LMFDB - Embedded newform 403.2.l.c.25.11

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			25.11
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.24

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

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

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	$-0.853570\pi$
$2$		−	1.25574i		−	0.887940i	0.896042	−	0.443970i	$-0.146430\pi$
$3$	−1.30537	−	2.26097i	−0.753656	−	1.30537i	−0.946040	−	0.324051i	$-0.894955\pi$
$3$	−1.30537	−	2.26097i	−0.753656	−	1.30537i	0.192384	−	0.981320i	$-0.438378\pi$
$4$	0.423126			0.211563
$5$	−3.09634	−	1.78767i	−1.38473	−	0.799472i	−0.392011	−	0.919960i	$-0.628221\pi$
$5$	−3.09634	−	1.78767i	−1.38473	−	0.799472i	−0.992715	+	0.120489i	$0.961554\pi$
$6$	−2.83918	+	1.63920i	−1.15909	+	0.669201i
$7$	4.10494	−	2.36999i	1.55152	−	0.895772i	0.553504	−	0.832847i	$-0.313291\pi$
$7$	4.10494	−	2.36999i	1.55152	−	0.895772i	0.998018	−	0.0629247i	$-0.0200428\pi$
$8$		−	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	0.00920887	−	0.999958i	$-0.497069\pi$
$11$	−2.82635	−	1.63179i	−0.852175	−	0.492004i	−0.861384	+	0.507954i	$0.830402\pi$
$12$	−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	0.857482	+	0.514514i	$0.172028\pi$
$17$	3.60493	+	6.24392i	0.874323	+	1.51437i	0.0168414	+	0.999858i	$0.494639\pi$
$18$	4.14987	+	2.39593i	0.978133	+	0.564725i
$19$	0.759270	−	0.438365i	0.174189	−	0.100568i	−0.410371	−	0.911919i	$-0.634601\pi$
$19$	0.759270	−	0.438365i	0.174189	−	0.100568i	0.584559	+	0.811351i	$0.301267\pi$
$20$	−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	−0.529714	−	0.848176i	$-0.677701\pi$
$37$	−0.365143	+	0.210815i	−0.0600291	+	0.0346578i	0.469685	+	0.882834i	$0.344367\pi$
$38$	−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	0.750269	−	0.661133i	$-0.229924\pi$
$41$	3.53994	+	2.04378i	0.552846	+	0.319186i	−0.197423	+	0.980318i	$0.563257\pi$
$42$	−7.76978	+	13.4576i	−1.19890	+	2.07656i
$43$	1.23636	+	2.14143i	0.188542	+	0.326565i	0.944764	−	0.327750i	$-0.106290\pi$
$43$	1.23636	+	2.14143i	0.188542	+	0.326565i	−0.756222	+	0.654315i	$0.772957\pi$
$44$	−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	$0.0257875\pi$
$47$			1.10959i			0.161851i	−0.996720	+	0.0809253i	$0.974212\pi$
$48$	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	−0.667752	−	0.744384i	$-0.732743\pi$
$53$	2.26251	−	3.91878i	0.310780	−	0.538286i	0.978531	+	0.206098i	$0.0660765\pi$
$54$		−	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	−0.203759	−	0.979021i	$-0.565316\pi$
$59$	4.16486	−	2.40458i	0.542218	−	0.313050i	0.745977	+	0.665971i	$0.231983\pi$
$60$			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	−0.0107625	−	0.999942i	$-0.503426\pi$
$67$	−7.22046	−	4.16873i	−0.882119	−	0.509292i	−0.871357	+	0.490650i	$0.836759\pi$
$68$	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	−0.125298	−	0.992119i	$-0.539989\pi$
$71$	−8.82343	−	5.09421i	−1.04715	−	0.604571i	−0.921850	+	0.387548i	$0.873322\pi$
$72$	10.0556	+	5.80563i	1.18507	+	0.684200i
$73$	0.353021	+	0.203817i	0.0413180	+	0.0238550i	0.520517	−	0.853851i	$-0.325739\pi$
$73$	0.353021	+	0.203817i	0.0413180	+	0.0238550i	−0.479199	+	0.877706i	$0.659073\pi$
