LMFDB - Embedded newform 75.10.e.g.32.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, degree $2$, 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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.18
Character	$\chi$	$=$	75.32
Dual form			75.10.e.g.68.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.0332 - 15.0332i) q^{2} +(65.5116 - 124.061i) q^{3} +60.0064i q^{4} +(-880.190 - 2849.89i) q^{6} +(4276.91 + 4276.91i) q^{7} +(8599.08 + 8599.08i) q^{8} +(-11099.5 - 16254.9i) q^{9} +O(q^{10})$	\(q+(15.0332 - 15.0332i) q^{2} +(65.5116 - 124.061i) q^{3} +60.0064i q^{4} +(-880.190 - 2849.89i) q^{6} +(4276.91 + 4276.91i) q^{7} +(8599.08 + 8599.08i) q^{8} +(-11099.5 - 16254.9i) q^{9} +58702.8i q^{11} +(7444.48 + 3931.12i) q^{12} +(-37919.1 + 37919.1i) q^{13} +128591. q^{14} +227820. q^{16} +(-316713. + 316713. i) q^{17} +(-411224. - 77503.2i) q^{18} +365693. i q^{19} +(810787. - 250412. i) q^{21} +(882490. + 882490. i) q^{22} +(1.50216e6 + 1.50216e6i) q^{23} +(1.63015e6 - 503474. i) q^{24} +1.14009e6i q^{26} +(-2.74375e6 + 312127. i) q^{27} +(-256642. + 256642. i) q^{28} +1.94930e6 q^{29} +954139. q^{31} +(-977869. + 977869. i) q^{32} +(7.28275e6 + 3.84571e6i) q^{33} +9.52242e6i q^{34} +(975400. - 666039. i) q^{36} +(-8.41718e6 - 8.41718e6i) q^{37} +(5.49753e6 + 5.49753e6i) q^{38} +(2.22015e6 + 7.18843e6i) q^{39} -1.47423e7i q^{41} +(8.42422e6 - 1.59532e7i) q^{42} +(2.54869e7 - 2.54869e7i) q^{43} -3.52254e6 q^{44} +4.51646e7 q^{46} +(-5.21954e6 + 5.21954e6i) q^{47} +(1.49249e7 - 2.82637e7i) q^{48} -3.76964e6i q^{49} +(1.85435e7 + 6.00402e7i) q^{51} +(-2.27539e6 - 2.27539e6i) q^{52} +(-8.10562e6 - 8.10562e6i) q^{53} +(-3.65551e7 + 4.59396e7i) q^{54} +7.35550e7i q^{56} +(4.53684e7 + 2.39571e7i) q^{57} +(2.93042e7 - 2.93042e7i) q^{58} -1.67070e8 q^{59} +2.01613e8 q^{61} +(1.43438e7 - 1.43438e7i) q^{62} +(2.20495e7 - 1.16992e8i) q^{63} +1.46045e8i q^{64} +(1.67296e8 - 5.16696e7i) q^{66} +(2.48357e7 + 2.48357e7i) q^{67} +(-1.90048e7 - 1.90048e7i) q^{68} +(2.84769e8 - 8.79513e7i) q^{69} +3.74056e7i q^{71} +(4.43323e7 - 2.35223e8i) q^{72} +(2.74232e8 - 2.74232e8i) q^{73} -2.53074e8 q^{74} -2.19439e7 q^{76} +(-2.51067e8 + 2.51067e8i) q^{77} +(1.41441e8 + 7.46891e7i) q^{78} +2.73806e8i q^{79} +(-1.41025e8 + 3.60842e8i) q^{81} +(-2.21625e8 - 2.21625e8i) q^{82} +(4.89787e8 + 4.89787e8i) q^{83} +(1.50263e7 + 4.86524e7i) q^{84} -7.66299e8i q^{86} +(1.27702e8 - 2.41833e8i) q^{87} +(-5.04790e8 + 5.04790e8i) q^{88} +4.96975e8 q^{89} -3.24353e8 q^{91} +(-9.01394e7 + 9.01394e7i) q^{92} +(6.25072e7 - 1.18372e8i) q^{93} +1.56933e8i q^{94} +(5.72540e7 + 1.85378e8i) q^{96} +(-2.56266e8 - 2.56266e8i) q^{97} +(-5.66697e7 - 5.66697e7i) q^{98} +(9.54209e8 - 6.51569e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10788 q^{6}+O(q^{10}) $ 48 * q + 10788 * q^6	$ 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) $ 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	15.0332	−	15.0332i	0.664379	−	0.664379i	−0.292030	−	0.956409i	$-0.594331\pi$
$2$	15.0332	−	15.0332i	0.664379	−	0.664379i	0.956409	+	0.292030i	$0.0943307\pi$
$3$	65.5116	−	124.061i	0.466952	−	0.884282i
$3$	65.5116	−	124.061i	0.466952	−	0.884282i
$4$			60.0064i			0.117200i
$5$		0			0
$5$		0			0
$6$	−880.190	−	2849.89i	−0.277265	−	0.897733i
$7$	4276.91	+	4276.91i	0.673270	+	0.673270i	0.958468	−	0.285199i	$-0.0920595\pi$
$7$	4276.91	+	4276.91i	0.673270	+	0.673270i	−0.285199	+	0.958468i	$0.592060\pi$
$8$	8599.08	+	8599.08i	0.742245	+	0.742245i
$9$	−11099.5	−	16254.9i	−0.563911	−	0.825836i
$10$		0			0
$11$			58702.8i			1.20890i	0.796642	+	0.604452i	$0.206608\pi$
$11$			58702.8i			1.20890i	−0.796642	+	0.604452i	$0.793392\pi$
$12$	7444.48	+	3931.12i	0.103638	+	0.0547269i
$13$	−37919.1	+	37919.1i	−0.368224	+	0.368224i	−0.866829	−	0.498605i	$-0.833846\pi$
$13$	−37919.1	+	37919.1i	−0.368224	+	0.368224i	0.498605	+	0.866829i	$0.333846\pi$
$14$	128591.			0.894613
$15$		0			0
$16$	227820.			0.869064
$17$	−316713.	+	316713.i	−0.919699	+	0.919699i	−0.997007	−	0.0773080i	$-0.975368\pi$
$17$	−316713.	+	316713.i	−0.919699	+	0.919699i	0.0773080	+	0.997007i	$0.475368\pi$
$18$	−411224.	−	77503.2i	−0.923319	−	0.174018i
$19$			365693.i			0.643762i	0.946780	+	0.321881i	$0.104315\pi$
$19$			365693.i			0.643762i	−0.946780	+	0.321881i	$0.895685\pi$
$20$		0			0
$21$	810787.	−	250412.i	0.909746	−	0.280976i
$22$	882490.	+	882490.i	0.803171	+	0.803171i
$23$	1.50216e6	+	1.50216e6i	1.11929	+	1.11929i	0.991846	+	0.127441i	$0.0406764\pi$
$23$	1.50216e6	+	1.50216e6i	1.11929	+	1.11929i	0.127441	+	0.991846i	$0.459324\pi$
$24$	1.63015e6	−	503474.i	1.00295	−	0.309761i
$25$		0			0
$26$			1.14009e6i			0.489282i
$27$	−2.74375e6	+	312127.i	−0.993592	+	0.113030i
$28$	−256642.	+	256642.i	−0.0789073	+	0.0789073i
$29$	1.94930e6			0.511786			0.255893	−	0.966705i	$-0.417631\pi$
$29$	1.94930e6			0.511786			0.255893	+	0.966705i	$0.417631\pi$
$30$		0			0
$31$	954139.			0.185560			0.0927800	−	0.995687i	$-0.470425\pi$
$31$	954139.			0.185560			0.0927800	+	0.995687i	$0.470425\pi$
$32$	−977869.	+	977869.i	−0.164856	+	0.164856i
$33$	7.28275e6	+	3.84571e6i	1.06901	+	0.564500i
$34$			9.52242e6i			1.22206i
$35$		0			0
$36$	975400.	−	666039.i	0.0967880	−	0.0660904i
$37$	−8.41718e6	−	8.41718e6i	−0.738345	−	0.738345i	0.233913	−	0.972258i	$-0.424847\pi$
$37$	−8.41718e6	−	8.41718e6i	−0.738345	−	0.738345i	−0.972258	+	0.233913i	$0.924847\pi$
$38$	5.49753e6	+	5.49753e6i	0.427702	+	0.427702i
$39$	2.22015e6	+	7.18843e6i	0.153671	+	0.497558i
$40$		0			0
$41$		−	1.47423e7i		−	0.814778i	−0.913255	−	0.407389i	$-0.866439\pi$
$41$		−	1.47423e7i		−	0.814778i	0.913255	−	0.407389i	$-0.133561\pi$
$42$	8.42422e6	−	1.59532e7i	0.417742	−	0.791091i
$43$	2.54869e7	−	2.54869e7i	1.13687	−	1.13687i	0.147857	−	0.989009i	$-0.452762\pi$
$43$	2.54869e7	−	2.54869e7i	1.13687	−	1.13687i	0.989009	−	0.147857i	$-0.0472375\pi$
$44$	−3.52254e6			−0.141684
$45$		0			0
$46$	4.51646e7			1.48726
$47$	−5.21954e6	+	5.21954e6i	−0.156024	+	0.156024i	−0.780802	−	0.624778i	$-0.785189\pi$
$47$	−5.21954e6	+	5.21954e6i	−0.156024	+	0.156024i	0.624778	+	0.780802i	$0.285189\pi$
$48$	1.49249e7	−	2.82637e7i	0.405812	−	0.768498i
$49$		−	3.76964e6i		−	0.0934151i
$50$		0			0
$51$	1.85435e7	+	6.00402e7i	0.383818	+	1.24273i
$52$	−2.27539e6	−	2.27539e6i	−0.0431559	−	0.0431559i
$53$	−8.10562e6	−	8.10562e6i	−0.141106	−	0.141106i	0.633025	−	0.774131i	$-0.281813\pi$
$53$	−8.10562e6	−	8.10562e6i	−0.141106	−	0.141106i	−0.774131	+	0.633025i	$0.781813\pi$
$54$	−3.65551e7	+	4.59396e7i	−0.585027	+	0.735217i
$55$		0			0
$56$			7.35550e7i			0.999462i
$57$	4.53684e7	+	2.39571e7i	0.569267	+	0.300606i
$58$	2.93042e7	−	2.93042e7i	0.340020	−	0.340020i
$59$	−1.67070e8			−1.79500			−0.897499	−	0.441016i	$-0.854618\pi$
$59$	−1.67070e8			−1.79500			−0.897499	+	0.441016i	$0.854618\pi$
$60$		0			0
$61$	2.01613e8			1.86438			0.932188	−	0.361974i	$-0.117897\pi$
$61$	2.01613e8			1.86438			0.932188	+	0.361974i	$0.117897\pi$
$62$	1.43438e7	−	1.43438e7i	0.123282	−	0.123282i
$63$	2.20495e7	−	1.16992e8i	0.176346	−	0.935675i
$64$			1.46045e8i			1.08812i
$65$		0			0
$66$	1.67296e8	−	5.16696e7i	1.08527	−	0.335187i
$67$	2.48357e7	+	2.48357e7i	0.150570	+	0.150570i	0.778373	−	0.627802i	$-0.216045\pi$
$67$	2.48357e7	+	2.48357e7i	0.150570	+	0.150570i	−0.627802	+	0.778373i	$0.716045\pi$
$68$	−1.90048e7	−	1.90048e7i	−0.107789	−	0.107789i
$69$	2.84769e8	−	8.79513e7i	1.51242	−	0.467112i
$70$		0			0
$71$			3.74056e7i			0.174693i	0.996178	+	0.0873463i	$0.0278387\pi$
$71$			3.74056e7i			0.174693i	−0.996178	+	0.0873463i	$0.972161\pi$
$72$	4.43323e7	−	2.35223e8i	0.194412	−	1.03153i
$73$	2.74232e8	−	2.74232e8i	1.13023	−	1.13023i	0.140087	−	0.990139i	$-0.455262\pi$
$73$	2.74232e8	−	2.74232e8i	1.13023	−	1.13023i	0.990139	−	0.140087i	$-0.0447383\pi$
$74$	−2.53074e8			−0.981082
$75$		0			0
$76$	−2.19439e7			−0.0754489
$77$	−2.51067e8	+	2.51067e8i	−0.813918	+	0.813918i
$78$	1.41441e8	+	7.46891e7i	0.432663	+	0.228471i
$79$			2.73806e8i			0.790899i	0.918488	+	0.395450i	$0.129411\pi$
$79$			2.73806e8i			0.790899i	−0.918488	+	0.395450i	$0.870589\pi$
$80$		0			0
$81$	−1.41025e8	+	3.60842e8i	−0.364009	+	0.931395i
