LMFDB - Embedded newform 180.7.f.e.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(19,180)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("180.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.f (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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} - 10x^{8} - 1775x^{6} - 1000x^{4} + 160000x^{2} + 1000000 $ x^12 + 16x^10 - 10x^8 - 1775x^6 - 1000x^4 + 160000*x^2 + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.7
Root			$3.06674 - 0.771446i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.7.f.e.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.68788 - 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 + 30.8579i) q^{5} +88.8045 q^{7} +(-507.445 + 68.1408i) q^{8} +O(q^{10})$	\(q+(3.68788 - 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 + 30.8579i) q^{5} +88.8045 q^{7} +(-507.445 + 68.1408i) q^{8} +(-227.649 + 973.743i) q^{10} +1790.06i q^{11} -3328.41i q^{13} +(327.500 - 630.447i) q^{14} +(-1387.65 + 3853.78i) q^{16} +3001.09i q^{17} +6872.67i q^{19} +(6073.32 + 5207.19i) q^{20} +(12708.1 + 6601.53i) q^{22} +5908.85 q^{23} +(13720.6 - 7475.70i) q^{25} +(-23629.3 - 12274.8i) q^{26} +(-3267.93 - 4650.02i) q^{28} +14040.2 q^{29} -51272.4i q^{31} +(22241.6 + 24063.5i) q^{32} +(21305.5 + 11067.6i) q^{34} +(-10757.0 + 2740.32i) q^{35} +18940.9i q^{37} +(48790.9 + 25345.6i) q^{38} +(59364.8 - 23912.7i) q^{40} +11762.3 q^{41} +100904. q^{43} +(93732.0 - 65872.8i) q^{44} +(21791.1 - 41948.5i) q^{46} +129204. q^{47} -109763. q^{49} +(-2472.19 - 124976. i) q^{50} +(-174284. + 122483. i) q^{52} -47508.5i q^{53} +(-55237.5 - 216833. i) q^{55} +(-45063.4 + 6051.21i) q^{56} +(51778.5 - 99675.1i) q^{58} +139889. i q^{59} +299920. q^{61} +(-363996. - 189086. i) q^{62} +(252858. - 69155.5i) q^{64} +(102708. + 403175. i) q^{65} +40858.7 q^{67} +(157144. - 110437. i) q^{68} +(-20216.3 + 86472.8i) q^{70} -222756. i q^{71} +633436. i q^{73} +(134467. + 69851.8i) q^{74} +(359870. - 252909. i) q^{76} +158966. i q^{77} -166771. i q^{79} +(49167.8 - 509634. i) q^{80} +(43378.0 - 83503.9i) q^{82} -328119. q^{83} +(-92607.1 - 363526. i) q^{85} +(372122. - 716345. i) q^{86} +(-121976. - 908359. i) q^{88} -27762.8 q^{89} -295578. i q^{91} +(-217441. - 309402. i) q^{92} +(476488. - 917254. i) q^{94} +(-212076. - 832496. i) q^{95} +220750. i q^{97} +(-404791. + 779235. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 64 q^{4} - 460 q^{5}+O(q^{10}) $ 12 * q + 64 * q^4 - 460 * q^5	$ 12 q + 64 q^{4} - 460 q^{5} + 2000 q^{10} - 512 q^{14} - 20928 q^{16} + 13760 q^{20} - 55700 q^{25} - 14496 q^{26} + 16072 q^{29} + 257216 q^{34} - 36800 q^{40} + 192136 q^{41} + 165120 q^{44} - 49472 q^{46} + 145796 q^{49} + 36000 q^{50} - 1078208 q^{56} + 215384 q^{61} - 6656 q^{64} - 710400 q^{65} + 530080 q^{70} + 1020384 q^{74} + 2515200 q^{76} + 127040 q^{80} - 44800 q^{85} + 5268832 q^{86} + 4346152 q^{89} + 4292992 q^{94}+O(q^{100}) $ 12 * q + 64 * q^4 - 460 * q^5 + 2000 * q^10 - 512 * q^14 - 20928 * q^16 + 13760 * q^20 - 55700 * q^25 - 14496 * q^26 + 16072 * q^29 + 257216 * q^34 - 36800 * q^40 + 192136 * q^41 + 165120 * q^44 - 49472 * q^46 + 145796 * q^49 + 36000 * q^50 - 1078208 * q^56 + 215384 * q^61 - 6656 * q^64 - 710400 * q^65 + 530080 * q^70 + 1020384 * q^74 + 2515200 * q^76 + 127040 * q^80 - 44800 * q^85 + 5268832 * q^86 + 4346152 * q^89 + 4292992 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	3.68788	−	7.09927i	0.460984	−	0.887408i
$2$	3.68788	−	7.09927i	0.460984	−	0.887408i
$3$		0			0
$3$		0			0
$4$	−36.7991	−	52.3624i	−0.574987	−	0.818163i
$5$	−121.131	+	30.8579i	−0.969050	+	0.246863i
$5$	−121.131	+	30.8579i	−0.969050	+	0.246863i
$6$		0			0
$7$	88.8045			0.258905			0.129453	−	0.991586i	$-0.458678\pi$
$7$	88.8045			0.258905			0.129453	+	0.991586i	$0.458678\pi$
$8$	−507.445	+	68.1408i	−0.991104	+	0.133088i
$9$		0			0
$10$	−227.649	+	973.743i	−0.227649	+	0.973743i
$11$			1790.06i			1.34490i	0.740142	+	0.672450i	$0.234758\pi$
$11$			1790.06i			1.34490i	−0.740142	+	0.672450i	$0.765242\pi$
$12$		0			0
$13$		−	3328.41i		−	1.51498i	−0.652847	−	0.757490i	$-0.726426\pi$
$13$		−	3328.41i		−	1.51498i	0.652847	−	0.757490i	$-0.273574\pi$
$14$	327.500	−	630.447i	0.119351	−	0.229755i
$15$		0			0
$16$	−1387.65	+	3853.78i	−0.338781	+	0.940865i
$17$			3001.09i			0.610846i	0.952217	+	0.305423i	$0.0987979\pi$
$17$			3001.09i			0.610846i	−0.952217	+	0.305423i	$0.901202\pi$
$18$		0			0
$19$			6872.67i			1.00199i	0.865449	+	0.500997i	$0.167033\pi$
$19$			6872.67i			1.00199i	−0.865449	+	0.500997i	$0.832967\pi$
$20$	6073.32	+	5207.19i	0.759165	+	0.650898i
$21$		0			0
$22$	12708.1	+	6601.53i	1.19348	+	0.619978i
$23$	5908.85			0.485646			0.242823	−	0.970071i	$-0.421927\pi$
$23$	5908.85			0.485646			0.242823	+	0.970071i	$0.421927\pi$
$24$		0			0
$25$	13720.6	−	7475.70i	0.878118	−	0.478445i
$26$	−23629.3	−	12274.8i	−1.34441	−	0.698382i
$27$		0			0
$28$	−3267.93	−	4650.02i	−0.148867	−	0.211827i
$29$	14040.2			0.575677			0.287839	−	0.957679i	$-0.407063\pi$
$29$	14040.2			0.575677			0.287839	+	0.957679i	$0.407063\pi$
$30$		0			0
$31$		−	51272.4i		−	1.72107i	−0.509392	−	0.860534i	$-0.670130\pi$
$31$		−	51272.4i		−	1.72107i	0.509392	−	0.860534i	$-0.329870\pi$
$32$	22241.6	+	24063.5i	0.678759	+	0.734361i
$33$		0			0
$34$	21305.5	+	11067.6i	0.542070	+	0.281591i
$35$	−10757.0	+	2740.32i	−0.250892	+	0.0639141i
$36$		0			0
$37$			18940.9i			0.373935i	0.982366	+	0.186967i	$0.0598659\pi$
$37$			18940.9i			0.373935i	−0.982366	+	0.186967i	$0.940134\pi$
$38$	48790.9	+	25345.6i	0.889177	+	0.461903i
$39$		0			0
$40$	59364.8	−	23912.7i	0.927576	−	0.373635i
$41$	11762.3			0.170664			0.0853320	−	0.996353i	$-0.472805\pi$
$41$	11762.3			0.170664			0.0853320	+	0.996353i	$0.472805\pi$
$42$		0			0
$43$	100904.			1.26912			0.634561	−	0.772873i	$-0.281181\pi$
$43$	100904.			1.26912			0.634561	+	0.772873i	$0.281181\pi$
$44$	93732.0	−	65872.8i	1.10035	−	0.773300i
$45$		0			0
$46$	21791.1	−	41948.5i	0.223875	−	0.430966i
$47$	129204.			1.24446			0.622232	−	0.782833i	$-0.286226\pi$
$47$	129204.			1.24446			0.622232	+	0.782833i	$0.286226\pi$
$48$		0			0
$49$	−109763.			−0.932968
$50$	−2472.19	−	124976.i	−0.0197775	−	0.999804i
$51$		0			0
$52$	−174284.	+	122483.i	−1.23950	+	0.871093i
$53$		−	47508.5i		−	0.319112i	−0.987189	−	0.159556i	$-0.948994\pi$
$53$		−	47508.5i		−	0.319112i	0.987189	−	0.159556i	$-0.0510063\pi$
$54$		0			0
$55$	−55237.5	−	216833.i	−0.332006	−	1.30328i
$56$	−45063.4	+	6051.21i	−0.256602	+	0.0344571i
$57$		0			0
$58$	51778.5	−	99675.1i	0.265378	−	0.510861i
$59$			139889.i			0.681127i	0.940221	+	0.340564i	$0.110618\pi$
$59$			139889.i			0.681127i	−0.940221	+	0.340564i	$0.889382\pi$
$60$		0			0
$61$	299920.			1.32134			0.660672	−	0.750675i	$-0.270271\pi$
$61$	299920.			1.32134			0.660672	+	0.750675i	$0.270271\pi$
$62$	−363996.	−	189086.i	−1.52729	−	0.793386i
$63$		0			0
$64$	252858.	−	69155.5i	0.964575	−	0.263807i
$65$	102708.	+	403175.i	0.373992	+	1.46809i
$66$		0			0
$67$	40858.7			0.135850			0.0679251	−	0.997690i	$-0.478362\pi$
$67$	40858.7			0.135850			0.0679251	+	0.997690i	$0.478362\pi$
$68$	157144.	−	110437.i	0.499772	−	0.351229i
