LMFDB - Embedded newform 95.11.f.a.58.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,11,Mod(58,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("95.58");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	95.f (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:	$60.3589390040$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			58.20
Character	$\chi$	$=$	95.58
Dual form			95.11.f.a.77.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-27.0389 + 27.0389i) q^{2} +(145.189 + 145.189i) q^{3} -438.207i q^{4} +(2114.71 + 2300.79i) q^{5} -7851.52 q^{6} +(-16374.3 + 16374.3i) q^{7} +(-15839.2 - 15839.2i) q^{8} -16889.2i q^{9} +O(q^{10})$	\(q+(-27.0389 + 27.0389i) q^{2} +(145.189 + 145.189i) q^{3} -438.207i q^{4} +(2114.71 + 2300.79i) q^{5} -7851.52 q^{6} +(-16374.3 + 16374.3i) q^{7} +(-15839.2 - 15839.2i) q^{8} -16889.2i q^{9} +(-119390. - 5031.30i) q^{10} -80719.3 q^{11} +(63623.0 - 63623.0i) q^{12} +(-311519. - 311519. i) q^{13} -885484. i q^{14} +(-27016.2 + 641083. i) q^{15} +1.30527e6 q^{16} +(546998. - 546998. i) q^{17} +(456665. + 456665. i) q^{18} +568056. i q^{19} +(1.00822e6 - 926682. i) q^{20} -4.75473e6 q^{21} +(2.18256e6 - 2.18256e6i) q^{22} +(1.07971e6 + 1.07971e6i) q^{23} -4.59937e6i q^{24} +(-821618. + 9.73100e6i) q^{25} +1.68463e7 q^{26} +(1.10254e7 - 1.10254e7i) q^{27} +(7.17531e6 + 7.17531e6i) q^{28} -1.08294e7i q^{29} +(-1.66037e7 - 1.80647e7i) q^{30} +9.14521e6 q^{31} +(-1.90739e7 + 1.90739e7i) q^{32} +(-1.17196e7 - 1.17196e7i) q^{33} +2.95805e7i q^{34} +(-7.23005e7 - 3.04686e6i) q^{35} -7.40095e6 q^{36} +(7.50094e7 - 7.50094e7i) q^{37} +(-1.53596e7 - 1.53596e7i) q^{38} -9.04585e7i q^{39} +(2.94730e6 - 6.99380e7i) q^{40} -1.51907e8 q^{41} +(1.28563e8 - 1.28563e8i) q^{42} +(-1.05527e8 - 1.05527e8i) q^{43} +3.53718e7i q^{44} +(3.88583e7 - 3.57157e7i) q^{45} -5.83884e7 q^{46} +(-5.91177e7 + 5.91177e7i) q^{47} +(1.89512e8 + 1.89512e8i) q^{48} -2.53757e8i q^{49} +(-2.40900e8 - 2.85332e8i) q^{50} +1.58837e8 q^{51} +(-1.36510e8 + 1.36510e8i) q^{52} +(1.09867e8 + 1.09867e8i) q^{53} +5.96230e8i q^{54} +(-1.70698e8 - 1.85718e8i) q^{55} +5.18710e8 q^{56} +(-8.24756e7 + 8.24756e7i) q^{57} +(2.92816e8 + 2.92816e8i) q^{58} -5.67366e8i q^{59} +(2.80927e8 + 1.18387e7i) q^{60} -1.66832e8 q^{61} +(-2.47277e8 + 2.47277e8i) q^{62} +(2.76547e8 + 2.76547e8i) q^{63} +3.05127e8i q^{64} +(5.79663e7 - 1.37551e9i) q^{65} +6.33770e8 q^{66} +(-6.78936e8 + 6.78936e8i) q^{67} +(-2.39699e8 - 2.39699e8i) q^{68} +3.13525e8i q^{69} +(2.03731e9 - 1.87254e9i) q^{70} -2.91266e9 q^{71} +(-2.67511e8 + 2.67511e8i) q^{72} +(1.75715e9 + 1.75715e9i) q^{73} +4.05635e9i q^{74} +(-1.53213e9 + 1.29355e9i) q^{75} +2.48926e8 q^{76} +(1.32172e9 - 1.32172e9i) q^{77} +(2.44590e9 + 2.44590e9i) q^{78} -2.53235e9i q^{79} +(2.76028e9 + 3.00316e9i) q^{80} +2.20425e9 q^{81} +(4.10741e9 - 4.10741e9i) q^{82} +(4.65193e9 + 4.65193e9i) q^{83} +2.08356e9i q^{84} +(2.41527e9 + 1.01783e8i) q^{85} +5.70667e9 q^{86} +(1.57232e9 - 1.57232e9i) q^{87} +(1.27853e9 + 1.27853e9i) q^{88} -5.39717e9i q^{89} +(-8.49743e7 + 2.01640e9i) q^{90} +1.02018e10 q^{91} +(4.73137e8 - 4.73137e8i) q^{92} +(1.32779e9 + 1.32779e9i) q^{93} -3.19696e9i q^{94} +(-1.30698e9 + 1.20127e9i) q^{95} -5.53864e9 q^{96} +(6.13404e9 - 6.13404e9i) q^{97} +(6.86131e9 + 6.86131e9i) q^{98} +1.36328e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8}+O(q^{10}) $ 180 * q - 64 * q^2 - 124 * q^3 + 8454 * q^5 - 24320 * q^6 + 32890 * q^7 + 98304 * q^8	\( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8} + 322576 q^{10} + 435480 q^{11} - 1494224 q^{12} - 48556 q^{13} + 4094384 q^{15} - 44262960 q^{16} - 505646 q^{17} - 6298560 q^{18} + 24709120 q^{20} + 38659000 q^{21} - 34179888 q^{22} - 16720612 q^{23} + 33791178 q^{25} + 86813120 q^{26} - 14436244 q^{27} - 133340704 q^{28} + 232195960 q^{30} + 64155640 q^{31} + 226208632 q^{32} + 11350832 q^{33} - 151622642 q^{35} + 1852895600 q^{36} - 373035252 q^{37} + 28746456 q^{40} - 461563640 q^{41} + 1629657056 q^{42} - 123615382 q^{43} - 1310415408 q^{45} - 462362320 q^{46} + 1397297450 q^{47} + 1422934764 q^{48} - 903150292 q^{50} + 786433560 q^{51} + 1822166628 q^{52} + 3614315976 q^{53} + 1190412472 q^{55} - 2951801640 q^{56} - 2958059232 q^{58} + 13343296716 q^{60} + 1705662680 q^{61} + 5674658712 q^{62} - 2955158450 q^{63} + 5908753192 q^{65} - 6577823720 q^{66} - 4198675868 q^{67} - 10832391640 q^{68} + 7095849220 q^{70} + 5547444200 q^{71} + 12902115940 q^{72} + 331620970 q^{73} - 11862069968 q^{75} - 10562822066 q^{77} - 12446121128 q^{78} + 9866450160 q^{80} - 63545444700 q^{81} + 9916048472 q^{82} - 1670597036 q^{83} - 25420912412 q^{85} - 54497853920 q^{86} + 20560091976 q^{87} - 4241912244 q^{88} + 1724884384 q^{90} - 9777438680 q^{91} + 57824442424 q^{92} + 49325339272 q^{93} - 5501891978 q^{95} - 7492787400 q^{96} - 74779609888 q^{97} - 60964218864 q^{98}+O(q^{100}) \) 180 * q - 64 * q^2 - 124 * q^3 + 8454 * q^5 - 24320 * q^6 + 32890 * q^7 + 98304 * q^8 + 322576 * q^10 + 435480 * q^11 - 1494224 * q^12 - 48556 * q^13 + 4094384 * q^15 - 44262960 * q^16 - 505646 * q^17 - 6298560 * q^18 + 24709120 * q^20 + 38659000 * q^21 - 34179888 * q^22 - 16720612 * q^23 + 33791178 * q^25 + 86813120 * q^26 - 14436244 * q^27 - 133340704 * q^28 + 232195960 * q^30 + 64155640 * q^31 + 226208632 * q^32 + 11350832 * q^33 - 151622642 * q^35 + 1852895600 * q^36 - 373035252 * q^37 + 28746456 * q^40 - 461563640 * q^41 + 1629657056 * q^42 - 123615382 * q^43 - 1310415408 * q^45 - 462362320 * q^46 + 1397297450 * q^47 + 1422934764 * q^48 - 903150292 * q^50 + 786433560 * q^51 + 1822166628 * q^52 + 3614315976 * q^53 + 1190412472 * q^55 - 2951801640 * q^56 - 2958059232 * q^58 + 13343296716 * q^60 + 1705662680 * q^61 + 5674658712 * q^62 - 2955158450 * q^63 + 5908753192 * q^65 - 6577823720 * q^66 - 4198675868 * q^67 - 10832391640 * q^68 + 7095849220 * q^70 + 5547444200 * q^71 + 12902115940 * q^72 + 331620970 * q^73 - 11862069968 * q^75 - 10562822066 * q^77 - 12446121128 * q^78 + 9866450160 * q^80 - 63545444700 * q^81 + 9916048472 * q^82 - 1670597036 * q^83 - 25420912412 * q^85 - 54497853920 * q^86 + 20560091976 * q^87 - 4241912244 * q^88 + 1724884384 * q^90 - 9777438680 * q^91 + 57824442424 * q^92 + 49325339272 * q^93 - 5501891978 * q^95 - 7492787400 * q^96 - 74779609888 * q^97 - 60964218864 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−27.0389	+	27.0389i	−0.844966	+	0.844966i	−0.989500	−	0.144533i	$-0.953832\pi$
$2$	−27.0389	+	27.0389i	−0.844966	+	0.844966i	0.144533	+	0.989500i	$0.453832\pi$
$3$	145.189	+	145.189i	0.597487	+	0.597487i	0.939643	−	0.342156i	$-0.111157\pi$
$3$	145.189	+	145.189i	0.597487	+	0.597487i	−0.342156	+	0.939643i	$0.611157\pi$
$4$		−	438.207i		−	0.427937i
$5$	2114.71	+	2300.79i	0.676708	+	0.736252i
$5$	2114.71	+	2300.79i	0.676708	+	0.736252i
$6$	−7851.52			−1.00971
$7$	−16374.3	+	16374.3i	−0.974252	+	0.974252i	−0.999677	−	0.0254249i	$-0.991906\pi$
$7$	−16374.3	+	16374.3i	−0.974252	+	0.974252i	0.0254249	+	0.999677i	$0.491906\pi$
$8$	−15839.2	−	15839.2i	−0.483374	−	0.483374i
$9$		−	16889.2i		−	0.286019i
$10$	−119390.	−	5031.30i	−1.19390	−	0.0503130i
$11$	−80719.3			−0.501203			−0.250602	−	0.968090i	$-0.580628\pi$
$11$	−80719.3			−0.501203			−0.250602	+	0.968090i	$0.580628\pi$
$12$	63623.0	−	63623.0i	0.255687	−	0.255687i
$13$	−311519.	−	311519.i	−0.839012	−	0.839012i	0.149717	−	0.988729i	$-0.452164\pi$
$13$	−311519.	−	311519.i	−0.839012	−	0.839012i	−0.988729	+	0.149717i	$0.952164\pi$
$14$		−	885484.i		−	1.64642i
$15$	−27016.2	+	641083.i	−0.0355769	+	0.844225i
$16$	1.30527e6			1.24481
$17$	546998.	−	546998.i	0.385249	−	0.385249i	−0.487740	−	0.872989i	$-0.662179\pi$
$17$	546998.	−	546998.i	0.385249	−	0.385249i	0.872989	+	0.487740i	$0.162179\pi$
$18$	456665.	+	456665.i	0.241677	+	0.241677i
$19$			568056.i			0.229416i
$19$			568056.i			0.229416i
$20$	1.00822e6	−	926682.i	0.315069	−	0.289588i
$21$	−4.75473e6			−1.16421
$22$	2.18256e6	−	2.18256e6i	0.423500	−	0.423500i
$23$	1.07971e6	+	1.07971e6i	0.167752	+	0.167752i	0.785991	−	0.618238i	$-0.212153\pi$
$23$	1.07971e6	+	1.07971e6i	0.167752	+	0.167752i	−0.618238	+	0.785991i	$0.712153\pi$
$24$		−	4.59937e6i		−	0.577619i
$25$	−821618.	+	9.73100e6i	−0.0841337	+	0.996454i
$26$	1.68463e7			1.41787
$27$	1.10254e7	−	1.10254e7i	0.768379	−	0.768379i
$28$	7.17531e6	+	7.17531e6i	0.416918	+	0.416918i
$29$		−	1.08294e7i		−	0.527978i	−0.964526	−	0.263989i	$-0.914962\pi$
$29$		−	1.08294e7i		−	0.527978i	0.964526	−	0.263989i	$-0.0850382\pi$
$30$	−1.66037e7	−	1.80647e7i	−0.683280	−	0.743403i
$31$	9.14521e6			0.319437			0.159719	−	0.987163i	$-0.448941\pi$
$31$	9.14521e6			0.319437			0.159719	+	0.987163i	$0.448941\pi$
$32$	−1.90739e7	+	1.90739e7i	−0.568446	+	0.568446i
$33$	−1.17196e7	−	1.17196e7i	−0.299462	−	0.299462i
$34$			2.95805e7i			0.651045i
$35$	−7.23005e7	−	3.04686e6i	−1.37658	−	0.0580112i
$36$	−7.40095e6			−0.122398
$37$	7.50094e7	−	7.50094e7i	1.08170	−	1.08170i	0.0853498	−	0.996351i	$-0.472799\pi$
$37$	7.50094e7	−	7.50094e7i	1.08170	−	1.08170i	0.996351	−	0.0853498i	$-0.0272008\pi$
$38$	−1.53596e7	−	1.53596e7i	−0.193849	−	0.193849i
$39$		−	9.04585e7i		−	1.00260i
$40$	2.94730e6	−	6.99380e7i	0.0287822	−	0.682988i
$41$	−1.51907e8			−1.31117			−0.655585	−	0.755121i	$-0.727578\pi$
$41$	−1.51907e8			−1.31117			−0.655585	+	0.755121i	$0.727578\pi$
$42$	1.28563e8	−	1.28563e8i	0.983714	−	0.983714i
$43$	−1.05527e8	−	1.05527e8i	−0.717829	−	0.717829i	0.250331	−	0.968160i	$-0.419461\pi$
$43$	−1.05527e8	−	1.05527e8i	−0.717829	−	0.717829i	−0.968160	+	0.250331i	$0.919461\pi$
