LMFDB - Embedded newform 700.2.be.e.107.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(107,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("700.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.be (of order $12$, degree $4$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.9
Character	$\chi$	$=$	700.107
Dual form			700.2.be.e.543.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.157385 + 1.40543i) q^{2} +(-0.290169 + 1.08292i) q^{3} +(-1.95046 - 0.442386i) q^{4} +(-1.47630 - 0.578247i) q^{6} +(2.16744 + 1.51730i) q^{7} +(0.928715 - 2.67161i) q^{8} +(1.50955 + 0.871538i) q^{9} +O(q^{10})$	\(q+(-0.157385 + 1.40543i) q^{2} +(-0.290169 + 1.08292i) q^{3} +(-1.95046 - 0.442386i) q^{4} +(-1.47630 - 0.578247i) q^{6} +(2.16744 + 1.51730i) q^{7} +(0.928715 - 2.67161i) q^{8} +(1.50955 + 0.871538i) q^{9} +(2.58391 - 1.49182i) q^{11} +(1.04503 - 1.98383i) q^{12} +(-4.05418 + 4.05418i) q^{13} +(-2.47357 + 2.80739i) q^{14} +(3.60859 + 1.72571i) q^{16} +(-0.617565 + 2.30478i) q^{17} +(-1.46247 + 1.98440i) q^{18} +(-1.25694 + 2.17708i) q^{19} +(-2.27204 + 1.90691i) q^{21} +(1.68998 + 3.86629i) q^{22} +(5.79414 - 1.55254i) q^{23} +(2.62367 + 1.78095i) q^{24} +(-5.05979 - 6.33592i) q^{26} +(-3.76010 + 3.76010i) q^{27} +(-3.55628 - 3.91827i) q^{28} +2.55433i q^{29} +(3.12248 - 1.80277i) q^{31} +(-2.99330 + 4.80001i) q^{32} +(0.865758 + 3.23105i) q^{33} +(-3.14202 - 1.23068i) q^{34} +(-2.55876 - 2.36770i) q^{36} +(-4.61014 + 1.23528i) q^{37} +(-2.86191 - 2.10918i) q^{38} +(-3.21397 - 5.56676i) q^{39} -7.93727 q^{41} +(-2.32244 - 3.49331i) q^{42} +(-7.62646 - 7.62646i) q^{43} +(-5.69977 + 1.76665i) q^{44} +(1.27007 + 8.38760i) q^{46} +(-0.765987 - 2.85870i) q^{47} +(-2.91592 + 3.40708i) q^{48} +(2.39563 + 6.57731i) q^{49} +(-2.31671 - 1.33755i) q^{51} +(9.70103 - 6.11400i) q^{52} +(2.47243 + 0.662485i) q^{53} +(-4.69277 - 5.87634i) q^{54} +(6.06656 - 4.38142i) q^{56} +(-1.99289 - 1.99289i) q^{57} +(-3.58993 - 0.402012i) q^{58} +(1.04694 + 1.81336i) q^{59} +(0.950478 - 1.64628i) q^{61} +(2.04223 + 4.67216i) q^{62} +(1.94948 + 4.17944i) q^{63} +(-6.27498 - 4.96233i) q^{64} +(-4.67727 + 0.708243i) q^{66} +(-3.00512 - 0.805219i) q^{67} +(2.22414 - 4.22219i) q^{68} +6.72512i q^{69} +8.09721i q^{71} +(3.73035 - 3.22351i) q^{72} +(9.41954 + 2.52396i) q^{73} +(-1.01054 - 6.67364i) q^{74} +(3.41472 - 3.69026i) q^{76} +(7.86400 + 0.687116i) q^{77} +(8.32952 - 3.64089i) q^{78} +(4.03058 - 6.98117i) q^{79} +(-0.366226 - 0.634322i) q^{81} +(1.24921 - 11.1553i) q^{82} +(5.99790 + 5.99790i) q^{83} +(5.27511 - 2.71422i) q^{84} +(11.9187 - 9.51816i) q^{86} +(-2.76614 - 0.741186i) q^{87} +(-1.58584 - 8.28866i) q^{88} +(-1.77990 - 1.02763i) q^{89} +(-14.9386 + 2.63582i) q^{91} +(-11.9881 + 0.464910i) q^{92} +(1.04621 + 3.90452i) q^{93} +(4.13826 - 0.626624i) q^{94} +(-4.32949 - 4.63434i) q^{96} +(-6.63160 - 6.63160i) q^{97} +(-9.62097 + 2.33171i) q^{98} +5.20071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	$ 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) $ 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.157385	+	1.40543i	−0.111288	+	0.993788i
$2$	−0.157385	+	1.40543i	−0.111288	+	0.993788i
$3$	−0.290169	+	1.08292i	−0.167529	+	0.625227i	0.830175	+	0.557503i	$0.188240\pi$
$3$	−0.290169	+	1.08292i	−0.167529	+	0.625227i	−0.997704	+	0.0677240i	$0.978426\pi$
$4$	−1.95046	−	0.442386i	−0.975230	−	0.221193i
$5$		0			0
$5$		0			0
$6$	−1.47630	−	0.578247i	−0.602699	−	0.236068i
$7$	2.16744	+	1.51730i	0.819217	+	0.573484i
$7$	2.16744	+	1.51730i	0.819217	+	0.573484i
$8$	0.928715	−	2.67161i	0.328350	−	0.944556i
$9$	1.50955	+	0.871538i	0.503183	+	0.290513i
$10$		0			0
$11$	2.58391	−	1.49182i	0.779077	−	0.449800i	−0.0570261	−	0.998373i	$-0.518162\pi$
$11$	2.58391	−	1.49182i	0.779077	−	0.449800i	0.836103	+	0.548572i	$0.184828\pi$
$12$	1.04503	−	1.98383i	0.301675	−	0.572684i
$13$	−4.05418	+	4.05418i	−1.12443	+	1.12443i	−0.133359	+	0.991068i	$0.542576\pi$
$13$	−4.05418	+	4.05418i	−1.12443	+	1.12443i	−0.991068	+	0.133359i	$0.957424\pi$
$14$	−2.47357	+	2.80739i	−0.661090	+	0.750306i
$15$		0			0
$16$	3.60859	+	1.72571i	0.902147	+	0.431428i
$17$	−0.617565	+	2.30478i	−0.149782	+	0.558992i	0.849714	+	0.527243i	$0.176774\pi$
$17$	−0.617565	+	2.30478i	−0.149782	+	0.558992i	−0.999496	+	0.0317490i	$0.989892\pi$
$18$	−1.46247	+	1.98440i	−0.344706	+	0.467727i
$19$	−1.25694	+	2.17708i	−0.288362	+	0.499457i	−0.973419	−	0.229032i	$-0.926444\pi$
$19$	−1.25694	+	2.17708i	−0.288362	+	0.499457i	0.685057	+	0.728489i	$0.259777\pi$
$20$		0			0
$21$	−2.27204	+	1.90691i	−0.495800	+	0.416121i
$22$	1.68998	+	3.86629i	0.360304	+	0.824295i
$23$	5.79414	−	1.55254i	1.20816	−	0.323726i	0.402122	−	0.915586i	$-0.368273\pi$
$23$	5.79414	−	1.55254i	1.20816	−	0.323726i	0.806041	+	0.591860i	$0.201606\pi$
$24$	2.62367	+	1.78095i	0.535553	+	0.363534i
$25$		0			0
$26$	−5.05979	−	6.33592i	−0.992307	−	1.24258i
$27$	−3.76010	+	3.76010i	−0.723632	+	0.723632i
$28$	−3.55628	−	3.91827i	−0.672074	−	0.740484i
$29$			2.55433i			0.474327i	0.971470	+	0.237163i	$0.0762177\pi$
$29$			2.55433i			0.474327i	−0.971470	+	0.237163i	$0.923782\pi$
$30$		0			0
$31$	3.12248	−	1.80277i	0.560815	−	0.323787i	−0.192658	−	0.981266i	$-0.561711\pi$
$31$	3.12248	−	1.80277i	0.560815	−	0.323787i	0.753472	+	0.657479i	$0.228377\pi$
$32$	−2.99330	+	4.80001i	−0.529147	+	0.848530i
$33$	0.865758	+	3.23105i	0.150709	+	0.562454i
$34$	−3.14202	−	1.23068i	−0.538851	−	0.211060i
$35$		0			0
$36$	−2.55876	−	2.36770i	−0.426460	−	0.394617i
$37$	−4.61014	+	1.23528i	−0.757903	+	0.203079i	−0.617021	−	0.786947i	$-0.711661\pi$
$37$	−4.61014	+	1.23528i	−0.757903	+	0.203079i	−0.140882	+	0.990026i	$0.544994\pi$
$38$	−2.86191	−	2.10918i	−0.464263	−	0.342154i
$39$	−3.21397	−	5.56676i	−0.514648	−	0.891396i
$40$		0			0
$41$	−7.93727			−1.23959			−0.619797	−	0.784763i	$-0.712785\pi$
$41$	−7.93727			−1.23959			−0.619797	+	0.784763i	$0.712785\pi$
$42$	−2.32244	−	3.49331i	−0.358360	−	0.539029i
$43$	−7.62646	−	7.62646i	−1.16302	−	1.16302i	−0.983810	−	0.179215i	$-0.942644\pi$
$43$	−7.62646	−	7.62646i	−1.16302	−	1.16302i	−0.179215	−	0.983810i	$-0.557356\pi$
$44$	−5.69977	+	1.76665i	−0.859272	+	0.266332i
$45$		0			0
$46$	1.27007	+	8.38760i	0.187261	+	1.23668i
$47$	−0.765987	−	2.85870i	−0.111731	−	0.416985i	0.887291	−	0.461210i	$-0.152585\pi$
$47$	−0.765987	−	2.85870i	−0.111731	−	0.416985i	−0.999022	+	0.0442256i	$0.985918\pi$
$48$	−2.91592	+	3.40708i	−0.420876	+	0.491770i
$49$	2.39563	+	6.57731i	0.342232	+	0.939615i
$50$		0			0
$51$	−2.31671	−	1.33755i	−0.324404	−	0.187295i
$52$	9.70103	−	6.11400i	1.34529	−	0.847859i
$53$	2.47243	+	0.662485i	0.339614	+	0.0909993i	0.424595	−	0.905383i	$-0.360416\pi$
$53$	2.47243	+	0.662485i	0.339614	+	0.0909993i	−0.0849813	+	0.996383i	$0.527083\pi$
$54$	−4.69277	−	5.87634i	−0.638605	−	0.799668i
$55$		0			0
$56$	6.06656	−	4.38142i	0.810678	−	0.585492i
$57$	−1.99289	−	1.99289i	−0.263965	−	0.263965i
$58$	−3.58993	−	0.402012i	−0.471380	−	0.0527868i
$59$	1.04694	+	1.81336i	0.136301	+	0.236079i	0.926094	−	0.377294i	$-0.123145\pi$
$59$	1.04694	+	1.81336i	0.136301	+	0.236079i	−0.789793	+	0.613374i	$0.789812\pi$
$60$		0			0
$61$	0.950478	−	1.64628i	0.121696	−	0.210784i	−0.798740	−	0.601676i	$-0.794500\pi$
$61$	0.950478	−	1.64628i	0.121696	−	0.210784i	0.920437	+	0.390892i	$0.127833\pi$
$62$	2.04223	+	4.67216i	0.259363	+	0.593365i
$63$	1.94948	+	4.17944i	0.245612	+	0.526560i
$64$	−6.27498	−	4.96233i	−0.784372	−	0.620291i
$65$		0			0
$66$	−4.67727	+	0.708243i	−0.575733	+	0.0871787i
$67$	−3.00512	−	0.805219i	−0.367134	−	0.0983732i	0.0705354	−	0.997509i	$-0.477529\pi$
$67$	−3.00512	−	0.805219i	−0.367134	−	0.0983732i	−0.437669	+	0.899136i	$0.644196\pi$
$68$	2.22414	−	4.22219i	0.269717	−	0.512016i
$69$			6.72512i			0.809609i
$70$		0			0
$71$			8.09721i			0.960962i	0.877005	+	0.480481i	$0.159538\pi$
$71$			8.09721i			0.960962i	−0.877005	+	0.480481i	$0.840462\pi$
$72$	3.73035	−	3.22351i	0.439626	−	0.379894i
$73$	9.41954	+	2.52396i	1.10247	+	0.295407i	0.763771	−	0.645487i	$-0.223345\pi$
$73$	9.41954	+	2.52396i	1.10247	+	0.295407i	0.338702	+	0.940894i	$0.390012\pi$
$74$	−1.01054	−	6.67364i	−0.117473	−	0.775795i
$75$		0			0
$76$	3.41472	−	3.69026i	0.391695	−	0.423302i
$77$	7.86400	+	0.687116i	0.896186	+	0.0783041i
$78$	8.32952	−	3.64089i	0.943133	−	0.412249i
$79$	4.03058	−	6.98117i	0.453476	−	0.785443i	−0.545123	−	0.838356i	$-0.683517\pi$
$79$	4.03058	−	6.98117i	0.453476	−	0.785443i	0.998599	+	0.0529126i	$0.0168505\pi$
$80$		0			0
$81$	−0.366226	−	0.634322i	−0.0406918	−	0.0704802i
$82$	1.24921	−	11.1553i	0.137952	−	1.23189i
