LMFDB - Embedded newform 177.7.c.a.58.14

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			58.14
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.91595i q^{2} +15.5885 q^{3} -34.3260 q^{4} -70.2821 q^{5} -154.574i q^{6} +315.675 q^{7} -294.246i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-9.91595i q^{2} +15.5885 q^{3} -34.3260 q^{4} -70.2821 q^{5} -154.574i q^{6} +315.675 q^{7} -294.246i q^{8} +243.000 q^{9} +696.914i q^{10} +1757.73i q^{11} -535.089 q^{12} +3990.02i q^{13} -3130.21i q^{14} -1095.59 q^{15} -5114.59 q^{16} -2601.72 q^{17} -2409.57i q^{18} -12139.0 q^{19} +2412.50 q^{20} +4920.88 q^{21} +17429.6 q^{22} +8281.58i q^{23} -4586.84i q^{24} -10685.4 q^{25} +39564.8 q^{26} +3788.00 q^{27} -10835.8 q^{28} -31786.7 q^{29} +10863.8i q^{30} -194.726i q^{31} +31884.3i q^{32} +27400.4i q^{33} +25798.5i q^{34} -22186.3 q^{35} -8341.21 q^{36} -16186.6i q^{37} +120370. i q^{38} +62198.2i q^{39} +20680.2i q^{40} +82067.8 q^{41} -48795.2i q^{42} +134723. i q^{43} -60335.9i q^{44} -17078.6 q^{45} +82119.7 q^{46} -34502.7i q^{47} -79728.6 q^{48} -17998.4 q^{49} +105956. i q^{50} -40556.8 q^{51} -136961. i q^{52} +38215.6 q^{53} -37561.6i q^{54} -123537. i q^{55} -92886.0i q^{56} -189229. q^{57} +315195. i q^{58} +(156402. - 133112. i) q^{59} +37607.2 q^{60} +267542. i q^{61} -1930.89 q^{62} +76709.0 q^{63} -11171.2 q^{64} -280427. i q^{65} +271700. q^{66} +23922.1i q^{67} +89306.6 q^{68} +129097. i q^{69} +219998. i q^{70} +213558. q^{71} -71501.8i q^{72} -140860. i q^{73} -160506. q^{74} -166569. q^{75} +416684. q^{76} +554872. i q^{77} +616754. q^{78} +369365. q^{79} +359464. q^{80} +59049.0 q^{81} -813780. i q^{82} -201363. i q^{83} -168914. q^{84} +182854. q^{85} +1.33590e6 q^{86} -495505. q^{87} +517206. q^{88} -8376.32i q^{89} +169350. i q^{90} +1.25955e6i q^{91} -284273. i q^{92} -3035.47i q^{93} -342126. q^{94} +853156. q^{95} +497026. i q^{96} +738936. i q^{97} +178471. i q^{98} +427129. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	9.91595i		−	1.23949i	−0.784802	−	0.619747i	$-0.787235\pi$
$2$		−	9.91595i		−	1.23949i	0.784802	−	0.619747i	$-0.212765\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−34.3260			−0.536344
$5$	−70.2821			−0.562257			−0.281128	−	0.959670i	$-0.590709\pi$
$5$	−70.2821			−0.562257			−0.281128	+	0.959670i	$0.590709\pi$
$6$		−	154.574i		−	0.715622i
$7$	315.675			0.920335			0.460167	−	0.887832i	$-0.347789\pi$
$7$	315.675			0.920335			0.460167	+	0.887832i	$0.347789\pi$
$8$		−	294.246i		−	0.574699i
$9$	243.000			0.333333
$10$			696.914i			0.696914i
$11$			1757.73i			1.32061i	0.750997	+	0.660306i	$0.229573\pi$
$11$			1757.73i			1.32061i	−0.750997	+	0.660306i	$0.770427\pi$
$12$	−535.089			−0.309658
$13$			3990.02i			1.81612i	0.418839	+	0.908060i	$0.362437\pi$
$13$			3990.02i			1.81612i	−0.418839	+	0.908060i	$0.637563\pi$
$14$		−	3130.21i		−	1.14075i
$15$	−1095.59			−0.324619
$16$	−5114.59			−1.24868
$17$	−2601.72			−0.529558			−0.264779	−	0.964309i	$-0.585299\pi$
$17$	−2601.72			−0.529558			−0.264779	+	0.964309i	$0.585299\pi$
$18$		−	2409.57i		−	0.413164i
$19$	−12139.0			−1.76980			−0.884898	−	0.465785i	$-0.845772\pi$
$19$	−12139.0			−1.76980			−0.884898	+	0.465785i	$0.845772\pi$
$20$	2412.50			0.301563
$21$	4920.88			0.531356
$22$	17429.6			1.63689
$23$			8281.58i			0.680659i	0.940306	+	0.340330i	$0.110539\pi$
$23$			8281.58i			0.680659i	−0.940306	+	0.340330i	$0.889461\pi$
$24$		−	4586.84i		−	0.331803i
$25$	−10685.4			−0.683867
$26$	39564.8			2.25107
$27$	3788.00			0.192450
$28$	−10835.8			−0.493616
$29$	−31786.7			−1.30332			−0.651660	−	0.758511i	$-0.725927\pi$
$29$	−31786.7			−1.30332			−0.651660	+	0.758511i	$0.725927\pi$
$30$			10863.8i			0.402363i
$31$		−	194.726i		−	0.00653639i	−0.999995	−	0.00326819i	$-0.998960\pi$
$31$		−	194.726i		−	0.00653639i	0.999995	−	0.00326819i	$-0.00104030\pi$
$32$			31884.3i			0.973030i
$33$			27400.4i			0.762455i
$34$			25798.5i			0.656384i
$35$	−22186.3			−0.517465
$36$	−8341.21			−0.178781
$37$		−	16186.6i		−	0.319559i	−0.987153	−	0.159779i	$-0.948922\pi$
$37$		−	16186.6i		−	0.319559i	0.987153	−	0.159779i	$-0.0510783\pi$
$38$			120370.i			2.19365i
$39$			62198.2i			1.04854i
$40$			20680.2i			0.323128i
$41$	82067.8			1.19075			0.595376	−	0.803447i	$-0.297003\pi$
$41$	82067.8			1.19075			0.595376	+	0.803447i	$0.297003\pi$
$42$		−	48795.2i		−	0.658612i
$43$			134723.i			1.69447i	0.531215	+	0.847237i	$0.321736\pi$
$43$			134723.i			1.69447i	−0.531215	+	0.847237i	$0.678264\pi$
$44$		−	60335.9i		−	0.708301i
$45$	−17078.6			−0.187419
$46$	82119.7			0.843673
$47$		−	34502.7i		−	0.332322i	−0.986099	−	0.166161i	$-0.946863\pi$
$47$		−	34502.7i		−	0.332322i	0.986099	−	0.166161i	$-0.0531371\pi$
$48$	−79728.6			−0.720925
$49$	−17998.4			−0.152984
$50$			105956.i			0.847649i
$51$	−40556.8			−0.305740
$52$		−	136961.i		−	0.974065i
$53$	38215.6			0.256692			0.128346	−	0.991729i	$-0.459033\pi$
$53$	38215.6			0.256692			0.128346	+	0.991729i	$0.459033\pi$
$54$		−	37561.6i		−	0.238541i
$55$		−	123537.i		−	0.742523i
$56$		−	92886.0i		−	0.528916i
$57$	−189229.			−1.02179
$58$			315195.i			1.61546i
$59$	156402.	−	133112.i	0.761531	−	0.648129i
$59$	156402.	−	133112.i	0.761531	−	0.648129i
$60$	37607.2			0.174107
$61$			267542.i			1.17870i	0.807879	+	0.589348i	$0.200615\pi$
$61$			267542.i			1.17870i	−0.807879	+	0.589348i	$0.799385\pi$
$62$	−1930.89			−0.00810181
$63$	76709.0			0.306778
$64$	−11171.2			−0.0426146
$65$		−	280427.i		−	1.02113i
$66$	271700.			0.945058
$67$			23922.1i			0.0795381i	0.999209	+	0.0397691i	$0.0126622\pi$
$67$			23922.1i			0.0795381i	−0.999209	+	0.0397691i	$0.987338\pi$
$68$	89306.6			0.284025
$69$			129097.i			0.392979i
$70$			219998.i			0.641394i
$71$	213558.			0.596680			0.298340	−	0.954460i	$-0.403567\pi$
$71$	213558.			0.596680			0.298340	+	0.954460i	$0.403567\pi$
$72$		−	71501.8i		−	0.191566i
$73$		−	140860.i		−	0.362093i	−0.983475	−	0.181046i	$-0.942052\pi$
$73$		−	140860.i		−	0.362093i	0.983475	−	0.181046i	$-0.0579484\pi$
$74$	−160506.			−0.396091
$75$	−166569.			−0.394831
$76$	416684.			0.949218
$77$			554872.i			1.21540i
$78$	616754.			1.29966
$79$	369365.			0.749160			0.374580	−	0.927195i	$-0.377787\pi$
$79$	369365.			0.749160			0.374580	+	0.927195i	$0.377787\pi$
$80$	359464.			0.702078
$81$	59049.0			0.111111
$82$		−	813780.i		−	1.47593i
$83$		−	201363.i		−	0.352165i	−0.984375	−	0.176082i	$-0.943657\pi$
$83$		−	201363.i		−	0.352165i	0.984375	−	0.176082i	$-0.0563425\pi$
