LMFDB - Embedded newform 700.2.be.e.207.17

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			207.17
Character	$\chi$	$=$	700.207
Dual form			700.2.be.e.443.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40543 - 0.157385i) q^{2} +(-1.08292 + 0.290169i) q^{3} +(1.95046 - 0.442386i) q^{4} +(-1.47630 + 0.578247i) q^{6} +(1.51730 + 2.16744i) q^{7} +(2.67161 - 0.928715i) q^{8} +(-1.50955 + 0.871538i) q^{9} +O(q^{10})$	\(q+(1.40543 - 0.157385i) q^{2} +(-1.08292 + 0.290169i) q^{3} +(1.95046 - 0.442386i) q^{4} +(-1.47630 + 0.578247i) q^{6} +(1.51730 + 2.16744i) q^{7} +(2.67161 - 0.928715i) q^{8} +(-1.50955 + 0.871538i) q^{9} +(2.58391 + 1.49182i) q^{11} +(-1.98383 + 1.04503i) q^{12} +(-4.05418 + 4.05418i) q^{13} +(2.47357 + 2.80739i) q^{14} +(3.60859 - 1.72571i) q^{16} +(2.30478 - 0.617565i) q^{17} +(-1.98440 + 1.46247i) q^{18} +(1.25694 + 2.17708i) q^{19} +(-2.27204 - 1.90691i) q^{21} +(3.86629 + 1.68998i) q^{22} +(1.55254 - 5.79414i) q^{23} +(-2.62367 + 1.78095i) q^{24} +(-5.05979 + 6.33592i) q^{26} +(3.76010 - 3.76010i) q^{27} +(3.91827 + 3.55628i) q^{28} +2.55433i q^{29} +(3.12248 + 1.80277i) q^{31} +(4.80001 - 2.99330i) q^{32} +(-3.23105 - 0.865758i) q^{33} +(3.14202 - 1.23068i) q^{34} +(-2.55876 + 2.36770i) q^{36} +(1.23528 - 4.61014i) q^{37} +(2.10918 + 2.86191i) q^{38} +(3.21397 - 5.56676i) q^{39} -7.93727 q^{41} +(-3.49331 - 2.32244i) q^{42} +(7.62646 + 7.62646i) q^{43} +(5.69977 + 1.76665i) q^{44} +(1.27007 - 8.38760i) q^{46} +(-2.85870 - 0.765987i) q^{47} +(-3.40708 + 2.91592i) q^{48} +(-2.39563 + 6.57731i) q^{49} +(-2.31671 + 1.33755i) q^{51} +(-6.11400 + 9.70103i) q^{52} +(-0.662485 - 2.47243i) q^{53} +(4.69277 - 5.87634i) q^{54} +(6.06656 + 4.38142i) q^{56} +(-1.99289 - 1.99289i) q^{57} +(0.402012 + 3.58993i) q^{58} +(-1.04694 + 1.81336i) q^{59} +(0.950478 + 1.64628i) q^{61} +(4.67216 + 2.04223i) q^{62} +(-4.17944 - 1.94948i) q^{63} +(6.27498 - 4.96233i) q^{64} +(-4.67727 - 0.708243i) q^{66} +(-0.805219 - 3.00512i) q^{67} +(4.22219 - 2.22414i) q^{68} +6.72512i q^{69} -8.09721i q^{71} +(-3.22351 + 3.73035i) q^{72} +(-2.52396 - 9.41954i) q^{73} +(1.01054 - 6.67364i) q^{74} +(3.41472 + 3.69026i) q^{76} +(0.687116 + 7.86400i) q^{77} +(3.64089 - 8.32952i) q^{78} +(-4.03058 - 6.98117i) q^{79} +(-0.366226 + 0.634322i) q^{81} +(-11.1553 + 1.24921i) q^{82} +(-5.99790 - 5.99790i) q^{83} +(-5.27511 - 2.71422i) q^{84} +(11.9187 + 9.51816i) q^{86} +(-0.741186 - 2.76614i) q^{87} +(8.28866 + 1.58584i) q^{88} +(1.77990 - 1.02763i) q^{89} +(-14.9386 - 2.63582i) q^{91} +(0.464910 - 11.9881i) q^{92} +(-3.90452 - 1.04621i) q^{93} +(-4.13826 - 0.626624i) q^{94} +(-4.32949 + 4.63434i) q^{96} +(-6.63160 - 6.63160i) q^{97} +(-2.33171 + 9.62097i) 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.40543	−	0.157385i	0.993788	−	0.111288i
$2$	1.40543	−	0.157385i	0.993788	−	0.111288i
$3$	−1.08292	+	0.290169i	−0.625227	+	0.167529i	−0.557503	−	0.830175i	$-0.688240\pi$
$3$	−1.08292	+	0.290169i	−0.625227	+	0.167529i	−0.0677240	+	0.997704i	$0.521574\pi$
$4$	1.95046	−	0.442386i	0.975230	−	0.221193i
$5$		0			0
$5$		0			0
$6$	−1.47630	+	0.578247i	−0.602699	+	0.236068i
$7$	1.51730	+	2.16744i	0.573484	+	0.819217i
$7$	1.51730	+	2.16744i	0.573484	+	0.819217i
$8$	2.67161	−	0.928715i	0.944556	−	0.328350i
$9$	−1.50955	+	0.871538i	−0.503183	+	0.290513i
$10$		0			0
$11$	2.58391	+	1.49182i	0.779077	+	0.449800i	0.836103	−	0.548572i	$-0.184828\pi$
$11$	2.58391	+	1.49182i	0.779077	+	0.449800i	−0.0570261	+	0.998373i	$0.518162\pi$
$12$	−1.98383	+	1.04503i	−0.572684	+	0.301675i
$13$	−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
$17$	2.30478	−	0.617565i	0.558992	−	0.149782i	0.0317490	−	0.999496i	$-0.489892\pi$
$17$	2.30478	−	0.617565i	0.558992	−	0.149782i	0.527243	+	0.849714i	$0.323226\pi$
$18$	−1.98440	+	1.46247i	−0.467727	+	0.344706i
$19$	1.25694	+	2.17708i	0.288362	+	0.499457i	0.973419	−	0.229032i	$-0.0735561\pi$
$19$	1.25694	+	2.17708i	0.288362	+	0.499457i	−0.685057	+	0.728489i	$0.740223\pi$
$20$		0			0
$21$	−2.27204	−	1.90691i	−0.495800	−	0.416121i
$22$	3.86629	+	1.68998i	0.824295	+	0.360304i
$23$	1.55254	−	5.79414i	0.323726	−	1.20816i	−0.591860	−	0.806041i	$-0.701606\pi$
$23$	1.55254	−	5.79414i	0.323726	−	1.20816i	0.915586	−	0.402122i	$-0.131727\pi$
$24$	−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
$28$	3.91827	+	3.55628i	0.740484	+	0.672074i
$29$			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	0.753472	−	0.657479i	$-0.228377\pi$
$31$	3.12248	+	1.80277i	0.560815	+	0.323787i	−0.192658	+	0.981266i	$0.561711\pi$
$32$	4.80001	−	2.99330i	0.848530	−	0.529147i
$33$	−3.23105	−	0.865758i	−0.562454	−	0.150709i
$34$	3.14202	−	1.23068i	0.538851	−	0.211060i
$35$		0			0
$36$	−2.55876	+	2.36770i	−0.426460	+	0.394617i
$37$	1.23528	−	4.61014i	0.203079	−	0.757903i	−0.786947	−	0.617021i	$-0.788339\pi$
$37$	1.23528	−	4.61014i	0.203079	−	0.757903i	0.990026	−	0.140882i	$-0.0449939\pi$
$38$	2.10918	+	2.86191i	0.342154	+	0.464263i
$39$	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	$0.712785\pi$
$42$	−3.49331	−	2.32244i	−0.539029	−	0.358360i
$43$	7.62646	+	7.62646i	1.16302	+	1.16302i	0.983810	+	0.179215i	$0.0573557\pi$
$43$	7.62646	+	7.62646i	1.16302	+	1.16302i	0.179215	+	0.983810i	$0.442644\pi$
$44$	5.69977	+	1.76665i	0.859272	+	0.266332i
$45$		0			0
$46$	1.27007	−	8.38760i	0.187261	−	1.23668i
$47$	−2.85870	−	0.765987i	−0.416985	−	0.111731i	0.0442256	−	0.999022i	$-0.485918\pi$
$47$	−2.85870	−	0.765987i	−0.416985	−	0.111731i	−0.461210	+	0.887291i	$0.652585\pi$
$48$	−3.40708	+	2.91592i	−0.491770	+	0.420876i
$49$	−2.39563	+	6.57731i	−0.342232	+	0.939615i
$50$		0			0
$51$	−2.31671	+	1.33755i	−0.324404	+	0.187295i
$52$	−6.11400	+	9.70103i	−0.847859	+	1.34529i
$53$	−0.662485	−	2.47243i	−0.0909993	−	0.339614i	0.905383	−	0.424595i	$-0.139584\pi$
$53$	−0.662485	−	2.47243i	−0.0909993	−	0.339614i	−0.996383	+	0.0849813i	$0.972917\pi$
$54$	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
$58$	0.402012	+	3.58993i	0.0527868	+	0.471380i
$59$	−1.04694	+	1.81336i	−0.136301	+	0.236079i	−0.926094	−	0.377294i	$-0.876855\pi$
$59$	−1.04694	+	1.81336i	−0.136301	+	0.236079i	0.789793	+	0.613374i	$0.210188\pi$
$60$		0			0
$61$	0.950478	+	1.64628i	0.121696	+	0.210784i	0.920437	−	0.390892i	$-0.127833\pi$
$61$	0.950478	+	1.64628i	0.121696	+	0.210784i	−0.798740	+	0.601676i	$0.794500\pi$
$62$	4.67216	+	2.04223i	0.593365	+	0.259363i
$63$	−4.17944	−	1.94948i	−0.526560	−	0.245612i
$64$	6.27498	−	4.96233i	0.784372	−	0.620291i
$65$		0			0
$66$	−4.67727	−	0.708243i	−0.575733	−	0.0871787i
$67$	−0.805219	−	3.00512i	−0.0983732	−	0.367134i	0.899136	−	0.437669i	$-0.144196\pi$
$67$	−0.805219	−	3.00512i	−0.0983732	−	0.367134i	−0.997509	+	0.0705354i	$0.977529\pi$
$68$	4.22219	−	2.22414i	0.512016	−	0.269717i
$69$			6.72512i			0.809609i
$70$		0			0
$71$		−	8.09721i		−	0.960962i	−0.877005	−	0.480481i	$-0.840462\pi$
$71$		−	8.09721i		−	0.960962i	0.877005	−	0.480481i	$-0.159538\pi$
$72$	−3.22351	+	3.73035i	−0.379894	+	0.439626i
$73$	−2.52396	−	9.41954i	−0.295407	−	1.10247i	−0.940894	−	0.338702i	$-0.890012\pi$
$73$	−2.52396	−	9.41954i	−0.295407	−	1.10247i	0.645487	−	0.763771i	$-0.276655\pi$
