LMFDB - Embedded newform 784.2.x.o.557.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.7
Character	$\chi$	$=$	784.557
Dual form			784.2.x.o.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236566 - 1.39429i) q^{2} +(-0.827840 + 0.221819i) q^{3} +(-1.88807 - 0.659683i) q^{4} +(-4.10878 - 1.10095i) q^{5} +(0.113440 + 1.20672i) q^{6} +(-1.36644 + 2.47646i) q^{8} +(-1.96196 + 1.13274i) q^{9} +O(q^{10})$	\(q+(0.236566 - 1.39429i) q^{2} +(-0.827840 + 0.221819i) q^{3} +(-1.88807 - 0.659683i) q^{4} +(-4.10878 - 1.10095i) q^{5} +(0.113440 + 1.20672i) q^{6} +(-1.36644 + 2.47646i) q^{8} +(-1.96196 + 1.13274i) q^{9} +(-2.50703 + 5.46838i) q^{10} +(-0.318576 - 1.18894i) q^{11} +(1.70935 + 0.127301i) q^{12} +(1.73092 + 1.73092i) q^{13} +3.64563 q^{15} +(3.12964 + 2.49106i) q^{16} +(0.931914 - 1.61412i) q^{17} +(1.11523 + 3.00350i) q^{18} +(0.989804 - 3.69400i) q^{19} +(7.03141 + 4.78916i) q^{20} +(-1.73309 + 0.162922i) q^{22} +(1.23305 - 0.711901i) q^{23} +(0.581870 - 2.35321i) q^{24} +(11.3399 + 6.54709i) q^{25} +(2.82287 - 2.00392i) q^{26} +(3.19099 - 3.19099i) q^{27} +(-0.181826 - 0.181826i) q^{29} +(0.862433 - 5.08305i) q^{30} +(-3.23200 + 5.59799i) q^{31} +(4.21362 - 3.77431i) q^{32} +(0.527459 + 0.913587i) q^{33} +(-2.03009 - 1.68120i) q^{34} +(4.45157 - 0.844420i) q^{36} +(0.238000 + 0.0637719i) q^{37} +(-4.91634 - 2.25395i) q^{38} +(-1.81687 - 1.04897i) q^{39} +(8.34086 - 8.67085i) q^{40} +0.440182i q^{41} +(-5.54503 + 5.54503i) q^{43} +(-0.182830 + 2.45496i) q^{44} +(9.30835 - 2.49417i) q^{45} +(-0.700896 - 1.88763i) q^{46} +(3.61427 + 6.26009i) q^{47} +(-3.14340 - 1.36799i) q^{48} +(11.8112 - 14.2623i) q^{50} +(-0.413433 + 1.54295i) q^{51} +(-2.12624 - 4.40996i) q^{52} +(-2.59716 - 9.69274i) q^{53} +(-3.69428 - 5.20404i) q^{54} +5.23583i q^{55} +3.27760i q^{57} +(-0.296532 + 0.210504i) q^{58} +(0.438601 + 1.63688i) q^{59} +(-6.88321 - 2.40496i) q^{60} +(-2.41596 + 9.01647i) q^{61} +(7.04063 + 5.83064i) q^{62} +(-4.26567 - 6.76787i) q^{64} +(-5.20632 - 9.01761i) q^{65} +(1.39858 - 0.519306i) q^{66} +(9.59422 - 2.57076i) q^{67} +(-2.82433 + 2.43281i) q^{68} +(-0.862854 + 0.862854i) q^{69} +11.2912i q^{71} +(-0.124272 - 6.40653i) q^{72} +(8.13092 + 4.69439i) q^{73} +(0.145219 - 0.316754i) q^{74} +(-10.8399 - 2.90454i) q^{75} +(-4.30569 + 6.32158i) q^{76} +(-1.89238 + 2.28509i) q^{78} +(6.52948 + 11.3094i) q^{79} +(-10.1165 - 13.6808i) q^{80} +(1.46441 - 2.53643i) q^{81} +(0.613739 + 0.104132i) q^{82} +(3.06926 + 3.06926i) q^{83} +(-5.60609 + 5.60609i) q^{85} +(6.41960 + 9.04313i) q^{86} +(0.190855 + 0.110190i) q^{87} +(3.37967 + 0.835679i) q^{88} +(5.66084 - 3.26829i) q^{89} +(-1.27554 - 13.5686i) q^{90} +(-2.79771 + 0.530699i) q^{92} +(1.43384 - 5.35117i) q^{93} +(9.58338 - 3.55840i) q^{94} +(-8.13378 + 14.0881i) q^{95} +(-2.65099 + 4.05919i) q^{96} -1.70409 q^{97} +(1.97179 + 1.97179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.236566	−	1.39429i	0.167278	−	0.985910i
$2$	0.236566	−	1.39429i	0.167278	−	0.985910i
$3$	−0.827840	+	0.221819i	−0.477954	+	0.128067i	−0.489750	−	0.871863i	$-0.662912\pi$
$3$	−0.827840	+	0.221819i	−0.477954	+	0.128067i	0.0117959	+	0.999930i	$0.496245\pi$
$4$	−1.88807	−	0.659683i	−0.944036	−	0.329841i
$5$	−4.10878	−	1.10095i	−1.83750	−	0.492358i	−0.838857	−	0.544352i	$-0.816775\pi$
$5$	−4.10878	−	1.10095i	−1.83750	−	0.492358i	−0.998647	+	0.0519945i	$0.983442\pi$
$6$	0.113440	+	1.20672i	0.0463118	+	0.492642i
$7$		0			0
$7$		0			0
$8$	−1.36644	+	2.47646i	−0.483110	+	0.875560i
$9$	−1.96196	+	1.13274i	−0.653987	+	0.377579i
$10$	−2.50703	+	5.46838i	−0.792794	+	1.72925i
$11$	−0.318576	−	1.18894i	−0.0960542	−	0.358479i	0.901123	−	0.433564i	$-0.142744\pi$
$11$	−0.318576	−	1.18894i	−0.0960542	−	0.358479i	−0.997177	+	0.0750845i	$0.976077\pi$
$12$	1.70935	+	0.127301i	0.493448	+	0.0367488i
$13$	1.73092	+	1.73092i	0.480070	+	0.480070i	0.905154	−	0.425084i	$-0.139755\pi$
$13$	1.73092	+	1.73092i	0.480070	+	0.480070i	−0.425084	+	0.905154i	$0.639755\pi$
$14$		0			0
$15$	3.64563			0.941297
$16$	3.12964	+	2.49106i	0.782409	+	0.622765i
$17$	0.931914	−	1.61412i	0.226022	−	0.391482i	−0.730603	−	0.682802i	$-0.760761\pi$
$17$	0.931914	−	1.61412i	0.226022	−	0.391482i	0.956626	+	0.291320i	$0.0940945\pi$
$18$	1.11523	+	3.00350i	0.262862	+	0.707933i
$19$	0.989804	−	3.69400i	0.227077	−	0.847462i	−0.754485	−	0.656317i	$-0.772113\pi$
$19$	0.989804	−	3.69400i	0.227077	−	0.847462i	0.981562	−	0.191145i	$-0.0612199\pi$
$20$	7.03141	+	4.78916i	1.57227	+	1.07089i
$21$		0			0
$22$	−1.73309	+	0.162922i	−0.369496	+	0.0347352i
$23$	1.23305	−	0.711901i	0.257108	−	0.148442i	−0.365906	−	0.930652i	$-0.619241\pi$
$23$	1.23305	−	0.711901i	0.257108	−	0.148442i	0.623015	+	0.782210i	$0.285908\pi$
$24$	0.581870	−	2.35321i	0.118774	−	0.480348i
$25$	11.3399	+	6.54709i	2.26798	+	1.30942i
$26$	2.82287	−	2.00392i	0.553611	−	0.393001i
$27$	3.19099	−	3.19099i	0.614106	−	0.614106i
$28$		0			0
$29$	−0.181826	−	0.181826i	−0.0337642	−	0.0337642i	0.690023	−	0.723787i	$-0.257600\pi$
$29$	−0.181826	−	0.181826i	−0.0337642	−	0.0337642i	−0.723787	+	0.690023i	$0.757600\pi$
$30$	0.862433	−	5.08305i	0.157458	−	0.928034i
$31$	−3.23200	+	5.59799i	−0.580485	+	1.00543i	0.414937	+	0.909850i	$0.363804\pi$
$31$	−3.23200	+	5.59799i	−0.580485	+	1.00543i	−0.995422	+	0.0955792i	$0.969530\pi$
$32$	4.21362	−	3.77431i	0.744869	−	0.667210i
$33$	0.527459	+	0.913587i	0.0918189	+	0.159035i
$34$	−2.03009	−	1.68120i	−0.348157	−	0.288324i
$35$		0			0
$36$	4.45157	−	0.844420i	0.741929	−	0.140737i
$37$	0.238000	+	0.0637719i	0.0391269	+	0.0104840i	0.278329	−	0.960486i	$-0.410219\pi$
$37$	0.238000	+	0.0637719i	0.0391269	+	0.0104840i	−0.239202	+	0.970970i	$0.576886\pi$
$38$	−4.91634	−	2.25395i	−0.797536	−	0.365639i
$39$	−1.81687	−	1.04897i	−0.290933	−	0.167970i
$40$	8.34086	−	8.67085i	1.31881	−	1.37098i
$41$			0.440182i			0.0687448i	0.999409	+	0.0343724i	$0.0109432\pi$
$41$			0.440182i			0.0687448i	−0.999409	+	0.0343724i	$0.989057\pi$
$42$		0			0
$43$	−5.54503	+	5.54503i	−0.845609	+	0.845609i	−0.989582	−	0.143972i	$-0.954012\pi$
$43$	−5.54503	+	5.54503i	−0.845609	+	0.845609i	0.143972	+	0.989582i	$0.454012\pi$
$44$	−0.182830	+	2.45496i	−0.0275626	+	0.370100i
$45$	9.30835	−	2.49417i	1.38761	−	0.371808i
$46$	−0.700896	−	1.88763i	−0.103341	−	0.278317i
$47$	3.61427	+	6.26009i	0.527195	+	0.913128i	0.999498	+	0.0316918i	$0.0100895\pi$
$47$	3.61427	+	6.26009i	0.527195	+	0.913128i	−0.472303	+	0.881436i	$0.656577\pi$
$48$	−3.14340	−	1.36799i	−0.453711	−	0.197452i
$49$		0			0
$50$	11.8112	−	14.2623i	1.67035	−	2.01699i
$51$	−0.413433	+	1.54295i	−0.0578921	+	0.216056i
$52$	−2.12624	−	4.40996i	−0.294857	−	0.611551i
$53$	−2.59716	−	9.69274i	−0.356747	−	1.33140i	−0.878271	−	0.478163i	$-0.841303\pi$
$53$	−2.59716	−	9.69274i	−0.356747	−	1.33140i	0.521524	−	0.853237i	$-0.325364\pi$
$54$	−3.69428	−	5.20404i	−0.502727	−	0.708180i
$55$			5.23583i			0.706000i
$56$		0			0
$57$			3.27760i			0.434129i
$58$	−0.296532	+	0.210504i	−0.0389365	+	0.0276405i
$59$	0.438601	+	1.63688i	0.0571010	+	0.213104i	0.988581	−	0.150688i	$-0.0481488\pi$
$59$	0.438601	+	1.63688i	0.0571010	+	0.213104i	−0.931480	+	0.363791i	$0.881482\pi$
$60$	−6.88321	−	2.40496i	−0.888619	−	0.310479i
$61$	−2.41596	+	9.01647i	−0.309331	+	1.15444i	0.619821	+	0.784743i	$0.287205\pi$
$61$	−2.41596	+	9.01647i	−0.309331	+	1.15444i	−0.929152	+	0.369697i	$0.879461\pi$
$62$	7.04063	+	5.83064i	0.894161	+	0.740492i
$63$		0			0
$64$	−4.26567	−	6.76787i	−0.533209	−	0.845984i
$65$	−5.20632	−	9.01761i	−0.645765	−	1.11850i
$66$	1.39858	−	0.519306i	0.172153	−	0.0639222i
$67$	9.59422	−	2.57076i	1.17212	−	0.314069i	0.380324	−	0.924853i	$-0.375813\pi$
$67$	9.59422	−	2.57076i	1.17212	−	0.314069i	0.791797	+	0.610785i	$0.209146\pi$
$68$	−2.82433	+	2.43281i	−0.342500	+	0.295022i
$69$	−0.862854	+	0.862854i	−0.103875	+	0.103875i
$70$		0			0
$71$			11.2912i			1.34002i	0.742352	+	0.670010i	$0.233710\pi$
$71$			11.2912i			1.34002i	−0.742352	+	0.670010i	$0.766290\pi$
$72$	−0.124272	−	6.40653i	−0.0146456	−	0.755017i
$73$	8.13092	+	4.69439i	0.951652	+	0.549437i	0.893594	−	0.448877i	$-0.148176\pi$
$73$	8.13092	+	4.69439i	0.951652	+	0.549437i	0.0580583	+	0.998313i	$0.481509\pi$
$74$	0.145219	−	0.316754i	0.0168814	−	0.0368219i
$75$	−10.8399	−	2.90454i	−1.25168	−	0.335388i
$76$	−4.30569	+	6.32158i	−0.493897	+	0.725135i
$77$		0			0
$78$	−1.89238	+	2.28509i	−0.214270	+	0.258736i
$79$	6.52948	+	11.3094i	0.734624	+	1.27241i	0.954888	+	0.296966i	$0.0959747\pi$
$79$	6.52948	+	11.3094i	0.734624	+	1.27241i	−0.220264	+	0.975440i	$0.570692\pi$
$80$	−10.1165	−	13.6808i	−1.13106	−	1.52956i