$84$	−168914.			−0.284989
$85$	182854.			0.297748
$86$	1.33590e6			2.10029
$87$	−495505.			−0.752473
$88$	517206.			0.758954
$89$		−	8376.32i		−	0.0118818i	−0.999982	−	0.00594091i	$-0.998109\pi$
$89$		−	8376.32i		−	0.0118818i	0.999982	−	0.00594091i	$-0.00189106\pi$
$90$			169350.i			0.232305i
$91$			1.25955e6i			1.67144i
$92$		−	284273.i		−	0.365067i
$93$		−	3035.47i		−	0.00377379i
$94$	−342126.			−0.411911
$95$	853156.			0.995080
$96$			497026.i			0.561779i
$97$			738936.i			0.809639i	0.914397	+	0.404820i	$0.132666\pi$
$97$			738936.i			0.809639i	−0.914397	+	0.404820i	$0.867334\pi$
$98$			178471.i			0.189623i
$99$			427129.i			0.440204i
$100$	366788.			0.366788
$101$		−	1.69788e6i		−	1.64795i	−0.566630	−	0.823973i	$-0.691753\pi$
$101$		−	1.69788e6i		−	1.64795i	0.566630	−	0.823973i	$-0.308247\pi$
$102$			402159.i			0.378963i
$103$			98537.6i			0.0901758i	0.998983	+	0.0450879i	$0.0143568\pi$
$103$			98537.6i			0.0901758i	−0.998983	+	0.0450879i	$0.985643\pi$
$104$	1.17405e6			1.04372
$105$	−345850.			−0.298758
$106$		−	378943.i		−	0.318168i
$107$	−563327.			−0.459842			−0.229921	−	0.973209i	$-0.573847\pi$
$107$	−563327.			−0.459842			−0.229921	+	0.973209i	$0.573847\pi$
$108$	−130027.			−0.103219
$109$			219893.i			0.169798i	0.996390	+	0.0848988i	$0.0270567\pi$
$109$			219893.i			0.169798i	−0.996390	+	0.0848988i	$0.972943\pi$
$110$	−1.22499e6			−0.920352
$111$		−	252324.i		−	0.184497i
$112$	−1.61455e6			−1.14920
$113$		−	1.22429e6i		−	0.848492i	−0.905547	−	0.424246i	$-0.860539\pi$
$113$		−	1.22429e6i		−	0.848492i	0.905547	−	0.424246i	$-0.139461\pi$
$114$			1.87638e6i			1.26650i
$115$		−	582047.i		−	0.382705i
$116$	1.09111e6			0.699028
$117$			969574.i			0.605374i
$118$	−1.31993e6	−	1.55088e6i	−0.803352	−	0.943912i
$119$	−821297.			−0.487371
$120$			322373.i			0.186558i
$121$	−1.31807e6			−0.744014
$122$	2.65293e6			1.46099
$123$	1.27931e6			0.687481
$124$			6684.15i			0.00350575i
$125$	1.84915e6			0.946766
$126$		−	760642.i		−	0.380250i
$127$	−2.62983e6			−1.28386			−0.641929	−	0.766764i	$-0.721866\pi$
$127$	−2.62983e6			−1.28386			−0.641929	+	0.766764i	$0.721866\pi$
$128$			2.15137e6i			1.02585i
$129$			2.10012e6i			0.978305i
$130$	−2.78070e6			−1.26568
$131$		−	2.92615e6i		−	1.30161i	−0.759243	−	0.650807i	$-0.774431\pi$
$131$		−	2.92615e6i		−	1.30161i	0.759243	−	0.650807i	$-0.225569\pi$
$132$		−	940544.i		−	0.408938i
$133$	−3.83199e6			−1.62880
$134$	237210.			0.0985870
$135$	−266228.			−0.108206
$136$			765545.i			0.304336i
$137$	1.96220e6			0.763101			0.381550	−	0.924348i	$-0.375390\pi$
$137$	1.96220e6			0.763101			0.381550	+	0.924348i	$0.375390\pi$
$138$	1.28012e6			0.487095
$139$	−3.16846e6			−1.17979			−0.589893	−	0.807481i	$-0.700830\pi$
$139$	−3.16846e6			−1.17979			−0.589893	+	0.807481i	$0.700830\pi$
$140$	761566.			0.277539
$141$		−	537843.i		−	0.191866i
$142$		−	2.11763e6i		−	0.739581i
$143$	−7.01339e6			−2.39839
$144$	−1.24285e6			−0.416226
$145$	2.23404e6			0.732801
$146$	−1.39676e6			−0.448811
$147$	−280567.			−0.0883253
$148$			555621.i			0.171393i
$149$			3.34972e6i			1.01263i	0.862350	+	0.506313i	$0.168992\pi$
$149$			3.34972e6i			1.01263i	−0.862350	+	0.506313i	$0.831008\pi$
$150$			1.65169e6i			0.489390i
$151$		−	3.55679e6i		−	1.03307i	−0.856267	−	0.516533i	$-0.827222\pi$
$151$		−	3.55679e6i		−	1.03307i	0.856267	−	0.516533i	$-0.172778\pi$
$152$			3.57186e6i			1.01710i
$153$	−632218.			−0.176519
$154$	5.50208e6			1.50649
$155$			13685.7i			0.00367513i
$156$		−	2.13502e6i		−	0.562376i
$157$			2.57388e6i			0.665104i	0.943085	+	0.332552i	$0.107910\pi$
$157$			2.57388e6i			0.665104i	−0.943085	+	0.332552i	$0.892090\pi$
$158$		−	3.66260e6i		−	0.928579i
$159$	595722.			0.148201
$160$		−	2.24089e6i		−	0.547093i
$161$			2.61429e6i			0.626434i
$162$		−	585527.i		−	0.137721i
$163$	−1.21026e6			−0.279457			−0.139729	−	0.990190i	$-0.544623\pi$
$163$	−1.21026e6			−0.279457			−0.139729	+	0.990190i	$0.544623\pi$
$164$	−2.81706e6			−0.638652
$165$		−	1.92575e6i		−	0.428696i
$166$	−1.99671e6			−0.436506
$167$	−6.75088e6			−1.44948			−0.724738	−	0.689024i	$-0.758039\pi$
$167$	−6.75088e6			−1.44948			−0.724738	+	0.689024i	$0.758039\pi$
$168$		−	1.44795e6i		−	0.305370i
$169$	−1.10934e7			−2.29829
$170$		−	1.81317e6i		−	0.369056i
$171$	−2.94978e6			−0.589932
$172$		−	4.62449e6i		−	0.908820i
$173$			4.51061e6i			0.871158i	0.900151	+	0.435579i	$0.143456\pi$
$173$			4.51061e6i			0.871158i	−0.900151	+	0.435579i	$0.856544\pi$
$174$			4.91340e6i			0.932685i
$175$	−3.37312e6			−0.629387
$176$		−	8.99009e6i		−	1.64902i
$177$	2.43807e6	−	2.07501e6i	0.439670	−	0.374197i
$178$	−83059.1			−0.0147274
$179$		−	2.01402e6i		−	0.351159i	−0.984465	−	0.175579i	$-0.943820\pi$
$179$		−	2.01402e6i		−	0.351159i	0.984465	−	0.175579i	$-0.0561799\pi$
$180$	586238.			0.100521
$181$	5.72471e6			0.965424			0.482712	−	0.875779i	$-0.339652\pi$
$181$	5.72471e6			0.965424			0.482712	+	0.875779i	$0.339652\pi$
$182$	1.24896e7			2.07174
$183$			4.17056e6i			0.680521i
$184$	2.43682e6			0.391174
$185$			1.13763e6i			0.179674i
$186$	−30099.6			−0.00467758
$187$		−	4.57313e6i		−	0.699340i
$188$			1.18434e6i			0.178239i
$189$	1.19577e6			0.177119
$190$		−	8.45985e6i		−	1.23339i
$191$			7.02854e6i			1.00871i	0.863497	+	0.504354i	$0.168269\pi$
$191$			7.02854e6i			1.00871i	−0.863497	+	0.504354i	$0.831731\pi$
$192$	−174141.			−0.0246035
$193$	1.27840e6			0.177825			0.0889126	−	0.996039i	$-0.471661\pi$
$193$	1.27840e6			0.177825			0.0889126	+	0.996039i	$0.471661\pi$
$194$	7.32725e6			1.00354
$195$		−	4.37142e6i		−	0.589548i
$196$	617813.			0.0820519
$197$	1.49210e7			1.95164			0.975819	−	0.218580i	$-0.0701425\pi$
$197$	1.49210e7			1.95164			0.975819	+	0.218580i	$0.0701425\pi$
$198$	4.23539e6			0.545630
$199$	1.18057e7			1.49807			0.749034	−	0.662532i	$-0.230518\pi$
$199$	1.18057e7			1.49807			0.749034	+	0.662532i	$0.230518\pi$
$200$			3.14414e6i			0.393018i
$201$			372909.i			0.0459214i
$202$	−1.68361e7			−2.04262
$203$	−1.00343e7			−1.19949
$204$	1.39215e6			0.163982
$205$	−5.76790e6			−0.669509
$206$	977093.			0.111772
$207$			2.01242e6i			0.226886i
$208$		−	2.04073e7i		−	2.26775i
$209$		−	2.13372e7i		−	2.33721i
$210$			3.42943e6i			0.370309i
$211$			5.57655e6i			0.593633i	0.954935	+	0.296816i	$0.0959249\pi$
$211$			5.57655e6i			0.593633i	−0.954935	+	0.296816i	$0.904075\pi$
$212$	−1.31179e6			−0.137675
$213$	3.32905e6			0.344493
$214$			5.58592e6i			0.569972i
$215$		−	9.46859e6i		−	0.952730i
$216$		−	1.11460e6i		−	0.110601i
