LMFDB - Embedded newform 75.12.e.d.68.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,12,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, 12, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
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:	$57.6257385420$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.19
Character	$\chi$	$=$	75.68
Dual form			75.12.e.d.32.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(57.5586 + 57.5586i) q^{2} +(-345.894 + 239.801i) q^{3} +4577.97i q^{4} +(-33711.7 - 6106.58i) q^{6} +(-53787.8 + 53787.8i) q^{7} +(-145622. + 145622. i) q^{8} +(62138.3 - 165891. i) q^{9} +O(q^{10})$	\(q+(57.5586 + 57.5586i) q^{2} +(-345.894 + 239.801i) q^{3} +4577.97i q^{4} +(-33711.7 - 6106.58i) q^{6} +(-53787.8 + 53787.8i) q^{7} +(-145622. + 145622. i) q^{8} +(62138.3 - 165891. i) q^{9} -299004. i q^{11} +(-1.09780e6 - 1.58349e6i) q^{12} +(-257611. - 257611. i) q^{13} -6.19189e6 q^{14} -7.38785e6 q^{16} +(-1.91096e6 - 1.91096e6i) q^{17} +(1.31250e7 - 5.97187e6i) q^{18} +1.22718e7i q^{19} +(5.70652e6 - 3.15032e7i) q^{21} +(1.72102e7 - 1.72102e7i) q^{22} +(16960.0 - 16960.0i) q^{23} +(1.54495e7 - 8.52898e7i) q^{24} -2.96554e7i q^{26} +(1.82876e7 + 7.22816e7i) q^{27} +(-2.46239e8 - 2.46239e8i) q^{28} -8.47515e7 q^{29} +5.68233e7 q^{31} +(-1.27001e8 - 1.27001e8i) q^{32} +(7.17013e7 + 1.03424e8i) q^{33} -2.19984e8i q^{34} +(7.59446e8 + 2.84468e8i) q^{36} +(2.28933e8 - 2.28933e8i) q^{37} +(-7.06349e8 + 7.06349e8i) q^{38} +(1.50881e8 + 2.73308e7i) q^{39} +4.14106e8i q^{41} +(2.14174e9 - 1.48482e9i) q^{42} +(-5.52861e8 - 5.52861e8i) q^{43} +1.36883e9 q^{44} +1.95238e6 q^{46} +(3.42474e8 + 3.42474e8i) q^{47} +(2.55541e9 - 1.77161e9i) q^{48} -3.80892e9i q^{49} +(1.11924e9 + 2.02740e8i) q^{51} +(1.17934e9 - 1.17934e9i) q^{52} +(1.12548e9 - 1.12548e9i) q^{53} +(-3.10782e9 + 5.21303e9i) q^{54} -1.56653e10i q^{56} +(-2.94279e9 - 4.24475e9i) q^{57} +(-4.87817e9 - 4.87817e9i) q^{58} +6.76703e9 q^{59} +3.58336e9 q^{61} +(3.27067e9 + 3.27067e9i) q^{62} +(5.58064e9 + 1.22652e10i) q^{63} +5.10338e8i q^{64} +(-1.82589e9 + 1.00799e10i) q^{66} +(-1.15389e10 + 1.15389e10i) q^{67} +(8.74832e9 - 8.74832e9i) q^{68} +(-1.79934e6 + 9.93336e6i) q^{69} +2.04369e10i q^{71} +(1.51087e10 + 3.32060e10i) q^{72} +(-8.20889e9 - 8.20889e9i) q^{73} +2.63541e10 q^{74} -5.61801e10 q^{76} +(1.60827e10 + 1.60827e10i) q^{77} +(7.11140e9 + 1.02576e10i) q^{78} -2.87419e10i q^{79} +(-2.36587e10 - 2.06164e10i) q^{81} +(-2.38354e10 + 2.38354e10i) q^{82} +(-6.21066e9 + 6.21066e9i) q^{83} +(1.44221e11 + 2.61243e10i) q^{84} -6.36438e10i q^{86} +(2.93150e10 - 2.03235e10i) q^{87} +(4.35414e10 + 4.35414e10i) q^{88} -9.02351e10 q^{89} +2.77126e10 q^{91} +(7.76423e7 + 7.76423e7i) q^{92} +(-1.96548e10 + 1.36263e10i) q^{93} +3.94246e10i q^{94} +(7.43838e10 + 1.34740e10i) q^{96} +(1.89037e9 - 1.89037e9i) q^{97} +(2.19236e11 - 2.19236e11i) q^{98} +(-4.96021e10 - 1.85796e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7}+O(q^{10}) $ 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7	$ 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) $ 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	57.5586	+	57.5586i	1.27188	+	1.27188i	0.945103	+	0.326774i	$0.105962\pi$
$2$	57.5586	+	57.5586i	1.27188	+	1.27188i	0.326774	+	0.945103i	$0.394038\pi$
$3$	−345.894	+	239.801i	−0.821819	+	0.569749i
$3$	−345.894	+	239.801i	−0.821819	+	0.569749i
$4$			4577.97i			2.23534i
$5$		0			0
$5$		0			0
$6$	−33711.7	−	6106.58i	−1.76990	−	0.320602i
$7$	−53787.8	+	53787.8i	−1.20961	+	1.20961i	−0.238452	+	0.971154i	$0.576640\pi$
$7$	−53787.8	+	53787.8i	−1.20961	+	1.20961i	−0.971154	+	0.238452i	$0.923360\pi$
$8$	−145622.	+	145622.i	−1.57120	+	1.57120i
$9$	62138.3	−	165891.i	0.350773	−	0.936461i
$10$		0			0
$11$		−	299004.i		−	0.559779i	−0.960032	−	0.279890i	$-0.909702\pi$
$11$		−	299004.i		−	0.559779i	0.960032	−	0.279890i	$-0.0902979\pi$
$12$	−1.09780e6	−	1.58349e6i	−1.27358	−	1.83704i
$13$	−257611.	−	257611.i	−0.192432	−	0.192432i	0.604314	−	0.796746i	$-0.293447\pi$
$13$	−257611.	−	257611.i	−0.192432	−	0.192432i	−0.796746	+	0.604314i	$0.793447\pi$
$14$	−6.19189e6			−3.07694
$15$		0			0
$16$	−7.38785e6			−1.76140
$17$	−1.91096e6	−	1.91096e6i	−0.326424	−	0.326424i	0.524801	−	0.851225i	$-0.324140\pi$
$17$	−1.91096e6	−	1.91096e6i	−0.326424	−	0.326424i	−0.851225	+	0.524801i	$0.824140\pi$
$18$	1.31250e7	−	5.97187e6i	1.63720	−	0.744923i
$19$			1.22718e7i			1.13701i	0.822680	+	0.568505i	$0.192478\pi$
$19$			1.22718e7i			1.13701i	−0.822680	+	0.568505i	$0.807522\pi$
$20$		0			0
$21$	5.70652e6	−	3.15032e7i	0.304906	−	1.68325i
$22$	1.72102e7	−	1.72102e7i	0.711970	−	0.711970i
$23$	16960.0	−	16960.0i	0.000549442	−	0.000549442i	−0.706832	−	0.707381i	$-0.749876\pi$
$23$	16960.0	−	16960.0i	0.000549442	−	0.000549442i	0.707381	+	0.706832i	$0.249876\pi$
$24$	1.54495e7	−	8.52898e7i	0.396052	−	2.18643i
$25$		0			0
$26$		−	2.96554e7i		−	0.489498i
$27$	1.82876e7	+	7.22816e7i	0.245276	+	0.969453i
$28$	−2.46239e8	−	2.46239e8i	−2.70388	−	2.70388i
$29$	−8.47515e7			−0.767288			−0.383644	−	0.923481i	$-0.625331\pi$
$29$	−8.47515e7			−0.767288			−0.383644	+	0.923481i	$0.625331\pi$
$30$		0			0
$31$	5.68233e7			0.356481			0.178241	−	0.983987i	$-0.442959\pi$
$31$	5.68233e7			0.356481			0.178241	+	0.983987i	$0.442959\pi$
$32$	−1.27001e8	−	1.27001e8i	−0.669086	−	0.669086i
$33$	7.17013e7	+	1.03424e8i	0.318934	+	0.460037i
$34$		−	2.19984e8i		−	0.830342i
$35$		0			0
$36$	7.59446e8	+	2.84468e8i	2.09331	+	0.784095i
$37$	2.28933e8	−	2.28933e8i	0.542748	−	0.542748i	−0.381586	−	0.924334i	$-0.624622\pi$
$37$	2.28933e8	−	2.28933e8i	0.542748	−	0.542748i	0.924334	+	0.381586i	$0.124622\pi$
$38$	−7.06349e8	+	7.06349e8i	−1.44614	+	1.44614i
$39$	1.50881e8	+	2.73308e7i	0.267781	+	0.0485062i
$40$		0			0
$41$			4.14106e8i			0.558214i	0.960260	+	0.279107i	$0.0900384\pi$
$41$			4.14106e8i			0.558214i	−0.960260	+	0.279107i	$0.909962\pi$
$42$	2.14174e9	−	1.48482e9i	2.52869	−	1.75308i
$43$	−5.52861e8	−	5.52861e8i	−0.573508	−	0.573508i	0.359599	−	0.933107i	$-0.382914\pi$
$43$	−5.52861e8	−	5.52861e8i	−0.573508	−	0.573508i	−0.933107	+	0.359599i	$0.882914\pi$
$44$	1.36883e9			1.25130
$45$		0			0
$46$	1.95238e6			0.00139764
$47$	3.42474e8	+	3.42474e8i	0.217816	+	0.217816i	0.807577	−	0.589762i	$-0.200778\pi$
$47$	3.42474e8	+	3.42474e8i	0.217816	+	0.217816i	−0.589762	+	0.807577i	$0.700778\pi$
$48$	2.55541e9	−	1.77161e9i	1.44755	−	1.00356i
$49$		−	3.80892e9i		−	1.92630i
$50$		0			0
$51$	1.11924e9	+	2.02740e8i	0.454241	+	0.0822817i
$52$	1.17934e9	−	1.17934e9i	0.430150	−	0.430150i
$53$	1.12548e9	−	1.12548e9i	0.369674	−	0.369674i	−0.497684	−	0.867358i	$-0.665816\pi$
$53$	1.12548e9	−	1.12548e9i	0.369674	−	0.369674i	0.867358	+	0.497684i	$0.165816\pi$
$54$	−3.10782e9	+	5.21303e9i	−0.921064	+	1.54499i
$55$		0			0
$56$		−	1.56653e10i		−	3.80106i
$57$	−2.94279e9	−	4.24475e9i	−0.647810	−	0.934416i
$58$	−4.87817e9	−	4.87817e9i	−0.975895	−	0.975895i
$59$	6.76703e9			1.23229			0.616144	−	0.787633i	$-0.288694\pi$
$59$	6.76703e9			1.23229			0.616144	+	0.787633i	$0.288694\pi$
$60$		0			0
$61$	3.58336e9			0.543221			0.271611	−	0.962407i	$-0.412444\pi$
$61$	3.58336e9			0.543221			0.271611	+	0.962407i	$0.412444\pi$
$62$	3.27067e9	+	3.27067e9i	0.453400	+	0.453400i
$63$	5.58064e9	+	1.22652e10i	0.708452	+	1.55705i
$64$			5.10338e8i			0.0594112i
$65$		0			0
$66$	−1.82589e9	+	1.00799e10i	−0.179466	+	0.990755i
$67$	−1.15389e10	+	1.15389e10i	−1.04413	+	1.04413i	−0.0451495	+	0.998980i	$0.514376\pi$
$67$	−1.15389e10	+	1.15389e10i	−1.04413	+	1.04413i	−0.998980	+	0.0451495i	$0.985624\pi$
$68$	8.74832e9	−	8.74832e9i	0.729668	−	0.729668i
$69$	−1.79934e6	+	9.93336e6i	−0.000138498	+	0.000764585i
$70$		0			0
$71$			2.04369e10i			1.34429i	0.740418	+	0.672147i	$0.234628\pi$
$71$			2.04369e10i			1.34429i	−0.740418	+	0.672147i	$0.765372\pi$
$72$	1.51087e10	+	3.32060e10i	0.920232	+	2.02250i
$73$	−8.20889e9	−	8.20889e9i	−0.463456	−	0.463456i	0.436330	−	0.899787i	$-0.356278\pi$
$73$	−8.20889e9	−	8.20889e9i	−0.463456	−	0.463456i	−0.899787	+	0.436330i	$0.856278\pi$
$74$	2.63541e10			1.38062
$75$		0			0
$76$	−5.61801e10			−2.54160
