LMFDB - Embedded newform 966.2.q.h.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			673.1
Character	$\chi$	$=$	966.673
Dual form			966.2.q.h.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.29551 + 0.832573i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.29551 + 0.832573i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.219161 - 1.52430i) q^{10} +(1.17932 + 2.58236i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(-0.0245143 - 0.170501i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-1.47759 + 0.433861i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.74635 + 2.01539i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-2.25620 - 2.60380i) q^{19} +(1.47759 + 0.433861i) q^{20} +(-0.415415 + 0.909632i) q^{21} -2.83890 q^{22} +(3.84724 + 2.86334i) q^{23} +1.00000 q^{24} +(-1.09191 + 2.39095i) q^{25} +(0.165277 + 0.0485297i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(0.291881 - 0.336848i) q^{29} +(0.219161 - 1.52430i) q^{30} +(-6.36689 + 1.86949i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.404018 + 2.81001i) q^{33} +(-1.10781 - 2.42575i) q^{34} +(-0.639729 - 1.40081i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-1.80815 - 1.16203i) q^{37} +(3.30576 - 0.970658i) q^{38} +(0.0245143 - 0.170501i) q^{39} +(-1.00847 + 1.16384i) q^{40} +(-4.38958 + 2.82101i) q^{41} +(-0.654861 - 0.755750i) q^{42} +(-0.783065 - 0.229929i) q^{43} +(1.17932 - 2.58236i) q^{44} -1.53997 q^{45} +(-4.20279 + 2.31010i) q^{46} -3.64621 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-1.72129 - 1.98647i) q^{50} +(-2.24341 + 1.44175i) q^{51} +(-0.112803 + 0.130181i) q^{52} +(-1.90322 + 13.2372i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-3.67782 - 2.36359i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-1.43124 - 3.13397i) q^{57} +(0.185156 + 0.405436i) q^{58} +(0.191349 + 1.33086i) q^{59} +(1.29551 + 0.832573i) q^{60} +(1.37837 - 0.404726i) q^{61} +(0.944356 - 6.56814i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(0.173713 + 0.200476i) q^{65} +(-2.72391 - 0.799811i) q^{66} +(-4.67799 + 10.2434i) q^{67} +2.66674 q^{68} +(2.88471 + 3.83125i) q^{69} +1.53997 q^{70} +(1.44827 - 3.17128i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-6.75250 - 7.79281i) q^{73} +(1.80815 - 1.16203i) q^{74} +(-1.72129 + 1.98647i) q^{75} +(-0.490320 + 3.41025i) q^{76} +(-2.72391 + 0.799811i) q^{77} +(0.144910 + 0.0931277i) q^{78} +(-1.26571 - 8.80318i) q^{79} +(-0.639729 - 1.40081i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.742585 - 5.16479i) q^{82} +(8.11279 + 5.21378i) q^{83} +(0.959493 - 0.281733i) q^{84} +(0.584447 - 4.06492i) q^{85} +(0.534448 - 0.616785i) q^{86} +(0.374959 - 0.240971i) q^{87} +(1.85909 + 2.14550i) q^{88} +(13.4154 + 3.93912i) q^{89} +(0.639729 - 1.40081i) q^{90} +0.172254 q^{91} +(-0.355443 - 4.78264i) q^{92} -6.63568 q^{93} +(1.51469 - 3.31671i) q^{94} +(5.09078 + 1.49479i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(9.45486 - 6.07627i) q^{97} +(0.654861 - 0.755750i) q^{98} +(-0.404018 + 2.81001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−1.29551	+	0.832573i	−0.579369	+	0.372338i	−0.797261	−	0.603635i	$-0.793718\pi$
$5$	−1.29551	+	0.832573i	−0.579369	+	0.372338i	0.217892	+	0.975973i	$0.430082\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.219161	−	1.52430i	−0.0693049	−	0.482026i
$11$	1.17932	+	2.58236i	0.355579	+	0.778610i	0.999904	+	0.0138578i	$0.00441121\pi$
$11$	1.17932	+	2.58236i	0.355579	+	0.778610i	−0.644325	+	0.764752i	$0.722862\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	−0.0245143	−	0.170501i	−0.00679906	−	0.0472885i	0.986139	−	0.165918i	$-0.0530589\pi$
$13$	−0.0245143	−	0.170501i	−0.00679906	−	0.0472885i	−0.992939	+	0.118630i	$0.962150\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	−1.47759	+	0.433861i	−0.381513	+	0.112022i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−1.74635	+	2.01539i	−0.423551	+	0.488804i	−0.926915	−	0.375270i	$-0.877550\pi$
$17$	−1.74635	+	2.01539i	−0.423551	+	0.488804i	0.503364	+	0.864074i	$0.332095\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	−2.25620	−	2.60380i	−0.517609	−	0.597352i	0.435422	−	0.900226i	$-0.356599\pi$
$19$	−2.25620	−	2.60380i	−0.517609	−	0.597352i	−0.953030	+	0.302874i	$0.902054\pi$
$20$	1.47759	+	0.433861i	0.330400	+	0.0970143i
$21$	−0.415415	+	0.909632i	−0.0906510	+	0.198498i
$22$	−2.83890			−0.605256
$23$	3.84724	+	2.86334i	0.802206	+	0.597047i
$23$	3.84724	+	2.86334i	0.802206	+	0.597047i
$24$	1.00000			0.204124
$25$	−1.09191	+	2.39095i	−0.218382	+	0.478190i
$26$	0.165277	+	0.0485297i	0.0324135	+	0.00951745i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	0.841254	−	0.540641i	0.158982	−	0.102172i
$29$	0.291881	−	0.336848i	0.0542009	−	0.0625512i	−0.728002	−	0.685575i	$-0.759551\pi$
$29$	0.291881	−	0.336848i	0.0542009	−	0.0625512i	0.782203	+	0.623024i	$0.214096\pi$
$30$	0.219161	−	1.52430i	0.0400132	−	0.278298i
$31$	−6.36689	+	1.86949i	−1.14353	+	0.335770i	−0.798011	−	0.602643i	$-0.794114\pi$
$31$	−6.36689	+	1.86949i	−1.14353	+	0.335770i	−0.345516	+	0.938413i	$0.612296\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.404018	+	2.81001i	0.0703305	+	0.489159i
$34$	−1.10781	−	2.42575i	−0.189987	−	0.416014i
$35$	−0.639729	−	1.40081i	−0.108134	−	0.236780i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−1.80815	−	1.16203i	−0.297258	−	0.191036i	0.383507	−	0.923538i	$-0.374716\pi$
$37$	−1.80815	−	1.16203i	−0.297258	−	0.191036i	−0.680765	+	0.732502i	$0.738353\pi$
$38$	3.30576	−	0.970658i	0.536265	−	0.157462i
$39$	0.0245143	−	0.170501i	0.00392544	−	0.0273020i
$40$	−1.00847	+	1.16384i	−0.159453	+	0.184018i
$41$	−4.38958	+	2.82101i	−0.685537	+	0.440568i	−0.836497	−	0.547972i	$-0.815400\pi$
$41$	−4.38958	+	2.82101i	−0.685537	+	0.440568i	0.150959	+	0.988540i	$0.451764\pi$
$42$	−0.654861	−	0.755750i	−0.101047	−	0.116615i
$43$	−0.783065	−	0.229929i	−0.119416	−	0.0350638i	0.221478	−	0.975165i	$-0.428912\pi$
$43$	−0.783065	−	0.229929i	−0.119416	−	0.0350638i	−0.340895	+	0.940101i	$0.610730\pi$
$44$	1.17932	−	2.58236i	0.177790	−	0.389305i
$45$	−1.53997			−0.229566
$46$	−4.20279	+	2.31010i	−0.619667	+	0.340606i
$47$	−3.64621			−0.531854			−0.265927	−	0.963993i	$-0.585678\pi$
$47$	−3.64621			−0.531854			−0.265927	+	0.963993i	$0.585678\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−1.72129	−	1.98647i	−0.243427	−	0.280929i
$51$	−2.24341	+	1.44175i	−0.314140	+	0.201885i
$52$	−0.112803	+	0.130181i	−0.0156429	+	0.0180529i
$53$	−1.90322	+	13.2372i	−0.261428	+	1.81827i	0.260718	+	0.965415i	$0.416041\pi$
$53$	−1.90322	+	13.2372i	−0.261428	+	1.81827i	−0.522146	+	0.852856i	$0.674869\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	−3.67782	−	2.36359i	−0.495918	−	0.318707i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	−1.43124	−	3.13397i	−0.189572	−	0.415105i
$58$	0.185156	+	0.405436i	0.0243122	+	0.0532363i
$59$	0.191349	+	1.33086i	0.0249115	+	0.173263i	0.998479	−	0.0551371i	$-0.0175596\pi$
$59$	0.191349	+	1.33086i	0.0249115	+	0.173263i	−0.973567	+	0.228400i	$0.926650\pi$
$60$	1.29551	+	0.832573i	0.167250	+	0.107485i
$61$	1.37837	−	0.404726i	0.176482	−	0.0518198i	−0.192298	−	0.981337i	$-0.561594\pi$
$61$	1.37837	−	0.404726i	0.176482	−	0.0518198i	0.368780	+	0.929517i	$0.379776\pi$
$62$	0.944356	−	6.56814i	0.119933	−	0.834155i
$63$	−0.654861	+	0.755750i	−0.0825047	+	0.0952155i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	0.173713	+	0.200476i	0.0215465	+	0.0248659i
$66$	−2.72391	−	0.799811i	−0.335290	−	0.0984500i
$67$	−4.67799	+	10.2434i	−0.571507	+	1.25143i	0.374483	+	0.927234i	$0.377820\pi$
$67$	−4.67799	+	10.2434i	−0.571507	+	1.25143i	−0.945991	+	0.324193i	$0.894907\pi$
$68$	2.66674			0.323390
$69$	2.88471	+	3.83125i	0.347278	+	0.461228i
$70$	1.53997			0.184062
$71$	1.44827	−	3.17128i	0.171879	−	0.376362i	−0.804015	−	0.594609i	$-0.797307\pi$
$71$	1.44827	−	3.17128i	0.171879	−	0.376362i	0.975893	+	0.218248i	$0.0700340\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	−6.75250	−	7.79281i	−0.790321	−	0.912079i	0.207488	−	0.978238i	$-0.433471\pi$
$73$	−6.75250	−	7.79281i	−0.790321	−	0.912079i	−0.997809	+	0.0661586i	$0.978926\pi$
$74$	1.80815	−	1.16203i	0.210193	−	0.135083i
$75$	−1.72129	+	1.98647i	−0.198757	+	0.229378i
$76$	−0.490320	+	3.41025i	−0.0562435	+	0.391182i
$77$	−2.72391	+	0.799811i	−0.310418	+	0.0911469i
$78$	0.144910	+	0.0931277i	0.0164078	+	0.0105446i
$79$	−1.26571	−	8.80318i	−0.142403	−	0.990435i	−0.928235	−	0.371995i	$-0.878674\pi$
$79$	−1.26571	−	8.80318i	−0.142403	−	0.990435i	0.785832	−	0.618440i	$-0.212235\pi$
$80$	−0.639729	−	1.40081i	−0.0715238	−	0.156615i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.742585	−	5.16479i	−0.0820048	−	0.570356i
$83$	8.11279	+	5.21378i	0.890495	+	0.572286i	0.903957	−	0.427623i	$-0.140649\pi$
$83$	8.11279	+	5.21378i	0.890495	+	0.572286i	−0.0134623	+	0.999909i	$0.504285\pi$
$84$	0.959493	−	0.281733i	0.104689	−	0.0307395i
$85$	0.584447	−	4.06492i	0.0633921	−	0.440902i
$86$	0.534448	−	0.616785i	0.0576310	−	0.0665097i
