LMFDB - Embedded newform 10.7.c.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,7,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	10.c (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:	$2.30054083620$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{129})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 65x^{2} + 1024 $ x^4 + 65*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-6.17891i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.7.c.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 4.00000i) q^{2} +(-32.8945 + 32.8945i) q^{3} +32.0000i q^{4} +(110.895 - 57.6836i) q^{5} -263.156 q^{6} +(261.840 + 261.840i) q^{7} +(-128.000 + 128.000i) q^{8} -1435.10i q^{9} +O(q^{10})$	\(q+(4.00000 + 4.00000i) q^{2} +(-32.8945 + 32.8945i) q^{3} +32.0000i q^{4} +(110.895 - 57.6836i) q^{5} -263.156 q^{6} +(261.840 + 261.840i) q^{7} +(-128.000 + 128.000i) q^{8} -1435.10i q^{9} +(674.313 + 212.844i) q^{10} +155.258 q^{11} +(-1052.63 - 1052.63i) q^{12} +(141.211 - 141.211i) q^{13} +2094.72i q^{14} +(-1750.35 + 5545.30i) q^{15} -1024.00 q^{16} +(1785.85 + 1785.85i) q^{17} +(5740.41 - 5740.41i) q^{18} -4680.83i q^{19} +(1845.88 + 3548.63i) q^{20} -17226.2 q^{21} +(621.032 + 621.032i) q^{22} +(6535.54 - 6535.54i) q^{23} -8421.00i q^{24} +(8970.20 - 12793.6i) q^{25} +1129.69 q^{26} +(23226.9 + 23226.9i) q^{27} +(-8378.88 + 8378.88i) q^{28} -1144.93i q^{29} +(-29182.6 + 15179.8i) q^{30} -24552.4 q^{31} +(-4096.00 - 4096.00i) q^{32} +(-5107.14 + 5107.14i) q^{33} +14286.8i q^{34} +(44140.5 + 13932.7i) q^{35} +45923.3 q^{36} +(-55456.0 - 55456.0i) q^{37} +(18723.3 - 18723.3i) q^{38} +9290.14i q^{39} +(-6811.00 + 21578.0i) q^{40} +100758. q^{41} +(-68904.8 - 68904.8i) q^{42} +(-68642.6 + 68642.6i) q^{43} +4968.26i q^{44} +(-82781.9 - 159145. i) q^{45} +52284.3 q^{46} +(99714.1 + 99714.1i) q^{47} +(33684.0 - 33684.0i) q^{48} +19471.3i q^{49} +(87055.2 - 15293.6i) q^{50} -117490. q^{51} +(4518.75 + 4518.75i) q^{52} +(-167132. + 167132. i) q^{53} +185815. i q^{54} +(17217.3 - 8955.85i) q^{55} -67031.0 q^{56} +(153974. + 153974. i) q^{57} +(4579.73 - 4579.73i) q^{58} -229247. i q^{59} +(-177450. - 56011.2i) q^{60} +199081. q^{61} +(-98209.6 - 98209.6i) q^{62} +(375767. - 375767. i) q^{63} -32768.0i q^{64} +(7513.96 - 23805.1i) q^{65} -40857.1 q^{66} +(-351757. - 351757. i) q^{67} +(-57147.2 + 57147.2i) q^{68} +429967. i q^{69} +(120831. + 232293. i) q^{70} -271358. q^{71} +(183693. + 183693. i) q^{72} +(134279. - 134279. i) q^{73} -443648. i q^{74} +(125769. + 715910. i) q^{75} +149787. q^{76} +(40652.8 + 40652.8i) q^{77} +(-37160.5 + 37160.5i) q^{78} -332838. i q^{79} +(-113556. + 59068.0i) q^{80} -481887. q^{81} +(403033. + 403033. i) q^{82} +(-495925. + 495925. i) q^{83} -551239. i q^{84} +(301056. + 95026.8i) q^{85} -549141. q^{86} +(37662.0 + 37662.0i) q^{87} +(-19873.0 + 19873.0i) q^{88} -19355.0i q^{89} +(305452. - 967707. i) q^{90} +73949.3 q^{91} +(209137. + 209137. i) q^{92} +(807640. - 807640. i) q^{93} +797713. i q^{94} +(-270007. - 519078. i) q^{95} +269472. q^{96} +(-229968. - 229968. i) q^{97} +(-77885.3 + 77885.3i) q^{98} -222811. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 18 q^{3} + 330 q^{5} - 144 q^{6} - 202 q^{7} - 512 q^{8}+O(q^{10}) $ 4 * q + 16 * q^2 - 18 * q^3 + 330 * q^5 - 144 * q^6 - 202 * q^7 - 512 * q^8	\( 4 q + 16 q^{2} - 18 q^{3} + 330 q^{5} - 144 q^{6} - 202 q^{7} - 512 q^{8} + 880 q^{10} - 2332 q^{11} - 576 q^{12} + 792 q^{13} + 4470 q^{15} - 4096 q^{16} + 12368 q^{17} + 14784 q^{18} - 3520 q^{20} - 69132 q^{21} - 9328 q^{22} + 35342 q^{23} - 1600 q^{25} + 6336 q^{26} + 61560 q^{27} + 6464 q^{28} - 37680 q^{30} - 18932 q^{31} - 16384 q^{32} - 73356 q^{33} + 130790 q^{35} + 118272 q^{36} - 67812 q^{37} + 44000 q^{38} - 56320 q^{40} + 110228 q^{41} - 276528 q^{42} - 293538 q^{43} - 72510 q^{45} + 282736 q^{46} + 195438 q^{47} + 18432 q^{48} - 1600 q^{50} + 185388 q^{51} + 25344 q^{52} - 121988 q^{53} - 108540 q^{55} + 51712 q^{56} + 268800 q^{57} + 229120 q^{58} - 444480 q^{60} - 243372 q^{61} - 75728 q^{62} + 451902 q^{63} + 100020 q^{65} - 586848 q^{66} - 773602 q^{67} - 395776 q^{68} + 895840 q^{70} - 1046132 q^{71} + 473088 q^{72} + 922372 q^{73} + 367350 q^{75} + 352000 q^{76} + 1040116 q^{77} + 23088 q^{78} - 337920 q^{80} + 360144 q^{81} + 440912 q^{82} - 1238058 q^{83} + 86840 q^{85} - 2348304 q^{86} - 1238640 q^{87} + 298496 q^{88} + 1161840 q^{90} - 221892 q^{91} + 1130944 q^{92} + 2336244 q^{93} - 355400 q^{95} + 147456 q^{96} - 1937532 q^{97} - 1321024 q^{98}+O(q^{100}) \) 4 * q + 16 * q^2 - 18 * q^3 + 330 * q^5 - 144 * q^6 - 202 * q^7 - 512 * q^8 + 880 * q^10 - 2332 * q^11 - 576 * q^12 + 792 * q^13 + 4470 * q^15 - 4096 * q^16 + 12368 * q^17 + 14784 * q^18 - 3520 * q^20 - 69132 * q^21 - 9328 * q^22 + 35342 * q^23 - 1600 * q^25 + 6336 * q^26 + 61560 * q^27 + 6464 * q^28 - 37680 * q^30 - 18932 * q^31 - 16384 * q^32 - 73356 * q^33 + 130790 * q^35 + 118272 * q^36 - 67812 * q^37 + 44000 * q^38 - 56320 * q^40 + 110228 * q^41 - 276528 * q^42 - 293538 * q^43 - 72510 * q^45 + 282736 * q^46 + 195438 * q^47 + 18432 * q^48 - 1600 * q^50 + 185388 * q^51 + 25344 * q^52 - 121988 * q^53 - 108540 * q^55 + 51712 * q^56 + 268800 * q^57 + 229120 * q^58 - 444480 * q^60 - 243372 * q^61 - 75728 * q^62 + 451902 * q^63 + 100020 * q^65 - 586848 * q^66 - 773602 * q^67 - 395776 * q^68 + 895840 * q^70 - 1046132 * q^71 + 473088 * q^72 + 922372 * q^73 + 367350 * q^75 + 352000 * q^76 + 1040116 * q^77 + 23088 * q^78 - 337920 * q^80 + 360144 * q^81 + 440912 * q^82 - 1238058 * q^83 + 86840 * q^85 - 2348304 * q^86 - 1238640 * q^87 + 298496 * q^88 + 1161840 * q^90 - 221892 * q^91 + 1130944 * q^92 + 2336244 * q^93 - 355400 * q^95 + 147456 * q^96 - 1937532 * q^97 - 1321024 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	4.00000	+	4.00000i	0.500000	+	0.500000i
$2$	4.00000	+	4.00000i	0.500000	+	0.500000i
$3$	−32.8945	+	32.8945i	−1.21832	+	1.21832i	−0.250095	+	0.968221i	$0.580462\pi$
$3$	−32.8945	+	32.8945i	−1.21832	+	1.21832i	−0.968221	+	0.250095i	$0.919538\pi$
$4$			32.0000i			0.500000i
$5$	110.895	−	57.6836i	0.887156	−	0.461469i
$5$	110.895	−	57.6836i	0.887156	−	0.461469i
$6$	−263.156			−1.21832
$7$	261.840	+	261.840i	0.763382	+	0.763382i	0.976932	−	0.213550i	$-0.0685027\pi$
$7$	261.840	+	261.840i	0.763382	+	0.763382i	−0.213550	+	0.976932i	$0.568503\pi$
$8$	−128.000	+	128.000i	−0.250000	+	0.250000i
$9$		−	1435.10i		−	1.96859i
$10$	674.313	+	212.844i	0.674313	+	0.212844i
$11$	155.258			0.116648			0.0583238	−	0.998298i	$-0.481424\pi$
$11$	155.258			0.116648			0.0583238	+	0.998298i	$0.481424\pi$
$12$	−1052.63	−	1052.63i	−0.609158	−	0.609158i
$13$	141.211	−	141.211i	0.0642744	−	0.0642744i	−0.674239	−	0.738513i	$-0.735528\pi$
$13$	141.211	−	141.211i	0.0642744	−	0.0642744i	0.738513	+	0.674239i	$0.235528\pi$
$14$			2094.72i			0.763382i
$15$	−1750.35	+	5545.30i	−0.518622	+	1.64305i
$16$	−1024.00			−0.250000
$17$	1785.85	+	1785.85i	0.363495	+	0.363495i	0.865098	−	0.501603i	$-0.167256\pi$
$17$	1785.85	+	1785.85i	0.363495	+	0.363495i	−0.501603	+	0.865098i	$0.667256\pi$
$18$	5740.41	−	5740.41i	0.984295	−	0.984295i
$19$		−	4680.83i		−	0.682436i	−0.939984	−	0.341218i	$-0.889161\pi$
$19$		−	4680.83i		−	0.682436i	0.939984	−	0.341218i	$-0.110839\pi$
$20$	1845.88	+	3548.63i	0.230735	+	0.443578i
$21$	−17226.2			−1.86008
$22$	621.032	+	621.032i	0.0583238	+	0.0583238i
$23$	6535.54	−	6535.54i	0.537153	−	0.537153i	−0.385539	−	0.922692i	$-0.625984\pi$
$23$	6535.54	−	6535.54i	0.537153	−	0.537153i	0.922692	+	0.385539i	$0.125984\pi$
$24$		−	8421.00i		−	0.609158i
$25$	8970.20	−	12793.6i	0.574093	−	0.818790i
$26$	1129.69			0.0642744
$27$	23226.9	+	23226.9i	1.18005	+	1.18005i
$28$	−8378.88	+	8378.88i	−0.381691	+	0.381691i
$29$		−	1144.93i		−	0.0469446i	−0.999724	−	0.0234723i	$-0.992528\pi$
$29$		−	1144.93i		−	0.0469446i	0.999724	−	0.0234723i	$-0.00747216\pi$
$30$	−29182.6	+	15179.8i	−1.08084	+	0.562215i
$31$	−24552.4			−0.824155			−0.412077	−	0.911149i	$-0.635197\pi$
$31$	−24552.4			−0.824155			−0.412077	+	0.911149i	$0.635197\pi$
$32$	−4096.00	−	4096.00i	−0.125000	−	0.125000i
$33$	−5107.14	+	5107.14i	−0.142114	+	0.142114i
$34$			14286.8i			0.363495i
$35$	44140.5	+	13932.7i	1.02952	+	0.324962i
$36$	45923.3			0.984295
$37$	−55456.0	−	55456.0i	−1.09482	−	1.09482i	−0.995006	−	0.0998157i	$-0.968175\pi$
$37$	−55456.0	−	55456.0i	−1.09482	−	1.09482i	−0.0998157	−	0.995006i	$-0.531825\pi$
$38$	18723.3	−	18723.3i	0.341218	−	0.341218i
$39$			9290.14i			0.156613i
$40$	−6811.00	+	21578.0i	−0.106422	+	0.337156i
$41$	100758.			1.46194			0.730968	−	0.682411i	$-0.239069\pi$
$41$	100758.			1.46194			0.730968	+	0.682411i	$0.239069\pi$
$42$	−68904.8	−	68904.8i	−0.930041	−	0.930041i
$43$	−68642.6	+	68642.6i	−0.863353	+	0.863353i	−0.991726	−	0.128373i	$-0.959025\pi$
$43$	−68642.6	+	68642.6i	−0.863353	+	0.863353i	0.128373	+	0.991726i	$0.459025\pi$
$44$			4968.26i			0.0583238i
$45$	−82781.9	−	159145.i	−0.908443	−	1.74645i
$46$	52284.3			0.537153
$47$	99714.1	+	99714.1i	0.960424	+	0.960424i	0.999246	−	0.0388219i	$-0.0123605\pi$
$47$	99714.1	+	99714.1i	0.960424	+	0.960424i	−0.0388219	+	0.999246i	$0.512361\pi$
$48$	33684.0	−	33684.0i	0.304579	−	0.304579i
