LMFDB - Embedded newform 403.2.l.c.129.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.32
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46210i q^{2} +(0.199198 - 0.345021i) q^{3} -4.06196 q^{4} +(3.00007 - 1.73209i) q^{5} +(0.849477 + 0.490446i) q^{6} +(-1.28546 - 0.742161i) q^{7} -5.07675i q^{8} +(1.42064 + 2.46062i) q^{9} +O(q^{10})$	\(q+2.46210i q^{2} +(0.199198 - 0.345021i) q^{3} -4.06196 q^{4} +(3.00007 - 1.73209i) q^{5} +(0.849477 + 0.490446i) q^{6} +(-1.28546 - 0.742161i) q^{7} -5.07675i q^{8} +(1.42064 + 2.46062i) q^{9} +(4.26458 + 7.38647i) q^{10} +(4.37174 - 2.52402i) q^{11} +(-0.809133 + 1.40146i) q^{12} +(-0.987523 + 3.46768i) q^{13} +(1.82728 - 3.16494i) q^{14} -1.38011i q^{15} +4.37557 q^{16} +(-1.11215 + 1.92631i) q^{17} +(-6.05831 + 3.49776i) q^{18} +(6.03502 + 3.48432i) q^{19} +(-12.1861 + 7.03567i) q^{20} +(-0.512122 + 0.295674i) q^{21} +(6.21441 + 10.7637i) q^{22} -4.24394 q^{23} +(-1.75158 - 1.01128i) q^{24} +(3.50026 - 6.06263i) q^{25} +(-8.53779 - 2.43138i) q^{26} +2.32714 q^{27} +(5.22148 + 3.01462i) q^{28} +2.92107 q^{29} +3.39798 q^{30} +(-2.38419 - 5.03146i) q^{31} +0.619609i q^{32} -2.01112i q^{33} +(-4.74276 - 2.73824i) q^{34} -5.14195 q^{35} +(-5.77058 - 9.99493i) q^{36} +(1.44635 + 0.835052i) q^{37} +(-8.57876 + 14.8588i) q^{38} +(0.999709 + 1.03147i) q^{39} +(-8.79338 - 15.2306i) q^{40} +(0.651993 - 0.376429i) q^{41} +(-0.727979 - 1.26090i) q^{42} +(-4.05686 + 7.02669i) q^{43} +(-17.7578 + 10.2525i) q^{44} +(8.52403 + 4.92135i) q^{45} -10.4490i q^{46} -8.29508i q^{47} +(0.871604 - 1.50966i) q^{48} +(-2.39840 - 4.15414i) q^{49} +(14.9268 + 8.61801i) q^{50} +(0.443077 + 0.767432i) q^{51} +(4.01127 - 14.0856i) q^{52} +(-1.69421 - 2.93446i) q^{53} +5.72966i q^{54} +(8.74366 - 15.1445i) q^{55} +(-3.76776 + 6.52596i) q^{56} +(2.40433 - 1.38814i) q^{57} +7.19198i q^{58} +(-5.22180 - 3.01481i) q^{59} +5.60596i q^{60} -3.30204 q^{61} +(12.3880 - 5.87013i) q^{62} -4.21737i q^{63} +7.22559 q^{64} +(3.04369 + 12.1137i) q^{65} +4.95159 q^{66} +(-6.91629 + 3.99312i) q^{67} +(4.51752 - 7.82457i) q^{68} +(-0.845383 + 1.46425i) q^{69} -12.6600i q^{70} +(4.65051 - 2.68498i) q^{71} +(12.4920 - 7.21223i) q^{72} +(-10.1346 + 5.85124i) q^{73} +(-2.05598 + 3.56107i) q^{74} +(-1.39449 - 2.41533i) q^{75} +(-24.5140 - 14.1532i) q^{76} -7.49292 q^{77} +(-2.53959 + 2.46139i) q^{78} +(-0.119947 + 0.207754i) q^{79} +(13.1270 - 7.57887i) q^{80} +(-3.79836 + 6.57895i) q^{81} +(0.926806 + 1.60528i) q^{82} +(13.9719 - 8.06666i) q^{83} +(2.08022 - 1.20101i) q^{84} +7.70539i q^{85} +(-17.3004 - 9.98841i) q^{86} +(0.581871 - 1.00783i) q^{87} +(-12.8138 - 22.1942i) q^{88} +11.9872i q^{89} +(-12.1169 + 20.9870i) q^{90} +(3.84300 - 3.72466i) q^{91} +17.2387 q^{92} +(-2.21089 - 0.179661i) q^{93} +20.4233 q^{94} +24.1406 q^{95} +(0.213778 + 0.123425i) q^{96} -14.2496i q^{97} +(10.2279 - 5.90510i) q^{98} +(12.4213 + 7.17146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$			2.46210i			1.74097i	0.492195	+	0.870485i	$0.336195\pi$
$2$			2.46210i			1.74097i	−0.492195	+	0.870485i	$0.663805\pi$
$3$	0.199198	−	0.345021i	0.115007	−	0.199198i	−0.802776	−	0.596281i	$-0.796644\pi$
$3$	0.199198	−	0.345021i	0.115007	−	0.199198i	0.917783	+	0.397083i	$0.129978\pi$
$4$	−4.06196			−2.03098
$5$	3.00007	−	1.73209i	1.34167	−	0.774614i	0.354618	−	0.935011i	$-0.384611\pi$
$5$	3.00007	−	1.73209i	1.34167	−	0.774614i	0.987052	+	0.160398i	$0.0512777\pi$
$6$	0.849477	+	0.490446i	0.346798	+	0.200224i
$7$	−1.28546	−	0.742161i	−0.485858	−	0.280510i	0.236996	−	0.971511i	$-0.423837\pi$
$7$	−1.28546	−	0.742161i	−0.485858	−	0.280510i	−0.722855	+	0.691000i	$0.757170\pi$
$8$		−	5.07675i		−	1.79490i
$9$	1.42064	+	2.46062i	0.473547	+	0.820207i
$10$	4.26458	+	7.38647i	1.34858	+	2.33581i
$11$	4.37174	−	2.52402i	1.31813	−	0.761022i	0.334701	−	0.942324i	$-0.391365\pi$
$11$	4.37174	−	2.52402i	1.31813	−	0.761022i	0.983427	+	0.181303i	$0.0580314\pi$
$12$	−0.809133	+	1.40146i	−0.233576	+	0.404566i
$13$	−0.987523	+	3.46768i	−0.273890	+	0.961761i
$13$	−0.987523	+	3.46768i	−0.273890	+	0.961761i
$14$	1.82728	−	3.16494i	0.488360	−	0.845865i
$15$		−	1.38011i		−	0.356344i
$16$	4.37557			1.09389
$17$	−1.11215	+	1.92631i	−0.269737	+	0.467198i	−0.968794	−	0.247868i	$-0.920270\pi$
$17$	−1.11215	+	1.92631i	−0.269737	+	0.467198i	0.699057	+	0.715066i	$0.253603\pi$
$18$	−6.05831	+	3.49776i	−1.42796	+	0.824431i
$19$	6.03502	+	3.48432i	1.38453	+	0.799358i	0.992692	−	0.120677i	$-0.0385065\pi$
$19$	6.03502	+	3.48432i	1.38453	+	0.799358i	0.391837	+	0.920035i	$0.371840\pi$
$20$	−12.1861	+	7.03567i	−2.72490	+	1.57322i
$21$	−0.512122	+	0.295674i	−0.111754	+	0.0645213i
$22$	6.21441	+	10.7637i	1.32492	+	2.29482i
$23$	−4.24394			−0.884922			−0.442461	−	0.896788i	$-0.645894\pi$
$23$	−4.24394			−0.884922			−0.442461	+	0.896788i	$0.645894\pi$
$24$	−1.75158	−	1.01128i	−0.357540	−	0.206426i
$25$	3.50026	−	6.06263i	0.700052	−	1.21253i
$26$	−8.53779	−	2.43138i	−1.67440	−	0.476834i
$27$	2.32714			0.447859
$28$	5.22148	+	3.01462i	0.986767	+	0.569710i
$29$	2.92107			0.542430			0.271215	−	0.962519i	$-0.412575\pi$
$29$	2.92107			0.542430			0.271215	+	0.962519i	$0.412575\pi$
$30$	3.39798			0.620384
$31$	−2.38419	−	5.03146i	−0.428214	−	0.903678i
$31$	−2.38419	−	5.03146i	−0.428214	−	0.903678i
$32$			0.619609i			0.109532i
$33$		−	2.01112i		−	0.350091i
$34$	−4.74276	−	2.73824i	−0.813377	−	0.469604i
$35$	−5.14195			−0.869149
$36$	−5.77058	−	9.99493i	−0.961763	−	1.66582i
$37$	1.44635	+	0.835052i	0.237779	+	0.137282i	0.614155	−	0.789185i	$-0.289497\pi$
$37$	1.44635	+	0.835052i	0.237779	+	0.137282i	−0.376377	+	0.926467i	$0.622830\pi$
$38$	−8.57876	+	14.8588i	−1.39166	+	2.41042i
$39$	0.999709	+	1.03147i	0.160082	+	0.165167i
$40$	−8.79338	−	15.2306i	−1.39035	−	2.40817i
$41$	0.651993	−	0.376429i	0.101824	−	0.0587883i	−0.448223	−	0.893922i	$-0.647943\pi$
$41$	0.651993	−	0.376429i	0.101824	−	0.0587883i	0.550047	+	0.835133i	$0.314610\pi$
$42$	−0.727979	−	1.26090i	−0.112330	−	0.194561i
$43$	−4.05686	+	7.02669i	−0.618666	+	1.07156i	0.371064	+	0.928607i	$0.378993\pi$
$43$	−4.05686	+	7.02669i	−0.618666	+	1.07156i	−0.989729	+	0.142953i	$0.954340\pi$
$44$	−17.7578	+	10.2525i	−2.67709	+	1.54562i
$45$	8.52403	+	4.92135i	1.27069	+	0.733632i
$46$		−	10.4490i		−	1.54062i
$47$		−	8.29508i		−	1.20996i	−0.796240	−	0.604981i	$-0.793181\pi$
$47$		−	8.29508i		−	1.20996i	0.796240	−	0.604981i	$-0.206819\pi$
$48$	0.871604	−	1.50966i	0.125805	−	0.217901i
$49$	−2.39840	−	4.15414i	−0.342628	−	0.593449i
$50$	14.9268	+	8.61801i	2.11097	+	1.21877i
$51$	0.443077	+	0.767432i	0.0620432	+	0.107462i
$52$	4.01127	−	14.0856i	0.556264	−	1.95332i
$53$	−1.69421	−	2.93446i	−0.232718	−	0.403079i	0.725889	−	0.687812i	$-0.241428\pi$
$53$	−1.69421	−	2.93446i	−0.232718	−	0.403079i	−0.958607	+	0.284733i	$0.908095\pi$
$54$			5.72966i			0.779708i
$55$	8.74366	−	15.1445i	1.17900	−	2.04208i
$56$	−3.76776	+	6.52596i	−0.503488	+	0.872067i
$57$	2.40433	−	1.38814i	0.318461	−	0.183863i
$58$			7.19198i			0.944354i
$59$	−5.22180	−	3.01481i	−0.679821	−	0.392495i	0.119967	−	0.992778i	$-0.461721\pi$
$59$	−5.22180	−	3.01481i	−0.679821	−	0.392495i	−0.799788	+	0.600283i	$0.795055\pi$
$60$			5.60596i			0.723726i
$61$	−3.30204			−0.422782			−0.211391	−	0.977402i	$-0.567799\pi$
$61$	−3.30204			−0.422782			−0.211391	+	0.977402i	$0.567799\pi$
$62$	12.3880	−	5.87013i	1.57328	−	0.745507i
$63$		−	4.21737i		−	0.531339i
$64$	7.22559			0.903199
$65$	3.04369	+	12.1137i	0.377524	+	1.50252i
$66$	4.95159			0.609498
$67$	−6.91629	+	3.99312i	−0.844960	+	0.487838i	−0.858947	−	0.512064i	$-0.828881\pi$
$67$	−6.91629	+	3.99312i	−0.844960	+	0.487838i	0.0139872	+	0.999902i	$0.495548\pi$
$68$	4.51752	−	7.82457i	0.547829	−	0.948868i
$69$	−0.845383	+	1.46425i	−0.101772	+	0.176275i
$70$		−	12.6600i		−	1.51316i
$71$	4.65051	−	2.68498i	0.551915	−	0.318648i	−0.197979	−	0.980206i	$-0.563438\pi$
$71$	4.65051	−	2.68498i	0.551915	−	0.318648i	0.749894	+	0.661558i	$0.230105\pi$
$72$	12.4920	−	7.21223i	1.47219	−	0.849970i
$73$	−10.1346	+	5.85124i	−1.18617	+	0.684836i	−0.957434	−	0.288653i	$-0.906793\pi$
$73$	−10.1346	+	5.85124i	−1.18617	+	0.684836i	−0.228736	+	0.973488i	$0.573459\pi$
$74$	−2.05598	+	3.56107i	−0.239003	+	0.413966i
$75$	−1.39449	−	2.41533i	−0.161022	−	0.278898i
$76$	−24.5140	−	14.1532i	−2.81195	−	1.62348i
$77$	−7.49292			−0.853898
$78$	−2.53959	+	2.46139i	−0.287552	+	0.278697i
