LMFDB - Embedded newform 56.2.p.a.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,2,Mod(37,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("56.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$56 = 2^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	56.p (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:	$0.447162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64$ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.6
Root			$1.26950 - 0.623187i$ of defining polynomial
Character	$\chi$	$=$	56.53
Dual form			56.2.p.a.37.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38687 + 0.276739i) q^{2} +(-1.36456 - 0.787829i) q^{3} +(1.84683 + 0.767603i) q^{4} +(-0.476087 + 0.274869i) q^{5} +(-1.67445 - 1.47024i) q^{6} +(-2.60755 + 0.447998i) q^{7} +(2.34889 + 1.57566i) q^{8} +(-0.258652 - 0.447998i) q^{9} +(-0.736339 + 0.249456i) q^{10} +(-2.07045 - 1.19538i) q^{11} +(-1.91537 - 2.50243i) q^{12} +3.96641i q^{13} +(-3.74031 - 0.100292i) q^{14} +0.866198 q^{15} +(2.82157 + 2.83527i) q^{16} +(2.10755 - 3.65038i) q^{17} +(-0.234739 - 0.692896i) q^{18} +(5.75174 - 3.32077i) q^{19} +(-1.09024 + 0.142191i) q^{20} +(3.91110 + 1.44298i) q^{21} +(-2.54065 - 2.23081i) q^{22} +(1.17445 + 2.03420i) q^{23} +(-1.96386 - 4.00060i) q^{24} +(-2.34889 + 4.06840i) q^{25} +(-1.09766 + 5.50090i) q^{26} +5.54207i q^{27} +(-5.15958 - 1.17418i) q^{28} -8.21720i q^{29} +(1.20131 + 0.239711i) q^{30} +(-0.433099 + 0.750150i) q^{31} +(3.12853 + 4.71299i) q^{32} +(1.88350 + 3.26232i) q^{33} +(3.93310 - 4.47937i) q^{34} +(1.11828 - 0.930019i) q^{35} +(-0.133802 - 1.02592i) q^{36} +(-0.229805 + 0.132678i) q^{37} +(8.89592 - 3.01376i) q^{38} +(3.12485 - 5.41240i) q^{39} +(-1.55138 - 0.104512i) q^{40} -6.24970 q^{41} +(5.02487 + 3.08358i) q^{42} +5.35027i q^{43} +(-2.90620 - 3.79694i) q^{44} +(0.246282 + 0.142191i) q^{45} +(1.06587 + 3.14619i) q^{46} +(-1.29930 - 2.25045i) q^{47} +(-1.61650 - 6.09180i) q^{48} +(6.59859 - 2.33635i) q^{49} +(-4.38350 + 4.99233i) q^{50} +(-5.75174 + 3.32077i) q^{51} +(-3.04463 + 7.32529i) q^{52} +(-9.36933 - 5.40939i) q^{53} +(-1.53370 + 7.68614i) q^{54} +1.31429 q^{55} +(-6.83074 - 3.05630i) q^{56} -10.4648 q^{57} +(2.27402 - 11.3962i) q^{58} +(-3.26891 - 1.88730i) q^{59} +(1.59972 + 0.664896i) q^{60} +(-6.18061 + 3.56837i) q^{61} +(-0.808249 + 0.920507i) q^{62} +(0.875150 + 1.05230i) q^{63} +(3.03461 + 7.40210i) q^{64} +(-1.09024 - 1.88835i) q^{65} +(1.70937 + 5.04566i) q^{66} +(2.31673 + 1.33757i) q^{67} +(6.69432 - 5.12387i) q^{68} -3.70105i q^{69} +(1.80828 - 0.980348i) q^{70} +8.76700 q^{71} +(0.0983458 - 1.45985i) q^{72} +(-2.33159 + 4.03843i) q^{73} +(-0.355428 + 0.120412i) q^{74} +(6.41041 - 3.70105i) q^{75} +(13.1715 - 1.71785i) q^{76} +(5.93432 + 2.18944i) q^{77} +(5.83159 - 6.64154i) q^{78} +(-0.308249 - 0.533903i) q^{79} +(-2.12264 - 0.574271i) q^{80} +(3.59024 - 6.21848i) q^{81} +(-8.66754 - 1.72953i) q^{82} +1.09948i q^{83} +(6.11550 + 5.66711i) q^{84} +2.31720i q^{85} +(-1.48063 + 7.42014i) q^{86} +(-6.47374 + 11.2129i) q^{87} +(-2.97977 - 6.07013i) q^{88} +(3.19779 + 5.53873i) q^{89} +(0.302212 + 0.265356i) q^{90} +(-1.77694 - 10.3426i) q^{91} +(0.607546 + 4.65834i) q^{92} +(1.18198 - 0.682416i) q^{93} +(-1.17917 - 3.48065i) q^{94} +(-1.82555 + 3.16195i) q^{95} +(-0.556038 - 8.89590i) q^{96} +12.9475 q^{97} +(9.79797 - 1.41414i) q^{98} +1.23675i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 2 q^{2} - 8 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{10} - 2 q^{12} - 16 q^{14} - 20 q^{15} + 8 q^{16} - 2 q^{17} + 6 q^{18} + 8 q^{20} + 12 q^{22} + 2 q^{23} + 18 q^{24} - 4 q^{25} - 2 q^{26} + 26 q^{28}+ \cdots + 52 q^{98}+O(q^{100})$ 12 * q - 2 * q^2 - 8 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^10 - 2 * q^12 - 16 * q^14 - 20 * q^15 + 8 * q^16 - 2 * q^17 + 6 * q^18 + 8 * q^20 + 12 * q^22 + 2 * q^23 + 18 * q^24 - 4 * q^25 - 2 * q^26 + 26 * q^28 + 14 * q^30 + 10 * q^31 - 12 * q^32 - 14 * q^33 + 32 * q^34 - 32 * q^36 + 18 * q^38 + 4 * q^39 + 10 * q^40 - 8 * q^41 + 22 * q^42 - 30 * q^44 - 4 * q^46 + 30 * q^47 - 56 * q^48 - 12 * q^49 - 16 * q^50 - 32 * q^52 + 2 * q^54 + 4 * q^55 - 40 * q^56 - 4 * q^57 - 22 * q^58 + 6 * q^60 - 28 * q^62 + 44 * q^63 + 24 * q^64 + 8 * q^65 - 38 * q^66 + 4 * q^68 - 48 * q^70 + 32 * q^71 + 20 * q^72 - 10 * q^73 + 18 * q^74 + 52 * q^76 + 52 * q^78 - 22 * q^79 + 36 * q^80 + 22 * q^81 - 26 * q^82 + 56 * q^84 + 40 * q^86 - 20 * q^87 - 14 * q^88 - 10 * q^89 + 52 * q^90 - 20 * q^92 + 42 * q^94 - 34 * q^95 + 16 * q^96 + 40 * q^97 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$ .

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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

)

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

$2$	1.38687	+	0.276739i	0.980667	+	0.195684i
$2$	1.38687	+	0.276739i	0.980667	+	0.195684i
$3$	−1.36456	−	0.787829i	−0.787829	−	0.454853i	0.0513689	−	0.998680i	$-0.483642\pi$
$3$	−1.36456	−	0.787829i	−0.787829	−	0.454853i	−0.839198	+	0.543827i	$0.816975\pi$
$4$	1.84683	+	0.767603i	0.923416	+	0.383801i
$5$	−0.476087	+	0.274869i	−0.212913	+	0.122925i	−0.602664	−	0.797995i	$-0.705894\pi$
$5$	−0.476087	+	0.274869i	−0.212913	+	0.122925i	0.389752	+	0.920920i	$0.372561\pi$
$6$	−1.67445	−	1.47024i	−0.683590	−	0.600225i
$7$	−2.60755	+	0.447998i	−0.985560	+	0.169327i
$7$	−2.60755	+	0.447998i	−0.985560	+	0.169327i
$8$	2.34889	+	1.57566i	0.830460	+	0.557079i
$9$	−0.258652	−	0.447998i	−0.0862173	−	0.149333i
$10$	−0.736339	+	0.249456i	−0.232851	+	0.0788850i
$11$	−2.07045	−	1.19538i	−0.624265	−	0.360419i	0.154263	−	0.988030i	$-0.450700\pi$
$11$	−2.07045	−	1.19538i	−0.624265	−	0.360419i	−0.778527	+	0.627611i	$0.784033\pi$
$12$	−1.91537	−	2.50243i	−0.552920	−	0.722388i
$13$			3.96641i			1.10008i	0.835137	+	0.550042i	$0.185388\pi$
$13$			3.96641i			1.10008i	−0.835137	+	0.550042i	$0.814612\pi$
$14$	−3.74031	−	0.100292i	−0.999641	−	0.0268043i
$15$	0.866198			0.223651
$16$	2.82157	+	2.83527i	0.705393	+	0.708817i
$17$	2.10755	−	3.65038i	0.511155	−	0.885347i	−0.488761	−	0.872418i	$-0.662551\pi$
$17$	2.10755	−	3.65038i	0.511155	−	0.885347i	0.999916	−	0.0129290i	$-0.00411554\pi$
$18$	−0.234739	−	0.692896i	−0.0553285	−	0.163317i
$19$	5.75174	−	3.32077i	1.31954	−	0.761837i	0.335886	−	0.941903i	$-0.390964\pi$
$19$	5.75174	−	3.32077i	1.31954	−	0.761837i	0.983655	+	0.180066i	$0.0576310\pi$
$20$	−1.09024	+	0.142191i	−0.243786	+	0.0317948i
$21$	3.91110	+	1.44298i	0.853471	+	0.314884i
$22$	−2.54065	−	2.23081i	−0.541667	−	0.475610i
$23$	1.17445	+	2.03420i	0.244889	+	0.424160i	0.962100	−	0.272695i	$-0.0879151\pi$
$23$	1.17445	+	2.03420i	0.244889	+	0.424160i	−0.717211	+	0.696856i	$0.754582\pi$
$24$	−1.96386	−	4.00060i	−0.400871	−	0.816620i
$25$	−2.34889	+	4.06840i	−0.469779	+	0.813681i
$26$	−1.09766	+	5.50090i	−0.215269	+	1.07882i
$27$			5.54207i			1.06657i
$28$	−5.15958	−	1.17418i	−0.975070	−	0.221900i
$29$		−	8.21720i		−	1.52590i	−0.646460	−	0.762948i	$-0.723751\pi$
$29$		−	8.21720i		−	1.52590i	0.646460	−	0.762948i	$-0.276249\pi$
$30$	1.20131	+	0.239711i	0.219328	+	0.0437650i
$31$	−0.433099	+	0.750150i	−0.0777869	+	0.134731i	−0.902295	−	0.431120i	$-0.858119\pi$
$31$	−0.433099	+	0.750150i	−0.0777869	+	0.134731i	0.824508	+	0.565850i	$0.191452\pi$
$32$	3.12853	+	4.71299i	0.553052	+	0.833147i
$33$	1.88350	+	3.26232i	0.327876	+	0.567897i
$34$	3.93310	−	4.47937i	0.674521	−	0.768205i
$35$	1.11828	−	0.930019i	0.189023	−	0.157202i
$36$	−0.133802	−	1.02592i	−0.0223003	−	0.170987i
$37$	−0.229805	+	0.132678i	−0.0377797	+	0.0218121i	−0.518771	−	0.854913i	$-0.673610\pi$
$37$	−0.229805	+	0.132678i	−0.0377797	+	0.0218121i	0.480991	+	0.876725i	$0.340277\pi$
$38$	8.89592	−	3.01376i	1.44311	−	0.488896i
$39$	3.12485	−	5.41240i	0.500377	−	0.866678i
$40$	−1.55138	−	0.104512i	−0.245294	−	0.0165248i
$41$	−6.24970			−0.976039			−0.488020	−	0.872833i	$-0.662281\pi$
$41$	−6.24970			−0.976039			−0.488020	+	0.872833i	$0.662281\pi$
$42$	5.02487	+	3.08358i	0.775354	+	0.475807i
$43$			5.35027i			0.815908i	0.913003	+	0.407954i	$0.133758\pi$
$43$			5.35027i			0.815908i	−0.913003	+	0.407954i	$0.866242\pi$
$44$	−2.90620	−	3.79694i	−0.438126	−	0.572410i
$45$	0.246282	+	0.142191i	0.0367135	+	0.0211965i
$46$	1.06587	+	3.14619i	0.157153	+	0.463881i
$47$	−1.29930	−	2.25045i	−0.189522	−	0.328262i	0.755569	−	0.655069i	$-0.227361\pi$
$47$	−1.29930	−	2.25045i	−0.189522	−	0.328262i	−0.945091	+	0.326807i	$0.894027\pi$
$48$	−1.61650	−	6.09180i	−0.233321	−	0.879276i
$49$	6.59859	−	2.33635i	0.942656	−	0.333765i
$50$	−4.38350	+	4.99233i	−0.619921	+	0.706022i
$51$	−5.75174	+	3.32077i	−0.805405	+	0.465001i
$52$	−3.04463	+	7.32529i	−0.422214	+	1.01583i
$53$	−9.36933	−	5.40939i	−1.28698	−	0.743037i	−0.308863	−	0.951107i	$-0.599948\pi$
$53$	−9.36933	−	5.40939i	−1.28698	−	0.743037i	−0.978114	+	0.208070i	$0.933282\pi$
$54$	−1.53370	+	7.68614i	−0.208711	+	1.04595i
$55$	1.31429			0.177218
$56$	−6.83074	−	3.05630i	−0.912796	−	0.408415i
