LMFDB - Embedded newform 56.2.p.a.37.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [56,2,Mod(37,56)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			37.6
Root			$1.26950 + 0.623187i$ of defining polynomial
Character	$\chi$	$=$	56.37
Dual form			56.2.p.a.53.6

$q$-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 $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

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

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	−0.839198	−	0.543827i	$-0.816975\pi$
$3$	−1.36456	+	0.787829i	−0.787829	+	0.454853i	0.0513689	+	0.998680i	$0.483642\pi$
$4$	1.84683	−	0.767603i	0.923416	−	0.383801i
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	0.389752	−	0.920920i	$-0.372561\pi$
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	−0.602664	+	0.797995i	$0.705894\pi$
$6$	−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	−0.778527	−	0.627611i	$-0.784033\pi$
$11$	−2.07045	+	1.19538i	−0.624265	+	0.360419i	0.154263	+	0.988030i	$0.450700\pi$
$12$	−1.91537	+	2.50243i	−0.552920	+	0.722388i
$13$		−	3.96641i		−	1.10008i	−0.835137	−	0.550042i	$-0.814612\pi$
$13$		−	3.96641i		−	1.10008i	0.835137	−	0.550042i	$-0.185388\pi$
$14$	−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	0.999916	+	0.0129290i	$0.00411554\pi$
$17$	2.10755	+	3.65038i	0.511155	+	0.885347i	−0.488761	+	0.872418i	$0.662551\pi$
$18$	−0.234739	+	0.692896i	−0.0553285	+	0.163317i
$19$	5.75174	+	3.32077i	1.31954	+	0.761837i	0.983655	−	0.180066i	$-0.0576310\pi$
$19$	5.75174	+	3.32077i	1.31954	+	0.761837i	0.335886	+	0.941903i	$0.390964\pi$
$20$	−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	−0.717211	−	0.696856i	$-0.754582\pi$
$23$	1.17445	−	2.03420i	0.244889	−	0.424160i	0.962100	+	0.272695i	$0.0879151\pi$
$24$	−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	$0.276249\pi$
$29$			8.21720i			1.52590i	−0.646460	+	0.762948i	$0.723751\pi$
$30$	1.20131	−	0.239711i	0.219328	−	0.0437650i
$31$	−0.433099	−	0.750150i	−0.0777869	−	0.134731i	0.824508	−	0.565850i	$-0.191452\pi$
$31$	−0.433099	−	0.750150i	−0.0777869	−	0.134731i	−0.902295	+	0.431120i	$0.858119\pi$
$32$	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	0.480991	−	0.876725i	$-0.340277\pi$
$37$	−0.229805	−	0.132678i	−0.0377797	−	0.0218121i	−0.518771	+	0.854913i	$0.673610\pi$
$38$	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	$-0.866242\pi$
$43$		−	5.35027i		−	0.815908i	0.913003	−	0.407954i	$-0.133758\pi$
$44$	−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	−0.945091	−	0.326807i	$-0.894027\pi$
$47$	−1.29930	+	2.25045i	−0.189522	+	0.328262i	0.755569	+	0.655069i	$0.227361\pi$
$48$	−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	−0.978114	−	0.208070i	$-0.933282\pi$
$53$	−9.36933	+	5.40939i	−1.28698	+	0.743037i	−0.308863	+	0.951107i	$0.599948\pi$
$54$	−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	−0.697460	−	0.716624i	$-0.745686\pi$
$59$	−3.26891	+	1.88730i	−0.425575	+	0.245706i	0.271884	+	0.962330i	$0.412353\pi$
$60$	1.59972	−	0.664896i	0.206523	−	0.0858377i
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	0.0490905	−	0.998794i	$-0.484368\pi$
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	−0.840436	+	0.541911i	$0.817701\pi$
$62$	−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	−0.351762	−	0.936089i	$-0.614417\pi$
$67$	2.31673	−	1.33757i	0.283034	−	0.163410i	0.634796	+	0.772680i	$0.281084\pi$
