LMFDB - Embedded newform 845.2.e.k.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.2
Root			$-1.62241 + 0.606458i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.k.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.285997 - 0.495361i) q^{2} +(0.214003 - 0.370665i) q^{3} +(0.836412 + 1.44871i) q^{4} +1.00000 q^{5} +(-0.122408 - 0.212018i) q^{6} +(-1.33641 - 2.31473i) q^{7} +2.10083 q^{8} +(1.40841 + 2.43943i) q^{9} +(0.285997 - 0.495361i) q^{10} +(2.55042 - 4.41745i) q^{11} +0.715980 q^{12} -1.52884 q^{14} +(0.214003 - 0.370665i) q^{15} +(-1.07199 + 1.85675i) q^{16} +(-2.67282 - 4.62947i) q^{17} +1.61120 q^{18} +(3.12241 + 5.40817i) q^{19} +(0.836412 + 1.44871i) q^{20} -1.14399 q^{21} +(-1.45882 - 2.52675i) q^{22} +(1.21400 - 2.10272i) q^{23} +(0.449585 - 0.778704i) q^{24} +1.00000 q^{25} +2.48963 q^{27} +(2.23558 - 3.87214i) q^{28} +(-1.33641 + 2.31473i) q^{29} +(-0.122408 - 0.212018i) q^{30} +0.244817 q^{31} +(2.71400 + 4.70079i) q^{32} +(-1.09159 - 1.89070i) q^{33} -3.05767 q^{34} +(-1.33641 - 2.31473i) q^{35} +(-2.35601 + 4.08074i) q^{36} +(1.66359 - 2.88142i) q^{37} +3.57199 q^{38} +2.10083 q^{40} +(3.24482 - 5.62019i) q^{41} +(-0.327176 + 0.566686i) q^{42} +(5.45882 + 9.45495i) q^{43} +8.53279 q^{44} +(1.40841 + 2.43943i) q^{45} +(-0.694402 - 1.20274i) q^{46} -2.67282 q^{47} +(0.458820 + 0.794700i) q^{48} +(-0.0719933 + 0.124696i) q^{49} +(0.285997 - 0.495361i) q^{50} -2.28797 q^{51} -4.20166 q^{53} +(0.712027 - 1.23327i) q^{54} +(2.55042 - 4.41745i) q^{55} +(-2.80757 - 4.86286i) q^{56} +2.67282 q^{57} +(0.764419 + 1.32401i) q^{58} +(-0.449585 - 0.778704i) q^{59} +0.715980 q^{60} +(2.90841 + 5.03751i) q^{61} +(0.0700168 - 0.121273i) q^{62} +(3.76442 - 6.52016i) q^{63} -1.18319 q^{64} -1.24877 q^{66} +(1.09159 - 1.89070i) q^{67} +(4.47116 - 7.74428i) q^{68} +(-0.519602 - 0.899976i) q^{69} -1.52884 q^{70} +(3.12241 + 5.40817i) q^{71} +(2.95882 + 5.12483i) q^{72} -10.9608 q^{73} +(-0.951561 - 1.64815i) q^{74} +(0.214003 - 0.370665i) q^{75} +(-5.22324 + 9.04692i) q^{76} -13.6336 q^{77} -3.63362 q^{79} +(-1.07199 + 1.85675i) q^{80} +(-3.69243 + 6.39547i) q^{81} +(-1.85601 - 3.21471i) q^{82} -9.81681 q^{83} +(-0.956844 - 1.65730i) q^{84} +(-2.67282 - 4.62947i) q^{85} +6.24482 q^{86} +(0.571993 + 0.990721i) q^{87} +(5.35799 - 9.28031i) q^{88} +(3.81681 - 6.61091i) q^{89} +1.61120 q^{90} +4.06163 q^{92} +(0.0523917 - 0.0907450i) q^{93} +(-0.764419 + 1.32401i) q^{94} +(3.12241 + 5.40817i) q^{95} +2.32322 q^{96} +(-5.67282 - 9.82562i) q^{97} +(0.0411797 + 0.0713253i) q^{98} +14.3681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 2 q^{3} - 5 q^{4} + 6 q^{5} + 10 q^{6} + 2 q^{7} - 6 q^{8} - 3 q^{9} + q^{10} + 6 q^{11} + 8 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 34 q^{18} + 8 q^{19} - 5 q^{20} - 4 q^{21} + 12 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) $ 6 * q + q^2 + 2 * q^3 - 5 * q^4 + 6 * q^5 + 10 * q^6 + 2 * q^7 - 6 * q^8 - 3 * q^9 + q^10 + 6 * q^11 + 8 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 34 * q^18 + 8 * q^19 - 5 * q^20 - 4 * q^21 + 12 * q^22 + 8 * q^23 + 12 * q^24 + 6 * q^25 - 28 * q^27 + 22 * q^28 + 2 * q^29 + 10 * q^30 - 20 * q^31 + 17 * q^32 - 18 * q^33 + 16 * q^34 + 2 * q^35 - 17 * q^36 + 20 * q^37 + 20 * q^38 - 6 * q^40 - 2 * q^41 - 22 * q^42 + 12 * q^43 + 24 * q^44 - 3 * q^45 + 8 * q^46 + 4 * q^47 - 18 * q^48 + q^49 + q^50 - 8 * q^51 + 12 * q^53 + 10 * q^54 + 6 * q^55 - 24 * q^56 - 4 * q^57 - 4 * q^58 - 12 * q^59 + 6 * q^61 + 4 * q^62 + 14 * q^63 - 30 * q^64 + 24 * q^66 + 18 * q^67 + 44 * q^68 - 16 * q^69 + 8 * q^70 + 8 * q^71 - 3 * q^72 - 40 * q^73 - 10 * q^74 + 2 * q^75 - 2 * q^76 - 36 * q^77 + 24 * q^79 - 5 * q^80 - 15 * q^81 - 14 * q^82 - 36 * q^83 + 10 * q^84 + 4 * q^85 + 16 * q^86 + 2 * q^87 + 30 * q^88 + 34 * q^90 - 20 * q^92 - 14 * q^93 + 4 * q^94 + 8 * q^95 + 44 * q^96 - 14 * q^97 + 21 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.285997	−	0.495361i	0.202230	−	0.350273i	−0.747017	−	0.664805i	$-0.768514\pi$
$2$	0.285997	−	0.495361i	0.202230	−	0.350273i	0.949247	+	0.314533i	$0.101848\pi$
$3$	0.214003	−	0.370665i	0.123555	−	0.214003i	−0.797612	−	0.603171i	$-0.793904\pi$
$3$	0.214003	−	0.370665i	0.123555	−	0.214003i	0.921167	+	0.389167i	$0.127237\pi$
$4$	0.836412	+	1.44871i	0.418206	+	0.724354i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.122408	−	0.212018i	−0.0499731	−	0.0865559i
$7$	−1.33641	−	2.31473i	−0.505116	−	0.874887i	−0.999982	−	0.00591779i	$-0.998116\pi$
$7$	−1.33641	−	2.31473i	−0.505116	−	0.874887i	0.494866	−	0.868969i	$-0.335217\pi$
$8$	2.10083			0.742756
$9$	1.40841	+	2.43943i	0.469468	+	0.813143i
$10$	0.285997	−	0.495361i	0.0904401	−	0.156647i
$11$	2.55042	−	4.41745i	0.768979	−	1.33191i	−0.169138	−	0.985592i	$-0.554098\pi$
$11$	2.55042	−	4.41745i	0.768979	−	1.33191i	0.938117	−	0.346319i	$-0.112568\pi$
$12$	0.715980			0.206686
$13$		0			0
$13$		0			0
$14$	−1.52884			−0.408599
$15$	0.214003	−	0.370665i	0.0552554	−	0.0957052i
$16$	−1.07199	+	1.85675i	−0.267998	+	0.464187i
$17$	−2.67282	−	4.62947i	−0.648255	−	1.12281i	−0.983539	−	0.180694i	$-0.942166\pi$
$17$	−2.67282	−	4.62947i	−0.648255	−	1.12281i	0.335284	−	0.942117i	$-0.391168\pi$
$18$	1.61120			0.379763
$19$	3.12241	+	5.40817i	0.716330	+	1.24072i	0.962444	+	0.271479i	$0.0875126\pi$
$19$	3.12241	+	5.40817i	0.716330	+	1.24072i	−0.246115	+	0.969241i	$0.579154\pi$
$20$	0.836412	+	1.44871i	0.187027	+	0.323941i
$21$	−1.14399			−0.249638
$22$	−1.45882	−	2.52675i	−0.311022	−	0.538705i
$23$	1.21400	−	2.10272i	0.253137	−	0.438446i	−0.711251	−	0.702938i	$-0.751871\pi$
$23$	1.21400	−	2.10272i	0.253137	−	0.438446i	0.964388	+	0.264492i	$0.0852043\pi$
$24$	0.449585	−	0.778704i	0.0917711	−	0.158952i
$25$	1.00000			0.200000
$26$		0			0
$27$	2.48963			0.479130
$28$	2.23558	−	3.87214i	0.422485	−	0.731766i
$29$	−1.33641	+	2.31473i	−0.248165	+	0.429835i	−0.963017	−	0.269441i	$-0.913161\pi$
$29$	−1.33641	+	2.31473i	−0.248165	+	0.429835i	0.714851	+	0.699276i	$0.246494\pi$
$30$	−0.122408	−	0.212018i	−0.0223486	−	0.0387090i
$31$	0.244817			0.0439704			0.0219852	−	0.999758i	$-0.493001\pi$
$31$	0.244817			0.0439704			0.0219852	+	0.999758i	$0.493001\pi$
$32$	2.71400	+	4.70079i	0.479773	+	0.830990i
$33$	−1.09159	−	1.89070i	−0.190022	−	0.329128i
$34$	−3.05767			−0.524387
$35$	−1.33641	−	2.31473i	−0.225895	−	0.391261i
$36$	−2.35601	+	4.08074i	−0.392669	+	0.680123i
$37$	1.66359	−	2.88142i	0.273492	−	0.473702i	−0.696261	−	0.717788i	$-0.745155\pi$
$37$	1.66359	−	2.88142i	0.273492	−	0.473702i	0.969754	+	0.244086i	$0.0784879\pi$
$38$	3.57199			0.579454
$39$		0			0
$40$	2.10083			0.332170
$41$	3.24482	−	5.62019i	0.506755	−	0.877726i	−0.493214	−	0.869908i	$-0.664178\pi$
$41$	3.24482	−	5.62019i	0.506755	−	0.877726i	0.999969	−	0.00781796i	$-0.00248856\pi$
$42$	−0.327176	+	0.566686i	−0.0504844	+	0.0874415i
$43$	5.45882	+	9.45495i	0.832462	+	1.44187i	0.896080	+	0.443893i	$0.146403\pi$
$43$	5.45882	+	9.45495i	0.832462	+	1.44187i	−0.0636177	+	0.997974i	$0.520264\pi$
$44$	8.53279			1.28637
$45$	1.40841	+	2.43943i	0.209953	+	0.363649i
$46$	−0.694402	−	1.20274i	−0.102384	−	0.177334i
$47$	−2.67282			−0.389871			−0.194936	−	0.980816i	$-0.562450\pi$
$47$	−2.67282			−0.389871			−0.194936	+	0.980816i	$0.562450\pi$
$48$	0.458820	+	0.794700i	0.0662250	+	0.114705i
$49$	−0.0719933	+	0.124696i	−0.0102848	+	0.0178137i
$50$	0.285997	−	0.495361i	0.0404460	−	0.0700546i
$51$	−2.28797			−0.320380
$52$		0			0
$53$	−4.20166			−0.577143			−0.288571	−	0.957458i	$-0.593180\pi$
$53$	−4.20166			−0.577143			−0.288571	+	0.957458i	$0.593180\pi$
$54$	0.712027	−	1.23327i	0.0968946	−	0.167826i
$55$	2.55042	−	4.41745i	0.343898	−	0.595649i
$56$	−2.80757	−	4.86286i	−0.375178	−	0.649827i
$57$	2.67282			0.354024
$58$	0.764419	+	1.32401i	0.100373	+	0.173851i
$59$	−0.449585	−	0.778704i	−0.0585310	−	0.101379i	0.835275	−	0.549832i	$-0.185308\pi$
$59$	−0.449585	−	0.778704i	−0.0585310	−	0.101379i	−0.893806	+	0.448454i	$0.851975\pi$
$60$	0.715980			0.0924326
$61$	2.90841	+	5.03751i	0.372383	+	0.644986i	0.989932	−	0.141546i	$-0.0452074\pi$
$61$	2.90841	+	5.03751i	0.372383	+	0.644986i	−0.617549	+	0.786533i	$0.711874\pi$
$62$	0.0700168	−	0.121273i	0.00889215	−	0.0154016i
$63$	3.76442	−	6.52016i	0.474272	−	0.821463i
$64$	−1.18319			−0.147899
$65$		0			0
$66$	−1.24877			−0.153713
$67$	1.09159	−	1.89070i	0.133360	−	0.230985i	−0.791610	−	0.611027i	$-0.790757\pi$
$67$	1.09159	−	1.89070i	0.133360	−	0.230985i	0.924970	+	0.380041i	$0.124090\pi$
