LMFDB - Embedded newform 8.11.d.b.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,11,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$5.08285802139$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 51x^{5} + 30855x^{4} - 121569x^{3} + 12144527x^{2} + 279415575x + 3348211684 $ x^8 - 3x^7 + 5x^6 - 51x^5 + 30855x^4 - 121569x^3 + 12144527x^2 + 279415575*x + 3348211684
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$-11.4287 - 6.91461i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.11.d.b.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(28.8575 + 13.8292i) q^{2} -196.684 q^{3} +(641.505 + 798.152i) q^{4} +5381.00i q^{5} +(-5675.81 - 2719.99i) q^{6} -6613.83i q^{7} +(7474.38 + 31904.2i) q^{8} -20364.2 q^{9} +(-74415.0 + 155282. i) q^{10} +221096. q^{11} +(-126174. - 156984. i) q^{12} -361689. i q^{13} +(91464.1 - 190858. i) q^{14} -1.05836e6i q^{15} +(-225518. + 1.02404e6i) q^{16} +776217. q^{17} +(-587659. - 281621. i) q^{18} +1.46186e6 q^{19} +(-4.29486e6 + 3.45194e6i) q^{20} +1.30084e6i q^{21} +(6.38025e6 + 3.05758e6i) q^{22} +2.34458e6i q^{23} +(-1.47009e6 - 6.27505e6i) q^{24} -1.91895e7 q^{25} +(5.00188e6 - 1.04374e7i) q^{26} +1.56193e7 q^{27} +(5.27884e6 - 4.24281e6i) q^{28} +2.88750e7i q^{29} +(1.46363e7 - 3.05415e7i) q^{30} -3.00762e7i q^{31} +(-2.06695e7 + 2.64324e7i) q^{32} -4.34861e7 q^{33} +(2.23996e7 + 1.07345e7i) q^{34} +3.55890e7 q^{35} +(-1.30637e7 - 1.62537e7i) q^{36} -1.16919e7i q^{37} +(4.21857e7 + 2.02164e7i) q^{38} +7.11386e7i q^{39} +(-1.71676e8 + 4.02196e7i) q^{40} +4.70330e7 q^{41} +(-1.79896e7 + 3.75389e7i) q^{42} +3.52427e7 q^{43} +(1.41834e8 + 1.76468e8i) q^{44} -1.09580e8i q^{45} +(-3.24238e7 + 6.76587e7i) q^{46} -4.23068e8i q^{47} +(4.43559e7 - 2.01412e8i) q^{48} +2.38733e8 q^{49} +(-5.53761e8 - 2.65376e8i) q^{50} -1.52670e8 q^{51} +(2.88683e8 - 2.32025e8i) q^{52} +9.16056e6i q^{53} +(4.50735e8 + 2.16003e8i) q^{54} +1.18971e9i q^{55} +(2.11009e8 - 4.94343e7i) q^{56} -2.87526e8 q^{57} +(-3.99319e8 + 8.33260e8i) q^{58} -1.03098e9 q^{59} +(8.44732e8 - 6.78943e8i) q^{60} +1.37140e8i q^{61} +(4.15930e8 - 8.67921e8i) q^{62} +1.34685e8i q^{63} +(-9.62009e8 + 4.76928e8i) q^{64} +1.94625e9 q^{65} +(-1.25490e9 - 6.01379e8i) q^{66} -7.94671e8 q^{67} +(4.97947e8 + 6.19539e8i) q^{68} -4.61143e8i q^{69} +(1.02701e9 + 4.92168e8i) q^{70} -2.04858e9i q^{71} +(-1.52210e8 - 6.49703e8i) q^{72} -1.88707e9 q^{73} +(1.61690e8 - 3.37399e8i) q^{74} +3.77428e9 q^{75} +(9.37794e8 + 1.16679e9i) q^{76} -1.46229e9i q^{77} +(-9.83792e8 + 2.05288e9i) q^{78} +1.04965e9i q^{79} +(-5.51035e9 - 1.21351e9i) q^{80} -1.86960e9 q^{81} +(1.35725e9 + 6.50430e8i) q^{82} +3.77162e9 q^{83} +(-1.03827e9 + 8.34494e8i) q^{84} +4.17682e9i q^{85} +(1.01702e9 + 4.87380e8i) q^{86} -5.67927e9i q^{87} +(1.65255e9 + 7.05387e9i) q^{88} -4.07338e9 q^{89} +(1.51540e9 - 3.16219e9i) q^{90} -2.39215e9 q^{91} +(-1.87133e9 + 1.50406e9i) q^{92} +5.91551e9i q^{93} +(5.85070e9 - 1.22087e10i) q^{94} +7.86629e9i q^{95} +(4.06538e9 - 5.19884e9i) q^{96} +1.76770e9 q^{97} +(6.88921e9 + 3.30149e9i) q^{98} -4.50244e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19}+ \cdots - 13646747232 q^{99}+O(q^{100}) $ 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9 + 9120 * q^10 + 143328 * q^11 + 180120 * q^12 - 400320 * q^14 - 1987312 * q^16 - 370800 * q^17 + 3067758 * q^18 + 1753312 * q^19 + 2557440 * q^20 + 1549180 * q^22 - 19794288 * q^24 - 18792760 * q^25 + 1891680 * q^26 + 28949184 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 64016928 * q^32 - 74308704 * q^33 - 115705388 * q^34 + 53736960 * q^35 + 50631516 * q^36 + 375128220 * q^38 - 357584640 * q^40 + 92669328 * q^41 - 576155520 * q^42 - 10190624 * q^43 + 727831512 * q^44 + 851947200 * q^46 - 1142760480 * q^48 - 80432248 * q^49 - 1669361190 * q^50 - 276714816 * q^51 + 2420759040 * q^52 + 1749768696 * q^54 - 2928529920 * q^56 + 1400712864 * q^57 - 3245264160 * q^58 - 965642016 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 5804705728 * q^64 - 839028480 * q^65 - 5970262296 * q^66 - 1225582880 * q^67 + 5258111400 * q^68 + 7723829760 * q^70 - 4343608728 * q^72 + 2800072720 * q^73 - 7669373280 * q^74 + 4485554400 * q^75 + 3753451288 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 - 11909065176 * q^81 - 3638778380 * q^82 + 1853422560 * q^83 - 2916218880 * q^84 + 3022180476 * q^86 + 5815578640 * q^88 + 6162596112 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 7877525568 * q^96 - 9697863536 * q^97 + 34759868298 * q^98 - 13646747232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	28.8575	+	13.8292i	0.901795	+	0.432163i
$2$	28.8575	+	13.8292i	0.901795	+	0.432163i
$3$	−196.684			−0.809401			−0.404701	−	0.914449i	$-0.632624\pi$
$3$	−196.684			−0.809401			−0.404701	+	0.914449i	$0.632624\pi$
$4$	641.505	+	798.152i	0.626470	+	0.779446i
$5$			5381.00i			1.72192i	0.508673	+	0.860960i	$0.330136\pi$
$5$			5381.00i			1.72192i	−0.508673	+	0.860960i	$0.669864\pi$
$6$	−5675.81	−	2719.99i	−0.729914	−	0.349793i
$7$		−	6613.83i		−	0.393516i	−0.980452	−	0.196758i	$-0.936959\pi$
$7$		−	6613.83i		−	0.393516i	0.980452	−	0.196758i	$-0.0630414\pi$
$8$	7474.38	+	31904.2i	0.228100	+	0.973638i
$9$	−20364.2			−0.344870
$10$	−74415.0	+	155282.i	−0.744150	+	1.55282i
$11$	221096.			1.37283			0.686415	−	0.727210i	$-0.259184\pi$
$11$	221096.			1.37283			0.686415	+	0.727210i	$0.259184\pi$
$12$	−126174.	−	156984.i	−0.507065	−	0.630884i
$13$		−	361689.i		−	0.974134i	−0.873365	−	0.487067i	$-0.838067\pi$
$13$		−	361689.i		−	0.974134i	0.873365	−	0.487067i	$-0.161933\pi$
$14$	91464.1	−	190858.i	0.170063	−	0.354871i
$15$		−	1.05836e6i		−	1.39372i
$16$	−225518.	+	1.02404e6i	−0.215071	+	0.976598i
$17$	776217.			0.546687			0.273343	−	0.961917i	$-0.411870\pi$
$17$	776217.			0.546687			0.273343	+	0.961917i	$0.411870\pi$
$18$	−587659.	−	281621.i	−0.311002	−	0.149040i
$19$	1.46186e6			0.590390			0.295195	−	0.955437i	$-0.404615\pi$
$19$	1.46186e6			0.590390			0.295195	+	0.955437i	$0.404615\pi$
$20$	−4.29486e6	+	3.45194e6i	−1.34214	+	1.07873i
$21$			1.30084e6i			0.318513i
$22$	6.38025e6	+	3.05758e6i	1.23801	+	0.593286i
$23$			2.34458e6i			0.364273i	0.983273	+	0.182136i	$0.0583012\pi$
$23$			2.34458e6i			0.364273i	−0.983273	+	0.182136i	$0.941699\pi$
$24$	−1.47009e6	−	6.27505e6i	−0.184624	−	0.788064i
$25$	−1.91895e7			−1.96501
$26$	5.00188e6	−	1.04374e7i	0.420985	−	0.878469i
$27$	1.56193e7			1.08854
$28$	5.27884e6	−	4.24281e6i	0.306725	−	0.246526i
$29$			2.88750e7i			1.40777i	0.710313	+	0.703886i	$0.248554\pi$
$29$			2.88750e7i			1.40777i	−0.710313	+	0.703886i	$0.751446\pi$
$30$	1.46363e7	−	3.05415e7i	0.602316	−	1.25685i
$31$		−	3.00762e7i		−	1.05054i	−0.850935	−	0.525272i	$-0.823964\pi$
$31$		−	3.00762e7i		−	1.05054i	0.850935	−	0.525272i	$-0.176036\pi$
$32$	−2.06695e7	+	2.64324e7i	−0.616000	+	0.787746i
$33$	−4.34861e7			−1.11117
$34$	2.23996e7	+	1.07345e7i	0.493000	+	0.236258i
$35$	3.55890e7			0.677604
$36$	−1.30637e7	−	1.62537e7i	−0.216050	−	0.268807i
$37$		−	1.16919e7i		−	0.168607i	−0.996440	−	0.0843037i	$-0.973133\pi$
$37$		−	1.16919e7i		−	0.168607i	0.996440	−	0.0843037i	$-0.0268666\pi$
$38$	4.21857e7	+	2.02164e7i	0.532411	+	0.255145i
$39$			7.11386e7i			0.788465i
$40$	−1.71676e8	+	4.02196e7i	−1.67653	+	0.392770i
$41$	4.70330e7			0.405960			0.202980	−	0.979183i	$-0.434937\pi$
$41$	4.70330e7			0.405960			0.202980	+	0.979183i	$0.434937\pi$
$42$	−1.79896e7	+	3.75389e7i	−0.137649	+	0.287233i
$43$	3.52427e7			0.239733			0.119866	−	0.992790i	$-0.461753\pi$
$43$	3.52427e7			0.239733			0.119866	+	0.992790i	$0.461753\pi$
$44$	1.41834e8	+	1.76468e8i	0.860036	+	1.07005i
$45$		−	1.09580e8i		−	0.593838i
$46$	−3.24238e7	+	6.76587e7i	−0.157425	+	0.328499i
$47$		−	4.23068e8i		−	1.84468i	−0.386380	−	0.922340i	$-0.626275\pi$
$47$		−	4.23068e8i		−	1.84468i	0.386380	−	0.922340i	$-0.373725\pi$
$48$	4.43559e7	−	2.01412e8i	0.174079	−	0.790460i
$49$	2.38733e8			0.845145
$50$	−5.53761e8	−	2.65376e8i	−1.77203	−	0.849204i
$51$	−1.52670e8			−0.442489
$52$	2.88683e8	−	2.32025e8i	0.759284	−	0.610265i
$53$			9.16056e6i			0.0219050i	0.999940	+	0.0109525i	$0.00348635\pi$
$53$			9.16056e6i			0.0219050i	−0.999940	+	0.0109525i	$0.996514\pi$
$54$	4.50735e8	+	2.16003e8i	0.981640	+	0.470427i
$55$			1.18971e9i			2.36390i
$56$	2.11009e8	−	4.94343e7i	0.383142	−	0.0897611i
$57$	−2.87526e8			−0.477862
$58$	−3.99319e8	+	8.33260e8i	−0.608388	+	1.26952i
$59$	−1.03098e9			−1.44209			−0.721044	−	0.692890i	$-0.756337\pi$
$59$	−1.03098e9			−1.44209			−0.721044	+	0.692890i	$0.756337\pi$
$60$	8.44732e8	−	6.78943e8i	1.08633	−	0.873126i
$61$			1.37140e8i			0.162374i	0.996699	+	0.0811869i	$0.0258711\pi$