$74$	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	−0.870749	−	0.491728i	$-0.836365\pi$
$79$	−7.65472	−	13.2584i	−0.861223	−	1.49168i	0.00952566	−	0.999955i	$-0.496968\pi$
$80$	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	0.914322	−	0.404989i	$-0.132724\pi$
$83$	9.29950	+	5.36907i	1.02075	+	0.589332i	0.106431	+	0.994320i	$0.466058\pi$
$84$	−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	$0.260754\pi$
$89$			13.7847i			1.46118i	−0.682818	+	0.730588i	$0.739246\pi$
$90$	−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	$0.115346\pi$
$97$			6.98265i			0.708981i	−0.935060	+	0.354490i	$0.884654\pi$
$98$	−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	−0.609064	−	0.793121i	$-0.708455\pi$
$103$	3.88023	−	6.72076i	0.382331	−	0.662216i	0.991395	+	0.130905i	$0.0417882\pi$
$104$	−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	0.569033	−	0.822315i	$-0.307318\pi$
$107$	−4.42343	−	7.66160i	−0.427629	−	0.740675i	−0.996662	+	0.0816397i	$0.973984\pi$
$108$	0.901379			0.0867352
$109$		−	6.25922i		−	0.599525i	−0.954014	−	0.299762i	$-0.903093\pi$
$109$		−	6.25922i		−	0.599525i	0.954014	−	0.299762i	$-0.0969074\pi$
$110$	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	−0.817026	−	0.576601i	$-0.804379\pi$
$113$	0.965617	−	1.67250i	0.0908376	−	0.157335i	0.907864	+	0.419265i	$0.137712\pi$
$114$	−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	0.998313	+	0.0580630i	$0.0184924\pi$
$127$	6.19188	+	10.7247i	0.549441	+	0.951659i	−0.448872	+	0.893596i	$0.648174\pi$
$128$			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	0.951962	−	0.306217i	$-0.0990632\pi$
$131$	2.41260	+	4.17874i	0.210789	+	0.365098i	−0.741172	+	0.671315i	$0.765730\pi$
$132$			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	0.788746	−	0.614719i	$-0.210731\pi$
$137$	7.61691	+	4.39762i	0.650756	+	0.375714i	−0.137990	+	0.990434i	$0.544064\pi$
$138$	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	−0.571659	−	0.820491i	$-0.693700\pi$
$149$	−1.79342	+	1.03543i	−0.146923	+	0.0848261i	0.424736	+	0.905317i	$0.360367\pi$
$150$	−22.0976	−	12.7581i	−1.80426	−	1.04169i
$151$			1.90494i			0.155022i	0.996991	+	0.0775111i	$0.0246973\pi$
$151$			1.90494i			0.155022i	−0.996991	+	0.0775111i	$0.975303\pi$
$152$	−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	$0.257367\pi$
$163$			18.4685i			1.44656i	−0.690554	+	0.723281i	$0.742633\pi$
$164$	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	−0.641003	−	0.767538i	$-0.721482\pi$
$167$	−3.83547	+	2.21441i	−0.296798	+	0.171356i	0.344206	+	0.938894i	$0.388148\pi$
$168$	−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	0.295948	+	0.955204i	$0.404365\pi$
$173$	−8.93423	+	15.4745i	−0.679257	+	1.17651i	−0.975205	+	0.221304i	$0.928969\pi$
$174$	−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	0.999863	+	0.0165789i	$0.00527745\pi$
$179$	6.88072	+	11.9178i	0.514289	+	0.890775i	−0.485574	+	0.874196i	$0.661389\pi$
$180$	4.99946	−	2.88644i	0.372638	−	0.215143i
$181$	−7.53510	+	13.0512i	−0.560079	+	0.970086i	0.437409	+	0.899262i	$0.355896\pi$
$181$	−7.53510	+	13.0512i	−0.560079	+	0.970086i	−0.997489	+	0.0708236i	$0.977437\pi$
$182$	−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	−0.893518	−	0.449027i	$-0.851771\pi$