$74$	1.01054	−	6.67364i	0.117473	−	0.775795i
$75$		0			0
$76$	3.41472	+	3.69026i	0.391695	+	0.423302i
$77$	0.687116	+	7.86400i	0.0783041	+	0.896186i
$78$	3.64089	−	8.32952i	0.412249	−	0.943133i
$79$	−4.03058	−	6.98117i	−0.453476	−	0.785443i	0.545123	−	0.838356i	$-0.316483\pi$
$79$	−4.03058	−	6.98117i	−0.453476	−	0.785443i	−0.998599	+	0.0529126i	$0.983150\pi$
$80$		0			0
$81$	−0.366226	+	0.634322i	−0.0406918	+	0.0704802i
$82$	−11.1553	+	1.24921i	−1.23189	+	0.137952i
$83$	−5.99790	−	5.99790i	−0.658356	−	0.658356i	0.296635	−	0.954991i	$-0.404135\pi$
$83$	−5.99790	−	5.99790i	−0.658356	−	0.658356i	−0.954991	+	0.296635i	$0.904135\pi$
$84$	−5.27511	−	2.71422i	−0.575562	−	0.296146i
$85$		0			0
$86$	11.9187	+	9.51816i	1.28523	+	1.02637i
$87$	−0.741186	−	2.76614i	−0.0794635	−	0.296562i
$88$	8.28866	+	1.58584i	0.883574	+	0.169051i
$89$	1.77990	−	1.02763i	0.188669	−	0.108928i	−0.402690	−	0.915336i	$-0.631925\pi$
$89$	1.77990	−	1.02763i	0.188669	−	0.108928i	0.591359	+	0.806408i	$0.298592\pi$
$90$		0			0
$91$	−14.9386	−	2.63582i	−1.56599	−	0.276309i
$92$	0.464910	−	11.9881i	0.0484702	−	1.24984i
$93$	−3.90452	−	1.04621i	−0.404880	−	0.108487i
$94$	−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	$0.907958\pi$
$98$	−2.33171	+	9.62097i	−0.235539	+	0.971865i
$99$	−5.20071			−0.522691
$100$		0			0
$101$	3.73273	−	6.46529i	0.371421	−	0.643320i	−0.618363	−	0.785892i	$-0.712204\pi$
$101$	3.73273	−	6.46529i	0.371421	−	0.643320i	0.989784	+	0.142572i	$0.0455373\pi$
$102$	−3.04546	+	2.24445i	−0.301545	+	0.222234i
$103$	1.06672	−	3.98105i	0.105107	−	0.392264i	−0.893250	−	0.449560i	$-0.851581\pi$
$103$	1.06672	−	3.98105i	0.105107	−	0.392264i	0.998357	+	0.0572952i	$0.0182476\pi$
$104$	−7.06600	+	14.5964i	−0.692878	+	1.43129i
$105$		0			0
$106$	−1.32020	−	3.37056i	−0.128229	−	0.327377i
$107$	10.0616	+	2.69601i	0.972696	+	0.260633i	0.709966	−	0.704236i	$-0.248710\pi$
$107$	10.0616	+	2.69601i	0.972696	+	0.260633i	0.262730	+	0.964869i	$0.415377\pi$
$108$	5.67051	−	8.99734i	0.545645	−	0.865770i
$109$	−8.88798	−	5.13148i	−0.851314	−	0.491507i	0.00977974	−	0.999952i	$-0.496887\pi$
$109$	−8.88798	−	5.13148i	−0.851314	−	0.491507i	−0.861094	+	0.508446i	$0.830220\pi$
$110$		0			0
$111$			5.35088i			0.507883i
$112$	9.21568	+	5.20300i	0.870800	+	0.491637i
$113$	−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
$117$	2.58661	−	9.65335i	0.239132	−	0.892453i
$118$	−1.18601	+	2.71332i	−0.109181	+	0.249782i
$119$	4.83558	+	4.05846i	0.443277	+	0.372039i
$120$		0			0
$121$	−1.04895	−	1.81684i	−0.0953593	−	0.165167i
$122$	1.59493	+	2.16413i	0.144398	+	0.195932i
$123$	8.59546	−	2.30315i	0.775027	−	0.207668i
$124$	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	$0.567290\pi$
$127$	−13.3832	+	13.3832i	−1.18756	+	1.18756i	−0.977739	+	0.209826i	$0.932710\pi$
$128$	8.03804	−	7.96178i	0.710469	−	0.703729i
$129$	−10.4718	−	6.04592i	−0.921994	−	0.532314i
$130$		0			0
$131$	13.2990	−	7.67817i	1.16194	−	0.670845i	0.210170	−	0.977665i	$-0.432598\pi$
$131$	13.2990	−	7.67817i	1.16194	−	0.670845i	0.951767	+	0.306820i	$0.0992651\pi$
$132$	−6.68504	−	0.259253i	−0.581858	−	0.0225651i
$133$	−2.81156	+	6.02762i	−0.243793	+	0.522661i
$134$	−1.60464	−	4.09675i	−0.138620	−	0.353905i
$135$		0			0
$136$	5.58394	−	3.79038i	0.478819	−	0.325022i
$137$	4.55145	−	1.21956i	0.388857	−	0.104194i	−0.0590931	−	0.998252i	$-0.518821\pi$
$137$	4.55145	−	1.21956i	0.388857	−	0.104194i	0.447950	+	0.894059i	$0.352154\pi$
$138$	1.05843	+	9.45167i	0.0900997	+	0.804580i
$139$	−10.3065			−0.874185			−0.437093	−	0.899417i	$-0.643992\pi$
$139$	−10.3065			−0.874185			−0.437093	+	0.899417i	$0.643992\pi$
$140$		0			0
$141$	3.31802			0.279428
$142$	−1.27438	−	11.3800i	−0.106943	−	0.954992i
$143$	−16.5237	+	4.42752i	−1.38178	+	0.370248i
$144$	−3.94332	+	5.75007i	−0.328610	+	0.479173i
$145$		0			0
$146$	−5.02973	−	12.8413i	−0.416264	−	1.06275i
$147$	0.685754	−	7.81786i	0.0565600	−	0.644806i
$148$	0.369908	−	9.53837i	0.0304063	−	0.784049i
$149$	8.37658	−	4.83622i	0.686236	−	0.396199i	−0.115964	−	0.993253i	$-0.536996\pi$
$149$	8.37658	−	4.83622i	0.686236	−	0.396199i	0.802201	+	0.597055i	$0.203662\pi$
$150$		0			0
$151$	0.955932	+	0.551908i	0.0777927	+	0.0449136i	0.538392	−	0.842695i	$-0.319032\pi$
$151$	0.955932	+	0.551908i	0.0777927	+	0.0449136i	−0.460599	+	0.887608i	$0.652365\pi$
$152$	5.37994	+	4.64897i	0.436371	+	0.377082i
$153$	−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
$157$	−8.39254	+	2.24878i	−0.669798	+	0.179472i	−0.577664	−	0.816275i	$-0.696036\pi$
$157$	−8.39254	+	2.24878i	−0.669798	+	0.179472i	−0.0921341	+	0.995747i	$0.529369\pi$
$158$	−6.76343	−	9.17719i	−0.538069	−	0.730098i
$159$	1.43484	+	2.48522i	0.113790	+	0.197091i
$160$		0			0
$161$	14.9141	−	5.42640i	1.17540	−	0.427660i
$162$	−0.414872	+	0.949133i	−0.0325954	+	0.0745709i
$163$	−0.278958	+	1.04108i	−0.0218496	+	0.0815440i	−0.975990	−	0.217816i	$-0.930107\pi$
$163$	−0.278958	+	1.04108i	−0.0218496	+	0.0815440i	0.954140	+	0.299360i	$0.0967733\pi$
$164$	−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	−0.786450	−	0.617654i	$-0.788083\pi$
$167$	−2.18132	+	2.18132i	−0.168796	+	0.168796i	0.617654	+	0.786450i	$0.288083\pi$
$168$	−7.84098	−	2.98443i	−0.604944	−	0.230253i
$169$		−	19.8727i		−	1.52867i
$170$		0			0
$171$	−3.79482	−	2.19094i	−0.290197	−	0.167546i
$172$	18.2490	+	11.5013i	1.39147	+	0.876963i
$173$	22.7858	+	6.10543i	1.73237	+	0.464187i	0.980727	−	0.195383i	$-0.0625948\pi$
$173$	22.7858	+	6.10543i	1.73237	+	0.464187i	0.751643	+	0.659570i	$0.229262\pi$
$174$	−1.47703	−	3.77097i	−0.111974	−	0.285876i
$175$		0			0
$176$	11.8987	+	0.924279i	0.896899	+	0.0696701i
$177$	0.607581	−	2.26752i	0.0456686	−	0.170437i
$178$	2.33979	−	1.72438i	0.175375	−	0.129248i
$179$	−3.53155	+	6.11682i	−0.263960	+	0.457193i	−0.967291	−	0.253670i	$-0.918362\pi$
$179$	−3.53155	+	6.11682i	−0.263960	+	0.457193i	0.703330	+	0.710863i	$0.251695\pi$
$180$		0			0
$181$	−2.37419			−0.176472			−0.0882360	−	0.996100i	$-0.528123\pi$
$181$	−2.37419			−0.176472			−0.0882360	+	0.996100i	$0.528123\pi$
$182$	−21.4100	−	1.35335i	−1.58701	−	0.100317i
$183$	−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
$187$	6.87664	+	1.84259i	0.502870	+	0.134744i
$188$	−5.91465	−	0.229376i	−0.431370	−	0.0167290i
$189$	13.8550	+	2.44462i	1.00780	+	0.177820i
$190$		0			0
$191$	5.46966	−	3.15791i	0.395771	−	0.228498i	−0.288887	−	0.957363i	$-0.593285\pi$
$191$	5.46966	−	3.15791i	0.395771	−	0.228498i	0.684658	+	0.728865i	$0.259952\pi$
$192$	−5.35541	+	7.19463i	−0.386494	+	0.519227i
$193$	−5.46675	−	20.4022i	−0.393505	−	1.46858i	−0.824311	−	0.566137i	$-0.808437\pi$
$193$	−5.46675	−	20.4022i	−0.393505	−	1.46858i	0.430806	−	0.902445i	$-0.358229\pi$
$194$	−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	$0.733740\pi$
$198$	−7.30923	+	0.818513i	−0.519444	+	0.0581692i
$199$	4.75738	−	8.24003i	0.337242	−	0.584120i	−0.646671	−	0.762769i	$-0.723839\pi$
$199$	4.75738	−	8.24003i	0.337242	−	0.584120i	0.983913	+	0.178649i	$0.0571727\pi$
$200$		0			0
$201$	1.74398	+	3.02067i	0.123011	+	0.213061i
$202$	4.22855	−	9.67397i	0.297520	−	0.680658i
$203$	−5.53636	+	3.87567i	−0.388576	+	0.272019i
$204$	−3.92693	+	3.63372i	−0.274940	+	0.254412i
