e8			−0.306010
$895$		−	2.02477e9i		−	2.82427i
$896$			2.70922e8i			0.376635i
$897$	2.55594e7			0.0354139
$898$		−	1.71360e8i		−	0.236636i
$899$			9.70570e7i			0.133582i
$900$	1.52780e8			0.209574
$901$	6.16693e8			0.843130
$902$	1.45509e9			1.98276
$903$		−	5.95094e8i		−	0.808206i
$904$	1.47274e8			0.199352
$905$	−6.91096e8			−0.932379
$906$	−2.34317e8			−0.315079
$907$	−1.00962e9			−1.35312			−0.676559	−	0.736389i	$-0.736529\pi$
$907$	−1.00962e9			−1.35312			−0.676559	+	0.736389i	$0.736529\pi$
$908$			2.54875e8i			0.340463i
$909$			6.41784e7i			0.0854471i
$910$	5.86222e8			0.777926
$911$	−9.28756e8			−1.22842			−0.614210	−	0.789143i	$-0.710525\pi$
$911$	−9.28756e8			−1.22842			−0.614210	+	0.789143i	$0.710525\pi$
$912$	−2.09217e7			−0.0275812
$913$	6.31026e7			0.0829154
$914$	−3.58958e8			−0.470116
$915$		−	1.28528e9i		−	1.67778i
$916$			1.94691e8i			0.253314i
$917$		−	4.55252e7i		−	0.0590396i
$918$			8.51371e7i			0.110050i
$919$		−	1.05932e8i		−	0.136483i	−0.997669	−	0.0682416i	$-0.978261\pi$
$919$		−	1.05932e8i		−	0.136483i	0.997669	−	0.0682416i	$-0.0217389\pi$
$920$	1.55141e8			0.199234
$921$	−1.82316e8			−0.233371
$922$			7.39668e8i			0.943722i
$923$		−	4.98943e8i		−	0.634521i
$924$			8.60169e7i			0.109036i
$925$			2.00236e9i			2.52998i
$926$	6.52089e8			0.821248
$927$		−	9.97312e7i		−	0.125196i
$928$		−	3.20999e8i		−	0.401661i
$929$			1.07899e9i			1.34577i	0.739746	+	0.672887i	$0.234946\pi$
$929$			1.07899e9i			1.34577i	−0.739746	+	0.672887i	$0.765054\pi$
$930$	−1.17367e8			−0.145914
$931$	2.66279e7			0.0329980
$932$			2.94158e7i			0.0363356i
$933$	−6.60302e8			−0.813014
$934$	6.41738e8			0.787621
$935$		−	1.20616e9i		−	1.47560i
$936$	1.89952e8			0.231641
$937$			1.20021e9i			1.45894i	0.684010	+	0.729472i	$0.260234\pi$
$937$			1.20021e9i			1.45894i	−0.684010	+	0.729472i	$0.739766\pi$
$938$	−4.06211e8			−0.492202
$939$			2.63384e8i			0.318121i
$940$		−	5.78476e8i		−	0.696468i
$941$		−	8.64892e8i		−	1.03799i	−0.854777	−	0.518995i	$-0.826306\pi$
$941$		−	8.64892e8i		−	1.03799i	0.854777	−	0.518995i	$-0.173694\pi$
$942$	−4.67510e8			−0.559291
$943$		−	1.54085e8i		−	0.183749i
$944$	−4.35108e7	+	6.04356e8i	−0.0517227	+	0.718418i
$945$	−2.23229e8			−0.264518
$946$		−	1.71805e9i		−	2.02937i
$947$	1.20025e9			1.41325			0.706627	−	0.707586i	$-0.250216\pi$
$947$	1.20025e9			1.41325			0.706627	+	0.707586i	$0.250216\pi$
$948$	−7.51259e6			−0.00881789
$949$	6.46250e8			0.756139
$950$			1.37902e8i			0.160842i
$951$	2.21315e8			0.257318
$952$		−	4.29414e8i		−	0.497697i
$953$	1.39575e9			1.61261			0.806303	−	0.591502i	$-0.201465\pi$
$953$	1.39575e9			1.61261			0.806303	+	0.591502i	$0.201465\pi$
$954$		−	3.29507e8i		−	0.379507i
$955$			2.19900e9i			2.52473i
$956$	1.84394e8			0.211044
$957$			5.32942e8i			0.608057i
$958$		−	1.15958e9i		−	1.31888i
$959$	−4.92419e8			−0.558315
$960$	1.10157e9			1.24508
$961$	8.67978e8			0.977999
$962$			4.61931e8i			0.518862i
$963$	2.69965e8			0.302293
$964$	3.18488e8			0.355519
$965$	−1.76818e9			−1.96764
$966$	−3.08731e7			−0.0342490
$967$		−	8.11424e8i		−	0.897363i	−0.893692	−	0.448682i	$-0.851894\pi$
$967$		−	8.11424e8i		−	0.897363i	0.893692	−	0.448682i	$-0.148106\pi$
$968$			3.59735e8i			0.396603i
$969$	2.26724e7			0.0249188
$970$	−2.48707e9			−2.72504
$971$	−8.07317e8			−0.881834			−0.440917	−	0.897548i	$-0.645347\pi$
$971$	−8.07317e8			−0.881834			−0.440917	+	0.897548i	$0.645347\pi$
$972$	−1.34211e7			−0.0146147