$83$	5.99790	+	5.99790i	0.658356	+	0.658356i	0.954991	−	0.296635i	$-0.0958646\pi$
$83$	5.99790	+	5.99790i	0.658356	+	0.658356i	−0.296635	+	0.954991i	$0.595865\pi$
$84$	5.27511	−	2.71422i	0.575562	−	0.296146i
$85$		0			0
$86$	11.9187	−	9.51816i	1.28523	−	1.02637i
$87$	−2.76614	−	0.741186i	−0.296562	−	0.0794635i
$88$	−1.58584	−	8.28866i	−0.169051	−	0.883574i
$89$	−1.77990	−	1.02763i	−0.188669	−	0.108928i	0.402690	−	0.915336i	$-0.368075\pi$
$89$	−1.77990	−	1.02763i	−0.188669	−	0.108928i	−0.591359	+	0.806408i	$0.701408\pi$
$90$		0			0
$91$	−14.9386	+	2.63582i	−1.56599	+	0.276309i
$92$	−11.9881	+	0.464910i	−1.24984	+	0.0484702i
$93$	1.04621	+	3.90452i	0.108487	+	0.404880i
$94$	4.13826	−	0.626624i	0.426829	−	0.0646313i
$95$		0			0
$96$	−4.32949	−	4.63434i	−0.441877	−	0.472990i
$97$	−6.63160	−	6.63160i	−0.673337	−	0.673337i	0.285147	−	0.958484i	$-0.407958\pi$
$97$	−6.63160	−	6.63160i	−0.673337	−	0.673337i	−0.958484	+	0.285147i	$0.907958\pi$
$98$	−9.62097	+	2.33171i	−0.971865	+	0.235539i
$99$	5.20071			0.522691
$100$		0			0
$101$	3.73273	+	6.46529i	0.371421	+	0.643320i	0.989784	−	0.142572i	$-0.0455373\pi$
$101$	3.73273	+	6.46529i	0.371421	+	0.643320i	−0.618363	+	0.785892i	$0.712204\pi$
$102$	2.24445	−	3.04546i	0.222234	−	0.301545i
$103$	3.98105	−	1.06672i	0.392264	−	0.105107i	−0.0572952	−	0.998357i	$-0.518248\pi$
$103$	3.98105	−	1.06672i	0.392264	−	0.105107i	0.449560	+	0.893250i	$0.351581\pi$
$104$	7.06600	+	14.5964i	0.692878	+	1.43129i
$105$		0			0
$106$	−1.32020	+	3.37056i	−0.128229	+	0.327377i
$107$	2.69601	+	10.0616i	0.260633	+	0.972696i	0.964869	+	0.262730i	$0.0846229\pi$
$107$	2.69601	+	10.0616i	0.260633	+	0.972696i	−0.704236	+	0.709966i	$0.748710\pi$
$108$	8.99734	−	5.67051i	0.865770	−	0.545645i
$109$	8.88798	−	5.13148i	0.851314	−	0.491507i	−0.00977974	−	0.999952i	$-0.503113\pi$
$109$	8.88798	−	5.13148i	0.851314	−	0.491507i	0.861094	+	0.508446i	$0.169780\pi$
$110$		0			0
$111$		−	5.35088i		−	0.507883i
$112$	5.20300	+	9.21568i	0.491637	+	0.870800i
$113$	−7.35551	+	7.35551i	−0.691948	+	0.691948i	−0.962660	−	0.270712i	$-0.912741\pi$
$113$	−7.35551	+	7.35551i	−0.691948	+	0.691948i	0.270712	+	0.962660i	$0.412741\pi$
$114$	3.11452	−	2.48722i	0.291701	−	0.232949i
$115$		0			0
$116$	1.13000	−	4.98211i	0.104918	−	0.462578i
$117$	−9.65335	+	2.58661i	−0.892453	+	0.239132i
$118$	−2.71332	+	1.18601i	−0.249782	+	0.109181i
$119$	−4.83558	+	4.05846i	−0.443277	+	0.372039i
$120$		0			0
$121$	−1.04895	+	1.81684i	−0.0953593	+	0.165167i
$122$	2.16413	+	1.59493i	0.195932	+	0.144398i
$123$	2.30315	−	8.59546i	0.207668	−	0.775027i
$124$	−6.88780	+	2.13488i	−0.618543	+	0.191718i
$125$		0			0
$126$	−6.18073	+	2.08208i	−0.550623	+	0.185486i
$127$	13.3832	−	13.3832i	1.18756	−	1.18756i	0.209826	−	0.977739i	$-0.432710\pi$
$127$	13.3832	−	13.3832i	1.18756	−	1.18756i	0.977739	−	0.209826i	$-0.0672898\pi$
$128$	7.96178	−	8.03804i	0.703729	−	0.710469i
$129$	10.4718	−	6.04592i	0.921994	−	0.532314i
$130$		0			0
$131$	13.2990	+	7.67817i	1.16194	+	0.670845i	0.951767	−	0.306820i	$-0.0992651\pi$
$131$	13.2990	+	7.67817i	1.16194	+	0.670845i	0.210170	+	0.977665i	$0.432598\pi$
$132$	−0.259253	−	6.68504i	−0.0225651	−	0.581858i
$133$	−6.02762	+	2.81156i	−0.522661	+	0.243793i
$134$	1.60464	−	4.09675i	0.138620	−	0.353905i
$135$		0			0
$136$	5.58394	+	3.79038i	0.478819	+	0.325022i
$137$	−1.21956	+	4.55145i	−0.104194	+	0.388857i	−0.998252	−	0.0590931i	$-0.981179\pi$
$137$	−1.21956	+	4.55145i	−0.104194	+	0.388857i	0.894059	+	0.447950i	$0.147846\pi$
$138$	−9.45167	−	1.05843i	−0.804580	−	0.0900997i
$139$	10.3065			0.874185			0.437093	−	0.899417i	$-0.356008\pi$
$139$	10.3065			0.874185			0.437093	+	0.899417i	$0.356008\pi$
$140$		0			0
$141$	3.31802			0.279428
$142$	−11.3800	−	1.27438i	−0.954992	−	0.106943i
$143$	−4.42752	+	16.5237i	−0.370248	+	1.38178i
$144$	3.94332	+	5.75007i	0.328610	+	0.479173i
$145$		0			0
$146$	−5.02973	+	12.8413i	−0.416264	+	1.06275i
$147$	−7.81786	+	0.685754i	−0.644806	+	0.0565600i
$148$	9.53837	−	0.369908i	0.784049	−	0.0304063i
$149$	−8.37658	−	4.83622i	−0.686236	−	0.396199i	0.115964	−	0.993253i	$-0.463004\pi$
$149$	−8.37658	−	4.83622i	−0.686236	−	0.396199i	−0.802201	+	0.597055i	$0.796338\pi$
$150$		0			0
$151$	0.955932	−	0.551908i	0.0777927	−	0.0449136i	−0.460599	−	0.887608i	$-0.652365\pi$
$151$	0.955932	−	0.551908i	0.0777927	−	0.0449136i	0.538392	+	0.842695i	$0.319032\pi$
$152$	4.64897	+	5.37994i	0.377082	+	0.436371i
$153$	−2.94095	+	2.94095i	−0.237762	+	0.237762i
$154$	−2.20337	+	10.9442i	−0.177552	+	0.881905i
$155$		0			0
$156$	3.80607	+	12.2796i	0.304729	+	0.983152i
$157$	2.24878	−	8.39254i	0.179472	−	0.669798i	−0.816275	−	0.577664i	$-0.803964\pi$
$157$	2.24878	−	8.39254i	0.179472	−	0.669798i	0.995747	−	0.0921341i	$-0.0293688\pi$
$158$	9.17719	+	6.76343i	0.730098	+	0.538069i
$159$	−1.43484	+	2.48522i	−0.113790	+	0.197091i
$160$		0			0
$161$	14.9141	+	5.42640i	1.17540	+	0.427660i
$162$	0.949133	−	0.414872i	0.0745709	−	0.0325954i
$163$	−1.04108	+	0.278958i	−0.0815440	+	0.0218496i	−0.299360	−	0.954140i	$-0.596773\pi$
$163$	−1.04108	+	0.278958i	−0.0815440	+	0.0218496i	0.217816	+	0.975990i	$0.430107\pi$
$164$	15.4813	+	3.51134i	1.20889	+	0.274190i
$165$		0			0
$166$	−9.37361	+	7.48565i	−0.727533	+	0.580999i
$167$	2.18132	−	2.18132i	0.168796	−	0.168796i	−0.617654	−	0.786450i	$-0.711917\pi$
$167$	2.18132	−	2.18132i	0.168796	−	0.168796i	0.786450	+	0.617654i	$0.211917\pi$
$168$	2.98443	+	7.84098i	0.230253	+	0.604944i
$169$		−	19.8727i		−	1.52867i
$170$		0			0
$171$	−3.79482	+	2.19094i	−0.290197	+	0.167546i
$172$	11.5013	+	18.2490i	0.876963	+	1.39147i
$173$	−6.10543	−	22.7858i	−0.464187	−	1.73237i	−0.659570	−	0.751643i	$-0.729262\pi$
$173$	−6.10543	−	22.7858i	−0.464187	−	1.73237i	0.195383	−	0.980727i	$-0.437405\pi$
$174$	1.47703	−	3.77097i	0.111974	−	0.285876i
$175$		0			0
$176$	11.8987	−	0.924279i	0.896899	−	0.0696701i
$177$	−2.26752	+	0.607581i	−0.170437	+	0.0456686i
$178$	1.72438	−	2.33979i	0.129248	−	0.175375i
$179$	3.53155	+	6.11682i	0.263960	+	0.457193i	0.967291	−	0.253670i	$-0.0816379\pi$
$179$	3.53155	+	6.11682i	0.263960	+	0.457193i	−0.703330	+	0.710863i	$0.748305\pi$
$180$		0			0
$181$	−2.37419			−0.176472			−0.0882360	−	0.996100i	$-0.528123\pi$
$181$	−2.37419			−0.176472			−0.0882360	+	0.996100i	$0.528123\pi$
$182$	−1.35335	−	21.4100i	−0.100317	−	1.58701i
$183$	1.50699	+	1.50699i	0.111400	+	0.111400i
$184$	1.23334	−	16.9215i	0.0909232	−	1.24747i
$185$		0			0
$186$	−5.65218	+	0.855866i	−0.414438	+	0.0627551i
$187$	1.84259	+	6.87664i	0.134744	+	0.502870i
$188$	0.229376	+	5.91465i	0.0167290	+	0.431370i
$189$	−13.8550	+	2.44462i	−1.00780	+	0.177820i
$190$		0			0
$191$	5.46966	+	3.15791i	0.395771	+	0.228498i	0.684658	−	0.728865i	$-0.259952\pi$
$191$	5.46966	+	3.15791i	0.395771	+	0.228498i	−0.288887	+	0.957363i	$0.593285\pi$
$192$	7.19463	−	5.35541i	0.519227	−	0.386494i
$193$	20.4022	+	5.46675i	1.46858	+	0.393505i	0.902445	−	0.430806i	$-0.141771\pi$
$193$	20.4022	+	5.46675i	1.46858	+	0.393505i	0.566137	+	0.824311i	$0.308437\pi$
$194$	10.3639	−	8.27652i	0.744088	−	0.594220i
$195$		0			0
$196$	−1.76286	−	13.8886i	−0.125919	−	0.992041i
$197$	1.01354	+	1.01354i	0.0722120	+	0.0722120i	0.742290	−	0.670078i	$-0.233740\pi$
$197$	1.01354	+	1.01354i	0.0722120	+	0.0722120i	−0.670078	+	0.742290i	$0.733740\pi$
$198$	−0.818513	+	7.30923i	−0.0581692	+	0.519444i
$199$	−4.75738	−	8.24003i	−0.337242	−	0.584120i	0.646671	−	0.762769i	$-0.276161\pi$
$199$	−4.75738	−	8.24003i	−0.337242	−	0.584120i	−0.983913	+	0.178649i	$0.942827\pi$
$200$		0			0
$201$	1.74398	−	3.02067i	0.123011	−	0.213061i
$202$	−9.67397	+	4.22855i	−0.680658	+	0.297520i
$203$	−3.87567	+	5.53636i	−0.272019	+	0.388576i
$204$	3.92693	+	3.63372i	0.274940	+	0.254412i
$205$		0			0
$206$	0.872641	+	5.76297i	0.0607998	+	0.401525i
$207$	10.0996	+	2.70619i	0.701973	+	0.188093i
$208$	−21.6262	+	7.63351i	−1.49951	+	0.529289i
$209$			7.50050i			0.518821i
$210$		0			0
$211$		−	26.9476i		−	1.85515i	−0.373634	−	0.927576i	$-0.621888\pi$
$211$		−	26.9476i		−	1.85515i	0.373634	−	0.927576i	$-0.378112\pi$
$212$	−4.52930	−	2.38592i	−0.311073	−	0.163866i
$213$	−8.76866	−	2.34956i	−0.600819	−	0.160989i
$214$	−14.5652	+	2.20550i	−0.995659	+	0.150765i
$215$		0			0
$216$	6.55345	+	13.5376i	0.445906	+	0.921116i
$217$	9.50314	+	0.830336i	0.645115	+	0.0563668i
$218$	5.81310	+	13.2990i	0.393712	+	0.900725i
$219$	−5.46651	+	9.46827i	−0.369393	+	0.639807i
$220$		0			0
$221$	−6.84029	−	11.8477i	−0.460128	−	0.796964i
$222$	7.52028	+	0.842147i	0.504728	+	0.0565212i
$223$	−2.22624	−	2.22624i	−0.149080	−	0.149080i	0.628627	−	0.777707i	$-0.283617\pi$
