LMFDB - Embedded newform 403.2.l.c.25.3

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			25.3
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.32

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

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

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	$-0.663805\pi$
$2$		−	2.46210i		−	1.74097i	0.492195	−	0.870485i	$-0.336195\pi$
$3$	0.199198	+	0.345021i	0.115007	+	0.199198i	0.917783	−	0.397083i	$-0.129978\pi$
$3$	0.199198	+	0.345021i	0.115007	+	0.199198i	−0.802776	+	0.596281i	$0.796644\pi$
$4$	−4.06196			−2.03098
$5$	3.00007	+	1.73209i	1.34167	+	0.774614i	0.987052	−	0.160398i	$-0.0512777\pi$
$5$	3.00007	+	1.73209i	1.34167	+	0.774614i	0.354618	+	0.935011i	$0.384611\pi$
$6$	0.849477	−	0.490446i	0.346798	−	0.200224i
$7$	−1.28546	+	0.742161i	−0.485858	+	0.280510i	−0.722855	−	0.691000i	$-0.757170\pi$
$7$	−1.28546	+	0.742161i	−0.485858	+	0.280510i	0.236996	+	0.971511i	$0.423837\pi$
$8$			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	0.983427	−	0.181303i	$-0.0580314\pi$
$11$	4.37174	+	2.52402i	1.31813	+	0.761022i	0.334701	+	0.942324i	$0.391365\pi$
$12$	−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	0.699057	−	0.715066i	$-0.253603\pi$
$17$	−1.11215	−	1.92631i	−0.269737	−	0.467198i	−0.968794	+	0.247868i	$0.920270\pi$
$18$	−6.05831	−	3.49776i	−1.42796	−	0.824431i
$19$	6.03502	−	3.48432i	1.38453	−	0.799358i	0.391837	−	0.920035i	$-0.371840\pi$
$19$	6.03502	−	3.48432i	1.38453	−	0.799358i	0.992692	+	0.120677i	$0.0385065\pi$
$20$	−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	−0.376377	−	0.926467i	$-0.622830\pi$
$37$	1.44635	−	0.835052i	0.237779	−	0.137282i	0.614155	+	0.789185i	$0.289497\pi$
$38$	−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	0.550047	−	0.835133i	$-0.314610\pi$
$41$	0.651993	+	0.376429i	0.101824	+	0.0587883i	−0.448223	+	0.893922i	$0.647943\pi$
$42$	−0.727979	+	1.26090i	−0.112330	+	0.194561i
$43$	−4.05686	−	7.02669i	−0.618666	−	1.07156i	−0.989729	−	0.142953i	$-0.954340\pi$
$43$	−4.05686	−	7.02669i	−0.618666	−	1.07156i	0.371064	−	0.928607i	$-0.378993\pi$
$44$	−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	$0.206819\pi$
$47$			8.29508i			1.20996i	−0.796240	+	0.604981i	$0.793181\pi$
$48$	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	−0.958607	−	0.284733i	$-0.908095\pi$
$53$	−1.69421	+	2.93446i	−0.232718	+	0.403079i	0.725889	+	0.687812i	$0.241428\pi$
$54$		−	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	−0.799788	−	0.600283i	$-0.795055\pi$
$59$	−5.22180	+	3.01481i	−0.679821	+	0.392495i	0.119967	+	0.992778i	$0.461721\pi$
$60$		−	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	0.0139872	−	0.999902i	$-0.495548\pi$
$67$	−6.91629	−	3.99312i	−0.844960	−	0.487838i	−0.858947	+	0.512064i	$0.828881\pi$
$68$	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	0.749894	−	0.661558i	$-0.230105\pi$
$71$	4.65051	+	2.68498i	0.551915	+	0.318648i	−0.197979	+	0.980206i	$0.563438\pi$
$72$	12.4920	+	7.21223i	1.47219	+	0.849970i
$73$	−10.1346	−	5.85124i	−1.18617	−	0.684836i	−0.228736	−	0.973488i	$-0.573459\pi$
$73$	−10.1346	−	5.85124i	−1.18617	−	0.684836i	−0.957434	+	0.288653i	$0.906793\pi$
$74$	−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	0.859199	−	0.511642i	$-0.170962\pi$
