LMFDB - Embedded newform 370.2.l.c.101.5

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			101.5
Root			$-1.07078 - 0.923815i$ of defining polynomial
Character	$\chi$	$=$	370.101
Dual form			370.2.l.c.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.529317i q^{6} +(1.80085 + 3.11916i) q^{7} +1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.529317i q^{6} +(1.80085 + 3.11916i) q^{7} +1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +1.00000 q^{10} -1.82324 q^{11} +(-0.264658 + 0.458402i) q^{12} +(-2.25314 + 1.30085i) q^{13} +3.60170i q^{14} +(0.458402 + 0.264658i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.42532 - 1.97761i) q^{17} +(2.35544 - 1.35991i) q^{18} +(6.48293 - 3.74292i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.953220 + 1.65102i) q^{21} +(-1.57897 - 0.911621i) q^{22} +6.10635i q^{23} +(-0.458402 + 0.264658i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.60170 q^{26} +3.02760 q^{27} +(-1.80085 + 3.11916i) q^{28} +7.96238i q^{29} +(0.264658 + 0.458402i) q^{30} -3.44189i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.482536 - 0.835777i) q^{33} +(-1.97761 - 3.42532i) q^{34} +(3.11916 + 1.80085i) q^{35} +2.71982 q^{36} +(-4.20419 - 4.39600i) q^{37} +7.48585 q^{38} +(-1.19262 - 0.688561i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.37841 - 9.31569i) q^{41} +(-1.65102 + 0.953220i) q^{42} -6.69206i q^{43} +(-0.911621 - 1.57897i) q^{44} -2.71982i q^{45} +(-3.05318 + 5.28826i) q^{46} -0.773560 q^{47} -0.529317 q^{48} +(-2.98612 + 5.17211i) q^{49} +(0.866025 - 0.500000i) q^{50} -2.09356i q^{51} +(-2.25314 - 1.30085i) q^{52} +(0.605365 - 1.04852i) q^{53} +(2.62198 + 1.51380i) q^{54} +(-1.57897 + 0.911621i) q^{55} +(-3.11916 + 1.80085i) q^{56} +(3.43152 + 1.98119i) q^{57} +(-3.98119 + 6.89563i) q^{58} +(-9.93254 - 5.73455i) q^{59} +0.529317i q^{60} +(-2.69140 + 1.55388i) q^{61} +(1.72094 - 2.98076i) q^{62} +9.79599 q^{63} -1.00000 q^{64} +(-1.30085 + 2.25314i) q^{65} -0.965073i q^{66} +(-2.92001 - 5.05761i) q^{67} -3.95521i q^{68} +(-2.79916 + 1.61610i) q^{69} +(1.80085 + 3.11916i) q^{70} +(-4.05440 - 7.02243i) q^{71} +(2.35544 + 1.35991i) q^{72} +11.9368 q^{73} +(-1.44293 - 5.90914i) q^{74} +0.529317 q^{75} +(6.48293 + 3.74292i) q^{76} +(-3.28339 - 5.68699i) q^{77} +(-0.688561 - 1.19262i) q^{78} +(12.0735 - 6.97065i) q^{79} +1.00000i q^{80} +(-3.27846 - 5.67845i) q^{81} -10.7568i q^{82} +(-2.08557 + 3.61231i) q^{83} -1.90644 q^{84} -3.95521 q^{85} +(3.34603 - 5.79550i) q^{86} +(-3.64997 + 2.10731i) q^{87} -1.82324i q^{88} +(15.4549 + 8.92289i) q^{89} +(1.35991 - 2.35544i) q^{90} +(-8.11513 - 4.68527i) q^{91} +(-5.28826 + 3.05318i) q^{92} +(1.57777 - 0.910924i) q^{93} +(-0.669923 - 0.386780i) q^{94} +(3.74292 - 6.48293i) q^{95} +(-0.458402 - 0.264658i) q^{96} +10.2216i q^{97} +(-5.17211 + 2.98612i) q^{98} +(-2.47945 + 4.29453i) 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
$3$	0.264658	+	0.458402i	0.152801	+	0.264658i	0.932256	−	0.361799i	$-0.117837\pi$
$3$	0.264658	+	0.458402i	0.152801	+	0.264658i	−0.779455	+	0.626458i	$0.784504\pi$
$4$	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
$6$			0.529317i			0.216093i
$7$	1.80085	+	3.11916i	0.680657	+	1.17893i	0.974781	+	0.223165i	$0.0716390\pi$
$7$	1.80085	+	3.11916i	0.680657	+	1.17893i	−0.294123	+	0.955767i	$0.595028\pi$
$8$			1.00000i			0.353553i
$9$	1.35991	−	2.35544i	0.453304	−	0.785146i
$10$	1.00000			0.316228
$11$	−1.82324			−0.549728			−0.274864	−	0.961483i	$-0.588633\pi$
$11$	−1.82324			−0.549728			−0.274864	+	0.961483i	$0.588633\pi$
$12$	−0.264658	+	0.458402i	−0.0764003	+	0.132329i
$13$	−2.25314	+	1.30085i	−0.624908	+	0.360791i	−0.778777	−	0.627300i	$-0.784160\pi$
$13$	−2.25314	+	1.30085i	−0.624908	+	0.360791i	0.153869	+	0.988091i	$0.450827\pi$
$14$			3.60170i			0.962595i
$15$	0.458402	+	0.264658i	0.118359	+	0.0683345i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.42532	−	1.97761i	−0.830761	−	0.479640i	0.0233520	−	0.999727i	$-0.492566\pi$
$17$	−3.42532	−	1.97761i	−0.830761	−	0.479640i	−0.854113	+	0.520087i	$0.825899\pi$
$18$	2.35544	−	1.35991i	0.555182	−	0.320534i
$19$	6.48293	−	3.74292i	1.48729	−	0.858685i	0.487392	−	0.873183i	$-0.337948\pi$
$19$	6.48293	−	3.74292i	1.48729	−	0.858685i	0.999895	+	0.0144978i	$0.00461495\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−0.953220	+	1.65102i	−0.208010	+	0.360283i
$22$	−1.57897	−	0.911621i	−0.336638	−	0.194358i
$23$			6.10635i			1.27326i	0.771168	+	0.636632i	$0.219673\pi$
$23$			6.10635i			1.27326i	−0.771168	+	0.636632i	$0.780327\pi$
$24$	−0.458402	+	0.264658i	−0.0935708	+	0.0540231i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.60170			−0.510235
$27$	3.02760			0.582661
$28$	−1.80085	+	3.11916i	−0.340329	+	0.589466i
$29$			7.96238i			1.47858i	0.673389	+	0.739289i	$0.264838\pi$
$29$			7.96238i			1.47858i	−0.673389	+	0.739289i	$0.735162\pi$
$30$	0.264658	+	0.458402i	0.0483198	+	0.0836923i
$31$		−	3.44189i		−	0.618181i	−0.951033	−	0.309091i	$-0.899975\pi$
$31$		−	3.44189i		−	0.618181i	0.951033	−	0.309091i	$-0.100025\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.482536	−	0.835777i	−0.0839988	−	0.145490i
$34$	−1.97761	−	3.42532i	−0.339157	−	0.587437i
$35$	3.11916	+	1.80085i	0.527235	+	0.304399i
$36$	2.71982			0.453304
$37$	−4.20419	−	4.39600i	−0.691164	−	0.722698i
$37$	−4.20419	−	4.39600i	−0.691164	−	0.722698i
$38$	7.48585			1.21436
$39$	−1.19262	−	0.688561i	−0.190973	−	0.110258i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.37841	−	9.31569i	−0.839967	−	1.45487i	−0.889921	−	0.456114i	$-0.849241\pi$
$41$	−5.37841	−	9.31569i	−0.839967	−	1.45487i	0.0499538	−	0.998752i	$-0.484093\pi$
$42$	−1.65102	+	0.953220i	−0.254759	+	0.147085i
$43$		−	6.69206i		−	1.02053i	−0.860017	−	0.510265i	$-0.829547\pi$
$43$		−	6.69206i		−	1.02053i	0.860017	−	0.510265i	$-0.170453\pi$
$44$	−0.911621	−	1.57897i	−0.137432	−	0.238039i
$45$		−	2.71982i		−	0.405447i
$46$	−3.05318	+	5.28826i	−0.450166	+	0.779711i
$47$	−0.773560			−0.112835			−0.0564177	−	0.998407i	$-0.517968\pi$
$47$	−0.773560			−0.112835			−0.0564177	+	0.998407i	$0.517968\pi$
$48$	−0.529317			−0.0764003
$49$	−2.98612	+	5.17211i	−0.426589	+	0.738873i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	2.09356i		−	0.293157i
$52$	−2.25314	−	1.30085i	−0.312454	−	0.180395i
$53$	0.605365	−	1.04852i	0.0831532	−	0.144026i	−0.821450	−	0.570281i	$-0.806834\pi$
$53$	0.605365	−	1.04852i	0.0831532	−	0.144026i	0.904603	+	0.426256i	$0.140168\pi$
$54$	2.62198	+	1.51380i	0.356806	+	0.206002i
$55$	−1.57897	+	0.911621i	−0.212909	+	0.122923i
$56$	−3.11916	+	1.80085i	−0.416816	+	0.240649i
$57$	3.43152	+	1.98119i	0.454516	+	0.262415i
$58$	−3.98119	+	6.89563i	−0.522756	+	0.905440i
$59$	−9.93254	−	5.73455i	−1.29311	−	0.746575i	−0.313903	−	0.949455i	$-0.601637\pi$
$59$	−9.93254	−	5.73455i	−1.29311	−	0.746575i	−0.979204	+	0.202880i	$0.934970\pi$
$60$			0.529317i			0.0683345i
$61$	−2.69140	+	1.55388i	−0.344598	+	0.198954i	−0.662304	−	0.749236i	$-0.730421\pi$
$61$	−2.69140	+	1.55388i	−0.344598	+	0.198954i	0.317705	+	0.948190i	$0.397088\pi$
$62$	1.72094	−	2.98076i	0.218560	−	0.378557i
$63$	9.79599			1.23418
$64$	−1.00000			−0.125000
$65$	−1.30085	+	2.25314i	−0.161351	+	0.279467i
$66$		−	0.965073i		−	0.118792i
$67$	−2.92001	−	5.05761i	−0.356736	−	0.617886i	0.630677	−	0.776045i	$-0.282777\pi$
$67$	−2.92001	−	5.05761i	−0.356736	−	0.617886i	−0.987414	+	0.158160i	$0.949444\pi$
$68$		−	3.95521i		−	0.479640i
$69$	−2.79916	+	1.61610i	−0.336980	+	0.194555i
$70$	1.80085	+	3.11916i	0.215243	+	0.372811i
$71$	−4.05440	−	7.02243i	−0.481169	−	0.833409i	0.518598	−	0.855018i	$-0.326454\pi$
$71$	−4.05440	−	7.02243i	−0.481169	−	0.833409i	−0.999766	+	0.0216095i	$0.993121\pi$
$72$	2.35544	+	1.35991i	0.277591	+	0.160267i
$73$	11.9368			1.39709			0.698546	−	0.715565i	$-0.253831\pi$
$73$	11.9368			1.39709			0.698546	+	0.715565i	$0.253831\pi$
$74$	−1.44293	−	5.90914i	−0.167738	−	0.686924i
$75$	0.529317			0.0611202
$76$	6.48293	+	3.74292i	0.743643	+	0.429343i
$77$	−3.28339	−	5.68699i	−0.374177	−	0.648093i
$78$	−0.688561	−	1.19262i	−0.0779642	−	0.135038i
$79$	12.0735	−	6.97065i	1.35838	−	0.784260i	0.368972	−	0.929440i	$-0.379710\pi$
$79$	12.0735	−	6.97065i	1.35838	−	0.784260i	0.989405	+	0.145181i	$0.0463764\pi$
$80$			1.00000i			0.111803i
$81$	−3.27846	−	5.67845i	−0.364273	−	0.630939i