$87$	0.374959	−	0.240971i	0.0401998	−	0.0258348i
$88$	1.85909	+	2.14550i	0.198179	+	0.228711i
$89$	13.4154	+	3.93912i	1.42203	+	0.417546i	0.900190	−	0.435498i	$-0.143428\pi$
$89$	13.4154	+	3.93912i	1.42203	+	0.417546i	0.521840	+	0.853043i	$0.325246\pi$
$90$	0.639729	−	1.40081i	0.0674333	−	0.147658i
$91$	0.172254			0.0180572
$92$	−0.355443	−	4.78264i	−0.0370575	−	0.498625i
$93$	−6.63568			−0.688088
$94$	1.51469	−	3.31671i	0.156228	−	0.342092i
$95$	5.09078	+	1.49479i	0.522303	+	0.153362i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	9.45486	−	6.07627i	0.959996	−	0.616952i	0.0359989	−	0.999352i	$-0.488539\pi$
$97$	9.45486	−	6.07627i	0.959996	−	0.616952i	0.923997	+	0.382400i	$0.124902\pi$
$98$	0.654861	−	0.755750i	0.0661509	−	0.0763422i
$99$	−0.404018	+	2.81001i	−0.0406053	+	0.282416i
$100$	2.52201	−	0.740528i	0.252201	−	0.0740528i
$101$	2.45862	+	1.58006i	0.244642	+	0.157222i	0.657216	−	0.753702i	$-0.271734\pi$
$101$	2.45862	+	1.58006i	0.244642	+	0.157222i	−0.412574	+	0.910924i	$0.635370\pi$
$102$	−0.379517	−	2.63960i	−0.0375778	−	0.261359i
$103$	1.89197	+	4.14283i	0.186421	+	0.408205i	0.979649	−	0.200720i	$-0.0643282\pi$
$103$	1.89197	+	4.14283i	0.186421	+	0.408205i	−0.793228	+	0.608925i	$0.791601\pi$
$104$	−0.0715570	−	0.156688i	−0.00701674	−	0.0153645i
$105$	−0.219161	−	1.52430i	−0.0213879	−	0.148756i
$106$	−11.2504	−	7.23017i	−1.09273	−	0.702256i
$107$	6.89328	−	2.02405i	0.666399	−	0.195672i	0.0689999	−	0.997617i	$-0.478019\pi$
$107$	6.89328	−	2.02405i	0.666399	−	0.195672i	0.597399	+	0.801944i	$0.296201\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	−9.25975	+	10.6863i	−0.886924	+	1.02356i	0.112628	+	0.993637i	$0.464073\pi$
$109$	−9.25975	+	10.6863i	−0.886924	+	1.02356i	−0.999552	+	0.0299273i	$0.990472\pi$
$110$	3.67782	−	2.36359i	0.350667	−	0.225360i
$111$	−1.40753	−	1.62437i	−0.133597	−	0.154179i
$112$	−0.959493	−	0.281733i	−0.0906636	−	0.0266212i
$113$	−0.761921	+	1.66838i	−0.0716755	+	0.156948i	−0.942078	−	0.335393i	$-0.891131\pi$
$113$	−0.761921	+	1.66838i	−0.0716755	+	0.156948i	0.870403	+	0.492340i	$0.163858\pi$
$114$	3.44532			0.322684
$115$	−7.36808	−	0.506368i	−0.687077	−	0.0472191i
$116$	−0.445714			−0.0413835
$117$	0.0715570	−	0.156688i	0.00661545	−	0.0144858i
$118$	−1.29008	−	0.378802i	−0.118762	−	0.0348716i
$119$	−1.74635	−	2.01539i	−0.160087	−	0.184751i
$120$	−1.29551	+	0.832573i	−0.118263	+	0.0760032i
$121$	1.92571	−	2.22238i	0.175064	−	0.202035i
$122$	−0.204444	+	1.42194i	−0.0185095	+	0.128736i
$123$	−5.00654	+	1.47005i	−0.451425	+	0.132550i
$124$	5.58229	+	3.58752i	0.501305	+	0.322169i
$125$	−1.67187	−	11.6281i	−0.149536	−	1.04005i
$126$	−0.415415	−	0.909632i	−0.0370081	−	0.0810365i
$127$	−0.626780	−	1.37246i	−0.0556178	−	0.121786i	0.879783	−	0.475376i	$-0.157688\pi$
$127$	−0.626780	−	1.37246i	−0.0556178	−	0.121786i	−0.935400	+	0.353590i	$0.884961\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−0.686567	−	0.441230i	−0.0604489	−	0.0388481i
$130$	−0.254522	+	0.0747344i	−0.0223231	+	0.00655464i
$131$	−0.138279	+	0.961754i	−0.0120815	+	0.0840289i	−0.994970	−	0.100172i	$-0.968061\pi$
$131$	−0.138279	+	0.961754i	−0.0120815	+	0.0840289i	0.982889	+	0.184201i	$0.0589697\pi$
$132$	1.85909	−	2.14550i	0.161813	−	0.186742i
$133$	2.89839	−	1.86268i	0.251322	−	0.161515i
$134$	−7.37439	−	8.51050i	−0.637050	−	0.735195i
$135$	−1.47759	−	0.433861i	−0.127171	−	0.0373408i
$136$	−1.10781	+	2.42575i	−0.0949935	+	0.208007i
$137$	6.85440			0.585611			0.292806	−	0.956172i	$-0.405411\pi$
$137$	6.85440			0.585611			0.292806	+	0.956172i	$0.405411\pi$
$138$	−4.68338	+	1.03247i	−0.398675	+	0.0878893i
$139$	1.74451			0.147967			0.0739837	−	0.997259i	$-0.476429\pi$
$139$	1.74451			0.147967			0.0739837	+	0.997259i	$0.476429\pi$
$140$	−0.639729	+	1.40081i	−0.0540669	+	0.118390i
$141$	−3.49851	−	1.02726i	−0.294628	−	0.0865105i
$142$	2.28306	+	2.63479i	0.191590	+	0.221107i
$143$	0.411384	−	0.264381i	0.0344017	−	0.0221086i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.0976833	+	0.679402i	−0.00811215	+	0.0564213i
$146$	9.89368	−	2.90505i	0.818807	−	0.240423i
$147$	−0.841254	−	0.540641i	−0.0693854	−	0.0445913i
$148$	0.305885	+	2.12748i	0.0251436	+	0.174877i
$149$	1.87111	+	4.09715i	0.153287	+	0.335652i	0.970660	−	0.240457i	$-0.0772975\pi$
$149$	1.87111	+	4.09715i	0.153287	+	0.335652i	−0.817373	+	0.576109i	$0.804570\pi$
$150$	−1.09191	−	2.39095i	−0.0891540	−	0.195220i
$151$	−0.636109	−	4.42424i	−0.0517658	−	0.360039i	−0.999197	−	0.0400783i	$-0.987239\pi$
$151$	−0.636109	−	4.42424i	−0.0517658	−	0.360039i	0.947431	−	0.319961i	$-0.103670\pi$
$152$	−2.89839	−	1.86268i	−0.235090	−	0.151083i
$153$	−2.55872	+	0.751308i	−0.206860	+	0.0607397i
$154$	0.404018	−	2.81001i	0.0325567	−	0.226437i
$155$	6.69188	−	7.72284i	0.537505	−	0.620313i
$156$	−0.144910	+	0.0931277i	−0.0116021	+	0.00745619i
$157$	−6.47102	−	7.46796i	−0.516444	−	0.596008i	0.436293	−	0.899805i	$-0.356291\pi$
$157$	−6.47102	−	7.46796i	−0.516444	−	0.596008i	−0.952737	+	0.303797i	$0.901746\pi$
$158$	8.53345	+	2.50565i	0.678885	+	0.199338i
$159$	−5.55548	+	12.1648i	−0.440578	+	0.964732i
$160$	1.53997			0.121746
$161$	−3.38171	+	3.40059i	−0.266516	+	0.268004i
$162$	−1.00000			−0.0785674
$163$	4.81092	−	10.5344i	0.376820	−	0.825121i	−0.622284	−	0.782792i	$-0.713795\pi$
$163$	4.81092	−	10.5344i	0.376820	−	0.825121i	0.999104	−	0.0423290i	$-0.0134778\pi$
$164$	5.00654	+	1.47005i	0.390945	+	0.114792i
$165$	−2.86294	−	3.30401i	−0.222880	−	0.257217i
$166$	−8.11279	+	5.21378i	−0.629675	+	0.404667i
$167$	−0.605382	+	0.698648i	−0.0468459	+	0.0540630i	−0.778689	−	0.627410i	$-0.784115\pi$
$167$	−0.605382	+	0.698648i	−0.0468459	+	0.0540630i	0.731843	+	0.681473i	$0.238660\pi$
$168$	−0.142315	+	0.989821i	−0.0109798	+	0.0763664i
$169$	12.4449	−	3.65416i	0.957303	−	0.281090i
$170$	3.45479	+	2.22026i	0.264970	+	0.170286i
$171$	−0.490320	−	3.41025i	−0.0374957	−	0.260788i
$172$	0.339030	+	0.742372i	0.0258508	+	0.0566054i
$173$	−5.90077	−	12.9209i	−0.448627	−	0.982356i	−0.989934	−	0.141531i	$-0.954797\pi$
$173$	−5.90077	−	12.9209i	−0.448627	−	0.982356i	0.541307	−	0.840825i	$-0.317930\pi$
$174$	0.0634317	+	0.441177i	0.00480875	+	0.0334456i
$175$	−2.21122	−	1.42106i	−0.167152	−	0.107422i
$176$	−2.72391	+	0.799811i	−0.205322	+	0.0602880i
$177$	−0.191349	+	1.33086i	−0.0143827	+	0.100034i
$178$	−9.15611	+	10.5667i	−0.686279	+	0.792008i
$179$	−2.04523	+	1.31439i	−0.152868	+	0.0982420i	−0.614839	−	0.788653i	$-0.710779\pi$
$179$	−2.04523	+	1.31439i	−0.152868	+	0.0982420i	0.461971	+	0.886895i	$0.347142\pi$
$180$	1.00847	+	1.16384i	0.0751668	+	0.0867471i
$181$	9.12673	+	2.67985i	0.678384	+	0.199192i	0.602733	−	0.797943i	$-0.294078\pi$
$181$	9.12673	+	2.67985i	0.678384	+	0.199192i	0.0756510	+	0.997134i	$0.475896\pi$
$182$	−0.0715570	+	0.156688i	−0.00530416	+	0.0116145i
$183$	1.43656			0.106194
$184$	4.49810	+	1.66346i	0.331604	+	0.122632i
$185$	3.30995			0.243352
$186$	2.75656	−	6.03603i	0.202121	−	0.442583i
$187$	−7.26396	−	2.13289i	−0.531193	−	0.155972i
$188$	2.38776	+	2.75562i	0.174145	+	0.200974i
$189$	−0.841254	+	0.540641i	−0.0611922	+	0.0393258i
$190$	−3.47450	+	4.00978i	−0.252066	+	0.290900i
$191$	−2.07127	+	14.4060i	−0.149872	+	1.04238i	0.766554	+	0.642180i	$0.221970\pi$
$191$	−2.07127	+	14.4060i	−0.149872	+	1.04238i	−0.916426	+	0.400204i	$0.868939\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	19.9102	+	12.7955i	1.43316	+	0.921039i	0.999804	+	0.0198187i	$0.00630891\pi$
$193$	19.9102	+	12.7955i	1.43316	+	0.921039i	0.433361	+	0.901220i	$0.357327\pi$
$194$	1.59948	+	11.1246i	0.114836	+	0.798701i
$195$	0.110196	+	0.241296i	0.00789130	+	0.0172795i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	−1.94738	−	13.5443i	−0.138745	−	0.964993i	−0.933632	−	0.358235i	$-0.883379\pi$
$197$	−1.94738	−	13.5443i	−0.138745	−	0.964993i	0.794886	−	0.606758i	$-0.207530\pi$
$198$	−2.38824	−	1.53483i	−0.169725	−	0.109075i
$199$	1.72873	−	0.507600i	0.122546	−	0.0359828i	−0.219884	−	0.975526i	$-0.570568\pi$
$199$	1.72873	−	0.507600i	0.122546	−	0.0359828i	0.342431	+	0.939543i	$0.388750\pi$
$200$	−0.374071	+	2.60172i	−0.0264508	+	0.183970i
$201$	−7.37439	+	8.51050i	−0.520149	+	0.600284i
$202$	−2.45862	+	1.58006i	−0.172988	+	0.111172i
$203$	0.291881	+	0.336848i	0.0204860	+	0.0236421i
$204$	2.55872	+	0.751308i	0.179146	+	0.0526021i
$205$	3.33804	−	7.30929i	0.233139	−	0.510503i
$206$	−4.55440			−0.317320
$207$	1.68847	+	4.48877i	0.117357	+	0.311991i
$208$	0.172254			0.0119437
$209$	4.06314	−	8.89704i	0.281053	−	0.615421i
$210$	1.47759	+	0.433861i	0.101964	+	0.0299393i
$211$	10.4241	+	12.0301i	0.717626	+	0.828184i	0.991019	−	0.133718i	$-0.0426916\pi$
$211$	10.4241	+	12.0301i	0.717626	+	0.828184i	−0.273394	+	0.961902i	$0.588146\pi$
$212$	11.2504	−	7.23017i	0.772678	−	0.496570i
$213$	2.28306	−	2.63479i	0.156433	−	0.180533i
$214$	−1.02243	+	7.11117i	−0.0698920	+	0.486110i
$215$	1.20590	−	0.354084i	0.0822417	−	0.0241484i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−0.944356	−	6.56814i	−0.0641071	−	0.445874i
$218$	−5.87398	−	12.8622i	−0.397836	−	0.871140i
$219$	−4.28349	−	9.37954i	−0.289452	−	0.633811i
