LMFDB - Embedded newform 700.2.g.j.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.6
Root			$-1.17915 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.j.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780776 - 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +(2.35829 - 3.56155i) q^{6} +(-2.17238 - 1.51022i) q^{7} +(-2.78078 - 0.516994i) q^{8} +6.12311 q^{9} +O(q^{10})$	\(q+(0.780776 - 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +(2.35829 - 3.56155i) q^{6} +(-2.17238 - 1.51022i) q^{7} +(-2.78078 - 0.516994i) q^{8} +6.12311 q^{9} -4.71659i q^{11} +(-2.35829 - 5.56155i) q^{12} +2.00000i q^{13} +(-3.47692 + 1.38241i) q^{14} +(-2.78078 + 2.87529i) q^{16} +1.12311i q^{17} +(4.78078 - 7.22004i) q^{18} +4.71659 q^{19} +(-6.56155 - 4.56155i) q^{21} +(-5.56155 - 3.68260i) q^{22} +6.41273i q^{23} +(-8.39919 - 1.56155i) q^{24} +(2.35829 + 1.56155i) q^{26} +9.43318 q^{27} +(-1.08464 + 5.17915i) q^{28} -2.00000 q^{29} +3.39228 q^{31} +(1.21922 + 5.52390i) q^{32} -14.2462i q^{33} +(1.32431 + 0.876894i) q^{34} +(-4.78078 - 11.2745i) q^{36} -2.00000 q^{37} +(3.68260 - 5.56155i) q^{38} +6.04090i q^{39} +1.12311i q^{41} +(-10.5018 + 4.17548i) q^{42} -0.371834i q^{43} +(-8.68466 + 3.68260i) q^{44} +(7.56155 + 5.00691i) q^{46} +5.08842 q^{47} +(-8.39919 + 8.68466i) q^{48} +(2.43845 + 6.56155i) q^{49} +3.39228i q^{51} +(3.68260 - 1.56155i) q^{52} -2.00000 q^{53} +(7.36520 - 11.1231i) q^{54} +(5.26012 + 5.32270i) q^{56} +14.2462 q^{57} +(-1.56155 + 2.35829i) q^{58} +2.06798 q^{59} -2.00000i q^{61} +(2.64861 - 4.00000i) q^{62} +(-13.3017 - 9.24726i) q^{63} +(7.46543 + 2.87529i) q^{64} +(-16.7984 - 11.1231i) q^{66} -3.76412i q^{67} +(2.06798 - 0.876894i) q^{68} +19.3693i q^{69} +7.36520i q^{71} +(-17.0270 - 3.16561i) q^{72} +15.3693i q^{73} +(-1.56155 + 2.35829i) q^{74} +(-3.68260 - 8.68466i) q^{76} +(-7.12311 + 10.2462i) q^{77} +(7.12311 + 4.71659i) q^{78} -1.32431i q^{79} +10.1231 q^{81} +(1.32431 + 0.876894i) q^{82} +3.02045 q^{83} +(-3.27608 + 15.6433i) q^{84} +(-0.438447 - 0.290319i) q^{86} -6.04090 q^{87} +(-2.43845 + 13.1158i) q^{88} -12.0000i q^{89} +(3.02045 - 4.34475i) q^{91} +(11.8078 - 5.00691i) q^{92} +10.2462 q^{93} +(3.97292 - 6.00000i) q^{94} +(3.68260 + 16.6847i) q^{96} -1.12311i q^{97} +(9.64092 + 2.24782i) q^{98} -28.8802i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9	$ 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9} - 6 q^{14} - 14 q^{16} + 30 q^{18} - 36 q^{21} - 28 q^{22} - 14 q^{28} - 16 q^{29} + 18 q^{32} - 30 q^{36} - 16 q^{37} - 8 q^{42} - 20 q^{44} + 44 q^{46} + 36 q^{49} - 16 q^{53} + 2 q^{56} + 48 q^{57} + 4 q^{58} + 2 q^{64} - 62 q^{72} + 4 q^{74} - 24 q^{77} + 24 q^{78} + 48 q^{81} + 8 q^{84} - 20 q^{86} - 36 q^{88} + 12 q^{92} + 16 q^{93} - 26 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9 - 6 * q^14 - 14 * q^16 + 30 * q^18 - 36 * q^21 - 28 * q^22 - 14 * q^28 - 16 * q^29 + 18 * q^32 - 30 * q^36 - 16 * q^37 - 8 * q^42 - 20 * q^44 + 44 * q^46 + 36 * q^49 - 16 * q^53 + 2 * q^56 + 48 * q^57 + 4 * q^58 + 2 * q^64 - 62 * q^72 + 4 * q^74 - 24 * q^77 + 24 * q^78 + 48 * q^81 + 8 * q^84 - 20 * q^86 - 36 * q^88 + 12 * q^92 + 16 * q^93 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.780776	−	1.17915i	0.552092	−	0.833783i
$2$	0.780776	−	1.17915i	0.552092	−	0.833783i
$3$	3.02045			1.74386			0.871928	−	0.489634i	$-0.162870\pi$
$3$	3.02045			1.74386			0.871928	+	0.489634i	$0.162870\pi$
$4$	−0.780776	−	1.84130i	−0.390388	−	0.920650i
$5$		0			0
$5$		0			0
$6$	2.35829	−	3.56155i	0.962770	−	1.45400i
$7$	−2.17238	−	1.51022i	−0.821081	−	0.570811i
$7$	−2.17238	−	1.51022i	−0.821081	−	0.570811i
$8$	−2.78078	−	0.516994i	−0.983153	−	0.182785i
$9$	6.12311			2.04104
$10$		0			0
$11$		−	4.71659i		−	1.42211i	−0.703139	−	0.711053i	$-0.748219\pi$
$11$		−	4.71659i		−	1.42211i	0.703139	−	0.711053i	$-0.251781\pi$
$12$	−2.35829	−	5.56155i	−0.680781	−	1.60548i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−3.47692	+	1.38241i	−0.929245	+	0.369463i
$15$		0			0
$16$	−2.78078	+	2.87529i	−0.695194	+	0.718822i
$17$			1.12311i			0.272393i	0.990682	+	0.136197i	$0.0434879\pi$
$17$			1.12311i			0.272393i	−0.990682	+	0.136197i	$0.956512\pi$
$18$	4.78078	−	7.22004i	1.12684	−	1.70178i
$19$	4.71659			1.08206			0.541030	−	0.841003i	$-0.318035\pi$
$19$	4.71659			1.08206			0.541030	+	0.841003i	$0.318035\pi$
$20$		0			0
$21$	−6.56155	−	4.56155i	−1.43185	−	0.995412i
$22$	−5.56155	−	3.68260i	−1.18573	−	0.785133i
$23$			6.41273i			1.33715i	0.743646	+	0.668573i	$0.233095\pi$
$23$			6.41273i			1.33715i	−0.743646	+	0.668573i	$0.766905\pi$
$24$	−8.39919	−	1.56155i	−1.71448	−	0.318751i
$25$		0			0
$26$	2.35829	+	1.56155i	0.462500	+	0.306246i
$27$	9.43318			1.81542
$28$	−1.08464	+	5.17915i	−0.204977	+	0.978767i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	3.39228			0.609272			0.304636	−	0.952469i	$-0.401465\pi$
$31$	3.39228			0.609272			0.304636	+	0.952469i	$0.401465\pi$
$32$	1.21922	+	5.52390i	0.215530	+	0.976497i
$33$		−	14.2462i		−	2.47995i
$34$	1.32431	+	0.876894i	0.227117	+	0.150386i
$35$		0			0
$36$	−4.78078	−	11.2745i	−0.796796	−	1.87908i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	3.68260	−	5.56155i	0.597397	−	0.902203i
$39$			6.04090i			0.967317i
$40$		0			0
$41$			1.12311i			0.175400i	0.996147	+	0.0876998i	$0.0279516\pi$
$41$			1.12311i			0.175400i	−0.996147	+	0.0876998i	$0.972048\pi$
$42$	−10.5018	+	4.17548i	−1.62047	+	0.644291i
$43$		−	0.371834i		−	0.0567042i	−0.999598	−	0.0283521i	$-0.990974\pi$
$43$		−	0.371834i		−	0.0567042i	0.999598	−	0.0283521i	$-0.00902596\pi$
$44$	−8.68466	+	3.68260i	−1.30926	+	0.555173i
$45$		0			0
$46$	7.56155	+	5.00691i	1.11489	+	0.738228i
$47$	5.08842			0.742223			0.371111	−	0.928588i	$-0.378977\pi$
$47$	5.08842			0.742223			0.371111	+	0.928588i	$0.378977\pi$
$48$	−8.39919	+	8.68466i	−1.21232	+	1.25352i
$49$	2.43845	+	6.56155i	0.348350	+	0.937365i
$50$		0			0
$51$			3.39228i			0.475014i
$52$	3.68260	−	1.56155i	0.510685	−	0.216548i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	7.36520	−	11.1231i	1.00228	−	1.51366i
$55$		0			0
$56$	5.26012	+	5.32270i	0.702913	+	0.711276i
$57$	14.2462			1.88696
$58$	−1.56155	+	2.35829i	−0.205042	+	0.309659i
$59$	2.06798			0.269227			0.134614	−	0.990898i	$-0.457021\pi$
$59$	2.06798			0.269227			0.134614	+	0.990898i	$0.457021\pi$
$60$		0			0
$61$		−	2.00000i		−	0.256074i	−0.991769	−	0.128037i	$-0.959132\pi$
$61$		−	2.00000i		−	0.256074i	0.991769	−	0.128037i	$-0.0408676\pi$
$62$	2.64861	−	4.00000i	0.336374	−	0.508001i
$63$	−13.3017	−	9.24726i	−1.67586	−	1.16505i
$64$	7.46543	+	2.87529i	0.933179	+	0.359411i
$65$		0			0
$66$	−16.7984	−	11.1231i	−2.06774	−	1.36916i
$67$		−	3.76412i		−	0.459860i	−0.973207	−	0.229930i	$-0.926150\pi$
$67$		−	3.76412i		−	0.459860i	0.973207	−	0.229930i	$-0.0738497\pi$
$68$	2.06798	−	0.876894i	0.250779	−	0.106339i
$69$			19.3693i			2.33179i
$70$		0			0
$71$			7.36520i			0.874089i	0.899440	+	0.437044i	$0.143975\pi$
$71$			7.36520i			0.874089i	−0.899440	+	0.437044i	$0.856025\pi$
$72$	−17.0270	−	3.16561i	−2.00665	−	0.373070i
$73$			15.3693i			1.79884i	0.437083	+	0.899421i	$0.356012\pi$
$73$			15.3693i			1.79884i	−0.437083	+	0.899421i	$0.643988\pi$
$74$	−1.56155	+	2.35829i	−0.181527	+	0.274146i
$75$		0			0
$76$	−3.68260	−	8.68466i	−0.422423	−	0.996199i
