LMFDB - Embedded newform 966.2.f.c.461.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.20
Character	$\chi$	$=$	966.461
Dual form			966.2.f.c.461.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.711304 - 1.57925i) q^{3} -1.00000 q^{4} +0.334212 q^{5} +(1.57925 - 0.711304i) q^{6} +(-0.168570 - 2.64038i) q^{7} -1.00000i q^{8} +(-1.98809 + 2.24666i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.711304 - 1.57925i) q^{3} -1.00000 q^{4} +0.334212 q^{5} +(1.57925 - 0.711304i) q^{6} +(-0.168570 - 2.64038i) q^{7} -1.00000i q^{8} +(-1.98809 + 2.24666i) q^{9} +0.334212i q^{10} +0.616447i q^{11} +(0.711304 + 1.57925i) q^{12} -3.23929i q^{13} +(2.64038 - 0.168570i) q^{14} +(-0.237727 - 0.527806i) q^{15} +1.00000 q^{16} -3.15851 q^{17} +(-2.24666 - 1.98809i) q^{18} +0.890178i q^{19} -0.334212 q^{20} +(-4.04992 + 2.14433i) q^{21} -0.616447 q^{22} +1.00000i q^{23} +(-1.57925 + 0.711304i) q^{24} -4.88830 q^{25} +3.23929 q^{26} +(4.96219 + 1.54164i) q^{27} +(0.168570 + 2.64038i) q^{28} -2.14128i q^{29} +(0.527806 - 0.237727i) q^{30} +2.97856i q^{31} +1.00000i q^{32} +(0.973527 - 0.438482i) q^{33} -3.15851i q^{34} +(-0.0563383 - 0.882446i) q^{35} +(1.98809 - 2.24666i) q^{36} -2.08345 q^{37} -0.890178 q^{38} +(-5.11567 + 2.30412i) q^{39} -0.334212i q^{40} -5.08253 q^{41} +(-2.14433 - 4.04992i) q^{42} -11.3381 q^{43} -0.616447i q^{44} +(-0.664445 + 0.750862i) q^{45} -1.00000 q^{46} +2.96029 q^{47} +(-0.711304 - 1.57925i) q^{48} +(-6.94317 + 0.890178i) q^{49} -4.88830i q^{50} +(2.24666 + 4.98809i) q^{51} +3.23929i q^{52} -0.00920039i q^{53} +(-1.54164 + 4.96219i) q^{54} +0.206024i q^{55} +(-2.64038 + 0.168570i) q^{56} +(1.40582 - 0.633187i) q^{57} +2.14128 q^{58} -13.1251 q^{59} +(0.237727 + 0.527806i) q^{60} -8.92731i q^{61} -2.97856 q^{62} +(6.26716 + 4.87059i) q^{63} -1.00000 q^{64} -1.08261i q^{65} +(0.438482 + 0.973527i) q^{66} +5.51592 q^{67} +3.15851 q^{68} +(1.57925 - 0.711304i) q^{69} +(0.882446 - 0.0563383i) q^{70} +4.57347i q^{71} +(2.24666 + 1.98809i) q^{72} -6.21012i q^{73} -2.08345i q^{74} +(3.47707 + 7.71988i) q^{75} -0.890178i q^{76} +(1.62765 - 0.103915i) q^{77} +(-2.30412 - 5.11567i) q^{78} -7.38606 q^{79} +0.334212 q^{80} +(-1.09498 - 8.93314i) q^{81} -5.08253i q^{82} +11.3888 q^{83} +(4.04992 - 2.14433i) q^{84} -1.05561 q^{85} -11.3381i q^{86} +(-3.38163 + 1.52310i) q^{87} +0.616447 q^{88} -15.6130 q^{89} +(-0.750862 - 0.664445i) q^{90} +(-8.55295 + 0.546049i) q^{91} -1.00000i q^{92} +(4.70391 - 2.11867i) q^{93} +2.96029i q^{94} +0.297508i q^{95} +(1.57925 - 0.711304i) q^{96} -10.2696i q^{97} +(-0.890178 - 6.94317i) q^{98} +(-1.38495 - 1.22555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.711304	−	1.57925i	−0.410672	−	0.911783i
$3$	−0.711304	−	1.57925i	−0.410672	−	0.911783i
$4$	−1.00000			−0.500000
$5$	0.334212			0.149464			0.0747321	−	0.997204i	$-0.476190\pi$
$5$	0.334212			0.149464			0.0747321	+	0.997204i	$0.476190\pi$
$6$	1.57925	−	0.711304i	0.644728	−	0.290389i
$7$	−0.168570	−	2.64038i	−0.0637136	−	0.997968i
$7$	−0.168570	−	2.64038i	−0.0637136	−	0.997968i
$8$		−	1.00000i		−	0.353553i
$9$	−1.98809	+	2.24666i	−0.662697	+	0.748887i
$10$			0.334212i			0.105687i
$11$			0.616447i			0.185866i	0.995672	+	0.0929329i	$0.0296242\pi$
$11$			0.616447i			0.185866i	−0.995672	+	0.0929329i	$0.970376\pi$
$12$	0.711304	+	1.57925i	0.205336	+	0.455892i
$13$		−	3.23929i		−	0.898419i	−0.893427	−	0.449209i	$-0.851706\pi$
$13$		−	3.23929i		−	0.898419i	0.893427	−	0.449209i	$-0.148294\pi$
$14$	2.64038	−	0.168570i	0.705670	−	0.0450523i
$15$	−0.237727	−	0.527806i	−0.0613808	−	0.136279i
$16$	1.00000			0.250000
$17$	−3.15851			−0.766051			−0.383026	−	0.923738i	$-0.625118\pi$
$17$	−3.15851			−0.766051			−0.383026	+	0.923738i	$0.625118\pi$
$18$	−2.24666	−	1.98809i	−0.529543	−	0.468598i
$19$			0.890178i			0.204221i	0.994773	+	0.102110i	$0.0325595\pi$
$19$			0.890178i			0.204221i	−0.994773	+	0.102110i	$0.967441\pi$
$20$	−0.334212			−0.0747321
$21$	−4.04992	+	2.14433i	−0.883765	+	0.467930i
$22$	−0.616447			−0.131427
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−1.57925	+	0.711304i	−0.322364	+	0.145194i
$25$	−4.88830			−0.977660
$26$	3.23929			0.635278
$27$	4.96219	+	1.54164i	0.954974	+	0.296689i
$28$	0.168570	+	2.64038i	0.0318568	+	0.498984i
$29$		−	2.14128i		−	0.397626i	−0.980037	−	0.198813i	$-0.936291\pi$
$29$		−	2.14128i		−	0.397626i	0.980037	−	0.198813i	$-0.0637086\pi$
$30$	0.527806	−	0.237727i	0.0963638	−	0.0434027i
$31$			2.97856i			0.534966i	0.963563	+	0.267483i	$0.0861919\pi$
$31$			2.97856i			0.534966i	−0.963563	+	0.267483i	$0.913808\pi$
$32$			1.00000i			0.176777i
$33$	0.973527	−	0.438482i	0.169469	−	0.0763298i
$34$		−	3.15851i		−	0.541680i
$35$	−0.0563383	−	0.882446i	−0.00952290	−	0.149161i
$36$	1.98809	−	2.24666i	0.331349	−	0.374444i
$37$	−2.08345			−0.342517			−0.171258	−	0.985226i	$-0.554783\pi$
$37$	−2.08345			−0.342517			−0.171258	+	0.985226i	$0.554783\pi$
$38$	−0.890178			−0.144406
$39$	−5.11567	+	2.30412i	−0.819163	+	0.368955i
$40$		−	0.334212i		−	0.0528436i
$41$	−5.08253			−0.793758			−0.396879	−	0.917871i	$-0.629907\pi$
$41$	−5.08253			−0.793758			−0.396879	+	0.917871i	$0.629907\pi$
$42$	−2.14433	−	4.04992i	−0.330877	−	0.624916i
$43$	−11.3381			−1.72905			−0.864526	−	0.502589i	$-0.832381\pi$
$43$	−11.3381			−1.72905			−0.864526	+	0.502589i	$0.832381\pi$