$82$		−	10.7568i		−	1.18789i
$83$	−2.08557	+	3.61231i	−0.228921	+	0.396502i	−0.957488	−	0.288472i	$-0.906853\pi$
$83$	−2.08557	+	3.61231i	−0.228921	+	0.396502i	0.728568	+	0.684974i	$0.240186\pi$
$84$	−1.90644			−0.208010
$85$	−3.95521			−0.429003
$86$	3.34603	−	5.79550i	0.360812	−	0.624945i
$87$	−3.64997	+	2.10731i	−0.391318	+	0.225927i
$88$		−	1.82324i		−	0.194358i
$89$	15.4549	+	8.92289i	1.63822	+	0.945825i	0.981447	+	0.191733i	$0.0614107\pi$
$89$	15.4549	+	8.92289i	1.63822	+	0.945825i	0.656769	+	0.754092i	$0.271923\pi$
$90$	1.35991	−	2.35544i	0.143347	−	0.248285i
$91$	−8.11513	−	4.68527i	−0.850696	−	0.491150i
$92$	−5.28826	+	3.05318i	−0.551339	+	0.318316i
$93$	1.57777	−	0.910924i	0.163607	−	0.0944584i
$94$	−0.669923	−	0.386780i	−0.0690972	−	0.0398933i
$95$	3.74292	−	6.48293i	0.384016	−	0.665135i
$96$	−0.458402	−	0.264658i	−0.0467854	−	0.0270116i
$97$			10.2216i			1.03785i	0.854821	+	0.518923i	$0.173667\pi$
$97$			10.2216i			1.03785i	−0.854821	+	0.518923i	$0.826333\pi$
$98$	−5.17211	+	2.98612i	−0.522462	+	0.301644i
$99$	−2.47945	+	4.29453i	−0.249194	+	0.431617i
$100$	1.00000			0.100000
$101$	−13.8037			−1.37352			−0.686760	−	0.726884i	$-0.740968\pi$
$101$	−13.8037			−1.37352			−0.686760	+	0.726884i	$0.740968\pi$
$102$	1.04678	−	1.81308i	0.103647	−	0.179521i
$103$			10.7623i			1.06045i	0.847858	+	0.530223i	$0.177892\pi$
$103$			10.7623i			1.06045i	−0.847858	+	0.530223i	$0.822108\pi$
$104$	−1.30085	−	2.25314i	−0.127559	−	0.220938i
$105$			1.90644i			0.186049i
$106$	1.04852	−	0.605365i	0.101841	−	0.0587982i
$107$	2.45517	+	4.25247i	0.237350	+	0.411102i	0.959953	−	0.280161i	$-0.0903879\pi$
$107$	2.45517	+	4.25247i	0.237350	+	0.411102i	−0.722603	+	0.691263i	$0.757055\pi$
$108$	1.51380	+	2.62198i	0.145665	+	0.252300i
$109$	−3.97600	−	2.29555i	−0.380832	−	0.219874i	0.297348	−	0.954769i	$-0.403898\pi$
$109$	−3.97600	−	2.29555i	−0.380832	−	0.219874i	−0.678180	+	0.734896i	$0.737231\pi$
$110$	−1.82324			−0.173839
$111$	0.902460	−	3.09064i	0.0856578	−	0.293351i
$112$	−3.60170			−0.340329
$113$	−3.61065	−	2.08461i	−0.339661	−	0.196104i	0.320461	−	0.947262i	$-0.396162\pi$
$113$	−3.61065	−	2.08461i	−0.339661	−	0.196104i	−0.660122	+	0.751158i	$0.729496\pi$
$114$	1.98119	+	3.43152i	0.185556	+	0.321392i
$115$	3.05318	+	5.28826i	0.284710	+	0.493133i
$116$	−6.89563	+	3.98119i	−0.640243	+	0.369644i
$117$			7.07617i			0.654192i
$118$	−5.73455	−	9.93254i	−0.527909	−	0.914364i
$119$		−	14.2455i		−	1.30588i
$120$	−0.264658	+	0.458402i	−0.0241599	+	0.0418461i
$121$	−7.67579			−0.697799
$122$	−3.10776			−0.281363
$123$	2.84688	−	4.93095i	0.256695	−	0.444609i
$124$	2.98076	−	1.72094i	0.267680	−	0.154545i
$125$		−	1.00000i		−	0.0894427i
$126$	8.48358	+	4.89799i	0.755777	+	0.436348i
$127$	−5.23545	+	9.06806i	−0.464571	+	0.804661i	−0.999182	−	0.0404376i	$-0.987125\pi$
$127$	−5.23545	+	9.06806i	−0.464571	+	0.804661i	0.534611	+	0.845098i	$0.320458\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.06765	−	1.77111i	0.270092	−	0.155938i
$130$	−2.25314	+	1.30085i	−0.197613	+	0.114092i
$131$	7.91382	+	4.56904i	0.691433	+	0.399199i	0.804149	−	0.594428i	$-0.202622\pi$
$131$	7.91382	+	4.56904i	0.691433	+	0.399199i	−0.112715	+	0.993627i	$0.535955\pi$
$132$	0.482536	−	0.835777i	0.0419994	−	0.0727451i
$133$	23.3496	+	13.4809i	2.02467	+	1.16894i
$134$		−	5.84003i		−	0.504501i
$135$	2.62198	−	1.51380i	0.225664	−	0.130287i
$136$	1.97761	−	3.42532i	0.169578	−	0.293718i
$137$	−1.54920			−0.132357			−0.0661785	−	0.997808i	$-0.521081\pi$
$137$	−1.54920			−0.132357			−0.0661785	+	0.997808i	$0.521081\pi$
$138$	−3.23219			−0.275143
$139$	3.45544	−	5.98499i	0.293086	−	0.507640i	−0.681452	−	0.731863i	$-0.738651\pi$
$139$	3.45544	−	5.98499i	0.293086	−	0.507640i	0.974538	+	0.224223i	$0.0719844\pi$
$140$			3.60170i			0.304399i
$141$	−0.204729	−	0.354601i	−0.0172413	−	0.0298628i
$142$		−	8.10880i		−	0.680476i
$143$	4.10802	−	2.37176i	0.343530	−	0.198337i
$144$	1.35991	+	2.35544i	0.113326	+	0.196286i
$145$	3.98119	+	6.89563i	0.330620	+	0.572651i
$146$	10.3375	+	5.96838i	0.855541	+	0.493947i
$147$	−3.16121			−0.260732
$148$	1.70495	−	5.83893i	0.140146	−	0.479957i
$149$	−19.4523			−1.59359			−0.796796	−	0.604248i	$-0.793473\pi$
$149$	−19.4523			−1.59359			−0.796796	+	0.604248i	$0.793473\pi$
$150$	0.458402	+	0.264658i	0.0374283	+	0.0216093i
$151$	0.873178	+	1.51239i	0.0710582	+	0.123076i	0.899365	−	0.437198i	$-0.144029\pi$
$151$	0.873178	+	1.51239i	0.0710582	+	0.123076i	−0.828307	+	0.560274i	$0.810696\pi$
$152$	3.74292	+	6.48293i	0.303591	+	0.525835i
$153$	−9.31626	+	5.37874i	−0.753175	+	0.434846i
$154$		−	6.56677i		−	0.529166i
$155$	−1.72094	−	2.98076i	−0.138230	−	0.239421i
$156$		−	1.37712i		−	0.110258i
$157$	−5.71307	+	9.89533i	−0.455953	+	0.789734i	−0.998742	−	0.0501351i	$-0.984035\pi$
$157$	−5.71307	+	9.89533i	−0.455953	+	0.789734i	0.542790	+	0.839869i	$0.317368\pi$
$158$	13.9413			1.10911
$159$	0.640859			0.0508234
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−19.0467	+	10.9966i	−1.50109	+	0.866656i
$162$		−	6.55691i		−	0.515160i
$163$	5.99013	+	3.45840i	0.469183	+	0.270883i	0.715898	−	0.698205i	$-0.246018\pi$
$163$	5.99013	+	3.45840i	0.469183	+	0.270883i	−0.246715	+	0.969088i	$0.579351\pi$
$164$	5.37841	−	9.31569i	0.419984	−	0.727433i
$165$	−0.835777	−	0.482536i	−0.0650652	−	0.0375654i
$166$	−3.61231	+	2.08557i	−0.280369	+	0.161871i
$167$	16.6192	−	9.59512i	1.28603	−	0.742493i	0.308090	−	0.951357i	$-0.400310\pi$
$167$	16.6192	−	9.59512i	1.28603	−	0.742493i	0.977945	+	0.208865i	$0.0669768\pi$
$168$	−1.65102	−	0.953220i	−0.127379	−	0.0735425i
$169$	−3.11558	+	5.39634i	−0.239660	+	0.415103i
$170$	−3.42532	−	1.97761i	−0.262710	−	0.151676i
$171$		−	20.3602i		−	1.55698i
$172$	5.79550	−	3.34603i	0.441903	−	0.255133i
$173$	7.50943	−	13.0067i	0.570931	−	0.988882i	−0.425539	−	0.904940i	$-0.639916\pi$
$173$	7.50943	−	13.0067i	0.570931	−	0.988882i	0.996471	−	0.0839420i	$-0.0267510\pi$
$174$	−4.21462			−0.319510
$175$	3.60170			0.272263
$176$	0.911621	−	1.57897i	0.0687160	−	0.119020i
$177$		−	6.07079i		−	0.456308i
$178$	8.92289	+	15.4549i	0.668799	+	1.15839i
$179$			23.2075i			1.73461i	0.497777	+	0.867305i	$0.334150\pi$
$179$			23.2075i			1.73461i	−0.497777	+	0.867305i	$0.665850\pi$
$180$	2.35544	−	1.35991i	0.175564	−	0.101362i
$181$	2.00037	+	3.46475i	0.148687	+	0.257533i	0.930742	−	0.365676i	$-0.119162\pi$
$181$	2.00037	+	3.46475i	0.148687	+	0.257533i	−0.782056	+	0.623209i	$0.785829\pi$
$182$	−4.68527	−	8.11513i	−0.347295	−	0.601533i
$183$	−1.42460	−	0.822495i	−0.105310	−	0.0608005i
$184$	−6.10635			−0.450166
$185$	−5.83893	−	1.70495i	−0.429287	−	0.125351i
$186$	1.82185			0.133584
$187$	6.24518	+	3.60566i	0.456693	+	0.263672i
$188$	−0.386780	−	0.669923i	−0.0282088	−	0.0488591i
$189$	5.45225	+	9.44357i	0.396593	+	0.686919i
$190$	6.48293	−	3.74292i	0.470321	−	0.271540i
$191$			21.5767i			1.56123i	0.625010	+	0.780616i	$0.285095\pi$
$191$			21.5767i			1.56123i	−0.625010	+	0.780616i	$0.714905\pi$
$192$	−0.264658	−	0.458402i	−0.0191001	−	0.0330823i
$193$			13.4206i			0.966039i	0.875610	+	0.483020i	$0.160460\pi$
$193$			13.4206i			0.966039i	−0.875610	+	0.483020i	$0.839540\pi$
$194$	−5.11079	+	8.85216i	−0.366934	+	0.635548i
$195$	−1.37712			−0.0986178
$196$	−5.97224			−0.426589
$197$	4.73638	−	8.20365i	0.337453	−	0.584486i	−0.646500	−	0.762914i	$-0.723768\pi$
$197$	4.73638	−	8.20365i	0.337453	−	0.584486i	0.983953	+	0.178428i	$0.0571012\pi$
$198$	−4.29453	+	2.47945i	−0.305199	+	0.176207i
$199$			11.7612i			0.833726i	0.908969	+	0.416863i	$0.136871\pi$
$199$			11.7612i			0.833726i	−0.908969	+	0.416863i	$0.863129\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	1.54561	−	2.67708i	0.109019	−	0.188826i
$202$	−11.9544	−	6.90185i	−0.841106	−	0.485613i
$203$	−24.8360	+	14.3391i	−1.74314	+	1.00640i
$204$	1.81308	−	1.04678i	0.126941	−	0.0732893i
$205$	−9.31569	−	5.37841i	−0.650636	−	0.375645i
$206$	−5.38117	+	9.32046i	−0.374924	+	0.649388i
$207$	14.3831	+	8.30411i	0.999697	+	0.577175i
$208$		−	2.60170i		−	0.180395i
$209$	−11.8200	+	6.82426i	−0.817604	+	0.472044i
$210$	−0.953220	+	1.65102i	−0.0657784	+	0.113932i
$211$	7.67248			0.528195			0.264098	−	0.964496i	$-0.414926\pi$
$211$	7.67248			0.528195			0.264098	+	0.964496i	$0.414926\pi$
$212$	1.21073			0.0831532
$213$	2.14606	−	3.71709i	0.147046	−	0.254691i
