LMFDB - Embedded newform 177.7.c.a.58.18

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			58.18
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.10973i q^{2} -15.5885 q^{3} +13.4517 q^{4} -5.28151 q^{5} +110.830i q^{6} -92.4639 q^{7} -550.661i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-7.10973i q^{2} -15.5885 q^{3} +13.4517 q^{4} -5.28151 q^{5} +110.830i q^{6} -92.4639 q^{7} -550.661i q^{8} +243.000 q^{9} +37.5501i q^{10} +24.8744i q^{11} -209.691 q^{12} -177.466i q^{13} +657.394i q^{14} +82.3307 q^{15} -3054.14 q^{16} -715.296 q^{17} -1727.66i q^{18} +11687.5 q^{19} -71.0454 q^{20} +1441.37 q^{21} +176.850 q^{22} -13557.4i q^{23} +8583.95i q^{24} -15597.1 q^{25} -1261.74 q^{26} -3788.00 q^{27} -1243.80 q^{28} -31537.4 q^{29} -585.349i q^{30} -37264.3i q^{31} -13528.2i q^{32} -387.753i q^{33} +5085.56i q^{34} +488.350 q^{35} +3268.76 q^{36} +17556.2i q^{37} -83094.9i q^{38} +2766.42i q^{39} +2908.32i q^{40} -64099.4 q^{41} -10247.8i q^{42} +76044.2i q^{43} +334.603i q^{44} -1283.41 q^{45} -96389.3 q^{46} +32613.7i q^{47} +47609.4 q^{48} -109099. q^{49} +110891. i q^{50} +11150.4 q^{51} -2387.22i q^{52} -56531.8 q^{53} +26931.6i q^{54} -131.374i q^{55} +50916.3i q^{56} -182190. q^{57} +224223. i q^{58} +(168147. + 117928. i) q^{59} +1107.49 q^{60} -290251. i q^{61} -264939. q^{62} -22468.7 q^{63} -291647. q^{64} +937.290i q^{65} -2756.82 q^{66} +149412. i q^{67} -9621.95 q^{68} +211339. i q^{69} -3472.03i q^{70} -683880. q^{71} -133811. i q^{72} +714312. i q^{73} +124820. q^{74} +243135. q^{75} +157217. q^{76} -2299.98i q^{77} +19668.5 q^{78} -489011. q^{79} +16130.5 q^{80} +59049.0 q^{81} +455730. i q^{82} -559911. i q^{83} +19388.9 q^{84} +3777.84 q^{85} +540654. q^{86} +491620. q^{87} +13697.3 q^{88} +783652. i q^{89} +9124.69i q^{90} +16409.2i q^{91} -182370. i q^{92} +580892. i q^{93} +231874. q^{94} -61727.6 q^{95} +210883. i q^{96} +1.32625e6i q^{97} +775668. i q^{98} +6044.47i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	7.10973i		−	0.888717i	−0.895849	−	0.444358i	$-0.853432\pi$
$2$		−	7.10973i		−	0.888717i	0.895849	−	0.444358i	$-0.146568\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	13.4517			0.210183
$5$	−5.28151			−0.0422521			−0.0211261	−	0.999777i	$-0.506725\pi$
$5$	−5.28151			−0.0422521			−0.0211261	+	0.999777i	$0.506725\pi$
$6$			110.830i			0.513101i
$7$	−92.4639			−0.269574			−0.134787	−	0.990875i	$-0.543035\pi$
$7$	−92.4639			−0.269574			−0.134787	+	0.990875i	$0.543035\pi$
$8$		−	550.661i		−	1.07551i
$9$	243.000			0.333333
$10$			37.5501i			0.0375501i
$11$			24.8744i			0.0186885i	0.999956	+	0.00934424i	$0.00297441\pi$
$11$			24.8744i			0.0186885i	−0.999956	+	0.00934424i	$0.997026\pi$
$12$	−209.691			−0.121349
$13$		−	177.466i		−	0.0807766i	−0.999184	−	0.0403883i	$-0.987141\pi$
$13$		−	177.466i		−	0.0807766i	0.999184	−	0.0403883i	$-0.0128595\pi$
$14$			657.394i			0.239575i
$15$	82.3307			0.0243943
$16$	−3054.14			−0.745640
$17$	−715.296			−0.145592			−0.0727962	−	0.997347i	$-0.523192\pi$
$17$	−715.296			−0.145592			−0.0727962	+	0.997347i	$0.523192\pi$
$18$		−	1727.66i		−	0.296239i
$19$	11687.5			1.70396			0.851981	−	0.523572i	$-0.175401\pi$
$19$	11687.5			1.70396			0.851981	+	0.523572i	$0.175401\pi$
$20$	−71.0454			−0.00888067
$21$	1441.37			0.155639
$22$	176.850			0.0166088
$23$		−	13557.4i		−	1.11427i	−0.830421	−	0.557137i	$-0.811900\pi$
$23$		−	13557.4i		−	1.11427i	0.830421	−	0.557137i	$-0.188100\pi$
$24$			8583.95i			0.620946i
$25$	−15597.1			−0.998215
$26$	−1261.74			−0.0717875
$27$	−3788.00			−0.192450
$28$	−1243.80			−0.0566599
$29$	−31537.4			−1.29310			−0.646551	−	0.762871i	$-0.723789\pi$
$29$	−31537.4			−1.29310			−0.646551	+	0.762871i	$0.723789\pi$
$30$		−	585.349i		−	0.0216796i
$31$		−	37264.3i		−	1.25086i	−0.780282	−	0.625428i	$-0.784924\pi$
$31$		−	37264.3i		−	1.25086i	0.780282	−	0.625428i	$-0.215076\pi$
$32$		−	13528.2i		−	0.412847i
$33$		−	387.753i		−	0.0107898i
$34$			5085.56i			0.129390i
$35$	488.350			0.0113901
$36$	3268.76			0.0700610
$37$			17556.2i			0.346598i	0.984869	+	0.173299i	$0.0554426\pi$
$37$			17556.2i			0.346598i	−0.984869	+	0.173299i	$0.944557\pi$
$38$		−	83094.9i		−	1.51434i
$39$			2766.42i			0.0466364i
$40$			2908.32i			0.0454425i
$41$	−64099.4			−0.930042			−0.465021	−	0.885300i	$-0.653953\pi$
$41$	−64099.4			−0.930042			−0.465021	+	0.885300i	$0.653953\pi$
$42$		−	10247.8i		−	0.138319i
$43$			76044.2i			0.956447i	0.878238	+	0.478224i	$0.158719\pi$
$43$			76044.2i			0.956447i	−0.878238	+	0.478224i	$0.841281\pi$
$44$			334.603i			0.00392800i
$45$	−1283.41			−0.0140840
$46$	−96389.3			−0.990274
$47$			32613.7i			0.314127i	0.987588	+	0.157064i	$0.0502028\pi$
$47$			32613.7i			0.314127i	−0.987588	+	0.157064i	$0.949797\pi$
$48$	47609.4			0.430496
$49$	−109099.			−0.927330
$50$			110891.i			0.887130i
$51$	11150.4			0.0840579
$52$		−	2387.22i		−	0.0169779i
$53$	−56531.8			−0.379721			−0.189861	−	0.981811i	$-0.560804\pi$
$53$	−56531.8			−0.379721			−0.189861	+	0.981811i	$0.560804\pi$
$54$			26931.6i			0.171034i
$55$		−	131.374i		−	0.000789627i
$56$			50916.3i			0.289930i
$57$	−182190.			−0.983783
$58$			224223.i			1.14920i
$59$	168147.	+	117928.i	0.818717	+	0.574197i
$59$	168147.	+	117928.i	0.818717	+	0.574197i
$60$	1107.49			0.00512726
$61$		−	290251.i		−	1.27875i	−0.768896	−	0.639373i	$-0.779194\pi$
$61$		−	290251.i		−	1.27875i	0.768896	−	0.639373i	$-0.220806\pi$
$62$	−264939.			−1.11166
$63$	−22468.7			−0.0898581
$64$	−291647.			−1.11254
$65$			937.290i			0.00341298i
$66$	−2756.82			−0.00958907
$67$			149412.i			0.496778i	0.968660	+	0.248389i	$0.0799011\pi$
$67$			149412.i			0.496778i	−0.968660	+	0.248389i	$0.920099\pi$
$68$	−9621.95			−0.0306010
$69$			211339.i			0.643326i
$70$		−	3472.03i		−	0.0101225i
$71$	−683880.			−1.91076			−0.955378	−	0.295388i	$-0.904551\pi$
$71$	−683880.			−1.91076			−0.955378	+	0.295388i	$0.904551\pi$
$72$		−	133811.i		−	0.358503i
$73$			714312.i			1.83620i	0.396353	+	0.918098i	$0.370276\pi$
$73$			714312.i			1.83620i	−0.396353	+	0.918098i	$0.629724\pi$
$74$	124820.			0.308027
$75$	243135.			0.576320
$76$	157217.			0.358144
$77$		−	2299.98i		−	0.00503793i
$78$	19668.5			0.0414465
$79$	−489011.			−0.991830			−0.495915	−	0.868371i	$-0.665167\pi$
$79$	−489011.			−0.991830			−0.495915	+	0.868371i	$0.665167\pi$
$80$	16130.5			0.0315049
$81$	59049.0			0.111111
$82$			455730.i			0.826544i
$83$		−	559911.i		−	0.979231i	−0.871939	−	0.489615i	$-0.837137\pi$
$83$		−	559911.i		−	0.979231i	0.871939	−	0.489615i	$-0.162863\pi$