$68$	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	0.696709	−	0.717354i	$-0.254647\pi$
$73$	−2.33159	−	4.03843i	−0.272892	−	0.472663i	−0.969601	+	0.244691i	$0.921313\pi$
$74$	−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	−0.882845	−	0.469665i	$-0.844375\pi$
$79$	−0.308249	+	0.533903i	−0.0346807	+	0.0600687i	0.848164	+	0.529734i	$0.177708\pi$
$80$	−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	$-0.980781\pi$
$83$		−	1.09948i		−	0.120683i	0.998178	−	0.0603416i	$-0.0192190\pi$
$84$	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	−0.645273	−	0.763952i	$-0.723257\pi$
$89$	3.19779	−	5.53873i	0.338965	−	0.587104i	0.984238	+	0.176847i	$0.0565899\pi$
$90$	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	0.378047	−	0.925787i	$-0.376596\pi$
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.990778	+	0.135495i	$0.0432625\pi$
$102$	−8.89592	−	3.01376i	−0.880827	−	0.298406i
$103$	−9.38954	+	16.2632i	−0.925179	+	1.60246i	−0.133906	+	0.990994i	$0.542752\pi$
$103$	−9.38954	+	16.2632i	−0.925179	+	1.60246i	−0.791273	+	0.611463i	$0.790581\pi$
$104$	−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	0.514120	−	0.857718i	$-0.328119\pi$
$107$	0.293506	+	0.169456i	0.0283743	+	0.0163819i	−0.485746	+	0.874100i	$0.661452\pi$
$108$	−4.25411	−	10.2353i	−0.409352	−	0.984888i
$109$	6.75910	−	3.90237i	0.647404	−	0.373779i	−0.140057	−	0.990143i	$-0.544729\pi$
$109$	6.75910	−	3.90237i	0.647404	−	0.373779i	0.787461	+	0.616365i	$0.211395\pi$
$110$	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	0.0695425	−	0.997579i	$-0.477846\pi$
$131$	−8.69419	−	5.01959i	−0.759615	−	0.438564i	−0.829157	+	0.559015i	$0.811179\pi$
$132$	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	0.788230	−	0.615381i	$-0.210998\pi$
$137$	−1.62485	−	2.81432i	−0.138820	−	0.240444i	−0.927050	+	0.374937i	$0.877664\pi$
$138$	1.02422	+	5.13289i	0.0871878	+	0.436940i
$139$			15.3349i			1.30069i	0.759639	+	0.650346i	$0.225376\pi$
$139$			15.3349i			1.30069i	−0.759639	+	0.650346i	$0.774624\pi$
$140$	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	0.738493	−	0.674261i	$-0.235538\pi$
$149$	6.39393	+	3.69154i	0.523812	+	0.302423i	−0.214681	+	0.976684i	$0.568871\pi$
$150$	9.91465	+	3.35888i	0.809528	+	0.274251i
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	0.645259	−	0.763964i	$-0.276750\pi$
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	−0.984242	+	0.176828i	$0.943416\pi$
$152$	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	−0.725928	−	0.687770i	$-0.758590\pi$
$157$	−6.18061	+	3.56837i	−0.493266	+	0.284787i	0.232662	+	0.972558i	$0.425256\pi$
$158$	−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	0.726987	−	0.686652i	$-0.240920\pi$
$163$	6.33023	+	3.65476i	0.495822	+	0.286263i	−0.231164	+	0.972915i	$0.574254\pi$
$164$	−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	−0.156329	−	0.987705i	$-0.549966\pi$
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.933542	+	0.358468i	$0.883299\pi$
$174$	−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	−0.309790	−	0.950805i	$-0.600259\pi$
$179$	4.79957	−	2.77103i	0.358737	−	0.207117i	0.668526	+	0.743688i	$0.266925\pi$
$180$	0.345695	−	0.451649i	0.0257666	−	0.0336639i
$181$			9.98466i			0.742154i	0.928602	+	0.371077i	$0.121011\pi$
$181$			9.98466i			0.742154i	−0.928602	+	0.371077i	$0.878989\pi$