$69$		0			0
$70$	−20216.3	+	86472.8i	−0.0589395	+	0.252107i
$71$		−	222756.i		−	0.622378i	−0.950348	−	0.311189i	$-0.899273\pi$
$71$		−	222756.i		−	0.622378i	0.950348	−	0.311189i	$-0.100727\pi$
$72$		0			0
$73$			633436.i			1.62830i	0.580656	+	0.814149i	$0.302796\pi$
$73$			633436.i			1.62830i	−0.580656	+	0.814149i	$0.697204\pi$
$74$	134467.	+	69851.8i	0.331833	+	0.172378i
$75$		0			0
$76$	359870.	−	252909.i	0.819794	−	0.576133i
$77$			158966.i			0.348202i
$78$		0			0
$79$		−	166771.i		−	0.338251i	−0.985594	−	0.169126i	$-0.945906\pi$
$79$		−	166771.i		−	0.338251i	0.985594	−	0.169126i	$-0.0540944\pi$
$80$	49167.8	−	509634.i	0.0960309	−	0.995378i
$81$		0			0
$82$	43378.0	−	83503.9i	0.0786734	−	0.151449i
$83$	−328119.			−0.573848			−0.286924	−	0.957953i	$-0.592633\pi$
$83$	−328119.			−0.573848			−0.286924	+	0.957953i	$0.592633\pi$
$84$		0			0
$85$	−92607.1	−	363526.i	−0.150795	−	0.591941i
$86$	372122.	−	716345.i	0.585046	−	1.12623i
$87$		0			0
$88$	−121976.	−	908359.i	−0.178990	−	1.33294i
$89$	−27762.8			−0.0393816			−0.0196908	−	0.999806i	$-0.506268\pi$
$89$	−27762.8			−0.0393816			−0.0196908	+	0.999806i	$0.506268\pi$
$90$		0			0
$91$		−	295578.i		−	0.392236i
$92$	−217441.	−	309402.i	−0.279240	−	0.397337i
$93$		0			0
$94$	476488.	−	917254.i	0.573679	−	1.10435i
$95$	−212076.	−	832496.i	−0.247355	−	0.970982i
$96$		0			0
$97$			220750.i			0.241872i	0.992660	+	0.120936i	$0.0385895\pi$
$97$			220750.i			0.241872i	−0.992660	+	0.120936i	$0.961410\pi$
$98$	−404791.	+	779235.i	−0.430084	+	0.827924i
$99$		0			0
$100$	−896352.	−	443344.i	−0.896352	−	0.443344i
$101$	−186720.			−0.181229			−0.0906144	−	0.995886i	$-0.528883\pi$
$101$	−186720.			−0.181229			−0.0906144	+	0.995886i	$0.528883\pi$
$102$		0			0
$103$	1.15683e6			1.05866			0.529332	−	0.848415i	$-0.322443\pi$
$103$	1.15683e6			1.05866			0.529332	+	0.848415i	$0.322443\pi$
$104$	226801.	+	1.68899e6i	0.201625	+	1.50150i
$105$		0			0
$106$	−337275.	−	175205.i	−0.283183	−	0.147106i
$107$	1.55229e6			1.26713			0.633566	−	0.773689i	$-0.281591\pi$
$107$	1.55229e6			1.26713			0.633566	+	0.773689i	$0.281591\pi$
$108$		0			0
$109$	1.76722e6			1.36462			0.682310	−	0.731063i	$-0.260975\pi$
$109$	1.76722e6			1.36462			0.682310	+	0.731063i	$0.260975\pi$
$110$	−1.74306e6	−	407506.i	−1.30959	−	0.306165i
$111$		0			0
$112$	−123229.	+	342233.i	−0.0877121	+	0.243595i
$113$			1.35571e6i			0.939572i	0.882780	+	0.469786i	$0.155669\pi$
$113$			1.35571e6i			0.939572i	−0.882780	+	0.469786i	$0.844331\pi$
$114$		0			0
$115$	−715747.	+	182335.i	−0.470615	+	0.119888i
$116$	−516667.	−	735178.i	−0.331007	−	0.470998i
$117$		0			0
$118$	993111.	+	515894.i	0.604438	+	0.313989i
$119$			266510.i			0.158151i
$120$		0			0
$121$	−1.43276e6			−0.808757
$122$	1.10607e6	−	2.12921e6i	0.609119	−	1.17257i
$123$		0			0
$124$	−2.68474e6	+	1.88678e6i	−1.40811	+	0.989592i
$125$	−1.43131e6	+	1.32893e6i	−0.732830	+	0.680412i
$126$		0			0
$127$	−933285.			−0.455620			−0.227810	−	0.973706i	$-0.573157\pi$
$127$	−933285.			−0.455620			−0.227810	+	0.973706i	$0.573157\pi$
$128$	441554.	−	2.05014e6i	0.210549	−	0.977583i
$129$		0			0
$130$	3.24102e6	+	757710.i	1.47520	+	0.344884i
$131$			10503.7i			0.00467227i	0.999997	+	0.00233614i	$0.000743616\pi$
$131$			10503.7i			0.00467227i	−0.999997	+	0.00233614i	$0.999256\pi$
$132$		0			0
$133$			610324.i			0.259421i
$134$	150682.	−	290067.i	0.0626248	−	0.120555i
$135$		0			0
$136$	−204497.	−	1.52289e6i	−0.0812961	−	0.605412i
$137$			2.10446e6i			0.818425i	0.912439	+	0.409213i	$0.134197\pi$
$137$			2.10446e6i			0.818425i	−0.912439	+	0.409213i	$0.865803\pi$
$138$		0			0
$139$			3.09139e6i			1.15109i	0.817770	+	0.575545i	$0.195210\pi$
$139$			3.09139e6i			1.15109i	−0.817770	+	0.575545i	$0.804790\pi$
$140$	539338.	+	462421.i	0.196552	+	0.168521i
$141$		0			0
$142$	−1.58140e6	−	821496.i	−0.552303	−	0.286906i
$143$	5.95806e6			2.03750
$144$		0			0
$145$	−1.70071e6	+	433250.i	−0.557860	+	0.142113i
$146$	4.49693e6	+	2.33603e6i	1.44497	+	0.750620i
$147$		0			0
$148$	991792.	−	697010.i	0.305940	−	0.215008i
$149$	−1.54748e6			−0.467806			−0.233903	−	0.972260i	$-0.575150\pi$
$149$	−1.54748e6			−0.467806			−0.233903	+	0.972260i	$0.575150\pi$
$150$		0			0
$151$			2.13696e6i			0.620677i	0.950626	+	0.310339i	$0.100442\pi$
$151$			2.13696e6i			0.620677i	−0.950626	+	0.310339i	$0.899558\pi$
$152$	−468310.	−	3.48751e6i	−0.133353	−	0.993080i
$153$		0			0
$154$	1.12854e6	+	586245.i	0.308997	+	0.160516i
$155$	1.58215e6	+	6.21069e6i	0.424868	+	1.66780i
$156$		0			0
$157$			6.53669e6i			1.68911i	0.535467	+	0.844556i	$0.320136\pi$
$157$			6.53669e6i			1.68911i	−0.535467	+	0.844556i	$0.679864\pi$
$158$	−1.18395e6	−	615031.i	−0.300167	−	0.155929i
$159$		0			0
$160$	−3.43670e6	−	2.22852e6i	−0.839038	−	0.544073i
$161$	524733.			0.125736
$162$		0			0
$163$	7.13681e6			1.64794			0.823970	−	0.566633i	$-0.191754\pi$
$163$	7.13681e6			1.64794			0.823970	+	0.566633i	$0.191754\pi$
$164$	−432844.	−	615904.i	−0.0981295	−	0.139631i
$165$		0			0
$166$	−1.21006e6	+	2.32940e6i	−0.264535	+	0.509237i
$167$	−4.55070e6			−0.977078			−0.488539	−	0.872542i	$-0.662470\pi$
$167$	−4.55070e6			−0.977078			−0.488539	+	0.872542i	$0.662470\pi$
$168$		0			0
$169$	−6.25151e6			−1.29516
$170$	−2.92229e6	−	683195.i	−0.594807	−	0.139059i
$171$		0			0
$172$	−3.71319e6	−	5.28358e6i	−0.729729	−	1.03835i
$173$			8.29944e6i			1.60292i	0.598051	+	0.801458i	$0.295942\pi$
$173$			8.29944e6i			1.60292i	−0.598051	+	0.801458i	$0.704058\pi$
$174$		0			0
$175$	1.21845e6	−	663876.i	0.227349	−	0.123872i
$176$	−6.89852e6	−	2.48397e6i	−1.26537	−	0.455626i
$177$		0			0
$178$	−102386.	+	197096.i	−0.0181543	+	0.0349476i
$179$		−	3.03619e6i		−	0.529384i	−0.964333	−	0.264692i	$-0.914730\pi$
$179$		−	3.03619e6i		−	0.529384i	0.964333	−	0.264692i	$-0.0852702\pi$
$180$		0			0
$181$	−644931.			−0.108762			−0.0543811	−	0.998520i	$-0.517319\pi$
$181$	−644931.			−0.108762			−0.0543811	+	0.998520i	$0.517319\pi$
$182$	−2.09839e6	−	1.09005e6i	−0.348074	−	0.180815i
$183$		0			0
$184$	−2.99842e6	+	402634.i	−0.481326	+	0.0646335i
$185$	−584476.	−	2.29434e6i	−0.0923106	−	0.362362i
$186$		0			0
$187$	−5.37214e6			−0.821528
$188$	−4.75460e6	−	6.76543e6i	−0.715550	−	1.01817i
$189$		0			0
$190$	−6.69222e6	−	1.56456e6i	−0.975684	−	0.228103i
$191$			4.62842e6i			0.664252i	0.943235	+	0.332126i	$0.107766\pi$
$191$			4.62842e6i			0.664252i	−0.943235	+	0.332126i	$0.892234\pi$
$192$		0			0
$193$		−	5.13781e6i		−	0.714671i	−0.933976	−	0.357335i	$-0.883685\pi$
$193$		−	5.13781e6i		−	0.714671i	0.933976	−	0.357335i	$-0.116315\pi$
$194$	1.56716e6	+	814098.i	0.214639	+	0.111499i
$195$		0			0
$196$	4.03918e6	+	5.74744e6i	0.536444	+	0.763320i
$197$			5.52253e6i			0.722337i	0.932501	+	0.361168i	$0.117622\pi$
$197$			5.52253e6i			0.722337i	−0.932501	+	0.361168i	$0.882378\pi$
$198$		0			0
$199$			4.29058e6i			0.544449i	0.962234	+	0.272224i	$0.0877593\pi$
$199$			4.29058e6i			0.544449i	−0.962234	+	0.272224i	$0.912241\pi$
$200$	−6.45305e6	+	4.72844e6i	−0.806631	+	0.591055i
$201$		0			0
$202$	−688601.	+	1.32558e6i	−0.0835437	+	0.160824i
$203$	1.24683e6			0.149046
$204$		0			0
$205$	−1.42479e6	+	362960.i	−0.165382	+	0.0421306i
$206$	4.26625e6	−	8.21265e6i	0.488028	−	0.939467i