$57$	−10.4648			−1.38610
$58$	2.27402	−	11.3962i	0.298593	−	1.49640i
$59$	−3.26891	−	1.88730i	−0.425575	−	0.245706i	0.271884	−	0.962330i	$-0.412353\pi$
$59$	−3.26891	−	1.88730i	−0.425575	−	0.245706i	−0.697460	+	0.716624i	$0.745686\pi$
$60$	1.59972	+	0.664896i	0.206523	+	0.0858377i
$61$	−6.18061	+	3.56837i	−0.791345	+	0.456884i	−0.840436	−	0.541911i	$-0.817701\pi$
$61$	−6.18061	+	3.56837i	−0.791345	+	0.456884i	0.0490905	+	0.998794i	$0.484368\pi$
$62$	−0.808249	+	0.920507i	−0.102648	+	0.116904i
$63$	0.875150	+	1.05230i	0.110259	+	0.132577i
$64$	3.03461	+	7.40210i	0.379326	+	0.925263i
$65$	−1.09024	−	1.88835i	−0.135228	−	0.234222i
$66$	1.70937	+	5.04566i	0.210409	+	0.621078i
$67$	2.31673	+	1.33757i	0.283034	+	0.163410i	0.634796	−	0.772680i	$-0.281084\pi$
$67$	2.31673	+	1.33757i	0.283034	+	0.163410i	−0.351762	+	0.936089i	$0.614417\pi$
$68$	6.69432	−	5.12387i	0.811806	−	0.621361i
$69$		−	3.70105i		−	0.445554i
$70$	1.80828	−	0.980348i	0.216131	−	0.117174i
$71$	8.76700			1.04045			0.520226	−	0.854029i	$-0.325848\pi$
$71$	8.76700			1.04045			0.520226	+	0.854029i	$0.325848\pi$
$72$	0.0983458	−	1.45985i	0.0115902	−	0.172045i
$73$	−2.33159	+	4.03843i	−0.272892	+	0.472663i	−0.969601	−	0.244691i	$-0.921313\pi$
$73$	−2.33159	+	4.03843i	−0.272892	+	0.472663i	0.696709	+	0.717354i	$0.254647\pi$
$74$	−0.355428	+	0.120412i	−0.0413176	+	0.0139976i
$75$	6.41041	−	3.70105i	0.740210	−	0.427361i
$76$	13.1715	−	1.71785i	1.51088	−	0.197051i
$77$	5.93432	+	2.18944i	0.676279	+	0.249510i
$78$	5.83159	−	6.64154i	0.660298	−	0.752006i
$79$	−0.308249	−	0.533903i	−0.0346807	−	0.0600687i	0.848164	−	0.529734i	$-0.177708\pi$
$79$	−0.308249	−	0.533903i	−0.0346807	−	0.0600687i	−0.882845	+	0.469665i	$0.844375\pi$
$80$	−2.12264	−	0.574271i	−0.237318	−	0.0642054i
$81$	3.59024	−	6.21848i	0.398916	−	0.690942i
$82$	−8.66754	−	1.72953i	−0.957170	−	0.190995i
$83$			1.09948i			0.120683i	0.998178	+	0.0603416i	$0.0192190\pi$
$83$			1.09948i			0.120683i	−0.998178	+	0.0603416i	$0.980781\pi$
$84$	6.11550	+	5.66711i	0.667256	+	0.618332i
$85$			2.31720i			0.251335i
$86$	−1.48063	+	7.42014i	−0.159660	+	0.800134i
$87$	−6.47374	+	11.2129i	−0.694058	+	1.20214i
$88$	−2.97977	−	6.07013i	−0.317644	−	0.647078i
$89$	3.19779	+	5.53873i	0.338965	+	0.587104i	0.984238	−	0.176847i	$-0.0565899\pi$
$89$	3.19779	+	5.53873i	0.338965	+	0.587104i	−0.645273	+	0.763952i	$0.723257\pi$
$90$	0.302212	+	0.265356i	0.0318559	+	0.0279710i
$91$	−1.77694	−	10.3426i	−0.186274	−	1.08420i
$92$	0.607546	+	4.65834i	0.0633411	+	0.485665i
$93$	1.18198	−	0.682416i	0.122565	−	0.0707632i
$94$	−1.17917	−	3.48065i	−0.121622	−	0.359002i
$95$	−1.82555	+	3.16195i	−0.187298	+	0.324409i
$96$	−0.556038	−	8.89590i	−0.0567504	−	0.907934i
$97$	12.9475			1.31462			0.657309	−	0.753621i	$-0.271695\pi$
$97$	12.9475			1.31462			0.657309	+	0.753621i	$0.271695\pi$
$98$	9.79797	−	1.41414i	0.989744	−	0.142849i
$99$			1.23675i			0.124298i
$100$	−7.46093	+	5.71064i	−0.746093	+	0.571064i
$101$	13.7565	+	7.94233i	1.36882	+	0.790291i	0.990778	−	0.135495i	$-0.0432625\pi$
$101$	13.7565	+	7.94233i	1.36882	+	0.790291i	0.378047	+	0.925787i	$0.376596\pi$
$102$	−8.89592	+	3.01376i	−0.880827	+	0.298406i
$103$	−9.38954	−	16.2632i	−0.925179	−	1.60246i	−0.791273	−	0.611463i	$-0.790581\pi$
$103$	−9.38954	−	16.2632i	−0.925179	−	1.60246i	−0.133906	−	0.990994i	$-0.542752\pi$
$104$	−6.24970	+	9.31667i	−0.612834	+	0.913575i
$105$	−2.25865	+	0.388055i	−0.220422	+	0.0378703i
$106$	−11.4971	−	10.0950i	−1.11670	−	0.980512i
$107$	0.293506	−	0.169456i	0.0283743	−	0.0163819i	−0.485746	−	0.874100i	$-0.661452\pi$
$107$	0.293506	−	0.169456i	0.0283743	−	0.0163819i	0.514120	+	0.857718i	$0.328119\pi$
$108$	−4.25411	+	10.2353i	−0.409352	+	0.984888i
$109$	6.75910	+	3.90237i	0.647404	+	0.373779i	0.787461	−	0.616365i	$-0.211395\pi$
$109$	6.75910	+	3.90237i	0.647404	+	0.373779i	−0.140057	+	0.990143i	$0.544729\pi$
$110$	1.82275	+	0.363714i	0.173792	+	0.0346788i
$111$	0.418110			0.0396853
$112$	−8.62757	−	6.12903i	−0.815229	−	0.579139i
$113$	2.51730			0.236808			0.118404	−	0.992966i	$-0.462222\pi$
$113$	2.51730			0.236808			0.118404	+	0.992966i	$0.462222\pi$
$114$	−14.5133	−	2.89601i	−1.35930	−	0.271237i
$115$	−1.11828	−	0.645638i	−0.104280	−	0.0602060i
$116$	6.30755	−	15.1758i	0.585641	−	1.40904i
$117$	1.77694	−	1.02592i	0.164279	−	0.0948463i
$118$	−4.01127	−	3.52208i	−0.369267	−	0.324234i
$119$	−3.86016	+	10.4627i	−0.353860	+	0.959115i
$120$	2.03461	+	1.36483i	0.185733	+	0.124592i
$121$	−2.64215	−	4.57635i	−0.240196	−	0.416031i
$122$	−9.55922	+	3.23847i	−0.865451	+	0.293197i
$123$	8.52809	+	4.92369i	0.768952	+	0.443954i
$124$	−1.37568	+	1.05295i	−0.123540	+	0.0945579i
$125$		−	5.33124i		−	0.476841i
$126$	0.922509	+	1.70160i	0.0821836	+	0.151590i
$127$	−5.30221			−0.470495			−0.235248	−	0.971935i	$-0.575590\pi$
$127$	−5.30221			−0.470495			−0.235248	+	0.971935i	$0.575590\pi$
$128$	2.16017	+	11.1056i	0.190933	+	0.981603i
$129$	4.21509	−	7.30075i	0.371118	−	0.642796i
$130$	−0.989446	−	2.92062i	−0.0867802	−	0.256155i
$131$	−8.69419	+	5.01959i	−0.759615	+	0.438564i	−0.829157	−	0.559015i	$-0.811179\pi$
$131$	−8.69419	+	5.01959i	−0.759615	+	0.438564i	0.0695425	+	0.997579i	$0.477846\pi$
$132$	0.974343	+	7.47074i	0.0848057	+	0.650244i
$133$	−13.5102	+	11.2358i	−1.17149	+	0.974270i
$134$	2.84286	+	2.49616i	0.245585	+	0.215636i
$135$	−1.52334	−	2.63850i	−0.131108	−	0.227086i
$136$	10.7021	−	5.25358i	0.917702	−	0.450491i
$137$	−1.62485	+	2.81432i	−0.138820	+	0.240444i	−0.927050	−	0.374937i	$-0.877664\pi$
$137$	−1.62485	+	2.81432i	−0.138820	+	0.240444i	0.788230	+	0.615381i	$0.210998\pi$
$138$	1.02422	−	5.13289i	0.0871878	−	0.436940i
$139$		−	15.3349i		−	1.30069i	−0.759639	−	0.650346i	$-0.774624\pi$
$139$		−	15.3349i		−	1.30069i	0.759639	−	0.650346i	$-0.225376\pi$
$140$	2.77916	−	0.859196i	0.234882	−	0.0726153i
$141$			4.09449i			0.344819i
$142$	12.1587	+	2.42617i	1.02034	+	0.203600i
$143$	4.74135	−	8.21226i	0.396491	−	0.686743i
$144$	0.540390	−	1.99741i	0.0450325	−	0.166451i
$145$	2.25865	+	3.91210i	0.187571	+	0.324882i
$146$	−4.35121	+	4.95555i	−0.360109	+	0.410124i
$147$	−10.8448	−	2.01047i	−0.894466	−	0.165821i
$148$	−0.526255	+	0.0686349i	−0.0432579	+	0.00564175i
$149$	6.39393	−	3.69154i	0.523812	−	0.302423i	−0.214681	−	0.976684i	$-0.568871\pi$
$149$	6.39393	−	3.69154i	0.523812	−	0.302423i	0.738493	+	0.674261i	$0.235538\pi$
$150$	9.91465	−	3.35888i	0.809528	−	0.274251i
$151$	−4.16550	+	7.21485i	−0.338983	+	0.587136i	−0.984242	−	0.176828i	$-0.943416\pi$
$151$	−4.16550	+	7.21485i	−0.338983	+	0.587136i	0.645259	+	0.763964i	$0.276750\pi$
$152$	18.7426	+	1.26264i	1.52023	+	0.102413i
$153$	−2.18048			−0.176282
$154$	7.62425	+	4.67873i	0.614379	+	0.377023i
$155$		−	0.476182i		−	0.0382478i
$156$	9.92564	−	7.59714i	0.794688	−	0.608258i
$157$	−6.18061	−	3.56837i	−0.493266	−	0.284787i	0.232662	−	0.972558i	$-0.425256\pi$
$157$	−6.18061	−	3.56837i	−0.493266	−	0.284787i	−0.725928	+	0.687770i	$0.758590\pi$
$158$	−0.279750	−	0.825759i	−0.0222557	−	0.0656939i
$159$	8.52334	+	14.7629i	0.675945	+	1.17077i
$160$	−2.78491	−	1.38386i	−0.220166	−	0.109404i
$161$	−3.97374	−	4.77813i	−0.313175	−	0.376569i
$162$	6.70010	−	7.63068i	0.526410	−	0.599523i
$163$	6.33023	−	3.65476i	0.495822	−	0.286263i	−0.231164	−	0.972915i	$-0.574254\pi$
$163$	6.33023	−	3.65476i	0.495822	−	0.286263i	0.726987	+	0.686652i	$0.240920\pi$
$164$	−11.5421	−	4.79729i	−0.901290	−	0.374605i
$165$	−1.79342	−	1.03543i	−0.139618	−	0.0806083i
$166$	−0.304268	+	1.52483i	−0.0236157	+	0.118350i
$167$	1.88873			0.146154			0.0730772	−	0.997326i	$-0.476718\pi$
$167$	1.88873			0.146154			0.0730772	+	0.997326i	$0.476718\pi$
$168$	6.91311	+	9.55195i	0.533358	+	0.736949i
$169$	−2.73240			−0.210184
$170$	−0.641258	+	3.21365i	−0.0491822	+	0.246476i
$171$	−2.97540	−	1.71785i	−0.227535	−	0.131367i
$172$	−4.10688	+	9.88104i	−0.313147	+	0.753422i
$173$	−14.3350	+	8.27632i	−1.08987	+	0.629237i	−0.933542	−	0.358468i	$-0.883299\pi$
$173$	−14.3350	+	8.27632i	−1.08987	+	0.629237i	−0.156329	+	0.987705i	$0.549966\pi$
$174$	−12.0813	+	13.7593i	−0.915880	+	1.04309i
$175$	4.30221	−	11.6609i	0.325217	−	0.881478i
$176$	−2.45272	−	9.24312i	−0.184881	−	0.696726i
$177$	2.97374	+	5.15068i	0.223520	+	0.387149i
$178$	2.90214	+	8.56647i	0.217525	+	0.642084i
$179$	4.79957	+	2.77103i	0.358737	+	0.207117i	0.668526	−	0.743688i	$-0.266925\pi$
$179$	4.79957	+	2.77103i	0.358737	+	0.207117i	−0.309790	+	0.950805i	$0.600259\pi$
$180$	0.345695	+	0.451649i	0.0257666	+	0.0336639i
$181$		−	9.98466i		−	0.742154i	−0.928602	−	0.371077i	$-0.878989\pi$
$181$		−	9.98466i		−	0.742154i	0.928602	−	0.371077i	$-0.121011\pi$
$182$	0.397801	−	14.8356i	0.0294870	−	1.09969i
$183$	11.2451			0.831259
$184$	−0.446553	+	6.62865i	−0.0329203	+	0.488671i
$185$	0.0729381	−	0.126333i	0.00536252	−	0.00928816i
$186$	1.82811	−	0.619324i	0.134043	−	0.0454111i
$187$	−8.72714	+	5.03862i	−0.638192	+	0.368460i
$188$	−0.672132	−	5.15354i	−0.0490202	−	0.375861i