$223$	−2.22624	−	2.22624i	−0.149080	−	0.149080i	−0.777707	+	0.628627i	$0.783617\pi$
$224$	−13.7709	+	5.86203i	−0.920104	+	0.391673i
$225$		0			0
$226$	−9.18000	−	11.4953i	−0.610645	−	0.764655i
$227$	7.79070	+	2.08751i	0.517087	+	0.138553i	0.507919	−	0.861405i	$-0.330415\pi$
$227$	7.79070	+	2.08751i	0.517087	+	0.138553i	0.00916824	+	0.999958i	$0.497082\pi$
$228$	3.00543	+	4.76868i	0.199039	+	0.315814i
$229$	−2.10701	−	1.21648i	−0.139235	−	0.0803873i	0.428764	−	0.903416i	$-0.358949\pi$
$229$	−2.10701	−	1.21648i	−0.139235	−	0.0803873i	−0.567999	+	0.823029i	$0.692282\pi$
$230$		0			0
$231$	−3.02598	+	8.31674i	−0.199095	+	0.547201i
$232$	6.82416	+	2.37224i	0.448028	+	0.155745i
$233$	−2.70941	−	10.1117i	−0.177499	−	0.662437i	−0.996112	−	0.0880913i	$-0.971923\pi$
$233$	−2.70941	−	10.1117i	−0.177499	−	0.662437i	0.818613	−	0.574346i	$-0.194743\pi$
$234$	−2.11600	−	13.9742i	−0.138327	−	0.913522i
$235$		0			0
$236$	−1.23982	−	4.00004i	−0.0807052	−	0.260381i
$237$	6.39053	+	6.39053i	0.415110	+	0.415110i
$238$	−4.94283	−	7.43480i	−0.320396	−	0.481927i
$239$	12.9050			0.834754			0.417377	−	0.908733i	$-0.362949\pi$
$239$	12.9050			0.834754			0.417377	+	0.908733i	$0.362949\pi$
$240$		0			0
$241$	−1.35695	−	2.35030i	−0.0874087	−	0.151396i	0.819006	−	0.573784i	$-0.194525\pi$
$241$	−1.35695	−	2.35030i	−0.0874087	−	0.151396i	−0.906415	+	0.422388i	$0.861192\pi$
$242$	−2.38835	−	1.76017i	−0.153529	−	0.113148i
$243$	−14.6160	+	3.91634i	−0.937616	+	0.251234i
$244$	−2.58216	+	2.79052i	−0.165306	+	0.178645i
$245$		0			0
$246$	11.7178	+	4.58970i	0.747101	+	0.292629i
$247$	−3.73043	−	13.9221i	−0.237361	−	0.885845i
$248$	−1.91639	−	10.0163i	−0.121691	−	0.636036i
$249$	−8.23568	+	4.75487i	−0.521915	+	0.301328i
$250$		0			0
$251$			3.15358i			0.199052i	0.995035	+	0.0995262i	$0.0317327\pi$
$251$			3.15358i			0.199052i	−0.995035	+	0.0995262i	$0.968267\pi$
$252$	−1.95346	−	9.01426i	−0.123056	−	0.567845i
$253$	12.6554	−	12.6554i	0.795640	−	0.795640i
$254$	16.7028	+	20.9154i	1.04803	+	1.31235i
$255$		0			0
$256$	10.0438	+	12.4548i	0.627739	+	0.778424i
$257$	15.9053	−	4.26180i	0.992143	−	0.265844i	0.273993	−	0.961732i	$-0.411656\pi$
$257$	15.9053	−	4.26180i	0.992143	−	0.265844i	0.718151	+	0.695888i	$0.244989\pi$
$258$	6.84900	+	15.6690i	0.426400	+	0.975507i
$259$	−11.8665	−	4.31754i	−0.737350	−	0.268279i
$260$		0			0
$261$	−2.22619	+	3.85588i	−0.137798	+	0.238673i
$262$	−12.8842	+	17.4823i	−0.795987	+	1.08006i
$263$	7.55474	−	28.1947i	0.465845	−	1.73856i	−0.188227	−	0.982126i	$-0.560274\pi$
$263$	7.55474	−	28.1947i	0.465845	−	1.73856i	0.654072	−	0.756432i	$-0.273059\pi$
$264$	9.43615	+	0.687763i	0.580755	+	0.0423289i
$265$		0			0
$266$	−3.00279	−	8.91389i	−0.184113	−	0.546546i
$267$	1.62931	−	1.62931i	0.0997123	−	0.0997123i
$268$	5.50515	+	2.89997i	0.336280	+	0.177144i
$269$	−5.29203	+	3.05536i	−0.322661	+	0.186288i	−0.652578	−	0.757721i	$-0.726313\pi$
$269$	−5.29203	+	3.05536i	−0.322661	+	0.186288i	0.329917	+	0.944010i	$0.392979\pi$
$270$		0			0
$271$	19.0699	+	11.0100i	1.15841	+	0.668810i	0.950923	−	0.309428i	$-0.100137\pi$
$271$	19.0699	+	11.0100i	1.15841	+	0.668810i	0.207489	+	0.978237i	$0.433471\pi$
$272$	−6.20594	+	7.25128i	−0.376290	+	0.439673i
$273$	1.48032	−	16.9422i	0.0895932	−	1.02539i
$274$	−6.20480	−	2.43033i	−0.374846	−	0.146822i
$275$		0			0
$276$	2.97510	−	13.1171i	0.179080	−	0.789555i
$277$	4.25922	−	15.8956i	0.255912	−	0.955077i	−0.711669	−	0.702515i	$-0.752060\pi$
$277$	4.25922	−	15.8956i	0.255912	−	0.955077i	0.967581	−	0.252561i	$-0.0812730\pi$
$278$	−1.62209	+	14.4850i	−0.0972862	+	0.868755i
$279$	6.28472			0.376257
$280$		0			0
$281$	6.79274			0.405221			0.202610	−	0.979259i	$-0.435057\pi$
$281$	6.79274			0.405221			0.202610	+	0.979259i	$0.435057\pi$
$282$	−0.522207	+	4.66325i	−0.0310970	+	0.277692i
$283$	3.37625	−	12.6003i	0.200697	−	0.749013i	−0.790021	−	0.613080i	$-0.789930\pi$
$283$	3.37625	−	12.6003i	0.200697	−	0.749013i	0.990718	−	0.135932i	$-0.0434030\pi$
$284$	3.58209	−	15.7933i	0.212558	−	0.937159i
$285$		0			0
$286$	−22.5261	−	8.82314i	−1.33200	−	0.521723i
$287$	−17.2036	−	12.0432i	−1.01550	−	0.710887i
$288$	−8.70194	+	4.63707i	−0.512767	+	0.273242i
$289$	9.79179	+	5.65329i	0.575987	+	0.332546i
$290$		0			0
$291$	9.10580	−	5.25724i	0.533791	−	0.308185i
$292$	−17.2559	−	9.08995i	−1.00982	−	0.531949i
$293$	1.28839	−	1.28839i	0.0752688	−	0.0752688i	−0.668470	−	0.743739i	$-0.733051\pi$
$293$	1.28839	−	1.28839i	0.0752688	−	0.0752688i	0.743739	+	0.668470i	$0.233051\pi$
$294$	0.266634	−	11.0954i	0.0155504	−	0.647095i
$295$		0			0
$296$	−0.981316	+	13.4637i	−0.0570378	+	0.782563i
$297$	−4.10636	+	15.3251i	−0.238275	+	0.889255i
$298$	8.11531	−	11.0115i	0.470107	−	0.637882i
$299$	−17.1962	+	29.7848i	−0.994484	+	1.72250i
$300$		0			0
$301$	−4.95833	−	28.1015i	−0.285793	−	1.61975i
$302$	0.625218	+	1.43036i	0.0359772	+	0.0823078i
$303$	−8.08454	+	2.16625i	−0.464445	+	0.124448i
$304$	−8.29280	+	5.68708i	−0.475625	+	0.326176i
$305$		0			0
$306$	−3.67044	−	4.59616i	−0.209825	−	0.262745i
$307$	−11.6465	+	11.6465i	−0.664701	+	0.664701i	−0.956484	−	0.291783i	$-0.905751\pi$
$307$	−11.6465	+	11.6465i	−0.664701	+	0.664701i	0.291783	+	0.956484i	$0.405751\pi$
$308$	−15.0345	−	4.81912i	−0.856667	−	0.274595i
$309$			4.62070i			0.262863i
$310$		0			0
$311$	−26.1398	+	15.0918i	−1.48225	+	0.855778i	−0.999797	−	0.0201436i	$-0.993588\pi$
$311$	−26.1398	+	15.0918i	−1.48225	+	0.855778i	−0.482454	+	0.875922i	$0.660254\pi$
$312$	−17.8571	+	3.41654i	−1.01096	+	0.193423i
$313$	−5.71023	−	21.3109i	−0.322761	−	1.20456i	−0.916543	−	0.399935i	$-0.869033\pi$
$313$	−5.71023	−	21.3109i	−0.322761	−	1.20456i	0.593782	−	0.804626i	$-0.297634\pi$
$314$	11.4412	+	4.48135i	0.645664	+	0.252897i
$315$		0			0
$316$	−10.9499	+	11.8334i	−0.615978	+	0.665682i
$317$	−1.40009	+	0.375154i	−0.0786372	+	0.0210708i	−0.297923	−	0.954590i	$-0.596294\pi$
$317$	−1.40009	+	0.375154i	−0.0786372	+	0.0210708i	0.219286	+	0.975661i	$0.429627\pi$
$318$	−3.26698	−	2.40770i	−0.183203	−	0.135017i
$319$	3.81059	+	6.60014i	0.213352	+	0.369537i
$320$		0			0
$321$	−11.6783			−0.651819
$322$	−9.97367	+	20.1067i	−0.555811	+	1.12050i
$323$	−4.24147	−	4.24147i	−0.236001	−	0.236001i
$324$	0.433694	+	1.39923i	0.0240941	+	0.0777352i
$325$		0			0
$326$	−0.228204	−	1.50707i	−0.0126391	−	0.0834691i
$327$	2.97799	+	11.1140i	0.164683	+	0.614606i
$328$	−7.37146	+	21.2053i	−0.407021	+	1.17087i
$329$	2.67726	−	7.35831i	0.147602	−	0.405677i
$330$		0			0
$331$	−24.5744	−	14.1881i	−1.35073	−	0.779846i	−0.362381	−	0.932030i	$-0.618036\pi$
$331$	−24.5744	−	14.1881i	−1.35073	−	0.779846i	−0.988352	+	0.152184i	$0.951369\pi$
$332$	−9.04528	−	14.3521i	−0.496424	−	0.787672i
$333$	−8.03583	−	2.15320i	−0.440361	−	0.117994i
$334$	2.72239	+	3.40900i	0.148962	+	0.186532i
$335$		0			0
$336$	−11.4896	+	2.96035i	−0.626811	+	0.161500i
$337$	11.7829	+	11.7829i	0.641857	+	0.641857i	0.951012	−	0.309155i	$-0.100046\pi$
$337$	11.7829	+	11.7829i	0.641857	+	0.641857i	−0.309155	+	0.951012i	$0.600046\pi$
$338$	27.9297	+	3.12767i	1.51918	+	0.170123i
$339$	−5.83112	−	10.0998i	−0.316703	−	0.548546i
$340$		0			0
$341$	5.37880	−	9.31636i	0.291279	−	0.504509i
$342$	−2.48197	−	5.67817i	−0.134209	−	0.307041i
$343$	−4.78733	+	17.8908i	−0.258492	+	0.966013i
$344$	−27.4577	+	13.2921i	−1.48042	+	0.716662i
$345$		0			0
$346$	32.9847	−	4.99461i	1.77327	−	0.268512i
$347$	15.4205	+	4.13190i	0.827815	+	0.221812i	0.647760	−	0.761844i	$-0.275706\pi$
$347$	15.4205	+	4.13190i	0.827815	+	0.221812i	0.180055	+	0.983657i	$0.442373\pi$
$348$	5.06736	+	2.66936i	0.271639	+	0.143093i
$349$		−	7.52656i		−	0.402888i	−0.979500	−	0.201444i	$-0.935437\pi$
$349$		−	7.52656i		−	0.402888i	0.979500	−	0.201444i	$-0.0645633\pi$
$350$		0			0
$351$		−	30.4882i		−	1.62734i
$352$	−0.573668	+	16.8683i	−0.0305766	+	0.899081i
$353$	5.41550	+	1.45108i	0.288238	+	0.0772331i	0.400041	−	0.916497i	$-0.368996\pi$
$353$	5.41550	+	1.45108i	0.288238	+	0.0772331i	−0.111803	+	0.993730i	$0.535663\pi$
$354$	−0.497038	−	3.28247i	−0.0264173	−	0.174461i
$355$		0			0
$356$	3.01702	+	2.79175i	0.159902	+	0.147962i
$357$	−2.99187	−	6.41420i	−0.158347	−	0.339476i
$358$	−9.15257	+	4.00064i	−0.483728	+	0.211441i
$359$	18.2143	−	31.5480i	0.961311	−	1.66504i	0.242097	−	0.970252i	$-0.422165\pi$
$359$	18.2143	−	31.5480i	0.961311	−	1.66504i	0.719215	−	0.694788i	$-0.244502\pi$
$360$		0			0
$361$	6.34021	+	10.9816i	0.333695	+	0.577977i
$362$	0.373661	−	3.33675i	0.0196392	−	0.175376i
$363$	−1.66313	−	1.66313i	−0.0872915	−	0.0872915i
$364$	30.3032	+	1.46757i	1.58832	+	0.0769217i