$77$	−7.12311	+	10.2462i	−0.811753	+	1.16766i
$78$	7.12311	+	4.71659i	0.806533	+	0.534049i
$79$		−	1.32431i		−	0.148996i	−0.997221	−	0.0744981i	$-0.976265\pi$
$79$		−	1.32431i		−	0.148996i	0.997221	−	0.0744981i	$-0.0237355\pi$
$80$		0			0
$81$	10.1231			1.12479
$82$	1.32431	+	0.876894i	0.146245	+	0.0968368i
$83$	3.02045			0.331537			0.165769	−	0.986165i	$-0.446990\pi$
$83$	3.02045			0.331537			0.165769	+	0.986165i	$0.446990\pi$
$84$	−3.27608	+	15.6433i	−0.357450	+	1.70683i
$85$		0			0
$86$	−0.438447	−	0.290319i	−0.0472790	−	0.0313059i
$87$	−6.04090			−0.647652
$88$	−2.43845	+	13.1158i	−0.259939	+	1.39815i
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		0			0
$91$	3.02045	−	4.34475i	0.316629	−	0.455454i
$92$	11.8078	−	5.00691i	1.23104	−	0.522006i
$93$	10.2462			1.06248
$94$	3.97292	−	6.00000i	0.409775	−	0.618853i
$95$		0			0
$96$	3.68260	+	16.6847i	0.375854	+	1.70287i
$97$		−	1.12311i		−	0.114034i	−0.998373	−	0.0570170i	$-0.981841\pi$
$97$		−	1.12311i		−	0.114034i	0.998373	−	0.0570170i	$-0.0181589\pi$
$98$	9.64092	+	2.24782i	0.973880	+	0.227064i
$99$		−	28.8802i		−	2.90257i
$100$		0			0
$101$			15.1231i			1.50481i	0.658703	+	0.752403i	$0.271105\pi$
$101$			15.1231i			1.50481i	−0.658703	+	0.752403i	$0.728895\pi$
$102$	4.00000	+	2.64861i	0.396059	+	0.262252i
$103$	−7.73704			−0.762353			−0.381176	−	0.924502i	$-0.624481\pi$
$103$	−7.73704			−0.762353			−0.381176	+	0.924502i	$0.624481\pi$
$104$	1.03399	−	5.56155i	0.101391	−	0.545355i
$105$		0			0
$106$	−1.56155	+	2.35829i	−0.151671	+	0.229058i
$107$		−	5.66906i		−	0.548049i	−0.961723	−	0.274024i	$-0.911645\pi$
$107$		−	5.66906i		−	0.548049i	0.961723	−	0.274024i	$-0.0883549\pi$
$108$	−7.36520	−	17.3693i	−0.708717	−	1.67136i
$109$	−7.12311			−0.682270			−0.341135	−	0.940014i	$-0.610811\pi$
$109$	−7.12311			−0.682270			−0.341135	+	0.940014i	$0.610811\pi$
$110$		0			0
$111$	−6.04090			−0.573376
$112$	10.3832	−	2.04662i	0.981123	−	0.193387i
$113$	−18.4924			−1.73962			−0.869810	−	0.493386i	$-0.835759\pi$
$113$	−18.4924			−1.73962			−0.869810	+	0.493386i	$0.835759\pi$
$114$	11.1231	−	16.7984i	1.04177	−	1.57331i
$115$		0			0
$116$	1.56155	+	3.68260i	0.144987	+	0.341921i
$117$			12.2462i			1.13216i
$118$	1.61463	−	2.43845i	0.148638	−	0.224477i
$119$	1.69614	−	2.43981i	0.155485	−	0.223657i
$120$		0			0
$121$	−11.2462			−1.02238
$122$	−2.35829	−	1.56155i	−0.213510	−	0.141376i
$123$			3.39228i			0.305872i
$124$	−2.64861	−	6.24621i	−0.237853	−	0.560926i
$125$		0			0
$126$	−21.2895	+	8.46462i	−1.89662	+	0.754088i
$127$		−	17.7509i		−	1.57513i	−0.616229	−	0.787567i	$-0.711341\pi$
$127$		−	17.7509i		−	1.57513i	0.616229	−	0.787567i	$-0.288659\pi$
$128$	9.21922	−	6.55789i	0.814872	−	0.579641i
$129$		−	1.12311i		−	0.0988839i
$130$		0			0
$131$	−17.5420			−1.53266			−0.766328	−	0.642450i	$-0.777918\pi$
$131$	−17.5420			−1.53266			−0.766328	+	0.642450i	$0.777918\pi$
$132$	−26.2316	+	11.1231i	−2.28316	+	0.968142i
$133$	−10.2462	−	7.12311i	−0.888459	−	0.617652i
$134$	−4.43845	−	2.93893i	−0.383423	−	0.253885i
$135$		0			0
$136$	0.580639	−	3.12311i	0.0497894	−	0.267804i
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$	22.8393	+	15.1231i	1.94421	+	1.28736i
$139$	−16.7984			−1.42482			−0.712410	−	0.701763i	$-0.752396\pi$
$139$	−16.7984			−1.42482			−0.712410	+	0.701763i	$0.752396\pi$
$140$		0			0
$141$	15.3693			1.29433
$142$	8.68466	+	5.75058i	0.728800	+	0.482578i
$143$	9.43318			0.788842
$144$	−17.0270	+	17.6057i	−1.41892	+	1.46714i
$145$		0			0
$146$	18.1227	+	12.0000i	1.49984	+	0.993127i
$147$	7.36520	+	19.8188i	0.607472	+	1.63463i
$148$	1.56155	+	3.68260i	0.128359	+	0.302708i
$149$	5.36932			0.439872			0.219936	−	0.975514i	$-0.429415\pi$
$149$	5.36932			0.439872			0.219936	+	0.975514i	$0.429415\pi$
$150$		0			0
$151$			10.0138i			0.814913i	0.913225	+	0.407456i	$0.133584\pi$
$151$			10.0138i			0.814913i	−0.913225	+	0.407456i	$0.866416\pi$
$152$	−13.1158	−	2.43845i	−1.06383	−	0.197784i
$153$			6.87689i			0.555964i
$154$	6.52024	+	16.3992i	0.525416	+	1.32148i
$155$		0			0
$156$	11.1231	−	4.71659i	0.890561	−	0.377629i
$157$		−	0.246211i		−	0.0196498i	−0.999952	−	0.00982490i	$-0.996873\pi$
$157$		−	0.246211i		−	0.0196498i	0.999952	−	0.00982490i	$-0.00312741\pi$
$158$	−1.56155	−	1.03399i	−0.124230	−	0.0822596i
$159$	−6.04090			−0.479074
$160$		0			0
$161$	9.68466	−	13.9309i	0.763258	−	1.09791i
$162$	7.90388	−	11.9366i	0.620988	−	0.937830i
$163$			3.02045i			0.236580i	0.992979	+	0.118290i	$0.0377412\pi$
$163$			3.02045i			0.236580i	−0.992979	+	0.118290i	$0.962259\pi$
$164$	2.06798	−	0.876894i	0.161482	−	0.0684739i
$165$		0			0
$166$	2.35829	−	3.56155i	0.183039	−	0.276430i
$167$	−19.8188			−1.53363			−0.766813	−	0.641870i	$-0.778159\pi$
$167$	−19.8188			−1.53363			−0.766813	+	0.641870i	$0.778159\pi$
$168$	15.8879	+	16.0769i	1.22578	+	1.24036i
$169$	9.00000			0.692308
$170$		0			0
$171$	28.8802			2.20852
$172$	−0.684658	+	0.290319i	−0.0522047	+	0.0221366i
$173$		−	16.2462i		−	1.23518i	−0.786502	−	0.617588i	$-0.788110\pi$
$173$		−	16.2462i		−	1.23518i	0.786502	−	0.617588i	$-0.211890\pi$
$174$	−4.71659	+	7.12311i	−0.357564	+	0.540001i
$175$		0			0
$176$	13.5616	+	13.1158i	1.02224	+	0.988639i
$177$	6.24621			0.469494
$178$	−14.1498	−	9.36932i	−1.06057	−	0.702260i
$179$			10.7575i			0.804052i	0.915628	+	0.402026i	$0.131694\pi$
$179$			10.7575i			0.804052i	−0.915628	+	0.402026i	$0.868306\pi$
$180$		0			0
$181$			15.1231i			1.12409i	0.827106	+	0.562046i	$0.189986\pi$
$181$			15.1231i			1.12409i	−0.827106	+	0.562046i	$0.810014\pi$
$182$	−2.76481	−	6.95383i	−0.204941	−	0.515453i
$183$		−	6.04090i		−	0.446556i
$184$	3.31534	−	17.8324i	0.244410	−	1.31462i
$185$		0			0
$186$	8.00000	−	12.0818i	0.586588	−	0.885880i
$187$	5.29723			0.387372
$188$	−3.97292	−	9.36932i	−0.289755	−	0.683328i
$189$	−20.4924	−	14.2462i	−1.49060	−	1.03626i
$190$		0			0
$191$		−	16.7984i		−	1.21549i	−0.794133	−	0.607744i	$-0.792075\pi$
$191$		−	16.7984i		−	1.21549i	0.794133	−	0.607744i	$-0.207925\pi$
$192$	22.5490	+	8.68466i	1.62733	+	0.626761i
$193$	22.4924			1.61904			0.809520	−	0.587092i	$-0.199727\pi$
$193$	22.4924			1.61904			0.809520	+	0.587092i	$0.199727\pi$
$194$	−1.32431	−	0.876894i	−0.0950797	−	0.0629573i
$195$		0			0
$196$	10.1779	−	9.61302i	0.726994	−	0.686644i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−34.0540	−	22.5490i	−2.42011	−	1.60248i
$199$	26.8122			1.90067			0.950333	−	0.311235i	$-0.100742\pi$
$199$	26.8122			1.90067			0.950333	+	0.311235i	$0.100742\pi$
$200$		0			0
$201$		−	11.3693i		−	0.801930i
$202$	17.8324	+	11.8078i	1.25468	+	0.830791i
$203$	4.34475	+	3.02045i	0.304942	+	0.211994i
$204$	6.24621	−	2.64861i	0.437322	−	0.185440i
$205$		0			0
$206$	−6.04090	+	9.12311i	−0.420889	+	0.635637i
$207$			39.2658i			2.72916i
$208$	−5.75058	−	5.56155i	−0.398731	−	0.385624i
$209$		−	22.2462i		−	1.53880i
$210$		0			0
$211$		−	22.0956i		−	1.52112i	−0.649265	−	0.760562i	$-0.724923\pi$
$211$		−	22.0956i		−	1.52112i	0.649265	−	0.760562i	$-0.275077\pi$
$212$	1.56155	+	3.68260i	0.107248	+	0.252922i
$213$			22.2462i			1.52429i
$214$	−6.68466	−	4.42627i	−0.456954	−	0.302574i
$215$		0			0
$216$	−26.2316	−	4.87689i	−1.78483	−	0.331831i
$217$	−7.36932	−	5.12311i	−0.500262	−	0.347779i
$218$	−5.56155	+	8.39919i	−0.376676	+	0.568865i
$219$			46.4222i			3.13692i
$220$		0			0
$221$	−2.24621			−0.151097
