LMFDB - Embedded newform 350.2.m.a.239.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.5
Character	$\chi$	$=$	350.239
Dual form			350.2.m.a.309.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.331395 - 0.107677i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.25842 + 1.84834i) q^{5} +(-0.107677 - 0.331395i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.32882 - 1.69199i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.331395 - 0.107677i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.25842 + 1.84834i) q^{5} +(-0.107677 - 0.331395i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.32882 - 1.69199i) q^{9} +(-2.23502 + 0.0683444i) q^{10} +(-2.18333 + 1.58628i) q^{11} +(0.204813 - 0.281901i) q^{12} +(-2.81761 + 3.87811i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.616058 - 0.477029i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.80718 - 1.88687i) q^{17} -2.87858i q^{18} +(1.15425 + 3.55243i) q^{19} +(-1.36901 - 1.76800i) q^{20} +(0.107677 - 0.331395i) q^{21} +(-2.56665 - 0.833956i) q^{22} +(-0.879367 - 1.21035i) q^{23} +0.348449 q^{24} +(-1.83275 - 4.65199i) q^{25} -4.79360 q^{26} +(1.20401 + 1.65718i) q^{27} +(-0.951057 - 0.309017i) q^{28} +(-2.88396 + 8.87591i) q^{29} +(0.748035 + 0.218011i) q^{30} +(-1.33918 - 4.12156i) q^{31} -1.00000i q^{32} +(0.894349 - 0.290592i) q^{33} +(4.93988 + 3.58903i) q^{34} +(-1.84834 - 1.25842i) q^{35} +(2.32882 - 1.69199i) q^{36} +(-2.24264 + 3.08673i) q^{37} +(-2.19552 + 3.02187i) q^{38} +(1.35132 - 0.981794i) q^{39} +(0.625661 - 2.14675i) q^{40} +(9.11384 + 6.62160i) q^{41} +(0.331395 - 0.107677i) q^{42} -7.26099i q^{43} +(-0.833956 - 2.56665i) q^{44} +(6.05802 - 2.17523i) q^{45} +(0.462311 - 1.42285i) q^{46} +(10.5529 + 3.42885i) q^{47} +(0.204813 + 0.281901i) q^{48} -1.00000 q^{49} +(2.68628 - 4.21710i) q^{50} -2.12764 q^{51} +(-2.81761 - 3.87811i) q^{52} +(0.496831 + 0.161430i) q^{53} +(-0.632987 + 1.94813i) q^{54} +(-0.184444 - 6.03175i) q^{55} +(-0.309017 - 0.951057i) q^{56} -1.30154i q^{57} +(-8.87591 + 2.88396i) q^{58} +(2.82686 + 2.05383i) q^{59} +(0.263309 + 0.733316i) q^{60} +(-2.73285 + 1.98553i) q^{61} +(2.54726 - 3.50601i) q^{62} +(1.69199 - 2.32882i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-3.62233 - 10.0882i) q^{65} +(0.760778 + 0.552738i) q^{66} +(13.2964 - 4.32028i) q^{67} +6.10603i q^{68} +(0.161092 + 0.495790i) q^{69} +(-0.0683444 - 2.23502i) q^{70} +(-2.84465 + 8.75495i) q^{71} +(2.73770 + 0.889531i) q^{72} +(-3.88608 - 5.34873i) q^{73} -3.81540 q^{74} +(0.106452 + 1.73899i) q^{75} -3.73524 q^{76} +(-1.58628 - 2.18333i) q^{77} +(1.58858 + 0.516160i) q^{78} +(3.21124 - 9.88319i) q^{79} +(2.10451 - 0.755660i) q^{80} +(2.44803 + 7.53426i) q^{81} +11.2653i q^{82} +(7.89465 - 2.56513i) q^{83} +(0.281901 + 0.204813i) q^{84} +(-3.82030 + 13.1081i) q^{85} +(5.87427 - 4.26790i) q^{86} +(1.91146 - 2.63090i) q^{87} +(1.58628 - 2.18333i) q^{88} +(-1.96248 + 1.42582i) q^{89} +(5.32061 + 3.62247i) q^{90} +(-3.87811 - 2.81761i) q^{91} +(1.42285 - 0.462311i) q^{92} +1.51006i q^{93} +(3.42885 + 10.5529i) q^{94} +(-8.01864 - 2.33699i) q^{95} +(-0.107677 + 0.331395i) q^{96} +(3.32974 + 1.08190i) q^{97} +(-0.587785 - 0.809017i) q^{98} +7.76855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−0.331395	−	0.107677i	−0.191331	−	0.0621672i	0.211784	−	0.977316i	$-0.432073\pi$
$3$	−0.331395	−	0.107677i	−0.191331	−	0.0621672i	−0.403115	+	0.915149i	$0.632073\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.25842	+	1.84834i	−0.562783	+	0.826604i
$5$	−1.25842	+	1.84834i	−0.562783	+	0.826604i
$6$	−0.107677	−	0.331395i	−0.0439588	−	0.135291i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−2.32882	−	1.69199i	−0.776274	−	0.563996i
$10$	−2.23502	+	0.0683444i	−0.706776	+	0.0216124i
$11$	−2.18333	+	1.58628i	−0.658298	+	0.478281i	−0.866088	−	0.499892i	$-0.833373\pi$
$11$	−2.18333	+	1.58628i	−0.658298	+	0.478281i	0.207790	+	0.978173i	$0.433373\pi$
$12$	0.204813	−	0.281901i	0.0591245	−	0.0813779i
$13$	−2.81761	+	3.87811i	−0.781464	+	1.07559i	0.213654	+	0.976909i	$0.431463\pi$
$13$	−2.81761	+	3.87811i	−0.781464	+	1.07559i	−0.995119	+	0.0986841i	$0.968537\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	0.616058	−	0.477029i	0.159066	−	0.123168i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.80718	−	1.88687i	1.40845	−	0.457632i	0.496535	−	0.868017i	$-0.334606\pi$
$17$	5.80718	−	1.88687i	1.40845	−	0.457632i	0.911912	+	0.410385i	$0.134606\pi$
$18$		−	2.87858i		−	0.678489i
$19$	1.15425	+	3.55243i	0.264804	+	0.814982i	0.991739	+	0.128276i	$0.0409443\pi$
$19$	1.15425	+	3.55243i	0.264804	+	0.814982i	−0.726935	+	0.686707i	$0.759056\pi$
$20$	−1.36901	−	1.76800i	−0.306119	−	0.395337i
$21$	0.107677	−	0.331395i	0.0234970	−	0.0723163i
$22$	−2.56665	−	0.833956i	−0.547212	−	0.177800i
$23$	−0.879367	−	1.21035i	−0.183361	−	0.252374i	0.707435	−	0.706778i	$-0.249852\pi$
$23$	−0.879367	−	1.21035i	−0.183361	−	0.252374i	−0.890796	+	0.454404i	$0.849852\pi$
$24$	0.348449			0.0711269
$25$	−1.83275	−	4.65199i	−0.366550	−	0.930398i
$26$	−4.79360			−0.940103
$27$	1.20401	+	1.65718i	0.231712	+	0.318925i
$28$	−0.951057	−	0.309017i	−0.179733	−	0.0583987i
$29$	−2.88396	+	8.87591i	−0.535538	+	1.64822i	0.206946	+	0.978352i	$0.433647\pi$
$29$	−2.88396	+	8.87591i	−0.535538	+	1.64822i	−0.742484	+	0.669864i	$0.766353\pi$
$30$	0.748035	+	0.218011i	0.136572	+	0.0398032i
$31$	−1.33918	−	4.12156i	−0.240523	−	0.740254i	−0.996341	−	0.0854717i	$-0.972760\pi$
$31$	−1.33918	−	4.12156i	−0.240523	−	0.740254i	0.755817	−	0.654782i	$-0.227240\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.894349	−	0.290592i	0.155686	−	0.0505855i
$34$	4.93988	+	3.58903i	0.847182	+	0.615514i
$35$	−1.84834	−	1.25842i	−0.312427	−	0.212712i
$36$	2.32882	−	1.69199i	0.388137	−	0.281998i
$37$	−2.24264	+	3.08673i	−0.368687	+	0.507455i	−0.952543	−	0.304403i	$-0.901543\pi$
$37$	−2.24264	+	3.08673i	−0.368687	+	0.507455i	0.583856	+	0.811857i	$0.301543\pi$
$38$	−2.19552	+	3.02187i	−0.356160	+	0.490213i
$39$	1.35132	−	0.981794i	0.216385	−	0.157213i
$40$	0.625661	−	2.14675i	0.0989257	−	0.339431i
$41$	9.11384	+	6.62160i	1.42334	+	1.03412i	0.991208	+	0.132311i	$0.0422396\pi$
$41$	9.11384	+	6.62160i	1.42334	+	1.03412i	0.432135	+	0.901809i	$0.357760\pi$
$42$	0.331395	−	0.107677i	0.0511354	−	0.0166149i
$43$		−	7.26099i		−	1.10729i	−0.832752	−	0.553645i	$-0.813236\pi$
$43$		−	7.26099i		−	1.10729i	0.832752	−	0.553645i	$-0.186764\pi$
$44$	−0.833956	−	2.56665i	−0.125724	−	0.386938i
$45$	6.05802	−	2.17523i	0.903076	−	0.324264i
$46$	0.462311	−	1.42285i	0.0681640	−	0.209787i
$47$	10.5529	+	3.42885i	1.53930	+	0.500149i	0.951183	−	0.308627i	$-0.0998694\pi$
$47$	10.5529	+	3.42885i	1.53930	+	0.500149i	0.588117	+	0.808776i	$0.299869\pi$
$48$	0.204813	+	0.281901i	0.0295623	+	0.0406890i
$49$	−1.00000			−0.142857
$50$	2.68628	−	4.21710i	0.379897	−	0.596388i
$51$	−2.12764			−0.297929
$52$	−2.81761	−	3.87811i	−0.390732	−	0.537797i
$53$	0.496831	+	0.161430i	0.0682450	+	0.0221742i	0.342941	−	0.939357i	$-0.388577\pi$
$53$	0.496831	+	0.161430i	0.0682450	+	0.0221742i	−0.274696	+	0.961531i	$0.588577\pi$
$54$	−0.632987	+	1.94813i	−0.0861386	+	0.265107i
$55$	−0.184444	−	6.03175i	−0.0248704	−	0.813320i
$56$	−0.309017	−	0.951057i	−0.0412941	−	0.127090i
$57$		−	1.30154i		−	0.172394i
$58$	−8.87591	+	2.88396i	−1.16546	+	0.378682i
$59$	2.82686	+	2.05383i	0.368026	+	0.267386i	0.756392	−	0.654119i	$-0.226960\pi$
$59$	2.82686	+	2.05383i	0.368026	+	0.267386i	−0.388366	+	0.921505i	$0.626960\pi$
$60$	0.263309	+	0.733316i	0.0339930	+	0.0946707i
$61$	−2.73285	+	1.98553i	−0.349906	+	0.254221i	−0.748829	−	0.662763i	$-0.769384\pi$
$61$	−2.73285	+	1.98553i	−0.349906	+	0.254221i	0.398924	+	0.916984i	$0.369384\pi$
$62$	2.54726	−	3.50601i	0.323503	−	0.445264i
$63$	1.69199	−	2.32882i	0.213171	−	0.293404i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−3.62233	−	10.0882i	−0.449295	−	1.25129i
$66$	0.760778	+	0.552738i	0.0936454	+	0.0680373i
$67$	13.2964	−	4.32028i	1.62442	−	0.527806i	0.651440	−	0.758700i	$-0.274165\pi$
$67$	13.2964	−	4.32028i	1.62442	−	0.527806i	0.972979	+	0.230894i	$0.0741652\pi$
$68$			6.10603i			0.740464i
$69$	0.161092	+	0.495790i	0.0193932	+	0.0596861i
$70$	−0.0683444	−	2.23502i	−0.00816872	−	0.267136i
$71$	−2.84465	+	8.75495i	−0.337598	+	1.03902i	0.627830	+	0.778351i	$0.283943\pi$
$71$	−2.84465	+	8.75495i	−0.337598	+	1.03902i	−0.965428	+	0.260670i	$0.916057\pi$
$72$	2.73770	+	0.889531i	0.322640	+	0.104832i
$73$	−3.88608	−	5.34873i	−0.454832	−	0.626022i	0.518595	−	0.855020i	$-0.326455\pi$
$73$	−3.88608	−	5.34873i	−0.454832	−	0.626022i	−0.973427	+	0.228998i	$0.926455\pi$
$74$	−3.81540			−0.443532
$75$	0.106452	+	1.73899i	0.0122920	+	0.200801i
$76$	−3.73524			−0.428462
$77$	−1.58628	−	2.18333i	−0.180773	−	0.248813i
$78$	1.58858	+	0.516160i	0.179871	+	0.0584436i
$79$	3.21124	−	9.88319i	0.361293	−	1.11195i	−0.590977	−	0.806689i	$-0.701258\pi$