$182$	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	−0.869056	−	0.494714i	$-0.835273\pi$
$191$	−0.0842049	+	0.145847i	−0.00609285	+	0.0105531i	0.862963	+	0.505267i	$0.168606\pi$
$192$	1.69069	+	12.4914i	0.122015	+	0.901486i
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	0.698450	−	0.715659i	$-0.253873\pi$
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	−0.969004	+	0.247046i	$0.920540\pi$
$194$	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	$0.0152664\pi$
$197$			1.34581i			0.0958847i	−0.998850	+	0.0479424i	$0.984734\pi$
$198$	−0.342255	−	1.71521i	−0.0243230	−	0.121895i
$199$	6.38059	+	11.0515i	0.452308	+	0.783420i	0.998529	−	0.0542208i	$-0.0172675\pi$
$199$	6.38059	+	11.0515i	0.452308	+	0.783420i	−0.546221	+	0.837641i	$0.683934\pi$
$200$	−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	$-0.905903\pi$
$211$		−	8.46353i		−	0.582653i	0.956624	−	0.291327i	$-0.0940967\pi$
$212$	−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	−0.134382	−	0.990930i	$-0.542905\pi$
$227$	9.89265	−	5.71152i	0.656598	−	0.379087i	0.790980	+	0.611843i	$0.209571\pi$
$228$	−19.3267	+	8.03281i	−1.27994	+	0.531986i
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.925164	−	0.379568i	$-0.123928\pi$
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.133866	+	0.990999i	$0.457261\pi$
$230$	−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	−0.626292	−	0.779589i	$-0.715428\pi$
$233$	5.52566	−	9.57072i	0.361998	−	0.626999i	0.988290	+	0.152590i	$0.0487615\pi$
$234$	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	0.549656	−	0.835391i	$-0.314759\pi$
$241$	−6.96479	−	12.0634i	−0.448642	−	0.777070i	−0.998298	+	0.0583207i	$0.981425\pi$
$242$	−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	$-0.992907\pi$
$251$		−	0.706033i		−	0.0445644i	0.999752	−	0.0222822i	$-0.00709323\pi$
$252$	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	0.335320	+	0.942104i	$0.391156\pi$
$257$	−10.3919	+	17.9992i	−0.648226	+	1.12276i	−0.983546	+	0.180656i	$0.942178\pi$
$258$	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	0.967654	+	0.252281i	$0.0811809\pi$
$263$	11.3895	+	19.7273i	0.702309	+	1.21644i	−0.265345	+	0.964154i	$0.585486\pi$
$264$	−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	−0.418839	−	0.908060i	$-0.637563\pi$
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	0.576984	+	0.816756i	$0.304230\pi$
$270$	−1.38250	+	4.08084i	−0.0841365	+	0.248352i
$271$	12.5926	−	21.8109i	0.764943	−	1.32492i	−0.175333	−	0.984509i	$-0.556100\pi$
$271$	12.5926	−	21.8109i	0.764943	−	1.32492i	0.940277	−	0.340412i	$-0.110566\pi$
$272$	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	−0.233724	−	0.972303i	$-0.575091\pi$
$277$	8.17940	−	4.72238i	0.491453	−	0.283740i	0.725177	+	0.688563i	$0.241758\pi$
$278$	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	−0.127118	−	0.991888i	$-0.540573\pi$
$283$	11.2429	−	6.49111i	0.668323	−	0.385856i	0.795441	+	0.606031i	$0.207239\pi$
$284$	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	$-0.909885\pi$
$293$		−	9.56300i		−	0.558677i	0.960193	−	0.279338i	$-0.0901151\pi$
$294$	−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	$0.113398\pi$
$307$			12.2217i			0.697527i	−0.937211	+	0.348763i	$0.886602\pi$
$308$	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	−0.822311	−	0.569038i	$-0.807316\pi$
