LMFDB - Embedded newform 1110.2.ba.a.619.14

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			619.14
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.16244 - 0.569075i) q^{5} +1.00000i q^{6} +(1.99912 - 1.15419i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.16244 - 0.569075i) 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} +(1.58819 - 1.57405i) 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} +(-1.57405 - 1.58819i) q^{20} +(1.15419 - 1.99912i) q^{21} +(-1.80333 + 3.12346i) q^{22} -0.748890 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.35231 - 2.46118i) q^{25} -4.16629 q^{26} -1.00000i q^{27} +(-1.99912 - 1.15419i) q^{28} -3.31885i q^{29} +(0.569075 + 2.16244i) q^{30} -4.54696i q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.12346 - 1.80333i) q^{33} +(-1.64189 - 2.84383i) q^{34} +(3.66615 - 3.63351i) q^{35} -1.00000 q^{36} +(-4.22132 + 4.37955i) q^{37} -4.08347i q^{38} +(3.60811 + 2.08315i) q^{39} +(2.16244 - 0.569075i) 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} +(-0.0447077 + 4.99980i) q^{50} +3.28377i q^{51} +(2.08315 - 3.60811i) q^{52} +(-2.02580 - 1.16959i) q^{53} +(0.866025 + 0.500000i) q^{54} +(7.79920 - 2.05246i) 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} +(6.55797 + 6.61687i) q^{65} +3.60666i q^{66} +(-6.87799 + 3.97101i) q^{67} +3.28377 q^{68} +(-0.648558 + 0.374445i) q^{69} +(1.31364 + 4.99174i) 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} +(1.57405 + 1.58819i) 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} +(-6.48534 + 6.42760i) 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} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	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
$5$	2.16244	−	0.569075i	0.967073	−	0.254498i
$5$	2.16244	−	0.569075i	0.967073	−	0.254498i
$6$			1.00000i			0.408248i
$7$	1.99912	−	1.15419i	0.755594	−	0.436243i	−0.0721173	−	0.997396i	$-0.522976\pi$
$7$	1.99912	−	1.15419i	0.755594	−	0.436243i	0.827712	+	0.561153i	$0.189642\pi$
$8$	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	0.995736	+	0.0922523i	$0.0294066\pi$
$13$	2.08315	+	3.60811i	0.577761	+	1.00071i	−0.417975	+	0.908459i	$0.637260\pi$
$14$			2.30838i			0.616940i
$15$	1.58819	−	1.57405i	0.410069	−	0.406419i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.64189	+	2.84383i	−0.398216	+	0.689730i	−0.993506	−	0.113781i	$-0.963704\pi$
$17$	−1.64189	+	2.84383i	−0.398216	+	0.689730i	0.595290	+	0.803511i	$0.297037\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.53639	+	2.04174i	−0.811303	+	0.468406i	−0.847408	−	0.530942i	$-0.821838\pi$
$19$	−3.53639	+	2.04174i	−0.811303	+	0.468406i	0.0361050	+	0.999348i	$0.488505\pi$
$20$	−1.57405	−	1.58819i	−0.351969	−	0.355131i
$21$	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	$-0.524878\pi$
$23$	−0.748890			−0.156154			−0.0780772	+	0.996947i	$0.524878\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	4.35231	−	2.46118i	0.870462	−	0.492236i
$26$	−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	$-0.900291\pi$
$29$		−	3.31885i		−	0.616295i	0.951339	−	0.308148i	$-0.0997091\pi$
$30$	0.569075	+	2.16244i	0.103898	+	0.394806i
$31$		−	4.54696i		−	0.816658i	−0.912835	−	0.408329i	$-0.866112\pi$
$31$		−	4.54696i		−	0.816658i	0.912835	−	0.408329i	$-0.133888\pi$
$32$	−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
$35$	3.66615	−	3.63351i	0.619692	−	0.614176i
$36$	−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
$40$	2.16244	−	0.569075i	0.341912	−	0.0899786i
$41$	−1.97387	−	3.41884i	−0.308266	−	0.533933i	0.669717	−	0.742616i	$-0.266415\pi$
$41$	−1.97387	−	3.41884i	−0.308266	−	0.533933i	−0.977983	+	0.208684i	$0.933082\pi$
$42$	1.15419	+	1.99912i	0.178095	+	0.308470i
$43$	11.6588			1.77796			0.888979	−	0.457949i	$-0.151416\pi$
$43$	11.6588			1.77796			0.888979	+	0.457949i	$0.151416\pi$
$44$	−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
$50$	−0.0447077	+	4.99980i	−0.00632263	+	0.707079i
$51$			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	$-0.384694\pi$
$53$	−2.02580	−	1.16959i	−0.278265	−	0.160656i	−0.632638	+	0.774448i	$0.718028\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	7.79920	−	2.05246i	1.05164	−	0.276754i
$56$	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	−0.337585	−	0.941295i	$-0.609610\pi$
$59$	−10.1511	−	5.86075i	−1.32156	−	0.763004i	−0.983978	+	0.178291i	$0.942943\pi$
$60$	−2.15727	−	0.588388i	−0.278502	−	0.0759605i
$61$	2.15821	−	1.24604i	0.276330	−	0.159539i	−0.355431	−	0.934703i	$-0.615666\pi$
$61$	2.15821	−	1.24604i	0.276330	−	0.159539i	0.631761	+	0.775163i	$0.282332\pi$
$62$	3.93778	+	2.27348i	0.500099	+	0.288732i
$63$		−	2.30838i		−	0.290828i
$64$	1.00000			0.125000
$65$	6.55797	+	6.61687i	0.813416	+	0.820722i
$66$			3.60666i			0.443950i
$67$	−6.87799	+	3.97101i	−0.840280	+	0.485136i	−0.857359	−	0.514718i	$-0.827896\pi$
$67$	−6.87799	+	3.97101i	−0.840280	+	0.485136i	0.0170795	+	0.999854i	$0.494563\pi$
$68$	3.28377			0.398216
$69$	−0.648558	+	0.374445i	−0.0780772	+	0.0450779i
$70$	1.31364	+	4.99174i	0.157010	+	0.596626i
$71$	0.361447	+	0.626045i	0.0428959	+	0.0742978i	0.886676	−	0.462391i	$-0.153008\pi$
$71$	0.361447	+	0.626045i	0.0428959	+	0.0742978i	−0.843780	+	0.536689i	$0.819675\pi$
$72$	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	−0.0127481	−	0.999919i	$-0.504058\pi$
$79$	7.52682	−	4.34561i	0.846833	−	0.488919i	0.859581	+	0.511000i	$0.170725\pi$
$80$	−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	$-0.447447\pi$