$81$	1.46441	−	2.53643i	0.162712	−	0.281825i
$82$	0.613739	+	0.104132i	0.0677762	+	0.0114995i
$83$	3.06926	+	3.06926i	0.336895	+	0.336895i	0.855198	−	0.518302i	$-0.173436\pi$
$83$	3.06926	+	3.06926i	0.336895	+	0.336895i	−0.518302	+	0.855198i	$0.673436\pi$
$84$		0			0
$85$	−5.60609	+	5.60609i	−0.608066	+	0.608066i
$86$	6.41960	+	9.04313i	0.692243	+	0.975146i
$87$	0.190855	+	0.110190i	0.0204618	+	0.0118137i
$88$	3.37967	+	0.835679i	0.360274	+	0.0890837i
$89$	5.66084	−	3.26829i	0.600047	−	0.346438i	−0.169013	−	0.985614i	$-0.554058\pi$
$89$	5.66084	−	3.26829i	0.600047	−	0.346438i	0.769060	+	0.639176i	$0.220725\pi$
$90$	−1.27554	−	13.5686i	−0.134454	−	1.43025i
$91$		0			0
$92$	−2.79771	+	0.530699i	−0.291682	+	0.0553292i
$93$	1.43384	−	5.35117i	0.148682	−	0.554890i
$94$	9.58338	−	3.55840i	0.988450	−	0.367021i
$95$	−8.13378	+	14.0881i	−0.834508	+	1.44541i
$96$	−2.65099	+	4.05919i	−0.270565	+	0.414289i
$97$	−1.70409			−0.173024			−0.0865122	−	0.996251i	$-0.527572\pi$
$97$	−1.70409			−0.173024			−0.0865122	+	0.996251i	$0.527572\pi$
$98$		0			0
$99$	1.97179	+	1.97179i	0.198172	+	0.198172i
$100$	−17.0915	−	19.8421i	−1.70915	−	1.98421i
$101$	−0.632838	−	2.36178i	−0.0629697	−	0.235006i	0.927267	−	0.374400i	$-0.122151\pi$
$101$	−0.632838	−	2.36178i	−0.0629697	−	0.235006i	−0.990237	+	0.139394i	$0.955485\pi$
$102$	2.05351	+	0.941454i	0.203328	+	0.0932178i
$103$	−12.6328	+	7.29353i	−1.24474	+	0.718653i	−0.970056	−	0.242881i	$-0.921908\pi$
$103$	−12.6328	+	7.29353i	−1.24474	+	0.718653i	−0.274687	+	0.961534i	$0.588574\pi$
$104$	−6.65174	+	1.92134i	−0.652257	+	0.188403i
$105$		0			0
$106$	−14.1289	+	1.32821i	−1.37232	+	0.129007i
$107$	−4.80256	−	1.28684i	−0.464281	−	0.124404i	0.0190927	−	0.999818i	$-0.493922\pi$
$107$	−4.80256	−	1.28684i	−0.464281	−	0.124404i	−0.483374	+	0.875414i	$0.660589\pi$
$108$	−8.12986	+	3.91978i	−0.782296	+	0.377181i
$109$	−9.76613	+	2.61683i	−0.935426	+	0.250647i	−0.694167	−	0.719814i	$-0.744227\pi$
$109$	−9.76613	+	2.61683i	−0.935426	+	0.250647i	−0.241259	+	0.970461i	$0.577560\pi$
$110$	7.30026	+	1.23862i	0.696052	+	0.118098i
$111$	−0.211172			−0.0200435
$112$		0			0
$113$	5.22780			0.491791			0.245895	−	0.969296i	$-0.420918\pi$
$113$	5.22780			0.491791			0.245895	+	0.969296i	$0.420918\pi$
$114$	4.56991	+	0.775370i	0.428012	+	0.0726200i
$115$	−5.85009	+	1.56753i	−0.545524	+	0.146173i
$116$	0.223353	+	0.463248i	0.0207378	+	0.0430115i
$117$	−5.35667	−	1.43532i	−0.495224	−	0.132695i
$118$	2.38604	−	0.224305i	0.219653	−	0.0206489i
$119$		0			0
$120$	−4.98154	+	9.02824i	−0.454750	+	0.824162i
$121$	8.21419	−	4.74247i	0.746745	−	0.431133i
$122$	12.0000	+	5.50153i	1.08643	+	0.498085i
$123$	−0.0976407	−	0.364400i	−0.00880396	−	0.0328568i
$124$	9.79516	−	8.43732i	0.879631	−	0.757694i
$125$	−24.3460	−	24.3460i	−2.17757	−	2.17757i
$126$		0			0
$127$	−1.20463			−0.106893			−0.0534467	−	0.998571i	$-0.517021\pi$
$127$	−1.20463			−0.106893			−0.0534467	+	0.998571i	$0.517021\pi$
$128$	−10.4455	+	4.34652i	−0.923257	+	0.384182i
$129$	3.36041	−	5.82039i	0.295867	−	0.512457i
$130$	−13.8048	+	5.12584i	−1.21076	+	0.449566i
$131$	0.809509	−	3.02113i	0.0707272	−	0.263957i	−0.921503	−	0.388370i	$-0.873038\pi$
$131$	0.809509	−	3.02113i	0.0707272	−	0.263957i	0.992231	+	0.124413i	$0.0397048\pi$
$132$	−0.393204	−	2.07287i	−0.0342240	−	0.180421i
$133$		0			0
$134$	−1.31471	−	13.9853i	−0.113574	−	1.20814i
$135$	−16.6242	+	9.59798i	−1.43078	+	0.826063i
$136$	2.72390	+	4.51345i	0.233572	+	0.387025i
$137$	0.286357	+	0.165329i	0.0244652	+	0.0141250i	0.512183	−	0.858877i	$-0.328837\pi$
$137$	0.286357	+	0.165329i	0.0244652	+	0.0141250i	−0.487718	+	0.873001i	$0.662170\pi$
$138$	0.998944	+	1.40719i	0.0850357	+	0.119788i
$139$	2.41295	−	2.41295i	0.204663	−	0.204663i	−0.597331	−	0.801995i	$-0.703772\pi$
$139$	2.41295	−	2.41295i	0.204663	−	0.204663i	0.801995	+	0.597331i	$0.203772\pi$
$140$		0			0
$141$	−4.38064	−	4.38064i	−0.368917	−	0.368917i
$142$	15.7432	+	2.67112i	1.32114	+	0.224155i
$143$	1.50653	−	2.60939i	0.125982	−	0.218208i
$144$	−8.96194	−	1.34230i	−0.746828	−	0.111858i
$145$	0.546903	+	0.947264i	0.0454179	+	0.0786660i
$146$	8.46883	−	10.2263i	0.700885	−	0.846335i
$147$		0			0
$148$	−0.407292	−	0.277410i	−0.0334792	−	0.0228030i
$149$	−2.36381	−	0.633381i	−0.193651	−	0.0518886i	0.160690	−	0.987005i	$-0.448628\pi$
$149$	−2.36381	−	0.633381i	−0.193651	−	0.0518886i	−0.354341	+	0.935116i	$0.615295\pi$
$150$	−6.61412	+	14.4268i	−0.540041	+	1.17794i
$151$	11.4320	+	6.60029i	0.930326	+	0.537124i	0.886915	−	0.461934i	$-0.152844\pi$
$151$	11.4320	+	6.60029i	0.930326	+	0.537124i	0.0434110	+	0.999057i	$0.486177\pi$
$152$	7.79552	+	7.49884i	0.632300	+	0.608236i
$153$			4.22246i			0.341365i
$154$		0			0
$155$	19.4427	−	19.4427i	1.56167	−	1.56167i
$156$	2.73840	+	3.17910i	0.219248	+	0.254532i
$157$	3.45433	−	0.925585i	0.275685	−	0.0738697i	−0.118327	−	0.992975i	$-0.537753\pi$
$157$	3.45433	−	0.925585i	0.275685	−	0.0738697i	0.394013	+	0.919105i	$0.371087\pi$
$158$	17.3132	−	6.42855i	1.37736	−	0.511428i
$159$	4.30007	+	7.44794i	0.341018	+	0.590660i
$160$	−21.4682	+	10.8689i	−1.69721	+	0.859259i
$161$		0			0
$162$	−3.19008	−	2.64184i	−0.250636	−	0.207562i
$163$	−2.90781	+	10.8521i	−0.227757	+	0.850001i	0.753524	+	0.657420i	$0.228352\pi$
$163$	−2.90781	+	10.8521i	−0.227757	+	0.850001i	−0.981281	+	0.192581i	$0.938314\pi$
$164$	0.290380	−	0.831095i	0.0226749	−	0.0648976i
$165$	−1.16141	−	4.33443i	−0.0904155	−	0.337435i
$166$	5.00552	−	3.55335i	0.388504	−	0.275793i
$167$			11.7171i			0.906693i	0.891334	+	0.453346i	$0.149770\pi$
$167$			11.7171i			0.906693i	−0.891334	+	0.453346i	$0.850230\pi$
$168$		0			0
$169$		−	7.00785i		−	0.539065i
$170$	6.49029	+	9.14271i	0.497782	+	0.701214i
$171$	2.24238	+	8.36867i	0.171479	+	0.639968i
$172$	14.1274	−	6.81146i	1.07720	−	0.519369i
$173$	−2.83415	+	10.5772i	−0.215476	+	0.804169i	0.770522	+	0.637413i	$0.219996\pi$
$173$	−2.83415	+	10.5772i	−0.215476	+	0.804169i	−0.985998	+	0.166755i	$0.946671\pi$
$174$	0.198787	−	0.240040i	0.0150700	−	0.0181974i
$175$		0			0
$176$	1.96469	−	4.51454i	0.148094	−	0.340296i
$177$	−0.726183	−	1.25779i	−0.0545833	−	0.0945410i
$178$	−3.21776	−	8.66600i	−0.241182	−	0.649544i
$179$	−16.1464	+	4.32641i	−1.20684	+	0.323371i	−0.805520	−	0.592568i	$-0.798114\pi$
$179$	−16.1464	+	4.32641i	−1.20684	+	0.323371i	−0.401317	+	0.915939i	$0.631447\pi$
$180$	−19.2202	−	1.43140i	−1.43259	−	0.106690i
$181$	15.9791	−	15.9791i	1.18772	−	1.18772i	0.210025	−	0.977696i	$-0.432646\pi$
$181$	15.9791	−	15.9791i	1.18772	−	1.18772i	0.977696	−	0.210025i	$-0.0673544\pi$
$182$		0			0
$183$		−	8.00010i		−	0.591385i
$184$	0.0781022	+	4.02636i	0.00575777	+	0.296827i
$185$	−0.907680	−	0.524050i	−0.0667340	−	0.0385289i
$186$	−7.12186	−	3.26509i	−0.522200	−	0.239408i
$187$	−2.21598	−	0.593770i	−0.162048	−	0.0434208i
$188$	−2.69432	−	14.2038i	−0.196503	−	1.03592i
$189$		0			0
$190$	17.7187	+	14.6736i	1.28545	+	1.06454i
$191$	4.97963	+	8.62497i	0.360313	+	0.624081i	0.988012	−	0.154375i	$-0.0493364\pi$
$191$	4.97963	+	8.62497i	0.360313	+	0.624081i	−0.627699	+	0.778456i	$0.716003\pi$
$192$	5.03254	+	4.65651i	0.363192	+	0.336054i
$193$	−4.02312	+	6.96824i	−0.289590	+	0.501585i	−0.973712	−	0.227783i	$-0.926852\pi$
$193$	−4.02312	+	6.96824i	−0.289590	+	0.501585i	0.684122	+	0.729368i	$0.260186\pi$
$194$	−0.403131	+	2.37599i	−0.0289431	+	0.170586i
$195$	6.31028	+	6.31028i	0.451889	+	0.451889i
$196$		0			0
$197$	6.01951	−	6.01951i	0.428873	−	0.428873i	−0.459372	−	0.888244i	$-0.651925\pi$
$197$	6.01951	−	6.01951i	0.428873	−	0.428873i	0.888244	+	0.459372i	$0.151925\pi$
$198$	3.21570	−	2.28278i	0.228530	−	0.162230i
$199$	−12.7812	−	7.37922i	−0.906035	−	0.523099i	−0.0268814	−	0.999639i	$-0.508558\pi$
$199$	−12.7812	−	7.37922i	−0.906035	−	0.523099i	−0.879153	+	0.476539i	$0.841891\pi$
$200$	−31.7089	+	19.1365i	−2.24216	+	1.35316i
$201$	−7.37224	+	4.25636i	−0.519998	+	0.300221i
$202$	−3.44271	+	0.323639i	−0.242228	+	0.0227712i
$203$		0			0
$204$	1.79845	−	2.64047i	0.125917	−	0.184870i
$205$	0.484616	−	1.80861i	0.0338470	−	0.126319i
$206$	7.18079	+	19.3391i	0.500309	+	1.34742i
$207$	−1.61279	+	2.79344i	−0.112097	+	0.194158i
$208$	1.10533	+	9.72896i	0.0766406	+	0.674582i
$209$	−4.70727			−0.325609
$210$		0			0
$211$	14.5016	+	14.5016i	0.998329	+	0.998329i	0.999999	−	0.00166940i	$-0.000531387\pi$
$211$	14.5016	+	14.5016i	0.998329	+	0.998329i	−0.00166940	+	0.999999i	$0.500531\pi$
$212$	−1.49050	+	20.0139i	−0.102368	+	1.37456i
$213$	−2.50461	−	9.34732i	−0.171613	−	0.640468i
$214$	−2.93035	+	6.39173i	−0.200315	+	0.436930i
$215$	28.8881	−	16.6786i	1.97015	−	1.13747i