$82$	−2.21625e8	−	2.21625e8i	−0.541322	−	0.541322i
$83$	4.89787e8	+	4.89787e8i	1.13281	+	1.13281i	0.989708	+	0.143098i	$0.0457065\pi$
$83$	4.89787e8	+	4.89787e8i	1.13281	+	1.13281i	0.143098	+	0.989708i	$0.454294\pi$
$84$	1.50263e7	+	4.86524e7i	0.0329304	+	0.106622i
$85$		0			0
$86$		−	7.66299e8i		−	1.51062i
$87$	1.27702e8	−	2.41833e8i	0.238980	−	0.452563i
$88$	−5.04790e8	+	5.04790e8i	−0.897302	+	0.897302i
$89$	4.96975e8			0.839614			0.419807	−	0.907613i	$-0.362098\pi$
$89$	4.96975e8			0.839614			0.419807	+	0.907613i	$0.362098\pi$
$90$		0			0
$91$	−3.24353e8			−0.495829
$92$	−9.01394e7	+	9.01394e7i	−0.131181	+	0.131181i
$93$	6.25072e7	−	1.18372e8i	0.0866477	−	0.164087i
$94$			1.56933e8i			0.207318i
$95$		0			0
$96$	5.72540e7	+	1.85378e8i	0.0687995	+	0.222760i
$97$	−2.56266e8	−	2.56266e8i	−0.293912	−	0.293912i	0.544711	−	0.838624i	$-0.316639\pi$
$97$	−2.56266e8	−	2.56266e8i	−0.293912	−	0.293912i	−0.838624	+	0.544711i	$0.816639\pi$
$98$	−5.66697e7	−	5.66697e7i	−0.0620631	−	0.0620631i
$99$	9.54209e8	−	6.51569e8i	0.998356	−	0.681714i
$100$		0			0
$101$		−	3.60064e8i		−	0.344297i	−0.985071	−	0.172149i	$-0.944929\pi$
$101$		−	3.60064e8i		−	0.344297i	0.985071	−	0.172149i	$-0.0550710\pi$
$102$	1.18136e9	+	6.23829e8i	1.08064	+	0.570643i
$103$	−8.25833e8	+	8.25833e8i	−0.722977	+	0.722977i	−0.969211	−	0.246233i	$-0.920807\pi$
$103$	−8.25833e8	+	8.25833e8i	−0.722977	+	0.722977i	0.246233	+	0.969211i	$0.420807\pi$
$104$	−6.52138e8			−0.546625
$105$		0			0
$106$	−2.43707e8			−0.187496
$107$	−1.88280e9	+	1.88280e9i	−1.38860	+	1.38860i	−0.560329	+	0.828270i	$0.689325\pi$
$107$	−1.88280e9	+	1.88280e9i	−1.38860	+	1.38860i	−0.828270	+	0.560329i	$0.810675\pi$
$108$	−1.87296e7	−	1.64643e8i	−0.0132472	−	0.116449i
$109$		−	1.44473e9i		−	0.980322i	−0.871632	−	0.490161i	$-0.836938\pi$
$109$		−	1.44473e9i		−	0.980322i	0.871632	−	0.490161i	$-0.163062\pi$
$110$		0			0
$111$	−1.59567e9	+	4.92824e8i	−0.997677	+	0.308133i
$112$	9.74366e8	+	9.74366e8i	0.585115	+	0.585115i
$113$	−2.00599e9	−	2.00599e9i	−1.15738	−	1.15738i	−0.985037	−	0.172343i	$-0.944866\pi$
$113$	−2.00599e9	−	2.00599e9i	−1.15738	−	1.15738i	−0.172343	−	0.985037i	$-0.555134\pi$
$114$	1.04218e9	−	3.21879e8i	0.577926	−	0.178493i
$115$		0			0
$116$			1.16971e8i			0.0599813i
$117$	1.03725e9	+	1.95491e8i	0.511739	+	0.0964472i
$118$	−2.51159e9	+	2.51159e9i	−1.19256	+	1.19256i
$119$	−2.70911e9			−1.23841
$120$		0			0
$121$	−1.08807e9			−0.461448
$122$	3.03088e9	−	3.03088e9i	1.23865	−	1.23865i
$123$	−1.82896e9	−	9.65795e8i	−0.720494	−	0.380463i
$124$			5.72545e7i			0.0217476i
$125$		0			0
$126$	−1.42729e9	−	2.09024e9i	−0.504482	−	0.738804i
$127$	−1.92166e9	−	1.92166e9i	−0.655480	−	0.655480i	0.298827	−	0.954307i	$-0.403405\pi$
$127$	−1.92166e9	−	1.92166e9i	−0.655480	−	0.655480i	−0.954307	+	0.298827i	$0.903405\pi$
$128$	1.69485e9	+	1.69485e9i	0.558067	+	0.558067i
$129$	−1.49225e9	−	4.83163e9i	−0.474448	−	1.53617i
$130$		0			0
$131$			1.60347e9i			0.475708i	0.971301	+	0.237854i	$0.0764439\pi$
$131$			1.60347e9i			0.475708i	−0.971301	+	0.237854i	$0.923556\pi$
$132$	−2.30768e8	+	4.37012e8i	−0.0661595	+	0.125288i
$133$	−1.56404e9	+	1.56404e9i	−0.433426	+	0.433426i
$134$	7.46719e8			0.200072
$135$		0			0
$136$	−5.44688e9			−1.36528
$137$	1.59065e8	−	1.59065e8i	0.0385774	−	0.0385774i	−0.687555	−	0.726132i	$-0.741316\pi$
$137$	1.59065e8	−	1.59065e8i	0.0385774	−	0.0385774i	0.726132	+	0.687555i	$0.241316\pi$
$138$	2.95881e9	−	5.60318e9i	0.694481	−	1.31516i
$139$			5.31088e9i			1.20670i	0.797476	+	0.603351i	$0.206168\pi$
$139$			5.31088e9i			1.20670i	−0.797476	+	0.603351i	$0.793832\pi$
$140$		0			0
$141$	3.05603e8	+	9.89484e8i	0.0651135	+	0.210825i
$142$	5.62326e8	+	5.62326e8i	0.116062	+	0.116062i
$143$	−2.22596e9	−	2.22596e9i	−0.445148	−	0.445148i
$144$	−2.52868e9	−	3.70320e9i	−0.490075	−	0.717704i
$145$		0			0
$146$		−	8.24517e9i		−	1.50180i
$147$	−4.67667e8	−	2.46955e8i	−0.0826054	−	0.0436204i
$148$	5.05085e8	−	5.05085e8i	0.0865340	−	0.0865340i
$149$	8.13798e9			1.35263			0.676314	−	0.736614i	$-0.263576\pi$
$149$	8.13798e9			1.35263			0.676314	+	0.736614i	$0.263576\pi$
$150$		0			0
$151$	6.40439e9			1.00249			0.501247	−	0.865304i	$-0.332875\pi$
$151$	6.40439e9			1.00249			0.501247	+	0.865304i	$0.332875\pi$
$152$	−3.14462e9	+	3.14462e9i	−0.477829	+	0.477829i
$153$	8.66349e9	+	1.63280e9i	1.27815	+	0.240892i
$154$			7.54867e9i			1.08150i
$155$		0			0
$156$	−4.31352e8	+	1.33223e8i	−0.0583138	+	0.0180103i
$157$	−6.49876e9	−	6.49876e9i	−0.853654	−	0.853654i	0.136927	−	0.990581i	$-0.456277\pi$
$157$	−6.49876e9	−	6.49876e9i	−0.853654	−	0.853654i	−0.990581	+	0.136927i	$0.956277\pi$
$158$	4.11618e9	+	4.11618e9i	0.525457	+	0.525457i
$159$	−1.53661e9	+	4.74582e8i	−0.190667	+	0.0588876i
$160$		0			0
$161$			1.28492e10i			1.50717i
$162$	3.30455e9	+	7.54465e9i	0.376960	+	0.860640i
$163$	−9.25166e9	+	9.25166e9i	−1.02654	+	1.02654i	−0.0269009	+	0.999638i	$0.508564\pi$
$163$	−9.25166e9	+	9.25166e9i	−1.02654	+	1.02654i	−0.999638	+	0.0269009i	$0.991436\pi$
$164$	8.84636e8			0.0954920
$165$		0			0
$166$	1.47261e10			1.50523
$167$	7.67500e9	−	7.67500e9i	0.763579	−	0.763579i	−0.213388	−	0.976967i	$-0.568450\pi$
$167$	7.67500e9	−	7.67500e9i	0.763579	−	0.763579i	0.976967	+	0.213388i	$0.0684500\pi$
$168$	9.12534e9	+	4.81871e9i	0.883807	+	0.466701i
$169$			7.72879e9i			0.728821i
$170$		0			0
$171$	5.94431e9	−	4.05899e9i	0.531642	−	0.363024i
$172$	1.52938e9	+	1.52938e9i	0.133241	+	0.133241i
$173$	5.16863e8	+	5.16863e8i	0.0438700	+	0.0438700i	0.728701	−	0.684831i	$-0.240124\pi$
$173$	5.16863e8	+	5.16863e8i	0.0438700	+	0.0438700i	−0.684831	+	0.728701i	$0.740124\pi$
$174$	−1.71576e9	−	5.55529e9i	−0.141900	−	0.459447i
$175$		0			0
$176$			1.33737e10i			1.05061i
$177$	−1.09450e10	+	2.07269e10i	−0.838179	+	1.58729i
$178$	7.47112e9	−	7.47112e9i	0.557822	−	0.557822i
$179$	1.26193e10			0.918747			0.459373	−	0.888243i	$-0.348074\pi$
$179$	1.26193e10			0.918747			0.459373	+	0.888243i	$0.348074\pi$
$180$		0			0
$181$	1.86530e10			1.29180			0.645899	−	0.763423i	$-0.276483\pi$
$181$	1.86530e10			1.29180			0.645899	+	0.763423i	$0.276483\pi$
$182$	−4.87606e9	+	4.87606e9i	−0.329419	+	0.329419i
$183$	1.32080e10	−	2.50123e10i	0.870575	−	1.64864i
$184$			2.58344e10i			1.66157i
$185$		0			0
$186$	−8.39824e8	−	2.71919e9i	−0.0514493	−	0.166583i
$187$	−1.85919e10	−	1.85919e10i	−1.11183	−	1.11183i
$188$	−3.13206e8	−	3.13206e8i	−0.0182860	−	0.0182860i
$189$	−1.30697e10	−	1.03998e10i	−0.745055	−	0.592855i
$190$		0			0
$191$		−	1.11678e10i		−	0.607182i	−0.952802	−	0.303591i	$-0.901814\pi$
$191$		−	1.11678e10i		−	0.607182i	0.952802	−	0.303591i	$-0.0981856\pi$
$192$	1.81185e10	+	9.56763e9i	0.962204	+	0.508100i
$193$	−3.98322e9	+	3.98322e9i	−0.206646	+	0.206646i	−0.802840	−	0.596194i	$-0.796679\pi$
$193$	−3.98322e9	+	3.98322e9i	−0.206646	+	0.206646i	0.596194	+	0.802840i	$0.296679\pi$
$194$	−7.70498e9			−0.390538
$195$		0			0
$196$	2.26203e8			0.0109483
$197$	2.21732e10	−	2.21732e10i	1.04889	−	1.04889i	0.0501502	−	0.998742i	$-0.484030\pi$
$197$	2.21732e10	−	2.21732e10i	1.04889	−	1.04889i	0.998742	−	0.0501502i	$-0.0159700\pi$
$198$	4.54965e9	−	2.41400e10i	0.210370	−	1.11620i
$199$		−	1.22079e10i		−	0.551826i	−0.961183	−	0.275913i	$-0.911020\pi$
$199$		−	1.22079e10i		−	0.551826i	0.961183	−	0.275913i	$-0.0889801\pi$
$200$		0			0
$201$	4.70818e9	−	1.45412e9i	0.203456	−	0.0628375i
$202$	−5.41291e9	−	5.41291e9i	−0.228744	−	0.228744i
$203$	8.33700e9	+	8.33700e9i	0.344570	+	0.344570i
$204$	−3.60280e9	+	1.11273e9i	−0.145648	+	0.0449835i
$205$		0			0
$206$			2.48298e10i			0.960662i
$207$	7.74435e9	−	4.10907e10i	0.293169	−	1.55553i
$208$	−8.63872e9	+	8.63872e9i	−0.320011	+	0.320011i
$209$	−2.14672e10			−0.778246
$210$		0			0
$211$	−1.11197e10			−0.386208			−0.193104	−	0.981178i	$-0.561855\pi$
$211$	−1.11197e10			−0.386208			−0.193104	+	0.981178i	$0.561855\pi$
$212$	4.86389e8	−	4.86389e8i	0.0165376	−	0.0165376i
$213$	4.64060e9	+	2.45050e9i	0.154478	+	0.0815732i
$214$			5.66089e10i			1.84511i
$215$		0			0
$216$	−2.62778e10	−	2.09097e10i	−0.821384	−	0.653592i
$217$	4.08077e9	+	4.08077e9i	0.124932	+	0.124932i