$79$	−0.119947	+	0.207754i	−0.0134951	+	0.0233742i	−0.872694	−	0.488267i	$-0.837629\pi$
$79$	−0.119947	+	0.207754i	−0.0134951	+	0.0233742i	0.859199	+	0.511642i	$0.170962\pi$
$80$	13.1270	−	7.57887i	1.46764	−	0.847344i
$81$	−3.79836	+	6.57895i	−0.422040	+	0.730995i
$82$	0.926806	+	1.60528i	0.102349	+	0.177273i
$83$	13.9719	−	8.06666i	1.53361	−	0.885431i	0.534419	−	0.845219i	$-0.320530\pi$
$83$	13.9719	−	8.06666i	1.53361	−	0.885431i	0.999191	−	0.0402111i	$-0.0128030\pi$
$84$	2.08022	−	1.20101i	0.226970	−	0.131041i
$85$			7.70539i			0.835767i
$86$	−17.3004	−	9.98841i	−1.86555	−	1.07708i
$87$	0.581871	−	1.00783i	0.0623832	−	0.108051i
$88$	−12.8138	−	22.1942i	−1.36596	−	2.36591i
$89$			11.9872i			1.27064i	0.772248	+	0.635322i	$0.219132\pi$
$89$			11.9872i			1.27064i	−0.772248	+	0.635322i	$0.780868\pi$
$90$	−12.1169	+	20.9870i	−1.27723	+	2.21223i
$91$	3.84300	−	3.72466i	0.402855	−	0.390451i
$92$	17.2387			1.79726
$93$	−2.21089	−	0.179661i	−0.229258	−	0.0186299i
$94$	20.4233			2.10651
$95$	24.1406			2.47677
$96$	0.213778	+	0.123425i	0.0218186	+	0.0125970i
$97$		−	14.2496i		−	1.44683i	−0.690415	−	0.723414i	$-0.742572\pi$
$97$		−	14.2496i		−	1.44683i	0.690415	−	0.723414i	$-0.257428\pi$
$98$	10.2279	−	5.90510i	1.03318	−	0.596505i
$99$	12.4213	+	7.17146i	1.24839	+	0.720759i
$100$	−14.2179	+	24.6261i	−1.42179	+	2.46261i
$101$	−3.84809			−0.382899			−0.191450	−	0.981502i	$-0.561319\pi$
$101$	−3.84809			−0.382899			−0.191450	+	0.981502i	$0.561319\pi$
$102$	−1.88950	+	1.09090i	−0.187088	+	0.108015i
$103$	−7.09556	−	12.2899i	−0.699146	−	1.21096i	−0.968763	−	0.247989i	$-0.920230\pi$
$103$	−7.09556	−	12.2899i	−0.699146	−	1.21096i	0.269616	−	0.962968i	$-0.413103\pi$
$104$	17.6045	+	5.01340i	1.72627	+	0.491605i
$105$	−1.02427	+	1.77408i	−0.0999581	+	0.173133i
$106$	7.22494	−	4.17132i	0.701748	−	0.405155i
$107$	−6.15370	+	10.6585i	−0.594900	+	1.03040i	0.398661	+	0.917099i	$0.369475\pi$
$107$	−6.15370	+	10.6585i	−0.594900	+	1.03040i	−0.993561	+	0.113299i	$0.963858\pi$
$108$	−9.45274			−0.909591
$109$			8.60809i			0.824505i	0.911070	+	0.412253i	$0.135258\pi$
$109$			8.60809i			0.824505i	−0.911070	+	0.412253i	$0.864742\pi$
$110$	37.2873	+	21.5278i	3.55520	+	2.05260i
$111$	0.576220	−	0.332681i	0.0546924	−	0.0315767i
$112$	−5.62462	−	3.24737i	−0.531476	−	0.306848i
$113$	5.06054	+	8.76510i	0.476055	+	0.824552i	0.999624	−	0.0274319i	$-0.00873294\pi$
$113$	5.06054	+	8.76510i	0.476055	+	0.824552i	−0.523569	+	0.851984i	$0.675400\pi$
$114$	3.41774	+	5.91970i	0.320101	+	0.554431i
$115$	−12.7321	+	7.35087i	−1.18727	+	0.685472i
$116$	−11.8653			−1.10166
$117$	−9.93556	+	2.49641i	−0.918543	+	0.230793i
$118$	7.42278	−	12.8566i	0.683322	−	1.18355i
$119$	2.85926	−	1.65079i	0.262108	−	0.151328i
$120$	−7.00649			−0.639602
$121$	7.24139	−	12.5425i	0.658308	−	1.14022i
$122$		−	8.12995i		−	0.736051i
$123$		−	0.299935i		−	0.0270442i
$124$	9.68448	+	20.4376i	0.869692	+	1.83535i
$125$		−	6.93017i		−	0.619853i
$126$	10.3836			0.925046
$127$	5.52173	−	9.56392i	0.489974	−	0.848661i	−0.509959	−	0.860199i	$-0.670339\pi$
$127$	5.52173	−	9.56392i	0.489974	−	0.848661i	0.999933	+	0.0115381i	$0.00367276\pi$
$128$			19.0294i			1.68198i
$129$	1.61624	+	2.79940i	0.142302	+	0.246474i
$130$	−29.8253	+	7.49389i	−2.61585	+	0.657258i
$131$	5.36778	−	9.29727i	0.468985	−	0.812306i	−0.530386	−	0.847756i	$-0.677953\pi$
$131$	5.36778	−	9.29727i	0.468985	−	0.812306i	0.999371	+	0.0354498i	$0.0112864\pi$
$132$			8.16908i			0.711027i
$133$	−5.17185	−	8.95791i	−0.448456	−	0.776749i
$134$	−9.83149	−	17.0286i	−0.849311	−	1.47105i
$135$	6.98158	−	4.03081i	0.600878	−	0.346917i
$136$	9.77937	+	5.64612i	0.838574	+	0.484151i
$137$	−16.6561	+	9.61638i	−1.42302	+	0.821583i	−0.996556	−	0.0829198i	$-0.973575\pi$
$137$	−16.6561	+	9.61638i	−1.42302	+	0.821583i	−0.426467	+	0.904503i	$0.640242\pi$
$138$	−3.60513	−	2.08142i	−0.306889	−	0.177182i
$139$	−7.93064			−0.672668			−0.336334	−	0.941743i	$-0.609187\pi$
$139$	−7.93064			−0.672668			−0.336334	+	0.941743i	$0.609187\pi$
$140$	20.8864			1.76522
$141$	−2.86197	−	1.65236i	−0.241022	−	0.139154i
$142$	6.61069	+	11.4500i	0.554757	+	0.960867i
$143$	4.43531	+	17.6523i	0.370899	+	1.47616i
$144$	6.21611	+	10.7666i	0.518009	+	0.897218i
$145$	8.76341	−	5.05956i	0.727761	−	0.420173i
$146$	−14.4064	−	24.9525i	−1.19228	−	2.06509i
$147$	−1.91102			−0.157618
$148$	−5.87502	−	3.39194i	−0.482923	−	0.278816i
$149$	−4.98855	−	2.88014i	−0.408678	−	0.235950i	0.281544	−	0.959548i	$-0.409154\pi$
$149$	−4.98855	−	2.88014i	−0.408678	−	0.235950i	−0.690222	+	0.723598i	$0.742487\pi$
$150$	5.94678	−	3.43338i	0.485553	−	0.280334i
$151$		−	22.9377i		−	1.86665i	−0.359037	−	0.933323i	$-0.616895\pi$
$151$		−	22.9377i		−	1.86665i	0.359037	−	0.933323i	$-0.383105\pi$
$152$	17.6890	−	30.6383i	1.43477	−	2.48509i
$153$	−6.31988			−0.510932
$154$		−	18.4484i		−	1.48661i
$155$	−15.8677	−	10.9651i	−1.27452	−	0.880737i
$156$	−4.06077	−	4.18979i	−0.325122	−	0.335451i
$157$	−6.13397			−0.489544			−0.244772	−	0.969581i	$-0.578713\pi$
$157$	−6.13397			−0.489544			−0.244772	+	0.969581i	$0.578713\pi$
$158$	−0.511513	−	0.295322i	−0.0406938	−	0.0234946i
$159$	−1.34993			−0.107057
$160$	1.07322	+	1.85887i	0.0848454	+	0.146956i
$161$	5.45541	+	3.14968i	0.429947	+	0.248230i
$162$	−16.1981	−	9.35196i	−1.27264	−	0.734759i
$163$		−	18.6598i		−	1.46155i	−0.682621	−	0.730773i	$-0.739160\pi$
$163$		−	18.6598i		−	1.46155i	0.682621	−	0.730773i	$-0.260840\pi$
$164$	−2.64837	+	1.52904i	−0.206803	+	0.119398i
$165$	−3.48344	−	6.03349i	−0.271185	−	0.469707i
$166$	19.8609	+	34.4002i	1.54151	+	2.66997i
$167$	−2.41317	−	1.39324i	−0.186737	−	0.107812i	0.403717	−	0.914884i	$-0.367718\pi$
$167$	−2.41317	−	1.39324i	−0.186737	−	0.107812i	−0.590454	+	0.807071i	$0.701051\pi$
$168$	1.50106	+	2.59991i	0.115809	+	0.200588i
$169$	−11.0496	−	6.84883i	−0.849969	−	0.526833i
$170$	−18.9715			−1.45505
$171$			19.7999i			1.51413i
$172$	16.4788	−	28.5421i	1.25650	−	2.17631i
$173$	−11.5632	−	20.0280i	−0.879131	−	1.52270i	−0.852296	−	0.523059i	$-0.824791\pi$
$173$	−11.5632	−	20.0280i	−0.879131	−	1.52270i	−0.0268346	−	0.999640i	$-0.508543\pi$
$174$	2.48138	+	1.43263i	0.188113	+	0.108607i
$175$	−8.99889	+	5.19551i	−0.680252	+	0.392744i
$176$	19.1288	−	11.0440i	1.44189	−	0.832476i
$177$	−2.08034	+	1.20109i	−0.156368	+	0.0902793i
$178$	−29.5138			−2.21215
$179$	−1.17909	+	2.04225i	−0.0881296	+	0.152645i	−0.906721	−	0.421732i	$-0.861422\pi$
$179$	−1.17909	+	2.04225i	−0.0881296	+	0.152645i	0.818591	+	0.574377i	$0.194756\pi$
$180$	−34.6242	−	19.9903i	−2.58074	−	1.48999i
$181$	7.21894	+	12.5036i	0.536579	+	0.929383i	0.999085	+	0.0427665i	$0.0136171\pi$
$181$	7.21894	+	12.5036i	0.536579	+	0.929383i	−0.462506	+	0.886616i	$0.653050\pi$
$182$	9.17050	+	9.46186i	0.679763	+	0.701359i
$183$	−0.657758	+	1.13927i	−0.0486229	+	0.0842173i
$184$			21.5454i			1.58835i
$185$	5.78554			0.425361
$186$	0.442343	−	5.44343i	0.0324342	−	0.399132i
$187$			11.2284i			0.821102i
$188$			33.6942i			2.45740i
$189$	−2.99145	−	1.72711i	−0.217596	−	0.125629i
$190$			59.4367i			4.31199i
$191$	−0.572538	−	0.991665i	−0.0414274	−	0.0717544i	0.844568	−	0.535448i	$-0.179857\pi$
$191$	−0.572538	−	0.991665i	−0.0414274	−	0.0717544i	−0.885996	+	0.463694i	$0.846524\pi$
$192$	1.43932	−	2.49298i	0.103874	−	0.179915i
$193$	−8.15663	−	4.70923i	−0.587127	−	0.338978i	0.176834	−	0.984241i	$-0.443415\pi$
$193$	−8.15663	−	4.70923i	−0.587127	−	0.338978i	−0.763961	+	0.645263i	$0.776748\pi$
$194$	35.0840			2.51888
$195$	4.78579	+	1.36289i	0.342718	+	0.0975988i
$196$	9.74217	+	16.8739i	0.695870	+	1.20528i
$197$	−8.47055	+	4.89047i	−0.603502	+	0.348432i	−0.770418	−	0.637539i	$-0.779952\pi$
$197$	−8.47055	+	4.89047i	−0.603502	+	0.348432i	0.166916	+	0.985971i	$0.446619\pi$
$198$	−17.6569	+	30.5826i	−1.25482	+	2.17341i
$199$	6.11906	+	10.5985i	0.433769	+	0.751309i	0.997194	−	0.0748575i	$-0.0238502\pi$
$199$	6.11906	+	10.5985i	0.433769	+	0.751309i	−0.563426	+	0.826167i	$0.690517\pi$
$200$	−30.7784	−	17.7699i	−2.17636	−	1.25652i
$201$			3.18169i			0.224419i
$202$		−	9.47439i		−	0.666616i
$203$	−3.75492	−	2.16790i	−0.263544	−	0.152157i
$204$	−1.79976	−	3.11727i	−0.126008	−	0.218253i
$205$	1.30402	−	2.25862i	0.0910764	−	0.157749i
$206$	30.2589	−	17.4700i	2.10824	−	1.21719i
$207$	−6.02911	−	10.4427i	−0.419052	−	0.725819i
$208$	−4.32097	+	15.1731i	−0.299606	+	1.05206i
$209$	35.1780			2.43331