$68$	4.47116	−	7.74428i	0.542208	−	0.939132i
$69$	−0.519602	−	0.899976i	−0.0625527	−	0.108344i
$70$	−1.52884			−0.182731
$71$	3.12241	+	5.40817i	0.370562	+	0.641832i	0.989652	−	0.143488i	$-0.0458319\pi$
$71$	3.12241	+	5.40817i	0.370562	+	0.641832i	−0.619090	+	0.785320i	$0.712499\pi$
$72$	2.95882	+	5.12483i	0.348700	+	0.603967i
$73$	−10.9608			−1.28286			−0.641432	−	0.767180i	$-0.721659\pi$
$73$	−10.9608			−1.28286			−0.641432	+	0.767180i	$0.721659\pi$
$74$	−0.951561	−	1.64815i	−0.110617	−	0.191594i
$75$	0.214003	−	0.370665i	0.0247110	−	0.0428007i
$76$	−5.22324	+	9.04692i	−0.599147	+	1.03775i
$77$	−13.6336			−1.55370
$78$		0			0
$79$	−3.63362			−0.408814			−0.204407	−	0.978886i	$-0.565527\pi$
$79$	−3.63362			−0.408814			−0.204407	+	0.978886i	$0.565527\pi$
$80$	−1.07199	+	1.85675i	−0.119852	+	0.207591i
$81$	−3.69243	+	6.39547i	−0.410269	+	0.710608i
$82$	−1.85601	−	3.21471i	−0.204962	−	0.355005i
$83$	−9.81681			−1.07753			−0.538767	−	0.842455i	$-0.681110\pi$
$83$	−9.81681			−1.07753			−0.538767	+	0.842455i	$0.681110\pi$
$84$	−0.956844	−	1.65730i	−0.104400	−	0.180826i
$85$	−2.67282	−	4.62947i	−0.289908	−	0.502136i
$86$	6.24482			0.673396
$87$	0.571993	+	0.990721i	0.0613241	+	0.106216i
$88$	5.35799	−	9.28031i	0.571164	−	0.989284i
$89$	3.81681	−	6.61091i	0.404581	−	0.700755i	−0.589692	−	0.807629i	$-0.700751\pi$
$89$	3.81681	−	6.61091i	0.404581	−	0.700755i	0.994273	+	0.106874i	$0.0340840\pi$
$90$	1.61120			0.169835
$91$		0			0
$92$	4.06163			0.423454
$93$	0.0523917	−	0.0907450i	0.00543276	−	0.00940982i
$94$	−0.764419	+	1.32401i	−0.0788438	+	0.136561i
$95$	3.12241	+	5.40817i	0.320352	+	0.554867i
$96$	2.32322			0.237113
$97$	−5.67282	−	9.82562i	−0.575988	−	0.997640i	−0.995934	−	0.0900911i	$-0.971284\pi$
$97$	−5.67282	−	9.82562i	−0.575988	−	0.997640i	0.419946	−	0.907549i	$-0.362049\pi$
$98$	0.0411797	+	0.0713253i	0.00415977	+	0.00720494i
$99$	14.3681			1.44405
$100$	0.836412	+	1.44871i	0.0836412	+	0.144871i
$101$	−5.42801	+	9.40158i	−0.540107	+	0.935493i	0.458790	+	0.888544i	$0.348283\pi$
$101$	−5.42801	+	9.40158i	−0.540107	+	0.935493i	−0.998897	+	0.0469480i	$0.985050\pi$
$102$	−0.654353	+	1.13337i	−0.0647906	+	0.112221i
$103$	10.6297			1.04737			0.523686	−	0.851911i	$-0.324556\pi$
$103$	10.6297			1.04737			0.523686	+	0.851911i	$0.324556\pi$
$104$		0			0
$105$	−1.14399			−0.111642
$106$	−1.20166	+	2.08134i	−0.116716	+	0.202157i
$107$	−0.0700168	+	0.121273i	−0.00676878	+	0.0117239i	−0.869390	−	0.494127i	$-0.835488\pi$
$107$	−0.0700168	+	0.121273i	−0.00676878	+	0.0117239i	0.862621	+	0.505850i	$0.168821\pi$
$108$	2.08236	+	3.60675i	0.200375	+	0.347060i
$109$	−9.05767			−0.867568			−0.433784	−	0.901017i	$-0.642822\pi$
$109$	−9.05767			−0.867568			−0.433784	+	0.901017i	$0.642822\pi$
$110$	−1.45882	−	2.52675i	−0.139093	−	0.240916i
$111$	−0.712027	−	1.23327i	−0.0675826	−	0.117057i
$112$	5.73050			0.541481
$113$	−6.48963	−	11.2404i	−0.610493	−	1.05741i	−0.991157	−	0.132692i	$-0.957638\pi$
$113$	−6.48963	−	11.2404i	−0.610493	−	1.05741i	0.380664	−	0.924713i	$-0.375695\pi$
$114$	0.764419	−	1.32401i	0.0715944	−	0.124005i
$115$	1.21400	−	2.10272i	0.113206	−	0.196079i
$116$	−4.47116			−0.415137
$117$		0			0
$118$	−0.514319			−0.0473469
$119$	−7.14399	+	12.3737i	−0.654888	+	1.13430i
$120$	0.449585	−	0.778704i	0.0410413	−	0.0710856i
$121$	−7.50924	−	13.0064i	−0.682658	−	1.18240i
$122$	3.32718			0.301228
$123$	−1.38880	−	2.40548i	−0.125224	−	0.216895i
$124$	0.204768	+	0.354668i	0.0183887	+	0.0318501i
$125$	1.00000			0.0894427
$126$	−2.15322	−	3.72949i	−0.191824	−	0.332249i
$127$	−6.03081	+	10.4457i	−0.535148	+	0.926904i	0.464008	+	0.885831i	$0.346411\pi$
$127$	−6.03081	+	10.4457i	−0.535148	+	0.926904i	−0.999156	+	0.0410728i	$0.986922\pi$
$128$	−5.76640	+	9.98769i	−0.509682	+	0.882795i
$129$	4.67282			0.411419
$130$		0			0
$131$	7.63362			0.666953			0.333476	−	0.942758i	$-0.391778\pi$
$131$	7.63362			0.666953			0.333476	+	0.942758i	$0.391778\pi$
$132$	1.82605	−	3.16280i	0.158937	−	0.275287i
$133$	8.34565	−	14.4551i	0.723659	−	1.25341i
$134$	−0.624385	−	1.08147i	−0.0539386	−	0.0934245i
$135$	2.48963			0.214274
$136$	−5.61515	−	9.72572i	−0.481495	−	0.833974i
$137$	−1.71598	−	2.97216i	−0.146606	−	0.253929i	0.783365	−	0.621562i	$-0.213502\pi$
$137$	−1.71598	−	2.97216i	−0.146606	−	0.253929i	−0.929971	+	0.367633i	$0.880168\pi$
$138$	−0.594417			−0.0506002
$139$	0.471163	+	0.816078i	0.0399635	+	0.0692188i	0.885315	−	0.464991i	$-0.153942\pi$
$139$	0.471163	+	0.816078i	0.0399635	+	0.0692188i	−0.845352	+	0.534210i	$0.820609\pi$
$140$	2.23558	−	3.87214i	0.188941	−	0.327256i
$141$	−0.571993	+	0.990721i	−0.0481705	+	0.0834338i
$142$	3.57199			0.299755
$143$		0			0
$144$	−6.03920			−0.503267
$145$	−1.33641	+	2.31473i	−0.110983	+	0.192228i
$146$	−3.13475	+	5.42955i	−0.259434	+	0.449353i
$147$	0.0308136	+	0.0533707i	0.00254146	+	0.00440194i
$148$	5.56578			0.457504
$149$	−5.67282	−	9.82562i	−0.464736	−	0.804946i	0.534454	−	0.845198i	$-0.320517\pi$
$149$	−5.67282	−	9.82562i	−0.464736	−	0.804946i	−0.999190	+	0.0402517i	$0.987184\pi$
$150$	−0.122408	−	0.212018i	−0.00999461	−	0.0173112i
$151$	−21.0224			−1.71078			−0.855390	−	0.517984i	$-0.826683\pi$
$151$	−21.0224			−1.71078			−0.855390	+	0.517984i	$0.826683\pi$
$152$	6.55965	+	11.3616i	0.532058	+	0.921551i
$153$	7.52884	−	13.0403i	0.608670	−	1.05425i
$154$	−3.89917	+	6.75356i	−0.314204	+	0.544217i
$155$	0.244817			0.0196642
$156$		0			0
$157$	−9.83528			−0.784941			−0.392470	−	0.919765i	$-0.628379\pi$
$157$	−9.83528			−0.784941			−0.392470	+	0.919765i	$0.628379\pi$
$158$	−1.03920	+	1.79995i	−0.0826746	+	0.143197i
$159$	−0.899170	+	1.55741i	−0.0713088	+	0.123510i
$160$	2.71400	+	4.70079i	0.214561	+	0.371630i
$161$	−6.48963			−0.511455
$162$	2.11204	+	3.65816i	0.165938	+	0.287413i
$163$	6.19243	+	10.7256i	0.485028	+	0.840093i	0.999852	−	0.0172025i	$-0.00547601\pi$
$163$	6.19243	+	10.7256i	0.485028	+	0.840093i	−0.514824	+	0.857296i	$0.672143\pi$
$164$	10.8560			0.847712
$165$	−1.09159	−	1.89070i	−0.0849805	−	0.147191i
$166$	−2.80757	+	4.86286i	−0.217910	+	0.377431i
$167$	−4.25405	+	7.36824i	−0.329188	+	0.570171i	−0.982351	−	0.187047i	$-0.940108\pi$
$167$	−4.25405	+	7.36824i	−0.329188	+	0.570171i	0.653163	+	0.757218i	$0.273442\pi$
$168$	−2.40332			−0.185420
$169$		0			0
$170$	−3.05767			−0.234513
$171$	−8.79523	+	15.2338i	−0.672588	+	1.16496i
$172$	−9.13164	+	15.8165i	−0.696281	+	1.20599i
$173$	10.7737	+	18.6605i	0.819106	+	1.41873i	0.906342	+	0.422545i	$0.138863\pi$
$173$	10.7737	+	18.6605i	0.819106	+	1.41873i	−0.0872361	+	0.996188i	$0.527803\pi$
$174$	0.654353			0.0496063
$175$	−1.33641	−	2.31473i	−0.101023	−	0.174977i
$176$	5.46806	+	9.47095i	0.412170	+	0.713900i
$177$	−0.384851			−0.0289271
$178$	−2.18319	−	3.78140i	−0.163637	−	0.283428i
$179$	−1.28402	+	2.22399i	−0.0959722	+	0.166229i	−0.910014	−	0.414578i	$-0.863929\pi$
$179$	−1.28402	+	2.22399i	−0.0959722	+	0.166229i	0.814042	+	0.580806i	$0.197263\pi$
$180$	−2.35601	+	4.08074i	−0.175607	+	0.304160i
$181$	−13.7305			−1.02058			−0.510290	−	0.860002i	$-0.670462\pi$
$181$	−13.7305			−1.02058			−0.510290	+	0.860002i	$0.670462\pi$
$182$		0			0
$183$	2.48963			0.184039
$184$	2.55042	−	4.41745i	0.188019	−	0.325659i
$185$	1.66359	−	2.88142i	0.122309	−	0.211846i
$186$	−0.0299677	−	0.0519055i	−0.00219734	−	0.00380590i
$187$	−27.2672			−1.99398
$188$	−2.23558	−	3.87214i	−0.163047	−	0.282405i
$189$	−3.32718	−	5.76284i	−0.242016	−	0.419185i
$190$	3.57199			0.259140
$191$	5.34565	+	9.25893i	0.386797	+	0.669953i	0.992017	−	0.126106i	$-0.0402479\pi$
$191$	5.34565	+	9.25893i	0.386797	+	0.669953i	−0.605219	+	0.796059i	$0.706915\pi$
$192$	−0.253207	+	0.438567i	−0.0182736	+	0.0316508i
$193$	−9.62967	+	16.6791i	−0.693159	+	1.20059i	0.277639	+	0.960686i	$0.410448\pi$
$193$	−9.62967	+	16.6791i	−0.693159	+	1.20059i	−0.970797	+	0.239900i	$0.922885\pi$
$194$	−6.48963			−0.465929
$195$		0			0
$196$	−0.240864			−0.0172046
$197$	−8.59046	+	14.8791i	−0.612045	+	1.06009i	0.378850	+	0.925458i	$0.376320\pi$
$197$	−8.59046	+	14.8791i	−0.612045	+	1.06009i	−0.990895	+	0.134635i	$0.957014\pi$
$198$	4.10922	−	7.11738i	0.292030	−	0.505810i
$199$	−5.77365	−	10.0003i	−0.409283	−	0.708900i	0.585526	−	0.810654i	$-0.300888\pi$
$199$	−5.77365	−	10.0003i	−0.409283	−	0.708900i	−0.994810	+	0.101754i	$0.967555\pi$
$200$	2.10083			0.148551
$201$	−0.467210	−	0.809231i	−0.0329544	−	0.0570788i
$202$	3.10478	+	5.37764i	0.218452	+	0.378370i
$203$	7.14399			0.501410