$84$	19388.9			0.0327126
$85$	3777.84			0.00615159
$86$	540654.			0.850010
$87$	491620.			0.746572
$88$	13697.3			0.0200996
$89$			783652.i			1.11161i	0.831312	+	0.555806i	$0.187590\pi$
$89$			783652.i			1.11161i	−0.831312	+	0.555806i	$0.812410\pi$
$90$			9124.69i			0.0125167i
$91$			16409.2i			0.0217753i
$92$		−	182370.i		−	0.234201i
$93$			580892.i			0.722182i
$94$	231874.			0.279170
$95$	−61727.6			−0.0719960
$96$			210883.i			0.238357i
$97$			1.32625e6i			1.45315i	0.687089	+	0.726573i	$0.258888\pi$
$97$			1.32625e6i			1.45315i	−0.687089	+	0.726573i	$0.741112\pi$
$98$			775668.i			0.824133i
$99$			6044.47i			0.00622949i
$100$	−209808.			−0.209808
$101$		−	1.69524e6i		−	1.64539i	−0.568486	−	0.822693i	$-0.692470\pi$
$101$		−	1.69524e6i		−	1.64539i	0.568486	−	0.822693i	$-0.307530\pi$
$102$		−	79276.1i		−	0.0747036i
$103$			1.22743e6i			1.12327i	0.827385	+	0.561635i	$0.189827\pi$
$103$			1.22743e6i			1.12327i	−0.827385	+	0.561635i	$0.810173\pi$
$104$	−97723.7			−0.0868760
$105$	−7612.62			−0.00657606
$106$			401926.i			0.337465i
$107$	−1.85505e6			−1.51427			−0.757137	−	0.653256i	$-0.773402\pi$
$107$	−1.85505e6			−1.51427			−0.757137	+	0.653256i	$0.773402\pi$
$108$	−50955.0			−0.0404497
$109$		−	1.82202e6i		−	1.40694i	−0.710727	−	0.703468i	$-0.751634\pi$
$109$		−	1.82202e6i		−	1.40694i	0.710727	−	0.703468i	$-0.248366\pi$
$110$	−934.036			−0.000701755
$111$		−	273674.i		−	0.200108i
$112$	282398.			0.201005
$113$		−	2.47615e6i		−	1.71609i	−0.513571	−	0.858047i	$-0.671678\pi$
$113$		−	2.47615e6i		−	1.71609i	0.513571	−	0.858047i	$-0.328322\pi$
$114$			1.29532e6i			0.874305i
$115$			71603.5i			0.0470804i
$116$	−424232.			−0.271788
$117$		−	43124.3i		−	0.0269255i
$118$	838437.	−	1.19548e6i	0.510298	−	0.727608i
$119$	66139.1			0.0392480
$120$		−	45336.3i		−	0.0262363i
$121$	1.77094e6			0.999651
$122$	−2.06361e6			−1.13644
$123$	999211.			0.536960
$124$		−	501268.i		−	0.262909i
$125$	164900.			0.0844288
$126$			159747.i			0.0798583i
$127$	−2.30876e6			−1.12711			−0.563557	−	0.826077i	$-0.690568\pi$
$127$	−2.30876e6			−1.12711			−0.563557	+	0.826077i	$0.690568\pi$
$128$			1.20773e6i			0.575889i
$129$		−	1.18541e6i		−	0.552205i
$130$	6663.88			0.00303317
$131$		−	3.34462e6i		−	1.48776i	−0.668313	−	0.743880i	$-0.732983\pi$
$131$		−	3.34462e6i		−	1.48776i	0.668313	−	0.743880i	$-0.267017\pi$
$132$		−	5215.94i		−	0.00226783i
$133$	−1.08067e6			−0.459344
$134$	1.06228e6			0.441495
$135$	20006.3			0.00813142
$136$			393885.i			0.156586i
$137$	1.22052e6			0.474660			0.237330	−	0.971429i	$-0.423728\pi$
$137$	1.22052e6			0.474660			0.237330	+	0.971429i	$0.423728\pi$
$138$	1.50256e6			0.571735
$139$	−4.97156e6			−1.85118			−0.925590	−	0.378529i	$-0.876430\pi$
$139$	−4.97156e6			−1.85118			−0.925590	+	0.378529i	$0.876430\pi$
$140$	6569.13			0.00239400
$141$		−	508397.i		−	0.181362i
$142$			4.86221e6i			1.69812i
$143$	4414.36			0.00150959
$144$	−742157.			−0.248547
$145$	166565.			0.0546362
$146$	5.07856e6			1.63186
$147$	1.70069e6			0.535394
$148$			236161.i			0.0728489i
$149$		−	74289.4i		−	0.0224578i	−0.999937	−	0.0112289i	$-0.996426\pi$
$149$		−	74289.4i		−	0.0224578i	0.999937	−	0.0112289i	$-0.00357435\pi$
$150$		−	1.72862e6i		−	0.512185i
$151$		−	628940.i		−	0.182675i	−0.995820	−	0.0913373i	$-0.970886\pi$
$151$		−	628940.i		−	0.182675i	0.995820	−	0.0913373i	$-0.0291141\pi$
$152$		−	6.43584e6i		−	1.83263i
$153$	−173817.			−0.0485308
$154$	−16352.2			−0.00447729
$155$			196812.i			0.0528513i
$156$			37213.1i			0.00980217i
$157$		−	4.07664e6i		−	1.05343i	−0.850043	−	0.526713i	$-0.823424\pi$
$157$		−	4.07664e6i		−	1.05343i	0.850043	−	0.526713i	$-0.176576\pi$
$158$			3.47673e6i			0.881455i
$159$	881243.			0.219232
$160$			71449.2i			0.0174436i
$161$			1.25357e6i			0.300380i
$162$		−	419823.i		−	0.0987463i
$163$	2.85092e6			0.658298			0.329149	−	0.944278i	$-0.393238\pi$
$163$	2.85092e6			0.658298			0.329149	+	0.944278i	$0.393238\pi$
$164$	−862247.			−0.195479
$165$			2047.92i			0.000455892i
$166$	−3.98082e6			−0.870259
$167$	5.22737e6			1.12236			0.561182	−	0.827693i	$-0.310347\pi$
$167$	5.22737e6			1.12236			0.561182	+	0.827693i	$0.310347\pi$
$168$		−	793706.i		−	0.167391i
$169$	4.79531e6			0.993475
$170$		−	26859.5i		−	0.00546702i
$171$	2.84006e6			0.567988
$172$			1.02292e6i			0.201029i
$173$		−	4.18140e6i		−	0.807576i	−0.914853	−	0.403788i	$-0.867693\pi$
$173$		−	4.18140e6i		−	0.807576i	0.914853	−	0.403788i	$-0.132307\pi$
$174$		−	3.49529e6i		−	0.663491i
$175$	1.44217e6			0.269093
$176$		−	75969.8i		−	0.0139349i
$177$	−2.62116e6	−	1.83832e6i	−0.472687	−	0.331513i
$178$	5.57155e6			0.987907
$179$		−	1.83198e6i		−	0.319419i	−0.987164	−	0.159709i	$-0.948944\pi$
$179$		−	1.83198e6i		−	0.319419i	0.987164	−	0.159709i	$-0.0510557\pi$
$180$	−17264.0			−0.00296022
$181$	−4.22034e6			−0.711725			−0.355862	−	0.934538i	$-0.615813\pi$
$181$	−4.22034e6			−0.711725			−0.355862	+	0.934538i	$0.615813\pi$
$182$	116665.			0.0193521
$183$			4.52457e6i			0.738285i
$184$	−7.46552e6			−1.19841
$185$		−	92723.3i		−	0.0146445i
$186$	4.12999e6			0.641815
$187$		−	17792.5i		−	0.00272090i
$188$			438709.i			0.0660242i
$189$	350253.			0.0518796
$190$			438867.i			0.0639841i
$191$		−	9.72301e6i		−	1.39541i	−0.716387	−	0.697703i	$-0.754206\pi$
$191$		−	9.72301e6i		−	1.39541i	0.716387	−	0.697703i	$-0.245794\pi$
$192$	4.54632e6			0.642328
$193$	8.09351e6			1.12581			0.562905	−	0.826522i	$-0.309684\pi$
$193$	8.09351e6			1.12581			0.562905	+	0.826522i	$0.309684\pi$
$194$	9.42926e6			1.29143
$195$		−	14610.9i		−	0.00197049i
$196$	−1.46757e6			−0.194909
$197$	1.05142e7			1.37523			0.687615	−	0.726075i	$-0.258658\pi$
$197$	1.05142e7			1.37523			0.687615	+	0.726075i	$0.258658\pi$
$198$	42974.6			0.00553625
$199$	1.83582e6			0.232955			0.116477	−	0.993193i	$-0.462840\pi$
$199$	1.83582e6			0.232955			0.116477	+	0.993193i	$0.462840\pi$
$200$			8.58872e6i			1.07359i
$201$		−	2.32911e6i		−	0.286815i
$202$	−1.20527e7			−1.46228
$203$	2.91608e6			0.348587
$204$	149991.			0.0176675
$205$	338542.			0.0392962
$206$	8.72668e6			0.998268
$207$		−	3.29444e6i		−	0.371425i
$208$			542007.i			0.0602303i
$209$			290719.i			0.0318445i
$210$			54123.7i			0.00584426i
$211$			1.44513e7i			1.53837i	0.639026	+	0.769185i	$0.279337\pi$
$211$			1.44513e7i			1.53837i	−0.639026	+	0.769185i	$0.720663\pi$
$212$	−760449.			−0.0798110
$213$	1.06606e7			1.10317
$214$			1.31889e7i			1.34576i
$215$		−	401629.i		−	0.0404119i
$216$			2.08590e6i			0.206982i
$217$			3.44560e6i			0.337199i