$216$	3.54205	+	12.2627i	0.241006	+	0.834368i
$217$		0			0
$218$	1.33827	+	14.2358i	0.0906391	+	0.964173i
$219$	−7.77241	−	2.08261i	−0.525211	−	0.140730i
$220$	3.45399	−	9.88563i	0.232868	−	0.666489i
$221$	4.40698	−	1.18085i	0.296445	−	0.0794323i
$222$	−0.0499561	+	0.294434i	−0.00335284	+	0.0197611i
$223$	−4.72461			−0.316383			−0.158192	−	0.987408i	$-0.550566\pi$
$223$	−4.72461			−0.316383			−0.158192	+	0.987408i	$0.550566\pi$
$224$		0			0
$225$	−29.6646			−1.97764
$226$	1.23672	−	7.28906i	0.0822656	−	0.484861i
$227$	−15.9081	+	4.26257i	−1.05586	+	0.282917i	−0.744671	−	0.667431i	$-0.767394\pi$
$227$	−15.9081	+	4.26257i	−1.05586	+	0.282917i	−0.311189	+	0.950348i	$0.600727\pi$
$228$	2.16218	−	6.18834i	0.143194	−	0.409833i
$229$	13.3085	+	3.56601i	0.879453	+	0.235649i	0.670171	−	0.742207i	$-0.266221\pi$
$229$	13.3085	+	3.56601i	0.879453	+	0.235649i	0.209282	+	0.977855i	$0.432887\pi$
$230$	0.801648	+	8.52753i	0.0528591	+	0.562289i
$231$		0			0
$232$	0.698739	−	0.201830i	0.0458745	−	0.0132508i
$233$	12.0806	−	6.97475i	0.791428	−	0.456931i	−0.0490370	−	0.998797i	$-0.515615\pi$
$233$	12.0806	−	6.97475i	0.791428	−	0.456931i	0.840465	+	0.541866i	$0.182282\pi$
$234$	−3.26845	+	7.12919i	−0.213665	+	0.466050i
$235$	−7.95822	−	29.7005i	−0.519137	−	1.93745i
$236$	0.251712	−	3.37989i	0.0163851	−	0.220012i
$237$	−7.91401	−	7.91401i	−0.514070	−	0.514070i
$238$		0			0
$239$	−23.1794			−1.49935			−0.749674	−	0.661807i	$-0.769790\pi$
$239$	−23.1794			−1.49935			−0.749674	+	0.661807i	$0.769790\pi$
$240$	11.4095	+	9.08147i	0.736479	+	0.586207i
$241$	−2.09690	+	3.63195i	−0.135073	+	0.233954i	−0.925626	−	0.378441i	$-0.876460\pi$
$241$	−2.09690	+	3.63195i	−0.135073	+	0.233954i	0.790552	+	0.612395i	$0.209794\pi$
$242$	−4.66916	−	12.5748i	−0.300145	−	0.808342i
$243$	−4.15362	+	15.5015i	−0.266455	+	0.994422i
$244$	10.5095	−	15.4300i	0.672803	−	0.987804i
$245$		0			0
$246$	−0.531177	+	0.0499343i	−0.0338666	+	0.00318370i
$247$	8.10728	−	4.68074i	0.515854	−	0.297828i
$248$	−9.44684	−	15.6532i	−0.599875	−	0.993982i
$249$	−3.22168	−	1.86004i	−0.204166	−	0.117875i
$250$	−39.7048	+	28.1859i	−2.51115	+	1.78263i
$251$	16.5937	−	16.5937i	1.04739	−	1.04739i	0.0485679	−	0.998820i	$-0.484534\pi$
$251$	16.5937	−	16.5937i	1.04739	−	1.04739i	0.998820	−	0.0485679i	$-0.0154657\pi$
$252$		0			0
$253$	−1.23923	−	1.23923i	−0.0779095	−	0.0779095i
$254$	−0.284974	+	1.67960i	−0.0178809	+	0.105387i
$255$	3.39741	−	5.88449i	0.212754	−	0.368501i
$256$	3.58925	+	15.5922i	0.224328	+	0.974514i
$257$	−5.52727	−	9.57351i	−0.344782	−	0.597179i	0.640532	−	0.767931i	$-0.278714\pi$
$257$	−5.52727	−	9.57351i	−0.344782	−	0.597179i	−0.985314	+	0.170752i	$0.945380\pi$
$258$	−7.32034	−	6.06228i	−0.455745	−	0.377421i
$259$		0			0
$260$	3.88115	+	20.4604i	0.240699	+	1.26890i
$261$	0.562697	+	0.150774i	0.0348301	+	0.00933269i
$262$	−4.02082	−	1.84339i	−0.248407	−	0.113885i
$263$	−14.1936	−	8.19466i	−0.875213	−	0.505304i	−0.00613562	−	0.999981i	$-0.501953\pi$
$263$	−14.1936	−	8.19466i	−0.875213	−	0.505304i	−0.869077	+	0.494677i	$0.835286\pi$
$264$	−2.98320	+	0.0578673i	−0.183603	+	0.00356148i
$265$			42.6847i			2.62210i
$266$		0			0
$267$	−3.96130	+	3.96130i	−0.242428	+	0.242428i
$268$	−19.8105	−	1.47536i	−1.21012	−	0.0901217i
$269$	1.24494	−	0.333581i	0.0759055	−	0.0203388i	−0.220666	−	0.975349i	$-0.570823\pi$
$269$	1.24494	−	0.333581i	0.0759055	−	0.0203388i	0.296572	+	0.955011i	$0.404157\pi$
$270$	9.44962	+	25.4495i	0.575085	+	1.54880i
$271$	−10.0688	−	17.4397i	−0.611639	−	1.05939i	−0.990964	−	0.134126i	$-0.957177\pi$
$271$	−10.0688	−	17.4397i	−0.611639	−	1.05939i	0.379326	−	0.925263i	$-0.376156\pi$
$272$	6.93742	−	2.73016i	0.420643	−	0.165540i
$273$		0			0
$274$	0.298258	−	0.360153i	0.0180184	−	0.0217577i
$275$	4.17149	−	15.5682i	0.251550	−	0.938798i
$276$	2.19834	−	1.05992i	0.132325	−	0.0637997i
$277$	8.35382	+	31.1769i	0.501932	+	1.87324i	0.487100	+	0.873346i	$0.338055\pi$
$277$	8.35382	+	31.1769i	0.501932	+	1.87324i	0.0148319	+	0.999890i	$0.495279\pi$
$278$	−2.79352	−	3.93516i	−0.167544	−	0.236015i
$279$		−	14.6441i		−	0.876717i
$280$		0			0
$281$			13.6466i			0.814089i	0.913408	+	0.407044i	$0.133441\pi$
$281$			13.6466i			0.814089i	−0.913408	+	0.407044i	$0.866559\pi$
$282$	−7.14419	+	5.07156i	−0.425430	+	0.302007i
$283$	4.86306	+	18.1492i	0.289079	+	1.07886i	0.945807	+	0.324730i	$0.105273\pi$
$283$	4.86306	+	18.1492i	0.289079	+	1.07886i	−0.656728	+	0.754128i	$0.728060\pi$
$284$	7.44862	−	21.3186i	0.441994	−	1.26503i
$285$	3.60846	−	13.4669i	0.213747	−	0.797713i
$286$	−3.28184	−	2.71783i	−0.194059	−	0.160709i
$287$		0			0
$288$	−3.99164	+	12.1780i	−0.235210	+	0.717594i
$289$	6.76307	+	11.7140i	0.397828	+	0.689058i
$290$	1.45014	−	0.538449i	0.0851550	−	0.0316188i
$291$	1.41072	−	0.378000i	0.0826977	−	0.0221588i
$292$	−12.2550	−	14.2272i	−0.717167	−	0.832582i
$293$	−2.19433	+	2.19433i	−0.128194	+	0.128194i	−0.768293	−	0.640099i	$-0.778893\pi$
$293$	−2.19433	+	2.19433i	−0.128194	+	0.128194i	0.640099	+	0.768293i	$0.278893\pi$
$294$		0			0
$295$		−	7.20847i		−	0.419693i
$296$	−0.483141	+	0.502256i	−0.0280820	+	0.0291930i
$297$	−4.81047	−	2.77733i	−0.279132	−	0.161157i
$298$	−1.44231	+	3.14599i	−0.0835510	+	0.182242i
$299$	3.36655	+	0.902063i	0.194692	+	0.0521677i
$300$	18.5504	+	12.6349i	1.07101	+	0.729475i
$301$		0			0
$302$	11.9071	−	14.3781i	0.685178	−	0.827368i
$303$	1.04778	+	1.81480i	0.0601932	+	0.104258i
$304$	12.2997	−	9.09522i	0.705436	−	0.521646i
$305$	19.8533	−	34.3869i	1.13680	−	1.96899i
$306$	5.88732	+	0.998891i	0.336555	+	0.0571028i
$307$	8.28029	+	8.28029i	0.472581	+	0.472581i	0.902749	−	0.430168i	$-0.141546\pi$
$307$	8.28029	+	8.28029i	0.472581	+	0.472581i	−0.430168	+	0.902749i	$0.641546\pi$
$308$		0			0
$309$	8.84007	−	8.84007i	0.502894	−	0.502894i
$310$	−22.5092	−	31.7082i	−1.27844	−	1.80090i
$311$	7.36500	+	4.25218i	0.417631	+	0.241119i	0.694063	−	0.719914i	$-0.255819\pi$
$311$	7.36500	+	4.25218i	0.417631	+	0.241119i	−0.276432	+	0.961033i	$0.589152\pi$
$312$	5.08039	−	3.06605i	0.287620	−	0.173581i
$313$	14.1001	−	8.14069i	0.796984	−	0.460139i	−0.0454317	−	0.998967i	$-0.514466\pi$
$313$	14.1001	−	8.14069i	0.796984	−	0.460139i	0.842415	+	0.538829i	$0.181133\pi$
$314$	−0.473353	−	5.03529i	−0.0267128	−	0.284158i
$315$		0			0
$316$	−4.86752	−	25.6603i	−0.273819	−	1.44351i
$317$	−5.85666	+	21.8574i	−0.328943	+	1.22763i	0.581345	+	0.813657i	$0.302526\pi$
$317$	−5.85666	+	21.8574i	−0.328943	+	1.22763i	−0.910288	+	0.413975i	$0.864140\pi$
$318$	11.4018	−	4.23360i	0.639382	−	0.237408i
$319$	−0.158255	+	0.274106i	−0.00886058	+	0.0153470i
$320$	10.0757	+	32.5040i	0.563247	+	1.81703i
$321$	4.26120			0.237837
$322$		0			0
$323$	−5.04015	−	5.04015i	−0.280442	−	0.280442i
$324$	−4.43815	+	3.82292i	−0.246564	+	0.212384i
$325$	8.29595	+	30.9609i	0.460177	+	1.71740i
$326$	14.4430	+	6.62156i	0.799926	+	0.366734i
$327$	7.50434	−	4.33263i	0.414991	−	0.239595i
$328$	−1.09009	−	0.601483i	−0.0601902	−	0.0332113i
$329$		0			0
$330$	−6.31820	+	0.593955i	−0.347805	+	0.0326961i
$331$	11.2314	+	3.00945i	0.617334	+	0.165414i	0.553915	−	0.832573i	$-0.313133\pi$
$331$	11.2314	+	3.00945i	0.617334	+	0.165414i	0.0634183	+	0.997987i	$0.479800\pi$
$332$	−3.77025	−	7.81973i	−0.206919	−	0.429164i
$333$	−0.539183	+	0.144474i	−0.0295470	+	0.00791711i
$334$	16.3369	+	2.77186i	0.893917	+	0.151670i
$335$	−42.2509			−2.30841
$336$		0			0
$337$	15.7590			0.858445			0.429223	−	0.903199i	$-0.358788\pi$
$337$	15.7590			0.858445			0.429223	+	0.903199i	$0.358788\pi$
$338$	−9.77095	−	1.65782i	−0.531470	−	0.0901736i
$339$	−4.32779	+	1.15963i	−0.235053	+	0.0629823i
$340$	14.2829	−	6.88646i	0.774602	−	0.373471i
$341$	7.68532	+	2.05928i	0.416183	+	0.111516i
$342$	12.1988	−	1.14677i	0.659635	−	0.0620104i
$343$		0			0
$344$	−6.15506	−	21.3090i	−0.331859	−	1.14890i
$345$	4.49523	−	2.59533i	0.242015	−	0.139728i
$346$	14.0772	+	6.45382i	0.756793	+	0.346960i
$347$	3.95167	+	14.7478i	0.212137	+	0.791706i	0.987155	+	0.159766i	$0.0510741\pi$
$347$	3.95167	+	14.7478i	0.212137	+	0.791706i	−0.775018	+	0.631939i	$0.782259\pi$
$348$	−0.287658	−	0.333952i	−0.0154201	−	0.0179017i
$349$	6.62124	+	6.62124i	0.354427	+	0.354427i	0.861754	−	0.507327i	$-0.169366\pi$
$349$	6.62124	+	6.62124i	0.354427	+	0.354427i	−0.507327	+	0.861754i	$0.669366\pi$
$350$		0			0
$351$	11.0467			0.589628
$352$	−5.82979	−	3.80734i	−0.310729	−	0.202932i
$353$	10.9032	−	18.8849i	0.580319	−	1.00514i	−0.415123	−	0.909765i	$-0.636261\pi$
$353$	10.9032	−	18.8849i	0.580319	−	1.00514i	0.995441	−	0.0953759i	$-0.0304053\pi$
$354$	−1.92551	+	0.714958i	−0.102339	+	0.0379996i
$355$	12.4310	−	46.3931i	0.659769	−	2.46229i
