LMFDB - Embedded newform 370.2.l.c.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.116304318664704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 6x^9 - 9x^8 - 2x^7 + 18x^6 - 4x^5 - 36x^4 + 48x^3 + 16x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$0.578188 - 1.29062i$ of defining polynomial
Character	$\chi$	$=$	370.101
Dual form			370.2.l.c.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -2.81361i q^{6} +(1.97465 + 3.42019i) q^{7} -1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -2.81361i q^{6} +(1.97465 + 3.42019i) q^{7} -1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +1.00000 q^{10} -5.23847 q^{11} +(-1.40680 + 2.43665i) q^{12} +(2.55417 - 1.47465i) q^{13} -3.94930i q^{14} +(-2.43665 - 1.40680i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18900 - 1.26382i) q^{17} +(4.25771 - 2.45819i) q^{18} +(4.20751 - 2.42920i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-5.55589 + 9.62308i) q^{21} +(4.53665 + 2.61923i) q^{22} -2.92572i q^{23} +(2.43665 - 1.40680i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.94930 q^{26} -5.39194 q^{27} +(-1.97465 + 3.42019i) q^{28} +9.66965i q^{29} +(1.40680 + 2.43665i) q^{30} -3.14682i q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.36950 - 12.7643i) q^{33} +(1.26382 + 2.18900i) q^{34} +(-3.42019 - 1.97465i) q^{35} -4.91638 q^{36} +(-6.01944 + 0.875392i) q^{37} -4.85841 q^{38} +(7.18643 + 4.14909i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.88220 + 6.72417i) q^{41} +(9.62308 - 5.55589i) q^{42} +1.68060i q^{43} +(-2.61923 - 4.53665i) q^{44} -4.91638i q^{45} +(-1.46286 + 2.53375i) q^{46} +11.8205 q^{47} -2.81361 q^{48} +(-4.29849 + 7.44520i) q^{49} +(-0.866025 + 0.500000i) q^{50} -7.11178i q^{51} +(2.55417 + 1.47465i) q^{52} +(-1.72422 + 2.98644i) q^{53} +(4.66956 + 2.69597i) q^{54} +(4.53665 - 2.61923i) q^{55} +(3.42019 - 1.97465i) q^{56} +(11.8383 + 6.83483i) q^{57} +(4.83483 - 8.37416i) q^{58} +(6.01430 + 3.47236i) q^{59} -2.81361i q^{60} +(8.76366 - 5.05970i) q^{61} +(-1.57341 + 2.72523i) q^{62} -19.4163 q^{63} -1.00000 q^{64} +(-1.47465 + 2.55417i) q^{65} +14.7390i q^{66} +(3.44554 + 5.96786i) q^{67} -2.52764i q^{68} +(7.12896 - 4.11591i) q^{69} +(1.97465 + 3.42019i) q^{70} +(-5.54009 - 9.59572i) q^{71} +(4.25771 + 2.45819i) q^{72} +1.02217 q^{73} +(5.65069 + 2.25161i) q^{74} +2.81361 q^{75} +(4.20751 + 2.42920i) q^{76} +(-10.3441 - 17.9166i) q^{77} +(-4.14909 - 7.18643i) q^{78} +(-7.07449 + 4.08446i) q^{79} -1.00000i q^{80} +(-0.210831 - 0.365171i) q^{81} -7.76440i q^{82} +(8.20899 - 14.2184i) q^{83} -11.1118 q^{84} +2.52764 q^{85} +(0.840298 - 1.45544i) q^{86} +(-23.5616 + 13.6033i) q^{87} +5.23847i q^{88} +(2.14759 + 1.23991i) q^{89} +(-2.45819 + 4.25771i) q^{90} +(10.0872 + 5.82384i) q^{91} +(2.53375 - 1.46286i) q^{92} +(7.66772 - 4.42696i) q^{93} +(-10.2369 - 5.91027i) q^{94} +(-2.42920 + 4.20751i) q^{95} +(2.43665 + 1.40680i) q^{96} -4.96273i q^{97} +(7.44520 - 4.29849i) q^{98} +(12.8772 - 22.3039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.40680	+	2.43665i	0.812218	+	1.40680i	0.911308	+	0.411725i	$0.135073\pi$
$3$	1.40680	+	2.43665i	0.812218	+	1.40680i	−0.0990900	+	0.995078i	$0.531593\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		−	2.81361i		−	1.14865i
$7$	1.97465	+	3.42019i	0.746348	+	1.29271i	0.949562	+	0.313578i	$0.101528\pi$
$7$	1.97465	+	3.42019i	0.746348	+	1.29271i	−0.203215	+	0.979134i	$0.565139\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.45819	+	4.25771i	−0.819397	+	1.41924i
$10$	1.00000			0.316228
$11$	−5.23847			−1.57946			−0.789729	−	0.613456i	$-0.789779\pi$
$11$	−5.23847			−1.57946			−0.789729	+	0.613456i	$0.789779\pi$
$12$	−1.40680	+	2.43665i	−0.406109	+	0.703402i
$13$	2.55417	−	1.47465i	0.708399	−	0.408994i	−0.102069	−	0.994777i	$-0.532546\pi$
$13$	2.55417	−	1.47465i	0.708399	−	0.408994i	0.810468	+	0.585783i	$0.199213\pi$
$14$		−	3.94930i		−	1.05550i
$15$	−2.43665	−	1.40680i	−0.629142	−	0.363235i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.18900	−	1.26382i	−0.530910	−	0.306521i	0.210477	−	0.977599i	$-0.432498\pi$
$17$	−2.18900	−	1.26382i	−0.530910	−	0.306521i	−0.741387	+	0.671078i	$0.765832\pi$
$18$	4.25771	−	2.45819i	1.00355	−	0.579401i
$19$	4.20751	−	2.42920i	0.965268	−	0.557298i	0.0674777	−	0.997721i	$-0.478505\pi$
$19$	4.20751	−	2.42920i	0.965268	−	0.557298i	0.897790	+	0.440423i	$0.145172\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−5.55589	+	9.62308i	−1.21239	+	2.09993i
$22$	4.53665	+	2.61923i	0.967217	+	0.558423i
$23$		−	2.92572i		−	0.610054i	−0.952344	−	0.305027i	$-0.901334\pi$
$23$		−	2.92572i		−	0.610054i	0.952344	−	0.305027i	$-0.0986655\pi$
$24$	2.43665	−	1.40680i	0.497380	−	0.287163i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.94930			−0.578406
$27$	−5.39194			−1.03768
$28$	−1.97465	+	3.42019i	−0.373174	+	0.646356i
$29$			9.66965i			1.79561i	0.440394	+	0.897805i	$0.354839\pi$
$29$			9.66965i			1.79561i	−0.440394	+	0.897805i	$0.645161\pi$
$30$	1.40680	+	2.43665i	0.256846	+	0.444870i
$31$		−	3.14682i		−	0.565186i	−0.959240	−	0.282593i	$-0.908805\pi$
$31$		−	3.14682i		−	0.565186i	0.959240	−	0.282593i	$-0.0911946\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−7.36950	−	12.7643i	−1.28286	−	2.22199i
$34$	1.26382	+	2.18900i	0.216743	+	0.375410i
$35$	−3.42019	−	1.97465i	−0.578118	−	0.333777i
$36$	−4.91638			−0.819397
$37$	−6.01944	+	0.875392i	−0.989590	+	0.143914i
$37$	−6.01944	+	0.875392i	−0.989590	+	0.143914i
$38$	−4.85841			−0.788138
$39$	7.18643	+	4.14909i	1.15075	+	0.664386i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	3.88220	+	6.72417i	0.606298	+	1.05014i	0.991845	+	0.127450i	$0.0406793\pi$
$41$	3.88220	+	6.72417i	0.606298	+	1.05014i	−0.385547	+	0.922688i	$0.625987\pi$
$42$	9.62308	−	5.55589i	1.48487	−	0.857292i
$43$			1.68060i			0.256289i	0.991756	+	0.128144i	$0.0409021\pi$
$43$			1.68060i			0.256289i	−0.991756	+	0.128144i	$0.959098\pi$
$44$	−2.61923	−	4.53665i	−0.394864	−	0.683925i
$45$		−	4.91638i		−	0.732891i
$46$	−1.46286	+	2.53375i	−0.215687	+	0.373580i
$47$	11.8205			1.72420			0.862102	−	0.506735i	$-0.169148\pi$
$47$	11.8205			1.72420			0.862102	+	0.506735i	$0.169148\pi$
$48$	−2.81361			−0.406109
$49$	−4.29849	+	7.44520i	−0.614070	+	1.06360i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		−	7.11178i		−	0.995848i
$52$	2.55417	+	1.47465i	0.354200	+	0.204497i
$53$	−1.72422	+	2.98644i	−0.236840	+	0.410219i	−0.959806	−	0.280665i	$-0.909445\pi$
$53$	−1.72422	+	2.98644i	−0.236840	+	0.410219i	0.722966	+	0.690884i	$0.242778\pi$
$54$	4.66956	+	2.69597i	0.635447	+	0.366875i
$55$	4.53665	−	2.61923i	0.611721	−	0.353178i
$56$	3.42019	−	1.97465i	0.457043	−	0.263874i
$57$	11.8383	+	6.83483i	1.56802	+	0.905295i
$58$	4.83483	−	8.37416i	0.634844	−	1.09958i
$59$	6.01430	+	3.47236i	0.782995	+	0.452062i	0.837491	−	0.546452i	$-0.184022\pi$
$59$	6.01430	+	3.47236i	0.782995	+	0.452062i	−0.0544958	+	0.998514i	$0.517355\pi$
$60$		−	2.81361i		−	0.363235i
$61$	8.76366	−	5.05970i	1.12207	−	0.647829i	0.180143	−	0.983640i	$-0.442344\pi$
$61$	8.76366	−	5.05970i	1.12207	−	0.647829i	0.941929	+	0.335812i	$0.109011\pi$
$62$	−1.57341	+	2.72523i	−0.199823	+	0.346104i
$63$	−19.4163			−2.44622
$64$	−1.00000			−0.125000
$65$	−1.47465	+	2.55417i	−0.182908	+	0.316806i
$66$			14.7390i			1.81424i
$67$	3.44554	+	5.96786i	0.420940	+	0.729090i	0.996032	−	0.0889992i	$-0.0283669\pi$
$67$	3.44554	+	5.96786i	0.420940	+	0.729090i	−0.575091	+	0.818089i	$0.695034\pi$
$68$		−	2.52764i		−	0.306521i
$69$	7.12896	−	4.11591i	0.858226	−	0.495497i
$70$	1.97465	+	3.42019i	0.236016	+	0.408791i
$71$	−5.54009	−	9.59572i	−0.657488	−	1.13880i	−0.981264	−	0.192669i	$-0.938286\pi$
$71$	−5.54009	−	9.59572i	−0.657488	−	1.13880i	0.323776	−	0.946134i	$-0.395048\pi$
$72$	4.25771	+	2.45819i	0.501776	+	0.289701i
$73$	1.02217			0.119636			0.0598182	−	0.998209i	$-0.480948\pi$
$73$	1.02217			0.119636			0.0598182	+	0.998209i	$0.480948\pi$
$74$	5.65069	+	2.25161i	0.656879	+	0.261744i
$75$	2.81361			0.324887
$76$	4.20751	+	2.42920i	0.482634	+	0.278649i
$77$	−10.3441	−	17.9166i	−1.17882	−	2.04178i
$78$	−4.14909	−	7.18643i	−0.469792	−	0.813703i
$79$	−7.07449	+	4.08446i	−0.795942	+	0.459537i	−0.842050	−	0.539399i	$-0.818651\pi$