$220$	0.622177	+	4.32734i	0.0419472	+	0.291749i
$221$	0.386437	+	0.248348i	0.0259945	+	0.0167057i
$222$	2.06229	−	0.605543i	0.138412	−	0.0406414i
$223$	−1.43517	+	9.98183i	−0.0961062	+	0.668433i	0.883637	+	0.468173i	$0.155088\pi$
$223$	−1.43517	+	9.98183i	−0.0961062	+	0.668433i	−0.979743	+	0.200260i	$0.935821\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	−2.21122	+	1.42106i	−0.147414	+	0.0947375i
$226$	−1.20109	−	1.38614i	−0.0798956	−	0.0922044i
$227$	23.6567	+	6.94623i	1.57015	+	0.461037i	0.947045	−	0.321101i	$-0.104053\pi$
$227$	23.6567	+	6.94623i	1.57015	+	0.461037i	0.623105	+	0.782139i	$0.285871\pi$
$228$	−1.43124	+	3.13397i	−0.0947860	+	0.207552i
$229$	6.12241			0.404580			0.202290	−	0.979326i	$-0.435162\pi$
$229$	6.12241			0.404580			0.202290	+	0.979326i	$0.435162\pi$
$230$	3.52142	−	6.49189i	0.232196	−	0.428062i
$231$	−2.83890			−0.186786
$232$	0.185156	−	0.405436i	0.0121561	−	0.0266182i
$233$	12.6487	+	3.71398i	0.828641	+	0.243311i	0.668433	−	0.743772i	$-0.266965\pi$
$233$	12.6487	+	3.71398i	0.828641	+	0.243311i	0.160208	+	0.987083i	$0.448783\pi$
$234$	0.112803	+	0.130181i	0.00737414	+	0.00851021i
$235$	4.72370	−	3.03573i	0.308140	−	0.198029i
$236$	0.880490	−	1.01614i	0.0573150	−	0.0661451i
$237$	1.26571	−	8.80318i	0.0822164	−	0.571828i
$238$	2.55872	−	0.751308i	0.165857	−	0.0487001i
$239$	4.96369	+	3.18997i	0.321074	+	0.206342i	0.691243	−	0.722623i	$-0.257064\pi$
$239$	4.96369	+	3.18997i	0.321074	+	0.206342i	−0.370168	+	0.928965i	$0.620700\pi$
$240$	−0.219161	−	1.52430i	−0.0141468	−	0.0983931i
$241$	1.41034	+	3.08822i	0.0908483	+	0.198930i	0.949602	−	0.313459i	$-0.101488\pi$
$241$	1.41034	+	3.08822i	0.0908483	+	0.198930i	−0.858753	+	0.512389i	$0.828761\pi$
$242$	1.22158	+	2.67489i	0.0785264	+	0.171949i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	−1.20851	−	0.776663i	−0.0773670	−	0.0497208i
$245$	1.47759	−	0.433861i	0.0944001	−	0.0277184i
$246$	0.742585	−	5.16479i	0.0473455	−	0.329295i
$247$	−0.388641	+	0.448515i	−0.0247286	+	0.0285384i
$248$	−5.58229	+	3.58752i	−0.354476	+	0.227808i
$249$	6.31528	+	7.28822i	0.400214	+	0.461872i
$250$	11.2718	+	3.30970i	0.712891	+	0.209324i
$251$	1.24566	−	2.72762i	0.0786255	−	0.172166i	−0.866237	−	0.499634i	$-0.833468\pi$
$251$	1.24566	−	2.72762i	0.0786255	−	0.172166i	0.944862	+	0.327468i	$0.106195\pi$
$252$	1.00000			0.0629941
$253$	−2.85702	+	13.3118i	−0.179619	+	0.836903i
$254$	1.50881			0.0946708
$255$	1.70599	−	3.73560i	0.106833	−	0.233932i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	8.84670	+	10.2096i	0.551842	+	0.636859i	0.961311	−	0.275464i	$-0.0888316\pi$
$257$	8.84670	+	10.2096i	0.551842	+	0.636859i	−0.409469	+	0.912324i	$0.634286\pi$
$258$	0.686567	−	0.441230i	0.0427438	−	0.0274698i
$259$	1.40753	−	1.62437i	0.0874595	−	0.100934i
$260$	0.0377515	−	0.262567i	0.00234125	−	0.0162837i
$261$	0.427660	−	0.125572i	0.0264715	−	0.00777272i
$262$	−0.817399	−	0.525311i	−0.0504991	−	0.0324538i
$263$	2.69347	+	18.7335i	0.166087	+	1.15516i	0.886877	+	0.462005i	$0.152870\pi$
$263$	2.69347	+	18.7335i	0.166087	+	1.15516i	−0.720790	+	0.693153i	$0.756221\pi$
$264$	1.17932	+	2.58236i	0.0725823	+	0.158933i
$265$	−8.55530	−	18.7335i	−0.525548	−	1.15079i
$266$	0.490320	+	3.41025i	0.0300634	+	0.209096i
$267$	11.7622	+	7.55911i	0.719835	+	0.462610i
$268$	10.8049	−	3.17259i	0.660012	−	0.193797i
$269$	1.71151	−	11.9038i	0.104353	−	0.725789i	−0.868722	−	0.495300i	$-0.835058\pi$
$269$	1.71151	−	11.9038i	0.104353	−	0.725789i	0.973075	−	0.230489i	$-0.0740327\pi$
$270$	1.00847	−	1.16384i	0.0613735	−	0.0708288i
$271$	−7.68585	+	4.93940i	−0.466882	+	0.300047i	−0.752850	−	0.658192i	$-0.771321\pi$
$271$	−7.68585	+	4.93940i	−0.466882	+	0.300047i	0.285968	+	0.958239i	$0.407685\pi$
$272$	−1.74635	−	2.01539i	−0.105888	−	0.122201i
$273$	0.165277	+	0.0485297i	0.0100030	+	0.00293715i
$274$	−2.84742	+	6.23499i	−0.172019	+	0.376669i
$275$	−7.46199			−0.449975
$276$	1.00638	−	4.68905i	0.0605770	−	0.282248i
$277$	12.6913			0.762545			0.381273	−	0.924463i	$-0.375486\pi$
$277$	12.6913			0.762545			0.381273	+	0.924463i	$0.375486\pi$
$278$	−0.724695	+	1.58686i	−0.0434643	+	0.0951736i
$279$	−6.36689	−	1.86949i	−0.381176	−	0.111923i
$280$	−1.00847	−	1.16384i	−0.0602675	−	0.0695525i
$281$	15.5321	−	9.98190i	0.926570	−	0.595470i	0.0120132	−	0.999928i	$-0.496176\pi$
$281$	15.5321	−	9.98190i	0.926570	−	0.595470i	0.914557	+	0.404457i	$0.132540\pi$
$282$	2.38776	−	2.75562i	0.142189	−	0.164095i
$283$	1.26076	−	8.76876i	0.0749443	−	0.521249i	−0.917421	−	0.397917i	$-0.869733\pi$
$283$	1.26076	−	8.76876i	0.0749443	−	0.521249i	0.992366	−	0.123331i	$-0.0393578\pi$
$284$	−3.34511	+	0.982213i	−0.198496	+	0.0582836i
$285$	4.46344	+	2.86848i	0.264391	+	0.169914i
$286$	0.0695938	+	0.484036i	0.00411517	+	0.0286216i
$287$	−2.16760	−	4.74637i	−0.127949	−	0.280170i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	1.40728	+	9.78783i	0.0827810	+	0.575755i
$290$	−0.577427	−	0.371090i	−0.0339077	−	0.0217911i
$291$	10.7838	−	3.16640i	0.632155	−	0.185617i
$292$	−1.46746	+	10.2064i	−0.0858766	+	0.597285i
$293$	11.4409	−	13.2035i	0.668386	−	0.771358i	−0.315737	−	0.948847i	$-0.602252\pi$
$293$	11.4409	−	13.2035i	0.668386	−	0.771358i	0.984123	+	0.177488i	$0.0567972\pi$
$294$	0.841254	−	0.540641i	0.0490629	−	0.0315308i
$295$	−1.35593	−	1.56483i	−0.0789454	−	0.0911079i
$296$	−2.06229	−	0.605543i	−0.119868	−	0.0351965i
$297$	−1.17932	+	2.58236i	−0.0684312	+	0.149844i
$298$	−4.50419			−0.260921
$299$	0.393889	−	0.726152i	0.0227792	−	0.0419945i
$300$	2.62848			0.151755
$301$	0.339030	−	0.742372i	0.0195414	−	0.0427896i
$302$	4.28868	+	1.25927i	0.246786	+	0.0724628i
$303$	1.91387	+	2.20873i	0.109949	+	0.126888i
$304$	2.89839	−	1.86268i	0.166234	−	0.106832i
$305$	−1.44873	+	1.67192i	−0.0829538	+	0.0957338i
$306$	0.379517	−	2.63960i	0.0216956	−	0.150896i
$307$	−24.8364	+	7.29263i	−1.41749	+	0.416212i	−0.898652	−	0.438662i	$-0.855453\pi$
$307$	−24.8364	+	7.29263i	−1.41749	+	0.416212i	−0.518836	+	0.854874i	$0.673635\pi$
$308$	2.38824	+	1.53483i	0.136082	+	0.0874549i
$309$	0.648159	+	4.50804i	0.0368725	+	0.256454i
$310$	4.24504	+	9.29533i	0.241102	+	0.527939i
$311$	−1.90848	−	4.17899i	−0.108220	−	0.236969i	0.847772	−	0.530360i	$-0.177943\pi$
$311$	−1.90848	−	4.17899i	−0.108220	−	0.236969i	−0.955992	+	0.293391i	$0.905216\pi$
$312$	−0.0245143	−	0.170501i	−0.00138785	−	0.00965272i
$313$	19.8094	+	12.7307i	1.11969	+	0.719582i	0.963384	−	0.268126i	$-0.0864044\pi$
$313$	19.8094	+	12.7307i	1.11969	+	0.719582i	0.156308	+	0.987708i	$0.450041\pi$
$314$	9.48125	−	2.78395i	0.535058	−	0.157107i
$315$	0.219161	−	1.52430i	0.0123483	−	0.0858846i
$316$	−5.82414	+	6.72141i	−0.327633	+	0.378109i
$317$	4.43284	−	2.84881i	0.248973	−	0.160005i	−0.410202	−	0.911995i	$-0.634542\pi$
$317$	4.43284	−	2.84881i	0.248973	−	0.160005i	0.659175	+	0.751989i	$0.270906\pi$
$318$	−8.75767	−	10.1069i	−0.491106	−	0.566766i
$319$	1.21408	+	0.356487i	0.0679756	+	0.0199595i
$320$	−0.639729	+	1.40081i	−0.0357619	+	0.0783077i
$321$	7.18430			0.400988
$322$	−1.68847	−	4.48877i	−0.0940948	−	0.250149i
$323$	9.18778			0.511222
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	0.434427	+	0.127559i	0.0240976	+	0.00707571i
$326$	7.58393	+	8.75233i	0.420035	+	0.484747i
$327$	−11.8954	+	7.64468i	−0.657815	+	0.422752i
$328$	−3.41700	+	3.94343i	−0.188672	+	0.217739i
$329$	0.518909	−	3.60909i	0.0286084	−	0.198976i
$330$	4.19475	−	1.23169i	0.230913	−	0.0678022i
$331$	−11.9475	−	7.67817i	−0.656692	−	0.422030i	0.169414	−	0.985545i	$-0.445812\pi$
$331$	−11.9475	−	7.67817i	−0.656692	−	0.422030i	−0.826106	+	0.563515i	$0.809449\pi$
$332$	−1.37244	−	9.54554i	−0.0753225	−	0.523879i
$333$	−0.892873	−	1.95512i	−0.0489292	−	0.107140i
$334$	−0.384028	−	0.840904i	−0.0210131	−	0.0460122i
$335$	−2.46798	−	17.1651i	−0.134840	−	0.937832i
$336$	−0.841254	−	0.540641i	−0.0458941	−	0.0294944i
$337$	31.6629	−	9.29706i	1.72479	−	0.506443i	0.738894	−	0.673822i	$-0.235349\pi$
$337$	31.6629	−	9.29706i	1.72479	−	0.506443i	0.985893	+	0.167379i	$0.0535304\pi$
$338$	−1.84587	+	12.8383i	−0.100402	+	0.698312i
$339$	−1.20109	+	1.38614i	−0.0652345	+	0.0752846i
$340$	−3.45479	+	2.22026i	−0.187362	+	0.120410i
$341$	−12.3363	−	14.2369i	−0.668048	−	0.770969i
$342$	3.30576	+	0.970658i	0.178755	+	0.0524872i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	−0.816124			−0.0440025
$345$	−6.92696	−	2.56168i	−0.372935	−	0.137916i
$346$	14.2045			0.763639
$347$	−4.50684	+	9.86860i	−0.241940	+	0.529774i	−0.991180	−	0.132525i	$-0.957692\pi$
$347$	−4.50684	+	9.86860i	−0.241940	+	0.529774i	0.749240	+	0.662299i	$0.230419\pi$
$348$	−0.427660	−	0.125572i	−0.0229250	−	0.00673138i
$349$	−21.0797	−	24.3272i	−1.12837	−	1.30221i	−0.947880	−	0.318629i	$-0.896778\pi$
$349$	−21.0797	−	24.3272i	−1.12837	−	1.30221i	−0.180488	−	0.983577i	$-0.557768\pi$
$350$	2.21122	−	1.42106i	0.118194	−	0.0759590i
$351$	0.112803	−	0.130181i	0.00602096	−	0.00694856i
$352$	0.404018	−	2.81001i	0.0215342	−	0.149774i
$353$	−23.6001	+	6.92961i	−1.25611	+	0.368826i	−0.841044	−	0.540967i	$-0.818058\pi$