$44$			3.53718e7i			0.214483i
$45$	3.88583e7	−	3.57157e7i	0.210582	−	0.193551i
$46$	−5.83884e7			−0.283490
$47$	−5.91177e7	+	5.91177e7i	−0.257767	+	0.257767i	−0.824146	−	0.566378i	$-0.808344\pi$
$47$	−5.91177e7	+	5.91177e7i	−0.257767	+	0.257767i	0.566378	+	0.824146i	$0.308344\pi$
$48$	1.89512e8	+	1.89512e8i	0.743756	+	0.743756i
$49$		−	2.53757e8i		−	0.898333i
$50$	−2.40900e8	−	2.85332e8i	−0.770880	−	0.913061i
$51$	1.58837e8			0.460362
$52$	−1.36510e8	+	1.36510e8i	−0.359044	+	0.359044i
$53$	1.09867e8	+	1.09867e8i	0.262718	+	0.262718i	0.826157	−	0.563440i	$-0.190522\pi$
$53$	1.09867e8	+	1.09867e8i	0.262718	+	0.262718i	−0.563440	+	0.826157i	$0.690522\pi$
$54$			5.96230e8i			1.29851i
$55$	−1.70698e8	−	1.85718e8i	−0.339168	−	0.369012i
$56$	5.18710e8			0.941857
$57$	−8.24756e7	+	8.24756e7i	−0.137073	+	0.137073i
$58$	2.92816e8	+	2.92816e8i	0.446124	+	0.446124i
$59$		−	5.67366e8i		−	0.793603i	−0.917905	−	0.396801i	$-0.870120\pi$
$59$		−	5.67366e8i		−	0.793603i	0.917905	−	0.396801i	$-0.129880\pi$
$60$	2.80927e8	+	1.18387e7i	0.361275	+	0.0152247i
$61$	−1.66832e8			−0.197529			−0.0987646	−	0.995111i	$-0.531489\pi$
$61$	−1.66832e8			−0.197529			−0.0987646	+	0.995111i	$0.531489\pi$
$62$	−2.47277e8	+	2.47277e8i	−0.269914	+	0.269914i
$63$	2.76547e8	+	2.76547e8i	0.278655	+	0.278655i
$64$			3.05127e8i			0.284172i
$65$	5.79663e7	−	1.37551e9i	0.0499584	−	1.18549i
$66$	6.33770e8			0.506071
$67$	−6.78936e8	+	6.78936e8i	−0.502869	+	0.502869i	−0.912328	−	0.409459i	$-0.865717\pi$
$67$	−6.78936e8	+	6.78936e8i	−0.502869	+	0.502869i	0.409459	+	0.912328i	$0.365717\pi$
$68$	−2.39699e8	−	2.39699e8i	−0.164862	−	0.164862i
$69$			3.13525e8i			0.200459i
$70$	2.03731e9	−	1.87254e9i	1.21218	−	1.11415i
$71$	−2.91266e9			−1.61435			−0.807175	−	0.590312i	$-0.799005\pi$
$71$	−2.91266e9			−1.61435			−0.807175	+	0.590312i	$0.799005\pi$
$72$	−2.67511e8	+	2.67511e8i	−0.138254	+	0.138254i
$73$	1.75715e9	+	1.75715e9i	0.847608	+	0.847608i	0.989834	−	0.142226i	$-0.0454261\pi$
$73$	1.75715e9	+	1.75715e9i	0.847608	+	0.847608i	−0.142226	+	0.989834i	$0.545426\pi$
$74$			4.05635e9i			1.82800i
$75$	−1.53213e9	+	1.29355e9i	−0.645637	+	0.545100i
$76$	2.48926e8			0.0981754
$77$	1.32172e9	−	1.32172e9i	0.488298	−	0.488298i
$78$	2.44590e9	+	2.44590e9i	0.847161	+	0.847161i
$79$		−	2.53235e9i		−	0.822976i	−0.911415	−	0.411488i	$-0.865009\pi$
$79$		−	2.53235e9i		−	0.822976i	0.911415	−	0.411488i	$-0.134991\pi$
$80$	2.76028e9	+	3.00316e9i	0.842370	+	0.916491i
$81$	2.20425e9			0.632174
$82$	4.10741e9	−	4.10741e9i	1.10789	−	1.10789i
$83$	4.65193e9	+	4.65193e9i	1.18098	+	1.18098i	0.979490	+	0.201490i	$0.0645785\pi$
$83$	4.65193e9	+	4.65193e9i	1.18098	+	1.18098i	0.201490	+	0.979490i	$0.435422\pi$
$84$			2.08356e9i			0.498206i
$85$	2.41527e9	+	1.01783e8i	0.544341	+	0.0229394i
$86$	5.70667e9			1.21308
$87$	1.57232e9	−	1.57232e9i	0.315460	−	0.315460i
$88$	1.27853e9	+	1.27853e9i	0.242269	+	0.242269i
$89$		−	5.39717e9i		−	0.966532i	−0.875473	−	0.483266i	$-0.839450\pi$
$89$		−	5.39717e9i		−	0.966532i	0.875473	−	0.483266i	$-0.160550\pi$
$90$	−8.49743e7	+	2.01640e9i	−0.0143905	+	0.341479i
$91$	1.02018e10			1.63482
$92$	4.73137e8	−	4.73137e8i	0.0717873	−	0.0717873i
$93$	1.32779e9	+	1.32779e9i	0.190859	+	0.190859i
$94$		−	3.19696e9i		−	0.435610i
$95$	−1.30698e9	+	1.20127e9i	−0.168908	+	0.155247i
$96$	−5.53864e9			−0.679278
$97$	6.13404e9	−	6.13404e9i	0.714312	−	0.714312i	−0.253122	−	0.967434i	$-0.581457\pi$
$97$	6.13404e9	−	6.13404e9i	0.714312	−	0.714312i	0.967434	+	0.253122i	$0.0814575\pi$
$98$	6.86131e9	+	6.86131e9i	0.759062	+	0.759062i
$99$			1.36328e9i			0.143354i
$100$	4.26419e9	+	3.60039e8i	0.426419	+	0.0360039i
$101$	4.04133e9			0.384518			0.192259	−	0.981344i	$-0.438419\pi$
$101$	4.04133e9			0.384518			0.192259	+	0.981344i	$0.438419\pi$
$102$	−4.29477e9	+	4.29477e9i	−0.388991	+	0.388991i
$103$	8.09997e9	+	8.09997e9i	0.698711	+	0.698711i	0.964132	−	0.265422i	$-0.0855112\pi$
$103$	8.09997e9	+	8.09997e9i	0.698711	+	0.698711i	−0.265422	+	0.964132i	$0.585511\pi$
$104$			9.86844e9i			0.811114i
$105$	−1.00549e10	−	1.09396e10i	−0.787826	−	0.857148i
$106$	−5.94139e9			−0.443975
$107$	−4.62414e9	+	4.62414e9i	−0.329695	+	0.329695i	−0.852470	−	0.522775i	$-0.824897\pi$
$107$	−4.62414e9	+	4.62414e9i	−0.329695	+	0.329695i	0.522775	+	0.852470i	$0.324897\pi$
$108$	−4.83141e9	−	4.83141e9i	−0.328818	−	0.328818i
$109$		−	2.70809e10i		−	1.76007i	−0.474904	−	0.880037i	$-0.657517\pi$
$109$		−	2.70809e10i		−	1.76007i	0.474904	−	0.880037i	$-0.342483\pi$
$110$	9.63711e9	+	4.06123e8i	0.598388	+	0.0252170i
$111$	2.17811e10			1.29260
$112$	−2.13729e10	+	2.13729e10i	−1.21276	+	1.21276i
$113$	1.76473e9	+	1.76473e9i	0.0957827	+	0.0957827i	0.753374	−	0.657592i	$-0.228425\pi$
$113$	1.76473e9	+	1.76473e9i	0.0957827	+	0.0957827i	−0.657592	+	0.753374i	$0.728425\pi$
$114$		−	4.46011e9i		−	0.231644i
$115$	−2.00908e8	+	4.76746e9i	−0.00998869	+	0.237027i
$116$	−4.74554e9			−0.225941
$117$	−5.26130e9	+	5.26130e9i	−0.239974	+	0.239974i
$118$	1.53410e10	+	1.53410e10i	0.670568	+	0.670568i
$119$			1.79134e10i			0.750659i
$120$	1.05822e10	−	9.72633e9i	0.425273	−	0.390879i
$121$	−1.94218e10			−0.748795
$122$	4.51097e9	−	4.51097e9i	0.166906	−	0.166906i
$123$	−2.20553e10	−	2.20553e10i	−0.783407	−	0.783407i
$124$		−	4.00750e9i		−	0.136699i
$125$	−2.41264e10	+	1.86879e10i	−0.790575	+	0.612365i
$126$	−1.49551e10			−0.470908
$127$	−3.17871e10	+	3.17871e10i	−0.962126	+	0.962126i	−0.999309	−	0.0371820i	$-0.988162\pi$
$127$	−3.17871e10	+	3.17871e10i	−0.962126	+	0.962126i	0.0371820	+	0.999309i	$0.488162\pi$
$128$	−2.77820e10	−	2.77820e10i	−0.808561	−	0.808561i
$129$		−	3.06428e10i		−	0.857787i
$130$	3.56250e10	+	3.87597e10i	0.959486	+	1.04391i
$131$	−3.32389e10			−0.861570			−0.430785	−	0.902455i	$-0.641763\pi$
$131$	−3.32389e10			−0.861570			−0.430785	+	0.902455i	$0.641763\pi$
$132$	−5.13560e9	+	5.13560e9i	−0.128151	+	0.128151i
$133$	−9.30149e9	−	9.30149e9i	−0.223509	−	0.223509i
$134$		−	3.67154e10i		−	0.849815i
$135$	4.86827e10	+	2.05156e9i	1.08569	+	0.0457526i
$136$	−1.73280e10			−0.372439
$137$	5.49156e10	−	5.49156e10i	1.13787	−	1.13787i	0.149038	−	0.988831i	$-0.452382\pi$
$137$	5.49156e10	−	5.49156e10i	1.13787	−	1.13787i	0.988831	−	0.149038i	$-0.0476178\pi$
$138$	−8.47737e9	−	8.47737e9i	−0.169381	−	0.169381i
$139$		−	7.96354e10i		−	1.53473i	−0.641210	−	0.767366i	$-0.721567\pi$
$139$		−	7.96354e10i		−	1.53473i	0.641210	−	0.767366i	$-0.278433\pi$
$140$	−1.33515e9	+	3.16826e10i	−0.0248251	+	0.589088i
$141$	−1.71665e10			−0.308025
$142$	7.87552e10	−	7.87552e10i	1.36407	−	1.36407i
$143$	2.51456e10	+	2.51456e10i	0.420516	+	0.420516i
$144$		−	2.20450e10i		−	0.356039i
$145$	2.49162e10	−	2.29011e10i	0.388725	−	0.357287i
$146$	−9.50230e10			−1.43240
$147$	3.68428e10	−	3.68428e10i	0.536742	−	0.536742i
$148$	−3.28697e10	−	3.28697e10i	−0.462900	−	0.462900i
$149$			5.38829e10i			0.733702i	0.930280	+	0.366851i	$0.119564\pi$
$149$			5.38829e10i			0.733702i	−0.930280	+	0.366851i	$0.880436\pi$
$150$	6.45096e9	−	7.64032e10i	0.0849509	−	1.00613i
$151$	5.57433e9			0.0710081			0.0355040	−	0.999370i	$-0.488696\pi$
$151$	5.57433e9			0.0710081			0.0355040	+	0.999370i	$0.488696\pi$
$152$	8.99756e9	−	8.99756e9i	0.110894	−	0.110894i
$153$	−9.23834e9	−	9.23834e9i	−0.110189	−	0.110189i
$154$			7.14757e10i			0.825191i
$155$	1.93395e10	+	2.10412e10i	0.216165	+	0.235186i
$156$	−3.96396e10			−0.429048
$157$	−2.90441e10	+	2.90441e10i	−0.304480	+	0.304480i	−0.842764	−	0.538284i	$-0.819073\pi$
$157$	−2.90441e10	+	2.90441e10i	−0.304480	+	0.304480i	0.538284	+	0.842764i	$0.319073\pi$
$158$	6.84719e10	+	6.84719e10i	0.695388	+	0.695388i
$159$			3.19031e10i			0.313941i
$160$	−8.42207e10	−	3.54919e9i	−0.803191	−	0.0338477i
$161$	−3.53589e10			−0.326866
$162$	−5.96006e10	+	5.96006e10i	−0.534166	+	0.534166i
$163$	6.98114e10	+	6.98114e10i	0.606720	+	0.606720i	0.942087	−	0.335368i	$-0.108861\pi$
$163$	6.98114e10	+	6.98114e10i	0.606720	+	0.606720i	−0.335368	+	0.942087i	$0.608861\pi$
$164$			6.65668e10i			0.561098i
$165$	2.18073e9	−	5.17478e10i	0.0178313	−	0.423128i
$166$	−2.51566e11			−1.99578
$167$	2.21679e10	−	2.21679e10i	0.170664	−	0.170664i	−0.616607	−	0.787271i	$-0.711493\pi$
$167$	2.21679e10	−	2.21679e10i	0.170664	−	0.170664i	0.787271	+	0.616607i	$0.211493\pi$
$168$	7.53112e10	+	7.53112e10i	0.562747	+	0.562747i
$169$			5.62300e10i			0.407882i
$170$	−6.80584e10	+	6.25542e10i	−0.479333	+	0.440567i
$171$	9.59399e9			0.0656173
$172$	−4.62427e10	+	4.62427e10i	−0.307185	+	0.307185i
$173$	−3.49329e10	−	3.49329e10i	−0.225426	−	0.225426i	0.585353	−	0.810779i	$-0.300956\pi$
$173$	−3.49329e10	−	3.49329e10i	−0.225426	−	0.225426i	−0.810779	+	0.585353i	$0.800956\pi$
$174$			8.50275e10i			0.533106i
$175$	−1.45884e11	−	1.72791e11i	−0.888830	−	1.05277i
$176$	−1.05361e11			−0.623901
$177$	8.23754e10	−	8.23754e10i	0.474167	−	0.474167i
$178$	1.45934e11	+	1.45934e11i	0.816687	+	0.816687i
$179$		−	1.68054e11i		−	0.914499i	−0.889339	−	0.457249i	$-0.848835\pi$
$179$		−	1.68054e11i		−	0.914499i	0.889339	−	0.457249i	$-0.151165\pi$
$180$	−1.56509e10	−	1.70280e10i	−0.0828278	−	0.0901159i
$181$	−2.51882e11			−1.29660			−0.648298	−	0.761387i	$-0.724519\pi$
$181$	−2.51882e11			−1.29660			−0.648298	+	0.761387i	$0.724519\pi$
$182$	−2.75845e11	+	2.75845e11i	−1.38137	+	1.38137i
$183$	−2.42223e10	−	2.42223e10i	−0.118021	−	0.118021i
$184$		−	3.42035e10i		−	0.162174i
$185$	3.31204e11	+	1.39575e10i	1.52840	+	0.0644092i
$186$	−7.18038e10			−0.322540
$187$	−4.41533e10	+	4.41533e10i	−0.193088	+	0.193088i
$188$	2.59058e10	+	2.59058e10i	0.110308	+	0.110308i