$356$	−12.8441	+	2.43640i	−0.680736	+	0.129129i
$357$		0			0
$358$	2.21257	+	23.5362i	0.116938	+	1.24393i
$359$	29.8216	−	17.2175i	1.57392	−	0.908704i	0.578241	−	0.815866i	$-0.303739\pi$
$359$	29.8216	−	17.2175i	1.57392	−	0.908704i	0.995681	−	0.0928386i	$-0.0295941\pi$
$360$	−6.54263	+	26.4599i	−0.344827	+	1.39456i
$361$	3.78856	+	2.18733i	0.199398	+	0.115123i
$362$	−18.4994	−	26.0596i	−0.972306	−	1.36966i
$363$	−5.74807	+	5.74807i	−0.301695	+	0.301695i
$364$		0			0
$365$	−28.2399	−	28.2399i	−1.47815	−	1.47815i
$366$	−11.1544	−	1.89256i	−0.583052	−	0.0989255i
$367$	1.65812	−	2.87195i	0.0865533	−	0.149915i	−0.819499	−	0.573081i	$-0.805748\pi$
$367$	1.65812	−	2.87195i	0.0865533	−	0.149915i	0.906052	+	0.423166i	$0.139081\pi$
$368$	5.63238	+	0.843605i	0.293608	+	0.0439759i
$369$	−0.498611	−	0.863619i	−0.0259566	−	0.0449582i
$370$	−0.945402	+	1.14159i	−0.0491491	+	0.0593487i
$371$		0			0
$372$	−6.23727	+	9.15751i	−0.323387	+	0.474795i
$373$	−22.4918	−	6.02667i	−1.16458	−	0.312049i	−0.375789	−	0.926705i	$-0.622628\pi$
$373$	−22.4918	−	6.02667i	−1.16458	−	0.312049i	−0.788795	+	0.614656i	$0.789295\pi$
$374$	−1.35211	+	2.94925i	−0.0699160	+	0.152502i
$375$	25.5550	+	14.7542i	1.31966	+	0.761903i
$376$	−20.4415	+	0.396519i	−1.05419	+	0.0204489i
$377$		−	0.629452i		−	0.0324184i
$378$		0			0
$379$	2.77271	−	2.77271i	0.142425	−	0.142425i	−0.632299	−	0.774724i	$-0.717889\pi$
$379$	2.77271	−	2.77271i	0.142425	−	0.142425i	0.774724	+	0.632299i	$0.217889\pi$
$380$	24.6509	−	21.2337i	1.26456	−	1.08927i
$381$	0.997239	−	0.267209i	0.0510901	−	0.0136895i
$382$	13.2037	−	4.90266i	0.675560	−	0.250842i
$383$	10.6953	+	18.5248i	0.546504	+	0.946572i	0.998511	+	0.0545578i	$0.0173749\pi$
$383$	10.6953	+	18.5248i	0.546504	+	0.946572i	−0.452007	+	0.892014i	$0.649292\pi$
$384$	7.68304	−	5.91523i	0.392073	−	0.301860i
$385$		0			0
$386$	8.76400	+	7.25783i	0.446076	+	0.369414i
$387$	4.59806	−	17.1602i	0.233733	−	0.872302i
$388$	3.21745	+	1.12416i	0.163341	+	0.0570706i
$389$	−6.51295	−	24.3067i	−0.330220	−	1.23240i	−0.908959	−	0.416885i	$-0.863122\pi$
$389$	−6.51295	−	24.3067i	−0.330220	−	1.23240i	0.578740	−	0.815512i	$-0.303545\pi$
$390$	10.2911	−	7.30554i	0.521112	−	0.369931i
$391$		−	2.65372i		−	0.134204i
$392$		0			0
$393$			2.68058i			0.135217i
$394$	−6.96892	−	9.81695i	−0.351089	−	0.494571i
$395$	−14.3772	−	53.6564i	−0.723395	−	2.69975i
$396$	−2.42213	−	5.02364i	−0.121717	−	0.252448i
$397$	−0.101204	+	0.377699i	−0.00507929	+	0.0189562i	−0.968419	−	0.249328i	$-0.919790\pi$
$397$	−0.101204	+	0.377699i	−0.00507929	+	0.0189562i	0.963340	+	0.268285i	$0.0864568\pi$
$398$	−13.3124	+	16.0750i	−0.667288	+	0.805765i
$399$		0			0
$400$	19.1806	+	48.7384i	0.959028	+	2.43692i
$401$	−9.92701	−	17.1941i	−0.495731	−	0.858631i	0.504257	−	0.863554i	$-0.331766\pi$
$401$	−9.92701	−	17.1941i	−0.495731	−	0.858631i	−0.999988	+	0.00492242i	$0.998433\pi$
$402$	4.19057	+	11.2859i	0.209007	+	0.562891i
$403$	−15.2840	+	4.09534i	−0.761350	+	0.204003i
$404$	−0.363184	+	4.87669i	−0.0180691	+	0.242624i
$405$	−8.80940	+	8.80940i	−0.437743	+	0.437743i
$406$		0			0
$407$		−	0.303284i		−	0.0150332i
$408$	−3.25612	−	3.13220i	−0.161202	−	0.155067i
$409$	−30.4501	−	17.5804i	−1.50566	−	0.869295i	−0.999978	−	0.00657643i	$-0.997907\pi$
$409$	−30.4501	−	17.5804i	−1.50566	−	0.869295i	−0.505685	−	0.862718i	$-0.668760\pi$
$410$	−2.40708	−	1.10355i	−0.118877	−	0.0545005i
$411$	−0.273731	−	0.0733461i	−0.0135022	−	0.00361789i
$412$	28.6630	−	5.43710i	1.41212	−	0.267866i
$413$		0			0
$414$	3.51333	+	2.90953i	0.172671	+	0.142996i
$415$	−9.23185	−	15.9900i	−0.453174	−	0.784920i
$416$	13.8264	+	0.760404i	0.677897	+	0.0372819i
$417$	−1.46230	+	2.53277i	−0.0716089	+	0.124030i
$418$	−1.11358	+	6.56329i	−0.0544671	+	0.321021i
$419$	17.1877	+	17.1877i	0.839673	+	0.839673i	0.988816	−	0.149142i	$-0.0476513\pi$
$419$	17.1877	+	17.1877i	0.839673	+	0.839673i	−0.149142	+	0.988816i	$0.547651\pi$
$420$		0			0
$421$	12.9543	−	12.9543i	0.631352	−	0.631352i	−0.317055	−	0.948407i	$-0.602694\pi$
$421$	12.9543	−	12.9543i	0.631352	−	0.631352i	0.948407	+	0.317055i	$0.102694\pi$
$422$	23.6499	−	16.7888i	1.15126	−	0.817264i
$423$	−14.1821	−	8.18803i	−0.689557	−	0.398116i
$424$	27.5525	+	6.81281i	1.33807	+	0.330859i
$425$	21.1356	−	12.2026i	1.02523	−	0.591915i
$426$	−13.6254	+	1.28088i	−0.660150	+	0.0620588i
$427$		0			0
$428$	8.21868	+	5.59782i	0.397265	+	0.270581i
$429$	−0.668354	+	2.49433i	−0.0322685	+	0.120427i
$430$	−16.4207	−	44.2239i	−0.791878	−	2.13267i
$431$	2.85225	−	4.94025i	0.137388	−	0.237963i	−0.789119	−	0.614240i	$-0.789463\pi$
$431$	2.85225	−	4.94025i	0.137388	−	0.237963i	0.926507	+	0.376277i	$0.122796\pi$
$432$	17.9356	−	2.03770i	0.862926	−	0.0980387i
$433$	8.09187			0.388870			0.194435	−	0.980915i	$-0.437713\pi$
$433$	8.09187			0.388870			0.194435	+	0.980915i	$0.437713\pi$
$434$		0			0
$435$	−0.662870	−	0.662870i	−0.0317822	−	0.0317822i
$436$	20.1654	+	1.50179i	0.965750	+	0.0719228i
$437$	−1.40928	−	5.25952i	−0.0674152	−	0.251597i
$438$	−4.74245	+	10.3443i	−0.226603	+	0.494269i
$439$	−6.11379	+	3.52980i	−0.291795	+	0.168468i	−0.638751	−	0.769413i	$-0.720549\pi$
$439$	−6.11379	+	3.52980i	−0.291795	+	0.168468i	0.346956	+	0.937881i	$0.387215\pi$
$440$	−12.9663	−	7.15446i	−0.618145	−	0.341076i
$441$		0			0
$442$	−0.603895	−	6.42394i	−0.0287244	−	0.305556i
$443$	−14.7590	−	3.95466i	−0.701221	−	0.187891i	−0.109443	−	0.993993i	$-0.534907\pi$
$443$	−14.7590	−	3.95466i	−0.701221	−	0.187891i	−0.591777	+	0.806102i	$0.701573\pi$
$444$	0.398707	+	0.139306i	0.0189218	+	0.00661119i
$445$	−26.8574	+	7.19641i	−1.27316	+	0.341142i
$446$	−1.11768	+	6.58746i	−0.0529238	+	0.311925i
$447$	2.09735			0.0992014
$448$		0			0
$449$	19.5020			0.920356			0.460178	−	0.887827i	$-0.347786\pi$
$449$	19.5020			0.920356			0.460178	+	0.887827i	$0.347786\pi$
$450$	−7.01764	+	41.3609i	−0.330815	+	1.94977i
$451$	0.523350	−	0.140231i	0.0246436	−	0.00660322i
$452$	−9.87048	−	3.44869i	−0.464268	−	0.162213i
$453$	−10.9280	−	2.92814i	−0.513441	−	0.137576i
$454$	2.17992	+	23.1889i	0.102309	+	1.08831i
$455$		0			0
$456$	−8.11683	−	4.47865i	−0.380105	−	0.209732i
$457$	−8.72578	+	5.03783i	−0.408175	+	0.235660i	−0.690005	−	0.723804i	$-0.742392\pi$
$457$	−8.72578	+	5.03783i	−0.408175	+	0.235660i	0.281830	+	0.959464i	$0.409058\pi$
$458$	8.12039	−	17.7123i	0.379441	−	0.827642i
$459$	−2.17692	−	8.12437i	−0.101610	−	0.379213i
$460$	12.0795	+	0.899601i	0.563208	+	0.0419441i
$461$	15.9419	+	15.9419i	0.742487	+	0.742487i	0.973056	−	0.230569i	$-0.0740587\pi$
$461$	15.9419	+	15.9419i	0.742487	+	0.742487i	−0.230569	+	0.973056i	$0.574059\pi$
$462$		0			0
$463$	−8.23452			−0.382690			−0.191345	−	0.981523i	$-0.561285\pi$
$463$	−8.23452			−0.382690			−0.191345	+	0.981523i	$0.561285\pi$
$464$	−0.116110	−	1.02199i	−0.00539028	−	0.0474446i
$465$	−11.7827	+	20.4082i	−0.546409	+	0.946408i
$466$	−6.86694	−	18.4938i	−0.318105	−	0.856711i
$467$	−8.94417	+	33.3801i	−0.413887	+	1.54465i	0.373169	+	0.927764i	$0.378271\pi$
$467$	−8.94417	+	33.3801i	−0.413887	+	1.54465i	−0.787055	+	0.616882i	$0.788395\pi$
$468$	9.16693	+	6.24368i	0.423741	+	0.288614i
$469$		0			0
$470$	−43.2936	+	4.06991i	−1.99699	+	0.187731i
$471$	−2.65432	+	1.53247i	−0.122305	+	0.0706126i
$472$	−4.65299	−	1.15053i	−0.214171	−	0.0529573i
$473$	8.35922	+	4.82620i	0.384357	+	0.221909i
$474$	−12.9066	+	9.16221i	−0.592819	+	0.420834i
$475$	35.4092	−	35.4092i	1.62469	−	1.62469i
$476$		0			0
$477$	16.0749	+	16.0749i	0.736017	+	0.736017i
$478$	−5.48346	+	32.3187i	−0.250808	+	1.47822i
$479$	−3.70229	+	6.41255i	−0.169162	+	0.292997i	−0.938125	−	0.346296i	$-0.887439\pi$
$479$	−3.70229	+	6.41255i	−0.169162	+	0.292997i	0.768964	+	0.639293i	$0.220773\pi$
$480$	15.3613	−	13.7597i	0.701143	−	0.628043i
$481$	0.301574	+	0.522342i	0.0137506	+	0.0238167i
$482$	4.56792	+	3.78288i	0.208063	+	0.172306i
$483$		0			0
$484$	−18.6375	+	3.53536i	−0.847160	+	0.160698i
$485$	7.00175	+	1.87611i	0.317933	+	0.0851899i
$486$	20.6310	+	9.45847i	0.935839	+	0.429045i
$487$	−29.4458	−	17.0005i	−1.33432	−	0.770368i	−0.348359	−	0.937361i	$-0.613261\pi$
$487$	−29.4458	−	17.0005i	−1.33432	−	0.770368i	−0.985958	+	0.166993i	$0.946594\pi$
$488$	−19.0276	−	18.3035i	−0.861340	−	0.828560i
$489$		−	9.62880i		−	0.435429i
$490$		0			0
$491$	2.03871	−	2.03871i	0.0920055	−	0.0920055i	−0.659606	−	0.751612i	$-0.729277\pi$
$491$	2.03871	−	2.03871i	0.0920055	−	0.0920055i	0.751612	+	0.659606i	$0.229277\pi$
$492$	−0.0560358	+	0.752426i	−0.00252629	+	0.0339220i
$493$	−0.462935	+	0.124043i	−0.0208496	+	0.00558662i
$494$	−4.60838	−	12.4112i	−0.207341	−	0.558405i