$79$	3.21124	−	9.88319i	0.361293	−	1.11195i	0.952270	−	0.305257i	$-0.0987425\pi$
$80$	2.10451	−	0.755660i	0.235292	−	0.0844853i
$81$	2.44803	+	7.53426i	0.272003	+	0.837140i
$82$			11.2653i			1.24405i
$83$	7.89465	−	2.56513i	0.866550	−	0.281559i	0.158189	−	0.987409i	$-0.449435\pi$
$83$	7.89465	−	2.56513i	0.866550	−	0.281559i	0.708362	+	0.705850i	$0.249435\pi$
$84$	0.281901	+	0.204813i	0.0307580	+	0.0223470i
$85$	−3.82030	+	13.1081i	−0.414370	+	1.42178i
$86$	5.87427	−	4.26790i	0.633438	−	0.460220i
$87$	1.91146	−	2.63090i	0.204930	−	0.282062i
$88$	1.58628	−	2.18333i	0.169098	−	0.232743i
$89$	−1.96248	+	1.42582i	−0.208022	+	0.151137i	−0.686918	−	0.726735i	$-0.741037\pi$
$89$	−1.96248	+	1.42582i	−0.208022	+	0.151137i	0.478896	+	0.877872i	$0.341037\pi$
$90$	5.32061	+	3.62247i	0.560842	+	0.381842i
$91$	−3.87811	−	2.81761i	−0.406536	−	0.295366i
$92$	1.42285	−	0.462311i	0.148342	−	0.0481992i
$93$			1.51006i			0.156586i
$94$	3.42885	+	10.5529i	0.353659	+	1.08845i
$95$	−8.01864	−	2.33699i	−0.822695	−	0.239771i
$96$	−0.107677	+	0.331395i	−0.0109897	+	0.0338229i
$97$	3.32974	+	1.08190i	0.338084	+	0.109850i	0.473139	−	0.880988i	$-0.343121\pi$
$97$	3.32974	+	1.08190i	0.338084	+	0.109850i	−0.135055	+	0.990838i	$0.543121\pi$
$98$	−0.587785	−	0.809017i	−0.0593753	−	0.0817231i
$99$	7.76855			0.780768
$100$	4.99066	−	0.305503i	0.499066	−	0.0305503i
$101$	−13.9936			−1.39242			−0.696209	−	0.717840i	$-0.745131\pi$
$101$	−13.9936			−1.39242			−0.696209	+	0.717840i	$0.745131\pi$
$102$	−1.25060	−	1.72130i	−0.123827	−	0.170434i
$103$	2.14610	+	0.697310i	0.211462	+	0.0687080i	0.412832	−	0.910807i	$-0.364540\pi$
$103$	2.14610	+	0.697310i	0.211462	+	0.0687080i	−0.201371	+	0.979515i	$0.564540\pi$
$104$	1.48131	−	4.55899i	0.145254	−	0.447046i
$105$	0.477029	+	0.616058i	0.0465533	+	0.0601211i
$106$	0.161430	+	0.496831i	0.0156795	+	0.0482565i
$107$		−	11.1542i		−	1.07832i	−0.842205	−	0.539158i	$-0.818743\pi$
$107$		−	11.1542i		−	1.07832i	0.842205	−	0.539158i	$-0.181257\pi$
$108$	−1.94813	+	0.632987i	−0.187459	+	0.0609092i
$109$	−4.99061	−	3.62589i	−0.478014	−	0.347297i	0.322543	−	0.946555i	$-0.395462\pi$
$109$	−4.99061	−	3.62589i	−0.478014	−	0.347297i	−0.800556	+	0.599258i	$0.795462\pi$
$110$	4.77137	−	3.69459i	0.454932	−	0.352265i
$111$	1.07557	−	0.781445i	0.102088	−	0.0741715i
$112$	0.587785	−	0.809017i	0.0555405	−	0.0764449i
$113$	−9.14676	+	12.5894i	−0.860454	+	1.18431i	0.121007	+	0.992652i	$0.461388\pi$
$113$	−9.14676	+	12.5894i	−0.860454	+	1.18431i	−0.981461	+	0.191662i	$0.938612\pi$
$114$	1.05297	−	0.765027i	0.0986197	−	0.0716514i
$115$	3.34375	−	0.102248i	0.311806	−	0.00953467i
$116$	−7.55030	−	5.48562i	−0.701028	−	0.509327i
$117$	13.1234	−	4.26406i	1.21326	−	0.394212i
$118$			3.49419i			0.321666i
$119$	1.88687	+	5.80718i	0.172969	+	0.532343i
$120$	−0.438496	+	0.644054i	−0.0400290	+	0.0587938i
$121$	−1.14856	+	3.53489i	−0.104414	+	0.321354i
$122$	−3.21266	−	1.04386i	−0.290860	−	0.0945063i
$123$	−2.30729	−	3.17571i	−0.208041	−	0.286344i
$124$	4.33366			0.389175
$125$	10.9049	+	2.46662i	0.975360	+	0.220621i
$126$	2.87858			0.256445
$127$	−2.07420	−	2.85489i	−0.184055	−	0.253330i	0.707012	−	0.707202i	$-0.250043\pi$
$127$	−2.07420	−	2.85489i	−0.184055	−	0.253330i	−0.891067	+	0.453871i	$0.850043\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−0.781840	+	2.40626i	−0.0688372	+	0.211859i
$130$	6.03238	−	8.86023i	0.529074	−	0.777093i
$131$	6.04586	+	18.6072i	0.528229	+	1.62572i	0.757841	+	0.652439i	$0.226254\pi$
$131$	6.04586	+	18.6072i	0.528229	+	1.62572i	−0.229612	+	0.973282i	$0.573746\pi$
$132$			0.940374i			0.0818490i
$133$	−3.55243	+	1.15425i	−0.308034	+	0.100086i
$134$	11.3106	+	8.21765i	0.977089	+	0.709897i
$135$	−4.57819	+	0.139996i	−0.394028	+	0.0120489i
$136$	−4.93988	+	3.58903i	−0.423591	+	0.307757i
$137$	−3.78816	+	5.21396i	−0.323644	+	0.445458i	−0.939576	−	0.342342i	$-0.888780\pi$
$137$	−3.78816	+	5.21396i	−0.323644	+	0.445458i	0.615931	+	0.787800i	$0.288780\pi$
$138$	−0.306415	+	0.421744i	−0.0260838	+	0.0359012i
$139$	−12.4397	+	9.03795i	−1.05512	+	0.766589i	−0.973179	−	0.230048i	$-0.926112\pi$
$139$	−12.4397	+	9.03795i	−1.05512	+	0.766589i	−0.0819401	+	0.996637i	$0.526112\pi$
$140$	1.76800	−	1.36901i	0.149423	−	0.115702i
$141$	−3.12797	−	2.27261i	−0.263423	−	0.191388i
$142$	−8.75495	+	2.84465i	−0.734699	+	0.238718i
$143$		−	12.9367i		−	1.08182i
$144$	0.889531	+	2.73770i	0.0741276	+	0.228141i
$145$	−12.7765	−	16.5002i	−1.06103	−	1.37027i
$146$	2.04303	−	6.28781i	0.169083	−	0.520383i
$147$	0.331395	+	0.107677i	0.0273330	+	0.00888103i
$148$	−2.24264	−	3.08673i	−0.184344	−	0.253727i
$149$	−1.24299			−0.101830			−0.0509148	−	0.998703i	$-0.516214\pi$
$149$	−1.24299			−0.101830			−0.0509148	+	0.998703i	$0.516214\pi$
$150$	−1.34430	+	1.10827i	−0.109762	+	0.0904903i
$151$	−19.6032			−1.59529			−0.797645	−	0.603128i	$-0.793921\pi$
$151$	−19.6032			−1.59529			−0.797645	+	0.603128i	$0.793921\pi$
$152$	−2.19552	−	3.02187i	−0.178080	−	0.245106i
$153$	−16.7164	−	5.43150i	−1.35144	−	0.439111i
$154$	0.833956	−	2.56665i	0.0672021	−	0.206827i
$155$	9.30331	+	2.71140i	0.747260	+	0.217785i
$156$	0.516160	+	1.58858i	0.0413258	+	0.127188i
$157$			8.00355i			0.638753i	0.947628	+	0.319377i	$0.103473\pi$
$157$			8.00355i			0.638753i	−0.947628	+	0.319377i	$0.896527\pi$
$158$	9.88319	−	3.21124i	0.786265	−	0.255473i
$159$	−0.147265	−	0.106994i	−0.0116789	−	0.00848520i
$160$	1.84834	+	1.25842i	0.146124	+	0.0994870i
$161$	1.21035	−	0.879367i	0.0953886	−	0.0693039i
$162$	−4.65643	+	6.40902i	−0.365844	+	0.503541i
$163$	6.29295	−	8.66150i	0.492902	−	0.678421i	−0.488018	−	0.872834i	$-0.662280\pi$
$163$	6.29295	−	8.66150i	0.492902	−	0.678421i	0.980920	+	0.194412i	$0.0622800\pi$
$164$	−9.11384	+	6.62160i	−0.711672	+	0.517060i
$165$	−0.588355	+	2.01875i	−0.0458034	+	0.157160i
$166$	6.71559	+	4.87916i	0.521231	+	0.378696i
$167$	−13.6109	+	4.42245i	−1.05324	+	0.342220i	−0.783941	−	0.620836i	$-0.786793\pi$
$167$	−13.6109	+	4.42245i	−1.05324	+	0.342220i	−0.269303	+	0.963055i	$0.586793\pi$
$168$			0.348449i			0.0268834i
$169$	−3.08357	−	9.49025i	−0.237198	−	0.730019i
$170$	−12.8502	+	4.61408i	−0.985567	+	0.353884i
$171$	3.32261	−	10.2260i	0.254087	−	0.781998i
$172$	6.90561	+	2.24377i	0.526548	+	0.171086i
$173$	−1.46116	−	2.01111i	−0.111090	−	0.152902i	0.749852	−	0.661606i	$-0.230125\pi$
$173$	−1.46116	−	2.01111i	−0.111090	−	0.152902i	−0.860942	+	0.508704i	$0.830125\pi$
$174$	3.25197			0.246531
$175$	4.65199	−	1.83275i	0.351658	−	0.138543i
$176$	2.69874			0.203425
$177$	−0.715657	−	0.985017i	−0.0537921	−	0.0740384i
$178$	−2.30703	−	0.749600i	−0.172919	−	0.0561849i
$179$	6.07986	−	18.7119i	0.454430	−	1.39859i	−0.417373	−	0.908735i	$-0.637049\pi$
$179$	6.07986	−	18.7119i	0.454430	−	1.39859i	0.871803	−	0.489857i	$-0.162951\pi$
$180$	0.196735	+	6.43370i	0.0146638	+	0.479540i
$181$	−4.01599	−	12.3599i	−0.298506	−	0.918707i	−0.982021	−	0.188771i	$-0.939550\pi$
$181$	−4.01599	−	12.3599i	−0.298506	−	0.918707i	0.683515	−	0.729936i	$-0.260450\pi$
$182$		−	4.79360i		−	0.355326i
$183$	1.11945	−	0.363731i	0.0827520	−	0.0268878i
$184$	1.21035	+	0.879367i	0.0892278	+	0.0648278i
$185$	−2.88315	−	8.02957i	−0.211973	−	0.590346i
$186$	−1.22167	+	0.887592i	−0.0895769	+	0.0650814i
$187$	−9.68586	+	13.3314i	−0.708300	+	0.974892i
$188$	−6.52206	+	8.97684i	−0.475670	+	0.654704i
$189$	−1.65718	+	1.20401i	−0.120542	+	0.0875790i
$190$	−2.82257	−	7.86087i	−0.204771	−	0.570287i
$191$	17.7842	+	12.9210i	1.28682	+	0.934929i	0.999736	−	0.0229762i	$-0.00731421\pi$
$191$	17.7842	+	12.9210i	1.28682	+	0.934929i	0.287084	+	0.957905i	$0.407314\pi$
$192$	−0.331395	+	0.107677i	−0.0239164	+	0.00777090i
$193$		−	12.2789i		−	0.883851i	−0.897052	−	0.441926i	$-0.854296\pi$
$193$		−	12.2789i		−	0.883851i	0.897052	−	0.441926i	$-0.145704\pi$
$194$	1.08190	+	3.32974i	0.0776758	+	0.239062i
$195$	0.114158	+	3.73322i	0.00817499	+	0.267342i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	7.49554	+	2.43545i	0.534035	+	0.173518i	0.563605	−	0.826044i	$-0.309414\pi$
$197$	7.49554	+	2.43545i	0.534035	+	0.173518i	−0.0295704	+	0.999563i	$0.509414\pi$
$198$	4.56624	+	6.28489i	0.324508	+	0.446647i
$199$	0.319409			0.0226423			0.0113211	−	0.999936i	$-0.496396\pi$
$199$	0.319409			0.0226423			0.0113211	+	0.999936i	$0.496396\pi$
$200$	3.18059	+	3.85796i	0.224902	+	0.272799i
$201$	−4.87157			−0.343614
$202$	−8.22524	−	11.3211i	−0.578726	−	0.796548i
$203$	−8.87591	−	2.88396i	−0.622967	−	0.202414i
$204$	0.657477	−	2.02351i	0.0460326	−	0.141674i
$205$	−23.7080	+	8.51276i	−1.65584	+	0.594557i
$206$	0.697310	+	2.14610i	0.0485839	+	0.149526i
$207$			4.30656i			0.299327i
$208$	4.55899	−	1.48131i	0.316109	−	0.102710i
$209$	−8.15525	−	5.92514i	−0.564111	−	0.409850i
$210$	−0.218011	+	0.748035i	−0.0150442	+	0.0516193i
$211$	−0.298513	+	0.216882i	−0.0205505	+	0.0149308i	−0.598013	−	0.801486i	$-0.704043\pi$
$211$	−0.298513	+	0.216882i	−0.0205505	+	0.0149308i	0.577463	+	0.816417i	$0.304043\pi$
