LMFDB - Embedded newform 403.2.l.c.25.5

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			25.5
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22973i q^{2} +(-0.613568 - 1.06273i) q^{3} -2.97169 q^{4} +(-2.33602 - 1.34870i) q^{5} +(-2.36960 + 1.36809i) q^{6} +(-1.24184 + 0.716977i) q^{7} +2.16660i q^{8} +(0.747068 - 1.29396i) q^{9} +O(q^{10})$	\(q-2.22973i q^{2} +(-0.613568 - 1.06273i) q^{3} -2.97169 q^{4} +(-2.33602 - 1.34870i) q^{5} +(-2.36960 + 1.36809i) q^{6} +(-1.24184 + 0.716977i) q^{7} +2.16660i q^{8} +(0.747068 - 1.29396i) q^{9} +(-3.00724 + 5.20869i) q^{10} +(1.17120 + 0.676192i) q^{11} +(1.82333 + 3.15811i) q^{12} +(-2.61537 - 2.48191i) q^{13} +(1.59866 + 2.76897i) q^{14} +3.31008i q^{15} -1.11245 q^{16} +(3.80956 + 6.59836i) q^{17} +(-2.88518 - 1.66576i) q^{18} +(-0.731192 + 0.422154i) q^{19} +(6.94192 + 4.00792i) q^{20} +(1.52391 + 0.879828i) q^{21} +(1.50772 - 2.61145i) q^{22} +5.80603 q^{23} +(2.30251 - 1.32936i) q^{24} +(1.13799 + 1.97106i) q^{25} +(-5.53397 + 5.83156i) q^{26} -5.51492 q^{27} +(3.69036 - 2.13063i) q^{28} -10.0152 q^{29} +7.38058 q^{30} +(4.29712 - 3.54044i) q^{31} +6.81365i q^{32} -1.65956i q^{33} +(14.7125 - 8.49429i) q^{34} +3.86795 q^{35} +(-2.22005 + 3.84525i) q^{36} +(0.0209981 - 0.0121233i) q^{37} +(0.941288 + 1.63036i) q^{38} +(-1.03289 + 4.30225i) q^{39} +(2.92210 - 5.06122i) q^{40} +(-6.84346 - 3.95107i) q^{41} +(1.96178 - 3.39790i) q^{42} +(-5.73802 - 9.93855i) q^{43} +(-3.48044 - 2.00943i) q^{44} +(-3.49033 + 2.01514i) q^{45} -12.9459i q^{46} -5.04640i q^{47} +(0.682561 + 1.18223i) q^{48} +(-2.47189 + 4.28144i) q^{49} +(4.39493 - 2.53741i) q^{50} +(4.67485 - 8.09709i) q^{51} +(7.77206 + 7.37545i) q^{52} +(2.94222 - 5.09607i) q^{53} +12.2968i q^{54} +(-1.82396 - 3.15919i) q^{55} +(-1.55340 - 2.69057i) q^{56} +(0.897272 + 0.518040i) q^{57} +22.3311i q^{58} +(-10.8705 + 6.27610i) q^{59} -9.83653i q^{60} +6.44491 q^{61} +(-7.89423 - 9.58141i) q^{62} +2.14252i q^{63} +12.9677 q^{64} +(2.76220 + 9.32513i) q^{65} -3.70036 q^{66} +(-4.50382 - 2.60028i) q^{67} +(-11.3208 - 19.6083i) q^{68} +(-3.56239 - 6.17024i) q^{69} -8.62448i q^{70} +(-1.65840 - 0.957475i) q^{71} +(2.80350 + 1.61860i) q^{72} +(7.01264 + 4.04875i) q^{73} +(-0.0270316 - 0.0468200i) q^{74} +(1.39647 - 2.41876i) q^{75} +(2.17287 - 1.25451i) q^{76} -1.93926 q^{77} +(9.59285 + 2.30307i) q^{78} +(-6.00014 - 10.3925i) q^{79} +(2.59870 + 1.50036i) q^{80} +(1.14257 + 1.97899i) q^{81} +(-8.80982 + 15.2591i) q^{82} +(6.84190 + 3.95017i) q^{83} +(-4.52858 - 2.61458i) q^{84} -20.5519i q^{85} +(-22.1603 + 12.7942i) q^{86} +(6.14500 + 10.6435i) q^{87} +(-1.46504 + 2.53752i) q^{88} +9.58894i q^{89} +(4.49323 + 7.78249i) q^{90} +(5.02734 + 1.20697i) q^{91} -17.2537 q^{92} +(-6.39912 - 2.39438i) q^{93} -11.2521 q^{94} +2.27744 q^{95} +(7.24108 - 4.18064i) q^{96} -5.23299i q^{97} +(9.54644 + 5.51164i) q^{98} +(1.74993 - 1.01032i) 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 $

$2$		−	2.22973i		−	1.57666i	−0.615255	−	0.788328i	$-0.710947\pi$
$2$		−	2.22973i		−	1.57666i	0.615255	−	0.788328i	$-0.289053\pi$
$3$	−0.613568	−	1.06273i	−0.354244	−	0.613568i	0.632745	−	0.774361i	$-0.281928\pi$
$3$	−0.613568	−	1.06273i	−0.354244	−	0.613568i	−0.986988	+	0.160793i	$0.948595\pi$
$4$	−2.97169			−1.48584
$5$	−2.33602	−	1.34870i	−1.04470	−	0.603158i	−0.123539	−	0.992340i	$-0.539424\pi$
$5$	−2.33602	−	1.34870i	−1.04470	−	0.603158i	−0.921161	+	0.389182i	$0.872758\pi$
$6$	−2.36960	+	1.36809i	−0.967386	+	0.558520i
$7$	−1.24184	+	0.716977i	−0.469372	+	0.270992i	−0.715977	−	0.698124i	$-0.754018\pi$
$7$	−1.24184	+	0.716977i	−0.469372	+	0.270992i	0.246605	+	0.969116i	$0.420685\pi$
$8$			2.16660i			0.766009i
$9$	0.747068	−	1.29396i	0.249023	−	0.431320i
$10$	−3.00724	+	5.20869i	−0.950972	+	1.64713i
$11$	1.17120	+	0.676192i	0.353130	+	0.203879i	0.666063	−	0.745896i	$-0.267978\pi$
$11$	1.17120	+	0.676192i	0.353130	+	0.203879i	−0.312933	+	0.949775i	$0.601312\pi$
$12$	1.82333	+	3.15811i	0.526351	+	0.911667i
$13$	−2.61537	−	2.48191i	−0.725372	−	0.688357i
$13$	−2.61537	−	2.48191i	−0.725372	−	0.688357i
$14$	1.59866	+	2.76897i	0.427261	+	0.740038i
$15$			3.31008i			0.854659i
$16$	−1.11245			−0.278112
$17$	3.80956	+	6.59836i	0.923955	+	1.60034i	0.793233	+	0.608918i	$0.208396\pi$
$17$	3.80956	+	6.59836i	0.923955	+	1.60034i	0.130722	+	0.991419i	$0.458270\pi$
$18$	−2.88518	−	1.66576i	−0.680043	−	0.392623i
$19$	−0.731192	+	0.422154i	−0.167747	+	0.0968487i	−0.581523	−	0.813530i	$-0.697543\pi$
$19$	−0.731192	+	0.422154i	−0.167747	+	0.0968487i	0.413776	+	0.910379i	$0.364210\pi$
$20$	6.94192	+	4.00792i	1.55226	+	0.896198i
$21$	1.52391	+	0.879828i	0.332544	+	0.191994i
$22$	1.50772	−	2.61145i	0.321448	−	0.556764i
$23$	5.80603			1.21064			0.605320	−	0.795982i	$-0.293045\pi$
$23$	5.80603			1.21064			0.605320	+	0.795982i	$0.293045\pi$
$24$	2.30251	−	1.32936i	0.469999	−	0.271354i
$25$	1.13799	+	1.97106i	0.227599	+	0.394212i
$26$	−5.53397	+	5.83156i	−1.08530	+	1.14366i
$27$	−5.51492			−1.06135
$28$	3.69036	−	2.13063i	0.697413	−	0.402652i
$29$	−10.0152			−1.85977			−0.929887	−	0.367846i	$-0.880095\pi$
$29$	−10.0152			−1.85977			−0.929887	+	0.367846i	$0.880095\pi$
$30$	7.38058			1.34750
$31$	4.29712	−	3.54044i	0.771786	−	0.635883i
$31$	4.29712	−	3.54044i	0.771786	−	0.635883i
$32$			6.81365i			1.20450i
$33$		−	1.65956i		−	0.288892i
$34$	14.7125	−	8.49429i	2.52318	−	1.45676i
$35$	3.86795			0.653803
$36$	−2.22005	+	3.84525i	−0.370009	+	0.640874i
$37$	0.0209981	−	0.0121233i	0.00345206	−	0.00199305i	−0.498273	−	0.867020i	$-0.666032\pi$
$37$	0.0209981	−	0.0121233i	0.00345206	−	0.00199305i	0.501725	+	0.865027i	$0.332699\pi$
$38$	0.941288	+	1.63036i	0.152697	+	0.264479i
$39$	−1.03289	+	4.30225i	−0.165395	+	0.688911i
$40$	2.92210	−	5.06122i	0.462024	−	0.800249i
$41$	−6.84346	−	3.95107i	−1.06877	−	0.617054i	−0.140924	−	0.990020i	$-0.545007\pi$
$41$	−6.84346	−	3.95107i	−1.06877	−	0.617054i	−0.927845	+	0.372966i	$0.878341\pi$
$42$	1.96178	−	3.39790i	0.302709	−	0.524307i
$43$	−5.73802	−	9.93855i	−0.875040	−	1.51561i	−0.856720	−	0.515782i	$-0.827501\pi$
$43$	−5.73802	−	9.93855i	−0.875040	−	1.51561i	−0.0183204	−	0.999832i	$-0.505832\pi$
$44$	−3.48044	−	2.00943i	−0.524695	−	0.302933i
$45$	−3.49033	+	2.01514i	−0.520308	+	0.300400i
$46$		−	12.9459i		−	1.90876i
$47$		−	5.04640i		−	0.736094i	−0.929807	−	0.368047i	$-0.880027\pi$
$47$		−	5.04640i		−	0.736094i	0.929807	−	0.368047i	$-0.119973\pi$
$48$	0.682561	+	1.18223i	0.0985193	+	0.170640i
$49$	−2.47189	+	4.28144i	−0.353127	+	0.611634i
$50$	4.39493	−	2.53741i	0.621537	−	0.358845i
$51$	4.67485	−	8.09709i	0.654611	−	1.13382i
$52$	7.77206	+	7.37545i	1.07779	+	1.02279i
$53$	2.94222	−	5.09607i	0.404144	−	0.699999i	−0.590077	−	0.807347i	$-0.700903\pi$
$53$	2.94222	−	5.09607i	0.404144	−	0.699999i	0.994221	+	0.107348i	$0.0342360\pi$
$54$			12.2968i			1.67338i
$55$	−1.82396	−	3.15919i	−0.245943	−	0.425986i
$56$	−1.55340	−	2.69057i	−0.207582	−	0.359543i
$57$	0.897272	+	0.518040i	0.118847	+	0.0686161i
$58$			22.3311i			2.93222i
$59$	−10.8705	+	6.27610i	−1.41522	+	0.817079i	−0.995874	−	0.0907468i	$-0.971075\pi$
$59$	−10.8705	+	6.27610i	−1.41522	+	0.817079i	−0.419348	+	0.907826i	$0.637741\pi$
$60$		−	9.83653i		−	1.26989i
$61$	6.44491			0.825186			0.412593	−	0.910916i	$-0.364623\pi$
$61$	6.44491			0.825186			0.412593	+	0.910916i	$0.364623\pi$
$62$	−7.89423	−	9.58141i	−1.00257	−	1.21684i
$63$			2.14252i			0.269933i
$64$	12.9677			1.62096
$65$	2.76220	+	9.32513i	0.342609	+	1.15664i
$66$	−3.70036			−0.455483
$67$	−4.50382	−	2.60028i	−0.550229	−	0.317675i	0.198985	−	0.980002i	$-0.436235\pi$
$67$	−4.50382	−	2.60028i	−0.550229	−	0.317675i	−0.749214	+	0.662328i	$0.769569\pi$
$68$	−11.3208	−	19.6083i	−1.37285	−	2.37785i
$69$	−3.56239	−	6.17024i	−0.428862	−	0.742810i
$70$		−	8.62448i		−	1.03082i
$71$	−1.65840	−	0.957475i	−0.196815	−	0.113631i	0.398354	−	0.917232i	$-0.369582\pi$
$71$	−1.65840	−	0.957475i	−0.196815	−	0.113631i	−0.595169	+	0.803600i	$0.702915\pi$
$72$	2.80350	+	1.61860i	0.330395	+	0.190754i
$73$	7.01264	+	4.04875i	0.820767	+	0.473870i	0.850681	−	0.525682i	$-0.176190\pi$
$73$	7.01264	+	4.04875i	0.820767	+	0.473870i	−0.0299137	+	0.999552i	$0.509523\pi$
$74$	−0.0270316	−	0.0468200i	−0.00314235	−	0.00544272i
$75$	1.39647	−	2.41876i	0.161251	−	0.279294i
$76$	2.17287	−	1.25451i	0.249246	−	0.143902i
$77$	−1.93926			−0.220999
$78$	9.59285	+	2.30307i	1.08618	+	0.260771i