$83$	−5.53660	−	3.19656i	−0.607721	−	0.350868i	−0.772073	+	0.635534i	$0.780780\pi$
$84$	−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	0.192928	−	0.981213i	$-0.438202\pi$
$89$	−5.28646	−	3.05214i	−0.560364	−	0.323526i	−0.753292	+	0.657687i	$0.771535\pi$
$90$	1.57405	+	1.58819i	0.165920	+	0.167410i
$91$	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
$95$	−6.48534	+	6.42760i	−0.665381	+	0.659458i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	4.51721			0.458653			0.229327	−	0.973350i	$-0.426348\pi$
$97$	4.51721			0.458653			0.229327	+	0.973350i	$0.426348\pi$
$98$	−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	$-0.278735\pi$
$103$	13.0004			1.28096			0.640482	+	0.767973i	$0.278735\pi$
$104$	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	$-0.775270\pi$
$107$	−5.99495	+	3.46119i	−0.579554	+	0.334606i	0.181402	+	0.983409i	$0.441936\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	8.88722	+	5.13104i	0.851242	+	0.491465i	0.861070	−	0.508487i	$-0.169795\pi$
$109$	8.88722	+	5.13104i	0.851242	+	0.491465i	−0.00982793	+	0.999952i	$0.503128\pi$
$110$	−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	$-0.836785\pi$
$113$	−0.115280	+	0.199671i	−0.0108446	+	0.0187835i	0.860552	+	0.509362i	$0.170119\pi$
$114$	−2.04174	−	3.53639i	−0.191226	−	0.331213i
$115$	−1.61943	+	0.426175i	−0.151013	+	0.0397410i
$116$	−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
$120$	1.58819	−	1.57405i	0.144981	−	0.143691i
$121$	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	$-0.531904\pi$
$127$	−11.4021	−	6.58300i	−1.01177	−	0.584147i	−0.911710	+	0.410834i	$0.865238\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	10.0969	−	5.82942i	0.888979	−	0.513252i
$130$	−9.00936	+	2.37093i	−0.790173	+	0.207944i
$131$	14.1821	+	8.18806i	1.23910	+	0.715394i	0.968910	−	0.247413i	$-0.0795804\pi$
$131$	14.1821	+	8.18806i	1.23910	+	0.715394i	0.270189	+	0.962807i	$0.412914\pi$
$132$	−3.12346	−	1.80333i	−0.271863	−	0.156960i
$133$	−4.71310	+	8.16333i	−0.408678	+	0.707850i
$134$		−	7.94202i		−	0.686086i
$135$	−0.569075	−	2.16244i	−0.0489782	−	0.186113i
$136$	−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	−0.561527	−	0.827459i	$-0.689786\pi$
$139$	5.13844	−	8.90004i	0.435837	−	0.754892i	0.997364	+	0.0725670i	$0.0231191\pi$
$140$	−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
$145$	−1.88867	−	7.17682i	−0.156846	−	0.596003i
$146$	−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	$0.815330\pi$
$150$	2.46118	+	4.35231i	0.200955	+	0.355364i
$151$	6.59299	+	11.4194i	0.536530	+	0.929297i	0.999088	+	0.0427080i	$0.0135985\pi$
$151$	6.59299	+	11.4194i	0.536530	+	0.929297i	−0.462558	+	0.886589i	$0.653068\pi$
$152$	−3.53639	+	2.04174i	−0.286839	+	0.165607i
$153$	1.64189	+	2.84383i	0.132739	+	0.229910i
$154$			8.32555i			0.670892i
$155$	−2.58756	−	9.83253i	−0.207838	−	0.789768i
$156$		−	4.16629i		−	0.333570i
$157$	−12.8251	−	7.40456i	−1.02355	−	0.590948i	−0.108421	−	0.994105i	$-0.534579\pi$
$157$	−12.8251	−	7.40456i	−1.02355	−	0.590948i	−0.915131	+	0.403157i	$0.867913\pi$
$158$			8.69122i			0.691436i
$159$	−2.33919			−0.185510
$160$	−1.57405	−	1.58819i	−0.124440	−	0.125558i
$161$	−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	$-0.977104\pi$
$163$	−5.57244	+	9.65175i	−0.436467	+	0.755984i	0.560947	+	0.827852i	$0.310437\pi$
$164$	−1.97387	+	3.41884i	−0.154133	+	0.266966i
$165$	5.72807	−	5.67708i	0.445930	−	0.441960i
$166$	5.53660	−	3.19656i	0.429723	−	0.248101i
$167$	−4.20425	−	7.28198i	−0.325335	−	0.563496i	0.656245	−	0.754548i	$-0.272144\pi$
$167$	−4.20425	−	7.28198i	−0.325335	−	0.563496i	−0.981580	+	0.191051i	$0.938810\pi$
$168$	1.15419	−	1.99912i	0.0890477	−	0.154235i
$169$	−2.17899	+	3.77413i	−0.167615	+	0.290317i
$170$	−5.16884	−	5.21526i	−0.396432	−	0.399992i
$171$			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	$-0.548172\pi$
$173$	−14.2350	−	8.21856i	−1.08226	−	0.624846i	−0.931506	+	0.363725i	$0.881505\pi$
$174$	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	$0.0174922\pi$
$179$			1.46972i			0.109852i	−0.998490	+	0.0549259i	$0.982508\pi$
$180$	−2.16244	+	0.569075i	−0.161179	+	0.0424163i
$181$	2.61171	+	4.52361i	0.194127	+	0.336237i	0.946614	−	0.322370i	$-0.104479\pi$
$181$	2.61171	+	4.52361i	0.194127	+	0.336237i	−0.752487	+	0.658607i	$0.771146\pi$
$182$	−8.32890	+	4.80869i	−0.617379	+	0.356444i
$183$	1.24604	−	2.15821i	0.0921100	−	0.159539i
$184$	−0.748890			−0.0552089
$185$	−6.63608	+	11.8728i	−0.487894	+	0.872903i
$186$	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
$190$	−2.32380	−	8.83027i	−0.168586	−	0.640615i
$191$			0.315810i			0.0228512i	0.999935	+	0.0114256i	$0.00363697\pi$
$191$			0.315810i			0.0228512i	−0.999935	+	0.0114256i	$0.996363\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−3.67336			−0.264414			−0.132207	−	0.991222i	$-0.542206\pi$
$193$	−3.67336			−0.264414			−0.132207	+	0.991222i	$0.542206\pi$
$194$	−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	$-0.613655\pi$
$197$	−18.7472	−	10.8237i	−1.33568	−	0.771157i	−0.986164	+	0.165772i	$0.946988\pi$
$198$	1.80333	+	3.12346i	0.128157	+	0.221975i
$199$			21.1121i			1.49660i	0.663360	+	0.748300i	$0.269130\pi$
$199$			21.1121i			1.49660i	−0.663360	+	0.748300i	$0.730870\pi$
$200$	4.35231	−	2.46118i	0.307755	−	0.174032i
$201$	−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
$205$	−6.21394	−	6.26976i	−0.434001	−	0.437899i
$206$	−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
