LMFDB - Embedded newform 966.2.q.b.463.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	966.463
Dual form			966.2.q.b.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.186393 + 0.215109i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.186393 + 0.215109i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.239446 + 0.153882i) q^{10} +(0.181716 - 1.26386i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-3.53631 - 2.27265i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.118239 + 0.258908i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-4.19227 - 1.23096i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(2.72514 - 0.800172i) q^{19} +(0.118239 - 0.258908i) q^{20} +(0.142315 + 0.989821i) q^{21} -1.27686 q^{22} +(-3.51302 + 3.26476i) q^{23} +1.00000 q^{24} +(0.700045 + 4.86892i) q^{25} +(-1.74625 + 3.82374i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.654861 - 0.755750i) q^{28} +(-4.85399 - 1.42526i) q^{29} +(0.239446 - 0.153882i) q^{30} +(-2.46834 - 5.40491i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-1.07416 - 0.690322i) q^{33} +(-0.621810 + 4.32479i) q^{34} +(0.0405070 - 0.281733i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-5.75825 - 6.64538i) q^{37} +(-1.17986 - 2.58352i) q^{38} +(-3.53631 + 2.27265i) q^{39} +(-0.273100 - 0.0801894i) q^{40} +(0.171292 - 0.197682i) q^{41} +(0.959493 - 0.281733i) q^{42} +(-2.02145 + 4.42636i) q^{43} +(0.181716 + 1.26386i) q^{44} +0.284630 q^{45} +(3.73149 + 3.01264i) q^{46} -5.56452 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(4.71973 - 1.38584i) q^{50} +(-2.86126 + 3.30207i) q^{51} +(4.03334 + 1.18430i) q^{52} +(-3.42550 + 2.20143i) q^{53} +(0.415415 + 0.909632i) q^{54} +(0.237997 + 0.274663i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(0.404200 - 2.81127i) q^{57} +(-0.719958 + 5.00742i) q^{58} +(-0.715900 - 0.460081i) q^{59} +(-0.186393 - 0.215109i) q^{60} +(5.19243 + 11.3698i) q^{61} +(-4.99862 + 3.21242i) q^{62} +(0.959493 + 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.14801 - 0.337086i) q^{65} +(-0.530426 + 1.16147i) q^{66} +(1.48241 + 10.3104i) q^{67} +4.36926 q^{68} +(1.51037 + 4.55179i) q^{69} -0.284630 q^{70} +(-2.19812 - 15.2883i) q^{71} +(0.415415 - 0.909632i) q^{72} +(6.50955 - 1.91138i) q^{73} +(-5.75825 + 6.64538i) q^{74} +(4.71973 + 1.38584i) q^{75} +(-2.38931 + 1.53552i) q^{76} +(0.530426 + 1.16147i) q^{77} +(2.75278 + 3.17688i) q^{78} +(0.0890471 + 0.0572271i) q^{79} +(-0.0405070 + 0.281733i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.220047 - 0.141416i) q^{82} +(-8.36616 - 9.65507i) q^{83} +(-0.415415 - 0.909632i) q^{84} +(1.04620 - 0.672352i) q^{85} +(4.66899 + 1.37094i) q^{86} +(-3.31288 + 3.82327i) q^{87} +(1.22514 - 0.359733i) q^{88} +(3.69269 - 8.08586i) q^{89} +(-0.0405070 - 0.281733i) q^{90} +4.20362 q^{91} +(2.45093 - 4.12225i) q^{92} -5.94187 q^{93} +(0.791914 + 5.50789i) q^{94} +(-0.335822 + 0.735347i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(4.54057 - 5.24010i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-1.07416 + 0.690322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 2 q^{10} + 7 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + 11 q^{19} + 2 q^{20} + q^{21} + 18 q^{22} + 21 q^{23} + 10 q^{24} + q^{25} - 2 q^{26} - q^{27} + q^{28} - 20 q^{29} + 2 q^{30} + 18 q^{31} - q^{32} - 15 q^{33} + 5 q^{34} + 9 q^{35} - q^{36} + 5 q^{37} - 22 q^{38} - 2 q^{39} + 2 q^{40} + 6 q^{41} + q^{42} - 12 q^{43} + 7 q^{44} + 2 q^{45} + 21 q^{46} - 32 q^{47} - q^{48} - q^{49} + 12 q^{50} - 17 q^{51} + 9 q^{52} - 39 q^{53} - q^{54} + 8 q^{55} + q^{56} + 22 q^{57} + 13 q^{58} + 15 q^{59} + 2 q^{60} + 21 q^{61} - 4 q^{62} + q^{63} - q^{64} - 7 q^{65} - 4 q^{66} - 26 q^{67} - 6 q^{68} - 12 q^{69} - 2 q^{70} + 27 q^{71} - q^{72} - 2 q^{73} + 5 q^{74} + 12 q^{75} + 4 q^{77} - 2 q^{78} + 47 q^{79} - 9 q^{80} - q^{81} + 6 q^{82} + 5 q^{83} + q^{84} + q^{85} - 12 q^{86} - 9 q^{87} - 4 q^{88} + 5 q^{89} - 9 q^{90} + 24 q^{91} + 10 q^{92} - 26 q^{93} + 23 q^{94} - 11 q^{95} - q^{96} + 2 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9 + 2 * q^10 + 7 * q^11 - q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 6 * q^17 - q^18 + 11 * q^19 + 2 * q^20 + q^21 + 18 * q^22 + 21 * q^23 + 10 * q^24 + q^25 - 2 * q^26 - q^27 + q^28 - 20 * q^29 + 2 * q^30 + 18 * q^31 - q^32 - 15 * q^33 + 5 * q^34 + 9 * q^35 - q^36 + 5 * q^37 - 22 * q^38 - 2 * q^39 + 2 * q^40 + 6 * q^41 + q^42 - 12 * q^43 + 7 * q^44 + 2 * q^45 + 21 * q^46 - 32 * q^47 - q^48 - q^49 + 12 * q^50 - 17 * q^51 + 9 * q^52 - 39 * q^53 - q^54 + 8 * q^55 + q^56 + 22 * q^57 + 13 * q^58 + 15 * q^59 + 2 * q^60 + 21 * q^61 - 4 * q^62 + q^63 - q^64 - 7 * q^65 - 4 * q^66 - 26 * q^67 - 6 * q^68 - 12 * q^69 - 2 * q^70 + 27 * q^71 - q^72 - 2 * q^73 + 5 * q^74 + 12 * q^75 + 4 * q^77 - 2 * q^78 + 47 * q^79 - 9 * q^80 - q^81 + 6 * q^82 + 5 * q^83 + q^84 + q^85 - 12 * q^86 - 9 * q^87 - 4 * q^88 + 5 * q^89 - 9 * q^90 + 24 * q^91 + 10 * q^92 - 26 * q^93 + 23 * q^94 - 11 * q^95 - q^96 + 2 * q^97 - q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.186393	+	0.215109i	−0.0833574	+	0.0961996i	−0.795896	−	0.605433i	$-0.793000\pi$
$5$	−0.186393	+	0.215109i	−0.0833574	+	0.0961996i	0.712539	+	0.701633i	$0.247545\pi$
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	0.239446	+	0.153882i	0.0757194	+	0.0486619i
$11$	0.181716	−	1.26386i	0.0547894	−	0.381069i	−0.943915	−	0.330188i	$-0.892888\pi$
$11$	0.181716	−	1.26386i	0.0547894	−	0.381069i	0.998705	−	0.0508810i	$-0.0162029\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	−3.53631	−	2.27265i	−0.980795	−	0.630319i	−0.0511173	−	0.998693i	$-0.516278\pi$
$13$	−3.53631	−	2.27265i	−0.980795	−	0.630319i	−0.929678	+	0.368374i	$0.879915\pi$
$14$	0.654861	+	0.755750i	0.175019	+	0.201983i
$15$	0.118239	+	0.258908i	0.0305293	+	0.0668498i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−4.19227	−	1.23096i	−1.01678	−	0.298552i	−0.269453	−	0.963014i	$-0.586843\pi$
$17$	−4.19227	−	1.23096i	−1.01678	−	0.298552i	−0.747323	+	0.664461i	$0.768661\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	2.72514	−	0.800172i	0.625189	−	0.183572i	0.0462329	−	0.998931i	$-0.485278\pi$
$19$	2.72514	−	0.800172i	0.625189	−	0.183572i	0.578956	+	0.815359i	$0.303460\pi$
$20$	0.118239	−	0.258908i	0.0264391	−	0.0578936i
$21$	0.142315	+	0.989821i	0.0310556	+	0.215997i
$22$	−1.27686			−0.272227
$23$	−3.51302	+	3.26476i	−0.732516	+	0.680750i
$23$	−3.51302	+	3.26476i	−0.732516	+	0.680750i
$24$	1.00000			0.204124
$25$	0.700045	+	4.86892i	0.140009	+	0.973784i
$26$	−1.74625	+	3.82374i	−0.342467	+	0.749898i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	0.654861	−	0.755750i	0.123757	−	0.142823i
$29$	−4.85399	−	1.42526i	−0.901363	−	0.264664i	−0.201962	−	0.979393i	$-0.564732\pi$
$29$	−4.85399	−	1.42526i	−0.901363	−	0.264664i	−0.699401	+	0.714729i	$0.746550\pi$
$30$	0.239446	−	0.153882i	0.0437166	−	0.0280950i
$31$	−2.46834	−	5.40491i	−0.443327	−	0.970751i	−0.990976	−	0.134042i	$-0.957204\pi$
$31$	−2.46834	−	5.40491i	−0.443327	−	0.970751i	0.547649	−	0.836708i	$-0.315523\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−1.07416	−	0.690322i	−0.186988	−	0.120170i
$34$	−0.621810	+	4.32479i	−0.106640	+	0.741695i
$35$	0.0405070	−	0.281733i	0.00684694	−	0.0476215i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−5.75825	−	6.64538i	−0.946651	−	1.09249i	−0.995601	−	0.0936919i	$-0.970133\pi$
$37$	−5.75825	−	6.64538i	−0.946651	−	1.09249i	0.0489506	−	0.998801i	$-0.484412\pi$
$38$	−1.17986	−	2.58352i	−0.191398	−	0.419103i
$39$	−3.53631	+	2.27265i	−0.566262	+	0.363915i
$40$	−0.273100	−	0.0801894i	−0.0431809	−	0.0126791i
$41$	0.171292	−	0.197682i	0.0267514	−	0.0308727i	−0.742216	−	0.670160i	$-0.766225\pi$
$41$	0.171292	−	0.197682i	0.0267514	−	0.0308727i	0.768968	+	0.639288i	$0.220771\pi$
$42$	0.959493	−	0.281733i	0.148053	−	0.0434723i
$43$	−2.02145	+	4.42636i	−0.308268	+	0.675014i	−0.998835	−	0.0482551i	$-0.984634\pi$
$43$	−2.02145	+	4.42636i	−0.308268	+	0.675014i	0.690567	+	0.723269i	$0.257361\pi$
$44$	0.181716	+	1.26386i	0.0273947	+	0.190534i
$45$	0.284630			0.0424301
$46$	3.73149	+	3.01264i	0.550178	+	0.444190i
$47$	−5.56452			−0.811669			−0.405835	−	0.913947i	$-0.633019\pi$
$47$	−5.56452			−0.811669			−0.405835	+	0.913947i	$0.633019\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	4.71973	−	1.38584i	0.667471	−	0.195987i
$51$	−2.86126	+	3.30207i	−0.400656	+	0.462382i
$52$	4.03334	+	1.18430i	0.559324	+	0.164232i
$53$	−3.42550	+	2.20143i	−0.470528	+	0.302390i	−0.754333	−	0.656492i	$-0.772040\pi$
$53$	−3.42550	+	2.20143i	−0.470528	+	0.302390i	0.283805	+	0.958882i	$0.408403\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	0.237997	+	0.274663i	0.0320915	+	0.0370356i
$56$	−0.841254	−	0.540641i	−0.112417	−	0.0722462i
$57$	0.404200	−	2.81127i	0.0535376	−	0.372362i
$58$	−0.719958	+	5.00742i	−0.0945351	+	0.657506i
$59$	−0.715900	−	0.460081i	−0.0932022	−	0.0598974i	0.493210	−	0.869911i	$-0.335824\pi$
$59$	−0.715900	−	0.460081i	−0.0932022	−	0.0598974i	−0.586412	+	0.810013i	$0.699460\pi$
$60$	−0.186393	−	0.215109i	−0.0240632	−	0.0277704i
$61$	5.19243	+	11.3698i	0.664822	+	1.45576i	0.877959	+	0.478736i	$0.158905\pi$
$61$	5.19243	+	11.3698i	0.664822	+	1.45576i	−0.213137	+	0.977022i	$0.568368\pi$
$62$	−4.99862	+	3.21242i	−0.634825	+	0.407977i
$63$	0.959493	+	0.281733i	0.120885	+	0.0354950i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	1.14801	−	0.337086i	0.142393	−	0.0418103i
$66$	−0.530426	+	1.16147i	−0.0652909	+	0.142967i
$67$	1.48241	+	10.3104i	0.181105	+	1.25961i	0.854156	+	0.520017i	$0.174074\pi$