$191$	−0.800061	+	1.38575i	−0.0578904	+	0.100269i	0.835628	+	0.549296i	$0.185104\pi$
$192$	11.6186	+	20.1240i	0.838500	+	1.45232i
$193$	−2.85669	+	1.64931i	−0.205629	+	0.118720i	−0.599278	−	0.800541i	$-0.704546\pi$
$193$	−2.85669	+	1.64931i	−0.205629	+	0.118720i	0.393649	+	0.919261i	$0.371212\pi$
$194$	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	0.0756977	−	0.997131i	$-0.475882\pi$
$197$	−10.5267	−	6.07757i	−0.749994	−	0.433009i	−0.825692	+	0.564122i	$0.809215\pi$
$198$	−7.81930	−	13.5434i	−0.555694	−	0.962490i
$199$	8.17718	−	14.1633i	0.579665	−	1.00401i	−0.415853	−	0.909432i	$-0.636517\pi$
$199$	8.17718	−	14.1633i	0.579665	−	1.00401i	0.995518	−	0.0945770i	$-0.0301499\pi$
$200$	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	0.819803	−	0.572646i	$-0.194083\pi$
$211$	−1.24958	−	2.16433i	−0.0860244	−	0.148999i	−0.905827	+	0.423647i	$0.860750\pi$
$212$	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	−0.641741	−	0.766922i	$-0.721787\pi$
$223$	−4.45662	+	2.57303i	−0.298437	+	0.172303i	0.343303	+	0.939225i	$0.388454\pi$
$224$	−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	0.134166	−	0.990959i	$-0.457164\pi$
$227$	−9.89789	−	5.71455i	−0.656946	−	0.379288i	−0.791112	+	0.611671i	$0.790498\pi$
$228$	−0.838745	−	0.484249i	−0.0555472	−	0.0320702i
$229$	−10.4386	+	6.02673i	−0.689803	+	0.398258i	−0.803538	−	0.595253i	$-0.797052\pi$
$229$	−10.4386	+	6.02673i	−0.689803	+	0.398258i	0.113735	+	0.993511i	$0.463718\pi$
$230$	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	0.263567	−	0.964641i	$-0.415101\pi$
$239$	−6.80305	−	3.92775i	−0.440053	−	0.254065i	−0.703620	+	0.710576i	$0.748434\pi$
$240$		−	27.7669i		−	1.79234i
$241$	0.640970	−	0.370064i	0.0412885	−	0.0238379i	−0.479214	−	0.877698i	$-0.659078\pi$
$241$	0.640970	−	0.370064i	0.0412885	−	0.0238379i	0.520502	+	0.853860i	$0.325745\pi$
$242$	−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	0.900701	−	0.434440i	$-0.143054\pi$
$251$	1.17419	+	2.03376i	0.0741142	+	0.128370i	−0.826587	+	0.562810i	$0.809720\pi$
$252$			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	−0.237885	−	0.971293i	$-0.576454\pi$
$257$	11.5781	−	20.0539i	0.722222	−	1.25093i	0.960107	−	0.279632i	$-0.0902124\pi$
$258$	−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	−0.674524	−	0.738253i	$-0.735651\pi$
$269$	4.95453	−	8.58150i	0.302083	−	0.523224i	0.976608	+	0.215029i	$0.0689846\pi$
$270$	−4.78216	+	8.28295i	−0.291033	+	0.504084i
$271$		−	12.9331i		−	0.785632i	−0.919617	−	0.392816i	$-0.871501\pi$
$271$		−	12.9331i		−	0.785632i	0.919617	−	0.392816i	$-0.128499\pi$
$272$	−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	$-0.883546\pi$
$281$		−	11.9938i		−	0.715489i	0.933819	−	0.357745i	$-0.116454\pi$
$282$	−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	−0.381057	−	0.924551i	$-0.624440\pi$
$293$	3.92154	−	2.26410i	0.229099	−	0.132270i	0.610156	+	0.792281i	$0.291107\pi$
$294$			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	−0.884525	−	0.466493i	$-0.845517\pi$
$307$	−16.1686	+	9.33496i	−0.922792	+	0.532774i	−0.0382675	+	0.999268i	$0.512184\pi$
$308$	−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	0.671908	−	0.740634i	$-0.265475\pi$
$313$	−5.40403	−	9.36005i	−0.305454	−	0.529062i	−0.977362	+	0.211573i	$0.932141\pi$