$61$			1.37140e8i			0.162374i	−0.996699	+	0.0811869i	$0.974129\pi$
$62$	4.15930e8	−	8.67921e8i	0.454006	−	0.947375i
$63$			1.34685e8i			0.135712i
$64$	−9.62009e8	+	4.76928e8i	−0.895941	+	0.444173i
$65$	1.94625e9			1.67738
$66$	−1.25490e9	−	6.01379e8i	−1.00205	−	0.480207i
$67$	−7.94671e8			−0.588591			−0.294295	−	0.955715i	$-0.595085\pi$
$67$	−7.94671e8			−0.588591			−0.294295	+	0.955715i	$0.595085\pi$
$68$	4.97947e8	+	6.19539e8i	0.342483	+	0.426113i
$69$		−	4.61143e8i		−	0.294843i
$70$	1.02701e9	+	4.92168e8i	0.611060	+	0.292835i
$71$		−	2.04858e9i		−	1.13543i	−0.823225	−	0.567716i	$-0.807827\pi$
$71$		−	2.04858e9i		−	1.13543i	0.823225	−	0.567716i	$-0.192173\pi$
$72$	−1.52210e8	−	6.49703e8i	−0.0786647	−	0.335778i
$73$	−1.88707e9			−0.910277			−0.455139	−	0.890421i	$-0.650410\pi$
$73$	−1.88707e9			−0.910277			−0.455139	+	0.890421i	$0.650410\pi$
$74$	1.61690e8	−	3.37399e8i	0.0728659	−	0.152049i
$75$	3.77428e9			1.59048
$76$	9.37794e8	+	1.16679e9i	0.369862	+	0.460177i
$77$		−	1.46229e9i		−	0.540231i
$78$	−9.83792e8	+	2.05288e9i	−0.340746	+	0.711034i
$79$			1.04965e9i			0.341120i	0.985347	+	0.170560i	$0.0545577\pi$
$79$			1.04965e9i			0.341120i	−0.985347	+	0.170560i	$0.945442\pi$
$80$	−5.51035e9	−	1.21351e9i	−1.68162	−	0.370335i
$81$	−1.86960e9			−0.536195
$82$	1.35725e9	+	6.50430e8i	0.366093	+	0.175441i
$83$	3.77162e9			0.957496			0.478748	−	0.877952i	$-0.341091\pi$
$83$	3.77162e9			0.957496			0.478748	+	0.877952i	$0.341091\pi$
$84$	−1.03827e9	+	8.34494e8i	−0.248263	+	0.199539i
$85$			4.17682e9i			0.941351i
$86$	1.01702e9	+	4.87380e8i	0.216190	+	0.103604i
$87$		−	5.67927e9i		−	1.13945i
$88$	1.65255e9	+	7.05387e9i	0.313142	+	1.33664i
$89$	−4.07338e9			−0.729465			−0.364733	−	0.931112i	$-0.618840\pi$
$89$	−4.07338e9			−0.729465			−0.364733	+	0.931112i	$0.618840\pi$
$90$	1.51540e9	−	3.16219e9i	0.256635	−	0.535520i
$91$	−2.39215e9			−0.383337
$92$	−1.87133e9	+	1.50406e9i	−0.283931	+	0.228206i
$93$			5.91551e9i			0.850311i
$94$	5.85070e9	−	1.22087e10i	0.797203	−	1.66352i
$95$			7.86629e9i			1.01660i
$96$	4.06538e9	−	5.19884e9i	0.498591	−	0.637603i
$97$	1.76770e9			0.205850			0.102925	−	0.994689i	$-0.467180\pi$
$97$	1.76770e9			0.205850			0.102925	+	0.994689i	$0.467180\pi$
$98$	6.88921e9	+	3.30149e9i	0.762148	+	0.365241i
$99$	−4.50244e9			−0.473447
$100$	−1.23102e10	−	1.53162e10i	−1.23102	−	1.53162i
$101$		−	1.09549e10i		−	1.04232i	−0.853459	−	0.521160i	$-0.825500\pi$
$101$		−	1.09549e10i		−	1.04232i	0.853459	−	0.521160i	$-0.174500\pi$
$102$	−4.40566e9	−	2.11131e9i	−0.399034	−	0.191227i
$103$			2.37007e8i			0.0204444i	0.999948	+	0.0102222i	$0.00325389\pi$
$103$			2.37007e8i			0.0204444i	−0.999948	+	0.0102222i	$0.996746\pi$
$104$	1.15394e10	−	2.70340e9i	0.948453	−	0.222200i
$105$	−6.99981e9			−0.548453
$106$	−1.26683e8	+	2.64350e8i	−0.00946652	+	0.0197538i
$107$	4.29761e9			0.306414			0.153207	−	0.988194i	$-0.451040\pi$
$107$	4.29761e9			0.306414			0.153207	+	0.988194i	$0.451040\pi$
$108$	1.00199e10	+	1.24666e10i	0.681937	+	0.848457i
$109$			2.92292e9i			0.189970i	0.995479	+	0.0949849i	$0.0302803\pi$
$109$			2.92292e9i			0.189970i	−0.995479	+	0.0949849i	$0.969720\pi$
$110$	−1.64528e10	+	3.43321e10i	−1.02159	+	2.13176i
$111$			2.29962e9i			0.136471i
$112$	6.77281e9	+	1.49154e9i	0.384307	+	0.0846339i
$113$	2.48941e10			1.35115			0.675575	−	0.737291i	$-0.263895\pi$
$113$	2.48941e10			1.35115			0.675575	+	0.737291i	$0.263895\pi$
$114$	−8.29727e9	−	3.97626e9i	−0.430934	−	0.206515i
$115$	−1.26162e10			−0.627248
$116$	−2.30467e10	+	1.85235e10i	−1.09728	+	0.881927i
$117$			7.36551e9i			0.335949i
$118$	−2.97516e10	−	1.42577e10i	−1.30047	−	0.623217i
$119$		−	5.13377e9i		−	0.215130i
$120$	3.37661e10	−	7.91058e9i	1.35698	−	0.317908i
$121$	2.29458e10			0.884661
$122$	−1.89654e9	+	3.95752e9i	−0.0701720	+	0.146428i
$123$	−9.25066e9			−0.328585
$124$	2.40054e10	−	1.92940e10i	0.818841	−	0.658134i
$125$		−	5.07100e10i		−	1.66167i
$126$	−1.86259e9	+	3.88668e9i	−0.0586497	+	0.122384i
$127$		−	1.86927e10i		−	0.565788i	−0.959151	−	0.282894i	$-0.908706\pi$
$127$		−	1.86927e10i		−	0.565788i	0.959151	−	0.282894i	$-0.0912945\pi$
$128$	−3.43567e10	+	4.59074e8i	−0.999911	+	0.0133608i
$129$	−6.93170e9			−0.194040
$130$	5.61638e10	+	2.69151e10i	1.51265	+	0.724902i
$131$	−1.62805e10			−0.421998			−0.210999	−	0.977486i	$-0.567672\pi$
$131$	−1.62805e10			−0.421998			−0.210999	+	0.977486i	$0.567672\pi$
$132$	−2.78965e10	−	3.47085e10i	−0.696114	−	0.866096i
$133$		−	9.66852e9i		−	0.232328i
$134$	−2.29322e10	−	1.09897e10i	−0.530788	−	0.254367i
$135$			8.40477e10i			1.87438i
$136$	5.80174e9	+	2.47646e10i	0.124699	+	0.532275i
$137$	3.24700e10			0.672791			0.336395	−	0.941721i	$-0.390792\pi$
$137$	3.24700e10			0.672791			0.336395	+	0.941721i	$0.390792\pi$
$138$	6.37725e9	−	1.33074e10i	0.127420	−	0.265888i
$139$	3.25763e10			0.627809			0.313905	−	0.949455i	$-0.398363\pi$
$139$	3.25763e10			0.627809			0.313905	+	0.949455i	$0.398363\pi$
$140$	2.28305e10	+	2.84055e10i	0.424498	+	0.528155i
$141$			8.32109e10i			1.49309i
$142$	2.83302e10	−	5.91168e10i	0.490692	−	1.02393i
$143$		−	7.99678e10i		−	1.33732i
$144$	4.59250e9	−	2.08537e10i	0.0741715	−	0.336799i
$145$	−1.55377e11			−2.42407
$146$	−5.44560e10	−	2.60967e10i	−0.820884	−	0.393388i
$147$	−4.69550e10			−0.684061
$148$	9.33192e9	−	7.50042e9i	0.131420	−	0.105627i
$149$			9.28139e10i			1.26381i	0.775046	+	0.631905i	$0.217727\pi$
$149$			9.28139e10i			1.26381i	−0.775046	+	0.631905i	$0.782273\pi$
$150$	1.08916e11	+	5.21954e10i	1.43429	+	0.687347i
$151$			1.62055e10i			0.206432i	0.994659	+	0.103216i	$0.0329133\pi$
$151$			1.62055e10i			0.206432i	−0.994659	+	0.103216i	$0.967087\pi$
$152$	1.09265e10	+	4.66396e10i	0.134668	+	0.574826i
$153$	−1.58070e10			−0.188536
$154$	2.02223e10	−	4.21979e10i	0.233468	−	0.487178i
$155$	1.61840e11			1.80895
$156$	−5.67794e10	+	4.56358e10i	−0.614565	+	0.493950i
$157$		−	2.39468e10i		−	0.251043i	−0.992091	−	0.125522i	$-0.959940\pi$
$157$		−	2.39468e10i		−	0.251043i	0.992091	−	0.125522i	$-0.0400605\pi$
$158$	−1.45158e10	+	3.02901e10i	−0.147420	+	0.307621i
$159$		−	1.80174e9i		−	0.0177299i
$160$	−1.42233e11	−	1.11223e11i	−1.35644	−	1.06070i
$161$	1.55067e10			0.143347
$162$	−5.39518e10	−	2.58551e10i	−0.483538	−	0.231724i
$163$	7.89570e10			0.686203			0.343101	−	0.939298i	$-0.388523\pi$
$163$	7.89570e10			0.686203			0.343101	+	0.939298i	$0.388523\pi$
$164$	3.01719e10	+	3.75395e10i	0.254322	+	0.316424i
$165$		−	2.33998e11i		−	1.91335i
$166$	1.08839e11	+	5.21585e10i	0.863466	+	0.413795i
$167$		−	1.85927e11i		−	1.43140i	−0.698408	−	0.715700i	$-0.746108\pi$
$167$		−	1.85927e11i		−	1.43140i	0.698408	−	0.715700i	$-0.253892\pi$
$168$	−4.15021e10	+	9.72295e9i	−0.310116	+	0.0726527i
$169$	7.03958e9			0.0510638
$170$	−5.77622e10	+	1.20532e11i	−0.406817	+	0.848906i
$171$	−2.97697e10			−0.203608
$172$	2.26084e10	+	2.81291e10i	0.150185	+	0.186859i
$173$		−	7.40712e9i		−	0.0477990i	−0.999714	−	0.0238995i	$-0.992392\pi$
$173$		−	7.40712e9i		−	0.0477990i	0.999714	−	0.0238995i	$-0.00760817\pi$
$174$	7.85399e10	−	1.63889e11i	0.492430	−	1.02755i
$175$			1.26916e11i			0.773263i
$176$	−4.98611e10	+	2.26410e11i	−0.295256	+	1.34070i
$177$	2.02778e11			1.16723
$178$	−1.17547e11	−	5.63317e10i	−0.657829	−	0.315248i
$179$	−3.09505e11			−1.68423			−0.842117	−	0.539295i	$-0.818691\pi$
$179$	−3.09505e11			−1.68423			−0.842117	+	0.539295i	$0.818691\pi$
$180$	8.74614e10	−	7.02960e10i	0.462864	−	0.372022i
$181$			3.52000e11i			1.81196i	0.423316	+	0.905982i	$0.360866\pi$
$181$			3.52000e11i			1.81196i	−0.423316	+	0.905982i	$0.639134\pi$
$182$	−6.90313e10	−	3.30816e10i	−0.345692	−	0.165664i
$183$		−	2.69734e10i		−	0.131425i
$184$	−7.48020e10	+	1.75243e10i	−0.354670	+	0.0830906i
$185$	6.29141e10			0.290328
$186$	−8.18070e10	+	1.70707e11i	−0.367473	+	0.766807i
$187$	1.71618e11			0.750508
$188$	3.37673e11	−	2.71400e11i	1.43783	−	1.15564i
$189$		−	1.03304e11i		−	0.428358i
$190$	−1.08785e11	+	2.27001e11i	−0.439339	+	0.916769i
$191$			4.23512e11i			1.66609i	0.553205	+	0.833045i	$0.313405\pi$
$191$			4.23512e11i			1.66609i	−0.553205	+	0.833045i	$0.686595\pi$
$192$	1.89212e11	−	9.38043e10i	0.725176	−	0.359514i
$193$	−2.50051e11			−0.933774			−0.466887	−	0.884317i	$-0.654625\pi$
$193$	−2.50051e11			−0.933774			−0.466887	+	0.884317i	$0.654625\pi$
$194$	5.10114e10	+	2.44459e10i	0.185634	+	0.0889607i
$195$	−3.82797e11			−1.35767
$196$	1.53148e11	+	1.90545e11i	0.529458	+	0.658744i
$197$		−	4.85950e11i		−	1.63780i	−0.573937	−	0.818899i	$-0.694585\pi$
$197$		−	4.85950e11i		−	1.63780i	0.573937	−	0.818899i	$-0.305415\pi$
$198$	−1.29929e11	−	6.22652e10i	−0.426953	−	0.204606i
$199$		−	1.41021e11i		−	0.451876i	−0.974142	−	0.225938i	$-0.927455\pi$
