LMFDB - Embedded newform 177.7.c.a.58.12

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			58.12
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.4738i q^{2} -15.5885 q^{3} -45.7013 q^{4} +65.8108 q^{5} +163.271i q^{6} +49.8494 q^{7} -191.658i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-10.4738i q^{2} -15.5885 q^{3} -45.7013 q^{4} +65.8108 q^{5} +163.271i q^{6} +49.8494 q^{7} -191.658i q^{8} +243.000 q^{9} -689.291i q^{10} +359.481i q^{11} +712.413 q^{12} +1757.21i q^{13} -522.114i q^{14} -1025.89 q^{15} -4932.27 q^{16} -2676.91 q^{17} -2545.14i q^{18} +1226.97 q^{19} -3007.64 q^{20} -777.075 q^{21} +3765.14 q^{22} +17806.6i q^{23} +2987.65i q^{24} -11293.9 q^{25} +18404.8 q^{26} -3788.00 q^{27} -2278.18 q^{28} -11354.5 q^{29} +10745.0i q^{30} +40936.7i q^{31} +39393.8i q^{32} -5603.75i q^{33} +28037.5i q^{34} +3280.63 q^{35} -11105.4 q^{36} +48303.0i q^{37} -12851.1i q^{38} -27392.2i q^{39} -12613.1i q^{40} +116179. q^{41} +8138.96i q^{42} -84100.8i q^{43} -16428.7i q^{44} +15992.0 q^{45} +186503. q^{46} +121248. i q^{47} +76886.6 q^{48} -115164. q^{49} +118291. i q^{50} +41728.9 q^{51} -80306.8i q^{52} +265316. q^{53} +39674.8i q^{54} +23657.7i q^{55} -9554.02i q^{56} -19126.6 q^{57} +118925. i q^{58} +(-205323. + 4783.75i) q^{59} +46884.4 q^{60} -288153. i q^{61} +428764. q^{62} +12113.4 q^{63} +96938.3 q^{64} +115643. i q^{65} -58692.8 q^{66} +150364. i q^{67} +122338. q^{68} -277577. i q^{69} -34360.7i q^{70} -157139. q^{71} -46572.8i q^{72} -15652.5i q^{73} +505918. q^{74} +176055. q^{75} -56074.3 q^{76} +17919.9i q^{77} -286902. q^{78} +756230. q^{79} -324597. q^{80} +59049.0 q^{81} -1.21684e6i q^{82} -669157. i q^{83} +35513.3 q^{84} -176169. q^{85} -880859. q^{86} +176999. q^{87} +68897.2 q^{88} +802081. i q^{89} -167498. i q^{90} +87595.9i q^{91} -813785. i q^{92} -638139. i q^{93} +1.26993e6 q^{94} +80748.1 q^{95} -614088. i q^{96} +879496. i q^{97} +1.20621e6i q^{98} +87353.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	10.4738i		−	1.30923i	−0.755963	−	0.654615i	$-0.772831\pi$
$2$		−	10.4738i		−	1.30923i	0.755963	−	0.654615i	$-0.227169\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	−45.7013			−0.714083
$5$	65.8108			0.526486			0.263243	−	0.964730i	$-0.415208\pi$
$5$	65.8108			0.526486			0.263243	+	0.964730i	$0.415208\pi$
$6$			163.271i			0.755884i
$7$	49.8494			0.145333			0.0726667	−	0.997356i	$-0.476849\pi$
$7$	49.8494			0.145333			0.0726667	+	0.997356i	$0.476849\pi$
$8$		−	191.658i		−	0.374331i
$9$	243.000			0.333333
$10$		−	689.291i		−	0.689291i
$11$			359.481i			0.270083i	0.990840	+	0.135042i	$0.0431168\pi$
$11$			359.481i			0.270083i	−0.990840	+	0.135042i	$0.956883\pi$
$12$	712.413			0.412276
$13$			1757.21i			0.799823i	0.916554	+	0.399912i	$0.130959\pi$
$13$			1757.21i			0.799823i	−0.916554	+	0.399912i	$0.869041\pi$
$14$		−	522.114i		−	0.190275i
$15$	−1025.89			−0.303967
$16$	−4932.27			−1.20417
$17$	−2676.91			−0.544862			−0.272431	−	0.962175i	$-0.587828\pi$
$17$	−2676.91			−0.544862			−0.272431	+	0.962175i	$0.587828\pi$
$18$		−	2545.14i		−	0.436410i
$19$	1226.97			0.178885			0.0894426	−	0.995992i	$-0.471491\pi$
$19$	1226.97			0.178885			0.0894426	+	0.995992i	$0.471491\pi$
$20$	−3007.64			−0.375955
$21$	−777.075			−0.0839083
$22$	3765.14			0.353601
$23$			17806.6i			1.46352i	0.681564	+	0.731758i	$0.261300\pi$
$23$			17806.6i			1.46352i	−0.681564	+	0.731758i	$0.738700\pi$
$24$			2987.65i			0.216120i
$25$	−11293.9			−0.722812
$26$	18404.8			1.04715
$27$	−3788.00			−0.192450
$28$	−2278.18			−0.103780
$29$	−11354.5			−0.465558			−0.232779	−	0.972530i	$-0.574782\pi$
$29$	−11354.5			−0.465558			−0.232779	+	0.972530i	$0.574782\pi$
$30$			10745.0i			0.397963i
$31$			40936.7i			1.37413i	0.726597	+	0.687064i	$0.241101\pi$
$31$			40936.7i			1.37413i	−0.726597	+	0.687064i	$0.758899\pi$
$32$			39393.8i			1.20220i
$33$		−	5603.75i		−	0.155933i
$34$			28037.5i			0.713350i
$35$	3280.63			0.0765161
$36$	−11105.4			−0.238028
$37$			48303.0i			0.953606i	0.879010	+	0.476803i	$0.158204\pi$
$37$			48303.0i			0.953606i	−0.879010	+	0.476803i	$0.841796\pi$
$38$		−	12851.1i		−	0.234202i
$39$		−	27392.2i		−	0.461778i
$40$		−	12613.1i		−	0.197080i
$41$	116179.			1.68569			0.842844	−	0.538158i	$-0.180880\pi$
$41$	116179.			1.68569			0.842844	+	0.538158i	$0.180880\pi$
$42$			8138.96i			0.109855i
$43$		−	84100.8i		−	1.05778i	−0.848691	−	0.528889i	$-0.822609\pi$
$43$		−	84100.8i		−	1.05778i	0.848691	−	0.528889i	$-0.177391\pi$
$44$		−	16428.7i		−	0.192862i
$45$	15992.0			0.175495
$46$	186503.			1.91608
$47$			121248.i			1.16783i	0.811814	+	0.583917i	$0.198481\pi$
$47$			121248.i			1.16783i	−0.811814	+	0.583917i	$0.801519\pi$
$48$	76886.6			0.695227
$49$	−115164.			−0.978878
$50$			118291.i			0.946327i
$51$	41728.9			0.314576
$52$		−	80306.8i		−	0.571140i
$53$	265316.			1.78211			0.891056	−	0.453893i	$-0.149965\pi$
$53$	265316.			1.78211			0.891056	+	0.453893i	$0.149965\pi$
$54$			39674.8i			0.251961i
$55$			23657.7i			0.142195i
$56$		−	9554.02i		−	0.0544029i
$57$	−19126.6			−0.103279
$58$			118925.i			0.609522i
$59$	−205323.	+	4783.75i	−0.999729	+	0.0232923i
$59$	−205323.	+	4783.75i	−0.999729	+	0.0232923i
$60$	46884.4			0.217058
$61$		−	288153.i		−	1.26950i	−0.772716	−	0.634752i	$-0.781102\pi$
$61$		−	288153.i		−	1.26950i	0.772716	−	0.634752i	$-0.218898\pi$
$62$	428764.			1.79905
$63$	12113.4			0.0484445
$64$	96938.3			0.369790
$65$			115643.i			0.421096i
$66$	−58692.8			−0.204152
$67$			150364.i			0.499941i	0.968253	+	0.249971i	$0.0804210\pi$
$67$			150364.i			0.499941i	−0.968253	+	0.249971i	$0.919579\pi$
$68$	122338.			0.389077
$69$		−	277577.i		−	0.844962i
$70$		−	34360.7i		−	0.100177i
$71$	−157139.			−0.439044			−0.219522	−	0.975608i	$-0.570450\pi$
$71$	−157139.			−0.439044			−0.219522	+	0.975608i	$0.570450\pi$
$72$		−	46572.8i		−	0.124777i
$73$		−	15652.5i		−	0.0402361i	−0.999798	−	0.0201181i	$-0.993596\pi$
$73$		−	15652.5i		−	0.0402361i	0.999798	−	0.0201181i	$-0.00640421\pi$
$74$	505918.			1.24849
$75$	176055.			0.417316
$76$	−56074.3			−0.127739
$77$			17919.9i			0.0392521i
$78$	−286902.			−0.604574
$79$	756230.			1.53381			0.766906	−	0.641759i	$-0.221795\pi$
$79$	756230.			1.53381			0.766906	+	0.641759i	$0.221795\pi$
$80$	−324597.			−0.633978
$81$	59049.0			0.111111
$82$		−	1.21684e6i		−	2.20695i
$83$		−	669157.i		−	1.17029i	−0.810929	−	0.585145i	$-0.801038\pi$
$83$		−	669157.i		−	1.17029i	0.810929	−	0.585145i	$-0.198962\pi$
$84$	35513.3			0.0599175