$210$	3.63351	+	3.66615i	0.250736	+	0.252988i
$211$	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
$215$	25.2116	−	6.63475i	1.71941	−	0.452486i
$216$		−	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
$220$	−5.67708	−	5.72807i	−0.382749	−	0.386187i
$221$	−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
$225$	0.0447077	−	4.99980i	0.00298052	−	0.333320i
$226$	−0.115280	−	0.199671i	−0.00766832	−	0.0132819i
$227$	−6.15062	−	10.6532i	−0.408231	−	0.707077i	0.586461	−	0.809978i	$-0.300521\pi$
$227$	−6.15062	−	10.6532i	−0.408231	−	0.707077i	−0.994692	+	0.102901i	$0.967188\pi$
$228$	4.08347			0.270434
$229$	−3.47120	−	6.01230i	−0.229383	−	0.397304i	0.728242	−	0.685320i	$-0.240338\pi$
$229$	−3.47120	−	6.01230i	−0.229383	−	0.397304i	−0.957626	+	0.288016i	$0.907004\pi$
$230$	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
$235$	0.887615	+	3.37287i	0.0579016	+	0.220022i
$236$			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	0.680341	−	0.732896i	$-0.261832\pi$
$239$	5.96439	+	3.44354i	0.385805	+	0.222744i	−0.294536	+	0.955640i	$0.595165\pi$
$240$	0.569075	+	2.16244i	0.0367336	+	0.139585i
$241$	14.4718	−	8.35532i	0.932213	−	0.538213i	0.0447019	−	0.999000i	$-0.485766\pi$
$241$	14.4718	−	8.35532i	0.932213	−	0.538213i	0.887511	+	0.460787i	$0.152433\pi$
$242$	−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
$250$	2.74858	+	10.8372i	0.173836	+	0.685406i
$251$			15.2154i			0.960385i	0.877163	+	0.480192i	$0.159433\pi$
$251$			15.2154i			0.960385i	−0.877163	+	0.480192i	$0.840567\pi$
$252$	−1.99912	+	1.15419i	−0.125932	+	0.0727071i
$253$	−2.70100			−0.169810
$254$	11.4021	−	6.58300i	0.715431	−	0.413054i
$255$	1.86871	+	7.10097i	0.117023	+	0.444680i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.53563	−	4.39185i	0.158168	−	0.273956i	−0.776040	−	0.630684i	$-0.782774\pi$
$257$	2.53563	−	4.39185i	0.158168	−	0.273956i	0.934208	+	0.356728i	$0.116108\pi$
$258$			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	$-0.716073\pi$
$263$	−4.34236	+	2.50706i	−0.267761	+	0.154592i	0.360109	+	0.932910i	$0.382740\pi$
$264$	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	−0.306267	−	0.951946i	$-0.599080\pi$
$271$	11.0506	−	19.1402i	0.671275	−	1.16268i	0.977543	−	0.210737i	$-0.0675865\pi$
$272$	−1.64189	−	2.84383i	−0.0995540	−	0.172433i
$273$	9.61738			0.582070
$274$	−7.03744	−	4.06307i	−0.425147	−	0.245459i
$275$	15.6973	−	8.87666i	0.946583	−	0.535283i
$276$	0.648558	+	0.374445i	0.0390386	+	0.0225390i
$277$	−0.00385131	−	0.00667067i	−0.000231403	−	0.000400802i	0.865910	−	0.500200i	$-0.166740\pi$
$277$	−0.00385131	−	0.00667067i	−0.000231403	−	0.000400802i	−0.866141	+	0.499800i	$0.833407\pi$
$278$	5.13844	+	8.90004i	0.308183	+	0.533789i
$279$	−3.93778	−	2.27348i	−0.235749	−	0.136110i
$280$	3.66615	−	3.63351i	0.219094	−	0.217144i
$281$	−21.1295	−	12.1991i	−1.26048	−	0.727739i	−0.287314	−	0.957837i	$-0.592762\pi$
$281$	−21.1295	−	12.1991i	−1.26048	−	0.727739i	−0.973168	+	0.230097i	$0.926095\pi$
$282$	−1.55975			−0.0928818
$283$	−12.8527	−	22.2615i	−0.764012	−	1.32331i	−0.940767	−	0.339053i	$-0.889893\pi$
$283$	−12.8527	−	22.2615i	−0.764012	−	1.32331i	0.176755	−	0.984255i	$-0.443440\pi$
$284$	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	$-0.569346\pi$
$293$	8.92404	−	5.15230i	0.521348	−	0.301000i	0.737486	+	0.675362i	$0.236013\pi$
$294$	−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
$300$	−4.99980	−	0.0447077i	−0.288664	−	0.00258120i
$301$	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
$305$	3.95790	−	3.92267i	0.226629	−	0.224612i
$306$	−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	−0.428475	−	0.903554i	$-0.640949\pi$
$311$	−25.1339	−	14.5111i	−1.42521	−	0.822847i	−0.996738	+	0.0807069i	$0.974282\pi$
$312$	3.60811	+	2.08315i	0.204269	+	0.117935i
$313$	−11.8894	+	20.5930i	−0.672028	+	1.16399i	0.305300	+	0.952256i	$0.401243\pi$
$313$	−11.8894	+	20.5930i	−0.672028	+	1.16399i	−0.977328	+	0.211731i	$0.932090\pi$
$314$	12.8251	−	7.40456i	0.723760	−	0.417863i
$315$	−1.31364	−	4.99174i	−0.0740153	−	0.281252i
$316$	−7.52682	−	4.34561i	−0.423416	−	0.244460i
$317$	−8.18665	−	4.72657i	−0.459808	−	0.265470i	0.252155	−	0.967687i	$-0.418861\pi$
$317$	−8.18665	−	4.72657i	−0.459808	−	0.265470i	−0.711964	+	0.702216i	$0.752194\pi$
$318$	1.16959	−	2.02580i	0.0655876	−	0.113601i
$319$		−	11.9700i		−	0.670190i
$320$	2.16244	−	0.569075i	0.120884	−	0.0318122i
$321$	−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
$330$	2.05246	+	7.79920i	0.112984	+	0.429332i
$331$	−29.2152	−	16.8674i	−1.60581	−	0.927115i	−0.990294	−	0.138992i	$-0.955614\pi$
$331$	−29.2152	−	16.8674i	−1.60581	−	0.927115i	−0.615517	−	0.788123i	$-0.711053\pi$
$332$			6.39311i			0.350868i
$333$	1.68214	+	5.84555i	0.0921805	+	0.320334i
$334$	8.40850			0.460093
$335$	−12.6134	+	12.5012i	−0.689146	+	0.683011i
$336$	1.15419	+	1.99912i	0.0629662	+	0.109061i
$337$	−29.0757	+	16.7869i	−1.58385	+	0.914439i	−0.589565	+	0.807721i	$0.700701\pi$
$337$	−29.0757	+	16.7869i	−1.58385	+	0.914439i	−0.994289	+	0.106717i	$0.965966\pi$
$338$	−2.17899	−	3.77413i	−0.118522	−	0.205285i
$339$			0.230560i			0.0125223i
$340$	7.10097	−	1.86871i	0.385104	−	0.101345i
$341$		−	16.3994i		−	0.888075i
$342$	−3.53639	−	2.04174i	−0.191226	−	0.110404i
$343$			20.0168i			1.08081i
$344$	11.6588			0.628603
$345$	−1.18938	+	1.17879i	−0.0640342	+	0.0634641i
$346$	14.2350	−	8.21856i	0.765277	−	0.441833i
$347$	11.3801			0.610915			0.305457	−	0.952206i	$-0.401191\pi$
