LMFDB - Embedded newform 403.2.l.c.129.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.24
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.25574i q^{2} +(-1.30537 + 2.26097i) q^{3} +0.423126 q^{4} +(-3.09634 + 1.78767i) q^{5} +(-2.83918 - 1.63920i) q^{6} +(4.10494 + 2.36999i) q^{7} +3.04281i q^{8} +(-1.90798 - 3.30473i) q^{9} +O(q^{10})$	\(q+1.25574i q^{2} +(-1.30537 + 2.26097i) q^{3} +0.423126 q^{4} +(-3.09634 + 1.78767i) q^{5} +(-2.83918 - 1.63920i) q^{6} +(4.10494 + 2.36999i) q^{7} +3.04281i q^{8} +(-1.90798 - 3.30473i) q^{9} +(-2.24485 - 3.88819i) q^{10} +(-2.82635 + 1.63179i) q^{11} +(-0.552336 + 0.956674i) q^{12} +(3.60302 + 0.135201i) q^{13} +(-2.97608 + 5.15472i) q^{14} -9.33430i q^{15} -2.97471 q^{16} +(3.60493 - 6.24392i) q^{17} +(4.14987 - 2.39593i) q^{18} +(0.759270 + 0.438365i) q^{19} +(-1.31014 + 0.756411i) q^{20} +(-10.7169 + 6.18743i) q^{21} +(-2.04910 - 3.54915i) q^{22} -1.57501 q^{23} +(-6.87969 - 3.97199i) q^{24} +(3.89155 - 6.74037i) q^{25} +(-0.169777 + 4.52444i) q^{26} +2.13028 q^{27} +(1.73691 + 1.00280i) q^{28} +8.05616 q^{29} +11.7214 q^{30} +(-2.77654 - 4.82606i) q^{31} +2.35016i q^{32} -8.52037i q^{33} +(7.84071 + 4.52684i) q^{34} -16.9471 q^{35} +(-0.807318 - 1.39832i) q^{36} +(-0.365143 - 0.210815i) q^{37} +(-0.550471 + 0.953443i) q^{38} +(-5.00896 + 7.96982i) q^{39} +(-5.43955 - 9.42157i) q^{40} +(3.53994 - 2.04378i) q^{41} +(-7.76978 - 13.4576i) q^{42} +(1.23636 - 2.14143i) q^{43} +(-1.19590 + 0.690453i) q^{44} +(11.8155 + 6.82171i) q^{45} -1.97780i q^{46} -1.10959i q^{47} +(3.88310 - 6.72573i) q^{48} +(7.73369 + 13.3951i) q^{49} +(8.46412 + 4.88676i) q^{50} +(9.41153 + 16.3013i) q^{51} +(1.52453 + 0.0572071i) q^{52} +(2.26251 + 3.91878i) q^{53} +2.67508i q^{54} +(5.83422 - 10.1052i) q^{55} +(-7.21142 + 12.4905i) q^{56} +(-1.98226 + 1.14446i) q^{57} +10.1164i q^{58} +(4.16486 + 2.40458i) q^{59} -3.94959i q^{60} -4.81018 q^{61} +(6.06026 - 3.48660i) q^{62} -18.0876i q^{63} -8.90061 q^{64} +(-11.3979 + 6.02239i) q^{65} +10.6993 q^{66} +(-7.22046 + 4.16873i) q^{67} +(1.52534 - 2.64196i) q^{68} +(2.05597 - 3.56105i) q^{69} -21.2810i q^{70} +(-8.82343 + 5.09421i) q^{71} +(10.0556 - 5.80563i) q^{72} +(0.353021 - 0.203817i) q^{73} +(0.264729 - 0.458523i) q^{74} +(10.1598 + 17.5973i) q^{75} +(0.321267 + 0.185484i) q^{76} -15.4693 q^{77} +(-10.0080 - 6.28993i) q^{78} +(-7.65472 + 13.2584i) q^{79} +(9.21072 - 5.31781i) q^{80} +(2.94314 - 5.09767i) q^{81} +(2.56645 + 4.44523i) q^{82} +(9.29950 - 5.36907i) q^{83} +(-4.53461 + 2.61806i) q^{84} +25.7777i q^{85} +(2.68907 + 1.55254i) q^{86} +(-10.5163 + 18.2147i) q^{87} +(-4.96523 - 8.60003i) q^{88} -13.7847i q^{89} +(-8.56627 + 14.8372i) q^{90} +(14.4697 + 9.09410i) q^{91} -0.666427 q^{92} +(14.5360 + 0.0221361i) q^{93} +1.39336 q^{94} -3.13461 q^{95} +(-5.31364 - 3.06783i) q^{96} -6.98265i q^{97} +(-16.8208 + 9.71148i) q^{98} +(10.7852 + 6.22687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.25574i			0.887940i	0.896042	+	0.443970i	$0.146430\pi$
$2$			1.25574i			0.887940i	−0.896042	+	0.443970i	$0.853570\pi$
$3$	−1.30537	+	2.26097i	−0.753656	+	1.30537i	0.192384	+	0.981320i	$0.438378\pi$
$3$	−1.30537	+	2.26097i	−0.753656	+	1.30537i	−0.946040	+	0.324051i	$0.894955\pi$
$4$	0.423126			0.211563
$5$	−3.09634	+	1.78767i	−1.38473	+	0.799472i	−0.992715	−	0.120489i	$-0.961554\pi$
$5$	−3.09634	+	1.78767i	−1.38473	+	0.799472i	−0.392011	+	0.919960i	$0.628221\pi$
$6$	−2.83918	−	1.63920i	−1.15909	−	0.669201i
$7$	4.10494	+	2.36999i	1.55152	+	0.895772i	0.998018	+	0.0629247i	$0.0200428\pi$
$7$	4.10494	+	2.36999i	1.55152	+	0.895772i	0.553504	+	0.832847i	$0.313291\pi$
$8$			3.04281i			1.07579i
$9$	−1.90798	−	3.30473i	−0.635995	−	1.10158i
$10$	−2.24485	−	3.88819i	−0.709883	−	1.22955i
$11$	−2.82635	+	1.63179i	−0.852175	+	0.492004i	−0.861384	−	0.507954i	$-0.830402\pi$
$11$	−2.82635	+	1.63179i	−0.852175	+	0.492004i	0.00920887	+	0.999958i	$0.497069\pi$
$12$	−0.552336	+	0.956674i	−0.159446	+	0.276168i
$13$	3.60302	+	0.135201i	0.999297	+	0.0374981i
$13$	3.60302	+	0.135201i	0.999297	+	0.0374981i
$14$	−2.97608	+	5.15472i	−0.795391	+	1.37766i
$15$		−	9.33430i		−	2.41011i
$16$	−2.97471			−0.743678
$17$	3.60493	−	6.24392i	0.874323	−	1.51437i	0.0168414	−	0.999858i	$-0.494639\pi$
$17$	3.60493	−	6.24392i	0.874323	−	1.51437i	0.857482	−	0.514514i	$-0.172028\pi$
$18$	4.14987	−	2.39593i	0.978133	−	0.564725i
$19$	0.759270	+	0.438365i	0.174189	+	0.100568i	0.584559	−	0.811351i	$-0.301267\pi$
$19$	0.759270	+	0.438365i	0.174189	+	0.100568i	−0.410371	+	0.911919i	$0.634601\pi$
$20$	−1.31014	+	0.756411i	−0.292957	+	0.169139i
$21$	−10.7169	+	6.18743i	−2.33863	+	1.35021i
$22$	−2.04910	−	3.54915i	−0.436870	−	0.756680i
$23$	−1.57501			−0.328412			−0.164206	−	0.986426i	$-0.552506\pi$
$23$	−1.57501			−0.328412			−0.164206	+	0.986426i	$0.552506\pi$
$24$	−6.87969	−	3.97199i	−1.40431	−	0.810779i
$25$	3.89155	−	6.74037i	0.778310	−	1.34807i
$26$	−0.169777	+	4.52444i	−0.0332960	+	0.887315i
$27$	2.13028			0.409973
$28$	1.73691	+	1.00280i	0.328245	+	0.189512i
$29$	8.05616			1.49599			0.747995	−	0.663704i	$-0.231017\pi$
$29$	8.05616			1.49599			0.747995	+	0.663704i	$0.231017\pi$
$30$	11.7214			2.14003
$31$	−2.77654	−	4.82606i	−0.498681	−	0.866786i
$31$	−2.77654	−	4.82606i	−0.498681	−	0.866786i
$32$			2.35016i			0.415454i
$33$		−	8.52037i		−	1.48321i
$34$	7.84071	+	4.52684i	1.34467	+	0.776346i
$35$	−16.9471			−2.86458
$36$	−0.807318	−	1.39832i	−0.134553	−	0.233053i
$37$	−0.365143	−	0.210815i	−0.0600291	−	0.0346578i	0.469685	−	0.882834i	$-0.344367\pi$
$37$	−0.365143	−	0.210815i	−0.0600291	−	0.0346578i	−0.529714	+	0.848176i	$0.677701\pi$
$38$	−0.550471	+	0.953443i	−0.0892981	+	0.154669i
$39$	−5.00896	+	7.96982i	−0.802075	+	1.27619i
$40$	−5.43955	−	9.42157i	−0.860068	−	1.48968i
$41$	3.53994	−	2.04378i	0.552846	−	0.319186i	−0.197423	−	0.980318i	$-0.563257\pi$
$41$	3.53994	−	2.04378i	0.552846	−	0.319186i	0.750269	+	0.661133i	$0.229924\pi$
$42$	−7.76978	−	13.4576i	−1.19890	−	2.07656i
$43$	1.23636	−	2.14143i	0.188542	−	0.326565i	−0.756222	−	0.654315i	$-0.772957\pi$
$43$	1.23636	−	2.14143i	0.188542	−	0.326565i	0.944764	+	0.327750i	$0.106290\pi$
$44$	−1.19590	+	0.690453i	−0.180289	+	0.104090i
$45$	11.8155	+	6.82171i	1.76136	+	1.01692i
$46$		−	1.97780i		−	0.291610i
$47$		−	1.10959i		−	0.161851i	−0.996720	−	0.0809253i	$-0.974212\pi$
$47$		−	1.10959i		−	0.161851i	0.996720	−	0.0809253i	$-0.0257875\pi$
$48$	3.88310	−	6.72573i	0.560478	−	0.970776i
$49$	7.73369	+	13.3951i	1.10481	+	1.91359i
$50$	8.46412	+	4.88676i	1.19701	+	0.691093i
$51$	9.41153	+	16.3013i	1.31788	+	2.28263i
$52$	1.52453	+	0.0572071i	0.211414	+	0.00793320i
$53$	2.26251	+	3.91878i	0.310780	+	0.538286i	0.978531	−	0.206098i	$-0.0660765\pi$
$53$	2.26251	+	3.91878i	0.310780	+	0.538286i	−0.667752	+	0.744384i	$0.732743\pi$
$54$			2.67508i			0.364032i
$55$	5.83422	−	10.1052i	0.786686	−	1.36258i
$56$	−7.21142	+	12.4905i	−0.963666	+	1.66912i
$57$	−1.98226	+	1.14446i	−0.262556	+	0.151587i
$58$			10.1164i			1.32835i
$59$	4.16486	+	2.40458i	0.542218	+	0.313050i	0.745977	−	0.665971i	$-0.231983\pi$
$59$	4.16486	+	2.40458i	0.542218	+	0.313050i	−0.203759	+	0.979021i	$0.565316\pi$
$60$		−	3.94959i		−	0.509889i
$61$	−4.81018			−0.615880			−0.307940	−	0.951406i	$-0.599640\pi$
$61$	−4.81018			−0.615880			−0.307940	+	0.951406i	$0.599640\pi$
$62$	6.06026	−	3.48660i	0.769654	−	0.442798i
$63$		−	18.0876i		−	2.27882i
$64$	−8.90061			−1.11258
$65$	−11.3979	+	6.02239i	−1.41373	+	0.746985i
$66$	10.6993			1.31700
$67$	−7.22046	+	4.16873i	−0.882119	+	0.509292i	−0.871357	−	0.490650i	$-0.836759\pi$
$67$	−7.22046	+	4.16873i	−0.882119	+	0.509292i	−0.0107625	+	0.999942i	$0.503426\pi$
$68$	1.52534	−	2.64196i	0.184974	−	0.320385i
$69$	2.05597	−	3.56105i	0.247510	−	0.428700i
$70$		−	21.2810i		−	2.54357i
$71$	−8.82343	+	5.09421i	−1.04715	+	0.604571i	−0.921850	−	0.387548i	$-0.873322\pi$
$71$	−8.82343	+	5.09421i	−1.04715	+	0.604571i	−0.125298	+	0.992119i	$0.539989\pi$
$72$	10.0556	−	5.80563i	1.18507	−	0.684200i
$73$	0.353021	−	0.203817i	0.0413180	−	0.0238550i	−0.479199	−	0.877706i	$-0.659073\pi$
$73$	0.353021	−	0.203817i	0.0413180	−	0.0238550i	0.520517	+	0.853851i	$0.325739\pi$
$74$	0.264729	−	0.458523i	0.0307741	−	0.0533023i
$75$	10.1598	+	17.5973i	1.17316	+	2.03197i
$76$	0.321267	+	0.185484i	0.0368518	+	0.0212764i
$77$	−15.4693			−1.76289
$78$	−10.0080	−	6.28993i	−1.13318	−	0.712194i
