LMFDB - Embedded newform 75.9.d.c.74.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(74,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.74");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.d (of order $2$, degree $1$, not 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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + \cdots + 336685801 $ x^20 + 943x^18 + 318815x^16 + 48938090x^14 + 3842259173x^12 + 159675554657x^10 + 3390679484573x^8 + 32981662033730x^6 + 124592584990175x^4 + 133865237486743*x^2 + 336685801
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{22}\cdot 5^{32} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			74.7
Root			$-1.32388i$ of defining polynomial
Character	$\chi$	$=$	75.74
Dual form			75.9.d.c.74.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.27106 q^{2} +(39.9876 - 70.4414i) q^{3} -187.590 q^{4} +(-330.740 + 582.625i) q^{6} +860.291i q^{7} +3668.96 q^{8} +(-3362.98 - 5633.57i) q^{9} +O(q^{10})$	\(q-8.27106 q^{2} +(39.9876 - 70.4414i) q^{3} -187.590 q^{4} +(-330.740 + 582.625i) q^{6} +860.291i q^{7} +3668.96 q^{8} +(-3362.98 - 5633.57i) q^{9} +8660.22i q^{11} +(-7501.26 + 13214.1i) q^{12} +18472.1i q^{13} -7115.52i q^{14} +17676.8 q^{16} +110116. q^{17} +(27815.4 + 46595.6i) q^{18} +71227.1 q^{19} +(60600.1 + 34401.0i) q^{21} -71629.2i q^{22} -369004. q^{23} +(146713. - 258446. i) q^{24} -152783. i q^{26} +(-531314. + 11620.0i) q^{27} -161382. i q^{28} +306317. i q^{29} +1.39489e6 q^{31} -1.08546e6 q^{32} +(610038. + 346302. i) q^{33} -910773. q^{34} +(630860. + 1.05680e6i) q^{36} -3.68589e6i q^{37} -589123. q^{38} +(1.30120e6 + 738653. i) q^{39} -5.05129e6i q^{41} +(-501227. - 284533. i) q^{42} +1.42558e6i q^{43} -1.62457e6i q^{44} +3.05206e6 q^{46} +779661. q^{47} +(706852. - 1.24518e6i) q^{48} +5.02470e6 q^{49} +(4.40326e6 - 7.75670e6i) q^{51} -3.46516e6i q^{52} +7.55943e6 q^{53} +(4.39453e6 - 96109.4i) q^{54} +3.15637e6i q^{56} +(2.84820e6 - 5.01733e6i) q^{57} -2.53356e6i q^{58} -2.08194e7i q^{59} +2.03126e7 q^{61} -1.15372e7 q^{62} +(4.84651e6 - 2.89314e6i) q^{63} +4.45264e6 q^{64} +(-5.04566e6 - 2.86428e6i) q^{66} -1.37810e6i q^{67} -2.06565e7 q^{68} +(-1.47556e7 + 2.59932e7i) q^{69} -4.19202e6i q^{71} +(-1.23386e7 - 2.06693e7i) q^{72} +2.57861e7i q^{73} +3.04862e7i q^{74} -1.33615e7 q^{76} -7.45030e6 q^{77} +(-1.07623e7 - 6.10945e6i) q^{78} -1.07664e7 q^{79} +(-2.04275e7 + 3.78911e7i) q^{81} +4.17795e7i q^{82} -1.63457e7 q^{83} +(-1.13679e7 - 6.45327e6i) q^{84} -1.17910e7i q^{86} +(2.15774e7 + 1.22489e7i) q^{87} +3.17740e7i q^{88} -5.98434e7i q^{89} -1.58913e7 q^{91} +6.92213e7 q^{92} +(5.57782e7 - 9.82577e7i) q^{93} -6.44862e6 q^{94} +(-4.34049e7 + 7.64612e7i) q^{96} +1.07731e8i q^{97} -4.15596e7 q^{98} +(4.87879e7 - 2.91241e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9}+O(q^{10}) $ 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9	$ 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9} + 560772 q^{16} + 463032 q^{19} + 579144 q^{21} - 2272668 q^{24} + 1763240 q^{31} + 2222552 q^{34} - 1337324 q^{36} - 3653584 q^{39} - 50849208 q^{46} - 18708428 q^{49} - 55465384 q^{51} + 15959596 q^{54} + 44834040 q^{61} + 45870004 q^{64} - 54839600 q^{66} - 67125264 q^{69} + 397844872 q^{76} - 324621848 q^{79} - 187150780 q^{81} + 394693536 q^{84} + 888576928 q^{91} + 184100072 q^{94} - 721614812 q^{96} + 67930400 q^{99}+O(q^{100}) $ 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9 + 560772 * q^16 + 463032 * q^19 + 579144 * q^21 - 2272668 * q^24 + 1763240 * q^31 + 2222552 * q^34 - 1337324 * q^36 - 3653584 * q^39 - 50849208 * q^46 - 18708428 * q^49 - 55465384 * q^51 + 15959596 * q^54 + 44834040 * q^61 + 45870004 * q^64 - 54839600 * q^66 - 67125264 * q^69 + 397844872 * q^76 - 324621848 * q^79 - 187150780 * q^81 + 394693536 * q^84 + 888576928 * q^91 + 184100072 * q^94 - 721614812 * q^96 + 67930400 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−8.27106			−0.516941			−0.258471	−	0.966019i	$-0.583219\pi$
$2$	−8.27106			−0.516941			−0.258471	+	0.966019i	$0.583219\pi$
$3$	39.9876	−	70.4414i	0.493674	−	0.869647i
$3$	39.9876	−	70.4414i	0.493674	−	0.869647i
$4$	−187.590			−0.732772
$5$		0			0
$5$		0			0
$6$	−330.740	+	582.625i	−0.255201	+	0.449556i
$7$			860.291i			0.358305i	0.983821	+	0.179153i	$0.0573356\pi$
$7$			860.291i			0.358305i	−0.983821	+	0.179153i	$0.942664\pi$
$8$	3668.96			0.895741
$9$	−3362.98	−	5633.57i	−0.512571	−	0.858645i
$10$		0			0
$11$			8660.22i			0.591505i	0.955265	+	0.295752i	$0.0955703\pi$
$11$			8660.22i			0.591505i	−0.955265	+	0.295752i	$0.904430\pi$
$12$	−7501.26	+	13214.1i	−0.361751	+	0.637253i
$13$			18472.1i			0.646758i	0.946270	+	0.323379i	$0.104819\pi$
$13$			18472.1i			0.646758i	−0.946270	+	0.323379i	$0.895181\pi$
$14$		−	7115.52i		−	0.185223i
$15$		0			0
$16$	17676.8			0.269726
$17$	110116.			1.31842			0.659209	−	0.751960i	$-0.270891\pi$
$17$	110116.			1.31842			0.659209	+	0.751960i	$0.270891\pi$
$18$	27815.4	+	46595.6i	0.264969	+	0.443869i
$19$	71227.1			0.546551			0.273275	−	0.961936i	$-0.411893\pi$
$19$	71227.1			0.546551			0.273275	+	0.961936i	$0.411893\pi$
$20$		0			0
$21$	60600.1	+	34401.0i	0.311599	+	0.176886i
$22$		−	71629.2i		−	0.305773i
$23$	−369004.			−1.31862			−0.659311	−	0.751871i	$-0.729152\pi$
$23$	−369004.			−1.31862			−0.659311	+	0.751871i	$0.729152\pi$
$24$	146713.	−	258446.i	0.442204	−	0.778978i
$25$		0			0
$26$		−	152783.i		−	0.334336i
$27$	−531314.	+	11620.0i	−0.999761	+	0.0218650i
$28$		−	161382.i		−	0.262556i
$29$			306317.i			0.433090i	0.976273	+	0.216545i	$0.0694788\pi$
$29$			306317.i			0.433090i	−0.976273	+	0.216545i	$0.930521\pi$
$30$		0			0
$31$	1.39489e6			1.51040			0.755200	−	0.655494i	$-0.227540\pi$
$31$	1.39489e6			1.51040			0.755200	+	0.655494i	$0.227540\pi$
$32$	−1.08546e6			−1.03517
$33$	610038.	+	346302.i	0.514400	+	0.292011i
$34$	−910773.			−0.681545
$35$		0			0
$36$	630860.	+	1.05680e6i	0.375598	+	0.629191i
$37$		−	3.68589e6i		−	1.96669i	−0.181751	−	0.983345i	$-0.558177\pi$
$37$		−	3.68589e6i		−	1.96669i	0.181751	−	0.983345i	$-0.441823\pi$
$38$	−589123.			−0.282535
$39$	1.30120e6	+	738653.i	0.562451	+	0.319288i
$40$		0			0
$41$		−	5.05129e6i		−	1.78758i	−0.448481	−	0.893792i	$-0.648035\pi$
$41$		−	5.05129e6i		−	1.78758i	0.448481	−	0.893792i	$-0.351965\pi$
$42$	−501227.	−	284533.i	−0.161078	−	0.0914397i
$43$			1.42558e6i			0.416981i	0.978024	+	0.208491i	$0.0668551\pi$
$43$			1.42558e6i			0.416981i	−0.978024	+	0.208491i	$0.933145\pi$
$44$		−	1.62457e6i		−	0.433438i
$45$		0			0
$46$	3.05206e6			0.681650
$47$	779661.			0.159777			0.0798885	−	0.996804i	$-0.474544\pi$
$47$	779661.			0.159777			0.0798885	+	0.996804i	$0.474544\pi$
$48$	706852.	−	1.24518e6i	0.133157	−	0.234566i
$49$	5.02470e6			0.871617
$50$		0			0
$51$	4.40326e6	−	7.75670e6i	0.650869	−	1.14656i
$52$		−	3.46516e6i		−	0.473926i
$53$	7.55943e6			0.958044			0.479022	−	0.877803i	$-0.340991\pi$
$53$	7.55943e6			0.958044			0.479022	+	0.877803i	$0.340991\pi$
$54$	4.39453e6	−	96109.4i	0.516818	−	0.0113029i
$55$		0			0
$56$			3.15637e6i			0.320949i
$57$	2.84820e6	−	5.01733e6i	0.269818	−	0.475306i
$58$		−	2.53356e6i		−	0.223882i
$59$		−	2.08194e7i		−	1.71814i	−0.511856	−	0.859071i	$-0.671042\pi$
$59$		−	2.08194e7i		−	1.71814i	0.511856	−	0.859071i	$-0.328958\pi$
$60$		0			0