$222$	−4.71659	+	7.12311i	−0.316557	+	0.478072i
$223$	20.5625			1.37697			0.688483	−	0.725252i	$-0.258277\pi$
$223$	20.5625			1.37697			0.688483	+	0.725252i	$0.258277\pi$
$224$	5.69372	−	13.8413i	0.380427	−	0.924811i
$225$		0			0
$226$	−14.4384	+	21.8053i	−0.960431	+	1.45047i
$227$	−3.76412			−0.249833			−0.124917	−	0.992167i	$-0.539866\pi$
$227$	−3.76412			−0.249833			−0.124917	+	0.992167i	$0.539866\pi$
$228$	−11.1231	−	26.2316i	−0.736646	−	1.73723i
$229$			12.8769i			0.850929i	0.904975	+	0.425465i	$0.139889\pi$
$229$			12.8769i			0.850929i	−0.904975	+	0.425465i	$0.860111\pi$
$230$		0			0
$231$	−21.5150	+	30.9481i	−1.41558	+	2.03624i
$232$	5.56155	+	1.03399i	0.365134	+	0.0678846i
$233$	−7.75379			−0.507968			−0.253984	−	0.967208i	$-0.581741\pi$
$233$	−7.75379			−0.507968			−0.253984	+	0.967208i	$0.581741\pi$
$234$	14.4401	+	9.56155i	0.943978	+	0.625058i
$235$		0			0
$236$	−1.61463	−	3.80776i	−0.105103	−	0.247864i
$237$		−	4.00000i		−	0.259828i
$238$	−1.55259	−	3.90495i	−0.100639	−	0.253120i
$239$		−	3.97292i		−	0.256987i	−0.991710	−	0.128493i	$-0.958986\pi$
$239$		−	3.97292i		−	0.256987i	0.991710	−	0.128493i	$-0.0410141\pi$
$240$		0			0
$241$			25.6155i			1.65004i	0.565103	+	0.825021i	$0.308837\pi$
$241$			25.6155i			1.65004i	−0.565103	+	0.825021i	$0.691163\pi$
$242$	−8.78078	+	13.2609i	−0.564450	+	0.852445i
$243$	2.27678			0.146055
$244$	−3.68260	+	1.56155i	−0.235754	+	0.0999682i
$245$		0			0
$246$	4.00000	+	2.64861i	0.255031	+	0.168869i
$247$			9.43318i			0.600219i
$248$	−9.43318	−	1.75379i	−0.599007	−	0.111366i
$249$	9.12311			0.578153
$250$		0			0
$251$	16.0547			1.01336			0.506682	−	0.862133i	$-0.330872\pi$
$251$	16.0547			1.01336			0.506682	+	0.862133i	$0.330872\pi$
$252$	−6.64134	+	31.7125i	−0.418365	+	1.99770i
$253$	30.2462			1.90156
$254$	−20.9309	−	13.8594i	−1.31332	−	0.869619i
$255$		0			0
$256$	−0.534565	−	15.9911i	−0.0334103	−	0.999442i
$257$		−	11.3693i		−	0.709199i	−0.935018	−	0.354599i	$-0.884617\pi$
$257$		−	11.3693i		−	0.709199i	0.935018	−	0.354599i	$-0.115383\pi$
$258$	−1.32431	−	0.876894i	−0.0824477	−	0.0545931i
$259$	4.34475	+	3.02045i	0.269970	+	0.187682i
$260$		0			0
$261$	−12.2462			−0.758021
$262$	−13.6964	+	20.6847i	−0.846168	+	1.27790i
$263$		−	18.4945i		−	1.14042i	−0.821499	−	0.570211i	$-0.806862\pi$
$263$		−	18.4945i		−	1.14042i	0.821499	−	0.570211i	$-0.193138\pi$
$264$	−7.36520	+	39.6155i	−0.453297	+	2.43817i
$265$		0			0
$266$	−16.3992	+	6.52024i	−1.00550	+	0.399781i
$267$		−	36.2454i		−	2.21818i
$268$	−6.93087	+	2.93893i	−0.423370	+	0.179524i
$269$			0.246211i			0.0150118i	0.999972	+	0.00750588i	$0.00238922\pi$
$269$			0.246211i			0.0150118i	−0.999972	+	0.00750588i	$0.997611\pi$
$270$		0			0
$271$	−1.90495			−0.115717			−0.0578586	−	0.998325i	$-0.518427\pi$
$271$	−1.90495			−0.115717			−0.0578586	+	0.998325i	$0.518427\pi$
$272$	−3.22925	−	3.12311i	−0.195802	−	0.189366i
$273$	9.12311	−	13.1231i	0.552155	−	0.794246i
$274$	10.9309	−	16.5081i	0.660358	−	0.997288i
$275$		0			0
$276$	35.6647	−	15.1231i	2.14676	−	0.910304i
$277$	−12.2462			−0.735804			−0.367902	−	0.929865i	$-0.619924\pi$
$277$	−12.2462			−0.735804			−0.367902	+	0.929865i	$0.619924\pi$
$278$	−13.1158	+	19.8078i	−0.786632	+	1.18799i
$279$	20.7713			1.24355
$280$		0			0
$281$	−29.3693			−1.75203			−0.876013	−	0.482287i	$-0.839806\pi$
$281$	−29.3693			−1.75203			−0.876013	+	0.482287i	$0.839806\pi$
$282$	12.0000	−	18.1227i	0.714590	−	1.07919i
$283$	−4.92539			−0.292784			−0.146392	−	0.989227i	$-0.546766\pi$
$283$	−4.92539			−0.292784			−0.146392	+	0.989227i	$0.546766\pi$
$284$	13.5616	−	5.75058i	0.804730	−	0.341234i
$285$		0			0
$286$	7.36520	−	11.1231i	0.435514	−	0.657723i
$287$	1.69614	−	2.43981i	0.100120	−	0.144017i
$288$	7.46543	+	33.8234i	0.439905	+	1.99307i
$289$	15.7386			0.925802
$290$		0			0
$291$		−	3.39228i		−	0.198859i
$292$	28.2995	−	12.0000i	1.65610	−	0.702247i
$293$		−	15.7538i		−	0.920346i	−0.887829	−	0.460173i	$-0.847787\pi$
$293$		−	15.7538i		−	0.920346i	0.887829	−	0.460173i	$-0.152213\pi$
$294$	29.1199	+	6.78942i	1.69831	+	0.395967i
$295$		0			0
$296$	5.56155	+	1.03399i	0.323259	+	0.0600993i
$297$		−	44.4924i		−	2.58171i
$298$	4.19224	−	6.33122i	0.242850	−	0.366757i
$299$	−12.8255			−0.741715
$300$		0			0
$301$	−0.561553	+	0.807764i	−0.0323674	+	0.0465587i
$302$	11.8078	+	7.81855i	0.679460	+	0.449907i
$303$			45.6786i			2.62416i
$304$	−13.1158	+	13.5616i	−0.752242	+	0.777808i
$305$		0			0
$306$	8.10887	+	5.36932i	0.463553	+	0.306943i
$307$	1.53311			0.0874993			0.0437496	−	0.999043i	$-0.486070\pi$
$307$	1.53311			0.0874993			0.0437496	+	0.999043i	$0.486070\pi$
$308$	24.4279	+	5.11578i	1.39191	+	0.291499i
$309$	−23.3693			−1.32943
$310$		0			0
$311$	−30.2045			−1.71274			−0.856369	−	0.516364i	$-0.827285\pi$
$311$	−30.2045			−1.71274			−0.856369	+	0.516364i	$0.827285\pi$
$312$	3.12311	−	16.7984i	0.176811	−	0.951021i
$313$			33.6155i			1.90006i	0.312156	+	0.950031i	$0.398949\pi$
$313$			33.6155i			1.90006i	−0.312156	+	0.950031i	$0.601051\pi$
$314$	−0.290319	−	0.192236i	−0.0163837	−	0.0108485i
$315$		0			0
$316$	−2.43845	+	1.03399i	−0.137173	+	0.0581663i
$317$	−12.2462			−0.687816			−0.343908	−	0.939003i	$-0.611751\pi$
$317$	−12.2462			−0.687816			−0.343908	+	0.939003i	$0.611751\pi$
$318$	−4.71659	+	7.12311i	−0.264493	+	0.399444i
$319$			9.43318i			0.528157i
$320$		0			0
$321$		−	17.1231i		−	0.955719i
$322$	−8.86499	−	22.2965i	−0.494027	−	1.24254i
$323$			5.29723i			0.294746i
$324$	−7.90388	−	18.6397i	−0.439105	−	1.03554i
$325$		0			0
$326$	3.56155	+	2.35829i	0.197256	+	0.130614i
$327$	−21.5150			−1.18978
$328$	0.580639	−	3.12311i	0.0320604	−	0.172445i
$329$	−11.0540	−	7.68466i	−0.609425	−	0.423669i
$330$		0			0
$331$		−	18.2857i		−	1.00507i	−0.864556	−	0.502537i	$-0.832400\pi$
$331$		−	18.2857i		−	1.00507i	0.864556	−	0.502537i	$-0.167600\pi$
$332$	−2.35829	−	5.56155i	−0.129428	−	0.305230i
$333$	−12.2462			−0.671088
$334$	−15.4741	+	23.3693i	−0.846704	+	1.27871i
$335$		0			0
$336$	31.3620	−	6.18170i	1.71094	−	0.337239i
$337$	12.2462			0.667094			0.333547	−	0.942734i	$-0.391754\pi$
$337$	12.2462			0.667094			0.333547	+	0.942734i	$0.391754\pi$
$338$	7.02699	−	10.6123i	0.382218	−	0.577234i
$339$	−55.8554			−3.03365
$340$		0			0
$341$		−	16.0000i		−	0.866449i
$342$	22.5490	−	34.0540i	1.21931	−	1.84143i
$343$	4.61219	−	17.9368i	0.249035	−	0.968495i
$344$	−0.192236	+	1.03399i	−0.0103647	+	0.0557489i
$345$		0			0
$346$	−19.1567	−	12.6847i	−1.02987	−	0.681931i
$347$		−	5.66906i		−	0.304331i	−0.988355	−	0.152166i	$-0.951375\pi$
$347$		−	5.66906i		−	0.304331i	0.988355	−	0.152166i	$-0.0486247\pi$
$348$	4.71659	+	11.1231i	0.252836	+	0.596261i
$349$		−	29.8617i		−	1.59846i	−0.601024	−	0.799231i	$-0.705240\pi$
$349$		−	29.8617i		−	1.59846i	0.601024	−	0.799231i	$-0.294760\pi$
$350$		0			0
$351$			18.8664i			1.00701i
$352$	26.0540	−	5.75058i	1.38868	−	0.306507i
$353$		−	19.3693i		−	1.03092i	−0.856912	−	0.515462i	$-0.827620\pi$
$353$		−	19.3693i		−	1.03092i	0.856912	−	0.515462i	$-0.172380\pi$
$354$	4.87689	−	7.36520i	0.259204	−	0.391456i
$355$		0			0
$356$	−22.0956	+	9.36932i	−1.17106	+	0.496573i
$357$	5.12311	−	7.36932i	0.271144	−	0.390026i
$358$	12.6847	+	8.39919i	0.670405	+	0.443911i
$359$		−	16.0547i		−	0.847335i	−0.905818	−	0.423668i	$-0.860742\pi$
$359$		−	16.0547i		−	0.847335i	0.905818	−	0.423668i	$-0.139258\pi$