$79$	−0.119947	−	0.207754i	−0.0134951	−	0.0233742i	−0.872694	+	0.488267i	$0.837629\pi$
$80$	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	0.999191	+	0.0402111i	$0.0128030\pi$
$83$	13.9719	+	8.06666i	1.53361	+	0.885431i	0.534419	+	0.845219i	$0.320530\pi$
$84$	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	$-0.780868\pi$
$89$		−	11.9872i		−	1.27064i	0.772248	−	0.635322i	$-0.219132\pi$
$90$	−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	$0.257428\pi$
$97$			14.2496i			1.44683i	−0.690415	+	0.723414i	$0.742572\pi$
$98$	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	0.269616	+	0.962968i	$0.413103\pi$
$103$	−7.09556	+	12.2899i	−0.699146	+	1.21096i	−0.968763	+	0.247989i	$0.920230\pi$
$104$	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	−0.993561	−	0.113299i	$-0.963858\pi$
$107$	−6.15370	−	10.6585i	−0.594900	−	1.03040i	0.398661	−	0.917099i	$-0.369475\pi$
$108$	−9.45274			−0.909591
$109$		−	8.60809i		−	0.824505i	−0.911070	−	0.412253i	$-0.864742\pi$
$109$		−	8.60809i		−	0.824505i	0.911070	−	0.412253i	$-0.135258\pi$
$110$	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	−0.523569	−	0.851984i	$-0.675400\pi$
$113$	5.06054	−	8.76510i	0.476055	−	0.824552i	0.999624	+	0.0274319i	$0.00873294\pi$
$114$	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	0.999933	−	0.0115381i	$-0.00367276\pi$
$127$	5.52173	+	9.56392i	0.489974	+	0.848661i	−0.509959	+	0.860199i	$0.670339\pi$
$128$		−	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	0.999371	−	0.0354498i	$-0.0112864\pi$
$131$	5.36778	+	9.29727i	0.468985	+	0.812306i	−0.530386	+	0.847756i	$0.677953\pi$
$132$		−	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	−0.426467	−	0.904503i	$-0.640242\pi$
$137$	−16.6561	−	9.61638i	−1.42302	−	0.821583i	−0.996556	+	0.0829198i	$0.973575\pi$
$138$	−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	−0.690222	−	0.723598i	$-0.742487\pi$
$149$	−4.98855	+	2.88014i	−0.408678	+	0.235950i	0.281544	+	0.959548i	$0.409154\pi$
$150$	5.94678	+	3.43338i	0.485553	+	0.280334i
$151$			22.9377i			1.86665i	0.359037	+	0.933323i	$0.383105\pi$
$151$			22.9377i			1.86665i	−0.359037	+	0.933323i	$0.616895\pi$
$152$	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	$0.260840\pi$
$163$			18.6598i			1.46155i	−0.682621	+	0.730773i	$0.739160\pi$
$164$	−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	−0.590454	−	0.807071i	$-0.701051\pi$
$167$	−2.41317	+	1.39324i	−0.186737	+	0.107812i	0.403717	+	0.914884i	$0.367718\pi$
$168$	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	−0.0268346	+	0.999640i	$0.508543\pi$
$173$	−11.5632	+	20.0280i	−0.879131	+	1.52270i	−0.852296	+	0.523059i	$0.824791\pi$
$174$	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	0.818591	−	0.574377i	$-0.194756\pi$
$179$	−1.17909	−	2.04225i	−0.0881296	−	0.152645i	−0.906721	+	0.421732i	$0.861422\pi$
$180$	−34.6242	+	19.9903i	−2.58074	+	1.48999i
$181$	7.21894	−	12.5036i	0.536579	−	0.929383i	−0.462506	−	0.886616i	$-0.653050\pi$
$181$	7.21894	−	12.5036i	0.536579	−	0.929383i	0.999085	−	0.0427665i	$-0.0136171\pi$
$182$	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	−0.885996	−	0.463694i	$-0.846524\pi$