$85$	−176169.			−0.286862
$86$	−880859.			−1.38488
$87$	176999.			0.268790
$88$	68897.2			0.101101
$89$			802081.i			1.13775i	0.822423	+	0.568877i	$0.192622\pi$
$89$			802081.i			1.13775i	−0.822423	+	0.568877i	$0.807378\pi$
$90$		−	167498.i		−	0.229764i
$91$			87595.9i			0.116241i
$92$		−	813785.i		−	1.04507i
$93$		−	638139.i		−	0.793353i
$94$	1.26993e6			1.52896
$95$	80748.1			0.0941806
$96$		−	614088.i		−	0.694092i
$97$			879496.i			0.963649i	0.876268	+	0.481824i	$0.160026\pi$
$97$			879496.i			0.963649i	−0.876268	+	0.481824i	$0.839974\pi$
$98$			1.20621e6i			1.28158i
$99$			87353.8i			0.0900277i
$100$	516148.			0.516148
$101$			958935.i			0.930733i	0.885118	+	0.465366i	$0.154077\pi$
$101$			958935.i			0.930733i	−0.885118	+	0.465366i	$0.845923\pi$
$102$		−	437061.i		−	0.411853i
$103$		−	501320.i		−	0.458779i	−0.973335	−	0.229389i	$-0.926327\pi$
$103$		−	501320.i		−	0.458779i	0.973335	−	0.229389i	$-0.0736729\pi$
$104$	336783.			0.299399
$105$	−51139.9			−0.0441766
$106$		−	2.77887e6i		−	2.33319i
$107$	1.15874e6			0.945878			0.472939	−	0.881095i	$-0.343193\pi$
$107$	1.15874e6			0.945878			0.472939	+	0.881095i	$0.343193\pi$
$108$	173116.			0.137425
$109$		−	369698.i		−	0.285474i	−0.989761	−	0.142737i	$-0.954410\pi$
$109$		−	369698.i		−	0.285474i	0.989761	−	0.142737i	$-0.0455904\pi$
$110$	247787.			0.186166
$111$		−	752969.i		−	0.550564i
$112$	−245871.			−0.175006
$113$			2.32947e6i			1.61444i	0.590253	+	0.807218i	$0.299028\pi$
$113$			2.32947e6i			1.61444i	−0.590253	+	0.807218i	$0.700972\pi$
$114$			200329.i			0.135216i
$115$			1.17187e6i			0.770521i
$116$	518915.			0.332447
$117$			427002.i			0.266608i
$118$	50104.2	+	2.15052e6i	0.0304950	+	1.30887i
$119$	−133442.			−0.0791867
$120$			196619.i			0.113784i
$121$	1.64233e6			0.927055
$122$	−3.01807e6			−1.66207
$123$	−1.81106e6			−0.973232
$124$		−	1.87086e6i		−	0.981241i
$125$	−1.77156e6			−0.907037
$126$		−	126874.i		−	0.0634250i
$127$	2.36785e6			1.15596			0.577981	−	0.816050i	$-0.303841\pi$
$127$	2.36785e6			1.15596			0.577981	+	0.816050i	$0.303841\pi$
$128$			1.50588e6i			0.718062i
$129$			1.31100e6i			0.610709i
$130$	1.21123e6			0.551311
$131$			3.73876e6i			1.66308i	0.555463	+	0.831541i	$0.312541\pi$
$131$			3.73876e6i			1.66308i	−0.555463	+	0.831541i	$0.687459\pi$
$132$			256099.i			0.111349i
$133$	61163.9			0.0259980
$134$	1.57489e6			0.654538
$135$	−249291.			−0.101322
$136$			513050.i			0.203959i
$137$	−4.53270e6			−1.76277			−0.881383	−	0.472402i	$-0.843387\pi$
$137$	−4.53270e6			−1.76277			−0.881383	+	0.472402i	$0.843387\pi$
$138$	−2.90730e6			−1.10625
$139$	−251519.			−0.0936541			−0.0468271	−	0.998903i	$-0.514911\pi$
$139$	−251519.			−0.0936541			−0.0468271	+	0.998903i	$0.514911\pi$
$140$	−149929.			−0.0546388
$141$		−	1.89007e6i		−	0.674249i
$142$			1.64585e6i			0.574810i
$143$	−631684.			−0.216019
$144$	−1.19854e6			−0.401390
$145$	−747248.			−0.245110
$146$	−163942.			−0.0526783
$147$	1.79523e6			0.565156
$148$		−	2.20751e6i		−	0.680953i
$149$			3.90999e6i			1.18200i	0.806673	+	0.590998i	$0.201266\pi$
$149$			3.90999e6i			1.18200i	−0.806673	+	0.590998i	$0.798734\pi$
$150$		−	1.84397e6i		−	0.546362i
$151$			2.04184e6i			0.593051i	0.955025	+	0.296525i	$0.0958279\pi$
$151$			2.04184e6i			0.593051i	−0.955025	+	0.296525i	$0.904172\pi$
$152$		−	235159.i		−	0.0669623i
$153$	−650489.			−0.181621
$154$	187690.			0.0513901
$155$			2.69407e6i			0.723460i
$156$			1.25186e6i			0.329748i
$157$		−	2.51585e6i		−	0.650109i	−0.945695	−	0.325054i	$-0.894617\pi$
$157$		−	2.51585e6i		−	0.650109i	0.945695	−	0.325054i	$-0.105383\pi$
$158$		−	7.92063e6i		−	2.00811i
$159$	−4.13586e6			−1.02890
$160$			2.59253e6i			0.632943i
$161$			887648.i			0.212698i
$162$		−	618470.i		−	0.145470i
$163$	−356307.			−0.0822739			−0.0411369	−	0.999154i	$-0.513098\pi$
$163$	−356307.			−0.0822739			−0.0411369	+	0.999154i	$0.513098\pi$
$164$	−5.30954e6			−1.20372
$165$		−	368787.i		−	0.0820964i
$166$	−7.00864e6			−1.53218
$167$	−1.08155e6			−0.232218			−0.116109	−	0.993236i	$-0.537042\pi$
$167$	−1.08155e6			−0.232218			−0.116109	+	0.993236i	$0.537042\pi$
$168$			148932.i			0.0314095i
$169$	1.73902e6			0.360283
$170$			1.84517e6i			0.375569i
$171$	298155.			0.0596284
$172$			3.84352e6i			0.755342i
$173$		−	8.25269e6i		−	1.59389i	−0.604054	−	0.796943i	$-0.706449\pi$
$173$		−	8.25269e6i		−	1.59389i	0.604054	−	0.796943i	$-0.293551\pi$
$174$		−	1.85386e6i		−	0.351908i
$175$	−562996.			−0.105049
$176$		−	1.77306e6i		−	0.325226i
$177$	3.20067e6	−	74571.3i	0.577194	−	0.0134478i
$178$	8.40087e6			1.48958
$179$			5.34005e6i			0.931078i	0.885027	+	0.465539i	$0.154140\pi$
$179$			5.34005e6i			0.931078i	−0.885027	+	0.465539i	$0.845860\pi$
$180$	−730856.			−0.125318
$181$	−6.53227e6			−1.10161			−0.550806	−	0.834633i	$-0.685680\pi$
$181$	−6.53227e6			−1.10161			−0.550806	+	0.834633i	$0.685680\pi$
$182$	917465.			0.152186
$183$			4.49187e6i			0.732949i
$184$	3.41277e6			0.547840
$185$			3.17886e6i			0.502060i
$186$	−6.68377e6			−1.03868
$187$		−	962297.i		−	0.147158i
$188$		−	5.54119e6i		−	0.833930i
$189$	−188829.			−0.0279694
$190$		−	845742.i		−	0.123304i
$191$		−	8.78274e6i		−	1.26046i	−0.776407	−	0.630232i	$-0.782960\pi$
$191$		−	8.78274e6i		−	1.26046i	0.776407	−	0.630232i	$-0.217040\pi$
$192$	−1.51112e6			−0.213498
$193$	−7.18375e6			−0.999261			−0.499631	−	0.866239i	$-0.666531\pi$
$193$	−7.18375e6			−0.999261			−0.499631	+	0.866239i	$0.666531\pi$
$194$	9.21170e6			1.26164
$195$		−	1.80270e6i		−	0.243120i
$196$	5.26315e6			0.699000
$197$	−1.13153e7			−1.48002			−0.740012	−	0.672594i	$-0.765180\pi$
$197$	−1.13153e7			−1.48002			−0.740012	+	0.672594i	$0.765180\pi$
$198$	914930.			0.117867
$199$	−7.22619e6			−0.916960			−0.458480	−	0.888705i	$-0.651606\pi$
$199$	−7.22619e6			−0.916960			−0.458480	+	0.888705i	$0.651606\pi$
$200$			2.16457e6i			0.270571i
$201$		−	2.34394e6i		−	0.288641i
$202$	1.00437e7			1.21854
$203$	−566014.			−0.0676611
$204$	−1.90706e6			−0.224634
$205$	7.64585e6			0.887491
$206$	−5.25075e6			−0.600647
$207$			4.32700e6i			0.487839i
$208$		−	8.66705e6i		−	0.963122i
$209$			441073.i			0.0483139i
$210$			535631.i			0.0578373i
$211$		−	3.44063e6i		−	0.366261i	−0.983089	−	0.183130i	$-0.941377\pi$
$211$		−	3.44063e6i		−	0.366261i	0.983089	−	0.183130i	$-0.0586230\pi$
$212$	−1.21253e7			−1.27258
$213$	2.44955e6			0.253482
$214$		−	1.21365e7i		−	1.23837i
$215$		−	5.53474e6i		−	0.556906i
$216$			725998.i			0.0720401i
$217$			2.04067e6i			0.199707i
$218$	−3.87215e6			−0.373752