$360$		0			0
$361$	3.24621			0.170853
$362$	17.8324	+	11.8078i	0.937248	+	0.620602i
$363$	−33.9686			−1.78289
$364$	−10.3583	−	2.16927i	−0.542922	−	0.113701i
$365$		0			0
$366$	−7.12311	−	4.71659i	−0.372331	−	0.246540i
$367$	−10.3857			−0.542127			−0.271063	−	0.962562i	$-0.587375\pi$
$367$	−10.3857			−0.542127			−0.271063	+	0.962562i	$0.587375\pi$
$368$	−18.4384	−	17.8324i	−0.961171	−	0.929576i
$369$			6.87689i			0.357997i
$370$		0			0
$371$	4.34475	+	3.02045i	0.225568	+	0.156814i
$372$	−8.00000	−	18.8664i	−0.414781	−	0.978175i
$373$	10.4924			0.543277			0.271639	−	0.962399i	$-0.412434\pi$
$373$	10.4924			0.543277			0.271639	+	0.962399i	$0.412434\pi$
$374$	4.13595	−	6.24621i	0.213865	−	0.322984i
$375$		0			0
$376$	−14.1498	−	2.63068i	−0.729719	−	0.135667i
$377$		−	4.00000i		−	0.206010i
$378$	−32.7984	+	13.0405i	−1.68697	+	0.670730i
$379$		−	14.8934i		−	0.765024i	−0.923950	−	0.382512i	$-0.875059\pi$
$379$		−	14.8934i		−	0.765024i	0.923950	−	0.382512i	$-0.124941\pi$
$380$		0			0
$381$		−	53.6155i		−	2.74681i
$382$	−19.8078	−	13.1158i	−1.01345	−	0.671062i
$383$	−19.0752			−0.974695			−0.487348	−	0.873208i	$-0.662036\pi$
$383$	−19.0752			−0.974695			−0.487348	+	0.873208i	$0.662036\pi$
$384$	27.8462	−	19.8078i	1.42102	−	1.01081i
$385$		0			0
$386$	17.5616	−	26.5219i	0.893860	−	1.34993i
$387$		−	2.27678i		−	0.115735i
$388$	−2.06798	+	0.876894i	−0.104986	+	0.0445176i
$389$	−7.12311			−0.361156			−0.180578	−	0.983561i	$-0.557797\pi$
$389$	−7.12311			−0.361156			−0.180578	+	0.983561i	$0.557797\pi$
$390$		0			0
$391$	−7.20217			−0.364230
$392$	−3.38849	−	19.5069i	−0.171145	−	0.985246i
$393$	−52.9848			−2.67273
$394$	−14.0540	+	21.2247i	−0.708029	+	1.06928i
$395$		0			0
$396$	−53.1771	+	22.5490i	−2.67225	+	1.13313i
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$	20.9343	−	31.6155i	1.04934	−	1.58474i
$399$	−30.9481	−	21.5150i	−1.54935	−	1.07710i
$400$		0			0
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−13.4061	−	8.87689i	−0.668635	−	0.442739i
$403$			6.78456i			0.337963i
$404$	27.8462	−	11.8078i	1.38540	−	0.587458i
$405$		0			0
$406$	6.95383	−	2.76481i	0.345113	−	0.137215i
$407$			9.43318i			0.467585i
$408$	1.75379	−	9.43318i	0.0868255	−	0.467012i
$409$			17.1231i			0.846683i	0.905970	+	0.423342i	$0.139143\pi$
$409$			17.1231i			0.846683i	−0.905970	+	0.423342i	$0.860857\pi$
$410$		0			0
$411$	42.2863			2.08583
$412$	6.04090	+	14.2462i	0.297614	+	0.701860i
$413$	−4.49242	−	3.12311i	−0.221058	−	0.153678i
$414$	46.3002	+	30.6578i	2.27553	+	1.50675i
$415$		0			0
$416$	−11.0478	+	2.43845i	−0.541663	+	0.119555i
$417$	−50.7386			−2.48468
$418$	−26.2316	−	17.3693i	−1.28303	−	0.849561i
$419$	23.5829			1.15210			0.576051	−	0.817414i	$-0.304593\pi$
$419$	23.5829			1.15210			0.576051	+	0.817414i	$0.304593\pi$
$420$		0			0
$421$	23.6155			1.15095			0.575475	−	0.817819i	$-0.304817\pi$
$421$	23.6155			1.15095			0.575475	+	0.817819i	$0.304817\pi$
$422$	−26.0540	−	17.2517i	−1.26829	−	0.839801i
$423$	31.1570			1.51490
$424$	5.56155	+	1.03399i	0.270093	+	0.0502149i
$425$		0			0
$426$	26.2316	+	17.3693i	1.27092	+	0.841546i
$427$	−3.02045	+	4.34475i	−0.146170	+	0.210257i
$428$	−10.4384	+	4.42627i	−0.504561	+	0.213952i
$429$	28.4924			1.37563
$430$		0			0
$431$		−	5.87787i		−	0.283127i	−0.989929	−	0.141563i	$-0.954787\pi$
$431$		−	5.87787i		−	0.283127i	0.989929	−	0.141563i	$-0.0452129\pi$
$432$	−26.2316	+	27.1231i	−1.26207	+	1.30496i
$433$			29.6155i			1.42323i	0.702569	+	0.711616i	$0.252036\pi$
$433$			29.6155i			1.42323i	−0.702569	+	0.711616i	$0.747964\pi$
$434$	−11.7947	+	4.68951i	−0.566163	+	0.225104i
$435$		0			0
$436$	5.56155	+	13.1158i	0.266350	+	0.628132i
$437$			30.2462i			1.44687i
$438$	54.7386	+	36.2454i	2.61551	+	1.73187i
$439$	−16.2177			−0.774031			−0.387015	−	0.922073i	$-0.626494\pi$
$439$	−16.2177			−0.774031			−0.387015	+	0.922073i	$0.626494\pi$
$440$		0			0
$441$	14.9309	+	40.1771i	0.710994	+	1.91319i
$442$	−1.75379	+	2.64861i	−0.0834192	+	0.125982i
$443$		−	23.0481i		−	1.09505i	−0.836790	−	0.547524i	$-0.815571\pi$
$443$		−	23.0481i		−	1.09505i	0.836790	−	0.547524i	$-0.184429\pi$
$444$	4.71659	+	11.1231i	0.223839	+	0.527879i
$445$		0			0
$446$	16.0547	−	24.2462i	0.760213	−	1.14809i
$447$	16.2177			0.767073
$448$	−11.8754	−	17.5207i	−0.561061	−	0.827775i
$449$	−15.6155			−0.736942			−0.368471	−	0.929639i	$-0.620119\pi$
$449$	−15.6155			−0.736942			−0.368471	+	0.929639i	$0.620119\pi$
$450$		0			0
$451$	5.29723			0.249437
$452$	14.4384	+	34.0501i	0.679127	+	1.60158i
$453$			30.2462i			1.42109i
$454$	−2.93893	+	4.43845i	−0.137931	+	0.208307i
$455$		0			0
$456$	−39.6155	−	7.36520i	−1.85517	−	0.344907i
$457$	−6.00000			−0.280668			−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000			−0.280668			−0.140334	+	0.990104i	$0.544818\pi$
$458$	15.1838	+	10.0540i	0.709490	+	0.469791i
$459$			10.5945i			0.494507i
$460$		0			0
$461$		−	3.61553i		−	0.168392i	−0.996449	−	0.0841960i	$-0.973168\pi$
$461$		−	3.61553i		−	0.168392i	0.996449	−	0.0841960i	$-0.0268322\pi$
$462$	19.6940	+	49.5329i	0.916250	+	2.30448i
$463$		−	28.6714i		−	1.33247i	−0.745741	−	0.666236i	$-0.767904\pi$
$463$		−	28.6714i		−	1.33247i	0.745741	−	0.666236i	$-0.232096\pi$
$464$	5.56155	−	5.75058i	0.258189	−	0.266964i
$465$		0			0
$466$	−6.05398	+	9.14286i	−0.280445	+	0.423535i
$467$	18.4945			0.855824			0.427912	−	0.903820i	$-0.359249\pi$
$467$	18.4945			0.855824			0.427912	+	0.903820i	$0.359249\pi$
$468$	22.5490	−	9.56155i	1.04233	−	0.441983i
$469$	−5.68466	+	8.17708i	−0.262493	+	0.377583i
$470$		0			0
$471$		−	0.743668i		−	0.0342664i
$472$	−5.75058	−	1.06913i	−0.264692	−	0.0492107i
$473$	−1.75379			−0.0806393
$474$	−4.71659	−	3.12311i	−0.216640	−	0.143449i
$475$		0			0
$476$	−5.81673	−	1.21816i	−0.266609	−	0.0558343i
$477$	−12.2462			−0.560715
$478$	−4.68466	−	3.10196i	−0.214271	−	0.141880i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		−	4.00000i		−	0.182384i
$482$	30.2045	+	20.0000i	1.37578	+	0.910975i
$483$	29.2520	−	42.0775i	1.33101	−	1.91459i
$484$	8.78078	+	20.7077i	0.399126	+	0.941257i
$485$		0			0
$486$	1.77766	−	2.68466i	0.0806361	−	0.121779i
$487$			13.1973i			0.598026i	0.954249	+	0.299013i	$0.0966575\pi$
$487$			13.1973i			0.598026i	−0.954249	+	0.299013i	$0.903343\pi$
$488$	−1.03399	+	5.56155i	−0.0468064	+	0.251760i
$489$			9.12311i			0.412561i
$490$		0			0
$491$			31.5288i			1.42287i	0.702750	+	0.711437i	$0.251955\pi$
$491$			31.5288i			1.42287i	−0.702750	+	0.711437i	$0.748045\pi$
$492$	6.24621	−	2.64861i	0.281601	−	0.119409i
$493$		−	2.24621i		−	0.101164i
$494$	11.1231	+	7.36520i	0.500452	+	0.331376i
$495$		0			0
$496$	−9.43318	+	9.75379i	−0.423562	+	0.437958i
$497$	11.1231	−	16.0000i	0.498939	−	0.717698i
$498$	7.12311	−	10.7575i	0.319194	−	0.482054i
$499$			24.3266i			1.08901i	0.838758	+	0.544504i	$0.183282\pi$
$499$			24.3266i			1.08901i	−0.838758	+	0.544504i	$0.816718\pi$
$500$		0			0
$501$	−59.8617			−2.67443
$502$	12.5351	−	18.9309i	0.559471	−	0.844926i
$503$	−17.9139			−0.798741			−0.399370	−	0.916790i	$-0.630771\pi$
$503$	−17.9139			−0.798741			−0.399370	+	0.916790i	$0.630771\pi$
$504$	32.2083	+	32.5915i	1.43467	+	1.45174i
$505$		0			0
$506$	23.6155	−	35.6647i	1.04984	−	1.58549i
$507$	27.1840			1.20729
$508$	−32.6847	+	13.8594i	−1.45015	+	0.614914i
$509$			23.6155i			1.04674i	0.852106	+	0.523370i	$0.175325\pi$