$79$	−7.65472	+	13.2584i	−0.861223	+	1.49168i	0.00952566	+	0.999955i	$0.496968\pi$
$79$	−7.65472	+	13.2584i	−0.861223	+	1.49168i	−0.870749	+	0.491728i	$0.836365\pi$
$80$	9.21072	−	5.31781i	1.02979	−	0.594550i
$81$	2.94314	−	5.09767i	0.327016	−	0.566408i
$82$	2.56645	+	4.44523i	0.283418	+	0.490894i
$83$	9.29950	−	5.36907i	1.02075	−	0.589332i	0.106431	−	0.994320i	$-0.466058\pi$
$83$	9.29950	−	5.36907i	1.02075	−	0.589332i	0.914322	+	0.404989i	$0.132724\pi$
$84$	−4.53461	+	2.61806i	−0.494767	+	0.285654i
$85$			25.7777i			2.79599i
$86$	2.68907	+	1.55254i	0.289970	+	0.167414i
$87$	−10.5163	+	18.2147i	−1.12746	+	1.95282i
$88$	−4.96523	−	8.60003i	−0.529295	−	0.916766i
$89$		−	13.7847i		−	1.46118i	−0.682818	−	0.730588i	$-0.739246\pi$
$89$		−	13.7847i		−	1.46118i	0.682818	−	0.730588i	$-0.260754\pi$
$90$	−8.56627	+	14.8372i	−0.902964	+	1.56398i
$91$	14.4697	+	9.09410i	1.51684	+	0.953321i
$92$	−0.666427			−0.0694799
$93$	14.5360	+	0.0221361i	1.50731	+	0.00229541i
$94$	1.39336			0.143714
$95$	−3.13461			−0.321604
$96$	−5.31364	−	3.06783i	−0.542321	−	0.313109i
$97$		−	6.98265i		−	0.708981i	−0.935060	−	0.354490i	$-0.884654\pi$
$97$		−	6.98265i		−	0.708981i	0.935060	−	0.354490i	$-0.115346\pi$
$98$	−16.8208	+	9.71148i	−1.69916	+	0.981008i
$99$	10.7852	+	6.22687i	1.08396	+	0.625824i
$100$	1.64662	−	2.85202i	0.164662	−	0.285202i
$101$	−0.504980			−0.0502474			−0.0251237	−	0.999684i	$-0.507998\pi$
$101$	−0.504980			−0.0502474			−0.0251237	+	0.999684i	$0.507998\pi$
$102$	−20.4701	+	11.8184i	−2.02684	+	1.17020i
$103$	3.88023	+	6.72076i	0.382331	+	0.662216i	0.991395	−	0.130905i	$-0.0417882\pi$
$103$	3.88023	+	6.72076i	0.382331	+	0.662216i	−0.609064	+	0.793121i	$0.708455\pi$
$104$	−0.411391	+	10.9633i	−0.0403402	+	1.07504i
$105$	22.1222	−	38.3168i	2.15891	−	3.73933i
$106$	−4.92096	+	2.84112i	−0.477966	+	0.275954i
$107$	−4.42343	+	7.66160i	−0.427629	+	0.740675i	−0.996662	−	0.0816397i	$-0.973984\pi$
$107$	−4.42343	+	7.66160i	−0.427629	+	0.740675i	0.569033	+	0.822315i	$0.307318\pi$
$108$	0.901379			0.0867352
$109$			6.25922i			0.599525i	0.954014	+	0.299762i	$0.0969074\pi$
$109$			6.25922i			0.599525i	−0.954014	+	0.299762i	$0.903093\pi$
$110$	12.6894	+	7.32624i	1.20989	+	0.698530i
$111$	0.953294	−	0.550384i	0.0904826	−	0.0522402i
$112$	−12.2110	−	7.05004i	−1.15383	−	0.666166i
$113$	0.965617	+	1.67250i	0.0908376	+	0.157335i	0.907864	−	0.419265i	$-0.137712\pi$
$113$	0.965617	+	1.67250i	0.0908376	+	0.157335i	−0.817026	+	0.576601i	$0.804379\pi$
$114$	−1.43714	−	2.48919i	−0.134600	−	0.233134i
$115$	4.87677	−	2.81560i	0.454761	−	0.262556i
$116$	3.40877			0.316496
$117$	−6.42770	−	12.1649i	−0.594241	−	1.12465i
$118$	−3.01952	+	5.22996i	−0.277969	+	0.481457i
$119$	29.5960	−	17.0873i	2.71306	−	1.56639i
$120$	28.4025			2.59278
$121$	−0.174512	+	0.302264i	−0.0158647	+	0.0274785i
$122$		−	6.04032i		−	0.546865i
$123$			10.6716i			0.962224i
$124$	−1.17482	−	2.04203i	−0.105502	−	0.183380i
$125$			9.95056i			0.890005i
$126$	22.7133			2.02346
$127$	6.19188	−	10.7247i	0.549441	−	0.951659i	−0.448872	−	0.893596i	$-0.648174\pi$
$127$	6.19188	−	10.7247i	0.549441	−	0.951659i	0.998313	−	0.0580630i	$-0.0184924\pi$
$128$		−	6.47650i		−	0.572447i
$129$	3.22780	+	5.59072i	0.284192	+	0.492236i
$130$	−7.56253	−	14.3127i	−0.663278	−	1.25531i
$131$	2.41260	−	4.17874i	0.210789	−	0.365098i	−0.741172	−	0.671315i	$-0.765730\pi$
$131$	2.41260	−	4.17874i	0.210789	−	0.365098i	0.951962	+	0.306217i	$0.0990632\pi$
$132$		−	3.60519i		−	0.313791i
$133$	2.07784	+	3.59892i	0.180172	+	0.312066i
$134$	−5.23483	−	9.06699i	−0.452220	−	0.783269i
$135$	−6.59609	+	3.80825i	−0.567701	+	0.327762i
$136$	18.9990	+	10.9691i	1.62915	+	0.940593i
$137$	7.61691	−	4.39762i	0.650756	−	0.375714i	−0.137990	−	0.990434i	$-0.544064\pi$
$137$	7.61691	−	4.39762i	0.650756	−	0.375714i	0.788746	+	0.614719i	$0.210731\pi$
$138$	4.47174	+	2.58176i	0.380659	+	0.219774i
$139$	3.91496			0.332062			0.166031	−	0.986121i	$-0.446905\pi$
$139$	3.91496			0.332062			0.166031	+	0.986121i	$0.446905\pi$
$140$	−7.17074			−0.606038
$141$	2.50875	+	1.44843i	0.211275	+	0.121980i
$142$	−6.39698	−	11.0799i	−0.536823	−	0.929804i
$143$	−10.4040	+	5.49725i	−0.870025	+	0.459703i
$144$	5.67571	+	9.83061i	0.472975	+	0.819218i
$145$	−24.9446	+	14.4018i	−2.07154	+	1.19600i
$146$	0.255940	+	0.443301i	0.0211818	+	0.0366879i
$147$	−40.3813			−3.33060
$148$	−0.154501	−	0.0892015i	−0.0126999	−	0.00733231i
$149$	−1.79342	−	1.03543i	−0.146923	−	0.0848261i	0.424736	−	0.905317i	$-0.360367\pi$
$149$	−1.79342	−	1.03543i	−0.146923	−	0.0848261i	−0.571659	+	0.820491i	$0.693700\pi$
$150$	−22.0976	+	12.7581i	−1.80426	+	1.04169i
$151$		−	1.90494i		−	0.155022i	−0.996991	−	0.0775111i	$-0.975303\pi$
$151$		−	1.90494i		−	0.155022i	0.996991	−	0.0775111i	$-0.0246973\pi$
$152$	−1.33386	+	2.31031i	−0.108190	+	0.187391i
$153$	−27.5126			−2.22426
$154$		−	19.4254i		−	1.56534i
$155$	17.2245	+	9.97959i	1.38351	+	0.801580i
$156$	−2.11942	+	3.37224i	−0.169689	+	0.269995i
$157$	0.668225			0.0533302			0.0266651	−	0.999644i	$-0.491511\pi$
$157$	0.668225			0.0533302			0.0266651	+	0.999644i	$0.491511\pi$
$158$	−16.6490	−	9.61231i	−1.32452	−	0.764714i
$159$	−11.8137			−0.936884
$160$	−4.20132	−	7.27690i	−0.332143	−	0.575289i
$161$	−6.46532	−	3.73276i	−0.509539	−	0.294182i
$162$	6.40133	+	3.69581i	0.502936	+	0.290370i
$163$		−	18.4685i		−	1.44656i	−0.690554	−	0.723281i	$-0.742633\pi$
$163$		−	18.4685i		−	1.44656i	0.690554	−	0.723281i	$-0.257367\pi$
$164$	1.49784	−	0.864778i	0.116962	−	0.0675278i
$165$	15.2316	+	26.3820i	1.18578	+	2.05383i
$166$	6.74213	+	11.6777i	0.523291	+	0.906367i
$167$	−3.83547	−	2.21441i	−0.296798	−	0.171356i	0.344206	−	0.938894i	$-0.388148\pi$
$167$	−3.83547	−	2.21441i	−0.296798	−	0.171356i	−0.641003	+	0.767538i	$0.721482\pi$
$168$	−18.8271	−	32.6096i	−1.45255	−	2.51588i
$169$	12.9634	+	0.974264i	0.997188	+	0.0749434i
$170$	−32.3700			−2.48267
$171$		−	3.34557i		−	0.255842i
$172$	0.523134	−	0.906095i	0.0398886	−	0.0690891i
$173$	−8.93423	−	15.4745i	−0.679257	−	1.17651i	−0.975205	−	0.221304i	$-0.928969\pi$
$173$	−8.93423	−	15.4745i	−0.679257	−	1.17651i	0.295948	−	0.955204i	$-0.404365\pi$
$174$	−22.8729	−	13.2057i	−1.73399	−	1.00112i
$175$	31.9492	−	18.4459i	2.41513	−	1.39438i
$176$	8.40757	−	4.85411i	0.633744	−	0.365892i
$177$	−10.8734	+	6.27774i	−0.817292	+	0.471864i
$178$	17.3100			1.29744
$179$	6.88072	−	11.9178i	0.514289	−	0.890775i	−0.485574	−	0.874196i	$-0.661389\pi$
$179$	6.88072	−	11.9178i	0.514289	−	0.890775i	0.999863	−	0.0165789i	$-0.00527745\pi$
$180$	4.99946	+	2.88644i	0.372638	+	0.215143i
$181$	−7.53510	−	13.0512i	−0.560079	−	0.970086i	−0.997489	−	0.0708236i	$-0.977437\pi$
$181$	−7.53510	−	13.0512i	−0.560079	−	0.970086i	0.437409	−	0.899262i	$-0.355896\pi$
$182$	−11.4198	+	18.1702i	−0.846491	+	1.34686i
$183$	6.27907	−	10.8757i	0.464162	−	0.803952i
$184$		−	4.79245i		−	0.353304i
$185$	1.50748			0.110832
$186$	−0.0277971	+	18.2534i	−0.00203818	+	1.33840i
$187$			23.5300i			1.72068i
$188$		−	0.469497i		−	0.0342416i
$189$	8.74469	+	5.04875i	0.636083	+	0.367243i
$190$		−	3.93625i		−	0.285565i
$191$	−0.800061	−	1.38575i	−0.0578904	−	0.100269i	0.835628	−	0.549296i	$-0.185104\pi$
$191$	−0.800061	−	1.38575i	−0.0578904	−	0.100269i	−0.893518	+	0.449027i	$0.851771\pi$
$192$	11.6186	−	20.1240i	0.838500	−	1.45232i
$193$	−2.85669	−	1.64931i	−0.205629	−	0.118720i	0.393649	−	0.919261i	$-0.371212\pi$
$193$	−2.85669	−	1.64931i	−0.205629	−	0.118720i	−0.599278	+	0.800541i	$0.704546\pi$
$194$	8.76837			0.629532
$195$	1.26201	−	33.6316i	0.0903744	−	2.40841i
$196$	3.27233	+	5.66783i	0.233738	+	0.404845i
$197$	−10.5267	+	6.07757i	−0.749994	+	0.433009i	−0.825692	−	0.564122i	$-0.809215\pi$
$197$	−10.5267	+	6.07757i	−0.749994	+	0.433009i	0.0756977	+	0.997131i	$0.475882\pi$
$198$	−7.81930	+	13.5434i	−0.555694	+	0.962490i
$199$	8.17718	+	14.1633i	0.579665	+	1.00401i	0.995518	+	0.0945770i	$0.0301499\pi$
$199$	8.17718	+	14.1633i	0.579665	+	1.00401i	−0.415853	+	0.909432i	$0.636517\pi$
$200$	20.5096	+	11.8412i	1.45025	+	0.837302i
$201$		−	21.7670i		−	1.53532i
$202$		−	0.634122i		−	0.0446166i
$203$	33.0700	+	19.0930i	2.32106	+	1.34007i
$204$	3.98226	+	6.89748i	0.278814	+	0.482920i
$205$	−7.30724	+	12.6565i	−0.510360	+	0.883969i
$206$	−8.43950	+	4.87255i	−0.588008	+	0.339487i
$207$	3.00509	+	5.20498i	0.208869	+	0.361771i
$208$	−10.7179	−	0.402185i	−0.743155	−	0.0278865i
$209$	−2.86128			−0.197919