$214$			4.91033i			0.335663i
$215$	−3.34603	−	5.79550i	−0.228198	−	0.395250i
$216$			3.02760i			0.206002i
$217$	10.7358	−	6.19832i	0.728794	−	0.420770i
$218$	−2.29555	−	3.97600i	−0.155474	−	0.269289i
$219$	3.15916	+	5.47183i	0.213477	+	0.369752i
$220$	−1.57897	−	0.911621i	−0.106454	−	0.0614615i
$221$	10.2903			0.692199
$222$	2.32688	−	2.22535i	0.156170	−	0.149355i
$223$	23.7522			1.59057			0.795283	−	0.606238i	$-0.207322\pi$
$223$	23.7522			1.59057			0.795283	+	0.606238i	$0.207322\pi$
$224$	−3.11916	−	1.80085i	−0.208408	−	0.120324i
$225$	−1.35991	−	2.35544i	−0.0906608	−	0.157029i
$226$	−2.08461	−	3.61065i	−0.138666	−	0.240177i
$227$	−6.03559	+	3.48465i	−0.400596	+	0.231284i	−0.686741	−	0.726902i	$-0.740959\pi$
$227$	−6.03559	+	3.48465i	−0.400596	+	0.231284i	0.286145	+	0.958186i	$0.407626\pi$
$228$			3.96238i			0.262415i
$229$	1.90185	+	3.29411i	0.125678	+	0.217681i	0.921998	−	0.387195i	$-0.126556\pi$
$229$	1.90185	+	3.29411i	0.125678	+	0.217681i	−0.796320	+	0.604876i	$0.793223\pi$
$230$			6.10635i			0.402641i
$231$	1.73795	−	3.01022i	0.114349	−	0.198058i
$232$	−7.96238			−0.522756
$233$	−22.4990			−1.47396			−0.736980	−	0.675914i	$-0.763749\pi$
$233$	−22.4990			−1.47396			−0.736980	+	0.675914i	$0.763749\pi$
$234$	−3.53808	+	6.12814i	−0.231292	+	0.400609i
$235$	−0.669923	+	0.386780i	−0.0437009	+	0.0252307i
$236$		−	11.4691i		−	0.746575i
$237$	6.39072	+	3.68968i	0.415122	+	0.239671i
$238$	7.12275	−	12.3370i	0.461699	−	0.799686i
$239$	−1.90418	−	1.09938i	−0.123171	−	0.0711131i	0.437148	−	0.899389i	$-0.355988\pi$
$239$	−1.90418	−	1.09938i	−0.123171	−	0.0711131i	−0.560320	+	0.828276i	$0.689322\pi$
$240$	−0.458402	+	0.264658i	−0.0295897	+	0.0170836i
$241$	22.2682	−	12.8565i	1.43442	−	0.828163i	0.436966	−	0.899478i	$-0.356053\pi$
$241$	22.2682	−	12.8565i	1.43442	−	0.828163i	0.997454	+	0.0713151i	$0.0227196\pi$
$242$	−6.64743	−	3.83789i	−0.427313	−	0.246709i
$243$	6.27674	−	10.8716i	0.402653	−	0.697415i
$244$	−2.69140	−	1.55388i	−0.172299	−	0.0994770i
$245$			5.97224i			0.381552i
$246$	4.93095	−	2.84688i	0.314386	−	0.181511i
$247$	−9.73796	+	16.8666i	−0.619612	+	1.07320i
$248$	3.44189			0.218560
$249$	−2.20785			−0.139917
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$		−	8.74327i		−	0.551870i	−0.961176	−	0.275935i	$-0.911013\pi$
$251$		−	8.74327i		−	0.551870i	0.961176	−	0.275935i	$-0.0889875\pi$
$252$	4.89799	+	8.48358i	0.308545	+	0.534415i
$253$		−	11.1334i		−	0.699949i
$254$	−9.06806	+	5.23545i	−0.568981	+	0.328501i
$255$	−1.04678	−	1.81308i	−0.0655519	−	0.113539i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.9581	+	6.90403i	0.745927	+	0.430661i	0.824220	−	0.566269i	$-0.191614\pi$
$257$	11.9581	+	6.90403i	0.745927	+	0.430661i	−0.0782932	+	0.996930i	$0.524947\pi$
$258$	3.54222			0.220529
$259$	6.14073	−	21.0301i	0.381567	−	1.30675i
$260$	−2.60170			−0.161351
$261$	18.7549	+	10.8281i	1.16090	+	0.670245i
$262$	4.56904	+	7.91382i	0.282276	+	0.488917i
$263$	8.36374	+	14.4864i	0.515730	+	0.893271i	0.999833	+	0.0182600i	$0.00581267\pi$
$263$	8.36374	+	14.4864i	0.515730	+	0.893271i	−0.484103	+	0.875011i	$0.660854\pi$
$264$	0.835777	−	0.482536i	0.0514385	−	0.0296981i
$265$		−	1.21073i		−	0.0743745i
$266$	13.4809	+	23.3496i	0.826566	+	1.43165i
$267$			9.44607i			0.578090i
$268$	2.92001	−	5.05761i	0.178368	−	0.308943i
$269$	−3.36208			−0.204989			−0.102495	−	0.994734i	$-0.532682\pi$
$269$	−3.36208			−0.204989			−0.102495	+	0.994734i	$0.532682\pi$
$270$	3.02760			0.184254
$271$	−5.97016	+	10.3406i	−0.362661	+	0.628148i	−0.988398	−	0.151887i	$-0.951465\pi$
$271$	−5.97016	+	10.3406i	−0.362661	+	0.628148i	0.625737	+	0.780034i	$0.284798\pi$
$272$	3.42532	−	1.97761i	0.207690	−	0.119910i
$273$		−	4.95998i		−	0.300192i
$274$	−1.34165	−	0.774599i	−0.0810518	−	0.0467953i
$275$	−0.911621	+	1.57897i	−0.0549728	+	0.0952157i
$276$	−2.79916	−	1.61610i	−0.168490	−	0.0972776i
$277$	2.81358	−	1.62442i	0.169052	−	0.0976020i	−0.413087	−	0.910692i	$-0.635549\pi$
$277$	2.81358	−	1.62442i	0.169052	−	0.0976020i	0.582139	+	0.813090i	$0.302216\pi$
$278$	5.98499	−	3.45544i	0.358956	−	0.207243i
$279$	−8.10715	−	4.68066i	−0.485362	−	0.280224i
$280$	−1.80085	+	3.11916i	−0.107621	+	0.186406i
$281$	−3.26660	−	1.88597i	−0.194869	−	0.112508i	0.399391	−	0.916781i	$-0.369222\pi$
$281$	−3.26660	−	1.88597i	−0.194869	−	0.112508i	−0.594260	+	0.804273i	$0.702555\pi$
$282$		−	0.409458i		−	0.0243829i
$283$	−4.63206	+	2.67432i	−0.275347	+	0.158972i	−0.631315	−	0.775526i	$-0.717485\pi$
$283$	−4.63206	+	2.67432i	−0.275347	+	0.158972i	0.355968	+	0.934498i	$0.384151\pi$
$284$	4.05440	−	7.02243i	0.240584	−	0.416704i
$285$	3.96238			0.234711
$286$	4.74353			0.280491
$287$	19.3714	−	33.5523i	1.14346	−	1.98053i
$288$			2.71982i			0.160267i
$289$	−0.678139	−	1.17457i	−0.0398905	−	0.0690924i
$290$			7.96238i			0.467567i
$291$	−4.68559	+	2.70523i	−0.274674	+	0.158583i
$292$	5.96838	+	10.3375i	0.349273	+	0.604959i
$293$	−3.84767	−	6.66436i	−0.224783	−	0.389336i	0.731471	−	0.681872i	$-0.238834\pi$
$293$	−3.84767	−	6.66436i	−0.224783	−	0.389336i	−0.956254	+	0.292536i	$0.905501\pi$
$294$	−2.73768	−	1.58060i	−0.159665	−	0.0921826i
$295$	−11.4691			−0.667757
$296$	4.39600	−	4.20419i	0.255512	−	0.244363i
$297$	−5.52004			−0.320305
$298$	−16.8462	−	9.72613i	−0.975872	−	0.563420i
$299$	−7.94345	−	13.7585i	−0.459382	−	0.795672i
$300$	0.264658	+	0.458402i	0.0152801	+	0.0264658i
$301$	20.8736	−	12.0514i	1.20314	−	0.694631i
$302$			1.74636i			0.100491i
$303$	−3.65326	−	6.32764i	−0.209875	−	0.363513i
$304$			7.48585i			0.429343i
$305$	−1.55388	+	2.69140i	−0.0889749	+	0.154109i
$306$	−10.7575			−0.614965
$307$	2.63342			0.150297			0.0751486	−	0.997172i	$-0.476057\pi$
$307$	2.63342			0.150297			0.0751486	+	0.997172i	$0.476057\pi$
$308$	3.28339	−	5.68699i	0.187088	−	0.324046i
$309$	−4.93348	+	2.84834i	−0.280656	+	0.162037i
$310$		−	3.44189i		−	0.195486i
$311$	−11.9202	−	6.88210i	−0.675930	−	0.390248i	0.122390	−	0.992482i	$-0.460944\pi$
$311$	−11.9202	−	6.88210i	−0.675930	−	0.390248i	−0.798320	+	0.602234i	$0.794277\pi$
$312$	0.688561	−	1.19262i	0.0389821	−	0.0675190i
$313$	−19.4375	−	11.2222i	−1.09867	−	0.634318i	−0.162800	−	0.986659i	$-0.552053\pi$
$313$	−19.4375	−	11.2222i	−1.09867	−	0.634318i	−0.935872	+	0.352341i	$0.885386\pi$
$314$	−9.89533	+	5.71307i	−0.558426	+	0.322407i
$315$	8.48358	−	4.89799i	0.477995	−	0.275971i
$316$	12.0735	+	6.97065i	0.679189	+	0.392130i
$317$	−15.5652	+	26.9596i	−0.874226	+	1.51420i	−0.0166418	+	0.999862i	$0.505297\pi$
$317$	−15.5652	+	26.9596i	−0.874226	+	1.51420i	−0.857585	+	0.514343i	$0.828036\pi$
$318$	0.555000	+	0.320430i	0.0311229	+	0.0179688i
$319$		−	14.5174i		−	0.812816i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	−1.29956	+	2.25090i	−0.0725344	+	0.125633i
$322$	−21.9933			−1.22564
$323$	−29.6081			−1.64744
$324$	3.27846	−	5.67845i	0.182137	−	0.315470i
$325$			2.60170i			0.144316i
$326$	3.45840	+	5.99013i	0.191543	+	0.331762i
$327$		−	2.43014i		−	0.134387i
$328$	9.31569	−	5.37841i	0.514373	−	0.296973i
$329$	−1.39307	−	2.41286i	−0.0768022	−	0.133025i
$330$	−0.482536	−	0.835777i	−0.0265627	−	0.0460080i
$331$	−7.69367	−	4.44194i	−0.422882	−	0.244151i	0.273427	−	0.961893i	$-0.411843\pi$
$331$	−7.69367	−	4.44194i	−0.422882	−	0.244151i	−0.696310	+	0.717741i	$0.745176\pi$
$332$	−4.17113			−0.228921
$333$	−16.0718	+	3.92452i	−0.880730	+	0.215063i
$334$	19.1902			1.05004
$335$	−5.05761	−	2.92001i	−0.276327	−	0.159537i
$336$	−0.953220	−	1.65102i	−0.0520024	−	0.0900708i
$337$	0.679720	+	1.17731i	0.0370267	+	0.0641322i	0.883945	−	0.467591i	$-0.154878\pi$
$337$	0.679720	+	1.17731i	0.0370267	+	0.0641322i	−0.846918	+	0.531723i	$0.821545\pi$
$338$	−5.39634	+	3.11558i	−0.293522	+	0.169465i
$339$		−	2.20684i		−	0.119859i
$340$	−1.97761	−	3.42532i	−0.107251	−	0.185764i
$341$			6.27540i			0.339832i
$342$	10.1801	−	17.6324i	0.550476	−	0.953453i
$343$	3.70168			0.199872
$344$	6.69206			0.360812
$345$	−1.61610	+	2.79916i	−0.0870078	+	0.150702i
$346$	13.0067	−	7.50943i	0.699245	−	0.403709i
$347$		−	2.31081i		−	0.124051i	−0.998075	−	0.0620253i	$-0.980244\pi$
$347$		−	2.31081i		−	0.124051i	0.998075	−	0.0620253i	$-0.0197560\pi$
$348$	−3.64997	−	2.10731i	−0.195659	−	0.112964i
$349$	−4.20057	+	7.27561i	−0.224852	+	0.389454i	−0.956275	−	0.292469i	$-0.905523\pi$
$349$	−4.20057	+	7.27561i	−0.224852	+	0.389454i	0.731423	+	0.681924i	$0.238856\pi$