$199$		−	1.41021e11i		−	0.451876i	0.974142	−	0.225938i	$-0.0725447\pi$
$200$	−1.43430e11	−	6.12226e11i	−0.448218	−	1.91321i
$201$	1.56299e11			0.476406
$202$	1.51498e11	−	3.16130e11i	0.450452	−	0.939959i
$203$	1.90975e11			0.553982
$204$	−9.79385e10	−	1.21854e11i	−0.277206	−	0.344896i
$205$			2.53085e11i			0.699031i
$206$	−3.27762e9	+	6.83941e9i	−0.00883532	+	0.0184367i
$207$		−	4.77456e10i		−	0.125627i
$208$	3.70383e11	+	8.15675e10i	0.951337	+	0.209508i
$209$	3.23212e11			0.810505
$210$	−2.01997e11	−	9.68019e10i	−0.494593	−	0.237021i
$211$	−4.54045e11			−1.08564			−0.542821	−	0.839848i	$-0.682644\pi$
$211$	−4.54045e11			−1.08564			−0.542821	+	0.839848i	$0.682644\pi$
$212$	−7.31152e9	+	5.87655e9i	−0.0170737	+	0.0137228i
$213$			4.02924e11i			0.919019i
$214$	1.24018e11	+	5.94327e10i	0.276323	+	0.132421i
$215$			1.89641e11i			0.412801i
$216$	1.16745e11	+	4.98322e11i	0.248296	+	1.05984i
$217$	−1.98919e11			−0.413406
$218$	−4.04217e10	+	8.43480e10i	−0.0820979	+	0.171314i
$219$	3.71157e11			0.736779
$220$	−9.49574e11	+	7.63208e11i	−1.84253	+	1.48091i
$221$		−	2.80749e11i		−	0.532546i
$222$	−3.18019e10	+	6.63611e10i	−0.0589778	+	0.123069i
$223$		−	7.10192e11i		−	1.28781i	−0.765106	−	0.643905i	$-0.777313\pi$
$223$		−	7.10192e11i		−	1.28781i	0.765106	−	0.643905i	$-0.222687\pi$
$224$	1.74819e11	+	1.36705e11i	0.309991	+	0.242406i
$225$	3.90780e11			0.677671
$226$	7.18380e11	+	3.44266e11i	1.21846	+	0.583918i
$227$	−1.75996e11			−0.291994			−0.145997	−	0.989285i	$-0.546639\pi$
$227$	−1.75996e11			−0.291994			−0.145997	+	0.989285i	$0.546639\pi$
$228$	−1.84449e11	−	2.29490e11i	−0.299366	−	0.372468i
$229$		−	3.96342e11i		−	0.629351i	−0.949199	−	0.314676i	$-0.898104\pi$
$229$		−	3.96342e11i		−	0.629351i	0.949199	−	0.314676i	$-0.101896\pi$
$230$	−3.64071e11	−	1.74472e11i	−0.565650	−	0.271074i
$231$			2.87609e11i			0.437264i
$232$	−9.21234e11	+	2.15823e11i	−1.37066	+	0.321113i
$233$	−9.14879e11			−1.33225			−0.666123	−	0.745842i	$-0.732047\pi$
$233$	−9.14879e11			−1.33225			−0.666123	+	0.745842i	$0.732047\pi$
$234$	−1.01859e11	+	2.12550e11i	−0.145185	+	0.302957i
$235$	2.27653e12			3.17639
$236$	−6.61381e11	−	8.22882e11i	−0.903424	−	1.12403i
$237$		−	2.06449e11i		−	0.276103i
$238$	7.09960e10	−	1.48147e11i	0.0929714	−	0.194003i
$239$		−	1.99248e11i		−	0.255508i	−0.991806	−	0.127754i	$-0.959223\pi$
$239$		−	1.99248e11i		−	0.255508i	0.991806	−	0.127754i	$-0.0407768\pi$
$240$	1.08380e12	+	2.38679e11i	1.36111	+	0.299750i
$241$	−5.21033e11			−0.640885			−0.320442	−	0.947268i	$-0.603832\pi$
$241$	−5.21033e11			−0.640885			−0.320442	+	0.947268i	$0.603832\pi$
$242$	6.62158e11	+	3.17323e11i	0.797783	+	0.382318i
$243$	−5.54586e11			−0.654542
$244$	−1.09459e11	+	8.79762e10i	−0.126561	+	0.101722i
$245$			1.28462e12i			1.45527i
$246$	−2.66951e11	−	1.27929e11i	−0.296316	−	0.142002i
$247$		−	5.28740e11i		−	0.575119i
$248$	9.59555e11	−	2.24801e11i	1.02285	−	0.239629i
$249$	−7.41819e11			−0.774999
$250$	7.01280e11	−	1.46336e12i	0.718111	−	1.49848i
$251$	−8.76908e11			−0.880209			−0.440104	−	0.897947i	$-0.645059\pi$
$251$	−8.76908e11			−0.880209			−0.440104	+	0.897947i	$0.645059\pi$
$252$	−1.07499e11	+	8.64014e10i	−0.105780	+	0.0850194i
$253$			5.18377e11i			0.500084i
$254$	2.58506e11	−	5.39424e11i	0.244513	−	0.510225i
$255$		−	8.21516e11i		−	0.761930i
$256$	−9.97795e11	−	4.61878e11i	−0.907489	−	0.420076i
$257$	6.77292e11			0.604102			0.302051	−	0.953292i	$-0.402329\pi$
$257$	6.77292e11			0.604102			0.302051	+	0.953292i	$0.402329\pi$
$258$	−2.00031e11	−	9.58601e10i	−0.174984	−	0.0838570i
$259$	−7.73283e10			−0.0663498
$260$	1.24853e12	+	1.55340e12i	1.05083	+	1.30743i
$261$		−	5.88017e11i		−	0.485498i
$262$	−4.69813e11	−	2.25146e11i	−0.380556	−	0.182372i
$263$			2.38906e12i			1.89867i	0.314269	+	0.949334i	$0.398241\pi$
$263$			2.38906e12i			1.89867i	−0.314269	+	0.949334i	$0.601759\pi$
$264$	−3.25031e11	−	1.38739e12i	−0.253458	−	1.08188i
$265$	−4.92930e10			−0.0377186
$266$	1.33708e11	−	2.79009e11i	0.100404	−	0.209512i
$267$	8.01170e11			0.590430
$268$	−5.09786e11	−	6.34269e11i	−0.368734	−	0.458774i
$269$			9.15425e11i			0.649922i	0.945727	+	0.324961i	$0.105351\pi$
$269$			9.15425e11i			0.649922i	−0.945727	+	0.324961i	$0.894649\pi$
$270$	−1.16231e12	+	2.42540e12i	−0.810037	+	1.69030i
$271$			7.01162e11i			0.479702i	0.970810	+	0.239851i	$0.0770986\pi$
$271$			7.01162e11i			0.479702i	−0.970810	+	0.239851i	$0.922901\pi$
$272$	−1.75051e11	+	7.94875e11i	−0.117576	+	0.533893i
$273$	4.70499e11			0.310274
$274$	9.37003e11	+	4.49035e11i	0.606720	+	0.290755i
$275$	−4.24272e12			−2.69762
$276$	3.68063e11	−	2.95826e11i	0.229814	−	0.184710i
$277$		−	2.10823e12i		−	1.29276i	−0.763014	−	0.646382i	$-0.776281\pi$
$277$		−	2.10823e12i		−	1.29276i	0.763014	−	0.646382i	$-0.223719\pi$
$278$	9.40069e11	+	4.50505e11i	0.566155	+	0.271316i
$279$			6.12477e11i			0.362301i
$280$	2.66006e11	+	1.13544e12i	0.154561	+	0.659740i
$281$	2.87581e12			1.64145			0.820727	−	0.571320i	$-0.193569\pi$
$281$	2.87581e12			1.64145			0.820727	+	0.571320i	$0.193569\pi$
$282$	−1.15074e12	+	2.40125e12i	−0.645257	+	1.34646i
$283$	2.12641e12			1.17142			0.585712	−	0.810519i	$-0.300815\pi$
$283$	2.12641e12			1.17142			0.585712	+	0.810519i	$0.300815\pi$
$284$	1.63508e12	−	1.31417e12i	0.885007	−	0.711313i
$285$		−	1.54718e12i		−	0.822841i
$286$	1.10589e12	−	2.30767e12i	0.577940	−	1.20599i
$287$		−	3.11068e11i		−	0.159752i
$288$	4.20919e11	−	5.38274e11i	0.212440	−	0.271670i
$289$	−1.41348e12			−0.701134
$290$	−4.48377e12	−	2.14874e12i	−2.18602	−	1.04759i
$291$	−3.47680e11			−0.166615
$292$	−1.21057e12	−	1.50617e12i	−0.570261	−	0.709512i
$293$			6.04754e11i			0.280053i	0.990148	+	0.140027i	$0.0447188\pi$
$293$			6.04754e11i			0.280053i	−0.990148	+	0.140027i	$0.955281\pi$
$294$	−1.35500e12	−	6.49351e11i	−0.616883	−	0.295626i
$295$		−	5.54772e12i		−	2.48316i
$296$	3.73021e11	−	8.73897e10i	0.164163	−	0.0384593i
$297$	3.45337e12			1.49438
$298$	−1.28354e12	+	2.67837e12i	−0.546172	+	1.13970i
$299$	8.48010e11			0.354850
$300$	2.42122e12	+	3.01245e12i	0.996387	+	1.23969i
$301$		−	2.33090e11i		−	0.0943388i
$302$	−2.24109e11	+	4.67648e11i	−0.0892122	+	0.186159i
$303$			2.15466e12i			0.843655i
$304$	−3.29677e11	+	1.49700e12i	−0.126976	+	0.576574i
$305$	−7.37952e11			−0.279595
$306$	−4.56151e11	−	2.18599e11i	−0.170021	−	0.0814782i
$307$	−3.39388e11			−0.124453			−0.0622264	−	0.998062i	$-0.519820\pi$
$307$	−3.39388e11			−0.124453			−0.0622264	+	0.998062i	$0.519820\pi$
$308$	1.16713e12	−	9.38065e11i	0.421081	−	0.338438i
$309$		−	4.66155e10i		−	0.0165477i
$310$	4.67028e12	+	2.23812e12i	1.63130	+	0.781762i
$311$			4.79193e11i			0.164706i	0.996603	+	0.0823528i	$0.0262434\pi$
$311$			4.79193e11i			0.164706i	−0.996603	+	0.0823528i	$0.973757\pi$
$312$	−2.26962e12	+	5.31717e11i	−0.767679	+	0.179849i
$313$	−3.15123e12			−1.04896			−0.524479	−	0.851423i	$-0.675740\pi$
$313$	−3.15123e12			−1.04896			−0.524479	+	0.851423i	$0.675740\pi$
$314$	3.31165e11	−	6.91043e11i	0.108492	−	0.226390i
$315$	−7.24742e11			−0.233685
$316$	−8.37778e11	+	6.73354e11i	−0.265885	+	0.213702i
$317$		−	7.24188e11i		−	0.226232i	−0.993582	−	0.113116i	$-0.963917\pi$
$317$		−	7.24188e11i		−	0.226232i	0.993582	−	0.113116i	$-0.0360832\pi$
$318$	2.49167e10	−	5.19936e10i	0.00766222	−	0.0159888i
$319$			6.38414e12i			1.93263i
$320$	−2.56635e12	−	5.17657e12i	−0.764831	−	1.54274i
$321$	−8.45274e11			−0.248012
$322$	4.47483e11	+	2.14445e11i	0.129270	+	0.0619494i
$323$	1.13472e12			0.322758
$324$	−1.19936e12	−	1.49222e12i	−0.335910	−	0.417935i
$325$			6.94064e12i			1.91418i
$326$	2.27850e12	+	1.09191e12i	0.618815	+	0.296552i
$327$		−	5.74893e11i		−	0.153762i
$328$	3.51542e11	+	1.50055e12i	0.0925995	+	0.395258i
$329$	−2.79810e12			−0.725911
$330$	3.23602e12	−	6.75260e12i	0.826877	−	1.72545i
$331$	1.89023e12			0.475745			0.237872	−	0.971296i	$-0.423550\pi$
$331$	1.89023e12			0.475745			0.237872	+	0.971296i	$0.423550\pi$
$332$	2.41951e12	+	3.01033e12i	0.599843	+	0.746316i
$333$			2.38096e11i			0.0581476i
$334$	2.57123e12	−	5.36539e12i	0.618599	−	1.29083i
$335$		−	4.27612e12i		−	1.01351i
$336$	−1.33211e12	−	2.93363e11i	−0.311059	−	0.0685028i
$337$	−2.44837e12			−0.563285			−0.281643	−	0.959519i	$-0.590879\pi$
$337$	−2.44837e12			−0.563285			−0.281643	+	0.959519i	$0.590879\pi$
$338$	2.03144e11	+	9.73520e10i	0.0460491	+	0.0220679i
$339$	−4.89628e12			−1.09362
$340$	−3.33374e12	+	2.67945e12i	−0.733732	+	0.589728i
$341$		−	6.64971e12i		−	1.44222i
$342$	−8.59078e11	−	4.11692e11i	−0.183612	−	0.0879917i
$343$		−	3.44718e12i		−	0.726095i
$344$	2.63418e11	+	1.12439e12i	0.0546830	+	0.233413i
$345$	2.48141e12			0.507695
$346$	1.02435e11	−	2.13750e11i	0.0206570	−	0.0431049i