$353$	−23.6001	+	6.92961i	−1.25611	+	0.368826i	−0.415063	+	0.909793i	$0.636240\pi$
$354$	−1.13110	−	0.726916i	−0.0601175	−	0.0386352i
$355$	0.764069	+	5.31422i	0.0405526	+	0.282049i
$356$	−5.80823	−	12.7183i	−0.307836	−	0.674066i
$357$	−1.10781	−	2.42575i	−0.0586313	−	0.128385i
$358$	−0.345991	−	2.40642i	−0.0182862	−	0.127183i
$359$	−23.0511	−	14.8140i	−1.21659	−	0.781855i	−0.234840	−	0.972034i	$-0.575457\pi$
$359$	−23.0511	−	14.8140i	−1.21659	−	0.781855i	−0.981749	+	0.190179i	$0.939093\pi$
$360$	−1.47759	+	0.433861i	−0.0778761	+	0.0228665i
$361$	1.01467	−	7.05722i	0.0534039	−	0.371432i
$362$	−6.22906	+	7.18871i	−0.327392	+	0.377830i
$363$	2.47382	−	1.58983i	0.129842	−	0.0834443i
$364$	−0.112803	−	0.130181i	−0.00591246	−	0.00682335i
$365$	15.2360	+	4.47370i	0.797489	+	0.234164i
$366$	−0.596769	+	1.30674i	−0.0311936	+	0.0683044i
$367$	−9.04166			−0.471971			−0.235985	−	0.971757i	$-0.575832\pi$
$367$	−9.04166			−0.471971			−0.235985	+	0.971757i	$0.575832\pi$
$368$	−3.38171	+	3.40059i	−0.176284	+	0.177268i
$369$	−5.21790			−0.271633
$370$	−1.37500	+	3.01084i	−0.0714830	+	0.156526i
$371$	−12.8316	−	3.76770i	−0.666184	−	0.195609i
$372$	4.34545	+	5.01491i	0.225301	+	0.260011i
$373$	18.6249	−	11.9695i	0.964359	−	0.619756i	0.0391576	−	0.999233i	$-0.487533\pi$
$373$	18.6249	−	11.9695i	0.964359	−	0.619756i	0.925201	+	0.379477i	$0.123896\pi$
$374$	4.95770	−	5.72150i	0.256357	−	0.295851i
$375$	1.67187	−	11.6281i	0.0863348	−	0.600472i
$376$	−3.49851	+	1.02726i	−0.180422	+	0.0529767i
$377$	−0.0645883	−	0.0415083i	−0.00332646	−	0.00213779i
$378$	−0.142315	−	0.989821i	−0.00731989	−	0.0509109i
$379$	−5.78602	−	12.6696i	−0.297208	−	0.650795i	0.700835	−	0.713323i	$-0.252811\pi$
$379$	−5.78602	−	12.6696i	−0.297208	−	0.650795i	−0.998043	+	0.0625286i	$0.980084\pi$
$380$	−2.20407	−	4.82624i	−0.113066	−	0.247581i
$381$	−0.214725	−	1.49345i	−0.0110007	−	0.0765116i
$382$	−12.2437	−	7.86857i	−0.626444	−	0.402591i
$383$	−20.2095	+	5.93404i	−1.03266	+	0.303215i	−0.753791	−	0.657115i	$-0.771777\pi$
$383$	−20.2095	+	5.93404i	−1.03266	+	0.303215i	−0.278866	+	0.960330i	$0.589959\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	2.86294	−	3.30401i	0.145909	−	0.168388i
$386$	−19.9102	+	12.7955i	−1.01340	+	0.651273i
$387$	−0.534448	−	0.616785i	−0.0271675	−	0.0313530i
$388$	−10.7838	−	3.16640i	−0.547462	−	0.160749i
$389$	−6.77436	+	14.8338i	−0.343474	+	0.752102i	−0.999998	−	0.00220275i	$-0.999299\pi$
$389$	−6.77436	+	14.8338i	−0.343474	+	0.752102i	0.656524	+	0.754305i	$0.272026\pi$
$390$	−0.265267			−0.0134323
$391$	−12.4894	+	2.75332i	−0.631614	+	0.139241i
$392$	−1.00000			−0.0505076
$393$	−0.403636	+	0.883839i	−0.0203607	+	0.0445838i
$394$	13.1293	+	3.85512i	0.661446	+	0.194218i
$395$	8.96902	+	10.3508i	0.451281	+	0.520806i
$396$	2.38824	−	1.53483i	0.120013	−	0.0771279i
$397$	−0.125681	+	0.145043i	−0.00630773	+	0.00727950i	−0.758895	−	0.651213i	$-0.774260\pi$
$397$	−0.125681	+	0.145043i	−0.00630773	+	0.00727950i	0.752587	+	0.658493i	$0.228806\pi$
$398$	−0.256410	+	1.78337i	−0.0128527	+	0.0893923i
$399$	3.30576	−	0.970658i	0.165495	−	0.0485937i
$400$	−2.21122	−	1.42106i	−0.110561	−	0.0710531i
$401$	5.58601	+	38.8515i	0.278952	+	1.94015i	0.336195	+	0.941792i	$0.390860\pi$
$401$	5.58601	+	38.8515i	0.278952	+	1.94015i	−0.0572430	+	0.998360i	$0.518231\pi$
$402$	−4.67799	−	10.2434i	−0.233317	−	0.510893i
$403$	0.474830	+	1.03973i	0.0236530	+	0.0517927i
$404$	−0.415924	−	2.89282i	−0.0206930	−	0.143923i
$405$	−1.29551	−	0.832573i	−0.0643744	−	0.0413709i
$406$	−0.427660	+	0.125572i	−0.0212244	+	0.00623204i
$407$	0.868377	−	6.03969i	0.0430439	−	0.299377i
$408$	−1.74635	+	2.01539i	−0.0864570	+	0.0997767i
$409$	32.2679	−	20.7373i	1.59554	−	1.02539i	0.626209	−	0.779656i	$-0.284606\pi$
$409$	32.2679	−	20.7373i	1.59554	−	1.02539i	0.969336	−	0.245739i	$-0.0790305\pi$
$410$	5.26209	+	6.07278i	0.259876	+	0.299913i
$411$	6.57675	+	1.93111i	0.324407	+	0.0952546i
$412$	1.89197	−	4.14283i	0.0932105	−	0.204103i
$413$	−1.34455			−0.0661608
$414$	−4.78455	−	0.328816i	−0.235148	−	0.0161604i
$415$	−14.8510			−0.729009
$416$	−0.0715570	+	0.156688i	−0.00350837	+	0.00768226i
$417$	1.67384	+	0.491485i	0.0819685	+	0.0240681i
$418$	6.40514	+	7.39193i	0.313286	+	0.361551i
$419$	−20.2460	+	13.0113i	−0.989083	+	0.635645i	−0.931899	−	0.362719i	$-0.881849\pi$
$419$	−20.2460	+	13.0113i	−0.989083	+	0.635645i	−0.0571840	+	0.998364i	$0.518212\pi$
$420$	−1.00847	+	1.16384i	−0.0492082	+	0.0567893i
$421$	−1.44083	+	10.0212i	−0.0702217	+	0.488403i	0.924114	+	0.382117i	$0.124805\pi$
$421$	−1.44083	+	10.0212i	−0.0702217	+	0.488403i	−0.994336	+	0.106286i	$0.966104\pi$
$422$	−15.2733	+	4.48464i	−0.743491	+	0.218309i
$423$	−3.06739	−	1.97129i	−0.149141	−	0.0958473i
$424$	1.90322	+	13.2372i	0.0924287	+	0.642856i
$425$	−2.91184	−	6.37604i	−0.141245	−	0.309284i
$426$	1.44827	+	3.17128i	0.0701692	+	0.153649i
$427$	0.204444	+	1.42194i	0.00989373	+	0.0688124i
$428$	−6.04381	−	3.88412i	−0.292139	−	0.187746i
$429$	0.469205	−	0.137771i	0.0226534	−	0.00665164i
$430$	−0.178863	+	1.24402i	−0.00862553	+	0.0599919i
$431$	−15.3113	+	17.6702i	−0.737519	+	0.851142i	−0.993297	−	0.115593i	$-0.963123\pi$
$431$	−15.3113	+	17.6702i	−0.737519	+	0.851142i	0.255778	+	0.966736i	$0.417669\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	−14.8296	−	17.1143i	−0.712665	−	0.822459i	0.277740	−	0.960656i	$-0.410415\pi$
$433$	−14.8296	−	17.1143i	−0.712665	−	0.822459i	−0.990405	+	0.138197i	$0.955869\pi$
$434$	6.36689	+	1.86949i	0.305621	+	0.0897383i
$435$	−0.285136	+	0.624361i	−0.0136712	+	0.0299358i
$436$	14.1400			0.677185
$437$	−1.22461	−	16.4777i	−0.0585812	−	0.788236i
$438$	10.3114			0.492696
$439$	−5.22885	+	11.4496i	−0.249560	+	0.546459i	−0.992406	−	0.123002i	$-0.960748\pi$
$439$	−5.22885	+	11.4496i	−0.249560	+	0.546459i	0.742847	+	0.669461i	$0.233475\pi$
$440$	−4.19475	−	1.23169i	−0.199977	−	0.0587185i
$441$	−0.654861	−	0.755750i	−0.0311838	−	0.0359881i
$442$	−0.386437	+	0.248348i	−0.0183809	+	0.0118127i
$443$	−23.1976	+	26.7714i	−1.10215	+	1.27195i	−0.142793	+	0.989753i	$0.545608\pi$
$443$	−23.1976	+	26.7714i	−1.10215	+	1.27195i	−0.959357	+	0.282196i	$0.908937\pi$
$444$	−0.305885	+	2.12748i	−0.0145167	+	0.100966i
$445$	−20.6594	+	6.06614i	−0.979348	+	0.287563i
$446$	−8.48360	−	5.45208i	−0.401710	−	0.258164i
$447$	0.641013	+	4.45834i	0.0303189	+	0.210872i
$448$	0.415415	+	0.909632i	0.0196265	+	0.0429761i
$449$	−7.87541	−	17.2447i	−0.371663	−	0.813829i	−0.999374	−	0.0353824i	$-0.988735\pi$
$449$	−7.87541	−	17.2447i	−0.371663	−	0.813829i	0.627710	−	0.778447i	$-0.283992\pi$
$450$	−0.374071	−	2.60172i	−0.0176339	−	0.122646i
$451$	−12.4616	−	8.00858i	−0.586793	−	0.377109i
$452$	1.75983	−	0.516732i	0.0827753	−	0.0243050i
$453$	0.636109	−	4.42424i	0.0298870	−	0.207869i
$454$	−16.1459	+	18.6333i	−0.757763	+	0.874505i
$455$	−0.223157	+	0.143414i	−0.0104618	+	0.00672337i
$456$	−2.25620	−	2.60380i	−0.105656	−	0.121934i
$457$	39.0323	+	11.4609i	1.82586	+	0.536120i	0.999630	−	0.0272185i	$-0.00866498\pi$
$457$	39.0323	+	11.4609i	1.82586	+	0.536120i	0.826226	+	0.563338i	$0.190483\pi$
$458$	−2.54334	+	5.56914i	−0.118843	+	0.260229i
$459$	−2.66674			−0.124473
$460$	4.44238	+	5.90002i	0.207127	+	0.275090i
$461$	−35.6795			−1.66176			−0.830879	−	0.556453i	$-0.812162\pi$
$461$	−35.6795			−1.66176			−0.830879	+	0.556453i	$0.812162\pi$
$462$	1.17932	−	2.58236i	0.0548671	−	0.120142i
$463$	11.0497	+	3.24449i	0.513524	+	0.150784i	0.528220	−	0.849108i	$-0.322860\pi$
$463$	11.0497	+	3.24449i	0.513524	+	0.150784i	−0.0146955	+	0.999892i	$0.504678\pi$
$464$	0.291881	+	0.336848i	0.0135502	+	0.0156378i
$465$	8.59659	−	5.52469i	0.398657	−	0.256201i
$466$	−8.63280	+	9.96278i	−0.399907	+	0.461517i
$467$	4.04224	−	28.1144i	0.187053	−	1.30098i	−0.652536	−	0.757758i	$-0.726295\pi$
$467$	4.04224	−	28.1144i	0.187053	−	1.30098i	0.839589	−	0.543222i	$-0.182796\pi$
$468$	−0.165277	+	0.0485297i	−0.00763992	+	0.00224328i
$469$	−9.47336	−	6.08816i	−0.437439	−	0.281125i
$470$	0.799107	+	5.55791i	0.0368601	+	0.256367i
$471$	−4.10493	−	8.98855i	−0.189145	−	0.414171i
$472$	0.558545	+	1.22304i	0.0257091	+	0.0562951i
$473$	−0.329729	−	2.29331i	−0.0151609	−	0.105447i
$474$	7.48186	+	4.80830i	0.343653	+	0.220853i
$475$	8.68911	−	2.55135i	0.398684	−	0.117064i
$476$	−0.379517	+	2.63960i	−0.0173951	+	0.120986i
$477$	−8.75767	+	10.1069i	−0.400986	+	0.462763i
$478$	−4.96369	+	3.18997i	−0.227034	+	0.145906i
$479$	−6.25583	−	7.21961i	−0.285836	−	0.329872i	0.594614	−	0.804011i	$-0.297305\pi$
$479$	−6.25583	−	7.21961i	−0.285836	−	0.329872i	−0.880450	+	0.474139i	$0.842759\pi$
$480$	1.47759	+	0.433861i	0.0674427	+	0.0198030i
$481$	−0.153801	+	0.336778i	−0.00701274	+	0.0153558i
$482$	−3.39503			−0.154639
$483$	−4.20279	+	2.31010i	−0.191233	+	0.105113i
$484$	−2.94063			−0.133665
$485$	−7.18992	+	15.7437i	−0.326477	+	0.714886i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	−16.7420	−	19.3213i	−0.758654	−	0.875533i	0.236723	−	0.971577i	$-0.423927\pi$
$487$	−16.7420	−	19.3213i	−0.758654	−	0.875533i	−0.995377	+	0.0960439i	$0.969381\pi$