$204$	−1.91369	−	3.31460i	−0.133985	−	0.232069i
$205$	3.24482	−	5.62019i	0.226628	−	0.392531i
$206$	3.04005	−	5.26552i	0.211810	−	0.366866i
$207$	6.83923			0.475360
$208$		0			0
$209$	31.8538			2.20337
$210$	−0.327176	+	0.566686i	−0.0225773	+	0.0391050i
$211$	−12.0616	+	20.8914i	−0.830357	+	1.43822i	0.0673990	+	0.997726i	$0.478530\pi$
$211$	−12.0616	+	20.8914i	−0.830357	+	1.43822i	−0.897756	+	0.440494i	$0.854803\pi$
$212$	−3.51432	−	6.08698i	−0.241364	−	0.418055i
$213$	2.67282			0.183139
$214$	0.0400492	+	0.0693672i	0.00273770	+	0.00474184i
$215$	5.45882	+	9.45495i	0.372288	+	0.644823i
$216$	5.23030			0.355877
$217$	−0.327176	−	0.566686i	−0.0222102	−	0.0384692i
$218$	−2.59046	+	4.48682i	−0.175448	+	0.303886i
$219$	−2.34565	+	4.06278i	−0.158504	+	0.274537i
$220$	8.53279			0.575281
$221$		0			0
$222$	−0.814549			−0.0546690
$223$	2.86525	−	4.96276i	0.191871	−	0.332331i	−0.753999	−	0.656875i	$-0.771878\pi$
$223$	2.86525	−	4.96276i	0.191871	−	0.332331i	0.945870	+	0.324545i	$0.105211\pi$
$224$	7.25405	−	12.5644i	0.484682	−	0.839493i
$225$	1.40841	+	2.43943i	0.0938937	+	0.162629i
$226$	−7.42405			−0.493841
$227$	1.47645	+	2.55728i	0.0979951	+	0.169733i	0.910855	−	0.412727i	$-0.135424\pi$
$227$	1.47645	+	2.55728i	0.0979951	+	0.169733i	−0.812860	+	0.582460i	$0.802090\pi$
$228$	2.23558	+	3.87214i	0.148055	+	0.256439i
$229$	−25.2593			−1.66918			−0.834592	−	0.550869i	$-0.814297\pi$
$229$	−25.2593			−1.66918			−0.834592	+	0.550869i	$0.814297\pi$
$230$	−0.694402	−	1.20274i	−0.0457875	−	0.0793063i
$231$	−2.91764	+	5.05350i	−0.191967	+	0.332496i
$232$	−2.80757	+	4.86286i	−0.184326	+	0.319263i
$233$	23.3456			1.52942			0.764712	−	0.644372i	$-0.222881\pi$
$233$	23.3456			1.52942			0.764712	+	0.644372i	$0.222881\pi$
$234$		0			0
$235$	−2.67282			−0.174356
$236$	0.752076	−	1.30263i	0.0489560	−	0.0847942i
$237$	−0.777607	+	1.34685i	−0.0505110	+	0.0874876i
$238$	4.08631	+	7.07770i	0.264876	+	0.458779i
$239$	3.79213			0.245292			0.122646	−	0.992450i	$-0.460862\pi$
$239$	3.79213			0.245292			0.122646	+	0.992450i	$0.460862\pi$
$240$	0.458820	+	0.794700i	0.0296167	+	0.0512977i
$241$	−1.71598	−	2.97216i	−0.110536	−	0.191454i	0.805451	−	0.592663i	$-0.201923\pi$
$241$	−1.71598	−	2.97216i	−0.110536	−	0.191454i	−0.915986	+	0.401209i	$0.868590\pi$
$242$	−8.59046			−0.552216
$243$	5.31483	+	9.20556i	0.340947	+	0.590537i
$244$	−4.86525	+	8.42686i	−0.311466	+	0.539474i
$245$	−0.0719933	+	0.124696i	−0.00459948	+	0.00796654i
$246$	−1.58877			−0.101296
$247$		0			0
$248$	0.514319			0.0326593
$249$	−2.10083	+	3.63875i	−0.133135	+	0.230596i
$250$	0.285997	−	0.495361i	0.0180880	−	0.0313294i
$251$	−12.7345	−	22.0567i	−0.803791	−	1.39221i	−0.917104	−	0.398648i	$-0.869479\pi$
$251$	−12.7345	−	22.0567i	−0.803791	−	1.39221i	0.113313	−	0.993559i	$-0.463854\pi$
$252$	12.5944			0.793374
$253$	−6.19243	−	10.7256i	−0.389314	−	0.674312i
$254$	3.44958	+	5.97486i	0.216446	+	0.374896i
$255$	−2.28797			−0.143278
$256$	2.11515	+	3.66355i	0.132197	+	0.228972i
$257$	4.63362	−	8.02567i	0.289037	−	0.500627i	−0.684543	−	0.728973i	$-0.739998\pi$
$257$	4.63362	−	8.02567i	0.289037	−	0.500627i	0.973580	+	0.228345i	$0.0733315\pi$
$258$	1.33641	−	2.31473i	0.0832014	−	0.144109i
$259$	−8.89296			−0.552581
$260$		0			0
$261$	−7.52884			−0.466023
$262$	2.18319	−	3.78140i	0.134878	−	0.233615i
$263$	4.07397	−	7.05632i	0.251212	−	0.435111i	−0.712648	−	0.701522i	$-0.752504\pi$
$263$	4.07397	−	7.05632i	0.251212	−	0.435111i	0.963860	+	0.266410i	$0.0858376\pi$
$264$	−2.29326	−	3.97204i	−0.141140	−	0.244462i
$265$	−4.20166			−0.258106
$266$	−4.77365	−	8.26821i	−0.292692	−	0.506957i
$267$	−1.63362	−	2.82951i	−0.0999759	−	0.173163i
$268$	3.65209			0.223087
$269$	−0.571993	−	0.990721i	−0.0348750	−	0.0604053i	0.848061	−	0.529899i	$-0.177770\pi$
$269$	−0.571993	−	0.990721i	−0.0348750	−	0.0604053i	−0.882936	+	0.469493i	$0.844437\pi$
$270$	0.712027	−	1.23327i	0.0433326	−	0.0750542i
$271$	−1.59357	+	2.76015i	−0.0968026	+	0.167667i	−0.910359	−	0.413818i	$-0.864195\pi$
$271$	−1.59357	+	2.76015i	−0.0968026	+	0.167667i	0.813557	+	0.581485i	$0.197528\pi$
$272$	11.4610			0.694925
$273$		0			0
$274$	−1.96306			−0.118593
$275$	2.55042	−	4.41745i	0.153796	−	0.266382i
$276$	0.869202	−	1.50550i	0.0523198	−	0.0906206i
$277$	3.81286	+	6.60406i	0.229092	+	0.396800i	0.957539	−	0.288303i	$-0.0930909\pi$
$277$	3.81286	+	6.60406i	0.229092	+	0.396800i	−0.728447	+	0.685102i	$0.759758\pi$
$278$	0.539004			0.0323273
$279$	0.344801	+	0.597214i	0.0206427	+	0.0357542i
$280$	−2.80757	−	4.86286i	−0.167785	−	0.290612i
$281$	20.2386			1.20733			0.603667	−	0.797237i	$-0.293706\pi$
$281$	20.2386			1.20733			0.603667	+	0.797237i	$0.293706\pi$
$282$	0.327176	+	0.566686i	0.0194831	+	0.0337457i
$283$	9.94845	−	17.2312i	0.591374	−	1.02429i	−0.402673	−	0.915344i	$-0.631919\pi$
$283$	9.94845	−	17.2312i	0.591374	−	1.02429i	0.994048	−	0.108946i	$-0.0347477\pi$
$284$	−5.22324	+	9.04692i	−0.309942	+	0.536836i
$285$	2.67282			0.158324
$286$		0			0
$287$	−17.3456			−1.02388
$288$	−7.64483	+	13.2412i	−0.450476	+	0.780247i
$289$	−5.78797	+	10.0251i	−0.340469	+	0.589710i
$290$	0.764419	+	1.32401i	0.0448882	+	0.0777487i
$291$	−4.85601			−0.284665
$292$	−9.16774	−	15.8790i	−0.536501	−	0.929248i
$293$	−13.0092	−	22.5327i	−0.760008	−	1.31637i	−0.942846	−	0.333229i	$-0.891862\pi$
$293$	−13.0092	−	22.5327i	−0.760008	−	1.31637i	0.182838	−	0.983143i	$-0.441472\pi$
$294$	0.0352503			0.00205584
$295$	−0.449585	−	0.778704i	−0.0261758	−	0.0453379i
$296$	3.49492	−	6.05337i	0.203138	−	0.351845i
$297$	6.34960	−	10.9978i	0.368441	−	0.638159i
$298$	−6.48963			−0.375934
$299$		0			0
$300$	0.715980			0.0413371
$301$	14.5905	−	25.2714i	0.840980	−	1.45662i
$302$	−6.01234	+	10.4137i	−0.345971	+	0.599240i
$303$	2.32322	+	4.02394i	0.133466	+	0.231169i
$304$	−13.3888			−0.767901
$305$	2.90841	+	5.03751i	0.166535	+	0.288447i
$306$	−4.30644	−	7.45898i	−0.246183	−	0.426402i
$307$	2.39276			0.136562			0.0682809	−	0.997666i	$-0.478249\pi$
$307$	2.39276			0.136562			0.0682809	+	0.997666i	$0.478249\pi$
$308$	−11.4033	−	19.7511i	−0.649765	−	1.12543i
$309$	2.27478	−	3.94004i	0.129408	−	0.224141i
$310$	0.0700168	−	0.121273i	0.00397669	−	0.00688783i
$311$	−3.54731			−0.201149			−0.100575	−	0.994930i	$-0.532068\pi$
$311$	−3.54731			−0.201149			−0.100575	+	0.994930i	$0.532068\pi$
$312$		0			0
$313$	4.97927			0.281445			0.140722	−	0.990049i	$-0.455057\pi$
$313$	4.97927			0.281445			0.140722	+	0.990049i	$0.455057\pi$
$314$	−2.81286	+	4.87201i	−0.158739	+	0.274944i
$315$	3.76442	−	6.52016i	0.212101	−	0.367370i
$316$	−3.03920	−	5.26405i	−0.170969	−	0.296126i
$317$	18.5944			1.04437			0.522183	−	0.852833i	$-0.325118\pi$
$317$	18.5944			1.04437			0.522183	+	0.852833i	$0.325118\pi$
$318$	0.514319	+	0.890827i	0.0288416	+	0.0499551i
$319$	6.81681	+	11.8071i	0.381668	+	0.661069i
$320$	−1.18319			−0.0661423
$321$	0.0299677	+	0.0519055i	0.00167263	+	0.00289708i
$322$	−1.85601	+	3.21471i	−0.103432	+	0.179149i
$323$	16.6913	−	28.9102i	0.928728	−	1.60860i
$324$	−12.3536			−0.686309
$325$		0			0
$326$	7.08405			0.392349
$327$	−1.93837	+	3.35736i	−0.107192	+	0.185662i
$328$	6.81681	−	11.8071i	0.376395	−	0.651936i
$329$	3.57199	+	6.18687i	0.196930	+	0.341093i
$330$	−1.24877			−0.0687425
$331$	2.95995	+	5.12679i	0.162694	+	0.281794i	0.935834	−	0.352442i	$-0.114648\pi$
$331$	2.95995	+	5.12679i	0.162694	+	0.281794i	−0.773140	+	0.634235i	$0.781315\pi$
$332$	−8.21090	−	14.2217i	−0.450631	−	0.780517i
$333$	9.37202			0.513584
$334$	2.43329	+	4.21458i	0.133144	+	0.230612i
$335$	1.09159	−	1.89070i	0.0596402	−	0.103300i
$336$	1.22635	−	2.12409i	0.0669027	−	0.115879i
$337$	−13.9216			−0.758358			−0.379179	−	0.925323i	$-0.623793\pi$
$337$	−13.9216			−0.758358			−0.379179	+	0.925323i	$0.623793\pi$
$338$		0			0
$339$	−5.55521			−0.301718
$340$	4.47116	−	7.74428i	0.242483	−	0.419993i
$341$	0.624385	−	1.08147i	0.0338123	−	0.0585647i
$342$	5.03081	+	8.71362i	0.272035	+	0.471179i
$343$	−18.3249			−0.989452
$344$	11.4681	+	19.8633i	0.618316	+	1.07095i
$345$	−0.519602	−	0.899976i	−0.0279744	−	0.0484531i
$346$	12.3249			0.662592
$347$	−3.82915	−	6.63229i	−0.205560	−	0.356040i	0.744751	−	0.667342i	$-0.232568\pi$
$347$	−3.82915	−	6.63229i	−0.205560	−	0.356040i	−0.950311	+	0.311302i	$0.899235\pi$
$348$	−0.956844	+	1.65730i	−0.0512922	+	0.0888407i
$349$	5.59046	−	9.68297i	0.299251	−	0.518317i	−0.676714	−	0.736246i	$-0.736597\pi$
$349$	5.59046	−	9.68297i	0.299251	−	0.518317i	0.975965	+	0.217929i	$0.0699300\pi$
