LMFDB - Embedded newform 770.2.m.f.43.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (of order $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.12
Character	$\chi$	$=$	770.43
Dual form			770.2.m.f.197.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.12640 - 1.12640i) q^{3} +1.00000i q^{4} +(-0.277104 + 2.21883i) q^{5} -1.59297i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.462431i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.12640 - 1.12640i) q^{3} +1.00000i q^{4} +(-0.277104 + 2.21883i) q^{5} -1.59297i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.462431i q^{9} +(-1.76489 + 1.37301i) q^{10} +(-2.89429 + 1.61960i) q^{11} +(1.12640 - 1.12640i) q^{12} +(-2.81773 + 2.81773i) q^{13} +1.00000i q^{14} +(2.81143 - 2.18717i) q^{15} -1.00000 q^{16} +(-4.15777 - 4.15777i) q^{17} +(0.326988 - 0.326988i) q^{18} +3.57054 q^{19} +(-2.21883 - 0.277104i) q^{20} -1.59297i q^{21} +(-3.19180 - 0.901340i) q^{22} +(1.88650 + 1.88650i) q^{23} +1.59297 q^{24} +(-4.84643 - 1.22969i) q^{25} -3.98487 q^{26} +(-3.90009 + 3.90009i) q^{27} +(-0.707107 + 0.707107i) q^{28} +1.22526 q^{29} +(3.53454 + 0.441420i) q^{30} -9.43245 q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.08446 + 1.43581i) q^{33} -5.87998i q^{34} +(-1.76489 + 1.37301i) q^{35} +0.462431 q^{36} +(-4.27744 + 4.27744i) q^{37} +(2.52475 + 2.52475i) q^{38} +6.34780 q^{39} +(-1.37301 - 1.76489i) q^{40} +4.51086i q^{41} +(1.12640 - 1.12640i) q^{42} +(4.32718 - 4.32718i) q^{43} +(-1.61960 - 2.89429i) q^{44} +(1.02606 + 0.128141i) q^{45} +2.66792i q^{46} +(-6.00076 + 6.00076i) q^{47} +(1.12640 + 1.12640i) q^{48} +1.00000i q^{49} +(-2.55742 - 4.29647i) q^{50} +9.36666i q^{51} +(-2.81773 - 2.81773i) q^{52} +(-0.325907 - 0.325907i) q^{53} -5.51557 q^{54} +(-2.79160 - 6.87073i) q^{55} -1.00000 q^{56} +(-4.02187 - 4.02187i) q^{57} +(0.866389 + 0.866389i) q^{58} +11.3516i q^{59} +(2.18717 + 2.81143i) q^{60} -10.7320i q^{61} +(-6.66975 - 6.66975i) q^{62} +(0.326988 - 0.326988i) q^{63} -1.00000i q^{64} +(-5.47126 - 7.03287i) q^{65} +(2.57998 + 4.61053i) q^{66} +(-2.64043 + 2.64043i) q^{67} +(4.15777 - 4.15777i) q^{68} -4.24992i q^{69} +(-2.21883 - 0.277104i) q^{70} +1.66704 q^{71} +(0.326988 + 0.326988i) q^{72} +(-4.06435 + 4.06435i) q^{73} -6.04921 q^{74} +(4.07390 + 6.84416i) q^{75} +3.57054i q^{76} +(-3.19180 - 0.901340i) q^{77} +(4.48857 + 4.48857i) q^{78} +13.5992 q^{79} +(0.277104 - 2.21883i) q^{80} +7.39887 q^{81} +(-3.18966 + 3.18966i) q^{82} +(-8.48702 + 8.48702i) q^{83} +1.59297 q^{84} +(10.3775 - 8.07327i) q^{85} +6.11956 q^{86} +(-1.38014 - 1.38014i) q^{87} +(0.901340 - 3.19180i) q^{88} -11.9972i q^{89} +(0.634921 + 0.816141i) q^{90} -3.98487 q^{91} +(-1.88650 + 1.88650i) q^{92} +(10.6247 + 10.6247i) q^{93} -8.48635 q^{94} +(-0.989412 + 7.92243i) q^{95} +1.59297i q^{96} +(5.77120 - 5.77120i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(0.748952 + 1.33841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3}+O(q^{10}) $ 36 * q - 4 * q^3	$ 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) $ 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.12640	−	1.12640i	−0.650329	−	0.650329i	0.302743	−	0.953072i	$-0.402098\pi$
$3$	−1.12640	−	1.12640i	−0.650329	−	0.650329i	−0.953072	+	0.302743i	$0.902098\pi$
$4$			1.00000i			0.500000i
$5$	−0.277104	+	2.21883i	−0.123925	+	0.992292i
$5$	−0.277104	+	2.21883i	−0.123925	+	0.992292i
$6$		−	1.59297i		−	0.650329i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	0.462431i		−	0.154144i
$10$	−1.76489	+	1.37301i	−0.558108	+	0.434183i
$11$	−2.89429	+	1.61960i	−0.872660	+	0.488328i
$11$	−2.89429	+	1.61960i	−0.872660	+	0.488328i
$12$	1.12640	−	1.12640i	0.325165	−	0.325165i
$13$	−2.81773	+	2.81773i	−0.781498	+	0.781498i	−0.980084	−	0.198586i	$-0.936365\pi$
$13$	−2.81773	+	2.81773i	−0.781498	+	0.781498i	0.198586	+	0.980084i	$0.436365\pi$
$14$			1.00000i			0.267261i
$15$	2.81143	−	2.18717i	0.725908	−	0.564724i
$16$	−1.00000			−0.250000
$17$	−4.15777	−	4.15777i	−1.00841	−	1.00841i	−0.999964	−	0.00844412i	$-0.997312\pi$
$17$	−4.15777	−	4.15777i	−1.00841	−	1.00841i	−0.00844412	−	0.999964i	$-0.502688\pi$
$18$	0.326988	−	0.326988i	0.0770718	−	0.0770718i
$19$	3.57054			0.819139			0.409569	−	0.912279i	$-0.365679\pi$
$19$	3.57054			0.819139			0.409569	+	0.912279i	$0.365679\pi$
$20$	−2.21883	−	0.277104i	−0.496146	−	0.0619623i
$21$		−	1.59297i		−	0.347616i
$22$	−3.19180	−	0.901340i	−0.680494	−	0.192166i
$23$	1.88650	+	1.88650i	0.393363	+	0.393363i	0.875884	−	0.482521i	$-0.160279\pi$
$23$	1.88650	+	1.88650i	0.393363	+	0.393363i	−0.482521	+	0.875884i	$0.660279\pi$
$24$	1.59297			0.325165
$25$	−4.84643	−	1.22969i	−0.969285	−	0.245939i
$26$	−3.98487			−0.781498
$27$	−3.90009	+	3.90009i	−0.750573	+	0.750573i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	1.22526			0.227525			0.113762	−	0.993508i	$-0.463710\pi$
$29$	1.22526			0.227525			0.113762	+	0.993508i	$0.463710\pi$
$30$	3.53454	+	0.441420i	0.645316	+	0.0805919i
$31$	−9.43245			−1.69412			−0.847059	−	0.531499i	$-0.821629\pi$
$31$	−9.43245			−1.69412			−0.847059	+	0.531499i	$0.821629\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.08446	+	1.43581i	0.885090	+	0.249943i
$34$		−	5.87998i		−	1.00841i
$35$	−1.76489	+	1.37301i	−0.298321	+	0.232081i
$36$	0.462431			0.0770718
$37$	−4.27744	+	4.27744i	−0.703207	+	0.703207i	−0.965098	−	0.261891i	$-0.915654\pi$
$37$	−4.27744	+	4.27744i	−0.703207	+	0.703207i	0.261891	+	0.965098i	$0.415654\pi$
$38$	2.52475	+	2.52475i	0.409569	+	0.409569i
$39$	6.34780			1.01646
$40$	−1.37301	−	1.76489i	−0.217092	−	0.279054i
$41$			4.51086i			0.704478i	0.935910	+	0.352239i	$0.114580\pi$
$41$			4.51086i			0.704478i	−0.935910	+	0.352239i	$0.885420\pi$
$42$	1.12640	−	1.12640i	0.173808	−	0.173808i
$43$	4.32718	−	4.32718i	0.659889	−	0.659889i	−0.295464	−	0.955354i	$-0.595474\pi$
$43$	4.32718	−	4.32718i	0.659889	−	0.659889i	0.955354	+	0.295464i	$0.0954744\pi$
$44$	−1.61960	−	2.89429i	−0.244164	−	0.436330i
$45$	1.02606	+	0.128141i	0.152955	+	0.0191022i
$46$			2.66792i			0.393363i
$47$	−6.00076	+	6.00076i	−0.875301	+	0.875301i	−0.993044	−	0.117743i	$-0.962434\pi$
$47$	−6.00076	+	6.00076i	−0.875301	+	0.875301i	0.117743	+	0.993044i	$0.462434\pi$
$48$	1.12640	+	1.12640i	0.162582	+	0.162582i
$49$			1.00000i			0.142857i
$50$	−2.55742	−	4.29647i	−0.361673	−	0.607612i
$51$			9.36666i			1.31160i
$52$	−2.81773	−	2.81773i	−0.390749	−	0.390749i
$53$	−0.325907	−	0.325907i	−0.0447668	−	0.0447668i	0.684369	−	0.729136i	$-0.260078\pi$
$53$	−0.325907	−	0.325907i	−0.0447668	−	0.0447668i	−0.729136	+	0.684369i	$0.760078\pi$
$54$	−5.51557			−0.750573
$55$	−2.79160	−	6.87073i	−0.376419	−	0.926449i
$56$	−1.00000			−0.133631
$57$	−4.02187	−	4.02187i	−0.532710	−	0.532710i
$58$	0.866389	+	0.866389i	0.113762	+	0.113762i
$59$			11.3516i			1.47785i	0.673788	+	0.738925i	$0.264666\pi$
$59$			11.3516i			1.47785i	−0.673788	+	0.738925i	$0.735334\pi$
$60$	2.18717	+	2.81143i	0.282362	+	0.362954i
$61$		−	10.7320i		−	1.37410i	−0.726611	−	0.687049i	$-0.758906\pi$
$61$		−	10.7320i		−	1.37410i	0.726611	−	0.687049i	$-0.241094\pi$
$62$	−6.66975	−	6.66975i	−0.847059	−	0.847059i
$63$	0.326988	−	0.326988i	0.0411966	−	0.0411966i
$64$		−	1.00000i		−	0.125000i
$65$	−5.47126	−	7.03287i	−0.678627	−	0.872321i
$66$	2.57998	+	4.61053i	0.317574	+	0.567517i
$67$	−2.64043	+	2.64043i	−0.322580	+	0.322580i	−0.849756	−	0.527176i	$-0.823251\pi$
$67$	−2.64043	+	2.64043i	−0.322580	+	0.322580i	0.527176	+	0.849756i	$0.323251\pi$
$68$	4.15777	−	4.15777i	0.504204	−	0.504204i
$69$		−	4.24992i		−	0.511631i
$70$	−2.21883	−	0.277104i	−0.265201	−	0.0331203i
$71$	1.66704			0.197842			0.0989209	−	0.995095i	$-0.468461\pi$
$71$	1.66704			0.197842			0.0989209	+	0.995095i	$0.468461\pi$
$72$	0.326988	+	0.326988i	0.0385359	+	0.0385359i
$73$	−4.06435	+	4.06435i	−0.475697	+	0.475697i	−0.903752	−	0.428056i	$-0.859199\pi$
$73$	−4.06435	+	4.06435i	−0.475697	+	0.475697i	0.428056	+	0.903752i	$0.359199\pi$
$74$	−6.04921			−0.703207
$75$	4.07390	+	6.84416i	0.470413	+	0.790296i
$76$			3.57054i			0.409569i
$77$	−3.19180	−	0.901340i	−0.363739	−	0.102717i
$78$	4.48857	+	4.48857i	0.508231	+	0.508231i
$79$	13.5992			1.53003			0.765016	−	0.644012i	$-0.222731\pi$