$49$			19471.3i			0.165504i
$50$	87055.2	−	15293.6i	0.696442	−	0.122349i
$51$	−117490.			−0.885704
$52$	4518.75	+	4518.75i	0.0321372	+	0.0321372i
$53$	−167132.	+	167132.i	−1.12261	+	1.12261i	−0.131268	+	0.991347i	$0.541905\pi$
$53$	−167132.	+	167132.i	−1.12261	+	1.12261i	−0.991347	+	0.131268i	$0.958095\pi$
$54$			185815.i			1.18005i
$55$	17217.3	−	8955.85i	0.103485	−	0.0538293i
$56$	−67031.0			−0.381691
$57$	153974.	+	153974.i	0.831423	+	0.831423i
$58$	4579.73	−	4579.73i	0.0234723	−	0.0234723i
$59$		−	229247.i		−	1.11621i	−0.829770	−	0.558106i	$-0.811528\pi$
$59$		−	229247.i		−	1.11621i	0.829770	−	0.558106i	$-0.188472\pi$
$60$	−177450.	−	56011.2i	−0.821526	−	0.259311i
$61$	199081.			0.877081			0.438540	−	0.898712i	$-0.355496\pi$
$61$	199081.			0.877081			0.438540	+	0.898712i	$0.355496\pi$
$62$	−98209.6	−	98209.6i	−0.412077	−	0.412077i
$63$	375767.	−	375767.i	1.50279	−	1.50279i
$64$		−	32768.0i		−	0.125000i
$65$	7513.96	−	23805.1i	0.0273608	−	0.0866821i
$66$	−40857.1			−0.142114
$67$	−351757.	−	351757.i	−1.16955	−	1.16955i	−0.982316	−	0.187233i	$-0.940048\pi$
$67$	−351757.	−	351757.i	−1.16955	−	1.16955i	−0.187233	−	0.982316i	$-0.559952\pi$
$68$	−57147.2	+	57147.2i	−0.181748	+	0.181748i
$69$			429967.i			1.30884i
$70$	120831.	+	232293.i	0.352277	+	0.677239i
$71$	−271358.			−0.758170			−0.379085	−	0.925362i	$-0.623761\pi$
$71$	−271358.			−0.758170			−0.379085	+	0.925362i	$0.623761\pi$
$72$	183693.	+	183693.i	0.492147	+	0.492147i
$73$	134279.	−	134279.i	0.345174	−	0.345174i	−0.513134	−	0.858308i	$-0.671516\pi$
$73$	134279.	−	134279.i	0.345174	−	0.345174i	0.858308	+	0.513134i	$0.171516\pi$
$74$		−	443648.i		−	1.09482i
$75$	125769.	+	715910.i	0.298119	+	1.69697i
$76$	149787.			0.341218
$77$	40652.8	+	40652.8i	0.0890467	+	0.0890467i
$78$	−37160.5	+	37160.5i	−0.0783066	+	0.0783066i
$79$		−	332838.i		−	0.675074i	−0.941312	−	0.337537i	$-0.890406\pi$
$79$		−	332838.i		−	0.675074i	0.941312	−	0.337537i	$-0.109594\pi$
$80$	−113556.	+	59068.0i	−0.221789	+	0.115367i
$81$	−481887.			−0.906755
$82$	403033.	+	403033.i	0.730968	+	0.730968i
$83$	−495925.	+	495925.i	−0.867324	+	0.867324i	−0.992175	−	0.124851i	$-0.960155\pi$
$83$	−495925.	+	495925.i	−0.867324	+	0.867324i	0.124851	+	0.992175i	$0.460155\pi$
$84$		−	551239.i		−	0.930041i
$85$	301056.	+	95026.8i	0.490219	+	0.154735i
$86$	−549141.			−0.863353
$87$	37662.0	+	37662.0i	0.0571934	+	0.0571934i
$88$	−19873.0	+	19873.0i	−0.0291619	+	0.0291619i
$89$		−	19355.0i		−	0.0274552i	−0.999906	−	0.0137276i	$-0.995630\pi$
$89$		−	19355.0i		−	0.0274552i	0.999906	−	0.0137276i	$-0.00436976\pi$
$90$	305452.	−	967707.i	0.419002	−	1.32744i
$91$	73949.3			0.0981319
$92$	209137.	+	209137.i	0.268577	+	0.268577i
$93$	807640.	−	807640.i	1.00408	−	1.00408i
$94$			797713.i			0.960424i
$95$	−270007.	−	519078.i	−0.314923	−	0.605427i
$96$	269472.			0.304579
$97$	−229968.	−	229968.i	−0.251972	−	0.251972i	0.569807	−	0.821779i	$-0.307018\pi$
$97$	−229968.	−	229968.i	−0.251972	−	0.251972i	−0.821779	+	0.569807i	$0.807018\pi$
$98$	−77885.3	+	77885.3i	−0.0827518	+	0.0827518i
$99$		−	222811.i		−	0.229631i
$100$	409395.	+	287046.i	0.409395	+	0.287046i
$101$	746356.			0.724405			0.362203	−	0.932099i	$-0.382025\pi$
$101$	746356.			0.724405			0.362203	+	0.932099i	$0.382025\pi$
$102$	−469958.	−	469958.i	−0.442852	−	0.442852i
$103$	13696.5	−	13696.5i	0.0125342	−	0.0125342i	−0.700812	−	0.713346i	$-0.747179\pi$
$103$	13696.5	−	13696.5i	0.0125342	−	0.0125342i	0.713346	+	0.700812i	$0.247179\pi$
$104$			36150.0i			0.0321372i
$105$	−1.91029e6	+	993670.i	−1.65018	+	0.858370i
$106$	−1.33705e6			−1.12261
$107$	−209124.	−	209124.i	−0.170707	−	0.170707i	0.616583	−	0.787290i	$-0.288517\pi$
$107$	−209124.	−	209124.i	−0.170707	−	0.170707i	−0.787290	+	0.616583i	$0.788517\pi$
$108$	−743261.	+	743261.i	−0.590024	+	0.590024i
$109$			1.50091e6i			1.15898i	0.814979	+	0.579490i	$0.196748\pi$
$109$			1.50091e6i			1.15898i	−0.814979	+	0.579490i	$0.803252\pi$
$110$	104692.	+	33045.7i	0.0786570	+	0.0248277i
$111$	3.64840e6			2.66768
$112$	−268124.	−	268124.i	−0.190845	−	0.190845i
$113$	419824.	−	419824.i	0.290959	−	0.290959i	−0.546500	−	0.837459i	$-0.684040\pi$
$113$	419824.	−	419824.i	0.290959	−	0.290959i	0.837459	+	0.546500i	$0.184040\pi$
$114$			1.23179e6i			0.831423i
$115$	347762.	−	1.10175e6i	0.228659	−	0.724418i
$116$	36637.8			0.0234723
$117$	−202652.	−	202652.i	−0.126530	−	0.126530i
$118$	916986.	−	916986.i	0.558106	−	0.558106i
$119$			935214.i			0.554971i
$120$	−485754.	−	933843.i	−0.281108	−	0.540419i
$121$	−1.74746e6			−0.986393
$122$	796323.	+	796323.i	0.438540	+	0.438540i
$123$	−3.31439e6	+	3.31439e6i	−1.78110	+	1.78110i
$124$		−	785676.i		−	0.412077i
$125$	256765.	−	1.93617e6i	0.131464	−	0.991321i
$126$	3.00614e6			1.50279
$127$	−1.33815e6	−	1.33815e6i	−0.653270	−	0.653270i	0.300509	−	0.953779i	$-0.402844\pi$
$127$	−1.33815e6	−	1.33815e6i	−0.653270	−	0.653270i	−0.953779	+	0.300509i	$0.902844\pi$
$128$	131072.	−	131072.i	0.0625000	−	0.0625000i
$129$		−	4.51593e6i		−	2.10367i
$130$	125276.	−	65164.5i	0.0570215	−	0.0296607i
$131$	−478487.			−0.212842			−0.106421	−	0.994321i	$-0.533939\pi$
$131$	−478487.			−0.212842			−0.106421	+	0.994321i	$0.533939\pi$
$132$	−163429.	−	163429.i	−0.0710569	−	0.0710569i
$133$	1.22563e6	−	1.22563e6i	0.520959	−	0.520959i
$134$		−	2.81405e6i		−	1.16955i
$135$	3.91555e6	+	1.23592e6i	1.59144	+	0.502332i
$136$	−457178.			−0.181748
$137$	3.04810e6	+	3.04810e6i	1.18541	+	1.18541i	0.978324	+	0.207082i	$0.0663967\pi$
$137$	3.04810e6	+	3.04810e6i	1.18541	+	1.18541i	0.207082	+	0.978324i	$0.433603\pi$
$138$	−1.71987e6	+	1.71987e6i	−0.654422	+	0.654422i
$139$			4.85015e6i			1.80597i	0.429672	+	0.902985i	$0.358629\pi$
$139$			4.85015e6i			1.80597i	−0.429672	+	0.902985i	$0.641371\pi$
$140$	−445848.	+	1.41250e6i	−0.162481	+	0.514758i
$141$	−6.56010e6			−2.34020
$142$	−1.08543e6	−	1.08543e6i	−0.379085	−	0.379085i
$143$	21924.1	−	21924.1i	0.00749746	−	0.00749746i
$144$			1.46954e6i			0.492147i
$145$	−66043.9	−	126967.i	−0.0216635	−	0.0416472i
$146$	1.07423e6			0.345174
$147$	−640500.	−	640500.i	−0.201636	−	0.201636i
$148$	1.77459e6	−	1.77459e6i	0.547411	−	0.547411i
$149$			1.71913e6i			0.519696i	0.965650	+	0.259848i	$0.0836725\pi$
$149$			1.71913e6i			0.519696i	−0.965650	+	0.259848i	$0.916328\pi$
$150$	−2.36056e6	+	3.36672e6i	−0.699427	+	0.997546i
$151$	2.24046e6			0.650739			0.325369	−	0.945587i	$-0.394511\pi$
$151$	2.24046e6			0.650739			0.325369	+	0.945587i	$0.394511\pi$
$152$	599146.	+	599146.i	0.170609	+	0.170609i
$153$	2.56288e6	−	2.56288e6i	0.715573	−	0.715573i
$154$			325222.i			0.0890467i
$155$	−2.72273e6	+	1.41627e6i	−0.731154	+	0.380322i
$156$	−297284.			−0.0783066
$157$	148996.	+	148996.i	0.0385012	+	0.0385012i	0.726095	−	0.687594i	$-0.241333\pi$
$157$	148996.	+	148996.i	0.0385012	+	0.0385012i	−0.687594	+	0.726095i	$0.741333\pi$
$158$	1.33135e6	−	1.33135e6i	0.337537	−	0.337537i
$159$		−	1.09954e7i		−	2.73540i
$160$	−690496.	−	217952.i	−0.168578	−	0.0532109i
$161$	3.42253e6			0.820106
$162$	−1.92755e6	−	1.92755e6i	−0.453378	−	0.453378i
$163$	703334.	−	703334.i	0.162405	−	0.162405i	−0.621226	−	0.783631i	$-0.713365\pi$
$163$	703334.	−	703334.i	0.162405	−	0.162405i	0.783631	+	0.621226i	$0.213365\pi$
$164$			3.22426e6i			0.730968i
$165$	−271756.	+	860953.i	−0.0604960	+	0.191658i
$166$	−3.96740e6			−0.867324
$167$	1.50752e6	+	1.50752e6i	0.323679	+	0.323679i	0.850177	−	0.526498i	$-0.176495\pi$
$167$	1.50752e6	+	1.50752e6i	0.323679	+	0.323679i	−0.526498	+	0.850177i	$0.676495\pi$
$168$	2.20495e6	−	2.20495e6i	0.465020	−	0.465020i
$169$			4.78693e6i			0.991738i
$170$	824115.	+	1.58433e6i	0.167742	+	0.322477i
$171$	−6.71747e6			−1.34344
$172$	−2.19656e6	−	2.19656e6i	−0.431677	−	0.431677i
$173$	1.83301e6	−	1.83301e6i	0.354018	−	0.354018i	−0.507584	−	0.861602i	$-0.669461\pi$
$173$	1.83301e6	−	1.83301e6i	0.354018	−	0.354018i	0.861602	+	0.507584i	$0.169461\pi$
$174$			301296.i			0.0571934i
$175$	5.69863e6	−	1.00112e6i	1.06330	−	0.186798i
$176$	−158984.			−0.0291619
$177$	7.54096e6	+	7.54096e6i	1.35990	+	1.35990i
$178$	77420.2	−	77420.2i	0.0137276	−	0.0137276i
$179$		−	1.01836e7i		−	1.77559i	−0.460241	−	0.887794i	$-0.652237\pi$
$179$		−	1.01836e7i		−	1.77559i	0.460241	−	0.887794i	$-0.347763\pi$
$180$	5.09264e6	−	2.64902e6i	0.873223	−	0.454222i
$181$	−5.43889e6			−0.917223			−0.458611	−	0.888637i	$-0.651653\pi$
$181$	−5.43889e6			−0.917223			−0.458611	+	0.888637i	$0.651653\pi$
$182$	295797.	+	295797.i	0.0490659	+	0.0490659i
$183$	−6.54867e6	+	6.54867e6i	−1.06856	+	1.06856i
$184$			1.67310e6i			0.268577i
$185$	−9.34867e6	−	2.95086e6i	−1.47650	−	0.466052i
$186$	6.46112e6			1.00408
$187$	277268.	+	277268.i	0.0424009	+	0.0424009i
$188$	−3.19085e6	+	3.19085e6i	−0.480212	+	0.480212i
$189$			1.21635e7i			1.80166i
$190$	996285.	−	3.15634e6i	0.145252	−	0.460175i
$191$	−54549.1			−0.00782866			−0.00391433	−	0.999992i	$-0.501246\pi$
$191$	−54549.1			−0.00782866			−0.00391433	+	0.999992i	$0.501246\pi$
$192$	1.07789e6	+	1.07789e6i	0.152290	+	0.152290i
$193$	−6.54855e6	+	6.54855e6i	−0.910905	+	0.910905i	−0.996343	−	0.0854388i	$-0.972771\pi$
$193$	−6.54855e6	+	6.54855e6i	−0.910905	+	0.910905i	0.0854388	+	0.996343i	$0.472771\pi$