$210$	48.1158	+	27.7796i	3.32030	+	1.91698i
$211$	−1.24958	+	2.16433i	−0.0860244	+	0.148999i	−0.905827	−	0.423647i	$-0.860750\pi$
$211$	−1.24958	+	2.16433i	−0.0860244	+	0.148999i	0.819803	+	0.572646i	$0.194083\pi$
$212$	0.957327	+	1.65814i	0.0657495	+	0.113881i
$213$		−	26.5993i		−	1.82255i
$214$	−9.62095	−	5.55466i	−0.657675	−	0.379709i
$215$			8.84080i			0.602937i
$216$			6.48205i			0.441047i
$217$	0.0401896	−	26.3910i	0.00272825	−	1.79154i
$218$	−7.85993			−0.532342
$219$			1.06423i			0.0719137i
$220$	2.46861	−	4.27576i	0.166434	−	0.288272i
$221$	13.8328	−	22.0095i	0.930494	−	1.48052i
$222$	0.691138	+	1.19709i	0.0463861	+	0.0803431i
$223$	−4.45662	−	2.57303i	−0.298437	−	0.172303i	0.343303	−	0.939225i	$-0.388454\pi$
$223$	−4.45662	−	2.57303i	−0.298437	−	0.172303i	−0.641741	+	0.766922i	$0.721787\pi$
$224$	−5.56985	+	9.64727i	−0.372151	+	0.644585i
$225$	−29.7001			−1.98001
$226$	−2.10022	+	1.21256i	−0.139704	+	0.0806583i
$227$	−9.89789	+	5.71455i	−0.656946	+	0.379288i	−0.791112	−	0.611671i	$-0.790498\pi$
$227$	−9.89789	+	5.71455i	−0.656946	+	0.379288i	0.134166	+	0.990959i	$0.457164\pi$
$228$	−0.838745	+	0.484249i	−0.0555472	+	0.0320702i
$229$	−10.4386	−	6.02673i	−0.689803	−	0.398258i	0.113735	−	0.993511i	$-0.463718\pi$
$229$	−10.4386	−	6.02673i	−0.689803	−	0.398258i	−0.803538	+	0.595253i	$0.797052\pi$
$230$	3.53566	+	6.12393i	0.233134	+	0.403800i
$231$	20.1932	−	34.9756i	1.32861	−	2.30123i
$232$			24.5133i			1.60938i
$233$	−14.9449			−0.979074			−0.489537	−	0.871983i	$-0.662834\pi$
$233$	−14.9449			−0.979074			−0.489537	+	0.871983i	$0.662834\pi$
$234$	15.2760	−	8.07149i	0.998621	−	0.527650i
$235$	1.98359	+	3.43568i	0.129395	+	0.224119i
$236$	1.76226	+	1.01744i	0.114713	+	0.0662297i
$237$	−19.9845	−	34.6142i	−1.29813	−	2.24843i
$238$	21.4571	+	37.1648i	1.39086	+	2.40904i
$239$	−6.80305	+	3.92775i	−0.440053	+	0.254065i	−0.703620	−	0.710576i	$-0.748434\pi$
$239$	−6.80305	+	3.92775i	−0.440053	+	0.254065i	0.263567	+	0.964641i	$0.415101\pi$
$240$			27.7669i			1.79234i
$241$	0.640970	+	0.370064i	0.0412885	+	0.0238379i	0.520502	−	0.853860i	$-0.325745\pi$
$241$	0.640970	+	0.370064i	0.0412885	+	0.0238379i	−0.479214	+	0.877698i	$0.659078\pi$
$242$	−0.379564	−	0.219141i	−0.0243993	−	0.0140869i
$243$	10.8792	+	18.8433i	0.697902	+	1.20880i
$244$	−2.03531			−0.130297
$245$	−47.8923	−	27.6506i	−3.05973	−	1.76653i
$246$	−13.4007			−0.854397
$247$	2.67639	+	1.68209i	0.170295	+	0.107029i
$248$	14.6848	−	8.44846i	0.932484	−	0.536478i
$249$			28.0345i			1.77661i
$250$	−12.4953			−0.790271
$251$	1.17419	−	2.03376i	0.0741142	−	0.128370i	−0.826587	−	0.562810i	$-0.809720\pi$
$251$	1.17419	−	2.03376i	0.0741142	−	0.128370i	0.900701	+	0.434440i	$0.143054\pi$
$252$		−	7.65334i		−	0.482115i
$253$	4.45152	−	2.57009i	0.279865	−	0.161580i
$254$	13.4673	+	7.77537i	0.845016	+	0.487870i
$255$	−58.2826	−	33.6495i	−3.64980	−	2.10721i
$256$	−9.66844			−0.604278
$257$	11.5781	+	20.0539i	0.722222	+	1.25093i	0.960107	+	0.279632i	$0.0902124\pi$
$257$	11.5781	+	20.0539i	0.722222	+	1.25093i	−0.237885	+	0.971293i	$0.576454\pi$
$258$	−7.02047	+	4.05327i	−0.437076	+	0.252346i
$259$	−0.999260	−	1.73077i	−0.0620910	−	0.107545i
$260$	−4.82273	+	2.54823i	−0.299093	+	0.158034i
$261$	−15.3710	−	26.6234i	−0.951442	−	1.64795i
$262$	5.24739	+	3.02958i	0.324185	+	0.187168i
$263$	28.9418			1.78463			0.892314	−	0.451416i	$-0.149081\pi$
$263$	28.9418			1.78463			0.892314	+	0.451416i	$0.149081\pi$
$264$	25.9258			1.59563
$265$	−14.0110	−	8.08926i	−0.860690	−	0.496919i
$266$	−4.51930	+	2.60922i	−0.277096	+	0.159981i
$267$	31.1668	+	17.9942i	1.90738	+	1.10122i
$268$	−3.05516	+	1.76390i	−0.186624	+	0.107747i
$269$	4.95453	+	8.58150i	0.302083	+	0.523224i	0.976608	−	0.215029i	$-0.0689846\pi$
$269$	4.95453	+	8.58150i	0.302083	+	0.523224i	−0.674524	+	0.738253i	$0.735651\pi$
$270$	−4.78216	−	8.28295i	−0.291033	−	0.504084i
$271$			12.9331i			0.785632i	0.919617	+	0.392816i	$0.128499\pi$
$271$			12.9331i			0.785632i	−0.919617	+	0.392816i	$0.871501\pi$
$272$	−10.7236	+	18.5739i	−0.650215	+	1.12621i
$273$	−39.4498	+	20.8445i	−2.38761	+	1.26156i
$274$	5.52226	+	9.56483i	0.333612	+	0.577832i
$275$			25.4008i			1.53173i
$276$	0.869935	−	1.50677i	0.0523639	−	0.0906970i
$277$	24.7975			1.48994			0.744968	−	0.667101i	$-0.232465\pi$
$277$	24.7975			1.48994			0.744968	+	0.667101i	$0.232465\pi$
$278$			4.91615i			0.294851i
$279$	−10.6512	+	18.3837i	−0.637672	+	1.10061i
$280$		−	51.5666i		−	3.08170i
$281$			11.9938i			0.715489i	0.933819	+	0.357745i	$0.116454\pi$
$281$			11.9938i			0.715489i	−0.933819	+	0.357745i	$0.883546\pi$
$282$	−1.81885	+	3.15033i	−0.108311	+	0.187600i
$283$	−12.0309			−0.715161			−0.357580	−	0.933882i	$-0.616398\pi$
$283$	−12.0309			−0.715161			−0.357580	+	0.933882i	$0.616398\pi$
$284$	−3.73342	+	2.15549i	−0.221538	+	0.127905i
$285$	4.09183	−	7.08726i	0.242379	−	0.419813i
$286$	−6.90309	−	13.0647i	−0.408188	−	0.772530i
$287$	19.3750			1.14367
$288$	7.76664	−	4.48407i	0.457653	−	0.264226i
$289$	−17.4910	−	30.2953i	−1.02888	−	1.78208i
$290$	−18.0848	−	31.3238i	−1.06198	−	1.83940i
$291$	15.7875	+	9.11494i	0.925482	+	0.534327i
$292$	0.149372	−	0.0862402i	0.00874136	−	0.00504682i
$293$	3.92154	+	2.26410i	0.229099	+	0.132270i	0.610156	−	0.792281i	$-0.291107\pi$
$293$	3.92154	+	2.26410i	0.229099	+	0.132270i	−0.381057	+	0.924551i	$0.624440\pi$
$294$		−	50.7083i		−	2.95737i
$295$	−17.1944			−1.00110
$296$	0.641471	−	1.11106i	0.0372847	−	0.0645790i
$297$	−6.02092	+	3.47618i	−0.349369	+	0.201708i
$298$	1.30023	−	2.25207i	0.0753204	−	0.130459i
$299$	−5.67478	−	0.212943i	−0.328181	−	0.0123148i
$300$	4.29889	+	7.44589i	0.248196	+	0.429889i
$301$	10.1503	−	5.86030i	0.585055	−	0.337782i
$302$	2.39211			0.137650
$303$	0.659186	−	1.14174i	0.0378692	−	0.0655915i
$304$	−2.25861	−	1.30401i	−0.129540	−	0.0747901i
$305$	14.8940	−	8.59903i	0.852825	−	0.492379i
$306$		−	34.5486i		−	1.97501i
$307$	−16.1686	−	9.33496i	−0.922792	−	0.532774i	−0.0382675	−	0.999268i	$-0.512184\pi$
$307$	−16.1686	−	9.33496i	−0.922792	−	0.532774i	−0.884525	+	0.466493i	$0.845517\pi$
$308$	−6.54547			−0.372963
$309$	−20.2606			−1.15258
$310$	−12.5317	+	21.6295i	−0.711754	+	1.22847i
$311$	27.2318			1.54418			0.772088	−	0.635516i	$-0.219212\pi$
$311$	27.2318			1.54418			0.772088	+	0.635516i	$0.219212\pi$
$312$	−24.2506	−	15.2413i	−1.37292	−	0.862868i
$313$	−5.40403	+	9.36005i	−0.305454	+	0.529062i	−0.977362	−	0.211573i	$-0.932141\pi$
$313$	−5.40403	+	9.36005i	−0.305454	+	0.529062i	0.671908	+	0.740634i	$0.265475\pi$
$314$			0.839115i			0.0473540i
$315$	32.3347	+	56.0054i	1.82186	+	3.15555i
$316$	−3.23891	+	5.60996i	−0.182203	+	0.315585i
$317$	14.4669	+	8.35245i	0.812540	+	0.469120i	0.847837	−	0.530257i	$-0.177904\pi$
$317$	14.4669	+	8.35245i	0.812540	+	0.469120i	−0.0352971	+	0.999377i	$0.511238\pi$
$318$		−	14.8348i		−	0.831897i
$319$	−22.7695	+	13.1460i	−1.27485	+	0.736033i
$320$	27.5593	−	15.9114i	1.54061	−	0.889473i
$321$	−11.5484	−	20.0025i	−0.644570	−	1.11643i
$322$	4.68736	−	8.11874i	0.261216	−	0.452440i
$323$	5.47423	−	3.16055i	0.304594	−	0.175858i
$324$	1.24532	−	2.15696i	0.0691845	−	0.119831i
$325$	14.9326	−	23.7595i	0.828313	−	1.31794i
$326$	23.1915			1.28446
$327$	−14.1519	−	8.17060i	−0.782602	−	0.451835i
$328$	6.21884	+	10.7714i	0.343378	+	0.594748i
$329$	2.62972	−	4.55481i	0.144981	−	0.251115i
$330$	−33.1288	+	19.1269i	−1.82368	+	1.05290i
$331$	12.3136	−	7.10928i	0.676818	−	0.390761i	−0.121837	−	0.992550i	$-0.538878\pi$
$331$	12.3136	−	7.10928i	0.676818	−	0.390761i	0.798655	+	0.601789i	$0.205545\pi$
$332$	3.93486	−	2.27179i	0.215953	−	0.124681i
$333$			1.60893i			0.0881688i
$334$	2.78072	−	4.81634i	0.152154	−	0.263538i
$335$	14.9047	−	25.8156i	0.814329	−	1.41046i
$336$	31.8798	−	18.4058i	1.73919	−	1.00412i
$337$	−5.25117			−0.286049			−0.143025	−	0.989719i	$-0.545683\pi$
$337$	−5.25117			−0.286049			−0.143025	+	0.989719i	$0.545683\pi$
$338$	−1.22342	+	16.2787i	−0.0665452	+	0.885443i
$339$	−5.04195			−0.273841
$340$			10.9072i			0.591527i
$341$	15.7226	+	9.10938i	0.851425	+	0.493301i
$342$	4.20116			0.227173
$343$			40.1352i			2.16710i
$344$	6.51596	+	3.76199i	0.351317	+	0.202833i
$345$			14.7016i			0.791509i
$346$	19.4320	−	11.2190i	1.04467	−	0.603139i
$347$	0.111427	−	0.192997i	0.00598171	−	0.0103606i	−0.863019	−	0.505171i	$-0.831429\pi$
$347$	0.111427	−	0.192997i	0.00598171	−	0.0103606i	0.869001	+	0.494811i	$0.164763\pi$
$348$	−4.44971	+	7.70712i	−0.238529	+	0.413145i