$79$	13.5992			1.53003			0.765016	+	0.644012i	$0.222731\pi$
$80$	0.277104	−	2.21883i	0.0309812	−	0.248073i
$81$	7.39887			0.822096
$82$	−3.18966	+	3.18966i	−0.352239	+	0.352239i
$83$	−8.48702	+	8.48702i	−0.931571	+	0.931571i	−0.997804	−	0.0662328i	$-0.978902\pi$
$83$	−8.48702	+	8.48702i	−0.931571	+	0.931571i	0.0662328	+	0.997804i	$0.478902\pi$
$84$	1.59297			0.173808
$85$	10.3775	−	8.07327i	1.12560	−	0.875669i
$86$	6.11956			0.659889
$87$	−1.38014	−	1.38014i	−0.147966	−	0.147966i
$88$	0.901340	−	3.19180i	0.0960832	−	0.340247i
$89$		−	11.9972i		−	1.27170i	−0.771812	−	0.635850i	$-0.780650\pi$
$89$		−	11.9972i		−	1.27170i	0.771812	−	0.635850i	$-0.219350\pi$
$90$	0.634921	+	0.816141i	0.0669266	+	0.0860288i
$91$	−3.98487			−0.417728
$92$	−1.88650	+	1.88650i	−0.196681	+	0.196681i
$93$	10.6247	+	10.6247i	1.10173	+	1.10173i
$94$	−8.48635			−0.875301
$95$	−0.989412	+	7.92243i	−0.101512	+	0.812824i
$96$			1.59297i			0.162582i
$97$	5.77120	−	5.77120i	0.585976	−	0.585976i	−0.350563	−	0.936539i	$-0.614010\pi$
$97$	5.77120	−	5.77120i	0.585976	−	0.585976i	0.936539	+	0.350563i	$0.114010\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	0.748952	+	1.33841i	0.0752726	+	0.134515i
$100$	1.22969	−	4.84643i	0.122969	−	0.484643i
$101$		−	2.51411i		−	0.250163i	−0.992146	−	0.125082i	$-0.960081\pi$
$101$		−	2.51411i		−	0.250163i	0.992146	−	0.125082i	$-0.0399192\pi$
$102$	−6.62323	+	6.62323i	−0.655798	+	0.655798i
$103$	9.99644	+	9.99644i	0.984979	+	0.984979i	0.999889	−	0.0149099i	$-0.00474614\pi$
$103$	9.99644	+	9.99644i	0.984979	+	0.984979i	−0.0149099	+	0.999889i	$0.504746\pi$
$104$		−	3.98487i		−	0.390749i
$105$	3.53454	+	0.441420i	0.344936	+	0.0430782i
$106$		−	0.460902i		−	0.0447668i
$107$	6.39894	+	6.39894i	0.618609	+	0.618609i	0.945175	−	0.326566i	$-0.105891\pi$
$107$	6.39894	+	6.39894i	0.618609	+	0.618609i	−0.326566	+	0.945175i	$0.605891\pi$
$108$	−3.90009	−	3.90009i	−0.375287	−	0.375287i
$109$	18.5158			1.77349			0.886745	−	0.462260i	$-0.152961\pi$
$109$	18.5158			1.77349			0.886745	+	0.462260i	$0.152961\pi$
$110$	2.88438	−	6.83230i	0.275015	−	0.651434i
$111$	9.63625			0.914632
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−3.61261	−	3.61261i	−0.339846	−	0.339846i	0.516464	−	0.856309i	$-0.327248\pi$
$113$	−3.61261	−	3.61261i	−0.339846	−	0.339846i	−0.856309	+	0.516464i	$0.827248\pi$
$114$		−	5.68779i		−	0.532710i
$115$	−4.70859	+	3.66307i	−0.439078	+	0.341583i
$116$			1.22526i			0.113762i
$117$	1.30301	+	1.30301i	0.120463	+	0.120463i
$118$	−8.02678	+	8.02678i	−0.738925	+	0.738925i
$119$		−	5.87998i		−	0.539017i
$120$	−0.441420	+	3.53454i	−0.0402959	+	0.322658i
$121$	5.75380	−	9.37517i	0.523072	−	0.852288i
$122$	7.58870	−	7.58870i	0.687049	−	0.687049i
$123$	5.08105	−	5.08105i	0.458143	−	0.458143i
$124$		−	9.43245i		−	0.847059i
$125$	4.07145	−	10.4127i	0.364161	−	0.931336i
$126$	0.462431			0.0411966
$127$	3.59755	+	3.59755i	0.319231	+	0.319231i	0.848472	−	0.529241i	$-0.177523\pi$
$127$	3.59755	+	3.59755i	0.319231	+	0.319231i	−0.529241	+	0.848472i	$0.677523\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−9.74831			−0.858291
$130$	1.10422	−	8.84176i	0.0968469	−	0.775474i
$131$			11.0741i			0.967545i	0.875194	+	0.483772i	$0.160734\pi$
$131$			11.0741i			0.967545i	−0.875194	+	0.483772i	$0.839266\pi$
$132$	−1.43581	+	5.08446i	−0.124971	+	0.442545i
$133$	2.52475	+	2.52475i	0.218924	+	0.218924i
$134$	−3.73414			−0.322580
$135$	−7.57292	−	9.73438i	−0.651773	−	0.837802i
$136$	5.87998			0.504204
$137$	−7.55794	+	7.55794i	−0.645718	+	0.645718i	−0.951955	−	0.306237i	$-0.900930\pi$
$137$	−7.55794	+	7.55794i	−0.645718	+	0.645718i	0.306237	+	0.951955i	$0.400930\pi$
$138$	3.00515	−	3.00515i	0.255815	−	0.255815i
$139$	4.37684			0.371238			0.185619	−	0.982622i	$-0.440571\pi$
$139$	4.37684			0.371238			0.185619	+	0.982622i	$0.440571\pi$
$140$	−1.37301	−	1.76489i	−0.116040	−	0.149161i
$141$	13.5185			1.13847
$142$	1.17878	+	1.17878i	0.0989209	+	0.0989209i
$143$	3.59173	−	12.7189i	0.300355	−	1.06361i
$144$			0.462431i			0.0385359i
$145$	−0.339524	+	2.71864i	−0.0281959	+	0.225771i
$146$	−5.74786			−0.475697
$147$	1.12640	−	1.12640i	0.0929042	−	0.0929042i
$148$	−4.27744	−	4.27744i	−0.351603	−	0.351603i
$149$	20.8793			1.71050			0.855248	−	0.518219i	$-0.173405\pi$
$149$	20.8793			1.71050			0.855248	+	0.518219i	$0.173405\pi$
$150$	−1.95887	+	7.72024i	−0.159941	+	0.630355i
$151$		−	5.07913i		−	0.413334i	−0.978411	−	0.206667i	$-0.933738\pi$
$151$		−	5.07913i		−	0.413334i	0.978411	−	0.206667i	$-0.0662616\pi$
$152$	−2.52475	+	2.52475i	−0.204785	+	0.204785i
$153$	−1.92268	+	1.92268i	−0.155440	+	0.155440i
$154$	−1.61960	−	2.89429i	−0.130511	−	0.233228i
$155$	2.61377	−	20.9290i	0.209943	−	1.68106i
$156$			6.34780i			0.508231i
$157$	1.01541	−	1.01541i	0.0810382	−	0.0810382i	−0.665426	−	0.746464i	$-0.731750\pi$
$157$	1.01541	−	1.01541i	0.0810382	−	0.0810382i	0.746464	+	0.665426i	$0.231750\pi$
$158$	9.61610	+	9.61610i	0.765016	+	0.765016i
$159$			0.734205i			0.0582263i
$160$	1.76489	−	1.37301i	0.139527	−	0.108546i
$161$			2.66792i			0.210261i
$162$	5.23179	+	5.23179i	0.411048	+	0.411048i
$163$	−12.0834	−	12.0834i	−0.946447	−	0.946447i	0.0521904	−	0.998637i	$-0.483380\pi$
$163$	−12.0834	−	12.0834i	−0.946447	−	0.946447i	−0.998637	+	0.0521904i	$0.983380\pi$
$164$	−4.51086			−0.352239
$165$	−4.59475	+	10.8837i	−0.357701	+	0.847294i
$166$	−12.0025			−0.931571
$167$	−11.9619	−	11.9619i	−0.925641	−	0.925641i	0.0717791	−	0.997421i	$-0.477132\pi$
$167$	−11.9619	−	11.9619i	−0.925641	−	0.925641i	−0.997421	+	0.0717791i	$0.977132\pi$
$168$	1.12640	+	1.12640i	0.0869039	+	0.0869039i
$169$		−	2.87921i		−	0.221478i
$170$	13.0467	+	1.62937i	1.00064	+	0.124967i
$171$		−	1.65113i		−	0.126265i
$172$	4.32718	+	4.32718i	0.329945	+	0.329945i
$173$	−5.48866	+	5.48866i	−0.417295	+	0.417295i	−0.884270	−	0.466975i	$-0.845344\pi$
$173$	−5.48866	+	5.48866i	−0.417295	+	0.417295i	0.466975	+	0.884270i	$0.345344\pi$
$174$		−	1.95181i		−	0.147966i
$175$	−2.55742	−	4.29647i	−0.193322	−	0.324782i
$176$	2.89429	−	1.61960i	0.218165	−	0.122082i
$177$	12.7865	−	12.7865i	0.961089	−	0.961089i
$178$	8.48330	−	8.48330i	0.635850	−	0.635850i
$179$			23.6849i			1.77029i	0.465311	+	0.885147i	$0.345942\pi$
$179$			23.6849i			1.77029i	−0.465311	+	0.885147i	$0.654058\pi$
$180$	−0.128141	+	1.02606i	−0.00955110	+	0.0764777i
$181$	−3.94998			−0.293600			−0.146800	−	0.989166i	$-0.546897\pi$
$181$	−3.94998			−0.293600			−0.146800	+	0.989166i	$0.546897\pi$
$182$	−2.81773	−	2.81773i	−0.208864	−	0.208864i
$183$	−12.0886	+	12.0886i	−0.893616	+	0.893616i
$184$	−2.66792			−0.196681
$185$	−8.30562	−	10.6762i	−0.610642	−	0.784931i
$186$			15.0257i			1.10173i
$187$	18.7677	+	5.29986i	1.37243	+	0.387564i
$188$	−6.00076	−	6.00076i	−0.437650	−	0.437650i
$189$	−5.51557			−0.401198
$190$	−6.30163	+	4.90239i	−0.457168	+	0.355656i
$191$	9.72468			0.703653			0.351827	−	0.936065i	$-0.385561\pi$
$191$	9.72468			0.703653			0.351827	+	0.936065i	$0.385561\pi$
$192$	−1.12640	+	1.12640i	−0.0812912	+	0.0812912i
$193$	8.28046	−	8.28046i	0.596041	−	0.596041i	−0.343216	−	0.939257i	$-0.611516\pi$
$193$	8.28046	−	8.28046i	0.596041	−	0.596041i	0.939257	+	0.343216i	$0.111516\pi$
$194$	8.16171			0.585976
$195$	−1.75900	+	14.0847i	−0.125965	+	1.00863i
$196$	−1.00000			−0.0714286
$197$	−2.11962	−	2.11962i	−0.151016	−	0.151016i	0.627555	−	0.778572i	$-0.284056\pi$
$197$	−2.11962	−	2.11962i	−0.151016	−	0.151016i	−0.778572	+	0.627555i	$0.784056\pi$
$198$	−0.416807	+	1.47599i	−0.0296212	+	0.104894i
$199$		−	25.2631i		−	1.79085i	−0.445210	−	0.895426i	$-0.646871\pi$
$199$		−	25.2631i		−	1.79085i	0.445210	−	0.895426i	$-0.353129\pi$
$200$	4.29647	−	2.55742i	0.303806	−	0.180837i
$201$	5.94839			0.419567
$202$	1.77774	−	1.77774i	0.125082	−	0.125082i
$203$	0.866389	+	0.866389i	0.0608086	+	0.0608086i
$204$	−9.36666			−0.655798
$205$	−10.0088	−	1.24998i	−0.699048	−	0.0873022i
$206$			14.1371i			0.984979i
$207$	0.872376	−	0.872376i	0.0606343	−	0.0606343i
$208$	2.81773	−	2.81773i	0.195374	−	0.195374i
$209$	−10.3342	+	5.78285i	−0.714830	+	0.400008i
$210$	2.18717	+	2.81143i	0.150929	+	0.194007i
$211$			12.8219i			0.882693i	0.897337	+	0.441346i	$0.145499\pi$
$211$			12.8219i			0.882693i	−0.897337	+	0.441346i	$0.854501\pi$