$67$	1.48241	+	10.3104i	0.181105	+	1.25961i	−0.673051	+	0.739596i	$0.735016\pi$
$68$	4.36926			0.529850
$69$	1.51037	+	4.55179i	0.181827	+	0.547971i
$70$	−0.284630			−0.0340198
$71$	−2.19812	−	15.2883i	−0.260869	−	1.81438i	−0.526350	−	0.850268i	$-0.676440\pi$
$71$	−2.19812	−	15.2883i	−0.260869	−	1.81438i	0.265481	−	0.964116i	$-0.414469\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	6.50955	−	1.91138i	0.761886	−	0.223710i	0.122366	−	0.992485i	$-0.460952\pi$
$73$	6.50955	−	1.91138i	0.761886	−	0.223710i	0.639519	+	0.768775i	$0.279133\pi$
$74$	−5.75825	+	6.64538i	−0.669383	+	0.772509i
$75$	4.71973	+	1.38584i	0.544988	+	0.160023i
$76$	−2.38931	+	1.53552i	−0.274073	+	0.176136i
$77$	0.530426	+	1.16147i	0.0604477	+	0.132362i
$78$	2.75278	+	3.17688i	0.311691	+	0.359711i
$79$	0.0890471	+	0.0572271i	0.0100186	+	0.00643855i	0.545641	−	0.838019i	$-0.316286\pi$
$79$	0.0890471	+	0.0572271i	0.0100186	+	0.00643855i	−0.535622	+	0.844458i	$0.679923\pi$
$80$	−0.0405070	+	0.281733i	−0.00452882	+	0.0314987i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.220047	−	0.141416i	−0.0243002	−	0.0156168i
$83$	−8.36616	−	9.65507i	−0.918306	−	1.05978i	−0.998016	−	0.0629633i	$-0.979945\pi$
$83$	−8.36616	−	9.65507i	−0.918306	−	1.05978i	0.0797100	−	0.996818i	$-0.474601\pi$
$84$	−0.415415	−	0.909632i	−0.0453255	−	0.0992490i
$85$	1.04620	−	0.672352i	0.113476	−	0.0729268i
$86$	4.66899	+	1.37094i	0.503470	+	0.147832i
$87$	−3.31288	+	3.82327i	−0.355178	+	0.409897i
$88$	1.22514	−	0.359733i	0.130600	−	0.0383476i
$89$	3.69269	−	8.08586i	0.391424	−	0.857100i	−0.606644	−	0.794974i	$-0.707485\pi$
$89$	3.69269	−	8.08586i	0.391424	−	0.857100i	0.998068	−	0.0621262i	$-0.0197881\pi$
$90$	−0.0405070	−	0.281733i	−0.00426982	−	0.0296972i
$91$	4.20362			0.440659
$92$	2.45093	−	4.12225i	0.255527	−	0.429774i
$93$	−5.94187			−0.616143
$94$	0.791914	+	5.50789i	0.0816797	+	0.568095i
$95$	−0.335822	+	0.735347i	−0.0344546	+	0.0754450i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	4.54057	−	5.24010i	0.461025	−	0.532051i	−0.476868	−	0.878975i	$-0.658228\pi$
$97$	4.54057	−	5.24010i	0.461025	−	0.532051i	0.937893	+	0.346923i	$0.112774\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	−1.07416	+	0.690322i	−0.107957	+	0.0693799i
$100$	−2.04342	−	4.47447i	−0.204342	−	0.447447i
$101$	6.81504	+	7.86498i	0.678122	+	0.782595i	0.985624	−	0.168953i	$-0.0540386\pi$
$101$	6.81504	+	7.86498i	0.678122	+	0.782595i	−0.307502	+	0.951547i	$0.599493\pi$
$102$	3.67565	+	2.36220i	0.363944	+	0.233893i
$103$	−0.228418	+	1.58868i	−0.0225067	+	0.156538i	−0.997975	−	0.0636004i	$-0.979742\pi$
$103$	−0.228418	+	1.58868i	−0.0225067	+	0.156538i	0.975469	+	0.220138i	$0.0706508\pi$
$104$	0.598237	−	4.16083i	0.0586620	−	0.408003i
$105$	−0.239446	−	0.153882i	−0.0233675	−	0.0150174i
$106$	2.66652	+	3.07733i	0.258996	+	0.298897i
$107$	1.85455	+	4.06089i	0.179286	+	0.392581i	0.977844	−	0.209337i	$-0.0671306\pi$
$107$	1.85455	+	4.06089i	0.179286	+	0.392581i	−0.798558	+	0.601918i	$0.794403\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	6.95106	+	2.04102i	0.665791	+	0.195494i	0.597128	−	0.802146i	$-0.296308\pi$
$109$	6.95106	+	2.04102i	0.665791	+	0.195494i	0.0686632	+	0.997640i	$0.478127\pi$
$110$	0.237997	−	0.274663i	0.0226921	−	0.0261881i
$111$	−8.43691	+	2.47730i	−0.800796	+	0.235135i
$112$	−0.415415	+	0.909632i	−0.0392530	+	0.0859521i
$113$	−0.0696638	−	0.484522i	−0.00655341	−	0.0455800i	0.986282	−	0.165067i	$-0.0527841\pi$
$113$	−0.0696638	−	0.484522i	−0.00655341	−	0.0455800i	−0.992836	+	0.119487i	$0.961875\pi$
$114$	−2.84018			−0.266008
$115$	−0.0474770	−	1.36421i	−0.00442725	−	0.127213i
$116$	5.05891			0.469708
$117$	0.598237	+	4.16083i	0.0553070	+	0.384669i
$118$	−0.353515	+	0.774089i	−0.0325437	+	0.0712607i
$119$	4.19227	−	1.23096i	0.384305	−	0.112842i
$120$	−0.186393	+	0.215109i	−0.0170153	+	0.0196367i
$121$	8.99010	+	2.63973i	0.817282	+	0.239976i
$122$	10.5151	−	6.75767i	0.951996	−	0.611811i
$123$	−0.108660	−	0.237933i	−0.00979758	−	0.0214537i
$124$	3.89109	+	4.49056i	0.349431	+	0.403264i
$125$	−2.37506	−	1.52636i	−0.212432	−	0.136522i
$126$	0.142315	−	0.989821i	0.0126784	−	0.0881803i
$127$	2.32137	−	16.1455i	0.205988	−	1.43268i	−0.580090	−	0.814553i	$-0.696983\pi$
$127$	2.32137	−	16.1455i	0.205988	−	1.43268i	0.786078	−	0.618127i	$-0.212108\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	3.18662	+	3.67755i	0.280566	+	0.323791i
$130$	−0.497033	−	1.08835i	−0.0435927	−	0.0954547i
$131$	−11.9976	+	7.71038i	−1.04823	+	0.673659i	−0.947010	−	0.321205i	$-0.895912\pi$
$131$	−11.9976	+	7.71038i	−1.04823	+	0.673659i	−0.101224	+	0.994864i	$0.532276\pi$
$132$	1.22514	+	0.359733i	0.106634	+	0.0313107i
$133$	−1.85992	+	2.14647i	−0.161276	+	0.186122i
$134$	9.99447	−	2.93464i	0.863391	−	0.253514i
$135$	0.118239	−	0.258908i	0.0101764	−	0.0222833i
$136$	−0.621810	−	4.32479i	−0.0533198	−	0.370847i
$137$	−17.0053			−1.45286			−0.726432	−	0.687238i	$-0.758823\pi$
$137$	−17.0053			−1.45286			−0.726432	+	0.687238i	$0.758823\pi$
$138$	4.29051	−	2.14278i	0.365232	−	0.182406i
$139$	−3.84405			−0.326048			−0.163024	−	0.986622i	$-0.552125\pi$
$139$	−3.84405			−0.326048			−0.163024	+	0.986622i	$0.552125\pi$
$140$	0.0405070	+	0.281733i	0.00342347	+	0.0238107i
$141$	−2.31159	+	5.06167i	−0.194671	+	0.426269i
$142$	−14.8198	+	4.35150i	−1.24365	+	0.365169i
$143$	−3.51491	+	4.05643i	−0.293932	+	0.339215i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	1.21133	−	0.778477i	0.100596	−	0.0646490i
$146$	−2.81833	−	6.17128i	−0.233247	−	0.510739i
$147$	−0.654861	−	0.755750i	−0.0540120	−	0.0623332i
$148$	7.39722	+	4.75390i	0.608048	+	0.390769i
$149$	2.91827	−	20.2970i	0.239074	−	1.66280i	−0.417605	−	0.908629i	$-0.637130\pi$
$149$	2.91827	−	20.2970i	0.239074	−	1.66280i	0.656679	−	0.754170i	$-0.271960\pi$
$150$	0.700045	−	4.86892i	0.0571584	−	0.397545i
$151$	−15.3388	−	9.85764i	−1.24825	−	0.802203i	−0.261621	−	0.965171i	$-0.584257\pi$
$151$	−15.3388	−	9.85764i	−1.24825	−	0.802203i	−0.986631	+	0.162968i	$0.947893\pi$
$152$	1.85992	+	2.14647i	0.150860	+	0.174102i
$153$	1.81506	+	3.97442i	0.146739	+	0.321313i
$154$	1.07416	−	0.690322i	0.0865584	−	0.0556277i
$155$	1.62272	+	0.476475i	0.130340	+	0.0382714i
$156$	2.75278	−	3.17688i	0.220399	−	0.254354i
$157$	15.5791	−	4.57442i	1.24334	−	0.365079i	0.407073	−	0.913395i	$-0.366549\pi$
$157$	15.5791	−	4.57442i	1.24334	−	0.365079i	0.836271	+	0.548317i	$0.184731\pi$
$158$	0.0439719	−	0.0962850i	0.00349821	−	0.00766002i
$159$	0.579491	+	4.03045i	0.0459566	+	0.319635i
$160$	0.284630			0.0225020
$161$	1.19028	−	4.64578i	0.0938071	−	0.366138i
$162$	1.00000			0.0785674
$163$	2.72747	+	18.9699i	0.213632	+	1.48584i	0.760892	+	0.648878i	$0.224762\pi$
$163$	2.72747	+	18.9699i	0.213632	+	1.48584i	−0.547261	+	0.836962i	$0.684329\pi$
$164$	−0.108660	+	0.237933i	−0.00848495	+	0.0185794i
$165$	0.348710	−	0.102391i	0.0271471	−	0.00797109i
$166$	−8.36616	+	9.65507i	−0.649340	+	0.749379i
$167$	−3.08464	−	0.905732i	−0.238696	−	0.0700876i	0.160196	−	0.987085i	$-0.448787\pi$
$167$	−3.08464	−	0.905732i	−0.238696	−	0.0700876i	−0.398893	+	0.916998i	$0.630605\pi$
$168$	−0.841254	+	0.540641i	−0.0649041	+	0.0417113i
$169$	1.94015	+	4.24833i	0.149242	+	0.326795i
$170$	−0.814398	−	0.939866i	−0.0624615	−	0.0720844i
$171$	−2.38931	−	1.53552i	−0.182715	−	0.117424i
$172$	0.692518	−	4.81657i	0.0528040	−	0.367260i
$173$	2.53606	−	17.6387i	0.192813	−	1.34105i	−0.631704	−	0.775210i	$-0.717644\pi$
$173$	2.53606	−	17.6387i	0.192813	−	1.34105i	0.824517	−	0.565837i	$-0.191447\pi$
$174$	4.25582	+	2.73505i	0.322633	+	0.207344i
$175$	−3.22125	−	3.71752i	−0.243504	−	0.281018i
$176$	−0.530426	−	1.16147i	−0.0399824	−	0.0875492i
$177$	−0.715900	+	0.460081i	−0.0538103	+	0.0345818i
$178$	−8.52909	−	2.50437i	−0.639282	−	0.187710i
$179$	−1.93456	+	2.23260i	−0.144596	+	0.166872i	−0.823427	−	0.567422i	$-0.807941\pi$
$179$	−1.93456	+	2.23260i	−0.144596	+	0.166872i	0.678832	+	0.734294i	$0.262486\pi$
$180$	−0.273100	+	0.0801894i	−0.0203557	+	0.00597697i
$181$	8.91460	−	19.5203i	0.662617	−	1.45093i	−0.217446	−	0.976072i	$-0.569773\pi$
$181$	8.91460	−	19.5203i	0.662617	−	1.45093i	0.880063	−	0.474857i	$-0.157500\pi$
$182$	−0.598237	−	4.16083i	−0.0443443	−	0.308421i
$183$	12.4994			0.923981
$184$	−4.42909	−	1.83933i	−0.326517	−	0.135597i
$185$	2.50278			0.184008
$186$	0.845616	+	5.88139i	0.0620035	+	0.431244i
$187$	−2.31757	+	5.07477i	−0.169477	+	0.371104i
$188$	5.33912	−	1.56771i	0.389396	−	0.114337i
$189$	0.654861	−	0.755750i	0.0476341	−	0.0549727i
$190$	0.775655	+	0.227753i	0.0562719	+	0.0165229i
$191$	3.80096	−	2.44273i	0.275028	−	0.176750i	−0.395855	−	0.918313i	$-0.629552\pi$
$191$	3.80096	−	2.44273i	0.275028	−	0.176750i	0.670883	+	0.741563i	$0.265915\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	15.3281	+	17.6896i	1.10334	+	1.27333i	0.958878	+	0.283817i	$0.0916009\pi$
$193$	15.3281	+	17.6896i	1.10334	+	1.27333i	0.144466	+	0.989510i	$0.453854\pi$
$194$	−5.83295	−	3.74861i	−0.418782	−	0.269135i
$195$	0.170276	−	1.18430i	0.0121937	−	0.0848092i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	−12.0263	−	7.72886i	−0.856841	−	0.550658i	0.0368606	−	0.999320i	$-0.488264\pi$
$197$	−12.0263	−	7.72886i	−0.856841	−	0.550658i	−0.893701	+	0.448662i	$0.851901\pi$
$198$	0.836164	+	0.964985i	0.0594236	+	0.0685785i
$199$	−1.73432	−	3.79764i	−0.122943	−	0.269208i	0.838146	−	0.545446i	$-0.183640\pi$
$199$	−1.73432	−	3.79764i	−0.122943	−	0.269208i	−0.961089	+	0.276238i	$0.910912\pi$
$200$	−4.13811	+	2.65940i	−0.292609	+	0.188048i
$201$	9.99447	+	2.93464i	0.704955	+	0.206994i