$77$	1.60827e10	+	1.60827e10i	0.677113	+	0.677113i
$78$	7.11140e9	+	1.02576e10i	0.278891	+	0.402279i
$79$		−	2.87419e10i		−	1.05091i	−0.850820	−	0.525457i	$-0.823894\pi$
$79$		−	2.87419e10i		−	1.05091i	0.850820	−	0.525457i	$-0.176106\pi$
$80$		0			0
$81$	−2.36587e10	−	2.06164e10i	−0.753917	−	0.656969i
$82$	−2.38354e10	+	2.38354e10i	−0.709979	+	0.709979i
$83$	−6.21066e9	+	6.21066e9i	−0.173065	+	0.173065i	−0.788324	−	0.615260i	$-0.789051\pi$
$83$	−6.21066e9	+	6.21066e9i	−0.173065	+	0.173065i	0.615260	+	0.788324i	$0.289051\pi$
$84$	1.44221e11	+	2.61243e10i	3.76263	+	0.681567i
$85$		0			0
$86$		−	6.36438e10i		−	1.45886i
$87$	2.93150e10	−	2.03235e10i	0.630572	−	0.437161i
$88$	4.35414e10	+	4.35414e10i	0.879524	+	0.879524i
$89$	−9.02351e10			−1.71289			−0.856447	−	0.516235i	$-0.827333\pi$
$89$	−9.02351e10			−1.71289			−0.856447	+	0.516235i	$0.827333\pi$
$90$		0			0
$91$	2.77126e10			0.465533
$92$	7.76423e7	+	7.76423e7i	0.00122819	+	0.00122819i
$93$	−1.96548e10	+	1.36263e10i	−0.292963	+	0.203105i
$94$			3.94246e10i			0.554069i
$95$		0			0
$96$	7.43838e10	+	1.34740e10i	0.931079	+	0.168657i
$97$	1.89037e9	−	1.89037e9i	0.0223513	−	0.0223513i	−0.695843	−	0.718194i	$-0.744969\pi$
$97$	1.89037e9	−	1.89037e9i	0.0223513	−	0.0223513i	0.718194	+	0.695843i	$0.244969\pi$
$98$	2.19236e11	−	2.19236e11i	2.45001	−	2.45001i
$99$	−4.96021e10	−	1.85796e10i	−0.524211	−	0.196355i
$100$		0			0
$101$		−	1.55162e11i		−	1.46899i	−0.678614	−	0.734495i	$-0.737419\pi$
$101$		−	1.55162e11i		−	1.46899i	0.678614	−	0.734495i	$-0.262581\pi$
$102$	5.27523e10	+	7.60911e10i	0.473086	+	0.682391i
$103$	−1.21425e11	−	1.21425e11i	−1.03205	−	1.03205i	−0.999469	−	0.0325848i	$-0.989626\pi$
$103$	−1.21425e11	−	1.21425e11i	−1.03205	−	1.03205i	−0.0325848	−	0.999469i	$-0.510374\pi$
$104$	7.50275e10			0.604696
$105$		0			0
$106$	1.29562e11			0.940360
$107$	−1.01184e11	−	1.01184e11i	−0.697434	−	0.697434i	0.266422	−	0.963856i	$-0.414158\pi$
$107$	−1.01184e11	−	1.01184e11i	−0.697434	−	0.697434i	−0.963856	+	0.266422i	$0.914158\pi$
$108$	−3.30903e11	+	8.37199e10i	−2.16706	+	0.548275i
$109$			4.72942e10i			0.294416i	0.989106	+	0.147208i	$0.0470287\pi$
$109$			4.72942e10i			0.294416i	−0.989106	+	0.147208i	$0.952971\pi$
$110$		0			0
$111$	−2.42882e10	+	1.34085e11i	−0.136810	+	0.755271i
$112$	3.97376e11	−	3.97376e11i	2.13060	−	2.13060i
$113$	1.85463e10	−	1.85463e10i	0.0946949	−	0.0946949i	−0.658172	−	0.752867i	$-0.728670\pi$
$113$	1.85463e10	−	1.85463e10i	0.0946949	−	0.0946949i	0.752867	+	0.658172i	$0.228670\pi$
$114$	7.49389e10	−	4.13705e11i	0.364528	−	2.01240i
$115$		0			0
$116$		−	3.87990e11i		−	1.71515i
$117$	−5.87429e10	+	2.67279e10i	−0.247704	+	0.112705i
$118$	3.89501e11	+	3.89501e11i	1.56732	+	1.56732i
$119$	2.05572e11			0.789689
$120$		0			0
$121$	1.95908e11			0.686647
$122$	2.06253e11	+	2.06253e11i	0.690910	+	0.690910i
$123$	−9.93030e10	−	1.43237e11i	−0.318042	−	0.458751i
$124$			2.60135e11i			0.796857i
$125$		0			0
$126$	−3.84754e11	+	1.02718e12i	−1.07931	+	2.88143i
$127$	3.04196e11	−	3.04196e11i	0.817022	−	0.817022i	−0.168654	−	0.985675i	$-0.553942\pi$
$127$	3.04196e11	−	3.04196e11i	0.817022	−	0.817022i	0.985675	+	0.168654i	$0.0539420\pi$
$128$	−2.89472e11	+	2.89472e11i	−0.744650	+	0.744650i
$129$	3.23808e11	+	5.86549e10i	0.798075	+	0.144564i
$130$		0			0
$131$			1.52397e11i			0.345131i	0.984998	+	0.172566i	$0.0552057\pi$
$131$			1.52397e11i			0.345131i	−0.984998	+	0.172566i	$0.944794\pi$
$132$	−4.73471e11	+	3.28247e11i	−1.02834	+	0.712925i
$133$	−6.60074e11	−	6.60074e11i	−1.37534	−	1.37534i
$134$	−1.32833e12			−2.65601
$135$		0			0
$136$	5.56554e11			1.02575
$137$	−5.49763e11	−	5.49763e11i	−0.973224	−	0.973224i	0.0264271	−	0.999651i	$-0.491587\pi$
$137$	−5.49763e11	−	5.49763e11i	−0.973224	−	0.973224i	−0.999651	+	0.0264271i	$0.991587\pi$
$138$	−6.75317e8	+	4.68182e8i	−0.00114861	+	0.000796306i
$139$		−	1.17207e12i		−	1.91590i	−0.286928	−	0.957952i	$-0.592634\pi$
$139$		−	1.17207e12i		−	1.91590i	0.286928	−	0.957952i	$-0.407366\pi$
$140$		0			0
$141$	−2.00585e11	−	3.63342e10i	−0.303105	−	0.0549048i
$142$	−1.17632e12	+	1.17632e12i	−1.70978	+	1.70978i
$143$	−7.70267e10	+	7.70267e10i	−0.107719	+	0.107719i
$144$	−4.59069e11	+	1.22558e12i	−0.617851	+	1.64948i
$145$		0			0
$146$		−	9.44984e11i		−	1.17892i
$147$	9.13381e11	+	1.31748e12i	1.09751	+	1.58307i
$148$	1.04805e12	+	1.04805e12i	1.21323	+	1.21323i
$149$	−5.22545e11			−0.582907			−0.291453	−	0.956585i	$-0.594139\pi$
$149$	−5.22545e11			−0.582907			−0.291453	+	0.956585i	$0.594139\pi$
$150$		0			0
$151$	−1.36055e12			−1.41040			−0.705198	−	0.709011i	$-0.749142\pi$
$151$	−1.36055e12			−1.41040			−0.705198	+	0.709011i	$0.749142\pi$
$152$	−1.78704e12	−	1.78704e12i	−1.78647	−	1.78647i
$153$	−4.35755e11	+	1.98267e11i	−0.420184	+	0.191183i
$154$			1.85140e12i			1.72241i
$155$		0			0
$156$	−1.25120e11	+	6.90731e11i	−0.108428	+	0.598582i
$157$	−1.08090e12	+	1.08090e12i	−0.904353	+	0.904353i	−0.995809	−	0.0914557i	$-0.970848\pi$
$157$	−1.08090e12	+	1.08090e12i	−0.904353	+	0.904353i	0.0914557	+	0.995809i	$0.470848\pi$
$158$	1.65434e12	−	1.65434e12i	1.33663	−	1.33663i
$159$	−1.19406e11	+	6.59186e11i	−0.0931838	+	0.514427i
$160$		0			0
$161$			1.82448e9i			0.00132922i
$162$	−1.75112e11	−	2.54841e12i	−0.123306	−	1.79447i
$163$	−2.74292e9	−	2.74292e9i	−0.00186716	−	0.00186716i	0.706173	−	0.708040i	$-0.250420\pi$
$163$	−2.74292e9	−	2.74292e9i	−0.00186716	−	0.00186716i	−0.708040	+	0.706173i	$0.750420\pi$
$164$	−1.89577e12			−1.24780
$165$		0			0
$166$	−7.14953e11			−0.440234
$167$	1.47832e12	+	1.47832e12i	0.880699	+	0.880699i	0.993606	−	0.112907i	$-0.0360162\pi$
$167$	1.47832e12	+	1.47832e12i	0.880699	+	0.880699i	−0.112907	+	0.993606i	$0.536016\pi$
$168$	3.75655e12	+	5.41854e12i	2.16565	+	3.12379i
$169$		−	1.65943e12i		−	0.925940i
$170$		0			0
$171$	2.03579e12	+	7.62550e11i	1.06477	+	0.398832i
$172$	2.53098e12	−	2.53098e12i	1.28199	−	1.28199i
$173$	−1.31945e12	+	1.31945e12i	−0.647350	+	0.647350i	−0.952352	−	0.305001i	$-0.901343\pi$
$173$	−1.31945e12	+	1.31945e12i	−0.647350	+	0.647350i	0.305001	+	0.952352i	$0.401343\pi$
$174$	2.85712e12	+	5.17542e11i	1.35802	+	0.245994i
$175$		0			0
$176$			2.20900e12i			0.985996i
$177$	−2.34068e12	+	1.62274e12i	−1.01272	+	0.702095i
$178$	−5.19380e12	−	5.19380e12i	−2.17859	−	2.17859i
$179$	1.75449e12			0.713606			0.356803	−	0.934180i	$-0.383867\pi$
$179$	1.75449e12			0.713606			0.356803	+	0.934180i	$0.383867\pi$
$180$		0			0
$181$	−2.14617e12			−0.821168			−0.410584	−	0.911823i	$-0.634675\pi$
$181$	−2.14617e12			−0.821168			−0.410584	+	0.911823i	$0.634675\pi$
$182$	1.59510e12	+	1.59510e12i	0.592100	+	0.592100i
$183$	−1.23946e12	+	8.59293e11i	−0.446429	+	0.309500i
$184$			4.93947e9i			0.00172656i
$185$		0			0
$186$	−1.91561e12	−	3.46996e11i	−0.630937	−	0.114289i
$187$	−5.71384e11	+	5.71384e11i	−0.182725	+	0.182725i
$188$	−1.56784e12	+	1.56784e12i	−0.486892	+	0.486892i
$189$	−4.87151e12	−	2.90422e12i	−1.46934	−	0.875970i
$190$		0			0
$191$			6.61199e12i			1.88212i	0.338233	+	0.941062i	$0.390171\pi$
$191$			6.61199e12i			1.88212i	−0.338233	+	0.941062i	$0.609829\pi$
$192$	−1.22379e11	−	1.76523e11i	−0.0338495	−	0.0488252i
$193$	−1.52315e12	−	1.52315e12i	−0.409428	−	0.409428i	0.472111	−	0.881539i	$-0.343492\pi$
$193$	−1.52315e12	−	1.52315e12i	−0.409428	−	0.409428i	−0.881539	+	0.472111i	$0.843492\pi$
$194$	2.17614e11			0.0568562
$195$		0			0
$196$	1.74371e13			4.30593
$197$	−2.90287e12	−	2.90287e12i	−0.697049	−	0.697049i	0.266724	−	0.963773i	$-0.414059\pi$
$197$	−2.90287e12	−	2.90287e12i	−0.697049	−	0.697049i	−0.963773	+	0.266724i	$0.914059\pi$
$198$	−1.78561e12	−	3.92444e12i	−0.416992	−	0.916472i
$199$		−	3.77492e12i		−	0.857464i	−0.903432	−	0.428732i	$-0.858960\pi$
$199$		−	3.77492e12i		−	0.857464i	0.903432	−	0.428732i	$-0.141040\pi$
$200$		0			0
$201$	1.22420e12	−	6.75829e12i	0.263194	−	1.45298i
$202$	8.93093e12	−	8.93093e12i	1.86837	−	1.86837i
$203$	4.55859e12	−	4.55859e12i	0.928116	−	0.928116i
$204$	−9.28138e11	+	5.12384e12i	−0.183928	+	1.01538i
$205$		0			0
$206$		−	1.39781e13i		−	2.62529i
$207$	−1.75964e9	−	3.86737e9i	−0.000321802	−	0.000707260i
$208$	1.90319e12	+	1.90319e12i	0.338949	+	0.338949i