$350$	3.11916	+	1.80085i	0.166726	+	0.0962595i
$351$	−6.82160	+	3.93845i	−0.364110	+	0.210219i
$352$	1.57897	−	0.911621i	0.0841596	−	0.0485896i
$353$	−1.43354	−	0.827653i	−0.0762995	−	0.0440515i	0.461365	−	0.887210i	$-0.347360\pi$
$353$	−1.43354	−	0.827653i	−0.0762995	−	0.0440515i	−0.537664	+	0.843159i	$0.680693\pi$
$354$	3.03539	−	5.25746i	0.161329	−	0.279431i
$355$	−7.02243	−	4.05440i	−0.372712	−	0.215185i
$356$			17.8458i			0.945825i
$357$	6.53016	−	3.77019i	0.345613	−	0.199540i
$358$	−11.6038	+	20.0983i	−0.613277	+	1.06223i
$359$	30.2373			1.59587			0.797933	−	0.602746i	$-0.205927\pi$
$359$	30.2373			1.59587			0.797933	+	0.602746i	$0.205927\pi$
$360$	2.71982			0.143347
$361$	18.5189	−	32.0758i	0.974682	−	1.68820i
$362$			4.00075i			0.210275i
$363$	−2.03146	−	3.51859i	−0.106624	−	0.184678i
$364$		−	9.37054i		−	0.491150i
$365$	10.3375	−	5.96838i	0.541092	−	0.312399i
$366$	−0.822495	−	1.42460i	−0.0429925	−	0.0744652i
$367$	−4.54463	−	7.87153i	−0.237228	−	0.410890i	0.722690	−	0.691172i	$-0.242905\pi$
$367$	−4.54463	−	7.87153i	−0.237228	−	0.410890i	−0.959918	+	0.280282i	$0.909572\pi$
$368$	−5.28826	−	3.05318i	−0.275670	−	0.159158i
$369$	−29.2567			−1.52304
$370$	−4.20419	−	4.39600i	−0.218565	−	0.228537i
$371$	4.36068			0.226395
$372$	1.57777	+	0.910924i	0.0818034	+	0.0472292i
$373$	−16.7256	−	28.9696i	−0.866020	−	1.49999i	−0.866031	−	0.499991i	$-0.833337\pi$
$373$	−16.7256	−	28.9696i	−0.866020	−	1.49999i	1.06354e−5	−	1.00000i	$-0.499997\pi$
$374$	3.60566	+	6.24518i	0.186444	+	0.322931i
$375$	0.458402	−	0.264658i	0.0236718	−	0.0136669i
$376$		−	0.773560i		−	0.0398933i
$377$	−10.3579	−	17.9403i	−0.533457	−	0.923975i
$378$			10.9045i			0.560867i
$379$	−8.65724	+	14.9948i	−0.444692	+	0.770230i	−0.998031	−	0.0627267i	$-0.980020\pi$
$379$	−8.65724	+	14.9948i	−0.444692	+	0.770230i	0.553338	+	0.832957i	$0.313354\pi$
$380$	7.48585			0.384016
$381$	−5.54242			−0.283947
$382$	−10.7883	+	18.6859i	−0.551979	+	0.956056i
$383$	10.2792	−	5.93471i	0.525244	−	0.303250i	−0.213834	−	0.976870i	$-0.568595\pi$
$383$	10.2792	−	5.93471i	0.525244	−	0.303250i	0.739077	+	0.673620i	$0.235262\pi$
$384$		−	0.529317i		−	0.0270116i
$385$	−5.68699	−	3.28339i	−0.289836	−	0.167337i
$386$	−6.71032	+	11.6226i	−0.341546	+	0.591576i
$387$	−15.7627	−	9.10062i	−0.801265	−	0.462610i
$388$	−8.85216	+	5.11079i	−0.449400	+	0.259461i
$389$	18.2160	−	10.5170i	0.923588	−	0.533234i	0.0388098	−	0.999247i	$-0.487643\pi$
$389$	18.2160	−	10.5170i	0.923588	−	0.533234i	0.884778	+	0.466013i	$0.154310\pi$
$390$	−1.19262	−	0.688561i	−0.0603908	−	0.0348667i
$391$	12.0760	−	20.9162i	0.610708	−	1.05778i
$392$	−5.17211	−	2.98612i	−0.261231	−	0.150822i
$393$			4.83694i			0.243991i
$394$	8.20365	−	4.73638i	0.413294	−	0.238615i
$395$	6.97065	−	12.0735i	0.350732	−	0.607485i
$396$	−4.95890			−0.249194
$397$	−4.08839			−0.205190			−0.102595	−	0.994723i	$-0.532715\pi$
$397$	−4.08839			−0.205190			−0.102595	+	0.994723i	$0.532715\pi$
$398$	−5.88058	+	10.1855i	−0.294767	+	0.510551i
$399$			14.2713i			0.714459i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			0.375392i			0.0187462i	0.999956	+	0.00937309i	$0.00298359\pi$
$401$			0.375392i			0.0187462i	−0.999956	+	0.00937309i	$0.997016\pi$
$402$	2.67708	−	1.54561i	0.133520	−	0.0770881i
$403$	4.47738	+	7.75505i	0.223034	+	0.386306i
$404$	−6.90185	−	11.9544i	−0.343380	−	0.594752i
$405$	−5.67845	−	3.27846i	−0.282165	−	0.162908i
$406$	−28.6781			−1.42327
$407$	7.66525	+	8.01497i	0.379952	+	0.397288i
$408$	2.09356			0.103647
$409$	26.8345	+	15.4929i	1.32688	+	0.766075i	0.984816	−	0.173602i	$-0.0555406\pi$
$409$	26.8345	+	15.4929i	1.32688	+	0.766075i	0.342064	+	0.939677i	$0.388874\pi$
$410$	−5.37841	−	9.31569i	−0.265621	−	0.460069i
$411$	−0.410008	−	0.710155i	−0.0202242	−	0.0350294i
$412$	−9.32046	+	5.38117i	−0.459186	+	0.265111i
$413$		−	41.3083i		−	2.03265i
$414$	8.30411	+	14.3831i	0.408125	+	0.706892i
$415$			4.17113i			0.204753i
$416$	1.30085	−	2.25314i	0.0637794	−	0.110469i
$417$	3.65804			0.179135
$418$	−13.6485			−0.667571
$419$	9.93508	−	17.2081i	0.485361	−	0.840669i	−0.514498	−	0.857492i	$-0.672022\pi$
$419$	9.93508	−	17.2081i	0.485361	−	0.840669i	0.999858	+	0.0168224i	$0.00535498\pi$
$420$	−1.65102	+	0.953220i	−0.0805618	+	0.0465124i
$421$			7.80166i			0.380230i	0.981762	+	0.190115i	$0.0608860\pi$
$421$			7.80166i			0.380230i	−0.981762	+	0.190115i	$0.939114\pi$
$422$	6.64456	+	3.83624i	0.323452	+	0.186745i
$423$	−1.05197	+	1.82207i	−0.0511487	+	0.0885922i
$424$	1.04852	+	0.605365i	0.0509207	+	0.0293991i
$425$	−3.42532	+	1.97761i	−0.166152	+	0.0959280i
$426$	3.71709	−	2.14606i	0.180094	−	0.103977i
$427$	−9.69361	−	5.59661i	−0.469107	−	0.270839i
$428$	−2.45517	+	4.25247i	−0.118675	+	0.205551i
$429$	2.17444	+	1.25541i	0.104983	+	0.0606120i
$430$		−	6.69206i		−	0.322720i
$431$	−20.3080	+	11.7248i	−0.978201	+	0.564765i	−0.901727	−	0.432307i	$-0.857700\pi$
$431$	−20.3080	+	11.7248i	−0.978201	+	0.564765i	−0.0764745	+	0.997072i	$0.524366\pi$
$432$	−1.51380	+	2.62198i	−0.0728327	+	0.126150i
$433$	−17.0424			−0.819008			−0.409504	−	0.912308i	$-0.634298\pi$
$433$	−17.0424			−0.819008			−0.409504	+	0.912308i	$0.634298\pi$
$434$	12.3966			0.595058
$435$	−2.10731	+	3.64997i	−0.101038	+	0.175003i
$436$		−	4.59109i		−	0.219874i
$437$	22.8556	+	39.5871i	1.09333	+	1.89371i
$438$			6.31833i			0.301901i
$439$	33.9642	−	19.6093i	1.62102	−	0.935899i	0.634378	−	0.773023i	$-0.281256\pi$
$439$	33.9642	−	19.6093i	1.62102	−	0.935899i	0.986647	−	0.162876i	$-0.0520769\pi$
$440$	−0.911621	−	1.57897i	−0.0434598	−	0.0752747i
$441$	8.12172	+	14.0672i	0.386749	+	0.669868i
$442$	8.91164	+	5.14514i	0.423884	+	0.244729i
$443$	−30.1536			−1.43264			−0.716321	−	0.697771i	$-0.754175\pi$
$443$	−30.1536			−1.43264			−0.716321	+	0.697771i	$0.754175\pi$
$444$	3.12781	−	0.763768i	0.148439	−	0.0362468i
$445$	17.8458			0.845971
$446$	20.5700	+	11.8761i	0.974019	+	0.562350i
$447$	−5.14820	−	8.91695i	−0.243502	−	0.421757i
$448$	−1.80085	−	3.11916i	−0.0850822	−	0.147367i
$449$	−12.3358	+	7.12208i	−0.582163	+	0.336112i	−0.761992	−	0.647586i	$-0.775779\pi$
$449$	−12.3358	+	7.12208i	−0.582163	+	0.336112i	0.179830	+	0.983698i	$0.442445\pi$
$450$		−	2.71982i		−	0.128214i
$451$	9.80615	+	16.9848i	0.461754	+	0.799781i
$452$		−	4.16922i		−	0.196104i
$453$	−0.462188	+	0.800532i	−0.0217155	+	0.0376123i
$454$	−6.96930			−0.327086
$455$	−9.37054			−0.439298
$456$	−1.98119	+	3.43152i	−0.0927778	+	0.160696i
$457$	−7.84680	+	4.53035i	−0.367058	+	0.211921i	−0.672172	−	0.740395i	$-0.734639\pi$
$457$	−7.84680	+	4.53035i	−0.367058	+	0.211921i	0.305114	+	0.952316i	$0.401305\pi$
$458$			3.80370i			0.177735i
$459$	−10.3705	−	5.98740i	−0.484053	−	0.279468i
$460$	−3.05318	+	5.28826i	−0.142355	+	0.246566i
$461$	−15.1541	−	8.74921i	−0.705795	−	0.407491i	0.103707	−	0.994608i	$-0.466930\pi$
$461$	−15.1541	−	8.74921i	−0.705795	−	0.407491i	−0.809502	+	0.587117i	$0.800263\pi$
$462$	3.01022	−	1.73795i	0.140048	−	0.0808568i
$463$	−27.2002	+	15.7040i	−1.26410	+	0.729828i	−0.973865	−	0.227127i	$-0.927067\pi$
$463$	−27.2002	+	15.7040i	−1.26410	+	0.729828i	−0.290234	+	0.956956i	$0.593733\pi$
$464$	−6.89563	−	3.98119i	−0.320121	−	0.184822i
$465$	0.910924	−	1.57777i	0.0422431	−	0.0731672i
$466$	−19.4847	−	11.2495i	−0.902613	−	0.521124i
$467$		−	40.0301i		−	1.85237i	−0.377066	−	0.926186i	$-0.623067\pi$
$467$		−	40.0301i		−	1.85237i	0.377066	−	0.926186i	$-0.376933\pi$
$468$	−6.12814	+	3.53808i	−0.283273	+	0.163548i
$469$	10.5170	−	18.2160i	0.485630	−	0.841137i
$470$	−0.773560			−0.0356817
$471$	−6.04805			−0.278679
$472$	5.73455	−	9.93254i	0.263954	−	0.457182i
$473$			12.2013i			0.561014i
$474$	3.68968	+	6.39072i	0.169473	+	0.293535i
$475$		−	7.48585i		−	0.343474i
$476$	12.3370	−	7.12275i	0.565464	−	0.326471i
$477$	−1.64649	−	2.85180i	−0.0753874	−	0.130575i
$478$	−1.09938	−	1.90418i	−0.0502845	−	0.0870954i
$479$	11.9653	+	6.90818i	0.546709	+	0.315643i	0.747794	−	0.663931i	$-0.231113\pi$
$479$	11.9653	+	6.90818i	0.546709	+	0.315643i	−0.201084	+	0.979574i	$0.564447\pi$
$480$	−0.529317			−0.0241599
$481$	15.1911	+	4.43578i	0.692657	+	0.202254i
$482$	25.7131			1.17120
$483$	−10.0817	−	5.82070i	−0.458735	−	0.264851i
$484$	−3.83789	−	6.64743i	−0.174450	−	0.302156i
$485$	5.11079	+	8.85216i	0.232069	+	0.401956i
$486$	10.8716	−	6.27674i	0.493147	−	0.284719i