$189$			3.61065e11i			1.49719i
$190$	2.85806e9	−	6.78204e10i	0.0115426	−	0.273900i
$191$	3.18328e11			1.25230			0.626149	−	0.779703i	$-0.284630\pi$
$191$	3.18328e11			1.25230			0.626149	+	0.779703i	$0.284630\pi$
$192$	−4.43011e10	+	4.43011e10i	−0.169789	+	0.169789i
$193$	−1.03544e11	−	1.03544e11i	−0.386667	−	0.386667i	0.486830	−	0.873497i	$-0.338153\pi$
$193$	−1.03544e11	−	1.03544e11i	−0.386667	−	0.386667i	−0.873497	+	0.486830i	$0.838153\pi$
$194$			3.31716e11i			1.20714i
$195$	2.08126e11	−	1.91294e11i	0.738164	−	0.678465i
$196$	−1.11198e11			−0.384430
$197$	3.35621e11	−	3.35621e11i	1.13115	−	1.13115i	0.141158	−	0.989987i	$-0.454917\pi$
$197$	3.35621e11	−	3.35621e11i	1.13115	−	1.13115i	0.989987	−	0.141158i	$-0.0450826\pi$
$198$	−3.68616e10	−	3.68616e10i	−0.121129	−	0.121129i
$199$			5.52704e9i			0.0177104i	0.999961	+	0.00885518i	$0.00281873\pi$
$199$			5.52704e9i			0.0177104i	−0.999961	+	0.00885518i	$0.997181\pi$
$200$	1.67145e11	−	1.41118e11i	0.522329	−	0.440992i
$201$	−1.97148e11			−0.600915
$202$	−1.09273e11	+	1.09273e11i	−0.324905	+	0.324905i
$203$	1.77324e11	+	1.77324e11i	0.514383	+	0.514383i
$204$		−	6.96033e10i		−	0.197006i
$205$	−3.21240e11	−	3.49506e11i	−0.887279	−	0.965351i
$206$	−4.38029e11			−1.18077
$207$	1.82354e10	−	1.82354e10i	0.0479803	−	0.0479803i
$208$	−4.06618e11	−	4.06618e11i	−1.04441	−	1.04441i
$209$		−	4.58531e10i		−	0.114984i
$210$	5.67669e11	+	2.39225e10i	1.38995	+	0.0585746i
$211$	1.22221e11			0.292235			0.146117	−	0.989267i	$-0.453322\pi$
$211$	1.22221e11			0.292235			0.146117	+	0.989267i	$0.453322\pi$
$212$	4.81447e10	−	4.81447e10i	0.112427	−	0.112427i
$213$	−4.22887e11	−	4.22887e11i	−0.964553	−	0.964553i
$214$		−	2.50064e11i		−	0.557163i
$215$	1.96360e10	−	4.65954e11i	0.0427427	−	1.01426i
$216$	−3.49267e11			−0.742830
$217$	−1.49746e11	+	1.49746e11i	−0.311212	+	0.311212i
$218$	7.32239e11	+	7.32239e11i	1.48720	+	1.48720i
$219$			5.10239e11i			1.01287i
$220$	−8.13829e10	+	7.48011e10i	−0.157914	+	0.145142i
$221$	−3.40801e11			−0.646457
$222$	−5.88938e11	+	5.88938e11i	−1.09221	+	1.09221i
$223$	6.52653e11	+	6.52653e11i	1.18347	+	1.18347i	0.978838	+	0.204634i	$0.0656005\pi$
$223$	6.52653e11	+	6.52653e11i	1.18347	+	1.18347i	0.204634	+	0.978838i	$0.434399\pi$
$224$		−	6.24641e11i		−	1.10762i
$225$	1.64348e11	+	1.38764e10i	0.285005	+	0.0240639i
$226$	−9.54330e10			−0.161866
$227$	6.41230e11	−	6.41230e11i	1.06386	−	1.06386i	0.0660433	−	0.997817i	$-0.478962\pi$
$227$	6.41230e11	−	6.41230e11i	1.06386	−	1.06386i	0.997817	−	0.0660433i	$-0.0210375\pi$
$228$	3.61414e10	+	3.61414e10i	0.0586585	+	0.0586585i
$229$		−	7.81070e11i		−	1.24026i	−0.784499	−	0.620130i	$-0.787080\pi$
$229$		−	7.81070e11i		−	1.24026i	0.784499	−	0.620130i	$-0.212920\pi$
$230$	−1.23475e11	−	1.34339e11i	−0.191840	−	0.208720i
$231$	3.83799e11			0.583503
$232$	−1.71530e11	+	1.71530e11i	−0.255211	+	0.255211i
$233$	1.40951e11	+	1.40951e11i	0.205252	+	0.205252i	0.802246	−	0.596994i	$-0.203638\pi$
$233$	1.40951e11	+	1.40951e11i	0.205252	+	0.205252i	−0.596994	+	0.802246i	$0.703638\pi$
$234$		−	2.84520e11i		−	0.405539i
$235$	−2.61034e11	−	1.10004e10i	−0.364215	−	0.0153486i
$236$	−2.48624e11			−0.339612
$237$	3.67669e11	−	3.67669e11i	0.491718	−	0.491718i
$238$	−4.84359e11	−	4.84359e11i	−0.634282	−	0.634282i
$239$			7.05814e11i			0.905109i	0.891737	+	0.452555i	$0.149487\pi$
$239$			7.05814e11i			0.905109i	−0.891737	+	0.452555i	$0.850513\pi$
$240$	−3.52636e10	+	8.36789e11i	−0.0442864	+	1.05090i
$241$	−1.11437e11			−0.137070			−0.0685351	−	0.997649i	$-0.521833\pi$
$241$	−1.11437e11			−0.137070			−0.0685351	+	0.997649i	$0.521833\pi$
$242$	5.25145e11	−	5.25145e11i	0.632707	−	0.632707i
$243$	−3.31005e11	−	3.31005e11i	−0.390664	−	0.390664i
$244$			7.31072e10i			0.0845300i
$245$	5.83841e11	−	5.36623e11i	0.661400	−	0.607909i
$246$	1.19270e12			1.32390
$247$	1.76960e11	−	1.76960e11i	0.192483	−	0.192483i
$248$	−1.44853e11	−	1.44853e11i	−0.154408	−	0.154408i
$249$			1.35082e12i			1.41124i
$250$	1.47053e11	−	1.15765e12i	0.150582	−	1.18544i
$251$	−5.88660e11			−0.590875			−0.295438	−	0.955362i	$-0.595465\pi$
$251$	−5.88660e11			−0.590875			−0.295438	+	0.955362i	$0.595465\pi$
$252$	1.21185e11	−	1.21185e11i	0.119247	−	0.119247i
$253$	−8.71534e10	−	8.71534e10i	−0.0840779	−	0.0840779i
$254$		−	1.71898e12i		−	1.62593i
$255$	3.35894e11	+	3.65449e11i	0.311531	+	0.338943i
$256$	1.18994e12			1.08224
$257$	6.93666e11	−	6.93666e11i	0.618706	−	0.618706i	−0.326493	−	0.945200i	$-0.605867\pi$
$257$	6.93666e11	−	6.93666e11i	0.618706	−	0.618706i	0.945200	+	0.326493i	$0.105867\pi$
$258$	8.28547e11	+	8.28547e11i	0.724801	+	0.724801i
$259$			2.45645e12i			2.10770i
$260$	−6.02760e11	−	2.54012e10i	−0.507315	−	0.0213790i
$261$	−1.82900e11			−0.151012
$262$	8.98745e11	−	8.98745e11i	0.727998	−	0.727998i
$263$	6.88929e9	+	6.88929e9i	0.00547514	+	0.00547514i	0.709839	−	0.704364i	$-0.248768\pi$
$263$	6.88929e9	+	6.88929e9i	0.00547514	+	0.00547514i	−0.704364	+	0.709839i	$0.748768\pi$
$264$			3.71258e11i			0.289505i
$265$	−2.04437e10	+	4.85119e11i	−0.0156434	+	0.371210i
$266$	5.03005e11			0.377715
$267$	7.83612e11	−	7.83612e11i	0.577490	−	0.577490i
$268$	2.97515e11	+	2.97515e11i	0.215196	+	0.215196i
$269$			2.30964e11i			0.163977i	0.996633	+	0.0819885i	$0.0261271\pi$
$269$			2.30964e11i			0.163977i	−0.996633	+	0.0819885i	$0.973873\pi$
$270$	−1.37180e12	+	1.26085e12i	−0.956030	+	0.878711i
$271$	−2.69357e11			−0.184281			−0.0921406	−	0.995746i	$-0.529371\pi$
$271$	−2.69357e11			−0.184281			−0.0921406	+	0.995746i	$0.529371\pi$
$272$	7.13983e11	−	7.13983e11i	0.479561	−	0.479561i
$273$	1.48119e12	+	1.48119e12i	0.976782	+	0.976782i
$274$			2.96972e12i			1.92292i
$275$	6.63205e10	−	7.85480e11i	0.0421681	−	0.499426i
$276$	1.37389e11			0.0857839
$277$	−2.55163e11	+	2.55163e11i	−0.156466	+	0.156466i	−0.780998	−	0.624533i	$-0.785289\pi$
$277$	−2.55163e11	+	2.55163e11i	−0.156466	+	0.156466i	0.624533	+	0.780998i	$0.285289\pi$
$278$	2.15326e12	+	2.15326e12i	1.29680	+	1.29680i
$279$		−	1.54455e11i		−	0.0913651i
$280$	1.09692e12	+	1.19344e12i	0.637361	+	0.693444i
$281$	−2.29778e12			−1.31152			−0.655762	−	0.754968i	$-0.727652\pi$
$281$	−2.29778e12			−1.31152			−0.655762	+	0.754968i	$0.727652\pi$
$282$	4.64164e11	−	4.64164e11i	0.260271	−	0.260271i
$283$	−2.21445e12	−	2.21445e12i	−1.21993	−	1.21993i	−0.967657	−	0.252270i	$-0.918823\pi$
$283$	−2.21445e12	−	2.21445e12i	−1.21993	−	1.21993i	−0.252270	−	0.967657i	$-0.581177\pi$
$284$			1.27635e12i			0.690840i
$285$	−3.64171e11	−	1.53467e10i	−0.193678	−	0.00816191i
$286$	−1.35982e12			−0.710643
$287$	2.48737e12	−	2.48737e12i	1.27741	−	1.27741i
$288$	3.22142e11	+	3.22142e11i	0.162586	+	0.162586i
$289$			1.41758e12i			0.703166i
$290$	−5.44861e10	+	1.29293e12i	−0.0265641	+	0.630355i
$291$	1.78119e12			0.853584
$292$	7.69997e11	−	7.69997e11i	0.362723	−	0.362723i
$293$	−2.43470e12	−	2.43470e12i	−1.12748	−	1.12748i	−0.990586	−	0.136891i	$-0.956289\pi$
$293$	−2.43470e12	−	2.43470e12i	−1.12748	−	1.12748i	−0.136891	−	0.990586i	$-0.543711\pi$
$294$			1.99238e12i			0.907058i
$295$	1.30539e12	−	1.19981e12i	0.584291	−	0.537037i
$296$	−2.37618e12			−1.04573
$297$	−8.89963e11	+	8.89963e11i	−0.385114	+	0.385114i
$298$	−1.45694e12	−	1.45694e12i	−0.619954	−	0.619954i
$299$		−	6.72701e11i		−	0.281492i
$300$	5.66842e11	+	6.71389e11i	0.233268	+	0.276292i
$301$	3.45585e12			1.39869
$302$	−1.50724e11	+	1.50724e11i	−0.0599994	+	0.0599994i
$303$	5.86757e11	+	5.86757e11i	0.229745	+	0.229745i
$304$			7.41469e11i			0.285578i
$305$	−3.52802e11	−	3.83846e11i	−0.133669	−	0.145431i
$306$	4.99590e11			0.186211
$307$	−2.90231e12	+	2.90231e12i	−1.06427	+	1.06427i	−0.0664846	+	0.997787i	$0.521178\pi$
$307$	−2.90231e12	+	2.90231e12i	−1.06427	+	1.06427i	−0.997787	+	0.0664846i	$0.978822\pi$
$308$	−5.79186e11	−	5.79186e11i	−0.208961	−	0.208961i
$309$			2.35206e12i			0.834941i
$310$	−1.09185e12	−	4.60123e10i	−0.381377	−	0.0160718i
$311$	−1.45095e12			−0.498714			−0.249357	−	0.968412i	$-0.580219\pi$
$311$	−1.45095e12			−0.498714			−0.249357	+	0.968412i	$0.580219\pi$
$312$	−1.43279e12	+	1.43279e12i	−0.484630	+	0.484630i
$313$	−4.49561e11	−	4.49561e11i	−0.149647	−	0.149647i	0.628314	−	0.777960i	$-0.283746\pi$
$313$	−4.49561e11	−	4.49561e11i	−0.149647	−	0.149647i	−0.777960	+	0.628314i	$0.783746\pi$
$314$		−	1.57064e12i		−	0.514551i
$315$	−5.14588e10	+	1.22109e12i	−0.0165923	+	0.393728i
$316$	−1.10969e12			−0.352182
$317$	3.92483e12	−	3.92483e12i	1.22610	−	1.22610i	0.260669	−	0.965428i	$-0.416057\pi$
$317$	3.92483e12	−	3.92483e12i	1.22610	−	1.22610i	0.965428	−	0.260669i	$-0.0839430\pi$
$318$	−8.62626e11	−	8.62626e11i	−0.265269	−	0.265269i
$319$			8.74144e11i			0.264624i
$320$	−7.02032e11	+	6.45255e11i	−0.209222	+	0.192301i
$321$	−1.34275e12			−0.393977
$322$	9.56066e11	−	9.56066e11i	0.276190	−	0.276190i
$323$	3.10726e11	+	3.10726e11i	0.0883822	+	0.0883822i
$324$		−	9.65920e11i		−	0.270530i
$325$	3.28734e12	−	2.77544e12i	0.906626	−	0.765448i
$326$	−3.77525e12			−1.02532
$327$	3.93186e12	−	3.93186e12i	1.05162	−	1.05162i
$328$	2.40609e12	+	2.40609e12i	0.633786	+	0.633786i
$329$		−	1.93601e12i		−	0.502261i
$330$	1.34024e12	+	1.45817e12i	0.342462	+	0.372596i
$331$	−2.40408e12			−0.605074			−0.302537	−	0.953138i	$-0.597834\pi$
$331$	−2.40408e12			−0.605074			−0.302537	+	0.953138i	$0.597834\pi$
$332$	2.03851e12	−	2.03851e12i	0.505385	−	0.505385i
$333$	−1.26685e12	−	1.26685e12i	−0.309387	−	0.309387i
$334$			1.19879e12i			0.288411i
$335$	−2.99784e12	−	1.26334e11i	−0.710533	−	0.0299430i
$336$	−6.20623e12			−1.44921
