LMFDB - Embedded newform 770.2.m.f.43.8

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			43.8
Character	$\chi$	$=$	770.43
Dual form			770.2.m.f.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.50262 + 1.50262i) q^{3} +1.00000i q^{4} +(2.23151 + 0.142694i) q^{5} -2.12502i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.51571i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.50262 + 1.50262i) q^{3} +1.00000i q^{4} +(2.23151 + 0.142694i) q^{5} -2.12502i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.51571i q^{9} +(-1.47702 - 1.67882i) q^{10} +(2.71114 + 1.91042i) q^{11} +(-1.50262 + 1.50262i) q^{12} +(0.722660 - 0.722660i) q^{13} +1.00000i q^{14} +(3.13869 + 3.56752i) q^{15} -1.00000 q^{16} +(1.53659 + 1.53659i) q^{17} +(1.07177 - 1.07177i) q^{18} +1.59091 q^{19} +(-0.142694 + 2.23151i) q^{20} -2.12502i q^{21} +(-0.566194 - 3.26794i) q^{22} +(-2.81042 - 2.81042i) q^{23} +2.12502 q^{24} +(4.95928 + 0.636844i) q^{25} -1.02200 q^{26} +(2.23032 - 2.23032i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.98984 q^{29} +(0.303227 - 4.74200i) q^{30} -6.13731 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.20317 + 6.94443i) q^{33} -2.17307i q^{34} +(-1.47702 - 1.67882i) q^{35} -1.51571 q^{36} +(-2.22460 + 2.22460i) q^{37} +(-1.12494 - 1.12494i) q^{38} +2.17176 q^{39} +(1.67882 - 1.47702i) q^{40} +7.43624i q^{41} +(-1.50262 + 1.50262i) q^{42} +(3.27964 - 3.27964i) q^{43} +(-1.91042 + 2.71114i) q^{44} +(-0.216282 + 3.38232i) q^{45} +3.97453i q^{46} +(-4.35707 + 4.35707i) q^{47} +(-1.50262 - 1.50262i) q^{48} +1.00000i q^{49} +(-3.05642 - 3.95706i) q^{50} +4.61781i q^{51} +(0.722660 + 0.722660i) q^{52} +(-0.605166 - 0.605166i) q^{53} -3.15415 q^{54} +(5.77734 + 4.64999i) q^{55} -1.00000 q^{56} +(2.39052 + 2.39052i) q^{57} +(-1.40703 - 1.40703i) q^{58} -1.98998i q^{59} +(-3.56752 + 3.13869i) q^{60} +5.67467i q^{61} +(4.33973 + 4.33973i) q^{62} +(1.07177 - 1.07177i) q^{63} -1.00000i q^{64} +(1.71574 - 1.50950i) q^{65} +(4.05968 - 5.76123i) q^{66} +(-2.05376 + 2.05376i) q^{67} +(-1.53659 + 1.53659i) q^{68} -8.44596i q^{69} +(-0.142694 + 2.23151i) q^{70} -3.29248 q^{71} +(1.07177 + 1.07177i) q^{72} +(3.33961 - 3.33961i) q^{73} +3.14605 q^{74} +(6.49496 + 8.40882i) q^{75} +1.59091i q^{76} +(-0.566194 - 3.26794i) q^{77} +(-1.53567 - 1.53567i) q^{78} -9.85037 q^{79} +(-2.23151 - 0.142694i) q^{80} +11.2498 q^{81} +(5.25821 - 5.25821i) q^{82} +(5.34891 - 5.34891i) q^{83} +2.12502 q^{84} +(3.20966 + 3.64818i) q^{85} -4.63812 q^{86} +(2.98997 + 2.98997i) q^{87} +(3.26794 - 0.566194i) q^{88} -1.14235i q^{89} +(2.54459 - 2.23873i) q^{90} -1.02200 q^{91} +(2.81042 - 2.81042i) q^{92} +(-9.22202 - 9.22202i) q^{93} +6.16183 q^{94} +(3.55012 + 0.227012i) q^{95} +2.12502i q^{96} +(0.767500 - 0.767500i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-2.89564 + 4.10930i) 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
$3$	1.50262	+	1.50262i	0.867536	+	0.867536i	0.992199	−	0.124664i	$-0.0397851\pi$
$3$	1.50262	+	1.50262i	0.867536	+	0.867536i	−0.124664	+	0.992199i	$0.539785\pi$
$4$			1.00000i			0.500000i
$5$	2.23151	+	0.142694i	0.997962	+	0.0638145i
$5$	2.23151	+	0.142694i	0.997962	+	0.0638145i
$6$		−	2.12502i		−	0.867536i
$7$	−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
$9$			1.51571i			0.505236i
$10$	−1.47702	−	1.67882i	−0.467074	−	0.530888i
$11$	2.71114	+	1.91042i	0.817440	+	0.576014i
$11$	2.71114	+	1.91042i	0.817440	+	0.576014i
$12$	−1.50262	+	1.50262i	−0.433768	+	0.433768i
$13$	0.722660	−	0.722660i	0.200430	−	0.200430i	−0.599754	−	0.800184i	$-0.704735\pi$
$13$	0.722660	−	0.722660i	0.200430	−	0.200430i	0.800184	+	0.599754i	$0.204735\pi$
$14$			1.00000i			0.267261i
$15$	3.13869	+	3.56752i	0.810406	+	0.921129i
$16$	−1.00000			−0.250000
$17$	1.53659	+	1.53659i	0.372678	+	0.372678i	0.868452	−	0.495774i	$-0.165115\pi$
$17$	1.53659	+	1.53659i	0.372678	+	0.372678i	−0.495774	+	0.868452i	$0.665115\pi$
$18$	1.07177	−	1.07177i	0.252618	−	0.252618i
$19$	1.59091			0.364979			0.182489	−	0.983208i	$-0.441584\pi$
$19$	1.59091			0.364979			0.182489	+	0.983208i	$0.441584\pi$
$20$	−0.142694	+	2.23151i	−0.0319073	+	0.498981i
$21$		−	2.12502i		−	0.463717i
$22$	−0.566194	−	3.26794i	−0.120713	−	0.696727i
$23$	−2.81042	−	2.81042i	−0.586013	−	0.586013i	0.350536	−	0.936549i	$-0.385999\pi$
$23$	−2.81042	−	2.81042i	−0.586013	−	0.586013i	−0.936549	+	0.350536i	$0.885999\pi$
$24$	2.12502			0.433768
$25$	4.95928	+	0.636844i	0.991855	+	0.127369i
$26$	−1.02200			−0.200430
$27$	2.23032	−	2.23032i	0.429225	−	0.429225i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	1.98984			0.369505			0.184752	−	0.982785i	$-0.440852\pi$
$29$	1.98984			0.369505			0.184752	+	0.982785i	$0.440852\pi$
$30$	0.303227	−	4.74200i	0.0553614	−	0.865767i
$31$	−6.13731			−1.10229			−0.551147	−	0.834408i	$-0.685810\pi$
$31$	−6.13731			−1.10229			−0.551147	+	0.834408i	$0.685810\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.20317	+	6.94443i	0.209446	+	1.20887i
$34$		−	2.17307i		−	0.372678i
$35$	−1.47702	−	1.67882i	−0.249661	−	0.283772i
$36$	−1.51571			−0.252618
$37$	−2.22460	+	2.22460i	−0.365721	+	0.365721i	−0.865914	−	0.500193i	$-0.833262\pi$
$37$	−2.22460	+	2.22460i	−0.365721	+	0.365721i	0.500193	+	0.865914i	$0.333262\pi$
$38$	−1.12494	−	1.12494i	−0.182489	−	0.182489i
$39$	2.17176			0.347760
$40$	1.67882	−	1.47702i	0.265444	−	0.233537i
$41$			7.43624i			1.16134i	0.814137	+	0.580672i	$0.197210\pi$
$41$			7.43624i			1.16134i	−0.814137	+	0.580672i	$0.802790\pi$
$42$	−1.50262	+	1.50262i	−0.231859	+	0.231859i
$43$	3.27964	−	3.27964i	0.500141	−	0.500141i	−0.411341	−	0.911482i	$-0.634939\pi$
$43$	3.27964	−	3.27964i	0.500141	−	0.500141i	0.911482	+	0.411341i	$0.134939\pi$
$44$	−1.91042	+	2.71114i	−0.288007	+	0.408720i
$45$	−0.216282	+	3.38232i	−0.0322414	+	0.504206i
$46$			3.97453i			0.586013i
$47$	−4.35707	+	4.35707i	−0.635544	+	0.635544i	−0.949453	−	0.313909i	$-0.898361\pi$
$47$	−4.35707	+	4.35707i	−0.635544	+	0.635544i	0.313909	+	0.949453i	$0.398361\pi$
$48$	−1.50262	−	1.50262i	−0.216884	−	0.216884i
$49$			1.00000i			0.142857i
$50$	−3.05642	−	3.95706i	−0.432243	−	0.559612i
$51$			4.61781i			0.646623i
$52$	0.722660	+	0.722660i	0.100215	+	0.100215i
$53$	−0.605166	−	0.605166i	−0.0831259	−	0.0831259i	0.664321	−	0.747447i	$-0.268721\pi$
$53$	−0.605166	−	0.605166i	−0.0831259	−	0.0831259i	−0.747447	+	0.664321i	$0.768721\pi$
$54$	−3.15415			−0.429225
$55$	5.77734	+	4.64999i	0.779016	+	0.627004i
$56$	−1.00000			−0.133631
$57$	2.39052	+	2.39052i	0.316632	+	0.316632i
$58$	−1.40703	−	1.40703i	−0.184752	−	0.184752i
$59$		−	1.98998i		−	0.259074i	−0.991575	−	0.129537i	$-0.958651\pi$
$59$		−	1.98998i		−	0.259074i	0.991575	−	0.129537i	$-0.0413491\pi$
$60$	−3.56752	+	3.13869i	−0.460564	+	0.405203i
$61$			5.67467i			0.726567i	0.931679	+	0.363284i	$0.118344\pi$
$61$			5.67467i			0.726567i	−0.931679	+	0.363284i	$0.881656\pi$
$62$	4.33973	+	4.33973i	0.551147	+	0.551147i
$63$	1.07177	−	1.07177i	0.135030	−	0.135030i
$64$		−	1.00000i		−	0.125000i
$65$	1.71574	−	1.50950i	0.212812	−	0.187231i
$66$	4.05968	−	5.76123i	0.499713	−	0.709158i
$67$	−2.05376	+	2.05376i	−0.250907	+	0.250907i	−0.821342	−	0.570436i	$-0.806774\pi$
$67$	−2.05376	+	2.05376i	−0.250907	+	0.250907i	0.570436	+	0.821342i	$0.306774\pi$
$68$	−1.53659	+	1.53659i	−0.186339	+	0.186339i
$69$		−	8.44596i		−	1.01677i
$70$	−0.142694	+	2.23151i	−0.0170551	+	0.266717i
$71$	−3.29248			−0.390746			−0.195373	−	0.980729i	$-0.562592\pi$
$71$	−3.29248			−0.390746			−0.195373	+	0.980729i	$0.562592\pi$
$72$	1.07177	+	1.07177i	0.126309	+	0.126309i
$73$	3.33961	−	3.33961i	0.390871	−	0.390871i	−0.484127	−	0.874998i	$-0.660863\pi$
$73$	3.33961	−	3.33961i	0.390871	−	0.390871i	0.874998	+	0.484127i	$0.160863\pi$
$74$	3.14605			0.365721
$75$	6.49496	+	8.40882i	0.749973	+	0.970967i
$76$			1.59091i			0.182489i
$77$	−0.566194	−	3.26794i	−0.0645238	−	0.372416i
$78$	−1.53567	−	1.53567i	−0.173880	−	0.173880i
$79$	−9.85037			−1.10825			−0.554127	−	0.832432i	$-0.686948\pi$
$79$	−9.85037			−1.10825			−0.554127	+	0.832432i	$0.686948\pi$
$80$	−2.23151	−	0.142694i	−0.249490	−	0.0159536i
$81$	11.2498			1.24997
$82$	5.25821	−	5.25821i	0.580672	−	0.580672i