$218$	−1.29541e7			−1.25037
$219$		−	1.11350e7i		−	1.06013i
$220$		−	1767.21i		−	0.000165966i
$221$			126941.i			0.0117605i
$222$	−1.94575e6			−0.177839
$223$	−1.05264e7			−0.949214			−0.474607	−	0.880198i	$-0.657410\pi$
$223$	−1.05264e7			−0.949214			−0.474607	+	0.880198i	$0.657410\pi$
$224$			1.25087e6i			0.111293i
$225$	−3.79010e6			−0.332738
$226$	−1.76047e7			−1.52512
$227$			8.08343e6i			0.691064i	0.938407	+	0.345532i	$0.112301\pi$
$227$			8.08343e6i			0.691064i	−0.938407	+	0.345532i	$0.887699\pi$
$228$	−2.45076e6			−0.206774
$229$		−	1.41787e7i		−	1.18067i	−0.807157	−	0.590336i	$-0.798995\pi$
$229$		−	1.41787e7i		−	1.18067i	0.807157	−	0.590336i	$-0.201005\pi$
$230$	509081.			0.0418412
$231$			35853.2i			0.00290865i
$232$			1.73664e7i			1.39074i
$233$			1.32063e7i			1.04403i	0.852935	+	0.522016i	$0.174820\pi$
$233$			1.32063e7i			1.04403i	−0.852935	+	0.522016i	$0.825180\pi$
$234$	−306602.			−0.0239292
$235$		−	172249.i		−	0.0132725i
$236$	2.26187e6	+	1.58633e6i	0.172080	+	0.120686i
$237$	7.62292e6			0.572633
$238$		−	470231.i		−	0.0348803i
$239$	1.69314e7			1.24022			0.620111	−	0.784514i	$-0.287088\pi$
$239$	1.69314e7			1.24022			0.620111	+	0.784514i	$0.287088\pi$
$240$	−251450.			−0.0181893
$241$	−1.23242e7			−0.880455			−0.440227	−	0.897886i	$-0.645102\pi$
$241$	−1.23242e7			−0.880455			−0.440227	+	0.897886i	$0.645102\pi$
$242$		−	1.25909e7i		−	0.888406i
$243$	−920483.			−0.0641500
$244$		−	3.90437e6i		−	0.268771i
$245$	576210.			0.0391816
$246$		−	7.10412e6i		−	0.477205i
$247$		−	2.07413e6i		−	0.137640i
$248$	−2.05200e7			−1.34531
$249$			8.72815e6i			0.565359i
$250$		−	1.17239e6i		−	0.0750333i
$251$	−404077.			−0.0255530			−0.0127765	−	0.999918i	$-0.504067\pi$
$251$	−404077.			−0.0255530			−0.0127765	+	0.999918i	$0.504067\pi$
$252$	−302243.			−0.0188866
$253$	337231.			0.0208241
$254$			1.64147e7i			1.00169i
$255$	−58890.8			−0.00355162
$256$	−1.00788e7			−0.600741
$257$	−8.33624e6			−0.491101			−0.245551	−	0.969384i	$-0.578969\pi$
$257$	−8.33624e6			−0.491101			−0.245551	+	0.969384i	$0.578969\pi$
$258$	−8.42797e6			−0.490754
$259$		−	1.62332e6i		−	0.0934337i
$260$			12608.2i			0.000717350i
$261$	−7.66360e6			−0.431034
$262$	−2.37794e7			−1.32220
$263$	−2.75857e6			−0.151641			−0.0758205	−	0.997121i	$-0.524158\pi$
$263$	−2.75857e6			−0.151641			−0.0758205	+	0.997121i	$0.524158\pi$
$264$	−213520.			−0.0116045
$265$	298573.			0.0160440
$266$			7.68328e6i			0.408227i
$267$		−	1.22159e7i		−	0.641789i
$268$			2.00985e6i			0.104414i
$269$		−	2.04406e7i		−	1.05012i	−0.851066	−	0.525058i	$-0.824043\pi$
$269$		−	2.04406e7i		−	1.05012i	0.851066	−	0.525058i	$-0.175957\pi$
$270$		−	142240.i		−	0.00722653i
$271$	−1.41673e7			−0.711835			−0.355918	−	0.934517i	$-0.615832\pi$
$271$	−1.41673e7			−0.711835			−0.355918	+	0.934517i	$0.615832\pi$
$272$	2.18462e6			0.108560
$273$		−	255794.i		−	0.0125720i
$274$		−	8.67757e6i		−	0.421839i
$275$		−	387968.i		−	0.0186551i
$276$			2.84286e6i			0.135216i
$277$	5.15145e6			0.242376			0.121188	−	0.992630i	$-0.461330\pi$
$277$	5.15145e6			0.242376			0.121188	+	0.992630i	$0.461330\pi$
$278$			3.53465e7i			1.64517i
$279$		−	9.05522e6i		−	0.416952i
$280$		−	268915.i		−	0.0122501i
$281$	−672904.			−0.0303273			−0.0151637	−	0.999885i	$-0.504827\pi$
$281$	−672904.			−0.0303273			−0.0151637	+	0.999885i	$0.504827\pi$
$282$	−3.61456e6			−0.161179
$283$			1.23913e7i			0.546711i	0.961913	+	0.273356i	$0.0881336\pi$
$283$			1.23913e7i			0.546711i	−0.961913	+	0.273356i	$0.911866\pi$
$284$	−9.19936e6			−0.401608
$285$	962238.			0.0415669
$286$		−	31384.9i		−	0.00134160i
$287$	5.92689e6			0.250715
$288$		−	3.28734e6i		−	0.137616i
$289$	−2.36259e7			−0.978803
$290$		−	1.18424e6i		−	0.0485561i
$291$		−	2.06741e7i		−	0.838974i
$292$			9.60871e6i			0.385937i
$293$	4.23495e7			1.68363			0.841813	−	0.539769i	$-0.181488\pi$
$293$	4.23495e7			1.68363			0.841813	+	0.539769i	$0.181488\pi$
$294$		−	1.20915e7i		−	0.475814i
$295$	−888072.	−	622838.i	−0.0345925	−	0.0242610i
$296$	9.66752e6			0.372769
$297$		−	94223.9i		−	0.00359660i
$298$	−528178.			−0.0199587
$299$	−2.40598e6			−0.0900073
$300$	3.27058e6			0.121133
$301$		−	7.03135e6i		−	0.257833i
$302$	−4.47159e6			−0.162346
$303$			2.64262e7i			0.949964i
$304$	−3.56952e7			−1.27054
$305$			1.53297e6i			0.0540298i
$306$			1.23579e6i			0.0431301i
$307$	−1.52601e7			−0.527402			−0.263701	−	0.964604i	$-0.584943\pi$
$307$	−1.52601e7			−0.527402			−0.263701	+	0.964604i	$0.584943\pi$
$308$		−	30938.7i		−	0.00105889i
$309$		−	1.91337e7i		−	0.648520i
$310$	1.39928e6			0.0469699
$311$	−6.21630e6			−0.206657			−0.103329	−	0.994647i	$-0.532949\pi$
$311$	−6.21630e6			−0.206657			−0.103329	+	0.994647i	$0.532949\pi$
$312$	1.52336e6			0.0501579
$313$		−	9.26899e6i		−	0.302273i	−0.988513	−	0.151137i	$-0.951707\pi$
$313$		−	9.26899e6i		−	0.302273i	0.988513	−	0.151137i	$-0.0482933\pi$
$314$	−2.89838e7			−0.936196
$315$	118669.			0.00379669
$316$	−6.57803e6			−0.208466
$317$	−5.63002e6			−0.176739			−0.0883694	−	0.996088i	$-0.528166\pi$
$317$	−5.63002e6			−0.176739			−0.0883694	+	0.996088i	$0.528166\pi$
$318$		−	6.26540e6i		−	0.194835i
$319$		−	784473.i		−	0.0241661i
$320$	1.54034e6			0.0470073
$321$	2.89174e7			0.874266
$322$	8.91253e6			0.266952
$323$	−8.36001e6			−0.248084
$324$	794310.			0.0233537
$325$			2.76796e6i			0.0806324i
$326$		−	2.02693e7i		−	0.585040i
$327$			2.84025e7i			0.812295i
$328$			3.52970e7i			1.00027i
$329$		−	3.01559e6i		−	0.0846807i
$330$	14560.2			0.000405158
$331$	5.30847e7			1.46381			0.731906	−	0.681405i	$-0.238631\pi$
$331$	5.30847e7			1.46381			0.731906	+	0.681405i	$0.238631\pi$
$332$		−	7.53176e6i		−	0.205818i
$333$			4.26616e6i			0.115533i
$334$		−	3.71652e7i		−	0.997463i
$335$		−	789123.i		−	0.0209899i
$336$	−4.40215e6			−0.116050
$337$			1.54982e7i			0.404940i	0.979288	+	0.202470i	$0.0648969\pi$
$337$			1.54982e7i			0.404940i	−0.979288	+	0.202470i	$0.935103\pi$
$338$		−	3.40934e7i		−	0.882918i
$339$			3.85993e7i			0.990787i
$340$	50818.5			0.00129296
$341$	926925.			0.0233766
$342$		−	2.01921e7i		−	0.504780i
$343$	2.09661e7			0.519558
$344$	4.18746e7			1.02867
$345$		−	1.11619e6i		−	0.0271819i
$346$	−2.97286e7			−0.717706
$347$			2.85902e6i			0.0684272i	0.999415	+	0.0342136i	$0.0108927\pi$
$347$			2.85902e6i			0.0684272i	−0.999415	+	0.0342136i	$0.989107\pi$
$348$	6.61313e6			0.156917
$349$			8.13353e7i			1.91339i	0.291097	+	0.956694i	$0.405980\pi$
$349$			8.13353e7i			1.91339i	−0.291097	+	0.956694i	$0.594020\pi$
$350$		−	1.02534e7i		−	0.239147i
