LMFDB - Embedded newform 30.10.e.a.23.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,10,Mod(17,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("30.17");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	30.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.4510750849$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.15
Character	$\chi$	$=$	30.23
Dual form			30.10.e.a.17.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.3137 + 11.3137i) q^{2} +(98.3235 + 100.077i) q^{3} +256.000i q^{4} +(-257.681 - 1373.58i) q^{5} +(-19.8436 + 2244.65i) q^{6} +(-6195.32 + 6195.32i) q^{7} +(-2896.31 + 2896.31i) q^{8} +(-347.984 + 19679.9i) q^{9} +O(q^{10})$	\(q+(11.3137 + 11.3137i) q^{2} +(98.3235 + 100.077i) q^{3} +256.000i q^{4} +(-257.681 - 1373.58i) q^{5} +(-19.8436 + 2244.65i) q^{6} +(-6195.32 + 6195.32i) q^{7} +(-2896.31 + 2896.31i) q^{8} +(-347.984 + 19679.9i) q^{9} +(12625.0 - 18455.6i) q^{10} +74250.3i q^{11} +(-25619.8 + 25170.8i) q^{12} +(-80669.6 - 80669.6i) q^{13} -140184. q^{14} +(112128. - 160843. i) q^{15} -65536.0 q^{16} +(82301.7 + 82301.7i) q^{17} +(-226590. + 218716. i) q^{18} +362317. i q^{19} +(351637. - 65966.4i) q^{20} +(-1.22916e6 - 10866.2i) q^{21} +(-840046. + 840046. i) q^{22} +(681933. - 681933. i) q^{23} +(-574630. - 5079.96i) q^{24} +(-1.82033e6 + 707892. i) q^{25} -1.82534e6i q^{26} +(-2.00373e6 + 1.90017e6i) q^{27} +(-1.58600e6 - 1.58600e6i) q^{28} +1.04307e6 q^{29} +(3.08832e6 - 551148. i) q^{30} +283662. q^{31} +(-741455. - 741455. i) q^{32} +(-7.43078e6 + 7.30055e6i) q^{33} +1.86227e6i q^{34} +(1.01062e7 + 6.91335e6i) q^{35} +(-5.03806e6 - 89083.8i) q^{36} +(5.07466e6 - 5.07466e6i) q^{37} +(-4.09915e6 + 4.09915e6i) q^{38} +(141490. - 1.60049e7i) q^{39} +(4.72464e6 + 3.23199e6i) q^{40} -1.81063e7i q^{41} +(-1.37834e7 - 1.40293e7i) q^{42} +(2.88345e7 + 2.88345e7i) q^{43} -1.90081e7 q^{44} +(2.71216e7 - 4.59317e6i) q^{45} +1.54304e7 q^{46} +(3.74010e7 + 3.74010e7i) q^{47} +(-6.44373e6 - 6.55867e6i) q^{48} -3.64103e7i q^{49} +(-2.86035e7 - 1.25857e7i) q^{50} +(-144352. + 1.63287e7i) q^{51} +(2.06514e7 - 2.06514e7i) q^{52} +(5.08597e7 - 5.08597e7i) q^{53} +(-4.41676e7 - 1.17162e6i) q^{54} +(1.01989e8 - 1.91329e7i) q^{55} -3.58871e7i q^{56} +(-3.62598e7 + 3.56243e7i) q^{57} +(1.18010e7 + 1.18010e7i) q^{58} -4.63070e7 q^{59} +(4.11759e7 + 2.87049e7i) q^{60} +3.55511e6 q^{61} +(3.20927e6 + 3.20927e6i) q^{62} +(-1.19767e8 - 1.24079e8i) q^{63} -1.67772e7i q^{64} +(-9.00192e7 + 1.31593e8i) q^{65} +(-1.66666e8 - 1.47339e6i) q^{66} +(-2.22768e8 + 2.22768e8i) q^{67} +(-2.10692e7 + 2.10692e7i) q^{68} +(1.35296e8 + 1.19607e6i) q^{69} +(3.61228e7 + 1.92554e8i) q^{70} +2.70212e8i q^{71} +(-5.59913e7 - 5.80070e7i) q^{72} +(2.47027e8 + 2.47027e8i) q^{73} +1.14826e8 q^{74} +(-2.49825e8 - 1.12571e8i) q^{75} -9.27532e7 q^{76} +(-4.60004e8 - 4.60004e8i) q^{77} +(1.82676e8 - 1.79474e8i) q^{78} -1.30605e8i q^{79} +(1.68874e7 + 9.00190e7i) q^{80} +(-3.87178e8 - 1.36966e7i) q^{81} +(2.04849e8 - 2.04849e8i) q^{82} +(5.26747e8 - 5.26747e8i) q^{83} +(2.78175e6 - 3.14664e8i) q^{84} +(9.18404e7 - 1.34256e8i) q^{85} +6.52451e8i q^{86} +(1.02559e8 + 1.04388e8i) q^{87} +(-2.15052e8 - 2.15052e8i) q^{88} -6.38029e8 q^{89} +(3.58812e8 + 2.54881e8i) q^{90} +9.99547e8 q^{91} +(1.74575e8 + 1.74575e8i) q^{92} +(2.78907e7 + 2.83882e7i) q^{93} +8.46288e8i q^{94} +(4.97672e8 - 9.33624e7i) q^{95} +(1.30047e6 - 1.47105e8i) q^{96} +(4.31943e8 - 4.31943e8i) q^{97} +(4.11935e8 - 4.11935e8i) q^{98} +(-1.46124e9 - 2.58379e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 296 q^{3} + 4544 q^{6} + 9756 q^{7}+O(q^{10}) $ 36 * q + 296 * q^3 + 4544 * q^6 + 9756 * q^7	$ 36 q + 296 q^{3} + 4544 q^{6} + 9756 q^{7} + 51264 q^{10} - 75776 q^{12} - 78120 q^{13} + 201428 q^{15} - 2359296 q^{16} - 276352 q^{18} - 1187968 q^{21} - 1065024 q^{22} - 8730936 q^{25} - 8987584 q^{27} + 2497536 q^{28} + 10183488 q^{30} - 19149912 q^{31} - 24042964 q^{33} + 7783424 q^{36} + 57972384 q^{37} - 20938752 q^{40} - 36541376 q^{42} + 129617424 q^{43} + 188714992 q^{45} - 10734336 q^{46} - 19398656 q^{48} + 61133728 q^{51} + 19998720 q^{52} - 84302028 q^{55} - 191033896 q^{57} + 129597120 q^{58} - 14761984 q^{60} - 258546456 q^{61} + 113024276 q^{63} - 177217408 q^{66} - 95099256 q^{67} - 64737216 q^{70} + 70746112 q^{72} - 744318180 q^{73} - 436271432 q^{75} + 274489344 q^{76} + 416094720 q^{78} - 2874828308 q^{81} - 1243259136 q^{82} - 93014352 q^{85} + 2750699540 q^{87} - 272646144 q^{88} - 319472512 q^{90} + 4799502000 q^{91} + 1861719848 q^{93} - 297795584 q^{96} - 2636190468 q^{97}+O(q^{100}) $ 36 * q + 296 * q^3 + 4544 * q^6 + 9756 * q^7 + 51264 * q^10 - 75776 * q^12 - 78120 * q^13 + 201428 * q^15 - 2359296 * q^16 - 276352 * q^18 - 1187968 * q^21 - 1065024 * q^22 - 8730936 * q^25 - 8987584 * q^27 + 2497536 * q^28 + 10183488 * q^30 - 19149912 * q^31 - 24042964 * q^33 + 7783424 * q^36 + 57972384 * q^37 - 20938752 * q^40 - 36541376 * q^42 + 129617424 * q^43 + 188714992 * q^45 - 10734336 * q^46 - 19398656 * q^48 + 61133728 * q^51 + 19998720 * q^52 - 84302028 * q^55 - 191033896 * q^57 + 129597120 * q^58 - 14761984 * q^60 - 258546456 * q^61 + 113024276 * q^63 - 177217408 * q^66 - 95099256 * q^67 - 64737216 * q^70 + 70746112 * q^72 - 744318180 * q^73 - 436271432 * q^75 + 274489344 * q^76 + 416094720 * q^78 - 2874828308 * q^81 - 1243259136 * q^82 - 93014352 * q^85 + 2750699540 * q^87 - 272646144 * q^88 - 319472512 * q^90 + 4799502000 * q^91 + 1861719848 * q^93 - 297795584 * q^96 - 2636190468 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	11.3137	+	11.3137i	0.500000	+	0.500000i
$2$	11.3137	+	11.3137i	0.500000	+	0.500000i
$3$	98.3235	+	100.077i	0.700828	+	0.713330i
$3$	98.3235	+	100.077i	0.700828	+	0.713330i
$4$			256.000i			0.500000i
$5$	−257.681	−	1373.58i	−0.184382	−	0.982855i
$5$	−257.681	−	1373.58i	−0.184382	−	0.982855i
$6$	−19.8436	+	2244.65i	−0.00625086	+	0.707079i
$7$	−6195.32	+	6195.32i	−0.975264	+	0.975264i	−0.999701	−	0.0244372i	$-0.992221\pi$
$7$	−6195.32	+	6195.32i	−0.975264	+	0.975264i	0.0244372	+	0.999701i	$0.492221\pi$
$8$	−2896.31	+	2896.31i	−0.250000	+	0.250000i
$9$	−347.984	+	19679.9i	−0.0176794	+	0.999844i
$10$	12625.0	−	18455.6i	0.399236	−	0.583618i
$11$			74250.3i			1.52908i	0.644574	+	0.764542i	$0.277035\pi$
$11$			74250.3i			1.52908i	−0.644574	+	0.764542i	$0.722965\pi$
$12$	−25619.8	+	25170.8i	−0.356665	+	0.350414i
$13$	−80669.6	−	80669.6i	−0.783366	−	0.783366i	0.197031	−	0.980397i	$-0.436870\pi$
$13$	−80669.6	−	80669.6i	−0.783366	−	0.783366i	−0.980397	+	0.197031i	$0.936870\pi$
$14$	−140184.			−0.975264
$15$	112128.	−	160843.i	0.571880	−	0.820337i
$16$	−65536.0			−0.250000
$17$	82301.7	+	82301.7i	0.238995	+	0.238995i	0.816434	−	0.577439i	$-0.195948\pi$
$17$	82301.7	+	82301.7i	0.238995	+	0.238995i	−0.577439	+	0.816434i	$0.695948\pi$
$18$	−226590.	+	218716.i	−0.508762	+	0.491082i
$19$			362317.i			0.637819i	0.947785	+	0.318910i	$0.103317\pi$
$19$			362317.i			0.637819i	−0.947785	+	0.318910i	$0.896683\pi$
$20$	351637.	−	65966.4i	0.491427	−	0.0921909i
$21$	−1.22916e6	−	10866.2i	−1.37918	−	0.0121925i
$22$	−840046.	+	840046.i	−0.764542	+	0.764542i
$23$	681933.	−	681933.i	0.508120	−	0.508120i	−0.405829	−	0.913949i	$-0.633017\pi$
$23$	681933.	−	681933.i	0.508120	−	0.508120i	0.913949	+	0.405829i	$0.133017\pi$
$24$	−574630.	−	5079.96i	−0.353540	−	0.00312543i
$25$	−1.82033e6	+	707892.i	−0.932007	+	0.362441i
$26$		−	1.82534e6i		−	0.783366i
$27$	−2.00373e6	+	1.90017e6i	−0.725609	+	0.688108i
$28$	−1.58600e6	−	1.58600e6i	−0.487632	−	0.487632i
$29$	1.04307e6			0.273857			0.136929	−	0.990581i	$-0.456277\pi$
$29$	1.04307e6			0.273857			0.136929	+	0.990581i	$0.456277\pi$
$30$	3.08832e6	−	551148.i	0.696109	−	0.124229i
$31$	283662.			0.0551663			0.0275832	−	0.999620i	$-0.491219\pi$
$31$	283662.			0.0551663			0.0275832	+	0.999620i	$0.491219\pi$
$32$	−741455.	−	741455.i	−0.125000	−	0.125000i
$33$	−7.43078e6	+	7.30055e6i	−1.09074	+	1.07162i
$34$			1.86227e6i			0.238995i
$35$	1.01062e7	+	6.91335e6i	1.13836	+	0.778722i
$36$	−5.03806e6	−	89083.8i	−0.499922	−	0.00883970i
$37$	5.07466e6	−	5.07466e6i	0.445142	−	0.445142i	−0.448593	−	0.893736i	$-0.648075\pi$
$37$	5.07466e6	−	5.07466e6i	0.445142	−	0.445142i	0.893736	+	0.448593i	$0.148075\pi$
$38$	−4.09915e6	+	4.09915e6i	−0.318910	+	0.318910i
$39$	141490.	−	1.60049e7i	0.00979342	−	1.10780i
$40$	4.72464e6	+	3.23199e6i	0.291809	+	0.199618i
$41$		−	1.81063e7i		−	1.00069i	−0.865825	−	0.500347i	$-0.833206\pi$
$41$		−	1.81063e7i		−	1.00069i	0.865825	−	0.500347i	$-0.166794\pi$
$42$	−1.37834e7	−	1.40293e7i	−0.683493	−	0.695685i
$43$	2.88345e7	+	2.88345e7i	1.28619	+	1.28619i	0.937083	+	0.349107i	$0.113515\pi$
$43$	2.88345e7	+	2.88345e7i	1.28619	+	1.28619i	0.349107	+	0.937083i	$0.386485\pi$
$44$	−1.90081e7			−0.764542
$45$	2.71216e7	−	4.59317e6i	0.985961	−	0.166977i
$46$	1.54304e7			0.508120
$47$	3.74010e7	+	3.74010e7i	1.11800	+	1.11800i	0.992034	+	0.125968i	$0.0402037\pi$
$47$	3.74010e7	+	3.74010e7i	1.11800	+	1.11800i	0.125968	+	0.992034i	$0.459796\pi$
$48$	−6.44373e6	−	6.55867e6i	−0.175207	−	0.178333i
$49$		−	3.64103e7i		−	0.902281i
$50$	−2.86035e7	−	1.25857e7i	−0.647224	−	0.284783i
$51$	−144352.	+	1.63287e7i	−0.00298785	+	0.337977i
$52$	2.06514e7	−	2.06514e7i	0.391683	−	0.391683i
$53$	5.08597e7	−	5.08597e7i	0.885385	−	0.885385i	−0.108690	−	0.994076i	$-0.534666\pi$
$53$	5.08597e7	−	5.08597e7i	0.885385	−	0.885385i	0.994076	+	0.108690i	$0.0346657\pi$
$54$	−4.41676e7	−	1.17162e6i	−0.706858	−	0.0187506i
$55$	1.01989e8	−	1.91329e7i	1.50287	−	0.281935i
$56$		−	3.58871e7i		−	0.487632i
$57$	−3.62598e7	+	3.56243e7i	−0.454976	+	0.447002i
$58$	1.18010e7	+	1.18010e7i	0.136929	+	0.136929i
$59$	−4.63070e7			−0.497522			−0.248761	−	0.968565i	$-0.580023\pi$