$219$			243999.i			0.0232303i
$220$		−	1.08119e6i		−	0.101539i
$221$		−	4.70389e6i		−	0.435793i
$222$	−7.88648e6			−0.720815
$223$	5.22189e6			0.470884			0.235442	−	0.971888i	$-0.424346\pi$
$223$	5.22189e6			0.470884			0.235442	+	0.971888i	$0.424346\pi$
$224$			1.96375e6i			0.174720i
$225$	−2.74443e6			−0.240937
$226$	2.43984e7			2.11367
$227$		−	8.28804e6i		−	0.708556i	−0.935140	−	0.354278i	$-0.884727\pi$
$227$		−	8.28804e6i		−	0.708556i	0.935140	−	0.354278i	$-0.115273\pi$
$228$	874111.			0.0737500
$229$		−	2.98348e6i		−	0.248438i	−0.992255	−	0.124219i	$-0.960358\pi$
$229$		−	2.98348e6i		−	0.248438i	0.992255	−	0.124219i	$-0.0396425\pi$
$230$	1.22739e7			1.00879
$231$		−	279343.i		−	0.0226622i
$232$			2.17618e6i			0.174273i
$233$		−	1.71585e6i		−	0.135647i	−0.997697	−	0.0678236i	$-0.978394\pi$
$233$		−	1.71585e6i		−	0.135647i	0.997697	−	0.0678236i	$-0.0216055\pi$
$234$	4.47235e6			0.349051
$235$			7.97942e6i			0.614848i
$236$	9.38354e6	−	218624.i	0.713889	−	0.0166326i
$237$	−1.17885e7			−0.885547
$238$			1.39765e6i			0.103674i
$239$	1.30840e6			0.0958397			0.0479198	−	0.998851i	$-0.484741\pi$
$239$	1.30840e6			0.0958397			0.0479198	+	0.998851i	$0.484741\pi$
$240$	5.05996e6			0.366027
$241$	−1.93506e7			−1.38243			−0.691217	−	0.722647i	$-0.742925\pi$
$241$	−1.93506e7			−1.38243			−0.691217	+	0.722647i	$0.742925\pi$
$242$		−	1.72015e7i		−	1.21373i
$243$	−920483.			−0.0641500
$244$			1.31690e7i			0.906531i
$245$	−7.57903e6			−0.515366
$246$			1.89687e7i			1.27418i
$247$			2.15605e6i			0.143077i
$248$	7.84582e6			0.514379
$249$			1.04311e7i			0.675667i
$250$			1.85550e7i			1.18752i
$251$	−1.33473e7			−0.844058			−0.422029	−	0.906582i	$-0.638682\pi$
$251$	−1.33473e7			−0.844058			−0.422029	+	0.906582i	$0.638682\pi$
$252$	−553598.			−0.0345934
$253$	−6.40113e6			−0.395271
$254$		−	2.48005e7i		−	1.51342i
$255$	2.74621e6			0.165620
$256$	2.19764e7			1.30990
$257$	−1.69761e7			−1.00009			−0.500045	−	0.866000i	$-0.666683\pi$
$257$	−1.69761e7			−1.00009			−0.500045	+	0.866000i	$0.666683\pi$
$258$	1.37312e7			0.799558
$259$			2.40787e6i			0.138591i
$260$		−	5.28505e6i		−	0.300697i
$261$	−2.75914e6			−0.155186
$262$	3.91592e7			2.17736
$263$	1.12084e6			0.0616135			0.0308068	−	0.999525i	$-0.490192\pi$
$263$	1.12084e6			0.0616135			0.0308068	+	0.999525i	$0.490192\pi$
$264$	−1.07400e6			−0.0583705
$265$	1.74606e7			0.938257
$266$		−	640620.i		−	0.0340374i
$267$		−	1.25032e7i		−	0.656883i
$268$		−	6.87182e6i		−	0.356999i
$269$			3.32729e7i			1.70936i	0.519155	+	0.854680i	$0.326247\pi$
$269$			3.32729e7i			1.70936i	−0.519155	+	0.854680i	$0.673753\pi$
$270$			2.61103e6i			0.132654i
$271$	3.33904e7			1.67770			0.838849	−	0.544365i	$-0.183229\pi$
$271$	3.33904e7			1.67770			0.838849	+	0.544365i	$0.183229\pi$
$272$	1.32032e7			0.656106
$273$		−	1.36549e6i		−	0.0671118i
$274$			4.74747e7i			2.30787i
$275$		−	4.05996e6i		−	0.195219i
$276$			1.26856e7i			0.603372i
$277$	1.66314e7			0.782509			0.391254	−	0.920283i	$-0.372041\pi$
$277$	1.66314e7			0.782509			0.391254	+	0.920283i	$0.372041\pi$
$278$			2.63437e6i			0.122615i
$279$			9.94761e6i			0.458043i
$280$		−	628757.i		−	0.0286424i
$281$	2.14792e7			0.968051			0.484026	−	0.875054i	$-0.339174\pi$
$281$	2.14792e7			0.968051			0.484026	+	0.875054i	$0.339174\pi$
$282$	−1.97963e7			−0.882747
$283$			2.69660e7i			1.18975i	0.803816	+	0.594877i	$0.202799\pi$
$283$			2.69660e7i			1.18975i	−0.803816	+	0.594877i	$0.797201\pi$
$284$	7.18144e6			0.313514
$285$	−1.25874e6			−0.0543752
$286$			6.61615e6i			0.282818i
$287$	5.79146e6			0.244987
$288$			9.57268e6i			0.400734i
$289$	−1.69717e7			−0.703125
$290$			7.82655e6i			0.320905i
$291$		−	1.37100e7i		−	0.556363i
$292$			715341.i			0.0287319i
$293$	2.18049e7			0.866864			0.433432	−	0.901186i	$-0.357303\pi$
$293$	2.18049e7			0.866864			0.433432	+	0.901186i	$0.357303\pi$
$294$		−	1.88029e7i		−	0.739919i
$295$	−1.35125e7	+	314822.i	−0.526343	+	0.0122631i
$296$	9.25764e6			0.356965
$297$		−	1.36171e6i		−	0.0519775i
$298$	4.09526e7			1.54751
$299$	−3.12900e7			−1.17055
$300$	−8.04595e6			−0.297998
$301$		−	4.19237e6i		−	0.153731i
$302$	2.13860e7			0.776440
$303$		−	1.49483e7i		−	0.537359i
$304$	−6.05177e6			−0.215408
$305$		−	1.89636e7i		−	0.668376i
$306$			6.81311e6i			0.237783i
$307$	−1.81303e6			−0.0626600			−0.0313300	−	0.999509i	$-0.509974\pi$
$307$	−1.81303e6			−0.0626600			−0.0313300	+	0.999509i	$0.509974\pi$
$308$		−	818962.i		−	0.0280293i
$309$			7.81481e6i			0.264876i
$310$	2.82173e7			0.947175
$311$	1.32810e7			0.441520			0.220760	−	0.975328i	$-0.429146\pi$
$311$	1.32810e7			0.441520			0.220760	+	0.975328i	$0.429146\pi$
$312$	−5.24993e6			−0.172858
$313$		−	4.08372e7i		−	1.33175i	−0.746062	−	0.665876i	$-0.768058\pi$
$313$		−	4.08372e7i		−	1.33175i	0.746062	−	0.665876i	$-0.231942\pi$
$314$	−2.63506e7			−0.851142
$315$	797192.			0.0255054
$316$	−3.45607e7			−1.09527
$317$	−5.33718e7			−1.67546			−0.837730	−	0.546085i	$-0.816117\pi$
$317$	−5.33718e7			−1.67546			−0.837730	+	0.546085i	$0.816117\pi$
$318$			4.33183e7i			1.34707i
$319$		−	4.08172e6i		−	0.125739i
$320$	6.37958e6			0.194689
$321$	−1.80630e7			−0.546103
$322$	9.29708e6			0.278470
$323$	−3.28449e6			−0.0974678
$324$	−2.69862e6			−0.0793425
$325$		−	1.98458e7i		−	0.578122i
$326$			3.73191e6i			0.107715i
$327$			5.76301e6i			0.164819i
$328$		−	2.22666e7i		−	0.631006i
$329$			6.04414e6i			0.169725i
$330$	−3.86262e6			−0.107483
$331$	4.11069e7			1.13352			0.566762	−	0.823881i	$-0.308196\pi$
$331$	4.11069e7			1.13352			0.566762	+	0.823881i	$0.308196\pi$
$332$			3.05813e7i			0.835684i
$333$			1.17376e7i			0.317869i
$334$			1.13279e7i			0.304026i
$335$			9.89556e6i			0.263212i
$336$	3.83275e6			0.101040
$337$		−	5.40856e6i		−	0.141316i	−0.997501	−	0.0706580i	$-0.977490\pi$
$337$		−	5.40856e6i		−	0.141316i	0.997501	−	0.0706580i	$-0.0225099\pi$
$338$		−	1.82142e7i		−	0.471693i
$339$		−	3.63128e7i		−	0.932095i
$340$	8.05117e6			0.204843
$341$	−1.47159e7			−0.371129
$342$		−	3.12282e6i		−	0.0780673i
$343$	−1.16056e7			−0.287597
$344$	−1.61186e7			−0.395960
$345$		−	1.82676e7i		−	0.444861i
$346$	−8.64374e7			−2.08676
$347$		−	1.65017e7i		−	0.394948i	−0.980308	−	0.197474i	$-0.936726\pi$
$347$		−	1.65017e7i		−	0.394948i	0.980308	−	0.197474i	$-0.0632738\pi$
$348$	−8.08908e6			−0.191938
$349$		−	7.68105e6i		−	0.180694i	−0.995910	−	0.0903471i	$-0.971202\pi$
$349$		−	7.68105e6i		−	0.180694i	0.995910	−	0.0903471i	$-0.0287977\pi$
$350$			5.89673e6i			0.137533i