$212$	0.325907	−	0.325907i	0.0223834	−	0.0223834i
$213$	−1.87776	−	1.87776i	−0.128662	−	0.128662i
$214$			9.04947i			0.618609i
$215$	8.40221	+	10.8004i	0.573026	+	0.736579i
$216$		−	5.51557i		−	0.375287i
$217$	−6.66975	−	6.66975i	−0.452772	−	0.452772i
$218$	13.0926	+	13.0926i	0.886745	+	0.886745i
$219$	9.15620			0.618719
$220$	6.87073	−	2.79160i	0.463225	−	0.188210i
$221$	23.4310			1.57614
$222$	6.81386	+	6.81386i	0.457316	+	0.457316i
$223$	5.25176	+	5.25176i	0.351684	+	0.351684i	0.860736	−	0.509052i	$-0.170004\pi$
$223$	5.25176	+	5.25176i	0.351684	+	0.351684i	−0.509052	+	0.860736i	$0.670004\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−0.568648	+	2.24114i	−0.0379099	+	0.149409i
$226$		−	5.10900i		−	0.339846i
$227$	−1.81746	−	1.81746i	−0.120629	−	0.120629i	0.644215	−	0.764844i	$-0.277184\pi$
$227$	−1.81746	−	1.81746i	−0.120629	−	0.120629i	−0.764844	+	0.644215i	$0.777184\pi$
$228$	4.02187	−	4.02187i	0.266355	−	0.266355i
$229$			18.5993i			1.22908i	0.788887	+	0.614538i	$0.210657\pi$
$229$			18.5993i			1.22908i	−0.788887	+	0.614538i	$0.789343\pi$
$230$	−5.91966	−	0.739290i	−0.390331	−	0.0487473i
$231$	2.57998	+	4.61053i	0.169750	+	0.303350i
$232$	−0.866389	+	0.866389i	−0.0568812	+	0.0568812i
$233$	−12.1716	+	12.1716i	−0.797386	+	0.797386i	−0.982683	−	0.185297i	$-0.940675\pi$
$233$	−12.1716	+	12.1716i	−0.797386	+	0.797386i	0.185297	+	0.982683i	$0.440675\pi$
$234$			1.84273i			0.120463i
$235$	−11.6518	−	14.9775i	−0.760082	−	0.977025i
$236$	−11.3516			−0.738925
$237$	−15.3182	−	15.3182i	−0.995024	−	0.995024i
$238$	4.15777	−	4.15777i	0.269508	−	0.269508i
$239$	−19.7037			−1.27452			−0.637262	−	0.770647i	$-0.719933\pi$
$239$	−19.7037			−1.27452			−0.637262	+	0.770647i	$0.719933\pi$
$240$	−2.81143	+	2.18717i	−0.181477	+	0.141181i
$241$		−	6.93411i		−	0.446665i	−0.974742	−	0.223333i	$-0.928306\pi$
$241$		−	6.93411i		−	0.446665i	0.974742	−	0.223333i	$-0.0716936\pi$
$242$	10.6978	−	2.56070i	0.687680	−	0.164608i
$243$	3.36617	+	3.36617i	0.215940	+	0.215940i
$244$	10.7320			0.687049
$245$	−2.21883	−	0.277104i	−0.141756	−	0.0177035i
$246$	7.18569			0.458143
$247$	−10.0608	+	10.0608i	−0.640155	+	0.640155i
$248$	6.66975	−	6.66975i	0.423529	−	0.423529i
$249$	19.1196			1.21166
$250$	10.2418	−	4.48391i	0.647749	−	0.283587i
$251$	17.5480			1.10762			0.553810	−	0.832643i	$-0.313173\pi$
$251$	17.5480			1.10762			0.553810	+	0.832643i	$0.313173\pi$
$252$	0.326988	+	0.326988i	0.0205983	+	0.0205983i
$253$	−8.51545	−	2.40470i	−0.535362	−	0.151182i
$254$			5.08770i			0.319231i
$255$	−20.7830	−	2.59554i	−1.30148	−	0.162539i
$256$	1.00000			0.0625000
$257$	−22.5745	+	22.5745i	−1.40816	+	1.40816i	−0.638709	+	0.769448i	$0.720531\pi$
$257$	−22.5745	+	22.5745i	−1.40816	+	1.40816i	−0.769448	+	0.638709i	$0.779469\pi$
$258$	−6.89310	−	6.89310i	−0.429145	−	0.429145i
$259$	−6.04921			−0.375880
$260$	7.03287	−	5.47126i	0.436160	−	0.339313i
$261$		−	0.566597i		−	0.0350715i
$262$	−7.83054	+	7.83054i	−0.483772	+	0.483772i
$263$	−6.27353	+	6.27353i	−0.386842	+	0.386842i	−0.873560	−	0.486717i	$-0.838194\pi$
$263$	−6.27353	+	6.27353i	−0.386842	+	0.386842i	0.486717	+	0.873560i	$0.338194\pi$
$264$	−4.61053	+	2.57998i	−0.283758	+	0.158787i
$265$	0.813443	−	0.632822i	0.0499694	−	0.0388740i
$266$			3.57054i			0.218924i
$267$	−13.5137	+	13.5137i	−0.827024	+	0.827024i
$268$	−2.64043	−	2.64043i	−0.161290	−	0.161290i
$269$		−	0.616625i		−	0.0375963i	−0.999823	−	0.0187982i	$-0.994016\pi$
$269$		−	0.616625i		−	0.0375963i	0.999823	−	0.0187982i	$-0.00598399\pi$
$270$	1.52839	−	12.2381i	0.0930146	−	0.744788i
$271$			24.3456i			1.47889i	0.673218	+	0.739444i	$0.264912\pi$
$271$			24.3456i			1.47889i	−0.673218	+	0.739444i	$0.735088\pi$
$272$	4.15777	+	4.15777i	0.252102	+	0.252102i
$273$	4.48857	+	4.48857i	0.271661	+	0.271661i
$274$	−10.6885			−0.645718
$275$	16.0186	−	4.29018i	0.965956	−	0.258708i
$276$	4.24992			0.255815
$277$	−11.1602	−	11.1602i	−0.670554	−	0.670554i	0.287290	−	0.957844i	$-0.407246\pi$
$277$	−11.1602	−	11.1602i	−0.670554	−	0.670554i	−0.957844	+	0.287290i	$0.907246\pi$
$278$	3.09489	+	3.09489i	0.185619	+	0.185619i
$279$			4.36185i			0.261137i
$280$	0.277104	−	2.21883i	0.0165601	−	0.132601i
$281$			18.1240i			1.08119i	0.841284	+	0.540593i	$0.181800\pi$
$281$			18.1240i			1.08119i	−0.841284	+	0.540593i	$0.818200\pi$
$282$	9.55906	+	9.55906i	0.569234	+	0.569234i
$283$	−13.7639	+	13.7639i	−0.818179	+	0.818179i	−0.985844	−	0.167665i	$-0.946377\pi$
$283$	−13.7639	+	13.7639i	−0.818179	+	0.818179i	0.167665	+	0.985844i	$0.446377\pi$
$284$			1.66704i			0.0989209i
$285$	10.0383	−	7.80938i	0.594619	−	0.462588i
$286$	11.5334	−	6.45390i	0.681982	−	0.381627i
$287$	−3.18966	+	3.18966i	−0.188280	+	0.188280i
$288$	−0.326988	+	0.326988i	−0.0192679	+	0.0192679i
$289$			17.5742i			1.03378i
$290$	−2.16245	+	1.68229i	−0.126983	+	0.0987875i
$291$	−13.0014			−0.762155
$292$	−4.06435	−	4.06435i	−0.237848	−	0.237848i
$293$	0.292794	−	0.292794i	0.0171052	−	0.0171052i	−0.698502	−	0.715608i	$-0.746150\pi$
$293$	0.292794	−	0.292794i	0.0171052	−	0.0171052i	0.715608	+	0.698502i	$0.246150\pi$
$294$	1.59297			0.0929042
$295$	−25.1872	−	3.14557i	−1.46646	−	0.183142i
$296$		−	6.04921i		−	0.351603i
$297$	4.97140	−	17.6046i	0.288470	−	1.02152i
$298$	14.7639	+	14.7639i	0.855248	+	0.855248i
$299$	−10.6313			−0.614824
$300$	−6.84416	+	4.07390i	−0.395148	+	0.235207i
$301$	6.11956			0.352726
$302$	3.59149	−	3.59149i	0.206667	−	0.206667i
$303$	−2.83190	+	2.83190i	−0.162688	+	0.162688i
$304$	−3.57054			−0.204785
$305$	23.8126	+	2.97389i	1.36351	+	0.170285i
$306$	−2.71908			−0.155440
$307$	16.2073	+	16.2073i	0.925000	+	0.925000i	0.997377	−	0.0723774i	$-0.0230586\pi$
$307$	16.2073	+	16.2073i	0.925000	+	0.925000i	−0.0723774	+	0.997377i	$0.523059\pi$
$308$	0.901340	−	3.19180i	0.0513586	−	0.181870i
$309$		−	22.5201i		−	1.28112i
$310$	16.6473	−	12.9508i	0.945501	−	0.735558i
$311$	−2.67455			−0.151660			−0.0758298	−	0.997121i	$-0.524161\pi$
$311$	−2.67455			−0.151660			−0.0758298	+	0.997121i	$0.524161\pi$
$312$	−4.48857	+	4.48857i	−0.254115	+	0.254115i
$313$	−17.6154	−	17.6154i	−0.995683	−	0.995683i	0.00430801	−	0.999991i	$-0.498629\pi$
$313$	−17.6154	−	17.6154i	−0.995683	−	0.995683i	−0.999991	+	0.00430801i	$0.998629\pi$
$314$	1.43600			0.0810382
$315$	0.634921	+	0.816141i	0.0357738	+	0.0459843i
$316$			13.5992i			0.765016i
$317$	2.40777	−	2.40777i	0.135234	−	0.135234i	−0.636249	−	0.771483i	$-0.719515\pi$
$317$	2.40777	−	2.40777i	0.135234	−	0.135234i	0.771483	+	0.636249i	$0.219515\pi$
$318$	−0.519161	+	0.519161i	−0.0291131	+	0.0291131i
$319$	−3.54625	+	1.98443i	−0.198552	+	0.111107i
$320$	2.21883	+	0.277104i	0.124036	+	0.0154906i
$321$		−	14.4156i		−	0.804599i
$322$	−1.88650	+	1.88650i	−0.105131	+	0.105131i
$323$	−14.8455	−	14.8455i	−0.826026	−	0.826026i
$324$			7.39887i			0.411048i
$325$	17.1209	−	10.1910i	0.949695	−	0.565294i
$326$		−	17.0885i		−	0.946447i
$327$	−20.8562	−	20.8562i	−1.15335	−	1.15335i
$328$	−3.18966	−	3.18966i	−0.176120	−	0.176120i
$329$	−8.48635			−0.467868
$330$	−10.9449	+	4.44695i	−0.602497	+	0.244796i
$331$	−12.5911			−0.692072			−0.346036	−	0.938221i	$-0.612472\pi$
$331$	−12.5911			−0.692072			−0.346036	+	0.938221i	$0.612472\pi$
$332$	−8.48702	−	8.48702i	−0.465786	−	0.465786i
$333$	1.97802	+	1.97802i	0.108395	+	0.108395i
$334$		−	16.9167i		−	0.925641i
$335$	−5.12700	−	6.59035i	−0.280118	−	0.360069i
$336$			1.59297i			0.0869039i
$337$	4.32809	+	4.32809i	0.235766	+	0.235766i	0.815094	−	0.579328i	$-0.196685\pi$
$337$	4.32809	+	4.32809i	0.235766	+	0.235766i	−0.579328	+	0.815094i	$0.696685\pi$
$338$	2.03591	−	2.03591i	0.110739	−	0.110739i
$339$			8.13851i			0.442023i
$340$	8.07327	+	10.3775i	0.437834	+	0.562801i
$341$	27.3002	−	15.2768i	1.47839	−	0.827284i
$342$	1.16752	−	1.16752i	0.0631325	−	0.0631325i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$			6.11956i			0.329945i
$345$	9.42986	+	1.17767i	0.507687	+	0.0634037i
$346$	−7.76213			−0.417295
$347$	−5.75319	−	5.75319i	−0.308847	−	0.308847i	0.535615	−	0.844462i	$-0.320080\pi$
$347$	−5.75319	−	5.75319i	−0.308847	−	0.308847i	−0.844462	+	0.535615i	$0.820080\pi$
$348$	1.38014	−	1.38014i	0.0739830	−	0.0739830i
$349$	24.2926			1.30035			0.650176	−	0.759784i	$-0.274695\pi$