$347$	11.3801			0.610915			0.305457	+	0.952206i	$0.401191\pi$
$348$	−1.65943	+	2.87421i	−0.0889546	+	0.154074i
$349$	−6.76004	+	11.7087i	−0.361856	+	0.626754i	−0.988266	−	0.152740i	$-0.951190\pi$
$349$	−6.76004	+	11.7087i	−0.361856	+	0.626754i	0.626410	+	0.779494i	$0.284524\pi$
$350$	5.68134	+	10.0468i	0.303680	+	0.537023i
$351$	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	$-0.901743\pi$
$353$	−4.00690	+	6.94015i	−0.213266	+	0.369387i	0.739469	+	0.673191i	$0.235077\pi$
$354$	5.86075	−	10.1511i	0.311495	−	0.539526i
$355$	1.13787	+	1.14809i	0.0603921	+	0.0609345i
$356$			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
$365$	0.158656	+	0.602883i	0.00830446	+	0.0315563i
$366$	1.24604	+	2.15821i	0.0651316	+	0.112811i
$367$	8.26280	−	4.77053i	0.431315	−	0.249020i	−0.268592	−	0.963254i	$-0.586558\pi$
$367$	8.26280	−	4.77053i	0.431315	−	0.249020i	0.699907	+	0.714234i	$0.253225\pi$
$368$	0.374445	−	0.648558i	0.0195193	−	0.0338084i
$369$	−3.94773			−0.205511
$370$	−6.96408	−	11.6834i	−0.362045	−	0.607391i
$371$	−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	$-0.870826\pi$
$373$	−20.0142	+	11.5552i	−1.03630	+	0.598305i	−0.117514	+	0.993071i	$0.537492\pi$
$374$	−5.92173	−	10.2567i	−0.306206	−	0.530364i
$375$	3.03827	−	10.7596i	0.156895	−	0.555623i
$376$			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	0.317702	+	0.948191i	$0.397089\pi$
$379$	−12.8937	+	22.3326i	−0.662306	+	1.14715i	−0.980008	+	0.198958i	$0.936244\pi$
$380$	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	0.888137	+	0.459578i	$0.151999\pi$
$383$	16.4797	+	28.5437i	0.842075	+	1.45852i	−0.0460621	+	0.998939i	$0.514667\pi$
$384$			1.00000i			0.0510310i
$385$	13.2226	−	13.1049i	0.673884	−	0.667886i
$386$	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	−0.954935	−	0.296815i	$-0.904076\pi$
$389$	−23.1816	+	13.3839i	−1.17535	+	0.678590i	−0.220418	+	0.975405i	$0.570742\pi$
$390$	−6.61687	+	6.55797i	−0.335058	+	0.332076i
$391$	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
$395$	13.8033	−	13.6804i	0.694521	−	0.688338i
$396$	−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
$400$	−0.0447077	+	4.99980i	−0.00223539	+	0.249990i
$401$			17.7454i			0.886161i	0.896482	+	0.443080i	$0.146114\pi$
$401$			17.7454i			0.886161i	−0.896482	+	0.443080i	$0.853886\pi$
$402$	−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
$405$	−1.57405	−	1.58819i	−0.0782154	−	0.0789179i
$406$	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	−0.296578	−	0.955009i	$-0.595846\pi$
$409$	−25.7232	−	14.8513i	−1.27193	−	0.734349i	−0.975351	+	0.220660i	$0.929179\pi$
$410$	8.53674	−	2.24655i	0.421600	−	0.110949i
$411$	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	−0.537741	−	0.843110i	$-0.680722\pi$
$419$	9.44226	−	16.3545i	0.461285	−	0.798968i	0.999025	+	0.0441419i	$0.0140554\pi$
$420$	−4.99174	+	1.31364i	−0.243572	+	0.0640991i
$421$			33.2036i			1.61825i	0.587639	+	0.809123i	$0.300058\pi$
$421$			33.2036i			1.61825i	−0.587639	+	0.809123i	$0.699942\pi$
$422$	−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
$425$	−0.146810	+	16.4182i	−0.00712133	+	0.796400i
$426$	−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	−0.724083	−	0.689713i	$-0.757737\pi$
$431$	−10.1481	+	5.85900i	−0.488816	+	0.282218i	0.235267	+	0.971931i	$0.424404\pi$
$432$	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
$435$	−5.22405	−	5.27097i	−0.250474	−	0.252724i
$436$		−	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	−0.974113	−	0.226062i	$-0.927415\pi$
$439$	−26.5130	+	15.3073i	−1.26539	+	0.730576i	−0.291281	+	0.956637i	$0.594082\pi$
$440$	7.79920	−	2.05246i	0.371812	−	0.0978473i
$441$	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	0.0365659	−	0.999331i	$-0.488358\pi$
$449$	19.5007	−	11.2587i	0.920295	−	0.531333i	0.883729	+	0.467999i	$0.155025\pi$
$450$	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	$-0.231051\pi$
$457$	−4.29461	−	7.43848i	−0.200893	−	0.347957i	−0.948816	+	0.315828i	$0.897718\pi$
$458$	6.94240			0.324397
$459$	2.84383	+	1.64189i	0.132739	+	0.0766367i
$460$	1.17879	+	1.18938i	0.0549615	+	0.0554552i
$461$	23.8184	+	13.7516i	1.10933	+	0.640474i	0.938657	−	0.344853i	$-0.112071\pi$
$461$	23.8184	+	13.7516i	1.10933	+	0.640474i	0.170677	+	0.985327i	$0.445404\pi$
$462$	4.16277	+	7.21014i	0.193670	+	0.335446i
$463$	7.63991	+	13.2327i	0.355057	+	0.614976i	0.987128	−	0.159934i	$-0.0511282\pi$
$463$	7.63991	+	13.2327i	0.355057	+	0.614976i	−0.632071	+	0.774911i	$0.717795\pi$
$464$	2.87421	+	1.65943i	0.133432	+	0.0770369i
$465$	−7.15716	−	7.22144i	−0.331905	−	0.334886i
$466$	5.85187	+	3.37858i	0.271083	+	0.156510i
$467$	31.5781			1.46126			0.730631	−	0.682773i	$-0.239226\pi$
$467$	31.5781			1.46126			0.730631	+	0.682773i	$0.239226\pi$
$468$	−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	0.992026	−	0.126032i	$-0.0402241\pi$
$479$	30.1785	+	17.4236i	1.37889	+	0.796104i	0.386866	+	0.922136i	$0.373557\pi$
$480$	−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
$485$	9.76821	−	2.57063i	0.443551	−	0.116726i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	32.7397			1.48358			0.741789	−	0.670633i	$-0.233977\pi$
$487$	32.7397			1.48358			0.741789	+	0.670633i	$0.233977\pi$
$488$	2.15821	−	1.24604i	0.0976974	−	0.0564056i
$489$			11.1449i			0.503989i
$490$	−2.63085	−	2.65448i	−0.118850	−	0.119917i
$491$	−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	−0.518925	−	0.854820i	$-0.673668\pi$