$347$	5.66030e12			1.12510			0.562551	−	0.826762i	$-0.309820\pi$
$347$	5.66030e12			1.12510			0.562551	+	0.826762i	$0.309820\pi$
$348$	4.53292e12	−	3.64328e12i	0.888142	−	0.713833i
$349$			8.20588e12i			1.58489i	0.609946	+	0.792443i	$0.291191\pi$
$349$			8.20588e12i			1.58489i	−0.609946	+	0.792443i	$0.708809\pi$
$350$	−1.75515e12	+	3.66248e12i	−0.334176	+	0.697325i
$351$		−	5.64935e12i		−	1.06038i
$352$	−4.56994e12	+	5.84408e12i	−0.845663	+	1.08144i
$353$	−7.02465e11			−0.128160			−0.0640798	−	0.997945i	$-0.520411\pi$
$353$	−7.02465e11			−0.128160			−0.0640798	+	0.997945i	$0.520411\pi$
$354$	5.85167e12	+	2.80427e12i	1.05260	+	0.504433i
$355$	1.10234e13			1.95512
$356$	−2.61309e12	−	3.25118e12i	−0.456988	−	0.568579i
$357$			1.00973e12i			0.174127i
$358$	−8.93153e12	−	4.28021e12i	−1.51883	−	0.727864i
$359$			5.97852e12i			1.00259i	0.865278	+	0.501293i	$0.167142\pi$
$359$			5.97852e12i			1.00259i	−0.865278	+	0.501293i	$0.832858\pi$
$360$	3.49605e12	−	8.19041e11i	0.578183	−	0.135454i
$361$	−3.99402e12			−0.651440
$362$	−4.86788e12	+	1.01578e13i	−0.783064	+	1.63402i
$363$	−4.51309e12			−0.716045
$364$	−1.53458e12	−	1.90930e12i	−0.240149	−	0.298791i
$365$		−	1.01543e13i		−	1.56742i
$366$	3.73021e11	−	7.78383e11i	0.0567973	−	0.118519i
$367$		−	1.90765e12i		−	0.286530i	−0.989684	−	0.143265i	$-0.954240\pi$
$367$		−	1.90765e12i		−	0.286530i	0.989684	−	0.143265i	$-0.0457601\pi$
$368$	−2.40094e12	−	5.28746e11i	−0.355748	−	0.0783445i
$369$	−9.57790e11			−0.140003
$370$	1.81554e12	+	8.70054e11i	0.261817	+	0.125469i
$371$	6.05864e10			0.00861996
$372$	−4.72148e12	+	3.79483e12i	−0.662771	+	0.532694i
$373$		−	4.41936e12i		−	0.612090i	−0.952017	−	0.306045i	$-0.900994\pi$
$373$		−	4.41936e12i		−	0.612090i	0.952017	−	0.306045i	$-0.0990058\pi$
$374$	4.95246e12	+	2.37335e12i	0.676804	+	0.324342i
$375$			9.97387e12i			1.34495i
$376$	1.34976e13	−	3.16217e12i	1.79605	−	0.420771i
$377$	1.04438e13			1.37136
$378$	1.42861e12	−	2.98108e12i	0.185121	−	0.386291i
$379$	−1.15746e13			−1.48017			−0.740083	−	0.672516i	$-0.765214\pi$
$379$	−1.15746e13			−1.48017			−0.740083	+	0.672516i	$0.765214\pi$
$380$	−6.27850e12	+	5.04627e12i	−0.792388	+	0.636872i
$381$			3.67657e12i			0.457949i
$382$	−5.85684e12	+	1.22215e13i	−0.720023	+	1.50247i
$383$		−	7.38843e12i		−	0.896517i	−0.893904	−	0.448259i	$-0.852044\pi$
$383$		−	7.38843e12i		−	0.896517i	0.893904	−	0.448259i	$-0.147956\pi$
$384$	6.75742e12	−	9.02928e10i	0.809329	−	0.0108143i
$385$	7.86857e12			0.930234
$386$	−7.21583e12	−	3.45801e12i	−0.842073	−	0.403543i
$387$	−7.17691e11			−0.0826766
$388$	1.13399e12	+	1.41090e12i	0.128959	+	0.160449i
$389$			8.41928e12i			0.945207i	0.881275	+	0.472603i	$0.156686\pi$
$389$			8.41928e12i			0.945207i	−0.881275	+	0.472603i	$0.843314\pi$
$390$	−1.10465e13	−	5.29378e12i	−1.22434	−	0.586736i
$391$			1.81991e12i			0.199143i
$392$	1.78438e12	+	7.61656e12i	0.192777	+	0.822865i
$393$	3.20212e12			0.341566
$394$	6.72031e12	−	1.40233e13i	0.707796	−	1.47696i
$395$	−5.64815e12			−0.587382
$396$	−2.88834e12	−	3.59363e12i	−0.296600	−	0.369026i
$397$		−	7.62252e12i		−	0.772940i	−0.922302	−	0.386470i	$-0.873694\pi$
$397$		−	7.62252e12i		−	0.772940i	0.922302	−	0.386470i	$-0.126306\pi$
$398$	1.95022e12	−	4.06952e12i	0.195284	−	0.407500i
$399$			1.90165e12i			0.188047i
$400$	4.32759e12	−	1.96508e13i	0.422616	−	1.91902i
$401$	1.08466e13			1.04610			0.523050	−	0.852302i	$-0.324794\pi$
$401$	1.08466e13			1.04610			0.523050	+	0.852302i	$0.324794\pi$
$402$	4.51040e12	+	2.16150e12i	0.429621	+	0.205885i
$403$	−1.08782e13			−1.02337
$404$	8.74366e12	−	7.02761e12i	0.812431	−	0.652982i
$405$		−	1.00603e13i		−	0.923285i
$406$	5.51104e12	+	2.64103e12i	0.499578	+	0.239410i
$407$		−	2.58503e12i		−	0.231469i
$408$	−1.14111e12	−	4.87080e12i	−0.100932	−	0.430824i
$409$	−1.74748e13			−1.52685			−0.763425	−	0.645897i	$-0.776484\pi$
$409$	−1.74748e13			−1.52685			−0.763425	+	0.645897i	$0.776484\pi$
$410$	−3.49996e12	+	7.30338e12i	−0.302095	+	0.630383i
$411$	−6.38635e12			−0.544558
$412$	−1.89167e11	+	1.52041e11i	−0.0159353	+	0.0128078i
$413$			6.81875e12i			0.567485i
$414$	6.60284e11	−	1.37782e12i	0.0542912	−	0.113289i
$415$			2.02951e13i			1.64873i
$416$	9.56030e12	+	7.47594e12i	0.767370	+	0.600066i
$417$	−6.40725e12			−0.508149
$418$	9.32707e12	+	4.46977e12i	0.730910	+	0.350270i
$419$	1.67775e13			1.29914			0.649572	−	0.760300i	$-0.274948\pi$
$419$	1.67775e13			1.29914			0.649572	+	0.760300i	$0.274948\pi$
$420$	−4.49041e12	−	5.58691e12i	−0.343589	−	0.427489i
$421$			4.09777e12i			0.309840i	0.987927	+	0.154920i	$0.0495120\pi$
$421$			4.09777e12i			0.309840i	−0.987927	+	0.154920i	$0.950488\pi$
$422$	−1.31026e13	−	6.27909e12i	−0.979027	−	0.469175i
$423$			8.61544e12i			0.636174i
$424$	−2.92260e11	+	6.84695e10i	−0.0213275	+	0.00499652i
$425$	−1.48952e13			−1.07424
$426$	−5.57212e12	+	1.16273e13i	−0.397166	+	0.828768i
$427$	9.07022e11			0.0638967
$428$	2.75694e12	+	3.43015e12i	0.191959	+	0.238833i
$429$			1.57284e13i			1.08243i
$430$	−2.62259e12	+	5.47256e12i	−0.178397	+	0.372262i
$431$		−	1.03214e13i		−	0.693985i	−0.937868	−	0.346993i	$-0.887203\pi$
$431$		−	1.03214e13i		−	0.693985i	0.937868	−	0.346993i	$-0.112797\pi$
$432$	−3.52245e12	+	1.59948e13i	−0.234113	+	1.06307i
$433$	2.17422e13			1.42844			0.714222	−	0.699919i	$-0.246781\pi$
$433$	2.17422e13			1.42844			0.714222	+	0.699919i	$0.246781\pi$
$434$	−5.74028e12	−	2.75089e12i	−0.372808	−	0.178659i
$435$	3.05602e13			1.96205
$436$	−2.33294e12	+	1.87507e12i	−0.148071	+	0.119010i
$437$			3.42746e12i			0.215063i
$438$	1.07107e13	+	5.13282e12i	0.664424	+	0.318409i
$439$		−	3.10509e13i		−	1.90437i	−0.305524	−	0.952184i	$-0.598832\pi$
$439$		−	3.10509e13i		−	1.90437i	0.305524	−	0.952184i	$-0.401168\pi$
$440$	−3.79569e13	+	8.89238e12i	−2.30158	+	0.539206i
$441$	−4.86160e12			−0.291465
$442$	3.88254e12	−	8.10170e12i	0.230147	−	0.480247i
$443$	−2.32225e13			−1.36110			−0.680552	−	0.732700i	$-0.738260\pi$
$443$	−2.32225e13			−1.36110			−0.680552	+	0.732700i	$0.738260\pi$
$444$	−1.83544e12	+	1.47522e12i	−0.106372	+	0.0854950i
$445$		−	2.19188e13i		−	1.25608i
$446$	9.82141e12	−	2.04943e13i	0.556544	−	1.16134i
$447$		−	1.82550e13i		−	1.02293i
$448$	3.15432e12	+	6.36256e12i	0.174789	+	0.352567i
$449$	−1.05020e13			−0.575493			−0.287747	−	0.957707i	$-0.592906\pi$
$449$	−1.05020e13			−0.575493			−0.287747	+	0.957707i	$0.592906\pi$
$450$	1.12769e13	+	5.40418e12i	0.611121	+	0.292865i
$451$	1.03988e13			0.557314
$452$	1.59697e13	+	1.98693e13i	0.846455	+	1.05315i
$453$		−	3.18736e12i		−	0.167086i
$454$	−5.07880e12	−	2.43389e12i	−0.263319	−	0.126189i
$455$		−	1.28722e13i		−	0.660076i
$456$	−2.14908e12	−	9.17328e12i	−0.109000	−	0.465265i
$457$	1.72386e13			0.864813			0.432407	−	0.901679i	$-0.357665\pi$
$457$	1.72386e13			0.864813			0.432407	+	0.901679i	$0.357665\pi$
$458$	5.48111e12	−	1.14374e13i	0.271982	−	0.567546i
$459$	1.21240e13			0.595090
$460$	−8.09336e12	−	1.00697e13i	−0.392952	−	0.488906i
$461$		−	8.78179e11i		−	0.0421773i	−0.999778	−	0.0210886i	$-0.993287\pi$
$461$		−	8.78179e11i		−	0.0421773i	0.999778	−	0.0210886i	$-0.00671322\pi$
$462$	−3.97742e12	+	8.29968e12i	−0.188969	+	0.394322i
$463$			3.73576e13i			1.75579i	0.478849	+	0.877897i	$0.341054\pi$
$463$			3.73576e13i			1.75579i	−0.478849	+	0.877897i	$0.658946\pi$
$464$	−2.95691e13	−	6.51185e12i	−1.37483	−	0.302771i
$465$	−3.18314e13			−1.46417
$466$	−2.64011e13	−	1.26521e13i	−1.20141	−	0.575748i
$467$	3.05749e13			1.37652			0.688258	−	0.725466i	$-0.258376\pi$
$467$	3.05749e13			1.37652			0.688258	+	0.725466i	$0.258376\pi$
$468$	−5.87880e12	+	4.72501e12i	−0.261854	+	0.210462i
$469$			5.25582e12i			0.231620i
$470$	6.56948e13	+	3.14826e13i	2.86445	+	1.37272i
$471$			4.70996e12i			0.203195i
$472$	−7.70596e12	−	3.28927e13i	−0.328940	−	1.40407i
$473$	7.79201e12			0.329112
$474$	2.85503e12	−	5.95760e12i	0.119322	−	0.248989i
$475$	−2.80525e13			−1.16012
$476$	4.09753e12	−	3.29334e12i	0.167682	−	0.134773i
$477$		−	1.86548e11i		−	0.00755436i
$478$	2.75545e12	−	5.74979e12i	0.110421	−	0.230416i
$479$			2.02856e13i			0.804470i	0.915536	+	0.402235i	$0.131767\pi$
$479$			2.02856e13i			0.804470i	−0.915536	+	0.402235i	$0.868233\pi$
$480$	2.79749e13	+	2.18758e13i	1.09790	+	0.858534i
$481$	−4.22883e12			−0.164246
$482$	−1.50357e13	−	7.20548e12i	−0.577947	−	0.276967i
$483$	−3.04992e12			−0.116025
$484$	1.47199e13	+	1.83143e13i	0.554213	+	0.689545i
$485$			9.51200e12i			0.354457i
$486$	−1.60039e13	−	7.66949e12i	−0.590263	−	0.282869i
$487$		−	2.31802e13i		−	0.846199i	−0.906083	−	0.423100i	$-0.860942\pi$
$487$		−	2.31802e13i		−	0.846199i	0.906083	−	0.423100i	$-0.139058\pi$
$488$	−4.37534e12	+	1.02504e12i	−0.158093	+	0.0370374i