$191$	−0.572538	+	0.991665i	−0.0414274	+	0.0717544i	0.844568	+	0.535448i	$0.179857\pi$
$192$	1.43932	+	2.49298i	0.103874	+	0.179915i
$193$	−8.15663	+	4.70923i	−0.587127	+	0.338978i	−0.763961	−	0.645263i	$-0.776748\pi$
$193$	−8.15663	+	4.70923i	−0.587127	+	0.338978i	0.176834	+	0.984241i	$0.443415\pi$
$194$	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	0.166916	−	0.985971i	$-0.446619\pi$
$197$	−8.47055	−	4.89047i	−0.603502	−	0.348432i	−0.770418	+	0.637539i	$0.779952\pi$
$198$	−17.6569	−	30.5826i	−1.25482	−	2.17341i
$199$	6.11906	−	10.5985i	0.433769	−	0.751309i	−0.563426	−	0.826167i	$-0.690517\pi$
$199$	6.11906	−	10.5985i	0.433769	−	0.751309i	0.997194	+	0.0748575i	$0.0238502\pi$
$200$	−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	0.973479	−	0.228776i	$-0.0734723\pi$
$211$	4.19236	+	7.26138i	0.288614	+	0.499894i	−0.684865	+	0.728670i	$0.740139\pi$
$212$	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	−0.397799	−	0.917472i	$-0.630226\pi$
$223$	2.95461	−	1.70585i	0.197856	−	0.114232i	0.595655	+	0.803241i	$0.296893\pi$
$224$	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	0.256683	−	0.966496i	$-0.417370\pi$
$227$	−6.80984	−	3.93166i	−0.451985	−	0.260954i	−0.708668	+	0.705542i	$0.750704\pi$
$228$	−9.76626	−	5.63855i	−0.646787	−	0.373422i
$229$	6.66003	−	3.84517i	0.440107	−	0.254096i	−0.263536	−	0.964650i	$-0.584889\pi$
$229$	6.66003	−	3.84517i	0.440107	−	0.254096i	0.703643	+	0.710553i	$0.251555\pi$
$230$	−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	−0.0311853	−	0.999514i	$-0.509928\pi$
$239$	−14.1051	−	8.14357i	−0.912382	−	0.526764i	−0.881197	+	0.472750i	$0.843262\pi$
$240$			6.03878i			0.389802i
$241$	−1.71627	+	0.990888i	−0.110555	+	0.0638287i	−0.554258	−	0.832345i	$-0.686998\pi$
$241$	−1.71627	+	0.990888i	−0.110555	+	0.0638287i	0.443703	+	0.896174i	$0.353664\pi$
$242$	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	0.795097	−	0.606483i	$-0.207420\pi$
$251$	−2.02285	−	3.50367i	−0.127681	−	0.221150i	−0.922778	+	0.385333i	$0.874087\pi$
$252$		−	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	−0.943398	−	0.331663i	$-0.892390\pi$
$257$	−2.95729	+	5.12217i	−0.184470	+	0.319512i	0.758927	+	0.651175i	$0.225724\pi$
$258$	−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	−0.151818	−	0.988409i	$-0.548513\pi$
$269$	12.7942	−	22.1603i	0.780078	−	1.35113i	0.931896	−	0.362726i	$-0.118154\pi$
$270$	9.92428	−	17.1894i	0.603973	−	1.04611i
$271$			2.87701i			0.174766i	0.996175	+	0.0873831i	$0.0278504\pi$
$271$			2.87701i			0.174766i	−0.996175	+	0.0873831i	$0.972150\pi$
$272$	−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	$0.0540095\pi$
$281$			5.66132i			0.337726i	−0.985640	+	0.168863i	$0.945990\pi$
$282$	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	0.660324	−	0.750981i	$-0.270419\pi$
$293$	28.0869	−	16.2160i	1.64085	−	0.947348i	0.980531	−	0.196367i	$-0.0629143\pi$
$294$			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	0.630998	−	0.775784i	$-0.282645\pi$
$307$	28.3557	−	16.3712i	1.61835	−	0.934353i	0.987348	−	0.158568i	$-0.0506878\pi$
$308$	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	−0.977029	−	0.213106i	$-0.931642\pi$
$313$	−11.9078	−	20.6249i	−0.673069	−	1.16579i	0.303960	−	0.952685i	$-0.401691\pi$