$83$	5.34891	−	5.34891i	0.587120	−	0.587120i	−0.349731	−	0.936850i	$-0.613727\pi$
$83$	5.34891	−	5.34891i	0.587120	−	0.587120i	0.936850	+	0.349731i	$0.113727\pi$
$84$	2.12502			0.231859
$85$	3.20966	+	3.64818i	0.348136	+	0.395701i
$86$	−4.63812			−0.500141
$87$	2.98997	+	2.98997i	0.320559	+	0.320559i
$88$	3.26794	−	0.566194i	0.348363	−	0.0603565i
$89$		−	1.14235i		−	0.121088i	−0.998166	−	0.0605442i	$-0.980716\pi$
$89$		−	1.14235i		−	0.121088i	0.998166	−	0.0605442i	$-0.0192836\pi$
$90$	2.54459	−	2.23873i	0.268224	−	0.235982i
$91$	−1.02200			−0.107134
$92$	2.81042	−	2.81042i	0.293007	−	0.293007i
$93$	−9.22202	−	9.22202i	−0.956279	−	0.956279i
$94$	6.16183			0.635544
$95$	3.55012	+	0.227012i	0.364235	+	0.0232909i
$96$			2.12502i			0.216884i
$97$	0.767500	−	0.767500i	0.0779278	−	0.0779278i	−0.667069	−	0.744996i	$-0.732451\pi$
$97$	0.767500	−	0.767500i	0.0779278	−	0.0779278i	0.744996	+	0.667069i	$0.232451\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	−2.89564	+	4.10930i	−0.291023	+	0.413000i
$100$	−0.636844	+	4.95928i	−0.0636844	+	0.495928i
$101$		−	4.18994i		−	0.416914i	−0.978031	−	0.208457i	$-0.933156\pi$
$101$		−	4.18994i		−	0.416914i	0.978031	−	0.208457i	$-0.0668442\pi$
$102$	3.26529	−	3.26529i	0.323311	−	0.323311i
$103$	7.45615	+	7.45615i	0.734676	+	0.734676i	0.971542	−	0.236866i	$-0.0761203\pi$
$103$	7.45615	+	7.45615i	0.734676	+	0.734676i	−0.236866	+	0.971542i	$0.576120\pi$
$104$		−	1.02200i		−	0.100215i
$105$	0.303227	−	4.74200i	0.0295919	−	0.462772i
$106$			0.855834i			0.0831259i
$107$	−12.1589	−	12.1589i	−1.17544	−	1.17544i	−0.980893	−	0.194548i	$-0.937676\pi$
$107$	−12.1589	−	12.1589i	−1.17544	−	1.17544i	−0.194548	−	0.980893i	$-0.562324\pi$
$108$	2.23032	+	2.23032i	0.214613	+	0.214613i
$109$	6.42608			0.615507			0.307754	−	0.951466i	$-0.400423\pi$
$109$	6.42608			0.615507			0.307754	+	0.951466i	$0.400423\pi$
$110$	−0.797154	−	7.37323i	−0.0760057	−	0.703010i
$111$	−6.68543			−0.634552
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−11.3035	−	11.3035i	−1.06335	−	1.06335i	−0.997853	−	0.0654947i	$-0.979137\pi$
$113$	−11.3035	−	11.3035i	−1.06335	−	1.06335i	−0.0654947	−	0.997853i	$-0.520863\pi$
$114$		−	3.38071i		−	0.316632i
$115$	−5.87045	−	6.67251i	−0.547423	−	0.622215i
$116$			1.98984i			0.184752i
$117$	1.09534	+	1.09534i	0.101264	+	0.101264i
$118$	−1.40713	+	1.40713i	−0.129537	+	0.129537i
$119$		−	2.17307i		−	0.199205i
$120$	4.74200	+	0.303227i	0.432884	+	0.0276807i
$121$	3.70058	+	10.3588i	0.336416	+	0.941714i
$122$	4.01260	−	4.01260i	0.363284	−	0.363284i
$123$	−11.1738	+	11.1738i	−1.00751	+	1.00751i
$124$		−	6.13731i		−	0.551147i
$125$	10.9758	+	2.12878i	0.981706	+	0.190404i
$126$	−1.51571			−0.135030
$127$	−14.6433	−	14.6433i	−1.29939	−	1.29939i	−0.928796	−	0.370591i	$-0.879155\pi$
$127$	−14.6433	−	14.6433i	−1.29939	−	1.29939i	−0.370591	−	0.928796i	$-0.620845\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	9.85609			0.867780
$130$	−2.28059	−	0.145832i	−0.200021	−	0.0127903i
$131$		−	5.49688i		−	0.480265i	−0.970740	−	0.240132i	$-0.922809\pi$
$131$		−	5.49688i		−	0.480265i	0.970740	−	0.240132i	$-0.0771908\pi$
$132$	−6.94443	+	1.20317i	−0.604435	+	0.104723i
$133$	−1.12494	−	1.12494i	−0.0975447	−	0.0975447i
$134$	2.90445			0.250907
$135$	5.29524	−	4.65873i	0.455741	−	0.400960i
$136$	2.17307			0.186339
$137$	14.1940	−	14.1940i	1.21268	−	1.21268i	0.242534	−	0.970143i	$-0.422021\pi$
$137$	14.1940	−	14.1940i	1.21268	−	1.21268i	0.970143	−	0.242534i	$-0.0779787\pi$
$138$	−5.97220	+	5.97220i	−0.508387	+	0.508387i
$139$	8.09694			0.686773			0.343387	−	0.939194i	$-0.388426\pi$
$139$	8.09694			0.686773			0.343387	+	0.939194i	$0.388426\pi$
$140$	1.67882	−	1.47702i	0.141886	−	0.124831i
$141$	−13.0940			−1.10271
$142$	2.32814	+	2.32814i	0.195373	+	0.195373i
$143$	3.33982	−	0.578648i	0.279290	−	0.0483889i
$144$		−	1.51571i		−	0.126309i
$145$	4.44036	+	0.283938i	0.368752	+	0.0235798i
$146$	−4.72292			−0.390871
$147$	−1.50262	+	1.50262i	−0.123934	+	0.123934i
$148$	−2.22460	−	2.22460i	−0.182861	−	0.182861i
$149$	−17.0157			−1.39398			−0.696989	−	0.717082i	$-0.745477\pi$
$149$	−17.0157			−1.39398			−0.696989	+	0.717082i	$0.745477\pi$
$150$	1.35331	−	10.5386i	0.110497	−	0.860470i
$151$			23.6173i			1.92195i	0.276641	+	0.960973i	$0.410779\pi$
$151$			23.6173i			1.92195i	−0.276641	+	0.960973i	$0.589221\pi$
$152$	1.12494	−	1.12494i	0.0912447	−	0.0912447i
$153$	−2.32902	+	2.32902i	−0.188290	+	0.188290i
$154$	−1.91042	+	2.71114i	−0.153946	+	0.218470i
$155$	−13.6955	−	0.875755i	−1.10005	−	0.0703423i
$156$			2.17176i			0.173880i
$157$	1.17423	−	1.17423i	0.0937140	−	0.0937140i	−0.658696	−	0.752410i	$-0.728891\pi$
$157$	1.17423	−	1.17423i	0.0937140	−	0.0937140i	0.752410	+	0.658696i	$0.228891\pi$
$158$	6.96527	+	6.96527i	0.554127	+	0.554127i
$159$		−	1.81866i		−	0.144229i
$160$	1.47702	+	1.67882i	0.116768	+	0.132722i
$161$			3.97453i			0.313237i
$162$	−7.95478	−	7.95478i	−0.624986	−	0.624986i
$163$	−5.65913	−	5.65913i	−0.443257	−	0.443257i	0.449848	−	0.893105i	$-0.351478\pi$
$163$	−5.65913	−	5.65913i	−0.443257	−	0.443257i	−0.893105	+	0.449848i	$0.851478\pi$
$164$	−7.43624			−0.580672
$165$	1.69397	+	15.6683i	0.131875	+	1.21977i
$166$	−7.56451			−0.587120
$167$	−15.9031	−	15.9031i	−1.23062	−	1.23062i	−0.963727	−	0.266891i	$-0.914004\pi$
$167$	−15.9031	−	15.9031i	−1.23062	−	1.23062i	−0.266891	−	0.963727i	$-0.585996\pi$
$168$	−1.50262	−	1.50262i	−0.115929	−	0.115929i
$169$			11.9555i			0.919656i
$170$	0.310083	−	4.84922i	0.0237823	−	0.371918i
$171$			2.41135i			0.184400i
$172$	3.27964	+	3.27964i	0.250071	+	0.250071i
$173$	−1.60073	+	1.60073i	−0.121701	+	0.121701i	−0.765334	−	0.643633i	$-0.777426\pi$
$173$	−1.60073	+	1.60073i	−0.121701	+	0.121701i	0.643633	+	0.765334i	$0.277426\pi$
$174$		−	4.22846i		−	0.320559i
$175$	−3.05642	−	3.95706i	−0.231044	−	0.299125i
$176$	−2.71114	−	1.91042i	−0.204360	−	0.144003i
$177$	2.99018	−	2.99018i	0.224756	−	0.224756i
$178$	−0.807760	+	0.807760i	−0.0605442	+	0.0605442i
$179$		−	11.7516i		−	0.878356i	−0.898400	−	0.439178i	$-0.855270\pi$
$179$		−	11.7516i		−	0.878356i	0.898400	−	0.439178i	$-0.144730\pi$
$180$	−3.38232	−	0.216282i	−0.252103	−	0.0161207i
$181$	−12.1351			−0.901998			−0.450999	−	0.892524i	$-0.648932\pi$
$181$	−12.1351			−0.901998			−0.450999	+	0.892524i	$0.648932\pi$
$182$	0.722660	+	0.722660i	0.0535671	+	0.0535671i
$183$	−8.52685	+	8.52685i	−0.630323	+	0.630323i
$184$	−3.97453			−0.293007
$185$	−5.28164	+	4.64677i	−0.388314	+	0.341638i
$186$			13.0419i			0.956279i
$187$	1.23038	+	7.10145i	0.0899741	+	0.519310i
$188$	−4.35707	−	4.35707i	−0.317772	−	0.317772i
$189$	−3.15415			−0.229431
$190$	−2.34979	−	2.67084i	−0.170472	−	0.193763i
$191$	6.63527			0.480111			0.240056	−	0.970759i	$-0.422834\pi$
$191$	6.63527			0.480111			0.240056	+	0.970759i	$0.422834\pi$
$192$	1.50262	−	1.50262i	0.108442	−	0.108442i
$193$	−14.3240	+	14.3240i	−1.03106	+	1.03106i	−0.0315612	+	0.999502i	$0.510048\pi$
$193$	−14.3240	+	14.3240i	−1.03106	+	1.03106i	−0.999502	+	0.0315612i	$0.989952\pi$
$194$	−1.08541			−0.0779278
$195$	4.84630	+	0.309896i	0.347051	+	0.0221921i
$196$	−1.00000			−0.0714286
$197$	−1.77392	−	1.77392i	−0.126387	−	0.126387i	0.641084	−	0.767471i	$-0.278485\pi$
$197$	−1.77392	−	1.77392i	−0.126387	−	0.126387i	−0.767471	+	0.641084i	$0.778485\pi$
$198$	4.95324	−	0.858185i	0.352011	−	0.0609885i
$199$			17.4009i			1.23352i	0.787152	+	0.616759i	$0.211555\pi$
$199$			17.4009i			1.23352i	−0.787152	+	0.616759i	$0.788445\pi$
$200$	3.95706	−	3.05642i	0.279806	−	0.216122i
$201$	−6.17202			−0.435341
$202$	−2.96273	+	2.96273i	−0.208457	+	0.208457i
$203$	−1.40703	−	1.40703i	−0.0987543	−	0.0987543i
$204$	−4.61781			−0.323311
$205$	−1.06110	+	16.5940i	−0.0741106	+	1.15898i
$206$		−	10.5446i		−	0.734676i
$207$	4.25978	−	4.25978i	0.296075	−	0.296075i
$208$	−0.722660	+	0.722660i	−0.0501074	+	0.0501074i
$209$	4.31317	+	3.03930i	0.298348	+	0.210233i
$210$	−3.56752	+	3.13869i	−0.246182	+	0.216590i
$211$			0.876221i			0.0603215i	0.999545	+	0.0301608i	$0.00960193\pi$
$211$			0.876221i			0.0603215i	−0.999545	+	0.0301608i	$0.990398\pi$
$212$	0.605166	−	0.605166i	0.0415630	−	0.0415630i
