LMFDB - Embedded newform 1110.2.ba.b.529.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.5
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.b.619.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57405 + 1.58819i) q^{5} -1.00000i q^{6} +(-1.99912 - 1.15419i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57405 + 1.58819i) q^{5} -1.00000i q^{6} +(-1.99912 - 1.15419i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.588388 + 2.15727i) q^{10} +3.60666 q^{11} +(0.866025 - 0.500000i) q^{12} +(-2.08315 + 3.60811i) q^{13} -2.30838i q^{14} +(-0.569075 - 2.16244i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.64189 + 2.84383i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-3.53639 - 2.04174i) q^{19} +(-2.16244 + 0.569075i) q^{20} +(1.15419 + 1.99912i) q^{21} +(1.80333 + 3.12346i) q^{22} +0.748890 q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.0447077 + 4.99980i) q^{25} -4.16629 q^{26} -1.00000i q^{27} +(1.99912 - 1.15419i) q^{28} +3.31885i q^{29} +(1.58819 - 1.57405i) q^{30} +4.54696i q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.12346 - 1.80333i) q^{33} +(-1.64189 + 2.84383i) q^{34} +(-1.31364 - 4.99174i) q^{35} -1.00000 q^{36} +(4.22132 + 4.37955i) q^{37} -4.08347i q^{38} +(3.60811 - 2.08315i) q^{39} +(-1.57405 - 1.58819i) q^{40} +(-1.97387 + 3.41884i) q^{41} +(-1.15419 + 1.99912i) q^{42} -11.6588 q^{43} +(-1.80333 + 3.12346i) q^{44} +(-0.588388 + 2.15727i) q^{45} +(0.374445 + 0.648558i) q^{46} +1.55975i q^{47} +1.00000i q^{48} +(-0.835693 - 1.44746i) q^{49} +(-4.35231 + 2.46118i) q^{50} -3.28377i q^{51} +(-2.08315 - 3.60811i) q^{52} +(2.02580 - 1.16959i) q^{53} +(0.866025 - 0.500000i) q^{54} +(5.67708 + 5.72807i) q^{55} +(1.99912 + 1.15419i) q^{56} +(2.04174 + 3.53639i) q^{57} +(-2.87421 + 1.65943i) q^{58} +(-10.1511 + 5.86075i) q^{59} +(2.15727 + 0.588388i) q^{60} +(2.15821 + 1.24604i) q^{61} +(-3.93778 + 2.27348i) q^{62} -2.30838i q^{63} +1.00000 q^{64} +(-9.00936 + 2.37093i) q^{65} -3.60666i q^{66} +(6.87799 + 3.97101i) q^{67} -3.28377 q^{68} +(-0.648558 - 0.374445i) q^{69} +(3.66615 - 3.63351i) q^{70} +(0.361447 - 0.626045i) q^{71} +(-0.500000 - 0.866025i) q^{72} +0.278797i q^{73} +(-1.68214 + 5.84555i) q^{74} +(2.53862 - 4.30760i) q^{75} +(3.53639 - 2.04174i) q^{76} +(-7.21014 - 4.16277i) q^{77} +(3.60811 + 2.08315i) q^{78} +(7.52682 + 4.34561i) q^{79} +(0.588388 - 2.15727i) q^{80} +(-0.500000 + 0.866025i) q^{81} -3.94773 q^{82} +(5.53660 - 3.19656i) q^{83} -2.30838 q^{84} +(-1.93213 + 7.08397i) q^{85} +(-5.82942 - 10.0969i) q^{86} +(1.65943 - 2.87421i) q^{87} -3.60666 q^{88} +(-5.28646 + 3.05214i) q^{89} +(-2.16244 + 0.569075i) q^{90} +(8.32890 - 4.80869i) q^{91} +(-0.374445 + 0.648558i) q^{92} +(2.27348 - 3.93778i) q^{93} +(-1.35078 + 0.779875i) q^{94} +(-2.32380 - 8.83027i) q^{95} +(-0.866025 + 0.500000i) q^{96} -4.51721 q^{97} +(0.835693 - 1.44746i) q^{98} +(1.80333 + 3.12346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.57405	+	1.58819i	0.703938	+	0.710261i
$5$	1.57405	+	1.58819i	0.703938	+	0.710261i
$6$		−	1.00000i		−	0.408248i
$7$	−1.99912	−	1.15419i	−0.755594	−	0.436243i	0.0721173	−	0.997396i	$-0.477024\pi$
$7$	−1.99912	−	1.15419i	−0.755594	−	0.436243i	−0.827712	+	0.561153i	$0.810358\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.588388	+	2.15727i	−0.186064	+	0.682188i
$11$	3.60666			1.08745			0.543725	−	0.839263i	$-0.317013\pi$
$11$	3.60666			1.08745			0.543725	+	0.839263i	$0.317013\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−2.08315	+	3.60811i	−0.577761	+	1.00071i	0.417975	+	0.908459i	$0.362740\pi$
$13$	−2.08315	+	3.60811i	−0.577761	+	1.00071i	−0.995736	+	0.0922523i	$0.970593\pi$
$14$		−	2.30838i		−	0.616940i
$15$	−0.569075	−	2.16244i	−0.146934	−	0.558340i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.64189	+	2.84383i	0.398216	+	0.689730i	0.993506	−	0.113781i	$-0.0362961\pi$
$17$	1.64189	+	2.84383i	0.398216	+	0.689730i	−0.595290	+	0.803511i	$0.702963\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−3.53639	−	2.04174i	−0.811303	−	0.468406i	0.0361050	−	0.999348i	$-0.488505\pi$
$19$	−3.53639	−	2.04174i	−0.811303	−	0.468406i	−0.847408	+	0.530942i	$0.821838\pi$
$20$	−2.16244	+	0.569075i	−0.483537	+	0.127249i
$21$	1.15419	+	1.99912i	0.251865	+	0.436243i
$22$	1.80333	+	3.12346i	0.384472	+	0.665924i
$23$	0.748890			0.156154			0.0780772	−	0.996947i	$-0.475122\pi$
$23$	0.748890			0.156154			0.0780772	+	0.996947i	$0.475122\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−0.0447077	+	4.99980i	−0.00894155	+	0.999960i
$26$	−4.16629			−0.817077
$27$		−	1.00000i		−	0.192450i
$28$	1.99912	−	1.15419i	0.377797	−	0.218121i
$29$			3.31885i			0.616295i	0.951339	+	0.308148i	$0.0997091\pi$
$29$			3.31885i			0.616295i	−0.951339	+	0.308148i	$0.900291\pi$
$30$	1.58819	−	1.57405i	0.289963	−	0.287382i
$31$			4.54696i			0.816658i	0.912835	+	0.408329i	$0.133888\pi$
$31$			4.54696i			0.816658i	−0.912835	+	0.408329i	$0.866112\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.12346	−	1.80333i	−0.543725	−	0.313920i
$34$	−1.64189	+	2.84383i	−0.281581	+	0.487713i
$35$	−1.31364	−	4.99174i	−0.222046	−	0.843757i
$36$	−1.00000			−0.166667
$37$	4.22132	+	4.37955i	0.693981	+	0.719993i
$37$	4.22132	+	4.37955i	0.693981	+	0.719993i
$38$		−	4.08347i		−	0.662426i
$39$	3.60811	−	2.08315i	0.577761	−	0.333570i
$40$	−1.57405	−	1.58819i	−0.248880	−	0.251115i
$41$	−1.97387	+	3.41884i	−0.308266	+	0.533933i	−0.977983	−	0.208684i	$-0.933082\pi$
$41$	−1.97387	+	3.41884i	−0.308266	+	0.533933i	0.669717	+	0.742616i	$0.266415\pi$
$42$	−1.15419	+	1.99912i	−0.178095	+	0.308470i
$43$	−11.6588			−1.77796			−0.888979	−	0.457949i	$-0.848584\pi$
$43$	−11.6588			−1.77796			−0.888979	+	0.457949i	$0.848584\pi$
$44$	−1.80333	+	3.12346i	−0.271863	+	0.470880i
$45$	−0.588388	+	2.15727i	−0.0877116	+	0.321586i
$46$	0.374445	+	0.648558i	0.0552089	+	0.0956247i
$47$			1.55975i			0.227513i	0.993509	+	0.113757i	$0.0362884\pi$
$47$			1.55975i			0.227513i	−0.993509	+	0.113757i	$0.963712\pi$
$48$			1.00000i			0.144338i
$49$	−0.835693	−	1.44746i	−0.119385	−	0.206780i
$50$	−4.35231	+	2.46118i	−0.615509	+	0.348064i
$51$		−	3.28377i		−	0.459820i
$52$	−2.08315	−	3.60811i	−0.288880	−	0.500355i
$53$	2.02580	−	1.16959i	0.278265	−	0.160656i	−0.354373	−	0.935104i	$-0.615306\pi$
$53$	2.02580	−	1.16959i	0.278265	−	0.160656i	0.632638	+	0.774448i	$0.281972\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	5.67708	+	5.72807i	0.765498	+	0.772373i
$56$	1.99912	+	1.15419i	0.267143	+	0.154235i
$57$	2.04174	+	3.53639i	0.270434	+	0.468406i
$58$	−2.87421	+	1.65943i	−0.377402	+	0.217893i
$59$	−10.1511	+	5.86075i	−1.32156	+	0.763004i	−0.983978	−	0.178291i	$-0.942943\pi$
$59$	−10.1511	+	5.86075i	−1.32156	+	0.763004i	−0.337585	+	0.941295i	$0.609610\pi$
$60$	2.15727	+	0.588388i	0.278502	+	0.0759605i
$61$	2.15821	+	1.24604i	0.276330	+	0.159539i	0.631761	−	0.775163i	$-0.282332\pi$
$61$	2.15821	+	1.24604i	0.276330	+	0.159539i	−0.355431	+	0.934703i	$0.615666\pi$
$62$	−3.93778	+	2.27348i	−0.500099	+	0.288732i
$63$		−	2.30838i		−	0.290828i
$64$	1.00000			0.125000
$65$	−9.00936	+	2.37093i	−1.11747	+	0.294078i
$66$		−	3.60666i		−	0.443950i
$67$	6.87799	+	3.97101i	0.840280	+	0.485136i	0.857359	−	0.514718i	$-0.172104\pi$
$67$	6.87799	+	3.97101i	0.840280	+	0.485136i	−0.0170795	+	0.999854i	$0.505437\pi$
$68$	−3.28377			−0.398216
$69$	−0.648558	−	0.374445i	−0.0780772	−	0.0450779i
$70$	3.66615	−	3.63351i	0.438189	−	0.434288i
$71$	0.361447	−	0.626045i	0.0428959	−	0.0742978i	−0.843780	−	0.536689i	$-0.819675\pi$
$71$	0.361447	−	0.626045i	0.0428959	−	0.0742978i	0.886676	+	0.462391i	$0.153008\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$			0.278797i			0.0326307i	0.999867	+	0.0163154i	$0.00519357\pi$
$73$			0.278797i			0.0326307i	−0.999867	+	0.0163154i	$0.994806\pi$
$74$	−1.68214	+	5.84555i	−0.195544	+	0.679531i
$75$	2.53862	−	4.30760i	0.293134	−	0.497399i
$76$	3.53639	−	2.04174i	0.405652	−	0.234203i
$77$	−7.21014	−	4.16277i	−0.821671	−	0.474392i
$78$	3.60811	+	2.08315i	0.408538	+	0.235870i
$79$	7.52682	+	4.34561i	0.846833	+	0.488919i	0.859581	−	0.511000i	$-0.170725\pi$
$79$	7.52682	+	4.34561i	0.846833	+	0.488919i	−0.0127481	+	0.999919i	$0.504058\pi$
$80$	0.588388	−	2.15727i	0.0657837	−	0.241190i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.94773			−0.435954
$83$	5.53660	−	3.19656i	0.607721	−	0.350868i	−0.164352	−	0.986402i	$-0.552553\pi$
$83$	5.53660	−	3.19656i	0.607721	−	0.350868i	0.772073	+	0.635534i	$0.219220\pi$
