LMFDB - Embedded newform 4.15.b.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,15,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.97315872608$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 88x^{4} - 1824x^{3} + 325632x^{2} + 21572352x + 982333440 $ x^6 - x^5 + 88x^4 - 1824x^3 + 325632x^2 + 21572352x + 982333440
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$-4.07037 + 30.9656i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.15.b.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-32.2815 + 123.862i) q^{2} -2369.41i q^{3} +(-14299.8 - 7996.93i) q^{4} +113343. q^{5} +(293481. + 76488.1i) q^{6} -697667. i q^{7} +(1.45214e6 - 1.51306e6i) q^{8} -831139. q^{9} +O(q^{10})$	\(q+(-32.2815 + 123.862i) q^{2} -2369.41i q^{3} +(-14299.8 - 7996.93i) q^{4} +113343. q^{5} +(293481. + 76488.1i) q^{6} -697667. i q^{7} +(1.45214e6 - 1.51306e6i) q^{8} -831139. q^{9} +(-3.65890e6 + 1.40390e7i) q^{10} -2.00895e7i q^{11} +(-1.89480e7 + 3.38821e7i) q^{12} -6.13899e7 q^{13} +(8.64148e7 + 2.25217e7i) q^{14} -2.68557e8i q^{15} +(1.40534e8 + 2.28709e8i) q^{16} +3.44542e8 q^{17} +(2.68304e7 - 1.02947e8i) q^{18} +3.17454e8i q^{19} +(-1.62079e9 - 9.06399e8i) q^{20} -1.65306e9 q^{21} +(2.48833e9 + 6.48519e8i) q^{22} +5.79264e9i q^{23} +(-3.58505e9 - 3.44071e9i) q^{24} +6.74323e9 q^{25} +(1.98176e9 - 7.60390e9i) q^{26} -9.36351e9i q^{27} +(-5.57919e9 + 9.97651e9i) q^{28} -3.72362e9 q^{29} +(3.32642e10 + 8.66943e9i) q^{30} -8.57575e8i q^{31} +(-3.28651e10 + 1.00238e10i) q^{32} -4.76003e10 q^{33} +(-1.11223e10 + 4.26758e10i) q^{34} -7.90760e10i q^{35} +(1.18851e10 + 6.64656e9i) q^{36} +9.83497e10 q^{37} +(-3.93207e10 - 1.02479e10i) q^{38} +1.45458e11i q^{39} +(1.64590e11 - 1.71495e11i) q^{40} -8.26198e9 q^{41} +(5.33632e10 - 2.04752e11i) q^{42} +1.16363e11i q^{43} +(-1.60654e11 + 2.87276e11i) q^{44} -9.42042e10 q^{45} +(-7.17490e11 - 1.86995e11i) q^{46} +3.17697e11i q^{47} +(5.41906e11 - 3.32982e11i) q^{48} +1.91484e11 q^{49} +(-2.17681e11 + 8.35233e11i) q^{50} -8.16362e11i q^{51} +(8.77864e11 + 4.90930e11i) q^{52} -6.36538e11 q^{53} +(1.15979e12 + 3.02268e11i) q^{54} -2.27701e12i q^{55} +(-1.05561e12 - 1.01311e12i) q^{56} +7.52180e11 q^{57} +(1.20204e11 - 4.61217e11i) q^{58} +2.87412e12i q^{59} +(-2.14763e12 + 3.84032e12i) q^{60} +8.45647e11 q^{61} +(1.06221e11 + 2.76838e10i) q^{62} +5.79859e11i q^{63} +(-1.80638e11 - 4.39434e12i) q^{64} -6.95814e12 q^{65} +(1.53661e12 - 5.89589e12i) q^{66} +6.82161e12i q^{67} +(-4.92689e12 - 2.75528e12i) q^{68} +1.37251e13 q^{69} +(9.79455e12 + 2.55269e12i) q^{70} -3.28972e12i q^{71} +(-1.20693e12 + 1.25756e12i) q^{72} +6.25122e10 q^{73} +(-3.17487e12 + 1.21818e13i) q^{74} -1.59775e13i q^{75} +(2.53866e12 - 4.53954e12i) q^{76} -1.40158e13 q^{77} +(-1.80168e13 - 4.69560e12i) q^{78} +1.05071e13i q^{79} +(1.59286e13 + 2.59227e13i) q^{80} -2.61613e13 q^{81} +(2.66709e11 - 1.02335e12i) q^{82} -2.38301e13i q^{83} +(2.36384e13 + 1.32194e13i) q^{84} +3.90516e13 q^{85} +(-1.44130e13 - 3.75636e12i) q^{86} +8.82279e12i q^{87} +(-3.03966e13 - 2.91727e13i) q^{88} +3.23837e13 q^{89} +(3.04105e12 - 1.16684e13i) q^{90} +4.28297e13i q^{91} +(4.63233e13 - 8.28336e13i) q^{92} -2.03195e12 q^{93} +(-3.93507e13 - 1.02557e13i) q^{94} +3.59814e13i q^{95} +(2.37505e13 + 7.78709e13i) q^{96} -1.34788e14 q^{97} +(-6.18138e12 + 2.37176e13i) q^{98} +1.66972e13i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9}+O(q^{10}) $ 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9	\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + 5796840 q^{10} + 193920 q^{12} - 80775396 q^{13} + 175232064 q^{14} - 353013504 q^{16} - 120131764 q^{17} + 1599402372 q^{18} - 5047343200 q^{20} + 1226658048 q^{21} + 9916985760 q^{22} - 24092176896 q^{24} + 3942973410 q^{25} + 39549467048 q^{26} - 65094731520 q^{28} - 8035796644 q^{29} + 99698873280 q^{30} - 85711465472 q^{32} - 37769804160 q^{33} + 98089165512 q^{34} - 27478990320 q^{36} + 31334118396 q^{37} - 165268841760 q^{38} + 435607171200 q^{40} + 83362750892 q^{41} - 830203906560 q^{42} + 915657452160 q^{44} + 271078769820 q^{45} - 1712365889856 q^{46} + 2292961843200 q^{48} - 551978693658 q^{49} - 1639579094580 q^{50} + 1057159118496 q^{52} + 76712275004 q^{53} + 445471858368 q^{54} - 560223046656 q^{56} - 2647253865600 q^{57} + 4483777382184 q^{58} - 9544013748480 q^{60} + 6210000787932 q^{61} + 10375644284160 q^{62} - 14398852657152 q^{64} - 7189912943720 q^{65} + 15071210499840 q^{66} - 18507298307296 q^{68} + 19348372347648 q^{69} + 12679529923200 q^{70} - 5286233111232 q^{72} - 29882649313236 q^{73} - 1536652566808 q^{74} + 21457134000000 q^{76} + 37339673521920 q^{77} - 29727224255040 q^{78} + 57843429624320 q^{80} - 98651978873946 q^{81} - 71900577251064 q^{82} + 102961968764928 q^{84} + 151199882653560 q^{85} - 100164269733216 q^{86} + 51557990330880 q^{88} - 180966014731924 q^{89} - 84934442792280 q^{90} + 82241452266240 q^{92} + 295002300748800 q^{93} - 40381697410176 q^{94} - 82703070928896 q^{96} - 345459072299124 q^{97} + 121406102961892 q^{98}+O(q^{100}) \) 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9 + 5796840 * q^10 + 193920 * q^12 - 80775396 * q^13 + 175232064 * q^14 - 353013504 * q^16 - 120131764 * q^17 + 1599402372 * q^18 - 5047343200 * q^20 + 1226658048 * q^21 + 9916985760 * q^22 - 24092176896 * q^24 + 3942973410 * q^25 + 39549467048 * q^26 - 65094731520 * q^28 - 8035796644 * q^29 + 99698873280 * q^30 - 85711465472 * q^32 - 37769804160 * q^33 + 98089165512 * q^34 - 27478990320 * q^36 + 31334118396 * q^37 - 165268841760 * q^38 + 435607171200 * q^40 + 83362750892 * q^41 - 830203906560 * q^42 + 915657452160 * q^44 + 271078769820 * q^45 - 1712365889856 * q^46 + 2292961843200 * q^48 - 551978693658 * q^49 - 1639579094580 * q^50 + 1057159118496 * q^52 + 76712275004 * q^53 + 445471858368 * q^54 - 560223046656 * q^56 - 2647253865600 * q^57 + 4483777382184 * q^58 - 9544013748480 * q^60 + 6210000787932 * q^61 + 10375644284160 * q^62 - 14398852657152 * q^64 - 7189912943720 * q^65 + 15071210499840 * q^66 - 18507298307296 * q^68 + 19348372347648 * q^69 + 12679529923200 * q^70 - 5286233111232 * q^72 - 29882649313236 * q^73 - 1536652566808 * q^74 + 21457134000000 * q^76 + 37339673521920 * q^77 - 29727224255040 * q^78 + 57843429624320 * q^80 - 98651978873946 * q^81 - 71900577251064 * q^82 + 102961968764928 * q^84 + 151199882653560 * q^85 - 100164269733216 * q^86 + 51557990330880 * q^88 - 180966014731924 * q^89 - 84934442792280 * q^90 + 82241452266240 * q^92 + 295002300748800 * q^93 - 40381697410176 * q^94 - 82703070928896 * q^96 - 345459072299124 * q^97 + 121406102961892 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−32.2815	+	123.862i	−0.252199	+	0.967675i
$2$	−32.2815	+	123.862i	−0.252199	+	0.967675i
$3$		−	2369.41i		−	1.08341i	−0.840570	−	0.541703i	$-0.817780\pi$
$3$		−	2369.41i		−	1.08341i	0.840570	−	0.541703i	$-0.182220\pi$
$4$	−14299.8	−	7996.93i	−0.872791	−	0.488094i
$5$	113343.			1.45080			0.725398	−	0.688329i	$-0.241656\pi$
$5$	113343.			1.45080			0.725398	+	0.688329i	$0.241656\pi$
$6$	293481.	+	76488.1i	1.04839	+	0.273234i
$7$		−	697667.i		−	0.847153i	−0.905860	−	0.423577i	$-0.860774\pi$
$7$		−	697667.i		−	0.847153i	0.905860	−	0.423577i	$-0.139226\pi$
$8$	1.45214e6	−	1.51306e6i	0.692433	−	0.721482i
$9$	−831139.			−0.173771
$10$	−3.65890e6	+	1.40390e7i	−0.365890	+	1.40390i
$11$		−	2.00895e7i		−	1.03091i	−0.856917	−	0.515454i	$-0.827623\pi$
$11$		−	2.00895e7i		−	1.03091i	0.856917	−	0.515454i	$-0.172377\pi$
$12$	−1.89480e7	+	3.38821e7i	−0.528804	+	0.945588i
$13$	−6.13899e7			−0.978348			−0.489174	−	0.872186i	$-0.662702\pi$
$13$	−6.13899e7			−0.978348			−0.489174	+	0.872186i	$0.662702\pi$
$14$	8.64148e7	+	2.25217e7i	0.819769	+	0.213651i
$15$		−	2.68557e8i		−	1.57180i
$16$	1.40534e8	+	2.28709e8i	0.523529	+	0.852008i
$17$	3.44542e8			0.839653			0.419827	−	0.907604i	$-0.362091\pi$
$17$	3.44542e8			0.839653			0.419827	+	0.907604i	$0.362091\pi$
$18$	2.68304e7	−	1.02947e8i	0.0438248	−	0.168154i
$19$			3.17454e8i			0.355145i	0.984108	+	0.177573i	$0.0568245\pi$
$19$			3.17454e8i			0.355145i	−0.984108	+	0.177573i	$0.943176\pi$
$20$	−1.62079e9	−	9.06399e8i	−1.26624	−	0.708125i
$21$	−1.65306e9			−0.917812
$22$	2.48833e9	+	6.48519e8i	0.997585	+	0.259994i
$23$			5.79264e9i			1.70130i	0.525731	+	0.850651i	$0.323792\pi$
$23$			5.79264e9i			1.70130i	−0.525731	+	0.850651i	$0.676208\pi$
$24$	−3.58505e9	−	3.44071e9i	−0.781659	−	0.750187i
$25$	6.74323e9			1.10481
$26$	1.98176e9	−	7.60390e9i	0.246738	−	0.946723i
$27$		−	9.36351e9i		−	0.895143i
$28$	−5.57919e9	+	9.97651e9i	−0.413490	+	0.739388i
$29$	−3.72362e9			−0.215864			−0.107932	−	0.994158i	$-0.534423\pi$
$29$	−3.72362e9			−0.215864			−0.107932	+	0.994158i	$0.534423\pi$
$30$	3.32642e10	+	8.66943e9i	1.52100	+	0.396407i
$31$		−	8.57575e8i		−	0.0311702i	−0.999879	−	0.0155851i	$-0.995039\pi$
$31$		−	8.57575e8i		−	0.0311702i	0.999879	−	0.0155851i	$-0.00496110\pi$
$32$	−3.28651e10	+	1.00238e10i	−0.956500	+	0.291731i
$33$	−4.76003e10			−1.11689
$34$	−1.11223e10	+	4.26758e10i	−0.211760	+	0.812512i
$35$		−	7.90760e10i		−	1.22905i
$36$	1.18851e10	+	6.64656e9i	0.151665	+	0.0848163i