$351$			672241.i			0.0155455i
$352$	336504.			0.00771547
$353$		−	2.35290e7i		−	0.534909i	−0.963570	−	0.267455i	$-0.913817\pi$
$353$		−	2.35290e7i		−	0.534909i	0.963570	−	0.267455i	$-0.0861825\pi$
$354$	−1.30699e7	+	1.86357e7i	−0.294621	+	0.420084i
$355$	3.61192e6			0.0807334
$356$			1.05415e7i			0.233642i
$357$	−1.03101e6			−0.0226598
$358$	−1.30249e7			−0.283873
$359$	−4.68770e7			−1.01316			−0.506579	−	0.862194i	$-0.669090\pi$
$359$	−4.68770e7			−1.01316			−0.506579	+	0.862194i	$0.669090\pi$
$360$			706723.i			0.0151475i
$361$	8.95514e7			1.90349
$362$			3.00055e7i			0.632522i
$363$	−2.76063e7			−0.577149
$364$			220732.i			0.00457679i
$365$		−	3.77265e6i		−	0.0775832i
$366$	3.21685e7			0.656126
$367$		−	5.44819e7i		−	1.10218i	−0.834445	−	0.551092i	$-0.814211\pi$
$367$		−	5.44819e7i		−	1.10218i	0.834445	−	0.551092i	$-0.185789\pi$
$368$			4.14061e7i			0.830848i
$369$	−1.55762e7			−0.310014
$370$	−659238.			−0.0130148
$371$	5.22715e6			0.102363
$372$			7.81399e6i			0.151790i
$373$	5.54160e7			1.06785			0.533923	−	0.845533i	$-0.320717\pi$
$373$	5.54160e7			1.06785			0.533923	+	0.845533i	$0.320717\pi$
$374$	−126500.			−0.00241811
$375$	−2.57054e6			−0.0487450
$376$	1.79591e7			0.337847
$377$			5.59683e6i			0.104452i
$378$		−	2.49020e6i		−	0.0461062i
$379$	8.30586e7			1.52569			0.762846	−	0.646580i	$-0.223801\pi$
$379$	8.30586e7			1.52569			0.762846	+	0.646580i	$0.223801\pi$
$380$	−830341.			−0.0151323
$381$	3.59900e7			0.650740
$382$	−6.91280e7			−1.24012
$383$	−1.23695e7			−0.220168			−0.110084	−	0.993922i	$-0.535112\pi$
$383$	−1.23695e7			−0.220168			−0.110084	+	0.993922i	$0.535112\pi$
$384$		−	1.88266e7i		−	0.332490i
$385$			12147.4i			0.000212863i
$386$		−	5.75427e7i		−	1.00053i
$387$			1.84788e7i			0.318816i
$388$			1.78403e7i			0.305426i
$389$	8.65306e6			0.147001			0.0735006	−	0.997295i	$-0.476583\pi$
$389$	8.65306e6			0.147001			0.0735006	+	0.997295i	$0.476583\pi$
$390$	−103880.			−0.00175120
$391$			9.69753e6i			0.162230i
$392$			6.00768e7i			0.997352i
$393$			5.21375e7i			0.858959i
$394$		−	7.47528e7i		−	1.22219i
$395$	2.58272e6			0.0419069
$396$			81308.4i			0.00130933i
$397$			5.99639e7i			0.958338i	0.877723	+	0.479169i	$0.159062\pi$
$397$			5.99639e7i			0.958338i	−0.877723	+	0.479169i	$0.840938\pi$
$398$		−	1.30522e7i		−	0.207031i
$399$	1.68460e7			0.265203
$400$	4.76358e7			0.744309
$401$		−	1.08704e8i		−	1.68582i	−0.538053	−	0.842911i	$-0.680840\pi$
$401$		−	1.08704e8i		−	1.68582i	0.538053	−	0.842911i	$-0.319160\pi$
$402$	−1.65593e7			−0.254897
$403$	−6.61315e6			−0.101040
$404$		−	2.28039e7i		−	0.345832i
$405$	−311868.			−0.00469468
$406$		−	2.07325e7i		−	0.309795i
$407$	−436699.			−0.00647738
$408$		−	6.14007e6i		−	0.0904050i
$409$		−	1.07716e8i		−	1.57439i	−0.616706	−	0.787193i	$-0.711533\pi$
$409$		−	1.07716e8i		−	1.57439i	0.616706	−	0.787193i	$-0.288467\pi$
$410$		−	2.40694e6i		−	0.0349232i
$411$	−1.90260e7			−0.274045
$412$			1.65110e7i			0.236092i
$413$	−1.55476e7	−	1.09041e7i	−0.220705	−	0.154789i
$414$	−2.34226e7			−0.330091
$415$			2.95718e6i			0.0413746i
$416$	−2.40079e6			−0.0333484
$417$	7.74990e7			1.06878
$418$	2.06693e6			0.0283007
$419$			4.18212e6i			0.0568531i	0.999596	+	0.0284265i	$0.00904967\pi$
$419$			4.18212e6i			0.0568531i	−0.999596	+	0.0284265i	$0.990950\pi$
$420$	−102403.			−0.00138218
$421$		−	2.52986e7i		−	0.339040i	−0.985527	−	0.169520i	$-0.945778\pi$
$421$		−	2.52986e7i		−	0.339040i	0.985527	−	0.169520i	$-0.0542217\pi$
$422$	1.02745e8			1.36717
$423$			7.92512e6i			0.104709i
$424$			3.11298e7i			0.408394i
$425$	1.11565e7			0.145333
$426$		−	7.57943e7i		−	0.980410i
$427$			2.68378e7i			0.344717i
$428$	−2.49536e7			−0.318274
$429$	−68813.0			−0.000871563
$430$	−2.85547e6			−0.0359147
$431$			1.36407e8i			1.70374i	0.523752	+	0.851871i	$0.324532\pi$
$431$			1.36407e8i			1.70374i	−0.523752	+	0.851871i	$0.675468\pi$
$432$	1.15691e7			0.143499
$433$	3.58849e7			0.442027			0.221013	−	0.975271i	$-0.429064\pi$
$433$	3.58849e7			0.442027			0.221013	+	0.975271i	$0.429064\pi$
$434$	2.44973e7			0.299674
$435$	−2.59650e6			−0.0315443
$436$		−	2.45093e7i		−	0.295714i
$437$		−	1.58452e8i		−	1.89868i
$438$	−7.91670e7			−0.942154
$439$	9.35625e7			1.10588			0.552940	−	0.833221i	$-0.313506\pi$
$439$	9.35625e7			1.10588			0.552940	+	0.833221i	$0.313506\pi$
$440$	−72342.7			−0.000849252
$441$	−2.65112e7			−0.309110
$442$	902515.			0.0104517
$443$		−	9.40911e7i		−	1.08227i	−0.840934	−	0.541137i	$-0.817994\pi$
$443$		−	9.40911e7i		−	1.08227i	0.840934	−	0.541137i	$-0.182006\pi$
$444$		−	3.68138e6i		−	0.0420593i
$445$		−	4.13887e6i		−	0.0469679i
$446$			7.48397e7i			0.843582i
$447$			1.15806e6i			0.0129660i
$448$	2.69668e7			0.299913
$449$	−1.35505e8			−1.49698			−0.748490	−	0.663146i	$-0.769221\pi$
$449$	−1.35505e8			−1.49698			−0.748490	+	0.663146i	$0.769221\pi$
$450$			2.69466e7i			0.295710i
$451$		−	1.59443e6i		−	0.0173811i
$452$		−	3.33084e7i		−	0.360694i
$453$			9.80420e6i			0.105467i
$454$	5.74710e7			0.614160
$455$		−	86665.5i		−	0.000920052i
$456$			1.00325e8i			1.05807i
$457$		−	3.81923e7i		−	0.400154i	−0.979780	−	0.200077i	$-0.935881\pi$
$457$		−	3.81923e7i		−	0.400154i	0.979780	−	0.200077i	$-0.0641192\pi$
$458$	−1.00807e8			−1.04928
$459$	2.70954e6			0.0280193
$460$			963189.i			0.00989550i
$461$	1.08095e8			1.10333			0.551663	−	0.834067i	$-0.313994\pi$
$461$	1.08095e8			1.10333			0.551663	+	0.834067i	$0.313994\pi$
$462$	254906.			0.00258496
$463$		−	1.29566e8i		−	1.30542i	−0.757610	−	0.652708i	$-0.773633\pi$
$463$		−	1.29566e8i		−	1.30542i	0.757610	−	0.652708i	$-0.226367\pi$
$464$	9.63198e7			0.964188
$465$		−	3.06799e6i		−	0.0305137i
$466$	9.38934e7			0.927849
$467$			2.80116e6i			0.0275035i	0.999905	+	0.0137517i	$0.00437745\pi$
$467$			2.80116e6i			0.0275035i	−0.999905	+	0.0137517i	$0.995623\pi$
$468$		−	580095.i		−	0.00565929i
$469$		−	1.38153e7i		−	0.133918i
$470$	−1.22465e6			−0.0117955
$471$			6.35486e7i			0.608195i
$472$	6.49383e7	−	9.25922e7i	0.617554	−	0.880538i
$473$	−1.89155e6			−0.0178745
$474$		−	5.41969e7i		−	0.508908i
$475$	−1.82291e8			−1.70092
$476$	889683.			0.00824925
$477$	−1.37372e7			−0.126574
$478$		−	1.20378e8i		−	1.10220i
$479$	−1.46808e8			−1.33581			−0.667905	−	0.744247i	$-0.732809\pi$
$479$	−1.46808e8			−1.33581			−0.667905	+	0.744247i	$0.732809\pi$
$480$		−	1.11378e6i		−	0.0100711i
$481$	3.11563e6			0.0279970
$482$			8.76216e7i			0.782475i
$483$		−	1.95412e7i		−	0.173424i
$484$	2.38222e7			0.210110
$485$		−	7.00459e6i		−	0.0613985i
$486$			6.54439e6i			0.0570112i