$337$	−2.22345e12	+	2.22345e12i	−0.511538	+	0.511538i	−0.914998	−	0.403459i	$-0.867808\pi$
$337$	−2.22345e12	+	2.22345e12i	−0.511538	+	0.511538i	0.403459	+	0.914998i	$0.367808\pi$
$338$	−1.52040e12	−	1.52040e12i	−0.344647	−	0.344647i
$339$			5.12441e11i			0.114458i
$340$	4.46022e10	−	1.05839e12i	0.00981661	−	0.232944i
$341$	−7.38195e11			−0.160103
$342$	−2.59411e11	+	2.59411e11i	−0.0554444	+	0.0554444i
$343$	−4.70241e11	−	4.70241e11i	−0.0990490	−	0.0990490i
$344$			3.34293e12i			0.693960i
$345$	−7.21353e11	+	6.63014e11i	−0.147589	+	0.135652i
$346$	1.88910e12			0.380955
$347$	−1.48717e11	+	1.48717e11i	−0.0295606	+	0.0295606i	−0.721733	−	0.692172i	$-0.756654\pi$
$347$	−1.48717e11	+	1.48717e11i	−0.0295606	+	0.0295606i	0.692172	+	0.721733i	$0.256654\pi$
$348$	−6.89001e11	−	6.89001e11i	−0.134997	−	0.134997i
$349$		−	9.32446e12i		−	1.80093i	−0.434929	−	0.900465i	$-0.643227\pi$
$349$		−	9.32446e12i		−	1.80093i	0.434929	−	0.900465i	$-0.356773\pi$
$350$	8.61665e12	+	7.27530e11i	1.64058	+	0.138519i
$351$	−6.86925e12			−1.28936
$352$	1.53963e12	−	1.53963e12i	0.284907	−	0.284907i
$353$	−2.60364e12	−	2.60364e12i	−0.475016	−	0.475016i	0.428518	−	0.903533i	$-0.359036\pi$
$353$	−2.60364e12	−	2.60364e12i	−0.475016	−	0.475016i	−0.903533	+	0.428518i	$0.859036\pi$
$354$			4.45469e12i			0.801310i
$355$	−6.15943e12	−	6.70141e12i	−1.09244	−	1.18857i
$356$	−2.36508e12			−0.413615
$357$	−2.60083e12	+	2.60083e12i	−0.448509	+	0.448509i
$358$	4.54399e12	+	4.54399e12i	0.772721	+	0.772721i
$359$		−	7.07878e12i		−	1.18710i	−0.804798	−	0.593548i	$-0.797727\pi$
$359$		−	7.07878e12i		−	1.18710i	0.804798	−	0.593548i	$-0.202273\pi$
$360$	−1.18119e12	−	4.97774e10i	−0.195348	−	0.00823226i
$361$	−3.22688e11			−0.0526316
$362$	6.81063e12	−	6.81063e12i	1.09558	−	1.09558i
$363$	−2.81984e12	−	2.81984e12i	−0.447395	−	0.447395i
$364$		−	4.47050e12i		−	0.699599i
$365$	−3.26964e11	+	7.75870e12i	−0.0504702	+	1.19764i
$366$	1.30989e12			0.199448
$367$	−3.87054e11	+	3.87054e11i	−0.0581355	+	0.0581355i	−0.735577	−	0.677441i	$-0.763089\pi$
$367$	−3.87054e11	+	3.87054e11i	−0.0581355	+	0.0581355i	0.677441	+	0.735577i	$0.263089\pi$
$368$	1.40932e12	+	1.40932e12i	0.208819	+	0.208819i
$369$			2.56558e12i			0.375020i
$370$	−9.33279e12	+	8.57801e12i	−1.34587	+	1.23702i
$371$	−3.59799e12			−0.511906
$372$	5.81846e11	−	5.81846e11i	0.0816757	−	0.0816757i
$373$	−1.59996e12	−	1.59996e12i	−0.221598	−	0.221598i	0.587573	−	0.809171i	$-0.300083\pi$
$373$	−1.59996e12	−	1.59996e12i	−0.221598	−	0.221598i	−0.809171	+	0.587573i	$0.800083\pi$
$374$		−	2.38772e12i		−	0.326306i
$375$	−6.21618e12	−	7.89621e11i	−0.838238	−	0.106479i
$376$	1.87275e12			0.249196
$377$	−3.37358e12	+	3.37358e12i	−0.442980	+	0.442980i
$378$	−9.76282e12	−	9.76282e12i	−1.26508	−	1.26508i
$379$		−	7.95902e12i		−	1.01780i	−0.860825	−	0.508901i	$-0.830052\pi$
$379$		−	7.95902e12i		−	1.01780i	0.860825	−	0.508901i	$-0.169948\pi$
$380$	5.26407e11	+	5.72726e11i	0.0664361	+	0.0722818i
$381$	−9.23029e12			−1.14972
$382$	−8.60724e12	+	8.60724e12i	−1.05815	+	1.05815i
$383$	−5.02552e12	−	5.02552e12i	−0.609799	−	0.609799i	0.333094	−	0.942894i	$-0.391907\pi$
$383$	−5.02552e12	−	5.02552e12i	−0.609799	−	0.609799i	−0.942894	+	0.333094i	$0.891907\pi$
$384$		−	8.06728e12i		−	0.966209i
$385$	5.83604e12	+	2.45940e11i	0.689946	+	0.0290754i
$386$	5.59942e12			0.653441
$387$	−1.78226e12	+	1.78226e12i	−0.205313	+	0.205313i
$388$	−2.68798e12	−	2.68798e12i	−0.305680	−	0.305680i
$389$		−	1.18313e13i		−	1.32827i	−0.747614	−	0.664134i	$-0.768800\pi$
$389$		−	1.18313e13i		−	1.32827i	0.747614	−	0.664134i	$-0.231200\pi$
$390$	−4.55124e11	+	1.07999e13i	−0.0504436	+	1.19700i
$391$	1.18120e12			0.129253
$392$	−4.01931e12	+	4.01931e12i	−0.434231	+	0.434231i
$393$	−4.82593e12	−	4.82593e12i	−0.514776	−	0.514776i
$394$			1.81497e13i			1.91156i
$395$	5.82639e12	−	5.35518e12i	0.605918	−	0.556914i
$396$	5.97399e11			0.0613464
$397$	−5.53707e12	+	5.53707e12i	−0.561471	+	0.561471i	−0.929725	−	0.368254i	$-0.879956\pi$
$397$	−5.53707e12	+	5.53707e12i	−0.561471	+	0.561471i	0.368254	+	0.929725i	$0.379956\pi$
$398$	−1.49445e11	−	1.49445e11i	−0.0149647	−	0.0149647i
$399$		−	2.70095e12i		−	0.267087i
$400$	−1.07244e12	+	1.27016e13i	−0.104730	+	1.24039i
$401$	1.90215e13			1.83452			0.917259	−	0.398291i	$-0.130397\pi$
$401$	1.90215e13			1.83452			0.917259	+	0.398291i	$0.130397\pi$
$402$	5.33068e12	−	5.33068e12i	0.507753	−	0.507753i
$403$	−2.84891e12	−	2.84891e12i	−0.268012	−	0.268012i
$404$		−	1.77094e12i		−	0.164550i
$405$	4.66136e12	+	5.07152e12i	0.427797	+	0.465439i
$406$	−9.58929e12			−0.869273
$407$	−6.05471e12	+	6.05471e12i	−0.542152	+	0.542152i
$408$	−2.51585e12	−	2.51585e12i	−0.222527	−	0.222527i
$409$			1.98375e13i			1.73329i	0.498929	+	0.866643i	$0.333727\pi$
$409$			1.98375e13i			1.73329i	−0.498929	+	0.866643i	$0.666273\pi$
$410$	1.81362e13	+	7.64290e11i	1.56541	+	0.0659689i
$411$	1.59463e13			1.35972
$412$	3.54947e12	−	3.54947e12i	0.299004	−	0.299004i
$413$	9.29019e12	+	9.29019e12i	0.773169	+	0.773169i
$414$			9.86131e11i			0.0810835i
$415$	−8.65613e11	+	2.05406e13i	−0.0703207	+	1.66868i
$416$	1.18838e13			0.953866
$417$	1.15622e13	−	1.15622e13i	0.916982	−	0.916982i
$418$	1.23982e12	+	1.23982e12i	0.0971576	+	0.0971576i
$419$			1.45812e13i			1.12908i	0.825406	+	0.564539i	$0.190946\pi$
$419$			1.45812e13i			1.12908i	−0.825406	+	0.564539i	$0.809054\pi$
$420$	−4.79382e12	+	4.40612e12i	−0.366805	+	0.337140i
$421$	−5.02625e12			−0.380044			−0.190022	−	0.981780i	$-0.560856\pi$
$421$	−5.02625e12			−0.380044			−0.190022	+	0.981780i	$0.560856\pi$
$422$	−3.30471e12	+	3.30471e12i	−0.246929	+	0.246929i
$423$	9.98447e11	+	9.98447e11i	0.0737264	+	0.0737264i
$424$		−	3.48042e12i		−	0.253982i
$425$	4.87342e12	+	5.77227e12i	0.351471	+	0.416295i
$426$	2.28688e13			1.63003
$427$	2.73176e12	−	2.73176e12i	0.192443	−	0.192443i
$428$	2.02633e12	+	2.02633e12i	0.141089	+	0.141089i
$429$			7.30175e12i			0.502505i
$430$	1.20680e13	+	1.31298e13i	0.820902	+	0.893135i
$431$	2.06517e13			1.38858			0.694288	−	0.719697i	$-0.255719\pi$
$431$	2.06517e13			1.38858			0.694288	+	0.719697i	$0.255719\pi$
$432$	1.43912e13	−	1.43912e13i	0.956484	−	0.956484i
$433$	−8.70581e12	−	8.70581e12i	−0.571965	−	0.571965i	0.360712	−	0.932677i	$-0.382534\pi$
$433$	−8.70581e12	−	8.70581e12i	−0.571965	−	0.571965i	−0.932677	+	0.360712i	$0.882534\pi$
$434$		−	8.09794e12i		−	0.525928i
$435$	6.94256e12	+	2.92571e11i	0.445732	+	0.0187838i
$436$	−1.18671e13			−0.753201
$437$	−6.13336e11	+	6.13336e11i	−0.0384850	+	0.0384850i
$438$	−1.37963e13	−	1.37963e13i	−0.855840	−	0.855840i
$439$		−	1.08556e13i		−	0.665782i	−0.942965	−	0.332891i	$-0.891976\pi$
$439$		−	1.08556e13i		−	0.665782i	0.942965	−	0.332891i	$-0.108024\pi$
$440$	−2.37904e11	+	5.64535e12i	−0.0144257	+	0.342316i
$441$	−4.28574e12			−0.256941
$442$	9.21490e12	−	9.21490e12i	0.546234	−	0.546234i
$443$	−1.80843e13	−	1.80843e13i	−1.05995	−	1.05995i	−0.998085	−	0.0618618i	$-0.980296\pi$
$443$	−1.80843e13	−	1.80843e13i	−1.05995	−	1.05995i	−0.0618618	−	0.998085i	$-0.519704\pi$
$444$		−	9.54465e12i		−	0.553153i
$445$	1.24177e13	−	1.14135e13i	0.711611	−	0.654060i
$446$	−3.52941e13			−1.99999
$447$	−7.82322e12	+	7.82322e12i	−0.438377	+	0.438377i
$448$	−4.99622e12	−	4.99622e12i	−0.276855	−	0.276855i
$449$		−	1.99105e13i		−	1.09106i	−0.838091	−	0.545531i	$-0.816328\pi$
$449$		−	1.99105e13i		−	1.09106i	0.838091	−	0.545531i	$-0.183672\pi$
$450$	−4.81901e12	+	4.06860e12i	−0.261153	+	0.220487i
$451$	1.22618e13			0.657163
$452$	7.73319e11	−	7.73319e11i	0.0409889	−	0.0409889i
$453$	8.09332e11	+	8.09332e11i	0.0424264	+	0.0424264i
$454$			3.46763e13i			1.79785i
$455$	2.15738e13	+	2.34721e13i	1.10629	+	1.20364i
$456$	2.61270e12			0.132515
$457$	1.41506e13	−	1.41506e13i	0.709895	−	0.709895i	−0.256618	−	0.966513i	$-0.582608\pi$
$457$	1.41506e13	−	1.41506e13i	0.709895	−	0.709895i	0.966513	+	0.256618i	$0.0826082\pi$
$458$	2.11193e13	+	2.11193e13i	1.04798	+	1.04798i
$459$		−	1.20618e13i		−	0.592035i
$460$	2.08913e12	+	8.80394e10i	0.101433	+	0.00427453i
$461$	2.73335e13			1.31278			0.656389	−	0.754423i	$-0.272083\pi$
$461$	2.73335e13			1.31278			0.656389	+	0.754423i	$0.272083\pi$
$462$	−1.03775e13	+	1.03775e13i	−0.493041	+	0.493041i
$463$	2.32832e13	+	2.32832e13i	1.09430	+	1.09430i	0.995064	+	0.0992373i	$0.0316403\pi$
$463$	2.32832e13	+	2.32832e13i	1.09430	+	1.09430i	0.0992373	+	0.995064i	$0.468360\pi$
$464$		−	1.41354e13i		−	0.657230i
$465$	−2.47069e11	+	5.86284e12i	−0.0113646	+	0.269677i
$466$	−7.62232e12			−0.346863
$467$	1.13442e13	−	1.13442e13i	0.510726	−	0.510726i	−0.404023	−	0.914749i	$-0.632388\pi$
$467$	1.13442e13	−	1.13442e13i	0.510726	−	0.510726i	0.914749	+	0.404023i	$0.132388\pi$
$468$	2.30554e12	+	2.30554e12i	0.102694	+	0.102694i
$469$		−	2.22341e13i		−	0.979842i
$470$	7.35552e12	−	6.76064e12i	0.320718	−	0.294780i
$471$	−8.43378e12			−0.363846
$472$	−8.98662e12	+	8.98662e12i	−0.383607	+	0.383607i
$473$	8.51806e12	+	8.51806e12i	0.359778	+	0.359778i
$474$			1.98828e13i			0.830970i
$475$	−5.52775e12	−	4.66725e11i	−0.228602	−	0.0193016i
$476$	7.84977e12			0.321235
$477$	1.85557e12	−	1.85557e12i	0.0751423	−	0.0751423i
$478$	−1.90845e13	−	1.90845e13i	−0.764787	−	0.764787i
$479$		−	8.28590e12i		−	0.328596i	−0.986411	−	0.164298i	$-0.947464\pi$
$479$		−	8.28590e12i		−	0.328596i	0.986411	−	0.164298i	$-0.0525358\pi$
$480$	−1.17126e13	−	1.27432e13i	−0.459672	−	0.500119i
$481$	−4.67338e13			−1.81512
$482$	3.01313e12	−	3.01313e12i	0.115820	−	0.115820i
$483$	−5.13373e12	−	5.13373e12i	−0.195298	−	0.195298i
$484$			8.51078e12i			0.320437i