$349$		−	13.0177i		−	0.696820i	−0.937342	−	0.348410i	$-0.886722\pi$
$349$		−	13.0177i		−	0.696820i	0.937342	−	0.348410i	$-0.113278\pi$
$350$	23.1631	+	40.1197i	1.23812	+	2.14449i
$351$	7.67545	+	0.288017i	0.409685	+	0.0153732i
$352$	−3.83497	−	6.64237i	−0.204405	−	0.354039i
$353$	4.46001	+	2.57499i	0.237382	+	0.137053i	0.613973	−	0.789327i	$-0.289570\pi$
$353$	4.46001	+	2.57499i	0.237382	+	0.137053i	−0.376591	+	0.926380i	$0.622904\pi$
$354$	−7.88318	−	13.6541i	−0.418987	−	0.725706i
$355$	18.2136	−	31.5468i	0.966675	−	1.67433i
$356$		−	5.83267i		−	0.309131i
$357$			89.2209i			4.72207i
$358$	14.9656	+	8.64037i	0.790954	+	0.456658i
$359$	−30.4181	+	17.5619i	−1.60540	+	0.926880i	−0.615023	+	0.788509i	$0.710853\pi$
$359$	−30.4181	+	17.5619i	−1.60540	+	0.926880i	−0.990380	+	0.138371i	$0.955813\pi$
$360$	−20.7571	+	35.9524i	−1.09400	+	1.89486i
$361$	−9.11567	−	15.7888i	−0.479772	−	0.830990i
$362$	16.3888	−	9.46210i	0.861378	−	0.497317i
$363$	−0.455606	−	0.789133i	−0.0239131	−	0.0414187i
$364$	6.12252	+	3.84795i	0.320907	+	0.201687i
$365$	−0.728716	+	1.26217i	−0.0381427	+	0.0660651i
$366$	13.6570	+	7.88485i	0.713861	+	0.412148i
$367$	−5.14087	−	8.90425i	−0.268351	−	0.464798i	0.700085	−	0.714059i	$-0.253145\pi$
$367$	−5.14087	−	8.90425i	−0.268351	−	0.464798i	−0.968436	+	0.249262i	$0.919812\pi$
$368$	4.68520			0.244233
$369$	−13.5083	−	7.79902i	−0.703214	−	0.406001i
$370$			1.89299i			0.0984120i
$371$			21.4485i			1.11355i
$372$	6.15055	+	0.00936636i	0.318891	+	0.000485623i
$373$	5.99170			0.310238			0.155119	−	0.987896i	$-0.450424\pi$
$373$	5.99170			0.310238			0.155119	+	0.987896i	$0.450424\pi$
$374$	−29.5474			−1.52786
$375$	−22.4979	−	12.9892i	−1.16179	−	0.670758i
$376$	3.37628			0.174118
$377$	29.0265	+	1.08920i	1.49494	+	0.0560968i
$378$	−6.33990	+	10.9810i	−0.326089	+	0.564803i
$379$	22.3775	+	12.9196i	1.14945	+	0.663638i	0.948754	−	0.316015i	$-0.102345\pi$
$379$	22.3775	+	12.9196i	1.14945	+	0.663638i	0.200700	+	0.979653i	$0.435678\pi$
$380$	−1.32634			−0.0680396
$381$	16.1654	+	27.9993i	0.828178	+	1.43445i
$382$	1.74013	−	1.00467i	0.0890329	−	0.0514032i
$383$	23.9478	−	13.8263i	1.22367	−	0.706489i	0.257975	−	0.966152i	$-0.416945\pi$
$383$	23.9478	−	13.8263i	1.22367	−	0.706489i	0.965699	+	0.259663i	$0.0836114\pi$
$384$	14.6432	+	8.45423i	0.747255	+	0.431428i
$385$	47.8983	−	27.6541i	2.44112	−	1.40938i
$386$	2.07110	−	3.58725i	0.105416	−	0.182586i
$387$	−9.43579			−0.479648
$388$		−	2.95454i		−	0.149994i
$389$	−11.6951	+	20.2565i	−0.592965	+	1.02704i	0.400866	+	0.916137i	$0.368709\pi$
$389$	−11.6951	+	20.2565i	−0.592965	+	1.02704i	−0.993831	+	0.110908i	$0.964624\pi$
$390$	42.2325	+	1.58475i	2.13852	+	0.0802470i
$391$	−5.67780	+	9.83423i	−0.287138	+	0.497338i
$392$	−40.7589	+	23.5321i	−2.05863	+	1.18855i
$393$	6.29866	+	10.9096i	0.317725	+	0.550317i
$394$	−7.63183	−	13.2187i	−0.384486	−	0.665950i
$395$		−	54.7366i		−	2.75409i
$396$	4.56352	+	2.63475i	0.229325	+	0.132401i
$397$	−15.6825	−	9.05431i	−0.787083	−	0.454423i	0.0518517	−	0.998655i	$-0.483488\pi$
$397$	−15.6825	−	9.05431i	−0.787083	−	0.454423i	−0.838935	+	0.544232i	$0.816821\pi$
$398$	−17.7854	+	10.2684i	−0.891500	+	0.514708i
$399$	−10.8494			−0.543149
$400$	−11.5762	+	20.0507i	−0.578812	+	1.00253i
$401$			11.0876i			0.553687i	0.960915	+	0.276844i	$0.0892884\pi$
$401$			11.0876i			0.553687i	−0.960915	+	0.276844i	$0.910712\pi$
$402$	27.3336			1.36327
$403$	−9.35141	−	17.7638i	−0.465827	−	0.884876i
$404$	−0.213670			−0.0106305
$405$			21.0455i			1.04576i
$406$	−23.9758	+	41.5273i	−1.18990	+	2.06096i
$407$	1.37603			0.0682071
$408$	−49.6016	+	28.6375i	−2.45564	+	1.41777i
$409$	−0.220582	−	0.127353i	−0.0109071	−	0.00629721i	0.494537	−	0.869157i	$-0.335338\pi$
$409$	−0.220582	−	0.127353i	−0.0109071	−	0.00629721i	−0.505444	+	0.862860i	$0.668671\pi$
$410$	−15.8932	−	9.17597i	−0.784911	−	0.453169i
$411$			22.9621i			1.13264i
$412$	1.64183	+	2.84373i	0.0808870	+	0.140100i
$413$	11.3977	+	19.7413i	0.560842	+	0.971407i
$414$	−6.53608	+	3.77361i	−0.321231	+	0.185463i
$415$	−19.1963	+	33.2489i	−0.942308	+	1.63213i
$416$	−0.317745	+	8.46766i	−0.0155787	+	0.415161i
$417$	−5.11047	+	8.85159i	−0.250261	+	0.433464i
$418$		−	3.59301i		−	0.175740i
$419$	−18.5419			−0.905830			−0.452915	−	0.891554i	$-0.649616\pi$
$419$	−18.5419			−0.905830			−0.452915	+	0.891554i	$0.649616\pi$
$420$	9.36047	−	16.2128i	0.456744	−	0.791104i
$421$	23.1824	−	13.3843i	1.12984	−	0.652313i	0.185945	−	0.982560i	$-0.440465\pi$
$421$	23.1824	−	13.3843i	1.12984	−	0.652313i	0.943895	+	0.330247i	$0.107132\pi$
$422$	−2.71783	−	1.56914i	−0.132302	−	0.0763845i
$423$	−3.66690	+	2.11709i	−0.178291	+	0.102936i
$424$	−11.9241	+	6.88439i	−0.579086	+	0.334335i
$425$	−28.0575	−	48.5971i	−1.36099	−	2.35730i
$426$	33.4017			1.61832
$427$	−19.7455	−	11.4001i	−0.955552	−	0.551688i
$428$	−1.87167	+	3.24182i	−0.0904704	+	0.156699i
$429$	1.15196	−	30.6990i	0.0556174	−	1.48216i
$430$	−11.1017			−0.535372
$431$	20.6252	+	11.9079i	0.993479	+	0.573586i	0.906313	−	0.422608i	$-0.138885\pi$
$431$	20.6252	+	11.9079i	0.993479	+	0.573586i	0.0871670	+	0.996194i	$0.472219\pi$
$432$	−6.33698			−0.304888
$433$	39.5363			1.89999			0.949997	−	0.312258i	$-0.101085\pi$
$433$	39.5363			1.89999			0.949997	+	0.312258i	$0.101085\pi$
$434$	33.1402	+	0.0504676i	1.59078	+	0.00242252i
$435$		−	75.1986i		−	3.60550i
$436$			2.64844i			0.126837i
$437$	−1.19586	−	0.690429i	−0.0572056	−	0.0330277i
$438$	−1.33639			−0.0638550
$439$	17.6308	+	30.5375i	0.841474	+	1.45748i	0.888648	+	0.458589i	$0.151645\pi$
$439$	17.6308	+	30.5375i	0.841474	+	1.45748i	−0.0471743	+	0.998887i	$0.515022\pi$
$440$	30.7481	+	17.7524i	1.46586	+	0.846313i
$441$	29.5115	−	51.1155i	1.40531	−	2.43407i
$442$	27.6382	+	17.3703i	1.31461	+	0.826223i
$443$	−3.71431	−	6.43338i	−0.176472	−	0.305659i	0.764197	−	0.644982i	$-0.223135\pi$
$443$	−3.71431	−	6.43338i	−0.176472	−	0.305659i	−0.940670	+	0.339323i	$0.889802\pi$
$444$	0.403363	−	0.232882i	0.0191428	−	0.0110521i
$445$	24.6426	+	42.6822i	1.16817	+	2.02333i
$446$	3.23105	−	5.59634i	0.152995	−	0.264994i
$447$	4.68217	−	2.70325i	0.221459	−	0.127859i
$448$	−36.5365	−	21.0943i	−1.72619	−	0.996614i
$449$		−	7.70296i		−	0.363525i	−0.983342	−	0.181763i	$-0.941820\pi$
$449$		−	7.70296i		−	0.363525i	0.983342	−	0.181763i	$-0.0581802\pi$
$450$		−	37.2955i		−	1.75813i
$451$	−6.67006	+	11.5529i	−0.314081	+	0.544004i
$452$	0.408577	+	0.707677i	0.0192179	+	0.0332863i
$453$	4.30702	+	2.48666i	0.202361	+	0.116833i
$454$	−7.17597	−	12.4291i	−0.336785	−	0.583329i
$455$	−61.0605	−	2.29126i	−2.86256	−	0.107416i
$456$	−3.48236	−	6.03163i	−0.163077	−	0.282457i
$457$		−	4.94195i		−	0.231175i	−0.993297	−	0.115587i	$-0.963125\pi$
$457$		−	4.94195i		−	0.231175i	0.993297	−	0.115587i	$-0.0368750\pi$
$458$	7.56799	−	13.1081i	0.353629	−	0.612503i
$459$	7.67952	−	13.3013i	0.358449	−	0.620852i
$460$	2.06349	−	1.19135i	0.0962106	−	0.0555472i
$461$		−	6.62597i		−	0.308602i	−0.988024	−	0.154301i	$-0.950687\pi$
$461$		−	6.62597i		−	0.308602i	0.988024	−	0.154301i	$-0.0493125\pi$
$462$	43.9202	+	25.3573i	2.04335	+	1.17973i
$463$		−	21.1097i		−	0.981052i	−0.871426	−	0.490526i	$-0.836805\pi$
$463$		−	21.1097i		−	0.981052i	0.871426	−	0.490526i	$-0.163195\pi$
$464$	−23.9647			−1.11254
$465$	−45.0479	+	25.9170i	−2.08905	+	1.20187i
$466$		−	18.7669i		−	0.869359i
$467$	−16.8413			−0.779323			−0.389661	−	0.920958i	$-0.627408\pi$
$467$	−16.8413			−0.779323			−0.389661	+	0.920958i	$0.627408\pi$
$468$	−2.71972	−	5.14730i	−0.125719	−	0.237934i
$469$	−39.5194			−1.82484
$470$	−4.31430	+	2.49086i	−0.199004	+	0.114895i
$471$	−0.872281	+	1.51084i	−0.0401926	+	0.0696156i
$472$	−7.31668	+	12.6729i	−0.336777	+	0.583315i
$473$			8.06990i			0.371054i
$474$	43.4663	−	25.0953i	1.99647	−	1.15266i
$475$	5.90948	−	3.41184i	0.271145	−	0.156546i
$476$	12.5228	−	7.23007i	0.573984	−	0.331390i
$477$	8.63367	−	14.9540i	0.395309	−	0.684695i
$478$	−4.93221	−	8.54284i	−0.225594	−	0.390741i
$479$	13.6537	+	7.88296i	0.623853	+	0.360182i	0.778368	−	0.627809i	$-0.216048\pi$
$479$	13.6537	+	7.88296i	0.623853	+	0.360182i	−0.154514	+	0.987991i	$0.549381\pi$
$480$	21.9371			1.00129
$481$	−1.28711	−	0.808939i	−0.0586873	−	0.0368844i
$482$	−0.464703	+	0.804889i	−0.0211666	+	0.0366617i
$483$	16.8793	−	9.74526i	0.768034	−	0.443425i
$484$	−0.0738406	+	0.127896i	−0.00335639	+	0.00581344i
$485$	12.4827	+	21.6207i	0.566810	+	0.981744i