$79$	−6.00014	−	10.3925i	−0.675068	−	1.16925i	−0.976449	−	0.215748i	$-0.930781\pi$
$79$	−6.00014	−	10.3925i	−0.675068	−	1.16925i	0.301381	−	0.953504i	$-0.402552\pi$
$80$	2.59870	+	1.50036i	0.290543	+	0.167745i
$81$	1.14257	+	1.97899i	0.126953	+	0.219888i
$82$	−8.80982	+	15.2591i	−0.972882	+	1.68508i
$83$	6.84190	+	3.95017i	0.750996	+	0.433588i	0.826054	−	0.563591i	$-0.190581\pi$
$83$	6.84190	+	3.95017i	0.750996	+	0.433588i	−0.0750574	+	0.997179i	$0.523914\pi$
$84$	−4.52858	−	2.61458i	−0.494108	−	0.285274i
$85$		−	20.5519i		−	2.22916i
$86$	−22.1603	+	12.7942i	−2.38960	+	1.37964i
$87$	6.14500	+	10.6435i	0.658813	+	1.14110i
$88$	−1.46504	+	2.53752i	−0.156173	+	0.270500i
$89$			9.58894i			1.01643i	0.861232	+	0.508213i	$0.169694\pi$
$89$			9.58894i			1.01643i	−0.861232	+	0.508213i	$0.830306\pi$
$90$	4.49323	+	7.78249i	0.473628	+	0.820347i
$91$	5.02734	+	1.20697i	0.527008	+	0.126525i
$92$	−17.2537			−1.79882
$93$	−6.39912	−	2.39438i	−0.663558	−	0.248286i
$94$	−11.2521			−1.16057
$95$	2.27744			0.233660
$96$	7.24108	−	4.18064i	0.739040	−	0.426685i
$97$		−	5.23299i		−	0.531329i	−0.964065	−	0.265665i	$-0.914409\pi$
$97$		−	5.23299i		−	0.531329i	0.964065	−	0.265665i	$-0.0855914\pi$
$98$	9.54644	+	5.51164i	0.964336	+	0.556760i
$99$	1.74993	−	1.01032i	0.175875	−	0.101541i
$100$	−3.38176	−	5.85738i	−0.338176	−	0.585738i
$101$	−0.692750			−0.0689312			−0.0344656	−	0.999406i	$-0.510973\pi$
$101$	−0.692750			−0.0689312			−0.0344656	+	0.999406i	$0.510973\pi$
$102$	−18.0543	−	10.4237i	−1.78764	−	1.03210i
$103$	−2.65162	+	4.59275i	−0.261272	+	0.452537i	−0.966580	−	0.256364i	$-0.917475\pi$
$103$	−2.65162	+	4.59275i	−0.261272	+	0.452537i	0.705308	+	0.708901i	$0.250809\pi$
$104$	5.37730	−	5.66646i	0.527287	−	0.555642i
$105$	−2.37325	−	4.11059i	−0.231606	−	0.401153i
$106$	−11.3628	−	6.56034i	−1.10366	−	0.637197i
$107$	−0.189589	−	0.328378i	−0.0183283	−	0.0317455i	0.856716	−	0.515789i	$-0.172501\pi$
$107$	−0.189589	−	0.328378i	−0.0183283	−	0.0317455i	−0.875044	+	0.484043i	$0.839168\pi$
$108$	16.3886			1.57700
$109$		−	6.21550i		−	0.595337i	−0.954669	−	0.297669i	$-0.903791\pi$
$109$		−	6.21550i		−	0.595337i	0.954669	−	0.297669i	$-0.0962090\pi$
$110$	−7.04414	+	4.06694i	−0.671633	+	0.387767i
$111$	−0.0257675	−	0.0148769i	−0.00244574	−	0.00141205i
$112$	1.38148	−	0.797598i	0.130538	−	0.0753660i
$113$	3.91958	−	6.78891i	0.368723	−	0.638647i	−0.620643	−	0.784093i	$-0.713128\pi$
$113$	3.91958	−	6.78891i	0.368723	−	0.638647i	0.989366	+	0.145446i	$0.0464618\pi$
$114$	1.15509	−	2.00067i	0.108184	−	0.187380i
$115$	−13.5630	−	7.83060i	−1.26476	−	0.730207i
$116$	29.7620			2.76333
$117$	−5.16535	+	1.53003i	−0.477536	+	0.141451i
$118$	13.9940	+	24.2383i	1.28825	+	2.23132i
$119$	−9.46174	−	5.46274i	−0.867357	−	0.500769i
$120$	−7.17162			−0.654677
$121$	−4.58553	−	7.94237i	−0.416866	−	0.722034i
$122$		−	14.3704i		−	1.30103i
$123$			9.69701i			0.874350i
$124$	−12.7697	+	10.5211i	−1.14675	+	0.944822i
$125$			7.34777i			0.657204i
$126$	4.77725			0.425591
$127$	−8.85528	−	15.3378i	−0.785779	−	1.36101i	−0.928532	−	0.371251i	$-0.878929\pi$
$127$	−8.85528	−	15.3378i	−0.785779	−	1.36101i	0.142753	−	0.989758i	$-0.454404\pi$
$128$		−	15.2871i		−	1.35121i
$129$	−7.04134	+	12.1960i	−0.619955	+	1.07379i
$130$	20.7925	−	6.15896i	1.82362	−	0.540176i
$131$	−6.67362	−	11.5590i	−0.583077	−	1.00992i	−0.995112	−	0.0987505i	$-0.968515\pi$
$131$	−6.67362	−	11.5590i	−0.583077	−	1.00992i	0.412036	−	0.911168i	$-0.364818\pi$
$132$			4.93169i			0.429248i
$133$	0.605349	−	1.04850i	0.0524904	−	0.0909161i
$134$	−5.79792	+	10.0423i	−0.500864	+	0.867522i
$135$	12.8830	+	7.43798i	1.10879	+	0.640159i
$136$	−14.2960	+	8.25380i	−1.22587	+	0.707758i
$137$	14.2090	+	8.20357i	1.21396	+	0.700878i	0.963619	−	0.267281i	$-0.0861251\pi$
$137$	14.2090	+	8.20357i	1.21396	+	0.700878i	0.250337	+	0.968159i	$0.419458\pi$
$138$	−13.7580	+	7.94317i	−1.17116	+	0.676167i
$139$	−4.89829			−0.415468			−0.207734	−	0.978185i	$-0.566609\pi$
$139$	−4.89829			−0.415468			−0.207734	+	0.978185i	$0.566609\pi$
$140$	−11.4943			−0.971450
$141$	−5.36297	+	3.09631i	−0.451643	+	0.260756i
$142$	−2.13491	+	3.69777i	−0.179158	+	0.310310i
$143$	−1.38487	−	4.67529i	−0.115809	−	0.390968i
$144$	−0.831073	+	1.43946i	−0.0692561	+	0.119955i
$145$	23.3957	+	13.5075i	1.94291	+	1.12174i
$146$	9.02761	−	15.6363i	0.747130	−	1.29407i
$147$	6.06669			0.500372
$148$	−0.0623998	+	0.0360265i	−0.00512923	+	0.00296136i
$149$	10.2864	−	5.93888i	0.842698	−	0.486532i	−0.0154823	−	0.999880i	$-0.504928\pi$
$149$	10.2864	−	5.93888i	0.842698	−	0.486532i	0.858180	+	0.513348i	$0.171595\pi$
$150$	−5.39318	−	3.11375i	−0.440351	−	0.254237i
$151$		−	19.3282i		−	1.57290i	−0.617652	−	0.786452i	$-0.711916\pi$
$151$		−	19.3282i		−	1.57290i	0.617652	−	0.786452i	$-0.288084\pi$
$152$	−0.914638	−	1.58420i	−0.0741870	−	0.128496i
$153$	11.3840			0.920344
$154$			4.32401i			0.348439i
$155$	−14.8132	+	2.47501i	−1.18982	+	0.198798i
$156$	3.06943	−	12.7849i	0.245751	−	1.02361i
$157$	10.2447			0.817615			0.408808	−	0.912621i	$-0.365945\pi$
$157$	10.2447			0.817615			0.408808	+	0.912621i	$0.365945\pi$
$158$	−23.1725	+	13.3787i	−1.84351	+	1.06435i
$159$	−7.22100			−0.572663
$160$	9.18959	−	15.9168i	0.726501	−	1.25834i
$161$	−7.21016	+	4.16279i	−0.568240	+	0.328074i
$162$	4.41262	−	2.54763i	0.346688	−	0.200160i
$163$			10.4433i			0.817980i	0.912539	+	0.408990i	$0.134119\pi$
$163$			10.4433i			0.817980i	−0.912539	+	0.408990i	$0.865881\pi$
$164$	20.3366	+	11.7414i	1.58802	+	0.916846i
$165$	−2.23825	+	3.87676i	−0.174247	+	0.301805i
$166$	8.80782	−	15.2556i	0.683619	−	1.18406i
$167$	16.2737	−	9.39565i	1.25930	−	0.727057i	0.286362	−	0.958122i	$-0.407554\pi$
$167$	16.2737	−	9.39565i	1.25930	−	0.727057i	0.972938	+	0.231064i	$0.0742208\pi$
$168$	−1.90624	+	3.30170i	−0.147069	+	0.254732i
$169$	0.680292	+	12.9822i	0.0523301	+	0.998630i
$170$	−45.8251			−3.51462
$171$			1.26151i			0.0964701i
$172$	17.0516	+	29.5343i	1.30017	+	2.25197i
$173$	−1.28786	+	2.23063i	−0.0979140	+	0.169592i	−0.910821	−	0.412801i	$-0.864550\pi$
$173$	−1.28786	+	2.23063i	−0.0979140	+	0.169592i	0.812907	+	0.582393i	$0.197884\pi$
$174$	23.7320	−	13.7017i	1.79912	−	1.03872i
$175$	−2.82641	−	1.63183i	−0.213657	−	0.123355i
$176$	−1.30289	−	0.752227i	−0.0982094	−	0.0567012i
$177$	13.3396	+	7.70163i	1.00267	+	0.578890i
$178$	21.3807			1.60255
$179$	5.45316	+	9.44515i	0.407588	+	0.705964i	0.994619	−	0.103601i	$-0.0330365\pi$
$179$	5.45316	+	9.44515i	0.407588	+	0.705964i	−0.587031	+	0.809565i	$0.699703\pi$
$180$	10.3722	−	5.98838i	0.773097	−	0.446348i
$181$	−4.21253	+	7.29632i	−0.313115	+	0.542331i	−0.979035	−	0.203692i	$-0.934706\pi$
$181$	−4.21253	+	7.29632i	−0.313115	+	0.542331i	0.665920	+	0.746023i	$0.268039\pi$
$182$	2.69122	−	11.2096i	0.199487	−	0.830911i
$183$	−3.95439	−	6.84920i	−0.292317	−	0.506308i
$184$			12.5793i			0.927361i
$185$	−0.0654026			−0.00480850
$186$	−5.33882	+	14.2683i	−0.391461	+	1.04620i
$187$			10.3040i			0.753502i
$188$			14.9963i			1.09372i
$189$	6.84865	−	3.95407i	0.498166	−	0.287616i
$190$		−	5.07807i		−	0.368402i
$191$	0.912194	−	1.57997i	0.0660040	−	0.114322i	−0.831135	−	0.556071i	$-0.812308\pi$
$191$	0.912194	−	1.57997i	0.0660040	−	0.114322i	0.897139	+	0.441749i	$0.145642\pi$
$192$	−7.95657	−	13.7812i	−0.574216	−	0.994571i
$193$	23.1356	−	13.3573i	1.66534	−	0.961482i	0.695234	−	0.718783i	$-0.255301\pi$
$193$	23.1356	−	13.3573i	1.66534	−	0.961482i	0.970102	−	0.242699i	$-0.0780327\pi$
$194$	−11.6681			−0.837724
$195$	8.21531	−	8.65708i	0.588310	−	0.619946i
$196$	7.34568	−	12.7231i	0.524691	−	0.908792i
$197$	−2.29398	−	1.32443i	−0.163440	−	0.0943618i	0.416049	−	0.909342i	$-0.363414\pi$
$197$	−2.29398	−	1.32443i	−0.163440	−	0.0943618i	−0.579489	+	0.814980i	$0.696748\pi$
$198$	−2.25274	−	3.90187i	−0.160096	−	0.277294i
$199$	6.56951	−	11.3787i	0.465700	−	0.806617i	−0.533533	−	0.845780i	$-0.679136\pi$
$199$	6.56951	−	11.3787i	0.465700	−	0.806617i	0.999233	+	0.0391630i	$0.0124692\pi$
$200$	−4.27050	+	2.46558i	−0.301970	+	0.174343i
$201$			6.38180i			0.450137i
$202$			1.54465i			0.108681i
$203$	12.4373	−	7.18066i	0.872925	−	0.503984i
$204$	−13.8922	+	24.0620i	−0.972649	+	1.68468i
$205$	10.6576	+	18.4596i	0.744362	+	1.28927i
$206$	10.2406	+	5.91240i	0.713495	+	0.411936i
$207$	4.33750	−	7.51277i	0.301477	−	0.522173i
$208$	2.90946	+	2.76099i	0.201734	+	0.191440i
$209$	−1.14183			−0.0789818
$210$	−9.16551	+	5.29171i	−0.632480	+	0.365163i