$485$	2.70848e13	+	1.14140e12i	1.00929	+	0.0425332i
$486$	1.79001e13			0.660196
$487$	2.58009e13	−	2.58009e13i	0.941869	−	0.941869i	−0.0565315	−	0.998401i	$-0.518004\pi$
$487$	2.58009e13	−	2.58009e13i	0.941869	−	0.941869i	0.998401	+	0.0565315i	$0.0180041\pi$
$488$	2.64249e12	+	2.64249e12i	0.0954805	+	0.0954805i
$489$			2.02717e13i			0.725014i
$490$	−1.27673e12	+	3.02961e13i	−0.0451978	+	1.07252i
$491$	−4.06699e13			−1.42517			−0.712584	−	0.701587i	$-0.752475\pi$
$491$	−4.06699e13			−1.42517			−0.712584	+	0.701587i	$0.752475\pi$
$492$	−9.66479e12	+	9.66479e12i	−0.335248	+	0.335248i
$493$	−5.92368e12	−	5.92368e12i	−0.203403	−	0.203403i
$494$			9.56964e12i			0.325283i
$495$	−3.13662e12	+	2.88294e12i	−0.105545	+	0.0970086i
$496$	1.19370e13			0.397637
$497$	4.76926e13	−	4.76926e13i	1.57278	−	1.57278i
$498$	−3.65248e13	−	3.65248e13i	−1.19245	−	1.19245i
$499$			2.07759e13i			0.671517i	0.941948	+	0.335758i	$0.108993\pi$
$499$			2.07759e13i			0.671517i	−0.941948	+	0.335758i	$0.891007\pi$
$500$	8.18917e12	+	1.05724e13i	0.262053	+	0.338316i
$501$	6.43709e12			0.203939
$502$	1.59167e13	−	1.59167e13i	0.499270	−	0.499270i
$503$	3.45589e12	+	3.45589e12i	0.107330	+	0.107330i	0.758732	−	0.651403i	$-0.225819\pi$
$503$	3.45589e12	+	3.45589e12i	0.107330	+	0.107330i	−0.651403	+	0.758732i	$0.725819\pi$
$504$		−	8.76058e12i		−	0.269389i
$505$	8.54624e12	+	9.29823e12i	0.260207	+	0.283102i
$506$	4.71307e12			0.142086
$507$	−8.16400e12	+	8.16400e12i	−0.243704	+	0.243704i
$508$	1.39293e13	+	1.39293e13i	0.411729	+	0.411729i
$509$		−	2.83330e13i		−	0.829285i	−0.909985	−	0.414642i	$-0.863907\pi$
$509$		−	2.83330e13i		−	0.829285i	0.909985	−	0.414642i	$-0.136093\pi$
$510$	−1.89636e13	−	7.99154e11i	−0.549628	−	0.0231622i
$511$	−5.75441e13			−1.65157
$512$	−3.72594e12	+	3.72594e12i	−0.105898	+	0.105898i
$513$	6.26305e12	+	6.26305e12i	0.176278	+	0.176278i
$514$			3.75120e13i			1.04557i
$515$	−1.50721e12	+	3.57654e13i	−0.0416043	+	0.987250i
$516$	−1.34279e13			−0.367078
$517$	4.77194e12	−	4.77194e12i	0.129194	−	0.129194i
$518$	−6.64197e13	−	6.64197e13i	−1.78093	−	1.78093i
$519$		−	1.01438e13i		−	0.269378i
$520$	−2.27052e13	+	2.08689e13i	−0.597184	+	0.548887i
$521$	−1.63463e12			−0.0425825			−0.0212913	−	0.999773i	$-0.506778\pi$
$521$	−1.63463e12			−0.0425825			−0.0212913	+	0.999773i	$0.506778\pi$
$522$	4.94542e12	−	4.94542e12i	0.127600	−	0.127600i
$523$	−1.88418e13	−	1.88418e13i	−0.481521	−	0.481521i	0.424096	−	0.905617i	$-0.360592\pi$
$523$	−1.88418e13	−	1.88418e13i	−0.481521	−	0.481521i	−0.905617	+	0.424096i	$0.860592\pi$
$524$			1.45655e13i			0.368697i
$525$	3.90657e12	−	4.62683e13i	0.0979489	−	1.16008i
$526$	−3.72558e11			−0.00925262
$527$	5.00242e12	−	5.00242e12i	0.123063	−	0.123063i
$528$	−1.52973e13	−	1.52973e13i	−0.372773	−	0.372773i
$529$		−	3.90950e13i		−	0.943718i
$530$	−1.25643e13	−	1.36699e13i	−0.300441	−	0.326878i
$531$	−9.58233e12			−0.226986
$532$	−4.07598e12	+	4.07598e12i	−0.0956476	+	0.0956476i
$533$	4.73220e13	+	4.73220e13i	1.10009	+	1.10009i
$534$			4.23760e13i			0.975920i
$535$	−2.04179e13	−	8.60442e11i	−0.465846	−	0.0196315i
$536$	2.15076e13			0.486148
$537$	2.43996e13	−	2.43996e13i	0.546401	−	0.546401i
$538$	−6.24502e12	−	6.24502e12i	−0.138555	−	0.138555i
$539$			2.04831e13i			0.450248i
$540$	8.99010e11	−	2.13331e13i	0.0195792	−	0.464606i
$541$	−4.58543e13			−0.989450			−0.494725	−	0.869050i	$-0.664731\pi$
$541$	−4.58543e13			−0.989450			−0.494725	+	0.869050i	$0.664731\pi$
$542$	7.28311e12	−	7.28311e12i	0.155712	−	0.155712i
$543$	−3.65706e13	−	3.65706e13i	−0.774699	−	0.774699i
$544$			2.08668e13i			0.437986i
$545$	6.23075e13	−	5.72683e13i	1.29586	−	1.19106i
$546$	−8.00996e13			−1.65070
$547$	−4.54090e13	+	4.54090e13i	−0.927268	+	0.927268i	−0.997529	−	0.0702605i	$-0.977617\pi$
$547$	−4.54090e13	+	4.54090e13i	−0.927268	+	0.927268i	0.0702605	+	0.997529i	$0.477617\pi$
$548$	−2.40644e13	−	2.40644e13i	−0.486936	−	0.486936i
$549$			2.81766e12i			0.0564971i
$550$	1.94453e13	+	2.30318e13i	0.386368	+	0.457629i
$551$	6.15172e12			0.121126
$552$	4.96598e12	−	4.96598e12i	0.0968969	−	0.0968969i
$553$	4.14653e13	+	4.14653e13i	0.801786	+	0.801786i
$554$		−	1.37987e13i		−	0.264416i
$555$	4.60608e13	+	5.01137e13i	0.874715	+	0.951682i
$556$	−3.48968e13			−0.656768
$557$	4.65490e13	−	4.65490e13i	0.868229	−	0.868229i	−0.124047	−	0.992276i	$-0.539587\pi$
$557$	4.65490e13	−	4.65490e13i	0.868229	−	0.868229i	0.992276	+	0.124047i	$0.0395874\pi$
$558$	4.17629e12	+	4.17629e12i	0.0772005	+	0.0772005i
$559$			6.57474e13i			1.20453i
$560$	−9.43720e13	−	3.97698e12i	−1.71357	−	0.0722127i
$561$	−1.28212e13			−0.230735
$562$	6.21294e13	−	6.21294e13i	1.10819	−	1.10819i
$563$	−1.87137e12	−	1.87137e12i	−0.0330839	−	0.0330839i	0.690371	−	0.723455i	$-0.257447\pi$
$563$	−1.87137e12	−	1.87137e12i	−0.0330839	−	0.0330839i	−0.723455	+	0.690371i	$0.757447\pi$
$564$			7.52248e12i			0.131815i
$565$	−3.28375e11	+	7.79218e12i	−0.00570331	+	0.135337i
$566$	1.19753e14			2.06159
$567$	−3.60930e13	+	3.60930e13i	−0.615896	+	0.615896i
$568$	4.61342e13	+	4.61342e13i	0.780336	+	0.780336i
$569$		−	7.07320e13i		−	1.18592i	−0.805232	−	0.592959i	$-0.797959\pi$
$569$		−	7.07320e13i		−	1.18592i	0.805232	−	0.592959i	$-0.202041\pi$
$570$	1.02618e13	−	9.43184e12i	0.170548	−	0.156755i
$571$	−7.32748e13			−1.20719			−0.603593	−	0.797292i	$-0.706265\pi$
$571$	−7.32748e13			−1.20719			−0.603593	+	0.797292i	$0.706265\pi$
$572$	1.10190e13	−	1.10190e13i	0.179954	−	0.179954i
$573$	4.62178e13	+	4.62178e13i	0.748231	+	0.748231i
$574$			1.34511e14i			2.15874i
$575$	−1.13938e13	+	9.61955e12i	−0.181271	+	0.153044i
$576$	5.15333e12			0.0812785
$577$	−3.88679e13	+	3.88679e13i	−0.607732	+	0.607732i	−0.942353	−	0.334621i	$-0.891392\pi$
$577$	−3.88679e13	+	3.88679e13i	−0.607732	+	0.607732i	0.334621	+	0.942353i	$0.391392\pi$
$578$	−3.83298e13	−	3.83298e13i	−0.594152	−	0.594152i
$579$		−	3.00669e13i		−	0.462057i
$580$	−1.00354e13	−	1.09185e13i	−0.152896	−	0.166350i
$581$	−1.52344e14			−2.30115
$582$	−4.81616e13	+	4.81616e13i	−0.721250	+	0.721250i
$583$	−8.86842e12	−	8.86842e12i	−0.131675	−	0.131675i
$584$		−	5.56638e13i		−	0.819424i
$585$	−2.32312e13	−	9.79001e11i	−0.339073	−	0.0142891i
$586$	1.31664e14			1.90536
$587$	−3.72230e13	+	3.72230e13i	−0.534099	+	0.534099i	−0.921789	−	0.387691i	$-0.873273\pi$
$587$	−3.72230e13	+	3.72230e13i	−0.534099	+	0.534099i	0.387691	+	0.921789i	$0.373273\pi$
$588$	−1.61448e13	−	1.61448e13i	−0.229692	−	0.229692i
$589$			5.19499e12i			0.0732839i
$590$	−2.85459e12	+	6.77380e13i	−0.0399285	+	0.947485i
$591$	9.74572e13			1.35169
$592$	9.79079e13	−	9.79079e13i	1.34651	−	1.34651i
$593$	2.99111e13	+	2.99111e13i	0.407905	+	0.407905i	0.881007	−	0.473102i	$-0.156866\pi$
$593$	2.99111e13	+	2.99111e13i	0.407905	+	0.407905i	−0.473102	+	0.881007i	$0.656866\pi$
$594$		−	4.81273e13i		−	0.650817i
$595$	−4.12149e13	+	3.78816e13i	−0.552674	+	0.507977i
$596$	2.36119e13			0.313978
$597$	−8.02467e11	+	8.02467e11i	−0.0105817	+	0.0105817i
$598$	1.81891e13	+	1.81891e13i	0.237851	+	0.237851i
$599$			1.26058e14i			1.63470i	0.576142	+	0.817350i	$0.304558\pi$
$599$			1.26058e14i			1.63470i	−0.576142	+	0.817350i	$0.695442\pi$
$600$	4.47564e13	+	3.77892e12i	0.575571	+	0.0485973i
$601$	−2.36867e12			−0.0302087			−0.0151044	−	0.999886i	$-0.504808\pi$
$601$	−2.36867e12			−0.0302087			−0.0151044	+	0.999886i	$0.504808\pi$
$602$	−9.34425e13	+	9.34425e13i	−1.18185	+	1.18185i
$603$	1.14667e13	+	1.14667e13i	0.143830	+	0.143830i
$604$		−	2.44271e12i		−	0.0303870i
$605$	−4.10715e13	−	4.46855e13i	−0.506715	−	0.551302i
$606$	−3.17306e13			−0.388253
$607$	9.07375e13	−	9.07375e13i	1.10114	−	1.10114i	0.106868	−	0.994273i	$-0.465918\pi$
$607$	9.07375e13	−	9.07375e13i	1.10114	−	1.10114i	0.994273	−	0.106868i	$-0.0340824\pi$
$608$	−1.08350e13	−	1.08350e13i	−0.130410	−	0.130410i
$609$			5.14910e13i			0.614674i
$610$	1.99182e13	+	8.39383e11i	0.235831	+	0.00993828i
$611$	3.68326e13			0.432540
$612$	−4.04831e12	+	4.04831e12i	−0.0471538	+	0.0471538i
$613$	−5.53290e13	−	5.53290e13i	−0.639220	−	0.639220i	0.311143	−	0.950363i	$-0.399288\pi$
$613$	−5.53290e13	−	5.53290e13i	−0.639220	−	0.639220i	−0.950363	+	0.311143i	$0.899288\pi$
$614$		−	1.56951e14i		−	1.79855i
$615$	4.10396e12	−	9.73851e13i	0.0466474	−	1.10692i
$616$	−4.18699e13			−0.472062
$617$	−3.86673e13	+	3.86673e13i	−0.432432	+	0.432432i	−0.889455	−	0.457023i	$-0.848916\pi$
$617$	−3.86673e13	+	3.86673e13i	−0.432432	+	0.432432i	0.457023	+	0.889455i	$0.348916\pi$
$618$	−6.35971e13	−	6.35971e13i	−0.705497	−	0.705497i
$619$		−	2.19139e13i		−	0.241139i	−0.992705	−	0.120569i	$-0.961528\pi$
$619$		−	2.19139e13i		−	0.241139i	0.992705	−	0.120569i	$-0.0384720\pi$
$620$	9.22040e12	−	8.47470e12i	0.100645	−	0.0925051i
$621$	2.38085e13			0.257795
$622$	3.92323e13	−	3.92323e13i	0.421397	−	0.421397i
$623$	8.83747e13	+	8.83747e13i	0.941646	+	0.941646i
$624$		−	1.18073e14i		−	1.24804i
$625$	−9.40173e13	−	1.59903e13i	−0.985843	−	0.167671i
$626$	2.43113e13			0.252893
$627$	6.65738e12	−	6.65738e12i	0.0687014	−	0.0687014i
$628$	1.27273e13	+	1.27273e13i	0.130298	+	0.130298i
$629$		−	8.20601e13i		−	0.833448i
$630$	−3.16257e13	−	3.44085e13i	−0.318667	−	0.346707i
$631$	−8.49708e13			−0.849421			−0.424710	−	0.905329i	$-0.639624\pi$
$631$	−8.49708e13			−0.849421			−0.424710	+	0.905329i	$0.639624\pi$
$632$	−4.01103e13	+	4.01103e13i	−0.397806	+	0.397806i
$633$	1.77451e13	+	1.77451e13i	0.174606	+	0.174606i
$634$			2.12247e14i			2.07202i
$635$	−1.40356e14	−	5.91482e12i	−1.35945	−	0.0572892i
$636$	1.39802e13			0.134347
$637$	−7.90502e13	+	7.90502e13i	−0.753712	+	0.753712i