$209$	3.66932e12			0.636475
$210$		0			0
$211$	−9.31282e12			−1.53295			−0.766475	−	0.642275i	$-0.777991\pi$
$211$	−9.31282e12			−1.53295			−0.766475	+	0.642275i	$0.777991\pi$
$212$	5.15240e12	+	5.15240e12i	0.826347	+	0.826347i
$213$	−4.90078e12	−	7.06900e12i	−0.765910	−	1.10477i
$214$		−	1.16481e13i		−	1.77410i
$215$		0			0
$216$	−1.31888e13	−	7.86270e12i	−1.90858	−	1.13783i
$217$	−3.05640e12	+	3.05640e12i	−0.431202	+	0.431202i
$218$	−2.72218e12	+	2.72218e12i	−0.374461	+	0.374461i
$219$	4.80790e12	+	8.70909e11i	0.644931	+	0.116823i
$220$		0			0
$221$			9.84568e11i			0.125629i
$222$	−9.11571e12	+	6.31972e12i	−1.13462	+	0.786605i
$223$	3.01429e12	+	3.01429e12i	0.366024	+	0.366024i	0.866025	−	0.500001i	$-0.166667\pi$
$223$	3.01429e12	+	3.01429e12i	0.366024	+	0.366024i	−0.500001	+	0.866025i	$0.666667\pi$
$224$	1.36622e13			1.61866
$225$		0			0
$226$	2.13500e12			0.240880
$227$	2.26550e12	+	2.26550e12i	0.249472	+	0.249472i	0.820754	−	0.571282i	$-0.193554\pi$
$227$	2.26550e12	+	2.26550e12i	0.249472	+	0.249472i	−0.571282	+	0.820754i	$0.693554\pi$
$228$	1.94324e13	−	1.34720e13i	2.08874	−	1.44808i
$229$			1.04987e13i			1.10164i	0.834625	+	0.550819i	$0.185684\pi$
$229$			1.04987e13i			1.10164i	−0.834625	+	0.550819i	$0.814316\pi$
$230$		0			0
$231$	−9.41957e12	−	1.70627e12i	−0.942248	−	0.170680i
$232$	1.23417e13	−	1.23417e13i	1.20556	−	1.20556i
$233$	−1.06708e13	+	1.06708e13i	−1.01798	+	1.01798i	−0.0181422	+	0.999835i	$0.505775\pi$
$233$	−1.06708e13	+	1.06708e13i	−1.01798	+	1.01798i	−0.999835	+	0.0181422i	$0.994225\pi$
$234$	−4.91958e12	−	1.84274e12i	−0.458396	−	0.171703i
$235$		0			0
$236$			3.09793e13i			2.75458i
$237$	6.89234e12	+	9.94166e12i	0.598757	+	0.863661i
$238$	1.18324e13	+	1.18324e13i	1.00439	+	1.00439i
$239$	2.58547e12			0.214462			0.107231	−	0.994234i	$-0.465802\pi$
$239$	2.58547e12			0.214462			0.107231	+	0.994234i	$0.465802\pi$
$240$		0			0
$241$	2.40423e13			1.90494			0.952471	−	0.304630i	$-0.0985329\pi$
$241$	2.40423e13			1.90494			0.952471	+	0.304630i	$0.0985329\pi$
$242$	1.12762e13	+	1.12762e13i	0.873330	+	0.873330i
$243$	1.31272e13	+	1.45771e12i	0.993891	+	0.110366i
$244$			1.64045e13i			1.21428i
$245$		0			0
$246$	2.52877e12	−	1.39602e13i	0.178964	−	0.987984i
$247$	3.16136e12	−	3.16136e12i	0.218797	−	0.218797i
$248$	−8.27470e12	+	8.27470e12i	−0.560103	+	0.560103i
$249$	6.58910e11	−	3.63755e12i	0.0436244	−	0.240831i
$250$		0			0
$251$			1.53527e13i			0.972704i	0.873763	+	0.486352i	$0.161673\pi$
$251$			1.53527e13i			0.972704i	−0.873763	+	0.486352i	$0.838327\pi$
$252$	−5.61497e13	+	2.55480e13i	−3.48053	+	1.58363i
$253$	−5.07109e9	−	5.07109e9i	−0.000307566	−	0.000307566i
$254$	3.50182e13			2.07830
$255$		0			0
$256$	−3.22780e13			−1.83479
$257$	−2.23552e12	−	2.23552e12i	−0.124379	−	0.124379i	0.642177	−	0.766556i	$-0.278031\pi$
$257$	−2.23552e12	−	2.23552e12i	−0.124379	−	0.124379i	−0.766556	+	0.642177i	$0.778031\pi$
$258$	1.52618e13	+	2.20140e13i	0.831185	+	1.19892i
$259$			2.46275e13i			1.31302i
$260$		0			0
$261$	−5.26631e12	+	1.40595e13i	−0.269143	+	0.718535i
$262$	−8.77175e12	+	8.77175e12i	−0.438964	+	0.438964i
$263$	−1.29466e13	+	1.29466e13i	−0.634454	+	0.634454i	−0.949182	−	0.314728i	$-0.898087\pi$
$263$	−1.29466e13	+	1.29466e13i	−0.634454	+	0.634454i	0.314728	+	0.949182i	$0.398087\pi$
$264$	−2.55020e13	−	4.61945e12i	−1.22392	−	0.221702i
$265$		0			0
$266$		−	7.59858e13i		−	3.49851i
$267$	3.12118e13	−	2.16384e13i	1.40769	−	0.975919i
$268$	−5.28250e13	−	5.28250e13i	−2.33398	−	2.33398i
$269$	7.20802e12			0.312017			0.156008	−	0.987756i	$-0.450137\pi$
$269$	7.20802e12			0.312017			0.156008	+	0.987756i	$0.450137\pi$
$270$		0			0
$271$	1.22507e13			0.509133			0.254566	−	0.967055i	$-0.418067\pi$
$271$	1.22507e13			0.509133			0.254566	+	0.967055i	$0.418067\pi$
$272$	1.41179e13	+	1.41179e13i	0.574964	+	0.574964i
$273$	−9.58564e12	+	6.64551e12i	−0.382584	+	0.265237i
$274$		−	6.32872e13i		−	2.47564i
$275$		0			0
$276$	−4.54747e10	−	8.23733e9i	−0.00170911	−	0.000309590i
$277$	−7.08002e12	+	7.08002e12i	−0.260853	+	0.260853i	−0.825400	−	0.564548i	$-0.809051\pi$
$277$	−7.08002e12	+	7.08002e12i	−0.260853	+	0.260853i	0.564548	+	0.825400i	$0.309051\pi$
$278$	6.74629e13	−	6.74629e13i	2.43679	−	2.43679i
$279$	3.53090e12	−	9.42648e12i	0.125044	−	0.333831i
$280$		0			0
$281$			3.72921e13i			1.26979i	0.772599	+	0.634895i	$0.218957\pi$
$281$			3.72921e13i			1.26979i	−0.772599	+	0.634895i	$0.781043\pi$
$282$	−9.45404e12	−	1.36367e13i	−0.315680	−	0.455345i
$283$	1.38836e13	+	1.38836e13i	0.454651	+	0.454651i	0.896895	−	0.442244i	$-0.145817\pi$
$283$	1.38836e13	+	1.38836e13i	0.454651	+	0.454651i	−0.442244	+	0.896895i	$0.645817\pi$
$284$	−9.35596e13			−3.00495
$285$		0			0
$286$	−8.86709e12			−0.274011
$287$	−2.22739e13	−	2.22739e13i	−0.675219	−	0.675219i
$288$	−2.89600e13	+	1.31767e13i	−0.861270	+	0.391876i
$289$		−	2.69684e13i		−	0.786895i
$290$		0			0
$291$	−2.00556e11	+	1.10718e12i	−0.00563409	+	0.0311033i
$292$	3.75801e13	−	3.75801e13i	1.03598	−	1.03598i
$293$	−1.53264e13	+	1.53264e13i	−0.414637	+	0.414637i	−0.883350	−	0.468713i	$-0.844718\pi$
$293$	−1.53264e13	+	1.53264e13i	−0.414637	+	0.414637i	0.468713	+	0.883350i	$0.344718\pi$
$294$	−2.32595e13	+	1.28405e14i	−0.617574	+	3.40936i
$295$		0			0
$296$			6.66751e13i			1.70553i
$297$	2.16125e13	−	5.46805e12i	0.542680	−	0.137300i
$298$	−3.00769e13	−	3.00769e13i	−0.741385	−	0.741385i
$299$	−8.73815e9			−0.000211460
$300$		0			0
$301$	5.94743e13			1.38744
$302$	−7.83112e13	−	7.83112e13i	−1.79385	−	1.79385i
$303$	3.72081e13	+	5.36698e13i	0.836956	+	1.20724i
$304$		−	9.06624e13i		−	2.00273i
$305$		0			0
$306$	−3.64934e13	−	1.36694e13i	−0.777583	−	0.291261i
$307$	3.56351e13	−	3.56351e13i	0.745791	−	0.745791i	−0.227895	−	0.973686i	$-0.573184\pi$
$307$	3.56351e13	−	3.56351e13i	0.745791	−	0.745791i	0.973686	+	0.227895i	$0.0731842\pi$
$308$	−7.36264e13	+	7.36264e13i	−1.51358	+	1.51358i
$309$	7.11178e13	+	1.28824e13i	1.43617	+	0.260150i
$310$		0			0
$311$		−	2.66600e13i		−	0.519610i	−0.965661	−	0.259805i	$-0.916342\pi$
$311$		−	2.66600e13i		−	0.519610i	0.965661	−	0.259805i	$-0.0836583\pi$
$312$	−2.59516e13	+	1.79916e13i	−0.496951	+	0.344525i
$313$	−1.43721e12	−	1.43721e12i	−0.0270412	−	0.0270412i	0.693457	−	0.720498i	$-0.256087\pi$
$313$	−1.43721e12	−	1.43721e12i	−0.0270412	−	0.0270412i	−0.720498	+	0.693457i	$0.756087\pi$
$314$	−1.24430e14			−2.30045
$315$		0			0
$316$	1.31580e14			2.34915
$317$	4.52632e13	+	4.52632e13i	0.794180	+	0.794180i	0.982171	−	0.187990i	$-0.0601974\pi$
$317$	4.52632e13	+	4.52632e13i	0.794180	+	0.794180i	−0.187990	+	0.982171i	$0.560197\pi$
$318$	−4.48146e13	+	3.10690e13i	−0.772805	+	0.535769i
$319$			2.53410e13i			0.429512i
$320$		0			0
$321$	5.92632e13	+	1.07350e13i	0.970527	+	0.175802i
$322$	−1.05014e11	+	1.05014e11i	−0.00169060	+	0.00169060i
$323$	2.34509e13	−	2.34509e13i	0.371147	−	0.371147i
$324$	9.43813e13	−	1.08309e14i	1.46855	−	1.68526i
$325$		0			0
$326$		−	3.15757e11i		−	0.00474959i
$327$	−1.13412e13	−	1.63588e13i	−0.167743	−	0.241957i
$328$	−6.03029e13	−	6.03029e13i	−0.877065	−	0.877065i
$329$	−3.68418e13			−0.526943
$330$		0			0
$331$	−6.58891e13			−0.911507			−0.455753	−	0.890106i	$-0.650630\pi$
$331$	−6.58891e13			−0.911507			−0.455753	+	0.890106i	$0.650630\pi$
$332$	−2.84322e13	−	2.84322e13i	−0.386858	−	0.386858i
$333$	−2.37524e13	−	5.22034e13i	−0.317881	−	0.698643i
$334$			1.70180e14i			2.24028i
$335$		0			0
$336$	−4.21589e13	+	2.32741e14i	−0.537061	+	2.96488i
$337$	−2.25852e13	+	2.25852e13i	−0.283047	+	0.283047i	−0.834323	−	0.551276i	$-0.814141\pi$
$337$	−2.25852e13	+	2.25852e13i	−0.283047	+	0.283047i	0.551276	+	0.834323i	$0.314141\pi$
$338$	9.55146e13	−	9.55146e13i	1.17768	−	1.17768i
$339$	−1.96764e12	+	1.08625e13i	−0.0238697	+	0.131774i
$340$		0			0
$341$		−	1.69904e13i		−	0.199551i
$342$	7.32857e13	+	1.61068e14i	0.846985	+	1.86151i
$343$	9.85171e13	+	9.85171e13i	1.12045	+	1.12045i
$344$	1.61017e14			1.80219
$345$		0			0
$346$	−1.51891e14			−1.64670
$347$	1.14067e13	+	1.14067e13i	0.121716	+	0.121716i	0.765341	−	0.643625i	$-0.222570\pi$
$347$	1.14067e13	+	1.14067e13i	0.121716	+	0.121716i	−0.643625	+	0.765341i	$0.722570\pi$