$351$		−	6.65631e6i		−	0.153926i
$352$	−1.41613e7			−0.324695
$353$			2.36300e7i			0.537206i	0.963251	+	0.268603i	$0.0865619\pi$
$353$			2.36300e7i			0.537206i	−0.963251	+	0.268603i	$0.913438\pi$
$354$	−781047.	−	3.35233e7i	−0.0176063	−	0.755679i
$355$	−1.03414e7			−0.231151
$356$		−	3.66562e7i		−	0.812451i
$357$	2.08016e6			0.0457185
$358$	5.59308e7			1.21900
$359$	3.66955e7			0.793102			0.396551	−	0.918013i	$-0.370207\pi$
$359$	3.66955e7			0.793102			0.396551	+	0.918013i	$0.370207\pi$
$360$		−	3.06499e6i		−	0.0656934i
$361$	−4.55404e7			−0.968000
$362$			6.84180e7i			1.44226i
$363$	−2.56015e7			−0.535235
$364$		−	4.00325e6i		−	0.0830057i
$365$		−	1.03010e6i		−	0.0211838i
$366$	4.70471e7			0.959598
$367$		−	9.00008e7i		−	1.82074i	−0.413795	−	0.910370i	$-0.635797\pi$
$367$		−	9.00008e7i		−	1.82074i	0.413795	−	0.910370i	$-0.364203\pi$
$368$		−	8.78271e7i		−	1.76232i
$369$	2.82316e7			0.561896
$370$	3.32948e7			0.657312
$371$	1.32258e7			0.259001
$372$			2.91638e7i			0.566520i
$373$	−7.07018e7			−1.36240			−0.681199	−	0.732098i	$-0.738541\pi$
$373$	−7.07018e7			−1.36240			−0.681199	+	0.732098i	$0.738541\pi$
$374$	−1.00789e7			−0.192664
$375$	2.76158e7			0.523678
$376$	2.32381e7			0.437157
$377$		−	1.99522e7i		−	0.372364i
$378$			1.97777e6i			0.0366184i
$379$	−1.87827e7			−0.345017			−0.172509	−	0.985008i	$-0.555187\pi$
$379$	−1.87827e7			−0.345017			−0.172509	+	0.985008i	$0.555187\pi$
$380$	−3.69029e6			−0.0672527
$381$	−3.69112e7			−0.667395
$382$	−9.19891e7			−1.65024
$383$	1.46187e7			0.260204			0.130102	−	0.991501i	$-0.458470\pi$
$383$	1.46187e7			0.260204			0.130102	+	0.991501i	$0.458470\pi$
$384$		−	2.34744e7i		−	0.414573i
$385$			1.17932e6i			0.0206657i
$386$			7.52414e7i			1.30826i
$387$		−	2.04365e7i		−	0.352593i
$388$		−	4.01941e7i		−	0.688125i
$389$	1.19705e7			0.203359			0.101679	−	0.994817i	$-0.467578\pi$
$389$	1.19705e7			0.203359			0.101679	+	0.994817i	$0.467578\pi$
$390$	−1.88812e7			−0.318300
$391$		−	4.76666e7i		−	0.797415i
$392$			2.20721e7i			0.366425i
$393$		−	5.82815e7i		−	0.960181i
$394$			1.18515e8i			1.93769i
$395$	4.97680e7			0.807531
$396$		−	3.99218e6i		−	0.0642873i
$397$		−	7.88120e7i		−	1.25957i	−0.776771	−	0.629783i	$-0.783144\pi$
$397$		−	7.88120e7i		−	1.25957i	0.776771	−	0.629783i	$-0.216856\pi$
$398$			7.56860e7i			1.20051i
$399$	−953450.			−0.0150100
$400$	5.57048e7			0.870388
$401$			2.81271e7i			0.436206i	0.975926	+	0.218103i	$0.0699868\pi$
$401$			2.81271e7i			0.436206i	−0.975926	+	0.218103i	$0.930013\pi$
$402$	−2.45501e7			−0.377898
$403$	−7.19344e7			−1.09906
$404$		−	4.38246e7i		−	0.664620i
$405$	3.88606e6			0.0584985
$406$			5.92834e6i			0.0885840i
$407$	−1.73640e7			−0.257553
$408$		−	7.99766e6i		−	0.117756i
$409$			5.77299e7i			0.843783i	0.906646	+	0.421891i	$0.138634\pi$
$409$			5.77299e7i			0.843783i	−0.906646	+	0.421891i	$0.861366\pi$
$410$		−	8.00814e7i		−	1.16193i
$411$	7.06577e7			1.01773
$412$			2.29110e7i			0.327606i
$413$	−1.02352e7	+	238467.i	−0.145294	+	0.00338515i
$414$	4.53203e7			0.638693
$415$		−	4.40377e7i		−	0.616142i
$416$	−6.92232e7			−0.961549
$417$	3.92080e6			0.0540712
$418$	4.61973e6			0.0632540
$419$			1.00992e8i			1.37292i	0.727167	+	0.686461i	$0.240837\pi$
$419$			1.00992e8i			1.37292i	−0.727167	+	0.686461i	$0.759163\pi$
$420$	2.33716e6			0.0315457
$421$			3.94968e7i			0.529317i	0.964342	+	0.264659i	$0.0852593\pi$
$421$			3.94968e7i			0.529317i	−0.964342	+	0.264659i	$0.914741\pi$
$422$	−3.60366e7			−0.479519
$423$			2.94633e7i			0.389278i
$424$		−	5.08498e7i		−	0.667101i
$425$	3.02328e7			0.393833
$426$		−	2.56562e7i		−	0.331867i
$427$		−	1.43643e7i		−	0.184501i
$428$	−5.29560e7			−0.675436
$429$	9.84698e6			0.124719
$430$	−5.79700e7			−0.729118
$431$			6.54180e7i			0.817082i	0.912740	+	0.408541i	$0.133962\pi$
$431$			6.54180e7i			0.817082i	−0.912740	+	0.408541i	$0.866038\pi$
$432$	1.86834e7			0.231742
$433$	−1.00605e8			−1.23924			−0.619619	−	0.784902i	$-0.712713\pi$
$433$	−1.00605e8			−1.23924			−0.619619	+	0.784902i	$0.712713\pi$
$434$	2.13736e7			0.261462
$435$	1.16484e7			0.141514
$436$			1.68957e7i			0.203852i
$437$			2.18482e7i			0.261801i
$438$	2.55560e6			0.0304138
$439$	−4.18830e7			−0.495044			−0.247522	−	0.968882i	$-0.579616\pi$
$439$	−4.18830e7			−0.495044			−0.247522	+	0.968882i	$0.579616\pi$
$440$	4.53418e6			0.0532281
$441$	−2.79849e7			−0.326293
$442$	−4.92678e7			−0.570554
$443$			1.28585e8i			1.47903i	0.673139	+	0.739516i	$0.264946\pi$
$443$			1.28585e8i			1.47903i	−0.673139	+	0.739516i	$0.735054\pi$
$444$			3.44117e7i			0.393149i
$445$			5.27856e7i			0.599012i
$446$		−	5.46933e7i		−	0.616495i
$447$		−	6.09506e7i		−	0.682426i
$448$	4.83231e6			0.0537429
$449$	−5.56187e7			−0.614443			−0.307221	−	0.951638i	$-0.599399\pi$
$449$	−5.56187e7			−0.614443			−0.307221	+	0.951638i	$0.599399\pi$
$450$			2.87447e7i			0.315442i
$451$			4.17642e7i			0.455276i
$452$		−	1.06460e8i		−	1.15284i
$453$		−	3.18292e7i		−	0.342398i
$454$	−8.68076e7			−0.927663
$455$			5.76475e6i			0.0611993i
$456$			3.66576e6i			0.0386607i
$457$		−	7.70912e7i		−	0.807711i	−0.914823	−	0.403855i	$-0.867670\pi$
$457$		−	7.70912e7i		−	0.807711i	0.914823	−	0.403855i	$-0.132330\pi$
$458$	−3.12485e7			−0.325262
$459$	1.01401e7			0.104859
$460$		−	5.35558e7i		−	0.550216i
$461$	−1.53553e7			−0.156731			−0.0783656	−	0.996925i	$-0.524970\pi$
$461$	−1.53553e7			−0.156731			−0.0783656	+	0.996925i	$0.524970\pi$
$462$	−2.92580e6			−0.0296701
$463$			6.06121e6i			0.0610684i	0.999534	+	0.0305342i	$0.00972084\pi$
$463$			6.06121e6i			0.0610684i	−0.999534	+	0.0305342i	$0.990279\pi$
$464$	5.60035e7			0.560610
$465$		−	4.19964e7i		−	0.417690i
$466$	−1.79715e7			−0.177593
$467$			1.17824e8i			1.15686i	0.815731	+	0.578431i	$0.196335\pi$
$467$			1.17824e8i			1.15686i	−0.815731	+	0.578431i	$0.803665\pi$
$468$		−	1.95146e7i		−	0.190380i
$469$			7.49554e6i			0.0726582i
$470$	8.35752e7			0.804977
$471$			3.92182e7i			0.375340i
$472$	916842.	+	3.93518e7i	0.00871904	+	0.374230i
$473$	3.02326e7			0.285688
$474$			1.23470e8i			1.15938i
$475$	−1.38574e7			−0.129300
$476$	6.09848e6			0.0565459
$477$	6.44717e7			0.594037
$478$		−	1.37039e7i		−	0.125476i
$479$	−1.66188e8			−1.51214			−0.756072	−	0.654488i	$-0.772884\pi$
$479$	−1.66188e8			−1.51214			−0.756072	+	0.654488i	$0.772884\pi$
$480$		−	4.04136e7i		−	0.365430i
$481$	−8.48786e7			−0.762716
$482$			2.02676e8i			1.80992i
$483$		−	1.38371e7i		−	0.122801i
$484$	−7.50568e7			−0.661994
$485$			5.78803e7i			0.507348i