$495$	−5.93083	−	10.2725i	−0.266571	−	0.461714i
$496$	−24.0599	+	9.46858i	−1.08032	+	0.425152i
$497$		0			0
$498$	−3.35557	+	4.05193i	−0.150367	+	0.181571i
$499$	−3.72332	+	13.8956i	−0.166679	+	0.622053i	0.831141	+	0.556061i	$0.187688\pi$
$499$	−3.72332	+	13.8956i	−0.166679	+	0.622053i	−0.997820	+	0.0659922i	$0.978979\pi$
$500$	29.9064	+	62.0277i	1.33745	+	2.77396i
$501$	−2.59907	−	9.69985i	−0.116118	−	0.433357i
$502$	−19.2109	−	27.0620i	−0.857425	−	1.20783i
$503$			27.2980i			1.21716i	0.793494	+	0.608579i	$0.208260\pi$
$503$			27.2980i			1.21716i	−0.793494	+	0.608579i	$0.791740\pi$
$504$		0			0
$505$			10.4008i			0.462828i
$506$	−2.02100	+	1.43468i	−0.0898443	+	0.0637792i
$507$	1.55447	+	5.80138i	0.0690366	+	0.257648i
$508$	2.27442	+	0.794672i	0.100911	+	0.0352579i
$509$	−5.34620	+	19.9523i	−0.236966	+	0.884370i	0.740286	+	0.672292i	$0.234690\pi$
$509$	−5.34620	+	19.9523i	−0.236966	+	0.884370i	−0.977253	+	0.212078i	$0.931977\pi$
$510$	−7.40095	−	6.12904i	−0.327720	−	0.271398i
$511$		0			0
$512$	22.5891	−	1.31585i	0.998308	−	0.0581530i
$513$	−8.62906	−	14.9460i	−0.380982	−	0.659881i
$514$	−14.6558	+	5.44183i	−0.646439	+	0.240029i
$515$	59.9351	−	16.0596i	2.64106	−	0.707669i
$516$	−10.1843	+	8.77252i	−0.448339	+	0.386189i
$517$	6.29146	−	6.29146i	0.276698	−	0.276698i
$518$		0			0
$519$		−	9.38489i		−	0.411951i
$520$	29.4459	−	0.571182i	1.29129	−	0.0250480i
$521$	9.46400	+	5.46404i	0.414625	+	0.239384i	0.692775	−	0.721154i	$-0.256388\pi$
$521$	9.46400	+	5.46404i	0.414625	+	0.239384i	−0.278150	+	0.960538i	$0.589721\pi$
$522$	0.343338	−	0.748893i	0.0150275	−	0.0327781i
$523$	−11.8976	−	3.18796i	−0.520247	−	0.139400i	−0.0108660	−	0.999941i	$-0.503459\pi$
$523$	−11.8976	−	3.18796i	−0.520247	−	0.139400i	−0.509381	+	0.860541i	$0.670125\pi$
$524$	−3.52140	+	5.17009i	−0.153833	+	0.225857i
$525$		0			0
$526$	−14.7834	+	17.8513i	−0.644588	+	0.778354i
$527$	6.02390	+	10.4337i	0.262405	+	0.454499i
$528$	−0.625041	+	4.17313i	−0.0272014	+	0.181612i
$529$	−10.4864	+	18.1630i	−0.455930	+	0.789694i
$530$	59.5147	+	10.0978i	2.58515	+	0.438619i
$531$	−2.71468	−	2.71468i	−0.117807	−	0.117807i
$532$		0			0
$533$	−0.761918	+	0.761918i	−0.0330023	+	0.0330023i
$534$	4.58608	+	6.46030i	0.198459	+	0.279565i
$535$	18.3160	+	10.5747i	0.791868	+	0.457185i
$536$	−6.74356	+	27.2725i	−0.291278	+	1.17799i
$537$	12.4069	−	7.16316i	0.535399	−	0.309113i
$538$	−0.170597	−	1.81472i	−0.00735494	−	0.0782382i
$539$		0			0
$540$	37.7193	−	7.15499i	1.62318	−	0.307902i
$541$	4.34231	−	16.2057i	0.186691	−	0.696739i	−0.807572	−	0.589769i	$-0.799219\pi$
$541$	4.34231	−	16.2057i	0.186691	−	0.696739i	0.994262	−	0.106969i	$-0.0341146\pi$
$542$	−26.6980	+	9.91320i	−1.14678	+	0.425808i
$543$	−9.68370	+	16.7727i	−0.415567	+	0.719784i
$544$	−2.16547	−	10.3186i	−0.0928437	−	0.442407i
$545$	43.0079			1.84226
$546$		0			0
$547$	−23.2429	−	23.2429i	−0.993797	−	0.993797i	0.00618416	−	0.999981i	$-0.498032\pi$
$547$	−23.2429	−	23.2429i	−0.993797	−	0.993797i	−0.999981	+	0.00618416i	$0.998032\pi$
$548$	−0.431599	−	0.501057i	−0.0184370	−	0.0214041i
$549$	−5.47329	−	20.4266i	−0.233594	−	0.871786i
$550$	−20.7197	−	9.49917i	−0.883492	−	0.405046i
$551$	−0.851637	+	0.491693i	−0.0362810	+	0.0209468i
$552$	−0.957780	−	3.31586i	−0.0407658	−	0.141132i
$553$		0			0
$554$	45.4457	−	4.27222i	1.93080	−	0.181509i
$555$	0.867659	+	0.232488i	0.0368301	+	0.00986858i
$556$	−6.14760	+	2.96404i	−0.260716	+	0.125703i
$557$	−22.7871	+	6.10578i	−0.965519	+	0.258710i	−0.706935	−	0.707279i	$-0.749923\pi$
$557$	−22.7871	+	6.10578i	−0.965519	+	0.258710i	−0.258584	+	0.965989i	$0.583256\pi$
$558$	−20.4180	−	3.46429i	−0.864364	−	0.146655i
$559$	−19.1960			−0.811904
$560$		0			0
$561$	1.96619			0.0830125
$562$	19.0273	+	3.22833i	0.802618	+	0.136179i
$563$	37.6366	−	10.0847i	1.58620	−	0.425020i	0.645358	−	0.763880i	$-0.276708\pi$
$563$	37.6366	−	10.0847i	1.58620	−	0.425020i	0.940837	+	0.338860i	$0.110041\pi$
$564$	5.38114	+	11.1608i	0.226587	+	0.469955i
$565$	−21.4799	−	5.75553i	−0.903667	−	0.242137i
$566$	26.4556	−	2.48701i	1.11201	−	0.104537i
$567$		0			0
$568$	−27.9622	−	15.4288i	−1.17327	−	0.647377i
$569$	10.2086	−	5.89395i	0.427968	−	0.247087i	−0.270513	−	0.962716i	$-0.587193\pi$
$569$	10.2086	−	5.89395i	0.427968	−	0.247087i	0.698481	+	0.715629i	$0.253860\pi$
$570$	−17.9231	−	8.21705i	−0.750718	−	0.344174i
$571$	−0.732074	−	2.73214i	−0.0306363	−	0.114336i	0.948914	−	0.315534i	$-0.102183\pi$
$571$	−0.732074	−	2.73214i	−0.0306363	−	0.114336i	−0.979551	+	0.201197i	$0.935517\pi$
$572$	−4.56581	+	3.93288i	−0.190906	+	0.164442i
$573$	−6.03552	−	6.03552i	−0.252138	−	0.252138i
$574$		0			0
$575$	18.6435			0.777489
$576$	16.0353	+	8.44640i	0.668138	+	0.351933i
$577$	−21.6020	+	37.4157i	−0.899302	+	1.55764i	−0.0709133	+	0.997482i	$0.522591\pi$
$577$	−21.6020	+	37.4157i	−0.899302	+	1.55764i	−0.828389	+	0.560154i	$0.810742\pi$
$578$	17.9326	−	6.65853i	0.745897	−	0.276958i
$579$	1.78481	−	6.66100i	0.0741741	−	0.276822i
$580$	−0.407699	−	2.14929i	−0.0169288	−	0.0892443i
$581$		0			0
$582$	−0.193313	−	2.05637i	−0.00801308	−	0.0852391i
$583$	−10.6967	+	6.17574i	−0.443012	+	0.255773i
$584$	−22.7359	+	13.7213i	−0.940817	+	0.567790i
$585$	20.4292	+	11.7948i	0.844643	+	0.487655i
$586$	2.54042	+	3.57863i	0.104944	+	0.147832i
$587$	−28.1127	+	28.1127i	−1.16034	+	1.16034i	−0.175935	+	0.984402i	$0.556295\pi$
$587$	−28.1127	+	28.1127i	−1.16034	+	1.16034i	−0.984402	+	0.175935i	$0.943705\pi$
$588$		0			0
$589$	17.4799	+	17.4799i	0.720248	+	0.720248i
$590$	−10.0507	−	1.70528i	−0.413780	−	0.0702053i
$591$	−3.64795	+	6.31844i	−0.150057	+	0.259906i
$592$	0.585993	+	0.792454i	0.0240842	+	0.0325697i
$593$	−8.44544	−	14.6279i	−0.346812	−	0.600697i	0.638869	−	0.769316i	$-0.279403\pi$
$593$	−8.44544	−	14.6279i	−0.346812	−	0.600697i	−0.985681	+	0.168619i	$0.946069\pi$
$594$	−5.01038	+	6.05015i	−0.205579	+	0.248241i
$595$		0			0
$596$	4.04521	+	2.75523i	0.165698	+	0.112859i
$597$	12.2176	+	3.27371i	0.500035	+	0.133984i
$598$	2.05415	−	4.48053i	0.0840003	−	0.183223i
$599$	25.7194	+	14.8491i	1.05087	+	0.606718i	0.922892	−	0.385059i	$-0.125819\pi$
$599$	25.7194	+	14.8491i	1.05087	+	0.606718i	0.127975	+	0.991777i	$0.459152\pi$
$600$	22.0051	−	22.8756i	0.898353	−	0.933894i
$601$		−	30.4663i		−	1.24275i	−0.783515	−	0.621373i	$-0.786575\pi$
$601$		−	30.4663i		−	1.24275i	0.783515	−	0.621373i	$-0.213425\pi$
$602$		0			0
$603$	−15.9115	+	15.9115i	−0.647966	+	0.647966i
$604$	−17.2304	−	20.0033i	−0.701095	−	0.813924i
$605$	−38.9715	+	10.4424i	−1.58442	+	0.424544i
$606$	2.77823	−	1.03158i	0.112858	−	0.0419051i
$607$	16.6272	+	28.7992i	0.674879	+	1.16892i	0.976504	+	0.215498i	$0.0691373\pi$
$607$	16.6272	+	28.7992i	0.674879	+	1.16892i	−0.301626	+	0.953426i	$0.597529\pi$
$608$	−9.77165	−	19.3009i	−0.396293	−	0.782756i
$609$		0			0
$610$	−43.2486	−	35.8160i	−1.75108	−	1.45015i
$611$	−4.57971	+	17.0917i	−0.185275	+	0.691456i
$612$	2.78548	−	7.97231i	0.112596	−	0.322261i
$613$	−5.29950	−	19.7780i	−0.214045	−	0.798827i	−0.986501	−	0.163758i	$-0.947638\pi$
$613$	−5.29950	−	19.7780i	−0.214045	−	0.798827i	0.772456	−	0.635069i	$-0.219028\pi$
$614$	13.5039	−	9.58626i	0.544974	−	0.386870i
$615$			1.60474i			0.0647093i
$616$		0			0
$617$		−	2.64884i		−	0.106638i	−0.998578	−	0.0533192i	$-0.983020\pi$
$617$		−	2.64884i		−	0.106638i	0.998578	−	0.0533192i	$-0.0169801\pi$
$618$	−10.2343	−	14.4169i	−0.411685	−	0.579931i
$619$	9.69816	+	36.1940i	0.389802	+	1.45476i	0.830456	+	0.557084i	$0.188080\pi$
$619$	9.69816	+	36.1940i	0.389802	+	1.45476i	−0.440654	+	0.897677i	$0.645253\pi$
$620$	−49.5352	+	23.8832i	−1.98938	+	0.959172i
$621$	1.66298	−	6.20631i	0.0667330	−	0.249051i
$622$	7.67108	−	9.26300i	0.307582	−	0.371412i
$623$		0			0
$624$	−3.07310	−	7.80884i	−0.123023	−	0.312604i
$625$	40.4934	+	70.1366i	1.61974	+	2.80546i
$626$	−8.01485	−	21.5854i	−0.320338	−	0.862725i
$627$	3.89687	−	1.04416i	0.155626	−	0.0416999i
$628$	−7.13262	−	0.531191i	−0.284622	−	0.0211968i
$629$	0.324731	−	0.324731i	0.0129479	−	0.0129479i
$630$		0			0
$631$			10.0919i			0.401753i	0.979617	+	0.200877i	$0.0643791\pi$
$631$			10.0919i			0.401753i	−0.979617	+	0.200877i	$0.935621\pi$
$632$	−36.9294	+	0.716345i	−1.46897	+	0.0284947i
$633$	−15.2217	−	8.78826i	−0.605009	−	0.349302i
$634$	29.0899	+	13.3366i	1.15531	+	0.529663i
$635$	4.94955	+	1.32623i	0.196417	+	0.0526298i
$636$	−3.20556	−	16.8989i	−0.127109	−	0.670086i
$637$		0			0
$638$	0.344744	+	0.285497i	0.0136486	+	0.0113029i
$639$	−12.7900	−	22.1529i	−0.505964	−	0.876355i
$640$	47.7034	−	6.35903i	1.88564	−	0.251363i
$641$	−15.3814	+	26.6413i	−0.607528	+	1.05227i	0.384118	+	0.923284i	$0.374505\pi$