$189$	−2.48284	−	14.4512i	−0.180600	−	1.05117i
$190$	−3.40684	+	3.88002i	−0.247158	+	0.281486i
$191$	−0.0842049	−	0.145847i	−0.00609285	−	0.0105531i	0.862963	−	0.505267i	$-0.168606\pi$
$191$	−0.0842049	−	0.145847i	−0.00609285	−	0.0105531i	−0.869056	+	0.494714i	$0.835273\pi$
$192$	1.69069	−	12.4914i	0.122015	−	0.901486i
$193$	−3.75865	+	6.51018i	−0.270554	+	0.468613i	−0.969004	−	0.247046i	$-0.920540\pi$
$193$	−3.75865	+	6.51018i	−0.270554	+	0.468613i	0.698450	+	0.715659i	$0.253873\pi$
$194$	17.9565	+	3.58307i	1.28920	+	0.257250i
$195$			3.43570i			0.246035i
$196$	13.9799	+	0.750250i	0.998563	+	0.0535893i
$197$		−	1.34581i		−	0.0958847i	−0.998850	−	0.0479424i	$-0.984734\pi$
$197$		−	1.34581i		−	0.0958847i	0.998850	−	0.0479424i	$-0.0152664\pi$
$198$	−0.342255	+	1.71521i	−0.0243230	+	0.121895i
$199$	6.38059	−	11.0515i	0.452308	−	0.783420i	−0.546221	−	0.837641i	$-0.683934\pi$
$199$	6.38059	−	11.0515i	0.452308	−	0.783420i	0.998529	+	0.0542208i	$0.0172675\pi$
$200$	−11.9277	+	5.85520i	−0.843417	+	0.414025i
$201$	−2.10755	−	3.65038i	−0.148655	−	0.257478i
$202$	16.8806	+	14.8220i	1.18771	+	1.04287i
$203$	3.68129	+	21.4267i	0.258376	+	1.50386i
$204$	−13.1715	+	1.71785i	−0.922192	+	0.120273i
$205$	2.97540	−	1.71785i	0.207811	−	0.119980i
$206$	−8.52145	−	25.1534i	−0.593717	−	1.75252i
$207$	0.607546	−	1.05230i	0.0422274	−	0.0731400i
$208$	−11.2458	+	11.1915i	−0.779758	+	0.775991i
$209$	−15.8783			−1.09832
$210$	−3.23985	−	0.0868731i	−0.223571	−	0.00599482i
$211$			8.46353i			0.582653i	0.956624	+	0.291327i	$0.0940967\pi$
$211$			8.46353i			0.582653i	−0.956624	+	0.291327i	$0.905903\pi$
$212$	−13.1513	−	17.1822i	−0.903236	−	1.18008i
$213$	−11.9631	−	6.90690i	−0.819698	−	0.473253i
$214$	0.453951	−	0.153789i	0.0310315	−	0.0105128i
$215$	−1.47062	−	2.54719i	−0.100296	−	0.173717i
$216$	−8.73240	+	13.0177i	−0.594164	+	0.885744i
$217$	0.793260	−	2.15008i	0.0538500	−	0.145957i
$218$	8.29407	+	7.28259i	0.561745	+	0.493239i
$219$	6.36319	−	3.67379i	0.429984	−	0.248252i
$220$	2.42726	+	1.00885i	0.163646	+	0.0680166i
$221$	14.4789	+	8.35939i	0.973955	+	0.562313i
$222$	0.579866	+	0.115707i	0.0389180	+	0.00776577i
$223$	−5.80161			−0.388505			−0.194252	−	0.980952i	$-0.562228\pi$
$223$	−5.80161			−0.388505			−0.194252	+	0.980952i	$0.562228\pi$
$224$	−10.2692	−	10.8878i	−0.686140	−	0.727469i
$225$	2.43018			0.162012
$226$	3.49118	+	0.696636i	0.232230	+	0.0463395i
$227$	9.89265	+	5.71152i	0.656598	+	0.379087i	0.790980	−	0.611843i	$-0.209571\pi$
$227$	9.89265	+	5.71152i	0.656598	+	0.379087i	−0.134382	+	0.990930i	$0.542905\pi$
$228$	−19.3267	−	8.03281i	−1.27994	−	0.531986i
$229$	16.0260	−	9.25263i	1.05903	−	0.611431i	0.133866	−	0.990999i	$-0.457261\pi$
$229$	16.0260	−	9.25263i	1.05903	−	0.611431i	0.925164	+	0.379568i	$0.123928\pi$
$230$	−1.37224	−	1.20489i	−0.0904825	−	0.0794480i
$231$	−6.37283	−	7.66285i	−0.419302	−	0.504178i
$232$	12.9475	−	19.3013i	0.850044	−	1.26719i
$233$	5.52566	+	9.57072i	0.361998	+	0.626999i	0.988290	−	0.152590i	$-0.0487615\pi$
$233$	5.52566	+	9.57072i	0.361998	+	0.626999i	−0.626292	+	0.779589i	$0.715428\pi$
$234$	2.74831	−	0.931070i	0.179663	−	0.0608660i
$235$	1.23716	+	0.714273i	0.0807032	+	0.0465940i
$236$	−4.58842	−	5.99475i	−0.298681	−	0.390225i
$237$			0.971389i			0.0630985i
$238$	−8.24899	+	13.4422i	−0.534702	+	0.871327i
$239$	−22.6107			−1.46256			−0.731281	−	0.682076i	$-0.761077\pi$
$239$	−22.6107			−1.46256			−0.731281	+	0.682076i	$0.761077\pi$
$240$	2.44404	+	2.45590i	0.157762	+	0.158528i
$241$	−6.96479	+	12.0634i	−0.448642	+	0.777070i	−0.998298	−	0.0583207i	$-0.981425\pi$
$241$	−6.96479	+	12.0634i	−0.448642	+	0.777070i	0.549656	+	0.835391i	$0.314759\pi$
$242$	−2.39788	−	7.07799i	−0.154142	−	0.454991i
$243$	4.60051	−	2.65611i	0.295123	−	0.170389i
$244$	−14.1536	+	1.84593i	−0.906093	+	0.118174i
$245$	−2.49931	+	2.92606i	−0.159675	+	0.186939i
$246$	10.4648	+	9.18859i	0.667211	+	0.585843i
$247$	13.1715	+	22.8138i	0.838085	+	1.45161i
$248$	−2.19928	+	1.07961i	−0.139655	+	0.0685551i
$249$	0.866198	−	1.50030i	0.0548931	−	0.0950776i
$250$	1.47536	−	7.39375i	0.0933100	−	0.467622i
$251$			0.706033i			0.0445644i	0.999752	+	0.0222822i	$0.00709323\pi$
$251$			0.706033i			0.0445644i	−0.999752	+	0.0222822i	$0.992907\pi$
$252$	0.808505	+	2.61519i	0.0509310	+	0.164741i
$253$		−	5.61562i		−	0.353051i
$254$	−7.35349	−	1.46733i	−0.461399	−	0.0920683i
$255$	1.82555	−	3.16195i	0.114321	−	0.198009i
$256$	−0.0774679	+	15.9998i	−0.00484175	+	0.999988i
$257$	−10.3919	−	17.9992i	−0.648226	−	1.12276i	−0.983546	−	0.180656i	$-0.942178\pi$
$257$	−10.3919	−	17.9992i	−0.648226	−	1.12276i	0.335320	−	0.942104i	$-0.391156\pi$
$258$	7.86620	−	8.95874i	0.489728	−	0.557747i
$259$	0.539788	−	0.448917i	0.0335408	−	0.0278943i
$260$	−0.563987	−	4.32435i	−0.0349770	−	0.268185i
$261$	−3.68129	+	2.12540i	−0.227866	+	0.131559i
$262$	−13.4469	+	4.55552i	−0.830749	+	0.281441i
$263$	11.3895	−	19.7273i	0.702309	−	1.21644i	−0.265345	−	0.964154i	$-0.585486\pi$
$263$	11.3895	−	19.7273i	0.702309	−	1.21644i	0.967654	−	0.252281i	$-0.0811809\pi$
$264$	−0.716153	+	10.6306i	−0.0440762	+	0.654268i
$265$	5.94749			0.365351
$266$	−21.8464	+	11.8439i	−1.33949	+	0.726194i
$267$		−	10.0772i		−	0.616717i
$268$	3.25189	+	4.24859i	0.198641	+	0.259524i
$269$	2.59376	+	1.49751i	0.158145	+	0.0913048i	0.576984	−	0.816756i	$-0.304230\pi$
$269$	2.59376	+	1.49751i	0.158145	+	0.0913048i	−0.418839	+	0.908060i	$0.637563\pi$
$270$	−1.38250	−	4.08084i	−0.0841365	−	0.248352i
$271$	12.5926	+	21.8109i	0.764943	+	1.32492i	0.940277	+	0.340412i	$0.110566\pi$
$271$	12.5926	+	21.8109i	0.764943	+	1.32492i	−0.175333	+	0.984509i	$0.556100\pi$
$272$	16.2964	−	4.32435i	0.988113	−	0.262202i
$273$	−5.72345	+	15.5130i	−0.346399	+	0.938890i
$274$	−3.03229	+	3.45345i	−0.183188	+	0.208630i
$275$	9.72654	−	5.61562i	0.586533	−	0.338635i
$276$	2.84094	−	6.83522i	0.171004	−	0.411432i
$277$	8.17940	+	4.72238i	0.491453	+	0.283740i	0.725177	−	0.688563i	$-0.241758\pi$
$277$	8.17940	+	4.72238i	0.491453	+	0.283740i	−0.233724	+	0.972303i	$0.575091\pi$
$278$	4.24377	−	21.2676i	0.254524	−	1.27554i
$279$	0.448088			0.0268263
$280$	4.09211	−	0.422495i	0.244550	−	0.0252489i
$281$	26.8425			1.60129			0.800644	−	0.599141i	$-0.204491\pi$
$281$	26.8425			1.60129			0.800644	+	0.599141i	$0.204491\pi$
$282$	−1.13311	+	5.67854i	−0.0674755	+	0.338152i
$283$	11.2429	+	6.49111i	0.668323	+	0.385856i	0.795441	−	0.606031i	$-0.207239\pi$
$283$	11.2429	+	6.49111i	0.668323	+	0.385856i	−0.127118	+	0.991888i	$0.540573\pi$
$284$	16.1912	+	6.72958i	0.960770	+	0.399327i
$285$	4.98215	−	2.87645i	0.295117	−	0.170386i
$286$	8.84830	−	10.0772i	0.523211	−	0.595880i
$287$	16.2964	−	2.79986i	0.961945	−	0.165270i
$288$	1.30221	−	2.62060i	0.0767336	−	0.154420i
$289$	−0.383502	−	0.664245i	−0.0225590	−	0.0390733i
$290$	2.04983	+	6.05064i	0.120370	+	0.355306i
$291$	−17.6676	−	10.2004i	−1.03569	−	0.597958i
$292$	−7.40597	+	5.66857i	−0.433401	+	0.331728i
$293$			9.56300i			0.558677i	0.960193	+	0.279338i	$0.0901151\pi$
$293$			9.56300i			0.558677i	−0.960193	+	0.279338i	$0.909885\pi$
$294$	−14.4840	−	5.78945i	−0.844725	−	0.337647i
$295$	2.07504			0.120814
$296$	−0.748843	−	0.0504474i	−0.0435256	−	0.00293220i
$297$	6.62485	−	11.4746i	0.384413	−	0.665823i
$298$	9.88916	−	3.35025i	0.572864	−	0.194075i
$299$	−8.06848	+	4.65834i	−0.466612	+	0.269399i
$300$	14.6799	−	1.91457i	0.847544	−	0.110538i
$301$	−2.39691	−	13.9511i	−0.138156	−	0.804126i
$302$	−7.77364	+	8.85332i	−0.447323	+	0.509452i
$303$	−12.5144	−	21.6756i	−0.718933	−	1.24523i
$304$	25.6442	+	6.93793i	1.47080	+	0.397918i
$305$	1.96167	−	3.39771i	0.112325	−	0.194552i
$306$	−3.02405	−	0.603425i	−0.172874	−	0.0344955i
$307$		−	12.2217i		−	0.697527i	−0.937211	−	0.348763i	$-0.886602\pi$
$307$		−	12.2217i		−	0.697527i	0.937211	−	0.348763i	$-0.113398\pi$
$308$	9.27908	+	8.59873i	0.528724	+	0.489958i
$309$			29.5894i			1.68328i
$310$	0.131778	−	0.660404i	0.00748449	−	0.0375084i
$311$	−15.9415	+	27.6114i	−0.903957	+	1.56570i	−0.0816453	+	0.996661i	$0.526017\pi$
$311$	−15.9415	+	27.6114i	−0.903957	+	1.56570i	−0.822311	+	0.569038i	$0.807316\pi$
$312$	15.8680	−	7.78946i	0.898350	−	0.440991i
$313$	−10.7618	−	18.6399i	−0.608291	−	1.05359i	−0.991522	−	0.129939i	$-0.958522\pi$
$313$	−10.7618	−	18.6399i	−0.608291	−	1.05359i	0.383230	−	0.923653i	$-0.374811\pi$
$314$	−7.58420	−	6.65929i	−0.428001	−	0.375806i
$315$	−0.705892	−	0.260435i	−0.0397725	−	0.0146739i
$316$	−0.159458	−	1.22264i	−0.00897023	−	0.0687789i
$317$	−20.0481	+	11.5747i	−1.12601	+	0.650103i	−0.942929	−	0.332995i	$-0.891941\pi$
$317$	−20.0481	+	11.5747i	−1.12601	+	0.650103i	−0.183082	+	0.983098i	$0.558607\pi$
$318$	7.73533	+	22.8329i	0.433776	+	1.28041i
$319$	−9.82264	+	17.0133i	−0.549962	+	0.952562i
$320$	−3.47935	−	2.68993i	−0.194501	−	0.150371i
$321$	−0.534009			−0.0298055
$322$	−4.18878	−	7.72634i	−0.233432	−	0.430572i
$323$		−	27.9947i		−	1.55767i
$324$	11.4039	−	8.72861i	0.633550	−	0.484923i
$325$	−16.1370	−	9.31667i	−0.895117	−	0.516796i