$212$	−0.307059	+	0.422630i	−0.0210889	+	0.0290263i
$213$	1.88541	−	2.59504i	0.129186	−	0.177809i
$214$	9.02392	−	6.55626i	0.616863	−	0.448177i
$215$	13.4208	+	9.13739i	0.915292	+	0.623165i
$216$	−1.65718	−	1.20401i	−0.112757	−	0.0819227i
$217$	4.12156	−	1.33918i	0.279790	−	0.0909092i
$218$		−	6.16873i		−	0.417799i
$219$	0.711894	+	2.19098i	0.0481053	+	0.148053i
$220$	5.79353	+	1.68850i	0.390600	+	0.113838i
$221$	−9.04489	+	27.8373i	−0.608425	+	1.87254i
$222$	1.26441	+	0.410830i	0.0848613	+	0.0275731i
$223$	8.90094	+	12.2511i	0.596051	+	0.820394i	0.995340	−	0.0964312i	$-0.0307428\pi$
$223$	8.90094	+	12.2511i	0.596051	+	0.820394i	−0.399288	+	0.916825i	$0.630743\pi$
$224$	1.00000			0.0668153
$225$	−3.60297	+	13.9347i	−0.240198	+	0.928977i
$226$	−15.5614			−1.03513
$227$	−13.8764	−	19.0992i	−0.921010	−	1.26766i	−0.963264	−	0.268555i	$-0.913454\pi$
$227$	−13.8764	−	19.0992i	−0.921010	−	1.26766i	0.0422544	−	0.999107i	$-0.486546\pi$
$228$	1.23784	+	0.402199i	0.0819780	+	0.0266363i
$229$	−3.37332	+	10.3820i	−0.222915	+	0.686062i	0.775582	+	0.631247i	$0.217457\pi$
$229$	−3.37332	+	10.3820i	−0.222915	+	0.686062i	−0.998497	+	0.0548145i	$0.982543\pi$
$230$	2.04813	+	2.64505i	0.135049	+	0.174409i
$231$	0.290592	+	0.894349i	0.0191195	+	0.0588438i
$232$		−	9.33269i		−	0.612721i
$233$	13.7558	−	4.46952i	0.901171	−	0.292808i	0.178451	−	0.983949i	$-0.442891\pi$
$233$	13.7558	−	4.46952i	0.901171	−	0.292808i	0.722720	+	0.691141i	$0.242891\pi$
$234$	11.1635	+	8.11072i	0.729778	+	0.530215i
$235$	−19.6177	+	15.1905i	−1.27972	+	0.990917i
$236$	−2.82686	+	2.05383i	−0.184013	+	0.133693i
$237$	−2.12838	+	2.92946i	−0.138253	+	0.190289i
$238$	−3.58903	+	4.93988i	−0.232642	+	0.320205i
$239$	12.4907	−	9.07500i	0.807954	−	0.587013i	−0.105283	−	0.994442i	$-0.533575\pi$
$239$	12.4907	−	9.07500i	0.807954	−	0.587013i	0.913237	+	0.407429i	$0.133575\pi$
$240$	−0.778792	+	0.0238146i	−0.0502708	+	0.00153722i
$241$	9.10158	+	6.61269i	0.586285	+	0.425961i	0.840984	−	0.541059i	$-0.181977\pi$
$241$	9.10158	+	6.61269i	0.586285	+	0.425961i	−0.254700	+	0.967020i	$0.581977\pi$
$242$	−3.53489	+	1.14856i	−0.227231	+	0.0738319i
$243$		−	8.90558i		−	0.571293i
$244$	−1.04386	−	3.21266i	−0.0668260	−	0.205669i
$245$	1.25842	−	1.84834i	0.0803976	−	0.118086i
$246$	1.21301	−	3.73327i	0.0773390	−	0.238025i
$247$	−17.0289	−	5.53303i	−1.08352	−	0.352058i
$248$	2.54726	+	3.50601i	0.161751	+	0.222632i
$249$	−2.89245			−0.183302
$250$	4.41417	+	10.2721i	0.279177	+	0.649662i
$251$	6.65358			0.419970			0.209985	−	0.977705i	$-0.432658\pi$
$251$	6.65358			0.419970			0.209985	+	0.977705i	$0.432658\pi$
$252$	1.69199	+	2.32882i	0.106585	+	0.146702i
$253$	3.83989	+	1.24766i	0.241412	+	0.0784395i
$254$	1.09047	−	3.35612i	0.0684222	−	0.210582i
$255$	2.67747	−	3.93261i	0.167670	−	0.246270i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			14.9756i			0.934152i	0.884217	+	0.467076i	$0.154693\pi$
$257$			14.9756i			0.934152i	−0.884217	+	0.467076i	$0.845307\pi$
$258$	−2.40626	+	0.781840i	−0.149807	+	0.0486752i
$259$	−3.08673	−	2.24264i	−0.191800	−	0.139351i
$260$	10.7138	−	0.327616i	0.664443	−	0.0203179i
$261$	21.7342	−	15.7908i	1.34531	−	0.977426i
$262$	−11.4999	+	15.8283i	−0.710466	+	0.977873i
$263$	7.09668	−	9.76775i	0.437600	−	0.602305i	−0.532076	−	0.846696i	$-0.678588\pi$
$263$	7.09668	−	9.76775i	0.437600	−	0.602305i	0.969677	+	0.244391i	$0.0785881\pi$
$264$	−0.760778	+	0.552738i	−0.0468227	+	0.0340187i
$265$	−0.923602	+	0.715168i	−0.0567364	+	0.0439324i
$266$	−3.02187	−	2.19552i	−0.185283	−	0.134616i
$267$	0.803883	−	0.261197i	0.0491968	−	0.0159850i
$268$			13.9807i			0.854008i
$269$	−2.19081	−	6.74263i	−0.133576	−	0.411105i	0.861790	−	0.507266i	$-0.169344\pi$
$269$	−2.19081	−	6.74263i	−0.133576	−	0.411105i	−0.995366	+	0.0961606i	$0.969344\pi$
$270$	−2.80425	−	3.62155i	−0.170661	−	0.220401i
$271$	2.38077	−	7.32725i	0.144621	−	0.445099i	−0.852341	−	0.522987i	$-0.824818\pi$
$271$	2.38077	−	7.32725i	0.144621	−	0.445099i	0.996962	+	0.0778881i	$0.0248177\pi$
$272$	−5.80718	−	1.88687i	−0.352112	−	0.114408i
$273$	0.981794	+	1.35132i	0.0594209	+	0.0817858i
$274$	−6.44480			−0.389345
$275$	11.3808	+	7.24957i	0.686291	+	0.437165i
$276$	−0.521304			−0.0313788
$277$	14.9909	+	20.6332i	0.900716	+	1.23973i	0.970239	+	0.242149i	$0.0778523\pi$
$277$	14.9909	+	20.6332i	0.900716	+	1.23973i	−0.0695228	+	0.997580i	$0.522148\pi$
$278$	−14.6237	−	4.75153i	−0.877072	−	0.284978i
$279$	−3.85493	+	11.8643i	−0.230789	+	0.710294i
$280$	2.14675	+	0.625661i	0.128293	+	0.0373904i
$281$	−4.10934	−	12.6473i	−0.245143	−	0.754472i	−0.995613	−	0.0935676i	$-0.970173\pi$
$281$	−4.10934	−	12.6473i	−0.245143	−	0.754472i	0.750470	−	0.660904i	$-0.229827\pi$
$282$		−	3.86639i		−	0.230240i
$283$	−19.0330	+	6.18420i	−1.13139	+	0.367612i	−0.814106	−	0.580717i	$-0.802772\pi$
$283$	−19.0330	+	6.18420i	−1.13139	+	0.367612i	−0.317289	+	0.948329i	$0.602772\pi$
$284$	−7.44740	−	5.41085i	−0.441922	−	0.321075i
$285$	2.40570	+	1.63789i	0.142501	+	0.0970202i
$286$	10.4660	−	7.60400i	0.618868	−	0.449634i
$287$	−6.62160	+	9.11384i	−0.390860	+	0.537973i
$288$	−1.69199	+	2.32882i	−0.0997014	+	0.137227i
$289$	16.4097	−	11.9224i	0.965279	−	0.701316i
$290$	5.83910	−	20.0350i	0.342884	−	1.17649i
$291$	−0.986965	−	0.717072i	−0.0578569	−	0.0420355i
$292$	6.28781	−	2.04303i	0.367966	−	0.119560i
$293$			17.6142i			1.02904i	0.857480	+	0.514518i	$0.172029\pi$
$293$			17.6142i			1.02904i	−0.857480	+	0.514518i	$0.827971\pi$
$294$	0.107677	+	0.331395i	0.00627984	+	0.0193273i
$295$	−7.35357	+	2.64042i	−0.428141	+	0.153731i
$296$	1.17902	−	3.62866i	0.0685294	−	0.210912i
$297$	−5.25750	−	1.70827i	−0.305071	−	0.0991237i
$298$	−0.730611	−	1.00560i	−0.0423231	−	0.0582528i
$299$	7.17156			0.414742
$300$	−1.68677	−	0.436136i	−0.0973860	−	0.0251803i
$301$	7.26099			0.418517
$302$	−11.5225	−	15.8594i	−0.663045	−	0.912603i
$303$	4.63741	+	1.50679i	0.266412	+	0.0865627i
$304$	1.15425	−	3.55243i	0.0662010	−	0.203746i
$305$	−0.230867	−	7.54988i	−0.0132194	−	0.432305i
$306$	−5.43150	−	16.7164i	−0.310498	−	0.955615i
$307$		−	22.9461i		−	1.30961i	−0.755800	−	0.654803i	$-0.772752\pi$
$307$		−	22.9461i		−	1.30961i	0.755800	−	0.654803i	$-0.227248\pi$
$308$	2.56665	−	0.833956i	0.146249	−	0.0475191i
$309$	−0.636123	−	0.462170i	−0.0361878	−	0.0262919i
$310$	3.27478	+	9.12026i	0.185995	+	0.517996i
$311$	17.4695	−	12.6923i	0.990604	−	0.719716i	0.0305506	−	0.999533i	$-0.490274\pi$
$311$	17.4695	−	12.6923i	0.990604	−	0.719716i	0.960053	+	0.279817i	$0.0902739\pi$
$312$	−0.981794	+	1.35132i	−0.0555831	+	0.0765036i
$313$	4.82694	−	6.64371i	0.272835	−	0.375524i	−0.650510	−	0.759498i	$-0.725445\pi$
$313$	4.82694	−	6.64371i	0.272835	−	0.375524i	0.923344	+	0.383974i	$0.125445\pi$
$314$	−6.47501	+	4.70437i	−0.365406	+	0.265483i
$315$	2.17523	+	6.05802i	0.122560	+	0.341331i
$316$	8.40714	+	6.10815i	0.472939	+	0.343610i
$317$	23.1610	−	7.52547i	1.30085	−	0.422672i	0.424974	−	0.905206i	$-0.360283\pi$
$317$	23.1610	−	7.52547i	1.30085	−	0.422672i	0.875878	+	0.482533i	$0.160283\pi$
$318$		−	0.182030i		−	0.0102077i
$319$	−7.78306	−	23.9538i	−0.435767	−	1.34115i
$320$	0.0683444	+	2.23502i	0.00382057	+	0.124942i
$321$	−1.20105	+	3.69644i	−0.0670359	+	0.206315i
$322$	1.42285	+	0.462311i	0.0792921	+	0.0257636i
$323$	13.4059	+	18.4516i	0.745924	+	1.02668i
$324$	−7.92199			−0.440111
$325$	23.2049	+	5.99990i	1.28718	+	0.332815i
$326$	10.7062			0.592962
$327$	1.26344	+	1.73897i	0.0698683	+	0.0961655i
$328$	−10.7140	−	3.48118i	−0.591580	−	0.192216i
$329$	−3.42885	+	10.5529i	−0.189039	+	0.581801i
$330$	−1.97903	+	0.710603i	−0.108942	+	0.0391174i
$331$	−2.74223	−	8.43971i	−0.150727	−	0.463889i	0.846976	−	0.531631i	$-0.178421\pi$
$331$	−2.74223	−	8.43971i	−0.150727	−	0.463889i	−0.997703	+	0.0677420i	$0.978421\pi$
$332$			8.30093i			0.455572i
$333$	10.4454	−	3.39392i	0.572405	−	0.185986i
$334$	−11.5781	−	8.41201i	−0.633527	−	0.460285i
$335$	−8.74718	+	30.0131i	−0.477909	+	1.63979i
$336$	−0.281901	+	0.204813i	−0.0153790	+	0.0111735i
$337$	−7.73256	+	10.6430i	−0.421219	+	0.579759i	−0.965910	−	0.258878i	$-0.916647\pi$
$337$	−7.73256	+	10.6430i	−0.421219	+	0.579759i	0.544690	+	0.838637i	$0.316647\pi$
$338$	5.86530	−	8.07289i	0.319030	−	0.439107i
$339$	4.38678	−	3.18718i	0.238257	−	0.173104i
$340$	−11.2860	−	7.68396i	−0.612071	−	0.416721i
$341$	9.46180	+	6.87440i	0.512385	+	0.372270i
$342$	10.2260	−	3.32261i	0.552956	−	0.179666i
$343$		−	1.00000i		−	0.0539949i
$344$	2.24377	+	6.90561i	0.120976	+	0.372326i
$345$	−1.11911	−	0.326160i	−0.0602509	−	0.0175598i
$346$	0.768177	−	2.36421i	0.0412975	−	0.127100i
$347$	12.0311	+	3.90915i	0.645865	+	0.209854i	0.613590	−	0.789625i	$-0.289725\pi$
$347$	12.0311	+	3.90915i	0.645865	+	0.209854i	0.0322751	+	0.999479i	$0.489725\pi$
$348$	1.91146	+	2.63090i	0.102465	+	0.141031i
$349$	25.3797			1.35855			0.679273	−	0.733885i	$-0.262295\pi$
$349$	25.3797			1.35855			0.679273	+	0.733885i	$0.262295\pi$
