LMFDB - Embedded newform 180.7.f.e.19.6

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			19.6
Root			$-3.06674 + 0.771446i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.7.f.e.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.68788 + 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 - 30.8579i) q^{5} -88.8045 q^{7} +(507.445 - 68.1408i) q^{8} +O(q^{10})$	\(q+(-3.68788 + 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 - 30.8579i) q^{5} -88.8045 q^{7} +(507.445 - 68.1408i) q^{8} +(665.785 - 746.143i) q^{10} +1790.06i q^{11} +3328.41i q^{13} +(327.500 - 630.447i) q^{14} +(-1387.65 + 3853.78i) q^{16} -3001.09i q^{17} +6872.67i q^{19} +(2841.74 + 7478.27i) q^{20} +(-12708.1 - 6601.53i) q^{22} -5908.85 q^{23} +(13720.6 + 7475.70i) q^{25} +(-23629.3 - 12274.8i) q^{26} +(3267.93 + 4650.02i) q^{28} +14040.2 q^{29} -51272.4i q^{31} +(-22241.6 - 24063.5i) q^{32} +(21305.5 + 11067.6i) q^{34} +(10757.0 + 2740.32i) q^{35} -18940.9i q^{37} +(-48790.9 - 25345.6i) q^{38} +(-63570.2 - 7404.68i) q^{40} +11762.3 q^{41} -100904. q^{43} +(93732.0 - 65872.8i) q^{44} +(21791.1 - 41948.5i) q^{46} -129204. q^{47} -109763. q^{49} +(-103672. + 69836.6i) q^{50} +(174284. - 122483. i) q^{52} +47508.5i q^{53} +(55237.5 - 216833. i) q^{55} +(-45063.4 + 6051.21i) q^{56} +(-51778.5 + 99675.1i) q^{58} +139889. i q^{59} +299920. q^{61} +(363996. + 189086. i) q^{62} +(252858. - 69155.5i) q^{64} +(102708. - 403175. i) q^{65} -40858.7 q^{67} +(-157144. + 110437. i) q^{68} +(-59124.7 + 66260.9i) q^{70} -222756. i q^{71} -633436. i q^{73} +(134467. + 69851.8i) q^{74} +(359870. - 252909. i) q^{76} -158966. i q^{77} -166771. i q^{79} +(287007. - 423994. i) q^{80} +(-43378.0 + 83503.9i) q^{82} +328119. q^{83} +(-92607.1 + 363526. i) q^{85} +(372122. - 716345. i) q^{86} +(121976. + 908359. i) q^{88} -27762.8 q^{89} -295578. i q^{91} +(217441. + 309402. i) q^{92} +(476488. - 917254. i) q^{94} +(212076. - 832496. i) q^{95} -220750. i q^{97} +(404791. - 779235. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.541322\pi$
$7$	−88.8045			−0.258905			−0.129453	+	0.991586i	$0.541322\pi$
$8$	507.445	−	68.1408i	0.991104	−	0.133088i
$9$		0			0
$10$	665.785	−	746.143i	0.665785	−	0.746143i
$11$			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	$0.273574\pi$
$13$			3328.41i			1.51498i	−0.652847	+	0.757490i	$0.726426\pi$
$14$	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	$-0.901202\pi$
$17$		−	3001.09i		−	0.610846i	0.952217	−	0.305423i	$-0.0987979\pi$
$18$		0			0
$19$			6872.67i			1.00199i	0.865449	+	0.500997i	$0.167033\pi$
$19$			6872.67i			1.00199i	−0.865449	+	0.500997i	$0.832967\pi$
$20$	2841.74	+	7478.27i	0.355217	+	0.934784i
$21$		0			0
$22$	−12708.1	−	6601.53i	−1.19348	−	0.619978i
$23$	−5908.85			−0.485646			−0.242823	−	0.970071i	$-0.578073\pi$
$23$	−5908.85			−0.485646			−0.242823	+	0.970071i	$0.578073\pi$
$24$		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	$-0.940134\pi$
$37$		−	18940.9i		−	0.373935i	0.982366	−	0.186967i	$-0.0598659\pi$
$38$	−48790.9	−	25345.6i	−0.889177	−	0.461903i
$39$		0			0
$40$	−63570.2	−	7404.68i	−0.993284	−	0.115698i
$41$	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	$-0.718819\pi$
$43$	−100904.			−1.26912			−0.634561	+	0.772873i	$0.718819\pi$
$44$	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	$-0.713774\pi$