$202$	6.81504	−	7.86498i	0.479505	−	0.553378i
$203$	4.85399	−	1.42526i	0.340683	−	0.100034i
$204$	1.81506	−	3.97442i	0.127079	−	0.278265i
$205$	0.0105955	+	0.0736930i	0.000740018	+	0.00514694i
$206$	1.60502			0.111827
$207$	4.76788	+	0.517000i	0.331391	+	0.0359340i
$208$	−4.20362			−0.291468
$209$	−0.516106	−	3.58960i	−0.0356998	−	0.248298i
$210$	−0.118239	+	0.258908i	−0.00815930	+	0.0178664i
$211$	−12.6501	+	3.71442i	−0.870872	+	0.255711i	−0.686486	−	0.727143i	$-0.740848\pi$
$211$	−12.6501	+	3.71442i	−0.870872	+	0.255711i	−0.184386	+	0.982854i	$0.559030\pi$
$212$	2.66652	−	3.07733i	0.183138	−	0.211352i
$213$	−14.8198	−	4.35150i	−1.01544	−	0.298160i
$214$	3.75563	−	2.41359i	0.256729	−	0.164990i
$215$	−0.575365	−	1.25987i	−0.0392396	−	0.0859227i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	4.99862	+	3.21242i	0.339328	+	0.218073i
$218$	1.03100	−	7.17078i	0.0698283	−	0.485666i
$219$	0.965516	−	6.71531i	0.0652435	−	0.453779i
$220$	−0.305738	−	0.196486i	−0.0206129	−	0.0132471i
$221$	12.0276	+	13.8806i	0.809065	+	0.933711i
$222$	3.65278	+	7.99848i	0.245159	+	0.536823i
$223$	6.07881	−	3.90661i	0.407067	−	0.261606i	−0.321045	−	0.947064i	$-0.604034\pi$
$223$	6.07881	−	3.90661i	0.407067	−	0.261606i	0.728113	+	0.685458i	$0.240398\pi$
$224$	0.959493	+	0.281733i	0.0641088	+	0.0188240i
$225$	3.22125	−	3.71752i	0.214750	−	0.247835i
$226$	−0.469676	+	0.137909i	−0.0312424	+	0.00917359i
$227$	7.27617	−	15.9326i	0.482937	−	1.05748i	−0.498709	−	0.866769i	$-0.666192\pi$
$227$	7.27617	−	15.9326i	0.482937	−	1.05748i	0.981646	−	0.190714i	$-0.0610804\pi$
$228$	0.404200	+	2.81127i	0.0267688	+	0.186181i
$229$	−4.31656			−0.285246			−0.142623	−	0.989777i	$-0.545554\pi$
$229$	−4.31656			−0.285246			−0.142623	+	0.989777i	$0.545554\pi$
$230$	−1.34357	+	0.241141i	−0.0885922	+	0.0159004i
$231$	1.27686			0.0840111
$232$	−0.719958	−	5.00742i	−0.0472675	−	0.328753i
$233$	−6.01483	+	13.1706i	−0.394045	+	0.862838i	0.603795	+	0.797140i	$0.293655\pi$
$233$	−6.01483	+	13.1706i	−0.394045	+	0.862838i	−0.997840	+	0.0656980i	$0.979073\pi$
$234$	4.03334	−	1.18430i	0.263668	−	0.0774198i
$235$	1.03719	−	1.19698i	0.0676586	−	0.0780822i
$236$	0.816521	+	0.239752i	0.0531510	+	0.0156065i
$237$	0.0890471	−	0.0572271i	0.00578423	−	0.00371730i
$238$	−1.81506	−	3.97442i	−0.117653	−	0.257623i
$239$	−10.9310	−	12.6151i	−0.707070	−	0.816002i	0.282620	−	0.959232i	$-0.408797\pi$
$239$	−10.9310	−	12.6151i	−0.707070	−	0.816002i	−0.989689	+	0.143230i	$0.954251\pi$
$240$	0.239446	+	0.153882i	0.0154562	+	0.00993307i
$241$	2.20399	−	15.3291i	0.141972	−	0.987434i	−0.786913	−	0.617064i	$-0.788322\pi$
$241$	2.20399	−	15.3291i	0.141972	−	0.987434i	0.928884	−	0.370370i	$-0.120769\pi$
$242$	1.33344	−	9.27426i	0.0857166	−	0.596172i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	−8.18535	−	9.44640i	−0.524013	−	0.604744i
$245$	0.118239	+	0.258908i	0.00755404	+	0.0165410i
$246$	−0.220047	+	0.141416i	−0.0140297	+	0.00901634i
$247$	−11.4554	−	3.36362i	−0.728891	−	0.214022i
$248$	3.89109	−	4.49056i	0.247085	−	0.285151i
$249$	−12.2580	+	3.59927i	−0.776819	+	0.228094i
$250$	−1.17282	+	2.56811i	−0.0741754	+	0.162421i
$251$	−3.16319	−	22.0005i	−0.199659	−	1.38866i	−0.805275	−	0.592901i	$-0.797983\pi$
$251$	−3.16319	−	22.0005i	−0.199659	−	1.38866i	0.605616	−	0.795757i	$-0.292927\pi$
$252$	−1.00000			−0.0629941
$253$	3.48784	+	5.03323i	0.219278	+	0.316437i
$254$	−16.3115			−1.02348
$255$	−0.176986	−	1.23096i	−0.0110833	−	0.0770859i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−0.891708	+	0.261829i	−0.0556232	+	0.0163324i	−0.309426	−	0.950924i	$-0.600137\pi$
$257$	−0.891708	+	0.261829i	−0.0556232	+	0.0163324i	0.253803	+	0.967256i	$0.418319\pi$
$258$	3.18662	−	3.67755i	0.198390	−	0.228954i
$259$	8.43691	+	2.47730i	0.524244	+	0.153932i
$260$	−1.00654	+	0.646863i	−0.0624228	+	0.0401167i
$261$	2.10155	+	4.60174i	0.130082	+	0.284841i
$262$	9.33933	+	10.7782i	0.576986	+	0.665877i
$263$	19.7972	+	12.7229i	1.22075	+	0.784528i	0.982425	−	0.186658i	$-0.0597657\pi$
$263$	19.7972	+	12.7229i	1.22075	+	0.784528i	0.238324	+	0.971186i	$0.423402\pi$
$264$	0.181716	−	1.26386i	0.0111838	−	0.0777853i
$265$	0.164940	−	1.14719i	0.0101322	−	0.0704710i
$266$	2.38931	+	1.53552i	0.146498	+	0.0941487i
$267$	−5.82116	−	6.71798i	−0.356249	−	0.411134i
$268$	−4.32713	−	9.47510i	−0.264322	−	0.578784i
$269$	13.6157	−	8.75025i	0.830161	−	0.533512i	−0.0551679	−	0.998477i	$-0.517569\pi$
$269$	13.6157	−	8.75025i	0.830161	−	0.533512i	0.885329	+	0.464965i	$0.153933\pi$
$270$	−0.273100	−	0.0801894i	−0.0166203	−	0.00488017i
$271$	7.04791	−	8.13373i	0.428130	−	0.494089i	−0.500166	−	0.865929i	$-0.666728\pi$
$271$	7.04791	−	8.13373i	0.428130	−	0.494089i	0.928297	+	0.371841i	$0.121273\pi$
$272$	−4.19227	+	1.23096i	−0.254194	+	0.0746381i
$273$	1.74625	−	3.82374i	0.105688	−	0.231423i
$274$	2.42011	+	16.8322i	0.146204	+	1.01687i
$275$	6.28085			0.378749
$276$	−2.73158	−	3.94189i	−0.164422	−	0.237274i
$277$	−19.3548			−1.16292			−0.581458	−	0.813576i	$-0.697518\pi$
$277$	−19.3548			−1.16292			−0.581458	+	0.813576i	$0.697518\pi$
$278$	0.547066	+	3.80493i	0.0328108	+	0.228204i
$279$	−2.46834	+	5.40491i	−0.147776	+	0.323584i
$280$	0.273100	−	0.0801894i	0.0163209	−	0.00479224i
$281$	7.98520	−	9.21541i	0.476357	−	0.549745i	−0.465812	−	0.884884i	$-0.654238\pi$
$281$	7.98520	−	9.21541i	0.476357	−	0.549745i	0.942169	+	0.335138i	$0.108783\pi$
$282$	5.33912	+	1.56771i	0.317940	+	0.0933556i
$283$	−3.04992	+	1.96007i	−0.181299	+	0.116514i	−0.628143	−	0.778098i	$-0.716185\pi$
$283$	−3.04992	+	1.96007i	−0.181299	+	0.116514i	0.446843	+	0.894612i	$0.352548\pi$
$284$	6.41629	+	14.0497i	0.380737	+	0.833697i
$285$	0.529390	+	0.610948i	0.0313583	+	0.0361895i
$286$	4.51536	+	2.90185i	0.266999	+	0.171590i
$287$	−0.0372254	+	0.258908i	−0.00219735	+	0.0152829i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	1.75858	+	1.13017i	0.103446	+	0.0664805i
$290$	−0.942944	−	1.08822i	−0.0553716	−	0.0639022i
$291$	−2.88034	−	6.30706i	−0.168849	−	0.369727i
$292$	−5.70737	+	3.66791i	−0.333999	+	0.214648i
$293$	6.20335	+	1.82147i	0.362404	+	0.106411i	0.457865	−	0.889022i	$-0.348614\pi$
$293$	6.20335	+	1.82147i	0.362404	+	0.106411i	−0.0954610	+	0.995433i	$0.530433\pi$
$294$	−0.654861	+	0.755750i	−0.0381923	+	0.0440762i
$295$	0.232406	−	0.0682406i	0.0135312	−	0.00397312i
$296$	3.65278	−	7.99848i	0.212314	−	0.464902i
$297$	0.181716	+	1.26386i	0.0105442	+	0.0733367i
$298$	−20.5058			−1.18787
$299$	19.8428	−	3.56134i	1.14754	−	0.205958i
$300$	−4.91899			−0.283998
$301$	−0.692518	−	4.81657i	−0.0399161	−	0.277623i
$302$	−7.57436	+	16.5855i	−0.435856	+	0.954391i
$303$	9.98531	−	2.93195i	0.573641	−	0.168436i
$304$	1.85992	−	2.14647i	0.106674	−	0.123108i
$305$	−3.41358	−	1.00232i	−0.195461	−	0.0573926i
$306$	3.67565	−	2.36220i	0.210123	−	0.135038i
$307$	2.09328	+	4.58364i	0.119470	+	0.261602i	0.959913	−	0.280297i	$-0.0904329\pi$
$307$	2.09328	+	4.58364i	0.119470	+	0.261602i	−0.840444	+	0.541899i	$0.817706\pi$
$308$	−0.836164	−	0.964985i	−0.0476449	−	0.0549851i
$309$	1.35023	+	0.867739i	0.0768118	+	0.0493640i
$310$	0.240687	−	1.67402i	0.0136701	−	0.0950778i
$311$	−1.27347	+	8.85719i	−0.0722120	+	0.502245i	0.921330	+	0.388781i	$0.127104\pi$
$311$	−1.27347	+	8.85719i	−0.0722120	+	0.502245i	−0.993542	+	0.113464i	$0.963805\pi$
$312$	−3.53631	−	2.27265i	−0.200204	−	0.128663i
$313$	18.5222	+	21.3757i	1.04693	+	1.20823i	0.977565	+	0.210636i	$0.0675535\pi$
$313$	18.5222	+	21.3757i	1.04693	+	1.20823i	0.0693701	+	0.997591i	$0.477901\pi$
$314$	−6.74499	−	14.7695i	−0.380642	−	0.833490i
$315$	−0.239446	+	0.153882i	−0.0134912	+	0.00867029i
$316$	−0.101563	−	0.0298215i	−0.00571335	−	0.00167759i
$317$	−16.2928	+	18.8029i	−0.915094	+	1.05607i	0.0831323	+	0.996539i	$0.473508\pi$
$317$	−16.2928	+	18.8029i	−0.915094	+	1.05607i	−0.998226	+	0.0595361i	$0.981038\pi$
$318$	3.90695	−	1.14719i	0.219091	−	0.0643310i
$319$	−2.68338	+	5.87578i	−0.150240	+	0.328980i
$320$	−0.0405070	−	0.281733i	−0.00226441	−	0.0157493i
$321$	4.46432			0.249174
$322$	−4.76788	−	0.517000i	−0.265704	−	0.0288113i
$323$	−12.4095			−0.690483
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	8.58975	−	18.8089i	0.476474	−	1.04333i
$326$	18.3887	−	5.39941i	1.01846	−	0.299046i
$327$	4.74415	−	5.47504i	0.262352	−	0.302770i
$328$	0.250975	+	0.0736930i	0.0138578	+	0.00406901i
$329$	4.68118	−	3.00841i	0.258082	−	0.165859i
$330$	−0.150975	−	0.330589i	−0.00831090	−	0.0181983i
$331$	−8.40676	−	9.70192i	−0.462077	−	0.533266i	0.476114	−	0.879384i	$-0.342045\pi$
$331$	−8.40676	−	9.70192i	−0.462077	−	0.533266i	−0.938191	+	0.346118i	$0.887500\pi$
$332$	10.7474	+	6.90695i	0.589841	+	0.379068i
$333$	−1.25139	+	8.70359i	−0.0685756	+	0.476954i
$334$	−0.457523	+	3.18214i	−0.0250345	+	0.174119i
$335$	−2.49416	−	1.60290i	−0.136271	−	0.0875759i
$336$	0.654861	+	0.755750i	0.0357256	+	0.0412295i
$337$	−8.35471	−	18.2943i	−0.455110	−	0.996552i	−0.988575	−	0.150730i	$-0.951838\pi$
$337$	−8.35471	−	18.2943i	−0.455110	−	0.996552i	0.533465	−	0.845822i	$-0.320890\pi$
$338$	3.92898	−	2.52500i	0.213708	−	0.137342i
$339$	−0.469676	−	0.137909i	−0.0255093	−	0.00749021i
$340$	−0.814398	+	0.939866i	−0.0441670	+	0.0509714i
$341$	−7.27960	+	2.13748i	−0.394212	+	0.115751i
$342$	−1.17986	+	2.58352i	−0.0637993	+	0.139701i
$343$	0.142315	+	0.989821i	0.00768428	+	0.0534453i
$344$	−4.86610			−0.262363
$345$	−1.26065	−	0.523527i	−0.0678712	−	0.0281857i
$346$	−17.8201			−0.958015
$347$	2.35880	+	16.4058i	0.126627	+	0.880709i	0.949786	+	0.312899i	$0.101300\pi$
$347$	2.35880	+	16.4058i	0.126627	+	0.880709i	−0.823160	+	0.567810i	$0.807791\pi$