$217$		−	61470.0i		−	0.00601567i
$218$	2.18044e6			0.210463
$219$		−	2.19579e6i		−	0.209054i
$220$			4.24054e6i			0.398247i
$221$		−	1.03809e7i		−	0.961741i
$222$	−2.50203e6			−0.228683
$223$	1.19173e7			1.07464			0.537322	−	0.843377i	$-0.319436\pi$
$223$	1.19173e7			1.07464			0.537322	+	0.843377i	$0.319436\pi$
$224$			1.00651e7i			0.895514i
$225$	−2.59656e6			−0.227956
$226$	−1.21400e7			−1.05170
$227$			2.29320e7i			1.96049i	0.197790	+	0.980245i	$0.436624\pi$
$227$			2.29320e7i			1.96049i	−0.197790	+	0.980245i	$0.563376\pi$
$228$	6.49546e6			0.548032
$229$			2.08608e6i			0.173710i	0.996221	+	0.0868550i	$0.0276817\pi$
$229$			2.08608e6i			0.173710i	−0.996221	+	0.0868550i	$0.972318\pi$
$230$	−5.77155e6			−0.474361
$231$			8.64960e6i			0.701714i
$232$			9.35310e6i			0.749017i
$233$			7.18787e6i			0.568241i	0.958789	+	0.284121i	$0.0917016\pi$
$233$			7.18787e6i			0.568241i	−0.958789	+	0.284121i	$0.908298\pi$
$234$	9.61425e6			0.750356
$235$			2.42492e6i			0.186850i
$236$	−5.36867e6	+	4.56920e6i	−0.408442	+	0.347620i
$237$	5.75783e6			0.432528
$238$			8.14394e6i			0.604093i
$239$	−1.69825e7			−1.24397			−0.621983	−	0.783031i	$-0.713673\pi$
$239$	−1.69825e7			−1.24397			−0.621983	+	0.783031i	$0.713673\pi$
$240$	5.60349e6			0.405345
$241$	3.37071e6			0.240808			0.120404	−	0.992725i	$-0.461581\pi$
$241$	3.37071e6			0.240808			0.120404	+	0.992725i	$0.461581\pi$
$242$			1.30699e7i			0.922200i
$243$	920483.			0.0641500
$244$		−	9.18363e6i		−	0.632186i
$245$	1.26497e6			0.0860163
$246$		−	1.26856e7i		−	0.852128i
$247$		−	4.84349e7i		−	3.21416i
$248$	−57297.2			−0.00375646
$249$		−	3.13894e6i		−	0.203323i
$250$		−	1.83361e7i		−	1.17351i
$251$	−1.81189e7			−1.14580			−0.572901	−	0.819624i	$-0.694182\pi$
$251$	−1.81189e7			−1.14580			−0.572901	+	0.819624i	$0.694182\pi$
$252$	−2.63311e6			−0.164539
$253$	−1.45568e7			−0.898886
$254$			2.60773e7i			1.59133i
$255$	2.85042e6			0.171905
$256$	2.06179e7			1.22892
$257$	−5.97124e6			−0.351775			−0.175887	−	0.984410i	$-0.556279\pi$
$257$	−5.97124e6			−0.351775			−0.175887	+	0.984410i	$0.556279\pi$
$258$	2.08246e7			1.21260
$259$		−	5.10971e6i		−	0.294101i
$260$			9.62593e6i			0.547675i
$261$	−7.72416e6			−0.434440
$262$	−2.90155e7			−1.61334
$263$	2.20924e7			1.21444			0.607220	−	0.794534i	$-0.292285\pi$
$263$	2.20924e7			1.21444			0.607220	+	0.794534i	$0.292285\pi$
$264$	8.06244e6			0.438182
$265$	−2.68587e6			−0.144327
$266$			3.79978e7i			2.01889i
$267$		−	130574.i		−	0.00685997i
$268$		−	821151.i		−	0.0426598i
$269$			2.95123e7i			1.51616i	0.652159	+	0.758082i	$0.273863\pi$
$269$			2.95123e7i			1.51616i	−0.652159	+	0.758082i	$0.726137\pi$
$270$			2.63991e6i			0.134121i
$271$	2.45049e7			1.23125			0.615624	−	0.788040i	$-0.288904\pi$
$271$	2.45049e7			1.23125			0.615624	+	0.788040i	$0.288904\pi$
$272$	1.33067e7			0.661248
$273$			1.96344e7i			0.965006i
$274$		−	1.94571e7i		−	0.945858i
$275$		−	1.87821e7i		−	0.903123i
$276$		−	4.43139e6i		−	0.210772i
$277$	−7.24719e6			−0.340981			−0.170491	−	0.985359i	$-0.554535\pi$
$277$	−7.24719e6			−0.340981			−0.170491	+	0.985359i	$0.554535\pi$
$278$			3.14182e7i			1.46234i
$279$		−	47318.3i		−	0.00217880i
$280$			6.52823e6i			0.297386i
$281$	4.38422e6			0.197594			0.0987969	−	0.995108i	$-0.468501\pi$
$281$	4.38422e6			0.197594			0.0987969	+	0.995108i	$0.468501\pi$
$282$	−5.33322e6			−0.237817
$283$		−	6.34579e6i		−	0.279980i	−0.990153	−	0.139990i	$-0.955293\pi$
$283$		−	6.34579e6i		−	0.279980i	0.990153	−	0.139990i	$-0.0447070\pi$
$284$	−7.33060e6			−0.320025
$285$	1.32994e7			0.574510
$286$			6.95444e7i			2.97279i
$287$	2.59068e7			1.09589
$288$			7.74787e6i			0.324343i
$289$	−1.73686e7			−0.719568
$290$		−	2.21526e7i		−	0.908302i
$291$			1.15189e7i			0.467445i
$292$			4.83516e6i			0.194206i
$293$	1.05299e7			0.418622			0.209311	−	0.977849i	$-0.432878\pi$
$293$	1.05299e7			0.418622			0.209311	+	0.977849i	$0.432878\pi$
$294$			2.78209e6i			0.109479i
$295$	−1.09923e7	+	9.35540e6i	−0.428176	+	0.364415i
$296$	−4.76284e6			−0.183650
$297$			6.65829e6i			0.254152i
$298$	3.32156e7			1.25514
$299$	−3.30437e7			−1.23616
$300$	5.71766e6			0.211765
$301$			4.25285e7i			1.55948i
$302$	−3.52690e7			−1.28048
$303$		−	2.64673e7i		−	0.951442i
$304$	6.20861e7			2.20991
$305$		−	1.88034e7i		−	0.662730i
$306$			6.26904e6i			0.218795i
$307$	−5.30124e7			−1.83215			−0.916077	−	0.401001i	$-0.868662\pi$
$307$	−5.30124e7			−1.83215			−0.916077	+	0.401001i	$0.868662\pi$
$308$		−	1.90465e7i		−	0.651874i
$309$			1.53605e6i			0.0520630i
$310$	135707.			0.00455530
$311$	2.41009e7			0.801219			0.400610	−	0.916249i	$-0.368798\pi$
$311$	2.41009e7			0.801219			0.400610	+	0.916249i	$0.368798\pi$
$312$	1.83016e7			0.602594
$313$			4.77031e7i			1.55566i	0.628477	+	0.777828i	$0.283679\pi$
$313$			4.77031e7i			1.55566i	−0.628477	+	0.777828i	$0.716321\pi$
$314$	2.55225e7			0.824393
$315$	−5.39127e6			−0.172488
$316$	−1.26788e7			−0.401807
$317$	1.81936e7			0.571137			0.285569	−	0.958358i	$-0.407818\pi$
$317$	1.81936e7			0.571137			0.285569	+	0.958358i	$0.407818\pi$
$318$		−	5.90714e6i		−	0.183695i
$319$		−	5.58725e7i		−	1.72118i
$320$	785133.			0.0239603
$321$	−8.78139e6			−0.265490
$322$	2.59231e7			0.776461
$323$	3.15823e7			0.937209
$324$	−2.02692e6			−0.0595937
$325$		−	4.26350e7i		−	1.24199i
$326$			1.20009e7i			0.346386i
$327$			3.42779e6i			0.0980326i
$328$		−	2.41481e7i		−	0.684324i
$329$		−	1.08916e7i		−	0.305847i
$330$	−1.90957e7			−0.531365
$331$	−6.20268e7			−1.71039			−0.855196	−	0.518305i	$-0.826563\pi$
$331$	−6.20268e7			−1.71039			−0.855196	+	0.518305i	$0.826563\pi$
$332$			6.91199e6i			0.188881i
$333$		−	3.93335e6i		−	0.106520i
$334$			6.69414e7i			1.79662i
$335$		−	1.68130e6i		−	0.0447209i
$336$	−2.51683e7			−0.663493
$337$		−	5.85561e7i		−	1.52997i	−0.644049	−	0.764984i	$-0.722747\pi$
$337$		−	5.85561e7i		−	1.52997i	0.644049	−	0.764984i	$-0.277253\pi$
$338$			1.10002e8i			2.84872i
$339$		−	1.90847e7i		−	0.489877i
$340$	−6.27665e6			−0.159695
$341$	342276.			0.00863203
$342$			2.92499e7i			0.731217i
$343$	−4.28205e7			−1.06113
$344$	3.96416e7			0.973813
$345$		−	9.07322e6i		−	0.220955i
$346$	4.47269e7			1.07979
$347$		−	7.33274e7i		−	1.75500i	−0.479574	−	0.877501i	$-0.659209\pi$
$347$		−	7.33274e7i		−	1.75500i	0.479574	−	0.877501i	$-0.340791\pi$
$348$	1.70087e7			0.403584
$349$		−	1.37662e6i		−	0.0323845i	−0.999869	−	0.0161923i	$-0.994846\pi$
$349$		−	1.37662e6i		−	0.0323845i	0.999869	−	0.0161923i	$-0.00515438\pi$
$350$			3.34477e7i			0.780121i