$47$	−129204.			−1.24446			−0.622232	+	0.782833i	$0.713774\pi$
$48$		0			0
$49$	−109763.			−0.932968
$50$	−103672.	+	69836.6i	−0.829375	+	0.558693i
$51$		0			0
$52$	174284.	−	122483.i	1.23950	−	0.871093i
$53$			47508.5i			0.319112i	0.987189	+	0.159556i	$0.0510063\pi$
$53$			47508.5i			0.319112i	−0.987189	+	0.159556i	$0.948994\pi$
$54$		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	$-0.521638\pi$
$67$	−40858.7			−0.135850			−0.0679251	+	0.997690i	$0.521638\pi$
$68$	−157144.	+	110437.i	−0.499772	+	0.351229i
$69$		0			0
$70$	−59124.7	+	66260.9i	−0.172375	+	0.193180i
$71$		−	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	$-0.697204\pi$
$73$		−	633436.i		−	1.62830i	0.580656	−	0.814149i	$-0.302796\pi$
$74$	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	$-0.0540944\pi$
$80$	287007.	−	423994.i	0.560560	−	0.828114i
$81$		0			0
$82$	−43378.0	+	83503.9i	−0.0786734	+	0.151449i
$83$	328119.			0.573848			0.286924	−	0.957953i	$-0.407367\pi$
$83$	328119.			0.573848			0.286924	+	0.957953i	$0.407367\pi$
$84$		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	$-0.961410\pi$
$97$		−	220750.i		−	0.241872i	0.992660	−	0.120936i	$-0.0385895\pi$
$98$	404791.	−	779235.i	0.430084	−	0.827924i
$99$		0			0
$100$	−113460.	−	993543.i	−0.113460	−	0.993543i
$101$	−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	$-0.677557\pi$
$103$	−1.15683e6			−1.05866			−0.529332	+	0.848415i	$0.677557\pi$
$104$	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	$-0.718409\pi$
$107$	−1.55229e6			−1.26713			−0.633566	+	0.773689i	$0.718409\pi$
$108$		0			0
$109$	1.76722e6			1.36462			0.682310	−	0.731063i	$-0.260975\pi$
$109$	1.76722e6			1.36462			0.682310	+	0.731063i	$0.260975\pi$
$110$	1.33564e6	+	1.19180e6i	1.00349	+	0.895415i
$111$		0			0
$112$	123229.	−	342233.i	0.0877121	−	0.243595i
$113$		−	1.35571e6i		−	0.939572i	−0.882780	−	0.469786i	$-0.844331\pi$
$113$		−	1.35571e6i		−	0.939572i	0.882780	−	0.469786i	$-0.155669\pi$
$114$		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	$-0.426843\pi$
$127$	933285.			0.455620			0.227810	+	0.973706i	$0.426843\pi$
$128$	−441554.	+	2.05014e6i	−0.210549	+	0.977583i
$129$		0			0
$130$	2.48347e6	+	2.21601e6i	1.13039	+	1.00865i
$131$			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	$-0.865803\pi$
$137$		−	2.10446e6i		−	0.818425i	0.912439	−	0.409213i	$-0.134197\pi$
$138$		0			0
$139$			3.09139e6i			1.15109i	0.817770	+	0.575545i	$0.195210\pi$
$139$			3.09139e6i			1.15109i	−0.817770	+	0.575545i	$0.804790\pi$
$140$	−252359.	−	664104.i	−0.0919676	−	0.242020i
$141$		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	$-0.679864\pi$
$157$		−	6.53669e6i		−	1.68911i	0.535467	−	0.844556i	$-0.320136\pi$
$158$	1.18395e6	+	615031.i	0.300167	+	0.155929i
$159$		0			0
$160$	1.95160e6	+	3.60118e6i	0.476465	+	0.879193i
$161$	524733.			0.125736
$162$		0			0
$163$	−7.13681e6			−1.64794			−0.823970	−	0.566633i	$-0.808246\pi$
$163$	−7.13681e6			−1.64794			−0.823970	+	0.566633i	$0.808246\pi$
$164$	−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	$-0.337530\pi$
$167$	4.55070e6			0.977078			0.488539	+	0.872542i	$0.337530\pi$
$168$		0			0
$169$	−6.25151e6			−1.29516
$170$	−2.23924e6	−	1.99808e6i	−0.455779	−	0.406692i
$171$		0			0
$172$	3.71319e6	+	5.28358e6i	0.729729	+	1.03835i