$44$		−	0.616447i		−	0.0929329i
$45$	−0.664445	+	0.750862i	−0.0990496	+	0.111932i
$46$	−1.00000			−0.147442
$47$	2.96029			0.431803			0.215901	−	0.976415i	$-0.430731\pi$
$47$	2.96029			0.431803			0.215901	+	0.976415i	$0.430731\pi$
$48$	−0.711304	−	1.57925i	−0.102668	−	0.227946i
$49$	−6.94317	+	0.890178i	−0.991881	+	0.127168i
$50$		−	4.88830i		−	0.691310i
$51$	2.24666	+	4.98809i	0.314596	+	0.698473i
$52$			3.23929i			0.449209i
$53$		−	0.00920039i		−	0.00126377i	−1.00000		0.000631885i	$-0.999799\pi$
$53$		−	0.00920039i		−	0.00126377i	1.00000		0.000631885i	$-0.000201135\pi$
$54$	−1.54164	+	4.96219i	−0.209791	+	0.675269i
$55$			0.206024i			0.0277803i
$56$	−2.64038	+	0.168570i	−0.352835	+	0.0225262i
$57$	1.40582	−	0.633187i	0.186205	−	0.0838677i
$58$	2.14128			0.281164
$59$	−13.1251			−1.70874			−0.854371	−	0.519663i	$-0.826058\pi$
$59$	−13.1251			−1.70874			−0.854371	+	0.519663i	$0.826058\pi$
$60$	0.237727	+	0.527806i	0.0306904	+	0.0681395i
$61$		−	8.92731i		−	1.14302i	−0.820594	−	0.571512i	$-0.806357\pi$
$61$		−	8.92731i		−	1.14302i	0.820594	−	0.571512i	$-0.193643\pi$
$62$	−2.97856			−0.378278
$63$	6.26716	+	4.87059i	0.789589	+	0.613637i
$64$	−1.00000			−0.125000
$65$		−	1.08261i		−	0.134281i
$66$	0.438482	+	0.973527i	0.0539733	+	0.119833i
$67$	5.51592			0.673877			0.336938	−	0.941527i	$-0.390609\pi$
$67$	5.51592			0.673877			0.336938	+	0.941527i	$0.390609\pi$
$68$	3.15851			0.383026
$69$	1.57925	−	0.711304i	0.190120	−	0.0856310i
$70$	0.882446	−	0.0563383i	0.105472	−	0.00673371i
$71$			4.57347i			0.542771i	0.962471	+	0.271386i	$0.0874819\pi$
$71$			4.57347i			0.542771i	−0.962471	+	0.271386i	$0.912518\pi$
$72$	2.24666	+	1.98809i	0.264772	+	0.234299i
$73$		−	6.21012i		−	0.726840i	−0.931625	−	0.363420i	$-0.881609\pi$
$73$		−	6.21012i		−	0.726840i	0.931625	−	0.363420i	$-0.118391\pi$
$74$		−	2.08345i		−	0.242196i
$75$	3.47707	+	7.71988i	0.401498	+	0.891414i
$76$		−	0.890178i		−	0.102110i
$77$	1.62765	−	0.103915i	0.185488	−	0.0118422i
$78$	−2.30412	−	5.11567i	−0.260891	−	0.579236i
$79$	−7.38606			−0.830997			−0.415499	−	0.909594i	$-0.636393\pi$
$79$	−7.38606			−0.830997			−0.415499	+	0.909594i	$0.636393\pi$
$80$	0.334212			0.0373661
$81$	−1.09498	−	8.93314i	−0.121664	−	0.992571i
$82$		−	5.08253i		−	0.561272i
$83$	11.3888			1.25008			0.625042	−	0.780592i	$-0.285082\pi$
$83$	11.3888			1.25008			0.625042	+	0.780592i	$0.285082\pi$
$84$	4.04992	−	2.14433i	0.441883	−	0.233965i
$85$	−1.05561			−0.114497
$86$		−	11.3381i		−	1.22262i
$87$	−3.38163	+	1.52310i	−0.362549	+	0.163294i
$88$	0.616447			0.0657135
$89$	−15.6130			−1.65498			−0.827490	−	0.561481i	$-0.810232\pi$
$89$	−15.6130			−1.65498			−0.827490	+	0.561481i	$0.810232\pi$
$90$	−0.750862	−	0.664445i	−0.0791478	−	0.0700386i
$91$	−8.55295	+	0.546049i	−0.896593	+	0.0572415i
$92$		−	1.00000i		−	0.104257i
$93$	4.70391	−	2.11867i	0.487773	−	0.219695i
$94$			2.96029i			0.305331i
$95$			0.297508i			0.0305237i
$96$	1.57925	−	0.711304i	0.161182	−	0.0725972i
$97$		−	10.2696i		−	1.04272i	−0.853338	−	0.521358i	$-0.825426\pi$
$97$		−	10.2696i		−	1.04272i	0.853338	−	0.521358i	$-0.174574\pi$
$98$	−0.890178	−	6.94317i	−0.0899215	−	0.701366i
$99$	−1.38495	−	1.22555i	−0.139193	−	0.123173i
$100$	4.88830			0.488830
$101$	−11.1328			−1.10775			−0.553875	−	0.832600i	$-0.686852\pi$
$101$	−11.1328			−1.10775			−0.553875	+	0.832600i	$0.686852\pi$
$102$	−4.98809	+	2.24666i	−0.493895	+	0.222453i
$103$			4.70411i			0.463510i	0.972774	+	0.231755i	$0.0744468\pi$
$103$			4.70411i			0.463510i	−0.972774	+	0.231755i	$0.925553\pi$
$104$	−3.23929			−0.317639
$105$	−1.35353	+	0.716660i	−0.132091	+	0.0699389i
$106$	0.00920039			0.000893620
$107$			6.66683i			0.644507i	0.946653	+	0.322254i	$0.104440\pi$
$107$			6.66683i			0.644507i	−0.946653	+	0.322254i	$0.895560\pi$
$108$	−4.96219	−	1.54164i	−0.477487	−	0.148345i
$109$	14.7101			1.40897			0.704486	−	0.709718i	$-0.251178\pi$
$109$	14.7101			1.40897			0.704486	+	0.709718i	$0.251178\pi$
$110$	−0.206024			−0.0196436
$111$	1.48196	+	3.29029i	0.140662	+	0.312301i
$112$	−0.168570	−	2.64038i	−0.0159284	−	0.249492i
$113$		−	16.9174i		−	1.59146i	−0.605653	−	0.795729i	$-0.707088\pi$
$113$		−	16.9174i		−	1.59146i	0.605653	−	0.795729i	$-0.292912\pi$
$114$	0.633187	+	1.40582i	0.0593034	+	0.131667i
$115$			0.334212i			0.0311655i
$116$			2.14128i			0.198813i
$117$	7.27760	+	6.44002i	0.672814	+	0.595380i
$118$		−	13.1251i		−	1.20826i
$119$	0.532431	+	8.33965i	0.0488079	+	0.764495i
$120$	−0.527806	+	0.237727i	−0.0481819	+	0.0217014i
$121$	10.6200			0.965454
$122$	8.92731			0.808240
$123$	3.61523	+	8.02661i	0.325974	+	0.723735i
$124$		−	2.97856i		−	0.267483i
$125$	−3.30479			−0.295590
$126$	−4.87059	+	6.26716i	−0.433907	+	0.558323i
$127$	1.27261			0.112926			0.0564631	−	0.998405i	$-0.482018\pi$
$127$	1.27261			0.112926			0.0564631	+	0.998405i	$0.482018\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	8.06487	+	17.9058i	0.710073	+	1.57652i
$130$	1.08261			0.0949513
$131$	3.12774			0.273272			0.136636	−	0.990621i	$-0.456371\pi$
$131$	3.12774			0.273272			0.136636	+	0.990621i	$0.456371\pi$
$132$	−0.973527	+	0.438482i	−0.0847347	+	0.0381649i
$133$	2.35040	−	0.150058i	0.203806	−	0.0130116i
$134$			5.51592i			0.476503i
$135$	1.65842	+	0.515236i	0.142734	+	0.0443445i
$136$			3.15851i			0.270840i
$137$			9.47914i			0.809858i	0.914348	+	0.404929i	$0.132704\pi$