$638$	−2.36359e13	−	2.36359e13i	−0.223599	−	0.223599i
$639$			4.91923e13i			0.461735i
$640$	5.16956e12	−	1.22671e14i	0.0481452	−	1.14246i
$641$	−1.44212e14			−1.33264			−0.666320	−	0.745666i	$-0.732131\pi$
$641$	−1.44212e14			−1.33264			−0.666320	+	0.745666i	$0.732131\pi$
$642$	3.63066e13	−	3.63066e13i	0.332897	−	0.332897i
$643$	9.42018e13	+	9.42018e13i	0.857047	+	0.857047i	0.990989	−	0.133942i	$-0.0427637\pi$
$643$	9.42018e13	+	9.42018e13i	0.857047	+	0.857047i	−0.133942	+	0.990989i	$0.542764\pi$
$644$			1.54945e13i			0.139878i
$645$	7.05025e13	−	6.48006e13i	0.631547	−	0.580471i
$646$	−1.68034e13			−0.149360
$647$	9.55149e13	−	9.55149e13i	0.842461	−	0.842461i	−0.146717	−	0.989178i	$-0.546871\pi$
$647$	9.55149e13	−	9.55149e13i	0.842461	−	0.842461i	0.989178	+	0.146717i	$0.0468708\pi$
$648$	−3.49136e13	−	3.49136e13i	−0.305577	−	0.305577i
$649$			4.57974e13i			0.397756i
$650$	−1.38412e13	+	1.63931e14i	−0.119291	+	1.41285i
$651$	−4.34830e13			−0.371890
$652$	3.05918e13	−	3.05918e13i	0.259638	−	0.259638i
$653$	1.72540e13	+	1.72540e13i	0.145319	+	0.145319i	0.776023	−	0.630704i	$-0.217234\pi$
$653$	1.72540e13	+	1.72540e13i	0.145319	+	0.145319i	−0.630704	+	0.776023i	$0.717234\pi$
$654$			2.12627e14i			1.77717i
$655$	−7.02907e13	−	7.64757e13i	−0.583031	−	0.634332i
$656$	−1.98281e14			−1.63215
$657$	2.96768e13	−	2.96768e13i	0.242432	−	0.242432i
$658$	5.23478e13	+	5.23478e13i	0.424393	+	0.424393i
$659$			4.28754e13i			0.344970i	0.985012	+	0.172485i	$0.0551797\pi$
$659$			4.28754e13i			0.344970i	−0.985012	+	0.172485i	$0.944820\pi$
$660$	−2.26762e13	−	9.55613e11i	−0.181072	−	0.00763066i
$661$	5.63895e13			0.446880			0.223440	−	0.974718i	$-0.428271\pi$
$661$	5.63895e13			0.446880			0.223440	+	0.974718i	$0.428271\pi$
$662$	6.50037e13	−	6.50037e13i	0.511267	−	0.511267i
$663$	−4.94807e13	−	4.94807e13i	−0.386249	−	0.386249i
$664$		−	1.47366e14i		−	1.14171i
$665$	1.73078e12	−	4.10707e13i	0.0133087	−	0.315809i
$666$	6.85083e13			0.522844
$667$	1.16926e13	−	1.16926e13i	0.0885694	−	0.0885694i
$668$	−9.71415e12	−	9.71415e12i	−0.0730335	−	0.0730335i
$669$			1.89517e14i			1.41422i
$670$	8.44743e13	−	7.76425e13i	0.625678	−	0.575076i
$671$	1.34666e13			0.0990023
$672$	9.06912e13	−	9.06912e13i	0.661787	−	0.661787i
$673$	−2.29087e13	−	2.29087e13i	−0.165930	−	0.165930i	0.619258	−	0.785188i	$-0.287434\pi$
$673$	−2.29087e13	−	2.29087e13i	−0.165930	−	0.165930i	−0.785188	+	0.619258i	$0.787434\pi$
$674$		−	1.20240e14i		−	0.864466i
$675$	9.82295e13	+	1.16347e14i	0.701008	+	0.830302i
$676$	2.46404e13			0.174548
$677$	−1.00291e14	+	1.00291e14i	−0.705211	+	0.705211i	−0.965524	−	0.260313i	$-0.916174\pi$
$677$	−1.00291e14	+	1.00291e14i	−0.705211	+	0.705211i	0.260313	+	0.965524i	$0.416174\pi$
$678$	−1.38558e13	−	1.38558e13i	−0.0967129	−	0.0967129i
$679$			2.00881e14i			1.39184i
$680$	−3.66438e13	−	3.98681e13i	−0.252032	−	0.274209i
$681$	1.86199e14			1.27128
$682$	1.99600e13	−	1.99600e13i	0.135282	−	0.135282i
$683$	−5.17923e13	−	5.17923e13i	−0.348467	−	0.348467i	0.511071	−	0.859538i	$-0.329249\pi$
$683$	−5.17923e13	−	5.17923e13i	−0.348467	−	0.348467i	−0.859538	+	0.511071i	$0.829249\pi$
$684$		−	4.20415e12i		−	0.0280801i
$685$	2.42480e14	+	1.02185e13i	1.60776	+	0.0677537i
$686$	2.54296e13			0.167386
$687$	1.13403e14	−	1.13403e14i	0.741039	−	0.741039i
$688$	−1.37742e14	−	1.37742e14i	−0.893559	−	0.893559i
$689$		−	6.84516e13i		−	0.440847i
$690$	1.57744e12	−	3.74318e13i	0.0100857	−	0.239329i
$691$	−5.71235e13			−0.362597			−0.181299	−	0.983428i	$-0.558030\pi$
$691$	−5.71235e13			−0.362597			−0.181299	+	0.983428i	$0.558030\pi$
$692$	−1.53079e13	+	1.53079e13i	−0.0964682	+	0.0964682i
$693$	−2.23227e13	−	2.23227e13i	−0.139663	−	0.139663i
$694$		−	8.04230e12i		−	0.0499554i
$695$	1.83224e14	−	1.68406e14i	1.12995	−	1.03856i
$696$	−4.98085e13			−0.304970
$697$	−8.30930e13	+	8.30930e13i	−0.505127	+	0.505127i
$698$	2.52123e14	+	2.52123e14i	1.52173	+	1.52173i
$699$			4.09291e13i			0.245271i
$700$	−7.57184e13	+	6.39276e13i	−0.450517	+	0.380363i
$701$	−1.80356e14			−1.06547			−0.532734	−	0.846283i	$-0.678836\pi$
$701$	−1.80356e14			−1.06547			−0.532734	+	0.846283i	$0.678836\pi$
$702$	1.85737e14	−	1.85737e14i	1.08947	−	1.08947i
$703$	4.26096e13	+	4.26096e13i	0.248159	+	0.248159i
$704$		−	2.46296e13i		−	0.142428i
$705$	−3.63022e13	−	3.94965e13i	−0.208443	−	0.226784i
$706$	1.40799e14			0.802745
$707$	−6.61737e13	+	6.61737e13i	−0.374618	+	0.374618i
$708$	−3.60975e13	−	3.60975e13i	−0.202913	−	0.202913i
$709$			1.46632e14i			0.818461i	0.912431	+	0.409230i	$0.134203\pi$
$709$			1.46632e14i			0.818461i	−0.912431	+	0.409230i	$0.865797\pi$
$710$	3.47743e14	+	1.46545e13i	1.92738	+	0.0812228i
$711$	−4.27692e13			−0.235387
$712$	−8.54870e13	+	8.54870e13i	−0.467197	+	0.467197i
$713$	9.87418e12	+	9.87418e12i	0.0535862	+	0.0535862i
$714$		−	1.40647e14i		−	0.757950i
$715$	−4.67900e12	+	1.11030e14i	−0.0250393	+	0.594172i
$716$	−7.36424e13			−0.391348
$717$	−1.02477e14	+	1.02477e14i	−0.540791	+	0.540791i
$718$	1.91403e14	+	1.91403e14i	1.00306	+	1.00306i
$719$			2.99675e13i			0.155957i	0.996955	+	0.0779787i	$0.0248466\pi$
$719$			2.99675e13i			0.155957i	−0.996955	+	0.0779787i	$0.975153\pi$
$720$	5.07208e13	−	4.66188e13i	0.262134	−	0.240934i
$721$	−2.65262e14			−1.36144
$722$	8.72513e12	−	8.72513e12i	0.0444719	−	0.0444719i
$723$	−1.61794e13	−	1.61794e13i	−0.0818976	−	0.0818976i
$724$			1.10377e14i			0.554861i
$725$	1.05381e14	+	8.89766e12i	0.526106	+	0.0444207i
$726$	1.52491e14			0.756068
$727$	−9.29680e12	+	9.29680e12i	−0.0457785	+	0.0457785i	−0.729625	−	0.683847i	$-0.760306\pi$
$727$	−9.29680e12	+	9.29680e12i	−0.0457785	+	0.0457785i	0.683847	+	0.729625i	$0.260306\pi$
$728$	−1.61588e14	−	1.61588e14i	−0.790229	−	0.790229i
$729$		−	2.26276e14i		−	1.09901i
$730$	−2.00946e14	−	2.18628e14i	−0.969316	−	1.05461i
$731$	−1.15446e14			−0.553086
$732$	−1.06144e13	+	1.06144e13i	−0.0505055	+	0.0505055i
$733$	7.44530e13	+	7.44530e13i	0.351854	+	0.351854i	0.860799	−	0.508945i	$-0.169964\pi$
$733$	7.44530e13	+	7.44530e13i	0.351854	+	0.351854i	−0.508945	+	0.860799i	$0.669964\pi$
$734$		−	2.09311e13i		−	0.0982451i
$735$	1.62679e14	+	6.85556e12i	0.758395	+	0.0319600i
$736$	−4.11885e13			−0.190716
$737$	5.48032e13	−	5.48032e13i	0.252040	−	0.252040i
$738$	−6.93706e13	−	6.93706e13i	−0.316879	−	0.316879i
$739$		−	1.61676e14i		−	0.733540i	−0.930312	−	0.366770i	$-0.880464\pi$
$739$		−	1.61676e14i		−	0.733540i	0.930312	−	0.366770i	$-0.119536\pi$
$740$	6.11626e12	−	1.45136e14i	0.0275630	−	0.654058i
$741$	5.13855e13			0.230012
$742$	9.72858e13	−	9.72858e13i	0.432544	−	0.432544i
$743$	1.33432e14	+	1.33432e14i	0.589272	+	0.589272i	0.937434	−	0.348162i	$-0.113194\pi$
$743$	1.33432e14	+	1.33432e14i	0.589272	+	0.589272i	−0.348162	+	0.937434i	$0.613194\pi$
$744$		−	4.20622e13i		−	0.184513i
$745$	−1.23973e14	+	1.13947e14i	−0.540190	+	0.496502i
$746$	8.65226e13			0.374486
$747$	7.85672e13	−	7.85672e13i	0.337783	−	0.337783i
$748$	1.93483e13	+	1.93483e13i	0.0826295	+	0.0826295i
$749$		−	1.51434e14i		−	0.642412i
$750$	1.89429e14	−	1.46728e14i	0.798254	−	0.618312i
$751$	−8.28332e13			−0.346740			−0.173370	−	0.984857i	$-0.555466\pi$
$751$	−8.28332e13			−0.346740			−0.173370	+	0.984857i	$0.555466\pi$
$752$	−7.71648e13	+	7.71648e13i	−0.320871	+	0.320871i
$753$	−8.54671e13	−	8.54671e13i	−0.353040	−	0.353040i
$754$		−	1.82436e14i		−	0.748606i
$755$	1.17881e13	+	1.28253e13i	0.0480517	+	0.0522798i
$756$	1.58222e14			0.640703
$757$	−3.44246e14	+	3.44246e14i	−1.38481	+	1.38481i	−0.548955	+	0.835852i	$0.684974\pi$
$757$	−3.44246e14	+	3.44246e14i	−1.38481	+	1.38481i	−0.835852	+	0.548955i	$0.815026\pi$
$758$	2.15203e14	+	2.15203e14i	0.860009	+	0.860009i
$759$		−	2.53075e13i		−	0.100471i
$760$	3.97287e13	+	1.67423e12i	0.156688	+	0.00660309i
$761$	3.22135e14			1.26216			0.631080	−	0.775718i	$-0.282612\pi$
$761$	3.22135e14			1.26216			0.631080	+	0.775718i	$0.282612\pi$
$762$	2.49577e14	−	2.49577e14i	0.971471	−	0.971471i
$763$	4.43430e14	+	4.43430e14i	1.71476	+	1.71476i
$764$		−	1.39494e14i		−	0.535904i
$765$	1.71903e12	−	4.07919e13i	0.00656111	−	0.155692i
$766$	2.71769e14			1.03052
$767$	−1.76745e14	+	1.76745e14i	−0.665842	+	0.665842i
$768$	1.72766e14	+	1.72766e14i	0.646626	+	0.646626i
$769$			3.56095e14i			1.32414i	0.749442	+	0.662070i	$0.230322\pi$
$769$			3.56095e14i			1.32414i	−0.749442	+	0.662070i	$0.769678\pi$
$770$	−1.64450e14	+	1.51150e14i	−0.607549	+	0.558413i
$771$	2.01426e14			0.739338
$772$	−4.53736e13	+	4.53736e13i	−0.165469	+	0.165469i
$773$	3.01190e14	+	3.01190e14i	1.09130	+	1.09130i	0.995390	+	0.0959064i	$0.0305749\pi$
$773$	3.01190e14	+	3.01190e14i	1.09130	+	1.09130i	0.0959064	+	0.995390i	$0.469425\pi$
$774$		−	9.63808e13i		−	0.346965i
$775$	−7.51387e12	+	8.89921e13i	−0.0268754	+	0.318304i
$776$	−1.94317e14			−0.690560
$777$	−3.56650e14	+	3.56650e14i	−1.25932	+	1.25932i
$778$	3.19907e14	+	3.19907e14i	1.12234	+	1.12234i
$779$		−	8.62918e13i		−	0.300803i
$780$	−8.38263e13	−	9.12022e13i	−0.290340	−	0.315887i
$781$	2.35108e14			0.809118
$782$	−3.19384e13	+	3.19384e13i	−0.109214	+	0.109214i
$783$	−1.19399e14	−	1.19399e14i	−0.405687	−	0.405687i
$784$		−	3.31222e14i		−	1.11825i
$785$	−1.28244e14	−	5.40441e12i	−0.430218	−	0.0181301i
$786$	2.60976e14			0.869938
$787$	−2.35613e14	+	2.35613e14i	−0.780415	+	0.780415i	−0.979901	−	0.199485i	$-0.936073\pi$
$787$	−2.35613e14	+	2.35613e14i	−0.780415	+	0.780415i	0.199485	+	0.979901i	$0.436073\pi$
$788$	−1.47072e14	−	1.47072e14i	−0.484059	−	0.484059i
$789$			2.00050e12i			0.00654265i
$790$	−1.27410e13	+	3.02338e14i	−0.0414064	+	0.982554i