$218$	−2.17190e10	−	2.17190e10i	−0.651305	−	0.651305i
$219$	−1.60562e10	−	5.19870e10i	−0.471677	−	1.52720i
$220$		0			0
$221$		−	2.40189e10i		−	0.677312i
$222$	−1.65793e10	+	3.13967e10i	−0.458119	+	0.867553i
$223$	−7.16715e9	+	7.16715e9i	−0.194077	+	0.194077i	−0.797455	−	0.603378i	$-0.793821\pi$
$223$	−7.16715e9	+	7.16715e9i	−0.194077	+	0.194077i	0.603378	+	0.797455i	$0.293821\pi$
$224$	−8.36452e9			−0.221986
$225$		0			0
$226$	−6.03129e10			−1.53788
$227$	−1.18533e10	+	1.18533e10i	−0.296293	+	0.296293i	−0.839560	−	0.543267i	$-0.817187\pi$
$227$	−1.18533e10	+	1.18533e10i	−0.296293	+	0.296293i	0.543267	+	0.839560i	$0.317187\pi$
$228$	−1.43758e9	+	2.72239e9i	−0.0352311	+	0.0667182i
$229$		−	4.34035e10i		−	1.04295i	−0.853265	−	0.521477i	$-0.825381\pi$
$229$		−	4.34035e10i		−	1.04295i	0.853265	−	0.521477i	$-0.174619\pi$
$230$		0			0
$231$	1.46999e10	+	4.75955e10i	0.339672	+	1.09979i
$232$	1.67622e10	+	1.67622e10i	0.379870	+	0.379870i
$233$	−2.50926e10	−	2.50926e10i	−0.557756	−	0.557756i	0.370912	−	0.928668i	$-0.379045\pi$
$233$	−2.50926e10	−	2.50926e10i	−0.557756	−	0.557756i	−0.928668	+	0.370912i	$0.879045\pi$
$234$	1.85321e10	−	1.26544e10i	0.404066	−	0.275911i
$235$		0			0
$236$		−	1.00253e10i		−	0.210374i
$237$	3.39688e10	+	1.79375e10i	0.699378	+	0.369312i
$238$	−4.07265e10	+	4.07265e10i	−0.822775	+	0.822775i
$239$	6.27536e10			1.24408			0.622040	−	0.782986i	$-0.286304\pi$
$239$	6.27536e10			1.24408			0.622040	+	0.782986i	$0.286304\pi$
$240$		0			0
$241$	5.35362e10			1.02228			0.511141	−	0.859497i	$-0.329223\pi$
$241$	5.35362e10			1.02228			0.511141	+	0.859497i	$0.329223\pi$
$242$	−1.63572e10	+	1.63572e10i	−0.306576	+	0.306576i
$243$	3.55278e10	+	4.11350e10i	0.653641	+	0.756804i
$244$			1.20981e10i			0.218505i
$245$		0			0
$246$	−4.20140e10	+	1.29761e10i	−0.731453	+	0.225910i
$247$	−1.38667e10	−	1.38667e10i	−0.237049	−	0.237049i
$248$	8.20472e9	+	8.20472e9i	0.137731	+	0.137731i
$249$	9.28504e10	−	2.86769e10i	1.53069	−	0.472754i
$250$		0			0
$251$		−	9.48545e10i		−	1.50843i	−0.656625	−	0.754217i	$-0.728017\pi$
$251$		−	9.48545e10i		−	1.50843i	0.656625	−	0.754217i	$-0.271983\pi$
$252$	7.02029e9	+	1.32311e9i	0.109661	+	0.0206678i
$253$	−8.81811e10	+	8.81811e10i	−1.35311	+	1.35311i
$254$	−5.77773e10			−0.870975
$255$		0			0
$256$	−2.38169e10			−0.346582
$257$	−5.10241e10	+	5.10241e10i	−0.729585	+	0.729585i	−0.970537	−	0.240952i	$-0.922540\pi$
$257$	−5.10241e10	+	5.10241e10i	−0.729585	+	0.729585i	0.240952	+	0.970537i	$0.422540\pi$
$258$	−9.50681e10	−	5.02015e10i	−1.33581	−	0.705388i
$259$		−	7.19991e10i		−	0.994210i
$260$		0			0
$261$	−2.16362e10	−	3.16858e10i	−0.288601	−	0.422651i
$262$	2.41053e10	+	2.41053e10i	0.316050	+	0.316050i
$263$	6.25001e10	+	6.25001e10i	0.805526	+	0.805526i	0.983953	−	0.178427i	$-0.0571008\pi$
$263$	6.25001e10	+	6.25001e10i	0.805526	+	0.805526i	−0.178427	+	0.983953i	$0.557101\pi$
$264$	2.95553e10	+	9.56946e10i	0.374471	+	1.21247i
$265$		0			0
$266$			4.70249e10i			0.575918i
$267$	3.25577e10	−	6.16554e10i	0.392060	−	0.742456i
$268$	−1.49030e9	+	1.49030e9i	−0.0176469	+	0.0176469i
$269$	3.82865e9			0.0445820			0.0222910	−	0.999752i	$-0.492904\pi$
$269$	3.82865e9			0.0445820			0.0222910	+	0.999752i	$0.492904\pi$
$270$		0			0
$271$	−9.96579e10			−1.12241			−0.561203	−	0.827678i	$-0.689661\pi$
$271$	−9.96579e10			−1.12241			−0.561203	+	0.827678i	$0.689661\pi$
$272$	−7.21536e10	+	7.21536e10i	−0.799278	+	0.799278i
$273$	−2.12489e10	+	4.02397e10i	−0.231529	+	0.438453i
$274$		−	4.78251e9i		−	0.0512600i
$275$		0			0
$276$	5.27764e9	+	1.70880e10i	0.0547456	+	0.177256i
$277$	−4.01414e10	−	4.01414e10i	−0.409670	−	0.409670i	0.471954	−	0.881623i	$-0.343549\pi$
$277$	−4.01414e10	−	4.01414e10i	−0.409670	−	0.409670i	−0.881623	+	0.471954i	$0.843549\pi$
$278$	7.98395e10	+	7.98395e10i	0.801708	+	0.801708i
$279$	−1.05904e10	−	1.55095e10i	−0.104639	−	0.153242i
$280$		0			0
$281$			4.70608e10i			0.450278i	0.974327	+	0.225139i	$0.0722836\pi$
$281$			4.70608e10i			0.450278i	−0.974327	+	0.225139i	$0.927716\pi$
$282$	1.94693e10	+	1.02809e10i	0.183328	+	0.0968079i
$283$	9.88934e10	−	9.88934e10i	0.916492	−	0.916492i	−0.0802806	−	0.996772i	$-0.525582\pi$
$283$	9.88934e10	−	9.88934e10i	0.916492	−	0.916492i	0.996772	+	0.0802806i	$0.0255816\pi$
$284$	−2.24458e9			−0.0204740
$285$		0			0
$286$	−6.69264e10			−0.591494
$287$	6.30517e10	−	6.30517e10i	0.548566	−	0.548566i
$288$	2.67490e10	+	5.04138e9i	0.229109	+	0.0431800i
$289$		−	8.20265e10i		−	0.691694i
$290$		0			0
$291$	−4.85810e10	+	1.50043e10i	−0.397144	+	0.122658i
$292$	1.64557e10	+	1.64557e10i	0.132463	+	0.132463i
$293$	−1.25197e11	−	1.25197e11i	−0.992409	−	0.992409i	0.00756274	−	0.999971i	$-0.497593\pi$
$293$	−1.25197e11	−	1.25197e11i	−0.992409	−	0.992409i	−0.999971	+	0.00756274i	$0.997593\pi$
$294$	−1.07430e10	+	3.31800e9i	−0.0838618	+	0.0259008i
$295$		0			0
$296$		−	1.44760e11i		−	1.09606i
$297$	−1.83227e10	−	1.61066e11i	−0.136643	−	1.20116i
$298$	1.22340e11	−	1.22340e11i	0.898658	−	0.898658i
$299$	−1.13921e11			−0.824298
$300$		0			0
$301$	2.18011e11			1.53084
$302$	9.62785e10	−	9.62785e10i	0.666036	−	0.666036i
$303$	−4.46701e10	−	2.35884e10i	−0.304456	−	0.160771i
$304$			8.33121e10i			0.559470i
$305$		0			0
$306$	1.54786e11	−	1.05694e11i	1.00922	−	0.689132i
$307$	−2.18198e10	−	2.18198e10i	−0.140194	−	0.140194i	0.633527	−	0.773721i	$-0.281607\pi$
$307$	−2.18198e10	−	2.18198e10i	−0.140194	−	0.140194i	−0.773721	+	0.633527i	$0.781607\pi$
$308$	−1.50656e10	−	1.50656e10i	−0.0953913	−	0.0953913i
$309$	4.83523e10	+	1.56556e11i	0.301720	+	0.976912i
$310$		0			0
$311$		−	3.16948e9i		−	0.0192117i	−0.999954	−	0.00960585i	$-0.996942\pi$
$311$		−	3.16948e9i		−	0.0192117i	0.999954	−	0.00960585i	$-0.00305768\pi$
$312$	−4.27226e10	+	8.09052e10i	−0.255248	+	0.483371i
$313$	1.00138e11	−	1.00138e11i	0.589728	−	0.589728i	−0.347830	−	0.937558i	$-0.613081\pi$
$313$	1.00138e11	−	1.00138e11i	0.589728	−	0.589728i	0.937558	+	0.347830i	$0.113081\pi$
$314$	−1.95394e11			−1.13430
$315$		0			0
$316$	−1.64301e10			−0.0926935
$317$	−2.05821e10	+	2.05821e10i	−0.114478	+	0.114478i	−0.762025	−	0.647547i	$-0.775795\pi$
$317$	−2.05821e10	+	2.05821e10i	−0.114478	+	0.114478i	0.647547	+	0.762025i	$0.275795\pi$
$318$	−1.59656e10	+	3.02346e10i	−0.0875515	+	0.165799i
$319$			1.14429e11i			0.618700i
$320$		0			0
$321$	1.10237e11	+	3.56928e11i	0.579504	+	1.87632i
$322$	1.93165e11	+	1.93165e11i	1.00133	+	1.00133i
$323$	−1.15820e11	−	1.15820e11i	−0.592067	−	0.592067i
$324$	−2.16528e10	−	8.46239e9i	−0.109160	−	0.0426619i
$325$		0			0
$326$			2.78164e11i			1.36402i
$327$	−1.79236e11	−	9.46468e10i	−0.866881	−	0.457764i
$328$	1.26771e11	−	1.26771e11i	0.604765	−	0.604765i
$329$	−4.46470e10			−0.210093
$330$		0			0
$331$	1.80028e11			0.824354			0.412177	−	0.911104i	$-0.364769\pi$
$331$	1.80028e11			0.824354			0.412177	+	0.911104i	$0.364769\pi$
$332$	−2.93904e10	+	2.93904e10i	−0.132765	+	0.132765i
$333$	−4.33945e10	+	2.30247e11i	−0.193391	+	1.02611i
$334$		−	2.30759e11i		−	1.01461i
$335$		0			0
$336$	1.84714e11	−	5.70489e10i	0.790627	−	0.244186i
$337$	1.08948e11	+	1.08948e11i	0.460133	+	0.460133i	0.898699	−	0.438566i	$-0.144514\pi$
$337$	1.08948e11	+	1.08948e11i	0.460133	+	0.460133i	−0.438566	+	0.898699i	$0.644514\pi$
$338$	1.16188e11	+	1.16188e11i	0.484214	+	0.484214i
$339$	−3.80282e11	+	1.17450e11i	−1.56389	+	0.483009i
$340$		0			0
$341$			5.60106e10i			0.224324i
$342$	2.83423e10	−	1.50382e11i	0.112026	−	0.594398i
$343$	1.88711e11	−	1.88711e11i	0.736164	−	0.736164i
$344$	4.38328e11			1.68767
$345$		0			0
$346$	1.55402e10			0.0582927
$347$	−7.90399e10	+	7.90399e10i	−0.292660	+	0.292660i	−0.838130	−	0.545470i	$-0.816351\pi$
$347$	−7.90399e10	+	7.90399e10i	−0.292660	+	0.292660i	0.545470	+	0.838130i	$0.316351\pi$
$348$	1.45115e10	+	7.66294e9i	0.0530404	+	0.0280084i
$349$		−	2.24682e11i		−	0.810686i	−0.914165	−	0.405343i	$-0.867152\pi$
$349$		−	2.24682e11i		−	0.810686i	0.914165	−	0.405343i	$-0.132848\pi$
$350$		0			0
$351$	9.22050e10	−	1.15876e11i	0.324244	−	0.407485i
$352$	−5.74036e10	−	5.74036e10i	−0.199295	−	0.199295i
