LMFDB - Embedded newform 200.2.v.c.3.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(3,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 10, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.v (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [208,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$26$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			3.18
Character	$\chi$	$=$	200.3
Dual form			200.2.v.c.67.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.746320 + 1.20125i) q^{2} +(0.238378 + 1.50506i) q^{3} +(-0.886011 + 1.79304i) q^{4} +(-2.20632 + 0.363530i) q^{5} +(-1.63005 + 1.40961i) q^{6} +(-0.599487 - 0.599487i) q^{7} +(-2.81514 + 0.273858i) q^{8} +(0.644782 - 0.209502i) q^{9} +(-2.08331 - 2.37903i) q^{10} +(-0.504364 + 1.55227i) q^{11} +(-2.90984 - 0.906081i) q^{12} +(5.16603 + 2.63223i) q^{13} +(0.272725 - 1.16754i) q^{14} +(-1.07307 - 3.23399i) q^{15} +(-2.42997 - 3.17730i) q^{16} +(0.424918 - 2.68282i) q^{17} +(0.732879 + 0.618190i) q^{18} +(1.03303 + 1.42184i) q^{19} +(1.30300 - 4.27811i) q^{20} +(0.759360 - 1.04517i) q^{21} +(-2.24109 + 0.552625i) q^{22} +(3.27737 + 6.43220i) q^{23} +(-1.08324 - 4.17168i) q^{24} +(4.73569 - 1.60413i) q^{25} +(0.693551 + 8.17019i) q^{26} +(2.54442 + 4.99370i) q^{27} +(1.60605 - 0.543750i) q^{28} +(-6.49732 - 4.72058i) q^{29} +(3.08398 - 3.70263i) q^{30} +(-1.09301 - 1.50440i) q^{31} +(2.00321 - 5.29029i) q^{32} +(-2.45650 - 0.389071i) q^{33} +(3.53987 - 1.49181i) q^{34} +(1.54059 + 1.10473i) q^{35} +(-0.195639 + 1.34174i) q^{36} +(-0.398349 + 0.781804i) q^{37} +(-0.937020 + 2.30208i) q^{38} +(-2.73019 + 8.40267i) q^{39} +(6.11154 - 1.62761i) q^{40} +(-1.42918 - 4.39856i) q^{41} +(1.82224 + 0.132151i) q^{42} +(3.23259 + 3.23259i) q^{43} +(-2.33641 - 2.27967i) q^{44} +(-1.34644 + 0.696627i) q^{45} +(-5.28072 + 8.73743i) q^{46} +(-1.01784 - 6.42640i) q^{47} +(4.20279 - 4.41465i) q^{48} -6.28123i q^{49} +(5.46131 + 4.49156i) q^{50} +4.13911 q^{51} +(-9.29685 + 6.93071i) q^{52} +(13.3108 - 2.10822i) q^{53} +(-4.09974 + 6.78339i) q^{54} +(0.548489 - 3.60816i) q^{55} +(1.85181 + 1.52346i) q^{56} +(-1.89371 + 1.89371i) q^{57} +(0.821520 - 11.3280i) q^{58} +(-2.90867 + 0.945085i) q^{59} +(6.74942 + 0.941288i) q^{60} +(-1.24919 - 0.405886i) q^{61} +(0.991428 - 2.43575i) q^{62} +(-0.512132 - 0.260944i) q^{63} +(7.85000 - 1.54190i) q^{64} +(-12.3548 - 3.92952i) q^{65} +(-1.36596 - 3.24124i) q^{66} +(1.73499 - 10.9543i) q^{67} +(4.43392 + 3.13891i) q^{68} +(-8.89961 + 6.46594i) q^{69} +(-0.177281 + 2.67512i) q^{70} +(-0.426288 + 0.586736i) q^{71} +(-1.75778 + 0.766357i) q^{72} +(4.64490 - 2.36670i) q^{73} +(-1.23644 + 0.104959i) q^{74} +(3.54320 + 6.74512i) q^{75} +(-3.46469 + 0.592491i) q^{76} +(1.23293 - 0.628207i) q^{77} +(-12.1313 + 2.99143i) q^{78} +(9.40528 + 6.83334i) q^{79} +(6.51633 + 6.12678i) q^{80} +(-5.26385 + 3.82441i) q^{81} +(4.21715 - 4.99954i) q^{82} +(-13.7683 - 2.18069i) q^{83} +(1.20123 + 2.28759i) q^{84} +(0.0377844 + 6.07364i) q^{85} +(-1.47061 + 6.29571i) q^{86} +(5.55594 - 10.9041i) q^{87} +(0.994752 - 4.50798i) q^{88} +(-4.46859 - 1.45193i) q^{89} +(-1.84170 - 1.09750i) q^{90} +(-1.51898 - 4.67495i) q^{91} +(-14.4370 + 0.177444i) q^{92} +(2.00367 - 2.00367i) q^{93} +(6.96009 - 6.01884i) q^{94} +(-2.79607 - 2.76150i) q^{95} +(8.43973 + 1.75386i) q^{96} +(-1.57229 + 0.249026i) q^{97} +(7.54534 - 4.68781i) q^{98} +1.10654i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q + 2 q^{2} - 16 q^{3} - 10 q^{4} - 26 q^{6} - 34 q^{8} - 20 q^{9} + 10 q^{10} - 4 q^{11} - 2 q^{12} - 30 q^{14} + 18 q^{16} - 32 q^{17} - 20 q^{18} - 10 q^{20} - 42 q^{22} - 40 q^{25} - 8 q^{26} - 28 q^{27}+ \cdots + 206 q^{98}+O(q^{100}) $ 208 * q + 2 * q^2 - 16 * q^3 - 10 * q^4 - 26 * q^6 - 34 * q^8 - 20 * q^9 + 10 * q^10 - 4 * q^11 - 2 * q^12 - 30 * q^14 + 18 * q^16 - 32 * q^17 - 20 * q^18 - 10 * q^20 - 42 * q^22 - 40 * q^25 - 8 * q^26 - 28 * q^27 + 30 * q^28 - 10 * q^30 + 22 * q^32 + 36 * q^33 + 30 * q^34 - 100 * q^35 - 38 * q^36 - 56 * q^38 + 20 * q^40 - 44 * q^41 - 70 * q^42 - 8 * q^43 + 60 * q^44 + 2 * q^46 + 104 * q^48 - 30 * q^50 + 8 * q^51 + 60 * q^52 - 140 * q^54 + 2 * q^56 + 92 * q^57 - 70 * q^58 - 40 * q^59 + 10 * q^60 - 120 * q^62 + 20 * q^64 - 40 * q^65 - 2 * q^66 - 12 * q^67 - 46 * q^68 + 30 * q^70 + 60 * q^72 - 16 * q^73 + 80 * q^75 - 24 * q^76 - 20 * q^78 + 30 * q^80 + 16 * q^81 - 22 * q^82 - 96 * q^83 - 10 * q^84 - 26 * q^86 + 134 * q^88 - 100 * q^89 + 130 * q^90 + 4 * q^91 + 70 * q^92 + 150 * q^94 - 26 * q^96 + 24 * q^97 + 206 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.746320	+	1.20125i	0.527728	+	0.849413i
$2$	0.746320	+	1.20125i	0.527728	+	0.849413i
$3$	0.238378	+	1.50506i	0.137628	+	0.868948i	0.955809	+	0.293988i	$0.0949825\pi$
$3$	0.238378	+	1.50506i	0.137628	+	0.868948i	−0.818181	+	0.574960i	$0.805018\pi$
$4$	−0.886011	+	1.79304i	−0.443006	+	0.896519i
$5$	−2.20632	+	0.363530i	−0.986696	+	0.162576i
$5$	−2.20632	+	0.363530i	−0.986696	+	0.162576i
$6$	−1.63005	+	1.40961i	−0.665466	+	0.575471i
$7$	−0.599487	−	0.599487i	−0.226585	−	0.226585i	0.584680	−	0.811264i	$-0.301220\pi$
$7$	−0.599487	−	0.599487i	−0.226585	−	0.226585i	−0.811264	+	0.584680i	$0.801220\pi$
$8$	−2.81514	+	0.273858i	−0.995302	+	0.0968234i
$9$	0.644782	−	0.209502i	0.214927	−	0.0698341i
$10$	−2.08331	−	2.37903i	−0.658801	−	0.752317i
$11$	−0.504364	+	1.55227i	−0.152071	+	0.468028i	−0.997852	−	0.0655026i	$-0.979135\pi$
$11$	−0.504364	+	1.55227i	−0.152071	+	0.468028i	0.845781	+	0.533530i	$0.179135\pi$
$12$	−2.90984	−	0.906081i	−0.839998	−	0.261563i
$13$	5.16603	+	2.63223i	1.43280	+	0.730048i	0.986335	−	0.164753i	$-0.0526827\pi$
$13$	5.16603	+	2.63223i	1.43280	+	0.730048i	0.446465	+	0.894801i	$0.352683\pi$
$14$	0.272725	−	1.16754i	0.0728889	−	0.312039i
$15$	−1.07307	−	3.23399i	−0.277067	−	0.835013i
$16$	−2.42997	−	3.17730i	−0.607492	−	0.794326i
$17$	0.424918	−	2.68282i	0.103058	−	0.650681i	−0.881039	−	0.473044i	$-0.843155\pi$
$17$	0.424918	−	2.68282i	0.103058	−	0.650681i	0.984096	−	0.177636i	$-0.0568450\pi$
$18$	0.732879	+	0.618190i	0.172741	+	0.145709i
$19$	1.03303	+	1.42184i	0.236993	+	0.326193i	0.910903	−	0.412621i	$-0.135386\pi$
$19$	1.03303	+	1.42184i	0.236993	+	0.326193i	−0.673910	+	0.738813i	$0.735386\pi$
$20$	1.30300	−	4.27811i	0.291360	−	0.956614i
$21$	0.759360	−	1.04517i	0.165706	−	0.228075i
$22$	−2.24109	+	0.552625i	−0.477801	+	0.117820i
$23$	3.27737	+	6.43220i	0.683379	+	1.34121i	0.928361	+	0.371679i	$0.121218\pi$
$23$	3.27737	+	6.43220i	0.683379	+	1.34121i	−0.244982	+	0.969528i	$0.578782\pi$
$24$	−1.08324	−	4.17168i	−0.221116	−	0.851540i
$25$	4.73569	−	1.60413i	0.947138	−	0.320826i
$26$	0.693551	+	8.17019i	0.136017	+	1.60231i
$27$	2.54442	+	4.99370i	0.489674	+	0.961039i
$28$	1.60605	−	0.543750i	0.303516	−	0.102759i
$29$	−6.49732	−	4.72058i	−1.20652	−	0.876589i	−0.211611	−	0.977354i	$-0.567871\pi$
$29$	−6.49732	−	4.72058i	−1.20652	−	0.876589i	−0.994910	+	0.100765i	$0.967871\pi$
$30$	3.08398	−	3.70263i	0.563055	−	0.676004i
$31$	−1.09301	−	1.50440i	−0.196311	−	0.270199i	0.699502	−	0.714631i	$-0.253405\pi$
$31$	−1.09301	−	1.50440i	−0.196311	−	0.270199i	−0.895812	+	0.444432i	$0.853405\pi$
$32$	2.00321	−	5.29029i	0.354120	−	0.935200i
$33$	−2.45650	−	0.389071i	−0.427621	−	0.0677285i
$34$	3.53987	−	1.49181i	0.607083	−	0.255844i
$35$	1.54059	+	1.10473i	0.260407	+	0.186733i
$36$	−0.195639	+	1.34174i	−0.0326064	+	0.223623i
$37$	−0.398349	+	0.781804i	−0.0654882	+	0.128528i	−0.921430	−	0.388544i	$-0.872978\pi$
$37$	−0.398349	+	0.781804i	−0.0654882	+	0.128528i	0.855942	+	0.517072i	$0.172978\pi$
$38$	−0.937020	+	2.30208i	−0.152005	+	0.373446i
$39$	−2.73019	+	8.40267i	−0.437181	+	1.34550i
$40$	6.11154	−	1.62761i	0.966319	−	0.257347i
$41$	−1.42918	−	4.39856i	−0.223200	−	0.686939i	−0.998469	−	0.0553084i	$-0.982386\pi$
$41$	−1.42918	−	4.39856i	−0.223200	−	0.686939i	0.775269	−	0.631631i	$-0.217614\pi$
$42$	1.82224	+	0.132151i	0.281177	+	0.0203914i
$43$	3.23259	+	3.23259i	0.492966	+	0.492966i	0.909239	−	0.416274i	$-0.136664\pi$
$43$	3.23259	+	3.23259i	0.492966	+	0.492966i	−0.416274	+	0.909239i	$0.636664\pi$
$44$	−2.33641	−	2.27967i	−0.352227	−	0.343674i
$45$	−1.34644	+	0.696627i	−0.200715	+	0.103847i
$46$	−5.28072	+	8.73743i	−0.778600	+	1.28826i
$47$	−1.01784	−	6.42640i	−0.148467	−	0.937387i	−0.943633	−	0.330994i	$-0.892616\pi$
$47$	−1.01784	−	6.42640i	−0.148467	−	0.937387i	0.795165	−	0.606393i	$-0.207384\pi$
$48$	4.20279	−	4.41465i	0.606620	−	0.637200i
$49$		−	6.28123i		−	0.897319i
$50$	5.46131	+	4.49156i	0.772345	+	0.635203i
$51$	4.13911			0.579591
$52$	−9.29685	+	6.93071i	−1.28924	+	0.961117i
$53$	13.3108	−	2.10822i	1.82838	−	0.289587i	0.854973	−	0.518673i	$-0.173574\pi$
$53$	13.3108	−	2.10822i	1.82838	−	0.289587i	0.973406	+	0.229086i	$0.0735736\pi$
$54$	−4.09974	+	6.78339i	−0.557904	+	0.923103i
$55$	0.548489	−	3.60816i	0.0739583	−	0.486524i
$56$	1.85181	+	1.52346i	0.247459	+	0.203581i
$57$	−1.89371	+	1.89371i	−0.250828	+	0.250828i
$58$	0.821520	−	11.3280i	0.107871	−	1.48744i
$59$	−2.90867	+	0.945085i	−0.378677	+	0.123040i	−0.492170	−	0.870499i	$-0.663796\pi$
$59$	−2.90867	+	0.945085i	−0.378677	+	0.123040i	0.113493	+	0.993539i	$0.463796\pi$
$60$	6.74942	+	0.941288i	0.871347	+	0.121520i
$61$	−1.24919	−	0.405886i	−0.159942	−	0.0519684i	0.227951	−	0.973673i	$-0.426797\pi$
$61$	−1.24919	−	0.405886i	−0.159942	−	0.0519684i	−0.387894	+	0.921704i	$0.626797\pi$
$62$	0.991428	−	2.43575i	0.125911	−	0.309340i
$63$	−0.512132	−	0.260944i	−0.0645226	−	0.0328759i
$64$	7.85000	−	1.54190i	0.981250	−	0.192737i
$65$	−12.3548	−	3.92952i	−1.53243	−	0.487397i
$66$	−1.36596	−	3.24124i	−0.168138	−	0.398969i
$67$	1.73499	−	10.9543i	0.211963	−	1.33828i	−0.620503	−	0.784204i	$-0.713071\pi$