$486$			9.64099e6i			0.0839871i
$487$	−1.81382e8			−1.57039			−0.785194	−	0.619250i	$-0.787437\pi$
$487$	−1.81382e8			−1.57039			−0.785194	+	0.619250i	$0.787437\pi$
$488$	−5.52268e7			−0.475215
$489$	5.55428e6			0.0475009
$490$			7.93816e7i			0.674732i
$491$	1.82057e8			1.53802			0.769010	−	0.639236i	$-0.220749\pi$
$491$	1.82057e8			1.53802			0.769010	+	0.639236i	$0.220749\pi$
$492$	8.27676e7			0.694968
$493$	3.03949e7			0.253665
$494$	2.25821e7			0.187320
$495$			5.74882e6i			0.0473984i
$496$		−	2.01911e8i		−	1.65468i
$497$	−7.83327e6			−0.0638078
$498$	1.09254e8			0.884604
$499$	7.94846e7			0.639707			0.319854	−	0.947467i	$-0.396366\pi$
$499$	7.94846e7			0.639707			0.319854	+	0.947467i	$0.396366\pi$
$500$	8.09624e7			0.647699
$501$	1.68596e7			0.134071
$502$			1.39797e8i			1.10507i
$503$			6.89633e7i			0.541894i	0.962594	+	0.270947i	$0.0873368\pi$
$503$			6.89633e7i			0.541894i	−0.962594	+	0.270947i	$0.912663\pi$
$504$		−	2.32163e6i		−	0.0181343i
$505$			6.31083e7i			0.490018i
$506$			6.70444e7i			0.517501i
$507$	−2.71086e7			−0.208009
$508$	−1.08214e8			−0.825453
$509$			1.38066e8i			1.04697i	0.852034	+	0.523486i	$0.175369\pi$
$509$			1.38066e8i			1.04697i	−0.852034	+	0.523486i	$0.824631\pi$
$510$		−	2.87633e7i		−	0.216835i
$511$		−	780269.i		−	0.00584765i
$512$		−	1.33801e8i		−	0.996896i
$513$	−4.64777e6			−0.0344265
$514$			1.77805e8i			1.30935i
$515$		−	3.29923e7i		−	0.241541i
$516$		−	5.99145e7i		−	0.436097i
$517$	−4.35863e7			−0.315412
$518$	2.52197e7			0.181447
$519$			1.28647e8i			0.920231i
$520$	2.21640e7			0.157629
$521$	2.63461e8			1.86296			0.931479	−	0.363795i	$-0.118519\pi$
$521$	2.63461e8			1.86296			0.931479	+	0.363795i	$0.118519\pi$
$522$			2.88988e7i			0.203174i
$523$	2.27713e8			1.59178			0.795889	−	0.605443i	$-0.207004\pi$
$523$	2.27713e8			1.59178			0.795889	+	0.605443i	$0.207004\pi$
$524$		−	1.70866e8i		−	1.18758i
$525$	8.77624e6			0.0606500
$526$		−	1.17395e7i		−	0.0806662i
$527$		−	1.09584e8i		−	0.748711i
$528$			2.76392e7i			0.187769i
$529$	−1.69039e8			−1.14188
$530$		−	1.82880e8i		−	1.22839i
$531$	−4.98936e7	+	1.16245e6i	−0.333243	+	0.00776410i
$532$	−2.79527e6			−0.0185647
$533$			2.04152e8i			1.34825i
$534$	−1.30957e8			−0.860010
$535$	7.62577e7			0.497992
$536$	2.88184e7			0.187144
$537$		−	8.32431e7i		−	0.537558i
$538$	3.48495e8			2.23795
$539$		−	4.13993e7i		−	0.264379i
$540$	1.13929e7			0.0723525
$541$		−	1.20606e8i		−	0.761687i	−0.924640	−	0.380843i	$-0.875634\pi$
$541$		−	1.20606e8i		−	0.761687i	0.924640	−	0.380843i	$-0.124366\pi$
$542$		−	3.49726e8i		−	2.19649i
$543$	1.01828e8			0.636016
$544$		−	1.05453e8i		−	0.655034i
$545$		−	2.43301e7i		−	0.150298i
$546$	−1.43019e7			−0.0878648
$547$	1.23169e8			0.752558			0.376279	−	0.926506i	$-0.377203\pi$
$547$	1.23169e8			0.752558			0.376279	+	0.926506i	$0.377203\pi$
$548$	2.07150e8			1.25876
$549$		−	7.00213e7i		−	0.423168i
$550$	−4.25233e7			−0.255587
$551$	−1.39317e7			−0.0832814
$552$	−5.31999e7			−0.316296
$553$	3.76976e7			0.222914
$554$		−	1.74194e8i		−	1.02448i
$555$		−	4.95535e7i		−	0.289865i
$556$	1.14948e7			0.0668768
$557$	−7.21947e7			−0.417772			−0.208886	−	0.977940i	$-0.566984\pi$
$557$	−7.21947e7			−0.417772			−0.208886	+	0.977940i	$0.566984\pi$
$558$	1.04190e8			0.599683
$559$	1.47783e8			0.846036
$560$	−1.61809e7			−0.0921382
$561$			1.50007e7i			0.0849618i
$562$		−	2.24969e8i		−	1.26740i
$563$		−	8.89719e7i		−	0.498572i	−0.968430	−	0.249286i	$-0.919804\pi$
$563$		−	8.89719e7i		−	0.498572i	0.968430	−	0.249286i	$-0.0801958\pi$
$564$			8.63786e7i			0.481469i
$565$			1.53304e8i			0.849978i
$566$	2.82438e8			1.55766
$567$	2.94356e6			0.0161482
$568$			3.01169e7i			0.164348i
$569$		−	1.17956e8i		−	0.640302i	−0.947367	−	0.320151i	$-0.896266\pi$
$569$		−	1.17956e8i		−	0.640302i	0.947367	−	0.320151i	$-0.103734\pi$
$570$			1.31838e7i			0.0711896i
$571$			3.46617e7i			0.186184i	0.995658	+	0.0930918i	$0.0296750\pi$
$571$			3.46617e7i			0.186184i	−0.995658	+	0.0930918i	$0.970325\pi$
$572$	2.88688e7			0.154255
$573$			1.36909e8i			0.727729i
$574$		−	6.06589e7i		−	0.320744i
$575$		−	2.01107e8i		−	1.05785i
$576$	2.35560e7			0.123263
$577$	−8.59270e7			−0.447303			−0.223652	−	0.974669i	$-0.571798\pi$
$577$	−8.59270e7			−0.447303			−0.223652	+	0.974669i	$0.571798\pi$
$578$			1.77759e8i			0.920552i
$579$	1.11984e8			0.576924
$580$	3.41502e7			0.175029
$581$		−	3.33570e7i		−	0.170082i
$582$	−1.43596e8			−0.728407
$583$			9.53758e7i			0.481319i
$584$	−2.99993e6			−0.0150616
$585$			2.81014e7i			0.140365i
$586$		−	2.28381e8i		−	1.13492i
$587$		−	3.82513e7i		−	0.189118i	−0.995519	−	0.0945589i	$-0.969856\pi$
$587$		−	3.82513e7i		−	0.189118i	0.995519	−	0.0945589i	$-0.0301441\pi$
$588$	−8.20443e7			−0.403568
$589$			5.02282e7i			0.245811i
$590$	3.29740e6	+	1.41528e8i	0.0160552	+	0.689104i
$591$	1.76389e8			0.854492
$592$		−	2.38244e8i		−	1.14830i
$593$	1.54007e8			0.738543			0.369271	−	0.929322i	$-0.379607\pi$
$593$	1.54007e8			0.738543			0.369271	+	0.929322i	$0.379607\pi$
$594$	−1.42623e7			−0.0680505
$595$	−8.78193e6			−0.0416907
$596$		−	1.78691e8i		−	0.844044i
$597$	1.12645e8			0.529407
$598$			3.27726e8i			1.53252i
$599$	2.97305e8			1.38332			0.691658	−	0.722225i	$-0.256881\pi$
$599$	2.97305e8			1.38332			0.691658	+	0.722225i	$0.256881\pi$
$600$		−	3.37423e7i		−	0.156214i
$601$			2.74162e8i			1.26294i	0.775399	+	0.631472i	$0.217549\pi$
$601$			2.74162e8i			1.26294i	−0.775399	+	0.631472i	$0.782451\pi$
$602$	−4.39102e7			−0.201269
$603$			3.65384e7i			0.166647i
$604$		−	9.33149e7i		−	0.423487i
$605$	1.08083e8			0.488082
$606$	−1.56566e8			−0.703526
$607$	−7.44553e7			−0.332912			−0.166456	−	0.986049i	$-0.553232\pi$
$607$	−7.44553e7			−0.332912			−0.166456	+	0.986049i	$0.553232\pi$
$608$			4.83351e7i			0.215056i
$609$	8.82329e6			0.0390642
$610$	−1.98622e8			−0.875058
$611$	−2.13058e8			−0.934060
$612$	2.97282e7			0.129692
$613$		−	1.19319e8i		−	0.517997i	−0.965878	−	0.258998i	$-0.916608\pi$
$613$		−	1.19319e8i		−	0.517997i	0.965878	−	0.258998i	$-0.0833924\pi$
$614$			1.89894e7i			0.0820364i
$615$	−1.19187e8			−0.512393
$616$	3.43449e6			0.0146933
$617$	−4.67089e7			−0.198859			−0.0994293	−	0.995045i	$-0.531702\pi$
$617$	−4.67089e7			−0.198859			−0.0994293	+	0.995045i	$0.531702\pi$
$618$	8.18510e7			0.346784
$619$	−3.82262e8			−1.61172			−0.805859	−	0.592107i	$-0.798296\pi$
$619$	−3.82262e8			−1.61172			−0.805859	+	0.592107i	$0.798296\pi$
$620$		−	1.23123e8i		−	0.516610i
$621$		−	6.74513e7i		−	0.281654i
$622$		−	1.39103e8i		−	0.578051i