$348$	9.30403e13	+	1.34203e14i	0.977204	+	1.40954i
$349$		−	2.00257e13i		−	0.207037i	−0.994628	−	0.103518i	$-0.966990\pi$
$349$		−	2.00257e13i		−	0.207037i	0.994628	−	0.103518i	$-0.0330101\pi$
$350$		0			0
$351$	1.39095e13	−	2.33316e13i	0.139355	−	0.233752i
$352$	−3.79738e13	+	3.79738e13i	−0.374541	+	0.374541i
$353$	4.19914e13	−	4.19914e13i	0.407755	−	0.407755i	−0.473200	−	0.880955i	$-0.656901\pi$
$353$	4.19914e13	−	4.19914e13i	0.407755	−	0.407755i	0.880955	+	0.473200i	$0.156901\pi$
$354$	−2.28128e14	−	4.13234e13i	−2.18103	−	0.395074i
$355$		0			0
$356$		−	4.13094e14i		−	3.82890i
$357$	−7.11062e13	+	4.92964e13i	−0.648982	+	0.449925i
$358$	1.00986e14	+	1.00986e14i	0.907619	+	0.907619i
$359$	−1.21733e12			−0.0107743			−0.00538716	−	0.999985i	$-0.501715\pi$
$359$	−1.21733e12			−0.0107743			−0.00538716	+	0.999985i	$0.501715\pi$
$360$		0			0
$361$	−3.41074e13			−0.292792
$362$	−1.23530e14	−	1.23530e14i	−1.04442	−	1.04442i
$363$	−6.77636e13	+	4.69790e13i	−0.564300	+	0.391216i
$364$			1.26868e14i			1.04062i
$365$		0			0
$366$	−1.20801e14	−	2.18821e13i	−0.961448	−	0.174158i
$367$	1.13749e14	−	1.13749e14i	0.891835	−	0.891835i	−0.102861	−	0.994696i	$-0.532800\pi$
$367$	1.13749e14	−	1.13749e14i	0.891835	−	0.891835i	0.994696	+	0.102861i	$0.0327996\pi$
$368$	−1.25298e11	+	1.25298e11i	−0.000967788	+	0.000967788i
$369$	6.86966e13	+	2.57319e13i	0.522745	+	0.195806i
$370$		0			0
$371$			1.21074e14i			0.894321i
$372$	−6.23807e13	−	8.99793e13i	−0.454008	−	0.654872i
$373$	1.90849e12	+	1.90849e12i	0.0136865	+	0.0136865i	0.713917	−	0.700230i	$-0.246919\pi$
$373$	1.90849e12	+	1.90849e12i	0.0136865	+	0.0136865i	−0.700230	+	0.713917i	$0.746919\pi$
$374$	−6.57760e13			−0.464808
$375$		0			0
$376$	−9.97432e13			−0.684463
$377$	2.18329e13	+	2.18329e13i	0.147650	+	0.147650i
$378$	−1.13235e14	−	4.47560e14i	−0.754699	−	2.98295i
$379$			4.34038e13i			0.285110i	0.989787	+	0.142555i	$0.0455317\pi$
$379$			4.34038e13i			0.285110i	−0.989787	+	0.142555i	$0.954468\pi$
$380$		0			0
$381$	−3.22732e13	+	1.78166e14i	−0.205947	+	1.13694i
$382$	−3.80576e14	+	3.80576e14i	−2.39383	+	2.39383i
$383$	−1.34929e14	+	1.34929e14i	−0.836590	+	0.836590i	−0.988408	−	0.151819i	$-0.951487\pi$
$383$	−1.34929e14	+	1.34929e14i	−0.836590	+	0.836590i	0.151819	+	0.988408i	$0.451487\pi$
$384$	3.07111e13	−	1.69542e14i	0.187704	−	1.03623i
$385$		0			0
$386$		−	1.75341e14i		−	1.04148i
$387$	−1.26069e14	+	5.73610e13i	−0.738239	+	0.335897i
$388$	8.65407e12	+	8.65407e12i	0.0499627	+	0.0499627i
$389$	1.34696e13			0.0766712			0.0383356	−	0.999265i	$-0.487794\pi$
$389$	1.34696e13			0.0766712			0.0383356	+	0.999265i	$0.487794\pi$
$390$		0			0
$391$	−6.48195e10			−0.000358702
$392$	5.54661e14	+	5.54661e14i	3.02659	+	3.02659i
$393$	−3.65449e13	−	5.27132e13i	−0.196638	−	0.283635i
$394$		−	3.34170e14i		−	1.77312i
$395$		0			0
$396$	8.50569e13	−	2.27077e14i	0.438920	−	1.17179i
$397$	5.76377e13	−	5.76377e13i	0.293331	−	0.293331i	−0.545063	−	0.838395i	$-0.683494\pi$
$397$	5.76377e13	−	5.76377e13i	0.293331	−	0.293331i	0.838395	+	0.545063i	$0.183494\pi$
$398$	2.17279e14	−	2.17279e14i	1.09059	−	1.09059i
$399$	3.86602e14	+	7.00294e13i	1.91387	+	0.346681i
$400$		0			0
$401$			3.27468e14i			1.57716i	0.614934	+	0.788578i	$0.289183\pi$
$401$			3.27468e14i			1.57716i	−0.614934	+	0.788578i	$0.710817\pi$
$402$	4.59461e14	−	3.18534e14i	2.18276	−	1.51326i
$403$	−1.46383e13	−	1.46383e13i	−0.0685983	−	0.0685983i
$404$	7.10330e14			3.28369
$405$		0			0
$406$	5.24772e14			2.36090
$407$	−6.84517e13	−	6.84517e13i	−0.303819	−	0.303819i
$408$	−1.92509e14	+	1.33462e14i	−0.842984	+	0.584422i
$409$		−	5.64062e13i		−	0.243696i	−0.992549	−	0.121848i	$-0.961118\pi$
$409$		−	5.64062e13i		−	0.243696i	0.992549	−	0.121848i	$-0.0388821\pi$
$410$		0			0
$411$	3.21993e14	+	5.83262e13i	1.35431	+	0.245321i
$412$	5.55879e14	−	5.55879e14i	2.30699	−	2.30699i
$413$	−3.63984e14	+	3.63984e14i	−1.49058	+	1.49058i
$414$	1.21318e11	−	3.23883e11i	0.000490255	−	0.00130884i
$415$		0			0
$416$			6.54337e13i			0.257507i
$417$	2.81064e14	+	4.05413e14i	1.09158	+	1.57453i
$418$	2.11201e14	+	2.11201e14i	0.809517	+	0.809517i
$419$	−2.65943e14			−1.00603			−0.503016	−	0.864277i	$-0.667776\pi$
$419$	−2.65943e14			−1.00603			−0.503016	+	0.864277i	$0.667776\pi$
$420$		0			0
$421$	−1.98860e14			−0.732818			−0.366409	−	0.930454i	$-0.619413\pi$
$421$	−1.98860e14			−0.732818			−0.366409	+	0.930454i	$0.619413\pi$
$422$	−5.36032e14	−	5.36032e14i	−1.94972	−	1.94972i
$423$	7.80941e13	−	3.55327e13i	0.280380	−	0.127572i
$424$			3.27787e14i			1.16166i
$425$		0			0
$426$	1.24800e14	−	6.88964e14i	0.430983	−	2.37927i
$427$	−1.92741e14	+	1.92741e14i	−0.657084	+	0.657084i
$428$	4.63220e14	−	4.63220e14i	1.55900	−	1.55900i
$429$	8.17202e12	−	4.51141e13i	0.0271528	−	0.149899i
$430$		0			0
$431$			1.58245e14i			0.512513i	0.966609	+	0.256257i	$0.0824892\pi$
$431$			1.58245e14i			0.512513i	−0.966609	+	0.256257i	$0.917511\pi$
$432$	−1.35106e14	−	5.34006e14i	−0.432029	−	1.70760i
$433$	−3.79240e14	−	3.79240e14i	−1.19737	−	1.19737i	−0.974950	−	0.222425i	$-0.928603\pi$
$433$	−3.79240e14	−	3.79240e14i	−1.19737	−	1.19737i	−0.222425	−	0.974950i	$-0.571397\pi$
$434$	−3.51843e14			−1.09687
$435$		0			0
$436$	−2.16511e14			−0.658120
$437$	2.08130e11	+	2.08130e11i	0.000624721	+	0.000624721i
$438$	2.26608e14	+	3.26864e14i	0.671687	+	0.968857i
$439$		−	4.38570e13i		−	0.128376i	−0.997938	−	0.0641881i	$-0.979554\pi$
$439$		−	4.38570e13i		−	0.128376i	0.997938	−	0.0641881i	$-0.0204458\pi$
$440$		0			0
$441$	−6.31866e14	−	2.36680e14i	−1.80390	−	0.675692i
$442$	−5.66703e13	+	5.66703e13i	−0.159784	+	0.159784i
$443$	9.14896e13	−	9.14896e13i	0.254772	−	0.254772i	−0.568152	−	0.822924i	$-0.692341\pi$
$443$	9.14896e13	−	9.14896e13i	0.254772	−	0.254772i	0.822924	+	0.568152i	$0.192341\pi$
$444$	−6.13836e14	−	1.11191e14i	−1.68829	−	0.305818i
$445$		0			0
$446$			3.46997e14i			0.931073i
$447$	1.80745e14	−	1.25307e14i	0.479044	−	0.332110i
$448$	−2.74499e13	−	2.74499e13i	−0.0718642	−	0.0718642i
$449$	−4.89331e14			−1.26546			−0.632730	−	0.774373i	$-0.718066\pi$
$449$	−4.89331e14			−1.26546			−0.632730	+	0.774373i	$0.718066\pi$
$450$		0			0
$451$	1.23819e14			0.312477
$452$	8.49046e13	+	8.49046e13i	0.211675	+	0.211675i
$453$	4.70606e14	−	3.26260e14i	1.15909	−	0.803571i
$454$			2.60798e14i			0.634595i
$455$		0			0
$456$	1.04666e15	+	1.89593e14i	2.48599	+	0.450315i
$457$	−1.82599e14	+	1.82599e14i	−0.428508	+	0.428508i	−0.888120	−	0.459612i	$-0.847988\pi$
$457$	−1.82599e14	+	1.82599e14i	−0.428508	+	0.428508i	0.459612	+	0.888120i	$0.347988\pi$
$458$	−6.04288e14	+	6.04288e14i	−1.40115	+	1.40115i
$459$	1.03180e14	−	1.73074e14i	0.236389	−	0.396517i
$460$		0			0
$461$		−	5.61548e14i		−	1.25612i	−0.778164	−	0.628061i	$-0.783849\pi$
$461$		−	5.61548e14i		−	1.25612i	0.778164	−	0.628061i	$-0.216151\pi$
$462$	−4.43966e14	−	6.40388e14i	−0.981340	−	1.41551i
$463$	−1.40372e14	−	1.40372e14i	−0.306608	−	0.306608i	0.536984	−	0.843592i	$-0.319564\pi$
$463$	−1.40372e14	−	1.40372e14i	−0.306608	−	0.306608i	−0.843592	+	0.536984i	$0.819564\pi$
$464$	6.26131e14			1.35150
$465$		0			0
$466$	−1.22839e15			−2.58948
$467$	2.20852e14	+	2.20852e14i	0.460106	+	0.460106i	0.898690	−	0.438584i	$-0.144520\pi$
$467$	2.20852e14	+	2.20852e14i	0.460106	+	0.460106i	−0.438584	+	0.898690i	$0.644520\pi$
$468$	−1.22360e14	−	2.68924e14i	−0.251934	−	0.553703i
$469$		−	1.24131e15i		−	2.52597i
$470$		0			0
$471$	1.14676e14	−	6.33078e14i	0.227960	−	1.25847i
$472$	−9.85427e14	+	9.85427e14i	−1.93617	+	1.93617i
$473$	−1.65308e14	+	1.65308e14i	−0.321038	+	0.321038i
$474$	−1.75515e14	+	9.68941e14i	−0.336925	+	1.86001i
$475$		0			0
$476$			9.41105e14i			1.76522i
$477$	−1.16771e14	−	2.56642e14i	−0.216514	−	0.475857i
$478$	1.48816e14	+	1.48816e14i	0.272769	+	0.272769i
$479$	4.06414e14			0.736417			0.368208	−	0.929743i	$-0.379971\pi$
$479$	4.06414e14			0.736417			0.368208	+	0.929743i	$0.379971\pi$
$480$		0			0
$481$	−1.17951e14			−0.208884
$482$	1.38384e15	+	1.38384e15i	2.42285	+	2.42285i
$483$	−4.37511e11	−	6.31075e11i	−0.000757320	−	0.00109238i
$484$			8.96864e14i			1.53489i
$485$		0			0
$486$	6.71681e14	+	8.39488e14i	1.12373	+	1.40448i