$487$	2.04812e8			1.77324			0.886622	−	0.462495i	$-0.153046\pi$
$487$	2.04812e8			1.77324			0.886622	+	0.462495i	$0.153046\pi$
$488$	−1.59830e8			−1.37530
$489$	−4.44414e7			−0.380068
$490$		−	4.09670e6i		−	0.0348214i
$491$	−1.51228e8			−1.27758			−0.638791	−	0.769381i	$-0.720565\pi$
$491$	−1.51228e8			−1.27758			−0.638791	+	0.769381i	$0.720565\pi$
$492$	1.34411e7			0.112860
$493$	2.25586e7			0.188266
$494$	−1.47465e7			−0.122323
$495$		−	31923.9i		−	0.000263209i
$496$			1.13810e8i			0.932689i
$497$	6.32343e7			0.515090
$498$	6.20548e7			0.502444
$499$	−4.19145e7			−0.337336			−0.168668	−	0.985673i	$-0.553947\pi$
$499$	−4.19145e7			−0.337336			−0.168668	+	0.985673i	$0.553947\pi$
$500$	2.21819e6			0.0177455
$501$	−8.14866e7			−0.647997
$502$			2.87288e6i			0.0227094i
$503$		−	2.33489e8i		−	1.83469i	−0.398094	−	0.917345i	$-0.630328\pi$
$503$		−	2.33489e8i		−	1.83469i	0.398094	−	0.917345i	$-0.369672\pi$
$504$			1.23727e7i			0.0966432i
$505$			8.95345e6i			0.0695211i
$506$		−	2.39762e6i		−	0.0185067i
$507$	−7.47516e7			−0.573583
$508$	−3.10568e7			−0.236900
$509$			9.20786e7i			0.698241i	0.937078	+	0.349121i	$0.113520\pi$
$509$			9.20786e7i			0.698241i	−0.937078	+	0.349121i	$0.886480\pi$
$510$			418698.i			0.00315638i
$511$		−	6.60481e7i		−	0.494991i
$512$			1.48952e8i			1.10978i
$513$	−4.42721e7			−0.327928
$514$			5.92685e7i			0.436450i
$515$		−	6.48267e6i		−	0.0474605i
$516$		−	1.59458e7i		−	0.116064i
$517$	−811244.			−0.00587056
$518$	−1.15413e7			−0.0830361
$519$			6.51816e7i			0.466254i
$520$	516129.			0.00367069
$521$	5.17563e7			0.365974			0.182987	−	0.983115i	$-0.441423\pi$
$521$	5.17563e7			0.365974			0.182987	+	0.983115i	$0.441423\pi$
$522$			5.44861e7i			0.383067i
$523$	−1.64753e8			−1.15167			−0.575834	−	0.817566i	$-0.695323\pi$
$523$	−1.64753e8			−1.15167			−0.575834	+	0.817566i	$0.695323\pi$
$524$		−	4.49909e7i		−	0.312702i
$525$	−2.24812e7			−0.155361
$526$			1.96127e7i			0.134766i
$527$			2.66550e7i			0.182115i
$528$			1.18425e6i			0.00804530i
$529$	−3.57665e7			−0.241607
$530$		−	2.12278e6i		−	0.0142586i
$531$	4.08598e7	+	2.86565e7i	0.272906	+	0.191399i
$532$	−1.45369e7			−0.0965463
$533$			1.13755e7i			0.0751256i
$534$	−8.68519e7			−0.570369
$535$	9.79747e6			0.0639813
$536$	8.22755e7			0.534289
$537$			2.85577e7i			0.184417i
$538$	−1.45327e8			−0.933256
$539$		−	2.71378e6i		−	0.0173304i
$540$	269120.			0.00170909
$541$			9.80167e7i			0.619025i	0.950895	+	0.309513i	$0.100166\pi$
$541$			9.80167e7i			0.619025i	−0.950895	+	0.309513i	$0.899834\pi$
$542$			1.00726e8i			0.632620i
$543$	6.57887e7			0.410915
$544$			9.67664e6i			0.0601074i
$545$			9.62304e6i			0.0594460i
$546$	−1.81863e6			−0.0111729
$547$	2.45510e8			1.50005			0.750027	−	0.661407i	$-0.230040\pi$
$547$	2.45510e8			1.50005			0.750027	+	0.661407i	$0.230040\pi$
$548$	1.64181e7			0.0997655
$549$		−	7.05311e7i		−	0.426249i
$550$	−2.75835e6			−0.0165791
$551$	−3.68593e8			−2.20340
$552$	1.16376e8			0.691904
$553$	4.52158e7			0.267372
$554$		−	3.66255e7i		−	0.215404i
$555$			1.44541e6i			0.00845499i
$556$	−6.68760e7			−0.389086
$557$	−2.60073e8			−1.50497			−0.752487	−	0.658607i	$-0.771146\pi$
$557$	−2.60073e8			−1.50497			−0.752487	+	0.658607i	$0.771146\pi$
$558$	−6.43802e7			−0.370552
$559$	1.34953e7			0.0772586
$560$	−1.49149e6			−0.00849290
$561$			277358.i			0.00157091i
$562$			4.78416e6i			0.0269524i
$563$			2.31232e8i			1.29575i	0.761745	+	0.647877i	$0.224343\pi$
$563$			2.31232e8i			1.29575i	−0.761745	+	0.647877i	$0.775657\pi$
$564$		−	6.83880e6i		−	0.0381191i
$565$			1.30778e7i			0.0725086i
$566$	8.80989e7			0.485871
$567$	−5.45990e6			−0.0299527
$568$			3.76586e8i			2.05504i
$569$			2.95772e8i			1.60554i	0.596289	+	0.802770i	$0.296641\pi$
$569$			2.95772e8i			1.60554i	−0.596289	+	0.802770i	$0.703359\pi$
$570$		−	6.84125e6i		−	0.0369412i
$571$			2.55594e8i			1.37291i	0.727171	+	0.686456i	$0.240835\pi$
$571$			2.55594e8i			1.37291i	−0.727171	+	0.686456i	$0.759165\pi$
$572$	59380.6			0.000317290
$573$			1.51567e8i			0.805638i
$574$		−	4.21386e7i		−	0.222815i
$575$			2.11456e8i			1.11228i
$576$	−7.08702e7			−0.370848
$577$	2.32931e8			1.21255			0.606276	−	0.795255i	$-0.292663\pi$
$577$	2.32931e8			1.21255			0.606276	+	0.795255i	$0.292663\pi$
$578$			1.67974e8i			0.869878i
$579$	−1.26165e8			−0.649986
$580$	2.24059e6			0.0114836
$581$			5.17716e7i			0.263975i
$582$	−1.46988e8			−0.745610
$583$		−	1.40619e6i		−	0.00709641i
$584$	3.93343e8			1.97485
$585$			227762.i			0.00113766i
$586$		−	3.01094e8i		−	1.49627i
$587$			1.57150e8i			0.776964i	0.921456	+	0.388482i	$0.127000\pi$
$587$			1.57150e8i			0.776964i	−0.921456	+	0.388482i	$0.873000\pi$
$588$	2.28772e7			0.112531
$589$		−	4.35525e8i		−	2.13141i
$590$	−4.42821e6	+	6.31396e6i	−0.0215612	+	0.0307430i
$591$	−1.63899e8			−0.793990
$592$		−	5.36192e7i		−	0.258437i
$593$	−6.64478e7			−0.318652			−0.159326	−	0.987226i	$-0.550932\pi$
$593$	−6.64478e7			−0.318652			−0.159326	+	0.987226i	$0.550932\pi$
$594$	−669907.			−0.00319636
$595$	−349314.			−0.00165831
$596$		−	999319.i		−	0.00472026i
$597$	−2.86177e7			−0.134497
$598$			1.71058e7i			0.0799910i
$599$	1.81573e8			0.844835			0.422417	−	0.906401i	$-0.361182\pi$
$599$	1.81573e8			0.844835			0.422417	+	0.906401i	$0.361182\pi$
$600$		−	1.33885e8i		−	0.619837i
$601$		−	3.47824e8i		−	1.60227i	−0.598483	−	0.801136i	$-0.704229\pi$
$601$		−	3.47824e8i		−	1.60227i	0.598483	−	0.801136i	$-0.295771\pi$
$602$	−4.99910e7			−0.229141
$603$			3.63072e7i			0.165593i
$604$		−	8.46031e6i		−	0.0383951i
$605$	−9.35326e6			−0.0422374
$606$	1.87883e8			0.844249
$607$	−1.91587e8			−0.856644			−0.428322	−	0.903626i	$-0.640895\pi$
$607$	−1.91587e8			−0.856644			−0.428322	+	0.903626i	$0.640895\pi$
$608$		−	1.58110e8i		−	0.703476i
$609$	−4.54571e7			−0.201257
$610$	1.08990e7			0.0480171
$611$	5.78782e6			0.0253742
$612$	−2.33813e6			−0.0102003
$613$			1.35949e8i			0.590193i	0.955468	+	0.295096i	$0.0953517\pi$
$613$			1.35949e8i			0.590193i	−0.955468	+	0.295096i	$0.904648\pi$
$614$			1.08495e8i			0.468711i
$615$	−5.27735e6			−0.0226877
$616$	−1.26651e6			−0.00541834
$617$	4.51298e7			0.192136			0.0960678	−	0.995375i	$-0.469373\pi$
$617$	4.51298e7			0.192136			0.0960678	+	0.995375i	$0.469373\pi$
$618$	−1.36035e8			−0.576351
$619$	−2.39592e8			−1.01018			−0.505092	−	0.863066i	$-0.668541\pi$
$619$	−2.39592e8			−1.01018			−0.505092	+	0.863066i	$0.668541\pi$
$620$			2.64745e6i			0.0111084i
$621$			5.13553e7i			0.214442i
$622$			4.41963e7i			0.183660i
$623$		−	7.24595e7i		−	0.299662i