$84$	−2.30838			−0.251865
$85$	−1.93213	+	7.08397i	−0.209569	+	0.768365i
$86$	−5.82942	−	10.0969i	−0.628603	−	1.08877i
$87$	1.65943	−	2.87421i	0.177909	−	0.308148i
$88$	−3.60666			−0.384472
$89$	−5.28646	+	3.05214i	−0.560364	+	0.323526i	−0.753292	−	0.657687i	$-0.771535\pi$
$89$	−5.28646	+	3.05214i	−0.560364	+	0.323526i	0.192928	+	0.981213i	$0.438202\pi$
$90$	−2.16244	+	0.569075i	−0.227941	+	0.0599857i
$91$	8.32890	−	4.80869i	0.873106	−	0.504088i
$92$	−0.374445	+	0.648558i	−0.0390386	+	0.0676169i
$93$	2.27348	−	3.93778i	0.235749	−	0.408329i
$94$	−1.35078	+	0.779875i	−0.139323	+	0.0804380i
$95$	−2.32380	−	8.83027i	−0.238417	−	0.905966i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−4.51721			−0.458653			−0.229327	−	0.973350i	$-0.573652\pi$
$97$	−4.51721			−0.458653			−0.229327	+	0.973350i	$0.573652\pi$
$98$	0.835693	−	1.44746i	0.0844177	−	0.146216i
$99$	1.80333	+	3.12346i	0.181242	+	0.313920i
$100$	−4.30760	−	2.53862i	−0.430760	−	0.253862i
$101$	−3.92973			−0.391022			−0.195511	−	0.980701i	$-0.562637\pi$
$101$	−3.92973			−0.391022			−0.195511	+	0.980701i	$0.562637\pi$
$102$	2.84383	−	1.64189i	0.281581	−	0.162571i
$103$	−13.0004			−1.28096			−0.640482	−	0.767973i	$-0.721265\pi$
$103$	−13.0004			−1.28096			−0.640482	+	0.767973i	$0.721265\pi$
$104$	2.08315	−	3.60811i	0.204269	−	0.353805i
$105$	−1.35822	+	4.97979i	−0.132549	+	0.485978i
$106$	2.02580	+	1.16959i	0.196763	+	0.113601i
$107$	5.99495	+	3.46119i	0.579554	+	0.334606i	0.760956	−	0.648803i	$-0.224730\pi$
$107$	5.99495	+	3.46119i	0.579554	+	0.334606i	−0.181402	+	0.983409i	$0.558064\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	8.88722	−	5.13104i	0.851242	−	0.491465i	−0.00982793	−	0.999952i	$-0.503128\pi$
$109$	8.88722	−	5.13104i	0.851242	−	0.491465i	0.861070	+	0.508487i	$0.169795\pi$
$110$	−2.12212	+	7.78054i	−0.202336	+	0.741845i
$111$	−1.46600	−	5.90346i	−0.139147	−	0.560332i
$112$			2.30838i			0.218121i
$113$	0.115280	+	0.199671i	0.0108446	+	0.0187835i	0.871397	−	0.490579i	$-0.163215\pi$
$113$	0.115280	+	0.199671i	0.0108446	+	0.0187835i	−0.860552	+	0.509362i	$0.829881\pi$
$114$	−2.04174	+	3.53639i	−0.191226	+	0.331213i
$115$	1.17879	+	1.18938i	0.109923	+	0.110910i
$116$	−2.87421	−	1.65943i	−0.266864	−	0.154074i
$117$	−4.16629			−0.385174
$118$	−10.1511	−	5.86075i	−0.934486	−	0.539526i
$119$		−	7.58019i		−	0.694875i
$120$	0.569075	+	2.16244i	0.0519492	+	0.197403i
$121$	2.00802			0.182548
$122$			2.49208i			0.225623i
$123$	3.41884	−	1.97387i	0.308266	−	0.177978i
$124$	−3.93778	−	2.27348i	−0.353623	−	0.204164i
$125$	−8.01101	+	7.79895i	−0.716527	+	0.697559i
$126$	1.99912	−	1.15419i	0.178095	−	0.102823i
$127$	11.4021	−	6.58300i	1.01177	−	0.584147i	0.100062	−	0.994981i	$-0.468096\pi$
$127$	11.4021	−	6.58300i	1.01177	−	0.584147i	0.911710	+	0.410834i	$0.134762\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	10.0969	+	5.82942i	0.888979	+	0.513252i
$130$	−6.55797	−	6.61687i	−0.575172	−	0.580338i
$131$	14.1821	−	8.18806i	1.23910	−	0.715394i	0.270189	−	0.962807i	$-0.412914\pi$
$131$	14.1821	−	8.18806i	1.23910	−	0.715394i	0.968910	+	0.247413i	$0.0795804\pi$
$132$	3.12346	−	1.80333i	0.271863	−	0.156960i
$133$	4.71310	+	8.16333i	0.408678	+	0.707850i
$134$			7.94202i			0.686086i
$135$	1.58819	−	1.57405i	0.136690	−	0.135473i
$136$	−1.64189	−	2.84383i	−0.140791	−	0.243856i
$137$			8.12613i			0.694263i	0.937817	+	0.347131i	$0.112844\pi$
$137$			8.12613i			0.694263i	−0.937817	+	0.347131i	$0.887156\pi$
$138$		−	0.748890i		−	0.0637498i
$139$	5.13844	+	8.90004i	0.435837	+	0.754892i	0.997364	−	0.0725670i	$-0.0231191\pi$
$139$	5.13844	+	8.90004i	0.435837	+	0.754892i	−0.561527	+	0.827459i	$0.689786\pi$
$140$	4.97979	+	1.35822i	0.420869	+	0.114791i
$141$	0.779875	−	1.35078i	0.0656774	−	0.113757i
$142$	0.722894			0.0606639
$143$	−7.51321	+	13.0133i	−0.628286	+	1.08822i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−5.27097	+	5.22405i	−0.437731	+	0.433834i
$146$	−0.241445	+	0.139399i	−0.0199822	+	0.0115367i
$147$			1.67139i			0.137854i
$148$	−5.90346	+	1.46600i	−0.485261	+	0.120504i
$149$	−20.4186			−1.67275			−0.836376	−	0.548156i	$-0.815330\pi$
$149$	−20.4186			−1.67275			−0.836376	+	0.548156i	$0.815330\pi$
$150$	4.99980	+	0.0447077i	0.408232	+	0.00365037i
$151$	6.59299	−	11.4194i	0.536530	−	0.929297i	−0.462558	−	0.886589i	$-0.653068\pi$
$151$	6.59299	−	11.4194i	0.536530	−	0.929297i	0.999088	−	0.0427080i	$-0.0135985\pi$
$152$	3.53639	+	2.04174i	0.286839	+	0.165607i
$153$	−1.64189	+	2.84383i	−0.132739	+	0.229910i
$154$		−	8.32555i		−	0.670892i
$155$	−7.22144	+	7.15716i	−0.580040	+	0.574877i
$156$			4.16629i			0.333570i
$157$	12.8251	−	7.40456i	1.02355	−	0.590948i	0.108421	−	0.994105i	$-0.465421\pi$
$157$	12.8251	−	7.40456i	1.02355	−	0.590948i	0.915131	+	0.403157i	$0.132087\pi$
$158$			8.69122i			0.691436i
$159$	−2.33919			−0.185510
$160$	2.16244	−	0.569075i	0.170956	−	0.0449893i
$161$	−1.49712	−	0.864361i	−0.117989	−	0.0681212i
$162$	−1.00000			−0.0785674
$163$	5.57244	+	9.65175i	0.436467	+	0.755984i	0.997414	−	0.0718681i	$-0.0228961\pi$
$163$	5.57244	+	9.65175i	0.436467	+	0.755984i	−0.560947	+	0.827852i	$0.689563\pi$
$164$	−1.97387	−	3.41884i	−0.154133	−	0.266966i
$165$	−2.05246	−	7.79920i	−0.159784	−	0.607167i
$166$	5.53660	+	3.19656i	0.429723	+	0.248101i
$167$	4.20425	−	7.28198i	0.325335	−	0.563496i	−0.656245	−	0.754548i	$-0.727856\pi$
$167$	4.20425	−	7.28198i	0.325335	−	0.563496i	0.981580	+	0.191051i	$0.0611897\pi$
$168$	−1.15419	−	1.99912i	−0.0890477	−	0.154235i
$169$	−2.17899	−	3.77413i	−0.167615	−	0.290317i
$170$	−7.10097	+	1.86871i	−0.544619	+	0.143324i
$171$		−	4.08347i		−	0.312271i
$172$	5.82942	−	10.0969i	0.444489	−	0.769878i
$173$	14.2350	−	8.21856i	1.08226	−	0.624846i	0.150758	−	0.988571i	$-0.451828\pi$
$173$	14.2350	−	8.21856i	1.08226	−	0.624846i	0.931506	+	0.363725i	$0.118495\pi$
$174$	3.31885			0.251601
$175$	5.86009	−	9.94357i	0.442981	−	0.751664i
$176$	−1.80333	−	3.12346i	−0.135931	−	0.235440i
$177$	11.7215			0.881042
$178$	−5.28646	−	3.05214i	−0.396237	−	0.228768i
$179$		−	1.46972i		−	0.109852i	−0.998490	−	0.0549259i	$-0.982508\pi$
$179$		−	1.46972i		−	0.109852i	0.998490	−	0.0549259i	$-0.0174922\pi$
$180$	−1.57405	−	1.58819i	−0.117323	−	0.118377i
$181$	2.61171	−	4.52361i	0.194127	−	0.336237i	−0.752487	−	0.658607i	$-0.771146\pi$
$181$	2.61171	−	4.52361i	0.194127	−	0.336237i	0.946614	+	0.322370i	$0.104479\pi$
$182$	8.32890	+	4.80869i	0.617379	+	0.356444i
$183$	−1.24604	−	2.15821i	−0.0921100	−	0.159539i
$184$	−0.748890			−0.0552089
$185$	−0.310969	+	13.5979i	−0.0228629	+	0.999739i
$186$	4.54696			0.333399
$187$	5.92173	+	10.2567i	0.433040	+	0.750047i
$188$	−1.35078	−	0.779875i	−0.0985160	−	0.0568783i
$189$	−1.15419	+	1.99912i	−0.0839549	+	0.145414i
$190$	6.48534	−	6.42760i	0.470496	−	0.466307i
$191$		−	0.315810i		−	0.0228512i	−0.999935	−	0.0114256i	$-0.996363\pi$
$191$		−	0.315810i		−	0.0228512i	0.999935	−	0.0114256i	$-0.00363697\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	3.67336			0.264414			0.132207	−	0.991222i	$-0.457794\pi$
$193$	3.67336			0.264414			0.132207	+	0.991222i	$0.457794\pi$
$194$	−2.25861	−	3.91202i	−0.162158	−	0.280867i
$195$	8.98780	+	2.45139i	0.643630	+	0.175548i
$196$	1.67139			0.119385
$197$	18.7472	−	10.8237i	1.33568	−	0.771157i	0.349519	−	0.936929i	$-0.386345\pi$
$197$	18.7472	−	10.8237i	1.33568	−	0.771157i	0.986164	+	0.165772i	$0.0530117\pi$
$198$	−1.80333	+	3.12346i	−0.128157	+	0.221975i
$199$		−	21.1121i		−	1.49660i	−0.663360	−	0.748300i	$-0.730870\pi$
$199$		−	21.1121i		−	1.49660i	0.663360	−	0.748300i	$-0.269130\pi$
$200$	0.0447077	−	4.99980i	0.00316131	−	0.353539i
$201$	−3.97101	−	6.87799i	−0.280093	−	0.485136i
$202$	−1.96486	−	3.40324i	−0.138247	−	0.239451i
$203$	3.83058	−	6.63477i	0.268854	−	0.465669i
$204$	2.84383	+	1.64189i	0.199108	+	0.114955i
$205$	−8.53674	+	2.24655i	−0.596232	+	0.156906i
$206$	−6.50018	−	11.2586i	−0.452889	−	0.784427i
$207$	0.374445	+	0.648558i	0.0260257	+	0.0450779i
$208$	4.16629			0.288880
$209$	−12.7546	−	7.36385i	−0.882252	−	0.509368i
$210$	−4.99174	+	1.31364i	−0.344462	+	0.0906498i
$211$	22.4890			1.54821			0.774104	−	0.633059i	$-0.218201\pi$
$211$	22.4890			1.54821			0.774104	+	0.633059i	$0.218201\pi$
$212$			2.33919i			0.160656i
$213$	−0.626045	+	0.361447i	−0.0428959	+	0.0247659i
$214$			6.92237i			0.473204i
$215$	−18.3517	−	18.5165i	−1.25157	−	1.26281i
$216$			1.00000i			0.0680414i
$217$	5.24805	−	9.08989i	0.356261	−	0.617062i
$218$	8.88722	+	5.13104i	0.601919	+	0.347518i