$210$	−4.36797	−	2.52185i	−0.301419	−	0.174024i
$211$	4.19236	−	7.26138i	0.288614	−	0.499894i	−0.684865	−	0.728670i	$-0.740139\pi$
$211$	4.19236	−	7.26138i	0.288614	−	0.499894i	0.973479	+	0.228776i	$0.0734723\pi$
$212$	6.88181	+	11.9196i	0.472644	+	0.818644i
$213$		−	2.13937i		−	0.146587i
$214$	−26.2424	−	15.1510i	−1.79389	−	1.03570i
$215$			28.1074i			1.91691i
$216$		−	11.8143i		−	0.803862i
$217$	−0.669370	+	8.23720i	−0.0454398	+	0.559177i
$218$	−21.1940			−1.43544
$219$			4.66222i			0.315043i
$220$	−35.5164	+	61.5162i	−2.39451	+	4.14742i
$221$	−5.58153	−	5.75886i	−0.375454	−	0.387383i
$222$	0.819095	+	1.41871i	0.0549741	+	0.0952179i
$223$	2.95461	+	1.70585i	0.197856	+	0.114232i	0.595655	−	0.803241i	$-0.296893\pi$
$223$	2.95461	+	1.70585i	0.197856	+	0.114232i	−0.397799	+	0.917472i	$0.630226\pi$
$224$	0.459850	−	0.796483i	0.0307250	−	0.0532173i
$225$	19.8905			1.32603
$226$	−21.5806	+	12.4596i	−1.43552	+	0.828798i
$227$	−6.80984	+	3.93166i	−0.451985	+	0.260954i	−0.708668	−	0.705542i	$-0.750704\pi$
$227$	−6.80984	+	3.93166i	−0.451985	+	0.260954i	0.256683	+	0.966496i	$0.417370\pi$
$228$	−9.76626	+	5.63855i	−0.646787	+	0.373422i
$229$	6.66003	+	3.84517i	0.440107	+	0.254096i	0.703643	−	0.710553i	$-0.251555\pi$
$229$	6.66003	+	3.84517i	0.440107	+	0.254096i	−0.263536	+	0.964650i	$0.584889\pi$
$230$	−18.0986	−	31.3477i	−1.19339	−	2.06701i
$231$	−1.49257	+	2.58521i	−0.0982042	+	0.170095i
$232$		−	14.8295i		−	0.973607i
$233$	24.7033			1.61836			0.809182	−	0.587558i	$-0.199911\pi$
$233$	24.7033			1.61836			0.809182	+	0.587558i	$0.199911\pi$
$234$	−6.14641	−	24.4624i	−0.401803	−	1.59916i
$235$	−14.3678	−	24.8858i	−0.937253	−	1.62337i
$236$	21.2107	+	12.2460i	1.38070	+	0.797148i
$237$	0.0477864	+	0.0827685i	0.00310406	+	0.00537639i
$238$	4.06442	+	7.03978i	0.263457	+	0.456321i
$239$	−14.1051	+	8.14357i	−0.912382	+	0.526764i	−0.881197	−	0.472750i	$-0.843262\pi$
$239$	−14.1051	+	8.14357i	−0.912382	+	0.526764i	−0.0311853	+	0.999514i	$0.509928\pi$
$240$		−	6.03878i		−	0.389802i
$241$	−1.71627	−	0.990888i	−0.110555	−	0.0638287i	0.443703	−	0.896174i	$-0.353664\pi$
$241$	−1.71627	−	0.990888i	−0.110555	−	0.0638287i	−0.554258	+	0.832345i	$0.686998\pi$
$242$	30.8808	+	17.8290i	1.98509	+	1.14609i
$243$	5.00396	+	8.66712i	0.321004	+	0.555996i
$244$	13.4127			0.858661
$245$	−14.3907	−	8.30847i	−0.919387	−	0.530808i
$246$	0.738471			0.0470832
$247$	−18.0422	+	17.4867i	−1.14800	+	1.11265i
$248$	−25.5435	+	12.1039i	−1.62201	+	0.768601i
$249$		−	6.42744i		−	0.407323i
$250$	17.0628			1.07915
$251$	−2.02285	+	3.50367i	−0.127681	+	0.221150i	−0.922778	−	0.385333i	$-0.874087\pi$
$251$	−2.02285	+	3.50367i	−0.127681	+	0.221150i	0.795097	+	0.606483i	$0.207420\pi$
$252$			17.1308i			1.07914i
$253$	−18.5534	+	10.7118i	−1.16644	+	0.673445i
$254$	23.5474	+	13.5951i	1.47749	+	0.853031i
$255$	2.65852	+	1.53490i	0.166483	+	0.0961190i
$256$	−32.4011			−2.02507
$257$	−2.95729	−	5.12217i	−0.184470	−	0.319512i	0.758927	−	0.651175i	$-0.225724\pi$
$257$	−2.95729	−	5.12217i	−0.184470	−	0.319512i	−0.943398	+	0.331663i	$0.892390\pi$
$258$	−6.89242	+	3.97934i	−0.429103	+	0.247743i
$259$	−1.23949	−	2.14685i	−0.0770179	−	0.133399i
$260$	−12.3633	−	49.2055i	−0.766742	−	3.05159i
$261$	4.14979	+	7.18765i	0.256866	+	0.444905i
$262$	22.8908	+	13.2160i	1.41420	+	0.816490i
$263$	−9.61129			−0.592658			−0.296329	−	0.955086i	$-0.595762\pi$
$263$	−9.61129			−0.592658			−0.296329	+	0.955086i	$0.595762\pi$
$264$	−10.2099			−0.628379
$265$	−10.1655	−	5.86905i	−0.624461	−	0.360533i
$266$	22.0553	−	12.7336i	1.35230	−	0.780749i
$267$	4.13584	+	2.38783i	0.253109	+	0.146133i
$268$	28.0937	−	16.2199i	1.71609	−	0.990788i
$269$	12.7942	+	22.1603i	0.780078	+	1.35113i	0.931896	+	0.362726i	$0.118154\pi$
$269$	12.7942	+	22.1603i	0.780078	+	1.35113i	−0.151818	+	0.988409i	$0.548513\pi$
$270$	9.92428	+	17.1894i	0.603973	+	1.04611i
$271$		−	2.87701i		−	0.174766i	−0.996175	−	0.0873831i	$-0.972150\pi$
$271$		−	2.87701i		−	0.174766i	0.996175	−	0.0873831i	$-0.0278504\pi$
$272$	−4.86630	+	8.42868i	−0.295063	+	0.511064i
$273$	−0.519569	−	2.06786i	−0.0314458	−	0.125152i
$274$	−23.6765	−	41.0090i	−1.43035	−	2.47744i
$275$		−	35.3390i		−	2.13102i
$276$	3.43391	−	5.94770i	0.206697	−	0.358010i
$277$	−4.47522			−0.268890			−0.134445	−	0.990921i	$-0.542925\pi$
$277$	−4.47522			−0.268890			−0.134445	+	0.990921i	$0.542925\pi$
$278$		−	19.5261i		−	1.17110i
$279$	8.99345	−	13.0145i	0.538424	−	0.779157i
$280$			26.1044i			1.56004i
$281$		−	5.66132i		−	0.337726i	−0.985640	−	0.168863i	$-0.945990\pi$
$281$		−	5.66132i		−	0.337726i	0.985640	−	0.168863i	$-0.0540095\pi$
$282$	4.06829	−	7.04648i	0.242263	−	0.419612i
$283$	13.1662			0.782648			0.391324	−	0.920253i	$-0.372017\pi$
$283$	13.1662			0.782648			0.391324	+	0.920253i	$0.372017\pi$
$284$	−18.8902	+	10.9063i	−1.12093	+	0.647167i
$285$	4.80876	−	8.32901i	0.284846	−	0.493368i
$286$	−43.4618	+	10.9202i	−2.56995	+	0.645725i
$287$	−1.11748			−0.0659629
$288$	−1.52462	+	0.880242i	−0.0898393	+	0.0518688i
$289$	6.02623	+	10.4377i	0.354484	+	0.613985i
$290$	12.4572	+	21.5764i	0.731509	+	1.26701i
$291$	−4.91641	−	2.83849i	−0.288205	−	0.166395i
$292$	41.1665	−	23.7675i	2.40909	−	1.39089i
$293$	28.0869	+	16.2160i	1.64085	+	0.947348i	0.980531	+	0.196367i	$0.0629143\pi$
$293$	28.0869	+	16.2160i	1.64085	+	0.947348i	0.660324	+	0.750981i	$0.270419\pi$
$294$		−	4.70513i		−	0.274409i
$295$	−20.8877			−1.21613
$296$	4.23935	−	7.34276i	0.246407	−	0.426790i
$297$	10.1736	−	5.87376i	0.590335	−	0.340830i
$298$	7.09121	−	12.2823i	0.410783	−	0.711496i
$299$	4.19098	−	14.7166i	0.242371	−	0.851083i
$300$	5.66435	+	9.81095i	0.327032	+	0.566435i
$301$	10.4299	−	6.02169i	0.601168	−	0.347084i
$302$	56.4751			3.24978
$303$	−0.766531	+	1.32767i	−0.0440361	+	0.0762727i
$304$	26.4066	+	15.2459i	1.51452	+	0.874411i
$305$	−9.90632	+	5.71942i	−0.567234	+	0.327493i
$306$		−	15.5602i		−	0.889517i
$307$	28.3557	+	16.3712i	1.61835	+	0.934353i	0.987348	+	0.158568i	$0.0506878\pi$
$307$	28.3557	+	16.3712i	1.61835	+	0.934353i	0.630998	+	0.775784i	$0.282645\pi$
$308$	30.4359			1.73425
$309$	−5.65368			−0.321627
$310$	26.9972	−	39.0679i	1.53334	−	2.21891i
$311$	−12.9861			−0.736376			−0.368188	−	0.929751i	$-0.620022\pi$
$311$	−12.9861			−0.736376			−0.368188	+	0.929751i	$0.620022\pi$
$312$	5.23651	−	5.07527i	0.296459	−	0.287331i
$313$	−11.9078	+	20.6249i	−0.673069	+	1.16579i	0.303960	+	0.952685i	$0.401691\pi$
$313$	−11.9078	+	20.6249i	−0.673069	+	1.16579i	−0.977029	+	0.213106i	$0.931642\pi$
$314$		−	15.1025i		−	0.852281i
$315$	−7.30486	−	12.6524i	−0.411583	−	0.712882i
$316$	0.487220	−	0.843889i	0.0274082	−	0.0474725i
$317$	14.9941	+	8.65687i	0.842154	+	0.486218i	0.857996	−	0.513657i	$-0.171709\pi$
$317$	14.9941	+	8.65687i	0.842154	+	0.486218i	−0.0158416	+	0.999875i	$0.505043\pi$
$318$		−	3.32367i		−	0.186382i
$319$	12.7702	−	7.37285i	0.714992	−	0.412801i
$320$	21.6773	−	12.5154i	1.21180	−	0.699630i
$321$	2.45161	+	4.24631i	0.136835	+	0.237006i
$322$	−7.75484	+	13.4318i	−0.432161	+	0.748524i
$323$	−13.4237	+	7.75019i	−0.746916	+	0.431232i
$324$	15.4288	−	26.7234i	0.857154	−	1.48463i
$325$	17.5667	+	18.1248i	0.974424	+	1.00538i
$326$	45.9423			2.54451
$327$	2.96997	+	1.71471i	0.164240	+	0.0948238i
$328$	−1.91103	−	3.31001i	−0.105519	−	0.182764i
$329$	−6.15628	+	10.6630i	−0.339407	+	0.587870i
$330$	14.8551	−	8.57659i	0.817745	−	0.472126i
$331$	−3.27545	+	1.89108i	−0.180035	+	0.103943i	−0.587309	−	0.809363i	$-0.699813\pi$
$331$	−3.27545	+	1.89108i	−0.180035	+	0.103943i	0.407274	+	0.913306i	$0.366479\pi$
$332$	−56.7531	+	32.7664i	−3.11473	+	1.79829i
$333$			4.74523i			0.260037i
$334$	3.43031	−	5.94147i	0.187698	−	0.325103i
$335$	−13.8329	+	23.9593i	−0.755772	+	1.30903i
$336$	−2.24082	+	1.29374i	−0.122247	+	0.0705793i
$337$	25.1289			1.36886			0.684429	−	0.729079i	$-0.260051\pi$
$337$	25.1289			1.36886			0.684429	+	0.729079i	$0.260051\pi$
$338$	16.8625	−	27.2053i	0.917200	−	1.47977i
$339$	4.03219			0.218999
$340$		−	31.2989i		−	1.69742i
$341$	−23.1226	−	15.9785i	−1.25216	−	0.865283i
$342$	−48.7493			−2.63606
$343$			17.5102i			0.945463i
$344$	35.6727	+	20.5957i	1.92334	+	1.11044i
$345$			5.85711i			0.315336i
$346$	49.3110	−	28.4697i	2.65097	−	1.53054i
$347$	−12.8766	+	22.3030i	−0.691253	+	1.19729i	0.280175	+	0.959949i	$0.409608\pi$
$347$	−12.8766	+	22.3030i	−0.691253	+	1.19729i	−0.971428	+	0.237336i	$0.923726\pi$