$487$			34.0763i			1.54414i	0.635535	+	0.772072i	$0.280779\pi$
$487$			34.0763i			1.54414i	−0.635535	+	0.772072i	$0.719221\pi$
$488$	−1.55388	−	2.69140i	−0.0703409	−	0.121834i
$489$			3.66118i			0.165564i
$490$	−2.98612	+	5.17211i	−0.134899	+	0.233652i
$491$	−5.20978			−0.235114			−0.117557	−	0.993066i	$-0.537506\pi$
$491$	−5.20978			−0.235114			−0.117557	+	0.993066i	$0.537506\pi$
$492$	5.69377			0.256695
$493$	15.7465	−	27.2737i	0.709185	−	1.22834i
$494$	−16.8666	+	9.73796i	−0.758866	+	0.438132i
$495$			4.95890i			0.222886i
$496$	2.98076	+	1.72094i	0.133840	+	0.0772727i
$497$	14.6027	−	25.2927i	0.655022	−	1.13453i
$498$	−1.91205	−	1.10392i	−0.0856812	−	0.0494680i
$499$	0.829455	−	0.478886i	0.0371315	−	0.0214379i	−0.481319	−	0.876545i	$-0.659842\pi$
$499$	0.829455	−	0.478886i	0.0371315	−	0.0214379i	0.518451	+	0.855107i	$0.326509\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	8.79683	+	5.07885i	0.393014	+	0.226907i
$502$	4.37163	−	7.57189i	0.195116	−	0.337950i
$503$	−11.1020	−	6.40975i	−0.495014	−	0.285797i	0.231638	−	0.972802i	$-0.425592\pi$
$503$	−11.1020	−	6.40975i	−0.495014	−	0.285797i	−0.726652	+	0.687005i	$0.758925\pi$
$504$			9.79599i			0.436348i
$505$	−11.9544	+	6.90185i	−0.531962	+	0.307128i
$506$	5.56668	−	9.64178i	0.247469	−	0.428629i
$507$	−3.29826			−0.146481
$508$	−10.4709			−0.464571
$509$	6.60643	−	11.4427i	0.292825	−	0.507188i	−0.681652	−	0.731677i	$-0.738738\pi$
$509$	6.60643	−	11.4427i	0.292825	−	0.507188i	0.974477	+	0.224489i	$0.0720713\pi$
$510$		−	2.09356i		−	0.0927044i
$511$	21.4963	+	37.2327i	0.950941	+	1.64708i
$512$		−	1.00000i		−	0.0441942i
$513$	19.6277	−	11.3321i	0.866585	−	0.500323i
$514$	6.90403	+	11.9581i	0.304524	+	0.527450i
$515$	5.38117	+	9.32046i	0.237123	+	0.410709i
$516$	3.06765	+	1.77111i	0.135046	+	0.0779688i
$517$	1.41039			0.0620288
$518$	15.8331	−	15.1422i	0.695665	−	0.665311i
$519$	7.94973			0.348954
$520$	−2.25314	−	1.30085i	−0.0988066	−	0.0570460i
$521$	15.9741	+	27.6680i	0.699838	+	1.21216i	0.968522	+	0.248927i	$0.0800780\pi$
$521$	15.9741	+	27.6680i	0.699838	+	1.21216i	−0.268684	+	0.963228i	$0.586589\pi$
$522$	10.8281	+	18.7549i	0.473935	+	0.820879i
$523$	0.402244	−	0.232235i	0.0175889	−	0.0101549i	−0.491180	−	0.871058i	$-0.663434\pi$
$523$	0.402244	−	0.232235i	0.0175889	−	0.0101549i	0.508769	+	0.860903i	$0.330101\pi$
$524$			9.13809i			0.399199i
$525$	0.953220	+	1.65102i	0.0416019	+	0.0720566i
$526$			16.7275i			0.729353i
$527$	−6.80670	+	11.7896i	−0.296505	+	0.513561i
$528$	0.965073			0.0419994
$529$	−14.2876			−0.621199
$530$	0.605365	−	1.04852i	0.0262954	−	0.0455449i
$531$	−27.0148	+	15.5970i	−1.17234	+	0.676851i
$532$			26.9618i			1.16894i
$533$	24.2366	+	13.9930i	1.04980	+	0.606105i
$534$	−4.72303	+	8.18053i	−0.204386	+	0.354006i
$535$	4.25247	+	2.45517i	0.183850	+	0.106146i
$536$	5.05761	−	2.92001i	0.218456	−	0.126125i
$537$	−10.6384	+	6.14206i	−0.459079	+	0.265049i
$538$	−2.91164	−	1.68104i	−0.125530	−	0.0724747i
$539$	5.44442	−	9.43002i	0.234508	−	0.406180i
$540$	2.62198	+	1.51380i	0.112832	+	0.0651435i
$541$		−	41.5176i		−	1.78498i	−0.451064	−	0.892491i	$-0.648955\pi$
$541$		−	41.5176i		−	1.78498i	0.451064	−	0.892491i	$-0.351045\pi$
$542$	−10.3406	+	5.97016i	−0.444167	+	0.256440i
$543$	−1.05883	+	1.83395i	−0.0454388	+	0.0787023i
$544$	3.95521			0.169578
$545$	−4.59109			−0.196661
$546$	2.47999	−	4.29547i	0.106134	−	0.183829i
$547$			36.4331i			1.55777i	0.627169	+	0.778883i	$0.284213\pi$
$547$			36.4331i			1.55777i	−0.627169	+	0.778883i	$0.715787\pi$
$548$	−0.774599	−	1.34165i	−0.0330892	−	0.0573122i
$549$			8.45256i			0.360747i
$550$	−1.57897	+	0.911621i	−0.0673277	+	0.0388717i
$551$	29.8026	+	51.6196i	1.26963	+	2.19907i
$552$	−1.61610	−	2.79916i	−0.0687857	−	0.119140i
$553$	43.4852	+	25.1062i	1.84918	+	1.06762i
$554$	3.24884			0.138030
$555$	−0.763768	−	3.12781i	−0.0324202	−	0.132768i
$556$	6.91087			0.293086
$557$	−21.8742	−	12.6291i	−0.926838	−	0.535110i	−0.0410278	−	0.999158i	$-0.513063\pi$
$557$	−21.8742	−	12.6291i	−0.926838	−	0.535110i	−0.885810	+	0.464048i	$0.846397\pi$
$558$	−4.68066	−	8.10715i	−0.198148	−	0.343203i
$559$	8.70537	+	15.0781i	0.368198	+	0.637738i
$560$	−3.11916	+	1.80085i	−0.131809	+	0.0760998i
$561$			3.81707i			0.161157i
$562$	−1.88597	−	3.26660i	−0.0795550	−	0.137793i
$563$		−	2.49484i		−	0.105145i	−0.998617	−	0.0525726i	$-0.983258\pi$
$563$		−	2.49484i		−	0.105145i	0.998617	−	0.0525726i	$-0.0167421\pi$
$564$	0.204729	−	0.354601i	0.00862065	−	0.0149314i
$565$	−4.16922			−0.175400
$566$	−5.34864			−0.224820
$567$	11.8080	−	20.4521i	0.495890	−	0.858907i
$568$	7.02243	−	4.05440i	0.294655	−	0.170119i
$569$			21.2914i			0.892581i	0.894888	+	0.446290i	$0.147255\pi$
$569$			21.2914i			0.892581i	−0.894888	+	0.446290i	$0.852745\pi$
$570$	3.43152	+	1.98119i	0.143731	+	0.0829830i
$571$	−6.21950	+	10.7725i	−0.260278	+	0.450814i	−0.966316	−	0.257360i	$-0.917147\pi$
$571$	−6.21950	+	10.7725i	−0.260278	+	0.450814i	0.706038	+	0.708174i	$0.250481\pi$
$572$	4.10802	+	2.37176i	0.171765	+	0.0991685i
$573$	−9.89078	+	5.71044i	−0.413193	+	0.238557i
$574$	33.5523	−	19.3714i	1.40045	−	0.808548i
$575$	5.28826	+	3.05318i	0.220536	+	0.127326i
$576$	−1.35991	+	2.35544i	−0.0566630	+	0.0981432i
$577$	15.8358	+	9.14279i	0.659252	+	0.380619i	0.791992	−	0.610532i	$-0.209044\pi$
$577$	15.8358	+	9.14279i	0.659252	+	0.380619i	−0.132740	+	0.991151i	$0.542378\pi$
$578$		−	1.35628i		−	0.0564137i
$579$	−6.15205	+	3.55189i	−0.255670	+	0.147611i
$580$	−3.98119	+	6.89563i	−0.165310	+	0.286325i
$581$	−15.0232			−0.623266
$582$	−5.41046			−0.224271
$583$	−1.10373	+	1.91171i	−0.0457117	+	0.0791750i
$584$			11.9368i			0.493947i
$585$	3.53808	+	6.12814i	0.146282	+	0.253367i
$586$		−	7.69534i		−	0.317892i
$587$	−14.8446	+	8.57054i	−0.612703	+	0.353744i	−0.774023	−	0.633158i	$-0.781758\pi$
$587$	−14.8446	+	8.57054i	−0.612703	+	0.353744i	0.161320	+	0.986902i	$0.448425\pi$
$588$	−1.58060	−	2.73768i	−0.0651830	−	0.112900i
$589$	−12.8827	−	22.3135i	−0.530823	−	0.919413i
$590$	−9.93254	−	5.73455i	−0.408916	−	0.236088i
$591$	5.01409			0.206252
$592$	5.90914	−	1.44293i	0.242864	−	0.0593042i
$593$	6.78758			0.278733			0.139366	−	0.990241i	$-0.455493\pi$
$593$	6.78758			0.278733			0.139366	+	0.990241i	$0.455493\pi$
$594$	−4.78050	−	2.76002i	−0.196146	−	0.113245i
$595$	−7.12275	−	12.3370i	−0.292004	−	0.505766i
$596$	−9.72613	−	16.8462i	−0.398398	−	0.690046i
$597$	−5.39133	+	3.11269i	−0.220653	+	0.127394i
$598$		−	15.8869i		−	0.649664i
$599$	7.37980	+	12.7822i	0.301530	+	0.522266i	0.976483	−	0.215595i	$-0.0691692\pi$
$599$	7.37980	+	12.7822i	0.301530	+	0.522266i	−0.674952	+	0.737861i	$0.735836\pi$
$600$			0.529317i			0.0216093i
$601$	12.2413	−	21.2025i	0.499333	−	0.864870i	−0.500667	−	0.865640i	$-0.666912\pi$
$601$	12.2413	−	21.2025i	0.499333	−	0.864870i	1.00000		0.000770196i	$0.000245161\pi$
$602$	24.1028			0.982357
$603$	−15.8838			−0.646840
$604$	−0.873178	+	1.51239i	−0.0355291	+	0.0615382i
$605$	−6.64743	+	3.83789i	−0.270256	+	0.156033i
$606$		−	7.30653i		−	0.296807i
$607$	29.0314	+	16.7613i	1.17835	+	0.680319i	0.955632	−	0.294565i	$-0.0951747\pi$
$607$	29.0314	+	16.7613i	1.17835	+	0.680319i	0.222715	+	0.974884i	$0.428508\pi$
$608$	−3.74292	+	6.48293i	−0.151796	+	0.262918i
$609$	−13.1461	−	7.58990i	−0.532707	−	0.307558i
$610$	−2.69140	+	1.55388i	−0.108972	+	0.0629148i
$611$	1.74294	−	1.00629i	0.0705117	−	0.0407100i
$612$	−9.31626	−	5.37874i	−0.376587	−	0.217423i
$613$	12.6035	−	21.8298i	0.509049	−	0.881699i	−0.490896	−	0.871218i	$-0.663331\pi$
$613$	12.6035	−	21.8298i	0.509049	−	0.881699i	0.999945	−	0.0104806i	$-0.00333615\pi$
$614$	2.28061	+	1.31671i	0.0920378	+	0.0531381i
$615$		−	5.69377i		−	0.229595i
$616$	5.68699	−	3.28339i	0.229135	−	0.132291i
$617$	18.0748	−	31.3064i	0.727662	−	1.26035i	−0.230207	−	0.973142i	$-0.573940\pi$
$617$	18.0748	−	31.3064i	0.727662	−	1.26035i	0.957869	−	0.287206i	$-0.0927264\pi$
$618$	−5.69669			−0.229154
$619$	4.03895			0.162339			0.0811695	−	0.996700i	$-0.474134\pi$
$619$	4.03895			0.162339			0.0811695	+	0.996700i	$0.474134\pi$
$620$	1.72094	−	2.98076i	0.0691148	−	0.119710i
$621$			18.4876i			0.741881i
$622$	−6.88210	−	11.9202i	−0.275947	−	0.477955i
$623$			64.2751i			2.57513i
$624$	1.19262	−	0.688561i	0.0477431	−	0.0275645i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.2222	−	19.4375i	−0.448531	−	0.776878i