$59$	−4.63070e7			−0.497522			−0.248761	+	0.968565i	$0.580023\pi$
$60$	4.11759e7	+	2.87049e7i	0.410169	+	0.285940i
$61$	3.55511e6			0.0328752			0.0164376	−	0.999865i	$-0.494768\pi$
$61$	3.55511e6			0.0328752			0.0164376	+	0.999865i	$0.494768\pi$
$62$	3.20927e6	+	3.20927e6i	0.0275832	+	0.0275832i
$63$	−1.19767e8	−	1.24079e8i	−0.957870	−	0.992354i
$64$		−	1.67772e7i		−	0.125000i
$65$	−9.00192e7	+	1.31593e8i	−0.625496	+	0.914373i
$66$	−1.66666e8	−	1.47339e6i	−1.08118	−	0.00955808i
$67$	−2.22768e8	+	2.22768e8i	−1.35057	+	1.35057i	−0.465544	+	0.885025i	$0.654141\pi$
$67$	−2.22768e8	+	2.22768e8i	−1.35057	+	1.35057i	−0.885025	+	0.465544i	$0.845859\pi$
$68$	−2.10692e7	+	2.10692e7i	−0.119497	+	0.119497i
$69$	1.35296e8	+	1.19607e6i	0.718562	+	0.00635237i
$70$	3.61228e7	+	1.92554e8i	0.179821	+	0.958543i
$71$			2.70212e8i			1.26195i	0.775804	+	0.630974i	$0.217345\pi$
$71$			2.70212e8i			1.26195i	−0.775804	+	0.630974i	$0.782655\pi$
$72$	−5.59913e7	−	5.80070e7i	−0.245541	−	0.254381i
$73$	2.47027e8	+	2.47027e8i	1.01810	+	1.01810i	0.999833	+	0.0182682i	$0.00581528\pi$
$73$	2.47027e8	+	2.47027e8i	1.01810	+	1.01810i	0.0182682	+	0.999833i	$0.494185\pi$
$74$	1.14826e8			0.445142
$75$	−2.49825e8	−	1.12571e8i	−0.911717	−	0.410819i
$76$	−9.27532e7			−0.318910
$77$	−4.60004e8	−	4.60004e8i	−1.49126	−	1.49126i
$78$	1.82676e8	−	1.79474e8i	0.558798	−	0.549005i
$79$		−	1.30605e8i		−	0.377258i	−0.982048	−	0.188629i	$-0.939596\pi$
$79$		−	1.30605e8i		−	0.377258i	0.982048	−	0.188629i	$-0.0604044\pi$
$80$	1.68874e7	+	9.00190e7i	0.0460954	+	0.245714i
$81$	−3.87178e8	−	1.36966e7i	−0.999375	−	0.0353533i
$82$	2.04849e8	−	2.04849e8i	0.500347	−	0.500347i
$83$	5.26747e8	−	5.26747e8i	1.21829	−	1.21829i	0.250061	−	0.968230i	$-0.419549\pi$
$83$	5.26747e8	−	5.26747e8i	1.21829	−	1.21829i	0.968230	−	0.250061i	$-0.0804506\pi$
$84$	2.78175e6	−	3.14664e8i	0.00609624	−	0.689589i
$85$	9.18404e7	−	1.34256e8i	0.190831	−	0.278964i
$86$			6.52451e8i			1.28619i
$87$	1.02559e8	+	1.04388e8i	0.191927	+	0.195351i
$88$	−2.15052e8	−	2.15052e8i	−0.382271	−	0.382271i
$89$	−6.38029e8			−1.07792			−0.538959	−	0.842332i	$-0.681182\pi$
$89$	−6.38029e8			−1.07792			−0.538959	+	0.842332i	$0.681182\pi$
$90$	3.58812e8	+	2.54881e8i	0.576469	+	0.409492i
$91$	9.99547e8			1.52798
$92$	1.74575e8	+	1.74575e8i	0.254060	+	0.254060i
$93$	2.78907e7	+	2.83882e7i	0.0386621	+	0.0393518i
$94$			8.46288e8i			1.11800i
$95$	4.97672e8	−	9.33624e7i	0.626884	−	0.117602i
$96$	1.30047e6	−	1.47105e8i	0.00156271	−	0.176770i
$97$	4.31943e8	−	4.31943e8i	0.495397	−	0.495397i	−0.414605	−	0.910002i	$-0.636080\pi$
$97$	4.31943e8	−	4.31943e8i	0.495397	−	0.495397i	0.910002	+	0.414605i	$0.136080\pi$
$98$	4.11935e8	−	4.11935e8i	0.451140	−	0.451140i
$99$	−1.46124e9	−	2.58379e7i	−1.52884	−	0.0270333i
$100$	−1.81220e8	−	4.66003e8i	−0.181220	−	0.466003i
$101$			4.84809e8i			0.463580i	0.972766	+	0.231790i	$0.0744582\pi$
$101$			4.84809e8i			0.463580i	−0.972766	+	0.231790i	$0.925542\pi$
$102$	−1.86372e8	+	1.83105e8i	−0.170482	+	0.167494i
$103$	4.02831e8	+	4.02831e8i	0.352659	+	0.352659i	0.861098	−	0.508439i	$-0.169777\pi$
$103$	4.02831e8	+	4.02831e8i	0.352659	+	0.352659i	−0.508439	+	0.861098i	$0.669777\pi$
$104$	4.67288e8			0.391683
$105$	3.01805e8	+	1.69115e9i	0.242312	+	1.35778i
$106$	1.15082e9			0.885385
$107$	−1.51799e9	−	1.51799e9i	−1.11955	−	1.11955i	−0.991808	−	0.127739i	$-0.959228\pi$
$107$	−1.51799e9	−	1.51799e9i	−1.11955	−	1.11955i	−0.127739	−	0.991808i	$-0.540772\pi$
$108$	−4.86444e8	−	5.12955e8i	−0.344054	−	0.362804i
$109$		−	4.04443e7i		−	0.0274434i	−0.999906	−	0.0137217i	$-0.995632\pi$
$109$		−	4.04443e7i		−	0.0274434i	0.999906	−	0.0137217i	$-0.00436789\pi$
$110$	1.37034e9	+	9.37408e8i	0.892401	+	0.610466i
$111$	1.00682e9	+	8.90066e6i	0.629502	+	0.00556504i
$112$	4.06016e8	−	4.06016e8i	0.243816	−	0.243816i
$113$	5.83546e8	−	5.83546e8i	0.336683	−	0.336683i	−0.518434	−	0.855118i	$-0.673485\pi$
$113$	5.83546e8	−	5.83546e8i	0.336683	−	0.336683i	0.855118	+	0.518434i	$0.173485\pi$
$114$	−8.13275e8	−	7.18967e6i	−0.450989	−	0.00398692i
$115$	−1.11241e9	−	7.60969e8i	−0.593096	−	0.405720i
$116$			2.67027e8i			0.136929i
$117$	1.61564e9	−	1.55950e9i	0.797093	−	0.769394i
$118$	−5.23904e8	−	5.23904e8i	−0.248761	−	0.248761i
$119$	−1.01977e9			−0.466166
$120$	1.41094e8	+	7.90611e8i	0.0621144	+	0.348054i
$121$	−3.15516e9			−1.33810
$122$	4.02215e7	+	4.02215e7i	0.0164376	+	0.0164376i
$123$	1.81203e9	−	1.78027e9i	0.713826	−	0.701315i
$124$			7.26175e7i			0.0275832i
$125$	1.44141e9	+	2.31795e9i	0.528072	+	0.849200i
$126$	4.87818e7	−	2.75881e9i	0.0172421	−	0.975112i
$127$	−2.96130e9	+	2.96130e9i	−1.01010	+	1.01010i	−0.0101533	+	0.999948i	$0.503232\pi$
$127$	−2.96130e9	+	2.96130e9i	−1.01010	+	1.01010i	−0.999948	+	0.0101533i	$0.996768\pi$
$128$	1.89813e8	−	1.89813e8i	0.0625000	−	0.0625000i
$129$	−5.05741e7	+	5.72080e9i	−0.0160796	+	1.81888i
$130$	−2.50726e9	+	4.70357e8i	−0.769935	+	0.144438i
$131$		−	3.40236e9i		−	1.00939i	−0.863298	−	0.504695i	$-0.831605\pi$
$131$		−	3.40236e9i		−	1.00939i	0.863298	−	0.504695i	$-0.168395\pi$
$132$	−1.86894e9	−	1.90228e9i	−0.535812	−	0.545370i
$133$	−2.24467e9	−	2.24467e9i	−0.622042	−	0.622042i
$134$	−5.04067e9			−1.35057
$135$	3.12637e9	+	2.26265e9i	0.810099	+	0.586293i
$136$	−4.76742e8			−0.119497
$137$	1.84631e9	+	1.84631e9i	0.447778	+	0.447778i	0.894615	−	0.446837i	$-0.147450\pi$
$137$	1.84631e9	+	1.84631e9i	0.447778	+	0.447778i	−0.446837	+	0.894615i	$0.647450\pi$
$138$	1.51717e9	+	1.54423e9i	0.356105	+	0.362457i
$139$		−	9.89105e8i		−	0.224738i	−0.993667	−	0.112369i	$-0.964156\pi$
$139$		−	9.89105e8i		−	0.224738i	0.993667	−	0.112369i	$-0.0358438\pi$
$140$	−1.76982e9	+	2.58718e9i	−0.389361	+	0.569182i
$141$	−6.55992e7	+	7.42039e9i	−0.0139769	+	1.58103i
$142$	−3.05710e9	+	3.05710e9i	−0.630974	+	0.630974i
$143$	5.98974e9	−	5.98974e9i	1.19783	−	1.19783i
$144$	2.28055e7	−	1.28974e9i	0.00441985	−	0.249961i
$145$	−2.68781e8	−	1.43275e9i	−0.0504943	−	0.269162i
$146$			5.58958e9i			1.01810i
$147$	3.64385e9	−	3.57999e9i	0.643624	−	0.632344i
$148$	1.29911e9	+	1.29911e9i	0.222571	+	0.222571i
$149$	−7.96464e9			−1.32382			−0.661909	−	0.749584i	$-0.730253\pi$
$149$	−7.96464e9			−1.32382			−0.661909	+	0.749584i	$0.730253\pi$
$150$	−1.55285e9	−	4.10004e9i	−0.250449	−	0.661268i
$151$	−2.83640e9			−0.443987			−0.221994	−	0.975048i	$-0.571256\pi$
$151$	−2.83640e9			−0.443987			−0.221994	+	0.975048i	$0.571256\pi$
$152$	−1.04938e9	−	1.04938e9i	−0.159455	−	0.159455i
$153$	−1.64833e9	+	1.59105e9i	−0.243183	+	0.234732i
$154$		−	1.04087e10i		−	1.49126i
$155$	−7.30945e7	−	3.89633e8i	−0.0101717	−	0.0542205i
$156$	4.09726e9	+	3.62214e7i	0.553902	+	0.00489671i
$157$	5.26775e9	−	5.26775e9i	0.691953	−	0.691953i	−0.270709	−	0.962661i	$-0.587258\pi$
$157$	5.26775e9	−	5.26775e9i	0.691953	−	0.691953i	0.962661	+	0.270709i	$0.0872580\pi$
$158$	1.47763e9	−	1.47763e9i	0.188629	−	0.188629i
$159$	1.00906e10	+	8.92050e7i	1.25207	+	0.0110688i
$160$	−8.27390e8	+	1.20951e9i	−0.0998091	+	0.145905i
$161$			8.44958e9i			0.991103i
$162$	−4.22546e9	−	4.53538e9i	−0.482011	−	0.517364i
$163$	4.35062e9	+	4.35062e9i	0.482732	+	0.482732i	0.906003	−	0.423271i	$-0.139118\pi$
$163$	4.35062e9	+	4.35062e9i	0.482732	+	0.482732i	−0.423271	+	0.906003i	$0.639118\pi$
$164$	4.63520e9			0.500347
$165$	1.19427e10	+	8.32556e9i	1.25436	+	0.874452i
$166$	1.19189e10			1.21829
$167$	−8.60080e9	−	8.60080e9i	−0.855686	−	0.855686i	0.135140	−	0.990826i	$-0.456851\pi$
$167$	−8.60080e9	−	8.60080e9i	−0.855686	−	0.855686i	−0.990826	+	0.135140i	$0.956851\pi$
$168$	3.59149e9	−	3.52855e9i	0.347843	−	0.341746i
$169$			2.41066e9i			0.227324i
$170$	2.55799e9	−	4.79873e8i	0.234897	−	0.0440663i
$171$	−7.13037e9	−	1.26080e8i	−0.637720	−	0.0112763i
$172$	−7.38164e9	+	7.38164e9i	−0.643095	+	0.643095i
$173$	−2.82046e8	+	2.82046e8i	−0.0239393	+	0.0239393i	−0.718975	−	0.695036i	$-0.755389\pi$
$173$	−2.82046e8	+	2.82046e8i	−0.0239393	+	0.0239393i	0.695036	+	0.718975i	$0.255389\pi$
$174$	−2.06983e7	+	2.34134e9i	−0.00171184	+	0.193639i
$175$	6.89188e9	−	1.56631e10i	0.555477	−	1.26243i
$176$		−	4.86607e9i		−	0.382271i
$177$	−4.55306e9	−	4.63428e9i	−0.348677	−	0.354897i
$178$	−7.21848e9	−	7.21848e9i	−0.538959	−	0.538959i
$179$	6.12927e9			0.446242			0.223121	−	0.974791i	$-0.428376\pi$
$179$	6.12927e9			0.446242			0.223121	+	0.974791i	$0.428376\pi$
$180$	1.17585e9	+	6.94314e9i	0.0834883	+	0.492980i
$181$	−3.81165e9			−0.263973			−0.131986	−	0.991252i	$-0.542136\pi$
$181$	−3.81165e9			−0.263973			−0.131986	+	0.991252i	$0.542136\pi$
$182$	1.13086e10	+	1.13086e10i	0.763989	+	0.763989i
$183$	3.49551e8	+	3.55786e8i	0.0230399	+	0.0234509i
$184$			3.95018e9i			0.254060i
$185$	−8.27810e9	−	5.66281e9i	−0.519586	−	0.355434i
$186$	−5.62888e6	+	6.36722e8i	−0.000344837	+	0.0390069i
$187$	−6.11092e9	+	6.11092e9i	−0.365443	+	0.365443i
$188$	−9.57465e9	+	9.57465e9i	−0.559001	+	0.559001i
$189$	6.41573e8	−	2.41859e10i	0.0365736	−	1.37875i
$190$	6.68679e9	+	4.57424e9i	0.372243	+	0.254641i
$191$		−	1.78564e10i		−	0.970832i	−0.874283	−	0.485416i	$-0.838668\pi$
$191$		−	1.78564e10i		−	0.970832i	0.874283	−	0.485416i	$-0.161332\pi$
$192$	1.67902e9	−	1.64959e9i	0.0891663	−	0.0876035i
$193$	1.96423e10	+	1.96423e10i	1.01902	+	1.01902i	0.999816	+	0.0192074i	$0.00611427\pi$
$193$	1.96423e10	+	1.96423e10i	1.01902	+	1.01902i	0.0192074	+	0.999816i	$0.493886\pi$
$194$	9.77374e9			0.495397
$195$	−2.20205e10	+	3.92982e9i	−1.09062	+	0.194633i
$196$	9.32103e9			0.451140
$197$	1.26115e10	+	1.26115e10i	0.596578	+	0.596578i	0.939400	−	0.342822i	$-0.111383\pi$
$197$	1.26115e10	+	1.26115e10i	0.596578	+	0.596578i	−0.342822	+	0.939400i	$0.611383\pi$
$198$	−1.62397e10	−	1.68244e10i	−0.750906	−	0.777939i