$207$		0			0
$208$	1.28270e7	+	4.61865e6i	1.42539	+	0.513246i
$209$	−1.23025e7			−1.34758
$210$		0			0
$211$		−	1.06723e7i		−	1.13608i	−0.823000	−	0.568041i	$-0.807702\pi$
$211$		−	1.06723e7i		−	1.13608i	0.823000	−	0.568041i	$-0.192298\pi$
$212$	−2.48766e6	+	1.74827e6i	−0.261086	+	0.183485i
$213$		0			0
$214$	5.72465e6	−	1.10201e7i	0.584128	−	1.12446i
$215$	−1.22226e7	+	3.11368e6i	−1.22984	+	0.313299i
$216$		0			0
$217$		−	4.55322e6i		−	0.445594i
$218$	6.51730e6	−	1.25460e7i	0.629069	−	1.21097i
$219$		0			0
$220$	−9.32119e6	+	1.08716e7i	−0.875393	+	1.02100i
$221$	9.98885e6			0.925420
$222$		0			0
$223$	−6.50950e6			−0.586993			−0.293497	−	0.955960i	$-0.594819\pi$
$223$	−6.50950e6			−0.586993			−0.293497	+	0.955960i	$0.594819\pi$
$224$	1.97515e6	+	2.13695e6i	0.175734	+	0.190130i
$225$		0			0
$226$	9.62451e6	+	4.99967e6i	0.833784	+	0.433128i
$227$	8.28329e6			0.708150			0.354075	−	0.935217i	$-0.384796\pi$
$227$	8.28329e6			0.708150			0.354075	+	0.935217i	$0.384796\pi$
$228$		0			0
$229$	5.99134e6			0.498904			0.249452	−	0.968387i	$-0.419749\pi$
$229$	5.99134e6			0.498904			0.249452	+	0.968387i	$0.419749\pi$
$230$	−1.34515e6	+	5.75371e6i	−0.110557	+	0.472895i
$231$		0			0
$232$	−7.12463e6	+	956711.i	−0.570556	+	0.0766155i
$233$		−	1.67538e6i		−	0.132448i	−0.997805	−	0.0662239i	$-0.978905\pi$
$233$		−	1.67538e6i		−	0.132448i	0.997805	−	0.0662239i	$-0.0210952\pi$
$234$		0			0
$235$	−1.56506e7	+	3.98696e6i	−1.20595	+	0.307212i
$236$	7.32494e6	−	5.14780e6i	0.557273	−	0.391639i
$237$		0			0
$238$	1.89203e6	+	982856.i	0.140345	+	0.0729053i
$239$		−	4.03994e6i		−	0.295925i	−0.988993	−	0.147962i	$-0.952729\pi$
$239$		−	4.03994e6i		−	0.295925i	0.988993	−	0.147962i	$-0.0472715\pi$
$240$		0			0
$241$	9.32032e6			0.665855			0.332928	−	0.942952i	$-0.391964\pi$
$241$	9.32032e6			0.665855			0.332928	+	0.942952i	$0.391964\pi$
$242$	−5.28385e6	+	1.01716e7i	−0.372824	+	0.717698i
$243$		0			0
$244$	−1.10368e7	−	1.57045e7i	−0.759755	−	1.08107i
$245$	1.32957e7	−	3.38704e6i	0.904093	−	0.230315i
$246$		0			0
$247$	2.28751e7			1.51800
$248$	3.49374e6	+	2.60179e7i	0.229053	+	1.70576i
$249$		0			0
$250$	4.15594e6	+	1.50622e7i	0.265980	+	0.963979i
$251$		−	2.59353e7i		−	1.64010i	−0.572291	−	0.820051i	$-0.693945\pi$
$251$		−	2.59353e7i		−	1.64010i	0.572291	−	0.820051i	$-0.306055\pi$
$252$		0			0
$253$			1.05772e7i			0.653146i
$254$	−3.44184e6	+	6.62564e6i	−0.210034	+	0.404321i
$255$		0			0
$256$	−1.29261e7	−	1.06954e7i	−0.770455	−	0.637494i
$257$		−	1.61283e7i		−	0.950146i	−0.879946	−	0.475073i	$-0.842422\pi$
$257$		−	1.61283e7i		−	0.950146i	0.879946	−	0.475073i	$-0.157578\pi$
$258$		0			0
$259$			1.68204e6i			0.0968137i
$260$	1.73316e7	−	2.02145e7i	0.986097	−	1.15012i
$261$		0			0
$262$	74568.5	+	38736.3i	0.00414621	+	0.00215385i
$263$	91845.2			0.00504881			0.00252441	−	0.999997i	$-0.499196\pi$
$263$	91845.2			0.00504881			0.00252441	+	0.999997i	$0.499196\pi$
$264$		0			0
$265$	1.46601e6	+	5.75476e6i	0.0787769	+	0.309236i
$266$	4.33285e6	+	2.25080e6i	0.230213	+	0.119589i
$267$		0			0
$268$	−1.50357e6	−	2.13946e6i	−0.0781121	−	0.111148i
$269$	5.38438e6			0.276617			0.138308	−	0.990389i	$-0.455833\pi$
$269$	5.38438e6			0.276617			0.138308	+	0.990389i	$0.455833\pi$
$270$		0			0
$271$		−	8.91843e6i		−	0.448106i	−0.974577	−	0.224053i	$-0.928071\pi$
$271$		−	8.91843e6i		−	0.448106i	0.974577	−	0.224053i	$-0.0719289\pi$
$272$	−1.15655e7	−	4.16445e6i	−0.574724	−	0.206943i
$273$		0			0
$274$	1.49401e7	+	7.76099e6i	0.726277	+	0.377281i
$275$	1.33820e7	+	2.45607e7i	0.643461	+	1.18098i
$276$		0			0
$277$		−	8.85192e6i		−	0.416484i	−0.978077	−	0.208242i	$-0.933226\pi$
$277$		−	8.85192e6i		−	0.416484i	0.978077	−	0.208242i	$-0.0667742\pi$
$278$	2.19466e7	+	1.14007e7i	1.02149	+	0.530635i
$279$		0			0
$280$	5.27186e6	−	2.12355e6i	0.240154	−	0.0967361i
$281$	−4.54352e6			−0.204774			−0.102387	−	0.994745i	$-0.532648\pi$
$281$	−4.54352e6			−0.204774			−0.102387	+	0.994745i	$0.532648\pi$
$282$		0			0
$283$	1.97987e7			0.873528			0.436764	−	0.899576i	$-0.356125\pi$
$283$	1.97987e7			0.873528			0.436764	+	0.899576i	$0.356125\pi$
$284$	−1.16640e7	+	8.19722e6i	−0.509206	+	0.357859i
$285$		0			0
$286$	2.19726e7	−	4.22979e7i	0.939254	−	1.80809i
$287$	1.04455e6			0.0441858
$288$		0			0
$289$	1.51310e7			0.626867
$290$	−3.19624e6	+	1.36715e7i	−0.131052	+	0.560562i
$291$		0			0
$292$	3.31682e7	−	2.33099e7i	1.33221	−	0.936250i
$293$		−	3.44412e7i		−	1.36923i	−0.728906	−	0.684614i	$-0.759971\pi$
$293$		−	3.44412e7i		−	1.36923i	0.728906	−	0.684614i	$-0.240029\pi$
$294$		0			0
$295$	−4.31668e6	−	1.69450e7i	−0.168145	−	0.660047i
$296$	−1.29065e6	−	9.61148e6i	−0.0497661	−	0.370608i
$297$		0			0
$298$	−5.70691e6	+	1.09860e7i	−0.215651	+	0.415135i
$299$		−	1.96671e7i		−	0.735744i
$300$		0			0
$301$	8.96074e6			0.328582
$302$	1.51709e7	+	7.88085e6i	0.550794	+	0.286123i
$303$		0			0
$304$	−2.64858e7	−	9.53683e6i	−0.942741	−	0.339456i
$305$	−3.63297e7	+	9.25489e6i	−1.28045	+	0.326191i
$306$		0			0
$307$	−1.94134e7			−0.670944			−0.335472	−	0.942050i	$-0.608896\pi$
$307$	−1.94134e7			−0.670944			−0.335472	+	0.942050i	$0.608896\pi$
$308$	8.32382e6	−	5.84980e6i	0.284886	−	0.200211i
$309$		0			0
$310$	4.99261e7	+	1.16721e7i	1.67588	+	0.391800i
$311$		−	2.64127e7i		−	0.878075i	−0.898469	−	0.439038i	$-0.855319\pi$
$311$		−	2.64127e7i		−	0.878075i	0.898469	−	0.439038i	$-0.144681\pi$
$312$		0			0
$313$			4.96526e6i			0.161923i	0.996717	+	0.0809616i	$0.0257991\pi$
$313$			4.96526e6i			0.161923i	−0.996717	+	0.0809616i	$0.974201\pi$
$314$	4.64057e7	+	2.41065e7i	1.49893	+	0.778655i
$315$		0			0
$316$	−8.73254e6	+	6.13704e6i	−0.276745	+	0.194490i
$317$			3.24542e7i			1.01881i	0.860527	+	0.509405i	$0.170135\pi$
$317$			3.24542e7i			1.01881i	−0.860527	+	0.509405i	$0.829865\pi$
$318$		0			0
$319$			2.51328e7i			0.774229i
$320$	−2.84950e7	+	1.61795e7i	−0.869598	+	0.493760i
$321$		0			0
$322$	1.93515e6	−	3.72522e6i	0.0579625	−	0.111579i
$323$	−2.06255e7			−0.612064
$324$		0			0
$325$	−2.48822e7	−	4.56677e7i	−0.724834	−	1.33033i
$326$	2.63197e7	−	5.06661e7i	0.759675	−	1.46240i
$327$		0			0
$328$	−5.96874e6	+	801495.i	−0.169146	+	0.0227133i
$329$	1.14739e7			0.322198
$330$		0			0
$331$		−	4.50251e7i		−	1.24157i	−0.783981	−	0.620784i	$-0.786814\pi$
$331$		−	4.50251e7i		−	1.24157i	0.783981	−	0.620784i	$-0.213186\pi$
$332$	1.20745e7	+	1.71811e7i	0.329955	+	0.469501i
$333$		0			0
$334$	−1.67824e7	+	3.23067e7i	−0.450418	+	0.867067i
$335$	−4.94927e6	+	1.26081e6i	−0.131646	+	0.0335364i
$336$		0			0
$337$			2.36631e6i			0.0618275i	0.999522	+	0.0309137i	$0.00984172\pi$
$337$			2.36631e6i			0.0618275i	−0.999522	+	0.0309137i	$0.990158\pi$
$338$	−2.30548e7	+	4.43811e7i	−0.597050	+	1.14934i
$339$		0			0
$340$	−1.56272e7	+	1.82266e7i	−0.397599	+	0.463733i
$341$	9.17807e7			2.31467
$342$		0			0
$343$	−2.01952e7			−0.500456
$344$	−5.12033e7	+	6.87569e6i	−1.25783	+	0.168904i
$345$		0			0
$346$	5.89200e7	+	3.06073e7i	1.42244	+	0.738919i
$347$	−3.57456e7			−0.855528			−0.427764	−	0.903890i	$-0.640699\pi$
$347$	−3.57456e7			−0.855528			−0.427764	+	0.903890i	$0.640699\pi$
$348$		0			0
$349$	2.95982e7			0.696288			0.348144	−	0.937441i	$-0.386812\pi$