$205$		0			0
$206$	0.872641	−	5.76297i	0.0607998	−	0.401525i
$207$	2.70619	+	10.0996i	0.188093	+	0.701973i
$208$	−7.63351	+	21.6262i	−0.529289	+	1.49951i
$209$			7.50050i			0.518821i
$210$		0			0
$211$			26.9476i			1.85515i	0.373634	+	0.927576i	$0.378112\pi$
$211$			26.9476i			1.85515i	−0.373634	+	0.927576i	$0.621888\pi$
$212$	−2.38592	−	4.52930i	−0.163866	−	0.311073i
$213$	2.34956	+	8.76866i	0.160989	+	0.600819i
$214$	14.5652	+	2.20550i	0.995659	+	0.150765i
$215$		0			0
$216$	6.55345	−	13.5376i	0.445906	−	0.921116i
$217$	0.830336	+	9.50314i	0.0563668	+	0.645115i
$218$	−13.2990	−	5.81310i	−0.900725	−	0.393712i
$219$	5.46651	+	9.46827i	0.369393	+	0.639807i
$220$		0			0
$221$	−6.84029	+	11.8477i	−0.460128	+	0.796964i
$222$	0.842147	+	7.52028i	0.0565212	+	0.504728i
$223$	2.22624	+	2.22624i	0.149080	+	0.149080i	0.777707	−	0.628627i	$-0.216383\pi$
$223$	2.22624	+	2.22624i	0.149080	+	0.149080i	−0.628627	+	0.777707i	$0.716383\pi$
$224$	13.7709	+	5.86203i	0.920104	+	0.391673i
$225$		0			0
$226$	−9.18000	+	11.4953i	−0.610645	+	0.764655i
$227$	2.08751	+	7.79070i	0.138553	+	0.517087i	0.999958	+	0.00916824i	$0.00291838\pi$
$227$	2.08751	+	7.79070i	0.138553	+	0.517087i	−0.861405	+	0.507919i	$0.830415\pi$
$228$	−4.76868	−	3.00543i	−0.315814	−	0.199039i
$229$	2.10701	−	1.21648i	0.139235	−	0.0803873i	−0.428764	−	0.903416i	$-0.641051\pi$
$229$	2.10701	−	1.21648i	0.139235	−	0.0803873i	0.567999	+	0.823029i	$0.307718\pi$
$230$		0			0
$231$	−3.02598	−	8.31674i	−0.199095	−	0.547201i
$232$	2.37224	+	6.82416i	0.155745	+	0.448028i
$233$	10.1117	+	2.70941i	0.662437	+	0.177499i	0.574346	−	0.818613i	$-0.305257\pi$
$233$	10.1117	+	2.70941i	0.662437	+	0.177499i	0.0880913	+	0.996112i	$0.471923\pi$
$234$	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
$238$	7.43480	+	4.94283i	0.481927	+	0.320396i
$239$	−12.9050			−0.834754			−0.417377	−	0.908733i	$-0.637051\pi$
$239$	−12.9050			−0.834754			−0.417377	+	0.908733i	$0.637051\pi$
$240$		0			0
$241$	−1.35695	+	2.35030i	−0.0874087	+	0.151396i	−0.906415	−	0.422388i	$-0.861192\pi$
$241$	−1.35695	+	2.35030i	−0.0874087	+	0.151396i	0.819006	+	0.573784i	$0.194525\pi$
$242$	−1.76017	−	2.38835i	−0.113148	−	0.153529i
$243$	−3.91634	+	14.6160i	−0.251234	+	0.937616i
$244$	2.58216	+	2.79052i	0.165306	+	0.178645i
$245$		0			0
$246$	11.7178	−	4.58970i	0.747101	−	0.292629i
$247$	−13.9221	−	3.73043i	−0.885845	−	0.237361i
$248$	10.0163	+	1.91639i	0.636036	+	0.121691i
$249$	8.23568	+	4.75487i	0.521915	+	0.301328i
$250$		0			0
$251$		−	3.15358i		−	0.199052i	−0.995035	−	0.0995262i	$-0.968267\pi$
$251$		−	3.15358i		−	0.199052i	0.995035	−	0.0995262i	$-0.0317327\pi$
$252$	−9.01426	−	1.95346i	−0.567845	−	0.123056i
$253$	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
$257$	−4.26180	+	15.9053i	−0.265844	+	0.992143i	0.695888	+	0.718151i	$0.255011\pi$
$257$	−4.26180	+	15.9053i	−0.265844	+	0.992143i	−0.961732	+	0.273993i	$0.911656\pi$
$258$	−15.6690	−	6.84900i	−0.975507	−	0.426400i
$259$	11.8665	−	4.31754i	0.737350	−	0.268279i
$260$		0			0
$261$	−2.22619	−	3.85588i	−0.137798	−	0.238673i
$262$	17.4823	−	12.8842i	1.08006	−	0.795987i
$263$	28.1947	−	7.55474i	1.73856	−	0.465845i	0.756432	−	0.654072i	$-0.226941\pi$
$263$	28.1947	−	7.55474i	1.73856	−	0.465845i	0.982126	+	0.188227i	$0.0602739\pi$
$264$	−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
$268$	−2.89997	−	5.50515i	−0.177144	−	0.336280i
$269$	5.29203	+	3.05536i	0.322661	+	0.186288i	0.652578	−	0.757721i	$-0.273687\pi$
$269$	5.29203	+	3.05536i	0.322661	+	0.186288i	−0.329917	+	0.944010i	$0.607021\pi$
$270$		0			0
$271$	19.0699	−	11.0100i	1.15841	−	0.668810i	0.207489	−	0.978237i	$-0.433471\pi$
$271$	19.0699	−	11.0100i	1.15841	−	0.668810i	0.950923	+	0.309428i	$0.100137\pi$
$272$	7.25128	−	6.20594i	0.439673	−	0.376290i
$273$	16.9422	−	1.48032i	1.02539	−	0.0895932i
$274$	6.20480	−	2.43033i	0.374846	−	0.146822i
$275$		0			0
$276$	2.97510	+	13.1171i	0.179080	+	0.789555i
$277$	−15.8956	+	4.25922i	−0.955077	+	0.255912i	−0.702515	−	0.711669i	$-0.747940\pi$
$277$	−15.8956	+	4.25922i	−0.955077	+	0.255912i	−0.252561	+	0.967581i	$0.581273\pi$
$278$	−14.4850	+	1.62209i	−0.868755	+	0.0972862i
$279$	−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	$0.435057\pi$
$282$	4.66325	−	0.522207i	0.277692	−	0.0310970i
$283$	12.6003	−	3.37625i	0.749013	−	0.200697i	0.135932	−	0.990718i	$-0.456597\pi$
$283$	12.6003	−	3.37625i	0.749013	−	0.200697i	0.613080	+	0.790021i	$0.289930\pi$
$284$	−3.58209	−	15.7933i	−0.212558	−	0.937159i
$285$		0			0
$286$	−22.5261	+	8.82314i	−1.33200	+	0.521723i
$287$	−12.0432	−	17.2036i	−0.710887	−	1.01550i
$288$	−4.63707	+	8.70194i	−0.273242	+	0.512767i
$289$	−9.79179	+	5.65329i	−0.575987	+	0.332546i
$290$		0			0
$291$	9.10580	+	5.25724i	0.533791	+	0.308185i
$292$	−9.08995	−	17.2559i	−0.531949	−	1.00982i
$293$	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
$297$	15.3251	−	4.10636i	0.889255	−	0.238275i
$298$	11.0115	−	8.11531i	0.637882	−	0.470107i
$299$	17.1962	+	29.7848i	0.994484	+	1.72250i
$300$		0			0
$301$	−4.95833	+	28.1015i	−0.285793	+	1.61975i
$302$	1.43036	+	0.625218i	0.0823078	+	0.0359772i
$303$	−2.16625	+	8.08454i	−0.124448	+	0.464445i
$304$	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	−0.291783	−	0.956484i	$-0.594249\pi$
$307$	11.6465	−	11.6465i	0.664701	−	0.664701i	0.956484	+	0.291783i	$0.0942486\pi$
$308$	4.81912	+	15.0345i	0.274595	+	0.856667i
$309$			4.62070i			0.262863i
$310$		0			0
$311$	−26.1398	−	15.0918i	−1.48225	−	0.855778i	−0.482454	−	0.875922i	$-0.660254\pi$
$311$	−26.1398	−	15.0918i	−1.48225	−	0.855778i	−0.999797	+	0.0201436i	$0.993588\pi$
$312$	3.41654	−	17.8571i	0.193423	−	1.01096i
$313$	21.3109	+	5.71023i	1.20456	+	0.322761i	0.804626	−	0.593782i	$-0.202366\pi$
$313$	21.3109	+	5.71023i	1.20456	+	0.322761i	0.399935	+	0.916543i	$0.369033\pi$
$314$	−11.4412	+	4.48135i	−0.645664	+	0.252897i
$315$		0			0
$316$	−10.9499	−	11.8334i	−0.615978	−	0.665682i
$317$	0.375154	−	1.40009i	0.0210708	−	0.0786372i	−0.954590	−	0.297923i	$-0.903706\pi$
$317$	0.375154	−	1.40009i	0.0210708	−	0.0786372i	0.975661	+	0.219286i	$0.0703728\pi$
$318$	2.40770	+	3.26698i	0.135017	+	0.183203i
$319$	−3.81059	+	6.60014i	−0.213352	+	0.369537i
$320$		0			0
$321$	−11.6783			−0.651819
$322$	20.1067	−	9.97367i	1.12050	−	0.555811i
$323$	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
$327$	11.1140	+	2.97799i	0.614606	+	0.164683i
$328$	−21.2053	+	7.37146i	−1.17087	+	0.407021i
$329$	−2.67726	−	7.35831i	−0.147602	−	0.405677i
$330$		0			0
$331$	−24.5744	+	14.1881i	−1.35073	+	0.779846i	−0.988352	−	0.152184i	$-0.951369\pi$
$331$	−24.5744	+	14.1881i	−1.35073	+	0.779846i	−0.362381	+	0.932030i	$0.618036\pi$
$332$	−14.3521	−	9.04528i	−0.787672	−	0.496424i
$333$	2.15320	+	8.03583i	0.117994	+	0.440361i
$334$	−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	$0.600046\pi$
$338$	−3.12767	−	27.9297i	−0.170123	−	1.51918i
$339$	5.83112	−	10.0998i	0.316703	−	0.548546i
$340$		0			0
$341$	5.37880	+	9.31636i	0.291279	+	0.504509i
$342$	−5.67817	−	2.48197i	−0.307041	−	0.134209i
$343$	−17.8908	+	4.78733i	−0.966013	+	0.258492i
$344$	27.4577	+	13.2921i	1.48042	+	0.716662i