$973$	−1.09011e8			−0.118340
$974$			1.02359e9i			1.10776i
$975$		−	9.51180e8i		−	1.02624i
$976$		−	1.00361e9i		−	1.07949i
$977$		−	1.60834e9i		−	1.72462i	−0.506377	−	0.862312i	$-0.669016\pi$
$977$		−	1.60834e9i		−	1.72462i	0.506377	−	0.862312i	$-0.330984\pi$
$978$		−	6.05116e8i		−	0.646877i
$979$	1.67258e9			1.78254
$980$	−2.06853e8			−0.219778
$981$		−	5.09805e8i		−	0.540004i
$982$		−	1.05666e9i		−	1.11583i
$983$		−	1.90194e8i		−	0.200234i	−0.994976	−	0.100117i	$-0.968078\pi$
$983$		−	1.90194e8i		−	0.200234i	0.994976	−	0.100117i	$-0.0319217\pi$
$984$		−	1.14512e9i		−	1.20189i
$985$	1.88347e8			0.197084
$986$		−	4.93663e8i		−	0.514991i
$987$			6.20410e8i			0.645249i
$988$		−	9.38600e6i		−	0.00973217i
$989$	−1.81931e8			−0.188069
$990$	−6.44465e8			−0.664193
$991$		−	5.02109e8i		−	0.515914i	−0.966156	−	0.257957i	$-0.916951\pi$
$991$		−	5.02109e8i		−	0.515914i	0.966156	−	0.257957i	$-0.0830493\pi$
$992$	6.45785e7			0.0661535
$993$	8.59409e8			0.877712
$994$			6.02670e8i			0.613649i
$995$	1.88058e9			1.90907
$996$		−	9.21441e6i		−	0.00932587i
$997$	9.76161e8			0.985000			0.492500	−	0.870313i	$-0.336083\pi$
$997$	9.76161e8			0.985000			0.492500	+	0.870313i	$0.336083\pi$
$998$		−	5.07187e8i		−	0.510242i
$999$		−	1.75899e8i		−	0.176428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.19	✓	60
59.58	odd	2	inner	177.7.c.a.58.42	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.19	✓	60	1.1	even	1	trivial
177.7.c.a.58.42	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)

\(f(q)\)	\(=\)	\(q-7.02990i q^{2} -15.5885 q^{3} +14.5805 q^{4} +242.375 q^{5} +109.585i q^{6} +243.138 q^{7} -552.413i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-7.02990i q^{2} -15.5885 q^{3} +14.5805 q^{4} +242.375 q^{5} +109.585i q^{6} +243.138 q^{7} -552.413i q^{8} +243.000 q^{9} -1703.87i q^{10} -1556.52i q^{11} -227.288 q^{12} +1415.05i q^{13} -1709.23i q^{14} -3778.26 q^{15} -2950.26 q^{16} +3197.13 q^{17} -1708.27i q^{18} -454.920 q^{19} +3533.96 q^{20} -3790.14 q^{21} -10942.2 q^{22} +1158.71i q^{23} +8611.27i q^{24} +43120.8 q^{25} +9947.68 q^{26} -3788.00 q^{27} +3545.07 q^{28} +21964.5 q^{29} +26560.8i q^{30} +4418.81i q^{31} -14614.4i q^{32} +24263.8i q^{33} -22475.5i q^{34} +58930.6 q^{35} +3543.06 q^{36} +46436.0i q^{37} +3198.04i q^{38} -22058.5i q^{39} -133891. i q^{40} -132979. q^{41} +26644.3i q^{42} +157011. i q^{43} -22694.9i q^{44} +58897.2 q^{45} +8145.63 q^{46} -163691. i q^{47} +45989.9 q^{48} -58533.1 q^{49} -303135. i q^{50} -49838.3 q^{51} +20632.2i q^{52} +192890. q^{53} +26629.2i q^{54} -377263. i q^{55} -134312. i q^{56} +7091.50 q^{57} -154408. i q^{58} +(14748.1 - 204849. i) q^{59} -55088.9 q^{60} +340178. i q^{61} +31063.8 q^{62} +59082.4 q^{63} -291554. q^{64} +342974. i q^{65} +170572. q^{66} -237657. i q^{67} +46615.8 q^{68} -18062.5i q^{69} -414276. i q^{70} -352597. q^{71} -134236. i q^{72} -456696. i q^{73} +326441. q^{74} -672187. q^{75} -6632.97 q^{76} -378450. i q^{77} -155069. q^{78} +33053.2 q^{79} -715069. q^{80} +59049.0 q^{81} +934832. i q^{82} +40540.7i q^{83} -55262.2 q^{84} +774905. q^{85} +1.10377e6 q^{86} -342393. q^{87} -859844. q^{88} +1.07456e6i q^{89} -414041. i q^{90} +344053. i q^{91} +16894.6i q^{92} -68882.5i q^{93} -1.15073e6 q^{94} -110261. q^{95} +227817. i q^{96} -1.45966e6i q^{97} +411482. i q^{98} -378235. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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