$194$		−	1.83974e6i		−	0.251972i
$195$	535889.	+	1.03023e6i	0.0722721	+	0.138940i
$196$	−623083.			−0.0827518
$197$	−8.84549e6	−	8.84549e6i	−1.15697	−	1.15697i	−0.985123	−	0.171850i	$-0.945026\pi$
$197$	−8.84549e6	−	8.84549e6i	−1.15697	−	1.15697i	−0.171850	−	0.985123i	$-0.554974\pi$
$198$	891245.	−	891245.i	0.114816	−	0.114816i
$199$			134874.i			0.0171147i	0.999963	+	0.00855733i	$0.00272392\pi$
$199$			134874.i			0.0171147i	−0.999963	+	0.00855733i	$0.997276\pi$
$200$	489395.	+	2.78577e6i	0.0611744	+	0.348221i
$201$	2.31418e7			2.84976
$202$	2.98542e6	+	2.98542e6i	0.362203	+	0.362203i
$203$	299789.	−	299789.i	0.0358367	−	0.0358367i
$204$		−	3.75966e6i		−	0.442852i
$205$	1.11735e7	−	5.81209e6i	1.29697	−	0.674638i
$206$	109572.			0.0125342
$207$	−9.37917e6	−	9.37917e6i	−1.05743	−	1.05743i
$208$	−144600.	+	144600.i	−0.0160686	+	0.0160686i
$209$		−	726737.i		−	0.0796046i
$210$	−1.16159e7	−	3.66649e6i	−1.25428	−	0.395906i
$211$	4.57148e6			0.486642			0.243321	−	0.969946i	$-0.421763\pi$
$211$	4.57148e6			0.486642			0.243321	+	0.969946i	$0.421763\pi$
$212$	−5.34821e6	−	5.34821e6i	−0.561307	−	0.561307i
$213$	8.92618e6	−	8.92618e6i	0.923691	−	0.923691i
$214$		−	1.67299e6i		−	0.170707i
$215$	−3.65254e6	+	1.15716e7i	−0.367518	+	1.16434i
$216$	−5.94608e6			−0.590024
$217$	−6.42880e6	−	6.42880e6i	−0.629145	−	0.629145i
$218$	−6.00365e6	+	6.00365e6i	−0.579490	+	0.579490i
$219$			8.83407e6i			0.841063i
$220$	286587.	+	550953.i	0.0269146	+	0.0517424i
$221$	504363.			0.0467269
$222$	1.45936e7	+	1.45936e7i	1.33384	+	1.33384i
$223$	8.58869e6	−	8.58869e6i	0.774484	−	0.774484i	−0.204403	−	0.978887i	$-0.565525\pi$
$223$	8.58869e6	−	8.58869e6i	0.774484	−	0.774484i	0.978887	+	0.204403i	$0.0655253\pi$
$224$		−	2.14499e6i		−	0.190845i
$225$	−1.83601e7	−	1.28731e7i	−1.61186	−	1.13015i
$226$	3.35859e6			0.290959
$227$	2.04614e6	+	2.04614e6i	0.174927	+	0.174927i	0.789140	−	0.614213i	$-0.210526\pi$
$227$	2.04614e6	+	2.04614e6i	0.174927	+	0.174927i	−0.614213	+	0.789140i	$0.710526\pi$
$228$	−4.92716e6	+	4.92716e6i	−0.415711	+	0.415711i
$229$			1.49421e7i			1.24424i	0.782922	+	0.622120i	$0.213728\pi$
$229$			1.49421e7i			1.24424i	−0.782922	+	0.622120i	$0.786272\pi$
$230$	5.79805e6	−	3.01595e6i	0.476539	−	0.247880i
$231$	−2.67451e6			−0.216974
$232$	146551.	+	146551.i	0.0117362	+	0.0117362i
$233$	−4.46396e6	+	4.46396e6i	−0.352900	+	0.352900i	−0.861188	−	0.508287i	$-0.830279\pi$
$233$	−4.46396e6	+	4.46396e6i	−0.352900	+	0.352900i	0.508287	+	0.861188i	$0.330279\pi$
$234$		−	1.62122e6i		−	0.126530i
$235$	1.68096e7	+	5.30588e6i	1.29525	+	0.408840i
$236$	7.33589e6			0.558106
$237$	1.09485e7	+	1.09485e7i	0.822453	+	0.822453i
$238$	−3.74086e6	+	3.74086e6i	−0.277485	+	0.277485i
$239$			9.83044e6i			0.720077i	0.932937	+	0.360039i	$0.117237\pi$
$239$			9.83044e6i			0.720077i	−0.932937	+	0.360039i	$0.882763\pi$
$240$	1.79236e6	−	5.67839e6i	0.129655	−	0.410763i
$241$	−1.98292e7			−1.41662			−0.708310	−	0.705902i	$-0.750542\pi$
$241$	−1.98292e7			−1.41662			−0.708310	+	0.705902i	$0.750542\pi$
$242$	−6.98982e6	−	6.98982e6i	−0.493197	−	0.493197i
$243$	−1.08096e6	+	1.08096e6i	−0.0753338	+	0.0753338i
$244$			6.37058e6i			0.438540i
$245$	1.12318e6	+	2.15926e6i	0.0763748	+	0.146828i
$246$	−2.65151e7			−1.78110
$247$	−660984.	−	660984.i	−0.0438632	−	0.0438632i
$248$	3.14271e6	−	3.14271e6i	0.206039	−	0.206039i
$249$		−	3.26264e7i		−	2.11335i
$250$	8.77176e6	−	6.71764e6i	0.561392	−	0.429929i
$251$	2.64803e6			0.167456			0.0837281	−	0.996489i	$-0.473317\pi$
$251$	2.64803e6			0.167456			0.0837281	+	0.996489i	$0.473317\pi$
$252$	1.20245e7	+	1.20245e7i	0.751393	+	0.751393i
$253$	1.01470e6	−	1.01470e6i	0.0626577	−	0.0626577i
$254$		−	1.07052e7i		−	0.653270i
$255$	−1.30289e7	+	6.77722e6i	−0.785758	+	0.408725i
$256$	1.04858e6			0.0625000
$257$	5.14082e6	+	5.14082e6i	0.302854	+	0.302854i	0.842129	−	0.539276i	$-0.181302\pi$
$257$	5.14082e6	+	5.14082e6i	0.302854	+	0.302854i	−0.539276	+	0.842129i	$0.681302\pi$
$258$	1.80637e7	−	1.80637e7i	1.05184	−	1.05184i
$259$		−	2.90412e7i		−	1.67153i
$260$	761762.	+	240447.i	0.0433411	+	0.0136804i
$261$	−1.64309e6			−0.0924147
$262$	−1.91395e6	−	1.91395e6i	−0.106421	−	0.106421i
$263$	4.13636e6	−	4.13636e6i	0.227379	−	0.227379i	−0.584218	−	0.811597i	$-0.698599\pi$
$263$	4.13636e6	−	4.13636e6i	0.227379	−	0.227379i	0.811597	+	0.584218i	$0.198599\pi$
$264$		−	1.30743e6i		−	0.0710569i
$265$	−8.89322e6	+	2.81747e7i	−0.477883	+	1.51399i
$266$	9.80502e6			0.520959
$267$	636675.	+	636675.i	0.0334491	+	0.0334491i
$268$	1.12562e7	−	1.12562e7i	0.584774	−	0.584774i
$269$		−	769267.i		−	0.0395203i	−0.999805	−	0.0197601i	$-0.993710\pi$
$269$		−	769267.i		−	0.0395203i	0.999805	−	0.0197601i	$-0.00629026\pi$
$270$	1.07185e7	+	2.06059e7i	0.544556	+	1.04689i
$271$	3.06018e6			0.153758			0.0768792	−	0.997040i	$-0.475504\pi$
$271$	3.06018e6			0.153758			0.0768792	+	0.997040i	$0.475504\pi$
$272$	−1.82871e6	−	1.82871e6i	−0.0908738	−	0.0908738i
$273$	−2.43253e6	+	2.43253e6i	−0.119556	+	0.119556i
$274$			2.43848e7i			1.18541i
$275$	1.39270e6	−	1.98631e6i	0.0669666	−	0.0955100i
$276$	−1.37590e7			−0.654422
$277$	−2.60549e7	−	2.60549e7i	−1.22589	−	1.22589i	−0.965506	−	0.260382i	$-0.916151\pi$
$277$	−2.60549e7	−	2.60549e7i	−1.22589	−	1.22589i	−0.260382	−	0.965506i	$-0.583849\pi$
$278$	−1.94006e7	+	1.94006e7i	−0.902985	+	0.902985i
$279$			3.52352e7i			1.62242i
$280$	−7.43338e6	+	3.86659e6i	−0.338620	+	0.176139i
$281$	6.85392e6			0.308901			0.154451	−	0.988000i	$-0.450639\pi$
$281$	6.85392e6			0.308901			0.154451	+	0.988000i	$0.450639\pi$
$282$	−2.62404e7	−	2.62404e7i	−1.17010	−	1.17010i
$283$	−9.67687e6	+	9.67687e6i	−0.426949	+	0.426949i	−0.887588	−	0.460639i	$-0.847620\pi$
$283$	−9.67687e6	+	9.67687e6i	−0.426949	+	0.426949i	0.460639	+	0.887588i	$0.347620\pi$
$284$		−	8.68344e6i		−	0.379085i
$285$	2.59566e7	+	8.19308e6i	1.12128	+	0.353926i
$286$	175393.			0.00749746
$287$	2.63825e7	+	2.63825e7i	1.11602	+	1.11602i
$288$	−5.87818e6	+	5.87818e6i	−0.246074	+	0.246074i
$289$		−	1.77590e7i		−	0.735743i
$290$	243692.	−	772043.i	0.00999187	−	0.0316554i
$291$	1.51294e7			0.613963
$292$	4.29692e6	+	4.29692e6i	0.172587	+	0.172587i
$293$	3.10247e7	−	3.10247e7i	1.23340	−	1.23340i	0.270752	−	0.962649i	$-0.412728\pi$
$293$	3.10247e7	−	3.10247e7i	1.23340	−	1.23340i	0.962649	−	0.270752i	$-0.0872724\pi$
$294$		−	5.12400e6i		−	0.201636i
$295$	−1.32238e7	−	2.54222e7i	−0.515097	−	0.990255i
$296$	1.41967e7			0.547411
$297$	3.60616e6	+	3.60616e6i	0.137650	+	0.137650i
$298$	−6.87651e6	+	6.87651e6i	−0.259848	+	0.259848i
$299$		−	1.84578e6i		−	0.0690504i
$300$	−2.29091e7	+	4.02461e6i	−0.848486	+	0.149060i
$301$	−3.59468e7			−1.31814
$302$	8.96185e6	+	8.96185e6i	0.325369	+	0.325369i
$303$	−2.45510e7	+	2.45510e7i	−0.882555	+	0.882555i
$304$			4.79317e6i			0.170609i
$305$	2.20770e7	−	1.14837e7i	0.778108	−	0.404746i
$306$	2.05030e7			0.715573
$307$	8.36685e6	+	8.36685e6i	0.289166	+	0.289166i	0.836750	−	0.547585i	$-0.184453\pi$
$307$	8.36685e6	+	8.36685e6i	0.289166	+	0.289166i	−0.547585	+	0.836750i	$0.684453\pi$
$308$	−1.30089e6	+	1.30089e6i	−0.0445234	+	0.0445234i
$309$			901080.i			0.0305413i
$310$	−1.65560e7	−	5.22582e6i	−0.555738	−	0.175416i
$311$	−3.85508e7			−1.28160			−0.640799	−	0.767708i	$-0.721397\pi$
$311$	−3.85508e7			−1.28160			−0.640799	+	0.767708i	$0.721397\pi$
$312$	−1.18914e6	−	1.18914e6i	−0.0391533	−	0.0391533i
$313$	−4.02122e6	+	4.02122e6i	−0.131137	+	0.131137i	−0.769629	−	0.638492i	$-0.779559\pi$
$313$	−4.02122e6	+	4.02122e6i	−0.131137	+	0.131137i	0.638492	+	0.769629i	$0.279559\pi$
$314$			1.19196e6i			0.0385012i
$315$	1.99949e7	−	6.33461e7i	0.639717	−	2.02669i
$316$	1.06508e7			0.337537
$317$	1.65473e7	+	1.65473e7i	0.519456	+	0.519456i	0.917407	−	0.397951i	$-0.130279\pi$
$317$	1.65473e7	+	1.65473e7i	0.519456	+	0.519456i	−0.397951	+	0.917407i	$0.630279\pi$
$318$	4.39817e7	−	4.39817e7i	1.36770	−	1.36770i
$319$		−	177760.i		−	0.00547598i
$320$	−1.89018e6	−	3.63379e6i	−0.0576836	−	0.110895i
$321$	1.37581e7			0.415951
$322$	1.36901e7	+	1.36901e7i	0.410053	+	0.410053i
$323$	8.35926e6	−	8.35926e6i	0.248062	−	0.248062i
$324$		−	1.54204e7i		−	0.453378i
$325$	−539906.	−	3.07329e6i	−0.0157278	−	0.0895268i
$326$	5.62667e6			0.162405
$327$	−4.93718e7	−	4.93718e7i	−1.41200	−	1.41200i
$328$	−1.28970e7	+	1.28970e7i	−0.365484	+	0.365484i
$329$			5.22183e7i			1.46634i
$330$	−4.53083e6	+	2.35679e6i	−0.126077	+	0.0655811i
$331$	5.77833e7			1.59337			0.796687	−	0.604391i	$-0.206584\pi$
$331$	5.77833e7			1.59337			0.796687	+	0.604391i	$0.206584\pi$
$332$	−1.58696e7	−	1.58696e7i	−0.433662	−	0.433662i
$333$	−7.95850e7	+	7.95850e7i	−2.15525	+	2.15525i
$334$			1.20602e7i			0.323679i
$335$	−5.92985e7	−	1.87173e7i	−1.57728	−	0.497862i
$336$	1.76396e7			0.465020
$337$	3.94556e7	+	3.94556e7i	1.03091	+	1.03091i	0.999507	+	0.0313983i	$0.00999603\pi$
$337$	3.94556e7	+	3.94556e7i	1.03091	+	1.03091i	0.0313983	+	0.999507i	$0.490004\pi$
$338$	−1.91477e7	+	1.91477e7i	−0.495869	+	0.495869i
$339$			2.76198e7i			0.708960i
$340$	−3.04086e6	+	9.63378e6i	−0.0773676	+	0.245109i
$341$	−3.81196e6			−0.0961357
$342$	−2.68699e7	−	2.68699e7i	−0.671718	−	0.671718i
$343$	2.57068e7	−	2.57068e7i	0.637039	−	0.637039i