$627$	−6.25650	−	3.61219i	−0.249861	−	0.144257i
$628$	−11.4261			−0.455953
$629$	5.70711	+	23.3719i	0.227557	+	0.931899i
$630$	9.79599			0.390282
$631$	8.41754	+	4.85987i	0.335097	+	0.193468i	0.658102	−	0.752929i	$-0.271360\pi$
$631$	8.41754	+	4.85987i	0.335097	+	0.193468i	−0.323005	+	0.946397i	$0.604693\pi$
$632$	6.97065	+	12.0735i	0.277278	+	0.480259i
$633$	2.03059	+	3.51708i	0.0807085	+	0.139791i
$634$	−26.9596	+	15.5652i	−1.07070	+	0.618171i
$635$			10.4709i			0.415525i
$636$	0.320430	+	0.555000i	0.0127059	+	0.0220072i
$637$		−	15.5380i		−	0.615637i
$638$	7.25868	−	12.5724i	0.287374	−	0.497746i
$639$	−22.0545			−0.872463
$640$	−1.00000			−0.0395285
$641$	15.8045	−	27.3743i	0.624241	−	1.08122i	−0.364446	−	0.931225i	$-0.618741\pi$
$641$	15.8045	−	27.3743i	0.624241	−	1.08122i	0.988687	−	0.149993i	$-0.0479252\pi$
$642$	−2.25090	+	1.29956i	−0.0888361	+	0.0512895i
$643$			36.9409i			1.45681i	0.685148	+	0.728404i	$0.259737\pi$
$643$			36.9409i			1.45681i	−0.685148	+	0.728404i	$0.740263\pi$
$644$	−19.0467	−	10.9966i	−0.750546	−	0.433328i
$645$	1.77111	−	3.06765i	0.0697374	−	0.120789i
$646$	−25.6414	−	14.8041i	−1.00885	−	0.582458i
$647$	10.8755	−	6.27896i	0.427559	−	0.246851i	−0.270747	−	0.962650i	$-0.587271\pi$
$647$	10.8755	−	6.27896i	0.427559	−	0.246851i	0.698306	+	0.715799i	$0.253937\pi$
$648$	5.67845	−	3.27846i	0.223071	−	0.128790i
$649$	18.1094	+	10.4555i	0.710857	+	0.410414i
$650$	−1.30085	+	2.25314i	−0.0510235	+	0.0883753i
$651$	5.68264	+	3.28088i	0.222720	+	0.128588i
$652$			6.91680i			0.270883i
$653$	18.7782	−	10.8416i	0.734846	−	0.424264i	−0.0853461	−	0.996351i	$-0.527200\pi$
$653$	18.7782	−	10.8416i	0.734846	−	0.424264i	0.820193	+	0.572088i	$0.193866\pi$
$654$	1.21507	−	2.10456i	0.0475130	−	0.0822950i
$655$	9.13809			0.357055
$656$	10.7568			0.419984
$657$	16.2330	−	28.1163i	0.633308	−	1.09692i
$658$		−	2.78613i		−	0.108615i
$659$	−9.54849	−	16.5385i	−0.371956	−	0.644247i	0.617910	−	0.786249i	$-0.287980\pi$
$659$	−9.54849	−	16.5385i	−0.371956	−	0.644247i	−0.989866	+	0.142001i	$0.954646\pi$
$660$		−	0.965073i		−	0.0375654i
$661$	−39.6128	+	22.8705i	−1.54076	+	0.889558i	−0.541968	+	0.840399i	$0.682321\pi$
$661$	−39.6128	+	22.8705i	−1.54076	+	0.889558i	−0.998791	+	0.0491589i	$0.984346\pi$
$662$	−4.44194	−	7.69367i	−0.172641	−	0.299023i
$663$	2.72341	+	4.71708i	0.105768	+	0.183196i
$664$	−3.61231	−	2.08557i	−0.140185	−	0.0809356i
$665$	26.9618			1.04553
$666$	−15.8809	−	4.63717i	−0.615371	−	0.179687i
$667$	−48.6211			−1.88262
$668$	16.6192	+	9.59512i	0.643017	+	0.371246i
$669$	6.28622	+	10.8881i	0.243039	+	0.420957i
$670$	−2.92001	−	5.05761i	−0.112810	−	0.195393i
$671$	4.90707	−	2.83310i	0.189435	−	0.109371i
$672$		−	1.90644i		−	0.0735425i
$673$	−20.8334	−	36.0846i	−0.803070	−	1.39096i	−0.917586	−	0.397537i	$-0.869865\pi$
$673$	−20.8334	−	36.0846i	−0.803070	−	1.39096i	0.114516	−	0.993421i	$-0.463468\pi$
$674$			1.35944i			0.0523637i
$675$	1.51380	−	2.62198i	0.0582661	−	0.100920i
$676$	−6.23116			−0.239660
$677$	34.6472			1.33160			0.665799	−	0.746131i	$-0.268091\pi$
$677$	34.6472			1.33160			0.665799	+	0.746131i	$0.268091\pi$
$678$	1.10342	−	1.91118i	0.0423765	−	0.0733983i
$679$	−31.8828	+	18.4075i	−1.22355	+	0.706417i
$680$		−	3.95521i		−	0.151676i
$681$	−3.19474	−	1.84448i	−0.122423	−	0.0706808i
$682$	−3.13770	+	5.43465i	−0.120149	+	0.208104i
$683$	5.40998	+	3.12345i	0.207007	+	0.119516i	0.599920	−	0.800060i	$-0.295199\pi$
$683$	5.40998	+	3.12345i	0.207007	+	0.119516i	−0.392913	+	0.919576i	$0.628533\pi$
$684$	17.6324	−	10.1801i	0.674193	−	0.389246i
$685$	−1.34165	+	0.774599i	−0.0512616	+	0.0295959i
$686$	3.20575	+	1.85084i	0.122396	+	0.0706654i
$687$	−1.00668	+	1.74362i	−0.0384073	+	0.0665234i
$688$	5.79550	+	3.34603i	0.220951	+	0.127566i
$689$			3.14995i			0.120004i
$690$	−2.79916	+	1.61610i	−0.106562	+	0.0615238i
$691$	17.0551	−	29.5403i	0.648806	−	1.12377i	−0.334602	−	0.942360i	$-0.608602\pi$
$691$	17.0551	−	29.5403i	0.648806	−	1.12377i	0.983408	−	0.181406i	$-0.0580648\pi$
$692$	15.0189			0.570931
$693$	−17.8605			−0.678463
$694$	1.15540	−	2.00122i	0.0438585	−	0.0759652i
$695$		−	6.91087i		−	0.262144i
$696$	−2.10731	−	3.64997i	−0.0798774	−	0.138352i
$697$			42.5456i			1.61153i
$698$	−7.27561	+	4.20057i	−0.275386	+	0.158994i
$699$	−5.95455	−	10.3136i	−0.225222	−	0.390096i
$700$	1.80085	+	3.11916i	0.0680657	+	0.117893i
$701$	16.0588	+	9.27155i	0.606532	+	0.350182i	0.771607	−	0.636099i	$-0.219453\pi$
$701$	16.0588	+	9.27155i	0.606532	+	0.350182i	−0.165075	+	0.986281i	$0.552787\pi$
$702$	−7.87690			−0.297294
$703$	−43.7094	−	12.7630i	−1.64853	−	0.481367i
$704$	1.82324			0.0687160
$705$	−0.354601	−	0.204729i	−0.0133551	−	0.00771054i
$706$	−0.827653	−	1.43354i	−0.0311491	−	0.0539519i
$707$	−24.8584	−	43.0560i	−0.934896	−	1.61929i
$708$	5.25746	−	3.03539i	0.197587	−	0.114077i
$709$		−	0.498672i		−	0.0187280i	−0.999956	−	0.00936401i	$-0.997019\pi$
$709$		−	0.498672i		−	0.0187280i	0.999956	−	0.00936401i	$-0.00298070\pi$
$710$	−4.05440	−	7.02243i	−0.152159	−	0.263547i
$711$		−	37.9179i		−	1.42203i
$712$	−8.92289	+	15.4549i	−0.334399	+	0.579197i
$713$	21.0174			0.787107
$714$	7.54038			0.282192
$715$	2.37176	−	4.10802i	0.0886990	−	0.153631i
$716$	−20.0983	+	11.6038i	−0.751108	+	0.433653i
$717$		−	1.16384i		−	0.0434645i
$718$	26.1863	+	15.1187i	0.977264	+	0.564224i
$719$	14.8275	−	25.6820i	0.552972	−	0.957775i	−0.445086	−	0.895488i	$-0.646827\pi$
$719$	14.8275	−	25.6820i	0.552972	−	0.957775i	0.998058	−	0.0622878i	$-0.0198396\pi$
$720$	2.35544	+	1.35991i	0.0877819	+	0.0506809i
$721$	−33.5695	+	19.3814i	−1.25019	+	0.721800i
$722$	32.0758	−	18.5189i	1.19374	−	0.689204i
$723$	11.7869	+	6.80518i	0.438360	+	0.253087i
$724$	−2.00037	+	3.46475i	−0.0743433	+	0.128766i
$725$	6.89563	+	3.98119i	0.256097	+	0.147858i
$726$		−	4.06292i		−	0.150789i
$727$	−28.7349	+	16.5901i	−1.06572	+	0.615293i	−0.927009	−	0.375040i	$-0.877629\pi$
$727$	−28.7349	+	16.5901i	−1.06572	+	0.615293i	−0.138711	+	0.990333i	$0.544296\pi$
$728$	4.68527	−	8.11513i	0.173648	−	0.300767i
$729$	−13.0260			−0.482444
$730$	11.9368			0.441800
$731$	−13.2343	+	22.9224i	−0.489487	+	0.847817i
$732$		−	1.64499i		−	0.0608005i
$733$	−1.77830	−	3.08011i	−0.0656830	−	0.113766i	0.831314	−	0.555803i	$-0.187589\pi$
$733$	−1.77830	−	3.08011i	−0.0656830	−	0.113766i	−0.896997	+	0.442037i	$0.854256\pi$
$734$		−	9.08926i		−	0.335491i
$735$	−2.73768	+	1.58060i	−0.100981	+	0.0583014i
$736$	−3.05318	−	5.28826i	−0.112542	−	0.194928i
$737$	5.32389	+	9.22125i	0.196108	+	0.339669i
$738$	−25.3370	−	14.6283i	−0.932669	−	0.538477i
$739$	37.9751			1.39693			0.698467	−	0.715642i	$-0.253866\pi$
$739$	37.9751			1.39693			0.698467	+	0.715642i	$0.253866\pi$
$740$	−1.44293	−	5.90914i	−0.0530433	−	0.217224i
$741$	−10.3089			−0.378708
$742$	3.77646	+	2.18034i	0.138638	+	0.0800429i
$743$	3.58987	+	6.21784i	0.131700	+	0.228111i	0.924332	−	0.381590i	$-0.124623\pi$
$743$	3.58987	+	6.21784i	0.131700	+	0.228111i	−0.792632	+	0.609700i	$0.791290\pi$
$744$	0.910924	+	1.57777i	0.0333961	+	0.0578437i
$745$	−16.8462	+	9.72613i	−0.617195	+	0.356338i
$746$		−	33.4513i		−	1.22474i
$747$	5.67237	+	9.82484i	0.207541	+	0.359472i
$748$			7.21132i			0.263672i
$749$	−8.84277	+	15.3161i	−0.323108	+	0.559639i
$750$	0.529317			0.0193279
$751$	−44.9332			−1.63964			−0.819818	−	0.572624i	$-0.805926\pi$
$751$	−44.9332			−1.63964			−0.819818	+	0.572624i	$0.805926\pi$
$752$	0.386780	−	0.669923i	0.0141044	−	0.0244296i
$753$	4.00793	−	2.31398i	0.146057	−	0.0843261i
$754$		−	20.7157i		−	0.754422i
$755$	1.51239	+	0.873178i	0.0550415	+	0.0317782i
$756$	−5.45225	+	9.44357i	−0.198296	+	0.343459i
$757$	−28.5757	−	16.4982i	−1.03860	−	0.599638i	−0.119166	−	0.992874i	$-0.538022\pi$
$757$	−28.5757	−	16.4982i	−1.03860	−	0.599638i	−0.919437	+	0.393237i	$0.871355\pi$
$758$	−14.9948	+	8.65724i	−0.544635	+	0.314445i
$759$	5.10355	−	2.94654i	0.185247	−	0.106953i
$760$	6.48293	+	3.74292i	0.235161	+	0.135770i
$761$	0.135420	−	0.234555i	0.00490898	−	0.00850259i	−0.863560	−	0.504245i	$-0.831771\pi$
$761$	0.135420	−	0.234555i	0.00490898	−	0.00850259i	0.868469	+	0.495743i	$0.165104\pi$
$762$	−4.79988	−	2.77121i	−0.173881	−	0.100390i
$763$		−	16.5357i		−	0.598634i
$764$	−18.6859	+	10.7883i	−0.676034	+	0.390308i
$765$	−5.37874	+	9.31626i	−0.194469	+	0.336830i