$213$	−4.94734	−	4.94734i	−0.338986	−	0.338986i
$214$			17.1952i			1.17544i
$215$	7.78654	−	6.85058i	0.531038	−	0.467205i
$216$		−	3.15415i		−	0.214613i
$217$	4.33973	+	4.33973i	0.294600	+	0.294600i
$218$	−4.54393	−	4.54393i	−0.307754	−	0.307754i
$219$	10.0363			0.678190
$220$	−4.64999	+	5.77734i	−0.313502	+	0.389508i
$221$	2.22086			0.149392
$222$	4.72731	+	4.72731i	0.317276	+	0.317276i
$223$	−16.2518	−	16.2518i	−1.08830	−	1.08830i	−0.995704	−	0.0925969i	$-0.970483\pi$
$223$	−16.2518	−	16.2518i	−1.08830	−	1.08830i	−0.0925969	−	0.995704i	$-0.529517\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−0.965270	+	7.51682i	−0.0643513	+	0.501121i
$226$			15.9856i			1.06335i
$227$	−17.2134	−	17.2134i	−1.14250	−	1.14250i	−0.987992	−	0.154503i	$-0.950622\pi$
$227$	−17.2134	−	17.2134i	−1.14250	−	1.14250i	−0.154503	−	0.987992i	$-0.549378\pi$
$228$	−2.39052	+	2.39052i	−0.158316	+	0.158316i
$229$		−	5.37750i		−	0.355355i	−0.984089	−	0.177678i	$-0.943142\pi$
$229$		−	5.37750i		−	0.355355i	0.984089	−	0.177678i	$-0.0568584\pi$
$230$	−0.567141	+	8.86922i	−0.0373961	+	0.584819i
$231$	4.05968	−	5.76123i	0.267108	−	0.379061i
$232$	1.40703	−	1.40703i	0.0923762	−	0.0923762i
$233$	3.53007	−	3.53007i	0.231262	−	0.231262i	−0.581957	−	0.813220i	$-0.697713\pi$
$233$	3.53007	−	3.53007i	0.231262	−	0.231262i	0.813220	+	0.581957i	$0.197713\pi$
$234$		−	1.54905i		−	0.101264i
$235$	−10.3446	+	9.10112i	−0.674805	+	0.593692i
$236$	1.98998			0.129537
$237$	−14.8013	−	14.8013i	−0.961449	−	0.961449i
$238$	−1.53659	+	1.53659i	−0.0996024	+	0.0996024i
$239$	24.6006			1.59128			0.795640	−	0.605769i	$-0.207135\pi$
$239$	24.6006			1.59128			0.795640	+	0.605769i	$0.207135\pi$
$240$	−3.13869	−	3.56752i	−0.202601	−	0.230282i
$241$		−	9.21230i		−	0.593416i	−0.954968	−	0.296708i	$-0.904111\pi$
$241$		−	9.21230i		−	0.593416i	0.954968	−	0.296708i	$-0.0958888\pi$
$242$	4.70811	−	9.94151i	0.302649	−	0.639065i
$243$	10.2131	+	10.2131i	0.655170	+	0.655170i
$244$	−5.67467			−0.363284
$245$	−0.142694	+	2.23151i	−0.00911636	+	0.142566i
$246$	15.8021			1.00751
$247$	1.14968	−	1.14968i	0.0731526	−	0.0731526i
$248$	−4.33973	+	4.33973i	−0.275573	+	0.275573i
$249$	16.0747			1.01869
$250$	−6.25579	−	9.26634i	−0.395651	−	0.586055i
$251$	−24.7521			−1.56234			−0.781169	−	0.624320i	$-0.785376\pi$
$251$	−24.7521			−1.56234			−0.781169	+	0.624320i	$0.785376\pi$
$252$	1.07177	+	1.07177i	0.0675150	+	0.0675150i
$253$	−2.25036	−	12.9885i	−0.141479	−	0.816582i
$254$			20.7088i			1.29939i
$255$	−0.658932	+	10.3047i	−0.0412639	+	0.645305i
$256$	1.00000			0.0625000
$257$	11.7331	−	11.7331i	0.731893	−	0.731893i	−0.239101	−	0.970995i	$-0.576853\pi$
$257$	11.7331	−	11.7331i	0.731893	−	0.731893i	0.970995	+	0.239101i	$0.0768528\pi$
$258$	−6.96931	−	6.96931i	−0.433890	−	0.433890i
$259$	3.14605			0.195486
$260$	1.50950	+	1.71574i	0.0936155	+	0.106406i
$261$			3.01602i			0.186687i
$262$	−3.88688	+	3.88688i	−0.240132	+	0.240132i
$263$	−13.9664	+	13.9664i	−0.861205	+	0.861205i	−0.991478	−	0.130273i	$-0.958415\pi$
$263$	−13.9664	+	13.9664i	−0.861205	+	0.861205i	0.130273	+	0.991478i	$0.458415\pi$
$264$	5.76123	+	4.05968i	0.354579	+	0.249856i
$265$	−1.26408	−	1.43679i	−0.0776519	−	0.0882612i
$266$			1.59091i			0.0975447i
$267$	1.71651	−	1.71651i	0.105048	−	0.105048i
$268$	−2.05376	−	2.05376i	−0.125453	−	0.125453i
$269$			5.09543i			0.310674i	0.987862	+	0.155337i	$0.0496463\pi$
$269$			5.09543i			0.310674i	−0.987862	+	0.155337i	$0.950354\pi$
$270$	−7.03852	−	0.450077i	−0.428351	−	0.0273908i
$271$		−	10.1283i		−	0.615252i	−0.951507	−	0.307626i	$-0.900465\pi$
$271$		−	10.1283i		−	0.615252i	0.951507	−	0.307626i	$-0.0995346\pi$
$272$	−1.53659	−	1.53659i	−0.0931695	−	0.0931695i
$273$	−1.53567	−	1.53567i	−0.0929427	−	0.0929427i
$274$	−20.0734			−1.21268
$275$	12.2287	+	11.2009i	0.737416	+	0.675439i
$276$	8.44596			0.508387
$277$	−3.09969	−	3.09969i	−0.186242	−	0.186242i	0.607827	−	0.794069i	$-0.292041\pi$
$277$	−3.09969	−	3.09969i	−0.186242	−	0.186242i	−0.794069	+	0.607827i	$0.792041\pi$
$278$	−5.72540	−	5.72540i	−0.343387	−	0.343387i
$279$		−	9.30237i		−	0.556918i
$280$	−2.23151	−	0.142694i	−0.133358	−	0.00852757i
$281$		−	1.26939i		−	0.0757257i	−0.999283	−	0.0378629i	$-0.987945\pi$
$281$		−	1.26939i		−	0.0757257i	0.999283	−	0.0378629i	$-0.0120550\pi$
$282$	9.25886	+	9.25886i	0.551357	+	0.551357i
$283$	−0.893747	+	0.893747i	−0.0531277	+	0.0531277i	−0.733172	−	0.680044i	$-0.761961\pi$
$283$	−0.893747	+	0.893747i	−0.0531277	+	0.0531277i	0.680044	+	0.733172i	$0.261961\pi$
$284$		−	3.29248i		−	0.195373i
$285$	4.99336	+	5.67558i	0.295781	+	0.336192i
$286$	−2.77077	−	1.95244i	−0.163839	−	0.115450i
$287$	5.25821	−	5.25821i	0.310382	−	0.310382i
$288$	−1.07177	+	1.07177i	−0.0631545	+	0.0631545i
$289$		−	12.2778i		−	0.722222i
$290$	−2.93903	−	3.34058i	−0.172586	−	0.196166i
$291$	2.30652			0.135210
$292$	3.33961	+	3.33961i	0.195436	+	0.195436i
$293$	19.4055	−	19.4055i	1.13368	−	1.13368i	0.144123	−	0.989560i	$-0.453964\pi$
$293$	19.4055	−	19.4055i	1.13368	−	1.13368i	0.989560	−	0.144123i	$-0.0460361\pi$
$294$	2.12502			0.123934
$295$	0.283958	−	4.44067i	0.0165327	−	0.258546i
$296$			3.14605i			0.182861i
$297$	10.3076	−	1.78586i	0.598106	−	0.103626i
$298$	12.0319	+	12.0319i	0.696989	+	0.696989i
$299$	−4.06196			−0.234909
$300$	−8.40882	+	6.49496i	−0.485483	+	0.374986i
$301$	−4.63812			−0.267337
$302$	16.6999	−	16.6999i	0.960973	−	0.960973i
$303$	6.29587	−	6.29587i	0.361688	−	0.361688i
$304$	−1.59091			−0.0912447
$305$	−0.809739	+	12.6631i	−0.0463655	+	0.725086i
$306$	3.29374			0.188290
$307$	−3.52752	−	3.52752i	−0.201326	−	0.201326i	0.599242	−	0.800568i	$-0.295469\pi$
$307$	−3.52752	−	3.52752i	−0.201326	−	0.201326i	−0.800568	+	0.599242i	$0.795469\pi$
$308$	3.26794	−	0.566194i	0.186208	−	0.0322619i
$309$			22.4075i			1.27472i
$310$	9.06491	+	10.3034i	0.514852	+	0.585195i
$311$	−10.2578			−0.581664			−0.290832	−	0.956774i	$-0.593932\pi$
$311$	−10.2578			−0.581664			−0.290832	+	0.956774i	$0.593932\pi$
$312$	1.53567	−	1.53567i	0.0869400	−	0.0869400i
$313$	−15.2152	−	15.2152i	−0.860016	−	0.860016i	0.131323	−	0.991340i	$-0.458077\pi$
$313$	−15.2152	−	15.2152i	−0.860016	−	0.860016i	−0.991340	+	0.131323i	$0.958077\pi$
$314$	−1.66062			−0.0937140
$315$	2.54459	−	2.23873i	0.143372	−	0.126138i
$316$		−	9.85037i		−	0.554127i
$317$	−4.17207	+	4.17207i	−0.234327	+	0.234327i	−0.814496	−	0.580169i	$-0.802986\pi$
$317$	−4.17207	+	4.17207i	−0.234327	+	0.234327i	0.580169	+	0.814496i	$0.302986\pi$
$318$	−1.28599	+	1.28599i	−0.0721147	+	0.0721147i
$319$	5.39475	+	3.80144i	0.302048	+	0.212840i
$320$	0.142694	−	2.23151i	0.00797681	−	0.124745i
$321$		−	36.5402i		−	2.03947i
$322$	2.81042	−	2.81042i	0.156619	−	0.156619i
$323$	2.44457	+	2.44457i	0.136020	+	0.136020i
$324$			11.2498i			0.624986i
$325$	4.04409	−	3.12365i	0.224326	−	0.173269i
$326$			8.00321i			0.443257i
$327$	9.65594	+	9.65594i	0.533974	+	0.533974i
$328$	5.25821	+	5.25821i	0.290336	+	0.290336i
$329$	6.16183			0.339712
$330$	9.88132	−	12.2769i	0.543949	−	0.675824i
$331$	25.1678			1.38335			0.691675	−	0.722209i	$-0.256873\pi$
$331$	25.1678			1.38335			0.691675	+	0.722209i	$0.256873\pi$
$332$	5.34891	+	5.34891i	0.293560	+	0.293560i
$333$	−3.37184	−	3.37184i	−0.184776	−	0.184776i
$334$			22.4904i			1.23062i
$335$	−4.87604	+	4.28993i	−0.266407	+	0.234384i
$336$			2.12502i			0.115929i
$337$	24.5005	+	24.5005i	1.33463	+	1.33463i	0.901177	+	0.433452i	$0.142705\pi$
$337$	24.5005	+	24.5005i	1.33463	+	1.33463i	0.433452	+	0.901177i	$0.357295\pi$
$338$	8.45383	−	8.45383i	0.459828	−	0.459828i
$339$		−	33.9698i		−	1.84498i
$340$	−3.64818	+	3.20966i	−0.197850	+	0.174068i
$341$	−16.6391	−	11.7249i	−0.901059	−	0.634936i
$342$	1.70508	−	1.70508i	0.0922002	−	0.0922002i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		−	4.63812i		−	0.250071i
$345$	1.20518	−	18.8473i	0.0648850	−	1.01470i
$346$	2.26377			0.121701
$347$	−13.1287	−	13.1287i	−0.704786	−	0.704786i	0.260648	−	0.965434i	$-0.416064\pi$
$347$	−13.1287	−	13.1287i	−0.704786	−	0.704786i	−0.965434	+	0.260648i	$0.916064\pi$
$348$	−2.98997	+	2.98997i	−0.160279	+	0.160279i
$349$	14.5097			0.776687			0.388343	−	0.921515i	$-0.373047\pi$