$348$	−2.36354	+	4.09376i	−0.126699	+	0.219449i
$349$		−	33.9441i		−	1.81699i	−0.417899	−	0.908493i	$-0.637233\pi$
$349$		−	33.9441i		−	1.81699i	0.417899	−	0.908493i	$-0.362767\pi$
$350$	−12.7919	−	22.1562i	−0.683755	−	1.18430i
$351$	−2.29811	+	8.06978i	−0.122664	+	0.430733i
$352$	1.56391	+	2.70877i	0.0833566	+	0.144378i
$353$	−23.3452	−	13.4783i	−1.24254	−	0.717380i	−0.272928	−	0.962034i	$-0.587992\pi$
$353$	−23.3452	−	13.4783i	−1.24254	−	0.717380i	−0.969610	+	0.244654i	$0.921326\pi$
$354$	−2.95720	−	5.12202i	−0.157173	−	0.272232i
$355$	9.30123	−	16.1102i	0.493658	−	0.855041i
$356$		−	48.6916i		−	2.58065i
$357$		−	1.31534i		−	0.0696150i
$358$	−5.02823	−	2.90305i	−0.265750	−	0.153431i
$359$	−21.2179	+	12.2502i	−1.11984	+	0.646540i	−0.941360	−	0.337404i	$-0.890451\pi$
$359$	−21.2179	+	12.2502i	−1.11984	+	0.646540i	−0.178480	+	0.983944i	$0.557118\pi$
$360$	24.9845	−	43.2743i	1.31680	−	2.28076i
$361$	14.7810	+	25.6014i	0.777946	+	1.34744i
$362$	−30.7851	+	17.7738i	−1.61803	+	0.934169i
$363$	−2.88494	−	4.99686i	−0.151420	−	0.262267i
$364$	−15.6101	+	15.1294i	−0.818190	+	0.792997i
$365$	−20.2697	+	35.1082i	−1.06097	+	1.83765i
$366$	−2.80500	−	1.61947i	−0.146620	−	0.0846510i
$367$	6.46581	+	11.1991i	0.337513	+	0.584589i	0.983964	−	0.178366i	$-0.0570811\pi$
$367$	6.46581	+	11.1991i	0.337513	+	0.584589i	−0.646452	+	0.762955i	$0.723748\pi$
$368$	−18.5696			−0.968009
$369$	1.85250	+	1.06954i	0.0964371	+	0.0556780i
$370$			14.2446i			0.740541i
$371$			5.02951i			0.261119i
$372$	8.98052	+	0.729774i	0.465618	+	0.0378370i
$373$	11.5002			0.595458			0.297729	−	0.954650i	$-0.403771\pi$
$373$	11.5002			0.595458			0.297729	+	0.954650i	$0.403771\pi$
$374$	−27.6455			−1.42951
$375$	−2.39105	−	1.38047i	−0.123473	−	0.0712874i
$376$	−42.1120			−2.17176
$377$	−2.88463	+	10.1293i	−0.148566	+	0.521688i
$378$	4.25233	−	7.36525i	0.218716	−	0.378828i
$379$	−1.36411	−	0.787568i	−0.0700695	−	0.0404547i	0.464556	−	0.885544i	$-0.346214\pi$
$379$	−1.36411	−	0.787568i	−0.0700695	−	0.0404547i	−0.534625	+	0.845089i	$0.679547\pi$
$380$	−98.0580			−5.03027
$381$	−2.19983	−	3.81022i	−0.112701	−	0.195204i
$382$	2.44158	−	1.40965i	0.124922	−	0.0721239i
$383$	10.8329	−	6.25438i	0.553536	−	0.319584i	−0.197011	−	0.980401i	$-0.563124\pi$
$383$	10.8329	−	6.25438i	0.553536	−	0.319584i	0.750547	+	0.660817i	$0.229790\pi$
$384$	6.56553	+	3.79061i	0.335046	+	0.193439i
$385$	−22.4793	+	12.9784i	−1.14565	+	0.661441i
$386$	11.5946	−	20.0825i	0.590151	−	1.02217i
$387$	−23.0534			−1.17187
$388$			57.8812i			2.93847i
$389$	−1.39417	+	2.41477i	−0.0706872	+	0.122434i	−0.899203	−	0.437532i	$-0.855853\pi$
$389$	−1.39417	+	2.41477i	−0.0706872	+	0.122434i	0.828515	+	0.559966i	$0.189186\pi$
$390$	−3.35559	+	11.7831i	−0.169917	+	0.596661i
$391$	4.71991	−	8.17512i	0.238696	−	0.413433i
$392$	−21.0895	+	12.1760i	−1.06518	+	0.614983i
$393$	−2.13850	−	3.70399i	−0.107873	−	0.186842i
$394$	−12.0409	−	20.8554i	−0.606609	−	1.05068i
$395$			0.831036i			0.0418140i
$396$	−50.4549	−	29.1301i	−2.53545	−	1.46384i
$397$	10.6286	+	6.13644i	0.533436	+	0.307979i	0.742414	−	0.669941i	$-0.233681\pi$
$397$	10.6286	+	6.13644i	0.533436	+	0.307979i	−0.208979	+	0.977920i	$0.567014\pi$
$398$	−26.0947	+	15.0658i	−1.30801	+	0.755178i
$399$	−4.12089			−0.206302
$400$	15.3156	−	26.5275i	0.765782	−	1.32637i
$401$		−	10.7458i		−	0.536618i	−0.963333	−	0.268309i	$-0.913535\pi$
$401$		−	10.7458i		−	0.536618i	0.963333	−	0.268309i	$-0.0864648\pi$
$402$	−7.83364			−0.390707
$403$	19.8019	−	3.29893i	0.986405	−	0.164331i
$404$	15.6308			0.777659
$405$			26.3164i			1.30767i
$406$	5.33761	−	9.24501i	0.264901	−	0.458822i
$407$	8.43076			0.417897
$408$	3.89606	−	2.24939i	0.192884	−	0.111361i
$409$	−8.12291	−	4.68976i	−0.401652	−	0.231894i	0.285545	−	0.958365i	$-0.407826\pi$
$409$	−8.12291	−	4.68976i	−0.401652	−	0.231894i	−0.687197	+	0.726472i	$0.741159\pi$
$410$	5.56096	+	3.21062i	0.274636	+	0.158561i
$411$			7.66225i			0.377951i
$412$	28.8218	+	49.9209i	1.41995	+	2.45943i
$413$	4.47495	+	7.75084i	0.220198	+	0.381394i
$414$	25.7111	−	14.8443i	1.26363	−	0.729557i
$415$	27.9443	−	48.4010i	1.37173	−	2.37591i
$416$	−2.14861	−	0.611878i	−0.105344	−	0.0299998i
$417$	−1.57977	+	2.73624i	−0.0773615	+	0.133994i
$418$			86.6119i			4.23633i
$419$	21.8811			1.06896			0.534482	−	0.845180i	$-0.320507\pi$
$419$	21.8811			1.06896			0.534482	+	0.845180i	$0.320507\pi$
$420$	4.16052	−	7.20623i	0.203013	−	0.351628i
$421$	10.0173	−	5.78349i	0.488213	−	0.281870i	−0.235620	−	0.971845i	$-0.575712\pi$
$421$	10.0173	−	5.78349i	0.488213	−	0.281870i	0.723833	+	0.689975i	$0.242379\pi$
$422$	17.8783	+	10.3220i	0.870301	+	0.502468i
$423$	20.4110	−	11.7843i	0.992419	−	0.572973i
$424$	−14.8975	+	8.60108i	−0.723487	+	0.417705i
$425$	7.78565	+	13.4851i	0.377660	+	0.654126i
$426$	5.26734			0.255203
$427$	4.24463	+	2.45064i	0.205412	+	0.118595i
$428$	24.9960	−	43.2944i	1.20823	−	2.09271i
$429$	6.97392	+	1.98603i	0.336704	+	0.0958863i
$430$	−69.2033			−3.33728
$431$	−5.95706	−	3.43931i	−0.286941	−	0.165666i	0.349620	−	0.936891i	$-0.386311\pi$
$431$	−5.95706	−	3.43931i	−0.286941	−	0.165666i	−0.636562	+	0.771226i	$0.719644\pi$
$432$	10.1826			0.489909
$433$	4.73695			0.227643			0.113822	−	0.993501i	$-0.463691\pi$
$433$	4.73695			0.227643			0.113822	+	0.993501i	$0.463691\pi$
$434$	−20.2808	−	1.64806i	−0.973511	−	0.0791094i
$435$		−	4.03141i		−	0.193291i
$436$		−	34.9657i		−	1.67455i
$437$	−25.6122	−	14.7872i	−1.22520	−	0.707369i
$438$	−11.4789			−0.548481
$439$	4.00379	+	6.93476i	0.191090	+	0.330978i	0.945612	−	0.325297i	$-0.105464\pi$
$439$	4.00379	+	6.93476i	0.191090	+	0.330978i	−0.754522	+	0.656275i	$0.772131\pi$
$440$	−76.8846	−	44.3894i	−3.66533	−	2.11618i
$441$	6.81451	−	11.8031i	0.324501	−	0.562052i
$442$	14.1789	−	13.7423i	0.674422	−	0.653655i
$443$	3.94248	+	6.82858i	0.187313	+	0.324436i	0.944354	−	0.328932i	$-0.106689\pi$
$443$	3.94248	+	6.82858i	0.187313	+	0.324436i	−0.757040	+	0.653368i	$0.773355\pi$
$444$	−2.34058	+	1.35134i	−0.111079	+	0.0641315i
$445$	20.7629	+	35.9625i	0.984257	+	1.70478i
$446$	−4.19997	+	7.27456i	−0.198874	+	0.344461i
$447$	−1.98742	+	1.14744i	−0.0940016	+	0.0542718i
$448$	−9.28821	−	5.36255i	−0.438827	−	0.253357i
$449$		−	35.0216i		−	1.65277i	−0.563106	−	0.826385i	$-0.690394\pi$
$449$		−	35.0216i		−	1.65277i	0.563106	−	0.826385i	$-0.309606\pi$
$450$			48.9724i			2.30858i
$451$	1.90023	−	3.29129i	0.0894783	−	0.154981i
$452$	−20.5557	−	35.6035i	−0.966857	−	1.67465i
$453$	−7.91400	−	4.56915i	−0.371832	−	0.214677i
$454$	−9.68016	−	16.7665i	−0.454312	−	0.786892i
$455$	5.07780	−	17.8306i	0.238051	−	0.835913i
$456$	−7.04723	−	12.2062i	−0.330017	−	0.571605i
$457$		−	17.0800i		−	0.798968i	−0.916740	−	0.399484i	$-0.869189\pi$
$457$		−	17.0800i		−	0.798968i	0.916740	−	0.399484i	$-0.130811\pi$
$458$	−9.46721	+	16.3977i	−0.442374	+	0.766214i
$459$	−2.58814	+	4.48278i	−0.120804	+	0.209238i
$460$	51.7172	−	29.8589i	2.41133	−	1.39218i
$461$			26.3842i			1.22884i	0.788981	+	0.614418i	$0.210609\pi$
$461$			26.3842i			1.22884i	−0.788981	+	0.614418i	$0.789391\pi$
$462$	−6.36507	−	3.67487i	−0.296130	−	0.170971i
$463$		−	24.9390i		−	1.15901i	−0.814968	−	0.579507i	$-0.803245\pi$
$463$		−	24.9390i		−	1.15901i	0.814968	−	0.579507i	$-0.196755\pi$
$464$	12.7814			0.593359
$465$	−6.94399	+	3.29046i	−0.322020	+	0.152591i
$466$			60.8220i			2.81752i
$467$	12.0669			0.558391			0.279195	−	0.960234i	$-0.409932\pi$
$467$	12.0669			0.558391			0.279195	+	0.960234i	$0.409932\pi$
$468$	40.3578	−	10.1403i	1.86554	−	0.468735i
$469$	11.8542			0.547374
$470$	61.2714	−	35.3750i	2.82624	−	1.63173i
$471$	−1.22187	+	2.11635i	−0.0563009	+	0.0975161i
$472$	−15.3054	+	26.5098i	−0.704489	+	1.22021i
$473$			40.9585i			1.88327i
$474$	−0.203785	+	0.117655i	−0.00936014	+	0.00540408i
$475$	42.2483	−	24.3921i	1.93848	−	1.11918i
$476$	−11.6142	+	6.70544i	−0.532335	+	0.307344i
$477$	4.81373	−	8.33762i	0.220405	−	0.381753i
$478$	−20.0503	−	34.7282i	−0.917081	−	1.58843i
$479$	22.2703	+	12.8578i	1.01756	+	0.587487i	0.913395	−	0.407073i	$-0.133451\pi$
$479$	22.2703	+	12.8578i	1.01756	+	0.587487i	0.104162	+	0.994560i	$0.466784\pi$
$480$	0.855131			0.0390312
$481$	−4.32400	+	4.19085i	−0.197157	+	0.191086i
$482$	2.43967	−	4.22563i	0.111124	−	0.192472i
$483$	2.17341	−	1.25482i	0.0988937	−	0.0570963i
$484$	−29.4142	+	50.9469i	−1.33701	+	2.31577i
$485$	−24.6816	−	42.7497i	−1.12073	−	1.94116i