$349$	2.95982e7			0.696288			0.348144	+	0.937441i	$0.386812\pi$
$350$	−219542.	−	1.10984e7i	−0.00512050	−	0.258855i
$351$		0			0
$352$	−4.30752e7	+	3.98138e7i	−0.987642	+	0.912863i
$353$		−	6.19569e7i		−	1.40853i	−0.709938	−	0.704264i	$-0.751277\pi$
$353$		−	6.19569e7i		−	1.40853i	0.709938	−	0.704264i	$-0.248723\pi$
$354$		0			0
$355$	6.87376e6	+	2.69827e7i	0.153642	+	0.603115i
$356$	1.02165e6	+	1.45373e6i	0.0226439	+	0.0322206i
$357$		0			0
$358$	−2.15547e7	−	1.11971e7i	−0.469779	−	0.244038i
$359$			4.08262e7i			0.882380i	0.897414	+	0.441190i	$0.145444\pi$
$359$			4.08262e7i			0.882380i	−0.897414	+	0.441190i	$0.854556\pi$
$360$		0			0
$361$	−187766.			−0.00399111
$362$	−2.37843e6	+	4.57854e6i	−0.0501377	+	0.0965164i
$363$		0			0
$364$	−1.54772e7	+	1.08770e7i	−0.320913	+	0.225531i
$365$	−1.95465e7	−	7.67289e7i	−0.401966	−	1.57790i
$366$		0			0
$367$	1.51049e7			0.305577			0.152788	−	0.988259i	$-0.451175\pi$
$367$	1.51049e7			0.305577			0.152788	+	0.988259i	$0.451175\pi$
$368$	−8.19940e6	+	2.27715e7i	−0.164527	+	0.456928i
$369$		0			0
$370$	−1.84436e7	−	4.31188e6i	−0.364117	−	0.0851259i
$371$		−	4.21896e6i		−	0.0826198i
$372$		0			0
$373$		−	5.32493e7i		−	1.02610i	−0.858360	−	0.513048i	$-0.828516\pi$
$373$		−	5.32493e7i		−	1.02610i	0.858360	−	0.513048i	$-0.171484\pi$
$374$	−1.98118e7	+	3.81382e7i	−0.378711	+	0.729030i
$375$		0			0
$376$	−6.55640e7	+	8.80407e6i	−1.23339	+	0.165623i
$377$		−	4.67315e7i		−	0.872139i
$378$		0			0
$379$			329020.i			0.00604373i	0.999995	+	0.00302187i	$0.000961891\pi$
$379$			329020.i			0.00604373i	−0.999995	+	0.00302187i	$0.999038\pi$
$380$	−3.57873e7	+	4.17400e7i	−0.652196	+	0.760679i
$381$		0			0
$382$	3.28584e7	+	1.70691e7i	0.589463	+	0.306210i
$383$	−8.05002e7			−1.43285			−0.716424	−	0.697665i	$-0.754223\pi$
$383$	−8.05002e7			−1.43285			−0.716424	+	0.697665i	$0.754223\pi$
$384$		0			0
$385$	−4.90534e6	−	1.92557e7i	−0.0859581	−	0.337425i
$386$	−3.64747e7	−	1.89476e7i	−0.634205	−	0.329452i
$387$		0			0
$388$	1.15590e7	−	8.12340e6i	0.197890	−	0.139073i
$389$	−4.89579e7			−0.831713			−0.415857	−	0.909430i	$-0.636518\pi$
$389$	−4.89579e7			−0.831713			−0.415857	+	0.909430i	$0.636518\pi$
$390$		0			0
$391$			1.77330e7i			0.296655i
$392$	5.56986e7	−	7.47933e6i	0.924669	−	0.124166i
$393$		0			0
$394$	3.92059e7	+	2.03664e7i	0.641008	+	0.332986i
$395$	5.14620e6	+	2.02012e7i	0.0835017	+	0.327783i
$396$		0			0
$397$			6.21417e7i			0.993142i	0.867996	+	0.496571i	$0.165408\pi$
$397$			6.21417e7i			0.993142i	−0.867996	+	0.496571i	$0.834592\pi$
$398$	3.04600e7	+	1.58231e7i	0.483148	+	0.250982i
$399$		0			0
$400$	9.77044e6	+	6.32498e7i	0.152663	+	0.988278i
$401$	−382303.			−0.00592891			−0.00296445	−	0.999996i	$-0.500944\pi$
$401$	−382303.			−0.00592891			−0.00296445	+	0.999996i	$0.500944\pi$
$402$		0			0
$403$	−1.70655e8			−2.60738
$404$	6.87115e6	+	9.77713e6i	0.104204	+	0.148275i
$405$		0			0
$406$	4.59816e6	−	8.85159e6i	0.0687078	−	0.132265i
$407$	−3.39054e7			−0.502905
$408$		0			0
$409$	−1.10847e8			−1.62015			−0.810074	−	0.586327i	$-0.800573\pi$
$409$	−1.10847e8			−1.62015			−0.810074	+	0.586327i	$0.800573\pi$
$410$	−2.67768e6	+	1.14535e7i	−0.0388515	+	0.166183i
$411$		0			0
$412$	−4.25704e7	−	6.05745e7i	−0.608718	−	0.866159i
$413$			1.24228e7i			0.176347i
$414$		0			0
$415$	3.97454e7	−	1.01250e7i	0.556087	−	0.141662i
$416$	8.00933e7	−	7.40291e7i	1.11254	−	1.02831i
$417$		0			0
$418$	−4.53701e7	+	8.73388e7i	−0.621214	+	1.19585i
$419$			1.21226e8i			1.64799i	0.566596	+	0.823995i	$0.308260\pi$
$419$			1.21226e8i			1.64799i	−0.566596	+	0.823995i	$0.691740\pi$
$420$		0			0
$421$	−826557.			−0.0110771			−0.00553856	−	0.999985i	$-0.501763\pi$
$421$	−826557.			−0.0110771			−0.00553856	+	0.999985i	$0.501763\pi$
$422$	−7.57653e7	−	3.93580e7i	−1.00817	−	0.523716i
$423$		0			0
$424$	3.23727e6	+	2.41080e7i	0.0424699	+	0.316273i
$425$	2.24352e7	+	4.11767e7i	0.292256	+	0.536395i
$426$		0			0
$427$	2.66342e7			0.342103
$428$	−5.71230e7	−	8.12817e7i	−0.728584	−	1.03672i
$429$		0			0
$430$	−2.29707e7	+	9.82547e7i	−0.288915	+	1.23580i
$431$		−	1.26492e8i		−	1.57990i	−0.613169	−	0.789952i	$-0.710106\pi$
$431$		−	1.26492e8i		−	1.57990i	0.613169	−	0.789952i	$-0.289894\pi$
$432$		0			0
$433$		−	1.05162e8i		−	1.29537i	−0.761907	−	0.647687i	$-0.775737\pi$
$433$		−	1.05162e8i		−	1.29537i	0.761907	−	0.647687i	$-0.224263\pi$
$434$	−3.23245e7	−	1.67917e7i	−0.395424	−	0.205412i
$435$		0			0
$436$	−6.50323e7	−	9.25360e7i	−0.784638	−	1.11648i
$437$			4.06096e7i			0.486614i
$438$		0			0
$439$			2.67453e7i			0.316122i	0.987429	+	0.158061i	$0.0505242\pi$
$439$			2.67453e7i			0.316122i	−0.987429	+	0.158061i	$0.949476\pi$
$440$	4.28052e7	+	1.06267e8i	0.502502	+	1.24750i
$441$		0			0
$442$	3.68376e7	−	7.09135e7i	0.426604	−	0.821225i
$443$	8.39480e7			0.965604			0.482802	−	0.875730i	$-0.339619\pi$
$443$	8.39480e7			0.965604			0.482802	+	0.875730i	$0.339619\pi$
$444$		0			0
$445$	3.36294e6	−	856700.i	0.0381628	−	0.00972185i
$446$	−2.40062e7	+	4.62127e7i	−0.270595	+	0.520903i
$447$		0			0
$448$	2.24549e7	−	6.14132e6i	0.249734	−	0.0683011i
$449$	3.85437e7			0.425808			0.212904	−	0.977073i	$-0.431708\pi$
$449$	3.85437e7			0.425808			0.212904	+	0.977073i	$0.431708\pi$
$450$		0			0
$451$			2.10553e7i			0.229526i
$452$	7.09880e7	−	4.98888e7i	0.768723	−	0.540241i
$453$		0			0
$454$	3.05477e7	−	5.88053e7i	0.326446	−	0.628418i
$455$	9.12089e6	+	3.58037e7i	0.0968285	+	0.380097i
$456$		0			0
$457$			1.01357e8i			1.06196i	0.847386	+	0.530978i	$0.178175\pi$
$457$			1.01357e8i			1.06196i	−0.847386	+	0.530978i	$0.821825\pi$
$458$	2.20953e7	−	4.25341e7i	0.229987	−	0.442732i
$459$		0			0
$460$	3.58864e7	+	3.07685e7i	0.368685	+	0.316106i
$461$	−9.49132e7			−0.968777			−0.484388	−	0.874853i	$-0.660958\pi$
$461$	−9.49132e7			−0.968777			−0.484388	+	0.874853i	$0.660958\pi$
$462$		0			0
$463$	1.18102e8			1.18991			0.594955	−	0.803759i	$-0.297170\pi$
$463$	1.18102e8			1.18991			0.594955	+	0.803759i	$0.297170\pi$
$464$	−1.94828e7	+	5.41079e7i	−0.195028	+	0.541635i
$465$		0			0
$466$	−1.18939e7	−	6.17858e6i	−0.117535	−	0.0610564i
$467$	1.86109e8			1.82733			0.913663	−	0.406473i	$-0.133241\pi$
$467$	1.86109e8			1.82733			0.913663	+	0.406473i	$0.133241\pi$
$468$		0			0
$469$	3.62844e6			0.0351723
$470$	−2.94132e7	+	1.25812e8i	−0.283301	+	1.21179i
$471$		0			0
$472$	−9.53217e6	−	7.09861e7i	−0.0906496	−	0.675068i
$473$			1.80625e8i			1.70684i
$474$		0			0
$475$	5.13781e7	+	9.42971e7i	0.479399	+	0.879868i
$476$	1.39551e7	−	9.80734e6i	0.129394	−	0.0909349i
$477$		0			0
$478$	−2.86806e7	−	1.48988e7i	−0.262606	−	0.136417i
$479$		−	5.01949e7i		−	0.456723i	−0.973576	−	0.228362i	$-0.926663\pi$
$479$		−	5.01949e7i		−	0.456723i	0.973576	−	0.228362i	$-0.0733368\pi$
$480$		0			0
$481$	6.30432e7			0.566504
$482$	3.43722e7	−	6.61674e7i	0.306949	−	0.590885i
$483$		0			0
$484$	5.27244e7	+	7.50229e7i	0.465025	+	0.661695i
$485$	−6.81186e6	−	2.67397e7i	−0.0597091	−	0.234386i
$486$		0			0
$487$	1.08896e8			0.942816			0.471408	−	0.881915i	$-0.343746\pi$
$487$	1.08896e8			0.942816			0.471408	+	0.881915i	$0.343746\pi$
$488$	−1.52193e8	+	2.04368e7i	−1.30959	+	0.175854i
$489$		0			0
$490$	2.49874e7	−	1.06881e8i	0.212389	−	0.908471i