$509$			23.6155i			1.04674i	−0.852106	+	0.523370i	$0.824675\pi$
$510$		0			0
$511$	23.2111	−	33.3880i	1.02680	−	1.47700i
$512$	−19.2732	−	11.8551i	−0.851763	−	0.523927i
$513$	44.4924			1.96439
$514$	−13.4061	−	8.87689i	−0.591318	−	0.391543i
$515$		0			0
$516$	−2.06798	+	0.876894i	−0.0910375	+	0.0386031i
$517$		−	24.0000i		−	1.05552i
$518$	6.95383	−	2.76481i	0.305534	−	0.121479i
$519$		−	49.0708i		−	2.15397i
$520$		0			0
$521$			9.75379i			0.427321i	0.976908	+	0.213661i	$0.0685387\pi$
$521$			9.75379i			0.427321i	−0.976908	+	0.213661i	$0.931461\pi$
$522$	−9.56155	+	14.4401i	−0.418498	+	0.632025i
$523$	19.2382			0.841227			0.420614	−	0.907240i	$-0.361815\pi$
$523$	19.2382			0.841227			0.420614	+	0.907240i	$0.361815\pi$
$524$	13.6964	+	32.3002i	0.598331	+	1.41104i
$525$		0			0
$526$	−21.8078	−	14.4401i	−0.950864	−	0.629618i
$527$			3.80989i			0.165961i
$528$	40.9620	+	39.6155i	1.78264	+	1.72404i
$529$	−18.1231			−0.787961
$530$		0			0
$531$	12.6624			0.549503
$532$	−5.11578	+	24.4279i	−0.221797	+	1.05908i
$533$	−2.24621			−0.0972942
$534$	−42.7386	−	28.2995i	−1.84948	−	1.22464i
$535$		0			0
$536$	−1.94602	+	10.4672i	−0.0840555	+	0.452113i
$537$			32.4924i			1.40215i
$538$	0.290319	+	0.192236i	0.0125166	+	0.00828788i
$539$	30.9481	−	11.5012i	1.33303	−	0.495390i
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	−1.48734	+	2.24621i	−0.0638866	+	0.0964830i
$543$			45.6786i			1.96025i
$544$	−6.20393	+	1.36932i	−0.265991	+	0.0587090i
$545$		0			0
$546$	−8.35097	−	21.0037i	−0.357388	−	0.898875i
$547$			30.5763i			1.30735i	0.756776	+	0.653674i	$0.226773\pi$
$547$			30.5763i			1.30735i	−0.756776	+	0.653674i	$0.773227\pi$
$548$	−10.9309	−	25.7782i	−0.466944	−	1.10119i
$549$		−	12.2462i		−	0.522656i
$550$		0			0
$551$	−9.43318			−0.401867
$552$	10.0138	−	53.8617i	0.426216	−	2.29251i
$553$	−2.00000	+	2.87689i	−0.0850487	+	0.122338i
$554$	−9.56155	+	14.4401i	−0.406231	+	0.613500i
$555$		0			0
$556$	13.1158	+	30.9309i	0.556233	+	1.31176i
$557$	26.4924			1.12252			0.561260	−	0.827640i	$-0.310317\pi$
$557$	26.4924			1.12252			0.561260	+	0.827640i	$0.310317\pi$
$558$	16.2177	−	24.4924i	0.686552	−	1.03685i
$559$	0.743668			0.0314538
$560$		0			0
$561$	16.0000			0.675521
$562$	−22.9309	+	34.6307i	−0.967280	+	1.46081i
$563$	−38.1045			−1.60592			−0.802958	−	0.596036i	$-0.796741\pi$
$563$	−38.1045			−1.60592			−0.802958	+	0.596036i	$0.796741\pi$
$564$	−12.0000	−	28.2995i	−0.505291	−	1.19163i
$565$		0			0
$566$	−3.84563	+	5.80776i	−0.161644	+	0.244119i
$567$	−21.9912	−	15.2882i	−0.923544	−	0.642042i
$568$	3.80776	−	20.4810i	0.159770	−	0.859363i
$569$	−28.8769			−1.21058			−0.605291	−	0.796004i	$-0.706943\pi$
$569$	−28.8769			−1.21058			−0.605291	+	0.796004i	$0.706943\pi$
$570$		0			0
$571$		−	3.22925i		−	0.135140i	−0.997715	−	0.0675700i	$-0.978475\pi$
$571$		−	3.22925i		−	0.135140i	0.997715	−	0.0675700i	$-0.0215246\pi$
$572$	−7.36520	−	17.3693i	−0.307955	−	0.726248i
$573$		−	50.7386i		−	2.11964i
$574$	−1.55259	−	3.90495i	−0.0648037	−	0.162989i
$575$		0			0
$576$	45.7116	+	17.6057i	1.90465	+	0.733571i
$577$			45.6155i			1.89900i	0.313768	+	0.949500i	$0.398409\pi$
$577$			45.6155i			1.89900i	−0.313768	+	0.949500i	$0.601591\pi$
$578$	12.2884	−	18.5582i	0.511128	−	0.771918i
$579$	67.9372			2.82337
$580$		0			0
$581$	−6.56155	−	4.56155i	−0.272219	−	0.189245i
$582$	−4.00000	−	2.64861i	−0.165805	−	0.109789i
$583$			9.43318i			0.390682i
$584$	7.94584	−	42.7386i	0.328801	−	1.76854i
$585$		0			0
$586$	−18.5760	−	12.3002i	−0.767369	−	0.508116i
$587$	−21.8868			−0.903365			−0.451683	−	0.892179i	$-0.649176\pi$
$587$	−21.8868			−0.903365			−0.451683	+	0.892179i	$0.649176\pi$
$588$	30.7418	−	29.0356i	1.26777	−	1.19741i
$589$	16.0000			0.659269
$590$		0			0
$591$	−54.3681			−2.23640
$592$	5.56155	−	5.75058i	0.228578	−	0.236347i
$593$		−	11.3693i		−	0.466882i	−0.972371	−	0.233441i	$-0.925001\pi$
$593$		−	11.3693i		−	0.466882i	0.972371	−	0.233441i	$-0.0749986\pi$
$594$	−52.4631	−	34.7386i	−2.15259	−	1.42534i
$595$		0			0
$596$	−4.19224	−	9.88653i	−0.171721	−	0.404968i
$597$	80.9848			3.31449
$598$	−10.0138	+	15.1231i	−0.409495	+	0.618430i
$599$			29.6238i			1.21040i	0.796074	+	0.605199i	$0.206906\pi$
$599$			29.6238i			1.21040i	−0.796074	+	0.605199i	$0.793094\pi$
$600$		0			0
$601$		−	17.1231i		−	0.698466i	−0.937036	−	0.349233i	$-0.886442\pi$
$601$		−	17.1231i		−	0.698466i	0.937036	−	0.349233i	$-0.113558\pi$
$602$	0.514026	+	1.29284i	0.0209501	+	0.0526921i
$603$		−	23.0481i		−	0.938590i
$604$	18.4384	−	7.81855i	0.750250	−	0.318132i
$605$		0			0
$606$	53.8617	+	35.6647i	2.18798	+	1.44878i
$607$	−37.9415			−1.54000			−0.769999	−	0.638045i	$-0.779743\pi$
$607$	−37.9415			−1.54000			−0.769999	+	0.638045i	$0.779743\pi$
$608$	5.75058	+	26.0540i	0.233217	+	1.05663i
$609$	13.1231	+	9.12311i	0.531775	+	0.369687i
$610$		0			0
$611$			10.1768i			0.411711i
$612$	12.6624	−	5.36932i	0.511848	−	0.217042i
$613$	−28.2462			−1.14085			−0.570427	−	0.821348i	$-0.693222\pi$
$613$	−28.2462			−1.14085			−0.570427	+	0.821348i	$0.693222\pi$
$614$	1.19702	−	1.80776i	0.0483077	−	0.0729554i
$615$		0			0
$616$	25.1050	−	24.8098i	1.01151	−	0.999616i
$617$	26.0000			1.04672			0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000			1.04672			0.523360	+	0.852111i	$0.324678\pi$
$618$	−18.2462	+	27.5559i	−0.733970	+	1.10846i
$619$	−20.6083			−0.828316			−0.414158	−	0.910205i	$-0.635924\pi$
$619$	−20.6083			−0.828316			−0.414158	+	0.910205i	$0.635924\pi$
$620$		0			0
$621$			60.4924i			2.42748i
$622$	−23.5829	+	35.6155i	−0.945590	+	1.42805i
$623$	−18.1227	+	26.0685i	−0.726070	+	1.04441i
$624$	−17.3693	−	16.7984i	−0.695329	−	0.672473i
$625$		0			0
$626$	39.6377	+	26.2462i	1.58424	+	1.04901i
$627$		−	67.1935i		−	2.68345i
$628$	−0.453349	+	0.192236i	−0.0180906	+	0.00767105i
$629$		−	2.24621i		−	0.0895623i
$630$		0			0
$631$			14.1498i			0.563293i	0.959518	+	0.281647i	$0.0908806\pi$
$631$			14.1498i			0.563293i	−0.959518	+	0.281647i	$0.909119\pi$
$632$	−0.684658	+	3.68260i	−0.0272343	+	0.146486i
$633$		−	66.7386i		−	2.65262i
$634$	−9.56155	+	14.4401i	−0.379738	+	0.573489i
$635$		0			0
$636$	4.71659	+	11.1231i	0.187025	+	0.441060i
$637$	−13.1231	+	4.87689i	−0.519956	+	0.193230i
$638$	11.1231	+	7.36520i	0.440368	+	0.291591i
$639$			45.0979i			1.78405i
$640$		0			0
$641$	−7.12311			−0.281346			−0.140673	−	0.990056i	$-0.544927\pi$
$641$	−7.12311			−0.281346			−0.140673	+	0.990056i	$0.544927\pi$
$642$	−20.1907	−	13.3693i	−0.796862	−	0.527645i
$643$	33.9686			1.33959			0.669795	−	0.742546i	$-0.266382\pi$
$643$	33.9686			1.33959			0.669795	+	0.742546i	$0.266382\pi$
$644$	−33.2125	−	6.95547i	−1.30875	−	0.274084i
$645$		0			0
$646$	6.24621	+	4.13595i	0.245754	+	0.162727i
$647$	40.1725			1.57934			0.789672	−	0.613529i	$-0.210251\pi$
$647$	40.1725			1.57934			0.789672	+	0.613529i	$0.210251\pi$
$648$	−28.1501	−	5.23358i	−1.10584	−	0.205595i
$649$		−	9.75379i		−	0.382870i
$650$		0			0
$651$	−22.2586	−	15.4741i	−0.872385	−	0.606477i
$652$	5.56155	−	2.35829i	0.217807	−	0.0923579i
$653$	22.9848			0.899466			0.449733	−	0.893163i	$-0.351519\pi$
$653$	22.9848			0.899466			0.449733	+	0.893163i	$0.351519\pi$
$654$	−16.7984	+	25.3693i	−0.656869	+	0.992019i
$655$		0			0
$656$	−3.22925	−	3.12311i	−0.126081	−	0.121937i
$657$			94.1080i			3.67150i