$344$		−	1.75725e7i		−	0.431677i
$345$	2.48021e7	+	4.76810e7i	0.603991	+	1.16115i
$346$	1.46641e7			0.354018
$347$	−5.59432e6	−	5.59432e6i	−0.133893	−	0.133893i	0.636984	−	0.770877i	$-0.280182\pi$
$347$	−5.59432e6	−	5.59432e6i	−0.133893	−	0.133893i	−0.770877	+	0.636984i	$0.780182\pi$
$348$	−1.20519e6	+	1.20519e6i	−0.0285967	+	0.0285967i
$349$		−	1.49144e7i		−	0.350858i	−0.984492	−	0.175429i	$-0.943869\pi$
$349$		−	1.49144e7i		−	0.350858i	0.984492	−	0.175429i	$-0.0561312\pi$
$350$	2.67990e7	+	1.87901e7i	0.625050	+	0.438252i
$351$	6.55978e6			0.151694
$352$	−635937.	−	635937.i	−0.0145810	−	0.0145810i
$353$	1.14916e7	−	1.14916e7i	0.261251	−	0.261251i	−0.564311	−	0.825562i	$-0.690858\pi$
$353$	1.14916e7	−	1.14916e7i	0.261251	−	0.261251i	0.825562	+	0.564311i	$0.190858\pi$
$354$			6.03277e7i			1.35990i
$355$	−3.00921e7	+	1.56529e7i	−0.672616	+	0.349872i
$356$	619361.			0.0137276
$357$	−3.07634e7	−	3.07634e7i	−0.676130	−	0.676130i
$358$	4.07344e7	−	4.07344e7i	0.887794	−	0.887794i
$359$			4.90540e6i			0.106021i	0.998594	+	0.0530104i	$0.0168817\pi$
$359$			4.90540e6i			0.106021i	−0.998594	+	0.0530104i	$0.983118\pi$
$360$	3.09666e7	+	9.77447e6i	0.663722	+	0.209501i
$361$	2.51357e7			0.534281
$362$	−2.17556e7	−	2.17556e7i	−0.458611	−	0.458611i
$363$	5.74818e7	−	5.74818e7i	1.20174	−	1.20174i
$364$			2.36638e6i			0.0490659i
$365$	7.14509e6	−	2.26365e7i	0.146936	−	0.465511i
$366$	−5.23893e7			−1.06856
$367$	154888.	+	154888.i	0.00313343	+	0.00313343i	0.708672	−	0.705538i	$-0.249295\pi$
$367$	154888.	+	154888.i	0.00313343	+	0.00313343i	−0.705538	+	0.708672i	$0.749295\pi$
$368$	−6.69240e6	+	6.69240e6i	−0.134288	+	0.134288i
$369$		−	1.44598e8i		−	2.87795i
$370$	−2.55912e7	−	4.91981e7i	−0.505226	−	0.971278i
$371$	−8.75234e7			−1.71397
$372$	2.58445e7	+	2.58445e7i	0.502041	+	0.502041i
$373$	−3.06497e7	+	3.06497e7i	−0.590609	+	0.590609i	−0.937796	−	0.347187i	$-0.887137\pi$
$373$	−3.06497e7	+	3.06497e7i	−0.590609	+	0.590609i	0.347187	+	0.937796i	$0.387137\pi$
$374$			2.21814e6i			0.0424009i
$375$	5.52434e7	+	7.21357e7i	1.04758	+	1.36791i
$376$	−2.55268e7			−0.480212
$377$	−161677.	−	161677.i	−0.00301734	−	0.00301734i
$378$	−4.86538e7	+	4.86538e7i	−0.900828	+	0.900828i
$379$		−	3.73773e7i		−	0.686579i	−0.939230	−	0.343290i	$-0.888459\pi$
$379$		−	3.73773e7i		−	0.686579i	0.939230	−	0.343290i	$-0.111541\pi$
$380$	1.66105e7	−	8.64023e6i	0.302714	−	0.157462i
$381$	8.80355e7			1.59178
$382$	−218196.	−	218196.i	−0.00391433	−	0.00391433i
$383$	−2.09069e7	+	2.09069e7i	−0.372128	+	0.372128i	−0.868252	−	0.496124i	$-0.834756\pi$
$383$	−2.09069e7	+	2.09069e7i	−0.372128	+	0.372128i	0.496124	+	0.868252i	$0.334756\pi$
$384$			8.62311e6i			0.152290i
$385$	6.85317e6	+	2.16317e6i	0.120091	+	0.0379061i
$386$	−5.23884e7			−0.910905
$387$	9.85091e7	+	9.85091e7i	1.69959	+	1.69959i
$388$	7.35897e6	−	7.35897e6i	0.125986	−	0.125986i
$389$		−	2.54717e7i		−	0.432723i	−0.976313	−	0.216361i	$-0.930581\pi$
$389$		−	2.54717e7i		−	0.432723i	0.976313	−	0.216361i	$-0.0694189\pi$
$390$	−1.97735e6	+	6.26446e6i	−0.0333341	+	0.105606i
$391$	2.33430e7			0.390505
$392$	−2.49233e6	−	2.49233e6i	−0.0413759	−	0.0413759i
$393$	1.57396e7	−	1.57396e7i	0.259308	−	0.259308i
$394$		−	7.07639e7i		−	1.15697i
$395$	−1.91993e7	−	3.69099e7i	−0.311526	−	0.598896i
$396$	7.12996e6			0.114816
$397$	−8.94817e6	−	8.94817e6i	−0.143009	−	0.143009i	0.631978	−	0.774987i	$-0.282243\pi$
$397$	−8.94817e6	−	8.94817e6i	−0.143009	−	0.143009i	−0.774987	+	0.631978i	$0.782243\pi$
$398$	−539495.	+	539495.i	−0.00855733	+	0.00855733i
$399$			8.06329e7i			1.26939i
$400$	−9.18548e6	+	1.31006e7i	−0.143523	+	0.204698i
$401$	−9.50200e7			−1.47361			−0.736804	−	0.676107i	$-0.763666\pi$
$401$	−9.50200e7			−1.47361			−0.736804	+	0.676107i	$0.763666\pi$
$402$	9.25670e7	+	9.25670e7i	1.42488	+	1.42488i
$403$	−3.46707e6	+	3.46707e6i	−0.0529721	+	0.0529721i
$404$			2.38834e7i			0.362203i
$405$	−5.34386e7	+	2.77970e7i	−0.804434	+	0.418439i
$406$	2.39831e6			0.0358367
$407$	−8.60999e6	−	8.60999e6i	−0.127708	−	0.127708i
$408$	1.50387e7	−	1.50387e7i	0.221426	−	0.221426i
$409$			1.28857e8i			1.88339i	0.336474	+	0.941693i	$0.390766\pi$
$409$			1.28857e8i			1.88339i	−0.336474	+	0.941693i	$0.609234\pi$
$410$	6.79425e7	+	2.14457e7i	0.985802	+	0.311164i
$411$	−2.00531e8			−2.88840
$412$	438288.	+	438288.i	0.00626712	+	0.00626712i
$413$	6.00259e7	−	6.00259e7i	0.852096	−	0.852096i
$414$		−	7.50333e7i		−	1.05743i
$415$	−2.63886e7	+	8.36021e7i	−0.369209	+	1.16970i
$416$	−1.15680e6			−0.0160686
$417$	−1.59543e8	−	1.59543e8i	−2.20024	−	2.20024i
$418$	2.90695e6	−	2.90695e6i	0.0398023	−	0.0398023i
$419$			4.82193e7i			0.655509i	0.944763	+	0.327755i	$0.106292\pi$
$419$			4.82193e7i			0.655509i	−0.944763	+	0.327755i	$0.893708\pi$
$420$	−3.17974e7	−	6.11294e7i	−0.429185	−	0.825091i
$421$	1.02360e8			1.37177			0.685886	−	0.727709i	$-0.259415\pi$
$421$	1.02360e8			1.37177			0.685886	+	0.727709i	$0.259415\pi$
$422$	1.82859e7	+	1.82859e7i	0.243321	+	0.243321i
$423$	1.43100e8	−	1.43100e8i	1.89068	−	1.89068i
$424$		−	4.27857e7i		−	0.561307i
$425$	3.88669e7	−	6.82802e6i	0.506306	−	0.0889464i
$426$	7.14094e7			0.923691
$427$	5.21273e7	+	5.21273e7i	0.669547	+	0.669547i
$428$	6.69196e6	−	6.69196e6i	0.0853537	−	0.0853537i
$429$			1.44237e6i			0.0182686i
$430$	−6.08967e7	+	3.16764e7i	−0.765929	+	0.398411i
$431$	1.38893e8			1.73480			0.867401	−	0.497610i	$-0.165789\pi$
$431$	1.38893e8			1.73480			0.867401	+	0.497610i	$0.165789\pi$
$432$	−2.37843e7	−	2.37843e7i	−0.295012	−	0.295012i
$433$	−8.14325e7	+	8.14325e7i	−1.00308	+	1.00308i	−0.00308136	+	0.999995i	$0.500981\pi$
$433$	−8.14325e7	+	8.14325e7i	−1.00308	+	1.00308i	−0.999995	+	0.00308136i	$0.999019\pi$
$434$		−	5.14304e7i		−	0.629145i
$435$	6.34900e6	+	2.00403e6i	0.0771325	+	0.0243465i
$436$	−4.80292e7			−0.579490
$437$	−3.05918e7	−	3.05918e7i	−0.366573	−	0.366573i
$438$	−3.53363e7	+	3.53363e7i	−0.420532	+	0.420532i
$439$		−	1.23204e8i		−	1.45623i	−0.685455	−	0.728115i	$-0.740397\pi$
$439$		−	1.23204e8i		−	1.45623i	0.685455	−	0.728115i	$-0.259603\pi$
$440$	−1.05746e6	+	3.35016e6i	−0.0124139	+	0.0393285i
$441$	2.79433e7			0.325809
$442$	2.01745e6	+	2.01745e6i	0.0233634	+	0.0233634i
$443$	−8.00035e6	+	8.00035e6i	−0.0920234	+	0.0920234i	−0.751620	−	0.659597i	$-0.770727\pi$
$443$	−8.00035e6	+	8.00035e6i	−0.0920234	+	0.0920234i	0.659597	+	0.751620i	$0.270727\pi$
$444$			1.16749e8i			1.33384i
$445$	−1.11647e6	−	2.14637e6i	−0.0126697	−	0.0243570i
$446$	6.87095e7			0.774484
$447$	−5.65499e7	−	5.65499e7i	−0.633154	−	0.633154i
$448$	8.57997e6	−	8.57997e6i	0.0954227	−	0.0954227i
$449$			1.07413e8i			1.18664i	0.804967	+	0.593320i	$0.202183\pi$
$449$			1.07413e8i			1.18664i	−0.804967	+	0.593320i	$0.797817\pi$
$450$	−2.19479e7	−	1.24933e8i	−0.240855	−	1.37101i
$451$	1.56435e7			0.170532
$452$	1.34344e7	+	1.34344e7i	0.145479	+	0.145479i
$453$	−7.36990e7	+	7.36990e7i	−0.792806	+	0.792806i
$454$			1.63691e7i			0.174927i
$455$	8.20058e6	−	4.26566e6i	0.0870583	−	0.0452848i
$456$	−3.94173e7			−0.415711
$457$	−4.63795e7	−	4.63795e7i	−0.485934	−	0.485934i	0.421087	−	0.907020i	$-0.361649\pi$
$457$	−4.63795e7	−	4.63795e7i	−0.485934	−	0.485934i	−0.907020	+	0.421087i	$0.861649\pi$
$458$	−5.97682e7	+	5.97682e7i	−0.622120	+	0.622120i
$459$			8.29595e7i			0.857883i
$460$	3.52560e7	+	1.11284e7i	0.362209	+	0.114330i
$461$	8.18127e7			0.835060			0.417530	−	0.908663i	$-0.362896\pi$
$461$	8.18127e7			0.835060			0.417530	+	0.908663i	$0.362896\pi$
$462$	−1.06980e7	−	1.06980e7i	−0.108487	−	0.108487i
$463$	−4.49737e7	+	4.49737e7i	−0.453123	+	0.453123i	−0.896390	−	0.443267i	$-0.853819\pi$
$463$	−4.49737e7	+	4.49737e7i	−0.453123	+	0.453123i	0.443267	+	0.896390i	$0.353819\pi$
$464$			1.17241e6i			0.0117362i
$465$	4.29752e7	−	1.36150e8i	0.427425	−	1.35413i
$466$	−3.57116e7			−0.352900
$467$	3.64476e7	+	3.64476e7i	0.357864	+	0.357864i	0.863025	−	0.505161i	$-0.168567\pi$
$467$	3.64476e7	+	3.64476e7i	0.357864	+	0.357864i	−0.505161	+	0.863025i	$0.668567\pi$
$468$	6.48487e6	−	6.48487e6i	0.0632650	−	0.0632650i
$469$		−	1.84208e8i		−	1.78562i
$470$	4.60150e7	+	8.84620e7i	0.443206	+	0.852046i
$471$	−9.80228e6			−0.0938133
$472$	2.93436e7	+	2.93436e7i	0.279053	+	0.279053i
$473$	−1.06573e7	+	1.06573e7i	−0.100708	+	0.100708i
$474$			8.75883e7i			0.822453i
$475$	−5.98846e7	−	4.19880e7i	−0.558772	−	0.391782i
$476$	−2.99269e7			−0.277485
$477$	2.39851e8	+	2.39851e8i	2.20997	+	2.20997i
$478$	−3.93217e7	+	3.93217e7i	−0.360039	+	0.360039i
$479$		−	2.14257e7i		−	0.194952i	−0.995238	−	0.0974762i	$-0.968923\pi$
$479$		−	2.14257e7i		−	0.194952i	0.995238	−	0.0974762i	$-0.0310770\pi$
$480$	2.98830e7	−	1.55441e7i	0.270209	−	0.140554i
$481$	−1.56620e7			−0.140738
$482$	−7.93166e7	−	7.93166e7i	−0.708310	−	0.708310i
$483$	−1.12583e8	+	1.12583e8i	−0.999148	+	0.999148i
$484$		−	5.59186e7i		−	0.493197i
$485$	−3.87676e7	−	1.22368e7i	−0.339816	−	0.107261i
$486$	−8.64766e6			−0.0753338
$487$	2.19968e7	+	2.19968e7i	0.190447	+	0.190447i	0.795889	−	0.605442i	$-0.207004\pi$
$487$	2.19968e7	+	2.19968e7i	0.190447	+	0.190447i	−0.605442	+	0.795889i	$0.707004\pi$
$488$	−2.54823e7	+	2.54823e7i	−0.219270	+	0.219270i
$489$			4.62717e7i			0.395721i
$490$	−4.14435e6	+	1.31298e7i	−0.0352264	+	0.111601i