$791$	−5.77924e13			−0.186633
$792$	2.15933e13	−	2.15933e13i	0.0692936	−	0.0692936i
$793$	5.19715e13	+	5.19715e13i	0.165729	+	0.165729i
$794$		−	2.99433e14i		−	0.948848i
$795$	−7.34023e13	+	6.74659e13i	−0.231139	+	0.212446i
$796$	2.42199e12			0.00757891
$797$	−2.37546e14	+	2.37546e14i	−0.738680	+	0.738680i	−0.972323	−	0.233642i	$-0.924936\pi$
$797$	−2.37546e14	+	2.37546e14i	−0.738680	+	0.738680i	0.233642	+	0.972323i	$0.424936\pi$
$798$	7.30309e13	+	7.30309e13i	0.225680	+	0.225680i
$799$			6.46745e13i			0.198609i
$800$	−1.69936e14	−	2.01279e14i	−0.518605	−	0.614256i
$801$	−9.11537e13			−0.276447
$802$	−5.14320e14	+	5.14320e14i	−1.55011	+	1.55011i
$803$	−1.41836e14	−	1.41836e14i	−0.424824	−	0.424824i
$804$			8.63919e13i			0.257154i
$805$	−7.47738e13	−	8.13533e13i	−0.221192	−	0.240655i
$806$	1.54063e14			0.452921
$807$	−3.35335e13	+	3.35335e13i	−0.0979740	+	0.0979740i
$808$	−6.40114e13	−	6.40114e13i	−0.185866	−	0.185866i
$809$			2.35444e14i			0.679430i	0.940528	+	0.339715i	$0.110331\pi$
$809$			2.35444e14i			0.679430i	−0.940528	+	0.339715i	$0.889669\pi$
$810$	−2.63167e14	−	1.10903e13i	−0.754754	−	0.0318065i
$811$	3.65303e14			1.04124			0.520618	−	0.853790i	$-0.325701\pi$
$811$	3.65303e14			1.04124			0.520618	+	0.853790i	$0.325701\pi$
$812$	7.77046e13	−	7.77046e13i	0.220124	−	0.220124i
$813$	−3.91077e13	−	3.91077e13i	−0.110106	−	0.110106i
$814$		−	3.27426e14i		−	0.916201i
$815$	−1.29902e13	+	3.08252e14i	−0.0361267	+	0.857270i
$816$	2.07325e14			0.573062
$817$	5.99452e13	−	5.99452e13i	0.164681	−	0.164681i
$818$	−5.36385e14	−	5.36385e14i	−1.46457	−	1.46457i
$819$		−	1.72300e14i		−	0.467589i
$820$	−1.53156e14	+	1.40770e14i	−0.413109	+	0.379699i
$821$	−6.66714e14			−1.78741			−0.893705	−	0.448655i	$-0.851903\pi$
$821$	−6.66714e14			−1.78741			−0.893705	+	0.448655i	$0.851903\pi$
$822$	−4.31171e14	+	4.31171e14i	−1.14892	+	1.14892i
$823$	−3.62093e14	−	3.62093e14i	−0.959004	−	0.959004i	0.0401877	−	0.999192i	$-0.487204\pi$
$823$	−3.62093e14	−	3.62093e14i	−0.959004	−	0.959004i	−0.999192	+	0.0401877i	$0.987204\pi$
$824$		−	2.56594e14i		−	0.675477i
$825$	1.23672e14	−	1.04414e14i	0.323595	−	0.273206i
$826$	−5.02393e14			−1.30660
$827$	1.24786e14	−	1.24786e14i	0.322582	−	0.322582i	−0.527175	−	0.849757i	$-0.676749\pi$
$827$	1.24786e14	−	1.24786e14i	0.322582	−	0.322582i	0.849757	+	0.527175i	$0.176749\pi$
$828$	−7.99088e12	−	7.99088e12i	−0.0205325	−	0.0205325i
$829$			6.37781e14i			1.62892i	0.580222	+	0.814458i	$0.302966\pi$
$829$			6.37781e14i			1.62892i	−0.580222	+	0.814458i	$0.697034\pi$
$830$	−5.31990e14	−	5.78801e14i	−1.35056	−	1.46940i
$831$	−7.40938e13			−0.186972
$832$	9.50529e13	−	9.50529e13i	0.238423	−	0.238423i
$833$	−1.38805e14	−	1.38805e14i	−0.346082	−	0.346082i
$834$			6.25260e14i			1.54964i
$835$	9.78824e13	+	4.12492e12i	0.241142	+	0.0101621i
$836$	−2.00932e13			−0.0492059
$837$	1.00830e14	−	1.00830e14i	0.245449	−	0.245449i
$838$	−3.94261e14	−	3.94261e14i	−0.954034	−	0.954034i
$839$		−	6.86733e14i		−	1.65188i	−0.563759	−	0.825940i	$-0.690645\pi$
$839$		−	6.86733e14i		−	1.65188i	0.563759	−	0.825940i	$-0.309355\pi$
$840$	−1.40136e13	+	3.32536e14i	−0.0335084	+	0.795138i
$841$	3.03431e14			0.721239
$842$	1.35905e14	−	1.35905e14i	0.321125	−	0.321125i
$843$	−3.33613e14	−	3.33613e14i	−0.783618	−	0.783618i
$844$		−	5.35579e13i		−	0.125058i
$845$	−1.29373e14	+	1.18910e14i	−0.300304	+	0.276017i
$846$	−5.39939e13			−0.124593
$847$	3.18018e14	−	3.18018e14i	0.729515	−	0.729515i
$848$	1.43407e14	+	1.43407e14i	0.327033	+	0.327033i
$849$		−	6.43029e14i		−	1.45778i
$850$	−2.87848e14	−	2.43039e13i	−0.648737	−	0.0547748i
$851$	1.61977e14			0.362915
$852$	−1.85312e14	+	1.85312e14i	−0.412768	+	0.412768i
$853$	−1.17817e14	−	1.17817e14i	−0.260893	−	0.260893i	0.564524	−	0.825417i	$-0.309060\pi$
$853$	−1.17817e14	−	1.17817e14i	−0.260893	−	0.260893i	−0.825417	+	0.564524i	$0.809060\pi$
$854$			1.47727e14i			0.325216i
$855$	2.02885e13	+	2.20737e13i	0.0444037	+	0.0483109i
$856$	1.46486e14			0.318732
$857$	−4.66329e14	+	4.66329e14i	−1.00876	+	1.00876i	−0.00880027	+	0.999961i	$0.502801\pi$
$857$	−4.66329e14	+	4.66329e14i	−1.00876	+	1.00876i	−0.999961	+	0.00880027i	$0.997199\pi$
$858$	−1.97431e14	−	1.97431e14i	−0.424600	−	0.424600i
$859$		−	7.04652e14i		−	1.50664i	−0.657655	−	0.753319i	$-0.728452\pi$
$859$		−	7.04652e14i		−	1.50664i	0.657655	−	0.753319i	$-0.271548\pi$
$860$	−2.04184e14	−	8.60465e12i	−0.434041	−	0.0182912i
$861$	7.22278e14			1.52647
$862$	−5.58400e14	+	5.58400e14i	−1.17330	+	1.17330i
$863$	−3.68927e14	−	3.68927e14i	−0.770701	−	0.770701i	0.207528	−	0.978229i	$-0.433458\pi$
$863$	−3.68927e14	−	3.68927e14i	−0.770701	−	0.770701i	−0.978229	+	0.207528i	$0.933458\pi$
$864$			4.20594e14i			0.873564i
$865$	6.50018e12	−	1.54246e14i	0.0134229	−	0.318518i
$866$	4.70791e14			0.966583
$867$	−2.05817e14	+	2.05817e14i	−0.420133	+	0.420133i
$868$	6.56198e13	+	6.56198e13i	0.133179	+	0.133179i
$869$			2.04409e14i			0.412479i
$870$	−1.95630e14	+	1.79809e14i	−0.392500	+	0.360757i
$871$	4.23003e14			0.843826
$872$	−4.28941e14	+	4.28941e14i	−0.850775	+	0.850775i
$873$	−1.03599e14	−	1.03599e14i	−0.204307	−	0.204307i
$874$		−	3.31679e13i		−	0.0650370i
$875$	8.90524e13	−	7.01053e14i	0.173622	−	1.36682i
$876$	2.23590e14			0.433444
$877$	6.14436e14	−	6.14436e14i	1.18435	−	1.18435i	0.205739	−	0.978607i	$-0.434040\pi$
$877$	6.14436e14	−	6.14436e14i	1.18435	−	1.18435i	0.978607	−	0.205739i	$-0.0659598\pi$
$878$	2.93524e14	+	2.93524e14i	0.562563	+	0.562563i
$879$		−	7.06985e14i		−	1.34731i
$880$	−2.22808e14	−	2.42413e14i	−0.422199	−	0.459349i
$881$	−4.99505e14			−0.941153			−0.470577	−	0.882359i	$-0.655954\pi$
$881$	−4.99505e14			−0.941153			−0.470577	+	0.882359i	$0.655954\pi$
$882$	1.15882e14	−	1.15882e14i	0.217106	−	0.217106i
$883$	1.65161e14	+	1.65161e14i	0.307683	+	0.307683i	0.844010	−	0.536327i	$-0.180189\pi$
$883$	1.65161e14	+	1.65161e14i	0.307683	+	0.307683i	−0.536327	+	0.844010i	$0.680189\pi$
$884$			1.49342e14i			0.276643i
$885$	3.63729e14	+	1.53281e13i	0.669979	+	0.0282340i
$886$	9.77962e14			1.79124
$887$	2.00070e14	−	2.00070e14i	0.364388	−	0.364388i	−0.501037	−	0.865426i	$-0.667048\pi$
$887$	2.00070e14	−	2.00070e14i	0.364388	−	0.364388i	0.865426	+	0.501037i	$0.167048\pi$
$888$	−3.44996e14	−	3.44996e14i	−0.624811	−	0.624811i
$889$		−	1.04098e15i		−	1.87471i
$890$	−2.71548e13	+	6.44370e14i	−0.0486291	+	1.15395i
$891$	−1.77926e14			−0.316848
$892$	2.85997e14	−	2.85997e14i	0.506452	−	0.506452i
$893$	−3.35821e13	−	3.35821e13i	−0.0591359	−	0.0591359i
$894$		−	4.23063e14i		−	0.740828i
$895$	3.86656e14	−	3.55385e14i	0.673301	−	0.618848i
$896$	9.09817e14			1.57548
$897$	9.76690e13	−	9.76690e13i	0.168188	−	0.168188i
$898$	5.38357e14	+	5.38357e14i	0.921911	+	0.921911i
$899$		−	9.90374e13i		−	0.168656i
$900$	6.08076e12	−	7.20186e13i	0.0102978	−	0.121964i
$901$	1.20195e14			0.202423
$902$	−3.31547e14	+	3.31547e14i	−0.555281	+	0.555281i
$903$	5.01752e14	+	5.01752e14i	0.835700	+	0.835700i
$904$		−	5.59040e13i		−	0.0925977i
$905$	−5.32658e14	−	5.79528e14i	−0.877417	−	0.954621i
$906$	−4.37670e13			−0.0716977
$907$	−7.11286e14	+	7.11286e14i	−1.15880	+	1.15880i	−0.174063	+	0.984735i	$0.555690\pi$
$907$	−7.11286e14	+	7.11286e14i	−1.15880	+	1.15880i	−0.984735	+	0.174063i	$0.944310\pi$
$908$	−2.80992e14	−	2.80992e14i	−0.455265	−	0.455265i
$909$		−	6.82546e13i		−	0.109980i
$910$	−1.21800e15	−	5.13282e13i	−1.95181	−	0.0822525i
$911$	9.07064e14			1.44559			0.722797	−	0.691061i	$-0.242856\pi$
$911$	9.07064e14			1.44559			0.722797	+	0.691061i	$0.242856\pi$
$912$	−1.07653e14	+	1.07653e14i	−0.170629	+	0.170629i
$913$	−3.75501e14	−	3.75501e14i	−0.591912	−	0.591912i
$914$			7.65234e14i			1.19967i
$915$	4.50719e12	−	1.06953e14i	0.00702748	−	0.166759i
$916$	−3.42271e14			−0.530753
$917$	5.44262e14	−	5.44262e14i	0.839386	−	0.839386i
$918$	3.26137e14	+	3.26137e14i	0.500250	+	0.500250i
$919$		−	1.00963e15i		−	1.54023i	−0.637905	−	0.770115i	$-0.720199\pi$
$919$		−	1.00963e15i		−	1.54023i	0.637905	−	0.770115i	$-0.279801\pi$
$920$	7.86950e13	−	7.23305e13i	0.119401	−	0.109744i
$921$	−8.42770e14			−1.27178
$922$	−7.39069e14	+	7.39069e14i	−1.10925	+	1.10925i
$923$	9.07350e14	+	9.07350e14i	1.35446	+	1.35446i
$924$		−	1.68183e14i		−	0.249703i
$925$	6.68288e14	+	7.91546e14i	0.986858	+	1.16887i
$926$	−1.25910e15			−1.84930
$927$	1.36802e14	−	1.36802e14i	0.199845	−	0.199845i
$928$	2.06559e14	+	2.06559e14i	0.300127	+	0.300127i
$929$			8.18867e14i			1.18341i	0.806155	+	0.591704i	$0.201545\pi$
$929$			8.18867e14i			1.18341i	−0.806155	+	0.591704i	$0.798455\pi$
$930$	−1.51844e14	−	1.65205e14i	−0.218265	−	0.237470i
$931$	1.44148e14			0.206092
$932$	6.17657e13	−	6.17657e13i	0.0878350	−	0.0878350i
$933$	−2.10663e14	−	2.10663e14i	−0.297975	−	0.297975i
$934$			6.13468e14i			0.863093i
$935$	−1.94959e14	−	8.21588e12i	−0.272826	−	0.0114973i
$936$	1.66670e14			0.231994
$937$	−7.82914e14	+	7.82914e14i	−1.08397	+	1.08397i	−0.0878323	+	0.996135i	$0.527994\pi$
$937$	−7.82914e14	+	7.82914e14i	−1.08397	+	1.08397i	−0.996135	+	0.0878323i	$0.972006\pi$
$938$	6.01187e14	+	6.01187e14i	0.827934	+	0.827934i
$939$		−	1.30543e14i		−	0.178824i
$940$	−4.82045e12	+	1.14387e14i	−0.00656822	+	0.155861i
$941$	−8.44829e14			−1.14504			−0.572520	−	0.819891i	$-0.694034\pi$
$941$	−8.44829e14			−1.14504			−0.572520	+	0.819891i	$0.694034\pi$
$942$	2.28040e14	−	2.28040e14i	0.307438	−	0.307438i
$943$	−1.64016e14	−	1.64016e14i	−0.219951	−	0.219951i
$944$		−	7.40568e14i		−	0.987882i
$945$	−8.30735e14	+	7.63549e14i	−1.10231	+	1.01316i
$946$	−4.60638e14			−0.608001