$499$	−0.850905	+	0.491270i	−0.0380917	+	0.0219923i	0.480833	+	0.876812i	$0.340334\pi$
$500$	−10.7596	−	3.03827i	−0.481184	−	0.135875i
$501$	−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	$-0.733450\pi$
$503$	6.92273	−	11.9905i	0.308669	−	0.534631i	0.978072	+	0.208269i	$0.0667830\pi$
$504$		−	2.30838i		−	0.102823i
$505$	−8.49780	+	2.23631i	−0.378147	+	0.0995144i
$506$	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	−0.936301	−	0.351198i	$-0.885774\pi$
$509$	−3.70010	+	6.40875i	−0.164004	+	0.284063i	0.772297	+	0.635261i	$0.219108\pi$
$510$	−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
$515$	28.1125	−	7.39818i	1.23879	−	0.326003i
$516$	−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
$520$	6.55797	+	6.61687i	0.287586	+	0.290169i
$521$	−15.1372	−	26.2185i	−0.663175	−	1.14865i	−0.979777	−	0.200094i	$-0.935875\pi$
$521$	−15.1372	−	26.2185i	−0.663175	−	1.14865i	0.316602	−	0.948558i	$-0.397458\pi$
$522$	2.87421	−	1.65943i	0.125801	−	0.0726311i
$523$	14.5571	+	25.2137i	0.636539	+	1.10252i	0.986187	+	0.165637i	$0.0529680\pi$
$523$	14.5571	+	25.2137i	0.636539	+	1.10252i	−0.349648	+	0.936881i	$0.613699\pi$
$524$		−	16.3761i		−	0.715394i
$525$	0.103202	−	11.5414i	0.00450412	−	0.503710i
$526$		−	5.01412i		−	0.218626i
$527$	12.9308	+	7.46559i	0.563274	+	0.325206i
$528$			3.60666i			0.156960i
$529$	−22.4392			−0.975616
$530$	3.71508	−	3.68201i	0.161373	−	0.159936i
$531$	−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
$535$	−10.9941	+	10.8962i	−0.475315	+	0.471083i
$536$	−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
$540$	−1.58819	+	1.57405i	−0.0683449	+	0.0677365i
$541$		−	28.7306i		−	1.23522i	−0.786483	−	0.617612i	$-0.788100\pi$
$541$		−	28.7306i		−	1.23522i	0.786483	−	0.617612i	$-0.211900\pi$
$542$	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	$-0.256248\pi$
$547$	32.4201			1.38618			0.693091	+	0.720850i	$0.256248\pi$
$548$	7.03744	−	4.06307i	0.300624	−	0.173566i
$549$		−	2.49208i		−	0.106359i
$550$	−0.161246	+	18.0326i	−0.00687554	+	0.768913i
$551$	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
$555$	0.189370	+	13.6002i	0.00803832	+	0.577294i
$556$	−10.2769			−0.435837
$557$	6.76342	−	11.7146i	0.286575	−	0.496363i	−0.686415	−	0.727210i	$-0.740817\pi$
$557$	6.76342	−	11.7146i	0.286575	−	0.496363i	0.972990	+	0.230848i	$0.0741499\pi$
$558$	3.93778	−	2.27348i	0.166700	−	0.0962441i
$559$	24.2871	+	42.0664i	1.02723	+	1.77922i
$560$	1.31364	+	4.99174i	0.0555114	+	0.210939i
$561$			11.8435i			0.500032i
$562$	21.1295	−	12.1991i	0.891295	−	0.514589i
$563$	−25.2768			−1.06529			−0.532645	−	0.846339i	$-0.678802\pi$
$563$	−25.2768			−1.06529			−0.532645	+	0.846339i	$0.678802\pi$
$564$	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	$0.364359\pi$
$569$			43.4411i			1.82114i	−0.413350	+	0.910572i	$0.635641\pi$
$570$	−6.42760	−	6.48534i	−0.269223	−	0.271641i
$571$	18.5642	−	32.1541i	0.776886	−	1.34561i	−0.156843	−	0.987624i	$-0.550132\pi$
$571$	18.5642	−	32.1541i	0.776886	−	1.34561i	0.933729	−	0.357982i	$-0.116535\pi$
$572$	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
$575$	−3.25940	+	1.84316i	−0.135926	+	0.0768649i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−12.4724	+	21.6029i	−0.519235	+	0.899341i	0.480515	+	0.876986i	$0.340450\pi$
$577$	−12.4724	+	21.6029i	−0.519235	+	0.899341i	−0.999750	+	0.0223548i	$0.992884\pi$
$578$	−6.21683			−0.258586
$579$	−3.18122	+	1.83668i	−0.132207	+	0.0763297i
$580$	−5.27097	+	5.22405i	−0.218865	+	0.216917i
$581$	−14.7577			−0.612254
$582$			4.51721i			0.187244i
$583$	−7.30637	−	4.21833i	−0.302599	−	0.174706i
$584$			0.278797i			0.0115367i
$585$	9.00936	−	2.37093i	0.372491	−	0.0980259i
$586$			10.3046i			0.425679i
$587$	−12.3953	−	21.4693i	−0.511608	−	0.886131i	−0.999909	−	0.0134561i	$-0.995717\pi$
$587$	−12.3953	−	21.4693i	−0.511608	−	0.886131i	0.488301	−	0.872675i	$-0.337617\pi$
$588$	1.44746	−	0.835693i	0.0596923	−	0.0344634i
$589$	9.28369	+	16.0798i	0.382528	+	0.662557i
$590$	18.6160	−	18.4503i	0.766408	−	0.759586i
$591$	−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
$595$	4.31370	+	16.3917i	0.176844	+	0.671995i
$596$	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	0.961677	−	0.274185i	$-0.0884082\pi$
$599$	5.95677	+	10.3174i	0.243387	+	0.421559i	−0.718290	+	0.695744i	$0.755075\pi$
$600$	2.53862	−	4.30760i	0.103639	−	0.175857i
$601$	18.2150	−	31.5493i	0.743006	−	1.28692i	−0.208114	−	0.978105i	$-0.566733\pi$
$601$	18.2150	−	31.5493i	0.743006	−	1.28692i	0.951120	−	0.308820i	$-0.0999341\pi$
$602$			26.9130i			1.09689i
$603$			7.94202i			0.323424i
$604$	6.59299	−	11.4194i	0.268265	−	0.464649i
$605$	4.34224	−	1.14272i	0.176537	−	0.0464580i
$606$		−	3.92973i		−	0.159634i
$607$	−2.82022	+	4.88477i	−0.114469	+	0.198267i	−0.917567	−	0.397580i	$-0.869850\pi$
$607$	−2.82022	+	4.88477i	−0.114469	+	0.198267i	0.803098	+	0.595847i	$0.203183\pi$
$608$	3.53639	+	2.04174i	0.143420	+	0.0828033i
$609$	−6.63477	−	3.83058i	−0.268854	−	0.155223i
$610$	1.41818	+	5.38898i	0.0574205	+	0.218194i
$611$	−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	$-0.345445\pi$
$613$	−1.63128	−	0.941819i	−0.0658867	−	0.0380397i	−0.532581	+	0.846379i	$0.678778\pi$
$614$	−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	$-0.507863\pi$
$617$	−22.4253	−	12.9473i	−0.902810	−	0.521238i	−0.878111	+	0.478457i	$0.841196\pi$
$618$			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	$0.380601\pi$
$620$	−7.22144	+	7.15716i	−0.290020	+	0.287438i