$658$	−17.6920	+	7.03426i	−0.689707	+	0.274224i
$659$		−	1.32431i		−	0.0515877i	−0.999667	−	0.0257938i	$-0.991789\pi$
$659$		−	1.32431i		−	0.0515877i	0.999667	−	0.0257938i	$-0.00821134\pi$
$660$		0			0
$661$			12.2462i			0.476322i	0.971226	+	0.238161i	$0.0765447\pi$
$661$			12.2462i			0.476322i	−0.971226	+	0.238161i	$0.923455\pi$
$662$	−21.5616	−	14.2771i	−0.838014	−	0.554894i
$663$	−6.78456			−0.263491
$664$	−8.39919	−	1.56155i	−0.325952	−	0.0606000i
$665$		0			0
$666$	−9.56155	+	14.4401i	−0.370503	+	0.559542i
$667$		−	12.8255i		−	0.496604i
$668$	15.4741	+	36.4924i	0.598710	+	1.41193i
$669$	62.1080			2.40123
$670$		0			0
$671$	−9.43318			−0.364164
$672$	17.1976	−	41.8069i	0.663411	−	1.61274i
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	9.56155	−	14.4401i	0.368297	−	0.556211i
$675$		0			0
$676$	−7.02699	−	16.5717i	−0.270269	−	0.637373i
$677$		−	32.7386i		−	1.25825i	−0.777305	−	0.629124i	$-0.783414\pi$
$677$		−	32.7386i		−	1.25825i	0.777305	−	0.629124i	$-0.216586\pi$
$678$	−43.6106	+	65.8617i	−1.67485	+	2.52940i
$679$	−1.69614	+	2.43981i	−0.0650919	+	0.0936313i
$680$		0			0
$681$	−11.3693			−0.435673
$682$	−18.8664	−	12.4924i	−0.722430	−	0.478360i
$683$		−	0.371834i		−	0.0142278i	−0.999975	−	0.00711392i	$-0.997736\pi$
$683$		−	0.371834i		−	0.0142278i	0.999975	−	0.00711392i	$-0.00226445\pi$
$684$	−22.5490	−	53.1771i	−0.862181	−	2.03328i
$685$		0			0
$686$	−17.5490	−	19.4431i	−0.670024	−	0.742339i
$687$			38.8940i			1.48390i
$688$	1.06913	+	1.03399i	0.0407602	+	0.0394204i
$689$		−	4.00000i		−	0.152388i
$690$		0			0
$691$	14.8934			0.566573			0.283286	−	0.959035i	$-0.408575\pi$
$691$	14.8934			0.566573			0.283286	+	0.959035i	$0.408575\pi$
$692$	−29.9142	+	12.6847i	−1.13717	+	0.482198i
$693$	−43.6155	+	62.7386i	−1.65682	+	2.38324i
$694$	−6.68466	−	4.42627i	−0.253746	−	0.168019i
$695$		0			0
$696$	16.7984	+	3.12311i	0.636741	+	0.118381i
$697$	−1.26137			−0.0477777
$698$	−35.2114	−	23.3153i	−1.33277	−	0.882499i
$699$	−23.4199			−0.885823
$700$		0			0
$701$	11.1231			0.420114			0.210057	−	0.977689i	$-0.432635\pi$
$701$	11.1231			0.420114			0.210057	+	0.977689i	$0.432635\pi$
$702$	22.2462	+	14.7304i	0.839629	+	0.555963i
$703$	−9.43318			−0.355779
$704$	13.5616	−	35.2114i	0.511120	−	1.32708i
$705$		0			0
$706$	−22.8393	−	15.1231i	−0.859568	−	0.569166i
$707$	22.8393	−	32.8531i	0.858959	−	1.23557i
$708$	−4.87689	−	11.5012i	−0.183285	−	0.432240i
$709$	44.7386			1.68019			0.840097	−	0.542436i	$-0.182498\pi$
$709$	44.7386			1.68019			0.840097	+	0.542436i	$0.182498\pi$
$710$		0			0
$711$		−	8.10887i		−	0.304106i
$712$	−6.20393	+	33.3693i	−0.232502	+	1.25057i
$713$			21.7538i			0.814686i
$714$	−4.68951	−	11.7947i	−0.175500	−	0.441405i
$715$		0			0
$716$	19.8078	−	8.39919i	0.740251	−	0.313892i
$717$		−	12.0000i		−	0.448148i
$718$	−18.9309	−	12.5351i	−0.706494	−	0.467807i
$719$	−22.6762			−0.845681			−0.422841	−	0.906204i	$-0.638967\pi$
$719$	−22.6762			−0.845681			−0.422841	+	0.906204i	$0.638967\pi$
$720$		0			0
$721$	16.8078	+	11.6847i	0.625954	+	0.435159i
$722$	2.53457	−	3.82776i	0.0943267	−	0.142455i
$723$			77.3704i			2.87743i
$724$	27.8462	−	11.8078i	1.03490	−	0.438832i
$725$		0			0
$726$	−26.5219	+	40.0540i	−0.984319	+	1.48654i
$727$	−9.64198			−0.357601			−0.178801	−	0.983885i	$-0.557222\pi$
$727$	−9.64198			−0.357601			−0.178801	+	0.983885i	$0.557222\pi$
$728$	−10.6454	+	10.5202i	−0.394545	+	0.389906i
$729$	−23.4924			−0.870090
$730$		0			0
$731$	0.417609			0.0154458
$732$	−11.1231	+	4.71659i	−0.411122	+	0.174330i
$733$			0.738634i			0.0272821i	0.999907	+	0.0136410i	$0.00434221\pi$
$733$			0.738634i			0.0272821i	−0.999907	+	0.0136410i	$0.995658\pi$
$734$	−8.10887	+	12.2462i	−0.299304	+	0.452016i
$735$		0			0
$736$	−35.4233	+	7.81855i	−1.30572	+	0.288196i
$737$	−17.7538			−0.653969
$738$	8.10887	+	5.36932i	0.298492	+	0.197647i
$739$		−	37.5697i		−	1.38202i	−0.722844	−	0.691012i	$-0.757165\pi$
$739$		−	37.5697i		−	1.38202i	0.722844	−	0.691012i	$-0.242835\pi$
$740$		0			0
$741$			28.4924i			1.04670i
$742$	6.95383	−	2.76481i	0.255283	−	0.101499i
$743$			23.7917i			0.872835i	0.899744	+	0.436417i	$0.143753\pi$
$743$			23.7917i			0.872835i	−0.899744	+	0.436417i	$0.856247\pi$
$744$	−28.4924	−	5.29723i	−1.04458	−	0.194206i
$745$		0			0
$746$	8.19224	−	12.3721i	0.299939	−	0.452975i
$747$	18.4945			0.676679
$748$	−4.13595	−	9.75379i	−0.151225	−	0.356634i
$749$	−8.56155	+	12.3153i	−0.312832	+	0.449993i
$750$		0			0
$751$			28.8802i			1.05385i	0.849911	+	0.526926i	$0.176656\pi$
$751$			28.8802i			1.05385i	−0.849911	+	0.526926i	$0.823344\pi$
$752$	−14.1498	+	14.6307i	−0.515989	+	0.533526i
$753$	48.4924			1.76716
$754$	−4.71659	−	3.12311i	−0.171768	−	0.113737i
$755$		0			0
$756$	−10.2316	+	48.8558i	−0.372118	+	1.77687i
$757$	−4.24621			−0.154331			−0.0771656	−	0.997018i	$-0.524587\pi$
$757$	−4.24621			−0.154331			−0.0771656	+	0.997018i	$0.524587\pi$
$758$	−17.5616	−	11.6284i	−0.637864	−	0.422364i
$759$	91.3571			3.31605
$760$		0			0
$761$			47.2311i			1.71212i	0.516873	+	0.856062i	$0.327096\pi$
$761$			47.2311i			1.71212i	−0.516873	+	0.856062i	$0.672904\pi$
$762$	−63.2206	−	41.8617i	−2.29024	−	1.51649i
$763$	15.4741	+	10.7575i	0.560199	+	0.389447i
$764$	−30.9309	+	13.1158i	−1.11904	+	0.474512i
$765$		0			0
$766$	−14.8934	+	22.4924i	−0.538122	+	0.812684i
$767$			4.13595i			0.149341i
$768$	−1.61463	−	48.3002i	−0.0582628	−	1.74288i
$769$			27.2311i			0.981977i	0.871166	+	0.490989i	$0.163364\pi$
$769$			27.2311i			0.981977i	−0.871166	+	0.490989i	$0.836636\pi$
$770$		0			0
$771$		−	34.3404i		−	1.23674i
$772$	−17.5616	−	41.4153i	−0.632054	−	1.49057i
$773$		−	32.7386i		−	1.17753i	−0.808305	−	0.588763i	$-0.799615\pi$
$773$		−	32.7386i		−	1.17753i	0.808305	−	0.588763i	$-0.200385\pi$
$774$	−2.68466	−	1.77766i	−0.0964981	−	0.0638965i
$775$		0			0
$776$	−0.580639	+	3.12311i	−0.0208437	+	0.112113i
$777$	13.1231	+	9.12311i	0.470789	+	0.327290i
$778$	−5.56155	+	8.39919i	−0.199391	+	0.301126i
$779$			5.29723i			0.189793i
$780$		0			0
$781$	34.7386			1.24305
$782$	−5.62329	+	8.49242i	−0.201088	+	0.303688i
$783$	−18.8664			−0.674229
$784$	−25.6471	−	11.2350i	−0.915969	−	0.401249i
$785$		0			0
$786$	−41.3693	+	62.4769i	−1.47559	+	2.22848i
$787$	3.02045			0.107667			0.0538337	−	0.998550i	$-0.482856\pi$
$787$	3.02045			0.107667			0.0538337	+	0.998550i	$0.482856\pi$
$788$	14.0540	+	33.1434i	0.500652	+	1.18069i
$789$		−	55.8617i		−	1.98873i
$790$		0			0
$791$	40.1725	+	27.9277i	1.42837	+	0.992995i
$792$	−14.9309	+	80.3093i	−0.530545	+	2.85367i
$793$	4.00000			0.142044
$794$	−16.5081	−	10.9309i	−0.585849	−	0.387922i
$795$		0			0
$796$	−20.9343	−	49.3693i	−0.741998	−	1.74985i
$797$		−	3.75379i		−	0.132966i	−0.997788	−	0.0664830i	$-0.978822\pi$
$797$		−	3.75379i		−	0.132966i	0.997788	−	0.0664830i	$-0.0211778\pi$
$798$	−49.5329	+	19.6940i	−1.75345	+	0.697162i
$799$			5.71484i			0.202176i
$800$		0			0
$801$		−	73.4773i		−	2.59619i
$802$	4.68466	−	7.07488i	0.165421	−	0.249823i
$803$	72.4908			2.55814
$804$	−20.9343	+	8.87689i	−0.738297	+	0.313064i
$805$		0			0
$806$	8.00000	+	5.29723i	0.281788	+	0.186587i
$807$			0.743668i			0.0261784i
$808$	7.81855	−	42.0540i	0.275056	−	1.47945i
$809$	46.9848			1.65190			0.825950	−	0.563744i	$-0.190640\pi$
$809$	46.9848			1.65190			0.825950	+	0.563744i	$0.190640\pi$
$810$		0			0