$311$	−15.9415	−	27.6114i	−0.903957	−	1.56570i	−0.0816453	−	0.996661i	$-0.526017\pi$
$312$	15.8680	+	7.78946i	0.898350	+	0.440991i
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	0.383230	+	0.923653i	$0.374811\pi$
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	−0.991522	+	0.129939i	$0.958522\pi$
$314$	−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	−0.183082	−	0.983098i	$-0.558607\pi$
$317$	−20.0481	−	11.5747i	−1.12601	−	0.650103i	−0.942929	+	0.332995i	$0.891941\pi$
$318$	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	−0.410086	−	0.912047i	$-0.634501\pi$
$331$	−25.5615	−	14.7579i	−1.40499	−	0.811169i	−0.994899	+	0.100878i	$0.967835\pi$
$332$	−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	−0.999528	−	0.0307361i	$-0.990215\pi$
$347$	−27.4329	+	15.8384i	−1.47267	+	0.850248i	−0.473146	+	0.880984i	$0.656882\pi$
$348$	−20.5629	−	15.7390i	−1.10229	−	0.843698i
$349$		−	28.4807i		−	1.52454i	−0.647260	−	0.762269i	$-0.724085\pi$
$349$		−	28.4807i		−	1.52454i	0.647260	−	0.762269i	$-0.275915\pi$
$350$	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	−0.998979	−	0.0451760i	$-0.985615\pi$
$353$	−10.1196	−	17.5277i	−0.538613	−	0.932905i	0.460366	−	0.887729i	$-0.347718\pi$
$354$	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	0.316889	+	0.948463i	$0.397362\pi$
$359$	−12.5611	+	21.7564i	−0.662948	+	1.14826i	−0.979837	+	0.199797i	$0.935972\pi$
$360$	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	0.924119	+	0.382104i	$0.124801\pi$
$367$	15.1912	+	26.3118i	0.792972	+	1.37347i	−0.131147	+	0.991363i	$0.541866\pi$
$368$	−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	0.620593	−	0.784133i	$-0.286892\pi$
$373$	4.86327	+	2.80781i	0.251811	+	0.145383i	−0.368782	+	0.929516i	$0.620225\pi$
$374$	−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	$-0.933543\pi$
$379$		−	8.07009i		−	0.414533i	0.978285	−	0.207266i	$-0.0664566\pi$
$380$	−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	−0.327022	−	0.945017i	$-0.606045\pi$
$383$	12.8166	−	22.1990i	0.654898	−	1.13432i	0.981919	−	0.189299i	$-0.0606216\pi$
$384$	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	−0.952655	−	0.304053i	$-0.901660\pi$
$389$	−22.9905	+	13.2736i	−1.16566	+	0.672997i	−0.213010	+	0.977050i	$0.568327\pi$
$390$	−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	0.999791	−	0.0204418i	$-0.00650729\pi$
$397$	29.5283	+	17.0482i	1.48198	+	0.855624i	0.482192	+	0.876065i	$0.339841\pi$
$398$	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	−0.998869	−	0.0475379i	$-0.984862\pi$
$401$	−9.17676	+	15.8946i	−0.458266	+	0.793739i	0.540604	+	0.841277i	$0.318196\pi$
$402$	−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	0.683445	−	0.730002i	$-0.260481\pi$
$409$	−5.87455	−	10.1750i	−0.290478	−	0.503122i	−0.973923	+	0.226880i	$0.927148\pi$
$410$	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	$-0.912729\pi$
$419$		−	11.0841i		−	0.541495i	0.962650	−	0.270748i	$-0.0872709\pi$
$420$	−4.46922	+	1.01707i	−0.218076	+	0.0496282i
$421$			0.137270i			0.00669012i	0.999994	+	0.00334506i	$0.00106477\pi$
$421$			0.137270i			0.00669012i	−0.999994	+	0.00334506i	$0.998935\pi$
$422$	−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	0.676064	−	0.736843i	$-0.263684\pi$
$431$	−6.23008	−	10.7908i	−0.300092	−	0.519775i	−0.976157	+	0.217067i	$0.930351\pi$
$432$	−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	−0.793510	−	0.608557i	$-0.791749\pi$