$79$	−7.07449	+	4.08446i	−0.795942	+	0.459537i	0.0461082	+	0.998936i	$0.485318\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.210831	−	0.365171i	−0.0234257	−	0.0405745i
$82$		−	7.76440i		−	0.857434i
$83$	8.20899	−	14.2184i	0.901054	−	1.56067i	0.0749251	−	0.997189i	$-0.476128\pi$
$83$	8.20899	−	14.2184i	0.901054	−	1.56067i	0.826129	−	0.563482i	$-0.190538\pi$
$84$	−11.1118			−1.21239
$85$	2.52764			0.274161
$86$	0.840298	−	1.45544i	0.0906117	−	0.156944i
$87$	−23.5616	+	13.6033i	−2.52607	+	1.45843i
$88$			5.23847i			0.558423i
$89$	2.14759	+	1.23991i	0.227644	+	0.131430i	0.609485	−	0.792798i	$-0.291376\pi$
$89$	2.14759	+	1.23991i	0.227644	+	0.131430i	−0.381841	+	0.924228i	$0.624710\pi$
$90$	−2.45819	+	4.25771i	−0.259116	+	0.448802i
$91$	10.0872	+	5.82384i	1.05742	+	0.610504i
$92$	2.53375	−	1.46286i	0.264161	−	0.152514i
$93$	7.66772	−	4.42696i	0.795106	−	0.459054i
$94$	−10.2369	−	5.91027i	−1.05586	−	0.609598i
$95$	−2.42920	+	4.20751i	−0.249231	+	0.431681i
$96$	2.43665	+	1.40680i	0.248690	+	0.143581i
$97$		−	4.96273i		−	0.503889i	−0.967742	−	0.251945i	$-0.918930\pi$
$97$		−	4.96273i		−	0.503889i	0.967742	−	0.251945i	$-0.0810701\pi$
$98$	7.44520	−	4.29849i	0.752079	−	0.434213i
$99$	12.8772	−	22.3039i	1.29420	−	2.24163i
$100$	1.00000			0.100000
$101$	−0.755513			−0.0751763			−0.0375882	−	0.999293i	$-0.511968\pi$
$101$	−0.755513			−0.0751763			−0.0375882	+	0.999293i	$0.511968\pi$
$102$	−3.55589	+	6.15898i	−0.352086	+	0.609830i
$103$		−	16.5377i		−	1.62951i	−0.579808	−	0.814753i	$-0.696873\pi$
$103$		−	16.5377i		−	1.62951i	0.579808	−	0.814753i	$-0.303127\pi$
$104$	−1.47465	−	2.55417i	−0.144601	−	0.250457i
$105$		−	11.1118i		−	1.08440i
$106$	2.98644	−	1.72422i	0.290069	−	0.167471i
$107$	−6.32318	−	10.9521i	−0.611285	−	1.05878i	−0.991024	−	0.133684i	$-0.957319\pi$
$107$	−6.32318	−	10.9521i	−0.611285	−	1.05878i	0.379739	−	0.925094i	$-0.376014\pi$
$108$	−2.69597	−	4.66956i	−0.259420	−	0.449329i
$109$	−4.60707	−	2.65989i	−0.441277	−	0.254772i	0.262862	−	0.964833i	$-0.415334\pi$
$109$	−4.60707	−	2.65989i	−0.441277	−	0.254772i	−0.704139	+	0.710062i	$0.748667\pi$
$110$	−5.23847			−0.499468
$111$	−10.6012	−	13.4358i	−1.00622	−	1.27527i
$112$	−3.94930			−0.373174
$113$	7.48250	+	4.32003i	0.703895	+	0.406394i	0.808796	−	0.588089i	$-0.200119\pi$
$113$	7.48250	+	4.32003i	0.703895	+	0.406394i	−0.104902	+	0.994483i	$0.533453\pi$
$114$	−6.83483	−	11.8383i	−0.640140	−	1.10876i
$115$	1.46286	+	2.53375i	0.136412	+	0.236273i
$116$	−8.37416	+	4.83483i	−0.777522	+	0.448902i
$117$			14.4999i			1.34052i
$118$	−3.47236	−	6.01430i	−0.319656	−	0.553661i
$119$		−	9.98240i		−	0.915085i
$120$	−1.40680	+	2.43665i	−0.128423	+	0.222435i
$121$	16.4416			1.49469
$122$	−10.1194			−0.916168
$123$	−10.9230	+	18.9192i	−0.984892	+	1.70588i
$124$	2.72523	−	1.57341i	0.244733	−	0.141297i
$125$			1.00000i			0.0894427i
$126$	16.8150	+	9.70814i	1.49800	+	0.864869i
$127$	4.04603	−	7.00792i	0.359027	−	0.621852i	−0.628772	−	0.777590i	$-0.716442\pi$
$127$	4.04603	−	7.00792i	0.359027	−	0.621852i	0.987798	+	0.155737i	$0.0497754\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.09503	+	2.36427i	−0.360548	+	0.208162i
$130$	2.55417	−	1.47465i	0.224015	−	0.129335i
$131$	3.43829	+	1.98510i	0.300405	+	0.173439i	0.642625	−	0.766181i	$-0.277845\pi$
$131$	3.43829	+	1.98510i	0.300405	+	0.173439i	−0.342220	+	0.939620i	$0.611179\pi$
$132$	7.36950	−	12.7643i	0.641432	−	1.11099i
$133$	16.6167	+	9.59366i	1.44085	+	0.831876i
$134$		−	6.89109i		−	0.595299i
$135$	4.66956	−	2.69597i	0.401892	−	0.232032i
$136$	−1.26382	+	2.18900i	−0.108372	+	0.187705i
$137$	20.7501			1.77280			0.886401	−	0.462918i	$-0.153197\pi$
$137$	20.7501			1.77280			0.886401	+	0.462918i	$0.153197\pi$
$138$	−8.23182			−0.700739
$139$	−9.05622	+	15.6858i	−0.768139	+	1.33046i	0.170433	+	0.985369i	$0.445484\pi$
$139$	−9.05622	+	15.6858i	−0.768139	+	1.33046i	−0.938571	+	0.345086i	$0.887850\pi$
$140$		−	3.94930i		−	0.333777i
$141$	16.6292	+	28.8026i	1.40043	+	2.42562i
$142$			11.0802i			0.929829i
$143$	−13.3799	+	7.72491i	−1.11889	+	0.645990i
$144$	−2.45819	−	4.25771i	−0.204849	−	0.354809i
$145$	−4.83483	−	8.37416i	−0.401510	−	0.695436i
$146$	−0.885228	−	0.511087i	−0.0732620	−	0.0422978i
$147$	−24.1885			−1.99504
$148$	−3.76783	−	4.77529i	−0.309714	−	0.392527i
$149$	−16.1234			−1.32088			−0.660441	−	0.750878i	$-0.729631\pi$
$149$	−16.1234			−1.32088			−0.660441	+	0.750878i	$0.729631\pi$
$150$	−2.43665	−	1.40680i	−0.198952	−	0.114865i
$151$	2.67163	+	4.62739i	0.217414	+	0.376572i	0.954017	−	0.299754i	$-0.0969045\pi$
$151$	2.67163	+	4.62739i	0.217414	+	0.376572i	−0.736603	+	0.676326i	$0.763571\pi$
$152$	−2.42920	−	4.20751i	−0.197035	−	0.341274i
$153$	10.7620	−	6.21342i	0.870052	−	0.502325i
$154$			20.6883i			1.66711i
$155$	1.57341	+	2.72523i	0.126379	+	0.218896i
$156$			8.29817i			0.664386i
$157$	−7.08298	+	12.2681i	−0.565283	+	0.979099i	0.431740	+	0.901998i	$0.357900\pi$
$157$	−7.08298	+	12.2681i	−0.565283	+	0.979099i	−0.997023	+	0.0771012i	$0.975434\pi$
$158$	8.16892			0.649884
$159$	−9.70257			−0.769464
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	10.0065	−	5.77727i	0.788625	−	0.455313i
$162$			0.421663i			0.0331290i
$163$	−0.975743	−	0.563345i	−0.0764261	−	0.0441246i	0.461300	−	0.887244i	$-0.347383\pi$
$163$	−0.975743	−	0.563345i	−0.0764261	−	0.0441246i	−0.537726	+	0.843120i	$0.680717\pi$
$164$	−3.88220	+	6.72417i	−0.303149	+	0.525069i
$165$	12.7643	+	7.36950i	0.993703	+	0.573714i
$166$	−14.2184	+	8.20899i	−1.10356	+	0.637141i
$167$	−9.17780	+	5.29881i	−0.710200	+	0.410034i	−0.811135	−	0.584859i	$-0.801150\pi$
$167$	−9.17780	+	5.29881i	−0.710200	+	0.410034i	0.100935	+	0.994893i	$0.467816\pi$
$168$	9.62308	+	5.55589i	0.742437	+	0.428646i
$169$	−2.15081	+	3.72532i	−0.165447	+	0.286563i
$170$	−2.18900	−	1.26382i	−0.167889	−	0.0969305i
$171$			23.8858i			1.82659i
$172$	−1.45544	+	0.840298i	−0.110976	+	0.0640722i
$173$	7.75419	−	13.4307i	0.589540	−	1.02111i	−0.404752	−	0.914426i	$-0.632642\pi$
$173$	7.75419	−	13.4307i	0.589540	−	1.02111i	0.994293	−	0.106688i	$-0.0340245\pi$
$174$	27.2066			2.06253
$175$	3.94930			0.298539
$176$	2.61923	−	4.53665i	0.197432	−	0.341963i
$177$			19.5397i			1.46869i
$178$	−1.23991	−	2.14759i	−0.0929351	−	0.160968i
$179$			8.16858i			0.610548i	0.952265	+	0.305274i	$0.0987481\pi$
$179$			8.16858i			0.610548i	−0.952265	+	0.305274i	$0.901252\pi$
$180$	4.25771	−	2.45819i	0.317351	−	0.183223i
$181$	−2.99877	−	5.19403i	−0.222897	−	0.386069i	0.732789	−	0.680455i	$-0.238218\pi$
$181$	−2.99877	−	5.19403i	−0.222897	−	0.386069i	−0.955686	+	0.294387i	$0.904885\pi$
$182$	−5.82384	−	10.0872i	−0.431692	−	0.747712i
$183$	24.6575	+	14.2360i	1.82273	+	1.05236i
$184$	−2.92572			−0.215687
$185$	4.77529	−	3.76783i	0.351087	−	0.277017i
$186$	−8.85392			−0.649201
$187$	11.4670	+	6.62048i	0.838550	+	0.484137i
$188$	5.91027	+	10.2369i	0.431051	+	0.746602i
$189$	−10.6472	−	18.4415i	−0.774470	−	1.34142i
$190$	4.20751	−	2.42920i	0.305245	−	0.176233i
$191$		−	12.8486i		−	0.929693i	−0.885391	−	0.464847i	$-0.846109\pi$
$191$		−	12.8486i		−	0.929693i	0.885391	−	0.464847i	$-0.153891\pi$
$192$	−1.40680	−	2.43665i	−0.101527	−	0.175850i
$193$		−	12.8968i		−	0.928330i	−0.885749	−	0.464165i	$-0.846354\pi$
$193$		−	12.8968i		−	0.928330i	0.885749	−	0.464165i	$-0.153646\pi$
$194$	−2.48137	+	4.29785i	−0.178152	+	0.308568i
$195$	−8.29817			−0.594244
$196$	−8.59698			−0.614070
$197$	5.03868	−	8.72726i	0.358991	−	0.621791i	−0.628801	−	0.777566i	$-0.716454\pi$
$197$	5.03868	−	8.72726i	0.358991	−	0.621791i	0.987793	+	0.155775i	$0.0497874\pi$
$198$	−22.3039	+	12.8772i	−1.58507	+	0.915140i
$199$		−	0.913815i		−	0.0647786i	−0.999475	−	0.0323893i	$-0.989688\pi$
$199$		−	0.913815i		−	0.0647786i	0.999475	−	0.0323893i	$-0.0103116\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−9.69441	+	16.7912i	−0.683791	+	1.18436i
$202$	0.654293	+	0.377756i	0.0460359	+	0.0265788i
$203$	−33.0721	+	19.0942i	−2.32121	+	1.34015i
$204$	6.15898	−	3.55589i	0.431215	−	0.248962i
$205$	−6.72417	−	3.88220i	−0.469636	−	0.271145i
$206$	−8.26884	+	14.3220i	−0.576117	+	0.997864i
$207$	12.4569	+	7.19197i	0.865812	+	0.499877i
$208$			2.94930i			0.204497i
$209$	−22.0409	+	12.7253i	−1.52460	+	0.880228i
$210$	−5.55589	+	9.62308i	−0.383393	+	0.664056i
$211$	−5.47592			−0.376978			−0.188489	−	0.982075i	$-0.560359\pi$