$766$	11.8694			0.428860
$767$	29.8392			1.07743
$768$	0.264658	−	0.458402i	0.00955003	−	0.0165411i
$769$		−	37.2643i		−	1.34378i	−0.740649	−	0.671892i	$-0.765482\pi$
$769$		−	37.2643i		−	1.34378i	0.740649	−	0.671892i	$-0.234518\pi$
$770$	−3.28339	−	5.68699i	−0.118325	−	0.204945i
$771$			7.30883i			0.263221i
$772$	−11.6226	+	6.71032i	−0.418307	+	0.241510i
$773$	2.07366	+	3.59168i	0.0745844	+	0.129184i	0.900905	−	0.434015i	$-0.142904\pi$
$773$	2.07366	+	3.59168i	0.0745844	+	0.129184i	−0.826321	+	0.563199i	$0.809570\pi$
$774$	−9.10062	−	15.7627i	−0.327115	−	0.566580i
$775$	−2.98076	−	1.72094i	−0.107072	−	0.0618181i
$776$	−10.2216			−0.366934
$777$	11.2654	−	2.75086i	0.404145	−	0.0986867i
$778$	21.0340			0.754106
$779$	−69.7358	−	40.2620i	−2.49854	−	1.44254i
$780$	−0.688561	−	1.19262i	−0.0246545	−	0.0427028i
$781$	7.39216	+	12.8036i	0.264512	+	0.458149i
$782$	20.9162	−	12.0760i	0.747962	−	0.431836i
$783$			24.1069i			0.861510i
$784$	−2.98612	−	5.17211i	−0.106647	−	0.184718i
$785$			11.4261i			0.407817i
$786$	−2.41847	+	4.18891i	−0.0862640	+	0.149414i
$787$	−43.0233			−1.53362			−0.766808	−	0.641877i	$-0.778156\pi$
$787$	−43.0233			−1.53362			−0.766808	+	0.641877i	$0.778156\pi$
$788$	9.47276			0.337453
$789$	−4.42707	+	7.66790i	−0.157608	+	0.272985i
$790$	12.0735	−	6.97065i	0.429557	−	0.248005i
$791$		−	15.0163i		−	0.533917i
$792$	−4.29453	−	2.47945i	−0.152600	−	0.0881034i
$793$	4.04273	−	7.00221i	0.143562	−	0.248656i
$794$	−3.54065	−	2.04419i	−0.125653	−	0.0725457i
$795$	0.555000	−	0.320430i	0.0196838	−	0.0113645i
$796$	−10.1855	+	5.88058i	−0.361014	+	0.208432i
$797$	8.57378	+	4.95008i	0.303699	+	0.175341i	0.644103	−	0.764938i	$-0.277231\pi$
$797$	8.57378	+	4.95008i	0.303699	+	0.175341i	−0.340404	+	0.940279i	$0.610564\pi$
$798$	−7.13566	+	12.3593i	−0.252599	+	0.437515i
$799$	2.64969	+	1.52980i	0.0937392	+	0.0541204i
$800$			1.00000i			0.0353553i
$801$	42.0346	−	24.2687i	1.48522	−	0.857492i
$802$	−0.187696	+	0.325099i	−0.00662778	+	0.0114796i
$803$	−21.7636			−0.768021
$804$	3.09122			0.109019
$805$	−10.9966	+	19.0467i	−0.387580	+	0.671309i
$806$			8.95476i			0.315418i
$807$	−0.889802	−	1.54118i	−0.0313225	−	0.0542522i
$808$		−	13.8037i		−	0.485613i
$809$	20.9742	−	12.1095i	0.737413	−	0.425746i	−0.0837147	−	0.996490i	$-0.526678\pi$
$809$	20.9742	−	12.1095i	0.737413	−	0.425746i	0.821128	+	0.570744i	$0.193345\pi$
$810$	−3.27846	−	5.67845i	−0.115193	−	0.199521i
$811$	5.85771	+	10.1458i	0.205692	+	0.356269i	0.950353	−	0.311174i	$-0.100722\pi$
$811$	5.85771	+	10.1458i	0.205692	+	0.356269i	−0.744661	+	0.667443i	$0.767389\pi$
$812$	−24.8360	−	14.3391i	−0.871572	−	0.503202i
$813$	−6.32021			−0.221659
$814$	2.63082	+	10.7738i	0.0922101	+	0.377621i
$815$	6.91680			0.242285
$816$	1.81308	+	1.04678i	0.0634704	+	0.0366446i
$817$	−25.0479	−	43.3842i	−0.876315	−	1.51782i
$818$	15.4929	+	26.8345i	0.541697	+	0.938246i
$819$	−22.0717	+	12.7431i	−0.771248	+	0.445280i
$820$		−	10.7568i		−	0.375645i
$821$	1.01873	+	1.76449i	0.0355539	+	0.0615812i	0.883255	−	0.468893i	$-0.155347\pi$
$821$	1.01873	+	1.76449i	0.0355539	+	0.0615812i	−0.847701	+	0.530474i	$0.822014\pi$
$822$		−	0.820016i		−	0.0286014i
$823$	−16.9307	+	29.3248i	−0.590166	+	1.02220i	0.404044	+	0.914740i	$0.367604\pi$
$823$	−16.9307	+	29.3248i	−0.590166	+	1.02220i	−0.994210	+	0.107458i	$0.965729\pi$
$824$	−10.7623			−0.374924
$825$	−0.965073			−0.0335995
$826$	20.6541	−	35.7740i	0.718650	−	1.24474i
$827$	−31.2396	+	18.0362i	−1.08631	+	0.627179i	−0.932591	−	0.360936i	$-0.882457\pi$
$827$	−31.2396	+	18.0362i	−1.08631	+	0.627179i	−0.153716	+	0.988115i	$0.549124\pi$
$828$			16.6082i			0.577175i
$829$	21.6666	+	12.5092i	0.752511	+	0.434462i	0.826600	−	0.562789i	$-0.190272\pi$
$829$	21.6666	+	12.5092i	0.752511	+	0.434462i	−0.0740896	+	0.997252i	$0.523605\pi$
$830$	−2.08557	+	3.61231i	−0.0723910	+	0.125385i
$831$	1.48927	+	0.859833i	0.0516624	+	0.0298273i
$832$	2.25314	−	1.30085i	0.0781135	−	0.0450989i
$833$	20.4568	−	11.8107i	0.708787	−	0.409218i
$834$	3.16795	+	1.82902i	0.109697	+	0.0633338i
$835$	9.59512	−	16.6192i	0.332053	−	0.575132i
$836$	−11.8200	−	6.82426i	−0.408802	−	0.236022i
$837$		−	10.4207i		−	0.360190i
$838$	17.2081	−	9.93508i	0.594443	−	0.343202i
$839$	10.1593	−	17.5964i	0.350737	−	0.607495i	−0.635641	−	0.771984i	$-0.719264\pi$
$839$	10.1593	−	17.5964i	0.350737	−	0.607495i	0.986379	+	0.164489i	$0.0525976\pi$
$840$	−1.90644			−0.0657784
$841$	−34.3995			−1.18619
$842$	−3.90083	+	6.75644i	−0.134432	+	0.232842i
$843$		−	1.99655i		−	0.0687650i
$844$	3.83624	+	6.64456i	0.132049	+	0.228715i
$845$			6.23116i			0.214358i
$846$	−1.82207	+	1.05197i	−0.0626441	+	0.0361676i
$847$	−13.8229	−	23.9420i	−0.474962	−	0.822658i
$848$	0.605365	+	1.04852i	0.0207883	+	0.0360064i
$849$	−2.45182	−	1.41556i	−0.0841464	−	0.0485819i
$850$	−3.95521			−0.135663
$851$	26.8435	−	25.6723i	0.920185	−	0.880034i
$852$	4.29212			0.147046
$853$	−4.78689	−	2.76371i	−0.163900	−	0.0946278i	0.415806	−	0.909453i	$-0.363499\pi$
$853$	−4.78689	−	2.76371i	−0.163900	−	0.0946278i	−0.579706	+	0.814825i	$0.696833\pi$
$854$	−5.59661	−	9.69361i	−0.191512	−	0.331709i
$855$	−10.1801	−	17.6324i	−0.348152	−	0.603017i
$856$	−4.25247	+	2.45517i	−0.145346	+	0.0839158i
$857$		−	40.8472i		−	1.39531i	−0.716433	−	0.697656i	$-0.754226\pi$
$857$		−	40.8472i		−	1.39531i	0.716433	−	0.697656i	$-0.245774\pi$
$858$	1.25541	+	2.17444i	0.0428591	+	0.0742342i
$859$			16.6315i			0.567458i	0.958904	+	0.283729i	$0.0915716\pi$
$859$			16.6315i			0.567458i	−0.958904	+	0.283729i	$0.908428\pi$
$860$	3.34603	−	5.79550i	0.114099	−	0.197625i
$861$	20.5072			0.698885
$862$	−23.4496			−0.798698
$863$	5.51014	−	9.54385i	0.187567	−	0.324876i	−0.756871	−	0.653564i	$-0.773273\pi$
$863$	5.51014	−	9.54385i	0.187567	−	0.324876i	0.944439	+	0.328688i	$0.106606\pi$
$864$	−2.62198	+	1.51380i	−0.0892015	+	0.0515005i
$865$		−	15.0189i		−	0.510656i
$866$	−14.7592	−	8.52122i	−0.501538	−	0.289563i
$867$	0.358950	−	0.621720i	0.0121906	−	0.0211147i
$868$	10.7358	+	6.19832i	0.364397	+	0.210385i
$869$	−22.0130	+	12.7092i	−0.746739	+	0.431130i
$870$	−3.64997	+	2.10731i	−0.123746	+	0.0714445i
$871$	13.1584	+	7.59700i	0.445855	+	0.257414i
$872$	2.29555	−	3.97600i	0.0777370	−	0.134644i
$873$	24.0763	+	13.9005i	0.814859	+	0.470459i
$874$			45.7112i			1.54621i
$875$	3.11916	−	1.80085i	0.105447	−	0.0608798i
$876$	−3.15916	+	5.47183i	−0.106738	+	0.184876i
$877$	−33.2095			−1.12141			−0.560703	−	0.828017i	$-0.689469\pi$
$877$	−33.2095			−1.12141			−0.560703	+	0.828017i	$0.689469\pi$
$878$	39.2185			1.32356
$879$	2.03664	−	3.52756i	0.0686940	−	0.118982i
$880$		−	1.82324i		−	0.0614615i
$881$	2.15537	+	3.73322i	0.0726164	+	0.125775i	0.900047	−	0.435792i	$-0.143532\pi$
$881$	2.15537	+	3.73322i	0.0726164	+	0.125775i	−0.827431	+	0.561568i	$0.810198\pi$
$882$			16.2434i			0.546945i
$883$	46.8394	−	27.0427i	1.57627	−	0.910060i	0.580897	−	0.813977i	$-0.302702\pi$
$883$	46.8394	−	27.0427i	1.57627	−	0.910060i	0.995373	−	0.0960828i	$-0.0306314\pi$
$884$	5.14514	+	8.91164i	0.173050	+	0.299731i
$885$	−3.03539	−	5.25746i	−0.102034	−	0.176728i
$886$	−26.1138	−	15.0768i	−0.877310	−	0.506515i
$887$	20.9463			0.703307			0.351654	−	0.936130i	$-0.385620\pi$
$887$	20.9463			0.703307			0.351654	+	0.936130i	$0.385620\pi$
$888$	3.09064	+	0.902460i	0.103715	+	0.0302846i
$889$	−37.7130			−1.26485
$890$	15.4549	+	8.92289i	0.518049	+	0.299096i
$891$	5.97742	+	10.3532i	0.200251	+	0.346845i
$892$	11.8761	+	20.5700i	0.397642	+	0.688735i
$893$	−5.01494	+	2.89538i	−0.167819	+	0.0968901i
$894$		−	10.2964i		−	0.344363i
$895$	11.6038	+	20.0983i	0.387871	+	0.671812i
$896$		−	3.60170i		−	0.120324i
$897$	4.20460	−	7.28258i	0.140388	−	0.243158i
$898$	−14.2442			−0.475334
$899$	27.4056			0.914029
$900$	1.35991	−	2.35544i	0.0453304	−	0.0785146i
$901$	−4.14713	+	2.39435i	−0.138161	+	0.0797673i
$902$			19.6123i			0.653018i
$903$	11.0488	+	6.37901i	0.367680	+	0.212280i
$904$	2.08461	−	3.61065i	0.0693331	−	0.120088i
$905$	3.46475	+	2.00037i	0.115172	+	0.0664947i
$906$	−0.800532	+	0.462188i	−0.0265959	+	0.0153552i
$907$	37.0391	−	21.3845i	1.22986	−	0.710062i	0.262862	−	0.964833i	$-0.415334\pi$
$907$	37.0391	−	21.3845i	1.22986	−	0.710062i	0.967001	+	0.254771i	$0.0820002\pi$
$908$	−6.03559	−	3.48465i	−0.200298	−	0.115642i
$909$	−18.7718	+	32.5138i	−0.622622	+	1.07841i