$947$	−7.89584e14	+	7.89584e14i	−1.03669	+	1.03669i	−0.0373886	+	0.999301i	$0.511904\pi$
$947$	−7.89584e14	+	7.89584e14i	−1.03669	+	1.03669i	−0.999301	+	0.0373886i	$0.988096\pi$
$948$	−1.61115e14	−	1.61115e14i	−0.210424	−	0.210424i
$949$		−	1.09477e15i		−	1.42231i
$950$	1.62084e14	−	1.36845e14i	0.209471	−	0.176852i
$951$	1.13969e15			1.46515
$952$	2.83734e14	−	2.83734e14i	0.362849	−	0.362849i
$953$	−5.01066e14	−	5.01066e14i	−0.637428	−	0.637428i	0.312493	−	0.949920i	$-0.398836\pi$
$953$	−5.01066e14	−	5.01066e14i	−0.637428	−	0.637428i	−0.949920	+	0.312493i	$0.898836\pi$
$954$			1.00345e14i			0.126986i
$955$	6.73171e14	+	7.32404e14i	0.847440	+	0.922007i
$956$	3.09293e14			0.387329
$957$	−1.26916e14	+	1.26916e14i	−0.158109	+	0.158109i
$958$	2.24042e14	+	2.24042e14i	0.277652	+	0.277652i
$959$			1.79840e15i			2.21714i
$960$	−1.95612e14	−	8.24338e12i	−0.239905	−	0.0101100i
$961$	−7.35993e14			−0.897960
$962$	1.26363e15	−	1.26363e15i	1.53372	−	1.53372i
$963$	7.80979e13	+	7.80979e13i	0.0942992	+	0.0942992i
$964$			4.88323e13i			0.0586573i
$965$	1.92670e13	−	4.57197e14i	0.0230238	−	0.546345i
$966$	2.77621e14			0.330040
$967$	4.18416e14	−	4.18416e14i	0.494853	−	0.494853i	−0.414978	−	0.909831i	$-0.636211\pi$
$967$	4.18416e14	−	4.18416e14i	0.494853	−	0.494853i	0.909831	+	0.414978i	$0.136211\pi$
$968$	3.07626e14	+	3.07626e14i	0.361948	+	0.361948i
$969$			9.02281e13i			0.105614i
$970$	−7.63207e14	+	7.01483e14i	−0.888759	+	0.816880i
$971$	1.67161e15			1.93659			0.968297	−	0.249801i	$-0.0803653\pi$
$971$	1.67161e15			1.93659			0.968297	+	0.249801i	$0.0803653\pi$
$972$	−1.45049e14	+	1.45049e14i	−0.167179	+	0.167179i
$973$	1.30397e15	+	1.30397e15i	1.49521	+	1.49521i
$974$			1.39526e15i			1.59170i
$975$	8.80252e14	+	7.43224e13i	0.999042	+	0.0843522i
$976$	−2.17762e14			−0.245886
$977$	1.08849e15	−	1.08849e15i	1.22279	−	1.22279i	0.256155	−	0.966636i	$-0.417544\pi$
$977$	1.08849e15	−	1.08849e15i	1.22279	−	1.22279i	0.966636	−	0.256155i	$-0.0824559\pi$
$978$	−5.48126e14	−	5.48126e14i	−0.612612	−	0.612612i
$979$			4.35656e14i			0.484429i
$980$	−2.35152e14	−	2.55843e14i	−0.260147	−	0.283037i
$981$	−4.57374e14			−0.503415
$982$	1.09967e15	−	1.09967e15i	1.20422	−	1.20422i
$983$	9.17415e13	+	9.17415e13i	0.0999536	+	0.0999536i	0.755315	−	0.655362i	$-0.227484\pi$
$983$	9.17415e13	+	9.17415e13i	0.0999536	+	0.0999536i	−0.655362	+	0.755315i	$0.727484\pi$
$984$			6.98677e14i			0.757357i
$985$	1.48194e15	+	6.24511e13i	1.59826	+	0.0673533i
$986$	3.20340e14			0.343737
$987$	2.81089e14	−	2.81089e14i	0.300094	−	0.300094i
$988$	−7.75453e13	−	7.75453e13i	−0.0823704	−	0.0823704i
$989$		−	2.27877e14i		−	0.240835i
$990$	6.85907e12	−	1.62763e14i	0.00721256	−	0.171151i
$991$	7.47146e14			0.781695			0.390848	−	0.920455i	$-0.372182\pi$
$991$	7.47146e14			0.781695			0.390848	+	0.920455i	$0.372182\pi$
$992$	−1.74435e14	+	1.74435e14i	−0.181583	+	0.181583i
$993$	−3.49046e14	−	3.49046e14i	−0.361524	−	0.361524i
$994$			2.57911e15i			2.65790i
$995$	−1.27165e13	+	1.16881e13i	−0.0130393	+	0.0119847i
$996$	5.91940e14			0.603922
$997$	−1.25142e15	+	1.25142e15i	−1.27036	+	1.27036i	−0.324459	+	0.945900i	$0.605182\pi$
$997$	−1.25142e15	+	1.25142e15i	−1.27036	+	1.27036i	−0.945900	+	0.324459i	$0.894818\pi$
$998$	−5.61758e14	−	5.61758e14i	−0.567409	−	0.567409i
$999$		−	1.65402e15i		−	1.66231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.11.f.a.58.20	✓	180
5.2	odd	4	inner	95.11.f.a.77.20	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.11.f.a.58.20	✓	180	1.1	even	1	trivial
95.11.f.a.77.20	yes	180	5.2	odd	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.0389 + 27.0389i) q^{2} +(145.189 + 145.189i) q^{3} -438.207i q^{4} +(2114.71 + 2300.79i) q^{5} -7851.52 q^{6} +(-16374.3 + 16374.3i) q^{7} +(-15839.2 - 15839.2i) q^{8} -16889.2i q^{9} +O(q^{10})\)	\(q+(-27.0389 + 27.0389i) q^{2} +(145.189 + 145.189i) q^{3} -438.207i q^{4} +(2114.71 + 2300.79i) q^{5} -7851.52 q^{6} +(-16374.3 + 16374.3i) q^{7} +(-15839.2 - 15839.2i) q^{8} -16889.2i q^{9} +(-119390. - 5031.30i) q^{10} -80719.3 q^{11} +(63623.0 - 63623.0i) q^{12} +(-311519. - 311519. i) q^{13} -885484. i q^{14} +(-27016.2 + 641083. i) q^{15} +1.30527e6 q^{16} +(546998. - 546998. i) q^{17} +(456665. + 456665. i) q^{18} +568056. i q^{19} +(1.00822e6 - 926682. i) q^{20} -4.75473e6 q^{21} +(2.18256e6 - 2.18256e6i) q^{22} +(1.07971e6 + 1.07971e6i) q^{23} -4.59937e6i q^{24} +(-821618. + 9.73100e6i) q^{25} +1.68463e7 q^{26} +(1.10254e7 - 1.10254e7i) q^{27} +(7.17531e6 + 7.17531e6i) q^{28} -1.08294e7i q^{29} +(-1.66037e7 - 1.80647e7i) q^{30} +9.14521e6 q^{31} +(-1.90739e7 + 1.90739e7i) q^{32} +(-1.17196e7 - 1.17196e7i) q^{33} +2.95805e7i q^{34} +(-7.23005e7 - 3.04686e6i) q^{35} -7.40095e6 q^{36} +(7.50094e7 - 7.50094e7i) q^{37} +(-1.53596e7 - 1.53596e7i) q^{38} -9.04585e7i q^{39} +(2.94730e6 - 6.99380e7i) q^{40} -1.51907e8 q^{41} +(1.28563e8 - 1.28563e8i) q^{42} +(-1.05527e8 - 1.05527e8i) q^{43} +3.53718e7i q^{44} +(3.88583e7 - 3.57157e7i) q^{45} -5.83884e7 q^{46} +(-5.91177e7 + 5.91177e7i) q^{47} +(1.89512e8 + 1.89512e8i) q^{48} -2.53757e8i q^{49} +(-2.40900e8 - 2.85332e8i) q^{50} +1.58837e8 q^{51} +(-1.36510e8 + 1.36510e8i) q^{52} +(1.09867e8 + 1.09867e8i) q^{53} +5.96230e8i q^{54} +(-1.70698e8 - 1.85718e8i) q^{55} +5.18710e8 q^{56} +(-8.24756e7 + 8.24756e7i) q^{57} +(2.92816e8 + 2.92816e8i) q^{58} -5.67366e8i q^{59} +(2.80927e8 + 1.18387e7i) q^{60} -1.66832e8 q^{61} +(-2.47277e8 + 2.47277e8i) q^{62} +(2.76547e8 + 2.76547e8i) q^{63} +3.05127e8i q^{64} +(5.79663e7 - 1.37551e9i) q^{65} +6.33770e8 q^{66} +(-6.78936e8 + 6.78936e8i) q^{67} +(-2.39699e8 - 2.39699e8i) q^{68} +3.13525e8i q^{69} +(2.03731e9 - 1.87254e9i) q^{70} -2.91266e9 q^{71} +(-2.67511e8 + 2.67511e8i) q^{72} +(1.75715e9 + 1.75715e9i) q^{73} +4.05635e9i q^{74} +(-1.53213e9 + 1.29355e9i) q^{75} +2.48926e8 q^{76} +(1.32172e9 - 1.32172e9i) q^{77} +(2.44590e9 + 2.44590e9i) q^{78} -2.53235e9i q^{79} +(2.76028e9 + 3.00316e9i) q^{80} +2.20425e9 q^{81} +(4.10741e9 - 4.10741e9i) q^{82} +(4.65193e9 + 4.65193e9i) q^{83} +2.08356e9i q^{84} +(2.41527e9 + 1.01783e8i) q^{85} +5.70667e9 q^{86} +(1.57232e9 - 1.57232e9i) q^{87} +(1.27853e9 + 1.27853e9i) q^{88} -5.39717e9i q^{89} +(-8.49743e7 + 2.01640e9i) q^{90} +1.02018e10 q^{91} +(4.73137e8 - 4.73137e8i) q^{92} +(1.32779e9 + 1.32779e9i) q^{93} -3.19696e9i q^{94} +(-1.30698e9 + 1.20127e9i) q^{95} -5.53864e9 q^{96} +(6.13404e9 - 6.13404e9i) q^{97} +(6.86131e9 + 6.86131e9i) q^{98} +1.36328e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8}+O(q^{10}) \) 180 * q - 64 * q^2 - 124 * q^3 + 8454 * q^5 - 24320 * q^6 + 32890 * q^7 + 98304 * q^8	\( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8} + 322576 q^{10} + 435480 q^{11} - 1494224 q^{12} - 48556 q^{13} + 4094384 q^{15} - 44262960 q^{16} - 505646 q^{17} - 6298560 q^{18} + 24709120 q^{20} + 38659000 q^{21} - 34179888 q^{22} - 16720612 q^{23} + 33791178 q^{25} + 86813120 q^{26} - 14436244 q^{27} - 133340704 q^{28} + 232195960 q^{30} + 64155640 q^{31} + 226208632 q^{32} + 11350832 q^{33} - 151622642 q^{35} + 1852895600 q^{36} - 373035252 q^{37} + 28746456 q^{40} - 461563640 q^{41} + 1629657056 q^{42} - 123615382 q^{43} - 1310415408 q^{45} - 462362320 q^{46} + 1397297450 q^{47} + 1422934764 q^{48} - 903150292 q^{50} + 786433560 q^{51} + 1822166628 q^{52} + 3614315976 q^{53} + 1190412472 q^{55} - 2951801640 q^{56} - 2958059232 q^{58} + 13343296716 q^{60} + 1705662680 q^{61} + 5674658712 q^{62} - 2955158450 q^{63} + 5908753192 q^{65} - 6577823720 q^{66} - 4198675868 q^{67} - 10832391640 q^{68} + 7095849220 q^{70} + 5547444200 q^{71} + 12902115940 q^{72} + 331620970 q^{73} - 11862069968 q^{75} - 10562822066 q^{77} - 12446121128 q^{78} + 9866450160 q^{80} - 63545444700 q^{81} + 9916048472 q^{82} - 1670597036 q^{83} - 25420912412 q^{85} - 54497853920 q^{86} + 20560091976 q^{87} - 4241912244 q^{88} + 1724884384 q^{90} - 9777438680 q^{91} + 57824442424 q^{92} + 49325339272 q^{93} - 5501891978 q^{95} - 7492787400 q^{96} - 74779609888 q^{97} - 60964218864 q^{98}+O(q^{100}) \) 180 * q - 64 * q^2 - 124 * q^3 + 8454 * q^5 - 24320 * q^6 + 32890 * q^7 + 98304 * q^8 + 322576 * q^10 + 435480 * q^11 - 1494224 * q^12 - 48556 * q^13 + 4094384 * q^15 - 44262960 * q^16 - 505646 * q^17 - 6298560 * q^18 + 24709120 * q^20 + 38659000 * q^21 - 34179888 * q^22 - 16720612 * q^23 + 33791178 * q^25 + 86813120 * q^26 - 14436244 * q^27 - 133340704 * q^28 + 232195960 * q^30 + 64155640 * q^31 + 226208632 * q^32 + 11350832 * q^33 - 151622642 * q^35 + 1852895600 * q^36 - 373035252 * q^37 + 28746456 * q^40 - 461563640 * q^41 + 1629657056 * q^42 - 123615382 * q^43 - 1310415408 * q^45 - 462362320 * q^46 + 1397297450 * q^47 + 1422934764 * q^48 - 903150292 * q^50 + 786433560 * q^51 + 1822166628 * q^52 + 3614315976 * q^53 + 1190412472 * q^55 - 2951801640 * q^56 - 2958059232 * q^58 + 13343296716 * q^60 + 1705662680 * q^61 + 5674658712 * q^62 - 2955158450 * q^63 + 5908753192 * q^65 - 6577823720 * q^66 - 4198675868 * q^67 - 10832391640 * q^68 + 7095849220 * q^70 + 5547444200 * q^71 + 12902115940 * q^72 + 331620970 * q^73 - 11862069968 * q^75 - 10562822066 * q^77 - 12446121128 * q^78 + 9866450160 * q^80 - 63545444700 * q^81 + 9916048472 * q^82 - 1670597036 * q^83 - 25420912412 * q^85 - 54497853920 * q^86 + 20560091976 * q^87 - 4241912244 * q^88 + 1724884384 * q^90 - 9777438680 * q^91 + 57824442424 * q^92 + 49325339272 * q^93 - 5501891978 * q^95 - 7492787400 * q^96 - 74779609888 * q^97 - 60964218864 * q^98

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