$211$	−5.47592			−0.376978			−0.188489	+	0.982075i	$0.560359\pi$
$212$	−3.44845			−0.236840
$213$	15.5876	−	26.9986i	1.06805	−	1.84991i
$214$			12.6464i			0.864488i
$215$	−0.840298	−	1.45544i	−0.0573079	−	0.0992602i
$216$			5.39194i			0.366875i
$217$	10.7627	−	6.21388i	0.730623	−	0.421825i
$218$	2.65989	+	4.60707i	0.180151	+	0.312030i
$219$	1.43800	+	2.49068i	0.0971708	+	0.168305i
$220$	4.53665	+	2.61923i	0.305861	+	0.176589i
$221$	−7.45477			−0.501462
$222$	2.46301	+	16.9363i	0.165306	+	1.13669i
$223$	12.6320			0.845899			0.422949	−	0.906153i	$-0.360995\pi$
$223$	12.6320			0.845899			0.422949	+	0.906153i	$0.360995\pi$
$224$	3.42019	+	1.97465i	0.228521	+	0.131937i
$225$	2.45819	+	4.25771i	0.163879	+	0.283847i
$226$	−4.32003	−	7.48250i	−0.287364	−	0.497729i
$227$	20.6340	−	11.9131i	1.36953	−	0.790697i	0.378660	−	0.925536i	$-0.376385\pi$
$227$	20.6340	−	11.9131i	1.36953	−	0.790697i	0.990868	+	0.134838i	$0.0430515\pi$
$228$			13.6697i			0.905295i
$229$	−4.62224	−	8.00596i	−0.305446	−	0.529049i	0.671914	−	0.740629i	$-0.265472\pi$
$229$	−4.62224	−	8.00596i	−0.305446	−	0.529049i	−0.977361	+	0.211580i	$0.932139\pi$
$230$		−	2.92572i		−	0.192916i
$231$	29.1044	−	50.4102i	1.91493	−	3.31675i
$232$	9.66965			0.634844
$233$	−1.79691			−0.117719			−0.0588596	−	0.998266i	$-0.518746\pi$
$233$	−1.79691			−0.117719			−0.0588596	+	0.998266i	$0.518746\pi$
$234$	7.24994	−	12.5573i	0.473944	−	0.820895i
$235$	−10.2369	+	5.91027i	−0.667781	+	0.385544i
$236$			6.94471i			0.452062i
$237$	−19.9048	−	11.4921i	−1.29296	−	0.746489i
$238$	−4.99120	+	8.64502i	−0.323532	+	0.560373i
$239$	0.845001	+	0.487862i	0.0546586	+	0.0315571i	0.527080	−	0.849816i	$-0.323287\pi$
$239$	0.845001	+	0.487862i	0.0546586	+	0.0315571i	−0.472422	+	0.881373i	$0.656620\pi$
$240$	2.43665	−	1.40680i	0.157285	−	0.0908088i
$241$	5.29039	−	3.05441i	0.340784	−	0.196752i	−0.319835	−	0.947473i	$-0.603627\pi$
$241$	5.29039	−	3.05441i	0.340784	−	0.196752i	0.660619	+	0.750722i	$0.270294\pi$
$242$	−14.2388	−	8.22078i	−0.915305	−	0.528452i
$243$	−7.49472	+	12.9812i	−0.480786	+	0.832747i
$244$	8.76366	+	5.05970i	0.561036	+	0.323914i
$245$		−	8.59698i		−	0.549241i
$246$	18.9192	−	10.9230i	1.20624	−	0.696424i
$247$	7.16446	−	12.4092i	0.455863	−	0.789579i
$248$	−3.14682			−0.199823
$249$	46.1937			2.92741
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			11.8413i			0.747418i	0.927546	+	0.373709i	$0.121914\pi$
$251$			11.8413i			0.747418i	−0.927546	+	0.373709i	$0.878086\pi$
$252$	−9.70814	−	16.8150i	−0.611555	−	1.05924i
$253$			15.3263i			0.963555i
$254$	−7.00792	+	4.04603i	−0.439716	+	0.253870i
$255$	3.55589	+	6.15898i	0.222678	+	0.385690i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.3403	+	7.12467i	0.769767	+	0.444425i	0.832791	−	0.553587i	$-0.186741\pi$
$257$	12.3403	+	7.12467i	0.769767	+	0.444425i	−0.0630248	+	0.998012i	$0.520075\pi$
$258$	4.72854			0.294386
$259$	−14.8803	−	18.8591i	−0.924617	−	1.17185i
$260$	−2.94930			−0.182908
$261$	−41.1706	−	23.7698i	−2.54840	−	1.47132i
$262$	−1.98510	−	3.43829i	−0.122640	−	0.212418i
$263$	−9.83222	−	17.0299i	−0.606281	−	1.05011i	−0.991848	−	0.127429i	$-0.959327\pi$
$263$	−9.83222	−	17.0299i	−0.606281	−	1.05011i	0.385567	−	0.922680i	$-0.374006\pi$
$264$	−12.7643	+	7.36950i	−0.785591	+	0.453561i
$265$		−	3.44845i		−	0.211836i
$266$	−9.59366	−	16.6167i	−0.588225	−	1.01884i
$267$			6.97723i			0.427000i
$268$	−3.44554	+	5.96786i	−0.210470	+	0.364545i
$269$	0.526562			0.0321051			0.0160525	−	0.999871i	$-0.494890\pi$
$269$	0.526562			0.0321051			0.0160525	+	0.999871i	$0.494890\pi$
$270$	−5.39194			−0.328143
$271$	4.54386	−	7.87019i	0.276020	−	0.478080i	−0.694372	−	0.719616i	$-0.744318\pi$
$271$	4.54386	−	7.87019i	0.276020	−	0.478080i	0.970392	+	0.241536i	$0.0776512\pi$
$272$	2.18900	−	1.26382i	0.132728	−	0.0766303i
$273$			32.7720i			1.98345i
$274$	−17.9701	−	10.3751i	−1.08562	−	0.626780i
$275$	−2.61923	+	4.53665i	−0.157946	+	0.273570i
$276$	7.12896	+	4.11591i	0.429113	+	0.247749i
$277$	−26.5155	+	15.3087i	−1.59316	+	0.919813i	−0.600402	+	0.799698i	$0.704993\pi$
$277$	−26.5155	+	15.3087i	−1.59316	+	0.919813i	−0.992760	+	0.120115i	$0.961674\pi$
$278$	15.6858	−	9.05622i	0.940774	−	0.543156i
$279$	13.3983	+	7.73549i	0.802133	+	0.463112i
$280$	−1.97465	+	3.42019i	−0.118008	+	0.204396i
$281$	−14.2745	−	8.24138i	−0.851545	−	0.491640i	0.00962696	−	0.999954i	$-0.496936\pi$
$281$	−14.2745	−	8.24138i	−0.851545	−	0.491640i	−0.861172	+	0.508314i	$0.830269\pi$
$282$		−	33.2584i		−	1.98051i
$283$	−24.8151	+	14.3270i	−1.47510	+	0.851652i	−0.999606	−	0.0280655i	$-0.991065\pi$
$283$	−24.8151	+	14.3270i	−1.47510	+	0.851652i	−0.475498	+	0.879717i	$0.657732\pi$
$284$	5.54009	−	9.59572i	0.328744	−	0.569401i
$285$	−13.6697			−0.809720
$286$	15.4498			0.913567
$287$	−15.3320	+	26.5558i	−0.905018	+	1.56754i
$288$			4.91638i			0.289701i
$289$	−5.30552	−	9.18944i	−0.312090	−	0.540555i
$290$			9.66965i			0.567822i
$291$	12.0925	−	6.98159i	0.708873	−	0.409268i
$292$	0.511087	+	0.885228i	0.0299091	+	0.0518041i
$293$	−10.5371	−	18.2509i	−0.615587	−	1.06623i	−0.990281	−	0.139079i	$-0.955586\pi$
$293$	−10.5371	−	18.2509i	−0.615587	−	1.06623i	0.374695	−	0.927148i	$-0.377748\pi$
$294$	20.9479	+	12.0943i	1.22170	+	0.705351i
$295$	−6.94471			−0.404337
$296$	0.875392	+	6.01944i	0.0508811	+	0.349873i
$297$	28.2455			1.63897
$298$	13.9633	+	8.06171i	0.808872	+	0.467003i
$299$	−4.31441	−	7.47278i	−0.249509	−	0.432162i
$300$	1.40680	+	2.43665i	0.0812218	+	0.140680i
$301$	−5.74797	+	3.31859i	−0.331307	+	0.191280i
$302$		−	5.34326i		−	0.307470i
$303$	−1.06286	−	1.84092i	−0.0610596	−	0.105758i
$304$			4.85841i			0.278649i
$305$	−5.05970	+	8.76366i	−0.289718	+	0.501806i
$306$	−12.4268			−0.710395
$307$	4.76704			0.272069			0.136035	−	0.990704i	$-0.456564\pi$
$307$	4.76704			0.272069			0.136035	+	0.990704i	$0.456564\pi$
$308$	10.3441	−	17.9166i	0.589412	−	1.02089i
$309$	40.2966	−	23.2653i	2.29239	−	1.32351i
$310$		−	3.14682i		−	0.178728i
$311$	−15.9677	−	9.21894i	−0.905444	−	0.522758i	−0.0264814	−	0.999649i	$-0.508430\pi$
$311$	−15.9677	−	9.21894i	−0.905444	−	0.522758i	−0.878962	+	0.476891i	$0.841764\pi$
$312$	4.14909	−	7.18643i	0.234896	−	0.406851i
$313$	−14.9405	−	8.62591i	−0.844487	−	0.487565i	0.0142997	−	0.999898i	$-0.495448\pi$
$313$	−14.9405	−	8.62591i	−0.844487	−	0.487565i	−0.858787	+	0.512333i	$0.828781\pi$
$314$	12.2681	−	7.08298i	0.692328	−	0.399716i
$315$	16.8150	−	9.70814i	0.947417	−	0.546991i
$316$	−7.07449	−	4.08446i	−0.397971	−	0.229769i
$317$	−16.3282	+	28.2813i	−0.917085	+	1.58844i	−0.113264	+	0.993565i	$0.536131\pi$
$317$	−16.3282	+	28.2813i	−0.917085	+	1.58844i	−0.803820	+	0.594872i	$0.797203\pi$
$318$	8.40267	+	4.85129i	0.471199	+	0.272047i
$319$		−	50.6542i		−	2.83609i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	17.7910	−	30.8148i	0.992994	−	1.71992i
$322$	−11.5545			−0.643909
$323$	−12.2803			−0.683294
$324$	0.210831	−	0.365171i	0.0117129	−	0.0202873i
$325$		−	2.94930i		−	0.163598i
$326$	0.563345	+	0.975743i	0.0312008	+	0.0540414i
$327$		−	14.9678i		−	0.827720i
$328$	6.72417	−	3.88220i	0.371280	−	0.214359i
$329$	23.3415	+	40.4286i	1.28686	+	2.22890i
$330$	−7.36950	−	12.7643i	−0.405677	−	0.702654i
$331$	−12.2922	−	7.09688i	−0.675638	−	0.390080i	0.122571	−	0.992460i	$-0.460886\pi$
$331$	−12.2922	−	7.09688i	−0.675638	−	0.390080i	−0.798210	+	0.602380i	$0.794219\pi$
$332$	16.4180			0.901054
$333$	11.0698	−	27.7809i	0.606620	−	1.52239i
$334$	10.5976			0.579876
$335$	−5.96786	−	3.44554i	−0.326059	−	0.188250i
$336$	−5.55589	−	9.62308i	−0.303099	−	0.524982i
$337$	12.3658	+	21.4182i	0.673608	+	1.16672i	0.976874	+	0.213818i	$0.0685898\pi$
$337$	12.3658	+	21.4182i	0.673608	+	1.16672i	−0.303265	+	0.952906i	$0.598077\pi$
$338$	3.72532	−	2.15081i	0.202630	−	0.116989i
$339$			24.3097i			1.32032i
$340$	1.26382	+	2.18900i	0.0685402	+	0.118715i
$341$			16.4845i			0.892688i
$342$	11.9429	−	20.6857i	0.645798	−	1.11855i
$343$	−6.30695			−0.340543
$344$	1.68060			0.0906117
$345$	−4.11591	+	7.12896i	−0.221593	+	0.383811i
$346$	−13.4307	+	7.75419i	−0.722037	+	0.416868i
$347$		−	8.11360i		−	0.435561i	−0.975998	−	0.217780i	$-0.930118\pi$
$347$		−	8.11360i		−	0.435561i	0.975998	−	0.217780i	$-0.0698817\pi$
$348$	−23.5616	−	13.6033i	−1.26303	−	0.729213i