$137$			9.47914i			0.809858i	−0.914348	+	0.404929i	$0.867296\pi$
$138$	0.711304	+	1.57925i	0.0605503	+	0.134435i
$139$		−	12.4667i		−	1.05741i	−0.848806	−	0.528704i	$-0.822678\pi$
$139$		−	12.4667i		−	1.05741i	0.848806	−	0.528704i	$-0.177322\pi$
$140$	0.0563383	+	0.882446i	0.00476145	+	0.0745803i
$141$	−2.10567	−	4.67505i	−0.177329	−	0.393711i
$142$	−4.57347			−0.383797
$143$	1.99685			0.166985
$144$	−1.98809	+	2.24666i	−0.165674	+	0.187222i
$145$		−	0.715642i		−	0.0594309i
$146$	6.21012			0.513953
$147$	6.34452	+	10.3318i	0.523287	+	0.852156i
$148$	2.08345			0.171258
$149$			11.1915i			0.916839i	0.888736	+	0.458420i	$0.151584\pi$
$149$			11.1915i			0.916839i	−0.888736	+	0.458420i	$0.848416\pi$
$150$	−7.71988	+	3.47707i	−0.630325	+	0.283902i
$151$	15.7569			1.28228			0.641141	−	0.767423i	$-0.278462\pi$
$151$	15.7569			1.28228			0.641141	+	0.767423i	$0.278462\pi$
$152$	0.890178			0.0722030
$153$	6.27941	−	7.09610i	0.507660	−	0.573686i
$154$	0.103915	+	1.62765i	0.00837368	+	0.131160i
$155$			0.995473i			0.0799583i
$156$	5.11567	−	2.30412i	0.409582	−	0.184478i
$157$			0.132472i			0.0105724i	0.999986	+	0.00528622i	$0.00168267\pi$
$157$			0.132472i			0.0105724i	−0.999986	+	0.00528622i	$0.998317\pi$
$158$		−	7.38606i		−	0.587604i
$159$	−0.0145298	+	0.00654428i	−0.00115228	+	0.000518995i
$160$			0.334212i			0.0264218i
$161$	2.64038	−	0.168570i	0.208091	−	0.0132852i
$162$	8.93314	−	1.09498i	0.701854	−	0.0860297i
$163$	−1.56309			−0.122430			−0.0612152	−	0.998125i	$-0.519498\pi$
$163$	−1.56309			−0.122430			−0.0612152	+	0.998125i	$0.519498\pi$
$164$	5.08253			0.396879
$165$	0.325365	−	0.146546i	0.0253296	−	0.0114086i
$166$			11.3888i			0.883942i
$167$	9.97417			0.771825			0.385912	−	0.922535i	$-0.373887\pi$
$167$	9.97417			0.771825			0.385912	+	0.922535i	$0.373887\pi$
$168$	2.14433	+	4.04992i	0.165438	+	0.312458i
$169$	2.50697			0.192844
$170$		−	1.05561i		−	0.0809618i
$171$	−1.99993	−	1.76976i	−0.152938	−	0.135337i
$172$	11.3381			0.864526
$173$	12.3935			0.942259			0.471129	−	0.882064i	$-0.343847\pi$
$173$	12.3935			0.942259			0.471129	+	0.882064i	$0.343847\pi$
$174$	−1.52310	−	3.38163i	−0.115466	−	0.256361i
$175$	0.824023	+	12.9070i	0.0622902	+	0.975674i
$176$			0.616447i			0.0464664i
$177$	9.33594	+	20.7279i	0.701732	+	1.55800i
$178$		−	15.6130i		−	1.17025i
$179$		−	4.94693i		−	0.369751i	−0.982762	−	0.184875i	$-0.940812\pi$
$179$		−	4.94693i		−	0.369751i	0.982762	−	0.184875i	$-0.0591881\pi$
$180$	0.664445	−	0.750862i	0.0495248	−	0.0559659i
$181$		−	11.2427i		−	0.835661i	−0.908525	−	0.417831i	$-0.862791\pi$
$181$		−	11.2427i		−	0.835661i	0.908525	−	0.417831i	$-0.137209\pi$
$182$	−0.546049	−	8.55295i	−0.0404758	−	0.633987i
$183$	−14.0985	+	6.35003i	−1.04219	+	0.469408i
$184$	1.00000			0.0737210
$185$	−0.696313			−0.0511940
$186$	2.11867	+	4.70391i	0.155348	+	0.344908i
$187$		−	1.94705i		−	0.142383i
$188$	−2.96029			−0.215901
$189$	3.23404	−	13.3619i	0.235242	−	0.971937i
$190$	−0.297508			−0.0215835
$191$			11.5303i			0.834304i	0.908837	+	0.417152i	$0.136972\pi$
$191$			11.5303i			0.834304i	−0.908837	+	0.417152i	$0.863028\pi$
$192$	0.711304	+	1.57925i	0.0513340	+	0.113973i
$193$	−5.65666			−0.407175			−0.203588	−	0.979057i	$-0.565260\pi$
$193$	−5.65666			−0.407175			−0.203588	+	0.979057i	$0.565260\pi$
$194$	10.2696			0.737312
$195$	−1.70972	+	0.770067i	−0.122436	+	0.0551456i
$196$	6.94317	−	0.890178i	0.495941	−	0.0635841i
$197$			3.68947i			0.262864i	0.991325	+	0.131432i	$0.0419575\pi$
$197$			3.68947i			0.262864i	−0.991325	+	0.131432i	$0.958042\pi$
$198$	1.22555	−	1.38495i	0.0870963	−	0.0984240i
$199$		−	9.66592i		−	0.685199i	−0.939482	−	0.342599i	$-0.888693\pi$
$199$		−	9.66592i		−	0.685199i	0.939482	−	0.342599i	$-0.111307\pi$
$200$			4.88830i			0.345655i
$201$	−3.92350	−	8.71104i	−0.276742	−	0.614430i
$202$		−	11.1328i		−	0.783298i
$203$	−5.65379	+	0.360956i	−0.396818	+	0.0253342i
$204$	−2.24666	−	4.98809i	−0.157298	−	0.349236i
$205$	−1.69864			−0.118638
$206$	−4.70411			−0.327751
$207$	−2.24666	−	1.98809i	−0.156154	−	0.138182i
$208$		−	3.23929i		−	0.224605i
$209$	−0.548748			−0.0379577
$210$	−0.716660	−	1.35353i	−0.0494542	−	0.0934027i
$211$	9.28923			0.639497			0.319748	−	0.947503i	$-0.396402\pi$
$211$	9.28923			0.639497			0.319748	+	0.947503i	$0.396402\pi$
$212$			0.00920039i			0.000631885i
$213$	7.22268	−	3.25313i	0.494890	−	0.222901i
$214$	−6.66683			−0.455735
$215$	−3.78935			−0.258431
$216$	1.54164	−	4.96219i	0.104896	−	0.337634i
$217$	7.86453	−	0.502098i	0.533879	−	0.0340846i
$218$			14.7101i			0.996293i
$219$	−9.80737	+	4.41729i	−0.662720	+	0.298493i
$220$		−	0.206024i		−	0.0138901i
$221$			10.2313i			0.688235i
$222$	−3.29029	+	1.48196i	−0.220830	+	0.0994630i
$223$		−	26.0351i		−	1.74344i	−0.490005	−	0.871720i	$-0.663005\pi$
$223$		−	26.0351i		−	1.74344i	0.490005	−	0.871720i	$-0.336995\pi$
$224$	2.64038	−	0.168570i	0.176418	−	0.0112631i
$225$	9.71840	−	10.9824i	0.647893	−	0.732157i
$226$	16.9174			1.12533
$227$	−1.73870			−0.115401			−0.0577006	−	0.998334i	$-0.518377\pi$
$227$	−1.73870			−0.115401			−0.0577006	+	0.998334i	$0.518377\pi$
$228$	−1.40582	+	0.633187i	−0.0931026	+	0.0419339i
$229$		−	5.40527i		−	0.357190i	−0.983923	−	0.178595i	$-0.942845\pi$
$229$		−	5.40527i		−	0.357190i	0.983923	−	0.178595i	$-0.0571552\pi$
$230$	−0.334212			−0.0220373