$219$	0.139399	−	0.241445i	0.00941968	−	0.0163154i
$220$	−7.79920	+	2.05246i	−0.525822	+	0.138377i
$221$	−13.6812			−0.920294
$222$	4.37955	−	4.22132i	0.293936	−	0.283317i
$223$		−	13.3114i		−	0.891397i	−0.895183	−	0.445699i	$-0.852955\pi$
$223$		−	13.3114i		−	0.891397i	0.895183	−	0.445699i	$-0.147045\pi$
$224$	−1.99912	+	1.15419i	−0.133571	+	0.0771175i
$225$	−4.35231	+	2.46118i	−0.290154	+	0.164079i
$226$	−0.115280	+	0.199671i	−0.00766832	+	0.0132819i
$227$	6.15062	−	10.6532i	0.408231	−	0.707077i	−0.586461	−	0.809978i	$-0.699479\pi$
$227$	6.15062	−	10.6532i	0.408231	−	0.707077i	0.994692	+	0.102901i	$0.0328125\pi$
$228$	−4.08347			−0.270434
$229$	−3.47120	+	6.01230i	−0.229383	+	0.397304i	−0.957626	−	0.288016i	$-0.907004\pi$
$229$	−3.47120	+	6.01230i	−0.229383	+	0.397304i	0.728242	+	0.685320i	$0.240338\pi$
$230$	−0.440638	+	1.61556i	−0.0290548	+	0.106527i
$231$	4.16277	+	7.21014i	0.273890	+	0.474392i
$232$		−	3.31885i		−	0.217893i
$233$		−	6.75716i		−	0.442676i	−0.975197	−	0.221338i	$-0.928958\pi$
$233$		−	6.75716i		−	0.442676i	0.975197	−	0.221338i	$-0.0710424\pi$
$234$	−2.08315	−	3.60811i	−0.136179	−	0.235870i
$235$	−2.47718	+	2.45513i	−0.161594	+	0.160155i
$236$		−	11.7215i		−	0.763004i
$237$	−4.34561	−	7.52682i	−0.282278	−	0.488919i
$238$	6.56464	−	3.79010i	0.425522	−	0.245675i
$239$	5.96439	−	3.44354i	0.385805	−	0.222744i	−0.294536	−	0.955640i	$-0.595165\pi$
$239$	5.96439	−	3.44354i	0.385805	−	0.222744i	0.680341	+	0.732896i	$0.261832\pi$
$240$	−1.58819	+	1.57405i	−0.102517	+	0.101605i
$241$	14.4718	+	8.35532i	0.932213	+	0.538213i	0.887511	−	0.460787i	$-0.152433\pi$
$241$	14.4718	+	8.35532i	0.932213	+	0.538213i	0.0447019	+	0.999000i	$0.485766\pi$
$242$	1.00401	+	1.73900i	0.0645403	+	0.111787i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−2.15821	+	1.24604i	−0.138165	+	0.0797696i
$245$	0.983422	−	3.60562i	0.0628286	−	0.230355i
$246$	3.41884	+	1.97387i	0.217977	+	0.125849i
$247$	14.7336	−	8.50646i	0.937478	−	0.541253i
$248$		−	4.54696i		−	0.288732i
$249$	−6.39311			−0.405147
$250$	−10.7596	−	3.03827i	−0.680497	−	0.192157i
$251$		−	15.2154i		−	0.960385i	−0.877163	−	0.480192i	$-0.840567\pi$
$251$		−	15.2154i		−	0.960385i	0.877163	−	0.480192i	$-0.159433\pi$
$252$	1.99912	+	1.15419i	0.125932	+	0.0727071i
$253$	2.70100			0.169810
$254$	11.4021	+	6.58300i	0.715431	+	0.413054i
$255$	5.21526	−	5.16884i	0.326592	−	0.323685i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.53563	−	4.39185i	−0.158168	−	0.273956i	0.776040	−	0.630684i	$-0.217226\pi$
$257$	−2.53563	−	4.39185i	−0.158168	−	0.273956i	−0.934208	+	0.356728i	$0.883892\pi$
$258$			11.6588i			0.725848i
$259$	−3.38408	−	13.6274i	−0.210277	−	0.846767i
$260$	2.45139	−	8.98780i	0.152029	−	0.557400i
$261$	−2.87421	+	1.65943i	−0.177909	+	0.102716i
$262$	14.1821	+	8.18806i	0.876176	+	0.505860i
$263$	4.34236	+	2.50706i	0.267761	+	0.154592i	0.627870	−	0.778318i	$-0.283927\pi$
$263$	4.34236	+	2.50706i	0.267761	+	0.154592i	−0.360109	+	0.932910i	$0.617260\pi$
$264$	3.12346	+	1.80333i	0.192236	+	0.110987i
$265$	5.04625	+	1.37635i	0.309989	+	0.0845485i
$266$	−4.71310	+	8.16333i	−0.288979	+	0.500526i
$267$	6.10428			0.373576
$268$	−6.87799	+	3.97101i	−0.420140	+	0.242568i
$269$	6.90387			0.420936			0.210468	−	0.977601i	$-0.432501\pi$
$269$	6.90387			0.420936			0.210468	+	0.977601i	$0.432501\pi$
$270$	2.15727	+	0.588388i	0.131287	+	0.0358081i
$271$	11.0506	+	19.1402i	0.671275	+	1.16268i	0.977543	+	0.210737i	$0.0675865\pi$
$271$	11.0506	+	19.1402i	0.671275	+	1.16268i	−0.306267	+	0.951946i	$0.599080\pi$
$272$	1.64189	−	2.84383i	0.0995540	−	0.172433i
$273$	−9.61738			−0.582070
$274$	−7.03744	+	4.06307i	−0.425147	+	0.245459i
$275$	−0.161246	+	18.0326i	−0.00972348	+	1.08741i
$276$	0.648558	−	0.374445i	0.0390386	−	0.0225390i
$277$	0.00385131	−	0.00667067i	0.000231403	−	0.000400802i	−0.865910	−	0.500200i	$-0.833260\pi$
$277$	0.00385131	−	0.00667067i	0.000231403	−	0.000400802i	0.866141	+	0.499800i	$0.166593\pi$
$278$	−5.13844	+	8.90004i	−0.308183	+	0.533789i
$279$	−3.93778	+	2.27348i	−0.235749	+	0.136110i
$280$	1.31364	+	4.99174i	0.0785050	+	0.298313i
$281$	−21.1295	+	12.1991i	−1.26048	+	0.727739i	−0.973168	−	0.230097i	$-0.926095\pi$
$281$	−21.1295	+	12.1991i	−1.26048	+	0.727739i	−0.287314	+	0.957837i	$0.592762\pi$
$282$	1.55975			0.0928818
$283$	12.8527	−	22.2615i	0.764012	−	1.32331i	−0.176755	−	0.984255i	$-0.556560\pi$
$283$	12.8527	−	22.2615i	0.764012	−	1.32331i	0.940767	−	0.339053i	$-0.110107\pi$
$284$	0.361447	+	0.626045i	0.0214479	+	0.0371489i
$285$	−2.40266	+	8.80914i	−0.142321	+	0.521808i
$286$	−15.0264			−0.888530
$287$	7.89197	−	4.55643i	0.465848	−	0.268958i
$288$	1.00000			0.0589256
$289$	3.10842	−	5.38394i	0.182848	−	0.316702i
$290$	−7.15965	−	1.95277i	−0.420429	−	0.114671i
$291$	3.91202	+	2.25861i	0.229327	+	0.132402i
$292$	−0.241445	−	0.139399i	−0.0141295	−	0.00815769i
$293$	−8.92404	−	5.15230i	−0.521348	−	0.301000i	0.216138	−	0.976363i	$-0.430654\pi$
$293$	−8.92404	−	5.15230i	−0.521348	−	0.301000i	−0.737486	+	0.675362i	$0.763987\pi$
$294$	−1.44746	+	0.835693i	−0.0844177	+	0.0487386i
$295$	−25.2864	−	6.89678i	−1.47223	−	0.401546i
$296$	−4.22132	−	4.37955i	−0.245359	−	0.254556i
$297$		−	3.60666i		−	0.209280i
$298$	−10.2093	−	17.6830i	−0.591407	−	1.02435i
$299$	−1.56005	+	2.70208i	−0.0902199	+	0.156265i
$300$	2.46118	+	4.35231i	0.142096	+	0.251281i
$301$	23.3074	+	13.4565i	1.34341	+	0.775621i
$302$	13.1860			0.758768
$303$	3.40324	+	1.96486i	0.195511	+	0.112878i
$304$			4.08347i			0.234203i
$305$	1.41818	+	5.38898i	0.0812048	+	0.308572i
$306$	−3.28377			−0.187721
$307$			25.1735i			1.43673i	0.695666	+	0.718365i	$0.255109\pi$
$307$			25.1735i			1.43673i	−0.695666	+	0.718365i	$0.744891\pi$
$308$	7.21014	−	4.16277i	0.410836	−	0.237196i
$309$	11.2586	+	6.50018i	0.640482	+	0.369782i
$310$	−9.80900	−	2.67537i	−0.557114	−	0.151951i
$311$	−25.1339	+	14.5111i	−1.42521	+	0.822847i	−0.996738	−	0.0807069i	$-0.974282\pi$
$311$	−25.1339	+	14.5111i	−1.42521	+	0.822847i	−0.428475	+	0.903554i	$0.640949\pi$
$312$	−3.60811	+	2.08315i	−0.204269	+	0.117935i
$313$	11.8894	+	20.5930i	0.672028	+	1.16399i	0.977328	+	0.211731i	$0.0679100\pi$
$313$	11.8894	+	20.5930i	0.672028	+	1.16399i	−0.305300	+	0.952256i	$0.598757\pi$
$314$	12.8251	+	7.40456i	0.723760	+	0.417863i
$315$	3.66615	−	3.63351i	0.206564	−	0.204725i
$316$	−7.52682	+	4.34561i	−0.423416	+	0.244460i
$317$	8.18665	−	4.72657i	0.459808	−	0.265470i	−0.252155	−	0.967687i	$-0.581139\pi$
$317$	8.18665	−	4.72657i	0.459808	−	0.265470i	0.711964	+	0.702216i	$0.247806\pi$
$318$	−1.16959	−	2.02580i	−0.0655876	−	0.113601i
$319$			11.9700i			0.670190i
$320$	1.57405	+	1.58819i	0.0879923	+	0.0887826i
$321$	−3.46119	−	5.99495i	−0.193185	−	0.334606i
$322$		−	1.72872i		−	0.0963380i
$323$		−	13.4092i		−	0.746107i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−17.9467	−	10.5766i	−0.995505	−	0.586685i
$326$	−5.57244	+	9.65175i	−0.308629	+	0.534561i
$327$	−10.2621			−0.567494
$328$	1.97387	−	3.41884i	0.108989	−	0.188774i
$329$	1.80025	−	3.11812i	0.0992509	−	0.171908i
$330$	5.72807	−	5.67708i	0.315320	−	0.312513i
$331$	−29.2152	+	16.8674i	−1.60581	+	0.927115i	−0.615517	+	0.788123i	$0.711053\pi$
$331$	−29.2152	+	16.8674i	−1.60581	+	0.927115i	−0.990294	+	0.138992i	$0.955614\pi$
$332$			6.39311i			0.350868i
$333$	−1.68214	+	5.84555i	−0.0921805	+	0.320334i
$334$	8.40850			0.460093
$335$	4.51960	+	17.1741i	0.246932	+	0.938324i
$336$	1.15419	−	1.99912i	0.0629662	−	0.109061i
$337$	29.0757	+	16.7869i	1.58385	+	0.914439i	0.994289	+	0.106717i	$0.0340340\pi$
$337$	29.0757	+	16.7869i	1.58385	+	0.914439i	0.589565	+	0.807721i	$0.299299\pi$
$338$	2.17899	−	3.77413i	0.118522	−	0.205285i
$339$		−	0.230560i		−	0.0125223i
$340$	−5.16884	−	5.21526i	−0.280320	−	0.282837i
$341$			16.3994i			0.888075i
$342$	3.53639	−	2.04174i	0.191226	−	0.110404i
$343$			20.0168i			1.08081i
$344$	11.6588			0.628603
$345$	−0.426175	−	1.61943i	−0.0229445	−	0.0871873i
$346$	14.2350	+	8.21856i	0.765277	+	0.441833i
$347$	−11.3801			−0.610915			−0.305457	−	0.952206i	$-0.598809\pi$
$347$	−11.3801			−0.610915			−0.305457	+	0.952206i	$0.598809\pi$
$348$	1.65943	+	2.87421i	0.0889546	+	0.154074i
$349$	−6.76004	−	11.7087i	−0.361856	−	0.626754i	0.626410	−	0.779494i	$-0.284524\pi$
$349$	−6.76004	−	11.7087i	−0.361856	−	0.626754i	−0.988266	+	0.152740i	$0.951190\pi$
$350$	11.5414	+	0.103202i	0.616916	+	0.00551640i
$351$	3.60811	+	2.08315i	0.192587	+	0.111190i
$352$	1.80333	−	3.12346i	0.0961179	−	0.166481i