$641$	−15.3814	+	26.6413i	−0.607528	+	1.05227i	−0.991646	+	0.128986i	$0.958828\pi$
$642$	1.00806	−	5.94134i	0.0397849	−	0.234486i
$643$	−22.2297	−	22.2297i	−0.876653	−	0.876653i	0.116533	−	0.993187i	$-0.462822\pi$
$643$	−22.2297	−	22.2297i	−0.876653	−	0.876653i	−0.993187	+	0.116533i	$0.962822\pi$
$644$		0			0
$645$	−20.2151	+	20.2151i	−0.795970	+	0.795970i
$646$	−8.21975	+	5.83509i	−0.323402	+	0.229578i
$647$	14.3410	+	8.27978i	0.563803	+	0.325512i	0.754670	−	0.656104i	$-0.227797\pi$
$647$	14.3410	+	8.27978i	0.563803	+	0.325512i	−0.190867	+	0.981616i	$0.561130\pi$
$648$	4.28033	+	7.09242i	0.168147	+	0.278617i
$649$	1.80643	−	1.04294i	0.0709085	−	0.0409390i
$650$	45.1309	−	4.24263i	1.77018	−	0.166409i
$651$		0			0
$652$	12.6491	−	18.5713i	0.495377	−	0.727308i
$653$	−9.67497	+	36.1075i	−0.378611	+	1.41300i	0.469385	+	0.882993i	$0.344476\pi$
$653$	−9.67497	+	36.1075i	−0.378611	+	1.41300i	−0.847996	+	0.530002i	$0.822191\pi$
$654$	−4.26566	−	11.4882i	−0.166800	−	0.449222i
$655$	−6.65220	+	11.5219i	−0.259923	+	0.450200i
$656$	−1.09652	+	1.37761i	−0.0428118	+	0.0537866i
$657$	−21.2701			−0.829824
$658$		0			0
$659$	−14.8808	−	14.8808i	−0.579674	−	0.579674i	0.355139	−	0.934813i	$-0.384433\pi$
$659$	−14.8808	−	14.8808i	−0.579674	−	0.579674i	−0.934813	+	0.355139i	$0.884433\pi$
$660$	−0.666529	+	8.94989i	−0.0259446	+	0.348374i
$661$	2.96488	+	11.0651i	0.115321	+	0.430382i	0.999311	−	0.0371232i	$-0.0118194\pi$
$661$	2.96488	+	11.0651i	0.115321	+	0.430382i	−0.883990	+	0.467506i	$0.845153\pi$
$662$	6.85300	−	14.9479i	0.266350	−	0.580965i
$663$	−3.38634	+	1.95510i	−0.131515	+	0.0759299i
$664$	−11.7949	+	3.40693i	−0.457730	+	0.132214i
$665$		0			0
$666$	0.0738851	+	0.785953i	0.00286299	+	0.0304551i
$667$	−0.353642	−	0.0947582i	−0.0136931	−	0.00366905i
$668$	7.72954	−	22.1226i	0.299065	−	0.855951i
$669$	3.91122	−	1.04801i	0.151217	−	0.0405183i
$670$	−9.99513	+	58.9098i	−0.386146	+	2.27588i
$671$	11.4897			0.443555
$672$		0			0
$673$	20.7704			0.800639			0.400319	−	0.916376i	$-0.368899\pi$
$673$	20.7704			0.800639			0.400319	+	0.916376i	$0.368899\pi$
$674$	3.72804	−	21.9725i	0.143599	−	0.846349i
$675$	57.0772	−	15.2938i	2.19690	−	0.588658i
$676$	−4.62296	+	13.2313i	−0.177806	+	0.508897i
$677$	−26.5605	−	7.11687i	−1.02080	−	0.273524i	−0.290667	−	0.956824i	$-0.593877\pi$
$677$	−26.5605	−	7.11687i	−1.02080	−	0.273524i	−0.730137	+	0.683301i	$0.760544\pi$
$678$	0.593044	+	6.30851i	0.0227757	+	0.242277i
$679$		0			0
$680$	−6.22284	−	21.5436i	−0.238635	−	0.826161i
$681$	12.2239	−	7.05746i	0.468420	−	0.270442i
$682$	4.68931	−	10.2284i	0.179563	−	0.391665i
$683$	−0.558762	−	2.08533i	−0.0213804	−	0.0797928i	0.954411	−	0.298495i	$-0.0964845\pi$
$683$	−0.558762	−	2.08533i	−0.0213804	−	0.0797928i	−0.975792	+	0.218702i	$0.929818\pi$
$684$	1.28690	−	17.2799i	0.0492057	−	0.660714i
$685$	−0.994563	−	0.994563i	−0.0380003	−	0.0380003i
$686$		0			0
$687$	−11.8083			−0.450517
$688$	−31.1669	+	3.54093i	−1.18823	+	0.134997i
$689$	12.2819	−	21.2728i	0.467902	−	0.810429i
$690$	−2.55521	−	6.88161i	−0.0972750	−	0.261979i
$691$	0.631272	−	2.35594i	0.0240147	−	0.0896242i	−0.952878	−	0.303352i	$-0.901894\pi$
$691$	0.631272	−	2.35594i	0.0240147	−	0.0896242i	0.976893	+	0.213728i	$0.0685607\pi$
$692$	12.3287	−	18.1009i	0.468666	−	0.688091i
$693$		0			0
$694$	21.4976	−	2.02092i	0.816036	−	0.0767131i
$695$	−12.5708	+	7.25775i	−0.476837	+	0.275302i
$696$	−0.533675	+	0.322076i	−0.0202289	+	0.0122083i
$697$	0.710506	+	0.410211i	0.0269124	+	0.0155379i
$698$	10.7983	−	7.66555i	0.408721	−	0.290145i
$699$	−8.45369	+	8.45369i	−0.319748	+	0.319748i
$700$		0			0
$701$	6.81795	+	6.81795i	0.257510	+	0.257510i	0.824041	−	0.566530i	$-0.191715\pi$
$701$	6.81795	+	6.81795i	0.257510	+	0.257510i	−0.566530	+	0.824041i	$0.691715\pi$
$702$	2.61327	−	15.4022i	0.0986317	−	0.581320i
$703$	0.471146	−	0.816049i	0.0177696	−	0.0307779i
$704$	−6.68765	+	7.22771i	−0.252050	+	0.272405i
$705$	13.1763	+	22.8220i	0.496247	+	0.859525i
$706$	−23.7516	−	19.6697i	−0.893904	−	0.740280i
$707$		0			0
$708$	0.541347	+	2.85384i	0.0203450	+	0.107254i
$709$	11.3630	+	3.04470i	0.426745	+	0.114346i	0.465798	−	0.884891i	$-0.345767\pi$
$709$	11.3630	+	3.04470i	0.426745	+	0.114346i	−0.0390527	+	0.999237i	$0.512434\pi$
$710$	−61.7446	−	28.3074i	−2.31723	−	1.06236i
$711$	−25.6212	−	14.7924i	−0.960869	−	0.554758i
$712$	0.358562	+	18.4847i	0.0134377	+	0.692745i
$713$			9.20346i			0.344672i
$714$		0			0
$715$	−9.06280	+	9.06280i	−0.338929	+	0.338929i
$716$	33.3396	+	2.48292i	1.24596	+	0.0927910i
$717$	19.1888	−	5.14163i	0.716619	−	0.192018i
$718$	−16.9513	−	45.6529i	−0.632619	−	1.70375i
$719$	16.4827	+	28.5490i	0.614703	+	1.06470i	0.990437	+	0.137969i	$0.0440573\pi$
$719$	16.4827	+	28.5490i	0.614703	+	1.06470i	−0.375734	+	0.926728i	$0.622609\pi$
$720$	35.3449	+	15.3818i	1.31723	+	0.573247i
$721$		0			0
$722$	3.94601	−	4.76490i	0.146855	−	0.177331i
$723$	0.930267	−	3.47180i	0.0345970	−	0.129118i
$724$	−40.7110	+	19.6286i	−1.51301	+	0.729492i
$725$	−0.871457	−	3.25232i	−0.0323651	−	0.120788i
$726$	6.65466	+	9.37426i	0.246977	+	0.347911i
$727$		−	13.8871i		−	0.515045i	−0.966272	−	0.257523i	$-0.917094\pi$
$727$		−	13.8871i		−	0.515045i	0.966272	−	0.257523i	$-0.0829062\pi$
$728$		0			0
$729$		−	4.96768i		−	0.183988i
$730$	−46.0552	+	32.6939i	−1.70458	+	1.21006i
$731$	3.78286	+	14.1178i	0.139914	+	0.522167i
$732$	−5.27753	+	15.1048i	−0.195063	+	0.558289i
$733$	2.86505	−	10.6925i	0.105823	−	0.394936i	−0.892614	−	0.450821i	$-0.851131\pi$
$733$	2.86505	−	10.6925i	0.105823	−	0.394936i	0.998437	+	0.0558846i	$0.0177979\pi$
$734$	−3.61207	−	2.99131i	−0.133324	−	0.110411i
$735$		0			0
$736$	2.50866	−	7.65359i	0.0924704	−	0.282115i
$737$	−6.11297	−	10.5880i	−0.225174	−	0.390013i
$738$	−1.32209	+	0.490903i	−0.0486667	+	0.0180704i
$739$	10.7856	−	2.88999i	0.396754	−	0.106310i	−0.0549249	−	0.998490i	$-0.517492\pi$
$739$	10.7856	−	2.88999i	0.396754	−	0.106310i	0.451679	+	0.892181i	$0.350825\pi$
$740$	1.36806	+	1.58822i	0.0502909	+	0.0583843i
$741$	−5.67325	+	5.67325i	−0.208412	+	0.208412i
$742$		0			0
$743$			49.5292i			1.81705i	0.417832	+	0.908524i	$0.362790\pi$
$743$			49.5292i			1.81705i	−0.417832	+	0.908524i	$0.637210\pi$
$744$	11.2927	+	10.8629i	0.414009	+	0.398253i
$745$	9.01507	+	5.20485i	0.330287	+	0.190691i
$746$	−13.7237	+	29.9344i	−0.502461	+	1.09598i
$747$	−9.49845	−	2.54510i	−0.347530	−	0.0931204i
$748$	3.79223	+	2.58292i	0.138658	+	0.0944411i
$749$		0			0
$750$	26.6170	−	32.1407i	0.971917	−	1.17361i
$751$	0.523146	+	0.906116i	0.0190899	+	0.0330646i	0.875413	−	0.483377i	$-0.160590\pi$
$751$	0.523146	+	0.906116i	0.0190899	+	0.0330646i	−0.856323	+	0.516441i	$0.827256\pi$
$752$	−4.28292	+	28.5952i	−0.156182	+	1.04276i
$753$	−10.0562	+	17.4178i	−0.366467	+	0.634739i
$754$	−0.877637	−	0.148907i	−0.0319616	−	0.00542288i
$755$	−39.7052	−	39.7052i	−1.44502	−	1.44502i
$756$		0			0
$757$	−29.5274	+	29.5274i	−1.07319	+	1.07319i	−0.0760892	+	0.997101i	$0.524243\pi$
$757$	−29.5274	+	29.5274i	−1.07319	+	1.07319i	−0.997101	+	0.0760892i	$0.975757\pi$
$758$	−3.21003	−	4.52189i	−0.116593	−	0.164242i
$759$	1.30077	+	0.750998i	0.0472148	+	0.0272595i
$760$	−23.7743	−	39.3936i	−0.862384	−	1.42895i
$761$	−33.9144	+	19.5805i	−1.22940	+	0.709793i	−0.966904	−	0.255141i	$-0.917878\pi$
$761$	−33.9144	+	19.5805i	−1.22940	+	0.709793i	−0.262493	+	0.964934i	$0.584545\pi$
$762$	−0.136653	−	1.45365i	−0.00495043	−	0.0526602i
$763$		0			0
$764$	−3.71216	−	19.5696i	−0.134301	−	0.708002i
$765$	4.64869	−	17.3492i	0.168074	−	0.627260i
$766$	28.3590	−	10.5300i	1.02465	−	0.380463i
$767$	−2.07412	+	3.59249i	−0.0748923	+	0.129717i
$768$	−6.42998	−	12.1117i	−0.232022	−	0.437043i
$769$	−28.7025			−1.03504			−0.517519	−	0.855672i	$-0.673144\pi$
$769$	−28.7025			−1.03504			−0.517519	+	0.855672i	$0.673144\pi$
$770$		0			0
$771$	6.69929	+	6.69929i	0.241269	+	0.241269i
$772$	12.1928	−	10.5026i	0.438827	−	0.377996i
$773$	−3.90180	−	14.5617i	−0.140338	−	0.523748i	−0.999919	−	0.0127485i	$-0.995942\pi$
$773$	−3.90180	−	14.5617i	−0.140338	−	0.523748i	0.859581	−	0.511000i	$-0.170725\pi$
$774$	−22.8385	−	10.4705i	−0.820913	−	0.376356i
$775$	−73.3012	+	42.3205i	−2.63306	+	1.52020i
$776$	2.32854	−	4.22011i	0.0835899	−	0.151493i
$777$		0			0
$778$	−35.4312	+	3.33078i	−1.27027	+	0.119414i
$779$	1.62603	+	0.435693i	0.0582586	+	0.0156103i
$780$	−7.75149	−	16.0771i	−0.277548	−	0.575651i
$781$	13.4246	−	3.59710i	0.480369	−	0.128715i
$782$	−3.70005	−	0.627781i	−0.132313	−	0.0224494i
$783$	−1.16041			−0.0414697
$784$		0			0
$785$	−15.2121			−0.542944
$786$	3.73750	+	0.634135i	0.133312	+	0.0226188i