$350$	−1.52884			−0.0817198
$351$		0			0
$352$	27.6873			1.47574
$353$	−4.82605	+	8.35896i	−0.256864	+	0.444902i	−0.965400	−	0.260773i	$-0.916023\pi$
$353$	−4.82605	+	8.35896i	−0.256864	+	0.444902i	0.708536	+	0.705675i	$0.249356\pi$
$354$	−0.110066	+	0.190640i	−0.00584994	+	0.0101324i
$355$	3.12241	+	5.40817i	0.165720	+	0.287036i
$356$	12.7697			0.676793
$357$	3.05767	+	5.29605i	0.161829	+	0.280297i
$358$	0.734451	+	1.27211i	0.0388169	+	0.0672329i
$359$	−9.51206			−0.502027			−0.251014	−	0.967984i	$-0.580764\pi$
$359$	−9.51206			−0.502027			−0.251014	+	0.967984i	$0.580764\pi$
$360$	2.95882	+	5.12483i	0.155944	+	0.270102i
$361$	−9.99887	+	17.3185i	−0.526256	+	0.911503i
$362$	−3.92688	+	6.80155i	−0.206392	+	0.357481i
$363$	−6.42801			−0.337383
$364$		0			0
$365$	−10.9608			−0.573714
$366$	0.712027	−	1.23327i	0.0372182	−	0.0644639i
$367$	8.50198	−	14.7259i	0.443800	−	0.768683i	−0.554168	−	0.832405i	$-0.686964\pi$
$367$	8.50198	−	14.7259i	0.443800	−	0.768683i	0.997968	+	0.0637213i	$0.0202969\pi$
$368$	2.60281	+	4.50819i	0.135681	+	0.235006i
$369$	18.2801			0.951622
$370$	−0.951561	−	1.64815i	−0.0494693	−	0.0856834i
$371$	5.61515	+	9.72572i	0.291524	+	0.504934i
$372$	0.175284			0.00908805
$373$	0.917641	+	1.58940i	0.0475136	+	0.0822960i	0.888804	−	0.458287i	$-0.151537\pi$
$373$	0.917641	+	1.58940i	0.0475136	+	0.0822960i	−0.841290	+	0.540583i	$0.818204\pi$
$374$	−7.79834	+	13.5071i	−0.403243	+	0.698437i
$375$	0.214003	−	0.370665i	0.0110511	−	0.0191410i
$376$	−5.61515			−0.289579
$377$		0			0
$378$	−3.80624			−0.195772
$379$	16.1840	−	28.0316i	0.831318	−	1.43989i	−0.0656752	−	0.997841i	$-0.520920\pi$
$379$	16.1840	−	28.0316i	0.831318	−	1.43989i	0.896993	−	0.442044i	$-0.145747\pi$
$380$	−5.22324	+	9.04692i	−0.267947	+	0.464097i
$381$	2.58123	+	4.47082i	0.132240	+	0.229047i
$382$	6.11535			0.312888
$383$	14.0709	+	24.3714i	0.718988	+	1.24532i	0.961401	+	0.275150i	$0.0887275\pi$
$383$	14.0709	+	24.3714i	0.718988	+	1.24532i	−0.242414	+	0.970173i	$0.577939\pi$
$384$	2.46806	+	4.27480i	0.125947	+	0.218147i
$385$	−13.6336			−0.694834
$386$	5.50811	+	9.54032i	0.280355	+	0.485589i
$387$	−15.3765	+	26.6328i	−0.781629	+	1.35382i
$388$	9.48963	−	16.4365i	0.481763	−	0.834438i
$389$	31.9585			1.62036			0.810181	−	0.586180i	$-0.199369\pi$
$389$	31.9585			1.62036			0.810181	+	0.586180i	$0.199369\pi$
$390$		0			0
$391$	−12.9793			−0.656390
$392$	−0.151246	+	0.261965i	−0.00763906	+	0.0132312i
$393$	1.63362	−	2.82951i	0.0824053	−	0.142730i
$394$	4.91369	+	8.51076i	0.247548	+	0.428766i
$395$	−3.63362			−0.182827
$396$	12.0176	+	20.8151i	0.603908	+	1.04600i
$397$	6.35488	+	11.0070i	0.318942	+	0.552424i	0.980268	−	0.197675i	$-0.0633390\pi$
$397$	6.35488	+	11.0070i	0.318942	+	0.552424i	−0.661325	+	0.750099i	$0.730006\pi$
$398$	−6.60498			−0.331078
$399$	−3.57199	−	6.18687i	−0.178823	−	0.309731i
$400$	−1.07199	+	1.85675i	−0.0535997	+	0.0928373i
$401$	−0.489634	+	0.848071i	−0.0244512	+	0.0423506i	−0.877992	−	0.478675i	$-0.841117\pi$
$401$	−0.489634	+	0.848071i	−0.0244512	+	0.0423506i	0.853541	+	0.521026i	$0.174450\pi$
$402$	−0.534482			−0.0266575
$403$		0			0
$404$	−18.1602			−0.903504
$405$	−3.69243	+	6.39547i	−0.183478	+	0.317793i
$406$	2.04316	−	3.53885i	0.101400	−	0.175630i
$407$	−8.48568	−	14.6976i	−0.420620	−	0.728535i
$408$	−4.80664			−0.237964
$409$	−3.89917	−	6.75356i	−0.192802	−	0.333942i	0.753376	−	0.657590i	$-0.228424\pi$
$409$	−3.89917	−	6.75356i	−0.192802	−	0.333942i	−0.946178	+	0.323648i	$0.895091\pi$
$410$	−1.85601	−	3.21471i	−0.0916620	−	0.158763i
$411$	−1.46890			−0.0724556
$412$	8.89078	+	15.3993i	0.438017	+	0.758668i
$413$	−1.20166	+	2.08134i	−0.0591299	+	0.102416i
$414$	1.95600	−	3.38789i	0.0961321	−	0.166506i
$415$	−9.81681			−0.481888
$416$		0			0
$417$	0.403322			0.0197508
$418$	9.11007	−	15.7791i	0.445588	−	0.771781i
$419$	−5.10083	+	8.83490i	−0.249192	+	0.431613i	−0.963302	−	0.268421i	$-0.913498\pi$
$419$	−5.10083	+	8.83490i	−0.249192	+	0.431613i	0.714110	+	0.700034i	$0.246832\pi$
$420$	−0.956844	−	1.65730i	−0.0466892	−	0.0808681i
$421$	31.1888			1.52005			0.760025	−	0.649893i	$-0.225186\pi$
$421$	31.1888			1.52005			0.760025	+	0.649893i	$0.225186\pi$
$422$	6.89917	+	11.9497i	0.335846	+	0.581703i
$423$	−3.76442	−	6.52016i	−0.183032	−	0.317021i
$424$	−8.82698			−0.428676
$425$	−2.67282	−	4.62947i	−0.129651	−	0.224562i
$426$	0.764419	−	1.32401i	0.0370362	−	0.0641486i
$427$	7.77365	−	13.4644i	0.376193	−	0.651586i
$428$	−0.234252			−0.0113230
$429$		0			0
$430$	6.24482			0.301152
$431$	−11.4681	+	19.8633i	−0.552397	+	0.956779i	0.445704	+	0.895180i	$0.352953\pi$
$431$	−11.4681	+	19.8633i	−0.552397	+	0.956779i	−0.998101	+	0.0615990i	$0.980380\pi$
$432$	−2.66887	+	4.62262i	−0.128406	+	0.222406i
$433$	−8.14399	−	14.1058i	−0.391375	−	0.677881i	0.601256	−	0.799056i	$-0.294667\pi$
$433$	−8.14399	−	14.1058i	−0.391375	−	0.677881i	−0.992631	+	0.121175i	$0.961334\pi$
$434$	−0.374285			−0.0179663
$435$	0.571993	+	0.990721i	0.0274250	+	0.0475015i
$436$	−7.57595	−	13.1219i	−0.362822	−	0.628426i
$437$	15.1625			0.725319
$438$	1.34169	+	2.32388i	0.0641086	+	0.111039i
$439$	11.8784	−	20.5741i	0.566927	−	0.981946i	−0.429941	−	0.902857i	$-0.641466\pi$
$439$	11.8784	−	20.5741i	0.566927	−	0.981946i	0.996868	−	0.0790890i	$-0.0252011\pi$
$440$	5.35799	−	9.28031i	0.255432	−	0.442421i
$441$	−0.405583			−0.0193135
$442$		0			0
$443$	−2.75292			−0.130795			−0.0653976	−	0.997859i	$-0.520832\pi$
$443$	−2.75292			−0.130795			−0.0653976	+	0.997859i	$0.520832\pi$
$444$	1.19110	−	2.06304i	0.0565269	−	0.0979074i
$445$	3.81681	−	6.61091i	0.180934	−	0.313387i
$446$	−1.63890	−	2.83866i	−0.0776043	−	0.134415i
$447$	−4.85601			−0.229682
$448$	1.58123	+	2.73877i	0.0747060	+	0.129395i
$449$	−13.5513	−	23.4715i	−0.639524	−	1.10769i	−0.985537	−	0.169458i	$-0.945798\pi$
$449$	−13.5513	−	23.4715i	−0.639524	−	1.10769i	0.346014	−	0.938229i	$-0.387535\pi$
$450$	1.61120			0.0759525
$451$	−16.5513	−	28.6676i	−0.779368	−	1.34991i
$452$	10.8560	−	18.8032i	0.510624	−	0.884427i
$453$	−4.49887	+	7.79227i	−0.211375	+	0.366113i
$454$	1.68903			0.0792703
$455$		0			0
$456$	5.61515			0.262953
$457$	20.0761	−	34.7729i	0.939122	−	1.62661i	0.172010	−	0.985095i	$-0.444974\pi$
$457$	20.0761	−	34.7729i	0.939122	−	1.62661i	0.767112	−	0.641513i	$-0.221693\pi$
$458$	−7.22408	+	12.5125i	−0.337559	+	0.584670i
$459$	−6.65435	−	11.5257i	−0.310599	−	0.537973i
$460$	4.06163			0.189374
$461$	1.00395	+	1.73890i	0.0467587	+	0.0809885i	0.888458	−	0.458959i	$-0.151777\pi$
$461$	1.00395	+	1.73890i	0.0467587	+	0.0809885i	−0.841699	+	0.539947i	$0.818444\pi$
$462$	1.66887	+	2.89057i	0.0776429	+	0.134481i
$463$	−2.67282			−0.124217			−0.0621083	−	0.998069i	$-0.519782\pi$
$463$	−2.67282			−0.124217			−0.0621083	+	0.998069i	$0.519782\pi$
$464$	−2.86525	−	4.96276i	−0.133016	−	0.230390i
$465$	0.0523917	−	0.0907450i	0.00242960	−	0.00420820i
$466$	6.67678	−	11.5645i	0.309296	−	0.535716i
$467$	−31.8890			−1.47565			−0.737824	−	0.674994i	$-0.764146\pi$
$467$	−31.8890			−1.47565			−0.737824	+	0.674994i	$0.764146\pi$
$468$		0			0
$469$	−5.83528			−0.269448
$470$	−0.764419	+	1.32401i	−0.0352600	+	0.0610721i
$471$	−2.10478	+	3.64559i	−0.0969833	+	0.167980i
$472$	−0.944501	−	1.63592i	−0.0434742	−	0.0752995i
$473$	55.6890			2.56058
$474$	0.444786	+	0.770392i	0.0204297	+	0.0353853i
$475$	3.12241	+	5.40817i	0.143266	+	0.248144i
$476$	−23.9013			−1.09551
$477$	−5.91764	−	10.2497i	−0.270950	−	0.469299i
$478$	1.08454	−	1.87847i	0.0496055	−	0.0859192i
$479$	−3.36723	+	5.83221i	−0.153852	+	0.266480i	−0.932641	−	0.360807i	$-0.882501\pi$
$479$	−3.36723	+	5.83221i	−0.153852	+	0.266480i	0.778788	+	0.627287i	$0.215835\pi$
$480$	2.32322			0.106040
$481$		0			0
$482$	−1.96306			−0.0894148
$483$	−1.38880	+	2.40548i	−0.0631927	+	0.109453i
$484$	12.5616	−	21.7574i	0.570983	−	0.988972i
$485$	−5.67282	−	9.82562i	−0.257590	−	0.446158i
$486$	6.08010			0.275799
$487$	19.8260	+	34.3397i	0.898404	+	1.55608i	0.829534	+	0.558456i	$0.188606\pi$
$487$	19.8260	+	34.3397i	0.898404	+	1.55608i	0.0688694	+	0.997626i	$0.478061\pi$
$488$	6.11007	+	10.5829i	0.276590	+	0.479067i
$489$	5.30080			0.239710
$490$	0.0411797	+	0.0713253i	0.00186031	+	0.00322215i
$491$	15.5473	−	26.9287i	0.701640	−	1.21528i	−0.266250	−	0.963904i	$-0.585785\pi$
$491$	15.5473	−	26.9287i	0.701640	−	1.21528i	0.967890	−	0.251373i	$-0.0808819\pi$
$492$	2.32322	−	4.02394i	0.104739	−	0.181413i
$493$	14.2880			0.643498
$494$		0			0
$495$	14.3681			0.645797