$173$		−	8.29944e6i		−	1.60292i	−0.598051	−	0.801458i	$-0.704058\pi$
$173$		−	8.29944e6i		−	1.60292i	0.598051	−	0.801458i	$-0.295942\pi$
$174$		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
$190$	5.12800e6	+	4.57572e6i	0.747631	+	0.667113i
$191$			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	$0.116315\pi$
$193$			5.13781e6i			0.714671i	−0.933976	+	0.357335i	$0.883685\pi$
$194$	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	$-0.882378\pi$
$197$		−	5.52253e6i		−	0.722337i	0.932501	−	0.361168i	$-0.117622\pi$
$198$		0			0
$199$			4.29058e6i			0.544449i	0.962234	+	0.272224i	$0.0877593\pi$
$199$			4.29058e6i			0.544449i	−0.962234	+	0.272224i	$0.912241\pi$
$200$	7.47185e6	+	2.85858e6i	0.933981	+	0.357322i
$201$		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
$220$	−1.33866e7	+	5.08689e6i	−1.25719	+	0.477732i
$221$	9.98885e6			0.925420
$222$		0			0
$223$	6.50950e6			0.586993			0.293497	−	0.955960i	$-0.405181\pi$
$223$	6.50950e6			0.586993			0.293497	+	0.955960i	$0.405181\pi$
$224$	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	$-0.615204\pi$
$227$	−8.28329e6			−0.708150			−0.354075	+	0.935217i	$0.615204\pi$
$228$		0			0
$229$	5.99134e6			0.498904			0.249452	−	0.968387i	$-0.419749\pi$
$229$	5.99134e6			0.498904			0.249452	+	0.968387i	$0.419749\pi$
$230$	−3.93403e6	+	4.40885e6i	−0.323336	+	0.362362i
$231$		0			0
$232$	7.12463e6	−	956711.i	0.570556	−	0.0766155i
$233$			1.67538e6i			0.132448i	0.997805	+	0.0662239i	$0.0210952\pi$
$233$			1.67538e6i			0.132448i	−0.997805	+	0.0662239i	$0.978905\pi$
$234$		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
$250$	1.47129e7	−	5.26031e6i	0.941626	−	0.336660i
$251$		−	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	$0.157578\pi$
$257$			1.61283e7i			0.950146i	−0.879946	+	0.475073i	$0.842422\pi$
$258$		0			0
$259$			1.68204e6i			0.0968137i
$260$	−2.48908e7	+	9.45847e6i	−1.41618	+	0.538147i
$261$		0			0
$262$	−74568.5	−	38736.3i	−0.00414621	−	0.00215385i
$263$	−91845.2			−0.00504881			−0.00252441	−	0.999997i	$-0.500804\pi$
$263$	−91845.2			−0.00504881			−0.00252441	+	0.999997i	$0.500804\pi$
$264$		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	$0.0667742\pi$
$277$			8.85192e6i			0.416484i	−0.978077	+	0.208242i	$0.933226\pi$
$278$	−2.19466e7	−	1.14007e7i	−1.02149	−	0.530635i
$279$		0			0
$280$	5.64532e6	+	657569.i	0.257167	+	0.0299549i
$281$	−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	$-0.643875\pi$
$283$	−1.97987e7			−0.873528			−0.436764	+	0.899576i	$0.643875\pi$
$284$	−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
$290$	9.34775e6	−	1.04760e7i	0.383277	−	0.429538i
$291$		0			0
$292$	−3.31682e7	+	2.33099e7i	−1.33221	+	0.936250i
$293$			3.44412e7i			1.36923i	0.728906	+	0.684614i	$0.240029\pi$
$293$			3.44412e7i			1.36923i	−0.728906	+	0.684614i	$0.759971\pi$
$294$		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	$-0.391104\pi$
$307$	1.94134e7			0.670944			0.335472	+	0.942050i	$0.391104\pi$
$308$	−8.32382e6	+	5.84980e6i	−0.284886	+	0.200211i
$309$		0			0
$310$	−3.82565e7	−	3.41364e7i	−1.28416	−	1.14586i
$311$		−	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	$-0.974201\pi$
$313$		−	4.96526e6i		−	0.161923i	0.996717	−	0.0809616i	$-0.0257991\pi$
$314$	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	$-0.829865\pi$