$488$	1.20851	−	0.776663i	0.0547067	−	0.0351579i
$489$	7.58393	−	8.75233i	0.342957	−	0.395794i
$490$	−0.219161	+	1.52430i	−0.00990070	+	0.0688608i
$491$	−16.8337	+	4.94281i	−0.759693	+	0.223066i	−0.638562	−	0.769571i	$-0.720470\pi$
$491$	−16.8337	+	4.94281i	−0.759693	+	0.223066i	−0.121131	+	0.992637i	$0.538652\pi$
$492$	4.38958	+	2.82101i	0.197898	+	0.127181i
$493$	0.169156	+	1.17651i	0.00761841	+	0.0529872i
$494$	−0.246537	−	0.539840i	−0.0110922	−	0.0242886i
$495$	−1.81613	−	3.97676i	−0.0816288	−	0.178742i
$496$	−0.944356	−	6.56814i	−0.0424028	−	0.294918i
$497$	2.93289	+	1.88485i	0.131558	+	0.0845472i
$498$	−9.25306	+	2.71694i	−0.414639	+	0.121749i
$499$	−1.25350	+	8.71829i	−0.0561144	+	0.390284i	0.942338	+	0.334664i	$0.108623\pi$
$499$	−1.25350	+	8.71829i	−0.0561144	+	0.390284i	−0.998452	+	0.0556204i	$0.982286\pi$
$500$	−7.69308	+	8.87829i	−0.344045	+	0.397049i
$501$	−0.777692	+	0.499792i	−0.0347447	+	0.0223291i
$502$	1.96366	+	2.26619i	0.0876426	+	0.101145i
$503$	21.1350	+	6.20580i	0.942363	+	0.276703i	0.716604	−	0.697480i	$-0.245696\pi$
$503$	21.1350	+	6.20580i	0.942363	+	0.276703i	0.225759	+	0.974183i	$0.427514\pi$
$504$	−0.415415	+	0.909632i	−0.0185041	+	0.0405182i
$505$	−4.50067			−0.200277
$506$	−10.9220	−	8.12874i	−0.485540	−	0.361366i
$507$	12.9703			0.576033
$508$	−0.626780	+	1.37246i	−0.0278089	+	0.0608929i
$509$	−22.3115	−	6.55126i	−0.988941	−	0.290379i	−0.253031	−	0.967458i	$-0.581427\pi$
$509$	−22.3115	−	6.55126i	−0.988941	−	0.290379i	−0.735910	+	0.677079i	$0.763246\pi$
$510$	2.68933	+	3.10365i	0.119085	+	0.137432i
$511$	8.67447	−	5.57474i	0.383736	−	0.246612i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.490320	−	3.41025i	0.0216481	−	0.150566i
$514$	−12.9621	+	3.80600i	−0.571732	+	0.167876i
$515$	−5.90027	−	3.79187i	−0.259997	−	0.167090i
$516$	0.116147	+	0.807817i	0.00511307	+	0.0355622i
$517$	−4.30006	−	9.41581i	−0.189116	−	0.414107i
$518$	0.892873	+	1.95512i	0.0392306	+	0.0859030i
$519$	−2.02151	−	14.0599i	−0.0887346	−	0.617163i
$520$	0.223157	+	0.143414i	0.00978608	+	0.00628913i
$521$	−13.6497	+	4.00791i	−0.598004	+	0.175590i	−0.566706	−	0.823920i	$-0.691782\pi$
$521$	−13.6497	+	4.00791i	−0.598004	+	0.175590i	−0.0312984	+	0.999510i	$0.509964\pi$
$522$	−0.0634317	+	0.441177i	−0.00277633	+	0.0193098i
$523$	−14.0198	+	16.1797i	−0.613044	+	0.707490i	−0.974371	−	0.224949i	$-0.927778\pi$
$523$	−14.0198	+	16.1797i	−0.613044	+	0.707490i	0.361327	+	0.932439i	$0.382324\pi$
$524$	0.817399	−	0.525311i	0.0357083	−	0.0229483i
$525$	−1.72129	−	1.98647i	−0.0751231	−	0.0866967i
$526$	−18.1595	−	5.33212i	−0.791793	−	0.232491i
$527$	7.35104	−	16.0965i	0.320216	−	0.701176i
$528$	−2.83890			−0.123547
$529$	6.60259	+	22.0319i	0.287069	+	0.957910i
$530$	20.5946			0.894572
$531$	−0.558545	+	1.22304i	−0.0242388	+	0.0530755i
$532$	−3.30576	−	0.970658i	−0.143323	−	0.0420834i
$533$	0.588593	+	0.679273i	0.0254948	+	0.0294226i
$534$	−11.7622	+	7.55911i	−0.509000	+	0.327115i
$535$	−7.24514	+	8.36134i	−0.313235	+	0.361492i
$536$	−1.60261	+	11.1464i	−0.0692221	+	0.481450i
$537$	−2.33269	+	0.684939i	−0.100663	+	0.0295573i
$538$	10.1171	+	6.50187i	0.436180	+	0.280316i
$539$	−0.404018	−	2.81001i	−0.0174023	−	0.121036i
$540$	0.639729	+	1.40081i	0.0275295	+	0.0602813i
$541$	−10.7912	−	23.6294i	−0.463949	−	1.01591i	−0.986570	−	0.163342i	$-0.947773\pi$
$541$	−10.7912	−	23.6294i	−0.463949	−	1.01591i	0.522620	−	0.852565i	$-0.324955\pi$
$542$	−1.30022	−	9.04320i	−0.0558491	−	0.388439i
$543$	8.00203	+	5.14259i	0.343400	+	0.220690i
$544$	2.55872	−	0.751308i	0.109704	−	0.0322121i
$545$	3.09895	−	21.5537i	0.132744	−	0.923257i
$546$	−0.112803	+	0.130181i	−0.00482751	+	0.00557124i
$547$	2.97966	−	1.91491i	0.127401	−	0.0818758i	−0.475388	−	0.879776i	$-0.657692\pi$
$547$	2.97966	−	1.91491i	0.127401	−	0.0818758i	0.602789	+	0.797900i	$0.294056\pi$
$548$	−4.48868	−	5.18021i	−0.191747	−	0.221288i
$549$	1.37837	+	0.404726i	0.0588274	+	0.0172733i
$550$	3.09982	−	6.78767i	0.132177	−	0.289427i
$551$	−1.53563			−0.0654199
$552$	3.84724	+	2.86334i	0.163750	+	0.121872i
$553$	8.89370			0.378199
$554$	−5.27215	+	11.5444i	−0.223992	+	0.490474i
$555$	3.17587	+	0.932520i	0.134808	+	0.0395833i
$556$	−1.14241	−	1.31841i	−0.0484490	−	0.0559131i
$557$	5.90633	−	3.79577i	0.250259	−	0.160832i	−0.409497	−	0.912311i	$-0.634296\pi$
$557$	5.90633	−	3.79577i	0.250259	−	0.160832i	0.659756	+	0.751480i	$0.270659\pi$
$558$	4.34545	−	5.01491i	0.183957	−	0.212298i
$559$	−0.0200067	+	0.139150i	−0.000846195	+	0.00588542i
$560$	1.47759	−	0.433861i	0.0624398	−	0.0183340i
$561$	−6.36881	−	4.09299i	−0.268892	−	0.172806i
$562$	2.62757	+	18.2752i	0.110837	+	0.770891i
$563$	4.77134	+	10.4478i	0.201088	+	0.440321i	0.983131	−	0.182903i	$-0.0585495\pi$
$563$	4.77134	+	10.4478i	0.201088	+	0.440321i	−0.782043	+	0.623225i	$0.785822\pi$
$564$	1.51469	+	3.31671i	0.0637799	+	0.139659i
$565$	−0.401968	−	2.79575i	−0.0169109	−	0.117618i
$566$	7.45261	+	4.78950i	0.313257	+	0.201318i
$567$	−0.959493	+	0.281733i	−0.0402949	+	0.0118317i
$568$	0.496157	−	3.45085i	0.0208183	−	0.144794i
$569$	−19.4648	+	22.4635i	−0.816006	+	0.941721i	−0.999144	−	0.0413665i	$-0.986829\pi$
$569$	−19.4648	+	22.4635i	−0.816006	+	0.941721i	0.183138	+	0.983087i	$0.441374\pi$
$570$	−4.46344	+	2.86848i	−0.186953	+	0.120147i
$571$	15.2260	+	17.5718i	0.637189	+	0.735355i	0.978875	−	0.204459i	$-0.0655434\pi$
$571$	15.2260	+	17.5718i	0.637189	+	0.735355i	−0.341686	+	0.939814i	$0.610998\pi$
$572$	−0.469205	−	0.137771i	−0.0196184	−	0.00576049i
$573$	−6.04602	+	13.2389i	−0.252576	+	0.553064i
$574$	5.21790			0.217791
$575$	−11.0469	+	6.07206i	−0.460689	+	0.253222i
$576$	1.00000			0.0416667
$577$	14.3925	−	31.5152i	0.599168	−	1.31199i	−0.330574	−	0.943780i	$-0.607242\pi$
$577$	14.3925	−	31.5152i	0.599168	−	1.31199i	0.929741	−	0.368214i	$-0.120031\pi$
$578$	−9.48793	−	2.78591i	−0.394646	−	0.115878i
$579$	15.4988	+	17.8865i	0.644106	+	0.743338i
$580$	0.577427	−	0.371090i	0.0239763	−	0.0154087i
$581$	−6.31528	+	7.28822i	−0.262002	+	0.302366i
$582$	−1.59948	+	11.1246i	−0.0663005	+	0.461130i
$583$	−36.4277	+	10.6961i	−1.50868	+	0.442989i
$584$	−8.67447	−	5.57474i	−0.358952	−	0.230684i
$585$	0.0377515	+	0.262567i	0.00156083	+	0.0108558i
$586$	7.25762	+	15.8920i	0.299810	+	0.656491i
$587$	−16.4969	−	36.1232i	−0.680900	−	1.49096i	−0.861687	−	0.507440i	$-0.830592\pi$
$587$	−16.4969	−	36.1232i	−0.680900	−	1.49096i	0.180788	−	0.983522i	$-0.442135\pi$
$588$	0.142315	+	0.989821i	0.00586897	+	0.0408195i
$589$	19.2328	+	12.3601i	0.792472	+	0.509291i
$590$	1.98669	−	0.583346i	0.0817909	−	0.0240160i
$591$	1.94738	−	13.5443i	0.0801045	−	0.557139i
$592$	1.40753	−	1.62437i	0.0578490	−	0.0667613i
$593$	15.1226	−	9.71873i	0.621012	−	0.399100i	−0.191960	−	0.981403i	$-0.561484\pi$
$593$	15.1226	−	9.71873i	0.621012	−	0.399100i	0.812972	+	0.582302i	$0.197848\pi$
$594$	−1.85909	−	2.14550i	−0.0762792	−	0.0880309i
$595$	3.94037	+	1.15700i	0.161539	+	0.0474322i
$596$	1.87111	−	4.09715i	0.0766436	−	0.167826i
$597$	1.80171			0.0737391
$598$	0.496904	+	0.659949i	0.0203199	+	0.0269873i
$599$	−18.7008			−0.764093			−0.382047	−	0.924143i	$-0.624781\pi$
$599$	−18.7008			−0.764093			−0.382047	+	0.924143i	$0.624781\pi$
$600$	−1.09191	+	2.39095i	−0.0445770	+	0.0976100i
$601$	−1.83538	−	0.538915i	−0.0748665	−	0.0219828i	0.244085	−	0.969754i	$-0.421512\pi$
$601$	−1.83538	−	0.538915i	−0.0748665	−	0.0219828i	−0.318951	+	0.947771i	$0.603331\pi$
$602$	0.534448	+	0.616785i	0.0217825	+	0.0251383i
$603$	−9.47336	+	6.08816i	−0.385785	+	0.247929i
$604$	−2.92705	+	3.37800i	−0.119100	+	0.137449i
$605$	−0.644473	+	4.48241i	−0.0262016	+	0.182236i
$606$	−2.80418	+	0.823381i	−0.113912	+	0.0334476i
$607$	4.30027	+	2.76362i	0.174543	+	0.112172i	0.624995	−	0.780629i	$-0.285101\pi$
$607$	4.30027	+	2.76362i	0.174543	+	0.112172i	−0.450452	+	0.892800i	$0.648737\pi$
$608$	0.490320	+	3.41025i	0.0198851	+	0.138304i
$609$	0.185156	+	0.405436i	0.00750291	+	0.0164291i
$610$	−0.919008	−	2.01235i	−0.0372096	−	0.0814776i
$611$	0.0893844	+	0.621682i	0.00361611	+	0.0251506i
$612$	2.24341	+	1.44175i	0.0906844	+	0.0582793i
$613$	15.2881	−	4.48899i	0.617480	−	0.181309i	0.0419912	−	0.999118i	$-0.486630\pi$
$613$	15.2881	−	4.48899i	0.617480	−	0.181309i	0.575489	+	0.817809i	$0.304812\pi$
$614$	3.68381	−	25.6215i	0.148666	−	1.03400i
$615$	5.26209	−	6.07278i	0.212188	−	0.244878i
$616$	−2.38824	+	1.53483i	−0.0962248	+	0.0618399i
$617$	−12.5310	−	14.4615i	−0.504478	−	0.582198i	0.445198	−	0.895432i	$-0.353133\pi$
$617$	−12.5310	−	14.4615i	−0.504478	−	0.582198i	−0.949676	+	0.313234i	$0.898588\pi$
$618$	−4.36992	−	1.28312i	−0.175784	−	0.0516148i
$619$	−3.21023	+	7.02941i	−0.129030	+	0.282536i	−0.963110	−	0.269107i	$-0.913272\pi$
$619$	−3.21023	+	7.02941i	−0.129030	+	0.282536i	0.834080	+	0.551643i	$0.185999\pi$
$620$	−10.2188			−0.410396
$621$	0.355443	+	4.78264i	0.0142634	+	0.191921i
$622$	4.59416			0.184209
$623$	−5.80823	+	12.7183i	−0.232702	+	0.509546i
$624$	0.165277	+	0.0485297i	0.00661637	+	0.00194274i
$625$	3.24072	+	3.73999i	0.129629	+	0.149599i