$496$	−0.262442	+	0.454563i	−0.0117840	+	0.0204105i
$497$	8.34565	−	14.4551i	0.374353	−	0.648399i
$498$	1.20166	+	2.08134i	0.0538477	+	0.0932670i
$499$	−13.1087			−0.586828			−0.293414	−	0.955986i	$-0.594791\pi$
$499$	−13.1087			−0.586828			−0.293414	+	0.955986i	$0.594791\pi$
$500$	0.836412	+	1.44871i	0.0374055	+	0.0647882i
$501$	1.82076	+	3.15365i	0.0813457	+	0.140895i
$502$	−14.5680			−0.650203
$503$	4.29636	+	7.44152i	0.191565	+	0.331801i	0.945769	−	0.324839i	$-0.105310\pi$
$503$	4.29636	+	7.44152i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$504$	7.90841	−	13.6978i	0.352268	−	0.610147i
$505$	−5.42801	+	9.40158i	−0.241543	+	0.418365i
$506$	−7.08405			−0.314924
$507$		0			0
$508$	−20.1770			−0.895209
$509$	14.9176	−	25.8381i	0.661213	−	1.14525i	−0.319084	−	0.947726i	$-0.603375\pi$
$509$	14.9176	−	25.8381i	0.661213	−	1.14525i	0.980297	−	0.197528i	$-0.0632913\pi$
$510$	−0.654353	+	1.13337i	−0.0289752	+	0.0501866i
$511$	14.6481	+	25.3713i	0.647996	+	1.12236i
$512$	−20.6459			−0.912428
$513$	7.77365	+	13.4644i	0.343215	+	0.594466i
$514$	−2.65040	−	4.59063i	−0.116904	−	0.202484i
$515$	10.6297			0.468399
$516$	3.90841	+	6.76956i	0.172058	+	0.298013i
$517$	−6.81681	+	11.8071i	−0.299803	+	0.519274i
$518$	−2.54336	+	4.40522i	−0.111749	+	0.193554i
$519$	9.22239			0.404818
$520$		0			0
$521$	10.0969			0.442352			0.221176	−	0.975234i	$-0.429010\pi$
$521$	10.0969			0.442352			0.221176	+	0.975234i	$0.429010\pi$
$522$	−2.15322	+	3.72949i	−0.0942440	+	0.163235i
$523$	−8.07397	+	13.9845i	−0.353050	+	0.611501i	−0.986782	−	0.162052i	$-0.948189\pi$
$523$	−8.07397	+	13.9845i	−0.353050	+	0.611501i	0.633732	+	0.773553i	$0.281522\pi$
$524$	6.38485	+	11.0589i	0.278923	+	0.483110i
$525$	−1.14399			−0.0499277
$526$	−2.33028	−	4.03617i	−0.101605	−	0.175985i
$527$	−0.654353	−	1.13337i	−0.0285040	−	0.0493705i
$528$	4.68073			0.203703
$529$	8.55239	+	14.8132i	0.371843	+	0.644051i
$530$	−1.20166	+	2.08134i	−0.0521968	+	0.0904075i
$531$	1.26640	−	2.19346i	0.0549569	−	0.0951881i
$532$	27.9216			1.21055
$533$		0			0
$534$	−1.86884			−0.0808726
$535$	−0.0700168	+	0.121273i	−0.00302709	+	0.00524308i
$536$	2.29326	−	3.97204i	0.0990536	−	0.171566i
$537$	0.549569	+	0.951882i	0.0237157	+	0.0410767i
$538$	−0.654353			−0.0282111
$539$	0.367225	+	0.636053i	0.0158175	+	0.0273967i
$540$	2.08236	+	3.60675i	0.0896105	+	0.155210i
$541$	−26.7776			−1.15126			−0.575630	−	0.817711i	$-0.695243\pi$
$541$	−26.7776			−1.15126			−0.575630	+	0.817711i	$0.695243\pi$
$542$	0.911512	+	1.57879i	0.0391528	+	0.0678146i
$543$	−2.93837	+	5.08941i	−0.126098	+	0.218408i
$544$	14.5081	−	25.1288i	0.622030	−	1.07739i
$545$	−9.05767			−0.387988
$546$		0			0
$547$	12.3865			0.529610			0.264805	−	0.964302i	$-0.414692\pi$
$547$	12.3865			0.529610			0.264805	+	0.964302i	$0.414692\pi$
$548$	2.87053	−	4.97191i	0.122623	−	0.212389i
$549$	−8.19243	+	14.1897i	−0.349644	+	0.605602i
$550$	−1.45882	−	2.52675i	−0.0622043	−	0.107741i
$551$	−16.6913			−0.711073
$552$	−1.09159	−	1.89070i	−0.0464614	−	0.0804734i
$553$	4.85601	+	8.41086i	0.206499	+	0.357666i
$554$	4.36186			0.185318
$555$	−0.712027	−	1.23327i	−0.0302239	−	0.0523493i
$556$	−0.788172	+	1.36515i	−0.0334260	+	0.0578954i
$557$	5.21090	−	9.02554i	0.220793	−	0.382424i	−0.734256	−	0.678873i	$-0.762469\pi$
$557$	5.21090	−	9.02554i	0.220793	−	0.382424i	0.955049	+	0.296448i	$0.0958022\pi$
$558$	0.394448			0.0166983
$559$		0			0
$560$	5.73050			0.242158
$561$	−5.83528	+	10.1070i	−0.246366	+	0.426718i
$562$	5.78817	−	10.0254i	0.244159	−	0.422896i
$563$	4.89078	+	8.47108i	0.206122	+	0.357013i	0.950490	−	0.310756i	$-0.100582\pi$
$563$	4.89078	+	8.47108i	0.206122	+	0.357013i	−0.744368	+	0.667770i	$0.767249\pi$
$564$	−1.91369			−0.0805808
$565$	−6.48963	−	11.2404i	−0.273021	−	0.472886i
$566$	−5.69045	−	9.85615i	−0.239187	−	0.414285i
$567$	19.7384			0.828935
$568$	6.55965	+	11.3616i	0.275237	+	0.476724i
$569$	−15.1101	+	26.1714i	−0.633447	+	1.09716i	0.353395	+	0.935474i	$0.385027\pi$
$569$	−15.1101	+	26.1714i	−0.633447	+	1.09716i	−0.986842	+	0.161688i	$0.948306\pi$
$570$	0.764419	−	1.32401i	0.0320180	−	0.0554568i
$571$	39.8643			1.66827			0.834135	−	0.551561i	$-0.185967\pi$
$571$	39.8643			1.66827			0.834135	+	0.551561i	$0.185967\pi$
$572$		0			0
$573$	4.57595			0.191163
$574$	−4.96080	+	8.59235i	−0.207060	+	0.358638i
$575$	1.21400	−	2.10272i	0.0506274	−	0.0876893i
$576$	−1.66641	−	2.88631i	−0.0694338	−	0.120263i
$577$	8.46326			0.352330			0.176165	−	0.984361i	$-0.443631\pi$
$577$	8.46326			0.352330			0.176165	+	0.984361i	$0.443631\pi$
$578$	3.31068	+	5.73427i	0.137706	+	0.238514i
$579$	4.12156	+	7.13876i	0.171286	+	0.296677i
$580$	−4.47116			−0.185655
$581$	13.1193	+	22.7233i	0.544280	+	0.942721i
$582$	−1.38880	+	2.40548i	−0.0575678	+	0.0997103i
$583$	−10.7160	+	18.5606i	−0.443811	+	0.768702i
$584$	−23.0268			−0.952855
$585$		0			0
$586$	−14.8824			−0.614786
$587$	−4.66359	+	8.07757i	−0.192487	+	0.333397i	−0.946074	−	0.323951i	$-0.894989\pi$
$587$	−4.66359	+	8.07757i	−0.192487	+	0.333397i	0.753587	+	0.657348i	$0.228322\pi$
$588$	−0.0515457	+	0.0892798i	−0.00212571	+	0.00368184i
$589$	0.764419	+	1.32401i	0.0314973	+	0.0545550i
$590$	−0.514319			−0.0211742
$591$	3.67678	+	6.36836i	0.151242	+	0.261959i
$592$	3.56671	+	6.17772i	0.146591	+	0.253903i
$593$	8.07841			0.331740			0.165870	−	0.986148i	$-0.446957\pi$
$593$	8.07841			0.331740			0.165870	+	0.986148i	$0.446957\pi$
$594$	−3.63193	−	6.29068i	−0.149020	−	0.258110i
$595$	−7.14399	+	12.3737i	−0.292875	+	0.507274i
$596$	9.48963	−	16.4365i	0.388711	−	0.673266i
$597$	−4.94233			−0.202276
$598$		0			0
$599$	19.1440			0.782202			0.391101	−	0.920348i	$-0.372094\pi$
$599$	19.1440			0.782202			0.391101	+	0.920348i	$0.372094\pi$
$600$	0.449585	−	0.778704i	0.0183542	−	0.0317904i
$601$	2.14399	−	3.71349i	0.0874550	−	0.151477i	−0.818980	−	0.573823i	$-0.805460\pi$
$601$	2.14399	−	3.71349i	0.0874550	−	0.151477i	0.906435	+	0.422346i	$0.138793\pi$
$602$	−8.34565	−	14.4551i	−0.340143	−	0.589145i
$603$	6.14963			0.250432
$604$	−17.5834	−	30.4554i	−0.715459	−	1.23921i
$605$	−7.50924	−	13.0064i	−0.305294	−	0.528784i
$606$	2.65774			0.107963
$607$	−14.6213	−	25.3248i	−0.593459	−	1.02790i	−0.993762	−	0.111519i	$-0.964428\pi$
$607$	−14.6213	−	25.3248i	−0.593459	−	1.02790i	0.400303	−	0.916383i	$-0.368905\pi$
$608$	−16.9485	+	29.3556i	−0.687351	+	1.19053i
$609$	1.52884	−	2.64802i	0.0619516	−	0.107303i
$610$	3.32718			0.134713
$611$		0			0
$612$	25.1888			1.01820
$613$	0.712027	−	1.23327i	0.0287585	−	0.0498112i	−0.851288	−	0.524699i	$-0.824178\pi$
$613$	0.712027	−	1.23327i	0.0287585	−	0.0498112i	0.880046	+	0.474888i	$0.157511\pi$
$614$	0.684320	−	1.18528i	0.0276169	−	0.0478339i
$615$	−1.38880	−	2.40548i	−0.0560020	−	0.0969982i
$616$	−28.6419			−1.15402
$617$	−23.2633	−	40.2932i	−0.936545	−	1.62214i	−0.771856	−	0.635797i	$-0.780671\pi$
$617$	−23.2633	−	40.2932i	−0.936545	−	1.62214i	−0.164689	−	0.986346i	$-0.552662\pi$
$618$	−1.30116	−	2.25368i	−0.0523404	−	0.0906562i
$619$	34.2818			1.37790			0.688950	−	0.724809i	$-0.258072\pi$
$619$	34.2818			1.37790			0.688950	+	0.724809i	$0.258072\pi$
$620$	0.204768	+	0.354668i	0.00822367	+	0.0142438i
$621$	3.02242	−	5.23499i	0.121286	−	0.210073i
$622$	−1.01452	+	1.75720i	−0.0406785	+	0.0704572i
$623$	−20.4033			−0.817442
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.42405	−	2.46653i	0.0569166	−	0.0985825i
$627$	6.81681	−	11.8071i	0.272237	−	0.471529i
$628$	−8.22635	−	14.2484i	−0.328267	−	0.568575i
$629$	−17.7859			−0.709171
$630$	−2.15322	−	3.72949i	−0.0857864	−	0.148586i
$631$	1.16161	+	2.01197i	0.0462430	+	0.0800953i	0.888220	−	0.459417i	$-0.151942\pi$
$631$	1.16161	+	2.01197i	0.0462430	+	0.0800953i	−0.841977	+	0.539513i	$0.818608\pi$
$632$	−7.63362			−0.303649
$633$	5.16246	+	8.94164i	0.205189	+	0.355398i
$634$	5.31794	−	9.21094i	0.211202	−	0.365813i
$635$	−6.03081	+	10.4457i	−0.239326	+	0.414524i
$636$	−3.00830			−0.119287
$637$		0			0
$638$	7.79834			0.308739
$639$	−8.79523	+	15.2338i	−0.347934	+	0.602639i
$640$	−5.76640	+	9.98769i	−0.227937	+	0.394798i
$641$	14.0656	+	24.3623i	0.555557	+	0.962253i	0.997860	+	0.0653873i	$0.0208283\pi$
$641$	14.0656	+	24.3623i	0.555557	+	0.962253i	−0.442303	+	0.896866i	$0.645838\pi$
$642$	0.0342826			0.00135303
$643$	−7.06691	−	12.2402i	−0.278692	−	0.482708i	0.692368	−	0.721544i	$-0.256567\pi$
$643$	−7.06691	−	12.2402i	−0.278692	−	0.482708i	−0.971060	+	0.238836i	$0.923234\pi$
$644$	−5.42801	−	9.40158i	−0.213893	−	0.370474i