$349$	14.5097			0.776687			0.388343	+	0.921515i	$0.373047\pi$
$350$	−0.636844	+	4.95928i	−0.0340408	+	0.265085i
$351$		−	3.22353i		−	0.172059i
$352$	0.566194	+	3.26794i	0.0301782	+	0.174182i
$353$	21.1170	+	21.1170i	1.12395	+	1.12395i	0.991142	+	0.132803i	$0.0423978\pi$
$353$	21.1170	+	21.1170i	1.12395	+	1.12395i	0.132803	+	0.991142i	$0.457602\pi$
$354$	−4.22875			−0.224756
$355$	−7.34721	−	0.469816i	−0.389949	−	0.0249352i
$356$	1.14235			0.0605442
$357$	3.26529	−	3.26529i	0.172817	−	0.172817i
$358$	−8.30964	+	8.30964i	−0.439178	+	0.439178i
$359$	−22.5774			−1.19159			−0.595794	−	0.803137i	$-0.703163\pi$
$359$	−22.5774			−1.19159			−0.595794	+	0.803137i	$0.703163\pi$
$360$	2.23873	+	2.54459i	0.117991	+	0.134112i
$361$	−16.4690			−0.866790
$362$	8.58084	+	8.58084i	0.450999	+	0.450999i
$363$	−10.0048	+	21.1259i	−0.525117	+	1.10882i
$364$		−	1.02200i		−	0.0535671i
$365$	7.92891	−	6.97583i	0.415018	−	0.365131i
$366$	12.0588			0.630323
$367$	−19.5032	+	19.5032i	−1.01806	+	1.01806i	−0.0182243	+	0.999834i	$0.505801\pi$
$367$	−19.5032	+	19.5032i	−1.01806	+	1.01806i	−0.999834	+	0.0182243i	$0.994199\pi$
$368$	2.81042	+	2.81042i	0.146503	+	0.146503i
$369$	−11.2712			−0.586753
$370$	7.02045	+	0.448922i	0.364976	+	0.0233383i
$371$			0.855834i			0.0444327i
$372$	9.22202	−	9.22202i	0.478139	−	0.478139i
$373$	24.0193	−	24.0193i	1.24367	−	1.24367i	0.285204	−	0.958467i	$-0.407939\pi$
$373$	24.0193	−	24.0193i	1.24367	−	1.24367i	0.958467	−	0.285204i	$-0.0920613\pi$
$374$	4.15148	−	5.89149i	0.214668	−	0.304642i
$375$	13.2937	+	19.6912i	0.686482	+	1.01685i
$376$			6.16183i			0.317772i
$377$	1.43798	−	1.43798i	0.0740598	−	0.0740598i
$378$	2.23032	+	2.23032i	0.114715	+	0.114715i
$379$			34.6660i			1.78067i	0.455304	+	0.890336i	$0.349531\pi$
$379$			34.6660i			1.78067i	−0.455304	+	0.890336i	$0.650469\pi$
$380$	−0.227012	+	3.55012i	−0.0116455	+	0.182117i
$381$		−	44.0067i		−	2.25453i
$382$	−4.69185	−	4.69185i	−0.240056	−	0.240056i
$383$	23.2224	+	23.2224i	1.18661	+	1.18661i	0.977999	+	0.208611i	$0.0668944\pi$
$383$	23.2224	+	23.2224i	1.18661	+	1.18661i	0.208611	+	0.977999i	$0.433106\pi$
$384$	−2.12502			−0.108442
$385$	−0.797154	−	7.37323i	−0.0406267	−	0.375775i
$386$	20.2572			1.03106
$387$	4.97098	+	4.97098i	0.252689	+	0.252689i
$388$	0.767500	+	0.767500i	0.0389639	+	0.0389639i
$389$			13.3981i			0.679309i	0.940550	+	0.339655i	$0.110310\pi$
$389$			13.3981i			0.679309i	−0.940550	+	0.339655i	$0.889690\pi$
$390$	−3.20773	−	3.64598i	−0.162429	−	0.184622i
$391$		−	8.63693i		−	0.436788i
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	8.25970	−	8.25970i	0.416647	−	0.416647i
$394$			2.50871i			0.126387i
$395$	−21.9812	−	1.40558i	−1.10599	−	0.0707227i
$396$	−4.10930	−	2.89564i	−0.206500	−	0.145511i
$397$	11.5150	−	11.5150i	0.577920	−	0.577920i	−0.356410	−	0.934330i	$-0.615999\pi$
$397$	11.5150	−	11.5150i	0.577920	−	0.577920i	0.934330	+	0.356410i	$0.115999\pi$
$398$	12.3043	−	12.3043i	0.616759	−	0.616759i
$399$		−	3.38071i		−	0.169247i
$400$	−4.95928	−	0.636844i	−0.247964	−	0.0318422i
$401$	10.4176			0.520229			0.260115	−	0.965578i	$-0.416240\pi$
$401$	10.4176			0.520229			0.260115	+	0.965578i	$0.416240\pi$
$402$	4.36428	+	4.36428i	0.217670	+	0.217670i
$403$	−4.43519	+	4.43519i	−0.220932	+	0.220932i
$404$	4.18994			0.208457
$405$	25.1039	+	1.60527i	1.24742	+	0.0797664i
$406$			1.98984i			0.0987543i
$407$	−10.2811	+	1.78128i	−0.509616	+	0.0882946i
$408$	3.26529	+	3.26529i	0.161656	+	0.161656i
$409$	24.6262			1.21769			0.608845	−	0.793289i	$-0.291633\pi$
$409$	24.6262			1.21769			0.608845	+	0.793289i	$0.291633\pi$
$410$	12.4841	−	10.9834i	0.616544	−	0.542434i
$411$	42.6563			2.10408
$412$	−7.45615	+	7.45615i	−0.367338	+	0.367338i
$413$	−1.40713	+	1.40713i	−0.0692404	+	0.0692404i
$414$	−6.02423			−0.296075
$415$	12.6994	−	11.1729i	0.623390	−	0.548456i
$416$	1.02200			0.0501074
$417$	12.1666	+	12.1666i	0.595800	+	0.595800i
$418$	−0.900761	−	5.19898i	−0.0440577	−	0.254291i
$419$			19.7765i			0.966145i	0.875580	+	0.483072i	$0.160479\pi$
$419$			19.7765i			0.966145i	−0.875580	+	0.483072i	$0.839521\pi$
$420$	4.74200	+	0.303227i	0.231386	+	0.0147959i
$421$	−27.3680			−1.33384			−0.666918	−	0.745131i	$-0.732387\pi$
$421$	−27.3680			−1.33384			−0.666918	+	0.745131i	$0.732387\pi$
$422$	0.619582	−	0.619582i	0.0301608	−	0.0301608i
$423$	−6.60404	−	6.60404i	−0.321100	−	0.321100i
$424$	−0.855834			−0.0415630
$425$	6.64181	+	8.59895i	0.322175	+	0.417110i
$426$			6.99659i			0.338986i
$427$	4.01260	−	4.01260i	0.194183	−	0.194183i
$428$	12.1589	−	12.1589i	0.587720	−	0.587720i
$429$	5.88795	+	4.14898i	0.284273	+	0.200315i
$430$	−10.3500	−	0.661830i	−0.499122	−	0.0319163i
$431$		−	18.2826i		−	0.880640i	−0.897841	−	0.440320i	$-0.854865\pi$
$431$		−	18.2826i		−	0.880640i	0.897841	−	0.440320i	$-0.145135\pi$
$432$	−2.23032	+	2.23032i	−0.107306	+	0.107306i
$433$	17.0592	+	17.0592i	0.819811	+	0.819811i	0.986080	−	0.166269i	$-0.0531721\pi$
$433$	17.0592	+	17.0592i	0.819811	+	0.819811i	−0.166269	+	0.986080i	$0.553172\pi$
$434$		−	6.13731i		−	0.294600i
$435$	6.24550	+	7.09880i	0.299449	+	0.340361i
$436$			6.42608i			0.307754i
$437$	−4.47111	−	4.47111i	−0.213882	−	0.213882i
$438$	−7.09673	−	7.09673i	−0.339095	−	0.339095i
$439$	10.7410			0.512639			0.256320	−	0.966592i	$-0.417490\pi$
$439$	10.7410			0.512639			0.256320	+	0.966592i	$0.417490\pi$
$440$	7.37323	−	0.797154i	0.351505	−	0.0380028i
$441$	−1.51571			−0.0721766
$442$	−1.57039	−	1.57039i	−0.0746958	−	0.0746958i
$443$	8.92355	+	8.92355i	0.423971	+	0.423971i	0.886568	−	0.462598i	$-0.153083\pi$
$443$	8.92355	+	8.92355i	0.423971	+	0.423971i	−0.462598	+	0.886568i	$0.653083\pi$
$444$		−	6.68543i		−	0.317276i
$445$	0.163005	−	2.54916i	0.00772720	−	0.120842i
$446$			22.9835i			1.08830i
$447$	−25.5680	−	25.5680i	−1.20932	−	1.20932i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$		−	15.0126i		−	0.708487i	−0.935153	−	0.354244i	$-0.884738\pi$
$449$		−	15.0126i		−	0.708487i	0.935153	−	0.354244i	$-0.115262\pi$
$450$	5.99774	−	4.63264i	0.282736	−	0.218385i
$451$	−14.2063	+	20.1607i	−0.668951	+	0.949330i
$452$	11.3035	−	11.3035i	0.531674	−	0.531674i
$453$	−35.4877	+	35.4877i	−1.66736	+	1.66736i
$454$			24.3435i			1.14250i
$455$	−2.28059	−	0.145832i	−0.106916	−	0.00683672i
$456$	3.38071			0.158316
$457$	26.6971	+	26.6971i	1.24884	+	1.24884i	0.956233	+	0.292606i	$0.0945223\pi$
$457$	26.6971	+	26.6971i	1.24884	+	1.24884i	0.292606	+	0.956233i	$0.405478\pi$
$458$	−3.80247	+	3.80247i	−0.177678	+	0.177678i
$459$	6.85418			0.319926
$460$	6.67251	−	5.87045i	0.311107	−	0.273711i
$461$		−	27.3974i		−	1.27602i	−0.770026	−	0.638012i	$-0.779757\pi$
$461$		−	27.3974i		−	1.27602i	0.770026	−	0.638012i	$-0.220243\pi$
$462$	−6.94443	+	1.20317i	−0.323084	+	0.0559767i
$463$	6.74568	+	6.74568i	0.313498	+	0.313498i	0.846263	−	0.532765i	$-0.178847\pi$
$463$	6.74568	+	6.74568i	0.313498	+	0.313498i	−0.532765	+	0.846263i	$0.678847\pi$
$464$	−1.98984			−0.0923762
$465$	−19.2631	−	21.8950i	−0.893305	−	1.01535i
$466$	−4.99227			−0.231262
$467$	13.9901	−	13.9901i	0.647385	−	0.647385i	−0.304975	−	0.952360i	$-0.598648\pi$
$467$	13.9901	−	13.9901i	0.647385	−	0.647385i	0.952360	+	0.304975i	$0.0986481\pi$
$468$	−1.09534	+	1.09534i	−0.0506322	+	0.0506322i
$469$	2.90445			0.134115
$470$	13.7502	+	0.879253i	0.634249	+	0.0405569i
$471$	3.52884			0.162600
$472$	−1.40713	−	1.40713i	−0.0647685	−	0.0647685i
$473$	15.1571	−	2.62607i	0.696923	−	0.120747i
$474$			20.9322i			0.961449i
$475$	7.88974	+	1.01316i	0.362006	+	0.0464869i
$476$	2.17307			0.0996024
$477$	0.917255	−	0.917255i	0.0419982	−	0.0419982i
$478$	−17.3953	−	17.3953i	−0.795640	−	0.795640i
$479$	27.3196			1.24826			0.624132	−	0.781319i	$-0.285453\pi$
$479$	27.3196			1.24826			0.624132	+	0.781319i	$0.285453\pi$
$480$	−0.303227	+	4.74200i	−0.0138403	+	0.216442i
$481$			3.21525i			0.146603i
$482$	−6.51408	+	6.51408i	−0.296708	+	0.296708i
$483$	−5.97220	+	5.97220i	−0.271744	+	0.271744i
$484$	−10.3588	+	3.70058i	−0.470857	+	0.168208i
$485$	1.82220	−	1.60317i	0.0827419	−	0.0727961i
$486$		−	14.4435i		−	0.655170i
$487$	−24.0101	+	24.0101i	−1.08800	+	1.08800i	−0.0922686	+	0.995734i	$0.529412\pi$
$487$	−24.0101	+	24.0101i	−1.08800	+	1.08800i	−0.995734	+	0.0922686i	$0.970588\pi$