$486$	−23.6623	+	13.6614i	−1.07334	+	0.619695i
$487$	11.6939	−	6.75150i	0.529903	−	0.305940i	−0.211074	−	0.977470i	$-0.567696\pi$
$487$	11.6939	−	6.75150i	0.529903	−	0.305940i	0.740977	+	0.671530i	$0.234363\pi$
$488$		−	14.6365i		−	0.662561i
$489$	41.7566	+	24.1082i	1.88830	+	1.09021i
$490$	34.7219	−	60.1401i	1.56858	−	2.71685i
$491$	9.96438	+	17.2588i	0.449686	+	0.778879i	0.998365	−	0.0571539i	$-0.0182026\pi$
$491$	9.96438	+	17.2588i	0.449686	+	0.778879i	−0.548679	+	0.836033i	$0.684869\pi$
$492$			4.51542i			0.203571i
$493$	29.0419	−	50.3020i	1.30798	−	2.26549i
$494$	−2.11226	+	3.36085i	−0.0950351	+	0.151212i
$495$	−44.5264			−2.00131
$496$	8.25940	+	14.3561i	0.370858	+	0.644610i
$497$	−48.2929			−2.16623
$498$	−35.2039			−1.57753
$499$	−6.21565	−	3.58861i	−0.278251	−	0.160648i	0.354381	−	0.935101i	$-0.384692\pi$
$499$	−6.21565	−	3.58861i	−0.278251	−	0.160648i	−0.632631	+	0.774453i	$0.718025\pi$
$500$			4.21034i			0.188292i
$501$	10.0134	−	5.78125i	0.447367	−	0.258287i
$502$	2.55386	+	1.47447i	0.113985	+	0.0658090i
$503$	5.88727	−	10.1971i	0.262501	−	0.454664i	−0.704405	−	0.709798i	$-0.748786\pi$
$503$	5.88727	−	10.1971i	0.262501	−	0.454664i	0.966906	+	0.255134i	$0.0821195\pi$
$504$	55.0371			2.45155
$505$	1.56359	−	0.902739i	0.0695788	−	0.0401714i
$506$	3.22735	+	5.58994i	0.143473	+	0.248503i
$507$	−19.1249	+	28.0382i	−0.849366	+	1.24522i
$508$	2.61994	−	4.53788i	0.116241	−	0.201336i
$509$	−32.9324	+	19.0135i	−1.45970	+	0.842761i	−0.998996	−	0.0447912i	$-0.985738\pi$
$509$	−32.9324	+	19.0135i	−1.45970	+	0.842761i	−0.460708	+	0.887552i	$0.652404\pi$
$510$	42.2549	−	73.1876i	1.87108	−	3.24080i
$511$	1.93217			0.0854743
$512$		−	25.0940i		−	1.10901i
$513$	1.61746	+	0.933842i	0.0714127	+	0.0412301i
$514$	−25.1824	+	14.5390i	−1.11075	+	0.641290i
$515$	−24.0290	−	13.8732i	−1.05885	−	0.611325i
$516$	1.36577	+	2.36558i	0.0601246	+	0.104139i
$517$	1.81062	+	3.13609i	0.0796311	+	0.137925i
$518$	2.17339	−	1.25481i	0.0954933	−	0.0551331i
$519$	46.6499			2.04771
$520$	−18.3250	−	34.6815i	−0.803603	−	1.52088i
$521$	−9.58274	+	16.5978i	−0.419827	+	0.727162i	−0.995922	−	0.0902208i	$-0.971243\pi$
$521$	−9.58274	+	16.5978i	−0.419827	+	0.727162i	0.576094	+	0.817383i	$0.304576\pi$
$522$	33.4320	−	19.3020i	1.46328	−	0.844823i
$523$	−40.6378			−1.77697			−0.888483	−	0.458910i	$-0.848240\pi$
$523$	−40.6378			−1.77697			−0.888483	+	0.458910i	$0.848240\pi$
$524$	1.02083	−	1.76813i	0.0445952	−	0.0772412i
$525$			96.3148i			4.20352i
$526$			36.3433i			1.58464i
$527$	−40.1427	−	0.0611314i	−1.74864	−	0.00266292i
$528$			25.3457i			1.10303i
$529$	−20.5193			−0.892145
$530$	10.1580	−	17.5941i	0.441235	−	0.764241i
$531$		−	18.3516i		−	0.796392i
$532$	0.879188	+	1.52280i	0.0381176	+	0.0660217i
$533$	13.0308	−	6.88518i	0.564426	−	0.298230i
$534$	−22.5959	+	39.1373i	−0.977821	+	1.69364i
$535$		−	31.6306i		−	1.36751i
$536$	−12.6846	−	21.9705i	−0.547893	−	0.948979i
$537$	17.9638	+	31.1142i	0.775194	+	1.34268i
$538$	−10.7761	+	6.22159i	−0.464591	+	0.268232i
$539$	−43.7162	−	25.2395i	−1.88299	−	1.08714i
$540$	−2.79098	+	1.61137i	−0.120104	+	0.0693423i
$541$	21.6985	+	12.5276i	0.932891	+	0.538605i	0.887725	−	0.460375i	$-0.152285\pi$
$541$	21.6985	+	12.5276i	0.932891	+	0.538605i	0.0451661	+	0.998979i	$0.485618\pi$
$542$	−16.2406			−0.697594
$543$	39.3444			1.68843
$544$	14.6742	+	8.47216i	0.629151	+	0.363241i
$545$	−11.1894	−	19.3807i	−0.479303	−	0.830177i
$546$	−26.1751	−	49.5386i	−1.12019	−	2.12006i
$547$	9.20026	+	15.9353i	0.393375	+	0.681345i	0.992892	−	0.119017i	$-0.0379742\pi$
$547$	9.20026	+	15.9353i	0.393375	+	0.681345i	−0.599517	+	0.800362i	$0.704641\pi$
$548$	3.22291	−	1.86075i	0.137676	−	0.0794872i
$549$	9.17775	+	15.8963i	0.391697	+	0.678439i
$550$	−31.8967			−1.36008
$551$	6.11680	+	3.53154i	0.260584	+	0.150448i
$552$	10.8356	+	6.25593i	0.461193	+	0.266270i
$553$	−62.8443	+	36.2832i	−2.67241	+	1.54292i
$554$			31.1391i			1.32297i
$555$	−1.96782	+	3.40836i	−0.0835291	+	0.144677i
$556$	1.65652			0.0702521
$557$		−	25.7036i		−	1.08910i	−0.838729	−	0.544549i	$-0.816701\pi$
$557$		−	25.7036i		−	1.08910i	0.838729	−	0.544549i	$-0.183299\pi$
$558$	−23.0851	−	13.3751i	−0.977272	−	0.566214i
$559$	4.74413	−	7.54845i	0.200655	−	0.319265i
$560$	50.4126			2.13032
$561$	−53.2005	−	30.7153i	−2.24613	−	1.29680i
$562$	−15.0610			−0.635311
$563$	−17.4276	−	30.1855i	−0.734486	−	1.27217i	−0.954948	−	0.296772i	$-0.904090\pi$
$563$	−17.4276	−	30.1855i	−0.734486	−	1.27217i	0.220462	−	0.975395i	$-0.429243\pi$
$564$	1.06152	+	0.612868i	0.0446980	+	0.0258064i
$565$	−5.97976	−	3.45241i	−0.251570	−	0.145244i
$566$		−	15.1076i		−	0.635020i
$567$	24.1629	−	13.9504i	1.01474	−	0.585863i
$568$	−15.5007	−	26.8480i	−0.650395	−	1.12652i
$569$	−2.96731	−	5.13953i	−0.124396	−	0.215460i	0.797101	−	0.603846i	$-0.206366\pi$
$569$	−2.96731	−	5.13953i	−0.124396	−	0.215460i	−0.921497	+	0.388386i	$0.873033\pi$
$570$	8.89973	+	5.13826i	0.372769	+	0.215218i
$571$	−13.0480	−	22.5998i	−0.546042	−	0.945773i	−0.998541	−	0.0540075i	$-0.982801\pi$
$571$	−13.0480	−	22.5998i	−0.546042	−	0.945773i	0.452498	−	0.891765i	$-0.350533\pi$
$572$	−4.40220	+	2.32603i	−0.184065	+	0.0972561i
$573$	4.17750			0.174518
$574$			24.3299i			1.01551i
$575$	−6.12923	+	10.6161i	−0.255607	+	0.442724i
$576$	16.9822	+	29.4141i	0.707593	+	1.22559i
$577$	11.1474	+	6.43595i	0.464072	+	0.267932i	0.713755	−	0.700396i	$-0.246993\pi$
$577$	11.1474	+	6.43595i	0.464072	+	0.267932i	−0.249683	+	0.968328i	$0.580326\pi$
$578$	38.0429	−	21.9641i	1.58238	−	0.913586i
$579$	7.45807	−	4.30592i	0.309947	−	0.178948i
$580$	−10.5547	+	6.09376i	−0.438260	+	0.253030i
$581$	50.8985			2.11163
$582$	−11.4460	+	19.8250i	−0.474451	+	0.821773i
$583$	−12.7893	−	7.38389i	−0.529678	−	0.305810i
$584$	0.620175	+	1.07418i	0.0256630	+	0.0444497i
$585$	41.6493	+	26.1762i	1.72199	+	1.08225i
$586$	−2.84312	+	4.92442i	−0.117448	+	0.203426i
$587$		−	38.9964i		−	1.60956i	−0.593576	−	0.804778i	$-0.702284\pi$
$587$		−	38.9964i		−	1.60956i	0.593576	−	0.804778i	$-0.297716\pi$
$588$	−17.0864			−0.704631
$589$	0.00743367	−	4.88142i	0.000306299	−	0.201135i
$590$		−	21.5917i		−	0.888915i
$591$		−	31.7339i		−	1.30536i
$592$	1.08620	+	0.627115i	0.0446424	+	0.0257743i
$593$		−	36.5125i		−	1.49939i	−0.661784	−	0.749695i	$-0.730200\pi$
$593$		−	36.5125i		−	1.49939i	0.661784	−	0.749695i	$-0.269800\pi$
$594$	−4.36517	−	7.56069i	−0.179105	−	0.310219i
$595$	−61.0929	+	105.816i	−2.50457	+	4.33804i
$596$	−0.758844	−	0.438119i	−0.0310835	−	0.0179461i
$597$	−42.6970			−1.74747
$598$	0.267401	−	7.12603i	0.0109348	−	0.291405i
$599$	−4.06005	−	7.03221i	−0.165889	−	0.287328i	0.771082	−	0.636736i	$-0.219716\pi$
$599$	−4.06005	−	7.03221i	−0.165889	−	0.287328i	−0.936971	+	0.349408i	$0.886383\pi$
$600$	−53.5453	+	30.9144i	−2.18598	+	1.26208i
$601$	−0.636150	+	1.10184i	−0.0259491	+	0.0449451i	−0.878708	−	0.477359i	$-0.841594\pi$
$601$	−0.636150	+	1.10184i	−0.0259491	+	0.0449451i	0.852759	+	0.522304i	$0.174927\pi$
$602$	7.35899	+	12.7461i	0.299930	+	0.519494i
$603$	27.5530	+	15.9078i	1.12205	+	0.647814i
$604$		−	0.806032i		−	0.0327970i
$605$		−	1.24788i		−	0.0507337i
$606$	1.43373	+	0.827764i	0.0582413	+	0.0336256i
$607$	−3.40727	−	5.90156i	−0.138297	−	0.239537i	0.788555	−	0.614964i	$-0.210829\pi$
$607$	−3.40727	−	5.90156i	−0.138297	−	0.239537i	−0.926852	+	0.375427i	$0.877496\pi$
$608$	−1.03023	+	1.78441i	−0.0417812	+	0.0723672i
$609$	−86.3373	+	49.8469i	−3.49856	+	2.01990i
$610$	10.7981	+	18.7029i	0.437203	+	0.757258i
$611$	0.150018	−	3.99788i	0.00606909	−	0.161737i
$612$	−11.6413			−0.470571
$613$	12.9148	+	7.45637i	0.521624	+	0.301160i	0.737599	−	0.675239i	$-0.235960\pi$
$613$	12.9148	+	7.45637i	0.521624	+	0.301160i	−0.215975	+	0.976399i	$0.569293\pi$
$614$	11.7223	−	20.3035i	0.473072	−	0.819384i
$615$	−19.0773	−	33.0429i	−0.769271	−	1.33242i
$616$		−	47.0701i		−	1.89651i
$617$	35.8948	+	20.7239i	1.44507	+	0.834313i	0.998182	−	0.0602763i	$-0.0191982\pi$
$617$	35.8948	+	20.7239i	1.44507	+	0.834313i	0.446890	+	0.894589i	$0.352532\pi$
$618$		−	25.4419i		−	1.02342i
$619$			29.9989i			1.20576i	0.797833	+	0.602878i	$0.205979\pi$
$619$			29.9989i			1.20576i	−0.797833	+	0.602878i	$0.794021\pi$
$620$	7.28814	+	4.22262i	0.292699	+	0.169585i
$621$	−3.35522			−0.134640
$622$			34.1960i			1.37114i
$623$	32.6696	−	56.5854i	1.30888	−	2.26705i
$624$	14.9002	−	23.7079i	0.596486	−	0.949076i
$625$	1.66941	+	2.89150i	0.0667764	+	0.115660i