$345$		0			0
$346$	32.9847	+	4.99461i	1.77327	+	0.268512i
$347$	4.13190	+	15.4205i	0.221812	+	0.827815i	0.983657	+	0.180055i	$0.0576274\pi$
$347$	4.13190	+	15.4205i	0.221812	+	0.827815i	−0.761844	+	0.647760i	$0.775706\pi$
$348$	−2.66936	−	5.06736i	−0.143093	−	0.271639i
$349$		−	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
$352$	16.8683	−	0.573668i	0.899081	−	0.0305766i
$353$	−1.45108	−	5.41550i	−0.0772331	−	0.288238i	0.916497	−	0.400041i	$-0.131004\pi$
$353$	−1.45108	−	5.41550i	−0.0772331	−	0.288238i	−0.993730	+	0.111803i	$0.964337\pi$
$354$	0.497038	−	3.28247i	0.0264173	−	0.174461i
$355$		0			0
$356$	3.01702	−	2.79175i	0.159902	−	0.147962i
$357$	−6.41420	−	2.99187i	−0.339476	−	0.158347i
$358$	−4.00064	+	9.15257i	−0.211441	+	0.483728i
$359$	−18.2143	−	31.5480i	−0.961311	−	1.66504i	−0.719215	−	0.694788i	$-0.755498\pi$
$359$	−18.2143	−	31.5480i	−0.961311	−	1.66504i	−0.242097	−	0.970252i	$-0.577835\pi$
$360$		0			0
$361$	6.34021	−	10.9816i	0.333695	−	0.577977i
$362$	−3.33675	+	0.373661i	−0.175376	+	0.0196392i
$363$	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
$367$	−8.46227	−	31.5816i	−0.441727	−	1.64855i	−0.724436	−	0.689342i	$-0.757900\pi$
$367$	−8.46227	−	31.5816i	−0.441727	−	1.64855i	0.282709	−	0.959206i	$-0.408767\pi$
$368$	−4.39657	−	23.5879i	−0.229187	−	1.22961i
$369$	11.9817	−	6.91763i	0.623742	−	0.360118i
$370$		0			0
$371$	4.35366	−	5.18730i	0.226031	−	0.269311i
$372$	−8.07844	−	0.313291i	−0.418848	−	0.0162434i
$373$	−25.2614	−	6.76877i	−1.30799	−	0.350474i	−0.463522	−	0.886086i	$-0.653414\pi$
$373$	−25.2614	−	6.76877i	−1.30799	−	0.350474i	−0.844464	+	0.535612i	$0.820081\pi$
$374$	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
$378$	19.8570	+	1.25518i	1.02133	+	0.0645594i
$379$	20.3769			1.04669			0.523344	−	0.852121i	$-0.324684\pi$
$379$	20.3769			1.04669			0.523344	+	0.852121i	$0.324684\pi$
$380$		0			0
$381$	10.6096	−	18.3763i	0.543546	−	0.941449i
$382$	7.19021	−	5.29906i	0.367883	−	0.271124i
$383$	6.60856	−	24.6635i	0.337682	−	1.26025i	−0.563250	−	0.826286i	$-0.690449\pi$
$383$	6.60856	−	24.6635i	0.337682	−	1.26025i	0.900932	−	0.433960i	$-0.142884\pi$
$384$	−6.39433	+	10.9544i	−0.326309	+	0.559014i
$385$		0			0
$386$	−10.8941	−	27.8134i	−0.554496	−	1.41567i
$387$	−18.1593	−	4.86576i	−0.923088	−	0.247341i
$388$	−15.8684	−	10.0009i	−0.805595	−	0.507721i
$389$	−15.6310	−	9.02458i	−0.792525	−	0.457564i	0.0483257	−	0.998832i	$-0.484611\pi$
$389$	−15.6310	−	9.02458i	−0.792525	−	0.457564i	−0.840851	+	0.541267i	$0.817945\pi$
$390$		0			0
$391$		−	14.3130i		−	0.723842i
$392$	−0.291730	+	19.7968i	−0.0147346	+	0.999891i
$393$	−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
$397$	−7.78706	+	29.0617i	−0.390821	+	1.45857i	0.437961	+	0.898994i	$0.355701\pi$
$397$	−7.78706	+	29.0617i	−0.390821	+	1.45857i	−0.828782	+	0.559571i	$0.810966\pi$
$398$	5.38931	−	12.3295i	0.270141	−	0.618022i
$399$	1.29568	−	7.34329i	0.0648649	−	0.367624i
$400$		0			0
$401$	−2.44780	−	4.23972i	−0.122237	−	0.211721i	0.798412	−	0.602111i	$-0.205674\pi$
$401$	−2.44780	−	4.23972i	−0.122237	−	0.211721i	−0.920650	+	0.390390i	$0.872340\pi$
$402$	2.92645	+	3.97086i	0.145958	+	0.198048i
$403$	−19.9678	+	5.35037i	−0.994669	+	0.266521i
$404$	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
$408$	−4.94713	+	5.72498i	−0.244920	+	0.283429i
$409$	29.0499	+	16.7720i	1.43642	+	0.829320i	0.997599	−	0.0692530i	$-0.0220616\pi$
$409$	29.0499	+	16.7720i	1.43642	+	0.829320i	0.438825	+	0.898573i	$0.355395\pi$
$410$		0			0
$411$	−4.57500	+	2.64138i	−0.225668	+	0.130290i
$412$	0.319431	−	8.23678i	0.0157372	−	0.405797i
$413$	−5.51888	+	0.482212i	−0.271566	+	0.0237281i
$414$	5.39289	+	13.7684i	0.265046	+	0.676680i
$415$		0			0
$416$	−7.32472	+	31.5955i	−0.359124	+	1.54910i
$417$	11.1611	−	2.99062i	0.546564	−	0.146451i
$418$	1.18047	+	10.5414i	0.0577385	+	0.515598i
$419$	36.3735			1.77696			0.888481	−	0.458914i	$-0.151761\pi$
$419$	36.3735			1.77696			0.888481	+	0.458914i	$0.151761\pi$
$420$		0			0
$421$	−33.2473			−1.62038			−0.810188	−	0.586170i	$-0.800635\pi$
$421$	−33.2473			−1.62038			−0.810188	+	0.586170i	$0.800635\pi$
$422$	4.24115	+	37.8730i	0.206456	+	1.84363i
$423$	4.98294	−	1.33517i	0.242279	−	0.0649184i
$424$	−4.06608	−	5.99010i	−0.197466	−	0.290905i
$425$		0			0
$426$	4.68219	+	11.9539i	0.226853	+	0.579171i
$427$	−2.12606	+	4.55800i	−0.102887	+	0.220577i
$428$	20.8175	+	0.807325i	1.00625	+	0.0390235i
$429$	16.6092	−	9.58933i	0.801900	−	0.462977i
$430$		0			0
$431$	26.9460	+	15.5573i	1.29794	+	0.749367i	0.980048	−	0.198759i	$-0.0636910\pi$
$431$	26.9460	+	15.5573i	1.29794	+	0.749367i	0.317894	+	0.948126i	$0.397024\pi$
$432$	7.07980	−	20.0575i	0.340627	−	0.965018i
$433$	−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
$437$	14.5658	−	3.90289i	0.696776	−	0.186700i
$438$	9.17295	+	12.4466i	0.438301	+	0.594723i
$439$	0.278565	+	0.482489i	0.0132952	+	0.0230280i	0.872596	−	0.488442i	$-0.162435\pi$
$439$	0.278565	+	0.482489i	0.0132952	+	0.0230280i	−0.859301	+	0.511470i	$0.829101\pi$
$440$		0			0
$441$	−2.11606	−	12.0166i	−0.100765	−	0.572221i
$442$	−7.74889	+	17.7277i	−0.368577	+	0.843221i
$443$	−6.31254	+	23.5587i	−0.299918	+	1.11931i	0.637315	+	0.770604i	$0.280045\pi$
$443$	−6.31254	+	23.5587i	−0.299918	+	1.11931i	−0.937233	+	0.348705i	$0.886621\pi$
$444$	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
$448$	20.2766	+	6.07134i	0.957977	+	0.286844i
$449$			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
$452$	−11.0927	+	17.6006i	−0.521754	+	0.827863i
$453$	−1.19535	−	0.320293i	−0.0561624	−	0.0150487i
$454$	4.15999	+	10.6207i	0.195238	+	0.498456i
$455$		0			0
$456$	−7.17505	−	3.47340i	−0.336003	−	0.162657i
$457$	−0.707473	+	2.64033i	−0.0330942	+	0.123509i	−0.980497	−	0.196535i	$-0.937031\pi$
$457$	−0.707473	+	2.64033i	−0.0330942	+	0.123509i	0.947403	+	0.320044i	$0.103698\pi$
$458$	2.76979	−	2.04129i	0.129424	−	0.0953831i
$459$	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	$0.144398\pi$
$462$	−5.56173	−	11.2123i	−0.258755	−	0.521645i
$463$	13.5055	+	13.5055i	0.627652	+	0.627652i	0.947477	−	0.319824i	$-0.103624\pi$
$463$	13.5055	+	13.5055i	0.627652	+	0.627652i	−0.319824	+	0.947477i	$0.603624\pi$
$464$	4.40804	+	9.21752i	0.204638	+	0.427913i
$465$		0			0
$466$	14.6376	+	2.21646i	0.678075	+	0.102676i
$467$	12.9076	+	3.45858i	0.597292	+	0.160044i	0.544784	−	0.838577i	$-0.316612\pi$
$467$	12.9076	+	3.45858i	0.597292	+	0.160044i	0.0525083	+	0.998620i	$0.483278\pi$
$468$	0.774565	−	19.9728i	0.0358043	−	0.923241i
$469$	5.29167	−	6.30492i	0.244347	−	0.291134i
$470$		0			0
$471$	8.43596	−	4.87051i	0.388709	−	0.224421i
$472$	−1.11293	+	5.81690i	−0.0512267	+	0.267745i
$473$	8.32876	+	31.0834i	0.382957	+	1.42921i
$474$	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
$478$	−18.1370	+	2.03105i	−0.829569	+	0.0928980i
$479$	3.91630	−	6.78323i	0.178940	−	0.309934i	−0.762578	−	0.646897i	$-0.776066\pi$
$479$	3.91630	−	6.78323i	0.178940	−	0.309934i	0.941518	+	0.336963i	$0.109400\pi$
$480$		0			0
$481$	13.6823	+	23.6984i	0.623858	+	1.08055i
$482$	−1.53719	+	3.51675i	−0.0700172	+	0.160183i
$483$	−14.5763	+	10.2040i	−0.663245	+	0.464298i