$211$	−4.92402	−	8.52865i	−0.338983	−	0.587137i	0.645258	−	0.763964i	$-0.276750\pi$
$211$	−4.92402	−	8.52865i	−0.338983	−	0.587137i	−0.984242	+	0.176828i	$0.943416\pi$
$212$	−8.74335	+	15.1439i	−0.600496	+	1.04009i
$213$			2.34990i			0.161013i
$214$	−0.732194	+	0.422732i	−0.0500518	+	0.0288974i
$215$			30.9555i			2.11115i
$216$		−	11.9486i		−	0.813001i
$217$	−2.79792	+	7.47761i	−0.189935	+	0.507613i
$218$	−13.8589			−0.938642
$219$		−	9.93673i		−	0.671462i
$220$	5.42024	+	9.38814i	0.365433	+	0.632948i
$221$	6.41309	−	26.7121i	0.431391	−	1.79685i
$222$	−0.0331714	+	0.0574546i	−0.00222632	+	0.00385610i
$223$	6.57720	−	3.79735i	0.440442	−	0.254289i	−0.263343	−	0.964702i	$-0.584825\pi$
$223$	6.57720	−	3.79735i	0.440442	−	0.254289i	0.703785	+	0.710413i	$0.251492\pi$
$224$	−4.88523	−	8.46147i	−0.326408	−	0.565356i
$225$	3.40063			0.226709
$226$	−15.1374	−	8.73960i	−1.00693	−	0.581349i
$227$	10.0912	+	5.82615i	0.669776	+	0.386695i	0.795992	−	0.605308i	$-0.206950\pi$
$227$	10.0912	+	5.82615i	0.669776	+	0.386695i	−0.126216	+	0.992003i	$0.540283\pi$
$228$	−2.66641	−	1.53945i	−0.176587	−	0.101953i
$229$	−11.2380	+	6.48829i	−0.742631	+	0.428758i	−0.823025	−	0.568005i	$-0.807715\pi$
$229$	−11.2380	+	6.48829i	−0.742631	+	0.428758i	0.0803942	+	0.996763i	$0.474382\pi$
$230$	−17.4601	+	30.2418i	−1.15129	+	1.99408i
$231$	1.18987	+	2.06091i	0.0782874	+	0.135598i
$232$		−	21.6989i		−	1.42460i
$233$	18.9837			1.24366			0.621831	−	0.783152i	$-0.286389\pi$
$233$	18.9837			1.24366			0.621831	+	0.783152i	$0.286389\pi$
$234$	3.41155	+	11.5173i	0.223020	+	0.752911i
$235$	−6.80609	+	11.7885i	−0.443981	+	0.768997i
$236$	32.3038	−	18.6506i	2.10280	−	1.21405i
$237$	−7.36299	+	12.7531i	−0.478277	+	0.828401i
$238$	−12.1804	+	21.0971i	−0.789540	+	1.36752i
$239$	−10.2691	−	5.92889i	−0.664255	−	0.383508i	0.129641	−	0.991561i	$-0.458617\pi$
$239$	−10.2691	−	5.92889i	−0.664255	−	0.383508i	−0.793896	+	0.608053i	$0.791951\pi$
$240$		−	3.68229i		−	0.237691i
$241$	−11.5118	+	6.64633i	−0.741539	+	0.428128i	−0.822629	−	0.568579i	$-0.807493\pi$
$241$	−11.5118	+	6.64633i	−0.741539	+	0.428128i	0.0810896	+	0.996707i	$0.474160\pi$
$242$	−17.7093	+	10.2245i	−1.13840	+	0.657255i
$243$	−6.87028	+	11.8997i	−0.440729	+	0.763365i
$244$	−19.1523			−1.22610
$245$	11.5488	−	6.66768i	0.737823	−	0.425982i
$246$	21.6217			1.37855
$247$	2.96008	+	0.710661i	0.188345	+	0.0452183i
$248$	7.67073	+	9.31014i	0.487092	+	0.591195i
$249$		−	9.69480i		−	0.614383i
$250$	16.3835			1.03618
$251$	−7.70363	−	13.3431i	−0.486249	−	0.842208i	0.513626	−	0.858014i	$-0.328302\pi$
$251$	−7.70363	−	13.3431i	−0.486249	−	0.842208i	−0.999875	+	0.0158061i	$0.994969\pi$
$252$		−	6.36691i		−	0.401078i
$253$	6.80001	+	3.92599i	0.427513	+	0.246825i
$254$	−34.1991	+	19.7449i	−2.14584	+	1.23890i
$255$	−21.8411	+	12.6100i	−1.36774	+	0.789667i
$256$	−8.15078			−0.509424
$257$	−3.82346	+	6.62242i	−0.238501	+	0.413095i	−0.960284	−	0.279024i	$-0.909989\pi$
$257$	−3.82346	+	6.62242i	−0.238501	+	0.413095i	0.721784	+	0.692119i	$0.243323\pi$
$258$	27.1937	+	15.7003i	1.69300	+	0.977456i
$259$	−0.0173842	+	0.0301103i	−0.00108020	+	0.00187096i
$260$	−8.20840	−	27.7114i	−0.509063	−	1.71859i
$261$	−7.48203	+	12.9593i	−0.463126	+	0.802158i
$262$	−25.7735	+	14.8804i	−1.59229	+	0.919311i
$263$	7.81272			0.481753			0.240877	−	0.970556i	$-0.422565\pi$
$263$	7.81272			0.481753			0.240877	+	0.970556i	$0.422565\pi$
$264$	3.59560			0.221294
$265$	−13.7462	+	7.93634i	−0.844419	+	0.487526i
$266$	−2.33786	−	1.34976i	−0.143343	−	0.0827593i
$267$	10.1905	−	5.88347i	0.623646	−	0.360062i
$268$	13.3839	+	7.72722i	0.817554	+	0.472015i
$269$	1.40551	−	2.43442i	0.0856956	−	0.148429i	−0.819992	−	0.572375i	$-0.806022\pi$
$269$	1.40551	−	2.43442i	0.0856956	−	0.148429i	0.905687	+	0.423946i	$0.139355\pi$
$270$	16.5847	−	28.7255i	1.00931	−	1.74818i
$271$		−	18.4025i		−	1.11787i	−0.829212	−	0.558935i	$-0.811210\pi$
$271$		−	18.4025i		−	1.11787i	0.829212	−	0.558935i	$-0.188790\pi$
$272$	−4.23794	−	7.34032i	−0.256963	−	0.445072i
$273$	−1.80193	−	6.08327i	−0.109058	−	0.368176i
$274$	18.2917	−	31.6822i	1.10504	−	1.91399i
$275$			3.07800i			0.185611i
$276$	10.5863	+	18.3360i	0.637221	+	1.10370i
$277$	−1.98129			−0.119044			−0.0595220	−	0.998227i	$-0.518958\pi$
$277$	−1.98129			−0.119044			−0.0595220	+	0.998227i	$0.518958\pi$
$278$			10.9219i			0.655050i
$279$	−1.37095	−	8.20526i	−0.0820767	−	0.491236i
$280$			8.38031i			0.500819i
$281$			3.12866i			0.186640i	0.995636	+	0.0933201i	$0.0297480\pi$
$281$			3.12866i			0.186640i	−0.995636	+	0.0933201i	$0.970252\pi$
$282$	6.90393	+	11.9580i	0.411123	+	0.712086i
$283$	10.9730			0.652279			0.326139	−	0.945322i	$-0.394252\pi$
$283$	10.9730			0.652279			0.326139	+	0.945322i	$0.394252\pi$
$284$	4.92823	+	2.84532i	0.292437	+	0.168839i
$285$	−1.39736	−	2.42030i	−0.0827726	−	0.143366i
$286$	−10.4246	+	3.08788i	−0.616421	+	0.182590i
$287$	11.3313			0.668867
$288$	8.81660	+	5.09026i	0.519523	+	0.299947i
$289$	−20.5256	+	35.5513i	−1.20739	+	2.09125i
$290$	30.1181	−	52.1660i	1.76859	−	3.06329i
$291$	−5.56126	+	3.21079i	−0.326007	+	0.188220i
$292$	−20.8394	−	12.0316i	−1.21953	−	0.704097i
$293$	−9.21064	+	5.31777i	−0.538091	+	0.310667i	−0.744305	−	0.667840i	$-0.767219\pi$
$293$	−9.21064	+	5.31777i	−0.538091	+	0.310667i	0.206214	+	0.978507i	$0.433886\pi$
$294$		−	13.5271i		−	0.788914i
$295$	33.8584			1.97131
$296$	0.0262662	+	0.0454945i	0.00152669	+	0.00264431i
$297$	−6.45906	−	3.72914i	−0.374793	−	0.216387i
$298$	−13.2421	−	22.9360i	−0.767094	−	1.32864i
$299$	−15.1849	−	14.4100i	−0.878165	−	0.833352i
$300$	−4.14988	+	7.18780i	−0.239593	+	0.414988i
$301$	14.2514	+	8.22806i	0.821438	+	0.474258i
$302$	−43.0965			−2.47993
$303$	0.425050	+	0.736207i	0.0244185	+	0.0422940i
$304$	0.813411	−	0.469623i	0.0466523	−	0.0269347i
$305$	−15.0554	−	8.69226i	−0.862071	−	0.497717i
$306$		−	25.3833i		−	1.45107i
$307$	−7.19715	+	4.15528i	−0.410763	+	0.237154i	−0.691118	−	0.722742i	$-0.742881\pi$
$307$	−7.19715	+	4.15528i	−0.410763	+	0.237154i	0.280354	+	0.959897i	$0.409548\pi$
$308$	5.76286			0.328370
$309$	6.50781			0.370216
$310$	5.51861	+	33.0293i	0.313436	+	1.87594i
$311$	−8.37729			−0.475033			−0.237516	−	0.971384i	$-0.576333\pi$
$311$	−8.37729			−0.475033			−0.237516	+	0.971384i	$0.576333\pi$
$312$	−9.32126	−	2.23786i	−0.527712	−	0.126694i
$313$	−14.1080	−	24.4358i	−0.797432	−	1.38119i	−0.921283	−	0.388893i	$-0.872858\pi$
$313$	−14.1080	−	24.4358i	−0.797432	−	1.38119i	0.123851	−	0.992301i	$-0.460476\pi$
$314$		−	22.8429i		−	1.28910i
$315$	2.88963	−	5.00498i	0.162812	−	0.281999i
$316$	17.8305	+	30.8834i	1.00305	+	1.73733i
$317$	−6.60773	+	3.81498i	−0.371127	+	0.214270i	−0.673951	−	0.738776i	$-0.735404\pi$
$317$	−6.60773	+	3.81498i	−0.371127	+	0.214270i	0.302824	+	0.953047i	$0.402071\pi$
$318$			16.1009i			0.902892i
$319$	−11.7298	−	6.77219i	−0.656741	−	0.379170i
$320$	−30.2928	−	17.4896i	−1.69342	−	0.977696i
$321$	−0.232652	+	0.402965i	−0.0129854	+	0.0224913i
$322$	9.28188	+	16.0767i	0.517259	+	0.895919i
$323$	−5.57104	−	3.21644i	−0.309981	−	0.178968i
$324$	−3.39537	−	5.88095i	−0.188632	−	0.326720i
$325$	1.91572	−	7.97944i	0.106265	−	0.442620i
$326$	23.2856			1.28967
$327$	−6.60541	+	3.81363i	−0.365280	+	0.210894i
$328$	8.56040	−	14.8270i	0.472669	−	0.818687i
$329$	3.61815	+	6.26683i	0.199475	+	0.345501i
$330$	8.64412	+	4.99069i	0.475843	+	0.274728i
$331$	−10.9320	−	6.31162i	−0.600879	−	0.346918i	0.168508	−	0.985700i	$-0.446105\pi$
$331$	−10.9320	−	6.31162i	−0.600879	−	0.346918i	−0.769387	+	0.638782i	$0.779438\pi$
$332$	−20.3320	−	11.7387i	−1.11586	−	0.644244i
$333$		−	0.0362276i		−	0.00198526i
$334$	−20.9497	−	36.2860i	−1.14632	−	1.98548i
$335$	7.01400	+	12.1486i	0.383216	+	0.663750i
$336$	−1.69527	−	0.978762i	−0.0924843	−	0.0533958i
$337$	−25.3673			−1.38185			−0.690923	−	0.722928i	$-0.742796\pi$
$337$	−25.3673			−1.38185			−0.690923	+	0.722928i	$0.742796\pi$
$338$	28.9468	−	1.51687i	1.57450	−	0.0825066i
$339$	−9.61972			−0.522471
$340$			61.0737i			3.31219i
$341$	7.42680	−	1.24088i	0.402184	−	0.0671977i
$342$	2.81283			0.152100
$343$		−	17.1268i		−	0.924762i
$344$	21.5329	−	12.4320i	1.16097	−	0.670289i
$345$			19.2184i			1.03468i
$346$	4.97371	+	2.87157i	0.267388	+	0.154377i
$347$	3.72055	+	6.44418i	0.199730	+	0.345942i	0.948441	−	0.316955i	$-0.102660\pi$
$347$	3.72055	+	6.44418i	0.199730	+	0.345942i	−0.748711	+	0.662896i	$0.769327\pi$