$353$	4.00690	+	6.94015i	0.213266	+	0.369387i	0.952735	−	0.303804i	$-0.0982567\pi$
$353$	4.00690	+	6.94015i	0.213266	+	0.369387i	−0.739469	+	0.673191i	$0.764923\pi$
$354$	5.86075	+	10.1511i	0.311495	+	0.539526i
$355$	1.56322	−	0.411381i	0.0829669	−	0.0218338i
$356$		−	6.10428i		−	0.323526i
$357$	−3.79010	+	6.56464i	−0.200593	+	0.347438i
$358$	1.27281	−	0.734858i	0.0672702	−	0.0388384i
$359$	22.9329			1.21035			0.605176	−	0.796092i	$-0.293103\pi$
$359$	22.9329			1.21035			0.605176	+	0.796092i	$0.293103\pi$
$360$	0.588388	−	2.15727i	0.0310107	−	0.113698i
$361$	−1.16263	−	2.01374i	−0.0611913	−	0.105986i
$362$	5.22341			0.274536
$363$	−1.73900	−	1.00401i	−0.0912738	−	0.0526970i
$364$			9.61738i			0.504088i
$365$	−0.442783	+	0.438842i	−0.0231763	+	0.0229700i
$366$	1.24604	−	2.15821i	0.0651316	−	0.112811i
$367$	−8.26280	−	4.77053i	−0.431315	−	0.249020i	0.268592	−	0.963254i	$-0.413442\pi$
$367$	−8.26280	−	4.77053i	−0.431315	−	0.249020i	−0.699907	+	0.714234i	$0.746775\pi$
$368$	−0.374445	−	0.648558i	−0.0195193	−	0.0338084i
$369$	−3.94773			−0.205511
$370$	−11.9316	+	6.52965i	−0.620296	+	0.339460i
$371$	−5.39973			−0.280340
$372$	2.27348	+	3.93778i	0.117874	+	0.204164i
$373$	20.0142	+	11.5552i	1.03630	+	0.598305i	0.918782	−	0.394766i	$-0.129174\pi$
$373$	20.0142	+	11.5552i	1.03630	+	0.598305i	0.117514	+	0.993071i	$0.462508\pi$
$374$	−5.92173	+	10.2567i	−0.306206	+	0.530364i
$375$	10.8372	−	2.74858i	0.559632	−	0.141936i
$376$		−	1.55975i		−	0.0804380i
$377$	−11.9748	−	6.91365i	−0.616733	−	0.356071i
$378$	−2.30838			−0.118730
$379$	−12.8937	−	22.3326i	−0.662306	−	1.14715i	−0.980008	−	0.198958i	$-0.936244\pi$
$379$	−12.8937	−	22.3326i	−0.662306	−	1.14715i	0.317702	−	0.948191i	$-0.397089\pi$
$380$	8.80914	+	2.40266i	0.451899	+	0.123254i
$381$	−13.1660			−0.674515
$382$	0.273500	−	0.157905i	0.0139935	−	0.00807913i
$383$	−16.4797	+	28.5437i	−0.842075	+	1.45852i	0.0460621	+	0.998939i	$0.485333\pi$
$383$	−16.4797	+	28.5437i	−0.842075	+	1.45852i	−0.888137	+	0.459578i	$0.848001\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−4.73786	−	18.0035i	−0.241464	−	0.917544i
$386$	1.83668	+	3.18122i	0.0934844	+	0.161920i
$387$	−5.82942	−	10.0969i	−0.296326	−	0.513252i
$388$	2.25861	−	3.91202i	0.114663	−	0.198603i
$389$	−23.1816	−	13.3839i	−1.17535	−	0.678590i	−0.220418	−	0.975405i	$-0.570742\pi$
$389$	−23.1816	−	13.3839i	−1.17535	−	0.678590i	−0.954935	+	0.296815i	$0.904076\pi$
$390$	2.37093	+	9.00936i	0.120057	+	0.456207i
$391$	1.22959	+	2.12972i	0.0621832	+	0.107704i
$392$	0.835693	+	1.44746i	0.0422089	+	0.0731079i
$393$	−16.3761			−0.826066
$394$	18.7472	+	10.8237i	0.944471	+	0.545290i
$395$	4.94595	+	18.7943i	0.248858	+	0.945641i
$396$	−3.60666			−0.181242
$397$			12.0526i			0.604905i	0.953164	+	0.302452i	$0.0978054\pi$
$397$			12.0526i			0.604905i	−0.953164	+	0.302452i	$0.902195\pi$
$398$	18.2837	−	10.5561i	0.916477	−	0.529128i
$399$		−	9.42620i		−	0.471900i
$400$	4.35231	−	2.46118i	0.217615	−	0.123059i
$401$		−	17.7454i		−	0.886161i	−0.896482	−	0.443080i	$-0.853886\pi$
$401$		−	17.7454i		−	0.886161i	0.896482	−	0.443080i	$-0.146114\pi$
$402$	3.97101	−	6.87799i	0.198056	−	0.343043i
$403$	−16.4059	−	9.47198i	−0.817238	−	0.471833i
$404$	1.96486	−	3.40324i	0.0977556	−	0.169318i
$405$	−2.16244	+	0.569075i	−0.107453	+	0.0282776i
$406$	7.66117			0.380217
$407$	15.2249	+	15.7956i	0.754670	+	0.782956i
$408$			3.28377i			0.162571i
$409$	−25.7232	+	14.8513i	−1.27193	+	0.734349i	−0.975351	−	0.220660i	$-0.929179\pi$
$409$	−25.7232	+	14.8513i	−1.27193	+	0.734349i	−0.296578	+	0.955009i	$0.595846\pi$
$410$	−6.21394	−	6.26976i	−0.306885	−	0.309641i
$411$	4.06307	−	7.03744i	0.200416	−	0.347131i
$412$	6.50018	−	11.2586i	0.320241	−	0.554673i
$413$	27.0577			1.33142
$414$	−0.374445	+	0.648558i	−0.0184030	+	0.0318749i
$415$	13.7917	+	3.76163i	0.677006	+	0.184651i
$416$	2.08315	+	3.60811i	0.102135	+	0.176902i
$417$		−	10.2769i		−	0.503261i
$418$		−	14.7277i		−	0.720356i
$419$	9.44226	+	16.3545i	0.461285	+	0.798968i	0.999025	−	0.0441419i	$-0.0140554\pi$
$419$	9.44226	+	16.3545i	0.461285	+	0.798968i	−0.537741	+	0.843110i	$0.680722\pi$
$420$	−3.63351	−	3.66615i	−0.177297	−	0.178890i
$421$		−	33.2036i		−	1.61825i	−0.587639	−	0.809123i	$-0.699942\pi$
$421$		−	33.2036i		−	1.61825i	0.587639	−	0.809123i	$-0.300058\pi$
$422$	11.2445	+	19.4761i	0.547374	+	0.948080i
$423$	−1.35078	+	0.779875i	−0.0656774	+	0.0379188i
$424$	−2.02580	+	1.16959i	−0.0983814	+	0.0568005i
$425$	−14.2920	+	8.08196i	−0.693263	+	0.392033i
$426$	−0.626045	−	0.361447i	−0.0303320	−	0.0175122i
$427$	−2.87634	−	4.98196i	−0.139196	−	0.241094i
$428$	−5.99495	+	3.46119i	−0.289777	+	0.167303i
$429$	13.0133	−	7.51321i	0.628286	−	0.362741i
$430$	6.85992	−	25.1512i	0.330815	−	1.21290i
$431$	−10.1481	−	5.85900i	−0.488816	−	0.282218i	0.235267	−	0.971931i	$-0.424404\pi$
$431$	−10.1481	−	5.85900i	−0.488816	−	0.282218i	−0.724083	+	0.689713i	$0.757737\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$		−	13.5422i		−	0.650796i	−0.945577	−	0.325398i	$-0.894502\pi$
$433$		−	13.5422i		−	0.650796i	0.945577	−	0.325398i	$-0.105498\pi$
$434$	10.4961			0.503829
$435$	7.17682	−	1.88867i	0.344102	−	0.0905550i
$436$			10.2621i			0.491465i
$437$	−2.64837	−	1.52904i	−0.126689	−	0.0731437i
$438$	0.278797			0.0133214
$439$	−26.5130	−	15.3073i	−1.26539	−	0.730576i	−0.291281	−	0.956637i	$-0.594082\pi$
$439$	−26.5130	−	15.3073i	−1.26539	−	0.730576i	−0.974113	+	0.226062i	$0.927415\pi$
$440$	−5.67708	−	5.72807i	−0.270644	−	0.273075i
$441$	0.835693	−	1.44746i	0.0397949	−	0.0689268i
$442$	−6.84058	−	11.8482i	−0.325373	−	0.563563i
$443$			3.95356i			0.187839i	0.995580	+	0.0939197i	$0.0299397\pi$
$443$			3.95356i			0.187839i	−0.995580	+	0.0939197i	$0.970060\pi$
$444$	5.84555	+	1.68214i	0.277417	+	0.0798307i
$445$	−13.1686	−	3.59168i	−0.624250	−	0.170262i
$446$	11.5280	−	6.65570i	0.545867	−	0.315157i
$447$	17.6830	+	10.2093i	0.836376	+	0.482882i
$448$	−1.99912	−	1.15419i	−0.0944493	−	0.0545303i
$449$	19.5007	+	11.2587i	0.920295	+	0.531333i	0.883729	−	0.467999i	$-0.155025\pi$
$449$	19.5007	+	11.2587i	0.920295	+	0.531333i	0.0365659	+	0.999331i	$0.488358\pi$
$450$	−4.30760	−	2.53862i	−0.203062	−	0.119672i
$451$	−7.11907	+	12.3306i	−0.335224	+	0.580625i
$452$	−0.230560			−0.0108446
$453$	−11.4194	+	6.59299i	−0.536530	+	0.309766i
$454$	12.3012			0.577326
$455$	20.7473	+	5.65875i	0.972646	+	0.265286i
$456$	−2.04174	−	3.53639i	−0.0956130	−	0.165607i
$457$	4.29461	−	7.43848i	0.200893	−	0.347957i	−0.747923	−	0.663785i	$-0.768949\pi$
$457$	4.29461	−	7.43848i	0.200893	−	0.347957i	0.948816	+	0.315828i	$0.102282\pi$
$458$	−6.94240			−0.324397
$459$	2.84383	−	1.64189i	0.132739	−	0.0766367i
$460$	−1.61943	+	0.426175i	−0.0755064	+	0.0198705i
$461$	23.8184	−	13.7516i	1.10933	−	0.640474i	0.170677	−	0.985327i	$-0.445404\pi$
$461$	23.8184	−	13.7516i	1.10933	−	0.640474i	0.938657	+	0.344853i	$0.112071\pi$
$462$	−4.16277	+	7.21014i	−0.193670	+	0.335446i
$463$	−7.63991	+	13.2327i	−0.355057	+	0.614976i	−0.987128	−	0.159934i	$-0.948872\pi$
$463$	−7.63991	+	13.2327i	−0.355057	+	0.614976i	0.632071	+	0.774911i	$0.282205\pi$
$464$	2.87421	−	1.65943i	0.133432	−	0.0770369i
$465$	9.83253	−	2.58756i	0.455973	−	0.119995i
$466$	5.85187	−	3.37858i	0.271083	−	0.156510i
$467$	−31.5781			−1.46126			−0.730631	−	0.682773i	$-0.760774\pi$
$467$	−31.5781			−1.46126			−0.730631	+	0.682773i	$0.760774\pi$
$468$	2.08315	−	3.60811i	0.0962934	−	0.166785i
$469$	−9.16659	−	15.8770i	−0.423274	−	0.733132i
$470$	−3.36480	−	0.917738i	−0.155207	−	0.0423321i
$471$	−14.8091			−0.682368
$472$	10.1511	−	5.86075i	0.467243	−	0.269763i
$473$	−42.0495			−1.93344
$474$	4.34561	−	7.52682i	0.199600	−	0.345718i
$475$	10.3664	−	17.5900i	0.475642	−	0.807083i
$476$	6.56464	+	3.79010i	0.300890	+	0.173719i
$477$	2.02580	+	1.16959i	0.0927549	+	0.0535520i
$478$	5.96439	+	3.44354i	0.272805	+	0.157504i
$479$	30.1785	−	17.4236i	1.37889	−	0.796104i	0.386866	−	0.922136i	$-0.373557\pi$
$479$	30.1785	−	17.4236i	1.37889	−	0.796104i	0.992026	+	0.126032i	$0.0402241\pi$
$480$	−2.15727	−	0.588388i	−0.0984653	−	0.0268561i
$481$	−24.5955	+	6.10778i	−1.12146	+	0.278491i
$482$			16.7106i			0.761148i
$483$	0.864361	+	1.49712i	0.0393298	+	0.0681212i
$484$	−1.00401	+	1.73900i	−0.0456369	+	0.0790455i
$485$	−7.11034	−	7.17420i	−0.322864	−	0.325764i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−32.7397			−1.48358			−0.741789	−	0.670633i	$-0.766023\pi$
$487$	−32.7397			−1.48358			−0.741789	+	0.670633i	$0.766023\pi$
$488$	−2.15821	−	1.24604i	−0.0976974	−	0.0564056i