$787$	−22.6434	+	6.06728i	−0.807150	+	0.216275i	−0.638721	−	0.769438i	$-0.720536\pi$
$787$	−22.6434	+	6.06728i	−0.807150	+	0.216275i	−0.168429	+	0.985714i	$0.553869\pi$
$788$	−15.3363	+	7.39431i	−0.546331	+	0.263411i
$789$	13.5677	+	3.63546i	0.483024	+	0.129426i
$790$	−78.2136	+	7.35263i	−2.78272	+	0.261595i
$791$		0			0
$792$	−7.57739	+	2.18872i	−0.269251	+	0.0777727i
$793$	−19.7886	+	11.4249i	−0.702713	+	0.405712i
$794$	0.502680	+	0.230459i	0.0178394	+	0.00817867i
$795$	−9.46828	−	35.3361i	−0.335805	−	1.25324i
$796$	19.2639	+	22.3640i	0.682790	+	0.792673i
$797$	−3.81531	−	3.81531i	−0.135145	−	0.135145i	0.636298	−	0.771443i	$-0.280465\pi$
$797$	−3.81531	−	3.81531i	−0.135145	−	0.135145i	−0.771443	+	0.636298i	$0.780465\pi$
$798$		0			0
$799$	13.4727			0.476631
$800$	72.4928	−	15.2134i	2.56301	−	0.537873i
$801$	−7.40422	+	12.8245i	−0.261615	+	0.453131i
$802$	−26.3219	+	9.77355i	−0.929458	+	0.345116i
$803$	2.99104	−	11.1627i	0.105551	−	0.393923i
$804$	16.7272	−	3.17298i	0.589922	−	0.111903i
$805$		0			0
$806$	2.09439	+	22.2791i	0.0737718	+	0.784748i
$807$	−0.956619	+	0.552304i	−0.0336746	+	0.0194420i
$808$	6.71359	+	1.66004i	0.236183	+	0.0584001i
$809$	−24.7881	−	14.3114i	−0.871505	−	0.503164i	−0.00365682	−	0.999993i	$-0.501164\pi$
$809$	−24.7881	−	14.3114i	−0.871505	−	0.503164i	−0.867848	+	0.496830i	$0.834497\pi$
$810$	10.1988	+	14.3668i	0.358350	+	0.504799i
$811$	−9.30808	+	9.30808i	−0.326851	+	0.326851i	−0.851388	−	0.524537i	$-0.824238\pi$
$811$	−9.30808	+	9.30808i	−0.326851	+	0.326851i	0.524537	+	0.851388i	$0.324238\pi$
$812$		0			0
$813$	12.2039	+	12.2039i	0.428008	+	0.428008i
$814$	−0.422865	−	0.0717467i	−0.0148214	−	0.00251472i
$815$	23.8951	−	41.3875i	0.837009	−	1.44974i
$816$	−5.13748	+	3.79899i	−0.179848	+	0.132991i
$817$	14.9948	+	25.9718i	0.524603	+	0.908639i
$818$	−31.7156	+	38.2973i	−1.10891	+	1.33903i
$819$		0			0
$820$	−2.10810	+	3.09510i	−0.0736180	+	0.108085i
$821$	−16.1169	−	4.31850i	−0.562482	−	0.150717i	−0.0336357	−	0.999434i	$-0.510709\pi$
$821$	−16.1169	−	4.31850i	−0.562482	−	0.150717i	−0.528846	+	0.848718i	$0.677375\pi$
$822$	−0.167021	+	0.364309i	−0.00582553	+	0.0127067i
$823$	9.41497	+	5.43573i	0.328185	+	0.189478i	0.655035	−	0.755598i	$-0.272654\pi$
$823$	9.41497	+	5.43573i	0.328185	+	0.189478i	−0.326850	+	0.945076i	$0.605987\pi$
$824$	−0.800169	−	41.2507i	−0.0278752	−	1.43704i
$825$			13.8133i			0.480918i
$826$		0			0
$827$	9.97483	−	9.97483i	0.346859	−	0.346859i	−0.512079	−	0.858938i	$-0.671125\pi$
$827$	9.97483	−	9.97483i	0.346859	−	0.346859i	0.858938	+	0.512079i	$0.171125\pi$
$828$	4.88786	−	4.21029i	0.169865	−	0.146318i
$829$	−24.9645	+	6.68921i	−0.867052	+	0.232326i	−0.664813	−	0.747010i	$-0.731489\pi$
$829$	−24.9645	+	6.68921i	−0.867052	+	0.232326i	−0.202240	+	0.979336i	$0.564822\pi$
$830$	−24.4786	+	9.08914i	−0.849666	+	0.315489i
$831$	−13.8312	−	23.9564i	−0.479801	−	0.831039i
$832$	4.33109	−	19.0982i	0.150154	−	0.662109i
$833$		0			0
$834$	3.18548	+	2.63803i	0.110304	+	0.0913475i
$835$	12.8998	−	48.1428i	0.446417	−	1.66605i
$836$	8.88767	+	3.10531i	0.307387	+	0.107399i
$837$	7.54985	+	28.1764i	0.260961	+	0.973920i
$838$	28.0306	−	19.8985i	0.968301	−	0.687384i
$839$		−	35.9931i		−	1.24262i	−0.783565	−	0.621310i	$-0.786601\pi$
$839$		−	35.9931i		−	1.24262i	0.783565	−	0.621310i	$-0.213399\pi$
$840$		0			0
$841$		−	28.9339i		−	0.997720i
$842$	−14.9974	−	21.1265i	−0.516845	−	0.728067i
$843$	−3.02708	−	11.2972i	−0.104258	−	0.389097i
$844$	−17.8136	−	36.9465i	−0.613169	−	1.27175i
$845$	−7.71526	+	28.7937i	−0.265413	+	0.990535i
$846$	−14.7715	+	17.8369i	−0.507854	+	0.613245i
$847$		0			0
$848$	16.0170	−	36.8044i	0.550026	−	1.26387i
$849$	−8.05167	−	13.9459i	−0.276333	−	0.478622i
$850$	−12.0140	−	32.3558i	−0.412078	−	1.10980i
$851$	0.338864	−	0.0907985i	0.0116161	−	0.00311253i
$852$	−1.43739	+	19.3007i	−0.0492441	+	0.661230i
$853$	−11.5045	+	11.5045i	−0.393906	+	0.393906i	−0.876077	−	0.482171i	$-0.839848\pi$
$853$	−11.5045	+	11.5045i	−0.393906	+	0.393906i	0.482171	+	0.876077i	$0.339848\pi$
$854$		0			0
$855$		−	36.8538i		−	1.26037i
$856$	9.74924	−	10.1349i	0.333222	−	0.346405i
$857$	46.8795	+	27.0659i	1.60137	+	0.924554i	0.991213	+	0.132276i	$0.0422286\pi$
$857$	46.8795	+	27.0659i	1.60137	+	0.924554i	0.610161	+	0.792277i	$0.291105\pi$
$858$	3.31970	+	1.52195i	0.113333	+	0.0519586i
$859$	6.87557	+	1.84230i	0.234591	+	0.0628586i	0.374199	−	0.927348i	$-0.377918\pi$
$859$	6.87557	+	1.84230i	0.234591	+	0.0628586i	−0.139608	+	0.990207i	$0.544584\pi$
$860$	−65.5454	+	12.4333i	−2.23508	+	0.423973i
$861$		0			0
$862$	−6.21337	−	5.14555i	−0.211628	−	0.175258i
$863$	−8.29596	−	14.3690i	−0.282398	−	0.489127i	0.689577	−	0.724212i	$-0.257796\pi$
$863$	−8.29596	−	14.3690i	−0.282398	−	0.489127i	−0.971975	+	0.235085i	$0.924463\pi$
$864$	1.40182	−	25.4894i	0.0476910	−	0.867167i
$865$	23.2898	−	40.3391i	0.791877	−	1.37157i
$866$	1.91426	−	11.2824i	0.0650493	−	0.383391i
$867$	−8.19713	−	8.19713i	−0.278389	−	0.278389i
$868$		0			0
$869$	11.3661	−	11.3661i	0.385567	−	0.385567i
$870$	−1.08104	+	0.767418i	−0.0366508	+	0.0260179i
$871$	21.0566	+	12.1570i	0.713475	+	0.411925i
$872$	6.86440	−	27.7611i	0.232458	−	0.940111i
$873$	3.34336	−	1.93029i	0.113156	−	0.0653305i
$874$	−7.66667	+	0.720721i	−0.259329	+	0.0243788i
$875$		0			0
$876$	13.3010	+	9.05944i	0.449399	+	0.306090i
$877$	−7.85634	+	29.3202i	−0.265290	+	0.990074i	0.696783	+	0.717282i	$0.254614\pi$
$877$	−7.85634	+	29.3202i	−0.265290	+	0.990074i	−0.962073	+	0.272793i	$0.912053\pi$
$878$	3.47524	+	9.35942i	0.117284	+	0.315865i
$879$	1.32981	−	2.30330i	0.0448534	−	0.0776883i
$880$	−13.0428	+	16.3863i	−0.439672	+	0.552381i
$881$	48.7213			1.64146			0.820731	−	0.571314i	$-0.193566\pi$
$881$	48.7213			1.64146			0.820731	+	0.571314i	$0.193566\pi$
$882$		0			0
$883$	2.32744	+	2.32744i	0.0783247	+	0.0783247i	0.745184	−	0.666859i	$-0.232362\pi$
$883$	2.32744	+	2.32744i	0.0783247	+	0.0783247i	−0.666859	+	0.745184i	$0.732362\pi$
$884$	−9.09968	−	0.677685i	−0.306055	−	0.0227930i
$885$	1.59898	+	5.96746i	0.0537490	+	0.200594i
$886$	−9.00541	+	19.6427i	−0.302543	+	0.659910i
$887$	45.9577	−	26.5337i	1.54311	−	0.890914i	0.544467	−	0.838782i	$-0.316732\pi$
$887$	45.9577	−	26.5337i	1.54311	−	0.890914i	0.998640	−	0.0521315i	$-0.0166015\pi$
$888$	0.288554	−	0.522957i	0.00968323	−	0.0175493i
$889$		0			0
$890$	3.68031	+	39.1493i	0.123364	+	1.31229i
$891$	−3.48219	−	0.933049i	−0.116658	−	0.0312583i
$892$	8.92040	+	3.11674i	0.298677	+	0.104356i
$893$	26.7022	−	7.15483i	0.893555	−	0.239427i
$894$	0.496163	−	2.92431i	0.0165942	−	0.0978036i
$895$	71.1052			2.37678
$896$		0			0
$897$	−2.98706			−0.0997350
$898$	4.61351	−	27.1914i	0.153955	−	0.907388i
$899$	1.60552	−	0.430199i	0.0535472	−	0.0143479i
$900$	56.0089	+	19.5692i	1.86696	+	0.652307i
$901$	−18.0656	−	4.84066i	−0.601852	−	0.161266i
$902$	−0.0717155	−	0.762874i	−0.00238786	−	0.0254009i
$903$		0			0
$904$	−7.14349	+	12.9464i	−0.237589	+	0.430592i
$905$	−83.2470	+	48.0627i	−2.76723	+	1.59766i
$906$	−6.66786	+	14.5440i	−0.221525	+	0.483193i
$907$	14.4466	+	53.9154i	0.479691	+	1.79023i	0.602863	+	0.797845i	$0.294027\pi$
$907$	14.4466	+	53.9154i	0.479691	+	1.79023i	−0.123172	+	0.992385i	$0.539307\pi$
$908$	32.8477	+	2.44628i	1.09009	+	0.0811827i
$909$	3.91688	+	3.91688i	0.129915	+	0.129915i
$910$		0			0
$911$	−44.7554			−1.48281			−0.741406	−	0.671057i	$-0.765841\pi$
$911$	−44.7554			−1.48281			−0.741406	+	0.671057i	$0.765841\pi$
$912$	−8.16469	+	10.2577i	−0.270360	+	0.339666i
$913$	2.67138	−	4.62696i	0.0884097	−	0.153130i
$914$	4.95995	+	13.3580i	0.164061	+	0.441844i
$915$	−8.80768	+	32.8707i	−0.291173	+	1.08667i
$916$	−22.7750	−	15.5123i	−0.752509	−	0.512541i
$917$		0			0
$918$	−11.8427	+	1.11330i	−0.390867	+	0.0367443i
$919$	19.8098	−	11.4372i	0.653464	−	0.377277i	−0.136318	−	0.990665i	$-0.543527\pi$
$919$	19.8098	−	11.4372i	0.653464	−	0.377277i	0.789782	+	0.613388i	$0.210194\pi$
$920$	4.11190	−	16.6294i	0.135565	−	0.548256i
$921$	−8.69148	−	5.01803i	−0.286394	−	0.165350i
$922$	25.9989	−	18.4562i	0.856227	−	0.607824i
$923$	−19.5442	+	19.5442i	−0.643304	+	0.643304i
$924$		0			0
$925$	2.28137	+	2.28137i	0.0750111	+	0.0750111i
$926$	−1.94801	+	11.4813i	−0.0640156	+	0.377298i
$927$	16.5233	−	28.6192i	0.542697	−	0.939979i
$928$	−1.45241	−	0.0798774i	−0.0476778	−	0.00262210i
$929$	−13.2871	−	23.0139i	−0.435935	−	0.755062i	0.561436	−	0.827520i	$-0.310249\pi$
$929$	−13.2871	−	23.0139i	−0.435935	−	0.755062i	−0.997371	+	0.0724577i	$0.976916\pi$
$930$	25.6675	+	21.2563i	0.841671	+	0.697023i
$931$		0			0
$932$	−27.4102	+	5.19946i	−0.897852	+	0.170314i