$314$			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	−0.0158416	−	0.999875i	$-0.505043\pi$
$317$	14.9941	−	8.65687i	0.842154	−	0.486218i	0.857996	+	0.513657i	$0.171709\pi$
$318$			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	0.407274	−	0.913306i	$-0.366479\pi$
$331$	−3.27545	−	1.89108i	−0.180035	−	0.103943i	−0.587309	+	0.809363i	$0.699813\pi$
$332$	−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	−0.971428	−	0.237336i	$-0.923726\pi$
$347$	−12.8766	−	22.3030i	−0.691253	−	1.19729i	0.280175	−	0.959949i	$-0.409608\pi$
$348$	−2.36354	−	4.09376i	−0.126699	−	0.219449i
$349$			33.9441i			1.81699i	0.417899	+	0.908493i	$0.362767\pi$
$349$			33.9441i			1.81699i	−0.417899	+	0.908493i	$0.637233\pi$
$350$	−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	−0.969610	−	0.244654i	$-0.921326\pi$
$353$	−23.3452	+	13.4783i	−1.24254	+	0.717380i	−0.272928	+	0.962034i	$0.587992\pi$
$354$	−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	−0.178480	−	0.983944i	$-0.557118\pi$
$359$	−21.2179	−	12.2502i	−1.11984	−	0.646540i	−0.941360	+	0.337404i	$0.890451\pi$
$360$	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	−0.646452	−	0.762955i	$-0.723748\pi$
$367$	6.46581	−	11.1991i	0.337513	−	0.584589i	0.983964	+	0.178366i	$0.0570811\pi$
$368$	−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	−0.534625	−	0.845089i	$-0.679547\pi$
$379$	−1.36411	+	0.787568i	−0.0700695	+	0.0404547i	0.464556	+	0.885544i	$0.346214\pi$
$380$	−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	0.750547	−	0.660817i	$-0.229790\pi$
$383$	10.8329	+	6.25438i	0.553536	+	0.319584i	−0.197011	+	0.980401i	$0.563124\pi$
$384$	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	0.828515	−	0.559966i	$-0.189186\pi$
$389$	−1.39417	−	2.41477i	−0.0706872	−	0.122434i	−0.899203	+	0.437532i	$0.855853\pi$
$390$	−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	−0.208979	−	0.977920i	$-0.567014\pi$
$397$	10.6286	−	6.13644i	0.533436	−	0.307979i	0.742414	+	0.669941i	$0.233681\pi$
$398$	−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	$0.0864648\pi$
$401$			10.7458i			0.536618i	−0.963333	+	0.268309i	$0.913535\pi$
$402$	−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	−0.687197	−	0.726472i	$-0.741159\pi$
$409$	−8.12291	+	4.68976i	−0.401652	+	0.231894i	0.285545	+	0.958365i	$0.407826\pi$
$410$	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	0.723833	−	0.689975i	$-0.242379\pi$
$421$	10.0173	+	5.78349i	0.488213	+	0.281870i	−0.235620	+	0.971845i	$0.575712\pi$
$422$	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	−0.636562	−	0.771226i	$-0.719644\pi$
$431$	−5.95706	+	3.43931i	−0.286941	+	0.165666i	0.349620	+	0.936891i	$0.386311\pi$
$432$	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	−0.754522	−	0.656275i	$-0.772131\pi$
$439$	4.00379	−	6.93476i	0.191090	−	0.330978i	0.945612	+	0.325297i	$0.105464\pi$
$440$	−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	−0.757040	−	0.653368i	$-0.773355\pi$
$443$	3.94248	−	6.82858i	0.187313	−	0.324436i	0.944354	+	0.328932i	$0.106689\pi$
$444$	−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	$0.309606\pi$
$449$			35.0216i			1.65277i	−0.563106	+	0.826385i	$0.690394\pi$
$450$		−	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	$0.130811\pi$