$484$	−2.84968	−	3.07963i	−0.129531	−	0.139983i
$485$		0			0
$486$	−3.20381	+	21.1581i	−0.145328	+	0.959751i
$487$	0.631456	+	2.35662i	0.0286140	+	0.106789i	0.978756	−	0.205029i	$-0.0657288\pi$
$487$	0.631456	+	2.35662i	0.0286140	+	0.106789i	−0.950142	+	0.311818i	$0.899062\pi$
$488$	4.06823	+	3.51548i	0.184160	+	0.159138i
$489$		−	1.20836i		−	0.0546439i
$490$		0			0
$491$			33.5206i			1.51276i	0.654130	+	0.756382i	$0.273035\pi$
$491$			33.5206i			1.51276i	−0.654130	+	0.756382i	$0.726965\pi$
$492$	15.7462	−	8.29471i	0.709895	−	0.373954i
$493$	1.57746	+	5.88718i	0.0710454	+	0.265145i
$494$	−20.1537	−	3.05171i	−0.906757	−	0.137303i
$495$		0			0
$496$	14.3788	+	1.11693i	0.645628	+	0.0501517i
$497$	17.5502	−	12.2859i	0.787236	−	0.551096i
$498$	12.3230	+	5.38646i	0.552207	+	0.241373i
$499$	10.3462	+	17.9201i	0.463159	+	0.802216i	0.999116	−	0.0420297i	$-0.0133824\pi$
$499$	10.3462	+	17.9201i	0.463159	+	0.802216i	−0.535957	+	0.844245i	$0.680049\pi$
$500$		0			0
$501$	1.72926	−	2.99516i	0.0772575	−	0.133814i
$502$	−0.496326	−	4.43214i	−0.0221521	−	0.197816i
$503$	−4.35918	−	4.35918i	−0.194366	−	0.194366i	0.603214	−	0.797580i	$-0.293887\pi$
$503$	−4.35918	−	4.35918i	−0.194366	−	0.194366i	−0.797580	+	0.603214i	$0.793887\pi$
$504$	−12.9763	−	1.32674i	−0.578012	−	0.0590975i
$505$		0			0
$506$	15.7945	−	19.7781i	0.702152	−	0.879242i
$507$	5.76644	+	21.5207i	0.256097	+	0.955766i
$508$	−20.1828	+	32.0239i	−0.895468	+	1.42083i
$509$	−26.4887	+	15.2933i	−1.17409	+	0.677862i	−0.954640	−	0.297761i	$-0.903760\pi$
$509$	−26.4887	+	15.2933i	−1.17409	+	0.677862i	−0.219451	+	0.975623i	$0.570427\pi$
$510$		0			0
$511$	16.5867	−	19.7628i	0.733754	−	0.874253i
$512$	12.1557	−	19.0851i	0.537211	−	0.843448i
$513$	12.9123	+	3.45983i	0.570091	+	0.152755i
$514$	−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
$518$	15.9980	−	7.93561i	0.702913	−	0.348671i
$519$	−26.4469			−1.16089
$520$		0			0
$521$	−4.68273	+	8.11072i	−0.205154	+	0.355337i	−0.950182	−	0.311696i	$-0.899103\pi$
$521$	−4.68273	+	8.11072i	−0.205154	+	0.355337i	0.745028	+	0.667033i	$0.232436\pi$
$522$	−3.73562	−	5.06880i	−0.163503	−	0.221855i
$523$	8.46836	−	31.6043i	0.370296	−	1.38196i	−0.489803	−	0.871833i	$-0.662931\pi$
$523$	8.46836	−	31.6043i	0.370296	−	1.38196i	0.860098	−	0.510128i	$-0.170402\pi$
$524$	22.5424	−	20.8592i	0.984770	−	0.911240i
$525$		0			0
$526$	38.4366	−	15.0551i	1.67592	−	0.656432i
$527$	8.30998	+	2.22665i	0.361988	+	0.0969945i
$528$	−13.1536	+	2.45171i	−0.572437	+	0.106697i
$529$	−11.2432	−	6.49124i	−0.488833	−	0.282228i
$530$		0			0
$531$		−	3.64981i		−	0.158388i
$532$	−2.81729	+	13.0004i	−0.122145	+	0.563640i
$533$	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
$537$	2.04949	−	7.64880i	0.0884420	−	0.330070i
$538$	7.91844	+	3.46120i	0.341388	+	0.149223i
$539$	−16.0022	+	13.4213i	−0.689265	+	0.578096i
$540$		0			0
$541$	2.73095	+	4.73015i	0.117413	+	0.203365i	0.918742	−	0.394859i	$-0.129207\pi$
$541$	2.73095	+	4.73015i	0.117413	+	0.203365i	−0.801329	+	0.598224i	$0.795873\pi$
$542$	25.0685	−	18.4751i	1.07679	−	0.793572i
$543$	2.57107	−	0.688915i	0.110335	−	0.0295642i
$544$	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	−0.600718	−	0.799461i	$-0.705118\pi$
$547$	4.64823	−	4.64823i	0.198744	−	0.198744i	0.799461	+	0.600718i	$0.205118\pi$
$548$	8.33791	−	4.39220i	0.356178	−	0.187626i
$549$	−2.86959	−	1.65676i	−0.122471	−	0.0707087i
$550$		0			0
$551$	−5.56098	+	3.21064i	−0.236906	+	0.136778i
$552$	6.24572	+	17.9669i	0.265835	+	0.764721i
$553$	9.01572	−	19.3286i	0.383387	−	0.821934i
$554$	−21.6699	+	8.48777i	−0.920664	+	0.360611i
$555$		0			0
$556$	−20.1024	+	4.55945i	−0.852532	+	0.193364i
$557$	12.0516	−	3.22921i	0.510642	−	0.136826i	0.00570726	−	0.999984i	$-0.498183\pi$
$557$	12.0516	−	3.22921i	0.510642	−	0.136826i	0.504934	+	0.863158i	$0.331517\pi$
$558$	−8.83273	+	0.989120i	−0.373919	+	0.0418728i
$559$	−61.8381			−2.61547
$560$		0			0
$561$	−7.98155			−0.336981
$562$	9.54671	−	1.06907i	0.402704	−	0.0450962i
$563$	−18.3414	+	4.91456i	−0.772997	+	0.207124i	−0.623695	−	0.781668i	$-0.714369\pi$
$563$	−18.3414	+	4.91456i	−0.772997	+	0.207124i	−0.149302	+	0.988792i	$0.547703\pi$
$564$	6.47167	−	1.46785i	0.272507	−	0.0618076i
$565$		0			0
$566$	17.1775	−	6.72818i	0.722025	−	0.282807i
$567$	−1.93053	+	0.168680i	−0.0810747	+	0.00708388i
$568$	−7.52000	−	21.6326i	−0.315532	−	0.907682i
$569$	−19.5330	+	11.2774i	−0.818868	+	0.472773i	−0.850026	−	0.526741i	$-0.823414\pi$
$569$	−19.5330	+	11.2774i	−0.818868	+	0.472773i	0.0311582	+	0.999514i	$0.490080\pi$
$570$		0			0
$571$	−22.8480	−	13.1913i	−0.956158	−	0.552038i	−0.0611692	−	0.998127i	$-0.519483\pi$
$571$	−22.8480	−	13.1913i	−0.956158	−	0.552038i	−0.894988	+	0.446090i	$0.852816\pi$
$572$	−30.2702	+	15.9456i	−1.26566	+	0.666717i
$573$	−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
$577$	−30.8143	+	8.25666i	−1.28282	+	0.343729i	−0.834927	−	0.550360i	$-0.814490\pi$
$577$	−30.8143	+	8.25666i	−1.28282	+	0.343729i	−0.447888	+	0.894090i	$0.647824\pi$
$578$	−12.8719	+	9.48637i	−0.535401	+	0.394581i
$579$	11.8402	+	20.5077i	0.492060	+	0.852273i
$580$		0			0
$581$	3.89953	−	22.1007i	0.161780	−	0.916892i
$582$	13.6250	+	5.95556i	0.564773	+	0.246866i
$583$	1.97662	−	7.37683i	0.0818630	−	0.305517i
$584$	−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	−0.944092	−	0.329682i	$-0.893058\pi$
$587$	−14.8860	+	14.8860i	−0.614410	+	0.614410i	0.329682	+	0.944092i	$0.393058\pi$
$588$	−2.12098	−	15.5518i	−0.0874677	−	0.641345i
$589$			9.06388i			0.373471i
$590$		0			0
$591$	−1.39169	−	0.803493i	−0.0572465	−	0.0330513i
$592$	−3.49815	−	18.7679i	−0.143773	−	0.771354i
$593$	−31.8592	−	8.53664i	−1.30830	−	0.350558i	−0.463717	−	0.885984i	$-0.653484\pi$
$593$	−31.8592	−	8.53664i	−1.30830	−	0.350558i	−0.844582	+	0.535426i	$0.820151\pi$
$594$	20.8921	−	8.18314i	0.857214	−	0.335758i
$595$		0			0
$596$	14.1987	−	13.1385i	0.581602	−	0.538176i
$597$	−2.76089	+	10.3038i	−0.112996	+	0.421705i
$598$	28.8558	+	39.1539i	1.18000	+	1.60112i
$599$	−8.79228	+	15.2287i	−0.359243	+	0.622227i	−0.987835	−	0.155509i	$-0.950298\pi$
$599$	−8.79228	+	15.2287i	−0.359243	+	0.622227i	0.628592	+	0.777736i	$0.283632\pi$
$600$		0			0
$601$	−17.7704			−0.724871			−0.362436	−	0.932009i	$-0.618055\pi$
$601$	−17.7704			−0.724871			−0.362436	+	0.932009i	$0.618055\pi$
$602$	−2.54583	+	40.2751i	−0.103760	+	1.64149i
$603$	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
$607$	−9.32548	−	2.49876i	−0.378510	−	0.101421i	0.0645477	−	0.997915i	$-0.479440\pi$
$607$	−9.32548	−	2.49876i	−0.378510	−	0.101421i	−0.443057	+	0.896493i	$0.646106\pi$
$608$	12.5500	+	6.68762i	0.508970	+	0.271219i
$609$	4.87086	−	5.80354i	0.197377	−	0.235171i
$610$		0			0
$611$	14.6951	−	8.48424i	0.594502	−	0.343236i
$612$	−4.43518	+	7.03725i	−0.179281	+	0.284464i
$613$	−2.25362	−	8.41064i	−0.0910230	−	0.339702i	0.905364	−	0.424637i	$-0.139598\pi$
$613$	−2.25362	−	8.41064i	−0.0910230	−	0.339702i	−0.996386	+	0.0849350i	$0.972932\pi$
$614$	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	$0.954023\pi$
$618$	0.727229	+	6.49407i	0.0292534	+	0.261230i
$619$	7.01153	−	12.1443i	0.281817	−	0.488121i	−0.690015	−	0.723795i	$-0.742396\pi$