$353$	7.92789e9	+	7.92789e9i	0.0271751	+	0.0271751i	0.720564	−	0.693389i	$-0.243883\pi$
$353$	7.92789e9	+	7.92789e9i	0.0271751	+	0.0271751i	−0.693389	+	0.720564i	$0.743883\pi$
$354$	1.47053e11	+	4.76130e11i	0.497691	+	1.61143i
$355$		0			0
$356$			2.98217e10i			0.0984028i
$357$	−1.77478e11	+	3.36096e11i	−0.578279	+	1.09511i
$358$	1.89708e11	−	1.89708e11i	0.610396	−	0.610396i
$359$	5.62393e11			1.78696			0.893480	−	0.449103i	$-0.148256\pi$
$359$	5.62393e11			1.78696			0.893480	+	0.449103i	$0.148256\pi$
$360$		0			0
$361$	1.88956e11			0.585571
$362$	2.80414e11	−	2.80414e11i	0.858244	−	0.858244i
$363$	−7.12812e10	+	1.34987e11i	−0.215474	+	0.408050i
$364$		−	1.94633e10i		−	0.0581112i
$365$		0			0
$366$	−1.77457e11	−	5.74573e11i	−0.516927	−	1.67371i
$367$	−1.06525e11	−	1.06525e11i	−0.306516	−	0.306516i	0.537040	−	0.843557i	$-0.319542\pi$
$367$	−1.06525e11	−	1.06525e11i	−0.306516	−	0.306516i	−0.843557	+	0.537040i	$0.819542\pi$
$368$	3.42223e11	+	3.42223e11i	0.972732	+	0.972732i
$369$	−2.39636e11	+	1.63632e11i	−0.672873	+	0.459462i
$370$		0			0
$371$		−	6.93340e10i		−	0.190005i
$372$	7.10307e9	+	3.75083e9i	0.0192310	+	0.0101551i
$373$	−1.55548e11	+	1.55548e11i	−0.416077	+	0.416077i	−0.883849	−	0.467772i	$-0.845057\pi$
$373$	−1.55548e11	+	1.55548e11i	−0.416077	+	0.416077i	0.467772	+	0.883849i	$0.345057\pi$
$374$	−5.58992e11			−1.47735
$375$		0			0
$376$	−8.97665e10			−0.231616
$377$	−7.39157e10	+	7.39157e10i	−0.188452	+	0.188452i
$378$	−3.52823e11	+	4.01369e10i	−0.888880	+	0.101118i
$379$			2.29013e11i			0.570144i	0.958506	+	0.285072i	$0.0920174\pi$
$379$			2.29013e11i			0.570144i	−0.958506	+	0.285072i	$0.907983\pi$
$380$		0			0
$381$	−3.64295e11	+	1.12513e11i	−0.885708	+	0.273552i
$382$	−1.67888e11	−	1.67888e11i	−0.403399	−	0.403399i
$383$	6.39342e10	+	6.39342e10i	0.151823	+	0.151823i	0.778932	−	0.627108i	$-0.215762\pi$
$383$	6.39342e10	+	6.39342e10i	0.151823	+	0.151823i	−0.627108	+	0.778932i	$0.715762\pi$
$384$	3.21298e11	−	9.92331e10i	0.754080	−	0.232898i
$385$		0			0
$386$			1.19761e11i			0.274582i
$387$	−6.97179e11	−	1.31397e11i	−1.57996	−	0.297774i
$388$	1.53776e10	−	1.53776e10i	0.0344465	−	0.0344465i
$389$	4.87453e11			1.07934			0.539672	−	0.841876i	$-0.318548\pi$
$389$	4.87453e11			1.07934			0.539672	+	0.841876i	$0.318548\pi$
$390$		0			0
$391$	−9.51509e11			−2.05882
$392$	3.24154e10	−	3.24154e10i	0.0693369	−	0.0693369i
$393$	1.98929e11	+	1.05046e11i	0.420660	+	0.222133i
$394$		−	6.66668e11i		−	1.39372i
$395$		0			0
$396$	3.90983e10	+	5.72587e10i	0.0798969	+	0.117007i
$397$	4.27138e11	+	4.27138e11i	0.863001	+	0.863001i	0.991686	−	0.128685i	$-0.0410755\pi$
$397$	4.27138e11	+	4.27138e11i	0.863001	+	0.863001i	−0.128685	+	0.991686i	$0.541075\pi$
$398$	−1.83524e11	−	1.83524e11i	−0.366622	−	0.366622i
$399$	9.15740e10	+	2.96499e11i	0.180881	+	0.585660i
$400$		0			0
$401$		−	1.38991e11i		−	0.268434i	−0.990952	−	0.134217i	$-0.957148\pi$
$401$		−	1.38991e11i		−	0.268434i	0.990952	−	0.134217i	$-0.0428519\pi$
$402$	4.89188e10	−	9.26390e10i	0.0934240	−	0.176920i
$403$	−3.61801e10	+	3.61801e10i	−0.0683277	+	0.0683277i
$404$	2.16062e10			0.0403517
$405$		0			0
$406$	2.50663e11			0.457850
$407$	4.94112e11	−	4.94112e11i	0.892587	−	0.892587i
$408$	−3.56834e11	+	6.75748e11i	−0.637523	+	1.20730i
$409$		−	7.31249e11i		−	1.29214i	−0.763277	−	0.646072i	$-0.776411\pi$
$409$		−	7.31249e11i		−	1.29214i	0.763277	−	0.646072i	$-0.223589\pi$
$410$		0			0
$411$	−9.31323e9	−	3.01545e10i	−0.0160995	−	0.0521271i
$412$	−4.95553e10	−	4.95553e10i	−0.0847330	−	0.0847330i
$413$	−7.14543e11	−	7.14543e11i	−1.20852	−	1.20852i
$414$	−5.01302e11	−	7.34147e11i	−0.838684	−	1.22823i
$415$		0			0
$416$		−	7.41598e10i		−	0.121408i
$417$	6.58875e11	+	3.47924e11i	1.06706	+	0.563472i
$418$	−3.22720e11	+	3.22720e11i	−0.517051	+	0.517051i
$419$	−2.26783e11			−0.359458			−0.179729	−	0.983716i	$-0.557522\pi$
$419$	−2.26783e11			−0.359458			−0.179729	+	0.983716i	$0.557522\pi$
$420$		0			0
$421$	−9.78678e11			−1.51834			−0.759172	−	0.650890i	$-0.774396\pi$
$421$	−9.78678e11			−1.51834			−0.759172	+	0.650890i	$0.774396\pi$
$422$	−1.67164e11	+	1.67164e11i	−0.256588	+	0.256588i
$423$	1.42777e11	+	2.69092e10i	0.216834	+	0.0408666i
$424$		−	1.39402e11i		−	0.209470i
$425$		0			0
$426$	1.06602e11	−	3.29241e10i	0.156827	−	0.0484362i
$427$	8.62280e11	+	8.62280e11i	1.25523	+	1.25523i
$428$	−1.12980e11	−	1.12980e11i	−0.162744	−	0.162744i
$429$	−4.21981e11	+	1.30329e11i	−0.601499	+	0.185774i
$430$		0			0
$431$		−	2.24677e10i		−	0.0313625i	−0.999877	−	0.0156812i	$-0.995008\pi$
$431$		−	2.24677e10i		−	0.0313625i	0.999877	−	0.0156812i	$-0.00499170\pi$
$432$	−6.25081e11	+	7.11088e10i	−0.863495	+	0.0982306i
$433$	−7.66183e10	+	7.66183e10i	−0.104746	+	0.104746i	−0.757538	−	0.652792i	$-0.773598\pi$
$433$	−7.66183e10	+	7.66183e10i	−0.104746	+	0.104746i	0.652792	+	0.757538i	$0.273598\pi$
$434$	1.22694e11			0.166004
$435$		0			0
$436$	8.66933e10			0.114894
$437$	−5.49330e11	+	5.49330e11i	−0.720555	+	0.720555i
$438$	−1.02291e12	−	5.40154e11i	−1.32801	−	0.701268i
$439$			5.84138e11i			0.750628i	0.926898	+	0.375314i	$0.122465\pi$
$439$			5.84138e11i			0.750628i	−0.926898	+	0.375314i	$0.877535\pi$
$440$		0			0
$441$	−6.12752e10	+	4.18409e10i	−0.0771456	+	0.0526778i
$442$	−3.61081e11	−	3.61081e11i	−0.449992	−	0.449992i
$443$	−1.14746e11	−	1.14746e11i	−0.141553	−	0.141553i	0.632779	−	0.774332i	$-0.281914\pi$
$443$	−1.14746e11	−	1.14746e11i	−0.141553	−	0.141553i	−0.774332	+	0.632779i	$0.781914\pi$
$444$	−2.95726e10	−	9.57505e10i	−0.0361132	−	0.116928i
$445$		0			0
$446$			2.15490e11i			0.257882i
$447$	5.33132e11	−	1.00961e12i	0.631613	−	1.19610i
$448$	−6.24621e11	+	6.24621e11i	−0.732597	+	0.732597i
$449$	−3.70236e11			−0.429902			−0.214951	−	0.976625i	$-0.568959\pi$
$449$	−3.70236e11			−0.429902			−0.214951	+	0.976625i	$0.568959\pi$
$450$		0			0
$451$	8.65417e11			0.984988
$452$	1.20372e11	−	1.20372e11i	0.135645	−	0.135645i
$453$	4.19562e11	−	7.94538e11i	0.468117	−	0.886488i
$454$			3.56385e11i			0.393702i
$455$		0			0
$456$	1.84117e11	+	5.96136e11i	0.199412	+	0.645659i
$457$	2.85790e11	+	2.85790e11i	0.306496	+	0.306496i	0.843549	−	0.537053i	$-0.180462\pi$
$457$	2.85790e11	+	2.85790e11i	0.306496	+	0.306496i	−0.537053	+	0.843549i	$0.680462\pi$
$458$	−6.52493e11	−	6.52493e11i	−0.692917	−	0.692917i
$459$	7.70127e11	−	9.67837e11i	0.809852	−	1.01776i
$460$		0			0
$461$		−	7.22179e11i		−	0.744716i	−0.928089	−	0.372358i	$-0.878549\pi$
$461$		−	7.22179e11i		−	0.744716i	0.928089	−	0.372358i	$-0.121451\pi$
$462$	9.36498e11	+	4.94525e11i	0.956352	+	0.505010i
$463$	5.12260e10	−	5.12260e10i	0.0518055	−	0.0518055i	−0.680729	−	0.732535i	$-0.738337\pi$
$463$	5.12260e10	−	5.12260e10i	0.0518055	−	0.0518055i	0.732535	+	0.680729i	$0.238337\pi$
$464$	4.44090e11			0.444775
$465$		0			0
$466$	−7.54444e11			−0.741123
$467$	−6.72730e11	+	6.72730e11i	−0.654508	+	0.654508i	−0.954075	−	0.299567i	$-0.903158\pi$
$467$	−6.72730e11	+	6.72730e11i	−0.654508	+	0.654508i	0.299567	+	0.954075i	$0.403158\pi$
$468$	−1.17307e10	+	6.22418e10i	−0.0113036	+	0.0599758i
$469$			2.12440e11i			0.202749i
$470$		0			0
$471$	−1.23199e12	+	3.80501e11i	−1.15349	+	0.356255i
$472$	−1.43665e12	−	1.43665e12i	−1.33233	−	1.33233i
$473$	1.49615e12	+	1.49615e12i	1.37436	+	1.37436i
$474$	7.80317e11	−	2.41001e11i	0.710016	−	0.219289i
$475$		0			0
$476$		−	1.62564e11i		−	0.145142i
$477$	−4.17883e10	+	2.21724e11i	−0.0369591	+	0.196101i
$478$	9.43387e11	−	9.43387e11i	0.826541	−	0.826541i
$479$	−2.12636e12			−1.84555			−0.922776	−	0.385337i	$-0.874085\pi$
$479$	−2.12636e12			−1.84555			−0.922776	+	0.385337i	$0.874085\pi$
$480$		0			0
$481$	6.38344e11			0.543753
$482$	8.04819e11	−	8.04819e11i	0.679183	−	0.679183i
$483$	1.59409e12	+	8.41774e11i	1.33276	+	0.703775i
$484$		−	6.52912e10i		−	0.0540817i
$485$		0			0
$486$	1.15249e12	+	8.42953e10i	0.937071	+	0.0685394i
$487$	−1.24347e10	−	1.24347e10i	−0.0100174	−	0.0100174i	0.702080	−	0.712098i	$-0.252255\pi$
$487$	−1.24347e10	−	1.24347e10i	−0.0100174	−	0.0100174i	−0.712098	+	0.702080i	$0.752255\pi$
$488$	1.73368e12	+	1.73368e12i	1.38382	+	1.38382i
$489$	5.41683e11	+	1.75387e12i	0.428405	+	1.38710i