$457$			17.0800i			0.798968i	−0.916740	+	0.399484i	$0.869189\pi$
$458$	−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	$-0.789391\pi$
$461$		−	26.3842i		−	1.22884i	0.788981	−	0.614418i	$-0.210609\pi$
$462$	−6.36507	+	3.67487i	−0.296130	+	0.170971i
$463$			24.9390i			1.15901i	0.814968	+	0.579507i	$0.196755\pi$
$463$			24.9390i			1.15901i	−0.814968	+	0.579507i	$0.803245\pi$
$464$	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	0.104162	−	0.994560i	$-0.466784\pi$
$479$	22.2703	−	12.8578i	1.01756	−	0.587487i	0.913395	+	0.407073i	$0.133451\pi$
$480$	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	0.525271	−	0.850935i	$-0.323964\pi$
$487$	1.12492	+	0.649473i	0.0509750	+	0.0294305i	−0.474296	+	0.880365i	$0.657297\pi$
$488$		−	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	−0.537140	−	0.843493i	$-0.680495\pi$
$491$	10.2354	−	17.7282i	0.461916	−	0.800062i	0.999056	+	0.0434305i	$0.0138287\pi$
$492$		−	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	−0.896497	−	0.443050i	$-0.853896\pi$
$499$	−21.4683	+	12.3947i	−0.961052	+	0.554864i	−0.0645556	+	0.997914i	$0.520563\pi$
$500$		−	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	0.744462	−	0.667665i	$-0.232706\pi$
$503$	−4.61974	−	8.00163i	−0.205984	−	0.356775i	−0.950446	+	0.310890i	$0.899373\pi$
$504$	−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	0.611765	−	0.791040i	$-0.290460\pi$
$509$	5.24740	+	3.02959i	0.232587	+	0.134284i	−0.379178	+	0.925324i	$0.623793\pi$
$510$	−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	0.728716	−	0.684816i	$-0.240117\pi$
$521$	−5.22040	−	9.04200i	−0.228710	−	0.396137i	−0.957426	+	0.288679i	$0.906784\pi$
$522$	−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	−0.655514	−	0.755183i	$-0.727548\pi$
$541$	−7.65848	+	4.42162i	−0.329264	+	0.190100i	0.326250	+	0.945283i	$0.394215\pi$
$542$	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	−0.752210	−	0.658923i	$-0.771012\pi$
$547$	4.54988	−	7.88063i	0.194539	−	0.336951i	0.946749	+	0.321972i	$0.104346\pi$
$548$	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	$-0.724748\pi$
$557$		−	35.9167i		−	1.52184i	0.648846	−	0.760919i	$-0.275252\pi$
$558$	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	−0.294481	−	0.955657i	$-0.595147\pi$
$563$	16.1439	−	27.9620i	0.680383	−	1.17846i	0.974864	−	0.222801i	$-0.0715200\pi$
$564$	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	−0.358526	−	0.933520i	$-0.616720\pi$
$569$	15.0085	−	25.9955i	0.629189	−	1.08979i	0.987715	−	0.156268i	$-0.0499462\pi$
$570$	20.5069	−	11.8397i	0.858939	−	0.495909i
$571$	3.20425	−	5.54993i	0.134094	−	0.232257i	−0.791157	−	0.611613i	$-0.790521\pi$
$571$	3.20425	−	5.54993i	0.134094	−	0.232257i	0.925251	+	0.379356i	$0.123854\pi$
$572$	−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	−0.0222295	−	0.999753i	$-0.507076\pi$
$577$	19.9965	−	11.5450i	0.832467	−	0.480625i	0.854697	+	0.519128i	$0.173743\pi$
$578$	−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	$-0.946934\pi$
$587$		−	8.04079i		−	0.331879i	0.986136	−	0.165940i	$-0.0530657\pi$
$588$	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	$0.0143090\pi$
$593$			2.18862i			0.0898759i	−0.998990	+	0.0449379i	$0.985691\pi$