$348$	−18.2610	−	31.6290i	−0.978894	−	1.69549i
$349$		−	9.40117i		−	0.503233i	−0.967827	−	0.251617i	$-0.919038\pi$
$349$		−	9.40117i		−	0.503233i	0.967827	−	0.251617i	$-0.0809622\pi$
$350$	−3.63854	+	6.30213i	−0.194488	+	0.336863i
$351$	14.4235	+	13.6875i	0.769871	+	0.730585i
$352$	−4.60733	+	7.98014i	−0.245572	+	0.425343i
$353$	−11.2505	+	6.49548i	−0.598803	+	0.345719i	−0.768571	−	0.639765i	$-0.779032\pi$
$353$	−11.2505	+	6.49548i	−0.598803	+	0.345719i	0.169767	+	0.985484i	$0.445698\pi$
$354$	17.1725	−	29.7437i	0.912710	−	1.58086i
$355$	2.58270	+	4.47336i	0.137075	+	0.237421i
$356$		−	28.4953i		−	1.51025i
$357$			13.4071i			0.709576i
$358$	21.0601	−	12.1591i	1.11306	−	0.642627i
$359$	4.09479	+	2.36413i	0.216115	+	0.124774i	0.604150	−	0.796871i	$-0.293513\pi$
$359$	4.09479	+	2.36413i	0.216115	+	0.124774i	−0.388035	+	0.921645i	$0.626846\pi$
$360$	−4.36601	−	7.56216i	−0.230109	−	0.398561i
$361$	−9.14357	+	15.8371i	−0.481241	+	0.833533i
$362$	16.2688	+	9.39280i	0.855069	+	0.493674i
$363$	−5.62707	+	9.74637i	−0.295345	+	0.511552i
$364$	−14.9397	−	3.58675i	−0.783052	−	0.187997i
$365$	−10.9211	−	18.9159i	−0.571637	−	0.990104i
$366$	−15.2719	+	8.81721i	−0.798273	+	0.460883i
$367$	0.534967	−	0.926590i	0.0279250	−	0.0483676i	−0.851725	−	0.523989i	$-0.824443\pi$
$367$	0.534967	−	0.926590i	0.0279250	−	0.0483676i	0.879650	+	0.475621i	$0.157777\pi$
$368$	−6.45889			−0.336693
$369$	−10.2251	+	5.90345i	−0.532296	+	0.307321i
$370$			0.145830i			0.00758134i
$371$			8.43801i			0.438079i
$372$	19.0162	+	7.11535i	0.985943	+	0.368914i
$373$	26.8258			1.38899			0.694493	−	0.719499i	$-0.255629\pi$
$373$	26.8258			1.38899			0.694493	+	0.719499i	$0.255629\pi$
$374$	22.9751			1.18801
$375$	7.80870	−	4.50836i	0.403240	−	0.232810i
$376$	10.9335			0.563854
$377$	26.1934	+	24.8567i	1.34903	+	1.28019i
$378$	−8.81650	−	15.2706i	−0.453472	−	0.785436i
$379$	7.66726	−	4.42670i	0.393841	−	0.227384i	−0.289982	−	0.957032i	$-0.593649\pi$
$379$	7.66726	−	4.42670i	0.393841	−	0.227384i	0.683823	+	0.729648i	$0.260316\pi$
$380$	−6.76783			−0.347183
$381$	−10.8666	+	18.8216i	−0.556715	+	0.964258i
$382$	−3.52289	−	2.03394i	−0.180247	−	0.104066i
$383$	−13.9865	−	8.07511i	−0.714677	−	0.412619i	0.0981133	−	0.995175i	$-0.468719\pi$
$383$	−13.9865	−	8.07511i	−0.714677	−	0.412619i	−0.812790	+	0.582556i	$0.802053\pi$
$384$	−16.2461	+	9.37971i	−0.829057	+	0.478656i
$385$	4.53014	+	2.61548i	0.230877	+	0.133297i
$386$	−29.7832	−	51.5861i	−1.51593	−	2.62566i
$387$	−17.1468			−0.871620
$388$			15.5508i			0.789473i
$389$	1.63417	+	2.83047i	0.0828559	+	0.143511i	0.904476	−	0.426525i	$-0.140263\pi$
$389$	1.63417	+	2.83047i	0.0828559	+	0.143511i	−0.821620	+	0.570036i	$0.806929\pi$
$390$	−19.3029	−	18.3179i	−0.977442	−	0.927563i
$391$	22.1184	+	38.3102i	1.11858	+	1.93743i
$392$	−9.27616	−	5.35559i	−0.468517	−	0.270498i
$393$	−8.18944	+	14.1845i	−0.413102	+	0.715514i
$394$	−2.95312	+	5.11496i	−0.148776	+	0.257688i
$395$			32.3696i			1.62869i
$396$	−5.20025	+	3.00236i	−0.261322	+	0.150874i
$397$	7.27323	−	4.19920i	0.365033	−	0.210752i	−0.306253	−	0.951950i	$-0.599075\pi$
$397$	7.27323	−	4.19920i	0.365033	−	0.210752i	0.671286	+	0.741198i	$0.265742\pi$
$398$	−25.3715	−	14.6482i	−1.27176	−	0.734249i
$399$	−1.48569			−0.0743776
$400$	−1.26596	−	2.19270i	−0.0632978	−	0.109635i
$401$		−	34.0952i		−	1.70264i	−0.524651	−	0.851318i	$-0.675804\pi$
$401$		−	34.0952i		−	1.70264i	0.524651	−	0.851318i	$-0.324196\pi$
$402$	14.2297			0.709711
$403$	−20.0256	−	1.40549i	−0.997546	−	0.0700122i
$404$	2.05864			0.102421
$405$		−	6.16396i		−	0.306290i
$406$	−16.0109	−	27.7317i	−0.794609	−	1.37630i
$407$	0.0327906			0.00162537
$408$	17.5431	+	10.1285i	0.868515	+	0.501438i
$409$	20.3528	−	11.7507i	1.00638	−	0.581033i	0.0962498	−	0.995357i	$-0.469315\pi$
$409$	20.3528	−	11.7507i	1.00638	−	0.581033i	0.910130	+	0.414324i	$0.135982\pi$
$410$	41.1598	−	23.7636i	2.03274	−	1.17360i
$411$		−	20.1338i		−	0.993126i
$412$	7.87980	−	13.6482i	0.388210	−	0.672399i
$413$	8.99964	−	15.5878i	0.442843	−	0.767027i
$414$	−16.7514	−	9.67144i	−0.823288	−	0.475325i
$415$	−10.6552	−	18.4554i	−0.523044	−	0.905939i
$416$	16.9108	−	17.8202i	0.829122	−	0.873707i
$417$	3.00544	+	5.20557i	0.147177	+	0.254918i
$418$			2.54596i			0.124527i
$419$	37.7384			1.84364			0.921821	−	0.387616i	$-0.126701\pi$
$419$	37.7384			1.84364			0.921821	+	0.387616i	$0.126701\pi$
$420$	7.05257	+	12.2154i	0.344130	+	0.596051i
$421$	15.2686	+	8.81532i	0.744145	+	0.429632i	0.823574	−	0.567208i	$-0.191977\pi$
$421$	15.2686	+	8.81532i	0.744145	+	0.429632i	−0.0794296	+	0.996840i	$0.525310\pi$
$422$	−19.0166	+	10.9792i	−0.925712	+	0.534460i
$423$	−6.52985	−	3.77001i	−0.317492	−	0.183304i
$424$	11.0411	+	6.37461i	0.536205	+	0.309578i
$425$	−8.67051	+	15.0178i	−0.420582	+	0.728469i
$426$	5.23965			0.253862
$427$	−8.00355	+	4.62085i	−0.387319	+	0.223619i
$428$	0.563400	+	0.975837i	0.0272330	+	0.0471689i
$429$	−4.11887	+	4.34035i	−0.198861	+	0.209554i
$430$	69.0224			3.32856
$431$	8.95150	−	5.16815i	0.431179	−	0.248941i	−0.268670	−	0.963232i	$-0.586584\pi$
$431$	8.95150	−	5.16815i	0.431179	−	0.248941i	0.699849	+	0.714291i	$0.253251\pi$
$432$	6.13505			0.295173
$433$	−13.7230			−0.659485			−0.329742	−	0.944071i	$-0.606962\pi$
$433$	−13.7230			−0.659485			−0.329742	+	0.944071i	$0.606962\pi$
$434$	16.6730	+	6.23861i	0.800331	+	0.299463i
$435$		−	33.1511i		−	1.58947i
$436$			18.4705i			0.884578i
$437$	−4.24532	+	2.45103i	−0.203081	+	0.117249i
$438$	−22.1562			−1.05866
$439$	−4.51215	+	7.81528i	−0.215353	+	0.373003i	−0.953382	−	0.301767i	$-0.902424\pi$
$439$	−4.51215	+	7.81528i	−0.215353	+	0.373003i	0.738028	+	0.674770i	$0.235757\pi$
$440$	6.84471	−	3.95180i	0.326309	−	0.188394i
$441$	3.69334	+	6.39705i	0.175873	+	0.304621i
$442$	−59.5607	−	14.2995i	−2.83302	−	0.680156i
$443$	0.523289	−	0.906363i	0.0248622	−	0.0430626i	−0.853327	−	0.521377i	$-0.825419\pi$
$443$	0.523289	−	0.906363i	0.0248622	−	0.0430626i	0.878189	+	0.478314i	$0.158752\pi$
$444$	0.0765730	+	0.0442095i	0.00363399	+	0.00209809i
$445$	12.9326	−	22.3999i	0.613065	−	1.06186i
$446$	−8.46705	−	14.6654i	−0.400926	−	0.694425i
$447$	−12.6229	−	7.28781i	−0.597041	−	0.344702i
$448$	−16.1038	+	9.29754i	−0.760834	+	0.439268i
$449$			16.6813i			0.787238i	0.919274	+	0.393619i	$0.128777\pi$
$449$			16.6813i			0.787238i	−0.919274	+	0.393619i	$0.871223\pi$
$450$		−	7.58249i		−	0.357442i
$451$	−5.34337	−	9.25498i	−0.251609	−	0.435800i
$452$	−11.6478	+	20.1745i	−0.547865	+	0.948930i
$453$	−20.5406	+	11.8591i	−0.965083	+	0.557191i
$454$	12.9907	−	22.5006i	0.609685	−	1.05601i
$455$	−10.1161	−	9.59989i	−0.474251	−	0.450050i
$456$	−1.12239	+	1.94403i	−0.0525605	+	0.0910375i
$457$			23.3381i			1.09171i	0.837879	+	0.545856i	$0.183795\pi$
$457$			23.3381i			1.09171i	−0.837879	+	0.545856i	$0.816205\pi$
$458$	14.4671	+	25.0578i	0.676004	+	1.17087i
$459$	−21.0094	−	36.3894i	−0.980636	−	1.69851i
$460$	40.3050	+	23.2701i	1.87923	+	1.08497i
$461$			27.4931i			1.28048i	0.768175	+	0.640240i	$0.221165\pi$
$461$			27.4931i			1.28048i	−0.768175	+	0.640240i	$0.778835\pi$
$462$	4.59526	−	2.65308i	0.213791	−	0.123432i
$463$			28.3883i			1.31932i	0.751565	+	0.659659i	$0.229299\pi$
$463$			28.3883i			1.31932i	−0.751565	+	0.659659i	$0.770701\pi$
$464$	11.1414			0.517225
$465$	11.7192	+	14.2238i	0.543463	+	0.659614i
$466$		−	42.3284i		−	1.96083i
$467$	8.29159			0.383689			0.191845	−	0.981425i	$-0.438553\pi$
$467$	8.29159			0.383689			0.191845	+	0.981425i	$0.438553\pi$
$468$	15.3498	−	4.54677i	0.709545	−	0.210174i
$469$	7.45736			0.344349
$470$	26.2851	+	15.1757i	1.21244	+	0.700005i
$471$	−6.28582	−	10.8874i	−0.289635	−	0.501663i
$472$	−13.5978	−	23.5521i	−0.625890	−	1.08407i
$473$		−	15.5200i		−	0.713611i
$474$	28.4359	+	16.4175i	1.30610	+	0.754079i
$475$	−1.66418	−	0.960815i	−0.0763579	−	0.0440852i
$476$	28.1174	+	16.2336i	1.28876	+	0.744064i
$477$	−4.39607	−	7.61422i	−0.201282	−	0.348631i
$478$	−13.2198	+	22.8974i	−0.604660	+	1.04730i
$479$	2.87951	−	1.66249i	0.131568	−	0.0759609i	−0.432771	−	0.901504i	$-0.642464\pi$
$479$	2.87951	−	1.66249i	0.131568	−	0.0759609i	0.564339	+	0.825543i	$0.309131\pi$
$480$	−22.5537			−1.02943
$481$	−0.0850065	−	0.0204085i	−0.00387596	−	0.000930548i
$482$	14.8195	+	25.6681i	0.675010	+	1.16915i
$483$	8.84785	+	5.10831i	0.402591	+	0.232436i
$484$	13.6268	+	23.6022i	0.619398	+	1.07283i
$485$	−7.05774	+	12.2244i	−0.320475	+	0.555080i