$489$		−	11.1449i		−	0.503989i
$490$	3.61427	−	0.951143i	0.163276	−	0.0429683i
$491$	−13.2696			−0.598851			−0.299425	−	0.954120i	$-0.596795\pi$
$491$	−13.2696			−0.598851			−0.299425	+	0.954120i	$0.596795\pi$
$492$			3.94773i			0.177978i
$493$	−9.43825	+	5.44918i	−0.425077	+	0.245419i
$494$	14.7336	+	8.50646i	0.662897	+	0.382724i
$495$	−2.12212	+	7.78054i	−0.0953820	+	0.349709i
$496$	3.93778	−	2.27348i	0.176812	−	0.102082i
$497$	−1.44515	+	0.834357i	−0.0648238	+	0.0374260i
$498$	−3.19656	−	5.53660i	−0.143241	−	0.248101i
$499$	−0.850905	−	0.491270i	−0.0380917	−	0.0219923i	0.480833	−	0.876812i	$-0.340334\pi$
$499$	−0.850905	−	0.491270i	−0.0380917	−	0.0219923i	−0.518925	+	0.854820i	$0.673668\pi$
$500$	−2.74858	−	10.8372i	−0.122920	−	0.484655i
$501$	−7.28198	+	4.20425i	−0.325335	+	0.187832i
$502$	13.1769	−	7.60768i	0.588113	−	0.339547i
$503$	−6.92273	−	11.9905i	−0.308669	−	0.534631i	0.669402	−	0.742900i	$-0.266550\pi$
$503$	−6.92273	−	11.9905i	−0.308669	−	0.534631i	−0.978072	+	0.208269i	$0.933217\pi$
$504$			2.30838i			0.102823i
$505$	−6.18560	−	6.24116i	−0.275256	−	0.277728i
$506$	1.35050	+	2.33913i	0.0600370	+	0.103987i
$507$			4.35798i			0.193545i
$508$			13.1660i			0.584147i
$509$	−3.70010	−	6.40875i	−0.164004	−	0.284063i	0.772297	−	0.635261i	$-0.219108\pi$
$509$	−3.70010	−	6.40875i	−0.164004	−	0.284063i	−0.936301	+	0.351198i	$0.885774\pi$
$510$	7.08397	+	1.93213i	0.313684	+	0.0855562i
$511$	0.321785	−	0.557348i	0.0142349	−	0.0246556i
$512$	−1.00000			−0.0441942
$513$	−2.04174	+	3.53639i	−0.0901448	+	0.156135i
$514$	2.53563	−	4.39185i	0.111842	−	0.193716i
$515$	−20.4633	−	20.6471i	−0.901719	−	0.909818i
$516$	−10.0969	+	5.82942i	−0.444489	+	0.256626i
$517$			5.62550i			0.247409i
$518$	10.1097	−	9.74442i	0.444193	−	0.428145i
$519$	−16.4371			−0.721510
$520$	9.00936	−	2.37093i	0.395087	−	0.103972i
$521$	−15.1372	+	26.2185i	−0.663175	+	1.14865i	0.316602	+	0.948558i	$0.397458\pi$
$521$	−15.1372	+	26.2185i	−0.663175	+	1.14865i	−0.979777	+	0.200094i	$0.935875\pi$
$522$	−2.87421	−	1.65943i	−0.125801	−	0.0726311i
$523$	−14.5571	+	25.2137i	−0.636539	+	1.10252i	0.349648	+	0.936881i	$0.386301\pi$
$523$	−14.5571	+	25.2137i	−0.636539	+	1.10252i	−0.986187	+	0.165637i	$0.947032\pi$
$524$			16.3761i			0.715394i
$525$	−10.0468	+	5.68134i	−0.438477	+	0.247954i
$526$			5.01412i			0.218626i
$527$	−12.9308	+	7.46559i	−0.563274	+	0.325206i
$528$			3.60666i			0.156960i
$529$	−22.4392			−0.975616
$530$	1.33117	+	5.05836i	0.0578225	+	0.219721i
$531$	−10.1511	−	5.86075i	−0.440521	−	0.254335i
$532$	−9.42620			−0.408678
$533$	−8.22370	−	14.2439i	−0.356208	−	0.616970i
$534$	3.05214	+	5.28646i	0.132079	+	0.228768i
$535$	3.93935	+	14.9692i	0.170313	+	0.647176i
$536$	−6.87799	−	3.97101i	−0.297084	−	0.171521i
$537$	−0.734858	+	1.27281i	−0.0317115	+	0.0549259i
$538$	3.45193	+	5.97892i	0.148823	+	0.257770i
$539$	−3.01406	−	5.22051i	−0.129825	−	0.224863i
$540$	0.569075	+	2.16244i	0.0244891	+	0.0930567i
$541$			28.7306i			1.23522i	0.786483	+	0.617612i	$0.211900\pi$
$541$			28.7306i			1.23522i	−0.786483	+	0.617612i	$0.788100\pi$
$542$	−11.0506	+	19.1402i	−0.474663	+	0.822141i
$543$	−4.52361	+	2.61171i	−0.194127	+	0.112079i
$544$	3.28377			0.140791
$545$	22.1380	+	6.03808i	0.948290	+	0.258643i
$546$	−4.80869	−	8.32890i	−0.205793	−	0.356444i
$547$	−32.4201			−1.38618			−0.693091	−	0.720850i	$-0.743752\pi$
$547$	−32.4201			−1.38618			−0.693091	+	0.720850i	$0.743752\pi$
$548$	−7.03744	−	4.06307i	−0.300624	−	0.173566i
$549$			2.49208i			0.106359i
$550$	−15.6973	+	8.87666i	−0.669336	+	0.378502i
$551$	6.77622	−	11.7367i	0.288676	−	0.500002i
$552$	0.648558	+	0.374445i	0.0276045	+	0.0159374i
$553$	−10.0313	−	17.3747i	−0.426575	−	0.738849i
$554$	0.00770262			0.000327253
$555$	7.06826	−	11.6207i	0.300031	−	0.493269i
$556$	−10.2769			−0.435837
$557$	−6.76342	−	11.7146i	−0.286575	−	0.496363i	0.686415	−	0.727210i	$-0.259183\pi$
$557$	−6.76342	−	11.7146i	−0.286575	−	0.496363i	−0.972990	+	0.230848i	$0.925850\pi$
$558$	−3.93778	−	2.27348i	−0.166700	−	0.0962441i
$559$	24.2871	−	42.0664i	1.02723	−	1.77922i
$560$	−3.66615	+	3.63351i	−0.154923	+	0.153544i
$561$		−	11.8435i		−	0.500032i
$562$	−21.1295	−	12.1991i	−0.891295	−	0.514589i
$563$	25.2768			1.06529			0.532645	−	0.846339i	$-0.321198\pi$
$563$	25.2768			1.06529			0.532645	+	0.846339i	$0.321198\pi$
$564$	0.779875	+	1.35078i	0.0328387	+	0.0568783i
$565$	−0.135659	+	0.497380i	−0.00570721	+	0.0209249i
$566$	25.7053			1.08048
$567$	1.99912	−	1.15419i	0.0839549	−	0.0484714i
$568$	−0.361447	+	0.626045i	−0.0151660	+	0.0262682i
$569$		−	43.4411i		−	1.82114i	−0.413350	−	0.910572i	$-0.635641\pi$
$569$		−	43.4411i		−	1.82114i	0.413350	−	0.910572i	$-0.364359\pi$
$570$	−8.83027	+	2.32380i	−0.369859	+	0.0973333i
$571$	18.5642	+	32.1541i	0.776886	+	1.34561i	0.933729	+	0.357982i	$0.116535\pi$
$571$	18.5642	+	32.1541i	0.776886	+	1.34561i	−0.156843	+	0.987624i	$0.550132\pi$
$572$	−7.51321	−	13.0133i	−0.314143	−	0.544112i
$573$	−0.157905	+	0.273500i	−0.00659658	+	0.0114256i
$574$	7.89197	+	4.55643i	0.329404	+	0.190182i
$575$	−0.0334812	+	3.74430i	−0.00139626	+	0.156148i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	12.4724	+	21.6029i	0.519235	+	0.899341i	0.999750	+	0.0223548i	$0.00711634\pi$
$577$	12.4724	+	21.6029i	0.519235	+	0.899341i	−0.480515	+	0.876986i	$0.659550\pi$
$578$	6.21683			0.258586
$579$	−3.18122	−	1.83668i	−0.132207	−	0.0763297i
$580$	−1.88867	−	7.17682i	−0.0784229	−	0.298001i
$581$	−14.7577			−0.612254
$582$			4.51721i			0.187244i
$583$	7.30637	−	4.21833i	0.302599	−	0.174706i
$584$		−	0.278797i		−	0.0115367i
$585$	−6.55797	−	6.61687i	−0.271139	−	0.273574i
$586$		−	10.3046i		−	0.425679i
$587$	12.3953	−	21.4693i	0.511608	−	0.886131i	−0.488301	−	0.872675i	$-0.662383\pi$
$587$	12.3953	−	21.4693i	0.511608	−	0.886131i	0.999909	−	0.0134561i	$-0.00428333\pi$
$588$	−1.44746	−	0.835693i	−0.0596923	−	0.0344634i
$589$	9.28369	−	16.0798i	0.382528	−	0.662557i
$590$	−6.67041	−	25.3471i	−0.274616	−	1.04352i
$591$	−21.6474			−0.890455
$592$	1.68214	−	5.84555i	0.0691354	−	0.240250i
$593$		−	30.1735i		−	1.23908i	−0.784966	−	0.619539i	$-0.787320\pi$
$593$		−	30.1735i		−	1.23908i	0.784966	−	0.619539i	$-0.212680\pi$
$594$	3.12346	−	1.80333i	0.128157	−	0.0739916i
$595$	12.0388	−	11.9316i	0.493543	−	0.489149i
$596$	10.2093	−	17.6830i	0.418188	−	0.724323i
$597$	−10.5561	+	18.2837i	−0.432031	+	0.748300i
$598$	−3.12010			−0.127590
$599$	5.95677	−	10.3174i	0.243387	−	0.421559i	−0.718290	−	0.695744i	$-0.755075\pi$
$599$	5.95677	−	10.3174i	0.243387	−	0.421559i	0.961677	+	0.274185i	$0.0884082\pi$
$600$	−2.53862	+	4.30760i	−0.103639	+	0.175857i
$601$	18.2150	+	31.5493i	0.743006	+	1.28692i	0.951120	+	0.308820i	$0.0999341\pi$
$601$	18.2150	+	31.5493i	0.743006	+	1.28692i	−0.208114	+	0.978105i	$0.566733\pi$
$602$			26.9130i			1.09689i
$603$			7.94202i			0.323424i
$604$	6.59299	+	11.4194i	0.268265	+	0.464649i
$605$	3.16074	+	3.18913i	0.128502	+	0.129656i
$606$			3.92973i			0.159634i
$607$	2.82022	+	4.88477i	0.114469	+	0.198267i	0.917567	−	0.397580i	$-0.130150\pi$
$607$	2.82022	+	4.88477i	0.114469	+	0.198267i	−0.803098	+	0.595847i	$0.796817\pi$
$608$	−3.53639	+	2.04174i	−0.143420	+	0.0828033i
$609$	−6.63477	+	3.83058i	−0.268854	+	0.155223i
$610$	−3.95790	+	3.92267i	−0.160251	+	0.158824i
$611$	−5.62776	−	3.24919i	−0.227675	−	0.131448i
$612$	−1.64189	−	2.84383i	−0.0663693	−	0.114955i
$613$	1.63128	−	0.941819i	0.0658867	−	0.0380397i	−0.466695	−	0.884418i	$-0.654555\pi$
$613$	1.63128	−	0.941819i	0.0658867	−	0.0380397i	0.532581	+	0.846379i	$0.321222\pi$
$614$	−21.8009	+	12.5868i	−0.879814	+	0.507961i
$615$	8.51631	+	2.32280i	0.343411	+	0.0936642i
$616$	7.21014	+	4.16277i	0.290505	+	0.167723i
$617$	22.4253	−	12.9473i	0.902810	−	0.521238i	0.0246992	−	0.999695i	$-0.492137\pi$
$617$	22.4253	−	12.9473i	0.902810	−	0.521238i	0.878111	+	0.478457i	$0.158804\pi$
$618$			13.0004i			0.522951i
$619$	18.2303			0.732737			0.366368	−	0.930470i	$-0.380601\pi$
$619$	18.2303			0.732737			0.366368	+	0.930470i	$0.380601\pi$
$620$	−2.58756	−	9.83253i	−0.103919	−	0.394884i
$621$		−	0.748890i		−	0.0300519i
$622$	−25.1339	−	14.5111i	−1.00778	−	0.581841i
$623$	14.0910			0.564544
$624$	−3.60811	−	2.08315i	−0.144440	−	0.0833926i
$625$	−24.9960	−	0.447059i	−0.999840	−	0.0178824i
$626$	−11.8894	+	20.5930i	−0.475196	+	0.823063i
$627$	7.36385	+	12.7546i	0.294084	+	0.509368i
$628$			14.8091i			0.590948i
$629$	−5.52376	+	19.1954i	−0.220247	+	0.765373i