$488$	4.01260	+	4.01260i	0.181642	+	0.181642i
$489$		−	17.0070i		−	0.769082i
$490$	1.67882	−	1.47702i	0.0758412	−	0.0667248i
$491$			27.0528i			1.22088i	0.792064	+	0.610438i	$0.209006\pi$
$491$			27.0528i			1.22088i	−0.792064	+	0.610438i	$0.790994\pi$
$492$	−11.1738	−	11.1738i	−0.503754	−	0.503754i
$493$	3.05758	+	3.05758i	0.137706	+	0.137706i
$494$	−1.62590			−0.0731526
$495$	−7.04802	+	8.75675i	−0.316785	+	0.393587i
$496$	6.13731			0.275573
$497$	2.32814	+	2.32814i	0.104431	+	0.104431i
$498$	−11.3665	−	11.3665i	−0.509347	−	0.509347i
$499$			21.9761i			0.983784i	0.870656	+	0.491892i	$0.163695\pi$
$499$			21.9761i			0.983784i	−0.870656	+	0.491892i	$0.836305\pi$
$500$	−2.12878	+	10.9758i	−0.0952020	+	0.490853i
$501$		−	47.7924i		−	2.13521i
$502$	17.5024	+	17.5024i	0.781169	+	0.781169i
$503$	−9.42657	+	9.42657i	−0.420310	+	0.420310i	−0.885311	−	0.465000i	$-0.846054\pi$
$503$	−9.42657	+	9.42657i	−0.420310	+	0.420310i	0.465000	+	0.885311i	$0.346054\pi$
$504$		−	1.51571i		−	0.0675150i
$505$	0.597877	−	9.34989i	0.0266052	−	0.416065i
$506$	−7.59304	+	10.7755i	−0.337552	+	0.479031i
$507$	−17.9646	+	17.9646i	−0.797834	+	0.797834i
$508$	14.6433	−	14.6433i	0.649694	−	0.649694i
$509$		−	22.3132i		−	0.989016i	−0.869173	−	0.494508i	$-0.835348\pi$
$509$		−	22.3132i		−	0.989016i	0.869173	−	0.494508i	$-0.164652\pi$
$510$	7.75245	−	6.82058i	0.343284	−	0.302020i
$511$	−4.72292			−0.208930
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.54823	−	3.54823i	0.156658	−	0.156658i
$514$	−16.5932			−0.731893
$515$	15.5745	+	17.7024i	0.686296	+	0.780062i
$516$			9.85609i			0.433890i
$517$	−20.1365	+	3.48879i	−0.885601	+	0.153437i
$518$	−2.22460	−	2.22460i	−0.0977431	−	0.0977431i
$519$	−4.81055			−0.211160
$520$	0.145832	−	2.28059i	0.00639516	−	0.100011i
$521$	−30.4145			−1.33248			−0.666241	−	0.745736i	$-0.732098\pi$
$521$	−30.4145			−1.33248			−0.666241	+	0.745736i	$0.732098\pi$
$522$	2.13265	−	2.13265i	0.0933435	−	0.0933435i
$523$	15.4051	−	15.4051i	0.673619	−	0.673619i	−0.284930	−	0.958548i	$-0.591970\pi$
$523$	15.4051	−	15.4051i	0.673619	−	0.673619i	0.958548	+	0.284930i	$0.0919702\pi$
$524$	5.49688			0.240132
$525$	1.35331	−	10.5386i	0.0590631	−	0.459940i
$526$	19.7515			0.861205
$527$	−9.43053	−	9.43053i	−0.410801	−	0.410801i
$528$	−1.20317	−	6.94443i	−0.0523614	−	0.302218i
$529$		−	7.20307i		−	0.313177i
$530$	−0.122122	+	1.90980i	−0.00530464	+	0.0829565i
$531$	3.01623			0.130893
$532$	1.12494	−	1.12494i	0.0487723	−	0.0487723i
$533$	5.37387	+	5.37387i	0.232768	+	0.232768i
$534$	−2.42751			−0.105048
$535$	−25.3976	−	28.8676i	−1.09803	−	1.24806i
$536$			2.90445i			0.125453i
$537$	17.6582	−	17.6582i	0.762005	−	0.762005i
$538$	3.60301	−	3.60301i	0.155337	−	0.155337i
$539$	−1.91042	+	2.71114i	−0.0822877	+	0.116777i
$540$	4.65873	+	5.29524i	0.200480	+	0.227871i
$541$			17.1463i			0.737178i	0.929593	+	0.368589i	$0.120159\pi$
$541$			17.1463i			0.737178i	−0.929593	+	0.368589i	$0.879841\pi$
$542$	−7.16181	+	7.16181i	−0.307626	+	0.307626i
$543$	−18.2345	−	18.2345i	−0.782515	−	0.782515i
$544$			2.17307i			0.0931695i
$545$	14.3399	+	0.916961i	0.614253	+	0.0392783i
$546$			2.17176i			0.0929427i
$547$	2.55264	+	2.55264i	0.109143	+	0.109143i	0.759569	−	0.650426i	$-0.225410\pi$
$547$	2.55264	+	2.55264i	0.109143	+	0.109143i	−0.650426	+	0.759569i	$0.725410\pi$
$548$	14.1940	+	14.1940i	0.606339	+	0.606339i
$549$	−8.60114			−0.367088
$550$	−0.726745	−	16.5672i	−0.0309885	−	0.706427i
$551$	3.16565			0.134861
$552$	−5.97220	−	5.97220i	−0.254194	−	0.254194i
$553$	6.96527	+	6.96527i	0.296193	+	0.296193i
$554$			4.38363i			0.186242i
$555$	−14.9186	−	0.953967i	−0.633259	−	0.0404937i
$556$			8.09694i			0.343387i
$557$	16.3281	+	16.3281i	0.691842	+	0.691842i	0.962637	−	0.270795i	$-0.0872865\pi$
$557$	16.3281	+	16.3281i	0.691842	+	0.691842i	−0.270795	+	0.962637i	$0.587286\pi$
$558$	−6.57777	+	6.57777i	−0.278459	+	0.278459i
$559$		−	4.74013i		−	0.200486i
$560$	1.47702	+	1.67882i	0.0624153	+	0.0709429i
$561$	−8.82197	+	12.5195i	−0.372464	+	0.528575i
$562$	−0.897598	+	0.897598i	−0.0378629	+	0.0378629i
$563$	−24.9720	+	24.9720i	−1.05244	+	1.05244i	−0.0538985	+	0.998546i	$0.517165\pi$
$563$	−24.9720	+	24.9720i	−1.05244	+	1.05244i	−0.998546	+	0.0538985i	$0.982835\pi$
$564$		−	13.0940i		−	0.551357i
$565$	−23.6110	−	26.8369i	−0.993323	−	1.12904i
$566$	1.26395			0.0531277
$567$	−7.95478	−	7.95478i	−0.334069	−	0.334069i
$568$	−2.32814	+	2.32814i	−0.0976864	+	0.0976864i
$569$	−24.7858			−1.03907			−0.519537	−	0.854448i	$-0.673896\pi$
$569$	−24.7858			−1.03907			−0.519537	+	0.854448i	$0.673896\pi$
$570$	0.482405	−	7.54408i	0.0202057	−	0.315987i
$571$			15.7851i			0.660585i	0.943879	+	0.330293i	$0.107147\pi$
$571$			15.7851i			0.660585i	−0.943879	+	0.330293i	$0.892853\pi$
$572$	0.578648	+	3.33982i	0.0241945	+	0.139645i
$573$	9.97026	+	9.97026i	0.416514	+	0.416514i
$574$	−7.43624			−0.310382
$575$	−12.1479	−	15.7275i	−0.506600	−	0.655880i
$576$	1.51571			0.0631545
$577$	−1.17852	+	1.17852i	−0.0490623	+	0.0490623i	−0.731212	−	0.682150i	$-0.761045\pi$
$577$	−1.17852	+	1.17852i	−0.0490623	+	0.0490623i	0.682150	+	0.731212i	$0.261045\pi$
$578$	−8.68170	+	8.68170i	−0.361111	+	0.361111i
$579$	−43.0469			−1.78897
$580$	−0.283938	+	4.44036i	−0.0117899	+	0.184376i
$581$	−7.56451			−0.313829
$582$	−1.63095	−	1.63095i	−0.0676052	−	0.0676052i
$583$	−0.484568	−	2.79681i	−0.0200688	−	0.115832i
$584$		−	4.72292i		−	0.195436i
$585$	2.28797	+	2.60056i	0.0945958	+	0.107520i
$586$	−27.4436			−1.13368
$587$	−30.6416	+	30.6416i	−1.26472	+	1.26472i	−0.315934	+	0.948781i	$0.602318\pi$
$587$	−30.6416	+	30.6416i	−1.26472	+	1.26472i	−0.948781	+	0.315934i	$0.897682\pi$
$588$	−1.50262	−	1.50262i	−0.0619668	−	0.0619668i
$589$	−9.76388			−0.402314
$590$	−3.34082	+	2.93924i	−0.137539	+	0.121007i
$591$		−	5.33105i		−	0.219290i
$592$	2.22460	−	2.22460i	0.0914303	−	0.0914303i
$593$	−13.6998	+	13.6998i	−0.562583	+	0.562583i	−0.930040	−	0.367457i	$-0.880228\pi$
$593$	−13.6998	+	13.6998i	−0.562583	+	0.562583i	0.367457	+	0.930040i	$0.380228\pi$
$594$	−8.55135	−	6.02576i	−0.350866	−	0.247240i
$595$	0.310083	−	4.84922i	0.0127122	−	0.198799i
$596$		−	17.0157i		−	0.696989i
$597$	−26.1469	+	26.1469i	−1.07012	+	1.07012i
$598$	2.87224	+	2.87224i	0.117454	+	0.117454i
$599$		−	8.26762i		−	0.337806i	−0.985633	−	0.168903i	$-0.945978\pi$
$599$		−	8.26762i		−	0.337806i	0.985633	−	0.168903i	$-0.0540224\pi$
$600$	10.5386	+	1.35331i	0.430235	+	0.0552485i
$601$		−	1.94042i		−	0.0791513i	−0.999217	−	0.0395756i	$-0.987399\pi$
$601$		−	1.94042i		−	0.0791513i	0.999217	−	0.0395756i	$-0.0126006\pi$
$602$	3.27964	+	3.27964i	0.133668	+	0.133668i
$603$	−3.11290	−	3.11290i	−0.126767	−	0.126767i
$604$	−23.6173			−0.960973
$605$	6.77973	+	23.6439i	0.275635	+	0.961262i
$606$	−8.90370			−0.361688
$607$	14.6773	+	14.6773i	0.595735	+	0.595735i	0.939175	−	0.343440i	$-0.111592\pi$
$607$	14.6773	+	14.6773i	0.595735	+	0.595735i	−0.343440	+	0.939175i	$0.611592\pi$
$608$	1.12494	+	1.12494i	0.0456224	+	0.0456224i
$609$		−	4.22846i		−	0.171346i
$610$	9.52673	−	8.38158i	0.385726	−	0.339360i
$611$			6.29736i			0.254764i
$612$	−2.32902	−	2.32902i	−0.0941452	−	0.0941452i
$613$	−29.7342	+	29.7342i	−1.20095	+	1.20095i	−0.227073	+	0.973878i	$0.572916\pi$
$613$	−29.7342	+	29.7342i	−1.20095	+	1.20095i	−0.973878	+	0.227073i	$0.927084\pi$
$614$			4.98866i			0.201326i
$615$	−26.5289	+	23.3400i	−1.06975	+	0.941161i
$616$	−2.71114	−	1.91042i	−0.109235	−	0.0769731i
$617$	9.94378	−	9.94378i	0.400322	−	0.400322i	−0.478025	−	0.878346i	$-0.658647\pi$
$617$	9.94378	−	9.94378i	0.400322	−	0.400322i	0.878346	+	0.478025i	$0.158647\pi$
$618$	15.8445	−	15.8445i	0.637358	−	0.637358i
$619$		−	39.5943i		−	1.59143i	−0.605673	−	0.795714i	$-0.707096\pi$
$619$		−	39.5943i		−	1.59143i	0.605673	−	0.795714i	$-0.292904\pi$
$620$	0.875755	−	13.6955i	0.0351712	−	0.550023i
$621$	−12.5363			−0.503063
$622$	7.25334	+	7.25334i	0.290832	+	0.290832i
$623$	−0.807760	+	0.807760i	−0.0323622	+	0.0323622i
$624$	−2.17176			−0.0869400
$625$	24.1889	+	6.31658i	0.967554	+	0.252663i
$626$			21.5176i			0.860016i
$627$	1.91414	+	11.0479i	0.0764432	+	0.441212i