$348$	2.10155	−	4.60174i	0.112655	−	0.246679i
$349$	31.8052	−	9.33885i	1.70249	−	0.499897i	0.721251	−	0.692673i	$-0.243567\pi$
$349$	31.8052	−	9.33885i	1.70249	−	0.499897i	0.981243	+	0.192776i	$0.0617490\pi$
$350$	−3.22125	+	3.71752i	−0.172183	+	0.198710i
$351$	4.03334	+	1.18430i	0.215284	+	0.0632130i
$352$	−1.07416	+	0.690322i	−0.0572530	+	0.0367943i
$353$	8.36137	+	18.3088i	0.445031	+	0.974481i	0.990647	+	0.136446i	$0.0435682\pi$
$353$	8.36137	+	18.3088i	0.445031	+	0.974481i	−0.545617	+	0.838035i	$0.683705\pi$
$354$	0.557281	+	0.643137i	0.0296192	+	0.0341823i
$355$	3.69836	+	2.37679i	0.196288	+	0.126147i
$356$	−1.26506	+	8.79868i	−0.0670480	+	0.466329i
$357$	0.621810	−	4.32479i	0.0329097	−	0.228892i
$358$	2.48519	+	1.59713i	0.131346	+	0.0844111i
$359$	0.825941	+	0.953187i	0.0435915	+	0.0503073i	0.777127	−	0.629344i	$-0.216676\pi$
$359$	0.825941	+	0.953187i	0.0435915	+	0.0503073i	−0.733535	+	0.679652i	$0.762131\pi$
$360$	0.118239	+	0.258908i	0.00623177	+	0.0136457i
$361$	−9.19772	+	5.91102i	−0.484091	+	0.311106i
$362$	−20.5902	−	6.04584i	−1.08220	−	0.317762i
$363$	6.13580	−	7.08110i	0.322046	−	0.371661i
$364$	−4.03334	+	1.18430i	−0.211404	+	0.0620739i
$365$	−0.802180	+	1.75653i	−0.0419880	+	0.0919409i
$366$	−1.77885	−	12.3722i	−0.0929818	−	0.646703i
$367$	−27.0308			−1.41100			−0.705499	−	0.708711i	$-0.749277\pi$
$367$	−27.0308			−1.41100			−0.705499	+	0.708711i	$0.749277\pi$
$368$	−1.19028	+	4.64578i	−0.0620476	+	0.242178i
$369$	−0.261571			−0.0136168
$370$	−0.356182	−	2.47730i	−0.0185170	−	0.128789i
$371$	1.69153	−	3.70393i	0.0878197	−	0.192298i
$372$	5.70118	−	1.67402i	0.295592	−	0.0867937i
$373$	−1.30370	+	1.50455i	−0.0675031	+	0.0779028i	−0.788497	−	0.615039i	$-0.789140\pi$
$373$	−1.30370	+	1.50455i	−0.0675031	+	0.0779028i	0.720994	+	0.692942i	$0.243686\pi$
$374$	5.35294	+	1.57176i	0.276794	+	0.0812740i
$375$	−2.37506	+	1.52636i	−0.122648	+	0.0788208i
$376$	−2.31159	−	5.06167i	−0.119211	−	0.261036i
$377$	13.9261	+	16.0715i	0.717229	+	0.827727i
$378$	−0.841254	−	0.540641i	−0.0432694	−	0.0278076i
$379$	−0.656687	+	4.56736i	−0.0337317	+	0.234609i	−0.999712	−	0.0240072i	$-0.992358\pi$
$379$	−0.656687	+	4.56736i	−0.0337317	+	0.234609i	0.965980	+	0.258617i	$0.0832666\pi$
$380$	0.115047	−	0.800172i	0.00590181	−	0.0410480i
$381$	−13.7221	−	8.81867i	−0.703005	−	0.451794i
$382$	−2.95880	−	3.41464i	−0.151385	−	0.174708i
$383$	4.65069	+	10.1836i	0.237639	+	0.520357i	0.990449	−	0.137881i	$-0.0440292\pi$
$383$	4.65069	+	10.1836i	0.237639	+	0.520357i	−0.752810	+	0.658238i	$0.771302\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	−0.348710	−	0.102391i	−0.0177719	−	0.00521831i
$386$	15.3281	−	17.6896i	0.780182	−	0.900378i
$387$	4.66899	−	1.37094i	0.237338	−	0.0696887i
$388$	−2.88034	+	6.30706i	−0.146227	+	0.320193i
$389$	4.06555	+	28.2765i	0.206132	+	1.43368i	0.785626	+	0.618702i	$0.212341\pi$
$389$	4.06555	+	28.2765i	0.206132	+	1.43368i	−0.579494	+	0.814976i	$0.696750\pi$
$390$	−1.19647			−0.0605858
$391$	18.7463	−	9.36238i	0.948044	−	0.473476i
$392$	1.00000			0.0505076
$393$	2.02963	+	14.1164i	0.102381	+	0.712078i
$394$	−5.93866	+	13.0039i	−0.299185	+	0.655125i
$395$	−0.0289078	+	0.00848809i	−0.00145451	+	0.000427082i
$396$	0.836164	−	0.964985i	0.0420188	−	0.0484923i
$397$	2.74538	+	0.806115i	0.137786	+	0.0404577i	0.349899	−	0.936788i	$-0.386216\pi$
$397$	2.74538	+	0.806115i	0.137786	+	0.0404577i	−0.212112	+	0.977245i	$0.568034\pi$
$398$	−3.51217	+	2.25713i	−0.176049	+	0.113140i
$399$	1.17986	+	2.58352i	0.0590666	+	0.129338i
$400$	3.22125	+	3.71752i	0.161063	+	0.185876i
$401$	28.9445	+	18.6015i	1.44542	+	0.928916i	0.999426	+	0.0338808i	$0.0107867\pi$
$401$	28.9445	+	18.6015i	1.44542	+	0.928916i	0.445996	+	0.895035i	$0.352850\pi$
$402$	1.48241	−	10.3104i	0.0739358	−	0.514235i
$403$	−3.55464	+	24.7231i	−0.177069	+	1.23154i
$404$	−8.75481	−	5.62637i	−0.435568	−	0.279922i
$405$	−0.186393	−	0.215109i	−0.00926193	−	0.0106888i
$406$	−2.10155	−	4.60174i	−0.104298	−	0.228381i
$407$	−9.44520	+	6.07006i	−0.468181	+	0.300882i
$408$	−4.19227	−	1.23096i	−0.207548	−	0.0609417i
$409$	−2.29797	+	2.65200i	−0.113627	+	0.131133i	−0.809714	−	0.586825i	$-0.800378\pi$
$409$	−2.29797	+	2.65200i	−0.113627	+	0.131133i	0.696086	+	0.717958i	$0.254923\pi$
$410$	0.0714350	−	0.0209752i	0.00352792	−	0.00103589i
$411$	−7.06427	+	15.4686i	−0.348455	+	0.763010i
$412$	−0.228418	−	1.58868i	−0.0112534	−	0.0782688i
$413$	0.850992			0.0418746
$414$	−0.166803	−	4.79293i	−0.00819790	−	0.235560i
$415$	3.63628			0.178498
$416$	0.598237	+	4.16083i	0.0293310	+	0.204001i
$417$	−1.59688	+	3.49667i	−0.0781994	+	0.171233i
$418$	−3.47961	+	1.02171i	−0.170193	+	0.0499733i
$419$	−5.51473	+	6.36434i	−0.269412	+	0.310918i	−0.874294	−	0.485397i	$-0.838675\pi$
$419$	−5.51473	+	6.36434i	−0.269412	+	0.310918i	0.604881	+	0.796316i	$0.293220\pi$
$420$	0.273100	+	0.0801894i	0.0133259	+	0.00391284i
$421$	−10.6395	+	6.83758i	−0.518537	+	0.333243i	−0.773593	−	0.633683i	$-0.781542\pi$
$421$	−10.6395	+	6.83758i	−0.518537	+	0.333243i	0.255056	+	0.966926i	$0.417906\pi$
$422$	5.47692	+	11.9928i	0.266612	+	0.583799i
$423$	3.64399	+	4.20539i	0.177177	+	0.204473i
$424$	−3.42550	−	2.20143i	−0.166357	−	0.106911i
$425$	3.05868	−	21.2736i	0.148368	−	1.03192i
$426$	−2.19812	+	15.2883i	−0.106499	+	0.740719i
$427$	−10.5151	−	6.75767i	−0.508864	−	0.327027i
$428$	−2.92351	−	3.37391i	−0.141313	−	0.163084i
$429$	2.22971	+	4.88238i	0.107651	+	0.235723i
$430$	−1.16517	+	0.748807i	−0.0561893	+	0.0361107i
$431$	−3.63363	−	1.06693i	−0.175026	−	0.0513922i	0.193045	−	0.981190i	$-0.438164\pi$
$431$	−3.63363	−	1.06693i	−0.175026	−	0.0513922i	−0.368071	+	0.929798i	$0.619982\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	27.5336	−	8.08460i	1.32318	−	0.388521i	0.457541	−	0.889189i	$-0.348730\pi$
$433$	27.5336	−	8.08460i	1.32318	−	0.388521i	0.865640	+	0.500668i	$0.166912\pi$
$434$	2.46834	−	5.40491i	0.118484	−	0.259444i
$435$	−0.204921	−	1.42526i	−0.00982522	−	0.0683359i
$436$	−7.24452			−0.346949
$437$	−6.96109	+	11.7079i	−0.332994	+	0.560067i
$438$	−6.78437			−0.324170
$439$	−3.27775	−	22.7973i	−0.156438	−	1.08805i	−0.905130	−	0.425135i	$-0.860227\pi$
$439$	−3.27775	−	22.7973i	−0.156438	−	1.08805i	0.748692	−	0.662919i	$-0.230682\pi$
$440$	−0.150975	+	0.330589i	−0.00719745	+	0.0157602i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	12.0276	−	13.8806i	0.572096	−	0.660233i
$443$	−13.6868	−	4.01882i	−0.650281	−	0.190940i	−0.0600771	−	0.998194i	$-0.519135\pi$
$443$	−13.6868	−	4.01882i	−0.650281	−	0.190940i	−0.590204	+	0.807254i	$0.700953\pi$
$444$	7.39722	−	4.75390i	0.351057	−	0.225610i
$445$	1.05105	+	2.30148i	0.0498245	+	0.109100i
$446$	−4.73196	−	5.46097i	−0.224065	−	0.258584i
$447$	−17.2505	−	11.0863i	−0.815923	−	0.524362i
$448$	0.142315	−	0.989821i	0.00672374	−	0.0467647i
$449$	−0.302505	+	2.10397i	−0.0142761	+	0.0992925i	−0.995714	−	0.0924895i	$-0.970518\pi$
$449$	−0.302505	+	2.10397i	−0.0142761	+	0.0992925i	0.981438	+	0.191782i	$0.0614266\pi$
$450$	−4.13811	−	2.65940i	−0.195073	−	0.125366i
$451$	−0.218716	−	0.252412i	−0.0102989	−	0.0118856i
$452$	0.203348	+	0.445269i	0.00956466	+	0.0209437i
$453$	−15.3388	+	9.85764i	−0.720679	+	0.463152i
$454$	−16.8059	−	4.93467i	−0.788742	−	0.231595i
$455$	−0.783524	+	0.904235i	−0.0367322	+	0.0423912i
$456$	2.72514	−	0.800172i	0.127616	−	0.0374715i
$457$	12.8936	−	28.2331i	0.603139	−	1.32069i	−0.324031	−	0.946047i	$-0.605038\pi$
$457$	12.8936	−	28.2331i	0.603139	−	1.32069i	0.927169	−	0.374643i	$-0.122235\pi$
$458$	0.614311	+	4.27263i	0.0287049	+	0.199647i
$459$	4.36926			0.203940
$460$	0.429896	+	1.29557i	0.0200440	+	0.0604065i
$461$	−12.9453			−0.602925			−0.301462	−	0.953478i	$-0.597475\pi$
$461$	−12.9453			−0.602925			−0.301462	+	0.953478i	$0.597475\pi$
$462$	−0.181716	−	1.26386i	−0.00845419	−	0.0588002i
$463$	−12.1968	+	26.7072i	−0.566832	+	1.24119i	0.381635	+	0.924313i	$0.375361\pi$
$463$	−12.1968	+	26.7072i	−0.566832	+	1.24119i	−0.948467	+	0.316876i	$0.897366\pi$
$464$	−4.85399	+	1.42526i	−0.225341	+	0.0661660i
$465$	1.10752	−	1.27815i	0.0513601	−	0.0592727i
$466$	13.8926	+	4.07923i	0.643562	+	0.188967i
$467$	−2.98660	+	1.91937i	−0.138203	+	0.0888178i	−0.607915	−	0.794002i	$-0.707994\pi$
$467$	−2.98660	+	1.91937i	−0.138203	+	0.0888178i	0.469712	+	0.882820i	$0.344358\pi$
$468$	−1.74625	−	3.82374i	−0.0807202	−	0.176753i
$469$	−6.82130	−	7.87219i	−0.314978	−	0.363504i
$470$	−1.33240	−	0.856282i	−0.0614591	−	0.0394974i
$471$	2.31073	−	16.0715i	0.106473	−	0.740535i
$472$	0.121109	−	0.842330i	0.00557448	−	0.0387714i
$473$	5.22698	+	3.35917i	0.240337	+	0.154455i
$474$	−0.0693173	−	0.0799964i	−0.00318385	−	0.00367436i
$475$	5.80369	+	12.7083i	0.266292	+	0.583097i
$476$	−3.67565	+	2.36220i	−0.168473	+	0.108271i
$477$	3.90695	+	1.14719i	0.178887	+	0.0525260i
$478$	−10.9310	+	12.6151i	−0.499974	+	0.577000i
$479$	−31.2589	+	9.17844i	−1.42825	+	0.419373i	−0.902289	−	0.431132i	$-0.858114\pi$
$479$	−31.2589	+	9.17844i	−1.42825	+	0.419373i	−0.525966	+	0.850506i	$0.676296\pi$
$480$	0.118239	−	0.258908i	0.00539687	−	0.0118175i
$481$	5.26035	+	36.5866i	0.239851	+	1.66820i
$482$	−15.4867			−0.705401
$483$	−3.73149	−	3.01264i	−0.169789	−	0.137080i
$484$	−9.36963			−0.425892
$485$	0.280861	+	1.95343i	0.0127533	+	0.0887008i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	0.949397	−	0.278768i	0.0430213	−	0.0126322i	−0.260151	−	0.965568i	$-0.583772\pi$
$487$	0.949397	−	0.278768i	0.0430213	−	0.0126322i	0.303172	+	0.952936i	$0.401954\pi$
$488$	−8.18535	+	9.44640i	−0.370533	+	0.427618i