$37$	9.83497e10			1.03600			0.518002	−	0.855380i	$-0.326676\pi$
$37$	9.83497e10			1.03600			0.518002	+	0.855380i	$0.326676\pi$
$38$	−3.93207e10	−	1.02479e10i	−0.343665	−	0.0895673i
$39$			1.45458e11i			1.05995i
$40$	1.64590e11	−	1.71495e11i	1.00458	−	1.04672i
$41$	−8.26198e9			−0.0424226			−0.0212113	−	0.999775i	$-0.506752\pi$
$41$	−8.26198e9			−0.0424226			−0.0212113	+	0.999775i	$0.506752\pi$
$42$	5.33632e10	−	2.04752e11i	0.231471	−	0.888144i
$43$			1.16363e11i			0.428089i	0.976824	+	0.214045i	$0.0686638\pi$
$43$			1.16363e11i			0.428089i	−0.976824	+	0.214045i	$0.931336\pi$
$44$	−1.60654e11	+	2.87276e11i	−0.503180	+	0.899768i
$45$	−9.42042e10			−0.252106
$46$	−7.17490e11	−	1.86995e11i	−1.64631	−	0.429067i
$47$			3.17697e11i			0.627087i	0.949574	+	0.313543i	$0.101516\pi$
$47$			3.17697e11i			0.627087i	−0.949574	+	0.313543i	$0.898484\pi$
$48$	5.41906e11	−	3.32982e11i	0.923071	−	0.567195i
$49$	1.91484e11			0.282332
$50$	−2.17681e11	+	8.35233e11i	−0.278632	+	1.06910i
$51$		−	8.16362e11i		−	0.909686i
$52$	8.77864e11	+	4.90930e11i	0.853894	+	0.477525i
$53$	−6.36538e11			−0.541867			−0.270934	−	0.962598i	$-0.587332\pi$
$53$	−6.36538e11			−0.541867			−0.270934	+	0.962598i	$0.587332\pi$
$54$	1.15979e12	+	3.02268e11i	0.866208	+	0.225754i
$55$		−	2.27701e12i		−	1.49564i
$56$	−1.05561e12	−	1.01311e12i	−0.611206	−	0.586597i
$57$	7.52180e11			0.384767
$58$	1.20204e11	−	4.61217e11i	0.0544406	−	0.208886i
$59$			2.87412e12i			1.15489i	0.816429	+	0.577445i	$0.195950\pi$
$59$			2.87412e12i			1.15489i	−0.816429	+	0.577445i	$0.804050\pi$
$60$	−2.14763e12	+	3.84032e12i	−0.767187	+	1.37186i
$61$	8.45647e11			0.269079			0.134540	−	0.990908i	$-0.457044\pi$
$61$	8.45647e11			0.269079			0.134540	+	0.990908i	$0.457044\pi$
$62$	1.06221e11	+	2.76838e10i	0.0301627	+	0.00786110i
$63$			5.79859e11i			0.147210i
$64$	−1.80638e11	−	4.39434e12i	−0.0410723	−	0.999156i
$65$	−6.95814e12			−1.41938
$66$	1.53661e12	−	5.89589e12i	0.281680	−	1.08079i
$67$			6.82161e12i			1.12555i	0.826611	+	0.562773i	$0.190266\pi$
$67$			6.82161e12i			1.12555i	−0.826611	+	0.562773i	$0.809734\pi$
$68$	−4.92689e12	−	2.75528e12i	−0.732842	−	0.409829i
$69$	1.37251e13			1.84320
$70$	9.79455e12	+	2.55269e12i	1.18932	+	0.309964i
$71$		−	3.28972e12i		−	0.361702i	−0.983511	−	0.180851i	$-0.942115\pi$
$71$		−	3.28972e12i		−	0.361702i	0.983511	−	0.180851i	$-0.0578851\pi$
$72$	−1.20693e12	+	1.25756e12i	−0.120325	+	0.125372i
$73$	6.25122e10			0.00565854			0.00282927	−	0.999996i	$-0.499099\pi$
$73$	6.25122e10			0.00565854			0.00282927	+	0.999996i	$0.499099\pi$
$74$	−3.17487e12	+	1.21818e13i	−0.261279	+	1.00251i
$75$		−	1.59775e13i		−	1.19696i
$76$	2.53866e12	−	4.53954e12i	0.173344	−	0.309968i
$77$	−1.40158e13			−0.873338
$78$	−1.80168e13	−	4.69560e12i	−1.02569	−	0.267318i
$79$			1.05071e13i			0.547135i	0.961853	+	0.273568i	$0.0882037\pi$
$79$			1.05071e13i			0.547135i	−0.961853	+	0.273568i	$0.911796\pi$
$80$	1.59286e13	+	2.59227e13i	0.759535	+	1.23609i
$81$	−2.61613e13			−1.14357
$82$	2.66709e11	−	1.02335e12i	0.0106989	−	0.0410513i
$83$		−	2.38301e13i		−	0.878171i	−0.898445	−	0.439086i	$-0.855302\pi$
$83$		−	2.38301e13i		−	0.878171i	0.898445	−	0.439086i	$-0.144698\pi$
$84$	2.36384e13	+	1.32194e13i	0.801058	+	0.447978i
$85$	3.90516e13			1.21817
$86$	−1.44130e13	−	3.75636e12i	−0.414251	−	0.107964i
$87$			8.82279e12i			0.233868i
$88$	−3.03966e13	−	2.91727e13i	−0.743782	−	0.713836i
$89$	3.23837e13			0.732143			0.366071	−	0.930587i	$-0.380703\pi$
$89$	3.23837e13			0.732143			0.366071	+	0.930587i	$0.380703\pi$
$90$	3.04105e12	−	1.16684e13i	0.0635808	−	0.243957i
$91$			4.28297e13i			0.828811i
$92$	4.63233e13	−	8.28336e13i	0.830395	−	1.48488i
$93$	−2.03195e12			−0.0337701
$94$	−3.93507e13	−	1.02557e13i	−0.606816	−	0.158151i
$95$			3.59814e13i			0.515243i
$96$	2.37505e13	+	7.78709e13i	0.316063	+	1.03628i
$97$	−1.34788e14			−1.66820			−0.834101	−	0.551612i	$-0.814013\pi$
$97$	−1.34788e14			−1.66820			−0.834101	+	0.551612i	$0.814013\pi$
$98$	−6.18138e12	+	2.37176e13i	−0.0712037	+	0.273205i
$99$			1.66972e13i			0.179142i
$100$	−9.64269e13	−	5.39251e13i	−0.964269	−	0.539251i
$101$	1.79994e14			1.67884			0.839419	−	0.543485i	$-0.182896\pi$
$101$	1.79994e14			1.67884			0.839419	+	0.543485i	$0.182896\pi$
$102$	1.01117e14	+	2.63534e13i	0.880281	+	0.229422i
$103$		−	5.09045e12i		−	0.0413900i	−0.999786	−	0.0206950i	$-0.993412\pi$
$103$		−	5.09045e12i		−	0.0413900i	0.999786	−	0.0206950i	$-0.00658790\pi$
$104$	−8.91466e13	+	9.28864e13i	−0.677441	+	0.705860i
$105$	−1.87364e14			−1.33156
$106$	2.05484e13	−	7.88431e13i	0.136658	−	0.524352i
$107$		−	2.79523e14i		−	1.74073i	−0.492407	−	0.870365i	$-0.663883\pi$
$107$		−	2.79523e14i		−	1.74073i	0.492407	−	0.870365i	$-0.336117\pi$
$108$	−7.48793e13	+	1.33896e14i	−0.436913	+	0.781273i
$109$	2.45434e14			1.34261			0.671305	−	0.741182i	$-0.265734\pi$
$109$	2.45434e14			1.34261			0.671305	+	0.741182i	$0.265734\pi$
$110$	2.82036e14	+	7.35054e13i	1.44729	+	0.377199i
$111$		−	2.33031e14i		−	1.12241i
$112$	1.59563e14	−	9.80458e13i	0.721781	−	0.443509i
$113$	−2.38170e14			−1.01237			−0.506184	−	0.862426i	$-0.668944\pi$
$113$	−2.38170e14			−1.01237			−0.506184	+	0.862426i	$0.668944\pi$
$114$	−2.42815e13	+	9.31668e13i	−0.0970378	+	0.372329i
$115$			6.56558e14i			2.46824i
$116$	5.32471e13	+	2.97775e13i	0.188404	+	0.105362i
$117$	5.10236e13			0.170008
$118$	−3.55995e14	−	9.27808e13i	−1.11756	−	0.291262i
$119$		−	2.40376e14i		−	0.711315i
$120$	−4.06343e14	−	3.89982e14i	−1.13403	−	1.08837i
$121$	−2.38380e13			−0.0627730
$122$	−2.72987e13	+	1.04744e14i	−0.0678616	+	0.260381i
$123$			1.95760e13i			0.0459609i
$124$	−6.85796e12	+	1.22632e13i	−0.0152140	+	0.0272051i
$125$	7.25076e13			0.152060
$126$	−7.18227e13	−	1.87187e13i	−0.142452	−	0.0371263i
$127$			9.50007e14i			1.78279i	0.453225	+	0.891396i	$0.350273\pi$
$127$			9.50007e14i			1.78279i	−0.453225	+	0.891396i	$0.649727\pi$
$128$	5.50124e14	+	1.19481e14i	0.977217	+	0.212242i
$129$	2.75711e14			0.463795
$130$	2.24619e14	−	8.61853e14i	0.357967	−	1.37350i
$131$		−	3.13334e14i		−	0.473270i	−0.971599	−	0.236635i	$-0.923955\pi$
$131$		−	3.13334e14i		−	0.473270i	0.971599	−	0.236635i	$-0.0760445\pi$
$132$	6.80675e14	+	3.80656e14i	0.974815	+	0.545149i
$133$	2.21477e14			0.300862
$134$	−8.44942e14	−	2.20212e14i	−1.08916	−	0.283862i
$135$		−	1.06129e15i		−	1.29867i
$136$	5.00323e14	−	5.21312e14i	0.581404	−	0.605794i
$137$	−1.05928e15			−1.16941			−0.584704	−	0.811247i	$-0.698789\pi$
$137$	−1.05928e15			−1.16941			−0.584704	+	0.811247i	$0.698789\pi$
$138$	−4.43068e14	+	1.70003e15i	−0.464854	+	1.78362i
$139$		−	1.02367e15i		−	1.02108i	−0.859855	−	0.510538i	$-0.829446\pi$
$139$		−	1.02367e15i		−	1.02108i	0.859855	−	0.510538i	$-0.170554\pi$
$140$	−6.32365e14	+	1.13077e15i	−0.599890	+	1.07270i
$141$	7.52754e14			0.679390
$142$	4.07473e14	+	1.06197e14i	0.350010	+	0.0912208i
$143$			1.23329e15i			1.00859i
$144$	−1.16803e14	−	1.90089e14i	−0.0909740	−	0.148054i
$145$	−4.22048e14			−0.313174
$146$	−2.01799e12	+	7.74291e12i	−0.00142708	+	0.00547563i
$147$		−	4.53704e14i		−	0.305880i
$148$	−1.40638e15	−	7.86495e14i	−0.904215	−	0.505667i
$149$	−9.53793e14			−0.584993			−0.292496	−	0.956267i	$-0.594486\pi$
$149$	−9.53793e14			−0.584993			−0.292496	+	0.956267i	$0.594486\pi$
$150$	1.97901e15	+	5.15777e14i	1.15827	+	0.301872i
$151$			2.50228e14i			0.139797i	0.997554	+	0.0698984i	$0.0222675\pi$
$151$			2.50228e14i			0.139797i	−0.997554	+	0.0698984i	$0.977732\pi$
$152$	4.80326e14	+	4.60987e14i	0.256231	+	0.245914i
$153$	−2.86363e14			−0.145907
$154$	4.52450e14	−	1.73603e15i	0.220255	−	0.845107i
$155$		−	9.72005e13i		−	0.0452217i
$156$	1.16322e15	−	2.08002e15i	0.517354	−	0.925114i
$157$	2.72276e15			1.15801			0.579005	−	0.815324i	$-0.303441\pi$
$157$	2.72276e15			1.15801			0.579005	+	0.815324i	$0.303441\pi$
$158$	−1.30144e15	−	3.39186e14i	−0.529449	−	0.137987i
$159$			1.50822e15i			0.587063i
$160$	−3.72505e15	+	1.13613e15i	−1.38769	+	0.423242i
$161$	4.04133e15			1.44126
$162$	8.44526e14	−	3.24040e15i	0.288408	−	1.10661i
$163$			4.12649e15i			1.34979i	0.737912	+	0.674897i	$0.235812\pi$
$163$			4.12649e15i			1.34979i	−0.737912	+	0.674897i	$0.764188\pi$
$164$	1.18145e14	+	6.60705e13i	0.0370261	+	0.0207062i
$165$	−5.39518e15			−1.62039
$166$	2.95166e15	+	7.69271e14i	0.849785	+	0.221474i
$167$		−	3.19518e15i		−	0.882024i	−0.897501	−	0.441012i	$-0.854620\pi$
$167$		−	3.19518e15i		−	0.882024i	0.897501	−	0.441012i	$-0.145380\pi$
$168$	−2.40047e15	+	2.50117e15i	−0.635523	+	0.662184i
$169$	−1.68658e14			−0.0428351
$170$	−1.26064e15	+	4.83703e15i	−0.307220	+	1.17879i
$171$		−	2.63849e14i		−	0.0617138i
$172$	9.30543e14	−	1.66396e15i	0.208948	−	0.373632i
$173$	−7.49126e15			−1.61522			−0.807611	−	0.589716i	$-0.799240\pi$
$173$	−7.49126e15			−1.61522			−0.807611	+	0.589716i	$0.799240\pi$
$174$	−1.09281e15	−	2.84813e14i	−0.226309	−	0.0589814i
$175$		−	4.70453e15i		−	0.935944i
$176$	4.59465e15	−	2.82325e15i	0.878342	−	0.539711i
$177$	6.80997e15			1.25122
$178$	−1.04539e15	+	4.01112e15i	−0.184646	+	0.708476i
$179$		−	1.06547e15i		−	0.180955i	−0.995899	−	0.0904773i	$-0.971161\pi$
$179$		−	1.06547e15i		−	0.180955i	0.995899	−	0.0904773i	$-0.0288393\pi$
$180$	1.34710e15	+	7.53344e14i	0.220036	+	0.123051i