$326$	9.79064	−	3.31687i	0.542253	−	0.183704i
$327$	−6.14879	−	10.6500i	−0.340029	−	0.588947i
$328$	−14.6799	−	9.84739i	−0.810561	−	0.543731i
$329$	4.39618	+	5.28607i	0.242369	+	0.291430i
$330$	−2.20070	−	1.93232i	−0.121145	−	0.106371i
$331$	−25.5615	+	14.7579i	−1.40499	+	0.811169i	−0.994899	−	0.100878i	$-0.967835\pi$
$331$	−25.5615	+	14.7579i	−1.40499	+	0.811169i	−0.410086	+	0.912047i	$0.634501\pi$
$332$	−0.843961	+	2.03055i	−0.0463184	+	0.111441i
$333$	0.118879	+	0.0686349i	0.00651454	+	0.00376117i
$334$	2.61943	+	0.522685i	0.143329	+	0.0286001i
$335$	−1.47062			−0.0803486
$336$	6.94421	+	15.1605i	0.378838	+	0.827071i
$337$	−3.28431			−0.178908			−0.0894538	−	0.995991i	$-0.528512\pi$
$337$	−3.28431			−0.178908			−0.0894538	+	0.995991i	$0.528512\pi$
$338$	−3.78949	−	0.756160i	−0.206121	−	0.0411297i
$339$	−3.43501	−	1.98320i	−0.186564	−	0.107713i
$340$	−1.77869	+	4.27947i	−0.0964628	+	0.232087i
$341$	1.79342	−	1.03543i	0.0971192	−	0.0560718i
$342$	−3.65111	−	3.20585i	−0.197429	−	0.173352i
$343$	−16.1595	+	9.04831i	−0.872529	+	0.488563i
$344$	−8.43018	+	12.5672i	−0.454525	+	0.677578i
$345$	1.01730	+	1.76202i	0.0547698	+	0.0948641i
$346$	−22.1712	+	7.51115i	−1.19193	+	0.403802i
$347$	−27.4329	−	15.8384i	−1.47267	−	0.850248i	−0.473146	−	0.880984i	$-0.656882\pi$
$347$	−27.4329	−	15.8384i	−1.47267	−	0.850248i	−0.999528	+	0.0307361i	$0.990215\pi$
$348$	−20.5629	+	15.7390i	−1.10229	+	0.843698i
$349$			28.4807i			1.52454i	0.647260	+	0.762269i	$0.275915\pi$
$349$			28.4807i			1.52454i	−0.647260	+	0.762269i	$0.724085\pi$
$350$	9.19363	−	14.9815i	0.491420	−	0.800796i
$351$	−21.9821			−1.17332
$352$	−0.843679	−	13.4978i	−0.0449682	−	0.719435i
$353$	−10.1196	+	17.5277i	−0.538613	+	0.932905i	0.460366	+	0.887729i	$0.347718\pi$
$353$	−10.1196	+	17.5277i	−0.538613	+	0.932905i	−0.998979	+	0.0451760i	$0.985615\pi$
$354$	2.69881	+	7.96628i	0.143440	+	0.423403i
$355$	−4.17386	+	2.40978i	−0.221525	+	0.127898i
$356$	1.65423	+	12.6837i	0.0876740	+	0.672237i
$357$	13.5102	−	11.2358i	0.715038	−	0.594663i
$358$	5.88954	+	5.17130i	0.311272	+	0.273312i
$359$	−12.5611	−	21.7564i	−0.662948	−	1.14826i	−0.979837	−	0.199797i	$-0.935972\pi$
$359$	−12.5611	−	21.7564i	−0.662948	−	1.14826i	0.316889	−	0.948463i	$-0.397362\pi$
$360$	0.354446	+	0.722047i	0.0186809	+	0.0380552i
$361$	12.5550	−	21.7460i	0.660791	−	1.14452i
$362$	2.76314	−	13.8474i	0.145228	−	0.727806i
$363$			8.32626i			0.437015i
$364$	4.65729	−	20.4650i	0.244108	−	1.07266i
$365$		−	2.56353i		−	0.134181i
$366$	15.5955	+	3.11195i	0.815189	+	0.162664i
$367$	15.1912	−	26.3118i	0.792972	−	1.37347i	−0.131147	−	0.991363i	$-0.541866\pi$
$367$	15.1912	−	26.3118i	0.792972	−	1.37347i	0.924119	−	0.382104i	$-0.124801\pi$
$368$	−2.45372	+	9.06952i	−0.127909	+	0.472781i
$369$	1.61650	+	2.79986i	0.0841515	+	0.145755i
$370$	0.136117	−	0.155022i	0.00707639	−	0.00805923i
$371$	26.8544	+	9.90778i	1.39421	+	0.514386i
$372$	2.70674	−	0.353016i	0.140338	−	0.0183031i
$373$	4.86327	−	2.80781i	0.251811	−	0.145383i	−0.368782	−	0.929516i	$-0.620225\pi$
$373$	4.86327	−	2.80781i	0.251811	−	0.145383i	0.620593	+	0.784133i	$0.286892\pi$
$374$	−13.4978	+	4.57278i	−0.697956	+	0.236453i
$375$	−4.20010	+	7.27479i	−0.216892	+	0.375669i
$376$	0.494024	−	7.33331i	0.0254774	−	0.378187i
$377$	32.5928			1.67861
$378$	0.555827	−	20.7291i	0.0285887	−	1.06619i
$379$			8.07009i			0.414533i	0.978285	+	0.207266i	$0.0664566\pi$
$379$			8.07009i			0.414533i	−0.978285	+	0.207266i	$0.933543\pi$
$380$	−5.79861	+	4.43829i	−0.297462	+	0.227679i
$381$	7.23518	+	4.17723i	0.370670	+	0.214006i
$382$	−0.0764199	−	0.225574i	−0.00390998	−	0.0115414i
$383$	12.8166	+	22.1990i	0.654898	+	1.13432i	0.981919	+	0.189299i	$0.0606216\pi$
$383$	12.8166	+	22.1990i	0.654898	+	1.13432i	−0.327022	+	0.945017i	$0.606045\pi$
$384$	5.80161	−	16.8560i	0.296062	−	0.860182i
$385$	−3.42706	+	0.588798i	−0.174659	+	0.0300079i
$386$	−7.01439	+	7.98862i	−0.357023	+	0.406610i
$387$	2.39691	−	1.38386i	0.121842	−	0.0703454i
$388$	23.9118	+	9.93853i	1.21394	+	0.504552i
$389$	−22.9905	−	13.2736i	−1.16566	−	0.672997i	−0.213010	−	0.977050i	$-0.568327\pi$
$389$	−22.9905	−	13.2736i	−1.16566	−	0.672997i	−0.952655	+	0.304053i	$0.901660\pi$
$390$	−0.950790	+	4.76487i	−0.0481451	+	0.241279i
$391$	9.90081			0.500705
$392$	19.1807	+	4.90928i	0.968771	+	0.247956i
$393$	15.8183			0.797929
$394$	0.372437	−	1.86646i	0.0187631	−	0.0940310i
$395$	0.293506	+	0.169456i	0.0147679	+	0.00852626i
$396$	−0.949329	+	2.28406i	−0.0477056	+	0.114778i
$397$	29.5283	−	17.0482i	1.48198	−	0.855624i	0.482192	−	0.876065i	$-0.339841\pi$
$397$	29.5283	−	17.0482i	1.48198	−	0.855624i	0.999791	+	0.0204418i	$0.00650729\pi$
$398$	11.9074	−	13.5613i	0.596866	−	0.679765i
$399$	27.2874	−	4.68821i	1.36608	−	0.234704i
$400$	−18.1626	+	4.81955i	−0.908129	+	0.240978i
$401$	−9.17676	−	15.8946i	−0.458266	−	0.793739i	0.540604	−	0.841277i	$-0.318196\pi$
$401$	−9.17676	−	15.8946i	−0.458266	−	0.793739i	−0.998869	+	0.0475379i	$0.984862\pi$
$402$	−1.91270	−	5.64585i	−0.0953967	−	0.281589i
$403$	−2.97540	−	1.71785i	−0.148215	−	0.0855721i
$404$	19.3094	+	25.2277i	0.960679	+	1.25512i
$405$			3.94738i			0.196147i
$406$	−0.824123	+	30.7349i	−0.0409005	+	1.52535i
$407$	0.634401			0.0314461
$408$	−18.7426	−	1.26264i	−0.927899	−	0.0625099i
$409$	−5.87455	+	10.1750i	−0.290478	+	0.503122i	−0.973923	−	0.226880i	$-0.927148\pi$
$409$	−5.87455	+	10.1750i	−0.290478	+	0.503122i	0.683445	+	0.730002i	$0.260481\pi$
$410$	4.60190	−	1.55903i	0.227271	−	0.0769949i
$411$	4.43441	−	2.56021i	0.218733	−	0.126286i
$412$	−4.85725	−	37.2427i	−0.239299	−	1.83482i
$413$	9.36933	+	3.45677i	0.461035	+	0.170096i
$414$	1.13380	−	1.29128i	0.0557233	−	0.0634627i
$415$	−0.302212	−	0.523446i	−0.0148350	−	0.0256949i
$416$	−18.6936	+	12.4090i	−0.916532	+	0.608403i
$417$	−12.0813	+	20.9254i	−0.591623	+	1.02472i
$418$	−22.0211	−	4.39413i	−1.07709	−	0.214924i
$419$			11.0841i			0.541495i	0.962650	+	0.270748i	$0.0872709\pi$
$419$			11.0841i			0.541495i	−0.962650	+	0.270748i	$0.912729\pi$
$420$	−4.46922	−	1.01707i	−0.218076	−	0.0496282i
$421$		−	0.137270i		−	0.00669012i	−0.999994	−	0.00334506i	$-0.998935\pi$
$421$		−	0.137270i		−	0.00669012i	0.999994	−	0.00334506i	$-0.00106477\pi$
$422$	−2.34219	+	11.7378i	−0.114016	+	0.571389i
$423$	−0.672132	+	1.16417i	−0.0326802	+	0.0566037i
$424$	−13.4842	−	27.4689i	−0.654852	−	1.33401i
$425$	9.90081	+	17.1487i	0.480260	+	0.831834i
$426$	−14.6799	−	12.8896i	−0.711243	−	0.624505i
$427$	14.5176	−	12.0736i	0.702555	−	0.584283i
$428$	0.672132	−	0.0876603i	0.0324887	−	0.00423722i
$429$	−12.9397	+	7.47074i	−0.624735	+	0.360691i
$430$	−1.33466	−	3.93961i	−0.0643629	−	0.189985i
$431$	−6.23008	+	10.7908i	−0.300092	+	0.519775i	−0.976157	−	0.217067i	$-0.930351\pi$
$431$	−6.23008	+	10.7908i	−0.300092	+	0.519775i	0.676064	+	0.736843i	$0.263684\pi$
$432$	−15.7132	+	15.6373i	−0.756003	+	0.752352i
$433$	−14.1563			−0.680310			−0.340155	−	0.940369i	$-0.610480\pi$
$433$	−14.1563			−0.680310			−0.340155	+	0.940369i	$0.610480\pi$
$434$	1.69516	−	2.76236i	0.0813703	−	0.132597i
$435$		−	7.11772i		−	0.341269i
$436$	9.48744	+	12.3953i	0.454366	+	0.593628i
$437$	13.5102	+	7.80014i	0.646282	+	0.373131i
$438$	9.84161	−	3.33413i	0.470250	−	0.159311i
$439$	2.72948	+	4.72760i	0.130271	+	0.225636i	0.923781	−	0.382921i	$-0.125082\pi$
$439$	2.72948	+	4.72760i	0.130271	+	0.225636i	−0.793510	+	0.608557i	$0.791749\pi$
$440$	3.08712	+	2.07086i	0.147173	+	0.0987246i
$441$	−2.75342	−	2.35186i	−0.131115	−	0.111993i
$442$	17.7670	+	15.6003i	0.845090	+	0.742030i
$443$	28.8691	−	16.6676i	1.37161	−	0.791900i	0.380480	−	0.924789i	$-0.375759\pi$
$443$	28.8691	−	16.6676i	1.37161	−	0.791900i	0.991131	+	0.132889i	$0.0424254\pi$
$444$	0.772179	+	0.320943i	0.0366460	+	0.0152313i
$445$	−3.04485	−	1.75794i	−0.144340	−	0.0833346i
$446$	−8.04610	−	1.60553i	−0.380994	−	0.0760241i
$447$	−11.6332			−0.550232
$448$	−11.2290	−	17.9418i	−0.530521	−	0.847672i
$449$	−26.9716			−1.27287			−0.636435	−	0.771330i	$-0.719592\pi$
$449$	−26.9716			−1.27287			−0.636435	+	0.771330i	$0.719592\pi$
$450$	3.37036	+	0.672526i	0.158880	+	0.0317032i
$451$	12.9397	+	7.47074i	0.609307	+	0.351783i
$452$	4.64904	+	1.93229i	0.218672	+	0.0908873i
$453$	11.3681	−	6.56339i	0.534121	−	0.308375i
$454$	12.1392	+	10.6588i	0.569723	+	0.500244i
$455$	3.68884	+	4.43555i	0.172935	+	0.207942i
$456$	−24.5807	−	16.4889i	−1.15110	−	0.772165i
$457$	−9.54668	−	16.5353i	−0.446575	−	0.773491i	0.551585	−	0.834118i	$-0.314023\pi$
$457$	−9.54668	−	16.5353i	−0.446575	−	0.773491i	−0.998160	+	0.0606278i	$0.980690\pi$
$458$	24.7866	−	8.39720i	1.15820	−	0.392375i
$459$	20.2306	+	11.6802i	0.944285	+	0.545183i
$460$	−1.56968	−	2.05078i	−0.0731865	−	0.0956180i
$461$		−	18.9177i		−	0.881087i	−0.897731	−	0.440543i	$-0.854786\pi$
$461$		−	18.9177i		−	0.881087i	0.897731	−	0.440543i	$-0.145214\pi$
$462$	−6.71770	−	12.3910i	−0.312536	−	0.576482i
$463$	0.860370			0.0399848			0.0199924	−	0.999800i	$-0.493636\pi$