$365$		0			0
$366$	−2.35515	+	1.88080i	−0.123106	+	0.0983107i
$367$	−31.5816	−	8.46227i	−1.64855	−	0.441727i	−0.689342	−	0.724436i	$-0.742100\pi$
$367$	−31.5816	−	8.46227i	−1.64855	−	0.441727i	−0.959206	+	0.282709i	$0.908767\pi$
$368$	23.5879	+	4.39657i	1.22961	+	0.229187i
$369$	−11.9817	−	6.91763i	−0.623742	−	0.360118i
$370$		0			0
$371$	4.35366	+	5.18730i	0.226031	+	0.269311i
$372$	−0.313291	−	8.07844i	−0.0162434	−	0.418848i
$373$	6.76877	+	25.2614i	0.350474	+	1.30799i	0.886086	+	0.463522i	$0.153414\pi$
$373$	6.76877	+	25.2614i	0.350474	+	1.30799i	−0.535612	+	0.844464i	$0.679919\pi$
$374$	−9.95463	+	1.50735i	−0.514742	+	0.0779433i
$375$		0			0
$376$	−8.34872	−	0.608504i	−0.430552	−	0.0313812i
$377$	−10.3557	−	10.3557i	−0.533346	−	0.533346i
$378$	−1.25518	−	19.8570i	−0.0645594	−	1.02133i
$379$	−20.3769			−1.04669			−0.523344	−	0.852121i	$-0.675316\pi$
$379$	−20.3769			−1.04669			−0.523344	+	0.852121i	$0.675316\pi$
$380$		0			0
$381$	10.6096	+	18.3763i	0.543546	+	0.941449i
$382$	−5.29906	+	7.19021i	−0.271124	+	0.367883i
$383$	24.6635	−	6.60856i	1.26025	−	0.337682i	0.433960	−	0.900932i	$-0.357116\pi$
$383$	24.6635	−	6.60856i	1.26025	−	0.337682i	0.826286	+	0.563250i	$0.190449\pi$
$384$	6.39433	+	10.9544i	0.326309	+	0.559014i
$385$		0			0
$386$	−10.8941	+	27.8134i	−0.554496	+	1.41567i
$387$	−4.86576	−	18.1593i	−0.247341	−	0.923088i
$388$	10.0009	+	15.8684i	0.507721	+	0.805595i
$389$	15.6310	−	9.02458i	0.792525	−	0.457564i	−0.0483257	−	0.998832i	$-0.515389\pi$
$389$	15.6310	−	9.02458i	0.792525	−	0.457564i	0.840851	+	0.541267i	$0.182055\pi$
$390$		0			0
$391$			14.3130i			0.723842i
$392$	19.7968	−	0.291730i	0.999891	−	0.0147346i
$393$	−12.1738	+	12.1738i	−0.614088	+	0.614088i
$394$	−1.58398	+	1.26495i	−0.0797998	+	0.0637272i
$395$		0			0
$396$	−10.1438	−	2.30072i	−0.509744	−	0.115616i
$397$	29.0617	−	7.78706i	1.45857	−	0.390821i	0.559571	−	0.828782i	$-0.310966\pi$
$397$	29.0617	−	7.78706i	1.45857	−	0.390821i	0.898994	+	0.437961i	$0.144299\pi$
$398$	12.3295	−	5.38931i	0.618022	−	0.270141i
$399$	−1.29568	−	7.34329i	−0.0648649	−	0.367624i
$400$		0			0
$401$	−2.44780	+	4.23972i	−0.122237	+	0.211721i	−0.920650	−	0.390390i	$-0.872340\pi$
$401$	−2.44780	+	4.23972i	−0.122237	+	0.211721i	0.798412	+	0.602111i	$0.205674\pi$
$402$	3.97086	+	2.92645i	0.198048	+	0.145958i
$403$	−5.35037	+	19.9678i	−0.266521	+	0.994669i
$404$	−4.42040	−	14.2616i	−0.219923	−	0.709541i
$405$		0			0
$406$	−7.17099	−	6.31832i	−0.355890	−	0.313573i
$407$	−10.0694	+	10.0694i	−0.499119	+	0.499119i
$408$	−5.72498	+	4.94713i	−0.283429	+	0.244920i
$409$	−29.0499	+	16.7720i	−1.43642	+	0.829320i	−0.997599	−	0.0692530i	$-0.977938\pi$
$409$	−29.0499	+	16.7720i	−1.43642	+	0.829320i	−0.438825	+	0.898573i	$0.644605\pi$
$410$		0			0
$411$	−4.57500	−	2.64138i	−0.225668	−	0.130290i
$412$	−8.23678	+	0.319431i	−0.405797	+	0.0157372i
$413$	−0.482212	+	5.51888i	−0.0237281	+	0.271566i
$414$	−5.39289	+	13.7684i	−0.265046	+	0.676680i
$415$		0			0
$416$	−7.32472	−	31.5955i	−0.359124	−	1.54910i
$417$	−2.99062	+	11.1611i	−0.146451	+	0.546564i
$418$	−10.5414	−	1.18047i	−0.515598	−	0.0577385i
$419$	−36.3735			−1.77696			−0.888481	−	0.458914i	$-0.848239\pi$
$419$	−36.3735			−1.77696			−0.888481	+	0.458914i	$0.848239\pi$
$420$		0			0
$421$	−33.2473			−1.62038			−0.810188	−	0.586170i	$-0.800635\pi$
$421$	−33.2473			−1.62038			−0.810188	+	0.586170i	$0.800635\pi$
$422$	37.8730	+	4.24115i	1.84363	+	0.206456i
$423$	1.33517	−	4.98294i	0.0649184	−	0.242279i
$424$	4.06608	−	5.99010i	0.197466	−	0.290905i
$425$		0			0
$426$	4.68219	−	11.9539i	0.226853	−	0.579171i
$427$	4.55800	−	2.12606i	0.220577	−	0.102887i
$428$	−0.807325	−	20.8175i	−0.0390235	−	1.00625i
$429$	−16.6092	−	9.58933i	−0.801900	−	0.462977i
$430$		0			0
$431$	26.9460	−	15.5573i	1.29794	−	0.749367i	0.317894	−	0.948126i	$-0.397024\pi$
$431$	26.9460	−	15.5573i	1.29794	−	0.749367i	0.980048	+	0.198759i	$0.0636910\pi$
$432$	−20.0575	+	7.07980i	−0.965018	+	0.340627i
$433$	−7.14603	+	7.14603i	−0.343416	+	0.343416i	−0.857650	−	0.514234i	$-0.828076\pi$
$433$	−7.14603	+	7.14603i	−0.343416	+	0.343416i	0.514234	+	0.857650i	$0.328076\pi$
$434$	−2.66263	+	13.2253i	−0.127810	+	0.634835i
$435$		0			0
$436$	−19.6058	+	6.07682i	−0.938945	+	0.291027i
$437$	−3.90289	+	14.5658i	−0.186700	+	0.696776i
$438$	−12.4466	−	9.17295i	−0.594723	−	0.438301i
$439$	−0.278565	+	0.482489i	−0.0132952	+	0.0230280i	−0.872596	−	0.488442i	$-0.837565\pi$
$439$	−0.278565	+	0.482489i	−0.0132952	+	0.0230280i	0.859301	+	0.511470i	$0.170899\pi$
$440$		0			0
$441$	−2.11606	+	12.0166i	−0.100765	+	0.572221i
$442$	17.7277	−	7.74889i	0.843221	−	0.368577i
$443$	−23.5587	+	6.31254i	−1.11931	+	0.299918i	−0.770604	−	0.637315i	$-0.780045\pi$
$443$	−23.5587	+	6.31254i	−1.11931	+	0.299918i	−0.348705	+	0.937233i	$0.613379\pi$
$444$	−2.36715	+	10.4367i	−0.112340	+	0.495302i
$445$		0			0
$446$	3.47920	−	2.77845i	0.164745	−	0.131563i
$447$	7.66789	−	7.66789i	0.362679	−	0.362679i
$448$	−6.07134	−	20.2766i	−0.286844	−	0.957977i
$449$			8.64441i			0.407955i	0.978976	+	0.203978i	$0.0653870\pi$
$449$			8.64441i			0.407955i	−0.978976	+	0.203978i	$0.934613\pi$
$450$		0			0
$451$	−20.5092	+	11.8410i	−0.965738	+	0.557569i
$452$	17.6006	−	11.0927i	0.827863	−	0.521754i
$453$	0.320293	+	1.19535i	0.0150487	+	0.0561624i
$454$	−4.15999	+	10.6207i	−0.195238	+	0.498456i
$455$		0			0
$456$	−7.17505	+	3.47340i	−0.336003	+	0.162657i
$457$	2.64033	−	0.707473i	0.123509	−	0.0330942i	−0.196535	−	0.980497i	$-0.562969\pi$
$457$	2.64033	−	0.707473i	0.123509	−	0.0330942i	0.320044	+	0.947403i	$0.396302\pi$
$458$	2.04129	−	2.76979i	0.0953831	−	0.129424i
$459$	−6.34412	−	10.9883i	−0.296118	−	0.512891i
$460$		0			0
$461$	38.5986			1.79772			0.898858	−	0.438239i	$-0.144398\pi$
$461$	38.5986			1.79772			0.898858	+	0.438239i	$0.144398\pi$
$462$	−11.2123	−	5.56173i	−0.521645	−	0.258755i
$463$	−13.5055	−	13.5055i	−0.627652	−	0.627652i	0.319824	−	0.947477i	$-0.396376\pi$
$463$	−13.5055	−	13.5055i	−0.627652	−	0.627652i	−0.947477	+	0.319824i	$0.896376\pi$
$464$	−4.40804	+	9.21752i	−0.204638	+	0.427913i
$465$		0			0
$466$	14.6376	−	2.21646i	0.678075	−	0.102676i
$467$	3.45858	+	12.9076i	0.160044	+	0.597292i	0.998620	+	0.0525083i	$0.0167216\pi$
$467$	3.45858	+	12.9076i	0.160044	+	0.597292i	−0.838577	+	0.544784i	$0.816612\pi$
$468$	19.9728	−	0.774565i	0.923241	−	0.0358043i
$469$	−5.29167	−	6.30492i	−0.244347	−	0.291134i
$470$		0			0
$471$	8.43596	+	4.87051i	0.388709	+	0.224421i
$472$	5.81690	−	1.11293i	0.267745	−	0.0512267i
$473$	−31.0834	−	8.32876i	−1.42921	−	0.382957i
$474$	−9.98721	+	7.97567i	−0.458728	+	0.366335i
$475$		0			0
$476$	11.2270	−	5.77668i	0.514589	−	0.264774i
$477$	3.15487	+	3.15487i	0.144452	+	0.144452i
$478$	−2.03105	+	18.1370i	−0.0928980	+	0.829569i
$479$	−3.91630	−	6.78323i	−0.178940	−	0.309934i	0.762578	−	0.646897i	$-0.223934\pi$
$479$	−3.91630	−	6.78323i	−0.178940	−	0.309934i	−0.941518	+	0.336963i	$0.890600\pi$
$480$		0			0
$481$	13.6823	−	23.6984i	0.623858	−	1.08055i
$482$	3.51675	−	1.53719i	0.160183	−	0.0700172i
$483$	−10.2040	+	14.5763i	−0.464298	+	0.663245i
$484$	2.84968	−	3.07963i	0.129531	−	0.139983i
$485$		0			0
$486$	−3.20381	−	21.1581i	−0.145328	−	0.959751i
$487$	2.35662	+	0.631456i	0.106789	+	0.0286140i	0.311818	−	0.950142i	$-0.399062\pi$
$487$	2.35662	+	0.631456i	0.106789	+	0.0286140i	−0.205029	+	0.978756i	$0.565729\pi$
$488$	−3.51548	−	4.06823i	−0.159138	−	0.184160i
$489$		−	1.20836i		−	0.0546439i
$490$		0			0
$491$		−	33.5206i		−	1.51276i	−0.654130	−	0.756382i	$-0.726965\pi$
$491$		−	33.5206i		−	1.51276i	0.654130	−	0.756382i	$-0.273035\pi$
$492$	−8.29471	+	15.7462i	−0.373954	+	0.709895i
$493$	−5.88718	−	1.57746i	−0.265145	−	0.0710454i
$494$	20.1537	−	3.05171i	0.906757	−	0.137303i
$495$		0			0
$496$	14.3788	−	1.11693i	0.645628	−	0.0501517i
$497$	−12.2859	+	17.5502i	−0.551096	+	0.787236i
$498$	−5.38646	−	12.3230i	−0.241373	−	0.552207i
$499$	−10.3462	+	17.9201i	−0.463159	+	0.802216i	−0.999116	−	0.0420297i	$-0.986618\pi$
$499$	−10.3462	+	17.9201i	−0.463159	+	0.802216i	0.535957	+	0.844245i	$0.319951\pi$
$500$		0			0
$501$	1.72926	+	2.99516i	0.0772575	+	0.133814i
$502$	−4.43214	−	0.496326i	−0.197816	−	0.0221521i
$503$	4.35918	+	4.35918i	0.194366	+	0.194366i	0.797580	−	0.603214i	$-0.206113\pi$
$503$	4.35918	+	4.35918i	0.194366	+	0.194366i	−0.603214	+	0.797580i	$0.706113\pi$
$504$	12.9763	−	1.32674i	0.578012	−	0.0590975i
$505$		0			0
$506$	15.7945	+	19.7781i	0.702152	+	0.879242i
$507$	21.5207	+	5.76644i	0.955766	+	0.256097i
$508$	−32.0239	+	20.1828i	−1.42083	+	0.895468i