$317$		−	3.24542e7i		−	1.01881i	0.860527	−	0.509405i	$-0.170135\pi$
$318$		0			0
$319$			2.51328e7i			0.774229i
$320$	−3.27630e7	+	574255.i	−0.999846	+	0.0175249i
$321$		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	$-0.990158\pi$
$337$		−	2.36631e6i		−	0.0618275i	0.999522	−	0.0309137i	$-0.00984172\pi$
$338$	2.30548e7	−	4.43811e7i	0.597050	−	1.14934i
$339$		0			0
$340$	2.24429e7	−	8.52830e6i	0.571009	−	0.216983i
$341$	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	$-0.359301\pi$
$347$	3.57456e7			0.855528			0.427764	+	0.903890i	$0.359301\pi$
$348$		0			0
$349$	2.95982e7			0.696288			0.348144	−	0.937441i	$-0.386812\pi$
$349$	2.95982e7			0.696288			0.348144	+	0.937441i	$0.386812\pi$
$350$	9.20652e6	−	6.20181e6i	0.214729	−	0.144649i
$351$		0			0
$352$	4.30752e7	−	3.98138e7i	0.987642	−	0.912863i
$353$			6.19569e7i			1.40853i	0.709938	+	0.704264i	$0.248723\pi$
$353$			6.19569e7i			1.40853i	−0.709938	+	0.704264i	$0.751277\pi$
$354$		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	$-0.548825\pi$
$367$	−1.51049e7			−0.305577			−0.152788	+	0.988259i	$0.548825\pi$
$368$	8.19940e6	−	2.27715e7i	0.164527	−	0.456928i
$369$		0			0
$370$	−1.41326e7	−	1.26106e7i	−0.279009	−	0.248960i
$371$		−	4.21896e6i		−	0.0826198i
$372$		0			0
$373$			5.32493e7i			1.02610i	0.858360	+	0.513048i	$0.171484\pi$
$373$			5.32493e7i			1.02610i	−0.858360	+	0.513048i	$0.828516\pi$
$374$	−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	$0.999038\pi$
$380$	−5.13957e7	+	1.95303e7i	−0.936647	+	0.355925i
$381$		0			0
$382$	−3.28584e7	−	1.70691e7i	−0.589463	−	0.306210i
$383$	8.05002e7			1.43285			0.716424	−	0.697665i	$-0.245777\pi$
$383$	8.05002e7			1.43285			0.716424	+	0.697665i	$0.245777\pi$
$384$		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	$-0.834592\pi$
$397$		−	6.21417e7i		−	0.993142i	0.867996	−	0.496571i	$-0.165408\pi$
$398$	−3.04600e7	−	1.58231e7i	−0.483148	−	0.250982i
$399$		0			0
$400$	−4.78491e7	+	4.25026e7i	−0.747642	+	0.664102i
$401$	−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	$0.800573\pi$
$410$	7.83119e6	−	8.77639e6i	0.113626	−	0.127340i
$411$		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
$430$	−6.71805e7	+	7.52890e7i	−0.844963	+	0.946948i
$431$		−	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	$0.224263\pi$
$433$			1.05162e8i			1.29537i	−0.761907	+	0.647687i	$0.775737\pi$
$434$	−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	$0.949476\pi$
$440$	1.32548e7	−	1.13795e8i	0.155603	−	1.33587i
$441$		0			0
$442$	−3.68376e7	+	7.09135e7i	−0.426604	+	0.821225i
$443$	−8.39480e7			−0.965604			−0.482802	−	0.875730i	$-0.660381\pi$
$443$	−8.39480e7			−0.965604			−0.482802	+	0.875730i	$0.660381\pi$
$444$		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	$-0.821825\pi$
$457$		−	1.01357e8i		−	1.06196i	0.847386	−	0.530978i	$-0.178175\pi$
$458$	−2.20953e7	+	4.25341e7i	−0.229987	+	0.442732i
$459$		0			0
$460$	−1.67914e7	−	4.41880e7i	−0.172510	−	0.453974i
$461$	−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	$-0.702830\pi$
$463$	−1.18102e8			−1.18991			−0.594955	+	0.803759i	$0.702830\pi$
$464$	−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	$-0.866759\pi$
$467$	−1.86109e8			−1.82733			−0.913663	+	0.406473i	$0.866759\pi$
$468$		0			0
$469$	3.62844e6			0.0351723
$470$	−8.60221e7	+	9.64047e7i	−0.828546	+	0.928549i