$231$	−1.32186	−	2.49656i	−0.0869723	−	0.164262i
$232$	−2.14128			−0.140582
$233$		−	13.3463i		−	0.874345i	−0.899378	−	0.437173i	$-0.855980\pi$
$233$		−	13.3463i		−	0.874345i	0.899378	−	0.437173i	$-0.144020\pi$
$234$	−6.44002	+	7.27760i	−0.420997	+	0.475752i
$235$	0.989366			0.0645391
$236$	13.1251			0.854371
$237$	5.25374	+	11.6645i	0.341267	+	0.757689i
$238$	−8.33965	+	0.532431i	−0.540579	+	0.0345124i
$239$			29.0538i			1.87933i	0.342093	+	0.939666i	$0.388864\pi$
$239$			29.0538i			1.87933i	−0.342093	+	0.939666i	$0.611136\pi$
$240$	−0.237727	−	0.527806i	−0.0153452	−	0.0340698i
$241$			16.1968i			1.04333i	0.853151	+	0.521664i	$0.174688\pi$
$241$			16.1968i			1.04333i	−0.853151	+	0.521664i	$0.825312\pi$
$242$			10.6200i			0.682679i
$243$	−13.3288	+	8.08343i	−0.855046	+	0.518553i
$244$			8.92731i			0.571512i
$245$	−2.32049	+	0.297508i	−0.148251	+	0.0190071i
$246$	−8.02661	+	3.61523i	−0.511758	+	0.230499i
$247$	2.88355			0.183476
$248$	2.97856			0.189139
$249$	−8.10090	−	17.9858i	−0.513374	−	1.13980i
$250$		−	3.30479i		−	0.209013i
$251$	2.17697			0.137409			0.0687047	−	0.997637i	$-0.478113\pi$
$251$	2.17697			0.137409			0.0687047	+	0.997637i	$0.478113\pi$
$252$	−6.26716	−	4.87059i	−0.394794	−	0.306818i
$253$	−0.616447			−0.0387557
$254$			1.27261i			0.0798509i
$255$	0.750862	+	1.66708i	0.0470208	+	0.104397i
$256$	1.00000			0.0625000
$257$	−12.3872			−0.772694			−0.386347	−	0.922353i	$-0.626263\pi$
$257$	−12.3872			−0.772694			−0.386347	+	0.922353i	$0.626263\pi$
$258$	−17.9058	+	8.06487i	−1.11477	+	0.502097i
$259$	0.351207	+	5.50108i	0.0218230	+	0.341821i
$260$			1.08261i			0.0671407i
$261$	4.81073	+	4.25706i	0.297777	+	0.263506i
$262$			3.12774i			0.193233i
$263$		−	15.9794i		−	0.985333i	−0.870218	−	0.492666i	$-0.836022\pi$
$263$		−	15.9794i		−	0.985333i	0.870218	−	0.492666i	$-0.163978\pi$
$264$	−0.438482	−	0.973527i	−0.0269867	−	0.0599165i
$265$		−	0.00307488i		−	0.000188888i
$266$	0.150058	+	2.35040i	0.00920062	+	0.144113i
$267$	11.1056	+	24.6570i	0.679653	+	1.50898i
$268$	−5.51592			−0.336938
$269$	−27.8643			−1.69892			−0.849459	−	0.527655i	$-0.823071\pi$
$269$	−27.8643			−1.69892			−0.849459	+	0.527655i	$0.823071\pi$
$270$	−0.515236	+	1.65842i	−0.0313563	+	0.100929i
$271$		−	13.5793i		−	0.824883i	−0.910984	−	0.412442i	$-0.864676\pi$
$271$		−	13.5793i		−	0.824883i	0.910984	−	0.412442i	$-0.135324\pi$
$272$	−3.15851			−0.191513
$273$	6.94610	+	13.1189i	0.420397	+	0.793991i
$274$	−9.47914			−0.572656
$275$		−	3.01338i		−	0.181714i
$276$	−1.57925	+	0.711304i	−0.0950600	+	0.0428155i
$277$	27.2647			1.63817			0.819087	−	0.573669i	$-0.194480\pi$
$277$	27.2647			1.63817			0.819087	+	0.573669i	$0.194480\pi$
$278$	12.4667			0.747700
$279$	−6.69183	−	5.92166i	−0.400629	−	0.354521i
$280$	−0.882446	+	0.0563383i	−0.0527362	+	0.00336685i
$281$		−	10.5377i		−	0.628626i	−0.949319	−	0.314313i	$-0.898226\pi$
$281$		−	10.5377i		−	0.628626i	0.949319	−	0.314313i	$-0.101774\pi$
$282$	4.67505	−	2.10567i	0.278395	−	0.125391i
$283$			15.1695i			0.901732i	0.892592	+	0.450866i	$0.148885\pi$
$283$			15.1695i			0.901732i	−0.892592	+	0.450866i	$0.851115\pi$
$284$		−	4.57347i		−	0.271386i
$285$	0.469842	−	0.211619i	0.0278310	−	0.0125352i
$286$			1.99685i			0.118076i
$287$	0.856764	+	13.4198i	0.0505732	+	0.792146i
$288$	−2.24666	−	1.98809i	−0.132386	−	0.117149i
$289$	−7.02382			−0.413166
$290$	0.715642			0.0420240
$291$	−16.2183	+	7.30479i	−0.950731	+	0.428214i
$292$			6.21012i			0.363420i
$293$	19.4813			1.13811			0.569055	−	0.822299i	$-0.307309\pi$
$293$	19.4813			1.13811			0.569055	+	0.822299i	$0.307309\pi$
$294$	−10.3318	+	6.34452i	−0.602565	+	0.370020i
$295$	−4.38657			−0.255396
$296$			2.08345i			0.121098i
$297$	−0.950342	+	3.05893i	−0.0551444	+	0.177497i
$298$	−11.1915			−0.648303
$299$	3.23929			0.187333
$300$	−3.47707	−	7.71988i	−0.200749	−	0.445707i
$301$	1.91127	+	29.9370i	0.110164	+	1.72554i
$302$			15.7569i			0.906710i
$303$	7.91878	+	17.5815i	0.454922	+	1.01003i
$304$			0.890178i			0.0510552i
$305$		−	2.98362i		−	0.170841i
$306$	7.09610	+	6.27941i	0.405657	+	0.358970i
$307$			11.1963i			0.639008i	0.947585	+	0.319504i	$0.103516\pi$
$307$			11.1963i			0.639008i	−0.947585	+	0.319504i	$0.896484\pi$
$308$	−1.62765	+	0.103915i	−0.0927441	+	0.00592109i
$309$	7.42900	−	3.34606i	0.422621	−	0.190351i
$310$	−0.995473			−0.0565391
$311$	−9.86492			−0.559388			−0.279694	−	0.960089i	$-0.590233\pi$
$311$	−9.86492			−0.559388			−0.279694	+	0.960089i	$0.590233\pi$
$312$	2.30412	+	5.11567i	0.130445	+	0.289618i
$313$		−	16.5493i		−	0.935423i	−0.883881	−	0.467711i	$-0.845079\pi$
$313$		−	16.5493i		−	0.935423i	0.883881	−	0.467711i	$-0.154921\pi$
$314$	−0.132472			−0.00747585
$315$	2.09456	+	1.62781i	0.118015	+	0.0917167i
$316$	7.38606			0.415499
$317$		−	12.6369i		−	0.709758i	−0.934912	−	0.354879i	$-0.884522\pi$
$317$		−	12.6369i		−	0.709758i	0.934912	−	0.354879i	$-0.115478\pi$
$318$	−0.00654428	−	0.0145298i	−0.000366985	−	0.000814788i
$319$	1.31999			0.0739050
$320$	−0.334212			−0.0186830
$321$	10.5286	−	4.74215i	0.587651	−	0.264681i
$322$	0.168570	+	2.64038i	0.00939406	+	0.147142i
$323$		−	2.81164i		−	0.156444i
$324$	1.09498	+	8.93314i	0.0608322	+	0.496286i
$325$			15.8347i			0.878348i
$326$		−	1.56309i		−	0.0865714i
$327$	−10.4634	−	23.2310i	−0.578625	−	1.28468i
$328$			5.08253i			0.280636i
