LMFDB - Embedded newform 20.9.b.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.14757220122$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{58}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.8
Root			$2.32463 - 7.96873i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41320 + 15.9375i) q^{2} -39.9624i q^{3} +(-252.006 - 45.0455i) q^{4} +279.508 q^{5} +(636.899 + 56.4746i) q^{6} -2633.20i q^{7} +(1074.04 - 3952.68i) q^{8} +4964.01 q^{9} +O(q^{10})$	\(q+(-1.41320 + 15.9375i) q^{2} -39.9624i q^{3} +(-252.006 - 45.0455i) q^{4} +279.508 q^{5} +(636.899 + 56.4746i) q^{6} -2633.20i q^{7} +(1074.04 - 3952.68i) q^{8} +4964.01 q^{9} +(-395.000 + 4454.66i) q^{10} +2484.31i q^{11} +(-1800.13 + 10070.7i) q^{12} +41319.8 q^{13} +(41966.5 + 3721.22i) q^{14} -11169.8i q^{15} +(61477.8 + 22703.5i) q^{16} -48625.0 q^{17} +(-7015.11 + 79113.7i) q^{18} -241516. i q^{19} +(-70437.8 - 12590.6i) q^{20} -105229. q^{21} +(-39593.7 - 3510.82i) q^{22} -57735.4i q^{23} +(-157958. - 42921.4i) q^{24} +78125.0 q^{25} +(-58392.9 + 658533. i) q^{26} -460567. i q^{27} +(-118614. + 663581. i) q^{28} -729286. q^{29} +(178019. + 15785.1i) q^{30} -134865. i q^{31} +(-448716. + 947716. i) q^{32} +99279.1 q^{33} +(68716.6 - 774960. i) q^{34} -736001. i q^{35} +(-1.25096e6 - 223606. i) q^{36} +1.68171e6 q^{37} +(3.84915e6 + 341309. i) q^{38} -1.65124e6i q^{39} +(300205. - 1.10481e6i) q^{40} -761790. q^{41} +(148709. - 1.67708e6i) q^{42} +2.54364e6i q^{43} +(111907. - 626061. i) q^{44} +1.38748e6 q^{45} +(920156. + 81591.4i) q^{46} +5.65990e6i q^{47} +(907284. - 2.45680e6i) q^{48} -1.16893e6 q^{49} +(-110406. + 1.24511e6i) q^{50} +1.94317e6i q^{51} +(-1.04128e7 - 1.86127e6i) q^{52} +1.14302e7 q^{53} +(7.34027e6 + 650871. i) q^{54} +694387. i q^{55} +(-1.04082e7 - 2.82817e6i) q^{56} -9.65155e6 q^{57} +(1.03062e6 - 1.16230e7i) q^{58} +2.12902e7i q^{59} +(-503150. + 2.81486e6i) q^{60} -2.63701e7 q^{61} +(2.14940e6 + 190590. i) q^{62} -1.30712e7i q^{63} +(-1.44701e7 - 8.49070e6i) q^{64} +1.15492e7 q^{65} +(-140301. + 1.58226e6i) q^{66} +1.53982e6i q^{67} +(1.22538e7 + 2.19034e6i) q^{68} -2.30724e6 q^{69} +(1.17300e7 + 1.04011e6i) q^{70} -2.06597e7i q^{71} +(5.33157e6 - 1.96211e7i) q^{72} +2.51296e7 q^{73} +(-2.37658e6 + 2.68022e7i) q^{74} -3.12206e6i q^{75} +(-1.08792e7 + 6.08634e7i) q^{76} +6.54169e6 q^{77} +(2.63165e7 + 2.33352e6i) q^{78} -1.95344e7i q^{79} +(1.71836e7 + 6.34581e6i) q^{80} +1.41635e7 q^{81} +(1.07656e6 - 1.21410e7i) q^{82} -2.37076e7i q^{83} +(2.65183e7 + 4.74009e6i) q^{84} -1.35911e7 q^{85} +(-4.05392e7 - 3.59466e6i) q^{86} +2.91440e7i q^{87} +(9.81968e6 + 2.66826e6i) q^{88} +3.86749e7 q^{89} +(-1.96078e6 + 2.21130e7i) q^{90} -1.08803e8i q^{91} +(-2.60072e6 + 1.45497e7i) q^{92} -5.38951e6 q^{93} +(-9.02045e7 - 7.99855e6i) q^{94} -6.75057e7i q^{95} +(3.78730e7 + 1.79317e7i) q^{96} -9.46443e7 q^{97} +(1.65192e6 - 1.86298e7i) q^{98} +1.23322e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.41320	+	15.9375i	−0.0883247	+	0.996092i
$2$	−1.41320	+	15.9375i	−0.0883247	+	0.996092i
$3$		−	39.9624i		−	0.493363i	−0.969097	−	0.246681i	$-0.920660\pi$
$3$		−	39.9624i		−	0.493363i	0.969097	−	0.246681i	$-0.0793401\pi$
$4$	−252.006	−	45.0455i	−0.984397	−	0.175959i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$	636.899	+	56.4746i	0.491435	+	0.0435761i
$7$		−	2633.20i		−	1.09671i	−0.836246	−	0.548354i	$-0.815255\pi$
$7$		−	2633.20i		−	1.09671i	0.836246	−	0.548354i	$-0.184745\pi$
$8$	1074.04	−	3952.68i	0.262218	−	0.965009i
$9$	4964.01			0.756593
$10$	−395.000	+	4454.66i	−0.0395000	+	0.445466i
$11$			2484.31i			0.169682i	0.996395	+	0.0848410i	$0.0270382\pi$
$11$			2484.31i			0.169682i	−0.996395	+	0.0848410i	$0.972962\pi$
$12$	−1800.13	+	10070.7i	−0.0868116	+	0.485665i
$13$	41319.8			1.44672			0.723360	−	0.690471i	$-0.242597\pi$
$13$	41319.8			1.44672			0.723360	+	0.690471i	$0.242597\pi$
$14$	41966.5	+	3721.22i	1.09242	+	0.0968665i
$15$		−	11169.8i		−	0.220639i
$16$	61477.8	+	22703.5i	0.938077	+	0.346427i
$17$	−48625.0			−0.582189			−0.291095	−	0.956694i	$-0.594019\pi$
$17$	−48625.0			−0.582189			−0.291095	+	0.956694i	$0.594019\pi$
$18$	−7015.11	+	79113.7i	−0.0668259	+	0.753636i
$19$		−	241516.i		−	1.85324i	−0.376002	−	0.926619i	$-0.622701\pi$
$19$		−	241516.i		−	1.85324i	0.376002	−	0.926619i	$-0.377299\pi$
$20$	−70437.8	−	12590.6i	−0.440236	−	0.0786913i
$21$	−105229.			−0.541075
$22$	−39593.7	−	3510.82i	−0.169019	−	0.0149871i
$23$		−	57735.4i		−	0.206315i	−0.994665	−	0.103158i	$-0.967105\pi$
$23$		−	57735.4i		−	0.206315i	0.994665	−	0.103158i	$-0.0328946\pi$
$24$	−157958.	−	42921.4i	−0.476099	−	0.129369i
$25$	78125.0			0.200000
$26$	−58392.9	+	658533.i	−0.127781	+	1.44107i
$27$		−	460567.i		−	0.866638i
$28$	−118614.	+	663581.i	−0.192976	+	1.07960i
$29$	−729286.			−1.03111			−0.515556	−	0.856856i	$-0.672415\pi$
$29$	−729286.			−1.03111			−0.515556	+	0.856856i	$0.672415\pi$
$30$	178019.	+	15785.1i	0.219776	+	0.0194878i
$31$		−	134865.i		−	0.146033i	−0.997331	−	0.0730165i	$-0.976737\pi$
$31$		−	134865.i		−	0.146033i	0.997331	−	0.0730165i	$-0.0232626\pi$
$32$	−448716.	+	947716.i	−0.427929	+	0.903813i
$33$	99279.1			0.0837147
$34$	68716.6	−	774960.i	0.0514217	−	0.579914i
$35$		−	736001.i		−	0.490463i
$36$	−1.25096e6	−	223606.i	−0.744788	−	0.133129i
$37$	1.68171e6			0.897313			0.448656	−	0.893704i	$-0.351903\pi$
$37$	1.68171e6			0.897313			0.448656	+	0.893704i	$0.351903\pi$
$38$	3.84915e6	+	341309.i	1.84599	+	0.163687i
$39$		−	1.65124e6i		−	0.713758i
$40$	300205.	−	1.10481e6i	0.117267	−	0.431565i
$41$	−761790.			−0.269588			−0.134794	−	0.990874i	$-0.543037\pi$
$41$	−761790.			−0.269588			−0.134794	+	0.990874i	$0.543037\pi$
$42$	148709.	−	1.67708e6i	0.0477903	−	0.538961i
$43$			2.54364e6i			0.744016i	0.928230	+	0.372008i	$0.121331\pi$
$43$			2.54364e6i			0.744016i	−0.928230	+	0.372008i	$0.878669\pi$
$44$	111907.	−	626061.i	0.0298571	−	0.167034i
$45$	1.38748e6			0.338359
$46$	920156.	+	81591.4i	0.205509	+	0.0182227i
$47$			5.65990e6i			1.15989i	0.814655	+	0.579946i	$0.196926\pi$
$47$			5.65990e6i			1.15989i	−0.814655	+	0.579946i	$0.803074\pi$
$48$	907284.	−	2.45680e6i	0.170914	−	0.462812i
$49$	−1.16893e6			−0.202770
$50$	−110406.	+	1.24511e6i	−0.0176649	+	0.199218i
$51$			1.94317e6i			0.287230i
$52$	−1.04128e7	−	1.86127e6i	−1.42415	−	0.254564i
$53$	1.14302e7			1.44861			0.724305	−	0.689480i	$-0.242161\pi$
$53$	1.14302e7			1.44861			0.724305	+	0.689480i	$0.242161\pi$
$54$	7.34027e6	+	650871.i	0.863251	+	0.0765455i
$55$			694387.i			0.0758841i
$56$	−1.04082e7	−	2.82817e6i	−1.05833	−	0.287577i
$57$	−9.65155e6			−0.914318
$58$	1.03062e6	−	1.16230e7i	0.0910727	−	1.02708i
$59$			2.12902e7i			1.75700i	0.477740	+	0.878501i	$0.341456\pi$
$59$			2.12902e7i			1.75700i	−0.477740	+	0.878501i	$0.658544\pi$
$60$	−503150.	+	2.81486e6i	−0.0388233	+	0.217196i
$61$	−2.63701e7			−1.90455			−0.952276	−	0.305238i	$-0.901264\pi$
$61$	−2.63701e7			−1.90455			−0.952276	+	0.305238i	$0.901264\pi$
$62$	2.14940e6	+	190590.i	0.145462	+	0.0128983i
$63$		−	1.30712e7i		−	0.829762i
$64$	−1.44701e7	−	8.49070e6i	−0.862483	−	0.506085i
$65$	1.15492e7			0.646993
$66$	−140301.	+	1.58226e6i	−0.00739408	+	0.0833876i
$67$			1.53982e6i			0.0764137i	0.999270	+	0.0382068i	$0.0121646\pi$
$67$			1.53982e6i			0.0764137i	−0.999270	+	0.0382068i	$0.987835\pi$
$68$	1.22538e7	+	2.19034e6i	0.573105	+	0.102441i
$69$	−2.30724e6			−0.101788
$70$	1.17300e7	+	1.04011e6i	0.488546	+	0.0433200i
$71$		−	2.06597e7i		−	0.813002i	−0.913650	−	0.406501i	$-0.866749\pi$
$71$		−	2.06597e7i		−	0.813002i	0.913650	−	0.406501i	$-0.133251\pi$
$72$	5.33157e6	−	1.96211e7i	0.198392	−	0.730119i
$73$	2.51296e7			0.884899			0.442449	−	0.896793i	$-0.354110\pi$
$73$	2.51296e7			0.884899			0.442449	+	0.896793i	$0.354110\pi$
$74$	−2.37658e6	+	2.68022e7i	−0.0792549	+	0.893806i
$75$		−	3.12206e6i		−	0.0986725i
$76$	−1.08792e7	+	6.08634e7i	−0.326094	+	1.82432i
$77$	6.54169e6			0.186092
$78$	2.63165e7	+	2.33352e6i	0.710968	+	0.0630425i
$79$		−	1.95344e7i		−	0.501525i	−0.968049	−	0.250762i	$-0.919319\pi$
$79$		−	1.95344e7i		−	0.501525i	0.968049	−	0.250762i	$-0.0806812\pi$
$80$	1.71836e7	+	6.34581e6i	0.419521	+	0.154927i
$81$	1.41635e7			0.329027
$82$	1.07656e6	−	1.21410e7i	0.0238113	−	0.268534i