$489$	−1.55296e13			−0.555413
$490$	−1.77653e13	+	3.70708e13i	−0.628915	+	1.31236i
$491$	−2.54719e13			−0.892593			−0.446296	−	0.894885i	$-0.647257\pi$
$491$	−2.54719e13			−0.892593			−0.446296	+	0.894885i	$0.647257\pi$
$492$	−5.93435e12	−	7.38344e12i	−0.205848	−	0.256114i
$493$			2.24133e13i			0.769611i
$494$	7.31207e12	−	1.52581e13i	0.248545	−	0.518639i
$495$		−	2.42276e13i		−	0.815238i
$496$	3.07991e13	+	6.78272e12i	1.02596	+	0.225941i
$497$	−1.35489e13			−0.446811
$498$	−2.14070e13	−	1.02588e13i	−0.698890	−	0.334926i
$499$	−6.30694e12			−0.203852			−0.101926	−	0.994792i	$-0.532501\pi$
$499$	−6.30694e12			−0.203852			−0.101926	+	0.994792i	$0.532501\pi$
$500$	4.04743e13	−	3.25307e13i	1.29518	−	1.04098i
$501$			3.65690e13i			1.15858i
$502$	−2.53053e13	−	1.21270e13i	−0.793768	−	0.380394i
$503$			5.04100e13i			1.56559i	0.622283	+	0.782793i	$0.286205\pi$
$503$			5.04100e13i			1.56559i	−0.622283	+	0.782793i	$0.713795\pi$
$504$	−4.29703e12	+	1.00669e12i	−0.132134	+	0.0309559i
$505$	5.89482e13			1.79479
$506$	−7.16875e12	+	1.49590e13i	−0.216118	+	0.450974i
$507$	−1.38458e12			−0.0413311
$508$	1.49196e13	−	1.19915e13i	0.441001	−	0.354449i
$509$		−	6.42360e12i		−	0.188014i	−0.995572	−	0.0940068i	$-0.970032\pi$
$509$		−	6.42360e12i		−	0.188014i	0.995572	−	0.0940068i	$-0.0299676\pi$
$510$	1.13609e13	−	2.37069e13i	0.329278	−	0.687105i
$511$			1.24808e13i			0.358209i
$512$	−2.24064e13	−	2.71274e13i	−0.636828	−	0.771006i
$513$	2.28334e13			0.642663
$514$	1.95449e13	+	9.36642e12i	0.544776	+	0.261071i
$515$	−1.27533e12			−0.0352036
$516$	−4.44672e12	−	5.53255e12i	−0.121560	−	0.151244i
$517$		−	9.35384e13i		−	2.53243i
$518$	−2.23150e12	−	1.06939e12i	−0.0598339	−	0.0286739i
$519$			1.45686e12i			0.0386886i
$520$	1.45470e13	+	6.20934e13i	0.382610	+	1.63316i
$521$	−2.69887e13			−0.703063			−0.351531	−	0.936176i	$-0.614339\pi$
$521$	−2.69887e13			−0.703063			−0.351531	+	0.936176i	$0.614339\pi$
$522$	8.13182e12	−	1.69687e13i	0.209814	−	0.437820i
$523$	−6.68036e13			−1.70723			−0.853613	−	0.520907i	$-0.825594\pi$
$523$	−6.68036e13			−1.70723			−0.853613	+	0.520907i	$0.825594\pi$
$524$	−1.04440e13	−	1.29943e13i	−0.264369	−	0.328924i
$525$		−	2.49625e13i		−	0.625880i
$526$	−3.30389e13	+	6.89423e13i	−0.820534	+	1.71221i
$527$		−	2.33456e13i		−	0.574318i
$528$	9.80690e12	−	4.45314e13i	0.238980	−	1.08517i
$529$	3.59294e13			0.867305
$530$	−1.42247e12	−	6.81683e11i	−0.0340145	−	0.0163006i
$531$	2.09952e13			0.497332
$532$	7.71695e12	−	6.20241e12i	0.181087	−	0.145547i
$533$		−	1.70113e13i		−	0.395459i
$534$	2.31197e13	+	1.10796e13i	0.532447	+	0.255162i
$535$			2.31255e13i			0.527620i
$536$	−5.93967e12	−	2.53533e13i	−0.134257	−	0.573074i
$537$	6.08748e13			1.36322
$538$	−1.26596e13	+	2.64168e13i	−0.280873	+	0.586097i
$539$	5.27827e13			1.16024
$540$	−6.70829e13	+	5.39170e13i	−1.46097	+	1.17424i
$541$		−	1.02428e11i		−	0.00221021i	−0.999999	−	0.00110511i	$-0.999648\pi$
$541$		−	1.02428e11i		−	0.00221021i	0.999999	−	0.00110511i	$-0.000351766\pi$
$542$	−9.69652e12	+	2.02337e13i	−0.207310	+	0.432593i
$543$		−	6.92329e13i		−	1.46661i
$544$	−1.60440e13	+	2.05173e13i	−0.336759	+	0.430650i
$545$	−1.57282e13			−0.327113
$546$	1.35774e13	+	6.50663e12i	0.279804	+	0.134089i
$547$	−1.84176e13			−0.376094			−0.188047	−	0.982160i	$-0.560216\pi$
$547$	−1.84176e13			−0.376094			−0.188047	+	0.982160i	$0.560216\pi$
$548$	2.08297e13	+	2.59160e13i	0.421483	+	0.524404i
$549$		−	2.79275e12i		−	0.0559978i
$550$	−1.22434e14	−	5.86735e13i	−2.43270	−	1.16581i
$551$			4.22114e13i			0.831135i
$552$	1.47124e13	−	3.44676e12i	0.287070	−	0.0672536i
$553$	6.94218e12			0.134236
$554$	2.91552e13	−	6.08382e13i	0.558685	−	1.16581i
$555$	−1.23742e13			−0.234992
$556$	2.08979e13	+	2.60008e13i	0.393303	+	0.489343i
$557$			7.26795e13i			1.35561i	0.735240	+	0.677807i	$0.237069\pi$
$557$			7.26795e13i			1.35561i	−0.735240	+	0.677807i	$0.762931\pi$
$558$	−8.47008e12	+	1.76745e13i	−0.156573	+	0.326721i
$559$		−	1.27469e13i		−	0.233532i
$560$	−8.02597e12	+	3.64445e13i	−0.145733	+	0.661747i
$561$	−3.37546e13			−0.607462
$562$	8.29886e13	+	3.97702e13i	1.48026	+	0.709376i
$563$	1.23522e13			0.218376			0.109188	−	0.994021i	$-0.465175\pi$
$563$	1.23522e13			0.218376			0.109188	+	0.994021i	$0.465175\pi$
$564$	−6.64150e13	+	5.33802e13i	−1.16378	+	0.935373i
$565$			1.33955e14i			2.32657i
$566$	6.13627e13	+	2.94066e13i	1.05638	+	0.506246i
$567$			1.23652e13i			0.211002i
$568$	6.53582e13	−	1.53118e13i	1.10550	−	0.258992i
$569$	−9.79422e13			−1.64213			−0.821067	−	0.570832i	$-0.806621\pi$
$569$	−9.79422e13			−1.64213			−0.821067	+	0.570832i	$0.806621\pi$
$570$	2.13963e13	−	4.46476e13i	0.355602	−	0.742034i
$571$	4.63676e13			0.763895			0.381948	−	0.924184i	$-0.375254\pi$
$571$	4.63676e13			0.763895			0.381948	+	0.924184i	$0.375254\pi$
$572$	6.38265e13	−	5.12998e13i	1.04237	−	0.837790i
$573$		−	8.32982e13i		−	1.34854i
$574$	4.30183e12	−	8.97664e12i	0.0690389	−	0.144064i
$575$		−	4.49914e13i		−	0.715798i
$576$	1.95906e13	−	9.71225e12i	0.308983	−	0.153182i
$577$	−7.69976e13			−1.20392			−0.601961	−	0.798526i	$-0.705614\pi$
$577$	−7.69976e13			−1.20392			−0.601961	+	0.798526i	$0.705614\pi$
$578$	−4.07895e13	−	1.95473e13i	−0.632279	−	0.303004i
$579$	4.91811e13			0.755798
$580$	−9.96748e13	−	1.24014e14i	−1.51861	−	1.88943i
$581$		−	2.49448e13i		−	0.376791i
$582$	−1.00331e13	−	4.80814e12i	−0.150253	−	0.0720049i
$583$			2.02536e12i			0.0300718i
$584$	−1.41047e13	−	6.02054e13i	−0.207634	−	0.886280i
$585$	−3.96338e13			−0.578477
$586$	−8.36328e12	+	1.74517e13i	−0.121029	+	0.252551i
$587$	2.22966e12			0.0319926			0.0159963	−	0.999872i	$-0.494908\pi$
$587$	2.22966e12			0.0319926			0.0159963	+	0.999872i	$0.494908\pi$
$588$	−3.01219e13	−	3.74772e13i	−0.428544	−	0.533189i
$589$		−	4.39673e13i		−	0.620230i
$590$	7.67207e13	−	1.60093e14i	1.07313	−	2.23930i
$591$			9.55788e13i			1.32564i
$592$	1.19730e13	+	2.63674e12i	0.164662	+	0.0362626i
$593$	4.14340e13			0.565045			0.282523	−	0.959261i	$-0.408829\pi$
$593$	4.14340e13			0.565045			0.282523	+	0.959261i	$0.408829\pi$
$594$	9.96554e13	+	4.77574e13i	1.34762	+	0.645815i
$595$	2.76248e13			0.370437
$596$	−7.40796e13	+	5.95406e13i	−0.985071	+	0.791738i
$597$			2.77367e13i			0.365749i
$598$	2.44714e13	+	1.17273e13i	0.320002	+	0.153353i
$599$		−	1.30467e14i		−	1.69187i	−0.533290	−	0.845933i	$-0.679045\pi$
$599$		−	1.30467e14i		−	1.69187i	0.533290	−	0.845933i	$-0.320955\pi$
$600$	2.82104e13	+	1.20415e14i	0.362788	+	1.54855i
$601$	6.20993e13			0.791980			0.395990	−	0.918255i	$-0.370401\pi$
$601$	6.20993e13			0.791980			0.395990	+	0.918255i	$0.370401\pi$
$602$	3.22345e12	−	6.72637e12i	0.0407698	−	0.0850743i
$603$	1.61828e13			0.202987
$604$	−1.29344e13	+	1.03959e13i	−0.160902	+	0.129323i
$605$			1.23471e14i			1.52331i
$606$	−2.97972e13	+	6.21779e13i	−0.364596	+	0.760804i
$607$			9.56403e13i			1.16064i	0.814389	+	0.580320i	$0.197072\pi$
$607$			9.56403e13i			1.16064i	−0.814389	+	0.580320i	$0.802928\pi$
$608$	−3.02160e13	+	3.86405e13i	−0.363680	+	0.465078i
$609$	−3.75617e13			−0.448393
$610$	−2.12954e13	−	1.02053e13i	−0.252137	−	0.120830i
$611$	−1.53019e14			−1.79696
$612$	−1.01403e13	−	1.26164e13i	−0.118112	−	0.146953i
$613$		−	7.01720e13i		−	0.810702i	−0.914161	−	0.405351i	$-0.867149\pi$
$613$		−	7.01720e13i		−	0.810702i	0.914161	−	0.405351i	$-0.132851\pi$
$614$	−9.79388e12	−	4.69347e12i	−0.112231	−	0.0537839i
$615$		−	4.97778e13i		−	0.565796i
$616$	4.66531e13	−	1.09297e13i	0.525989	−	0.123227i
$617$	−4.75331e13			−0.531582			−0.265791	−	0.964031i	$-0.585633\pi$
$617$	−4.75331e13			−0.531582			−0.265791	+	0.964031i	$0.585633\pi$
$618$	6.44657e11	−	1.34521e12i	0.00715132	−	0.0149227i
$619$	7.55113e13			0.830919			0.415459	−	0.909612i	$-0.363621\pi$
$619$	7.55113e13			0.830919			0.415459	+	0.909612i	$0.363621\pi$
$620$	1.03821e14	+	1.29173e14i	1.13325	+	1.40998i
$621$			3.66209e13i			0.396525i
$622$	−6.62686e12	+	1.38283e13i	−0.0711797	+	0.148531i
$623$			2.69406e13i			0.287057i
$624$	−7.28486e13	−	1.60431e13i	−0.770014	−	0.169576i
$625$	8.54727e13			0.896247
$626$	−9.09365e13	−	4.35791e13i	−0.945946	−	0.453321i
$627$	−6.35707e13			−0.656024
$628$	1.91132e13	−	1.53620e13i	0.195675	−	0.157271i
$629$		−	9.07546e12i		−	0.0921755i
$630$	−2.09142e13	−	1.00226e13i	−0.210736	−	0.100990i
$631$		−	7.50751e13i		−	0.750498i	−0.926924	−	0.375249i	$-0.877557\pi$
$631$		−	7.50751e13i		−	0.750498i	0.926924	−	0.375249i	$-0.122443\pi$
$632$	−3.34881e13	+	7.84546e12i	−0.332128	+	0.0778095i
$633$	8.93037e13			0.878720
$634$	1.00150e13	−	2.08982e13i	0.0977694	−	0.204015i
$635$	1.00585e14			0.974241
$636$	1.43806e12	−	1.15583e12i	0.0138195	−	0.0111073i