$61$	2.03126e7			1.46706			0.733528	−	0.679659i	$-0.237872\pi$
$61$	2.03126e7			1.46706			0.733528	+	0.679659i	$0.237872\pi$
$62$	−1.15372e7			−0.780788
$63$	4.84651e6	−	2.89314e6i	0.307657	−	0.183657i
$64$	4.45264e6			0.265398
$65$		0			0
$66$	−5.04566e6	−	2.86428e6i	−0.265915	−	0.150952i
$67$		−	1.37810e6i		−	0.0683884i	−0.999415	−	0.0341942i	$-0.989114\pi$
$67$		−	1.37810e6i		−	0.0683884i	0.999415	−	0.0341942i	$-0.0108865\pi$
$68$	−2.06565e7			−0.966100
$69$	−1.47556e7	+	2.59932e7i	−0.650969	+	1.14673i
$70$		0			0
$71$		−	4.19202e6i		−	0.164964i	−0.996593	−	0.0824821i	$-0.973715\pi$
$71$		−	4.19202e6i		−	0.164964i	0.996593	−	0.0824821i	$-0.0262847\pi$
$72$	−1.23386e7	−	2.06693e7i	−0.459131	−	0.769123i
$73$			2.57861e7i			0.908018i	0.890997	+	0.454009i	$0.150007\pi$
$73$			2.57861e7i			0.908018i	−0.890997	+	0.454009i	$0.849993\pi$
$74$			3.04862e7i			1.01666i
$75$		0			0
$76$	−1.33615e7			−0.400497
$77$	−7.45030e6			−0.211939
$78$	−1.07623e7	−	6.10945e6i	−0.290754	−	0.165053i
$79$	−1.07664e7			−0.276416			−0.138208	−	0.990403i	$-0.544134\pi$
$79$	−1.07664e7			−0.276416			−0.138208	+	0.990403i	$0.544134\pi$
$80$		0			0
$81$	−2.04275e7	+	3.78911e7i	−0.474542	+	0.880233i
$82$			4.17795e7i			0.924076i
$83$	−1.63457e7			−0.344422			−0.172211	−	0.985060i	$-0.555091\pi$
$83$	−1.63457e7			−0.344422			−0.172211	+	0.985060i	$0.555091\pi$
$84$	−1.13679e7	−	6.45327e6i	−0.228331	−	0.129617i
$85$		0			0
$86$		−	1.17910e7i		−	0.215555i
$87$	2.15774e7	+	1.22489e7i	0.376636	+	0.213806i
$88$			3.17740e7i			0.529835i
$89$		−	5.98434e7i		−	0.953798i	−0.878958	−	0.476899i	$-0.841761\pi$
$89$		−	5.98434e7i		−	0.953798i	0.878958	−	0.476899i	$-0.158239\pi$
$90$		0			0
$91$	−1.58913e7			−0.231737
$92$	6.92213e7			0.966248
$93$	5.57782e7	−	9.82577e7i	0.745646	−	1.31351i
$94$	−6.44862e6			−0.0825954
$95$		0			0
$96$	−4.34049e7	+	7.64612e7i	−0.511039	+	0.900236i
$97$			1.07731e8i			1.21690i	0.793593	+	0.608449i	$0.208208\pi$
$97$			1.07731e8i			1.21690i	−0.793593	+	0.608449i	$0.791792\pi$
$98$	−4.15596e7			−0.450575
$99$	4.87879e7	−	2.91241e7i	0.507892	−	0.303188i
$100$		0			0
$101$			7.89183e7i			0.758390i	0.925317	+	0.379195i	$0.123799\pi$
$101$			7.89183e7i			0.758390i	−0.925317	+	0.379195i	$0.876201\pi$
$102$	−3.64196e7	+	6.41561e7i	−0.336461	+	0.592703i
$103$			9.16877e6i			0.0814634i	0.999170	+	0.0407317i	$0.0129689\pi$
$103$			9.16877e6i			0.0814634i	−0.999170	+	0.0407317i	$0.987031\pi$
$104$			6.77731e7i			0.579328i
$105$		0			0
$106$	−6.25245e7			−0.495252
$107$	1.58104e8			1.20617			0.603084	−	0.797678i	$-0.293938\pi$
$107$	1.58104e8			1.20617			0.603084	+	0.797678i	$0.293938\pi$
$108$	9.96690e7	−	2.17978e6i	0.732597	−	0.0160221i
$109$	−6.69807e7			−0.474508			−0.237254	−	0.971448i	$-0.576247\pi$
$109$	−6.69807e7			−0.474508			−0.237254	+	0.971448i	$0.576247\pi$
$110$		0			0
$111$	−2.59639e8	−	1.47390e8i	−1.71032	−	0.970904i
$112$			1.52072e7i			0.0966443i
$113$	5.15107e7			0.315925			0.157962	−	0.987445i	$-0.449508\pi$
$113$	5.15107e7			0.315925			0.157962	+	0.987445i	$0.449508\pi$
$114$	−2.35576e7	+	4.14987e7i	−0.139480	+	0.245705i
$115$		0			0
$116$		−	5.74618e7i		−	0.317356i
$117$	1.04064e8	−	6.21211e7i	0.555335	−	0.331509i
$118$			1.72198e8i			0.888179i
$119$			9.47314e7i			0.472396i
$120$		0			0
$121$	1.39360e8			0.650122
$122$	−1.68007e8			−0.758382
$123$	−3.55820e8	−	2.01989e8i	−1.55457	−	0.882485i
$124$	−2.61666e8			−1.10678
$125$		0			0
$126$	−4.00857e7	+	2.39293e7i	−0.159041	+	0.0949398i
$127$		−	1.00091e8i		−	0.384751i	−0.981321	−	0.192376i	$-0.938381\pi$
$127$		−	1.00091e8i		−	0.384751i	0.981321	−	0.192376i	$-0.0616192\pi$
$128$	2.41049e8			0.897979
$129$	1.00420e8	+	5.70054e7i	0.362627	+	0.205853i
$130$		0			0
$131$			2.06368e8i			0.700741i	0.936611	+	0.350371i	$0.113944\pi$
$131$			2.06368e8i			0.700741i	−0.936611	+	0.350371i	$0.886056\pi$
$132$	−1.14437e8	−	6.49626e7i	−0.376938	−	0.213977i
$133$			6.12760e7i			0.195832i
$134$			1.13984e7i			0.0353528i
$135$		0			0
$136$	4.04009e8			1.18096
$137$	−5.13588e8			−1.45792			−0.728958	−	0.684558i	$-0.759995\pi$
$137$	−5.13588e8			−1.45792			−0.728958	+	0.684558i	$0.759995\pi$
$138$	1.22044e8	−	2.14991e8i	0.336513	−	0.592794i
$139$	4.42986e8			1.18667			0.593337	−	0.804955i	$-0.297810\pi$
$139$	4.42986e8			1.18667			0.593337	+	0.804955i	$0.297810\pi$
$140$		0			0
$141$	3.11768e7	−	5.49204e7i	0.0788778	−	0.138950i
$142$			3.46724e7i			0.0852768i
$143$	−1.59972e8			−0.382560
$144$	−5.94466e7	−	9.95833e7i	−0.138254	−	0.231599i
$145$		0			0
$146$		−	2.13279e8i		−	0.469392i
$147$	2.00926e8	−	3.53947e8i	0.430295	−	0.757999i
$148$			6.91435e8i			1.44113i
$149$		−	6.58947e8i		−	1.33692i	−0.743748	−	0.668460i	$-0.766954\pi$
$149$		−	6.58947e8i		−	1.33692i	0.743748	−	0.668460i	$-0.233046\pi$
$150$		0			0
$151$	9.73120e8			1.87180			0.935898	−	0.352270i	$-0.114590\pi$
$151$	9.73120e8			1.87180			0.935898	+	0.352270i	$0.114590\pi$
$152$	2.61329e8			0.489568
$153$	−3.70317e8	−	6.20344e8i	−0.675783	−	1.13205i
$154$	6.16219e7			0.109560
$155$		0			0
$156$	−2.44091e8	−	1.38564e8i	−0.412148	−	0.233965i
$157$			1.40153e8i			0.230677i	0.993326	+	0.115338i	$0.0367952\pi$
$157$			1.40153e8i			0.230677i	−0.993326	+	0.115338i	$0.963205\pi$
$158$	8.90496e7			0.142891
$159$	3.02284e8	−	5.32497e8i	0.472962	−	0.833160i
$160$		0			0
$161$		−	3.17451e8i		−	0.472469i
$162$	1.68957e8	−	3.13400e8i	0.245310	−	0.455029i
$163$			7.69236e8i			1.08970i	0.838532	+	0.544852i	$0.183414\pi$
$163$			7.69236e8i			1.08970i	−0.838532	+	0.544852i	$0.816586\pi$
$164$			9.47569e8i			1.30989i
$165$		0			0
$166$	1.35196e8			0.178046
$167$	1.29661e8			0.166703			0.0833513	−	0.996520i	$-0.473438\pi$
$167$	1.29661e8			0.166703			0.0833513	+	0.996520i	$0.473438\pi$
$168$	2.22339e8	+	1.26216e8i	0.279112	+	0.158444i
$169$	4.74514e8			0.581704
$170$		0			0
$171$	−2.39535e8	−	4.01263e8i	−0.280146	−	0.469293i
$172$		−	2.67423e8i		−	0.305552i
$173$	1.60800e8			0.179516			0.0897578	−	0.995964i	$-0.471391\pi$
$173$	1.60800e8			0.179516			0.0897578	+	0.995964i	$0.471391\pi$
$174$	−1.78468e8	−	1.01311e8i	−0.194698	−	0.110525i
$175$		0			0
$176$			1.53085e8i			0.159544i
$177$	−1.46654e9	−	8.32517e8i	−1.49418	−	0.848203i
$178$			4.94968e8i			0.493057i
$179$			6.02527e8i			0.586900i	0.955974	+	0.293450i	$0.0948034\pi$
$179$			6.02527e8i			0.586900i	−0.955974	+	0.293450i	$0.905197\pi$
$180$		0			0
$181$	1.13516e9			1.05765			0.528824	−	0.848732i	$-0.322633\pi$
$181$	1.13516e9			1.05765			0.528824	+	0.848732i	$0.322633\pi$
$182$	1.31438e8			0.119794
$183$	8.12254e8	−	1.43085e9i	0.724248	−	1.27582i
$184$	−1.35386e9			−1.18114
$185$		0			0
$186$	−4.61345e8	+	8.12695e8i	−0.385455	+	0.679010i
$187$			9.53625e8i			0.779850i
$188$	−1.46256e8			−0.117080
$189$	−9.99655e6	−	4.57084e8i	−0.00783435	−	0.358220i
$190$		0			0
$191$		−	7.00191e8i		−	0.526118i	−0.964780	−	0.263059i	$-0.915269\pi$
$191$		−	7.00191e8i		−	0.526118i	0.964780	−	0.263059i	$-0.0847314\pi$
$192$	1.78050e8	−	3.13650e8i	0.131020	−	0.230802i
$193$		−	1.04738e9i		−	0.754872i	−0.926036	−	0.377436i	$-0.876806\pi$
$193$		−	1.04738e9i		−	0.754872i	0.926036	−	0.377436i	$-0.123194\pi$
$194$		−	8.91051e8i		−	0.629065i
$195$		0			0
$196$	−9.42581e8			−0.638697
$197$	2.30634e8			0.153129			0.0765646	−	0.997065i	$-0.475605\pi$