$628$	1.17423	+	1.17423i	0.0468570	+	0.0468570i
$629$	−6.83659			−0.272593
$630$	−3.38232	−	0.216282i	−0.134755	−	0.00861687i
$631$	−4.42688			−0.176231			−0.0881157	−	0.996110i	$-0.528085\pi$
$631$	−4.42688			−0.176231			−0.0881157	+	0.996110i	$0.528085\pi$
$632$	−6.96527	+	6.96527i	−0.277063	+	0.277063i
$633$	−1.31662	+	1.31662i	−0.0523311	+	0.0523311i
$634$	5.90020			0.234327
$635$	−30.5873	−	34.7663i	−1.21382	−	1.37966i
$636$	1.81866			0.0721147
$637$	0.722660	+	0.722660i	0.0286328	+	0.0286328i
$638$	−1.12664	−	6.50269i	−0.0446040	−	0.257444i
$639$		−	4.99044i		−	0.197419i
$640$	−1.67882	+	1.47702i	−0.0663610	+	0.0583842i
$641$	−2.07075			−0.0817896			−0.0408948	−	0.999163i	$-0.513021\pi$
$641$	−2.07075			−0.0817896			−0.0408948	+	0.999163i	$0.513021\pi$
$642$	−25.8378	+	25.8378i	−1.01974	+	1.01974i
$643$	−19.0190	−	19.0190i	−0.750036	−	0.750036i	0.224450	−	0.974486i	$-0.427941\pi$
$643$	−19.0190	−	19.0190i	−0.750036	−	0.750036i	−0.974486	+	0.224450i	$0.927941\pi$
$644$	−3.97453			−0.156619
$645$	21.9940	+	1.40640i	0.866012	+	0.0553770i
$646$		−	3.45715i		−	0.136020i
$647$	−16.1775	+	16.1775i	−0.636002	+	0.636002i	−0.949567	−	0.313565i	$-0.898477\pi$
$647$	−16.1775	+	16.1775i	−0.636002	+	0.636002i	0.313565	+	0.949567i	$0.398477\pi$
$648$	7.95478	−	7.95478i	0.312493	−	0.312493i
$649$	3.80171	−	5.39513i	0.149230	−	0.211777i
$650$	−5.06836	−	0.650852i	−0.198797	−	0.0255285i
$651$			13.0419i			0.511153i
$652$	5.65913	−	5.65913i	0.221628	−	0.221628i
$653$	2.30114	+	2.30114i	0.0900505	+	0.0900505i	0.750697	−	0.660647i	$-0.229718\pi$
$653$	2.30114	+	2.30114i	0.0900505	+	0.0900505i	−0.660647	+	0.750697i	$0.729718\pi$
$654$		−	13.6556i		−	0.533974i
$655$	0.784370	−	12.2663i	0.0306479	−	0.479286i
$656$		−	7.43624i		−	0.290336i
$657$	5.06187	+	5.06187i	0.197482	+	0.197482i
$658$	−4.35707	−	4.35707i	−0.169856	−	0.169856i
$659$	−11.6329			−0.453155			−0.226578	−	0.973993i	$-0.572754\pi$
$659$	−11.6329			−0.453155			−0.226578	+	0.973993i	$0.572754\pi$
$660$	−15.6683	+	1.69397i	−0.609886	+	0.0659376i
$661$	44.0704			1.71414			0.857070	−	0.515200i	$-0.172282\pi$
$661$	44.0704			1.71414			0.857070	+	0.515200i	$0.172282\pi$
$662$	−17.7964	−	17.7964i	−0.691675	−	0.691675i
$663$	3.33711	+	3.33711i	0.129602	+	0.129602i
$664$		−	7.56451i		−	0.293560i
$665$	−2.34979	−	2.67084i	−0.0911211	−	0.103571i
$666$			4.76850i			0.184776i
$667$	−5.59230	−	5.59230i	−0.216535	−	0.216535i
$668$	15.9031	−	15.9031i	0.615309	−	0.615309i
$669$		−	48.8404i		−	1.88828i
$670$	6.48132	+	0.414447i	0.250395	+	0.0160115i
$671$	−10.8410	+	15.3848i	−0.418513	+	0.593925i
$672$	1.50262	−	1.50262i	0.0579647	−	0.0579647i
$673$	−26.2264	+	26.2264i	−1.01095	+	1.01095i	−0.0110122	+	0.999939i	$0.503505\pi$
$673$	−26.2264	+	26.2264i	−1.01095	+	1.01095i	−0.999939	+	0.0110122i	$0.996495\pi$
$674$		−	34.6490i		−	1.33463i
$675$	12.4811	−	9.64041i	0.480400	−	0.371060i
$676$	−11.9555			−0.459828
$677$	−8.29440	−	8.29440i	−0.318780	−	0.318780i	0.529519	−	0.848298i	$-0.322373\pi$
$677$	−8.29440	−	8.29440i	−0.318780	−	0.318780i	−0.848298	+	0.529519i	$0.822373\pi$
$678$	−24.0202	+	24.0202i	−0.922492	+	0.922492i
$679$	−1.08541			−0.0416542
$680$	4.84922	+	0.310083i	0.185959	+	0.0118911i
$681$		−	51.7303i		−	1.98231i
$682$	3.47491	+	20.0564i	0.133061	+	0.767998i
$683$	22.8312	+	22.8312i	0.873613	+	0.873613i	0.992864	−	0.119251i	$-0.0380494\pi$
$683$	22.8312	+	22.8312i	0.873613	+	0.873613i	−0.119251	+	0.992864i	$0.538049\pi$
$684$	−2.41135			−0.0922002
$685$	33.6995	−	29.6487i	1.28759	−	1.13282i
$686$	−1.00000			−0.0381802
$687$	8.08032	−	8.08032i	0.308283	−	0.308283i
$688$	−3.27964	+	3.27964i	−0.125035	+	0.125035i
$689$	−0.874658			−0.0333218
$690$	−14.1792	+	12.4748i	−0.539794	+	0.474909i
$691$	31.5705			1.20100			0.600498	−	0.799626i	$-0.294969\pi$
$691$	31.5705			1.20100			0.600498	+	0.799626i	$0.294969\pi$
$692$	−1.60073	−	1.60073i	−0.0608505	−	0.0608505i
$693$	4.95324	−	0.858185i	0.188158	−	0.0325997i
$694$			18.5668i			0.704786i
$695$	18.0684	+	1.15538i	0.685373	+	0.0438261i
$696$	4.22846			0.160279
$697$	−11.4265	+	11.4265i	−0.432808	+	0.432808i
$698$	−10.2599	−	10.2599i	−0.388343	−	0.388343i
$699$	10.6087			0.401257
$700$	3.95706	−	3.05642i	0.149563	−	0.115522i
$701$			43.8064i			1.65454i	0.561802	+	0.827272i	$0.310108\pi$
$701$			43.8064i			1.65454i	−0.561802	+	0.827272i	$0.689892\pi$
$702$	−2.27938	+	2.27938i	−0.0860296	+	0.0860296i
$703$	−3.53912	+	3.53912i	−0.133481	+	0.133481i
$704$	1.91042	−	2.71114i	0.0720017	−	0.102180i
$705$	−29.2194	−	1.86843i	−1.10047	−	0.0703691i
$706$		−	29.8640i		−	1.12395i
$707$	−2.96273	+	2.96273i	−0.111425	+	0.111425i
$708$	2.99018	+	2.99018i	0.112378	+	0.112378i
$709$			18.9738i			0.712576i	0.934376	+	0.356288i	$0.115958\pi$
$709$			18.9738i			0.712576i	−0.934376	+	0.356288i	$0.884042\pi$
$710$	4.86305	+	5.52747i	0.182507	+	0.207442i
$711$		−	14.9303i		−	0.559930i
$712$	−0.807760	−	0.807760i	−0.0302721	−	0.0302721i
$713$	17.2484	+	17.2484i	0.645958	+	0.645958i
$714$	−4.61781			−0.172817
$715$	7.53541	−	0.814688i	0.281808	−	0.0304676i
$716$	11.7516			0.439178
$717$	36.9653	+	36.9653i	1.38049	+	1.38049i
$718$	15.9646	+	15.9646i	0.595794	+	0.595794i
$719$		−	26.2694i		−	0.979683i	−0.871811	−	0.489842i	$-0.837055\pi$
$719$		−	26.2694i		−	0.979683i	0.871811	−	0.489842i	$-0.162945\pi$
$720$	0.216282	−	3.38232i	0.00806035	−	0.126052i
$721$		−	10.5446i		−	0.392701i
$722$	11.6454	+	11.6454i	0.433395	+	0.433395i
$723$	13.8425	−	13.8425i	0.514810	−	0.514810i
$724$		−	12.1351i		−	0.450999i
$725$	9.86819	+	1.26722i	0.366495	+	0.0470634i
$726$	22.0128	−	7.86379i	0.816970	−	0.291853i
$727$	6.78964	−	6.78964i	0.251814	−	0.251814i	−0.569900	−	0.821714i	$-0.693018\pi$
$727$	6.78964	−	6.78964i	0.251814	−	0.251814i	0.821714	+	0.569900i	$0.193018\pi$
$728$	−0.722660	+	0.722660i	−0.0267836	+	0.0267836i
$729$		−	3.05655i		−	0.113206i
$730$	−10.5392	−	0.673930i	−0.390075	−	0.0249433i
$731$	10.0789			0.372783
$732$	−8.52685	−	8.52685i	−0.315161	−	0.315161i
$733$	25.6822	−	25.6822i	0.948595	−	0.948595i	−0.0501466	−	0.998742i	$-0.515969\pi$
$733$	25.6822	−	25.6822i	0.948595	−	0.948595i	0.998742	+	0.0501466i	$0.0159689\pi$
$734$	27.5817			1.01806
$735$	−3.56752	+	3.13869i	−0.131590	+	0.115772i
$736$		−	3.97453i		−	0.146503i
$737$	−9.49158	+	1.64448i	−0.349627	+	0.0605754i
$738$	7.96991	+	7.96991i	0.293377	+	0.293377i
$739$	−2.27131			−0.0835515			−0.0417758	−	0.999127i	$-0.513302\pi$
$739$	−2.27131			−0.0835515			−0.0417758	+	0.999127i	$0.513302\pi$
$740$	−4.64677	−	5.28164i	−0.170819	−	0.194157i
$741$	3.45507			0.126925
$742$	0.605166	−	0.605166i	0.0222163	−	0.0222163i
$743$	27.9143	−	27.9143i	1.02407	−	1.02407i	0.0243717	−	0.999703i	$-0.492241\pi$
$743$	27.9143	−	27.9143i	1.02407	−	1.02407i	0.999703	−	0.0243717i	$-0.00775851\pi$
$744$	−13.0419			−0.478139
$745$	−37.9706	−	2.42803i	−1.39114	−	0.0889560i
$746$	−33.9684			−1.24367
$747$	8.10739	+	8.10739i	0.296634	+	0.296634i
$748$	−7.10145	+	1.23038i	−0.259655	+	0.0449871i
$749$			17.1952i			0.628300i
$750$	4.52370	−	23.3238i	0.165182	−	0.851665i
$751$	32.7338			1.19447			0.597237	−	0.802065i	$-0.296265\pi$
$751$	32.7338			1.19447			0.597237	+	0.802065i	$0.296265\pi$
$752$	4.35707	−	4.35707i	0.158886	−	0.158886i
$753$	−37.1929	−	37.1929i	−1.35538	−	1.35538i
$754$	−2.03361			−0.0740598
$755$	−3.37003	+	52.7022i	−0.122648	+	1.91803i
$756$		−	3.15415i		−	0.114715i
$757$	−10.7487	+	10.7487i	−0.390668	+	0.390668i	−0.874926	−	0.484257i	$-0.839090\pi$
$757$	−10.7487	+	10.7487i	−0.390668	+	0.390668i	0.484257	+	0.874926i	$0.339090\pi$
$758$	24.5126	−	24.5126i	0.890336	−	0.890336i
$759$	16.1354	−	22.8982i	0.585676	−	0.831152i
$760$	2.67084	−	2.34979i	0.0968815	−	0.0852360i
$761$			15.5665i			0.564285i	0.959373	+	0.282142i	$0.0910451\pi$
$761$			15.5665i			0.564285i	−0.959373	+	0.282142i	$0.908955\pi$
$762$	−31.1174	+	31.1174i	−1.12726	+	1.12726i
$763$	−4.54393	−	4.54393i	−0.164501	−	0.164501i
$764$			6.63527i			0.240056i
$765$	−5.52957	+	4.86490i	−0.199922	+	0.175891i
$766$		−	32.8415i		−	1.18661i
$767$	−1.43808	−	1.43808i	−0.0519261	−	0.0519261i
$768$	1.50262	+	1.50262i	0.0542210	+	0.0542210i
$769$	48.4835			1.74836			0.874180	−	0.485602i	$-0.161400\pi$