$350$	4.21710	+	2.68628i	0.225413	+	0.143588i
$351$	−9.81916			−0.524108
$352$	1.58628	+	2.18333i	0.0845490	+	0.116372i
$353$	14.0328	+	4.55952i	0.746889	+	0.242679i	0.657642	−	0.753331i	$-0.271554\pi$
$353$	14.0328	+	4.55952i	0.746889	+	0.242679i	0.0892467	+	0.996010i	$0.471554\pi$
$354$	0.376243	−	1.15796i	0.0199971	−	0.0615447i
$355$	−12.6024	−	16.2753i	−0.668865	−	0.863804i
$356$	−0.749600	−	2.30703i	−0.0397287	−	0.122272i
$357$		−	2.12764i		−	0.112607i
$358$	18.7119	−	6.07986i	0.988954	−	0.321331i
$359$	−18.9224	−	13.7479i	−0.998688	−	0.725589i	−0.0368812	−	0.999320i	$-0.511742\pi$
$359$	−18.9224	−	13.7479i	−0.998688	−	0.725589i	−0.961806	+	0.273731i	$0.911742\pi$
$360$	−5.08933	+	3.94080i	−0.268232	+	0.207698i
$361$	4.08389	−	2.96712i	0.214942	−	0.156164i
$362$	7.63886	−	10.5140i	0.401490	−	0.552603i
$363$	0.761251	−	1.04777i	0.0399553	−	0.0549938i
$364$	3.87811	−	2.81761i	0.203268	−	0.147683i
$365$	14.7766	−	0.451852i	0.773444	−	0.0236510i
$366$	0.952260	+	0.691857i	0.0497754	+	0.0361640i
$367$	27.1422	−	8.81904i	1.41681	−	0.460350i	0.502225	−	0.864737i	$-0.332515\pi$
$367$	27.1422	−	8.81904i	1.41681	−	0.460350i	0.914588	+	0.404387i	$0.132515\pi$
$368$			1.49607i			0.0779880i
$369$	−10.0209	−	30.8410i	−0.521665	−	1.60552i
$370$	4.80139	−	7.05218i	0.249612	−	0.366625i
$371$	−0.161430	+	0.496831i	−0.00838104	+	0.0257942i
$372$	−1.43615	−	0.466635i	−0.0744611	−	0.0241939i
$373$	15.3908	+	21.1837i	0.796908	+	1.09685i	0.993213	+	0.116307i	$0.0371055\pi$
$373$	15.3908	+	21.1837i	0.796908	+	1.09685i	−0.196306	+	0.980543i	$0.562894\pi$
$374$	−16.4786			−0.852087
$375$	−3.34822	−	1.99162i	−0.172901	−	0.102847i
$376$	−11.0960			−0.572232
$377$	−26.2959	−	36.1932i	−1.35431	−	1.86404i
$378$	−1.94813	−	0.632987i	−0.100201	−	0.0325573i
$379$	−2.93098	+	9.02063i	−0.150554	+	0.463358i	−0.997683	−	0.0680287i	$-0.978329\pi$
$379$	−2.93098	+	9.02063i	−0.150554	+	0.463358i	0.847129	+	0.531387i	$0.178329\pi$
$380$	4.70051	−	6.90401i	0.241131	−	0.354168i
$381$	0.379974	+	1.16944i	0.0194666	+	0.0599122i
$382$			21.9825i			1.12472i
$383$	28.7028	−	9.32609i	1.46664	−	0.476541i	0.536551	−	0.843868i	$-0.319727\pi$
$383$	28.7028	−	9.32609i	1.46664	−	0.476541i	0.930092	+	0.367327i	$0.119727\pi$
$384$	−0.281901	−	0.204813i	−0.0143857	−	0.0104518i
$385$	6.03175	−	0.184444i	0.307406	−	0.00940012i
$386$	9.93380	−	7.21733i	0.505617	−	0.367352i
$387$	−12.2855	+	16.9096i	−0.624508	+	0.859561i
$388$	−2.05789	+	2.83245i	−0.104474	+	0.143796i
$389$	−24.6651	+	17.9202i	−1.25057	+	0.908591i	−0.998255	−	0.0590544i	$-0.981191\pi$
$389$	−24.6651	+	17.9202i	−1.25057	+	0.908591i	−0.252314	+	0.967646i	$0.581191\pi$
$390$	−2.95314	+	2.28669i	−0.149538	+	0.115791i
$391$	−7.39040	−	5.36944i	−0.373749	−	0.271544i
$392$	0.951057	−	0.309017i	0.0480356	−	0.0156077i
$393$		−	6.81734i		−	0.343889i
$394$	2.43545	+	7.49554i	0.122696	+	0.377620i
$395$	14.2264	+	18.3727i	0.715810	+	0.924431i
$396$	−2.40061	+	7.38833i	−0.120635	+	0.371277i
$397$	−2.27470	−	0.739096i	−0.114164	−	0.0370942i	0.251378	−	0.967889i	$-0.419116\pi$
$397$	−2.27470	−	0.739096i	−0.114164	−	0.0370942i	−0.365542	+	0.930795i	$0.619116\pi$
$398$	0.187744	+	0.258407i	0.00941075	+	0.0129528i
$399$	1.30154			0.0651586
$400$	−1.25165	+	4.84080i	−0.0625824	+	0.242040i
$401$	6.99536			0.349332			0.174666	−	0.984628i	$-0.444115\pi$
$401$	6.99536			0.349332			0.174666	+	0.984628i	$0.444115\pi$
$402$	−2.86344	−	3.94118i	−0.142815	−	0.196568i
$403$	19.7571	+	6.41948i	0.984173	+	0.319777i
$404$	4.32427	−	13.3087i	0.215140	−	0.662134i
$405$	−17.0066	−	4.95648i	−0.845063	−	0.246289i
$406$	−2.88396	−	8.87591i	−0.143128	−	0.440504i
$407$		−	10.2968i		−	0.510392i
$408$	2.02351	−	0.657477i	0.100178	−	0.0325500i
$409$	−1.27387	−	0.925522i	−0.0629889	−	0.0457641i	0.555845	−	0.831286i	$-0.312395\pi$
$409$	−1.27387	−	0.925522i	−0.0629889	−	0.0457641i	−0.618834	+	0.785522i	$0.712395\pi$
$410$	−20.8222	−	14.1765i	−1.02834	−	0.700129i
$411$	1.81680	−	1.31998i	0.0896161	−	0.0651099i
$412$	−1.32636	+	1.82558i	−0.0653452	+	0.0899400i
$413$	−2.05383	+	2.82686i	−0.101063	+	0.139101i
$414$	−3.48408	+	2.53133i	−0.171233	+	0.124408i
$415$	−5.19356	+	17.8200i	−0.254942	+	0.874751i
$416$	3.87811	+	2.81761i	0.190140	+	0.138145i
$417$	5.09562	−	1.65567i	0.249534	−	0.0810784i
$418$		−	10.0804i		−	0.493051i
$419$	1.10714	+	3.40744i	0.0540875	+	0.166464i	0.974451	−	0.224599i	$-0.0721073\pi$
$419$	1.10714	+	3.40744i	0.0540875	+	0.166464i	−0.920364	+	0.391063i	$0.872107\pi$
$420$	−0.733316	+	0.263309i	−0.0357822	+	0.0128482i
$421$	10.3430	−	31.8324i	0.504086	−	1.55142i	−0.298216	−	0.954498i	$-0.596392\pi$
$421$	10.3430	−	31.8324i	0.504086	−	1.55142i	0.802302	−	0.596918i	$-0.203608\pi$
$422$	−0.350923	−	0.114022i	−0.0170827	−	0.00555049i
$423$	−18.7743	−	25.8406i	−0.912837	−	1.25641i
$424$	−0.522399			−0.0253700
$425$	−19.4208	−	23.5568i	−0.942046	−	1.14267i
$426$	3.20765			0.155411
$427$	−1.98553	−	2.73285i	−0.0960866	−	0.132252i
$428$	10.6083	+	3.44683i	0.512770	+	0.166609i
$429$	−1.39298	+	4.28715i	−0.0672537	+	0.206986i
$430$	0.496248	+	16.2285i	0.0239312	+	0.782607i
$431$	5.98425	+	18.4176i	0.288251	+	0.887146i	0.985405	+	0.170225i	$0.0544494\pi$
$431$	5.98425	+	18.4176i	0.288251	+	0.887146i	−0.697154	+	0.716921i	$0.745551\pi$
$432$		−	2.04839i		−	0.0985531i
$433$	−10.9250	+	3.54976i	−0.525024	+	0.170591i	−0.559524	−	0.828814i	$-0.689016\pi$
$433$	−10.9250	+	3.54976i	−0.525024	+	0.170591i	0.0345001	+	0.999405i	$0.489016\pi$
$434$	3.50601	+	2.54726i	0.168294	+	0.122273i
$435$	2.45738	+	6.84381i	0.117822	+	0.328136i
$436$	4.99061	−	3.62589i	0.239007	−	0.173649i
$437$	3.28465	−	4.52093i	0.157126	−	0.216266i
$438$	−1.35410	+	1.86376i	−0.0647015	+	0.0890540i
$439$	3.00890	−	2.18609i	0.143607	−	0.104337i	−0.513662	−	0.857993i	$-0.671712\pi$
$439$	3.00890	−	2.18609i	0.143607	−	0.104337i	0.657269	+	0.753656i	$0.271712\pi$
$440$	2.03933	+	5.67954i	0.0972212	+	0.270761i
$441$	2.32882	+	1.69199i	0.110896	+	0.0805709i
$442$	−27.8373	+	9.04489i	−1.32409	+	0.430221i
$443$			5.12662i			0.243573i	0.992556	+	0.121786i	$0.0388623\pi$
$443$			5.12662i			0.243573i	−0.992556	+	0.121786i	$0.961138\pi$
$444$	0.410830	+	1.26441i	0.0194971	+	0.0600060i
$445$	−0.165787	−	5.42162i	−0.00785904	−	0.257009i
$446$	−4.67950	+	14.4020i	−0.221581	+	0.681956i
$447$	0.411920	+	0.133841i	0.0194832	+	0.00633046i
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	−27.2386			−1.28547			−0.642735	−	0.766089i	$-0.722200\pi$
$449$	−27.2386			−1.28547			−0.642735	+	0.766089i	$0.722200\pi$
$450$	−13.3911	+	5.27572i	−0.631265	+	0.248700i
$451$	−30.4022			−1.43158
$452$	−9.14676	−	12.5894i	−0.430227	−	0.592157i
$453$	6.49642	+	2.11081i	0.305228	+	0.0991747i
$454$	7.29526	−	22.4525i	0.342384	−	1.05375i
$455$	10.0882	−	3.62233i	0.472942	−	0.169818i
$456$	0.402199	+	1.23784i	0.0188347	+	0.0579672i
$457$			33.1627i			1.55129i	0.631172	+	0.775643i	$0.282574\pi$
$457$			33.1627i			1.55129i	−0.631172	+	0.775643i	$0.717426\pi$
$458$	−10.3820	+	3.37332i	−0.485119	+	0.157625i
$459$	10.1188	+	7.35173i	0.472305	+	0.343149i
$460$	−0.936032	+	3.21169i	−0.0436427	+	0.149746i
$461$	29.3585	−	21.3302i	1.36736	−	0.993448i	0.369426	−	0.929260i	$-0.379554\pi$
$461$	29.3585	−	21.3302i	1.36736	−	0.993448i	0.997938	−	0.0641875i	$-0.0204456\pi$
$462$	−0.552738	+	0.760778i	−0.0257157	+	0.0353946i
$463$	−12.7721	+	17.5793i	−0.593571	+	0.816980i	−0.995101	−	0.0988659i	$-0.968479\pi$
$463$	−12.7721	+	17.5793i	−0.593571	+	0.816980i	0.401530	+	0.915846i	$0.368479\pi$
$464$	7.55030	−	5.48562i	0.350514	−	0.254663i
$465$	−2.79111	−	1.90030i	−0.129435	−	0.0881241i
$466$	11.7014	+	8.50154i	0.542055	+	0.393826i
$467$	0.0408807	−	0.0132830i	0.00189174	−	0.000614662i	−0.308071	−	0.951363i	$-0.599683\pi$
$467$	0.0408807	−	0.0132830i	0.00189174	−	0.000614662i	0.309963	+	0.950749i	$0.399683\pi$
$468$			13.7988i			0.637849i
$469$	4.32028	+	13.2964i	0.199492	+	0.613973i
$470$	−23.8203	−	6.94233i	−1.09875	−	0.320226i
$471$	0.861796	−	2.65234i	0.0397095	−	0.122213i
$472$	−3.32317	−	1.07976i	−0.152961	−	0.0497002i
$473$	11.5180	+	15.8531i	0.529596	+	0.728927i
$474$	−3.62102			−0.166319
$475$	14.4104	−	11.8803i	0.661195	−	0.545105i
$476$	−6.10603			−0.279869
$477$	−0.883894	−	1.21658i	−0.0404707	−	0.0557032i
$478$	14.6837	+	4.77101i	0.671615	+	0.218221i
$479$	−6.99144	+	21.5175i	−0.319447	+	0.983157i	0.654438	+	0.756116i	$0.272905\pi$
$479$	−6.99144	+	21.5175i	−0.319447	+	0.983157i	−0.973885	+	0.227042i	$0.927095\pi$
$480$	−0.477029	−	0.616058i	−0.0217733	−	0.0281191i
$481$	−5.65178	−	17.3944i	−0.257699	−	0.793115i
$482$			11.2502i			0.512432i
$483$	−0.495790	+	0.161092i	−0.0225592	+	0.00732993i
$484$	−3.00696	−	2.18468i	−0.136680	−	0.0993037i
$485$	−6.18994	+	4.79302i	−0.281071	+	0.217640i
$486$	7.20476	−	5.23457i	0.326815	−	0.237445i
$487$	−15.4751	+	21.2997i	−0.701246	+	0.965182i	0.298696	+	0.954348i	$0.403448\pi$