$349$	24.2926			1.30035			0.650176	+	0.759784i	$0.274695\pi$
$350$	1.22969	−	4.84643i	0.0657299	−	0.259052i
$351$		−	21.9788i		−	1.17314i
$352$	3.19180	+	0.901340i	0.170123	+	0.0480416i
$353$	3.20025	+	3.20025i	0.170332	+	0.170332i	0.787125	−	0.616793i	$-0.211568\pi$
$353$	3.20025	+	3.20025i	0.170332	+	0.170332i	−0.616793	+	0.787125i	$0.711568\pi$
$354$	18.0828			0.961089
$355$	−0.461945	+	3.69889i	−0.0245175	+	0.196317i
$356$	11.9972			0.635850
$357$	−6.62323	+	6.62323i	−0.350539	+	0.350539i
$358$	−16.7478	+	16.7478i	−0.885147	+	0.885147i
$359$	−33.3310			−1.75914			−0.879570	−	0.475769i	$-0.842170\pi$
$359$	−33.3310			−1.75914			−0.879570	+	0.475769i	$0.842170\pi$
$360$	−0.816141	+	0.634921i	−0.0430144	+	0.0334633i
$361$	−6.25122			−0.329012
$362$	−2.79306	−	2.79306i	−0.146800	−	0.146800i
$363$	−17.0413	+	4.07913i	−0.894437	+	0.214099i
$364$		−	3.98487i		−	0.208864i
$365$	−7.89187	−	10.1444i	−0.413079	−	0.530980i
$366$	−17.0959			−0.893616
$367$	20.3363	−	20.3363i	1.06155	−	1.06155i	0.0635703	−	0.997977i	$-0.479751\pi$
$367$	20.3363	−	20.3363i	1.06155	−	1.06155i	0.997977	−	0.0635703i	$-0.0202487\pi$
$368$	−1.88650	−	1.88650i	−0.0983407	−	0.0983407i
$369$	2.08596			0.108591
$370$	1.67626	−	13.4222i	0.0871447	−	0.697786i
$371$		−	0.460902i		−	0.0239288i
$372$	−10.6247	+	10.6247i	−0.550867	+	0.550867i
$373$	7.61185	−	7.61185i	0.394127	−	0.394127i	−0.482029	−	0.876155i	$-0.660100\pi$
$373$	7.61185	−	7.61185i	0.394127	−	0.394127i	0.876155	+	0.482029i	$0.160100\pi$
$374$	9.52321	+	17.0184i	0.492434	+	0.879998i
$375$	−16.3149	+	7.14275i	−0.842500	+	0.368850i
$376$		−	8.48635i		−	0.437650i
$377$	−3.45245	+	3.45245i	−0.177810	+	0.177810i
$378$	−3.90009	−	3.90009i	−0.200599	−	0.200599i
$379$		−	17.3663i		−	0.892047i	−0.895021	−	0.446024i	$-0.852840\pi$
$379$		−	17.3663i		−	0.892047i	0.895021	−	0.446024i	$-0.147160\pi$
$380$	−7.92243	−	0.989412i	−0.406412	−	0.0507558i
$381$		−	8.10458i		−	0.415210i
$382$	6.87639	+	6.87639i	0.351827	+	0.351827i
$383$	6.98576	+	6.98576i	0.356956	+	0.356956i	0.862690	−	0.505734i	$-0.168778\pi$
$383$	6.98576	+	6.98576i	0.356956	+	0.356956i	−0.505734	+	0.862690i	$0.668778\pi$
$384$	−1.59297			−0.0812912
$385$	2.88438	−	6.83230i	0.147002	−	0.348206i
$386$	11.7103			0.596041
$387$	−2.00102	−	2.00102i	−0.101718	−	0.101718i
$388$	5.77120	+	5.77120i	0.292988	+	0.292988i
$389$		−	16.4103i		−	0.832035i	−0.909357	−	0.416017i	$-0.863426\pi$
$389$		−	16.4103i		−	0.832035i	0.909357	−	0.416017i	$-0.136574\pi$
$390$	−11.2032	+	8.71559i	−0.567296	+	0.441331i
$391$		−	15.6873i		−	0.793341i
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	12.4739	−	12.4739i	0.629223	−	0.629223i
$394$		−	2.99759i		−	0.151016i
$395$	−3.76840	+	30.1744i	−0.189609	+	1.51824i
$396$	−1.33841	+	0.748952i	−0.0672575	+	0.0376363i
$397$	7.52706	−	7.52706i	0.377773	−	0.377773i	−0.492526	−	0.870298i	$-0.663926\pi$
$397$	7.52706	−	7.52706i	0.377773	−	0.377773i	0.870298	+	0.492526i	$0.163926\pi$
$398$	17.8637	−	17.8637i	0.895426	−	0.895426i
$399$		−	5.68779i		−	0.284745i
$400$	4.84643	+	1.22969i	0.242321	+	0.0614847i
$401$	−30.9786			−1.54700			−0.773499	−	0.633797i	$-0.781495\pi$
$401$	−30.9786			−1.54700			−0.773499	+	0.633797i	$0.781495\pi$
$402$	4.20614	+	4.20614i	0.209783	+	0.209783i
$403$	26.5781	−	26.5781i	1.32395	−	1.32395i
$404$	2.51411			0.125082
$405$	−2.05026	+	16.4168i	−0.101878	+	0.815759i
$406$			1.22526i			0.0608086i
$407$	5.45240	−	19.3079i	0.270266	−	0.957056i
$408$	−6.62323	−	6.62323i	−0.327899	−	0.327899i
$409$	−21.4365			−1.05997			−0.529984	−	0.848008i	$-0.677802\pi$
$409$	−21.4365			−1.05997			−0.529984	+	0.848008i	$0.677802\pi$
$410$	−6.19345	−	7.96119i	−0.305873	−	0.393175i
$411$	17.0266			0.839859
$412$	−9.99644	+	9.99644i	−0.492489	+	0.492489i
$413$	−8.02678	+	8.02678i	−0.394972	+	0.394972i
$414$	1.23373			0.0606343
$415$	−16.4795	−	21.1831i	−0.808946	−	1.03984i
$416$	3.98487			0.195374
$417$	−4.93008	−	4.93008i	−0.241427	−	0.241427i
$418$	−11.3965	−	3.21827i	−0.557419	−	0.157411i
$419$			8.68655i			0.424366i	0.977230	+	0.212183i	$0.0680572\pi$
$419$			8.68655i			0.424366i	−0.977230	+	0.212183i	$0.931943\pi$
$420$	−0.441420	+	3.53454i	−0.0215391	+	0.172468i
$421$	−25.4300			−1.23938			−0.619690	−	0.784846i	$-0.712742\pi$
$421$	−25.4300			−1.23938			−0.619690	+	0.784846i	$0.712742\pi$
$422$	−9.06642	+	9.06642i	−0.441346	+	0.441346i
$423$	2.77493	+	2.77493i	0.134922	+	0.134922i
$424$	0.460902			0.0223834
$425$	15.0376	+	25.2631i	0.729429	+	1.22544i
$426$		−	2.65556i		−	0.128662i
$427$	7.58870	−	7.58870i	0.367243	−	0.367243i
$428$	−6.39894	+	6.39894i	−0.309304	+	0.309304i
$429$	−18.3724	+	10.2809i	−0.887026	+	0.496366i
$430$	−1.69576	+	13.5783i	−0.0817766	+	0.654803i
$431$		−	4.07589i		−	0.196329i	−0.995170	−	0.0981644i	$-0.968703\pi$
$431$		−	4.07589i		−	0.196329i	0.995170	−	0.0981644i	$-0.0312971\pi$
$432$	3.90009	−	3.90009i	0.187643	−	0.187643i
$433$	−0.718614	−	0.718614i	−0.0345344	−	0.0345344i	0.689629	−	0.724163i	$-0.257774\pi$
$433$	−0.718614	−	0.718614i	−0.0345344	−	0.0345344i	−0.724163	+	0.689629i	$0.757774\pi$
$434$		−	9.43245i		−	0.452772i
$435$	3.44473	−	2.67985i	0.165162	−	0.128489i
$436$			18.5158i			0.886745i
$437$	6.73583	+	6.73583i	0.322219	+	0.322219i
$438$	6.47441	+	6.47441i	0.309359	+	0.309359i
$439$	−14.4503			−0.689674			−0.344837	−	0.938663i	$-0.612066\pi$
$439$	−14.4503			−0.689674			−0.344837	+	0.938663i	$0.612066\pi$
$440$	6.83230	+	2.88438i	0.325717	+	0.137508i
$441$	0.462431			0.0220205
$442$	16.5682	+	16.5682i	0.788069	+	0.788069i
$443$	2.18234	+	2.18234i	0.103686	+	0.103686i	0.757047	−	0.653361i	$-0.226641\pi$
$443$	2.18234	+	2.18234i	0.103686	+	0.103686i	−0.653361	+	0.757047i	$0.726641\pi$
$444$			9.63625i			0.457316i
$445$	26.6198	+	3.32447i	1.26190	+	0.157595i
$446$			7.42711i			0.351684i
$447$	−23.5185	−	23.5185i	−1.11239	−	1.11239i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$			15.2868i			0.721427i	0.932677	+	0.360713i	$0.117467\pi$
$449$			15.2868i			0.721427i	−0.932677	+	0.360713i	$0.882533\pi$
$450$	−1.98682	+	1.18263i	−0.0936595	+	0.0557496i
$451$	−7.30579	−	13.0557i	−0.344016	−	0.614770i
$452$	3.61261	−	3.61261i	0.169923	−	0.169923i
$453$	−5.72115	+	5.72115i	−0.268803	+	0.268803i
$454$		−	2.57027i		−	0.120629i
$455$	1.10422	−	8.84176i	0.0517668	−	0.414508i
$456$	5.68779			0.266355
$457$	3.30121	+	3.30121i	0.154424	+	0.154424i	0.780091	−	0.625667i	$-0.215173\pi$
$457$	3.30121	+	3.30121i	0.154424	+	0.154424i	−0.625667	+	0.780091i	$0.715173\pi$
$458$	−13.1517	+	13.1517i	−0.614538	+	0.614538i
$459$	32.4314			1.51377
$460$	−3.66307	−	4.70859i	−0.170792	−	0.219539i
$461$		−	34.2913i		−	1.59710i	−0.601926	−	0.798552i	$-0.705600\pi$
$461$		−	34.2913i		−	1.59710i	0.601926	−	0.798552i	$-0.294400\pi$
$462$	−1.43581	+	5.08446i	−0.0668001	+	0.236550i
$463$	16.7483	+	16.7483i	0.778360	+	0.778360i	0.979552	−	0.201192i	$-0.0644814\pi$
$463$	16.7483	+	16.7483i	0.778360	+	0.778360i	−0.201192	+	0.979552i	$0.564481\pi$
$464$	−1.22526			−0.0568812
$465$	−26.5187	+	20.6304i	−1.22977	+	0.956710i
$466$	−17.2132			−0.797386
$467$	−10.3472	+	10.3472i	−0.478812	+	0.478812i	−0.904752	−	0.425939i	$-0.859944\pi$
$467$	−10.3472	+	10.3472i	−0.478812	+	0.478812i	0.425939	+	0.904752i	$0.359944\pi$
$468$	−1.30301	+	1.30301i	−0.0602314	+	0.0602314i
$469$	−3.73414			−0.172426
$470$	2.35160	−	18.8298i	0.108471	−	0.868553i
$471$	−2.28751			−0.105403
$472$	−8.02678	−	8.02678i	−0.369463	−	0.369463i
$473$	−5.51581	+	19.5324i	−0.253617	+	0.898101i
$474$		−	21.6632i		−	0.995024i
$475$	−17.3044	−	4.39068i	−0.793979	−	0.201458i
$476$	5.87998			0.269508
$477$	−0.150709	+	0.150709i	−0.00690051	+	0.00690051i
$478$	−13.9326	−	13.9326i	−0.637262	−	0.637262i
$479$	42.6579			1.94909			0.974546	−	0.224189i	$-0.0719732\pi$
$479$	42.6579			1.94909			0.974546	+	0.224189i	$0.0719732\pi$
$480$	−3.53454	−	0.441420i	−0.161329	−	0.0201480i
$481$		−	24.1054i		−	1.09911i
$482$	4.90316	−	4.90316i	0.223333	−	0.223333i
$483$	3.00515	−	3.00515i	0.136739	−	0.136739i
$484$	9.37517	+	5.75380i	0.426144	+	0.261536i
$485$	11.2061	+	14.4045i	0.508842	+	0.654076i
$486$			4.76049i			0.215940i
$487$	−20.8575	+	20.8575i	−0.945144	+	0.945144i	−0.998572	−	0.0534277i	$-0.982985\pi$