$83$		−	2.37076e7i		−	0.499547i	−0.968304	−	0.249773i	$-0.919644\pi$
$83$		−	2.37076e7i		−	0.499547i	0.968304	−	0.249773i	$-0.0803561\pi$
$84$	2.65183e7	+	4.74009e6i	0.532633	+	0.0952071i
$85$	−1.35911e7			−0.260363
$86$	−4.05392e7	−	3.59466e6i	−0.741108	−	0.0657150i
$87$			2.91440e7i			0.508712i
$88$	9.81968e6	+	2.66826e6i	0.163745	+	0.0444937i
$89$	3.86749e7			0.616410			0.308205	−	0.951320i	$-0.400272\pi$
$89$	3.86749e7			0.616410			0.308205	+	0.951320i	$0.400272\pi$
$90$	−1.96078e6	+	2.21130e7i	−0.0298854	+	0.337036i
$91$		−	1.08803e8i		−	1.58663i
$92$	−2.60072e6	+	1.45497e7i	−0.0363030	+	0.203096i
$93$	−5.38951e6			−0.0720473
$94$	−9.02045e7	−	7.99855e6i	−1.15536	−	0.102447i
$95$		−	6.75057e7i		−	0.828793i
$96$	3.78730e7	+	1.79317e7i	0.445907	+	0.211124i
$97$	−9.46443e7			−1.06907			−0.534537	−	0.845145i	$-0.679514\pi$
$97$	−9.46443e7			−1.06907			−0.534537	+	0.845145i	$0.679514\pi$
$98$	1.65192e6	−	1.86298e7i	0.0179096	−	0.201978i
$99$			1.23322e7i			0.128380i
$100$	−1.96879e7	−	3.51918e6i	−0.196879	−	0.0351918i
$101$	−6.52649e7			−0.627183			−0.313591	−	0.949558i	$-0.601532\pi$
$101$	−6.52649e7			−0.627183			−0.313591	+	0.949558i	$0.601532\pi$
$102$	−3.09692e7	−	2.74608e6i	−0.286108	−	0.0253695i
$103$			1.47000e8i			1.30607i	0.757326	+	0.653037i	$0.226505\pi$
$103$			1.47000e8i			1.30607i	−0.757326	+	0.653037i	$0.773495\pi$
$104$	4.43793e7	−	1.63324e8i	0.379356	−	1.39610i
$105$	−2.94124e7			−0.241976
$106$	−1.61531e7	+	1.82169e8i	−0.127948	+	1.44295i
$107$			2.42429e8i			1.84948i	0.380603	+	0.924739i	$0.375716\pi$
$107$			2.42429e8i			1.84948i	−0.380603	+	0.924739i	$0.624284\pi$
$108$	−2.07465e7	+	1.16065e8i	−0.152493	+	0.853116i
$109$	−5.93486e7			−0.420440			−0.210220	−	0.977654i	$-0.567418\pi$
$109$	−5.93486e7			−0.420440			−0.210220	+	0.977654i	$0.567418\pi$
$110$	−1.10668e7	−	981304.i	−0.0755875	−	0.00670244i
$111$		−	6.72051e7i		−	0.442701i
$112$	5.97827e7	−	1.61883e8i	0.379930	−	1.02880i
$113$	5.46199e7			0.334994			0.167497	−	0.985873i	$-0.446432\pi$
$113$	5.46199e7			0.334994			0.167497	+	0.985873i	$0.446432\pi$
$114$	1.36395e7	−	1.53821e8i	0.0807569	−	0.910745i
$115$		−	1.61375e7i		−	0.0922669i
$116$	1.83784e8	+	3.28511e7i	1.01502	+	0.181434i
$117$	2.05112e8			1.09458
$118$	−3.39312e8	−	3.00873e7i	−1.75014	−	0.155187i
$119$			1.28039e8i			0.638492i
$120$	−4.41507e7	−	1.19969e7i	−0.212918	−	0.0578554i
$121$	2.08187e8			0.971208
$122$	3.72661e7	−	4.20273e8i	0.168219	−	1.89711i
$123$			3.04430e7i			0.133005i
$124$	−6.07505e6	+	3.39867e7i	−0.0256958	+	0.143755i
$125$	2.18366e7			0.0894427
$126$	2.08322e8	+	1.84722e7i	0.826519	+	0.0732885i
$127$			2.01099e8i			0.773026i	0.922284	+	0.386513i	$0.126321\pi$
$127$			2.01099e8i			0.773026i	−0.922284	+	0.386513i	$0.873679\pi$
$128$	1.55769e8	−	2.18617e8i	0.580286	−	0.814413i
$129$	1.01650e8			0.367070
$130$	−1.63213e7	+	1.84065e8i	−0.0571455	+	0.644464i
$131$		−	4.36365e8i		−	1.48172i	−0.671662	−	0.740858i	$-0.734419\pi$
$131$		−	4.36365e8i		−	1.48172i	0.671662	−	0.740858i	$-0.265581\pi$
$132$	−2.50189e7	−	4.47208e6i	−0.0824086	−	0.0147304i
$133$	−6.35959e8			−2.03246
$134$	−2.45409e7	−	2.17607e6i	−0.0761151	−	0.00674922i
$135$		−	1.28732e8i		−	0.387572i
$136$	−5.22254e7	+	1.92199e8i	−0.152660	+	0.561818i
$137$	4.48301e8			1.27259			0.636293	−	0.771447i	$-0.280467\pi$
$137$	4.48301e8			1.27259			0.636293	+	0.771447i	$0.280467\pi$
$138$	3.26059e6	−	3.67716e7i	0.00899041	−	0.101390i
$139$			4.73879e8i			1.26943i	0.772747	+	0.634714i	$0.218882\pi$
$139$			4.73879e8i			1.26943i	−0.772747	+	0.634714i	$0.781118\pi$
$140$	−3.31535e7	+	1.85477e8i	−0.0863014	+	0.482811i
$141$	2.26183e8			0.572248
$142$	3.29264e8	+	2.91963e7i	0.809825	+	0.0718082i
$143$			1.02651e8i			0.245482i
$144$	3.05176e8	+	1.12700e8i	0.709743	+	0.262105i
$145$	−2.03842e8			−0.461128
$146$	−3.55130e7	+	4.00502e8i	−0.0781584	+	0.881440i
$147$			4.67132e7i			0.100039i
$148$	−4.23800e8	−	7.57534e7i	−0.883312	−	0.157890i
$149$	−2.98504e8			−0.605627			−0.302814	−	0.953050i	$-0.597926\pi$
$149$	−2.98504e8			−0.605627			−0.302814	+	0.953050i	$0.597926\pi$
$150$	4.97577e7	+	4.41208e6i	0.0982869	+	0.00871522i
$151$		−	7.25032e8i		−	1.39460i	−0.716780	−	0.697299i	$-0.754385\pi$
$151$		−	7.25032e8i		−	1.39460i	0.716780	−	0.697299i	$-0.245615\pi$
$152$	−9.54634e8	−	2.59399e8i	−1.78839	−	0.485952i
$153$	−2.41375e8			−0.440480
$154$	−9.24468e6	+	1.04258e8i	−0.0164365	+	0.185364i
$155$		−	3.76958e7i		−	0.0653080i
$156$	−7.43808e7	+	4.16121e8i	−0.125592	+	0.702621i
$157$	−6.70288e8			−1.10322			−0.551611	−	0.834101i	$-0.685987\pi$
$157$	−6.70288e8			−1.10322			−0.551611	+	0.834101i	$0.685987\pi$
$158$	3.11329e8	+	2.76060e7i	0.499564	+	0.0442970i
$159$		−	4.56779e8i		−	0.714690i
$160$	−1.25420e8	+	2.64895e8i	−0.191376	+	0.404197i
$161$	−1.52029e8			−0.226268
$162$	−2.00158e7	+	2.25731e8i	−0.0290612	+	0.327741i
$163$		−	9.70735e8i		−	1.37515i	−0.726113	−	0.687575i	$-0.758675\pi$
$163$		−	9.70735e8i		−	1.37515i	0.726113	−	0.687575i	$-0.241325\pi$
$164$	1.91976e8	+	3.43152e7i	0.265381	+	0.0474364i
$165$	2.77493e7			0.0374384
$166$	3.77840e8	+	3.35035e7i	0.497594	+	0.0441223i
$167$			7.98683e8i			1.02685i	0.858133	+	0.513427i	$0.171624\pi$
$167$			7.98683e8i			1.02685i	−0.858133	+	0.513427i	$0.828376\pi$
$168$	−1.13020e8	+	4.15935e8i	−0.141880	+	0.522142i
$169$	8.91594e8			1.09300
$170$	1.92069e7	−	2.16608e8i	0.0229965	−	0.259345i
$171$		−	1.19889e9i		−	1.40215i
$172$	1.14580e8	−	6.41013e8i	0.130916	−	0.732408i
$173$	6.00425e8			0.670308			0.335154	−	0.942163i	$-0.391212\pi$
$173$	6.00425e8			0.670308			0.335154	+	0.942163i	$0.391212\pi$
$174$	−4.64482e8	−	4.11862e7i	−0.506724	−	0.0449319i
$175$		−	2.05719e8i		−	0.219342i
$176$	−5.64025e7	+	1.52730e8i	−0.0587824	+	0.159175i
$177$	8.50809e8			0.866840
$178$	−5.46552e7	+	6.16380e8i	−0.0544442	+	0.614001i
$179$			1.15845e9i			1.12840i	0.825637	+	0.564202i	$0.190816\pi$
$179$			1.15845e9i			1.12840i	−0.825637	+	0.564202i	$0.809184\pi$
$180$	−3.49654e8	−	6.24999e7i	−0.333080	−	0.0595373i
$181$	−7.96493e8			−0.742109			−0.371055	−	0.928611i	$-0.621004\pi$
$181$	−7.96493e8			−0.742109			−0.371055	+	0.928611i	$0.621004\pi$
$182$	1.73405e9	+	1.53760e8i	1.58043	+	0.140139i
$183$			1.05381e9i			0.939635i
$184$	−2.28209e8	−	6.20104e7i	−0.199096	−	0.0540995i
$185$	4.70052e8			0.401290
$186$	7.61643e6	−	8.58952e7i	0.00636355	−	0.0717657i
$187$		−	1.20800e8i		−	0.0987870i
$188$	2.54953e8	−	1.42633e9i	0.204094	−	1.14180i
$189$	−1.21276e9			−0.950449
$190$	1.07587e9	+	9.53988e7i	0.825554	+	0.0732029i
$191$			1.84245e9i			1.38440i	0.721706	+	0.692200i	$0.243358\pi$
$191$			1.84245e9i			1.38440i	−0.721706	+	0.692200i	$0.756642\pi$
$192$	−3.39309e8	+	5.78258e8i	−0.249684	+	0.425517i
$193$	2.34201e9			1.68795			0.843975	−	0.536382i	$-0.180209\pi$
$193$	2.34201e9			1.68795			0.843975	+	0.536382i	$0.180209\pi$
$194$	1.33751e8	−	1.50839e9i	0.0944256	−	1.06490i
$195$		−	4.61535e8i		−	0.319202i
$196$	2.94577e8	+	5.26550e7i	0.199606	+	0.0356792i
$197$	−1.86381e9			−1.23747			−0.618737	−	0.785598i	$-0.712356\pi$
$197$	−1.86381e9			−1.23747			−0.618737	+	0.785598i	$0.712356\pi$
$198$	−1.96543e8	−	1.74277e7i	−0.127878	−	0.0113391i
$199$		−	1.82005e9i		−	1.16057i	−0.814413	−	0.580286i	$-0.802941\pi$
$199$		−	1.82005e9i		−	1.16057i	0.814413	−	0.580286i	$-0.197059\pi$
$200$	8.39097e7	−	3.08803e8i	0.0524436	−	0.193002i
$201$	6.15349e7			0.0376997
$202$	9.22320e7	−	1.04016e9i	0.0553957	−	0.624732i
$203$			1.92035e9i			1.13083i
$204$	8.75311e7	−	4.89690e8i	0.0505408	−	0.282749i
$205$	−2.12927e8			−0.120563
$206$	−2.34280e9	−	2.07739e8i	−1.30097	−	0.115359i
$207$		−	2.86599e8i		−	0.156097i
$208$	2.54025e9	+	9.38102e8i	1.35713	+	0.501183i
$209$	6.00001e8			0.314461
$210$	4.15654e7	−	4.68758e8i	0.0213725	−	0.241030i
$211$			2.89129e9i			1.45869i	0.684148	+	0.729344i	$0.260174\pi$
$211$			2.89129e9i			1.45869i	−0.684148	+	0.729344i	$0.739826\pi$
$212$	−2.88048e9	−	5.14880e8i	−1.42601	−	0.254896i
$213$	−8.25613e8			−0.401105
$214$	−3.86370e9	−	3.42599e8i	−1.84225	−	0.163355i
$215$			7.10970e8i			0.332734i
$216$	−1.82047e9	−	4.94669e8i	−0.836313	−	0.227248i
$217$	−3.55125e8			−0.160156
$218$	8.38711e7	−	9.45866e8i	0.0371353	−	0.418797i
$219$		−	1.00424e9i		−	0.436576i