$314$		−	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	−0.0352971	−	0.999377i	$-0.511238\pi$
$317$	14.4669	−	8.35245i	0.812540	−	0.469120i	0.847837	+	0.530257i	$0.177904\pi$
$318$			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	0.798655	−	0.601789i	$-0.205545\pi$
$331$	12.3136	+	7.10928i	0.676818	+	0.390761i	−0.121837	+	0.992550i	$0.538878\pi$
$332$	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	0.869001	−	0.494811i	$-0.164763\pi$
$347$	0.111427	+	0.192997i	0.00598171	+	0.0103606i	−0.863019	+	0.505171i	$0.831429\pi$
$348$	−4.44971	−	7.70712i	−0.238529	−	0.413145i
$349$			13.0177i			0.696820i	0.937342	+	0.348410i	$0.113278\pi$
$349$			13.0177i			0.696820i	−0.937342	+	0.348410i	$0.886722\pi$
$350$	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	−0.376591	−	0.926380i	$-0.622904\pi$
$353$	4.46001	−	2.57499i	0.237382	−	0.137053i	0.613973	+	0.789327i	$0.289570\pi$
$354$	−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	−0.990380	−	0.138371i	$-0.955813\pi$
$359$	−30.4181	−	17.5619i	−1.60540	−	0.926880i	−0.615023	−	0.788509i	$-0.710853\pi$
$360$	−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	−0.968436	−	0.249262i	$-0.919812\pi$
$367$	−5.14087	+	8.90425i	−0.268351	+	0.464798i	0.700085	+	0.714059i	$0.253145\pi$
$368$	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	0.200700	−	0.979653i	$-0.435678\pi$
$379$	22.3775	−	12.9196i	1.14945	−	0.663638i	0.948754	+	0.316015i	$0.102345\pi$
$380$	−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	0.965699	−	0.259663i	$-0.0836114\pi$
$383$	23.9478	+	13.8263i	1.22367	+	0.706489i	0.257975	+	0.966152i	$0.416945\pi$
$384$	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	−0.993831	−	0.110908i	$-0.964624\pi$
$389$	−11.6951	−	20.2565i	−0.592965	−	1.02704i	0.400866	−	0.916137i	$-0.368709\pi$
$390$	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	−0.838935	−	0.544232i	$-0.816821\pi$
$397$	−15.6825	+	9.05431i	−0.787083	+	0.454423i	0.0518517	+	0.998655i	$0.483488\pi$
$398$	−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	$-0.910712\pi$
$401$		−	11.0876i		−	0.553687i	0.960915	−	0.276844i	$-0.0892884\pi$
$402$	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	−0.505444	−	0.862860i	$-0.668671\pi$
$409$	−0.220582	+	0.127353i	−0.0109071	+	0.00629721i	0.494537	+	0.869157i	$0.335338\pi$
$410$	−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	0.943895	−	0.330247i	$-0.107132\pi$
$421$	23.1824	+	13.3843i	1.12984	+	0.652313i	0.185945	+	0.982560i	$0.440465\pi$
$422$	−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	0.0871670	−	0.996194i	$-0.472219\pi$
$431$	20.6252	−	11.9079i	0.993479	−	0.573586i	0.906313	+	0.422608i	$0.138885\pi$
$432$	−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	−0.0471743	−	0.998887i	$-0.515022\pi$
$439$	17.6308	−	30.5375i	0.841474	−	1.45748i	0.888648	−	0.458589i	$-0.151645\pi$
$440$	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	−0.940670	−	0.339323i	$-0.889802\pi$
$443$	−3.71431	+	6.43338i	−0.176472	+	0.305659i	0.764197	+	0.644982i	$0.223135\pi$
$444$	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	$0.0581802\pi$
$449$			7.70296i			0.363525i	−0.983342	+	0.181763i	$0.941820\pi$