$626$	−19.8094	+	12.7307i	−0.791742	+	0.508822i
$627$	6.40514	−	7.39193i	0.255797	−	0.295205i
$628$	−1.40629	+	9.78094i	−0.0561170	+	0.390302i
$629$	5.49960	−	1.61483i	0.219283	−	0.0643874i
$630$	1.29551	+	0.832573i	0.0516143	+	0.0331705i
$631$	2.74160	+	19.0682i	0.109141	+	0.759094i	0.968732	+	0.248110i	$0.0798096\pi$
$631$	2.74160	+	19.0682i	0.109141	+	0.759094i	−0.859591	+	0.510983i	$0.829281\pi$
$632$	−3.69458	−	8.09000i	−0.146962	−	0.321803i
$633$	6.61260	+	14.4796i	0.262827	+	0.575512i
$634$	0.749903	+	5.21569i	0.0297824	+	0.207141i
$635$	1.95467	+	1.25619i	0.0775687	+	0.0498504i
$636$	12.8316	−	3.76770i	0.508807	−	0.149399i
$637$	−0.0245143	+	0.170501i	−0.000971294	+	0.00675550i
$638$	−0.828621	+	0.956279i	−0.0328054	+	0.0378595i
$639$	2.93289	−	1.88485i	0.116023	−	0.0745637i
$640$	−1.00847	−	1.16384i	−0.0398632	−	0.0460046i
$641$	9.86312	+	2.89607i	0.389570	+	0.114388i	0.470651	−	0.882320i	$-0.344019\pi$
$641$	9.86312	+	2.89607i	0.389570	+	0.114388i	−0.0810812	+	0.996707i	$0.525837\pi$
$642$	−2.98446	+	6.53507i	−0.117787	+	0.257918i
$643$	−2.36602			−0.0933066			−0.0466533	−	0.998911i	$-0.514856\pi$
$643$	−2.36602			−0.0933066			−0.0466533	+	0.998911i	$0.514856\pi$
$644$	4.78455	+	0.328816i	0.188538	+	0.0129572i
$645$	1.25681			0.0494869
$646$	−3.81674	+	8.35750i	−0.150168	+	0.328821i
$647$	43.7292	+	12.8401i	1.71917	+	0.504795i	0.984762	−	0.173909i	$-0.0556400\pi$
$647$	43.7292	+	12.8401i	1.71917	+	0.504795i	0.734412	+	0.678704i	$0.237458\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−3.21109	+	2.06364i	−0.126046	+	0.0810051i
$650$	−0.296499	+	0.342178i	−0.0116297	+	0.0134213i
$651$	0.944356	−	6.56814i	0.0370122	−	0.257426i
$652$	−11.1119	+	3.26274i	−0.435175	+	0.127779i
$653$	9.68691	+	6.22540i	0.379078	+	0.243619i	0.716279	−	0.697814i	$-0.245844\pi$
$653$	9.68691	+	6.22540i	0.379078	+	0.243619i	−0.337201	+	0.941433i	$0.609480\pi$
$654$	−2.01234	−	13.9961i	−0.0786886	−	0.547291i
$655$	−0.621589	−	1.36109i	−0.0242875	−	0.0531822i
$656$	−2.16760	−	4.74637i	−0.0846304	−	0.185315i
$657$	−1.46746	−	10.2064i	−0.0572510	−	0.398190i
$658$	3.06739	+	1.97129i	0.119579	+	0.0768488i
$659$	−16.0692	+	4.71834i	−0.625966	+	0.183800i	−0.579306	−	0.815110i	$-0.696676\pi$
$659$	−16.0692	+	4.71834i	−0.625966	+	0.183800i	−0.0466608	+	0.998911i	$0.514858\pi$
$660$	−0.622177	+	4.32734i	−0.0242182	+	0.168441i
$661$	17.2260	−	19.8799i	0.670014	−	0.773237i	−0.314365	−	0.949302i	$-0.601791\pi$
$661$	17.2260	−	19.8799i	0.670014	−	0.773237i	0.984379	+	0.176065i	$0.0563370\pi$
$662$	11.9475	−	7.67817i	0.464351	−	0.298420i
$663$	0.300816	+	0.347160i	0.0116827	+	0.0134826i
$664$	9.25306	+	2.71694i	0.359088	+	0.105438i
$665$	−2.20407	+	4.82624i	−0.0854701	+	0.187153i
$666$	2.14935			0.0832857
$667$	2.08745	−	0.460185i	0.0808263	−	0.0178184i
$668$	0.924444			0.0357678
$669$	−4.18924	+	9.17317i	−0.161966	+	0.354655i
$670$	16.6392	+	4.88571i	0.642828	+	0.188751i
$671$	2.67069	+	3.08214i	0.103101	+	0.118985i
$672$	0.841254	−	0.540641i	0.0324521	−	0.0208557i
$673$	15.4303	−	17.8075i	0.594793	−	0.686427i	−0.375925	−	0.926650i	$-0.622675\pi$
$673$	15.4303	−	17.8075i	0.594793	−	0.686427i	0.970718	+	0.240223i	$0.0772205\pi$
$674$	−4.69633	+	32.6637i	−0.180896	+	1.25816i
$675$	−2.52201	+	0.740528i	−0.0970721	+	0.0285029i
$676$	−10.9113	−	7.01229i	−0.419667	−	0.269703i
$677$	−5.72070	−	39.7884i	−0.219865	−	1.52919i	−0.738534	−	0.674217i	$-0.764481\pi$
$677$	−5.72070	−	39.7884i	−0.219865	−	1.52919i	0.518669	−	0.854975i	$-0.326428\pi$
$678$	−0.761921	−	1.66838i	−0.0292614	−	0.0640736i
$679$	4.66886	+	10.2234i	0.179174	+	0.392337i
$680$	−0.584447	−	4.06492i	−0.0224125	−	0.155882i
$681$	20.7414	+	13.3297i	0.794814	+	0.510796i
$682$	18.0750	−	5.30729i	0.692127	−	0.203227i
$683$	0.146298	−	1.01753i	0.00559795	−	0.0389346i	−0.986831	−	0.161755i	$-0.948285\pi$
$683$	0.146298	−	1.01753i	0.00559795	−	0.0389346i	0.992429	+	0.122820i	$0.0391938\pi$
$684$	−2.25620	+	2.60380i	−0.0862681	+	0.0995587i
$685$	−8.87994	+	5.70679i	−0.339285	+	0.218045i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	5.87441	+	1.72488i	0.224123	+	0.0658083i
$688$	0.339030	−	0.742372i	0.0129254	−	0.0283027i
$689$	2.30361			0.0877607
$690$	5.20775	−	5.23682i	0.198256	−	0.199362i
$691$	8.74157			0.332545			0.166273	−	0.986080i	$-0.446827\pi$
$691$	8.74157			0.332545			0.166273	+	0.986080i	$0.446827\pi$
$692$	−5.90077	+	12.9209i	−0.224314	+	0.491178i
$693$	−2.72391	−	0.799811i	−0.103473	−	0.0303823i
$694$	−7.10458	−	8.19913i	−0.269686	−	0.311235i
$695$	−2.26003	+	1.45243i	−0.0857278	+	0.0550939i
$696$	0.291881	−	0.336848i	0.0110637	−	0.0127682i
$697$	1.98028	−	13.7732i	0.0750086	−	0.521696i
$698$	30.8856	−	9.06884i	1.16904	−	0.343260i
$699$	11.0900	+	7.12708i	0.419460	+	0.269571i
$700$	0.374071	+	2.60172i	0.0141386	+	0.0983359i
$701$	−6.67147	−	14.6085i	−0.251978	−	0.551755i	0.740799	−	0.671726i	$-0.234447\pi$
$701$	−6.67147	−	14.6085i	−0.251978	−	0.551755i	−0.992777	+	0.119972i	$0.961720\pi$
$702$	0.0715570	+	0.156688i	0.00270075	+	0.00591381i
$703$	1.05387	+	7.32983i	0.0397475	+	0.276450i
$704$	2.38824	+	1.53483i	0.0900101	+	0.0578459i
$705$	5.38762	−	1.58195i	0.202909	−	0.0595796i
$706$	3.50044	−	24.3461i	0.131741	−	0.916276i
$707$	−1.91387	+	2.20873i	−0.0719786	+	0.0830677i
$708$	1.13110	−	0.726916i	0.0425095	−	0.0273192i
$709$	−25.2829	−	29.1780i	−0.949520	−	1.09580i	−0.995299	−	0.0968528i	$-0.969122\pi$
$709$	−25.2829	−	29.1780i	−0.949520	−	1.09580i	0.0457788	−	0.998952i	$-0.485423\pi$
$710$	−5.15139	−	1.51258i	−0.193328	−	0.0567663i
$711$	3.69458	−	8.09000i	0.138558	−	0.303399i
$712$	13.9818			0.523989
$713$	−29.8480	−	11.0382i	−1.11782	−	0.413383i
$714$	2.66674			0.0998004
$715$	−0.312836	+	0.685015i	−0.0116994	+	0.0256181i
$716$	2.33269	+	0.684939i	0.0871767	+	0.0255974i
$717$	3.86391	+	4.45919i	0.144300	+	0.166531i
$718$	23.0511	−	14.8140i	0.860259	−	0.552855i
$719$	−2.74235	+	3.16484i	−0.102272	+	0.118028i	−0.804578	−	0.593847i	$-0.797608\pi$
$719$	−2.74235	+	3.16484i	−0.102272	+	0.118028i	0.702306	+	0.711875i	$0.252154\pi$
$720$	0.219161	−	1.52430i	0.00816766	−	0.0568073i
$721$	−4.36992	+	1.28312i	−0.162744	+	0.0477860i
$722$	5.99796	+	3.85465i	0.223221	+	0.143455i
$723$	0.483163	+	3.36047i	0.0179690	+	0.124977i
$724$	−3.95144	−	8.65245i	−0.146854	−	0.321566i
$725$	0.486679	+	1.06568i	0.0180748	+	0.0395783i
$726$	0.418496	+	2.91070i	0.0155318	+	0.108026i
$727$	12.2020	+	7.84172i	0.452546	+	0.290833i	0.746990	−	0.664835i	$-0.231498\pi$
$727$	12.2020	+	7.84172i	0.452546	+	0.290833i	−0.294444	+	0.955669i	$0.595135\pi$
$728$	0.165277	−	0.0485297i	0.00612557	−	0.00179863i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−10.3987	+	12.0007i	−0.384873	+	0.444167i
$731$	1.83090	−	1.17665i	0.0677182	−	0.0435199i
$732$	−0.940747	−	1.08568i	−0.0347710	−	0.0401279i
$733$	18.0732	+	5.30677i	0.667549	+	0.196010i	0.597911	−	0.801562i	$-0.295998\pi$
$733$	18.0732	+	5.30677i	0.667549	+	0.196010i	0.0696375	+	0.997572i	$0.477816\pi$
$734$	3.75604	−	8.22458i	0.138638	−	0.303575i
$735$	1.53997			0.0568028
$736$	−1.68847	−	4.48877i	−0.0622379	−	0.165458i
$737$	−31.9689			−1.17759
$738$	2.16760	−	4.74637i	0.0797903	−	0.174716i
$739$	−19.9888	−	5.86925i	−0.735301	−	0.215904i	−0.107420	−	0.994214i	$-0.534259\pi$
$739$	−19.9888	−	5.86925i	−0.735301	−	0.215904i	−0.627880	+	0.778310i	$0.716077\pi$
$740$	−2.16756	−	2.50149i	−0.0796809	−	0.0919567i
$741$	−0.499259	+	0.320855i	−0.0183408	+	0.0117869i
$742$	8.75767	−	10.1069i	0.321504	−	0.371036i
$743$	−3.47175	+	24.1466i	−0.127366	+	0.885852i	0.821508	+	0.570197i	$0.193133\pi$
$743$	−3.47175	+	24.1466i	−0.127366	+	0.885852i	−0.948874	+	0.315655i	$0.897776\pi$
$744$	−6.36689	+	1.86949i	−0.233422	+	0.0685387i
$745$	−5.83522	−	3.75007i	−0.213786	−	0.137392i
$746$	3.15077	+	21.9141i	0.115358	+	0.802331i
$747$	4.00614	+	8.77221i	0.146577	+	0.320959i
$748$	3.14495	+	6.88648i	0.114991	+	0.251795i
$749$	1.02243	+	7.11117i	0.0373588	+	0.259837i
$750$	9.88276	+	6.35127i	0.360867	+	0.231915i
$751$	21.2249	−	6.23219i	0.774508	−	0.227416i	0.129487	−	0.991581i	$-0.458667\pi$
$751$	21.2249	−	6.23219i	0.774508	−	0.227416i	0.645021	+	0.764165i	$0.276849\pi$
$752$	0.518909	−	3.60909i	0.0189227	−	0.131610i
$753$	1.96366	−	2.26619i	0.0715599	−	0.0825845i
$754$	0.0645883	−	0.0415083i	0.00235217	−	0.00151164i
$755$	4.50759	+	5.20203i	0.164048	+	0.189321i
$756$	0.959493	+	0.281733i	0.0348964	+	0.0102465i
$757$	11.5686	−	25.3317i	0.420469	−	0.920698i	−0.574310	−	0.818638i	$-0.694729\pi$
$757$	11.5686	−	25.3317i	0.420469	−	0.920698i	0.994778	−	0.102060i	$-0.0325433\pi$
$758$	13.9283			0.505898
$759$	−6.49164	+	11.9676i	−0.235632	+	0.434397i
$760$	5.30570			0.192458
$761$	4.65231	−	10.1871i	0.168646	−	0.369283i	−0.806372	−	0.591408i	$-0.798572\pi$
$761$	4.65231	−	10.1871i	0.168646	−	0.369283i	0.975018	+	0.222125i	$0.0712994\pi$
$762$	1.44769	+	0.425080i	0.0524442	+	0.0153990i
$763$	−9.25975	−	10.6863i	−0.335226	−	0.386871i
$764$	12.2437	−	7.86857i	0.442963	−	0.284675i
$765$	2.68933	−	3.10365i	0.0972328	−	0.112213i