$486$	−21.3393	+	12.3203i	−0.967972	+	0.558859i
$487$	1.12492	−	0.649473i	0.0509750	−	0.0294305i	−0.474296	−	0.880365i	$-0.657297\pi$
$487$	1.12492	−	0.649473i	0.0509750	−	0.0294305i	0.525271	+	0.850935i	$0.323964\pi$
$488$			16.7636i			0.758852i
$489$	−6.43801	−	3.71699i	−0.291137	−	0.168088i
$490$	20.4563	−	35.4314i	0.924122	−	1.60063i
$491$	10.2354	+	17.7282i	0.461916	+	0.800062i	0.999056	−	0.0434305i	$-0.0138287\pi$
$491$	10.2354	+	17.7282i	0.461916	+	0.800062i	−0.537140	+	0.843493i	$0.680495\pi$
$492$			1.21832i			0.0549262i
$493$	−3.24868	+	5.62688i	−0.146313	+	0.253422i
$494$	−43.0540	−	44.4218i	−1.93709	−	1.99863i
$495$	49.6864			2.23324
$496$	−10.4322	−	22.0155i	−0.468420	−	0.988526i
$497$	−7.97073			−0.357536
$498$	15.8250			0.709136
$499$	−21.4683	−	12.3947i	−0.961052	−	0.554864i	−0.0645556	−	0.997914i	$-0.520563\pi$
$499$	−21.4683	−	12.3947i	−0.961052	−	0.554864i	−0.896497	+	0.443050i	$0.853896\pi$
$500$			28.1500i			1.25891i
$501$	−0.961396	+	0.555062i	−0.0429520	+	0.0247984i
$502$	−8.62641	−	4.98046i	−0.385015	−	0.222289i
$503$	−4.61974	+	8.00163i	−0.205984	+	0.356775i	−0.950446	−	0.310890i	$-0.899373\pi$
$503$	−4.61974	+	8.00163i	−0.205984	+	0.356775i	0.744462	+	0.667665i	$0.232706\pi$
$504$	−21.4105			−0.953701
$505$	−11.5445	+	6.66523i	−0.513724	+	0.296599i
$506$	−26.3735	−	45.6803i	−1.17245	−	2.03074i
$507$	−4.56404	+	2.44807i	−0.202696	+	0.108723i
$508$	−22.4290	+	38.8482i	−0.995127	+	1.72361i
$509$	5.24740	−	3.02959i	0.232587	−	0.134284i	−0.379178	−	0.925324i	$-0.623793\pi$
$509$	5.24740	−	3.02959i	0.232587	−	0.134284i	0.611765	+	0.791040i	$0.290460\pi$
$510$	−3.77908	+	6.54555i	−0.167340	+	0.289842i
$511$	17.3702			0.768414
$512$		−	41.7162i		−	1.84361i
$513$	14.0443	+	8.10850i	0.620073	+	0.357999i
$514$	12.6113	−	7.28115i	0.556261	−	0.321158i
$515$	−42.5743	−	24.5803i	−1.87605	−	1.08314i
$516$	−6.56508	−	11.3710i	−0.289011	−	0.500583i
$517$	−20.9370	−	36.2639i	−0.920807	−	1.59488i
$518$	5.28577	−	3.05174i	0.232243	−	0.134086i
$519$	−9.21343			−0.404425
$520$	61.4984	−	15.4521i	2.69688	−	0.677618i
$521$	−5.22040	+	9.04200i	−0.228710	+	0.396137i	−0.957426	−	0.288679i	$-0.906784\pi$
$521$	−5.22040	+	9.04200i	−0.228710	+	0.396137i	0.728716	+	0.684816i	$0.240117\pi$
$522$	−17.6967	+	10.2172i	−0.774566	+	0.447196i
$523$	−18.7336			−0.819163			−0.409581	−	0.912274i	$-0.634325\pi$
$523$	−18.7336			−0.819163			−0.409581	+	0.912274i	$0.634325\pi$
$524$	−21.8037	+	37.7651i	−0.952499	+	1.64978i
$525$			4.13974i			0.180673i
$526$		−	23.6640i		−	1.03180i
$527$	12.3437	+	1.00307i	0.537701	+	0.0436946i
$528$		−	8.79979i		−	0.382962i
$529$	−4.98901			−0.216913
$530$	14.4502	−	25.0285i	0.627677	−	1.08717i
$531$		−	17.1318i		−	0.743459i
$532$	21.0078	+	36.3866i	0.910805	+	1.57756i
$533$	0.661475	+	2.63264i	0.0286517	+	0.114032i
$534$	−5.87908	+	10.1829i	−0.254413	+	0.440656i
$535$			42.6350i			1.84327i
$536$	20.2721	+	35.1123i	0.875621	+	1.51662i
$537$	0.469746	+	0.813624i	0.0202710	+	0.0351105i
$538$	−54.5609	+	31.5007i	−2.35229	+	1.35809i
$539$	−20.9703	−	12.1072i	−0.903255	−	0.521494i
$540$	−28.3588	+	16.3730i	−1.22037	+	0.704581i
$541$	−7.65848	−	4.42162i	−0.329264	−	0.190100i	0.326250	−	0.945283i	$-0.394215\pi$
$541$	−7.65848	−	4.42162i	−0.329264	−	0.190100i	−0.655514	+	0.755183i	$0.727548\pi$
$542$	7.08351			0.304263
$543$	5.75199			0.246841
$544$	−1.19356	−	0.689100i	−0.0511733	−	0.0295449i
$545$	14.9100	+	25.8248i	0.638673	+	1.10621i
$546$	5.09128	−	1.27923i	0.217887	−	0.0547461i
$547$	4.54988	+	7.88063i	0.194539	+	0.336951i	0.946749	−	0.321972i	$-0.104346\pi$
$547$	4.54988	+	7.88063i	0.194539	+	0.336951i	−0.752210	+	0.658923i	$0.771012\pi$
$548$	67.6562	−	39.0613i	2.89013	−	1.66862i
$549$	−4.69100	−	8.12506i	−0.200207	−	0.346769i
$550$	87.0082			3.71004
$551$	17.6287	+	10.1780i	0.751009	+	0.433595i
$552$	7.43361	+	4.29180i	0.316395	+	0.182671i
$553$	0.308374	−	0.178040i	0.0131134	−	0.00757103i
$554$		−	11.0185i		−	0.468130i
$555$	1.15247	−	1.99613i	0.0489195	−	0.0847310i
$556$	32.2139			1.36617
$557$			35.9167i			1.52184i	0.648846	+	0.760919i	$0.275252\pi$
$557$			35.9167i			1.52184i	−0.648846	+	0.760919i	$0.724748\pi$
$558$	32.0430	+	22.1428i	1.35649	+	0.937379i
$559$	−20.3601	−	21.0069i	−0.861139	−	0.888498i
$560$	−22.4990			−0.950755
$561$	3.87403	+	2.23667i	0.163562	+	0.0944324i
$562$	13.9388			0.587971
$563$	16.1439	+	27.9620i	0.680383	+	1.17846i	0.974864	+	0.222801i	$0.0715200\pi$
$563$	16.1439	+	27.9620i	0.680383	+	1.17846i	−0.294481	+	0.955657i	$0.595147\pi$
$564$	11.6252	+	6.71182i	0.489510	+	0.282619i
$565$	30.3639	+	17.5306i	1.27742	+	0.737518i
$566$			32.4165i			1.36257i
$567$	9.76528	−	5.63799i	0.410103	−	0.236773i
$568$	−13.6309	−	23.6095i	−0.571942	−	0.990632i
$569$	15.0085	+	25.9955i	0.629189	+	1.08979i	0.987715	+	0.156268i	$0.0499462\pi$
$569$	15.0085	+	25.9955i	0.629189	+	1.08979i	−0.358526	+	0.933520i	$0.616720\pi$
$570$	20.5069	+	11.8397i	0.858939	+	0.495909i
$571$	3.20425	+	5.54993i	0.134094	+	0.232257i	0.925251	−	0.379356i	$-0.123854\pi$
$571$	3.20425	+	5.54993i	0.134094	+	0.232257i	−0.791157	+	0.611613i	$0.790521\pi$
$572$	−18.0160	−	71.7029i	−0.753289	−	2.99805i
$573$	−0.456194			−0.0190578
$574$		−	2.75136i		−	0.114839i
$575$	−14.8549	+	25.7294i	−0.619492	+	1.07299i
$576$	10.2650	+	17.7795i	0.427707	+	0.740811i
$577$	19.9965	+	11.5450i	0.832467	+	0.480625i	0.854697	−	0.519128i	$-0.173743\pi$
$577$	19.9965	+	11.5450i	0.832467	+	0.480625i	−0.0222295	+	0.999753i	$0.507076\pi$
$578$	−25.6988	+	14.8372i	−1.06893	+	0.617147i
$579$	−3.24957	+	1.87614i	−0.135047	+	0.0779696i
$580$	−35.5966	+	20.5517i	−1.47807	+	0.853362i
$581$	−23.9470			−0.993490
$582$	6.98865	−	12.1047i	0.289689	−	0.501756i
$583$	−14.8133	−	8.55245i	−0.613504	−	0.354206i
$584$	29.7053	+	51.4510i	1.22921	+	2.12906i
$585$	−25.4833	+	24.6987i	−1.05361	+	1.02116i
$586$	−39.9254	+	69.1529i	−1.64930	+	2.85668i
$587$			8.04079i			0.331879i	0.986136	+	0.165940i	$0.0530657\pi$
$587$			8.04079i			0.331879i	−0.986136	+	0.165940i	$0.946934\pi$
$588$	7.76248			0.320119
$589$	3.14258	−	38.6723i	0.129488	−	1.59346i
$590$		−	51.4276i		−	2.11724i
$591$			3.89669i			0.160288i
$592$	6.32861	+	3.65383i	0.260104	+	0.150171i
$593$		−	2.18862i		−	0.0898759i	−0.998990	−	0.0449379i	$-0.985691\pi$
$593$		−	2.18862i		−	0.0898759i	0.998990	−	0.0449379i	$-0.0143090\pi$
$594$	14.4618	+	25.0486i	0.593375	+	1.02776i
$595$	5.71864	−	9.90497i	0.234441	−	0.406064i
$596$	20.2633	+	11.6990i	0.830016	+	0.479210i
$597$	4.87561			0.199546
$598$	36.2338	+	10.3186i	1.48171	+	0.421960i
$599$	−17.5330	−	30.3680i	−0.716377	−	1.24080i	−0.962426	−	0.271544i	$-0.912466\pi$
$599$	−17.5330	−	30.3680i	−0.716377	−	1.24080i	0.246049	−	0.969257i	$-0.420868\pi$
$600$	−12.2620	+	7.07947i	−0.500594	+	0.289018i
$601$	−10.1110	+	17.5128i	−0.412436	+	0.714360i	−0.995156	−	0.0983131i	$-0.968655\pi$
$601$	−10.1110	+	17.5128i	−0.412436	+	0.714360i	0.582719	+	0.812673i	$0.301989\pi$
$602$	14.8260	+	25.6794i	0.604263	+	1.04661i
$603$	−19.6511	−	11.3456i	−0.800256	−	0.462028i
$604$			93.1721i			3.79112i
$605$		−	50.1709i		−	2.03974i
$606$	−3.26886	−	1.88728i	−0.132788	−	0.0766655i
$607$	−14.4354	−	25.0029i	−0.585917	−	1.01484i	−0.994760	−	0.102233i	$-0.967401\pi$
$607$	−14.4354	−	25.0029i	−0.585917	−	1.01484i	0.408844	−	0.912604i	$-0.365932\pi$
$608$	−2.15892	+	3.73935i	−0.0875557	+	0.151651i
$609$	−1.49594	+	0.863684i	−0.0606187	+	0.0349982i
$610$	−14.0818	−	24.3904i	−0.570155	−	0.987538i
$611$	28.7647	+	8.19158i	1.16369	+	0.331396i
$612$	25.6711			1.03769
$613$	−29.0142	−	16.7513i	−1.17187	−	0.676581i	−0.217752	−	0.976004i	$-0.569872\pi$
$613$	−29.0142	−	16.7513i	−1.17187	−	0.676581i	−0.954120	+	0.299424i	$0.903206\pi$
$614$	−40.3075	+	69.8147i	−1.62668	+	2.81749i
$615$	−0.519514	−	0.899825i	−0.0209488	−	0.0362844i
$616$			38.0397i			1.53266i
$617$	0.0633847	+	0.0365952i	0.00255177	+	0.00147327i	0.501275	−	0.865288i	$-0.332864\pi$
$617$	0.0633847	+	0.0365952i	0.00255177	+	0.00147327i	−0.498724	+	0.866761i	$0.666198\pi$
$618$		−	13.9200i		−	0.559943i
$619$			11.9477i			0.480218i	0.970746	+	0.240109i	$0.0771832\pi$
$619$			11.9477i			0.480218i	−0.970746	+	0.240109i	$0.922817\pi$
$620$	64.4538	+	44.5397i	2.58853	+	1.78876i
$621$	−9.87624			−0.396320
$622$		−	31.9732i		−	1.28201i
$623$	8.89644	−	15.4091i	0.356429	−	0.617352i
$624$	4.37429	+	4.51327i	0.175112	+	0.180675i