$619$	7.01153	−	12.1443i	0.281817	−	0.488121i	0.971832	+	0.235673i	$0.0757296\pi$
$620$		0			0
$621$	−15.9489	−	27.6243i	−0.640006	−	1.10852i
$622$	−39.1128	−	17.0965i	−1.56828	−	0.685505i
$623$	4.92796	+	2.29862i	0.197434	+	0.0920923i
$624$	1.99127	−	25.6346i	0.0797144	−	1.02620i
$625$		0			0
$626$	30.8496	+	4.67131i	1.23300	+	0.186703i
$627$	−2.17641	−	8.12248i	−0.0869175	−	0.324381i
$628$	−15.3745	+	8.09889i	−0.613509	+	0.323181i
$629$		−	11.3883i		−	0.454080i
$630$		0			0
$631$		−	25.9447i		−	1.03284i	−0.856334	−	0.516422i	$-0.827264\pi$
$631$		−	25.9447i		−	1.03284i	0.856334	−	0.516422i	$-0.172736\pi$
$632$	−17.2517	−	14.9077i	−0.686234	−	0.592996i
$633$	−7.81936	−	29.1823i	−0.310792	−	1.15989i
$634$	0.306899	−	2.02678i	0.0121885	−	0.0804936i
$635$		0			0
$636$	3.89803	+	4.21257i	0.154567	+	0.167039i
$637$	−16.9533	−	36.3779i	−0.671713	−	1.44134i
$638$	−4.31676	+	9.87576i	−0.170902	+	0.390985i
$639$	7.05703	+	12.2231i	0.279172	+	0.483540i
$640$		0			0
$641$	−2.50802	+	4.34403i	−0.0990610	+	0.171579i	−0.911296	−	0.411751i	$-0.864917\pi$
$641$	−2.50802	+	4.34403i	−0.0990610	+	0.171579i	0.812235	+	0.583330i	$0.198251\pi$
$642$	−16.4130	+	1.83799i	−0.647770	+	0.0725396i
$643$	−5.68565	−	5.68565i	−0.224220	−	0.224220i	0.586053	−	0.810273i	$-0.300681\pi$
$643$	−5.68565	−	5.68565i	−0.224220	−	0.224220i	−0.810273	+	0.586053i	$0.800681\pi$
$644$	26.6889	−	17.1818i	1.05169	−	0.677057i
$645$		0			0
$646$	6.62862	+	5.29354i	0.260800	+	0.208271i
$647$	5.04946	+	18.8448i	0.198515	+	0.740867i	0.991329	+	0.131404i	$0.0419484\pi$
$647$	5.04946	+	18.8448i	0.198515	+	0.740867i	−0.792814	+	0.609463i	$0.791385\pi$
$648$	−0.389308	+	2.03478i	−0.0152934	+	0.0799337i
$649$	−5.41041	+	3.12370i	−0.212377	+	0.122616i
$650$		0			0
$651$	−3.65670	−	10.0502i	−0.143318	−	0.393900i
$652$	−0.0835344	+	2.15400i	−0.00327146	+	0.0843572i
$653$	−25.9460	−	6.95220i	−1.01534	−	0.272061i	−0.287483	−	0.957786i	$-0.592819\pi$
$653$	−25.9460	−	6.95220i	−1.01534	−	0.272061i	−0.727861	+	0.685725i	$0.759485\pi$
$654$	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
$658$	−4.92079	−	9.92022i	−0.191832	−	0.386730i
$659$	−2.47864			−0.0965543			−0.0482771	−	0.998834i	$-0.515373\pi$
$659$	−2.47864			−0.0965543			−0.0482771	+	0.998834i	$0.515373\pi$
$660$		0			0
$661$	−6.04270	+	10.4663i	−0.235034	+	0.407091i	−0.959283	−	0.282448i	$-0.908853\pi$
$661$	−6.04270	+	10.4663i	−0.235034	+	0.407091i	0.724249	+	0.689539i	$0.242187\pi$
$662$	−32.3046	+	23.8080i	−1.25556	+	0.925322i
$663$	3.96968	−	14.8150i	0.154169	−	0.575368i
$664$	−21.5944	−	10.4537i	−0.838025	−	0.405682i
$665$		0			0
$666$	4.29088	+	10.9549i	0.166268	+	0.424494i
$667$	14.8001	+	3.96569i	0.573064	+	0.153552i
$668$	−3.28960	+	5.21957i	−0.127278	+	0.201951i
$669$	−3.05684	−	1.76487i	−0.118184	−	0.0682337i
$670$		0			0
$671$			5.67177i			0.218956i
$672$	−16.6138	−	2.35226i	−0.640890	−	0.0907405i
$673$	−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
$677$	8.74919	−	32.6524i	0.336259	−	1.25493i	−0.566240	−	0.824241i	$-0.691602\pi$
$677$	8.74919	−	32.6524i	0.336259	−	1.25493i	0.902498	−	0.430693i	$-0.141731\pi$
$678$	6.60567	−	15.1123i	0.253689	−	0.580384i
$679$	4.31152	−	24.4357i	0.165461	−	0.937756i
$680$		0			0
$681$	−4.52124	−	7.83101i	−0.173254	−	0.300085i
$682$	9.02578	+	12.2469i	0.345615	+	0.468960i
$683$	7.23810	−	1.93944i	0.276958	−	0.0742107i	−0.117666	−	0.993053i	$-0.537541\pi$
$683$	7.23810	−	1.93944i	0.276958	−	0.0742107i	0.394625	+	0.918842i	$0.370875\pi$
$684$	−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
$688$	40.6819	+	14.3597i	1.55098	+	0.547458i
$689$	12.7095	+	7.33783i	0.484193	+	0.279549i
$690$		0			0
$691$	16.5249	−	9.54066i	0.628637	−	0.362944i	−0.151587	−	0.988444i	$-0.548438\pi$
$691$	16.5249	−	9.54066i	0.628637	−	0.362944i	0.780224	+	0.625500i	$0.215105\pi$
$692$	47.1437	+	1.82828i	1.79213	+	0.0695009i
$693$	−7.89102	−	11.2722i	−0.299755	−	0.428197i
$694$	8.23405	+	21.0221i	0.312560	+	0.797987i
$695$		0			0
$696$	−4.54912	−	6.70170i	−0.172434	−	0.254027i
$697$	−18.2937	+	4.90178i	−0.692923	+	0.185668i
$698$	−1.18457	−	10.5780i	−0.0448365	−	0.400385i
$699$	−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	$0.692000\pi$
$702$	4.79839	+	42.8490i	0.181103	+	1.61723i
$703$	11.5893	−	3.10535i	0.437100	−	0.117121i
$704$	23.6168	−	3.46106i	0.890093	−	0.130443i
$705$		0			0
$706$	−2.89170	−	7.38272i	−0.108831	−	0.277852i
$707$	19.6768	−	1.71926i	0.740023	−	0.0646594i
$708$	0.181941	−	4.69150i	0.00683777	−	0.176317i
$709$	−23.7012	+	13.6839i	−0.890117	+	0.513909i	−0.873981	−	0.485960i	$-0.838470\pi$
$709$	−23.7012	+	13.6839i	−0.890117	+	0.513909i	−0.0161363	+	0.999870i	$0.505137\pi$
$710$		0			0
$711$	12.1687	+	7.02562i	0.456363	+	0.263481i
$712$	3.80082	−	4.39843i	0.142442	−	0.164838i
$713$	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
$717$	13.9751	−	3.74462i	0.521911	−	0.139846i
$718$	−30.5640	−	41.4718i	−1.14064	−	1.54771i
$719$	−21.7523	−	37.6760i	−0.811223	−	1.40508i	−0.912009	−	0.410171i	$-0.865469\pi$
$719$	−21.7523	−	37.6760i	−0.811223	−	1.40508i	0.100786	−	0.994908i	$-0.467864\pi$
$720$		0			0
$721$	10.2472	−	3.72838i	0.381627	−	0.138852i
$722$	7.18238	−	16.4317i	0.267300	−	0.611523i
$723$	0.787488	−	2.93894i	0.0292870	−	0.109300i
$724$	−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	−0.927771	−	0.373151i	$-0.878277\pi$
$727$	−14.9542	+	14.9542i	−0.554620	+	0.554620i	0.373151	+	0.927771i	$0.378277\pi$
$728$	−42.3580	+	6.83183i	−1.56989	+	0.253204i
$729$		−	19.1618i		−	0.709695i
$730$		0			0
$731$	22.2872	+	12.8675i	0.824322	+	0.475922i
$732$	−3.60601	−	2.27266i	−0.133282	−	0.0839999i
$733$	−30.6917	−	8.22383i	−1.13363	−	0.303754i	−0.357240	−	0.934013i	$-0.616282\pi$
$733$	−30.6917	−	8.22383i	−1.13363	−	0.303754i	−0.776385	+	0.630259i	$0.782949\pi$
$734$	−16.8636	−	43.0539i	−0.622446	−	1.58915i
$735$		0			0
$736$	−9.89144	−	32.4592i	−0.364603	−	1.19646i
$737$	2.40248	−	8.96619i	0.0884966	−	0.330274i
$738$	15.7507	−	11.6080i	0.579791	−	0.427296i
$739$	−0.495453	+	0.858149i	−0.0182255	+	0.0315675i	−0.874994	−	0.484133i	$-0.839135\pi$
$739$	−0.495453	+	0.858149i	−0.0182255	+	0.0315675i	0.856769	+	0.515701i	$0.172468\pi$
$740$		0			0
$741$	16.1591			0.593619
$742$	5.30236	−	7.97559i	0.194656	−	0.292793i
$743$	−9.00016	−	9.00016i	−0.330184	−	0.330184i	0.522472	−	0.852656i	$-0.325010\pi$
$743$	−9.00016	−	9.00016i	−0.330184	−	0.330184i	−0.852656	+	0.522472i	$0.825010\pi$
$744$	−11.4030	+	0.831117i	−0.418054	+	0.0304702i
$745$		0			0
$746$	−36.5684	−	5.53727i	−1.33886	−	0.202734i
$747$	14.2815	+	3.82673i	0.522534	+	0.140013i
$748$	14.2278	+	0.551767i	0.520218	+	0.0201746i
$749$	9.42304	+	25.8987i	0.344310	+	0.946318i
$750$		0			0
$751$	−11.3279	+	6.54015i	−0.413360	+	0.238653i	−0.692232	−	0.721675i	$-0.743373\pi$
$751$	−11.3279	+	6.54015i	−0.413360	+	0.238653i	0.278872	+	0.960328i	$0.410039\pi$
$752$	−11.6378	+	2.16917i	−0.424385	+	0.0791015i
$753$	0.915071	+	3.41509i	0.0333470	+	0.124453i
$754$	−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	$0.782203\pi$
$758$	28.6382	−	3.20701i	1.04019	−	0.116484i
$759$	−10.0327	+	17.3771i	−0.364162	+	0.630748i