$594$	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	0.246049	+	0.969257i	$0.420868\pi$
$599$	−17.5330	+	30.3680i	−0.716377	+	1.24080i	−0.962426	+	0.271544i	$0.912466\pi$
$600$	−12.2620	−	7.07947i	−0.500594	−	0.289018i
$601$	−10.1110	−	17.5128i	−0.412436	−	0.714360i	0.582719	−	0.812673i	$-0.301989\pi$
$601$	−10.1110	−	17.5128i	−0.412436	−	0.714360i	−0.995156	+	0.0983131i	$0.968655\pi$
$602$	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	0.408844	+	0.912604i	$0.365932\pi$
$607$	−14.4354	+	25.0029i	−0.585917	+	1.01484i	−0.994760	+	0.102233i	$0.967401\pi$
$608$	−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	−0.954120	−	0.299424i	$-0.903206\pi$
$613$	−29.0142	+	16.7513i	−1.17187	+	0.676581i	−0.217752	+	0.976004i	$0.569872\pi$
$614$	−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	−0.498724	−	0.866761i	$-0.666198\pi$
$617$	0.0633847	−	0.0365952i	0.00255177	−	0.00147327i	0.501275	+	0.865288i	$0.332864\pi$
$618$			13.9200i			0.559943i
$619$		−	11.9477i		−	0.480218i	−0.970746	−	0.240109i	$-0.922817\pi$
$619$		−	11.9477i		−	0.480218i	0.970746	−	0.240109i	$-0.0771832\pi$
$620$	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	0.277167	−	0.960822i	$-0.410605\pi$
$631$	−10.4585	−	6.03822i	−0.416346	−	0.240378i	−0.693513	+	0.720444i	$0.743938\pi$
$632$	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	0.485640	+	0.874159i	$0.338587\pi$
$641$	−13.0191	+	22.5498i	−0.514224	+	0.890663i	−0.999864	+	0.0165034i	$0.994747\pi$
$642$	−10.4548	−	6.03611i	−0.412620	−	0.238226i
$643$			10.0878i			0.397824i	0.980017	+	0.198912i	$0.0637408\pi$
$643$			10.0878i			0.397824i	−0.980017	+	0.198912i	$0.936259\pi$
$644$	−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	0.941567	−	0.336826i	$-0.109353\pi$
$661$	28.8118	+	16.6345i	1.12065	+	0.647008i	0.179084	+	0.983834i	$0.442687\pi$
$662$	−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	−0.995608	−	0.0936185i	$-0.970157\pi$
$673$	−10.8109	+	18.7250i	−0.416728	+	0.721794i	0.578880	+	0.815413i	$0.303490\pi$
$674$		−	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	−0.866656	−	0.498906i	$-0.833735\pi$
$677$	−0.0328535	+	0.0569039i	−0.00126266	+	0.00218699i	0.865393	+	0.501093i	$0.167069\pi$
$678$		−	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	$-0.745987\pi$
$683$		−	37.4224i		−	1.43193i	0.698137	−	0.715964i	$-0.254013\pi$
$684$			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	0.394071	−	0.919080i	$-0.371066\pi$
$691$	−5.38461	−	3.10881i	−0.204840	−	0.118265i	−0.598911	+	0.800815i	$0.704400\pi$
$692$	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	0.642530	+	0.766261i	$0.277885\pi$
$701$	26.0757	+	45.1645i	0.984866	+	1.70584i	0.342337	+	0.939577i	$0.388782\pi$
$702$	−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	$-0.750714\pi$
$709$		−	37.5718i		−	1.41104i	0.708690	−	0.705520i	$-0.249286\pi$
$710$	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	0.995683	−	0.0928181i	$-0.0295875\pi$
$719$	11.1938	+	19.3882i	0.417459	+	0.723060i	−0.578224	+	0.815878i	$0.696254\pi$
$720$	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	0.982242	−	0.187620i	$-0.0600774\pi$
$727$	8.86102	+	15.3477i	0.328637	+	0.569216i	−0.653605	+	0.756836i	$0.726744\pi$