$351$			1.51142e7i			0.349513i
$352$	−5.60440e7			−1.28499
$353$		−	3.05310e7i		−	0.694091i	−0.937848	−	0.347045i	$-0.887185\pi$
$353$		−	3.05310e7i		−	0.694091i	0.937848	−	0.347045i	$-0.112815\pi$
$354$	−2.05757e7	−	2.41758e7i	−0.463815	−	0.544968i
$355$	−1.50093e7			−0.335487
$356$			287525.i			0.00637274i
$357$	−1.28028e7			−0.281384
$358$	−1.99709e7			−0.435259
$359$	4.05307e7			0.875993			0.437997	−	0.898977i	$-0.355688\pi$
$359$	4.05307e7			0.875993			0.437997	+	0.898977i	$0.355688\pi$
$360$			5.02529e6i			0.107709i
$361$	1.00310e8			2.13218
$362$		−	5.67660e7i		−	1.19664i
$363$	−2.05466e7			−0.429557
$364$		−	4.32352e7i		−	0.896466i
$365$			9.89995e6i			0.203589i
$366$	4.13551e7			0.843501
$367$		−	2.60127e7i		−	0.526244i	−0.964763	−	0.263122i	$-0.915248\pi$
$367$		−	2.60127e7i		−	0.526244i	0.964763	−	0.263122i	$-0.0847522\pi$
$368$		−	4.23569e7i		−	0.849925i
$369$	1.99425e7			0.396917
$370$	1.12807e7			0.222705
$371$	1.20637e7			0.236243
$372$			104196.i			0.00202405i
$373$	−7.67396e7			−1.47874			−0.739372	−	0.673298i	$-0.764877\pi$
$373$	−7.67396e7			−1.47874			−0.739372	+	0.673298i	$0.764877\pi$
$374$	−4.53469e7			−0.866827
$375$	2.88254e7			0.546616
$376$	−1.01523e7			−0.190985
$377$		−	1.26829e8i		−	2.36699i
$378$		−	1.18572e7i		−	0.219537i
$379$	1.05935e8			1.94591			0.972955	−	0.230994i	$-0.0741979\pi$
$379$	1.05935e8			1.94591			0.972955	+	0.230994i	$0.0741979\pi$
$380$	−2.92854e7			−0.533705
$381$	−4.09950e7			−0.741235
$382$	6.96947e7			1.25029
$383$	−7.76856e7			−1.38275			−0.691376	−	0.722495i	$-0.742995\pi$
$383$	−7.76856e7			−1.38275			−0.691376	+	0.722495i	$0.742995\pi$
$384$			3.35365e7i			0.592275i
$385$		−	3.89976e7i		−	0.683369i
$386$		−	1.26765e7i		−	0.220413i
$387$			3.27376e7i			0.564825i
$388$		−	2.53647e7i		−	0.434245i
$389$	−1.60025e7			−0.271855			−0.135928	−	0.990719i	$-0.543401\pi$
$389$	−1.60025e7			−0.271855			−0.135928	+	0.990719i	$0.543401\pi$
$390$	−4.33468e7			−0.730740
$391$		−	2.15463e7i		−	0.360449i
$392$			5.29596e6i			0.0879197i
$393$		−	4.56141e7i		−	0.751487i
$394$		−	1.47956e8i		−	2.41904i
$395$	−2.59597e7			−0.421220
$396$		−	1.46616e7i		−	0.236100i
$397$			9.53672e7i			1.52415i	0.647489	+	0.762074i	$0.275819\pi$
$397$			9.53672e7i			1.52415i	−0.647489	+	0.762074i	$0.724181\pi$
$398$		−	1.17064e8i		−	1.85685i
$399$	−5.97347e7			−0.940391
$400$	5.46516e7			0.853931
$401$		−	7.34361e7i		−	1.13888i	−0.822034	−	0.569438i	$-0.807161\pi$
$401$		−	7.34361e7i		−	1.13888i	0.822034	−	0.569438i	$-0.192839\pi$
$402$	3.69775e6			0.0569192
$403$	776958.			0.0118709
$404$			5.82814e7i			0.883865i
$405$	−4.15009e6			−0.0624730
$406$			9.94991e7i			1.48676i
$407$	2.84517e7			0.422013
$408$			1.19337e7i			0.175709i
$409$			6.32248e7i			0.924097i	0.886855	+	0.462048i	$0.152885\pi$
$409$			6.32248e7i			0.924097i	−0.886855	+	0.462048i	$0.847115\pi$
$410$			5.71942e7i			0.829851i
$411$	3.05877e7			0.440576
$412$		−	3.38240e6i		−	0.0483652i
$413$	4.93723e7	−	4.20201e7i	0.700863	−	0.596496i
$414$	1.99551e7			0.281224
$415$			1.41522e7i			0.198007i
$416$	−1.27219e8			−1.76714
$417$	−4.93913e7			−0.681150
$418$	−2.11578e8			−2.89696
$419$			1.15918e7i			0.157583i	0.996891	+	0.0787916i	$0.0251062\pi$
$419$			1.15918e7i			0.157583i	−0.996891	+	0.0787916i	$0.974894\pi$
$420$	1.18716e7			0.160237
$421$			1.15562e8i			1.54870i	0.632755	+	0.774352i	$0.281924\pi$
$421$			1.15562e8i			1.54870i	−0.632755	+	0.774352i	$0.718076\pi$
$422$	5.52967e7			0.735804
$423$		−	8.38414e6i		−	0.110774i
$424$		−	1.12448e7i		−	0.147521i
$425$	2.78005e7			0.362147
$426$		−	3.30106e7i		−	0.426997i
$427$			8.44562e7i			1.08480i
$428$	1.93367e7			0.246634
$429$	−1.09328e8			−1.38471
$430$	−9.38900e7			−1.18090
$431$		−	3.80235e7i		−	0.474920i	−0.971397	−	0.237460i	$-0.923685\pi$
$431$		−	3.80235e7i		−	0.474920i	0.971397	−	0.237460i	$-0.0763149\pi$
$432$	−1.93740e7			−0.240308
$433$	−4.82860e7			−0.594782			−0.297391	−	0.954756i	$-0.596117\pi$
$433$	−4.82860e7			−0.594782			−0.297391	+	0.954756i	$0.596117\pi$
$434$	−609533.			−0.00745638
$435$	3.48252e7			0.423083
$436$		−	7.54803e6i		−	0.0910698i
$437$		−	1.00530e8i		−	1.20463i
$438$	−2.17734e7			−0.259121
$439$	−5.04082e6			−0.0595809			−0.0297905	−	0.999556i	$-0.509484\pi$
$439$	−5.04082e6			−0.0595809			−0.0297905	+	0.999556i	$0.509484\pi$
$440$	−3.63503e7			−0.426727
$441$	−4.37361e6			−0.0509946
$442$	−1.02936e8			−1.19207
$443$			1.24562e8i			1.43276i	0.697711	+	0.716379i	$0.254202\pi$
$443$			1.24562e8i			1.43276i	−0.697711	+	0.716379i	$0.745798\pi$
$444$			8.66128e6i			0.0989540i
$445$			588705.i			0.00668064i
$446$		−	1.18172e8i		−	1.33201i
$447$			5.22169e7i			0.584640i
$448$	−3.52645e6			−0.0392197
$449$	2.91679e7			0.322230			0.161115	−	0.986936i	$-0.448491\pi$
$449$	2.91679e7			0.322230			0.161115	+	0.986936i	$0.448491\pi$
$450$			2.57473e7i			0.282550i
$451$			1.44253e8i			1.57252i
$452$			4.20248e7i			0.455083i
$453$		−	5.54449e7i		−	0.596441i
$454$	2.27393e8			2.43001
$455$		−	8.85237e7i		−	0.939778i
$456$			5.56798e7i			0.587223i
$457$		−	1.21827e7i		−	0.127643i	−0.997961	−	0.0638213i	$-0.979671\pi$
$457$		−	1.21827e7i		−	0.127643i	0.997961	−	0.0638213i	$-0.0203288\pi$
$458$	2.06855e7			0.215312
$459$	−9.85530e6			−0.101913
$460$			1.99793e7i			0.205262i
$461$	3.02369e7			0.308628			0.154314	−	0.988022i	$-0.450683\pi$
$461$	3.02369e7			0.308628			0.154314	+	0.988022i	$0.450683\pi$
$462$	8.57690e7			0.869770
$463$			2.77245e7i			0.279332i	0.990199	+	0.139666i	$0.0446028\pi$
$463$			2.77245e7i			0.279332i	−0.990199	+	0.139666i	$0.955397\pi$
$464$	1.62576e8			1.62743
$465$			213339.i			0.00212184i
$466$	7.12746e7			0.704331
$467$			8.09525e7i			0.794840i	0.917637	+	0.397420i	$0.130094\pi$
$467$			8.09525e7i			0.794840i	−0.917637	+	0.397420i	$0.869906\pi$
$468$		−	3.32816e7i		−	0.324688i
$469$			7.55161e6i			0.0732017i
$470$	2.40454e7			0.231600
$471$			4.01229e7i			0.383998i
$472$	−3.91677e7	−	4.60208e7i	−0.372479	−	0.437651i
$473$	−2.36806e8			−2.23774
$474$		−	5.70943e7i		−	0.536115i
$475$	1.29711e8			1.21031
$476$	2.81918e7			0.261398
$477$	9.28638e6			0.0855641
$478$			1.68398e8i			1.54189i
$479$	−1.78760e8			−1.62654			−0.813269	−	0.581888i	$-0.802314\pi$
$479$	−1.78760e8			−1.62654			−0.813269	+	0.581888i	$0.802314\pi$
$480$		−	3.49321e7i		−	0.315864i
$481$	6.45849e7			0.580357
$482$		−	3.34238e7i		−	0.298480i
$483$			4.07527e7i			0.361672i
$484$	4.52439e7			0.399047
$485$		−	5.19340e7i		−	0.455225i