$623$			3.99833e7i			0.165354i
$624$			1.35106e8i			0.556059i
$625$	5.98804e7			0.245270
$626$	−4.27723e8			−1.74357
$627$		−	6.87565e6i		−	0.0278940i
$628$			1.14978e8i			0.464231i
$629$		−	1.29303e8i		−	0.519584i
$630$		−	8.34966e6i		−	0.0333924i
$631$	3.27902e8			1.30514			0.652568	−	0.757730i	$-0.273692\pi$
$631$	3.27902e8			1.30514			0.652568	+	0.757730i	$0.273692\pi$
$632$		−	1.44937e8i		−	0.574154i
$633$			5.36341e7i			0.211461i
$634$			5.59007e8i			2.19356i
$635$	1.55830e8			0.608598
$636$	1.89014e8			0.734722
$637$		−	2.02368e8i		−	0.782929i
$638$	−4.27513e7			−0.164622
$639$	−3.81847e7			−0.146348
$640$			9.91034e7i			0.378050i
$641$	−1.03508e8			−0.393005			−0.196503	−	0.980503i	$-0.562958\pi$
$641$	−1.03508e8			−0.393005			−0.196503	+	0.980503i	$0.562958\pi$
$642$			1.89189e8i			0.714975i
$643$	−1.45263e8			−0.546413			−0.273207	−	0.961955i	$-0.588084\pi$
$643$	−1.45263e8			−0.546413			−0.273207	+	0.961955i	$0.588084\pi$
$644$		−	4.05667e7i		−	0.151884i
$645$			8.62781e7i			0.321530i
$646$			3.44013e7i			0.127608i
$647$	−4.05992e7			−0.149901			−0.0749505	−	0.997187i	$-0.523880\pi$
$647$	−4.05992e7			−0.149901			−0.0749505	+	0.997187i	$0.523880\pi$
$648$		−	1.13172e7i		−	0.0415924i
$649$	−1.71967e6	−	7.38098e7i	−0.00629086	−	0.270010i
$650$	−2.07862e8			−0.756895
$651$		−	3.18108e7i		−	0.115301i
$652$	1.62837e7			0.0587504
$653$	2.85932e8			1.02689			0.513445	−	0.858123i	$-0.328369\pi$
$653$	2.85932e8			1.02689			0.513445	+	0.858123i	$0.328369\pi$
$654$	6.03609e7			0.215786
$655$			2.46051e8i			0.875590i
$656$	−5.73028e8			−2.02985
$657$		−	3.80356e6i		−	0.0134120i
$658$	6.33053e7			0.222209
$659$		−	1.76873e8i		−	0.618024i	−0.951058	−	0.309012i	$-0.900002\pi$
$659$		−	1.76873e8i		−	0.618024i	0.951058	−	0.309012i	$-0.0999983\pi$
$660$			1.68540e7i			0.0586236i
$661$	−7.79873e7			−0.270035			−0.135017	−	0.990843i	$-0.543109\pi$
$661$	−7.79873e7			−0.270035			−0.135017	+	0.990843i	$0.543109\pi$
$662$		−	4.30547e8i		−	1.48404i
$663$			7.33264e7i			0.251605i
$664$	−1.28249e8			−0.438076
$665$	4.02524e6			0.0136876
$666$	1.22938e8			0.416163
$667$		−	2.02185e8i		−	0.681352i
$668$	4.94280e7			0.165823
$669$	−8.14013e7			−0.271865
$670$	1.03644e8			0.344605
$671$	1.03586e8			0.342872
$672$		−	3.06119e7i		−	0.100875i
$673$		−	2.77194e8i		−	0.909367i	−0.890653	−	0.454684i	$-0.849752\pi$
$673$		−	2.77194e8i		−	0.909367i	0.890653	−	0.454684i	$-0.150248\pi$
$674$	−5.66483e7			−0.185015
$675$	4.27814e7			0.139105
$676$	−7.94753e7			−0.257272
$677$	3.25221e8			1.04812			0.524061	−	0.851681i	$-0.324416\pi$
$677$	3.25221e8			1.04812			0.524061	+	0.851681i	$0.324416\pi$
$678$	−3.80334e8			−1.22033
$679$			4.38423e7i			0.140050i
$680$			3.37642e7i			0.107382i
$681$			1.29198e8i			0.409085i
$682$			1.54132e8i			0.485893i
$683$			1.09553e8i			0.343844i	0.985111	+	0.171922i	$0.0549977\pi$
$683$			1.09553e8i			0.343844i	−0.985111	+	0.171922i	$0.945002\pi$
$684$	−1.36260e7			−0.0425796
$685$	−2.98300e8			−0.928072
$686$			1.21555e8i			0.376531i
$687$			4.65079e7i			0.143436i
$688$			4.14808e8i			1.27374i
$689$			4.66216e8i			1.42537i
$690$	−1.91332e8			−0.582425
$691$			2.79823e8i			0.848105i	0.905638	+	0.424052i	$0.139393\pi$
$691$			2.79823e8i			0.848105i	−0.905638	+	0.424052i	$0.860607\pi$
$692$			3.77159e8i			1.13817i
$693$			4.35453e6i			0.0130840i
$694$	−1.72836e8			−0.517078
$695$	−1.65527e7			−0.0493076
$696$		−	3.39232e7i		−	0.100617i
$697$	−3.11001e8			−0.918467
$698$	−8.04501e7			−0.236570
$699$			2.67474e7i			0.0783159i
$700$	2.57296e7			0.0750136
$701$		−	2.76329e8i		−	0.802181i	−0.916038	−	0.401091i	$-0.868631\pi$
$701$		−	2.76329e8i		−	0.802181i	0.916038	−	0.401091i	$-0.131369\pi$
$702$	−6.97171e7			−0.201525
$703$			5.92665e7i			0.170586i
$704$			3.48474e7i			0.0998741i
$705$		−	1.24387e8i		−	0.354983i
$706$	2.47497e8			0.703326
$707$			4.78023e7i			0.135267i
$708$	−1.46275e8	+	3.40800e6i	−0.412164	+	0.00960285i
$709$	5.87199e8			1.64758			0.823791	−	0.566894i	$-0.191855\pi$
$709$	5.87199e8			1.64758			0.823791	+	0.566894i	$0.191855\pi$
$710$			1.08314e8i			0.302629i
$711$	1.83764e8			0.511271
$712$	1.53725e8			0.425897
$713$	−7.28943e8			−2.01106
$714$		−	2.17872e7i		−	0.0598560i
$715$	−4.15716e7			−0.113731
$716$		−	2.44047e8i		−	0.664867i
$717$	−2.03959e7			−0.0553331
$718$		−	3.84342e8i		−	1.03835i
$719$			1.61463e8i			0.434395i	0.976128	+	0.217198i	$0.0696916\pi$
$719$			1.61463e8i			0.434395i	−0.976128	+	0.217198i	$0.930308\pi$
$720$	−7.88770e7			−0.211326
$721$		−	2.49905e7i		−	0.0666759i
$722$			4.76983e8i			1.26733i
$723$	3.01647e8			0.798148
$724$	2.98533e8			0.786642
$725$	1.28237e8			0.336511
$726$			2.68146e8i			0.700746i
$727$	2.22627e8			0.579394			0.289697	−	0.957118i	$-0.406446\pi$
$727$	2.22627e8			0.579394			0.289697	+	0.957118i	$0.406446\pi$
$728$	1.67884e7			0.0435127
$729$	1.43489e7			0.0370370
$730$	−1.07892e7			−0.0277344
$731$			2.25130e8i			0.576344i
$732$		−	2.05284e8i		−	0.523386i
$733$	2.35665e8			0.598388			0.299194	−	0.954192i	$-0.403282\pi$
$733$	2.35665e8			0.598388			0.299194	+	0.954192i	$0.403282\pi$
$734$	−9.42653e8			−2.38377
$735$	1.18145e8			0.297547
$736$	−7.01469e8			−1.75944
$737$	−5.40529e7			−0.135026
$738$		−	2.95693e8i		−	0.735651i
$739$		−	6.19496e8i		−	1.53499i	−0.641055	−	0.767495i	$-0.721503\pi$
$739$		−	6.19496e8i		−	1.53499i	0.641055	−	0.767495i	$-0.278497\pi$
$740$		−	1.45278e8i		−	0.358512i
$741$		−	3.36095e7i		−	0.0826053i
$742$		−	1.38525e8i		−	0.339091i
$743$	3.35713e8			0.818469			0.409234	−	0.912429i	$-0.365796\pi$
$743$	3.35713e8			0.818469			0.409234	+	0.912429i	$0.365796\pi$
$744$	−1.22304e8			−0.296977
$745$			2.57319e8i			0.622305i
$746$			7.40519e8i			1.78369i
$747$		−	1.62605e8i		−	0.390097i
$748$			4.39782e7i			0.105083i
$749$	5.77626e7			0.137468
$750$		−	2.89244e8i		−	0.685615i
$751$			6.69314e8i			1.58019i	0.612982	+	0.790097i	$0.289970\pi$
$751$			6.69314e8i			1.58019i	−0.612982	+	0.790097i	$0.710030\pi$
$752$		−	5.98028e8i		−	1.40627i
$753$	2.08064e8			0.487317
$754$	−2.08977e8			−0.487510
$755$			1.34375e8i			0.312233i
$756$	8.62974e6			0.0199725
$757$	−8.01456e8			−1.84753			−0.923767	−	0.382956i	$-0.874906\pi$
$757$	−8.01456e8			−1.84753			−0.923767	+	0.382956i	$0.874906\pi$
$758$			1.96727e8i			0.451707i
$759$	9.97838e7			0.228210
$760$		−	1.54760e7i		−	0.0352547i
$761$	−1.79814e8			−0.408008			−0.204004	−	0.978970i	$-0.565396\pi$
$761$	−1.79814e8			−0.408008			−0.204004	+	0.978970i	$0.565396\pi$