$630$	4.97979	+	1.35822i	0.198400	+	0.0541128i
$631$	20.7274	−	11.9669i	0.825143	−	0.476397i	−0.0270438	−	0.999634i	$-0.508609\pi$
$631$	20.7274	−	11.9669i	0.825143	−	0.476397i	0.852187	+	0.523238i	$0.175276\pi$
$632$	−7.52682	−	4.34561i	−0.299401	−	0.172859i
$633$	−19.4761	−	11.2445i	−0.774104	−	0.446929i
$634$	8.18665	+	4.72657i	0.325134	+	0.187716i
$635$	28.4026	+	7.74671i	1.12712	+	0.307419i
$636$	1.16959	−	2.02580i	0.0463774	−	0.0803281i
$637$	6.96348			0.275903
$638$	−10.3663	+	5.98499i	−0.410406	+	0.236948i
$639$	0.722894			0.0285972
$640$	−0.588388	+	2.15727i	−0.0232581	+	0.0852735i
$641$	23.8781	+	41.3581i	0.943128	+	1.63355i	0.759456	+	0.650559i	$0.225465\pi$
$641$	23.8781	+	41.3581i	0.943128	+	1.63355i	0.183672	+	0.982988i	$0.441201\pi$
$642$	3.46119	−	5.99495i	0.136602	−	0.236602i
$643$	−41.6635			−1.64305			−0.821524	−	0.570175i	$-0.806876\pi$
$643$	−41.6635			−1.64305			−0.821524	+	0.570175i	$0.806876\pi$
$644$	1.49712	−	0.864361i	0.0589947	−	0.0340606i
$645$	6.63475	+	25.2116i	0.261243	+	0.992705i
$646$	11.6127	−	6.70460i	0.456896	−	0.263789i
$647$	−14.5351	+	25.1755i	−0.571433	+	0.989751i	0.424986	+	0.905200i	$0.360279\pi$
$647$	−14.5351	+	25.1755i	−0.571433	+	0.989751i	−0.996419	+	0.0845511i	$0.973054\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−36.6117	+	21.1377i	−1.43713	+	0.829729i
$650$	0.186265	−	20.8306i	0.00730593	−	0.817044i
$651$	−9.08989	+	5.24805i	−0.356261	+	0.205687i
$652$	−11.1449			−0.436467
$653$	−23.6468	+	40.9575i	−0.925371	+	1.60279i	−0.134407	+	0.990926i	$0.542913\pi$
$653$	−23.6468	+	40.9575i	−0.925371	+	1.60279i	−0.790964	+	0.611863i	$0.790420\pi$
$654$	−5.13104	−	8.88722i	−0.200640	−	0.347518i
$655$	35.3277	+	9.63551i	1.38037	+	0.376491i
$656$	3.94773			0.154133
$657$	−0.241445	+	0.139399i	−0.00941968	+	0.00543846i
$658$	3.60050			0.140362
$659$	9.93900	−	17.2149i	0.387169	−	0.670596i	−0.604899	−	0.796302i	$-0.706786\pi$
$659$	9.93900	−	17.2149i	0.387169	−	0.670596i	0.992067	+	0.125707i	$0.0401198\pi$
$660$	7.78054	+	2.12212i	0.302857	+	0.0826033i
$661$	−5.66878	−	3.27287i	−0.220490	−	0.127300i	0.385687	−	0.922630i	$-0.373964\pi$
$661$	−5.66878	−	3.27287i	−0.220490	−	0.127300i	−0.606177	+	0.795330i	$0.707298\pi$
$662$	−29.2152	−	16.8674i	−1.13548	−	0.655570i
$663$	11.8482	+	6.84058i	0.460147	+	0.265666i
$664$	−5.53660	+	3.19656i	−0.214862	+	0.124050i
$665$	−5.54626	+	20.3348i	−0.215075	+	0.788551i
$666$	−5.90346	+	1.46600i	−0.228754	+	0.0568064i
$667$			2.48546i			0.0962372i
$668$	4.20425	+	7.28198i	0.162667	+	0.281748i
$669$	−6.65570	+	11.5280i	−0.257324	+	0.445699i
$670$	−12.6134	+	12.5012i	−0.487300	+	0.482962i
$671$	7.78392	+	4.49405i	0.300495	+	0.173491i
$672$	2.30838			0.0890477
$673$	38.8931	+	22.4549i	1.49922	+	0.865574i	1.00000		0.000903078i	$-0.000287459\pi$
$673$	38.8931	+	22.4549i	1.49922	+	0.865574i	0.499218	+	0.866477i	$0.333621\pi$
$674$			33.5737i			1.29321i
$675$	4.99980	+	0.0447077i	0.192442	+	0.00172080i
$676$	4.35798			0.167615
$677$			27.1822i			1.04470i	0.852732	+	0.522348i	$0.174944\pi$
$677$			27.1822i			1.04470i	−0.852732	+	0.522348i	$0.825056\pi$
$678$	0.199671	−	0.115280i	0.00766832	−	0.00442731i
$679$	9.03043	+	5.21372i	0.346556	+	0.200084i
$680$	1.93213	−	7.08397i	0.0740939	−	0.271658i
$681$	−10.6532	+	6.15062i	−0.408231	+	0.235692i
$682$	−14.2023	+	8.19968i	−0.543833	+	0.313982i
$683$	−24.2086	−	41.9305i	−0.926316	−	1.60443i	−0.789431	−	0.613840i	$-0.789624\pi$
$683$	−24.2086	−	41.9305i	−0.926316	−	1.60443i	−0.136885	−	0.990587i	$-0.543709\pi$
$684$	3.53639	+	2.04174i	0.135217	+	0.0780677i
$685$	−12.9059	+	12.7910i	−0.493108	+	0.488718i
$686$	−17.3351	+	10.0084i	−0.661857	+	0.382123i
$687$	6.01230	−	3.47120i	0.229383	−	0.132435i
$688$	5.82942	+	10.0969i	0.222245	+	0.384939i
$689$			9.74574i			0.371283i
$690$	1.18938	−	1.17879i	0.0452790	−	0.0448759i
$691$	−18.3449	−	31.7743i	−0.697872	−	1.20875i	−0.969203	−	0.246264i	$-0.920797\pi$
$691$	−18.3449	−	31.7743i	−0.697872	−	1.20875i	0.271330	−	0.962486i	$-0.412536\pi$
$692$			16.4371i			0.624846i
$693$		−	8.32555i		−	0.316261i
$694$	−5.69004	−	9.85544i	−0.215991	−	0.374107i
$695$	−6.04679	+	22.1700i	−0.229368	+	0.840955i
$696$	−1.65943	+	2.87421i	−0.0629004	+	0.108947i
$697$	−12.9635			−0.491026
$698$	6.76004	−	11.7087i	0.255871	−	0.443182i
$699$	−3.37858	+	5.85187i	−0.127790	+	0.221338i
$700$	5.68134	+	10.0468i	0.214735	+	0.379732i
$701$	39.0071	−	22.5207i	1.47328	−	0.850597i	0.473729	−	0.880670i	$-0.342907\pi$
$701$	39.0071	−	22.5207i	1.47328	−	0.850597i	0.999548	+	0.0300735i	$0.00957412\pi$
$702$			4.16629i			0.157247i
$703$	−5.98637	−	24.1066i	−0.225780	−	0.909198i
$704$	3.60666			0.135931
$705$	3.37287	−	0.887615i	0.127030	−	0.0334295i
$706$	−4.00690	+	6.94015i	−0.150802	+	0.261196i
$707$	7.85597	+	4.53565i	0.295454	+	0.170581i
$708$	−5.86075	+	10.1511i	−0.220260	+	0.381502i
$709$		−	41.1960i		−	1.54715i	−0.633705	−	0.773575i	$-0.718467\pi$
$709$		−	41.1960i		−	1.54715i	0.633705	−	0.773575i	$-0.281533\pi$
$710$	1.13787	+	1.14809i	0.0427037	+	0.0430872i
$711$			8.69122i			0.325946i
$712$	5.28646	−	3.05214i	0.198119	−	0.114384i
$713$			3.40517i			0.127525i
$714$	−7.58019			−0.283682
$715$	−32.4937	+	8.55115i	−1.21520	+	0.319795i
$716$	1.27281	+	0.734858i	0.0475672	+	0.0274629i
$717$	−6.88709			−0.257203
$718$	11.4664	+	19.8605i	0.427924	+	0.741186i
$719$	9.93211	+	17.2029i	0.370405	+	0.641560i	0.989628	−	0.143655i	$-0.0458856\pi$
$719$	9.93211	+	17.2029i	0.370405	+	0.641560i	−0.619223	+	0.785215i	$0.712552\pi$
$720$	2.16244	−	0.569075i	0.0805894	−	0.0212082i
$721$	25.9892	+	15.0049i	0.967889	+	0.558811i
$722$	1.16263	−	2.01374i	0.0432688	−	0.0749437i
$723$	−8.35532	−	14.4718i	−0.310738	−	0.538213i
$724$	2.61171	+	4.52361i	0.0970633	+	0.168119i
$725$	−16.5936	−	0.148378i	−0.616271	−	0.00551063i
$726$		−	2.00802i		−	0.0745248i
$727$	5.99437	−	10.3825i	0.222319	−	0.385067i	−0.733193	−	0.680021i	$-0.761971\pi$
$727$	5.99437	−	10.3825i	0.222319	−	0.385067i	0.955512	+	0.294953i	$0.0953041\pi$
$728$	−8.32890	+	4.80869i	−0.308689	+	0.178222i
$729$	−1.00000			−0.0370370
$730$	−0.601440	−	0.164041i	−0.0222603	−	0.00607142i
$731$	−19.1425	−	33.1558i	−0.708011	−	1.22631i
$732$	2.49208			0.0921100
$733$	14.4350	+	8.33404i	0.533168	+	0.307825i	0.742306	−	0.670061i	$-0.233732\pi$
$733$	14.4350	+	8.33404i	0.533168	+	0.307825i	−0.209137	+	0.977886i	$0.567066\pi$
$734$		−	9.54106i		−	0.352167i
$735$	−2.65448	+	2.63085i	−0.0979120	+	0.0970404i
$736$	0.374445	−	0.648558i	0.0138022	−	0.0239062i
$737$	24.8066	+	14.3221i	0.913762	+	0.527561i
$738$	−1.97387	−	3.41884i	−0.0726590	−	0.125849i
$739$	13.8748			0.510394			0.255197	−	0.966889i	$-0.417860\pi$
$739$	13.8748			0.510394			0.255197	+	0.966889i	$0.417860\pi$
$740$	−11.6207	−	7.06826i	−0.427184	−	0.259835i
$741$	−17.0129			−0.624986
$742$	−2.69987	−	4.67631i	−0.0991152	−	0.171673i
$743$	43.4777	+	25.1019i	1.59504	+	0.920899i	0.992423	+	0.122871i	$0.0392102\pi$
$743$	43.4777	+	25.1019i	1.59504	+	0.920899i	0.602621	+	0.798028i	$0.294123\pi$
$744$	−2.27348	+	3.93778i	−0.0833498	+	0.144366i
$745$	−32.1399	−	32.4286i	−1.17751	−	1.18809i
$746$			23.1104i			0.846132i
$747$	5.53660	+	3.19656i	0.202574	+	0.116956i
$748$	−11.8435			−0.433040
$749$	−7.98973	−	13.8386i	−0.291938	−	0.505652i
$750$	7.79895	+	8.01101i	0.284777	+	0.292521i
$751$	26.7710			0.976888			0.488444	−	0.872595i	$-0.337565\pi$
$751$	26.7710			0.976888			0.488444	+	0.872595i	$0.337565\pi$
$752$	1.35078	−	0.779875i	0.0492580	−	0.0284391i
$753$	−7.60768	+	13.1769i	−0.277239	+	0.480192i
$754$		−	13.8273i		−	0.503561i
$755$	28.5139	−	7.50381i	1.03773	−	0.273092i
$756$	−1.15419	−	1.99912i	−0.0419775	−	0.0727071i
$757$	−0.848563	−	1.46975i	−0.0308416	−	0.0534191i	0.850193	−	0.526472i	$-0.176485\pi$
$757$	−0.848563	−	1.46975i	−0.0308416	−	0.0534191i	−0.881034	+	0.473053i	$0.843152\pi$
$758$	12.8937	−	22.3326i	0.468321	−	0.811156i
$759$	−2.33913	−	1.35050i	−0.0849051	−	0.0490200i
$760$	2.32380	+	8.83027i	0.0842931	+	0.320307i
$761$	13.8079	+	23.9160i	0.500536	+	0.866953i	1.00000		0.000618665i	$0.000196927\pi$
$761$	13.8079	+	23.9160i	0.500536	+	0.866953i	−0.499464	+	0.866335i	$0.666470\pi$
$762$	−6.58300	−	11.4021i	−0.238477	−	0.413054i
$763$	−23.6888			−0.857591
$764$	0.273500	+	0.157905i	0.00989487	+	0.00571281i
$765$	−7.10097	+	1.86871i	−0.256736	+	0.0675634i
$766$	−32.9595			−1.19087
$767$		−	48.8352i		−	1.76334i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$			41.1203i			1.48284i	0.671043	+	0.741418i	$0.265846\pi$