$491$	1.27586e8			1.07785			0.538926	−	0.842353i	$-0.318830\pi$
$491$	1.27586e8			1.07785			0.538926	+	0.842353i	$0.318830\pi$
$492$	−1.06061e8	−	1.06061e8i	−0.890551	−	0.890551i
$493$	2.04468e6	−	2.04468e6i	0.0170641	−	0.0170641i
$494$		−	5.28787e6i		−	0.0438632i
$495$	−1.28526e7	−	2.47085e7i	−0.105968	−	0.203719i
$496$	2.51416e7			0.206039
$497$	−7.10522e7	−	7.10522e7i	−0.578773	−	0.578773i
$498$	1.30506e8	−	1.30506e8i	1.05668	−	1.05668i
$499$		−	1.19270e8i		−	0.959905i	−0.877295	−	0.479952i	$-0.840654\pi$
$499$		−	1.19270e8i		−	0.959905i	0.877295	−	0.479952i	$-0.159346\pi$
$500$	6.19576e7	+	8.21648e6i	0.495660	+	0.0657318i
$501$	−9.91785e7			−0.788687
$502$	1.05921e7	+	1.05921e7i	0.0837281	+	0.0837281i
$503$	6.37213e7	−	6.37213e7i	0.500704	−	0.500704i	−0.410953	−	0.911657i	$-0.634804\pi$
$503$	6.37213e7	−	6.37213e7i	0.500704	−	0.500704i	0.911657	+	0.410953i	$0.134804\pi$
$504$			9.61963e7i			0.751393i
$505$	8.27668e7	−	4.30525e7i	0.642661	−	0.334291i
$506$	8.11757e6			0.0626577
$507$	−1.57464e8	−	1.57464e8i	−1.20825	−	1.20825i
$508$	4.28207e7	−	4.28207e7i	0.326635	−	0.326635i
$509$			2.96382e7i			0.224749i	0.993666	+	0.112375i	$0.0358456\pi$
$509$			2.96382e7i			0.224749i	−0.993666	+	0.112375i	$0.964154\pi$
$510$	−7.92247e7	−	2.50069e7i	−0.597241	−	0.188516i
$511$	7.03191e7			0.527000
$512$	4.19430e6	+	4.19430e6i	0.0312500	+	0.0312500i
$513$	1.08721e8	−	1.08721e8i	0.805308	−	0.805308i
$514$			4.11266e7i			0.302854i
$515$	728803.	−	2.30893e6i	0.00533567	−	0.0169040i
$516$	1.44510e8			1.05184
$517$	1.54814e7	+	1.54814e7i	0.112031	+	0.112031i
$518$	1.16165e8	−	1.16165e8i	0.835767	−	0.835767i
$519$			1.20592e8i			0.862612i
$520$	2.08526e6	+	4.00884e6i	0.0148303	+	0.0285107i
$521$	−8.99036e7			−0.635717			−0.317859	−	0.948138i	$-0.602964\pi$
$521$	−8.99036e7			−0.635717			−0.317859	+	0.948138i	$0.602964\pi$
$522$	−6.57238e6	−	6.57238e6i	−0.0462074	−	0.0462074i
$523$	−1.34982e8	+	1.34982e8i	−0.943560	+	0.943560i	−0.998490	−	0.0549303i	$-0.982506\pi$
$523$	−1.34982e8	+	1.34982e8i	−0.943560	+	0.943560i	0.0549303	+	0.998490i	$0.482506\pi$
$524$		−	1.53116e7i		−	0.106421i
$525$	−1.54523e8	+	2.20385e8i	−1.06786	+	1.52302i
$526$	3.30909e7			0.227379
$527$	−4.38469e7	−	4.38469e7i	−0.299576	−	0.299576i
$528$	5.22971e6	−	5.22971e6i	0.0355284	−	0.0355284i
$529$			6.26093e7i			0.422933i
$530$	−1.48272e8	+	7.71260e7i	−0.995935	+	0.518052i
$531$	−3.28992e8			−2.19736
$532$	3.92201e7	+	3.92201e7i	0.260480	+	0.260480i
$533$	1.42281e7	−	1.42281e7i	0.0939651	−	0.0939651i
$534$			5.09340e6i			0.0334491i
$535$	−3.52537e7	−	1.11277e7i	−0.230220	−	0.0726679i
$536$	9.00498e7			0.584774
$537$	3.34985e8	+	3.34985e8i	2.16323	+	2.16323i
$538$	3.07707e6	−	3.07707e6i	0.0197601	−	0.0197601i
$539$			3.02308e6i			0.0193056i
$540$	−3.95496e7	+	1.25298e8i	−0.251166	+	0.795722i
$541$	−1.32893e8			−0.839288			−0.419644	−	0.907689i	$-0.637845\pi$
$541$	−1.32893e8			−0.839288			−0.419644	+	0.907689i	$0.637845\pi$
$542$	1.22407e7	+	1.22407e7i	0.0768792	+	0.0768792i
$543$	1.78910e8	−	1.78910e8i	1.11747	−	1.11747i
$544$		−	1.46297e7i		−	0.0908738i
$545$	8.65781e7	+	1.66443e8i	0.534833	+	1.02820i
$546$	−1.94602e7			−0.119556
$547$	8.92181e7	+	8.92181e7i	0.545119	+	0.545119i	0.925025	−	0.379906i	$-0.124044\pi$
$547$	8.92181e7	+	8.92181e7i	0.545119	+	0.545119i	−0.379906	+	0.925025i	$0.624044\pi$
$548$	−9.75391e7	+	9.75391e7i	−0.592703	+	0.592703i
$549$		−	2.85701e8i		−	1.72661i
$550$	1.35160e7	−	2.37445e6i	0.0812383	−	0.0142717i
$551$	−5.35923e6			−0.0320367
$552$	−5.50358e7	−	5.50358e7i	−0.327211	−	0.327211i
$553$	8.71502e7	−	8.71502e7i	0.515339	−	0.515339i
$554$		−	2.08440e8i		−	1.22589i
$555$	4.04588e8	−	2.10453e8i	2.36665	−	1.23105i
$556$	−1.55205e8			−0.902985
$557$	−3.45522e7	−	3.45522e7i	−0.199945	−	0.199945i	0.600032	−	0.799976i	$-0.295155\pi$
$557$	−3.45522e7	−	3.45522e7i	−0.199945	−	0.199945i	−0.799976	+	0.600032i	$0.795155\pi$
$558$	−1.40941e8	+	1.40941e8i	−0.811211	+	0.811211i
$559$			1.93862e7i			0.110983i
$560$	−4.51999e7	−	1.42671e7i	−0.257379	−	0.0812405i
$561$	−1.82412e7			−0.103315
$562$	2.74157e7	+	2.74157e7i	0.154451	+	0.154451i
$563$	−1.41480e8	+	1.41480e8i	−0.792811	+	0.792811i	−0.981950	−	0.189139i	$-0.939430\pi$
$563$	−1.41480e8	+	1.41480e8i	−0.792811	+	0.792811i	0.189139	+	0.981950i	$0.439430\pi$
$564$		−	2.09923e8i		−	1.17010i
$565$	2.23392e7	−	7.07731e7i	0.123857	−	0.392394i
$566$	−7.74150e7			−0.426949
$567$	−1.26177e8	−	1.26177e8i	−0.692200	−	0.692200i
$568$	3.47338e7	−	3.47338e7i	0.189543	−	0.189543i
$569$			2.25682e8i			1.22507i	0.790445	+	0.612533i	$0.209849\pi$
$569$			2.25682e8i			1.22507i	−0.790445	+	0.612533i	$0.790151\pi$
$570$	7.10541e7	+	1.36599e8i	0.383676	+	0.737602i
$571$	−1.79933e7			−0.0966501			−0.0483251	−	0.998832i	$-0.515388\pi$
$571$	−1.79933e7			−0.0966501			−0.0483251	+	0.998832i	$0.515388\pi$
$572$	701572.	+	701572.i	0.00374873	+	0.00374873i
$573$	1.79437e6	−	1.79437e6i	0.00953778	−	0.00953778i
$574$			2.11060e8i			1.11602i
$575$	−2.49880e7	−	1.42238e8i	−0.131440	−	0.748191i
$576$	−4.70254e7			−0.246074
$577$	−9.98078e7	−	9.98078e7i	−0.519562	−	0.519562i	0.397877	−	0.917439i	$-0.369747\pi$
$577$	−9.98078e7	−	9.98078e7i	−0.519562	−	0.519562i	−0.917439	+	0.397877i	$0.869747\pi$
$578$	7.10362e7	−	7.10362e7i	0.367871	−	0.367871i
$579$		−	4.30823e8i		−	2.21954i
$580$	4.06294e6	−	2.11340e6i	0.0208236	−	0.0108317i
$581$	−2.59706e8			−1.32420
$582$	6.05175e7	+	6.05175e7i	0.306981	+	0.306981i
$583$	−2.59485e7	+	2.59485e7i	−0.130950	+	0.130950i
$584$			3.43754e7i			0.172587i
$585$	−3.41627e7	−	1.07833e7i	−0.170642	−	0.0538622i
$586$	2.48197e8			1.23340
$587$	1.63890e8	+	1.63890e8i	0.810285	+	0.810285i	0.984676	−	0.174391i	$-0.0557957\pi$
$587$	1.63890e8	+	1.63890e8i	0.810285	+	0.810285i	−0.174391	+	0.984676i	$0.555796\pi$
$588$	2.04960e7	−	2.04960e7i	0.100818	−	0.100818i
$589$			1.14926e8i			0.562433i
$590$	4.87937e7	−	1.54584e8i	0.237579	−	0.752676i
$591$	5.81937e8			2.81912
$592$	5.67869e7	+	5.67869e7i	0.273705	+	0.273705i
$593$	2.01862e8	−	2.01862e8i	0.968035	−	0.968035i	−0.0314699	−	0.999505i	$-0.510019\pi$
$593$	2.01862e8	−	2.01862e8i	0.968035	−	0.968035i	0.999505	+	0.0314699i	$0.0100188\pi$
$594$			2.88493e7i			0.137650i
$595$	5.39466e7	+	1.03710e8i	0.256102	+	0.492346i
$596$	−5.50121e7			−0.259848
$597$	−4.43661e6	−	4.43661e6i	−0.0208511	−	0.0208511i
$598$	7.38312e6	−	7.38312e6i	0.0345252	−	0.0345252i
$599$			1.19257e7i			0.0554887i	0.999615	+	0.0277443i	$0.00883243\pi$
$599$			1.19257e7i			0.0554887i	−0.999615	+	0.0277443i	$0.991168\pi$
$600$	−1.07735e8	−	7.55381e7i	−0.498773	−	0.349713i
$601$	−1.44542e7			−0.0665843			−0.0332921	−	0.999446i	$-0.510599\pi$
$601$	−1.44542e7			−0.0665843			−0.0332921	+	0.999446i	$0.510599\pi$
$602$	−1.43787e8	−	1.43787e8i	−0.659068	−	0.659068i
$603$	−5.04807e8	+	5.04807e8i	−2.30236	+	2.30236i
$604$			7.16948e7i			0.325369i
$605$	−1.93783e8	+	1.00800e8i	−0.875085	+	0.455190i
$606$	−1.96408e8			−0.882555
$607$	−2.13752e8	−	2.13752e8i	−0.955750	−	0.955750i	0.0433118	−	0.999062i	$-0.486209\pi$
$607$	−2.13752e8	−	2.13752e8i	−0.955750	−	0.955750i	−0.999062	+	0.0433118i	$0.986209\pi$
$608$	−1.91727e7	+	1.91727e7i	−0.0853045	+	0.0853045i
$609$			1.97229e7i			0.0873208i
$610$	1.34243e8	+	4.23731e7i	0.591427	+	0.186681i
$611$	2.81614e7			0.123461
$612$	8.20121e7	+	8.20121e7i	0.357786	+	0.357786i
$613$	2.28955e8	−	2.28955e8i	0.993961	−	0.993961i	−0.00602111	−	0.999982i	$-0.501917\pi$
$613$	2.28955e8	−	2.28955e8i	0.993961	−	0.993961i	0.999982	+	0.00602111i	$0.00191659\pi$
$614$			6.69348e7i			0.289166i
$615$	−1.76362e8	+	5.58734e8i	−0.758192	+	2.40204i
$616$	−1.04071e7			−0.0445234
$617$	−1.26144e8	−	1.26144e8i	−0.537045	−	0.537045i	0.385615	−	0.922660i	$-0.373989\pi$
$617$	−1.26144e8	−	1.26144e8i	−0.537045	−	0.537045i	−0.922660	+	0.385615i	$0.873989\pi$
$618$	−3.60432e6	+	3.60432e6i	−0.0152707	+	0.0152707i
$619$			3.79865e8i			1.60161i	0.598922	+	0.800807i	$0.295596\pi$
$619$			3.79865e8i			1.60161i	−0.598922	+	0.800807i	$0.704404\pi$
$620$	−4.53207e7	−	8.71272e7i	−0.190161	−	0.365577i
$621$	3.03601e8			1.26773
$622$	−1.54203e8	−	1.54203e8i	−0.640799	−	0.640799i
$623$	5.06792e6	−	5.06792e6i	0.0209588	−	0.0209588i
$624$		−	9.51310e6i		−	0.0391533i
$625$	−8.32117e7	−	2.29522e8i	−0.340835	−	0.940123i
$626$	−3.21698e7			−0.131137
$627$	2.39057e7	+	2.39057e7i	0.0969836	+	0.0969836i
$628$	−4.76786e6	+	4.76786e6i	−0.0192506	+	0.0192506i
$629$		−	1.98072e8i		−	0.795924i
$630$	3.33364e8	−	1.73405e8i	1.33321	−	0.693489i
$631$	−2.31401e7			−0.0921039			−0.0460519	−	0.998939i	$-0.514664\pi$
$631$	−2.31401e7			−0.0921039			−0.0460519	+	0.998939i	$0.514664\pi$
$632$	4.26032e7	+	4.26032e7i	0.168768	+	0.168768i
$633$	−1.50377e8	+	1.50377e8i	−0.592884	+	0.592884i
$634$			1.32378e8i			0.519456i
$635$	−2.25583e8	−	7.12041e7i	−0.881017	−	0.278089i
$636$	3.51854e8			1.36770
$637$	2.74956e6	+	2.74956e6i	0.0106376	+	0.0106376i
$638$	711040.	−	711040.i	0.00273799	−	0.00273799i
$639$			3.89426e8i			1.49253i
$640$	6.97446e6	−	2.20959e7i	0.0266055	−	0.0842891i
$641$	−9.07974e6			−0.0344746			−0.0172373	−	0.999851i	$-0.505487\pi$
$641$	−9.07974e6			−0.0344746			−0.0172373	+	0.999851i	$0.505487\pi$