$762$			3.86602e8i			0.873774i
$763$		−	1.84292e7i		−	0.0414890i
$764$			4.01383e8i			0.900075i
$765$	−4.28092e7			−0.0956208
$766$		−	1.53114e8i		−	0.340667i
$767$	−8.40606e6	−	3.60796e8i	−0.0186297	−	0.799606i
$768$	−3.42579e8			−0.756270
$769$			7.98304e8i			1.75545i	0.479161	+	0.877727i	$0.340941\pi$
$769$			7.98304e8i			1.75545i	−0.479161	+	0.877727i	$0.659059\pi$
$770$	1.23520e7			0.0270562
$771$	2.64631e8			0.577402
$772$	3.28306e8			0.713555
$773$		−	5.06230e8i		−	1.09600i	−0.836479	−	0.547998i	$-0.815390\pi$
$773$		−	5.06230e8i		−	1.09600i	0.836479	−	0.547998i	$-0.184610\pi$
$774$	−2.14049e8			−0.461625
$775$		−	4.62336e8i		−	0.993237i
$776$	1.68562e8			0.360724
$777$		−	3.75350e7i		−	0.0800154i
$778$		−	1.25377e8i		−	0.266243i
$779$	1.42549e8			0.301544
$780$			8.23859e7i			0.173608i
$781$		−	5.64884e7i		−	0.118578i
$782$	−4.99253e8			−1.04400
$783$	4.30108e7			0.0895967
$784$	5.68021e8			1.17873
$785$		−	1.65570e8i		−	0.342273i
$786$	−6.10431e8			−1.25710
$787$	1.04243e8			0.213857			0.106929	−	0.994267i	$-0.465898\pi$
$787$	1.04243e8			0.213857			0.106929	+	0.994267i	$0.465898\pi$
$788$	5.17125e8			1.05686
$789$	−1.74721e7			−0.0355726
$790$		−	5.21262e8i		−	1.05724i
$791$			1.16122e8i			0.234632i
$792$	1.67420e7			0.0337002
$793$	5.06346e8			1.01538
$794$	−8.25464e8			−1.64906
$795$	−2.72184e8			−0.541703
$796$	3.30246e8			0.654785
$797$			3.91390e8i			0.773099i	0.922269	+	0.386549i	$0.126333\pi$
$797$			3.91390e8i			0.773099i	−0.922269	+	0.386549i	$0.873667\pi$
$798$			9.98628e6i			0.0196515i
$799$		−	3.24570e8i		−	0.636308i
$800$		−	4.44911e8i		−	0.868966i
$801$			1.94906e8i			0.379251i
$802$	2.94598e8			0.571094
$803$	5.62678e6			0.0108671
$804$			1.07121e8i			0.206114i
$805$			5.84168e7i			0.111982i
$806$			7.53429e8i			1.43892i
$807$		−	5.18673e8i		−	0.986900i
$808$	1.83787e8			0.348403
$809$			2.10422e8i			0.397416i	0.980059	+	0.198708i	$0.0636745\pi$
$809$			2.10422e8i			0.397416i	−0.980059	+	0.198708i	$0.936326\pi$
$810$		−	4.07020e7i		−	0.0765879i
$811$		−	6.55133e8i		−	1.22819i	−0.789230	−	0.614097i	$-0.789520\pi$
$811$		−	6.55133e8i		−	1.22819i	0.789230	−	0.614097i	$-0.210480\pi$
$812$	2.58676e7			0.0483157
$813$	−5.20505e8			−0.968619
$814$			1.81868e8i			0.337196i
$815$	−2.34489e7			−0.0433161
$816$	−2.05818e8			−0.378803
$817$		−	1.03189e8i		−	0.189221i
$818$	6.04653e8			1.10471
$819$			2.12858e7i			0.0387470i
$820$	−3.49425e8			−0.633742
$821$		−	8.95844e8i		−	1.61884i	−0.587233	−	0.809418i	$-0.699783\pi$
$821$		−	8.95844e8i		−	1.61884i	0.587233	−	0.809418i	$-0.300217\pi$
$822$		−	7.40058e8i		−	1.33245i
$823$		−	9.58993e8i		−	1.72035i	−0.510002	−	0.860173i	$-0.670355\pi$
$823$		−	9.58993e8i		−	1.72035i	0.510002	−	0.860173i	$-0.329645\pi$
$824$	−9.60819e7			−0.171735
$825$			6.32884e7i			0.112710i
$826$	2.49766e6	+	1.07202e8i	0.00443194	+	0.190223i
$827$	3.79102e8			0.670254			0.335127	−	0.942173i	$-0.391221\pi$
$827$	3.79102e8			0.670254			0.335127	+	0.942173i	$0.391221\pi$
$828$		−	1.97750e8i		−	0.348357i
$829$	−3.95084e8			−0.693468			−0.346734	−	0.937964i	$-0.612709\pi$
$829$	−3.95084e8			−0.693468			−0.346734	+	0.937964i	$0.612709\pi$
$830$	−4.61244e8			−0.806671
$831$	−2.59258e8			−0.451782
$832$			1.70341e8i			0.295767i
$833$	3.08284e8			0.533354
$834$		−	4.10658e7i		−	0.0707917i
$835$	−7.11773e7			−0.122259
$836$		−	2.01576e7i		−	0.0345001i
$837$		−	1.55068e8i		−	0.264451i
$838$	1.05778e9			1.79747
$839$			2.92121e8i			0.494627i	0.968936	+	0.247313i	$0.0795477\pi$
$839$			2.92121e8i			0.494627i	−0.968936	+	0.247313i	$0.920452\pi$
$840$			9.80135e6i			0.0165367i
$841$	−4.65899e8			−0.783256
$842$	4.13684e8			0.692998
$843$	−3.34827e8			−0.558905
$844$			1.57241e8i			0.261540i
$845$	1.14446e8			0.189684
$846$	3.08593e8			0.509654
$847$	8.18694e7			0.134732
$848$	−1.30861e9			−2.14596
$849$		−	4.20359e8i		−	0.686905i
$850$		−	3.16654e8i		−	0.515618i
$851$	−8.60112e8			−1.39562
$852$	−1.11948e8			−0.181007
$853$	3.39905e8			0.547659			0.273829	−	0.961778i	$-0.411710\pi$
$853$	3.39905e8			0.547659			0.273829	+	0.961778i	$0.411710\pi$
$854$	−1.50449e8			−0.241555
$855$	1.96218e7			0.0313935
$856$		−	2.22082e8i		−	0.354072i
$857$		−	1.12529e9i		−	1.78782i	−0.448247	−	0.893910i	$-0.647952\pi$
$857$		−	1.12529e9i		−	1.78782i	0.448247	−	0.893910i	$-0.352048\pi$
$858$		−	1.03136e8i		−	0.163285i
$859$			7.21578e7i			0.113842i	0.998379	+	0.0569211i	$0.0181284\pi$
$859$			7.21578e7i			0.113842i	−0.998379	+	0.0569211i	$0.981872\pi$
$860$			2.52945e8i			0.397677i
$861$	−9.02800e7			−0.141443
$862$	6.85178e8			1.06975
$863$			6.80620e8i			1.05894i	0.848328	+	0.529471i	$0.177609\pi$
$863$			6.80620e8i			1.05894i	−0.848328	+	0.529471i	$0.822391\pi$
$864$		−	1.49223e8i		−	0.231364i
$865$		−	5.43116e8i		−	0.839159i
$866$			1.05372e9i			1.62245i
$867$	2.64563e8			0.405950
$868$		−	9.32611e7i		−	0.142607i
$869$			2.71850e8i			0.414257i
$870$		−	1.22004e8i		−	0.185275i
$871$	−2.64221e8			−0.399865
$872$	−7.08554e7			−0.106862
$873$			2.13718e8i			0.321216i
$874$	2.28835e8			0.342758
$875$	−8.83110e7			−0.131823
$876$		−	1.11511e7i		−	0.0165884i
$877$	4.98285e8			0.738719			0.369359	−	0.929287i	$-0.379577\pi$
$877$	4.98285e8			0.738719			0.369359	+	0.929287i	$0.379577\pi$
$878$			4.38675e8i			0.648127i
$879$	−3.39904e8			−0.500484
$880$		−	1.16686e8i		−	0.171227i
$881$		−	5.62164e8i		−	0.822121i	−0.911608	−	0.411060i	$-0.865159\pi$
$881$		−	5.62164e8i		−	0.822121i	0.911608	−	0.411060i	$-0.134841\pi$
$882$			2.93109e8i			0.427192i
$883$	6.42211e8			0.932816			0.466408	−	0.884570i	$-0.345548\pi$
$883$	6.42211e8			0.932816			0.466408	+	0.884570i	$0.345548\pi$
$884$			2.14974e8i			0.311193i
$885$	2.10639e8	−	4.90759e6i	0.303884	−	0.00708009i
$886$	1.34677e9			1.93639
$887$		−	5.48309e8i		−	0.785696i	−0.919603	−	0.392848i	$-0.871490\pi$
$887$		−	5.48309e8i		−	0.785696i	0.919603	−	0.392848i	$-0.128510\pi$
$888$	−1.44312e8			−0.206094
$889$	1.18036e8			0.168000
$890$	5.52868e8			0.784244
$891$			2.12270e7i			0.0300092i
$892$	−2.38647e8			−0.336250
$893$			1.48768e8i			0.208908i
$894$	−6.38387e8			−0.893453
$895$			3.51433e8i			0.490200i
$896$			7.50674e7i			0.104358i
$897$	4.87762e8			0.675820
$898$			5.82541e8i			0.804447i
$899$		−	4.64815e8i		−	0.639736i
$900$	1.25424e8			0.172049
$901$	−7.10225e8			−0.971006
$902$	4.37432e8			0.596061
$903$			6.53526e7i			0.0887564i
$904$	4.46460e8			0.604334
$905$	−4.29894e8			−0.579983
$906$	−3.33374e8			−0.448278