$439$	2.72948	−	4.72760i	0.130271	−	0.225636i	0.923781	+	0.382921i	$0.125082\pi$
$440$	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	0.991131	−	0.132889i	$-0.0424254\pi$
$443$	28.8691	+	16.6676i	1.37161	+	0.791900i	0.380480	+	0.924789i	$0.375759\pi$
$444$	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	−0.998160	−	0.0606278i	$-0.980690\pi$
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	0.551585	+	0.834118i	$0.314023\pi$
$458$	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	$0.145214\pi$
$461$			18.9177i			0.881087i	−0.897731	+	0.440543i	$0.854786\pi$
$462$	−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	0.0763871	−	0.997078i	$-0.475662\pi$
$467$	−16.1842	−	9.34394i	−0.748914	−	0.432386i	−0.825302	+	0.564692i	$0.808995\pi$
$468$	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	0.996300	−	0.0859405i	$-0.0273895\pi$
$479$	9.27364	+	16.0624i	0.423723	+	0.733911i	−0.572577	+	0.819851i	$0.694056\pi$
$480$	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	0.999750	+	0.0223676i	$0.00712041\pi$
$487$	11.4588	+	19.8471i	0.519246	+	0.899360i	−0.480504	+	0.876993i	$0.659546\pi$
$488$	−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	$0.189036\pi$
$491$			24.7987i			1.11915i	−0.828780	+	0.559575i	$0.810964\pi$
$492$	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	−0.999701	−	0.0244624i	$-0.992213\pi$
$499$	−33.9707	−	19.6130i	−1.52074	−	0.877997i	−0.521035	−	0.853535i	$-0.674454\pi$
$500$	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	0.413596	−	0.910460i	$-0.364272\pi$
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	−0.581684	+	0.813415i	$0.697606\pi$
$510$	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	0.959455	−	0.281863i	$-0.0909525\pi$
$521$	5.37827	+	9.31544i	0.235626	+	0.408117i	−0.723828	+	0.689980i	$0.757619\pi$
$522$	−5.69366	−	1.92890i	−0.249205	−	0.0844255i
$523$	2.43561	+	1.40620i	0.106502	+	0.0614889i	0.552305	−	0.833642i	$-0.313748\pi$
$523$	2.43561	+	1.40620i	0.106502	+	0.0614889i	−0.445803	+	0.895131i	$0.647082\pi$
$524$	−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	0.952218	−	0.305419i	$-0.0987966\pi$
$541$	27.0699	+	15.6288i	1.16383	+	0.671935i	0.211608	+	0.977355i	$0.432130\pi$
$542$	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	$-0.783035\pi$
$547$		−	29.4711i		−	1.26010i	0.776556	−	0.630048i	$-0.216965\pi$
$548$	−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	−0.850744	−	0.525580i	$-0.823848\pi$
$557$	−19.3751	+	11.1862i	−0.820950	+	0.473976i	0.0297941	+	0.999556i	$0.490515\pi$
$558$	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	−0.956542	−	0.291594i	$-0.905814\pi$
$563$	−28.0528	+	16.1963i	−1.18229	+	0.682593i	−0.225743	+	0.974187i	$0.572481\pi$
$564$	−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	−0.157029	−	0.987594i	$-0.550192\pi$
$569$	18.5288	−	32.0928i	0.776767	−	1.34540i	0.933796	−	0.357806i	$-0.116475\pi$
$570$	7.70563	+	2.61051i	0.322753	+	0.109342i
$571$	−19.4303	+	11.2181i	−0.813132	+	0.469462i	−0.848042	−	0.529928i	$-0.822219\pi$
$571$	−19.4303	+	11.2181i	−0.813132	+	0.469462i	0.0349102	+	0.999390i	$0.488885\pi$
$572$	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	0.749087	−	0.662471i	$-0.230492\pi$
$577$	−4.78431	−	8.28667i	−0.199173	−	0.344978i	−0.948261	+	0.317493i	$0.897159\pi$