$487$	−20.8575	+	20.8575i	−0.945144	+	0.945144i	0.0534277	+	0.998572i	$0.482985\pi$
$488$	7.58870	+	7.58870i	0.343524	+	0.343524i
$489$			27.2216i			1.23100i
$490$	−1.37301	−	1.76489i	−0.0620262	−	0.0797297i
$491$		−	2.87041i		−	0.129540i	−0.997900	−	0.0647700i	$-0.979369\pi$
$491$		−	2.87041i		−	0.129540i	0.997900	−	0.0647700i	$-0.0206314\pi$
$492$	5.08105	+	5.08105i	0.229071	+	0.229071i
$493$	−5.09435	−	5.09435i	−0.229438	−	0.229438i
$494$	−14.2282			−0.640155
$495$	−3.17724	+	1.29092i	−0.142806	+	0.0580226i
$496$	9.43245			0.423529
$497$	1.17878	+	1.17878i	0.0528754	+	0.0528754i
$498$	13.5196	+	13.5196i	0.605828	+	0.605828i
$499$		−	28.5037i		−	1.27600i	−0.770037	−	0.638000i	$-0.779762\pi$
$499$		−	28.5037i		−	1.27600i	0.770037	−	0.638000i	$-0.220238\pi$
$500$	10.4127	+	4.07145i	0.465668	+	0.182081i
$501$			26.9479i			1.20394i
$502$	12.4083	+	12.4083i	0.553810	+	0.553810i
$503$	−24.6457	+	24.6457i	−1.09890	+	1.09890i	−0.104357	+	0.994540i	$0.533279\pi$
$503$	−24.6457	+	24.6457i	−1.09890	+	1.09890i	−0.994540	+	0.104357i	$0.966721\pi$
$504$			0.462431i			0.0205983i
$505$	5.57838	+	0.696669i	0.248235	+	0.0310014i
$506$	−4.32095	−	7.72171i	−0.192090	−	0.343272i
$507$	−3.24315	+	3.24315i	−0.144033	+	0.144033i
$508$	−3.59755	+	3.59755i	−0.159615	+	0.159615i
$509$			28.3718i			1.25756i	0.777584	+	0.628779i	$0.216445\pi$
$509$			28.3718i			1.25756i	−0.777584	+	0.628779i	$0.783555\pi$
$510$	−12.8605	−	16.5312i	−0.569473	−	0.732012i
$511$	−5.74786			−0.254271
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−13.9255	+	13.9255i	−0.614824	+	0.614824i
$514$	−31.9251			−1.40816
$515$	−24.9505	+	19.4104i	−1.09945	+	0.855323i
$516$		−	9.74831i		−	0.429145i
$517$	7.64909	−	27.0867i	0.336407	−	1.19127i
$518$	−4.27744	−	4.27744i	−0.187940	−	0.187940i
$519$	12.3649			0.542758
$520$	8.84176	+	1.10422i	0.387737	+	0.0484234i
$521$	0.927122			0.0406180			0.0203090	−	0.999794i	$-0.493535\pi$
$521$	0.927122			0.0406180			0.0203090	+	0.999794i	$0.493535\pi$
$522$	0.400645	−	0.400645i	0.0175357	−	0.0175357i
$523$	27.2331	−	27.2331i	1.19082	−	1.19082i	0.213981	−	0.976838i	$-0.431357\pi$
$523$	27.2331	−	27.2331i	1.19082	−	1.19082i	0.976838	−	0.213981i	$-0.0686430\pi$
$524$	−11.0741			−0.483772
$525$	−1.95887	+	7.72024i	−0.0854922	+	0.336939i
$526$	−8.87211			−0.386842
$527$	39.2180	+	39.2180i	1.70836	+	1.70836i
$528$	−5.08446	−	1.43581i	−0.221273	−	0.0624857i
$529$		−	15.8822i		−	0.690532i
$530$	1.02266	+	0.127718i	0.0444217	+	0.00554771i
$531$	5.24932			0.227801
$532$	−2.52475	+	2.52475i	−0.109462	+	0.109462i
$533$	−12.7104	−	12.7104i	−0.550548	−	0.550548i
$534$	−19.1112			−0.827024
$535$	−15.9713	+	12.4250i	−0.690501	+	0.537180i
$536$		−	3.73414i		−	0.161290i
$537$	26.6788	−	26.6788i	1.15127	−	1.15127i
$538$	0.436020	−	0.436020i	0.0187982	−	0.0187982i
$539$	−1.61960	−	2.89429i	−0.0697611	−	0.124666i
$540$	9.73438	−	7.57292i	0.418901	−	0.325887i
$541$			28.7473i			1.23594i	0.786200	+	0.617972i	$0.212045\pi$
$541$			28.7473i			1.23594i	−0.786200	+	0.617972i	$0.787955\pi$
$542$	−17.2149	+	17.2149i	−0.739444	+	0.739444i
$543$	4.44927	+	4.44927i	0.190937	+	0.190937i
$544$			5.87998i			0.252102i
$545$	−5.13079	+	41.0834i	−0.219779	+	1.75982i
$546$			6.34780i			0.271661i
$547$	−3.32935	−	3.32935i	−0.142353	−	0.142353i	0.632339	−	0.774692i	$-0.282095\pi$
$547$	−3.32935	−	3.32935i	−0.142353	−	0.142353i	−0.774692	+	0.632339i	$0.782095\pi$
$548$	−7.55794	−	7.55794i	−0.322859	−	0.322859i
$549$	−4.96283			−0.211808
$550$	14.3605	+	8.29322i	0.612332	+	0.353624i
$551$	4.37484			0.186374
$552$	3.00515	+	3.00515i	0.127908	+	0.127908i
$553$	9.61610	+	9.61610i	0.408918	+	0.408918i
$554$		−	15.7830i		−	0.670554i
$555$	−2.67024	+	21.3812i	−0.113346	+	0.907582i
$556$			4.37684i			0.185619i
$557$	13.6361	+	13.6361i	0.577778	+	0.577778i	0.934291	−	0.356512i	$-0.116034\pi$
$557$	13.6361	+	13.6361i	0.577778	+	0.577778i	−0.356512	+	0.934291i	$0.616034\pi$
$558$	−3.08430	+	3.08430i	−0.130569	+	0.130569i
$559$			24.3857i			1.03140i
$560$	1.76489	−	1.37301i	0.0745803	−	0.0580202i
$561$	−15.1702	−	27.1098i	−0.640488	−	1.14458i
$562$	−12.8156	+	12.8156i	−0.540593	+	0.540593i
$563$	20.0216	−	20.0216i	0.843808	−	0.843808i	−0.145544	−	0.989352i	$-0.546493\pi$
$563$	20.0216	−	20.0216i	0.843808	−	0.843808i	0.989352	+	0.145544i	$0.0464932\pi$
$564$			13.5185i			0.569234i
$565$	9.01684	−	7.01470i	0.379341	−	0.295111i
$566$	−19.4651			−0.818179
$567$	5.23179	+	5.23179i	0.219714	+	0.219714i
$568$	−1.17878	+	1.17878i	−0.0494604	+	0.0494604i
$569$	−3.34126			−0.140073			−0.0700365	−	0.997544i	$-0.522312\pi$
$569$	−3.34126			−0.140073			−0.0700365	+	0.997544i	$0.522312\pi$
$570$	12.6202	+	1.57611i	0.528604	+	0.0660159i
$571$			19.4315i			0.813183i	0.913610	+	0.406592i	$0.133283\pi$
$571$			19.4315i			0.813183i	−0.913610	+	0.406592i	$0.866717\pi$
$572$	12.7189	+	3.59173i	0.531805	+	0.150178i
$573$	−10.9539	−	10.9539i	−0.457606	−	0.457606i
$574$	−4.51086			−0.188280
$575$	−6.82297	−	11.4626i	−0.284538	−	0.478024i
$576$	−0.462431			−0.0192679
$577$	28.8647	−	28.8647i	1.20165	−	1.20165i	0.227988	−	0.973664i	$-0.426785\pi$
$577$	28.8647	−	28.8647i	1.20165	−	1.20165i	0.973664	−	0.227988i	$-0.0732148\pi$
$578$	−12.4268	+	12.4268i	−0.516888	+	0.516888i
$579$	−18.6543			−0.775246
$580$	−2.71864	−	0.339524i	−0.112885	−	0.0140980i
$581$	−12.0025			−0.497946
$582$	−9.19337	−	9.19337i	−0.381078	−	0.381078i
$583$	1.47111	+	0.415429i	0.0609270	+	0.0172053i
$584$		−	5.74786i		−	0.237848i
$585$	−3.25222	+	2.53008i	−0.134463	+	0.104606i
$586$	0.414073			0.0171052
$587$	−21.9999	+	21.9999i	−0.908032	+	0.908032i	−0.996113	−	0.0880816i	$-0.971926\pi$
$587$	−21.9999	+	21.9999i	−0.908032	+	0.908032i	0.0880816	+	0.996113i	$0.471926\pi$
$588$	1.12640	+	1.12640i	0.0464521	+	0.0464521i
$589$	−33.6790			−1.38772
$590$	−15.5858	−	20.0343i	−0.641658	−	0.824800i
$591$			4.77509i			0.196421i
$592$	4.27744	−	4.27744i	0.175802	−	0.175802i
$593$	−6.34070	+	6.34070i	−0.260381	+	0.260381i	−0.825209	−	0.564828i	$-0.808943\pi$
$593$	−6.34070	+	6.34070i	−0.260381	+	0.260381i	0.564828	+	0.825209i	$0.308943\pi$
$594$	15.9636	−	8.93301i	0.654996	−	0.366526i
$595$	13.0467	+	1.62937i	0.534862	+	0.0667975i
$596$			20.8793i			0.855248i
$597$	−28.4564	+	28.4564i	−1.16464	+	1.16464i
$598$	−7.51747	−	7.51747i	−0.307412	−	0.307412i
$599$		−	17.4692i		−	0.713771i	−0.934148	−	0.356886i	$-0.883839\pi$
$599$		−	17.4692i		−	0.713771i	0.934148	−	0.356886i	$-0.116161\pi$
$600$	−7.72024	−	1.95887i	−0.315177	−	0.0799706i
$601$		−	30.2953i		−	1.23577i	−0.786268	−	0.617886i	$-0.787989\pi$
$601$		−	30.2953i		−	1.23577i	0.786268	−	0.617886i	$-0.212011\pi$
$602$	4.32718	+	4.32718i	0.176363	+	0.176363i
$603$	1.22102	+	1.22102i	0.0497237	+	0.0497237i
$604$	5.07913			0.206667
$605$	19.2075	+	15.3646i	0.780897	+	0.624660i
$606$	−4.00491			−0.162688
$607$	1.64597	+	1.64597i	0.0668080	+	0.0668080i	0.739721	−	0.672913i	$-0.234957\pi$
$607$	1.64597	+	1.64597i	0.0668080	+	0.0668080i	−0.672913	+	0.739721i	$0.734957\pi$
$608$	−2.52475	−	2.52475i	−0.102392	−	0.102392i
$609$		−	1.95181i		−	0.0790912i
$610$	14.7352	+	18.9409i	0.596610	+	0.766895i
$611$		−	33.8170i		−	1.36809i
$612$	−1.92268	−	1.92268i	−0.0777198	−	0.0777198i
$613$	−2.65043	+	2.65043i	−0.107050	+	0.107050i	−0.758603	−	0.651553i	$-0.774118\pi$
$613$	−2.65043	+	2.65043i	−0.107050	+	0.107050i	0.651553	+	0.758603i	$0.274118\pi$
$614$			22.9206i			0.925000i
$615$	9.86602	+	12.6820i	0.397836	+	0.511387i
$616$	2.89429	−	1.61960i	0.116614	−	0.0652555i
$617$	−15.5890	+	15.5890i	−0.627588	+	0.627588i	−0.947461	−	0.319872i	$-0.896360\pi$
$617$	−15.5890	+	15.5890i	−0.627588	+	0.627588i	0.319872	+	0.947461i	$0.396360\pi$
$618$	15.9241	−	15.9241i	0.640561	−	0.640561i
$619$		−	12.6487i		−	0.508394i	−0.967152	−	0.254197i	$-0.918189\pi$
$619$		−	12.6487i		−	0.508394i	0.967152	−	0.254197i	$-0.0818112\pi$
$620$	20.9290	+	2.61377i	0.840529	+	0.104972i
$621$	−14.7151			−0.590495
$622$	−1.89119	−	1.89119i	−0.0758298	−	0.0758298i
$623$	8.48330	−	8.48330i	0.339876	−	0.339876i
$624$	−6.34780			−0.254115
$625$	21.9757	+	11.9192i	0.879028	+	0.476770i
$626$		−	24.9120i		−	0.995683i
$627$	18.1543	+	5.12663i	0.725012	+	0.204738i