$199$			1.02047e10i			0.461277i	0.973040	+	0.230638i	$0.0740814\pi$
$199$			1.02047e10i			0.461277i	−0.973040	+	0.230638i	$0.925919\pi$
$200$	3.22195e9	−	7.32250e9i	0.142391	−	0.323612i
$201$	−4.41974e10	−	3.90723e8i	−1.90992	−	0.0168844i
$202$	−5.48499e9	+	5.48499e9i	−0.231790	+	0.231790i
$203$	−6.46217e9	+	6.46217e9i	−0.267083	+	0.267083i
$204$	−4.18015e9	−	3.69542e7i	−0.168988	−	0.00149392i
$205$	−2.48704e10	+	4.66565e9i	−0.983538	+	0.184510i
$206$			9.11502e9i			0.352659i
$207$	1.31831e10	+	1.36577e10i	0.499057	+	0.517024i
$208$	5.28676e9	+	5.28676e9i	0.195841	+	0.195841i
$209$	−2.69022e10			−0.975279
$210$	−1.57186e10	+	2.25477e10i	−0.557734	+	0.800046i
$211$	−5.64080e9			−0.195916			−0.0979580	−	0.995191i	$-0.531231\pi$
$211$	−5.64080e9			−0.195916			−0.0979580	+	0.995191i	$0.531231\pi$
$212$	1.30201e10	+	1.30201e10i	0.442693	+	0.442693i
$213$	−2.70421e10	+	2.65681e10i	−0.900185	+	0.884409i
$214$		−	3.43482e10i		−	1.11955i
$215$	3.21765e10	−	4.70367e10i	1.02699	−	1.50129i
$216$	2.99935e8	−	1.13069e10i	0.00937531	−	0.353429i
$217$	−1.75738e9	+	1.75738e9i	−0.0538017	+	0.0538017i
$218$	4.57575e8	−	4.57575e8i	0.0137217	−	0.0137217i
$219$	−4.33271e8	+	4.90103e10i	−0.0127280	+	1.43976i
$220$	4.89803e9	+	2.61091e10i	0.140968	+	0.751433i
$221$		−	1.32785e10i		−	0.374441i
$222$	1.12901e10	+	1.14915e10i	0.311968	+	0.317533i
$223$	6.96117e9	+	6.96117e9i	0.188499	+	0.188499i	0.795047	−	0.606548i	$-0.207446\pi$
$223$	6.96117e9	+	6.96117e9i	0.188499	+	0.188499i	−0.606548	+	0.795047i	$0.707446\pi$
$224$	9.18710e9			0.243816
$225$	−1.32978e10	−	3.60702e10i	−0.345907	−	0.938269i
$226$	1.32041e10			0.336683
$227$	1.17543e10	+	1.17543e10i	0.293820	+	0.293820i	0.838587	−	0.544767i	$-0.183382\pi$
$227$	1.17543e10	+	1.17543e10i	0.293820	+	0.293820i	−0.544767	+	0.838587i	$0.683382\pi$
$228$	−9.11982e9	−	9.28250e9i	−0.223501	−	0.227488i
$229$			1.57912e10i			0.379451i	0.981837	+	0.189726i	$0.0607599\pi$
$229$			1.57912e10i			0.379451i	−0.981837	+	0.189726i	$0.939240\pi$
$230$	−3.97612e9	−	2.11949e10i	−0.0936881	−	0.499408i
$231$	8.06821e8	−	9.12652e10i	0.0186433	−	2.10888i
$232$	−3.02106e9	+	3.02106e9i	−0.0684643	+	0.0684643i
$233$	−5.90307e10	+	5.90307e10i	−1.31213	+	1.31213i	−0.392283	+	0.919845i	$0.628315\pi$
$233$	−5.90307e10	+	5.90307e10i	−1.31213	+	1.31213i	−0.919845	+	0.392283i	$0.871685\pi$
$234$	3.59226e10	+	6.35190e8i	0.783243	+	0.0138494i
$235$	4.17358e10	−	6.10108e10i	0.892695	−	1.30497i
$236$		−	1.18546e10i		−	0.248761i
$237$	1.30706e10	−	1.28416e10i	0.269110	−	0.264393i
$238$	−1.15374e10	−	1.15374e10i	−0.233083	−	0.233083i
$239$	3.94275e10			0.781644			0.390822	−	0.920466i	$-0.372191\pi$
$239$	3.94275e10			0.781644			0.390822	+	0.920466i	$0.372191\pi$
$240$	−7.34844e9	+	1.05410e10i	−0.142970	+	0.205084i
$241$	8.63663e10			1.64918			0.824589	−	0.565732i	$-0.191406\pi$
$241$	8.63663e10			1.64918			0.824589	+	0.565732i	$0.191406\pi$
$242$	−3.56966e10	−	3.56966e10i	−0.669048	−	0.669048i
$243$	−3.66980e10	−	4.00945e10i	−0.675172	−	0.737661i
$244$			9.10108e8i			0.0164376i
$245$	−5.00125e10	+	9.38225e9i	−0.886811	+	0.166364i
$246$	4.06422e10	+	3.59293e8i	0.707570	+	0.00625520i
$247$	2.92280e10	−	2.92280e10i	0.499646	−	0.499646i
$248$	−8.21574e8	+	8.21574e8i	−0.0137916	+	0.0137916i
$249$	1.04507e11	+	9.23885e8i	1.72286	+	0.0152307i
$250$	−9.91695e9	+	4.25324e10i	−0.160564	+	0.688636i
$251$			8.54919e10i			1.35954i	0.733423	+	0.679772i	$0.237921\pi$
$251$			8.54919e10i			1.35954i	−0.733423	+	0.679772i	$0.762079\pi$
$252$	3.17643e10	−	3.06605e10i	0.496177	−	0.478935i
$253$	5.06337e10	+	5.06337e10i	0.776958	+	0.776958i
$254$	−6.70065e10			−1.01010
$255$	2.24660e10	−	4.00933e9i	0.332733	−	0.0593801i
$256$	4.29497e9			0.0625000
$257$	7.46653e10	+	7.46653e10i	1.06763	+	1.06763i	0.997541	+	0.0700860i	$0.0223274\pi$
$257$	7.46653e10	+	7.46653e10i	1.06763	+	1.06763i	0.0700860	+	0.997541i	$0.477673\pi$
$258$	−6.52956e10	+	6.41513e10i	−0.917478	+	0.901398i
$259$			6.28782e10i			0.868263i
$260$	−3.36879e10	−	2.30449e10i	−0.457187	−	0.312748i
$261$	−3.62973e8	+	2.05276e10i	−0.00484163	+	0.273814i
$262$	3.84933e10	−	3.84933e10i	0.504695	−	0.504695i
$263$	3.02888e10	−	3.02888e10i	0.390375	−	0.390375i	−0.484446	−	0.874821i	$-0.660979\pi$
$263$	3.02888e10	−	3.02888e10i	0.390375	−	0.390375i	0.874821	+	0.484446i	$0.160979\pi$
$264$	3.77188e8	−	4.26665e10i	0.00477904	−	0.540591i
$265$	−8.29655e10	−	5.67543e10i	−1.03345	−	0.706956i
$266$		−	5.07911e10i		−	0.622042i
$267$	−6.27333e10	−	6.38523e10i	−0.755435	−	0.768911i
$268$	−5.70287e10	−	5.70287e10i	−0.675284	−	0.675284i
$269$	6.01206e10			0.700065			0.350033	−	0.936738i	$-0.386171\pi$
$269$	6.01206e10			0.700065			0.350033	+	0.936738i	$0.386171\pi$
$270$	9.77186e9	+	6.09697e10i	0.111903	+	0.698196i
$271$	−1.45800e11			−1.64208			−0.821040	−	0.570871i	$-0.806606\pi$
$271$	−1.45800e11			−1.64208			−0.821040	+	0.570871i	$0.806606\pi$
$272$	−5.39372e9	−	5.39372e9i	−0.0597487	−	0.0597487i
$273$	9.82789e10	+	1.00032e11i	1.07085	+	1.08995i
$274$			4.17773e10i			0.447778i
$275$	−5.25612e10	−	1.35160e11i	−0.554202	−	1.42512i
$276$	−3.06194e8	+	3.46358e10i	−0.00317619	+	0.359281i
$277$	−9.48841e9	+	9.48841e9i	−0.0968355	+	0.0968355i	−0.753865	−	0.657029i	$-0.771813\pi$
$277$	−9.48841e9	+	9.48841e9i	−0.0968355	+	0.0968355i	0.657029	+	0.753865i	$0.271813\pi$
$278$	1.11904e10	−	1.11904e10i	0.112369	−	0.112369i
$279$	−9.87098e7	+	5.58245e9i	−0.000975307	+	0.0551577i
$280$	−4.92939e10	+	9.24744e9i	−0.479272	+	0.0899105i
$281$			8.81955e10i			0.843855i	0.906630	+	0.421928i	$0.138646\pi$
$281$			8.81955e10i			0.843855i	−0.906630	+	0.421928i	$0.861354\pi$
$282$	−8.46943e10	+	8.32100e10i	−0.797505	+	0.783528i
$283$	−3.86882e10	−	3.86882e10i	−0.358542	−	0.358542i	0.504733	−	0.863275i	$-0.331591\pi$
$283$	−3.86882e10	−	3.86882e10i	−0.358542	−	0.358542i	−0.863275	+	0.504733i	$0.831591\pi$
$284$	−6.91742e10			−0.630974
$285$	5.82763e10	+	4.06260e10i	0.523227	+	0.364756i
$286$	1.35532e11			1.19783
$287$	1.12174e11	+	1.12174e11i	0.975942	+	0.975942i
$288$	1.48498e10	−	1.43338e10i	0.127190	−	0.122771i
$289$		−	1.05041e11i		−	0.885763i
$290$	1.31688e10	−	1.92506e10i	0.109334	−	0.159828i
$291$	8.56978e10	+	7.57602e8i	0.700569	+	0.00619331i
$292$	−6.32388e10	+	6.32388e10i	−0.509051	+	0.509051i
$293$	9.67535e10	−	9.67535e10i	0.766942	−	0.766942i	−0.210625	−	0.977567i	$-0.567550\pi$
$293$	9.67535e10	−	9.67535e10i	0.766942	−	0.766942i	0.977567	+	0.210625i	$0.0675499\pi$
$294$	8.17283e10	+	7.22511e8i	0.637984	+	0.00564003i
$295$	1.19324e10	+	6.36064e10i	0.0917340	+	0.488992i
$296$			2.93956e10i			0.222571i
$297$	−1.41088e11	−	1.48778e11i	−1.05217	−	1.10952i
$298$	−9.01096e10	−	9.01096e10i	−0.661909	−	0.661909i
$299$	−1.10022e11			−0.796088
$300$	2.88182e10	−	6.39552e10i	0.205410	−	0.455858i
$301$	−3.57278e11			−2.50875
$302$	−3.20902e10	−	3.20902e10i	−0.221994	−	0.221994i
$303$	−4.85184e10	+	4.76681e10i	−0.330685	+	0.324890i
$304$		−	2.37448e10i		−	0.159455i
$305$	−9.16086e8	−	4.88323e9i	−0.00606159	−	0.0323116i
$306$	−3.66494e10	−	6.48041e8i	−0.238958	−	0.00422529i
$307$	5.66781e9	−	5.66781e9i	0.0364161	−	0.0364161i	−0.688664	−	0.725080i	$-0.741803\pi$
$307$	5.66781e9	−	5.66781e9i	0.0364161	−	0.0364161i	0.725080	+	0.688664i	$0.241803\pi$
$308$	1.17761e11	−	1.17761e11i	0.745630	−	0.745630i
$309$	−7.06542e8	+	7.99220e10i	−0.00440885	+	0.498716i
$310$	3.58123e9	−	5.23516e9i	0.0220244	−	0.0321961i
$311$			2.52579e10i			0.153100i	0.997066	+	0.0765500i	$0.0243905\pi$
$311$			2.52579e10i			0.153100i	−0.997066	+	0.0765500i	$0.975610\pi$
$312$	4.59454e10	+	4.67650e10i	0.274502	+	0.279399i
$313$	−3.00136e10	−	3.00136e10i	−0.176754	−	0.176754i	0.613185	−	0.789939i	$-0.289888\pi$
$313$	−3.00136e10	−	3.00136e10i	−0.176754	−	0.176754i	−0.789939	+	0.613185i	$0.789888\pi$
$314$	1.19196e11			0.691953
$315$	−1.39571e11	+	1.96483e11i	−0.798726	+	1.12442i
$316$	3.34349e10			0.188629
$317$	−2.38220e8	−	2.38220e8i	−0.00132499	−	0.00132499i	0.706444	−	0.707769i	$-0.250298\pi$
$317$	−2.38220e8	−	2.38220e8i	−0.00132499	−	0.00132499i	−0.707769	+	0.706444i	$0.750298\pi$
$318$	1.13153e11	+	1.15171e11i	0.620503	+	0.631572i
$319$			7.74486e10i			0.418750i
$320$	−2.30449e10	+	4.32318e9i	−0.122857	+	0.0230477i
$321$	2.66247e9	−	3.01171e11i	0.0139963	−	1.58322i
$322$	−9.55961e10	+	9.55961e10i	−0.495551	+	0.495551i
$323$	−2.98193e10	+	2.98193e10i	−0.152436	+	0.152436i
$324$	3.50633e9	−	9.91176e10i	0.0176766	−	0.499687i
$325$	2.03950e11	+	8.97395e10i	1.01403	+	0.446178i
$326$			9.84432e10i			0.482732i
$327$	4.04756e9	−	3.97663e9i	0.0195762	−	0.0192331i
$328$	5.24414e10	+	5.24414e10i	0.250174	+	0.250174i
$329$	−4.63422e11			−2.18070
$330$	4.09229e10	+	2.29309e11i	0.189956	+	1.06441i
$331$	−3.48325e9			−0.0159499			−0.00797496	−	0.999968i	$-0.502539\pi$
$331$	−3.48325e9			−0.0159499			−0.00797496	+	0.999968i	$0.502539\pi$
$332$	1.34847e11	+	1.34847e11i	0.609145	+	0.609145i
$333$	9.81030e10	+	1.01635e11i	0.437203	+	0.452943i
$334$		−	1.94614e11i		−	0.855686i
$335$	3.63394e11	+	2.48587e11i	1.57643	+	1.07839i
$336$	8.05540e10	+	7.12129e8i	0.344794	+	0.00304812i
$337$	1.27549e11	−	1.27549e11i	0.538694	−	0.538694i	−0.384451	−	0.923145i	$-0.625609\pi$
$337$	1.27549e11	−	1.27549e11i	0.538694	−	0.538694i	0.923145	+	0.384451i	$0.125609\pi$
$338$	−2.72735e10	+	2.72735e10i	−0.113662	+	0.113662i
$339$	1.15776e11	+	1.02351e9i	0.476124	+	0.00420912i
$340$	3.43694e10	+	2.35112e10i	0.139482	+	0.0954155i
$341$			2.10620e10i			0.0843539i
$342$	−7.92445e10	−	8.20974e10i	−0.313222	−	0.324498i
$343$	−2.44302e10	−	2.44302e10i	−0.0953023	−	0.0953023i
$344$	−1.67028e11			−0.643095
$345$	−3.32204e10	−	1.86148e11i	−0.126246	−	0.707414i
$346$	−6.38197e9			−0.0239393