$181$	7.52697e14			0.118269			0.0591344	−	0.998250i	$-0.481166\pi$
$181$	7.52697e14			0.118269			0.0591344	+	0.998250i	$0.481166\pi$
$182$	−5.30499e15	−	1.38261e15i	−0.802020	−	0.209025i
$183$		−	2.00369e15i		−	0.291522i
$184$	8.76459e15	+	8.41171e15i	1.22746	+	1.17804i
$185$	1.11473e16			1.50303
$186$	6.55943e13	−	2.51682e14i	0.00851678	−	0.0326785i
$187$		−	6.92168e15i		−	0.865606i
$188$	2.54060e15	−	4.54300e15i	0.306077	−	0.547316i
$189$	−6.53261e15			−0.758323
$190$	−4.45674e15	−	1.16153e15i	−0.498588	−	0.129944i
$191$			9.65360e15i			1.04101i	0.853858	+	0.520506i	$0.174257\pi$
$191$			9.65360e15i			1.04101i	−0.853858	+	0.520506i	$0.825743\pi$
$192$	−1.04120e16	+	4.28005e14i	−1.08249	+	0.0444980i
$193$	−1.80058e16			−1.80515			−0.902573	−	0.430538i	$-0.858324\pi$
$193$	−1.80058e16			−1.80515			−0.902573	+	0.430538i	$0.858324\pi$
$194$	4.35115e15	−	1.66951e16i	0.420719	−	1.61428i
$195$			1.64867e16i			1.53777i
$196$	−2.73818e15	−	1.53128e15i	−0.246416	−	0.137804i
$197$	4.30570e15			0.373921			0.186961	−	0.982367i	$-0.440136\pi$
$197$	4.30570e15			0.373921			0.186961	+	0.982367i	$0.440136\pi$
$198$	−2.06815e15	−	5.39009e14i	−0.173351	−	0.0451794i
$199$			3.57983e15i			0.289662i	0.989456	+	0.144831i	$0.0462638\pi$
$199$			3.57983e15i			0.289662i	−0.989456	+	0.144831i	$0.953736\pi$
$200$	9.79210e15	−	1.02029e16i	0.765008	−	0.797101i
$201$	1.61632e16			1.21942
$202$	−5.81048e15	+	2.22945e16i	−0.423401	+	1.62457i
$203$			2.59785e15i			0.182870i
$204$	−6.52839e15	+	1.16738e16i	−0.444012	+	0.793966i
$205$	−9.36442e14			−0.0615466
$206$	6.30516e14	+	1.64327e14i	0.0400521	+	0.0104385i
$207$		−	4.81449e15i		−	0.295636i
$208$	−8.62736e15	−	1.40404e16i	−0.512194	−	0.833560i
$209$	6.37750e15			0.366122
$210$	6.04837e15	−	2.32073e16i	0.335818	−	1.28852i
$211$		−	3.54222e16i		−	1.90238i	−0.308599	−	0.951192i	$-0.599860\pi$
$211$		−	3.54222e16i		−	1.90238i	0.308599	−	0.951192i	$-0.400140\pi$
$212$	9.10237e15	+	5.09034e15i	0.472937	+	0.264482i
$213$	−7.79470e15			−0.391870
$214$	3.46224e16	+	9.02343e15i	1.68446	+	0.439011i
$215$			1.31889e16i			0.621070i
$216$	−1.41675e16	−	1.35971e16i	−0.645829	−	0.619827i
$217$	−5.98302e14			−0.0264060
$218$	−7.92298e15	+	3.04001e16i	−0.338605	+	1.29921i
$219$		−	1.48117e14i		−	0.00613051i
$220$	−1.82091e16	+	3.25609e16i	−0.730012	+	1.30538i
$221$	−2.11514e16			−0.821473
$222$	2.88638e16	+	7.52258e15i	1.08613	+	0.283071i
$223$		−	1.98330e16i		−	0.723194i	−0.932335	−	0.361597i	$-0.882232\pi$
$223$		−	1.98330e16i		−	0.723194i	0.932335	−	0.361597i	$-0.117768\pi$
$224$	6.99327e15	+	2.29289e16i	0.247141	+	0.810302i
$225$	−5.60457e15			−0.191984
$226$	7.68849e15	−	2.95003e16i	0.255318	−	0.979643i
$227$		−	1.14566e16i		−	0.368870i	−0.982845	−	0.184435i	$-0.940955\pi$
$227$		−	1.14566e16i		−	0.368870i	0.982845	−	0.184435i	$-0.0590455\pi$
$228$	−1.07560e16	−	6.01512e15i	−0.335821	−	0.187802i
$229$	1.23732e16			0.374657			0.187328	−	0.982297i	$-0.440017\pi$
$229$	1.23732e16			0.374657			0.187328	+	0.982297i	$0.440017\pi$
$230$	−8.13228e16	−	2.11947e16i	−2.38846	−	0.622489i
$231$			3.32091e16i			0.946180i
$232$	−5.40721e15	+	5.63406e15i	−0.149471	+	0.155742i
$233$	3.86944e15			0.103790			0.0518951	−	0.998653i	$-0.483474\pi$
$233$	3.86944e15			0.103790			0.0518951	+	0.998653i	$0.483474\pi$
$234$	−1.64712e15	+	6.31990e15i	−0.0428759	+	0.164513i
$235$			3.60088e16i			0.909775i
$236$	2.29841e16	−	4.10994e16i	0.563695	−	1.00798i
$237$	2.48957e16			0.592770
$238$	2.97735e16	+	7.75968e15i	0.688322	+	0.179393i
$239$		−	1.42837e16i		−	0.320668i	−0.987063	−	0.160334i	$-0.948743\pi$
$239$		−	1.42837e16i		−	0.320668i	0.987063	−	0.160334i	$-0.0512572\pi$
$240$	6.14215e16	−	3.77414e16i	1.33919	−	0.822885i
$241$	−4.35287e15			−0.0921841			−0.0460921	−	0.998937i	$-0.514677\pi$
$241$	−4.35287e15			−0.0921841			−0.0460921	+	0.998937i	$0.514677\pi$
$242$	7.69527e14	−	2.95264e15i	0.0158313	−	0.0607439i
$243$			1.72015e16i			0.343814i
$244$	−1.20926e16	−	6.76258e15i	−0.234850	−	0.131336i
$245$	2.17034e16			0.409606
$246$	−2.42474e15	−	6.31943e14i	−0.0444753	−	0.0115913i
$247$		−	1.94885e16i		−	0.347456i
$248$	−1.29756e15	−	1.24532e15i	−0.0224888	−	0.0215833i
$249$	−5.64633e16			−0.951417
$250$	−2.34065e15	+	8.98097e15i	−0.0383493	+	0.147144i
$251$			1.03484e17i			1.64876i	0.566040	+	0.824378i	$0.308475\pi$
$251$			1.03484e17i			1.64876i	−0.566040	+	0.824378i	$0.691525\pi$
$252$	4.63709e15	−	8.29187e15i	0.0718524	−	0.128484i
$253$	1.16371e17			1.75389
$254$	−1.17670e17	−	3.06676e16i	−1.72516	−	0.449618i
$255$		−	9.25293e16i		−	1.31977i
$256$	−3.25581e16	+	6.42827e16i	−0.451834	+	0.892102i
$257$	−1.39119e17			−1.87868			−0.939342	−	0.342981i	$-0.888563\pi$
$257$	−1.39119e17			−1.87868			−0.939342	+	0.342981i	$0.888563\pi$
$258$	−8.90035e15	+	3.41502e16i	−0.116969	+	0.448803i
$259$		−	6.86154e16i		−	0.877653i
$260$	9.95002e16	+	5.56438e16i	1.23883	+	0.692792i
$261$	3.09485e15			0.0375108
$262$	3.88103e16	+	1.01149e16i	0.457972	+	0.119358i
$263$		−	2.95629e16i		−	0.339669i	−0.985473	−	0.169835i	$-0.945677\pi$
$263$		−	2.95629e16i		−	0.339669i	0.985473	−	0.169835i	$-0.0543234\pi$
$264$	−6.91222e16	+	7.20219e16i	−0.773374	+	0.805819i
$265$	−7.21474e16			−0.786139
$266$	−7.14962e15	+	2.74327e16i	−0.0758772	+	0.291137i
$267$		−	7.67302e16i		−	0.793209i
$268$	5.45519e16	−	9.75478e16i	0.549372	−	0.982367i
$269$	8.72957e16			0.856499			0.428249	−	0.903661i	$-0.359130\pi$
$269$	8.72957e16			0.856499			0.428249	+	0.903661i	$0.359130\pi$
$270$	1.31454e17	+	3.42601e16i	1.25669	+	0.327523i
$271$			1.77937e17i			1.65760i	0.559543	+	0.828801i	$0.310977\pi$
$271$			1.77937e17i			1.65760i	−0.559543	+	0.828801i	$0.689023\pi$
$272$	4.84198e16	+	7.87999e16i	0.439583	+	0.715391i
$273$	1.01481e17			0.897939
$274$	3.41950e16	−	1.31205e17i	0.294923	−	1.13161i
$275$		−	1.35468e17i		−	1.13896i
$276$	−1.96267e17	−	1.09759e17i	−1.60873	−	0.899655i
$277$	−1.24976e17			−0.998778			−0.499389	−	0.866378i	$-0.666442\pi$
$277$	−1.24976e17			−0.998778			−0.499389	+	0.866378i	$0.666442\pi$
$278$	1.26795e17	+	3.30457e16i	0.988071	+	0.257515i
$279$			7.12764e14i			0.00541647i
$280$	−1.19647e17	−	1.14829e17i	−0.886735	−	0.851033i
$281$	9.16435e16			0.662457			0.331228	−	0.943551i	$-0.392537\pi$
$281$	9.16435e16			0.662457			0.331228	+	0.943551i	$0.392537\pi$
$282$	−2.43000e16	+	9.32379e16i	−0.171342	+	0.657429i
$283$			7.61168e16i			0.523571i	0.965126	+	0.261785i	$0.0843112\pi$
$283$			7.61168e16i			0.523571i	−0.965126	+	0.261785i	$0.915689\pi$
$284$	−2.63077e16	+	4.70424e16i	−0.176544	+	0.315690i
$285$	8.52547e16			0.558218
$286$	−1.52759e17	−	3.98125e16i	−0.975985	−	0.254365i
$287$			5.76411e15i			0.0359384i
$288$	2.73155e16	−	8.33117e15i	0.166212	−	0.0506942i
$289$	−4.96686e16			−0.294983
$290$	1.36243e16	−	5.22760e16i	0.0789823	−	0.303051i
$291$			3.19368e17i			1.80734i
$292$	−8.93913e14	−	4.99905e14i	−0.00493873	−	0.00276190i
$293$	−8.23784e16			−0.444365			−0.222183	−	0.975005i	$-0.571318\pi$
$293$	−8.23784e16			−0.444365			−0.222183	+	0.975005i	$0.571318\pi$
$294$	5.61968e16	+	1.46462e16i	0.295992	+	0.0771426i
$295$			3.25763e17i			1.67551i
$296$	1.42817e17	−	1.48809e17i	0.717363	−	0.747458i
$297$	−1.88108e17			−0.922810
$298$	3.07899e16	−	1.18139e17i	0.147535	−	0.566083i
$299$		−	3.55609e17i		−	1.66447i
$300$	−1.27771e17	+	2.28475e17i	−0.584229	+	1.04470i
$301$	8.11823e16			0.362657
$302$	−3.09938e16	−	8.07773e15i	−0.135278	−	0.0352566i
$303$		−	4.26480e17i		−	1.81886i
$304$	−7.26047e16	+	4.46131e16i	−0.302586	+	0.185929i
$305$	9.58486e16			0.390379
$306$	9.24421e15	−	3.54696e16i	0.0367976	−	0.141191i
$307$		−	1.52343e17i		−	0.592726i	−0.955075	−	0.296363i	$-0.904226\pi$
$307$		−	1.52343e17i		−	0.592726i	0.955075	−	0.296363i	$-0.0957738\pi$
$308$	2.00423e17	+	1.12083e17i	0.762242	+	0.426271i
$309$	−1.20614e16			−0.0448422
$310$	1.20395e16	+	3.13778e15i	0.0437599	+	0.0114049i
$311$		−	1.11654e16i		−	0.0396781i	−0.999803	−	0.0198390i	$-0.993685\pi$
$311$		−	1.11654e16i		−	0.0396781i	0.999803	−	0.0198390i	$-0.00631538\pi$
$312$	2.20086e17	+	2.11225e17i	0.764734	+	0.733944i
$313$	4.49996e17			1.52897			0.764483	−	0.644644i	$-0.222994\pi$
$313$	4.49996e17			1.52897			0.764483	+	0.644644i	$0.222994\pi$
$314$	−8.78948e16	+	3.37248e17i	−0.292049	+	1.12058i
$315$			6.57232e16i			0.213572i
$316$	8.40248e16	−	1.50250e17i	0.267053	−	0.477535i
$317$	2.34027e16			0.0727531			0.0363766	−	0.999338i	$-0.488418\pi$
$317$	2.34027e16			0.0727531			0.0363766	+	0.999338i	$0.488418\pi$
$318$	−1.86812e17	−	4.86875e16i	−0.568086	−	0.148057i
$319$			7.48057e16i			0.222536i
$320$	−2.04741e16	−	4.98069e17i	−0.0595875	−	1.44957i
$321$	−6.62306e17			−1.88592
$322$	−1.30460e17	+	5.00569e17i	−0.363485	+	1.39468i
$323$			1.09376e17i			0.298199i
$324$	3.74102e17	+	2.09210e17i	0.998102	+	0.558171i
$325$	−4.13966e17			−1.08089
$326$	−5.11117e17	−	1.33209e17i	−1.30616	−	0.340417i
$327$		−	5.81535e17i		−	1.45459i
$328$	−1.19975e16	+	1.25009e16i	−0.0293748	+	0.0306071i
$329$	2.21646e17			0.531239
$330$	1.74164e17	−	6.68260e17i	0.408660	−	1.56801i
$331$			4.74292e17i			1.08956i	0.838580	+	0.544778i	$0.183386\pi$
$331$			4.74292e17i			1.08956i	−0.838580	+	0.544778i	$0.816614\pi$