$491$			1.71108e7i			0.144553i	0.997385	+	0.0722764i	$0.0230264\pi$
$491$			1.71108e7i			0.144553i	−0.997385	+	0.0722764i	$0.976974\pi$
$492$		0			0
$493$			4.21359e7i			0.351650i
$494$	8.43604e7	−	1.62396e8i	0.699774	−	1.34709i
$495$		0			0
$496$	1.97593e8	+	7.11479e7i	1.61929	+	0.583065i
$497$		−	1.97817e7i		−	0.161137i
$498$		0			0
$499$			2.08493e7i			0.167799i	0.996474	+	0.0838994i	$0.0267374\pi$
$499$			2.08493e7i			0.167799i	−0.996474	+	0.0838994i	$0.973263\pi$
$500$	1.22257e8	+	2.60433e7i	0.978055	+	0.208346i
$501$		0			0
$502$	−1.84122e8	−	9.56463e7i	−1.45544	−	0.756061i
$503$	−1.34897e7			−0.105998			−0.0529991	−	0.998595i	$-0.516878\pi$
$503$	−1.34897e7			−0.105998			−0.0529991	+	0.998595i	$0.516878\pi$
$504$		0			0
$505$	2.26177e7	−	5.76179e6i	0.175620	−	0.0447387i
$506$	7.50905e7	+	3.90075e7i	0.579607	+	0.301090i
$507$		0			0
$508$	3.43441e7	+	4.88691e7i	0.261976	+	0.372772i
$509$	−1.73454e8			−1.31531			−0.657657	−	0.753317i	$-0.728453\pi$
$509$	−1.73454e8			−1.31531			−0.657657	+	0.753317i	$0.728453\pi$
$510$		0			0
$511$			5.62519e7i			0.421575i
$512$	−1.23599e8	+	5.23226e7i	−0.920885	+	0.389834i
$513$		0			0
$514$	−1.14499e8	−	5.94793e7i	−0.843167	−	0.438002i
$515$	−1.40128e8	+	3.56973e7i	−1.02590	+	0.261345i
$516$		0			0
$517$			2.31283e8i			1.67368i
$518$	1.19412e7	+	6.20315e6i	0.0859133	+	0.0446296i
$519$		0			0
$520$	−7.95912e7	−	1.97591e8i	−0.566050	−	1.40526i
$521$	1.78879e8			1.26487			0.632437	−	0.774612i	$-0.282055\pi$
$521$	1.78879e8			1.26487			0.632437	+	0.774612i	$0.282055\pi$
$522$		0			0
$523$	−1.77417e8			−1.24020			−0.620098	−	0.784525i	$-0.712907\pi$
$523$	−1.77417e8			−1.24020			−0.620098	+	0.784525i	$0.712907\pi$
$524$	549999.	−	386527.i	0.00382268	−	0.00268649i
$525$		0			0
$526$	338714.	−	652034.i	0.00232742	−	0.00448036i
$527$	1.53873e8			1.05131
$528$		0			0
$529$	−1.13121e8			−0.764148
$530$	4.62610e7	+	1.08153e7i	0.310733	+	0.0726456i
$531$		0			0
$532$	3.19581e7	−	2.24594e7i	0.212249	−	0.149164i
$533$		−	3.91499e7i		−	0.258552i
$534$		0			0
$535$	−1.88031e8	+	4.79003e7i	−1.22791	+	0.312808i
$536$	−2.07336e7	+	2.78415e6i	−0.134642	+	0.0180800i
$537$		0			0
$538$	1.98569e7	−	3.82251e7i	0.127516	−	0.245472i
$539$		−	1.96482e8i		−	1.25475i
$540$		0			0
$541$	1.34835e8			0.851553			0.425777	−	0.904828i	$-0.360001\pi$
$541$	1.34835e8			0.851553			0.425777	+	0.904828i	$0.360001\pi$
$542$	−6.33143e7	−	3.28901e7i	−0.397653	−	0.206570i
$543$		0			0
$544$	−7.22168e7	+	6.67489e7i	−0.448582	+	0.414617i
$545$	−2.14066e8	+	5.45327e7i	−1.32239	+	0.336874i
$546$		0			0
$547$	2.22069e8			1.35683			0.678416	−	0.734678i	$-0.262667\pi$
$547$	2.22069e8			1.35683			0.678416	+	0.734678i	$0.262667\pi$
$548$	1.10195e8	−	7.74423e7i	0.669605	−	0.470583i
$549$		0			0
$550$	2.23714e8	−	4.42538e6i	1.34464	−	0.0265988i
$551$			9.64937e7i			0.576825i
$552$		0			0
$553$		−	1.48100e7i		−	0.0875751i
$554$	−6.28422e7	−	3.26448e7i	−0.369591	−	0.191993i
$555$		0			0
$556$	1.61873e8	−	1.13760e8i	0.941779	−	0.661861i
$557$			2.84443e8i			1.64600i	0.568042	+	0.823000i	$0.307701\pi$
$557$			2.84443e8i			1.64600i	−0.568042	+	0.823000i	$0.692299\pi$
$558$		0			0
$559$		−	3.35850e8i		−	1.92269i
$560$	4.36632e6	−	4.52578e7i	0.0248629	−	0.257709i
$561$		0			0
$562$	−1.67560e7	+	3.22557e7i	−0.0943974	+	0.181718i
$563$	−4.28842e7			−0.240310			−0.120155	−	0.992755i	$-0.538339\pi$
$563$	−4.28842e7			−0.240310			−0.120155	+	0.992755i	$0.538339\pi$
$564$		0			0
$565$	−4.18341e7	−	1.64218e8i	−0.231945	−	0.910492i
$566$	7.30150e7	−	1.40556e8i	0.402683	−	0.775176i
$567$		0			0
$568$	1.51788e7	+	1.13036e8i	0.0828307	+	0.616841i
$569$	3.24019e8			1.75887			0.879435	−	0.476019i	$-0.157921\pi$
$569$	3.24019e8			1.75887			0.879435	+	0.476019i	$0.157921\pi$
$570$		0			0
$571$		−	3.28824e8i		−	1.76626i	−0.469126	−	0.883131i	$-0.655431\pi$
$571$		−	3.28824e8i		−	1.76626i	0.469126	−	0.883131i	$-0.344569\pi$
$572$	−2.19252e8	−	3.11979e8i	−1.17153	−	1.66700i
$573$		0			0
$574$	3.85216e6	−	7.41552e6i	0.0203690	−	0.0392108i
$575$	8.10730e7	−	4.41728e7i	0.426454	−	0.232355i
$576$		0			0
$577$			9.48080e7i			0.493534i	0.969075	+	0.246767i	$0.0793683\pi$
$577$			9.48080e7i			0.493534i	−0.969075	+	0.246767i	$0.920632\pi$
$578$	5.58014e7	−	1.07419e8i	0.288976	−	0.556287i
$579$		0			0
$580$	8.52706e7	+	7.31099e7i	0.437034	+	0.374707i
$581$	−2.91384e7			−0.148572
$582$		0			0
$583$	8.50431e7			0.429174
$584$	−4.31628e7	−	3.21434e8i	−0.216706	−	1.61381i
$585$		0			0
$586$	−2.44507e8	−	1.27015e8i	−1.21506	−	0.631193i
$587$	5.12804e7			0.253534			0.126767	−	0.991932i	$-0.459540\pi$
$587$	5.12804e7			0.253534			0.126767	+	0.991932i	$0.459540\pi$
$588$		0			0
$589$	3.52378e8			1.72450
$590$	−1.36216e8	−	3.18457e7i	−0.663243	−	0.155058i
$591$		0			0
$592$	−7.29942e7	−	2.62833e7i	−0.351822	−	0.126682i
$593$			2.12368e7i			0.101842i	0.998703	+	0.0509208i	$0.0162156\pi$
$593$			2.12368e7i			0.101842i	−0.998703	+	0.0509208i	$0.983784\pi$
$594$		0			0
$595$	−8.22393e6	−	3.22827e7i	−0.0390417	−	0.153257i
$596$	5.69459e7	+	8.10297e7i	0.268982	+	0.382741i
$597$		0			0
$598$	−1.39622e8	−	7.25298e7i	−0.652905	−	0.339166i
$599$			2.38008e8i			1.10742i	0.832710	+	0.553709i	$0.186788\pi$
$599$			2.38008e8i			1.10742i	−0.832710	+	0.553709i	$0.813212\pi$
$600$		0			0
$601$	−1.59516e8			−0.734822			−0.367411	−	0.930059i	$-0.619756\pi$
$601$	−1.59516e8			−0.734822			−0.367411	+	0.930059i	$0.619756\pi$
$602$	3.30461e7	−	6.36147e7i	0.151471	−	0.291587i
$603$		0			0
$604$	1.11896e8	−	7.86384e7i	0.507815	−	0.356881i
$605$	1.73552e8	−	4.42120e7i	0.783727	−	0.199652i
$606$		0			0
$607$	−1.87552e8			−0.838602			−0.419301	−	0.907847i	$-0.637725\pi$
$607$	−1.87552e8			−0.838602			−0.419301	+	0.907847i	$0.637725\pi$
$608$	−1.65381e8	+	1.52859e8i	−0.735825	+	0.680112i
$609$		0			0
$610$	−6.82765e7	+	2.92045e8i	−0.300803	+	1.28665i
$611$		−	4.30044e8i		−	1.88534i
$612$		0			0
$613$		−	1.96888e7i		−	0.0854749i	−0.999086	−	0.0427374i	$-0.986392\pi$
$613$		−	1.96888e7i		−	0.0854749i	0.999086	−	0.0427374i	$-0.0136079\pi$
$614$	−7.15942e7	+	1.37821e8i	−0.309295	+	0.595401i
$615$		0			0
$616$	−1.08320e7	−	8.06664e7i	−0.0463413	−	0.345104i
$617$			2.99111e8i			1.27344i	0.771096	+	0.636719i	$0.219709\pi$
$617$			2.99111e8i			1.27344i	−0.771096	+	0.636719i	$0.780291\pi$
$618$		0			0
$619$		−	6.73241e7i		−	0.283856i	−0.989877	−	0.141928i	$-0.954670\pi$
$619$		−	6.73241e7i		−	0.283856i	0.989877	−	0.141928i	$-0.0453302\pi$
$620$	2.66985e8	−	3.11393e8i	1.12024	−	1.30658i
$621$		0			0
$622$	−1.87511e8	−	9.74068e7i	−0.779211	−	0.404779i
$623$	−2.46546e6			−0.0101961
$624$		0			0
$625$	1.32368e8	−	2.05142e8i	0.542181	−	0.840262i
$626$	3.52497e7	+	1.83113e7i	0.143692	+	0.0746441i
$627$		0			0
$628$	3.42277e8	−	2.40544e8i	1.38197	−	0.971217i
$629$	−5.68434e7			−0.228417
$630$		0			0
$631$			3.74586e8i			1.49095i	0.666533	+	0.745476i	$0.267778\pi$
$631$			3.74586e8i			1.49095i	−0.666533	+	0.745476i	$0.732222\pi$
$632$	1.13639e7	+	8.46272e7i	0.0450171	+	0.335242i
$633$		0			0
$634$	2.30401e8	+	1.19687e8i	0.904101	+	0.469656i
$635$	1.13050e8	−	2.87992e7i	0.441519	−	0.112476i
$636$		0			0
$637$			3.65335e8i			1.41343i
$638$	1.78425e8	+	9.26867e7i	0.687057	+	0.356907i