$490$		0			0
$491$		−	8.62627e11i		−	0.669817i	−0.942251	−	0.334909i	$-0.891295\pi$
$491$		−	8.62627e11i		−	0.669817i	0.942251	−	0.334909i	$-0.108705\pi$
$492$	5.79539e10	−	1.09749e11i	0.0445902	−	0.0844419i
$493$	−6.17369e11	+	6.17369e11i	−0.470689	+	0.470689i
$494$	−4.16922e11			−0.314981
$495$		0			0
$496$	2.17372e11			0.161263
$497$	−1.59981e11	+	1.59981e11i	−0.117615	+	0.117615i
$498$	9.64732e11	−	1.82694e12i	0.702869	−	1.33105i
$499$			1.50755e12i			1.08848i	0.838931	+	0.544238i	$0.183181\pi$
$499$			1.50755e12i			1.08848i	−0.838931	+	0.544238i	$0.816819\pi$
$500$		0			0
$501$	−4.49369e11	−	1.45497e12i	−0.318664	−	1.03177i
$502$	−1.42597e12	−	1.42597e12i	−1.00217	−	1.00217i
$503$	−3.55435e11	−	3.55435e11i	−0.247574	−	0.247574i	0.572401	−	0.819974i	$-0.306012\pi$
$503$	−3.55435e11	−	3.55435e11i	−0.247574	−	0.247574i	−0.819974	+	0.572401i	$0.806012\pi$
$504$	1.19563e12	−	8.16421e11i	0.825392	−	0.563607i
$505$		0			0
$506$			2.65129e12i			1.79796i
$507$	9.58844e11	+	5.06325e11i	0.644484	+	0.340325i
$508$	1.15312e11	−	1.15312e11i	0.0768223	−	0.0768223i
$509$	1.44389e12			0.953463			0.476731	−	0.879049i	$-0.341821\pi$
$509$	1.44389e12			0.953463			0.476731	+	0.879049i	$0.341821\pi$
$510$		0			0
$511$	2.34573e12			1.52189
$512$	−1.22581e12	+	1.22581e12i	−0.788329	+	0.788329i
$513$	−1.14143e11	−	1.00337e12i	−0.0727646	−	0.639636i
$514$			1.53411e12i			0.969443i
$515$		0			0
$516$	2.89929e11	−	8.95448e10i	0.180040	−	0.0556053i
$517$	−3.06401e11	−	3.06401e11i	−0.188618	−	0.188618i
$518$	−1.08238e12	−	1.08238e12i	−0.660533	−	0.660533i
$519$	9.79832e10	−	3.02622e10i	0.0592787	−	0.0183083i
$520$		0			0
$521$		−	1.98009e12i		−	1.17738i	−0.808360	−	0.588688i	$-0.799645\pi$
$521$		−	1.98009e12i		−	1.17738i	0.808360	−	0.588688i	$-0.200355\pi$
$522$	−8.01599e11	−	1.51077e11i	−0.472541	−	0.0890597i
$523$	−4.47532e11	+	4.47532e11i	−0.261557	+	0.261557i	−0.825686	−	0.564129i	$-0.809212\pi$
$523$	−4.47532e11	+	4.47532e11i	−0.261557	+	0.261557i	0.564129	+	0.825686i	$0.309212\pi$
$524$	−9.62186e10			−0.0557530
$525$		0			0
$526$	1.87915e12			1.07035
$527$	−3.02188e11	+	3.02188e11i	−0.170659	+	0.170659i
$528$	1.65916e12	+	8.76130e11i	0.929040	+	0.490587i
$529$			2.71183e12i			1.50561i
$530$		0			0
$531$	1.85438e12	+	2.71571e12i	1.01222	+	1.48237i
$532$	−9.38522e10	−	9.38522e10i	−0.0507975	−	0.0507975i
$533$	5.59016e11	+	5.59016e11i	0.300021	+	0.300021i
$534$	−4.37433e11	−	1.41632e12i	−0.232796	−	0.753749i
$535$		0			0
$536$			4.27128e11i			0.223520i
$537$	8.26709e11	−	1.56557e12i	0.429011	−	0.812432i
$538$	5.75568e10	−	5.75568e10i	0.0296194	−	0.0296194i
$539$	2.21288e11			0.112930
$540$		0			0
$541$	7.47488e10			0.0375160			0.0187580	−	0.999824i	$-0.494029\pi$
$541$	7.47488e10			0.0375160			0.0187580	+	0.999824i	$0.494029\pi$
$542$	−1.49818e12	+	1.49818e12i	−0.745703	+	0.745703i
$543$	1.22199e12	−	2.31411e12i	0.603208	−	1.14231i
$544$		−	6.19408e11i		−	0.303237i
$545$		0			0
$546$	2.85492e11	+	9.24370e11i	0.137476	+	0.445122i
$547$	1.82795e12	+	1.82795e12i	0.873013	+	0.873013i	0.992800	−	0.119786i	$-0.0382209\pi$
$547$	1.82795e12	+	1.82795e12i	0.873013	+	0.873013i	−0.119786	+	0.992800i	$0.538221\pi$
$548$	9.54493e9	+	9.54493e9i	0.00452127	+	0.00452127i
$549$	−2.23779e12	−	3.27720e12i	−1.05134	−	1.53967i
$550$		0			0
$551$			7.12846e11i			0.329468i
$552$	3.20506e12	+	1.69246e12i	1.46930	+	0.775874i
$553$	−1.17105e12	+	1.17105e12i	−0.532489	+	0.532489i
$554$	−1.20691e12			−0.544352
$555$		0			0
$556$	−3.18687e11			−0.141425
$557$	2.45120e12	−	2.45120e12i	1.07902	−	1.07902i	0.0824246	−	0.996597i	$-0.473734\pi$
$557$	2.45120e12	−	2.45120e12i	1.07902	−	1.07902i	0.996597	−	0.0824246i	$-0.0262664\pi$
$558$	−3.92365e11	−	7.39488e10i	−0.171331	−	0.0322907i
$559$			1.93288e12i			0.837244i
$560$		0			0
$561$	−3.52453e12	+	1.08855e12i	−1.50234	+	0.463999i
$562$	7.07473e11	+	7.07473e11i	0.299155	+	0.299155i
$563$	−2.92630e11	−	2.92630e11i	−0.122753	−	0.122753i	0.643062	−	0.765814i	$-0.277664\pi$
$563$	−2.92630e11	−	2.92630e11i	−0.122753	−	0.122753i	−0.765814	+	0.643062i	$0.777664\pi$
$564$	−5.93754e10	+	1.83381e10i	−0.0247087	+	0.00763131i
$565$		0			0
$566$		−	2.97337e12i		−	1.21780i
$567$	−2.14644e12	+	9.40138e11i	−0.872157	+	0.382004i
$568$	−3.21654e11	+	3.21654e11i	−0.129665	+	0.129665i
$569$	−3.06312e12			−1.22506			−0.612532	−	0.790446i	$-0.709849\pi$
$569$	−3.06312e12			−1.22506			−0.612532	+	0.790446i	$0.709849\pi$
$570$		0			0
$571$	8.84316e11			0.348133			0.174066	−	0.984734i	$-0.444309\pi$
$571$	8.84316e11			0.348133			0.174066	+	0.984734i	$0.444309\pi$
$572$	1.33572e11	−	1.33572e11i	0.0521714	−	0.0521714i
$573$	−1.38550e12	−	7.31623e11i	−0.536920	−	0.283525i
$574$		−	1.89574e12i		−	0.728911i
$575$		0			0
$576$	2.37395e12	−	1.62102e12i	0.898607	−	0.613602i
$577$	−1.57741e12	−	1.57741e12i	−0.592452	−	0.592452i	0.345841	−	0.938293i	$-0.387594\pi$
$577$	−1.57741e12	−	1.57741e12i	−0.592452	−	0.592452i	−0.938293	+	0.345841i	$0.887594\pi$
$578$	−1.23312e12	−	1.23312e12i	−0.459547	−	0.459547i
$579$	2.33217e11	+	7.55111e11i	0.0862394	+	0.279227i
$580$		0			0
$581$			4.18955e12i			1.52537i
$582$	−5.04765e11	+	9.55890e11i	−0.182363	+	0.345346i
$583$	4.75822e11	−	4.75822e11i	0.170583	−	0.170583i
$584$	4.71629e12			1.67781
$585$		0			0
$586$	−3.76423e12			−1.31867
$587$	8.25436e11	−	8.25436e11i	0.286954	−	0.286954i	−0.548921	−	0.835874i	$-0.684961\pi$
$587$	8.25436e11	−	8.25436e11i	0.286954	−	0.286954i	0.835874	+	0.548921i	$0.184961\pi$
$588$	1.48189e10	−	2.80630e10i	0.00511232	−	0.00968135i
$589$			3.48922e11i			0.119456i
$590$		0			0
$591$	−1.29824e12	−	4.20344e12i	−0.437734	−	1.41730i
$592$	−1.91760e12	−	1.91760e12i	−0.641669	−	0.641669i
$593$	−2.35719e12	−	2.35719e12i	−0.782796	−	0.782796i	0.197506	−	0.980302i	$-0.436716\pi$
$593$	−2.35719e12	−	2.35719e12i	−0.782796	−	0.782796i	−0.980302	+	0.197506i	$0.936716\pi$
$594$	−2.69678e12	−	2.14588e12i	−0.888806	−	0.707241i
$595$		0			0
$596$			4.88331e11i			0.158528i
$597$	−1.51453e12	−	7.99759e11i	−0.487970	−	0.257676i
$598$	−1.71260e12	+	1.71260e12i	−0.547647	+	0.547647i
$599$	−6.20595e11			−0.196964			−0.0984822	−	0.995139i	$-0.531399\pi$
$599$	−6.20595e11			−0.196964			−0.0984822	+	0.995139i	$0.531399\pi$
$600$		0			0
$601$	−1.81726e12			−0.568176			−0.284088	−	0.958798i	$-0.591691\pi$
$601$	−1.81726e12			−0.568176			−0.284088	+	0.958798i	$0.591691\pi$
$602$	3.27739e12	−	3.27739e12i	1.01706	−	1.01706i
$603$	1.28040e11	−	6.79365e11i	0.0394381	−	0.209255i
$604$			3.84305e11i			0.117492i
$605$		0			0
$606$	−1.02614e12	+	3.16925e11i	−0.309087	+	0.0954618i
$607$	3.29545e11	+	3.29545e11i	0.0985294	+	0.0985294i	0.754653	−	0.656124i	$-0.227805\pi$
$607$	3.29545e11	+	3.29545e11i	0.0985294	+	0.0985294i	−0.656124	+	0.754653i	$0.727805\pi$
$608$	−3.57600e11	−	3.57600e11i	−0.106128	−	0.106128i
$609$	1.58047e12	−	4.88129e11i	0.465595	−	0.143799i
$610$		0			0
$611$		−	3.95840e11i		−	0.114904i
$612$	−9.79788e10	+	5.19865e11i	−0.0282326	+	0.149799i
$613$	−3.58258e12	+	3.58258e12i	−1.02476	+	1.02476i	−0.0250770	+	0.999686i	$0.507983\pi$
$613$	−3.58258e12	+	3.58258e12i	−1.02476	+	1.02476i	−0.999686	+	0.0250770i	$0.992017\pi$
$614$	−6.56043e11			−0.186284
$615$		0			0
$616$	−4.31789e12			−1.20825
$617$	4.93643e11	−	4.93643e11i	0.137129	−	0.137129i	−0.635210	−	0.772339i	$-0.719087\pi$
$617$	4.93643e11	−	4.93643e11i	0.137129	−	0.137129i	0.772339	+	0.635210i	$0.219087\pi$
$618$	3.08042e12	+	1.62664e12i	0.849497	+	0.448584i
$619$		−	3.37713e12i		−	0.924569i	−0.886732	−	0.462285i	$-0.847030\pi$
$619$		−	3.37713e12i		−	0.924569i	0.886732	−	0.462285i	$-0.152970\pi$
$620$		0			0
$621$	−4.59043e12	−	3.65269e12i	−1.23863	−	0.985601i
$622$	−4.76473e10	−	4.76473e10i	−0.0127639	−	0.0127639i
$623$	2.12552e12	+	2.12552e12i	0.565287	+	0.565287i
$624$	5.05795e11	+	1.63767e12i	0.133550	+	0.432410i
$625$		0			0
$626$		−	3.01080e12i		−	0.783606i
$627$	−1.40635e12	+	2.66325e12i	−0.363404	+	0.688189i
$628$	3.89967e11	−	3.89967e11i	0.100048	−	0.100048i
$629$	5.33166e12			1.35811
$630$		0			0
$631$	3.13188e12			0.786453			0.393227	−	0.919442i	$-0.371359\pi$