$67$	1.73499	−	10.9543i	0.211963	−	1.33828i	0.832466	−	0.554077i	$-0.186929\pi$
$68$	4.43392	+	3.13891i	0.537692	+	0.380648i
$69$	−8.89961	+	6.46594i	−1.07139	+	0.778408i
$70$	−0.177281	+	2.67512i	−0.0211892	+	0.319738i
$71$	−0.426288	+	0.586736i	−0.0505911	+	0.0696327i	−0.833563	−	0.552424i	$-0.813703\pi$
$71$	−0.426288	+	0.586736i	−0.0505911	+	0.0696327i	0.782972	+	0.622057i	$0.213703\pi$
$72$	−1.75778	+	0.766357i	−0.207156	+	0.0903160i
$73$	4.64490	−	2.36670i	0.543645	−	0.277001i	−0.160526	−	0.987032i	$-0.551319\pi$
$73$	4.64490	−	2.36670i	0.543645	−	0.277001i	0.704171	+	0.710031i	$0.251319\pi$
$74$	−1.23644	+	0.104959i	−0.143733	+	0.0122012i
$75$	3.54320	+	6.74512i	0.409133	+	0.778859i
$76$	−3.46469	+	0.592491i	−0.397427	+	0.0679634i
$77$	1.23293	−	0.628207i	0.140505	−	0.0715909i
$78$	−12.1313	+	2.99143i	−1.37360	+	0.338713i
$79$	9.40528	+	6.83334i	1.05818	+	0.768810i	0.973750	−	0.227619i	$-0.0730942\pi$
$79$	9.40528	+	6.83334i	1.05818	+	0.768810i	0.0844264	+	0.996430i	$0.473094\pi$
$80$	6.51633	+	6.12678i	0.728548	+	0.684995i
$81$	−5.26385	+	3.82441i	−0.584872	+	0.424934i
$82$	4.21715	−	4.99954i	0.465706	−	0.552107i
$83$	−13.7683	−	2.18069i	−1.51127	−	0.239362i	−0.654897	−	0.755718i	$-0.727288\pi$
$83$	−13.7683	−	2.18069i	−1.51127	−	0.239362i	−0.856374	+	0.516357i	$0.827288\pi$
$84$	1.20123	+	2.28759i	0.131065	+	0.249597i
$85$	0.0377844	+	6.07364i	0.00409829	+	0.658779i
$86$	−1.47061	+	6.29571i	−0.158580	+	0.678884i
$87$	5.55594	−	10.9041i	0.595659	−	1.16905i
$88$	0.994752	−	4.50798i	0.106041	−	0.480553i
$89$	−4.46859	−	1.45193i	−0.473670	−	0.153905i	0.0624475	−	0.998048i	$-0.480109\pi$
$89$	−4.46859	−	1.45193i	−0.473670	−	0.153905i	−0.536117	+	0.844144i	$0.680109\pi$
$90$	−1.84170	−	1.09750i	−0.194132	−	0.115687i
$91$	−1.51898	−	4.67495i	−0.159233	−	0.490068i
$92$	−14.4370	+	0.177444i	−1.50516	+	0.0184998i
$93$	2.00367	−	2.00367i	0.207771	−	0.207771i
$94$	6.96009	−	6.01884i	0.717878	−	0.620796i
$95$	−2.79607	−	2.76150i	−0.286871	−	0.283324i
$96$	8.43973	+	1.75386i	0.861377	+	0.179003i
$97$	−1.57229	+	0.249026i	−0.159642	+	0.0252848i	−0.235744	−	0.971815i	$-0.575753\pi$
$97$	−1.57229	+	0.249026i	−0.159642	+	0.0252848i	0.0761018	+	0.997100i	$0.475753\pi$
$98$	7.54534	−	4.68781i	0.762194	−	0.473540i
$99$			1.10654i			0.111212i
$100$	−1.31961	+	9.91255i	−0.131961	+	0.991255i
$101$		−	10.7533i		−	1.06999i	−0.844855	−	0.534995i	$-0.820314\pi$
$101$		−	10.7533i		−	1.06999i	0.844855	−	0.534995i	$-0.179686\pi$
$102$	3.08910	+	4.97211i	0.305867	+	0.492312i
$103$	−14.0081	+	2.21866i	−1.38025	+	0.218611i	−0.802038	−	0.597273i	$-0.796251\pi$
$103$	−14.0081	+	2.21866i	−1.38025	+	0.218611i	−0.578216	+	0.815883i	$0.696251\pi$
$104$	−15.2640	−	5.99532i	−1.49675	−	0.587889i
$105$	−1.29544	+	2.58203i	−0.126422	+	0.251980i
$106$	12.4666	+	14.4162i	1.21087	+	1.40023i
$107$	−11.1004	+	11.1004i	−1.07312	+	1.07312i	−0.0760098	+	0.997107i	$0.524218\pi$
$107$	−11.1004	+	11.1004i	−1.07312	+	1.07312i	−0.997107	+	0.0760098i	$0.975782\pi$
$108$	−11.2083	+	0.137760i	−1.07852	+	0.0132560i
$109$	0.0984171	+	0.302897i	0.00942665	+	0.0290122i	0.955659	−	0.294475i	$-0.0951447\pi$
$109$	0.0984171	+	0.302897i	0.00942665	+	0.0290122i	−0.946233	+	0.323487i	$0.895145\pi$
$110$	4.74366	−	2.03397i	0.452290	−	0.193931i
$111$	−1.27162	−	0.413175i	−0.120697	−	0.0392168i
$112$	−0.448018	+	3.36149i	−0.0423337	+	0.317630i
$113$	−4.80088	+	9.42226i	−0.451629	+	0.886372i	0.547153	+	0.837033i	$0.315712\pi$
$113$	−4.80088	+	9.42226i	−0.451629	+	0.886372i	−0.998782	+	0.0493393i	$0.984288\pi$
$114$	−3.68813	−	0.861507i	−0.345425	−	0.0806875i
$115$	−9.56923	−	13.0001i	−0.892335	−	1.21226i
$116$	14.2209	−	7.46745i	1.32037	−	0.693335i
$117$	3.88242	+	0.614916i	0.358930	+	0.0568490i
$118$	−3.30609	−	2.78871i	−0.304350	−	0.256722i
$119$	−1.86305	+	1.35359i	−0.170786	+	0.124083i
$120$	3.90651	+	8.81026i	0.356614	+	0.804263i
$121$	6.74402	+	4.89982i	0.613093	+	0.445438i
$122$	−0.444724	−	1.80351i	−0.0402634	−	0.163282i
$123$	6.27942	−	3.19952i	0.566196	−	0.288491i
$124$	3.66587	−	0.626894i	0.329205	−	0.0562968i
$125$	−9.86530	+	5.26079i	−0.882379	+	0.470539i
$126$	−0.0687549	−	0.809948i	−0.00612517	−	0.0721559i
$127$	10.4147	−	5.30653i	0.924152	−	0.470879i	0.0739061	−	0.997265i	$-0.476453\pi$
$127$	10.4147	−	5.30653i	0.924152	−	0.470879i	0.850245	+	0.526386i	$0.176453\pi$
$128$	7.71082	+	8.27908i	0.681547	+	0.731774i
$129$	−4.09467	+	5.63583i	−0.360516	+	0.496208i
$130$	−4.50031	−	17.7739i	−0.394703	−	1.55888i
$131$	−9.80424	+	7.12319i	−0.856600	+	0.622356i	−0.926958	−	0.375165i	$-0.877586\pi$
$131$	−9.80424	+	7.12319i	−0.856600	+	0.622356i	0.0703578	+	0.997522i	$0.477586\pi$
$132$	2.87410	−	4.05987i	0.250158	−	0.353366i
$133$	0.233088	−	1.47166i	0.0202113	−	0.127609i
$134$	14.4537	−	6.09126i	1.24861	−	0.526205i
$135$	−7.42917	−	10.0927i	−0.639401	−	0.868644i
$136$	−0.461489	+	7.66889i	−0.0395724	+	0.657602i
$137$	9.47288	+	4.82667i	0.809322	+	0.412370i	0.809130	−	0.587630i	$-0.199939\pi$
$137$	9.47288	+	4.82667i	0.809322	+	0.412370i	0.000192369		1.00000i	$0.499939\pi$
$138$	−14.4092	−	5.86500i	−1.22659	−	0.499262i
$139$	−10.9546	−	3.55938i	−0.929161	−	0.301903i	−0.194941	−	0.980815i	$-0.562452\pi$
$139$	−10.9546	−	3.55938i	−0.929161	−	0.301903i	−0.734219	+	0.678912i	$0.762452\pi$
$140$	−3.34580	+	1.78354i	−0.282772	+	0.150736i
$141$	9.42950	−	3.06383i	0.794107	−	0.258021i
$142$	−1.02296	−	0.0741868i	−0.0858453	−	0.00622562i
$143$	−6.69149	+	6.69149i	−0.559571	+	0.559571i
$144$	−2.23245	−	1.53958i	−0.186038	−	0.128299i
$145$	16.0512	+	8.05313i	1.33298	+	0.668776i
$146$	6.30958	+	3.81338i	0.522185	+	0.315598i
$147$	9.45364	−	1.49731i	0.779723	−	0.123496i
$148$	−1.04886	−	1.40694i	−0.0862160	−	0.115650i
$149$	−10.5617			−0.865244			−0.432622	−	0.901575i	$-0.642412\pi$
$149$	−10.5617			−0.865244			−0.432622	+	0.901575i	$0.642412\pi$
$150$	−5.45822	+	9.29030i	−0.445662	+	0.758549i
$151$			5.53163i			0.450158i	0.974341	+	0.225079i	$0.0722640\pi$
$151$			5.53163i			0.450158i	−0.974341	+	0.225079i	$0.927736\pi$
$152$	−3.29750	−	3.71978i	−0.267463	−	0.301714i
$153$	−0.288079	−	1.81886i	−0.0232898	−	0.147046i
$154$	1.67479	+	1.01221i	0.134959	+	0.0815663i
$155$	2.95843	+	2.92185i	0.237627	+	0.234688i
$156$	−12.6473	−	12.3402i	−1.01260	−	0.988006i
$157$	−2.85061	−	2.85061i	−0.227503	−	0.227503i	0.584146	−	0.811649i	$-0.301430\pi$
$157$	−2.85061	−	2.85061i	−0.227503	−	0.227503i	−0.811649	+	0.584146i	$0.801430\pi$
$158$	−1.18920	+	16.3980i	−0.0946079	+	1.30455i
$159$	6.34601	+	19.5310i	0.503272	+	1.54891i
$160$	−2.49653	+	12.4003i	−0.197368	+	0.980329i
$161$	1.89128	−	5.82076i	0.149054	−	0.458740i
$162$	−8.52259	−	3.46897i	−0.669598	−	0.272548i
$163$	7.00084	−	13.7399i	0.548348	−	1.07619i	−0.435998	−	0.899948i	$-0.643605\pi$
$163$	7.00084	−	13.7399i	0.548348	−	1.07619i	0.984346	−	0.176246i	$-0.0563954\pi$
$164$	9.15305	+	1.33460i	0.714733	+	0.104215i
$165$	5.56125	−	0.0345968i	0.432943	−	0.00269336i
$166$	−7.65603	−	18.1667i	−0.594223	−	1.41001i
$167$	21.8863	+	3.46646i	1.69362	+	0.268243i	0.927327	−	0.374253i	$-0.122101\pi$
$167$	21.8863	+	3.46646i	1.69362	+	0.268243i	0.766290	+	0.642495i	$0.222101\pi$
$168$	−1.85148	+	3.15025i	−0.142844	+	0.243047i
$169$	12.1181	+	16.6791i	0.932161	+	1.28301i
$170$	−7.26777	+	4.57827i	−0.557413	+	0.351137i
$171$	0.963958	+	0.700356i	0.0737157	+	0.0535576i
$172$	−8.66028	+	2.93205i	−0.660340	+	0.223566i
$173$	5.69578	+	11.1786i	0.433042	+	0.849893i	0.999664	+	0.0259151i	$0.00824996\pi$
$173$	5.69578	+	11.1786i	0.433042	+	0.849893i	−0.566622	+	0.823978i	$0.691750\pi$
$174$	17.2451	−	1.46391i	1.30735	−	0.110978i
$175$	−3.80064	−	1.87733i	−0.287301	−	0.141913i
$176$	6.15763	−	2.16945i	0.464149	−	0.163529i
$177$	−2.11578	−	4.15244i	−0.159031	−	0.312117i
$178$	−1.59086	−	6.45151i	−0.119240	−	0.483561i
$179$	12.0112	−	16.5320i	0.897761	−	1.23566i	−0.0734160	−	0.997301i	$-0.523390\pi$
$179$	12.0112	−	16.5320i	0.897761	−	1.23566i	0.971177	−	0.238360i	$-0.0766099\pi$
$180$	−0.0561221	−	3.03143i	−0.00418309	−	0.225949i
$181$	−13.1045	−	18.0368i	−0.974049	−	1.34066i	−0.939975	−	0.341244i	$-0.889152\pi$
$181$	−13.1045	−	18.0368i	−0.974049	−	1.34066i	−0.0340747	−	0.999419i	$-0.510848\pi$
$182$	4.48215	−	5.31370i	0.332239	−	0.393877i
$183$	0.313104	−	1.97686i	0.0231453	−	0.146134i
$184$	−10.9878	−	17.2100i	−0.810028	−	1.26874i
$185$	0.594676	−	1.86972i	0.0437214	−	0.137465i
$186$	3.90229	+	0.911531i	0.286130	+	0.0668367i
$187$	3.95016	+	2.01271i	0.288864	+	0.147184i
$188$	12.4246	+	3.86884i	0.906157	+	0.282164i
$189$	1.46831	−	4.51901i	0.106804	−	0.328709i
$190$	1.23049	−	5.41975i	0.0892691	−	0.393190i
$191$	−10.5039	+	3.41293i	−0.760036	+	0.246951i	−0.663294	−	0.748359i	$-0.730842\pi$
$191$	−10.5039	+	3.41293i	−0.760036	+	0.246951i	−0.0967418	+	0.995310i	$0.530842\pi$
$192$	4.19192	+	11.4472i	0.302526	+	0.826130i
$193$	2.33162	+	2.33162i	0.167834	+	0.167834i	0.786027	−	0.618193i	$-0.212135\pi$
$193$	2.33162	+	2.33162i	0.167834	+	0.167834i	−0.618193	+	0.786027i	$0.712135\pi$
$194$	−1.47258	−	1.70286i	−0.105725	−	0.122258i
$195$	2.96905	−	19.5315i	0.212618	−	1.39868i
$196$	11.2625	+	5.56524i	0.804463	+	0.397517i
$197$	2.13910	+	13.5058i	0.152405	+	0.962246i	0.938785	+	0.344503i	$0.111953\pi$
$197$	2.13910	+	13.5058i	0.152405	+	0.962246i	−0.786380	+	0.617743i	$0.788047\pi$
$198$	−1.32924	+	0.825836i	−0.0944647	+	0.0586896i
$199$	10.9851			0.778711			0.389355	−	0.921088i	$-0.372698\pi$
$199$	10.9851			0.778711			0.389355	+	0.921088i	$0.372698\pi$
$200$	−12.8923	+	5.81275i	−0.911625	+	0.411024i
$201$	16.9005			1.19207
$202$	12.9174	−	8.02538i	0.908863	−	0.564664i