$642$	5.50323e7	+	5.50323e7i	0.207976	+	0.207976i
$643$	3.19089e8	−	3.19089e8i	1.20027	−	1.20027i	0.226186	−	0.974084i	$-0.427374\pi$
$643$	3.19089e8	−	3.19089e8i	1.20027	−	1.20027i	0.974084	−	0.226186i	$-0.0726258\pi$
$644$			1.09521e8i			0.410053i
$645$	−2.60495e8	−	5.00792e8i	−0.970780	−	1.86629i
$646$	6.68741e7			0.248062
$647$	1.30690e8	+	1.30690e8i	0.482537	+	0.482537i	0.905941	−	0.423404i	$-0.139165\pi$
$647$	1.30690e8	+	1.30690e8i	0.482537	+	0.482537i	−0.423404	+	0.905941i	$0.639165\pi$
$648$	6.16815e7	−	6.16815e7i	0.226689	−	0.226689i
$649$		−	3.55924e7i		−	0.130204i
$650$	1.01335e7	−	1.44528e7i	0.0368995	−	0.0526273i
$651$	4.22945e8			1.53299
$652$	2.25067e7	+	2.25067e7i	0.0812024	+	0.0812024i
$653$	−1.71577e8	+	1.71577e8i	−0.616195	+	0.616195i	−0.944553	−	0.328358i	$-0.893505\pi$
$653$	−1.71577e8	+	1.71577e8i	−0.616195	+	0.616195i	0.328358	+	0.944553i	$0.393505\pi$
$654$		−	3.94975e8i		−	1.41200i
$655$	−5.30616e7	+	2.76009e7i	−0.188824	+	0.0982198i
$656$	−1.03176e8			−0.365484
$657$	−1.92704e8	−	1.92704e8i	−0.679507	−	0.679507i
$658$	−2.08873e8	+	2.08873e8i	−0.733170	+	0.733170i
$659$		−	4.79318e8i		−	1.67482i	−0.546577	−	0.837409i	$-0.684070\pi$
$659$		−	4.79318e8i		−	1.67482i	0.546577	−	0.837409i	$-0.315930\pi$
$660$	−2.75505e7	−	8.69619e6i	−0.0958291	−	0.0302480i
$661$	−8.22224e7			−0.284699			−0.142349	−	0.989816i	$-0.545466\pi$
$661$	−8.22224e7			−0.284699			−0.142349	+	0.989816i	$0.545466\pi$
$662$	2.31133e8	+	2.31133e8i	0.796687	+	0.796687i
$663$	−1.65908e7	+	1.65908e7i	−0.0569281	+	0.0569281i
$664$		−	1.26957e8i		−	0.433662i
$665$	6.52168e7	−	2.06614e8i	0.221766	−	0.702579i
$666$	−6.36680e8			−2.15525
$667$	−7.48276e6	−	7.48276e6i	−0.0252165	−	0.0252165i
$668$	−4.82407e7	+	4.82407e7i	−0.161839	+	0.161839i
$669$			5.65042e8i			1.88713i
$670$	−1.62325e8	−	3.12063e8i	−0.539710	−	1.03757i
$671$	3.09089e7			0.102309
$672$	7.05586e7	+	7.05586e7i	0.232510	+	0.232510i
$673$	7.15687e7	−	7.15687e7i	0.234789	−	0.234789i	−0.579899	−	0.814688i	$-0.696908\pi$
$673$	7.15687e7	−	7.15687e7i	0.234789	−	0.234789i	0.814688	+	0.579899i	$0.196908\pi$
$674$			3.15645e8i			1.03091i
$675$	5.05505e8	−	8.88057e7i	1.64367	−	0.288755i
$676$	−1.53182e8			−0.495869
$677$	2.59011e8	+	2.59011e8i	0.834740	+	0.834740i	0.988161	−	0.153421i	$-0.0490289\pi$
$677$	2.59011e8	+	2.59011e8i	0.834740	+	0.834740i	−0.153421	+	0.988161i	$0.549029\pi$
$678$	−1.10479e8	+	1.10479e8i	−0.354480	+	0.354480i
$679$		−	1.20430e8i		−	0.384701i
$680$	−5.06985e7	+	2.63717e7i	−0.161238	+	0.0838708i
$681$	−1.34614e8			−0.426234
$682$	−1.52478e7	−	1.52478e7i	−0.0480679	−	0.0480679i
$683$	1.24272e8	−	1.24272e8i	0.390041	−	0.390041i	−0.484661	−	0.874702i	$-0.661057\pi$
$683$	1.24272e8	−	1.24272e8i	0.390041	−	0.390041i	0.874702	+	0.484661i	$0.161057\pi$
$684$		−	2.14959e8i		−	0.671718i
$685$	5.13842e8	+	1.62192e8i	1.59867	+	0.504612i
$686$	2.05655e8			0.637039
$687$	−4.91512e8	−	4.91512e8i	−1.51588	−	1.51588i
$688$	7.02900e7	−	7.02900e7i	0.215838	−	0.215838i
$689$			4.72016e7i			0.144311i
$690$	−9.15158e7	+	2.89932e8i	−0.278579	+	0.882571i
$691$	−5.18169e8			−1.57050			−0.785249	−	0.619181i	$-0.787465\pi$
$691$	−5.18169e8			−1.57050			−0.785249	+	0.619181i	$0.787465\pi$
$692$	5.86562e7	+	5.86562e7i	0.177009	+	0.177009i
$693$	5.83409e7	−	5.83409e7i	0.175296	−	0.175296i
$694$		−	4.47546e7i		−	0.133893i
$695$	2.79774e8	+	5.37855e8i	0.833399	+	1.60218i
$696$	−9.64148e6			−0.0285967
$697$	1.79939e8	+	1.79939e8i	0.531407	+	0.531407i
$698$	5.96578e7	−	5.96578e7i	0.175429	−	0.175429i
$699$		−	2.93680e8i		−	0.859889i
$700$	3.20358e7	+	1.82356e8i	0.0933988	+	0.531651i
$701$	5.59711e8			1.62484			0.812419	−	0.583074i	$-0.198150\pi$
$701$	5.59711e8			1.62484			0.812419	+	0.583074i	$0.198150\pi$
$702$	2.62391e7	+	2.62391e7i	0.0758469	+	0.0758469i
$703$	−2.59580e8	+	2.59580e8i	−0.747146	+	0.747146i
$704$		−	5.08750e6i		−	0.0145810i
$705$	−7.27479e8	+	3.78410e8i	−2.07612	+	1.07993i
$706$	9.19331e7			0.261251
$707$	1.95426e8	+	1.95426e8i	0.552998	+	0.552998i
$708$	−2.41311e8	+	2.41311e8i	−0.679950	+	0.679950i
$709$			6.14417e8i			1.72395i	0.506951	+	0.861975i	$0.330772\pi$
$709$			6.14417e8i			1.72395i	−0.506951	+	0.861975i	$0.669228\pi$
$710$	−1.82980e8	−	5.77567e7i	−0.511244	−	0.161372i
$711$	−4.77656e8			−1.32894
$712$	2.47745e6	+	2.47745e6i	0.00686379	+	0.00686379i
$713$	−1.60463e8	+	1.60463e8i	−0.442697	+	0.442697i
$714$		−	2.46108e8i		−	0.676130i
$715$	1.16660e6	−	3.69593e6i	0.00319158	−	0.0101113i
$716$	3.25875e8			0.887794
$717$	−3.23368e8	−	3.23368e8i	−0.877282	−	0.877282i
$718$	−1.96216e7	+	1.96216e7i	−0.0530104	+	0.0530104i
$719$		−	5.02779e8i		−	1.35267i	−0.736596	−	0.676333i	$-0.763568\pi$
$719$		−	5.02779e8i		−	1.35267i	0.736596	−	0.676333i	$-0.236432\pi$
$720$	8.47686e7	+	1.62964e8i	0.227111	+	0.436612i
$721$	7.17258e6			0.0191368
$722$	1.00543e8	+	1.00543e8i	0.267141	+	0.267141i
$723$	6.52271e8	−	6.52271e8i	1.72589	−	1.72589i
$724$		−	1.74045e8i		−	0.458611i
$725$	−1.46478e7	−	1.02703e7i	−0.0384378	−	0.0269506i
$726$	4.59854e8			1.20174
$727$	−2.31315e8	−	2.31315e8i	−0.602005	−	0.602005i	0.338839	−	0.940844i	$-0.389966\pi$
$727$	−2.31315e8	−	2.31315e8i	−0.602005	−	0.602005i	−0.940844	+	0.338839i	$0.889966\pi$
$728$	−9.46551e6	+	9.46551e6i	−0.0245330	+	0.0245330i
$729$		−	4.22411e8i		−	1.09032i
$730$	1.19126e8	−	6.19655e7i	0.306224	−	0.159287i
$731$	−2.45171e8			−0.627649
$732$	−2.09557e8	−	2.09557e8i	−0.534281	−	0.534281i
$733$	3.51387e8	−	3.51387e8i	0.892224	−	0.892224i	−0.102508	−	0.994732i	$-0.532687\pi$
$733$	3.51387e8	−	3.51387e8i	0.892224	−	0.892224i	0.994732	+	0.102508i	$0.0326869\pi$
$734$			1.23911e6i			0.00313343i
$735$	−1.07974e8	−	3.40816e7i	−0.271931	−	0.0858338i
$736$	−5.35392e7			−0.134288
$737$	−5.46131e7	−	5.46131e7i	−0.136425	−	0.136425i
$738$	5.78393e8	−	5.78393e8i	1.43898	−	1.43898i
$739$			3.30414e8i			0.818701i	0.912377	+	0.409350i	$0.134245\pi$
$739$			3.30414e8i			0.818701i	−0.912377	+	0.409350i	$0.865755\pi$
$740$	9.44277e7	−	2.99157e8i	0.233026	−	0.738252i
$741$	4.34855e7			0.106878
$742$	−3.50094e8	−	3.50094e8i	−0.856984	−	0.856984i
$743$	−2.08570e8	+	2.08570e8i	−0.508494	+	0.508494i	−0.914064	−	0.405570i	$-0.867073\pi$
$743$	−2.08570e8	+	2.08570e8i	−0.508494	+	0.508494i	0.405570	+	0.914064i	$0.367073\pi$
$744$			2.06756e8i			0.502041i
$745$	9.91655e7	+	1.90642e8i	0.239824	+	0.461052i
$746$	−2.45198e8			−0.590609
$747$	7.11702e8	+	7.11702e8i	1.70741	+	1.70741i
$748$	−8.87257e6	+	8.87257e6i	−0.0212004	+	0.0212004i
$749$		−	1.09514e8i		−	0.260630i
$750$	−6.75693e7	+	5.09516e8i	−0.160164	+	1.20774i
$751$	−4.62858e8			−1.09277			−0.546384	−	0.837535i	$-0.683996\pi$
$751$	−4.62858e8			−1.09277			−0.546384	+	0.837535i	$0.683996\pi$
$752$	−1.02107e8	−	1.02107e8i	−0.240106	−	0.240106i
$753$	−8.71056e7	+	8.71056e7i	−0.204015	+	0.204015i
$754$		−	1.29342e6i		−	0.00301734i
$755$	2.48455e8	−	1.29238e8i	0.577307	−	0.300296i
$756$	−3.89231e8			−0.900828
$757$	−3.57918e7	−	3.57918e7i	−0.0825080	−	0.0825080i	0.664648	−	0.747156i	$-0.268581\pi$
$757$	−3.57918e7	−	3.57918e7i	−0.0825080	−	0.0825080i	−0.747156	+	0.664648i	$0.768581\pi$
$758$	1.49509e8	−	1.49509e8i	0.343290	−	0.343290i
$759$			6.67559e7i			0.152674i
$760$	1.01003e8	+	3.18811e7i	0.230088	+	0.0726261i
$761$	1.44943e8			0.328884			0.164442	−	0.986387i	$-0.447418\pi$
$761$	1.44943e8			0.328884			0.164442	+	0.986387i	$0.447418\pi$
$762$	3.52142e8	+	3.52142e8i	0.795890	+	0.795890i
$763$	−3.92999e8	+	3.92999e8i	−0.884744	+	0.884744i
$764$		−	1.74557e6i		−	0.00391433i
$765$	1.36373e8	−	4.32045e8i	0.304610	−	0.965039i
$766$	−1.67255e8			−0.372128
$767$	−3.23721e7	−	3.23721e7i	−0.0717439	−	0.0717439i
$768$	−3.44924e7	+	3.44924e7i	−0.0761448	+	0.0761448i
$769$		−	5.46294e8i		−	1.20129i	−0.799516	−	0.600644i	$-0.794911\pi$
$769$		−	5.46294e8i		−	1.20129i	0.799516	−	0.600644i	$-0.205089\pi$
$770$	1.87600e7	+	3.60654e7i	0.0410923	+	0.0789984i
$771$	−3.38210e8			−0.737943
$772$	−2.09553e8	−	2.09553e8i	−0.455452	−	0.455452i
$773$	−4.39326e8	+	4.39326e8i	−0.951149	+	0.951149i	−0.998861	−	0.0477120i	$-0.984807\pi$
$773$	−4.39326e8	+	4.39326e8i	−0.951149	+	0.951149i	0.0477120	+	0.998861i	$0.484807\pi$
$774$			7.88073e8i			1.69959i
$775$	−2.20240e8	+	3.14113e8i	−0.473141	+	0.674810i
$776$	5.88718e7			0.125986
$777$	9.55297e8	+	9.55297e8i	2.03646	+	2.03646i
$778$	1.01887e8	−	1.01887e8i	0.216361	−	0.216361i
$779$		−	4.71632e8i		−	0.997678i
$780$	−3.29672e7	+	1.71484e7i	−0.0694702	+	0.0361361i
$781$	−4.21304e7			−0.0884388
$782$	9.33720e7	+	9.33720e7i	0.195252	+	0.195252i
$783$	2.65932e7	−	2.65932e7i	0.0553969	−	0.0553969i
$784$		−	1.99386e7i		−	0.0413759i
$785$	2.51174e7	+	7.92819e6i	0.0519237	+	0.0163895i
$786$	1.25917e8			0.259308
$787$	4.05694e7	+	4.05694e7i	0.0832290	+	0.0832290i	0.747496	−	0.664267i	$-0.231256\pi$
$787$	4.05694e7	+	4.05694e7i	0.0832290	+	0.0832290i	−0.664267	+	0.747496i	$0.731256\pi$
$788$	2.83056e8	−	2.83056e8i	0.578486	−	0.578486i
$789$			2.72127e8i			0.554040i
$790$	7.08424e7	−	2.24437e8i	0.143685	−	0.455211i
$791$	2.19853e8			0.444225
$792$	2.85198e7	+	2.85198e7i	0.0574079	+	0.0574079i
$793$	2.81124e7	−	2.81124e7i	0.0563739	−	0.0563739i
$794$		−	7.15854e7i		−	0.143009i
$795$	−6.34256e8	−	1.21933e9i	−1.26230	−	2.42673i