$728$	−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	0.819459	−	0.573138i	$-0.194274\pi$
$733$	19.8408	+	11.4551i	0.732835	+	0.423103i	−0.0866231	+	0.996241i	$0.527608\pi$
$734$	−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	0.563365	−	0.826208i	$-0.309506\pi$
$739$	3.52125	+	2.03300i	0.129531	+	0.0747849i	−0.433834	+	0.900993i	$0.642840\pi$
$740$	−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	$0.0195620\pi$
$743$			3.34822i			0.122834i	−0.998112	+	0.0614172i	$0.980438\pi$
$744$	−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	0.988820	−	0.149112i	$-0.0476414\pi$
$751$	10.0102	+	17.3381i	0.365276	+	0.632676i	−0.623545	+	0.781788i	$0.714308\pi$
$752$			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	−0.236271	−	0.971687i	$-0.575925\pi$
$757$	19.9026	−	34.4722i	0.723371	−	1.25291i	0.959641	−	0.281227i	$-0.0907415\pi$
$758$	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	−0.141951	−	0.989874i	$-0.545338\pi$
$761$	17.7746	−	10.2622i	0.644329	−	0.372004i	0.786280	+	0.617870i	$0.212004\pi$
$762$	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	0.380293	−	0.924866i	$-0.375823\pi$
$769$	38.0300	−	21.9566i	1.37140	−	0.791776i	0.991104	+	0.133090i	$0.0424899\pi$
$770$	−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	$0.219151\pi$
$773$			35.3300i			1.27073i	−0.772211	+	0.635366i	$0.780849\pi$
$774$			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	−0.286477	−	0.958087i	$-0.592484\pi$
$787$	11.2217	−	6.47887i	0.400012	−	0.230947i	0.686489	+	0.727140i	$0.259151\pi$
$788$	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	−0.961962	−	0.273182i	$-0.911924\pi$
$797$	−6.89968	+	11.9506i	−0.244399	+	0.423312i	0.717563	+	0.696493i	$0.245257\pi$
$798$			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	0.764331	+	0.644824i	$0.223069\pi$
$809$	26.7534	+	46.3383i	0.940599	+	1.62917i	0.176268	+	0.984342i	$0.443597\pi$
$810$	−64.7937			−2.27662
$811$	−16.7996	−	9.69927i	−0.589915	−	0.340587i	0.175149	−	0.984542i	$-0.443959\pi$
$811$	−16.7996	−	9.69927i	−0.589915	−	0.340587i	−0.765064	+	0.643954i	$0.777293\pi$
$812$	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	$0.0804614\pi$
$821$			14.3319i			0.500187i	−0.968222	+	0.250094i	$0.919539\pi$
$822$	−18.8653			−0.658001
$823$	−10.6888	−	18.5136i	−0.372588	−	0.645342i	0.617375	−	0.786669i	$-0.288196\pi$
$823$	−10.6888	−	18.5136i	−0.372588	−	0.645342i	−0.989963	+	0.141327i	$0.954863\pi$
$824$	−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	0.835820	−	0.549004i	$-0.184993\pi$
$827$	22.3814	+	12.9219i	0.778278	+	0.449339i	−0.0575417	+	0.998343i	$0.518326\pi$
$828$	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	$-0.862066\pi$
$839$		−	24.3251i		−	0.839795i	0.907571	−	0.419898i	$-0.137934\pi$
$840$	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	$0.136978\pi$
$853$			24.3678i			0.834338i	−0.908829	+	0.417169i	$0.863022\pi$
$854$	−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	0.405109	+	0.914268i	$0.367233\pi$
$857$	−17.2493	+	29.8767i	−0.589225	+	1.02057i	−0.994334	+	0.106299i	$0.966100\pi$
$858$	−4.88980	−	17.1705i	−0.166935	−	0.586192i
$859$	−23.3035	+	40.3628i	−0.795105	+	1.37716i	0.127667	+	0.991817i	$0.459251\pi$