$349$	−12.0052	+	20.7936i	−0.642622	+	1.11305i	0.342223	+	0.939619i	$0.388820\pi$
$349$	−12.0052	+	20.7936i	−0.642622	+	1.11305i	−0.984845	+	0.173435i	$0.944513\pi$
$350$	−3.42019	−	1.97465i	−0.182817	−	0.105550i
$351$	−13.7719	+	7.95123i	−0.735092	+	0.424405i
$352$	−4.53665	+	2.61923i	−0.241804	+	0.139606i
$353$	18.8909	+	10.9067i	1.00546	+	0.580504i	0.909860	−	0.414915i	$-0.136189\pi$
$353$	18.8909	+	10.9067i	1.00546	+	0.580504i	0.0956030	+	0.995420i	$0.469522\pi$
$354$	9.76984	−	16.9219i	0.519261	−	0.899387i
$355$	9.59572	+	5.54009i	0.509288	+	0.294038i
$356$			2.47982i			0.131430i
$357$	24.3237	−	14.0433i	1.28735	−	0.743249i
$358$	4.08429	−	7.07419i	0.215861	−	0.373883i
$359$	−14.6216			−0.771696			−0.385848	−	0.922562i	$-0.626091\pi$
$359$	−14.6216			−0.771696			−0.385848	+	0.922562i	$0.626091\pi$
$360$	−4.91638			−0.259116
$361$	2.30207	−	3.98730i	0.121162	−	0.209858i
$362$			5.99754i			0.315224i
$363$	23.1300	+	40.0624i	1.21401	+	2.10273i
$364$			11.6477i			0.610504i
$365$	−0.885228	+	0.511087i	−0.0463350	+	0.0267515i
$366$	−14.2360	−	24.6575i	−0.744128	−	1.28887i
$367$	−4.67210	−	8.09232i	−0.243882	−	0.422415i	0.717935	−	0.696110i	$-0.245088\pi$
$367$	−4.67210	−	8.09232i	−0.243882	−	0.422415i	−0.961817	+	0.273695i	$0.911754\pi$
$368$	2.53375	+	1.46286i	0.132081	+	0.0762568i
$369$	−38.1727			−1.98719
$370$	−6.01944	+	0.875392i	−0.312936	+	0.0455095i
$371$	−13.6190			−0.707061
$372$	7.66772	+	4.42696i	0.397553	+	0.229527i
$373$	1.13370	+	1.96362i	0.0587007	+	0.101673i	0.893882	−	0.448301i	$-0.147971\pi$
$373$	1.13370	+	1.96362i	0.0587007	+	0.101673i	−0.835182	+	0.549974i	$0.814638\pi$
$374$	−6.62048	−	11.4670i	−0.342337	−	0.592945i
$375$	−2.43665	+	1.40680i	−0.125828	+	0.0726470i
$376$		−	11.8205i		−	0.609598i
$377$	14.2594	+	24.6979i	0.734394	+	1.27201i
$378$			21.2944i			1.09527i
$379$	1.23608	−	2.14096i	0.0634932	−	0.109974i	−0.832531	−	0.553978i	$-0.813109\pi$
$379$	1.23608	−	2.14096i	0.0634932	−	0.109974i	0.896025	+	0.444004i	$0.146443\pi$
$380$	−4.85841			−0.249231
$381$	22.7678			1.16643
$382$	−6.42431	+	11.1272i	−0.328696	+	0.569319i
$383$	30.3399	−	17.5167i	1.55029	−	0.895063i	0.552177	−	0.833727i	$-0.313797\pi$
$383$	30.3399	−	17.5167i	1.55029	−	0.895063i	0.998117	−	0.0613362i	$-0.0195362\pi$
$384$			2.81361i			0.143581i
$385$	17.9166	+	10.3441i	0.913114	+	0.527187i
$386$	−6.44839	+	11.1689i	−0.328214	+	0.568484i
$387$	−7.15550	−	4.13123i	−0.363734	−	0.210002i
$388$	4.29785	−	2.48137i	0.218190	−	0.125972i
$389$	23.5689	−	13.6075i	1.19499	−	0.689927i	0.235555	−	0.971861i	$-0.424309\pi$
$389$	23.5689	−	13.6075i	1.19499	−	0.689927i	0.959434	+	0.281934i	$0.0909758\pi$
$390$	7.18643	+	4.14909i	0.363899	+	0.210097i
$391$	−3.69758	+	6.40439i	−0.186995	+	0.323884i
$392$	7.44520	+	4.29849i	0.376039	+	0.217106i
$393$			11.1706i			0.563481i
$394$	−8.72726	+	5.03868i	−0.439673	+	0.253845i
$395$	4.08446	−	7.07449i	0.205511	−	0.355956i
$396$	25.7543			1.29420
$397$	2.34614			0.117750			0.0588748	−	0.998265i	$-0.481249\pi$
$397$	2.34614			0.117750			0.0588748	+	0.998265i	$0.481249\pi$
$398$	−0.456907	+	0.791387i	−0.0229027	+	0.0396686i
$399$			53.9856i			2.70266i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$		−	20.5055i		−	1.02400i	−0.858987	−	0.511998i	$-0.828906\pi$
$401$		−	20.5055i		−	1.02400i	0.858987	−	0.511998i	$-0.171094\pi$
$402$	16.7912	−	9.69441i	0.837469	−	0.483513i
$403$	−4.64046	−	8.03752i	−0.231158	−	0.400377i
$404$	−0.377756	−	0.654293i	−0.0187941	−	0.0325523i
$405$	0.365171	+	0.210831i	0.0181455	+	0.0104763i
$406$	38.1884			1.89526
$407$	31.5327	−	4.58572i	1.56302	−	0.227305i
$408$	−7.11178			−0.352086
$409$	−31.9761	−	18.4614i	−1.58112	−	0.912859i	−0.994697	−	0.102853i	$-0.967203\pi$
$409$	−31.9761	−	18.4614i	−1.58112	−	0.912859i	−0.586421	−	0.810006i	$-0.699464\pi$
$410$	3.88220	+	6.72417i	0.191728	+	0.332083i
$411$	29.1913	+	50.5609i	1.43990	+	2.49398i
$412$	14.3220	−	8.26884i	0.705597	−	0.407376i
$413$			27.4268i			1.34958i
$414$	−7.19197	−	12.4569i	−0.353466	−	0.612221i
$415$			16.4180i			0.805927i
$416$	1.47465	−	2.55417i	0.0723007	−	0.125228i
$417$	−50.9613			−2.49558
$418$	25.4506			1.24483
$419$	4.73126	−	8.19479i	0.231137	−	0.400342i	−0.727006	−	0.686631i	$-0.759089\pi$
$419$	4.73126	−	8.19479i	0.231137	−	0.400342i	0.958143	+	0.286290i	$0.0924220\pi$
$420$	9.62308	−	5.55589i	0.469558	−	0.271100i
$421$			12.5632i			0.612293i	0.951984	+	0.306146i	$0.0990397\pi$
$421$			12.5632i			0.612293i	−0.951984	+	0.306146i	$0.900960\pi$
$422$	4.74229	+	2.73796i	0.230851	+	0.133282i
$423$	−29.0572	+	50.3285i	−1.41281	+	2.44705i
$424$	2.98644	+	1.72422i	0.145034	+	0.0837357i
$425$	−2.18900	+	1.26382i	−0.106182	+	0.0613042i
$426$	−26.9986	+	15.5876i	−1.30809	+	0.755224i
$427$	34.6103	+	19.9823i	1.67491	+	0.967011i
$428$	6.32318	−	10.9521i	0.305643	−	0.529389i
$429$	−37.6459	−	21.7349i	−1.81756	−	1.04937i
$430$			1.68060i			0.0810456i
$431$	24.7659	−	14.2986i	1.19293	−	0.688740i	0.233962	−	0.972246i	$-0.424831\pi$
$431$	24.7659	−	14.2986i	1.19293	−	0.688740i	0.958971	+	0.283506i	$0.0914975\pi$
$432$	2.69597	−	4.66956i	0.129710	−	0.224664i
$433$	−10.2506			−0.492613			−0.246306	−	0.969192i	$-0.579217\pi$
$433$	−10.2506			−0.492613			−0.246306	+	0.969192i	$0.579217\pi$
$434$	−12.4278			−0.596551
$435$	13.6033	−	23.5616i	0.652228	−	1.12969i
$436$		−	5.31979i		−	0.254772i
$437$	−7.10717	−	12.3100i	−0.339982	−	0.588866i
$438$		−	2.87599i		−	0.137420i
$439$	−9.52996	+	5.50213i	−0.454840	+	0.262602i	−0.709872	−	0.704330i	$-0.751247\pi$
$439$	−9.52996	+	5.50213i	−0.454840	+	0.262602i	0.255032	+	0.966933i	$0.417914\pi$
$440$	−2.61923	−	4.53665i	−0.124867	−	0.216276i
$441$	−21.1330	−	36.6035i	−1.00633	−	1.74302i
$442$	6.45602	+	3.72738i	0.307081	+	0.177294i
$443$	3.49848			0.166218			0.0831089	−	0.996540i	$-0.473515\pi$
$443$	3.49848			0.166218			0.0831089	+	0.996540i	$0.473515\pi$
$444$	6.33514	−	15.8988i	0.300653	−	0.754524i
$445$	−2.47982			−0.117555
$446$	−10.9396	−	6.31598i	−0.518005	−	0.299070i
$447$	−22.6825	−	39.2872i	−1.07284	−	1.85822i
$448$	−1.97465	−	3.42019i	−0.0932935	−	0.161589i
$449$	13.6898	−	7.90382i	0.646063	−	0.373005i	−0.140883	−	0.990026i	$-0.544994\pi$
$449$	13.6898	−	7.90382i	0.646063	−	0.373005i	0.786946	+	0.617022i	$0.211661\pi$
$450$		−	4.91638i		−	0.231760i
$451$	−20.3368	−	35.2243i	−0.957622	−	1.65865i
$452$			8.64005i			0.406394i
$453$	−7.51691	+	13.0197i	−0.353175	+	0.611717i
$454$	−23.8261			−1.11821
$455$	−11.6477			−0.546052
$456$	6.83483	−	11.8383i	0.320070	−	0.554378i
$457$	23.8050	−	13.7438i	1.11355	−	0.642908i	0.173803	−	0.984780i	$-0.444394\pi$
$457$	23.8050	−	13.7438i	1.11355	−	0.642908i	0.939746	+	0.341873i	$0.111061\pi$
$458$			9.24449i			0.431967i
$459$	11.8030	+	6.81444i	0.550915	+	0.318071i
$460$	−1.46286	+	2.53375i	−0.0682061	+	0.118137i
$461$	−17.9712	−	10.3757i	−0.837002	−	0.483243i	0.0192421	−	0.999815i	$-0.493875\pi$
$461$	−17.9712	−	10.3757i	−0.837002	−	0.483243i	−0.856244	+	0.516572i	$0.827208\pi$
$462$	−50.4102	+	29.1044i	−2.34530	+	1.35406i
$463$	12.5685	−	7.25643i	0.584108	−	0.337235i	−0.178656	−	0.983912i	$-0.557175\pi$
$463$	12.5685	−	7.25643i	0.584108	−	0.337235i	0.762764	+	0.646677i	$0.223842\pi$
$464$	−8.37416	−	4.83483i	−0.388761	−	0.224451i
$465$	−4.42696	+	7.66772i	−0.205295	+	0.355582i
$466$	1.55617	+	0.898453i	0.0720880	+	0.0416200i
$467$			1.19790i			0.0554322i	0.999616	+	0.0277161i	$0.00882343\pi$
$467$			1.19790i			0.0554322i	−0.999616	+	0.0277161i	$0.991177\pi$
$468$	−12.5573	+	7.24994i	−0.580460	+	0.335129i
$469$	−13.6075	+	23.5689i	−0.628336	+	1.08831i
$470$	11.8205			0.545241
$471$	−39.8574			−1.83653
$472$	3.47236	−	6.01430i	0.159828	−	0.276830i
$473$		−	8.80376i		−	0.404797i
$474$	11.4921	+	19.9048i	0.527848	+	0.914259i
$475$		−	4.85841i		−	0.222919i
$476$	8.64502	−	4.99120i	0.396244	−	0.228771i
$477$	−8.47694	−	14.6825i	−0.388132	−	0.672265i
$478$	−0.487862	−	0.845001i	−0.0223143	−	0.0386495i
$479$	12.0118	+	6.93504i	0.548835	+	0.316870i	0.748652	−	0.662963i	$-0.230701\pi$
$479$	12.0118	+	6.93504i	0.548835	+	0.316870i	−0.199817	+	0.979833i	$0.564035\pi$
$480$	−2.81361			−0.128423
$481$	−14.0838	+	11.1125i	−0.642165	+	0.506685i
$482$	−6.10881			−0.278249
$483$	28.1544	+	16.2550i	1.28107	+	0.739626i
$484$	8.22078	+	14.2388i	0.373672	+	0.647219i