$220$	3.12790e7	−	1.74989e8i	0.0133525	−	0.0747001i
$221$	−2.00917e9			−0.842265
$222$	1.07108e9	+	9.49739e7i	0.440970	+	0.0391014i
$223$		−	2.26023e9i		−	0.913973i	−0.889474	−	0.456986i	$-0.848929\pi$
$223$		−	2.26023e9i		−	0.913973i	0.889474	−	0.456986i	$-0.151071\pi$
$224$	2.49552e9	+	1.18156e9i	0.991219	+	0.469313i
$225$	3.87813e8			0.151319
$226$	−7.71886e7	+	8.70503e8i	−0.0295882	+	0.333685i
$227$			1.08021e9i			0.406823i	0.979093	+	0.203412i	$0.0652029\pi$
$227$			1.08021e9i			0.406823i	−0.979093	+	0.203412i	$0.934797\pi$
$228$	2.43225e9	+	4.34759e8i	0.900053	+	0.160883i
$229$	6.30352e8			0.229214			0.114607	−	0.993411i	$-0.463439\pi$
$229$	6.30352e8			0.229214			0.114607	+	0.993411i	$0.463439\pi$
$230$	2.57192e8	+	2.28055e7i	0.0919063	+	0.00814945i
$231$		−	2.61421e8i		−	0.0918107i
$232$	−7.83286e8	+	2.88263e9i	−0.270376	+	0.995032i
$233$	1.17430e9			0.398435			0.199217	−	0.979955i	$-0.436160\pi$
$233$	1.17430e9			0.398435			0.199217	+	0.979955i	$0.436160\pi$
$234$	−2.89863e8	+	3.26896e9i	−0.0966784	+	1.09030i
$235$			1.58199e9i			0.518720i
$236$	9.59030e8	−	5.36526e9i	0.309161	−	1.72959i
$237$	−7.80642e8			−0.247434
$238$	−2.04062e9	−	1.80944e8i	−0.635996	−	0.0563946i
$239$			3.05182e9i			0.935334i	0.883905	+	0.467667i	$0.154905\pi$
$239$			3.05182e9i			0.935334i	−0.883905	+	0.467667i	$0.845095\pi$
$240$	2.53594e8	−	6.86696e8i	0.0764352	−	0.206976i
$241$	2.81871e9			0.835570			0.417785	−	0.908546i	$-0.362807\pi$
$241$	2.81871e9			0.835570			0.417785	+	0.908546i	$0.362807\pi$
$242$	−2.94209e8	+	3.31797e9i	−0.0857817	+	0.967412i
$243$		−	3.58779e9i		−	1.02897i
$244$	6.64542e9	+	1.18786e9i	1.87484	+	0.335123i
$245$	−3.26726e8			−0.0906815
$246$	−4.85184e8	−	4.30218e7i	−0.132485	−	0.0117476i
$247$		−	9.97938e9i		−	2.68112i
$248$	−5.33076e8	−	1.44851e8i	−0.140923	−	0.0382925i
$249$	−9.47414e8			−0.246458
$250$	−3.08594e7	+	3.48020e8i	−0.00790000	+	0.0890932i
$251$		−	2.92571e8i		−	0.0737116i	−0.999321	−	0.0368558i	$-0.988266\pi$
$251$		−	2.92571e8i		−	0.0737116i	0.999321	−	0.0368558i	$-0.0117342\pi$
$252$	−5.88800e8	+	3.29402e9i	−0.146004	+	0.816816i
$253$	1.43433e8			0.0350079
$254$	−3.20500e9	−	2.84192e8i	−0.770005	−	0.0682773i
$255$			5.43133e8i			0.128453i
$256$	3.26407e9	+	2.79152e9i	0.759976	+	0.649951i
$257$	3.03746e9			0.696270			0.348135	−	0.937444i	$-0.386815\pi$
$257$	3.03746e9			0.696270			0.348135	+	0.937444i	$0.386815\pi$
$258$	−1.43651e8	+	1.62004e9i	−0.0324213	+	0.365635i
$259$		−	4.42827e9i		−	0.984091i
$260$	−2.91047e9	−	5.20241e8i	−0.636898	−	0.113844i
$261$	−3.62018e9			−0.780133
$262$	6.95456e9	+	6.16669e8i	1.47593	+	0.130872i
$263$		−	1.69827e9i		−	0.354964i	−0.984124	−	0.177482i	$-0.943205\pi$
$263$		−	1.69827e9i		−	0.354964i	0.984124	−	0.177482i	$-0.0567951\pi$
$264$	1.06630e8	−	3.92418e8i	0.0219515	−	0.0807855i
$265$	3.19485e9			0.647838
$266$	8.98734e8	−	1.01356e10i	0.179517	−	2.02452i
$267$		−	1.54554e9i		−	0.304114i
$268$	6.93621e7	−	3.88044e8i	0.0134457	−	0.0752215i
$269$	−8.70547e8			−0.166258			−0.0831291	−	0.996539i	$-0.526491\pi$
$269$	−8.70547e8			−0.166258			−0.0831291	+	0.996539i	$0.526491\pi$
$270$	2.05167e9	+	1.81924e8i	0.386057	+	0.0342322i
$271$			7.36841e9i			1.36614i	0.730351	+	0.683072i	$0.239357\pi$
$271$			7.36841e9i			1.36614i	−0.730351	+	0.683072i	$0.760643\pi$
$272$	−2.98936e9	−	1.10396e9i	−0.546138	−	0.201686i
$273$	−4.34803e9			−0.782785
$274$	−6.33537e8	+	7.14478e9i	−0.112401	+	1.26761i
$275$			1.94087e8i			0.0339364i
$276$	5.81439e8	+	1.03931e8i	0.100200	+	0.0179105i
$277$	2.37339e9			0.403135			0.201568	−	0.979475i	$-0.435396\pi$
$277$	2.37339e9			0.403135			0.201568	+	0.979475i	$0.435396\pi$
$278$	−7.55243e9	−	6.69684e8i	−1.26447	−	0.112122i
$279$		−	6.69469e8i		−	0.110488i
$280$	−2.90917e9	−	7.90498e8i	−0.473301	−	0.128608i
$281$	5.50733e9			0.883315			0.441657	−	0.897184i	$-0.354391\pi$
$281$	5.50733e9			0.883315			0.441657	+	0.897184i	$0.354391\pi$
$282$	−3.19641e8	+	3.60479e9i	−0.0505436	+	0.570011i
$283$			4.55904e9i			0.710768i	0.934720	+	0.355384i	$0.115650\pi$
$283$			4.55904e9i			0.710768i	−0.934720	+	0.355384i	$0.884350\pi$
$284$	−9.30629e8	+	5.20638e9i	−0.143055	+	0.800317i
$285$	−2.69769e9			−0.408896
$286$	−1.63600e9	−	1.45066e8i	−0.244523	−	0.0216822i
$287$			2.00594e9i			0.295659i
$288$	−2.22743e9	+	4.70447e9i	−0.323768	+	0.683818i
$289$	−4.61137e9			−0.661056
$290$	2.88068e8	−	3.24872e9i	0.0407290	−	0.459325i
$291$			3.78221e9i			0.527441i
$292$	−6.33280e9	−	1.13197e9i	−0.871092	−	0.155706i
$293$	−8.27611e9			−1.12294			−0.561469	−	0.827498i	$-0.689763\pi$
$293$	−8.27611e9			−1.12294			−0.561469	+	0.827498i	$0.689763\pi$
$294$	−7.44490e8	−	6.60148e7i	−0.0996482	−	0.00883593i
$295$			5.95080e9i			0.785756i
$296$	1.80623e9	−	6.64725e9i	0.235291	−	0.865914i
$297$	1.14419e9			0.147053
$298$	4.21845e8	−	4.75740e9i	0.0534918	−	0.603260i
$299$		−	2.38562e9i		−	0.298480i
$300$	−1.40635e8	+	7.86777e8i	−0.0173623	+	0.0971330i
$301$	6.69791e9			0.815969
$302$	1.15552e10	+	1.02461e9i	1.38915	+	0.123178i
$303$			2.60814e9i			0.309429i
$304$	5.48324e9	−	1.48479e10i	0.642012	−	1.73848i
$305$	−7.37067e9			−0.851742
$306$	3.41110e8	−	3.84691e9i	0.0389053	−	0.438759i
$307$		−	7.73582e9i		−	0.870869i	−0.900221	−	0.435434i	$-0.856595\pi$
$307$		−	7.73582e9i		−	0.870869i	0.900221	−	0.435434i	$-0.143405\pi$
$308$	−1.64854e9	−	2.94674e8i	−0.183188	−	0.0327445i
$309$	5.87446e9			0.644368
$310$	6.00776e8	+	5.32715e7i	0.0650527	+	0.00576831i
$311$			1.08068e10i			1.15520i	0.816321	+	0.577599i	$0.196010\pi$
$311$			1.08068e10i			1.15520i	−0.816321	+	0.577599i	$0.803990\pi$
$312$	−6.52680e9	−	1.77350e9i	−0.688783	−	0.187160i
$313$	−4.73025e9			−0.492841			−0.246421	−	0.969163i	$-0.579254\pi$
$313$	−4.73025e9			−0.492841			−0.246421	+	0.969163i	$0.579254\pi$
$314$	9.47248e8	−	1.06827e10i	0.0974418	−	1.09891i
$315$		−	3.65352e9i		−	0.371081i
$316$	−8.79938e8	+	4.92279e9i	−0.0882478	+	0.493700i
$317$	−5.44758e9			−0.539469			−0.269735	−	0.962935i	$-0.586936\pi$
$317$	−5.44758e9			−0.539469			−0.269735	+	0.962935i	$0.586936\pi$
$318$	7.27990e9	+	6.45518e8i	0.711897	+	0.0631248i
$319$		−	1.81178e9i		−	0.174961i
$320$	−4.04451e9	−	2.37322e9i	−0.385714	−	0.226328i
$321$	9.68803e9			0.912463
$322$	2.14846e8	−	2.42295e9i	0.0199850	−	0.225383i
$323$			1.17437e10i			1.07893i
$324$	−3.56929e9	−	6.38003e8i	−0.323893	−	0.0578952i
$325$	3.22811e9			0.289344
$326$	1.54711e10	+	1.37184e9i	1.36978	+	0.121460i
$327$			2.37171e9i			0.207429i
$328$	−8.18197e8	+	3.01111e9i	−0.0706907	+	0.260154i
$329$	1.49036e10			1.27206
$330$	−3.92152e7	+	4.42254e8i	−0.00330673	+	0.0372921i
$331$			8.65354e8i			0.0720911i	0.999350	+	0.0360456i	$0.0114761\pi$
$331$			8.65354e8i			0.0720911i	−0.999350	+	0.0360456i	$0.988524\pi$
$332$	−1.06792e9	+	5.97446e9i	−0.0878997	+	0.491752i
$333$	8.34801e9			0.678901
$334$	−1.27290e10	−	1.12870e9i	−1.02284	−	0.0906966i
$335$			4.30393e8i			0.0341732i
$336$	−6.46924e9	−	2.38906e9i	−0.507570	−	0.187443i
$337$	8.64475e8			0.0670244			0.0335122	−	0.999438i	$-0.489331\pi$
$337$	8.64475e8			0.0670244			0.0335122	+	0.999438i	$0.489331\pi$
$338$	−1.26000e9	+	1.42097e10i	−0.0965389	+	1.08873i
$339$		−	2.18274e9i		−	0.165274i
$340$	3.42504e9	+	6.12218e8i	0.256301	+	0.0458132i
$341$	3.35046e8			0.0247792
$342$	1.91072e10	+	1.69426e9i	1.39667	+	0.123844i
$343$		−	1.21018e10i		−	0.874329i
$344$	1.00542e10	+	2.73199e9i	0.717982	+	0.195094i
$345$	−6.44895e8			−0.0455211
$346$	−8.48518e8	+	9.56926e9i	−0.0592048	+	0.667689i
$347$			1.10077e10i			0.759239i	0.925143	+	0.379620i	$0.123945\pi$
$347$			1.10077e10i			0.759239i	−0.925143	+	0.379620i	$0.876055\pi$
$348$	1.31281e9	−	7.34446e9i	0.0895125	−	0.500775i
$349$	−1.99631e10			−1.34563			−0.672816	−	0.739810i	$-0.734915\pi$
$349$	−1.99631e10			−1.34563			−0.672816	+	0.739810i	$0.734915\pi$
$350$	3.27863e9	+	2.90721e8i	0.218484	+	0.0193733i
$351$		−	1.90305e10i		−	1.25378i
$352$	−2.35442e9	−	1.11475e9i	−0.153361	−	0.0726118i
$353$	1.32468e10			0.853126			0.426563	−	0.904458i	$-0.359724\pi$
$353$	1.32468e10			0.853126			0.426563	+	0.904458i	$0.359724\pi$
$354$	−1.20236e9	+	1.35597e10i	−0.0765634	+	0.863452i
$355$		−	5.77457e9i		−	0.363586i
$356$	−9.74630e9	−	1.74213e9i	−0.606792	−	0.108463i
$357$	5.11675e9			0.315008