$626$	−11.7538	−	6.78604i	−0.469775	−	0.271225i
$627$	3.73503	−	6.46926i	0.149163	−	0.258357i
$628$	0.282743			0.0112827
$629$	−2.63263	+	1.51995i	−0.104970	+	0.0606043i
$630$	−70.3280	+	40.6039i	−2.80194	+	1.61770i
$631$	−10.4605	+	6.03937i	−0.416426	+	0.240424i	−0.693547	−	0.720411i	$-0.743953\pi$
$631$	−10.4605	+	6.03937i	−0.416426	+	0.240424i	0.277121	+	0.960835i	$0.410620\pi$
$632$	−40.3427	−	23.2918i	−1.60474	−	0.926500i
$633$	−3.26232	−	5.65051i	−0.129666	−	0.224588i
$634$	−10.4885	+	18.1666i	−0.416551	+	0.721487i
$635$			44.2762i			1.75705i
$636$	−4.99867			−0.198210
$637$	26.0536	+	49.3085i	1.03228	+	1.95368i
$638$	−16.5079	−	28.5925i	−0.653553	−	1.13199i
$639$	33.6699	+	19.4393i	1.33196	+	0.769008i
$640$	11.5779	+	20.0534i	0.457655	+	0.792682i
$641$	−15.3801	−	26.6392i	−0.607479	−	1.05218i	−0.991654	−	0.128924i	$-0.958848\pi$
$641$	−15.3801	−	26.6392i	−0.607479	−	1.05218i	0.384176	−	0.923260i	$-0.374486\pi$
$642$	25.1178	−	14.5018i	0.991321	−	0.572339i
$643$			15.8255i			0.624097i	0.950066	+	0.312048i	$0.101015\pi$
$643$			15.8255i			0.624097i	−0.950066	+	0.312048i	$0.898985\pi$
$644$	−2.73565	−	1.57943i	−0.107800	−	0.0622381i
$645$	−19.9888	−	11.5405i	−0.787057	−	0.454407i
$646$	3.96881	+	6.87419i	0.156151	+	0.270461i
$647$	−34.3028			−1.34858			−0.674291	−	0.738466i	$-0.735550\pi$
$647$	−34.3028			−1.34858			−0.674291	+	0.738466i	$0.735550\pi$
$648$	15.5112	+	8.95542i	0.609339	+	0.351802i
$649$	−15.6951			−0.616087
$650$	29.8357	+	18.7514i	1.17025	+	0.735492i
$651$	59.6169	+	34.5410i	2.33657	+	1.35377i
$652$		−	7.81448i		−	0.306039i
$653$	5.38877			0.210879			0.105439	−	0.994426i	$-0.466375\pi$
$653$	5.38877			0.210879			0.105439	+	0.994426i	$0.466375\pi$
$654$	10.2601	−	17.7711i	0.401203	−	0.694903i
$655$			17.2517i			0.674081i
$656$	−10.5303	+	6.07967i	−0.411139	+	0.237371i
$657$	−1.34712	−	0.777759i	−0.0525561	−	0.0303433i
$658$	5.71964	+	3.30224i	0.222975	+	0.128735i
$659$	11.5594			0.450292			0.225146	−	0.974325i	$-0.427714\pi$
$659$	11.5594			0.450292			0.225146	+	0.974325i	$0.427714\pi$
$660$	6.44490	+	11.1629i	0.250867	+	0.434515i
$661$	4.89343	−	2.82522i	0.190332	−	0.109888i	−0.401806	−	0.915725i	$-0.631617\pi$
$661$	4.89343	−	2.82522i	0.190332	−	0.109888i	0.592138	+	0.805837i	$0.298284\pi$
$662$	8.92738	+	15.4627i	0.346972	+	0.600974i
$663$	31.7059	+	60.0061i	1.23136	+	2.33044i
$664$	16.3370	+	28.2966i	0.634000	+	1.09812i
$665$	−12.8674	−	7.42900i	−0.498976	−	0.288084i
$666$	−2.02039			−0.0782886
$667$	−12.6885			−0.491302
$668$	−1.62289	−	0.936974i	−0.0627914	−	0.0362526i
$669$	11.6351	−	6.71752i	0.449838	−	0.259714i
$670$	32.4176	+	18.7163i	1.25240	+	0.723075i
$671$	13.5952	−	7.84921i	0.524838	−	0.303015i
$672$	−14.5414	−	25.1865i	−0.560948	−	0.971591i
$673$	−16.4517	−	28.4951i	−0.634165	−	1.09841i	−0.986691	−	0.162604i	$-0.948011\pi$
$673$	−16.4517	−	28.4951i	−0.634165	−	1.09841i	0.352526	−	0.935802i	$-0.385323\pi$
$674$		−	6.59408i		−	0.253995i
$675$	8.29011	−	14.3589i	0.319087	−	0.552674i
$676$	5.48517	+	0.412236i	0.210968	+	0.0158552i
$677$	11.5473	+	20.0006i	0.443800	+	0.768684i	0.997968	−	0.0637207i	$-0.0202967\pi$
$677$	11.5473	+	20.0006i	0.443800	+	0.768684i	−0.554168	+	0.832405i	$0.686963\pi$
$678$		−	6.33136i		−	0.243154i
$679$	16.5488	−	28.6634i	0.635085	−	1.10000i
$680$	−78.4367			−3.00791
$681$		−	29.8384i		−	1.14341i
$682$	−11.4390	+	19.7434i	−0.438021	+	0.756014i
$683$			32.2899i			1.23554i	0.786360	+	0.617769i	$0.211963\pi$
$683$			32.2899i			1.23554i	−0.786360	+	0.617769i	$0.788037\pi$
$684$		−	1.41560i		−	0.0541268i
$685$	−15.7230	+	27.2331i	−0.600746	+	1.04052i
$686$	−50.3993			−1.92425
$687$	27.2525	−	15.7342i	1.03975	−	0.600299i
$688$	−3.67780	+	6.37014i	−0.140215	+	0.242859i
$689$	7.62204	+	14.4253i	0.290377	+	0.549561i
$690$	−18.4614			−0.702812
$691$	−23.8539	+	13.7721i	−0.907446	+	0.523914i	−0.879609	−	0.475698i	$-0.842196\pi$
$691$	−23.8539	+	13.7721i	−0.907446	+	0.523914i	−0.0278378	+	0.999612i	$0.508862\pi$
$692$	−3.78031	−	6.54768i	−0.143706	−	0.248905i
$693$	29.5152	+	51.1218i	1.12119	+	1.94196i
$694$	0.242354	+	0.139923i	0.00919962	+	0.00531140i
$695$	−12.1220	+	6.99866i	−0.459815	+	0.265474i
$696$	−55.4239	−	31.9990i	−2.10084	−	1.21292i
$697$		−	29.4708i		−	1.11629i
$698$	16.3468			0.618735
$699$	19.5087	−	33.7900i	0.737885	−	1.27805i
$700$	13.5185	−	7.80492i	0.510952	−	0.294998i
$701$	−18.3905	+	31.8534i	−0.694601	+	1.20308i	0.275714	+	0.961240i	$0.411086\pi$
$701$	−18.3905	+	31.8534i	−0.694601	+	1.20308i	−0.970315	+	0.241845i	$0.922247\pi$
$702$	−0.361674	+	9.63834i	−0.0136505	+	0.363776i
$703$	−0.184828	−	0.320132i	−0.00697092	−	0.0120740i
$704$	25.1562	−	14.5239i	0.948110	−	0.547391i
$705$	−10.3573			−0.390077
$706$	−3.23350	+	5.60059i	−0.121695	+	0.210781i
$707$	−2.07291	−	1.19680i	−0.0779599	−	0.0450102i
$708$	−4.60080	+	2.65627i	−0.172909	+	0.0998289i
$709$			0.855978i			0.0321469i	0.999871	+	0.0160735i	$0.00511656\pi$
$709$			0.855978i			0.0321469i	−0.999871	+	0.0160735i	$0.994883\pi$
$710$	39.6145	+	22.8714i	1.48670	+	0.858349i
$711$	58.4204			2.19093
$712$	41.9442			1.57193
$713$	4.37307	+	7.60109i	0.163773	+	0.284663i
$714$	−112.038			−4.19291
$715$	22.3870	−	35.6203i	0.837227	−	1.33212i
$716$	2.91141	−	5.04271i	0.108804	−	0.188455i
$717$		−	20.5087i		−	0.765910i
$718$	−22.0531	−	38.1971i	−0.823014	−	1.42550i
$719$	18.6527	−	32.3074i	0.695629	−	1.20486i	−0.274340	−	0.961633i	$-0.588459\pi$
$719$	18.6527	−	32.3074i	0.695629	−	1.20486i	0.969968	−	0.243231i	$-0.0782074\pi$
$720$	−35.1478	−	20.2926i	−1.30988	−	0.756261i
$721$			36.7844i			1.36992i
$722$	19.8266	−	11.4469i	0.737869	−	0.426009i
$723$	−1.67341	+	0.966142i	−0.0622347	+	0.0359312i
$724$	−3.18830	−	5.52229i	−0.118492	−	0.205234i
$725$	31.3509	−	54.3014i	1.16434	−	2.01670i
$726$	0.990943	−	0.572121i	0.0367773	−	0.0212334i
$727$	23.3377	−	40.4220i	0.865546	−	1.49917i	−0.000957310	−	1.00000i	$-0.500305\pi$
$727$	23.3377	−	40.4220i	0.865546	−	1.49917i	0.866504	−	0.499171i	$-0.166362\pi$
$728$	−27.6716	+	44.0286i	−1.02558	+	1.63181i
$729$	−39.1468			−1.44988
$730$	−1.58496	−	0.915075i	−0.0586619	−	0.0338684i
$731$	−8.91394	−	15.4394i	−0.329694	−	0.571047i
$732$	2.65684	−	4.60177i	0.0981995	−	0.170086i
$733$	45.6376	−	26.3489i	1.68566	−	0.973218i	0.727890	−	0.685694i	$-0.240501\pi$
$733$	45.6376	−	26.3489i	1.68566	−	0.973218i	0.957773	−	0.287524i	$-0.0928322\pi$
$734$	11.1814	−	6.45558i	0.412712	−	0.238280i
$735$	125.034	−	72.1886i	4.61196	−	2.66272i
$736$		−	3.70152i		−	0.136440i
$737$	13.6050	−	23.5646i	0.501147	−	0.868012i
$738$	9.79351	−	16.9629i	0.360504	−	0.624412i
$739$	−1.43816	+	0.830321i	−0.0529035	+	0.0305438i	−0.526218	−	0.850349i	$-0.676391\pi$
$739$	−1.43816	+	0.830321i	−0.0529035	+	0.0305438i	0.473315	+	0.880893i	$0.343057\pi$
$740$	0.637852			0.0234479
$741$	−7.29684	+	3.85549i	−0.268056	+	0.141635i
$742$	−26.9337			−0.988766
$743$		−	21.6565i		−	0.794500i	−0.917711	−	0.397250i	$-0.869965\pi$
$743$		−	21.6565i		−	0.794500i	0.917711	−	0.397250i	$-0.130035\pi$
$744$	−0.0673559	+	44.2302i	−0.00246939	+	1.62156i
$745$	7.40407			0.271264
$746$			7.52399i			0.275473i
$747$	−35.4866	−	20.4882i	−1.29839	−	0.749624i
$748$			9.95614i			0.364032i
$749$	−36.3158	+	20.9669i	−1.32695	+	0.766116i
$750$	16.3110	−	28.2514i	0.595592	−	1.03160i
$751$	15.0407	−	26.0512i	0.548841	−	0.950621i	−0.449513	−	0.893274i	$-0.648402\pi$
$751$	15.0407	−	26.0512i	0.548841	−	0.950621i	0.998354	−	0.0573474i	$-0.0182643\pi$
$752$			3.30072i			0.120365i
$753$	3.06551	+	5.30961i	0.111713	+	0.193493i
$754$	−1.36775	+	36.4496i	−0.0498105	+	1.32742i
$755$	3.40542	+	5.89836i	0.123936	+	0.214663i
$756$	3.70011	+	2.13626i	0.134572	+	0.0776949i
$757$	−0.863766	−	1.49609i	−0.0313941	−	0.0543762i	0.849901	−	0.526942i	$-0.176661\pi$
$757$	−0.863766	−	1.49609i	−0.0313941	−	0.0543762i	−0.881296	+	0.472565i	$0.843328\pi$
$758$	−16.2237	+	28.1002i	−0.589270	+	1.02065i
$759$			13.4197i			0.487103i
$760$		−	9.53802i		−	0.345980i
$761$	−5.93772	−	3.42814i	−0.215242	−	0.124270i	0.388503	−	0.921447i	$-0.372992\pi$
$761$	−5.93772	−	3.42814i	−0.215242	−	0.124270i	−0.603745	+	0.797177i	$0.706326\pi$
$762$	−35.1597	+	20.2995i	−1.27370	+	0.735372i
$763$	−14.8343	+	25.6937i	−0.537037	+	0.930175i
$764$	−0.338527	−	0.586345i	−0.0122475	−	0.0212132i
$765$	85.1883	−	49.1835i	3.07999	−	1.77823i
$766$	17.3621	+	30.0721i	0.627319	+	1.08655i