$578$	−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	$0.162595\pi$
$587$			23.6894i			0.977766i	−0.872349	+	0.488883i	$0.837405\pi$
$588$	−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	−0.779375	−	0.626558i	$-0.784463\pi$
$593$	3.72404	−	6.45023i	0.152928	−	0.264879i	0.932303	+	0.361679i	$0.117796\pi$
$594$	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	0.848406	−	0.529346i	$-0.177563\pi$
$599$	−0.837627	−	1.45081i	−0.0342245	−	0.0592786i	−0.882630	+	0.470068i	$0.844229\pi$
$600$	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	−0.460593	−	0.887611i	$-0.652363\pi$
$607$	13.2647	−	22.9751i	0.538397	−	0.932531i	0.998991	−	0.0449200i	$-0.0143033\pi$
$608$	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	0.167788	−	0.985823i	$-0.446338\pi$
$613$	27.3692	−	15.8016i	1.10543	−	0.638220i	0.937642	+	0.347603i	$0.113004\pi$
$614$	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	−0.593184	−	0.805067i	$-0.702129\pi$
$619$	−4.79105	+	2.76611i	−0.192568	+	0.111179i	0.400616	+	0.916246i	$0.368796\pi$
$620$	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	0.757287	−	0.653082i	$-0.226524\pi$
$641$	−4.73300	−	8.19779i	−0.186942	−	0.323793i	−0.944229	+	0.329289i	$0.893191\pi$
$642$	−0.740603	+	0.147781i	−0.0292293	+	0.00583245i
$643$			13.0085i			0.513007i	0.966543	+	0.256503i	$0.0825705\pi$
$643$			13.0085i			0.513007i	−0.966543	+	0.256503i	$0.917430\pi$
$644$	−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	−0.998847	−	0.0480078i	$-0.984713\pi$
$647$	−13.7610	−	23.8347i	−0.540999	−	0.937039i	0.457848	−	0.889031i	$-0.348621\pi$
$648$	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	0.958572	−	0.284850i	$-0.0919439\pi$
$653$	30.4390	+	17.5740i	1.19117	+	0.687723i	0.232598	+	0.972573i	$0.425277\pi$
$654$	−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	$-0.976001\pi$
$659$		−	3.86719i		−	0.150644i	0.997159	−	0.0753222i	$-0.0239985\pi$
$660$	−2.51735	+	3.28890i	−0.0979875	+	0.128020i
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	−0.192403	−	0.981316i	$-0.561628\pi$
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	0.753643	+	0.657284i	$0.228295\pi$
$662$	−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	−0.380334	−	0.924849i	$-0.624191\pi$
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.991110	+	0.133045i	$0.957524\pi$
$678$	−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	0.161427	−	0.986885i	$-0.448390\pi$
$683$	28.6643	−	16.5493i	1.09681	−	0.633242i	0.935381	+	0.353642i	$0.115057\pi$
$684$	−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	0.724897	−	0.688857i	$-0.241887\pi$
$691$	12.9010	+	7.44840i	0.490777	+	0.283350i	−0.234120	+	0.972208i	$0.575221\pi$
$692$	−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	$-0.789090\pi$
$701$		−	32.5746i		−	1.23032i	0.788401	−	0.615162i	$-0.210910\pi$
$702$	−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	0.675169	−	0.737663i	$-0.264071\pi$
$709$	9.95635	+	5.74830i	0.373918	+	0.215882i	−0.301251	+	0.953545i	$0.597404\pi$
$710$	−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	−0.496949	−	0.867780i	$-0.665546\pi$
$719$	13.4887	−	23.3632i	0.503045	−	0.871299i	0.999994	−	0.00351948i	$-0.00112029\pi$
$720$	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	0.131428	−	0.991326i	$-0.458044\pi$
$733$	−17.9059	−	10.3380i	−0.661371	−	0.381843i	−0.792799	+	0.609483i	$0.791377\pi$