$358$	−1.84627e10	−	1.63711e9i	−1.12399	−	0.0996659i
$359$		−	2.59685e9i		−	0.156340i	−0.996940	−	0.0781699i	$-0.975092\pi$
$359$		−	2.59685e9i		−	0.156340i	0.996940	−	0.0781699i	$-0.0249076\pi$
$360$	1.49022e9	−	5.48427e9i	0.0887237	−	0.326519i
$361$	−4.13463e10			−2.43449
$362$	1.12560e9	−	1.26941e10i	0.0655466	−	0.739209i
$363$		−	8.31965e9i		−	0.479158i
$364$	−4.90109e9	+	2.74190e10i	−0.279182	+	1.56188i
$365$	7.02393e9			0.395739
$366$	−1.67951e10	−	1.48924e9i	−0.935963	−	0.0829930i
$367$		−	3.62330e9i		−	0.199728i	−0.995001	−	0.0998642i	$-0.968159\pi$
$367$		−	3.62330e9i		−	0.199728i	0.995001	−	0.0998642i	$-0.0318408\pi$
$368$	1.31079e9	−	3.54945e9i	0.0714732	−	0.193539i
$369$	−3.78153e9			−0.203968
$370$	−6.64275e8	+	7.49144e9i	−0.0354439	+	0.399722i
$371$		−	3.00981e10i		−	1.58870i
$372$	1.35819e9	+	2.42773e8i	0.0709232	+	0.0126774i
$373$	4.15162e9			0.214478			0.107239	−	0.994233i	$-0.465799\pi$
$373$	4.15162e9			0.214478			0.107239	+	0.994233i	$0.465799\pi$
$374$	1.92524e9	+	1.70714e8i	0.0984009	+	0.00872533i
$375$		−	8.72643e8i		−	0.0441277i
$376$	2.23718e10	+	6.07899e9i	1.11931	+	0.304145i
$377$	−3.01339e10			−1.49173
$378$	1.71387e9	−	1.93284e10i	0.0839481	−	0.946734i
$379$			1.89551e10i			0.918692i	0.888257	+	0.459346i	$0.151916\pi$
$379$			1.89551e10i			0.918692i	−0.888257	+	0.459346i	$0.848084\pi$
$380$	−3.04083e9	+	1.70118e10i	−0.145834	+	0.815862i
$381$	8.03638e9			0.381382
$382$	−2.93639e10	−	2.60374e9i	−1.37899	−	0.122277i
$383$		−	8.87673e9i		−	0.412532i	−0.978496	−	0.206266i	$-0.933869\pi$
$383$		−	8.87673e9i		−	0.412532i	0.978496	−	0.206266i	$-0.0661313\pi$
$384$	−8.73647e9	−	6.22491e9i	−0.401801	−	0.286291i
$385$	1.82846e9			0.0832227
$386$	−3.30972e9	+	3.73257e10i	−0.149088	+	1.68135i
$387$			1.26267e10i			0.562918i
$388$	2.38509e10	+	4.26330e9i	1.05239	+	0.188113i
$389$	2.05595e10			0.897872			0.448936	−	0.893564i	$-0.351803\pi$
$389$	2.05595e10			0.897872			0.448936	+	0.893564i	$0.351803\pi$
$390$	7.35569e9	+	6.52239e8i	0.317955	+	0.0281934i
$391$			2.80739e9i			0.120114i
$392$	−1.25548e9	+	4.62040e9i	−0.0531699	+	0.195675i
$393$	−1.74382e10			−0.731023
$394$	2.63393e9	−	2.97044e10i	0.109300	−	1.23264i
$395$		−	5.46004e9i		−	0.224289i
$396$	5.55508e8	−	3.10777e9i	0.0225897	−	0.126377i
$397$	2.04868e10			0.824733			0.412366	−	0.911018i	$-0.364702\pi$
$397$	2.04868e10			0.824733			0.412366	+	0.911018i	$0.364702\pi$
$398$	2.90071e10	+	2.57209e9i	1.15604	+	0.102507i
$399$			2.54144e10i			1.00274i
$400$	4.80295e9	+	1.77371e9i	0.187615	+	0.0692854i
$401$	−7.30576e9			−0.282545			−0.141273	−	0.989971i	$-0.545119\pi$
$401$	−7.30576e9			−0.282545			−0.141273	+	0.989971i	$0.545119\pi$
$402$	−8.69609e7	+	9.80711e8i	−0.00332981	+	0.0375523i
$403$		−	5.57258e9i		−	0.211269i
$404$	1.64471e10	+	2.93989e9i	0.617397	+	0.110358i
$405$	3.95882e9			0.147145
$406$	−3.06056e10	−	2.71384e9i	−1.12641	−	0.0998802i
$407$			4.17789e9i			0.152258i
$408$	7.68073e9	+	2.08705e9i	0.277180	+	0.0753170i
$409$	−1.05889e10			−0.378406			−0.189203	−	0.981938i	$-0.560590\pi$
$409$	−1.05889e10			−0.378406			−0.189203	+	0.981938i	$0.560590\pi$
$410$	3.00907e8	−	3.39352e9i	0.0106487	−	0.120092i
$411$		−	1.79152e10i		−	0.627847i
$412$	6.62168e9	−	3.70448e10i	0.229815	−	1.28570i
$413$	5.60614e10			1.92692
$414$	4.56766e9	+	4.05021e8i	0.155487	+	0.0137872i
$415$		−	6.62649e9i		−	0.223404i
$416$	−1.85408e10	+	3.91594e10i	−0.619093	+	1.30756i
$417$	1.89373e10			0.626289
$418$	−8.47919e8	+	9.56250e9i	−0.0277747	+	0.313232i
$419$			2.61037e9i			0.0846928i	0.999103	+	0.0423464i	$0.0134833\pi$
$419$			2.61037e9i			0.0846928i	−0.999103	+	0.0423464i	$0.986517\pi$
$420$	7.41208e9	+	1.32489e9i	0.238201	+	0.0425779i
$421$	9.29505e9			0.295885			0.147943	−	0.988996i	$-0.452735\pi$
$421$	9.29505e9			0.295885			0.147943	+	0.988996i	$0.452735\pi$
$422$	−4.60799e10	−	4.08596e9i	−1.45299	−	0.128838i
$423$			2.80958e10i			0.877567i
$424$	1.22766e10	−	4.51800e10i	0.379852	−	1.39792i
$425$	−3.79883e9			−0.116438
$426$	1.16675e9	−	1.31582e10i	0.0354275	−	0.399537i
$427$			6.94377e10i			2.08874i
$428$	1.09203e10	−	6.10934e10i	0.325432	−	1.82062i
$429$	4.10219e9			0.121112
$430$	−1.13311e10	−	1.00474e9i	−0.331434	−	0.0293886i
$431$		−	1.86560e10i		−	0.540642i	−0.962770	−	0.270321i	$-0.912870\pi$
$431$		−	1.86560e10i		−	0.540642i	0.962770	−	0.270321i	$-0.0871298\pi$
$432$	1.04565e10	−	2.83146e10i	0.300227	−	0.812973i
$433$	−1.66970e10			−0.474994			−0.237497	−	0.971388i	$-0.576327\pi$
$433$	−1.66970e10			−0.474994			−0.237497	+	0.971388i	$0.576327\pi$
$434$	5.01861e8	−	5.65980e9i	0.0141457	−	0.159530i
$435$			8.14600e9i			0.227503i
$436$	1.49562e10	+	2.67339e9i	0.413880	+	0.0739802i
$437$	−1.39440e10			−0.382351
$438$	1.60050e10	+	1.41918e9i	0.434870	+	0.0385605i
$439$		−	5.48360e9i		−	0.147641i	−0.997272	−	0.0738206i	$-0.976481\pi$
$439$		−	5.48360e9i		−	0.147641i	0.997272	−	0.0738206i	$-0.0235192\pi$
$440$	2.74469e9	+	7.45802e8i	0.0732288	+	0.0198982i
$441$	−5.80257e9			−0.153414
$442$	2.83936e9	−	3.20212e10i	0.0743928	−	0.838973i
$443$		−	5.97812e9i		−	0.155221i	−0.996984	−	0.0776104i	$-0.975271\pi$
$443$		−	5.97812e9i		−	0.155221i	0.996984	−	0.0776104i	$-0.0247290\pi$
$444$	−3.02729e9	+	1.69361e10i	−0.0778972	+	0.435793i
$445$	1.08100e10			0.275667
$446$	3.60223e10	+	3.19415e9i	0.910401	+	0.0807264i
$447$			1.19289e10i			0.298794i
$448$	−2.23577e10	+	3.81026e10i	−0.555028	+	0.945893i
$449$	−3.11696e10			−0.766913			−0.383456	−	0.923559i	$-0.625266\pi$
$449$	−3.11696e10			−0.766913			−0.383456	+	0.923559i	$0.625266\pi$
$450$	−5.48056e8	+	6.18076e9i	−0.0133652	+	0.150727i
$451$		−	1.89253e9i		−	0.0457442i
$452$	−1.37645e10	−	2.46038e9i	−0.329767	−	0.0589452i
$453$	−2.89740e10			−0.688043
$454$	−1.72158e10	−	1.52655e9i	−0.405233	−	0.0359325i
$455$		−	3.04114e10i		−	0.709563i
$456$	−1.03662e10	+	3.81494e10i	−0.239751	+	0.882325i
$457$	−4.33966e9			−0.0994927			−0.0497463	−	0.998762i	$-0.515841\pi$
$457$	−4.33966e9			−0.0994927			−0.0497463	+	0.998762i	$0.515841\pi$
$458$	−8.90810e8	+	1.00462e10i	−0.0202453	+	0.228318i
$459$			2.23951e10i			0.504547i
$460$	−7.26924e8	+	4.06675e9i	−0.0162352	+	0.0908273i
$461$	−5.16164e10			−1.14284			−0.571418	−	0.820659i	$-0.693607\pi$
$461$	−5.16164e10			−1.14284			−0.571418	+	0.820659i	$0.693607\pi$
$462$	4.16640e9	+	3.69440e8i	0.0914519	+	0.00810915i
$463$			6.86820e10i			1.49458i	0.664499	+	0.747289i	$0.268645\pi$
$463$			6.86820e10i			1.49458i	−0.664499	+	0.747289i	$0.731355\pi$
$464$	−4.48349e10	−	1.65573e10i	−0.967263	−	0.357205i
$465$	−1.50641e9			−0.0322205
$466$	−1.65952e9	+	1.87154e10i	−0.0351916	+	0.396877i
$467$		−	2.14596e10i		−	0.451185i	−0.974222	−	0.225592i	$-0.927568\pi$
$467$		−	2.14596e10i		−	0.451185i	0.974222	−	0.225592i	$-0.0724317\pi$
$468$	−5.16893e10	−	9.23936e9i	−1.07750	−	0.192601i
$469$	4.05465e9			0.0838036
$470$	−2.52129e10	−	2.23566e9i	−0.516692	−	0.0458158i
$471$			2.67863e10i			0.544289i
$472$	8.41534e10	+	2.28667e10i	1.69552	+	0.460718i
$473$	−6.31921e9			−0.126246
$474$	1.10320e9	−	1.24415e10i	0.0218545	−	0.246466i
$475$		−	1.88684e10i		−	0.370648i
$476$	5.76759e9	−	3.22666e10i	0.112348	−	0.628530i
$477$	5.67397e10			1.09601
$478$	−4.86382e10	−	4.31281e9i	−0.931679	−	0.0826131i
$479$		−	8.24617e10i		−	1.56643i	−0.621753	−	0.783213i	$-0.713579\pi$
$479$		−	8.24617e10i		−	1.56643i	0.621753	−	0.783213i	$-0.286421\pi$
$480$	1.05858e10	+	5.01208e9i	0.199416	+	0.0944175i
$481$	6.94878e10			1.29816
$482$	−3.98339e9	+	4.49231e10i	−0.0738014	+	0.832304i
$483$			6.07543e9i			0.111632i
$484$	−5.24643e10	−	9.37789e9i	−0.956055	−	0.170893i
$485$	−2.64539e10			−0.478104
$486$	5.71802e10	+	5.07024e9i	1.02495	+	0.0908832i
$487$		−	2.94674e9i		−	0.0523874i	−0.999657	−	0.0261937i	$-0.991661\pi$
$487$		−	2.94674e9i		−	0.0523874i	0.999657	−	0.0261937i	$-0.00833866\pi$
$488$	−2.83227e10	+	1.04233e11i	−0.499408	+	1.83791i
$489$	−3.87929e10			−0.678448
$490$	4.61727e8	−	5.20718e9i	0.00800942	−	0.0903271i
$491$		−	8.17812e10i		−	1.40711i	−0.710642	−	0.703554i	$-0.751595\pi$
$491$		−	8.17812e10i		−	1.40711i	0.710642	−	0.703554i	$-0.248405\pi$
$492$	1.37132e9	−	7.67180e9i	0.0234033	−	0.130929i
$493$	3.54616e10			0.600302
$494$	1.59046e11	+	1.41028e10i	2.67064	+	0.236809i
$495$			3.44694e9i			0.0574134i