$621$			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
$625$	12.8852	−	21.4236i	0.515407	−	0.856946i
$626$	−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	0.852187	−	0.523238i	$-0.175276\pi$
$631$	20.7274	+	11.9669i	0.825143	+	0.476397i	−0.0270438	+	0.999634i	$0.508609\pi$
$632$	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	0.183672	−	0.982988i	$-0.441201\pi$
$641$	23.8781	−	41.3581i	0.943128	−	1.63355i	0.759456	−	0.650559i	$-0.225465\pi$
$642$	−3.46119	−	5.99495i	−0.136602	−	0.236602i
$643$	41.6635			1.64305			0.821524	−	0.570175i	$-0.193124\pi$
$643$	41.6635			1.64305			0.821524	+	0.570175i	$0.193124\pi$
$644$	1.49712	+	0.864361i	0.0589947	+	0.0340606i
$645$	18.5165	−	18.3517i	0.729086	−	0.722596i
$646$	11.6127	+	6.70460i	0.456896	+	0.263789i
$647$	14.5351	+	25.1755i	0.571433	+	0.989751i	0.996419	+	0.0845511i	$0.0269456\pi$
$647$	14.5351	+	25.1755i	0.571433	+	0.989751i	−0.424986	+	0.905200i	$0.639721\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−36.6117	−	21.1377i	−1.43713	−	0.829729i
$650$	−18.1330	+	10.2540i	−0.711234	+	0.402195i
$651$	−9.08989	−	5.24805i	−0.356261	−	0.205687i
$652$	11.1449			0.436467
$653$	23.6468	+	40.9575i	0.925371	+	1.60279i	0.790964	+	0.611863i	$0.209580\pi$
$653$	23.6468	+	40.9575i	0.925371	+	1.60279i	0.134407	+	0.990926i	$0.457087\pi$
$654$	−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	0.992067	−	0.125707i	$-0.0401198\pi$
$659$	9.93900	+	17.2149i	0.387169	+	0.670596i	−0.604899	+	0.796302i	$0.706786\pi$
$660$	−7.78054	−	2.12212i	−0.302857	−	0.0826033i
$661$	−5.66878	+	3.27287i	−0.220490	+	0.127300i	−0.606177	−	0.795330i	$-0.707298\pi$
$661$	−5.66878	+	3.27287i	−0.220490	+	0.127300i	0.385687	+	0.922630i	$0.373964\pi$
$662$	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
$670$	−4.51960	−	17.1741i	−0.174607	−	0.663495i
$671$	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	$-0.999713\pi$
$673$	−38.8931	+	22.4549i	−1.49922	+	0.865574i	−0.499218	+	0.866477i	$0.666379\pi$
$674$		−	33.5737i		−	1.29321i
$675$	−2.46118	−	4.35231i	−0.0947309	−	0.167520i
$676$	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	0.136885	−	0.990587i	$-0.456291\pi$
$683$	24.2086	−	41.9305i	0.926316	−	1.60443i	0.789431	−	0.613840i	$-0.210376\pi$
$684$	3.53639	−	2.04174i	0.135217	−	0.0780677i
$685$	4.62438	+	17.5723i	0.176688	+	0.671403i
$686$	−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
$690$	−0.426175	−	1.61943i	−0.0162242	−	0.0616507i
$691$	−18.3449	+	31.7743i	−0.697872	+	1.20875i	0.271330	+	0.962486i	$0.412536\pi$
$691$	−18.3449	+	31.7743i	−0.697872	+	1.20875i	−0.969203	+	0.246264i	$0.920797\pi$
$692$			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
$700$	−11.5414	−	0.103202i	−0.436225	−	0.00390068i
$701$	39.0071	+	22.5207i	1.47328	+	0.850597i	0.999548	−	0.0300735i	$-0.00957412\pi$
$701$	39.0071	+	22.5207i	1.47328	+	0.850597i	0.473729	+	0.880670i	$0.342907\pi$
$702$			4.16629i			0.157247i
$703$	5.98637	−	24.1066i	0.225780	−	0.909198i
$704$	3.60666			0.135931
$705$	2.45513	+	2.47718i	0.0924656	+	0.0932961i
$706$	−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	$0.281533\pi$
$709$			41.1960i			1.54715i	−0.633705	+	0.773575i	$0.718467\pi$
$710$	−1.56322	+	0.411381i	−0.0586665	+	0.0154388i
$711$		−	8.69122i		−	0.325946i
$712$	−5.28646	−	3.05214i	−0.198119	−	0.114384i
$713$			3.40517i			0.127525i
$714$	−7.58019			−0.283682
$715$	23.6524	+	23.8648i	0.884549	+	0.892494i
$716$	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	−0.619223	−	0.785215i	$-0.712552\pi$
$719$	9.93211	−	17.2029i	0.370405	−	0.641560i	0.989628	+	0.143655i	$0.0458856\pi$
$720$	1.57405	+	1.58819i	0.0586615	+	0.0591884i
$721$	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
$725$	−8.16830	−	14.4447i	−0.303363	−	0.536461i
$726$			2.00802i			0.0745248i
$727$	−5.99437	−	10.3825i	−0.222319	−	0.385067i	0.733193	−	0.680021i	$-0.238029\pi$
$727$	−5.99437	−	10.3825i	−0.222319	−	0.385067i	−0.955512	+	0.294953i	$0.904696\pi$
$728$	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	$-0.766268\pi$
$733$	−14.4350	+	8.33404i	−0.533168	+	0.307825i	0.209137	+	0.977886i	$0.432934\pi$
$734$			9.54106i			0.352167i
$735$	0.951143	+	3.61427i	0.0350834	+	0.133314i
$736$	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	$0.417860\pi$
$740$	13.6002	−	0.189370i	0.499952	−	0.00696139i
$741$	−17.0129			−0.624986
$742$	2.69987	−	4.67631i	0.0991152	−	0.171673i
$743$	−43.4777	+	25.1019i	−1.59504	+	0.920899i	−0.602621	+	0.798028i	$0.705877\pi$
$743$	−43.4777	+	25.1019i	−1.59504	+	0.920899i	−0.992423	+	0.122871i	$0.960790\pi$
$744$	−2.27348	−	3.93778i	−0.0833498	−	0.144366i
$745$	−44.1539	+	11.6197i	−1.61767	+	0.425712i
$746$		−	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
$755$	20.7554	+	20.9419i	0.755368	+	0.762153i
$756$	−1.15419	+	1.99912i	−0.0419775	+	0.0727071i
$757$	0.848563	−	1.46975i	0.0308416	−	0.0534191i	−0.850193	−	0.526472i	$-0.823515\pi$
$757$	0.848563	−	1.46975i	0.0308416	−	0.0534191i	0.881034	+	0.473053i	$0.156848\pi$
$758$	−12.8937	−	22.3326i	−0.468321	−	0.811156i
$759$	−2.33913	+	1.35050i	−0.0849051	+	0.0490200i
$760$	−6.48534	+	6.42760i	−0.235248	+	0.233154i
$761$	13.8079	−	23.9160i	0.500536	−	0.866953i	−0.499464	−	0.866335i	$-0.666470\pi$
$761$	13.8079	−	23.9160i	0.500536	−	0.866953i	1.00000		0.000618665i	$-0.000196927\pi$
$762$	6.58300	−	11.4021i	0.238477	−	0.413054i
$763$	23.6888			0.857591
$764$	0.273500	−	0.157905i	0.00989487	−	0.00571281i