$811$	−8.10887			−0.284741			−0.142370	−	0.989813i	$-0.545472\pi$
$811$	−8.10887			−0.284741			−0.142370	+	0.989813i	$0.545472\pi$
$812$	2.16927	−	10.3583i	0.0761265	−	0.363505i
$813$	−5.75379			−0.201794
$814$	11.1231	+	7.36520i	0.389865	+	0.258150i
$815$		0			0
$816$	−9.75379	−	9.43318i	−0.341451	−	0.330227i
$817$		−	1.75379i		−	0.0613573i
$818$	20.1907	+	13.3693i	0.705950	+	0.467447i
$819$	18.4945	−	26.6034i	0.646251	−	0.929598i
$820$		0			0
$821$	15.6155			0.544986			0.272493	−	0.962158i	$-0.412152\pi$
$821$	15.6155			0.544986			0.272493	+	0.962158i	$0.412152\pi$
$822$	33.0161	−	49.8617i	1.15157	−	1.73913i
$823$		−	29.0890i		−	1.01398i	−0.861953	−	0.506989i	$-0.830758\pi$
$823$		−	29.0890i		−	1.01398i	0.861953	−	0.506989i	$-0.169242\pi$
$824$	21.5150	+	4.00000i	0.749509	+	0.139347i
$825$		0			0
$826$	−7.19018	+	2.85878i	−0.250178	+	0.0994697i
$827$		−	24.5354i		−	0.853180i	−0.904445	−	0.426590i	$-0.859715\pi$
$827$		−	24.5354i		−	0.853180i	0.904445	−	0.426590i	$-0.140285\pi$
$828$	72.3002	−	30.6578i	2.51261	−	1.06543i
$829$		−	15.7538i		−	0.547152i	−0.961850	−	0.273576i	$-0.911794\pi$
$829$		−	15.7538i		−	0.547152i	0.961850	−	0.273576i	$-0.0882065\pi$
$830$		0			0
$831$	−36.9890			−1.28314
$832$	−5.75058	+	14.9309i	−0.199365	+	0.517635i
$833$	−7.36932	+	2.73863i	−0.255332	+	0.0948880i
$834$	−39.6155	+	59.8283i	−1.37177	+	2.07169i
$835$		0			0
$836$	−40.9620	+	17.3693i	−1.41670	+	0.600730i
$837$	32.0000			1.10608
$838$	18.4130	−	27.8078i	0.636067	−	0.960603i
$839$	−10.9205			−0.377018			−0.188509	−	0.982071i	$-0.560365\pi$
$839$	−10.9205			−0.377018			−0.188509	+	0.982071i	$0.560365\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	18.4384	−	27.8462i	0.635431	−	0.959643i
$843$	−88.7085			−3.05528
$844$	−40.6847	+	17.2517i	−1.40042	+	0.593829i
$845$		0			0
$846$	24.3266	−	36.7386i	0.836366	−	1.26310i
$847$	24.4310	+	16.9843i	0.839460	+	0.583587i
$848$	5.56155	−	5.75058i	0.190985	−	0.197476i
$849$	−14.8769			−0.510574
$850$		0			0
$851$		−	12.8255i		−	0.439651i
$852$	40.9620	−	17.3693i	1.40333	−	0.595063i
$853$			24.2462i			0.830174i	0.909782	+	0.415087i	$0.136249\pi$
$853$			24.2462i			0.830174i	−0.909782	+	0.415087i	$0.863751\pi$
$854$	2.76481	+	6.95383i	0.0946099	+	0.237955i
$855$		0			0
$856$	−2.93087	+	15.7644i	−0.100175	+	0.538816i
$857$			25.6155i			0.875010i	0.899216	+	0.437505i	$0.144138\pi$
$857$			25.6155i			0.875010i	−0.899216	+	0.437505i	$0.855862\pi$
$858$	22.2462	−	33.5968i	0.759473	−	1.14697i
$859$	3.55531			0.121306			0.0606528	−	0.998159i	$-0.480682\pi$
$859$	3.55531			0.121306			0.0606528	+	0.998159i	$0.480682\pi$
$860$		0			0
$861$	5.12311	−	7.36932i	0.174595	−	0.251146i
$862$	−6.93087	−	4.58930i	−0.236066	−	0.156312i
$863$		−	10.2226i		−	0.347982i	−0.984747	−	0.173991i	$-0.944334\pi$
$863$		−	10.2226i		−	0.347982i	0.984747	−	0.173991i	$-0.0556664\pi$
$864$	11.5012	+	52.1080i	0.391277	+	1.77275i
$865$		0			0
$866$	34.9211	+	23.1231i	1.18667	+	0.785755i
$867$	47.5377			1.61447
$868$	−3.67939	+	17.5691i	−0.124887	+	0.596335i
$869$	−6.24621			−0.211888
$870$		0			0
$871$	7.52823			0.255084
$872$	19.8078	+	3.68260i	0.670776	+	0.124709i
$873$		−	6.87689i		−	0.232748i
$874$	35.6647	+	23.6155i	1.20638	+	0.798807i
$875$		0			0
$876$	85.4773	−	36.2454i	2.88801	−	1.22462i
$877$	−0.738634			−0.0249419			−0.0124709	−	0.999922i	$-0.503970\pi$
$877$	−0.738634			−0.0249419			−0.0124709	+	0.999922i	$0.503970\pi$
$878$	−12.6624	+	19.1231i	−0.427336	+	0.645374i
$879$		−	47.5835i		−	1.60495i
$880$		0			0
$881$		−	31.3693i		−	1.05686i	−0.848977	−	0.528430i	$-0.822781\pi$
$881$		−	31.3693i		−	1.05686i	0.848977	−	0.528430i	$-0.177219\pi$
$882$	59.0324	+	13.7636i	1.98772	+	0.463445i
$883$		−	31.3200i		−	1.05400i	−0.849865	−	0.527001i	$-0.823317\pi$
$883$		−	31.3200i		−	1.05400i	0.849865	−	0.527001i	$-0.176683\pi$
$884$	1.75379	+	4.13595i	0.0589863	+	0.139107i
$885$		0			0
$886$	−27.1771	−	17.9954i	−0.913032	−	0.604567i
$887$	29.9957			1.00716			0.503578	−	0.863950i	$-0.332017\pi$
$887$	29.9957			1.00716			0.503578	+	0.863950i	$0.332017\pi$
$888$	16.7984	+	3.12311i	0.563717	+	0.104805i
$889$	−26.8078	+	38.5616i	−0.899104	+	1.29331i
$890$		0			0
$891$		−	47.7465i		−	1.59957i
$892$	−16.0547	−	37.8617i	−0.537552	−	1.26770i
$893$	24.0000			0.803129
$894$	12.6624	−	19.1231i	0.423495	−	0.639572i
$895$		0			0
$896$	−29.9315	+	0.323119i	−0.999942	+	0.0107946i
$897$	−38.7386			−1.29345
$898$	−12.1922	+	18.4130i	−0.406860	+	0.614450i
$899$	−6.78456			−0.226278
$900$		0			0
$901$		−	2.24621i		−	0.0748321i
$902$	4.13595	−	6.24621i	0.137712	−	0.207976i
$903$	−1.69614	+	2.43981i	−0.0564440	+	0.0811918i
$904$	51.4233	+	9.56047i	1.71031	+	0.317976i
$905$		0			0
$906$	35.6647	+	23.6155i	1.18488	+	0.784573i
$907$			52.8350i			1.75436i	0.480166	+	0.877178i	$0.340577\pi$
$907$			52.8350i			1.75436i	−0.480166	+	0.877178i	$0.659423\pi$
$908$	2.93893	+	6.93087i	0.0975319	+	0.230009i
$909$			92.6004i			3.07136i
$910$		0			0
$911$		−	2.06798i		−	0.0685151i	−0.999413	−	0.0342575i	$-0.989093\pi$
$911$		−	2.06798i		−	0.0685151i	0.999413	−	0.0342575i	$-0.0109066\pi$
$912$	−39.6155	+	40.9620i	−1.31180	+	1.35639i
$913$		−	14.2462i		−	0.471481i
$914$	−4.68466	+	7.07488i	−0.154955	+	0.234016i
$915$		0			0
$916$	23.7102	−	10.0540i	0.783408	−	0.332193i
$917$	38.1080	+	26.4924i	1.25844	+	0.874857i
$918$	12.4924	+	8.27190i	0.412311	+	0.273013i
$919$			9.27015i			0.305794i	0.988242	+	0.152897i	$0.0488603\pi$
$919$			9.27015i			0.305794i	−0.988242	+	0.152897i	$0.951140\pi$
$920$		0			0
$921$	4.63068			0.152586
$922$	−4.26324	−	2.82292i	−0.140402	−	0.0929679i
$923$	−14.7304			−0.484857
$924$	73.7832	+	15.4519i	2.42729	+	0.508332i
$925$		0			0
$926$	−33.8078	−	22.3859i	−1.11099	−	0.735647i
$927$	−47.3747			−1.55599
$928$	−2.43845	−	11.0478i	−0.0800460	−	0.362662i
$929$			21.1231i			0.693027i	0.938045	+	0.346513i	$0.112634\pi$
$929$			21.1231i			0.693027i	−0.938045	+	0.346513i	$0.887366\pi$
$930$		0			0
$931$	11.5012	+	30.9481i	0.376935	+	1.01428i
$932$	6.05398	+	14.2771i	0.198305	+	0.467661i
$933$	−91.2311			−2.98677
$934$	14.4401	−	21.8078i	0.472494	−	0.713572i
$935$		0			0
$936$	6.33122	−	34.0540i	0.206942	−	1.11309i
$937$		−	38.1080i		−	1.24493i	−0.782647	−	0.622466i	$-0.786131\pi$
$937$		−	38.1080i		−	1.24493i	0.782647	−	0.622466i	$-0.213869\pi$
$938$	5.20354	+	13.0875i	0.169901	+	0.427323i
$939$			101.534i			3.31344i
$940$		0			0
$941$		−	26.6307i		−	0.868135i	−0.900880	−	0.434068i	$-0.857078\pi$
$941$		−	26.6307i		−	0.868135i	0.900880	−	0.434068i	$-0.142922\pi$
$942$	−0.876894	−	0.580639i	−0.0285708	−	0.0189182i
$943$	−7.20217			−0.234535
$944$	−5.75058	+	5.94602i	−0.187165	+	0.193527i
$945$		0			0
$946$	−1.36932	+	2.06798i	−0.0445203	+	0.0672357i
$947$			35.8735i			1.16573i	0.812568	+	0.582867i	$0.198069\pi$
$947$			35.8735i			1.16573i	−0.812568	+	0.582867i	$0.801931\pi$
$948$	−7.36520	+	3.12311i	−0.239211	+	0.101434i
$949$	−30.7386			−0.997818
$950$		0			0
$951$	−36.9890			−1.19945
$952$	−5.97796	+	5.90767i	−0.193747	+	0.191469i
$953$	−28.2462			−0.914985			−0.457492	−	0.889214i	$-0.651252\pi$
$953$	−28.2462			−0.914985			−0.457492	+	0.889214i	$0.651252\pi$
$954$	−9.56155	+	14.4401i	−0.309567	+	0.467515i
$955$		0			0
$956$	−7.31534	+	3.10196i	−0.236595	+	0.100325i
$957$			28.4924i			0.921029i
$958$		0			0
$959$	−30.4133	−	21.1431i	−0.982096	−	0.682747i