$487$	−15.4751	+	21.2997i	−0.701246	+	0.965182i	−0.999941	+	0.0108334i	$0.996552\pi$
$488$	1.98553	−	2.73285i	0.0898808	−	0.123710i
$489$	−3.01809	+	2.19277i	−0.136483	+	0.0991607i
$490$	2.23502	−	0.0683444i	0.100968	−	0.00308748i
$491$	6.59692	+	4.79294i	0.297715	+	0.216302i	0.726607	−	0.687053i	$-0.241096\pi$
$491$	6.59692	+	4.79294i	0.297715	+	0.216302i	−0.428892	+	0.903356i	$0.641096\pi$
$492$	3.73327	−	1.21301i	0.168309	−	0.0546869i
$493$			56.9856i			2.56650i
$494$	−5.53303	−	17.0289i	−0.248943	−	0.766168i
$495$	−9.77611	+	14.3589i	−0.439403	+	0.645387i
$496$	−1.33918	+	4.12156i	−0.0601308	+	0.185064i
$497$	−8.75495	−	2.84465i	−0.392713	−	0.127600i
$498$	−1.70014	−	2.34004i	−0.0761851	−	0.104860i
$499$	−7.07119			−0.316550			−0.158275	−	0.987395i	$-0.550593\pi$
$499$	−7.07119			−0.316550			−0.158275	+	0.987395i	$0.550593\pi$
$500$	−5.71568	+	9.60890i	−0.255613	+	0.429723i
$501$	4.98678			0.222793
$502$	3.91088	+	5.38286i	0.174551	+	0.240249i
$503$	14.7756	+	4.80087i	0.658810	+	0.214060i	0.619295	−	0.785159i	$-0.287419\pi$
$503$	14.7756	+	4.80087i	0.658810	+	0.214060i	0.0395153	+	0.999219i	$0.487419\pi$
$504$	−0.889531	+	2.73770i	−0.0396229	+	0.121947i
$505$	17.6099	−	25.8650i	0.783629	−	1.15098i
$506$	1.24766	+	3.83989i	0.0554651	+	0.170704i
$507$			3.47705i			0.154421i
$508$	3.35612	−	1.09047i	0.148904	−	0.0483818i
$509$	−22.9770	−	16.6938i	−1.01844	−	0.739938i	−0.0524757	−	0.998622i	$-0.516711\pi$
$509$	−22.9770	−	16.6938i	−1.01844	−	0.739938i	−0.965962	+	0.258684i	$0.916711\pi$
$510$	4.75533	−	0.145412i	0.210569	−	0.00643896i
$511$	5.34873	−	3.88608i	0.236614	−	0.171910i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−4.49728	+	6.18997i	−0.198560	+	0.273294i
$514$	−12.1155	+	8.80244i	−0.534392	+	0.388259i
$515$	−3.98957	+	3.08922i	−0.175801	+	0.136127i
$516$	−2.04688	−	1.48715i	−0.0901090	−	0.0654680i
$517$	−28.4796	+	9.25357i	−1.25253	+	0.406972i
$518$		−	3.81540i		−	0.167639i
$519$	0.267671	+	0.823806i	0.0117494	+	0.0361611i
$520$	6.56247	+	8.47509i	0.287783	+	0.371657i
$521$	2.00610	−	6.17415i	0.0878889	−	0.270494i	−0.897446	−	0.441124i	$-0.854580\pi$
$521$	2.00610	−	6.17415i	0.0878889	−	0.270494i	0.985335	+	0.170629i	$0.0545801\pi$
$522$	25.5501	+	8.30172i	1.11830	+	0.363356i
$523$	−1.14042	−	1.56966i	−0.0498672	−	0.0686363i	0.783355	−	0.621574i	$-0.213507\pi$
$523$	−1.14042	−	1.56966i	−0.0498672	−	0.0686363i	−0.833222	+	0.552938i	$0.813507\pi$
$524$	−19.5648			−0.854692
$525$	−1.73899	+	0.106452i	−0.0758958	+	0.00464595i
$526$	12.0736			0.526434
$527$	−15.5537	−	21.4078i	−0.677528	−	0.932537i
$528$	−0.894349	−	0.290592i	−0.0389215	−	0.0126464i
$529$	6.41574	−	19.7456i	0.278945	−	0.858505i
$530$	−1.12146	−	0.326845i	−0.0487132	−	0.0141972i
$531$	−3.10819	−	9.56603i	−0.134884	−	0.415130i
$532$		−	3.73524i		−	0.161943i
$533$	−51.3585	+	16.6874i	−2.22458	+	0.722811i
$534$	0.683824	+	0.496827i	0.0295919	+	0.0214998i
$535$	20.6168	+	14.0367i	0.891340	+	0.606858i
$536$	−11.3106	+	8.21765i	−0.488545	+	0.354949i
$537$	−4.02967	+	5.54636i	−0.173893	+	0.239343i
$538$	4.16717	−	5.73562i	0.179660	−	0.247280i
$539$	2.18333	−	1.58628i	0.0940425	−	0.0683259i
$540$	1.28160	−	4.39738i	0.0551511	−	0.189233i
$541$	1.44508	+	1.04991i	0.0621286	+	0.0451391i	0.618416	−	0.785851i	$-0.287775\pi$
$541$	1.44508	+	1.04991i	0.0621286	+	0.0451391i	−0.556287	+	0.830990i	$0.687775\pi$
$542$	7.32725	−	2.38077i	0.314732	−	0.102263i
$543$			4.52845i			0.194334i
$544$	−1.88687	−	5.80718i	−0.0808987	−	0.248981i
$545$	12.9822	−	4.66146i	0.556096	−	0.199675i
$546$	−0.516160	+	1.58858i	−0.0220896	+	0.0679848i
$547$	−16.0406	−	5.21191i	−0.685846	−	0.222845i	−0.0546932	−	0.998503i	$-0.517418\pi$
$547$	−16.0406	−	5.21191i	−0.685846	−	0.222845i	−0.631153	+	0.775658i	$0.717418\pi$
$548$	−3.78816	−	5.21396i	−0.161822	−	0.222729i
$549$	9.72382			0.415003
$550$	0.824472	+	13.4685i	0.0351556	+	0.574298i
$551$	−34.8599			−1.48508
$552$	−0.306415	−	0.421744i	−0.0130419	−	0.0179506i
$553$	9.88319	+	3.21124i	0.420276	+	0.136556i
$554$	−7.88119	+	24.2558i	−0.334839	+	1.03053i
$555$	0.0908621	+	2.97141i	0.00385688	+	0.126129i
$556$	−4.75153	−	14.6237i	−0.201510	−	0.620184i
$557$			8.93662i			0.378657i	0.981914	+	0.189328i	$0.0606311\pi$
$557$			8.93662i			0.378657i	−0.981914	+	0.189328i	$0.939369\pi$
$558$	−11.8643	+	3.85493i	−0.502254	+	0.163192i
$559$	28.1589	+	20.4586i	1.19099	+	0.865308i
$560$	0.755660	+	2.10451i	0.0319324	+	0.0889319i
$561$	4.64533	−	3.37503i	0.196126	−	0.142494i
$562$	7.81643	−	10.7584i	0.329716	−	0.453816i
$563$	−12.6463	+	17.4061i	−0.532977	+	0.733580i	−0.987580	−	0.157114i	$-0.949781\pi$
$563$	−12.6463	+	17.4061i	−0.532977	+	0.733580i	0.454603	+	0.890694i	$0.349781\pi$
$564$	3.12797	−	2.27261i	0.131711	−	0.0956940i
$565$	−11.7591	−	32.7492i	−0.494710	−	1.37777i
$566$	−16.1904	−	11.7630i	−0.680535	−	0.494437i
$567$	−7.53426	+	2.44803i	−0.316409	+	0.102808i
$568$		−	9.20550i		−	0.386254i
$569$	−4.52285	−	13.9199i	−0.189608	−	0.583553i	0.810389	−	0.585892i	$-0.199256\pi$
$569$	−4.52285	−	13.9199i	−0.189608	−	0.583553i	−0.999997	+	0.00233871i	$0.999256\pi$
$570$	0.0889531	+	2.90898i	0.00372584	+	0.121844i
$571$	−6.38256	+	19.6435i	−0.267102	+	0.822054i	0.724100	+	0.689695i	$0.242255\pi$
$571$	−6.38256	+	19.6435i	−0.267102	+	0.822054i	−0.991202	+	0.132360i	$0.957745\pi$
$572$	12.3035	+	3.99766i	0.514436	+	0.167150i
$573$	−4.50231	−	6.19689i	−0.188087	−	0.258879i
$574$	−11.2653			−0.470206
$575$	−4.01886	+	6.30907i	−0.167598	+	0.263106i
$576$	−2.87858			−0.119941
$577$	4.09998	+	5.64314i	0.170684	+	0.234927i	0.885786	−	0.464093i	$-0.153620\pi$
$577$	4.09998	+	5.64314i	0.170684	+	0.234927i	−0.715102	+	0.699020i	$0.753620\pi$
$578$	19.2908	+	6.26796i	0.802392	+	0.260713i
$579$	−1.32215	+	4.06915i	−0.0549465	+	0.169108i
$580$	19.6408	−	7.05234i	0.815539	−	0.292832i
$581$	2.56513	+	7.89465i	0.106419	+	0.327525i
$582$		−	1.21996i		−	0.0505688i
$583$	−1.34082	+	0.435658i	−0.0555310	+	0.0180431i
$584$	5.34873	+	3.88608i	0.221332	+	0.160807i
$585$	−8.63336	+	29.6226i	−0.356946	+	1.22474i
$586$	−14.2502	+	10.3534i	−0.588671	+	0.427695i
$587$	−4.59181	+	6.32009i	−0.189524	+	0.260858i	−0.893196	−	0.449667i	$-0.851543\pi$
$587$	−4.59181	+	6.32009i	−0.189524	+	0.260858i	0.703672	+	0.710525i	$0.251543\pi$
$588$	−0.204813	+	0.281901i	−0.00844636	+	0.0116254i
$589$	13.0958	−	9.51465i	0.539603	−	0.392044i
$590$	−6.45846	−	4.39717i	−0.265891	−	0.181028i
$591$	−2.22174	−	1.61419i	−0.0913902	−	0.0663989i
$592$	3.62866	−	1.17902i	0.149137	−	0.0484576i
$593$		−	29.3675i		−	1.20598i	−0.797750	−	0.602988i	$-0.793977\pi$
$593$		−	29.3675i		−	1.20598i	0.797750	−	0.602988i	$-0.206023\pi$
$594$	−1.70827	−	5.25750i	−0.0700910	−	0.215718i
$595$	−13.1081	−	3.82030i	−0.537381	−	0.156617i
$596$	0.384105	−	1.18215i	0.0157335	−	0.0484229i
$597$	−0.105850	−	0.0343929i	−0.00433217	−	0.00140761i
$598$	4.21534	+	5.80192i	0.172378	+	0.237258i
$599$	12.3378			0.504107			0.252053	−	0.967713i	$-0.418894\pi$
$599$	12.3378			0.504107			0.252053	+	0.967713i	$0.418894\pi$
$600$	−0.638620	−	1.62098i	−0.0260715	−	0.0661764i
$601$	23.0581			0.940558			0.470279	−	0.882518i	$-0.344153\pi$
$601$	23.0581			0.940558			0.470279	+	0.882518i	$0.344153\pi$
$602$	4.26790	+	5.87427i	0.173947	+	0.239417i
$603$	−38.2749	−	12.4363i	−1.55867	−	0.506444i
$604$	6.05773	−	18.6438i	0.246486	−	0.758605i
$605$	−5.08832	−	6.57131i	−0.206870	−	0.267162i
$606$	1.50679	+	4.63741i	0.0612090	+	0.188382i
$607$		−	8.06026i		−	0.327156i	−0.986530	−	0.163578i	$-0.947696\pi$
$607$		−	8.06026i		−	0.327156i	0.986530	−	0.163578i	$-0.0523035\pi$
$608$	3.55243	−	1.15425i	0.144070	−	0.0468112i
$609$	2.63090	+	1.91146i	0.106609	+	0.0774562i
$610$	5.97229	−	4.62449i	0.241811	−	0.187240i
$611$	−43.0314	+	31.2642i	−1.74087	+	1.26481i
$612$	10.3313	−	14.2199i	0.417619	−	0.574803i
$613$	19.7478	−	27.1805i	0.797604	−	1.09781i	−0.195515	−	0.980701i	$-0.562638\pi$
$613$	19.7478	−	27.1805i	0.797604	−	1.09781i	0.993119	−	0.117107i	$-0.0373622\pi$
$614$	18.5638	−	13.4874i	0.749175	−	0.544307i
$615$	8.77335	−	0.268279i	0.353776	−	0.0108180i
$616$	2.18333	+	1.58628i	0.0879687	+	0.0639130i
$617$	32.9164	−	10.6952i	1.32516	−	0.430572i	0.440898	−	0.897557i	$-0.354660\pi$
$617$	32.9164	−	10.6952i	1.32516	−	0.430572i	0.884265	+	0.466986i	$0.154660\pi$
$618$		−	0.786291i		−	0.0316293i
$619$	8.66382	+	26.6645i	0.348228	+	1.07174i	0.959833	+	0.280573i	$0.0905245\pi$
$619$	8.66382	+	26.6645i	0.348228	+	1.07174i	−0.611604	+	0.791164i	$0.709476\pi$
$620$	−5.45358	+	8.01010i	−0.219021	+	0.321693i
$621$	0.946992	−	2.91454i	0.0380015	−	0.116957i
$622$	20.5366	+	6.67275i	0.823443	+	0.267553i
$623$	−1.42582	−	1.96248i	−0.0571244	−	0.0786250i
$624$	−1.67033			−0.0668666
$625$	−18.2821	+	17.0519i	−0.731283	+	0.682075i
$626$	8.21207			0.328220
$627$	2.06461	+	2.84169i	0.0824526	+	0.113486i
$628$	−7.61183	−	2.47323i	−0.303745	−	0.0986928i
$629$	−7.19915	+	22.1567i	−0.287049	+	0.883446i