$486$		−	9.12746e6i		−	0.0795135i
$487$	1.00111e8			0.866752			0.433376	−	0.901213i	$-0.357322\pi$
$487$	1.00111e8			0.866752			0.433376	+	0.901213i	$0.357322\pi$
$488$	7.87230e7			0.677396
$489$	−1.88661e7			−0.161345
$490$		−	1.25433e7i		−	0.106617i
$491$	1.22140e8			1.03184			0.515920	−	0.856637i	$-0.327450\pi$
$491$	1.22140e8			1.03184			0.515920	+	0.856637i	$0.327450\pi$
$492$	−4.39136e7			−0.368726
$493$	8.27000e7			0.690184
$494$	−4.80278e8			−3.98393
$495$		−	3.00195e7i		−	0.247508i
$496$			995941.i			0.00816185i
$497$	6.74150e7			0.549145
$498$	−3.11256e7			−0.252017
$499$	−6.22366e7			−0.500892			−0.250446	−	0.968131i	$-0.580577\pi$
$499$	−6.22366e7			−0.500892			−0.250446	+	0.968131i	$0.580577\pi$
$500$	−6.34740e7			−0.507792
$501$	−1.05236e8			−0.836856
$502$			1.79666e8i			1.42021i
$503$		−	5.88439e7i		−	0.462378i	−0.972909	−	0.231189i	$-0.925738\pi$
$503$		−	5.88439e7i		−	0.462378i	0.972909	−	0.231189i	$-0.0742616\pi$
$504$		−	2.25713e7i		−	0.176305i
$505$			1.19331e8i			0.926569i
$506$			1.44345e8i			1.11416i
$507$	−1.72929e8			−1.32692
$508$	9.02716e7			0.688589
$509$		−	7.99767e6i		−	0.0606471i	−0.999540	−	0.0303236i	$-0.990346\pi$
$509$		−	7.99767e6i		−	0.0606471i	0.999540	−	0.0303236i	$-0.00965377\pi$
$510$		−	2.82646e7i		−	0.213075i
$511$		−	4.44660e7i		−	0.333246i
$512$		−	6.67583e7i		−	0.497388i
$513$	−4.59826e7			−0.340597
$514$			5.92104e7i			0.436023i
$515$		−	6.92543e6i		−	0.0507020i
$516$		−	7.20886e7i		−	0.524708i
$517$	6.06465e7			0.438868
$518$	−5.06676e7			−0.364536
$519$			7.03134e7i			0.502963i
$520$	−8.25144e7			−0.586840
$521$	1.52735e8			1.08000			0.540002	−	0.841664i	$-0.318424\pi$
$521$	1.52735e8			1.08000			0.540002	+	0.841664i	$0.318424\pi$
$522$			7.65924e7i			0.538486i
$523$	−1.44484e8			−1.00998			−0.504992	−	0.863124i	$-0.668504\pi$
$523$	−1.44484e8			−1.00998			−0.504992	+	0.863124i	$0.668504\pi$
$524$			1.00443e8i			0.698113i
$525$	−5.25817e7			−0.363377
$526$		−	2.19067e8i		−	1.50529i
$527$			506621.i			0.00346140i
$528$		−	1.40142e8i		−	0.952062i
$529$	7.94513e7			0.536703
$530$			2.66329e7i			0.178892i
$531$	3.80058e7	−	3.23462e7i	0.253844	−	0.216043i
$532$	1.31537e8			0.873599
$533$			3.27452e8i			2.16255i
$534$	−1.29476e6			−0.00850289
$535$	3.95918e7			0.258550
$536$	7.03899e6			0.0457105
$537$		−	3.13954e7i		−	0.202742i
$538$	2.92642e8			1.87927
$539$		−	3.16364e7i		−	0.202032i
$540$	9.13855e6			0.0580358
$541$		−	2.14241e8i		−	1.35304i	−0.736423	−	0.676522i	$-0.763487\pi$
$541$		−	2.14241e8i		−	1.35304i	0.736423	−	0.676522i	$-0.236513\pi$
$542$		−	2.42990e8i		−	1.52612i
$543$	8.92395e7			0.557388
$544$		−	8.29539e7i		−	0.515276i
$545$		−	1.54545e7i		−	0.0954698i
$546$	1.94694e8			1.19612
$547$	2.40800e8			1.47128			0.735639	−	0.677373i	$-0.236882\pi$
$547$	2.40800e8			1.47128			0.735639	+	0.677373i	$0.236882\pi$
$548$	−6.73545e7			−0.409284
$549$			6.50126e7i			0.392899i
$550$	−1.86243e8			−1.11941
$551$	3.85859e8			2.30661
$552$	3.79863e7			0.225845
$553$	1.16599e8			0.689478
$554$			7.18627e7i			0.422644i
$555$			1.77339e7i			0.103735i
$556$	1.08760e8			0.632771
$557$	−3.76529e7			−0.217888			−0.108944	−	0.994048i	$-0.534747\pi$
$557$	−3.76529e7			−0.217888			−0.108944	+	0.994048i	$0.534747\pi$
$558$	−469206.			−0.00270060
$559$	−5.37545e8			−3.07737
$560$	1.13474e8			0.646147
$561$		−	7.12880e7i		−	0.403764i
$562$		−	4.34737e7i		−	0.244916i
$563$			1.25482e8i			0.703162i	0.936157	+	0.351581i	$0.114356\pi$
$563$			1.25482e8i			0.703162i	−0.936157	+	0.351581i	$0.885644\pi$
$564$			1.84620e7i			0.102906i
$565$			8.60454e7i			0.477070i
$566$	−6.29245e7			−0.347033
$567$	1.86403e7			0.102259
$568$		−	6.28387e7i		−	0.342911i
$569$			1.90978e8i			1.03668i	0.855173	+	0.518342i	$0.173451\pi$
$569$			1.90978e8i			1.03668i	−0.855173	+	0.518342i	$0.826549\pi$
$570$		−	1.31876e8i		−	0.712101i
$571$			3.02963e8i			1.62735i	0.581321	+	0.813675i	$0.302536\pi$
$571$			3.02963e8i			1.62735i	−0.581321	+	0.813675i	$0.697464\pi$
$572$	2.40741e8			1.28636
$573$			1.09564e8i			0.582378i
$574$		−	2.56890e8i		−	1.35835i
$575$		−	8.84922e7i		−	0.465481i
$576$	−2.71459e6			−0.0142049
$577$	2.82315e8			1.46962			0.734812	−	0.678271i	$-0.237271\pi$
$577$	2.82315e8			1.46962			0.734812	+	0.678271i	$0.237271\pi$
$578$			1.72226e8i			0.891900i
$579$	1.99282e7			0.102667
$580$	−7.66855e7			−0.393033
$581$		−	6.35653e7i		−	0.324110i
$582$	1.14220e8			0.579395
$583$			6.71728e7i			0.338991i
$584$	−4.14475e7			−0.208094
$585$		−	6.81437e7i		−	0.340375i
$586$		−	1.04414e8i		−	0.518880i
$587$		−	3.55786e7i		−	0.175904i	−0.996125	−	0.0879518i	$-0.971968\pi$
$587$		−	3.55786e7i		−	0.175904i	0.996125	−	0.0879518i	$-0.0280321\pi$
$588$	9.63075e6			0.0473727
$589$			2.36378e6i			0.0115681i
$590$	9.27676e7	+	1.08999e8i	0.451690	+	0.530721i
$591$	2.32595e8			1.12678
$592$			8.27879e7i			0.399026i
$593$	−2.37978e8			−1.14123			−0.570614	−	0.821218i	$-0.693295\pi$
$593$	−2.37978e8			−1.14123			−0.570614	+	0.821218i	$0.693295\pi$
$594$	6.60232e7			0.315019
$595$	5.77225e7			0.274027
$596$		−	1.14982e8i		−	0.543116i
$597$	1.84032e8			0.864910
$598$			3.27659e8i			1.53221i
$599$	−3.35138e8			−1.55935			−0.779674	−	0.626185i	$-0.784615\pi$
$599$	−3.35138e8			−1.55935			−0.779674	+	0.626185i	$0.784615\pi$
$600$			4.90123e7i			0.226909i
$601$		−	5.73297e7i		−	0.264093i	−0.991244	−	0.132046i	$-0.957845\pi$
$601$		−	5.73297e7i		−	0.264093i	0.991244	−	0.132046i	$-0.0421548\pi$
$602$	4.21711e8			1.93297
$603$			5.81308e6i			0.0265127i
$604$			1.22090e8i			0.554078i
$605$	9.26364e7			0.418327
$606$	−2.62449e8			−1.17931
$607$	−5.69967e7			−0.254849			−0.127425	−	0.991848i	$-0.540671\pi$
$607$	−5.69967e7			−0.254849			−0.127425	+	0.991848i	$0.540671\pi$
$608$		−	3.87044e8i		−	1.72206i
$609$	−1.56419e8			−0.692527
$610$	−1.86453e8			−0.821449
$611$	1.37666e8			0.603537
$612$	2.17015e7			0.0946750
$613$			1.77064e8i			0.768685i	0.923191	+	0.384342i	$0.125572\pi$
$613$			1.77064e8i			0.768685i	−0.923191	+	0.384342i	$0.874428\pi$
$614$			5.25668e8i			2.27094i
$615$	−8.99127e7			−0.386541
$616$	1.63269e8			0.698492
$617$	−1.07770e8			−0.458820			−0.229410	−	0.973330i	$-0.573680\pi$
$617$	−1.07770e8			−0.458820			−0.229410	+	0.973330i	$0.573680\pi$
$618$	1.52314e7			0.0645318
$619$	2.76526e8			1.16591			0.582953	−	0.812506i	$-0.301897\pi$
$619$	2.76526e8			1.16591			0.582953	+	0.812506i	$0.301897\pi$
$620$		−	469776.i		−	0.00197113i
$621$			3.13706e7i			0.130993i
$622$		−	2.38983e8i		−	0.993106i