$496$	3.06189e9	−	8.29118e9i	0.0505898	−	0.136990i
$497$	−5.44012e10			−0.891626
$498$	1.33888e9	−	1.50994e10i	0.0217683	−	0.245494i
$499$			4.69562e10i			0.757340i	0.925532	+	0.378670i	$0.123618\pi$
$499$			4.69562e10i			0.757340i	−0.925532	+	0.378670i	$0.876382\pi$
$500$	−5.50295e9	−	9.83641e8i	−0.0880472	−	0.0157383i
$501$	3.19173e10			0.506612
$502$	4.66284e9	+	4.13460e8i	0.0734236	+	0.00651056i
$503$		−	8.89245e10i		−	1.38915i	−0.719420	−	0.694575i	$-0.755592\pi$
$503$		−	8.89245e10i		−	1.38915i	0.719420	−	0.694575i	$-0.244408\pi$
$504$	−5.16663e10	−	1.40391e10i	−0.800728	−	0.217579i
$505$	−1.82421e10			−0.280485
$506$	−2.02699e8	+	2.28596e9i	−0.00309207	+	0.0348711i
$507$		−	3.56302e10i		−	0.539245i
$508$	9.05859e9	−	5.06780e10i	0.136021	−	0.760965i
$509$	1.30873e11			1.94975			0.974877	−	0.222745i	$-0.0715019\pi$
$509$	1.30873e11			1.94975			0.974877	+	0.222745i	$0.0715019\pi$
$510$	−8.65616e9	−	7.67553e8i	−0.127951	−	0.0113456i
$511$		−	6.61711e10i		−	0.970476i
$512$	−4.91025e10	+	4.80761e10i	−0.714535	+	0.699599i
$513$	−1.11234e11			−1.60609
$514$	−4.29252e9	+	4.84094e10i	−0.0614978	+	0.693549i
$515$			4.10877e10i			0.584094i
$516$	−2.56164e10	−	4.57888e9i	−0.361343	−	0.0645892i
$517$	−1.40610e10			−0.196813
$518$	7.05754e10	+	6.25801e9i	0.980245	+	0.0869195i
$519$		−	2.39944e10i		−	0.330705i
$520$	1.24044e10	−	4.56504e10i	0.169653	−	0.624354i
$521$	7.03085e10			0.954238			0.477119	−	0.878839i	$-0.341681\pi$
$521$	7.03085e10			0.954238			0.477119	+	0.878839i	$0.341681\pi$
$522$	5.11603e9	−	5.76966e10i	0.0689050	−	0.777084i
$523$		−	7.40744e10i		−	0.990060i	−0.868876	−	0.495030i	$-0.835157\pi$
$523$		−	7.40744e10i		−	0.990060i	0.868876	−	0.495030i	$-0.164843\pi$
$524$	−1.96563e10	+	1.09967e11i	−0.260721	+	1.45860i
$525$	−8.22100e9			−0.108215
$526$	2.70661e10	+	2.39999e9i	0.353577	+	0.0313521i
$527$			6.55779e9i			0.0850189i
$528$	6.10346e9	+	2.25398e9i	0.0785309	+	0.0290011i
$529$	7.49776e10			0.957434
$530$	−4.51494e9	+	5.09178e10i	−0.0572201	+	0.645306i
$531$			1.05685e11i			1.32934i
$532$	1.60265e11	+	2.86471e10i	2.00075	+	0.357630i
$533$	−3.14770e10			−0.390018
$534$	2.46320e10	+	2.18415e9i	0.302925	+	0.0268607i
$535$			6.77609e10i			0.827111i
$536$	6.08642e9	+	1.65384e9i	0.0737399	+	0.0200370i
$537$	4.62943e10			0.556712
$538$	1.23025e9	−	1.38743e10i	0.0146847	−	0.165608i
$539$		−	2.90399e9i		−	0.0344064i
$540$	−5.79881e9	+	3.24413e10i	−0.0681968	+	0.381525i
$541$	3.35458e9			0.0391605			0.0195803	−	0.999808i	$-0.493767\pi$
$541$	3.35458e9			0.0391605			0.0195803	+	0.999808i	$0.493767\pi$
$542$	−1.17434e11	−	1.04130e10i	−1.36081	−	0.120664i
$543$			3.18298e10i			0.366129i
$544$	2.18188e10	−	4.60827e10i	0.249135	−	0.526190i
$545$	−1.65884e10			−0.188027
$546$	6.14462e9	−	6.92966e10i	0.0691392	−	0.779725i
$547$		−	1.13812e11i		−	1.27128i	−0.771987	−	0.635638i	$-0.780737\pi$
$547$		−	1.13812e11i		−	1.27128i	0.771987	−	0.635638i	$-0.219263\pi$
$548$	−1.12974e11	−	2.01939e10i	−1.25273	−	0.223923i
$549$	−1.30902e11			−1.44097
$550$	−3.09325e9	−	2.74283e8i	−0.0338038	−	0.00299742i
$551$			1.76134e11i			1.91090i
$552$	−2.47808e9	+	9.11979e9i	−0.0266907	+	0.0982265i
$553$	−5.14380e10			−0.550026
$554$	−3.35407e9	+	3.78259e10i	−0.0356068	+	0.401560i
$555$		−	1.87844e10i		−	0.197982i
$556$	2.13461e10	−	1.19420e11i	0.223367	−	1.24962i
$557$	−1.05403e11			−1.09505			−0.547524	−	0.836790i	$-0.684430\pi$
$557$	−1.05403e11			−1.09505			−0.547524	+	0.836790i	$0.684430\pi$
$558$	1.06696e10	+	9.46091e8i	0.110056	+	0.00975879i
$559$			1.05103e11i			1.07638i
$560$	1.67098e10	−	4.52477e10i	0.169910	−	0.460092i
$561$	−4.82745e9			−0.0487378
$562$	−7.78293e9	+	8.77728e10i	−0.0780185	+	0.879862i
$563$			7.97945e10i			0.794217i	0.917772	+	0.397108i	$0.129986\pi$
$563$			7.97945e10i			0.794217i	−0.917772	+	0.397108i	$0.870014\pi$
$564$	−5.69995e10	−	1.01885e10i	−0.563319	−	0.100692i
$565$	1.52667e10			0.149814
$566$	−7.26596e10	−	6.44282e9i	−0.707990	−	0.0627784i
$567$		−	3.72953e10i		−	0.360846i
$568$	−8.16613e10	−	2.21895e10i	−0.784554	−	0.213184i
$569$	−4.57243e10			−0.436212			−0.218106	−	0.975925i	$-0.569988\pi$
$569$	−4.57243e10			−0.436212			−0.218106	+	0.975925i	$0.569988\pi$
$570$	3.81236e9	−	4.29943e10i	0.0361156	−	0.407298i
$571$			2.16780e10i			0.203927i	0.994788	+	0.101964i	$0.0325126\pi$
$571$			2.16780e10i			0.203927i	−0.994788	+	0.101964i	$0.967487\pi$
$572$	4.62398e9	−	2.58687e10i	0.0431948	−	0.241652i
$573$	7.36286e10			0.683011
$574$	−3.19697e10	−	2.83479e9i	−0.294504	−	0.0261140i
$575$		−	4.51058e9i		−	0.0412630i
$576$	−7.18296e10	−	4.21479e10i	−0.652549	−	0.382901i
$577$	1.69273e11			1.52716			0.763579	−	0.645715i	$-0.223440\pi$
$577$	1.69273e11			1.52716			0.763579	+	0.645715i	$0.223440\pi$
$578$	6.51676e9	−	7.34935e10i	0.0583876	−	0.658472i
$579$		−	9.35923e10i		−	0.832772i
$580$	5.13693e10	+	9.18215e9i	0.453933	+	0.0811395i
$581$	−6.24269e10			−0.547857
$582$	−6.02789e10	−	5.34500e9i	−0.525380	−	0.0465861i
$583$			2.83963e10i			0.245803i
$584$	2.69903e10	−	9.93290e10i	0.232036	−	0.853935i
$585$	5.73305e10			0.489511
$586$	1.16958e10	−	1.31900e11i	0.0991831	−	1.11855i
$587$		−	3.75401e10i		−	0.316187i	−0.987424	−	0.158093i	$-0.949465\pi$
$587$		−	3.75401e10i		−	0.316187i	0.987424	−	0.158093i	$-0.0505347\pi$
$588$	2.10422e9	−	1.17720e10i	0.0176028	−	0.0984783i
$589$	−3.25719e10			−0.270634
$590$	−9.48407e10	−	8.40965e9i	−0.782685	−	0.0694016i
$591$			7.44822e10i			0.610524i
$592$	1.03388e11	+	3.81806e10i	0.841748	+	0.310854i
$593$	1.04118e11			0.841994			0.420997	−	0.907062i	$-0.361680\pi$
$593$	1.04118e11			0.841994			0.420997	+	0.907062i	$0.361680\pi$
$594$	−1.61697e9	+	1.82355e10i	−0.0129884	+	0.146478i
$595$			3.57881e10i			0.285542i
$596$	7.52248e10	+	1.34463e10i	0.596178	+	0.106566i
$597$	−7.27337e10			−0.572583
$598$	3.80207e10	+	3.37134e9i	0.297314	+	0.0263632i
$599$		−	4.81442e10i		−	0.373970i	−0.982363	−	0.186985i	$-0.940128\pi$
$599$		−	4.81442e10i		−	0.373970i	0.982363	−	0.186985i	$-0.0598716\pi$
$600$	−1.23405e10	−	3.35323e9i	−0.0952199	−	0.0258737i
$601$	−1.48443e11			−1.13779			−0.568896	−	0.822410i	$-0.692629\pi$
$601$	−1.48443e11			−1.13779			−0.568896	+	0.822410i	$0.692629\pi$
$602$	−9.46546e9	+	1.06748e11i	−0.0720702	+	0.812780i
$603$			7.64369e9i			0.0578141i
$604$	−3.26594e10	+	1.82712e11i	−0.245392	+	1.37284i
$605$	5.81901e10			0.434337
$606$	−4.15672e10	−	3.68581e9i	−0.308219	−	0.0273302i
$607$			5.44460e10i			0.401062i	0.979687	+	0.200531i	$0.0642667\pi$
$607$			5.44460e10i			0.401062i	−0.979687	+	0.200531i	$0.935733\pi$
$608$	2.28888e11	+	1.08372e11i	1.67498	+	0.793054i
$609$	7.67419e10			0.557909
$610$	1.04162e10	−	1.17470e11i	0.0752298	−	0.848413i
$611$			2.33866e11i			1.67804i
$612$	6.08279e10	+	1.08729e10i	0.433608	+	0.0775065i
$613$	1.16278e11			0.823484			0.411742	−	0.911301i	$-0.364921\pi$
$613$	1.16278e11			0.823484			0.411742	+	0.911301i	$0.364921\pi$
$614$	1.23289e11	+	1.09322e10i	0.867465	+	0.0769192i
$615$			8.50906e9i			0.0594814i
$616$	7.02607e9	−	2.58572e10i	0.0487966	−	0.179580i
$617$	−4.87411e10			−0.336321			−0.168161	−	0.985760i	$-0.553783\pi$
$617$	−4.87411e10			−0.336321			−0.168161	+	0.985760i	$0.553783\pi$
$618$	−8.30176e9	+	9.36240e10i	−0.0569136	+	0.641850i
$619$		−	4.92280e10i		−	0.335312i	−0.985846	−	0.167656i	$-0.946380\pi$
$619$		−	4.92280e10i		−	0.335312i	0.985846	−	0.167656i	$-0.0536198\pi$
$620$	−1.69803e9	+	9.49956e9i	−0.0114915	+	0.0642890i
$621$	−2.65910e10			−0.178800
$622$	−1.72233e11	−	1.52721e10i	−1.15068	−	0.102033i
$623$		−	1.01839e11i		−	0.676022i
$624$	3.74888e10	−	1.01514e11i	0.247265	−	0.669560i
$625$	6.10352e9			0.0400000
$626$	6.68477e9	−	7.53882e10i	0.0435300	−	0.490915i
$627$		−	2.39775e10i		−	0.155143i
$628$	1.68916e11	+	3.01935e10i	1.08601	+	0.194122i
$629$	−8.17731e10			−0.522406
$630$	5.82278e10	+	5.16313e9i	0.369631	+	0.0327756i
$631$		−	1.10376e11i		−	0.696240i	−0.937450	−	0.348120i	$-0.886820\pi$
$631$		−	1.10376e11i		−	0.696240i	0.937450	−	0.348120i	$-0.113180\pi$
$632$	−7.72132e10	−	2.09808e10i	−0.483976	−	0.131509i
$633$	1.15543e11			0.719662
$634$	7.69850e9	−	8.68207e10i	0.0476485	−	0.537361i
$635$			5.62088e10i			0.345708i
$636$	−2.05758e10	+	1.15111e11i	−0.125756	+	0.703539i
$637$	−4.82999e10			−0.293352