$489$	18.3887	+	5.39941i	0.831566	+	0.244170i
$490$	0.239446	−	0.153882i	0.0108171	−	0.00695170i
$491$	−8.26503	−	18.0979i	−0.372996	−	0.816747i	−0.999309	−	0.0371750i	$-0.988164\pi$
$491$	−8.26503	−	18.0979i	−0.372996	−	0.816747i	0.626313	−	0.779572i	$-0.284563\pi$
$492$	0.171292	+	0.197682i	0.00772246	+	0.00891219i
$493$	18.5948	+	11.9502i	0.837468	+	0.538208i
$494$	−1.69910	+	11.8175i	−0.0764462	+	0.531695i
$495$	0.0517217	−	0.359733i	0.00232472	−	0.0161688i
$496$	−4.99862	−	3.21242i	−0.224444	−	0.144242i
$497$	10.1146	+	11.6729i	0.453704	+	0.523602i
$498$	5.30713	+	11.6210i	0.237818	+	0.520749i
$499$	−26.6766	+	17.1440i	−1.19421	+	0.767471i	−0.977945	−	0.208863i	$-0.933024\pi$
$499$	−26.6766	+	17.1440i	−1.19421	+	0.767471i	−0.216264	+	0.976335i	$0.569387\pi$
$500$	2.70888	+	0.795398i	0.121145	+	0.0355713i
$501$	−2.10529	+	2.42963i	−0.0940573	+	0.108548i
$502$	−21.3264	+	6.26199i	−0.951843	+	0.279486i
$503$	9.81856	−	21.4996i	0.437788	−	0.958622i	−0.554211	−	0.832376i	$-0.686980\pi$
$503$	9.81856	−	21.4996i	0.437788	−	0.958622i	0.991999	−	0.126246i	$-0.0402928\pi$
$504$	0.142315	+	0.989821i	0.00633921	+	0.0440902i
$505$	−2.96210			−0.131812
$506$	4.48563	−	4.16864i	0.199411	−	0.185319i
$507$	4.67038			0.207419
$508$	2.32137	+	16.1455i	0.102994	+	0.716340i
$509$	−16.7543	+	36.6868i	−0.742621	+	1.62611i	0.0365743	+	0.999331i	$0.488355\pi$
$509$	−16.7543	+	36.6868i	−0.742621	+	1.62611i	−0.779195	+	0.626782i	$0.784372\pi$
$510$	−1.19325	+	0.350368i	−0.0528378	+	0.0155146i
$511$	−4.44282	+	5.12728i	−0.196539	+	0.226818i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−2.38931	+	1.53552i	−0.105491	+	0.0677948i
$514$	0.386067	+	0.845369i	0.0170287	+	0.0372876i
$515$	−0.299164	−	0.345254i	−0.0131827	−	0.0152137i
$516$	−4.09362	−	2.63081i	−0.180212	−	0.115815i
$517$	−1.01116	+	7.03279i	−0.0444709	+	0.309302i
$518$	1.25139	−	8.70359i	0.0549828	−	0.382414i
$519$	−14.9912	−	9.63427i	−0.658042	−	0.422898i
$520$	0.783524	+	0.904235i	0.0343598	+	0.0396533i
$521$	8.12357	+	17.7881i	0.355900	+	0.779312i	0.999898	+	0.0142851i	$0.00454724\pi$
$521$	8.12357	+	17.7881i	0.355900	+	0.779312i	−0.643998	+	0.765027i	$0.722725\pi$
$522$	4.25582	−	2.73505i	0.186272	−	0.119710i
$523$	−4.90347	−	1.43979i	−0.214414	−	0.0629575i	0.172762	−	0.984964i	$-0.444731\pi$
$523$	−4.90347	−	1.43979i	−0.214414	−	0.0629575i	−0.387175	+	0.922006i	$0.626549\pi$
$524$	9.33933	−	10.7782i	0.407990	−	0.470846i
$525$	−4.71973	+	1.38584i	−0.205986	+	0.0604830i
$526$	9.77596	−	21.4064i	0.426252	−	0.933362i
$527$	3.69471	+	25.6973i	0.160944	+	1.11939i
$528$	−1.27686			−0.0555681
$529$	1.68265	−	22.9384i	0.0731588	−	0.997320i
$530$	−1.15898			−0.0503430
$531$	0.121109	+	0.842330i	0.00525567	+	0.0365540i
$532$	1.17986	−	2.58352i	0.0511532	−	0.112010i
$533$	−1.05500	+	0.309777i	−0.0456973	+	0.0134179i
$534$	−5.82116	+	6.71798i	−0.251906	+	0.290715i
$535$	−1.21921	−	0.357992i	−0.0527109	−	0.0154773i
$536$	−8.76284	+	5.63153i	−0.378497	+	0.243245i
$537$	1.22720	+	2.68719i	0.0529575	+	0.115961i
$538$	−10.5989	−	12.2318i	−0.456951	−	0.527349i
$539$	−1.07416	−	0.690322i	−0.0462674	−	0.0297343i
$540$	−0.0405070	+	0.281733i	−0.00174314	+	0.0121238i
$541$	−1.92091	+	13.3602i	−0.0825865	+	0.574402i	0.905946	+	0.423393i	$0.139161\pi$
$541$	−1.92091	+	13.3602i	−0.0825865	+	0.574402i	−0.988532	+	0.151008i	$0.951748\pi$
$542$	−9.05396	−	5.81863i	−0.388901	−	0.249931i
$543$	−14.0530	−	16.2180i	−0.603071	−	0.695981i
$544$	1.81506	+	3.97442i	0.0778199	+	0.170402i
$545$	−1.73467	+	1.11480i	−0.0743050	+	0.0477530i
$546$	−4.03334	−	1.18430i	−0.172611	−	0.0506832i
$547$	−27.5688	+	31.8161i	−1.17876	+	1.36036i	−0.259965	+	0.965618i	$0.583711\pi$
$547$	−27.5688	+	31.8161i	−1.17876	+	1.36036i	−0.918793	+	0.394741i	$0.870834\pi$
$548$	16.3165	−	4.79096i	0.697006	−	0.204660i
$549$	5.19243	−	11.3698i	0.221607	−	0.485253i
$550$	−0.893858	−	6.21692i	−0.0381142	−	0.265090i
$551$	−14.3682			−0.612107
$552$	−3.51302	+	3.26476i	−0.149524	+	0.138958i
$553$	−0.105850			−0.00450122
$554$	2.75447	+	19.1578i	0.117026	+	0.813936i
$555$	1.03969	−	2.27660i	0.0441324	−	0.0966365i
$556$	3.68834	−	1.08300i	0.156421	−	0.0459292i
$557$	−16.5607	+	19.1121i	−0.701699	+	0.809804i	−0.988981	−	0.148042i	$-0.952703\pi$
$557$	−16.5607	+	19.1121i	−0.701699	+	0.809804i	0.287282	+	0.957846i	$0.407248\pi$
$558$	5.70118	+	1.67402i	0.241350	+	0.0708668i
$559$	17.2080	−	11.0589i	0.727822	−	0.467743i
$560$	−0.118239	−	0.258908i	−0.00499653	−	0.0109409i
$561$	3.65342	+	4.21627i	0.154247	+	0.178011i
$562$	−10.2580	−	6.59243i	−0.432709	−	0.278085i
$563$	3.26822	−	22.7310i	0.137739	−	0.957996i	−0.797333	−	0.603539i	$-0.793757\pi$
$563$	3.26822	−	22.7310i	0.137739	−	0.957996i	0.935072	−	0.354457i	$-0.115334\pi$
$564$	0.791914	−	5.50789i	0.0333456	−	0.231924i
$565$	0.117210	+	0.0753261i	0.00493105	+	0.00316899i
$566$	2.37417	+	2.73993i	0.0997937	+	0.115168i
$567$	−0.415415	−	0.909632i	−0.0174458	−	0.0382010i
$568$	12.9936	−	8.35046i	0.545198	−	0.350378i
$569$	17.7151	+	5.20163i	0.742657	+	0.218064i	0.631108	−	0.775695i	$-0.282601\pi$
$569$	17.7151	+	5.20163i	0.742657	+	0.218064i	0.111549	+	0.993759i	$0.464419\pi$
$570$	0.529390	−	0.610948i	0.0221737	−	0.0255898i
$571$	16.5516	−	4.85999i	0.692663	−	0.203384i	0.0835921	−	0.996500i	$-0.473361\pi$
$571$	16.5516	−	4.85999i	0.692663	−	0.203384i	0.609071	+	0.793116i	$0.291543\pi$
$572$	2.22971	−	4.88238i	0.0932287	−	0.204142i
$573$	−0.643009	−	4.47222i	−0.0268621	−	0.186830i
$574$	0.261571			0.0109177
$575$	−18.3551	−	14.8191i	−0.765462	−	0.618001i
$576$	1.00000			0.0416667
$577$	−3.84985	−	26.7763i	−0.160271	−	1.11471i	−0.898122	−	0.439747i	$-0.855068\pi$
$577$	−3.84985	−	26.7763i	−0.160271	−	1.11471i	0.737850	−	0.674964i	$-0.235841\pi$
$578$	0.868393	−	1.90152i	0.0361204	−	0.0790926i
$579$	22.4586	−	6.59444i	0.933347	−	0.274055i
$580$	−0.942944	+	1.08822i	−0.0391536	+	0.0451857i
$581$	12.2580	+	3.59927i	0.508547	+	0.149323i
$582$	−5.83295	+	3.74861i	−0.241784	+	0.155385i
$583$	2.15984	+	4.72939i	0.0894514	+	0.195871i
$584$	4.44282	+	5.12728i	0.183845	+	0.212168i
$585$	−1.00654	−	0.646863i	−0.0416152	−	0.0267445i
$586$	0.920100	−	6.39943i	0.0380090	−	0.264358i
$587$	0.210342	−	1.46296i	0.00868175	−	0.0603829i	−0.985020	−	0.172440i	$-0.944835\pi$
$587$	0.210342	−	1.46296i	0.00868175	−	0.0603829i	0.993702	+	0.112057i	$0.0357440\pi$
$588$	0.841254	+	0.540641i	0.0346927	+	0.0222957i
$589$	−11.0514	−	12.7540i	−0.455366	−	0.525520i
$590$	−0.100621	−	0.220329i	−0.00414249	−	0.00907079i
$591$	−12.0263	+	7.72886i	−0.494697	+	0.317923i
$592$	−8.43691	−	2.47730i	−0.346755	−	0.101816i
$593$	−15.2453	+	17.5940i	−0.626048	+	0.722497i	−0.976844	−	0.213954i	$-0.931366\pi$
$593$	−15.2453	+	17.5940i	−0.626048	+	0.722497i	0.350796	+	0.936452i	$0.385911\pi$
$594$	1.22514	−	0.359733i	0.0502680	−	0.0147600i
$595$	−0.516619	+	1.13124i	−0.0211793	+	0.0463762i
$596$	2.91827	+	20.2970i	0.119537	+	0.831399i
$597$	−4.17492			−0.170868
$598$	−6.34902	−	19.1340i	−0.259631	−	0.782446i
$599$	6.52873			0.266757			0.133378	−	0.991065i	$-0.457417\pi$
$599$	6.52873			0.266757			0.133378	+	0.991065i	$0.457417\pi$
$600$	0.700045	+	4.86892i	0.0285792	+	0.198773i
$601$	−1.13517	+	2.48567i	−0.0463045	+	0.101393i	−0.931370	−	0.364073i	$-0.881386\pi$
$601$	−1.13517	+	2.48567i	−0.0463045	+	0.101393i	0.885066	+	0.465466i	$0.154113\pi$
$602$	−4.66899	+	1.37094i	−0.190294	+	0.0558753i
$603$	6.82130	−	7.87219i	0.277785	−	0.320581i
$604$	17.4947	+	5.13690i	0.711848	+	0.209017i
$605$	−2.24352	+	1.44182i	−0.0912120	+	0.0586184i
$606$	−4.32316	−	9.46641i	−0.175617	−	0.384547i
$607$	1.70571	+	1.96849i	0.0692325	+	0.0798985i	0.789309	−	0.613996i	$-0.210439\pi$
$607$	1.70571	+	1.96849i	0.0692325	+	0.0798985i	−0.720077	+	0.693894i	$0.755893\pi$
$608$	−2.38931	−	1.53552i	−0.0968995	−	0.0622735i
$609$	0.719958	−	5.00742i	0.0291742	−	0.202911i
$610$	−0.506313	+	3.52148i	−0.0205000	+	0.142581i
$611$	19.6779	+	12.6462i	0.796081	+	0.511610i
$612$	−2.86126	−	3.30207i	−0.115659	−	0.133478i
$613$	−2.19347	−	4.80304i	−0.0885935	−	0.193993i	0.860149	−	0.510043i	$-0.170370\pi$
$613$	−2.19347	−	4.80304i	−0.0885935	−	0.193993i	−0.948742	+	0.316050i	$0.897643\pi$
$614$	4.23908	−	2.72429i	0.171075	−	0.109943i
$615$	0.0714350	+	0.0209752i	0.00288054	+	0.000845802i
$616$	−0.836164	+	0.964985i	−0.0336900	+	0.0388804i
$617$	−5.65535	+	1.66056i	−0.227676	+	0.0668516i	−0.393580	−	0.919290i	$-0.628764\pi$
$617$	−5.65535	+	1.66056i	−0.227676	+	0.0668516i	0.165905	+	0.986142i	$0.446946\pi$
$618$	0.666749	−	1.45998i	0.0268206	−	0.0587289i
$619$	−2.94468	−	20.4807i	−0.118357	−	0.823188i	−0.959365	−	0.282167i	$-0.908947\pi$
$619$	−2.94468	−	20.4807i	−0.118357	−	0.823188i	0.841009	−	0.541022i	$-0.181962\pi$
$620$	−1.69123			−0.0679215
$621$	2.45093	−	4.12225i	0.0983524	−	0.165420i
$622$	8.94827			0.358793
$623$	1.26506	+	8.79868i	0.0506835	+	0.352512i
$624$	−1.74625	+	3.82374i	−0.0699057	+	0.153072i
$625$	−22.8276	+	6.70280i	−0.913105	+	0.268112i
$626$	18.5222	−	21.3757i	0.740295	−	0.854346i
$627$	−3.47961	−	1.02171i	−0.138962	−	0.0408030i
$628$	−13.6592	+	8.77826i	−0.545063	+	0.350291i
$629$	15.9600	+	34.9474i	0.636365	+	1.39344i
$630$	0.186393	+	0.215109i	0.00742607	+	0.00857014i
$631$	7.97178	+	5.12315i	0.317351	+	0.203949i	0.689612	−	0.724179i	$-0.257781\pi$
$631$	7.97178	+	5.12315i	0.317351	+	0.203949i	−0.372261	+	0.928128i	$0.621417\pi$
$632$	−0.0150641	+	0.104773i	−0.000599217	+	0.00416765i
$633$	−1.87631	+	13.0500i	−0.0745765	+	0.518691i
$634$	20.9302	+	13.4510i	0.831244	+	0.534208i
$635$	3.04035	+	3.50875i	0.120653	+	0.139240i