$734$	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	−0.661294	−	0.750126i	$-0.729993\pi$
$739$	−9.30563	+	5.37261i	−0.342313	+	0.197635i	0.318981	+	0.947761i	$0.396659\pi$
$740$	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	−0.978654	−	0.205513i	$-0.934114\pi$
$751$	−8.53229	+	14.7784i	−0.311348	+	0.539270i	0.667307	+	0.744783i	$0.267447\pi$
$752$	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	$0.318560\pi$
$757$			46.3272i			1.68379i	−0.539641	+	0.841895i	$0.681440\pi$
$758$	−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	−0.702714	−	0.711473i	$-0.748029\pi$
$761$	7.30474	−	12.6522i	0.264796	−	0.458641i	0.967510	+	0.252832i	$0.0813619\pi$
$762$	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	−0.516147	−	0.856500i	$-0.672634\pi$
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	0.483677	+	0.875246i	$0.339301\pi$
$774$	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	0.273847	−	0.961773i	$-0.411704\pi$
$787$	34.8899	−	20.1437i	1.24369	−	0.718045i	0.969844	+	0.243728i	$0.0783705\pi$
$788$	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	$0.193789\pi$
$797$			32.2902i			1.14378i	−0.820331	+	0.571889i	$0.806211\pi$
$798$	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	−0.956135	−	0.292926i	$-0.905371\pi$
$809$	−20.8131	−	36.0493i	−0.731749	−	1.26743i	0.224386	−	0.974500i	$-0.427962\pi$
$810$	−1.09239	−	5.47452i	−0.0383828	−	0.192355i
$811$			18.7227i			0.657444i	0.944427	+	0.328722i	$0.106618\pi$
$811$			18.7227i			0.657444i	−0.944427	+	0.328722i	$0.893382\pi$
$812$	−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	0.189274	−	0.981924i	$-0.439386\pi$
$821$	−16.2308	−	9.37088i	−0.566460	−	0.327046i	−0.755734	+	0.654878i	$0.772720\pi$
$822$	6.85847	+	2.32351i	0.239217	+	0.0810417i
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	0.987337	−	0.158636i	$-0.0507095\pi$
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	−0.631051	+	0.775741i	$0.717376\pi$
$824$	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	$-0.679341\pi$
$827$		−	48.6254i		−	1.69087i	0.534079	−	0.845435i	$-0.320659\pi$
$828$	1.92978	+	1.47707i	0.0670647	+	0.0513317i
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	−0.601559	−	0.798829i	$-0.705453\pi$
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	0.391026	+	0.920379i	$0.372120\pi$
$830$	−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	$-0.823164\pi$
$853$		−	30.8071i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$854$	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	0.725014	−	0.688734i	$-0.241833\pi$
$857$	−6.84889	−	11.8626i	−0.233954	−	0.405220i	−0.958968	+	0.283514i	$0.908500\pi$
$858$	−20.0132	−	6.78005i	−0.683238	−	0.231467i
$859$	7.52869	+	4.34669i	0.256876	+	0.148307i	0.622908	−	0.782295i	$-0.285951\pi$
$859$	7.52869	+	4.34669i	0.256876	+	0.148307i	−0.366033	+	0.930602i	$0.619284\pi$
$860$	−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	−0.860940	−	0.508706i	$-0.830124\pi$
$863$	0.296174	−	0.512989i	0.0100819	−	0.0174623i	0.871022	+	0.491243i	$0.163457\pi$
$864$	−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	0.259690	−	0.965692i	$-0.416380\pi$
$877$	−13.2310	−	7.63892i	−0.446779	−	0.257948i	−0.706469	+	0.707744i	$0.749713\pi$
$878$	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	$0.110536\pi$
$883$			20.2255i			0.680642i	−0.940309	+	0.340321i	$0.889464\pi$