$624$		−	8.44905e6i		−	0.0347740i
$625$	2.42834e8			0.994647
$626$	−6.59001e7			−0.268635
$627$		−	4.53185e6i		−	0.0183854i
$628$		−	5.48378e7i		−	0.221412i
$629$		−	1.25579e7i		−	0.0504620i
$630$		−	843704.i		−	0.00337418i
$631$	2.71459e8			1.08048			0.540240	−	0.841511i	$-0.318333\pi$
$631$	2.71459e8			1.08048			0.540240	+	0.841511i	$0.318333\pi$
$632$			2.69279e8i			1.06672i
$633$		−	2.25274e8i		−	0.888178i
$634$			4.00279e7i			0.157071i
$635$	1.21938e7			0.0476230
$636$	1.18542e7			0.0460789
$637$			1.93615e7i			0.0749065i
$638$	−5.57740e6			−0.0214768
$639$	−1.66183e8			−0.636918
$640$		−	6.37863e6i		−	0.0243325i
$641$	3.22726e8			1.22535			0.612675	−	0.790335i	$-0.290093\pi$
$641$	3.22726e8			1.22535			0.612675	+	0.790335i	$0.290093\pi$
$642$		−	2.05595e8i		−	0.776975i
$643$	−4.58458e8			−1.72451			−0.862256	−	0.506472i	$-0.830949\pi$
$643$	−4.58458e8			−1.72451			−0.862256	+	0.506472i	$0.830949\pi$
$644$			1.68626e7i			0.0631346i
$645$			6.26077e6i			0.0233318i
$646$			5.94374e7i			0.220477i
$647$	−1.30910e8			−0.483349			−0.241675	−	0.970357i	$-0.577697\pi$
$647$	−1.30910e8			−0.483349			−0.241675	+	0.970357i	$0.577697\pi$
$648$		−	3.25160e7i		−	0.119501i
$649$	−2.93338e6	+	4.18256e6i	−0.0107309	+	0.0153006i
$650$	1.96794e7			0.0716593
$651$		−	5.37116e7i		−	0.194682i
$652$	3.83497e7			0.138363
$653$	−5.20303e8			−1.86860			−0.934300	−	0.356487i	$-0.883974\pi$
$653$	−5.20303e8			−1.86860			−0.934300	+	0.356487i	$0.883974\pi$
$654$	2.01934e8			0.721900
$655$			1.76647e7i			0.0628610i
$656$	1.95769e8			0.693477
$657$			1.73578e8i			0.612065i
$658$	−2.14400e7			−0.0752571
$659$		−	3.84699e8i		−	1.34420i	−0.740459	−	0.672102i	$-0.765392\pi$
$659$		−	3.84699e8i		−	1.34420i	0.740459	−	0.672102i	$-0.234608\pi$
$660$			27548.0i			9.58206e-5i
$661$	−3.53367e6			−0.0122355			−0.00611775	−	0.999981i	$-0.501947\pi$
$661$	−3.53367e6			−0.0122355			−0.00611775	+	0.999981i	$0.501947\pi$
$662$		−	3.77418e8i		−	1.30091i
$663$		−	1.97881e6i		−	0.00678991i
$664$	−3.08321e8			−1.05317
$665$	5.70758e6			0.0194083
$666$	3.03312e7			0.102676
$667$			4.27565e8i			1.44087i
$668$	7.03170e7			0.235902
$669$	1.64090e8			0.548029
$670$	−5.61046e6			−0.0186541
$671$	7.21981e6			0.0238978
$672$		−	1.94991e7i		−	0.0642549i
$673$		−	2.92865e8i		−	0.960776i	−0.877056	−	0.480388i	$-0.840496\pi$
$673$		−	2.92865e8i		−	0.960776i	0.877056	−	0.480388i	$-0.159504\pi$
$674$	1.10188e8			0.359877
$675$	5.90818e7			0.192107
$676$	6.45052e7			0.208811
$677$	4.31519e8			1.39070			0.695351	−	0.718670i	$-0.255249\pi$
$677$	4.31519e8			1.39070			0.695351	+	0.718670i	$0.255249\pi$
$678$	2.74431e8			0.880529
$679$		−	1.22630e8i		−	0.391731i
$680$		−	2.08031e6i		−	0.00661609i
$681$		−	1.26008e8i		−	0.398986i
$682$		−	6.59019e6i		−	0.0207752i
$683$			3.46467e8i			1.08742i	0.839272	+	0.543712i	$0.182982\pi$
$683$			3.46467e8i			1.08742i	−0.839272	+	0.543712i	$0.817018\pi$
$684$	3.82036e7			0.119381
$685$	−6.44619e6			−0.0200554
$686$		−	1.49063e8i		−	0.461740i
$687$			2.21024e8i			0.681662i
$688$		−	2.32250e8i		−	0.713166i
$689$			1.00325e7i			0.0306726i
$690$	−7.93579e6			−0.0241570
$691$		−	2.41016e8i		−	0.730485i	−0.930912	−	0.365243i	$-0.880986\pi$
$691$		−	2.41016e8i		−	0.730485i	0.930912	−	0.365243i	$-0.119014\pi$
$692$		−	5.62470e7i		−	0.169739i
$693$		−	558895.i		−	0.00167931i
$694$	2.03269e7			0.0608124
$695$	2.62574e7			0.0782162
$696$		−	2.70716e8i		−	0.802946i
$697$	4.58501e7			0.135407
$698$	5.78272e8			1.70046
$699$		−	2.05866e8i		−	0.602773i
$700$	1.93996e7			0.0565587
$701$		−	3.94108e7i		−	0.114409i	−0.998362	−	0.0572046i	$-0.981781\pi$
$701$		−	3.94108e7i		−	0.114409i	0.998362	−	0.0572046i	$-0.0182187\pi$
$702$	4.77945e6			0.0138155
$703$			2.05188e8i			0.590589i
$704$		−	7.25452e6i		−	0.0207917i
$705$			2.68510e6i			0.00766291i
$706$	−1.67285e8			−0.475383
$707$			1.56749e8i			0.443554i
$708$	−3.52590e7	−	2.47285e7i	−0.0993506	−	0.0696783i
$709$	6.41700e7			0.180050			0.0900250	−	0.995940i	$-0.471305\pi$
$709$	6.41700e7			0.180050			0.0900250	+	0.995940i	$0.471305\pi$
$710$		−	2.56798e7i		−	0.0717491i
$711$	−1.18830e8			−0.330610
$712$	4.31526e8			1.19555
$713$	−5.05206e8			−1.39380
$714$			7.33018e6i			0.0201382i
$715$	−23314.5			−6.37834e−5
$716$		−	2.46432e7i		−	0.0671364i
$717$	−2.63934e8			−0.716042
$718$			3.33283e8i			0.900409i
$719$		−	7.86926e7i		−	0.211713i	−0.994381	−	0.105856i	$-0.966242\pi$
$719$		−	7.86926e7i		−	0.211713i	0.994381	−	0.105856i	$-0.0337584\pi$
$720$	3.91971e6			0.0105016
$721$		−	1.13493e8i		−	0.302805i
$722$		−	6.36686e8i		−	1.69166i
$723$	1.92115e8			0.508331
$724$	−5.67708e7			−0.149592
$725$	4.91893e8			1.29079
$726$			1.96273e8i			0.512922i
$727$	1.84082e8			0.479080			0.239540	−	0.970886i	$-0.423003\pi$
$727$	1.84082e8			0.479080			0.239540	+	0.970886i	$0.423003\pi$
$728$	9.03592e6			0.0234195
$729$	1.43489e7			0.0370370
$730$	−2.68225e7			−0.0689495
$731$		−	5.43941e7i		−	0.139252i
$732$			6.08632e7i			0.155175i
$733$	−4.12617e8			−1.04770			−0.523848	−	0.851812i	$-0.675504\pi$
$733$	−4.12617e8			−1.04770			−0.523848	+	0.851812i	$0.675504\pi$
$734$	−3.87351e8			−0.979528
$735$	−8.98223e6			−0.0226215
$736$	−1.83406e8			−0.460024
$737$	−3.71654e6			−0.00928402
$738$			1.10742e8i			0.275515i
$739$		−	4.38567e8i		−	1.08668i	−0.839512	−	0.543342i	$-0.817159\pi$
$739$		−	4.38567e8i		−	1.08668i	0.839512	−	0.543342i	$-0.182841\pi$
$740$		−	1.24729e6i		−	0.00307802i
$741$			3.23325e7i			0.0794667i
$742$		−	3.71637e7i		−	0.0909718i
$743$	−1.55606e8			−0.379367			−0.189683	−	0.981845i	$-0.560746\pi$
$743$	−1.55606e8			−0.379367			−0.189683	+	0.981845i	$0.560746\pi$
$744$	3.19875e8			0.776714
$745$			392361.i			0.000948891i
$746$		−	3.93993e8i		−	0.949013i
$747$		−	1.36058e8i		−	0.326410i
$748$		−	239340.i		−	0.000571887i
$749$	1.71525e8			0.408209
$750$			1.82758e7i			0.0433205i
$751$		−	1.66999e8i		−	0.394270i	−0.980376	−	0.197135i	$-0.936836\pi$
$751$		−	1.66999e8i		−	0.394270i	0.980376	−	0.197135i	$-0.0631637\pi$
$752$		−	9.96068e7i		−	0.234226i
$753$	6.29893e6			0.0147531
$754$	3.97920e7			0.0928285
$755$			3.32175e6i			0.00771839i
$756$	4.71150e6			0.0109042
$757$	−1.60340e8			−0.369619			−0.184810	−	0.982774i	$-0.559167\pi$
$757$	−1.60340e8			−0.369619			−0.184810	+	0.982774i	$0.559167\pi$
$758$		−	5.90524e8i		−	1.35591i
$759$	−5.25691e6			−0.0120228
$760$			3.39910e7i			0.0774324i
$761$	−2.04852e8			−0.464821			−0.232410	−	0.972618i	$-0.574661\pi$
$761$	−2.04852e8			−0.464821			−0.232410	+	0.972618i	$0.574661\pi$