$637$		−	8.63469e13i		−	0.823284i
$638$	−8.82877e13	+	1.84230e14i	−0.835212	+	1.74284i
$639$			4.17177e13i			0.391576i
$640$	−2.47028e12	−	1.84873e14i	−0.0230063	−	1.72177i
$641$	1.92038e14			1.77458			0.887291	−	0.461210i	$-0.152584\pi$
$641$	1.92038e14			1.77458			0.887291	+	0.461210i	$0.152584\pi$
$642$	−2.43925e13	−	1.16895e13i	−0.223656	−	0.107182i
$643$	−1.14745e14			−1.04395			−0.521975	−	0.852961i	$-0.674805\pi$
$643$	−1.14745e14			−1.04395			−0.521975	+	0.852961i	$0.674805\pi$
$644$	9.94761e12	+	1.23767e13i	0.0898027	+	0.111731i
$645$		−	3.72995e13i		−	0.334121i
$646$	3.27452e13	+	1.56924e13i	0.291062	+	0.139484i
$647$			5.82025e13i			0.513358i	0.966497	+	0.256679i	$0.0826284\pi$
$647$			5.82025e13i			0.513358i	−0.966497	+	0.256679i	$0.917372\pi$
$648$	−1.39741e13	−	5.96479e13i	−0.122306	−	0.522060i
$649$	−2.27946e14			−1.97974
$650$	−9.59837e13	+	2.00289e14i	−0.827238	+	1.72620i
$651$	3.91242e13			0.334611
$652$	5.06513e13	+	6.30197e13i	0.429885	+	0.534858i
$653$		−	1.62553e14i		−	1.36908i	−0.728974	−	0.684542i	$-0.760002\pi$
$653$		−	1.62553e14i		−	1.36908i	0.728974	−	0.684542i	$-0.239998\pi$
$654$	7.95032e12	−	1.65899e13i	0.0664502	−	0.138662i
$655$		−	8.76052e13i		−	0.726647i
$656$	−1.06068e13	+	4.81636e13i	−0.0873102	+	0.396460i
$657$	3.84287e13			0.313927
$658$	−8.07460e13	−	3.86955e13i	−0.654624	−	0.313712i
$659$	1.20273e14			0.967704			0.483852	−	0.875150i	$-0.339237\pi$
$659$	1.20273e14			0.967704			0.483852	+	0.875150i	$0.339237\pi$
$660$	1.86766e14	−	1.50111e14i	1.49135	−	1.19865i
$661$		−	1.23883e14i		−	0.981758i	−0.871228	−	0.490879i	$-0.836676\pi$
$661$		−	1.23883e14i		−	0.981758i	0.871228	−	0.490879i	$-0.163324\pi$
$662$	5.45471e13	+	2.61404e13i	0.429024	+	0.205599i
$663$			5.52190e13i			0.431043i
$664$	2.81905e13	+	1.20330e14i	0.218405	+	0.932255i
$665$	5.20263e13			0.400050
$666$	−3.29269e12	+	6.87086e12i	−0.0251293	+	0.0524372i
$667$	−6.76999e13			−0.512813
$668$	1.48398e14	−	1.19273e14i	1.11570	−	0.896729i
$669$			1.39684e14i			1.04235i
$670$	5.91355e13	−	1.23398e14i	0.438000	−	0.913975i
$671$			3.03211e13i			0.222911i
$672$	−3.43842e13	−	2.68877e13i	−0.250907	−	0.196204i
$673$	7.76604e13			0.562502			0.281251	−	0.959634i	$-0.409251\pi$
$673$	7.76604e13			0.562502			0.281251	+	0.959634i	$0.409251\pi$
$674$	−7.06538e13	−	3.38591e13i	−0.507968	−	0.243431i
$675$	−2.99728e14			−2.13899
$676$	4.51593e12	+	5.61866e12i	0.0319900	+	0.0398015i
$677$			1.79880e14i			1.26485i	0.774621	+	0.632426i	$0.217941\pi$
$677$			1.79880e14i			1.26485i	−0.774621	+	0.632426i	$0.782059\pi$
$678$	−1.41294e14	−	6.77117e13i	−0.986224	−	0.472624i
$679$		−	1.16913e13i		−	0.0810053i
$680$	−1.33258e14	+	3.12192e13i	−0.916535	+	0.214722i
$681$	3.46157e13			0.236340
$682$	9.19603e13	−	1.91894e14i	0.623273	−	1.30058i
$683$	−1.46057e13			−0.0982698			−0.0491349	−	0.998792i	$-0.515646\pi$
$683$	−1.46057e13			−0.0982698			−0.0491349	+	0.998792i	$0.515646\pi$
$684$	−1.90974e13	−	2.37608e13i	−0.127554	−	0.158701i
$685$			1.74721e14i			1.15849i
$686$	4.76718e13	−	9.94768e13i	0.313791	−	0.654789i
$687$			7.79544e13i			0.509398i
$688$	−7.94788e12	+	3.60899e13i	−0.0515596	+	0.234123i
$689$	3.31327e12			0.0213384
$690$	7.16072e13	+	3.43160e13i	0.457837	+	0.219407i
$691$	−1.80286e14			−1.14438			−0.572191	−	0.820120i	$-0.693906\pi$
$691$	−1.80286e14			−1.14438			−0.572191	+	0.820120i	$0.693906\pi$
$692$	5.91201e12	−	4.75170e12i	0.0372567	−	0.0299446i
$693$			2.97783e13i			0.186309i
$694$	1.63342e14	+	7.82776e13i	1.01461	+	0.486228i
$695$			1.75293e14i			1.08104i
$696$	1.81192e14	−	4.24490e13i	1.10941	−	0.259909i
$697$	3.65078e13			0.221933
$698$	−1.13481e14	+	2.36801e14i	−0.684929	+	1.42924i
$699$	1.79943e14			1.07832
$700$	−1.01298e14	+	8.14174e13i	−0.602716	+	0.484426i
$701$		−	2.61562e14i		−	1.54520i	−0.634895	−	0.772598i	$-0.718957\pi$
$701$		−	2.61562e14i		−	1.54520i	0.634895	−	0.772598i	$-0.281043\pi$
$702$	7.81261e13	−	1.63026e14i	0.458258	−	0.956248i
$703$		−	1.70920e13i		−	0.0995442i
$704$	−2.12696e14	+	1.05447e14i	−1.22997	+	0.609774i
$705$	−4.47758e14			−2.57097
$706$	−2.02714e13	−	9.71455e12i	−0.115574	−	0.0553859i
$707$	−7.24537e13			−0.410170
$708$	1.30083e14	+	1.61848e14i	0.731233	+	0.909790i
$709$			2.37281e14i			1.32444i	0.749310	+	0.662219i	$0.230385\pi$
$709$			2.37281e14i			1.32444i	−0.749310	+	0.662219i	$0.769615\pi$
$710$	3.18107e14	+	1.52445e14i	1.76312	+	0.844932i
$711$		−	2.13752e13i		−	0.117642i
$712$	−3.04460e13	−	1.29958e14i	−0.166391	−	0.710235i
$713$	7.05161e13			0.382684
$714$	−1.39638e13	+	2.91383e13i	−0.0752511	+	0.157027i
$715$	4.30307e14			2.30276
$716$	−1.98549e14	−	2.47032e14i	−1.05512	−	1.31277i
$717$			3.91890e13i			0.206808i
$718$	−8.26783e13	+	1.72525e14i	−0.433280	+	0.904127i
$719$		−	2.61945e14i		−	1.36322i	−0.731717	−	0.681609i	$-0.761281\pi$
$719$		−	2.61945e14i		−	1.36322i	0.731717	−	0.681609i	$-0.238719\pi$
$720$	1.12214e14	+	2.47122e13i	0.579941	+	0.127717i
$721$	1.56752e12			0.00804521
$722$	−1.15257e14	−	5.52342e13i	−0.587465	−	0.281528i
$723$	1.02479e14			0.518733
$724$	−2.80949e14	+	2.25810e14i	−1.41233	+	1.13514i
$725$		−	5.54098e14i		−	2.76628i
$726$	−1.30236e14	−	6.24125e13i	−0.645726	−	0.309448i
$727$			1.58213e14i			0.779058i	0.921014	+	0.389529i	$0.127362\pi$
$727$			1.58213e14i			0.779058i	−0.921014	+	0.389529i	$0.872638\pi$
$728$	−1.78798e13	−	7.63195e13i	−0.0874393	−	0.373232i
$729$	2.19476e14			1.06598
$730$	1.40426e14	−	2.93028e14i	0.677383	−	1.41350i
$731$	2.73560e13			0.131059
$732$	2.15289e13	−	1.73036e13i	0.102439	−	0.0823341i
$733$			2.50230e14i			1.18255i	0.806469	+	0.591276i	$0.201376\pi$
$733$			2.50230e14i			1.18255i	−0.806469	+	0.591276i	$0.798624\pi$
$734$	2.63814e13	−	5.50501e13i	0.123828	−	0.258391i
$735$		−	2.52665e14i		−	1.17790i
$736$	−6.19729e13	−	4.84614e13i	−0.286954	−	0.224392i
$737$	−1.75698e14			−0.808035
$738$	−2.76394e13	−	1.32455e13i	−0.126254	−	0.0605043i
$739$	3.08452e14			1.39948			0.699738	−	0.714400i	$-0.253300\pi$
$739$	3.08452e14			1.39948			0.699738	+	0.714400i	$0.253300\pi$
$740$	4.03597e13	+	5.02151e13i	0.181882	+	0.226295i
$741$			1.03995e14i			0.465502i
$742$	1.74837e12	+	8.37863e11i	0.00777344	+	0.00372523i
$743$		−	2.42121e14i		−	1.06927i	−0.845082	−	0.534637i	$-0.820448\pi$
$743$		−	2.42121e14i		−	1.06927i	0.845082	−	0.534637i	$-0.179552\pi$
$744$	−1.88730e14	+	4.42148e13i	−0.827895	+	0.193956i
$745$	−4.99431e14			−2.17618
$746$	6.11163e13	−	1.27531e14i	0.264523	−	0.551980i
$747$	−7.68060e13			−0.330211
$748$	1.10094e14	+	1.36977e14i	0.470170	+	0.584980i
$749$		−	2.84237e13i		−	0.120579i
$750$	−1.37931e14	+	2.87820e14i	−0.581240	+	1.21287i
$751$		−	2.94510e14i		−	1.23282i	−0.787424	−	0.616412i	$-0.788586\pi$
$751$		−	2.94510e14i		−	1.23282i	0.787424	−	0.616412i	$-0.211414\pi$
$752$	4.33238e14	+	9.54095e13i	1.80151	+	0.396737i
$753$	1.72474e14			0.712442
$754$	3.01381e14	+	1.44429e14i	1.23668	+	0.592651i
$755$	−8.72015e13			−0.355459
$756$	8.24521e13	−	6.62699e13i	0.333882	−	0.268353i
$757$			2.90155e14i			1.16721i	0.812036	+	0.583607i	$0.198359\pi$
$757$			2.90155e14i			1.16721i	−0.812036	+	0.583607i	$0.801641\pi$
$758$	−3.34014e14	−	1.60068e14i	−1.33481	−	0.639673i
$759$		−	1.01957e14i		−	0.404769i
$760$	−2.50967e14	+	5.87956e13i	−0.989804	+	0.231887i
$761$	4.11236e14			1.61127			0.805635	−	0.592412i	$-0.201824\pi$
$761$	4.11236e14			1.61127			0.805635	+	0.592412i	$0.201824\pi$
$762$	−5.08441e13	+	1.06096e14i	−0.197909	+	0.412977i
$763$	1.93317e13			0.0747562
$764$	−3.38027e14	+	2.71685e14i	−1.29863	+	1.04376i
$765$		−	8.50577e13i		−	0.324643i
$766$	1.02176e14	−	2.13211e14i	0.387442	−	0.808475i
$767$			3.72895e14i			1.40479i
$768$	1.96251e14	+	9.08443e13i	0.734523	+	0.340010i
$769$	−1.42100e14			−0.528400			−0.264200	−	0.964468i	$-0.585108\pi$
$769$	−1.42100e14			−0.528400			−0.264200	+	0.964468i	$0.585108\pi$
$770$	2.27067e14	+	1.08816e14i	0.838881	+	0.402013i
$771$	−1.33213e14			−0.488961
$772$	−1.60409e14	−	1.99579e14i	−0.584981	−	0.727826i
$773$			2.58504e14i			0.936635i	0.883560	+	0.468317i	$0.155140\pi$
$773$			2.58504e14i			0.936635i	−0.883560	+	0.468317i	$0.844860\pi$
$774$	−2.07107e13	−	9.92510e12i	−0.0745574	−	0.0357298i
$775$			5.77147e14i			2.06433i
$776$	1.32125e13	+	5.63970e13i	0.0469543	+	0.200423i
$777$	1.52093e13			0.0537036
$778$	−1.16432e14	+	2.42959e14i	−0.408484	+	0.852383i
$779$	6.87559e13			0.239675
$780$	−2.45566e14	−	3.05530e14i	−0.850541	−	1.05823i
$781$		−	4.52932e14i		−	1.55875i
$782$	−2.51679e13	+	5.25178e13i	−0.0860623	+	0.179586i
$783$			4.51009e14i			1.53242i
$784$	−5.38385e13	+	2.44471e14i	−0.181766	+	0.825367i
$785$	1.28858e14			0.432277
$786$	9.24049e13	+	4.42828e13i	0.308022	+	0.147612i