$639$		0			0
$640$	9.77690e6	+	2.61962e8i	0.0372959	+	0.999304i
$641$	−3.70848e8			−1.40806			−0.704031	−	0.710169i	$-0.748618\pi$
$641$	−3.70848e8			−1.40806			−0.704031	+	0.710169i	$0.748618\pi$
$642$		0			0
$643$	4.50751e8			1.69552			0.847761	−	0.530378i	$-0.177950\pi$
$643$	4.50751e8			1.69552			0.847761	+	0.530378i	$0.177950\pi$
$644$	−1.93097e7	−	2.74763e7i	−0.0722967	−	0.102873i
$645$		0			0
$646$	−7.60643e7	+	1.46426e8i	−0.282152	+	0.543151i
$647$	−3.12382e8			−1.15338			−0.576691	−	0.816962i	$-0.695656\pi$
$647$	−3.12382e8			−1.15338			−0.576691	+	0.816962i	$0.695656\pi$
$648$		0			0
$649$	−2.50410e8			−0.916048
$650$	−4.15970e8	+	8.22846e6i	−1.51468	+	0.0299625i
$651$		0			0
$652$	−2.62629e8	−	3.73701e8i	−0.947544	−	1.34828i
$653$		−	1.75008e8i		−	0.628519i	−0.949337	−	0.314260i	$-0.898244\pi$
$653$		−	1.75008e8i		−	0.628519i	0.949337	−	0.314260i	$-0.101756\pi$
$654$		0			0
$655$	−324121.	−	1.27233e6i	−0.00115341	−	0.00452767i
$656$	−1.63219e7	+	4.53295e7i	−0.0578176	+	0.160572i
$657$		0			0
$658$	4.23143e7	−	8.14562e7i	0.148528	−	0.285921i
$659$			5.04270e8i			1.76200i	0.473113	+	0.881002i	$0.343130\pi$
$659$			5.04270e8i			1.76200i	−0.473113	+	0.881002i	$0.656870\pi$
$660$		0			0
$661$	−3.10890e8			−1.07647			−0.538236	−	0.842794i	$-0.680909\pi$
$661$	−3.10890e8			−1.07647			−0.538236	+	0.842794i	$0.680909\pi$
$662$	−3.19645e8	−	1.66047e8i	−1.10178	−	0.572344i
$663$		0			0
$664$	1.66502e8	−	2.23583e7i	0.568743	−	0.0763720i
$665$	−1.88333e7	−	7.39294e7i	−0.0640415	−	0.251392i
$666$		0			0
$667$	8.29615e7			0.279575
$668$	1.67462e8	+	2.38286e8i	0.561807	+	0.799409i
$669$		0			0
$670$	−9.30145e6	+	3.97859e7i	−0.0309262	+	0.132283i
$671$			5.36875e8i			1.77708i
$672$		0			0
$673$			4.42525e8i			1.45175i	0.687826	+	0.725876i	$0.258565\pi$
$673$			4.42525e8i			1.45175i	−0.687826	+	0.725876i	$0.741435\pi$
$674$	1.67990e7	+	8.72665e6i	0.0548662	+	0.0285015i
$675$		0			0
$676$	2.30050e8	+	3.27344e8i	0.744702	+	1.05965i
$677$			3.01059e8i			0.970255i	0.874443	+	0.485128i	$0.161227\pi$
$677$			3.01059e8i			0.970255i	−0.874443	+	0.485128i	$0.838773\pi$
$678$		0			0
$679$			1.96036e7i			0.0626218i
$680$	7.17640e7	+	1.78159e8i	0.228234	+	0.566606i
$681$		0			0
$682$	3.38476e8	−	6.51576e8i	1.06703	−	2.05405i
$683$	2.52236e8			0.791673			0.395836	−	0.918321i	$-0.370455\pi$
$683$	2.52236e8			0.791673			0.395836	+	0.918321i	$0.370455\pi$
$684$		0			0
$685$	−6.49391e7	−	2.54916e8i	−0.202039	−	0.793095i
$686$	−7.44773e7	+	1.43371e8i	−0.230702	+	0.444108i
$687$		0			0
$688$	−1.40019e8	+	3.88863e8i	−0.429954	+	1.19407i
$689$	−1.58128e8			−0.483448
$690$		0			0
$691$		−	6.69200e7i		−	0.202825i	−0.994844	−	0.101413i	$-0.967664\pi$
$691$		−	6.69200e7i		−	0.202825i	0.994844	−	0.101413i	$-0.0323362\pi$
$692$	4.34579e8	−	3.05413e8i	1.31145	−	0.921655i
$693$		0			0
$694$	−1.31825e8	+	2.53768e8i	−0.394385	+	0.759203i
$695$	−9.53936e7	−	3.74464e8i	−0.284161	−	1.11546i
$696$		0			0
$697$			3.52998e7i			0.104249i
$698$	1.09154e8	−	2.10125e8i	0.320978	−	0.617892i
$699$		0			0
$700$	−7.96001e7	−	3.93709e7i	−0.232070	−	0.114784i
$701$	4.07068e8			1.18171			0.590857	−	0.806776i	$-0.298790\pi$
$701$	4.07068e8			1.18171			0.590857	+	0.806776i	$0.298790\pi$
$702$		0			0
$703$	−1.30175e8			−0.374680
$704$	1.23793e8	+	4.52631e8i	0.354795	+	1.29726i
$705$		0			0
$706$	−4.39849e8	−	2.28489e8i	−1.24994	−	0.649310i
$707$	−1.65816e7			−0.0469211
$708$		0			0
$709$	2.14836e7			0.0602793			0.0301396	−	0.999546i	$-0.490405\pi$
$709$	2.14836e7			0.0602793			0.0301396	+	0.999546i	$0.490405\pi$
$710$	2.16907e8	+	5.07102e7i	0.606036	+	0.141684i
$711$		0			0
$712$	1.40881e7	−	1.89178e6i	0.0390313	−	0.00524120i
$713$		−	3.02961e8i		−	0.835830i
$714$		0			0
$715$	−7.21708e8	+	1.83853e8i	−1.97444	+	0.502982i
$716$	−1.58982e8	+	1.11729e8i	−0.433122	+	0.304388i
$717$		0			0
$718$	2.89836e8	+	1.50562e8i	0.783031	+	0.406764i
$719$		−	4.75458e8i		−	1.27916i	−0.768724	−	0.639581i	$-0.779108\pi$
$719$		−	4.75458e8i		−	1.27916i	0.768724	−	0.639581i	$-0.220892\pi$
$720$		0			0
$721$	1.02732e8			0.274094
$722$	−692456.	+	1.33300e6i	−0.00183984	+	0.00354175i
$723$		0			0
$724$	2.37329e7	+	3.37702e7i	0.0625368	+	0.0889851i
$725$	1.92640e8	−	1.04960e8i	0.505512	−	0.275430i
$726$		0			0
$727$	6.11316e8			1.59097			0.795486	−	0.605972i	$-0.207216\pi$
$727$	6.11316e8			1.59097			0.795486	+	0.605972i	$0.207216\pi$
$728$	2.01409e7	+	1.49990e8i	0.0522018	+	0.388747i
$729$		0			0
$730$	−6.16804e8	−	1.44201e8i	−1.58554	−	0.370681i
$731$			3.02822e8i			0.775239i
$732$		0			0
$733$		−	5.86490e8i		−	1.48919i	−0.667519	−	0.744593i	$-0.732644\pi$
$733$		−	5.86490e8i		−	1.48919i	0.667519	−	0.744593i	$-0.267356\pi$
$734$	5.57050e7	−	1.07234e8i	0.140866	−	0.271171i
$735$		0			0
$736$	1.31422e8	+	1.42188e8i	0.329637	+	0.356639i
$737$			7.31397e7i			0.182705i
$738$		0			0
$739$			5.79830e8i			1.43671i	0.695679	+	0.718353i	$0.255104\pi$
$739$			5.79830e8i			1.43671i	−0.695679	+	0.718353i	$0.744896\pi$
$740$	−9.86289e7	+	1.15034e8i	−0.243394	+	0.283878i
$741$		0			0
$742$	−2.99516e7	−	1.55590e7i	−0.0733175	−	0.0380864i
$743$	3.73947e8			0.911681			0.455841	−	0.890061i	$-0.349339\pi$
$743$	3.73947e8			0.911681			0.455841	+	0.890061i	$0.349339\pi$
$744$		0			0
$745$	1.87448e8	−	4.77518e7i	0.453327	−	0.115484i
$746$	−3.78031e8	−	1.96377e8i	−0.910565	−	0.473014i
$747$		0			0
$748$	1.97690e8	+	2.81298e8i	0.472367	+	0.672143i
$749$	1.37850e8			0.328067
$750$		0			0
$751$			1.27510e8i			0.301041i	0.988607	+	0.150521i	$0.0480950\pi$
$751$			1.27510e8i			0.301041i	−0.988607	+	0.150521i	$0.951905\pi$
$752$	−1.79289e8	+	4.97924e8i	−0.421600	+	1.17087i
$753$		0			0
$754$	−3.31760e8	−	1.72340e8i	−0.773944	−	0.402043i
$755$	−6.59421e7	−	2.58853e8i	−0.153222	−	0.601468i
$756$		0			0
$757$			2.33748e7i			0.0538841i	0.999637	+	0.0269420i	$0.00857696\pi$
$757$			2.33748e7i			0.0538841i	−0.999637	+	0.0269420i	$0.991423\pi$
$758$	2.33580e6	+	1.21339e6i	0.00536326	+	0.00278607i
$759$		0			0
$760$	1.64344e8	+	4.07995e8i	0.374380	+	0.929425i
$761$	−7.53332e8			−1.70936			−0.854678	−	0.519159i	$-0.826245\pi$
$761$	−7.53332e8			−1.70936			−0.854678	+	0.519159i	$0.826245\pi$
$762$		0			0
$763$	1.56937e8			0.353307
$764$	2.42355e8	−	1.70322e8i	0.543467	−	0.381936i
$765$		0			0
$766$	−2.96875e8	+	5.71492e8i	−0.660521	+	1.27152i
$767$	4.65609e8			1.03189
$768$		0			0
$769$	−6.33859e8			−1.39384			−0.696921	−	0.717148i	$-0.745447\pi$
$769$	−6.33859e8			−1.39384			−0.696921	+	0.717148i	$0.745447\pi$
$770$	−1.54792e8	−	3.61884e7i	−0.339059	−	0.0792678i
$771$		0			0
$772$	−2.69028e8	+	1.89067e8i	−0.584717	+	0.410926i
$773$		−	1.08448e8i		−	0.234793i	−0.993085	−	0.117396i	$-0.962545\pi$
$773$		−	1.08448e8i		−	0.234793i	0.993085	−	0.117396i	$-0.0374548\pi$
$774$		0			0
$775$	−3.83297e8	−	7.03487e8i	−0.823437	−	1.51130i
$776$	−1.50421e7	−	1.12018e8i	−0.0321901	−	0.239720i
$777$		0			0
$778$	−1.80551e8	+	3.47565e8i	−0.383407	+	0.738069i
$779$			8.08387e7i			0.171004i
$780$		0			0
$781$	3.98747e8			0.837036
$782$	1.25891e8	+	6.53971e7i	0.263254	+	0.136753i
$783$		0			0
$784$	1.52312e8	−	4.23002e8i	0.316072	−	0.877797i
$785$	−2.01708e8	−	7.91797e8i	−0.416979	−	1.63684i