$884$	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	−0.988294	−	0.152563i	$-0.951247\pi$
$887$	−10.7820	+	18.6750i	−0.362024	+	0.627044i	0.626270	+	0.779606i	$0.284581\pi$
$888$	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	0.0280482	−	0.999607i	$-0.491071\pi$
$907$	27.3384	−	15.7838i	0.907757	−	0.524094i	0.879709	+	0.475513i	$0.157737\pi$
$908$	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	−0.965464	−	0.260535i	$-0.916101\pi$
$919$	−7.79407	+	13.4997i	−0.257103	+	0.445315i	0.708362	+	0.705849i	$0.249434\pi$
$920$	−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	0.296411	+	0.955060i	$0.404210\pi$
$929$	−20.6926	+	35.8406i	−0.678901	+	1.17589i	−0.975312	+	0.220830i	$0.929123\pi$
$930$	−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	0.153841	−	0.988096i	$-0.450836\pi$
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.932636	+	0.360818i	$0.117502\pi$
$942$	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	0.629673	−	0.776861i	$-0.283189\pi$
$947$	8.36198	+	4.82779i	0.271728	+	0.156882i	−0.357945	+	0.933743i	$0.616522\pi$
$948$	−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	0.968022	−	0.250865i	$-0.0807151\pi$
$971$	38.4767	+	22.2146i	1.23478	+	0.712899i	0.266755	+	0.963764i	$0.414048\pi$
$972$	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	0.997155	−	0.0753795i	$-0.0240168\pi$
$977$	13.5436	+	23.4581i	0.433297	+	0.750492i	−0.563858	+	0.825872i	$0.690684\pi$
$978$	−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	0.593635	−	0.804735i	$-0.297692\pi$
$983$	−12.5444	−	21.7275i	−0.400103	−	0.692999i	−0.993738	+	0.111736i	$0.964359\pi$
$984$	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	0.691258	−	0.722608i	$-0.257057\pi$
$991$	−8.81972	−	15.2762i	−0.280168	−	0.485265i	−0.971426	+	0.237343i	$0.923723\pi$
$992$	−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	−0.857583	−	0.514345i	$-0.828035\pi$
$997$	−26.5529	+	15.3303i	−0.840939	+	0.485516i	0.0166442	+	0.999861i	$0.494702\pi$
$998$	−52.5407	−	17.7997i	−1.66315	−	0.563440i
$999$	−0.735311	+	1.27360i	−0.0232642	+	0.0402948i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	8.5	even	2	inner
56.2.p.a.37.6	yes	12	1.1	even	1	trivial
56.2.p.a.53.3	yes	12	7.4	even	3	inner
56.2.p.a.53.6	yes	12	56.53	even	6	inner
224.2.t.a.81.2		12	28.11	odd	6
224.2.t.a.81.5		12	56.11	odd	6
224.2.t.a.177.2		12	8.3	odd	2
224.2.t.a.177.5		12	4.3	odd	2
392.2.b.e.197.1		6	7.2	even	3
392.2.b.e.197.2		6	56.37	even	6
392.2.b.f.197.1		6	7.5	odd	6
392.2.b.f.197.2		6	56.5	odd	6
392.2.p.g.165.3		12	7.3	odd	6
392.2.p.g.165.6		12	56.45	odd	6
392.2.p.g.373.3		12	56.13	odd	2
392.2.p.g.373.6		12	7.6	odd	2
504.2.cj.c.37.1		12	3.2	odd	2
504.2.cj.c.37.4		12	24.5	odd	2
504.2.cj.c.109.1		12	168.53	odd	6
504.2.cj.c.109.4		12	21.11	odd	6
1568.2.b.e.785.2		6	28.19	even	6
1568.2.b.e.785.5		6	56.19	even	6
1568.2.b.f.785.2		6	56.51	odd	6
1568.2.b.f.785.5		6	28.23	odd	6
1568.2.t.g.177.2		12	28.27	even	2
1568.2.t.g.177.5		12	56.27	even	2
1568.2.t.g.753.2		12	56.3	even	6
1568.2.t.g.753.5		12	28.3	even	6
2016.2.cr.c.1297.3		12	24.11	even	2
2016.2.cr.c.1297.4		12	12.11	even	2
2016.2.cr.c.1873.3		12	84.11	even	6
2016.2.cr.c.1873.4		12	168.11	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(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

Introduction

L-functions

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