$203$	1.06513	+	6.72498i	0.0747576	+	0.472001i
$204$	−3.66730	+	7.42158i	−0.256762	+	0.519614i
$205$	4.75223	+	9.18508i	0.331910	+	0.641513i
$206$	−13.1197	−	15.1714i	−0.914090	−	1.05704i
$207$	3.46075	+	3.46075i	0.240539	+	0.240539i
$208$	−4.18991	−	22.8103i	−0.290518	−	1.58161i
$209$	−2.72811	+	0.886416i	−0.188707	+	0.0613147i
$210$	−4.06848	+	0.370871i	−0.280752	+	0.0255925i
$211$	5.60549	−	17.2519i	0.385898	−	1.18767i	−0.549929	−	0.835212i	$-0.685345\pi$
$211$	5.60549	−	17.2519i	0.385898	−	1.18767i	0.935827	−	0.352461i	$-0.114655\pi$
$212$	−8.01340	+	25.7347i	−0.550362	+	1.76746i
$213$	−0.984691	−	0.501725i	−0.0674699	−	0.0343777i
$214$	−21.6188	−	5.04992i	−1.47783	−	0.345206i
$215$	−8.30728	−	5.95699i	−0.566552	−	0.406263i
$216$	−8.53046	−	13.3612i	−0.580424	−	0.909112i
$217$	−0.246623	+	1.55712i	−0.0167418	+	0.105704i
$218$	−0.290405	+	0.344282i	−0.0196687	+	0.0233177i
$219$	4.66927	+	6.42670i	0.315520	+	0.434276i
$220$	5.98360	+	4.18033i	0.403414	+	0.281838i
$221$	9.25694	−	12.7411i	0.622689	−	0.857058i
$222$	−0.452710	−	1.83590i	−0.0303839	−	0.123217i
$223$	−8.42226	−	16.5296i	−0.563996	−	1.10691i	−0.980270	−	0.197666i	$-0.936664\pi$
$223$	−8.42226	−	16.5296i	−0.563996	−	1.10691i	0.416273	−	0.909240i	$-0.363336\pi$
$224$	−4.37235	+	1.97056i	−0.292140	+	0.131664i
$225$	2.71742	−	2.02645i	0.181161	−	0.135097i
$226$	−14.9015	+	1.26496i	−0.991233	+	0.0841438i
$227$	−4.71320	−	9.25018i	−0.312826	−	0.613956i	0.680042	−	0.733173i	$-0.261962\pi$
$227$	−4.71320	−	9.25018i	−0.312826	−	0.613956i	−0.992868	+	0.119217i	$0.961962\pi$
$228$	−1.71764	−	5.07334i	−0.113754	−	0.335990i
$229$	5.69094	+	4.13471i	0.376068	+	0.273229i	0.759723	−	0.650247i	$-0.225335\pi$
$229$	5.69094	+	4.13471i	0.376068	+	0.273229i	−0.383655	+	0.923477i	$0.625335\pi$
$230$	8.47464	−	21.1973i	0.558801	−	1.39771i
$231$	1.23939	+	1.70588i	0.0815461	+	0.112239i
$232$	19.5836	+	11.5097i	1.28573	+	0.755651i
$233$	4.44895	+	0.704644i	0.291460	+	0.0461628i	0.300452	−	0.953797i	$-0.402862\pi$
$233$	4.44895	+	0.704644i	0.291460	+	0.0461628i	−0.00899219	+	0.999960i	$0.502862\pi$
$234$	2.15886	+	5.12269i	0.141129	+	0.334881i
$235$	4.58188	+	13.8087i	0.298889	+	0.900779i
$236$	0.882544	−	6.05271i	0.0574487	−	0.393998i
$237$	−8.04258	+	15.7844i	−0.522422	+	1.02531i
$238$	−3.01643	−	1.22778i	−0.195526	−	0.0795854i
$239$	7.49866	−	23.0785i	0.485048	−	1.49282i	−0.346863	−	0.937916i	$-0.612753\pi$
$239$	7.49866	−	23.0785i	0.485048	−	1.49282i	0.831911	−	0.554909i	$-0.187247\pi$
$240$	−7.66783	+	11.2680i	−0.494956	+	0.727345i
$241$	2.40482	+	7.40128i	0.154908	+	0.476758i	0.998152	−	0.0607736i	$-0.0193568\pi$
$241$	2.40482	+	7.40128i	0.154908	+	0.476758i	−0.843243	+	0.537532i	$0.819357\pi$
$242$	−0.852714	+	11.7581i	−0.0548145	+	0.755839i
$243$	4.87832	+	4.87832i	0.312944	+	0.312944i
$244$	1.83457	−	1.88022i	0.117446	−	0.120369i
$245$	2.28342	+	13.8584i	0.145882	+	0.885381i
$246$	8.52989	+	5.15529i	0.543846	+	0.328689i
$247$	1.59405	+	10.0644i	0.101427	+	0.640386i
$248$	3.48897	+	3.93577i	0.221550	+	0.249922i
$249$		−	21.2420i		−	1.34616i
$250$	−13.6822	−	7.92447i	−0.865339	−	0.501188i
$251$	17.0826			1.07824			0.539121	−	0.842228i	$-0.318756\pi$
$251$	17.0826			1.07824			0.539121	+	0.842228i	$0.318756\pi$
$252$	0.921638	−	0.687073i	0.0580578	−	0.0432815i
$253$	−11.6375	+	1.84320i	−0.731644	+	0.115881i
$254$	14.1472	+	8.55025i	0.887672	+	0.536491i
$255$	−9.13220	+	1.50469i	−0.571880	+	0.0942275i
$256$	−4.19052	+	15.4415i	−0.261907	+	0.965093i
$257$	−9.52969	+	9.52969i	−0.594445	+	0.594445i	−0.938829	−	0.344384i	$-0.888088\pi$
$257$	−9.52969	+	9.52969i	−0.594445	+	0.594445i	0.344384	+	0.938829i	$0.388088\pi$
$258$	−9.82599	−	0.712595i	−0.611740	−	0.0443642i
$259$	0.707486	−	0.229876i	0.0439611	−	0.0142838i
$260$	17.9923	−	18.6710i	1.11583	−	1.15793i
$261$	−5.17833	−	1.68254i	−0.320530	−	0.104147i
$262$	−15.8739	−	6.46117i	−0.980690	−	0.399172i
$263$	−8.45079	−	4.30589i	−0.521098	−	0.265513i	0.173597	−	0.984817i	$-0.444461\pi$
$263$	−8.45079	−	4.30589i	−0.521098	−	0.265513i	−0.694695	+	0.719304i	$0.744461\pi$
$264$	7.02192	+	0.422557i	0.432169	+	0.0260066i
$265$	−28.6015	+	9.49030i	−1.75697	+	0.582984i
$266$	1.94180	−	0.818334i	0.119059	−	0.0501753i
$267$	1.12003	−	7.07161i	0.0685449	−	0.432776i
$268$	18.1043	+	12.8165i	1.10589	+	0.782895i
$269$	12.5762	−	9.13718i	0.766787	−	0.557104i	−0.134197	−	0.990955i	$-0.542846\pi$
$269$	12.5762	−	9.13718i	0.766787	−	0.557104i	0.900985	+	0.433851i	$0.142846\pi$
$270$	6.57937	−	16.4567i	0.400408	−	1.00152i
$271$	−10.0546	+	13.8390i	−0.610775	+	0.840660i	−0.996641	−	0.0818949i	$-0.973903\pi$
$271$	−10.0546	+	13.8390i	−0.610775	+	0.840660i	0.385866	+	0.922555i	$0.373903\pi$
$272$	−9.55668	+	5.16908i	−0.579459	+	0.313422i
$273$	6.67400	−	3.40057i	0.403929	−	0.205812i
$274$	1.27175	+	14.9816i	0.0768295	+	0.905069i
$275$	0.101533	+	8.16015i	0.00612269	+	0.492075i
$276$	−3.70853	−	21.6862i	−0.223227	−	1.30536i
$277$	−15.6458	+	7.97194i	−0.940066	+	0.478987i	−0.855714	−	0.517449i	$-0.826882\pi$
$277$	−15.6458	+	7.97194i	−0.940066	+	0.478987i	−0.0843515	+	0.996436i	$0.526882\pi$
$278$	−3.89996	−	15.8157i	−0.233904	−	0.948564i
$279$	−1.01993	−	0.741023i	−0.0610616	−	0.0443639i
$280$	−4.63952	−	2.68806i	−0.277264	−	0.160642i
$281$	−21.3524	+	15.5134i	−1.27378	+	0.925454i	−0.999346	−	0.0361521i	$-0.988490\pi$
$281$	−21.3524	+	15.5134i	−1.27378	+	0.925454i	−0.274432	+	0.961606i	$0.588490\pi$
$282$	10.7179	+	9.04060i	0.638239	+	0.538360i
$283$	−15.9498	−	2.52621i	−0.948119	−	0.150167i	−0.336822	−	0.941568i	$-0.609352\pi$
$283$	−15.9498	−	2.52621i	−0.948119	−	0.150167i	−0.611297	+	0.791401i	$0.709352\pi$
$284$	−0.674343	−	1.28421i	−0.0400149	−	0.0762036i
$285$	3.48971	−	4.86655i	0.206712	−	0.288269i
$286$	−13.0322	−	3.04417i	−0.770608	−	0.180005i
$287$	−1.78010	+	3.49365i	−0.105076	+	0.206224i
$288$	0.183304	−	3.83076i	0.0108013	−	0.225730i
$289$	9.15097	+	2.97333i	0.538292	+	0.174902i
$290$	2.30553	+	25.2918i	0.135385	+	1.48518i
$291$	−0.749600	−	2.30703i	−0.0439424	−	0.135241i
$292$	0.128138	+	10.4254i	0.00749871	+	0.610101i
$293$	9.63162	−	9.63162i	0.562685	−	0.562685i	−0.367384	−	0.930069i	$-0.619747\pi$
$293$	9.63162	−	9.63162i	0.562685	−	0.562685i	0.930069	+	0.367384i	$0.119747\pi$
$294$	8.85409	+	10.2387i	0.516381	+	0.597135i
$295$	6.07389	−	3.14255i	0.353636	−	0.182966i
$296$	0.907305	−	2.30998i	0.0527360	−	0.134265i
$297$	−9.03490	+	1.43099i	−0.524258	+	0.0830343i
$298$	−7.88238	−	12.6872i	−0.456614	−	0.734950i
$299$			41.8558i			2.42058i
$300$	−15.2336	+	0.376837i	−0.879510	+	0.0217567i
$301$		−	3.87579i		−	0.223397i
$302$	−6.64488	+	4.12837i	−0.382370	+	0.237561i
$303$	16.1843	−	2.56335i	0.929765	−	0.147260i
$304$	2.00740	−	6.73727i	0.115132	−	0.386409i
$305$	2.90366	+	0.441396i	0.166263	+	0.0252743i
$306$	1.96991	−	1.70351i	0.112612	−	0.0973830i
$307$	−15.0324	+	15.0324i	−0.857947	+	0.857947i	−0.991096	−	0.133149i	$-0.957491\pi$
$307$	−15.0324	+	15.0324i	−0.857947	+	0.857947i	0.133149	+	0.991096i	$0.457491\pi$
$308$	0.0340125	+	2.76728i	0.00193804	+	0.157681i
$309$	−6.67844	−	20.5541i	−0.379923	−	1.16928i
$310$	−1.30194	+	5.73445i	−0.0739451	+	0.325695i
$311$	9.39383	+	3.05224i	0.532675	+	0.173077i	0.562990	−	0.826464i	$-0.309651\pi$
$311$	9.39383	+	3.05224i	0.532675	+	0.173077i	−0.0303149	+	0.999540i	$0.509651\pi$
$312$	5.38473	−	24.4024i	0.304850	−	1.38151i
$313$	−8.14863	+	15.9926i	−0.460588	+	0.903954i	0.537566	+	0.843221i	$0.319344\pi$
$313$	−8.14863	+	15.9926i	−0.460588	+	0.903954i	−0.998154	+	0.0607328i	$0.980656\pi$
$314$	1.29683	−	5.55176i	0.0731844	−	0.313304i
$315$	1.22479	+	0.389551i	0.0690090	+	0.0219487i
$316$	−20.5856	+	10.8096i	−1.15803	+	0.608088i
$317$	−27.1533	−	4.30065i	−1.52508	−	0.241549i	−0.663115	−	0.748518i	$-0.730766\pi$
$317$	−27.1533	−	4.30065i	−1.52508	−	0.241549i	−0.861964	+	0.506969i	$0.830766\pi$
$318$	−18.7255	+	22.1996i	−1.05007	+	1.24489i
$319$	10.6046	−	7.70471i	0.593745	−	0.431381i
$320$	−16.7591	+	6.25563i	−0.936862	+	0.349700i
$321$	−19.3529	−	14.0607i	−1.08017	−	0.784792i
$322$	8.40370	−	2.07225i	0.468320	−	0.115482i
$323$	4.25350	−	2.16727i	0.236671	−	0.120590i
$324$	−2.19348	−	12.8267i	−0.121860	−	0.712597i
$325$	28.6872	+	4.17842i	1.59128	+	0.231777i
$326$	21.7300	−	1.84461i	1.20351	−	0.102164i
$327$	−0.432418	+	0.220328i	−0.0239128	+	0.0121842i
$328$	5.22791	+	11.9912i	0.288663	+	0.662101i
$329$	−3.24236	+	4.46273i	−0.178757	+	0.246038i
$330$	4.19204	+	6.65464i	0.230764	+	0.366326i
$331$	−20.4129	+	14.8308i	−1.12199	+	0.815175i	−0.984510	−	0.175329i	$-0.943901\pi$
$331$	−20.4129	+	14.8308i	−1.12199	+	0.815175i	−0.137483	+	0.990504i	$0.543901\pi$
$332$	16.1090	−	22.7550i	0.884094	−	1.24884i
$333$	−0.0930586	+	0.587549i	−0.00509958	+	0.0321975i
$334$	12.1701	+	28.8781i	0.665921	+	1.58014i
$335$	0.154278	+	24.7994i	0.00842913	+	1.35494i
$336$	−5.16604	+	0.127010i	−0.281831	+	0.00692898i
$337$	23.0657	+	11.7526i	1.25647	+	0.640204i	0.950170	−	0.311731i	$-0.100909\pi$
$337$	23.0657	+	11.7526i	1.25647	+	0.640204i	0.306300	+	0.951935i	$0.400909\pi$
$338$	−10.9918	+	27.0048i	−0.597877	+	1.46887i
$339$	−15.3255	−	4.97956i	−0.832368	−	0.270453i
$340$	−10.9237	−	5.31356i	−0.592423	−	0.288169i
$341$	2.88652	−	0.937886i	0.156314	−	0.0507894i
$342$	−0.121883	+	1.68065i	−0.00659067	+	0.0908789i
$343$	−7.96192	+	7.96192i	−0.429903	+	0.429903i
$344$	−9.98547	−	8.21493i	−0.538380	−	0.442919i
$345$	17.2848	−	17.5012i	0.930583	−	0.942234i
$346$	−9.17743	+	15.1849i	−0.493382	+	0.816344i
$347$	12.6639	−	2.00576i	0.679832	−	0.107675i	0.193038	−	0.981191i	$-0.438166\pi$
$347$	12.6639	−	2.00576i	0.679832	−	0.107675i	0.486795	+	0.873516i	$0.338166\pi$
$348$	14.6289	+	19.6232i	0.784192	+	1.05191i