$762$		−	2.55880e8i		−	0.578323i
$763$			1.68471e8i			0.379273i
$764$		−	1.30791e8i		−	0.293290i
$765$	918016.			0.00205053
$766$			8.79436e7i			0.195667i
$767$	2.09282e7	−	2.98405e7i	0.0463817	−	0.0661332i
$768$	1.57112e8			0.346838
$769$			6.58830e8i			1.44875i	0.689405	+	0.724377i	$0.257872\pi$
$769$			6.58830e8i			1.44875i	−0.689405	+	0.724377i	$0.742128\pi$
$770$	86364.6			0.000189175
$771$	1.29949e8			0.283537
$772$	1.08871e8			0.236626
$773$		−	6.88094e8i		−	1.48974i	−0.667211	−	0.744868i	$-0.732512\pi$
$773$		−	6.88094e8i		−	1.48974i	0.667211	−	0.744868i	$-0.267488\pi$
$774$	1.31379e8			0.283337
$775$			5.81215e8i			1.24862i
$776$	7.30312e8			1.56287
$777$			2.53050e7i			0.0539440i
$778$		−	6.15209e7i		−	0.130642i
$779$	−7.49161e8			−1.58476
$780$		−	196542.i		−	0.000414162i
$781$		−	1.70111e7i		−	0.0357091i
$782$	6.89469e7			0.144176
$783$	1.19464e8			0.248857
$784$	3.33205e8			0.691454
$785$			2.15308e7i			0.0445094i
$786$	3.70684e8			0.763371
$787$	3.15091e8			0.646415			0.323208	−	0.946328i	$-0.395239\pi$
$787$	3.15091e8			0.646415			0.323208	+	0.946328i	$0.395239\pi$
$788$	1.41433e8			0.289050
$789$	4.30019e7			0.0875500
$790$		−	1.83624e7i		−	0.0372433i
$791$			2.28954e8i			0.462615i
$792$	3.32845e6			0.00669988
$793$	−5.15098e7			−0.103293
$794$	4.26328e8			0.851691
$795$	−4.65430e6			−0.00926303
$796$	2.46950e7			0.0489631
$797$			7.92808e8i			1.56600i	0.622019	+	0.783002i	$0.286313\pi$
$797$			7.92808e8i			1.56600i	−0.622019	+	0.783002i	$0.713687\pi$
$798$		−	1.19770e8i		−	0.235690i
$799$		−	2.33284e7i		−	0.0457346i
$800$			2.11000e8i			0.412110i
$801$			1.90427e8i			0.370537i
$802$	−7.72855e8			−1.49822
$803$	−1.77680e7			−0.0343157
$804$		−	3.13305e7i		−	0.0602836i
$805$		−	6.62074e6i		−	0.0126917i
$806$			4.70177e7i			0.0897959i
$807$			3.18638e8i			0.606285i
$808$	−9.33504e8			−1.76963
$809$			6.09963e7i			0.115201i	0.998340	+	0.0576007i	$0.0183450\pi$
$809$			6.09963e7i			0.115201i	−0.998340	+	0.0576007i	$0.981655\pi$
$810$			2.21730e6i			0.00417224i
$811$			3.64050e8i			0.682493i	0.939974	+	0.341246i	$0.110849\pi$
$811$			3.64050e8i			0.682493i	−0.939974	+	0.341246i	$0.889151\pi$
$812$	3.92262e7			0.0732670
$813$	2.20847e8			0.410978
$814$			3.10481e6i			0.00575655i
$815$	−1.50572e7			−0.0278145
$816$	−3.40548e7			−0.0626769
$817$			8.88766e8i			1.62975i
$818$	−7.65834e8			−1.39918
$819$			3.98744e6i			0.00725843i
$820$	4.55397e6			0.00825940
$821$		−	1.53827e8i		−	0.277973i	−0.990294	−	0.138987i	$-0.955615\pi$
$821$		−	1.53827e8i		−	0.277973i	0.990294	−	0.138987i	$-0.0443845\pi$
$822$			1.35270e8i			0.243549i
$823$		−	4.02308e8i		−	0.721704i	−0.932623	−	0.360852i	$-0.882486\pi$
$823$		−	4.02308e8i		−	0.721704i	0.932623	−	0.360852i	$-0.117514\pi$
$824$	6.75896e8			1.20809
$825$			6.04782e6i			0.0107705i
$826$	−7.75251e7	+	1.10539e8i	−0.137563	+	0.196144i
$827$	8.60824e8			1.52194			0.760971	−	0.648786i	$-0.224723\pi$
$827$	8.60824e8			1.52194			0.760971	+	0.648786i	$0.224723\pi$
$828$		−	4.43159e7i		−	0.0780671i
$829$	3.78821e8			0.664921			0.332461	−	0.943117i	$-0.392121\pi$
$829$	3.78821e8			0.664921			0.332461	+	0.943117i	$0.392121\pi$
$830$	2.10248e7			0.0367703
$831$	−8.03032e7			−0.139936
$832$			5.17574e7i			0.0898675i
$833$	7.80384e7			0.135012
$834$		−	5.50997e8i		−	0.949841i
$835$	−2.76084e7			−0.0474222
$836$			3.91066e6i			0.00669316i
$837$			1.41157e8i			0.240727i
$838$	2.97337e7			0.0505263
$839$		−	2.12664e8i		−	0.360088i	−0.983659	−	0.180044i	$-0.942376\pi$
$839$		−	2.12664e8i		−	0.360088i	0.983659	−	0.180044i	$-0.0576241\pi$
$840$			4.19197e6i			0.00707262i
$841$	3.99787e8			0.672110
$842$	−1.79867e8			−0.301310
$843$	1.04895e7			0.0175095
$844$			1.94395e8i			0.323339i
$845$	−2.53265e7			−0.0419764
$846$	5.63455e7			0.0930568
$847$	−1.63748e8			−0.269480
$848$	1.72656e8			0.283136
$849$		−	1.93161e8i		−	0.315644i
$850$		−	7.93200e7i		−	0.129159i
$851$	2.38016e8			0.386205
$852$	1.43404e8			0.231869
$853$	5.13419e8			0.827228			0.413614	−	0.910452i	$-0.364266\pi$
$853$	5.13419e8			0.827228			0.413614	+	0.910452i	$0.364266\pi$
$854$	1.90809e8			0.306356
$855$	−1.49998e7			−0.0239987
$856$			1.02150e9i			1.62862i
$857$			4.10711e8i			0.652520i	0.945280	+	0.326260i	$0.105788\pi$
$857$			4.10711e8i			0.652520i	−0.945280	+	0.326260i	$0.894212\pi$
$858$			489242.i			0.000774572i
$859$		−	6.78867e8i		−	1.07104i	−0.844523	−	0.535519i	$-0.820116\pi$
$859$		−	6.78867e8i		−	1.07104i	0.844523	−	0.535519i	$-0.179884\pi$
$860$		−	5.40259e6i		−	0.00849389i
$861$	−9.23910e7			−0.144751
$862$	9.69815e8			1.51414
$863$			8.96658e8i			1.39506i	0.716553	+	0.697532i	$0.245719\pi$
$863$			8.96658e8i			1.39506i	−0.716553	+	0.697532i	$0.754281\pi$
$864$			5.12446e7i			0.0794524i
$865$			2.20841e7i			0.0341218i
$866$		−	2.55132e8i		−	0.392836i
$867$	3.68292e8			0.565112
$868$			4.63492e7i			0.0708734i
$869$		−	1.21638e7i		−	0.0185358i
$870$			1.84604e7i			0.0280339i
$871$	2.65156e7			0.0401280
$872$	−1.00332e9			−1.51317
$873$			3.22278e8i			0.484382i
$874$	−1.12655e9			−1.68739
$875$	−1.52473e7			−0.0227598
$876$		−	1.49785e8i		−	0.222821i
$877$	−2.40821e8			−0.357022			−0.178511	−	0.983938i	$-0.557128\pi$
$877$	−2.40821e8			−0.357022			−0.178511	+	0.983938i	$0.557128\pi$
$878$		−	6.65204e8i		−	0.982815i
$879$	−6.60164e8			−0.972042
$880$			401236.i			0.000588778i
$881$		−	1.26491e9i		−	1.84983i	−0.380173	−	0.924915i	$-0.624136\pi$
$881$		−	1.26491e9i		−	1.84983i	0.380173	−	0.924915i	$-0.375864\pi$
$882$			1.88487e8i			0.274711i
$883$	4.79498e8			0.696474			0.348237	−	0.937407i	$-0.386780\pi$
$883$	4.79498e8			0.696474			0.348237	+	0.937407i	$0.386780\pi$
$884$			1.70757e6i			0.00247185i
$885$	1.38437e7	+	9.70909e6i	0.0199720	+	0.0140071i
$886$	−6.68963e8			−0.961836
$887$		−	7.51852e8i		−	1.07736i	−0.842510	−	0.538681i	$-0.818923\pi$
$887$		−	7.51852e8i		−	1.07736i	0.842510	−	0.538681i	$-0.181077\pi$
$888$	−1.50702e8			−0.215218
$889$	2.13477e8			0.303841
$890$	−2.94262e7			−0.0417412
$891$			1.46881e6i			0.00207650i
$892$	−1.41598e8			−0.199509
$893$			3.81172e8i			0.535262i
$894$	8.23348e6			0.0115231
$895$			9.67561e6i			0.0134961i
$896$		−	1.11671e8i		−	0.155245i
$897$	3.75054e7			0.0519657
$898$			9.63403e8i			1.33039i
$899$			1.17522e9i			1.61748i
$900$	−5.09833e7			−0.0699359
$901$	4.04370e7			0.0552846
$902$	−1.13360e7			−0.0154468
$903$			1.09608e8i			0.148860i
$904$	−1.36352e9			−1.84568
$905$	2.22898e7			0.0300719
$906$	6.97052e7			0.0937305