$329$	−0.499017	−	7.81628i	−0.0275117	−	0.430926i
$330$	0.146546	+	0.325365i	0.00806709	+	0.0179107i
$331$	−19.5688			−1.07560			−0.537799	−	0.843073i	$-0.680744\pi$
$331$	−19.5688			−1.07560			−0.537799	+	0.843073i	$0.680744\pi$
$332$	−11.3888			−0.625042
$333$	4.14208	−	4.68080i	0.226985	−	0.256506i
$334$			9.97417i			0.545763i
$335$	1.84349			0.100721
$336$	−4.04992	+	2.14433i	−0.220941	+	0.116983i
$337$	19.1229			1.04169			0.520846	−	0.853651i	$-0.325617\pi$
$337$	19.1229			1.04169			0.520846	+	0.853651i	$0.325617\pi$
$338$			2.50697i			0.136361i
$339$	−26.7169	+	12.0334i	−1.45106	+	0.653567i
$340$	1.05561			0.0572486
$341$	−1.83613			−0.0994319
$342$	1.76976	−	1.99993i	0.0956974	−	0.108144i
$343$	3.52082	+	18.1825i	0.190106	+	0.981764i
$344$			11.3381i			0.611312i
$345$	0.527806	−	0.237727i	0.0284161	−	0.0127988i
$346$			12.3935i			0.666277i
$347$			13.6981i			0.735354i	0.929954	+	0.367677i	$0.119847\pi$
$347$			13.6981i			0.735354i	−0.929954	+	0.367677i	$0.880153\pi$
$348$	3.38163	−	1.52310i	0.181274	−	0.0816469i
$349$		−	11.7210i		−	0.627412i	−0.949520	−	0.313706i	$-0.898429\pi$
$349$		−	11.7210i		−	0.627412i	0.949520	−	0.313706i	$-0.101571\pi$
$350$	−12.9070	+	0.824023i	−0.689906	+	0.0440459i
$351$	4.99384	−	16.0740i	0.266551	−	0.857966i
$352$	−0.616447			−0.0328567
$353$	8.43379			0.448885			0.224443	−	0.974487i	$-0.427944\pi$
$353$	8.43379			0.448885			0.224443	+	0.974487i	$0.427944\pi$
$354$	−20.7279	+	9.33594i	−1.10167	+	0.496200i
$355$			1.52851i			0.0811249i
$356$	15.6130			0.827490
$357$	12.7917	−	6.77288i	0.677009	−	0.358459i
$358$	4.94693			0.261453
$359$		−	22.4082i		−	1.18266i	−0.806430	−	0.591330i	$-0.798603\pi$
$359$		−	22.4082i		−	1.18266i	0.806430	−	0.591330i	$-0.201397\pi$
$360$	0.750862	+	0.664445i	0.0395739	+	0.0350193i
$361$	18.2076			0.958294
$362$	11.2427			0.590902
$363$	−7.55405	−	16.7717i	−0.396485	−	0.880285i
$364$	8.55295	−	0.546049i	0.448297	−	0.0286207i
$365$		−	2.07550i		−	0.108637i
$366$	−6.35003	−	14.0985i	−0.331922	−	0.736940i
$367$		−	23.8207i		−	1.24343i	−0.783244	−	0.621714i	$-0.786436\pi$
$367$		−	23.8207i		−	1.24343i	0.783244	−	0.621714i	$-0.213564\pi$
$368$			1.00000i			0.0521286i
$369$	10.1045	−	11.4187i	0.526022	−	0.594435i
$370$		−	0.696313i		−	0.0361996i
$371$	−0.0242925	+	0.00155091i	−0.00126120	+	8.05193e-5i
$372$	−4.70391	+	2.11867i	−0.243887	+	0.109848i
$373$	−36.8075			−1.90582			−0.952910	−	0.303254i	$-0.901927\pi$
$373$	−36.8075			−1.90582			−0.952910	+	0.303254i	$0.901927\pi$
$374$	1.94705			0.100680
$375$	2.35071	+	5.21911i	0.121390	+	0.269514i
$376$		−	2.96029i		−	0.152665i
$377$	−6.93624			−0.357235
$378$	13.3619	+	3.23404i	0.687263	+	0.166341i
$379$	0.647490			0.0332593			0.0166297	−	0.999862i	$-0.494706\pi$
$379$	0.647490			0.0332593			0.0166297	+	0.999862i	$0.494706\pi$
$380$		−	0.297508i		−	0.0152619i
$381$	−0.905216	−	2.00978i	−0.0463756	−	0.102964i
$382$	−11.5303			−0.589942
$383$	−23.8151			−1.21689			−0.608447	−	0.793595i	$-0.708207\pi$
$383$	−23.8151			−1.21689			−0.608447	+	0.793595i	$0.708207\pi$
$384$	−1.57925	+	0.711304i	−0.0805910	+	0.0362986i
$385$	0.543981	−	0.0347296i	0.0277239	−	0.00176998i
$386$		−	5.65666i		−	0.287916i
$387$	22.5413	−	25.4730i	1.14584	−	1.29486i
$388$			10.2696i			0.521358i
$389$		−	33.3678i		−	1.69182i	−0.533329	−	0.845908i	$-0.679059\pi$
$389$		−	33.3678i		−	1.69182i	0.533329	−	0.845908i	$-0.320941\pi$
$390$	−0.770067	−	1.70972i	−0.0389938	−	0.0865750i
$391$		−	3.15851i		−	0.159733i
$392$	0.890178	+	6.94317i	0.0449608	+	0.350683i
$393$	−2.22478	−	4.93950i	−0.112225	−	0.249165i
$394$	−3.68947			−0.185873
$395$	−2.46851			−0.124204
$396$	1.38495	+	1.22555i	0.0695963	+	0.0615864i
$397$			6.35096i			0.318745i	0.987218	+	0.159373i	$0.0509472\pi$
$397$			6.35096i			0.318745i	−0.987218	+	0.159373i	$0.949053\pi$
$398$	9.66592			0.484509
$399$	−1.90883	−	3.60515i	−0.0955611	−	0.180483i
$400$	−4.88830			−0.244415
$401$		−	30.0803i		−	1.50214i	−0.660223	−	0.751069i	$-0.729538\pi$
$401$		−	30.0803i		−	1.50214i	0.660223	−	0.751069i	$-0.270462\pi$
$402$	8.71104	−	3.92350i	0.434467	−	0.195686i
$403$	9.64845			0.480623
$404$	11.1328			0.553875
$405$	−0.365956	−	2.98557i	−0.0181845	−	0.148354i
$406$	−0.360956	−	5.65379i	−0.0179140	−	0.280593i
$407$		−	1.28433i		−	0.0636621i
$408$	4.98809	−	2.24666i	0.246947	−	0.111226i
$409$			7.71976i			0.381718i	0.981617	+	0.190859i	$0.0611273\pi$
$409$			7.71976i			0.381718i	−0.981617	+	0.190859i	$0.938873\pi$
$410$		−	1.69864i		−	0.0838901i
$411$	14.9700	−	6.74255i	0.738415	−	0.332586i
$412$		−	4.70411i		−	0.231755i
$413$	2.21250	+	34.6552i	0.108870	+	1.70527i
$414$	1.98809	−	2.24666i	0.0977094	−	0.110417i
$415$	3.80628			0.186843
$416$	3.23929			0.158819
$417$	−19.6880	+	8.86759i	−0.964127	+	0.434248i
$418$		−	0.548748i		−	0.0268401i
$419$	27.4462			1.34083			0.670417	−	0.741984i	$-0.266115\pi$
$419$	27.4462			1.34083			0.670417	+	0.741984i	$0.266115\pi$
$420$	1.35353	−	0.716660i	0.0660457	−	0.0349694i
$421$	−1.72287			−0.0839678			−0.0419839	−	0.999118i	$-0.513368\pi$
$421$	−1.72287			−0.0839678			−0.0419839	+	0.999118i	$0.513368\pi$
$422$			9.28923i			0.452192i
$423$	−5.88533	+	6.65077i	−0.286155	+	0.323372i
$424$	−0.00920039			−0.000446810
$425$	15.4398			0.748938
$426$	3.25313	+	7.22268i	0.157615	+	0.349940i
$427$	−23.5714	+	1.50488i	−1.14070	+	0.0728262i