$960$		0			0
$961$	−19.4924			−0.628788
$962$	−4.71659	−	3.12311i	−0.152069	−	0.100693i
$963$		−	34.7123i		−	1.11859i
$964$	47.1659	−	20.0000i	1.51911	−	0.644157i
$965$		0			0
$966$	−26.7763	−	67.3455i	−0.861512	−	2.16681i
$967$			3.43806i			0.110560i	0.998471	+	0.0552802i	$0.0176052\pi$
$967$			3.43806i			0.110560i	−0.998471	+	0.0552802i	$0.982395\pi$
$968$	31.2732	+	5.81422i	1.00516	+	0.186876i
$969$			16.0000i			0.513994i
$970$		0			0
$971$	10.7575			0.345224			0.172612	−	0.984990i	$-0.444779\pi$
$971$	10.7575			0.345224			0.172612	+	0.984990i	$0.444779\pi$
$972$	−1.77766	−	4.19224i	−0.0570183	−	0.134466i
$973$	36.4924	+	25.3693i	1.16989	+	0.813303i
$974$	15.5616	+	10.3041i	0.498624	+	0.330166i
$975$		0			0
$976$	5.75058	+	5.56155i	0.184071	+	0.178021i
$977$	−22.4924			−0.719596			−0.359798	−	0.933030i	$-0.617154\pi$
$977$	−22.4924			−0.719596			−0.359798	+	0.933030i	$0.617154\pi$
$978$	10.7575	+	7.12311i	0.343986	+	0.227772i
$979$	−56.5991			−1.80891
$980$		0			0
$981$	−43.6155			−1.39254
$982$	37.1771	+	24.6169i	1.18637	+	0.785558i
$983$	28.5083			0.909275			0.454637	−	0.890677i	$-0.349769\pi$
$983$	28.5083			0.909275			0.454637	+	0.890677i	$0.349769\pi$
$984$	1.75379	−	9.43318i	0.0559087	−	0.300719i
$985$		0			0
$986$	−2.64861	−	1.75379i	−0.0843490	−	0.0558520i
$987$	−33.3880	−	23.2111i	−1.06275	−	0.738818i
$988$	17.3693	−	7.36520i	0.552592	−	0.234318i
$989$	2.38447			0.0758218
$990$		0			0
$991$			48.9078i			1.55361i	0.629743	+	0.776804i	$0.283160\pi$
$991$			48.9078i			1.55361i	−0.629743	+	0.776804i	$0.716840\pi$
$992$	4.13595	+	18.7386i	0.131317	+	0.594952i
$993$		−	55.2311i		−	1.75270i
$994$	−10.1817	−	25.6082i	−0.322944	−	0.812243i
$995$		0			0
$996$	−7.12311	−	16.7984i	−0.225704	−	0.532277i
$997$		−	5.50758i		−	0.174427i	−0.996190	−	0.0872134i	$-0.972204\pi$
$997$		−	5.50758i		−	0.174427i	0.996190	−	0.0872134i	$-0.0277962\pi$
$998$	28.6847	+	18.9936i	0.907997	+	0.601233i
$999$	−18.8664			−0.596905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.g.j.251.6		8
4.3	odd	2	inner	700.2.g.j.251.7		8
5.2	odd	4		700.2.c.j.699.8		8
5.3	odd	4		700.2.c.i.699.1		8
5.4	even	2		140.2.g.c.111.3	yes	8
7.6	odd	2	inner	700.2.g.j.251.5		8
15.14	odd	2		1260.2.c.c.811.6		8
20.3	even	4		700.2.c.i.699.7		8
20.7	even	4		700.2.c.j.699.2		8
20.19	odd	2		140.2.g.c.111.2	yes	8
28.27	even	2	inner	700.2.g.j.251.8		8
35.4	even	6		980.2.o.e.411.4		16
35.9	even	6		980.2.o.e.31.8		16
35.13	even	4		700.2.c.j.699.1		8
35.19	odd	6		980.2.o.e.31.7		16
35.24	odd	6		980.2.o.e.411.3		16
35.27	even	4		700.2.c.i.699.8		8
35.34	odd	2		140.2.g.c.111.4	yes	8
40.19	odd	2		2240.2.k.e.1791.2		8
40.29	even	2		2240.2.k.e.1791.8		8
60.59	even	2		1260.2.c.c.811.8		8
105.104	even	2		1260.2.c.c.811.5		8
140.19	even	6		980.2.o.e.31.4		16
140.27	odd	4		700.2.c.i.699.2		8
140.39	odd	6		980.2.o.e.411.7		16
140.59	even	6		980.2.o.e.411.8		16
140.79	odd	6		980.2.o.e.31.3		16
140.83	odd	4		700.2.c.j.699.7		8
140.139	even	2		140.2.g.c.111.1	✓	8
280.69	odd	2		2240.2.k.e.1791.1		8
280.139	even	2		2240.2.k.e.1791.7		8
420.419	odd	2		1260.2.c.c.811.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.1	✓	8	140.139	even	2
140.2.g.c.111.2	yes	8	20.19	odd	2
140.2.g.c.111.3	yes	8	5.4	even	2
140.2.g.c.111.4	yes	8	35.34	odd	2
700.2.c.i.699.1		8	5.3	odd	4
700.2.c.i.699.2		8	140.27	odd	4
700.2.c.i.699.7		8	20.3	even	4
700.2.c.i.699.8		8	35.27	even	4
700.2.c.j.699.1		8	35.13	even	4
700.2.c.j.699.2		8	20.7	even	4
700.2.c.j.699.7		8	140.83	odd	4
700.2.c.j.699.8		8	5.2	odd	4
700.2.g.j.251.5		8	7.6	odd	2	inner
700.2.g.j.251.6		8	1.1	even	1	trivial
700.2.g.j.251.7		8	4.3	odd	2	inner
700.2.g.j.251.8		8	28.27	even	2	inner
980.2.o.e.31.3		16	140.79	odd	6
980.2.o.e.31.4		16	140.19	even	6
980.2.o.e.31.7		16	35.19	odd	6
980.2.o.e.31.8		16	35.9	even	6
980.2.o.e.411.3		16	35.24	odd	6
980.2.o.e.411.4		16	35.4	even	6
980.2.o.e.411.7		16	140.39	odd	6
980.2.o.e.411.8		16	140.59	even	6
1260.2.c.c.811.5		8	105.104	even	2
1260.2.c.c.811.6		8	15.14	odd	2
1260.2.c.c.811.7		8	420.419	odd	2
1260.2.c.c.811.8		8	60.59	even	2
2240.2.k.e.1791.1		8	280.69	odd	2
2240.2.k.e.1791.2		8	40.19	odd	2
2240.2.k.e.1791.7		8	280.139	even	2
2240.2.k.e.1791.8		8	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.780776 - 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +(2.35829 - 3.56155i) q^{6} +(-2.17238 - 1.51022i) q^{7} +(-2.78078 - 0.516994i) q^{8} +6.12311 q^{9} +O(q^{10})\)	\(q+(0.780776 - 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +(2.35829 - 3.56155i) q^{6} +(-2.17238 - 1.51022i) q^{7} +(-2.78078 - 0.516994i) q^{8} +6.12311 q^{9} -4.71659i q^{11} +(-2.35829 - 5.56155i) q^{12} +2.00000i q^{13} +(-3.47692 + 1.38241i) q^{14} +(-2.78078 + 2.87529i) q^{16} +1.12311i q^{17} +(4.78078 - 7.22004i) q^{18} +4.71659 q^{19} +(-6.56155 - 4.56155i) q^{21} +(-5.56155 - 3.68260i) q^{22} +6.41273i q^{23} +(-8.39919 - 1.56155i) q^{24} +(2.35829 + 1.56155i) q^{26} +9.43318 q^{27} +(-1.08464 + 5.17915i) q^{28} -2.00000 q^{29} +3.39228 q^{31} +(1.21922 + 5.52390i) q^{32} -14.2462i q^{33} +(1.32431 + 0.876894i) q^{34} +(-4.78078 - 11.2745i) q^{36} -2.00000 q^{37} +(3.68260 - 5.56155i) q^{38} +6.04090i q^{39} +1.12311i q^{41} +(-10.5018 + 4.17548i) q^{42} -0.371834i q^{43} +(-8.68466 + 3.68260i) q^{44} +(7.56155 + 5.00691i) q^{46} +5.08842 q^{47} +(-8.39919 + 8.68466i) q^{48} +(2.43845 + 6.56155i) q^{49} +3.39228i q^{51} +(3.68260 - 1.56155i) q^{52} -2.00000 q^{53} +(7.36520 - 11.1231i) q^{54} +(5.26012 + 5.32270i) q^{56} +14.2462 q^{57} +(-1.56155 + 2.35829i) q^{58} +2.06798 q^{59} -2.00000i q^{61} +(2.64861 - 4.00000i) q^{62} +(-13.3017 - 9.24726i) q^{63} +(7.46543 + 2.87529i) q^{64} +(-16.7984 - 11.1231i) q^{66} -3.76412i q^{67} +(2.06798 - 0.876894i) q^{68} +19.3693i q^{69} +7.36520i q^{71} +(-17.0270 - 3.16561i) q^{72} +15.3693i q^{73} +(-1.56155 + 2.35829i) q^{74} +(-3.68260 - 8.68466i) q^{76} +(-7.12311 + 10.2462i) q^{77} +(7.12311 + 4.71659i) q^{78} -1.32431i q^{79} +10.1231 q^{81} +(1.32431 + 0.876894i) q^{82} +3.02045 q^{83} +(-3.27608 + 15.6433i) q^{84} +(-0.438447 - 0.290319i) q^{86} -6.04090 q^{87} +(-2.43845 + 13.1158i) q^{88} -12.0000i q^{89} +(3.02045 - 4.34475i) q^{91} +(11.8078 - 5.00691i) q^{92} +10.2462 q^{93} +(3.97292 - 6.00000i) q^{94} +(3.68260 + 16.6847i) q^{96} -1.12311i q^{97} +(9.64092 + 2.24782i) q^{98} -28.8802i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9	\( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 16 q^{9} - 6 q^{14} - 14 q^{16} + 30 q^{18} - 36 q^{21} - 28 q^{22} - 14 q^{28} - 16 q^{29} + 18 q^{32} - 30 q^{36} - 16 q^{37} - 8 q^{42} - 20 q^{44} + 44 q^{46} + 36 q^{49} - 16 q^{53} + 2 q^{56} + 48 q^{57} + 4 q^{58} + 2 q^{64} - 62 q^{72} + 4 q^{74} - 24 q^{77} + 24 q^{78} + 48 q^{81} + 8 q^{84} - 20 q^{86} - 36 q^{88} + 12 q^{92} + 16 q^{93} - 26 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^4 - 14 * q^8 + 16 * q^9 - 6 * q^14 - 14 * q^16 + 30 * q^18 - 36 * q^21 - 28 * q^22 - 14 * q^28 - 16 * q^29 + 18 * q^32 - 30 * q^36 - 16 * q^37 - 8 * q^42 - 20 * q^44 + 44 * q^46 + 36 * q^49 - 16 * q^53 + 2 * q^56 + 48 * q^57 + 4 * q^58 + 2 * q^64 - 62 * q^72 + 4 * q^74 - 24 * q^77 + 24 * q^78 + 48 * q^81 + 8 * q^84 - 20 * q^86 - 36 * q^88 + 12 * q^92 + 16 * q^93 - 26 * q^98

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