$463$	0.860370			0.0399848			0.0199924	+	0.999800i	$0.493636\pi$
$464$	23.2979	−	23.1854i	1.08158	−	1.07636i
$465$	−0.375150	+	0.649778i	−0.0173972	+	0.0301328i
$466$	5.01479	+	14.8025i	0.232306	+	0.685714i
$467$	−16.1842	+	9.34394i	−0.748914	+	0.432386i	−0.825302	−	0.564692i	$-0.808995\pi$
$467$	−16.1842	+	9.34394i	−0.748914	+	0.432386i	0.0763871	+	0.997078i	$0.475662\pi$
$468$	4.06922	−	0.530712i	0.188100	−	0.0245322i
$469$	−6.64022	−	2.44987i	−0.306617	−	0.113125i
$470$	1.51811	+	1.33297i	0.0700253	+	0.0614855i
$471$	5.62253	+	9.73852i	0.259073	+	0.448727i
$472$	−4.70457	−	9.58375i	−0.216545	−	0.441128i
$473$	6.39558	−	11.0775i	0.294069	−	0.509342i
$474$	−0.268821	+	1.34719i	−0.0123474	+	0.0618786i
$475$			31.2006i			1.43158i
$476$	−15.1603	+	16.3598i	−0.694870	+	0.749849i
$477$			5.59660i			0.256251i
$478$	−31.3581	−	6.25725i	−1.43429	−	0.286200i
$479$	9.27364	−	16.0624i	0.423723	−	0.733911i	−0.572577	−	0.819851i	$-0.694056\pi$
$479$	9.27364	−	16.0624i	0.423723	−	0.733911i	0.996300	+	0.0859405i	$0.0273895\pi$
$480$	2.70993	+	4.08238i	0.123691	+	0.186335i
$481$	−0.526255	−	0.911501i	−0.0239952	−	0.0415609i
$482$	−12.9977	+	14.8029i	−0.592028	+	0.674255i
$483$	1.65807	+	9.65067i	0.0754446	+	0.439120i
$484$	−1.36680	−	10.4799i	−0.0621271	−	0.476357i
$485$	−6.16413	+	3.55886i	−0.279899	+	0.161600i
$486$	7.11537	−	2.41054i	0.322760	−	0.109344i
$487$	11.4588	−	19.8471i	0.519246	−	0.899360i	−0.480504	−	0.876993i	$-0.659546\pi$
$487$	11.4588	−	19.8471i	0.519246	−	0.899360i	0.999750	−	0.0223676i	$-0.00712041\pi$
$488$	−20.1401	−	1.35678i	−0.911701	−	0.0614187i
$489$	−11.5173			−0.520830
$490$	−4.27598	+	3.36641i	−0.193169	+	0.152079i
$491$		−	24.7987i		−	1.11915i	−0.828780	−	0.559575i	$-0.810964\pi$
$491$		−	24.7987i		−	1.11915i	0.828780	−	0.559575i	$-0.189036\pi$
$492$	11.9705	+	15.6394i	0.539672	+	0.705079i
$493$	−29.9959	−	17.3181i	−1.35095	−	0.779969i
$494$	11.9538	+	35.2849i	0.537826	+	1.58754i
$495$	−0.339943	−	0.588798i	−0.0152793	−	0.0264645i
$496$	−3.34889	+	0.888650i	−0.150370	+	0.0399016i
$497$	−22.8604	+	3.92760i	−1.02543	+	0.176177i
$498$	1.61650	−	1.84101i	0.0724370	−	0.0824978i
$499$	−33.9707	+	19.6130i	−1.52074	+	0.877997i	−0.521035	+	0.853535i	$0.674454\pi$
$499$	−33.9707	+	19.6130i	−1.52074	+	0.877997i	−0.999701	+	0.0244624i	$0.992213\pi$
$500$	4.09228	−	9.84590i	0.183012	−	0.440322i
$501$	−2.57729	−	1.48800i	−0.115145	−	0.0664788i
$502$	−0.195387	+	0.979178i	−0.00872054	+	0.0437028i
$503$	7.59396			0.338598			0.169299	−	0.985565i	$-0.445850\pi$
$503$	7.59396			0.338598			0.169299	+	0.985565i	$0.445850\pi$
$504$	0.397568	+	3.85068i	0.0177091	+	0.171523i
$505$	−8.73240			−0.388587
$506$	1.55406	−	7.78815i	0.0690864	−	0.346226i
$507$	3.72852	+	2.15266i	0.165589	+	0.0956030i
$508$	−9.79229	−	4.06999i	−0.434463	−	0.180577i
$509$	−3.79222	+	2.18944i	−0.168087	+	0.0970451i	−0.581684	−	0.813415i	$-0.697606\pi$
$509$	−3.79222	+	2.18944i	−0.168087	+	0.0970451i	0.413596	+	0.910460i	$0.364272\pi$
$510$	3.40684	−	3.88002i	0.150858	−	0.171810i
$511$	4.27052	−	11.5749i	0.188917	−	0.512046i
$512$	−4.53521	+	22.1683i	−0.200430	+	0.979708i
$513$	18.4039	+	31.8765i	0.812553	+	1.40738i
$514$	−9.43110	−	27.8385i	−0.415988	−	1.22790i
$515$	8.94047	+	5.16178i	0.393964	+	0.227455i
$516$	13.3886	−	10.2477i	0.589402	−	0.451132i
$517$			6.21259i			0.273230i
$518$	0.872850	−	0.473210i	0.0383508	−	0.0207916i
$519$	26.0813			1.14484
$520$	0.414537	−	6.15339i	0.0181786	−	0.269844i
$521$	5.37827	−	9.31544i	0.235626	−	0.408117i	−0.723828	−	0.689980i	$-0.757619\pi$
$521$	5.37827	−	9.31544i	0.235626	−	0.408117i	0.959455	+	0.281863i	$0.0909525\pi$
$522$	−5.69366	+	1.92890i	−0.249205	+	0.0844255i
$523$	2.43561	−	1.40620i	0.106502	−	0.0614889i	−0.445803	−	0.895131i	$-0.647082\pi$
$523$	2.43561	−	1.40620i	0.106502	−	0.0614889i	0.552305	+	0.833642i	$0.313748\pi$
$524$	−19.9098	+	2.59666i	−0.869762	+	0.113435i
$525$	−15.0574	+	12.5225i	−0.657158	+	0.546528i
$526$	21.2551	−	24.2073i	0.926768	−	1.05549i
$527$	1.82555	+	3.16195i	0.0795223	+	0.137737i
$528$	−3.93511	+	14.5451i	−0.171254	+	0.632994i
$529$	8.74135	−	15.1405i	0.380059	−	0.658281i
$530$	8.24841	+	1.64590i	0.358288	+	0.0714934i
$531$			1.95262i			0.0847365i
$532$	−33.5758	+	10.3802i	−1.45570	+	0.450039i
$533$		−	24.7889i		−	1.07372i
$534$	2.78876	−	13.9758i	0.120682	−	0.604794i
$535$	−0.0931564	+	0.161352i	−0.00402750	+	0.00697584i
$536$	3.33421	+	6.79218i	0.144016	+	0.293377i
$537$	−4.36620	−	7.56248i	−0.188415	−	0.326345i
$538$	3.18280	+	2.79465i	0.137220	+	0.120486i
$539$	−16.4549	−	3.05049i	−0.708762	−	0.131394i
$540$	−0.788031	−	6.04219i	−0.0339114	−	0.260015i
$541$	27.0699	−	15.6288i	1.16383	−	0.671935i	0.211608	−	0.977355i	$-0.432130\pi$
$541$	27.0699	−	15.6288i	1.16383	−	0.671935i	0.952218	+	0.305419i	$0.0987966\pi$
$542$	11.4283	+	33.7339i	0.490889	+	1.44899i
$543$	−7.86620	+	13.6247i	−0.337571	+	0.584690i
$544$	23.7977	−	1.48748i	1.02032	−	0.0637750i
$545$	−4.29055			−0.183787
$546$	−12.2307	+	19.9307i	−0.523427	+	0.852954i
$547$			29.4711i			1.26010i	0.776556	+	0.630048i	$0.216965\pi$
$547$			29.4711i			1.26010i	−0.776556	+	0.630048i	$0.783035\pi$
$548$	−5.16111	+	3.95034i	−0.220472	+	0.168750i
$549$	3.19725	+	1.84593i	0.136455	+	0.0787826i
$550$	15.0435	−	5.09644i	0.641458	−	0.217313i
$551$	−27.2874	−	47.2632i	−1.16248	−	2.01348i
$552$	5.83159	−	8.69338i	0.248209	−	0.370015i
$553$	1.04296	+	1.25408i	0.0443512	+	0.0533289i
$554$	10.0369	+	8.81290i	0.426428	+	0.374424i
$555$	−0.199057	+	0.114926i	−0.00844949	+	0.00487832i
$556$	11.7711	−	28.3210i	0.499207	−	1.20108i
$557$	−19.3751	−	11.1862i	−0.820950	−	0.473976i	0.0297941	−	0.999556i	$-0.490515\pi$
$557$	−19.3751	−	11.1862i	−0.820950	−	0.473976i	−0.850744	+	0.525580i	$0.823848\pi$
$558$	0.621441	+	0.124003i	0.0263077	+	0.00524948i
$559$	−21.2213			−0.897567
$560$	5.79215	+	0.546498i	0.244763	+	0.0230938i
$561$	15.8783			0.670381
$562$	37.2271	+	7.42835i	1.57033	+	0.313346i
$563$	−28.0528	−	16.1963i	−1.18229	−	0.682593i	−0.225743	−	0.974187i	$-0.572481\pi$
$563$	−28.0528	−	16.1963i	−1.18229	−	0.682593i	−0.956542	+	0.291594i	$0.905814\pi$
$564$	−3.14295	+	7.56184i	−0.132342	+	0.318411i
$565$	−1.19846	+	0.691928i	−0.0504194	+	0.0291097i
$566$	13.7962	+	12.1137i	0.579896	+	0.509177i
$567$	−6.57585	+	17.8234i	−0.276160	+	0.748513i
$568$	20.5928	+	13.8138i	0.864053	+	0.579614i
$569$	18.5288	+	32.0928i	0.776767	+	1.34540i	0.933796	+	0.357806i	$0.116475\pi$
$569$	18.5288	+	32.0928i	0.776767	+	1.34540i	−0.157029	+	0.987594i	$0.550192\pi$
$570$	7.70563	−	2.61051i	0.322753	−	0.109342i
$571$	−19.4303	−	11.2181i	−0.813132	−	0.469462i	0.0349102	−	0.999390i	$-0.488885\pi$
$571$	−19.4303	−	11.2181i	−0.813132	−	0.469462i	−0.848042	+	0.529928i	$0.822219\pi$
$572$	15.0602	−	11.5272i	0.629699	−	0.481976i
$573$			0.265356i			0.0110854i
$574$	23.3758	+	0.626798i	0.975689	+	0.0261620i
$575$	−11.0346			−0.460175
$576$	2.53122	−	3.27407i	0.105468	−	0.136420i
$577$	−4.78431	+	8.28667i	−0.199173	+	0.344978i	−0.948261	−	0.317493i	$-0.897159\pi$
$577$	−4.78431	+	8.28667i	−0.199173	+	0.344978i	0.749087	+	0.662471i	$0.230492\pi$
$578$	−0.348046	−	1.02735i	−0.0144768	−	0.0427323i
$579$	10.2578	−	5.92235i	0.426300	−	0.246124i
$580$	1.16841	+	8.95874i	0.0485156	+	0.371991i
$581$	−0.492563	−	2.86693i	−0.0204350	−	0.118940i
$582$	−21.6799	−	19.0360i	−0.898660	−	0.789067i
$583$	12.9325	+	22.3997i	0.535609	+	0.927703i
$584$	−11.8398	+	5.81206i	−0.489936	+	0.240505i
$585$	−0.563987	+	0.976854i	−0.0233180	+	0.0403879i
$586$	−2.64645	+	13.2627i	−0.109324	+	0.547876i
$587$		−	23.6894i		−	0.977766i	−0.872349	−	0.488883i	$-0.837405\pi$
$587$		−	23.6894i		−	0.977766i	0.872349	−	0.488883i	$-0.162595\pi$
$588$	−18.4853	−	12.0375i	−0.762321	−	0.496419i
$589$			5.75289i			0.237044i
$590$	2.87782	+	0.574245i	0.118478	+	0.0236413i
$591$	−1.06026	+	1.83643i	−0.0436135	+	0.0755407i
$592$	−1.02459	−	0.277198i	−0.0421104	−	0.0113928i
$593$	3.72404	+	6.45023i	0.152928	+	0.264879i	0.932303	−	0.361679i	$-0.117796\pi$
$593$	3.72404	+	6.45023i	0.152928	+	0.264879i	−0.779375	+	0.626558i	$0.784463\pi$
$594$	12.3633	−	14.0804i	0.507272	−	0.577727i
$595$	−1.03810	−	6.04219i	−0.0425579	−	0.247706i
$596$	14.6422	−	1.90965i	0.599766	−	0.0782222i
$597$	−17.4134	+	10.0536i	−0.712682	+	0.411467i
$598$	−12.4791	+	4.22766i	−0.510308	+	0.172882i
$599$	−0.837627	+	1.45081i	−0.0342245	+	0.0592786i	−0.882630	−	0.470068i	$-0.844229\pi$
$599$	−0.837627	+	1.45081i	−0.0342245	+	0.0592786i	0.848406	+	0.529346i	$0.177563\pi$
$600$	20.8890	+	1.40723i	0.852788	+	0.0574499i
$601$	−8.27385			−0.337497			−0.168749	−	0.985659i	$-0.553973\pi$
$601$	−8.27385			−0.337497			−0.168749	+	0.985659i	$0.553973\pi$
$602$	0.536591	−	20.0117i	0.0218698	−	0.815615i
$603$		−	1.38386i		−	0.0563550i
$604$	−13.2311	+	10.1272i	−0.538366	+	0.412068i
$605$	2.51579	+	1.45249i	0.102281	+	0.0590522i
$606$	−11.3574	−	33.5245i	−0.461363	−	1.36184i