$349$	9.62259			0.515086			0.257543	−	0.966267i	$-0.417087\pi$
$349$	9.62259			0.515086			0.257543	+	0.966267i	$0.417087\pi$
$350$	−0.581348	−	5.96661i	−0.0310744	−	0.318929i
$351$			32.4951i			1.73446i
$352$	7.20162	+	5.77775i	0.383848	+	0.307955i
$353$	−4.16891	−	26.3215i	−0.221889	−	1.40095i	−0.807266	−	0.590188i	$-0.799053\pi$
$353$	−4.16891	−	26.3215i	−0.221889	−	1.40095i	0.585377	−	0.810761i	$-0.300947\pi$
$354$	3.40908	−	5.64063i	0.181191	−	0.299796i
$355$	0.727232	−	1.44950i	0.0385975	−	0.0769312i
$356$	6.56259	−	6.72592i	0.347817	−	0.356473i
$357$	−2.48134	−	2.48134i	−0.131326	−	0.131326i
$358$	28.8233	+	2.09031i	1.52336	+	0.110476i
$359$	−11.0131	−	33.8947i	−0.581247	−	1.78889i	−0.613845	−	0.789426i	$-0.710378\pi$
$359$	−11.0131	−	33.8947i	−0.581247	−	1.78889i	0.0325983	−	0.999469i	$-0.489622\pi$
$360$	3.59962	−	2.32983i	0.189717	−	0.122793i
$361$	4.91684	−	15.1325i	0.258781	−	0.796446i
$362$	11.8866	−	29.2030i	0.624744	−	1.53488i
$363$	−5.76690	+	11.3182i	−0.302684	+	0.594050i
$364$	9.72821	+	1.41847i	0.509897	+	0.0743478i
$365$	−9.38777	+	6.91025i	−0.491379	+	0.361699i
$366$	2.60839	−	1.09926i	0.136343	−	0.0574590i
$367$	−25.2411	−	3.99779i	−1.31757	−	0.208683i	−0.542234	−	0.840228i	$-0.682421\pi$
$367$	−25.2411	−	3.99779i	−1.31757	−	0.208683i	−0.775339	+	0.631545i	$0.782421\pi$
$368$	12.4732	−	26.0432i	0.650208	−	1.35760i
$369$	−1.84302	−	2.53670i	−0.0959437	−	0.132055i
$370$	2.68983	−	0.681057i	0.139837	−	0.0354064i
$371$	−9.24350	−	6.71580i	−0.479899	−	0.348667i
$372$	1.81738	+	5.36792i	0.0942267	+	0.278314i
$373$	−1.19470	−	2.34473i	−0.0618592	−	0.121406i	0.858007	−	0.513638i	$-0.171703\pi$
$373$	−1.19470	−	2.34473i	−0.0618592	−	0.121406i	−0.919866	+	0.392233i	$0.871703\pi$
$374$	0.530318	+	6.24726i	0.0274221	+	0.323038i
$375$	−10.2695	−	13.5938i	−0.530314	−	0.701982i
$376$	4.62529	+	17.8125i	0.238531	+	0.918607i
$377$	−21.1397	−	41.4891i	−1.08875	−	2.13680i
$378$	6.52430	−	1.60881i	0.335574	−	0.0827484i
$379$	13.0709	−	17.9905i	0.671405	−	0.924110i	−0.328386	−	0.944544i	$-0.606505\pi$
$379$	13.0709	−	17.9905i	0.671405	−	0.924110i	0.999791	+	0.0204337i	$0.00650470\pi$
$380$	7.42883	−	2.56674i	0.381091	−	0.131671i
$381$	10.4693	+	14.4097i	0.536358	+	0.738234i
$382$	−11.9391	−	10.0707i	−0.610855	−	0.515262i
$383$	0.408510	−	2.57923i	0.0208739	−	0.131793i	−0.975051	−	0.221982i	$-0.928747\pi$
$383$	0.408510	−	2.57923i	0.0208739	−	0.131793i	0.995925	+	0.0901896i	$0.0287473\pi$
$384$	−10.6224	+	13.5788i	−0.542074	+	0.692941i
$385$	−2.49186	+	1.83423i	−0.126997	+	0.0934811i
$386$	−1.06073	+	4.54100i	−0.0539896	+	0.231131i
$387$	2.76156	+	1.40708i	0.140378	+	0.0715260i
$388$	0.946554	−	3.03982i	0.0480540	−	0.154323i
$389$	−2.82279	+	8.68765i	−0.143121	+	0.440481i	−0.996765	−	0.0803764i	$-0.974388\pi$
$389$	−2.82279	+	8.68765i	−0.143121	+	0.440481i	0.853644	+	0.520858i	$0.174388\pi$
$390$	25.6781	−	11.0102i	1.30026	−	0.557521i
$391$	18.6491	−	6.05945i	0.943125	−	0.306440i
$392$	1.72016	+	17.6825i	0.0868814	+	0.893103i
$393$	−13.0580	−	13.0580i	−0.658687	−	0.658687i
$394$	−14.6274	+	12.6492i	−0.736916	+	0.637259i
$395$	−23.2352	−	11.6574i	−1.16909	−	0.586548i
$396$	−1.98407	−	0.980410i	−0.0997034	−	0.0492674i
$397$	−3.48764	−	22.0201i	−0.175040	−	1.10516i	−0.906169	−	0.422917i	$-0.861006\pi$
$397$	−3.48764	−	22.0201i	−0.175040	−	1.10516i	0.731129	−	0.682239i	$-0.238994\pi$
$398$	8.19838	+	13.1958i	0.410948	+	0.661447i
$399$	2.27051			0.113667
$400$	−16.6044	−	11.1487i	−0.830219	−	0.557437i
$401$	24.5825			1.22759			0.613795	−	0.789465i	$-0.289642\pi$
$401$	24.5825			1.22759			0.613795	+	0.789465i	$0.289642\pi$
$402$	12.6132	+	20.3017i	0.629088	+	1.01256i
$403$	−1.68661	−	10.6488i	−0.0840161	−	0.530457i
$404$	19.2810	+	9.52751i	0.959266	+	0.474012i
$405$	10.2234	−	10.3514i	0.508007	−	0.514367i
$406$	−7.28346	+	6.29848i	−0.361472	+	0.312588i
$407$	−1.01266	−	1.01266i	−0.0501957	−	0.0501957i
$408$	−11.6522	+	1.13353i	−0.576868	+	0.0561180i
$409$	−12.4251	+	4.03716i	−0.614381	+	0.199624i	−0.599644	−	0.800267i	$-0.704691\pi$
$409$	−12.4251	+	4.03716i	−0.614381	+	0.199624i	−0.0147370	+	0.999891i	$0.504691\pi$
$410$	−7.48690	+	12.5636i	−0.369752	+	0.620474i
$411$	−5.00631	+	15.4078i	−0.246943	+	0.760013i
$412$	8.43316	−	27.0827i	0.415472	−	1.33427i
$413$	2.31028	+	1.17714i	0.113681	+	0.0579235i
$414$	−1.57440	+	6.74006i	−0.0773777	+	0.331256i
$415$	31.1701	−	0.193911i	1.53008	−	0.00951870i
$416$	24.2739	−	22.0569i	1.19012	−	1.08143i
$417$	2.74574	−	17.3359i	0.134459	−	0.848942i
$418$	−3.10085	−	2.61559i	−0.151668	−	0.127933i
$419$	−13.5174	−	18.6051i	−0.660367	−	0.908918i	0.339126	−	0.940741i	$-0.389869\pi$
$419$	−13.5174	−	18.6051i	−0.660367	−	0.908918i	−0.999494	+	0.0318232i	$0.989869\pi$
$420$	−3.48190	−	4.61048i	−0.169899	−	0.224968i
$421$	−1.27992	+	1.76165i	−0.0623792	+	0.0858577i	−0.839067	−	0.544028i	$-0.816898\pi$
$421$	−1.27992	+	1.76165i	−0.0623792	+	0.0858577i	0.776688	+	0.629886i	$0.216898\pi$
$422$	24.9074	−	6.14186i	1.21247	−	0.298981i
$423$	−2.00263	−	3.93039i	−0.0973713	−	0.191102i
$424$	−36.8944	+	9.58021i	−1.79175	+	0.465256i
$425$	−2.29132	−	13.3867i	−0.111145	−	0.649348i
$426$	−0.132197	−	1.55731i	−0.00640496	−	0.0754519i
$427$	0.505549	+	0.992196i	0.0244652	+	0.0480158i
$428$	−10.0684	−	29.7385i	−0.486673	−	1.43747i
$429$	−11.6662	−	8.47600i	−0.563250	−	0.409225i
$430$	0.955948	−	14.4250i	0.0460999	−	0.695633i
$431$	3.07549	+	4.23304i	0.148141	+	0.203899i	0.876638	−	0.481150i	$-0.159781\pi$
$431$	3.07549	+	4.23304i	0.148141	+	0.203899i	−0.728497	+	0.685049i	$0.759781\pi$
$432$	9.68366	−	20.2189i	0.465905	−	0.972784i
$433$	16.4529	+	2.60589i	0.790677	+	0.125231i	0.538695	−	0.842501i	$-0.318918\pi$
$433$	16.4529	+	2.60589i	0.790677	+	0.125231i	0.251982	+	0.967732i	$0.418918\pi$
$434$	−2.05455	+	0.865851i	−0.0986214	+	0.0415622i
$435$	−8.29419	+	26.0778i	−0.397676	+	1.25033i
$436$	−0.630304	−	0.0919044i	−0.0301861	−	0.00440142i
$437$	−5.75996	+	11.3046i	−0.275536	+	0.540770i
$438$	−4.23531	+	10.4053i	−0.202371	+	0.497187i
$439$	−4.46164	+	13.7315i	−0.212943	+	0.655370i	0.786351	+	0.617780i	$0.211968\pi$
$439$	−4.46164	+	13.7315i	−0.212943	+	0.655370i	−0.999293	+	0.0375894i	$0.988032\pi$
$440$	−0.555950	+	10.3077i	−0.0265039	+	0.491399i
$441$	−1.31593	−	4.05003i	−0.0626635	−	0.192858i
$442$	22.2139	+	1.61098i	1.05661	+	0.0766266i
$443$	17.2334	+	17.2334i	0.818783	+	0.818783i	0.985932	−	0.167149i	$-0.0534560\pi$
$443$	17.2334	+	17.2334i	0.818783	+	0.818783i	−0.167149	+	0.985932i	$0.553456\pi$
$444$	1.86751	−	1.91399i	0.0886281	−	0.0908338i
$445$	10.3870	+	1.57896i	0.492389	+	0.0748498i
$446$	13.5705	−	22.4537i	0.642583	−	1.06321i
$447$	−2.51767	−	15.8959i	−0.119082	−	0.751852i
$448$	−5.63032	−	3.78163i	−0.266008	−	0.178665i
$449$		−	29.7838i		−	1.40558i	−0.711396	−	0.702792i	$-0.751937\pi$
$449$		−	29.7838i		−	1.40558i	0.711396	−	0.702792i	$-0.248063\pi$
$450$	4.46235	+	1.75192i	0.210357	+	0.0825864i
$451$	7.54859			0.355449
$452$	−12.6408	−	16.9564i	−0.594575	−	0.797562i
$453$	−8.32544	+	1.31862i	−0.391164	+	0.0619542i
$454$	7.59424	−	12.5653i	0.356415	−	0.589721i
$455$	5.05085	+	9.76224i	0.236788	+	0.457661i
$456$	4.81244	−	5.84966i	0.225363	−	0.273935i
$457$	−2.99043	+	2.99043i	−0.139887	+	0.139887i	−0.773582	−	0.633696i	$-0.781537\pi$
$457$	−2.99043	+	2.99043i	−0.139887	+	0.139887i	0.633696	+	0.773582i	$0.281537\pi$
$458$	−0.719562	+	9.92207i	−0.0336229	+	0.463628i
$459$	14.4784	−	4.70432i	0.675794	−	0.219579i
$460$	31.7881	−	5.63978i	1.48213	−	0.262956i
$461$	25.4014	+	8.25343i	1.18306	+	0.384400i	0.833504	−	0.552514i	$-0.186331\pi$
$461$	25.4014	+	8.25343i	1.18306	+	0.384400i	0.349559	+	0.936914i	$0.386331\pi$
$462$	−1.12421	+	2.76196i	−0.0523028	+	0.128498i
$463$	−14.4305	−	7.35271i	−0.670643	−	0.341710i	0.0852925	−	0.996356i	$-0.472818\pi$
$463$	−14.4305	−	7.35271i	−0.670643	−	0.341710i	−0.755935	+	0.654646i	$0.772818\pi$
$464$	0.789562	+	32.1148i	0.0366545	+	1.49089i
$465$	−3.69234	+	5.14912i	−0.171228	+	0.238785i
$466$	2.47389	+	5.87020i	0.114601	+	0.271932i
$467$	1.52271	−	9.61404i	0.0704628	−	0.444885i	−0.927082	−	0.374858i	$-0.877692\pi$
$467$	1.52271	−	9.61404i	0.0704628	−	0.444885i	0.997545	−	0.0700268i	$-0.0223085\pi$
$468$	−4.54244	+	6.41651i	−0.209974	+	0.296603i
$469$	−7.60707	+	5.52686i	−0.351262	+	0.255207i
$470$	−13.1681	+	15.8097i	−0.607401	+	0.729246i
$471$	3.61082	−	4.96986i	0.166378	−	0.228999i
$472$	7.92949	−	3.45711i	0.364985	−	0.159126i
$473$	−6.64827	+	3.38746i	−0.305688	+	0.155756i
$474$	−24.9634	+	2.11910i	−1.14661	+	0.0973333i
$475$	7.17292	+	5.07629i	0.329116	+	0.232916i
$476$	−0.776345	−	4.53981i	−0.0355837	−	0.208082i
$477$	8.14089	−	4.14799i	0.372746	−	0.189923i
$478$	33.3195	−	8.21619i	1.52400	−	0.375800i
$479$	−9.26622	−	6.73230i	−0.423384	−	0.307607i	0.355614	−	0.934633i	$-0.384272\pi$
$479$	−9.26622	−	6.73230i	−0.423384	−	0.307607i	−0.778998	+	0.627026i	$0.784272\pi$
$480$	−19.2583	−	0.801475i	−0.879019	−	0.0365821i
$481$	−4.11577	+	2.99028i	−0.187663	+	0.136345i
$482$	−7.09603	+	8.41252i	−0.323215	+	0.383180i
$483$	9.21145	+	1.45895i	0.419135	+	0.0663845i
$484$	−14.7608	+	7.75099i	−0.670947	+	0.352318i
$485$	3.37845	−	1.12101i	0.153407	−	0.0509023i
$486$	−2.21930	+	9.50088i	−0.100669	+	0.430969i
$487$	−9.45591	+	18.5583i	−0.428488	+	0.840955i	0.571307	+	0.820736i	$0.306436\pi$
$487$	−9.45591	+	18.5583i	−0.428488	+	0.840955i	−0.999796	+	0.0202192i	$0.993564\pi$
$488$	3.62780	+	0.800526i	0.164223	+	0.0362381i
$489$	22.3483	+	7.26140i	1.01062	+	0.328372i
$490$	−14.9433	+	13.0858i	−0.675068	+	0.591155i
$491$	6.15155	+	18.9325i	0.277616	+	0.854413i	0.988515	+	0.151120i	$0.0482879\pi$