$796$	−4.31596e6			−0.00855733
$797$	−2.42931e8	−	2.42931e8i	−0.479854	−	0.479854i	0.425231	−	0.905085i	$-0.360193\pi$
$797$	−2.42931e8	−	2.42931e8i	−0.479854	−	0.479854i	−0.905085	+	0.425231i	$0.860193\pi$
$798$	−3.22532e8	+	3.22532e8i	−0.634693	+	0.634693i
$799$			3.56149e8i			0.698219i
$800$	−8.91445e7	+	1.56606e7i	−0.174110	+	0.0305872i
$801$	−2.77765e7			−0.0540479
$802$	−3.80080e8	−	3.80080e8i	−0.736804	−	0.736804i
$803$	2.08479e7	−	2.08479e7i	0.0402638	−	0.0402638i
$804$			7.40536e8i			1.42488i
$805$	3.79540e8	−	1.97424e8i	0.727562	−	0.378453i
$806$	−2.77365e7			−0.0529721
$807$	2.53047e7	+	2.53047e7i	0.0481482	+	0.0481482i
$808$	−9.55335e7	+	9.55335e7i	−0.181101	+	0.181101i
$809$			1.42702e8i			0.269515i	0.990879	+	0.134758i	$0.0430256\pi$
$809$			1.42702e8i			0.269515i	−0.990879	+	0.134758i	$0.956974\pi$
$810$	−3.24942e8	−	1.02567e8i	−0.611436	−	0.192997i
$811$	8.49716e8			1.59298			0.796491	−	0.604650i	$-0.206687\pi$
$811$	8.49716e8			1.59298			0.796491	+	0.604650i	$0.206687\pi$
$812$	9.59325e6	+	9.59325e6i	0.0179183	+	0.0179183i
$813$	−1.00663e8	+	1.00663e8i	−0.187326	+	0.187326i
$814$		−	6.88799e7i		−	0.127708i
$815$	3.74251e7	−	1.18567e8i	0.0691337	−	0.219023i
$816$	1.20309e8			0.221426
$817$	3.21304e8	+	3.21304e8i	0.589183	+	0.589183i
$818$	−5.15429e8	+	5.15429e8i	−0.941693	+	0.941693i
$819$		−	1.06125e8i		−	0.193181i
$820$	1.85987e8	+	3.57553e8i	0.337319	+	0.648483i
$821$	−7.22390e8			−1.30540			−0.652698	−	0.757618i	$-0.726363\pi$
$821$	−7.22390e8			−1.30540			−0.652698	+	0.757618i	$0.726363\pi$
$822$	−8.02126e8	−	8.02126e8i	−1.44420	−	1.44420i
$823$	5.66866e8	−	5.66866e8i	1.01691	−	1.01691i	0.0170518	−	0.999855i	$-0.494572\pi$
$823$	5.66866e8	−	5.66866e8i	1.01691	−	1.01691i	0.999855	−	0.0170518i	$-0.00542801\pi$
$824$			3.50630e6i			0.00626712i
$825$	1.95267e7	+	1.11151e8i	0.0347749	+	0.197948i
$826$	4.80207e8			0.852096
$827$	−4.65387e8	−	4.65387e8i	−0.822806	−	0.822806i	0.163704	−	0.986510i	$-0.447656\pi$
$827$	−4.65387e8	−	4.65387e8i	−0.822806	−	0.822806i	−0.986510	+	0.163704i	$0.947656\pi$
$828$	3.00133e8	−	3.00133e8i	0.528717	−	0.528717i
$829$			1.75143e8i			0.307418i	0.988116	+	0.153709i	$0.0491219\pi$
$829$			1.75143e8i			0.307418i	−0.988116	+	0.153709i	$0.950878\pi$
$830$	−4.39963e8	+	2.28854e8i	−0.769452	+	0.400243i
$831$	1.71413e9			2.98704
$832$	−4.62720e6	−	4.62720e6i	−0.00803430	−	0.00803430i
$833$	−3.47729e7	+	3.47729e7i	−0.0601597	+	0.0601597i
$834$		−	1.27635e9i		−	2.20024i
$835$	2.54135e8	+	8.02167e7i	0.436522	+	0.137786i
$836$	2.32556e7			0.0398023
$837$	−5.70276e8	−	5.70276e8i	−0.972542	−	0.972542i
$838$	−1.92877e8	+	1.92877e8i	−0.327755	+	0.327755i
$839$			2.61932e8i			0.443509i	0.975103	+	0.221754i	$0.0711783\pi$
$839$			2.61932e8i			0.443509i	−0.975103	+	0.221754i	$0.928822\pi$
$840$	1.17328e8	−	3.71707e8i	0.197953	−	0.627138i
$841$	5.93512e8			0.997796
$842$	4.09438e8	+	4.09438e8i	0.685886	+	0.685886i
$843$	−2.25457e8	+	2.25457e8i	−0.376340	+	0.376340i
$844$			1.46287e8i			0.243321i
$845$	2.76127e8	+	5.30844e8i	0.457656	+	0.879826i
$846$	1.14480e9			1.89068
$847$	−4.57554e8	−	4.57554e8i	−0.752995	−	0.752995i
$848$	1.71143e8	−	1.71143e8i	0.280654	−	0.280654i
$849$		−	6.36632e8i		−	1.04032i
$850$	1.82780e8	+	1.28156e8i	0.297626	+	0.208680i
$851$	−7.24870e8			−1.17617
$852$	2.85638e8	+	2.85638e8i	0.461846	+	0.461846i
$853$	−1.49027e8	+	1.49027e8i	−0.240114	+	0.240114i	−0.816897	−	0.576783i	$-0.804308\pi$
$853$	−1.49027e8	+	1.49027e8i	−0.240114	+	0.240114i	0.576783	+	0.816897i	$0.304308\pi$
$854$			4.17018e8i			0.669547i
$855$	−7.44930e8	+	3.87488e8i	−1.19184	+	0.619954i
$856$	5.35357e7			0.0853537
$857$	−7.23056e8	−	7.23056e8i	−1.14876	−	1.14876i	−0.986797	−	0.161964i	$-0.948217\pi$
$857$	−7.23056e8	−	7.23056e8i	−1.14876	−	1.14876i	−0.161964	−	0.986797i	$-0.551783\pi$
$858$	−5.76948e6	+	5.76948e6i	−0.00913428	+	0.00913428i
$859$			7.65128e8i			1.20713i	0.797313	+	0.603565i	$0.206254\pi$
$859$			7.65128e8i			1.20713i	−0.797313	+	0.603565i	$0.793746\pi$
$860$	−3.70293e8	−	1.16881e8i	−0.582170	−	0.183759i
$861$	−1.73568e9			−2.71932
$862$	5.55574e8	+	5.55574e8i	0.867401	+	0.867401i
$863$	−6.06587e8	+	6.06587e8i	−0.943758	+	0.943758i	−0.998501	−	0.0547422i	$-0.982566\pi$
$863$	−6.06587e8	+	6.06587e8i	−0.943758	+	0.943758i	0.0547422	+	0.998501i	$0.482566\pi$
$864$		−	1.90275e8i		−	0.295012i
$865$	9.75359e7	−	3.09005e8i	0.150701	−	0.477438i
$866$	−6.51460e8			−1.00308
$867$	5.84176e8	+	5.84176e8i	0.896367	+	0.896367i
$868$	2.05721e8	−	2.05721e8i	0.314572	−	0.314572i
$869$		−	5.16757e7i		−	0.0787458i
$870$	1.73799e7	+	3.34121e7i	0.0263930	+	0.0507395i
$871$	−9.93438e7			−0.150344
$872$	−1.92117e8	−	1.92117e8i	−0.289745	−	0.289745i
$873$	−3.30027e8	+	3.30027e8i	−0.496029	+	0.496029i
$874$		−	2.44734e8i		−	0.366573i
$875$	5.74199e8	−	4.39736e8i	0.857113	−	0.656399i
$876$	−2.82690e8			−0.420532
$877$	−1.13289e8	−	1.13289e8i	−0.167953	−	0.167953i	0.618126	−	0.786079i	$-0.287892\pi$
$877$	−1.13289e8	−	1.13289e8i	−0.167953	−	0.167953i	−0.786079	+	0.618126i	$0.787892\pi$
$878$	4.92814e8	−	4.92814e8i	0.728115	−	0.728115i
$879$			2.04109e9i			3.00535i
$880$	−1.76305e7	+	9.17079e6i	−0.0258712	+	0.0134573i
$881$	1.29336e9			1.89144			0.945718	−	0.324989i	$-0.105361\pi$
$881$	1.29336e9			1.89144			0.945718	+	0.324989i	$0.105361\pi$
$882$	1.11773e8	+	1.11773e8i	0.162904	+	0.162904i
$883$	−3.61691e8	+	3.61691e8i	−0.525358	+	0.525358i	−0.919185	−	0.393827i	$-0.871151\pi$
$883$	−3.61691e8	+	3.61691e8i	−0.525358	+	0.525358i	0.393827	+	0.919185i	$0.371151\pi$
$884$			1.61396e7i			0.0233634i
$885$	1.27124e9	+	4.01261e8i	1.83400	+	0.578892i
$886$	−6.40028e7			−0.0920234
$887$	3.90226e8	+	3.90226e8i	0.559172	+	0.559172i	0.929072	−	0.369899i	$-0.120608\pi$
$887$	3.90226e8	+	3.90226e8i	0.559172	+	0.559172i	−0.369899	+	0.929072i	$0.620608\pi$
$888$	−4.66995e8	+	4.66995e8i	−0.666920	+	0.666920i
$889$		−	7.00761e8i		−	0.997390i
$890$	4.11960e6	−	1.30513e7i	0.00584366	−	0.0185134i
$891$	−7.48168e7			−0.105771
$892$	2.74838e8	+	2.74838e8i	0.387242	+	0.387242i
$893$	4.66745e8	−	4.66745e8i	0.655428	−	0.655428i
$894$		−	4.52399e8i		−	0.633154i
$895$	−5.87427e8	−	1.12931e9i	−0.819379	−	1.57522i
$896$	6.86398e7			0.0954227
$897$	6.07161e7	+	6.07161e7i	0.0841253	+	0.0841253i
$898$	−4.29653e8	+	4.29653e8i	−0.593320	+	0.593320i
$899$			2.81108e7i			0.0386896i
$900$	4.11941e8	−	5.87524e8i	0.565076	−	0.805931i
$901$	−5.96944e8			−0.816130
$902$	6.25741e7	+	6.25741e7i	0.0852658	+	0.0852658i
$903$	1.18245e9	−	1.18245e9i	1.60591	−	1.60591i
$904$			1.07475e8i			0.145479i
$905$	−6.03143e8	+	3.13735e8i	−0.813720	+	0.423270i
$906$	−5.89592e8			−0.792806
$907$	7.36666e8	+	7.36666e8i	0.987299	+	0.987299i	0.999920	−	0.0126210i	$-0.00401749\pi$
$907$	7.36666e8	+	7.36666e8i	0.987299	+	0.987299i	−0.0126210	+	0.999920i	$0.504017\pi$
$908$	−6.54765e7	+	6.54765e7i	−0.0874637	+	0.0874637i
$909$		−	1.07110e9i		−	1.42606i
$910$	4.98650e7	+	1.57396e7i	0.0661716	+	0.0208867i
$911$	−2.02041e8			−0.267230			−0.133615	−	0.991033i	$-0.542659\pi$
$911$	−2.02041e8			−0.267230			−0.133615	+	0.991033i	$0.542659\pi$
$912$	−1.57669e8	−	1.57669e8i	−0.207856	−	0.207856i
$913$	−7.69963e7	+	7.69963e7i	−0.101171	+	0.101171i
$914$		−	3.71036e8i		−	0.485934i
$915$	−3.48461e8	+	1.10396e9i	−0.454873	+	1.44109i
$916$	−4.78146e8			−0.622120
$917$	−1.25287e8	−	1.25287e8i	−0.162479	−	0.162479i
$918$	−3.31838e8	+	3.31838e8i	−0.428942	+	0.428942i
$919$		−	1.34043e9i		−	1.72702i	−0.504328	−	0.863512i	$-0.668260\pi$
$919$		−	1.34043e9i		−	1.72702i	0.504328	−	0.863512i	$-0.331740\pi$
$920$	9.65104e7	+	1.85538e8i	0.123940	+	0.238269i
$921$	−5.50448e8			−0.704591
$922$	3.27251e8	+	3.27251e8i	0.417530	+	0.417530i
$923$	−3.83186e7	+	3.83186e7i	−0.0487310	+	0.0487310i
$924$		−	8.55843e7i		−	0.108487i
$925$	−1.20693e9	+	2.12030e8i	−1.52496	+	0.267900i
$926$	−3.59790e8			−0.453123
$927$	−1.96559e7	−	1.96559e7i	−0.0246748	−	0.0246748i
$928$	−4.68964e6	+	4.68964e6i	−0.00586808	+	0.00586808i
$929$		−	5.54786e8i		−	0.691956i	−0.938243	−	0.345978i	$-0.887547\pi$
$929$		−	5.54786e8i		−	0.691956i	0.938243	−	0.345978i	$-0.112453\pi$
$930$	7.16503e8	−	3.72701e8i	0.890777	−	0.463352i
$931$	9.11420e7			0.112946
$932$	−1.42847e8	−	1.42847e8i	−0.176450	−	0.176450i
$933$	1.26811e9	−	1.26811e9i	1.56139	−	1.56139i
$934$			2.91581e8i			0.357864i
$935$	4.67413e7	+	1.47537e7i	0.0571829	+	0.0180495i
$936$	5.18789e7			0.0632650
$937$	−9.35798e7	−	9.35798e7i	−0.113753	−	0.113753i	0.647939	−	0.761692i	$-0.275631\pi$
$937$	−9.35798e7	−	9.35798e7i	−0.113753	−	0.113753i	−0.761692	+	0.647939i	$0.775631\pi$
$938$	7.36832e8	−	7.36832e8i	0.892812	−	0.892812i
$939$		−	2.64552e8i		−	0.319532i
$940$	−1.69788e8	+	5.37908e8i	−0.204420	+	0.647626i
$941$	1.32412e9			1.58912			0.794560	−	0.607185i	$-0.207701\pi$
$941$	1.32412e9			1.58912			0.794560	+	0.607185i	$0.207701\pi$
$942$	−3.92091e7	−	3.92091e7i	−0.0469066	−	0.0469066i
$943$	6.58509e8	−	6.58509e8i	0.785284	−	0.785284i
$944$			2.34748e8i			0.279053i
$945$	7.01632e8	+	1.34886e9i	0.831408	+	1.59835i
$946$	−8.52586e7			−0.100708
$947$	−1.97318e8	−	1.97318e8i	−0.232336	−	0.232336i	0.581331	−	0.813667i	$-0.302532\pi$