$628$	1.01541	+	1.01541i	0.0405191	+	0.0405191i
$629$	35.5693			1.41824
$630$	−0.128141	+	1.02606i	−0.00510528	+	0.0408790i
$631$	−4.68529			−0.186519			−0.0932593	−	0.995642i	$-0.529729\pi$
$631$	−4.68529			−0.186519			−0.0932593	+	0.995642i	$0.529729\pi$
$632$	−9.61610	+	9.61610i	−0.382508	+	0.382508i
$633$	14.4426	−	14.4426i	0.574041	−	0.574041i
$634$	3.40510			0.135234
$635$	−8.97925	+	6.98546i	−0.356331	+	0.277209i
$636$	−0.734205			−0.0291131
$637$	−2.81773	−	2.81773i	−0.111643	−	0.111643i
$638$	−3.91078	−	1.10438i	−0.154829	−	0.0437226i
$639$		−	0.770892i		−	0.0304960i
$640$	1.37301	+	1.76489i	0.0542729	+	0.0697635i
$641$	45.8756			1.81198			0.905989	−	0.423301i	$-0.139129\pi$
$641$	45.8756			1.81198			0.905989	+	0.423301i	$0.139129\pi$
$642$	10.1934	−	10.1934i	0.402300	−	0.402300i
$643$	25.2698	+	25.2698i	0.996544	+	0.996544i	0.999994	−	0.00344978i	$-0.00109810\pi$
$643$	25.2698	+	25.2698i	0.996544	+	0.996544i	−0.00344978	+	0.999994i	$0.501098\pi$
$644$	−2.66792			−0.105131
$645$	2.70130	−	21.6299i	0.106363	−	0.851675i
$646$		−	20.9947i		−	0.826026i
$647$	29.9289	−	29.9289i	1.17662	−	1.17662i	0.196026	−	0.980599i	$-0.437196\pi$
$647$	29.9289	−	29.9289i	1.17662	−	1.17662i	0.980599	−	0.196026i	$-0.0628037\pi$
$648$	−5.23179	+	5.23179i	−0.205524	+	0.205524i
$649$	−18.3850	−	32.8547i	−0.721675	−	1.28966i
$650$	19.3124	+	4.90018i	0.757494	+	0.192201i
$651$			15.0257i			0.588902i
$652$	12.0834	−	12.0834i	0.473223	−	0.473223i
$653$	−15.5924	−	15.5924i	−0.610176	−	0.610176i	0.332816	−	0.942992i	$-0.392001\pi$
$653$	−15.5924	−	15.5924i	−0.610176	−	0.610176i	−0.942992	+	0.332816i	$0.892001\pi$
$654$		−	29.4952i		−	1.15335i
$655$	−24.5715	−	3.06867i	−0.960087	−	0.119903i
$656$		−	4.51086i		−	0.176120i
$657$	1.87948	+	1.87948i	0.0733256	+	0.0733256i
$658$	−6.00076	−	6.00076i	−0.233934	−	0.233934i
$659$	17.1249			0.667093			0.333547	−	0.942734i	$-0.391755\pi$
$659$	17.1249			0.667093			0.333547	+	0.942734i	$0.391755\pi$
$660$	−10.8837	−	4.59475i	−0.423647	−	0.178850i
$661$	−17.1311			−0.666322			−0.333161	−	0.942870i	$-0.608115\pi$
$661$	−17.1311			−0.666322			−0.333161	+	0.942870i	$0.608115\pi$
$662$	−8.90328	−	8.90328i	−0.346036	−	0.346036i
$663$	−26.3927	−	26.3927i	−1.02501	−	1.02501i
$664$		−	12.0025i		−	0.465786i
$665$	−6.30163	+	4.90239i	−0.244367	+	0.190106i
$666$			2.79734i			0.108395i
$667$	2.31145	+	2.31145i	0.0894998	+	0.0894998i
$668$	11.9619	−	11.9619i	0.462821	−	0.462821i
$669$		−	11.8312i		−	0.457420i
$670$	1.03474	−	8.28542i	0.0399757	−	0.320094i
$671$	17.3816	+	31.0616i	0.671010	+	1.19912i
$672$	−1.12640	+	1.12640i	−0.0434520	+	0.0434520i
$673$	−26.5222	+	26.5222i	−1.02235	+	1.02235i	−0.0226106	+	0.999744i	$0.507198\pi$
$673$	−26.5222	+	26.5222i	−1.02235	+	1.02235i	−0.999744	+	0.0226106i	$0.992802\pi$
$674$			6.12084i			0.235766i
$675$	23.6974	−	14.1056i	0.912115	−	0.542925i
$676$	2.87921			0.110739
$677$	10.2042	+	10.2042i	0.392178	+	0.392178i	0.875463	−	0.483285i	$-0.160557\pi$
$677$	10.2042	+	10.2042i	0.392178	+	0.392178i	−0.483285	+	0.875463i	$0.660557\pi$
$678$	−5.75479	+	5.75479i	−0.221012	+	0.221012i
$679$	8.16171			0.313217
$680$	−1.62937	+	13.0467i	−0.0624834	+	0.500318i
$681$			4.09438i			0.156897i
$682$	30.1065	+	8.50185i	1.15284	+	0.325553i
$683$	13.5415	+	13.5415i	0.518150	+	0.518150i	0.917011	−	0.398862i	$-0.130595\pi$
$683$	13.5415	+	13.5415i	0.518150	+	0.518150i	−0.398862	+	0.917011i	$0.630595\pi$
$684$	1.65113			0.0631325
$685$	−14.6755	−	18.8641i	−0.560720	−	0.720761i
$686$	−1.00000			−0.0381802
$687$	20.9503	−	20.9503i	0.799304	−	0.799304i
$688$	−4.32718	+	4.32718i	−0.164972	+	0.164972i
$689$	1.83664			0.0699702
$690$	5.83518	+	7.50066i	0.222142	+	0.285545i
$691$	−25.3633			−0.964865			−0.482432	−	0.875933i	$-0.660247\pi$
$691$	−25.3633			−0.964865			−0.482432	+	0.875933i	$0.660247\pi$
$692$	−5.48866	−	5.48866i	−0.208647	−	0.208647i
$693$	−0.416807	+	1.47599i	−0.0158332	+	0.0560681i
$694$		−	8.13624i		−	0.308847i
$695$	−1.21284	+	9.71146i	−0.0460056	+	0.368377i
$696$	1.95181			0.0739830
$697$	18.7551	−	18.7551i	0.710402	−	0.710402i
$698$	17.1774	+	17.1774i	0.650176	+	0.650176i
$699$	27.4202			1.03713
$700$	4.29647	−	2.55742i	0.162391	−	0.0966612i
$701$		−	22.1826i		−	0.837824i	−0.908027	−	0.418912i	$-0.862412\pi$
$701$		−	22.1826i		−	0.837824i	0.908027	−	0.418912i	$-0.137588\pi$
$702$	15.5414	−	15.5414i	0.586571	−	0.586571i
$703$	−15.2728	+	15.2728i	−0.576024	+	0.576024i
$704$	1.61960	+	2.89429i	0.0610409	+	0.109083i
$705$	−3.74604	+	29.9954i	−0.141084	+	1.12969i
$706$			4.52584i			0.170332i
$707$	1.77774	−	1.77774i	0.0668589	−	0.0668589i
$708$	12.7865	+	12.7865i	0.480545	+	0.480545i
$709$		−	9.21272i		−	0.345991i	−0.984923	−	0.172995i	$-0.944655\pi$
$709$		−	9.21272i		−	0.345991i	0.984923	−	0.172995i	$-0.0553446\pi$
$710$	−2.94215	+	2.28887i	−0.110417	+	0.0858996i
$711$		−	6.28870i		−	0.235845i
$712$	8.48330	+	8.48330i	0.317925	+	0.317925i
$713$	−17.7943	−	17.7943i	−0.666403	−	0.666403i
$714$	−9.36666			−0.350539
$715$	27.2258	+	11.4939i	1.01819	+	0.429847i
$716$	−23.6849			−0.885147
$717$	22.1943	+	22.1943i	0.828861	+	0.828861i
$718$	−23.5685	−	23.5685i	−0.879570	−	0.879570i
$719$		−	4.78036i		−	0.178277i	−0.996019	−	0.0891386i	$-0.971589\pi$
$719$		−	4.78036i		−	0.178277i	0.996019	−	0.0891386i	$-0.0284114\pi$
$720$	−1.02606	−	0.128141i	−0.0382388	−	0.00477555i
$721$			14.1371i			0.526493i
$722$	−4.42028	−	4.42028i	−0.164506	−	0.164506i
$723$	−7.81061	+	7.81061i	−0.290480	+	0.290480i
$724$		−	3.94998i		−	0.146800i
$725$	−5.93813	−	1.50669i	−0.220536	−	0.0559572i
$726$	−14.9344	−	9.16565i	−0.554268	−	0.340169i
$727$	−6.64578	+	6.64578i	−0.246478	+	0.246478i	−0.819524	−	0.573045i	$-0.805762\pi$
$727$	−6.64578	+	6.64578i	−0.246478	+	0.246478i	0.573045	+	0.819524i	$0.305762\pi$
$728$	2.81773	−	2.81773i	0.104432	−	0.104432i
$729$		−	29.7799i		−	1.10296i
$730$	1.59276	−	12.7535i	0.0589506	−	0.472030i
$731$	−35.9829			−1.33088
$732$	−12.0886	−	12.0886i	−0.446808	−	0.446808i
$733$	31.5358	−	31.5358i	1.16480	−	1.16480i	0.181391	−	0.983411i	$-0.441940\pi$
$733$	31.5358	−	31.5358i	1.16480	−	1.16480i	0.983411	−	0.181391i	$-0.0580600\pi$
$734$	28.7599			1.06155
$735$	2.18717	+	2.81143i	0.0806749	+	0.103701i
$736$		−	2.66792i		−	0.0983407i
$737$	3.36573	−	11.9186i	0.123978	−	0.439028i
$738$	1.47500	+	1.47500i	0.0542954	+	0.0542954i
$739$	−23.8380			−0.876893			−0.438447	−	0.898757i	$-0.644471\pi$
$739$	−23.8380			−0.876893			−0.438447	+	0.898757i	$0.644471\pi$
$740$	10.6762	−	8.30562i	0.392466	−	0.305321i
$741$	22.6651			0.832623
$742$	0.325907	−	0.325907i	0.0119644	−	0.0119644i
$743$	19.1554	−	19.1554i	0.702744	−	0.702744i	−0.262255	−	0.964999i	$-0.584466\pi$
$743$	19.1554	−	19.1554i	0.702744	−	0.702744i	0.964999	+	0.262255i	$0.0844660\pi$
$744$	−15.0257			−0.550867
$745$	−5.78573	+	46.3276i	−0.211973	+	1.69731i
$746$	10.7648			0.394127
$747$	3.92466	+	3.92466i	0.143596	+	0.143596i
$748$	−5.29986	+	18.7677i	−0.193782	+	0.686216i
$749$			9.04947i			0.330660i
$750$	−16.5871	−	6.48572i	−0.605675	−	0.236825i
$751$	16.2825			0.594157			0.297078	−	0.954853i	$-0.403988\pi$
$751$	16.2825			0.594157			0.297078	+	0.954853i	$0.403988\pi$
$752$	6.00076	−	6.00076i	0.218825	−	0.218825i
$753$	−19.7661	−	19.7661i	−0.720318	−	0.720318i
$754$	−4.88250			−0.177810
$755$	11.2697	+	1.40745i	0.410147	+	0.0512222i
$756$		−	5.51557i		−	0.200599i
$757$	−38.6196	+	38.6196i	−1.40365	+	1.40365i	−0.615570	+	0.788083i	$0.711074\pi$
$757$	−38.6196	+	38.6196i	−1.40365	+	1.40365i	−0.788083	+	0.615570i	$0.788926\pi$
$758$	12.2798	−	12.2798i	0.446024	−	0.446024i
$759$	6.88317	+	12.3005i	0.249843	+	0.446480i
$760$	−4.90239	−	6.30163i	−0.177828	−	0.228584i
$761$			52.1150i			1.88917i	0.328268	+	0.944584i	$0.393535\pi$
$761$			52.1150i			1.88917i	−0.328268	+	0.944584i	$0.606465\pi$
$762$	5.73080	−	5.73080i	0.207605	−	0.207605i
$763$	13.0926	+	13.0926i	0.473985	+	0.473985i
$764$			9.72468i			0.351827i
$765$	−3.73333	−	4.79889i	−0.134979	−	0.173504i
$766$			9.87936i			0.356956i
$767$	−31.9857	−	31.9857i	−1.15494	−	1.15494i
$768$	−1.12640	−	1.12640i	−0.0406456	−	0.0406456i
$769$	21.2836			0.767506			0.383753	−	0.923436i	$-0.374631\pi$