$623$		−	2.64419e6i		−	0.0109353i
$624$		−	3.18118e8i		−	1.30929i
$625$	3.69975e7			0.151542
$626$	4.73021e8			1.92823
$627$		−	3.32614e8i		−	1.34939i
$628$		−	8.83511e7i		−	0.356724i
$629$			4.21130e7i			0.169225i
$630$			5.34595e7i			0.213798i
$631$	2.00851e8			0.799442			0.399721	−	0.916637i	$-0.369107\pi$
$631$	2.00851e8			0.799442			0.399721	+	0.916637i	$0.369107\pi$
$632$		−	1.08684e8i		−	0.430541i
$633$			8.69297e7i			0.342734i
$634$		−	1.80407e8i		−	0.707921i
$635$	1.84830e8			0.721858
$636$	−2.04487e7			−0.0794868
$637$		−	7.18139e7i		−	0.277837i
$638$	−5.54029e8			−2.13339
$639$	5.18947e7			0.198893
$640$		−	1.51202e8i		−	0.576792i
$641$	−3.76806e8			−1.43068			−0.715341	−	0.698775i	$-0.753729\pi$
$641$	−3.76806e8			−1.43068			−0.715341	+	0.698775i	$0.753729\pi$
$642$			8.70758e7i			0.329073i
$643$	1.11916e8			0.420979			0.210489	−	0.977596i	$-0.432494\pi$
$643$	1.11916e8			0.420979			0.210489	+	0.977596i	$0.432494\pi$
$644$		−	8.97380e7i		−	0.335984i
$645$		−	1.47601e8i		−	0.550059i
$646$		−	3.13169e8i		−	1.16166i
$647$	9.73243e7			0.359342			0.179671	−	0.983727i	$-0.442497\pi$
$647$	9.73243e7			0.359342			0.179671	+	0.983727i	$0.442497\pi$
$648$		−	1.73749e7i		−	0.0638554i
$649$	2.33976e8	+	2.74914e8i	0.855926	+	1.00569i
$650$	−4.22767e8			−1.53943
$651$		−	958222.i		−	0.00347315i
$652$	4.15434e7			0.149885
$653$	−7.12719e7			−0.255964			−0.127982	−	0.991777i	$-0.540850\pi$
$653$	−7.12719e7			−0.255964			−0.127982	+	0.991777i	$0.540850\pi$
$654$	3.39898e7			0.121511
$655$			2.05656e8i			0.731842i
$656$	−4.19743e8			−1.48687
$657$		−	3.42290e7i		−	0.120698i
$658$	−1.08001e8			−0.379096
$659$			1.41719e8i			0.495190i	0.968864	+	0.247595i	$0.0796402\pi$
$659$			1.41719e8i			0.495190i	−0.968864	+	0.247595i	$0.920360\pi$
$660$			6.61034e7i			0.229928i
$661$	−3.46865e8			−1.20104			−0.600519	−	0.799611i	$-0.705039\pi$
$661$	−3.46865e8			−1.20104			−0.600519	+	0.799611i	$0.705039\pi$
$662$			6.15055e8i			2.12002i
$663$		−	1.61822e8i		−	0.555262i
$664$	−5.92503e7			−0.202389
$665$	2.69320e8			0.915806
$666$	−3.90028e7			−0.132030
$667$		−	2.63244e8i		−	0.887117i
$668$	2.31731e8			0.777417
$669$	1.85773e8			0.620445
$670$	−1.66717e7			−0.0554312
$671$	−4.70267e8			−1.55660
$672$			1.56899e8i			0.517025i
$673$		−	1.27064e8i		−	0.416849i	−0.978038	−	0.208424i	$-0.933166\pi$
$673$		−	1.27064e8i		−	0.416849i	0.978038	−	0.208424i	$-0.0668336\pi$
$674$	−5.80639e8			−1.89639
$675$	−4.04763e7			−0.131610
$676$	3.80793e8			1.23268
$677$	−4.88993e8			−1.57593			−0.787964	−	0.615722i	$-0.788865\pi$
$677$	−4.88993e8			−1.57593			−0.787964	+	0.615722i	$0.788865\pi$
$678$	−1.89243e8			−0.607199
$679$			2.33263e8i			0.745139i
$680$		−	5.38041e7i		−	0.171115i
$681$			3.57475e8i			1.13189i
$682$		−	3.39399e6i		−	0.0106993i
$683$		−	3.15064e8i		−	0.988864i	−0.869216	−	0.494432i	$-0.835376\pi$
$683$		−	3.15064e8i		−	0.988864i	0.869216	−	0.494432i	$-0.164624\pi$
$684$	1.01254e8			0.316406
$685$	−1.37908e8			−0.429058
$686$			4.24605e8i			1.31526i
$687$			3.25188e7i			0.100292i
$688$		−	6.89051e8i		−	2.11585i
$689$			1.52481e8i			0.466184i
$690$	−8.99695e7			−0.273872
$691$			6.17270e8i			1.87086i	0.353513	+	0.935430i	$0.384987\pi$
$691$			6.17270e8i			1.87086i	−0.353513	+	0.935430i	$0.615013\pi$
$692$		−	1.54831e8i		−	0.467240i
$693$			1.34834e8i			0.405135i
$694$	−7.27110e8			−2.17531
$695$	2.22686e8			0.663343
$696$			1.45800e8i			0.432445i
$697$	−2.13517e8			−0.630572
$698$	−1.36505e7			−0.0401404
$699$			1.12048e8i			0.328074i
$700$	1.15786e8			0.337568
$701$			4.33185e8i			1.25753i	0.777594	+	0.628766i	$0.216440\pi$
$701$			4.33185e8i			1.25753i	−0.777594	+	0.628766i	$0.783560\pi$
$702$	1.49871e8			0.433219
$703$			1.96490e8i			0.565554i
$704$		−	1.96359e7i		−	0.0562773i
$705$			3.78007e7i			0.107878i
$706$	−3.02743e8			−0.860321
$707$		−	5.35978e8i		−	1.51666i
$708$	−8.36892e7	+	7.12268e7i	−0.235814	+	0.200698i
$709$	−5.33293e7			−0.149633			−0.0748165	−	0.997197i	$-0.523837\pi$
$709$	−5.33293e7			−0.149633			−0.0748165	+	0.997197i	$0.523837\pi$
$710$			1.48832e8i			0.415834i
$711$	8.97557e7			0.249720
$712$	−2.46470e6			−0.00682847
$713$	1.61264e6			0.00444905
$714$			1.26951e8i			0.348773i
$715$	4.92916e8			1.34851
$716$			6.91331e7i			0.188342i
$717$	−2.64731e8			−0.718204
$718$		−	4.01900e8i		−	1.08579i
$719$			1.43489e8i			0.386039i	0.981195	+	0.193020i	$0.0618281\pi$
$719$			1.43489e8i			0.386039i	−0.981195	+	0.193020i	$0.938172\pi$
$720$	8.73498e7			0.234026
$721$			3.11058e7i			0.0829920i
$722$		−	9.94670e8i		−	2.64282i
$723$	5.25442e7			0.139030
$724$	−1.96506e8			−0.517799
$725$	3.39654e8			0.891298
$726$			2.03739e8i			0.532432i
$727$	−3.66892e8			−0.954850			−0.477425	−	0.878672i	$-0.658430\pi$
$727$	−3.66892e8			−0.954850			−0.477425	+	0.878672i	$0.658430\pi$
$728$	3.70617e8			0.960574
$729$	1.43489e7			0.0370370
$730$	9.81674e7			0.252347
$731$		−	3.50510e8i		−	0.897322i
$732$		−	1.43159e8i		−	0.364993i
$733$	3.01738e8			0.766158			0.383079	−	0.923715i	$-0.374864\pi$
$733$	3.01738e8			0.766158			0.383079	+	0.923715i	$0.374864\pi$
$734$	−2.57940e8			−0.652276
$735$	1.97189e7			0.0496615
$736$	−2.64052e8			−0.662302
$737$	−4.20487e7			−0.105039
$738$		−	1.97749e8i		−	0.491976i
$739$			4.84655e8i			1.20088i	0.799670	+	0.600440i	$0.205008\pi$
$739$			4.84655e8i			1.20088i	−0.799670	+	0.600440i	$0.794992\pi$
$740$		−	3.90502e7i		−	0.0963670i
$741$		−	7.55026e8i		−	1.85570i
$742$		−	1.19623e8i		−	0.292821i
$743$	7.54774e8			1.84014			0.920069	−	0.391755i	$-0.128132\pi$
$743$	7.54774e8			1.84014			0.920069	+	0.391755i	$0.128132\pi$
$744$	−893175.			−0.00216879
$745$		−	2.35425e8i		−	0.569356i
$746$			7.60945e8i			1.83289i
$747$		−	4.89313e7i		−	0.117388i
$748$			1.56977e8i			0.375087i
$749$	−1.77828e8			−0.423209
$750$		−	2.85831e8i		−	0.677526i
$751$		−	2.39183e8i		−	0.564691i	−0.959313	−	0.282345i	$-0.908888\pi$
$751$		−	2.39183e8i		−	0.564691i	0.959313	−	0.282345i	$-0.0911124\pi$
$752$			1.76467e8i			0.414963i
$753$	−2.82445e8			−0.661529
$754$	−1.25763e9			−2.93387
$755$			2.49979e8i			0.580848i
$756$	−4.10461e7			−0.0949964
$757$	1.77949e8			0.410211			0.205106	−	0.978740i	$-0.434246\pi$
$757$	1.77949e8			0.410211			0.205106	+	0.978740i	$0.434246\pi$
$758$		−	1.05045e9i		−	2.41194i
$759$	−2.26918e8			−0.518972
$760$		−	2.51038e8i		−	0.571871i
$761$	7.08378e7			0.160735			0.0803676	−	0.996765i	$-0.474391\pi$
$761$	7.08378e7			0.160735			0.0803676	+	0.996765i	$0.474391\pi$