$197$	2.30634e8			0.153129			0.0765646	+	0.997065i	$0.475605\pi$
$198$	−4.03528e8	+	2.40887e8i	−0.262550	+	0.156730i
$199$	1.31166e9			0.836389			0.418195	−	0.908357i	$-0.362663\pi$
$199$	1.31166e9			0.836389			0.418195	+	0.908357i	$0.362663\pi$
$200$		0			0
$201$	−9.70755e7	−	5.51070e7i	−0.0594737	−	0.0337616i
$202$		−	6.52738e8i		−	0.392043i
$203$	−2.63521e8			−0.155178
$204$	−8.26006e8	+	1.45508e9i	−0.476939	+	0.840166i
$205$		0			0
$206$		−	7.58355e7i		−	0.0421118i
$207$	1.24095e9	+	2.07881e9i	0.675887	+	1.13223i
$208$			3.26526e8i			0.174447i
$209$			6.16842e8i			0.323287i
$210$		0			0
$211$	−2.00097e9			−1.00951			−0.504756	−	0.863262i	$-0.668417\pi$
$211$	−2.00097e9			−1.00951			−0.504756	+	0.863262i	$0.668417\pi$
$212$	−1.41807e9			−0.702027
$213$	−2.95292e8	−	1.67629e8i	−0.143461	−	0.0814386i
$214$	−1.30769e9			−0.623518
$215$		0			0
$216$	−1.94937e9	+	4.26331e7i	−0.895527	+	0.0195854i
$217$			1.20001e9i			0.541184i
$218$	5.54001e8			0.245293
$219$	1.81641e9	+	1.03113e9i	0.789655	+	0.448265i
$220$		0			0
$221$			2.03406e9i			0.852697i
$222$	2.14749e9	+	1.21907e9i	0.884138	+	0.501900i
$223$			6.09667e8i			0.246532i	0.992374	+	0.123266i	$0.0393368\pi$
$223$			6.09667e8i			0.246532i	−0.992374	+	0.123266i	$0.960663\pi$
$224$		−	9.33810e8i		−	0.370908i
$225$		0			0
$226$	−4.26048e8			−0.163314
$227$	3.91198e9			1.47331			0.736654	−	0.676270i	$-0.236405\pi$
$227$	3.91198e9			1.47331			0.736654	+	0.676270i	$0.236405\pi$
$228$	−5.34293e8	+	9.41199e8i	−0.197715	+	0.348291i
$229$	−5.02295e8			−0.182649			−0.0913244	−	0.995821i	$-0.529110\pi$
$229$	−5.02295e8			−0.182649			−0.0913244	+	0.995821i	$0.529110\pi$
$230$		0			0
$231$	−2.97920e8	+	5.24810e8i	−0.104629	+	0.184312i
$232$			1.12386e9i			0.387937i
$233$	−3.16835e9			−1.07500			−0.537502	−	0.843263i	$-0.680632\pi$
$233$	−3.16835e9			−1.07500			−0.537502	+	0.843263i	$0.680632\pi$
$234$	−8.60716e8	+	5.13808e8i	−0.287076	+	0.171371i
$235$		0			0
$236$			3.90549e9i			1.25901i
$237$	−4.30523e8	+	7.58401e8i	−0.136459	+	0.240384i
$238$		−	7.83530e8i		−	0.244201i
$239$		−	4.48748e9i		−	1.37534i	−0.726022	−	0.687672i	$-0.758633\pi$
$239$		−	4.48748e9i		−	1.37534i	0.726022	−	0.687672i	$-0.241367\pi$
$240$		0			0
$241$	−1.29718e9			−0.384532			−0.192266	−	0.981343i	$-0.561584\pi$
$241$	−1.29718e9			−0.384532			−0.192266	+	0.981343i	$0.561584\pi$
$242$	−1.15265e9			−0.336075
$243$	1.85226e9	+	2.95412e9i	0.531223	+	0.847232i
$244$	−3.81044e9			−1.07502
$245$		0			0
$246$	2.94301e9	+	1.67066e9i	0.803620	+	0.456193i
$247$			1.31571e9i			0.353486i
$248$	5.11778e9			1.35293
$249$	−6.53625e8	+	1.15141e9i	−0.170032	+	0.299525i
$250$		0			0
$251$		−	2.67142e9i		−	0.673050i	−0.941675	−	0.336525i	$-0.890748\pi$
$251$		−	2.67142e9i		−	0.673050i	0.941675	−	0.336525i	$-0.109252\pi$
$252$	−9.09154e8	+	5.42723e8i	−0.225442	+	0.134579i
$253$		−	3.19566e9i		−	0.779970i
$254$			8.27858e8i			0.198894i
$255$		0			0
$256$	−3.13361e9			−0.729600
$257$	−3.44128e9			−0.788838			−0.394419	−	0.918931i	$-0.629054\pi$
$257$	−3.44128e9			−0.788838			−0.394419	+	0.918931i	$0.629054\pi$
$258$	−8.30576e8	−	4.71495e8i	−0.187457	−	0.106414i
$259$	3.17094e9			0.704675
$260$		0			0
$261$	1.72565e9	−	1.03014e9i	0.371871	−	0.221990i
$262$		−	1.70688e9i		−	0.362242i
$263$	−5.78459e9			−1.20906			−0.604532	−	0.796581i	$-0.706640\pi$
$263$	−5.78459e9			−1.20906			−0.604532	+	0.796581i	$0.706640\pi$
$264$	2.23820e9	+	1.27057e9i	0.460769	+	0.261566i
$265$		0			0
$266$		−	5.06817e8i		−	0.101234i
$267$	−4.21545e9	−	2.39300e9i	−0.829467	−	0.470865i
$268$			2.58518e8i			0.0501131i
$269$			7.11504e9i			1.35884i	0.733749	+	0.679420i	$0.237769\pi$
$269$			7.11504e9i			1.35884i	−0.733749	+	0.679420i	$0.762231\pi$
$270$		0			0
$271$	1.82473e9			0.338314			0.169157	−	0.985589i	$-0.445895\pi$
$271$	1.82473e9			0.338314			0.169157	+	0.985589i	$0.445895\pi$
$272$	1.94649e9			0.355612
$273$	−6.35457e8	+	1.11941e9i	−0.114402	+	0.201529i
$274$	4.24792e9			0.753657
$275$		0			0
$276$	2.76800e9	−	4.87605e9i	0.477012	−	0.840295i
$277$		−	8.53355e9i		−	1.44947i	−0.689025	−	0.724737i	$-0.741961\pi$
$277$		−	8.53355e9i		−	1.44947i	0.689025	−	0.724737i	$-0.258039\pi$
$278$	−3.66397e9			−0.613440
$279$	−4.69097e9	−	7.85819e9i	−0.774187	−	1.29690i
$280$		0			0
$281$		−	5.59999e9i		−	0.898177i	−0.893487	−	0.449088i	$-0.851749\pi$
$281$		−	5.59999e9i		−	0.898177i	0.893487	−	0.449088i	$-0.148251\pi$
$282$	−2.57865e8	+	4.54250e8i	−0.0407752	+	0.0718288i
$283$		−	1.05463e10i		−	1.64420i	−0.569344	−	0.822099i	$-0.692803\pi$
$283$		−	1.05463e10i		−	1.64420i	0.569344	−	0.822099i	$-0.307197\pi$
$284$			7.86379e8i			0.120881i
$285$		0			0
$286$	1.32314e9			0.197761
$287$	4.34558e9			0.640501
$288$	3.65037e9	+	6.11500e9i	0.530600	+	0.888847i
$289$	5.14969e9			0.738227
$290$		0			0
$291$	7.58873e9	+	4.30791e9i	1.05827	+	0.600752i
$292$		−	4.83721e9i		−	0.665370i
$293$	7.76813e9			1.05401			0.527006	−	0.849861i	$-0.323314\pi$
$293$	7.76813e9			1.05401			0.527006	+	0.849861i	$0.323314\pi$
$294$	−1.66187e9	+	2.92752e9i	−0.222437	+	0.391841i
$295$		0			0
$296$		−	1.35234e10i		−	1.76164i
$297$	−1.00631e8	−	4.60129e9i	−0.0129333	−	0.591363i
$298$			5.45019e9i			0.691109i
$299$		−	6.81627e9i		−	0.852829i
$300$		0			0
$301$	−1.22641e9			−0.149407
$302$	−8.04874e9			−0.967609
$303$	5.55912e9	+	3.15576e9i	0.659531	+	0.374398i
$304$	1.25906e9			0.147419
$305$		0			0
$306$	3.06291e9	+	5.13090e9i	0.349340	+	0.585205i
$307$			4.13874e9i			0.465924i	0.972486	+	0.232962i	$0.0748417\pi$
$307$			4.13874e9i			0.465924i	−0.972486	+	0.232962i	$0.925158\pi$
$308$	1.39760e9			0.155303
$309$	6.45861e8	+	3.66637e8i	0.0708444	+	0.0402164i
$310$		0			0
$311$			1.50911e10i			1.61316i	0.591124	+	0.806581i	$0.298685\pi$
$311$			1.50911e10i			1.61316i	−0.591124	+	0.806581i	$0.701315\pi$
$312$	4.77403e9	+	2.71009e9i	0.503810	+	0.285999i
$313$		−	2.10030e9i		−	0.218829i	−0.993996	−	0.109414i	$-0.965102\pi$
$313$		−	2.10030e9i		−	0.218829i	0.993996	−	0.109414i	$-0.0348976\pi$
$314$		−	1.15921e9i		−	0.119246i
$315$		0			0
$316$	2.01967e9			0.202550
$317$	−2.98247e9			−0.295351			−0.147676	−	0.989036i	$-0.547179\pi$
$317$	−2.98247e9			−0.295351			−0.147676	+	0.989036i	$0.547179\pi$
$318$	−2.50021e9	+	4.40431e9i	−0.244493	+	0.430695i
$319$	−2.65277e9			−0.256175
$320$		0			0
$321$	6.32221e9	−	1.11371e10i	0.595454	−	1.04894i
$322$			2.62566e9i			0.244239i
$323$	7.84321e9			0.720583
$324$	3.83198e9	−	7.10798e9i	0.347731	−	0.645010i
$325$		0			0
$326$		−	6.36239e9i		−	0.563313i
$327$	−2.67840e9	+	4.71821e9i	−0.234253	+	0.412655i
$328$		−	1.85330e10i		−	1.60121i
$329$			6.70735e8i			0.0572490i
$330$		0			0
$331$	−7.32884e9			−0.610553			−0.305277	−	0.952264i	$-0.598749\pi$
$331$	−7.32884e9			−0.610553			−0.305277	+	0.952264i	$0.598749\pi$
$332$	3.06628e9			0.252383
$333$	−2.07647e10	+	1.23956e10i	−1.68869	+	1.00807i
$334$	−1.07243e9			−0.0861754
$335$		0			0
$336$	1.07121e9	+	6.08098e8i	0.0840464	+	0.0477108i
$337$		−	1.13784e10i		−	0.882191i	−0.897460	−	0.441095i	$-0.854590\pi$
$337$		−	1.13784e10i		−	0.882191i	0.897460	−	0.441095i	$-0.145410\pi$
$338$	−3.92473e9			−0.300707
$339$	2.05979e9	−	3.62848e9i	0.155964	−	0.274743i
$340$		0			0
$341$			1.20800e10i			0.893408i
$342$	1.98121e9	+	3.31887e9i	0.144819	+	0.242597i
$343$			9.28211e9i			0.670610i
$344$			5.23038e9i			0.373507i