$332$	−1.90568e17	+	3.40766e17i	−0.428630	+	0.766460i
$333$	−8.17423e16			−0.180027
$334$	3.95763e17	+	1.03145e17i	0.853513	+	0.222446i
$335$			7.73185e17i			1.63294i
$336$	−2.32311e17	−	3.78070e17i	−0.480501	−	0.781983i
$337$	6.48884e17			1.31449			0.657245	−	0.753677i	$-0.271722\pi$
$337$	6.48884e17			1.31449			0.657245	+	0.753677i	$0.271722\pi$
$338$	5.44452e15	−	2.08904e16i	0.0108030	−	0.0414504i
$339$			5.64323e17i			1.09681i
$340$	−5.58431e17	−	3.12293e17i	−1.06320	−	0.594579i
$341$	−1.72282e16			−0.0321337
$342$	3.26810e16	+	8.51743e15i	0.0597189	+	0.0155642i
$343$		−	6.06766e17i		−	1.08633i
$344$	1.76063e17	+	1.68975e17i	0.308859	+	0.296423i
$345$	1.55565e18			2.67411
$346$	2.41829e17	−	9.27885e17i	0.407357	−	1.56301i
$347$		−	7.04504e17i		−	1.16299i	−0.813549	−	0.581496i	$-0.802468\pi$
$347$		−	7.04504e17i		−	1.16299i	0.813549	−	0.581496i	$-0.197532\pi$
$348$	7.05552e16	−	1.26164e17i	0.114150	−	0.204118i
$349$	−9.26668e17			−1.46942			−0.734711	−	0.678381i	$-0.762682\pi$
$349$	−9.26668e17			−1.46942			−0.734711	+	0.678381i	$0.762682\pi$
$350$	5.82715e17	+	1.51869e17i	0.905690	+	0.236044i
$351$			5.74825e17i			0.875761i
$352$	2.01373e17	+	6.60243e17i	0.300748	+	0.986065i
$353$	−1.15975e18			−1.69801			−0.849005	−	0.528385i	$-0.822798\pi$
$353$	−1.15975e18			−1.69801			−0.849005	+	0.528385i	$0.822798\pi$
$354$	−2.19836e17	+	8.43500e17i	−0.315556	+	1.21077i
$355$		−	3.72868e17i		−	0.524756i
$356$	−4.63080e17	−	2.58970e17i	−0.639008	−	0.357354i
$357$	−5.69549e17			−0.770643
$358$	1.31972e17	+	3.43949e16i	0.175105	+	0.0456366i
$359$		−	8.35881e16i		−	0.108764i	−0.998520	−	0.0543818i	$-0.982681\pi$
$359$		−	8.35881e16i		−	0.108764i	0.998520	−	0.0543818i	$-0.0173188\pi$
$360$	−1.36798e17	+	1.42536e17i	−0.174566	+	0.181890i
$361$	6.98229e17			0.873872
$362$	−2.42982e16	+	9.32309e16i	−0.0298273	+	0.114446i
$363$			5.64821e16i			0.0680087i
$364$	3.42506e17	−	6.12457e17i	0.404537	−	0.723379i
$365$	7.08535e15			0.00820940
$366$	2.48181e17	+	6.46819e16i	0.282099	+	0.0735217i
$367$		−	8.77749e17i		−	0.978831i	−0.872051	−	0.489416i	$-0.837210\pi$
$367$		−	8.77749e17i		−	0.978831i	0.872051	−	0.489416i	$-0.162790\pi$
$368$	−1.32483e18	+	8.14061e17i	−1.44952	+	0.890681i
$369$	6.86686e15			0.00737180
$370$	−3.59851e17	+	1.38073e18i	−0.379063	+	1.45445i
$371$			4.44091e17i			0.459045i
$372$	2.90565e16	+	1.62493e16i	0.0294742	+	0.0164829i
$373$	−5.51683e17			−0.549196			−0.274598	−	0.961559i	$-0.588545\pi$
$373$	−5.51683e17			−0.549196			−0.274598	+	0.961559i	$0.588545\pi$
$374$	8.57336e17	+	2.23442e17i	0.837625	+	0.218305i
$375$		−	1.71800e17i		−	0.164742i
$376$	4.80693e17	+	4.61339e17i	0.452432	+	0.434216i
$377$	2.28593e17			0.211190
$378$	2.10882e17	−	8.09145e17i	0.191248	−	0.733810i
$379$		−	1.91257e18i		−	1.70272i	−0.524580	−	0.851361i	$-0.675778\pi$
$379$		−	1.91257e18i		−	1.70272i	0.524580	−	0.851361i	$-0.324222\pi$
$380$	2.87740e17	−	5.14527e17i	0.251487	−	0.449700i
$381$	2.25096e18			1.93149
$382$	−1.19572e18	−	3.11632e17i	−1.00736	−	0.262542i
$383$			1.96195e18i			1.62291i	0.584412	+	0.811457i	$0.301325\pi$
$383$			1.96195e18i			1.62291i	−0.584412	+	0.811457i	$0.698675\pi$
$384$	2.83101e17	−	1.30347e18i	0.229944	−	1.05872i
$385$	−1.58860e18			−1.26704
$386$	5.81255e17	−	2.23025e18i	0.455256	−	1.74679i
$387$		−	9.67135e16i		−	0.0743893i
$388$	1.92744e18	+	1.07789e18i	1.45599	+	0.814239i
$389$	−2.25076e17			−0.166987			−0.0834933	−	0.996508i	$-0.526608\pi$
$389$	−2.25076e17			−0.166987			−0.0834933	+	0.996508i	$0.526608\pi$
$390$	−2.04208e18	−	5.32215e17i	−1.48806	−	0.387824i
$391$			1.99581e18i			1.42850i
$392$	2.78061e17	−	2.89726e17i	0.195496	−	0.203697i
$393$	−7.42418e17			−0.512744
$394$	−1.38994e17	+	5.33314e17i	−0.0943026	+	0.361834i
$395$			1.19092e18i			0.793782i
$396$	1.33526e17	−	2.38766e17i	0.0874379	−	0.156353i
$397$	2.10584e18			1.35485			0.677427	−	0.735590i	$-0.263095\pi$
$397$	2.10584e18			1.35485			0.677427	+	0.735590i	$0.263095\pi$
$398$	−4.43407e17	−	1.15562e17i	−0.280299	−	0.0730524i
$399$		−	5.24771e17i		−	0.325956i
$400$	9.47652e17	+	1.54224e18i	0.578401	+	0.941308i
$401$	1.01874e18			0.611014			0.305507	−	0.952190i	$-0.401174\pi$
$401$	1.01874e18			0.611014			0.305507	+	0.952190i	$0.401174\pi$
$402$	−5.21772e17	+	2.00201e18i	−0.307538	+	1.18001i
$403$			5.26464e16i			0.0304953i
$404$	−2.57388e18	−	1.43940e18i	−1.46527	−	0.819430i
$405$	−2.96521e18			−1.65909
$406$	−3.21776e17	−	8.38624e16i	−0.176958	−	0.0461196i
$407$		−	1.97580e18i		−	1.06802i
$408$	−1.23520e18	−	1.18547e18i	−0.656322	−	0.629897i
$409$	−5.09887e17			−0.266324			−0.133162	−	0.991094i	$-0.542513\pi$
$409$	−5.09887e17			−0.266324			−0.133162	+	0.991094i	$0.542513\pi$
$410$	3.02297e16	−	1.15990e17i	0.0155220	−	0.0595571i
$411$			2.50986e18i			1.26694i
$412$	−4.07080e16	+	7.27925e16i	−0.0202022	+	0.0361249i
$413$	2.00518e18			0.978369
$414$	5.96334e17	+	1.55419e17i	0.286080	+	0.0745592i
$415$		−	2.70099e18i		−	1.27405i
$416$	2.01759e18	−	6.15360e17i	0.935790	−	0.285414i
$417$	−2.42551e18			−1.10624
$418$	−2.05875e17	+	7.89932e17i	−0.0923357	+	0.354288i
$419$		−	1.48939e18i		−	0.656917i	−0.944518	−	0.328459i	$-0.893471\pi$
$419$		−	1.48939e18i		−	0.656917i	0.944518	−	0.328459i	$-0.106529\pi$
$420$	2.67926e18	+	1.49833e18i	1.16217	+	0.649925i
$421$	−3.84687e17			−0.164109			−0.0820546	−	0.996628i	$-0.526148\pi$
$421$	−3.84687e17			−0.164109			−0.0820546	+	0.996628i	$0.526148\pi$
$422$	4.38748e18	+	1.14348e18i	1.84089	+	0.479780i
$423$		−	2.64050e17i		−	0.108969i
$424$	−9.24340e17	+	9.63118e17i	−0.375207	+	0.390948i
$425$	2.32333e18			0.927658
$426$	2.51624e17	−	9.65471e17i	0.0988293	−	0.379203i
$427$		−	5.89980e17i		−	0.227951i
$428$	−2.23533e18	+	3.99713e18i	−0.849640	+	1.51929i
$429$	2.92218e18			1.09271
$430$	−1.63361e18	−	4.25759e17i	−0.600994	−	0.156633i
$431$		−	3.54760e18i		−	1.28408i	−0.766669	−	0.642042i	$-0.778087\pi$
$431$		−	3.54760e18i		−	1.28408i	0.766669	−	0.642042i	$-0.221913\pi$
$432$	2.14152e18	−	1.31589e18i	0.762668	−	0.468633i
$433$	−2.75629e18			−0.965849			−0.482925	−	0.875662i	$-0.660426\pi$
$433$	−2.75629e18			−0.965849			−0.482925	+	0.875662i	$0.660426\pi$
$434$	1.93141e16	−	7.41071e16i	0.00665956	−	0.0255524i
$435$			1.00001e18i			0.339295i
$436$	−3.50966e18	−	1.96272e18i	−1.17182	−	0.655319i
$437$	−1.83890e18			−0.604209
$438$	1.83461e16	+	4.78144e15i	0.00593234	+	0.00154611i
$439$			3.70584e18i			1.17933i	0.807648	+	0.589665i	$0.200740\pi$
$439$			3.70584e18i			1.17933i	−0.807648	+	0.589665i	$0.799260\pi$
$440$	−3.44525e18	−	3.30654e18i	−1.07908	−	1.03563i
$441$	−1.59150e17			−0.0490609
$442$	6.82799e17	−	2.61986e18i	0.207175	−	0.794919i
$443$			1.77582e18i			0.530362i	0.964199	+	0.265181i	$0.0854317\pi$
$443$			1.77582e18i			0.530362i	−0.964199	+	0.265181i	$0.914568\pi$
$444$	−1.86353e18	+	3.33230e18i	−0.547843	+	0.979632i
$445$	3.67048e18			1.06219
$446$	2.45657e18	+	6.40239e17i	0.699817	+	0.182389i
$447$			2.25993e18i			0.633785i
$448$	−3.06578e18	+	1.26025e17i	−0.846438	+	0.0347945i
$449$	−3.86648e18			−1.05097			−0.525486	−	0.850802i	$-0.676116\pi$
$449$	−3.86648e18			−1.05097			−0.525486	+	0.850802i	$0.676116\pi$
$450$	1.80924e17	−	6.94195e17i	0.0484181	−	0.185778i
$451$			1.65979e17i			0.0437338i
$452$	3.40579e18	+	1.90463e18i	0.883586	+	0.494130i
$453$	5.92893e17			0.151457
$454$	1.41904e18	+	3.69835e17i	0.356946	+	0.0930286i
$455$			4.85447e18i			1.20244i
$456$	1.09227e18	−	1.13809e18i	0.266425	−	0.277602i
$457$	−1.78862e18			−0.429639			−0.214820	−	0.976654i	$-0.568916\pi$
$457$	−1.78862e18			−0.429639			−0.214820	+	0.976654i	$0.568916\pi$
$458$	−3.99425e17	+	1.53257e18i	−0.0944881	+	0.362546i
$459$		−	3.22612e18i		−	0.751609i
$460$	5.25044e18	−	9.38865e18i	1.20473	−	2.15426i
$461$	3.38458e18			0.764889			0.382444	−	0.923979i	$-0.375082\pi$
$461$	3.38458e18			0.764889			0.382444	+	0.923979i	$0.375082\pi$
$462$	−4.11337e18	−	1.07204e18i	−0.915595	−	0.238626i
$463$			1.27172e18i			0.278821i	0.990235	+	0.139410i	$0.0445207\pi$
$463$			1.27172e18i			0.278821i	−0.990235	+	0.139410i	$0.955479\pi$
$464$	−5.23295e17	−	8.51626e17i	−0.113011	−	0.183918i
$465$	−2.30308e17			−0.0489935
$466$	−1.24911e17	+	4.79278e17i	−0.0261758	+	0.100435i
$467$		−	1.67912e18i		−	0.346628i	−0.984867	−	0.173314i	$-0.944553\pi$
$467$		−	1.67912e18i		−	0.346628i	0.984867	−	0.173314i	$-0.0554475\pi$
$468$	−7.29627e17	−	4.08032e17i	−0.148382	−	0.0829799i
$469$	4.75921e18			0.953510
$470$	−4.46014e18	−	1.16242e18i	−0.880367	−	0.229444i
$471$		−	6.45134e18i		−	1.25460i
$472$	4.34871e18	+	4.17362e18i	0.833232	+	0.799684i
$473$	2.33767e18			0.441321
$474$	−8.03671e17	+	3.08365e18i	−0.149496	+	0.573609i
$475$			2.14067e18i			0.392368i
$476$	−1.92227e18	+	3.43733e18i	−0.347188	+	0.620829i
$477$	5.29052e17			0.0941606
$478$	1.76922e18	+	4.61100e17i	0.310303	+	0.0808722i
$479$		−	2.63877e18i		−	0.456092i	−0.973650	−	0.228046i	$-0.926766\pi$
$479$		−	2.63877e18i		−	0.456092i	0.973650	−	0.228046i	$-0.0732337\pi$
$480$	2.69196e18	+	8.82616e18i	0.458543	+	1.50343i
$481$	−6.03768e18			−1.01357
$482$	1.40517e17	−	5.39157e17i	0.0232488	−	0.0892043i
$483$		−	9.57558e18i		−	1.56147i