$630$	−3.62247	+	5.32061i	−0.144323	+	0.211978i
$631$	−7.08798	−	21.8146i	−0.282168	−	0.868424i	−0.987233	−	0.159281i	$-0.949082\pi$
$631$	−7.08798	−	21.8146i	−0.282168	−	0.868424i	0.705065	−	0.709142i	$-0.250918\pi$
$632$			10.3918i			0.413364i
$633$	0.122279	−	0.0397308i	0.00486015	−	0.00157916i
$634$	19.7019	+	14.3143i	0.782463	+	0.568493i
$635$	7.88703	−	0.241176i	0.312987	−	0.00957078i
$636$	0.147265	−	0.106994i	0.00583944	−	0.00424260i
$637$	2.81761	−	3.87811i	0.111638	−	0.153656i
$638$	14.8043	−	20.3763i	0.586106	−	0.806706i
$639$	21.4380	−	15.5756i	0.848073	−	0.616161i
$640$	−1.76800	+	1.36901i	−0.0698863	+	0.0541147i
$641$	−23.6455	−	17.1795i	−0.933943	−	0.678549i	0.0130122	−	0.999915i	$-0.495858\pi$
$641$	−23.6455	−	17.1795i	−0.933943	−	0.678549i	−0.946955	+	0.321366i	$0.895858\pi$
$642$	−3.69644	+	1.20105i	−0.145887	+	0.0474015i
$643$		−	26.9456i		−	1.06263i	−0.847175	−	0.531314i	$-0.821698\pi$
$643$		−	26.9456i		−	1.06263i	0.847175	−	0.531314i	$-0.178302\pi$
$644$	0.462311	+	1.42285i	0.0182176	+	0.0560680i
$645$	−3.46370	−	4.47319i	−0.136383	−	0.176132i
$646$	−7.04790	+	21.6912i	−0.277296	+	0.853429i
$647$	−20.3789	−	6.62151i	−0.801178	−	0.260318i	−0.120321	−	0.992735i	$-0.538392\pi$
$647$	−20.3789	−	6.62151i	−0.801178	−	0.260318i	−0.680857	+	0.732417i	$0.738392\pi$
$648$	−4.65643	−	6.40902i	−0.182922	−	0.251770i
$649$	−9.42991			−0.370156
$650$	8.78547	+	22.2998i	0.344594	+	0.874671i
$651$	−1.51006			−0.0591840
$652$	6.29295	+	8.66150i	0.246451	+	0.339211i
$653$	−17.2018	−	5.58921i	−0.673160	−	0.218723i	−0.0475615	−	0.998868i	$-0.515145\pi$
$653$	−17.2018	−	5.58921i	−0.673160	−	0.218723i	−0.625598	+	0.780145i	$0.715145\pi$
$654$	−0.664229	+	2.04429i	−0.0259734	+	0.0799379i
$655$	−42.0008	−	12.2409i	−1.64111	−	0.478293i
$656$	−3.48118	−	10.7140i	−0.135917	−	0.418310i
$657$			19.0315i			0.742488i
$658$	−10.5529	+	3.42885i	−0.411395	+	0.133670i
$659$	−32.7786	−	23.8150i	−1.27687	−	0.927702i	−0.277419	−	0.960749i	$-0.589479\pi$
$659$	−32.7786	−	23.8150i	−1.27687	−	0.927702i	−0.999454	+	0.0330466i	$0.989479\pi$
$660$	−1.73813	−	1.18339i	−0.0676568	−	0.0460633i
$661$	29.1613	−	21.1869i	1.13424	−	0.824077i	0.147937	−	0.988997i	$-0.452737\pi$
$661$	29.1613	−	21.1869i	1.13424	−	0.824077i	0.986307	+	0.164920i	$0.0527366\pi$
$662$	5.21603	−	7.17925i	0.202727	−	0.279029i
$663$	5.99486	−	8.25122i	0.232821	−	0.320451i
$664$	−6.71559	+	4.87916i	−0.260615	+	0.189348i
$665$	2.33699	−	8.01864i	0.0906248	−	0.310950i
$666$	8.88540	+	6.45562i	0.344302	+	0.250150i
$667$	13.2790	−	4.31460i	0.514164	−	0.167062i
$668$		−	14.3114i		−	0.553723i
$669$	−1.63057	−	5.01838i	−0.0630415	−	0.194022i
$670$	−29.4226	+	10.5647i	−1.13669	+	0.408148i
$671$	2.81710	−	8.67013i	0.108753	−	0.334707i
$672$	−0.331395	−	0.107677i	−0.0127838	−	0.00415372i
$673$	0.391712	+	0.539145i	0.0150994	+	0.0207825i	0.816500	−	0.577346i	$-0.195911\pi$
$673$	0.391712	+	0.539145i	0.0150994	+	0.0207825i	−0.801401	+	0.598128i	$0.795911\pi$
$674$	−13.1554			−0.506728
$675$	5.50254	−	8.63825i	0.211793	−	0.332486i
$676$	9.97864			0.383794
$677$	−17.7889	−	24.4844i	−0.683684	−	0.941010i	0.316287	−	0.948664i	$-0.397564\pi$
$677$	−17.7889	−	24.4844i	−0.683684	−	0.941010i	−0.999971	+	0.00765324i	$0.997564\pi$
$678$	5.15697	+	1.67560i	0.198052	+	0.0643510i
$679$	−1.08190	+	3.32974i	−0.0415195	+	0.127784i
$680$	−0.417313	−	13.6471i	−0.0160032	−	0.523343i
$681$	2.54203	+	7.82356i	0.0974108	+	0.299800i
$682$			11.6954i			0.447841i
$683$	37.3993	−	12.1518i	1.43104	−	0.464975i	0.511951	−	0.859014i	$-0.328923\pi$
$683$	37.3993	−	12.1518i	1.43104	−	0.464975i	0.919093	+	0.394040i	$0.128923\pi$
$684$	8.69872	+	6.31999i	0.332604	+	0.241651i
$685$	−4.87008	−	13.5632i	−0.186076	−	0.518222i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	2.23580	−	3.07732i	0.0853011	−	0.117407i
$688$	−4.26790	+	5.87427i	−0.162712	+	0.223954i
$689$	−2.02592	+	1.47192i	−0.0771814	+	0.0560756i
$690$	−0.393928	−	1.09709i	−0.0149966	−	0.0417656i
$691$	33.7659	+	24.5324i	1.28452	+	0.933255i	0.999679	−	0.0253209i	$-0.00806074\pi$
$691$	33.7659	+	24.5324i	1.28452	+	0.933255i	0.284836	+	0.958576i	$0.408061\pi$
$692$	2.36421	−	0.768177i	0.0898736	−	0.0292017i
$693$			7.76855i			0.295103i
$694$	3.90915	+	12.0311i	0.148389	+	0.456696i
$695$	−1.05088	−	34.3663i	−0.0398622	−	1.30359i
$696$	−1.00491	+	3.09281i	−0.0380911	+	0.117233i
$697$	65.4198	+	21.2562i	2.47795	+	0.805135i
$698$	14.9178	+	20.5326i	0.564649	+	0.777172i
$699$	−5.03986			−0.190625
$700$	0.305503	+	4.99066i	0.0115469	+	0.188629i
$701$	25.1217			0.948832			0.474416	−	0.880301i	$-0.342659\pi$
$701$	25.1217			0.948832			0.474416	+	0.880301i	$0.342659\pi$
$702$	−5.77156	−	7.94387i	−0.217833	−	0.299822i
$703$	−13.5539	−	4.40394i	−0.511196	−	0.166098i
$704$	−0.833956	+	2.56665i	−0.0314309	+	0.0967344i
$705$	8.13687	−	2.92167i	0.306452	−	0.110037i
$706$	4.55952	+	14.0328i	0.171600	+	0.528130i
$707$		−	13.9936i		−	0.526284i
$708$	1.15796	−	0.376243i	0.0435187	−	0.0141401i
$709$	15.9593	+	11.5951i	0.599365	+	0.435464i	0.845654	−	0.533732i	$-0.179211\pi$
$709$	15.9593	+	11.5951i	0.599365	+	0.435464i	−0.246288	+	0.969197i	$0.579211\pi$
$710$	5.75952	−	19.7619i	0.216151	−	0.741652i
$711$	−24.2007	+	17.5828i	−0.907596	+	0.659407i
$712$	1.42582	−	1.96248i	0.0534350	−	0.0735469i
$713$	−3.81088	+	5.24523i	−0.142719	+	0.196435i
$714$	1.72130	−	1.25060i	0.0644179	−	0.0468024i
$715$	23.9114	+	16.2798i	0.894237	+	0.608831i
$716$	15.9173	+	11.5646i	0.594857	+	0.432189i
$717$	−5.11651	+	1.66246i	−0.191080	+	0.0620855i
$718$		−	23.3894i		−	0.872885i
$719$	10.6140	+	32.6666i	0.395836	+	1.21826i	0.928308	+	0.371811i	$0.121263\pi$
$719$	10.6140	+	32.6666i	0.395836	+	1.21826i	−0.532472	+	0.846448i	$0.678737\pi$
$720$	−6.17961	−	1.80102i	−0.230300	−	0.0671199i
$721$	−0.697310	+	2.14610i	−0.0259692	+	0.0799250i
$722$	4.80090	+	1.55991i	0.178671	+	0.0580537i
$723$	−2.30419	−	3.17144i	−0.0856936	−	0.117947i
$724$	12.9960			0.482993
$725$	46.5763	−	2.85116i	1.72980	−	0.105889i
$726$	1.29512			0.0480663
$727$	−9.52326	−	13.1076i	−0.353198	−	0.486136i	0.595040	−	0.803696i	$-0.297136\pi$
$727$	−9.52326	−	13.1076i	−0.353198	−	0.486136i	−0.948238	+	0.317561i	$0.897136\pi$
$728$	4.55899	+	1.48131i	0.168967	+	0.0549008i
$729$	6.38517	−	19.6515i	0.236488	−	0.727834i
$730$	9.05104	+	11.6890i	0.334994	+	0.432628i
$731$	−13.7005	−	42.1659i	−0.506732	−	1.55956i
$732$			1.17706i			0.0435053i
$733$	−12.5062	+	4.06350i	−0.461926	+	0.150089i	−0.530729	−	0.847542i	$-0.678082\pi$
$733$	−12.5062	+	4.06350i	−0.461926	+	0.150089i	0.0688036	+	0.997630i	$0.478082\pi$
$734$	23.0886	+	16.7748i	0.852214	+	0.619170i
$735$	−0.616058	+	0.477029i	−0.0227237	+	0.0175955i
$736$	−1.21035	+	0.879367i	−0.0446139	+	0.0324139i
$737$	−22.1773	+	30.5244i	−0.816912	+	1.12438i
$738$	19.0608	−	26.2350i	0.701638	−	0.965722i
$739$	17.2330	−	12.5205i	0.633926	−	0.460574i	−0.223832	−	0.974628i	$-0.571857\pi$
$739$	17.2330	−	12.5205i	0.633926	−	0.460574i	0.857758	+	0.514053i	$0.171857\pi$
$740$	8.52751	−	0.260761i	0.313478	−	0.00958578i
$741$	5.04752	+	3.66724i	0.185425	+	0.134719i
$742$	−0.496831	+	0.161430i	−0.0182393	+	0.00592629i
$743$			39.4418i			1.44698i	0.690336	+	0.723489i	$0.257463\pi$
$743$			39.4418i			1.44698i	−0.690336	+	0.723489i	$0.742537\pi$
$744$	−0.466635	−	1.43615i	−0.0171077	−	0.0526520i
$745$	1.56420	−	2.29747i	0.0573080	−	0.0841728i
$746$	−8.09145	+	24.9029i	−0.296249	+	0.911760i
$747$	−22.7254	−	7.38393i	−0.831479	−	0.270164i
$748$	−9.68586	−	13.3314i	−0.354150	−	0.487446i
$749$	11.1542			0.407565
$750$	−0.356773	−	3.87941i	−0.0130275	−	0.141656i
$751$	21.5265			0.785514			0.392757	−	0.919642i	$-0.371521\pi$
$751$	21.5265			0.785514			0.392757	+	0.919642i	$0.371521\pi$
$752$	−6.52206	−	8.97684i	−0.237835	−	0.327352i
$753$	−2.20496	−	0.716436i	−0.0803533	−	0.0261084i
$754$	13.8246	−	42.5476i	0.503461	−	1.54949i
$755$	24.6691	−	36.2335i	0.897802	−	1.31867i
$756$	−0.632987	−	1.94813i	−0.0230215	−	0.0708529i
$757$		−	49.6653i		−	1.80512i	−0.430568	−	0.902558i	$-0.641687\pi$
$757$		−	49.6653i		−	1.80512i	0.430568	−	0.902558i	$-0.358313\pi$
$758$	−9.02063	+	2.93098i	−0.327644	+	0.106458i
$759$	−1.13818	−	0.826934i	−0.0413132	−	0.0300158i
$760$	8.34835	−	0.255283i	0.302827	−	0.00926008i
$761$	−23.0714	+	16.7623i	−0.836336	+	0.607634i	−0.921345	−	0.388746i	$-0.872908\pi$
$761$	−23.0714	+	16.7623i	−0.836336	+	0.607634i	0.0850084	+	0.996380i	$0.472908\pi$
$762$	−0.722753	+	0.994784i	−0.0261826	+	0.0360372i
$763$	3.62589	−	4.99061i	0.131266	−	0.180672i
$764$	−17.7842	+	12.9210i	−0.643410	+	0.467465i
$765$	31.0756	−	24.0626i	1.12354	−	0.869985i
$766$	24.4160	+	17.7393i	0.882187	+	0.640946i
$767$	−15.9300	+	5.17596i	−0.575198	+	0.186893i
$768$		−	0.348449i		−	0.0125736i
$769$	−0.759565	−	2.33770i	−0.0273906	−	0.0842996i	0.936427	−	0.350863i	$-0.114112\pi$
$769$	−0.759565	−	2.33770i	−0.0273906	−	0.0842996i	−0.963817	+	0.266564i	$0.914112\pi$