$450$			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	$0.0368750\pi$
$457$			4.94195i			0.231175i	−0.993297	+	0.115587i	$0.963125\pi$
$458$	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	$0.0493125\pi$
$461$			6.62597i			0.308602i	−0.988024	+	0.154301i	$0.950687\pi$
$462$	43.9202	−	25.3573i	2.04335	−	1.17973i
$463$			21.1097i			0.981052i	0.871426	+	0.490526i	$0.163195\pi$
$463$			21.1097i			0.981052i	−0.871426	+	0.490526i	$0.836805\pi$
$464$	−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	−0.154514	−	0.987991i	$-0.549381\pi$
$479$	13.6537	−	7.88296i	0.623853	−	0.360182i	0.778368	+	0.627809i	$0.216048\pi$
$480$	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	0.740977	−	0.671530i	$-0.234363\pi$
$487$	11.6939	+	6.75150i	0.529903	+	0.305940i	−0.211074	+	0.977470i	$0.567696\pi$
$488$			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	−0.548679	−	0.836033i	$-0.684869\pi$
$491$	9.96438	−	17.2588i	0.449686	−	0.778879i	0.998365	+	0.0571539i	$0.0182026\pi$
$492$		−	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	−0.632631	−	0.774453i	$-0.718025\pi$
$499$	−6.21565	+	3.58861i	−0.278251	+	0.160648i	0.354381	+	0.935101i	$0.384692\pi$
$500$		−	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	0.966906	−	0.255134i	$-0.0821195\pi$
$503$	5.88727	+	10.1971i	0.262501	+	0.454664i	−0.704405	+	0.709798i	$0.748786\pi$
$504$	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	−0.460708	−	0.887552i	$-0.652404\pi$
$509$	−32.9324	−	19.0135i	−1.45970	−	0.842761i	−0.998996	+	0.0447912i	$0.985738\pi$
$510$	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	0.576094	−	0.817383i	$-0.304576\pi$
$521$	−9.58274	−	16.5978i	−0.419827	−	0.727162i	−0.995922	+	0.0902208i	$0.971243\pi$
$522$	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	0.0451661	−	0.998979i	$-0.485618\pi$
$541$	21.6985	−	12.5276i	0.932891	−	0.538605i	0.887725	+	0.460375i	$0.152285\pi$
$542$	−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	−0.599517	−	0.800362i	$-0.704641\pi$
$547$	9.20026	−	15.9353i	0.393375	−	0.681345i	0.992892	+	0.119017i	$0.0379742\pi$
$548$	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	$0.183299\pi$
$557$			25.7036i			1.08910i	−0.838729	+	0.544549i	$0.816701\pi$
$558$	−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	0.220462	+	0.975395i	$0.429243\pi$
$563$	−17.4276	+	30.1855i	−0.734486	+	1.27217i	−0.954948	+	0.296772i	$0.904090\pi$
$564$	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	−0.921497	−	0.388386i	$-0.873033\pi$
$569$	−2.96731	+	5.13953i	−0.124396	+	0.215460i	0.797101	+	0.603846i	$0.206366\pi$
$570$	8.89973	−	5.13826i	0.372769	−	0.215218i
$571$	−13.0480	+	22.5998i	−0.546042	+	0.945773i	0.452498	+	0.891765i	$0.350533\pi$
$571$	−13.0480	+	22.5998i	−0.546042	+	0.945773i	−0.998541	+	0.0540075i	$0.982801\pi$
$572$	−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	−0.249683	−	0.968328i	$-0.580326\pi$
$577$	11.1474	−	6.43595i	0.464072	−	0.267932i	0.713755	+	0.700396i	$0.246993\pi$
$578$	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	$0.297716\pi$
$587$			38.9964i			1.60956i	−0.593576	+	0.804778i	$0.702284\pi$
$588$	−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	$0.269800\pi$
$593$			36.5125i			1.49939i	−0.661784	+	0.749695i	$0.730200\pi$