$638$	2.88751e10	+	2.56039e9i	0.174277	+	0.0154534i
$639$		−	1.02555e11i		−	0.615112i
$640$	4.35388e10	−	6.11054e10i	0.259512	−	0.364217i
$641$	2.15342e11			1.27554			0.637772	−	0.770225i	$-0.279856\pi$
$641$	2.15342e11			1.27554			0.637772	+	0.770225i	$0.279856\pi$
$642$	−1.36911e10	+	1.54403e11i	−0.0805930	+	0.908897i
$643$		−	1.22051e11i		−	0.713996i	−0.934105	−	0.356998i	$-0.883800\pi$
$643$		−	1.22051e11i		−	0.713996i	0.934105	−	0.356998i	$-0.116200\pi$
$644$	3.83121e10	+	6.84821e9i	0.222737	+	0.0398138i
$645$	2.84120e10			0.164159
$646$	−1.87165e11	−	1.65962e10i	−1.07472	−	0.0952966i
$647$		−	2.92452e11i		−	1.66893i	−0.551064	−	0.834463i	$-0.685778\pi$
$647$		−	2.92452e11i		−	1.66893i	0.551064	−	0.834463i	$-0.314222\pi$
$648$	1.52122e10	−	5.59838e10i	0.0862767	−	0.317514i
$649$	−5.28916e10			−0.298132
$650$	−4.56195e9	+	5.14479e10i	−0.0255562	+	0.288213i
$651$			1.41916e10i			0.0790149i
$652$	−4.37272e10	+	2.44631e11i	−0.241970	+	1.35369i
$653$	−2.80990e10			−0.154539			−0.0772696	−	0.997010i	$-0.524620\pi$
$653$	−2.80990e10			−0.154539			−0.0772696	+	0.997010i	$0.524620\pi$
$654$	−3.77990e10	−	3.35169e9i	−0.206619	−	0.0183211i
$655$		−	1.21968e11i		−	0.662644i
$656$	−4.68332e10	−	1.72953e10i	−0.252894	−	0.0933925i
$657$	1.24743e11			0.669509
$658$	−2.10618e10	+	2.37526e11i	−0.112355	+	1.26709i
$659$		−	2.51394e11i		−	1.33295i	−0.745529	−	0.666473i	$-0.767803\pi$
$659$		−	2.51394e11i		−	1.33295i	0.745529	−	0.666473i	$-0.232197\pi$
$660$	−6.99299e9	−	1.24998e9i	−0.0368542	−	0.00658762i
$661$	−2.53415e11			−1.32748			−0.663738	−	0.747965i	$-0.731031\pi$
$661$	−2.53415e11			−1.32748			−0.663738	+	0.747965i	$0.731031\pi$
$662$	−1.37915e10	−	1.22291e9i	−0.0718094	−	0.00636743i
$663$			8.02914e10i			0.415542i
$664$	−9.37086e10	−	2.54631e10i	−0.482067	−	0.130990i
$665$	−1.77756e11			−0.908945
$666$	−1.17974e10	+	1.33046e11i	−0.0599637	+	0.676247i
$667$			4.21056e10i			0.212734i
$668$	3.59771e10	−	2.01273e11i	0.180684	−	1.01083i
$669$	−9.03242e10			−0.450920
$670$	−6.85938e9	−	6.08230e8i	−0.0340397	−	0.00301834i
$671$		−	6.55116e10i		−	0.323168i
$672$	4.72178e10	−	9.97271e10i	0.231542	−	0.489031i
$673$	−1.77857e11			−0.866981			−0.433491	−	0.901158i	$-0.642718\pi$
$673$	−1.77857e11			−0.866981			−0.433491	+	0.901158i	$0.642718\pi$
$674$	−1.22167e9	+	1.37775e10i	−0.00591991	+	0.0667624i
$675$		−	3.59818e10i		−	0.173328i
$676$	−2.24687e11	−	4.01623e10i	−1.07595	−	0.192323i
$677$	−2.43910e11			−1.16111			−0.580556	−	0.814220i	$-0.697165\pi$
$677$	−2.43910e11			−1.16111			−0.580556	+	0.814220i	$0.697165\pi$
$678$	3.47874e10	+	3.08464e9i	0.164628	+	0.0145977i
$679$			2.49217e11i			1.17246i
$680$	−1.45975e10	+	5.37212e10i	−0.0682718	+	0.251252i
$681$	4.31678e10			0.200711
$682$	−4.73485e8	+	5.33978e9i	−0.00218861	+	0.0246823i
$683$			2.74209e11i			1.26008i	0.776562	+	0.630041i	$0.216962\pi$
$683$			2.74209e11i			1.26008i	−0.776562	+	0.630041i	$0.783038\pi$
$684$	−5.40045e10	+	3.02126e11i	−0.246720	+	1.38027i
$685$	1.25304e11			0.569118
$686$	1.92873e11	+	1.71023e10i	0.870912	+	0.0772249i
$687$		−	2.51904e10i		−	0.113086i
$688$	−5.77495e10	+	1.56378e11i	−0.257747	+	0.697944i
$689$	4.72295e11			2.09573
$690$	9.11362e8	−	1.02780e10i	0.00402063	−	0.0453431i
$691$			1.07912e11i			0.473323i	0.971592	+	0.236661i	$0.0760532\pi$
$691$			1.07912e11i			0.473323i	−0.971592	+	0.236661i	$0.923947\pi$
$692$	−1.51311e11	−	2.70465e10i	−0.659850	−	0.117947i
$693$	3.24730e10			0.140796
$694$	−1.75435e11	−	1.55560e10i	−0.756272	−	0.0670596i
$695$			1.32453e11i			0.567706i
$696$	1.15197e11	+	3.13020e10i	0.490912	+	0.133394i
$697$	3.70421e10			0.156951
$698$	2.82118e10	−	3.18161e11i	0.118853	−	1.34037i
$699$		−	4.69280e10i		−	0.196573i
$700$	−9.26670e9	+	5.18423e10i	−0.0385952	+	0.215919i
$701$	−1.00364e11			−0.415630			−0.207815	−	0.978168i	$-0.566635\pi$
$701$	−1.00364e11			−0.415630			−0.207815	+	0.978168i	$0.566635\pi$
$702$	3.03298e11	+	2.68938e10i	1.24888	+	0.110740i
$703$		−	4.06159e11i		−	1.66293i
$704$	2.10936e10	−	3.59482e10i	0.0858735	−	0.146348i
$705$	6.32201e10			0.255917
$706$	−1.87204e10	+	2.11121e11i	−0.0753521	+	0.849791i
$707$			1.71855e11i			0.687837i
$708$	−2.14409e11	−	3.83251e10i	−0.853315	−	0.152528i
$709$	−4.36108e11			−1.72587			−0.862937	−	0.505311i	$-0.831378\pi$
$709$	−4.36108e11			−1.72587			−0.862937	+	0.505311i	$0.831378\pi$
$710$	9.20321e10	+	8.16060e9i	0.362165	+	0.0321136i
$711$		−	9.69690e10i		−	0.379450i
$712$	4.15386e10	−	1.52869e11i	0.161634	−	0.594841i
$713$	−7.78647e9			−0.0301288
$714$	−7.23097e9	+	8.15481e10i	−0.0278230	+	0.313777i
$715$			2.86919e10i			0.109783i
$716$	5.21829e10	−	2.91936e11i	0.198553	−	1.11080i
$717$	1.21958e11			0.461459
$718$	4.13872e10	+	3.66986e9i	0.155729	+	0.0138087i
$719$			3.29910e11i			1.23447i	0.786780	+	0.617234i	$0.211747\pi$
$719$			3.29910e11i			1.23447i	−0.786780	+	0.617234i	$0.788253\pi$
$720$	8.52994e10	+	3.15006e10i	0.317407	+	0.117217i
$721$	3.87079e11			1.43238
$722$	5.84304e10	−	6.58956e11i	0.215026	−	2.42498i
$723$		−	1.12642e11i		−	0.412239i
$724$	2.00721e11	+	3.58784e10i	0.730531	+	0.130581i
$725$	−5.69755e10			−0.206222
$726$	1.32594e11	+	1.17573e10i	0.477285	+	0.0423215i
$727$			2.87638e11i			1.02969i	0.857282	+	0.514847i	$0.172151\pi$
$727$			2.87638e11i			1.02969i	−0.857282	+	0.514847i	$0.827849\pi$
$728$	−4.30064e11	−	1.16859e11i	−1.53111	−	0.416043i
$729$	−5.04496e10			−0.178627
$730$	−9.92618e9	+	1.11944e11i	−0.0349535	+	0.394192i
$731$		−	1.23685e11i		−	0.433158i
$732$	4.74695e10	−	2.65567e11i	0.165337	−	0.924974i
$733$	7.34639e10			0.254483			0.127241	−	0.991872i	$-0.459388\pi$
$733$	7.34639e10			0.254483			0.127241	+	0.991872i	$0.459388\pi$
$734$	5.77462e10	+	5.12043e9i	0.198948	+	0.0176410i
$735$			1.30567e10i			0.0447389i
$736$	5.47168e10	+	2.59068e10i	0.186470	+	0.0882881i
$737$	−3.82540e9			−0.0129660
$738$	5.34405e9	−	6.02681e10i	0.0180154	−	0.203171i
$739$			3.53166e11i			1.18413i	0.805889	+	0.592067i	$0.201688\pi$
$739$			3.53166e11i			1.18413i	−0.805889	+	0.592067i	$0.798312\pi$
$740$	−1.18456e11	−	2.11737e10i	−0.395029	−	0.0706107i
$741$	−3.98800e11			−1.32276
$742$	4.79687e11	+	4.25344e10i	1.58249	+	0.140322i
$743$			2.51184e11i			0.824208i	0.911137	+	0.412104i	$0.135206\pi$
$743$			2.51184e11i			0.824208i	−0.911137	+	0.412104i	$0.864794\pi$
$744$	−5.78858e9	+	2.13030e10i	−0.0188921	+	0.0695263i
$745$	−8.34345e10			−0.270845
$746$	−5.86705e9	+	6.61663e10i	−0.0189437	+	0.213639i
$747$		−	1.17685e11i		−	0.377954i
$748$	−5.44149e9	+	3.04422e10i	−0.0173825	+	0.0972456i
$749$	6.38363e11			2.02834
$750$	1.39077e10	+	1.23321e9i	0.0439552	+	0.00389757i
$751$		−	5.06685e11i		−	1.59286i	−0.604729	−	0.796431i	$-0.706719\pi$
$751$		−	5.06685e11i		−	1.59286i	0.604729	−	0.796431i	$-0.293281\pi$
$752$	−1.28499e11	+	3.47958e11i	−0.401818	+	1.08807i
$753$	−1.16918e10			−0.0363666
$754$	4.25852e10	−	4.80259e11i	0.131757	−	1.48590i
$755$		−	2.02653e11i		−	0.623684i
$756$	3.05623e11	+	5.46295e10i	0.935620	+	0.167240i
$757$	9.66712e10			0.294384			0.147192	−	0.989108i	$-0.452977\pi$
$757$	9.66712e10			0.294384			0.147192	+	0.989108i	$0.452977\pi$
$758$	−3.02097e11	−	2.67873e10i	−0.915102	−	0.0811432i
$759$		−	5.73192e9i		−	0.0172716i
$760$	−2.66828e11	−	7.25042e10i	−0.799793	−	0.217324i
$761$	5.18752e11			1.54675			0.773376	−	0.633947i	$-0.218566\pi$
$761$	5.18752e11			1.54675			0.773376	+	0.633947i	$0.218566\pi$
$762$	−1.13570e10	+	1.28079e11i	−0.0336855	+	0.379892i
$763$			1.56276e11i			0.461100i
$764$	8.29940e10	−	4.64307e11i	0.243598	−	1.36280i
$765$	−6.74664e10			−0.196989
$766$	1.41473e11	+	1.25446e10i	0.410920	+	0.0364368i
$767$			8.79708e11i			2.54189i
$768$	1.11556e11	−	1.30440e11i	0.320661	−	0.374944i
$769$	1.06291e11			0.303943			0.151972	−	0.988385i	$-0.451438\pi$
$769$	1.06291e11			0.303943			0.151972	+	0.988385i	$0.451438\pi$
$770$	−2.58397e9	+	2.91410e10i	−0.00735062	+	0.0828975i
$771$		−	1.21384e11i		−	0.343514i
$772$	−5.90200e11	−	1.05497e11i	−1.66161	−	0.297010i
$773$	−9.89630e10			−0.277176			−0.138588	−	0.990350i	$-0.544256\pi$
$773$	−9.89630e10			−0.277176			−0.138588	+	0.990350i	$0.544256\pi$
$774$	−2.01237e11	−	1.78439e10i	−0.560717	−	0.0497195i
$775$		−	1.05363e10i		−	0.0292066i