$484$	3.40879e17	+	1.90631e17i	0.0547877	+	0.0306391i
$485$	−1.52773e19			−2.42022
$486$	−2.13062e18	−	5.55291e17i	−0.332700	−	0.0867095i
$487$			6.02454e18i			0.927303i	0.886018	+	0.463651i	$0.153461\pi$
$487$			6.02454e18i			0.927303i	−0.886018	+	0.463651i	$0.846539\pi$
$488$	1.22800e18	−	1.27951e18i	0.186320	−	0.194136i
$489$	9.77735e18			1.46238
$490$	−7.00619e17	+	2.68824e18i	−0.103302	+	0.396365i
$491$			3.04593e18i			0.442741i	0.975190	+	0.221371i	$0.0710531\pi$
$491$			3.04593e18i			0.442741i	−0.975190	+	0.221371i	$0.928947\pi$
$492$	1.56548e17	−	2.79934e17i	0.0224332	−	0.0401143i
$493$	−1.28295e18			−0.181251
$494$	2.41389e18	+	6.29117e17i	0.336224	+	0.0876280i
$495$			1.89252e18i			0.259898i
$496$	1.96135e17	−	1.20518e17i	0.0265573	−	0.0163185i
$497$	−2.29513e18			−0.306417
$498$	1.82272e18	−	6.99368e18i	0.239946	−	0.920663i
$499$			4.15397e18i			0.539212i	0.962971	+	0.269606i	$0.0868935\pi$
$499$			4.15397e18i			0.539212i	−0.962971	+	0.269606i	$0.913106\pi$
$500$	−1.03685e18	−	5.79838e17i	−0.132716	−	0.0742193i
$501$	−7.57070e18			−0.955591
$502$	−1.28178e19	−	3.34061e18i	−1.59546	−	0.415815i
$503$		−	8.28512e18i		−	1.01700i	−0.861061	−	0.508502i	$-0.830199\pi$
$503$		−	8.28512e18i		−	1.01700i	0.861061	−	0.508502i	$-0.169801\pi$
$504$	8.77359e17	+	8.42035e17i	0.106210	+	0.101933i
$505$	2.04012e19			2.43565
$506$	−3.75663e18	+	1.44140e19i	−0.442329	+	1.69719i
$507$			3.99620e17i			0.0464078i
$508$	7.59713e18	−	1.35849e19i	0.870169	−	1.55601i
$509$	−1.06268e17			−0.0120054			−0.00600270	−	0.999982i	$-0.501911\pi$
$509$	−1.06268e17			−0.0120054			−0.00600270	+	0.999982i	$0.501911\pi$
$510$	1.14609e19	+	2.98698e18i	1.27711	+	0.332845i
$511$		−	4.36127e16i		−	0.00479365i
$512$	−6.91119e18	−	6.10787e18i	−0.749313	−	0.662216i
$513$	2.97249e18			0.317906
$514$	4.49096e18	−	1.72316e19i	0.473803	−	1.81796i
$515$		−	5.76970e17i		−	0.0600485i
$516$	−3.94261e18	−	2.20484e18i	−0.404796	−	0.226375i
$517$	6.38237e18			0.646469
$518$	8.49887e18	+	2.21501e18i	0.849284	+	0.221343i
$519$			1.77499e19i			1.74994i
$520$	−1.01042e19	+	1.05281e19i	−0.982829	+	1.02406i
$521$	5.25175e18			0.504011			0.252006	−	0.967726i	$-0.418910\pi$
$521$	5.25175e18			0.504011			0.252006	+	0.967726i	$0.418910\pi$
$522$	−9.99063e16	+	3.83336e17i	−0.00946018	+	0.0362983i
$523$			1.39466e19i			1.30304i	0.758632	+	0.651519i	$0.225868\pi$
$523$			1.39466e19i			1.30304i	−0.758632	+	0.651519i	$0.774132\pi$
$524$	−2.50571e18	+	4.48062e18i	−0.231000	+	0.413066i
$525$	−1.11470e19			−1.01401
$526$	3.66173e18	+	9.54333e17i	0.328690	+	0.0856643i
$527$		−	2.95471e17i		−	0.0261722i
$528$	−6.68945e18	−	1.08866e19i	−0.584727	−	0.951602i
$529$	−2.19618e19			−1.89443
$530$	2.32902e18	−	8.93635e18i	0.198264	−	0.760728i
$531$		−	2.38879e18i		−	0.200686i
$532$	−3.16708e18	−	1.77114e18i	−0.262590	−	0.146849i
$533$	5.07202e17			0.0415041
$534$	9.50399e18	+	2.47696e18i	0.767568	+	0.200046i
$535$		−	3.16821e19i		−	2.52545i
$536$	1.03215e19	+	9.90592e18i	0.812061	+	0.779366i
$537$	−2.52454e18			−0.196048
$538$	−2.81803e18	+	1.08127e19i	−0.216008	+	0.828813i
$539$		−	3.84681e18i		−	0.291058i
$540$	−8.48708e18	+	1.51763e19i	−0.633873	+	1.13347i
$541$	−7.44833e18			−0.549134			−0.274567	−	0.961568i	$-0.588534\pi$
$541$	−7.44833e18			−0.549134			−0.274567	+	0.961568i	$0.588534\pi$
$542$	−2.20397e19	−	5.74406e18i	−1.60402	−	0.418046i
$543$		−	1.78345e18i		−	0.128133i
$544$	−1.13234e19	+	3.45362e18i	−0.803129	+	0.244953i
$545$	2.78184e19			1.94785
$546$	−3.27596e18	+	1.25697e19i	−0.226459	+	0.868914i
$547$			1.84776e19i			1.26106i	0.776167	+	0.630528i	$0.217162\pi$
$547$			1.84776e19i			1.26106i	−0.776167	+	0.630528i	$0.782838\pi$
$548$	1.51475e19	+	8.47096e18i	1.02065	+	0.570780i
$549$	−7.02851e17			−0.0467581
$550$	1.67794e19	+	4.37311e18i	1.10214	+	0.287244i
$551$		−	1.18208e18i		−	0.0766630i
$552$	1.99308e19	−	2.07669e19i	1.27629	−	1.32984i
$553$	7.33048e18			0.463507
$554$	4.03442e18	−	1.54799e19i	0.251891	−	0.966493i
$555$		−	2.64125e19i		−	1.62839i
$556$	−8.18625e18	+	1.46384e19i	−0.498381	+	0.891187i
$557$	1.27693e19			0.767683			0.383841	−	0.923399i	$-0.374601\pi$
$557$	1.27693e19			0.767683			0.383841	+	0.923399i	$0.374601\pi$
$558$	−8.82847e16	−	2.30091e16i	−0.00524139	−	0.00136603i
$559$		−	7.14349e18i		−	0.418820i
$560$	1.80854e19	−	1.11129e19i	1.04716	−	0.643442i
$561$	−1.64003e19			−0.937803
$562$	−2.95839e18	+	1.13512e19i	−0.167071	+	0.641043i
$563$			1.53198e18i			0.0854467i	0.999087	+	0.0427234i	$0.0136034\pi$
$563$			1.53198e18i			0.0854467i	−0.999087	+	0.0427234i	$0.986397\pi$
$564$	−1.07642e19	−	6.01972e18i	−0.592966	−	0.331606i
$565$	−2.69950e19			−1.46874
$566$	−9.42801e18	−	2.45716e18i	−0.506646	−	0.132044i
$567$			1.82519e19i			0.968783i
$568$	−4.97754e18	−	4.77713e18i	−0.260961	−	0.250454i
$569$	−1.27708e19			−0.661350			−0.330675	−	0.943745i	$-0.607276\pi$
$569$	−1.27708e19			−0.661350			−0.330675	+	0.943745i	$0.607276\pi$
$570$	−2.75215e18	+	1.05599e19i	−0.140782	+	0.540174i
$571$		−	3.30749e19i		−	1.67127i	−0.549286	−	0.835635i	$-0.685100\pi$
$571$		−	3.30749e19i		−	1.67127i	0.549286	−	0.835635i	$-0.314900\pi$
$572$	9.86254e18	−	1.76358e19i	0.492285	−	0.880287i
$573$	2.28733e19			1.12784
$574$	−7.13957e17	−	1.86074e17i	−0.0347767	−	0.00906364i
$575$			3.90611e19i			1.87962i
$576$	1.50135e17	+	3.65231e18i	0.00713715	+	0.173624i
$577$	2.53825e19			1.19207			0.596037	−	0.802957i	$-0.296741\pi$
$577$	2.53825e19			1.19207			0.596037	+	0.802957i	$0.296741\pi$
$578$	1.60337e18	−	6.15207e18i	0.0743944	−	0.285448i
$579$			4.26632e19i			1.95571i
$580$	6.03521e18	+	3.37509e18i	0.273336	+	0.152858i
$581$	−1.66255e19			−0.743946
$582$	−3.95577e19	−	1.03097e19i	−1.74892	−	0.455810i
$583$			1.27877e19i			0.558616i
$584$	9.07763e16	−	9.45845e16i	0.00391816	−	0.00408254i
$585$	5.78319e18			0.246647
$586$	2.65930e18	−	1.02036e19i	0.112068	−	0.430001i
$587$			8.66644e18i			0.360889i	0.983585	+	0.180445i	$0.0577537\pi$
$587$			8.66644e18i			0.360889i	−0.983585	+	0.180445i	$0.942246\pi$
$588$	−3.62823e18	+	6.48788e18i	−0.149298	+	0.266969i
$589$	2.72241e17			0.0110700
$590$	−4.03498e19	−	1.05161e19i	−1.62135	−	0.422562i
$591$		−	1.02020e19i		−	0.405109i
$592$	1.38215e19	+	2.24935e19i	0.542378	+	0.882683i
$593$	1.33237e18			0.0516704			0.0258352	−	0.999666i	$-0.491775\pi$
$593$	1.33237e18			0.0516704			0.0258352	+	0.999666i	$0.491775\pi$
$594$	6.07241e18	−	2.32995e19i	0.232732	−	0.892981i
$595$		−	2.72450e19i		−	1.03197i
$596$	1.36391e19	+	7.62741e18i	0.510576	+	0.285531i
$597$	8.48210e18			0.313822
$598$	4.40466e19	+	1.14796e19i	1.61066	+	0.419777i
$599$		−	3.49944e19i		−	1.26477i	−0.774656	−	0.632383i	$-0.782077\pi$
$599$		−	3.49944e19i		−	1.26477i	0.774656	−	0.632383i	$-0.217923\pi$
$600$	−2.41749e19	−	2.32015e19i	−0.863585	−	0.828815i
$601$	−2.22716e19			−0.786376			−0.393188	−	0.919458i	$-0.628628\pi$
$601$	−2.22716e19			−0.786376			−0.393188	+	0.919458i	$0.628628\pi$
$602$	−2.62069e18	+	1.00554e19i	−0.0914618	+	0.350934i
$603$		−	5.66971e18i		−	0.195587i
$604$	2.00105e18	−	3.57821e18i	0.0682339	−	0.122013i
$605$	−2.70189e18			−0.0910709
$606$	5.28249e19	+	1.37674e19i	1.76007	+	0.458716i
$607$			2.81797e19i			0.928145i	0.885797	+	0.464073i	$0.153612\pi$
$607$			2.81797e19i			0.928145i	−0.885797	+	0.464073i	$0.846388\pi$
$608$	−3.18210e18	−	1.04332e19i	−0.103607	−	0.339697i
$609$	6.15537e18			0.198122
$610$	−3.09413e18	+	1.18720e19i	−0.0984533	+	0.377761i
$611$		−	1.95034e19i		−	0.613509i
$612$	4.09493e18	+	2.29002e18i	0.127346	+	0.0712163i
$613$	2.19343e19			0.674372			0.337186	−	0.941438i	$-0.390525\pi$
$613$	2.19343e19			0.674372			0.337186	+	0.941438i	$0.390525\pi$
$614$	1.88696e19	+	4.91786e18i	0.573566	+	0.149485i
$615$			2.21882e18i			0.0666800i
$616$	−2.03528e19	+	2.12067e19i	−0.604728	+	0.630097i
$617$	−4.07723e19			−1.19776			−0.598879	−	0.800840i	$-0.704387\pi$
$617$	−4.07723e19			−1.19776			−0.598879	+	0.800840i	$0.704387\pi$
$618$	3.89359e17	−	1.49395e18i	0.0113092	−	0.0433927i
$619$		−	1.07476e19i		−	0.308658i	−0.988019	−	0.154329i	$-0.950678\pi$
$619$		−	1.07476e19i		−	0.308658i	0.988019	−	0.154329i	$-0.0493216\pi$
$620$	−7.77305e17	+	1.38995e18i	−0.0220724	+	0.0394691i
$621$	5.42394e19			1.52291
$622$	1.38297e18	+	3.60435e17i	0.0383955	+	0.0100068i
$623$		−	2.25930e19i		−	0.620237i
$624$	−3.32675e19	+	2.04418e19i	−0.903085	+	0.554914i
$625$	−3.29391e19			−0.884204
$626$	−1.45265e19	+	5.57375e19i	−0.385604	+	1.47954i
$627$		−	1.51109e19i		−	0.396659i
$628$	−3.89350e19	−	2.17737e19i	−1.01070	−	0.565217i
$629$	3.38856e19			0.869883
$630$	−8.14064e18	−	2.12164e18i	−0.206669	−	0.0538627i
$631$		−	6.39901e19i		−	1.60660i	−0.595575	−	0.803300i	$-0.703076\pi$
$631$		−	6.39901e19i		−	1.60660i	0.595575	−	0.803300i	$-0.296924\pi$
$632$	1.58979e19	+	1.52578e19i	0.394748	+	0.378855i
$633$	−8.39297e19			−2.06106
$634$	−7.55475e17	+	2.89872e18i	−0.0183483	+	0.0704014i
$635$			1.07677e20i			2.58647i
$636$	1.20611e19	−	2.15673e19i	0.286542	−	0.512383i
$637$	−1.17552e19			−0.276218
$638$	−9.26562e18	−	2.41484e18i	−0.215342	−	0.0561233i
$639$			2.73422e18i			0.0628531i
$640$	6.23530e19	+	1.35424e19i	1.41774	+	0.307919i
$641$	5.57952e18			0.125485			0.0627423	−	0.998030i	$-0.480015\pi$