$645$	4.67282			0.183992
$646$	−9.54731	−	16.5364i	−0.375634	−	0.650617i
$647$	22.9485	−	39.7479i	0.902197	−	1.56265i	0.0775604	−	0.996988i	$-0.475287\pi$
$647$	22.9485	−	39.7479i	0.902197	−	1.56265i	0.824636	−	0.565663i	$-0.191380\pi$
$648$	−7.75716	+	13.4358i	−0.304730	+	0.527808i
$649$	−4.58651			−0.180036
$650$		0			0
$651$	−0.280067			−0.0109767
$652$	−10.3588	+	17.9420i	−0.405683	+	0.702664i
$653$	−25.2241	+	43.6894i	−0.987095	+	1.70970i	−0.354864	+	0.934918i	$0.615473\pi$
$653$	−25.2241	+	43.6894i	−0.987095	+	1.70970i	−0.632230	+	0.774780i	$0.717860\pi$
$654$	1.10874	+	1.92039i	0.0433550	+	0.0750931i
$655$	7.63362			0.298270
$656$	6.95684	+	12.0496i	0.271619	+	0.470458i
$657$	−15.4372	−	26.7381i	−0.602264	−	1.04315i
$658$	4.08631			0.159301
$659$	22.9361	+	39.7265i	0.893464	+	1.54753i	0.835694	+	0.549195i	$0.185066\pi$
$659$	22.9361	+	39.7265i	0.893464	+	1.54753i	0.0577700	+	0.998330i	$0.481601\pi$
$660$	1.82605	−	3.16280i	0.0710787	−	0.123112i
$661$	−12.9216	+	22.3809i	−0.502592	+	0.870514i	0.497404	+	0.867519i	$0.334287\pi$
$661$	−12.9216	+	22.3809i	−0.502592	+	0.870514i	−0.999996	+	0.00299527i	$0.999047\pi$
$662$	3.38614			0.131606
$663$		0			0
$664$	−20.6235			−0.800345
$665$	8.34565	−	14.4551i	0.323630	−	0.560544i
$666$	2.68037	−	4.64253i	0.103862	−	0.179894i
$667$	3.24482	+	5.62019i	0.125640	+	0.217615i
$668$	−14.2326			−0.550674
$669$	−1.22635	−	2.12409i	−0.0474133	−	0.0821222i
$670$	−0.624385	−	1.08147i	−0.0241221	−	0.0417807i
$671$	29.6706			1.14542
$672$	−3.10478	−	5.37764i	−0.119770	−	0.207447i
$673$	−2.48963	+	4.31217i	−0.0959683	+	0.166222i	−0.910012	−	0.414581i	$-0.863928\pi$
$673$	−2.48963	+	4.31217i	−0.0959683	+	0.166222i	0.814044	+	0.580803i	$0.197261\pi$
$674$	−3.98153	+	6.89621i	−0.153363	+	0.265632i
$675$	2.48963			0.0958261
$676$		0			0
$677$	−35.8353			−1.37726			−0.688631	−	0.725112i	$-0.741788\pi$
$677$	−35.8353			−1.37726			−0.688631	+	0.725112i	$0.741788\pi$
$678$	−1.58877	+	2.75183i	−0.0610164	+	0.105684i
$679$	−15.1625	+	26.2621i	−0.581882	+	1.00785i
$680$	−5.61515	−	9.72572i	−0.215331	−	0.372964i
$681$	1.26386			0.0484311
$682$	−0.357144	−	0.618592i	−0.0136757	−	0.0236871i
$683$	20.2356	+	35.0491i	0.774293	+	1.34111i	0.935191	+	0.354144i	$0.115228\pi$
$683$	20.2356	+	35.0491i	0.774293	+	1.34111i	−0.160898	+	0.986971i	$0.551439\pi$
$684$	−29.4257			−1.12512
$685$	−1.71598	−	2.97216i	−0.0655642	−	0.113561i
$686$	−5.24086	+	9.07744i	−0.200097	+	0.346578i
$687$	−5.40558	+	9.36274i	−0.206236	+	0.357211i
$688$	−23.4073			−0.892394
$689$		0			0
$690$	−0.594417			−0.0226291
$691$	6.12241	−	10.6043i	0.232907	−	0.403407i	−0.725755	−	0.687953i	$-0.758509\pi$
$691$	6.12241	−	10.6043i	0.232907	−	0.403407i	0.958662	+	0.284546i	$0.0918428\pi$
$692$	−18.0224	+	31.2158i	−0.685110	+	1.18664i
$693$	−19.2017	−	33.2583i	−0.729411	−	1.26338i
$694$	−4.38050			−0.166281
$695$	0.471163	+	0.816078i	0.0178722	+	0.0309556i
$696$	1.20166	+	2.08134i	0.0455488	+	0.0788929i
$697$	−34.6913			−1.31403
$698$	−3.19771	−	5.53859i	−0.121035	−	0.209639i
$699$	4.99605	−	8.65341i	0.188968	−	0.327302i
$700$	2.23558	−	3.87214i	0.0844970	−	0.146353i
$701$	11.8353			0.447012			0.223506	−	0.974703i	$-0.428250\pi$
$701$	11.8353			0.447012			0.223506	+	0.974703i	$0.428250\pi$
$702$		0			0
$703$	20.7776			0.783642
$704$	−3.01763	+	5.22668i	−0.113731	+	0.196988i
$705$	−0.571993	+	0.990721i	−0.0215425	+	0.0373127i
$706$	2.76047	+	4.78127i	0.103891	+	0.179945i
$707$	29.0162			1.09127
$708$	−0.321894	−	0.557536i	−0.0120975	−	0.0209535i
$709$	3.18714	+	5.52029i	0.119696	+	0.207319i	0.919647	−	0.392746i	$-0.128475\pi$
$709$	3.18714	+	5.52029i	0.119696	+	0.207319i	−0.799951	+	0.600065i	$0.795141\pi$
$710$	3.57199			0.134055
$711$	−5.11761	−	8.86396i	−0.191925	−	0.332424i
$712$	8.01847	−	13.8884i	0.300505	−	0.520490i
$713$	0.297209	−	0.514780i	0.0111306	−	0.0192787i
$714$	3.49794			0.130907
$715$		0			0
$716$	−4.29588			−0.160545
$717$	0.811528	−	1.40561i	0.0303071	−	0.0524934i
$718$	−2.72042	+	4.71190i	−0.101525	+	0.175847i
$719$	17.4504	+	30.2250i	0.650791	+	1.12720i	0.982931	+	0.183973i	$0.0588960\pi$
$719$	17.4504	+	30.2250i	0.650791	+	1.12720i	−0.332140	+	0.943230i	$0.607771\pi$
$720$	−6.03920			−0.225068
$721$	−14.2056	−	24.6048i	−0.529045	−	0.916332i
$722$	5.71929	+	9.90609i	0.212850	+	0.368667i
$723$	−1.46890			−0.0546290
$724$	−11.4844	−	19.8915i	−0.426813	−	0.739261i
$725$	−1.33641	+	2.31473i	−0.0496331	+	0.0859670i
$726$	−1.83839	+	3.18418i	−0.0682290	+	0.118176i
$727$	19.8106			0.734734			0.367367	−	0.930076i	$-0.380259\pi$
$727$	19.8106			0.734734			0.367367	+	0.930076i	$0.380259\pi$
$728$		0			0
$729$	−17.6050			−0.652036
$730$	−3.13475	+	5.42955i	−0.116022	+	0.200957i
$731$	29.1809	−	50.5429i	1.07930	−	1.86939i
$732$	2.08236	+	3.60675i	0.0769662	+	0.133309i
$733$	−12.6050			−0.465576			−0.232788	−	0.972528i	$-0.574785\pi$
$733$	−12.6050			−0.465576			−0.232788	+	0.972528i	$0.574785\pi$
$734$	−4.86307	−	8.42309i	−0.179499	−	0.310902i
$735$	0.0308136	+	0.0533707i	0.00113658	+	0.00196861i
$736$	13.1792			0.485793
$737$	−5.56804	−	9.64413i	−0.205101	−	0.355246i
$738$	5.22804	−	9.05523i	0.192447	−	0.333328i
$739$	−18.5874	+	32.1942i	−0.683747	+	1.18428i	0.290082	+	0.957002i	$0.406317\pi$
$739$	−18.5874	+	32.1942i	−0.683747	+	1.18428i	−0.973829	+	0.227283i	$0.927016\pi$
$740$	5.56578			0.204602
$741$		0			0
$742$	6.42366			0.235820
$743$	−13.9661	+	24.1900i	−0.512366	+	0.887444i	0.487531	+	0.873105i	$0.337897\pi$
$743$	−13.9661	+	24.1900i	−0.512366	+	0.887444i	−0.999897	+	0.0143381i	$0.995436\pi$
$744$	0.110066	−	0.190640i	0.00403521	−	0.00698920i
$745$	−5.67282	−	9.82562i	−0.207836	−	0.359983i
$746$	1.04977			0.0384348
$747$	−13.8260	−	23.9474i	−0.505869	−	0.876190i
$748$	−22.8066	−	39.5023i	−0.833893	−	1.44435i
$749$	0.374285			0.0136761
$750$	−0.122408	−	0.212018i	−0.00446973	−	0.00774179i
$751$	6.81286	−	11.8002i	0.248605	−	0.430596i	−0.714534	−	0.699600i	$-0.753361\pi$
$751$	6.81286	−	11.8002i	0.248605	−	0.430596i	0.963139	+	0.269005i	$0.0866947\pi$
$752$	2.86525	−	4.96276i	0.104485	−	0.180973i
$753$	−10.9009			−0.397249
$754$		0			0
$755$	−21.0224			−0.765084
$756$	5.56578	−	9.64021i	0.202425	−	0.350611i
$757$	15.4280	−	26.7221i	0.560740	−	0.971231i	−0.436692	−	0.899611i	$-0.643850\pi$
$757$	15.4280	−	26.7221i	0.560740	−	0.971231i	0.997432	−	0.0716196i	$-0.0228168\pi$
$758$	−9.25716	−	16.0339i	−0.336235	−	0.582376i
$759$	−5.30080			−0.192407
$760$	6.55965	+	11.3616i	0.237944	+	0.412130i
$761$	8.50811	+	14.7365i	0.308419	+	0.534197i	0.978017	−	0.208527i	$-0.0668669\pi$
$761$	8.50811	+	14.7365i	0.308419	+	0.534197i	−0.669598	+	0.742724i	$0.733534\pi$
$762$	2.95289			0.106972
$763$	12.1048	+	20.9661i	0.438223	+	0.759024i
$764$	−8.94233	+	15.4886i	−0.323522	+	0.560357i
$765$	7.52884	−	13.0403i	0.272206	−	0.471474i
$766$	16.0969			0.581604
$767$		0			0
$768$	1.81060			0.0653343
$769$	−14.5081	+	25.1288i	−0.523176	+	0.906167i	0.476461	+	0.879196i	$0.341919\pi$
$769$	−14.5081	+	25.1288i	−0.523176	+	0.906167i	−0.999636	+	0.0269710i	$0.991414\pi$
$770$	−3.89917	+	6.75356i	−0.140516	+	0.243381i
$771$	−1.98322	−	3.43504i	−0.0714240	−	0.123710i
$772$	−32.2175			−1.15953
$773$	−20.2580	−	35.0879i	−0.728630	−	1.26202i	−0.957462	−	0.288558i	$-0.906824\pi$
$773$	−20.2580	−	35.0879i	−0.728630	−	1.26202i	0.228833	−	0.973466i	$-0.426509\pi$
$774$	8.79523	+	15.2338i	0.316138	+	0.547567i
$775$	0.244817			0.00879409
$776$	−11.9176	−	20.6420i	−0.427818	−	0.741003i
$777$	−1.90312	+	3.29630i	−0.0682741	+	0.118254i
$778$	9.14003	−	15.8310i	0.327686	−	0.567569i
$779$	40.5266			1.45202
$780$		0			0
$781$	31.8538			1.13982
$782$	−3.71203	+	6.42942i	−0.132742	+	0.229916i
$783$	−3.32718	+	5.76284i	−0.118904	+	0.205947i
$784$	−0.154353	−	0.267347i	−0.00551259	−	0.00954809i
$785$	−9.83528			−0.351036
$786$	−0.934420	−	1.61846i	−0.0333297	−	0.0577287i
$787$	17.0132	+	29.4677i	0.606455	+	1.05041i	0.991820	+	0.127646i	$0.0407422\pi$
$787$	17.0132	+	29.4677i	0.606455	+	1.05041i	−0.385365	+	0.922764i	$0.625924\pi$
$788$	−28.7407			−1.02384
$789$	−1.74369	−	3.02015i	−0.0620769	−	0.107520i
$790$	−1.03920	+	1.79995i	−0.0369732	+	0.0640394i
$791$	−17.3456	+	30.0435i	−0.616740	+	1.06823i
$792$	30.1849			1.07257
$793$		0			0
$794$	7.26990			0.257999
$795$	−0.899170	+	1.55741i	−0.0318903	+	0.0552355i
$796$	9.65831	−	16.7287i	0.342330	−	0.592932i
$797$	7.38880	+	12.7978i	0.261725	+	0.453321i	0.966700	−	0.255911i	$-0.0823754\pi$