$786$		0			0
$787$	−3.53415e8			−0.725039			−0.362519	−	0.931976i	$-0.618083\pi$
$787$	−3.53415e8			−0.725039			−0.362519	+	0.931976i	$0.618083\pi$
$788$	2.89173e8	−	2.03225e8i	0.590989	−	0.415334i
$789$		0			0
$790$	1.62392e8	+	3.79653e7i	0.329370	+	0.0770026i
$791$			1.20393e8i			0.243260i
$792$		0			0
$793$		−	9.98257e8i		−	2.00181i
$794$	4.41160e8	+	2.29171e8i	0.881322	+	0.457823i
$795$		0			0
$796$	2.24665e8	−	1.57890e8i	0.445448	−	0.313051i
$797$		−	5.64122e8i		−	1.11429i	−0.830415	−	0.557145i	$-0.811897\pi$
$797$		−	5.64122e8i		−	1.11429i	0.830415	−	0.557145i	$-0.188103\pi$
$798$		0			0
$799$			3.87753e8i			0.760176i
$800$	4.85059e8	+	1.63894e8i	0.947382	+	0.320106i
$801$		0			0
$802$	−1.40989e6	+	2.71407e6i	−0.00273313	+	0.00526136i
$803$	−1.13389e9			−2.18990
$804$		0			0
$805$	−6.35616e7	+	1.61921e7i	−0.121845	+	0.0310396i
$806$	−6.29356e8	+	1.21153e9i	−1.20196	+	2.31381i
$807$		0			0
$808$	9.47504e7	−	1.27233e7i	0.179617	−	0.0241193i
$809$	2.93587e8			0.554487			0.277243	−	0.960800i	$-0.410579\pi$
$809$	2.93587e8			0.554487			0.277243	+	0.960800i	$0.410579\pi$
$810$		0			0
$811$			7.58312e8i			1.42163i	0.703381	+	0.710813i	$0.251673\pi$
$811$			7.58312e8i			1.42163i	−0.703381	+	0.710813i	$0.748327\pi$
$812$	−4.58824e7	−	6.52871e7i	−0.0856994	−	0.121944i
$813$		0			0
$814$	−1.25039e8	+	2.40704e8i	−0.231831	+	0.446282i
$815$	−8.64492e8	+	2.20227e8i	−1.59694	+	0.406815i
$816$		0			0
$817$			6.93481e8i			1.27165i
$818$	−4.08791e8	+	7.86934e8i	−0.746863	+	1.43773i
$819$		0			0
$820$	7.14364e7	+	6.12486e7i	0.129562	+	0.111085i
$821$	2.11510e7			0.0382209			0.0191104	−	0.999817i	$-0.493917\pi$
$821$	2.11510e7			0.0382209			0.0191104	+	0.999817i	$0.493917\pi$
$822$		0			0
$823$	−9.99192e8			−1.79246			−0.896230	−	0.443590i	$-0.853705\pi$
$823$	−9.99192e8			−1.79246			−0.896230	+	0.443590i	$0.853705\pi$
$824$	−5.87028e8	+	7.88274e7i	−1.04925	+	0.140895i
$825$		0			0
$826$	8.81927e7	+	4.58137e7i	0.156492	+	0.0812934i
$827$	−5.08817e8			−0.899591			−0.449796	−	0.893131i	$-0.648503\pi$
$827$	−5.08817e8			−0.899591			−0.449796	+	0.893131i	$0.648503\pi$
$828$		0			0
$829$	9.05552e8			1.58946			0.794730	−	0.606963i	$-0.207612\pi$
$829$	9.05552e8			1.58946			0.794730	+	0.606963i	$0.207612\pi$
$830$	7.46959e7	−	3.19503e8i	0.130636	−	0.558780i
$831$		0			0
$832$	−2.30178e8	−	8.41614e8i	−0.399663	−	1.46131i
$833$		−	3.29408e8i		−	0.569900i
$834$		0			0
$835$	5.51233e8	−	1.40425e8i	0.946838	−	0.241204i
$836$	4.52722e8	+	6.44189e8i	0.774841	+	1.10254i
$837$		0			0
$838$	8.60618e8	+	4.47068e8i	1.46244	+	0.759698i
$839$		−	8.22611e8i		−	1.39286i	−0.717623	−	0.696432i	$-0.754770\pi$
$839$		−	8.22611e8i		−	1.39286i	0.717623	−	0.696432i	$-0.245230\pi$
$840$		0			0
$841$	−3.97696e8			−0.668596
$842$	−3.04824e6	+	5.86795e6i	−0.00510638	+	0.00982992i
$843$		0			0
$844$	−5.58826e8	+	3.92730e8i	−0.929500	+	0.653232i
$845$	7.57253e8	−	1.92908e8i	1.25508	−	0.319728i
$846$		0			0
$847$	−1.27236e8			−0.209391
$848$	1.83087e8	+	6.59249e7i	0.300242	+	0.108109i
$849$		0			0
$850$	3.75063e8	−	7.41926e6i	0.610727	−	0.0120810i
$851$			1.11919e8i			0.181600i
$852$		0			0
$853$			1.56058e8i			0.251443i	0.992066	+	0.125722i	$0.0401246\pi$
$853$			1.56058e8i			0.251443i	−0.992066	+	0.125722i	$0.959875\pi$
$854$	9.82238e7	−	1.89084e8i	0.157704	−	0.303585i
$855$		0			0
$856$	−7.87703e8	+	1.05774e8i	−1.25586	+	0.168639i
$857$		−	3.39476e8i		−	0.539345i	−0.962952	−	0.269672i	$-0.913085\pi$
$857$		−	3.39476e8i		−	0.539345i	0.962952	−	0.269672i	$-0.0869154\pi$
$858$		0			0
$859$		−	6.27544e8i		−	0.990068i	−0.868874	−	0.495034i	$-0.835156\pi$
$859$		−	6.27544e8i		−	0.990068i	0.868874	−	0.495034i	$-0.164844\pi$
$860$	6.12823e8	+	5.25427e8i	0.963474	+	0.826070i
$861$		0			0
$862$	−8.97999e8	−	4.66486e8i	−1.40202	−	0.728311i
$863$	5.09291e8			0.792381			0.396190	−	0.918168i	$-0.370332\pi$
$863$	5.09291e8			0.792381			0.396190	+	0.918168i	$0.370332\pi$
$864$		0			0
$865$	−2.56103e8	−	1.00532e9i	−0.395700	−	1.55331i
$866$	−7.46573e8	−	3.87824e8i	−1.14953	−	0.597147i
$867$		0			0
$868$	−2.38417e8	+	1.67554e8i	−0.364568	+	0.256210i
$869$	2.98531e8			0.454914
$870$		0			0
$871$		−	1.35995e8i		−	0.205810i
$872$	−8.96769e8	+	1.20420e8i	−1.35248	+	0.181614i
$873$		0			0
$874$	2.88299e8	+	1.49763e8i	0.431825	+	0.224322i
$875$	−1.27107e8	+	1.18015e8i	−0.189733	+	0.176162i
$876$		0			0
$877$			6.30685e8i			0.935004i	0.883992	+	0.467502i	$0.154846\pi$
$877$			6.30685e8i			0.935004i	−0.883992	+	0.467502i	$0.845154\pi$
$878$	1.89872e8	+	9.86334e7i	0.280529	+	0.145727i
$879$		0			0
$880$	9.12276e8	+	8.80134e7i	1.33868	+	0.129152i
$881$	−2.54533e8			−0.372235			−0.186117	−	0.982528i	$-0.559590\pi$
$881$	−2.54533e8			−0.372235			−0.186117	+	0.982528i	$0.559590\pi$
$882$		0			0
$883$	−3.28879e7			−0.0477698			−0.0238849	−	0.999715i	$-0.507604\pi$
$883$	−3.28879e7			−0.0477698			−0.0238849	+	0.999715i	$0.507604\pi$
$884$	−3.67581e8	−	5.23040e8i	−0.532104	−	0.757144i
$885$		0			0
$886$	3.09590e8	−	5.95969e8i	0.445128	−	0.856885i
$887$	−2.38053e8			−0.341116			−0.170558	−	0.985348i	$-0.554557\pi$
$887$	−2.38053e8			−0.341116			−0.170558	+	0.985348i	$0.554557\pi$
$888$		0			0
$889$	−8.28799e7			−0.117962
$890$	6.32018e6	−	2.70338e7i	0.00896519	−	0.0383476i
$891$		0			0
$892$	2.39544e8	+	3.40853e8i	0.337513	+	0.480256i
$893$			8.87977e8i			1.24695i
$894$		0			0
$895$	9.36904e7	+	3.67778e8i	0.130685	+	0.512999i
$896$	3.92120e7	−	1.82062e8i	0.0545123	−	0.253101i
$897$		0			0
$898$	1.42144e8	−	2.73632e8i	0.196291	−	0.377866i
$899$		−	7.19874e8i		−	0.990780i
$900$		0			0
$901$	1.42577e8			0.194928
$902$	1.49477e8	+	7.76493e7i	0.203683	+	0.105808i
$903$		0			0
$904$	−9.23789e7	−	6.87946e8i	−0.125045	−	0.931213i
$905$	7.81214e7	−	1.99012e7i	0.105396	−	0.0268493i
$906$		0			0
$907$	8.69796e8			1.16572			0.582861	−	0.812572i	$-0.301933\pi$
$907$	8.69796e8			1.16572			0.582861	+	0.812572i	$0.301933\pi$
$908$	−3.04818e8	−	4.33733e8i	−0.407177	−	0.579382i
$909$		0			0
$910$	2.87817e8	+	6.72880e7i	0.381937	+	0.0892922i
$911$			3.98390e8i			0.526931i	0.964669	+	0.263466i	$0.0848655\pi$
$911$			3.98390e8i			0.526931i	−0.964669	+	0.263466i	$0.915134\pi$
$912$		0			0
$913$		−	5.87353e8i		−	0.771768i
$914$	7.19563e8	+	3.73793e8i	0.942388	+	0.489545i
$915$		0			0
$916$	−2.20476e8	−	3.13721e8i	−0.286863	−	0.408185i
$917$			932775.i			0.00120968i
$918$		0			0
$919$		−	1.03935e9i		−	1.33911i	−0.742762	−	0.669555i	$-0.766485\pi$
$919$		−	1.03935e9i		−	1.33911i	0.742762	−	0.669555i	$-0.233515\pi$
$920$	3.50778e8	−	1.41296e8i	0.450473	−	0.181455i
$921$		0			0
$922$	−3.50028e8	+	6.73814e8i	−0.446591	+	0.859700i
$923$	−7.41423e8			−0.942889
$924$		0			0
$925$	1.41597e8	+	2.59881e8i	0.178907	+	0.328359i
$926$	4.35545e8	−	8.38437e8i	0.548530	−	1.05594i
$927$		0			0
$928$	3.12276e8	+	3.37857e8i	0.390746	+	0.422755i
$929$	−9.01112e8			−1.12391			−0.561955	−	0.827168i	$-0.689951\pi$
$929$	−9.01112e8			−1.12391			−0.561955	+	0.827168i	$0.689951\pi$
$930$		0			0
$931$		−	7.54364e8i		−	0.934828i
$932$	−8.77268e7	+	6.16525e7i	−0.108364	+	0.0761557i
$933$		0			0
$934$	6.86346e8	−	1.32123e9i	0.842369	−	1.62158i
$935$	6.50734e8	−	1.65773e8i	0.796102	−	0.202805i