$345$		0			0
$346$	−1.32999e9			−0.0927990
$347$	3.88679e9			0.268086			0.134043	−	0.990976i	$-0.457204\pi$
$347$	3.88679e9			0.268086			0.134043	+	0.990976i	$0.457204\pi$
$348$	−4.04769e9	−	2.29776e9i	−0.275988	−	0.156671i
$349$	−4.13731e9			−0.278879			−0.139440	−	0.990231i	$-0.544530\pi$
$349$	−4.13731e9			−0.278879			−0.139440	+	0.990231i	$0.544530\pi$
$350$		0			0
$351$	−2.14645e8	−	9.81446e9i	−0.0141414	−	0.646603i
$352$		−	9.40031e9i		−	0.612310i
$353$	−4.18048e9			−0.269232			−0.134616	−	0.990898i	$-0.542980\pi$
$353$	−4.18048e9			−0.269232			−0.134616	+	0.990898i	$0.542980\pi$
$354$	1.21299e10	+	6.88580e9i	0.772402	+	0.438471i
$355$		0			0
$356$			1.12260e10i			0.698916i
$357$	6.67302e9	+	3.78809e9i	0.410818	+	0.233210i
$358$		−	4.98353e9i		−	0.303393i
$359$			1.48870e10i			0.896249i	0.893971	+	0.448124i	$0.147908\pi$
$359$			1.48870e10i			0.896249i	−0.893971	+	0.448124i	$0.852092\pi$
$360$		0			0
$361$	−1.19103e10			−0.701282
$362$	−9.38894e9			−0.546742
$363$	5.57266e9	−	9.81668e9i	0.320949	−	0.565377i
$364$	2.98105e9			0.169810
$365$		0			0
$366$	−6.71820e9	+	1.18346e10i	−0.374394	+	0.659525i
$367$			1.50821e10i			0.831374i	0.909508	+	0.415687i	$0.136459\pi$
$367$			1.50821e10i			0.831374i	−0.909508	+	0.415687i	$0.863541\pi$
$368$	−6.52280e9			−0.355667
$369$	−2.84568e10	+	1.69874e10i	−1.53490	+	0.916265i
$370$		0			0
$371$			6.50331e9i			0.343272i
$372$	−1.04634e10	+	1.84321e10i	−0.546388	+	0.962506i
$373$			6.56465e9i			0.339138i	0.985518	+	0.169569i	$0.0542375\pi$
$373$			6.56465e9i			0.339138i	−0.985518	+	0.169569i	$0.945762\pi$
$374$		−	7.88749e9i		−	0.403137i
$375$		0			0
$376$	2.86054e9			0.143119
$377$	−5.65829e9			−0.280105
$378$	8.26820e7	+	3.78057e9i	0.00404990	+	0.185178i
$379$	−2.75446e10			−1.33499			−0.667497	−	0.744612i	$-0.732634\pi$
$379$	−2.75446e10			−1.33499			−0.667497	+	0.744612i	$0.732634\pi$
$380$		0			0
$381$	−7.05055e9	−	4.00240e9i	−0.334598	−	0.189942i
$382$			5.79132e9i			0.271972i
$383$	1.76457e10			0.820058			0.410029	−	0.912073i	$-0.365519\pi$
$383$	1.76457e10			0.820058			0.410029	+	0.912073i	$0.365519\pi$
$384$	9.63899e9	−	1.69798e10i	0.443309	−	0.780924i
$385$		0			0
$386$			8.66290e9i			0.390224i
$387$	8.03108e9	−	4.79418e9i	0.358039	−	0.213733i
$388$		−	2.02092e10i		−	0.891709i
$389$		−	1.70171e9i		−	0.0743167i	−0.999309	−	0.0371583i	$-0.988169\pi$
$389$		−	1.70171e9i		−	0.0743167i	0.999309	−	0.0371583i	$-0.0118306\pi$
$390$		0			0
$391$	−4.06331e10			−1.73849
$392$	1.84354e10			0.780744
$393$	1.45369e10	+	8.25218e9i	0.609397	+	0.345938i
$394$	−1.90759e9			−0.0791588
$395$		0			0
$396$	−9.15211e9	+	5.46338e9i	−0.372169	+	0.222168i
$397$			3.12255e10i			1.25703i	0.777796	+	0.628517i	$0.216338\pi$
$397$			3.12255e10i			1.25703i	−0.777796	+	0.628517i	$0.783662\pi$
$398$	−1.08488e10			−0.432364
$399$	4.31637e9	+	2.45028e9i	0.170305	+	0.0966773i
$400$		0			0
$401$		−	1.81268e10i		−	0.701041i	−0.936555	−	0.350521i	$-0.886005\pi$
$401$		−	1.81268e10i		−	0.701041i	0.936555	−	0.350521i	$-0.113995\pi$
$402$	8.02917e8	+	4.55794e8i	0.0307444	+	0.0174528i
$403$			2.57664e10i			0.976863i
$404$		−	1.48043e10i		−	0.555726i
$405$		0			0
$406$	2.17960e9			0.0802182
$407$	3.19206e10			1.16331
$408$	1.61554e10	−	2.84590e10i	0.583011	−	1.02702i
$409$	1.54793e10			0.553171			0.276585	−	0.960989i	$-0.410797\pi$
$409$	1.54793e10			0.553171			0.276585	+	0.960989i	$0.410797\pi$
$410$		0			0
$411$	−2.05372e10	+	3.61778e10i	−0.719736	+	1.26787i
$412$		−	1.71997e9i		−	0.0596941i
$413$	1.79107e10			0.615620
$414$	−1.02640e10	−	1.71940e10i	−0.349394	−	0.585295i
$415$		0			0
$416$		−	2.00506e10i		−	0.669507i
$417$	1.77140e10	−	3.12046e10i	0.585830	−	1.03199i
$418$		−	5.10194e9i		−	0.167121i
$419$			3.93876e10i			1.27792i	0.769240	+	0.638960i	$0.220635\pi$
$419$			3.93876e10i			1.27792i	−0.769240	+	0.638960i	$0.779365\pi$
$420$		0			0
$421$	4.76055e10			1.51540			0.757702	−	0.652601i	$-0.226322\pi$
$421$	4.76055e10			1.51540			0.757702	+	0.652601i	$0.226322\pi$
$422$	1.65502e10			0.521858
$423$	−2.62198e9	−	4.39227e9i	−0.0818971	−	0.137192i
$424$	2.77352e10			0.858159
$425$		0			0
$426$	2.44237e9	+	1.38647e9i	0.0741607	+	0.0420990i
$427$			1.74748e10i			0.525654i
$428$	−2.96587e10			−0.883846
$429$	−6.39690e9	+	1.12686e10i	−0.188860	+	0.332692i
$430$		0			0
$431$		−	3.36447e10i		−	0.975007i	−0.873121	−	0.487503i	$-0.837908\pi$
$431$		−	3.36447e10i		−	0.975007i	0.873121	−	0.487503i	$-0.162092\pi$
$432$	−9.39192e9	+	2.05403e8i	−0.269662	+	0.00589756i
$433$			4.21393e10i			1.19877i	0.800461	+	0.599384i	$0.204588\pi$
$433$			4.21393e10i			1.19877i	−0.800461	+	0.599384i	$0.795412\pi$
$434$		−	9.92533e9i		−	0.279760i
$435$		0			0
$436$	1.25649e10			0.347706
$437$	−2.62831e10			−0.720694
$438$	−1.50236e10	−	8.52850e9i	−0.408205	−	0.231727i
$439$	1.50964e10			0.406458			0.203229	−	0.979131i	$-0.434856\pi$
$439$	1.50964e10			0.406458			0.203229	+	0.979131i	$0.434856\pi$
$440$		0			0
$441$	−1.68980e10	−	2.83070e10i	−0.446766	−	0.748410i
$442$		−	1.68238e10i		−	0.440794i
$443$	−2.67455e10			−0.694442			−0.347221	−	0.937783i	$-0.612875\pi$
$443$	−2.67455e10			−0.694442			−0.347221	+	0.937783i	$0.612875\pi$
$444$	4.87056e10	+	2.76488e10i	1.25328	+	0.711451i
$445$		0			0
$446$		−	5.04259e9i		−	0.127443i
$447$	−4.64172e10	−	2.63497e10i	−1.16265	−	0.660003i
$448$			3.83056e9i			0.0950934i
$449$		−	7.24234e10i		−	1.78194i	−0.454061	−	0.890970i	$-0.650025\pi$
$449$		−	7.24234e10i		−	1.78194i	0.454061	−	0.890970i	$-0.349975\pi$
$450$		0			0
$451$	4.37452e10			1.05736
$452$	−9.66286e9			−0.231501
$453$	3.89128e10	−	6.85479e10i	0.924058	−	1.62780i
$454$	−3.23562e10			−0.761613
$455$		0			0
$456$	1.04499e10	−	1.84084e10i	0.241687	−	0.425751i
$457$			1.17186e10i			0.268665i	0.990936	+	0.134332i	$0.0428890\pi$
$457$			1.17186e10i			0.268665i	−0.990936	+	0.134332i	$0.957111\pi$
$458$	4.15451e9			0.0944187
$459$	−5.85060e10	+	1.27954e9i	−1.31810	+	0.0288272i
$460$		0			0
$461$			8.60209e10i			1.90458i	0.305189	+	0.952292i	$0.401280\pi$
$461$			8.60209e10i			1.90458i	−0.305189	+	0.952292i	$0.598720\pi$
$462$	2.46411e9	−	4.34073e9i	0.0540870	−	0.0952786i
$463$			3.65148e10i			0.794594i	0.917690	+	0.397297i	$0.130052\pi$
$463$			3.65148e10i			0.794594i	−0.917690	+	0.397297i	$0.869948\pi$
$464$			5.41469e9i			0.116816i
$465$		0			0
$466$	2.62056e10			0.555714
$467$	−8.61531e10			−1.81135			−0.905677	−	0.423969i	$-0.860637\pi$
$467$	−8.61531e10			−1.81135			−0.905677	+	0.423969i	$0.860637\pi$
$468$	−1.95212e10	+	1.16533e10i	−0.406934	+	0.242921i
$469$	1.18557e9			0.0245039
$470$		0			0
$471$	9.87257e9	+	5.60438e9i	0.200607	+	0.113879i
$472$		−	7.63853e10i		−	1.53901i
$473$	−1.23458e10			−0.246646
$474$	3.56088e9	−	6.27278e9i	0.0705415	−	0.124264i
$475$		0			0
$476$		−	1.77706e10i		−	0.346159i
$477$	−2.54222e10	−	4.25865e10i	−0.491066	−	0.822619i
$478$			3.71162e10i			0.710972i
$479$			4.44469e10i			0.844306i	0.906525	+	0.422153i	$0.138725\pi$
$479$			4.44469e10i			0.844306i	−0.906525	+	0.422153i	$0.861275\pi$
$480$		0			0
$481$	6.80860e10			1.27197
$482$	1.07291e10			0.198781
$483$	−2.23617e10	−	1.26941e10i	−0.410881	−	0.233246i
$484$	−2.61424e10			−0.476391
$485$		0			0
$486$	−1.53202e10	−	2.44337e10i	−0.274611	−	0.437969i
$487$			4.69494e9i			0.0834668i	0.999129	+	0.0417334i	$0.0132880\pi$