$509$	26.4887	+	15.2933i	1.17409	+	0.677862i	0.954640	−	0.297761i	$-0.0962400\pi$
$509$	26.4887	+	15.2933i	1.17409	+	0.677862i	0.219451	+	0.975623i	$0.429573\pi$
$510$		0			0
$511$	16.5867	+	19.7628i	0.733754	+	0.874253i
$512$	−19.0851	+	12.1557i	−0.843448	+	0.537211i
$513$	−3.45983	−	12.9123i	−0.152755	−	0.570091i
$514$	3.48641	+	23.0245i	0.153779	+	1.01557i
$515$		0			0
$516$	−23.0995	+	7.15973i	−1.01690	+	0.315189i
$517$	−6.24391	−	6.24391i	−0.274607	−	0.274607i
$518$	7.93561	−	15.9980i	0.348671	−	0.702913i
$519$	26.4469			1.16089
$520$		0			0
$521$	−4.68273	−	8.11072i	−0.205154	−	0.355337i	0.745028	−	0.667033i	$-0.232436\pi$
$521$	−4.68273	−	8.11072i	−0.205154	−	0.355337i	−0.950182	+	0.311696i	$0.899103\pi$
$522$	−5.06880	−	3.73562i	−0.221855	−	0.163503i
$523$	31.6043	−	8.46836i	1.38196	−	0.370296i	0.510128	−	0.860098i	$-0.329598\pi$
$523$	31.6043	−	8.46836i	1.38196	−	0.370296i	0.871833	+	0.489803i	$0.162931\pi$
$524$	−22.5424	−	20.8592i	−0.984770	−	0.911240i
$525$		0			0
$526$	38.4366	+	15.0551i	1.67592	+	0.656432i
$527$	2.22665	+	8.30998i	0.0969945	+	0.361988i
$528$	−2.45171	+	13.1536i	−0.106697	+	0.572437i
$529$	11.2432	−	6.49124i	0.488833	−	0.282228i
$530$		0			0
$531$			3.64981i			0.158388i
$532$	13.0004	−	2.81729i	0.563640	−	0.122145i
$533$	32.1791	−	32.1791i	1.39383	−	1.39383i
$534$	2.03345	+	2.54631i	0.0879961	+	0.110190i
$535$		0			0
$536$	−4.94213	+	7.28068i	−0.213468	+	0.314478i
$537$	−7.64880	+	2.04949i	−0.330070	+	0.0884420i
$538$	−3.46120	−	7.91844i	−0.149223	−	0.341388i
$539$	16.0022	+	13.4213i	0.689265	+	0.578096i
$540$		0			0
$541$	2.73095	−	4.73015i	0.117413	−	0.203365i	−0.801329	−	0.598224i	$-0.795873\pi$
$541$	2.73095	−	4.73015i	0.117413	−	0.203365i	0.918742	+	0.394859i	$0.129207\pi$
$542$	−18.4751	+	25.0685i	−0.793572	+	1.07679i
$543$	0.688915	−	2.57107i	0.0295642	−	0.110335i
$544$	−9.21444	−	9.86325i	−0.395066	−	0.422883i
$545$		0			0
$546$	23.5781	+	4.74693i	1.00905	+	0.203150i
$547$	−4.64823	+	4.64823i	−0.198744	+	0.198744i	−0.799461	−	0.600718i	$-0.794882\pi$
$547$	−4.64823	+	4.64823i	−0.198744	+	0.198744i	0.600718	+	0.799461i	$0.294882\pi$
$548$	4.39220	−	8.33791i	0.187626	−	0.356178i
$549$	2.86959	−	1.65676i	0.122471	−	0.0707087i
$550$		0			0
$551$	−5.56098	−	3.21064i	−0.236906	−	0.136778i
$552$	17.9669	+	6.24572i	0.764721	+	0.265835i
$553$	19.3286	−	9.01572i	0.821934	−	0.383387i
$554$	21.6699	+	8.48777i	0.920664	+	0.360611i
$555$		0			0
$556$	−20.1024	−	4.55945i	−0.852532	−	0.193364i
$557$	−3.22921	+	12.0516i	−0.136826	+	0.510642i	0.863158	+	0.504934i	$0.168483\pi$
$557$	−3.22921	+	12.0516i	−0.136826	+	0.510642i	−0.999984	+	0.00570726i	$0.998183\pi$
$558$	−0.989120	+	8.83273i	−0.0418728	+	0.373919i
$559$	61.8381			2.61547
$560$		0			0
$561$	−7.98155			−0.336981
$562$	−1.06907	+	9.54671i	−0.0450962	+	0.402704i
$563$	−4.91456	+	18.3414i	−0.207124	+	0.772997i	0.781668	+	0.623695i	$0.214369\pi$
$563$	−4.91456	+	18.3414i	−0.207124	+	0.772997i	−0.988792	+	0.149302i	$0.952297\pi$
$564$	−6.47167	−	1.46785i	−0.272507	−	0.0618076i
$565$		0			0
$566$	17.1775	+	6.72818i	0.722025	+	0.282807i
$567$	0.168680	−	1.93053i	0.00708388	−	0.0810747i
$568$	21.6326	+	7.52000i	0.907682	+	0.315532i
$569$	19.5330	+	11.2774i	0.818868	+	0.472773i	0.850026	−	0.526741i	$-0.176586\pi$
$569$	19.5330	+	11.2774i	0.818868	+	0.472773i	−0.0311582	+	0.999514i	$0.509920\pi$
$570$		0			0
$571$	−22.8480	+	13.1913i	−0.956158	+	0.552038i	−0.894988	−	0.446090i	$-0.852816\pi$
$571$	−22.8480	+	13.1913i	−0.956158	+	0.552038i	−0.0611692	+	0.998127i	$0.519483\pi$
$572$	15.9456	−	30.2702i	0.666717	−	1.26566i
$573$	−5.00690	+	5.00690i	−0.209166	+	0.209166i
$574$	19.6334	−	22.2830i	0.819483	−	0.930074i
$575$		0			0
$576$	−5.14753	−	12.9598i	−0.214480	−	0.539990i
$577$	8.25666	−	30.8143i	0.343729	−	1.28282i	−0.550360	−	0.834927i	$-0.685510\pi$
$577$	8.25666	−	30.8143i	0.343729	−	1.28282i	0.894090	−	0.447888i	$-0.147824\pi$
$578$	−9.48637	+	12.8719i	−0.394581	+	0.535401i
$579$	−11.8402	+	20.5077i	−0.492060	+	0.852273i
$580$		0			0
$581$	3.89953	+	22.1007i	0.161780	+	0.916892i
$582$	5.95556	+	13.6250i	0.246866	+	0.564773i
$583$	7.37683	−	1.97662i	0.305517	−	0.0818630i
$584$	15.4911	−	22.8213i	0.641026	−	0.944351i
$585$		0			0
$586$	1.60797	+	2.01352i	0.0664248	+	0.0831778i
$587$	14.8860	−	14.8860i	0.614410	−	0.614410i	−0.329682	−	0.944092i	$-0.606942\pi$
$587$	14.8860	−	14.8860i	0.614410	−	0.614410i	0.944092	+	0.329682i	$0.106942\pi$
$588$	15.5518	+	2.12098i	0.641345	+	0.0874677i
$589$			9.06388i			0.373471i
$590$		0			0
$591$	−1.39169	+	0.803493i	−0.0572465	+	0.0330513i
$592$	−18.7679	−	3.49815i	−0.771354	−	0.143773i
$593$	8.53664	+	31.8592i	0.350558	+	1.30830i	0.885984	+	0.463717i	$0.153484\pi$
$593$	8.53664	+	31.8592i	0.350558	+	1.30830i	−0.535426	+	0.844582i	$0.679849\pi$
$594$	−20.8921	−	8.18314i	−0.857214	−	0.335758i
$595$		0			0
$596$	14.1987	+	13.1385i	0.581602	+	0.538176i
$597$	10.3038	−	2.76089i	0.421705	−	0.112996i
$598$	−39.1539	−	28.8558i	−1.60112	−	1.18000i
$599$	8.79228	+	15.2287i	0.359243	+	0.622227i	0.987835	−	0.155509i	$-0.0497016\pi$
$599$	8.79228	+	15.2287i	0.359243	+	0.622227i	−0.628592	+	0.777736i	$0.716368\pi$
$600$		0			0
$601$	−17.7704			−0.724871			−0.362436	−	0.932009i	$-0.618055\pi$
$601$	−17.7704			−0.724871			−0.362436	+	0.932009i	$0.618055\pi$
$602$	40.2751	−	2.54583i	1.64149	−	0.103760i
$603$	−3.83460	−	3.83460i	−0.156157	−	0.156157i
$604$	−2.10866	+	0.653583i	−0.0858003	+	0.0265939i
$605$		0			0
$606$	−1.77212	−	11.7032i	−0.0719875	−	0.475409i
$607$	−2.49876	−	9.32548i	−0.101421	−	0.378510i	0.896493	−	0.443057i	$-0.146106\pi$
$607$	−2.49876	−	9.32548i	−0.101421	−	0.378510i	−0.997915	+	0.0645477i	$0.979440\pi$
$608$	−6.68762	−	12.5500i	−0.271219	−	0.508970i
$609$	−4.87086	−	5.80354i	−0.197377	−	0.235171i
$610$		0			0
$611$	14.6951	+	8.48424i	0.594502	+	0.343236i
$612$	7.03725	−	4.43518i	0.284464	−	0.179281i
$613$	8.41064	+	2.25362i	0.339702	+	0.0910230i	0.424637	−	0.905364i	$-0.360402\pi$
$613$	8.41064	+	2.25362i	0.339702	+	0.0910230i	−0.0849350	+	0.996386i	$0.527068\pi$
$614$	−14.5354	−	18.2013i	−0.586599	−	0.734546i
$615$		0			0
$616$	9.13912	−	20.3714i	0.368226	−	0.820787i
$617$	−21.0055	−	21.0055i	−0.845648	−	0.845648i	0.143938	−	0.989587i	$-0.454023\pi$
$617$	−21.0055	−	21.0055i	−0.845648	−	0.845648i	−0.989587	+	0.143938i	$0.954023\pi$
$618$	−6.49407	−	0.727229i	−0.261230	−	0.0292534i
$619$	−7.01153	−	12.1443i	−0.281817	−	0.488121i	0.690015	−	0.723795i	$-0.257604\pi$
$619$	−7.01153	−	12.1443i	−0.281817	−	0.488121i	−0.971832	+	0.235673i	$0.924270\pi$
$620$		0			0
$621$	−15.9489	+	27.6243i	−0.640006	+	1.10852i
$622$	−17.0965	−	39.1128i	−0.685505	−	1.56828i
$623$	−2.29862	−	4.92796i	−0.0920923	−	0.197434i
$624$	−1.99127	−	25.6346i	−0.0797144	−	1.02620i
$625$		0			0
$626$	30.8496	−	4.67131i	1.23300	−	0.186703i
$627$	−8.12248	−	2.17641i	−0.324381	−	0.0869175i
$628$	−8.09889	+	15.3745i	−0.323181	+	0.613509i
$629$		−	11.3883i		−	0.454080i
$630$		0			0
$631$			25.9447i			1.03284i	0.856334	+	0.516422i	$0.172736\pi$
$631$			25.9447i			1.03284i	−0.856334	+	0.516422i	$0.827264\pi$
$632$	−14.9077	−	17.2517i	−0.592996	−	0.686234i
$633$	29.1823	+	7.81936i	1.15989	+	0.310792i
$634$	−0.306899	−	2.02678i	−0.0121885	−	0.0804936i
$635$		0			0
$636$	3.89803	−	4.21257i	0.154567	−	0.167039i
$637$	−36.3779	−	16.9533i	−1.44134	−	0.671713i
$638$	−9.87576	+	4.31676i	−0.390985	+	0.170902i
$639$	−7.05703	+	12.2231i	−0.279172	+	0.483540i
$640$		0			0
$641$	−2.50802	−	4.34403i	−0.0990610	−	0.171579i	0.812235	−	0.583330i	$-0.198251\pi$
$641$	−2.50802	−	4.34403i	−0.0990610	−	0.171579i	−0.911296	+	0.411751i	$0.864917\pi$
$642$	1.83799	−	16.4130i	0.0725396	−	0.647770i
$643$	5.68565	+	5.68565i	0.224220	+	0.224220i	0.810273	−	0.586053i	$-0.199319\pi$
$643$	5.68565	+	5.68565i	0.224220	+	0.224220i	−0.586053	+	0.810273i	$0.699319\pi$
$644$	−26.6889	−	17.1818i	−1.05169	−	0.677057i
$645$		0			0
$646$	6.62862	−	5.29354i	0.260800	−	0.208271i
$647$	18.8448	+	5.04946i	0.740867	+	0.198515i	0.609463	−	0.792814i	$-0.291385\pi$
$647$	18.8448	+	5.04946i	0.740867	+	0.198515i	0.131404	+	0.991329i	$0.458052\pi$
$648$	−2.03478	+	0.389308i	−0.0799337	+	0.0152934i
$649$	5.41041	+	3.12370i	0.212377	+	0.122616i
$650$		0			0
$651$	−3.65670	+	10.0502i	−0.143318	+	0.393900i
$652$	2.15400	−	0.0835344i	0.0843572	−	0.00327146i
$653$	6.95220	+	25.9460i	0.272061	+	1.01534i	0.957786	+	0.287483i	$0.0928186\pi$
$653$	6.95220	+	25.9460i	0.272061	+	1.01534i	−0.685725	+	0.727861i	$0.740515\pi$
$654$	−16.0886	+	2.43618i	−0.629115	+	0.0952620i
$655$		0			0
$656$	−28.6423	−	13.6975i	−1.11830	−	0.534796i