$636$	−1.69153	−	3.70393i	−0.0670734	−	0.146870i
$637$	−3.53631	+	2.27265i	−0.140114	+	0.0900455i
$638$	6.19785	+	1.81985i	0.245375	+	0.0720487i
$639$	−10.1146	+	11.6729i	−0.400129	+	0.461774i
$640$	−0.273100	+	0.0801894i	−0.0107952	+	0.00316977i
$641$	−7.38608	+	16.1733i	−0.291733	+	0.638805i	−0.997578	−	0.0695610i	$-0.977840\pi$
$641$	−7.38608	+	16.1733i	−0.291733	+	0.638805i	0.705845	+	0.708366i	$0.250567\pi$
$642$	−0.635339	−	4.41888i	−0.0250748	−	0.174399i
$643$	−25.8280			−1.01856			−0.509278	−	0.860602i	$-0.670087\pi$
$643$	−25.8280			−1.01856			−0.509278	+	0.860602i	$0.670087\pi$
$644$	0.166803	+	4.79293i	0.00657294	+	0.188868i
$645$	−1.38504			−0.0545358
$646$	1.76606	+	12.2832i	0.0694845	+	0.483276i
$647$	−4.88644	+	10.6998i	−0.192106	+	0.420653i	−0.981035	−	0.193831i	$-0.937909\pi$
$647$	−4.88644	+	10.6998i	−0.192106	+	0.420653i	0.788929	+	0.614484i	$0.210636\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−0.711569	+	0.821194i	−0.0279315	+	0.0322347i
$650$	−19.8399	−	5.82553i	−0.778187	−	0.228496i
$651$	4.99862	−	3.21242i	0.195911	−	0.125904i
$652$	−7.96143	−	17.4331i	−0.311794	−	0.682733i
$653$	18.1747	+	20.9747i	0.711231	+	0.820805i	0.990224	−	0.139489i	$-0.0445458\pi$
$653$	18.1747	+	20.9747i	0.711231	+	0.820805i	−0.278992	+	0.960293i	$0.590000\pi$
$654$	−6.09448	−	3.91668i	−0.238313	−	0.153154i
$655$	0.577693	−	4.01794i	0.0225723	−	0.156994i
$656$	0.0372254	−	0.258908i	0.00145341	−	0.0101087i
$657$	−5.70737	−	3.66791i	−0.222666	−	0.143099i
$658$	−3.64399	−	4.20539i	−0.142057	−	0.163943i
$659$	12.1099	+	26.5169i	0.471734	+	1.03295i	0.984654	+	0.174517i	$0.0558363\pi$
$659$	12.1099	+	26.5169i	0.471734	+	1.03295i	−0.512921	+	0.858436i	$0.671436\pi$
$660$	−0.305738	+	0.196486i	−0.0119008	+	0.00764821i
$661$	0.114543	+	0.0336330i	0.00445522	+	0.00130817i	0.283959	−	0.958836i	$-0.408352\pi$
$661$	0.114543	+	0.0336330i	0.00445522	+	0.00130817i	−0.279504	+	0.960144i	$0.590170\pi$
$662$	−8.40676	+	9.70192i	−0.326738	+	0.377076i
$663$	17.6227	−	5.17449i	0.684409	−	0.200961i
$664$	5.30713	−	11.6210i	0.205957	−	0.450982i
$665$	−0.115047	−	0.800172i	−0.00446135	−	0.0310293i
$666$	8.79309			0.340725
$667$	21.7053	−	10.8401i	0.840432	−	0.419732i
$668$	3.21486			0.124387
$669$	−1.02835	−	7.15235i	−0.0397584	−	0.276526i
$670$	−1.23163	+	2.69689i	−0.0475820	+	0.104190i
$671$	15.3134	−	4.49643i	0.591169	−	0.173583i
$672$	0.654861	−	0.755750i	0.0252618	−	0.0291537i
$673$	9.27689	+	2.72394i	0.357598	+	0.105000i	0.455597	−	0.890186i	$-0.349426\pi$
$673$	9.27689	+	2.72394i	0.357598	+	0.105000i	−0.0979988	+	0.995187i	$0.531244\pi$
$674$	−16.9190	+	10.8732i	−0.651697	+	0.418820i
$675$	−2.04342	−	4.47447i	−0.0786513	−	0.172222i
$676$	−3.05845	−	3.52964i	−0.117633	−	0.135755i
$677$	−42.1556	−	27.0917i	−1.62017	−	1.04122i	−0.955885	−	0.293742i	$-0.905099\pi$
$677$	−42.1556	−	27.0917i	−1.62017	−	1.04122i	−0.664286	−	0.747479i	$-0.731264\pi$
$678$	−0.0696638	+	0.484522i	−0.00267542	+	0.0186080i
$679$	−0.986760	+	6.86307i	−0.0378684	+	0.263380i
$680$	1.04620	+	0.672352i	0.0401200	+	0.0257835i
$681$	−11.4702	−	13.2373i	−0.439538	−	0.507254i
$682$	3.15172	+	6.90131i	0.120686	+	0.264265i
$683$	−10.2016	+	6.55615i	−0.390352	+	0.250864i	−0.721065	−	0.692867i	$-0.756347\pi$
$683$	−10.2016	+	6.55615i	−0.390352	+	0.250864i	0.330713	+	0.943731i	$0.392711\pi$
$684$	2.72514	+	0.800172i	0.104198	+	0.0305954i
$685$	3.16967	−	3.65800i	0.121107	−	0.139765i
$686$	0.959493	−	0.281733i	0.0366336	−	0.0107566i
$687$	−1.79316	+	3.92648i	−0.0684135	+	0.149805i
$688$	0.692518	+	4.81657i	0.0264020	+	0.183630i
$689$	17.1167			0.652094
$690$	−0.338789	+	1.32233i	−0.0128975	+	0.0503401i
$691$	−5.37949			−0.204645			−0.102323	−	0.994751i	$-0.532627\pi$
$691$	−5.37949			−0.204645			−0.102323	+	0.994751i	$0.532627\pi$
$692$	2.53606	+	17.6387i	0.0964067	+	0.670523i
$693$	0.530426	−	1.16147i	0.0201492	−	0.0441206i
$694$	15.9031	−	4.66958i	0.603674	−	0.177255i
$695$	0.716504	−	0.826890i	0.0271785	−	0.0313657i
$696$	−4.85399	−	1.42526i	−0.183990	−	0.0540243i
$697$	−0.961443	+	0.617882i	−0.0364173	+	0.0234040i
$698$	−13.7702	−	30.1524i	−0.521208	−	1.14129i
$699$	9.48179	+	10.9426i	0.358634	+	0.413886i
$700$	4.13811	+	2.65940i	0.156406	+	0.100516i
$701$	2.65219	−	18.4464i	0.100172	−	0.696709i	−0.876411	−	0.481565i	$-0.840069\pi$
$701$	2.65219	−	18.4464i	0.100172	−	0.696709i	0.976582	−	0.215145i	$-0.0690223\pi$
$702$	0.598237	−	4.16083i	0.0225790	−	0.157040i
$703$	−21.0095	−	13.5020i	−0.792387	−	0.509236i
$704$	0.836164	+	0.964985i	0.0315141	+	0.0363692i
$705$	−0.657946	−	1.44070i	−0.0247797	−	0.0542600i
$706$	16.9325	−	10.8819i	0.637264	−	0.409545i
$707$	−9.98531	−	2.93195i	−0.375536	−	0.110267i
$708$	0.557281	−	0.643137i	0.0209439	−	0.0241706i
$709$	6.21452	−	1.82475i	0.233391	−	0.0685298i	−0.162946	−	0.986635i	$-0.552100\pi$
$709$	6.21452	−	1.82475i	0.233391	−	0.0685298i	0.396337	+	0.918105i	$0.370281\pi$
$710$	1.82627	−	3.99896i	0.0685385	−	0.150078i
$711$	−0.0150641	−	0.104773i	−0.000564947	−	0.00392930i
$712$	8.88916			0.333135
$713$	26.3171	+	10.9290i	0.985583	+	0.409295i
$714$	−4.36926			−0.163515
$715$	−0.217418	−	1.51218i	−0.00813098	−	0.0565522i
$716$	1.22720	−	2.68719i	0.0458625	−	0.100425i
$717$	−16.0160	+	4.70272i	−0.598128	+	0.175626i
$718$	0.825941	−	0.953187i	0.0308239	−	0.0355726i
$719$	7.44550	+	2.18620i	0.277670	+	0.0815314i	0.417603	−	0.908630i	$-0.362870\pi$
$719$	7.44550	+	2.18620i	0.277670	+	0.0815314i	−0.139932	+	0.990161i	$0.544689\pi$
$720$	0.239446	−	0.153882i	0.00892362	−	0.00573486i
$721$	−0.666749	−	1.45998i	−0.0248310	−	0.0543724i
$722$	7.15983	+	8.26288i	0.266461	+	0.307513i
$723$	−13.0283	−	8.37276i	−0.484526	−	0.311386i
$724$	−3.05401	+	21.2411i	−0.113501	+	0.789418i
$725$	3.54146	−	24.6314i	0.131527	−	0.914787i
$726$	−7.88224	−	5.06561i	−0.292537	−	0.188002i
$727$	−16.8632	−	19.4612i	−0.625423	−	0.721776i	0.351305	−	0.936261i	$-0.385738\pi$
$727$	−16.8632	−	19.4612i	−0.625423	−	0.721776i	−0.976727	+	0.214485i	$0.931193\pi$
$728$	1.74625	+	3.82374i	0.0647201	+	0.141717i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	1.85281	+	0.544035i	0.0685757	+	0.0201356i
$731$	13.9232	−	16.0682i	0.514967	−	0.594303i
$732$	−11.9931	+	3.52148i	−0.443276	+	0.130158i
$733$	17.1466	−	37.5458i	0.633323	−	1.38678i	−0.272098	−	0.962270i	$-0.587717\pi$
$733$	17.1466	−	37.5458i	0.633323	−	1.38678i	0.905421	−	0.424515i	$-0.139555\pi$
$734$	3.84689	+	26.7557i	0.141991	+	0.987571i
$735$	0.284630			0.0104987
$736$	4.76788	+	0.517000i	0.175747	+	0.0190569i
$737$	13.3003			0.489922
$738$	0.0372254	+	0.258908i	0.00137029	+	0.00953054i
$739$	18.4136	−	40.3201i	0.677353	−	1.48320i	−0.188070	−	0.982156i	$-0.560223\pi$
$739$	18.4136	−	40.3201i	0.677353	−	1.48320i	0.865423	−	0.501042i	$-0.167050\pi$
$740$	−2.40140	+	0.705113i	−0.0882770	+	0.0259205i
$741$	−7.81841	+	9.02293i	−0.287216	+	0.331465i
$742$	−3.90695	−	1.14719i	−0.143429	−	0.0421145i
$743$	25.5558	−	16.4237i	0.937551	−	0.602528i	0.0198518	−	0.999803i	$-0.493681\pi$
$743$	25.5558	−	16.4237i	0.937551	−	0.602528i	0.917699	+	0.397275i	$0.130044\pi$
$744$	−2.46834	−	5.40491i	−0.0904937	−	0.198154i
$745$	3.82213	+	4.41097i	0.140032	+	0.161605i
$746$	1.67477	+	1.07631i	0.0613178	+	0.0394066i
$747$	−1.81814	+	12.6455i	−0.0665223	+	0.462673i
$748$	0.793964	−	5.52214i	0.0290302	−	0.201909i
$749$	−3.75563	−	2.41359i	−0.137228	−	0.0881908i
$750$	1.84883	+	2.13366i	0.0675096	+	0.0779103i
$751$	13.4146	+	29.3738i	0.489504	+	1.07186i	0.979740	+	0.200274i	$0.0641833\pi$
$751$	13.4146	+	29.3738i	0.489504	+	1.07186i	−0.490236	+	0.871590i	$0.663089\pi$
$752$	−4.68118	+	3.00841i	−0.170705	+	0.109705i
$753$	−21.3264	−	6.26199i	−0.777176	−	0.228200i
$754$	13.9261	−	16.0715i	0.507158	−	0.585291i
$755$	4.97950	−	1.46211i	0.181223	−	0.0532118i
$756$	−0.415415	+	0.909632i	−0.0151085	+	0.0330830i
$757$	2.10139	+	14.6155i	0.0763762	+	0.531208i	0.991708	+	0.128509i	$0.0410190\pi$
$757$	2.10139	+	14.6155i	0.0763762	+	0.531208i	−0.915332	+	0.402700i	$0.868072\pi$
$758$	4.61432			0.167600
$759$	6.02729	−	1.08177i	0.218777	−	0.0392656i
$760$	−0.808401			−0.0293238
$761$	−3.66744	−	25.5076i	−0.132945	−	0.924649i	−0.941688	−	0.336488i	$-0.890761\pi$
$761$	−3.66744	−	25.5076i	−0.132945	−	0.924649i	0.808743	−	0.588162i	$-0.200148\pi$
$762$	−6.77605	+	14.8375i	−0.245470	+	0.537505i
$763$	−6.95106	+	2.04102i	−0.251645	+	0.0738898i
$764$	−2.95880	+	3.41464i	−0.107046	+	0.123537i
$765$	−1.19325	−	0.350368i	−0.0431419	−	0.0126676i
$766$	9.41807	−	6.05263i	0.340289	−	0.218690i
$767$	1.48604	+	3.25397i	0.0536578	+	0.117494i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	43.4534	+	27.9258i	1.56697	+	1.00703i	0.980373	+	0.197153i	$0.0631694\pi$
$769$	43.4534	+	27.9258i	1.56697	+	1.00703i	0.586598	+	0.809878i	$0.300467\pi$
$770$	−0.0517217	+	0.359733i	−0.00186392	+	0.0129639i
$771$	−0.132261	+	0.919894i	−0.00476325	+	0.0331292i
$772$	−19.6910	−	12.6546i	−0.708694	−	0.455450i
$773$	−28.6623	−	33.0780i	−1.03091	−	1.18973i	−0.981600	−	0.190950i	$-0.938843\pi$
$773$	−28.6623	−	33.0780i	−1.03091	−	1.18973i	−0.0493106	−	0.998783i	$-0.515702\pi$
$774$	−2.02145	−	4.42636i	−0.0726596	−	0.159102i
$775$	24.5881	−	15.8018i	0.883231	−	0.567618i
$776$	6.65278	+	1.95343i	0.238821	+	0.0701242i
$777$	5.75825	−	6.64538i	0.206576	−	0.238402i
$778$	27.4101	−	8.04834i	0.982701	−	0.288547i
$779$	0.308615	−	0.675774i	0.0110573	−	0.0242121i
$780$	0.170276	+	1.18430i	0.00609686	+	0.0424046i
$781$	−19.7217			−0.705698
$782$	−11.9350	−	17.2231i	−0.426794	−	0.615898i
$783$	5.05891			0.180791