$762$			4.06504e8i			0.918756i
$763$			6.94146e7i			0.156271i
$764$		−	2.41262e8i		−	0.541014i
$765$	4.44336e7			0.0992492
$766$			7.70326e8i			1.71391i
$767$	5.31120e8	+	6.24048e8i	1.17708	+	1.38303i
$768$	3.21401e8			0.709518
$769$		−	7.07471e8i		−	1.55571i	−0.628441	−	0.777857i	$-0.716307\pi$
$769$		−	7.07471e8i		−	1.55571i	0.628441	−	0.777857i	$-0.283693\pi$
$770$	−3.86698e8			−0.847032
$771$	−9.30823e7			−0.203097
$772$	−4.38822e7			−0.0953754
$773$		−	7.54245e8i		−	1.63295i	−0.577378	−	0.816477i	$-0.695924\pi$
$773$		−	7.54245e8i		−	1.63295i	0.577378	−	0.816477i	$-0.304076\pi$
$774$	3.24624e8			0.700097
$775$			2.08073e6i			0.00447002i
$776$	2.17429e8			0.465299
$777$		−	7.96524e7i		−	0.169799i
$778$			1.58680e8i			0.336963i
$779$	−9.96224e8			−2.10739
$780$			1.50053e8i			0.316200i
$781$			3.75379e8i			0.787982i
$782$	−2.13652e8			−0.446774
$783$	−1.20408e8			−0.250824
$784$	9.20545e7			0.191028
$785$		−	1.80898e8i		−	0.373960i
$786$	−4.52307e8			−0.931464
$787$	9.33623e8			1.91535			0.957673	−	0.287858i	$-0.0929432\pi$
$787$	9.33623e8			1.91535			0.957673	+	0.287858i	$0.0929432\pi$
$788$	−5.12178e8			−1.04675
$789$	3.44387e8			0.701157
$790$			2.57415e8i			0.522100i
$791$		−	3.86476e8i		−	0.780896i
$792$	1.25681e8			0.252985
$793$	−1.06750e9			−2.14065
$794$	9.45656e8			1.88917
$795$	−4.18686e7			−0.0833272
$796$	−4.05241e8			−0.803479
$797$			1.17506e8i			0.232105i	0.993243	+	0.116053i	$0.0370241\pi$
$797$			1.17506e8i			0.232105i	−0.993243	+	0.116053i	$0.962976\pi$
$798$			5.92326e8i			1.16561i
$799$			8.97662e7i			0.175984i
$800$		−	3.40697e8i		−	0.665424i
$801$		−	2.03545e6i		−	0.00396061i
$802$	−7.28188e8			−1.41163
$803$	2.47595e8			0.478183
$804$		−	1.28005e7i		−	0.0246296i
$805$		−	1.83738e8i		−	0.352217i
$806$		−	7.70428e6i		−	0.0147139i
$807$			4.60051e8i			0.875358i
$808$	−4.99594e8			−0.947073
$809$		−	1.88296e8i		−	0.355628i	−0.984064	−	0.177814i	$-0.943097\pi$
$809$		−	1.88296e8i		−	0.355628i	0.984064	−	0.177814i	$-0.0569026\pi$
$810$			4.11520e7i			0.0774348i
$811$		−	2.20121e8i		−	0.412665i	−0.978482	−	0.206333i	$-0.933847\pi$
$811$		−	2.20121e8i		−	0.412665i	0.978482	−	0.206333i	$-0.0661529\pi$
$812$	3.44436e8			0.643339
$813$	3.81994e8			0.710861
$814$		−	2.82126e8i		−	0.523082i
$815$	8.50596e7			0.157127
$816$	2.07431e8			0.381772
$817$		−	1.63540e9i		−	2.99887i
$818$	6.26934e8			1.14541
$819$			3.06070e8i			0.557146i
$820$	1.97989e8			0.359087
$821$		−	7.39414e8i		−	1.33616i	−0.744090	−	0.668079i	$-0.767117\pi$
$821$		−	7.39414e8i		−	1.33616i	0.744090	−	0.668079i	$-0.232883\pi$
$822$		−	3.03306e8i		−	0.546091i
$823$		−	6.64646e8i		−	1.19231i	−0.802868	−	0.596157i	$-0.796694\pi$
$823$		−	6.64646e8i		−	1.19231i	0.802868	−	0.596157i	$-0.203306\pi$
$824$	2.89943e7			0.0518240
$825$		−	2.92784e8i		−	0.521418i
$826$	−4.16669e8	−	4.89573e8i	−0.739352	−	0.868715i
$827$	2.88615e6			0.00510273			0.00255136	−	0.999997i	$-0.499188\pi$
$827$	2.88615e6			0.00510273			0.00255136	+	0.999997i	$0.499188\pi$
$828$		−	6.90785e7i		−	0.121689i
$829$	−2.72554e8			−0.478398			−0.239199	−	0.970971i	$-0.576885\pi$
$829$	−2.72554e8			−0.478398			−0.239199	+	0.970971i	$0.576885\pi$
$830$	1.40333e8			0.245429
$831$	−1.12972e8			−0.196866
$832$		−	4.45731e7i		−	0.0773932i
$833$	4.68268e7			0.0810139
$834$			4.89762e8i			0.844281i
$835$	4.74466e8			0.814978
$836$			7.32420e8i			1.25355i
$837$		−	737619.i		−	0.00125793i
$838$	1.14944e8			0.195323
$839$		−	6.88782e8i		−	1.16626i	−0.812378	−	0.583131i	$-0.801827\pi$
$839$		−	6.88782e8i		−	1.16626i	0.812378	−	0.583131i	$-0.198173\pi$
$840$			1.01765e8i			0.171696i
$841$	4.15570e8			0.698645
$842$	1.14591e9			1.91961
$843$	6.83432e7			0.114081
$844$		−	1.91420e8i		−	0.318391i
$845$	7.79670e8			1.29223
$846$	−8.31367e7			−0.137304
$847$	−4.16080e8			−0.684742
$848$	−1.95457e8			−0.320526
$849$		−	9.89211e7i		−	0.161646i
$850$		−	2.75668e8i		−	0.448879i
$851$	1.34051e8			0.217511
$852$	−1.14273e8			−0.184767
$853$	−1.04472e7			−0.0168327			−0.00841636	−	0.999965i	$-0.502679\pi$
$853$	−1.04472e7			−0.0168327			−0.00841636	+	0.999965i	$0.502679\pi$
$854$	8.37463e8			1.34460
$855$	2.07317e8			0.331693
$856$			1.65757e8i			0.264271i
$857$			8.15501e8i			1.29563i	0.761797	+	0.647816i	$0.224318\pi$
$857$			8.15501e8i			1.29563i	−0.761797	+	0.647816i	$0.775682\pi$
$858$			1.08409e9i			1.71634i
$859$			1.32357e7i			0.0208818i	0.999945	+	0.0104409i	$0.00332350\pi$
$859$			1.32357e7i			0.0208818i	−0.999945	+	0.0104409i	$0.996676\pi$
$860$			3.25019e8i			0.510990i
$861$	4.03846e8			0.632713
$862$	−3.77039e8			−0.588661
$863$			3.34465e8i			0.520377i	0.965558	+	0.260188i	$0.0837846\pi$
$863$			3.34465e8i			0.520377i	−0.965558	+	0.260188i	$0.916215\pi$
$864$			1.20777e8i			0.187260i
$865$		−	3.17015e8i		−	0.489814i
$866$			4.78802e8i			0.737228i
$867$	−2.70750e8			−0.415443
$868$			2.11002e6i			0.00322646i
$869$			6.49245e8i			0.989349i
$870$		−	3.45324e8i		−	0.524408i
$871$	−9.54497e7			−0.144451
$872$	6.47025e7			0.0975825
$873$			1.79561e8i			0.269880i
$874$	−9.96854e8			−1.49313
$875$	5.83731e8			0.871342
$876$			7.53727e7i			0.112125i
$877$	6.21918e8			0.922008			0.461004	−	0.887398i	$-0.347489\pi$
$877$	6.21918e8			0.922008			0.461004	+	0.887398i	$0.347489\pi$
$878$			4.99845e7i			0.0738502i
$879$	1.64145e8			0.241692
$880$			6.31842e8i			0.927173i
$881$		−	1.57387e8i		−	0.230166i	−0.993356	−	0.115083i	$-0.963287\pi$
$881$		−	1.57387e8i		−	0.230166i	0.993356	−	0.115083i	$-0.0367135\pi$
$882$			4.33685e7i			0.0632075i
$883$	5.18082e8			0.752517			0.376258	−	0.926515i	$-0.377210\pi$
$883$	5.18082e8			0.752517			0.376258	+	0.926515i	$0.377210\pi$
$884$			3.56335e8i			0.515824i
$885$	−1.71353e8	+	1.45836e8i	−0.247207	+	0.210395i
$886$	1.23515e9			1.77589
$887$			3.32997e6i			0.00477166i	0.999997	+	0.00238583i	$0.000759434\pi$
$887$			3.32997e6i			0.00477166i	−0.999997	+	0.00238583i	$0.999241\pi$
$888$	−7.42454e7			−0.106030
$889$	−8.30172e8			−1.18158
$890$	5.83757e6			0.00828061
$891$			1.03792e8i			0.146735i
$892$	−4.09074e8			−0.576378
$893$			4.18829e8i			0.588142i
$894$	5.17780e8			0.724657
$895$			1.41549e8i			0.197442i
$896$			6.79132e8i			0.944126i
$897$	−5.15100e8			−0.713697
$898$		−	2.89227e8i		−	0.399402i
$899$			6.18968e6i			0.00851901i
$900$	8.91294e7			0.122263
$901$	−9.94261e7			−0.135933
$902$	1.43041e9			1.94913
$903$			6.62954e8i			0.900368i
$904$	−3.60241e8			−0.487627
$905$	−4.02345e8			−0.542816
$906$	−5.49789e8			−0.739284