$657$	12.0195	+	12.0195i	0.468926	+	0.468926i
$658$	9.92022	+	4.92079i	0.386730	+	0.191832i
$659$	2.47864			0.0965543			0.0482771	−	0.998834i	$-0.484627\pi$
$659$	2.47864			0.0965543			0.0482771	+	0.998834i	$0.484627\pi$
$660$		0			0
$661$	−6.04270	−	10.4663i	−0.235034	−	0.407091i	0.724249	−	0.689539i	$-0.242187\pi$
$661$	−6.04270	−	10.4663i	−0.235034	−	0.407091i	−0.959283	+	0.282448i	$0.908853\pi$
$662$	23.8080	−	32.3046i	0.925322	−	1.25556i
$663$	14.8150	−	3.96968i	0.575368	−	0.154169i
$664$	21.5944	−	10.4537i	0.838025	−	0.405682i
$665$		0			0
$666$	4.29088	−	10.9549i	0.166268	−	0.424494i
$667$	3.96569	+	14.8001i	0.153552	+	0.573064i
$668$	−5.21957	+	3.28960i	−0.201951	+	0.127278i
$669$	3.05684	−	1.76487i	0.118184	−	0.0682337i
$670$		0			0
$671$		−	5.67177i		−	0.218956i
$672$	−2.35226	−	16.6138i	−0.0907405	−	0.640890i
$673$	−34.0874	+	34.0874i	−1.31397	+	1.31397i	−0.395511	+	0.918461i	$0.629432\pi$
$673$	−34.0874	+	34.0874i	−1.31397	+	1.31397i	−0.918461	+	0.395511i	$0.870568\pi$
$674$	−18.4145	+	14.7056i	−0.709301	+	0.566439i
$675$		0			0
$676$	−8.79142	+	38.7610i	−0.338132	+	1.49081i
$677$	−32.6524	+	8.74919i	−1.25493	+	0.336259i	−0.824241	−	0.566240i	$-0.808398\pi$
$677$	−32.6524	+	8.74919i	−1.25493	+	0.336259i	−0.430693	+	0.902498i	$0.641731\pi$
$678$	15.1123	−	6.60567i	0.580384	−	0.253689i
$679$	−4.31152	−	24.4357i	−0.165461	−	0.937756i
$680$		0			0
$681$	−4.52124	+	7.83101i	−0.173254	+	0.300085i
$682$	12.2469	+	9.02578i	0.468960	+	0.345615i
$683$	1.93944	−	7.23810i	0.0742107	−	0.276958i	−0.918842	−	0.394625i	$-0.870875\pi$
$683$	1.93944	−	7.23810i	0.0742107	−	0.276958i	0.993053	+	0.117666i	$0.0375413\pi$
$684$	8.37089	−	2.59457i	0.320069	−	0.0992058i
$685$		0			0
$686$	−24.3908	−	9.54400i	−0.931246	−	0.364392i
$687$	1.92874	−	1.92874i	0.0735862	−	0.0735862i
$688$	−14.3597	−	40.6819i	−0.547458	−	1.55098i
$689$	−12.7095	+	7.33783i	−0.484193	+	0.279549i
$690$		0			0
$691$	16.5249	+	9.54066i	0.628637	+	0.362944i	0.780224	−	0.625500i	$-0.215105\pi$
$691$	16.5249	+	9.54066i	0.628637	+	0.362944i	−0.151587	+	0.988444i	$0.548438\pi$
$692$	1.82828	+	47.1437i	0.0695009	+	1.79213i
$693$	11.2722	+	7.89102i	0.428197	+	0.299755i
$694$	−8.23405	+	21.0221i	−0.312560	+	0.797987i
$695$		0			0
$696$	−4.54912	+	6.70170i	−0.172434	+	0.254027i
$697$	4.90178	−	18.2937i	0.185668	−	0.692923i
$698$	10.5780	+	1.18457i	0.400385	+	0.0448365i
$699$	11.7363			0.443909
$700$		0			0
$701$	−30.0384			−1.13454			−0.567268	−	0.823533i	$-0.692000\pi$
$701$	−30.0384			−1.13454			−0.567268	+	0.823533i	$0.692000\pi$
$702$	42.8490	+	4.79839i	1.61723	+	0.181103i
$703$	3.10535	−	11.5893i	0.117121	−	0.437100i
$704$	−23.6168	−	3.46106i	−0.890093	−	0.130443i
$705$		0			0
$706$	−2.89170	+	7.38272i	−0.108831	+	0.277852i
$707$	−1.71926	+	19.6768i	−0.0646594	+	0.740023i
$708$	4.69150	−	0.181941i	0.176317	−	0.00683777i
$709$	23.7012	+	13.6839i	0.890117	+	0.513909i	0.873981	−	0.485960i	$-0.161530\pi$
$709$	23.7012	+	13.6839i	0.890117	+	0.513909i	0.0161363	+	0.999870i	$0.494863\pi$
$710$		0			0
$711$	12.1687	−	7.02562i	0.456363	−	0.263481i
$712$	−4.39843	+	3.80082i	−0.164838	+	0.142442i
$713$	15.2933	−	15.2933i	0.572737	−	0.572737i
$714$	9.48558	−	3.19537i	0.354989	−	0.119584i
$715$		0			0
$716$	−4.18215	−	13.4929i	−0.156294	−	0.504254i
$717$	−3.74462	+	13.9751i	−0.139846	+	0.521911i
$718$	41.4718	+	30.5640i	1.54771	+	1.14064i
$719$	21.7523	−	37.6760i	0.811223	−	1.40508i	−0.100786	−	0.994908i	$-0.532136\pi$
$719$	21.7523	−	37.6760i	0.811223	−	1.40508i	0.912009	−	0.410171i	$-0.134531\pi$
$720$		0			0
$721$	10.2472	+	3.72838i	0.381627	+	0.138852i
$722$	−16.4317	+	7.18238i	−0.611523	+	0.267300i
$723$	2.93894	−	0.787488i	0.109300	−	0.0292870i
$724$	4.63076	+	1.05031i	0.172101	+	0.0390344i
$725$		0			0
$726$	2.59916	−	2.07565i	0.0964637	−	0.0770348i
$727$	14.9542	−	14.9542i	0.554620	−	0.554620i	−0.373151	−	0.927771i	$-0.621723\pi$
$727$	14.9542	−	14.9542i	0.554620	−	0.554620i	0.927771	+	0.373151i	$0.121723\pi$
$728$	−6.83183	+	42.3580i	−0.253204	+	1.56989i
$729$		−	19.1618i		−	0.709695i
$730$		0			0
$731$	22.2872	−	12.8675i	0.824322	−	0.475922i
$732$	−2.27266	−	3.60601i	−0.0839999	−	0.133282i
$733$	8.22383	+	30.6917i	0.303754	+	1.13363i	0.934013	+	0.357240i	$0.116282\pi$
$733$	8.22383	+	30.6917i	0.303754	+	1.13363i	−0.630259	+	0.776385i	$0.717051\pi$
$734$	16.8636	−	43.0539i	0.622446	−	1.58915i
$735$		0			0
$736$	−9.89144	+	32.4592i	−0.364603	+	1.19646i
$737$	−8.96619	+	2.40248i	−0.330274	+	0.0884966i
$738$	11.6080	−	15.7507i	0.427296	−	0.579791i
$739$	0.495453	+	0.858149i	0.0182255	+	0.0315675i	0.874994	−	0.484133i	$-0.160865\pi$
$739$	0.495453	+	0.858149i	0.0182255	+	0.0315675i	−0.856769	+	0.515701i	$0.827532\pi$
$740$		0			0
$741$	16.1591			0.593619
$742$	−7.97559	+	5.30236i	−0.292793	+	0.194656i
$743$	9.00016	+	9.00016i	0.330184	+	0.330184i	0.852656	−	0.522472i	$-0.174990\pi$
$743$	9.00016	+	9.00016i	0.330184	+	0.330184i	−0.522472	+	0.852656i	$0.674990\pi$
$744$	11.4030	+	0.831117i	0.418054	+	0.0304702i
$745$		0			0
$746$	−36.5684	+	5.53727i	−1.33886	+	0.202734i
$747$	3.82673	+	14.2815i	0.140013	+	0.522534i
$748$	−0.551767	−	14.2278i	−0.0201746	−	0.520218i
$749$	−9.42304	+	25.8987i	−0.344310	+	0.946318i
$750$		0			0
$751$	−11.3279	−	6.54015i	−0.413360	−	0.238653i	0.278872	−	0.960328i	$-0.410039\pi$
$751$	−11.3279	−	6.54015i	−0.413360	−	0.238653i	−0.692232	+	0.721675i	$0.743373\pi$
$752$	2.16917	−	11.6378i	0.0791015	−	0.424385i
$753$	−3.41509	−	0.915071i	−0.124453	−	0.0333470i
$754$	16.1840	−	12.9244i	0.589388	−	0.470678i
$755$		0			0
$756$	28.1051	+	1.36112i	1.02217	+	0.0495035i
$757$	−3.92981	−	3.92981i	−0.142831	−	0.142831i	0.632076	−	0.774907i	$-0.282203\pi$
$757$	−3.92981	−	3.92981i	−0.142831	−	0.142831i	−0.774907	+	0.632076i	$0.782203\pi$
$758$	3.20701	−	28.6382i	0.116484	−	1.04019i
$759$	10.0327	+	17.3771i	0.364162	+	0.630748i
$760$		0			0
$761$	11.1617	−	19.3326i	0.404612	−	0.700808i	−0.589665	−	0.807648i	$-0.700740\pi$
$761$	11.1617	−	19.3326i	0.404612	−	0.700808i	0.994276	+	0.106840i	$0.0340734\pi$
$762$	−27.4964	+	12.0189i	−0.996091	+	0.435397i
$763$	27.0502	+	2.36351i	0.979282	+	0.0855646i
$764$	−9.27134	−	8.57908i	−0.335425	−	0.310380i
$765$		0			0
$766$	5.40621	+	35.7029i	0.195334	+	1.29000i
$767$	−11.5962	−	3.10719i	−0.418714	−	0.112194i
$768$	−16.4020	+	7.26271i	−0.591856	+	0.262071i
$769$		−	27.9731i		−	1.00873i	−0.863489	−	0.504367i	$-0.831726\pi$
$769$		−	27.9731i		−	1.00873i	0.863489	−	0.504367i	$-0.168274\pi$
$770$		0			0
$771$			18.4608i			0.664851i
$772$	−37.3752	−	19.6883i	−1.34516	−	0.708598i
$773$	−43.0144	−	11.5257i	−1.54712	−	0.414550i	−0.618562	−	0.785736i	$-0.712285\pi$
$773$	−43.0144	−	11.5257i	−1.54712	−	0.414550i	−0.928559	+	0.371186i	$0.878951\pi$
$774$	26.2874	−	3.98049i	0.944880	−	0.143076i
$775$		0			0
$776$	−23.8759	+	11.5582i	−0.857094	+	0.414914i
$777$	8.11886	−	11.5977i	0.291263	−	0.416066i
$778$	10.2233	+	23.3886i	0.366524	+	0.838523i
$779$	9.97667	−	17.2801i	0.357451	−	0.619124i
$780$		0			0
$781$	12.0796	+	20.9224i	0.432241	+	0.748663i
$782$	−20.1160	−	2.25266i	−0.719346	−	0.0805548i
$783$	−9.60453	−	9.60453i	−0.343238	−	0.343238i
$784$	−2.70572	+	27.8690i	−0.0966327	+	0.995320i
$785$		0			0
$786$	−15.1935	−	19.0254i	−0.541933	−	0.678614i
$787$	−39.0901	−	10.4742i	−1.39341	−	0.373363i	−0.517437	−	0.855722i	$-0.673114\pi$
$787$	−39.0901	−	10.4742i	−1.39341	−	0.373363i	−0.875974	+	0.482358i	$0.839780\pi$
$788$	−1.52850	−	2.42526i	−0.0544505	−	0.0863962i
$789$	28.3405	+	16.3624i	1.00895	+	0.582518i
$790$		0			0
$791$	−27.1031	+	4.78217i	−0.963677	+	0.170034i
$792$	4.82998	−	13.8943i	0.171626	−	0.493711i
$793$	2.82089	+	10.5277i	0.100173	+	0.373850i
$794$	6.37029	+	42.0697i	0.226073	+	1.49300i
$795$		0			0
$796$	5.63381	+	18.1764i	0.199685	+	0.644247i
$797$	−3.10654	−	3.10654i	−0.110039	−	0.110039i	0.649943	−	0.759983i	$-0.274793\pi$
$797$	−3.10654	−	3.10654i	−0.110039	−	0.110039i	−0.759983	+	0.649943i	$0.774793\pi$
$798$	10.5244	−	0.665257i	0.372559	−	0.0235498i
$799$	7.06174			0.249826
$800$		0			0
$801$	−1.79123	−	3.10250i	−0.0632900	−	0.109622i
$802$	−5.57337	−	4.10748i	−0.196803	−	0.145040i
$803$	28.1045	−	7.53057i	0.991786	−	0.265748i
$804$	−4.73787	+	5.12018i	−0.167092	+	0.180575i
$805$		0			0
$806$	−27.2213	−	10.6622i	−0.958830	−	0.375560i
$807$	−1.77314	−	6.61744i	−0.0624174	−	0.232945i
$808$	20.7394	−	3.96799i	0.729608	−	0.139594i
$809$	−26.5415	+	15.3237i	−0.933148	+	0.538753i	−0.887806	−	0.460218i	$-0.847771\pi$
$809$	−26.5415	+	15.3237i	−0.933148	+	0.538753i	−0.0453422	+	0.998972i	$0.514438\pi$