$487$			4.69494e9i			0.0834668i	−0.999129	+	0.0417334i	$0.986712\pi$
$488$	7.45262e10			1.31410
$489$	5.41860e10	+	3.07599e10i	0.947658	+	0.537959i
$490$		0			0
$491$		−	5.52069e10i		−	0.949876i	−0.880019	−	0.474938i	$-0.842470\pi$
$491$		−	5.52069e10i		−	0.949876i	0.880019	−	0.474938i	$-0.157530\pi$
$492$	6.67481e10	+	3.78910e10i	1.13914	+	0.646660i
$493$			3.37302e10i			0.570994i
$494$		−	1.08823e10i		−	0.182732i
$495$		0			0
$496$	2.46571e10			0.407394
$497$	3.60635e9			0.0591075
$498$	5.40617e9	−	9.52341e9i	0.0878967	−	0.154837i
$499$	1.49484e10			0.241097			0.120548	−	0.992707i	$-0.461535\pi$
$499$	1.49484e10			0.241097			0.120548	+	0.992707i	$0.461535\pi$
$500$		0			0
$501$	5.18482e9	−	9.13347e9i	0.0822968	−	0.144972i
$502$			2.20955e10i			0.347927i
$503$	−4.72327e10			−0.737854			−0.368927	−	0.929458i	$-0.620275\pi$
$503$	−4.72327e10			−0.737854			−0.368927	+	0.929458i	$0.620275\pi$
$504$	1.77816e10	−	1.06148e10i	0.275581	−	0.164509i
$505$		0			0
$506$			2.64315e10i			0.403199i
$507$	1.89747e10	−	3.34254e10i	0.287172	−	0.505877i
$508$			1.87760e10i			0.281935i
$509$		−	5.95408e10i		−	0.887041i	−0.896264	−	0.443520i	$-0.853729\pi$
$509$		−	5.95408e10i		−	0.887041i	0.896264	−	0.443520i	$-0.146271\pi$
$510$		0			0
$511$	−2.21836e10			−0.325348
$512$	−3.57904e10			−0.520818
$513$	−3.78439e10	+	8.27656e8i	−0.546420	+	0.0119503i
$514$	2.84630e10			0.407783
$515$		0			0
$516$	−1.88377e10	−	1.06936e10i	−0.265722	−	0.150843i
$517$			6.75204e9i			0.0945089i
$518$	−2.62270e10			−0.364276
$519$	6.43002e9	−	1.13270e10i	0.0886222	−	0.156115i
$520$		0			0
$521$		−	5.61267e10i		−	0.761761i	−0.924624	−	0.380880i	$-0.875621\pi$
$521$		−	5.61267e10i		−	0.761761i	0.924624	−	0.380880i	$-0.124379\pi$
$522$	−1.42730e10	+	8.52032e9i	−0.192235	+	0.114756i
$523$		−	3.49100e10i		−	0.466599i	−0.972405	−	0.233299i	$-0.925048\pi$
$523$		−	3.49100e10i		−	0.466599i	0.972405	−	0.233299i	$-0.0749522\pi$
$524$		−	3.87125e10i		−	0.513483i
$525$		0			0
$526$	4.78447e10			0.625015
$527$	1.53599e11			1.99134
$528$	1.07835e10	+	6.12149e9i	0.138747	+	0.0787629i
$529$	5.78531e10			0.738762
$530$		0			0
$531$	−1.17287e11	+	7.00151e10i	−1.47527	+	0.880671i
$532$		−	1.14947e10i		−	0.143500i
$533$	9.33076e10			1.15613
$534$	3.48663e10	+	1.97926e10i	0.428786	+	0.243410i
$535$		0			0
$536$		−	5.05620e9i		−	0.0612583i
$537$	4.24428e10	+	2.40936e10i	0.510396	+	0.289738i
$538$		−	5.88489e10i		−	0.702441i
$539$			4.35150e10i			0.515566i
$540$		0			0
$541$	−3.13461e10			−0.365927			−0.182963	−	0.983120i	$-0.558569\pi$
$541$	−3.13461e10			−0.365927			−0.182963	+	0.983120i	$0.558569\pi$
$542$	−1.50924e10			−0.174889
$543$	4.53922e10	−	7.99619e10i	0.522133	−	0.919780i
$544$	−1.19526e11			−1.36479
$545$		0			0
$546$	5.25590e9	−	9.25869e9i	0.0591394	−	0.104179i
$547$			5.00255e10i			0.558781i	0.960178	+	0.279391i	$0.0901324\pi$
$547$			5.00255e10i			0.558781i	−0.960178	+	0.279391i	$0.909868\pi$
$548$	9.63437e10			1.06832
$549$	−6.83110e10	−	1.14433e11i	−0.751971	−	1.25968i
$550$		0			0
$551$			2.18180e10i			0.236706i
$552$	−5.41377e10	+	9.53678e10i	−0.583100	+	1.02718i
$553$		−	9.26224e9i		−	0.0990412i
$554$			7.05815e10i			0.749293i
$555$		0			0
$556$	−8.30996e10			−0.869560
$557$	−6.39723e10			−0.664617			−0.332309	−	0.943171i	$-0.607828\pi$
$557$	−6.39723e10			−0.664617			−0.332309	+	0.943171i	$0.607828\pi$
$558$	3.87993e10	+	6.49955e10i	0.400209	+	0.670420i
$559$	−2.63333e10			−0.269686
$560$		0			0
$561$	6.71747e10	+	3.81332e10i	0.678194	+	0.384992i
$562$			4.63178e10i			0.464305i
$563$	−1.47936e11			−1.47245			−0.736225	−	0.676736i	$-0.763394\pi$
$563$	−1.47936e11			−1.47245			−0.736225	+	0.676736i	$0.763394\pi$
$564$	−5.84844e9	+	1.03025e10i	−0.0577995	+	0.101818i
$565$		0			0
$566$			8.72290e10i			0.849954i
$567$	−3.25974e10	−	1.75736e10i	−0.315392	−	0.170031i
$568$		−	1.53803e10i		−	0.147765i
$569$			1.24543e11i			1.18815i	0.804410	+	0.594075i	$0.202482\pi$
$569$			1.24543e11i			1.18815i	−0.804410	+	0.594075i	$0.797518\pi$
$570$		0			0
$571$	−1.25257e11			−1.17830			−0.589151	−	0.808023i	$-0.700538\pi$
$571$	−1.25257e11			−1.17830			−0.589151	+	0.808023i	$0.700538\pi$
$572$	3.00091e10			0.280329
$573$	−4.93224e10	−	2.79990e10i	−0.457537	−	0.259731i
$574$	−3.59425e10			−0.331101
$575$		0			0
$576$	−1.49741e10	−	2.50842e10i	−0.136035	−	0.227883i
$577$			1.59567e10i			0.143959i	0.997406	+	0.0719797i	$0.0229317\pi$
$577$			1.59567e10i			0.143959i	−0.997406	+	0.0719797i	$0.977068\pi$
$578$	−4.25934e10			−0.381620
$579$	−7.37786e10	−	4.18820e10i	−0.656472	−	0.372661i
$580$		0			0
$581$		−	1.40620e10i		−	0.123408i
$582$	−6.27669e10	−	3.56310e10i	−0.547065	−	0.310553i
$583$			6.54663e10i			0.566687i
$584$			9.46081e10i			0.813349i
$585$		0			0
$586$	−6.42506e10			−0.544863
$587$	8.97851e10			0.756226			0.378113	−	0.925759i	$-0.376573\pi$
$587$	8.97851e10			0.756226			0.378113	+	0.925759i	$0.376573\pi$
$588$	−3.76916e10	+	6.63967e10i	−0.315308	+	0.555440i
$589$	9.93536e10			0.825510
$590$		0			0
$591$	9.22250e9	−	1.62462e10i	0.0755960	−	0.133168i
$592$		−	6.51547e10i		−	0.530467i
$593$	4.22870e10			0.341970			0.170985	−	0.985274i	$-0.445305\pi$
$593$	4.22870e10			0.341970			0.170985	+	0.985274i	$0.445305\pi$
$594$	8.32328e8	+	3.80576e10i	0.00668573	+	0.305700i
$595$		0			0
$596$			1.23612e11i			0.979657i
$597$	5.24501e10	−	9.23951e10i	0.412904	−	0.727363i
$598$			5.63777e10i			0.440862i
$599$			7.21992e10i			0.560822i	0.959880	+	0.280411i	$0.0904707\pi$
$599$			7.21992e10i			0.560822i	−0.959880	+	0.280411i	$0.909529\pi$
$600$		0			0
$601$	−6.40453e10			−0.490896			−0.245448	−	0.969410i	$-0.578935\pi$
$601$	−6.40453e10			−0.490896			−0.245448	+	0.969410i	$0.578935\pi$
$602$	1.01437e10			0.0772344
$603$	−7.76363e9	+	4.63453e9i	−0.0587213	+	0.0350539i
$604$	−1.82547e11			−1.37160
$605$		0			0
$606$	−4.59798e10	−	2.61015e10i	−0.340939	−	0.193542i
$607$			2.21809e11i			1.63390i	0.576711	+	0.816949i	$0.304336\pi$
$607$			2.21809e11i			1.63390i	−0.576711	+	0.816949i	$0.695664\pi$
$608$	−7.73140e10			−0.565775
$609$	−1.05376e10	+	1.85628e10i	−0.0766076	+	0.134950i
$610$		0			0
$611$			1.44019e10i			0.103337i
$612$	6.94675e10	+	1.16370e11i	0.495195	+	0.829536i
$613$		−	1.52452e11i		−	1.07967i	−0.841771	−	0.539835i	$-0.818487\pi$
$613$		−	1.52452e11i		−	1.07967i	0.841771	−	0.539835i	$-0.181513\pi$
$614$		−	3.42318e10i		−	0.240855i
$615$		0			0
$616$	−2.73348e10			−0.189843
$617$	8.38162e9			0.0578345			0.0289173	−	0.999582i	$-0.490794\pi$
$617$	8.38162e9			0.0578345			0.0289173	+	0.999582i	$0.490794\pi$
$618$	−5.34196e9	−	3.03248e9i	−0.0366224	−	0.0207895i
$619$	1.86669e11			1.27148			0.635741	−	0.771902i	$-0.280695\pi$
$619$	1.86669e11			1.27148			0.635741	+	0.771902i	$0.280695\pi$
$620$		0			0
$621$	1.96057e11	−	4.28782e9i	1.31831	−	0.0288317i
$622$		−	1.24819e11i		−	0.833910i
$623$	5.14827e10			0.341751
$624$	2.30010e10	+	1.30570e10i	0.151708	+	0.0861203i
$625$		0			0
$626$			1.73717e10i			0.113122i
$627$	4.34512e10	+	2.46660e10i	0.281146	+	0.159599i
$628$		−	2.62912e10i		−	0.169033i
$629$		−	4.05874e11i		−	2.59292i
$630$		0			0
$631$	1.95553e10			0.123352			0.0616761	−	0.998096i	$-0.480355\pi$
$631$	1.95553e10			0.123352			0.0616761	+	0.998096i	$0.480355\pi$
$632$	−3.95015e10			−0.247597
$633$	−8.00142e10	+	1.40951e11i	−0.498370	+	0.877919i