$491$	6.15155	+	18.9325i	0.277616	+	0.854413i	−0.710900	+	0.703293i	$0.751712\pi$
$492$	0.173229	+	14.0940i	0.00780977	+	0.635409i
$493$	−15.4253	+	15.4253i	−0.694721	+	0.694721i
$494$	−10.9003	+	9.42616i	−0.490426	+	0.424103i
$495$	−0.402262	−	2.44139i	−0.0180803	−	0.109732i
$496$	−2.12396	+	7.12848i	−0.0953685	+	0.320078i
$497$	0.607295	−	0.0961860i	0.0272409	−	0.00431453i
$498$	25.5170	−	15.8534i	1.14344	−	0.710406i
$499$			25.0399i			1.12094i	0.828175	+	0.560469i	$0.189379\pi$
$499$			25.0399i			1.12094i	−0.828175	+	0.560469i	$0.810621\pi$
$500$	−0.692025	−	22.3500i	−0.0309483	−	0.999521i
$501$			33.7666i			1.50858i
$502$	12.7491	+	20.5205i	0.569019	+	0.915873i
$503$	−2.49218	+	0.394723i	−0.111121	+	0.0175998i	−0.211747	−	0.977324i	$-0.567915\pi$
$503$	−2.49218	+	0.394723i	−0.111121	+	0.0175998i	0.100626	+	0.994924i	$0.467915\pi$
$504$	1.51319	+	0.594343i	0.0674026	+	0.0264742i
$505$	3.90914	+	23.7251i	0.173954	+	1.05575i
$506$	−10.8995	−	12.6040i	−0.484540	−	0.560315i
$507$	−22.2144	+	22.2144i	−0.986577	+	0.986577i
$508$	0.287307	+	23.3755i	0.0127472	+	1.03712i
$509$	1.71006	+	5.26302i	0.0757970	+	0.233279i	0.981775	−	0.190045i	$-0.0608632\pi$
$509$	1.71006	+	5.26302i	0.0757970	+	0.233279i	−0.905978	+	0.423324i	$0.860863\pi$
$510$	−8.62306	−	9.84708i	−0.381835	−	0.436036i
$511$	−4.20336	−	1.36575i	−0.185946	−	0.0604174i
$512$	−21.6766	+	6.49043i	−0.957979	+	0.286839i
$513$	−4.47180	+	8.77640i	−0.197435	+	0.387488i
$514$	−18.5598	−	4.33535i	−0.818636	−	0.191224i
$515$	30.0997	−	9.98742i	1.32635	−	0.440099i
$516$	−6.47733	−	12.3353i	−0.285149	−	0.543032i
$517$	10.4889	+	1.66128i	0.461301	+	0.0730628i
$518$	0.804151	+	0.678308i	0.0353324	+	0.0298031i
$519$	−15.4667	+	11.2372i	−0.678914	+	0.493260i
$520$	35.8566	+	7.67868i	1.57242	+	0.336732i
$521$	−2.44987	−	1.77994i	−0.107331	−	0.0779804i	0.532825	−	0.846225i	$-0.321130\pi$
$521$	−2.44987	−	1.77994i	−0.107331	−	0.0779804i	−0.640156	+	0.768245i	$0.721130\pi$
$522$	−1.84354	−	7.47619i	−0.0806894	−	0.327224i
$523$	−7.76863	+	3.95831i	−0.339698	+	0.173085i	−0.615515	−	0.788125i	$-0.711052\pi$
$523$	−7.76863	+	3.95831i	−0.339698	+	0.173085i	0.275816	+	0.961210i	$0.411052\pi$
$524$	−4.08549	−	23.8906i	−0.178475	−	1.04367i
$525$	1.91951	−	6.16771i	0.0837742	−	0.269181i
$526$	−1.13454	−	13.3651i	−0.0494682	−	0.582746i
$527$	−4.50049	+	2.29311i	−0.196044	+	0.0998895i
$528$	4.73301	+	8.75046i	0.205978	+	0.380815i
$529$	−17.1130	+	23.5540i	−0.744043	+	1.02409i
$530$	−32.7461	−	27.2748i	−1.42240	−	1.18474i
$531$	−1.67746	+	1.21875i	−0.0727957	+	0.0528891i
$532$	2.43223	+	1.72185i	0.105450	+	0.0746515i
$533$	4.19482	−	26.4850i	0.181698	−	1.14719i
$534$	9.33069	−	3.93225i	0.403779	−	0.170165i
$535$	20.4557	−	28.5264i	0.884377	−	1.23330i
$536$	−1.88432	+	31.3130i	−0.0813901	+	1.35252i
$537$	27.7449	+	14.1368i	1.19728	+	0.610046i
$538$	20.3620	+	8.28798i	0.877867	+	0.357320i
$539$	9.75018	+	3.16803i	0.419970	+	0.136457i
$540$	24.6790	−	4.37850i	1.06201	−	0.188420i
$541$	−17.7647	+	5.77210i	−0.763764	+	0.248162i	−0.664894	−	0.746938i	$-0.731523\pi$
$541$	−17.7647	+	5.77210i	−0.763764	+	0.248162i	−0.0988709	+	0.995100i	$0.531523\pi$
$542$	−24.1281	−	1.74980i	−1.03639	−	0.0751605i
$543$	24.0227	−	24.0227i	1.03091	−	1.03091i
$544$	−13.3417	−	7.62219i	−0.572022	−	0.326799i
$545$	−0.327252	−	0.632509i	−0.0140179	−	0.0270937i
$546$	9.06589	+	5.47924i	0.387984	+	0.234490i
$547$	6.61028	−	1.04697i	0.282635	−	0.0447650i	−0.0135073	−	0.999909i	$-0.504300\pi$
$547$	6.61028	−	1.04697i	0.282635	−	0.0447650i	0.296143	+	0.955144i	$0.404300\pi$
$548$	−17.0475	+	12.7087i	−0.728232	+	0.542890i
$549$	−0.890490			−0.0380052
$550$	−9.72661	+	6.21205i	−0.414744	+	0.264883i
$551$		−	14.1146i		−	0.601304i
$552$	23.2829	−	20.6398i	0.990985	−	0.878486i
$553$	−1.54185	−	9.73483i	−0.0655660	−	0.413967i
$554$	−21.2531	−	12.8449i	−0.902958	−	0.545729i
$555$	2.95581	+	0.449323i	0.125467	+	0.0190727i
$556$	16.0880	−	16.4884i	0.682285	−	0.699265i
$557$	−8.28968	−	8.28968i	−0.351245	−	0.351245i	0.509328	−	0.860573i	$-0.329894\pi$
$557$	−8.28968	−	8.28968i	−0.351245	−	0.351245i	−0.860573	+	0.509328i	$0.829894\pi$
$558$	0.128960	−	1.77823i	0.00545931	−	0.0752786i
$559$	8.19077	+	25.2086i	0.346433	+	1.06621i
$560$	−0.233531	−	7.57938i	−0.00986849	−	0.320287i
$561$	−2.08762	+	6.42502i	−0.0881392	+	0.271265i
$562$	−34.5713	−	14.0716i	−1.45830	−	0.593576i
$563$	4.90781	−	9.63212i	0.206840	−	0.405946i	−0.764160	−	0.645027i	$-0.776846\pi$
$563$	4.90781	−	9.63212i	0.206840	−	0.405946i	0.971000	+	0.239081i	$0.0768462\pi$
$564$	−2.86108	+	19.6220i	−0.120473	+	0.826237i
$565$	7.16700	−	22.5338i	0.301518	−	0.948004i
$566$	−8.86908	−	21.0451i	−0.372795	−	0.884593i
$567$	5.44829	+	0.862924i	0.228807	+	0.0362394i
$568$	1.03938	−	1.76848i	0.0436114	−	0.0742039i
$569$	−13.6521	−	18.7905i	−0.572326	−	0.787739i	0.420502	−	0.907292i	$-0.361854\pi$
$569$	−13.6521	−	18.7905i	−0.572326	−	0.787739i	−0.992828	+	0.119552i	$0.961854\pi$
$570$	8.45039	+	0.560011i	0.353948	+	0.0234563i
$571$	−1.84713	−	1.34202i	−0.0772998	−	0.0561616i	0.548464	−	0.836174i	$-0.315213\pi$
$571$	−1.84713	−	1.34202i	−0.0772998	−	0.0561616i	−0.625764	+	0.780012i	$0.715213\pi$
$572$	−6.06936	−	17.9268i	−0.253773	−	0.749559i
$573$	−7.64057	−	14.9955i	−0.319189	−	0.626444i
$574$	−5.52528	+	0.469030i	−0.230621	+	0.0195769i
$575$	25.8387	+	25.2036i	1.07755	+	1.05106i
$576$	4.73851	−	2.63878i	0.197438	−	0.109949i
$577$	−5.48015	−	10.7554i	−0.228142	−	0.447753i	0.748351	−	0.663303i	$-0.230846\pi$
$577$	−5.48015	−	10.7554i	−0.228142	−	0.447753i	−0.976493	+	0.215549i	$0.930846\pi$
$578$	3.25784	+	13.2117i	0.135508	+	0.549533i
$579$	−2.95343	+	4.06504i	−0.122740	+	0.168937i
$580$	−28.6611	+	21.6453i	−1.19009	+	0.898772i
$581$	6.94664	+	9.56123i	0.288195	+	0.396667i
$582$	2.21189	−	2.62224i	0.0916856	−	0.108696i
$583$	−3.44095	+	21.7253i	−0.142510	+	0.899770i
$584$	−12.4279	+	7.93462i	−0.514270	+	0.328337i
$585$	−8.78941	+	0.0546794i	−0.363397	+	0.00226071i
$586$	18.7583	+	4.38172i	0.774897	+	0.181007i
$587$	26.0399	+	13.2680i	1.07478	+	0.547628i	0.899514	−	0.436893i	$-0.143921\pi$
$587$	26.0399	+	13.2680i	1.07478	+	0.547628i	0.175267	+	0.984521i	$0.443921\pi$
$588$	−5.69130	+	18.2774i	−0.234705	+	0.753746i
$589$	1.00991	−	3.10818i	0.0416126	−	0.128070i
$590$	8.30806	+	4.95092i	0.342038	+	0.203826i
$591$	−19.8171	+	6.43897i	−0.815167	+	0.264864i
$592$	3.45201	−	0.634083i	0.141877	−	0.0260606i
$593$	10.4158	+	10.4158i	0.427727	+	0.427727i	0.887853	−	0.460126i	$-0.152196\pi$
$593$	10.4158	+	10.4158i	0.427727	+	0.427727i	−0.460126	+	0.887853i	$0.652196\pi$
$594$	−8.46191	−	9.78522i	−0.347196	−	0.401492i
$595$	3.61842	−	3.66372i	0.148341	−	0.150198i
$596$	9.35775	−	18.9374i	0.383308	−	0.775708i
$597$	2.61860	+	16.5332i	0.107172	+	0.676659i
$598$	−50.2793	+	31.2378i	−2.05607	+	1.27741i
$599$	−25.5565			−1.04421			−0.522105	−	0.852881i	$-0.674853\pi$
$599$	−25.5565			−1.04421			−0.522105	+	0.852881i	$0.674853\pi$
$600$	−11.8218	−	18.0181i	−0.482623	−	0.735586i
$601$	−27.3859			−1.11709			−0.558547	−	0.829473i	$-0.688641\pi$
$601$	−27.3859			−1.11709			−0.558547	+	0.829473i	$0.688641\pi$
$602$	4.65580	−	2.89258i	0.189756	−	0.117893i
$603$	−1.17626	−	7.42663i	−0.0479011	−	0.302436i
$604$	−9.91842	−	4.90109i	−0.403575	−	0.199422i
$605$	−16.6607	−	8.35891i	−0.677354	−	0.339838i
$606$	15.1579	+	17.5284i	0.615748	+	0.712041i
$607$	−33.4675	−	33.4675i	−1.35841	−	1.35841i	−0.875884	−	0.482522i	$-0.839721\pi$
$607$	−33.4675	−	33.4675i	−1.35841	−	1.35841i	−0.482522	−	0.875884i	$-0.660279\pi$
$608$	9.59133	−	2.61678i	0.388980	−	0.106124i
$609$	−9.86760	+	3.20618i	−0.399856	+	0.129921i
$610$	1.63684	+	3.81745i	0.0662735	+	0.154564i
$611$	11.6575	−	35.8782i	0.471613	−	1.45148i
$612$	3.51652	+	1.09499i	0.142147	+	0.0442625i
$613$	−20.0105	−	10.1959i	−0.808218	−	0.411808i	0.000502907	−	1.00000i	$-0.499840\pi$
$613$	−20.0105	−	10.1959i	−0.808218	−	0.411808i	−0.808721	+	0.588192i	$0.799840\pi$
$614$	−29.2768	−	6.83873i	−1.18151	−	0.275989i
$615$	−12.6913	+	9.34193i	−0.511762	+	0.376703i
$616$	−3.29882	+	2.10614i	−0.132913	+	0.0848587i
$617$	−6.16968	+	38.9539i	−0.248382	+	1.56822i	0.476390	+	0.879234i	$0.341945\pi$
$617$	−6.16968	+	38.9539i	−0.248382	+	1.56822i	−0.724772	+	0.688989i	$0.758055\pi$
$618$	19.7064	−	23.3624i	0.792708	−	0.939775i
$619$	−10.9094	−	15.0155i	−0.438487	−	0.603525i	0.531388	−	0.847128i	$-0.321671\pi$
$619$	−10.9094	−	15.0155i	−0.438487	−	0.603525i	−0.969875	+	0.243603i	$0.921671\pi$
$620$	−7.86018	+	2.71578i	−0.315673	+	0.109069i
$621$	−23.7815	+	32.7324i	−0.954319	+	1.31351i
$622$	3.34430	+	13.5623i	0.134094	+	0.543799i
$623$	1.80845	+	3.54927i	0.0724539	+	0.142199i
$624$	33.3321	−	11.7436i	1.33435	−	0.470119i
$625$	19.8535	−	15.1933i	0.794142	−	0.607733i
$626$	−25.2926	+	2.14704i	−1.01090	+	0.0858129i
$627$	−1.98443	−	3.89467i	−0.0792506	−	0.155538i
$628$	7.63692	−	2.58557i	0.304746	−	0.103176i
$629$	1.92818	+	1.40090i	0.0768815	+	0.0558577i
$630$	0.446136	+	1.76201i	0.0177745	+	0.0702002i
$631$	4.93488	+	6.79228i	0.196454	+	0.270396i	0.895867	−	0.444321i	$-0.146555\pi$
$631$	4.93488	+	6.79228i	0.196454	+	0.270396i	−0.699413	+	0.714718i	$0.746555\pi$
$632$	−28.3485	−	16.6611i	−1.12764	−	0.662742i
$633$	27.3015	+	4.32413i	1.08514	+	0.171869i
$634$	−15.0989	−	35.8276i	−0.599653	−	1.42289i
$635$	−21.0490	+	15.4940i	−0.835303	+	0.614859i
$636$	−40.6425	−	5.92607i	−1.61158	−	0.234984i
$637$	16.5336	−	32.4491i	0.655086	−	1.28568i
$638$	17.1698	+	6.98864i	0.679757	+	0.276683i
$639$	−0.151941	+	0.467625i	−0.00601068	+	0.0184990i
$640$	−20.0222	−	15.4632i	−0.791448	−	0.611236i
$641$	1.94986	+	6.00105i	0.0770148	+	0.237027i	0.982151	−	0.188095i	$-0.0602312\pi$