$631$	3.13188e12			0.786453			0.393227	+	0.919442i	$0.371359\pi$
$632$	−2.35448e12	+	2.35448e12i	−0.587041	+	0.587041i
$633$	−7.28468e11	+	1.37952e12i	−0.180341	+	0.341517i
$634$			6.18830e11i			0.152114i
$635$		0			0
$636$	−2.84780e10	−	9.22063e10i	−0.00690164	−	0.0223462i
$637$	1.42941e11	+	1.42941e11i	0.0343977	+	0.0343977i
$638$	1.72024e12	+	1.72024e12i	0.411051	+	0.411051i
$639$	6.08026e11	−	4.15182e11i	0.144267	−	0.0985111i
$640$		0			0
$641$			1.82672e12i			0.427378i	0.976902	+	0.213689i	$0.0685479\pi$
$641$			1.82672e12i			0.427378i	−0.976902	+	0.213689i	$0.931452\pi$
$642$	7.02298e12	+	3.70854e12i	1.63160	+	0.861580i
$643$	−1.21362e12	+	1.21362e12i	−0.279984	+	0.279984i	−0.833103	−	0.553119i	$-0.813438\pi$
$643$	−1.21362e12	+	1.21362e12i	−0.279984	+	0.279984i	0.553119	+	0.833103i	$0.313438\pi$
$644$	−7.71037e11			−0.176640
$645$		0			0
$646$	−3.48228e12			−0.786715
$647$	−2.74547e12	+	2.74547e12i	−0.615954	+	0.615954i	−0.944491	−	0.328537i	$-0.893444\pi$
$647$	−2.74547e12	+	2.74547e12i	−0.615954	+	0.615954i	0.328537	+	0.944491i	$0.393444\pi$
$648$	−4.31559e12	+	1.89022e12i	−0.961507	+	0.421139i
$649$		−	9.80747e12i		−	2.16998i
$650$		0			0
$651$	7.73604e11	−	2.38928e11i	0.168812	−	0.0521378i
$652$	−5.55159e11	−	5.55159e11i	−0.120310	−	0.120310i
$653$	2.27677e12	+	2.27677e12i	0.490016	+	0.490016i	0.908311	−	0.418295i	$-0.137372\pi$
$653$	2.27677e12	+	2.27677e12i	0.490016	+	0.490016i	−0.418295	+	0.908311i	$0.637372\pi$
$654$	−4.11733e12	+	1.27164e12i	−0.880067	+	0.271809i
$655$		0			0
$656$		−	3.35860e12i		−	0.708094i
$657$	−7.50145e12	−	1.41380e12i	−1.57073	−	0.296035i
$658$	−6.71187e11	+	6.71187e11i	−0.139581	+	0.139581i
$659$	7.34764e12			1.51762			0.758811	−	0.651311i	$-0.225780\pi$
$659$	7.34764e12			1.51762			0.758811	+	0.651311i	$0.225780\pi$
$660$		0			0
$661$	−1.49359e11			−0.0304316			−0.0152158	−	0.999884i	$-0.504844\pi$
$661$	−1.49359e11			−0.0304316			−0.0152158	+	0.999884i	$0.504844\pi$
$662$	2.70639e12	−	2.70639e12i	0.547684	−	0.547684i
$663$	−2.97982e12	−	1.57352e12i	−0.598935	−	0.316272i
$664$			8.42344e12i			1.68164i
$665$		0			0
$666$	2.80899e12	+	4.11370e12i	0.553243	+	0.810212i
$667$	2.92817e12	+	2.92817e12i	0.572835	+	0.572835i
$668$	4.60549e11	+	4.60549e11i	0.0894915	+	0.0894915i
$669$	4.19635e11	+	1.35870e12i	0.0809943	+	0.262244i
$670$		0			0
$671$			1.18352e13i			2.25385i
$672$	−5.47973e11	+	1.03771e12i	−0.103657	+	0.196298i
$673$	−1.63669e11	+	1.63669e11i	−0.0307538	+	0.0307538i	−0.722316	−	0.691563i	$-0.756923\pi$
$673$	−1.63669e11	+	1.63669e11i	−0.0307538	+	0.0307538i	0.691563	+	0.722316i	$0.256923\pi$
$674$	3.27566e12			0.611405
$675$		0			0
$676$	−4.63777e11			−0.0854179
$677$	−1.86211e12	+	1.86211e12i	−0.340688	+	0.340688i	−0.856626	−	0.515938i	$-0.827443\pi$
$677$	−1.86211e12	+	1.86211e12i	−0.340688	+	0.340688i	0.515938	+	0.856626i	$0.327443\pi$
$678$	−3.95119e12	+	7.48250e12i	−0.718116	+	1.35992i
$679$		−	2.19205e12i		−	0.395764i
$680$		0			0
$681$	6.94006e11	+	2.24706e12i	0.123652	+	0.400362i
$682$	8.42018e11	+	8.42018e11i	0.149036	+	0.149036i
$683$	−4.86679e12	−	4.86679e12i	−0.855755	−	0.855755i	0.135080	−	0.990835i	$-0.456871\pi$
$683$	−4.86679e12	−	4.86679e12i	−0.855755	−	0.855755i	−0.990835	+	0.135080i	$0.956871\pi$
$684$	2.43566e11	+	3.56697e11i	0.0425465	+	0.0623084i
$685$		0			0
$686$		−	5.67386e12i		−	0.978184i
$687$	−5.38470e12	−	2.84343e12i	−0.922266	−	0.487010i
$688$	5.80643e12	−	5.80643e12i	0.988009	−	0.988009i
$689$	6.14715e11			0.103917
$690$		0			0
$691$	9.61042e12			1.60358			0.801791	−	0.597604i	$-0.203881\pi$
$691$	9.61042e12			1.60358			0.801791	+	0.597604i	$0.203881\pi$
$692$	−3.10151e10	+	3.10151e10i	−0.00514157	+	0.00514157i
$693$	6.86777e12	+	1.29437e12i	1.13114	+	0.213186i
$694$			2.37644e12i			0.388875i
$695$		0			0
$696$	3.17766e12	−	9.81423e11i	0.513294	−	0.158531i
$697$	4.66909e12	+	4.66909e12i	0.749351	+	0.749351i
$698$	−3.37768e12	−	3.37768e12i	−0.538603	−	0.538603i
$699$	−4.75688e12	+	1.46917e12i	−0.753660	+	0.232768i
$700$		0			0
$701$		−	1.11771e13i		−	1.74823i	−0.485719	−	0.874115i	$-0.661442\pi$
$701$		−	1.11771e13i		−	1.74823i	0.485719	−	0.874115i	$-0.338558\pi$
$702$	−3.55853e11	−	3.12812e12i	−0.0553036	−	0.486146i
$703$	3.07810e12	−	3.07810e12i	0.475318	−	0.475318i
$704$	−8.57324e12			−1.31543
$705$		0			0
$706$	2.38363e11			0.0361092
$707$	1.53996e12	−	1.53996e12i	0.231805	−	0.231805i
$708$	−1.24375e12	−	6.56771e11i	−0.186030	−	0.0982346i
$709$		−	4.28809e12i		−	0.637318i	−0.947870	−	0.318659i	$-0.896768\pi$
$709$		−	4.28809e12i		−	0.637318i	0.947870	−	0.318659i	$-0.103232\pi$
$710$		0			0
$711$	4.45070e12	−	3.03910e12i	0.653153	−	0.445997i
$712$	4.27353e12	+	4.27353e12i	0.623199	+	0.623199i
$713$	1.43327e12	+	1.43327e12i	0.207695	+	0.207695i
$714$	2.38453e12	+	7.72065e12i	0.343369	+	1.11176i
$715$		0			0
$716$			7.57238e11i			0.107677i
$717$	4.11109e12	−	7.78530e12i	0.580926	−	1.10012i
$718$	8.45456e12	−	8.45456e12i	1.18722	−	1.18722i
$719$	−9.33578e12			−1.30278			−0.651389	−	0.758744i	$-0.725813\pi$
$719$	−9.33578e12			−1.30278			−0.651389	+	0.758744i	$0.725813\pi$
$720$		0			0
$721$	−7.06403e12			−0.973518
$722$	2.84062e12	−	2.84062e12i	0.389041	−	0.389041i
$723$	3.50724e12	−	6.64177e12i	0.477357	−	0.903985i
$724$			1.11930e12i			0.151399i
$725$		0			0
$726$	9.57707e11	+	3.10087e12i	0.127943	+	0.414257i
$727$	−8.95394e12	−	8.95394e12i	−1.18880	−	1.18880i	−0.977399	−	0.211403i	$-0.932197\pi$
$727$	−8.95394e12	−	8.95394e12i	−1.18880	−	1.18880i	−0.211403	−	0.977399i	$-0.567803\pi$
$728$	−2.78914e12	−	2.78914e12i	−0.368026	−	0.368026i
$729$	7.43075e12	−	1.71280e12i	0.974448	−	0.224612i
$730$		0			0
$731$			1.61441e13i			2.09115i
$732$	1.50090e12	+	7.92563e11i	0.193220	+	0.102031i
$733$	5.84770e12	−	5.84770e12i	0.748199	−	0.748199i	−0.225942	−	0.974141i	$-0.572546\pi$
$733$	5.84770e12	−	5.84770e12i	0.748199	−	0.748199i	0.974141	+	0.225942i	$0.0725460\pi$
$734$	−3.20282e12			−0.407286
$735$		0			0
$736$	−2.93784e12			−0.369043
$737$	−1.45792e12	+	1.45792e12i	−0.182025	+	0.182025i
$738$	−1.14258e12	+	6.06240e12i	−0.141786	+	0.752300i
$739$		−	6.38216e12i		−	0.787169i	−0.919289	−	0.393584i	$-0.871235\pi$
$739$		−	6.38216e12i		−	0.787169i	0.919289	−	0.393584i	$-0.128765\pi$
$740$		0			0
$741$	−2.62876e12	+	8.11894e11i	−0.320309	+	0.0989276i
$742$	−1.04231e12	−	1.04231e12i	−0.126235	−	0.126235i
$743$	9.98098e12	+	9.98098e12i	1.20150	+	1.20150i	0.973710	+	0.227789i	$0.0731497\pi$
$743$	9.98098e12	+	9.98098e12i	1.20150	+	1.20150i	0.227789	+	0.973710i	$0.426850\pi$
$744$	1.55539e12	−	4.80384e11i	0.186107	−	0.0574792i
$745$		0			0
$746$			4.67676e12i			0.552866i
$747$	2.52508e12	−	1.33978e13i	0.296710	−	1.57431i
$748$	1.11564e12	−	1.11564e12i	0.130306	−	0.130306i
$749$	−1.61051e13			−1.86980
$750$		0			0
$751$	1.58721e13			1.82077			0.910386	−	0.413761i	$-0.135785\pi$
$751$	1.58721e13			1.82077			0.910386	+	0.413761i	$0.135785\pi$
$752$	−1.18912e12	+	1.18912e12i	−0.135595	+	0.135595i
$753$	−1.17678e13	−	6.21407e12i	−1.33388	−	0.704367i
$754$			2.22238e12i			0.250407i
$755$		0			0
$756$	6.24058e11	−	7.84268e11i	0.0694827	−	0.0873205i
$757$	2.26504e12	+	2.26504e12i	0.250694	+	0.250694i	0.821255	−	0.570561i	$-0.193274\pi$
$757$	2.26504e12	+	2.26504e12i	0.250694	+	0.250694i	−0.570561	+	0.821255i	$0.693274\pi$
$758$	3.44280e12	+	3.44280e12i	0.378792	+	0.378792i
$759$	5.16298e12	+	1.67168e13i	0.564693	+	1.82837i
$760$		0			0
$761$		−	7.82985e12i		−	0.846296i	−0.906061	−	0.423148i	$-0.860925\pi$
$761$		−	7.82985e12i		−	0.846296i	0.906061	−	0.423148i	$-0.139075\pi$
$762$	−3.78509e12	+	7.16794e12i	−0.406704	+	0.770188i
$763$	6.17900e12	−	6.17900e12i	0.660021	−	0.660021i
$764$	6.70142e11			0.0711617
$765$		0			0
$766$	1.92227e12			0.201737
$767$	6.33514e12	−	6.33514e12i	0.660962	−	0.660962i
$768$	−1.56029e12	+	2.95476e12i	−0.161837	+	0.306476i
$769$		−	1.77000e12i		−	0.182517i	−0.995827	−	0.0912586i	$-0.970911\pi$
$769$		−	1.77000e12i		−	0.182517i	0.995827	−	0.0912586i	$-0.0290890\pi$
$770$		0			0
$771$	2.98745e12	+	9.67279e12i	0.304478	+	0.985841i
$772$	−2.39019e11	−	2.39019e11i	−0.0242189	−	0.0242189i