$625$	5.49764	+	9.52219i	0.219906	+	0.380888i
$626$	−50.7807	−	29.3183i	−2.02961	−	1.17179i
$627$	7.00739	−	12.1371i	0.279848	−	0.484711i
$628$	24.9159			0.994252
$629$	−3.21713	+	1.85741i	−0.128275	+	0.0740598i
$630$	31.1515	−	17.9853i	1.24111	−	0.716553i
$631$	−10.4585	+	6.03822i	−0.416346	+	0.240378i	−0.693513	−	0.720444i	$-0.743938\pi$
$631$	−10.4585	+	6.03822i	−0.416346	+	0.240378i	0.277167	+	0.960822i	$0.410605\pi$
$632$	1.05472	+	0.608941i	0.0419544	+	0.0242224i
$633$	−1.67022	−	2.89290i	−0.0663852	−	0.114983i
$634$	−21.3141	+	36.9171i	−0.846491	+	1.46617i
$635$		−	38.2565i		−	1.51816i
$636$	5.48336			0.217430
$637$	16.7737	−	4.21455i	0.664598	−	0.166987i
$638$	18.1527	+	31.4415i	0.718674	+	1.24478i
$639$	13.2134	+	7.62877i	0.522715	+	0.301789i
$640$	32.9606	+	57.0894i	1.30288	+	2.25666i
$641$	−13.0191	−	22.5498i	−0.514224	−	0.890663i	−0.999864	−	0.0165034i	$-0.994747\pi$
$641$	−13.0191	−	22.5498i	−0.514224	−	0.890663i	0.485640	−	0.874159i	$-0.338587\pi$
$642$	−10.4548	+	6.03611i	−0.412620	+	0.238226i
$643$		−	10.0878i		−	0.397824i	−0.980017	−	0.198912i	$-0.936259\pi$
$643$		−	10.0878i		−	0.397824i	0.980017	−	0.198912i	$-0.0637408\pi$
$644$	−22.1596	−	12.7939i	−0.873212	−	0.504149i
$645$	9.69763	+	5.59893i	0.381844	+	0.220458i
$646$	−19.0818	−	33.0506i	−0.750763	−	1.30036i
$647$	−45.5255			−1.78979			−0.894896	−	0.446275i	$-0.852750\pi$
$647$	−45.5255			−1.78979			−0.894896	+	0.446275i	$0.852750\pi$
$648$	33.3997	+	19.2833i	1.31206	+	0.757520i
$649$	−30.4378			−1.19479
$650$	−44.6251	+	43.2510i	−1.75034	+	1.69644i
$651$	2.70867	+	1.87178i	0.106161	+	0.0733608i
$652$			75.7951i			2.96837i
$653$	2.71514			0.106252			0.0531259	−	0.998588i	$-0.483082\pi$
$653$	2.71514			0.106252			0.0531259	+	0.998588i	$0.483082\pi$
$654$	−4.22180	+	7.31237i	−0.165085	+	0.285936i
$655$		−	37.1899i		−	1.45313i
$656$	2.85284	−	1.64709i	0.111385	−	0.0643080i
$657$	−28.7954	−	16.6250i	−1.12341	−	0.648604i
$658$	−26.2534	−	15.1574i	−1.02346	−	0.590897i
$659$	38.9080			1.51564			0.757819	−	0.652464i	$-0.226265\pi$
$659$	38.9080			1.51564			0.757819	+	0.652464i	$0.226265\pi$
$660$	14.1496	+	24.5078i	0.550771	+	0.953964i
$661$	28.8118	−	16.6345i	1.12065	−	0.647008i	0.179084	−	0.983834i	$-0.442687\pi$
$661$	28.8118	−	16.6345i	1.12065	−	0.647008i	0.941567	+	0.336826i	$0.109353\pi$
$662$	−4.65604	−	8.06450i	−0.180962	−	0.313436i
$663$	−3.09876	+	0.778592i	−0.120346	+	0.0302380i
$664$	−40.9524	−	70.9316i	−1.58926	−	2.75268i
$665$	−31.0318	−	17.9162i	−1.20336	−	0.694761i
$666$	−11.6833			−0.452717
$667$	−12.3968			−0.480008
$668$	9.80218	+	5.65929i	0.379258	+	0.218965i
$669$	1.17711	−	0.679602i	0.0455095	−	0.0262749i
$670$	−58.9902	−	34.0580i	−2.27899	−	1.31578i
$671$	−14.4356	+	8.33441i	−0.557281	+	0.321746i
$672$	−0.183202	−	0.317315i	−0.00706718	−	0.0122407i
$673$	−10.8109	−	18.7250i	−0.416728	−	0.721794i	0.578880	−	0.815413i	$-0.303490\pi$
$673$	−10.8109	−	18.7250i	−0.416728	−	0.721794i	−0.995608	+	0.0936185i	$0.970157\pi$
$674$			61.8700i			2.38314i
$675$	8.14560	−	14.1086i	0.313524	−	0.543040i
$676$	44.8830	+	27.8196i	1.72627	+	1.06999i
$677$	−0.0328535	−	0.0569039i	−0.00126266	−	0.00218699i	0.865393	−	0.501093i	$-0.167069\pi$
$677$	−0.0328535	−	0.0569039i	−0.00126266	−	0.00218699i	−0.866656	+	0.498906i	$0.833735\pi$
$678$			9.92767i			0.381270i
$679$	−10.5755	+	18.3173i	−0.405850	+	0.702953i
$680$	39.1183			1.50012
$681$			3.13271i			0.120046i
$682$	39.3407	−	56.9302i	1.50643	−	2.17997i
$683$			37.4224i			1.43193i	0.698137	+	0.715964i	$0.254013\pi$
$683$			37.4224i			1.43193i	−0.698137	+	0.715964i	$0.745987\pi$
$684$		−	80.4262i		−	3.07517i
$685$	−33.3129	+	57.6996i	−1.27282	+	2.20459i
$686$	−43.1120			−1.64602
$687$	2.65333	−	1.53190i	0.101231	−	0.0584456i
$688$	−17.7511	+	30.7458i	−0.676753	+	1.17217i
$689$	11.8488	−	2.97713i	0.451405	−	0.113420i
$690$	−14.4208			−0.548991
$691$	−5.38461	+	3.10881i	−0.204840	+	0.118265i	−0.598911	−	0.800815i	$-0.704400\pi$
$691$	−5.38461	+	3.10881i	−0.204840	+	0.118265i	0.394071	+	0.919080i	$0.371066\pi$
$692$	46.9690	+	81.3528i	1.78549	+	3.09257i
$693$	−10.6447	−	18.4372i	−0.404361	−	0.700373i
$694$	−54.9122	−	31.7036i	−2.08444	−	1.20345i
$695$	−23.7924	+	13.7366i	−0.902499	+	0.521058i
$696$	−5.11650	−	2.95401i	−0.193940	−	0.111972i
$697$			1.67458i			0.0634294i
$698$	83.5739			3.16332
$699$	4.92084	−	8.52314i	0.186123	−	0.322375i
$700$	36.5531	−	21.1039i	1.38158	−	0.797654i
$701$	26.0757	−	45.1645i	0.984866	−	1.70584i	0.342337	−	0.939577i	$-0.388782\pi$
$701$	26.0757	−	45.1645i	0.984866	−	1.70584i	0.642530	−	0.766261i	$-0.277885\pi$
$702$	−19.8686	−	5.65817i	−0.749893	−	0.213554i
$703$	5.81918	+	10.0791i	0.219474	+	0.380141i
$704$	31.5884	−	18.2376i	1.19053	−	0.687354i
$705$	−11.4481			−0.431162
$706$	33.1851	−	57.4783i	1.24894	−	2.16322i
$707$	4.94656	+	2.85590i	0.186035	+	0.107407i
$708$	8.45026	−	4.87876i	0.317580	−	0.183355i
$709$			37.5718i			1.41104i	0.708690	+	0.705520i	$0.249286\pi$
$709$			37.5718i			1.41104i	−0.708690	+	0.705520i	$0.750714\pi$
$710$	39.6650	+	22.9006i	1.48860	+	0.859444i
$711$	−0.681607			−0.0255623
$712$	60.8561			2.28068
$713$	10.1184	+	21.3532i	0.378936	+	0.799684i
$714$	3.23850			0.121198
$715$	43.8816	+	45.2757i	1.64108	+	1.69322i
$716$	4.78943	−	8.29553i	0.178989	−	0.310019i
$717$			6.48873i			0.242326i
$718$	−30.1612	−	52.2408i	−1.12561	−	1.94961i
$719$	11.1938	−	19.3882i	0.417459	−	0.723060i	−0.578224	−	0.815878i	$-0.696254\pi$
$719$	11.1938	−	19.3882i	0.417459	−	0.723060i	0.995683	+	0.0928181i	$0.0295875\pi$
$720$	37.2975	+	21.5337i	1.38999	+	0.802514i
$721$			21.0642i			0.784471i
$722$	−63.0333	+	36.3923i	−2.34586	+	1.35438i
$723$	−0.683754	+	0.394766i	−0.0254291	+	0.0146815i
$724$	−29.3230	−	50.7889i	−1.08978	−	1.88756i
$725$	10.2245	−	17.7094i	0.379729	−	0.657710i
$726$	12.3028	−	7.10302i	0.456599	−	0.263618i
$727$	8.86102	−	15.3477i	0.328637	−	0.569216i	−0.653605	−	0.756836i	$-0.726744\pi$
$727$	8.86102	−	15.3477i	0.328637	−	0.569216i	0.982242	+	0.187620i	$0.0600774\pi$
$728$	−18.9092	−	19.5099i	−0.700820	−	0.723086i
$729$	−18.8030			−0.696409
$730$	−86.4400	−	49.9062i	−3.19929	−	1.84711i
$731$	−9.02370	−	15.6295i	−0.333754	−	0.578078i
$732$	2.67178	−	4.62767i	0.0987520	−	0.171043i
$733$	19.8408	−	11.4551i	0.732835	−	0.423103i	−0.0866231	−	0.996241i	$-0.527608\pi$
$733$	19.8408	−	11.4551i	0.732835	−	0.423103i	0.819459	+	0.573138i	$0.194274\pi$
$734$	−27.5734	+	15.9195i	−1.01775	+	0.587599i
$735$	−5.73319	+	3.31006i	−0.211472	+	0.122093i
$736$		−	2.62958i		−	0.0969277i
$737$	−20.1575	+	34.9138i	−0.742510	+	1.28607i
$738$	−2.63332	+	4.56104i	−0.0969337	+	0.167894i
$739$	3.52125	−	2.03300i	0.129531	−	0.0747849i	−0.433834	−	0.900993i	$-0.642840\pi$
$739$	3.52125	−	2.03300i	0.129531	−	0.0747849i	0.563365	+	0.826208i	$0.309506\pi$
$740$	−23.5006			−0.863899
$741$	2.43929	+	9.70825i	0.0896096	+	0.356641i
$742$	−12.3832			−0.454600
$743$		−	3.34822i		−	0.122834i	−0.998112	−	0.0614172i	$-0.980438\pi$
$743$		−	3.34822i		−	0.122834i	0.998112	−	0.0614172i	$-0.0195620\pi$
$744$	−0.912092	+	11.2241i	−0.0334389	+	0.411496i
$745$	−19.9546			−0.731081
$746$			28.3147i			1.03667i
$747$	39.6980	+	22.9196i	1.45247	+	0.838586i
$748$		−	45.6093i		−	1.66764i
$749$	15.8207	−	9.13406i	0.578074	−	0.333751i
$750$	3.39887	−	5.88702i	0.124109	−	0.214964i
$751$	10.0102	−	17.3381i	0.365276	−	0.632676i	−0.623545	−	0.781788i	$-0.714308\pi$
$751$	10.0102	−	17.3381i	0.365276	−	0.632676i	0.988820	+	0.149112i	$0.0476414\pi$
$752$		−	36.2957i		−	1.32357i
$753$	0.805894	+	1.39585i	0.0293684	+	0.0508676i
$754$	−24.9395	−	7.10225i	−0.908243	−	0.258649i
$755$	−39.7302	−	68.8147i	−1.44593	−	2.50442i
$756$	12.1511	+	7.01545i	0.441932	+	0.255150i
$757$	19.9026	+	34.4722i	0.723371	+	1.25291i	0.959641	+	0.281227i	$0.0907415\pi$
$757$	19.9026	+	34.4722i	0.723371	+	1.25291i	−0.236271	+	0.971687i	$0.575925\pi$
$758$	1.93907	−	3.35858i	0.0704304	−	0.121989i
$759$			8.53506i			0.309803i
$760$		−	122.556i		−	4.44556i
$761$	17.7746	+	10.2622i	0.644329	+	0.372004i	0.786280	−	0.617870i	$-0.212004\pi$
$761$	17.7746	+	10.2622i	0.644329	+	0.372004i	−0.141951	+	0.989874i	$0.545338\pi$
$762$	9.38117	−	5.41622i	0.339844	−	0.196209i
$763$	6.38859	−	11.0654i	0.231282	−	0.400593i
$764$	2.32562	+	4.02810i	0.0841382	+	0.145732i
$765$	−18.9600	+	10.9466i	−0.685502	+	0.395775i
$766$	15.3989	+	26.6717i	0.556386	+	0.963689i