$487$	−6.48096e14	+	6.48096e14i	−1.07209	+	1.07209i	−0.0748952	+	0.997191i	$0.523862\pi$
$487$	−6.48096e14	+	6.48096e14i	−1.07209	+	1.07209i	−0.997191	+	0.0748952i	$0.976138\pi$
$488$	−5.21815e14	+	5.21815e14i	−0.853508	+	0.853508i
$489$	1.60651e12	+	2.91005e11i	0.00259828	+	0.000470655i
$490$		0			0
$491$			9.20026e14i			1.45496i	0.686127	+	0.727481i	$0.259309\pi$
$491$			9.20026e14i			1.45496i	−0.686127	+	0.727481i	$0.740691\pi$
$492$	6.55735e14	−	4.54606e14i	1.02546	−	0.710931i
$493$	1.61957e14	+	1.61957e14i	0.250461	+	0.250461i
$494$	3.63926e14			0.556564
$495$		0			0
$496$	−4.19802e14			−0.627907
$497$	−1.09926e15	−	1.09926e15i	−1.62607	−	1.62607i
$498$	2.47298e14	−	1.71446e14i	0.361792	−	0.250823i
$499$			1.00870e15i			1.45952i	0.683705	+	0.729759i	$0.260368\pi$
$499$			1.00870e15i			1.45952i	−0.683705	+	0.729759i	$0.739632\pi$
$500$		0			0
$501$	−8.65843e14	−	1.56840e14i	−1.22555	−	0.221998i
$502$	−8.83682e14	+	8.83682e14i	−1.23716	+	1.23716i
$503$	5.32566e14	−	5.32566e14i	0.737479	−	0.737479i	−0.234611	−	0.972089i	$-0.575382\pi$
$503$	5.32566e14	−	5.32566e14i	0.737479	−	0.737479i	0.972089	+	0.234611i	$0.0753816\pi$
$504$	−2.59874e15	−	9.73417e14i	−3.55955	−	1.33331i
$505$		0			0
$506$		−	5.83769e11i		−	0.000782372i
$507$	3.97933e14	+	5.73988e14i	0.527553	+	0.760955i
$508$	1.39260e15	+	1.39260e15i	1.82632	+	1.82632i
$509$	−1.54706e14			−0.200706			−0.100353	−	0.994952i	$-0.531997\pi$
$509$	−1.54706e14			−0.200706			−0.100353	+	0.994952i	$0.531997\pi$
$510$		0			0
$511$	8.83076e14			1.12120
$512$	−1.26504e15	−	1.26504e15i	−1.58898	−	1.58898i
$513$	−8.87027e14	+	2.24422e14i	−1.10228	+	0.278881i
$514$		−	2.57347e14i		−	0.316389i
$515$		0			0
$516$	−2.68521e14	+	1.48238e15i	−0.323150	+	1.78397i
$517$	1.02401e14	−	1.02401e14i	0.121929	−	0.121929i
$518$	−1.41753e15	+	1.41753e15i	−1.67000	+	1.67000i
$519$	1.39985e14	−	7.72795e14i	0.163178	−	0.900832i
$520$		0			0
$521$			1.07048e15i			1.22171i	0.791741	+	0.610857i	$0.209175\pi$
$521$			1.07048e15i			1.22171i	−0.791741	+	0.610857i	$0.790825\pi$
$522$	−1.11237e15	+	5.06125e14i	−1.25620	+	0.571570i
$523$	−5.12638e14	−	5.12638e14i	−0.572864	−	0.572864i	0.360064	−	0.932928i	$-0.382755\pi$
$523$	−5.12638e14	−	5.12638e14i	−0.572864	−	0.572864i	−0.932928	+	0.360064i	$0.882755\pi$
$524$	−6.97669e14			−0.771485
$525$		0			0
$526$	−1.49038e15			−1.61389
$527$	−1.08587e14	−	1.08587e14i	−0.116364	−	0.116364i
$528$	−5.29719e14	−	7.64078e14i	−0.561770	−	0.810310i
$529$			9.52809e14i			0.999999i
$530$		0			0
$531$	4.20492e14	−	1.12259e15i	0.432253	−	1.15399i
$532$	3.02180e15	−	3.02180e15i	3.07434	−	3.07434i
$533$	1.06678e14	−	1.06678e14i	0.107418	−	0.107418i
$534$	3.04198e15	+	5.51028e14i	3.03166	+	0.549157i
$535$		0			0
$536$		−	3.36064e15i		−	3.28107i
$537$	−6.06867e14	+	4.20727e14i	−0.586455	+	0.406576i
$538$	4.14883e14	+	4.14883e14i	0.396847	+	0.396847i
$539$	−1.13888e15			−1.07830
$540$		0			0
$541$	8.22414e14			0.762967			0.381483	−	0.924376i	$-0.375413\pi$
$541$	8.22414e14			0.762967			0.381483	+	0.924376i	$0.375413\pi$
$542$	7.05134e14	+	7.05134e14i	0.647554	+	0.647554i
$543$	7.42348e14	−	5.14653e14i	0.674852	−	0.467860i
$544$			4.85387e14i			0.436812i
$545$		0			0
$546$	−9.34241e14	−	1.69229e14i	−0.823948	−	0.149251i
$547$	1.52786e15	−	1.52786e15i	1.33399	−	1.33399i	0.432220	−	0.901768i	$-0.357730\pi$
$547$	1.52786e15	−	1.52786e15i	1.33399	−	1.33399i	0.901768	−	0.432220i	$-0.142270\pi$
$548$	2.51680e15	−	2.51680e15i	2.17548	−	2.17548i
$549$	2.22664e14	−	5.94448e14i	0.190547	−	0.508705i
$550$		0			0
$551$		−	1.04006e15i		−	0.872414i
$552$	−1.18449e12	−	1.70853e12i	−0.000983708	−	0.00141892i
$553$	1.54596e15	+	1.54596e15i	1.27119	+	1.27119i
$554$	−8.15031e14			−0.663545
$555$		0			0
$556$	5.36573e15			4.28270
$557$	9.40171e13	+	9.40171e13i	0.0743025	+	0.0743025i	0.743281	−	0.668979i	$-0.233268\pi$
$557$	9.40171e13	+	9.40171e13i	0.0743025	+	0.0743025i	−0.668979	+	0.743281i	$0.733268\pi$
$558$	7.45808e14	−	3.39341e14i	0.583632	−	0.265551i
$559$			2.84846e14i			0.220722i
$560$		0			0
$561$	6.06200e13	−	3.34656e14i	0.0460596	−	0.254275i
$562$	−2.14648e15	+	2.14648e15i	−1.61502	+	1.61502i
$563$	−8.33319e14	+	8.33319e14i	−0.620891	+	0.620891i	−0.945759	−	0.324869i	$-0.894680\pi$
$563$	−8.33319e14	+	8.33319e14i	−0.620891	+	0.620891i	0.324869	+	0.945759i	$0.394680\pi$
$564$	1.66337e14	−	9.18273e14i	0.122731	−	0.677543i
$565$		0			0
$566$			1.59824e15i			1.15652i
$567$	2.38146e15	−	1.63640e14i	1.70662	−	0.117269i
$568$	−2.97606e15	−	2.97606e15i	−2.11215	−	2.11215i
$569$	−4.61379e14			−0.324295			−0.162147	−	0.986767i	$-0.551842\pi$
$569$	−4.61379e14			−0.324295			−0.162147	+	0.986767i	$0.551842\pi$
$570$		0			0
$571$	−1.65817e15			−1.14322			−0.571612	−	0.820524i	$-0.693682\pi$
$571$	−1.65817e15			−1.14322			−0.571612	+	0.820524i	$0.693682\pi$
$572$	−3.52626e14	−	3.52626e14i	−0.240789	−	0.240789i
$573$	−1.58556e15	−	2.28705e15i	−1.07234	−	1.54677i
$574$		−	2.56410e15i		−	1.71759i
$575$		0			0
$576$	8.46606e13	+	3.17115e13i	0.0556362	+	0.0208398i
$577$	1.82744e15	−	1.82744e15i	1.18953	−	1.18953i	0.212333	−	0.977197i	$-0.431894\pi$
$577$	1.82744e15	−	1.82744e15i	1.18953	−	1.18953i	0.977197	−	0.212333i	$-0.0681061\pi$
$578$	1.55226e15	−	1.55226e15i	1.00083	−	1.00083i
$579$	8.92102e14	+	1.61596e14i	0.569747	+	0.103205i
$580$		0			0
$581$		−	6.68115e14i		−	0.418680i
$582$	−7.52714e13	+	5.21840e13i	−0.0467255	+	0.0323937i
$583$	−3.36522e14	−	3.36522e14i	−0.206936	−	0.206936i
$584$	2.39078e15			1.45636
$585$		0			0
$586$	−1.76433e15			−1.05473
$587$	−1.48506e15	−	1.48506e15i	−0.879499	−	0.879499i	0.113983	−	0.993483i	$-0.463639\pi$
$587$	−1.48506e15	−	1.48506e15i	−0.879499	−	0.879499i	−0.993483	+	0.113983i	$0.963639\pi$
$588$	−6.03140e15	+	4.18143e15i	−3.53869	+	2.45330i
$589$			6.97325e14i			0.405323i
$590$		0			0
$591$	1.70019e15	+	3.07975e14i	0.969990	+	0.175705i
$592$	−1.69132e15	+	1.69132e15i	−0.955997	+	0.955997i
$593$	−1.44655e15	+	1.44655e15i	−0.810088	+	0.810088i	−0.984647	−	0.174559i	$-0.944150\pi$
$593$	−1.44655e15	+	1.44655e15i	−0.810088	+	0.810088i	0.174559	+	0.984647i	$0.444150\pi$
$594$	1.55871e15	+	9.29249e14i	0.864851	+	0.515593i
$595$		0			0
$596$		−	2.39220e15i		−	1.30299i
$597$	9.05229e14	+	1.30572e15i	0.488539	+	0.704680i
$598$	−5.02955e11	−	5.02955e11i	−0.000268951	−	0.000268951i
$599$	−1.31768e15			−0.698171			−0.349085	−	0.937091i	$-0.613508\pi$
$599$	−1.31768e15			−0.698171			−0.349085	+	0.937091i	$0.613508\pi$
$600$		0			0
$601$	1.08147e15			0.562605			0.281303	−	0.959619i	$-0.409234\pi$
$601$	1.08147e15			0.562605			0.281303	+	0.959619i	$0.409234\pi$
$602$	3.42326e15	+	3.42326e15i	1.76465	+	1.76465i
$603$	1.19720e15	+	2.63122e15i	0.611534	+	1.34404i
$604$		−	6.22856e15i		−	3.15271i
$605$		0			0
$606$	−9.47512e14	+	5.23079e15i	−0.470961	+	2.59997i
$607$	−1.60205e15	+	1.60205e15i	−0.789112	+	0.789112i	−0.981349	−	0.192236i	$-0.938426\pi$
$607$	−1.60205e15	+	1.60205e15i	−0.789112	+	0.789112i	0.192236	+	0.981349i	$0.438426\pi$
$608$	1.55853e15	−	1.55853e15i	0.760758	−	0.760758i
$609$	−4.83636e14	+	2.66994e15i	−0.233950	+	1.29154i
$610$		0			0
$611$		−	1.76450e14i		−	0.0838292i
$612$	−9.07663e14	−	1.99487e15i	−0.427358	−	0.939253i
$613$	2.11687e15	+	2.11687e15i	0.987784	+	0.987784i	0.999926	−	0.0121419i	$-0.00386497\pi$
$613$	2.11687e15	+	2.11687e15i	0.987784	+	0.987784i	−0.0121419	+	0.999926i	$0.503865\pi$
$614$	4.10221e15			1.89711
$615$		0			0
$616$	−4.68399e15			−2.12776
$617$	−9.98345e14	−	9.98345e14i	−0.449482	−	0.449482i	0.445700	−	0.895182i	$-0.352955\pi$
$617$	−9.98345e14	−	9.98345e14i	−0.449482	−	0.449482i	−0.895182	+	0.445700i	$0.852955\pi$
$618$	3.35195e15	+	4.83493e15i	1.49576	+	2.15751i
$619$			2.29252e15i			1.01395i	0.861962	+	0.506973i	$0.169236\pi$
$619$			2.29252e15i			1.01395i	−0.861962	+	0.506973i	$0.830764\pi$
$620$		0			0
$621$	1.53605e12	+	9.15736e11i	0.000667423	+	0.000397893i
$622$	1.53451e15	−	1.53451e15i	0.660880	−	0.660880i
$623$	4.85354e15	−	4.85354e15i	2.07193	−	2.07193i
$624$	−1.11469e15	−	2.01916e14i	−0.471671	−	0.0854389i
$625$		0			0
$626$		−	1.65447e14i		−	0.0687861i