$810$		0			0
$811$		−	47.0428i		−	1.65190i	−0.563747	−	0.825948i	$-0.690641\pi$
$811$		−	47.0428i		−	1.65190i	0.563747	−	0.825948i	$-0.309359\pi$
$812$	10.0086	−	9.08391i	0.351231	−	0.318783i
$813$	−17.4565	+	17.4565i	−0.612225	+	0.612225i
$814$	−12.5670	−	15.7365i	−0.440473	−	0.551565i
$815$		0			0
$816$	−6.05182	−	8.82466i	−0.211856	−	0.308925i
$817$	26.1894	−	7.01744i	0.916253	−	0.245509i
$818$	−18.9998	−	43.4672i	−0.664312	−	1.51979i
$819$	−24.8478	−	9.04066i	−0.868251	−	0.315906i
$820$		0			0
$821$	0.415401	−	0.719496i	0.0144976	−	0.0251106i	−0.858686	−	0.512503i	$-0.828718\pi$
$821$	0.415401	−	0.719496i	0.0144976	−	0.0251106i	0.873183	+	0.487392i	$0.162052\pi$
$822$	4.43231	−	6.01413i	0.154594	−	0.209767i
$823$	0.0598810	−	0.223479i	0.00208732	−	0.00778999i	−0.964874	−	0.262712i	$-0.915383\pi$
$823$	0.0598810	−	0.223479i	0.00208732	−	0.00778999i	0.966962	+	0.254922i	$0.0820498\pi$
$824$	0.847407	−	11.6265i	0.0295208	−	0.405028i
$825$		0			0
$826$	−7.68050	−	1.54630i	−0.267239	−	0.0538027i
$827$	0.00150949	−	0.00150949i	5.24902e−5	−	5.24902e-5i	−0.707081	−	0.707133i	$-0.749988\pi$
$827$	0.00150949	−	0.00150949i	5.24902e−5	−	5.24902e-5i	0.707133	+	0.707081i	$0.249988\pi$
$828$	−18.5018	−	9.74626i	−0.642981	−	0.338706i
$829$	36.8314	−	21.2646i	1.27921	−	0.738551i	0.302506	−	0.953148i	$-0.402177\pi$
$829$	36.8314	−	21.2646i	1.27921	−	0.738551i	0.976703	+	0.214596i	$0.0688435\pi$
$830$		0			0
$831$	15.9779	+	9.22484i	0.554267	+	0.320006i
$832$	45.5580	−	5.32172i	1.57944	−	0.184497i
$833$	−16.6387	+	1.45949i	−0.576498	+	0.0505683i
$834$	−15.2155	−	5.95970i	−0.526870	−	0.206368i
$835$		0			0
$836$	3.31812	−	14.6294i	0.114760	−	0.505970i
$837$	−4.96227	+	18.5194i	−0.171521	+	0.640126i
$838$	5.72464	−	51.1204i	0.197754	−	1.76592i
$839$	−49.4733			−1.70801			−0.854004	−	0.520267i	$-0.825832\pi$
$839$	−49.4733			−1.70801			−0.854004	+	0.520267i	$0.825832\pi$
$840$		0			0
$841$	22.4754			0.775014
$842$	5.23262	−	46.7267i	0.180328	−	1.61031i
$843$	−1.97104	+	7.35602i	−0.0678862	+	0.253355i
$844$	−11.9213	+	52.5603i	−0.410347	+	1.80920i
$845$		0			0
$846$	6.79303	+	2.66073i	0.233549	+	0.0914778i
$847$	−5.03023	+	2.34633i	−0.172841	+	0.0806207i
$848$	7.77872	+	6.65734i	0.267122	+	0.228614i
$849$	12.6655	+	7.31245i	0.434680	+	0.250963i
$850$		0			0
$851$	−24.7940	+	14.3148i	−0.849928	+	0.490706i
$852$	16.0635	+	8.46185i	0.550327	+	0.289898i
$853$	−9.16674	+	9.16674i	−0.313863	+	0.313863i	−0.846404	−	0.532541i	$-0.821237\pi$
$853$	−9.16674	+	9.16674i	−0.313863	+	0.313863i	0.532541	+	0.846404i	$0.321237\pi$
$854$	2.27066	+	6.74055i	0.0777004	+	0.230657i
$855$		0			0
$856$	29.3846	+	2.14172i	1.00434	+	0.0732026i
$857$	−5.81720	+	21.7101i	−0.198712	+	0.741602i	0.792563	+	0.609790i	$0.208746\pi$
$857$	−5.81720	+	21.7101i	−0.198712	+	0.741602i	−0.991275	+	0.131812i	$0.957920\pi$
$858$	16.0912	−	21.8338i	0.549343	−	0.745395i
$859$	−4.05858	+	7.02967i	−0.138477	+	0.239849i	−0.926920	−	0.375258i	$-0.877554\pi$
$859$	−4.05858	+	7.02967i	−0.138477	+	0.239849i	0.788443	+	0.615107i	$0.210887\pi$
$860$		0			0
$861$	18.0338	−	15.1356i	0.614590	−	0.515821i
$862$	17.6237	+	40.3191i	0.600267	+	1.37328i
$863$	0.470041	−	0.125947i	0.0160004	−	0.00428729i	−0.250810	−	0.968036i	$-0.580697\pi$
$863$	0.470041	−	0.125947i	0.0160004	−	0.00428729i	0.266810	+	0.963749i	$0.414030\pi$
$864$	−6.79341	−	29.3037i	−0.231116	−	0.996931i
$865$		0			0
$866$	−8.91856	−	11.1679i	−0.303065	−	0.379501i
$867$	−8.96335	+	8.96335i	−0.304411	+	0.304411i
$868$	−18.1682	−	5.82360i	−0.616668	−	0.197666i
$869$		−	24.0516i		−	0.815895i
$870$		0			0
$871$	15.4478	−	8.91879i	0.523428	−	0.302202i
$872$	−5.45489	−	28.5109i	−0.184726	−	0.965500i
$873$	−4.23103	−	15.7904i	−0.143199	−	0.534424i
$874$	−19.8569	−	7.77766i	−0.671670	−	0.263083i
$875$		0			0
$876$	14.8508	−	16.0492i	0.501763	−	0.542251i
$877$	17.2678	−	4.62691i	0.583094	−	0.156240i	0.0447988	−	0.998996i	$-0.485735\pi$
$877$	17.2678	−	4.62691i	0.583094	−	0.156240i	0.538295	+	0.842757i	$0.319069\pi$
$878$	−0.634262	−	0.467440i	−0.0214053	−	0.0157753i
$879$	1.02138	+	1.76909i	0.0344504	+	0.0596698i
$880$		0			0
$881$	−5.27459			−0.177705			−0.0888527	−	0.996045i	$-0.528320\pi$
$881$	−5.27459			−0.177705			−0.0888527	+	0.996045i	$0.528320\pi$
$882$	−16.5555	−	4.86521i	−0.557453	−	0.163820i
$883$	−5.20270	−	5.20270i	−0.175085	−	0.175085i	0.614124	−	0.789209i	$-0.289509\pi$
$883$	−5.20270	−	5.20270i	−0.175085	−	0.175085i	−0.789209	+	0.614124i	$0.789509\pi$
$884$	8.10044	+	26.1346i	0.272447	+	0.879001i
$885$		0			0
$886$	−5.16404	−	34.1036i	−0.173489	−	1.14573i
$887$	−11.5714	−	43.1849i	−0.388528	−	1.45001i	−0.832529	−	0.553981i	$-0.813108\pi$
$887$	−11.5714	−	43.1849i	−0.388528	−	1.45001i	0.444001	−	0.896026i	$-0.353559\pi$
$888$	−14.2954	−	4.96944i	−0.479724	−	0.166764i
$889$	49.3135	−	8.70105i	1.65392	−	0.291824i
$890$		0			0
$891$	−1.89259	−	1.09269i	−0.0634040	−	0.0366063i
$892$	3.35734	+	5.32706i	0.112412	+	0.178363i
$893$	7.18643	+	1.92560i	0.240485	+	0.0644377i
$894$	9.56986	+	11.9835i	0.320064	+	0.400787i
$895$		0			0
$896$	29.4528	−	5.34162i	0.983949	−	0.178451i
$897$	−27.2648	−	27.2648i	−0.910346	−	0.910346i
$898$	−12.1491	−	1.36050i	−0.405421	−	0.0454005i
$899$	4.60486	+	7.97585i	0.153581	+	0.266009i
$900$		0			0
$901$	−3.05377	+	5.28929i	−0.101736	+	0.176212i
$902$	−13.4138	−	30.6877i	−0.446631	−	1.02179i
$903$	31.8706	+	2.78469i	1.06059	+	0.0926686i
$904$	12.8199	+	26.4822i	0.426382	+	0.880785i
$905$		0			0
$906$	−1.73039	+	0.262019i	−0.0574882	+	0.00870499i
$907$	9.45206	+	2.53267i	0.313851	+	0.0840960i	0.412306	−	0.911045i	$-0.364723\pi$
$907$	9.45206	+	2.53267i	0.313851	+	0.0840960i	−0.0984553	+	0.995141i	$0.531390\pi$
$908$	−14.2720	−	7.51811i	−0.473632	−	0.249497i
$909$			13.0129i			0.431610i
$910$		0			0
$911$			5.81294i			0.192591i	0.995353	+	0.0962957i	$0.0306994\pi$
$911$			5.81294i			0.192591i	−0.995353	+	0.0962957i	$0.969301\pi$
$912$	−3.75237	−	10.6307i	−0.124253	−	0.352017i
$913$	24.4458	+	6.55024i	0.809038	+	0.216781i
$914$	0.578756	+	3.82213i	0.0191435	+	0.126425i
$915$		0			0
$916$	3.57148	+	3.30481i	0.118005	+	0.109194i
$917$	17.1747	+	36.8205i	0.567160	+	1.21592i
$918$	16.4418	−	7.18681i	0.542660	−	0.237200i
$919$	−10.6688	+	18.4789i	−0.351930	+	0.609561i	−0.986588	−	0.163232i	$-0.947808\pi$
$919$	−10.6688	+	18.4789i	−0.351930	+	0.609561i	0.634657	+	0.772794i	$0.281141\pi$
$920$		0			0
$921$	−9.23283	−	15.9917i	−0.304232	−	0.526946i
$922$	−6.07484	+	54.2476i	−0.200064	+	1.78655i
$923$	−32.8275	−	32.8275i	−1.08053	−	1.08053i
$924$	9.58127	−	14.8828i	0.315201	−	0.489609i
$925$		0			0
$926$	21.1065	−	16.8554i	0.693604	−	0.553903i
$927$	6.93927	+	1.85937i	0.227916	+	0.0610698i
$928$	−12.2608	−	7.64588i	−0.402481	−	0.250988i
$929$	−12.5925	−	7.27026i	−0.413145	−	0.238529i	0.278995	−	0.960293i	$-0.409999\pi$
$929$	−12.5925	−	7.27026i	−0.413145	−	0.238529i	−0.692140	+	0.721763i	$0.743332\pi$
$930$		0			0
$931$	−17.3305	−	3.05180i	−0.567984	−	0.100019i
$932$	0.811338	+	20.9210i	0.0265763	+	0.685290i
$933$	−8.75834	−	32.6866i	−0.286735	−	1.07011i
$934$	−18.6850	+	2.82933i	−0.611393	+	0.0925784i
$935$		0			0
$936$	−2.05481	+	28.1922i	−0.0671637	+	0.921491i
$937$	−5.05360	−	5.05360i	−0.165094	−	0.165094i	0.619725	−	0.784819i	$-0.287244\pi$
$937$	−5.05360	−	5.05360i	−0.165094	−	0.165094i	−0.784819	+	0.619725i	$0.787244\pi$
$938$	9.69395	−	6.44477i	0.316519	−	0.210429i
$939$	24.7350			0.807195
$940$		0			0
$941$	1.44742	+	2.50700i	0.0471845	+	0.0817259i	0.888653	−	0.458580i	$-0.151642\pi$
$941$	1.44742	+	2.50700i	0.0471845	+	0.0817259i	−0.841469	+	0.540306i	$0.818308\pi$
$942$	−8.17284	+	11.0896i	−0.266286	+	0.361319i
$943$	−45.9897	+	12.3229i	−1.49763	+	0.401289i
$944$	0.648650	+	8.35040i	0.0211118	+	0.271782i
$945$		0			0
$946$	16.5975	−	42.3746i	0.539632	−	1.37772i
$947$	8.72837	+	32.5747i	0.283634	+	1.05854i	0.949832	+	0.312761i	$0.101254\pi$
$947$	8.72837	+	32.5747i	0.283634	+	1.05854i	−0.666198	+	0.745775i	$0.732079\pi$
$948$	−9.63740	−	15.2916i	−0.313008	−	0.496647i
$949$	−48.4211	+	27.9559i	−1.57181	+	0.907487i
$950$		0			0
$951$		−	1.62505i		−	0.0526960i
$952$	6.35175	+	16.6879i	0.205861	+	0.540859i
$953$	−23.9098	+	23.9098i	−0.774513	+	0.774513i	−0.978892	−	0.204379i	$-0.934483\pi$
$953$	−23.9098	+	23.9098i	−0.774513	+	0.774513i	0.204379	+	0.978892i	$0.434483\pi$
$954$	−4.93047	+	3.93742i	−0.159630	+	0.127479i
$955$		0			0
$956$	−25.1707	−	5.70899i	−0.814077	−	0.184642i
$957$	−8.25317	+	2.21143i	−0.266787	+	0.0714854i
$958$	10.1497	−	4.43650i	0.327922	−	0.143337i