$347$	−2.20653e11	−	2.20653e11i	−0.817009	−	0.817009i	0.168665	−	0.985673i	$-0.446054\pi$
$347$	−2.20653e11	−	2.20653e11i	−0.817009	−	0.817009i	−0.985673	+	0.168665i	$0.946054\pi$
$348$	−2.67234e10	+	2.62550e10i	−0.0976753	+	0.0959634i
$349$		−	2.46071e11i		−	0.887865i	−0.896060	−	0.443932i	$-0.853583\pi$
$349$		−	2.46071e11i		−	0.887865i	0.896060	−	0.443932i	$-0.146417\pi$
$350$	2.55181e11	−	9.92352e10i	0.908953	−	0.353476i
$351$	3.14926e11	+	8.35396e9i	1.10746	+	0.0293772i
$352$	5.50533e10	−	5.50533e10i	0.191135	−	0.191135i
$353$	3.30409e11	−	3.30409e11i	1.13257	−	1.13257i	0.142822	−	0.989748i	$-0.454382\pi$
$353$	3.30409e11	−	3.30409e11i	1.13257	−	1.13257i	0.989748	−	0.142822i	$-0.0456178\pi$
$354$	9.18896e8	−	1.03943e11i	0.00310994	−	0.351787i
$355$	3.71158e11	−	6.96285e10i	1.24031	−	0.232680i
$356$		−	1.63336e11i		−	0.538959i
$357$	−1.00267e11	−	1.02056e11i	−0.326703	−	0.332530i
$358$	6.93448e10	+	6.93448e10i	0.223121	+	0.223121i
$359$	−4.25333e11			−1.35146			−0.675731	−	0.737148i	$-0.736172\pi$
$359$	−4.25333e11			−1.35146			−0.675731	+	0.737148i	$0.736172\pi$
$360$	−6.52494e10	+	9.18559e10i	−0.204746	+	0.288234i
$361$	1.91414e11			0.593186
$362$	−4.31239e10	−	4.31239e10i	−0.131986	−	0.131986i
$363$	−3.10226e11	−	3.15760e11i	−0.937775	−	0.954504i
$364$			2.55884e11i			0.763989i
$365$	2.75657e11	−	4.02965e11i	0.812926	−	1.18837i
$366$	−7.05462e7	+	7.97998e9i	−0.000205498	+	0.0232454i
$367$	−2.91625e9	+	2.91625e9i	−0.00839126	+	0.00839126i	−0.711290	−	0.702899i	$-0.751889\pi$
$367$	−2.91625e9	+	2.91625e9i	−0.00839126	+	0.00839126i	0.702899	+	0.711290i	$0.251889\pi$
$368$	−4.46912e10	+	4.46912e10i	−0.127030	+	0.127030i
$369$	3.56330e11	+	6.30069e9i	1.00054	+	0.0176917i
$370$	−2.95886e10	−	1.57723e11i	−0.0820761	−	0.437510i
$371$			6.30184e11i			1.72697i
$372$	−7.26738e9	+	7.14001e9i	−0.0196759	+	0.0193311i
$373$	1.30026e11	+	1.30026e11i	0.347810	+	0.347810i	0.859293	−	0.511484i	$-0.170904\pi$
$373$	1.30026e11	+	1.30026e11i	0.347810	+	0.347810i	−0.511484	+	0.859293i	$0.670904\pi$
$374$	−1.38274e11			−0.365443
$375$	−9.02503e10	+	3.72162e11i	−0.235672	+	0.971833i
$376$	−2.16650e11			−0.559001
$377$	−8.41443e10	−	8.41443e10i	−0.214530	−	0.214530i
$378$	2.80891e11	−	2.66374e11i	0.707660	−	0.671087i
$379$			3.25136e11i			0.809448i	0.914439	+	0.404724i	$0.132632\pi$
$379$			3.25136e11i			0.809448i	−0.914439	+	0.404724i	$0.867368\pi$
$380$	2.39008e10	+	1.27404e11i	0.0588011	+	0.313442i
$381$	−5.87524e11	−	5.19394e9i	−1.42844	−	0.0126280i
$382$	2.02022e11	−	2.02022e11i	0.485416	−	0.485416i
$383$	−2.29649e10	+	2.29649e10i	−0.0545344	+	0.0545344i	−0.733848	−	0.679314i	$-0.762278\pi$
$383$	−2.29649e10	+	2.29649e10i	−0.0545344	+	0.0545344i	0.679314	+	0.733848i	$0.262278\pi$
$384$	3.76590e10	+	3.32920e8i	0.0883849	+	0.000781357i
$385$	−5.13318e11	+	7.50387e11i	−1.19073	+	1.74065i
$386$			4.44454e11i			1.01902i
$387$	−5.77496e11	+	5.57428e11i	−1.30873	+	1.26325i
$388$	1.10577e11	+	1.10577e11i	0.247698	+	0.247698i
$389$	−4.26592e11			−0.944581			−0.472291	−	0.881443i	$-0.656573\pi$
$389$	−4.26592e11			−0.944581			−0.472291	+	0.881443i	$0.656573\pi$
$390$	−2.93594e11	−	2.04673e11i	−0.642624	−	0.447991i
$391$	1.12248e11			0.242876
$392$	1.05455e11	+	1.05455e11i	0.225570	+	0.225570i
$393$	3.40499e11	−	3.34532e11i	0.720028	−	0.707409i
$394$			2.85365e11i			0.596578i
$395$	−1.79397e11	+	3.36545e10i	−0.370790	+	0.0695595i
$396$	6.61450e9	−	3.74078e11i	0.0135166	−	0.764422i
$397$	3.15635e11	−	3.15635e11i	0.637717	−	0.637717i	−0.312275	−	0.949992i	$-0.601091\pi$
$397$	3.15635e11	−	3.15635e11i	0.637717	−	0.637717i	0.949992	+	0.312275i	$0.101091\pi$
$398$	−1.15453e11	+	1.15453e11i	−0.230638	+	0.230638i
$399$	3.93702e9	−	4.45344e11i	0.00777660	−	0.879666i
$400$	1.19297e11	−	4.63924e10i	0.233002	−	0.0906102i
$401$		−	6.10464e10i		−	0.117899i	−0.998261	−	0.0589496i	$-0.981225\pi$
$401$		−	6.10464e10i		−	0.117899i	0.998261	−	0.0589496i	$-0.0187751\pi$
$402$	−4.95616e11	−	5.04457e11i	−0.946517	−	0.963401i
$403$	−2.28829e10	−	2.28829e10i	−0.0432154	−	0.0432154i
$404$	−1.24111e11			−0.231790
$405$	8.09553e10	+	5.35350e11i	0.149519	+	0.988759i
$406$	−1.46222e11			−0.267083
$407$	3.76795e11	+	3.76795e11i	0.680660	+	0.680660i
$408$	−4.68750e10	−	4.77111e10i	−0.0837472	−	0.0852411i
$409$			3.72503e10i			0.0658225i	0.999458	+	0.0329113i	$0.0104779\pi$
$409$			3.72503e10i			0.0658225i	−0.999458	+	0.0329113i	$0.989522\pi$
$410$	−3.34163e11	−	2.28591e11i	−0.584024	−	0.399514i
$411$	−3.23832e9	+	3.66310e11i	−0.00559799	+	0.633229i
$412$	−1.03125e11	+	1.03125e11i	−0.176330	+	0.176330i
$413$	2.86886e11	−	2.86886e11i	0.485215	−	0.485215i
$414$	−5.36952e9	+	3.03669e11i	−0.00898326	+	0.508041i
$415$	−8.59263e11	−	5.87797e11i	−1.42203	−	0.972772i
$416$			1.19626e11i			0.195841i
$417$	9.89871e10	−	9.72523e10i	0.160312	−	0.157503i
$418$	−3.04363e11	−	3.04363e11i	−0.487639	−	0.487639i
$419$	6.08061e11			0.963793			0.481897	−	0.876228i	$-0.339948\pi$
$419$	6.08061e11			0.963793			0.481897	+	0.876228i	$0.339948\pi$
$420$	−4.32933e11	+	7.72621e10i	−0.678890	+	0.121156i
$421$	7.33671e11			1.13824			0.569118	−	0.822256i	$-0.307285\pi$
$421$	7.33671e11			1.13824			0.569118	+	0.822256i	$0.307285\pi$
$422$	−6.38184e10	−	6.38184e10i	−0.0979580	−	0.0979580i
$423$	−7.49064e11	+	7.23034e11i	−1.13759	+	1.09806i
$424$			2.94611e11i			0.442693i
$425$	−2.08077e11	−	9.15551e10i	−0.309366	−	0.136123i
$426$	−6.06531e11	−	5.36197e9i	−0.892297	−	0.00788826i
$427$	−2.20250e10	+	2.20250e10i	−0.0320620	+	0.0320620i
$428$	3.88606e11	−	3.88606e11i	0.559774	−	0.559774i
$429$	1.18837e12	+	1.05057e10i	1.69392	+	0.0149750i
$430$	8.96195e11	−	1.68125e11i	1.26414	−	0.237150i
$431$		−	6.23292e11i		−	0.870050i	−0.900418	−	0.435025i	$-0.856740\pi$
$431$		−	6.23292e11i		−	0.870050i	0.900418	−	0.435025i	$-0.143260\pi$
$432$	1.31317e11	−	1.24530e11i	0.181402	−	0.172027i
$433$	−3.19154e11	−	3.19154e11i	−0.436320	−	0.436320i	0.454452	−	0.890771i	$-0.349835\pi$
$433$	−3.19154e11	−	3.19154e11i	−0.436320	−	0.436320i	−0.890771	+	0.454452i	$0.849835\pi$
$434$	−3.97649e10			−0.0538017
$435$	1.16958e11	−	1.67772e11i	0.156613	−	0.224655i
$436$	1.03537e10			0.0137217
$437$	2.47076e11	+	2.47076e11i	0.324089	+	0.324089i
$438$	−5.59390e11	+	5.49587e11i	−0.726242	+	0.713514i
$439$			6.67890e11i			0.858251i	0.903245	+	0.429126i	$0.141178\pi$
$439$			6.67890e11i			0.858251i	−0.903245	+	0.429126i	$0.858822\pi$
$440$	−2.39976e11	+	3.50806e11i	−0.305233	+	0.446200i
$441$	7.16551e11	+	1.26702e10i	0.902140	+	0.0159518i
$442$	1.50229e11	−	1.50229e11i	0.187220	−	0.187220i
$443$	1.01051e12	−	1.01051e12i	1.24659	−	1.24659i	0.289379	−	0.957215i	$-0.406551\pi$
$443$	1.01051e12	−	1.01051e12i	1.24659	−	1.24659i	0.957215	−	0.289379i	$-0.0934488\pi$
$444$	−2.27857e9	+	2.57745e11i	−0.00278252	+	0.314751i
$445$	1.64408e11	+	8.76385e11i	0.198748	+	1.05944i
$446$			1.57513e11i			0.188499i
$447$	−7.83111e11	−	7.97081e11i	−0.927769	−	0.944319i
$448$	1.03940e11	+	1.03940e11i	0.121908	+	0.121908i
$449$	−3.49275e11			−0.405563			−0.202782	−	0.979224i	$-0.564998\pi$
$449$	−3.49275e11			−0.405563			−0.202782	+	0.979224i	$0.564998\pi$
$450$	2.57640e11	−	5.58536e11i	0.296181	−	0.642088i
$451$	1.34440e12			1.53015
$452$	1.49388e11	+	1.49388e11i	0.168342	+	0.168342i
$453$	−2.78884e11	−	2.83859e11i	−0.311159	−	0.316710i
$454$			2.65970e11i			0.293820i
$455$	−2.57565e11	−	1.37296e12i	−0.281731	−	1.50178i
$456$	1.84056e9	−	2.08198e11i	0.00199346	−	0.225494i
$457$	−5.71768e11	+	5.71768e11i	−0.613192	+	0.613192i	−0.943776	−	0.330584i	$-0.892754\pi$
$457$	−5.71768e11	+	5.71768e11i	−0.613192	+	0.613192i	0.330584	+	0.943776i	$0.392754\pi$
$458$	−1.78657e11	+	1.78657e11i	−0.189726	+	0.189726i
$459$	−3.21298e11	−	8.52298e9i	−0.337871	−	0.00896260i
$460$	1.94808e11	−	2.84777e11i	0.202860	−	0.296548i
$461$			2.45545e11i			0.253208i	0.991953	+	0.126604i	$0.0404077\pi$
$461$			2.45545e11i			0.253208i	−0.991953	+	0.126604i	$0.959592\pi$
$462$	1.04168e12	−	1.02342e12i	1.06376	−	1.04512i
$463$	4.26706e11	+	4.26706e11i	0.431534	+	0.431534i	0.889150	−	0.457616i	$-0.151297\pi$
$463$	4.26706e11	+	4.26706e11i	0.431534	+	0.431534i	−0.457616	+	0.889150i	$0.651297\pi$
$464$	−6.83589e10			−0.0684643
$465$	3.18066e10	−	4.56252e10i	0.0315485	−	0.0452550i
$466$	−1.33571e12			−1.31213
$467$	1.16348e12	+	1.16348e12i	1.13197	+	1.13197i	0.989850	+	0.142117i	$0.0453908\pi$
$467$	1.16348e12	+	1.16348e12i	1.13197	+	1.13197i	0.142117	+	0.989850i	$0.454609\pi$
$468$	3.99232e11	+	4.13605e11i	0.384697	+	0.398546i
$469$		−	2.76024e12i		−	2.63432i
$470$	1.16245e12	−	2.18073e11i	1.09883	−	0.206139i
$471$	1.04513e12	+	9.23932e9i	0.978531	+	0.00865060i
$472$	1.34119e11	−	1.34119e11i	0.124380	−	0.124380i
$473$	−2.14097e12	+	2.14097e12i	−1.96669	+	1.96669i
$474$	2.93163e11	+	2.59168e9i	0.266751	+	0.00235819i
$475$	−2.56482e11	−	6.59535e11i	−0.231172	−	0.594452i
$476$		−	2.61061e11i		−	0.233083i
$477$	9.83216e11	+	1.01861e12i	0.869594	+	0.900900i
$478$	4.46071e11	+	4.46071e11i	0.390822	+	0.390822i
$479$	−9.79330e11			−0.850001			−0.425000	−	0.905193i	$-0.639726\pi$
$479$	−9.79330e11			−0.850001			−0.425000	+	0.905193i	$0.639726\pi$
$480$	−2.02396e11	+	3.61200e10i	−0.174027	+	0.0310572i
$481$	−8.18741e11			−0.697419
$482$	9.77123e11	+	9.77123e11i	0.824589	+	0.824589i
$483$	−8.45612e11	+	8.30792e11i	−0.706983	+	0.694593i
$484$		−	8.07721e11i		−	0.669048i
$485$	−7.04612e11	−	4.82005e11i	−0.578245	−	0.395561i
$486$	3.84271e10	−	8.68808e11i	0.0312445	−	0.706416i
$487$	6.43843e11	−	6.43843e11i	0.518680	−	0.518680i	−0.398492	−	0.917172i	$-0.630466\pi$
$487$	6.43843e11	−	6.43843e11i	0.518680	−	0.518680i	0.917172	+	0.398492i	$0.130466\pi$
$488$	−1.02967e10	+	1.02967e10i	−0.00821881	+	0.00821881i
$489$	−7.63073e9	+	8.63166e11i	−0.00603498	+	0.682660i