$760$		0			0
$761$	11.1617	+	19.3326i	0.404612	+	0.700808i	0.994276	−	0.106840i	$-0.0340734\pi$
$761$	11.1617	+	19.3326i	0.404612	+	0.700808i	−0.589665	+	0.807648i	$0.700740\pi$
$762$	12.0189	−	27.4964i	0.435397	−	0.996091i
$763$	−2.36351	−	27.0502i	−0.0855646	−	0.979282i
$764$	9.27134	−	8.57908i	0.335425	−	0.310380i
$765$		0			0
$766$	5.40621	−	35.7029i	0.195334	−	1.29000i
$767$	−3.10719	−	11.5962i	−0.112194	−	0.418714i
$768$	−7.26271	+	16.4020i	−0.262071	+	0.591856i
$769$		−	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
$772$	−19.6883	−	37.3752i	−0.708598	−	1.34516i
$773$	11.5257	+	43.0144i	0.414550	+	1.54712i	0.785736	+	0.618562i	$0.212285\pi$
$773$	11.5257	+	43.0144i	0.414550	+	1.54712i	−0.371186	+	0.928559i	$0.621049\pi$
$774$	−26.2874	−	3.98049i	−0.944880	−	0.143076i
$775$		0			0
$776$	−23.8759	−	11.5582i	−0.857094	−	0.414914i
$777$	−11.5977	+	8.11886i	−0.416066	+	0.291263i
$778$	−23.3886	−	10.2233i	−0.838523	−	0.366524i
$779$	−9.97667	−	17.2801i	−0.357451	−	0.619124i
$780$		0			0
$781$	12.0796	−	20.9224i	0.432241	−	0.748663i
$782$	−2.25266	−	20.1160i	−0.0805548	−	0.719346i
$783$	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
$787$	−10.4742	−	39.0901i	−0.373363	−	1.39341i	−0.855722	−	0.517437i	$-0.826886\pi$
$787$	−10.4742	−	39.0901i	−0.373363	−	1.39341i	0.482358	−	0.875974i	$-0.339780\pi$
$788$	2.42526	+	1.52850i	0.0863962	+	0.0544505i
$789$	−28.3405	+	16.3624i	−1.00895	+	0.582518i
$790$		0			0
$791$	−27.1031	−	4.78217i	−0.963677	−	0.170034i
$792$	−13.8943	+	4.82998i	−0.493711	+	0.171626i
$793$	−10.5277	−	2.82089i	−0.373850	−	0.100173i
$794$	−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	$0.774793\pi$
$798$	0.665257	−	10.5244i	0.0235498	−	0.372559i
$799$	−7.06174			−0.249826
$800$		0			0
$801$	−1.79123	+	3.10250i	−0.0632900	+	0.109622i
$802$	−4.10748	−	5.57337i	−0.145040	−	0.196803i
$803$	7.53057	−	28.1045i	0.265748	−	0.991786i
$804$	4.73787	+	5.12018i	0.167092	+	0.180575i
$805$		0			0
$806$	−27.2213	+	10.6622i	−0.958830	+	0.375560i
$807$	−6.61744	−	1.77314i	−0.232945	−	0.0624174i
$808$	3.96799	−	20.7394i	0.139594	−	0.729608i
$809$	26.5415	+	15.3237i	0.933148	+	0.538753i	0.887806	−	0.460218i	$-0.152229\pi$
$809$	26.5415	+	15.3237i	0.933148	+	0.538753i	0.0453422	+	0.998972i	$0.485562\pi$
$810$		0			0
$811$			47.0428i			1.65190i	0.563747	+	0.825948i	$0.309359\pi$
$811$			47.0428i			1.65190i	−0.563747	+	0.825948i	$0.690641\pi$
$812$	−9.08391	+	10.0086i	−0.318783	+	0.351231i
$813$	−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
$817$	−7.01744	+	26.1894i	−0.245509	+	0.916253i
$818$	43.4672	+	18.9998i	1.51979	+	0.664312i
$819$	24.8478	−	9.04066i	0.868251	−	0.315906i
$820$		0			0
$821$	0.415401	+	0.719496i	0.0144976	+	0.0251106i	0.873183	−	0.487392i	$-0.162052\pi$
$821$	0.415401	+	0.719496i	0.0144976	+	0.0251106i	−0.858686	+	0.512503i	$0.828718\pi$
$822$	−6.01413	+	4.43231i	−0.209767	+	0.154594i
$823$	0.223479	−	0.0598810i	0.00778999	−	0.00208732i	−0.254922	−	0.966962i	$-0.582050\pi$
$823$	0.223479	−	0.0598810i	0.00778999	−	0.00208732i	0.262712	+	0.964874i	$0.415383\pi$
$824$	−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	−0.707133	−	0.707081i	$-0.750012\pi$
$827$	−0.00150949	+	0.00150949i	−5.24902e−5	+	5.24902e-5i	0.707081	+	0.707133i	$0.250012\pi$
$828$	9.74626	+	18.5018i	0.338706	+	0.642981i
$829$	−36.8314	−	21.2646i	−1.27921	−	0.738551i	−0.302506	−	0.953148i	$-0.597823\pi$
$829$	−36.8314	−	21.2646i	−1.27921	−	0.738551i	−0.976703	+	0.214596i	$0.931156\pi$
$830$		0			0
$831$	15.9779	−	9.22484i	0.554267	−	0.320006i
$832$	−5.32172	+	45.5580i	−0.184497	+	1.57944i
$833$	−1.45949	+	16.6387i	−0.0505683	+	0.576498i
$834$	15.2155	−	5.95970i	0.526870	−	0.206368i
$835$		0			0
$836$	3.31812	+	14.6294i	0.114760	+	0.505970i
$837$	18.5194	−	4.96227i	0.640126	−	0.171521i
$838$	51.1204	−	5.72464i	1.76592	−	0.197754i
$839$	49.4733			1.70801			0.854004	−	0.520267i	$-0.174168\pi$
$839$	49.4733			1.70801			0.854004	+	0.520267i	$0.174168\pi$
$840$		0			0
$841$	22.4754			0.775014
$842$	−46.7267	+	5.23262i	−1.61031	+	0.180328i
$843$	−7.35602	+	1.97104i	−0.253355	+	0.0678862i
$844$	11.9213	+	52.5603i	0.410347	+	1.80920i
$845$		0			0
$846$	6.79303	−	2.66073i	0.233549	−	0.0914778i
$847$	2.34633	−	5.03023i	0.0806207	−	0.172841i
$848$	−6.65734	−	7.77872i	−0.228614	−	0.267122i
$849$	−12.6655	+	7.31245i	−0.434680	+	0.250963i
$850$		0			0
$851$	−24.7940	−	14.3148i	−0.849928	−	0.490706i
$852$	8.46185	+	16.0635i	0.289898	+	0.550327i
$853$	−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
$857$	21.7101	−	5.81720i	0.741602	−	0.198712i	0.131812	−	0.991275i	$-0.457920\pi$
$857$	21.7101	−	5.81720i	0.741602	−	0.198712i	0.609790	+	0.792563i	$0.291254\pi$
$858$	21.8338	−	16.0912i	0.745395	−	0.549343i
$859$	4.05858	+	7.02967i	0.138477	+	0.239849i	0.926920	−	0.375258i	$-0.122446\pi$
$859$	4.05858	+	7.02967i	0.138477	+	0.239849i	−0.788443	+	0.615107i	$0.789113\pi$
$860$		0			0
$861$	18.0338	+	15.1356i	0.614590	+	0.515821i
$862$	40.3191	+	17.6237i	1.37328	+	0.600267i
$863$	0.125947	−	0.470041i	0.00428729	−	0.0160004i	−0.963749	−	0.266810i	$-0.914030\pi$
$863$	0.125947	−	0.470041i	0.00428729	−	0.0160004i	0.968036	+	0.250810i	$0.0806969\pi$
$864$	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
$868$	5.82360	+	18.1682i	0.197666	+	0.616668i
$869$		−	24.0516i		−	0.815895i
$870$		0			0
$871$	15.4478	+	8.91879i	0.523428	+	0.302202i
$872$	−28.5109	−	5.45489i	−0.965500	−	0.184726i
$873$	15.7904	+	4.23103i	0.534424	+	0.143199i
$874$	19.8569	−	7.77766i	0.671670	−	0.263083i
$875$		0			0
$876$	14.8508	+	16.0492i	0.501763	+	0.542251i
$877$	−4.62691	+	17.2678i	−0.156240	+	0.583094i	0.842757	+	0.538295i	$0.180931\pi$
$877$	−4.62691	+	17.2678i	−0.156240	+	0.583094i	−0.998996	+	0.0447988i	$0.985735\pi$
$878$	0.467440	+	0.634262i	0.0157753	+	0.0214053i
$879$	−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	$0.528320\pi$
$882$	−4.86521	−	16.5555i	−0.163820	−	0.557453i
$883$	5.20270	+	5.20270i	0.175085	+	0.175085i	0.789209	−	0.614124i	$-0.210491\pi$
$883$	5.20270	+	5.20270i	0.175085	+	0.175085i	−0.614124	+	0.789209i	$0.710491\pi$
$884$	−8.10044	+	26.1346i	−0.272447	+	0.879001i
$885$		0			0
$886$	−5.16404	+	34.1036i	−0.173489	+	1.14573i
$887$	−43.1849	−	11.5714i	−1.45001	−	0.388528i	−0.553981	−	0.832529i	$-0.686892\pi$
$887$	−43.1849	−	11.5714i	−1.45001	−	0.388528i	−0.896026	+	0.444001i	$0.853559\pi$
$888$	4.96944	+	14.2954i	0.166764	+	0.479724i
$889$	−49.3135	−	8.70105i	−1.65392	−	0.291824i
$890$		0			0
$891$	−1.89259	+	1.09269i	−0.0634040	+	0.0366063i
$892$	5.32706	+	3.35734i	0.178363	+	0.112412i
$893$	−1.92560	−	7.18643i	−0.0644377	−	0.240485i
$894$	−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
$898$	1.36050	+	12.1491i	0.0454005	+	0.405421i
$899$	−4.60486	+	7.97585i	−0.153581	+	0.266009i
$900$		0			0
$901$	−3.05377	−	5.28929i	−0.101736	−	0.176212i
$902$	−30.6877	−	13.4138i	−1.02179	−	0.446631i
$903$	−2.78469	−	31.8706i	−0.0926686	−	1.06059i
$904$	−12.8199	+	26.4822i	−0.426382	+	0.880785i
$905$		0			0
$906$	−1.73039	−	0.262019i	−0.0574882	−	0.00870499i
$907$	2.53267	+	9.45206i	0.0840960	+	0.313851i	0.995141	−	0.0984553i	$-0.0313902\pi$