$627$	−1.26920e15	+	8.79906e14i	−0.523067	+	0.362631i
$628$	−4.94834e15	−	4.94834e15i	−2.02154	−	2.02154i
$629$	−8.74961e14			−0.354332
$630$		0			0
$631$	−1.58425e15			−0.630467			−0.315233	−	0.949014i	$-0.602083\pi$
$631$	−1.58425e15			−0.630467			−0.315233	+	0.949014i	$0.602083\pi$
$632$	4.18545e15	+	4.18545e15i	1.65119	+	1.65119i
$633$	3.22125e15	−	2.23322e15i	1.25981	−	0.873396i
$634$			5.21057e15i			2.02020i
$635$		0			0
$636$	−3.01773e15	−	5.46636e14i	−1.14992	−	0.208297i
$637$	−9.81220e14	+	9.81220e14i	−0.370680	+	0.370680i
$638$	−1.45859e15	+	1.45859e15i	−0.546286	+	0.546286i
$639$	3.39030e15	+	1.26991e15i	1.25888	+	0.471541i
$640$		0			0
$641$		−	2.53471e15i		−	0.925143i	−0.886582	−	0.462571i	$-0.846927\pi$
$641$		−	2.53471e15i		−	0.925143i	0.886582	−	0.462571i	$-0.153073\pi$
$642$	2.79321e15	+	4.02899e15i	1.01079	+	1.45799i
$643$	1.42370e15	+	1.42370e15i	0.510810	+	0.510810i	0.914775	−	0.403965i	$-0.132368\pi$
$643$	1.42370e15	+	1.42370e15i	0.510810	+	0.510810i	−0.403965	+	0.914775i	$0.632368\pi$
$644$	−8.35240e12			−0.00297125
$645$		0			0
$646$	2.69961e15			0.944107
$647$	−3.56918e15	−	3.56918e15i	−1.23764	−	1.23764i	−0.960962	−	0.276681i	$-0.910766\pi$
$647$	−3.56918e15	−	3.56918e15i	−1.23764	−	1.23764i	−0.276681	−	0.960962i	$-0.589234\pi$
$648$	6.44742e15	−	4.43029e14i	2.21678	−	0.152324i
$649$		−	2.02337e15i		−	0.689809i
$650$		0			0
$651$	3.24263e14	−	1.79011e15i	0.108693	−	0.600047i
$652$	1.25570e13	−	1.25570e13i	0.00417373	−	0.00417373i
$653$	4.85810e14	−	4.85810e14i	0.160119	−	0.160119i	−0.622500	−	0.782620i	$-0.713883\pi$
$653$	4.85810e14	−	4.85810e14i	0.160119	−	0.160119i	0.782620	+	0.622500i	$0.213883\pi$
$654$	2.88806e14	−	1.59437e15i	0.0943904	−	0.521088i
$655$		0			0
$656$		−	3.05936e15i		−	0.983239i
$657$	−1.87187e15	+	8.51696e14i	−0.596576	+	0.271441i
$658$	−2.12056e15	−	2.12056e15i	−0.670206	−	0.670206i
$659$	−2.29364e15			−0.718879			−0.359439	−	0.933168i	$-0.617032\pi$
$659$	−2.29364e15			−0.718879			−0.359439	+	0.933168i	$0.617032\pi$
$660$		0			0
$661$	−2.41660e15			−0.744898			−0.372449	−	0.928053i	$-0.621482\pi$
$661$	−2.41660e15			−0.744898			−0.372449	+	0.928053i	$0.621482\pi$
$662$	−3.79248e15	−	3.79248e15i	−1.15932	−	1.15932i
$663$	−2.36100e14	−	3.40556e14i	−0.0715767	−	0.103244i
$664$		−	1.80881e15i		−	0.543838i
$665$		0			0
$666$	1.63760e15	−	4.37191e15i	0.484282	−	1.29289i
$667$	−1.43738e12	+	1.43738e12i	−0.000421580	+	0.000421580i
$668$	−6.76770e15	+	6.76770e15i	−1.96866	+	1.96866i
$669$	−1.76546e15	−	3.19797e14i	−0.509347	−	0.0922636i
$670$		0			0
$671$		−	1.07144e15i		−	0.304084i
$672$	−4.72567e15	+	3.27620e15i	−1.33025	+	0.922231i
$673$	−2.10399e15	−	2.10399e15i	−0.587437	−	0.587437i	0.349500	−	0.936937i	$-0.386352\pi$
$673$	−2.10399e15	−	2.10399e15i	−0.587437	−	0.587437i	−0.936937	+	0.349500i	$0.886352\pi$
$674$	−2.59994e15			−0.720003
$675$		0			0
$676$	7.59684e15			2.06979
$677$	1.71633e15	+	1.71633e15i	0.463836	+	0.463836i	0.899911	−	0.436075i	$-0.143632\pi$
$677$	1.71633e15	+	1.71633e15i	0.463836	+	0.463836i	−0.436075	+	0.899911i	$0.643632\pi$
$678$	−7.38483e14	+	5.11974e14i	−0.197960	+	0.137241i
$679$			2.03358e14i			0.0540725i
$680$		0			0
$681$	−1.32689e15	−	2.40354e14i	−0.347157	−	0.0628844i
$682$	9.77941e14	−	9.77941e14i	0.253804	−	0.253804i
$683$	−2.81651e15	+	2.81651e15i	−0.725100	+	0.725100i	−0.969639	−	0.244539i	$-0.921363\pi$
$683$	−2.81651e15	+	2.81651e15i	−0.725100	+	0.725100i	0.244539	+	0.969639i	$0.421363\pi$
$684$	−3.49094e15	+	9.31978e15i	−0.891525	+	2.38011i
$685$		0			0
$686$			1.13410e16i			2.85016i
$687$	−2.51759e15	−	3.63142e15i	−0.627657	−	0.905347i
$688$	4.08446e15	+	4.08446e15i	1.01018	+	1.01018i
$689$	−5.79871e14			−0.142274
$690$		0			0
$691$	−7.28776e14			−0.175981			−0.0879903	−	0.996121i	$-0.528044\pi$
$691$	−7.28776e14			−0.175981			−0.0879903	+	0.996121i	$0.528044\pi$
$692$	−6.04041e15	−	6.04041e15i	−1.44705	−	1.44705i
$693$	3.66734e15	−	1.66863e15i	0.871602	−	0.396577i
$694$			1.31311e15i			0.309615i
$695$		0			0
$696$	−1.30937e15	+	7.22844e15i	−0.303886	+	1.67762i
$697$	7.91340e14	−	7.91340e14i	0.182214	−	0.182214i
$698$	1.15265e15	−	1.15265e15i	0.263325	−	0.263325i
$699$	1.13210e15	−	6.24981e15i	0.256602	−	1.41658i
$700$		0			0
$701$			4.32718e14i			0.0965508i	0.998834	+	0.0482754i	$0.0153725\pi$
$701$			4.32718e14i			0.0965508i	−0.998834	+	0.0482754i	$0.984627\pi$
$702$	2.14354e15	−	5.42326e14i	0.474546	−	0.120062i
$703$	2.80942e15	+	2.80942e15i	0.617110	+	0.617110i
$704$	1.52593e14			0.0332572
$705$		0			0
$706$	4.83393e15			1.03723
$707$	8.34584e15	+	8.34584e15i	1.77690	+	1.77690i
$708$	−7.42886e15	−	1.07156e16i	−1.56942	−	2.26377i
$709$		−	1.80415e14i		−	0.0378198i	−0.999821	−	0.0189099i	$-0.993980\pi$
$709$		−	1.80415e14i		−	0.0378198i	0.999821	−	0.0189099i	$-0.00601957\pi$
$710$		0			0
$711$	−4.76804e15	−	1.78598e15i	−0.984139	−	0.368632i
$712$	1.31402e16	−	1.31402e16i	2.69130	−	2.69130i
$713$	9.63720e11	−	9.63720e11i	0.000195866	−	0.000195866i
$714$	−6.93020e15	−	1.25534e15i	−1.39767	−	0.253176i
$715$		0			0
$716$			8.03200e15i			1.59515i
$717$	−8.94298e14	+	6.19997e14i	−0.176249	+	0.122190i
$718$	−7.00679e13	−	7.00679e13i	−0.0137036	−	0.0137036i
$719$	−1.79368e15			−0.348125			−0.174062	−	0.984735i	$-0.555689\pi$
$719$	−1.79368e15			−0.348125			−0.174062	+	0.984735i	$0.555689\pi$
$720$		0			0
$721$	1.30623e16			2.49676
$722$	−1.96317e15	−	1.96317e15i	−0.372395	−	0.372395i
$723$	−8.31607e15	+	5.76535e15i	−1.56552	+	1.08534i
$724$		−	9.82512e15i		−	1.83559i
$725$		0			0
$726$	−6.60441e15	−	1.19633e15i	−1.21530	−	0.220140i
$727$	3.29802e15	−	3.29802e15i	0.602302	−	0.602302i	−0.338621	−	0.940923i	$-0.609960\pi$
$727$	3.29802e15	−	3.29802e15i	0.602302	−	0.602302i	0.940923	+	0.338621i	$0.109960\pi$
$728$	−4.03556e15	+	4.03556e15i	−0.731445	+	0.731445i
$729$	−4.89019e15	+	2.64371e15i	−0.879679	+	0.475567i
$730$		0			0
$731$			2.11299e15i			0.374414i
$732$	−3.93382e15	−	5.67423e15i	−0.691837	−	0.997921i
$733$	−2.27006e15	−	2.27006e15i	−0.396246	−	0.396246i	0.480661	−	0.876907i	$-0.340397\pi$
$733$	−2.27006e15	−	2.27006e15i	−0.396246	−	0.396246i	−0.876907	+	0.480661i	$0.840397\pi$
$734$	1.30945e16			2.26861
$735$		0			0
$736$	−4.30786e12			−0.000735248
$737$	3.45019e15	+	3.45019e15i	0.584482	+	0.584482i
$738$	2.47299e15	+	5.43517e15i	0.415826	+	0.913909i
$739$		−	3.80388e15i		−	0.634867i	−0.948280	−	0.317434i	$-0.897179\pi$
$739$		−	3.80388e15i		−	0.634867i	0.948280	−	0.317434i	$-0.102821\pi$
$740$		0			0
$741$	−3.35399e14	+	1.85159e15i	−0.0551521	+	0.304470i
$742$	−6.96883e15	+	6.96883e15i	−1.13747	+	1.13747i
$743$	1.51492e15	−	1.51492e15i	0.245443	−	0.245443i	−0.573654	−	0.819098i	$-0.694475\pi$
$743$	1.51492e15	−	1.51492e15i	0.245443	−	0.245443i	0.819098	+	0.573654i	$0.194475\pi$
$744$	8.77890e14	−	4.84645e15i	0.141185	−	0.779421i
$745$		0			0
$746$			2.19700e14i			0.0348150i
$747$	6.44374e14	+	1.41621e15i	0.101362	+	0.222775i
$748$	−2.61578e15	−	2.61578e15i	−0.408453	−	0.408453i
$749$	1.08850e16			1.68724
$750$		0			0
$751$	−7.32884e15			−1.11948			−0.559739	−	0.828669i	$-0.689099\pi$
$751$	−7.32884e15			−1.11948			−0.559739	+	0.828669i	$0.689099\pi$
$752$	−2.53015e15	−	2.53015e15i	−0.383661	−	0.383661i
$753$	−3.68160e15	−	5.31042e15i	−0.554197	−	0.799386i
$754$			2.51334e15i			0.375586i
$755$		0			0
$756$	1.32954e16	−	2.23016e16i	1.95809	−	3.28448i
$757$	−4.77508e15	+	4.77508e15i	−0.698157	+	0.698157i	−0.964013	−	0.265856i	$-0.914345\pi$
$757$	−4.77508e15	+	4.77508e15i	−0.698157	+	0.698157i	0.265856	+	0.964013i	$0.414345\pi$
$758$	−2.49826e15	+	2.49826e15i	−0.362624	+	0.362624i
$759$	2.97011e12	+	5.38009e11i	0.000427999	+	7.75282e-5i
$760$		0			0
$761$			1.12966e15i			0.160447i	0.996777	+	0.0802236i	$0.0255634\pi$
$761$			1.12966e15i			0.160447i	−0.996777	+	0.0802236i	$0.974437\pi$
$762$	−1.21126e16	+	8.39739e15i	−1.70799	+	1.18411i
$763$	−2.54385e15	−	2.54385e15i	−0.356128	−	0.356128i
$764$	−3.02695e16			−4.20719
$765$		0			0
$766$	−1.55327e16			−2.12808
$767$	−1.74326e15	−	1.74326e15i	−0.237131	−	0.237131i
$768$	1.11648e16	−	7.74030e15i	1.50787	−	1.04537i
$769$			9.34099e15i			1.25256i	0.779599	+	0.626279i	$0.215423\pi$