$776$	−1.01652e11	+	3.74098e11i	−0.280330	+	1.03167i
$777$	−1.76964e11			−0.485514
$778$	−2.90546e10	+	3.27666e11i	−0.0793043	+	0.894363i
$779$			1.83984e11i			0.499610i
$780$	−2.07901e10	+	1.16309e11i	−0.0561665	+	0.314222i
$781$	5.13253e10			0.137952
$782$	−4.47426e10	−	3.96738e9i	−0.119645	−	0.0106091i
$783$			3.35885e11i			0.893601i
$784$	−7.18632e10	−	2.65387e10i	−0.190214	−	0.0702451i
$785$	−1.87351e11			−0.493376
$786$	2.46436e10	−	2.77921e11i	0.0645674	−	0.728166i
$787$		−	3.29755e11i		−	0.859592i	−0.902926	−	0.429796i	$-0.858585\pi$
$787$		−	3.29755e11i		−	0.859592i	0.902926	−	0.429796i	$-0.141415\pi$
$788$	4.69690e11	+	8.39562e10i	1.21817	+	0.217745i
$789$	−6.78670e10			−0.175126
$790$	8.70192e10	+	7.71610e9i	0.223412	+	0.0198102i
$791$		−	1.43825e11i		−	0.367391i
$792$	4.87450e10	+	1.32453e10i	0.123888	+	0.0336636i
$793$	−1.08961e12			−2.75535
$794$	−2.89519e10	+	3.26509e11i	−0.0728443	+	0.821509i
$795$		−	1.27674e11i		−	0.319619i
$796$	−8.19853e10	+	4.58664e11i	−0.204213	+	1.14246i
$797$	6.85369e10			0.169860			0.0849300	−	0.996387i	$-0.472933\pi$
$797$	6.85369e10			0.169860			0.0849300	+	0.996387i	$0.472933\pi$
$798$	−4.05042e11	−	3.59156e10i	−0.998822	−	0.0885668i
$799$		−	2.75213e11i		−	0.675277i
$800$	−3.50559e10	+	7.40403e10i	−0.0855857	+	0.180763i
$801$	1.91983e11			0.466371
$802$	1.03245e10	−	1.16435e11i	0.0249557	−	0.281441i
$803$			6.24297e10i			0.150151i
$804$	−1.55072e10	−	2.77187e9i	−0.0371115	−	0.00663360i
$805$	−4.24933e10			−0.101190
$806$	8.88128e10	+	7.87514e9i	0.210443	+	0.0186603i
$807$			3.47891e10i			0.0820256i
$808$	−7.00974e10	+	2.57971e11i	−0.164459	+	0.605237i
$809$	−7.62508e11			−1.78012			−0.890062	−	0.455840i	$-0.849339\pi$
$809$	−7.62508e11			−1.78012			−0.890062	+	0.455840i	$0.849339\pi$
$810$	−5.59459e9	+	6.30936e10i	−0.0129966	+	0.146570i
$811$		−	4.40805e11i		−	1.01897i	−0.860478	−	0.509487i	$-0.829835\pi$
$811$		−	4.40805e11i		−	1.01897i	0.860478	−	0.509487i	$-0.170165\pi$
$812$	8.65034e10	−	4.83940e11i	0.198980	−	1.11319i
$813$	2.94459e11			0.674005
$814$	−6.65850e10	−	5.90418e9i	−0.151663	−	0.0134481i
$815$		−	2.71329e11i		−	0.614986i
$816$	−4.41167e10	+	1.19462e11i	−0.0995044	+	0.269444i
$817$	6.14330e11			1.37884
$818$	1.49642e10	−	1.68761e11i	0.0334226	−	0.376927i
$819$		−	5.40100e11i		−	1.20043i
$820$	5.36588e10	+	9.59140e9i	0.118682	+	0.0212142i
$821$	−2.67657e11			−0.589123			−0.294562	−	0.955632i	$-0.595174\pi$
$821$	−2.67657e11			−0.589123			−0.294562	+	0.955632i	$0.595174\pi$
$822$	2.85522e11	+	2.53176e10i	0.625393	+	0.0554544i
$823$		−	3.84869e11i		−	0.838906i	−0.907777	−	0.419453i	$-0.862222\pi$
$823$		−	3.84869e11i		−	0.838906i	0.907777	−	0.419453i	$-0.137778\pi$
$824$	5.81042e11	+	1.57884e11i	1.26037	+	0.342476i
$825$	7.75618e9			0.0167429
$826$	−7.92257e10	+	8.93477e11i	−0.170195	+	1.91939i
$827$			4.88174e11i			1.04364i	0.853054	+	0.521822i	$0.174747\pi$
$827$			4.88174e11i			1.04364i	−0.853054	+	0.521822i	$0.825253\pi$
$828$	−1.29100e10	+	7.22246e10i	−0.0274666	+	0.153661i
$829$	−1.47134e11			−0.311526			−0.155763	−	0.987794i	$-0.549784\pi$
$829$	−1.47134e11			−0.311526			−0.155763	+	0.987794i	$0.549784\pi$
$830$	1.05609e11	+	9.36452e9i	0.222531	+	0.0197321i
$831$		−	9.48464e10i		−	0.198892i
$832$	−5.97900e11	−	3.50834e11i	−1.24777	−	0.732164i
$833$	5.68392e10			0.118050
$834$	−2.67622e10	+	3.01813e11i	−0.0553168	+	0.623841i
$835$			2.23239e11i			0.459223i
$836$	−1.51204e11	−	2.70273e10i	−0.309555	−	0.0553323i
$837$	−6.21142e10			−0.126558
$838$	−4.16027e10	−	3.68896e9i	−0.0843617	−	0.00748046i
$839$		−	4.39919e11i		−	0.887821i	−0.896071	−	0.443910i	$-0.853591\pi$
$839$		−	4.39919e11i		−	0.887821i	0.896071	−	0.443910i	$-0.146409\pi$
$840$	−3.15902e10	+	1.16257e11i	−0.0634505	+	0.233509i
$841$	3.16120e10			0.0631929
$842$	−1.31357e10	+	1.48140e11i	−0.0261340	+	0.294729i
$843$		−	2.20086e11i		−	0.435794i
$844$	1.30240e11	−	7.28622e11i	0.256669	−	1.43593i
$845$	2.49208e11			0.488804
$846$	−4.47776e11	−	3.97049e10i	−0.874137	−	0.0775108i
$847$		−	5.48198e11i		−	1.06513i
$848$	7.02705e11	+	2.59506e11i	1.35891	+	0.501838i
$849$	1.82190e11			0.350666
$850$	5.36849e9	−	6.05437e10i	0.0102843	−	0.115983i
$851$		−	9.70941e10i		−	0.185129i
$852$	2.08059e11	+	3.71901e10i	0.394847	+	0.0705780i
$853$	6.98819e11			1.31998			0.659992	−	0.751273i	$-0.270560\pi$
$853$	6.98819e11			1.31998			0.659992	+	0.751273i	$0.270560\pi$
$854$	−1.10666e12	−	9.81291e10i	−2.08058	−	0.184487i
$855$		−	3.35099e11i		−	0.627059i
$856$	9.58242e11	+	2.60379e11i	1.78476	+	0.484966i
$857$	3.28226e10			0.0608485			0.0304242	−	0.999537i	$-0.490314\pi$
$857$	3.28226e10			0.0608485			0.0304242	+	0.999537i	$0.490314\pi$
$858$	−5.79719e9	+	6.53785e10i	−0.0106972	+	0.120638i
$859$			6.28697e11i			1.15470i	0.816497	+	0.577349i	$0.195913\pi$
$859$			6.28697e11i			1.15470i	−0.816497	+	0.577349i	$0.804087\pi$
$860$	3.20260e10	−	1.79168e11i	0.0585476	−	0.327543i
$861$	8.01623e10			0.145867
$862$	2.97330e11	+	2.63646e10i	0.538529	+	0.0477521i
$863$			7.90308e11i			1.42480i	0.701775	+	0.712399i	$0.252391\pi$
$863$			7.90308e11i			1.42480i	−0.701775	+	0.712399i	$0.747609\pi$
$864$	4.36487e11	+	2.06664e11i	0.783278	+	0.370859i
$865$	1.67824e11			0.299771
$866$	2.35962e10	−	2.66109e11i	0.0419537	−	0.473138i
$867$			1.84281e11i			0.326140i
$868$	8.94936e10	+	1.59968e10i	0.157657	+	0.0281809i
$869$	4.85296e10			0.0850997
$870$	−1.29827e11	−	1.15119e10i	−0.226614	−	0.0200941i
$871$			6.36251e10i			0.110549i
$872$	−6.37430e10	+	2.34586e11i	−0.110247	+	0.405728i
$873$	−4.69815e11			−0.808854
$874$	1.97056e10	−	2.22232e11i	0.0337710	−	0.380857i
$875$		−	5.75001e10i		−	0.0980926i
$876$	−4.52364e10	+	2.53074e11i	−0.0768195	+	0.429764i
$877$	7.21024e10			0.121885			0.0609427	−	0.998141i	$-0.480589\pi$
$877$	7.21024e10			0.121885			0.0609427	+	0.998141i	$0.480589\pi$
$878$	8.73947e10	+	7.74940e9i	0.147064	+	0.0130404i
$879$			3.30733e11i			0.554015i
$880$	−1.57650e10	+	4.26894e10i	−0.0262883	+	0.0711851i
$881$	−5.33265e11			−0.885196			−0.442598	−	0.896720i	$-0.645943\pi$
$881$	−5.33265e11			−0.885196			−0.442598	+	0.896720i	$0.645943\pi$
$882$	8.20017e9	−	9.24783e10i	0.0135503	−	0.152815i
$883$		−	3.49301e11i		−	0.574589i	−0.957842	−	0.287295i	$-0.907244\pi$
$883$		−	3.49301e11i		−	0.574589i	0.957842	−	0.287295i	$-0.0927559\pi$
$884$	5.06324e11	+	9.05043e10i	0.829123	+	0.148204i
$885$	2.37808e11			0.387662
$886$	9.52761e10	+	8.44825e9i	0.154614	+	0.0137098i
$887$		−	2.17981e11i		−	0.352148i	−0.984377	−	0.176074i	$-0.943660\pi$
$887$		−	2.17981e11i		−	0.352148i	0.984377	−	0.176074i	$-0.0563398\pi$
$888$	−2.65640e11	−	7.21812e10i	−0.427210	−	0.116084i
$889$	5.29532e11			0.847784
$890$	−1.52766e10	+	1.72284e11i	−0.0243482	+	0.274589i
$891$			3.51866e10i			0.0558299i
$892$	−1.01813e11	+	5.69591e11i	−0.160822	+	0.899712i
$893$	1.36696e12			2.14956
$894$	−1.90117e11	−	1.68579e10i	−0.297626	−	0.0263909i
$895$			3.23796e11i			0.504637i
$896$	−5.75663e11	−	4.10171e11i	−0.893174	−	0.636405i
$897$	−9.53348e10			−0.147259
$898$	4.40488e10	−	4.96765e11i	0.0677374	−	0.763916i
$899$			9.83549e10i			0.150577i
$900$	−9.77311e10	−	1.74692e10i	−0.148958	−	0.0266259i
$901$	−5.55795e11			−0.843365
$902$	3.01621e10	+	2.67451e9i	0.0455654	+	0.00404034i
$903$		−	2.67665e11i		−	0.402569i
$904$	5.86642e10	−	2.15895e11i	0.0878414	−	0.323272i
$905$	−2.22627e11			−0.331881
$906$	4.09459e10	−	4.61772e11i	0.0607712	−	0.685354i
$907$		−	6.26742e9i		−	0.00926104i	−0.999989	−	0.00463052i	$-0.998526\pi$
$907$		−	6.26742e9i		−	0.00926104i	0.999989	−	0.00463052i	$-0.00147395\pi$
$908$	4.86587e10	−	2.72220e11i	0.0715842	−	0.400476i
$909$	−3.23975e11			−0.474522
$910$	4.84681e11	+	4.29773e10i	0.706790	+	0.0626719i
$911$			6.22008e11i			0.903073i	0.892253	+	0.451536i	$0.149124\pi$
$911$			6.22008e11i			0.903073i	−0.892253	+	0.451536i	$0.850876\pi$
$912$	−5.93356e11	−	2.19123e11i	−0.857701	−	0.316745i
$913$	5.88972e10			0.0847640
$914$	6.13279e9	−	6.91632e10i	0.00878766	−	0.0991038i
$915$			2.94550e11i			0.420217i
$916$	−1.58852e11	−	2.83945e10i	−0.225638	−	0.0403323i
$917$	−1.14904e12			−1.62501
$918$	−3.56921e11	−	3.16486e10i	−0.502575	−	0.0445640i
$919$			8.27760e11i			1.16049i	0.814441	+	0.580246i	$0.197044\pi$
$919$			8.27760e11i			1.16049i	−0.814441	+	0.580246i	$0.802956\pi$