$769$	48.4835			1.74836			0.874180	+	0.485602i	$0.161400\pi$
$770$	−4.64999	+	5.77734i	−0.167574	+	0.208201i
$771$	35.2608			1.26989
$772$	−14.3240	−	14.3240i	−0.515532	−	0.515532i
$773$	24.4300	+	24.4300i	0.878686	+	0.878686i	0.993399	−	0.114713i	$-0.0365948\pi$
$773$	24.4300	+	24.4300i	0.878686	+	0.878686i	−0.114713	+	0.993399i	$0.536595\pi$
$774$		−	7.03003i		−	0.252689i
$775$	−30.4366	−	3.90851i	−1.09332	−	0.140398i
$776$		−	1.08541i		−	0.0389639i
$777$	4.72731	+	4.72731i	0.169591	+	0.169591i
$778$	9.47387	−	9.47387i	0.339655	−	0.339655i
$779$			11.8304i			0.423866i
$780$	−0.309896	+	4.84630i	−0.0110961	+	0.173526i
$781$	−8.92638	−	6.29003i	−0.319411	−	0.225075i
$782$	−6.10723	+	6.10723i	−0.218394	+	0.218394i
$783$	4.43799	−	4.43799i	0.158601	−	0.158601i
$784$		−	1.00000i		−	0.0357143i
$785$	2.78787	−	2.45276i	0.0995033	−	0.0875426i
$786$	−11.6810			−0.416647
$787$	34.8553	+	34.8553i	1.24246	+	1.24246i	0.958979	+	0.283478i	$0.0914883\pi$
$787$	34.8553	+	34.8553i	1.24246	+	1.24246i	0.283478	+	0.958979i	$0.408512\pi$
$788$	1.77392	−	1.77392i	0.0631934	−	0.0631934i
$789$	−41.9723			−1.49425
$790$	14.5492	+	16.5370i	0.517636	+	0.588359i
$791$			15.9856i			0.568383i
$792$	0.858185	+	4.95324i	0.0304943	+	0.176006i
$793$	4.10086	+	4.10086i	0.145626	+	0.145626i
$794$	−16.2846			−0.577920
$795$	0.259512	−	4.05837i	0.00920393	−	0.143935i
$796$	−17.4009			−0.616759
$797$	30.1352	−	30.1352i	1.06744	−	1.06744i	0.0698898	−	0.997555i	$-0.477735\pi$
$797$	30.1352	−	30.1352i	1.06744	−	1.06744i	0.997555	−	0.0698898i	$-0.0222648\pi$
$798$	−2.39052	+	2.39052i	−0.0846235	+	0.0846235i
$799$	−13.3901			−0.473706
$800$	3.05642	+	3.95706i	0.108061	+	0.139903i
$801$	1.73146			0.0611782
$802$	−7.36634	−	7.36634i	−0.260115	−	0.260115i
$803$	15.4342	−	2.67409i	0.544661	−	0.0943665i
$804$		−	6.17202i		−	0.217670i
$805$	−0.567141	+	8.86922i	−0.0199891	+	0.312599i
$806$	6.27230			0.220932
$807$	−7.65647	+	7.65647i	−0.269521	+	0.269521i
$808$	−2.96273	−	2.96273i	−0.104229	−	0.104229i
$809$	−21.0391			−0.739697			−0.369848	−	0.929092i	$-0.620590\pi$
$809$	−21.0391			−0.739697			−0.369848	+	0.929092i	$0.620590\pi$
$810$	−16.6161	−	18.8863i	−0.583829	−	0.663596i
$811$			50.2439i			1.76430i	0.470967	+	0.882151i	$0.343905\pi$
$811$			50.2439i			1.76430i	−0.470967	+	0.882151i	$0.656095\pi$
$812$	1.40703	−	1.40703i	0.0493771	−	0.0493771i
$813$	15.2190	−	15.2190i	0.533753	−	0.533753i
$814$	8.52940	+	6.01029i	0.298955	+	0.210661i
$815$	−11.8209	−	13.4359i	−0.414067	−	0.470640i
$816$		−	4.61781i		−	0.161656i
$817$	5.21761	−	5.21761i	0.182541	−	0.182541i
$818$	−17.4134	−	17.4134i	−0.608845	−	0.608845i
$819$		−	1.54905i		−	0.0541281i
$820$	−16.5940	−	1.06110i	−0.579489	−	0.0370553i
$821$			11.9807i			0.418128i	0.977902	+	0.209064i	$0.0670417\pi$
$821$			11.9807i			0.418128i	−0.977902	+	0.209064i	$0.932958\pi$
$822$	−30.1626	−	30.1626i	−1.05204	−	1.05204i
$823$	6.00990	+	6.00990i	0.209492	+	0.209492i	0.804051	−	0.594560i	$-0.202674\pi$
$823$	6.00990	+	6.00990i	0.209492	+	0.209492i	−0.594560	+	0.804051i	$0.702674\pi$
$824$	10.5446			0.367338
$825$	1.54435	+	35.2056i	0.0537673	+	1.22570i
$826$	1.98998			0.0692404
$827$	21.0570	+	21.0570i	0.732223	+	0.732223i	0.971060	−	0.238837i	$-0.0767660\pi$
$827$	21.0570	+	21.0570i	0.732223	+	0.732223i	−0.238837	+	0.971060i	$0.576766\pi$
$828$	4.25978	+	4.25978i	0.148037	+	0.148037i
$829$		−	0.791497i		−	0.0274898i	−0.999906	−	0.0137449i	$-0.995625\pi$
$829$		−	0.791497i		−	0.0274898i	0.999906	−	0.0137449i	$-0.00437528\pi$
$830$	−16.8803	−	1.07941i	−0.585923	−	0.0374667i
$831$		−	9.31529i		−	0.323144i
$832$	−0.722660	−	0.722660i	−0.0250537	−	0.0250537i
$833$	−1.53659	+	1.53659i	−0.0532397	+	0.0532397i
$834$		−	17.2061i		−	0.595800i
$835$	−33.2186	−	37.7572i	−1.14958	−	1.30664i
$836$	−3.03930	+	4.31317i	−0.105116	+	0.149174i
$837$	−13.6882	+	13.6882i	−0.473132	+	0.473132i
$838$	13.9841	−	13.9841i	0.483072	−	0.483072i
$839$		−	54.7496i		−	1.89016i	−0.326832	−	0.945082i	$-0.605981\pi$
$839$		−	54.7496i		−	1.89016i	0.326832	−	0.945082i	$-0.394019\pi$
$840$	−3.13869	−	3.56752i	−0.108295	−	0.123091i
$841$	−25.0405			−0.863466
$842$	19.3521	+	19.3521i	0.666918	+	0.666918i
$843$	1.90741	−	1.90741i	0.0656948	−	0.0656948i
$844$	−0.876221			−0.0301608
$845$	−1.70598	+	26.6789i	−0.0586874	+	0.917781i
$846$			9.33953i			0.321100i
$847$	4.70811	−	9.94151i	0.161773	−	0.341594i
$848$	0.605166	+	0.605166i	0.0207815	+	0.0207815i
$849$	−2.68592			−0.0921804
$850$	1.38391	−	10.7768i	0.0474676	−	0.369643i
$851$	12.5041			0.428635
$852$	4.94734	−	4.94734i	0.169493	−	0.169493i
$853$	3.11758	−	3.11758i	0.106744	−	0.106744i	−0.651718	−	0.758462i	$-0.725951\pi$
$853$	3.11758	−	3.11758i	0.106744	−	0.106744i	0.758462	+	0.651718i	$0.225951\pi$
$854$	−5.67467			−0.194183
$855$	−0.344084	+	5.38095i	−0.0117674	+	0.184025i
$856$	−17.1952			−0.587720
$857$	19.1026	+	19.1026i	0.652533	+	0.652533i	0.953602	−	0.301070i	$-0.0973436\pi$
$857$	19.1026	+	19.1026i	0.652533	+	0.652533i	−0.301070	+	0.953602i	$0.597344\pi$
$858$	−1.22964	−	7.09718i	−0.0419791	−	0.242294i
$859$		−	45.6584i		−	1.55785i	−0.627120	−	0.778923i	$-0.715766\pi$
$859$		−	45.6584i		−	1.55785i	0.627120	−	0.778923i	$-0.284234\pi$
$860$	6.85058	+	7.78654i	0.233603	+	0.265519i
$861$	15.8021			0.538536
$862$	−12.9277	+	12.9277i	−0.440320	+	0.440320i
$863$	−14.9342	−	14.9342i	−0.508365	−	0.508365i	0.405659	−	0.914024i	$-0.367042\pi$
$863$	−14.9342	−	14.9342i	−0.508365	−	0.508365i	−0.914024	+	0.405659i	$0.867042\pi$
$864$	3.15415			0.107306
$865$	−3.80045	+	3.34362i	−0.129219	+	0.113687i
$866$		−	24.1253i		−	0.819811i
$867$	18.4488	−	18.4488i	0.626553	−	0.626553i
$868$	−4.33973	+	4.33973i	−0.147300	+	0.147300i
$869$	−26.7058	−	18.8184i	−0.905931	−	0.638369i
$870$	0.603374	−	9.43585i	0.0204563	−	0.319905i
$871$			2.96834i			0.100578i
$872$	4.54393	−	4.54393i	0.153877	−	0.153877i
$873$	1.16331	+	1.16331i	0.0393719	+	0.0393719i
$874$			6.32311i			0.213882i
$875$	−6.25579	−	9.26634i	−0.211484	−	0.313260i
$876$			10.0363i			0.339095i
$877$	11.9521	+	11.9521i	0.403593	+	0.403593i	0.879497	−	0.475904i	$-0.157879\pi$
$877$	11.9521	+	11.9521i	0.403593	+	0.403593i	−0.475904	+	0.879497i	$0.657879\pi$
$878$	−7.59502	−	7.59502i	−0.256320	−	0.256320i
$879$	58.3181			1.96702
$880$	−5.77734	−	4.64999i	−0.194754	−	0.156751i
$881$	7.71798			0.260025			0.130013	−	0.991512i	$-0.458498\pi$
$881$	7.71798			0.260025			0.130013	+	0.991512i	$0.458498\pi$
$882$	1.07177	+	1.07177i	0.0360883	+	0.0360883i
$883$	23.3810	+	23.3810i	0.786834	+	0.786834i	0.980974	−	0.194140i	$-0.0621915\pi$
$883$	23.3810	+	23.3810i	0.786834	+	0.786834i	−0.194140	+	0.980974i	$0.562191\pi$
$884$			2.22086i			0.0746958i
$885$	7.09930	−	6.24594i	0.238640	−	0.209955i
$886$		−	12.6198i		−	0.423971i
$887$	−30.2409	−	30.2409i	−1.01539	−	1.01539i	−0.999880	−	0.0155119i	$-0.995062\pi$
$887$	−30.2409	−	30.2409i	−1.01539	−	1.01539i	−0.0155119	−	0.999880i	$-0.504938\pi$
$888$	−4.72731	+	4.72731i	−0.158638	+	0.158638i
$889$			20.7088i			0.694552i
$890$	−1.91779	+	1.68726i	−0.0642844	+	0.0565572i
$891$	30.4997	+	21.4918i	1.02178	+	0.720002i
$892$	16.2518	−	16.2518i	0.544150	−	0.544150i
$893$	−6.93169	+	6.93169i	−0.231960	+	0.231960i
$894$			36.1586i			1.20932i
$895$	1.67688	−	26.2238i	0.0560519	−	0.876566i
$896$	1.00000			0.0334077
$897$	−6.10356	−	6.10356i	−0.203792	−	0.203792i
$898$	−10.6155	+	10.6155i	−0.354244	+	0.354244i
$899$	−12.2123			−0.407303
$900$	−7.51682	−	0.965270i	−0.250561	−	0.0321757i
$901$		−	1.85979i		−	0.0619584i
$902$	24.3012	−	4.21035i	0.809140	−	0.140189i
$903$	−6.96931	−	6.96931i	−0.231924	−	0.231924i
$904$	−15.9856			−0.531674
$905$	−27.0797	−	1.73161i	−0.900159	−	0.0575605i
$906$	50.1872			1.66736
$907$	−3.07983	+	3.07983i	−0.102264	+	0.102264i	−0.756388	−	0.654124i	$-0.773038\pi$
$907$	−3.07983	+	3.07983i	−0.102264	+	0.102264i	0.654124	+	0.756388i	$0.273038\pi$
$908$	17.2134	−	17.2134i	0.571248	−	0.571248i
$909$	6.35072			0.210640
$910$	1.50950	+	1.71574i	0.0500396	+	0.0568763i
$911$	−34.6790			−1.14897			−0.574484	−	0.818516i	$-0.694797\pi$
$911$	−34.6790			−1.14897			−0.574484	+	0.818516i	$0.694797\pi$