$594$	−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	−0.936971	−	0.349408i	$-0.886383\pi$
$599$	−4.06005	+	7.03221i	−0.165889	+	0.287328i	0.771082	+	0.636736i	$0.219716\pi$
$600$	−53.5453	−	30.9144i	−2.18598	−	1.26208i
$601$	−0.636150	−	1.10184i	−0.0259491	−	0.0449451i	0.852759	−	0.522304i	$-0.174927\pi$
$601$	−0.636150	−	1.10184i	−0.0259491	−	0.0449451i	−0.878708	+	0.477359i	$0.841594\pi$
$602$	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	−0.926852	−	0.375427i	$-0.877496\pi$
$607$	−3.40727	+	5.90156i	−0.138297	+	0.239537i	0.788555	+	0.614964i	$0.210829\pi$
$608$	−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	−0.215975	−	0.976399i	$-0.569293\pi$
$613$	12.9148	−	7.45637i	0.521624	−	0.301160i	0.737599	+	0.675239i	$0.235960\pi$
$614$	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	0.446890	−	0.894589i	$-0.352532\pi$
$617$	35.8948	−	20.7239i	1.44507	−	0.834313i	0.998182	+	0.0602763i	$0.0191982\pi$
$618$			25.4419i			1.02342i
$619$		−	29.9989i		−	1.20576i	−0.797833	−	0.602878i	$-0.794021\pi$
$619$		−	29.9989i		−	1.20576i	0.797833	−	0.602878i	$-0.205979\pi$
$620$	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	0.277121	−	0.960835i	$-0.410620\pi$
$631$	−10.4605	−	6.03937i	−0.416426	−	0.240424i	−0.693547	+	0.720411i	$0.743953\pi$
$632$	−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	0.384176	+	0.923260i	$0.374486\pi$
$641$	−15.3801	+	26.6392i	−0.607479	+	1.05218i	−0.991654	+	0.128924i	$0.958848\pi$
$642$	25.1178	+	14.5018i	0.991321	+	0.572339i
$643$		−	15.8255i		−	0.624097i	−0.950066	−	0.312048i	$-0.898985\pi$
$643$		−	15.8255i		−	0.624097i	0.950066	−	0.312048i	$-0.101015\pi$
$644$	−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	0.592138	−	0.805837i	$-0.298284\pi$
$661$	4.89343	+	2.82522i	0.190332	+	0.109888i	−0.401806	+	0.915725i	$0.631617\pi$
$662$	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	0.352526	+	0.935802i	$0.385323\pi$
$673$	−16.4517	+	28.4951i	−0.634165	+	1.09841i	−0.986691	+	0.162604i	$0.948011\pi$
$674$			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	−0.554168	−	0.832405i	$-0.686963\pi$
$677$	11.5473	−	20.0006i	0.443800	−	0.768684i	0.997968	+	0.0637207i	$0.0202967\pi$
$678$			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	$-0.788037\pi$
$683$		−	32.2899i		−	1.23554i	0.786360	−	0.617769i	$-0.211963\pi$
$684$			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	−0.0278378	−	0.999612i	$-0.508862\pi$
$691$	−23.8539	−	13.7721i	−0.907446	−	0.523914i	−0.879609	+	0.475698i	$0.842196\pi$
$692$	−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	−0.970315	−	0.241845i	$-0.922247\pi$
$701$	−18.3905	−	31.8534i	−0.694601	−	1.20308i	0.275714	−	0.961240i	$-0.411086\pi$
$702$	−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	$-0.994883\pi$
$709$		−	0.855978i		−	0.0321469i	0.999871	−	0.0160735i	$-0.00511656\pi$
$710$	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	0.969968	+	0.243231i	$0.0782074\pi$
$719$	18.6527	+	32.3074i	0.695629	+	1.20486i	−0.274340	+	0.961633i	$0.588459\pi$
$720$	−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	0.866504	+	0.499171i	$0.166362\pi$
$727$	23.3377	+	40.4220i	0.865546	+	1.49917i	−0.000957310		1.00000i	$0.500305\pi$