$770$	3.69459	+	4.77137i	0.133144	+	0.171948i
$771$	1.61252	−	4.96284i	0.0580736	−	0.178732i
$772$	11.6779	+	3.79437i	0.420296	+	0.136562i
$773$	−5.42837	−	7.47152i	−0.195245	−	0.268732i	0.700158	−	0.713988i	$-0.253113\pi$
$773$	−5.42837	−	7.47152i	−0.195245	−	0.268732i	−0.895403	+	0.445256i	$0.853113\pi$
$774$	−20.9014			−0.751284
$775$	−16.7191	+	13.7836i	−0.600568	+	0.495122i
$776$	−3.50110			−0.125682
$777$	0.781445	+	1.07557i	0.0280342	+	0.0385858i
$778$	−28.9955	−	9.42122i	−1.03954	−	0.337767i
$779$	−13.0030	+	40.0193i	−0.465882	+	1.43384i
$780$	−3.58578	−	1.04506i	−0.128392	−	0.0374191i
$781$	−7.67698	−	23.6273i	−0.274704	−	0.845452i
$782$		−	9.13504i		−	0.326668i
$783$	−18.1813	+	5.90747i	−0.649747	+	0.211116i
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	−14.7933	−	10.0718i	−0.527996	−	0.359480i
$786$	5.51534	−	4.00713i	0.196726	−	0.142930i
$787$	−6.44986	+	8.87747i	−0.229913	+	0.316447i	−0.908350	−	0.418211i	$-0.862657\pi$
$787$	−6.44986	+	8.87747i	−0.229913	+	0.316447i	0.678438	+	0.734658i	$0.262657\pi$
$788$	−4.63250	+	6.37608i	−0.165026	+	0.227139i
$789$	−3.40356	+	2.47283i	−0.121170	+	0.0880352i
$790$	−6.50174	+	22.3086i	−0.231322	+	0.793706i
$791$	−12.5894	−	9.14676i	−0.447629	−	0.325221i
$792$	−7.38833	+	2.40061i	−0.262533	+	0.0853021i
$793$		−	16.1927i		−	0.575021i
$794$	−0.739096	−	2.27470i	−0.0262295	−	0.0807262i
$795$	0.383084	−	0.137552i	0.0135866	−	0.00487848i
$796$	−0.0987027	+	0.303776i	−0.00349843	+	0.0107670i
$797$	−2.18645	−	0.710420i	−0.0774480	−	0.0251644i	0.270037	−	0.962850i	$-0.412964\pi$
$797$	−2.18645	−	0.710420i	−0.0774480	−	0.0251644i	−0.347485	+	0.937686i	$0.612964\pi$
$798$	0.765027	+	1.05297i	0.0270817	+	0.0372747i
$799$	67.7524			2.39691
$800$	−4.65199	+	1.83275i	−0.164473	+	0.0647974i
$801$	6.98274			0.246723
$802$	4.11177	+	5.65937i	0.145192	+	0.199839i
$803$	16.9692	+	5.51362i	0.598829	+	0.194571i
$804$	1.50540	−	4.63314i	0.0530913	−	0.163398i
$805$	0.102248	+	3.34375i	0.00360377	+	0.117852i
$806$	6.41948	+	19.7571i	0.226117	+	0.695915i
$807$			2.47037i			0.0869612i
$808$	13.3087	−	4.32427i	0.468199	−	0.152127i
$809$	−30.2797	−	21.9995i	−1.06458	−	0.773461i	−0.0896483	−	0.995973i	$-0.528574\pi$
$809$	−30.2797	−	21.9995i	−1.06458	−	0.773461i	−0.974930	+	0.222512i	$0.928574\pi$
$810$	−5.98633	−	16.6719i	−0.210338	−	0.585792i
$811$	−21.7427	+	15.7970i	−0.763490	+	0.554708i	−0.899979	−	0.435933i	$-0.856418\pi$
$811$	−21.7427	+	15.7970i	−0.763490	+	0.554708i	0.136488	+	0.990642i	$0.456418\pi$
$812$	5.48562	−	7.55030i	0.192507	−	0.264964i
$813$	−1.57795	+	2.17186i	−0.0553411	+	0.0761705i
$814$	8.33027	−	6.05229i	0.291976	−	0.212133i
$815$	8.09025	+	22.5314i	0.283389	+	0.789239i
$816$	1.72130	+	1.25060i	0.0602575	+	0.0437796i
$817$	25.7941	−	8.38102i	0.902423	−	0.293215i
$818$		−	1.57459i		−	0.0550543i
$819$	4.26406	+	13.1234i	0.148998	+	0.458570i
$820$	−0.769922	−	25.1783i	−0.0268868	−	0.879264i
$821$	−12.9101	+	39.7331i	−0.450564	+	1.38669i	0.425700	+	0.904864i	$0.360028\pi$
$821$	−12.9101	+	39.7331i	−0.450564	+	1.38669i	−0.876265	+	0.481830i	$0.839972\pi$
$822$	2.13578	+	0.693956i	0.0744937	+	0.0242045i
$823$	−11.9564	−	16.4566i	−0.416774	−	0.573640i	0.548080	−	0.836426i	$-0.315359\pi$
$823$	−11.9564	−	16.4566i	−0.416774	−	0.573640i	−0.964854	+	0.262786i	$0.915359\pi$
$824$	−2.25654			−0.0786104
$825$	−2.99095	−	3.62792i	−0.104131	−	0.126308i
$826$	−3.49419			−0.121578
$827$	6.59625	+	9.07896i	0.229374	+	0.315706i	0.908155	−	0.418635i	$-0.137491\pi$
$827$	6.59625	+	9.07896i	0.229374	+	0.315706i	−0.678781	+	0.734341i	$0.737491\pi$
$828$	−4.09578	−	1.33080i	−0.142338	−	0.0462485i
$829$	−6.48419	+	19.9563i	−0.225205	+	0.693110i	0.773066	+	0.634326i	$0.218722\pi$
$829$	−6.48419	+	19.9563i	−0.225205	+	0.693110i	−0.998271	+	0.0587839i	$0.981278\pi$
$830$	−17.4694	+	6.27267i	−0.606372	+	0.217728i
$831$	−2.74619	−	8.45191i	−0.0952644	−	0.293194i
$832$			4.79360i			0.166188i
$833$	−5.80718	+	1.88687i	−0.201207	+	0.0653760i
$834$	4.33460	+	3.14927i	0.150095	+	0.109050i
$835$	8.95406	−	30.7230i	0.309868	−	1.06321i
$836$	8.15525	−	5.92514i	0.282055	−	0.204925i
$837$	5.21779	−	7.18167i	0.180353	−	0.248235i
$838$	−2.10591	+	2.89854i	−0.0727475	+	0.100128i
$839$	−8.04271	+	5.84337i	−0.277665	+	0.201736i	−0.717898	−	0.696148i	$-0.754896\pi$
$839$	−8.04271	+	5.84337i	−0.277665	+	0.201736i	0.440233	+	0.897884i	$0.354896\pi$
$840$	−0.644054	−	0.438496i	−0.0222220	−	0.0151296i
$841$	−47.0031	−	34.1498i	−1.62080	−	1.17758i
$842$	31.8324	−	10.3430i	1.09702	−	0.356442i
$843$			4.63372i			0.159594i
$844$	−0.114022	−	0.350923i	−0.00392479	−	0.0120793i
$845$	21.4217	+	6.24324i	0.736928	+	0.214774i
$846$	9.87023	−	30.3774i	0.339345	−	1.04440i
$847$	−3.53489	−	1.14856i	−0.121460	−	0.0394648i
$848$	−0.307059	−	0.422630i	−0.0105444	−	0.0145132i
$849$	6.97333			0.239324
$850$	7.64259	−	29.5581i	0.262139	−	1.01383i
$851$	5.70811			0.195671
$852$	1.88541	+	2.59504i	0.0645930	+	0.0889047i
$853$	−12.5465	−	4.07661i	−0.429585	−	0.139581i	0.0862404	−	0.996274i	$-0.472515\pi$
$853$	−12.5465	−	4.07661i	−0.429585	−	0.139581i	−0.515825	+	0.856694i	$0.672515\pi$
$854$	1.04386	−	3.21266i	0.0357200	−	0.109935i
$855$	14.7198	+	19.0099i	0.503407	+	0.650125i
$856$	3.44683	+	10.6083i	0.117810	+	0.362583i
$857$		−	14.2425i		−	0.486514i	−0.969962	−	0.243257i	$-0.921784\pi$
$857$		−	14.2425i		−	0.486514i	0.969962	−	0.243257i	$-0.0782159\pi$
$858$	−4.28715	+	1.39298i	−0.146361	+	0.0475556i
$859$	14.2108	+	10.3247i	0.484865	+	0.352275i	0.803206	−	0.595701i	$-0.203126\pi$
$859$	14.2108	+	10.3247i	0.484865	+	0.352275i	−0.318341	+	0.947976i	$0.603126\pi$
$860$	−12.8374	+	9.94034i	−0.437753	+	0.338963i
$861$	3.17571	−	2.30729i	0.108228	−	0.0786322i
$862$	−11.3827	+	15.6670i	−0.387697	+	0.533619i
$863$	21.0011	−	28.9056i	0.714887	−	0.983957i	−0.284791	−	0.958590i	$-0.591924\pi$
$863$	21.0011	−	28.9056i	0.714887	−	0.983957i	0.999678	−	0.0253678i	$-0.00807568\pi$
$864$	1.65718	−	1.20401i	0.0563784	−	0.0409613i
$865$	5.55598	−	0.169895i	0.188909	−	0.00577662i
$866$	−9.29340	−	6.75205i	−0.315802	−	0.229444i
$867$	−6.72187	+	2.18407i	−0.228287	+	0.0741748i
$868$			4.33366i			0.147094i
$869$	8.66631	+	26.6722i	0.293984	+	0.904791i
$870$	−4.09235	+	6.01076i	−0.138744	+	0.203784i
$871$	−20.7097	+	63.7379i	−0.701721	+	2.15968i
$872$	5.86681	+	1.90624i	0.198675	+	0.0645535i
$873$	−5.92382	−	8.15344i	−0.200491	−	0.275952i
$874$	5.58818			0.189023
$875$	−2.46662	+	10.9049i	−0.0833870	+	0.368651i
$876$	−2.30374			−0.0778361
$877$	14.0307	+	19.3116i	0.473782	+	0.652105i	0.977295	−	0.211883i	$-0.0679595\pi$
$877$	14.0307	+	19.3116i	0.473782	+	0.652105i	−0.503513	+	0.863988i	$0.667959\pi$
$878$	3.53717	+	1.14930i	0.119374	+	0.0387869i
$879$	1.89664	−	5.83727i	0.0639722	−	0.196886i
$880$	−3.39615	+	4.98820i	−0.114484	+	0.168152i
$881$	2.61762	+	8.05620i	0.0881898	+	0.271420i	0.985419	−	0.170145i	$-0.0544235\pi$
$881$	2.61762	+	8.05620i	0.0881898	+	0.271420i	−0.897229	+	0.441565i	$0.854424\pi$
$882$			2.87858i			0.0969269i
$883$	2.79558	−	0.908338i	0.0940787	−	0.0305680i	−0.261599	−	0.965177i	$-0.584250\pi$
$883$	2.79558	−	0.908338i	0.0940787	−	0.0305680i	0.355678	+	0.934609i	$0.384250\pi$
$884$	−23.6798	−	17.2044i	−0.796439	−	0.578647i
$885$	2.72125	−	0.0832126i	0.0914737	−	0.00279716i
$886$	−4.14752	+	3.01335i	−0.139339	+	0.101235i
$887$	−3.72943	+	5.13312i	−0.125222	+	0.172353i	−0.867025	−	0.498264i	$-0.833971\pi$
$887$	−3.72943	+	5.13312i	−0.125222	+	0.172353i	0.741803	+	0.670618i	$0.233971\pi$
$888$	−0.781445	+	1.07557i	−0.0262236	+	0.0360937i
$889$	2.85489	−	2.07420i	0.0957499	−	0.0695664i
$890$	4.28874	−	3.32087i	0.143759	−	0.111316i
$891$	−17.2963	−	12.5665i	−0.579447	−	0.420993i
$892$	−14.4020	+	4.67950i	−0.482216	+	0.156681i
$893$			41.4462i			1.38694i
$894$	0.133841	+	0.411920i	0.00447631	+	0.0137767i
$895$	26.9350	+	34.7851i	0.900337	+	1.16274i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	−2.37662	−	0.772211i	−0.0793530	−	0.0257834i
$898$	−16.0105	−	22.0365i	−0.534276	−	0.735368i
$899$	40.4447			1.34891
$900$	−12.1393	−	7.73268i	−0.404642	−	0.257756i
$901$	3.18978			0.106267
$902$	−17.8700	−	24.5959i	−0.595005	−	0.818954i
$903$	−2.40626	−	0.781840i	−0.0800752	−	0.0260180i
$904$	4.80873	−	14.7998i	0.159936	−	0.492233i
$905$	27.8992	+	8.13109i	0.927402	+	0.270287i
$906$	2.11081	+	6.49642i	0.0701271	+	0.215829i
$907$		−	27.9028i		−	0.926496i	−0.886229	−	0.463248i	$-0.846684\pi$
$907$		−	27.9028i		−	0.926496i	0.886229	−	0.463248i	$-0.153316\pi$
$908$	22.4525	−	7.29526i	0.745113	−	0.242102i
$909$	32.5887	+	23.6770i	1.08090	+	0.785318i
$910$	8.86023	+	6.03238i	0.293714	+	0.199971i
$911$	−22.8716	+	16.6172i	−0.757771	+	0.550553i	−0.898226	−	0.439534i	$-0.855143\pi$
$911$	−22.8716	+	16.6172i	−0.757771	+	0.550553i	0.140455	+	0.990087i	$0.455143\pi$
$912$	−0.765027	+	1.05297i	−0.0253326	+	0.0348673i
$913$	−13.1676	+	18.1236i	−0.435784	+	0.599805i