$907$	1.18399e9			1.58682			0.793409	−	0.608689i	$-0.208304\pi$
$907$	1.18399e9			1.58682			0.793409	+	0.608689i	$0.208304\pi$
$908$		−	7.87164e8i		−	1.05150i
$909$		−	4.12585e8i		−	0.549315i
$910$	−8.77796e8			−1.16485
$911$	−1.32176e9			−1.74823			−0.874113	−	0.485723i	$-0.838556\pi$
$911$	−1.32176e9			−1.74823			−0.874113	+	0.485723i	$0.838556\pi$
$912$	9.67827e8			1.27589
$913$	3.53943e8			0.465073
$914$	−1.20803e8			−0.158212
$915$		−	2.93116e8i		−	0.382627i
$916$		−	7.16068e7i		−	0.0931682i
$917$		−	9.23711e8i		−	1.19792i
$918$			9.77246e7i			0.126321i
$919$			1.24056e9i			1.59835i	0.601099	+	0.799174i	$0.294730\pi$
$919$			1.24056e9i			1.59835i	−0.601099	+	0.799174i	$0.705270\pi$
$920$	−1.71265e8			−0.219940
$921$	−8.26381e8			−1.05780
$922$		−	2.99828e8i		−	0.382542i
$923$			8.52102e8i			1.08364i
$924$		−	2.96906e8i		−	0.376360i
$925$			1.72961e8i			0.218536i
$926$	2.74914e8			0.346230
$927$			2.39446e7i			0.0300586i
$928$		−	1.01349e9i		−	1.26817i
$929$			4.94718e8i			0.617036i	0.951219	+	0.308518i	$0.0998329\pi$
$929$			4.94718e8i			0.617036i	−0.951219	+	0.308518i	$0.900167\pi$
$930$	2.11546e6			0.00263000
$931$	2.18483e8			0.270750
$932$		−	2.46731e8i		−	0.304772i
$933$	3.75695e8			0.462584
$934$	8.02720e8			0.985198
$935$			3.21409e8i			0.393209i
$936$	2.85293e8			0.347908
$937$			5.43292e8i			0.660411i	0.943909	+	0.330206i	$0.107118\pi$
$937$			5.43292e8i			0.660411i	−0.943909	+	0.330206i	$0.892882\pi$
$938$	7.48814e7			0.0907330
$939$			7.43618e8i			0.898159i
$940$		−	8.32377e7i		−	0.100216i
$941$		−	8.59260e8i		−	1.03123i	−0.856820	−	0.515615i	$-0.827564\pi$
$941$		−	8.59260e8i		−	1.03123i	0.856820	−	0.515615i	$-0.172436\pi$
$942$	3.97856e8			0.475963
$943$			6.79652e8i			0.810497i
$944$	−7.99934e8	+	6.80814e8i	−0.950907	+	0.809305i
$945$	−8.40416e7			−0.0995861
$946$			2.34816e9i			2.77367i
$947$	6.98045e8			0.821927			0.410964	−	0.911652i	$-0.365192\pi$
$947$	6.98045e8			0.821927			0.410964	+	0.911652i	$0.365192\pi$
$948$	−1.97643e8			−0.231983
$949$	5.62034e8			0.657604
$950$		−	1.28620e9i		−	1.50017i
$951$	2.83610e8			0.329746
$952$			2.41663e8i			0.280091i
$953$	6.69808e8			0.773877			0.386938	−	0.922106i	$-0.373533\pi$
$953$	6.69808e8			0.773877			0.386938	+	0.922106i	$0.373533\pi$
$954$		−	9.20833e7i		−	0.106056i
$955$		−	4.93981e8i		−	0.567153i
$956$	5.82942e8			0.667193
$957$		−	8.70966e8i		−	0.993724i
$958$			1.77258e9i			2.01608i
$959$	6.19417e8			0.702308
$960$	1.22390e7			0.0138335
$961$	8.87466e8			0.999957
$962$		−	6.40420e8i		−	0.719349i
$963$	−1.36888e8			−0.153281
$964$	−1.15703e8			−0.129156
$965$	−8.98483e7			−0.0999834
$966$	4.04102e8			0.448290
$967$			1.53958e9i			1.70264i	0.524648	+	0.851319i	$0.324197\pi$
$967$			1.53958e9i			1.70264i	−0.524648	+	0.851319i	$0.675803\pi$
$968$			3.87835e8i			0.427584i
$969$	4.92320e8			0.541098
$970$	−5.14974e8			−0.564249
$971$	−1.73667e9			−1.89696			−0.948481	−	0.316833i	$-0.897381\pi$
$971$	−1.73667e9			−1.89696			−0.948481	+	0.316833i	$0.897381\pi$
$972$	−3.15965e7			−0.0344065
$973$	−1.00020e9			−1.08580
$974$		−	9.92695e8i		−	1.07433i
$975$		−	6.64614e8i		−	0.717061i
$976$		−	1.36837e9i		−	1.47181i
$977$			3.38520e8i			0.362995i	0.983391	+	0.181498i	$0.0580945\pi$
$977$			3.38520e8i			0.362995i	−0.983391	+	0.181498i	$0.941906\pi$
$978$			1.87075e8i			0.199986i
$979$	1.47233e7			0.0156913
$980$	−4.34212e7			−0.0461343
$981$			5.34339e7i			0.0565992i
$982$		−	1.21113e9i		−	1.27896i
$983$			1.67105e9i			1.75925i	0.475667	+	0.879626i	$0.342207\pi$
$983$			1.67105e9i			1.75925i	−0.475667	+	0.879626i	$0.657793\pi$
$984$		−	3.76432e8i		−	0.395095i
$985$	−1.04868e9			−1.09732
$986$		−	8.20049e8i		−	0.855478i
$987$		−	1.69784e8i		−	0.176581i
$988$			1.66258e9i			1.72390i
$989$	−1.11572e9			−1.15336
$990$	−2.97672e8			−0.306784
$991$		−	1.46763e9i		−	1.50798i	−0.656886	−	0.753990i	$-0.728127\pi$
$991$		−	1.46763e9i		−	1.50798i	0.656886	−	0.753990i	$-0.271873\pi$
$992$	6.20868e6			0.00636010
$993$	−9.66902e8			−0.987495
$994$		−	6.68483e8i		−	0.680662i
$995$	−8.29728e8			−0.842299
$996$			1.07747e8i			0.109051i
$997$	−5.01587e8			−0.506129			−0.253064	−	0.967449i	$-0.581438\pi$
$997$	−5.01587e8			−0.506129			−0.253064	+	0.967449i	$0.581438\pi$
$998$			6.17135e8i			0.620852i
$999$		−	6.13148e7i		−	0.0614991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.14	✓	60
59.58	odd	2	inner	177.7.c.a.58.47	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.14	✓	60	1.1	even	1	trivial
177.7.c.a.58.47	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)

\(f(q)\)	\(=\)	\(q-9.91595i q^{2} +15.5885 q^{3} -34.3260 q^{4} -70.2821 q^{5} -154.574i q^{6} +315.675 q^{7} -294.246i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-9.91595i q^{2} +15.5885 q^{3} -34.3260 q^{4} -70.2821 q^{5} -154.574i q^{6} +315.675 q^{7} -294.246i q^{8} +243.000 q^{9} +696.914i q^{10} +1757.73i q^{11} -535.089 q^{12} +3990.02i q^{13} -3130.21i q^{14} -1095.59 q^{15} -5114.59 q^{16} -2601.72 q^{17} -2409.57i q^{18} -12139.0 q^{19} +2412.50 q^{20} +4920.88 q^{21} +17429.6 q^{22} +8281.58i q^{23} -4586.84i q^{24} -10685.4 q^{25} +39564.8 q^{26} +3788.00 q^{27} -10835.8 q^{28} -31786.7 q^{29} +10863.8i q^{30} -194.726i q^{31} +31884.3i q^{32} +27400.4i q^{33} +25798.5i q^{34} -22186.3 q^{35} -8341.21 q^{36} -16186.6i q^{37} +120370. i q^{38} +62198.2i q^{39} +20680.2i q^{40} +82067.8 q^{41} -48795.2i q^{42} +134723. i q^{43} -60335.9i q^{44} -17078.6 q^{45} +82119.7 q^{46} -34502.7i q^{47} -79728.6 q^{48} -17998.4 q^{49} +105956. i q^{50} -40556.8 q^{51} -136961. i q^{52} +38215.6 q^{53} -37561.6i q^{54} -123537. i q^{55} -92886.0i q^{56} -189229. q^{57} +315195. i q^{58} +(156402. - 133112. i) q^{59} +37607.2 q^{60} +267542. i q^{61} -1930.89 q^{62} +76709.0 q^{63} -11171.2 q^{64} -280427. i q^{65} +271700. q^{66} +23922.1i q^{67} +89306.6 q^{68} +129097. i q^{69} +219998. i q^{70} +213558. q^{71} -71501.8i q^{72} -140860. i q^{73} -160506. q^{74} -166569. q^{75} +416684. q^{76} +554872. i q^{77} +616754. q^{78} +369365. q^{79} +359464. q^{80} +59049.0 q^{81} -813780. i q^{82} -201363. i q^{83} -168914. q^{84} +182854. q^{85} +1.33590e6 q^{86} -495505. q^{87} +517206. q^{88} -8376.32i q^{89} +169350. i q^{90} +1.25955e6i q^{91} -284273. i q^{92} -3035.47i q^{93} -342126. q^{94} +853156. q^{95} +497026. i q^{96} +738936. i q^{97} +178471. i q^{98} +427129. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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