$641$	1.94986	+	6.00105i	0.0770148	+	0.237027i	−0.905136	+	0.425122i	$0.860231\pi$
$642$	2.44698	−	33.7415i	0.0965746	−	1.33167i
$643$	−9.08027	−	9.08027i	−0.358091	−	0.358091i	0.505018	−	0.863109i	$-0.331486\pi$
$643$	−9.08027	−	9.08027i	−0.358091	−	0.358091i	−0.863109	+	0.505018i	$0.831486\pi$
$644$	8.76115	+	8.54840i	0.345238	+	0.336854i
$645$	6.98536	−	13.9230i	0.275048	−	0.548217i
$646$	5.77791	+	3.49205i	0.227329	+	0.137393i
$647$	4.99520	+	31.5384i	0.196381	+	1.23990i	0.867078	+	0.498172i	$0.165995\pi$
$647$	4.99520	+	31.5384i	0.196381	+	1.23990i	−0.670697	+	0.741731i	$0.734005\pi$
$648$	13.7711	−	12.2078i	0.540980	−	0.479567i
$649$		−	4.99172i		−	0.195942i
$650$	16.3905	+	37.5790i	0.642888	+	1.47397i
$651$	−2.40234			−0.0941553
$652$	18.4334	+	24.7265i	0.721906	+	0.968364i
$653$	24.8409	−	3.93441i	0.972099	−	0.153965i	0.349868	−	0.936799i	$-0.386227\pi$
$653$	24.8409	−	3.93441i	0.972099	−	0.153965i	0.622231	+	0.782834i	$0.286227\pi$
$654$	−0.587392	−	0.355007i	−0.0229688	−	0.0138819i
$655$	19.0418	−	19.2802i	0.744024	−	0.753339i
$656$	−10.5027	+	15.2293i	−0.410061	+	0.594604i
$657$	2.49912	−	2.49912i	0.0975000	−	0.0975000i
$658$	−7.78070	−	0.564267i	−0.303323	−	0.0219974i
$659$	19.1414	−	6.21943i	0.745645	−	0.242275i	0.0885388	−	0.996073i	$-0.471780\pi$
$659$	19.1414	−	6.21943i	0.745645	−	0.242275i	0.657106	+	0.753798i	$0.271780\pi$
$660$	−4.86530	+	10.0022i	−0.189382	+	0.389335i
$661$	−12.2360	−	3.97571i	−0.475924	−	0.154637i	0.0612256	−	0.998124i	$-0.480499\pi$
$661$	−12.2360	−	3.97571i	−0.475924	−	0.154637i	−0.537150	+	0.843487i	$0.680499\pi$
$662$	−33.0501	−	13.4524i	−1.28453	−	0.522844i
$663$	21.3828	+	10.8951i	0.830438	+	0.423129i
$664$	39.3569	+	2.36838i	1.52735	+	0.0919108i
$665$	0.0207266	+	3.33169i	0.000803744	+	0.129197i
$666$	−0.775245	+	0.326713i	−0.0300401	+	0.0126599i
$667$	9.06959	−	57.2631i	0.351176	−	2.21724i
$668$	−25.6070	+	36.1717i	−0.990766	+	1.39953i
$669$	22.8704	−	16.6163i	0.884221	−	0.642424i
$670$	−29.6752	+	18.6936i	−1.14645	+	0.722198i
$671$	1.26009	−	1.73437i	0.0486453	−	0.0669545i
$672$	−4.00809	−	6.11093i	−0.154616	−	0.235734i
$673$	−15.9689	+	8.13657i	−0.615557	+	0.313642i	−0.733824	−	0.679340i	$-0.762266\pi$
$673$	−15.9689	+	8.13657i	−0.615557	+	0.313642i	0.118267	+	0.992982i	$0.462266\pi$
$674$	3.09662	+	36.4789i	0.119278	+	1.40512i
$675$	20.0601	+	19.5671i	0.772115	+	0.753137i
$676$	−40.6430	+	6.95030i	−1.56319	+	0.267319i
$677$	10.1219	−	5.15738i	0.389017	−	0.198214i	−0.248532	−	0.968624i	$-0.579948\pi$
$677$	10.1219	−	5.15738i	0.389017	−	0.198214i	0.637549	+	0.770409i	$0.279948\pi$
$678$	−5.45604	−	22.1262i	−0.209538	−	0.849750i
$679$	1.09186	+	0.793280i	0.0419016	+	0.0304433i
$680$	−1.76968	−	17.0878i	−0.0678642	−	0.655287i
$681$	12.7986	−	9.29870i	0.490442	−	0.356327i
$682$	3.28090	+	2.76747i	0.125632	+	0.105972i
$683$	0.869222	+	0.137671i	0.0332598	+	0.00526784i	0.173042	−	0.984914i	$-0.444640\pi$
$683$	0.869222	+	0.137671i	0.0332598	+	0.00526784i	−0.139782	+	0.990182i	$0.544640\pi$
$684$	−2.10984	+	1.10789i	−0.0806719	+	0.0423612i
$685$	−22.6548	−	7.20550i	−0.865597	−	0.275308i
$686$	−15.5064	−	3.62213i	−0.592038	−	0.138293i
$687$	−4.86640	+	9.55084i	−0.185665	+	0.364387i
$688$	2.41583	−	18.1260i	0.0921028	−	0.691048i
$689$	74.3134	+	24.1459i	2.83111	+	0.919885i
$690$	33.9234	+	7.70189i	1.29144	+	0.293206i
$691$	4.21965	+	12.9867i	0.160523	+	0.494039i	0.998679	−	0.0513922i	$-0.0163659\pi$
$691$	4.21965	+	12.9867i	0.160523	+	0.494039i	−0.838155	+	0.545431i	$0.816366\pi$
$692$	−25.0902	+	0.308382i	−0.953785	+	0.0117229i
$693$	0.663358	−	0.663358i	0.0251989	−	0.0251989i
$694$	11.8607	+	13.7156i	0.450227	+	0.520636i
$695$	25.4634	+	3.87078i	0.965881	+	0.146827i
$696$	−12.6546	+	32.2182i	−0.479670	+	1.22123i
$697$	−12.4078	+	1.96521i	−0.469981	+	0.0744376i
$698$	7.18154	+	11.5592i	0.271825	+	0.437521i
$699$			6.86391i			0.259617i
$700$	6.73353	−	5.15135i	0.254504	−	0.194703i
$701$			30.3530i			1.14642i	0.819410	+	0.573208i	$0.194301\pi$
$701$			30.3530i			1.14642i	−0.819410	+	0.573208i	$0.805699\pi$
$702$	−39.0348	+	24.2518i	−1.47327	+	0.915325i
$703$	−1.52311	+	0.241237i	−0.0574451	+	0.00909841i
$704$	−1.56582	+	12.9630i	−0.0590139	+	0.488562i
$705$	−19.6907	+	10.1877i	−0.741594	+	0.383691i
$706$	28.5074	−	24.6522i	1.07289	−	0.927796i
$707$	−6.44644	+	6.44644i	−0.242443	+	0.242443i
$708$	9.32009	−	0.114553i	0.350270	−	0.00430515i
$709$	8.73436	+	26.8816i	0.328026	+	1.00956i	0.970056	+	0.242880i	$0.0780922\pi$
$709$	8.73436	+	26.8816i	0.328026	+	1.00956i	−0.642031	+	0.766679i	$0.721908\pi$
$710$	2.28396	−	0.208199i	0.0857154	−	0.00781357i
$711$	7.49596	+	2.43558i	0.281120	+	0.0913415i
$712$	12.9773	+	2.86363i	0.486346	+	0.107319i
$713$	6.09441	−	11.9610i	0.228237	−	0.447941i
$714$	1.12884	−	4.83259i	0.0422458	−	0.180855i
$715$	12.3310	−	17.1961i	0.461154	−	0.643099i
$716$	19.0005	+	36.1841i	0.710081	+	1.35226i
$717$	36.5221	+	5.78453i	1.36394	+	0.216027i
$718$	32.4968	−	38.5258i	1.21277	−	1.43777i
$719$	37.2617	−	27.0722i	1.38963	−	1.00962i	0.393719	−	0.919231i	$-0.371188\pi$
$719$	37.2617	−	27.0722i	1.38963	−	1.00962i	0.995906	−	0.0903910i	$-0.0288117\pi$
$720$	5.48519	+	2.58525i	0.204421	+	0.0963466i
$721$	9.72770	+	7.06759i	0.362279	+	0.263211i
$722$	21.8474	−	5.38731i	0.813077	−	0.200495i
$723$	−10.5661	+	5.38371i	−0.392958	+	0.200222i
$724$	43.9514	−	7.51605i	1.63344	−	0.279332i
$725$	−38.3417	−	11.9327i	−1.42397	−	0.443168i
$726$	−17.8999	+	1.51949i	−0.664329	+	0.0563936i
$727$	−25.7138	+	13.1018i	−0.953672	+	0.485920i	−0.860343	−	0.509715i	$-0.829751\pi$
$727$	−25.7138	+	13.1018i	−0.953672	+	0.485920i	−0.0933286	+	0.995635i	$0.529751\pi$
$728$	5.55642	+	12.7447i	0.205935	+	0.472348i
$729$	−17.6525	+	24.2966i	−0.653797	+	0.899874i
$730$	−15.3072	−	6.11982i	−0.566546	−	0.226505i
$731$	10.0461	−	7.29890i	0.371567	−	0.269959i
$732$	3.26718	+	2.31293i	0.120758	+	0.0854884i
$733$	−7.76752	+	49.0422i	−0.286900	+	1.81142i	0.250532	+	0.968108i	$0.419394\pi$
$733$	−7.76752	+	49.0422i	−0.286900	+	1.81142i	−0.537432	+	0.843307i	$0.680606\pi$
$734$	−14.0356	−	33.3045i	−0.518062	−	1.22929i
$735$	−20.3134	+	6.74023i	−0.749272	+	0.248617i
$736$	40.5935	−	4.45321i	1.49629	−	0.164147i
$737$	16.1290	+	8.21813i	0.594119	+	0.302719i
$738$	1.67173	−	4.10712i	0.0615372	−	0.151185i
$739$	−26.6502	−	8.65917i	−0.980343	−	0.318533i	−0.225359	−	0.974276i	$-0.572355\pi$
$739$	−26.6502	−	8.65917i	−0.980343	−	0.318533i	−0.754984	+	0.655743i	$0.772355\pi$
$740$	2.82559	+	2.72287i	0.103871	+	0.100095i
$741$	−14.7676	+	4.79829i	−0.542502	+	0.176270i
$742$	1.16875	−	16.1159i	0.0429061	−	0.591634i
$743$	−17.1558	+	17.1558i	−0.629384	+	0.629384i	−0.947913	−	0.318529i	$-0.896811\pi$
$743$	−17.1558	+	17.1558i	−0.629384	+	0.629384i	0.318529	+	0.947913i	$0.396811\pi$
$744$	−5.09188	+	6.18932i	−0.186677	+	0.226911i
$745$	23.3024	−	3.83948i	0.853733	−	0.140668i
$746$	1.92498	−	3.18506i	0.0704786	−	0.116613i
$747$	−9.33443	+	1.47843i	−0.341529	+	0.0540929i
$748$	−7.10875	+	5.29950i	−0.259922	+	0.193769i
$749$	13.3091			0.486304
$750$	8.66528	−	22.4816i	0.316411	−	0.820912i
$751$		−	54.0781i		−	1.97334i	−0.162738	−	0.986669i	$-0.552032\pi$
$751$		−	54.0781i		−	1.97334i	0.162738	−	0.986669i	$-0.447968\pi$
$752$	−17.9453	+	18.8499i	−0.654398	+	0.687386i
$753$	4.07212	+	25.7103i	0.148396	+	0.936936i
$754$	34.0618	−	56.3583i	1.24046	−	2.05245i
$755$	−2.01092	−	12.2045i	−0.0731847	−	0.444169i
$756$	6.80180	+	6.63663i	0.247379	+	0.241372i
$757$	23.3426	+	23.3426i	0.848401	+	0.848401i	0.989934	−	0.141532i	$-0.0452029\pi$
$757$	23.3426	+	23.3426i	0.848401	+	0.848401i	−0.141532	+	0.989934i	$0.545203\pi$
$758$	31.3662	+	2.27472i	1.13927	+	0.0826215i
$759$	−5.54826	−	17.0758i	−0.201389	−	0.619812i
$760$	8.62759	+	7.00828i	0.312956	+	0.254217i
$761$	−1.58617	+	4.88172i	−0.0574985	+	0.176962i	−0.975681	−	0.219196i	$-0.929657\pi$
$761$	−1.58617	+	4.88172i	−0.0574985	+	0.176962i	0.918182	+	0.396158i	$0.129657\pi$
$762$	−9.49628	+	23.3305i	−0.344014	+	0.845176i
$763$	0.122583	−	0.240582i	0.00443780	−	0.00870967i
$764$	3.18708	−	21.8578i	0.115304	−	0.790787i
$765$	1.29680	+	3.90826i	0.0468861	+	0.141303i
$766$	3.40319	−	1.43421i	0.122962	−	0.0518201i
$767$	−17.5140	−	2.77394i	−0.632393	−	0.100161i
$768$	−24.2393	−	2.62607i	−0.874661	−	0.0947601i
$769$	−10.5565	−	14.5298i	−0.380679	−	0.523959i	0.575085	−	0.818093i	$-0.304969\pi$
$769$	−10.5565	−	14.5298i	−0.380679	−	0.523959i	−0.955764	+	0.294134i	$0.904969\pi$
$770$	−4.06310	−	1.62442i	−0.146424	−	0.0585401i
$771$	−16.6144	−	12.0711i	−0.598354	−	0.434730i
$772$	−6.24653	+	2.11484i	−0.224817	+	0.0761148i
$773$	−11.5035	−	22.5768i	−0.413751	−	0.812033i	−0.999998	−	0.00190030i	$-0.999395\pi$
$773$	−11.5035	−	22.5768i	−0.413751	−	0.812033i	0.586247	−	0.810133i	$-0.300605\pi$
$774$	0.370745	+	4.36746i	0.0133261	+	0.156985i
$775$	−7.58942	−	5.37105i	−0.272620	−	0.192934i
$776$	4.35802	−	1.13163i	0.156444	−	0.0406231i
$777$	0.514628	+	1.01001i	0.0184622	+	0.0362340i
$778$	−12.5428	+	3.09289i	−0.449680	+	0.110885i
$779$	4.77767	−	6.57590i	0.171178	−	0.235606i
$780$	32.3901	+	22.6287i	1.15975	+	0.810239i
$781$	−0.695769	−	0.957644i	−0.0248966	−	0.0342672i
$782$	21.1971	+	17.8799i	0.758007	+	0.639386i
$783$	7.04127	−	44.4568i	0.251634	−	1.58876i
$784$	−19.9574	+	15.2632i	−0.712764	+	0.545114i
$785$	7.32563	+	5.25307i	0.261463	+	0.187490i
$786$	5.94048	−	25.4313i	0.211890	−	0.907106i
$787$	−30.5479	−	15.5649i	−1.08891	−	0.554829i	−0.185085	−	0.982723i	$-0.559256\pi$
$787$	−30.5479	−	15.5649i	−1.08891	−	0.554829i	−0.903829	+	0.427893i	$0.859256\pi$
$788$	−26.1116	−	8.13077i	−0.930188	−	0.289647i
$789$	4.46615	−	13.7454i	0.158999	−	0.489349i