$765$	5.16884	+	5.21526i	0.186880	+	0.188558i
$766$	−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	$-0.734154\pi$
$769$		−	41.1203i		−	1.48284i	0.671043	−	0.741418i	$-0.265846\pi$
$770$	4.73786	+	18.0035i	0.170741	+	0.648802i
$771$		−	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	$-0.691125\pi$
$773$	−3.69664	+	2.13426i	−0.132959	+	0.0767639i	0.432045	+	0.901852i	$0.357792\pi$
$774$	5.82942	+	10.0969i	0.209534	+	0.362924i
$775$	−11.1909	−	19.7898i	−0.401989	−	0.710869i
$776$	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
$780$	−2.37093	−	9.00936i	−0.0848930	−	0.322587i
$781$	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
$790$	4.94595	+	18.7943i	0.175969	+	0.668669i
$791$			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
$795$	−5.05836	+	1.33117i	−0.179401	+	0.0472118i
$796$	18.2837	−	10.5561i	0.648047	−	0.374150i
$797$	9.96472	−	17.2594i	0.352969	−	0.611360i	−0.633799	−	0.773497i	$-0.718506\pi$
$797$	9.96472	−	17.2594i	0.352969	−	0.611360i	0.986768	+	0.162138i	$0.0518389\pi$
$798$	−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
$805$	−2.74554	+	2.72110i	−0.0967677	+	0.0959063i
$806$			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	−0.971861	−	0.235556i	$-0.924309\pi$
$809$	−35.6616	+	20.5892i	−1.25379	+	0.723878i	−0.281933	+	0.959434i	$0.590976\pi$
$810$	2.16244	−	0.569075i	0.0759805	−	0.0199952i
$811$	−3.81494	−	6.60766i	−0.133961	−	0.232026i	0.791239	−	0.611507i	$-0.209436\pi$
$811$	−3.81494	−	6.60766i	−0.133961	−	0.232026i	−0.925200	+	0.379480i	$0.876103\pi$
$812$	−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	0.985615	−	0.169006i	$-0.0540557\pi$
$821$	9.92670	+	17.1935i	0.346444	+	0.600059i	−0.639171	+	0.769065i	$0.720722\pi$
$822$	−8.12613			−0.283431
$823$	0.0766940	+	0.0442793i	0.00267339	+	0.00154348i	0.501336	−	0.865253i	$-0.332842\pi$
$823$	0.0766940	+	0.0442793i	0.00267339	+	0.00154348i	−0.498663	+	0.866796i	$0.666175\pi$
$824$	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	−0.953800	−	0.300443i	$-0.902865\pi$
$827$	−21.1970	−	36.7143i	−0.737092	−	1.27668i	0.216708	−	0.976236i	$-0.430468\pi$
$828$	0.748890			0.0260257
$829$	−26.2357	−	15.1472i	−0.911204	−	0.526084i	−0.0303859	−	0.999538i	$-0.509674\pi$
$829$	−26.2357	−	15.1472i	−0.911204	−	0.526084i	−0.880818	+	0.473454i	$0.843007\pi$
$830$	10.1535	−	10.0631i	0.352433	−	0.349296i
$831$	−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
$835$	−13.2354	−	13.3543i	−0.458031	−	0.462145i
$836$	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	−0.893769	−	0.448528i	$-0.851949\pi$
$839$	−1.69298	+	2.93233i	−0.0584482	+	0.101235i	0.835321	+	0.549763i	$0.185282\pi$
$840$	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	−0.307729	−	0.951474i	$-0.599569\pi$
$853$	19.5721	−	33.8999i	0.670136	−	1.16071i	0.977865	−	0.209236i	$-0.0670977\pi$
$854$	2.87634	+	4.98196i	0.0984262	+	0.170479i
$855$	2.32380	+	8.83027i	0.0794723	+	0.301989i
$856$	−5.99495	+	3.46119i	−0.204903	+	0.118301i
$857$	0.165876			0.00566621			0.00283311	−	0.999996i	$-0.499098\pi$
$857$	0.165876			0.00566621			0.00283311	+	0.999996i	$0.499098\pi$
$858$	−13.0133	+	7.51321i	−0.444265	+	0.256497i
$859$		−	47.9739i		−	1.63685i	−0.574615	−	0.818424i	$-0.694848\pi$
$859$		−	47.9739i		−	1.63685i	0.574615	−	0.818424i	$-0.305152\pi$
$860$	−18.3517	−	18.5165i	−0.625786	−	0.631407i
$861$	−9.11286			−0.310566
$862$		−	11.7180i		−	0.399117i
$863$	−39.1758	−	22.6182i	−1.33356	−	0.769931i	−0.347717	−	0.937600i	$-0.613043\pi$
$863$	−39.1758	−	22.6182i	−1.33356	−	0.769931i	−0.985843	+	0.167668i	$0.946376\pi$
$864$	−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
$870$	7.17682	−	1.88867i	0.243317	−	0.0640321i
$871$	−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
$875$	7.01347	−	24.8372i	0.237099	−	0.839652i
$876$	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	0.783140	−	0.621846i	$-0.213617\pi$
$881$	−4.36215	−	7.55546i	−0.146965	−	0.254550i	−0.930104	+	0.367296i	$0.880284\pi$
$882$	−1.67139			−0.0562785
$883$	−5.24023	−	9.07635i	−0.176348	−	0.305444i	0.764279	−	0.644886i	$-0.223095\pi$
$883$	−5.24023	−	9.07635i	−0.176348	−	0.305444i	−0.940627	+	0.339442i	$0.889762\pi$
$884$	6.84058	+	11.8482i	0.230074	+	0.398499i
$885$	−25.3471	+	6.67041i	−0.852032	+	0.224223i
$886$	−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
$890$	9.69477	−	9.60847i	0.324970	−	0.322077i
$891$	−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
$895$	0.836378	+	3.17817i	0.0279570	+	0.106235i
$896$			2.30838i			0.0771175i
$897$	−2.70208	−	1.56005i	−0.0902199	−	0.0520885i
$898$			22.5175i			0.751418i
$899$	−15.0907			−0.503302
$900$	−4.35231	+	2.46118i	−0.145077	+	0.0820394i
$901$	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
$905$	8.22193	+	8.29578i	0.273306	+	0.275761i
$906$	−11.4194	+	6.59299i	−0.379384	+	0.219037i
$907$	5.25683	+	9.10510i	0.174550	+	0.302330i	0.940006	−	0.341159i	$-0.110820\pi$
$907$	5.25683	+	9.10510i	0.174550	+	0.302330i	−0.765455	+	0.643489i	$0.777486\pi$
$908$	−6.15062	+	10.6532i	−0.204115	+	0.353538i
$909$	−1.96486	+	3.40324i	−0.0651704	+	0.112878i
$910$	−15.2742	+	15.1383i	−0.506336	+	0.501829i
$911$		−	35.2304i		−	1.16724i	−0.812029	−	0.583618i	$-0.801637\pi$
$911$		−	35.2304i		−	1.16724i	0.812029	−	0.583618i	$-0.198363\pi$
$912$	−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	$-0.914866\pi$
$919$		−	16.0232i		−	0.528556i	0.964447	−	0.264278i	$-0.0851336\pi$
$920$	−1.61943	+	0.426175i	−0.0533911	+	0.0140506i