$914$	−26.8292	+	19.4925i	−0.887430	+	0.644756i
$915$	−0.736439	+	2.52685i	−0.0243459	+	0.0835352i
$916$	−8.83146	−	6.41643i	−0.291800	−	0.212005i
$917$	−18.6072	+	6.04586i	−0.614465	+	0.199652i
$918$			12.5075i			0.412809i
$919$	7.23143	+	22.2560i	0.238543	+	0.734159i	0.996632	+	0.0820080i	$0.0261333\pi$
$919$	7.23143	+	22.2560i	0.238543	+	0.734159i	−0.758089	+	0.652151i	$0.773867\pi$
$920$	−3.14850	+	1.13052i	−0.103803	+	0.0372721i
$921$	−2.47077	+	7.60424i	−0.0814145	+	0.250568i
$922$	34.5130	+	11.2140i	1.13663	+	0.369312i
$923$	−25.9375	−	35.6999i	−0.853743	−	1.17508i
$924$	−0.940374			−0.0309360
$925$	18.4696	+	4.77554i	0.607277	+	0.157019i
$926$	−21.7292			−0.714067
$927$	−3.81805	−	5.25509i	−0.125401	−	0.172600i
$928$	8.87591	+	2.88396i	0.291366	+	0.0946706i
$929$	−7.34867	+	22.6169i	−0.241102	+	0.742036i	0.755151	+	0.655551i	$0.227563\pi$
$929$	−7.34867	+	22.6169i	−0.241102	+	0.742036i	−0.996253	+	0.0864849i	$0.972437\pi$
$930$	−0.103204	−	3.37502i	−0.00338420	−	0.110671i
$931$	−1.15425	−	3.55243i	−0.0378291	−	0.116426i
$932$			14.4637i			0.473774i
$933$	−7.15597	+	2.32512i	−0.234276	+	0.0761209i
$934$	0.0347752	+	0.0252657i	0.00113788	+	0.000826719i
$935$	−12.4522	−	34.6794i	−0.407230	−	1.13414i
$936$	−11.1635	+	8.11072i	−0.364889	+	0.265107i
$937$	26.5326	−	36.5190i	0.866783	−	1.19302i	−0.113126	−	0.993581i	$-0.536086\pi$
$937$	26.5326	−	36.5190i	0.866783	−	1.19302i	0.979909	−	0.199444i	$-0.0639136\pi$
$938$	−8.21765	+	11.3106i	−0.268316	+	0.369305i
$939$	−2.31499	+	1.68194i	−0.0755470	+	0.0548881i
$940$	−8.38479	−	23.3517i	−0.273482	−	0.761647i
$941$	4.95051	+	3.59676i	0.161382	+	0.117251i	0.665545	−	0.746357i	$-0.268199\pi$
$941$	4.95051	+	3.59676i	0.161382	+	0.117251i	−0.504163	+	0.863608i	$0.668199\pi$
$942$	2.65234	−	0.861796i	0.0864178	−	0.0280788i
$943$		−	16.8537i		−	0.548832i
$944$	−1.07976	−	3.32317i	−0.0351433	−	0.108160i
$945$	−0.139996	−	4.57819i	−0.00455406	−	0.148929i
$946$	−6.05535	+	18.6365i	−0.196876	+	0.605923i
$947$	−40.2498	−	13.0780i	−1.30794	−	0.424977i	−0.429606	−	0.903017i	$-0.641347\pi$
$947$	−40.2498	−	13.0780i	−1.30794	−	0.424977i	−0.878338	+	0.478040i	$0.841347\pi$
$948$	−2.12838	−	2.92946i	−0.0691266	−	0.0951446i
$949$	31.6924			1.02878
$950$	18.0816	+	4.67521i	0.586644	+	0.151684i
$951$	−8.48576			−0.275169
$952$	−3.58903	−	4.93988i	−0.116321	−	0.160102i
$953$	2.66659	+	0.866426i	0.0863792	+	0.0280663i	0.351888	−	0.936042i	$-0.385540\pi$
$953$	2.66659	+	0.866426i	0.0863792	+	0.0280663i	−0.265509	+	0.964108i	$0.585540\pi$
$954$	0.464690	−	1.43017i	0.0150449	−	0.0463035i
$955$	−46.2624	+	16.6113i	−1.49702	+	0.537528i
$956$	4.77101	+	14.6837i	0.154306	+	0.474904i
$957$			8.77622i			0.283695i
$958$	−21.5175	+	6.99144i	−0.695197	+	0.225883i
$959$	−5.21396	−	3.78816i	−0.168367	−	0.122326i
$960$	0.218011	−	0.748035i	0.00703628	−	0.0241427i
$961$	9.88566	−	7.18235i	0.318892	−	0.231689i
$962$	10.7503	−	14.7965i	0.346604	−	0.477060i
$963$	−18.8728	+	25.9761i	−0.608166	+	0.837069i
$964$	−9.10158	+	6.61269i	−0.293142	+	0.212980i
$965$	22.6955	+	15.4520i	0.730595	+	0.497417i
$966$	−0.421744	−	0.306415i	−0.0135694	−	0.00985874i
$967$	39.7055	−	12.9011i	1.27684	−	0.414871i	0.409376	−	0.912366i	$-0.365747\pi$
$967$	39.7055	−	12.9011i	1.27684	−	0.414871i	0.867467	+	0.497495i	$0.165747\pi$
$968$		−	3.71680i		−	0.119463i
$969$	−2.45584	−	7.55829i	−0.0788928	−	0.242807i
$970$	−7.51599	−	2.19050i	−0.241324	−	0.0703327i
$971$	−11.0420	+	33.9838i	−0.354355	+	1.09059i	0.602028	+	0.798475i	$0.294360\pi$
$971$	−11.0420	+	33.9838i	−0.354355	+	1.09059i	−0.956383	+	0.292117i	$0.905640\pi$
$972$	8.46971	+	2.75197i	0.271666	+	0.0882696i
$973$	−9.03795	−	12.4397i	−0.289743	−	0.398798i
$974$	−26.3279			−0.843600
$975$	−7.04393	−	4.48697i	−0.225586	−	0.143698i
$976$	3.37799			0.108127
$977$	28.4446	+	39.1506i	0.910024	+	1.25254i	0.967159	+	0.254173i	$0.0818034\pi$
$977$	28.4446	+	39.1506i	0.910024	+	1.25254i	−0.0571351	+	0.998366i	$0.518197\pi$
$978$	−3.54798	−	1.15281i	−0.113452	−	0.0368628i
$979$	2.02297	−	6.22607i	0.0646545	−	0.198986i
$980$	1.36901	+	1.76800i	0.0437313	+	0.0564767i
$981$	5.48728	+	16.8881i	0.175195	+	0.539196i
$982$			8.15424i			0.260212i
$983$	−2.95452	+	0.959981i	−0.0942345	+	0.0306186i	−0.355755	−	0.934579i	$-0.615776\pi$
$983$	−2.95452	+	0.959981i	−0.0942345	+	0.0306186i	0.261520	+	0.965198i	$0.415776\pi$
$984$	3.17571	+	2.30729i	0.101238	+	0.0735537i
$985$	−13.9341	+	10.7895i	−0.443977	+	0.343782i
$986$	−46.1023	+	33.4953i	−1.46820	+	1.06671i
$987$	2.27261	−	3.12797i	0.0723379	−	0.0995645i
$988$	10.5245	−	14.4857i	0.334828	−	0.460851i
$989$	−8.78831	+	6.38508i	−0.279452	+	0.203034i
$990$	−17.3629	+	0.530937i	−0.551829	+	0.0168743i
$991$	11.6719	+	8.48016i	0.370771	+	0.269381i	0.757531	−	0.652800i	$-0.226406\pi$
$991$	11.6719	+	8.48016i	0.370771	+	0.269381i	−0.386759	+	0.922181i	$0.626406\pi$
$992$	−4.12156	+	1.33918i	−0.130860	+	0.0425189i
$993$			3.09215i			0.0981265i
$994$	−2.84465	−	8.75495i	−0.0902270	−	0.277690i
$995$	−0.401951	+	0.590377i	−0.0127427	+	0.0187162i
$996$	0.893817	−	2.75088i	0.0283217	−	0.0871651i
$997$	−13.2433	−	4.30300i	−0.419418	−	0.136277i	0.0917019	−	0.995787i	$-0.470769\pi$
$997$	−13.2433	−	4.30300i	−0.419418	−	0.136277i	−0.511120	+	0.859509i	$0.670769\pi$
$998$	−4.15634	−	5.72071i	−0.131567	−	0.181086i
$999$	−7.81543			−0.247269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.239.5	✓	24
25.3	odd	20		8750.2.a.z.1.7		12
25.9	even	10	inner	350.2.m.a.309.5	yes	24
25.22	odd	20		8750.2.a.bb.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.239.5	✓	24	1.1	even	1	trivial
350.2.m.a.309.5	yes	24	25.9	even	10	inner
8750.2.a.z.1.7		12	25.3	odd	20
8750.2.a.bb.1.6		12	25.22	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.331395 - 0.107677i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.25842 + 1.84834i) q^{5} +(-0.107677 - 0.331395i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.32882 - 1.69199i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.331395 - 0.107677i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.25842 + 1.84834i) q^{5} +(-0.107677 - 0.331395i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-2.32882 - 1.69199i) q^{9} +(-2.23502 + 0.0683444i) q^{10} +(-2.18333 + 1.58628i) q^{11} +(0.204813 - 0.281901i) q^{12} +(-2.81761 + 3.87811i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.616058 - 0.477029i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.80718 - 1.88687i) q^{17} -2.87858i q^{18} +(1.15425 + 3.55243i) q^{19} +(-1.36901 - 1.76800i) q^{20} +(0.107677 - 0.331395i) q^{21} +(-2.56665 - 0.833956i) q^{22} +(-0.879367 - 1.21035i) q^{23} +0.348449 q^{24} +(-1.83275 - 4.65199i) q^{25} -4.79360 q^{26} +(1.20401 + 1.65718i) q^{27} +(-0.951057 - 0.309017i) q^{28} +(-2.88396 + 8.87591i) q^{29} +(0.748035 + 0.218011i) q^{30} +(-1.33918 - 4.12156i) q^{31} -1.00000i q^{32} +(0.894349 - 0.290592i) q^{33} +(4.93988 + 3.58903i) q^{34} +(-1.84834 - 1.25842i) q^{35} +(2.32882 - 1.69199i) q^{36} +(-2.24264 + 3.08673i) q^{37} +(-2.19552 + 3.02187i) q^{38} +(1.35132 - 0.981794i) q^{39} +(0.625661 - 2.14675i) q^{40} +(9.11384 + 6.62160i) q^{41} +(0.331395 - 0.107677i) q^{42} -7.26099i q^{43} +(-0.833956 - 2.56665i) q^{44} +(6.05802 - 2.17523i) q^{45} +(0.462311 - 1.42285i) q^{46} +(10.5529 + 3.42885i) q^{47} +(0.204813 + 0.281901i) q^{48} -1.00000 q^{49} +(2.68628 - 4.21710i) q^{50} -2.12764 q^{51} +(-2.81761 - 3.87811i) q^{52} +(0.496831 + 0.161430i) q^{53} +(-0.632987 + 1.94813i) q^{54} +(-0.184444 - 6.03175i) q^{55} +(-0.309017 - 0.951057i) q^{56} -1.30154i q^{57} +(-8.87591 + 2.88396i) q^{58} +(2.82686 + 2.05383i) q^{59} +(0.263309 + 0.733316i) q^{60} +(-2.73285 + 1.98553i) q^{61} +(2.54726 - 3.50601i) q^{62} +(1.69199 - 2.32882i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-3.62233 - 10.0882i) q^{65} +(0.760778 + 0.552738i) q^{66} +(13.2964 - 4.32028i) q^{67} +6.10603i q^{68} +(0.161092 + 0.495790i) q^{69} +(-0.0683444 - 2.23502i) q^{70} +(-2.84465 + 8.75495i) q^{71} +(2.73770 + 0.889531i) q^{72} +(-3.88608 - 5.34873i) q^{73} -3.81540 q^{74} +(0.106452 + 1.73899i) q^{75} -3.73524 q^{76} +(-1.58628 - 2.18333i) q^{77} +(1.58858 + 0.516160i) q^{78} +(3.21124 - 9.88319i) q^{79} +(2.10451 - 0.755660i) q^{80} +(2.44803 + 7.53426i) q^{81} +11.2653i q^{82} +(7.89465 - 2.56513i) q^{83} +(0.281901 + 0.204813i) q^{84} +(-3.82030 + 13.1081i) q^{85} +(5.87427 - 4.26790i) q^{86} +(1.91146 - 2.63090i) q^{87} +(1.58628 - 2.18333i) q^{88} +(-1.96248 + 1.42582i) q^{89} +(5.32061 + 3.62247i) q^{90} +(-3.87811 - 2.81761i) q^{91} +(1.42285 - 0.462311i) q^{92} +1.51006i q^{93} +(3.42885 + 10.5529i) q^{94} +(-8.01864 - 2.33699i) q^{95} +(-0.107677 + 0.331395i) q^{96} +(3.32974 + 1.08190i) q^{97} +(-0.587785 - 0.809017i) q^{98} +7.76855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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