$486$	26.5331	+	15.3189i	1.20356	+	0.694878i
$487$	−29.3104	−	16.9224i	−1.32818	−	0.766825i	−0.343162	−	0.939276i	$-0.611498\pi$
$487$	−29.3104	−	16.9224i	−1.32818	−	0.766825i	−0.985018	+	0.172451i	$0.944831\pi$
$488$			13.9635i			0.632100i
$489$	11.0984	−	6.40765i	0.501886	−	0.289764i
$490$	−14.8671	−	25.7506i	−0.671628	−	1.16329i
$491$	10.9019	−	18.8827i	0.491997	−	0.852164i	−0.507961	−	0.861380i	$-0.669600\pi$
$491$	10.9019	−	18.8827i	0.491997	−	0.852164i	0.999958	+	0.00921654i	$0.00293376\pi$
$492$		−	28.8165i		−	1.29915i
$493$	−38.1535	−	66.0838i	−1.71835	−	2.97627i
$494$	1.58458	−	6.60017i	0.0712937	−	0.296956i
$495$	−5.45050			−0.244982
$496$	−4.78032	+	3.93855i	−0.214643	+	0.176846i
$497$	2.74595			0.123173
$498$	−21.6168			−0.968671
$499$	11.1752	−	6.45201i	0.500271	−	0.288832i	−0.228554	−	0.973531i	$-0.573400\pi$
$499$	11.1752	−	6.45201i	0.500271	−	0.288832i	0.728826	+	0.684699i	$0.240067\pi$
$500$		−	21.8353i		−	0.976503i
$501$	−19.9701	−	11.5297i	−0.892198	−	0.515111i
$502$	−29.7515	+	17.1770i	−1.32787	+	0.766647i
$503$	7.45166	+	12.9066i	0.332253	+	0.575479i	0.982953	−	0.183856i	$-0.0588579\pi$
$503$	7.45166	+	12.9066i	0.332253	+	0.575479i	−0.650700	+	0.759335i	$0.725525\pi$
$504$	−4.64199			−0.206771
$505$	1.61828	+	0.934314i	0.0720125	+	0.0415764i
$506$	8.75388	−	15.1622i	0.389157	−	0.674041i
$507$	13.3792	−	8.68842i	0.594190	−	0.385866i
$508$	26.3151	+	45.5792i	1.16755	+	2.02225i
$509$	−23.7551	−	13.7150i	−1.05293	−	0.607907i	−0.129459	−	0.991585i	$-0.541324\pi$
$509$	−23.7551	−	13.7150i	−1.05293	−	0.607907i	−0.923467	+	0.383678i	$0.874657\pi$
$510$	28.1168	+	48.6997i	1.24503	+	2.15646i
$511$	−11.6114			−0.513660
$512$		−	12.4003i		−	0.548020i
$513$	4.03246	−	2.32814i	0.178038	−	0.102790i
$514$	14.7662	+	8.52527i	0.651309	+	0.376033i
$515$	12.3885	−	7.15250i	0.545902	−	0.315177i
$516$	20.9247	−	36.2426i	0.921156	−	1.59549i
$517$	3.41233	−	5.91034i	0.150074	−	0.259936i
$518$	0.0671378	+	0.0387620i	0.00294986	+	0.00170310i
$519$	3.16075			0.138742
$520$	−20.2038	+	5.98458i	−0.885997	+	0.262441i
$521$	19.2009	+	33.2570i	0.841208	+	1.45702i	0.888874	+	0.458152i	$0.151489\pi$
$521$	19.2009	+	33.2570i	0.841208	+	1.45702i	−0.0476655	+	0.998863i	$0.515178\pi$
$522$	28.8956	+	16.6829i	1.26473	+	0.730190i
$523$	−5.53479			−0.242020			−0.121010	−	0.992651i	$-0.538613\pi$
$523$	−5.53479			−0.242020			−0.121010	+	0.992651i	$0.538613\pi$
$524$	19.8319	+	34.3499i	0.866361	+	1.50058i
$525$			4.00495i			0.174790i
$526$		−	17.4203i		−	0.759559i
$527$	39.7313	+	14.8664i	1.73072	+	0.647591i
$528$			1.84617i			0.0803442i
$529$	10.7099			0.465649
$530$	17.6959	+	30.6502i	0.768660	+	1.33136i
$531$			18.7547i			0.813885i
$532$	−1.79891	+	3.11580i	−0.0779926	+	0.135087i
$533$	8.09197	+	27.3183i	0.350502	+	1.18329i
$534$	−13.1185	−	22.7220i	−0.567694	−	0.983275i
$535$			1.02280i			0.0442194i
$536$	5.63377	−	9.75797i	0.243342	−	0.421480i
$537$	6.69177	−	11.5905i	0.288771	−	0.500166i
$538$	−5.42809	−	3.13391i	−0.234022	−	0.135112i
$539$	−5.79014	+	3.34294i	−0.249399	+	0.143991i
$540$	−38.2841	−	22.1034i	−1.64749	−	0.951177i
$541$	−6.61874	+	3.82133i	−0.284562	+	0.164292i	−0.635487	−	0.772112i	$-0.719201\pi$
$541$	−6.61874	+	3.82133i	−0.284562	+	0.164292i	0.350925	+	0.936404i	$0.385867\pi$
$542$	−41.0325			−1.76250
$543$	10.3387			0.443676
$544$	−44.9589	+	25.9571i	−1.92760	+	1.11290i
$545$	−8.38286	+	14.5195i	−0.359082	+	0.621949i
$546$	−13.5640	+	4.01781i	−0.580487	+	0.171946i
$547$	20.6818	−	35.8219i	0.884290	−	1.53163i	0.0377643	−	0.999287i	$-0.487976\pi$
$547$	20.6818	−	35.8219i	0.884290	−	1.53163i	0.846526	−	0.532348i	$-0.178690\pi$
$548$	−42.2247	−	24.3784i	−1.80375	−	1.04140i
$549$	4.81479	−	8.33945i	0.205490	−	0.355919i
$550$	6.86311			0.292644
$551$	7.32302	−	4.22795i	0.311971	−	0.180117i
$552$	13.3685	−	7.71828i	0.568999	−	0.328512i
$553$	14.9024	+	8.60392i	0.633716	+	0.365876i
$554$			4.41773i			0.187691i
$555$	0.0401290	+	0.0695054i	0.00170338	+	0.00295034i
$556$	14.5562			0.617320
$557$		−	4.53716i		−	0.192246i	−0.995369	−	0.0961228i	$-0.969356\pi$
$557$		−	4.53716i		−	0.192246i	0.995369	−	0.0961228i	$-0.0306442\pi$
$558$	−18.2955	+	3.05685i	−0.774510	+	0.129407i
$559$	−9.65950	+	40.2342i	−0.408553	+	1.70172i
$560$	−4.30289			−0.181830
$561$	10.9504	−	6.32219i	0.462325	−	0.266923i
$562$	6.97606			0.294267
$563$	−11.0672	+	19.1689i	−0.466426	+	0.807873i	−0.999265	−	0.0383438i	$-0.987792\pi$
$563$	−11.0672	+	19.1689i	−0.466426	+	0.807873i	0.532839	+	0.846217i	$0.321125\pi$
$564$	15.9371	−	9.20127i	0.671072	−	0.387443i
$565$	−18.3124	+	10.5727i	−0.770410	+	0.444796i
$566$		−	24.4669i		−	1.02842i
$567$	−2.83779	−	1.63840i	−0.119176	−	0.0688062i
$568$	2.07447	−	3.59308i	0.0870427	−	0.150762i
$569$	−14.1220	+	24.4599i	−0.592023	+	1.02541i	0.401937	+	0.915667i	$0.368337\pi$
$569$	−14.1220	+	24.4599i	−0.592023	+	1.02541i	−0.993960	+	0.109746i	$0.964996\pi$
$570$	−5.39662	+	3.11574i	−0.226040	+	0.130504i
$571$	0.0857072	−	0.148449i	0.00358673	−	0.00621241i	−0.864226	−	0.503103i	$-0.832192\pi$
$571$	0.0857072	−	0.148449i	0.00358673	−	0.00621241i	0.867813	+	0.496891i	$0.165525\pi$
$572$	4.11540	+	13.8935i	0.172074	+	0.580917i
$573$	−2.23877			−0.0935260
$574$		−	25.2658i		−	1.05457i
$575$	6.60721	+	11.4440i	0.275540	+	0.477249i
$576$	9.68776	−	16.7797i	0.403657	−	0.699154i
$577$	−30.6784	+	17.7122i	−1.27716	+	0.737367i	−0.976325	−	0.216310i	$-0.930598\pi$
$577$	−30.6784	+	17.7122i	−1.27716	+	0.737367i	−0.300832	+	0.953677i	$0.597264\pi$
$578$	79.2698	+	45.7664i	3.29719	+	1.90363i
$579$	−28.3905	−	16.3913i	−1.17987	−	0.681198i
$580$	−69.5247	−	40.1401i	−2.88685	−	1.66673i
$581$	−11.3287			−0.469995
$582$	7.15920	+	12.4001i	0.296758	+	0.514001i
$583$	6.89184	−	3.97900i	0.285431	−	0.164793i
$584$	−8.77202	+	15.1936i	−0.362989	+	0.628715i
$585$	14.1299	+	3.39233i	0.584200	+	0.140256i
$586$	11.8572	+	20.5372i	0.489815	+	0.848385i
$587$		−	33.8469i		−	1.39701i	−0.715605	−	0.698505i	$-0.753849\pi$
$587$		−	33.8469i		−	1.39701i	0.715605	−	0.698505i	$-0.246151\pi$
$588$	−18.0283			−0.743475
$589$	−1.64741	+	4.40279i	−0.0678802	+	0.181414i
$590$		−	75.4949i		−	3.10808i
$591$			3.25052i			0.133708i
$592$	−0.0233592	+	0.0134865i	−0.000960059	+	0.000554290i
$593$		−	34.2584i		−	1.40682i	−0.710783	−	0.703411i	$-0.751659\pi$
$593$		−	34.2584i		−	1.40682i	0.710783	−	0.703411i	$-0.248341\pi$
$594$	−8.31497	+	14.4020i	−0.341167	+	0.590919i
$595$	14.7352	+	25.5221i	0.604085	+	1.04631i
$596$	−30.5681	+	17.6485i	−1.25212	+	0.722911i
$597$	−16.1234			−0.659886
$598$	−32.1304	+	33.8582i	−1.31391	+	1.38456i
$599$	−21.2517	+	36.8090i	−0.868321	+	1.50398i	−0.00460964	+	0.999989i	$0.501467\pi$
$599$	−21.2517	+	36.8090i	−0.868321	+	1.50398i	−0.863711	+	0.503987i	$0.831866\pi$
$600$	5.24049	+	3.02560i	0.213942	+	0.123519i
$601$	19.8651	+	34.4073i	0.810313	+	1.40350i	0.912645	+	0.408753i	$0.134036\pi$
$601$	19.8651	+	34.4073i	0.810313	+	1.40350i	−0.102332	+	0.994750i	$0.532630\pi$
$602$	18.3463	−	31.7768i	0.747741	−	1.29513i
$603$	−6.72932	+	3.88517i	−0.274039	+	0.158217i
$604$			57.4373i			2.33709i
$605$			24.7380i			1.00574i
$606$	1.64154	−	0.947745i	0.0666831	−	0.0384995i
$607$	−10.6451	+	18.4378i	−0.432070	+	0.748366i	−0.997051	−	0.0767369i	$-0.975550\pi$
$607$	−10.6451	+	18.4378i	−0.432070	+	0.748366i	0.564982	+	0.825103i	$0.308883\pi$
$608$	−2.87641	−	4.98209i	−0.116654	−	0.202050i
$609$	−15.2622	−	8.81165i	−0.618456	−	0.357066i
$610$	−19.3814	+	33.5695i	−0.784729	+	1.35919i
$611$	−12.5247	+	13.1982i	−0.506695	+	0.533942i
$612$	−33.8298			−1.36749
$613$	12.9248	−	7.46212i	0.522026	−	0.301392i	−0.215737	−	0.976452i	$-0.569215\pi$
$613$	12.9248	−	7.46212i	0.522026	−	0.301392i	0.737763	+	0.675059i	$0.235882\pi$
$614$	9.26514	+	16.0477i	0.373911	+	0.647632i
$615$	13.0784	−	22.6524i	0.527371	−	0.913433i
$616$		−	4.20159i		−	0.169287i
$617$	−37.1590	+	21.4538i	−1.49597	+	0.863696i	−0.999989	−	0.00463942i	$-0.998523\pi$
$617$	−37.1590	+	21.4538i	−1.49597	+	0.863696i	−0.495977	+	0.868336i	$0.665190\pi$
$618$		−	14.5106i		−	0.583704i
$619$		−	20.2790i		−	0.815082i	−0.913187	−	0.407541i	$-0.866386\pi$
$619$		−	20.2790i		−	0.815082i	0.913187	−	0.407541i	$-0.133614\pi$
$620$	44.0201	−	7.35497i	1.76789	−	0.295383i
$621$	−32.0198			−1.28491
$622$			18.6791i			0.748963i
$623$	−6.87505	−	11.9079i	−0.275443	−	0.477081i
$624$	1.14904	−	4.78602i	0.0459983	−	0.191594i
$625$	15.5999	−	27.0198i	0.623996	−	1.08079i