$797$	7.38880	+	12.7978i	0.261725	+	0.453321i	−0.704976	+	0.709232i	$0.749042\pi$
$798$	−4.08631			−0.144654
$799$	7.14399	+	12.3737i	0.252736	+	0.437752i
$800$	2.71400	+	4.70079i	0.0959545	+	0.166198i
$801$	21.5025			0.759752
$802$	0.280067	+	0.485091i	0.00988952	+	0.0171292i
$803$	−27.9546	+	48.4188i	−0.986496	+	1.70866i
$804$	0.781560	−	1.35370i	0.0275635	−	0.0477414i
$805$	−6.48963			−0.228730
$806$		0			0
$807$	−0.489634			−0.0172359
$808$	−11.4033	+	19.7511i	−0.401167	+	0.694842i
$809$	18.0277	−	31.2249i	0.633820	−	1.09781i	−0.352943	−	0.935645i	$-0.614819\pi$
$809$	18.0277	−	31.2249i	0.633820	−	1.09781i	0.986764	−	0.162164i	$-0.0518475\pi$
$810$	2.11204	+	3.65816i	0.0742096	+	0.128535i
$811$	5.31040			0.186473			0.0932366	−	0.995644i	$-0.470279\pi$
$811$	5.31040			0.186473			0.0932366	+	0.995644i	$0.470279\pi$
$812$	5.97531	+	10.3495i	0.209692	+	0.363198i
$813$	0.682059	+	1.18136i	0.0239209	+	0.0414321i
$814$	−9.70750			−0.340248
$815$	6.19243	+	10.7256i	0.216911	+	0.375701i
$816$	2.45269	−	4.24819i	0.0858614	−	0.148716i
$817$	−34.0893	+	59.0445i	−1.19263	+	2.06570i
$818$	−4.46060			−0.155961
$819$		0			0
$820$	10.8560			0.379108
$821$	−6.81681	+	11.8071i	−0.237908	+	0.412069i	−0.960114	−	0.279609i	$-0.909795\pi$
$821$	−6.81681	+	11.8071i	−0.237908	+	0.412069i	0.722206	+	0.691678i	$0.243128\pi$
$822$	−0.420101	+	0.727636i	−0.0146527	+	0.0253792i
$823$	−19.8229	−	34.3343i	−0.690984	−	1.19682i	−0.971516	−	0.236975i	$-0.923844\pi$
$823$	−19.8229	−	34.3343i	−0.690984	−	1.19682i	0.280532	−	0.959845i	$-0.409489\pi$
$824$	22.3311			0.777942
$825$	−1.09159	−	1.89070i	−0.0380045	−	0.0658256i
$826$	0.687342	+	1.19051i	0.0239157	+	0.0414232i
$827$	23.8952			0.830918			0.415459	−	0.909612i	$-0.363621\pi$
$827$	23.8952			0.830918			0.415459	+	0.909612i	$0.363621\pi$
$828$	5.72042	+	9.90805i	0.198798	+	0.344329i
$829$	13.6781	−	23.6912i	0.475060	−	0.822829i	−0.524532	−	0.851391i	$-0.675760\pi$
$829$	13.6781	−	23.6912i	0.475060	−	0.822829i	0.999592	+	0.0285624i	$0.00909292\pi$
$830$	−2.80757	+	4.86286i	−0.0974523	+	0.168792i
$831$	3.26386			0.113222
$832$		0			0
$833$	0.769701			0.0266686
$834$	0.115349	−	0.199790i	0.00399420	−	0.00691815i
$835$	−4.25405	+	7.36824i	−0.147218	+	0.254988i
$836$	26.6429	+	46.1468i	0.921462	+	1.59602i
$837$	0.609505			0.0210676
$838$	2.91764	+	5.05350i	0.100788	+	0.174570i
$839$	14.7705	+	25.5833i	0.509936	+	0.883235i	0.999934	+	0.0115113i	$0.00366423\pi$
$839$	14.7705	+	25.5833i	0.509936	+	0.883235i	−0.489998	+	0.871724i	$0.663002\pi$
$840$	−2.40332			−0.0829225
$841$	10.9280	+	18.9279i	0.376828	+	0.652685i
$842$	8.91990	−	15.4497i	0.307400	−	0.532433i
$843$	4.33113	−	7.50174i	0.149172	−	0.258374i
$844$	−40.3540			−1.38904
$845$		0			0
$846$	−4.30644			−0.148059
$847$	−20.0709	+	34.7638i	−0.689643	+	1.19450i
$848$	4.50415	−	7.80142i	0.154673	−	0.267902i
$849$	−4.25801	−	7.37508i	−0.146134	−	0.253112i
$850$	−3.05767			−0.104877
$851$	−4.03920	−	6.99611i	−0.138462	−	0.239823i
$852$	2.23558	+	3.87214i	0.0765898	+	0.132657i
$853$	5.61515			0.192259			0.0961295	−	0.995369i	$-0.469354\pi$
$853$	5.61515			0.192259			0.0961295	+	0.995369i	$0.469354\pi$
$854$	−4.44648	−	7.70153i	−0.152155	−	0.263541i
$855$	−8.79523	+	15.2338i	−0.300791	+	0.520985i
$856$	−0.147093	+	0.254773i	−0.00502755	+	0.00870798i
$857$	−39.9216			−1.36370			−0.681848	−	0.731494i	$-0.738823\pi$
$857$	−39.9216			−1.36370			−0.681848	+	0.731494i	$0.738823\pi$
$858$		0			0
$859$	28.6498			0.977520			0.488760	−	0.872418i	$-0.337449\pi$
$859$	28.6498			0.977520			0.488760	+	0.872418i	$0.337449\pi$
$860$	−9.13164	+	15.8165i	−0.311386	+	0.539337i
$861$	−3.71203	+	6.42942i	−0.126506	+	0.219114i
$862$	6.55965	+	11.3616i	0.223423	+	0.386979i
$863$	−38.5530			−1.31236			−0.656179	−	0.754605i	$-0.727828\pi$
$863$	−38.5530			−1.31236			−0.656179	+	0.754605i	$0.727828\pi$
$864$	6.75687	+	11.7033i	0.229874	+	0.398153i
$865$	10.7737	+	18.6605i	0.366315	+	0.634477i
$866$	−9.31661			−0.316591
$867$	2.47729	+	4.29079i	0.0841332	+	0.145723i
$868$	0.547308	−	0.947966i	0.0185769	−	0.0321761i
$869$	−9.26724	+	16.0513i	−0.314370	+	0.544504i
$870$	0.654353			0.0221846
$871$		0			0
$872$	−19.0286			−0.644391
$873$	15.9793	−	27.6769i	0.540816	−	0.936721i
$874$	4.33641	−	7.51089i	0.146681	−	0.254059i
$875$	−1.33641	−	2.31473i	−0.0451790	−	0.0782523i
$876$	−7.84771			−0.265150
$877$	13.6913	+	23.7140i	0.462322	+	0.800765i	0.999076	−	0.0429733i	$-0.0136830\pi$
$877$	13.6913	+	23.7140i	0.462322	+	0.800765i	−0.536754	+	0.843739i	$0.680350\pi$
$878$	−6.79439	−	11.7682i	−0.229299	−	0.397158i
$879$	−11.1361			−0.375611
$880$	5.46806	+	9.47095i	0.184328	+	0.319266i
$881$	12.5420	−	21.7234i	0.422552	−	0.731881i	−0.573637	−	0.819110i	$-0.694468\pi$
$881$	12.5420	−	21.7234i	0.422552	−	0.731881i	0.996188	+	0.0872290i	$0.0278012\pi$
$882$	−0.115995	+	0.200910i	−0.00390576	+	0.00676498i
$883$	−50.5513			−1.70119			−0.850593	−	0.525825i	$-0.823757\pi$
$883$	−50.5513			−1.70119			−0.850593	+	0.525825i	$0.823757\pi$
$884$		0			0
$885$	−0.384851			−0.0129366
$886$	−0.787326	+	1.36369i	−0.0264507	+	0.0458140i
$887$	9.82915	−	17.0246i	0.330031	−	0.571630i	−0.652487	−	0.757800i	$-0.726274\pi$
$887$	9.82915	−	17.0246i	0.330031	−	0.571630i	0.982518	+	0.186170i	$0.0596076\pi$
$888$	−1.49585	−	2.59088i	−0.0501974	−	0.0869444i
$889$	32.2386			1.08125
$890$	−2.18319	−	3.78140i	−0.0731807	−	0.126753i
$891$	18.8344	+	32.6222i	0.630977	+	1.09288i
$892$	9.58611			0.320967
$893$	−8.34565	−	14.4551i	−0.279276	−	0.483721i
$894$	−1.38880	+	2.40548i	−0.0464485	+	0.0804512i
$895$	−1.28402	+	2.22399i	−0.0429201	+	0.0743397i
$896$	30.8251			1.02979
$897$		0			0
$898$	−15.5025			−0.517324
$899$	−0.327176	+	0.566686i	−0.0109119	+	0.0189000i
$900$	−2.35601	+	4.08074i	−0.0785338	+	0.136025i
$901$	11.2303	+	19.4514i	0.374135	+	0.648022i
$902$	−18.9344			−0.630447
$903$	−6.24482	−	10.8163i	−0.207814	−	0.359945i
$904$	−13.6336	−	23.6141i	−0.453447	−	0.785394i
$905$	−13.7305			−0.456417
$906$	2.57332	+	4.45713i	0.0854929	+	0.148078i
$907$	−11.0269	+	19.0991i	−0.366141	+	0.634175i	−0.988959	−	0.148192i	$-0.952655\pi$
$907$	−11.0269	+	19.0991i	−0.366141	+	0.634175i	0.622818	+	0.782367i	$0.285988\pi$
$908$	−2.46983	+	4.27788i	−0.0819643	+	0.141966i
$909$	−30.5793			−1.01425
$910$		0			0
$911$	−14.0079			−0.464103			−0.232051	−	0.972704i	$-0.574544\pi$
$911$	−14.0079			−0.464103			−0.232051	+	0.972704i	$0.574544\pi$
$912$	−2.86525	+	4.96276i	−0.0948779	+	0.164333i
$913$	−25.0369	+	43.3653i	−0.828602	+	1.43518i
$914$	−11.4834	−	19.8899i	−0.379838	−	0.657898i
$915$	2.48963			0.0823048
$916$	−21.1272	−	36.5934i	−0.698063	−	1.20908i
$917$	−10.2017	−	17.6698i	−0.336889	−	0.583508i
$918$	−7.61249			−0.251250
$919$	−10.9176	−	18.9099i	−0.360140	−	0.623780i	0.627844	−	0.778339i	$-0.283938\pi$
$919$	−10.9176	−	18.9099i	−0.360140	−	0.623780i	−0.987984	+	0.154559i	$0.950604\pi$
$920$	2.55042	−	4.41745i	0.0840847	−	0.145639i
$921$	0.512058	−	0.886910i	0.0168729	−	0.0292247i
$922$	1.14851			0.0378241
$923$		0			0
$924$	−9.76140			−0.321126
$925$	1.66359	−	2.88142i	0.0546984	−	0.0947405i
$926$	−0.764419	+	1.32401i	−0.0251204	+	0.0435097i
$927$	14.9709	+	25.9303i	0.491708	+	0.851664i
$928$	−14.5081			−0.476252
$929$	7.61120	+	13.1830i	0.249715	+	0.432520i	0.963447	−	0.267900i	$-0.0863296\pi$
$929$	7.61120	+	13.1830i	0.249715	+	0.432520i	−0.713731	+	0.700419i	$0.752996\pi$
$930$	−0.0299677	−	0.0519055i	−0.000982679	−	0.00170205i
$931$	−0.899170			−0.0294691
$932$	19.5266	+	33.8210i	0.639614	+	1.10784i
$933$	−0.759136	+	1.31486i	−0.0248530	+	0.0430466i
$934$	−9.12015	+	15.7966i	−0.298420	+	0.516879i
$935$	−27.2672			−0.891734
$936$		0			0
$937$	−25.4610			−0.831774			−0.415887	−	0.909416i	$-0.636529\pi$
$937$	−25.4610			−0.831774			−0.415887	+	0.909416i	$0.636529\pi$
$938$	−1.66887	+	2.89057i	−0.0544906	+	0.0943804i
$939$	1.06558	−	1.84564i	0.0347739	−	0.0602301i
$940$	−2.23558	−	3.87214i	−0.0729166	−	0.126295i
$941$	24.9299			0.812691			0.406346	−	0.913719i	$-0.366803\pi$
$941$	24.9299			0.812691			0.406346	+	0.913719i	$0.366803\pi$
$942$	1.20392	+	2.08525i	0.0392259	+	0.0679412i
$943$	−7.87844	−	13.6459i	−0.256557	−	0.444370i
$944$	1.92781			0.0627448
$945$	−3.32718	−	5.76284i	−0.108233	−	0.187465i
$946$	15.9269	−	27.5862i	0.517827	−	0.896903i
$947$	8.34036	−	14.4459i	0.271025	−	0.469430i	−0.698099	−	0.716001i	$-0.745971\pi$
$947$	8.34036	−	14.4459i	0.271025	−	0.469430i	0.969125	+	0.246571i	$0.0793039\pi$
$948$	−2.60160			−0.0844960