$920$	−6.37865e10	−	1.73324e10i	−0.0890384	−	0.0241940i
$921$	−3.09142e11			−0.429654
$922$	7.29441e10	−	8.22635e11i	0.100941	−	1.13837i
$923$		−	8.53656e11i		−	1.17619i
$924$	−1.17759e10	+	6.58797e10i	−0.0161549	+	0.0903782i
$925$	1.31383e11			0.179463
$926$	−1.09462e12	−	9.70610e10i	−1.48874	−	0.132008i
$927$			7.29708e11i			0.988167i
$928$	3.27242e11	−	6.91156e11i	0.441243	−	0.931932i
$929$	−6.50031e11			−0.872713			−0.436356	−	0.899774i	$-0.643731\pi$
$929$	−6.50031e11			−0.872713			−0.436356	+	0.899774i	$0.643731\pi$
$930$	2.12886e9	−	2.40084e10i	0.00284587	−	0.0320946i
$931$			2.82315e11i			0.375781i
$932$	−2.95931e11	−	5.28971e10i	−0.392218	−	0.0701082i
$933$	4.31866e11			0.569932
$934$	3.42012e11	+	3.03266e10i	0.449421	+	0.0398508i
$935$		−	3.37646e10i		−	0.0441789i
$936$	2.20299e11	−	8.10740e11i	0.287018	−	1.05628i
$937$	−6.60322e11			−0.856639			−0.428319	−	0.903627i	$-0.640894\pi$
$937$	−6.60322e11			−0.856639			−0.428319	+	0.903627i	$0.640894\pi$
$938$	−5.73002e9	+	6.46209e10i	−0.00740193	+	0.0834760i
$939$			1.89032e11i			0.243149i
$940$	7.12616e10	−	3.98671e11i	0.0912734	−	0.510626i
$941$	−2.13315e11			−0.272059			−0.136029	−	0.990705i	$-0.543434\pi$
$941$	−2.13315e11			−0.272059			−0.136029	+	0.990705i	$0.543434\pi$
$942$	−4.26906e11	−	3.78543e10i	−0.542161	−	0.0480741i
$943$			4.39823e10i			0.0556200i
$944$	−4.83362e11	+	1.30888e12i	−0.608674	+	1.64820i
$945$	−3.38978e11			−0.425054
$946$	8.93027e9	−	1.00712e11i	0.0111506	−	0.125753i
$947$			1.23955e10i			0.0154121i	0.999970	+	0.00770607i	$0.00245294\pi$
$947$			1.23955e10i			0.0154121i	−0.999970	+	0.00770607i	$0.997547\pi$
$948$	1.96726e11	+	3.51644e10i	0.243573	+	0.0435382i
$949$	1.03835e12			1.28020
$950$	3.00715e11	+	2.66648e10i	0.369199	+	0.0327373i
$951$			2.17698e11i			0.266154i
$952$	5.06098e11	+	1.37520e11i	0.616150	+	0.167424i
$953$	−1.59801e12			−1.93734			−0.968672	−	0.248344i	$-0.920114\pi$
$953$	−1.59801e12			−1.93734			−0.968672	+	0.248344i	$0.920114\pi$
$954$	−8.01843e10	+	9.04288e11i	−0.0968046	+	1.09172i
$955$			5.14980e11i			0.619122i
$956$	1.37471e11	−	7.69076e11i	0.164581	−	0.920741i
$957$	−7.24029e10			−0.0863193
$958$	1.31423e12	+	1.16534e11i	1.56030	+	0.138354i
$959$		−	1.18046e12i		−	1.39566i
$960$	−9.48396e10	+	1.61628e11i	−0.111662	+	0.190297i
$961$	8.34703e11			0.978674
$962$	−9.81999e10	+	1.10746e12i	−0.114660	+	1.29309i
$963$			1.20342e12i			1.39930i
$964$	−7.10332e11	−	1.26970e11i	−0.822533	−	0.147026i
$965$	6.54612e11			0.754875
$966$	−9.68270e10	−	8.58577e9i	−0.111196	−	0.00985986i
$967$		−	4.54304e11i		−	0.519566i	−0.965667	−	0.259783i	$-0.916349\pi$
$967$		−	4.54304e11i		−	0.519566i	0.965667	−	0.259783i	$-0.0836510\pi$
$968$	2.23602e11	−	8.22896e11i	0.254668	−	0.937224i
$969$	4.69307e11			0.532306
$970$	3.73845e10	−	4.21608e11i	0.0422284	−	0.476236i
$971$			3.98175e11i			0.447917i	0.974599	+	0.223958i	$0.0718979\pi$
$971$			3.98175e11i			0.447917i	−0.974599	+	0.223958i	$0.928102\pi$
$972$	−1.61614e11	+	9.04143e11i	−0.181056	+	1.01291i
$973$	1.24782e12			1.39219
$974$	4.69636e10	+	4.16432e9i	0.0521826	+	0.00462710i
$975$		−	1.29003e11i		−	0.142752i
$976$	−1.62118e12	−	5.98693e11i	−1.78662	−	0.659789i
$977$	1.61846e12			1.77633			0.888165	−	0.459525i	$-0.151980\pi$
$977$	1.61846e12			1.77633			0.888165	+	0.459525i	$0.151980\pi$
$978$	5.48219e10	−	6.18260e11i	0.0599237	−	0.675796i
$979$			9.60806e10i			0.104594i
$980$	8.23367e10	+	1.47175e10i	0.0892667	+	0.0159562i
$981$	−2.94607e11			−0.318102
$982$	1.30339e12	+	1.15573e11i	1.40161	+	0.124282i
$983$		−	7.83368e10i		−	0.0838980i	−0.999120	−	0.0419490i	$-0.986643\pi$
$983$		−	7.83368e10i		−	0.0838980i	0.999120	−	0.0419490i	$-0.0133567\pi$
$984$	1.20331e11	+	3.26971e10i	0.128351	+	0.0348762i
$985$	−5.20950e11			−0.553416
$986$	−5.01141e10	+	5.65167e11i	−0.0530215	+	0.597956i
$987$		−	5.95585e11i		−	0.627589i
$988$	−4.49526e11	+	2.51486e12i	−0.471767	+	2.63929i
$989$	1.46858e11			0.153502
$990$	−5.49355e10	−	4.87120e9i	−0.0571890	−	0.00507102i
$991$			1.11925e12i			1.16046i	0.814451	+	0.580232i	$0.197038\pi$
$991$			1.11925e12i			1.16046i	−0.814451	+	0.580232i	$0.802962\pi$
$992$	1.27813e11	+	6.05159e10i	0.131987	+	0.0624917i
$993$	3.45816e10			0.0355671
$994$	7.68795e10	−	8.67017e11i	0.0787526	−	0.888142i
$995$		−	5.08721e11i		−	0.519023i
$996$	2.38754e11	+	4.26767e10i	0.242612	+	0.0433665i
$997$	−8.38483e11			−0.848621			−0.424311	−	0.905517i	$-0.639483\pi$
$997$	−8.38483e11			−0.848621			−0.424311	+	0.905517i	$0.639483\pi$
$998$	−7.48363e11	−	6.63583e10i	−0.754380	−	0.0668918i
$999$		−	7.74539e11i		−	0.777645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.8	yes	16
3.2	odd	2		180.9.c.a.91.9		16
4.3	odd	2	inner	20.9.b.a.11.7	✓	16
5.2	odd	4		100.9.d.c.99.1		32
5.3	odd	4		100.9.d.c.99.32		32
5.4	even	2		100.9.b.d.51.9		16
8.3	odd	2		320.9.b.d.191.6		16
8.5	even	2		320.9.b.d.191.11		16
12.11	even	2		180.9.c.a.91.10		16
20.3	even	4		100.9.d.c.99.2		32
20.7	even	4		100.9.d.c.99.31		32
20.19	odd	2		100.9.b.d.51.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.7	✓	16	4.3	odd	2	inner
20.9.b.a.11.8	yes	16	1.1	even	1	trivial
100.9.b.d.51.9		16	5.4	even	2
100.9.b.d.51.10		16	20.19	odd	2
100.9.d.c.99.1		32	5.2	odd	4
100.9.d.c.99.2		32	20.3	even	4
100.9.d.c.99.31		32	20.7	even	4
100.9.d.c.99.32		32	5.3	odd	4
180.9.c.a.91.9		16	3.2	odd	2
180.9.c.a.91.10		16	12.11	even	2
320.9.b.d.191.6		16	8.3	odd	2
320.9.b.d.191.11		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41320 + 15.9375i) q^{2} -39.9624i q^{3} +(-252.006 - 45.0455i) q^{4} +279.508 q^{5} +(636.899 + 56.4746i) q^{6} -2633.20i q^{7} +(1074.04 - 3952.68i) q^{8} +4964.01 q^{9} +O(q^{10})\)	\(q+(-1.41320 + 15.9375i) q^{2} -39.9624i q^{3} +(-252.006 - 45.0455i) q^{4} +279.508 q^{5} +(636.899 + 56.4746i) q^{6} -2633.20i q^{7} +(1074.04 - 3952.68i) q^{8} +4964.01 q^{9} +(-395.000 + 4454.66i) q^{10} +2484.31i q^{11} +(-1800.13 + 10070.7i) q^{12} +41319.8 q^{13} +(41966.5 + 3721.22i) q^{14} -11169.8i q^{15} +(61477.8 + 22703.5i) q^{16} -48625.0 q^{17} +(-7015.11 + 79113.7i) q^{18} -241516. i q^{19} +(-70437.8 - 12590.6i) q^{20} -105229. q^{21} +(-39593.7 - 3510.82i) q^{22} -57735.4i q^{23} +(-157958. - 42921.4i) q^{24} +78125.0 q^{25} +(-58392.9 + 658533. i) q^{26} -460567. i q^{27} +(-118614. + 663581. i) q^{28} -729286. q^{29} +(178019. + 15785.1i) q^{30} -134865. i q^{31} +(-448716. + 947716. i) q^{32} +99279.1 q^{33} +(68716.6 - 774960. i) q^{34} -736001. i q^{35} +(-1.25096e6 - 223606. i) q^{36} +1.68171e6 q^{37} +(3.84915e6 + 341309. i) q^{38} -1.65124e6i q^{39} +(300205. - 1.10481e6i) q^{40} -761790. q^{41} +(148709. - 1.67708e6i) q^{42} +2.54364e6i q^{43} +(111907. - 626061. i) q^{44} +1.38748e6 q^{45} +(920156. + 81591.4i) q^{46} +5.65990e6i q^{47} +(907284. - 2.45680e6i) q^{48} -1.16893e6 q^{49} +(-110406. + 1.24511e6i) q^{50} +1.94317e6i q^{51} +(-1.04128e7 - 1.86127e6i) q^{52} +1.14302e7 q^{53} +(7.34027e6 + 650871. i) q^{54} +694387. i q^{55} +(-1.04082e7 - 2.82817e6i) q^{56} -9.65155e6 q^{57} +(1.03062e6 - 1.16230e7i) q^{58} +2.12902e7i q^{59} +(-503150. + 2.81486e6i) q^{60} -2.63701e7 q^{61} +(2.14940e6 + 190590. i) q^{62} -1.30712e7i q^{63} +(-1.44701e7 - 8.49070e6i) q^{64} +1.15492e7 q^{65} +(-140301. + 1.58226e6i) q^{66} +1.53982e6i q^{67} +(1.22538e7 + 2.19034e6i) q^{68} -2.30724e6 q^{69} +(1.17300e7 + 1.04011e6i) q^{70} -2.06597e7i q^{71} +(5.33157e6 - 1.96211e7i) q^{72} +2.51296e7 q^{73} +(-2.37658e6 + 2.68022e7i) q^{74} -3.12206e6i q^{75} +(-1.08792e7 + 6.08634e7i) q^{76} +6.54169e6 q^{77} +(2.63165e7 + 2.33352e6i) q^{78} -1.95344e7i q^{79} +(1.71836e7 + 6.34581e6i) q^{80} +1.41635e7 q^{81} +(1.07656e6 - 1.21410e7i) q^{82} -2.37076e7i q^{83} +(2.65183e7 + 4.74009e6i) q^{84} -1.35911e7 q^{85} +(-4.05392e7 - 3.59466e6i) q^{86} +2.91440e7i q^{87} +(9.81968e6 + 2.66826e6i) q^{88} +3.86749e7 q^{89} +(-1.96078e6 + 2.21130e7i) q^{90} -1.08803e8i q^{91} +(-2.60072e6 + 1.45497e7i) q^{92} -5.38951e6 q^{93} +(-9.02045e7 - 7.99855e6i) q^{94} -6.75057e7i q^{95} +(3.78730e7 + 1.79317e7i) q^{96} -9.46443e7 q^{97} +(1.65192e6 - 1.86298e7i) q^{98} +1.23322e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

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