$471$		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	$-0.656254\pi$
$487$	−1.08896e8			−0.942816			−0.471408	+	0.881915i	$0.656254\pi$
$488$	1.52193e8	−	2.04368e7i	1.30959	−	0.175854i
$489$		0			0
$490$	−7.30784e7	+	8.18988e7i	−0.621156	+	0.696128i
$491$			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	$0.973263\pi$
$500$	−1.69150e7	+	1.23850e8i	−0.135320	+	0.990802i
$501$		0			0
$502$	1.84122e8	+	9.56463e7i	1.45544	+	0.756061i
$503$	1.34897e7			0.105998			0.0529991	−	0.998595i	$-0.483122\pi$
$503$	1.34897e7			0.105998			0.0529991	+	0.998595i	$0.483122\pi$
$504$		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
$520$	2.46458e7	−	2.11588e8i	0.175280	−	1.50481i
$521$	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	$-0.287093\pi$
$523$	1.77417e8			1.24020			0.620098	+	0.784525i	$0.287093\pi$
$524$	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
$530$	3.54481e7	+	3.16304e7i	0.238103	+	0.212460i
$531$		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	$-0.737333\pi$
$547$	−2.22069e8			−1.35683			−0.678416	+	0.734678i	$0.737333\pi$
$548$	−1.10195e8	+	7.74423e7i	−0.669605	+	0.470583i
$549$		0			0
$550$	−1.25012e8	−	1.85579e8i	−0.751386	−	1.11543i
$551$			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	$-0.692299\pi$
$557$		−	2.84443e8i		−	1.64600i	0.568042	−	0.823000i	$-0.307701\pi$
$558$		0			0
$559$		−	3.35850e8i		−	1.92269i
$560$	−2.54875e7	+	3.76526e7i	−0.145132	+	0.214403i
$561$		0			0
$562$	1.67560e7	−	3.22557e7i	0.0943974	−	0.181718i
$563$	4.28842e7			0.240310			0.120155	−	0.992755i	$-0.461661\pi$
$563$	4.28842e7			0.240310			0.120155	+	0.992755i	$0.461661\pi$
$564$		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	$-0.920632\pi$
$577$		−	9.48080e7i		−	0.493534i	0.969075	−	0.246767i	$-0.0793683\pi$
$578$	−5.58014e7	+	1.07419e8i	−0.288976	+	0.556287i
$579$		0			0
$580$	3.98985e7	+	1.04996e8i	0.204490	+	0.538134i
$581$	−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	$-0.540460\pi$
$587$	−5.12804e7			−0.253534			−0.126767	+	0.991932i	$0.540460\pi$
$588$		0			0
$589$	3.52378e8			1.72450
$590$	1.04377e8	+	9.31362e7i	0.508219	+	0.453484i
$591$		0			0
$592$	7.29942e7	+	2.62833e7i	0.351822	+	0.126682i
$593$		−	2.12368e7i		−	0.101842i	−0.998703	−	0.0509208i	$-0.983784\pi$
$593$		−	2.12368e7i		−	0.101842i	0.998703	−	0.0509208i	$-0.0162156\pi$
$594$		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	$-0.362275\pi$
$607$	1.87552e8			0.838602			0.419301	+	0.907847i	$0.362275\pi$
$608$	1.65381e8	−	1.52859e8i	0.735825	−	0.680112i
$609$		0			0
$610$	1.99682e8	−	2.23783e8i	0.879731	−	0.985912i
$611$		−	4.30044e8i		−	1.88534i
$612$		0			0
$613$			1.96888e7i			0.0854749i	0.999086	+	0.0427374i	$0.0136079\pi$
$613$			1.96888e7i			0.0854749i	−0.999086	+	0.0427374i	$0.986392\pi$
$614$	−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	$-0.780291\pi$
$617$		−	2.99111e8i		−	1.27344i	0.771096	−	0.636719i	$-0.219709\pi$
$618$		0			0
$619$		−	6.73241e7i		−	0.283856i	−0.989877	−	0.141928i	$-0.954670\pi$
$619$		−	6.73241e7i		−	0.283856i	0.989877	−	0.141928i	$-0.0453302\pi$
$620$	3.83429e8	−	1.45703e8i	1.60883	−	0.611353i
$621$		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
$640$	1.16749e8	−	2.34711e8i	0.445362	−	0.895351i
$641$	−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	$-0.822050\pi$