$766$	2.99753	−	20.8483i	0.108305	−	0.753279i
$767$	0.222222	−	0.0652503i	0.00802398	−	0.00235605i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	2.87758	+	20.0140i	0.103768	+	0.721723i	0.973581	+	0.228341i	$0.0733302\pi$
$769$	2.87758	+	20.0140i	0.103768	+	0.721723i	−0.869813	+	0.493381i	$0.835761\pi$
$770$	1.81613	+	3.97676i	0.0654487	+	0.143313i
$771$	5.61196	+	12.2885i	0.202110	+	0.442559i
$772$	−3.36820	−	23.4264i	−0.121224	−	0.843133i
$773$	5.16717	+	3.32074i	0.185850	+	0.119439i	0.630258	−	0.776386i	$-0.282949\pi$
$773$	5.16717	+	3.32074i	0.185850	+	0.119439i	−0.444407	+	0.895825i	$0.646586\pi$
$774$	0.783065	−	0.229929i	0.0281467	−	0.00826462i
$775$	2.48222	−	17.2642i	0.0891640	−	0.620149i
$776$	7.35999	−	8.49388i	0.264208	−	0.304913i
$777$	1.80815	−	1.16203i	0.0648670	−	0.0416875i
$778$	−10.6791	−	12.3243i	−0.382865	−	0.441849i
$779$	17.2491	+	5.06480i	0.618014	+	0.181465i
$780$	0.110196	−	0.241296i	0.00394565	−	0.00863977i
$781$	9.89736			0.354155
$782$	2.68376	−	12.5045i	0.0959710	−	0.447160i
$783$	0.445714			0.0159285
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	14.6009	+	4.28721i	0.521128	+	0.153017i
$786$	−0.636292	−	0.734320i	−0.0226958	−	0.0261923i
$787$	−3.37235	+	2.16728i	−0.120211	+	0.0772550i	−0.599365	−	0.800476i	$-0.704580\pi$
$787$	−3.37235	+	2.16728i	−0.120211	+	0.0772550i	0.479154	+	0.877731i	$0.340944\pi$
$788$	−8.96085	+	10.3414i	−0.319217	+	0.368396i
$789$	−2.69347	+	18.7335i	−0.0958902	+	0.666931i
$790$	−13.1413	+	3.85863i	−0.467546	+	0.137284i
$791$	−1.54296	−	0.991601i	−0.0548614	−	0.0352573i
$792$	0.404018	+	2.81001i	0.0143562	+	0.0998492i
$793$	−0.102796	−	0.225092i	−0.00365039	−	0.00799324i
$794$	−0.0797262	−	0.174576i	−0.00282938	−	0.00619547i
$795$	−2.93092	−	20.3850i	−0.103949	−	0.722980i
$796$	−1.51570	−	0.974078i	−0.0537224	−	0.0345253i
$797$	29.1962	−	8.57279i	1.03418	−	0.303664i	0.279773	−	0.960066i	$-0.409741\pi$
$797$	29.1962	−	8.57279i	1.03418	−	0.303664i	0.754411	+	0.656403i	$0.227923\pi$
$798$	−0.490320	+	3.41025i	−0.0173571	+	0.120722i
$799$	6.36754	−	7.34853i	0.225267	−	0.259972i
$800$	2.21122	−	1.42106i	0.0781783	−	0.0502422i
$801$	9.15611	+	10.5667i	0.323515	+	0.373356i
$802$	−37.6611	−	11.0583i	−1.32986	−	0.390482i
$803$	12.1604	−	26.6276i	0.429132	−	0.939668i
$804$	11.2610			0.397145
$805$	1.54980	−	7.22102i	0.0546233	−	0.254507i
$806$	−1.14303			−0.0402613
$807$	4.99588	−	10.9395i	0.175863	−	0.385087i
$808$	2.80418	+	0.823381i	0.0986507	+	0.0289665i
$809$	29.6903	+	34.2645i	1.04386	+	1.20468i	0.978379	+	0.206821i	$0.0663118\pi$
$809$	29.6903	+	34.2645i	1.04386	+	1.20468i	0.0654782	+	0.997854i	$0.479143\pi$
$810$	1.29551	−	0.832573i	0.0455195	−	0.0292536i
$811$	−27.1658	+	31.3510i	−0.953920	+	1.10088i	0.0408933	+	0.999164i	$0.486980\pi$
$811$	−27.1658	+	31.3510i	−0.953920	+	1.10088i	−0.994813	+	0.101719i	$0.967566\pi$
$812$	0.0634317	−	0.441177i	0.00222602	−	0.0154823i
$813$	−8.76611	+	2.57396i	−0.307441	+	0.0902728i
$814$	5.13316	+	3.29888i	0.179917	+	0.115626i
$815$	2.53810	+	17.6529i	0.0889059	+	0.618354i
$816$	−1.10781	−	2.42575i	−0.0387809	−	0.0849184i
$817$	1.16807	+	2.55771i	0.0408655	+	0.0894829i
$818$	5.45876	+	37.9665i	0.190861	+	1.32747i
$819$	0.144910	+	0.0931277i	0.00506355	+	0.00325415i
$820$	−7.70995	+	2.26385i	−0.269243	+	0.0790569i
$821$	−3.61584	+	25.1487i	−0.126194	+	0.877696i	0.824123	+	0.566411i	$0.191669\pi$
$821$	−3.61584	+	25.1487i	−0.126194	+	0.877696i	−0.950317	+	0.311285i	$0.899241\pi$
$822$	−4.48868	+	5.18021i	−0.156561	+	0.180681i
$823$	30.8897	−	19.8516i	1.07675	−	0.691984i	0.122944	−	0.992414i	$-0.460767\pi$
$823$	30.8897	−	19.8516i	1.07675	−	0.691984i	0.953804	+	0.300430i	$0.0971302\pi$
$824$	2.98250	+	3.44199i	0.103900	+	0.119907i
$825$	−7.15973	−	2.10229i	−0.249270	−	0.0731922i
$826$	0.558545	−	1.22304i	0.0194342	−	0.0425551i
$827$	−8.73138			−0.303620			−0.151810	−	0.988410i	$-0.548510\pi$
$827$	−8.73138			−0.303620			−0.151810	+	0.988410i	$0.548510\pi$
$828$	2.28667	−	4.21558i	0.0794674	−	0.146502i
$829$	19.2843			0.669770			0.334885	−	0.942259i	$-0.391303\pi$
$829$	19.2843			0.669770			0.334885	+	0.942259i	$0.391303\pi$
$830$	6.16935	−	13.5090i	0.214141	−	0.468904i
$831$	12.1772	+	3.57555i	0.422422	+	0.124034i
$832$	−0.112803	−	0.130181i	−0.00391073	−	0.00451322i
$833$	2.24341	−	1.44175i	0.0777295	−	0.0499537i
$834$	−1.14241	+	1.31841i	−0.0395585	+	0.0456529i
$835$	0.202602	−	1.40913i	0.00701134	−	0.0487650i
$836$	−9.38472	+	2.75560i	−0.324577	+	0.0953045i
$837$	−5.58229	−	3.58752i	−0.192952	−	0.124003i
$838$	−3.42502	−	23.8215i	−0.118315	−	0.822901i
$839$	6.31988	+	13.8386i	0.218186	+	0.477762i	0.986798	−	0.161954i	$-0.0517795\pi$
$839$	6.31988	+	13.8386i	0.218186	+	0.477762i	−0.768612	+	0.639715i	$0.779052\pi$
$840$	−0.639729	−	1.40081i	−0.0220727	−	0.0483325i
$841$	4.09886	+	28.5082i	0.141340	+	0.983041i
$842$	−8.51705	−	5.47358i	−0.293517	−	0.188632i
$843$	17.7152	−	5.20165i	0.610144	−	0.179155i
$844$	2.26538	−	15.7560i	0.0779775	−	0.542345i
$845$	−13.0802	+	15.0953i	−0.449972	+	0.519295i
$846$	3.06739	−	1.97129i	0.105459	−	0.0677743i
$847$	1.92571	+	2.22238i	0.0661680	+	0.0763620i
$848$	−12.8316	−	3.76770i	−0.440640	−	0.129383i
$849$	3.68013	−	8.05837i	0.126302	−	0.276562i
$850$	7.00948			0.240423
$851$	−3.62912	−	9.64795i	−0.124405	−	0.330728i
$852$	−3.48633			−0.119440
$853$	−17.7340	+	38.8321i	−0.607202	+	1.32959i	0.317269	+	0.948336i	$0.397234\pi$
$853$	−17.7340	+	38.8321i	−0.607202	+	1.32959i	−0.924471	+	0.381252i	$0.875493\pi$
$854$	−1.37837	−	0.404726i	−0.0471668	−	0.0138494i
$855$	3.47450	+	4.00978i	0.118825	+	0.137132i
$856$	6.04381	−	3.88412i	0.206573	−	0.132757i
$857$	2.34958	−	2.71156i	0.0802602	−	0.0926252i	−0.714199	−	0.699943i	$-0.753209\pi$
$857$	2.34958	−	2.71156i	0.0802602	−	0.0926252i	0.794459	+	0.607317i	$0.207754\pi$
$858$	−0.0695938	+	0.484036i	−0.00237589	+	0.0165247i
$859$	−32.7736	+	9.62319i	−1.11822	+	0.328339i	−0.788067	−	0.615589i	$-0.788918\pi$
$859$	−32.7736	+	9.62319i	−1.11822	+	0.328339i	−0.330152	+	0.943928i	$0.607100\pi$
$860$	−1.05730	−	0.679483i	−0.0360535	−	0.0231702i
$861$	−0.742585	−	5.16479i	−0.0253072	−	0.176016i
$862$	−9.71282	−	21.2681i	−0.330820	−	0.724394i
$863$	−1.49193	−	3.26686i	−0.0507857	−	0.111205i	0.882538	−	0.470241i	$-0.155833\pi$
$863$	−1.49193	−	3.26686i	−0.0507857	−	0.111205i	−0.933324	+	0.359036i	$0.883106\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	18.4021	+	11.8263i	0.625689	+	0.402106i
$866$	21.7281	−	6.37995i	0.738352	−	0.216800i
$867$	−1.40728	+	9.78783i	−0.0477936	+	0.332412i
$868$	−4.34545	+	5.01491i	−0.147494	+	0.170217i
$869$	21.2403	−	13.6503i	0.720527	−	0.463054i
$870$	−0.449489	−	0.518738i	−0.0152391	−	0.0175869i
$871$	1.86118	+	0.546493i	0.0630638	+	0.0185172i
$872$	−5.87398	+	12.8622i	−0.198918	+	0.435570i
$873$	11.2390			0.380383
$874$	15.4974	+	5.73114i	0.524207	+	0.193859i
$875$	11.7477			0.397143
$876$	−4.28349	+	9.37954i	−0.144726	+	0.316905i
$877$	−12.7739	−	3.75076i	−0.431344	−	0.126654i	0.0588508	−	0.998267i	$-0.481256\pi$
$877$	−12.7739	−	3.75076i	−0.431344	−	0.126654i	−0.490195	+	0.871613i	$0.663075\pi$
$878$	−8.24277	−	9.51267i	−0.278180	−	0.321037i
$879$	14.6974	−	9.44541i	0.495729	−	0.318586i
$880$	2.86294	−	3.30401i	0.0965098	−	0.111378i
$881$	−3.22186	+	22.4085i	−0.108547	+	0.754962i	0.860743	+	0.509040i	$0.170000\pi$
$881$	−3.22186	+	22.4085i	−0.108547	+	0.754962i	−0.969290	+	0.245922i	$0.920909\pi$
$882$	0.959493	−	0.281733i	0.0323078	−	0.00948643i
$883$	29.8590	+	19.1892i	1.00484	+	0.645768i	0.936051	−	0.351863i	$-0.114452\pi$
$883$	29.8590	+	19.1892i	1.00484	+	0.645768i	0.0687838	+	0.997632i	$0.478088\pi$
$884$	−0.0653735	−	0.454682i	−0.00219875	−	0.0152926i
$885$	−0.860144	−	1.88345i	−0.0289134	−	0.0633116i
$886$	−14.7155	−	32.2225i	−0.494378	−	1.08254i
$887$	−5.03396	−	35.0120i	−0.169024	−	1.17559i	−0.880907	−	0.473289i	$-0.843067\pi$
$887$	−5.03396	−	35.0120i	−0.169024	−	1.17559i	0.711883	−	0.702298i	$-0.247843\pi$
$888$	−1.80815	−	1.16203i	−0.0606776	−	0.0389951i
$889$	1.44769	−	0.425080i	0.0485539	−	0.0142567i
$890$	3.06426	−	21.3124i	0.102714	−	0.714393i
$891$	−1.85909	+	2.14550i	−0.0622817	+	0.0718769i
$892$	8.48360	−	5.45208i	0.284052	−	0.182549i
$893$	8.22659	+	9.49399i	0.275292	+	0.317704i
$894$	−4.32174	−	1.26898i	−0.144541	−	0.0424409i
$895$	1.55529	−	3.40561i	0.0519875	−	0.113837i
$896$	−1.00000			−0.0334077
$897$	0.582515	−	0.585766i	0.0194496	−	0.0195582i
$898$	18.9579			0.632634
$899$	−1.22864	+	2.69034i	−0.0409774	+	0.0897280i
$900$	2.52201	+	0.740528i	0.0840669	+	0.0246843i
$901$	−23.3545	−	26.9525i	−0.778050	−	0.897917i
$902$	12.4616	−	8.00858i	0.414926	−	0.266656i
$903$	0.534448	−	0.616785i	0.0177853	−	0.0205253i
$904$	−0.261023	+	1.81545i	−0.00868148	+	0.0603810i
$905$	−14.0549	+	4.12690i	−0.467202	+	0.137183i
$906$	3.76018	+	2.41652i	0.124924	+	0.0802835i
$907$	−1.43245	−	9.96293i	−0.0475638	−	0.330814i	−0.999685	−	0.0250931i	$-0.992012\pi$
$907$	−1.43245	−	9.96293i	−0.0475638	−	0.330814i	0.952121	−	0.305721i	$-0.0988973\pi$
$908$	−10.2422	−	22.4273i	−0.339900	−	0.744278i