$910$	−8.11513	−	4.68527i	−0.269014	−	0.155315i
$911$		−	0.0374463i		−	0.00124065i	−1.00000		0.000620326i	$-0.999803\pi$
$911$		−	0.0374463i		−	0.00124065i	1.00000		0.000620326i	$-0.000197456\pi$
$912$	−3.43152	+	1.98119i	−0.113629	+	0.0656038i
$913$	3.80249	−	6.58611i	0.125844	−	0.217968i
$914$	−9.06071			−0.299702
$915$	−1.64499			−0.0543817
$916$	−1.90185	+	3.29411i	−0.0628390	+	0.108840i
$917$			32.9126i			1.08687i
$918$	−5.98740	−	10.3705i	−0.197614	−	0.342277i
$919$		−	14.1285i		−	0.466056i	−0.972470	−	0.233028i	$-0.925137\pi$
$919$		−	14.1285i		−	0.466056i	0.972470	−	0.233028i	$-0.0748633\pi$
$920$	−5.28826	+	3.05318i	−0.174349	+	0.100660i
$921$	0.696956	+	1.20716i	0.0229655	+	0.0397774i
$922$	−8.74921	−	15.1541i	−0.288140	−	0.499073i
$923$	18.2703	+	10.5483i	0.601373	+	0.347203i
$924$	3.47590			0.114349
$925$	−5.90914	+	1.44293i	−0.194291	+	0.0474433i
$926$	−31.4081			−1.03213
$927$	25.3500	+	14.6358i	0.832604	+	0.480704i
$928$	−3.98119	−	6.89563i	−0.130689	−	0.226360i
$929$	2.46073	+	4.26211i	0.0807340	+	0.139835i	0.903565	−	0.428450i	$-0.140940\pi$
$929$	2.46073	+	4.26211i	0.0807340	+	0.139835i	−0.822831	+	0.568286i	$0.807607\pi$
$930$	1.57777	−	0.910924i	0.0517370	−	0.0298704i
$931$			44.7073i			1.46522i
$932$	−11.2495	−	19.4847i	−0.368490	−	0.638244i
$933$		−	7.28562i		−	0.238521i
$934$	20.0151	−	34.6671i	0.654913	−	1.13434i
$935$	7.21132			0.235835
$936$	−7.07617			−0.231292
$937$	−13.2829	+	23.0066i	−0.433933	+	0.751593i	−0.997208	−	0.0746761i	$-0.976208\pi$
$937$	−13.2829	+	23.0066i	−0.433933	+	0.751593i	0.563275	+	0.826269i	$0.309541\pi$
$938$	18.2160	−	10.5170i	0.594773	−	0.343393i
$939$		−	11.8802i		−	0.387697i
$940$	−0.669923	−	0.386780i	−0.0218505	−	0.0126154i
$941$	14.0089	−	24.2641i	0.456676	−	0.790986i	−0.542107	−	0.840310i	$-0.682373\pi$
$941$	14.0089	−	24.2641i	0.456676	−	0.790986i	0.998783	+	0.0493234i	$0.0157065\pi$
$942$	−5.23776	−	3.02402i	−0.170656	−	0.0985280i
$943$	56.8849	−	32.8425i	1.85243	−	1.06950i
$944$	9.93254	−	5.73455i	0.323277	−	0.186644i
$945$	9.44357	+	5.45225i	0.307199	+	0.177362i
$946$	−6.10063	+	10.5666i	−0.198349	+	0.343550i
$947$	−5.33284	−	3.07892i	−0.173294	−	0.100051i	0.410844	−	0.911706i	$-0.365234\pi$
$947$	−5.33284	−	3.07892i	−0.173294	−	0.100051i	−0.584138	+	0.811654i	$0.698567\pi$
$948$			7.37936i			0.239671i
$949$	−26.8952	+	15.5279i	−0.873055	+	0.504058i
$950$	3.74292	−	6.48293i	0.121436	−	0.210334i
$951$	−16.4778			−0.534329
$952$	14.2455			0.461699
$953$	−6.06112	+	10.4982i	−0.196339	+	0.340069i	−0.947339	−	0.320233i	$-0.896239\pi$
$953$	−6.06112	+	10.4982i	−0.196339	+	0.340069i	0.751000	+	0.660303i	$0.229572\pi$
$954$		−	3.29297i		−	0.106614i
$955$	10.7883	+	18.6859i	0.349102	+	0.604663i
$956$		−	2.19876i		−	0.0711131i
$957$	6.65478	−	3.84214i	0.215118	−	0.124199i
$958$	6.90818	+	11.9653i	0.223193	+	0.386582i
$959$	−2.78987	−	4.83220i	−0.0900897	−	0.156040i
$960$	−0.458402	−	0.264658i	−0.0147948	−	0.00854181i
$961$	19.1534			0.617852
$962$	10.9380	+	11.4371i	0.352656	+	0.368746i
$963$	13.3552			0.430366
$964$	22.2682	+	12.8565i	0.717210	+	0.414081i
$965$	6.71032	+	11.6226i	0.216013	+	0.374145i
$966$	−5.82070	−	10.0817i	−0.187278	−	0.324375i
$967$	−2.16508	+	1.25001i	−0.0696243	+	0.0401976i	−0.534408	−	0.845227i	$-0.679465\pi$
$967$	−2.16508	+	1.25001i	−0.0696243	+	0.0401976i	0.464784	+	0.885424i	$0.346132\pi$
$968$		−	7.67579i		−	0.246709i
$969$	−7.83604	−	13.5724i	−0.251730	−	0.436009i
$970$			10.2216i			0.328195i
$971$	1.24277	−	2.15254i	0.0398825	−	0.0690784i	−0.845395	−	0.534141i	$-0.820635\pi$
$971$	1.24277	−	2.15254i	0.0398825	−	0.0690784i	0.885278	+	0.465063i	$0.153968\pi$
$972$	12.5535			0.402653
$973$	24.8909			0.797965
$974$	−17.0381	+	29.5109i	−0.545937	+	0.945591i
$975$	−1.19262	+	0.688561i	−0.0381945	+	0.0220516i
$976$		−	3.10776i		−	0.0994770i
$977$	15.0492	+	8.68866i	0.481467	+	0.277975i	0.721027	−	0.692906i	$-0.243670\pi$
$977$	15.0492	+	8.68866i	0.481467	+	0.277975i	−0.239561	+	0.970881i	$0.577003\pi$
$978$	−1.83059	+	3.17067i	−0.0585358	+	0.101387i
$979$	−28.1780	−	16.2686i	−0.900574	−	0.519947i
$980$	−5.17211	+	2.98612i	−0.165217	+	0.0953881i
$981$	−10.8140	+	6.24348i	−0.345265	+	0.199339i
$982$	−4.51180	−	2.60489i	−0.143977	−	0.0831254i
$983$	3.60240	−	6.23954i	0.114899	−	0.199010i	−0.802841	−	0.596194i	$-0.796679\pi$
$983$	3.60240	−	6.23954i	0.114899	−	0.199010i	0.917739	+	0.397183i	$0.130012\pi$
$984$	4.93095	+	2.84688i	0.157193	+	0.0907554i
$985$		−	9.47276i		−	0.301827i
$986$	27.2737	−	15.7465i	0.868571	−	0.501470i
$987$	0.737373	−	1.27717i	0.0234708	−	0.0406527i
$988$	−19.4759			−0.619612
$989$	40.8641			1.29940
$990$	−2.47945	+	4.29453i	−0.0788021	+	0.136489i
$991$			14.6406i			0.465076i	0.972587	+	0.232538i	$0.0747029\pi$
$991$			14.6406i			0.465076i	−0.972587	+	0.232538i	$0.925297\pi$
$992$	1.72094	+	2.98076i	0.0546400	+	0.0946393i
$993$		−	4.70239i		−	0.149226i
$994$	25.2927	−	14.6027i	0.802235	−	0.463171i
$995$	5.88058	+	10.1855i	0.186427	+	0.322901i
$996$	−1.10392	−	1.91205i	−0.0349792	−	0.0605857i
$997$	−29.5198	−	17.0433i	−0.934902	−	0.539766i	−0.0465432	−	0.998916i	$-0.514821\pi$
$997$	−29.5198	−	17.0433i	−0.934902	−	0.539766i	−0.888358	+	0.459151i	$0.848154\pi$
$998$	0.957772			0.0303177
$999$	−12.7286	−	13.3093i	−0.402715	−	0.421088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.c.101.5	yes	12
37.11	even	6	inner	370.2.l.c.11.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.c.11.5	✓	12	37.11	even	6	inner
370.2.l.c.101.5	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.529317i q^{6} +(1.80085 + 3.11916i) q^{7} +1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.264658 + 0.458402i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +0.529317i q^{6} +(1.80085 + 3.11916i) q^{7} +1.00000i q^{8} +(1.35991 - 2.35544i) q^{9} +1.00000 q^{10} -1.82324 q^{11} +(-0.264658 + 0.458402i) q^{12} +(-2.25314 + 1.30085i) q^{13} +3.60170i q^{14} +(0.458402 + 0.264658i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.42532 - 1.97761i) q^{17} +(2.35544 - 1.35991i) q^{18} +(6.48293 - 3.74292i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.953220 + 1.65102i) q^{21} +(-1.57897 - 0.911621i) q^{22} +6.10635i q^{23} +(-0.458402 + 0.264658i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.60170 q^{26} +3.02760 q^{27} +(-1.80085 + 3.11916i) q^{28} +7.96238i q^{29} +(0.264658 + 0.458402i) q^{30} -3.44189i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.482536 - 0.835777i) q^{33} +(-1.97761 - 3.42532i) q^{34} +(3.11916 + 1.80085i) q^{35} +2.71982 q^{36} +(-4.20419 - 4.39600i) q^{37} +7.48585 q^{38} +(-1.19262 - 0.688561i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.37841 - 9.31569i) q^{41} +(-1.65102 + 0.953220i) q^{42} -6.69206i q^{43} +(-0.911621 - 1.57897i) q^{44} -2.71982i q^{45} +(-3.05318 + 5.28826i) q^{46} -0.773560 q^{47} -0.529317 q^{48} +(-2.98612 + 5.17211i) q^{49} +(0.866025 - 0.500000i) q^{50} -2.09356i q^{51} +(-2.25314 - 1.30085i) q^{52} +(0.605365 - 1.04852i) q^{53} +(2.62198 + 1.51380i) q^{54} +(-1.57897 + 0.911621i) q^{55} +(-3.11916 + 1.80085i) q^{56} +(3.43152 + 1.98119i) q^{57} +(-3.98119 + 6.89563i) q^{58} +(-9.93254 - 5.73455i) q^{59} +0.529317i q^{60} +(-2.69140 + 1.55388i) q^{61} +(1.72094 - 2.98076i) q^{62} +9.79599 q^{63} -1.00000 q^{64} +(-1.30085 + 2.25314i) q^{65} -0.965073i q^{66} +(-2.92001 - 5.05761i) q^{67} -3.95521i q^{68} +(-2.79916 + 1.61610i) q^{69} +(1.80085 + 3.11916i) q^{70} +(-4.05440 - 7.02243i) q^{71} +(2.35544 + 1.35991i) q^{72} +11.9368 q^{73} +(-1.44293 - 5.90914i) q^{74} +0.529317 q^{75} +(6.48293 + 3.74292i) q^{76} +(-3.28339 - 5.68699i) q^{77} +(-0.688561 - 1.19262i) q^{78} +(12.0735 - 6.97065i) q^{79} +1.00000i q^{80} +(-3.27846 - 5.67845i) q^{81} -10.7568i q^{82} +(-2.08557 + 3.61231i) q^{83} -1.90644 q^{84} -3.95521 q^{85} +(3.34603 - 5.79550i) q^{86} +(-3.64997 + 2.10731i) q^{87} -1.82324i q^{88} +(15.4549 + 8.92289i) q^{89} +(1.35991 - 2.35544i) q^{90} +(-8.11513 - 4.68527i) q^{91} +(-5.28826 + 3.05318i) q^{92} +(1.57777 - 0.910924i) q^{93} +(-0.669923 - 0.386780i) q^{94} +(3.74292 - 6.48293i) q^{95} +(-0.458402 - 0.264658i) q^{96} +10.2216i q^{97} +(-5.17211 + 2.98612i) q^{98} +(-2.47945 + 4.29453i) 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

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