$641$	5.57952e18			0.125485			0.0627423	+	0.998030i	$0.480015\pi$
$642$	2.13802e19	−	8.20348e19i	0.475627	−	1.82496i
$643$			3.16664e19i			0.696822i	0.937342	+	0.348411i	$0.113279\pi$
$643$			3.16664e19i			0.696822i	−0.937342	+	0.348411i	$0.886721\pi$
$644$	−5.77903e19	−	3.23182e19i	−1.25792	−	0.703471i
$645$	3.12500e19			0.672872
$646$	−1.35476e19	−	3.53083e18i	−0.288560	−	0.0752054i
$647$			4.14438e19i			0.873231i	0.899648	+	0.436616i	$0.143823\pi$
$647$			4.14438e19i			0.873231i	−0.899648	+	0.436616i	$0.856177\pi$
$648$	−3.79898e19	+	3.95836e19i	−0.791849	+	0.825068i
$649$	5.77396e19			1.19059
$650$	1.33634e19	−	5.12749e19i	0.272599	−	1.04595i
$651$			1.41762e18i			0.0286084i
$652$	3.29992e19	−	5.90080e19i	0.658826	−	1.17809i
$653$	−3.03333e19			−0.599138			−0.299569	−	0.954075i	$-0.596843\pi$
$653$	−3.03333e19			−0.599138			−0.299569	+	0.954075i	$0.596843\pi$
$654$	7.20303e19	+	1.87728e19i	1.40757	+	0.366847i
$655$		−	3.55144e19i		−	0.686618i
$656$	−1.16109e18	−	1.88959e18i	−0.0222095	−	0.0361444i
$657$	−5.19563e16			−0.000983289
$658$	−7.15508e18	+	2.74537e19i	−0.133978	+	0.514066i
$659$		−	5.74518e18i		−	0.106440i	−0.998583	−	0.0532201i	$-0.983051\pi$
$659$		−	5.74518e18i		−	0.106440i	0.998583	−	0.0532201i	$-0.0169485\pi$
$660$	7.71501e19	+	4.31449e19i	1.41426	+	0.790900i
$661$	7.51512e19			1.36309			0.681547	−	0.731775i	$-0.261308\pi$
$661$	7.51512e19			1.36309			0.681547	+	0.731775i	$0.261308\pi$
$662$	−5.87469e19	−	1.53108e19i	−1.05434	−	0.274785i
$663$			5.01164e19i			0.889989i
$664$	−3.60563e19	−	3.46046e19i	−0.633585	−	0.608075i
$665$	2.51030e19			0.436490
$666$	2.63876e18	−	1.01248e19i	0.0454026	−	0.174208i
$667$		−	2.15696e19i		−	0.367249i
$668$	−2.55516e19	+	4.56905e19i	−0.430510	+	0.769823i
$669$	−4.69926e19			−0.783513
$670$	−9.57686e19	−	2.49596e19i	−1.58015	−	0.411826i
$671$		−	1.69886e19i		−	0.277396i
$672$	5.43280e19	−	1.65699e19i	0.877887	−	0.267754i
$673$	−2.08259e19			−0.333041			−0.166521	−	0.986038i	$-0.553253\pi$
$673$	−2.08259e19			−0.333041			−0.166521	+	0.986038i	$0.553253\pi$
$674$	−2.09469e19	+	8.03723e19i	−0.331513	+	1.27200i
$675$		−	6.31403e19i		−	0.988964i
$676$	2.41178e18	+	1.34874e18i	0.0373861	+	0.0209075i
$677$	−1.13345e19			−0.173893			−0.0869464	−	0.996213i	$-0.527711\pi$
$677$	−1.13345e19			−0.173893			−0.0869464	+	0.996213i	$0.527711\pi$
$678$	−6.98984e19	−	1.82172e19i	−1.06135	−	0.276614i
$679$			9.40370e19i			1.41322i
$680$	5.67083e19	−	5.90873e19i	0.843499	−	0.878885i
$681$	−2.71453e19			−0.399636
$682$	5.56153e17	−	2.13393e18i	0.00810408	−	0.0310950i
$683$		−	7.73552e19i		−	1.11569i	−0.829944	−	0.557846i	$-0.811628\pi$
$683$		−	7.73552e19i		−	1.11569i	0.829944	−	0.557846i	$-0.188372\pi$
$684$	−2.10998e18	+	3.77299e18i	−0.0301221	+	0.0538633i
$685$	−1.20062e20			−1.69657
$686$	7.51555e19	+	1.95873e19i	1.05122	+	0.273972i
$687$		−	2.93172e19i		−	0.405906i
$688$	−2.66132e19	+	1.63529e19i	−0.364735	+	0.224117i
$689$	3.90770e19			0.530135
$690$	−5.02188e19	+	1.92687e20i	−0.674408	+	2.58767i
$691$			7.17459e19i			0.953786i	0.878961	+	0.476893i	$0.158237\pi$
$691$			7.17459e19i			0.953786i	−0.878961	+	0.476893i	$0.841763\pi$
$692$	1.07124e20	+	5.99070e19i	1.40975	+	0.788379i
$693$	1.16491e19			0.151760
$694$	8.72615e19	+	2.27424e19i	1.12540	+	0.293306i
$695$		−	1.16027e20i		−	1.48137i
$696$	1.33494e19	+	1.28119e19i	0.168732	+	0.161938i
$697$	−2.84660e18			−0.0356203
$698$	2.99142e19	−	1.14779e20i	0.370587	−	1.42192i
$699$		−	9.16829e18i		−	0.112447i
$700$	−3.76218e19	+	6.72739e19i	−0.456828	+	0.816884i
$701$	−2.41146e19			−0.289904			−0.144952	−	0.989439i	$-0.546303\pi$
$701$	−2.41146e19			−0.289904			−0.144952	+	0.989439i	$0.546303\pi$
$702$	−7.11992e19	−	1.85562e19i	−0.847452	−	0.220866i
$703$			3.12215e19i			0.367932i
$704$	−8.82800e19	+	3.62892e18i	−1.03004	+	0.0423418i
$705$	8.53198e19			0.985657
$706$	3.74383e19	−	1.43649e20i	0.428236	−	1.64312i
$707$		−	1.25576e20i		−	1.42223i
$708$	−9.73813e19	−	5.44588e19i	−1.09205	−	0.610711i
$709$	1.28450e20			1.42630			0.713151	−	0.701011i	$-0.247268\pi$
$709$	1.28450e20			1.42630			0.713151	+	0.701011i	$0.247268\pi$
$710$	4.61844e19	+	1.20367e19i	0.507793	+	0.132343i
$711$		−	8.73289e18i		−	0.0950760i
$712$	4.70255e19	−	4.89983e19i	0.506960	−	0.528228i
$713$	4.96762e18			0.0530300
$714$	1.83859e19	−	7.05457e19i	0.194356	−	0.745733i
$715$			1.39786e20i			1.46326i
$716$	−8.52048e18	+	1.52360e19i	−0.0883228	+	0.157936i
$717$	−3.38440e19			−0.347414
$718$	1.03534e19	+	2.69835e18i	0.105248	+	0.0274301i
$719$			4.82643e19i			0.485874i	0.970042	+	0.242937i	$0.0781109\pi$
$719$			4.82643e19i			0.485874i	−0.970042	+	0.242937i	$0.921889\pi$
$720$	−1.32389e19	−	2.15454e19i	−0.131985	−	0.214796i
$721$	−3.55144e18			−0.0350637
$722$	−2.25399e19	+	8.64844e19i	−0.220390	+	0.845624i
$723$			1.03137e19i			0.0998729i
$724$	−1.07634e19	−	6.01926e18i	−0.103224	−	0.0577263i
$725$	−2.51093e19			−0.238489
$726$	−6.99601e18	−	1.82333e18i	−0.0658103	−	0.0171517i
$727$			1.76865e20i			1.64779i	0.566743	+	0.823895i	$0.308203\pi$
$727$			1.76865e20i			1.64779i	−0.566743	+	0.823895i	$0.691797\pi$
$728$	6.48038e19	+	6.21946e19i	0.597972	+	0.573896i
$729$	−8.43712e19			−0.771084
$730$	−2.28726e17	+	8.77609e17i	−0.00207040	+	0.00794403i
$731$			4.00918e19i			0.359446i
$732$	−1.60233e19	+	2.86523e19i	−0.142290	+	0.254438i
$733$	−6.10273e19			−0.536780			−0.268390	−	0.963310i	$-0.586492\pi$
$733$	−6.10273e19			−0.536780			−0.268390	+	0.963310i	$0.586492\pi$
$734$	1.08720e20	+	2.83350e19i	0.947191	+	0.246860i
$735$		−	5.14244e19i		−	0.443770i
$736$	−5.80642e19	−	1.90376e20i	−0.496322	−	1.62730i
$737$	1.37043e20			1.16034
$738$	−2.21672e17	+	8.50546e17i	−0.00185916	+	0.00713351i
$739$		−	8.22272e19i		−	0.683131i	−0.939858	−	0.341566i	$-0.889043\pi$
$739$		−	8.22272e19i		−	0.683131i	0.939858	−	0.341566i	$-0.110957\pi$
$740$	−1.59404e20	−	8.91441e19i	−1.31183	−	0.733619i
$741$	−4.61762e19			−0.376436
$742$	−5.50062e19	−	1.43359e19i	−0.444206	−	0.115771i
$743$			1.41500e20i			1.13197i	0.824417	+	0.565983i	$0.191503\pi$
$743$			1.41500e20i			1.13197i	−0.824417	+	0.565983i	$0.808497\pi$
$744$	−2.95067e18	+	3.07445e18i	−0.0233835	+	0.0243645i
$745$	−1.08106e20			−0.848705
$746$	1.78091e19	−	6.83328e19i	0.138507	−	0.531444i
$747$			1.98061e19i			0.152600i
$748$	−5.53521e19	+	9.89787e19i	−0.422497	+	0.755493i
$749$	−1.95014e20			−1.47467
$750$	2.12796e19	+	5.54597e18i	0.159417	+	0.0415479i
$751$		−	1.20048e20i		−	0.890996i	−0.895283	−	0.445498i	$-0.853027\pi$
$751$		−	1.20048e20i		−	0.890996i	0.895283	−	0.445498i	$-0.146973\pi$
$752$	−7.26601e19	+	4.46471e19i	−0.534283	+	0.328298i
$753$	2.45196e20			1.78627
$754$	−7.37931e18	+	2.83141e19i	−0.0532619	+	0.204363i
$755$			2.83617e19i			0.202817i
$756$	9.34151e19	+	5.22408e19i	0.661858	+	0.370133i
$757$	1.53107e20			1.07479			0.537395	−	0.843331i	$-0.319408\pi$
$757$	1.53107e20			1.07479			0.537395	+	0.843331i	$0.319408\pi$
$758$	2.36896e20	+	6.17407e19i	1.64768	+	0.429425i
$759$		−	2.75731e20i		−	1.90017i
$760$	5.44419e19	+	5.22499e19i	0.371739	+	0.356772i
$761$	2.17872e20			1.47404			0.737018	−	0.675873i	$-0.236233\pi$
$761$	2.17872e20			1.47404			0.737018	+	0.675873i	$0.236233\pi$
$762$	−7.26642e19	+	2.78809e20i	−0.487120	+	1.86905i
$763$		−	1.71231e20i		−	1.13740i
$764$	7.71991e19	−	1.38045e20i	0.508111	−	0.908586i
$765$	−3.24573e19			−0.211681
$766$	−2.43011e20	−	6.33345e19i	−1.57045	−	0.409297i
$767$		−	1.76442e20i		−	1.12988i
$768$	1.52312e20	+	7.71435e19i	0.966509	+	0.489520i
$769$	−7.62132e19			−0.479232			−0.239616	−	0.970868i	$-0.577022\pi$
$769$	−7.62132e19			−0.479232			−0.239616	+	0.970868i	$0.577022\pi$
$770$	5.12823e19	−	1.96768e20i	0.319545	−	1.22608i
$771$			3.29630e20i			2.03538i
$772$	2.57480e20	+	1.43991e20i	1.57552	+	0.881080i
$773$	−2.83396e20			−1.71845			−0.859226	−	0.511597i	$-0.829054\pi$
$773$	−2.83396e20			−1.71845			−0.859226	+	0.511597i	$0.829054\pi$
$774$	1.19792e19	+	3.12206e18i	0.0719847	+	0.0187609i
$775$		−	5.78283e18i		−	0.0344372i
$776$	−1.95731e20	+	2.03942e20i	−1.15512	+	1.20358i
$777$	−1.62578e20			−0.950856
$778$	7.26578e18	−	2.78784e19i	0.0421139	−	0.161589i
$779$		−	2.62280e18i		−	0.0150662i
$780$	1.31843e20	−	2.35757e20i	0.750576	−	1.34215i
$781$	−6.60888e19			−0.372882
$782$	−2.47206e20	−	6.44276e19i	−1.38233	−	0.360267i
$783$			3.48662e19i			0.193229i
$784$	2.69099e19	+	4.37941e19i	0.147809	+	0.240549i
$785$	3.08607e20			1.68004
$786$	2.39663e19	−	9.19577e19i	0.129313	−	0.496170i
$787$		−	1.63309e20i		−	0.873345i	−0.899621	−	0.436672i	$-0.856157\pi$
$787$		−	1.63309e20i		−	0.873345i	0.899621	−	0.436672i	$-0.143843\pi$
$788$	−6.15707e19	−	3.44324e19i	−0.326355	−	0.182509i
$789$	−7.00466e19			−0.368000
$790$	−1.47510e20	−	3.84445e19i	−0.768123	−	0.200191i
$791$			1.66164e20i			0.857631i
$792$	2.52638e19	+	2.42466e19i	0.129247	+	0.124044i
$793$	−5.19142e19			−0.263253
$794$	−6.79797e19	+	2.60835e20i	−0.341693	+	1.31106i
$795$			1.70947e20i			0.851709i
$796$	2.86277e19	−	5.11909e19i	0.141382	−	0.252814i
$797$	−8.26020e19			−0.404373			−0.202187	−	0.979347i	$-0.564805\pi$
$797$	−8.26020e19			−0.404373			−0.202187	+	0.979347i	$0.564805\pi$