$921$	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
$925$	−7.59364	+	29.4506i	−0.249677	+	0.968329i
$926$	−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	0.620983	−	0.783824i	$-0.286734\pi$
$929$	−11.2262	−	19.4444i	−0.368320	−	0.637949i	−0.989303	+	0.145875i	$0.953400\pi$
$930$	9.83253	−	2.58756i	0.322421	−	0.0848494i
$931$		−	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	$-0.358184\pi$
$937$	−4.13499	−	2.38734i	−0.135084	−	0.0779909i	−0.566019	+	0.824392i	$0.691517\pi$
$938$	−9.16659	−	15.8770i	−0.299300	−	0.518402i
$939$			23.7788i			0.775991i
$940$	2.47718	−	2.45513i	0.0807968	−	0.0800776i
$941$	18.1220	−	31.3883i	0.590762	−	1.02323i	−0.403368	−	0.915038i	$-0.632161\pi$
$941$	18.1220	−	31.3883i	0.590762	−	1.02323i	0.994130	−	0.108192i	$-0.0345060\pi$
$942$	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
$945$	−3.63351	−	3.66615i	−0.118198	−	0.119260i
$946$	−21.0248	+	36.4160i	−0.683574	+	1.18399i
$947$	1.39999	−	2.42486i	0.0454937	−	0.0787974i	−0.842382	−	0.538881i	$-0.818847\pi$
$947$	1.39999	−	2.42486i	0.0454937	−	0.0787974i	0.887876	+	0.460084i	$0.152181\pi$
$948$	−8.69122			−0.282278
$949$	−1.00593	+	0.580775i	−0.0326539	+	0.0188528i
$950$	−10.0502	−	17.7725i	−0.326070	−	0.576617i
$951$	−9.45313			−0.306539
$952$			7.58019i			0.245675i
$953$	6.35576	+	3.66950i	0.205883	+	0.118867i	0.599397	−	0.800452i	$-0.295407\pi$
$953$	6.35576	+	3.66950i	0.205883	+	0.118867i	−0.393513	+	0.919319i	$0.628741\pi$
$954$		−	2.33919i		−	0.0757340i
$955$	0.179720	+	0.682921i	0.00581559	+	0.0220988i
$956$		−	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
$960$	1.58819	−	1.57405i	0.0512587	−	0.0508024i
$961$	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
$965$	−7.94342	+	2.09041i	−0.255708	+	0.0672928i
$966$	−0.864361	−	1.49712i	−0.0278104	−	0.0481690i
$967$	10.9128	+	18.9016i	0.350933	+	0.607833i	0.986413	−	0.164284i	$-0.0525313\pi$
$967$	10.9128	+	18.9016i	0.350933	+	0.607833i	−0.635481	+	0.772117i	$0.719198\pi$
$968$	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	0.164367	+	0.986399i	$0.447442\pi$
$971$	−24.0582	+	41.6700i	−0.772063	+	1.33725i	−0.936430	+	0.350853i	$0.885892\pi$
$972$			1.00000i			0.0320750i
$973$		−	23.7229i		−	0.760523i
$974$	−16.3699	+	28.3534i	−0.524524	+	0.908502i
$975$	20.8306	+	0.186265i	0.667114	+	0.00596527i
$976$			2.49208i			0.0797696i
$977$	13.1493	−	22.7753i	0.420685	−	0.728647i	−0.575322	−	0.817927i	$-0.695123\pi$
$977$	13.1493	−	22.7753i	0.420685	−	0.728647i	0.996007	+	0.0892800i	$0.0284566\pi$
$978$	−9.65175	−	5.57244i	−0.308629	−	0.178187i
$979$	−19.0665	−	11.0080i	−0.609368	−	0.351819i
$980$	3.61427	−	0.951143i	0.115454	−	0.0303832i
$981$	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	$-0.270647\pi$
$983$	10.6255	+	6.13466i	0.338902	+	0.195665i	−0.320884	+	0.947118i	$0.603980\pi$
$984$	−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
$990$	5.67708	+	5.72807i	0.180430	+	0.182050i
$991$		−	16.1880i		−	0.514229i	−0.966381	−	0.257114i	$-0.917228\pi$
$991$		−	16.1880i		−	0.514229i	0.966381	−	0.257114i	$-0.0827717\pi$
$992$	−3.93778	+	2.27348i	−0.125025	+	0.0721830i
$993$	−33.7348			−1.07054
$994$	−1.44515	+	0.834357i	−0.0458373	+	0.0264642i
$995$	12.0144	+	45.6538i	0.380882	+	1.44732i
$996$	3.19656	+	5.53660i	0.101287	+	0.175434i
$997$	1.31257	−	2.27343i	0.0415694	−	0.0720003i	−0.844492	−	0.535568i	$-0.820098\pi$
$997$	1.31257	−	2.27343i	0.0415694	−	0.0720003i	0.886062	+	0.463568i	$0.153431\pi$
$998$		−	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.a.619.14	yes	36
5.4	even	2		1110.2.ba.b.619.5	yes	36
37.11	even	6		1110.2.ba.b.529.5	yes	36
185.159	even	6	inner	1110.2.ba.a.529.14	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.14	✓	36	185.159	even	6	inner
1110.2.ba.a.619.14	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.5	yes	36	37.11	even	6
1110.2.ba.b.619.5	yes	36	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.16244 - 0.569075i) q^{5} +1.00000i q^{6} +(1.99912 - 1.15419i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.16244 - 0.569075i) 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} +(1.58819 - 1.57405i) 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} +(-1.57405 - 1.58819i) q^{20} +(1.15419 - 1.99912i) q^{21} +(-1.80333 + 3.12346i) q^{22} -0.748890 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.35231 - 2.46118i) q^{25} -4.16629 q^{26} -1.00000i q^{27} +(-1.99912 - 1.15419i) q^{28} -3.31885i q^{29} +(0.569075 + 2.16244i) q^{30} -4.54696i q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.12346 - 1.80333i) q^{33} +(-1.64189 - 2.84383i) q^{34} +(3.66615 - 3.63351i) q^{35} -1.00000 q^{36} +(-4.22132 + 4.37955i) q^{37} -4.08347i q^{38} +(3.60811 + 2.08315i) q^{39} +(2.16244 - 0.569075i) 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} +(-0.0447077 + 4.99980i) q^{50} +3.28377i q^{51} +(2.08315 - 3.60811i) q^{52} +(-2.02580 - 1.16959i) q^{53} +(0.866025 + 0.500000i) q^{54} +(7.79920 - 2.05246i) 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} +(6.55797 + 6.61687i) q^{65} +3.60666i q^{66} +(-6.87799 + 3.97101i) q^{67} +3.28377 q^{68} +(-0.648558 + 0.374445i) q^{69} +(1.31364 + 4.99174i) 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} +(1.57405 + 1.58819i) 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} +(-6.48534 + 6.42760i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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