$859$	−23.3035	+	40.3628i	−0.795105	+	1.37716i	−0.922772	+	0.385345i	$0.874082\pi$
$860$			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	0.848125	−	0.529796i	$-0.177732\pi$
$863$	23.8943	+	13.7954i	0.813370	+	0.469600i	−0.0347546	+	0.999396i	$0.511065\pi$
$864$		−	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	0.775174	−	0.631748i	$-0.217662\pi$
$877$	18.2320	+	10.5263i	0.615652	+	0.355447i	−0.159522	+	0.987194i	$0.550995\pi$
$878$	−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	−0.266207	−	0.963916i	$-0.585771\pi$
$881$	20.8268	−	36.0730i	0.701672	−	1.21533i	0.967879	−	0.251416i	$-0.0808961\pi$
$882$	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	−0.863743	−	0.503932i	$-0.831886\pi$
$887$	−25.8599	−	44.7906i	−0.868290	−	1.50392i	−0.00454624	−	0.999990i	$-0.501447\pi$
$888$	−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	−0.884877	−	0.465825i	$-0.845757\pi$
$911$	−25.5303	−	44.2197i	−0.845855	−	1.46506i	0.0390218	−	0.999238i	$-0.487576\pi$
$912$	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	−0.961569	−	0.274562i	$-0.911467\pi$
$919$	−7.36675	+	12.7596i	−0.243007	+	0.420900i	0.718563	+	0.695462i	$0.244800\pi$
$920$	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	$0.0917372\pi$
$929$			17.3262i			0.568456i	−0.958757	+	0.284228i	$0.908263\pi$
$930$	−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	0.986184	−	0.165654i	$-0.0529736\pi$
$937$	10.7024	+	18.5370i	0.349631	+	0.605579i	−0.636553	+	0.771233i	$0.719640\pi$
$938$		−	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	0.943253	−	0.332074i	$-0.107748\pi$
$941$	34.5806	+	19.9651i	1.12730	+	0.650844i	0.184042	+	0.982918i	$0.441082\pi$
$942$	−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	−0.895280	−	0.445504i	$-0.853024\pi$
$947$	−29.4533	+	17.0048i	−0.957102	+	0.552583i	−0.0618221	+	0.998087i	$0.519691\pi$
$948$	−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	−0.136487	−	0.990642i	$-0.543581\pi$
$967$	20.3120	−	11.7271i	0.653190	−	0.377119i	0.789677	+	0.613522i	$0.210248\pi$
$968$	−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	−0.984848	−	0.173419i	$-0.944518\pi$
$971$	−10.6645	+	18.4714i	−0.342239	+	0.592775i	0.642609	+	0.766194i	$0.277852\pi$
$972$	−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	$0.00692286\pi$
$977$			1.35950i			0.0434942i	−0.999764	+	0.0217471i	$0.993077\pi$
$978$	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	0.449670	−	0.893195i	$-0.351542\pi$
$983$	−3.10469	−	1.79249i	−0.0990241	−	0.0571716i	−0.548694	+	0.836023i	$0.684875\pi$
$984$	−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	−0.902645	−	0.430386i	$-0.858377\pi$
$997$	−2.48173	+	4.29849i	−0.0785972	+	0.136134i	0.824048	+	0.566520i	$0.191711\pi$
$998$	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.25.3	✓	68
13.12	even	2	inner	403.2.l.c.25.32	yes	68
31.5	even	3	inner	403.2.l.c.129.3	yes	68
403.129	even	6	inner	403.2.l.c.129.32	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.3	✓	68	1.1	even	1	trivial
403.2.l.c.25.32	yes	68	13.12	even	2	inner
403.2.l.c.129.3	yes	68	31.5	even	3	inner
403.2.l.c.129.32	yes	68	403.129	even	6	inner

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

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