$959$	−9.54923	+	8.01459i	−0.308361	+	0.258805i
$960$		0			0
$961$	−9.00006	+	15.5886i	−0.290325	+	0.502857i
$962$	31.1530	+	22.9592i	1.00441	+	0.740236i
$963$	−4.69935	+	17.5382i	−0.151435	+	0.565161i
$964$	1.60693	+	5.18447i	0.0517558	+	0.166980i
$965$		0			0
$966$	−18.8800	−	16.6351i	−0.607455	−	0.535225i
$967$	2.13618	−	2.13618i	0.0686949	−	0.0686949i	−0.671925	−	0.740620i	$-0.734532\pi$
$967$	2.13618	−	2.13618i	0.0686949	−	0.0686949i	0.740620	+	0.671925i	$0.234532\pi$
$968$	3.87970	+	4.48972i	0.124698	+	0.144305i
$969$	5.82393	−	3.36245i	0.187092	−	0.108017i
$970$		0			0
$971$	14.3494	+	8.28465i	0.460495	+	0.265867i	0.712252	−	0.701923i	$-0.247675\pi$
$971$	14.3494	+	8.28465i	0.460495	+	0.265867i	−0.251757	+	0.967790i	$0.581008\pi$
$972$	30.2404	−	1.17276i	0.969963	−	0.0376162i
$973$	22.3387	+	15.6380i	0.716147	+	0.501331i
$974$	−1.25836	+	3.21269i	−0.0403206	+	0.102941i
$975$		0			0
$976$	6.27089	−	4.30048i	0.200726	−	0.137655i
$977$	0.0810094	−	0.302331i	0.00259172	−	0.00967243i	−0.964618	−	0.263652i	$-0.915073\pi$
$977$	0.0810094	−	0.302331i	0.00259172	−	0.00967243i	0.967210	+	0.253980i	$0.0817396\pi$
$978$	1.69826	+	0.190178i	0.0543045	+	0.00608121i
$979$	−6.13213			−0.195984
$980$		0			0
$981$	17.8891			0.571156
$982$	47.1108	+	5.27563i	1.50337	+	0.168352i
$983$	−14.9395	+	55.7548i	−0.476495	+	1.77830i	0.139142	+	0.990272i	$0.455566\pi$
$983$	−14.9395	+	55.7548i	−0.476495	+	1.77830i	−0.615636	+	0.788030i	$0.711101\pi$
$984$	−20.8247	−	14.1358i	−0.663868	−	0.450634i
$985$		0			0
$986$	3.14357	−	8.02574i	0.100112	−	0.255592i
$987$	7.19163	+	5.03442i	0.228912	+	0.160247i
$988$	1.11708	+	28.8049i	0.0355391	+	0.916405i
$989$	−56.0292	−	32.3485i	−1.78162	−	1.02862i
$990$		0			0
$991$	19.0262	−	10.9848i	0.604386	−	0.348942i	−0.166379	−	0.986062i	$-0.553208\pi$
$991$	19.0262	−	10.9848i	0.604386	−	0.348942i	0.770765	+	0.637120i	$0.219874\pi$
$992$	−0.693241	+	20.3842i	−0.0220104	+	0.647199i
$993$	22.4953	−	22.4953i	0.713868	−	0.713868i
$994$	−22.7320	−	20.0290i	−0.721015	−	0.635283i
$995$		0			0
$996$	18.1669	−	5.63084i	0.575639	−	0.178420i
$997$	2.18286	−	8.14653i	0.0691317	−	0.258003i	−0.922707	−	0.385502i	$-0.874028\pi$
$997$	2.18286	−	8.14653i	0.0691317	−	0.258003i	0.991839	+	0.127499i	$0.0406949\pi$
$998$	−23.5571	−	17.3612i	−0.745688	−	0.549559i
$999$	12.6898	−	21.9794i	0.401488	−	0.695397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.be.e.107.9		72
4.3	odd	2	inner	700.2.be.e.107.6		72
5.2	odd	4		140.2.w.b.23.2	✓	72
5.3	odd	4	inner	700.2.be.e.443.17		72
5.4	even	2		140.2.w.b.107.10	yes	72
7.4	even	3	inner	700.2.be.e.207.5		72
20.3	even	4	inner	700.2.be.e.443.5		72
20.7	even	4		140.2.w.b.23.14	yes	72
20.19	odd	2		140.2.w.b.107.13	yes	72
28.11	odd	6	inner	700.2.be.e.207.17		72
35.2	odd	12		980.2.k.k.883.13		36
35.4	even	6		140.2.w.b.67.14	yes	72
35.9	even	6		980.2.k.k.687.3		36
35.12	even	12		980.2.k.j.883.13		36
35.17	even	12		980.2.x.m.263.13		72
35.18	odd	12	inner	700.2.be.e.543.6		72
35.19	odd	6		980.2.k.j.687.3		36
35.24	odd	6		980.2.x.m.67.14		72
35.27	even	4		980.2.x.m.863.2		72
35.32	odd	12		140.2.w.b.123.13	yes	72
35.34	odd	2		980.2.x.m.667.10		72
140.19	even	6		980.2.k.j.687.13		36
140.27	odd	4		980.2.x.m.863.14		72
140.39	odd	6		140.2.w.b.67.2	yes	72
140.47	odd	12		980.2.k.j.883.3		36
140.59	even	6		980.2.x.m.67.2		72
140.67	even	12		140.2.w.b.123.10	yes	72
140.79	odd	6		980.2.k.k.687.13		36
140.87	odd	12		980.2.x.m.263.10		72
140.107	even	12		980.2.k.k.883.3		36
140.123	even	12	inner	700.2.be.e.543.9		72
140.139	even	2		980.2.x.m.667.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.2	✓	72	5.2	odd	4
140.2.w.b.23.14	yes	72	20.7	even	4
140.2.w.b.67.2	yes	72	140.39	odd	6
140.2.w.b.67.14	yes	72	35.4	even	6
140.2.w.b.107.10	yes	72	5.4	even	2
140.2.w.b.107.13	yes	72	20.19	odd	2
140.2.w.b.123.10	yes	72	140.67	even	12
140.2.w.b.123.13	yes	72	35.32	odd	12
700.2.be.e.107.6		72	4.3	odd	2	inner
700.2.be.e.107.9		72	1.1	even	1	trivial
700.2.be.e.207.5		72	7.4	even	3	inner
700.2.be.e.207.17		72	28.11	odd	6	inner
700.2.be.e.443.5		72	20.3	even	4	inner
700.2.be.e.443.17		72	5.3	odd	4	inner
700.2.be.e.543.6		72	35.18	odd	12	inner
700.2.be.e.543.9		72	140.123	even	12	inner
980.2.k.j.687.3		36	35.19	odd	6
980.2.k.j.687.13		36	140.19	even	6
980.2.k.j.883.3		36	140.47	odd	12
980.2.k.j.883.13		36	35.12	even	12
980.2.k.k.687.3		36	35.9	even	6
980.2.k.k.687.13		36	140.79	odd	6
980.2.k.k.883.3		36	140.107	even	12
980.2.k.k.883.13		36	35.2	odd	12
980.2.x.m.67.2		72	140.59	even	6
980.2.x.m.67.14		72	35.24	odd	6
980.2.x.m.263.10		72	140.87	odd	12
980.2.x.m.263.13		72	35.17	even	12
980.2.x.m.667.10		72	35.34	odd	2
980.2.x.m.667.13		72	140.139	even	2
980.2.x.m.863.2		72	35.27	even	4
980.2.x.m.863.14		72	140.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.157385 + 1.40543i) q^{2} +(-0.290169 + 1.08292i) q^{3} +(-1.95046 - 0.442386i) q^{4} +(-1.47630 - 0.578247i) q^{6} +(2.16744 + 1.51730i) q^{7} +(0.928715 - 2.67161i) q^{8} +(1.50955 + 0.871538i) q^{9} +O(q^{10})\)	\(q+(-0.157385 + 1.40543i) q^{2} +(-0.290169 + 1.08292i) q^{3} +(-1.95046 - 0.442386i) q^{4} +(-1.47630 - 0.578247i) q^{6} +(2.16744 + 1.51730i) q^{7} +(0.928715 - 2.67161i) q^{8} +(1.50955 + 0.871538i) q^{9} +(2.58391 - 1.49182i) q^{11} +(1.04503 - 1.98383i) q^{12} +(-4.05418 + 4.05418i) q^{13} +(-2.47357 + 2.80739i) q^{14} +(3.60859 + 1.72571i) q^{16} +(-0.617565 + 2.30478i) q^{17} +(-1.46247 + 1.98440i) q^{18} +(-1.25694 + 2.17708i) q^{19} +(-2.27204 + 1.90691i) q^{21} +(1.68998 + 3.86629i) q^{22} +(5.79414 - 1.55254i) q^{23} +(2.62367 + 1.78095i) q^{24} +(-5.05979 - 6.33592i) q^{26} +(-3.76010 + 3.76010i) q^{27} +(-3.55628 - 3.91827i) q^{28} +2.55433i q^{29} +(3.12248 - 1.80277i) q^{31} +(-2.99330 + 4.80001i) q^{32} +(0.865758 + 3.23105i) q^{33} +(-3.14202 - 1.23068i) q^{34} +(-2.55876 - 2.36770i) q^{36} +(-4.61014 + 1.23528i) q^{37} +(-2.86191 - 2.10918i) q^{38} +(-3.21397 - 5.56676i) q^{39} -7.93727 q^{41} +(-2.32244 - 3.49331i) q^{42} +(-7.62646 - 7.62646i) q^{43} +(-5.69977 + 1.76665i) q^{44} +(1.27007 + 8.38760i) q^{46} +(-0.765987 - 2.85870i) q^{47} +(-2.91592 + 3.40708i) q^{48} +(2.39563 + 6.57731i) q^{49} +(-2.31671 - 1.33755i) q^{51} +(9.70103 - 6.11400i) q^{52} +(2.47243 + 0.662485i) q^{53} +(-4.69277 - 5.87634i) q^{54} +(6.06656 - 4.38142i) q^{56} +(-1.99289 - 1.99289i) q^{57} +(-3.58993 - 0.402012i) q^{58} +(1.04694 + 1.81336i) q^{59} +(0.950478 - 1.64628i) q^{61} +(2.04223 + 4.67216i) q^{62} +(1.94948 + 4.17944i) q^{63} +(-6.27498 - 4.96233i) q^{64} +(-4.67727 + 0.708243i) q^{66} +(-3.00512 - 0.805219i) q^{67} +(2.22414 - 4.22219i) q^{68} +6.72512i q^{69} +8.09721i q^{71} +(3.73035 - 3.22351i) q^{72} +(9.41954 + 2.52396i) q^{73} +(-1.01054 - 6.67364i) q^{74} +(3.41472 - 3.69026i) q^{76} +(7.86400 + 0.687116i) q^{77} +(8.32952 - 3.64089i) q^{78} +(4.03058 - 6.98117i) q^{79} +(-0.366226 - 0.634322i) q^{81} +(1.24921 - 11.1553i) q^{82} +(5.99790 + 5.99790i) q^{83} +(5.27511 - 2.71422i) q^{84} +(11.9187 - 9.51816i) q^{86} +(-2.76614 - 0.741186i) q^{87} +(-1.58584 - 8.28866i) q^{88} +(-1.77990 - 1.02763i) q^{89} +(-14.9386 + 2.63582i) q^{91} +(-11.9881 + 0.464910i) q^{92} +(1.04621 + 3.90452i) q^{93} +(4.13826 - 0.626624i) q^{94} +(-4.32949 - 4.63434i) q^{96} +(-6.63160 - 6.63160i) q^{97} +(-9.62097 + 2.33171i) q^{98} +5.20071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8}+O(q^{10}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8	\( 72 q - 2 q^{2} - 16 q^{6} + 4 q^{8} - 10 q^{12} - 28 q^{16} - 4 q^{17} + 20 q^{18} + 4 q^{21} + 16 q^{22} - 4 q^{26} - 42 q^{28} + 38 q^{32} + 64 q^{33} + 16 q^{36} + 4 q^{37} - 12 q^{38} - 40 q^{41} - 78 q^{42} - 28 q^{46} - 12 q^{48} - 48 q^{52} + 24 q^{53} + 36 q^{56} + 16 q^{57} - 30 q^{58} - 20 q^{61} - 56 q^{62} + 44 q^{66} + 12 q^{68} - 44 q^{72} + 12 q^{73} + 112 q^{76} - 16 q^{77} - 64 q^{78} - 52 q^{81} + 34 q^{82} + 64 q^{86} - 16 q^{88} - 44 q^{92} - 12 q^{93} - 48 q^{96} + 24 q^{97} + 90 q^{98}+O(q^{100}) \) 72 * q - 2 * q^2 - 16 * q^6 + 4 * q^8 - 10 * q^12 - 28 * q^16 - 4 * q^17 + 20 * q^18 + 4 * q^21 + 16 * q^22 - 4 * q^26 - 42 * q^28 + 38 * q^32 + 64 * q^33 + 16 * q^36 + 4 * q^37 - 12 * q^38 - 40 * q^41 - 78 * q^42 - 28 * q^46 - 12 * q^48 - 48 * q^52 + 24 * q^53 + 36 * q^56 + 16 * q^57 - 30 * q^58 - 20 * q^61 - 56 * q^62 + 44 * q^66 + 12 * q^68 - 44 * q^72 + 12 * q^73 + 112 * q^76 - 16 * q^77 - 64 * q^78 - 52 * q^81 + 34 * q^82 + 64 * q^86 - 16 * q^88 - 44 * q^92 - 12 * q^93 - 48 * q^96 + 24 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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