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	−1.91983	+	4.20383i	−0.0685215	+	0.150041i
$786$	13.6839	−	4.01794i	0.488087	−	0.143315i
$787$	19.9613	−	23.0366i	0.711545	−	0.821167i	−0.278718	−	0.960373i	$-0.589910\pi$
$787$	19.9613	−	23.0366i	0.711545	−	0.821167i	0.990263	+	0.139206i	$0.0444551\pi$
$788$	13.7167	+	4.02757i	0.488636	+	0.143476i
$789$	19.7972	−	12.7229i	0.704800	−	0.452947i
$790$	0.0125157	+	0.0274056i	0.000445289	+	0.000975046i
$791$	0.320557	+	0.369943i	0.0113977	+	0.0131537i
$792$	−1.07416	−	0.690322i	−0.0381687	−	0.0245295i
$793$	7.47759	−	52.0078i	0.265537	−	1.84685i
$794$	0.407202	−	2.83215i	0.0144511	−	0.100509i
$795$	−0.974998	−	0.626593i	−0.0345796	−	0.0222230i
$796$	2.73399	+	3.15519i	0.0969038	+	0.111833i
$797$	−9.86438	−	21.6000i	−0.349414	−	0.765111i	−0.999984	−	0.00566414i	$-0.998197\pi$
$797$	−9.86438	−	21.6000i	−0.349414	−	0.765111i	0.650570	−	0.759447i	$-0.274530\pi$
$798$	2.38931	−	1.53552i	0.0845808	−	0.0543568i
$799$	23.3280	+	6.84972i	0.825286	+	0.242326i
$800$	3.22125	−	3.71752i	0.113888	−	0.131434i
$801$	−8.52909	+	2.50437i	−0.301360	+	0.0884874i
$802$	14.2930	−	31.2972i	0.504702	−	1.10514i
$803$	−1.23283	−	8.57450i	−0.0435055	−	0.302588i
$804$	−10.4164			−0.367358
$805$	0.777488	+	1.12198i	0.0274028	+	0.0395445i
$806$	24.9773			0.879789
$807$	−2.30336	−	16.0202i	−0.0810821	−	0.563939i
$808$	−4.32316	+	9.46641i	−0.152088	+	0.333027i
$809$	13.4150	−	3.93900i	0.471646	−	0.138488i	−0.0372675	−	0.999305i	$-0.511865\pi$
$809$	13.4150	−	3.93900i	0.471646	−	0.138488i	0.508914	+	0.860817i	$0.330047\pi$
$810$	−0.186393	+	0.215109i	−0.00654918	+	0.00755815i
$811$	−27.2084	−	7.98911i	−0.955417	−	0.280536i	−0.233376	−	0.972387i	$-0.574977\pi$
$811$	−27.2084	−	7.98911i	−0.955417	−	0.280536i	−0.722040	+	0.691851i	$0.756796\pi$
$812$	−4.25582	+	2.73505i	−0.149350	+	0.0959815i
$813$	−4.47089	−	9.78988i	−0.156801	−	0.343346i
$814$	7.35247	+	8.48520i	0.257704	+	0.297406i
$815$	−4.58898	−	2.94916i	−0.160745	−	0.103305i
$816$	−0.621810	+	4.32479i	−0.0217677	+	0.151398i
$817$	−1.96688	+	13.6799i	−0.0688124	+	0.478601i
$818$	2.95204	+	1.89716i	0.103216	+	0.0663326i
$819$	−2.75278	−	3.17688i	−0.0961900	−	0.111009i
$820$	−0.0309280	−	0.0677228i	−0.00108005	−	0.00236498i
$821$	16.9973	−	10.9235i	0.593210	−	0.381233i	−0.209318	−	0.977848i	$-0.567124\pi$
$821$	16.9973	−	10.9235i	0.593210	−	0.381233i	0.802528	+	0.596615i	$0.203488\pi$
$822$	16.3165	+	4.79096i	0.569103	+	0.167104i
$823$	−19.2517	+	22.2176i	−0.671072	+	0.774458i	−0.984544	−	0.175140i	$-0.943962\pi$
$823$	−19.2517	+	22.2176i	−0.671072	+	0.774458i	0.313472	+	0.949597i	$0.398508\pi$
$824$	−1.54001	+	0.452186i	−0.0536486	+	0.0157527i
$825$	2.60916	−	5.71326i	0.0908392	−	0.198910i
$826$	−0.121109	−	0.842330i	−0.00421391	−	0.0293084i
$827$	−45.1183			−1.56892			−0.784459	−	0.620181i	$-0.787059\pi$
$827$	−45.1183			−1.56892			−0.784459	+	0.620181i	$0.787059\pi$
$828$	−4.72041	+	0.847210i	−0.164045	+	0.0294426i
$829$	−13.4218			−0.466157			−0.233079	−	0.972458i	$-0.574880\pi$
$829$	−13.4218			−0.466157			−0.233079	+	0.972458i	$0.574880\pi$
$830$	−0.517497	−	3.59927i	−0.0179626	−	0.124933i
$831$	−8.04027	+	17.6057i	−0.278914	+	0.610736i
$832$	4.03334	−	1.18430i	0.139831	−	0.0410581i
$833$	−2.86126	+	3.30207i	−0.0991366	+	0.114410i
$834$	3.68834	+	1.08300i	0.127717	+	0.0375011i
$835$	0.769785	−	0.494711i	0.0266395	−	0.0171202i
$836$	1.50651	+	3.29879i	0.0521037	+	0.114091i
$837$	3.89109	+	4.49056i	0.134496	+	0.155217i
$838$	7.08439	+	4.55286i	0.244726	+	0.157276i
$839$	3.22932	−	22.4604i	0.111488	−	0.775419i	−0.854985	−	0.518652i	$-0.826434\pi$
$839$	3.22932	−	22.4604i	0.111488	−	0.775419i	0.966474	−	0.256766i	$-0.0826570\pi$
$840$	0.0405070	−	0.281733i	0.00139763	−	0.00972070i
$841$	−2.86653	−	1.84221i	−0.0988459	−	0.0635244i
$842$	8.28214	+	9.55810i	0.285422	+	0.329394i
$843$	−5.06546	−	11.0918i	−0.174464	−	0.382022i
$844$	11.0913	−	7.12792i	0.381777	−	0.245353i
$845$	−1.27548	−	0.374516i	−0.0438779	−	0.0128837i
$846$	3.64399	−	4.20539i	0.125283	−	0.144584i
$847$	−8.99010	+	2.63973i	−0.308903	+	0.0907022i
$848$	−1.69153	+	3.70393i	−0.0580873	+	0.127193i
$849$	0.515956	+	3.58855i	0.0177076	+	0.123159i
$850$	−21.4923			−0.737181
$851$	41.9244	+	4.54603i	1.43715	+	0.155836i
$852$	15.4455			0.529154
$853$	8.20395	+	57.0597i	0.280898	+	1.95369i	0.300207	+	0.953874i	$0.402944\pi$
$853$	8.20395	+	57.0597i	0.280898	+	1.95369i	−0.0193095	+	0.999814i	$0.506147\pi$
$854$	−5.19243	+	11.3698i	−0.177681	+	0.389068i
$855$	0.775655	−	0.227753i	0.0265268	−	0.00778898i
$856$	−2.92351	+	3.37391i	−0.0999235	+	0.115318i
$857$	−41.2383	−	12.1087i	−1.40867	−	0.413624i	−0.513020	−	0.858377i	$-0.671473\pi$
$857$	−41.2383	−	12.1087i	−1.40867	−	0.413624i	−0.895653	+	0.444753i	$0.853292\pi$
$858$	4.51536	−	2.90185i	0.154152	−	0.0990674i
$859$	23.5980	+	51.6724i	0.805153	+	1.76304i	0.626972	+	0.779041i	$0.284294\pi$
$859$	23.5980	+	51.6724i	0.805153	+	1.76304i	0.178181	+	0.983998i	$0.442979\pi$
$860$	0.907006	+	1.04674i	0.0309286	+	0.0356936i
$861$	0.220047	+	0.141416i	0.00749919	+	0.00481944i
$862$	−0.538950	+	3.74848i	−0.0183567	+	0.127674i
$863$	0.780567	−	5.42897i	0.0265708	−	0.184804i	−0.972214	−	0.234095i	$-0.924787\pi$
$863$	0.780567	−	5.42897i	0.0265708	−	0.184804i	0.998784	+	0.0492913i	$0.0156963\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	3.32154	+	3.83326i	0.112936	+	0.130335i
$866$	−11.9207	−	26.1028i	−0.405083	−	0.887009i
$867$	1.75858	−	1.13017i	0.0597244	−	0.0383825i
$868$	−5.70118	−	1.67402i	−0.193511	−	0.0568198i
$869$	0.0885084	−	0.102144i	0.00300244	−	0.00346500i
$870$	−1.38159	+	0.405671i	−0.0468402	+	0.0137535i
$871$	18.1896	−	39.8297i	0.616331	−	1.34958i
$872$	1.03100	+	7.17078i	0.0349141	+	0.242833i
$873$	−6.93364			−0.234668
$874$	12.5794	+	5.22402i	0.425506	+	0.176705i
$875$	2.82324			0.0954429
$876$	0.965516	+	6.71531i	0.0326218	+	0.226889i
$877$	10.2358	−	22.4133i	0.345639	−	0.756843i	−0.654361	−	0.756182i	$-0.727062\pi$
$877$	10.2358	−	22.4133i	0.345639	−	0.756843i	1.00000		0.000661062i	$-0.000210423\pi$
$878$	−22.0987	+	6.48877i	−0.745796	+	0.218986i
$879$	4.23383	−	4.88610i	0.142804	−	0.164804i
$880$	0.348710	+	0.102391i	0.0117550	+	0.00345158i
$881$	−6.92201	+	4.44850i	−0.233208	+	0.149874i	−0.652026	−	0.758196i	$-0.726081\pi$
$881$	−6.92201	+	4.44850i	−0.233208	+	0.149874i	0.418818	+	0.908070i	$0.362445\pi$
$882$	0.415415	+	0.909632i	0.0139878	+	0.0306289i
$883$	−9.09890	−	10.5007i	−0.306202	−	0.353376i	0.581704	−	0.813401i	$-0.302386\pi$
$883$	−9.09890	−	10.5007i	−0.306202	−	0.353376i	−0.887906	+	0.460024i	$0.847841\pi$
$884$	−15.4510	−	9.92978i	−0.519675	−	0.333975i
$885$	0.0344712	−	0.239752i	0.00115874	−	0.00805918i
$886$	−2.03007	+	14.1195i	−0.0682016	+	0.474353i
$887$	−40.3552	−	25.9347i	−1.35499	−	0.870801i	−0.356999	−	0.934105i	$-0.616200\pi$
$887$	−40.3552	−	25.9347i	−1.35499	−	0.870801i	−0.997994	+	0.0633034i	$0.979836\pi$
$888$	−5.75825	−	6.64538i	−0.193234	−	0.223004i
$889$	6.77605	+	14.8375i	0.227261	+	0.497633i
$890$	2.12847	−	1.36789i	0.0713465	−	0.0458516i
$891$	1.22514	+	0.359733i	0.0410436	+	0.0120515i
$892$	−4.73196	+	5.46097i	−0.158438	+	0.182847i
$893$	−15.1641	+	4.45258i	−0.507447	+	0.149000i
$894$	−8.51840	+	18.6527i	−0.284898	+	0.623839i
$895$	−0.119664	−	0.832280i	−0.00399992	−	0.0278201i
$896$	−1.00000			−0.0334077
$897$	5.00347	−	19.5291i	0.167061	−	0.652056i
$898$	2.12561			0.0709324
$899$	4.27789	+	29.7534i	0.142676	+	0.992331i
$900$	−2.04342	+	4.47447i	−0.0681140	+	0.149149i
$901$	17.0705	−	5.01235i	0.568701	−	0.166986i
$902$	−0.218716	+	0.252412i	−0.00728245	+	0.00840439i
$903$	−4.66899	−	1.37094i	−0.155374	−	0.0456220i
$904$	0.411797	−	0.264646i	0.0136962	−	0.00880200i
$905$	2.53736	+	5.55604i	0.0843447	+	0.184689i
$906$	11.9402	+	13.7798i	0.396688	+	0.457802i
$907$	−31.3873	−	20.1714i	−1.04220	−	0.669780i	−0.0966690	−	0.995317i	$-0.530819\pi$
$907$	−31.3873	−	20.1714i	−1.04220	−	0.669780i	−0.945530	+	0.325536i	$0.894455\pi$
$908$	−2.49271	+	17.3372i	−0.0827234	+	0.575354i
$909$	1.48105	−	10.3009i	0.0491233	−	0.341660i
$910$	1.00654	+	0.646863i	0.0333664	+	0.0214433i
$911$	−5.24585	−	6.05403i	−0.173803	−	0.200579i	0.662164	−	0.749359i	$-0.269638\pi$
$911$	−5.24585	−	6.05403i	−0.173803	−	0.200579i	−0.835967	+	0.548780i	$0.815093\pi$
$912$	−1.17986	−	2.58352i	−0.0390689	−	0.0855490i
$913$	−13.7229	+	8.81920i	−0.454163	+	0.291873i
$914$	−29.7807	−	8.74440i	−0.985058	−	0.289239i
$915$	−2.32979	+	2.68873i	−0.0770206	+	0.0888865i
$916$	4.14171	−	1.21612i	0.136846	−	0.0401816i
$917$	5.92446	−	12.9728i	0.195643	−	0.428398i
$918$	−0.621810	−	4.32479i	−0.0205228	−	0.142739i
$919$	−7.83011			−0.258291			−0.129146	−	0.991626i	$-0.541223\pi$
$919$	−7.83011			−0.258291			−0.129146	+	0.991626i	$0.541223\pi$
$920$	1.22121	−	0.609900i	0.0402620	−	0.0201078i
$921$	5.03900			0.166041
$922$	1.84231	+	12.8136i	0.0606734	+	0.421993i
$923$	−26.9716	+	59.0596i	−0.887781	+	1.94397i
$924$	−1.22514	+	0.359733i	−0.0403040	+	0.0118343i
$925$	28.3248	−	32.6885i	0.931312	−	1.07479i
$926$	28.1711	+	8.27179i	0.925761	+	0.271828i
$927$	1.35023	−	0.867739i	0.0443473	−	0.0285003i
$928$	2.10155	+	4.60174i	0.0689866	+	0.151060i
$929$	−8.67404	−	10.0104i	−0.284586	−	0.328430i	0.595400	−	0.803429i	$-0.296994\pi$
$929$	−8.67404	−	10.0104i	−0.284586	−	0.328430i	−0.879986	+	0.475000i	$0.842448\pi$
$930$	−1.42275	−	0.914349i	−0.0466540	−	0.0299827i
$931$	0.404200	−	2.81127i	0.0132471	−	0.0921358i
$932$	2.06059	−	14.3317i	0.0674969	−	0.469451i
$933$	7.52777	+	4.83780i	0.246448	+	0.158382i