$428$		−	6.66683i		−	0.322254i
$429$	−1.42037	−	3.15354i	−0.0685762	−	0.152254i
$430$		−	3.78935i		−	0.182739i
$431$		−	28.3079i		−	1.36354i	−0.731566	−	0.681771i	$-0.761210\pi$
$431$		−	28.3079i		−	1.36354i	0.731566	−	0.681771i	$-0.238790\pi$
$432$	4.96219	+	1.54164i	0.238744	+	0.0741724i
$433$			3.77079i			0.181213i	0.995887	+	0.0906064i	$0.0288805\pi$
$433$			3.77079i			0.181213i	−0.995887	+	0.0906064i	$0.971119\pi$
$434$	0.502098	+	7.86453i	0.0241015	+	0.377510i
$435$	−1.13018	+	0.509040i	−0.0541881	+	0.0244066i
$436$	−14.7101			−0.704486
$437$	−0.890178			−0.0425830
$438$	−4.41729	−	9.80737i	−0.211066	−	0.468614i
$439$		−	4.15471i		−	0.198293i	−0.995073	−	0.0991467i	$-0.968389\pi$
$439$		−	4.15471i		−	0.198293i	0.995073	−	0.0991467i	$-0.0316113\pi$
$440$	0.206024			0.00982182
$441$	11.8037	−	17.3687i	0.562082	−	0.827081i
$442$	−10.2313			−0.486655
$443$		−	16.9438i		−	0.805025i	−0.915414	−	0.402513i	$-0.868137\pi$
$443$		−	16.9438i		−	0.805025i	0.915414	−	0.402513i	$-0.131863\pi$
$444$	−1.48196	−	3.29029i	−0.0703309	−	0.156150i
$445$	−5.21807			−0.247360
$446$	26.0351			1.23280
$447$	17.6742	−	7.96053i	0.835959	−	0.376520i
$448$	0.168570	+	2.64038i	0.00796420	+	0.124746i
$449$		−	19.5254i		−	0.921459i	−0.887541	−	0.460730i	$-0.847588\pi$
$449$		−	19.5254i		−	0.921459i	0.887541	−	0.460730i	$-0.152412\pi$
$450$	10.9824	+	9.71840i	0.517714	+	0.458130i
$451$		−	3.13311i		−	0.147533i
$452$			16.9174i			0.795729i
$453$	−11.2080	−	24.8842i	−0.526597	−	1.16916i
$454$		−	1.73870i		−	0.0816010i
$455$	−2.85850	+	0.182496i	−0.134009	+	0.00855555i
$456$	−0.633187	−	1.40582i	−0.0296517	−	0.0658334i
$457$	−19.7471			−0.923729			−0.461864	−	0.886951i	$-0.652819\pi$
$457$	−19.7471			−0.923729			−0.461864	+	0.886951i	$0.652819\pi$
$458$	5.40527			0.252572
$459$	−15.6731	−	4.86930i	−0.731559	−	0.227279i
$460$		−	0.334212i		−	0.0155827i
$461$	−24.1439			−1.12449			−0.562247	−	0.826969i	$-0.690063\pi$
$461$	−24.1439			−1.12449			−0.562247	+	0.826969i	$0.690063\pi$
$462$	2.49656	−	1.32186i	0.116151	−	0.0614987i
$463$	−34.1392			−1.58658			−0.793292	−	0.608841i	$-0.791635\pi$
$463$	−34.1392			−1.58658			−0.793292	+	0.608841i	$0.791635\pi$
$464$		−	2.14128i		−	0.0994065i
$465$	1.57211	−	0.708084i	0.0729046	−	0.0328366i
$466$	13.3463			0.618255
$467$	17.3020			0.800642			0.400321	−	0.916375i	$-0.368899\pi$
$467$	17.3020			0.800642			0.400321	+	0.916375i	$0.368899\pi$
$468$	−7.27760	−	6.44002i	−0.336407	−	0.297690i
$469$	−0.929820	−	14.5641i	−0.0429351	−	0.672508i
$470$			0.989366i			0.0456360i
$471$	0.209208	−	0.0942282i	0.00963978	−	0.00434181i
$472$			13.1251i			0.604132i
$473$		−	6.98937i		−	0.321371i
$474$	−11.6645	+	5.25374i	−0.535767	+	0.241312i
$475$		−	4.35146i		−	0.199659i
$476$	−0.532431	−	8.33965i	−0.0244039	−	0.382247i
$477$	0.0206702	+	0.0182912i	0.000946421	+	0.000837497i
$478$	−29.0538			−1.32889
$479$	−6.66557			−0.304558			−0.152279	−	0.988338i	$-0.548661\pi$
$479$	−6.66557			−0.304558			−0.152279	+	0.988338i	$0.548661\pi$
$480$	0.527806	−	0.237727i	0.0240910	−	0.0108507i
$481$			6.74890i			0.307723i
$482$	−16.1968			−0.737744
$483$	−2.14433	−	4.04992i	−0.0975702	−	0.184278i
$484$	−10.6200			−0.482727
$485$		−	3.43221i		−	0.155849i
$486$	−8.08343	−	13.3288i	−0.366672	−	0.604609i
$487$	16.2562			0.736637			0.368319	−	0.929700i	$-0.379934\pi$
$487$	16.2562			0.736637			0.368319	+	0.929700i	$0.379934\pi$
$488$	−8.92731			−0.404120
$489$	1.11183	+	2.46851i	0.0502787	+	0.111630i
$490$	−0.297508	−	2.32049i	−0.0134401	−	0.104829i
$491$			24.7150i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$491$			24.7150i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$492$	−3.61523	−	8.02661i	−0.162987	−	0.361868i
$493$			6.76326i			0.304602i
$494$			2.88355i			0.129737i
$495$	−0.462867	−	0.409595i	−0.0208043	−	0.0184099i
$496$			2.97856i			0.133742i
$497$	12.0757	−	0.770951i	0.541668	−	0.0345819i
$498$	17.9858	−	8.10090i	0.805964	−	0.363010i
$499$	14.1996			0.635662			0.317831	−	0.948147i	$-0.397045\pi$
$499$	14.1996			0.635662			0.317831	+	0.948147i	$0.397045\pi$
$500$	3.30479			0.147795
$501$	−7.09467	−	15.7518i	−0.316967	−	0.703737i
$502$			2.17697i			0.0971631i
$503$	−3.22976			−0.144008			−0.0720038	−	0.997404i	$-0.522939\pi$
$503$	−3.22976			−0.144008			−0.0720038	+	0.997404i	$0.522939\pi$
$504$	4.87059	−	6.26716i	0.216953	−	0.279162i
$505$	−3.72070			−0.165569
$506$		−	0.616447i		−	0.0274044i
$507$	−1.78322	−	3.95915i	−0.0791955	−	0.175832i
$508$	−1.27261			−0.0564631
$509$	−34.5726			−1.53240			−0.766202	−	0.642600i	$-0.777856\pi$
$509$	−34.5726			−1.53240			−0.766202	+	0.642600i	$0.777856\pi$
$510$	−1.66708	+	0.750862i	−0.0738196	+	0.0332487i
$511$	−16.3971	+	1.04684i	−0.725363	+	0.0463096i
$512$			1.00000i			0.0441942i
$513$	−1.37234	+	4.41723i	−0.0605902	+	0.195026i
$514$		−	12.3872i		−	0.546377i
$515$			1.57217i			0.0692782i
$516$	−8.06487	−	17.9058i	−0.355036	−	0.788260i
$517$			1.82486i			0.0802574i
$518$	−5.50108	+	0.351207i	−0.241704	+	0.0154312i
$519$	−8.81553	−	19.5725i	−0.386959	−	0.859136i
$520$	−1.08261			−0.0474757
$521$	19.4594			0.852530			0.426265	−	0.904598i	$-0.359829\pi$
$521$	19.4594			0.852530			0.426265	+	0.904598i	$0.359829\pi$
$522$	−4.25706	+	4.81073i	−0.186327	+	0.210560i
$523$		−	0.456621i		−	0.0199667i	−0.999950	−	0.00998333i	$-0.996822\pi$