$936$		0			0
$937$			8.08145e7i			0.0982360i	0.998793	+	0.0491180i	$0.0156410\pi$
$937$			8.08145e7i			0.0982360i	−0.998793	+	0.0491180i	$0.984359\pi$
$938$	1.33812e7	−	2.57592e7i	0.0162139	−	0.0312122i
$939$		0			0
$940$	7.84697e8	+	6.72789e8i	0.944754	+	0.810019i
$941$	5.21062e8			0.625346			0.312673	−	0.949861i	$-0.398776\pi$
$941$	5.21062e8			0.625346			0.312673	+	0.949861i	$0.398776\pi$
$942$		0			0
$943$	6.95019e7			0.0828823
$944$	−5.39103e8	−	1.94117e8i	−0.640849	−	0.230753i
$945$		0			0
$946$	1.28230e9	+	6.66121e8i	1.51467	+	0.786828i
$947$	1.67327e9			1.97023			0.985114	−	0.171902i	$-0.0549911\pi$
$947$	1.67327e9			1.97023			0.985114	+	0.171902i	$0.0549911\pi$
$948$		0			0
$949$	2.10833e9			2.46684
$950$	8.58916e8	−	1.69906e7i	1.00180	−	0.0198170i
$951$		0			0
$952$	−1.81602e7	−	1.35239e8i	−0.0210480	−	0.156744i
$953$		−	5.89780e8i		−	0.681414i	−0.940170	−	0.340707i	$-0.889334\pi$
$953$		−	5.89780e8i		−	0.681414i	0.940170	−	0.340707i	$-0.110666\pi$
$954$		0			0
$955$	−1.42823e8	−	5.60647e8i	−0.163979	−	0.643694i
$956$	−2.11541e8	+	1.48666e8i	−0.242115	+	0.170153i
$957$		0			0
$958$	−3.56347e8	−	1.85112e8i	−0.405300	−	0.210542i
$959$			1.86885e8i			0.211895i
$960$		0			0
$961$	−1.74135e9			−1.96208
$962$	2.32495e8	−	4.47560e8i	0.261149	−	0.502720i
$963$		0			0
$964$	−3.42980e8	−	4.88035e8i	−0.382858	−	0.544778i
$965$	1.58542e8	+	6.22350e8i	0.176426	+	0.692552i
$966$		0			0
$967$	9.41406e8			1.04111			0.520556	−	0.853828i	$-0.325725\pi$
$967$	9.41406e8			1.04111			0.520556	+	0.853828i	$0.325725\pi$
$968$	7.27049e8	−	9.76297e7i	0.801563	−	0.107636i
$969$		0			0
$970$	−2.14954e8	−	5.02535e7i	−0.235521	−	0.0550619i
$971$			1.61734e9i			1.76662i	0.468787	+	0.883311i	$0.344691\pi$
$971$			1.61734e9i			1.76662i	−0.468787	+	0.883311i	$0.655309\pi$
$972$		0			0
$973$			2.74529e8i			0.298023i
$974$	4.01597e8	−	7.73085e8i	0.434623	−	0.836662i
$975$		0			0
$976$	−4.16183e8	+	1.15583e9i	−0.447646	+	1.24321i
$977$			6.67855e8i			0.716141i	0.933695	+	0.358070i	$0.116565\pi$
$977$			6.67855e8i			0.716141i	−0.933695	+	0.358070i	$0.883435\pi$
$978$		0			0
$979$		−	4.96972e7i		−	0.0529643i
$980$	−6.66624e8	−	5.71555e8i	−0.708277	−	0.607267i
$981$		0			0
$982$	1.21474e8	+	6.31026e7i	0.128277	+	0.0666366i
$983$	8.58744e7			0.0904073			0.0452036	−	0.998978i	$-0.485606\pi$
$983$	8.58744e7			0.0904073			0.0452036	+	0.998978i	$0.485606\pi$
$984$		0			0
$985$	−1.70414e8	−	6.68952e8i	−0.178318	−	0.699981i
$986$	2.99134e8	+	1.55392e8i	0.312057	+	0.162105i
$987$		0			0
$988$	−8.41783e8	−	1.19779e9i	−0.872830	−	1.24197i
$989$	5.96228e8			0.616344
$990$		0			0
$991$		−	6.76605e8i		−	0.695208i	−0.937642	−	0.347604i	$-0.886995\pi$
$991$		−	6.76605e8i		−	0.695208i	0.937642	−	0.347604i	$-0.113005\pi$
$992$	1.23379e9	−	1.14038e9i	1.26389	−	1.16819i
$993$		0			0
$994$	−1.40436e8	−	7.29525e7i	−0.142994	−	0.0742816i
$995$	−1.32398e8	−	5.19724e8i	−0.134404	−	0.527598i
$996$		0			0
$997$			1.53009e9i			1.54394i	0.635659	+	0.771970i	$0.280728\pi$
$997$			1.53009e9i			1.54394i	−0.635659	+	0.771970i	$0.719272\pi$
$998$	1.48014e8	+	7.68895e7i	0.148906	+	0.0773526i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.f.e.19.7		12
3.2	odd	2		20.7.d.d.19.6	yes	12
4.3	odd	2	inner	180.7.f.e.19.5		12
5.4	even	2	inner	180.7.f.e.19.6		12
12.11	even	2		20.7.d.d.19.8	yes	12
15.2	even	4		100.7.b.f.51.1		12
15.8	even	4		100.7.b.f.51.12		12
15.14	odd	2		20.7.d.d.19.7	yes	12
20.19	odd	2	inner	180.7.f.e.19.8		12
24.5	odd	2		320.7.h.f.319.10		12
24.11	even	2		320.7.h.f.319.4		12
60.23	odd	4		100.7.b.f.51.11		12
60.47	odd	4		100.7.b.f.51.2		12
60.59	even	2		20.7.d.d.19.5	✓	12
120.29	odd	2		320.7.h.f.319.3		12
120.59	even	2		320.7.h.f.319.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.5	✓	12	60.59	even	2
20.7.d.d.19.6	yes	12	3.2	odd	2
20.7.d.d.19.7	yes	12	15.14	odd	2
20.7.d.d.19.8	yes	12	12.11	even	2
100.7.b.f.51.1		12	15.2	even	4
100.7.b.f.51.2		12	60.47	odd	4
100.7.b.f.51.11		12	60.23	odd	4
100.7.b.f.51.12		12	15.8	even	4
180.7.f.e.19.5		12	4.3	odd	2	inner
180.7.f.e.19.6		12	5.4	even	2	inner
180.7.f.e.19.7		12	1.1	even	1	trivial
180.7.f.e.19.8		12	20.19	odd	2	inner
320.7.h.f.319.3		12	120.29	odd	2
320.7.h.f.319.4		12	24.11	even	2
320.7.h.f.319.9		12	120.59	even	2
320.7.h.f.319.10		12	24.5	odd	2

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.68788 - 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 + 30.8579i) q^{5} +88.8045 q^{7} +(-507.445 + 68.1408i) q^{8} +O(q^{10})\)	\(q+(3.68788 - 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 + 30.8579i) q^{5} +88.8045 q^{7} +(-507.445 + 68.1408i) q^{8} +(-227.649 + 973.743i) q^{10} +1790.06i q^{11} -3328.41i q^{13} +(327.500 - 630.447i) q^{14} +(-1387.65 + 3853.78i) q^{16} +3001.09i q^{17} +6872.67i q^{19} +(6073.32 + 5207.19i) q^{20} +(12708.1 + 6601.53i) q^{22} +5908.85 q^{23} +(13720.6 - 7475.70i) q^{25} +(-23629.3 - 12274.8i) q^{26} +(-3267.93 - 4650.02i) q^{28} +14040.2 q^{29} -51272.4i q^{31} +(22241.6 + 24063.5i) q^{32} +(21305.5 + 11067.6i) q^{34} +(-10757.0 + 2740.32i) q^{35} +18940.9i q^{37} +(48790.9 + 25345.6i) q^{38} +(59364.8 - 23912.7i) q^{40} +11762.3 q^{41} +100904. q^{43} +(93732.0 - 65872.8i) q^{44} +(21791.1 - 41948.5i) q^{46} +129204. q^{47} -109763. q^{49} +(-2472.19 - 124976. i) q^{50} +(-174284. + 122483. i) q^{52} -47508.5i q^{53} +(-55237.5 - 216833. i) q^{55} +(-45063.4 + 6051.21i) q^{56} +(51778.5 - 99675.1i) q^{58} +139889. i q^{59} +299920. q^{61} +(-363996. - 189086. i) q^{62} +(252858. - 69155.5i) q^{64} +(102708. + 403175. i) q^{65} +40858.7 q^{67} +(157144. - 110437. i) q^{68} +(-20216.3 + 86472.8i) q^{70} -222756. i q^{71} +633436. i q^{73} +(134467. + 69851.8i) q^{74} +(359870. - 252909. i) q^{76} +158966. i q^{77} -166771. i q^{79} +(49167.8 - 509634. i) q^{80} +(43378.0 - 83503.9i) q^{82} -328119. q^{83} +(-92607.1 - 363526. i) q^{85} +(372122. - 716345. i) q^{86} +(-121976. - 908359. i) q^{88} -27762.8 q^{89} -295578. i q^{91} +(-217441. - 309402. i) q^{92} +(476488. - 917254. i) q^{94} +(-212076. - 832496. i) q^{95} +220750. i q^{97} +(-404791. + 779235. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 64 q^{4} - 460 q^{5}+O(q^{10}) \) 12 * q + 64 * q^4 - 460 * q^5	\( 12 q + 64 q^{4} - 460 q^{5} + 2000 q^{10} - 512 q^{14} - 20928 q^{16} + 13760 q^{20} - 55700 q^{25} - 14496 q^{26} + 16072 q^{29} + 257216 q^{34} - 36800 q^{40} + 192136 q^{41} + 165120 q^{44} - 49472 q^{46} + 145796 q^{49} + 36000 q^{50} - 1078208 q^{56} + 215384 q^{61} - 6656 q^{64} - 710400 q^{65} + 530080 q^{70} + 1020384 q^{74} + 2515200 q^{76} + 127040 q^{80} - 44800 q^{85} + 5268832 q^{86} + 4346152 q^{89} + 4292992 q^{94}+O(q^{100}) \) 12 * q + 64 * q^4 - 460 * q^5 + 2000 * q^10 - 512 * q^14 - 20928 * q^16 + 13760 * q^20 - 55700 * q^25 - 14496 * q^26 + 16072 * q^29 + 257216 * q^34 - 36800 * q^40 + 192136 * q^41 + 165120 * q^44 - 49472 * q^46 + 145796 * q^49 + 36000 * q^50 - 1078208 * q^56 + 215384 * q^61 - 6656 * q^64 - 710400 * q^65 + 530080 * q^70 + 1020384 * q^74 + 2515200 * q^76 + 127040 * q^80 - 44800 * q^85 + 5268832 * q^86 + 4346152 * q^89 + 4292992 * q^94

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