$933$	−7.04026	−	1.88643i	−0.230488	−	0.0617590i
$934$	44.4255	+	20.3673i	1.45365	+	0.666440i
$935$	8.45127	+	4.87934i	0.276386	+	0.159572i
$936$	10.8741	−	11.3043i	0.355430	−	0.369492i
$937$		−	11.8582i		−	0.387391i	−0.981062	−	0.193696i	$-0.937953\pi$
$937$		−	11.8582i		−	0.387391i	0.981062	−	0.193696i	$-0.0620474\pi$
$938$		0			0
$939$	−9.86686	+	9.86686i	−0.321993	+	0.321993i
$940$	−4.56720	+	61.3265i	−0.148966	+	2.00025i
$941$	2.04535	−	0.548049i	0.0666764	−	0.0178659i	−0.225327	−	0.974283i	$-0.572345\pi$
$941$	2.04535	−	0.548049i	0.0666764	−	0.0178659i	0.292003	+	0.956417i	$0.405678\pi$
$942$	1.50878	+	4.06342i	0.0491588	+	0.132393i
$943$	0.313366	+	0.542765i	0.0102046	+	0.0176749i
$944$	−2.70491	+	6.21542i	−0.0880372	+	0.202295i
$945$		0			0
$946$	8.70662	−	10.5134i	0.283077	−	0.341821i
$947$	1.38876	−	5.18291i	0.0451285	−	0.168422i	−0.939684	−	0.342045i	$-0.888881\pi$
$947$	1.38876	−	5.18291i	0.0451285	−	0.168422i	0.984812	+	0.173623i	$0.0555473\pi$
$948$	9.72148	+	20.1630i	0.315739	+	0.654862i
$949$	5.94835	+	22.1995i	0.193092	+	0.720628i
$950$	−40.9940	−	57.7473i	−1.33002	−	1.87357i
$951$		−	19.3935i		−	0.628878i
$952$		0			0
$953$		−	3.43130i		−	0.111151i	−0.998454	−	0.0555753i	$-0.982301\pi$
$953$		−	3.43130i		−	0.111151i	0.998454	−	0.0555753i	$-0.0176993\pi$
$954$	26.2157	−	18.6102i	0.848766	−	0.602527i
$955$	−10.9646	−	40.9205i	−0.354806	−	1.32415i
$956$	43.7643	+	15.2910i	1.41544	+	0.494547i
$957$	0.0702080	−	0.262020i	0.00226950	−	0.00846989i
$958$	8.06510	+	6.67905i	0.260572	+	0.215790i
$959$		0			0
$960$	−15.5511	−	24.6731i	−0.501908	−	0.796322i
$961$	−5.39169	−	9.33869i	−0.173926	−	0.301248i
$962$	0.799637	−	0.296913i	0.0257813	−	0.00957284i
$963$	10.8801	−	2.91531i	0.350606	−	0.0939446i
$964$	6.35504	−	5.47408i	0.204682	−	0.176308i
$965$	24.2018	−	24.2018i	0.779083	−	0.779083i
$966$		0			0
$967$		−	19.4110i		−	0.624217i	−0.950046	−	0.312108i	$-0.898965\pi$
$967$		−	19.4110i		−	0.624217i	0.950046	−	0.312108i	$-0.101035\pi$
$968$	0.520293	+	26.8224i	0.0167229	+	0.862104i
$969$	5.29044	+	3.05444i	0.169954	+	0.0981227i
$970$	4.27222	−	9.31862i	0.137173	−	0.299203i
$971$	−19.4567	−	5.21341i	−0.624396	−	0.167306i	−0.0672705	−	0.997735i	$-0.521429\pi$
$971$	−19.4567	−	5.21341i	−0.624396	−	0.167306i	−0.557125	+	0.830428i	$0.688096\pi$
$972$	18.0684	−	26.5279i	0.579545	−	0.850883i
$973$		0			0
$974$	−30.6695	+	37.0342i	−0.982715	+	1.18665i
$975$	−13.7354	−	23.7905i	−0.439886	−	0.761905i
$976$	−30.0216	+	22.2000i	−0.960969	+	0.710604i
$977$	−8.78731	+	15.2201i	−0.281131	+	0.486933i	−0.971664	−	0.236368i	$-0.924043\pi$
$977$	−8.78731	+	15.2201i	−0.281131	+	0.486933i	0.690533	+	0.723301i	$0.257376\pi$
$978$	−13.4253	−	2.27785i	−0.429294	−	0.0728376i
$979$	−5.68920	−	5.68920i	−0.181828	−	0.181828i
$980$		0			0
$981$	16.1966	−	16.1966i	0.517117	−	0.517117i
$982$	−2.36025	−	3.32483i	−0.0753187	−	0.106100i
$983$	−47.7497	−	27.5683i	−1.52298	−	0.879292i	−0.999631	−	0.0271723i	$-0.991350\pi$
$983$	−47.7497	−	27.5683i	−1.52298	−	0.879292i	−0.523347	−	0.852119i	$-0.675317\pi$
$984$	1.03584	+	0.256129i	0.0330214	+	0.00816508i
$985$	−31.3600	+	18.1057i	−0.999214	+	0.576896i
$986$	0.0634368	+	0.674809i	0.00202024	+	0.0214903i
$987$		0			0
$988$	−18.3949	+	3.48934i	−0.585221	+	0.111011i
$989$	−2.88978	+	10.7848i	−0.0918896	+	0.342937i
$990$	−15.7258	+	5.83915i	−0.499800	+	0.185580i
$991$	18.4719	−	31.9943i	0.586781	−	1.01633i	−0.407870	−	0.913040i	$-0.633728\pi$
$991$	18.4719	−	31.9943i	0.586781	−	1.01633i	0.994651	−	0.103294i	$-0.0329382\pi$
$992$	7.51014	+	35.7864i	0.238447	+	1.13622i
$993$	−9.96536			−0.316241
$994$		0			0
$995$	44.3910	+	44.3910i	1.40729	+	1.40729i
$996$	4.85573	+	5.63718i	0.153860	+	0.178621i
$997$	0.959891	+	3.58236i	0.0304001	+	0.113455i	0.979459	−	0.201645i	$-0.0646287\pi$
$997$	0.959891	+	3.58236i	0.0304001	+	0.113455i	−0.949059	+	0.315100i	$0.897962\pi$
$998$	18.4937	+	8.47861i	0.585407	+	0.268386i
$999$	0.962950	−	0.555960i	0.0304664	−	0.0175898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.557.7		48
7.2	even	3	inner	784.2.x.o.765.2		48
7.3	odd	6		784.2.m.j.589.9		24
7.4	even	3		784.2.m.k.589.9		24
7.5	odd	6		112.2.w.c.93.2	yes	48
7.6	odd	2		112.2.w.c.109.7	yes	48
16.5	even	4	inner	784.2.x.o.165.2		48
28.19	even	6		448.2.ba.c.401.7		48
28.27	even	2		448.2.ba.c.81.6		48
56.5	odd	6		896.2.ba.f.289.7		48
56.13	odd	2		896.2.ba.f.417.6		48
56.19	even	6		896.2.ba.e.289.6		48
56.27	even	2		896.2.ba.e.417.7		48
112.5	odd	12		112.2.w.c.37.7	✓	48
112.13	odd	4		896.2.ba.f.865.7		48
112.19	even	12		896.2.ba.e.737.7		48
112.27	even	4		448.2.ba.c.305.7		48
112.37	even	12	inner	784.2.x.o.373.7		48
112.53	even	12		784.2.m.k.197.9		24
112.61	odd	12		896.2.ba.f.737.6		48
112.69	odd	4		112.2.w.c.53.2	yes	48
112.75	even	12		448.2.ba.c.177.6		48
112.83	even	4		896.2.ba.e.865.6		48
112.101	odd	12		784.2.m.j.197.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.7	✓	48	112.5	odd	12
112.2.w.c.53.2	yes	48	112.69	odd	4
112.2.w.c.93.2	yes	48	7.5	odd	6
112.2.w.c.109.7	yes	48	7.6	odd	2
448.2.ba.c.81.6		48	28.27	even	2
448.2.ba.c.177.6		48	112.75	even	12
448.2.ba.c.305.7		48	112.27	even	4
448.2.ba.c.401.7		48	28.19	even	6
784.2.m.j.197.9		24	112.101	odd	12
784.2.m.j.589.9		24	7.3	odd	6
784.2.m.k.197.9		24	112.53	even	12
784.2.m.k.589.9		24	7.4	even	3
784.2.x.o.165.2		48	16.5	even	4	inner
784.2.x.o.373.7		48	112.37	even	12	inner
784.2.x.o.557.7		48	1.1	even	1	trivial
784.2.x.o.765.2		48	7.2	even	3	inner
896.2.ba.e.289.6		48	56.19	even	6
896.2.ba.e.417.7		48	56.27	even	2
896.2.ba.e.737.7		48	112.19	even	12
896.2.ba.e.865.6		48	112.83	even	4
896.2.ba.f.289.7		48	56.5	odd	6
896.2.ba.f.417.6		48	56.13	odd	2
896.2.ba.f.737.6		48	112.61	odd	12
896.2.ba.f.865.7		48	112.13	odd	4

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.236566 - 1.39429i) q^{2} +(-0.827840 + 0.221819i) q^{3} +(-1.88807 - 0.659683i) q^{4} +(-4.10878 - 1.10095i) q^{5} +(0.113440 + 1.20672i) q^{6} +(-1.36644 + 2.47646i) q^{8} +(-1.96196 + 1.13274i) q^{9} +O(q^{10})\)	\(q+(0.236566 - 1.39429i) q^{2} +(-0.827840 + 0.221819i) q^{3} +(-1.88807 - 0.659683i) q^{4} +(-4.10878 - 1.10095i) q^{5} +(0.113440 + 1.20672i) q^{6} +(-1.36644 + 2.47646i) q^{8} +(-1.96196 + 1.13274i) q^{9} +(-2.50703 + 5.46838i) q^{10} +(-0.318576 - 1.18894i) q^{11} +(1.70935 + 0.127301i) q^{12} +(1.73092 + 1.73092i) q^{13} +3.64563 q^{15} +(3.12964 + 2.49106i) q^{16} +(0.931914 - 1.61412i) q^{17} +(1.11523 + 3.00350i) q^{18} +(0.989804 - 3.69400i) q^{19} +(7.03141 + 4.78916i) q^{20} +(-1.73309 + 0.162922i) q^{22} +(1.23305 - 0.711901i) q^{23} +(0.581870 - 2.35321i) q^{24} +(11.3399 + 6.54709i) q^{25} +(2.82287 - 2.00392i) q^{26} +(3.19099 - 3.19099i) q^{27} +(-0.181826 - 0.181826i) q^{29} +(0.862433 - 5.08305i) q^{30} +(-3.23200 + 5.59799i) q^{31} +(4.21362 - 3.77431i) q^{32} +(0.527459 + 0.913587i) q^{33} +(-2.03009 - 1.68120i) q^{34} +(4.45157 - 0.844420i) q^{36} +(0.238000 + 0.0637719i) q^{37} +(-4.91634 - 2.25395i) q^{38} +(-1.81687 - 1.04897i) q^{39} +(8.34086 - 8.67085i) q^{40} +0.440182i q^{41} +(-5.54503 + 5.54503i) q^{43} +(-0.182830 + 2.45496i) q^{44} +(9.30835 - 2.49417i) q^{45} +(-0.700896 - 1.88763i) q^{46} +(3.61427 + 6.26009i) q^{47} +(-3.14340 - 1.36799i) q^{48} +(11.8112 - 14.2623i) q^{50} +(-0.413433 + 1.54295i) q^{51} +(-2.12624 - 4.40996i) q^{52} +(-2.59716 - 9.69274i) q^{53} +(-3.69428 - 5.20404i) q^{54} +5.23583i q^{55} +3.27760i q^{57} +(-0.296532 + 0.210504i) q^{58} +(0.438601 + 1.63688i) q^{59} +(-6.88321 - 2.40496i) q^{60} +(-2.41596 + 9.01647i) q^{61} +(7.04063 + 5.83064i) q^{62} +(-4.26567 - 6.76787i) q^{64} +(-5.20632 - 9.01761i) q^{65} +(1.39858 - 0.519306i) q^{66} +(9.59422 - 2.57076i) q^{67} +(-2.82433 + 2.43281i) q^{68} +(-0.862854 + 0.862854i) q^{69} +11.2912i q^{71} +(-0.124272 - 6.40653i) q^{72} +(8.13092 + 4.69439i) q^{73} +(0.145219 - 0.316754i) q^{74} +(-10.8399 - 2.90454i) q^{75} +(-4.30569 + 6.32158i) q^{76} +(-1.89238 + 2.28509i) q^{78} +(6.52948 + 11.3094i) q^{79} +(-10.1165 - 13.6808i) q^{80} +(1.46441 - 2.53643i) q^{81} +(0.613739 + 0.104132i) q^{82} +(3.06926 + 3.06926i) q^{83} +(-5.60609 + 5.60609i) q^{85} +(6.41960 + 9.04313i) q^{86} +(0.190855 + 0.110190i) q^{87} +(3.37967 + 0.835679i) q^{88} +(5.66084 - 3.26829i) q^{89} +(-1.27554 - 13.5686i) q^{90} +(-2.79771 + 0.530699i) q^{92} +(1.43384 - 5.35117i) q^{93} +(9.58338 - 3.55840i) q^{94} +(-8.13378 + 14.0881i) q^{95} +(-2.65099 + 4.05919i) q^{96} -1.70409 q^{97} +(1.97179 + 1.97179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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