$798$	6.49994e19	+	1.69404e19i	0.315420	+	0.0822059i
$799$			1.09460e20i			0.526535i
$800$	−2.21617e20	+	6.75928e19i	−1.05675	+	0.322307i
$801$	−2.69153e19			−0.127225
$802$	−3.28863e19	+	1.26183e20i	−0.154097	+	0.591263i
$803$		−	1.25584e18i		−	0.00583344i
$804$	−2.31131e20	−	1.29256e20i	−1.06430	−	0.595193i
$805$	4.58059e20			2.09098
$806$	−6.52091e18	−	1.69950e18i	−0.0295096	−	0.00769090i
$807$		−	2.06839e20i		−	0.927937i
$808$	2.61376e20	−	2.72341e20i	1.16248	−	1.21125i
$809$	−2.49148e20			−1.09854			−0.549272	−	0.835643i	$-0.685095\pi$
$809$	−2.49148e20			−1.09854			−0.549272	+	0.835643i	$0.685095\pi$
$810$	9.57215e19	−	3.67279e20i	0.418422	−	1.60546i
$811$			1.92894e20i			0.835937i	0.908462	+	0.417968i	$0.137258\pi$
$811$			1.92894e20i			0.835937i	−0.908462	+	0.417968i	$0.862742\pi$
$812$	2.07748e19	−	3.71488e19i	0.0892575	−	0.159607i
$813$	4.21605e20			1.79586
$814$	2.44727e20	+	6.37816e19i	1.03350	+	0.269355i
$815$			4.67711e20i			1.95828i
$816$	1.86709e20	−	1.14726e20i	0.775059	−	0.476247i
$817$	−3.69398e19			−0.152034
$818$	1.64599e19	−	6.31559e19i	0.0671667	−	0.257715i
$819$		−	3.55975e19i		−	0.144023i
$820$	1.33909e19	+	7.48866e18i	0.0537173	+	0.0300405i
$821$	−1.20724e20			−0.480167			−0.240084	−	0.970752i	$-0.577175\pi$
$821$	−1.20724e20			−0.480167			−0.240084	+	0.970752i	$0.577175\pi$
$822$	−3.10878e20	−	8.10221e19i	−1.22599	−	0.319522i
$823$		−	1.98153e20i		−	0.774821i	−0.921907	−	0.387411i	$-0.873370\pi$
$823$		−	1.98153e20i		−	0.774821i	0.921907	−	0.387411i	$-0.126630\pi$
$824$	−7.70214e18	−	7.39204e18i	−0.0298622	−	0.0286598i
$825$	−3.20980e20			−1.23396
$826$	−6.47301e19	+	2.48366e20i	−0.246744	+	0.946744i
$827$		−	4.73938e20i		−	1.79136i	−0.444699	−	0.895680i	$-0.646689\pi$
$827$		−	4.73938e20i		−	1.79136i	0.444699	−	0.895680i	$-0.353311\pi$
$828$	−3.85011e19	+	6.88463e19i	−0.144298	+	0.258029i
$829$	6.87626e19			0.255547			0.127773	−	0.991803i	$-0.459217\pi$
$829$	6.87626e19			0.255547			0.127773	+	0.991803i	$0.459217\pi$
$830$	3.34551e20	+	8.71919e19i	1.23287	+	0.321314i
$831$			2.96120e20i			1.08208i
$832$	1.10893e19	+	2.69768e20i	0.0401830	+	0.977523i
$833$	6.59742e19			0.237061
$834$	7.82989e19	−	3.00429e20i	0.278993	−	1.07048i
$835$		−	3.62153e20i		−	1.27964i
$836$	−9.11970e19	−	5.10004e19i	−0.319548	−	0.178702i
$837$	−8.02991e18			−0.0279018
$838$	1.84480e20	+	4.80798e19i	0.635683	+	0.165674i
$839$		−	9.49839e19i		−	0.324576i	−0.986743	−	0.162288i	$-0.948113\pi$
$839$		−	9.49839e19i		−	0.324576i	0.986743	−	0.162288i	$-0.0518874\pi$
$840$	−2.72078e20	+	2.83492e20i	−0.922015	+	0.960695i
$841$	−2.83693e20			−0.953403
$842$	1.24183e19	−	4.76483e19i	0.0413882	−	0.158804i
$843$		−	2.17141e20i		−	0.717710i
$844$	−2.83269e20	+	5.06531e20i	−0.928542	+	1.66038i
$845$	−1.91163e19			−0.0621450
$846$	3.27059e19	+	8.52393e18i	0.105447	+	0.0274819i
$847$			1.66310e19i			0.0531783i
$848$	−8.94551e19	−	1.45582e20i	−0.283683	−	0.461675i
$849$	1.80352e20			0.567240
$850$	−7.50004e19	+	2.87773e20i	−0.233954	+	0.897672i
$851$			5.69704e20i			1.76255i
$852$	1.11463e20	+	6.23336e19i	0.342021	+	0.191269i
$853$	2.02272e20			0.615593			0.307796	−	0.951452i	$-0.400408\pi$
$853$	2.02272e20			0.615593			0.307796	+	0.951452i	$0.400408\pi$
$854$	7.30764e19	+	1.90454e19i	0.220583	+	0.0574891i
$855$		−	2.99055e19i		−	0.0895342i
$856$	−4.22935e20	−	4.05906e20i	−1.25591	−	1.20534i
$857$	4.20343e19			0.123805			0.0619025	−	0.998082i	$-0.480283\pi$
$857$	4.20343e19			0.123805			0.0619025	+	0.998082i	$0.480283\pi$
$858$	−9.43321e19	+	3.61948e20i	−0.275581	+	1.05739i
$859$		−	2.14936e20i		−	0.622811i	−0.950277	−	0.311406i	$-0.899200\pi$
$859$		−	2.14936e20i		−	0.622811i	0.950277	−	0.311406i	$-0.100800\pi$
$860$	1.05471e20	−	1.88599e20i	0.303140	−	0.542065i
$861$	1.36576e19			0.0389360
$862$	4.39414e20	+	1.14522e20i	1.24258	+	0.323845i
$863$		−	2.61596e20i		−	0.733762i	−0.930268	−	0.366881i	$-0.880426\pi$
$863$		−	2.61596e20i		−	0.733762i	0.930268	−	0.366881i	$-0.119574\pi$
$864$	9.38579e19	+	3.07733e20i	0.261141	+	0.856204i
$865$	−8.49085e20			−2.34336
$866$	8.89771e19	−	3.41401e20i	0.243586	−	0.934629i
$867$			1.17685e20i			0.319586i
$868$	8.55560e18	+	4.78457e18i	0.0230469	+	0.0128886i
$869$	2.11083e20			0.564047
$870$	−1.23863e20	−	3.22817e19i	−0.328328	−	0.0855700i
$871$		−	4.18778e20i		−	1.10118i
$872$	3.56404e20	−	3.71356e20i	0.929667	−	0.968668i
$873$	1.12027e20			0.289884
$874$	5.93623e19	−	2.27770e20i	0.152381	−	0.584678i
$875$		−	5.05862e19i		−	0.128818i
$876$	−1.18448e18	+	2.11805e18i	−0.00299226	+	0.00535065i
$877$	−3.90992e20			−0.979875			−0.489938	−	0.871758i	$-0.662980\pi$
$877$	−3.90992e20			−0.979875			−0.489938	+	0.871758i	$0.662980\pi$
$878$	−4.59014e20	−	1.19630e20i	−1.14121	−	0.297426i
$879$			1.95188e20i			0.481428i
$880$	5.20774e20	−	3.19997e20i	1.27430	−	0.783011i
$881$	5.40581e20			1.31229			0.656144	−	0.754636i	$-0.272186\pi$
$881$	5.40581e20			1.31229			0.656144	+	0.754636i	$0.272186\pi$
$882$	5.13759e18	−	1.97127e19i	0.0123731	−	0.0474750i
$883$			3.86863e20i			0.924342i	0.886791	+	0.462171i	$0.152929\pi$
$883$			3.86863e20i			0.924342i	−0.886791	+	0.462171i	$0.847071\pi$
$884$	3.02461e20	+	1.69146e20i	0.716974	+	0.400956i
$885$	7.71866e20			1.81526
$886$	−2.19957e20	−	5.73260e19i	−0.513218	−	0.133757i
$887$			6.78127e20i			1.56981i	0.619619	+	0.784903i	$0.287287\pi$
$887$			6.78127e20i			1.56981i	−0.619619	+	0.784903i	$0.712713\pi$
$888$	−3.52589e20	−	3.38393e20i	−0.809801	−	0.777196i
$889$	6.62788e20			1.51030
$890$	−1.18488e20	+	4.54634e20i	−0.267883	+	1.02786i
$891$			5.25568e20i			1.17892i
$892$	−1.58603e20	+	2.83608e20i	−0.352986	+	0.631197i
$893$	−1.00854e20			−0.222707
$894$	−2.79920e20	−	7.29538e19i	−0.613298	−	0.159840i
$895$		−	1.20764e20i		−	0.262528i
$896$	8.33582e19	−	3.83804e20i	0.179801	−	0.827853i
$897$	−8.42585e20			−1.80329
$898$	1.24816e20	−	4.78911e20i	0.265054	−	1.01700i
$899$			3.19329e18i			0.00672853i
$900$	8.01442e19	+	4.48193e19i	0.167562	+	0.0937060i
$901$	−2.19314e20			−0.454981
$902$	−2.05586e19	−	5.35805e18i	−0.0423202	−	0.0110296i
$903$		−	1.92354e20i		−	0.392905i
$904$	−3.45856e20	+	3.60365e20i	−0.700997	+	0.730405i
$905$	8.53133e19			0.171584
$906$	−1.91395e19	+	7.34371e19i	−0.0381973	+	0.146561i
$907$		−	9.18773e18i		−	0.0181952i	−0.999959	−	0.00909761i	$-0.997104\pi$
$907$		−	9.18773e18i		−	0.0181952i	0.999959	−	0.00909761i	$-0.00289590\pi$
$908$	−9.16173e19	+	1.63827e20i	−0.180043	+	0.321946i
$909$	−1.49600e20			−0.291733
$910$	−6.01286e20	−	1.56709e20i	−1.16357	−	0.303253i
$911$		−	1.02841e21i		−	1.97486i	−0.158046	−	0.987432i	$-0.550519\pi$
$911$		−	1.02841e21i		−	1.97486i	0.158046	−	0.987432i	$-0.449481\pi$
$912$	1.05707e20	+	1.72030e20i	0.201437	+	0.327824i
$913$	−4.78735e20			−0.905315
$914$	5.77392e19	−	2.21542e20i	0.108355	−	0.415751i
$915$		−	2.27105e20i		−	0.422940i
$916$	−1.76934e20	−	9.89476e19i	−0.326997	−	0.182868i
$917$	−2.18603e20			−0.400932
$918$	3.99595e20	+	1.04144e20i	0.727314	+	0.189555i
$919$			8.16694e20i			1.47520i	0.675238	+	0.737600i	$0.264041\pi$
$919$			8.16694e20i			1.47520i	−0.675238	+	0.737600i	$0.735959\pi$
$920$	9.93409e20	+	9.53412e20i	1.78079	+	1.70909i
$921$	−3.60963e20			−0.642163
$922$	−1.09259e20	+	4.19222e20i	−0.192904	+	0.740164i
$923$			2.01956e20i			0.353870i
$924$	2.65571e20	−	4.74885e20i	0.461824	−	0.825818i
$925$	6.63195e20			1.14459
$926$	−1.57519e20	−	4.10530e19i	−0.269808	−	0.0703183i
$927$			4.23088e18i			0.00719237i
$928$	1.22377e20	−	3.73248e19i	0.206474	−	0.0629741i
$929$	7.17263e19			0.120107			0.0600535	−	0.998195i	$-0.480873\pi$
$929$	7.17263e19			0.120107			0.0600535	+	0.998195i	$0.480873\pi$
$930$	7.43468e18	−	2.85265e19i	0.0123561	−	0.0474098i
$931$			6.07873e19i			0.100269i
$932$	−5.53323e19	−	3.09436e19i	−0.0905873	−	0.0506594i
$933$	−2.64554e19			−0.0429875
$934$	2.07980e20	+	5.42044e19i	0.335423	+	0.0874191i
$935$		−	7.84527e20i		−	1.25582i
$936$	7.40932e19	−	7.72016e19i	0.117719	−	0.122658i
$937$	9.33303e20			1.47179			0.735894	−	0.677096i	$-0.236762\pi$
$937$	9.33303e20			1.47179			0.735894	+	0.677096i	$0.236762\pi$
$938$	−1.53634e20	+	5.89488e20i	−0.240474	+	0.922688i
$939$		−	1.06622e21i		−	1.65649i
$940$	2.87960e20	−	5.14920e20i	0.444056	−	0.794044i
$941$	3.59055e20			0.549583			0.274791	−	0.961504i	$-0.411391\pi$
$941$	3.59055e20			0.549583			0.274791	+	0.961504i	$0.411391\pi$
$942$	7.99079e20	+	2.08259e20i	1.21404	+	0.316408i
$943$		−	4.78587e19i		−	0.0721737i
$944$	−6.57337e20	+	4.03911e20i	−0.983975	+	0.604619i
$945$	−7.40429e20			−1.10017
$946$	−7.54633e19	+	2.89549e20i	−0.111301	+	0.427055i
$947$		−	8.55162e20i		−	1.25198i	−0.779830	−	0.625991i	$-0.784695\pi$
$947$		−	8.55162e20i		−	1.25198i	0.779830	−	0.625991i	$-0.215305\pi$
$948$	−3.56004e20	−	1.99089e20i	−0.517365	−	0.289327i
$949$	−3.83762e18			−0.00553603
$950$	−2.65148e20	−	6.91039e19i	−0.379685	−	0.0989549i
$951$		−	5.54507e19i		−	0.0788212i
$952$	−3.63702e20	−	3.49059e20i	−0.513201	−	0.492538i
$953$	−1.03188e20			−0.144538			−0.0722688	−	0.997385i	$-0.523024\pi$
$953$	−1.03188e20			−0.144538			−0.0722688	+	0.997385i	$0.523024\pi$
$954$	−1.70786e19	+	6.55296e19i	−0.0237472	+	0.0911169i
$955$			1.09417e21i			1.51030i