$607$	13.2647	+	22.9751i	0.538397	+	0.932531i	0.998991	+	0.0449200i	$0.0143033\pi$
$607$	13.2647	+	22.9751i	0.538397	+	0.932531i	−0.460593	+	0.887611i	$0.652363\pi$
$608$	33.6453	+	16.7188i	1.36450	+	0.678036i
$609$	11.8572	−	32.1383i	0.480480	−	1.30231i
$610$	3.66087	−	4.16932i	0.148224	−	0.168811i
$611$	8.92620	−	5.15354i	0.361115	−	0.208490i
$612$	−4.02699	−	1.67375i	−0.162781	−	0.0676572i
$613$	27.3692	+	15.8016i	1.10543	+	0.638220i	0.937642	−	0.347603i	$-0.113004\pi$
$613$	27.3692	+	15.8016i	1.10543	+	0.638220i	0.167788	+	0.985823i	$0.446338\pi$
$614$	3.38221	−	16.9499i	0.136495	−	0.684042i
$615$	−5.41348			−0.218293
$616$	10.4893	+	14.4932i	0.422626	+	0.583948i
$617$	10.1113			0.407064			0.203532	−	0.979068i	$-0.434758\pi$
$617$	10.1113			0.407064			0.203532	+	0.979068i	$0.434758\pi$
$618$	−8.18853	+	41.0367i	−0.329391	+	1.65074i
$619$	−4.79105	−	2.76611i	−0.192568	−	0.111179i	0.400616	−	0.916246i	$-0.368796\pi$
$619$	−4.79105	−	2.76611i	−0.192568	−	0.111179i	−0.593184	+	0.805067i	$0.702129\pi$
$620$	0.365519	−	0.879428i	0.0146796	−	0.0353187i
$621$	−11.2737	+	6.50886i	−0.452397	+	0.261192i
$622$	−29.7499	+	33.8819i	−1.19286	+	1.35854i
$623$	−10.8197	−	13.0099i	−0.433483	−	0.521230i
$624$	24.1626	−	6.41169i	0.967277	−	0.256673i
$625$	−10.2791	−	17.8039i	−0.411163	−	0.712155i
$626$	−9.76682	−	28.8294i	−0.390360	−	1.15226i
$627$	21.6668	+	12.5094i	0.865290	+	0.499576i
$628$	−8.67544	−	11.3344i	−0.346188	−	0.452293i
$629$			1.11850i			0.0445975i
$630$	−0.906910	−	0.556538i	−0.0361322	−	0.0221730i
$631$	35.5582			1.41555			0.707774	−	0.706439i	$-0.249700\pi$
$631$	35.5582			1.41555			0.707774	+	0.706439i	$0.249700\pi$
$632$	0.117204	−	1.73978i	0.00466211	−	0.0692046i
$633$	6.66781	−	11.5490i	0.265022	−	0.459031i
$634$	−31.0073	+	10.5046i	−1.23146	+	0.417192i
$635$	2.52431	−	1.45741i	0.100174	−	0.0578357i
$636$	4.40916	+	33.8071i	0.174835	+	1.34054i
$637$	9.26693	+	26.1727i	0.367169	+	1.03700i
$638$	−18.3310	+	20.8770i	−0.725731	+	0.826528i
$639$	−2.26760	−	3.92760i	−0.0897050	−	0.155374i
$640$	−4.08100	−	4.69345i	−0.161316	−	0.185525i
$641$	−4.73300	+	8.19779i	−0.186942	+	0.323793i	−0.944229	−	0.329289i	$-0.893191\pi$
$641$	−4.73300	+	8.19779i	−0.186942	+	0.323793i	0.757287	+	0.653082i	$0.226524\pi$
$642$	−0.740603	−	0.147781i	−0.0292293	−	0.00583245i
$643$		−	13.0085i		−	0.513007i	−0.966543	−	0.256503i	$-0.917430\pi$
$643$		−	13.0085i		−	0.513007i	0.966543	−	0.256503i	$-0.0825705\pi$
$644$	−3.67113	−	11.8746i	−0.144663	−	0.467927i
$645$			4.63439i			0.182479i
$646$	7.74722	−	38.8251i	0.304810	−	1.52755i
$647$	−13.7610	+	23.8347i	−0.540999	+	0.937039i	0.457848	+	0.889031i	$0.348621\pi$
$647$	−13.7610	+	23.8347i	−0.540999	+	0.937039i	−0.998847	+	0.0480078i	$0.984713\pi$
$648$	18.2313	−	8.94956i	0.716193	−	0.351572i
$649$	4.51207	+	7.81514i	0.177114	+	0.306771i
$650$	−19.8016	−	17.3868i	−0.776683	−	0.681965i
$651$	−2.77634	+	2.30896i	−0.108813	+	0.0904951i
$652$	14.4963	−	1.89062i	0.567718	−	0.0740425i
$653$	30.4390	−	17.5740i	1.19117	−	0.687723i	0.232598	−	0.972573i	$-0.425277\pi$
$653$	30.4390	−	17.5740i	1.19117	−	0.687723i	0.958572	+	0.284850i	$0.0919439\pi$
$654$	−5.58032	−	16.4718i	−0.218208	−	0.644099i
$655$	2.75946	−	4.77952i	0.107821	−	0.186751i
$656$	−17.6340	−	17.7196i	−0.688491	−	0.691833i
$657$	2.41228			0.0941121
$658$	4.63408	+	8.54769i	0.180655	+	0.333224i
$659$			3.86719i			0.150644i	0.997159	+	0.0753222i	$0.0239985\pi$
$659$			3.86719i			0.150644i	−0.997159	+	0.0753222i	$0.976001\pi$
$660$	−2.51735	−	3.28890i	−0.0979875	−	0.128020i
$661$	14.4295	+	8.33085i	0.561241	+	0.324033i	0.753643	−	0.657284i	$-0.228295\pi$
$661$	14.4295	+	8.33085i	0.561241	+	0.324033i	−0.192403	+	0.981316i	$0.561628\pi$
$662$	−39.5346	+	13.3935i	−1.53656	+	0.520553i
$663$	−13.1715	−	22.8138i	−0.511540	−	0.886013i
$664$	−1.73240	+	2.58255i	−0.0672300	+	0.100222i
$665$	3.34366	−	9.06278i	0.129662	−	0.351439i
$666$	0.145876	+	0.128086i	0.00565259	+	0.00496325i
$667$	16.7154	−	9.65067i	0.647225	−	0.373675i
$668$	3.48817	+	1.44980i	0.134961	+	0.0560943i
$669$	7.91664	+	4.57068i	0.306075	+	0.176713i
$670$	−2.03956	−	0.406978i	−0.0787953	−	0.0157229i
$671$	17.0622			0.658679
$672$	5.43525	+	22.9474i	0.209669	+	0.885214i
$673$	−3.95795			−0.152568			−0.0762838	−	0.997086i	$-0.524306\pi$
$673$	−3.95795			−0.152568			−0.0762838	+	0.997086i	$0.524306\pi$
$674$	−4.55492	−	0.908896i	−0.175449	−	0.0350094i
$675$	−22.5474	−	13.0177i	−0.867848	−	0.501053i
$676$	−5.04628	−	2.09740i	−0.194088	−	0.0806691i
$677$	−35.6839	+	20.6021i	−1.37144	+	0.791804i	−0.991110	−	0.133045i	$-0.957524\pi$
$677$	−35.6839	+	20.6021i	−1.37144	+	0.791804i	−0.380334	+	0.924849i	$0.624191\pi$
$678$	−4.21509	−	3.70105i	−0.161880	−	0.142138i
$679$	−33.7612	+	5.80045i	−1.29564	+	0.222601i
$680$	−3.65111	+	5.44285i	−0.140014	+	0.208724i
$681$	−8.99940	−	15.5874i	−0.344858	−	0.597311i
$682$	2.77379	−	0.939703i	0.106214	−	0.0359831i
$683$	28.6643	+	16.5493i	1.09681	+	0.633242i	0.935381	−	0.353642i	$-0.115057\pi$
$683$	28.6643	+	16.5493i	1.09681	+	0.633242i	0.161427	+	0.986885i	$0.448390\pi$
$684$	−4.17644	−	5.45650i	−0.159690	−	0.208635i
$685$		−	1.78648i		−	0.0682580i
$686$	−24.9151	+	8.07690i	−0.951264	+	0.308378i
$687$	−29.1580			−1.11245
$688$	−15.1694	+	15.0962i	−0.578329	+	0.575536i
$689$	21.4558	−	37.1626i	0.817402	−	1.41578i
$690$	0.923251	+	2.72523i	0.0351476	+	0.103748i
$691$	12.9010	−	7.44840i	0.490777	−	0.283350i	−0.234120	−	0.972208i	$-0.575221\pi$
$691$	12.9010	−	7.44840i	0.490777	−	0.283350i	0.724897	+	0.688857i	$0.241887\pi$
$692$	−32.8273	+	4.28137i	−1.24791	+	0.162753i
$693$	−0.554060	−	3.22487i	−0.0210470	−	0.122503i
$694$	−33.6628	−	29.5575i	−1.27782	−	1.12199i
$695$	4.21509	+	7.30075i	0.159888	+	0.276933i
$696$	−32.8738	+	16.1374i	−1.24608	+	0.611687i
$697$	−13.1715	+	22.8138i	−0.498907	+	0.864133i
$698$	−7.88172	+	39.4992i	−0.298328	+	1.49506i
$699$		−	17.4131i		−	0.658623i
$700$	16.8964	−	18.2332i	0.638623	−	0.689152i
$701$			32.5746i			1.23032i	0.788401	+	0.615162i	$0.210910\pi$
$701$			32.5746i			1.23032i	−0.788401	+	0.615162i	$0.789090\pi$
$702$	−30.4864	−	6.08330i	−1.15063	−	0.229599i
$703$	−0.881187	+	1.52626i	−0.0332346	+	0.0575640i
$704$	2.56529	−	18.9532i	0.0966829	−	0.714325i
$705$	−1.12545	−	1.94934i	−0.0423869	−	0.0734162i
$706$	−18.8852	+	21.5082i	−0.710755	+	0.809471i
$707$	−39.4289	−	14.5471i	−1.48288	−	0.547100i
$708$	1.53833	+	11.7951i	0.0578140	+	0.443286i
$709$	9.95635	−	5.74830i	0.373918	−	0.215882i	−0.301251	−	0.953545i	$-0.597404\pi$
$709$	9.95635	−	5.74830i	0.373918	−	0.215882i	0.675169	+	0.737663i	$0.264071\pi$
$710$	−6.45548	+	2.18699i	−0.242270	+	0.0820761i
$711$	−0.159458	+	0.276190i	−0.00598016	+	0.0103579i
$712$	−1.21588	+	18.0485i	−0.0455669	+	0.676397i
$713$	−2.03461			−0.0761967
$714$	21.8464	−	11.8439i	0.817580	−	0.443246i
$715$			5.21300i			0.194955i
$716$	6.73694	+	8.80179i	0.251771	+	0.328938i
$717$	30.8536	+	17.8133i	1.15225	+	0.665251i
$718$	−11.3998	−	33.6495i	−0.425435	−	1.25579i
$719$	13.4887	+	23.3632i	0.503045	+	0.871299i	0.999994	+	0.00351948i	$0.00112029\pi$
$719$	13.4887	+	23.3632i	0.503045	+	0.871299i	−0.496949	+	0.867780i	$0.665546\pi$
$720$	0.291753	+	1.09948i	0.0108730	+	0.0409750i
$721$	31.7695	+	38.2004i	1.18316	+	1.42266i
$722$	23.4302	−	26.6844i	0.871981	−	0.993091i
$723$	19.0077	−	10.9741i	0.706906	−	0.408132i
$724$	7.66425	−	18.4400i	0.284840	−	0.685316i
$725$	33.4309	+	19.3013i	1.24159	+	0.716833i
$726$	−2.30420	+	11.5475i	−0.0855168	+	0.428566i
$727$	−27.0230			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$727$	−27.0230			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$728$	12.1225	−	27.0935i	0.449291	−	1.00415i
$729$	−29.9117			−1.10784
$730$	0.709427	−	3.55528i	0.0262571	−	0.131587i
$731$	19.5305	+	11.2759i	0.722361	+	0.417055i
$732$	20.7677	+	8.63175i	0.767598	+	0.319039i
$733$	−17.9059	+	10.3380i	−0.661371	+	0.381843i	−0.792799	−	0.609483i	$-0.791377\pi$
$733$	−17.9059	+	10.3380i	−0.661371	+	0.381843i	0.131428	+	0.991326i	$0.458044\pi$
$734$	28.3497	−	32.2872i	1.04641	−	1.19174i
$735$	5.71569	−	2.02375i	0.210826	−	0.0746470i
$736$	−5.91288	+	11.8992i	−0.217952	+	0.438611i
$737$	−3.19779	−	5.53873i	−0.117792	−	0.204022i
$738$	1.46705	+	4.33039i	0.0540028	+	0.159404i
$739$	−9.30563	−	5.37261i	−0.342313	−	0.197635i	0.318981	−	0.947761i	$-0.396659\pi$
$739$	−9.30563	−	5.37261i	−0.342313	−	0.197635i	−0.661294	+	0.750126i	$0.729993\pi$
$740$	0.231678	−	0.177327i	0.00851664	−	0.00651869i
$741$		−	41.5076i		−	1.52482i
$742$	34.5017	+	21.1725i	1.26660	+	0.777266i
$743$	11.8708			0.435498			0.217749	−	0.976005i	$-0.430129\pi$
$743$	11.8708			0.435498			0.217749	+	0.976005i	$0.430129\pi$
$744$	3.85160	+	0.259471i	0.141206	+	0.00951267i
$745$	−2.02938	+	3.51499i	−0.0743507	+	0.128779i
$746$	7.52177	−	2.54822i	0.275391	−	0.0932970i
$747$	0.492563	−	0.284382i	0.0180219	−	0.0104050i
$748$	−19.9852	+	2.60650i	−0.730732	+	0.0953030i
$749$	−0.689416	+	0.573355i	−0.0251907	+	0.0209499i