$485$	2.48137	+	4.29785i	0.112673	+	0.195155i
$486$	12.9812	−	7.49472i	0.588841	−	0.339967i
$487$		−	35.3465i		−	1.60170i	−0.598862	−	0.800852i	$-0.704380\pi$
$487$		−	35.3465i		−	1.60170i	0.598862	−	0.800852i	$-0.295620\pi$
$488$	−5.05970	−	8.76366i	−0.229042	−	0.396712i
$489$		−	3.17006i		−	0.143355i
$490$	−4.29849	+	7.44520i	−0.194186	+	0.336340i
$491$	−2.11115			−0.0952751			−0.0476375	−	0.998865i	$-0.515169\pi$
$491$	−2.11115			−0.0952751			−0.0476375	+	0.998865i	$0.515169\pi$
$492$	−21.8460			−0.984892
$493$	12.2207	−	21.1669i	0.550392	−	0.953307i
$494$	−12.4092	+	7.16446i	−0.558316	+	0.322344i
$495$			25.7543i			1.15757i
$496$	2.72523	+	1.57341i	0.122366	+	0.0706483i
$497$	21.8795	−	37.8964i	0.981430	−	1.69989i
$498$	−40.0049	−	23.0969i	−1.79266	−	1.03500i
$499$	5.62547	−	3.24787i	0.251831	−	0.145395i	−0.368772	−	0.929520i	$-0.620222\pi$
$499$	5.62547	−	3.24787i	0.251831	−	0.145395i	0.620602	+	0.784126i	$0.286888\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−25.8227	−	14.9088i	−1.15367	−	0.666074i
$502$	5.92066	−	10.2549i	0.264252	−	0.457698i
$503$	−27.3930	−	15.8153i	−1.22139	−	0.705171i	−0.256177	−	0.966630i	$-0.582463\pi$
$503$	−27.3930	−	15.8153i	−1.22139	−	0.705171i	−0.965215	+	0.261459i	$0.915796\pi$
$504$			19.4163i			0.864869i
$505$	0.654293	−	0.377756i	0.0291157	−	0.0168099i
$506$	7.66314	−	13.2730i	0.340668	−	0.590055i
$507$	−12.1031			−0.537516
$508$	8.09205			0.359027
$509$	−19.7306	+	34.1744i	−0.874543	+	1.51475i	−0.0172943	+	0.999850i	$0.505505\pi$
$509$	−19.7306	+	34.1744i	−0.874543	+	1.51475i	−0.857249	+	0.514903i	$0.827828\pi$
$510$		−	7.11178i		−	0.314915i
$511$	2.01844	+	3.49603i	0.0892903	+	0.154655i
$512$			1.00000i			0.0441942i
$513$	−22.6866	+	13.0981i	−1.00164	+	0.578297i
$514$	−7.12467	−	12.3403i	−0.314256	−	0.544307i
$515$	8.26884	+	14.3220i	0.364369	+	0.631105i
$516$	−4.09503	−	2.36427i	−0.180274	−	0.104081i
$517$	−61.9216			−2.72331
$518$	3.45719	+	23.7726i	0.151900	+	1.04451i
$519$	43.6345			1.91534
$520$	2.55417	+	1.47465i	0.112008	+	0.0646677i
$521$	−3.16429	−	5.48070i	−0.138630	−	0.240114i	0.788348	−	0.615229i	$-0.210937\pi$
$521$	−3.16429	−	5.48070i	−0.138630	−	0.240114i	−0.926978	+	0.375115i	$0.877603\pi$
$522$	23.7698	+	41.1706i	1.04038	+	1.80199i
$523$	2.77181	−	1.60030i	0.121203	−	0.0699764i	−0.438173	−	0.898891i	$-0.644374\pi$
$523$	2.77181	−	1.60030i	0.121203	−	0.0699764i	0.559376	+	0.828914i	$0.311041\pi$
$524$			3.97020i			0.173439i
$525$	5.55589	+	9.62308i	0.242479	+	0.419986i
$526$			19.6644i			0.857410i
$527$	−3.97701	+	6.88839i	−0.173241	+	0.300063i
$528$	14.7390			0.641432
$529$	14.4402			0.627834
$530$	−1.72422	+	2.98644i	−0.0748955	+	0.129723i
$531$	−29.5686	+	17.0714i	−1.28317	+	0.740837i
$532$			19.1873i			0.831876i
$533$	19.8316	+	11.4498i	0.859002	+	0.495945i
$534$	3.48862	−	6.04246i	0.150967	−	0.261483i
$535$	10.9521	+	6.32318i	0.473500	+	0.273375i
$536$	5.96786	−	3.44554i	0.257772	−	0.148825i
$537$	−19.9040	+	11.4916i	−0.858921	+	0.495898i
$538$	−0.456016	−	0.263281i	−0.0196603	−	0.0113509i
$539$	22.5175	−	39.0015i	0.969898	−	1.67991i
$540$	4.66956	+	2.69597i	0.200946	+	0.116016i
$541$		−	6.72644i		−	0.289192i	−0.989491	−	0.144596i	$-0.953812\pi$
$541$		−	6.72644i		−	0.289192i	0.989491	−	0.144596i	$-0.0461883\pi$
$542$	−7.87019	+	4.54386i	−0.338054	+	0.195175i
$543$	8.43736	−	14.6139i	0.362082	−	0.627144i
$544$	−2.52764			−0.108372
$545$	5.31979			0.227875
$546$	16.3860	−	28.3814i	0.701256	−	1.21461i
$547$		−	34.7721i		−	1.48675i	−0.668877	−	0.743373i	$-0.733225\pi$
$547$		−	34.7721i		−	1.48675i	0.668877	−	0.743373i	$-0.266775\pi$
$548$	10.3751	+	17.9701i	0.443201	+	0.767646i
$549$			49.7509i			2.12331i
$550$	4.53665	−	2.61923i	0.193443	−	0.111685i
$551$	23.4896	+	40.6851i	1.00069	+	1.73324i
$552$	−4.11591	−	7.12896i	−0.175185	−	0.303429i
$553$	−27.9393	−	16.1308i	−1.18810	−	0.685949i
$554$	30.6175			1.30081
$555$	15.8988	+	6.33514i	0.674867	+	0.268912i
$556$	−18.1124			−0.768139
$557$	−5.21849	−	3.01290i	−0.221115	−	0.127661i	0.385352	−	0.922770i	$-0.374080\pi$
$557$	−5.21849	−	3.01290i	−0.221115	−	0.127661i	−0.606466	+	0.795109i	$0.707413\pi$
$558$	−7.73549	−	13.3983i	−0.327469	−	0.567194i
$559$	2.47829	+	4.29253i	0.104821	+	0.181555i
$560$	3.42019	−	1.97465i	0.144530	−	0.0834442i
$561$			37.2548i			1.57290i
$562$	8.24138	+	14.2745i	0.347642	+	0.602133i
$563$			30.3059i			1.27724i	0.769522	+	0.638620i	$0.220495\pi$
$563$			30.3059i			1.27724i	−0.769522	+	0.638620i	$0.779505\pi$
$564$	−16.6292	+	28.8026i	−0.700215	+	1.21281i
$565$	−8.64005			−0.363490
$566$	28.6540			1.20442
$567$	0.832637	−	1.44217i	0.0349675	−	0.0605654i
$568$	−9.59572	+	5.54009i	−0.402628	+	0.232457i
$569$		−	9.64599i		−	0.404381i	−0.979346	−	0.202190i	$-0.935194\pi$
$569$		−	9.64599i		−	0.404381i	0.979346	−	0.202190i	$-0.0648060\pi$
$570$	11.8383	+	6.83483i	0.495850	+	0.286279i
$571$	11.5120	−	19.9394i	0.481762	−	0.834436i	−0.518019	−	0.855369i	$-0.673330\pi$
$571$	11.5120	−	19.9394i	0.481762	−	0.834436i	0.999781	+	0.0209328i	$0.00666361\pi$
$572$	−13.3799	−	7.72491i	−0.559443	−	0.322995i
$573$	31.3076	−	18.0755i	1.30790	−	0.755114i
$574$	26.5558	−	15.3320i	1.10842	−	0.639944i
$575$	−2.53375	−	1.46286i	−0.105665	−	0.0610054i
$576$	2.45819	−	4.25771i	0.102425	−	0.177405i
$577$	28.1896	+	16.2753i	1.17355	+	0.677548i	0.954513	−	0.298169i	$-0.0963760\pi$
$577$	28.1896	+	16.2753i	1.17355	+	0.677548i	0.219034	+	0.975717i	$0.429709\pi$
$578$			10.6110i			0.441361i
$579$	31.4250	−	18.1432i	1.30598	−	0.754007i
$580$	4.83483	−	8.37416i	0.200755	−	0.347718i
$581$	64.8395			2.69000
$582$	−13.9632			−0.578792
$583$	9.03229	−	15.6444i	0.374079	−	0.647924i
$584$		−	1.02217i		−	0.0422978i
$585$	−7.24994	−	12.5573i	−0.299748	−	0.519179i
$586$			21.0743i			0.870571i
$587$	−28.9200	+	16.6969i	−1.19365	+	0.689157i	−0.959133	−	0.282954i	$-0.908685\pi$
$587$	−28.9200	+	16.6969i	−1.19365	+	0.689157i	−0.234521	+	0.972111i	$0.575352\pi$
$588$	−12.0943	−	20.9479i	−0.498759	−	0.863876i
$589$	−7.64428	−	13.2403i	−0.314977	−	0.545556i
$590$	6.01430	+	3.47236i	0.247605	+	0.142955i
$591$	28.3537			1.16632
$592$	2.25161	−	5.65069i	0.0925406	−	0.232242i
$593$	19.1069			0.784626			0.392313	−	0.919832i	$-0.371675\pi$
$593$	19.1069			0.784626			0.392313	+	0.919832i	$0.371675\pi$
$594$	−24.4613	−	14.1228i	−1.00366	−	0.579464i
$595$	4.99120	+	8.64502i	0.204619	+	0.354411i
$596$	−8.06171	−	13.9633i	−0.330221	−	0.571959i
$597$	2.22665	−	1.28556i	0.0911308	−	0.0526144i
$598$			8.62882i			0.352859i
$599$	0.677086	+	1.17275i	0.0276650	+	0.0479172i	0.879526	−	0.475850i	$-0.157860\pi$
$599$	0.677086	+	1.17275i	0.0276650	+	0.0479172i	−0.851861	+	0.523767i	$0.824526\pi$
$600$		−	2.81361i		−	0.114865i
$601$	−14.4676	+	25.0586i	−0.590145	+	1.02216i	0.404067	+	0.914729i	$0.367596\pi$
$601$	−14.4676	+	25.0586i	−0.590145	+	1.02216i	−0.994212	+	0.107432i	$0.965737\pi$
$602$	6.63718			0.270511
$603$	−33.8792			−1.37967
$604$	−2.67163	+	4.62739i	−0.108707	+	0.188286i
$605$	−14.2388	+	8.22078i	−0.578890	+	0.334222i
$606$			2.12572i			0.0863513i
$607$	−7.40617	−	4.27596i	−0.300607	−	0.173556i	0.342108	−	0.939661i	$-0.388859\pi$
$607$	−7.40617	−	4.27596i	−0.300607	−	0.173556i	−0.642716	+	0.766105i	$0.722192\pi$
$608$	2.42920	−	4.20751i	0.0985173	−	0.170637i
$609$	−93.0519	−	53.7235i	−3.77065	−	2.17699i
$610$	8.76366	−	5.05970i	0.354830	−	0.204861i
$611$	30.1917	−	17.4312i	1.22142	−	0.705190i
$612$	10.7620	+	6.21342i	0.435026	+	0.251162i
$613$	−20.0120	+	34.6618i	−0.808278	+	1.39998i	0.105777	+	0.994390i	$0.466267\pi$
$613$	−20.0120	+	34.6618i	−0.808278	+	1.39998i	−0.914056	+	0.405589i	$0.867066\pi$
$614$	−4.12838	−	2.38352i	−0.166608	−	0.0961911i
$615$		−	21.8460i		−	0.880914i
$616$	−17.9166	+	10.3441i	−0.721880	+	0.416778i
$617$	0.0533952	−	0.0924832i	0.00214961	−	0.00372323i	−0.864949	−	0.501860i	$-0.832649\pi$
$617$	0.0533952	−	0.0924832i	0.00214961	−	0.00372323i	0.867098	+	0.498137i	$0.165982\pi$
$618$	−46.5305			−1.87173
$619$	34.5582			1.38901			0.694505	−	0.719488i	$-0.255623\pi$
$619$	34.5582			1.38901			0.694505	+	0.719488i	$0.255623\pi$
$620$	−1.57341	+	2.72523i	−0.0631897	+	0.109448i
$621$			15.7753i			0.633041i
$622$	9.21894	+	15.9677i	0.369646	+	0.640245i
$623$			9.79355i			0.392370i