$490$	−6.71975e11	−	4.59678e11i	−0.526587	−	0.360223i
$491$		−	1.00928e12i		−	0.783694i	−0.920030	−	0.391847i	$-0.871836\pi$
$491$		−	1.00928e12i		−	0.783694i	0.920030	−	0.391847i	$-0.128164\pi$
$492$	4.55750e11	+	4.63879e11i	0.350658	+	0.356913i
$493$	8.58467e10	+	8.58467e10i	0.0654505	+	0.0654505i
$494$	6.61353e11			0.499646
$495$	3.41044e11	+	2.01379e12i	0.255321	+	1.50762i
$496$	−1.85901e10			−0.0137916
$497$	−1.67405e12	−	1.67405e12i	−1.23073	−	1.23073i
$498$	1.17191e12	+	1.19282e12i	0.853813	+	0.869044i
$499$		−	3.96768e11i		−	0.286473i	−0.989688	−	0.143237i	$-0.954249\pi$
$499$		−	3.96768e11i		−	0.286473i	0.989688	−	0.143237i	$-0.0457510\pi$
$500$	−5.93396e11	+	3.69001e11i	−0.424600	+	0.264036i
$501$	1.50853e10	−	1.70641e12i	0.0106975	−	1.21008i
$502$	−9.67231e11	+	9.67231e11i	−0.679772	+	0.679772i
$503$	−3.93374e11	+	3.93374e11i	−0.274000	+	0.274000i	−0.830708	−	0.556708i	$-0.812064\pi$
$503$	−3.93374e11	+	3.93374e11i	−0.274000	+	0.274000i	0.556708	+	0.830708i	$0.312064\pi$
$504$	7.06255e11	+	1.24881e10i	0.487556	+	0.00862105i
$505$	6.65925e11	−	1.24926e11i	0.455632	−	0.0854757i
$506$			1.14571e12i			0.776958i
$507$	−2.41252e11	+	2.37024e11i	−0.162157	+	0.159315i
$508$	−7.58092e11	−	7.58092e11i	−0.505051	−	0.505051i
$509$	1.46268e12			0.965869			0.482934	−	0.875657i	$-0.339571\pi$
$509$	1.46268e12			0.965869			0.482934	+	0.875657i	$0.339571\pi$
$510$	2.99535e11	+	2.08814e11i	0.196056	+	0.136676i
$511$	−3.06082e12			−1.98584
$512$	4.85920e10	+	4.85920e10i	0.0312500	+	0.0312500i
$513$	−6.88465e11	−	7.25986e11i	−0.438888	−	0.462807i
$514$			1.68948e12i			1.06763i
$515$	4.49519e11	−	6.57123e11i	0.281589	−	0.411637i
$516$	−1.46452e12	−	1.29470e10i	−0.909438	−	0.00803979i
$517$	−2.77704e12	+	2.77704e12i	−1.70952	+	1.70952i
$518$	−7.11386e11	+	7.11386e11i	−0.434131	+	0.434131i
$519$	−5.59582e10	−	4.94692e8i	−0.0338540	−	0.000299283i
$520$	−1.20411e11	−	6.41858e11i	−0.0722192	−	0.384967i
$521$		−	1.11588e11i		−	0.0663512i	−0.999450	−	0.0331756i	$-0.989438\pi$
$521$		−	1.11588e11i		−	0.0663512i	0.999450	−	0.0331756i	$-0.0105621\pi$
$522$	−2.36350e11	+	2.28137e11i	−0.139328	+	0.134486i
$523$	−1.33574e12	−	1.33574e12i	−0.780666	−	0.780666i	0.199277	−	0.979943i	$-0.436141\pi$
$523$	−1.33574e12	−	1.33574e12i	−0.780666	−	0.780666i	−0.979943	+	0.199277i	$0.936141\pi$
$524$	8.71003e11			0.504695
$525$	2.24516e12	−	8.50331e11i	1.28982	−	0.488507i
$526$	6.85358e11			0.390375
$527$	2.33459e10	+	2.33459e10i	0.0131845	+	0.0131845i
$528$	4.86984e11	−	4.78449e11i	0.272685	−	0.267906i
$529$			8.71088e11i			0.483628i
$530$	−2.96546e11	−	1.58075e12i	−0.163249	−	0.870205i
$531$	1.61141e10	−	9.11318e11i	0.00879589	−	0.497444i
$532$	5.74635e11	−	5.74635e11i	0.311021	−	0.311021i
$533$	−1.46062e12	+	1.46062e12i	−0.783910	+	0.783910i
$534$	1.26608e10	−	1.43215e12i	0.00673791	−	0.762173i
$535$	−1.69393e12	+	2.47624e12i	−0.893928	+	1.30678i
$536$		−	1.29041e12i		−	0.675284i
$537$	6.02651e11	+	6.13402e11i	0.312739	+	0.318318i
$538$	6.80187e11	+	6.80187e11i	0.350033	+	0.350033i
$539$	2.70347e12			1.37966
$540$	−5.79238e11	+	8.00350e11i	−0.293147	+	0.405049i
$541$	2.09107e12			1.04950			0.524748	−	0.851257i	$-0.324159\pi$
$541$	2.09107e12			1.04950			0.524748	+	0.851257i	$0.324159\pi$
$542$	−1.64953e12	−	1.64953e12i	−0.821040	−	0.821040i
$543$	−3.74774e11	−	3.81460e11i	−0.185000	−	0.188300i
$544$		−	1.22046e11i		−	0.0597487i
$545$	−5.55536e10	+	1.04217e10i	−0.0269729	+	0.00506007i
$546$	−1.98346e10	+	2.24363e12i	−0.00955117	+	1.08040i
$547$	3.52076e11	−	3.52076e11i	0.168149	−	0.168149i	−0.618017	−	0.786165i	$-0.712064\pi$
$547$	3.52076e11	−	3.52076e11i	0.168149	−	0.168149i	0.786165	+	0.618017i	$0.212064\pi$
$548$	−4.72656e11	+	4.72656e11i	−0.223889	+	0.223889i
$549$	−1.23712e9	+	6.99643e10i	−0.000581215	+	0.0328701i
$550$	9.34495e11	−	2.12382e12i	0.435457	−	0.989659i
$551$			3.77924e11i			0.174671i
$552$	−3.95324e11	+	3.88395e11i	−0.181229	+	0.178052i
$553$	8.09141e11	+	8.09141e11i	0.367926	+	0.367926i
$554$	−2.14698e11			−0.0968355
$555$	−2.47212e11	−	1.38524e12i	−0.110599	−	0.619735i
$556$	2.53211e11			0.112369
$557$	1.59723e12	+	1.59723e12i	0.703103	+	0.703103i	0.965075	−	0.261972i	$-0.0843729\pi$
$557$	1.59723e12	+	1.59723e12i	0.703103	+	0.703103i	−0.261972	+	0.965075i	$0.584373\pi$
$558$	−6.42750e10	+	6.20414e10i	−0.0280665	+	0.0270912i
$559$		−	4.65214e12i		−	2.01511i
$560$	−6.62319e11	−	4.53073e11i	−0.284591	−	0.194681i
$561$	−1.21241e12	−	1.07182e10i	−0.516794	−	0.00456867i
$562$	−9.97818e11	+	9.97818e11i	−0.421928	+	0.421928i
$563$	1.64573e12	−	1.64573e12i	0.690353	−	0.690353i	−0.271957	−	0.962309i	$-0.587671\pi$
$563$	1.64573e12	−	1.64573e12i	0.690353	−	0.690353i	0.962309	+	0.271957i	$0.0876708\pi$
$564$	−1.89962e12	−	1.67934e10i	−0.790516	−	0.00698847i
$565$	−9.51916e11	−	6.51178e11i	−0.392989	−	0.268833i
$566$		−	8.75415e11i		−	0.358542i
$567$	2.48355e12	−	2.31384e12i	1.00913	−	0.940176i
$568$	−7.82616e11	−	7.82616e11i	−0.315487	−	0.315487i
$569$	−3.80308e12			−1.52100			−0.760502	−	0.649336i	$-0.775047\pi$
$569$	−3.80308e12			−1.52100			−0.760502	+	0.649336i	$0.775047\pi$
$570$	1.99690e11	+	1.11895e12i	0.0792355	+	0.443992i
$571$	2.03319e12			0.800417			0.400208	−	0.916424i	$-0.368938\pi$
$571$	2.03319e12			0.800417			0.400208	+	0.916424i	$0.368938\pi$
$572$	1.53337e12	+	1.53337e12i	0.598916	+	0.598916i
$573$	1.78702e12	−	1.75570e12i	0.692524	−	0.680387i
$574$			2.53821e12i			0.975942i
$575$	−7.58605e11	+	1.72408e12i	−0.289408	+	0.657735i
$576$	3.30174e11	+	5.83820e9i	0.124980	+	0.00220993i
$577$	2.77918e12	−	2.77918e12i	1.04382	−	1.04382i	0.0448251	−	0.998995i	$-0.485727\pi$
$577$	2.77918e12	−	2.77918e12i	1.04382	−	1.04382i	0.998995	−	0.0448251i	$-0.0142731\pi$
$578$	1.18840e12	−	1.18840e12i	0.442881	−	0.442881i
$579$	−3.44514e10	+	3.89705e12i	−0.0127395	+	1.44106i
$580$	3.66783e11	−	6.88079e10i	0.134581	−	0.0252471i
$581$			6.52673e12i			2.37631i
$582$	9.60989e11	+	9.78131e11i	0.347188	+	0.353381i
$583$	3.77635e12	+	3.77635e12i	1.35383	+	1.35383i
$584$	−1.43093e12			−0.509051
$585$	−2.55842e12	−	1.81736e12i	−0.903172	−	0.641564i
$586$	2.18928e12			0.766942
$587$	−1.86538e11	−	1.86538e11i	−0.0648480	−	0.0648480i	0.673939	−	0.738787i	$-0.264601\pi$
$587$	−1.86538e11	−	1.86538e11i	−0.0648480	−	0.0648480i	−0.738787	+	0.673939i	$0.764601\pi$
$588$	9.16476e11	+	9.32825e11i	0.316172	+	0.321812i
$589$			1.02776e11i			0.0351861i
$590$	−5.84624e11	+	8.54624e11i	−0.198629	+	0.290363i
$591$	−2.21198e10	+	2.50212e12i	−0.00745825	+	0.843656i
$592$	−3.32573e11	+	3.32573e11i	−0.111286	+	0.111286i
$593$	8.72498e11	−	8.72498e11i	0.289747	−	0.289747i	−0.547233	−	0.836980i	$-0.684319\pi$
$593$	8.72498e11	−	8.72498e11i	0.289747	−	0.289747i	0.836980	+	0.547233i	$0.184319\pi$
$594$	8.69933e10	−	3.27946e12i	0.0286713	−	1.08084i
$595$	2.62776e11	+	1.40074e12i	0.0859526	+	0.458174i
$596$		−	2.03895e12i		−	0.661909i
$597$	−1.02126e12	+	1.00336e12i	−0.329043	+	0.323276i
$598$	−1.24476e12	−	1.24476e12i	−0.398044	−	0.398044i
$599$	5.84880e12			1.85629			0.928145	−	0.372219i	$-0.121403\pi$
$599$	5.84880e12			1.85629			0.928145	+	0.372219i	$0.121403\pi$
$600$	1.04961e12	−	3.97529e11i	0.330634	−	0.125224i
$601$	−3.50113e11			−0.109464			−0.0547322	−	0.998501i	$-0.517431\pi$
$601$	−3.50113e11			−0.109464			−0.0547322	+	0.998501i	$0.517431\pi$
$602$	−4.04214e12	−	4.04214e12i	−1.25437	−	1.25437i
$603$	−4.30654e12	−	4.46158e12i	−1.32648	−	1.37424i
$604$		−	7.26117e11i		−	0.221994i
$605$	8.13026e11	+	4.33387e12i	0.246720	+	1.31515i
$606$	−1.08823e12	−	9.62035e9i	−0.327788	−	0.00289777i
$607$	2.69941e12	−	2.69941e12i	0.807085	−	0.807085i	−0.177107	−	0.984192i	$-0.556674\pi$
$607$	2.69941e12	−	2.69941e12i	0.807085	−	0.807085i	0.984192	+	0.177107i	$0.0566738\pi$
$608$	2.68642e11	−	2.68642e11i	0.0797274	−	0.0797274i
$609$	−1.28210e12	−	1.13343e10i	−0.377698	−	0.00333900i
$610$	4.48831e10	−	6.56118e10i	0.0131250	−	0.0191866i
$611$		−	6.03424e12i		−	1.75161i
$612$	−4.07309e11	−	4.21973e11i	−0.117366	−	0.121591i
$613$	5.53700e11	+	5.53700e11i	0.158381	+	0.158381i	0.781849	−	0.623468i	$-0.214277\pi$
$613$	5.53700e11	+	5.53700e11i	0.158381	+	0.158381i	−0.623468	+	0.781849i	$0.714277\pi$
$614$	1.28248e11			0.0364161
$615$	−2.91227e12	−	2.03023e12i	−0.820907	−	0.572277i
$616$	2.66463e12			0.745630
$617$	−7.39652e11	−	7.39652e11i	−0.205468	−	0.205468i	0.596870	−	0.802338i	$-0.296411\pi$
$617$	−7.39652e11	−	7.39652e11i	−0.205468	−	0.205468i	−0.802338	+	0.596870i	$0.796411\pi$
$618$	−9.12208e11	+	8.96221e11i	−0.251562	+	0.247154i
$619$			5.91391e12i			1.61907i	0.587068	+	0.809537i	$0.300282\pi$
$619$			5.91391e12i			1.61907i	−0.587068	+	0.809537i	$0.699718\pi$
$620$	9.97461e10	−	1.87122e10i	0.0271102	−	0.00508583i
$621$	−7.06194e10	+	2.66220e12i	−0.0190551	+	0.718338i
$622$	−2.85760e11	+	2.85760e11i	−0.0765500	+	0.0765500i
$623$	3.95279e12	−	3.95279e12i	1.05125	−	1.05125i
$624$	−9.27267e9	+	1.04890e12i	−0.00244835	+	0.276951i
$625$	2.81247e12	−	2.57719e12i	0.737273	−	0.675595i
$626$		−	6.79130e11i		−	0.176754i
$627$	−2.64511e12	−	2.69230e12i	−0.683503	−	0.695696i
$628$	1.34854e12	+	1.34854e12i	0.345976	+	0.345976i
$629$	8.35306e11			0.212774
$630$	−3.80202e12	+	6.43888e11i	−0.961572	+	0.162846i
$631$	−5.52009e11			−0.138616			−0.0693082	−	0.997595i	$-0.522079\pi$
$631$	−5.52009e11			−0.138616			−0.0693082	+	0.997595i	$0.522079\pi$
$632$	3.78273e11	+	3.78273e11i	0.0943145	+	0.0943145i
$633$	−5.54623e11	−	5.64517e11i	−0.137303	−	0.139753i
$634$		−	5.39030e9i		−	0.00132499i
$635$	4.83065e12	+	3.30451e12i	1.17903	+	0.806539i
$636$	−2.28365e10	+	2.58320e12i	−0.00553442	+	0.626037i
$637$	−2.93720e12	+	2.93720e12i	−0.706816	+	0.706816i
$638$	−8.76230e11	+	8.76230e11i	−0.209375	+	0.209375i