$750$	−7.83823	+	8.92688i	−0.286212	+	0.325964i
$751$	−8.53229	−	14.7784i	−0.311348	−	0.539270i	0.667307	−	0.744783i	$-0.267447\pi$
$751$	−8.53229	−	14.7784i	−0.311348	−	0.539270i	−0.978654	+	0.205513i	$0.934114\pi$
$752$	2.71456	−	10.0337i	0.0989899	−	0.365890i
$753$	0.556233	−	0.963424i	0.0202703	−	0.0351091i
$754$	45.2020	+	9.01968i	1.64616	+	0.328477i
$755$		−	4.57986i		−	0.166678i
$756$	6.50740	−	28.5947i	0.236672	−	1.03998i
$757$		−	46.3272i		−	1.68379i	−0.539641	−	0.841895i	$-0.681440\pi$
$757$		−	46.3272i		−	1.68379i	0.539641	−	0.841895i	$-0.318560\pi$
$758$	−2.23331	+	11.1922i	−0.0811173	+	0.406518i
$759$	−4.42415	+	7.66285i	−0.160586	+	0.278144i
$760$	−9.27018	+	4.55064i	−0.336265	+	0.165069i
$761$	7.30474	+	12.6522i	0.264796	+	0.458641i	0.967510	−	0.252832i	$-0.0813619\pi$
$761$	7.30474	+	12.6522i	0.264796	+	0.458641i	−0.702714	+	0.711473i	$0.748029\pi$
$762$	8.87827	+	7.79555i	0.321626	+	0.282403i
$763$	−19.3729	−	7.14753i	−0.701346	−	0.258758i
$764$	−0.0435595	−	0.333991i	−0.00157593	−	0.0120834i
$765$	1.03810	−	0.599347i	0.0375326	−	0.0216694i
$766$	11.6317	+	34.3340i	0.420269	+	1.24054i
$767$	7.48582	−	12.9658i	0.270297	−	0.468169i
$768$	12.7108	−	21.7717i	0.458662	−	0.785617i
$769$	49.3177			1.77844			0.889221	−	0.457477i	$-0.151247\pi$
$769$	49.3177			1.77844			0.889221	+	0.457477i	$0.151247\pi$
$770$	−4.91584	−	0.131813i	−0.177155	−	0.00475021i
$771$			32.7480i			1.17939i
$772$	−11.9388	+	9.13804i	−0.429688	+	0.328885i
$773$	−0.902744	−	0.521200i	−0.0324695	−	0.0187462i	0.483677	−	0.875246i	$-0.339301\pi$
$773$	−0.902744	−	0.521200i	−0.0324695	−	0.0187462i	−0.516147	+	0.856500i	$0.672634\pi$
$774$	3.70718	−	1.25592i	0.133252	−	0.0451429i
$775$	−2.03461	−	3.52404i	−0.0730853	−	0.126587i
$776$	30.4123	+	20.4008i	1.09174	+	0.732346i
$777$	−1.09024	+	0.187313i	−0.0391122	+	0.00671981i
$778$	−28.2116	−	24.7711i	−1.01143	−	0.888087i
$779$	−35.9467	+	20.7538i	−1.28792	+	0.743583i
$780$	−2.63725	+	6.34515i	−0.0944287	+	0.227193i
$781$	−18.1517	−	10.4799i	−0.649517	−	0.374999i
$782$	13.7312	+	2.73994i	0.491025	+	0.0979800i
$783$	45.5403			1.62748
$784$	25.2426	+	12.1166i	0.901521	+	0.432735i
$785$	3.92334			0.140030
$786$	21.9380	+	4.37754i	0.782502	+	0.156142i
$787$	34.8899	+	20.1437i	1.24369	+	0.718045i	0.969844	−	0.243728i	$-0.0783705\pi$
$787$	34.8899	+	20.1437i	1.24369	+	0.718045i	0.273847	+	0.961773i	$0.411704\pi$
$788$	1.03304	−	2.48548i	0.0368007	−	0.0885415i
$789$	−31.0834	+	17.9460i	−1.10660	+	0.638895i
$790$	0.360161	+	0.316239i	0.0128140	+	0.0112513i
$791$	−6.56399	+	1.12775i	−0.233388	+	0.0400981i
$792$	−1.94869	+	2.90498i	−0.0692436	+	0.103224i
$793$	−14.1536	−	24.5148i	−0.502610	−	0.870546i
$794$	45.6699	−	15.4720i	1.62076	−	0.549082i
$795$	−8.11570	−	4.68560i	−0.287834	−	0.166181i
$796$	20.2670	−	15.5125i	0.718346	−	0.549826i
$797$		−	32.2902i		−	1.14378i	−0.820331	−	0.571889i	$-0.806211\pi$
$797$		−	32.2902i		−	1.14378i	0.820331	−	0.571889i	$-0.193789\pi$
$798$	39.1416	+	1.04954i	1.38560	+	0.0371533i
$799$	−10.9533			−0.387501
$800$	−26.5229	+	1.65782i	−0.937728	+	0.0586126i
$801$	1.65423	−	2.86521i	0.0584493	−	0.101237i
$802$	−8.32834	−	24.5834i	−0.294084	−	0.868069i
$803$	9.65489	−	5.57425i	0.340714	−	0.196711i
$804$	−1.09024	−	8.35939i	−0.0384499	−	0.294813i
$805$	3.20521	+	1.18254i	0.112969	+	0.0416792i
$806$	−3.65111	−	3.20585i	−0.128605	−	0.112921i
$807$	−2.35956	−	4.08688i	−0.0830605	−	0.143865i
$808$	19.7982	+	40.3313i	0.696499	+	1.41885i
$809$	−20.8131	+	36.0493i	−0.731749	+	1.26743i	0.224386	+	0.974500i	$0.427962\pi$
$809$	−20.8131	+	36.0493i	−0.731749	+	1.26743i	−0.956135	+	0.292926i	$0.905371\pi$
$810$	−1.09239	+	5.47452i	−0.0383828	+	0.192355i
$811$		−	18.7227i		−	0.657444i	−0.944427	−	0.328722i	$-0.893382\pi$
$811$		−	18.7227i		−	0.657444i	0.944427	−	0.328722i	$-0.106618\pi$
$812$	−9.64849	+	42.3973i	−0.338596	+	1.48785i
$813$		−	39.6831i		−	1.39175i
$814$	0.879833	+	0.175563i	0.0308381	+	0.00615349i
$815$	−2.00916	+	3.47997i	−0.0703778	+	0.121898i
$816$	−25.6442	−	6.93793i	−0.897727	−	0.242876i
$817$	17.7670	+	30.7734i	0.621589	+	1.07662i
$818$	−10.9631	+	12.4857i	−0.383315	+	0.436554i
$819$	−4.17386	+	3.47120i	−0.145846	+	0.121294i
$820$	6.81369	−	0.888650i	0.237944	−	0.0310330i
$821$	−16.2308	+	9.37088i	−0.566460	+	0.327046i	−0.755734	−	0.654878i	$-0.772720\pi$
$821$	−16.2308	+	9.37088i	−0.566460	+	0.327046i	0.189274	+	0.981924i	$0.439386\pi$
$822$	6.85847	−	2.32351i	0.239217	−	0.0810417i
$823$	10.2211	−	17.7035i	0.356286	−	0.617106i	−0.631051	−	0.775741i	$-0.717376\pi$
$823$	10.2211	−	17.7035i	0.356286	−	0.617106i	0.987337	+	0.158636i	$0.0507095\pi$
$824$	3.57013	−	52.9951i	0.124371	−	1.84617i
$825$	−17.6966			−0.616116
$826$	12.0375	+	7.38695i	0.418837	+	0.257025i
$827$			48.6254i			1.69087i	0.534079	+	0.845435i	$0.320659\pi$
$827$			48.6254i			1.69087i	−0.534079	+	0.845435i	$0.679341\pi$
$828$	1.92978	−	1.47707i	0.0670647	−	0.0513317i
$829$	−6.06173	−	3.49974i	−0.210532	−	0.121551i	0.391026	−	0.920379i	$-0.372120\pi$
$829$	−6.06173	−	3.49974i	−0.210532	−	0.121551i	−0.601559	+	0.798829i	$0.705453\pi$
$830$	−0.274271	−	0.809586i	−0.00952009	−	0.0281012i
$831$	−7.44085	−	12.8879i	−0.258120	−	0.447078i
$832$	−29.3598	+	12.0365i	−1.01787	+	0.417290i
$833$	5.37827	−	29.0113i	0.186346	−	1.00518i
$834$	−22.5461	+	25.6775i	−0.780707	+	0.889140i
$835$	−0.899200	+	0.519154i	−0.0311181	+	0.0179660i
$836$	−29.3245	−	12.1882i	−1.01421	−	0.421538i
$837$	−4.15738	−	2.40026i	−0.143700	−	0.0829653i
$838$	−3.06741	+	15.3723i	−0.105962	+	0.531027i
$839$	40.1867			1.38740			0.693700	−	0.720264i	$-0.255979\pi$
$839$	40.1867			1.38740			0.693700	+	0.720264i	$0.255979\pi$
$840$	−5.91678	−	2.64736i	−0.204148	−	0.0913426i
$841$	−38.5224			−1.32836
$842$	0.0379879	−	0.190376i	0.00130915	−	0.00656078i
$843$	−36.6281	−	21.1473i	−1.26154	−	0.728350i
$844$	−6.49663	+	15.6307i	−0.223623	+	0.538031i
$845$	1.30086	−	0.751051i	0.0447509	−	0.0258369i
$846$	−1.25433	+	1.42855i	−0.0431248	+	0.0491144i
$847$	8.93974	+	10.7494i	0.307173	+	0.369352i
$848$	−11.0992	−	41.8275i	−0.381148	−	1.43636i
$849$	−10.2278	−	17.7150i	−0.351016	−	0.607978i
$850$	8.98545	+	26.5230i	0.308198	+	0.909731i
$851$	−0.539788	−	0.311647i	−0.0185037	−	0.0106831i
$852$	−16.7921	−	21.9388i	−0.575287	−	0.751610i
$853$			30.8071i			1.05482i	0.849612	+	0.527408i	$0.176836\pi$
$853$			30.8071i			1.05482i	−0.849612	+	0.527408i	$0.823164\pi$
$854$	23.4753	−	12.7270i	0.803308	−	0.435508i
$855$	1.88873			0.0645933
$856$	0.956420	+	0.0644313i	0.0326898	+	0.00220222i
$857$	−6.84889	+	11.8626i	−0.233954	+	0.405220i	−0.958968	−	0.283514i	$-0.908500\pi$
$857$	−6.84889	+	11.8626i	−0.233954	+	0.405220i	0.725014	+	0.688734i	$0.241833\pi$
$858$	−20.0132	+	6.78005i	−0.683238	+	0.231467i
$859$	7.52869	−	4.34669i	0.256876	−	0.148307i	−0.366033	−	0.930602i	$-0.619284\pi$
$859$	7.52869	−	4.34669i	0.256876	−	0.148307i	0.622908	+	0.782295i	$0.285951\pi$
$860$	−0.760758	−	5.83309i	−0.0259416	−	0.198907i
$861$	−24.4432	−	9.01819i	−0.833022	−	0.307339i
$862$	−11.6266	+	13.2414i	−0.396002	+	0.451003i
$863$	0.296174	+	0.512989i	0.0100819	+	0.0174623i	0.871022	−	0.491243i	$-0.163457\pi$
$863$	0.296174	+	0.512989i	0.0100819	+	0.0174623i	−0.860940	+	0.508706i	$0.830124\pi$
$864$	−26.1197	+	17.3385i	−0.888610	+	0.589869i
$865$	4.54981	−	7.88049i	0.154698	−	0.267945i
$866$	−19.6330	−	3.91761i	−0.667158	−	0.133126i
$867$			1.20854i			0.0410440i
$868$	3.11542	−	3.36192i	0.105744	−	0.114111i
$869$			1.47389i			0.0499984i
$870$	1.96975	−	9.87138i	0.0667808	−	0.334671i
$871$	−5.30533	+	9.18911i	−0.179764	+	0.311361i
$872$	9.72761	+	19.8163i	0.329418	+	0.671063i
$873$	−3.34889	−	5.80045i	−0.113343	−	0.196316i
$874$	16.5784	+	14.5566i	0.560772	+	0.492385i
$875$	2.38839	+	13.9015i	0.0807422	+	0.469955i
$876$	14.5717	−	1.90046i	0.492333	−	0.0642108i
$877$	−13.2310	+	7.63892i	−0.446779	+	0.257948i	−0.706469	−	0.707744i	$-0.749713\pi$
$877$	−13.2310	+	7.63892i	−0.446779	+	0.257948i	0.259690	+	0.965692i	$0.416380\pi$
$878$	2.47713	+	7.31194i	0.0835992	+	0.246766i
$879$	7.53401	−	13.0493i	0.254116	−	0.440142i
$880$	3.70835	+	3.72635i	0.125009	+	0.125615i
$881$	−43.1280			−1.45302			−0.726509	−	0.687157i	$-0.758859\pi$
$881$	−43.1280			−1.45302			−0.726509	+	0.687157i	$0.758859\pi$
$882$	−3.16780	−	4.02371i	−0.106665	−	0.135485i
$883$		−	20.2255i		−	0.680642i	−0.940309	−	0.340321i	$-0.889464\pi$
$883$		−	20.2255i		−	0.680642i	0.940309	−	0.340321i	$-0.110536\pi$
$884$	20.3234	+	26.5524i	0.683549	+	0.893054i
$885$	−2.83152	−	1.63478i	−0.0951805	−	0.0549525i
$886$	44.6503	−	15.1266i	1.50006	−	0.508188i
$887$	−10.7820	−	18.6750i	−0.362024	−	0.627044i	0.626270	−	0.779606i	$-0.284581\pi$
$887$	−10.7820	−	18.6750i	−0.362024	−	0.627044i	−0.988294	+	0.152563i	$0.951247\pi$
$888$	0.982097	+	0.658799i	0.0329570	+	0.0221078i
$889$	13.8258	−	2.37538i	0.463701	−	0.0796678i
$890$	−3.73633	−	3.28067i	−0.125242	−	0.109968i