$907$	2.53267	+	9.45206i	0.0840960	+	0.313851i	−0.911045	+	0.412306i	$0.864723\pi$
$908$	7.51811	+	14.2720i	0.249497	+	0.473632i
$909$			13.0129i			0.431610i
$910$		0			0
$911$		−	5.81294i		−	0.192591i	−0.995353	−	0.0962957i	$-0.969301\pi$
$911$		−	5.81294i		−	0.192591i	0.995353	−	0.0962957i	$-0.0306994\pi$
$912$	−10.6307	−	3.75237i	−0.352017	−	0.124253i
$913$	−6.55024	−	24.4458i	−0.216781	−	0.809038i
$914$	−0.578756	+	3.82213i	−0.0191435	+	0.126425i
$915$		0			0
$916$	3.57148	−	3.30481i	0.118005	−	0.109194i
$917$	36.8205	+	17.1747i	1.21592	+	0.567160i
$918$	7.18681	−	16.4418i	0.237200	−	0.542660i
$919$	10.6688	+	18.4789i	0.351930	+	0.609561i	0.986588	−	0.163232i	$-0.0521921\pi$
$919$	10.6688	+	18.4789i	0.351930	+	0.609561i	−0.634657	+	0.772794i	$0.718859\pi$
$920$		0			0
$921$	−9.23283	+	15.9917i	−0.304232	+	0.526946i
$922$	54.2476	−	6.07484i	1.78655	−	0.200064i
$923$	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
$927$	1.85937	+	6.93927i	0.0610698	+	0.227916i
$928$	7.64588	+	12.2608i	0.250988	+	0.402481i
$929$	12.5925	−	7.27026i	0.413145	−	0.238529i	−0.278995	−	0.960293i	$-0.590001\pi$
$929$	12.5925	−	7.27026i	0.413145	−	0.238529i	0.692140	+	0.721763i	$0.256668\pi$
$930$		0			0
$931$	−17.3305	+	3.05180i	−0.567984	+	0.100019i
$932$	20.9210	+	0.811338i	0.685290	+	0.0265763i
$933$	32.6866	+	8.75834i	1.07011	+	0.286735i
$934$	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	$0.787244\pi$
$938$	6.44477	−	9.69395i	0.210429	−	0.316519i
$939$	−24.7350			−0.807195
$940$		0			0
$941$	1.44742	−	2.50700i	0.0471845	−	0.0817259i	−0.841469	−	0.540306i	$-0.818308\pi$
$941$	1.44742	−	2.50700i	0.0471845	−	0.0817259i	0.888653	+	0.458580i	$0.151642\pi$
$942$	11.0896	−	8.17284i	0.361319	−	0.266286i
$943$	−12.3229	+	45.9897i	−0.401289	+	1.49763i
$944$	−0.648650	+	8.35040i	−0.0211118	+	0.271782i
$945$		0			0
$946$	16.5975	+	42.3746i	0.539632	+	1.37772i
$947$	32.5747	+	8.72837i	1.05854	+	0.283634i	0.745775	−	0.666198i	$-0.232079\pi$
$947$	32.5747	+	8.72837i	1.05854	+	0.283634i	0.312761	+	0.949832i	$0.398746\pi$
$948$	15.2916	+	9.63740i	0.496647	+	0.313008i
$949$	48.4211	+	27.9559i	1.57181	+	0.907487i
$950$		0			0
$951$			1.62505i			0.0526960i
$952$	16.6879	+	6.35175i	0.540859	+	0.205861i
$953$	−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
$957$	2.21143	−	8.25317i	0.0714854	−	0.266787i
$958$	4.43650	−	10.1497i	0.143337	−	0.327922i
$959$	9.54923	+	8.01459i	0.308361	+	0.258805i
$960$		0			0
$961$	−9.00006	−	15.5886i	−0.290325	−	0.502857i
$962$	22.9592	+	31.1530i	0.740236	+	1.00441i
$963$	−17.5382	+	4.69935i	−0.565161	+	0.151435i
$964$	−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	−0.740620	−	0.671925i	$-0.765468\pi$
$967$	−2.13618	+	2.13618i	−0.0686949	+	0.0686949i	0.671925	+	0.740620i	$0.265468\pi$
$968$	−4.48972	−	3.87970i	−0.144305	−	0.124698i
$969$	−5.82393	−	3.36245i	−0.187092	−	0.108017i
$970$		0			0
$971$	14.3494	−	8.28465i	0.460495	−	0.265867i	−0.251757	−	0.967790i	$-0.581008\pi$
$971$	14.3494	−	8.28465i	0.460495	−	0.265867i	0.712252	+	0.701923i	$0.247675\pi$
$972$	−1.17276	+	30.2404i	−0.0376162	+	0.969963i
$973$	−15.6380	−	22.3387i	−0.501331	−	0.716147i
$974$	1.25836	+	3.21269i	0.0403206	+	0.102941i
$975$		0			0
$976$	6.27089	+	4.30048i	0.200726	+	0.137655i
$977$	−0.302331	+	0.0810094i	−0.00967243	+	0.00259172i	−0.263652	−	0.964618i	$-0.584927\pi$
$977$	−0.302331	+	0.0810094i	−0.00967243	+	0.00259172i	0.253980	+	0.967210i	$0.418260\pi$
$978$	−0.190178	−	1.69826i	−0.00608121	−	0.0543045i
$979$	6.13213			0.195984
$980$		0			0
$981$	17.8891			0.571156
$982$	5.27563	+	47.1108i	0.168352	+	1.50337i
$983$	−55.7548	+	14.9395i	−1.77830	+	0.476495i	−0.990272	−	0.139142i	$-0.955566\pi$
$983$	−55.7548	+	14.9395i	−1.77830	+	0.476495i	−0.788030	+	0.615636i	$0.788899\pi$
$984$	20.8247	−	14.1358i	0.663868	−	0.450634i
$985$		0			0
$986$	3.14357	+	8.02574i	0.100112	+	0.255592i
$987$	5.03442	+	7.19163i	0.160247	+	0.228912i
$988$	−28.8049	−	1.11708i	−0.916405	−	0.0355391i
$989$	56.0292	−	32.3485i	1.78162	−	1.02862i
$990$		0			0
$991$	19.0262	+	10.9848i	0.604386	+	0.348942i	0.770765	−	0.637120i	$-0.219874\pi$
$991$	19.0262	+	10.9848i	0.604386	+	0.348942i	−0.166379	+	0.986062i	$0.553208\pi$
$992$	20.3842	−	0.693241i	0.647199	−	0.0220104i
$993$	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
$997$	−8.14653	+	2.18286i	−0.258003	+	0.0691317i	−0.385502	−	0.922707i	$-0.625972\pi$
$997$	−8.14653	+	2.18286i	−0.258003	+	0.0691317i	0.127499	+	0.991839i	$0.459305\pi$
$998$	17.3612	+	23.5571i	0.549559	+	0.745688i
$999$	−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.207.17		72
4.3	odd	2	inner	700.2.be.e.207.5		72
5.2	odd	4		140.2.w.b.123.10	yes	72
5.3	odd	4	inner	700.2.be.e.543.9		72
5.4	even	2		140.2.w.b.67.2	yes	72
7.2	even	3	inner	700.2.be.e.107.6		72
20.3	even	4	inner	700.2.be.e.543.6		72
20.7	even	4		140.2.w.b.123.13	yes	72
20.19	odd	2		140.2.w.b.67.14	yes	72
28.23	odd	6	inner	700.2.be.e.107.9		72
35.2	odd	12		140.2.w.b.23.14	yes	72
35.4	even	6		980.2.k.k.687.13		36
35.9	even	6		140.2.w.b.107.13	yes	72
35.12	even	12		980.2.x.m.863.14		72
35.17	even	12		980.2.k.j.883.3		36
35.19	odd	6		980.2.x.m.667.13		72
35.23	odd	12	inner	700.2.be.e.443.5		72
35.24	odd	6		980.2.k.j.687.13		36
35.27	even	4		980.2.x.m.263.10		72
35.32	odd	12		980.2.k.k.883.3		36
35.34	odd	2		980.2.x.m.67.2		72
140.19	even	6		980.2.x.m.667.10		72
140.23	even	12	inner	700.2.be.e.443.17		72
140.27	odd	4		980.2.x.m.263.13		72
140.39	odd	6		980.2.k.k.687.3		36
140.47	odd	12		980.2.x.m.863.2		72
140.59	even	6		980.2.k.j.687.3		36
140.67	even	12		980.2.k.k.883.13		36
140.79	odd	6		140.2.w.b.107.10	yes	72
140.87	odd	12		980.2.k.j.883.13		36
140.107	even	12		140.2.w.b.23.2	✓	72
140.139	even	2		980.2.x.m.67.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.2	✓	72	140.107	even	12
140.2.w.b.23.14	yes	72	35.2	odd	12
140.2.w.b.67.2	yes	72	5.4	even	2
140.2.w.b.67.14	yes	72	20.19	odd	2
140.2.w.b.107.10	yes	72	140.79	odd	6
140.2.w.b.107.13	yes	72	35.9	even	6
140.2.w.b.123.10	yes	72	5.2	odd	4
140.2.w.b.123.13	yes	72	20.7	even	4
700.2.be.e.107.6		72	7.2	even	3	inner
700.2.be.e.107.9		72	28.23	odd	6	inner
700.2.be.e.207.5		72	4.3	odd	2	inner
700.2.be.e.207.17		72	1.1	even	1	trivial
700.2.be.e.443.5		72	35.23	odd	12	inner
700.2.be.e.443.17		72	140.23	even	12	inner
700.2.be.e.543.6		72	20.3	even	4	inner
700.2.be.e.543.9		72	5.3	odd	4	inner
980.2.k.j.687.3		36	140.59	even	6
980.2.k.j.687.13		36	35.24	odd	6
980.2.k.j.883.3		36	35.17	even	12
980.2.k.j.883.13		36	140.87	odd	12
980.2.k.k.687.3		36	140.39	odd	6
980.2.k.k.687.13		36	35.4	even	6
980.2.k.k.883.3		36	35.32	odd	12
980.2.k.k.883.13		36	140.67	even	12
980.2.x.m.67.2		72	35.34	odd	2
980.2.x.m.67.14		72	140.139	even	2
980.2.x.m.263.10		72	35.27	even	4
980.2.x.m.263.13		72	140.27	odd	4
980.2.x.m.667.10		72	140.19	even	6
980.2.x.m.667.13		72	35.19	odd	6
980.2.x.m.863.2		72	140.47	odd	12
980.2.x.m.863.14		72	35.12	even	12

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)

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

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Database

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