$773$	−8.22129e12	−	8.22129e12i	−0.828194	−	0.828194i	0.159073	−	0.987267i	$-0.449150\pi$
$773$	−8.22129e12	−	8.22129e12i	−0.828194	−	0.828194i	−0.987267	+	0.159073i	$0.949150\pi$
$774$	−1.24561e13	+	8.50550e12i	−1.24752	+	0.851855i
$775$		0			0
$776$		−	4.40730e12i		−	0.436309i
$777$	−8.93231e12	−	4.71678e12i	−0.879163	−	0.464249i
$778$	7.32797e12	−	7.32797e12i	0.717093	−	0.717093i
$779$	5.39117e12			0.524523
$780$		0			0
$781$	−2.19582e12			−0.211187
$782$	−1.43042e13	+	1.43042e13i	−1.36783	+	1.36783i
$783$	−5.34840e12	+	6.08430e11i	−0.508506	+	0.0578473i
$784$		−	8.58799e11i		−	0.0811838i
$785$		0			0
$786$	4.56971e12	−	1.41136e12i	0.427058	−	0.131897i
$787$	8.13867e12	+	8.13867e12i	0.756253	+	0.756253i	0.975638	−	0.219386i	$-0.0704052\pi$
$787$	8.13867e12	+	8.13867e12i	0.756253	+	0.756253i	−0.219386	+	0.975638i	$0.570405\pi$
$788$	1.33054e12	+	1.33054e12i	0.122930	+	0.122930i
$789$	1.18483e13	−	3.65936e12i	1.08846	−	0.336170i
$790$		0			0
$791$		−	1.71589e13i		−	1.55846i
$792$	1.38082e13	+	2.60243e12i	1.24702	+	0.235026i
$793$	−7.64497e12	+	7.64497e12i	−0.686509	+	0.686509i
$794$	1.28425e13			1.14672
$795$		0			0
$796$	7.32552e11			0.0646740
$797$	−3.42528e12	+	3.42528e12i	−0.300700	+	0.300700i	−0.841288	−	0.540588i	$-0.818202\pi$
$797$	−3.42528e12	+	3.42528e12i	−0.300700	+	0.300700i	0.540588	+	0.841288i	$0.318202\pi$
$798$	5.83398e12	+	3.08068e12i	0.509274	+	0.268926i
$799$		−	3.30619e12i		−	0.286991i
$800$		0			0
$801$	−5.51616e12	−	8.07830e12i	−0.473467	−	0.693383i
$802$	−2.08948e12	−	2.08948e12i	−0.178342	−	0.178342i
$803$	1.60982e13	+	1.60982e13i	1.36633	+	1.36633i
$804$	8.72568e10	+	2.82521e11i	0.00736456	+	0.0238450i
$805$		0			0
$806$			1.08780e12i			0.0907910i
$807$	2.50821e11	−	4.74987e11i	0.0208177	−	0.0394231i
$808$	3.09622e12	−	3.09622e12i	0.255553	−	0.255553i
$809$	1.10348e13			0.905726			0.452863	−	0.891580i	$-0.350403\pi$
$809$	1.10348e13			0.905726			0.452863	+	0.891580i	$0.350403\pi$
$810$		0			0
$811$	1.72147e13			1.39736			0.698678	−	0.715437i	$-0.253772\pi$
$811$	1.72147e13			1.39736			0.698678	+	0.715437i	$0.253772\pi$
$812$	−5.00273e11	+	5.00273e11i	−0.0403836	+	0.0403836i
$813$	−6.52875e12	+	1.23637e13i	−0.524110	+	0.992524i
$814$		−	1.48562e13i		−	1.18603i
$815$		0			0
$816$	4.22457e12	+	1.36784e13i	0.333562	+	1.08001i
$817$	9.32038e12	+	9.32038e12i	0.731871	+	0.731871i
$818$	−1.09930e13	−	1.09930e13i	−0.858473	−	0.858473i
$819$	3.60014e12	+	5.27234e12i	0.279603	+	0.409473i
$820$		0			0
$821$			2.18942e13i			1.68184i	0.541161	+	0.840919i	$0.317985\pi$
$821$			2.18942e13i			1.68184i	−0.541161	+	0.840919i	$0.682015\pi$
$822$	−5.93325e11	−	3.13310e11i	−0.0453283	−	0.0239360i
$823$	−1.21626e13	+	1.21626e13i	−0.924116	+	0.924116i	−0.997317	−	0.0732014i	$-0.976678\pi$
$823$	−1.21626e13	+	1.21626e13i	−0.924116	+	0.924116i	0.0732014	+	0.997317i	$0.476678\pi$
$824$	−1.42028e13			−1.07325
$825$		0			0
$826$	−2.14837e13			−1.60583
$827$	−6.26933e12	+	6.26933e12i	−0.466065	+	0.466065i	−0.900637	−	0.434572i	$-0.856900\pi$
$827$	−6.26933e12	+	6.26933e12i	−0.466065	+	0.466065i	0.434572	+	0.900637i	$0.356900\pi$
$828$	2.46571e12	+	4.64711e11i	0.182308	+	0.0343595i
$829$		−	4.46429e12i		−	0.328290i	−0.986436	−	0.164145i	$-0.947514\pi$
$829$		−	4.46429e12i		−	0.328290i	0.986436	−	0.164145i	$-0.0524864\pi$
$830$		0			0
$831$	−7.60973e12	+	2.35027e12i	−0.553560	+	0.170967i
$832$	−5.53788e12	−	5.53788e12i	−0.400672	−	0.400672i
$833$	1.19389e12	+	1.19389e12i	0.0859138	+	0.0859138i
$834$	1.51354e13	−	4.67458e12i	1.08330	−	0.334577i
$835$		0			0
$836$		−	1.28817e12i		−	0.0912105i
$837$	−2.61792e12	+	2.97813e11i	−0.184371	+	0.0209739i
$838$	−3.40928e12	+	3.40928e12i	−0.238816	+	0.238816i
$839$	−7.35559e12			−0.512494			−0.256247	−	0.966611i	$-0.582486\pi$
$839$	−7.35559e12			−0.512494			−0.256247	+	0.966611i	$0.582486\pi$
$840$		0			0
$841$	−1.07074e13			−0.738075
$842$	−1.47126e13	+	1.47126e13i	−1.00876	+	1.00876i
$843$	5.83842e12	+	3.08303e12i	0.398173	+	0.210258i
$844$		−	6.67252e11i		−	0.0452636i
$845$		0			0
$846$	2.55093e12	−	1.74187e12i	0.171211	−	0.116909i
$847$	−4.65358e12	−	4.65358e12i	−0.310679	−	0.310679i
$848$	−1.84662e12	−	1.84662e12i	−0.122630	−	0.122630i
$849$	−5.79019e12	−	1.87475e13i	−0.382479	−	1.23840i
$850$		0			0
$851$		−	2.52880e13i		−	1.65284i
$852$	−1.47046e11	+	2.78466e11i	−0.00956038	+	0.0181048i
$853$	−1.68333e13	+	1.68333e13i	−1.08868	+	1.08868i	−0.0930106	+	0.995665i	$0.529649\pi$
$853$	−1.68333e13	+	1.68333e13i	−1.08868	+	1.08868i	−0.995665	+	0.0930106i	$0.970351\pi$
$854$	2.59256e13			1.66790
$855$		0			0
$856$	−3.23807e13			−2.06136
$857$	1.88407e13	−	1.88407e13i	1.19312	−	1.19312i	0.216934	−	0.976186i	$-0.430394\pi$
$857$	1.88407e13	−	1.88407e13i	1.19312	−	1.19312i	0.976186	−	0.216934i	$-0.0696055\pi$
$858$	−4.38446e12	+	8.30298e12i	−0.276200	+	0.523048i
$859$			1.59297e13i			0.998250i	0.866530	+	0.499125i	$0.166345\pi$
$859$			1.59297e13i			0.998250i	−0.866530	+	0.499125i	$0.833655\pi$
$860$		0			0
$861$	−3.69166e12	−	1.19529e13i	−0.228933	−	0.741241i
$862$	−3.37761e11	−	3.37761e11i	−0.0208366	−	0.0208366i
$863$	−1.70113e13	−	1.70113e13i	−1.04397	−	1.04397i	−0.998988	−	0.0449837i	$-0.985676\pi$
$863$	−1.70113e13	−	1.70113e13i	−1.04397	−	1.04397i	−0.0449837	−	0.998988i	$-0.514324\pi$
$864$	2.37781e12	−	2.98825e12i	0.145166	−	0.182434i
$865$		0			0
$866$			2.30363e12i			0.139182i
$867$	−1.01763e13	−	5.37369e12i	−0.611652	−	0.322988i
$868$	−2.44872e11	+	2.44872e11i	−0.0146420	+	0.0146420i
$869$	−1.60732e13			−0.956121
$870$		0			0
$871$	−1.88349e12			−0.110887
$872$	1.24234e13	−	1.24234e13i	0.727639	−	0.727639i
$873$	−1.32117e12	+	7.00998e12i	−0.0769829	+	0.408463i
$874$			1.65164e13i			0.957443i
$875$		0			0
$876$	3.11955e12	−	9.63477e11i	0.178988	−	0.0552806i
$877$	1.04180e13	+	1.04180e13i	0.594686	+	0.594686i	0.938894	−	0.344207i	$-0.111852\pi$
$877$	1.04180e13	+	1.04180e13i	0.594686	+	0.594686i	−0.344207	+	0.938894i	$0.611852\pi$
$878$	8.78145e12	+	8.78145e12i	0.498702	+	0.498702i
$879$	−2.37340e13	+	7.33027e12i	−1.34098	+	0.414162i
$880$		0			0
$881$		−	1.50295e13i		−	0.840530i	−0.907401	−	0.420265i	$-0.861937\pi$
$881$		−	1.50295e13i		−	0.840530i	0.907401	−	0.420265i	$-0.138063\pi$
$882$	−2.92159e11	+	1.55016e12i	−0.0162559	+	0.0862520i
$883$	2.26491e13	−	2.26491e13i	1.25380	−	1.25380i	0.299795	−	0.954004i	$-0.403082\pi$
$883$	2.26491e13	−	2.26491e13i	1.25380	−	1.25380i	0.954004	−	0.299795i	$-0.0969183\pi$
$884$	1.44129e12			0.0793810
$885$		0			0
$886$	−3.44999e12			−0.188090
$887$	9.52793e12	−	9.52793e12i	0.516824	−	0.516824i	−0.399785	−	0.916609i	$-0.630915\pi$
$887$	9.52793e12	−	9.52793e12i	0.516824	−	0.516824i	0.916609	+	0.399785i	$0.130915\pi$
$888$	−1.79591e13	−	9.48347e12i	−0.969231	−	0.511810i
$889$		−	1.64375e13i		−	0.882630i
$890$		0			0
$891$	−2.11824e13	−	8.27854e12i	−1.12597	−	0.440052i
$892$	−4.30075e11	−	4.30075e11i	−0.0227459	−	0.0227459i
$893$	−1.90875e12	−	1.90875e12i	−0.100442	−	0.100442i
$894$	−7.16296e12	−	2.31923e13i	−0.375037	−	1.21430i
$895$		0			0
$896$			1.44975e13i			0.751460i
$897$	−7.46316e12	+	1.41332e13i	−0.384908	+	0.728912i
$898$	−5.56582e12	+	5.56582e12i	−0.285618	+	0.285618i
$899$	1.85991e12			0.0949669
$900$		0			0
$901$	5.13431e12			0.259550
$902$	1.30100e13	−	1.30100e13i	0.654406	−	0.654406i
$903$	1.42822e13	−	2.70467e13i	0.714827	−	1.35369i
$904$		−	3.44993e13i		−	1.71812i
$905$		0			0
$906$	−5.63708e12	−	1.82518e13i	−0.277957	−	0.899971i
$907$	−1.19308e13	−	1.19308e13i	−0.585380	−	0.585380i	0.350997	−	0.936377i	$-0.385843\pi$
$907$	−1.19308e13	−	1.19308e13i	−0.585380	−	0.585380i	−0.936377	+	0.350997i	$0.885843\pi$
$908$	−7.11272e11	−	7.11272e11i	−0.0347256	−	0.0347256i
$909$	−5.85282e12	+	3.99652e12i	−0.284333	+	0.194153i
$910$		0			0
$911$			2.17430e13i			1.04589i	0.852366	+	0.522946i	$0.175167\pi$
$911$			2.17430e13i			1.04589i	−0.852366	+	0.522946i	$0.824833\pi$
$912$	1.03358e13	+	5.45791e12i	0.494730	+	0.261246i
$913$	−2.87519e13	+	2.87519e13i	−1.36945	+	1.36945i
$914$	8.59268e12			0.407259
$915$		0			0
$916$	2.60449e12			0.122234
$917$	−6.85791e12	+	6.85791e12i	−0.320280	+	0.320280i