$639$	−5.31774e12	−	9.40292e10i	−1.26175	−	0.0223105i
$640$	−3.09634e11	−	2.11812e11i	−0.0729523	−	0.0499046i
$641$		−	2.62900e12i		−	0.615077i	−0.951536	−	0.307538i	$-0.900495\pi$
$641$		−	2.62900e12i		−	0.615077i	0.951536	−	0.307538i	$-0.0995053\pi$
$642$	3.43748e12	−	3.37724e12i	0.798607	−	0.784610i
$643$	1.53760e12	+	1.53760e12i	0.354727	+	0.354727i	0.861865	−	0.507138i	$-0.169297\pi$
$643$	1.53760e12	+	1.53760e12i	0.354727	+	0.354727i	−0.507138	+	0.861865i	$0.669297\pi$
$644$	−2.16309e12			−0.495551
$645$	7.87102e12	−	1.40468e12i	1.79066	−	0.319564i
$646$	−6.74734e11			−0.152436
$647$	−2.44071e12	−	2.44071e12i	−0.547578	−	0.547578i	0.378161	−	0.925740i	$-0.376556\pi$
$647$	−2.44071e12	−	2.44071e12i	−0.547578	−	0.547578i	−0.925740	+	0.378161i	$0.876556\pi$
$648$	1.16106e12	−	1.08172e12i	0.258682	−	0.241005i
$649$		−	3.43831e12i		−	0.760753i
$650$	1.29215e12	+	3.32272e12i	0.283924	+	0.730102i
$651$	−3.48665e11	−	3.08234e9i	−0.0760842	−	0.000672614i
$652$	−1.11376e12	+	1.11376e12i	−0.241366	+	0.241366i
$653$	−4.30645e12	+	4.30645e12i	−0.926851	+	0.926851i	−0.997501	−	0.0706501i	$-0.977493\pi$
$653$	−4.30645e12	+	4.30645e12i	−0.926851	+	0.926851i	0.0706501	+	0.997501i	$0.477493\pi$
$654$	9.07834e10	+	8.02561e8i	0.0194047	+	0.000171545i
$655$	−4.67341e12	+	8.76724e11i	−0.992084	+	0.186113i
$656$			1.18661e12i			0.250174i
$657$	−4.94743e12	+	4.77551e12i	−1.03594	+	0.999943i
$658$	−5.24302e12	−	5.24302e12i	−1.09035	−	1.09035i
$659$	−4.33577e12			−0.895534			−0.447767	−	0.894150i	$-0.647781\pi$
$659$	−4.33577e12			−0.895534			−0.447767	+	0.894150i	$0.647781\pi$
$660$	−2.13134e12	+	3.05732e12i	−0.437226	+	0.627182i
$661$	−5.66140e12			−1.15350			−0.576749	−	0.816921i	$-0.695679\pi$
$661$	−5.66140e12			−1.15350			−0.576749	+	0.816921i	$0.695679\pi$
$662$	−3.94084e10	−	3.94084e10i	−0.00797496	−	0.00797496i
$663$	1.32888e12	−	1.30559e12i	0.267100	−	0.262419i
$664$			3.05125e12i			0.609145i
$665$	−2.50483e12	+	3.66165e12i	−0.496684	+	0.726071i
$666$	−3.99577e10	+	2.25977e12i	−0.00786985	+	0.445073i
$667$	7.11306e11	−	7.11306e11i	0.139152	−	0.139152i
$668$	2.20180e12	−	2.20180e12i	0.427843	−	0.427843i
$669$	−1.22095e10	+	1.38110e12i	−0.00235657	+	0.266568i
$670$	1.29889e12	+	6.92377e12i	0.249020	+	1.32741i
$671$			2.63968e11i			0.0502690i
$672$	9.03308e11	+	9.19421e11i	0.170873	+	0.173921i
$673$	−9.29730e9	−	9.29730e9i	−0.00174699	−	0.00174699i	0.706233	−	0.707980i	$-0.250393\pi$
$673$	−9.29730e9	−	9.29730e9i	−0.00174699	−	0.00174699i	−0.707980	+	0.706233i	$0.750393\pi$
$674$	2.88610e12			0.538694
$675$	2.30232e12	−	4.87736e12i	0.426874	−	0.904311i
$676$	−6.17128e11			−0.113662
$677$	1.03272e12	+	1.03272e12i	0.188945	+	0.188945i	0.795240	−	0.606295i	$-0.207345\pi$
$677$	1.03272e12	+	1.03272e12i	0.188945	+	0.188945i	−0.606295	+	0.795240i	$0.707345\pi$
$678$	1.29828e12	+	1.32144e12i	0.235957	+	0.240166i
$679$			5.35204e12i			0.966285i
$680$	1.22848e11	+	6.54844e11i	0.0220331	+	0.117449i
$681$	−2.06164e10	+	2.33207e12i	−0.00367325	+	0.415508i
$682$	−2.38289e11	+	2.38289e11i	−0.0421769	+	0.0421769i
$683$	−3.70944e12	+	3.70944e12i	−0.652252	+	0.652252i	−0.953535	−	0.301283i	$-0.902585\pi$
$683$	−3.70944e12	+	3.70944e12i	−0.652252	+	0.652252i	0.301283	+	0.953535i	$0.402585\pi$
$684$	3.22766e10	−	1.82538e12i	0.00563813	−	0.318860i
$685$	2.06030e12	−	3.01182e12i	0.357538	−	0.522662i
$686$		−	5.52792e11i		−	0.0953023i
$687$	−1.58034e12	+	1.55265e12i	−0.270674	+	0.265930i
$688$	−1.88970e12	−	1.88970e12i	−0.321547	−	0.321547i
$689$	−8.20566e12			−1.38716
$690$	1.73018e12	−	2.48187e12i	0.290584	−	0.416830i
$691$	2.02525e12			0.337930			0.168965	−	0.985622i	$-0.445958\pi$
$691$	2.02525e12			0.337930			0.168965	+	0.985622i	$0.445958\pi$
$692$	−7.22038e10	−	7.22038e10i	−0.0119697	−	0.0119697i
$693$	9.21292e12	−	8.89277e12i	1.51739	−	1.46466i
$694$		−	4.99280e12i		−	0.817009i
$695$	−1.35862e12	+	2.54874e11i	−0.220884	+	0.0414375i
$696$	−5.99382e11	−	5.29877e9i	−0.0968193	−	0.000855921i
$697$	1.49018e12	−	1.49018e12i	0.239161	−	0.239161i
$698$	2.78398e12	−	2.78398e12i	0.443932	−	0.443932i
$699$	−1.17117e13	−	1.03536e11i	−1.85556	−	0.0164038i
$700$	4.00976e12	+	1.76432e12i	0.631214	+	0.277739i
$701$		−	3.87840e12i		−	0.606627i	−0.952891	−	0.303313i	$-0.901907\pi$
$701$		−	3.87840e12i		−	0.606627i	0.952891	−	0.303313i	$-0.0980929\pi$
$702$	3.46847e12	+	3.65750e12i	0.539040	+	0.568417i
$703$	1.83864e12	+	1.83864e12i	0.283920	+	0.283920i
$704$	1.24571e12			0.191135
$705$	1.02094e13	−	1.82199e12i	1.55650	−	0.277776i
$706$	7.47630e12			1.13257
$707$	−3.00355e12	−	3.00355e12i	−0.452113	−	0.452113i
$708$	1.18638e12	−	1.16558e12i	0.177449	−	0.174339i
$709$			1.90038e12i			0.282444i	0.989978	+	0.141222i	$0.0451031\pi$
$709$			1.90038e12i			0.282444i	−0.989978	+	0.141222i	$0.954897\pi$
$710$	4.98693e12	+	3.41141e12i	0.736496	+	0.503816i
$711$	2.57030e12	+	4.54485e10i	0.377199	+	0.00666970i
$712$	1.84793e12	−	1.84793e12i	0.269479	−	0.269479i
$713$	1.93439e11	−	1.93439e11i	0.0280311	−	0.0280311i
$714$	2.02359e10	−	2.28903e12i	0.00291394	−	0.329616i
$715$	−9.77084e12	−	6.68395e12i	−1.39815	−	0.956436i
$716$			1.56909e12i			0.223121i
$717$	3.87665e12	+	3.94580e12i	0.547798	+	0.557570i
$718$	−4.81209e12	−	4.81209e12i	−0.675731	−	0.675731i
$719$	8.22405e12			1.14764			0.573820	−	0.818982i	$-0.305461\pi$
$719$	8.22405e12			1.14764			0.573820	+	0.818982i	$0.305461\pi$
$720$	−1.77744e12	+	3.01018e11i	−0.246490	+	0.0417442i
$721$	−4.99133e12			−0.687872
$722$	2.16560e12	+	2.16560e12i	0.296593	+	0.296593i
$723$	8.49184e12	+	8.64332e12i	1.15579	+	1.17641i
$724$		−	9.75782e11i		−	0.131986i
$725$	−1.89873e12	+	7.38384e11i	−0.255237	+	0.0992571i
$726$	6.26097e10	−	7.08223e12i	0.00836425	−	0.946140i
$727$	6.86906e12	−	6.86906e12i	0.911995	−	0.911995i	−0.0844339	−	0.996429i	$-0.526908\pi$
$727$	6.86906e12	−	6.86906e12i	0.911995	−	0.911995i	0.996429	+	0.0844339i	$0.0269082\pi$
$728$	−2.89500e12	+	2.89500e12i	−0.381994	+	0.381994i
$729$	4.04280e11	−	7.61487e12i	0.0530161	−	0.998594i
$730$	7.67774e12	−	1.44033e12i	1.00065	−	0.187719i
$731$			4.74626e12i			0.614786i
$732$	−9.10813e10	+	8.94850e10i	−0.0117254	+	0.0115199i
$733$	4.60323e12	+	4.60323e12i	0.588973	+	0.588973i	0.937353	−	0.348380i	$-0.113268\pi$
$733$	4.60323e12	+	4.60323e12i	0.588973	+	0.588973i	−0.348380	+	0.937353i	$0.613268\pi$
$734$	−6.59872e10			−0.00839126
$735$	−5.85635e12	−	4.08262e12i	−0.740175	−	0.515996i
$736$	−1.01125e12			−0.127030
$737$	−1.65406e13	−	1.65406e13i	−2.06513	−	2.06513i
$738$	3.96013e12	+	4.10270e12i	0.491423	+	0.509115i
$739$		−	1.43693e13i		−	1.77230i	−0.463401	−	0.886149i	$-0.653371\pi$
$739$		−	1.43693e13i		−	1.77230i	0.463401	−	0.886149i	$-0.346629\pi$
$740$	1.44968e12	−	2.11919e12i	0.177717	−	0.259793i
$741$	5.79886e12	+	5.12642e10i	0.706578	+	0.00624643i
$742$	−7.12971e12	+	7.12971e12i	−0.863485	+	0.863485i
$743$	5.02396e12	−	5.02396e12i	0.604778	−	0.604778i	−0.336798	−	0.941577i	$-0.609344\pi$
$743$	5.02396e12	−	5.02396e12i	0.604778	−	0.604778i	0.941577	+	0.336798i	$0.109344\pi$
$744$	−1.63001e11	−	1.44099e9i	−0.0195035	−	0.000172418i
$745$	2.05234e12	+	1.09401e13i	0.244088	+	1.30112i
$746$			2.94216e12i			0.347810i
$747$	1.01831e13	+	1.05496e13i	1.19656	+	1.23964i
$748$	−1.56440e12	−	1.56440e12i	−0.182722	−	0.182722i
$749$	1.88089e13			2.18371
$750$	−5.23160e12	+	3.18947e12i	−0.603752	+	0.368080i
$751$	−1.21196e13			−1.39030			−0.695149	−	0.718866i	$-0.744661\pi$
$751$	−1.21196e13			−1.39030			−0.695149	+	0.718866i	$0.744661\pi$
$752$	−2.45111e12	−	2.45111e12i	−0.279501	−	0.279501i
$753$	−8.55581e12	+	8.40587e12i	−0.969804	+	0.952807i
$754$		−	1.90397e12i		−	0.214530i
$755$	7.30886e11	+	3.89602e12i	0.0818632	+	0.436375i
$756$	6.19160e12	+	1.64243e11i	0.689373	+	0.0182868i
$757$	7.96991e12	−	7.96991e12i	0.882108	−	0.882108i	−0.111641	−	0.993749i	$-0.535611\pi$
$757$	7.96991e12	−	7.96991e12i	0.882108	−	0.882108i	0.993749	+	0.111641i	$0.0356106\pi$
$758$	−3.67850e12	+	3.67850e12i	−0.404724	+	0.404724i
$759$	−8.88086e10	+	1.00458e13i	−0.00971331	+	1.09874i
$760$	−1.17101e12	+	1.71182e12i	−0.127320	+	0.186122i
$761$		−	6.30342e12i		−	0.681311i	−0.940188	−	0.340656i	$-0.889351\pi$
$761$		−	6.30342e12i		−	0.681311i	0.940188	−	0.340656i	$-0.110649\pi$
$762$	−6.58831e12	−	6.70584e12i	−0.707908	−	0.720536i
$763$	2.50565e11	+	2.50565e11i	0.0267646	+	0.0267646i
$764$	4.57124e12			0.485416
$765$	2.61018e12	+	1.85413e12i	0.275546	+	0.195733i
$766$	−5.19637e11			−0.0545344
$767$	3.73556e12	+	3.73556e12i	0.389742	+	0.389742i
$768$	4.22296e11	+	4.29829e11i	0.0438018	+	0.0445831i
$769$			1.08153e12i			0.111525i	0.998444	+	0.0557623i	$0.0177589\pi$
$769$			1.08153e12i			0.111525i	−0.998444	+	0.0557623i	$0.982241\pi$
$770$	−1.42972e13	+	2.68213e12i	−1.46569	+	0.274961i
$771$	−1.30959e11	+	1.48137e13i	−0.0133472	+	1.50979i
$772$	−5.02842e12	+	5.02842e12i	−0.509511	+	0.509511i
$773$	8.13903e12	−	8.13903e12i	0.819908	−	0.819908i	−0.166186	−	0.986094i	$-0.553145\pi$
$773$	8.13903e12	−	8.13903e12i	0.819908	−	0.819908i	0.986094	+	0.166186i	$0.0531454\pi$
$774$	−1.28402e13	−	2.27042e11i	−1.28599	−	0.0227391i
$775$	−5.16358e11	+	2.00802e11i	−0.0514154	+	0.0199945i
$776$			2.50208e12i			0.247698i
$777$	−6.29269e12	+	6.18241e12i	−0.619358	+	0.608503i
$778$	−4.82634e12	−	4.82634e12i	−0.472291	−	0.472291i
$779$	6.56021e12			0.638263
$780$	−1.00603e12	−	5.63725e12i	−0.0973166	−	0.545308i
$781$	−2.00633e13			−1.92962
$782$	1.26995e12	+	1.26995e12i	0.121438	+	0.121438i
$783$	−2.09004e12	+	1.98202e12i	−0.198713	+	0.188443i
$784$			2.38618e12i			0.225570i
$785$	−8.59308e12	−	5.87828e12i	−0.807673	−	0.552506i
$786$	7.63710e12	+	6.75150e10i	0.713719	+	0.00630955i
$787$	−6.29656e12	+	6.29656e12i	−0.585082	+	0.585082i	−0.936295	−	0.351213i	$-0.885769\pi$