$790$	−3.33740	−	36.6115i	−0.118739	−	1.30258i
$791$	8.52659	−	2.77046i	0.303171	−	0.0985061i
$792$	−0.303036	−	3.11507i	−0.0107679	−	0.110689i
$793$	−5.38497	−	5.38497i	−0.191226	−	0.191226i
$794$	23.8488	−	20.6236i	0.846361	−	0.731903i
$795$	−21.1015	−	40.7847i	−0.748392	−	1.44648i
$796$	−9.73289	+	19.6966i	−0.344973	+	0.698129i
$797$	−1.16928	−	7.38252i	−0.0414179	−	0.261502i	0.958287	−	0.285809i	$-0.0922622\pi$
$797$	−1.16928	−	7.38252i	−0.0414179	−	0.261502i	−0.999705	+	0.0243065i	$0.992262\pi$
$798$	1.69453	+	2.72745i	0.0599856	+	0.0965507i
$799$	−17.6734			−0.625240
$800$	1.00026	−	28.2666i	0.0353647	−	0.999374i
$801$	−3.18545			−0.112552
$802$	18.3464	+	29.5297i	0.647834	+	1.04273i
$803$	1.33104	+	8.40383i	0.0469712	+	0.296565i
$804$	−14.9740	+	30.3032i	−0.528093	+	1.06871i
$805$	−2.05674	+	13.5300i	−0.0724907	+	0.476870i
$806$	11.5332	−	9.97350i	0.406239	−	0.351301i
$807$	16.7499	+	16.7499i	0.589625	+	0.589625i
$808$	2.94487	+	30.2719i	0.103600	+	1.06496i
$809$	−6.69119	+	2.17410i	−0.235250	+	0.0764373i	−0.424269	−	0.905536i	$-0.639469\pi$
$809$	−6.69119	+	2.17410i	−0.235250	+	0.0764373i	0.189020	+	0.981973i	$0.439469\pi$
$810$	20.0646	+	4.55543i	0.705000	+	0.160062i
$811$	1.88146	−	5.79054i	0.0660670	−	0.203333i	−0.912573	−	0.408913i	$-0.865908\pi$
$811$	1.88146	−	5.79054i	0.0660670	−	0.203333i	0.978640	+	0.205580i	$0.0659080\pi$
$812$	−13.0019	−	4.04859i	−0.456276	−	0.142078i
$813$	−23.2254	−	11.8339i	−0.814550	−	0.415034i
$814$	0.460691	−	1.97223i	0.0161472	−	0.0691266i
$815$	−10.4512	+	32.8597i	−0.366090	+	1.15102i
$816$	−10.0579	−	13.1512i	−0.352097	−	0.460384i
$817$	−1.25688	+	7.93560i	−0.0439725	+	0.277631i
$818$	−14.1227	−	11.9126i	−0.493790	−	0.416516i
$819$	−1.95883	−	2.69610i	−0.0684470	−	0.0942092i
$820$	−20.6797	+	0.382852i	−0.722167	+	0.0133698i
$821$	−4.36281	+	6.00490i	−0.152263	+	0.209572i	−0.878334	−	0.478048i	$-0.841345\pi$
$821$	−4.36281	+	6.00490i	−0.152263	+	0.209572i	0.726071	+	0.687620i	$0.241345\pi$
$822$	−22.2450	+	5.48535i	−0.775884	+	0.191323i
$823$	19.6217	+	38.5098i	0.683970	+	1.34237i	0.927993	+	0.372598i	$0.121533\pi$
$823$	19.6217	+	38.5098i	0.683970	+	1.34237i	−0.244023	+	0.969769i	$0.578467\pi$
$824$	38.8270	−	10.0820i	1.35260	−	0.351225i
$825$	−12.2573	+	2.09802i	−0.426745	+	0.0730436i
$826$	0.310160	+	3.65375i	0.0107918	+	0.127130i
$827$	0.278491	+	0.546569i	0.00968408	+	0.0190061i	0.895798	−	0.444462i	$-0.146605\pi$
$827$	0.278491	+	0.546569i	0.00968408	+	0.0190061i	−0.886114	+	0.463468i	$0.846605\pi$
$828$	−9.27152	+	3.13899i	−0.322208	+	0.109088i
$829$	25.2713	+	18.3607i	0.877709	+	0.637693i	0.932644	−	0.360797i	$-0.117495\pi$
$829$	25.2713	+	18.3607i	0.877709	+	0.637693i	−0.0549352	+	0.998490i	$0.517495\pi$
$830$	23.4958	+	37.2984i	0.815551	+	1.29465i
$831$	−15.7279	−	21.6476i	−0.545594	−	0.750946i
$832$	44.6120	+	12.6975i	1.54664	+	0.440207i
$833$	−16.8514	−	2.66901i	−0.583868	−	0.0924756i
$834$	22.8740	−	9.63981i	0.792061	−	0.333799i
$835$	−49.5484	+	0.308243i	−1.71469	+	0.0106672i
$836$	0.827758	−	5.67697i	0.0286286	−	0.196342i
$837$	4.73146	−	9.28601i	0.163543	−	0.320971i
$838$	12.2611	−	30.1231i	0.423552	−	1.04059i
$839$	2.67652	−	8.23749i	0.0924038	−	0.284390i	−0.894165	−	0.447738i	$-0.852230\pi$
$839$	2.67652	−	8.23749i	0.0924038	−	0.284390i	0.986568	+	0.163349i	$0.0522296\pi$
$840$	2.93973	−	7.62353i	0.101430	−	0.263037i
$841$	10.9698	+	33.7615i	0.378268	+	1.16419i
$842$	−3.07141	−	0.222743i	−0.105848	−	0.00767624i
$843$	−28.4386	−	28.4386i	−0.979479	−	0.979479i
$844$	25.9668	+	25.3363i	0.893815	+	0.872111i
$845$	−32.7997	−	32.3942i	−1.12835	−	1.11439i
$846$	3.22678	−	5.33900i	0.110939	−	0.183558i
$847$	−1.10558	−	6.98033i	−0.0379880	−	0.239847i
$848$	−39.0433	−	37.1695i	−1.34075	−	1.27641i
$849$		−	24.6077i		−	0.844534i
$850$	14.3707	−	12.7432i	0.492910	−	0.437088i
$851$	−6.33426			−0.217136
$852$	1.77206	−	1.32105i	0.0607098	−	0.0452586i
$853$	−9.13882	+	1.44745i	−0.312907	+	0.0495596i	−0.310913	−	0.950438i	$-0.600635\pi$
$853$	−9.13882	+	1.44745i	−0.312907	+	0.0495596i	−0.00199425	+	0.999998i	$0.500635\pi$
$854$	−0.814576	+	1.34779i	−0.0278742	+	0.0461204i
$855$	−2.38140	−	1.19478i	−0.0814422	−	0.0408607i
$856$	28.2092	−	34.2891i	0.964172	−	1.17198i
$857$	25.2568	−	25.2568i	0.862757	−	0.862757i	−0.128901	−	0.991658i	$-0.541145\pi$
$857$	25.2568	−	25.2568i	0.862757	−	0.862757i	0.991658	+	0.128901i	$0.0411449\pi$
$858$	1.47508	−	20.3399i	0.0503583	−	0.694392i
$859$	3.73920	−	1.21494i	0.127580	−	0.0414532i	−0.244531	−	0.969641i	$-0.578634\pi$
$859$	3.73920	−	1.21494i	0.127580	−	0.0414532i	0.372111	+	0.928188i	$0.378634\pi$
$860$	18.0414	−	9.61731i	0.615208	−	0.327947i
$861$	−5.68250	−	1.84636i	−0.193659	−	0.0629237i
$862$	−2.78965	+	6.85364i	−0.0950160	+	0.233436i
$863$	34.4560	+	17.5562i	1.17290	+	0.597620i	0.928237	−	0.371989i	$-0.121324\pi$
$863$	34.4560	+	17.5562i	1.17290	+	0.597620i	0.244659	+	0.969609i	$0.421324\pi$
$864$	31.5151	−	3.45729i	1.07217	−	0.117619i
$865$	−16.6305	−	22.5930i	−0.565453	−	0.768184i
$866$	9.14882	+	21.7089i	0.310890	+	0.737699i
$867$	−2.29365	+	14.4816i	−0.0778965	+	0.491819i
$868$	−2.57346	−	1.82183i	−0.0873488	−	0.0618368i
$869$	−15.3509	+	11.1531i	−0.520743	+	0.378342i
$870$	−37.5161	+	9.49898i	−1.27192	+	0.322045i
$871$	37.7972	−	52.0234i	1.28071	−	1.76275i
$872$	−0.360008	−	0.825744i	−0.0121914	−	0.0279632i
$873$	−0.961614	+	0.489967i	−0.0325457	+	0.0165829i
$874$	−17.8784	+	1.51766i	−0.604745	+	0.0513356i
$875$	9.06789	+	2.76034i	0.306551	+	0.0933166i
$876$	−15.6603	+	2.67805i	−0.529114	+	0.0904828i
$877$	15.7980	−	8.04946i	0.533459	−	0.271811i	−0.166441	−	0.986051i	$-0.553228\pi$
$877$	15.7980	−	8.04946i	0.533459	−	0.271811i	0.699901	+	0.714240i	$0.253228\pi$
$878$	−19.8248	+	4.88856i	−0.669055	+	0.164981i
$879$	16.7922	+	12.2002i	0.566385	+	0.411503i
$880$	−12.7970	+	7.02499i	−0.431388	+	0.236812i
$881$	−0.144449	+	0.104948i	−0.00486661	+	0.00353580i	−0.590216	−	0.807245i	$-0.700957\pi$
$881$	−0.144449	+	0.104948i	−0.00486661	+	0.00353580i	0.585349	+	0.810781i	$0.300957\pi$
$882$	3.88299	−	4.60338i	0.130747	−	0.155004i
$883$	33.7769	+	5.34973i	1.13668	+	0.180033i	0.696282	−	0.717769i	$-0.254836\pi$
$883$	33.7769	+	5.34973i	1.13668	+	0.180033i	0.440400	+	0.897801i	$0.354836\pi$
$884$	14.6435	+	27.8868i	0.492514	+	0.937934i
$885$	6.17762	+	8.39247i	0.207658	+	0.282110i
$886$	−7.84001	+	33.5633i	−0.263390	+	1.12758i
$887$	4.49102	−	8.81412i	0.150794	−	0.295949i	−0.803236	−	0.595661i	$-0.796890\pi$
$887$	4.49102	−	8.81412i	0.150794	−	0.295949i	0.954030	+	0.299711i	$0.0968904\pi$
$888$	3.69294	+	0.814901i	0.123927	+	0.0273463i
$889$	−9.42465	−	3.06225i	−0.316093	−	0.102705i
$890$	5.85527	+	13.6558i	0.196269	+	0.457742i
$891$	−3.28163	−	10.0998i	−0.109939	−	0.338357i
$892$	37.1005	−	0.456000i	1.24221	−	0.0152680i
$893$	8.08587	−	8.08587i	0.270583	−	0.270583i
$894$	17.2160	−	14.8878i	0.575791	−	0.497923i
$895$	−20.4907	+	40.8414i	−0.684928	+	1.36518i
$896$	0.340664	−	9.58574i	0.0113808	−	0.320237i
$897$	−62.9955	+	9.97751i	−2.10336	+	0.333139i
$898$	35.7778	−	22.2282i	1.19392	−	0.741766i
$899$			14.9342i			0.498084i
$900$	1.22584	+	6.66790i	0.0408613	+	0.222263i
$901$		−	36.6064i		−	1.21953i
$902$	5.63366	+	9.06775i	0.187580	+	0.301923i
$903$	5.83331	−	0.923906i	0.194120	−	0.0307457i
$904$	10.9348	−	27.8397i	0.363686	−	0.925936i
$905$	35.4696	+	35.0310i	1.17905	+	1.16447i
$906$	−7.79745	−	9.01684i	−0.259053	−	0.299564i
$907$	−7.87950	+	7.87950i	−0.261634	+	0.261634i	−0.825718	−	0.564083i	$-0.809230\pi$
$907$	−7.87950	+	7.87950i	−0.261634	+	0.261634i	0.564083	+	0.825718i	$0.309230\pi$
$908$	20.7619	−	0.255183i	0.689007	−	0.00846855i
$909$	−2.25283	−	6.93351i	−0.0747218	−	0.229970i
$910$	−7.95736	+	13.3531i	−0.263784	+	0.442651i
$911$	−25.3951	−	8.25137i	−0.841377	−	0.273380i	−0.143547	−	0.989643i	$-0.545851\pi$
$911$	−25.3951	−	8.25137i	−0.841377	−	0.273380i	−0.697830	+	0.716263i	$0.745851\pi$
$912$	10.6185	+	1.41524i	0.351615	+	0.0468632i
$913$	10.3293	−	20.2723i	0.341849	−	0.670916i
$914$	−5.82409	−	1.36044i	−0.192644	−	0.0449994i
$915$	0.0278418	+	4.47541i	0.000920421	+	0.147953i
$916$	−12.4559	+	6.54067i	−0.411555	+	0.216110i
$917$	10.1478	+	1.60725i	0.335109	+	0.0530760i
$918$	16.4566	+	13.8813i	0.543149	+	0.458150i
$919$	−46.3097	+	33.6460i	−1.52762	+	1.10988i	−0.570071	+	0.821596i	$0.693084\pi$
$919$	−46.3097	+	33.6460i	−1.52762	+	1.10988i	−0.957545	+	0.288282i	$0.906916\pi$
$920$	30.4989	+	33.9764i	1.00552	+	1.12017i
$921$	−26.2082	−	19.0414i	−0.863589	−	0.627434i
$922$	9.04317	+	36.6732i	0.297821	+	1.20777i
$923$	−3.74664	+	1.90901i	−0.123322	+	0.0628358i
$924$	−4.15682	+	0.710851i	−0.136749	+	0.0233853i
$925$	−0.632344	+	4.34139i	−0.0207913	+	0.142744i
$926$	−1.93733	−	22.8222i	−0.0636645	−	0.749983i
$927$	−8.56733	+	4.36527i	−0.281388	+	0.143374i
$928$	−37.9887	+	24.9164i	−1.24704	+	0.817921i
$929$	−23.3033	+	32.0743i	−0.764557	+	1.05232i	0.232264	+	0.972653i	$0.425387\pi$
$929$	−23.3033	+	32.0743i	−0.764557	+	1.05232i	−0.996821	+	0.0796697i	$0.974613\pi$
$930$	−8.94106	−	0.592528i	−0.293189	−	0.0194298i
$931$	8.93092	−	6.48869i	0.292699	−	0.212658i
$932$	−5.20527	+	7.35281i	−0.170504	+	0.240849i
$933$	−2.35452	+	14.8659i	−0.0770837	+	0.486687i
$934$	12.6853	−	5.34599i	0.415076	−	0.174926i
$935$	−9.44700	−	3.00467i	−0.308950	−	0.0982633i
$936$	−11.0980	−	0.667840i	−0.362748	−	0.0218290i
$937$	13.9394	+	7.10250i	0.455381	+	0.232028i	0.666608	−	0.745409i	$-0.267746\pi$
$937$	13.9394	+	7.10250i	0.455381	+	0.232028i	−0.211226	+	0.977437i	$0.567746\pi$
$938$	−12.3165	−	5.01319i	−0.402147	−	0.163687i
$939$	−26.0123	−	8.45190i	−0.848879	−	0.275817i