$891$	−14.8668	+	8.58338i	−0.498058	+	0.287554i
$892$	−10.7146	−	4.45333i	−0.358751	−	0.149109i
$893$	−14.9465	−	8.62934i	−0.500164	−	0.288770i
$894$	−16.1338	−	3.21936i	−0.539594	−	0.107671i
$895$	−3.04668			−0.101839
$896$	−10.6080	−	27.9905i	−0.354389	−	0.935098i
$897$	14.6799			0.490147
$898$	−37.4062	−	7.46410i	−1.24826	−	0.249080i
$899$	6.16413	+	3.55886i	0.205585	+	0.118695i
$900$	4.48814	+	1.86542i	0.149605	+	0.0621806i
$901$	−39.4926	+	22.8011i	−1.31569	+	0.759614i
$902$	15.8783	+	13.9419i	0.528689	+	0.464214i
$903$	−7.72032	+	20.9254i	−0.256916	+	0.696354i
$904$	5.91288	+	3.96641i	0.196659	+	0.131921i
$905$	2.74447	+	4.75356i	0.0912293	+	0.158014i
$906$	17.5825	−	5.95659i	0.584139	−	0.197894i
$907$	27.3384	+	15.7838i	0.907757	+	0.524094i	0.879709	−	0.475513i	$-0.157737\pi$
$907$	27.3384	+	15.7838i	0.907757	+	0.524094i	0.0280482	+	0.999607i	$0.491071\pi$
$908$	13.8859	+	18.1418i	0.460819	+	0.602058i
$909$		−	8.21720i		−	0.272547i
$910$	3.88846	+	7.17238i	0.128901	+	0.237762i
$911$	15.6873			0.519744			0.259872	−	0.965643i	$-0.416320\pi$
$911$	15.6873			0.519744			0.259872	+	0.965643i	$0.416320\pi$
$912$	−29.5272	−	29.6705i	−0.977742	−	0.982488i
$913$	1.31429	−	2.27641i	0.0434965	−	0.0753382i
$914$	−8.66406	−	25.5743i	−0.286582	−	0.845924i
$915$	−5.35363	+	3.09092i	−0.176986	+	0.102183i
$916$	36.6997	−	4.78642i	1.21259	−	0.158148i
$917$	20.4217	−	16.9838i	0.674385	−	0.560855i
$918$	24.8250	+	21.7975i	0.819346	+	0.719425i
$919$	−7.79407	−	13.4997i	−0.257103	−	0.445315i	0.708362	−	0.705849i	$-0.249434\pi$
$919$	−7.79407	−	13.4997i	−0.257103	−	0.445315i	−0.965464	+	0.260535i	$0.916101\pi$
$920$	−1.60941	−	3.27856i	−0.0530607	−	0.108091i
$921$	−9.62857	+	16.6772i	−0.317272	+	0.549532i
$922$	5.23527	−	26.2365i	0.172414	−	0.864052i
$923$			34.7735i			1.14458i
$924$	−5.88753	−	19.0438i	−0.193685	−	0.626495i
$925$		−	1.24659i		−	0.0409875i
$926$	1.19322	+	0.238098i	0.0392118	+	0.00782438i
$927$	−4.85725	+	8.41300i	−0.159533	+	0.276319i
$928$	38.7276	−	25.7078i	1.27130	−	0.843899i
$929$	−20.6926	−	35.8406i	−0.678901	−	1.17589i	−0.975312	−	0.220830i	$-0.929123\pi$
$929$	−20.6926	−	35.8406i	−0.678901	−	1.17589i	0.296411	−	0.955060i	$-0.404210\pi$
$930$	−0.700104	+	0.797341i	−0.0229573	+	0.0261459i
$931$	30.1949	−	35.3505i	0.989599	−	1.15857i
$932$	2.85844	+	21.9170i	0.0936315	+	0.717916i
$933$	43.5061	−	25.1183i	1.42433	−	0.822335i
$934$	−25.0312	+	8.48006i	−0.819047	+	0.277476i
$935$	2.76992	−	4.79764i	0.0905860	−	0.156900i
$936$	5.79035	+	0.390080i	0.189264	+	0.0127501i
$937$	−23.9308			−0.781785			−0.390892	−	0.920436i	$-0.627834\pi$
$937$	−23.9308			−0.781785			−0.390892	+	0.920436i	$0.627834\pi$
$938$	−8.53116	−	5.23527i	−0.278552	−	0.170938i
$939$			33.9137i			1.10673i
$940$	1.73654	+	2.26879i	0.0566398	+	0.0739997i
$941$	33.3285	+	19.2422i	1.08648	+	0.627278i	0.932636	−	0.360818i	$-0.117502\pi$
$941$	33.3285	+	19.2422i	1.08648	+	0.627278i	0.153841	+	0.988096i	$0.450836\pi$
$942$	5.10271	+	15.0621i	0.166255	+	0.490748i
$943$	−7.33994	−	12.7132i	−0.239021	−	0.413997i
$944$	−3.87244	−	14.5934i	−0.126037	−	0.474974i
$945$	5.15423	+	6.19757i	0.167667	+	0.201607i
$946$	11.9354	−	13.5931i	0.388054	−	0.441951i
$947$	8.36198	−	4.82779i	0.271728	−	0.156882i	−0.357945	−	0.933743i	$-0.616522\pi$
$947$	8.36198	−	4.82779i	0.271728	−	0.156882i	0.629673	+	0.776861i	$0.283189\pi$
$948$	−0.745641	+	1.79399i	−0.0242173	+	0.0582661i
$949$	−16.0181	−	9.24804i	−0.519969	−	0.300204i
$950$	−8.63440	+	43.2712i	−0.280137	+	1.40390i
$951$	36.4757			1.18280
$952$	−25.5527	+	18.4935i	−0.828169	+	0.599378i
$953$	−19.3777			−0.627704			−0.313852	−	0.949472i	$-0.601620\pi$
$953$	−19.3777			−0.627704			−0.313852	+	0.949472i	$0.601620\pi$
$954$	−1.54880	+	7.76177i	−0.0501441	+	0.251296i
$955$	0.0801777	+	0.0462906i	0.00259449	+	0.00149793i
$956$	−41.7581	−	17.3560i	−1.35055	−	0.561334i
$957$	26.8071	−	15.4771i	0.866552	−	0.500304i
$958$	17.3065	−	19.7101i	0.559146	−	0.636806i
$959$	2.97606	−	8.06641i	0.0961020	−	0.260478i
$960$	2.62857	+	6.41169i	0.0848368	+	0.206936i
$961$	15.1249	+	26.1970i	0.487898	+	0.845065i
$962$	−0.477602	−	1.40977i	−0.0153985	−	0.0454529i
$963$	−0.151832	−	0.0876603i	−0.00489272	−	0.00282481i
$964$	−22.1227	+	16.9328i	−0.712524	+	0.545370i
$965$		−	4.13255i		−	0.133031i
$966$	−0.371188	+	13.8431i	−0.0119428	+	0.445394i
$967$	34.8845			1.12181			0.560905	−	0.827880i	$-0.310453\pi$
$967$	34.8845			1.12181			0.560905	+	0.827880i	$0.310453\pi$
$968$	1.00461	−	14.9125i	0.0322894	−	0.479305i
$969$	−22.0550	+	38.2004i	−0.708510	+	1.22717i
$970$	−9.53374	+	3.22983i	−0.306110	+	0.103704i
$971$	38.4767	−	22.2146i	1.23478	−	0.712899i	0.266755	−	0.963764i	$-0.414048\pi$
$971$	38.4767	−	22.2146i	1.23478	−	0.712899i	0.968022	+	0.250865i	$0.0807151\pi$
$972$	10.5352	−	1.37402i	0.337917	−	0.0440716i
$973$	6.87002	+	39.9865i	0.220243	+	1.28191i
$974$	21.3843	−	24.3544i	0.685197	−	0.780365i
$975$	14.6799	+	25.4263i	0.470133	+	0.814294i
$976$	−27.5563	−	7.45524i	−0.882056	−	0.238636i
$977$	13.5436	−	23.4581i	0.433297	−	0.750492i	−0.563858	−	0.825872i	$-0.690684\pi$
$977$	13.5436	−	23.4581i	0.433297	−	0.750492i	0.997155	+	0.0753795i	$0.0240168\pi$
$978$	−15.9730	−	3.18728i	−0.510761	−	0.101918i
$979$		−	15.2902i		−	0.488678i
$980$	−6.86186	+	3.48545i	−0.219194	+	0.111339i
$981$		−	4.03742i		−	0.128905i
$982$	6.86276	−	34.3926i	0.219000	−	1.09751i
$983$	−12.5444	+	21.7275i	−0.400103	+	0.692999i	−0.993738	−	0.111736i	$-0.964359\pi$
$983$	−12.5444	+	21.7275i	−0.400103	+	0.692999i	0.593635	+	0.804735i	$0.297692\pi$
$984$	12.2735	+	25.0026i	0.391266	+	0.797053i
$985$	0.369920	+	0.640721i	0.0117866	+	0.0204151i
$986$	−36.8079	−	32.3191i	−1.17220	−	1.02925i
$987$	−1.83433	−	10.6766i	−0.0583873	−	0.339839i
$988$	6.81369	+	52.2437i	0.216772	+	1.66209i
$989$	−10.8835	+	6.28360i	−0.346076	+	0.199807i
$990$	−0.308514	−	0.910663i	−0.00980522	−	0.0289428i
$991$	−8.81972	+	15.2762i	−0.280168	+	0.485265i	−0.971426	−	0.237343i	$-0.923723\pi$
$991$	−8.81972	+	15.2762i	−0.280168	+	0.485265i	0.691258	+	0.722608i	$0.257057\pi$
$992$	−4.89041	+	0.305675i	−0.155271	+	0.00970519i
$993$	46.5068			1.47585
$994$	−32.7913	−	0.879264i	−1.04008	−	0.0278886i
$995$			7.01530i			0.222400i
$996$	2.75136	−	2.10590i	0.0871801	−	0.0667281i
$997$	−26.5529	−	15.3303i	−0.840939	−	0.485516i	0.0166442	−	0.999861i	$-0.494702\pi$
$997$	−26.5529	−	15.3303i	−0.840939	−	0.485516i	−0.857583	+	0.514345i	$0.828035\pi$
$998$	−52.5407	+	17.7997i	−1.66315	+	0.563440i
$999$	−0.735311	−	1.27360i	−0.0232642	−	0.0402948i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.2.p.a.53.6	yes	12
3.2	odd	2		504.2.cj.c.109.1		12
4.3	odd	2		224.2.t.a.81.5		12
7.2	even	3	inner	56.2.p.a.37.3	✓	12
7.3	odd	6		392.2.b.f.197.2		6
7.4	even	3		392.2.b.e.197.2		6
7.5	odd	6		392.2.p.g.373.3		12
7.6	odd	2		392.2.p.g.165.6		12
8.3	odd	2		224.2.t.a.81.2		12
8.5	even	2	inner	56.2.p.a.53.3	yes	12
12.11	even	2		2016.2.cr.c.1873.4		12
21.2	odd	6		504.2.cj.c.37.4		12
24.5	odd	2		504.2.cj.c.109.4		12
24.11	even	2		2016.2.cr.c.1873.3		12
28.3	even	6		1568.2.b.e.785.5		6
28.11	odd	6		1568.2.b.f.785.2		6
28.19	even	6		1568.2.t.g.177.5		12
28.23	odd	6		224.2.t.a.177.2		12
28.27	even	2		1568.2.t.g.753.2		12
56.3	even	6		1568.2.b.e.785.2		6
56.5	odd	6		392.2.p.g.373.6		12
56.11	odd	6		1568.2.b.f.785.5		6
56.13	odd	2		392.2.p.g.165.3		12
56.19	even	6		1568.2.t.g.177.2		12
56.27	even	2		1568.2.t.g.753.5		12
56.37	even	6	inner	56.2.p.a.37.6	yes	12
56.45	odd	6		392.2.b.f.197.1		6
56.51	odd	6		224.2.t.a.177.5		12
56.53	even	6		392.2.b.e.197.1		6
84.23	even	6		2016.2.cr.c.1297.3		12
168.107	even	6		2016.2.cr.c.1297.4		12
168.149	odd	6		504.2.cj.c.37.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	7.2	even	3	inner
56.2.p.a.37.6	yes	12	56.37	even	6	inner
56.2.p.a.53.3	yes	12	8.5	even	2	inner
56.2.p.a.53.6	yes	12	1.1	even	1	trivial
224.2.t.a.81.2		12	8.3	odd	2
224.2.t.a.81.5		12	4.3	odd	2
224.2.t.a.177.2		12	28.23	odd	6
224.2.t.a.177.5		12	56.51	odd	6
392.2.b.e.197.1		6	56.53	even	6
392.2.b.e.197.2		6	7.4	even	3
392.2.b.f.197.1		6	56.45	odd	6
392.2.b.f.197.2		6	7.3	odd	6
392.2.p.g.165.3		12	56.13	odd	2
392.2.p.g.165.6		12	7.6	odd	2
392.2.p.g.373.3		12	7.5	odd	6
392.2.p.g.373.6		12	56.5	odd	6
504.2.cj.c.37.1		12	168.149	odd	6
504.2.cj.c.37.4		12	21.2	odd	6
504.2.cj.c.109.1		12	3.2	odd	2
504.2.cj.c.109.4		12	24.5	odd	2
1568.2.b.e.785.2		6	56.3	even	6
1568.2.b.e.785.5		6	28.3	even	6
1568.2.b.f.785.2		6	28.11	odd	6
1568.2.b.f.785.5		6	56.11	odd	6
1568.2.t.g.177.2		12	56.19	even	6
1568.2.t.g.177.5		12	28.19	even	6
1568.2.t.g.753.2		12	28.27	even	2
1568.2.t.g.753.5		12	56.27	even	2
2016.2.cr.c.1297.3		12	84.23	even	6
2016.2.cr.c.1297.4		12	168.107	even	6
2016.2.cr.c.1873.3		12	24.11	even	2
2016.2.cr.c.1873.4		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	56.2.p.a.53.6

Level	$56$
Weight	$2$
Character	56.53
Analytic conductor	$0.447$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$