$767$	15.6110	−	15.1303i	0.563682	−	0.546325i
$768$	−6.45423	+	11.1791i	−0.232897	+	0.403390i
$769$	38.0300	+	21.9566i	1.37140	+	0.791776i	0.991104	−	0.133090i	$-0.0424899\pi$
$769$	38.0300	+	21.9566i	1.37140	+	0.791776i	0.380293	+	0.924866i	$0.375823\pi$
$770$	−31.9542	−	55.3463i	−1.15155	−	1.99454i
$771$	−2.35634			−0.0848615
$772$	33.1319	+	19.1287i	1.19244	+	0.688457i
$773$		−	35.3300i		−	1.27073i	−0.772211	−	0.635366i	$-0.780849\pi$
$773$		−	35.3300i		−	1.27073i	0.772211	−	0.635366i	$-0.219151\pi$
$774$		−	56.7598i		−	2.04019i
$775$	−38.8492	−	3.15696i	−1.39550	−	0.113401i
$776$	−72.3416			−2.59691
$777$	−0.987611			−0.0354304
$778$	−5.94542	−	3.43259i	−0.213154	−	0.123064i
$779$	5.24639			0.187971
$780$	−19.4397	−	5.53601i	−0.696052	−	0.198221i
$781$	13.5539	−	23.4760i	0.484996	−	0.840038i
$782$	20.1280	+	11.6209i	0.719775	+	0.415562i
$783$	6.79775			0.242932
$784$	−10.4943	−	18.1767i	−0.374798	−	0.649169i
$785$	−18.4023	+	10.6246i	−0.656806	+	0.379207i
$786$	9.11962	−	5.26521i	0.325286	−	0.187804i
$787$	11.2217	+	6.47887i	0.400012	+	0.230947i	0.686489	−	0.727140i	$-0.259151\pi$
$787$	11.2217	+	6.47887i	0.400012	+	0.230947i	−0.286477	+	0.958087i	$0.592484\pi$
$788$	34.4070	−	19.8649i	1.22570	−	0.707657i
$789$	−1.91455	+	3.31609i	−0.0681597	+	0.118056i
$790$	−2.04610			−0.0727969
$791$		−	15.0229i		−	0.534154i
$792$	36.4077	−	63.0600i	1.29369	−	2.24074i
$793$	3.26084	−	11.4504i	0.115796	−	0.406616i
$794$	−15.1086	+	26.1688i	−0.536183	+	0.928695i
$795$	−4.04989	+	2.33820i	−0.143635	+	0.0829275i
$796$	−24.8553	−	43.0507i	−0.880974	−	1.52589i
$797$	−6.89968	−	11.9506i	−0.244399	−	0.423312i	0.717563	−	0.696493i	$-0.245257\pi$
$797$	−6.89968	−	11.9506i	−0.244399	−	0.423312i	−0.961962	+	0.273182i	$0.911924\pi$
$798$		−	10.1460i		−	0.359166i
$799$	15.9789	+	9.22539i	0.565291	+	0.326371i
$800$	3.75646	+	2.16880i	0.132811	+	0.0766785i
$801$	−29.4960	+	17.0295i	−1.04219	+	0.601709i
$802$	26.4572			0.934236
$803$	−29.5373	+	51.1601i	−1.04235	+	1.80540i
$804$		−	12.9239i		−	0.455790i
$805$	21.8221			0.769129
$806$	8.12231	+	48.7544i	0.286096	+	1.71730i
$807$	10.1943			0.358858
$808$			19.5358i			0.687266i
$809$	26.7534	−	46.3383i	0.940599	−	1.62917i	0.176268	−	0.984342i	$-0.443597\pi$
$809$	26.7534	−	46.3383i	0.940599	−	1.62917i	0.764331	−	0.644824i	$-0.223069\pi$
$810$	−64.7937			−2.27662
$811$	−16.7996	+	9.69927i	−0.589915	+	0.340587i	−0.765064	−	0.643954i	$-0.777293\pi$
$811$	−16.7996	+	9.69927i	−0.589915	+	0.340587i	0.175149	+	0.984542i	$0.443959\pi$
$812$	15.2523	+	8.80593i	0.535252	+	0.309028i
$813$	−0.992630	−	0.573095i	−0.0348130	−	0.0200993i
$814$			20.7574i			0.727547i
$815$	−32.3204	−	55.9805i	−1.13213	−	1.96091i
$816$	1.93871	+	3.35795i	0.0678685	+	0.117552i
$817$	−48.9665	+	28.2708i	−1.71312	+	0.989070i
$818$	11.5467	−	19.9994i	0.403720	−	0.699264i
$819$	14.6245	+	4.16475i	0.511021	+	0.145528i
$820$	−5.29685	+	9.17442i	−0.184974	+	0.320384i
$821$		−	14.3319i		−	0.500187i	−0.968222	−	0.250094i	$-0.919539\pi$
$821$		−	14.3319i		−	0.500187i	0.968222	−	0.250094i	$-0.0804614\pi$
$822$	−18.8653			−0.658001
$823$	−10.6888	+	18.5136i	−0.372588	+	0.645342i	−0.989963	−	0.141327i	$-0.954863\pi$
$823$	−10.6888	+	18.5136i	−0.372588	+	0.645342i	0.617375	+	0.786669i	$0.288196\pi$
$824$	−62.3926	+	36.0224i	−2.17355	+	1.25490i
$825$	−12.1927	−	7.03945i	−0.424495	−	0.245082i
$826$	−19.0834	+	11.0178i	−0.663995	+	0.383358i
$827$	22.3814	−	12.9219i	0.778278	−	0.449339i	−0.0575417	−	0.998343i	$-0.518326\pi$
$827$	22.3814	−	12.9219i	0.778278	−	0.449339i	0.835820	+	0.549004i	$0.184993\pi$
$828$	24.4900	+	42.4179i	0.851085	+	1.47412i
$829$	15.9724			0.554745			0.277373	−	0.960762i	$-0.410536\pi$
$829$	15.9724			0.554745			0.277373	+	0.960762i	$0.410536\pi$
$830$	119.168	+	68.8018i	4.13639	+	2.38815i
$831$	−0.891455	+	1.54405i	−0.0309242	+	0.0535623i
$832$	−7.13544	+	25.0560i	−0.247377	+	0.868662i
$833$	10.6695			0.369677
$834$	−6.73690	−	3.88955i	−0.233280	−	0.134684i
$835$	−9.65289			−0.334052
$836$	−142.892			−4.94201
$837$	−5.54835	−	11.7089i	−0.191779	−	0.404720i
$838$			53.8736i			1.86103i
$839$			24.3251i			0.839795i	0.907571	+	0.419898i	$0.137934\pi$
$839$			24.3251i			0.839795i	−0.907571	+	0.419898i	$0.862066\pi$
$840$	9.00656	+	5.19994i	0.310756	+	0.179415i
$841$	−20.4673			−0.705770
$842$	14.2395	+	24.6636i	0.490727	+	0.849965i
$843$	−1.95327	−	1.12772i	−0.0672743	−	0.0388408i
$844$	−17.0292	+	29.4954i	−0.586168	+	1.01527i
$845$	−45.0123	−	1.40804i	−1.54847	−	0.0484381i
$846$	29.0142	+	50.2541i	0.997530	+	1.72777i
$847$	−18.6170	+	10.7485i	−0.639689	+	0.369324i
$848$	−7.41313	−	12.8399i	−0.254568	−	0.440925i
$849$	2.62267	−	4.54260i	0.0900099	−	0.155902i
$850$	−33.2018	+	19.1691i	−1.13881	+	0.657494i
$851$	−6.13823	−	3.54391i	−0.210416	−	0.121484i
$852$			8.69001i			0.297715i
$853$		−	24.3678i		−	0.834338i	−0.908829	−	0.417169i	$-0.863022\pi$
$853$		−	24.3678i		−	0.834338i	0.908829	−	0.417169i	$-0.136978\pi$
$854$	−6.03373	+	10.4507i	−0.206470	+	0.357617i
$855$	34.2951	+	59.4009i	1.17287	+	2.03147i
$856$	54.1106	+	31.2408i	1.84946	+	1.06779i
$857$	−17.2493	−	29.8767i	−0.589225	−	1.02057i	−0.994334	−	0.106299i	$-0.966100\pi$
$857$	−17.2493	−	29.8767i	−0.589225	−	1.02057i	0.405109	−	0.914268i	$-0.367233\pi$
$858$	−4.88980	+	17.1705i	−0.166935	+	0.586192i
$859$	−23.3035	−	40.3628i	−0.795105	−	1.37716i	−0.922772	−	0.385345i	$-0.874082\pi$
$859$	−23.3035	−	40.3628i	−0.795105	−	1.37716i	0.127667	−	0.991817i	$-0.459251\pi$
$860$		−	114.171i		−	3.89320i
$861$	−0.222600	+	0.385554i	−0.00758619	+	0.0131397i
$862$	8.46794	−	14.6669i	0.288419	−	0.499556i
$863$	23.8943	−	13.7954i	0.813370	−	0.469600i	−0.0347546	−	0.999396i	$-0.511065\pi$
$863$	23.8943	−	13.7954i	0.813370	−	0.469600i	0.848125	+	0.529796i	$0.177732\pi$
$864$			1.44192i			0.0490551i
$865$	−69.3805	−	40.0568i	−2.35901	−	1.36197i
$866$			11.6629i			0.396320i
$867$	4.80165			0.163073
$868$	2.71895	−	33.4591i	0.0922872	−	1.13568i
$869$			1.21100i			0.0410803i
$870$	9.92575			0.336514
$871$	−7.01687	−	27.9268i	−0.237758	−	0.946263i
$872$	43.7011			1.47991
$873$	35.0629	−	20.2436i	1.18670	−	0.685140i
$874$	36.4077	−	63.0600i	1.23151	−	2.13304i
$875$	−5.14330	+	8.90846i	−0.173875	+	0.301161i
$876$		−	18.9377i		−	0.639846i
$877$	18.2320	−	10.5263i	0.615652	−	0.355447i	−0.159522	−	0.987194i	$-0.550995\pi$
$877$	18.2320	−	10.5263i	0.615652	−	0.355447i	0.775174	+	0.631748i	$0.217662\pi$
$878$	−17.0741	+	9.85774i	−0.576223	+	0.332683i
$879$	11.1897	−	6.46038i	0.377419	−	0.217903i
$880$	38.2585	−	66.2657i	1.28969	−	2.23382i
$881$	20.8268	+	36.0730i	0.701672	+	1.21533i	0.967879	+	0.251416i	$0.0808961\pi$
$881$	20.8268	+	36.0730i	0.701672	+	1.21533i	−0.266207	+	0.963916i	$0.585771\pi$
$882$	29.0604	+	16.7780i	0.978515	+	0.564946i
$883$	−36.8362			−1.23964			−0.619818	−	0.784746i	$-0.712793\pi$
$883$	−36.8362			−1.23964			−0.619818	+	0.784746i	$0.712793\pi$
$884$	22.6719	+	23.3922i	0.762540	+	0.786766i
$885$	−4.16078	+	7.20668i	−0.139863	+	0.242250i
$886$	−16.8127	+	9.70681i	−0.564833	+	0.326107i
$887$	−25.8599	+	44.7906i	−0.868290	+	1.50392i	−0.00454624	+	0.999990i	$0.501447\pi$
$887$	−25.8599	+	44.7906i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$888$	−1.68894	−	2.92533i	−0.0566770	−	0.0981675i
$889$	−14.1959	+	8.19602i	−0.476116	+	0.274886i
$890$	−88.5433	+	51.1205i	−2.96798	+	1.71356i
$891$			38.3486i			1.28473i
$892$	−12.0015	−	6.92907i	−0.401840	−	0.232003i
$893$	28.9027	−	50.0610i	0.967192	−	1.67523i
$894$	−2.82511	−	4.89323i	−0.0944857	−	0.163654i
$895$			8.16918i			0.273066i
$896$	14.1229	−	24.4615i	0.471812	−	0.817202i
$897$	−4.24270	−	4.37749i	−0.141660	−	0.146160i
$898$	86.2267			2.87742
$899$	−6.96440	−	14.6973i	−0.232276	−	0.490181i
$900$	−80.7941			−2.69314
$901$	7.53688			0.251090
$902$	8.10351	+	4.67856i	0.269817	+	0.155779i
$903$		−	4.79803i		−	0.159668i
$904$	44.4982	−	25.6911i	1.47999	−	0.854472i
$905$	43.3146	+	25.0077i	1.43983	+	0.831283i
$906$	11.2497	−	19.4851i	0.373747	−	0.647348i
$907$	−20.9112			−0.694343			−0.347172	−	0.937802i	$-0.612858\pi$
$907$	−20.9112			−0.694343			−0.347172	+	0.937802i	$0.612858\pi$
$908$	27.6613	−	15.9702i	0.917971	−	0.529991i
$909$	−5.46675	−	9.46869i	−0.181321	−	0.314057i
$910$	43.9009	+	12.5021i	1.45530	+	0.414439i
$911$	−25.5303	+	44.2197i	−0.845855	+	1.46506i	0.0390218	+	0.999238i	$0.487576\pi$