$949$		0			0
$950$	3.57199			0.115891
$951$	3.97927	−	6.89229i	0.129037	−	0.223498i
$952$	−15.0083	+	25.9951i	−0.486422	+	0.842508i
$953$	−13.5865	−	23.5325i	−0.440110	−	0.762293i	0.557587	−	0.830119i	$-0.311727\pi$
$953$	−13.5865	−	23.5325i	−0.440110	−	0.762293i	−0.997697	+	0.0678252i	$0.978394\pi$
$954$	−6.76970			−0.219177
$955$	5.34565	+	9.25893i	0.172981	+	0.299612i
$956$	3.17178	+	5.49368i	0.102583	+	0.177678i
$957$	5.83528			0.188628
$958$	1.92603	+	3.33598i	0.0622272	+	0.107781i
$959$	−4.58651	+	7.94407i	−0.148106	+	0.256527i
$960$	−0.253207	+	0.438567i	−0.00817221	+	0.0141547i
$961$	−30.9401			−0.998067
$962$		0			0
$963$	−0.394448			−0.0127109
$964$	2.87053	−	4.97191i	0.0924536	−	0.160134i
$965$	−9.62967	+	16.6791i	−0.309990	+	0.536918i
$966$	0.794386	+	1.37592i	0.0255590	+	0.0442694i
$967$	6.75914			0.217359			0.108680	−	0.994077i	$-0.465338\pi$
$967$	6.75914			0.217359			0.108680	+	0.994077i	$0.465338\pi$
$968$	−15.7756	−	27.3242i	−0.507048	−	0.878233i
$969$	−7.14399	−	12.3737i	−0.229498	−	0.397502i
$970$	−6.48963			−0.208370
$971$	−23.3210	−	40.3931i	−0.748405	−	1.29628i	−0.948587	−	0.316517i	$-0.897487\pi$
$971$	−23.3210	−	40.3931i	−0.748405	−	1.29628i	0.200181	−	0.979759i	$-0.435847\pi$
$972$	−8.89078	+	15.3993i	−0.285172	+	0.493932i
$973$	1.25934	−	2.18123i	0.0403724	−	0.0699271i
$974$	22.6807			0.726737
$975$		0			0
$976$	−12.4712			−0.399192
$977$	26.3734	−	45.6800i	0.843758	−	1.46143i	−0.0429368	−	0.999078i	$-0.513671\pi$
$977$	26.3734	−	45.6800i	0.843758	−	1.46143i	0.886695	−	0.462355i	$-0.152995\pi$
$978$	1.51601	−	2.62581i	0.0484767	−	0.0839641i
$979$	−19.4689	−	33.7211i	−0.622229	−	1.07773i
$980$	−0.240864			−0.00769412
$981$	−12.7569	−	22.0956i	−0.407296	−	0.705457i
$982$	−8.89296	−	15.4031i	−0.283786	−	0.491531i
$983$	20.9977			0.669724			0.334862	−	0.942267i	$-0.391310\pi$
$983$	20.9977			0.669724			0.334862	+	0.942267i	$0.391310\pi$
$984$	−2.91764	−	5.05350i	−0.0930110	−	0.161100i
$985$	−8.59046	+	14.8791i	−0.273715	+	0.474088i
$986$	4.08631	−	7.07770i	0.130135	−	0.225400i
$987$	3.05767			0.0973268
$988$		0			0
$989$	26.5081			0.842909
$990$	4.10922	−	7.11738i	0.130600	−	0.226205i
$991$	16.1585	−	27.9874i	0.513292	−	0.889048i	−0.486589	−	0.873631i	$-0.661759\pi$
$991$	16.1585	−	27.9874i	0.513292	−	0.889048i	0.999881	−	0.0154167i	$-0.00490748\pi$
$992$	0.664434	+	1.15083i	0.0210958	+	0.0365390i
$993$	2.53376			0.0804064
$994$	−4.77365	−	8.26821i	−0.151411	−	0.262252i
$995$	−5.77365	−	10.0003i	−0.183037	−	0.317030i
$996$	−7.02864			−0.222711
$997$	10.6952	+	18.5247i	0.338722	+	0.586684i	0.984193	−	0.177102i	$-0.0566721\pi$
$997$	10.6952	+	18.5247i	0.338722	+	0.586684i	−0.645471	+	0.763785i	$0.723339\pi$
$998$	−3.74905	+	6.49355i	−0.118674	+	0.205550i
$999$	4.14173	−	7.17368i	0.131038	−	0.226965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.k.191.2		6
13.2	odd	12		845.2.m.h.361.4		12
13.3	even	3	inner	845.2.e.k.146.2		6
13.4	even	6		845.2.a.k.1.2		3
13.5	odd	4		845.2.m.h.316.3		12
13.6	odd	12		65.2.c.a.51.4	yes	6
13.7	odd	12		65.2.c.a.51.3	✓	6
13.8	odd	4		845.2.m.h.316.4		12
13.9	even	3		845.2.a.i.1.2		3
13.10	even	6		845.2.e.i.146.2		6
13.11	odd	12		845.2.m.h.361.3		12
13.12	even	2		845.2.e.i.191.2		6
39.17	odd	6		7605.2.a.bs.1.2		3
39.20	even	12		585.2.b.g.181.4		6
39.32	even	12		585.2.b.g.181.3		6
39.35	odd	6		7605.2.a.cc.1.2		3
52.7	even	12		1040.2.k.d.961.4		6
52.19	even	12		1040.2.k.d.961.3		6
65.4	even	6		4225.2.a.bc.1.2		3
65.7	even	12		325.2.d.f.324.4		6
65.9	even	6		4225.2.a.be.1.2		3
65.19	odd	12		325.2.c.g.51.3		6
65.32	even	12		325.2.d.e.324.4		6
65.33	even	12		325.2.d.e.324.3		6
65.58	even	12		325.2.d.f.324.3		6
65.59	odd	12		325.2.c.g.51.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.3	✓	6	13.7	odd	12
65.2.c.a.51.4	yes	6	13.6	odd	12
325.2.c.g.51.3		6	65.19	odd	12
325.2.c.g.51.4		6	65.59	odd	12
325.2.d.e.324.3		6	65.33	even	12
325.2.d.e.324.4		6	65.32	even	12
325.2.d.f.324.3		6	65.58	even	12
325.2.d.f.324.4		6	65.7	even	12
585.2.b.g.181.3		6	39.32	even	12
585.2.b.g.181.4		6	39.20	even	12
845.2.a.i.1.2		3	13.9	even	3
845.2.a.k.1.2		3	13.4	even	6
845.2.e.i.146.2		6	13.10	even	6
845.2.e.i.191.2		6	13.12	even	2
845.2.e.k.146.2		6	13.3	even	3	inner
845.2.e.k.191.2		6	1.1	even	1	trivial
845.2.m.h.316.3		12	13.5	odd	4
845.2.m.h.316.4		12	13.8	odd	4
845.2.m.h.361.3		12	13.11	odd	12
845.2.m.h.361.4		12	13.2	odd	12
1040.2.k.d.961.3		6	52.19	even	12
1040.2.k.d.961.4		6	52.7	even	12
4225.2.a.bc.1.2		3	65.4	even	6
4225.2.a.be.1.2		3	65.9	even	6
7605.2.a.bs.1.2		3	39.17	odd	6
7605.2.a.cc.1.2		3	39.35	odd	6

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.285997 - 0.495361i) q^{2} +(0.214003 - 0.370665i) q^{3} +(0.836412 + 1.44871i) q^{4} +1.00000 q^{5} +(-0.122408 - 0.212018i) q^{6} +(-1.33641 - 2.31473i) q^{7} +2.10083 q^{8} +(1.40841 + 2.43943i) q^{9} +(0.285997 - 0.495361i) q^{10} +(2.55042 - 4.41745i) q^{11} +0.715980 q^{12} -1.52884 q^{14} +(0.214003 - 0.370665i) q^{15} +(-1.07199 + 1.85675i) q^{16} +(-2.67282 - 4.62947i) q^{17} +1.61120 q^{18} +(3.12241 + 5.40817i) q^{19} +(0.836412 + 1.44871i) q^{20} -1.14399 q^{21} +(-1.45882 - 2.52675i) q^{22} +(1.21400 - 2.10272i) q^{23} +(0.449585 - 0.778704i) q^{24} +1.00000 q^{25} +2.48963 q^{27} +(2.23558 - 3.87214i) q^{28} +(-1.33641 + 2.31473i) q^{29} +(-0.122408 - 0.212018i) q^{30} +0.244817 q^{31} +(2.71400 + 4.70079i) q^{32} +(-1.09159 - 1.89070i) q^{33} -3.05767 q^{34} +(-1.33641 - 2.31473i) q^{35} +(-2.35601 + 4.08074i) q^{36} +(1.66359 - 2.88142i) q^{37} +3.57199 q^{38} +2.10083 q^{40} +(3.24482 - 5.62019i) q^{41} +(-0.327176 + 0.566686i) q^{42} +(5.45882 + 9.45495i) q^{43} +8.53279 q^{44} +(1.40841 + 2.43943i) q^{45} +(-0.694402 - 1.20274i) q^{46} -2.67282 q^{47} +(0.458820 + 0.794700i) q^{48} +(-0.0719933 + 0.124696i) q^{49} +(0.285997 - 0.495361i) q^{50} -2.28797 q^{51} -4.20166 q^{53} +(0.712027 - 1.23327i) q^{54} +(2.55042 - 4.41745i) q^{55} +(-2.80757 - 4.86286i) q^{56} +2.67282 q^{57} +(0.764419 + 1.32401i) q^{58} +(-0.449585 - 0.778704i) q^{59} +0.715980 q^{60} +(2.90841 + 5.03751i) q^{61} +(0.0700168 - 0.121273i) q^{62} +(3.76442 - 6.52016i) q^{63} -1.18319 q^{64} -1.24877 q^{66} +(1.09159 - 1.89070i) q^{67} +(4.47116 - 7.74428i) q^{68} +(-0.519602 - 0.899976i) q^{69} -1.52884 q^{70} +(3.12241 + 5.40817i) q^{71} +(2.95882 + 5.12483i) q^{72} -10.9608 q^{73} +(-0.951561 - 1.64815i) q^{74} +(0.214003 - 0.370665i) q^{75} +(-5.22324 + 9.04692i) q^{76} -13.6336 q^{77} -3.63362 q^{79} +(-1.07199 + 1.85675i) q^{80} +(-3.69243 + 6.39547i) q^{81} +(-1.85601 - 3.21471i) q^{82} -9.81681 q^{83} +(-0.956844 - 1.65730i) q^{84} +(-2.67282 - 4.62947i) q^{85} +6.24482 q^{86} +(0.571993 + 0.990721i) q^{87} +(5.35799 - 9.28031i) q^{88} +(3.81681 - 6.61091i) q^{89} +1.61120 q^{90} +4.06163 q^{92} +(0.0523917 - 0.0907450i) q^{93} +(-0.764419 + 1.32401i) q^{94} +(3.12241 + 5.40817i) q^{95} +2.32322 q^{96} +(-5.67282 - 9.82562i) q^{97} +(0.0411797 + 0.0713253i) q^{98} +14.3681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 2 q^{3} - 5 q^{4} + 6 q^{5} + 10 q^{6} + 2 q^{7} - 6 q^{8} - 3 q^{9} + q^{10} + 6 q^{11} + 8 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 34 q^{18} + 8 q^{19} - 5 q^{20} - 4 q^{21} + 12 q^{22}+ \cdots - 24 q^{99}+O(q^{100}) \) 6 * q + q^2 + 2 * q^3 - 5 * q^4 + 6 * q^5 + 10 * q^6 + 2 * q^7 - 6 * q^8 - 3 * q^9 + q^10 + 6 * q^11 + 8 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 34 * q^18 + 8 * q^19 - 5 * q^20 - 4 * q^21 + 12 * q^22 + 8 * q^23 + 12 * q^24 + 6 * q^25 - 28 * q^27 + 22 * q^28 + 2 * q^29 + 10 * q^30 - 20 * q^31 + 17 * q^32 - 18 * q^33 + 16 * q^34 + 2 * q^35 - 17 * q^36 + 20 * q^37 + 20 * q^38 - 6 * q^40 - 2 * q^41 - 22 * q^42 + 12 * q^43 + 24 * q^44 - 3 * q^45 + 8 * q^46 + 4 * q^47 - 18 * q^48 + q^49 + q^50 - 8 * q^51 + 12 * q^53 + 10 * q^54 + 6 * q^55 - 24 * q^56 - 4 * q^57 - 4 * q^58 - 12 * q^59 + 6 * q^61 + 4 * q^62 + 14 * q^63 - 30 * q^64 + 24 * q^66 + 18 * q^67 + 44 * q^68 - 16 * q^69 + 8 * q^70 + 8 * q^71 - 3 * q^72 - 40 * q^73 - 10 * q^74 + 2 * q^75 - 2 * q^76 - 36 * q^77 + 24 * q^79 - 5 * q^80 - 15 * q^81 - 14 * q^82 - 36 * q^83 + 10 * q^84 + 4 * q^85 + 16 * q^86 + 2 * q^87 + 30 * q^88 + 34 * q^90 - 20 * q^92 - 14 * q^93 + 4 * q^94 + 8 * q^95 + 44 * q^96 - 14 * q^97 + 21 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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Database

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