$769$			9.34099e15i			1.25256i	−0.779599	+	0.626279i	$0.784577\pi$
$770$		0			0
$771$	1.30933e15	+	2.37174e14i	0.173082	+	0.0313522i
$772$	6.97295e15	−	6.97295e15i	0.915211	−	0.915211i
$773$	−2.41111e15	+	2.41111e15i	−0.314217	+	0.314217i	−0.846541	−	0.532324i	$-0.821319\pi$
$773$	−2.41111e15	+	2.41111e15i	−0.314217	+	0.314217i	0.532324	+	0.846541i	$0.321319\pi$
$774$	−1.05579e16	−	3.95472e15i	−1.36617	−	0.511729i
$775$		0			0
$776$			5.50558e14i			0.0702366i
$777$	−5.90570e15	−	8.51852e15i	−0.748093	−	1.07907i
$778$	7.75291e14	+	7.75291e14i	0.0975163	+	0.0975163i
$779$	−5.08184e15			−0.634695
$780$		0			0
$781$	6.11071e15			0.752508
$782$	−3.73092e12	−	3.73092e12i	−0.000456225	−	0.000456225i
$783$	−1.54990e15	−	6.12597e15i	−0.188197	−	0.743850i
$784$			2.81397e16i			3.39298i
$785$		0			0
$786$	9.30624e14	−	5.13756e15i	0.110650	−	0.610848i
$787$	8.03949e14	−	8.03949e14i	0.0949221	−	0.0949221i	−0.658051	−	0.752973i	$-0.728619\pi$
$787$	8.03949e14	−	8.03949e14i	0.0949221	−	0.0949221i	0.752973	+	0.658051i	$0.228619\pi$
$788$	1.32893e16	−	1.32893e16i	1.55814	−	1.55814i
$789$	1.37355e15	−	7.58277e15i	0.159927	−	0.882886i
$790$		0			0
$791$			1.99513e15i			0.229087i
$792$	9.92873e15	−	4.51755e15i	1.13215	−	0.515127i
$793$	−9.23114e14	−	9.23114e14i	−0.104533	−	0.104533i
$794$	6.63508e15			0.746163
$795$		0			0
$796$	1.72815e16			1.91672
$797$	−4.46616e15	−	4.46616e15i	−0.491942	−	0.491942i	0.416976	−	0.908918i	$-0.363090\pi$
$797$	−4.46616e15	−	4.46616e15i	−0.491942	−	0.491942i	−0.908918	+	0.416976i	$0.863090\pi$
$798$	1.82214e16	+	2.62830e16i	1.99327	+	2.87514i
$799$		−	1.30891e15i		−	0.142201i
$800$		0			0
$801$	−5.60706e15	+	1.49692e16i	−0.600836	+	1.60406i
$802$	−1.88486e16	+	1.88486e16i	−2.00595	+	2.00595i
$803$	−2.45449e15	+	2.45449e15i	−0.259433	+	0.259433i
$804$	3.09393e16	+	5.60438e15i	3.24790	+	0.588327i
$805$		0			0
$806$		−	1.68512e15i		−	0.174497i
$807$	−2.49321e15	+	1.72849e15i	−0.256421	+	0.177771i
$808$	2.25950e16	+	2.25950e16i	2.30808	+	2.30808i
$809$	−1.55678e15			−0.157947			−0.0789734	−	0.996877i	$-0.525164\pi$
$809$	−1.55678e15			−0.157947			−0.0789734	+	0.996877i	$0.525164\pi$
$810$		0			0
$811$	−8.47541e15			−0.848293			−0.424147	−	0.905593i	$-0.639426\pi$
$811$	−8.47541e15			−0.848293			−0.424147	+	0.905593i	$0.639426\pi$
$812$	2.08691e16	+	2.08691e16i	2.07465	+	2.07465i
$813$	−4.23745e15	+	2.93773e15i	−0.418415	+	0.290078i
$814$		−	7.87996e15i		−	0.772841i
$815$		0			0
$816$	−8.26877e15	−	1.49781e15i	−0.800101	−	0.144931i
$817$	6.78462e15	−	6.78462e15i	0.652085	−	0.652085i
$818$	3.24666e15	−	3.24666e15i	0.309951	−	0.309951i
$819$	1.72202e15	−	4.59728e15i	0.163296	−	0.435953i
$820$		0			0
$821$		−	6.57614e15i		−	0.615295i	−0.951500	−	0.307648i	$-0.900458\pi$
$821$		−	6.57614e15i		−	0.615295i	0.951500	−	0.307648i	$-0.0995418\pi$
$822$	1.51763e16	+	2.18906e16i	1.41049	+	2.03453i
$823$	−1.03415e16	−	1.03415e16i	−0.954739	−	0.954739i	0.0442803	−	0.999019i	$-0.485901\pi$
$823$	−1.03415e16	−	1.03415e16i	−0.954739	−	0.954739i	−0.999019	+	0.0442803i	$0.985901\pi$
$824$	3.53641e16			3.24312
$825$		0			0
$826$	−4.19007e16			−3.79168
$827$	−1.18033e15	−	1.18033e15i	−0.106102	−	0.106102i	0.652063	−	0.758165i	$-0.273904\pi$
$827$	−1.18033e15	−	1.18033e15i	−0.106102	−	0.106102i	−0.758165	+	0.652063i	$0.773904\pi$
$828$	1.77047e13	−	8.05561e12i	0.00158097	−	0.000719336i
$829$		−	1.17502e16i		−	1.04230i	−0.853464	−	0.521152i	$-0.825502\pi$
$829$		−	1.17502e16i		−	1.04230i	0.853464	−	0.521152i	$-0.174498\pi$
$830$		0			0
$831$	7.51143e14	−	4.14673e15i	0.0657532	−	0.362994i
$832$	1.31469e14	−	1.31469e14i	0.0114326	−	0.0114326i
$833$	−7.27868e15	+	7.27868e15i	−0.628789	+	0.628789i
$834$	−7.15736e15	+	3.95127e16i	−0.614243	+	3.39096i
$835$		0			0
$836$			1.67981e16i			1.42274i
$837$	1.03916e15	+	4.10728e15i	0.0874363	+	0.345592i
$838$	−1.53073e16	−	1.53073e16i	−1.27955	−	1.27955i
$839$	2.04023e16			1.69430			0.847148	−	0.531358i	$-0.178318\pi$
$839$	2.04023e16			1.69430			0.847148	+	0.531358i	$0.178318\pi$
$840$		0			0
$841$	−5.01770e15			−0.411269
$842$	−1.14461e16	−	1.14461e16i	−0.932054	−	0.932054i
$843$	−8.94266e15	−	1.28991e16i	−0.723461	−	1.04354i
$844$		−	4.26339e16i		−	3.42666i
$845$		0			0
$846$	6.54019e15	+	2.44978e15i	0.518864	+	0.194352i
$847$	−1.05375e16	+	1.05375e16i	−0.830573	+	0.830573i
$848$	−8.31485e15	+	8.31485e15i	−0.651145	+	0.651145i
$849$	−8.13157e15	−	1.47296e15i	−0.632677	−	0.114604i
$850$		0			0
$851$		−	7.76538e12i		−	0.000596417i
$852$	3.23617e16	−	2.24357e16i	2.46953	−	1.71207i
$853$	1.50285e16	+	1.50285e16i	1.13945	+	1.13945i	0.988549	+	0.150903i	$0.0482181\pi$
$853$	1.50285e16	+	1.50285e16i	1.13945	+	1.13945i	0.150903	+	0.988549i	$0.451782\pi$
$854$	−2.21878e16			−1.67146
$855$		0			0
$856$	2.94693e16			2.19161
$857$	−1.22985e14	−	1.22985e14i	−0.00908778	−	0.00908778i	0.702548	−	0.711636i	$-0.252045\pi$
$857$	−1.22985e14	−	1.22985e14i	−0.00908778	−	0.00908778i	−0.711636	+	0.702548i	$0.752045\pi$
$858$	3.06707e15	−	2.12633e15i	0.225187	−	0.156117i
$859$			3.56216e15i			0.259867i	0.991523	+	0.129933i	$0.0414763\pi$
$859$			3.56216e15i			0.259867i	−0.991523	+	0.129933i	$0.958524\pi$
$860$		0			0
$861$	1.30457e16	+	2.36311e15i	0.939613	+	0.170203i
$862$	−9.10835e15	+	9.10835e15i	−0.651853	+	0.651853i
$863$	1.72351e16	−	1.72351e16i	1.22561	−	1.22561i	0.260007	−	0.965607i	$-0.416275\pi$
$863$	1.72351e16	−	1.72351e16i	1.22561	−	1.22561i	0.965607	−	0.260007i	$-0.0837250\pi$
$864$	6.85729e15	−	1.15024e16i	0.484537	−	0.812759i
$865$		0			0
$866$		−	4.36570e16i		−	3.04583i
$867$	6.46703e15	+	9.32820e15i	0.448332	+	0.646685i
$868$	−1.39921e16	−	1.39921e16i	−0.963883	−	0.963883i
$869$	−8.59395e15			−0.588280
$870$		0			0
$871$	5.94512e15			0.401847
$872$	−6.88706e15	−	6.88706e15i	−0.462586	−	0.462586i
$873$	−1.96132e14	−	4.31060e14i	−0.0130909	−	0.0287713i
$874$			2.39593e13i			0.00158914i
$875$		0			0
$876$	−3.98700e15	+	2.20105e16i	−0.261140	+	1.44164i
$877$	2.17604e15	−	2.17604e15i	0.141635	−	0.141635i	−0.632734	−	0.774369i	$-0.718067\pi$
$877$	2.17604e15	−	2.17604e15i	0.141635	−	0.141635i	0.774369	+	0.632734i	$0.218067\pi$
$878$	2.52435e15	−	2.52435e15i	0.163279	−	0.163279i
$879$	1.62603e15	−	8.97659e15i	0.104518	−	0.576996i
$880$		0			0
$881$		−	1.72749e16i		−	1.09660i	−0.836283	−	0.548299i	$-0.815276\pi$
$881$		−	1.72749e16i		−	1.09660i	0.836283	−	0.548299i	$-0.184724\pi$
$882$	−2.27463e16	−	4.99922e16i	−1.43494	−	3.15374i
$883$	1.52847e16	+	1.52847e16i	0.958240	+	0.958240i	0.999162	−	0.0409223i	$-0.0130296\pi$
$883$	1.52847e16	+	1.52847e16i	0.958240	+	0.958240i	−0.0409223	+	0.999162i	$0.513030\pi$
$884$	−4.50733e15			−0.280822
$885$		0			0
$886$	1.05320e16			0.648076
$887$	1.88072e16	+	1.88072e16i	1.15012	+	1.15012i	0.986528	+	0.163594i	$0.0523088\pi$
$887$	1.88072e16	+	1.88072e16i	1.15012	+	1.15012i	0.163594	+	0.986528i	$0.447691\pi$
$888$	−1.59887e16	−	2.30625e16i	−0.971723	−	1.40164i
$889$			3.27241e16i			1.97655i
$890$		0			0
$891$	−6.16438e15	+	7.07405e15i	−0.367758	+	0.422027i
$892$	−1.37994e16	+	1.37994e16i	−0.818187	+	0.818187i
$893$	−4.20278e15	+	4.20278e15i	−0.247659	+	0.247659i
$894$	1.76159e16	+	3.19096e15i	1.03169	+	0.186881i
$895$		0			0
$896$		−	3.11401e16i		−	1.80147i
$897$	3.02247e12	−	2.09541e12i	0.000173782	−	0.000120479i
$898$	−2.81652e16	−	2.81652e16i	−1.60951	−	1.60951i
$899$	−4.81586e15			−0.273524
$900$		0			0
$901$	−4.30148e15			−0.241341
$902$	7.12686e15	+	7.12686e15i	0.397432	+	0.397432i
$903$	−2.05718e16	+	1.42620e16i	−1.14022	+	0.790492i
$904$			5.40149e15i			0.297569i
$905$		0			0
$906$	4.58665e16	+	8.30830e15i	2.49626	+	0.452176i
$907$	1.45135e16	−	1.45135e16i	0.785112	−	0.785112i	−0.195577	−	0.980688i	$-0.562658\pi$
$907$	1.45135e16	−	1.45135e16i	0.785112	−	0.785112i	0.980688	+	0.195577i	$0.0626579\pi$
$908$	−1.03714e16	+	1.03714e16i	−0.557654	+	0.557654i
$909$	−2.57401e16	−	9.64153e15i	−1.37565	−	0.515282i
$910$		0			0
$911$			4.51742e15i			0.238528i	0.992863	+	0.119264i	$0.0380535\pi$
$911$			4.51742e15i			0.238528i	−0.992863	+	0.119264i	$0.961946\pi$
$912$	2.17409e16	+	3.13596e16i	1.14105	+	1.64588i
$913$	1.85701e15	+	1.85701e15i	0.0968780	+	0.0968780i