$626$	−54.4852	+	31.4571i	−2.17767	+	1.25728i
$627$	0.700589	+	1.21346i	0.0279788	+	0.0484607i
$628$	−30.4440			−1.21485
$629$	0.159987	+	0.0923686i	0.00637911	+	0.00368298i
$630$	−11.1597	−	6.44308i	−0.444615	−	0.256698i
$631$	13.6722	+	7.89367i	0.544283	+	0.314242i	0.746813	−	0.665034i	$-0.231583\pi$
$631$	13.6722	+	7.89367i	0.544283	+	0.314242i	−0.202530	+	0.979276i	$0.564916\pi$
$632$	22.5165	−	12.9999i	0.895658	−	0.517108i
$633$	−6.04244	+	10.4658i	−0.240166	+	0.415979i
$634$	8.50636	+	14.7334i	0.337831	+	0.585140i
$635$			47.7725i			1.89580i
$636$	21.4586			0.850887
$637$	17.0910	−	5.06253i	0.677171	−	0.200585i
$638$	−15.1001	+	26.1542i	−0.597820	+	1.03545i
$639$	−2.47787	+	1.43060i	−0.0980230	+	0.0565936i
$640$	−20.6178	+	35.7111i	−0.814990	+	1.41160i
$641$	7.57293	−	13.1167i	0.299113	−	0.518078i	−0.676820	−	0.736148i	$-0.736643\pi$
$641$	7.57293	−	13.1167i	0.299113	−	0.518078i	0.975933	+	0.218070i	$0.0699760\pi$
$642$	0.898502	+	0.518750i	0.0354610	+	0.0204734i
$643$			3.63466i			0.143337i	0.997429	+	0.0716685i	$0.0228324\pi$
$643$			3.63466i			0.143337i	−0.997429	+	0.0716685i	$0.977168\pi$
$644$	21.4263	−	12.3705i	0.844316	−	0.487466i
$645$	32.8974	−	18.9933i	1.29533	−	0.747861i
$646$	−7.17179	+	12.4219i	−0.282170	+	0.488734i
$647$	26.2555			1.03221			0.516105	−	0.856525i	$-0.327381\pi$
$647$	26.2555			1.03221			0.516105	+	0.856525i	$0.327381\pi$
$648$	−4.28769	+	2.47550i	−0.168436	+	0.0972467i
$649$	−16.9754			−0.666342
$650$	−17.7920	−	4.27153i	−0.697859	−	0.167543i
$651$	9.66340	−	1.61458i	0.378738	−	0.0632804i
$652$		−	31.0341i		−	1.21539i
$653$	29.3099			1.14699			0.573493	−	0.819210i	$-0.305588\pi$
$653$	29.3099			1.14699			0.573493	+	0.819210i	$0.305588\pi$
$654$	8.50337	+	14.7283i	0.332508	+	0.575921i
$655$			36.0029i			1.40675i
$656$	7.61298	+	4.39536i	0.297237	+	0.171610i
$657$	10.4778	−	6.04938i	0.408779	−	0.236009i
$658$	13.9733	−	8.06750i	0.544737	−	0.314504i
$659$	9.83901			0.383273			0.191637	−	0.981466i	$-0.438620\pi$
$659$	9.83901			0.383273			0.191637	+	0.981466i	$0.438620\pi$
$660$	6.65138	−	11.5205i	0.258905	−	0.448436i
$661$	13.0224	+	7.51851i	0.506514	+	0.292436i	0.731400	−	0.681949i	$-0.238867\pi$
$661$	13.0224	+	7.51851i	0.506514	+	0.292436i	−0.224885	+	0.974385i	$0.572201\pi$
$662$	−14.0732	+	24.3755i	−0.546970	+	0.947380i
$663$	−32.3227	+	9.57431i	−1.25531	+	0.371835i
$664$	−8.55845	+	14.8237i	−0.332132	+	0.575270i
$665$	−2.82821	+	1.63287i	−0.109673	+	0.0633200i
$666$	−0.0807777			−0.00313007
$667$	−58.1484			−2.25152
$668$	−48.3605	+	27.9209i	−1.87112	+	1.08029i
$669$	−8.07112	−	4.65986i	−0.312047	−	0.180161i
$670$	27.0881	−	15.6393i	1.04650	−	0.604200i
$671$	7.54826	+	4.35799i	0.291397	+	0.168238i
$672$	−5.99485	+	10.3834i	−0.231256	+	0.400547i
$673$	7.22214	−	12.5091i	0.278393	−	0.482191i	−0.692592	−	0.721329i	$-0.743532\pi$
$673$	7.22214	−	12.5091i	0.278393	−	0.482191i	0.970986	+	0.239138i	$0.0768649\pi$
$674$			56.5623i			2.17870i
$675$	−6.27594	−	10.8702i	−0.241561	−	0.418396i
$676$	−2.02161	−	38.5790i	−0.0777544	−	1.48381i
$677$	1.22146	−	2.11563i	0.0469444	−	0.0813101i	−0.841598	−	0.540104i	$-0.818385\pi$
$677$	1.22146	−	2.11563i	0.0469444	−	0.0813101i	0.888543	+	0.458794i	$0.151718\pi$
$678$			21.4494i			0.823757i
$679$	3.75193	+	6.49854i	0.143986	+	0.249391i
$680$	44.5277			1.70756
$681$		−	14.2990i		−	0.547937i
$682$	−2.76684	−	16.5597i	−0.105948	−	0.634105i
$683$		−	24.7764i		−	0.948042i	−0.880514	−	0.474021i	$-0.842802\pi$
$683$		−	24.7764i		−	0.948042i	0.880514	−	0.474021i	$-0.157198\pi$
$684$		−	3.74882i		−	0.143340i
$685$	−22.1283	−	38.3274i	−0.845480	−	1.46441i
$686$	−38.1882			−1.45803
$687$	13.7906	+	7.96201i	0.526145	+	0.303770i
$688$	6.38324	+	11.0561i	0.243359	+	0.421510i
$689$	−20.3429	+	6.02579i	−0.775004	+	0.229564i
$690$	42.8518			1.63134
$691$	19.3377	+	11.1646i	0.735641	+	0.424722i	0.820482	−	0.571672i	$-0.193705\pi$
$691$	19.3377	+	11.1646i	0.735641	+	0.424722i	−0.0848414	+	0.996394i	$0.527038\pi$
$692$	3.82711	−	6.62875i	0.145485	−	0.251987i
$693$	−1.44876	+	2.50932i	−0.0550337	+	0.0953212i
$694$	14.3688	−	8.29581i	0.545431	−	0.314905i
$695$	11.4425	+	6.60634i	0.434039	+	0.250593i
$696$	−23.0601	+	13.3138i	−0.874091	+	0.504657i
$697$		−	60.2075i		−	2.28052i
$698$	−20.9621			−0.793425
$699$	−11.6478	−	20.1745i	−0.440559	−	0.763071i
$700$	8.39921	+	4.84929i	0.317460	+	0.183286i
$701$	−12.3273	−	21.3514i	−0.465594	−	0.806432i	0.533634	−	0.845715i	$-0.320826\pi$
$701$	−12.3273	−	21.3514i	−0.465594	−	0.806432i	−0.999228	+	0.0392831i	$0.987493\pi$
$702$	30.5194	−	32.1606i	1.15188	−	1.21382i
$703$	−0.0102358	+	0.0177288i	−0.000386049	+	0.000668656i
$704$	15.1877	+	8.76865i	0.572410	+	0.330481i
$705$	16.7040			0.629109
$706$	14.4831	+	25.0855i	0.545080	+	0.944107i
$707$	0.860286	−	0.496686i	0.0323544	−	0.0186798i
$708$	−39.6412	−	22.8868i	−1.48981	−	0.860140i
$709$		−	50.4937i		−	1.89633i	−0.317776	−	0.948166i	$-0.602936\pi$
$709$		−	50.4937i		−	1.89633i	0.317776	−	0.948166i	$-0.397064\pi$
$710$	9.97438	−	5.75871i	0.374332	−	0.216121i
$711$	−17.9301			−0.672429
$712$	−20.7754			−0.778591
$713$	24.9492	−	20.5559i	0.934355	−	0.769825i
$714$	29.8941			1.11876
$715$	−3.07049	+	12.7894i	−0.114830	+	0.478295i
$716$	−16.2051	−	28.0680i	−0.605613	−	1.04895i
$717$			14.5511i			0.543421i
$718$	5.27136	−	9.13027i	0.196726	−	0.340739i
$719$	4.78687	+	8.29110i	0.178520	+	0.309206i	0.941374	−	0.337365i	$-0.109536\pi$
$719$	4.78687	+	8.29110i	0.178520	+	0.309206i	−0.762854	+	0.646571i	$0.776202\pi$
$720$	3.88281	−	2.24174i	0.144704	−	0.0835447i
$721$		−	7.60461i		−	0.283211i
$722$	35.3125	+	20.3877i	1.31420	+	0.758751i
$723$	14.1265	+	8.15595i	0.525371	+	0.303323i
$724$	12.5183	−	21.6824i	0.465240	−	0.805819i
$725$	−11.3972	−	19.7405i	−0.423282	−	0.733146i
$726$	21.7318	+	12.5468i	0.806541	+	0.465657i
$727$	−15.4541	−	26.7673i	−0.573161	−	0.992744i	−0.996239	−	0.0866507i	$-0.972384\pi$
$727$	−15.4541	−	26.7673i	−0.573161	−	0.992744i	0.423078	−	0.906093i	$-0.360950\pi$
$728$	−2.61503	+	10.8922i	−0.0969194	+	0.403693i
$729$	23.7170			0.878407
$730$	−42.1773	+	24.3511i	−1.56105	+	0.901275i
$731$	43.7187	−	75.7231i	1.61700	−	2.80072i
$732$	11.7512	+	20.3537i	0.434337	+	0.752294i
$733$	20.3009	+	11.7207i	0.749831	+	0.432915i	0.825633	−	0.564208i	$-0.190818\pi$
$733$	20.3009	+	11.7207i	0.749831	+	0.432915i	−0.0758022	+	0.997123i	$0.524152\pi$
$734$	−2.06604	−	1.19283i	−0.0762591	−	0.0440282i
$735$	−14.1719	−	8.18215i	−0.522738	−	0.301803i
$736$			39.5602i			1.45821i
$737$	−3.51657	−	6.09089i	−0.129535	−	0.224361i
$738$	13.1631	+	22.7991i	0.484540	+	0.839247i
$739$	28.3079	+	16.3436i	1.04132	+	0.601208i	0.920208	−	0.391430i	$-0.128020\pi$
$739$	28.3079	+	16.3436i	1.04132	+	0.601208i	0.121115	+	0.992638i	$0.461353\pi$
$740$	0.194356			0.00714467
$741$	−1.06097	−	3.58181i	−0.0389757	−	0.131581i
$742$	18.8145			0.690701
$743$		−	40.3386i		−	1.47988i	−0.672673	−	0.739940i	$-0.734854\pi$
$743$		−	40.3386i		−	1.47988i	0.672673	−	0.739940i	$-0.265146\pi$
$744$	5.18767	−	13.8643i	0.190189	−	0.508291i
$745$	−32.0391			−1.17382
$746$		−	59.8142i		−	2.18995i
$747$	10.2227	−	5.90210i	0.374030	−	0.215947i
$748$		−	30.6202i		−	1.11959i
$749$	0.470879	+	0.271862i	0.0172056	+	0.00993363i
$750$	−10.0524	−	17.4113i	−0.367062	−	0.635770i
$751$	−8.69213	−	15.0552i	−0.317180	−	0.549372i	0.662718	−	0.748869i	$-0.269403\pi$
$751$	−8.69213	−	15.0552i	−0.317180	−	0.549372i	−0.979899	+	0.199496i	$0.936069\pi$
$752$			5.61385i			0.204716i
$753$	−9.45341	+	16.3738i	−0.344501	+	0.596694i
$754$	55.4238	−	58.4042i	2.01842	−	2.12695i
$755$	−26.0679	+	45.1510i	−0.948709	+	1.64321i
$756$	−20.3520	+	11.7503i	−0.740197	+	0.427353i
$757$	2.95482	−	5.11789i	0.107395	−	0.186013i	−0.807319	−	0.590115i	$-0.799083\pi$
$757$	2.95482	−	5.11789i	0.107395	−	0.186013i	0.914714	+	0.404102i	$0.132416\pi$
$758$	−9.87033	−	17.0959i	−0.358506	−	0.620951i
$759$		−	9.63544i		−	0.349744i
$760$			4.93430i			0.178986i
$761$	9.38418	−	5.41796i	0.340176	−	0.196401i	−0.320174	−	0.947359i	$-0.603741\pi$
$761$	9.38418	−	5.41796i	0.340176	−	0.196401i	0.660350	+	0.750958i	$0.270408\pi$
$762$	41.9670	+	24.2296i	1.52030	+	0.877748i
$763$	4.45637	+	7.71866i	0.161331	+	0.279434i
$764$	−2.71075	+	4.69516i	−0.0980717	+	0.169865i
$765$	−26.5933	−	15.3536i	−0.961483	−	0.555112i
$766$	−18.0053	+	31.1861i	−0.650558	+	1.12680i
$767$	44.0071	+	10.5653i	1.58900	+	0.381491i