$907$	3.19987e8			0.428855			0.214427	−	0.976740i	$-0.431211\pi$
$907$	3.19987e8			0.428855			0.214427	+	0.976740i	$0.431211\pi$
$908$			3.78774e8i			0.505968i
$909$			2.33021e8i			0.310244i
$910$	6.03791e7			0.0801240
$911$	1.35316e9			1.78975			0.894877	−	0.446313i	$-0.147263\pi$
$911$	1.35316e9			1.78975			0.894877	+	0.446313i	$0.147263\pi$
$912$	9.43378e7			0.124366
$913$	2.40549e8			0.316076
$914$	−8.07440e8			−1.05748
$915$			2.95613e8i			0.385887i
$916$			1.36349e8i			0.177405i
$917$			1.86375e8i			0.241701i
$918$		−	1.06206e8i		−	0.137284i
$919$			3.20508e8i			0.412945i	0.978452	+	0.206472i	$0.0661983\pi$
$919$			3.20508e8i			0.412945i	−0.978452	+	0.206472i	$0.933802\pi$
$920$	2.24597e8			0.288430
$921$	2.82624e7			0.0361768
$922$			1.60829e8i			0.205197i
$923$		−	2.76126e8i		−	0.351158i
$924$			1.27664e7i			0.0161827i
$925$		−	5.45531e8i		−	0.689278i
$926$	6.34841e7			0.0799525
$927$		−	1.21821e8i		−	0.152926i
$928$		−	4.47296e8i		−	0.559695i
$929$			1.49525e9i			1.86495i	0.361238	+	0.932474i	$0.382354\pi$
$929$			1.49525e9i			1.86495i	−0.361238	+	0.932474i	$0.617646\pi$
$930$	−4.39864e8			−0.546852
$931$	−1.41303e8			−0.175107
$932$			7.84164e7i			0.0968633i
$933$	−2.07031e8			−0.254912
$934$	1.23407e9			1.51460
$935$		−	6.33295e7i		−	0.0774767i
$936$	8.18383e7			0.0997996
$937$		−	8.00505e8i		−	0.973072i	−0.873660	−	0.486536i	$-0.838260\pi$
$937$		−	8.00505e8i		−	0.973072i	0.873660	−	0.486536i	$-0.161740\pi$
$938$	7.85071e7			0.0951263
$939$			6.36590e8i			0.768887i
$940$		−	3.64670e8i		−	0.439052i
$941$			3.67953e8i			0.441594i	0.975320	+	0.220797i	$0.0708659\pi$
$941$			3.67953e8i			0.441594i	−0.975320	+	0.220797i	$0.929134\pi$
$942$	4.10765e8			0.491407
$943$			2.06876e9i			2.46703i
$944$	1.01271e9	−	2.35948e7i	1.20384	−	0.0280479i
$945$	−1.24270e7			−0.0147255
$946$		−	3.16652e8i		−	0.374032i
$947$	1.21053e9			1.42537			0.712683	−	0.701486i	$-0.247480\pi$
$947$	1.21053e9			1.42537			0.712683	+	0.701486i	$0.247480\pi$
$948$	5.38748e8			0.632354
$949$	2.75048e7			0.0321818
$950$			1.45140e8i			0.169284i
$951$	8.31984e8			0.967327
$952$			2.55752e7i			0.0296421i
$953$	−1.25588e9			−1.45101			−0.725503	−	0.688219i	$-0.758393\pi$
$953$	−1.25588e9			−1.45101			−0.725503	+	0.688219i	$0.758393\pi$
$954$		−	6.75266e8i		−	0.777732i
$955$		−	5.77999e8i		−	0.663616i
$956$	−5.97954e7			−0.0684375
$957$			6.36277e7i			0.0725957i
$958$			1.74063e9i			1.97974i
$959$	−2.25952e8			−0.256189
$960$	−9.94478e7			−0.112404
$961$	−7.88306e8			−0.888229
$962$			8.89004e8i			0.998570i
$963$	2.81574e8			0.315293
$964$	8.84349e8			0.987172
$965$	−4.72768e8			−0.526097
$966$	−1.44927e8			−0.160775
$967$			1.10105e8i			0.121767i	0.998145	+	0.0608833i	$0.0193917\pi$
$967$			1.10105e8i			0.121767i	−0.998145	+	0.0608833i	$0.980608\pi$
$968$		−	3.14766e8i		−	0.347026i
$969$	5.12002e7			0.0562730
$970$	6.06229e8			0.664235
$971$	1.47243e9			1.60833			0.804167	−	0.594404i	$-0.202612\pi$
$971$	1.47243e9			1.60833			0.804167	+	0.594404i	$0.202612\pi$
$972$	4.20673e7			0.0458084
$973$	−1.25381e7			−0.0136111
$974$			1.89976e9i			2.05600i
$975$			3.09366e8i			0.333779i
$976$			1.42125e9i			1.52870i
$977$		−	1.41112e9i		−	1.51315i	−0.653909	−	0.756573i	$-0.726872\pi$
$977$		−	1.41112e9i		−	1.51315i	0.653909	−	0.756573i	$-0.273128\pi$
$978$		−	5.81747e7i		−	0.0621895i
$979$	−2.88333e8			−0.307288
$980$	3.46372e8			0.368014
$981$		−	8.98365e7i		−	0.0951581i
$982$		−	1.90683e9i		−	2.01362i
$983$		−	1.99332e8i		−	0.209854i	−0.994480	−	0.104927i	$-0.966539\pi$
$983$		−	1.99332e8i		−	0.209854i	0.994480	−	0.104927i	$-0.0334609\pi$
$984$			3.47103e8i			0.364311i
$985$	−7.44671e8			−0.779212
$986$		−	3.18352e8i		−	0.332106i
$987$		−	9.42187e7i		−	0.0979909i
$988$		−	9.85344e7i		−	0.102168i
$989$	1.49755e9			1.54808
$990$	6.02122e7			0.0620553
$991$			1.46633e8i			0.150664i	0.997158	+	0.0753322i	$0.0240017\pi$
$991$			1.46633e8i			0.150664i	−0.997158	+	0.0753322i	$0.975998\pi$
$992$	−1.61265e9			−1.65198
$993$	−6.40794e8			−0.654441
$994$			8.20444e7i			0.0835391i
$995$	−4.75561e8			−0.482767
$996$		−	4.76716e8i		−	0.482482i
$997$	−1.31432e9			−1.32622			−0.663111	−	0.748521i	$-0.730764\pi$
$997$	−1.31432e9			−1.32622			−0.663111	+	0.748521i	$0.730764\pi$
$998$		−	8.32509e8i		−	0.837524i
$999$		−	1.82971e8i		−	0.183521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.12	✓	60
59.58	odd	2	inner	177.7.c.a.58.49	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.12	✓	60	1.1	even	1	trivial
177.7.c.a.58.49	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)

\(f(q)\)	\(=\)	\(q-10.4738i q^{2} -15.5885 q^{3} -45.7013 q^{4} +65.8108 q^{5} +163.271i q^{6} +49.8494 q^{7} -191.658i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-10.4738i q^{2} -15.5885 q^{3} -45.7013 q^{4} +65.8108 q^{5} +163.271i q^{6} +49.8494 q^{7} -191.658i q^{8} +243.000 q^{9} -689.291i q^{10} +359.481i q^{11} +712.413 q^{12} +1757.21i q^{13} -522.114i q^{14} -1025.89 q^{15} -4932.27 q^{16} -2676.91 q^{17} -2545.14i q^{18} +1226.97 q^{19} -3007.64 q^{20} -777.075 q^{21} +3765.14 q^{22} +17806.6i q^{23} +2987.65i q^{24} -11293.9 q^{25} +18404.8 q^{26} -3788.00 q^{27} -2278.18 q^{28} -11354.5 q^{29} +10745.0i q^{30} +40936.7i q^{31} +39393.8i q^{32} -5603.75i q^{33} +28037.5i q^{34} +3280.63 q^{35} -11105.4 q^{36} +48303.0i q^{37} -12851.1i q^{38} -27392.2i q^{39} -12613.1i q^{40} +116179. q^{41} +8138.96i q^{42} -84100.8i q^{43} -16428.7i q^{44} +15992.0 q^{45} +186503. q^{46} +121248. i q^{47} +76886.6 q^{48} -115164. q^{49} +118291. i q^{50} +41728.9 q^{51} -80306.8i q^{52} +265316. q^{53} +39674.8i q^{54} +23657.7i q^{55} -9554.02i q^{56} -19126.6 q^{57} +118925. i q^{58} +(-205323. + 4783.75i) q^{59} +46884.4 q^{60} -288153. i q^{61} +428764. q^{62} +12113.4 q^{63} +96938.3 q^{64} +115643. i q^{65} -58692.8 q^{66} +150364. i q^{67} +122338. q^{68} -277577. i q^{69} -34360.7i q^{70} -157139. q^{71} -46572.8i q^{72} -15652.5i q^{73} +505918. q^{74} +176055. q^{75} -56074.3 q^{76} +17919.9i q^{77} -286902. q^{78} +756230. q^{79} -324597. q^{80} +59049.0 q^{81} -1.21684e6i q^{82} -669157. i q^{83} +35513.3 q^{84} -176169. q^{85} -880859. q^{86} +176999. q^{87} +68897.2 q^{88} +802081. i q^{89} -167498. i q^{90} +87595.9i q^{91} -813785. i q^{92} -638139. i q^{93} +1.26993e6 q^{94} +80748.1 q^{95} -614088. i q^{96} +879496. i q^{97} +1.20621e6i q^{98} +87353.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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