$728$	−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	0.957773	+	0.287524i	$0.0928322\pi$
$733$	45.6376	+	26.3489i	1.68566	+	0.973218i	0.727890	+	0.685694i	$0.240501\pi$
$734$	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	0.473315	−	0.880893i	$-0.343057\pi$
$739$	−1.43816	−	0.830321i	−0.0529035	−	0.0305438i	−0.526218	+	0.850349i	$0.676391\pi$
$740$	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	$0.130035\pi$
$743$			21.6565i			0.794500i	−0.917711	+	0.397250i	$0.869965\pi$
$744$	−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	0.998354	+	0.0573474i	$0.0182643\pi$
$751$	15.0407	+	26.0512i	0.548841	+	0.950621i	−0.449513	+	0.893274i	$0.648402\pi$
$752$		−	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	−0.881296	−	0.472565i	$-0.843328\pi$
$757$	−0.863766	+	1.49609i	−0.0313941	+	0.0543762i	0.849901	+	0.526942i	$0.176661\pi$
$758$	−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	−0.603745	−	0.797177i	$-0.706326\pi$
$761$	−5.93772	+	3.42814i	−0.215242	+	0.124270i	0.388503	+	0.921447i	$0.372992\pi$
$762$	−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	−0.120748	−	0.992683i	$-0.538529\pi$
$769$	18.8172	−	10.8641i	0.678567	−	0.391771i	0.799315	+	0.600912i	$0.205196\pi$
$770$	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	$0.0197011\pi$
$773$			3.43940i			0.123706i	−0.998085	+	0.0618532i	$0.980299\pi$
$774$			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	−0.116681	−	0.993169i	$-0.537225\pi$
$787$	19.2192	−	11.0962i	0.685089	−	0.395536i	0.801770	+	0.597633i	$0.203892\pi$
$788$	−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	−0.615544	−	0.788103i	$-0.711064\pi$
$797$	10.5795	−	18.3242i	0.374745	−	0.649077i	0.990289	+	0.139025i	$0.0443970\pi$
$798$			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	0.961642	−	0.274309i	$-0.0884492\pi$
$809$	6.91908	+	11.9842i	0.243262	+	0.421342i	−0.718380	+	0.695651i	$0.755116\pi$
$810$	−26.4276			−0.928572
$811$	−13.7339	−	7.92926i	−0.482262	−	0.278434i	0.239097	−	0.970996i	$-0.423149\pi$
$811$	−13.7339	−	7.92926i	−0.482262	−	0.278434i	−0.721359	+	0.692562i	$0.756482\pi$
$812$	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	$0.185695\pi$
$821$			31.5669i			1.10169i	−0.834607	+	0.550845i	$0.814305\pi$
$822$	−28.8344			−1.00571
$823$	9.62086	+	16.6638i	0.335362	+	0.580864i	0.983554	−	0.180612i	$-0.0578080\pi$
$823$	9.62086	+	16.6638i	0.335362	+	0.580864i	−0.648192	+	0.761477i	$0.724475\pi$
$824$	−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	0.313803	−	0.949488i	$-0.398397\pi$
$827$	−10.1105	−	5.83729i	−0.351576	−	0.202983i	−0.665379	+	0.746506i	$0.731730\pi$
$828$	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	$-0.904320\pi$
$839$		−	17.1523i		−	0.592163i	0.955163	−	0.296081i	$-0.0956800\pi$
$840$	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	$-0.896615\pi$
$853$		−	18.6402i		−	0.638227i	0.947717	−	0.319113i	$-0.103385\pi$
$854$	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	−0.969082	−	0.246739i	$-0.920641\pi$
$857$	−7.92928	+	13.7339i	−0.270859	+	0.469142i	0.698223	+	0.715880i	$0.253974\pi$
$858$	38.5499	−	1.44656i	1.31607	−	0.0493849i
$859$	−12.7218	+	22.0348i	−0.434062	+	0.751817i	−0.997219	−	0.0745332i	$-0.976253\pi$