$768$	5.00106	+	8.66209i	0.180460	+	0.312566i
$769$	25.6743	−	14.8231i	0.925840	−	0.534534i	0.0403462	−	0.999186i	$-0.487154\pi$
$769$	25.6743	−	14.8231i	0.925840	−	0.534534i	0.885493	+	0.464652i	$0.153821\pi$
$770$	5.83180	−	10.1010i	0.210164	−	0.364014i
$771$	9.38380			0.337949
$772$	−68.7517	+	39.6938i	−2.47443	+	1.42861i
$773$			52.9042i			1.90283i	0.307911	+	0.951415i	$0.400370\pi$
$773$			52.9042i			1.90283i	−0.307911	+	0.951415i	$0.599630\pi$
$774$			38.2327i			1.37424i
$775$	11.8685	+	4.44089i	0.426330	+	0.159521i
$776$	11.3378			0.407003
$777$	0.0426655			0.00153062
$778$	6.31118	−	3.64376i	0.226267	−	0.130635i
$779$	6.67184			0.239044
$780$	−24.4133	+	25.7261i	−0.874138	+	0.921143i
$781$	−1.29487	−	2.24279i	−0.0463342	−	0.0802532i
$782$	85.4214	−	49.3181i	3.05466	−	1.76361i
$783$	55.2329			1.97386
$784$	2.74984	−	4.76287i	0.0982086	−	0.170102i
$785$	−23.9318	−	13.8170i	−0.854163	−	0.493151i
$786$	31.6276	+	18.2602i	1.12812	+	0.651320i
$787$	8.10458	−	4.67918i	0.288897	−	0.166795i	−0.348547	−	0.937291i	$-0.613325\pi$
$787$	8.10458	−	4.67918i	0.288897	−	0.166795i	0.637444	+	0.770496i	$0.279992\pi$
$788$	6.81700	+	3.93580i	0.242846	+	0.140207i
$789$	−4.79364	−	8.30282i	−0.170658	−	0.295588i
$790$	72.1754			2.56788
$791$			11.2410i			0.399684i
$792$	2.18897	+	3.79140i	0.0777815	+	0.134722i
$793$	−16.8558	−	15.9956i	−0.598567	−	0.568022i
$794$	−9.36308	−	16.2173i	−0.332283	−	0.575531i
$795$	16.8684	+	9.73898i	0.598260	+	0.345406i
$796$	−19.5225	+	33.8140i	−0.691958	+	1.19851i
$797$	−6.88968	+	11.9333i	−0.244045	+	0.422698i	−0.961863	−	0.273533i	$-0.911808\pi$
$797$	−6.88968	+	11.9333i	−0.244045	+	0.422698i	0.717818	+	0.696231i	$0.245141\pi$
$798$			3.31269i			0.117268i
$799$	33.2980	−	19.2246i	1.17800	−	0.680117i
$800$	−13.4301	+	7.75389i	−0.474827	+	0.274141i
$801$	12.4077	+	7.16359i	0.438405	+	0.253113i
$802$	−76.0231			−2.68447
$803$	5.47546	+	9.48377i	0.193225	+	0.334675i
$804$		−	18.9647i		−	0.668834i
$805$	22.4574			0.791520
$806$	−3.13385	+	44.6516i	−0.110385	+	1.57279i
$807$	−3.44951			−0.121428
$808$		−	1.50091i		−	0.0528019i
$809$	7.44097	+	12.8881i	0.261611	+	0.453123i	0.966670	−	0.256025i	$-0.0824130\pi$
$809$	7.44097	+	12.8881i	0.261611	+	0.453123i	−0.705059	+	0.709148i	$0.749080\pi$
$810$	−13.7440			−0.482913
$811$	−34.0772	−	19.6745i	−1.19661	−	0.690864i	−0.236814	−	0.971555i	$-0.576103\pi$
$811$	−34.0772	−	19.6745i	−1.19661	−	0.690864i	−0.959798	+	0.280691i	$0.909436\pi$
$812$	−36.9597	+	21.3387i	−1.29703	+	0.748841i
$813$	−19.5569	+	11.2912i	−0.685889	+	0.395998i
$814$		−	0.0731140i		−	0.00256265i
$815$	14.0848	−	24.3957i	0.493371	−	0.854543i
$816$	−5.20052	+	9.00757i	−0.182055	+	0.315328i
$817$	8.39119	+	4.84465i	0.293570	+	0.169493i
$818$	−26.2008	−	45.3811i	−0.916090	−	1.58671i
$819$	5.31754	−	5.60349i	0.185810	−	0.195802i
$820$	−31.6712	−	54.8561i	−1.10601	−	1.91566i
$821$		−	26.6714i		−	0.930839i	−0.885090	−	0.465420i	$-0.845903\pi$
$821$		−	26.6714i		−	0.930839i	0.885090	−	0.465420i	$-0.154097\pi$
$822$	−44.8929			−1.56582
$823$	1.10858	+	1.92011i	0.0386425	+	0.0669308i	0.884700	−	0.466161i	$-0.154363\pi$
$823$	1.10858	+	1.92011i	0.0386425	+	0.0669308i	−0.846057	+	0.533092i	$0.821030\pi$
$824$	−9.95065	−	5.74501i	−0.346647	−	0.200137i
$825$	3.27109	−	1.88857i	0.113885	−	0.0657514i
$826$	−34.7566	−	20.0668i	−1.20934	−	0.698212i
$827$	21.7233	+	12.5419i	0.755392	+	0.436126i	0.827639	−	0.561261i	$-0.189684\pi$
$827$	21.7233	+	12.5419i	0.755392	+	0.436126i	−0.0722470	+	0.997387i	$0.523017\pi$
$828$	−12.8897	+	22.3256i	−0.447948	+	0.775868i
$829$	−10.1424			−0.352258			−0.176129	−	0.984367i	$-0.556358\pi$
$829$	−10.1424			−0.352258			−0.176129	+	0.984367i	$0.556358\pi$
$830$	−41.1505	+	23.7582i	−1.42835	+	0.824660i
$831$	1.21565	+	2.10557i	0.0421706	+	0.0730415i
$832$	−33.9153	−	32.1846i	−1.17580	−	1.11580i
$833$	−37.6673			−1.30509
$834$	11.6070	−	6.70131i	0.401918	−	0.232047i
$835$	−50.6877			−1.75412
$836$	3.39315			0.117355
$837$	−23.6983	+	19.5253i	−0.819132	+	0.674892i
$838$		−	84.1464i		−	2.90679i
$839$			3.73108i			0.128811i	0.997924	+	0.0644055i	$0.0205151\pi$
$839$			3.73108i			0.128811i	−0.997924	+	0.0644055i	$0.979485\pi$
$840$	8.90601	−	5.14189i	0.307287	−	0.177412i
$841$	71.3040			2.45876
$842$	19.6558	−	34.0448i	0.677382	−	1.17326i
$843$	3.32492	−	1.91965i	0.114516	−	0.0661161i
$844$	14.6326	+	25.3445i	0.503677	+	0.872393i
$845$	15.9199	−	31.2442i	0.547662	−	1.07483i
$846$	−8.40609	+	14.5598i	−0.289007	+	0.500576i
$847$	11.3890	+	6.57544i	0.391330	+	0.225935i
$848$	−3.27306	+	5.66910i	−0.112397	+	0.194678i
$849$	−6.73270	−	11.6614i	−0.231066	−	0.400217i
$850$	33.4855	+	19.3329i	1.14854	+	0.663113i
$851$	0.121915	−	0.0703879i	0.00417921	−	0.00241287i
$852$		−	6.98318i		−	0.239240i
$853$		−	2.74076i		−	0.0938417i	−0.998899	−	0.0469209i	$-0.985059\pi$
$853$		−	2.74076i		−	0.0938417i	0.998899	−	0.0469209i	$-0.0149409\pi$
$854$	10.3032	+	17.8457i	0.352570	+	0.610668i
$855$	1.70140	−	2.94691i	0.0581867	−	0.100782i
$856$	0.711464	−	0.410764i	0.0243173	−	0.0140396i
$857$	6.58107	−	11.3987i	0.224805	−	0.389374i	−0.731456	−	0.681889i	$-0.761159\pi$
$857$	6.58107	−	11.3987i	0.224805	−	0.389374i	0.956261	+	0.292515i	$0.0944922\pi$
$858$	9.67781	+	9.18395i	0.330395	+	0.313535i
$859$	−7.12253	+	12.3366i	−0.243018	+	0.420919i	−0.961572	−	0.274551i	$-0.911471\pi$
$859$	−7.12253	+	12.3366i	−0.243018	+	0.420919i	0.718555	+	0.695470i	$0.244804\pi$
$860$		−	91.9902i		−	3.13684i
$861$	−6.95254	−	12.0421i	−0.236942	−	0.410395i
$862$	−11.5236	−	19.9594i	−0.392494	−	0.679820i
$863$	30.8292	+	17.7993i	1.04944	+	0.605894i	0.922492	−	0.386015i	$-0.126149\pi$
$863$	30.8292	+	17.7993i	1.04944	+	0.605894i	0.126947	+	0.991909i	$0.459482\pi$
$864$		−	37.5767i		−	1.27839i
$865$	6.01692	−	3.47387i	0.204581	−	0.118115i
$866$			30.5985i			1.03978i
$867$	50.3753			1.71084
$868$	8.31455	−	22.2211i	0.282214	−	0.754234i
$869$		−	16.2290i		−	0.550530i
$870$	−73.9179			−2.50605
$871$	5.32549	+	17.9787i	0.180447	+	0.609186i
$872$	13.4665			0.456033
$873$	−6.77128	−	3.90940i	−0.229173	−	0.132313i
$874$	5.46514	+	9.46590i	0.184861	+	0.320189i
$875$	−5.26818	−	9.12476i	−0.178097	−	0.308473i
$876$			29.5289i			0.997688i
$877$	29.5678	+	17.0710i	0.998435	+	0.576447i	0.907785	−	0.419436i	$-0.137772\pi$
$877$	29.5678	+	17.0710i	0.998435	+	0.576447i	0.0906503	+	0.995883i	$0.471105\pi$
$878$	17.4260	+	10.0609i	0.588097	+	0.339538i
$879$	11.3027	+	6.52562i	0.381231	+	0.220104i
$880$	2.02906	+	3.51443i	0.0683996	+	0.118472i
$881$	20.1548	−	34.9091i	0.679031	−	1.17612i	−0.296242	−	0.955113i	$-0.595734\pi$
$881$	20.1548	−	34.9091i	0.679031	−	1.17612i	0.975273	−	0.221003i	$-0.0709331\pi$
$882$	14.2637	−	8.23514i	0.480283	−	0.277292i
$883$	13.4842			0.453780			0.226890	−	0.973920i	$-0.427144\pi$
$883$	13.4842			0.453780			0.226890	+	0.973920i	$0.427144\pi$
$884$	−19.0577	+	79.3801i	−0.640980	+	2.66984i
$885$	−20.7744	−	35.9823i	−0.698324	−	1.20953i
$886$	−2.02094	−	1.16679i	−0.0678949	−	0.0391991i
$887$	−12.9381	−	22.4094i	−0.434417	−	0.752433i	0.562831	−	0.826572i	$-0.309712\pi$
$887$	−12.9381	−	22.4094i	−0.434417	−	0.752433i	−0.997248	+	0.0741395i	$0.976379\pi$
$888$	0.0322323	−	0.0558279i	0.00108164	−	0.00187346i
$889$	21.9937	+	12.6981i	0.737645	+	0.425880i
$890$	−49.9458	−	28.8362i	−1.67419	−	0.966592i
$891$			3.09039i			0.103532i
$892$	−19.5454	+	11.2845i	−0.654428	+	0.377834i
$893$	2.13036	+	3.68989i	0.0712897	+	0.123477i
$894$	−16.2498	+	28.1456i	−0.543476	+	0.941328i
$895$		−	29.4187i		−	0.983360i
$896$	10.9605	+	18.9842i	0.366166	+	0.634218i
$897$	−5.99700	+	24.9790i	−0.200234	+	0.834024i
$898$	37.1947			1.24120
$899$	−43.0365	+	35.4582i	−1.43535	+	1.18260i
$900$	−10.1056			−0.336854
$901$	44.8342			1.49365
$902$	−20.6361	+	11.9143i	−0.687107	+	0.396701i
$903$		−	20.1939i		−	0.672011i
$904$	14.7089	+	8.49216i	0.489209	+	0.282445i
$905$	19.6811	−	11.3629i	0.654222	−	0.377715i
$906$	26.4427	+	45.8000i	0.878499	+	1.52160i
$907$	−4.70920			−0.156366			−0.0781831	−	0.996939i	$-0.524912\pi$
$907$	−4.70920			−0.156366			−0.0781831	+	0.996939i	$0.524912\pi$
$908$	−29.9879	−	17.3135i	−0.995183	−	0.574569i
$909$	−0.517532	+	0.896392i	−0.0171655	+	0.0297314i
$910$	−21.4052	+	22.5562i	−0.709574	+	0.747730i
$911$	21.3155	+	36.9195i	0.706213	+	1.22320i	0.966252	+	0.257599i	$0.0829314\pi$
$911$	21.3155	+	36.9195i	0.706213	+	1.22320i	−0.260039	+	0.965598i	$0.583735\pi$