$624$	−7.18643	+	4.14909i	−0.287687	+	0.166096i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.62591	+	14.9405i	0.344761	+	0.597143i
$627$	−62.0144	−	35.8040i	−2.47662	−	1.42988i
$628$	−14.1660			−0.565283
$629$	14.2829	+	5.69125i	0.569496	+	0.226925i
$630$	−19.4163			−0.773563
$631$	5.54791	+	3.20309i	0.220859	+	0.127513i	0.606348	−	0.795199i	$-0.292634\pi$
$631$	5.54791	+	3.20309i	0.220859	+	0.127513i	−0.385489	+	0.922712i	$0.625967\pi$
$632$	4.08446	+	7.07449i	0.162471	+	0.281408i
$633$	−7.70355	−	13.3429i	−0.306188	−	0.530334i
$634$	28.2813	−	16.3282i	1.12319	−	0.648477i
$635$			8.09205i			0.321123i
$636$	−4.85129	−	8.40267i	−0.192366	−	0.333188i
$637$			25.3551i			1.00460i
$638$	−25.3271	+	43.8678i	−1.00271	+	1.73674i
$639$	54.4744			2.15497
$640$	−1.00000			−0.0395285
$641$	−14.9665	+	25.9228i	−0.591142	+	1.02389i	0.402936	+	0.915228i	$0.367990\pi$
$641$	−14.9665	+	25.9228i	−0.591142	+	1.02389i	−0.994079	+	0.108661i	$0.965344\pi$
$642$	−30.8148	+	17.7910i	−1.21616	+	0.702153i
$643$		−	15.8086i		−	0.623431i	−0.950175	−	0.311716i	$-0.899096\pi$
$643$		−	15.8086i		−	0.623431i	0.950175	−	0.311716i	$-0.100904\pi$
$644$	10.0065	+	5.77727i	0.394312	+	0.227656i
$645$	2.36427	−	4.09503i	0.0930930	−	0.161242i
$646$	10.6351	+	6.14015i	0.418431	+	0.241581i
$647$	−9.27416	+	5.35444i	−0.364605	+	0.210505i	−0.671099	−	0.741368i	$-0.734177\pi$
$647$	−9.27416	+	5.35444i	−0.364605	+	0.210505i	0.306494	+	0.951873i	$0.400844\pi$
$648$	−0.365171	+	0.210831i	−0.0143453	+	0.00828224i
$649$	−31.5057	−	18.1898i	−1.23671	−	0.714013i
$650$	−1.47465	+	2.55417i	−0.0578406	+	0.100183i
$651$	30.2821	+	17.4834i	1.18685	+	0.685228i
$652$		−	1.12669i		−	0.0441246i
$653$	−19.5406	+	11.2818i	−0.764682	+	0.441489i	−0.830974	−	0.556311i	$-0.812216\pi$
$653$	−19.5406	+	11.2818i	−0.764682	+	0.441489i	0.0662922	+	0.997800i	$0.478883\pi$
$654$	−7.48389	+	12.9625i	−0.292643	+	0.506873i
$655$	−3.97020			−0.155129
$656$	−7.76440			−0.303149
$657$	−2.51270	+	4.35212i	−0.0980297	+	0.169792i
$658$		−	46.6829i		−	1.81989i
$659$	24.5615	+	42.5417i	0.956779	+	1.65719i	0.730243	+	0.683187i	$0.239407\pi$
$659$	24.5615	+	42.5417i	0.956779	+	1.65719i	0.226536	+	0.974003i	$0.427260\pi$
$660$			14.7390i			0.573714i
$661$	10.6409	−	6.14350i	0.413882	−	0.238955i	−0.278575	−	0.960415i	$-0.589862\pi$
$661$	10.6409	−	6.14350i	0.413882	−	0.238955i	0.692456	+	0.721460i	$0.256529\pi$
$662$	7.09688	+	12.2922i	0.275828	+	0.477749i
$663$	−10.4874	−	18.1647i	−0.407296	−	0.705458i
$664$	−14.2184	−	8.20899i	−0.551780	−	0.318571i
$665$	−19.1873			−0.744052
$666$	−23.4772	+	18.5241i	−0.909722	+	0.717795i
$667$	28.2907			1.09542
$668$	−9.17780	−	5.29881i	−0.355100	−	0.205017i
$669$	17.7707	+	30.7797i	0.687054	+	1.19001i
$670$	3.44554	+	5.96786i	0.133113	+	0.230558i
$671$	−45.9082	+	26.5051i	−1.77227	+	1.02322i
$672$			11.1118i			0.428646i
$673$	−8.94312	−	15.4899i	−0.344732	−	0.597093i	0.640573	−	0.767897i	$-0.278697\pi$
$673$	−8.94312	−	15.4899i	−0.344732	−	0.597093i	−0.985305	+	0.170804i	$0.945364\pi$
$674$		−	24.7316i		−	0.952626i
$675$	−2.69597	+	4.66956i	−0.103768	+	0.179731i
$676$	−4.30162			−0.165447
$677$	−39.4953			−1.51793			−0.758964	−	0.651133i	$-0.774294\pi$
$677$	−39.4953			−1.51793			−0.758964	+	0.651133i	$0.774294\pi$
$678$	12.1549	−	21.0528i	0.466804	−	0.808529i
$679$	16.9735	−	9.79966i	0.651384	−	0.376076i
$680$		−	2.52764i		−	0.0969305i
$681$	58.0560	+	33.5187i	2.22471	+	1.28444i
$682$	8.24227	−	14.2760i	0.315613	−	0.546657i
$683$	16.2450	+	9.37906i	0.621598	+	0.358880i	0.777491	−	0.628894i	$-0.216492\pi$
$683$	16.2450	+	9.37906i	0.621598	+	0.358880i	−0.155893	+	0.987774i	$0.549825\pi$
$684$	−20.6857	+	11.9429i	−0.790938	+	0.456648i
$685$	−17.9701	+	10.3751i	−0.686603	+	0.396411i
$686$	5.46198	+	3.15347i	0.208539	+	0.120400i
$687$	13.0052	−	22.5256i	0.496178	−	0.859406i
$688$	−1.45544	−	0.840298i	−0.0554881	−	0.0320361i
$689$			10.1705i			0.387465i
$690$	7.12896	−	4.11591i	0.271395	−	0.156690i
$691$	18.8718	−	32.6869i	0.717916	−	1.24347i	−0.243907	−	0.969799i	$-0.578429\pi$
$691$	18.8718	−	32.6869i	0.717916	−	1.24347i	0.961824	−	0.273669i	$-0.0882374\pi$
$692$	15.5084			0.589540
$693$	101.712			3.86370
$694$	−4.05680	+	7.02659i	−0.153994	+	0.266726i
$695$		−	18.1124i		−	0.687044i
$696$	13.6033	+	23.5616i	0.515632	+	0.893100i
$697$		−	19.6256i		−	0.743372i
$698$	20.7936	−	12.0052i	0.787048	−	0.454402i
$699$	−2.52789	−	4.37844i	−0.0956137	−	0.165608i
$700$	1.97465	+	3.42019i	0.0746348	+	0.129271i
$701$	−8.56876	−	4.94718i	−0.323638	−	0.186852i	0.329375	−	0.944199i	$-0.393162\pi$
$701$	−8.56876	−	4.94718i	−0.323638	−	0.186852i	−0.653013	+	0.757347i	$0.726495\pi$
$702$	15.9025			0.600200
$703$	−23.2003	+	18.3057i	−0.875017	+	0.690412i
$704$	5.23847			0.197432
$705$	−28.8026	−	16.6292i	−1.08477	−	0.626291i
$706$	−10.9067	−	18.8909i	−0.410479	−	0.710970i
$707$	−1.49187	−	2.58400i	−0.0561077	−	0.0971813i
$708$	−16.9219	+	9.76984i	−0.635963	+	0.367173i
$709$			8.15882i			0.306411i	0.988194	+	0.153206i	$0.0489597\pi$
$709$			8.15882i			0.306411i	−0.988194	+	0.153206i	$0.951040\pi$
$710$	−5.54009	−	9.59572i	−0.207916	−	0.360121i
$711$		−	40.1615i		−	1.50617i
$712$	1.23991	−	2.14759i	0.0464676	−	0.0804842i
$713$	−9.20671			−0.344794
$714$	−28.0866			−1.05111
$715$	7.72491	−	13.3799i	0.288895	−	0.500381i
$716$	−7.07419	+	4.08429i	−0.264375	+	0.152637i
$717$			2.74530i			0.102525i
$718$	12.6626	+	7.31078i	0.472565	+	0.272836i
$719$	−21.5544	+	37.3334i	−0.803845	+	1.39230i	0.113223	+	0.993570i	$0.463883\pi$
$719$	−21.5544	+	37.3334i	−0.803845	+	1.39230i	−0.917068	+	0.398731i	$0.869451\pi$
$720$	4.25771	+	2.45819i	0.158676	+	0.0916114i
$721$	56.5621	−	32.6561i	2.10648	−	1.21618i
$722$	−3.98730	+	2.30207i	−0.148392	+	0.0856742i
$723$	14.8851	+	8.59390i	0.553582	+	0.319611i
$724$	2.99877	−	5.19403i	0.111448	−	0.193034i
$725$	8.37416	+	4.83483i	0.311009	+	0.179561i
$726$		−	46.2601i		−	1.71687i
$727$	40.4823	−	23.3724i	1.50140	−	0.866836i	0.501406	−	0.865212i	$-0.332816\pi$
$727$	40.4823	−	23.3724i	1.50140	−	0.866836i	0.999999	−	0.00162370i	$-0.000516841\pi$
$728$	5.82384	−	10.0872i	0.215846	−	0.373856i
$729$	−43.4394			−1.60887
$730$	1.02217			0.0378323
$731$	2.12397	−	3.67882i	0.0785579	−	0.136066i
$732$			28.4720i			1.05236i
$733$	−4.55451	−	7.88864i	−0.168225	−	0.291373i	0.769571	−	0.638561i	$-0.220470\pi$
$733$	−4.55451	−	7.88864i	−0.168225	−	0.291373i	−0.937796	+	0.347188i	$0.887137\pi$
$734$			9.34420i			0.344901i
$735$	20.9479	−	12.0943i	0.772674	−	0.446103i
$736$	−1.46286	−	2.53375i	−0.0539217	−	0.0933951i
$737$	−18.0494	−	31.2624i	−0.664857	−	1.15157i
$738$	33.0586	+	19.0864i	1.21690	+	0.702579i
$739$	−22.5334			−0.828905			−0.414453	−	0.910071i	$-0.636027\pi$
$739$	−22.5334			−0.828905			−0.414453	+	0.910071i	$0.636027\pi$
$740$	5.65069	+	2.25161i	0.207723	+	0.0827708i
$741$	40.3159			1.48104
$742$	11.7944	+	6.80948i	0.432985	+	0.249984i
$743$	−4.07129	−	7.05169i	−0.149361	−	0.258701i	0.781630	−	0.623742i	$-0.214388\pi$
$743$	−4.07129	−	7.05169i	−0.149361	−	0.258701i	−0.930992	+	0.365041i	$0.881055\pi$
$744$	−4.42696	−	7.66772i	−0.162300	−	0.281112i
$745$	13.9633	−	8.06171i	0.511576	−	0.295358i
$746$		−	2.26740i		−	0.0830154i
$747$	40.3585	+	69.9030i	1.47664	+	2.55762i
$748$			13.2410i			0.484137i
$749$	24.9722	−	43.2530i	0.912463	−	1.58043i
$750$	2.81361			0.102738
$751$	−49.7026			−1.81367			−0.906837	−	0.421481i	$-0.861511\pi$
$751$	−49.7026			−1.81367			−0.906837	+	0.421481i	$0.861511\pi$
$752$	−5.91027	+	10.2369i	−0.215526	+	0.373301i
$753$	−28.8532	+	16.6584i	−1.05147	+	0.607066i
$754$		−	28.5187i		−	1.03859i
$755$	−4.62739	−	2.67163i	−0.168408	−	0.0972305i
$756$	10.6472	−	18.4415i	0.387235	−	0.670711i
$757$	9.10485	+	5.25669i	0.330921	+	0.191057i	0.656250	−	0.754543i	$-0.272142\pi$
$757$	9.10485	+	5.25669i	0.330921	+	0.191057i	−0.325329	+	0.945601i	$0.605475\pi$
$758$	−2.14096	+	1.23608i	−0.0777630	+	0.0448965i
$759$	−37.3449	+	21.5611i	−1.35553	+	0.782617i
$760$	4.20751	+	2.42920i	0.152622	+	0.0881165i
$761$	1.43338	−	2.48268i	0.0519598	−	0.0899971i	−0.838876	−	0.544323i	$-0.816787\pi$
$761$	1.43338	−	2.48268i	0.0519598	−	0.0899971i	0.890835	+	0.454326i	$0.150120\pi$
$762$	−19.7175	−	11.3839i	−0.714291	−	0.412396i
$763$		−	21.0094i		−	0.760593i
$764$	11.1272	−	6.42431i	0.402569	−	0.232423i