$634$	2.46682e10			0.152679
$635$		0			0
$636$	−5.67052e10	+	9.98908e10i	−0.346573	+	0.610516i
$637$			9.28165e10i			0.563725i
$638$	2.19412e10			0.132427
$639$	−2.36160e10	+	1.40977e10i	−0.141646	+	0.0845559i
$640$		0			0
$641$		−	1.22798e11i		−	0.727373i	−0.931521	−	0.363687i	$-0.881518\pi$
$641$		−	1.22798e11i		−	0.727373i	0.931521	−	0.363687i	$-0.118482\pi$
$642$	−5.22914e10	+	9.21154e10i	−0.307815	+	0.542241i
$643$		−	2.19260e11i		−	1.28267i	−0.767259	−	0.641337i	$-0.778380\pi$
$643$		−	2.19260e11i		−	1.28267i	0.767259	−	0.641337i	$-0.221620\pi$
$644$			5.95505e10i			0.346212i
$645$		0			0
$646$	−6.48717e10			−0.372499
$647$	−2.09093e11			−1.19322			−0.596611	−	0.802530i	$-0.703487\pi$
$647$	−2.09093e11			−1.19322			−0.596611	+	0.802530i	$0.703487\pi$
$648$	−7.49474e10	+	1.39021e11i	−0.425066	+	0.788461i
$649$	1.80300e11			1.01629
$650$		0			0
$651$	8.45302e10	+	4.79855e10i	0.470639	+	0.267169i
$652$		−	1.44301e11i		−	0.798505i
$653$	1.89323e11			1.04124			0.520621	−	0.853788i	$-0.325700\pi$
$653$	1.89323e11			1.04124			0.520621	+	0.853788i	$0.325700\pi$
$654$	2.21532e10	−	3.90246e10i	0.121095	−	0.213318i
$655$		0			0
$656$		−	8.92905e10i		−	0.482158i
$657$	1.45268e11	−	8.67182e10i	0.779665	−	0.465424i
$658$		−	5.54769e9i		−	0.0295943i
$659$		−	1.58406e11i		−	0.839904i	−0.907546	−	0.419952i	$-0.862047\pi$
$659$		−	1.58406e11i		−	0.839904i	0.907546	−	0.419952i	$-0.137953\pi$
$660$		0			0
$661$	3.37961e11			1.77036			0.885178	−	0.465252i	$-0.154036\pi$
$661$	3.37961e11			1.77036			0.885178	+	0.465252i	$0.154036\pi$
$662$	6.06173e10			0.315620
$663$	1.43282e11	+	8.13373e10i	0.741546	+	0.420955i
$664$	−5.99716e10			−0.308513
$665$		0			0
$666$	1.71746e11	−	1.02525e11i	0.872952	−	0.521112i
$667$		−	1.13032e11i		−	0.571082i
$668$	−2.43230e10			−0.122155
$669$	4.29458e10	+	2.43791e10i	0.214396	+	0.121707i
$670$		0			0
$671$			1.75912e11i			0.867771i
$672$	−6.57789e10	−	3.73408e10i	−0.322559	−	0.183108i
$673$		−	3.10614e10i		−	0.151412i	−0.997130	−	0.0757061i	$-0.975879\pi$
$673$		−	3.10614e10i		−	0.151412i	0.997130	−	0.0757061i	$-0.0241211\pi$
$674$			9.41116e10i			0.456041i
$675$		0			0
$676$	−8.90139e10			−0.426256
$677$	−5.35620e10			−0.254978			−0.127489	−	0.991840i	$-0.540692\pi$
$677$	−5.35620e10			−0.254978			−0.127489	+	0.991840i	$0.540692\pi$
$678$	−1.70366e10	+	3.00114e10i	−0.0806242	+	0.142026i
$679$	−9.26801e10			−0.436021
$680$		0			0
$681$	1.56431e11	−	2.75565e11i	0.727334	−	1.28126i
$682$		−	9.99145e10i		−	0.461840i
$683$	1.38214e10			0.0635139			0.0317570	−	0.999496i	$-0.489890\pi$
$683$	1.38214e10			0.0635139			0.0317570	+	0.999496i	$0.489890\pi$
$684$	4.49343e10	+	7.52727e10i	0.205283	+	0.343885i
$685$		0			0
$686$		−	7.67729e10i		−	0.346666i
$687$	−2.00856e10	+	3.53823e10i	−0.0901690	+	0.158840i
$688$			2.51996e10i			0.112471i
$689$			1.39638e11i			0.619622i
$690$		0			0
$691$	−2.88658e11			−1.26611			−0.633054	−	0.774107i	$-0.718199\pi$
$691$	−2.88658e11			−1.26611			−0.633054	+	0.774107i	$0.718199\pi$
$692$	−3.01644e10			−0.131544
$693$	2.50552e10	+	4.19718e10i	0.108634	+	0.181980i
$694$	−3.21479e10			−0.138584
$695$		0			0
$696$	7.91664e10	+	4.49406e10i	0.337368	+	0.191514i
$697$		−	5.56226e11i		−	2.35678i
$698$	3.42199e10			0.144164
$699$	−1.26695e11	+	2.23183e11i	−0.530702	+	0.934873i
$700$		0			0
$701$		−	4.28713e11i		−	1.77539i	−0.460429	−	0.887696i	$-0.652305\pi$
$701$		−	4.28713e11i		−	1.77539i	0.460429	−	0.887696i	$-0.347695\pi$
$702$	1.77534e9	+	8.11760e10i	0.00731026	+	0.334256i
$703$		−	2.62535e11i		−	1.07490i
$704$			3.85608e10i			0.156984i
$705$		0			0
$706$	3.45770e10			0.139177
$707$	−6.78927e10			−0.271735
$708$	2.75108e11	+	1.56171e11i	1.09489	+	0.621539i
$709$	1.93857e11			0.767179			0.383589	−	0.923504i	$-0.374688\pi$
$709$	1.93857e11			0.767179			0.383589	+	0.923504i	$0.374688\pi$
$710$		0			0
$711$	3.62072e10	+	6.06533e10i	0.141683	+	0.237343i
$712$		−	2.19563e11i		−	0.854356i
$713$	−5.14719e11			−1.99165
$714$	−5.51929e10	−	3.13315e10i	−0.212369	−	0.120556i
$715$		0			0
$716$		−	1.13028e11i		−	0.430064i
$717$	−3.16105e11	−	1.79444e11i	−1.19606	−	0.678972i
$718$		−	1.23131e11i		−	0.463308i
$719$		−	9.46617e10i		−	0.354208i	−0.984192	−	0.177104i	$-0.943327\pi$
$719$		−	9.46617e10i		−	0.354208i	0.984192	−	0.177104i	$-0.0566730\pi$
$720$		0			0
$721$	−7.88781e9			−0.0291887
$722$	9.85105e10			0.362522
$723$	−5.18712e10	+	9.13753e10i	−0.189834	+	0.334407i
$724$	−2.12943e11			−0.775014
$725$		0			0
$726$	−4.60918e10	+	8.11943e10i	−0.165912	+	0.292267i
$727$			3.90262e11i			1.39707i	0.715575	+	0.698536i	$0.246165\pi$
$727$			3.90262e11i			1.39707i	−0.715575	+	0.698536i	$0.753835\pi$
$728$	−5.83046e10			−0.207576
$729$	2.82159e11	−	1.23477e10i	0.999044	−	0.0437196i
$730$		0			0
$731$			1.56978e11i			0.549756i
$732$	−1.52370e11	+	2.68413e11i	−0.530709	+	0.934886i
$733$			2.42553e11i			0.840215i	0.907474	+	0.420108i	$0.138008\pi$
$733$			2.42553e11i			0.840215i	−0.907474	+	0.420108i	$0.861992\pi$
$734$		−	1.24745e11i		−	0.429771i
$735$		0			0
$736$	4.00539e11			1.36500
$737$	1.19347e10			0.0404520
$738$	2.35368e11	−	1.40504e11i	0.793453	−	0.473655i
$739$	−4.33550e9			−0.0145365			−0.00726827	−	0.999974i	$-0.502314\pi$
$739$	−4.33550e9			−0.0145365			−0.00726827	+	0.999974i	$0.502314\pi$
$740$		0			0
$741$	9.26804e10	+	5.26121e10i	0.307408	+	0.174507i
$742$		−	5.37892e10i		−	0.177452i
$743$	1.85138e11			0.607493			0.303746	−	0.952753i	$-0.401762\pi$
$743$	1.85138e11			0.607493			0.303746	+	0.952753i	$0.401762\pi$
$744$	2.04648e11	−	3.60503e11i	0.667906	−	1.17657i
$745$		0			0
$746$		−	5.42966e10i		−	0.175314i
$747$	5.49702e10	+	9.20845e10i	0.176541	+	0.295736i
$748$		−	1.78890e11i		−	0.571452i
$749$			1.36015e11i			0.432176i
$750$		0			0
$751$	−1.76039e11			−0.553414			−0.276707	−	0.960954i	$-0.589243\pi$
$751$	−1.76039e11			−0.553414			−0.276707	+	0.960954i	$0.589243\pi$
$752$	1.37819e10			0.0430961
$753$	−1.88178e11	−	1.06824e11i	−0.585315	−	0.332267i
$754$	4.68001e10			0.144798
$755$		0			0
$756$	1.87525e9	+	8.57443e10i	0.00574079	+	0.262493i
$757$			1.04686e11i			0.318789i	0.987215	+	0.159395i	$0.0509542\pi$
$757$			1.04686e11i			0.318789i	−0.987215	+	0.159395i	$0.949046\pi$
$758$	2.27823e11			0.690114
$759$	−2.25107e11	−	1.27787e11i	−0.678299	−	0.385051i
$760$		0			0
$761$			1.31591e11i			0.392362i	0.980568	+	0.196181i	$0.0628541\pi$
$761$			1.31591e11i			0.392362i	−0.980568	+	0.196181i	$0.937146\pi$
$762$	5.83155e10	+	3.31041e10i	0.172967	+	0.0981887i
$763$		−	5.76229e10i		−	0.170019i
$764$			1.31349e11i			0.385524i
$765$		0			0
$766$	−1.45949e11			−0.423922
$767$	3.84576e11			1.11122
$768$	−1.25306e11	+	2.20736e11i	−0.360185	+	0.634494i
$769$	2.25269e9			0.00644165			0.00322082	−	0.999995i	$-0.498975\pi$
$769$	2.25269e9			0.00644165			0.00322082	+	0.999995i	$0.498975\pi$
$770$		0			0
$771$	−1.37609e11	+	2.42409e11i	−0.389429	+	0.686010i
$772$			1.96477e11i			0.553149i
$773$	−1.83457e11			−0.513825			−0.256913	−	0.966435i	$-0.582705\pi$
$773$	−1.83457e11			−0.513825			−0.256913	+	0.966435i	$0.582705\pi$
$774$	−6.64256e10	+	3.96530e10i	−0.185085	+	0.110487i
$775$		0			0
$776$			3.95261e11i			1.09003i
$777$	1.26798e11	−	2.23365e11i	0.347880	−	0.612818i
$778$			1.40749e10i			0.0384174i
$779$		−	3.59788e11i		−	0.977006i