$643$	−4.50751e8			−1.69552			−0.847761	+	0.530378i	$0.822050\pi$
$644$	−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	$-0.304344\pi$
$647$	3.12382e8			1.15338			0.576691	+	0.816962i	$0.304344\pi$
$648$		0			0
$649$	−2.50410e8			−0.916048
$650$	−2.32445e8	−	3.45062e8i	−0.846408	−	1.25649i
$651$		0			0
$652$	2.62629e8	+	3.73701e8i	0.947544	+	1.34828i
$653$			1.75008e8i			0.628519i	0.949337	+	0.314260i	$0.101756\pi$
$653$			1.75008e8i			0.628519i	−0.949337	+	0.314260i	$0.898244\pi$
$654$		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
$670$	−2.72031e7	+	3.04865e7i	−0.0904471	+	0.101364i
$671$			5.36875e8i			1.77708i
$672$		0			0
$673$		−	4.42525e8i		−	1.45175i	−0.687826	−	0.725876i	$-0.741435\pi$
$673$		−	4.42525e8i		−	1.45175i	0.687826	−	0.725876i	$-0.258565\pi$
$674$	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	$-0.838773\pi$
$677$		−	3.01059e8i		−	0.970255i	0.874443	−	0.485128i	$-0.161227\pi$
$678$		0			0
$679$			1.96036e7i			0.0626218i
$680$	−2.22221e7	+	1.90780e8i	−0.0706738	+	0.606744i
$681$		0			0
$682$	−3.38476e8	+	6.51576e8i	−1.06703	+	2.05405i
$683$	−2.52236e8			−0.791673			−0.395836	−	0.918321i	$-0.629545\pi$
$683$	−2.52236e8			−0.791673			−0.395836	+	0.918321i	$0.629545\pi$
$684$		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
$700$	1.00758e7	+	8.82310e7i	0.0293754	+	0.257233i
$701$	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	$0.490405\pi$
$710$	−1.66208e8	−	1.48308e8i	−0.464383	−	0.414370i
$711$		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	$-0.792784\pi$
$727$	−6.11316e8			−1.59097			−0.795486	+	0.605972i	$0.792784\pi$
$728$	−2.01409e7	−	1.49990e8i	−0.0522018	−	0.388747i
$729$		0			0
$730$	−4.72634e8	−	4.21732e8i	−1.21494	−	1.08410i
$731$			3.02822e8i			0.775239i
$732$		0			0
$733$			5.86490e8i			1.48919i	0.667519	+	0.744593i	$0.267356\pi$
$733$			5.86490e8i			1.48919i	−0.667519	+	0.744593i	$0.732644\pi$
$734$	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	$0.744896\pi$
$740$	1.41645e8	−	5.38251e7i	0.349548	−	0.132828i
$741$		0			0
$742$	2.99516e7	+	1.55590e7i	0.0733175	+	0.0380864i
$743$	−3.73947e8			−0.911681			−0.455841	−	0.890061i	$-0.650661\pi$
$743$	−3.73947e8			−0.911681			−0.455841	+	0.890061i	$0.650661\pi$
$744$		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	$-0.991423\pi$
$757$		−	2.33748e7i		−	0.0538841i	0.999637	−	0.0269420i	$-0.00857696\pi$
$758$	−2.33580e6	−	1.21339e6i	−0.00536326	−	0.00278607i
$759$		0			0
$760$	5.08900e7	−	4.36897e8i	0.115929	−	0.995265i
$761$	−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	$0.745447\pi$
$770$	−1.18611e8	−	1.05837e8i	−0.259808	−	0.231828i
$771$		0			0
$772$	2.69028e8	−	1.89067e8i	0.584717	−	0.410926i
$773$			1.08448e8i			0.234793i	0.993085	+	0.117396i	$0.0374548\pi$
$773$			1.08448e8i			0.234793i	−0.993085	+	0.117396i	$0.962545\pi$
$774$		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	$-0.381917\pi$
$787$	3.53415e8			0.725039			0.362519	+	0.931976i	$0.381917\pi$
$788$	−2.89173e8	+	2.03225e8i	−0.590989	+	0.415334i
$789$		0			0
$790$	−1.24435e8	−	1.11034e8i	−0.252384	−	0.225203i
$791$			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	$0.188103\pi$
$797$			5.64122e8i			1.11429i	−0.830415	+	0.557145i	$0.811897\pi$
$798$		0			0
$799$			3.87753e8i			0.760176i
$800$	−1.25276e8	−	4.96437e8i	−0.244679	−	0.969604i