$956$	−1.14226e20	+	2.04255e20i	−0.156516	+	0.279877i
$957$	1.77246e20			0.241097
$958$	3.26844e20	+	8.51834e19i	0.441349	+	0.115026i
$959$			7.39023e20i			0.990667i
$960$	−1.18013e21	+	4.85116e19i	−1.57048	+	0.0645575i
$961$	7.56209e20			0.999028
$962$	1.94905e20	−	7.47842e20i	0.255622	−	0.980808i
$963$			2.32323e20i			0.302488i
$964$	6.22452e19	+	3.48096e19i	0.0804575	+	0.0449945i
$965$	−2.04084e21			−2.61890
$966$	1.18605e21	+	3.09114e20i	1.51100	+	0.393802i
$967$			8.55095e20i			1.08151i	0.841181	+	0.540753i	$0.181861\pi$
$967$			8.55095e20i			1.08151i	−0.841181	+	0.540753i	$0.818139\pi$
$968$	−3.46161e19	+	3.60683e19i	−0.0434661	+	0.0452896i
$969$	2.59158e20			0.323071
$970$	4.93175e20	−	1.89229e21i	0.610377	−	2.34199i
$971$			4.99804e20i			0.614136i	0.951688	+	0.307068i	$0.0993480\pi$
$971$			4.99804e20i			0.614136i	−0.951688	+	0.307068i	$0.900652\pi$
$972$	1.37559e20	−	2.45979e20i	0.167813	−	0.300078i
$973$	−7.14184e20			−0.865008
$974$	−7.46215e20	−	1.94481e20i	−0.897328	−	0.233865i
$975$			9.80856e20i			1.17104i
$976$	1.18842e20	+	1.93407e20i	0.140871	+	0.229258i
$977$	1.26501e21			1.48879			0.744395	−	0.667739i	$-0.232738\pi$
$977$	1.26501e21			1.48879			0.744395	+	0.667739i	$0.232738\pi$
$978$	−3.15627e20	+	1.21105e21i	−0.368810	+	1.41511i
$979$		−	6.50571e20i		−	0.754772i
$980$	−3.10355e20	−	1.73561e20i	−0.357500	−	0.199926i
$981$	−2.03990e20			−0.233306
$982$	−3.77277e20	−	9.83272e19i	−0.428430	−	0.111659i
$983$			4.78813e20i			0.539873i	0.962878	+	0.269936i	$0.0870026\pi$
$983$			4.78813e20i			0.539873i	−0.962878	+	0.269936i	$0.912997\pi$
$984$	2.96197e19	+	2.84271e19i	0.0331600	+	0.0318249i
$985$	4.88023e20			0.542484
$986$	4.14154e19	−	1.58909e20i	0.0457112	−	0.175392i
$987$		−	5.25172e20i		−	0.575548i
$988$	−1.55848e20	+	2.78682e20i	−0.169591	+	0.303256i
$989$	−6.74046e20			−0.728309
$990$	−2.34412e20	−	6.10932e19i	−0.251497	−	0.0655461i
$991$		−	1.15848e21i		−	1.23417i	−0.786897	−	0.617085i	$-0.788314\pi$
$991$		−	1.15848e21i		−	1.23417i	0.786897	−	0.617085i	$-0.211686\pi$
$992$	8.59615e18	+	2.81843e19i	0.00909332	+	0.0298143i
$993$	1.12379e21			1.18043
$994$	7.40902e19	−	2.84280e20i	0.0772780	−	0.296512i
$995$			4.05751e20i			0.420240i
$996$	8.07415e20	+	4.51533e20i	0.830388	+	0.464381i
$997$	−1.22877e20			−0.125488			−0.0627442	−	0.998030i	$-0.519985\pi$
$997$	−1.22877e20			−0.125488			−0.0627442	+	0.998030i	$0.519985\pi$
$998$	−5.14521e20	−	1.34096e20i	−0.521783	−	0.135989i
$999$		−	9.20898e20i		−	0.927371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.15.b.a.3.4	yes	6
3.2	odd	2		36.15.d.c.19.3		6
4.3	odd	2	inner	4.15.b.a.3.3	✓	6
8.3	odd	2		64.15.c.d.63.2		6
8.5	even	2		64.15.c.d.63.5		6
12.11	even	2		36.15.d.c.19.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.15.b.a.3.3	✓	6	4.3	odd	2	inner
4.15.b.a.3.4	yes	6	1.1	even	1	trivial
36.15.d.c.19.3		6	3.2	odd	2
36.15.d.c.19.4		6	12.11	even	2
64.15.c.d.63.2		6	8.3	odd	2
64.15.c.d.63.5		6	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-32.2815 + 123.862i) q^{2} -2369.41i q^{3} +(-14299.8 - 7996.93i) q^{4} +113343. q^{5} +(293481. + 76488.1i) q^{6} -697667. i q^{7} +(1.45214e6 - 1.51306e6i) q^{8} -831139. q^{9} +O(q^{10})\)	\(q+(-32.2815 + 123.862i) q^{2} -2369.41i q^{3} +(-14299.8 - 7996.93i) q^{4} +113343. q^{5} +(293481. + 76488.1i) q^{6} -697667. i q^{7} +(1.45214e6 - 1.51306e6i) q^{8} -831139. q^{9} +(-3.65890e6 + 1.40390e7i) q^{10} -2.00895e7i q^{11} +(-1.89480e7 + 3.38821e7i) q^{12} -6.13899e7 q^{13} +(8.64148e7 + 2.25217e7i) q^{14} -2.68557e8i q^{15} +(1.40534e8 + 2.28709e8i) q^{16} +3.44542e8 q^{17} +(2.68304e7 - 1.02947e8i) q^{18} +3.17454e8i q^{19} +(-1.62079e9 - 9.06399e8i) q^{20} -1.65306e9 q^{21} +(2.48833e9 + 6.48519e8i) q^{22} +5.79264e9i q^{23} +(-3.58505e9 - 3.44071e9i) q^{24} +6.74323e9 q^{25} +(1.98176e9 - 7.60390e9i) q^{26} -9.36351e9i q^{27} +(-5.57919e9 + 9.97651e9i) q^{28} -3.72362e9 q^{29} +(3.32642e10 + 8.66943e9i) q^{30} -8.57575e8i q^{31} +(-3.28651e10 + 1.00238e10i) q^{32} -4.76003e10 q^{33} +(-1.11223e10 + 4.26758e10i) q^{34} -7.90760e10i q^{35} +(1.18851e10 + 6.64656e9i) q^{36} +9.83497e10 q^{37} +(-3.93207e10 - 1.02479e10i) q^{38} +1.45458e11i q^{39} +(1.64590e11 - 1.71495e11i) q^{40} -8.26198e9 q^{41} +(5.33632e10 - 2.04752e11i) q^{42} +1.16363e11i q^{43} +(-1.60654e11 + 2.87276e11i) q^{44} -9.42042e10 q^{45} +(-7.17490e11 - 1.86995e11i) q^{46} +3.17697e11i q^{47} +(5.41906e11 - 3.32982e11i) q^{48} +1.91484e11 q^{49} +(-2.17681e11 + 8.35233e11i) q^{50} -8.16362e11i q^{51} +(8.77864e11 + 4.90930e11i) q^{52} -6.36538e11 q^{53} +(1.15979e12 + 3.02268e11i) q^{54} -2.27701e12i q^{55} +(-1.05561e12 - 1.01311e12i) q^{56} +7.52180e11 q^{57} +(1.20204e11 - 4.61217e11i) q^{58} +2.87412e12i q^{59} +(-2.14763e12 + 3.84032e12i) q^{60} +8.45647e11 q^{61} +(1.06221e11 + 2.76838e10i) q^{62} +5.79859e11i q^{63} +(-1.80638e11 - 4.39434e12i) q^{64} -6.95814e12 q^{65} +(1.53661e12 - 5.89589e12i) q^{66} +6.82161e12i q^{67} +(-4.92689e12 - 2.75528e12i) q^{68} +1.37251e13 q^{69} +(9.79455e12 + 2.55269e12i) q^{70} -3.28972e12i q^{71} +(-1.20693e12 + 1.25756e12i) q^{72} +6.25122e10 q^{73} +(-3.17487e12 + 1.21818e13i) q^{74} -1.59775e13i q^{75} +(2.53866e12 - 4.53954e12i) q^{76} -1.40158e13 q^{77} +(-1.80168e13 - 4.69560e12i) q^{78} +1.05071e13i q^{79} +(1.59286e13 + 2.59227e13i) q^{80} -2.61613e13 q^{81} +(2.66709e11 - 1.02335e12i) q^{82} -2.38301e13i q^{83} +(2.36384e13 + 1.32194e13i) q^{84} +3.90516e13 q^{85} +(-1.44130e13 - 3.75636e12i) q^{86} +8.82279e12i q^{87} +(-3.03966e13 - 2.91727e13i) q^{88} +3.23837e13 q^{89} +(3.04105e12 - 1.16684e13i) q^{90} +4.28297e13i q^{91} +(4.63233e13 - 8.28336e13i) q^{92} -2.03195e12 q^{93} +(-3.93507e13 - 1.02557e13i) q^{94} +3.59814e13i q^{95} +(2.37505e13 + 7.78709e13i) q^{96} -1.34788e14 q^{97} +(-6.18138e12 + 2.37176e13i) q^{98} +1.66972e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9}+O(q^{10}) \) 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9	\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + 5796840 q^{10} + 193920 q^{12} - 80775396 q^{13} + 175232064 q^{14} - 353013504 q^{16} - 120131764 q^{17} + 1599402372 q^{18} - 5047343200 q^{20} + 1226658048 q^{21} + 9916985760 q^{22} - 24092176896 q^{24} + 3942973410 q^{25} + 39549467048 q^{26} - 65094731520 q^{28} - 8035796644 q^{29} + 99698873280 q^{30} - 85711465472 q^{32} - 37769804160 q^{33} + 98089165512 q^{34} - 27478990320 q^{36} + 31334118396 q^{37} - 165268841760 q^{38} + 435607171200 q^{40} + 83362750892 q^{41} - 830203906560 q^{42} + 915657452160 q^{44} + 271078769820 q^{45} - 1712365889856 q^{46} + 2292961843200 q^{48} - 551978693658 q^{49} - 1639579094580 q^{50} + 1057159118496 q^{52} + 76712275004 q^{53} + 445471858368 q^{54} - 560223046656 q^{56} - 2647253865600 q^{57} + 4483777382184 q^{58} - 9544013748480 q^{60} + 6210000787932 q^{61} + 10375644284160 q^{62} - 14398852657152 q^{64} - 7189912943720 q^{65} + 15071210499840 q^{66} - 18507298307296 q^{68} + 19348372347648 q^{69} + 12679529923200 q^{70} - 5286233111232 q^{72} - 29882649313236 q^{73} - 1536652566808 q^{74} + 21457134000000 q^{76} + 37339673521920 q^{77} - 29727224255040 q^{78} + 57843429624320 q^{80} - 98651978873946 q^{81} - 71900577251064 q^{82} + 102961968764928 q^{84} + 151199882653560 q^{85} - 100164269733216 q^{86} + 51557990330880 q^{88} - 180966014731924 q^{89} - 84934442792280 q^{90} + 82241452266240 q^{92} + 295002300748800 q^{93} - 40381697410176 q^{94} - 82703070928896 q^{96} - 345459072299124 q^{97} + 121406102961892 q^{98}+O(q^{100}) \) 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9 + 5796840 * q^10 + 193920 * q^12 - 80775396 * q^13 + 175232064 * q^14 - 353013504 * q^16 - 120131764 * q^17 + 1599402372 * q^18 - 5047343200 * q^20 + 1226658048 * q^21 + 9916985760 * q^22 - 24092176896 * q^24 + 3942973410 * q^25 + 39549467048 * q^26 - 65094731520 * q^28 - 8035796644 * q^29 + 99698873280 * q^30 - 85711465472 * q^32 - 37769804160 * q^33 + 98089165512 * q^34 - 27478990320 * q^36 + 31334118396 * q^37 - 165268841760 * q^38 + 435607171200 * q^40 + 83362750892 * q^41 - 830203906560 * q^42 + 915657452160 * q^44 + 271078769820 * q^45 - 1712365889856 * q^46 + 2292961843200 * q^48 - 551978693658 * q^49 - 1639579094580 * q^50 + 1057159118496 * q^52 + 76712275004 * q^53 + 445471858368 * q^54 - 560223046656 * q^56 - 2647253865600 * q^57 + 4483777382184 * q^58 - 9544013748480 * q^60 + 6210000787932 * q^61 + 10375644284160 * q^62 - 14398852657152 * q^64 - 7189912943720 * q^65 + 15071210499840 * q^66 - 18507298307296 * q^68 + 19348372347648 * q^69 + 12679529923200 * q^70 - 5286233111232 * q^72 - 29882649313236 * q^73 - 1536652566808 * q^74 + 21457134000000 * q^76 + 37339673521920 * q^77 - 29727224255040 * q^78 + 57843429624320 * q^80 - 98651978873946 * q^81 - 71900577251064 * q^82 + 102961968764928 * q^84 + 151199882653560 * q^85 - 100164269733216 * q^86 + 51557990330880 * q^88 - 180966014731924 * q^89 - 84934442792280 * q^90 + 82241452266240 * q^92 + 295002300748800 * q^93 - 40381697410176 * q^94 - 82703070928896 * q^96 - 345459072299124 * q^97 + 121406102961892 * q^98

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