$780$		0			0
$781$	3.63038e10			0.0975771
$782$	3.36079e11			0.898699
$783$	−3.55939e9	−	1.62750e11i	−0.00946952	−	0.432987i
$784$	8.88205e10			0.235098
$785$		0			0
$786$	−1.20235e11	−	6.82542e10i	−0.315023	−	0.178830i
$787$			5.90552e11i			1.53943i	0.638389	+	0.769714i	$0.279601\pi$
$787$			5.90552e11i			1.53943i	−0.638389	+	0.769714i	$0.720399\pi$
$788$	−4.32645e10			−0.112209
$789$	−2.31312e11	+	4.07474e11i	−0.596884	+	1.05146i
$790$		0			0
$791$			4.43141e10i			0.113197i
$792$	1.79001e11	−	1.06855e11i	0.454940	−	0.271578i
$793$			3.75216e11i			0.948830i
$794$		−	2.58268e11i		−	0.649813i
$795$		0			0
$796$	−2.46053e11			−0.612882
$797$	−5.88219e11			−1.45783			−0.728914	−	0.684606i	$-0.759974\pi$
$797$	−5.88219e11			−1.45783			−0.728914	+	0.684606i	$0.759974\pi$
$798$	−3.57009e10	−	2.02664e10i	−0.0880375	−	0.0499765i
$799$	8.58529e10			0.210653
$800$		0			0
$801$	−3.37132e11	+	2.01252e11i	−0.818973	+	0.488889i
$802$			1.49928e11i			0.362397i
$803$	−2.23313e11			−0.537097
$804$	1.82103e10	+	1.03375e10i	0.0435807	+	0.0247395i
$805$		0			0
$806$		−	2.13116e11i		−	0.504981i
$807$	5.01194e11	+	2.84514e11i	1.18171	+	0.670825i
$808$			2.89548e11i			0.679321i
$809$			5.05936e11i			1.18114i	0.806987	+	0.590570i	$0.201097\pi$
$809$			5.05936e11i			1.18114i	−0.806987	+	0.590570i	$0.798903\pi$
$810$		0			0
$811$	−5.19700e11			−1.20135			−0.600674	−	0.799494i	$-0.705101\pi$
$811$	−5.19700e11			−1.20135			−0.600674	+	0.799494i	$0.705101\pi$
$812$	4.94338e10			0.113710
$813$	7.29664e10	−	1.28536e11i	0.167017	−	0.294214i
$814$	−2.64017e11			−0.601361
$815$		0			0
$816$	7.78355e10	−	1.37113e11i	0.175556	−	0.309257i
$817$			1.01540e11i			0.227902i
$818$	−1.28030e11			−0.285957
$819$	5.34422e10	+	8.95249e10i	0.118782	+	0.198979i
$820$		0			0
$821$			1.31370e11i			0.289150i	0.989494	+	0.144575i	$0.0461815\pi$
$821$			1.31370e11i			0.289150i	−0.989494	+	0.144575i	$0.953819\pi$
$822$	1.69864e11	−	2.99229e11i	0.372061	−	0.655415i
$823$			5.04661e11i			1.10002i	0.835158	+	0.550010i	$0.185376\pi$
$823$			5.04661e11i			1.10002i	−0.835158	+	0.550010i	$0.814624\pi$
$824$			3.36398e10i			0.0729701i
$825$		0			0
$826$	−1.48140e11			−0.318239
$827$	1.62367e10			0.0347117			0.0173559	−	0.999849i	$-0.494475\pi$
$827$	1.62367e10			0.0347117			0.0173559	+	0.999849i	$0.494475\pi$
$828$	−2.32790e11	−	3.89963e11i	−0.495271	−	0.829664i
$829$	−3.49989e11			−0.741031			−0.370515	−	0.928826i	$-0.620819\pi$
$829$	−3.49989e11			−0.741031			−0.370515	+	0.928826i	$0.620819\pi$
$830$		0			0
$831$	−6.01115e11	−	3.41236e11i	−1.26053	−	0.715569i
$832$			8.22494e10i			0.171648i
$833$	5.53298e11			1.14916
$834$	−1.46513e11	+	2.58095e11i	−0.302840	+	0.533476i
$835$		0			0
$836$		−	1.15713e11i		−	0.236896i
$837$	−7.41122e11	+	1.62085e10i	−1.51004	+	0.0330249i
$838$		−	3.25777e11i		−	0.660609i
$839$			5.47730e11i			1.10540i	0.833381	+	0.552699i	$0.186402\pi$
$839$			5.47730e11i			1.10540i	−0.833381	+	0.552699i	$0.813598\pi$
$840$		0			0
$841$	4.06417e11			0.812433
$842$	−3.93748e11			−0.783375
$843$	−3.94471e11	−	2.23930e11i	−0.781097	−	0.443407i
$844$	3.75362e11			0.739742
$845$		0			0
$846$	2.16866e10	+	3.63288e10i	0.0423360	+	0.0709201i
$847$			1.19890e11i			0.232942i
$848$	1.33626e11			0.258409
$849$	−7.42896e11	−	4.21721e11i	−1.42987	−	0.811699i
$850$		0			0
$851$			1.36011e12i			2.59332i
$852$	5.53936e10	+	3.14454e10i	0.105124	+	0.0596759i
$853$		−	2.92272e11i		−	0.552067i	−0.961148	−	0.276033i	$-0.910980\pi$
$853$		−	2.92272e11i		−	0.552067i	0.961148	−	0.276033i	$-0.0890200\pi$
$854$		−	1.44535e11i		−	0.271732i
$855$		0			0
$856$	5.80077e11			1.08041
$857$	2.42186e11			0.448979			0.224490	−	0.974476i	$-0.427929\pi$
$857$	2.42186e11			0.448979			0.224490	+	0.974476i	$0.427929\pi$
$858$	5.29091e10	−	9.32037e10i	0.0976296	−	0.171982i
$859$	−2.79708e11			−0.513727			−0.256864	−	0.966448i	$-0.582689\pi$
$859$	−2.79708e11			−0.513727			−0.256864	+	0.966448i	$0.582689\pi$
$860$		0			0
$861$	1.73769e11	−	3.06108e11i	0.316199	−	0.557010i
$862$			2.78277e11i			0.504021i
$863$	7.52248e11			1.35618			0.678091	−	0.734978i	$-0.262807\pi$
$863$	7.52248e11			1.35618			0.678091	+	0.734978i	$0.262807\pi$
$864$	5.76719e11	−	1.26130e10i	1.03493	−	0.0226341i
$865$		0			0
$866$		−	3.48536e11i		−	0.619693i
$867$	2.05924e11	−	3.62751e11i	0.364444	−	0.641997i
$868$		−	2.25109e11i		−	0.396564i
$869$		−	9.32395e10i		−	0.163501i
$870$		0			0
$871$	2.54564e10			0.0442307
$872$	−2.45749e11			−0.425037
$873$	6.06911e11	−	3.62298e11i	1.04488	−	0.623747i
$874$	2.17389e11			0.372556
$875$		0			0
$876$	−3.40740e11	−	1.93428e11i	−0.578637	−	0.328476i
$877$		−	9.81199e11i		−	1.65866i	−0.558756	−	0.829332i	$-0.688721\pi$
$877$		−	9.81199e11i		−	1.65866i	0.558756	−	0.829332i	$-0.311279\pi$
$878$	−1.24863e11			−0.210115
$879$	3.10629e11	−	5.47198e11i	0.520339	−	0.916619i
$880$		0			0
$881$		−	5.64513e11i		−	0.937067i	−0.883446	−	0.468533i	$-0.844783\pi$
$881$		−	5.64513e11i		−	0.937067i	0.883446	−	0.468533i	$-0.155217\pi$
$882$	1.39764e11	+	2.34129e11i	0.230952	+	0.386884i
$883$			8.27626e11i			1.36142i	0.732555	+	0.680708i	$0.238328\pi$
$883$			8.27626e11i			1.36142i	−0.732555	+	0.680708i	$0.761672\pi$
$884$		−	3.81569e11i		−	0.624833i
$885$		0			0
$886$	2.21214e11			0.358986
$887$	7.27364e11			1.17505			0.587526	−	0.809205i	$-0.300102\pi$
$887$	7.27364e11			1.17505			0.587526	+	0.809205i	$0.300102\pi$
$888$	−9.52605e11	−	5.40768e11i	−1.53201	−	0.869679i
$889$	8.61073e10			0.137858
$890$		0			0
$891$	−3.28146e11	−	1.76906e11i	−0.520662	−	0.280693i
$892$		−	1.14367e11i		−	0.180652i
$893$	5.55330e10			0.0873263
$894$	3.83919e11	+	2.17940e11i	0.601021	+	0.341183i
$895$		0			0
$896$			2.07372e11i			0.321750i
$897$	−4.80147e11	−	2.72566e11i	−0.741660	−	0.421020i
$898$			5.99018e11i			0.921159i
$899$			4.27277e11i			0.654139i
$900$		0			0
$901$	8.32411e11			1.26310
$902$	−3.61820e11			−0.546595
$903$	−4.90412e10	+	8.63900e10i	−0.0737582	+	0.129931i
$904$	1.88990e11			0.282987
$905$		0			0
$906$	−3.21850e11	+	5.66964e11i	−0.477684	+	0.841478i
$907$			1.16923e12i			1.72771i	0.503743	+	0.863853i	$0.331956\pi$
$907$			1.16923e12i			1.72771i	−0.503743	+	0.863853i	$0.668044\pi$
$908$	−7.33847e11			−1.07960
$909$	4.44592e11	−	2.65401e11i	0.651187	−	0.388729i
$910$		0			0
$911$		−	1.19802e12i		−	1.73936i	−0.493614	−	0.869681i	$-0.664324\pi$
$911$		−	1.19802e12i		−	1.73936i	0.493614	−	0.869681i	$-0.335676\pi$
$912$	5.03470e10	−	8.86903e10i	0.0727770	−	0.128203i
$913$		−	1.41557e11i		−	0.203727i
$914$		−	9.69253e10i		−	0.138884i
$915$		0			0
$916$	9.42252e10			0.133840
$917$	−1.77537e11			−0.251079
$918$	4.83906e11	−	1.05831e10i	0.681382	−	0.0149020i
$919$	−9.42803e11			−1.32178			−0.660890	−	0.750483i	$-0.729821\pi$
$919$	−9.42803e11			−1.32178			−0.660890	+	0.750483i	$0.729821\pi$
$920$		0			0
$921$	2.91539e11	+	1.65498e11i	0.405189	+	0.230015i
$922$		−	7.11484e11i		−	0.984558i
$923$	7.74352e10			0.106692
$924$	5.58867e10	−	9.84489e10i	0.0766691	−	0.135059i
$925$		0			0
$926$		−	3.02016e11i		−	0.410758i
$927$	5.16529e10	−	3.08344e10i	0.0699481	−	0.0417558i
$928$		−	3.32494e11i		−	0.448324i
$929$			5.40213e11i			0.725274i	0.931930	+	0.362637i	$0.118124\pi$
$929$			5.40213e11i			0.725274i	−0.931930	+	0.362637i	$0.881876\pi$
$930$		0			0
$931$	3.57895e11			0.476383