$801$		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
$820$	3.34255e7	+	8.79619e7i	0.0606228	+	0.159534i
$821$	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	$-0.146295\pi$
$823$	9.99192e8			1.79246			0.896230	+	0.443590i	$0.146295\pi$
$824$	−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	$-0.351497\pi$
$827$	5.08817e8			0.899591			0.449796	+	0.893131i	$0.351497\pi$
$828$		0			0
$829$	9.05552e8			1.58946			0.794730	−	0.606963i	$-0.207612\pi$
$829$	9.05552e8			1.58946			0.794730	+	0.606963i	$0.207612\pi$
$830$	2.18457e8	−	2.44824e8i	0.382059	−	0.428173i
$831$		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
$850$	2.09586e8	+	3.11128e8i	0.341276	+	0.506620i
$851$			1.11919e8i			0.181600i
$852$		0			0
$853$		−	1.56058e8i		−	0.251443i	−0.992066	−	0.125722i	$-0.959875\pi$
$853$		−	1.56058e8i		−	0.251443i	0.992066	−	0.125722i	$-0.0401246\pi$
$854$	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	$0.0869154\pi$
$857$			3.39476e8i			0.539345i	−0.962952	+	0.269672i	$0.913085\pi$
$858$		0			0
$859$		−	6.27544e8i		−	0.990068i	−0.868874	−	0.495034i	$-0.835156\pi$
$859$		−	6.27544e8i		−	0.990068i	0.868874	−	0.495034i	$-0.164844\pi$
$860$	−2.86743e8	−	7.54588e8i	−0.450814	−	1.18636i
$861$		0			0
$862$	8.97999e8	+	4.66486e8i	1.40202	+	0.728311i
$863$	−5.09291e8			−0.792381			−0.396190	−	0.918168i	$-0.629668\pi$
$863$	−5.09291e8			−0.792381			−0.396190	+	0.918168i	$0.629668\pi$
$864$		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	$-0.845154\pi$
$877$		−	6.30685e8i		−	0.935004i	0.883992	−	0.467502i	$-0.154846\pi$
$878$	−1.89872e8	−	9.86334e7i	−0.280529	−	0.145727i
$879$		0			0
$880$	7.58976e8	+	5.13760e8i	1.11373	+	0.753898i
$881$	−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	$-0.492396\pi$
$883$	3.28879e7			0.0477698			0.0238849	+	0.999715i	$0.492396\pi$
$884$	−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	$-0.445443\pi$
$887$	2.38053e8			0.341116			0.170558	+	0.985348i	$0.445443\pi$
$888$		0			0
$889$	−8.28799e7			−0.117962
$890$	−1.84841e7	+	2.07150e7i	−0.0262197	+	0.0293843i
$891$		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	$-0.698067\pi$
$907$	−8.69796e8			−1.16572			−0.582861	+	0.812572i	$0.698067\pi$
$908$	3.04818e8	+	4.33733e8i	0.407177	+	0.579382i
$909$		0			0
$910$	−2.20543e8	−	1.96791e8i	−0.292664	−	0.261145i
$911$			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	$-0.233515\pi$
$920$	3.75627e8	+	4.37532e7i	0.482385	+	0.0561884i
$921$		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	$-0.984359\pi$
$937$		−	8.08145e7i		−	0.0982360i	0.998793	−	0.0491180i	$-0.0156410\pi$
$938$	−1.33812e7	+	2.57592e7i	−0.0162139	+	0.0312122i
$939$		0			0
$940$	−3.67164e8	−	9.66223e8i	−0.442055	−	1.16330i
$941$	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	$-0.945009\pi$
$947$	−1.67327e9			−1.97023			−0.985114	+	0.171902i	$0.945009\pi$
$948$		0			0
$949$	2.10833e9			2.46684
$950$	−4.79964e8	−	7.12503e8i	−0.559807	−	0.831028i
$951$		0			0
$952$	1.81602e7	+	1.35239e8i	0.0210480	+	0.156744i
$953$			5.89780e8i			0.681414i	0.940170	+	0.340707i	$0.110666\pi$
$953$			5.89780e8i			0.681414i	−0.940170	+	0.340707i	$0.889334\pi$
$954$		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	$-0.674275\pi$
$967$	−9.41406e8			−1.04111			−0.520556	+	0.853828i	$0.674275\pi$