$911$	−25.5303	+	44.2197i	−0.845855	+	1.46506i	−0.884877	+	0.465825i	$0.845757\pi$
$912$	10.5203	−	6.07389i	0.348362	−	0.201127i
$913$	40.7209	−	70.5306i	1.34766	−	2.33422i
$914$	42.0527			1.39098
$915$			4.55718i			0.150656i
$916$	−27.0528	−	15.6189i	−0.893848	−	0.516064i
$917$	−13.8001	+	7.96751i	−0.455721	+	0.263110i
$918$	−11.0371	−	6.37226i	−0.364278	−	0.210316i
$919$	−7.36675	−	12.7596i	−0.243007	−	0.420900i	0.718563	−	0.695462i	$-0.244800\pi$
$919$	−7.36675	−	12.7596i	−0.243007	−	0.420900i	−0.961569	+	0.274562i	$0.911467\pi$
$920$	37.3185	+	64.6376i	1.23036	+	2.13104i
$921$	11.2968	−	6.52221i	0.372242	−	0.214914i
$922$	−64.9607			−2.13937
$923$	4.71814	+	18.7780i	0.155300	+	0.618084i
$924$	6.06277	−	10.5010i	0.199450	−	0.345458i
$925$	10.1252	−	5.84580i	0.332915	−	0.192209i
$926$	61.4024			2.01781
$927$	20.1605	−	34.9190i	0.662157	−	1.14689i
$928$			1.80992i			0.0594137i
$929$		−	17.3262i		−	0.568456i	−0.958757	−	0.284228i	$-0.908263\pi$
$929$		−	17.3262i		−	0.568456i	0.958757	−	0.284228i	$-0.0917372\pi$
$930$	−8.10144	−	17.0968i	−0.265657	−	0.560627i
$931$		−	33.4271i		−	1.09553i
$932$	−100.344			−3.28686
$933$	−2.58681	+	4.48048i	−0.0846883	+	0.146684i
$934$			29.7100i			0.972142i
$935$	19.4486	+	33.6859i	0.636037	+	1.10165i
$936$	12.6736	+	50.4403i	0.414250	+	1.64869i
$937$	10.7024	−	18.5370i	0.349631	−	0.605579i	−0.636553	−	0.771233i	$-0.719640\pi$
$937$	10.7024	−	18.5370i	0.349631	−	0.605579i	0.986184	+	0.165654i	$0.0529736\pi$
$938$			29.1862i			0.952962i
$939$	4.74402	+	8.21689i	0.154815	+	0.268148i
$940$	58.3614	+	101.085i	1.90354	+	3.29703i
$941$	34.5806	−	19.9651i	1.12730	−	0.650844i	0.184042	−	0.982918i	$-0.441082\pi$
$941$	34.5806	−	19.9651i	1.12730	−	0.650844i	0.943253	+	0.332074i	$0.107748\pi$
$942$	−5.21066	−	3.00838i	−0.169773	−	0.0980182i
$943$	−2.76702	+	1.59754i	−0.0901065	+	0.0520230i
$944$	−22.8484	−	13.1915i	−0.743651	−	0.429347i
$945$	−11.9660			−0.389256
$946$	−100.844			−3.27872
$947$	−29.4533	−	17.0048i	−0.957102	−	0.552583i	−0.0618221	−	0.998087i	$-0.519691\pi$
$947$	−29.4533	−	17.0048i	−0.957102	−	0.552583i	−0.895280	+	0.445504i	$0.853024\pi$
$948$	−0.194106	−	0.336202i	−0.00630428	−	0.0109193i
$949$	−10.2820	−	40.9219i	−0.333769	−	1.32838i
$950$	60.0558	+	104.020i	1.94847	+	3.37484i
$951$	5.97360	−	3.44886i	0.193707	−	0.111837i
$952$	−8.38065	−	14.5157i	−0.271619	−	0.470457i
$953$	34.7885			1.12691			0.563455	−	0.826146i	$-0.309472\pi$
$953$	34.7885			1.12691			0.563455	+	0.826146i	$0.309472\pi$
$954$	20.5281	+	11.8519i	0.664621	+	0.383719i
$955$	−3.43531	−	1.98337i	−0.111164	−	0.0641805i
$956$	57.2942	−	33.0788i	1.85303	−	1.06985i
$957$		−	5.87463i		−	0.189900i
$958$	−31.6572	+	54.8319i	−1.02280	+	1.77154i
$959$	28.5476			0.921850
$960$		−	9.97214i		−	0.321849i
$961$	−19.6313	+	23.9920i	−0.633266	+	0.773934i
$962$	−10.3183	−	10.6461i	−0.332676	−	0.343245i
$963$	−34.9688			−1.12685
$964$	6.97141	+	4.02494i	0.224534	+	0.129635i
$965$	−32.6272			−1.05031
$966$	3.08950	+	5.35117i	0.0994029	+	0.172171i
$967$	20.3120	+	11.7271i	0.653190	+	0.377119i	0.789677	−	0.613522i	$-0.210248\pi$
$967$	20.3120	+	11.7271i	0.653190	+	0.377119i	−0.136487	+	0.990642i	$0.543581\pi$
$968$	−63.6749	−	36.7627i	−2.04659	−	1.18160i
$969$			6.17529i			0.198379i
$970$	105.254	−	60.7686i	3.37951	−	1.95116i
$971$	−10.6645	−	18.4714i	−0.342239	−	0.592775i	0.642609	−	0.766194i	$-0.277852\pi$
$971$	−10.6645	−	18.4714i	−0.342239	−	0.592775i	−0.984848	+	0.173419i	$0.944518\pi$
$972$	−20.3259	−	35.2054i	−0.651953	−	1.12921i
$973$	10.1945	+	5.88581i	0.326821	+	0.188690i
$974$	1.59907	+	2.76967i	0.0512375	+	0.0887460i
$975$	9.75267	−	2.45045i	0.312335	−	0.0784773i
$976$	−14.4483			−0.462478
$977$		−	1.35950i		−	0.0434942i	−0.999764	−	0.0217471i	$-0.993077\pi$
$977$		−	1.35950i		−	0.0434942i	0.999764	−	0.0217471i	$-0.00692286\pi$
$978$	9.15160	−	15.8510i	0.292636	−	0.506860i
$979$	30.2560	+	52.4050i	0.966987	+	1.67487i
$980$	58.4543	+	33.7486i	1.86725	+	1.07806i
$981$	−21.1812	+	12.2290i	−0.676265	+	0.390442i
$982$	−43.6487	+	25.2006i	−1.39288	+	0.804183i
$983$	−3.10469	+	1.79249i	−0.0990241	+	0.0571716i	−0.548694	−	0.836023i	$-0.684875\pi$
$983$	−3.10469	+	1.79249i	−0.0990241	+	0.0571716i	0.449670	+	0.893195i	$0.351542\pi$
$984$	−1.52269			−0.0485417
$985$	−16.9415	+	29.3435i	−0.539800	+	0.934961i
$986$	−13.8540	−	7.99859i	−0.441200	−	0.254727i
$987$	2.45264	+	4.24809i	0.0780682	+	0.135218i
$988$	73.2867	−	71.0300i	2.33156	−	2.25977i
$989$	17.2171	−	29.8208i	0.547471	−	0.948247i
$990$			122.333i			3.88800i
$991$	4.59832			0.146071			0.0730353	−	0.997329i	$-0.476731\pi$
$991$	4.59832			0.146071			0.0730353	+	0.997329i	$0.476731\pi$
$992$	3.11754	−	1.47727i	0.0989821	−	0.0469033i
$993$			1.50680i			0.0478168i
$994$		−	19.6248i		−	0.622460i
$995$	36.7152	+	21.1975i	1.16395	+	0.672006i
$996$			26.1080i			0.827263i
$997$	−2.48173	−	4.29849i	−0.0785972	−	0.136134i	0.824048	−	0.566520i	$-0.191711\pi$
$997$	−2.48173	−	4.29849i	−0.0785972	−	0.136134i	−0.902645	+	0.430386i	$0.858377\pi$
$998$	30.5171	−	52.8571i	0.966001	−	1.67316i
$999$	3.36587	+	1.94328i	0.106491	+	0.0614828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.129.32	yes	68
13.12	even	2	inner	403.2.l.c.129.3	yes	68
31.25	even	3	inner	403.2.l.c.25.32	yes	68
403.25	even	6	inner	403.2.l.c.25.3	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.3	✓	68	403.25	even	6	inner
403.2.l.c.25.32	yes	68	31.25	even	3	inner
403.2.l.c.129.3	yes	68	13.12	even	2	inner
403.2.l.c.129.32	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.46210i q^{2} +(0.199198 - 0.345021i) q^{3} -4.06196 q^{4} +(3.00007 - 1.73209i) q^{5} +(0.849477 + 0.490446i) q^{6} +(-1.28546 - 0.742161i) q^{7} -5.07675i q^{8} +(1.42064 + 2.46062i) q^{9} +O(q^{10})\)	\(q+2.46210i q^{2} +(0.199198 - 0.345021i) q^{3} -4.06196 q^{4} +(3.00007 - 1.73209i) q^{5} +(0.849477 + 0.490446i) q^{6} +(-1.28546 - 0.742161i) q^{7} -5.07675i q^{8} +(1.42064 + 2.46062i) q^{9} +(4.26458 + 7.38647i) q^{10} +(4.37174 - 2.52402i) q^{11} +(-0.809133 + 1.40146i) q^{12} +(-0.987523 + 3.46768i) q^{13} +(1.82728 - 3.16494i) q^{14} -1.38011i q^{15} +4.37557 q^{16} +(-1.11215 + 1.92631i) q^{17} +(-6.05831 + 3.49776i) q^{18} +(6.03502 + 3.48432i) q^{19} +(-12.1861 + 7.03567i) q^{20} +(-0.512122 + 0.295674i) q^{21} +(6.21441 + 10.7637i) q^{22} -4.24394 q^{23} +(-1.75158 - 1.01128i) q^{24} +(3.50026 - 6.06263i) q^{25} +(-8.53779 - 2.43138i) q^{26} +2.32714 q^{27} +(5.22148 + 3.01462i) q^{28} +2.92107 q^{29} +3.39798 q^{30} +(-2.38419 - 5.03146i) q^{31} +0.619609i q^{32} -2.01112i q^{33} +(-4.74276 - 2.73824i) q^{34} -5.14195 q^{35} +(-5.77058 - 9.99493i) q^{36} +(1.44635 + 0.835052i) q^{37} +(-8.57876 + 14.8588i) q^{38} +(0.999709 + 1.03147i) q^{39} +(-8.79338 - 15.2306i) q^{40} +(0.651993 - 0.376429i) q^{41} +(-0.727979 - 1.26090i) q^{42} +(-4.05686 + 7.02669i) q^{43} +(-17.7578 + 10.2525i) q^{44} +(8.52403 + 4.92135i) q^{45} -10.4490i q^{46} -8.29508i q^{47} +(0.871604 - 1.50966i) q^{48} +(-2.39840 - 4.15414i) q^{49} +(14.9268 + 8.61801i) q^{50} +(0.443077 + 0.767432i) q^{51} +(4.01127 - 14.0856i) q^{52} +(-1.69421 - 2.93446i) q^{53} +5.72966i q^{54} +(8.74366 - 15.1445i) q^{55} +(-3.76776 + 6.52596i) q^{56} +(2.40433 - 1.38814i) q^{57} +7.19198i q^{58} +(-5.22180 - 3.01481i) q^{59} +5.60596i q^{60} -3.30204 q^{61} +(12.3880 - 5.87013i) q^{62} -4.21737i q^{63} +7.22559 q^{64} +(3.04369 + 12.1137i) q^{65} +4.95159 q^{66} +(-6.91629 + 3.99312i) q^{67} +(4.51752 - 7.82457i) q^{68} +(-0.845383 + 1.46425i) q^{69} -12.6600i q^{70} +(4.65051 - 2.68498i) q^{71} +(12.4920 - 7.21223i) q^{72} +(-10.1346 + 5.85124i) q^{73} +(-2.05598 + 3.56107i) q^{74} +(-1.39449 - 2.41533i) q^{75} +(-24.5140 - 14.1532i) q^{76} -7.49292 q^{77} +(-2.53959 + 2.46139i) q^{78} +(-0.119947 + 0.207754i) q^{79} +(13.1270 - 7.57887i) q^{80} +(-3.79836 + 6.57895i) q^{81} +(0.926806 + 1.60528i) q^{82} +(13.9719 - 8.06666i) q^{83} +(2.08022 - 1.20101i) q^{84} +7.70539i q^{85} +(-17.3004 - 9.98841i) q^{86} +(0.581871 - 1.00783i) q^{87} +(-12.8138 - 22.1942i) q^{88} +11.9872i q^{89} +(-12.1169 + 20.9870i) q^{90} +(3.84300 - 3.72466i) q^{91} +17.2387 q^{92} +(-2.21089 - 0.179661i) q^{93} +20.4233 q^{94} +24.1406 q^{95} +(0.213778 + 0.123425i) q^{96} -14.2496i q^{97} +(10.2279 - 5.90510i) q^{98} +(12.4213 + 7.17146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more