$523$		−	0.456621i		−	0.0199667i	0.999950	−	0.00998333i	$-0.00317784\pi$
$524$	−3.12774			−0.136636
$525$	19.7972	−	10.4821i	0.864022	−	0.457477i
$526$	15.9794			0.696735
$527$		−	9.40783i		−	0.409811i
$528$	0.973527	−	0.438482i	0.0423673	−	0.0190825i
$529$	−1.00000			−0.0434783
$530$	0.00307488			0.000133564
$531$	26.0939	−	29.4877i	1.13238	−	1.27966i
$532$	−2.35040	+	0.150058i	−0.101903	+	0.00650582i
$533$			16.4638i			0.713127i
$534$	−24.6570	+	11.1056i	−1.06701	+	0.480588i
$535$			2.22814i			0.0963308i
$536$		−	5.51592i		−	0.238251i
$537$	−7.81246	+	3.51877i	−0.337132	+	0.151846i
$538$		−	27.8643i		−	1.20132i
$539$	−0.548748	−	4.28010i	−0.0236362	−	0.184357i
$540$	−1.65842	−	0.515236i	−0.0713672	−	0.0221722i
$541$	−36.4914			−1.56889			−0.784445	−	0.620199i	$-0.787052\pi$
$541$	−36.4914			−1.56889			−0.784445	+	0.620199i	$0.787052\pi$
$542$	13.5793			0.583281
$543$	−17.7550	+	7.99696i	−0.761942	+	0.343182i
$544$		−	3.15851i		−	0.135420i
$545$	4.91629			0.210591
$546$	−13.1189	+	6.94610i	−0.561437	+	0.297266i
$547$	21.9239			0.937398			0.468699	−	0.883358i	$-0.344723\pi$
$547$	21.9239			0.937398			0.468699	+	0.883358i	$0.344723\pi$
$548$		−	9.47914i		−	0.404929i
$549$	20.0566	+	17.7483i	0.855997	+	0.757479i
$550$	3.01338			0.128491
$551$	1.90612			0.0812035
$552$	−0.711304	−	1.57925i	−0.0302751	−	0.0672176i
$553$	1.24507	+	19.5020i	0.0529458	+	0.829309i
$554$			27.2647i			1.15836i
$555$	0.495291	+	1.09966i	0.0210239	+	0.0466778i
$556$			12.4667i			0.528704i
$557$			18.2808i			0.774583i	0.921957	+	0.387292i	$0.126589\pi$
$557$			18.2808i			0.774583i	−0.921957	+	0.387292i	$0.873411\pi$
$558$	5.92166	−	6.69183i	0.250684	−	0.283288i
$559$			36.7276i			1.55341i
$560$	−0.0563383	−	0.882446i	−0.00238073	−	0.0372901i
$561$	−3.07489	+	1.38495i	−0.129822	+	0.0584726i
$562$	10.5377			0.444505
$563$	15.4798			0.652397			0.326198	−	0.945301i	$-0.394232\pi$
$563$	15.4798			0.652397			0.326198	+	0.945301i	$0.394232\pi$
$564$	2.10567	+	4.67505i	0.0886646	+	0.196855i
$565$		−	5.65401i		−	0.237866i
$566$	−15.1695			−0.637621
$567$	−23.4023	+	4.39702i	−0.982803	+	0.184657i
$568$	4.57347			0.191899
$569$		−	41.5182i		−	1.74053i	−0.492579	−	0.870267i	$-0.663946\pi$
$569$		−	41.5182i		−	1.74053i	0.492579	−	0.870267i	$-0.336054\pi$
$570$	0.211619	+	0.469842i	0.00886374	+	0.0196795i
$571$	−5.38690			−0.225435			−0.112717	−	0.993627i	$-0.535955\pi$
$571$	−5.38690			−0.225435			−0.112717	+	0.993627i	$0.535955\pi$
$572$	−1.99685			−0.0834927
$573$	18.2093	−	8.20156i	0.760705	−	0.342625i
$574$	−13.4198	+	0.856764i	−0.560131	+	0.0357606i
$575$		−	4.88830i		−	0.203856i
$576$	1.98809	−	2.24666i	0.0828372	−	0.0936109i
$577$			32.6637i			1.35981i	0.733301	+	0.679905i	$0.237979\pi$
$577$			32.6637i			1.35981i	−0.733301	+	0.679905i	$0.762021\pi$
$578$		−	7.02382i		−	0.292152i
$579$	4.02361	+	8.93330i	0.167215	+	0.371255i
$580$			0.715642i			0.0297154i
$581$	−1.91981	−	30.0707i	−0.0796473	−	1.24754i
$582$	−7.30479	−	16.2183i	−0.302793	−	0.672269i
$583$	0.00567155			0.000234892
$584$	−6.21012			−0.256977
$585$	2.43226	+	2.15233i	0.100562	+	0.0889880i
$586$			19.4813i			0.804766i
$587$	28.9317			1.19414			0.597070	−	0.802189i	$-0.296332\pi$
$587$	28.9317			1.19414			0.597070	+	0.802189i	$0.296332\pi$
$588$	−6.34452	−	10.3318i	−0.261644	−	0.426078i
$589$	−2.65145			−0.109251
$590$		−	4.38657i		−	0.180592i
$591$	5.82662	−	2.62434i	0.239675	−	0.107951i
$592$	−2.08345			−0.0856291
$593$	4.62778			0.190040			0.0950200	−	0.995475i	$-0.469708\pi$
$593$	4.62778			0.190040			0.0950200	+	0.995475i	$0.469708\pi$
$594$	−3.05893	−	0.950342i	−0.125509	−	0.0389930i
$595$	0.177945	+	2.78721i	0.00729503	+	0.114265i
$596$		−	11.1915i		−	0.458420i
$597$	−15.2649	+	6.87541i	−0.624753	+	0.281392i
$598$			3.23929i			0.132465i
$599$			23.0851i			0.943230i	0.881804	+	0.471615i	$0.156329\pi$
$599$			23.0851i			0.943230i	−0.881804	+	0.471615i	$0.843671\pi$
$600$	7.71988	−	3.47707i	0.315163	−	0.141951i
$601$		−	18.8377i		−	0.768405i	−0.923249	−	0.384203i	$-0.874476\pi$
$601$		−	18.8377i		−	0.768405i	0.923249	−	0.384203i	$-0.125524\pi$
$602$	−29.9370	+	1.91127i	−1.22014	+	0.0778977i
$603$	−10.9662	+	12.3924i	−0.446576	+	0.504658i
$604$	−15.7569			−0.641141
$605$	3.54933			0.144301
$606$	−17.5815	+	7.91878i	−0.714198	+	0.321678i
$607$		−	2.17865i		−	0.0884286i	−0.999022	−	0.0442143i	$-0.985922\pi$
$607$		−	2.17865i		−	0.0884286i	0.999022	−	0.0442143i	$-0.0140784\pi$
$608$	−0.890178			−0.0361015
$609$	4.59160	+	8.67202i	0.186061	+	0.351408i
$610$	2.98362			0.120803
$611$		−	9.58925i		−	0.387940i
$612$	−6.27941	+	7.09610i	−0.253830	+	0.286843i
$613$	−18.6916			−0.754947			−0.377473	−	0.926020i	$-0.623207\pi$
$613$	−18.6916			−0.754947			−0.377473	+	0.926020i	$0.623207\pi$
$614$	−11.1963			−0.451847
$615$	1.20825	+	2.68259i	0.0487215	+	0.108173i
$616$	−0.103915	−	1.62765i	−0.00418684	−	0.0655800i
$617$		−	43.5422i		−	1.75294i	−0.481454	−	0.876471i	$-0.659891\pi$
$617$		−	43.5422i		−	1.75294i	0.481454	−	0.876471i	$-0.340109\pi$
$618$	3.34606	+	7.42900i	0.134598	+	0.298838i
$619$			1.99564i			0.0802115i	0.999195	+	0.0401057i	$0.0127695\pi$
$619$			1.99564i			0.0802115i	−0.999195	+	0.0401057i	$0.987231\pi$
$620$		−	0.995473i		−	0.0399792i
$621$	−1.54164	+	4.96219i	−0.0618640	+	0.199126i
$622$		−	9.86492i		−	0.395547i