$934$	2.32487	+	2.68304i	0.0760721	+	0.0877918i
$935$	−0.659649	−	1.44443i	−0.0215728	−	0.0472379i
$936$	−3.53631	+	2.27265i	−0.115588	+	0.0742838i
$937$	10.6192	+	3.11807i	0.346913	+	0.101863i	0.450547	−	0.892753i	$-0.351229\pi$
$937$	10.6192	+	3.11807i	0.346913	+	0.101863i	−0.103634	+	0.994615i	$0.533047\pi$
$938$	−6.82130	+	7.87219i	−0.222723	+	0.257036i
$939$	27.1384	−	7.96856i	0.885629	−	0.260044i
$940$	−0.657946	+	1.44070i	−0.0214598	+	0.0469905i
$941$	8.11494	+	56.4406i	0.264539	+	1.83991i	0.497548	+	0.867437i	$0.334234\pi$
$941$	8.11494	+	56.4406i	0.264539	+	1.83991i	−0.233008	+	0.972475i	$0.574857\pi$
$942$	−16.2368			−0.529022
$943$	0.0436307	+	1.25369i	0.00142081	+	0.0408258i
$944$	−0.850992			−0.0276974
$945$	0.0405070	+	0.281733i	0.00131769	+	0.00916476i
$946$	2.58111	−	5.65183i	0.0839190	−	0.183757i
$947$	51.9646	−	15.2582i	1.68862	−	0.495824i	0.710472	−	0.703726i	$-0.248482\pi$
$947$	51.9646	−	15.2582i	1.68862	−	0.495824i	0.978150	+	0.207902i	$0.0666634\pi$
$948$	−0.0693173	+	0.0799964i	−0.00225132	+	0.00259816i
$949$	−27.3637	−	8.03470i	−0.888262	−	0.260817i
$950$	11.7530	−	7.55320i	0.381318	−	0.245058i
$951$	10.3354	+	22.6314i	0.335149	+	0.733874i
$952$	2.86126	+	3.30207i	0.0927338	+	0.107021i
$953$	0.287208	+	0.184577i	0.00930357	+	0.00597904i	0.545284	−	0.838251i	$-0.316422\pi$
$953$	0.287208	+	0.184577i	0.00930357	+	0.00597904i	−0.535981	+	0.844230i	$0.680058\pi$
$954$	0.579491	−	4.03045i	0.0187617	−	0.130491i
$955$	−0.183019	+	1.27293i	−0.00592237	+	0.0411910i
$956$	14.0423	+	9.02445i	0.454161	+	0.291872i
$957$	4.23008	+	4.88177i	0.136739	+	0.157805i
$958$	13.5336	+	29.6345i	0.437251	+	0.957447i
$959$	14.3058	−	9.19378i	0.461958	−	0.296883i
$960$	−0.273100	−	0.0801894i	−0.00881427	−	0.00258810i
$961$	−2.81968	+	3.25408i	−0.0909574	+	0.104970i
$962$	35.4655	−	10.4136i	1.14345	−	0.335749i
$963$	1.85455	−	4.06089i	0.0597619	−	0.130860i
$964$	2.20399	+	15.3291i	0.0709858	+	0.493717i
$965$	−6.66225			−0.214465
$966$	−2.45093	+	4.12225i	−0.0788574	+	0.132631i
$967$	−28.3144			−0.910529			−0.455264	−	0.890356i	$-0.650455\pi$
$967$	−28.3144			−0.910529			−0.455264	+	0.890356i	$0.650455\pi$
$968$	1.33344	+	9.27426i	0.0428583	+	0.298086i
$969$	−5.15509	+	11.2881i	−0.165605	+	0.362625i
$970$	1.89358	−	0.556005i	0.0607992	−	0.0178522i
$971$	6.17793	−	7.12971i	0.198259	−	0.228803i	−0.647911	−	0.761716i	$-0.724357\pi$
$971$	6.17793	−	7.12971i	0.198259	−	0.228803i	0.846170	+	0.532913i	$0.178903\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	3.23382	−	2.07825i	0.103672	−	0.0666257i
$974$	−0.411044	−	0.900061i	−0.0131707	−	0.0288398i
$975$	−13.5409	−	15.6270i	−0.433656	−	0.500466i
$976$	10.5151	+	6.75767i	0.336582	+	0.216308i
$977$	1.99348	−	13.8650i	0.0637772	−	0.443580i	−0.932764	−	0.360486i	$-0.882611\pi$
$977$	1.99348	−	13.8650i	0.0637772	−	0.443580i	0.996542	−	0.0830940i	$-0.0264802\pi$
$978$	2.72747	−	18.9699i	0.0872147	−	0.606592i
$979$	−9.54839	−	6.13638i	−0.305168	−	0.196120i
$980$	−0.186393	−	0.215109i	−0.00595410	−	0.00687140i
$981$	−3.00948	−	6.58985i	−0.0960854	−	0.210398i
$982$	−16.7374	+	10.7565i	−0.534113	+	0.343254i
$983$	17.0100	+	4.99459i	0.542535	+	0.159303i	0.541506	−	0.840697i	$-0.317854\pi$
$983$	17.0100	+	4.99459i	0.542535	+	0.159303i	0.00102896	+	0.999999i	$0.499672\pi$
$984$	0.171292	−	0.197682i	0.00546060	−	0.00630187i
$985$	3.90417	−	1.14637i	0.124397	−	0.0365263i
$986$	9.18220	−	20.1062i	0.292421	−	0.640312i
$987$	−0.791914	−	5.50789i	−0.0252069	−	0.175318i
$988$	11.9390			0.379832
$989$	−7.34961	−	22.1495i	−0.233704	−	0.704312i
$990$	−0.363432			−0.0115506
$991$	−7.79690	−	54.2286i	−0.247677	−	1.72263i	−0.611572	−	0.791189i	$-0.709463\pi$
$991$	−7.79690	−	54.2286i	−0.247677	−	1.72263i	0.363896	−	0.931440i	$-0.381446\pi$
$992$	−2.46834	+	5.40491i	−0.0783699	+	0.171606i
$993$	−12.3175	+	3.61674i	−0.390883	+	0.114774i
$994$	10.1146	−	11.6729i	0.320817	−	0.370243i
$995$	1.14017	+	0.334785i	0.0361459	+	0.0106134i
$996$	10.7474	−	6.90695i	0.340545	−	0.218855i
$997$	−0.333973	−	0.731298i	−0.0105770	−	0.0231604i	0.904270	−	0.426962i	$-0.140416\pi$
$997$	−0.333973	−	0.731298i	−0.0105770	−	0.0231604i	−0.914847	+	0.403801i	$0.867689\pi$
$998$	20.7660	+	23.9652i	0.657336	+	0.758606i
$999$	7.39722	+	4.75390i	0.234038	+	0.150407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.b.463.1	yes	10
23.8	even	11	inner	966.2.q.b.169.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.b.169.1	✓	10	23.8	even	11	inner
966.2.q.b.463.1	yes	10	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)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.186393 + 0.215109i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.186393 + 0.215109i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.239446 + 0.153882i) q^{10} +(0.181716 - 1.26386i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-3.53631 - 2.27265i) q^{13} +(0.654861 + 0.755750i) q^{14} +(0.118239 + 0.258908i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-4.19227 - 1.23096i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(2.72514 - 0.800172i) q^{19} +(0.118239 - 0.258908i) q^{20} +(0.142315 + 0.989821i) q^{21} -1.27686 q^{22} +(-3.51302 + 3.26476i) q^{23} +1.00000 q^{24} +(0.700045 + 4.86892i) q^{25} +(-1.74625 + 3.82374i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.654861 - 0.755750i) q^{28} +(-4.85399 - 1.42526i) q^{29} +(0.239446 - 0.153882i) q^{30} +(-2.46834 - 5.40491i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-1.07416 - 0.690322i) q^{33} +(-0.621810 + 4.32479i) q^{34} +(0.0405070 - 0.281733i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-5.75825 - 6.64538i) q^{37} +(-1.17986 - 2.58352i) q^{38} +(-3.53631 + 2.27265i) q^{39} +(-0.273100 - 0.0801894i) q^{40} +(0.171292 - 0.197682i) q^{41} +(0.959493 - 0.281733i) q^{42} +(-2.02145 + 4.42636i) q^{43} +(0.181716 + 1.26386i) q^{44} +0.284630 q^{45} +(3.73149 + 3.01264i) q^{46} -5.56452 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(4.71973 - 1.38584i) q^{50} +(-2.86126 + 3.30207i) q^{51} +(4.03334 + 1.18430i) q^{52} +(-3.42550 + 2.20143i) q^{53} +(0.415415 + 0.909632i) q^{54} +(0.237997 + 0.274663i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(0.404200 - 2.81127i) q^{57} +(-0.719958 + 5.00742i) q^{58} +(-0.715900 - 0.460081i) q^{59} +(-0.186393 - 0.215109i) q^{60} +(5.19243 + 11.3698i) q^{61} +(-4.99862 + 3.21242i) q^{62} +(0.959493 + 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.14801 - 0.337086i) q^{65} +(-0.530426 + 1.16147i) q^{66} +(1.48241 + 10.3104i) q^{67} +4.36926 q^{68} +(1.51037 + 4.55179i) q^{69} -0.284630 q^{70} +(-2.19812 - 15.2883i) q^{71} +(0.415415 - 0.909632i) q^{72} +(6.50955 - 1.91138i) q^{73} +(-5.75825 + 6.64538i) q^{74} +(4.71973 + 1.38584i) q^{75} +(-2.38931 + 1.53552i) q^{76} +(0.530426 + 1.16147i) q^{77} +(2.75278 + 3.17688i) q^{78} +(0.0890471 + 0.0572271i) q^{79} +(-0.0405070 + 0.281733i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.220047 - 0.141416i) q^{82} +(-8.36616 - 9.65507i) q^{83} +(-0.415415 - 0.909632i) q^{84} +(1.04620 - 0.672352i) q^{85} +(4.66899 + 1.37094i) q^{86} +(-3.31288 + 3.82327i) q^{87} +(1.22514 - 0.359733i) q^{88} +(3.69269 - 8.08586i) q^{89} +(-0.0405070 - 0.281733i) q^{90} +4.20362 q^{91} +(2.45093 - 4.12225i) q^{92} -5.94187 q^{93} +(0.791914 + 5.50789i) q^{94} +(-0.335822 + 0.735347i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(4.54057 - 5.24010i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-1.07416 + 0.690322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 2 q^{10} + 7 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + 11 q^{19} + 2 q^{20} + q^{21} + 18 q^{22} + 21 q^{23} + 10 q^{24} + q^{25} - 2 q^{26} - q^{27} + q^{28} - 20 q^{29} + 2 q^{30} + 18 q^{31} - q^{32} - 15 q^{33} + 5 q^{34} + 9 q^{35} - q^{36} + 5 q^{37} - 22 q^{38} - 2 q^{39} + 2 q^{40} + 6 q^{41} + q^{42} - 12 q^{43} + 7 q^{44} + 2 q^{45} + 21 q^{46} - 32 q^{47} - q^{48} - q^{49} + 12 q^{50} - 17 q^{51} + 9 q^{52} - 39 q^{53} - q^{54} + 8 q^{55} + q^{56} + 22 q^{57} + 13 q^{58} + 15 q^{59} + 2 q^{60} + 21 q^{61} - 4 q^{62} + q^{63} - q^{64} - 7 q^{65} - 4 q^{66} - 26 q^{67} - 6 q^{68} - 12 q^{69} - 2 q^{70} + 27 q^{71} - q^{72} - 2 q^{73} + 5 q^{74} + 12 q^{75} + 4 q^{77} - 2 q^{78} + 47 q^{79} - 9 q^{80} - q^{81} + 6 q^{82} + 5 q^{83} + q^{84} + q^{85} - 12 q^{86} - 9 q^{87} - 4 q^{88} + 5 q^{89} - 9 q^{90} + 24 q^{91} + 10 q^{92} - 26 q^{93} + 23 q^{94} - 11 q^{95} - q^{96} + 2 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 + q^7 - q^8 - q^9 + 2 * q^10 + 7 * q^11 - q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 6 * q^17 - q^18 + 11 * q^19 + 2 * q^20 + q^21 + 18 * q^22 + 21 * q^23 + 10 * q^24 + q^25 - 2 * q^26 - q^27 + q^28 - 20 * q^29 + 2 * q^30 + 18 * q^31 - q^32 - 15 * q^33 + 5 * q^34 + 9 * q^35 - q^36 + 5 * q^37 - 22 * q^38 - 2 * q^39 + 2 * q^40 + 6 * q^41 + q^42 - 12 * q^43 + 7 * q^44 + 2 * q^45 + 21 * q^46 - 32 * q^47 - q^48 - q^49 + 12 * q^50 - 17 * q^51 + 9 * q^52 - 39 * q^53 - q^54 + 8 * q^55 + q^56 + 22 * q^57 + 13 * q^58 + 15 * q^59 + 2 * q^60 + 21 * q^61 - 4 * q^62 + q^63 - q^64 - 7 * q^65 - 4 * q^66 - 26 * q^67 - 6 * q^68 - 12 * q^69 - 2 * q^70 + 27 * q^71 - q^72 - 2 * q^73 + 5 * q^74 + 12 * q^75 + 4 * q^77 - 2 * q^78 + 47 * q^79 - 9 * q^80 - q^81 + 6 * q^82 + 5 * q^83 + q^84 + q^85 - 12 * q^86 - 9 * q^87 - 4 * q^88 + 5 * q^89 - 9 * q^90 + 24 * q^91 + 10 * q^92 - 26 * q^93 + 23 * q^94 - 11 * q^95 - q^96 + 2 * q^97 - q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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