$940$	−28.8191	−	4.01917i	−0.939974	−	0.131091i
$941$	0.332851	−	0.108150i	0.0108506	−	0.00352559i	−0.303587	−	0.952804i	$-0.598184\pi$
$941$	0.332851	−	0.108150i	0.0108506	−	0.00352559i	0.314437	+	0.949278i	$0.398184\pi$
$942$	8.66488	+	0.628389i	0.282317	+	0.0204740i
$943$	23.6085	−	23.6085i	0.768797	−	0.768797i
$944$	10.0708	+	6.94521i	0.327777	+	0.226047i
$945$	−1.59677	+	10.5041i	−0.0519430	+	0.341700i
$946$	−9.03093	−	5.45811i	−0.293621	−	0.177459i
$947$	18.7583	−	2.97102i	0.609561	−	0.0965450i	0.155980	−	0.987760i	$-0.450146\pi$
$947$	18.7583	−	2.97102i	0.609561	−	0.0965450i	0.453581	+	0.891215i	$0.350146\pi$
$948$	−21.1763	−	28.4058i	−0.687774	−	0.922579i
$949$	30.2254			0.981158
$950$	−0.744607	+	12.4050i	−0.0241583	+	0.402472i
$951$		−	41.8925i		−	1.35846i
$952$	4.87405	−	4.32074i	0.157969	−	0.140036i
$953$	4.31977	+	27.2740i	0.139931	+	0.883491i	0.953362	+	0.301829i	$0.0975972\pi$
$953$	4.31977	+	27.2740i	0.139931	+	0.883491i	−0.813431	+	0.581662i	$0.802403\pi$
$954$	11.0585	+	6.68353i	0.358032	+	0.216387i
$955$	21.9343	−	11.3485i	0.709776	−	0.367229i
$956$	34.7367	+	33.8932i	1.12347	+	1.09618i
$957$	14.1240	+	14.1240i	0.456564	+	0.456564i
$958$	1.17162	−	16.1555i	0.0378533	−	0.521961i
$959$	−2.78534	−	8.57239i	−0.0899433	−	0.276817i
$960$	−13.4101	−	23.7323i	−0.432810	−	0.765955i
$961$	8.51098	−	26.1941i	0.274548	−	0.844971i
$962$	−6.66377	−	2.71237i	−0.214848	−	0.0874502i
$963$	−4.83178	+	9.48291i	−0.155702	+	0.305582i
$964$	−15.4015	−	2.24568i	−0.496048	−	0.0723286i
$965$	−5.99192	−	4.29669i	−0.192887	−	0.138315i
$966$	5.12212	+	12.1541i	0.164802	+	0.391052i
$967$	22.7152	+	3.59773i	0.730471	+	0.115695i	0.510581	−	0.859830i	$-0.329430\pi$
$967$	22.7152	+	3.59773i	0.730471	+	0.115695i	0.219890	+	0.975525i	$0.429430\pi$
$968$	−20.3272	−	11.9468i	−0.653341	−	0.383983i
$969$	4.27582	+	5.88516i	0.137359	+	0.189059i
$970$	3.86802	+	3.22173i	0.124195	+	0.103444i
$971$	−5.28369	−	3.83882i	−0.169562	−	0.123194i	0.499768	−	0.866159i	$-0.333419\pi$
$971$	−5.28369	−	3.83882i	−0.169562	−	0.123194i	−0.669330	+	0.742966i	$0.733419\pi$
$972$	−13.0693	+	4.42476i	−0.419197	+	0.141924i
$973$	4.43336	+	8.70096i	0.142127	+	0.278940i
$974$	−29.3503	+	2.49149i	−0.940444	+	0.0798324i
$975$	0.549614	+	44.1720i	0.0176017	+	1.41464i
$976$	1.74587	+	4.95535i	0.0558838	+	0.158617i
$977$	−5.81313	−	11.4089i	−0.185978	−	0.365003i	0.779126	−	0.626867i	$-0.215663\pi$
$977$	−5.81313	−	11.4089i	−0.185978	−	0.365003i	−0.965105	+	0.261863i	$0.915663\pi$
$978$	7.95621	+	32.2652i	0.254412	+	1.03173i
$979$	4.50759	−	6.20416i	0.144063	−	0.198286i
$980$	−26.8718	−	8.18445i	−0.858387	−	0.261443i
$981$	0.126915	+	0.174684i	0.00405209	+	0.00557722i
$982$	−18.1517	+	21.5193i	−0.579244	+	0.686708i
$983$	−4.63549	+	29.2673i	−0.147849	+	0.933482i	0.796524	+	0.604607i	$0.206670\pi$
$983$	−4.63549	+	29.2673i	−0.147849	+	0.933482i	−0.944373	+	0.328876i	$0.893330\pi$
$984$	−16.8012	+	10.7268i	−0.535603	+	0.341957i
$985$	−9.62931	−	29.0204i	−0.306815	−	0.924667i
$986$	−30.0419	−	7.01745i	−0.956729	−	0.223481i
$987$	−7.48959	−	3.81613i	−0.238396	−	0.121469i
$988$	−19.4583	−	6.05902i	−0.619050	−	0.192763i
$989$	−10.1983	+	31.3871i	−0.324287	+	0.998052i
$990$	2.63250	−	2.30528i	0.0836665	−	0.0732665i
$991$	22.3204	−	7.25233i	0.709030	−	0.230378i	0.0677695	−	0.997701i	$-0.478412\pi$
$991$	22.3204	−	7.25233i	0.709030	−	0.230378i	0.641261	+	0.767323i	$0.278412\pi$
$992$	−10.1482	+	2.76872i	−0.322207	+	0.0879070i
$993$	−27.1873	−	27.1873i	−0.862762	−	0.862762i
$994$	0.568780	+	0.657728i	0.0180406	+	0.0208619i
$995$	−24.2366	+	3.99341i	−0.768351	+	0.126599i
$996$	38.0877	+	18.8207i	1.20686	+	0.596356i
$997$	−7.01416	−	44.2857i	−0.222141	−	1.40254i	−0.806590	−	0.591111i	$-0.798690\pi$
$997$	−7.01416	−	44.2857i	−0.222141	−	1.40254i	0.584450	−	0.811430i	$-0.301310\pi$
$998$	−30.0792	+	18.6878i	−0.952140	+	0.591551i
$999$	−4.91767			−0.155588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.v.c.3.18	yes	208
4.3	odd	2		800.2.bp.c.303.5		208
5.2	odd	4		1000.2.v.g.507.5		208
5.3	odd	4		1000.2.v.i.507.22		208
5.4	even	2		1000.2.v.h.243.9		208
8.3	odd	2	inner	200.2.v.c.3.15	✓	208
8.5	even	2		800.2.bp.c.303.6		208
25.6	even	5		1000.2.v.g.643.4		208
25.8	odd	20		1000.2.v.h.107.12		208
25.17	odd	20	inner	200.2.v.c.67.15	yes	208
25.19	even	10		1000.2.v.i.643.23		208
40.3	even	4		1000.2.v.i.507.23		208
40.19	odd	2		1000.2.v.h.243.12		208
40.27	even	4		1000.2.v.g.507.4		208
100.67	even	20		800.2.bp.c.367.6		208
200.19	odd	10		1000.2.v.i.643.22		208
200.67	even	20	inner	200.2.v.c.67.18	yes	208
200.83	even	20		1000.2.v.h.107.9		208
200.117	odd	20		800.2.bp.c.367.5		208
200.131	odd	10		1000.2.v.g.643.5		208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.v.c.3.15	✓	208	8.3	odd	2	inner
200.2.v.c.3.18	yes	208	1.1	even	1	trivial
200.2.v.c.67.15	yes	208	25.17	odd	20	inner
200.2.v.c.67.18	yes	208	200.67	even	20	inner
800.2.bp.c.303.5		208	4.3	odd	2
800.2.bp.c.303.6		208	8.5	even	2
800.2.bp.c.367.5		208	200.117	odd	20
800.2.bp.c.367.6		208	100.67	even	20
1000.2.v.g.507.4		208	40.27	even	4
1000.2.v.g.507.5		208	5.2	odd	4
1000.2.v.g.643.4		208	25.6	even	5
1000.2.v.g.643.5		208	200.131	odd	10
1000.2.v.h.107.9		208	200.83	even	20
1000.2.v.h.107.12		208	25.8	odd	20
1000.2.v.h.243.9		208	5.4	even	2
1000.2.v.h.243.12		208	40.19	odd	2
1000.2.v.i.507.22		208	5.3	odd	4
1000.2.v.i.507.23		208	40.3	even	4
1000.2.v.i.643.22		208	200.19	odd	10
1000.2.v.i.643.23		208	25.19	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.v (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.746320 + 1.20125i) q^{2} +(0.238378 + 1.50506i) q^{3} +(-0.886011 + 1.79304i) q^{4} +(-2.20632 + 0.363530i) q^{5} +(-1.63005 + 1.40961i) q^{6} +(-0.599487 - 0.599487i) q^{7} +(-2.81514 + 0.273858i) q^{8} +(0.644782 - 0.209502i) q^{9} +(-2.08331 - 2.37903i) q^{10} +(-0.504364 + 1.55227i) q^{11} +(-2.90984 - 0.906081i) q^{12} +(5.16603 + 2.63223i) q^{13} +(0.272725 - 1.16754i) q^{14} +(-1.07307 - 3.23399i) q^{15} +(-2.42997 - 3.17730i) q^{16} +(0.424918 - 2.68282i) q^{17} +(0.732879 + 0.618190i) q^{18} +(1.03303 + 1.42184i) q^{19} +(1.30300 - 4.27811i) q^{20} +(0.759360 - 1.04517i) q^{21} +(-2.24109 + 0.552625i) q^{22} +(3.27737 + 6.43220i) q^{23} +(-1.08324 - 4.17168i) q^{24} +(4.73569 - 1.60413i) q^{25} +(0.693551 + 8.17019i) q^{26} +(2.54442 + 4.99370i) q^{27} +(1.60605 - 0.543750i) q^{28} +(-6.49732 - 4.72058i) q^{29} +(3.08398 - 3.70263i) q^{30} +(-1.09301 - 1.50440i) q^{31} +(2.00321 - 5.29029i) q^{32} +(-2.45650 - 0.389071i) q^{33} +(3.53987 - 1.49181i) q^{34} +(1.54059 + 1.10473i) q^{35} +(-0.195639 + 1.34174i) q^{36} +(-0.398349 + 0.781804i) q^{37} +(-0.937020 + 2.30208i) q^{38} +(-2.73019 + 8.40267i) q^{39} +(6.11154 - 1.62761i) q^{40} +(-1.42918 - 4.39856i) q^{41} +(1.82224 + 0.132151i) q^{42} +(3.23259 + 3.23259i) q^{43} +(-2.33641 - 2.27967i) q^{44} +(-1.34644 + 0.696627i) q^{45} +(-5.28072 + 8.73743i) q^{46} +(-1.01784 - 6.42640i) q^{47} +(4.20279 - 4.41465i) q^{48} -6.28123i q^{49} +(5.46131 + 4.49156i) q^{50} +4.13911 q^{51} +(-9.29685 + 6.93071i) q^{52} +(13.3108 - 2.10822i) q^{53} +(-4.09974 + 6.78339i) q^{54} +(0.548489 - 3.60816i) q^{55} +(1.85181 + 1.52346i) q^{56} +(-1.89371 + 1.89371i) q^{57} +(0.821520 - 11.3280i) q^{58} +(-2.90867 + 0.945085i) q^{59} +(6.74942 + 0.941288i) q^{60} +(-1.24919 - 0.405886i) q^{61} +(0.991428 - 2.43575i) q^{62} +(-0.512132 - 0.260944i) q^{63} +(7.85000 - 1.54190i) q^{64} +(-12.3548 - 3.92952i) q^{65} +(-1.36596 - 3.24124i) q^{66} +(1.73499 - 10.9543i) q^{67} +(4.43392 + 3.13891i) q^{68} +(-8.89961 + 6.46594i) q^{69} +(-0.177281 + 2.67512i) q^{70} +(-0.426288 + 0.586736i) q^{71} +(-1.75778 + 0.766357i) q^{72} +(4.64490 - 2.36670i) q^{73} +(-1.23644 + 0.104959i) q^{74} +(3.54320 + 6.74512i) q^{75} +(-3.46469 + 0.592491i) q^{76} +(1.23293 - 0.628207i) q^{77} +(-12.1313 + 2.99143i) q^{78} +(9.40528 + 6.83334i) q^{79} +(6.51633 + 6.12678i) q^{80} +(-5.26385 + 3.82441i) q^{81} +(4.21715 - 4.99954i) q^{82} +(-13.7683 - 2.18069i) q^{83} +(1.20123 + 2.28759i) q^{84} +(0.0377844 + 6.07364i) q^{85} +(-1.47061 + 6.29571i) q^{86} +(5.55594 - 10.9041i) q^{87} +(0.994752 - 4.50798i) q^{88} +(-4.46859 - 1.45193i) q^{89} +(-1.84170 - 1.09750i) q^{90} +(-1.51898 - 4.67495i) q^{91} +(-14.4370 + 0.177444i) q^{92} +(2.00367 - 2.00367i) q^{93} +(6.96009 - 6.01884i) q^{94} +(-2.79607 - 2.76150i) q^{95} +(8.43973 + 1.75386i) q^{96} +(-1.57229 + 0.249026i) q^{97} +(7.54534 - 4.68781i) q^{98} +1.10654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q + 2 q^{2} - 16 q^{3} - 10 q^{4} - 26 q^{6} - 34 q^{8} - 20 q^{9} + 10 q^{10} - 4 q^{11} - 2 q^{12} - 30 q^{14} + 18 q^{16} - 32 q^{17} - 20 q^{18} - 10 q^{20} - 42 q^{22} - 40 q^{25} - 8 q^{26} - 28 q^{27}+ \cdots + 206 q^{98}+O(q^{100}) \) 208 * q + 2 * q^2 - 16 * q^3 - 10 * q^4 - 26 * q^6 - 34 * q^8 - 20 * q^9 + 10 * q^10 - 4 * q^11 - 2 * q^12 - 30 * q^14 + 18 * q^16 - 32 * q^17 - 20 * q^18 - 10 * q^20 - 42 * q^22 - 40 * q^25 - 8 * q^26 - 28 * q^27 + 30 * q^28 - 10 * q^30 + 22 * q^32 + 36 * q^33 + 30 * q^34 - 100 * q^35 - 38 * q^36 - 56 * q^38 + 20 * q^40 - 44 * q^41 - 70 * q^42 - 8 * q^43 + 60 * q^44 + 2 * q^46 + 104 * q^48 - 30 * q^50 + 8 * q^51 + 60 * q^52 - 140 * q^54 + 2 * q^56 + 92 * q^57 - 70 * q^58 - 40 * q^59 + 10 * q^60 - 120 * q^62 + 20 * q^64 - 40 * q^65 - 2 * q^66 - 12 * q^67 - 46 * q^68 + 30 * q^70 + 60 * q^72 - 16 * q^73 + 80 * q^75 - 24 * q^76 - 20 * q^78 + 30 * q^80 + 16 * q^81 - 22 * q^82 - 96 * q^83 - 10 * q^84 - 26 * q^86 + 134 * q^88 - 100 * q^89 + 130 * q^90 + 4 * q^91 + 70 * q^92 + 150 * q^94 - 26 * q^96 + 24 * q^97 + 206 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more