$914$	−2.10202e16			−1.09002
$915$		0			0
$916$	−4.80626e16			−2.46253
$917$	−8.19709e15	−	8.19709e15i	−0.417473	−	0.417473i
$918$	1.59008e16	−	4.02297e15i	0.804978	−	0.203663i
$919$		−	2.70898e16i		−	1.36323i	−0.731710	−	0.681616i	$-0.761277\pi$
$919$		−	2.70898e16i		−	1.36323i	0.731710	−	0.681616i	$-0.238723\pi$
$920$		0			0
$921$	−3.78065e15	+	2.08713e16i	−0.187992	+	1.03782i
$922$	3.23219e16	−	3.23219e16i	1.59763	−	1.59763i
$923$	5.26478e15	−	5.26478e15i	0.258685	−	0.258685i
$924$	7.81127e15	−	4.31226e16i	0.381527	−	2.10624i
$925$		0			0
$926$		−	1.61592e16i		−	0.779936i
$927$	−2.76884e16	+	1.25982e16i	−1.32849	+	0.604462i
$928$	1.07635e16	+	1.07635e16i	0.513382	+	0.513382i
$929$	3.02780e16			1.43562			0.717812	−	0.696237i	$-0.245144\pi$
$929$	3.02780e16			1.43562			0.717812	+	0.696237i	$0.245144\pi$
$930$		0			0
$931$	4.67424e16			2.19022
$932$	−4.88505e16	−	4.88505e16i	−2.27553	−	2.27553i
$933$	6.39308e15	+	9.22153e15i	0.296047	+	0.427026i
$934$			2.54238e16i			1.17040i
$935$		0			0
$936$	4.66208e15	−	1.24464e16i	0.212111	−	0.566274i
$937$	1.09260e16	−	1.09260e16i	0.494192	−	0.494192i	−0.415432	−	0.909624i	$-0.636370\pi$
$937$	1.09260e16	−	1.09260e16i	0.494192	−	0.494192i	0.909624	+	0.415432i	$0.136370\pi$
$938$	7.14478e16	−	7.14478e16i	3.21272	−	3.21272i
$939$	8.41765e14	+	1.52478e14i	0.0376296	+	0.00681627i
$940$		0			0
$941$			3.35190e16i			1.48098i	0.672069	+	0.740488i	$0.265406\pi$
$941$			3.35190e16i			1.48098i	−0.672069	+	0.740488i	$0.734594\pi$
$942$	4.30397e16	−	2.98385e16i	1.89055	−	1.31068i
$943$	7.02323e12	+	7.02323e12i	0.000306706	+	0.000306706i
$944$	−4.99938e16			−2.17055
$945$		0			0
$946$	−1.90297e16			−0.816641
$947$	2.02296e16	+	2.02296e16i	0.863104	+	0.863104i	0.991697	−	0.128594i	$-0.0410463\pi$
$947$	2.02296e16	+	2.02296e16i	0.863104	+	0.863104i	−0.128594	+	0.991697i	$0.541046\pi$
$948$	−4.55127e16	+	3.15529e16i	−1.93057	+	1.33842i
$949$			4.22940e15i			0.178367i
$950$		0			0
$951$	−2.65104e16	−	4.80212e15i	−1.10516	−	0.200189i
$952$	−2.99358e16	+	2.99358e16i	−1.24076	+	1.24076i
$953$	−2.82571e16	+	2.82571e16i	−1.16444	+	1.16444i	−0.180944	+	0.983493i	$0.557915\pi$
$953$	−2.82571e16	+	2.82571e16i	−1.16444	+	1.16444i	−0.983493	+	0.180944i	$0.942085\pi$
$954$	8.05074e15	−	2.14931e16i	0.329852	−	0.880610i
$955$		0			0
$956$			1.18362e16i			0.479396i
$957$	−6.07679e15	−	8.76530e15i	−0.244714	−	0.352981i
$958$	2.33926e16	+	2.33926e16i	0.936631	+	0.936631i
$959$	5.91411e16			2.35444
$960$		0			0
$961$	−2.21796e16			−0.872921
$962$	−6.78910e15	−	6.78910e15i	−0.265674	−	0.265674i
$963$	−2.30730e16	+	1.04982e16i	−0.897760	+	0.408479i
$964$			1.10065e17i			4.25819i
$965$		0			0
$966$	1.11413e13	−	6.15063e13i	0.000426149	−	0.00235258i
$967$	5.09218e15	−	5.09218e15i	0.193668	−	0.193668i	−0.603611	−	0.797279i	$-0.706272\pi$
$967$	5.09218e15	−	5.09218e15i	0.193668	−	0.193668i	0.797279	+	0.603611i	$0.206272\pi$
$968$	−2.85285e16	+	2.85285e16i	−1.07886	+	1.07886i
$969$	−2.48799e15	+	1.37351e16i	−0.0935552	+	0.516477i
$970$		0			0
$971$			4.90090e16i			1.82209i	0.412306	+	0.911046i	$0.364724\pi$
$971$			4.90090e16i			1.82209i	−0.412306	+	0.911046i	$0.635276\pi$
$972$	−6.67336e15	+	6.00961e16i	−0.246706	+	2.22168i
$973$	6.30432e16	+	6.30432e16i	2.31749	+	2.31749i
$974$	−7.46069e16			−2.72712
$975$		0			0
$976$	−2.64734e16			−0.956831
$977$	−1.20684e16	−	1.20684e16i	−0.433741	−	0.433741i	0.456158	−	0.889899i	$-0.349225\pi$
$977$	−1.20684e16	−	1.20684e16i	−0.433741	−	0.433741i	−0.889899	+	0.456158i	$0.849225\pi$
$978$	7.57187e13	+	1.09218e14i	0.00270607	+	0.00390330i
$979$			2.69806e16i			0.958843i
$980$		0			0
$981$	7.84569e15	+	2.93878e15i	0.275709	+	0.103273i
$982$	−5.29554e16	+	5.29554e16i	−1.85053	+	1.85053i
$983$	1.15454e16	−	1.15454e16i	0.401204	−	0.401204i	−0.477453	−	0.878657i	$-0.658440\pi$
$983$	1.15454e16	−	1.15454e16i	0.401204	−	0.401204i	0.878657	+	0.477453i	$0.158440\pi$
$984$	3.53191e16	+	6.39773e15i	1.22050	+	0.221082i
$985$		0			0
$986$			1.86440e16i			0.637111i
$987$	1.27434e16	−	8.83469e15i	0.433051	−	0.300225i
$988$	1.44726e16	+	1.44726e16i	0.489085	+	0.489085i
$989$	−1.87530e13			−0.000630219
$990$		0			0
$991$	2.39536e16			0.796098			0.398049	−	0.917364i	$-0.369687\pi$
$991$	2.39536e16			0.796098			0.398049	+	0.917364i	$0.369687\pi$
$992$	−7.21661e15	−	7.21661e15i	−0.238517	−	0.238517i
$993$	2.27907e16	−	1.58003e16i	0.749093	−	0.519330i
$994$		−	1.26543e17i		−	4.13631i
$995$		0			0
$996$	1.66526e16	+	3.01647e15i	0.538339	+	0.0975153i
$997$	−1.58579e16	+	1.58579e16i	−0.509825	+	0.509825i	−0.914473	−	0.404648i	$-0.867394\pi$
$997$	−1.58579e16	+	1.58579e16i	−0.509825	+	0.509825i	0.404648	+	0.914473i	$0.367394\pi$
$998$	−5.80593e16	+	5.80593e16i	−1.85633	+	1.85633i
$999$	2.07342e16	+	1.23610e16i	0.659292	+	0.393046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.12.e.d.68.19		40
3.2	odd	2	inner	75.12.e.d.68.2		40
5.2	odd	4	inner	75.12.e.d.32.2		40
5.3	odd	4		15.12.e.a.2.19	yes	40
5.4	even	2		15.12.e.a.8.2	yes	40
15.2	even	4	inner	75.12.e.d.32.19		40
15.8	even	4		15.12.e.a.2.2	✓	40
15.14	odd	2		15.12.e.a.8.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.e.a.2.2	✓	40	15.8	even	4
15.12.e.a.2.19	yes	40	5.3	odd	4
15.12.e.a.8.2	yes	40	5.4	even	2
15.12.e.a.8.19	yes	40	15.14	odd	2
75.12.e.d.32.2		40	5.2	odd	4	inner
75.12.e.d.32.19		40	15.2	even	4	inner
75.12.e.d.68.2		40	3.2	odd	2	inner
75.12.e.d.68.19		40	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(57.5586 + 57.5586i) q^{2} +(-345.894 + 239.801i) q^{3} +4577.97i q^{4} +(-33711.7 - 6106.58i) q^{6} +(-53787.8 + 53787.8i) q^{7} +(-145622. + 145622. i) q^{8} +(62138.3 - 165891. i) q^{9} +O(q^{10})\)	\(q+(57.5586 + 57.5586i) q^{2} +(-345.894 + 239.801i) q^{3} +4577.97i q^{4} +(-33711.7 - 6106.58i) q^{6} +(-53787.8 + 53787.8i) q^{7} +(-145622. + 145622. i) q^{8} +(62138.3 - 165891. i) q^{9} -299004. i q^{11} +(-1.09780e6 - 1.58349e6i) q^{12} +(-257611. - 257611. i) q^{13} -6.19189e6 q^{14} -7.38785e6 q^{16} +(-1.91096e6 - 1.91096e6i) q^{17} +(1.31250e7 - 5.97187e6i) q^{18} +1.22718e7i q^{19} +(5.70652e6 - 3.15032e7i) q^{21} +(1.72102e7 - 1.72102e7i) q^{22} +(16960.0 - 16960.0i) q^{23} +(1.54495e7 - 8.52898e7i) q^{24} -2.96554e7i q^{26} +(1.82876e7 + 7.22816e7i) q^{27} +(-2.46239e8 - 2.46239e8i) q^{28} -8.47515e7 q^{29} +5.68233e7 q^{31} +(-1.27001e8 - 1.27001e8i) q^{32} +(7.17013e7 + 1.03424e8i) q^{33} -2.19984e8i q^{34} +(7.59446e8 + 2.84468e8i) q^{36} +(2.28933e8 - 2.28933e8i) q^{37} +(-7.06349e8 + 7.06349e8i) q^{38} +(1.50881e8 + 2.73308e7i) q^{39} +4.14106e8i q^{41} +(2.14174e9 - 1.48482e9i) q^{42} +(-5.52861e8 - 5.52861e8i) q^{43} +1.36883e9 q^{44} +1.95238e6 q^{46} +(3.42474e8 + 3.42474e8i) q^{47} +(2.55541e9 - 1.77161e9i) q^{48} -3.80892e9i q^{49} +(1.11924e9 + 2.02740e8i) q^{51} +(1.17934e9 - 1.17934e9i) q^{52} +(1.12548e9 - 1.12548e9i) q^{53} +(-3.10782e9 + 5.21303e9i) q^{54} -1.56653e10i q^{56} +(-2.94279e9 - 4.24475e9i) q^{57} +(-4.87817e9 - 4.87817e9i) q^{58} +6.76703e9 q^{59} +3.58336e9 q^{61} +(3.27067e9 + 3.27067e9i) q^{62} +(5.58064e9 + 1.22652e10i) q^{63} +5.10338e8i q^{64} +(-1.82589e9 + 1.00799e10i) q^{66} +(-1.15389e10 + 1.15389e10i) q^{67} +(8.74832e9 - 8.74832e9i) q^{68} +(-1.79934e6 + 9.93336e6i) q^{69} +2.04369e10i q^{71} +(1.51087e10 + 3.32060e10i) q^{72} +(-8.20889e9 - 8.20889e9i) q^{73} +2.63541e10 q^{74} -5.61801e10 q^{76} +(1.60827e10 + 1.60827e10i) q^{77} +(7.11140e9 + 1.02576e10i) q^{78} -2.87419e10i q^{79} +(-2.36587e10 - 2.06164e10i) q^{81} +(-2.38354e10 + 2.38354e10i) q^{82} +(-6.21066e9 + 6.21066e9i) q^{83} +(1.44221e11 + 2.61243e10i) q^{84} -6.36438e10i q^{86} +(2.93150e10 - 2.03235e10i) q^{87} +(4.35414e10 + 4.35414e10i) q^{88} -9.02351e10 q^{89} +2.77126e10 q^{91} +(7.76423e7 + 7.76423e7i) q^{92} +(-1.96548e10 + 1.36263e10i) q^{93} +3.94246e10i q^{94} +(7.43838e10 + 1.34740e10i) q^{96} +(1.89037e9 - 1.89037e9i) q^{97} +(2.19236e11 - 2.19236e11i) q^{98} +(-4.96021e10 - 1.85796e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7}+O(q^{10}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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