$767$	14.6809	+	9.22684i	0.530098	+	0.333162i
$768$	12.6209	−	21.8600i	0.455417	−	0.788806i
$769$	18.8172	+	10.8641i	0.678567	+	0.391771i	0.799315	−	0.600912i	$-0.205196\pi$
$769$	18.8172	+	10.8641i	0.678567	+	0.391771i	−0.120748	+	0.992683i	$0.538529\pi$
$770$	34.7262	+	60.1476i	1.25145	+	2.16757i
$771$	−60.4548			−2.17723
$772$	−1.20874	−	0.697866i	−0.0435035	−	0.0251167i
$773$		−	3.43940i		−	0.123706i	−0.998085	−	0.0618532i	$-0.980299\pi$
$773$		−	3.43940i		−	0.123706i	0.998085	−	0.0618532i	$-0.0197011\pi$
$774$		−	11.8489i		−	0.425899i
$775$	−43.3344	−	0.0659919i	−1.55662	−	0.00237050i
$776$	21.2469			0.762718
$777$	5.21762			0.187181
$778$	−25.4368	−	14.6859i	−0.911954	−	0.526517i
$779$	3.58369			0.128399
$780$	0.533989	−	14.2304i	0.0191199	−	0.509531i
$781$	16.6254	−	28.7960i	0.594902	−	1.03040i
$782$	−12.3492	−	7.12981i	−0.441607	−	0.254962i
$783$	17.1619			0.613316
$784$	−23.0055	−	39.8467i	−0.821625	−	1.42310i
$785$	−2.06905	+	1.19457i	−0.0738477	+	0.0426360i
$786$	−13.6996	+	7.90946i	−0.488648	+	0.282121i
$787$	19.2192	+	11.0962i	0.685089	+	0.395536i	0.801770	−	0.597633i	$-0.203892\pi$
$787$	19.2192	+	11.0962i	0.685089	+	0.395536i	−0.116681	+	0.993169i	$0.537225\pi$
$788$	−4.45411	+	2.57158i	−0.158671	+	0.0916087i
$789$	−37.7798	+	65.4365i	−1.34500	+	2.32960i
$790$	68.7347			2.44547
$791$			9.15400i			0.325479i
$792$	−18.9472	+	32.8174i	−0.673258	+	1.16612i
$793$	−17.3312	−	0.650342i	−0.615447	−	0.0230943i
$794$	11.3698	−	19.6931i	0.403500	−	0.698882i
$795$	36.5791	−	21.1190i	1.29733	−	0.749013i
$796$	3.45998	+	5.99286i	0.122636	+	0.212411i
$797$	10.5795	+	18.3242i	0.374745	+	0.649077i	0.990289	−	0.139025i	$-0.0443970\pi$
$797$	10.5795	+	18.3242i	0.374745	+	0.649077i	−0.615544	+	0.788103i	$0.711064\pi$
$798$		−	13.6240i		−	0.482284i
$799$	−6.92820	−	4.00000i	−0.245102	−	0.141510i
$800$	15.8409	+	9.14577i	0.560062	+	0.323352i
$801$	−45.5547	+	26.3010i	−1.60960	+	0.929301i
$802$	−13.9231			−0.491641
$803$	−0.665173	+	1.15211i	−0.0234734	+	0.0406572i
$804$		−	9.21016i		−	0.324817i
$805$	26.6918			0.940762
$806$	22.3066	−	11.7429i	0.785716	−	0.413626i
$807$	−25.8700			−0.910667
$808$		−	1.53656i		−	0.0540559i
$809$	6.91908	−	11.9842i	0.243262	−	0.421342i	−0.718380	−	0.695651i	$-0.755116\pi$
$809$	6.91908	−	11.9842i	0.243262	−	0.421342i	0.961642	+	0.274309i	$0.0884492\pi$
$810$	−26.4276			−0.928572
$811$	−13.7339	+	7.92926i	−0.482262	+	0.278434i	−0.721359	−	0.692562i	$-0.756482\pi$
$811$	−13.7339	+	7.92926i	−0.482262	+	0.278434i	0.239097	+	0.970996i	$0.423149\pi$
$812$	13.9928	+	8.07874i	0.491051	+	0.283508i
$813$	−29.2414	−	16.8825i	−1.02554	−	0.592096i
$814$			1.72793i			0.0605638i
$815$	33.0156	+	57.1846i	1.15649	+	2.00309i
$816$	−27.9966	−	48.4915i	−0.980077	−	1.69754i
$817$	1.87746	−	1.08395i	0.0656839	−	0.0379226i
$818$	0.159922	−	0.276993i	0.00559154	−	0.00968483i
$819$	2.44547	−	65.1699i	0.0854515	−	2.27722i
$820$	−3.09188	+	5.35530i	−0.107973	+	0.187015i
$821$		−	31.5669i		−	1.10169i	−0.834607	−	0.550845i	$-0.814305\pi$
$821$		−	31.5669i		−	1.10169i	0.834607	−	0.550845i	$-0.185695\pi$
$822$	−28.8344			−1.00571
$823$	9.62086	−	16.6638i	0.335362	−	0.580864i	−0.648192	−	0.761477i	$-0.724475\pi$
$823$	9.62086	−	16.6638i	0.335362	−	0.580864i	0.983554	+	0.180612i	$0.0578080\pi$
$824$	−20.4500	+	11.8068i	−0.712409	+	0.411309i
$825$	−57.4304	−	33.1575i	−1.99947	−	1.15439i
$826$	−24.7899	+	14.3125i	−0.862551	+	0.497994i
$827$	−10.1105	+	5.83729i	−0.351576	+	0.202983i	−0.665379	−	0.746506i	$-0.731730\pi$
$827$	−10.1105	+	5.83729i	−0.351576	+	0.202983i	0.313803	+	0.949488i	$0.398397\pi$
$828$	1.27153	+	2.20236i	0.0441888	+	0.0765373i
$829$	−11.4786			−0.398667			−0.199334	−	0.979932i	$-0.563878\pi$
$829$	−11.4786			−0.398667			−0.199334	+	0.979932i	$0.563878\pi$
$830$	−41.7519	−	24.1055i	−1.44923	−	0.836713i
$831$	−32.3699	+	56.0663i	−1.12290	+	1.94492i
$832$	−32.0690	−	1.20337i	−1.11179	−	0.0417195i
$833$	111.518			3.86386
$834$	−11.1153	−	6.41740i	−0.384890	−	0.222216i
$835$	15.8346			0.547978
$836$	−1.21068			−0.0418723
$837$	−5.91481	−	10.2809i	−0.204446	−	0.355359i
$838$		−	23.2837i		−	0.804322i
$839$			17.1523i			0.592163i	0.955163	+	0.296081i	$0.0956800\pi$
$839$			17.1523i			0.592163i	−0.955163	+	0.296081i	$0.904320\pi$
$840$	116.591	+	67.3136i	4.02276	+	2.32254i
$841$	35.9016			1.23799
$842$	16.8072	+	29.1109i	0.579215	+	1.00323i
$843$	−27.1176	−	15.6563i	−0.933979	−	0.539233i
$844$	−0.528728	+	0.915784i	−0.0181996	+	0.0315226i
$845$	−41.8809	+	20.1577i	−1.44075	+	0.693447i
$846$	−2.65850	−	4.60466i	−0.0914011	−	0.158311i
$847$	−1.43272	+	0.827184i	−0.0492290	+	0.0284224i
$848$	−6.73032	−	11.6573i	−0.231120	−	0.400312i
$849$	15.7047	−	27.2014i	0.538985	−	0.933550i
$850$	61.0251	−	35.2329i	2.09314	−	1.20848i
$851$	0.575104	+	0.332036i	0.0197143	+	0.0113821i
$852$		−	11.2549i		−	0.385585i
$853$			18.6402i			0.638227i	0.947717	+	0.319113i	$0.103385\pi$
$853$			18.6402i			0.638227i	−0.947717	+	0.319113i	$0.896615\pi$
$854$	14.3155	−	24.7951i	0.489866	−	0.848472i
$855$	5.98079	+	10.3590i	0.204539	+	0.354272i
$856$	−23.3128	−	13.4596i	−0.796814	−	0.460041i
$857$	−7.92928	−	13.7339i	−0.270859	−	0.469142i	0.698223	−	0.715880i	$-0.253974\pi$
$857$	−7.92928	−	13.7339i	−0.270859	−	0.469142i	−0.969082	+	0.246739i	$0.920641\pi$
$858$	38.5499	+	1.44656i	1.31607	+	0.0493849i
$859$	−12.7218	−	22.0348i	−0.434062	−	0.751817i	0.563157	−	0.826350i	$-0.309587\pi$
$859$	−12.7218	−	22.0348i	−0.434062	−	0.751817i	−0.997219	+	0.0745332i	$0.976253\pi$
$860$			3.74077i			0.127559i
$861$	−25.2915	+	43.8062i	−0.861933	+	1.49291i
$862$	−14.9532	+	25.8998i	−0.509310	+	0.882150i
$863$	29.4586	−	17.0079i	1.00278	−	0.578957i	0.0937124	−	0.995599i	$-0.470127\pi$
$863$	29.4586	−	17.0079i	1.00278	−	0.578957i	0.909070	+	0.416642i	$0.136793\pi$
$864$			5.00651i			0.170325i
$865$	55.3269	+	31.9430i	1.88117	+	1.08609i
$866$			49.6472i			1.68708i
$867$	91.3289			3.10169
$868$	0.0170053	−	11.1667i	0.000577196	−	0.379024i
$869$		−	49.9636i		−	1.69490i
$870$	94.4296			3.20146
$871$	−26.5790	+	14.0438i	−0.900596	+	0.475856i
$872$	−19.0456			−0.644965
$873$	−23.0757	+	13.3228i	−0.780996	+	0.450908i
$874$	0.866997	−	1.50168i	0.0293266	−	0.0507952i
$875$	−23.5827	+	40.8465i	−0.797241	+	1.38086i
$876$			0.450302i			0.0152143i
$877$	31.1102	−	17.9615i	1.05052	−	0.606516i	0.127722	−	0.991810i	$-0.459233\pi$
$877$	31.1102	−	17.9615i	1.05052	−	0.606516i	0.922794	+	0.385294i	$0.125900\pi$
$878$	−38.3471	+	22.1397i	−1.29415	+	0.747178i
$879$	−10.2381	+	5.91099i	−0.345324	+	0.199373i
$880$	−17.3551	+	30.0600i	−0.585041	+	1.01332i
$881$	−23.1467	−	40.0912i	−0.779832	−	1.35071i	−0.932038	−	0.362360i	$-0.881971\pi$
$881$	−23.1467	−	40.0912i	−0.779832	−	1.35071i	0.152207	−	0.988349i	$-0.451362\pi$
$882$	64.1876	+	37.0587i	2.16131	+	1.24783i
$883$	15.3676			0.517162			0.258581	−	0.965990i	$-0.416745\pi$
$883$	15.3676			0.517162			0.258581	+	0.965990i	$0.416745\pi$
$884$	5.85301	−	9.31281i	0.196858	−	0.313224i
$885$	22.4451	−	38.8760i	0.754483	−	1.30680i
$886$	8.07863	−	4.66420i	0.271407	−	0.156697i
$887$	12.1051	−	20.9667i	0.406450	−	0.703992i	−0.588039	−	0.808832i	$-0.700100\pi$
$887$	12.1051	−	20.9667i	0.406450	−	0.703992i	0.994489	+	0.104841i	$0.0334332\pi$
$888$	1.67471	+	2.90069i	0.0561997	+	0.0973408i
$889$	50.8346	−	29.3494i	1.70494	−	0.984346i
$890$	−53.5975	+	30.9446i	−1.79659	+	1.03726i
$891$			19.2104i			0.643572i
$892$	−1.88571	−	1.08872i	−0.0631383	−	0.0364529i
$893$	0.486406	−	0.842480i	0.0162770	−	0.0281925i
$894$	3.39457	+	5.87957i	0.113531	+	0.196642i
$895$			49.2019i			1.64464i
$896$	15.3492	−	26.5856i	0.512782	−	0.888164i
$897$	7.88915	−	12.5525i	0.263411	−	0.419117i
$898$	9.67289			0.322788
$899$	−22.3682	−	38.8795i	−0.746021	−	1.29670i
$900$	−12.5669			−0.418896
$901$	32.6248			1.08689
$902$	−14.5074	−	8.37584i	−0.483043	−	0.278885i
$903$			30.5994i			1.01829i
$904$	−5.08909	+	2.93819i	−0.169261	+	0.0977226i
$905$	46.6625	+	26.9406i	1.55111	+	0.895535i
$906$	−3.12259	+	5.40848i	−0.103741	+	0.179685i
$907$	−47.8340			−1.58830			−0.794150	−	0.607721i	$-0.792084\pi$
$907$	−47.8340			−1.58830			−0.794150	+	0.607721i	$0.792084\pi$
$908$	−4.18805	+	2.41797i	−0.138985	+	0.0802433i
$909$	0.963494	+	1.66882i	0.0319571	+	0.0553513i
$910$	2.87722	−	76.6759i	0.0953790	−	2.54178i
$911$	−27.6368	+	47.8684i	−0.915649	+	1.58595i	−0.109702	+	0.993965i	$0.534990\pi$