$787$	−6.29656e12	+	6.29656e12i	−0.585082	+	0.585082i	0.351213	+	0.936295i	$0.385769\pi$
$788$	−3.22853e12	+	3.22853e12i	−0.298289	+	0.298289i
$789$	6.00933e12	+	5.31248e10i	0.552051	+	0.00488035i
$790$	−2.41040e12	−	1.64889e12i	−0.220175	−	0.150615i
$791$			7.23050e12i			0.656711i
$792$	4.30704e12	−	4.15737e12i	0.388969	−	0.375453i
$793$	−2.86789e11	−	2.86789e11i	−0.0257533	−	0.0257533i
$794$	7.14201e12			0.637717
$795$	−2.47763e12	−	1.38833e13i	−0.219981	−	1.23265i
$796$	−2.61240e12			−0.230638
$797$	1.01860e13	+	1.01860e13i	0.894211	+	0.894211i	0.994916	−	0.100705i	$-0.0321100\pi$
$797$	1.01860e13	+	1.01860e13i	0.894211	+	0.894211i	−0.100705	+	0.994916i	$0.532110\pi$
$798$	5.08304e12	−	4.99396e12i	0.443722	−	0.435945i
$799$			6.15633e12i			0.534394i
$800$	1.87456e12	+	8.24819e11i	0.161806	+	0.0711957i
$801$	2.22024e11	−	1.25564e13i	0.0190569	−	1.07775i
$802$	6.90661e11	−	6.90661e11i	0.0589496	−	0.0589496i
$803$	−1.83418e13	+	1.83418e13i	−1.55676	+	1.55676i
$804$	1.00025e11	−	1.13145e13i	0.00844221	−	0.954959i
$805$	1.16062e13	−	2.17730e12i	0.974110	−	0.182741i
$806$		−	5.17781e11i		−	0.0432154i
$807$	5.91127e12	+	6.01672e12i	0.490625	+	0.499377i
$808$	−1.40416e12	−	1.40416e12i	−0.115895	−	0.115895i
$809$	−1.74942e12			−0.143591			−0.0717953	−	0.997419i	$-0.522873\pi$
$809$	−1.74942e12			−0.143591			−0.0717953	+	0.997419i	$0.522873\pi$
$810$	−5.14089e12	+	6.97270e12i	−0.419620	+	0.569139i
$811$	1.37773e13			1.11833			0.559167	−	0.829055i	$-0.311121\pi$
$811$	1.37773e13			1.11833			0.559167	+	0.829055i	$0.311121\pi$
$812$	−1.65432e12	−	1.65432e12i	−0.133542	−	0.133542i
$813$	−1.43355e13	−	1.45912e13i	−1.15082	−	1.17134i
$814$			8.52589e12i			0.680660i
$815$	4.85485e12	−	7.09700e12i	0.385449	−	0.563463i
$816$	9.46028e9	−	1.07012e12i	0.000746961	−	0.0844941i
$817$	−1.04473e13	+	1.04473e13i	−0.820357	+	0.820357i
$818$	−4.21439e11	+	4.21439e11i	−0.0329113	+	0.0329113i
$819$	−3.47826e11	+	1.96710e13i	−0.0270137	+	1.52774i
$820$	−1.19441e12	−	6.36683e12i	−0.0922549	−	0.491769i
$821$		−	1.67796e13i		−	1.28896i	−0.764622	−	0.644479i	$-0.777074\pi$
$821$		−	1.67796e13i		−	1.28896i	0.764622	−	0.644479i	$-0.222926\pi$
$822$	−4.18096e12	+	4.10769e12i	−0.319413	+	0.313815i
$823$	−8.22947e12	−	8.22947e12i	−0.625277	−	0.625277i	0.321599	−	0.946876i	$-0.395780\pi$
$823$	−8.22947e12	−	8.22947e12i	−0.625277	−	0.625277i	−0.946876	+	0.321599i	$0.895780\pi$
$824$	−2.33345e12			−0.176330
$825$	8.35843e12	−	1.85496e13i	0.628177	−	1.39409i
$826$	6.49150e12			0.485215
$827$	1.65009e12	+	1.65009e12i	0.122669	+	0.122669i	0.765776	−	0.643107i	$-0.222355\pi$
$827$	1.65009e12	+	1.65009e12i	0.122669	+	0.122669i	−0.643107	+	0.765776i	$0.722355\pi$
$828$	−3.49637e12	+	3.37487e12i	−0.258512	+	0.249529i
$829$		−	6.21039e12i		−	0.456692i	−0.973580	−	0.228346i	$-0.926668\pi$
$829$		−	6.21039e12i		−	0.456692i	0.973580	−	0.228346i	$-0.0733318\pi$
$830$	−3.07129e12	−	1.63716e13i	−0.224631	−	1.19740i
$831$	−1.88251e12	−	1.66421e10i	−0.136941	−	0.00121061i
$832$	−1.35341e12	+	1.35341e12i	−0.0979207	+	0.0979207i
$833$	2.99663e12	−	2.99663e12i	0.215640	−	0.215640i
$834$	2.22019e12	+	1.96274e10i	0.158907	+	0.00140480i
$835$	−9.59763e12	+	1.40302e13i	−0.683242	+	0.998788i
$836$		−	6.88695e12i		−	0.487639i
$837$	−5.68383e11	+	5.39007e11i	−0.0400292	+	0.0379603i
$838$	6.87942e12	+	6.87942e12i	0.481897	+	0.481897i
$839$	−5.11575e12			−0.356435			−0.178217	−	0.983991i	$-0.557033\pi$
$839$	−5.11575e12			−0.356435			−0.178217	+	0.983991i	$0.557033\pi$
$840$	−5.77220e12	−	4.02396e12i	−0.400023	−	0.278867i
$841$	−1.34191e13			−0.925002
$842$	8.30054e12	+	8.30054e12i	0.569118	+	0.569118i
$843$	−8.82638e12	+	8.67169e12i	−0.601947	+	0.591397i
$844$		−	1.44405e12i		−	0.0979580i
$845$	3.31123e12	−	6.21182e11i	0.223427	−	0.0419144i
$846$	−1.66549e13	−	2.94494e11i	−1.11783	−	0.0197656i
$847$	1.95472e13	−	1.95472e13i	1.30500	−	1.30500i
$848$	−3.33314e12	+	3.33314e12i	−0.221346	+	0.221346i
$849$	6.78569e10	−	7.67578e12i	0.00448239	−	0.507035i
$850$	−1.31829e12	−	3.38995e12i	−0.0866215	−	0.222745i
$851$		−	6.92115e12i		−	0.452372i
$852$	−6.80145e12	−	6.92277e12i	−0.442204	−	0.450093i
$853$	1.29557e13	+	1.29557e13i	0.837894	+	0.837894i	0.988581	−	0.150687i	$-0.0481486\pi$
$853$	1.29557e13	+	1.29557e13i	0.837894	+	0.837894i	−0.150687	+	0.988581i	$0.548149\pi$
$854$	−4.98370e11			−0.0320620
$855$	1.66418e12	+	9.82664e12i	0.106501	+	0.628865i
$856$	8.79315e12			0.559774
$857$	6.69947e12	+	6.69947e12i	0.424255	+	0.424255i	0.886666	−	0.462411i	$-0.153016\pi$
$857$	6.69947e12	+	6.69947e12i	0.424255	+	0.424255i	−0.462411	+	0.886666i	$0.653016\pi$
$858$	1.33260e13	+	1.35637e13i	0.839474	+	0.854449i
$859$			2.35671e13i			1.47685i	0.674335	+	0.738425i	$0.264430\pi$
$859$			2.35671e13i			1.47685i	−0.674335	+	0.738425i	$0.735570\pi$
$860$	1.20414e13	+	8.23718e12i	0.750644	+	0.513494i
$861$	−1.96747e11	+	2.22554e13i	−0.0122009	+	1.38014i
$862$	7.05175e12	−	7.05175e12i	0.435025	−	0.435025i
$863$	−1.15134e13	+	1.15134e13i	−0.706568	+	0.706568i	−0.965812	−	0.259244i	$-0.916527\pi$
$863$	−1.15134e13	+	1.15134e13i	−0.706568	+	0.706568i	0.259244	+	0.965812i	$0.416527\pi$
$864$	2.89457e12	+	7.67834e10i	0.176715	+	0.00468765i
$865$	4.60091e11	+	3.14735e11i	0.0279429	+	0.0191149i
$866$		−	7.22163e12i		−	0.436320i
$867$	1.05122e13	−	1.03280e13i	0.631841	−	0.620768i
$868$	−4.49889e11	−	4.49889e11i	−0.0269009	−	0.0269009i
$869$	9.69748e12			0.576859
$870$	3.22135e12	−	5.74888e11i	0.190634	−	0.0340209i
$871$	3.59412e13			2.11598
$872$	1.17139e11	+	1.17139e11i	0.00686086	+	0.00686086i
$873$	8.35029e12	+	8.65090e12i	0.486561	+	0.504078i
$874$			5.59069e12i			0.324089i
$875$	−2.32905e13	−	5.43046e12i	−1.34320	−	0.313185i
$876$	−1.25466e13	−	1.10917e11i	−0.719878	−	0.00636401i
$877$	1.51731e13	−	1.51731e13i	0.866116	−	0.866116i	−0.125924	−	0.992040i	$-0.540190\pi$
$877$	1.51731e13	−	1.51731e13i	0.866116	−	0.866116i	0.992040	+	0.125924i	$0.0401896\pi$
$878$	−7.55631e12	+	7.55631e12i	−0.429126	+	0.429126i
$879$	1.91960e13	+	1.69700e11i	1.08458	+	0.00958809i
$880$	−6.68394e12	+	1.25389e12i	−0.375717	+	0.0704838i
$881$		−	1.13021e13i		−	0.632075i	−0.948747	−	0.316037i	$-0.897648\pi$
$881$		−	1.13021e13i		−	0.632075i	0.948747	−	0.316037i	$-0.102352\pi$
$882$	7.96351e12	+	8.25020e12i	0.443094	+	0.459046i
$883$	−1.26911e13	−	1.26911e13i	−0.702548	−	0.702548i	0.262409	−	0.964957i	$-0.415483\pi$
$883$	−1.26911e13	−	1.26911e13i	−0.702548	−	0.702548i	−0.964957	+	0.262409i	$0.915483\pi$
$884$	3.39929e12			0.187220
$885$	−5.19232e12	+	7.44817e12i	−0.284523	+	0.408136i
$886$	2.28653e13			1.24659
$887$	−1.23026e13	−	1.23026e13i	−0.667332	−	0.667332i	0.289765	−	0.957098i	$-0.406423\pi$
$887$	−1.23026e13	−	1.23026e13i	−0.667332	−	0.667332i	−0.957098	+	0.289765i	$0.906423\pi$
$888$	−2.94183e12	+	2.89027e12i	−0.158767	+	0.155984i
$889$		−	3.66923e13i		−	1.97023i
$890$	−8.05510e12	+	1.17752e13i	−0.430344	+	0.629093i
$891$	1.01698e12	−	2.87481e13i	0.0540581	−	1.52813i
$892$	−1.78206e12	+	1.78206e12i	−0.0942497	+	0.0942497i
$893$	−1.35510e13	+	1.35510e13i	−0.713084	+	0.713084i
$894$	1.58047e11	−	1.78778e13i	0.00827499	−	0.936044i
$895$	−1.57940e12	−	8.41905e12i	−0.0822788	−	0.438591i
$896$			2.35190e12i			0.121908i
$897$	−1.08178e13	−	1.10108e13i	−0.557921	−	0.567873i
$898$	−3.95159e12	−	3.95159e12i	−0.202782	−	0.202782i
$899$	2.95881e11			0.0151077
$900$	9.23397e12	−	3.40424e12i	0.469134	−	0.172953i
$901$	8.37168e12			0.423205
$902$	1.52101e13	+	1.52101e13i	0.765073	+	0.765073i
$903$	−3.51288e13	−	3.57555e13i	−1.75820	−	1.78957i
$904$			3.38026e12i			0.168342i
$905$	9.82190e11	+	5.23561e12i	0.0486718	+	0.259447i
$906$	5.62843e10	−	6.36672e12i	0.00277530	−	0.313934i
$907$	−2.13398e12	+	2.13398e12i	−0.104702	+	0.104702i	−0.757517	−	0.652815i	$-0.773588\pi$
$907$	−2.13398e12	+	2.13398e12i	−0.104702	+	0.104702i	0.652815	+	0.757517i	$0.273588\pi$
$908$	−3.00911e12	+	3.00911e12i	−0.146910	+	0.146910i
$909$	−9.54100e12	−	1.68706e11i	−0.463507	−	0.00819582i
$910$	1.26192e13	−	1.84473e13i	0.610024	−	0.891755i
$911$		−	1.03488e13i		−	0.497805i	−0.968529	−	0.248902i	$-0.919930\pi$
$911$		−	1.03488e13i		−	0.497805i	0.968529	−	0.248902i	$-0.0800699\pi$
$912$	2.37632e12	−	2.33467e12i	0.113744	−	0.111750i
$913$	3.91112e13	+	3.91112e13i	1.86287	+	1.86287i
$914$	−1.29376e13			−0.613192
$915$	3.98629e11	−	5.71816e11i	0.0188007	−	0.0269688i
$916$	−4.04255e12			−0.189726
$917$	2.10787e13	+	2.10787e13i	0.984422	+	0.984422i
$918$	−3.53864e12	−	3.73150e12i	−0.164454	−	0.173417i
$919$			3.85780e13i			1.78410i	0.451932	+	0.892052i	$0.350735\pi$
$919$			3.85780e13i			1.78410i	−0.451932	+	0.892052i	$0.649265\pi$
$920$	5.42589e12	−	1.01789e12i	0.249704	−	0.0468440i
$921$	1.12450e12	+	9.94102e9i	0.0514981	+	0.000455263i
$922$	−2.77803e12	+	2.77803e12i	−0.126604	+	0.126604i
$923$	2.17979e13	−	2.17979e13i	0.988567	−	0.988567i
$924$	2.33639e13	+	2.06546e11i	1.05444	+	0.00932166i
$925$	−5.64522e12	+	1.28298e13i	−0.253538	+	0.576214i
$926$			9.65526e12i			0.431534i
$927$	−8.06786e12	+	7.78750e12i	−0.358839	+	0.346369i
$928$	−7.73393e11	−	7.73393e11i	−0.0342321	−	0.0342321i
$929$	−3.70374e13			−1.63143			−0.815717	−	0.578451i	$-0.803657\pi$
$929$	−3.70374e13			−1.63143			−0.815717	+	0.578451i	$0.803657\pi$
$930$	8.76040e11	−	1.56340e11i	0.0384017	−	0.00685324i
$931$	1.31921e13			0.575492
$932$	−1.51118e13	−	1.51118e13i	−0.656064	−	0.656064i
$933$	−2.52774e12	+	2.48344e12i	−0.109211	+	0.107297i
$934$			2.63266e13i			1.13197i
$935$	9.96852e12	+	6.81918e12i	0.426558	+	0.291796i
$936$	−1.62609e11	+	9.19619e12i	−0.00692472	+	0.391622i
$937$	−2.57771e13	+	2.57771e13i	−1.09246	+	1.09246i	−0.0971940	+	0.995265i	$0.530987\pi$