$947$	−1.97318e8	−	1.97318e8i	−0.232336	−	0.232336i	−0.813667	+	0.581331i	$0.802532\pi$
$948$	−3.50353e8	+	3.50353e8i	−0.411227	+	0.411227i
$949$		−	3.79232e7i		−	0.0443718i
$950$	−7.15867e7	−	4.07490e8i	−0.0834952	−	0.475277i
$951$	−1.08863e9			−1.26572
$952$	−1.19707e8	−	1.19707e8i	−0.138743	−	0.138743i
$953$	2.45239e8	−	2.45239e8i	0.283342	−	0.283342i	−0.551098	−	0.834440i	$-0.685791\pi$
$953$	2.45239e8	−	2.45239e8i	0.283342	−	0.283342i	0.834440	+	0.551098i	$0.185791\pi$
$954$			1.91881e9i			2.20997i
$955$	−6.04920e6	+	3.14659e6i	−0.00694525	+	0.00361268i
$956$	−3.14574e8			−0.360039
$957$	5.84734e6	+	5.84734e6i	0.00667148	+	0.00667148i
$958$	8.57028e7	−	8.57028e7i	0.0974762	−	0.0974762i
$959$			1.59623e9i			1.80983i
$960$	1.81708e8	+	5.73554e7i	0.205382	+	0.0648277i
$961$	−2.84684e8			−0.320769
$962$	−6.26479e7	−	6.26479e7i	−0.0703690	−	0.0703690i
$963$	−3.00114e8	+	3.00114e8i	−0.336053	+	0.336053i
$964$		−	6.34533e8i		−	0.708310i
$965$	−3.48454e8	+	1.10394e9i	−0.387761	+	1.22847i
$966$	−9.00661e8			−0.999148
$967$	1.51940e8	+	1.51940e8i	0.168033	+	0.168033i	0.786114	−	0.618082i	$-0.212090\pi$
$967$	1.51940e8	+	1.51940e8i	0.168033	+	0.168033i	−0.618082	+	0.786114i	$0.712090\pi$
$968$	2.23674e8	−	2.23674e8i	0.246598	−	0.246598i
$969$			5.49948e8i			0.604436i
$970$	−1.06123e8	−	2.04017e8i	−0.116277	−	0.223538i
$971$	5.44968e8			0.595269			0.297635	−	0.954680i	$-0.403802\pi$
$971$	5.44968e8			0.595269			0.297635	+	0.954680i	$0.403802\pi$
$972$	−3.45907e7	−	3.45907e7i	−0.0376669	−	0.0376669i
$973$	−1.26996e9	+	1.26996e9i	−1.37864	+	1.37864i
$974$			1.75975e8i			0.190447i
$975$	1.18854e8	+	8.33344e7i	0.128233	+	0.0899105i
$976$	−2.03859e8			−0.219270
$977$	−1.83840e8	−	1.83840e8i	−0.197132	−	0.197132i	0.601638	−	0.798769i	$-0.294515\pi$
$977$	−1.83840e8	−	1.83840e8i	−0.197132	−	0.197132i	−0.798769	+	0.601638i	$0.794515\pi$
$978$	−1.85087e8	+	1.85087e8i	−0.197860	+	0.197860i
$979$		−	3.00503e6i		−	0.00320258i
$980$	−6.90964e7	+	3.59417e7i	−0.0734138	+	0.0381874i
$981$	2.15396e9			2.28156
$982$	5.10345e8	+	5.10345e8i	0.538926	+	0.538926i
$983$	7.53744e8	−	7.53744e8i	0.793530	−	0.793530i	−0.188536	−	0.982066i	$-0.560374\pi$
$983$	7.53744e8	−	7.53744e8i	0.793530	−	0.793530i	0.982066	+	0.188536i	$0.0603743\pi$
$984$		−	8.48484e8i		−	0.890551i
$985$	−1.49116e9	−	4.70677e8i	−1.56032	−	0.492509i
$986$	1.63574e7			0.0170641
$987$	−1.71770e9	−	1.71770e9i	−1.78647	−	1.78647i
$988$	2.11515e7	−	2.11515e7i	0.0219316	−	0.0219316i
$989$			8.97233e8i			0.927506i
$990$	4.74239e7	−	1.50244e8i	0.0488756	−	0.154843i
$991$	4.47089e8			0.459381			0.229690	−	0.973264i	$-0.426229\pi$
$991$	4.47089e8			0.459381			0.229690	+	0.973264i	$0.426229\pi$
$992$	1.00567e8	+	1.00567e8i	0.103019	+	0.103019i
$993$	−1.90075e9	+	1.90075e9i	−1.94123	+	1.94123i
$994$		−	5.68418e8i		−	0.578773i
$995$	7.78001e6	+	1.49568e7i	0.00789789	+	0.0151834i
$996$	1.04405e9			1.05668
$997$	5.22406e8	+	5.22406e8i	0.527136	+	0.527136i	0.919717	−	0.392581i	$-0.128418\pi$
$997$	5.22406e8	+	5.22406e8i	0.527136	+	0.527136i	−0.392581	+	0.919717i	$0.628418\pi$
$998$	4.77078e8	−	4.77078e8i	0.479952	−	0.479952i
$999$		−	2.57614e9i		−	2.58389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.7.c.b.7.1	yes	4
3.2	odd	2		90.7.g.b.37.1		4
4.3	odd	2		80.7.p.c.17.2		4
5.2	odd	4		50.7.c.d.43.2		4
5.3	odd	4	inner	10.7.c.b.3.1	✓	4
5.4	even	2		50.7.c.d.7.2		4
15.2	even	4		450.7.g.m.343.1		4
15.8	even	4		90.7.g.b.73.1		4
15.14	odd	2		450.7.g.m.307.1		4
20.3	even	4		80.7.p.c.33.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.7.c.b.3.1	✓	4	5.3	odd	4	inner
10.7.c.b.7.1	yes	4	1.1	even	1	trivial
50.7.c.d.7.2		4	5.4	even	2
50.7.c.d.43.2		4	5.2	odd	4
80.7.p.c.17.2		4	4.3	odd	2
80.7.p.c.33.2		4	20.3	even	4
90.7.g.b.37.1		4	3.2	odd	2
90.7.g.b.73.1		4	15.8	even	4
450.7.g.m.307.1		4	15.14	odd	2
450.7.g.m.343.1		4	15.2	even	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 4.00000i) q^{2} +(-32.8945 + 32.8945i) q^{3} +32.0000i q^{4} +(110.895 - 57.6836i) q^{5} -263.156 q^{6} +(261.840 + 261.840i) q^{7} +(-128.000 + 128.000i) q^{8} -1435.10i q^{9} +O(q^{10})\)	\(q+(4.00000 + 4.00000i) q^{2} +(-32.8945 + 32.8945i) q^{3} +32.0000i q^{4} +(110.895 - 57.6836i) q^{5} -263.156 q^{6} +(261.840 + 261.840i) q^{7} +(-128.000 + 128.000i) q^{8} -1435.10i q^{9} +(674.313 + 212.844i) q^{10} +155.258 q^{11} +(-1052.63 - 1052.63i) q^{12} +(141.211 - 141.211i) q^{13} +2094.72i q^{14} +(-1750.35 + 5545.30i) q^{15} -1024.00 q^{16} +(1785.85 + 1785.85i) q^{17} +(5740.41 - 5740.41i) q^{18} -4680.83i q^{19} +(1845.88 + 3548.63i) q^{20} -17226.2 q^{21} +(621.032 + 621.032i) q^{22} +(6535.54 - 6535.54i) q^{23} -8421.00i q^{24} +(8970.20 - 12793.6i) q^{25} +1129.69 q^{26} +(23226.9 + 23226.9i) q^{27} +(-8378.88 + 8378.88i) q^{28} -1144.93i q^{29} +(-29182.6 + 15179.8i) q^{30} -24552.4 q^{31} +(-4096.00 - 4096.00i) q^{32} +(-5107.14 + 5107.14i) q^{33} +14286.8i q^{34} +(44140.5 + 13932.7i) q^{35} +45923.3 q^{36} +(-55456.0 - 55456.0i) q^{37} +(18723.3 - 18723.3i) q^{38} +9290.14i q^{39} +(-6811.00 + 21578.0i) q^{40} +100758. q^{41} +(-68904.8 - 68904.8i) q^{42} +(-68642.6 + 68642.6i) q^{43} +4968.26i q^{44} +(-82781.9 - 159145. i) q^{45} +52284.3 q^{46} +(99714.1 + 99714.1i) q^{47} +(33684.0 - 33684.0i) q^{48} +19471.3i q^{49} +(87055.2 - 15293.6i) q^{50} -117490. q^{51} +(4518.75 + 4518.75i) q^{52} +(-167132. + 167132. i) q^{53} +185815. i q^{54} +(17217.3 - 8955.85i) q^{55} -67031.0 q^{56} +(153974. + 153974. i) q^{57} +(4579.73 - 4579.73i) q^{58} -229247. i q^{59} +(-177450. - 56011.2i) q^{60} +199081. q^{61} +(-98209.6 - 98209.6i) q^{62} +(375767. - 375767. i) q^{63} -32768.0i q^{64} +(7513.96 - 23805.1i) q^{65} -40857.1 q^{66} +(-351757. - 351757. i) q^{67} +(-57147.2 + 57147.2i) q^{68} +429967. i q^{69} +(120831. + 232293. i) q^{70} -271358. q^{71} +(183693. + 183693. i) q^{72} +(134279. - 134279. i) q^{73} -443648. i q^{74} +(125769. + 715910. i) q^{75} +149787. q^{76} +(40652.8 + 40652.8i) q^{77} +(-37160.5 + 37160.5i) q^{78} -332838. i q^{79} +(-113556. + 59068.0i) q^{80} -481887. q^{81} +(403033. + 403033. i) q^{82} +(-495925. + 495925. i) q^{83} -551239. i q^{84} +(301056. + 95026.8i) q^{85} -549141. q^{86} +(37662.0 + 37662.0i) q^{87} +(-19873.0 + 19873.0i) q^{88} -19355.0i q^{89} +(305452. - 967707. i) q^{90} +73949.3 q^{91} +(209137. + 209137. i) q^{92} +(807640. - 807640. i) q^{93} +797713. i q^{94} +(-270007. - 519078. i) q^{95} +269472. q^{96} +(-229968. - 229968. i) q^{97} +(-77885.3 + 77885.3i) q^{98} -222811. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 18 q^{3} + 330 q^{5} - 144 q^{6} - 202 q^{7} - 512 q^{8}+O(q^{10}) \) 4 * q + 16 * q^2 - 18 * q^3 + 330 * q^5 - 144 * q^6 - 202 * q^7 - 512 * q^8	\( 4 q + 16 q^{2} - 18 q^{3} + 330 q^{5} - 144 q^{6} - 202 q^{7} - 512 q^{8} + 880 q^{10} - 2332 q^{11} - 576 q^{12} + 792 q^{13} + 4470 q^{15} - 4096 q^{16} + 12368 q^{17} + 14784 q^{18} - 3520 q^{20} - 69132 q^{21} - 9328 q^{22} + 35342 q^{23} - 1600 q^{25} + 6336 q^{26} + 61560 q^{27} + 6464 q^{28} - 37680 q^{30} - 18932 q^{31} - 16384 q^{32} - 73356 q^{33} + 130790 q^{35} + 118272 q^{36} - 67812 q^{37} + 44000 q^{38} - 56320 q^{40} + 110228 q^{41} - 276528 q^{42} - 293538 q^{43} - 72510 q^{45} + 282736 q^{46} + 195438 q^{47} + 18432 q^{48} - 1600 q^{50} + 185388 q^{51} + 25344 q^{52} - 121988 q^{53} - 108540 q^{55} + 51712 q^{56} + 268800 q^{57} + 229120 q^{58} - 444480 q^{60} - 243372 q^{61} - 75728 q^{62} + 451902 q^{63} + 100020 q^{65} - 586848 q^{66} - 773602 q^{67} - 395776 q^{68} + 895840 q^{70} - 1046132 q^{71} + 473088 q^{72} + 922372 q^{73} + 367350 q^{75} + 352000 q^{76} + 1040116 q^{77} + 23088 q^{78} - 337920 q^{80} + 360144 q^{81} + 440912 q^{82} - 1238058 q^{83} + 86840 q^{85} - 2348304 q^{86} - 1238640 q^{87} + 298496 q^{88} + 1161840 q^{90} - 221892 q^{91} + 1130944 q^{92} + 2336244 q^{93} - 355400 q^{95} + 147456 q^{96} - 1937532 q^{97} - 1321024 q^{98}+O(q^{100}) \) 4 * q + 16 * q^2 - 18 * q^3 + 330 * q^5 - 144 * q^6 - 202 * q^7 - 512 * q^8 + 880 * q^10 - 2332 * q^11 - 576 * q^12 + 792 * q^13 + 4470 * q^15 - 4096 * q^16 + 12368 * q^17 + 14784 * q^18 - 3520 * q^20 - 69132 * q^21 - 9328 * q^22 + 35342 * q^23 - 1600 * q^25 + 6336 * q^26 + 61560 * q^27 + 6464 * q^28 - 37680 * q^30 - 18932 * q^31 - 16384 * q^32 - 73356 * q^33 + 130790 * q^35 + 118272 * q^36 - 67812 * q^37 + 44000 * q^38 - 56320 * q^40 + 110228 * q^41 - 276528 * q^42 - 293538 * q^43 - 72510 * q^45 + 282736 * q^46 + 195438 * q^47 + 18432 * q^48 - 1600 * q^50 + 185388 * q^51 + 25344 * q^52 - 121988 * q^53 - 108540 * q^55 + 51712 * q^56 + 268800 * q^57 + 229120 * q^58 - 444480 * q^60 - 243372 * q^61 - 75728 * q^62 + 451902 * q^63 + 100020 * q^65 - 586848 * q^66 - 773602 * q^67 - 395776 * q^68 + 895840 * q^70 - 1046132 * q^71 + 473088 * q^72 + 922372 * q^73 + 367350 * q^75 + 352000 * q^76 + 1040116 * q^77 + 23088 * q^78 - 337920 * q^80 + 360144 * q^81 + 440912 * q^82 - 1238058 * q^83 + 86840 * q^85 - 2348304 * q^86 - 1238640 * q^87 + 298496 * q^88 + 1161840 * q^90 - 221892 * q^91 + 1130944 * q^92 + 2336244 * q^93 - 355400 * q^95 + 147456 * q^96 - 1937532 * q^97 - 1321024 * q^98

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