$912$	−0.998166	−	0.576292i	−0.0330526	−	0.0190829i
$913$	5.34215	+	9.25287i	0.176799	+	0.306225i
$914$	52.0377			1.72125
$915$			21.3332i			0.705253i
$916$	33.3960	−	19.2812i	1.10343	−	0.637068i
$917$	16.5751	+	9.56966i	0.547359	+	0.316018i
$918$	−81.1385	+	46.8453i	−2.67797	+	1.54613i
$919$	−5.58475	+	9.67308i	−0.184224	+	0.319085i	−0.943315	−	0.331899i	$-0.892311\pi$
$919$	−5.58475	+	9.67308i	−0.184224	+	0.319085i	0.759091	+	0.650985i	$0.225644\pi$
$920$	16.9658	−	29.3856i	0.559345	−	0.968814i
$921$	8.83189	+	5.09909i	0.291021	+	0.168021i
$922$	61.3021			2.01888
$923$	1.96095	+	6.62013i	0.0645455	+	0.217904i
$924$	−3.53591	−	6.12437i	−0.116323	−	0.201477i
$925$	0.0477913	+	0.0275923i	0.00157137	+	0.000907231i
$926$	63.2982			2.08011
$927$	3.96189	+	6.86219i	0.130125	+	0.225384i
$928$		−	68.2400i		−	2.24009i
$929$		−	8.08502i		−	0.265261i	−0.991166	−	0.132630i	$-0.957658\pi$
$929$		−	8.08502i		−	0.265261i	0.991166	−	0.132630i	$-0.0423423\pi$
$930$	31.7153	−	26.1305i	1.03998	−	0.856854i
$931$		−	4.17407i		−	0.136799i
$932$	−56.4135			−1.84789
$933$	5.14004	+	8.90281i	0.168277	+	0.291465i
$934$		−	18.4880i		−	0.604946i
$935$	13.8970	−	24.0703i	0.454480	−	0.787183i
$936$	−3.31496	−	11.1912i	−0.108353	−	0.365797i
$937$	8.15627	+	14.1271i	0.266454	+	0.461511i	0.967943	−	0.251168i	$-0.0808147\pi$
$937$	8.15627	+	14.1271i	0.266454	+	0.461511i	−0.701490	+	0.712680i	$0.747481\pi$
$938$		−	16.6279i		−	0.542920i
$939$	−17.3125	+	29.9861i	−0.564971	+	0.978558i
$940$	20.2256	−	35.0317i	0.659686	−	1.14261i
$941$	0.780833	+	0.450814i	0.0254544	+	0.0146961i	0.512673	−	0.858584i	$-0.328655\pi$
$941$	0.780833	+	0.450814i	0.0254544	+	0.0146961i	−0.487219	+	0.873280i	$0.661989\pi$
$942$	−24.2758	+	14.0157i	−0.790950	+	0.456655i
$943$	−39.7333	−	22.9400i	−1.29389	−	0.747030i
$944$	12.0929	−	6.98182i	0.393590	−	0.227239i
$945$	−21.3314			−0.693912
$946$	−34.6054			−1.12512
$947$	45.6723	−	26.3689i	1.48415	−	0.856875i	0.484313	−	0.874895i	$-0.339070\pi$
$947$	45.6723	−	26.3689i	1.48415	−	0.856875i	0.999838	+	0.0180205i	$0.00573642\pi$
$948$	21.8805	−	37.8981i	0.710645	−	1.23087i
$949$	−8.29201	−	27.9937i	−0.269170	−	0.908713i
$950$	−2.14236	+	3.71067i	−0.0695073	+	0.120390i
$951$	8.10859	+	4.68150i	0.262939	+	0.151808i
$952$	11.8356	−	20.4998i	0.383593	−	0.664403i
$953$	−15.1184			−0.489734			−0.244867	−	0.969557i	$-0.578744\pi$
$953$	−15.1184			−0.489734			−0.244867	+	0.969557i	$0.578744\pi$
$954$	−16.9776	+	9.80205i	−0.549672	+	0.317353i
$955$	−4.26180	+	2.46055i	−0.137909	+	0.0796217i
$956$	30.5167	+	17.6188i	0.986979	+	0.569833i
$957$			16.6208i			0.537274i
$958$	−3.70689	−	6.42053i	−0.119764	−	0.207438i
$959$	−23.5271			−0.759729
$960$			42.9242i			1.38537i
$961$	5.93051	−	30.4274i	0.191307	−	0.981530i
$962$	−0.0455054	+	0.189541i	−0.00146715	+	0.00611106i
$963$	−0.566544			−0.0182566
$964$	34.2094	−	19.7508i	1.10181	−	0.636131i
$965$	−72.0603			−2.31970
$966$	11.3901	−	19.7283i	0.366472	−	0.634747i
$967$	−2.26734	+	1.30905i	−0.0729128	+	0.0420962i	−0.536013	−	0.844210i	$-0.680070\pi$
$967$	−2.26734	+	1.30905i	−0.0729128	+	0.0420962i	0.463100	+	0.886306i	$0.346737\pi$
$968$	17.2079	−	9.93501i	0.553084	−	0.319323i
$969$			7.89403i			0.253593i
$970$	27.2570	+	15.7368i	0.875170	+	0.505280i
$971$	−27.8082	+	48.1652i	−0.892408	+	1.54570i	−0.0554277	+	0.998463i	$0.517652\pi$
$971$	−27.8082	+	48.1652i	−0.892408	+	1.54570i	−0.836980	+	0.547233i	$0.815681\pi$
$972$	20.4163	−	35.3621i	0.654855	−	1.13424i
$973$	6.08290	−	3.51196i	0.195009	−	0.112588i
$974$	−37.7323	+	65.3542i	−1.20902	+	2.09408i
$975$	−9.65542	+	2.86004i	−0.309221	+	0.0915944i
$976$	−7.16961			−0.229494
$977$			36.5483i			1.16928i	0.811291	+	0.584642i	$0.198765\pi$
$977$			36.5483i			1.16928i	−0.811291	+	0.584642i	$0.801235\pi$
$978$	−14.2873	−	24.7464i	−0.456858	−	0.791302i
$979$	−6.48396	+	11.2305i	−0.207228	+	0.358930i
$980$	−34.3193	+	19.8143i	−1.09629	+	0.632943i
$981$	−8.04261	−	4.64340i	−0.256781	−	0.148252i
$982$	−42.1033	−	24.3083i	−1.34357	−	0.775710i
$983$	−33.7076	−	19.4611i	−1.07511	−	0.620713i	−0.145535	−	0.989353i	$-0.546490\pi$
$983$	−33.7076	−	19.4611i	−1.07511	−	0.620713i	−0.929572	+	0.368640i	$0.879824\pi$
$984$	−21.0096			−0.669760
$985$	3.57253	+	6.18780i	0.113830	+	0.197160i
$986$	−147.349	+	85.0719i	−4.69255	+	2.70924i
$987$	4.43997	−	7.69025i	0.141326	−	0.244783i
$988$	−8.79643	−	2.11186i	−0.279852	−	0.0671873i
$989$	−33.3151	−	57.7035i	−1.05936	−	1.83486i
$990$			12.1531i			0.386252i
$991$	−48.0001			−1.52477			−0.762386	−	0.647122i	$-0.775972\pi$
$991$	−48.0001			−1.52477			−0.762386	+	0.647122i	$0.775972\pi$
$992$	24.1234	+	29.2791i	0.765917	+	0.929612i
$993$			15.4904i			0.491574i
$994$		−	6.12272i		−	0.194201i
$995$	−30.6930	+	17.7206i	−0.973034	+	0.561781i
$996$			28.8099i			0.912878i
$997$	10.0217	−	17.3581i	0.317390	−	0.549735i	−0.662553	−	0.749015i	$-0.730527\pi$
$997$	10.0217	−	17.3581i	0.317390	−	0.549735i	0.979943	+	0.199280i	$0.0638603\pi$
$998$	−14.3862	−	24.9177i	−0.455388	−	0.788756i
$999$	−0.115803	+	0.0668587i	−0.00366384	+	0.00211532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.5	✓	68
13.12	even	2	inner	403.2.l.c.25.30	yes	68
31.5	even	3	inner	403.2.l.c.129.5	yes	68
403.129	even	6	inner	403.2.l.c.129.30	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.5	✓	68	1.1	even	1	trivial
403.2.l.c.25.30	yes	68	13.12	even	2	inner
403.2.l.c.129.5	yes	68	31.5	even	3	inner
403.2.l.c.129.30	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)

\(f(q)\)	\(=\)	\(q-2.22973i q^{2} +(-0.613568 - 1.06273i) q^{3} -2.97169 q^{4} +(-2.33602 - 1.34870i) q^{5} +(-2.36960 + 1.36809i) q^{6} +(-1.24184 + 0.716977i) q^{7} +2.16660i q^{8} +(0.747068 - 1.29396i) q^{9} +O(q^{10})\)	\(q-2.22973i q^{2} +(-0.613568 - 1.06273i) q^{3} -2.97169 q^{4} +(-2.33602 - 1.34870i) q^{5} +(-2.36960 + 1.36809i) q^{6} +(-1.24184 + 0.716977i) q^{7} +2.16660i q^{8} +(0.747068 - 1.29396i) q^{9} +(-3.00724 + 5.20869i) q^{10} +(1.17120 + 0.676192i) q^{11} +(1.82333 + 3.15811i) q^{12} +(-2.61537 - 2.48191i) q^{13} +(1.59866 + 2.76897i) q^{14} +3.31008i q^{15} -1.11245 q^{16} +(3.80956 + 6.59836i) q^{17} +(-2.88518 - 1.66576i) q^{18} +(-0.731192 + 0.422154i) q^{19} +(6.94192 + 4.00792i) q^{20} +(1.52391 + 0.879828i) q^{21} +(1.50772 - 2.61145i) q^{22} +5.80603 q^{23} +(2.30251 - 1.32936i) q^{24} +(1.13799 + 1.97106i) q^{25} +(-5.53397 + 5.83156i) q^{26} -5.51492 q^{27} +(3.69036 - 2.13063i) q^{28} -10.0152 q^{29} +7.38058 q^{30} +(4.29712 - 3.54044i) q^{31} +6.81365i q^{32} -1.65956i q^{33} +(14.7125 - 8.49429i) q^{34} +3.86795 q^{35} +(-2.22005 + 3.84525i) q^{36} +(0.0209981 - 0.0121233i) q^{37} +(0.941288 + 1.63036i) q^{38} +(-1.03289 + 4.30225i) q^{39} +(2.92210 - 5.06122i) q^{40} +(-6.84346 - 3.95107i) q^{41} +(1.96178 - 3.39790i) q^{42} +(-5.73802 - 9.93855i) q^{43} +(-3.48044 - 2.00943i) q^{44} +(-3.49033 + 2.01514i) q^{45} -12.9459i q^{46} -5.04640i q^{47} +(0.682561 + 1.18223i) q^{48} +(-2.47189 + 4.28144i) q^{49} +(4.39493 - 2.53741i) q^{50} +(4.67485 - 8.09709i) q^{51} +(7.77206 + 7.37545i) q^{52} +(2.94222 - 5.09607i) q^{53} +12.2968i q^{54} +(-1.82396 - 3.15919i) q^{55} +(-1.55340 - 2.69057i) q^{56} +(0.897272 + 0.518040i) q^{57} +22.3311i q^{58} +(-10.8705 + 6.27610i) q^{59} -9.83653i q^{60} +6.44491 q^{61} +(-7.89423 - 9.58141i) q^{62} +2.14252i q^{63} +12.9677 q^{64} +(2.76220 + 9.32513i) q^{65} -3.70036 q^{66} +(-4.50382 - 2.60028i) q^{67} +(-11.3208 - 19.6083i) q^{68} +(-3.56239 - 6.17024i) q^{69} -8.62448i q^{70} +(-1.65840 - 0.957475i) q^{71} +(2.80350 + 1.61860i) q^{72} +(7.01264 + 4.04875i) q^{73} +(-0.0270316 - 0.0468200i) q^{74} +(1.39647 - 2.41876i) q^{75} +(2.17287 - 1.25451i) q^{76} -1.93926 q^{77} +(9.59285 + 2.30307i) q^{78} +(-6.00014 - 10.3925i) q^{79} +(2.59870 + 1.50036i) q^{80} +(1.14257 + 1.97899i) q^{81} +(-8.80982 + 15.2591i) q^{82} +(6.84190 + 3.95017i) q^{83} +(-4.52858 - 2.61458i) q^{84} -20.5519i q^{85} +(-22.1603 + 12.7942i) q^{86} +(6.14500 + 10.6435i) q^{87} +(-1.46504 + 2.53752i) q^{88} +9.58894i q^{89} +(4.49323 + 7.78249i) q^{90} +(5.02734 + 1.20697i) q^{91} -17.2537 q^{92} +(-6.39912 - 2.39438i) q^{93} -11.2521 q^{94} +2.27744 q^{95} +(7.24108 - 4.18064i) q^{96} -5.23299i q^{97} +(9.54644 + 5.51164i) q^{98} +(1.74993 - 1.01032i) 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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