$787$	−4.24394e14			−1.40571			−0.702855	−	0.711333i	$-0.748092\pi$
$787$	−4.24394e14			−1.40571			−0.702855	+	0.711333i	$0.748092\pi$
$788$	3.87862e14	−	3.11739e14i	1.27657	−	1.02603i
$789$		−	4.69892e14i		−	1.53678i
$790$	−1.62991e14	−	7.81095e13i	−0.529698	−	0.253845i
$791$		−	1.64645e14i		−	0.531700i
$792$	−3.36529e13	−	1.43646e14i	−0.107993	−	0.460966i
$793$	4.96021e13			0.158174
$794$	1.05413e14	−	2.19966e14i	0.334036	−	0.697034i
$795$	9.69516e12			0.0305295
$796$	1.12556e14	−	9.04659e13i	0.352213	−	0.283087i
$797$			3.84509e14i			1.19568i	0.801616	+	0.597839i	$0.203974\pi$
$797$			3.84509e14i			1.19568i	−0.801616	+	0.597839i	$0.796026\pi$
$798$	−2.62983e13	+	5.48767e13i	−0.0812669	+	0.169580i
$799$		−	3.28393e14i		−	1.00846i
$800$	3.96638e14	−	5.07225e14i	1.21044	−	1.54793i
$801$	8.29511e13			0.251570
$802$	3.13006e14	+	1.50001e14i	0.943369	+	0.452086i
$803$	−4.17223e14			−1.24966
$804$	1.00267e14	+	1.24751e14i	0.298454	+	0.371333i
$805$			8.34414e13i			0.246832i
$806$	−3.13918e14	−	1.50437e14i	−0.922870	−	0.442263i
$807$		−	1.80050e14i		−	0.526048i
$808$	3.49506e14	−	8.18809e13i	1.01484	−	0.237753i
$809$	−2.91643e14			−0.841606			−0.420803	−	0.907152i	$-0.638252\pi$
$809$	−2.91643e14			−0.841606			−0.420803	+	0.907152i	$0.638252\pi$
$810$	1.39126e14	−	2.90315e14i	0.399010	−	0.832614i
$811$	−1.84338e14			−0.525424			−0.262712	−	0.964874i	$-0.584617\pi$
$811$	−1.84338e14			−0.525424			−0.262712	+	0.964874i	$0.584617\pi$
$812$	1.22511e14	+	1.52427e14i	0.347053	+	0.431799i
$813$		−	1.37908e14i		−	0.388271i
$814$	3.57489e13	−	7.45973e13i	0.100033	−	0.208738i
$815$			4.24867e14i			1.18159i
$816$	3.44298e13	−	1.56340e14i	0.0951665	−	0.432134i
$817$	5.15201e13			0.141536
$818$	−5.04279e14	−	2.41663e14i	−1.37691	−	0.659848i
$819$	4.87142e13			0.132201
$820$	−2.02000e14	+	1.62355e14i	−0.544856	+	0.437922i
$821$			3.88449e14i			1.04140i	0.853740	+	0.520700i	$0.174329\pi$
$821$			3.88449e14i			1.04140i	−0.853740	+	0.520700i	$0.825671\pi$
$822$	−1.84294e14	−	8.83183e13i	−0.491080	−	0.235338i
$823$		−	2.91752e14i		−	0.772707i	−0.922351	−	0.386354i	$-0.873734\pi$
$823$		−	2.91752e14i		−	0.772707i	0.922351	−	0.386354i	$-0.126266\pi$
$824$	−7.56150e12	+	1.77148e12i	−0.0199054	+	0.00466337i
$825$	8.34477e14			2.18346
$826$	−9.42980e13	+	1.96772e14i	−0.245246	+	0.511755i
$827$	−2.48060e14			−0.641253			−0.320626	−	0.947206i	$-0.603893\pi$
$827$	−2.48060e14			−0.641253			−0.320626	+	0.947206i	$0.603893\pi$
$828$	3.81083e13	−	3.06290e13i	0.0979191	−	0.0787013i
$829$			1.64039e14i			0.418962i	0.977813	+	0.209481i	$0.0671774\pi$
$829$			1.64039e14i			0.418962i	−0.977813	+	0.209481i	$0.932823\pi$
$830$	−2.80665e14	+	5.85664e14i	−0.712521	+	1.48682i
$831$			4.14656e14i			1.04637i
$832$	1.72499e14	+	3.47948e14i	0.432684	+	0.872766i
$833$	1.85308e14			0.462030
$834$	−1.84897e14	−	8.86073e13i	−0.458247	−	0.219604i
$835$	1.00048e15			2.46476
$836$	2.07342e14	+	2.57972e14i	0.507757	+	0.631744i
$837$		−	4.69770e14i		−	1.14356i
$838$	4.84156e14	+	2.32020e14i	1.17156	+	0.561443i
$839$		−	5.19240e14i		−	1.24899i	−0.781030	−	0.624494i	$-0.785305\pi$
$839$		−	5.19240e14i		−	1.24899i	0.781030	−	0.624494i	$-0.214695\pi$
$840$	−5.23192e13	−	2.23323e14i	−0.125102	−	0.533995i
$841$	−4.13060e14			−0.981824
$842$	−5.66690e13	+	1.18251e14i	−0.133901	+	0.279412i
$843$	−5.65628e14			−1.32860
$844$	−2.91272e14	−	3.62397e14i	−0.680122	−	0.846199i
$845$			3.78800e13i			0.0879278i
$846$	−1.19145e14	+	2.48620e14i	−0.274931	+	0.573699i
$847$		−	1.51760e14i		−	0.348128i
$848$	−9.38076e12	−	2.06587e12i	−0.0213924	−	0.00471112i
$849$	−4.18231e14			−0.948152
$850$	−4.29839e14	−	2.05990e14i	−0.968748	−	0.464249i
$851$	2.74127e13			0.0614191
$852$	−3.21594e14	+	2.58478e14i	−0.716326	+	0.575738i
$853$		−	8.40549e14i		−	1.86131i	−0.365903	−	0.930653i	$-0.619240\pi$
$853$		−	8.40549e14i		−	1.86131i	0.365903	−	0.930653i	$-0.380760\pi$
$854$	2.61744e13	+	1.25434e13i	0.0576218	+	0.0276138i
$855$		−	1.60191e14i		−	0.350596i
$856$	3.21220e13	+	1.37112e14i	0.0698930	+	0.298336i
$857$	9.08205e13			0.196463			0.0982313	−	0.995164i	$-0.468681\pi$
$857$	9.08205e13			0.196463			0.0982313	+	0.995164i	$0.468681\pi$
$858$	−2.17512e14	+	4.53882e14i	−0.467785	+	0.976128i
$859$	5.90738e14			1.26307			0.631537	−	0.775346i	$-0.282424\pi$
$859$	5.90738e14			1.26307			0.631537	+	0.775346i	$0.282424\pi$
$860$	−1.51363e14	+	1.21656e14i	−0.321756	+	0.258607i
$861$			6.11823e13i			0.129303i
$862$	1.42736e14	−	2.97848e14i	0.299915	−	0.625833i
$863$			5.07805e14i			1.06082i	0.847740	+	0.530411i	$0.177963\pi$
$863$			5.07805e14i			1.06082i	−0.847740	+	0.530411i	$0.822037\pi$
$864$	−3.22845e14	+	4.12856e14i	−0.670540	+	0.857493i
$865$	3.98577e13			0.0823060
$866$	6.27424e14	+	3.00677e14i	1.28816	+	0.617321i
$867$	2.78010e14			0.567498
$868$	−1.27607e14	−	1.58767e14i	−0.258986	−	0.322227i
$869$			2.32072e14i			0.468300i
$870$	8.81888e14	+	4.22623e14i	1.76936	+	0.847924i
$871$			2.87424e14i			0.573366i
$872$	−9.32533e13	+	2.18470e13i	−0.184962	+	0.0433321i
$873$	−3.59979e13			−0.0709913
$874$	−4.73992e13	+	9.89079e13i	−0.0929423	+	0.193943i
$875$	−3.35387e14			−0.653892
$876$	2.38099e14	+	2.96240e14i	0.461570	+	0.574280i
$877$			2.07322e14i			0.399620i	0.979835	+	0.199810i	$0.0640325\pi$
$877$			2.07322e14i			0.399620i	−0.979835	+	0.199810i	$0.935968\pi$
$878$	4.29409e14	−	8.96049e14i	0.822998	−	1.71735i
$879$		−	1.18946e14i		−	0.226676i
$880$	−1.21831e15	−	2.68302e14i	−2.30858	−	0.508407i
$881$	3.62994e14			0.683943			0.341971	−	0.939710i	$-0.388905\pi$
$881$	3.62994e14			0.683943			0.341971	+	0.939710i	$0.388905\pi$
$882$	−1.40293e14	−	6.72321e13i	−0.262842	−	0.125960i
$883$	5.88143e12			0.0109567			0.00547835	−	0.999985i	$-0.498256\pi$
$883$	5.88143e12			0.0109567			0.00547835	+	0.999985i	$0.498256\pi$
$884$	2.24081e14	−	1.80102e14i	0.415091	−	0.333624i
$885$			1.09115e15i			2.00987i
$886$	−6.70143e14	−	3.21150e14i	−1.22744	−	0.588219i
$887$			4.25024e13i			0.0774096i	0.999251	+	0.0387048i	$0.0123232\pi$
$887$			4.25024e13i			0.0774096i	−0.999251	+	0.0387048i	$0.987677\pi$
$888$	−7.33674e13	+	1.71882e13i	−0.132873	+	0.0311290i
$889$	−1.23630e14			−0.222647
$890$	3.03121e14	−	6.32522e14i	0.542832	−	1.13273i
$891$	−4.13360e14			−0.736105
$892$	5.66841e14	−	4.55592e14i	1.00378	−	0.806774i
$893$		−	6.18468e14i		−	1.08908i
$894$	2.52453e14	−	5.26794e14i	0.442072	−	0.922472i
$895$		−	1.66545e15i		−	2.90012i
$896$	3.03624e12	+	2.27229e14i	0.00525770	+	0.393481i
$897$	−1.66790e14			−0.287216
$898$	−3.03061e14	−	1.45235e14i	−0.518977	−	0.248707i
$899$	8.68450e14			1.47893
$900$	2.50687e14	+	3.11902e14i	0.424541	+	0.528208i
$901$			7.11058e12i			0.0119752i
$902$	3.00083e14	+	1.43807e14i	0.502583	+	0.240851i
$903$			4.58451e13i			0.0763579i
$904$	1.86068e14	+	7.94225e14i	0.308197	+	1.31553i
$905$	−1.89411e15			−3.12006
$906$	4.40787e13	−	9.19791e13i	0.0722085	−	0.150677i
$907$	2.03986e14			0.332326			0.166163	−	0.986098i	$-0.446862\pi$
$907$	2.03986e14			0.332326			0.166163	+	0.986098i	$0.446862\pi$
$908$	−1.12903e14	−	1.40472e14i	−0.182926	−	0.227594i
$909$			2.23087e14i			0.359464i
$910$	1.78012e14	−	3.71458e14i	0.285261	−	0.595254i
$911$			1.49719e14i			0.238608i	0.992858	+	0.119304i	$0.0380664\pi$
$911$			1.49719e14i			0.238608i	−0.992858	+	0.119304i	$0.961934\pi$
$912$	6.48424e13	−	2.94438e14i	0.102774	−	0.466680i
$913$	8.33888e14			1.31448
$914$	4.97464e14	+	2.38397e14i	0.779884	+	0.373740i
$915$	1.45144e14			0.226304
$916$	3.16342e14	−	2.54256e14i	0.490545	−	0.394270i
$917$			1.07676e14i			0.166063i
$918$	3.49868e14	+	1.67666e14i	0.536649	+	0.257176i
$919$			9.31781e14i			1.42146i	0.703463	+	0.710732i	$0.251636\pi$
$919$			9.31781e14i			1.42146i	−0.703463	+	0.710732i	$0.748364\pi$
$920$	−9.42983e13	−	4.02509e14i	−0.143075	−	0.610713i
$921$	6.67524e13			0.100732
$922$	1.21445e13	−	2.53420e13i	0.0182275	−	0.0380353i
$923$	−7.40948e14			−1.10606
$924$	−2.29556e14	+	1.84503e14i	−0.340823	+	0.273932i
$925$			2.24362e14i			0.331315i
$926$	−5.16626e14	+	1.07804e15i	−0.758790	+	1.58337i
$927$		−	4.82645e12i		−	0.00705066i
$928$	−7.63236e14	−	5.96833e14i	−1.10897	−	0.867188i
$929$	−9.29163e14			−1.34281			−0.671403	−	0.741093i	$-0.734308\pi$
$929$	−9.29163e14			−1.34281			−0.671403	+	0.741093i	$0.734308\pi$
$930$	−9.18572e14	−	4.40203e14i	−1.32038	−	0.632759i
$931$	3.48995e14			0.498965
$932$	−5.86900e14	−	7.30213e14i	−0.834612	−	1.03841i
$933$		−	9.42498e13i		−	0.133313i
$934$	8.82315e14	+	4.22828e14i	1.24134	+	0.594879i
$935$			9.23477e14i			1.29231i
$936$	−2.34990e14	+	5.50526e13i	−0.327093	+	0.0766300i
$937$	−3.08132e14			−0.426618			−0.213309	−	0.976985i	$-0.568424\pi$