$968$	−7.27049e8	+	9.76297e7i	−0.801563	+	0.107636i
$969$		0			0
$970$	−1.64711e8	−	1.46972e8i	−0.180471	−	0.161035i
$971$			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	$-0.883435\pi$
$977$		−	6.67855e8i		−	0.716141i	0.933695	−	0.358070i	$-0.116565\pi$
$978$		0			0
$979$		−	4.96972e7i		−	0.0529643i
$980$	−3.11917e8	−	8.20836e8i	−0.331406	−	0.872123i
$981$		0			0
$982$	−1.21474e8	−	6.31026e7i	−0.128277	−	0.0666366i
$983$	−8.58744e7			−0.0904073			−0.0452036	−	0.998978i	$-0.514394\pi$
$983$	−8.58744e7			−0.0904073			−0.0452036	+	0.998978i	$0.514394\pi$
$984$		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	$-0.719272\pi$
$997$		−	1.53009e9i		−	1.54394i	0.635659	−	0.771970i	$-0.280728\pi$
$998$	−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.19.6		12
3.2	odd	2		20.7.d.d.19.7	yes	12
4.3	odd	2	inner	180.7.f.e.19.8		12
5.4	even	2	inner	180.7.f.e.19.7		12
12.11	even	2		20.7.d.d.19.5	✓	12
15.2	even	4		100.7.b.f.51.12		12
15.8	even	4		100.7.b.f.51.1		12
15.14	odd	2		20.7.d.d.19.6	yes	12
20.19	odd	2	inner	180.7.f.e.19.5		12
24.5	odd	2		320.7.h.f.319.3		12
24.11	even	2		320.7.h.f.319.9		12
60.23	odd	4		100.7.b.f.51.2		12
60.47	odd	4		100.7.b.f.51.11		12
60.59	even	2		20.7.d.d.19.8	yes	12
120.29	odd	2		320.7.h.f.319.10		12
120.59	even	2		320.7.h.f.319.4		12

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

\(f(q)\)	\(=\)	\(q+(-3.68788 + 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 - 30.8579i) q^{5} -88.8045 q^{7} +(507.445 - 68.1408i) q^{8} +O(q^{10})\)	\(q+(-3.68788 + 7.09927i) q^{2} +(-36.7991 - 52.3624i) q^{4} +(-121.131 - 30.8579i) q^{5} -88.8045 q^{7} +(507.445 - 68.1408i) q^{8} +(665.785 - 746.143i) q^{10} +1790.06i q^{11} +3328.41i q^{13} +(327.500 - 630.447i) q^{14} +(-1387.65 + 3853.78i) q^{16} -3001.09i q^{17} +6872.67i q^{19} +(2841.74 + 7478.27i) q^{20} +(-12708.1 - 6601.53i) q^{22} -5908.85 q^{23} +(13720.6 + 7475.70i) q^{25} +(-23629.3 - 12274.8i) q^{26} +(3267.93 + 4650.02i) q^{28} +14040.2 q^{29} -51272.4i q^{31} +(-22241.6 - 24063.5i) q^{32} +(21305.5 + 11067.6i) q^{34} +(10757.0 + 2740.32i) q^{35} -18940.9i q^{37} +(-48790.9 - 25345.6i) q^{38} +(-63570.2 - 7404.68i) q^{40} +11762.3 q^{41} -100904. q^{43} +(93732.0 - 65872.8i) q^{44} +(21791.1 - 41948.5i) q^{46} -129204. q^{47} -109763. q^{49} +(-103672. + 69836.6i) q^{50} +(174284. - 122483. i) q^{52} +47508.5i q^{53} +(55237.5 - 216833. i) q^{55} +(-45063.4 + 6051.21i) q^{56} +(-51778.5 + 99675.1i) q^{58} +139889. i q^{59} +299920. q^{61} +(363996. + 189086. i) q^{62} +(252858. - 69155.5i) q^{64} +(102708. - 403175. i) q^{65} -40858.7 q^{67} +(-157144. + 110437. i) q^{68} +(-59124.7 + 66260.9i) q^{70} -222756. i q^{71} -633436. i q^{73} +(134467. + 69851.8i) q^{74} +(359870. - 252909. i) q^{76} -158966. i q^{77} -166771. i q^{79} +(287007. - 423994. i) q^{80} +(-43378.0 + 83503.9i) q^{82} +328119. q^{83} +(-92607.1 + 363526. i) q^{85} +(372122. - 716345. i) q^{86} +(121976. + 908359. i) q^{88} -27762.8 q^{89} -295578. i q^{91} +(217441. + 309402. i) q^{92} +(476488. - 917254. i) q^{94} +(212076. - 832496. i) q^{95} -220750. i q^{97} +(404791. - 779235. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 64 q^{4} - 460 q^{5}+O(q^{10}) \) 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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