$912$	−2.39052	−	2.39052i	−0.0791580	−	0.0791580i
$913$	24.7203	−	4.28298i	0.818124	−	0.141746i
$914$		−	37.7554i		−	1.24884i
$915$	−20.2445	+	17.8110i	−0.669262	+	0.588814i
$916$	5.37750			0.177678
$917$	−3.88688	+	3.88688i	−0.128356	+	0.128356i
$918$	−4.84664	−	4.84664i	−0.159963	−	0.159963i
$919$	16.9875			0.560366			0.280183	−	0.959947i	$-0.409605\pi$
$919$	16.9875			0.560366			0.280183	+	0.959947i	$0.409605\pi$
$920$	−8.86922	−	0.567141i	−0.292409	−	0.0186981i
$921$		−	10.6010i		−	0.349315i
$922$	−19.3729	+	19.3729i	−0.638012	+	0.638012i
$923$	−2.37934	+	2.37934i	−0.0783171	+	0.0783171i
$924$	5.76123	+	4.05968i	0.189530	+	0.133554i
$925$	−12.4491	+	9.61567i	−0.409324	+	0.316161i
$926$		−	9.53983i		−	0.313498i
$927$	−11.3013	+	11.3013i	−0.371185	+	0.371185i
$928$	1.40703	+	1.40703i	0.0461881	+	0.0461881i
$929$			30.0027i			0.984358i	0.870494	+	0.492179i	$0.163799\pi$
$929$			30.0027i			0.984358i	−0.870494	+	0.492179i	$0.836201\pi$
$930$	−1.86100	+	29.1031i	−0.0610245	+	0.954330i
$931$			1.59091i			0.0521398i
$932$	3.53007	+	3.53007i	0.115631	+	0.115631i
$933$	−15.4135	−	15.4135i	−0.504615	−	0.504615i
$934$	−19.7850			−0.647385
$935$	1.73227	+	16.0225i	0.0566513	+	0.523993i
$936$	1.54905			0.0506322
$937$	6.82471	+	6.82471i	0.222954	+	0.222954i	0.809741	−	0.586787i	$-0.199608\pi$
$937$	6.82471	+	6.82471i	0.222954	+	0.222954i	−0.586787	+	0.809741i	$0.699608\pi$
$938$	−2.05376	−	2.05376i	−0.0670576	−	0.0670576i
$939$		−	45.7253i		−	1.49219i
$940$	−9.10112	−	10.3446i	−0.296846	−	0.337403i
$941$			17.1242i			0.558233i	0.960257	+	0.279117i	$0.0900416\pi$
$941$			17.1242i			0.558233i	−0.960257	+	0.279117i	$0.909958\pi$
$942$	−2.49527	−	2.49527i	−0.0813002	−	0.0813002i
$943$	20.8989	−	20.8989i	0.680563	−	0.680563i
$944$			1.98998i			0.0647685i
$945$	−7.03852	−	0.450077i	−0.228963	−	0.0146410i
$946$	−12.5746	−	8.86076i	−0.408835	−	0.288088i
$947$	15.8997	−	15.8997i	0.516670	−	0.516670i	−0.399892	−	0.916562i	$-0.630952\pi$
$947$	15.8997	−	15.8997i	0.516670	−	0.516670i	0.916562	+	0.399892i	$0.130952\pi$
$948$	14.8013	−	14.8013i	0.480725	−	0.480725i
$949$		−	4.82680i		−	0.156685i
$950$	−4.86248	−	6.29530i	−0.157760	−	0.204247i
$951$	−12.5380			−0.406574
$952$	−1.53659	−	1.53659i	−0.0498012	−	0.0498012i
$953$	−19.6337	+	19.6337i	−0.635998	+	0.635998i	−0.949566	−	0.313568i	$-0.898476\pi$
$953$	−19.6337	+	19.6337i	−0.635998	+	0.635998i	0.313568	+	0.949566i	$0.398476\pi$
$954$	−1.29719			−0.0419982
$955$	14.8067	+	0.946811i	0.479133	+	0.0306381i
$956$			24.6006i			0.795640i
$957$	2.39413	+	13.8183i	0.0773911	+	0.446683i
$958$	−19.3179	−	19.3179i	−0.624132	−	0.624132i
$959$	−20.0734			−0.648203
$960$	3.56752	−	3.13869i	0.115141	−	0.101301i
$961$	6.66658			0.215051
$962$	2.27353	−	2.27353i	0.0733014	−	0.0733014i
$963$	18.4293	−	18.4293i	0.593875	−	0.593875i
$964$	9.21230			0.296708
$965$	−34.0081	+	29.9202i	−1.09476	+	0.963165i
$966$	8.44596			0.271744
$967$	−7.70407	−	7.70407i	−0.247746	−	0.247746i	0.572299	−	0.820045i	$-0.306052\pi$
$967$	−7.70407	−	7.70407i	−0.247746	−	0.247746i	−0.820045	+	0.572299i	$0.806052\pi$
$968$	9.94151	+	4.70811i	0.319532	+	0.151324i
$969$			7.34650i			0.236004i
$970$	−2.42210	−	0.154881i	−0.0777690	−	0.00497293i
$971$	−5.50534			−0.176675			−0.0883374	−	0.996091i	$-0.528155\pi$
$971$	−5.50534			−0.176675			−0.0883374	+	0.996091i	$0.528155\pi$
$972$	−10.2131	+	10.2131i	−0.327585	+	0.327585i
$973$	−5.72540	−	5.72540i	−0.183548	−	0.183548i
$974$	33.9554			1.08800
$975$	10.7704	+	1.38307i	0.344928	+	0.0442938i
$976$		−	5.67467i		−	0.181642i
$977$	−22.4851	+	22.4851i	−0.719361	+	0.719361i	−0.968474	−	0.249113i	$-0.919861\pi$
$977$	−22.4851	+	22.4851i	−0.719361	+	0.719361i	0.249113	+	0.968474i	$0.419861\pi$
$978$	−12.0258	+	12.0258i	−0.384541	+	0.384541i
$979$	2.18236	−	3.09706i	0.0697486	−	0.0989825i
$980$	−2.23151	−	0.142694i	−0.0712830	−	0.00455818i
$981$			9.74007i			0.310976i
$982$	19.1292	−	19.1292i	0.610438	−	0.610438i
$983$	32.5406	+	32.5406i	1.03789	+	1.03789i	0.999254	+	0.0386315i	$0.0122999\pi$
$983$	32.5406	+	32.5406i	1.03789	+	1.03789i	0.0386315	+	0.999254i	$0.487700\pi$
$984$			15.8021i			0.503754i
$985$	−3.70540	−	4.21165i	−0.118064	−	0.134194i
$986$		−	4.32407i		−	0.137706i
$987$	9.25886	+	9.25886i	0.294713	+	0.294713i
$988$	1.14968	+	1.14968i	0.0365763	+	0.0365763i
$989$	−18.4344			−0.586179
$990$	11.1757	−	1.20825i	0.355186	−	0.0384008i
$991$	−8.05431			−0.255854			−0.127927	−	0.991784i	$-0.540832\pi$
$991$	−8.05431			−0.255854			−0.127927	+	0.991784i	$0.540832\pi$
$992$	−4.33973	−	4.33973i	−0.137787	−	0.137787i
$993$	37.8176	+	37.8176i	1.20011	+	1.20011i
$994$		−	3.29248i		−	0.104431i
$995$	−2.48300	+	38.8303i	−0.0787163	+	1.23100i
$996$			16.0747i			0.509347i
$997$	−24.6166	−	24.6166i	−0.779615	−	0.779615i	0.200150	−	0.979765i	$-0.435857\pi$
$997$	−24.6166	−	24.6166i	−0.779615	−	0.779615i	−0.979765	+	0.200150i	$0.935857\pi$
$998$	15.5394	−	15.5394i	0.491892	−	0.491892i
$999$			9.92312i			0.313954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.43.8	✓	36
5.2	odd	4	inner	770.2.m.f.197.17	yes	36
11.10	odd	2	inner	770.2.m.f.43.17	yes	36
55.32	even	4	inner	770.2.m.f.197.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.8	✓	36	1.1	even	1	trivial
770.2.m.f.43.17	yes	36	11.10	odd	2	inner
770.2.m.f.197.8	yes	36	55.32	even	4	inner
770.2.m.f.197.17	yes	36	5.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.50262 + 1.50262i) q^{3} +1.00000i q^{4} +(2.23151 + 0.142694i) q^{5} -2.12502i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.51571i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.50262 + 1.50262i) q^{3} +1.00000i q^{4} +(2.23151 + 0.142694i) q^{5} -2.12502i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.51571i q^{9} +(-1.47702 - 1.67882i) q^{10} +(2.71114 + 1.91042i) q^{11} +(-1.50262 + 1.50262i) q^{12} +(0.722660 - 0.722660i) q^{13} +1.00000i q^{14} +(3.13869 + 3.56752i) q^{15} -1.00000 q^{16} +(1.53659 + 1.53659i) q^{17} +(1.07177 - 1.07177i) q^{18} +1.59091 q^{19} +(-0.142694 + 2.23151i) q^{20} -2.12502i q^{21} +(-0.566194 - 3.26794i) q^{22} +(-2.81042 - 2.81042i) q^{23} +2.12502 q^{24} +(4.95928 + 0.636844i) q^{25} -1.02200 q^{26} +(2.23032 - 2.23032i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.98984 q^{29} +(0.303227 - 4.74200i) q^{30} -6.13731 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.20317 + 6.94443i) q^{33} -2.17307i q^{34} +(-1.47702 - 1.67882i) q^{35} -1.51571 q^{36} +(-2.22460 + 2.22460i) q^{37} +(-1.12494 - 1.12494i) q^{38} +2.17176 q^{39} +(1.67882 - 1.47702i) q^{40} +7.43624i q^{41} +(-1.50262 + 1.50262i) q^{42} +(3.27964 - 3.27964i) q^{43} +(-1.91042 + 2.71114i) q^{44} +(-0.216282 + 3.38232i) q^{45} +3.97453i q^{46} +(-4.35707 + 4.35707i) q^{47} +(-1.50262 - 1.50262i) q^{48} +1.00000i q^{49} +(-3.05642 - 3.95706i) q^{50} +4.61781i q^{51} +(0.722660 + 0.722660i) q^{52} +(-0.605166 - 0.605166i) q^{53} -3.15415 q^{54} +(5.77734 + 4.64999i) q^{55} -1.00000 q^{56} +(2.39052 + 2.39052i) q^{57} +(-1.40703 - 1.40703i) q^{58} -1.98998i q^{59} +(-3.56752 + 3.13869i) q^{60} +5.67467i q^{61} +(4.33973 + 4.33973i) q^{62} +(1.07177 - 1.07177i) q^{63} -1.00000i q^{64} +(1.71574 - 1.50950i) q^{65} +(4.05968 - 5.76123i) q^{66} +(-2.05376 + 2.05376i) q^{67} +(-1.53659 + 1.53659i) q^{68} -8.44596i q^{69} +(-0.142694 + 2.23151i) q^{70} -3.29248 q^{71} +(1.07177 + 1.07177i) q^{72} +(3.33961 - 3.33961i) q^{73} +3.14605 q^{74} +(6.49496 + 8.40882i) q^{75} +1.59091i q^{76} +(-0.566194 - 3.26794i) q^{77} +(-1.53567 - 1.53567i) q^{78} -9.85037 q^{79} +(-2.23151 - 0.142694i) q^{80} +11.2498 q^{81} +(5.25821 - 5.25821i) q^{82} +(5.34891 - 5.34891i) q^{83} +2.12502 q^{84} +(3.20966 + 3.64818i) q^{85} -4.63812 q^{86} +(2.98997 + 2.98997i) q^{87} +(3.26794 - 0.566194i) q^{88} -1.14235i q^{89} +(2.54459 - 2.23873i) q^{90} -1.02200 q^{91} +(2.81042 - 2.81042i) q^{92} +(-9.22202 - 9.22202i) q^{93} +6.16183 q^{94} +(3.55012 + 0.227012i) q^{95} +2.12502i q^{96} +(0.767500 - 0.767500i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-2.89564 + 4.10930i) 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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