$769$			41.1203i			1.48284i	−0.671043	+	0.741418i	$0.734154\pi$
$770$	13.2226	−	13.1049i	0.476508	−	0.472266i
$771$			5.07127i			0.182637i
$772$	−1.83668	+	3.18122i	−0.0661035	+	0.114495i
$773$	3.69664	+	2.13426i	0.132959	+	0.0767639i	0.565004	−	0.825088i	$-0.308875\pi$
$773$	3.69664	+	2.13426i	0.132959	+	0.0767639i	−0.432045	+	0.901852i	$0.642208\pi$
$774$	5.82942	−	10.0969i	0.209534	−	0.362924i
$775$	−22.7339	−	0.203284i	−0.816625	−	0.00730218i
$776$	4.51721			0.162158
$777$	−3.88301	+	13.4937i	−0.139302	+	0.484085i
$778$		−	26.7678i		−	0.959672i
$779$	13.9607	−	8.06022i	0.500195	−	0.288787i
$780$	−6.61687	+	6.55797i	−0.236922	+	0.234813i
$781$	1.30362	−	2.25793i	0.0466471	−	0.0807952i
$782$	−1.22959	+	2.12972i	−0.0439702	+	0.0761585i
$783$	3.31885			0.118606
$784$	−0.835693	+	1.44746i	−0.0298462	+	0.0516951i
$785$	31.9472	+	8.71350i	1.14024	+	0.310998i
$786$	−8.18806	−	14.1821i	−0.292059	−	0.505860i
$787$			19.0243i			0.678143i	0.940761	+	0.339072i	$0.110113\pi$
$787$			19.0243i			0.678143i	−0.940761	+	0.339072i	$0.889887\pi$
$788$			21.6474i			0.771157i
$789$	−2.50706	−	4.34236i	−0.0892538	−	0.154592i
$790$	−13.8033	+	13.6804i	−0.491100	+	0.486728i
$791$		−	0.532220i		−	0.0189236i
$792$	−1.80333	−	3.12346i	−0.0640786	−	0.110987i
$793$	−8.99172	+	5.19137i	−0.319305	+	0.184351i
$794$	−10.4379	+	6.02632i	−0.370427	+	0.213866i
$795$	−3.68201	−	3.71508i	−0.130587	−	0.131760i
$796$	18.2837	+	10.5561i	0.648047	+	0.374150i
$797$	−9.96472	−	17.2594i	−0.352969	−	0.611360i	0.633799	−	0.773497i	$-0.281494\pi$
$797$	−9.96472	−	17.2594i	−0.352969	−	0.611360i	−0.986768	+	0.162138i	$0.948161\pi$
$798$	8.16333	−	4.71310i	0.288979	−	0.166842i
$799$	−4.43567	+	2.56093i	−0.156923	+	0.0905993i
$800$	4.30760	+	2.53862i	0.152297	+	0.0897537i
$801$	−5.28646	−	3.05214i	−0.186788	−	0.107842i
$802$	15.3679	−	8.87268i	0.542660	−	0.313305i
$803$			1.00553i			0.0354843i
$804$	7.94202			0.280093
$805$	−0.983773	−	3.73826i	−0.0346734	−	0.131756i
$806$		−	18.9440i		−	0.667272i
$807$	−5.97892	−	3.45193i	−0.210468	−	0.121514i
$808$	3.92973			0.138247
$809$	−35.6616	−	20.5892i	−1.25379	−	0.723878i	−0.281933	−	0.959434i	$-0.590976\pi$
$809$	−35.6616	−	20.5892i	−1.25379	−	0.723878i	−0.971861	+	0.235556i	$0.924309\pi$
$810$	−1.57405	−	1.58819i	−0.0553066	−	0.0558034i
$811$	−3.81494	+	6.60766i	−0.133961	+	0.232026i	−0.925200	−	0.379480i	$-0.876103\pi$
$811$	−3.81494	+	6.60766i	−0.133961	+	0.232026i	0.791239	+	0.611507i	$0.209436\pi$
$812$	3.83058	+	6.63477i	0.134427	+	0.232835i
$813$		−	22.1012i		−	0.775122i
$814$	−6.06690	+	21.0829i	−0.212645	+	0.738956i
$815$	−6.55751	+	24.0425i	−0.229700	+	0.842172i
$816$	−2.84383	+	1.64189i	−0.0995540	+	0.0574775i
$817$	41.2302	+	23.8043i	1.44246	+	0.832806i
$818$	−25.7232	−	14.8513i	−0.899390	−	0.519263i
$819$	8.32890	+	4.80869i	0.291035	+	0.168029i
$820$	2.32280	−	8.51631i	0.0811156	−	0.297403i
$821$	9.92670	−	17.1935i	0.346444	−	0.600059i	−0.639171	−	0.769065i	$-0.720722\pi$
$821$	9.92670	−	17.1935i	0.346444	−	0.600059i	0.985615	+	0.169006i	$0.0540557\pi$
$822$	8.12613			0.283431
$823$	−0.0766940	+	0.0442793i	−0.00267339	+	0.00154348i	−0.501336	−	0.865253i	$-0.667158\pi$
$823$	−0.0766940	+	0.0442793i	−0.00267339	+	0.00154348i	0.498663	+	0.866796i	$0.333825\pi$
$824$	13.0004			0.452889
$825$	9.15594	−	15.5361i	0.318769	−	0.540896i
$826$	13.5288	+	23.4326i	0.470728	+	0.815325i
$827$	21.1970	−	36.7143i	0.737092	−	1.27668i	−0.216708	−	0.976236i	$-0.569532\pi$
$827$	21.1970	−	36.7143i	0.737092	−	1.27668i	0.953800	−	0.300443i	$-0.0971347\pi$
$828$	−0.748890			−0.0260257
$829$	−26.2357	+	15.1472i	−0.911204	+	0.526084i	−0.880818	−	0.473454i	$-0.843007\pi$
$829$	−26.2357	+	15.1472i	−0.911204	+	0.526084i	−0.0303859	+	0.999538i	$0.509674\pi$
$830$	3.63816	+	13.8247i	0.126282	+	0.479864i
$831$	−0.00667067	+	0.00385131i	−0.000231403	+	0.000133601i
$832$	−2.08315	+	3.60811i	−0.0722201	+	0.125089i
$833$	2.74423	−	4.75314i	0.0950818	−	0.164686i
$834$	8.90004	−	5.13844i	0.308183	−	0.177930i
$835$	18.1829	−	4.78507i	0.629245	−	0.165594i
$836$	12.7546	−	7.36385i	0.441126	−	0.254684i
$837$	4.54696			0.157166
$838$	−9.44226	+	16.3545i	−0.326177	+	0.564956i
$839$	−1.69298	−	2.93233i	−0.0584482	−	0.101235i	0.835321	−	0.549763i	$-0.185282\pi$
$839$	−1.69298	−	2.93233i	−0.0584482	−	0.101235i	−0.893769	+	0.448528i	$0.851949\pi$
$840$	1.35822	−	4.97979i	0.0468631	−	0.171819i
$841$	17.9852			0.620180
$842$	28.7552	−	16.6018i	0.990970	−	0.572137i
$843$	24.3983			0.840321
$844$	−11.2445	+	19.4761i	−0.387052	+	0.670394i
$845$	2.56418	−	9.40133i	0.0882106	−	0.323416i
$846$	−1.35078	−	0.779875i	−0.0464409	−	0.0268127i
$847$	−4.01427	−	2.31764i	−0.137932	−	0.0796351i
$848$	−2.02580	−	1.16959i	−0.0695661	−	0.0401640i
$849$	−22.2615	+	12.8527i	−0.764012	+	0.441103i
$850$	−14.1452	−	8.33625i	−0.485176	−	0.285931i
$851$	3.16131	+	3.27980i	0.108368	+	0.112430i
$852$		−	0.722894i		−	0.0247659i
$853$	−19.5721	−	33.8999i	−0.670136	−	1.16071i	−0.977865	−	0.209236i	$-0.932902\pi$
$853$	−19.5721	−	33.8999i	−0.670136	−	1.16071i	0.307729	−	0.951474i	$-0.400431\pi$
$854$	2.87634	−	4.98196i	0.0984262	−	0.170479i
$855$	6.48534	−	6.42760i	0.221794	−	0.219819i
$856$	−5.99495	−	3.46119i	−0.204903	−	0.118301i
$857$	−0.165876			−0.00566621			−0.00283311	−	0.999996i	$-0.500902\pi$
$857$	−0.165876			−0.00566621			−0.00283311	+	0.999996i	$0.500902\pi$
$858$	13.0133	+	7.51321i	0.444265	+	0.256497i
$859$			47.9739i			1.63685i	0.574615	+	0.818424i	$0.305152\pi$
$859$			47.9739i			1.63685i	−0.574615	+	0.818424i	$0.694848\pi$
$860$	25.2116	−	6.63475i	0.859707	−	0.226243i
$861$	−9.11286			−0.310566
$862$		−	11.7180i		−	0.399117i
$863$	39.1758	−	22.6182i	1.33356	−	0.769931i	0.347717	−	0.937600i	$-0.386957\pi$
$863$	39.1758	−	22.6182i	1.33356	−	0.769931i	0.985843	+	0.167668i	$0.0536238\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	35.4593	+	9.67140i	1.20565	+	0.328838i
$866$	11.7279	−	6.77110i	0.398530	−	0.230091i
$867$	−5.38394	+	3.10842i	−0.182848	+	0.105567i
$868$	5.24805	+	9.08989i	0.178131	+	0.308531i
$869$	27.1467	+	15.6732i	0.920889	+	0.531675i
$870$	5.22405	+	5.27097i	0.177112	+	0.178703i
$871$	−28.6557	+	16.5444i	−0.970961	+	0.560585i
$872$	−8.88722	+	5.13104i	−0.300959	+	0.173759i
$873$	−2.25861	−	3.91202i	−0.0764422	−	0.132402i
$874$		−	3.05807i		−	0.103441i
$875$	25.0164	−	6.34477i	0.845709	−	0.214492i
$876$	0.139399	+	0.241445i	0.00470984	+	0.00815769i
$877$		−	14.1700i		−	0.478487i	−0.970960	−	0.239244i	$-0.923101\pi$
$877$		−	14.1700i		−	0.478487i	0.970960	−	0.239244i	$-0.0768995\pi$
$878$		−	30.6145i		−	1.03319i
$879$	5.15230	+	8.92404i	0.173783	+	0.301000i
$880$	2.12212	−	7.78054i	0.0715365	−	0.262282i
$881$	−4.36215	+	7.55546i	−0.146965	+	0.254550i	−0.930104	−	0.367296i	$-0.880284\pi$
$881$	−4.36215	+	7.55546i	−0.146965	+	0.254550i	0.783140	+	0.621846i	$0.213617\pi$
$882$	1.67139			0.0562785
$883$	5.24023	−	9.07635i	0.176348	−	0.305444i	−0.764279	−	0.644886i	$-0.776905\pi$
$883$	5.24023	−	9.07635i	0.176348	−	0.305444i	0.940627	+	0.339442i	$0.110238\pi$
$884$	6.84058	−	11.8482i	0.230074	−	0.398499i
$885$	18.4503	+	18.6160i	0.620199	+	0.625770i
$886$	−3.42389	+	1.97678i	−0.115028	+	0.0664113i
$887$		−	6.48431i		−	0.217722i	−0.994057	−	0.108861i	$-0.965280\pi$
$887$		−	6.48431i		−	0.217722i	0.994057	−	0.108861i	$-0.0347203\pi$
$888$	1.46600	+	5.90346i	0.0491957	+	0.198107i
$889$	−30.3921			−1.01932
$890$	−3.47379	−	13.2002i	−0.116442	−	0.442470i
$891$	−1.80333	+	3.12346i	−0.0604139	+	0.104640i
$892$	11.5280	+	6.65570i	0.385986	+	0.222849i
$893$	3.18460	−	5.51589i	0.106569	−	0.184582i
$894$			20.4186i			0.682898i
$895$	2.33419	−	2.31341i	0.0780234	−	0.0773288i
$896$		−	2.30838i		−	0.0771175i
$897$	2.70208	−	1.56005i	0.0902199	−	0.0520885i
$898$			22.5175i			0.751418i
$899$	−15.0907			−0.503302
$900$	0.0447077	−	4.99980i	0.00149026	−	0.166660i
$901$	6.65226	+	3.84068i	0.221619	+	0.127952i
$902$	−14.2381			−0.474078
$903$	−13.4565	−	23.3074i	−0.447805	−	0.775621i
$904$	−0.115280	−	0.199671i	−0.00383416	−	0.00664096i
$905$	11.2953	−	2.97251i	0.375469	−	0.0988096i
$906$	−11.4194	−	6.59299i	−0.379384	−	0.219037i
$907$	−5.25683	+	9.10510i	−0.174550	+	0.302330i	−0.940006	−	0.341159i	$-0.889180\pi$
$907$	−5.25683	+	9.10510i	−0.174550	+	0.302330i	0.765455	+	0.643489i	$0.222514\pi$
$908$	6.15062	+	10.6532i	0.204115	+	0.353538i
$909$	−1.96486	−	3.40324i	−0.0651704	−	0.112878i
$910$	5.47301	+	20.7970i	0.181428	+	0.689415i
$911$			35.2304i			1.16724i	0.812029	+	0.583618i	$0.198363\pi$