$909$	1.21408	+	2.65846i	0.0402684	+	0.0881755i
$910$	−0.0377515	−	0.262567i	−0.00125145	−	0.00870402i
$911$	−14.4019	−	9.25557i	−0.477158	−	0.306651i	0.279865	−	0.960039i	$-0.409710\pi$
$911$	−14.4019	−	9.25557i	−0.477158	−	0.306651i	−0.757023	+	0.653389i	$0.773347\pi$
$912$	3.30576	−	0.970658i	0.109465	−	0.0321417i
$913$	−3.89623	+	27.0988i	−0.128946	+	0.896841i
$914$	−26.6398	+	30.7440i	−0.881168	+	1.01692i
$915$	−1.86108	+	1.19604i	−0.0615253	+	0.0395399i
$916$	−4.00933	−	4.62701i	−0.132472	−	0.152881i
$917$	−0.932286	−	0.273744i	−0.0307868	−	0.00903982i
$918$	1.10781	−	2.42575i	0.0365630	−	0.0800618i
$919$	−15.3959			−0.507864			−0.253932	−	0.967222i	$-0.581724\pi$
$919$	−15.3959			−0.507864			−0.253932	+	0.967222i	$0.581724\pi$
$920$	−7.21228	+	1.58997i	−0.237782	+	0.0524198i
$921$	−25.8849			−0.852937
$922$	14.8218	−	32.4552i	0.488129	−	1.06885i
$923$	−0.576210	−	0.169191i	−0.0189662	−	0.00556897i
$924$	1.85909	+	2.14550i	0.0611594	+	0.0705817i
$925$	4.75268	−	3.05436i	0.156267	−	0.100427i
$926$	−7.54152	+	8.70337i	−0.247830	+	0.286011i
$927$	−0.648159	+	4.50804i	−0.0212883	+	0.148064i
$928$	−0.427660	+	0.125572i	−0.0140386	+	0.00412211i
$929$	28.2466	+	18.1530i	0.926740	+	0.595580i	0.914606	−	0.404347i	$-0.132501\pi$
$929$	28.2466	+	18.1530i	0.926740	+	0.595580i	0.0121344	+	0.999926i	$0.496137\pi$
$930$	1.45428	+	10.1148i	0.0476879	+	0.331676i
$931$	1.43124	+	3.13397i	0.0469069	+	0.102712i
$932$	−5.47627	−	11.9914i	−0.179381	−	0.392790i
$933$	−0.653817	−	4.54740i	−0.0214050	−	0.148875i
$934$	23.8946	+	15.3561i	0.781854	+	0.502467i
$935$	11.1863	−	3.28460i	0.365832	−	0.107418i
$936$	0.0245143	−	0.170501i	0.000801277	−	0.00557300i
$937$	−9.07766	+	10.4762i	−0.296554	+	0.342242i	−0.884399	−	0.466732i	$-0.845431\pi$
$937$	−9.07766	+	10.4762i	−0.296554	+	0.342242i	0.587844	+	0.808974i	$0.299977\pi$
$938$	9.47336	−	6.08816i	0.309316	−	0.198785i
$939$	15.4203	+	17.7960i	0.503222	+	0.580750i
$940$	−5.38762	−	1.58195i	−0.175725	−	0.0515974i
$941$	−15.6489	+	34.2663i	−0.510139	+	1.11705i	0.462901	+	0.886410i	$0.346809\pi$
$941$	−15.6489	+	34.2663i	−0.510139	+	1.11705i	−0.973040	+	0.230638i	$0.925919\pi$
$942$	9.88152			0.321957
$943$	−24.9653	−	1.71573i	−0.812982	−	0.0558718i
$944$	−1.34455			−0.0437612
$945$	0.639729	−	1.40081i	0.0208104	−	0.0455684i
$946$	2.22305	+	0.652745i	0.0722774	+	0.0212226i
$947$	12.7545	+	14.7195i	0.414465	+	0.478318i	0.924143	−	0.382047i	$-0.124781\pi$
$947$	12.7545	+	14.7195i	0.414465	+	0.478318i	−0.509678	+	0.860365i	$0.670235\pi$
$948$	−7.48186	+	4.80830i	−0.243000	+	0.156166i
$949$	−1.16315	+	1.34234i	−0.0377574	+	0.0435744i
$950$	−1.28879	+	8.96377i	−0.0418140	+	0.290823i
$951$	5.05588	−	1.48454i	0.163948	−	0.0481395i
$952$	−2.24341	−	1.44175i	−0.0727092	−	0.0467274i
$953$	2.04514	+	14.2243i	0.0662486	+	0.460769i	0.995761	+	0.0919783i	$0.0293191\pi$
$953$	2.04514	+	14.2243i	0.0662486	+	0.460769i	−0.929512	+	0.368791i	$0.879772\pi$
$954$	−5.55548	−	12.1648i	−0.179865	−	0.393850i
$955$	−9.31071	−	20.3876i	−0.301288	−	0.659728i
$956$	−0.839707	−	5.84029i	−0.0271581	−	0.188889i
$957$	1.06447	+	0.684094i	0.0344095	+	0.0221136i
$958$	9.16595	−	2.69137i	0.296138	−	0.0869541i
$959$	−0.975484	+	6.78464i	−0.0315000	+	0.219087i
$960$	−1.00847	+	1.16384i	−0.0325482	+	0.0375626i
$961$	10.9635	−	7.04578i	0.353660	−	0.227283i
$962$	−0.242453	−	0.279805i	−0.00781699	−	0.00902128i
$963$	6.89328	+	2.02405i	0.222133	+	0.0652241i
$964$	1.41034	−	3.08822i	0.0454242	−	0.0994650i
$965$	−36.4470			−1.17327
$966$	−0.355443	−	4.78264i	−0.0114362	−	0.153879i
$967$	37.8529			1.21727			0.608634	−	0.793451i	$-0.291718\pi$
$967$	37.8529			1.21727			0.608634	+	0.793451i	$0.291718\pi$
$968$	1.22158	−	2.67489i	0.0392632	−	0.0859744i
$969$	8.81561	+	2.58850i	0.283198	+	0.0831545i
$970$	−11.3342	−	13.0804i	−0.363919	−	0.419985i
$971$	30.8882	−	19.8506i	0.991249	−	0.637037i	0.0587737	−	0.998271i	$-0.481281\pi$
$971$	30.8882	−	19.8506i	0.991249	−	0.637037i	0.932475	+	0.361234i	$0.117645\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−0.248270	+	1.72675i	−0.00795916	+	0.0553572i
$974$	24.5302	−	7.20271i	0.785998	−	0.230790i
$975$	0.380892	+	0.244784i	0.0121983	+	0.00783937i
$976$	0.204444	+	1.42194i	0.00654409	+	0.0455151i
$977$	9.37241	+	20.5227i	0.299850	+	0.656580i	0.998250	−	0.0591273i	$-0.0188318\pi$
$977$	9.37241	+	20.5227i	0.299850	+	0.656580i	−0.698400	+	0.715707i	$0.746105\pi$
$978$	4.81092	+	10.5344i	0.153836	+	0.336854i
$979$	5.64888	+	39.2888i	0.180539	+	1.25568i
$980$	−1.29551	−	0.832573i	−0.0413835	−	0.0265956i
$981$	−13.5673	+	3.98371i	−0.433169	+	0.127190i
$982$	2.49682	−	17.3658i	0.0796767	−	0.554164i
$983$	−1.40978	+	1.62697i	−0.0449650	+	0.0518923i	−0.777787	−	0.628529i	$-0.783658\pi$
$983$	−1.40978	+	1.62697i	−0.0449650	+	0.0518923i	0.732822	+	0.680421i	$0.238203\pi$
$984$	−4.38958	+	2.82101i	−0.139935	+	0.0899306i
$985$	13.7995	+	15.9255i	0.439688	+	0.507427i
$986$	−1.14046	−	0.334869i	−0.0363196	−	0.0106644i
$987$	1.51469	−	3.31671i	0.0482131	−	0.105572i
$988$	0.593471			0.0188808
$989$	−2.35428	−	3.12677i	−0.0748618	−	0.0994256i
$990$	4.37184			0.138946
$991$	1.13011	−	2.47460i	0.0358992	−	0.0786082i	−0.890833	−	0.454331i	$-0.849878\pi$
$991$	1.13011	−	2.47460i	0.0358992	−	0.0786082i	0.926732	+	0.375723i	$0.122606\pi$
$992$	6.36689	+	1.86949i	0.202149	+	0.0593563i
$993$	−9.30032	−	10.7331i	−0.295137	−	0.340606i
$994$	−2.93289	+	1.88485i	−0.0930256	+	0.0597839i
$995$	−1.81697	+	2.09689i	−0.0576018	+	0.0664760i
$996$	1.37244	−	9.54554i	0.0434875	−	0.302462i
$997$	−51.8758	+	15.2321i	−1.64292	+	0.482405i	−0.967044	−	0.254609i	$-0.918053\pi$
$997$	−51.8758	+	15.2321i	−1.64292	+	0.482405i	−0.675878	+	0.737014i	$0.736235\pi$
$998$	−7.40971	−	4.76193i	−0.234550	−	0.150736i
$999$	−0.305885	−	2.12748i	−0.00967777	−	0.0673103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.h.673.1	yes	30
23.4	even	11	inner	966.2.q.h.211.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.h.211.1	✓	30	23.4	even	11	inner
966.2.q.h.673.1	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.29551 + 0.832573i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.29551 + 0.832573i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.219161 - 1.52430i) q^{10} +(1.17932 + 2.58236i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(-0.0245143 - 0.170501i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-1.47759 + 0.433861i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.74635 + 2.01539i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-2.25620 - 2.60380i) q^{19} +(1.47759 + 0.433861i) q^{20} +(-0.415415 + 0.909632i) q^{21} -2.83890 q^{22} +(3.84724 + 2.86334i) q^{23} +1.00000 q^{24} +(-1.09191 + 2.39095i) q^{25} +(0.165277 + 0.0485297i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(0.291881 - 0.336848i) q^{29} +(0.219161 - 1.52430i) q^{30} +(-6.36689 + 1.86949i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.404018 + 2.81001i) q^{33} +(-1.10781 - 2.42575i) q^{34} +(-0.639729 - 1.40081i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-1.80815 - 1.16203i) q^{37} +(3.30576 - 0.970658i) q^{38} +(0.0245143 - 0.170501i) q^{39} +(-1.00847 + 1.16384i) q^{40} +(-4.38958 + 2.82101i) q^{41} +(-0.654861 - 0.755750i) q^{42} +(-0.783065 - 0.229929i) q^{43} +(1.17932 - 2.58236i) q^{44} -1.53997 q^{45} +(-4.20279 + 2.31010i) q^{46} -3.64621 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-1.72129 - 1.98647i) q^{50} +(-2.24341 + 1.44175i) q^{51} +(-0.112803 + 0.130181i) q^{52} +(-1.90322 + 13.2372i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-3.67782 - 2.36359i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-1.43124 - 3.13397i) q^{57} +(0.185156 + 0.405436i) q^{58} +(0.191349 + 1.33086i) q^{59} +(1.29551 + 0.832573i) q^{60} +(1.37837 - 0.404726i) q^{61} +(0.944356 - 6.56814i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(0.173713 + 0.200476i) q^{65} +(-2.72391 - 0.799811i) q^{66} +(-4.67799 + 10.2434i) q^{67} +2.66674 q^{68} +(2.88471 + 3.83125i) q^{69} +1.53997 q^{70} +(1.44827 - 3.17128i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-6.75250 - 7.79281i) q^{73} +(1.80815 - 1.16203i) q^{74} +(-1.72129 + 1.98647i) q^{75} +(-0.490320 + 3.41025i) q^{76} +(-2.72391 + 0.799811i) q^{77} +(0.144910 + 0.0931277i) q^{78} +(-1.26571 - 8.80318i) q^{79} +(-0.639729 - 1.40081i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.742585 - 5.16479i) q^{82} +(8.11279 + 5.21378i) q^{83} +(0.959493 - 0.281733i) q^{84} +(0.584447 - 4.06492i) q^{85} +(0.534448 - 0.616785i) q^{86} +(0.374959 - 0.240971i) q^{87} +(1.85909 + 2.14550i) q^{88} +(13.4154 + 3.93912i) q^{89} +(0.639729 - 1.40081i) q^{90} +0.172254 q^{91} +(-0.355443 - 4.78264i) q^{92} -6.63568 q^{93} +(1.51469 - 3.31671i) q^{94} +(5.09078 + 1.49479i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(9.45486 - 6.07627i) q^{97} +(0.654861 - 0.755750i) q^{98} +(-0.404018 + 2.81001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

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