$769$	21.2836			0.767506			0.383753	+	0.923436i	$0.374631\pi$
$770$	6.87073	−	2.79160i	0.247604	−	0.100602i
$771$	50.8559			1.83153
$772$	8.28046	+	8.28046i	0.298020	+	0.298020i
$773$	12.9076	+	12.9076i	0.464255	+	0.464255i	0.900047	−	0.435793i	$-0.143532\pi$
$773$	12.9076	+	12.9076i	0.464255	+	0.464255i	−0.435793	+	0.900047i	$0.643532\pi$
$774$		−	2.82987i		−	0.101718i
$775$	45.7137	+	11.5990i	1.64208	+	0.416649i
$776$			8.16171i			0.292988i
$777$	6.81386	+	6.81386i	0.244446	+	0.244446i
$778$	11.6038	−	11.6038i	0.416017	−	0.416017i
$779$			16.1062i			0.577065i
$780$	−14.0847	−	1.75900i	−0.504313	−	0.0629824i
$781$	−4.82490	+	2.69994i	−0.172649	+	0.0966116i
$782$	11.0926	−	11.0926i	0.396670	−	0.396670i
$783$	−4.77862	+	4.77862i	−0.170774	+	0.170774i
$784$		−	1.00000i		−	0.0357143i
$785$	1.97164	+	2.53439i	0.0703709	+	0.0904561i
$786$	17.6407			0.629223
$787$	10.4428	+	10.4428i	0.372244	+	0.372244i	0.868294	−	0.496050i	$-0.165217\pi$
$787$	10.4428	+	10.4428i	0.372244	+	0.372244i	−0.496050	+	0.868294i	$0.665217\pi$
$788$	2.11962	−	2.11962i	0.0755082	−	0.0755082i
$789$	14.1330			0.503150
$790$	−24.0012	+	18.6718i	−0.853923	+	0.664314i
$791$		−	5.10900i		−	0.181655i
$792$	−1.47599	−	0.416807i	−0.0524469	−	0.0148106i
$793$	30.2400	+	30.2400i	1.07385	+	1.07385i
$794$	10.6449			0.377773
$795$	−1.62908	−	0.203451i	−0.0577774	−	0.00721567i
$796$	25.2631			0.895426
$797$	17.1425	−	17.1425i	0.607217	−	0.607217i	−0.335001	−	0.942218i	$-0.608737\pi$
$797$	17.1425	−	17.1425i	0.607217	−	0.607217i	0.942218	+	0.335001i	$0.108737\pi$
$798$	4.02187	−	4.02187i	0.142373	−	0.142373i
$799$	49.8996			1.76532
$800$	2.55742	+	4.29647i	0.0904183	+	0.151903i
$801$	−5.54787			−0.196024
$802$	−21.9052	−	21.9052i	−0.773499	−	0.773499i
$803$	5.18078	−	18.3460i	0.182826	−	0.647417i
$804$			5.94839i			0.209783i
$805$	−5.91966	−	0.739290i	−0.208640	−	0.0260566i
$806$	37.5871			1.32395
$807$	−0.694569	+	0.694569i	−0.0244500	+	0.0244500i
$808$	1.77774	+	1.77774i	0.0625408	+	0.0625408i
$809$	9.35192			0.328796			0.164398	−	0.986394i	$-0.447432\pi$
$809$	9.35192			0.328796			0.164398	+	0.986394i	$0.447432\pi$
$810$	−13.0582	+	10.1587i	−0.458819	+	0.356941i
$811$		−	9.97185i		−	0.350159i	−0.984554	−	0.175079i	$-0.943982\pi$
$811$		−	9.97185i		−	0.350159i	0.984554	−	0.175079i	$-0.0560182\pi$
$812$	−0.866389	+	0.866389i	−0.0304043	+	0.0304043i
$813$	27.4229	−	27.4229i	0.961765	−	0.961765i
$814$	17.5082	−	9.79730i	0.613661	−	0.343395i
$815$	30.1594	−	23.4627i	1.05644	−	0.821863i
$816$		−	9.36666i		−	0.327899i
$817$	15.4504	−	15.4504i	0.540541	−	0.540541i
$818$	−15.1579	−	15.1579i	−0.529984	−	0.529984i
$819$			1.84273i			0.0643901i
$820$	1.24998	−	10.0088i	0.0436511	−	0.349524i
$821$			13.1710i			0.459671i	0.973230	+	0.229835i	$0.0738188\pi$
$821$			13.1710i			0.459671i	−0.973230	+	0.229835i	$0.926181\pi$
$822$	12.0396	+	12.0396i	0.419929	+	0.419929i
$823$	−7.98644	−	7.98644i	−0.278390	−	0.278390i	0.554076	−	0.832466i	$-0.313072\pi$
$823$	−7.98644	−	7.98644i	−0.278390	−	0.278390i	−0.832466	+	0.554076i	$0.813072\pi$
$824$	−14.1371			−0.492489
$825$	−22.8758	−	13.2109i	−0.796434	−	0.459944i
$826$	−11.3516			−0.394972
$827$	16.2693	+	16.2693i	0.565739	+	0.565739i	0.930932	−	0.365193i	$-0.118997\pi$
$827$	16.2693	+	16.2693i	0.565739	+	0.565739i	−0.365193	+	0.930932i	$0.618997\pi$
$828$	0.872376	+	0.872376i	0.0303172	+	0.0303172i
$829$		−	19.2029i		−	0.666945i	−0.942760	−	0.333472i	$-0.891780\pi$
$829$		−	19.2029i		−	0.666945i	0.942760	−	0.333472i	$-0.108220\pi$
$830$	3.32593	−	26.6314i	0.115445	−	0.924390i
$831$			25.1419i			0.872162i
$832$	2.81773	+	2.81773i	0.0976872	+	0.0976872i
$833$	4.15777	−	4.15777i	0.144058	−	0.144058i
$834$		−	6.97219i		−	0.241427i
$835$	29.8562	−	23.2268i	1.03322	−	0.803796i
$836$	−5.78285	−	10.3342i	−0.200004	−	0.357415i
$837$	36.7874	−	36.7874i	1.27156	−	1.27156i
$838$	−6.14232	+	6.14232i	−0.212183	+	0.212183i
$839$			24.0992i			0.831997i	0.909365	+	0.415998i	$0.136568\pi$
$839$			24.0992i			0.831997i	−0.909365	+	0.415998i	$0.863432\pi$
$840$	−2.81143	+	2.18717i	−0.0970036	+	0.0754645i
$841$	−27.4987			−0.948232
$842$	−17.9817	−	17.9817i	−0.619690	−	0.619690i
$843$	20.4149	−	20.4149i	0.703127	−	0.703127i
$844$	−12.8219			−0.441346
$845$	6.38848	+	0.797841i	0.219770	+	0.0274466i
$846$			3.92435i			0.134922i
$847$	10.6978	−	2.56070i	0.367581	−	0.0879867i
$848$	0.325907	+	0.325907i	0.0111917	+	0.0111917i
$849$	31.0074			1.06417
$850$	−7.23058	+	28.4969i	−0.248007	+	0.977436i
$851$	−16.1388			−0.553231
$852$	1.87776	−	1.87776i	0.0643311	−	0.0643311i
$853$	−16.4503	+	16.4503i	−0.563249	+	0.563249i	−0.930229	−	0.366980i	$-0.880392\pi$
$853$	−16.4503	+	16.4503i	−0.563249	+	0.563249i	0.366980	+	0.930229i	$0.380392\pi$
$854$	10.7320			0.367243
$855$	3.66358	+	0.457534i	0.125292	+	0.0156473i
$856$	−9.04947			−0.309304
$857$	−23.8563	−	23.8563i	−0.814917	−	0.814917i	0.170449	−	0.985366i	$-0.445478\pi$
$857$	−23.8563	−	23.8563i	−0.814917	−	0.814917i	−0.985366	+	0.170449i	$0.945478\pi$
$858$	−20.2609	−	5.72153i	−0.691696	−	0.195330i
$859$			40.7880i			1.39167i	0.718202	+	0.695835i	$0.244965\pi$
$859$			40.7880i			1.39167i	−0.718202	+	0.695835i	$0.755035\pi$
$860$	−10.8004	+	8.40221i	−0.368290	+	0.286513i
$861$	7.18569			0.244888
$862$	2.88209	−	2.88209i	0.0981644	−	0.0981644i
$863$	−18.2523	−	18.2523i	−0.621317	−	0.621317i	0.324551	−	0.945868i	$-0.394787\pi$
$863$	−18.2523	−	18.2523i	−0.621317	−	0.621317i	−0.945868	+	0.324551i	$0.894787\pi$
$864$	5.51557			0.187643
$865$	−10.6575	−	13.6993i	−0.362365	−	0.465791i
$866$		−	1.01627i		−	0.0345344i
$867$	19.7956	−	19.7956i	0.672294	−	0.672294i
$868$	6.66975	−	6.66975i	0.226386	−	0.226386i
$869$	−39.3600	+	22.0253i	−1.33520	+	0.747157i
$870$	4.33073	+	0.540853i	0.146825	+	0.0183366i
$871$		−	14.8801i		−	0.504192i
$872$	−13.0926	+	13.0926i	−0.443372	+	0.443372i
$873$	−2.66878	−	2.66878i	−0.0903245	−	0.0903245i
$874$			9.52591i			0.322219i
$875$	10.2418	−	4.48391i	0.346236	−	0.151584i
$876$			9.15620i			0.309359i
$877$	−15.2913	−	15.2913i	−0.516349	−	0.516349i	0.400115	−	0.916465i	$-0.368970\pi$
$877$	−15.2913	−	15.2913i	−0.516349	−	0.516349i	−0.916465	+	0.400115i	$0.868970\pi$
$878$	−10.2179	−	10.2179i	−0.344837	−	0.344837i
$879$	−0.659608			−0.0222480
$880$	2.79160	+	6.87073i	0.0941048	+	0.231612i
$881$	−50.4122			−1.69843			−0.849216	−	0.528046i	$-0.822925\pi$
$881$	−50.4122			−1.69843			−0.849216	+	0.528046i	$0.822925\pi$
$882$	0.326988	+	0.326988i	0.0110103	+	0.0110103i
$883$	0.957578	+	0.957578i	0.0322251	+	0.0322251i	0.723036	−	0.690811i	$-0.242746\pi$
$883$	0.957578	+	0.957578i	0.0322251	+	0.0322251i	−0.690811	+	0.723036i	$0.742746\pi$
$884$			23.4310i			0.788069i
$885$	24.8278	+	31.9142i	0.834578	+	1.07278i
$886$			3.08629i			0.103686i
$887$	−23.7656	−	23.7656i	−0.797971	−	0.797971i	0.184804	−	0.982775i	$-0.440835\pi$
$887$	−23.7656	−	23.7656i	−0.797971	−	0.797971i	−0.982775	+	0.184804i	$0.940835\pi$
$888$	−6.81386	+	6.81386i	−0.228658	+	0.228658i
$889$			5.08770i			0.170636i
$890$	16.4723	+	21.1738i	0.552151	+	0.709746i
$891$	−21.4144	+	11.9832i	−0.717411	+	0.401452i
$892$	−5.25176	+	5.25176i	−0.175842	+	0.175842i
$893$	−21.4260	+	21.4260i	−0.716993	+	0.716993i
$894$		−	33.2601i		−	1.11239i
$895$	−52.5529	−	6.56319i	−1.75665	−	0.219383i
$896$	1.00000			0.0334077
$897$	11.9751	+	11.9751i	0.399838	+	0.399838i
$898$	−10.8094	+	10.8094i	−0.360713	+	0.360713i
$899$	−11.5572			−0.385454
$900$	−2.24114	−	0.568648i	−0.0747045	−	0.0189549i
$901$			2.71009i			0.0902863i
$902$	4.06582	−	14.3978i	0.135377	−	0.479393i
$903$	−6.89310	−	6.89310i	−0.229388	−	0.229388i
$904$	5.10900			0.169923
$905$	1.09456	−	8.76435i	0.0363843	−	0.291337i
$906$	−8.09092			−0.268803
$907$	−9.37776	+	9.37776i	−0.311383	+	0.311383i	−0.845445	−	0.534062i	$-0.820665\pi$
$907$	−9.37776	+	9.37776i	−0.311383	+	0.311383i	0.534062	+	0.845445i	$0.320665\pi$
$908$	1.81746	−	1.81746i	0.0603144	−	0.0603144i
$909$	−1.16260			−0.0385610
$910$	7.03287	−	5.47126i	0.233137	−	0.181371i
$911$	−47.1255			−1.56134			−0.780669	−	0.624945i	$-0.785121\pi$
$911$	−47.1255			−1.56134			−0.780669	+	0.624945i	$0.785121\pi$
$912$	4.02187	+	4.02187i	0.133177	+	0.133177i
$913$	10.8183	−	38.3094i	0.358033	−	1.26786i