$859$	−12.7218	+	22.0348i	−0.434062	+	0.751817i	0.563157	+	0.826350i	$0.309587\pi$
$860$		−	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	0.909070	−	0.416642i	$-0.136793\pi$
$863$	29.4586	+	17.0079i	1.00278	+	0.578957i	0.0937124	+	0.995599i	$0.470127\pi$
$864$		−	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	0.922794	−	0.385294i	$-0.125900\pi$
$877$	31.1102	+	17.9615i	1.05052	+	0.606516i	0.127722	+	0.991810i	$0.459233\pi$
$878$	−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	0.152207	+	0.988349i	$0.451362\pi$
$881$	−23.1467	+	40.0912i	−0.779832	+	1.35071i	−0.932038	+	0.362360i	$0.881971\pi$
$882$	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	0.994489	−	0.104841i	$-0.0334332\pi$
$887$	12.1051	+	20.9667i	0.406450	+	0.703992i	−0.588039	+	0.808832i	$0.700100\pi$
$888$	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	−0.805948	−	0.591987i	$-0.798344\pi$
$911$	−27.6368	−	47.8684i	−0.915649	−	1.58595i	−0.109702	−	0.993965i	$-0.534990\pi$
$912$	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	−0.469584	−	0.882888i	$-0.655596\pi$
$919$	16.0612	−	27.8189i	0.529812	−	0.917661i	0.999395	−	0.0347728i	$-0.0110707\pi$
$920$	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	$-0.892948\pi$
$929$		−	20.1170i		−	0.660019i	0.943978	−	0.330009i	$-0.107052\pi$
$930$	−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	0.578228	−	0.815875i	$-0.303744\pi$
$937$	−12.7785	−	22.1330i	−0.417455	−	0.723053i	−0.995683	+	0.0928226i	$0.970411\pi$
$938$			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	−0.100818	−	0.994905i	$-0.532146\pi$
$941$	−31.0696	−	17.9380i	−1.01284	−	0.584764i	−0.912022	+	0.410141i	$0.865479\pi$
$942$	−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	−0.995924	−	0.0901967i	$-0.971250\pi$
$947$	−43.5681	+	25.1541i	−1.41577	+	0.817397i	−0.419849	+	0.907594i	$0.637917\pi$
$948$	−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	0.151557	−	0.988448i	$-0.451571\pi$
$967$	33.6888	−	19.4502i	1.08336	−	0.625477i	0.931800	+	0.362972i	$0.118238\pi$
$968$	−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	−0.385139	−	0.922859i	$-0.625846\pi$
$971$	18.9037	−	32.7422i	0.606650	−	1.05075i	0.991788	−	0.127889i	$-0.0408202\pi$
$972$	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	$0.115173\pi$
$977$			22.1288i			0.707964i	−0.935252	+	0.353982i	$0.884827\pi$
$978$	−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	0.979751	−	0.200219i	$-0.0641654\pi$
$983$	40.6405	+	23.4638i	1.29623	+	0.748380i	0.316481	+	0.948599i	$0.397499\pi$
$984$	−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	0.494360	+	0.869257i	$0.335402\pi$
$997$	−15.9651	+	27.6523i	−0.505619	+	0.875757i	−0.999979	+	0.00650016i	$0.997931\pi$
$998$	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.25.11	✓	68
13.12	even	2	inner	403.2.l.c.25.24	yes	68
31.5	even	3	inner	403.2.l.c.129.11	yes	68
403.129	even	6	inner	403.2.l.c.129.24	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.11	✓	68	1.1	even	1	trivial
403.2.l.c.25.24	yes	68	13.12	even	2	inner
403.2.l.c.129.11	yes	68	31.5	even	3	inner
403.2.l.c.129.24	yes	68	403.129	even	6	inner

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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