$932$	5.94350e11			0.787732
$933$	1.06303e12	+	6.03455e11i	1.40288	+	0.796377i
$934$	7.12577e11			0.936363
$935$		0			0
$936$	3.81805e11	−	2.27920e11i	0.497437	−	0.296947i
$937$		−	8.00616e11i		−	1.03864i	−0.854579	−	0.519321i	$-0.826185\pi$
$937$		−	8.00616e11i		−	1.03864i	0.854579	−	0.519321i	$-0.173815\pi$
$938$	−9.80591e9			−0.0126671
$939$	−1.47948e11	−	8.39862e10i	−0.190304	−	0.108030i
$940$		0			0
$941$		−	4.51353e11i		−	0.575649i	−0.957683	−	0.287825i	$-0.907068\pi$
$941$		−	4.51353e11i		−	0.575649i	0.957683	−	0.287825i	$-0.0929321\pi$
$942$	−8.16566e10	−	4.63542e10i	−0.103702	−	0.0588688i
$943$			1.86395e12i			2.35715i
$944$		−	3.68019e11i		−	0.463428i
$945$		0			0
$946$	1.02113e11			0.127502
$947$	3.43776e11			0.427441			0.213720	−	0.976895i	$-0.431442\pi$
$947$	3.43776e11			0.427441			0.213720	+	0.976895i	$0.431442\pi$
$948$	8.07617e10	−	1.42268e11i	0.0999935	−	0.176147i
$949$	−4.76323e11			−0.587268
$950$		0			0
$951$	−1.19262e11	+	2.10089e11i	−0.145807	+	0.256851i
$952$			3.47566e11i			0.423145i
$953$	−7.01344e11			−0.850275			−0.425138	−	0.905129i	$-0.639774\pi$
$953$	−7.01344e11			−0.850275			−0.425138	+	0.905129i	$0.639774\pi$
$954$	2.10269e11	+	3.52236e11i	0.253852	+	0.425246i
$955$		0			0
$956$			8.41805e11i			1.00781i
$957$	−1.06078e11	+	1.86865e11i	−0.126467	+	0.222782i
$958$		−	3.67623e11i		−	0.436456i
$959$		−	4.41835e11i		−	0.522379i
$960$		0			0
$961$	1.09282e12			1.28131
$962$	−5.63143e11			−0.657535
$963$	−5.31701e11	−	8.90690e11i	−0.618247	−	1.03567i
$964$	2.43338e11			0.281774
$965$		0			0
$966$	1.84955e11	+	1.04994e11i	0.212401	+	0.120574i
$967$		−	1.29211e12i		−	1.47773i	−0.673855	−	0.738863i	$-0.735363\pi$
$967$		−	1.29211e12i		−	1.47773i	0.673855	−	0.738863i	$-0.264637\pi$
$968$	5.11304e11			0.582341
$969$	3.13631e11	−	5.52487e11i	0.355733	−	0.626653i
$970$		0			0
$971$			3.10599e11i			0.349400i	0.984622	+	0.174700i	$0.0558955\pi$
$971$			3.10599e11i			0.349400i	−0.984622	+	0.174700i	$0.944104\pi$
$972$	−3.47465e11	−	5.54161e11i	−0.389265	−	0.620828i
$973$			3.81097e11i			0.425191i
$974$		−	3.88321e10i		−	0.0431475i
$975$		0			0
$976$	3.59062e11			0.395704
$977$	−1.06003e12			−1.16343			−0.581716	−	0.813392i	$-0.697618\pi$
$977$	−1.06003e12			−1.16343			−0.581716	+	0.813392i	$0.697618\pi$
$978$	−4.48176e11	−	2.54417e11i	−0.489884	−	0.278093i
$979$	5.18257e11			0.564176
$980$		0			0
$981$	2.25255e11	+	3.77340e11i	0.243219	+	0.407434i
$982$			4.56619e11i			0.491030i
$983$	−1.23511e11			−0.132279			−0.0661395	−	0.997810i	$-0.521068\pi$
$983$	−1.23511e11			−0.132279			−0.0661395	+	0.997810i	$0.521068\pi$
$984$	−1.30549e12	−	7.41089e11i	−1.39249	−	0.790478i
$985$		0			0
$986$		−	2.78985e11i		−	0.295170i
$987$	4.72475e10	+	2.68211e10i	0.0497864	+	0.0282623i
$988$		−	2.46813e11i		−	0.259025i
$989$		−	5.26044e11i		−	0.549840i
$990$		0			0
$991$	−1.19256e11			−0.123648			−0.0618238	−	0.998087i	$-0.519692\pi$
$991$	−1.19256e11			−0.123648			−0.0618238	+	0.998087i	$0.519692\pi$
$992$	−1.51409e12			−1.56353
$993$	−2.93063e11	+	5.16254e11i	−0.301414	+	0.530966i
$994$	−2.98284e10			−0.0305551
$995$		0			0
$996$	1.22613e11	−	2.15993e11i	0.124595	−	0.219484i
$997$			2.68628e11i			0.271876i	0.990717	+	0.135938i	$0.0434048\pi$
$997$			2.68628e11i			0.271876i	−0.990717	+	0.135938i	$0.956595\pi$
$998$	−1.23639e11			−0.124633
$999$	4.28299e10	+	1.95837e12i	0.0430017	+	1.96622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.d.c.74.7		20
3.2	odd	2	inner	75.9.d.c.74.13		20
5.2	odd	4		75.9.c.g.26.4		10
5.3	odd	4		15.9.c.a.11.7	yes	10
5.4	even	2	inner	75.9.d.c.74.14		20
15.2	even	4		75.9.c.g.26.7		10
15.8	even	4		15.9.c.a.11.4	✓	10
15.14	odd	2	inner	75.9.d.c.74.8		20
20.3	even	4		240.9.l.b.161.1		10
60.23	odd	4		240.9.l.b.161.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.4	✓	10	15.8	even	4
15.9.c.a.11.7	yes	10	5.3	odd	4
75.9.c.g.26.4		10	5.2	odd	4
75.9.c.g.26.7		10	15.2	even	4
75.9.d.c.74.7		20	1.1	even	1	trivial
75.9.d.c.74.8		20	15.14	odd	2	inner
75.9.d.c.74.13		20	3.2	odd	2	inner
75.9.d.c.74.14		20	5.4	even	2	inner
240.9.l.b.161.1		10	20.3	even	4
240.9.l.b.161.2		10	60.23	odd	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-8.27106 q^{2} +(39.9876 - 70.4414i) q^{3} -187.590 q^{4} +(-330.740 + 582.625i) q^{6} +860.291i q^{7} +3668.96 q^{8} +(-3362.98 - 5633.57i) q^{9} +O(q^{10})\)	\(q-8.27106 q^{2} +(39.9876 - 70.4414i) q^{3} -187.590 q^{4} +(-330.740 + 582.625i) q^{6} +860.291i q^{7} +3668.96 q^{8} +(-3362.98 - 5633.57i) q^{9} +8660.22i q^{11} +(-7501.26 + 13214.1i) q^{12} +18472.1i q^{13} -7115.52i q^{14} +17676.8 q^{16} +110116. q^{17} +(27815.4 + 46595.6i) q^{18} +71227.1 q^{19} +(60600.1 + 34401.0i) q^{21} -71629.2i q^{22} -369004. q^{23} +(146713. - 258446. i) q^{24} -152783. i q^{26} +(-531314. + 11620.0i) q^{27} -161382. i q^{28} +306317. i q^{29} +1.39489e6 q^{31} -1.08546e6 q^{32} +(610038. + 346302. i) q^{33} -910773. q^{34} +(630860. + 1.05680e6i) q^{36} -3.68589e6i q^{37} -589123. q^{38} +(1.30120e6 + 738653. i) q^{39} -5.05129e6i q^{41} +(-501227. - 284533. i) q^{42} +1.42558e6i q^{43} -1.62457e6i q^{44} +3.05206e6 q^{46} +779661. q^{47} +(706852. - 1.24518e6i) q^{48} +5.02470e6 q^{49} +(4.40326e6 - 7.75670e6i) q^{51} -3.46516e6i q^{52} +7.55943e6 q^{53} +(4.39453e6 - 96109.4i) q^{54} +3.15637e6i q^{56} +(2.84820e6 - 5.01733e6i) q^{57} -2.53356e6i q^{58} -2.08194e7i q^{59} +2.03126e7 q^{61} -1.15372e7 q^{62} +(4.84651e6 - 2.89314e6i) q^{63} +4.45264e6 q^{64} +(-5.04566e6 - 2.86428e6i) q^{66} -1.37810e6i q^{67} -2.06565e7 q^{68} +(-1.47556e7 + 2.59932e7i) q^{69} -4.19202e6i q^{71} +(-1.23386e7 - 2.06693e7i) q^{72} +2.57861e7i q^{73} +3.04862e7i q^{74} -1.33615e7 q^{76} -7.45030e6 q^{77} +(-1.07623e7 - 6.10945e6i) q^{78} -1.07664e7 q^{79} +(-2.04275e7 + 3.78911e7i) q^{81} +4.17795e7i q^{82} -1.63457e7 q^{83} +(-1.13679e7 - 6.45327e6i) q^{84} -1.17910e7i q^{86} +(2.15774e7 + 1.22489e7i) q^{87} +3.17740e7i q^{88} -5.98434e7i q^{89} -1.58913e7 q^{91} +6.92213e7 q^{92} +(5.57782e7 - 9.82577e7i) q^{93} -6.44862e6 q^{94} +(-4.34049e7 + 7.64612e7i) q^{96} +1.07731e8i q^{97} -4.15596e7 q^{98} +(4.87879e7 - 2.91241e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9}+O(q^{10}) \) 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9	\( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9} + 560772 q^{16} + 463032 q^{19} + 579144 q^{21} - 2272668 q^{24} + 1763240 q^{31} + 2222552 q^{34} - 1337324 q^{36} - 3653584 q^{39} - 50849208 q^{46} - 18708428 q^{49} - 55465384 q^{51} + 15959596 q^{54} + 44834040 q^{61} + 45870004 q^{64} - 54839600 q^{66} - 67125264 q^{69} + 397844872 q^{76} - 324621848 q^{79} - 187150780 q^{81} + 394693536 q^{84} + 888576928 q^{91} + 184100072 q^{94} - 721614812 q^{96} + 67930400 q^{99}+O(q^{100}) \) 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9 + 560772 * q^16 + 463032 * q^19 + 579144 * q^21 - 2272668 * q^24 + 1763240 * q^31 + 2222552 * q^34 - 1337324 * q^36 - 3653584 * q^39 - 50849208 * q^46 - 18708428 * q^49 - 55465384 * q^51 + 15959596 * q^54 + 44834040 * q^61 + 45870004 * q^64 - 54839600 * q^66 - 67125264 * q^69 + 397844872 * q^76 - 324621848 * q^79 - 187150780 * q^81 + 394693536 * q^84 + 888576928 * q^91 + 184100072 * q^94 - 721614812 * q^96 + 67930400 * q^99

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