$937$	−2.57771e13	+	2.57771e13i	−1.09246	+	1.09246i	−0.995265	+	0.0971940i	$0.969013\pi$
$938$	3.12285e13	−	3.12285e13i	1.31716	−	1.31716i
$939$	5.26421e10	−	5.95473e12i	0.00220972	−	0.249958i
$940$	1.56188e13	+	1.06844e13i	0.652487	+	0.446347i
$941$			2.05819e13i			0.855720i	0.903845	+	0.427860i	$0.140732\pi$
$941$			2.05819e13i			0.855720i	−0.903845	+	0.427860i	$0.859268\pi$
$942$	1.17197e13	+	1.19288e13i	0.484940	+	0.493591i
$943$	−1.23473e13	−	1.23473e13i	−0.508473	−	0.508473i
$944$	3.03477e12			0.124380
$945$	−3.33867e13	+	5.35101e12i	−1.36185	+	0.218269i
$946$	−4.84447e13			−1.96669
$947$	4.18394e11	+	4.18394e11i	0.0169048	+	0.0169048i	0.715509	−	0.698604i	$-0.246195\pi$
$947$	4.18394e11	+	4.18394e11i	0.0169048	+	0.0169048i	−0.698604	+	0.715509i	$0.746195\pi$
$948$	3.28744e12	+	3.34608e12i	0.132197	+	0.134555i
$949$		−	3.98551e13i		−	1.59509i
$950$	4.56003e12	−	1.03635e13i	0.181640	−	0.412812i
$951$	4.17824e8	−	4.72631e10i	1.65646e−5	−	0.00187374i
$952$	2.95357e12	−	2.95357e12i	0.116542	−	0.116542i
$953$	3.38102e12	−	3.38102e12i	0.132779	−	0.132779i	−0.637594	−	0.770373i	$-0.720070\pi$
$953$	3.38102e12	−	3.38102e12i	0.132779	−	0.132779i	0.770373	+	0.637594i	$0.220070\pi$
$954$	−4.00468e11	+	2.26481e13i	−0.0156531	+	0.885247i
$955$	−2.45272e13	+	4.60126e12i	−0.954187	+	0.179004i
$956$			1.00934e13i			0.390822i
$957$	−7.75085e12	+	7.61501e12i	−0.298707	+	0.293472i
$958$	−1.10799e13	−	1.10799e13i	−0.425000	−	0.425000i
$959$	−2.28770e13			−0.873403
$960$	−2.69850e12	−	1.88120e12i	−0.102542	−	0.0714850i
$961$	−2.63592e13			−0.996957
$962$	−9.26300e12	−	9.26300e12i	−0.348709	−	0.348709i
$963$	3.04022e13	−	2.93457e13i	1.13917	−	1.09958i
$964$			2.21098e13i			0.824589i
$965$	2.19188e13	−	3.20417e13i	0.813662	−	1.18944i
$966$	−1.89663e13	−	1.67670e11i	−0.700788	−	0.00619524i
$967$	−1.13306e13	+	1.13306e13i	−0.416709	+	0.416709i	−0.884068	−	0.467359i	$-0.845206\pi$
$967$	−1.13306e13	+	1.13306e13i	−0.416709	+	0.416709i	0.467359	+	0.884068i	$0.345206\pi$
$968$	9.13832e12	−	9.13832e12i	0.334524	−	0.334524i
$969$	−5.91618e12	−	5.23014e10i	−0.215568	−	0.00190571i
$970$	−2.51851e12	−	1.34250e13i	−0.0913421	−	0.486903i
$971$			2.93515e13i			1.05960i	0.848122	+	0.529801i	$0.177734\pi$
$971$			2.93515e13i			1.05960i	−0.848122	+	0.529801i	$0.822266\pi$
$972$	1.02642e13	−	9.39469e12i	0.368830	−	0.337586i
$973$	6.12782e12	+	6.12782e12i	0.219179	+	0.219179i
$974$	1.45685e13			0.518680
$975$	1.10722e13	+	2.92343e13i	0.392386	+	1.03603i
$976$	−2.32988e11			−0.00821881
$977$	−2.27132e13	−	2.27132e13i	−0.797539	−	0.797539i	0.185168	−	0.982707i	$-0.440717\pi$
$977$	−2.27132e13	−	2.27132e13i	−0.797539	−	0.797539i	−0.982707	+	0.185168i	$0.940717\pi$
$978$	−9.85194e12	+	9.67928e12i	−0.344348	+	0.338313i
$979$		−	4.73739e13i		−	1.64823i
$980$	−2.40186e12	−	1.28032e13i	−0.0831820	−	0.443405i
$981$	7.95941e11	+	1.40740e10i	0.0274391	+	0.000485183i
$982$	1.14187e13	−	1.14187e13i	0.391847	−	0.391847i
$983$	−1.45774e13	+	1.45774e13i	−0.497953	+	0.497953i	−0.910800	−	0.412847i	$-0.864534\pi$
$983$	−1.45774e13	+	1.45774e13i	−0.497953	+	0.497953i	0.412847	+	0.910800i	$0.364534\pi$
$984$	−9.19791e10	+	1.04044e13i	−0.00312760	+	0.353785i
$985$	1.40731e13	−	2.05726e13i	0.476351	−	0.696348i
$986$			1.94249e12i			0.0654505i
$987$	−4.55653e13	−	4.63781e13i	−1.52829	−	1.55556i
$988$	7.48236e12	+	7.48236e12i	0.249823	+	0.249823i
$989$	3.93264e13			1.30708
$990$	−1.89250e13	+	2.66419e13i	−0.626148	+	0.881469i
$991$	5.09135e12			0.167688			0.0838440	−	0.996479i	$-0.473280\pi$
$991$	5.09135e12			0.167688			0.0838440	+	0.996479i	$0.473280\pi$
$992$	−2.10323e11	−	2.10323e11i	−0.00689579	−	0.00689579i
$993$	−3.42485e11	−	3.48594e11i	−0.0111782	−	0.0113776i
$994$		−	3.78793e13i		−	1.23073i
$995$	1.40170e13	−	2.62956e12i	0.453368	−	0.0850510i
$996$	−2.36514e11	+	2.67538e13i	−0.00761536	+	0.861428i
$997$	−3.73941e13	+	3.73941e13i	−1.19860	+	1.19860i	−0.224015	+	0.974586i	$0.571917\pi$
$997$	−3.73941e13	+	3.73941e13i	−1.19860	+	1.19860i	−0.974586	+	0.224015i	$0.928083\pi$
$998$	4.48892e12	−	4.48892e12i	0.143237	−	0.143237i
$999$	−5.25520e11	+	1.98110e13i	−0.0166934	+	0.629305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.10.e.a.23.15	yes	36
3.2	odd	2	inner	30.10.e.a.23.8	yes	36
5.2	odd	4	inner	30.10.e.a.17.8	✓	36
15.2	even	4	inner	30.10.e.a.17.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.10.e.a.17.8	✓	36	5.2	odd	4	inner
30.10.e.a.17.15	yes	36	15.2	even	4	inner
30.10.e.a.23.8	yes	36	3.2	odd	2	inner
30.10.e.a.23.15	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.3137 + 11.3137i) q^{2} +(98.3235 + 100.077i) q^{3} +256.000i q^{4} +(-257.681 - 1373.58i) q^{5} +(-19.8436 + 2244.65i) q^{6} +(-6195.32 + 6195.32i) q^{7} +(-2896.31 + 2896.31i) q^{8} +(-347.984 + 19679.9i) q^{9} +O(q^{10})\)	\(q+(11.3137 + 11.3137i) q^{2} +(98.3235 + 100.077i) q^{3} +256.000i q^{4} +(-257.681 - 1373.58i) q^{5} +(-19.8436 + 2244.65i) q^{6} +(-6195.32 + 6195.32i) q^{7} +(-2896.31 + 2896.31i) q^{8} +(-347.984 + 19679.9i) q^{9} +(12625.0 - 18455.6i) q^{10} +74250.3i q^{11} +(-25619.8 + 25170.8i) q^{12} +(-80669.6 - 80669.6i) q^{13} -140184. q^{14} +(112128. - 160843. i) q^{15} -65536.0 q^{16} +(82301.7 + 82301.7i) q^{17} +(-226590. + 218716. i) q^{18} +362317. i q^{19} +(351637. - 65966.4i) q^{20} +(-1.22916e6 - 10866.2i) q^{21} +(-840046. + 840046. i) q^{22} +(681933. - 681933. i) q^{23} +(-574630. - 5079.96i) q^{24} +(-1.82033e6 + 707892. i) q^{25} -1.82534e6i q^{26} +(-2.00373e6 + 1.90017e6i) q^{27} +(-1.58600e6 - 1.58600e6i) q^{28} +1.04307e6 q^{29} +(3.08832e6 - 551148. i) q^{30} +283662. q^{31} +(-741455. - 741455. i) q^{32} +(-7.43078e6 + 7.30055e6i) q^{33} +1.86227e6i q^{34} +(1.01062e7 + 6.91335e6i) q^{35} +(-5.03806e6 - 89083.8i) q^{36} +(5.07466e6 - 5.07466e6i) q^{37} +(-4.09915e6 + 4.09915e6i) q^{38} +(141490. - 1.60049e7i) q^{39} +(4.72464e6 + 3.23199e6i) q^{40} -1.81063e7i q^{41} +(-1.37834e7 - 1.40293e7i) q^{42} +(2.88345e7 + 2.88345e7i) q^{43} -1.90081e7 q^{44} +(2.71216e7 - 4.59317e6i) q^{45} +1.54304e7 q^{46} +(3.74010e7 + 3.74010e7i) q^{47} +(-6.44373e6 - 6.55867e6i) q^{48} -3.64103e7i q^{49} +(-2.86035e7 - 1.25857e7i) q^{50} +(-144352. + 1.63287e7i) q^{51} +(2.06514e7 - 2.06514e7i) q^{52} +(5.08597e7 - 5.08597e7i) q^{53} +(-4.41676e7 - 1.17162e6i) q^{54} +(1.01989e8 - 1.91329e7i) q^{55} -3.58871e7i q^{56} +(-3.62598e7 + 3.56243e7i) q^{57} +(1.18010e7 + 1.18010e7i) q^{58} -4.63070e7 q^{59} +(4.11759e7 + 2.87049e7i) q^{60} +3.55511e6 q^{61} +(3.20927e6 + 3.20927e6i) q^{62} +(-1.19767e8 - 1.24079e8i) q^{63} -1.67772e7i q^{64} +(-9.00192e7 + 1.31593e8i) q^{65} +(-1.66666e8 - 1.47339e6i) q^{66} +(-2.22768e8 + 2.22768e8i) q^{67} +(-2.10692e7 + 2.10692e7i) q^{68} +(1.35296e8 + 1.19607e6i) q^{69} +(3.61228e7 + 1.92554e8i) q^{70} +2.70212e8i q^{71} +(-5.59913e7 - 5.80070e7i) q^{72} +(2.47027e8 + 2.47027e8i) q^{73} +1.14826e8 q^{74} +(-2.49825e8 - 1.12571e8i) q^{75} -9.27532e7 q^{76} +(-4.60004e8 - 4.60004e8i) q^{77} +(1.82676e8 - 1.79474e8i) q^{78} -1.30605e8i q^{79} +(1.68874e7 + 9.00190e7i) q^{80} +(-3.87178e8 - 1.36966e7i) q^{81} +(2.04849e8 - 2.04849e8i) q^{82} +(5.26747e8 - 5.26747e8i) q^{83} +(2.78175e6 - 3.14664e8i) q^{84} +(9.18404e7 - 1.34256e8i) q^{85} +6.52451e8i q^{86} +(1.02559e8 + 1.04388e8i) q^{87} +(-2.15052e8 - 2.15052e8i) q^{88} -6.38029e8 q^{89} +(3.58812e8 + 2.54881e8i) q^{90} +9.99547e8 q^{91} +(1.74575e8 + 1.74575e8i) q^{92} +(2.78907e7 + 2.83882e7i) q^{93} +8.46288e8i q^{94} +(4.97672e8 - 9.33624e7i) q^{95} +(1.30047e6 - 1.47105e8i) q^{96} +(4.31943e8 - 4.31943e8i) q^{97} +(4.11935e8 - 4.11935e8i) q^{98} +(-1.46124e9 - 2.58379e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 296 q^{3} + 4544 q^{6} + 9756 q^{7}+O(q^{10}) \) 36 * q + 296 * q^3 + 4544 * q^6 + 9756 * q^7	\( 36 q + 296 q^{3} + 4544 q^{6} + 9756 q^{7} + 51264 q^{10} - 75776 q^{12} - 78120 q^{13} + 201428 q^{15} - 2359296 q^{16} - 276352 q^{18} - 1187968 q^{21} - 1065024 q^{22} - 8730936 q^{25} - 8987584 q^{27} + 2497536 q^{28} + 10183488 q^{30} - 19149912 q^{31} - 24042964 q^{33} + 7783424 q^{36} + 57972384 q^{37} - 20938752 q^{40} - 36541376 q^{42} + 129617424 q^{43} + 188714992 q^{45} - 10734336 q^{46} - 19398656 q^{48} + 61133728 q^{51} + 19998720 q^{52} - 84302028 q^{55} - 191033896 q^{57} + 129597120 q^{58} - 14761984 q^{60} - 258546456 q^{61} + 113024276 q^{63} - 177217408 q^{66} - 95099256 q^{67} - 64737216 q^{70} + 70746112 q^{72} - 744318180 q^{73} - 436271432 q^{75} + 274489344 q^{76} + 416094720 q^{78} - 2874828308 q^{81} - 1243259136 q^{82} - 93014352 q^{85} + 2750699540 q^{87} - 272646144 q^{88} - 319472512 q^{90} + 4799502000 q^{91} + 1861719848 q^{93} - 297795584 q^{96} - 2636190468 q^{97}+O(q^{100}) \) 36 * q + 296 * q^3 + 4544 * q^6 + 9756 * q^7 + 51264 * q^10 - 75776 * q^12 - 78120 * q^13 + 201428 * q^15 - 2359296 * q^16 - 276352 * q^18 - 1187968 * q^21 - 1065024 * q^22 - 8730936 * q^25 - 8987584 * q^27 + 2497536 * q^28 + 10183488 * q^30 - 19149912 * q^31 - 24042964 * q^33 + 7783424 * q^36 + 57972384 * q^37 - 20938752 * q^40 - 36541376 * q^42 + 129617424 * q^43 + 188714992 * q^45 - 10734336 * q^46 - 19398656 * q^48 + 61133728 * q^51 + 19998720 * q^52 - 84302028 * q^55 - 191033896 * q^57 + 129597120 * q^58 - 14761984 * q^60 - 258546456 * q^61 + 113024276 * q^63 - 177217408 * q^66 - 95099256 * q^67 - 64737216 * q^70 + 70746112 * q^72 - 744318180 * q^73 - 436271432 * q^75 + 274489344 * q^76 + 416094720 * q^78 - 2874828308 * q^81 - 1243259136 * q^82 - 93014352 * q^85 + 2750699540 * q^87 - 272646144 * q^88 - 319472512 * q^90 + 4799502000 * q^91 + 1861719848 * q^93 - 297795584 * q^96 - 2636190468 * q^97

Introduction

L-functions

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