$918$	−2.97221e12	−	2.61271e13i	−0.138130	−	1.21423i
$919$			1.86612e13i			0.863016i	0.902109	+	0.431508i	$0.142018\pi$
$919$			1.86612e13i			0.863016i	−0.902109	+	0.431508i	$0.857982\pi$
$920$		0			0
$921$	−4.13645e12	+	1.27754e12i	−0.189435	+	0.0585070i
$922$	−1.08567e13	−	1.08567e13i	−0.494774	−	0.494774i
$923$	−1.41839e12	−	1.41839e12i	−0.0643261	−	0.0643261i
$924$	−2.85603e12	+	8.82088e11i	−0.128896	+	0.0398096i
$925$		0			0
$926$		−	1.54018e12i		−	0.0688370i
$927$	2.25901e13	+	4.25756e12i	1.00476	+	0.189366i
$928$	−1.90616e12	+	1.90616e12i	−0.0843712	+	0.0843712i
$929$	2.24364e13			0.988284			0.494142	−	0.869381i	$-0.335482\pi$
$929$	2.24364e13			0.988284			0.494142	+	0.869381i	$0.335482\pi$
$930$		0			0
$931$	1.37853e12			0.0601371
$932$	1.50572e12	−	1.50572e12i	0.0653691	−	0.0653691i
$933$	−3.93210e11	−	2.07638e11i	−0.0169886	−	0.00897095i
$934$			2.02266e13i			0.869683i
$935$		0			0
$936$	7.23838e12	+	1.06005e13i	0.308248	+	0.451423i
$937$	1.28204e13	+	1.28204e13i	0.543340	+	0.543340i	0.924507	−	0.381166i	$-0.124477\pi$
$937$	1.28204e13	+	1.28204e13i	0.543340	+	0.543340i	−0.381166	+	0.924507i	$0.624477\pi$
$938$	3.19365e12	+	3.19365e12i	0.134702	+	0.134702i
$939$	−5.86308e12	−	1.89836e13i	−0.246111	−	0.796861i
$940$		0			0
$941$			3.50035e13i			1.45532i	0.685938	+	0.727660i	$0.259392\pi$
$941$			3.50035e13i			1.45532i	−0.685938	+	0.727660i	$0.740608\pi$
$942$	−1.28006e13	+	2.42409e13i	−0.529664	+	1.00304i
$943$	2.21454e13	−	2.21454e13i	0.911971	−	0.911971i
$944$	−3.80619e13			−1.55997
$945$		0			0
$946$	4.49839e13			1.82619
$947$	−1.38968e13	+	1.38968e13i	−0.561488	+	0.561488i	−0.929730	−	0.368242i	$-0.879960\pi$
$947$	−1.38968e13	+	1.38968e13i	−0.561488	+	0.561488i	0.368242	+	0.929730i	$0.379960\pi$
$948$	−1.07636e12	+	2.03834e12i	−0.0432834	+	0.0819672i
$949$			2.07973e13i			0.832354i
$950$		0			0
$951$	1.20508e12	+	3.90182e12i	0.0477753	+	0.154687i
$952$	−2.32958e13	−	2.32958e13i	−0.919205	−	0.919205i
$953$	−1.16170e13	−	1.16170e13i	−0.456220	−	0.456220i	0.441192	−	0.897413i	$-0.354556\pi$
$953$	−1.16170e13	−	1.16170e13i	−0.456220	−	0.456220i	−0.897413	+	0.441192i	$0.854556\pi$
$954$	2.70501e12	+	3.96143e12i	0.105731	+	0.154840i
$955$		0			0
$956$			3.76562e12i			0.145806i
$957$	1.41963e13	+	7.49646e12i	0.547105	+	0.288903i
$958$	−3.19659e13	+	3.19659e13i	−1.22615	+	1.22615i
$959$	1.36062e12			0.0519459
$960$		0			0
$961$	−2.55292e13			−0.965568
$962$	9.59634e12	−	9.59634e12i	0.361258	−	0.361258i
$963$	5.15028e13	+	9.70671e12i	1.92980	+	0.363709i
$964$			3.21251e12i			0.119811i
$965$		0			0
$966$	3.66189e13	−	1.13098e13i	1.35303	−	0.417885i
$967$	1.56646e13	+	1.56646e13i	0.576103	+	0.576103i	0.933827	−	0.357724i	$-0.116447\pi$
$967$	1.56646e13	+	1.56646e13i	0.576103	+	0.576103i	−0.357724	+	0.933827i	$0.616447\pi$
$968$	−9.35640e12	−	9.35640e12i	−0.342507	−	0.342507i
$969$	−2.19563e13	+	6.78122e12i	−0.800022	+	0.247087i
$970$		0			0
$971$		−	2.39671e13i		−	0.865224i	−0.901580	−	0.432612i	$-0.857592\pi$
$971$		−	2.39671e13i		−	0.865224i	0.901580	−	0.432612i	$-0.142408\pi$
$972$	−2.46837e12	+	2.13189e12i	−0.0886975	+	0.0766068i
$973$	−2.27142e13	+	2.27142e13i	−0.812436	+	0.812436i
$974$	−3.73866e11			−0.0133107
$975$		0			0
$976$	4.59314e13			1.62026
$977$	1.15859e12	−	1.15859e12i	0.0406821	−	0.0406821i	−0.686473	−	0.727155i	$-0.740842\pi$
$977$	1.15859e12	−	1.15859e12i	0.0406821	−	0.0406821i	0.727155	+	0.686473i	$0.240842\pi$
$978$	3.45094e13	+	1.82230e13i	1.20618	+	0.636934i
$979$			2.91738e13i			1.01501i
$980$		0			0
$981$	−2.34840e13	+	1.60358e13i	−0.809585	+	0.552814i
$982$	−1.29680e13	−	1.29680e13i	−0.445013	−	0.445013i
$983$	1.13857e13	+	1.13857e13i	0.388927	+	0.388927i	0.874304	−	0.485378i	$-0.161318\pi$
$983$	1.13857e13	+	1.13857e13i	0.388927	+	0.388927i	−0.485378	+	0.874304i	$0.661318\pi$
$984$	−7.42239e12	−	2.40323e13i	−0.252386	−	0.817179i
$985$		0			0
$986$			1.85621e13i			0.625432i
$987$	−2.92490e12	+	5.53897e12i	−0.0981033	+	0.185781i
$988$	8.32093e11	−	8.32093e11i	0.0277821	−	0.0277821i
$989$	7.65710e13			2.54496
$990$		0			0
$991$	5.64713e13			1.85993			0.929965	−	0.367648i	$-0.119837\pi$
$991$	5.64713e13			1.85993			0.929965	+	0.367648i	$0.119837\pi$
$992$	−9.33023e11	+	9.33023e11i	−0.0305907	+	0.0305907i
$993$	1.17939e13	−	2.23345e13i	0.384934	−	0.728962i
$994$			4.81004e12i			0.156282i
$995$		0			0
$996$	1.72080e12	+	5.57162e12i	0.0554068	+	0.179397i
$997$	−1.09158e13	−	1.09158e13i	−0.349885	−	0.349885i	0.510182	−	0.860067i	$-0.329578\pi$
$997$	−1.09158e13	−	1.09158e13i	−0.349885	−	0.349885i	−0.860067	+	0.510182i	$0.829578\pi$
$998$	2.26633e13	+	2.26633e13i	0.723162	+	0.723162i
$999$	2.57219e13	+	2.04674e13i	0.817068	+	0.650158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.g.32.18	yes	48
3.2	odd	2	inner	75.10.e.g.32.8	yes	48
5.2	odd	4	inner	75.10.e.g.68.17	yes	48
5.3	odd	4	inner	75.10.e.g.68.8	yes	48
5.4	even	2	inner	75.10.e.g.32.7	✓	48
15.2	even	4	inner	75.10.e.g.68.7	yes	48
15.8	even	4	inner	75.10.e.g.68.18	yes	48
15.14	odd	2	inner	75.10.e.g.32.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.e.g.32.7	✓	48	5.4	even	2	inner
75.10.e.g.32.8	yes	48	3.2	odd	2	inner
75.10.e.g.32.17	yes	48	15.14	odd	2	inner
75.10.e.g.32.18	yes	48	1.1	even	1	trivial
75.10.e.g.68.7	yes	48	15.2	even	4	inner
75.10.e.g.68.8	yes	48	5.3	odd	4	inner
75.10.e.g.68.17	yes	48	5.2	odd	4	inner
75.10.e.g.68.18	yes	48	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(15.0332 - 15.0332i) q^{2} +(65.5116 - 124.061i) q^{3} +60.0064i q^{4} +(-880.190 - 2849.89i) q^{6} +(4276.91 + 4276.91i) q^{7} +(8599.08 + 8599.08i) q^{8} +(-11099.5 - 16254.9i) q^{9} +O(q^{10})\)	\(q+(15.0332 - 15.0332i) q^{2} +(65.5116 - 124.061i) q^{3} +60.0064i q^{4} +(-880.190 - 2849.89i) q^{6} +(4276.91 + 4276.91i) q^{7} +(8599.08 + 8599.08i) q^{8} +(-11099.5 - 16254.9i) q^{9} +58702.8i q^{11} +(7444.48 + 3931.12i) q^{12} +(-37919.1 + 37919.1i) q^{13} +128591. q^{14} +227820. q^{16} +(-316713. + 316713. i) q^{17} +(-411224. - 77503.2i) q^{18} +365693. i q^{19} +(810787. - 250412. i) q^{21} +(882490. + 882490. i) q^{22} +(1.50216e6 + 1.50216e6i) q^{23} +(1.63015e6 - 503474. i) q^{24} +1.14009e6i q^{26} +(-2.74375e6 + 312127. i) q^{27} +(-256642. + 256642. i) q^{28} +1.94930e6 q^{29} +954139. q^{31} +(-977869. + 977869. i) q^{32} +(7.28275e6 + 3.84571e6i) q^{33} +9.52242e6i q^{34} +(975400. - 666039. i) q^{36} +(-8.41718e6 - 8.41718e6i) q^{37} +(5.49753e6 + 5.49753e6i) q^{38} +(2.22015e6 + 7.18843e6i) q^{39} -1.47423e7i q^{41} +(8.42422e6 - 1.59532e7i) q^{42} +(2.54869e7 - 2.54869e7i) q^{43} -3.52254e6 q^{44} +4.51646e7 q^{46} +(-5.21954e6 + 5.21954e6i) q^{47} +(1.49249e7 - 2.82637e7i) q^{48} -3.76964e6i q^{49} +(1.85435e7 + 6.00402e7i) q^{51} +(-2.27539e6 - 2.27539e6i) q^{52} +(-8.10562e6 - 8.10562e6i) q^{53} +(-3.65551e7 + 4.59396e7i) q^{54} +7.35550e7i q^{56} +(4.53684e7 + 2.39571e7i) q^{57} +(2.93042e7 - 2.93042e7i) q^{58} -1.67070e8 q^{59} +2.01613e8 q^{61} +(1.43438e7 - 1.43438e7i) q^{62} +(2.20495e7 - 1.16992e8i) q^{63} +1.46045e8i q^{64} +(1.67296e8 - 5.16696e7i) q^{66} +(2.48357e7 + 2.48357e7i) q^{67} +(-1.90048e7 - 1.90048e7i) q^{68} +(2.84769e8 - 8.79513e7i) q^{69} +3.74056e7i q^{71} +(4.43323e7 - 2.35223e8i) q^{72} +(2.74232e8 - 2.74232e8i) q^{73} -2.53074e8 q^{74} -2.19439e7 q^{76} +(-2.51067e8 + 2.51067e8i) q^{77} +(1.41441e8 + 7.46891e7i) q^{78} +2.73806e8i q^{79} +(-1.41025e8 + 3.60842e8i) q^{81} +(-2.21625e8 - 2.21625e8i) q^{82} +(4.89787e8 + 4.89787e8i) q^{83} +(1.50263e7 + 4.86524e7i) q^{84} -7.66299e8i q^{86} +(1.27702e8 - 2.41833e8i) q^{87} +(-5.04790e8 + 5.04790e8i) q^{88} +4.96975e8 q^{89} -3.24353e8 q^{91} +(-9.01394e7 + 9.01394e7i) q^{92} +(6.25072e7 - 1.18372e8i) q^{93} +1.56933e8i q^{94} +(5.72540e7 + 1.85378e8i) q^{96} +(-2.56266e8 - 2.56266e8i) q^{97} +(-5.66697e7 - 5.66697e7i) q^{98} +(9.54209e8 - 6.51569e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10788 q^{6}+O(q^{10}) \) 48 * q + 10788 * q^6	\( 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) \) 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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