$765$	−6.21342	+	10.7620i	−0.224647	+	0.389099i
$766$	−35.0335			−1.26581
$767$	20.4820			0.739564
$768$	1.40680	−	2.43665i	0.0507636	−	0.0879252i
$769$			18.9984i			0.685099i	0.939500	+	0.342549i	$0.111290\pi$
$769$			18.9984i			0.685099i	−0.939500	+	0.342549i	$0.888710\pi$
$770$	−10.3441	−	17.9166i	−0.372777	−	0.645669i
$771$			40.0921i			1.44388i
$772$	11.1689	−	6.44839i	0.401979	−	0.232083i
$773$	−1.36501	−	2.36427i	−0.0490960	−	0.0850368i	0.840433	−	0.541915i	$-0.182301\pi$
$773$	−1.36501	−	2.36427i	−0.0490960	−	0.0850368i	−0.889529	+	0.456879i	$0.848967\pi$
$774$	4.13123	+	7.15550i	0.148494	+	0.257199i
$775$	−2.72523	−	1.57341i	−0.0978931	−	0.0565186i
$776$	−4.96273			−0.178152
$777$	25.0194	−	62.7892i	0.897565	−	2.25255i
$778$	−27.2150			−0.975704
$779$	32.6688	+	18.8613i	1.17048	+	0.675777i
$780$	−4.14909	−	7.18643i	−0.148561	−	0.257315i
$781$	29.0216	+	50.2669i	1.03847	+	1.79869i
$782$	6.40439	−	3.69758i	0.229021	−	0.132225i
$783$		−	52.1382i		−	1.86327i
$784$	−4.29849	−	7.44520i	−0.153517	−	0.265900i
$785$		−	14.1660i		−	0.505605i
$786$	5.58529	−	9.67401i	0.199221	−	0.345060i
$787$	1.07558			0.0383404			0.0191702	−	0.999816i	$-0.493898\pi$
$787$	1.07558			0.0383404			0.0191702	+	0.999816i	$0.493898\pi$
$788$	10.0774			0.358991
$789$	27.6640	−	47.9154i	0.984864	−	1.70584i
$790$	−7.07449	+	4.08446i	−0.251699	+	0.145318i
$791$			34.1222i			1.21324i
$792$	−22.3039	−	12.8772i	−0.792534	−	0.457570i
$793$	14.9226	−	25.8467i	0.529917	−	0.917842i
$794$	−2.03182	−	1.17307i	−0.0721066	−	0.0416308i
$795$	8.40267	−	4.85129i	0.298012	−	0.172057i
$796$	0.791387	−	0.456907i	0.0280500	−	0.0161947i
$797$	−10.9159	−	6.30233i	−0.386663	−	0.223240i	0.294050	−	0.955790i	$-0.404997\pi$
$797$	−10.9159	−	6.30233i	−0.386663	−	0.223240i	−0.680713	+	0.732550i	$0.738330\pi$
$798$	26.9928	−	46.7529i	0.955534	−	1.65503i
$799$	−25.8752	−	14.9390i	−0.915398	−	0.528505i
$800$		−	1.00000i		−	0.0353553i
$801$	−10.5584	+	6.09587i	−0.373061	+	0.215387i
$802$	−10.2527	+	17.7583i	−0.362037	+	0.627067i
$803$	−5.35463			−0.188961
$804$	−19.3888			−0.683791
$805$	−5.77727	+	10.0065i	−0.203622	+	0.352684i
$806$			9.28093i			0.326907i
$807$	0.740770	+	1.28305i	0.0260763	+	0.0451655i
$808$			0.755513i			0.0265788i
$809$	−7.43655	+	4.29349i	−0.261455	+	0.150951i	−0.624998	−	0.780626i	$-0.714900\pi$
$809$	−7.43655	+	4.29349i	−0.261455	+	0.150951i	0.363543	+	0.931577i	$0.381567\pi$
$810$	−0.210831	−	0.365171i	−0.00740786	−	0.0128308i
$811$	8.94230	+	15.4885i	0.314007	+	0.543876i	0.979226	−	0.202773i	$-0.0649952\pi$
$811$	8.94230	+	15.4885i	0.314007	+	0.543876i	−0.665219	+	0.746648i	$0.731662\pi$
$812$	−33.0721	−	19.0942i	−1.16060	−	0.670074i
$813$	25.5693			0.896753
$814$	−29.6009	−	11.7950i	−1.03751	−	0.413414i
$815$	1.12669			0.0394662
$816$	6.15898	+	3.55589i	0.215607	+	0.124481i
$817$	4.08251	+	7.07112i	0.142829	+	0.247387i
$818$	18.4614	+	31.9761i	0.645489	+	1.11802i
$819$	−49.5924	+	28.6322i	−1.73290	+	1.00049i
$820$		−	7.76440i		−	0.271145i
$821$	−12.4019	−	21.4808i	−0.432831	−	0.749685i	0.564285	−	0.825580i	$-0.309152\pi$
$821$	−12.4019	−	21.4808i	−0.432831	−	0.749685i	−0.997116	+	0.0758952i	$0.975819\pi$
$822$		−	58.3827i		−	2.03633i
$823$	−7.01240	+	12.1458i	−0.244437	+	0.423377i	−0.961973	−	0.273144i	$-0.911936\pi$
$823$	−7.01240	+	12.1458i	−0.244437	+	0.423377i	0.717536	+	0.696521i	$0.245270\pi$
$824$	−16.5377			−0.576117
$825$	−14.7390			−0.513146
$826$	13.7134	−	23.7523i	0.477150	−	0.826447i
$827$	−39.5761	+	22.8493i	−1.37620	+	0.794548i	−0.991699	−	0.128578i	$-0.958959\pi$
$827$	−39.5761	+	22.8493i	−1.37620	+	0.794548i	−0.384498	+	0.923126i	$0.625625\pi$
$828$			14.3839i			0.499877i
$829$	15.8025	+	9.12361i	0.548845	+	0.316876i	0.748656	−	0.662959i	$-0.230699\pi$
$829$	15.8025	+	9.12361i	0.548845	+	0.316876i	−0.199811	+	0.979834i	$0.564033\pi$
$830$	8.20899	−	14.2184i	0.284938	−	0.493527i
$831$	−74.6042	−	43.0728i	−2.58799	−	1.49418i
$832$	−2.55417	+	1.47465i	−0.0885499	+	0.0511243i
$833$	18.8188	−	10.8650i	0.652032	−	0.376451i
$834$	44.1338	+	25.4806i	1.52823	+	0.882322i
$835$	5.29881	−	9.17780i	0.183373	−	0.317611i
$836$	−22.0409	−	12.7253i	−0.762300	−	0.440114i
$837$			16.9675i			0.586482i
$838$	−8.19479	+	4.73126i	−0.283084	+	0.163439i
$839$	21.0651	−	36.4858i	0.727247	−	1.25963i	−0.230795	−	0.973002i	$-0.574133\pi$
$839$	21.0651	−	36.4858i	0.727247	−	1.25963i	0.958042	−	0.286627i	$-0.0925341\pi$
$840$	−11.1118			−0.383393
$841$	−64.5022			−2.22421
$842$	6.28160	−	10.8800i	0.216478	−	0.374951i
$843$		−	46.3760i		−	1.59727i
$844$	−2.73796	−	4.74229i	−0.0942445	−	0.163236i
$845$		−	4.30162i		−	0.147980i
$846$	50.3285	−	29.0572i	1.73033	−	0.999006i
$847$	32.4663	+	56.2334i	1.11556	+	1.93220i
$848$	−1.72422	−	2.98644i	−0.0592101	−	0.102555i
$849$	−69.8199	−	40.3105i	−2.39621	−	1.38345i
$850$	2.52764			0.0866973
$851$	2.56115	+	17.6112i	0.0877951	+	0.603704i
$852$	31.1753			1.06805
$853$	14.9470	+	8.62964i	0.511775	+	0.295473i	0.733563	−	0.679622i	$-0.237856\pi$
$853$	14.9470	+	8.62964i	0.511775	+	0.295473i	−0.221788	+	0.975095i	$0.571189\pi$
$854$	−19.9823	−	34.6103i	−0.683780	−	1.18434i
$855$	−11.9429	−	20.6857i	−0.408438	−	0.707436i
$856$	−10.9521	+	6.32318i	−0.374334	+	0.216122i
$857$		−	35.1582i		−	1.20098i	−0.799631	−	0.600491i	$-0.794972\pi$
$857$		−	35.1582i		−	1.20098i	0.799631	−	0.600491i	$-0.205028\pi$
$858$	21.7349	+	37.6459i	0.742016	+	1.28521i
$859$			12.8084i			0.437018i	0.975835	+	0.218509i	$0.0701193\pi$
$859$			12.8084i			0.437018i	−0.975835	+	0.218509i	$0.929881\pi$
$860$	0.840298	−	1.45544i	0.0286539	−	0.0496301i
$861$	−86.2763			−2.94029
$862$	−28.5972			−0.974025
$863$	7.35393	−	12.7374i	0.250331	−	0.433585i	−0.713286	−	0.700873i	$-0.752794\pi$
$863$	7.35393	−	12.7374i	0.250331	−	0.433585i	0.963617	+	0.267288i	$0.0861274\pi$
$864$	−4.66956	+	2.69597i	−0.158862	+	0.0917188i
$865$			15.5084i			0.527301i
$866$	8.87728	+	5.12530i	0.301662	+	0.174165i
$867$	14.9277	−	25.8555i	0.506970	−	0.878097i
$868$	10.7627	+	6.21388i	0.365311	+	0.210913i
$869$	37.0595	−	21.3963i	1.25716	−	0.725820i
$870$	−23.5616	+	13.6033i	−0.798813	+	0.461195i
$871$	17.6010	+	10.1619i	0.596387	+	0.344324i
$872$	−2.65989	+	4.60707i	−0.0900753	+	0.156015i
$873$	21.1299	+	12.1993i	0.715138	+	0.412885i
$874$			14.2143i			0.480807i
$875$	−3.42019	+	1.97465i	−0.115624	+	0.0667554i
$876$	−1.43800	+	2.49068i	−0.0485854	+	0.0841524i
$877$	32.7004			1.10422			0.552108	−	0.833773i	$-0.313824\pi$
$877$	32.7004			1.10422			0.552108	+	0.833773i	$0.313824\pi$
$878$	11.0043			0.371376
$879$	29.6474	−	51.3508i	0.999981	−	1.73202i
$880$			5.23847i			0.176589i
$881$	14.8534	+	25.7268i	0.500423	+	0.866759i	1.00000		0.000488989i	$0.000155650\pi$
$881$	14.8534	+	25.7268i	0.500423	+	0.866759i	−0.499576	+	0.866270i	$0.666511\pi$
$882$			42.2660i			1.42317i
$883$	−26.6656	+	15.3954i	−0.897368	+	0.518096i	−0.876345	−	0.481683i	$-0.840026\pi$
$883$	−26.6656	+	15.3954i	−0.897368	+	0.518096i	−0.0210227	+	0.999779i	$0.506692\pi$
$884$	−3.72738	−	6.45602i	−0.125365	−	0.217139i
$885$	−9.76984	−	16.9219i	−0.328410	−	0.568822i
$886$	−3.02977	−	1.74924i	−0.101787	−	0.0587669i
$887$	1.18778			0.0398817			0.0199409	−	0.999801i	$-0.493652\pi$
$887$	1.18778			0.0398817			0.0199409	+	0.999801i	$0.493652\pi$
$888$	−13.4358	+	10.6012i	−0.450876	+	0.355753i
$889$	31.9579			1.07184
$890$	2.14759	+	1.23991i	0.0719872	+	0.0415619i
$891$	1.10443	+	1.91294i	0.0369999	+	0.0640858i
$892$	6.31598	+	10.9396i	0.211475	+	0.366285i
$893$	49.7350	−	28.7145i	1.66432	−	0.960895i
$894$			45.3650i			1.51723i
$895$	−4.08429	−	7.07419i	−0.136523	−	0.236464i
$896$			3.94930i			0.131937i
$897$	12.1391	−	21.0255i	0.405311	−	0.702020i
$898$	−15.8076			−0.527508
$899$	30.4287			1.01485
$900$	−2.45819	+	4.25771i	−0.0819397	+	0.141924i
$901$	7.54864	−	4.35821i	0.251482	−	0.145193i
$902$			40.6736i			1.35428i
$903$	−16.1725	−	9.33721i	−0.538188	−	0.310723i
$904$	4.32003	−	7.48250i	0.143682	−	0.248864i
$905$	5.19403	+	2.99877i	0.172655	+	0.0996825i
$906$	13.0197	−	7.51691i	0.432549	−	0.249733i
$907$	23.3777	−	13.4971i	0.776244	−	0.448165i	−0.0588537	−	0.998267i	$-0.518745\pi$
$907$	23.3777	−	13.4971i	0.776244	−	0.448165i	0.835097	+	0.550102i	$0.185411\pi$
$908$	20.6340	+	11.9131i	0.684764	+	0.395349i