$914$			4.66862i			0.154424i
$915$	−23.4728	−	30.1724i	−0.775986	−	0.997468i
$916$	−18.5993			−0.614538
$917$	−7.83054	+	7.83054i	−0.258587	+	0.258587i
$918$	22.9325	+	22.9325i	0.756885	+	0.756885i
$919$	−34.1248			−1.12567			−0.562836	−	0.826568i	$-0.690290\pi$
$919$	−34.1248			−1.12567			−0.562836	+	0.826568i	$0.690290\pi$
$920$	0.739290	−	5.91966i	0.0243737	−	0.195165i
$921$		−	36.5119i		−	1.20311i
$922$	24.2476	−	24.2476i	0.798552	−	0.798552i
$923$	−4.69728	+	4.69728i	−0.154613	+	0.154613i
$924$	−4.61053	+	2.57998i	−0.151675	+	0.0848752i
$925$	25.9902	−	15.4704i	0.854554	−	0.508662i
$926$			23.6857i			0.778360i
$927$	4.62266	−	4.62266i	0.151828	−	0.151828i
$928$	−0.866389	−	0.866389i	−0.0284406	−	0.0284406i
$929$			22.5508i			0.739868i	0.929058	+	0.369934i	$0.120620\pi$
$929$			22.5508i			0.739868i	−0.929058	+	0.369934i	$0.879380\pi$
$930$	−33.3394	−	4.16367i	−1.09324	−	0.136532i
$931$			3.57054i			0.117020i
$932$	−12.1716	−	12.1716i	−0.398693	−	0.398693i
$933$	3.01262	+	3.01262i	0.0986287	+	0.0986287i
$934$	−14.6332			−0.478812
$935$	−16.9601	+	40.1738i	−0.554655	+	1.31382i
$936$	−1.84273			−0.0602314
$937$	−32.5537	−	32.5537i	−1.06348	−	1.06348i	−0.997843	−	0.0656397i	$-0.979091\pi$
$937$	−32.5537	−	32.5537i	−1.06348	−	1.06348i	−0.0656397	−	0.997843i	$-0.520909\pi$
$938$	−2.64043	−	2.64043i	−0.0862132	−	0.0862132i
$939$			39.6842i			1.29504i
$940$	14.9775	−	11.6518i	0.488512	−	0.380041i
$941$		−	21.5108i		−	0.701231i	−0.936519	−	0.350616i	$-0.885972\pi$
$941$		−	21.5108i		−	0.701231i	0.936519	−	0.350616i	$-0.114028\pi$
$942$	−1.61752	−	1.61752i	−0.0527015	−	0.0527015i
$943$	−8.50975	+	8.50975i	−0.277115	+	0.277115i
$944$		−	11.3516i		−	0.369463i
$945$	1.52839	−	12.2381i	0.0497184	−	0.398106i
$946$	−17.7118	+	9.91124i	−0.575859	+	0.322242i
$947$	19.3572	−	19.3572i	0.629024	−	0.629024i	−0.318798	−	0.947823i	$-0.603279\pi$
$947$	19.3572	−	19.3572i	0.629024	−	0.629024i	0.947823	+	0.318798i	$0.103279\pi$
$948$	15.3182	−	15.3182i	0.497512	−	0.497512i
$949$		−	22.9045i		−	0.743512i
$950$	−9.13136	−	15.3407i	−0.296261	−	0.497719i
$951$	−5.42424			−0.175893
$952$	4.15777	+	4.15777i	0.134754	+	0.134754i
$953$	36.3981	−	36.3981i	1.17905	−	1.17905i	0.199065	−	0.979986i	$-0.436209\pi$
$953$	36.3981	−	36.3981i	1.17905	−	1.17905i	0.979986	−	0.199065i	$-0.0637905\pi$
$954$	−0.213135			−0.00690051
$955$	−2.69475	+	21.5774i	−0.0872000	+	0.698229i
$956$		−	19.7037i		−	0.637262i
$957$	6.22978	+	1.75924i	0.201380	+	0.0568682i
$958$	30.1637	+	30.1637i	0.974546	+	0.974546i
$959$	−10.6885			−0.345151
$960$	−2.18717	−	2.81143i	−0.0705906	−	0.0907385i
$961$	57.9711			1.87004
$962$	17.0451	−	17.0451i	0.549555	−	0.549555i
$963$	2.95907	−	2.95907i	0.0953546	−	0.0953546i
$964$	6.93411			0.223333
$965$	16.0784	+	20.6675i	0.517582	+	0.665311i
$966$	4.24992			0.136739
$967$	33.4497	+	33.4497i	1.07567	+	1.07567i	0.996892	+	0.0787789i	$0.0251021\pi$
$967$	33.4497	+	33.4497i	1.07567	+	1.07567i	0.0787789	+	0.996892i	$0.474898\pi$
$968$	2.56070	+	10.6978i	0.0823040	+	0.343840i
$969$			33.4441i			1.07438i
$970$	−2.26164	+	18.1094i	−0.0726169	+	0.581459i
$971$	−16.9411			−0.543666			−0.271833	−	0.962344i	$-0.587630\pi$
$971$	−16.9411			−0.543666			−0.271833	+	0.962344i	$0.587630\pi$
$972$	−3.36617	+	3.36617i	−0.107970	+	0.107970i
$973$	3.09489	+	3.09489i	0.0992176	+	0.0992176i
$974$	−29.4970			−0.945144
$975$	−30.7642	−	7.80586i	−0.985242	−	0.249987i
$976$			10.7320i			0.343524i
$977$	15.7563	−	15.7563i	0.504089	−	0.504089i	−0.408617	−	0.912706i	$-0.633989\pi$
$977$	15.7563	−	15.7563i	0.504089	−	0.504089i	0.912706	+	0.408617i	$0.133989\pi$
$978$	−19.2486	+	19.2486i	−0.615502	+	0.615502i
$979$	19.4307	+	34.7233i	0.621006	+	1.10976i
$980$	0.277104	−	2.21883i	0.00885176	−	0.0708780i
$981$		−	8.56226i		−	0.273372i
$982$	2.02969	−	2.02969i	0.0647700	−	0.0647700i
$983$	−5.72822	−	5.72822i	−0.182702	−	0.182702i	0.609830	−	0.792532i	$-0.291238\pi$
$983$	−5.72822	−	5.72822i	−0.182702	−	0.182702i	−0.792532	+	0.609830i	$0.791238\pi$
$984$			7.18569i			0.229071i
$985$	5.29043	−	4.11572i	0.168567	−	0.131138i
$986$		−	7.20450i		−	0.229438i
$987$	9.55906	+	9.55906i	0.304268	+	0.304268i
$988$	−10.0608	−	10.0608i	−0.320078	−	0.320078i
$989$	16.3265			0.519152
$990$	−3.15947	−	1.33383i	−0.100414	−	0.0423918i
$991$	−30.1008			−0.956184			−0.478092	−	0.878310i	$-0.658671\pi$
$991$	−30.1008			−0.956184			−0.478092	+	0.878310i	$0.658671\pi$
$992$	6.66975	+	6.66975i	0.211765	+	0.211765i
$993$	14.1827	+	14.1827i	0.450075	+	0.450075i
$994$			1.66704i			0.0528754i
$995$	56.0545	+	7.00050i	1.77705	+	0.221931i
$996$			19.1196i			0.605828i
$997$	11.6690	+	11.6690i	0.369561	+	0.369561i	0.867317	−	0.497756i	$-0.165842\pi$
$997$	11.6690	+	11.6690i	0.369561	+	0.369561i	−0.497756	+	0.867317i	$0.665842\pi$
$998$	20.1551	−	20.1551i	0.638000	−	0.638000i
$999$		−	33.3648i		−	1.05562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.43.12	yes	36
5.2	odd	4	inner	770.2.m.f.197.3	yes	36
11.10	odd	2	inner	770.2.m.f.43.3	✓	36
55.32	even	4	inner	770.2.m.f.197.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.3	✓	36	11.10	odd	2	inner
770.2.m.f.43.12	yes	36	1.1	even	1	trivial
770.2.m.f.197.3	yes	36	5.2	odd	4	inner
770.2.m.f.197.12	yes	36	55.32	even	4	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.12640 - 1.12640i) q^{3} +1.00000i q^{4} +(-0.277104 + 2.21883i) q^{5} -1.59297i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.462431i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.12640 - 1.12640i) q^{3} +1.00000i q^{4} +(-0.277104 + 2.21883i) q^{5} -1.59297i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.462431i q^{9} +(-1.76489 + 1.37301i) q^{10} +(-2.89429 + 1.61960i) q^{11} +(1.12640 - 1.12640i) q^{12} +(-2.81773 + 2.81773i) q^{13} +1.00000i q^{14} +(2.81143 - 2.18717i) q^{15} -1.00000 q^{16} +(-4.15777 - 4.15777i) q^{17} +(0.326988 - 0.326988i) q^{18} +3.57054 q^{19} +(-2.21883 - 0.277104i) q^{20} -1.59297i q^{21} +(-3.19180 - 0.901340i) q^{22} +(1.88650 + 1.88650i) q^{23} +1.59297 q^{24} +(-4.84643 - 1.22969i) q^{25} -3.98487 q^{26} +(-3.90009 + 3.90009i) q^{27} +(-0.707107 + 0.707107i) q^{28} +1.22526 q^{29} +(3.53454 + 0.441420i) q^{30} -9.43245 q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.08446 + 1.43581i) q^{33} -5.87998i q^{34} +(-1.76489 + 1.37301i) q^{35} +0.462431 q^{36} +(-4.27744 + 4.27744i) q^{37} +(2.52475 + 2.52475i) q^{38} +6.34780 q^{39} +(-1.37301 - 1.76489i) q^{40} +4.51086i q^{41} +(1.12640 - 1.12640i) q^{42} +(4.32718 - 4.32718i) q^{43} +(-1.61960 - 2.89429i) q^{44} +(1.02606 + 0.128141i) q^{45} +2.66792i q^{46} +(-6.00076 + 6.00076i) q^{47} +(1.12640 + 1.12640i) q^{48} +1.00000i q^{49} +(-2.55742 - 4.29647i) q^{50} +9.36666i q^{51} +(-2.81773 - 2.81773i) q^{52} +(-0.325907 - 0.325907i) q^{53} -5.51557 q^{54} +(-2.79160 - 6.87073i) q^{55} -1.00000 q^{56} +(-4.02187 - 4.02187i) q^{57} +(0.866389 + 0.866389i) q^{58} +11.3516i q^{59} +(2.18717 + 2.81143i) q^{60} -10.7320i q^{61} +(-6.66975 - 6.66975i) q^{62} +(0.326988 - 0.326988i) q^{63} -1.00000i q^{64} +(-5.47126 - 7.03287i) q^{65} +(2.57998 + 4.61053i) q^{66} +(-2.64043 + 2.64043i) q^{67} +(4.15777 - 4.15777i) q^{68} -4.24992i q^{69} +(-2.21883 - 0.277104i) q^{70} +1.66704 q^{71} +(0.326988 + 0.326988i) q^{72} +(-4.06435 + 4.06435i) q^{73} -6.04921 q^{74} +(4.07390 + 6.84416i) q^{75} +3.57054i q^{76} +(-3.19180 - 0.901340i) q^{77} +(4.48857 + 4.48857i) q^{78} +13.5992 q^{79} +(0.277104 - 2.21883i) q^{80} +7.39887 q^{81} +(-3.18966 + 3.18966i) q^{82} +(-8.48702 + 8.48702i) q^{83} +1.59297 q^{84} +(10.3775 - 8.07327i) q^{85} +6.11956 q^{86} +(-1.38014 - 1.38014i) q^{87} +(0.901340 - 3.19180i) q^{88} -11.9972i q^{89} +(0.634921 + 0.816141i) q^{90} -3.98487 q^{91} +(-1.88650 + 1.88650i) q^{92} +(10.6247 + 10.6247i) q^{93} -8.48635 q^{94} +(-0.989412 + 7.92243i) q^{95} +1.59297i q^{96} +(5.77120 - 5.77120i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(0.748952 + 1.33841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3}+O(q^{10}) \) 36 * q - 4 * q^3	\( 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) \) 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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