$911$	−27.6368	+	47.8684i	−0.915649	+	1.58595i	−0.805948	+	0.591987i	$0.798344\pi$
$912$	5.89665	−	3.40443i	0.195258	−	0.112732i
$913$	−17.5224	+	30.3497i	−0.579907	+	1.00443i
$914$	6.20579			0.205269
$915$			44.8997i			1.48434i
$916$	−4.41685	−	2.55007i	−0.145937	−	0.0842566i
$917$	19.8071	−	11.4356i	0.654089	−	0.377638i
$918$	16.7030	+	9.64345i	0.551280	+	0.318281i
$919$	16.0612	+	27.8189i	0.529812	+	0.917661i	0.999395	+	0.0347728i	$0.0110707\pi$
$919$	16.0612	+	27.8189i	0.529812	+	0.917661i	−0.469584	+	0.882888i	$0.655596\pi$
$920$	8.56734	+	14.8391i	0.282457	+	0.489229i
$921$	42.2121	−	24.3712i	1.39094	−	0.803057i
$922$	8.32047			0.274020
$923$	−32.4797	+	17.1616i	−1.06908	+	0.564880i
$924$	8.54426	−	14.7991i	0.281085	−	0.486854i
$925$	−2.84195	+	1.64080i	−0.0934426	+	0.0539491i
$926$	26.5083			0.871115
$927$	14.8068	−	25.6462i	0.486321	−	0.842332i
$928$			18.9333i			0.621515i
$929$			20.1170i			0.660019i	0.943978	+	0.330009i	$0.107052\pi$
$929$			20.1170i			0.660019i	−0.943978	+	0.330009i	$0.892948\pi$
$930$	−32.5450	−	56.5683i	−1.06719	−	1.85495i
$931$			13.5607i			0.444434i
$932$	−6.32358			−0.207136
$933$	−35.5476	+	61.5703i	−1.16378	+	2.01572i
$934$		−	21.1482i		−	0.691992i
$935$	−42.0639	−	72.8568i	−1.37564	−	2.38267i
$936$	37.0156	−	19.5582i	1.20989	−	0.639281i
$937$	−12.7785	+	22.1330i	−0.417455	+	0.723053i	−0.995683	−	0.0928226i	$-0.970411\pi$
$937$	−12.7785	+	22.1330i	−0.417455	+	0.723053i	0.578228	+	0.815875i	$0.303744\pi$
$938$		−	49.6259i		−	1.62034i
$939$	−14.1085	−	24.4367i	−0.460414	−	0.797461i
$940$	0.839308	+	1.45372i	0.0273752	+	0.0474152i
$941$	−31.0696	+	17.9380i	−1.01284	+	0.584764i	−0.912022	−	0.410141i	$-0.865479\pi$
$941$	−31.0696	+	17.9380i	−1.01284	+	0.584764i	−0.100818	+	0.994905i	$0.532146\pi$
$942$	−1.89721	−	1.09536i	−0.0618145	−	0.0356886i
$943$	−5.57544	+	3.21898i	−0.181561	+	0.104824i
$944$	−12.3892	−	7.15294i	−0.403236	−	0.232808i
$945$	−36.1021			−1.17440
$946$	−10.1337			−0.329474
$947$	−43.5681	−	25.1541i	−1.41577	−	0.817397i	−0.419849	−	0.907594i	$-0.637917\pi$
$947$	−43.5681	−	25.1541i	−1.41577	−	0.817397i	−0.995924	+	0.0901967i	$0.971250\pi$
$948$	−8.45596	−	14.6461i	−0.274637	−	0.475685i
$949$	1.29950	−	0.686626i	0.0421834	−	0.0222888i
$950$	4.28437	+	7.42075i	0.139003	+	0.240761i
$951$	−37.7692	+	21.8061i	−1.22475	+	0.707111i
$952$	51.9933	+	90.0550i	1.68511	+	2.91870i
$953$	2.72952			0.0884179			0.0442089	−	0.999022i	$-0.485923\pi$
$953$	2.72952			0.0884179			0.0442089	+	0.999022i	$0.485923\pi$
$954$	18.7782	+	10.8416i	0.607968	+	0.351010i
$955$	4.95452	+	2.86050i	0.160325	+	0.0925635i
$956$	−2.87855	+	1.66193i	−0.0930989	+	0.0537507i
$957$		−	68.6414i		−	2.21886i
$958$	−9.89893	+	17.1454i	−0.319820	+	0.553944i
$959$	41.6893			1.34622
$960$			83.0810i			2.68143i
$961$	−15.5817	+	26.7995i	−0.502635	+	0.864499i
$962$	1.01581	−	1.61628i	0.0327512	−	0.0521108i
$963$	33.7593			1.08788
$964$	0.271211	+	0.156584i	0.00873512	+	0.00504322i
$965$	11.7937			0.379653
$966$	12.2375	+	21.1959i	0.393734	+	0.681968i
$967$	33.6888	+	19.4502i	1.08336	+	0.625477i	0.931800	−	0.362972i	$-0.118238\pi$
$967$	33.6888	+	19.4502i	1.08336	+	0.625477i	0.151557	+	0.988448i	$0.451571\pi$
$968$	−0.919731	−	0.531007i	−0.0295613	−	0.0170672i
$969$			16.5027i			0.530144i
$970$	−27.1499	+	15.6750i	−0.871729	+	0.503293i
$971$	18.9037	+	32.7422i	0.606650	+	1.05075i	0.991788	+	0.127889i	$0.0408202\pi$
$971$	18.9037	+	32.7422i	0.606650	+	1.05075i	−0.385139	+	0.922859i	$0.625846\pi$
$972$	4.60328	+	7.97311i	0.147650	+	0.255738i
$973$	16.0707	+	9.27840i	0.515202	+	0.297452i
$974$	8.47810	+	14.6845i	0.271656	+	0.470522i
$975$	34.2269	+	64.7771i	1.09614	+	2.07453i
$976$	14.3089			0.458017
$977$		−	22.1288i		−	0.707964i	−0.935252	−	0.353982i	$-0.884827\pi$
$977$		−	22.1288i		−	0.707964i	0.935252	−	0.353982i	$-0.115173\pi$
$978$	−30.2735	+	52.4353i	−0.968041	+	1.67670i
$979$	22.4938	+	38.9604i	0.718904	+	1.24518i
$980$	−20.2645	−	11.6997i	−0.647325	−	0.373733i
$981$	20.6850	−	11.9425i	0.660421	−	0.381295i
$982$	−21.6725	+	12.5126i	−0.691598	+	0.399294i
$983$	40.6405	−	23.4638i	1.29623	−	0.748380i	0.316481	−	0.948599i	$-0.397499\pi$
$983$	40.6405	−	23.4638i	1.29623	−	0.748380i	0.979751	+	0.200219i	$0.0641654\pi$
$984$	−32.4716			−1.03516
$985$	21.7294	−	37.6365i	0.692357	−	1.19920i
$986$	63.1660	+	36.4689i	2.01162	+	1.16141i
$987$	6.86552	+	11.8914i	0.218532	+	0.378508i
$988$	1.13245	+	0.711736i	0.0360281	+	0.0226433i
$989$	−1.94727	+	3.37277i	−0.0619196	+	0.107248i
$990$		−	55.9134i		−	1.77705i
$991$	−53.8622			−1.71099			−0.855495	−	0.517811i	$-0.826747\pi$
$991$	−53.8622			−1.71099			−0.855495	+	0.517811i	$0.826747\pi$
$992$	11.3420	−	6.52530i	0.360109	−	0.207179i
$993$			37.1210i			1.17800i
$994$		−	60.6431i		−	1.92348i
$995$	−50.6387	−	29.2363i	−1.60535	−	0.926851i
$996$			11.8621i			0.375866i
$997$	−15.9651	−	27.6523i	−0.505619	−	0.875757i	−0.999979	−	0.00650016i	$-0.997931\pi$
$997$	−15.9651	−	27.6523i	−0.505619	−	0.875757i	0.494360	−	0.869257i	$-0.335402\pi$
$998$	4.50635	−	7.80522i	0.142646	−	0.247070i
$999$	−0.777858	−	0.449097i	−0.0246103	−	0.0142088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.129.24	yes	68
13.12	even	2	inner	403.2.l.c.129.11	yes	68
31.25	even	3	inner	403.2.l.c.25.24	yes	68
403.25	even	6	inner	403.2.l.c.25.11	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.11	✓	68	403.25	even	6	inner
403.2.l.c.25.24	yes	68	31.25	even	3	inner
403.2.l.c.129.11	yes	68	13.12	even	2	inner
403.2.l.c.129.24	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.25574i q^{2} +(-1.30537 + 2.26097i) q^{3} +0.423126 q^{4} +(-3.09634 + 1.78767i) q^{5} +(-2.83918 - 1.63920i) q^{6} +(4.10494 + 2.36999i) q^{7} +3.04281i q^{8} +(-1.90798 - 3.30473i) q^{9} +O(q^{10})\)	\(q+1.25574i q^{2} +(-1.30537 + 2.26097i) q^{3} +0.423126 q^{4} +(-3.09634 + 1.78767i) q^{5} +(-2.83918 - 1.63920i) q^{6} +(4.10494 + 2.36999i) q^{7} +3.04281i q^{8} +(-1.90798 - 3.30473i) q^{9} +(-2.24485 - 3.88819i) q^{10} +(-2.82635 + 1.63179i) q^{11} +(-0.552336 + 0.956674i) q^{12} +(3.60302 + 0.135201i) q^{13} +(-2.97608 + 5.15472i) q^{14} -9.33430i q^{15} -2.97471 q^{16} +(3.60493 - 6.24392i) q^{17} +(4.14987 - 2.39593i) q^{18} +(0.759270 + 0.438365i) q^{19} +(-1.31014 + 0.756411i) q^{20} +(-10.7169 + 6.18743i) q^{21} +(-2.04910 - 3.54915i) q^{22} -1.57501 q^{23} +(-6.87969 - 3.97199i) q^{24} +(3.89155 - 6.74037i) q^{25} +(-0.169777 + 4.52444i) q^{26} +2.13028 q^{27} +(1.73691 + 1.00280i) q^{28} +8.05616 q^{29} +11.7214 q^{30} +(-2.77654 - 4.82606i) q^{31} +2.35016i q^{32} -8.52037i q^{33} +(7.84071 + 4.52684i) q^{34} -16.9471 q^{35} +(-0.807318 - 1.39832i) q^{36} +(-0.365143 - 0.210815i) q^{37} +(-0.550471 + 0.953443i) q^{38} +(-5.00896 + 7.96982i) q^{39} +(-5.43955 - 9.42157i) q^{40} +(3.53994 - 2.04378i) q^{41} +(-7.76978 - 13.4576i) q^{42} +(1.23636 - 2.14143i) q^{43} +(-1.19590 + 0.690453i) q^{44} +(11.8155 + 6.82171i) q^{45} -1.97780i q^{46} -1.10959i q^{47} +(3.88310 - 6.72573i) q^{48} +(7.73369 + 13.3951i) q^{49} +(8.46412 + 4.88676i) q^{50} +(9.41153 + 16.3013i) q^{51} +(1.52453 + 0.0572071i) q^{52} +(2.26251 + 3.91878i) q^{53} +2.67508i q^{54} +(5.83422 - 10.1052i) q^{55} +(-7.21142 + 12.4905i) q^{56} +(-1.98226 + 1.14446i) q^{57} +10.1164i q^{58} +(4.16486 + 2.40458i) q^{59} -3.94959i q^{60} -4.81018 q^{61} +(6.06026 - 3.48660i) q^{62} -18.0876i q^{63} -8.90061 q^{64} +(-11.3979 + 6.02239i) q^{65} +10.6993 q^{66} +(-7.22046 + 4.16873i) q^{67} +(1.52534 - 2.64196i) q^{68} +(2.05597 - 3.56105i) q^{69} -21.2810i q^{70} +(-8.82343 + 5.09421i) q^{71} +(10.0556 - 5.80563i) q^{72} +(0.353021 - 0.203817i) q^{73} +(0.264729 - 0.458523i) q^{74} +(10.1598 + 17.5973i) q^{75} +(0.321267 + 0.185484i) q^{76} -15.4693 q^{77} +(-10.0080 - 6.28993i) q^{78} +(-7.65472 + 13.2584i) q^{79} +(9.21072 - 5.31781i) q^{80} +(2.94314 - 5.09767i) q^{81} +(2.56645 + 4.44523i) q^{82} +(9.29950 - 5.36907i) q^{83} +(-4.53461 + 2.61806i) q^{84} +25.7777i q^{85} +(2.68907 + 1.55254i) q^{86} +(-10.5163 + 18.2147i) q^{87} +(-4.96523 - 8.60003i) q^{88} -13.7847i q^{89} +(-8.56627 + 14.8372i) q^{90} +(14.4697 + 9.09410i) q^{91} -0.666427 q^{92} +(14.5360 + 0.0221361i) q^{93} +1.39336 q^{94} -3.13461 q^{95} +(-5.31364 - 3.06783i) q^{96} -6.98265i q^{97} +(-16.8208 + 9.71148i) q^{98} +(10.7852 + 6.22687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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