$937$	−3.08132e14			−0.426618			−0.213309	+	0.976985i	$0.568424\pi$
$938$	−7.26839e13	+	1.51670e14i	−0.100098	+	0.208874i
$939$	6.19798e14			0.849029
$940$	1.46040e15	+	1.81702e15i	1.98991	+	2.47582i
$941$			6.11614e14i			0.828952i	0.910060	+	0.414476i	$0.136035\pi$
$941$			6.11614e14i			0.828952i	−0.910060	+	0.414476i	$0.863965\pi$
$942$	−6.51351e13	+	1.35917e14i	−0.0878134	+	0.183240i
$943$			1.10273e14i			0.147880i
$944$	2.32506e14	−	1.05577e15i	0.310151	−	1.40834i
$945$	5.55877e14			0.737598
$946$	2.24858e14	+	1.07758e14i	0.296792	+	0.142230i
$947$	7.23883e14			0.950427			0.475213	−	0.879871i	$-0.342371\pi$
$947$	7.23883e14			0.950427			0.475213	+	0.879871i	$0.342371\pi$
$948$	1.64778e14	−	1.32438e14i	0.215207	−	0.172970i
$949$			6.82532e14i			0.886732i
$950$	−8.09523e14	−	3.87944e14i	−1.04619	−	0.501362i
$951$			1.42437e14i			0.183113i
$952$	1.63789e14	−	3.83717e13i	0.209459	−	0.0490712i
$953$	1.17221e15			1.49122			0.745608	−	0.666385i	$-0.232159\pi$
$953$	1.17221e15			1.49122			0.745608	+	0.666385i	$0.232159\pi$
$954$	2.57981e12	−	5.38329e12i	0.00326472	−	0.00681249i
$955$	−2.27892e15			−2.86887
$956$	1.59030e14	−	1.27819e14i	0.199155	−	0.160068i
$957$		−	1.25566e15i		−	1.56427i
$958$	−2.80534e14	+	5.85390e14i	−0.347662	+	0.725468i
$959$		−	2.14751e14i		−	0.264754i
$960$	5.04761e14	+	1.01815e15i	0.619055	+	1.24869i
$961$	−8.49472e13			−0.103641
$962$	−1.22033e14	−	5.84815e13i	−0.148116	−	0.0709812i
$963$	−8.75175e13			−0.105673
$964$	−3.34245e14	−	4.15864e14i	−0.401495	−	0.499535i
$965$		−	1.34552e15i		−	1.60788i
$966$	−8.80130e13	−	4.21781e13i	−0.104631	−	0.0501419i
$967$		−	1.04445e15i		−	1.23525i	−0.786471	−	0.617627i	$-0.788094\pi$
$967$		−	1.04445e15i		−	1.23525i	0.786471	−	0.617627i	$-0.211906\pi$
$968$	1.71506e14	+	7.32067e14i	0.201791	+	0.861339i
$969$	−2.23183e14			−0.261241
$970$	−1.31544e14	+	2.74492e14i	−0.153183	+	0.319647i
$971$	−3.97256e13			−0.0460230			−0.0230115	−	0.999735i	$-0.507325\pi$
$971$	−3.97256e13			−0.0460230			−0.0230115	+	0.999735i	$0.507325\pi$
$972$	−3.55770e14	−	4.42644e14i	−0.410051	−	0.510180i
$973$		−	2.15454e14i		−	0.247053i
$974$	3.20564e14	−	6.68922e14i	0.365696	−	0.763099i
$975$		−	1.36512e15i		−	1.54934i
$976$	−1.40437e14	−	3.09276e13i	−0.158574	−	0.0349219i
$977$	1.61456e15			1.81377			0.906884	−	0.421381i	$-0.138454\pi$
$977$	1.61456e15			1.81377			0.906884	+	0.421381i	$0.138454\pi$
$978$	−4.48145e14	−	2.14763e14i	−0.500869	−	0.240029i
$979$	−9.00606e14			−1.00143
$980$	−1.02532e15	+	8.24090e14i	−1.13431	+	0.911684i
$981$		−	5.95230e13i		−	0.0655148i
$982$	−7.35053e14	−	3.52256e14i	−0.804936	−	0.385746i
$983$		−	1.09516e14i		−	0.119319i	−0.998219	−	0.0596597i	$-0.980998\pi$
$983$		−	1.09516e14i		−	0.119319i	0.998219	−	0.0596597i	$-0.0190016\pi$
$984$	−6.91430e13	−	2.95135e14i	−0.0749501	−	0.319922i
$985$	2.61490e15			2.82016
$986$	−3.09958e14	+	6.46791e14i	−0.332597	+	0.694031i
$987$	5.50343e14			0.587554
$988$	4.22015e14	−	3.39190e14i	0.448274	−	0.360295i
$989$			8.26296e13i			0.0873281i
$990$	3.35049e14	−	6.99147e14i	0.352316	−	0.735178i
$991$			1.73875e15i			1.81915i	0.415536	+	0.909577i	$0.363594\pi$
$991$			1.73875e15i			1.81915i	−0.415536	+	0.909577i	$0.636406\pi$
$992$	7.94984e14	+	6.21660e14i	0.827561	+	0.647135i
$993$	−3.71778e14			−0.385068
$994$	−3.90988e14	−	1.87371e14i	−0.402932	−	0.193095i
$995$	7.58836e14			0.778094
$996$	−4.75881e14	−	5.92084e14i	−0.485513	−	0.604069i
$997$		−	1.61791e15i		−	1.64240i	−0.570641	−	0.821200i	$-0.693305\pi$
$997$		−	1.61791e15i		−	1.64240i	0.570641	−	0.821200i	$-0.306695\pi$
$998$	−1.82002e14	−	8.72200e13i	−0.183833	−	0.0880975i
$999$		−	1.82620e14i		−	0.183536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.11.d.b.3.8	yes	8
3.2	odd	2		72.11.b.b.19.1		8
4.3	odd	2		32.11.d.b.15.8		8
8.3	odd	2	inner	8.11.d.b.3.7	✓	8
8.5	even	2		32.11.d.b.15.7		8
12.11	even	2		288.11.b.b.271.1		8
16.3	odd	4		256.11.c.m.255.12		16
16.5	even	4		256.11.c.m.255.11		16
16.11	odd	4		256.11.c.m.255.5		16
16.13	even	4		256.11.c.m.255.6		16
24.5	odd	2		288.11.b.b.271.8		8
24.11	even	2		72.11.b.b.19.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.11.d.b.3.7	✓	8	8.3	odd	2	inner
8.11.d.b.3.8	yes	8	1.1	even	1	trivial
32.11.d.b.15.7		8	8.5	even	2
32.11.d.b.15.8		8	4.3	odd	2
72.11.b.b.19.1		8	3.2	odd	2
72.11.b.b.19.2		8	24.11	even	2
256.11.c.m.255.5		16	16.11	odd	4
256.11.c.m.255.6		16	16.13	even	4
256.11.c.m.255.11		16	16.5	even	4
256.11.c.m.255.12		16	16.3	odd	4
288.11.b.b.271.1		8	12.11	even	2
288.11.b.b.271.8		8	24.5	odd	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(28.8575 + 13.8292i) q^{2} -196.684 q^{3} +(641.505 + 798.152i) q^{4} +5381.00i q^{5} +(-5675.81 - 2719.99i) q^{6} -6613.83i q^{7} +(7474.38 + 31904.2i) q^{8} -20364.2 q^{9} +(-74415.0 + 155282. i) q^{10} +221096. q^{11} +(-126174. - 156984. i) q^{12} -361689. i q^{13} +(91464.1 - 190858. i) q^{14} -1.05836e6i q^{15} +(-225518. + 1.02404e6i) q^{16} +776217. q^{17} +(-587659. - 281621. i) q^{18} +1.46186e6 q^{19} +(-4.29486e6 + 3.45194e6i) q^{20} +1.30084e6i q^{21} +(6.38025e6 + 3.05758e6i) q^{22} +2.34458e6i q^{23} +(-1.47009e6 - 6.27505e6i) q^{24} -1.91895e7 q^{25} +(5.00188e6 - 1.04374e7i) q^{26} +1.56193e7 q^{27} +(5.27884e6 - 4.24281e6i) q^{28} +2.88750e7i q^{29} +(1.46363e7 - 3.05415e7i) q^{30} -3.00762e7i q^{31} +(-2.06695e7 + 2.64324e7i) q^{32} -4.34861e7 q^{33} +(2.23996e7 + 1.07345e7i) q^{34} +3.55890e7 q^{35} +(-1.30637e7 - 1.62537e7i) q^{36} -1.16919e7i q^{37} +(4.21857e7 + 2.02164e7i) q^{38} +7.11386e7i q^{39} +(-1.71676e8 + 4.02196e7i) q^{40} +4.70330e7 q^{41} +(-1.79896e7 + 3.75389e7i) q^{42} +3.52427e7 q^{43} +(1.41834e8 + 1.76468e8i) q^{44} -1.09580e8i q^{45} +(-3.24238e7 + 6.76587e7i) q^{46} -4.23068e8i q^{47} +(4.43559e7 - 2.01412e8i) q^{48} +2.38733e8 q^{49} +(-5.53761e8 - 2.65376e8i) q^{50} -1.52670e8 q^{51} +(2.88683e8 - 2.32025e8i) q^{52} +9.16056e6i q^{53} +(4.50735e8 + 2.16003e8i) q^{54} +1.18971e9i q^{55} +(2.11009e8 - 4.94343e7i) q^{56} -2.87526e8 q^{57} +(-3.99319e8 + 8.33260e8i) q^{58} -1.03098e9 q^{59} +(8.44732e8 - 6.78943e8i) q^{60} +1.37140e8i q^{61} +(4.15930e8 - 8.67921e8i) q^{62} +1.34685e8i q^{63} +(-9.62009e8 + 4.76928e8i) q^{64} +1.94625e9 q^{65} +(-1.25490e9 - 6.01379e8i) q^{66} -7.94671e8 q^{67} +(4.97947e8 + 6.19539e8i) q^{68} -4.61143e8i q^{69} +(1.02701e9 + 4.92168e8i) q^{70} -2.04858e9i q^{71} +(-1.52210e8 - 6.49703e8i) q^{72} -1.88707e9 q^{73} +(1.61690e8 - 3.37399e8i) q^{74} +3.77428e9 q^{75} +(9.37794e8 + 1.16679e9i) q^{76} -1.46229e9i q^{77} +(-9.83792e8 + 2.05288e9i) q^{78} +1.04965e9i q^{79} +(-5.51035e9 - 1.21351e9i) q^{80} -1.86960e9 q^{81} +(1.35725e9 + 6.50430e8i) q^{82} +3.77162e9 q^{83} +(-1.03827e9 + 8.34494e8i) q^{84} +4.17682e9i q^{85} +(1.01702e9 + 4.87380e8i) q^{86} -5.67927e9i q^{87} +(1.65255e9 + 7.05387e9i) q^{88} -4.07338e9 q^{89} +(1.51540e9 - 3.16219e9i) q^{90} -2.39215e9 q^{91} +(-1.87133e9 + 1.50406e9i) q^{92} +5.91551e9i q^{93} +(5.85070e9 - 1.22087e10i) q^{94} +7.86629e9i q^{95} +(4.06538e9 - 5.19884e9i) q^{96} +1.76770e9 q^{97} +(6.88921e9 + 3.30149e9i) q^{98} -4.50244e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19}+ \cdots - 13646747232 q^{99}+O(q^{100}) \) 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9 + 9120 * q^10 + 143328 * q^11 + 180120 * q^12 - 400320 * q^14 - 1987312 * q^16 - 370800 * q^17 + 3067758 * q^18 + 1753312 * q^19 + 2557440 * q^20 + 1549180 * q^22 - 19794288 * q^24 - 18792760 * q^25 + 1891680 * q^26 + 28949184 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 64016928 * q^32 - 74308704 * q^33 - 115705388 * q^34 + 53736960 * q^35 + 50631516 * q^36 + 375128220 * q^38 - 357584640 * q^40 + 92669328 * q^41 - 576155520 * q^42 - 10190624 * q^43 + 727831512 * q^44 + 851947200 * q^46 - 1142760480 * q^48 - 80432248 * q^49 - 1669361190 * q^50 - 276714816 * q^51 + 2420759040 * q^52 + 1749768696 * q^54 - 2928529920 * q^56 + 1400712864 * q^57 - 3245264160 * q^58 - 965642016 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 5804705728 * q^64 - 839028480 * q^65 - 5970262296 * q^66 - 1225582880 * q^67 + 5258111400 * q^68 + 7723829760 * q^70 - 4343608728 * q^72 + 2800072720 * q^73 - 7669373280 * q^74 + 4485554400 * q^75 + 3753451288 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 - 11909065176 * q^81 - 3638778380 * q^82 + 1853422560 * q^83 - 2916218880 * q^84 + 3022180476 * q^86 + 5815578640 * q^88 + 6162596112 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 7877525568 * q^96 - 9697863536 * q^97 + 34759868298 * q^98 - 13646747232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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