$911$			35.2304i			1.16724i	−0.812029	+	0.583618i	$0.801637\pi$
$912$	2.04174	−	3.53639i	0.0676086	−	0.117102i
$913$	19.9687	−	11.5289i	0.660866	−	0.381551i
$914$	8.58921			0.284106
$915$	1.46631	−	5.37609i	0.0484747	−	0.177728i
$916$	−3.47120	−	6.01230i	−0.114692	−	0.198652i
$917$	−37.8023			−1.24834
$918$	2.84383	+	1.64189i	0.0938604	+	0.0541903i
$919$			16.0232i			0.528556i	0.964447	+	0.264278i	$0.0851336\pi$
$919$			16.0232i			0.528556i	−0.964447	+	0.264278i	$0.914866\pi$
$920$	−1.17879	−	1.18938i	−0.0388637	−	0.0392128i
$921$	12.5868	−	21.8009i	0.414748	−	0.718365i
$922$	23.8184	+	13.7516i	0.784418	+	0.452884i
$923$	1.50589	+	2.60828i	0.0495671	+	0.0858527i
$924$	−8.32555			−0.273890
$925$	−22.0856	+	20.9100i	−0.726169	+	0.687516i
$926$	−15.2798			−0.502126
$927$	−6.50018	−	11.2586i	−0.213494	−	0.369782i
$928$	2.87421	+	1.65943i	0.0943506	+	0.0544733i
$929$	−11.2262	+	19.4444i	−0.368320	+	0.637949i	−0.989303	−	0.145875i	$-0.953400\pi$
$929$	−11.2262	+	19.4444i	−0.368320	+	0.637949i	0.620983	+	0.783824i	$0.286734\pi$
$930$	7.15716	+	7.22144i	0.234693	+	0.236800i
$931$			6.82505i			0.223682i
$932$	5.85187	+	3.37858i	0.191684	+	0.110669i
$933$	29.0221			0.950142
$934$	−15.7891	−	27.3475i	−0.516634	−	0.894836i
$935$	−6.96855	+	25.5495i	−0.227896	+	0.835559i
$936$	4.16629			0.136179
$937$	4.13499	−	2.38734i	0.135084	−	0.0779909i	−0.430935	−	0.902383i	$-0.641816\pi$
$937$	4.13499	−	2.38734i	0.135084	−	0.0779909i	0.566019	+	0.824392i	$0.308483\pi$
$938$	9.16659	−	15.8770i	0.299300	−	0.518402i
$939$		−	23.7788i		−	0.775991i
$940$	−0.887615	−	3.37287i	−0.0289508	−	0.110011i
$941$	18.1220	+	31.3883i	0.590762	+	1.02323i	0.994130	+	0.108192i	$0.0345060\pi$
$941$	18.1220	+	31.3883i	0.590762	+	1.02323i	−0.403368	+	0.915038i	$0.632161\pi$
$942$	−7.40456	−	12.8251i	−0.241253	−	0.417863i
$943$	−1.47821	+	2.56033i	−0.0481371	+	0.0833759i
$944$	10.1511	+	5.86075i	0.330391	+	0.190751i
$945$	−4.99174	+	1.31364i	−0.162381	+	0.0427327i
$946$	−21.0248	−	36.4160i	−0.683574	−	1.18399i
$947$	−1.39999	−	2.42486i	−0.0454937	−	0.0787974i	0.842382	−	0.538881i	$-0.181153\pi$
$947$	−1.39999	−	2.42486i	−0.0454937	−	0.0787974i	−0.887876	+	0.460084i	$0.847819\pi$
$948$	8.69122			0.282278
$949$	−1.00593	−	0.580775i	−0.0326539	−	0.0188528i
$950$	20.4165	+	0.182563i	0.662400	+	0.00592312i
$951$	−9.45313			−0.306539
$952$			7.58019i			0.245675i
$953$	−6.35576	+	3.66950i	−0.205883	+	0.118867i	−0.599397	−	0.800452i	$-0.704593\pi$
$953$	−6.35576	+	3.66950i	−0.205883	+	0.118867i	0.393513	+	0.919319i	$0.371259\pi$
$954$			2.33919i			0.0757340i
$955$	0.501567	−	0.497102i	0.0162303	−	0.0160859i
$956$			6.88709i			0.222744i
$957$	5.98499	−	10.3663i	0.193467	−	0.335095i
$958$	30.1785	+	17.4236i	0.975024	+	0.562931i
$959$	9.37910	−	16.2451i	0.302867	−	0.524581i
$960$	−0.569075	−	2.16244i	−0.0183668	−	0.0697925i
$961$	10.3252			0.333070
$962$	−17.5873	−	18.2465i	−0.567036	−	0.588290i
$963$			6.92237i			0.223070i
$964$	−14.4718	+	8.35532i	−0.466106	+	0.269107i
$965$	5.78206	+	5.83399i	0.186131	+	0.187803i
$966$	−0.864361	+	1.49712i	−0.0278104	+	0.0481690i
$967$	−10.9128	+	18.9016i	−0.350933	+	0.607833i	−0.986413	−	0.164284i	$-0.947469\pi$
$967$	−10.9128	+	18.9016i	−0.350933	+	0.607833i	0.635481	+	0.772117i	$0.280802\pi$
$968$	−2.00802			−0.0645403
$969$	−6.70460	+	11.6127i	−0.215383	+	0.373054i
$970$	2.65787	−	9.74483i	0.0853391	−	0.312888i
$971$	−24.0582	−	41.6700i	−0.772063	−	1.33725i	−0.936430	−	0.350853i	$-0.885892\pi$
$971$	−24.0582	−	41.6700i	−0.772063	−	1.33725i	0.164367	−	0.986399i	$-0.447442\pi$
$972$			1.00000i			0.0320750i
$973$		−	23.7229i		−	0.760523i
$974$	−16.3699	−	28.3534i	−0.524524	−	0.908502i
$975$	10.2540	+	18.1330i	0.328391	+	0.580720i
$976$		−	2.49208i		−	0.0797696i
$977$	−13.1493	−	22.7753i	−0.420685	−	0.728647i	0.575322	−	0.817927i	$-0.304877\pi$
$977$	−13.1493	−	22.7753i	−0.420685	−	0.728647i	−0.996007	+	0.0892800i	$0.971543\pi$
$978$	9.65175	−	5.57244i	0.308629	−	0.178187i
$979$	−19.0665	+	11.0080i	−0.609368	+	0.351819i
$980$	2.63085	+	2.65448i	0.0840395	+	0.0847943i
$981$	8.88722	+	5.13104i	0.283747	+	0.163822i
$982$	−6.63482	−	11.4919i	−0.211726	−	0.366720i
$983$	−10.6255	+	6.13466i	−0.338902	+	0.195665i	−0.659787	−	0.751453i	$-0.729353\pi$
$983$	−10.6255	+	6.13466i	−0.338902	+	0.195665i	0.320884	+	0.947118i	$0.396020\pi$
$984$	−3.41884	+	1.97387i	−0.108989	+	0.0629246i
$985$	46.6992	+	12.7371i	1.48796	+	0.405837i
$986$	−9.43825	−	5.44918i	−0.300575	−	0.173537i
$987$	−3.11812	+	1.80025i	−0.0992509	+	0.0573025i
$988$			17.0129i			0.541253i
$989$	−8.73120			−0.277636
$990$	−7.79920	+	2.05246i	−0.247875	+	0.0652315i
$991$			16.1880i			0.514229i	0.966381	+	0.257114i	$0.0827717\pi$
$991$			16.1880i			0.514229i	−0.966381	+	0.257114i	$0.917228\pi$
$992$	3.93778	+	2.27348i	0.125025	+	0.0721830i
$993$	33.7348			1.07054
$994$	−1.44515	−	0.834357i	−0.0458373	−	0.0264642i
$995$	33.5301	−	33.2317i	1.06298	−	1.05351i
$996$	3.19656	−	5.53660i	0.101287	−	0.175434i
$997$	−1.31257	−	2.27343i	−0.0415694	−	0.0720003i	0.844492	−	0.535568i	$-0.179902\pi$
$997$	−1.31257	−	2.27343i	−0.0415694	−	0.0720003i	−0.886062	+	0.463568i	$0.846569\pi$
$998$		−	0.982540i		−	0.0311018i
$999$	4.37955	−	4.22132i	0.138563	−	0.133557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.529.5	yes	36
5.4	even	2		1110.2.ba.a.529.14	✓	36
37.27	even	6		1110.2.ba.a.619.14	yes	36
185.64	even	6	inner	1110.2.ba.b.619.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.14	✓	36	5.4	even	2
1110.2.ba.a.619.14	yes	36	37.27	even	6
1110.2.ba.b.529.5	yes	36	1.1	even	1	trivial
1110.2.ba.b.619.5	yes	36	185.64	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57405 + 1.58819i) q^{5} -1.00000i q^{6} +(-1.99912 - 1.15419i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57405 + 1.58819i) q^{5} -1.00000i q^{6} +(-1.99912 - 1.15419i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.588388 + 2.15727i) q^{10} +3.60666 q^{11} +(0.866025 - 0.500000i) q^{12} +(-2.08315 + 3.60811i) q^{13} -2.30838i q^{14} +(-0.569075 - 2.16244i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.64189 + 2.84383i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-3.53639 - 2.04174i) q^{19} +(-2.16244 + 0.569075i) q^{20} +(1.15419 + 1.99912i) q^{21} +(1.80333 + 3.12346i) q^{22} +0.748890 q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.0447077 + 4.99980i) q^{25} -4.16629 q^{26} -1.00000i q^{27} +(1.99912 - 1.15419i) q^{28} +3.31885i q^{29} +(1.58819 - 1.57405i) q^{30} +4.54696i q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.12346 - 1.80333i) q^{33} +(-1.64189 + 2.84383i) q^{34} +(-1.31364 - 4.99174i) q^{35} -1.00000 q^{36} +(4.22132 + 4.37955i) q^{37} -4.08347i q^{38} +(3.60811 - 2.08315i) q^{39} +(-1.57405 - 1.58819i) q^{40} +(-1.97387 + 3.41884i) q^{41} +(-1.15419 + 1.99912i) q^{42} -11.6588 q^{43} +(-1.80333 + 3.12346i) q^{44} +(-0.588388 + 2.15727i) q^{45} +(0.374445 + 0.648558i) q^{46} +1.55975i q^{47} +1.00000i q^{48} +(-0.835693 - 1.44746i) q^{49} +(-4.35231 + 2.46118i) q^{50} -3.28377i q^{51} +(-2.08315 - 3.60811i) q^{52} +(2.02580 - 1.16959i) q^{53} +(0.866025 - 0.500000i) q^{54} +(5.67708 + 5.72807i) q^{55} +(1.99912 + 1.15419i) q^{56} +(2.04174 + 3.53639i) q^{57} +(-2.87421 + 1.65943i) q^{58} +(-10.1511 + 5.86075i) q^{59} +(2.15727 + 0.588388i) q^{60} +(2.15821 + 1.24604i) q^{61} +(-3.93778 + 2.27348i) q^{62} -2.30838i q^{63} +1.00000 q^{64} +(-9.00936 + 2.37093i) q^{65} -3.60666i q^{66} +(6.87799 + 3.97101i) q^{67} -3.28377 q^{68} +(-0.648558 - 0.374445i) q^{69} +(3.66615 - 3.63351i) q^{70} +(0.361447 - 0.626045i) q^{71} +(-0.500000 - 0.866025i) q^{72} +0.278797i q^{73} +(-1.68214 + 5.84555i) q^{74} +(2.53862 - 4.30760i) q^{75} +(3.53639 - 2.04174i) q^{76} +(-7.21014 - 4.16277i) q^{77} +(3.60811 + 2.08315i) q^{78} +(7.52682 + 4.34561i) q^{79} +(0.588388 - 2.15727i) q^{80} +(-0.500000 + 0.866025i) q^{81} -3.94773 q^{82} +(5.53660 - 3.19656i) q^{83} -2.30838 q^{84} +(-1.93213 + 7.08397i) q^{85} +(-5.82942 - 10.0969i) q^{86} +(1.65943 - 2.87421i) q^{87} -3.60666 q^{88} +(-5.28646 + 3.05214i) q^{89} +(-2.16244 + 0.569075i) q^{90} +(8.32890 - 4.80869i) q^{91} +(-0.374445 + 0.648558i) q^{92} +(2.27348 - 3.93778i) q^{93} +(-1.35078 + 0.779875i) q^{94} +(-2.32380 - 8.83027i) q^{95} +(-0.866025 + 0.500000i) q^{96} -4.51721 q^{97} +(0.835693 - 1.44746i) q^{98} +(1.80333 + 3.12346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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