$909$	1.85719	−	3.21675i	0.0615992	−	0.106693i
$910$	10.0872	+	5.82384i	0.334387	+	0.193058i
$911$			28.3992i			0.940908i	0.882425	+	0.470454i	$0.155910\pi$
$911$			28.3992i			0.940908i	−0.882425	+	0.470454i	$0.844090\pi$
$912$	−11.8383	+	6.83483i	−0.392004	+	0.226324i
$913$	−43.0025	+	74.4826i	−1.42318	+	2.46501i
$914$	−27.4876			−0.909209
$915$	−28.4720			−0.941256
$916$	4.62224	−	8.00596i	0.152723	−	0.264524i
$917$			15.6795i			0.517783i
$918$	−6.81444	−	11.8030i	−0.224910	−	0.389556i
$919$		−	33.2492i		−	1.09679i	−0.836219	−	0.548395i	$-0.815239\pi$
$919$		−	33.2492i		−	1.09679i	0.836219	−	0.548395i	$-0.184761\pi$
$920$	2.53375	−	1.46286i	0.0835351	−	0.0482290i
$921$	6.70629	+	11.6156i	0.220980	+	0.382748i
$922$	10.3757	+	17.9712i	0.341705	+	0.591850i
$923$	−28.3007	−	16.3394i	−0.931528	−	0.537818i
$924$	58.2087			1.91493
$925$	−2.25161	+	5.65069i	−0.0740325	+	0.185793i
$926$	−14.5129			−0.476922
$927$	70.4127	+	40.6528i	2.31265	+	1.33521i
$928$	4.83483	+	8.37416i	0.158711	+	0.274895i
$929$	20.2744	+	35.1164i	0.665183	+	1.15213i	0.979236	+	0.202725i	$0.0649797\pi$
$929$	20.2744	+	35.1164i	0.665183	+	1.15213i	−0.314053	+	0.949405i	$0.601687\pi$
$930$	7.66772	−	4.42696i	0.251434	−	0.145166i
$931$			41.7676i			1.36888i
$932$	−0.898453	−	1.55617i	−0.0294298	−	0.0509739i
$933$		−	51.8769i		−	1.69838i
$934$	0.598950	−	1.03741i	0.0195982	−	0.0339451i
$935$	−13.2410			−0.433026
$936$	14.4999			0.473944
$937$	21.3445	−	36.9697i	0.697294	−	1.20775i	−0.272107	−	0.962267i	$-0.587721\pi$
$937$	21.3445	−	36.9697i	0.697294	−	1.20775i	0.969401	−	0.245482i	$-0.0789461\pi$
$938$	23.5689	−	13.6075i	0.769551	−	0.444300i
$939$		−	48.5398i		−	1.58404i
$940$	−10.2369	−	5.91027i	−0.333891	−	0.192772i
$941$	13.5253	−	23.4265i	0.440912	−	0.763682i	−0.556845	−	0.830616i	$-0.687988\pi$
$941$	13.5253	−	23.4265i	0.440912	−	0.763682i	0.997757	+	0.0669343i	$0.0213218\pi$
$942$	34.5175	+	19.9287i	1.12464	+	0.649313i
$943$	19.6730	−	11.3582i	0.640641	−	0.369874i
$944$	−6.01430	+	3.47236i	−0.195749	+	0.113016i
$945$	18.4415	+	10.6472i	0.599902	+	0.346354i
$946$	−4.40188	+	7.62428i	−0.143117	+	0.247887i
$947$	−7.62016	−	4.39950i	−0.247622	−	0.142965i	0.371053	−	0.928612i	$-0.378997\pi$
$947$	−7.62016	−	4.39950i	−0.247622	−	0.142965i	−0.618675	+	0.785647i	$0.712330\pi$
$948$		−	22.9841i		−	0.746489i
$949$	2.61080	−	1.50735i	0.0847503	−	0.0489306i
$950$	−2.42920	+	4.20751i	−0.0788138	+	0.136510i
$951$	−91.8824			−2.97949
$952$	−9.98240			−0.323532
$953$	−13.9400	+	24.1447i	−0.451559	+	0.782124i	−0.998483	−	0.0550587i	$-0.982465\pi$
$953$	−13.9400	+	24.1447i	−0.451559	+	0.782124i	0.546924	+	0.837182i	$0.315799\pi$
$954$			16.9539i			0.548902i
$955$	6.42431	+	11.1272i	0.207886	+	0.360069i
$956$			0.975723i			0.0315571i
$957$	123.427	−	71.2605i	3.98982	−	2.30352i
$958$	−6.93504	−	12.0118i	−0.224061	−	0.388085i
$959$	40.9742	+	70.9695i	1.32313	+	2.29172i
$960$	2.43665	+	1.40680i	0.0786427	+	0.0454044i
$961$	21.0975			0.680565
$962$	17.7531	−	2.58180i	0.572384	−	0.0832404i
$963$	62.1744			2.00354
$964$	5.29039	+	3.05441i	0.170392	+	0.0983758i
$965$	6.44839	+	11.1689i	0.207581	+	0.359541i
$966$	−16.2550	−	28.1544i	−0.522995	−	0.905854i
$967$	−23.6814	+	13.6724i	−0.761541	+	0.439676i	−0.829849	−	0.557988i	$-0.811573\pi$
$967$	−23.6814	+	13.6724i	−0.761541	+	0.439676i	0.0683075	+	0.997664i	$0.478240\pi$
$968$		−	16.4416i		−	0.528452i
$969$	−17.2760	−	29.9229i	−0.554984	−	0.961260i
$970$		−	4.96273i		−	0.159344i
$971$	−13.2341	+	22.9221i	−0.424702	+	0.735606i	−0.996393	−	0.0848636i	$-0.972955\pi$
$971$	−13.2341	+	22.9221i	−0.424702	+	0.735606i	0.571690	+	0.820469i	$0.306288\pi$
$972$	−14.9894			−0.480786
$973$	−71.5315			−2.29319
$974$	−17.6733	+	30.6110i	−0.566288	+	0.980840i
$975$	7.18643	−	4.14909i	0.230150	−	0.132877i
$976$			10.1194i			0.323914i
$977$	−22.2269	−	12.8327i	−0.711101	−	0.410554i	0.100367	−	0.994950i	$-0.467998\pi$
$977$	−22.2269	−	12.8327i	−0.711101	−	0.410554i	−0.811469	+	0.584396i	$0.801332\pi$
$978$	−1.58503	+	2.74536i	−0.0506837	+	0.0877868i
$979$	−11.2501	−	6.49523i	−0.359554	−	0.207588i
$980$	7.44520	−	4.29849i	0.237828	−	0.137310i
$981$	22.6501	−	13.0770i	0.723162	−	0.417518i
$982$	1.82831	+	1.05558i	0.0583438	+	0.0336848i
$983$	−7.32713	+	12.6910i	−0.233699	+	0.404779i	−0.958894	−	0.283765i	$-0.908416\pi$
$983$	−7.32713	+	12.6910i	−0.233699	+	0.404779i	0.725195	+	0.688544i	$0.241750\pi$
$984$	18.9192	+	10.9230i	0.603121	+	0.348212i
$985$			10.0774i			0.321092i
$986$	−21.1669	+	12.2207i	−0.674090	+	0.389186i
$987$	−65.6737	+	113.750i	−2.09042	+	3.62071i
$988$	14.3289			0.455863
$989$	4.91695			0.156350
$990$	12.8772	−	22.3039i	0.409263	−	0.708864i
$991$			53.0936i			1.68657i	0.537463	+	0.843287i	$0.319383\pi$
$991$			53.0936i			1.68657i	−0.537463	+	0.843287i	$0.680617\pi$
$992$	−1.57341	−	2.72523i	−0.0499559	−	0.0865261i
$993$		−	39.9357i		−	1.26732i
$994$	−37.8964	+	21.8795i	−1.20200	+	0.693975i
$995$	0.456907	+	0.791387i	0.0144849	+	0.0250887i
$996$	23.0969	+	40.0049i	0.731852	+	1.26761i
$997$	10.2660	+	5.92705i	0.325126	+	0.187712i	0.653675	−	0.756775i	$-0.273226\pi$
$997$	10.2660	+	5.92705i	0.325126	+	0.187712i	−0.328549	+	0.944487i	$0.606560\pi$
$998$	−6.49573			−0.205619
$999$	32.4565	−	4.72007i	1.02688	−	0.149336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.c.101.3	yes	12
37.11	even	6	inner	370.2.l.c.11.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.c.11.3	✓	12	37.11	even	6	inner
370.2.l.c.101.3	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -2.81361i q^{6} +(1.97465 + 3.42019i) q^{7} -1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.40680 + 2.43665i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -2.81361i q^{6} +(1.97465 + 3.42019i) q^{7} -1.00000i q^{8} +(-2.45819 + 4.25771i) q^{9} +1.00000 q^{10} -5.23847 q^{11} +(-1.40680 + 2.43665i) q^{12} +(2.55417 - 1.47465i) q^{13} -3.94930i q^{14} +(-2.43665 - 1.40680i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.18900 - 1.26382i) q^{17} +(4.25771 - 2.45819i) q^{18} +(4.20751 - 2.42920i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-5.55589 + 9.62308i) q^{21} +(4.53665 + 2.61923i) q^{22} -2.92572i q^{23} +(2.43665 - 1.40680i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.94930 q^{26} -5.39194 q^{27} +(-1.97465 + 3.42019i) q^{28} +9.66965i q^{29} +(1.40680 + 2.43665i) q^{30} -3.14682i q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.36950 - 12.7643i) q^{33} +(1.26382 + 2.18900i) q^{34} +(-3.42019 - 1.97465i) q^{35} -4.91638 q^{36} +(-6.01944 + 0.875392i) q^{37} -4.85841 q^{38} +(7.18643 + 4.14909i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.88220 + 6.72417i) q^{41} +(9.62308 - 5.55589i) q^{42} +1.68060i q^{43} +(-2.61923 - 4.53665i) q^{44} -4.91638i q^{45} +(-1.46286 + 2.53375i) q^{46} +11.8205 q^{47} -2.81361 q^{48} +(-4.29849 + 7.44520i) q^{49} +(-0.866025 + 0.500000i) q^{50} -7.11178i q^{51} +(2.55417 + 1.47465i) q^{52} +(-1.72422 + 2.98644i) q^{53} +(4.66956 + 2.69597i) q^{54} +(4.53665 - 2.61923i) q^{55} +(3.42019 - 1.97465i) q^{56} +(11.8383 + 6.83483i) q^{57} +(4.83483 - 8.37416i) q^{58} +(6.01430 + 3.47236i) q^{59} -2.81361i q^{60} +(8.76366 - 5.05970i) q^{61} +(-1.57341 + 2.72523i) q^{62} -19.4163 q^{63} -1.00000 q^{64} +(-1.47465 + 2.55417i) q^{65} +14.7390i q^{66} +(3.44554 + 5.96786i) q^{67} -2.52764i q^{68} +(7.12896 - 4.11591i) q^{69} +(1.97465 + 3.42019i) q^{70} +(-5.54009 - 9.59572i) q^{71} +(4.25771 + 2.45819i) q^{72} +1.02217 q^{73} +(5.65069 + 2.25161i) q^{74} +2.81361 q^{75} +(4.20751 + 2.42920i) q^{76} +(-10.3441 - 17.9166i) q^{77} +(-4.14909 - 7.18643i) q^{78} +(-7.07449 + 4.08446i) q^{79} -1.00000i q^{80} +(-0.210831 - 0.365171i) q^{81} -7.76440i q^{82} +(8.20899 - 14.2184i) q^{83} -11.1118 q^{84} +2.52764 q^{85} +(0.840298 - 1.45544i) q^{86} +(-23.5616 + 13.6033i) q^{87} +5.23847i q^{88} +(2.14759 + 1.23991i) q^{89} +(-2.45819 + 4.25771i) q^{90} +(10.0872 + 5.82384i) q^{91} +(2.53375 - 1.46286i) q^{92} +(7.66772 - 4.42696i) q^{93} +(-10.2369 - 5.91027i) q^{94} +(-2.42920 + 4.20751i) q^{95} +(2.43665 + 1.40680i) q^{96} -4.96273i q^{97} +(7.44520 - 4.29849i) q^{98} +(12.8772 - 22.3039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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