$907$	−6.69829e8			−0.897723			−0.448862	−	0.893601i	$-0.648170\pi$
$907$	−6.69829e8			−0.897723			−0.448862	+	0.893601i	$0.648170\pi$
$908$			1.08736e8i			0.145250i
$909$		−	4.11944e8i		−	0.548462i
$910$	−616169.			−0.000817665
$911$	−6.71306e8			−0.887902			−0.443951	−	0.896051i	$-0.646424\pi$
$911$	−6.71306e8			−0.887902			−0.443951	+	0.896051i	$0.646424\pi$
$912$	5.56434e8			0.733549
$913$	1.39274e7			0.0183003
$914$	−2.71537e8			−0.355623
$915$		−	2.38966e7i		−	0.0311941i
$916$		−	1.90727e8i		−	0.248157i
$917$			3.09257e8i			0.401062i
$918$		−	1.92641e7i		−	0.0249012i
$919$		−	2.66964e8i		−	0.343959i	−0.985101	−	0.171979i	$-0.944984\pi$
$919$		−	2.66964e8i		−	0.343959i	0.985101	−	0.171979i	$-0.0550163\pi$
$920$	3.94292e7			0.0506355
$921$	2.37881e8			0.304496
$922$		−	7.68528e8i		−	0.980543i
$923$			1.21366e8i			0.154344i
$924$			482286.i			0.000611348i
$925$		−	2.73826e8i		−	0.345979i
$926$	−9.21181e8			−1.16014
$927$			2.98265e8i			0.374423i
$928$			4.26644e8i			0.533853i
$929$		−	9.17577e8i		−	1.14445i	−0.820098	−	0.572223i	$-0.806081\pi$
$929$		−	9.17577e8i		−	1.14445i	0.820098	−	0.572223i	$-0.193919\pi$
$930$	−2.18126e7			−0.0271181
$931$	−1.27510e9			−1.58014
$932$			1.77648e8i			0.219438i
$933$	9.69026e7			0.119314
$934$	1.99155e7			0.0244428
$935$			93971.4i			0.000114964i
$936$	−2.37469e7			−0.0289587
$937$			4.04281e8i			0.491433i	0.969342	+	0.245717i	$0.0790232\pi$
$937$			4.04281e8i			0.491433i	−0.969342	+	0.245717i	$0.920977\pi$
$938$	−9.82228e7			−0.119016
$939$			1.44489e8i			0.174517i
$940$		−	2.31705e6i		−	0.00278966i
$941$		−	7.69801e8i		−	0.923867i	−0.886915	−	0.461933i	$-0.847156\pi$
$941$		−	7.69801e8i		−	0.923867i	0.886915	−	0.461933i	$-0.152844\pi$
$942$	4.51813e8			0.540513
$943$			8.69020e8i			1.03632i
$944$	−5.13546e8	−	3.60169e8i	−0.610468	−	0.428144i
$945$	−1.84987e6			−0.00219202
$946$			1.34484e7i			0.0158854i
$947$	9.93572e8			1.16990			0.584951	−	0.811069i	$-0.301114\pi$
$947$	9.93572e8			1.16990			0.584951	+	0.811069i	$0.301114\pi$
$948$	1.02541e8			0.120358
$949$	1.26766e8			0.148322
$950$			1.29604e9i			1.51164i
$951$	8.77633e7			0.102040
$952$		−	3.64202e7i		−	0.0422116i
$953$	−5.64373e8			−0.652060			−0.326030	−	0.945359i	$-0.605711\pi$
$953$	−5.64373e8			−0.652060			−0.326030	+	0.945359i	$0.605711\pi$
$954$			9.76680e7i			0.112488i
$955$			5.13522e7i			0.0589588i
$956$	2.27756e8			0.260673
$957$			1.22287e7i			0.0139523i
$958$			1.04377e9i			1.18716i
$959$	−1.12854e8			−0.127956
$960$	−2.40115e7			−0.0271397
$961$	−5.01122e8			−0.564642
$962$		−	2.21513e7i		−	0.0248814i
$963$	−4.50777e8			−0.504758
$964$	−1.65781e8			−0.185057
$965$	−4.27460e7			−0.0475678
$966$	−1.38933e8			−0.154125
$967$		−	1.04721e9i		−	1.15812i	−0.815284	−	0.579061i	$-0.803419\pi$
$967$		−	1.04721e9i		−	1.15812i	0.815284	−	0.579061i	$-0.196581\pi$
$968$		−	9.75189e8i		−	1.07513i
$969$	1.30320e8			0.143231
$970$	−4.98008e7			−0.0545659
$971$	−1.53371e9			−1.67527			−0.837635	−	0.546230i	$-0.816062\pi$
$971$	−1.53371e9			−1.67527			−0.837635	+	0.546230i	$0.816062\pi$
$972$	−1.23821e7			−0.0134832
$973$	4.59690e8			0.499030
$974$		−	1.45616e9i		−	1.57591i
$975$		−	4.31482e7i		−	0.0465531i
$976$			8.86469e8i			0.953485i
$977$			6.65628e8i			0.713753i	0.934152	+	0.356876i	$0.116158\pi$
$977$			6.65628e8i			0.713753i	−0.934152	+	0.356876i	$0.883842\pi$
$978$			3.15967e8i			0.337773i
$979$	−1.94928e7			−0.0207743
$980$	7.75101e6			0.00823531
$981$		−	4.42751e8i		−	0.468978i
$982$			1.07519e9i			1.13541i
$983$			7.86895e8i			0.828431i	0.910179	+	0.414215i	$0.135944\pi$
$983$			7.86895e8i			0.828431i	−0.910179	+	0.414215i	$0.864056\pi$
$984$		−	5.50227e8i		−	0.577506i
$985$	−5.55306e7			−0.0581064
$986$		−	1.60386e8i		−	0.167315i
$987$			4.70084e7i			0.0488904i
$988$		−	2.79006e7i		−	0.0289296i
$989$	1.03096e9			1.06574
$990$	−226971.			−0.000233918
$991$			1.03857e9i			1.06712i	0.845761	+	0.533562i	$0.179147\pi$
$991$			1.03857e9i			1.06712i	−0.845761	+	0.533562i	$0.820853\pi$
$992$	−5.04117e8			−0.516412
$993$	−8.27509e8			−0.845133
$994$		−	4.49579e8i		−	0.457769i
$995$	−9.69593e6			−0.00984283
$996$			1.17409e8i			0.118829i
$997$	1.18891e8			0.119968			0.0599839	−	0.998199i	$-0.480895\pi$
$997$	1.18891e8			0.119968			0.0599839	+	0.998199i	$0.480895\pi$
$998$			2.98001e8i			0.299796i
$999$		−	6.65028e7i		−	0.0667027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.18	✓	60
59.58	odd	2	inner	177.7.c.a.58.43	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.18	✓	60	1.1	even	1	trivial
177.7.c.a.58.43	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)

\(f(q)\)	\(=\)	\(q-7.10973i q^{2} -15.5885 q^{3} +13.4517 q^{4} -5.28151 q^{5} +110.830i q^{6} -92.4639 q^{7} -550.661i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-7.10973i q^{2} -15.5885 q^{3} +13.4517 q^{4} -5.28151 q^{5} +110.830i q^{6} -92.4639 q^{7} -550.661i q^{8} +243.000 q^{9} +37.5501i q^{10} +24.8744i q^{11} -209.691 q^{12} -177.466i q^{13} +657.394i q^{14} +82.3307 q^{15} -3054.14 q^{16} -715.296 q^{17} -1727.66i q^{18} +11687.5 q^{19} -71.0454 q^{20} +1441.37 q^{21} +176.850 q^{22} -13557.4i q^{23} +8583.95i q^{24} -15597.1 q^{25} -1261.74 q^{26} -3788.00 q^{27} -1243.80 q^{28} -31537.4 q^{29} -585.349i q^{30} -37264.3i q^{31} -13528.2i q^{32} -387.753i q^{33} +5085.56i q^{34} +488.350 q^{35} +3268.76 q^{36} +17556.2i q^{37} -83094.9i q^{38} +2766.42i q^{39} +2908.32i q^{40} -64099.4 q^{41} -10247.8i q^{42} +76044.2i q^{43} +334.603i q^{44} -1283.41 q^{45} -96389.3 q^{46} +32613.7i q^{47} +47609.4 q^{48} -109099. q^{49} +110891. i q^{50} +11150.4 q^{51} -2387.22i q^{52} -56531.8 q^{53} +26931.6i q^{54} -131.374i q^{55} +50916.3i q^{56} -182190. q^{57} +224223. i q^{58} +(168147. + 117928. i) q^{59} +1107.49 q^{60} -290251. i q^{61} -264939. q^{62} -22468.7 q^{63} -291647. q^{64} +937.290i q^{65} -2756.82 q^{66} +149412. i q^{67} -9621.95 q^{68} +211339. i q^{69} -3472.03i q^{70} -683880. q^{71} -133811. i q^{72} +714312. i q^{73} +124820. q^{74} +243135. q^{75} +157217. q^{76} -2299.98i q^{77} +19668.5 q^{78} -489011. q^{79} +16130.5 q^{80} +59049.0 q^{81} +455730. i q^{82} -559911. i q^{83} +19388.9 q^{84} +3777.84 q^{85} +540654. q^{86} +491620. q^{87} +13697.3 q^{88} +783652. i q^{89} +9124.69i q^{90} +16409.2i q^{91} -182370. i q^{92} +580892. i q^{93} +231874. q^{94} -61727.6 q^{95} +210883. i q^{96} +1.32625e6i q^{97} +775668. i q^{98} +6044.47i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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