$623$	2.63190	+	41.2243i	0.105445	+	1.65162i
$624$	−5.11567	+	2.30412i	−0.204791	+	0.0922388i
$625$	23.3370			0.933480
$626$	16.5493			0.661444
$627$	0.390327	+	0.866612i	0.0155881	+	0.0346092i
$628$		−	0.132472i		−	0.00528622i
$629$	6.58059			0.262385
$630$	−1.62781	+	2.09456i	−0.0648535	+	0.0834494i
$631$	24.2580			0.965696			0.482848	−	0.875704i	$-0.339602\pi$
$631$	24.2580			0.965696			0.482848	+	0.875704i	$0.339602\pi$
$632$			7.38606i			0.293802i
$633$	−6.60747	−	14.6701i	−0.262623	−	0.583082i
$634$	12.6369			0.501874
$635$	0.425323			0.0168784
$636$	0.0145298	−	0.00654428i	0.000576142	−	0.000259497i
$637$	2.88355	+	22.4910i	0.114250	+	0.891125i
$638$			1.31999i			0.0522588i
$639$	−10.2750	−	9.09248i	−0.406474	−	0.359693i
$640$		−	0.334212i		−	0.0132109i
$641$		−	26.6761i		−	1.05364i	−0.849976	−	0.526821i	$-0.823384\pi$
$641$		−	26.6761i		−	1.05364i	0.849976	−	0.526821i	$-0.176616\pi$
$642$	4.74215	+	10.5286i	0.187158	+	0.415532i
$643$			48.6820i			1.91983i	0.280288	+	0.959916i	$0.409570\pi$
$643$			48.6820i			1.91983i	−0.280288	+	0.959916i	$0.590430\pi$
$644$	−2.64038	+	0.168570i	−0.104045	+	0.00664260i
$645$	2.69538	+	5.98435i	0.106130	+	0.235633i
$646$	2.81164			0.110622
$647$	−10.9109			−0.428953			−0.214477	−	0.976729i	$-0.568805\pi$
$647$	−10.9109			−0.428953			−0.214477	+	0.976729i	$0.568805\pi$
$648$	−8.93314	+	1.09498i	−0.350927	+	0.0430149i
$649$		−	8.09093i		−	0.317597i
$650$	−15.8347			−0.621086
$651$	−6.38702	−	12.0630i	−0.250327	−	0.472784i
$652$	1.56309			0.0612152
$653$			28.1573i			1.10188i	0.834545	+	0.550940i	$0.185731\pi$
$653$			28.1573i			1.10188i	−0.834545	+	0.550940i	$0.814269\pi$
$654$	23.2310	−	10.4634i	0.908404	−	0.409150i
$655$	1.04533			0.0408444
$656$	−5.08253			−0.198440
$657$	13.9520	+	12.3463i	0.544321	+	0.481675i
$658$	7.81628	−	0.499017i	0.304710	−	0.0194537i
$659$		−	8.33441i		−	0.324663i	−0.986736	−	0.162331i	$-0.948099\pi$
$659$		−	8.33441i		−	0.324663i	0.986736	−	0.162331i	$-0.0519013\pi$
$660$	−0.325365	+	0.146546i	−0.0126648	+	0.00570429i
$661$			10.3792i			0.403705i	0.979416	+	0.201853i	$0.0646962\pi$
$661$			10.3792i			0.403705i	−0.979416	+	0.201853i	$0.935304\pi$
$662$		−	19.5688i		−	0.760562i
$663$	16.1579	−	7.27760i	0.627521	−	0.282639i
$664$		−	11.3888i		−	0.441971i
$665$	0.785534	−	0.0501511i	0.0304617	−	0.00194478i
$666$	4.68080	+	4.14208i	0.181377	+	0.160502i
$667$	2.14128			0.0829107
$668$	−9.97417			−0.385912
$669$	−41.1161	+	18.5189i	−1.58964	+	0.715981i
$670$			1.84349i			0.0712202i
$671$	5.50321			0.212449
$672$	−2.14433	−	4.04992i	−0.0827192	−	0.156229i
$673$	37.1417			1.43171			0.715854	−	0.698250i	$-0.246038\pi$
$673$	37.1417			1.43171			0.715854	+	0.698250i	$0.246038\pi$
$674$			19.1229i			0.736587i
$675$	−24.2567	−	7.53602i	−0.933640	−	0.290062i
$676$	−2.50697			−0.0964219
$677$	−51.1129			−1.96443			−0.982215	−	0.187762i	$-0.939877\pi$
$677$	−51.1129			−1.96443			−0.982215	+	0.187762i	$0.939877\pi$
$678$	−12.0334	−	26.7169i	−0.462141	−	1.02606i
$679$	−27.1155	+	1.73114i	−1.04060	+	0.0664352i
$680$			1.05561i			0.0404809i
$681$	1.23674	+	2.74584i	0.0473921	+	0.105221i
$682$		−	1.83613i		−	0.0703090i
$683$			9.54141i			0.365092i	0.983197	+	0.182546i	$0.0584338\pi$
$683$			9.54141i			0.365092i	−0.983197	+	0.182546i	$0.941566\pi$
$684$	1.99993	+	1.76976i	0.0764692	+	0.0676683i
$685$			3.16804i			0.121045i
$686$	−18.1825	+	3.52082i	−0.694212	+	0.134425i
$687$	−8.53630	+	3.84479i	−0.325680	+	0.146688i
$688$	−11.3381			−0.432263
$689$	−0.0298028			−0.00113539
$690$	0.237727	+	0.527806i	0.00905010	+	0.0200932i
$691$			9.55799i			0.363603i	0.983335	+	0.181802i	$0.0581929\pi$
$691$			9.55799i			0.363603i	−0.983335	+	0.181802i	$0.941807\pi$
$692$	−12.3935			−0.471129
$693$	−3.00246	+	3.86338i	−0.114054	+	0.146758i
$694$	−13.6981			−0.519974
$695$		−	4.16651i		−	0.158045i
$696$	1.52310	+	3.38163i	0.0577330	+	0.128180i
$697$	16.0532			0.608059
$698$	11.7210			0.443647
$699$	−21.0772	+	9.49328i	−0.797213	+	0.359069i
$700$	−0.824023	−	12.9070i	−0.0311451	−	0.487837i
$701$			28.0103i			1.05793i	0.848642	+	0.528967i	$0.177421\pi$
$701$			28.0103i			1.05793i	−0.848642	+	0.528967i	$0.822579\pi$
$702$	16.0740	+	4.99384i	0.606674	+	0.188480i
$703$		−	1.85464i		−	0.0699490i
$704$		−	0.616447i		−	0.0232332i
$705$	−0.703740	−	1.56246i	−0.0265044	−	0.0588457i
$706$			8.43379i			0.317410i
$707$	1.87665	+	29.3947i	0.0705788	+	1.10550i
$708$	−9.33594	−	20.7279i	−0.350866	−	0.779002i
$709$	15.2373			0.572248			0.286124	−	0.958193i	$-0.407633\pi$
$709$	15.2373			0.572248			0.286124	+	0.958193i	$0.407633\pi$
$710$	−1.52851			−0.0573640
$711$	14.6842	−	16.5940i	0.550700	−	0.622323i
$712$			15.6130i			0.585124i
$713$	−2.97856			−0.111548
$714$	6.77288	+	12.7917i	0.253469	+	0.478718i
$715$	0.667373			0.0249583
$716$			4.94693i			0.184875i
$717$	45.8833	−	20.6661i	1.71354	−	0.771789i
$718$	22.4082			0.836267
$719$	−44.6979			−1.66695			−0.833475	−	0.552558i	$-0.813652\pi$
$719$	−44.6979			−1.66695			−0.833475	+	0.552558i	$0.813652\pi$
$720$	−0.664445	+	0.750862i	−0.0247624	+	0.0279830i
$721$	12.4206	−	0.792974i	0.462568	−	0.0295319i
$722$			18.2076i			0.677616i
$723$	25.5789	−	11.5208i	0.951288	−	0.428465i
$724$			11.2427i			0.417831i
$725$			10.4672i			0.388743i
$726$	16.7717	−	7.55405i	0.622455	−	0.280357i
$727$		−	24.8349i		−	0.921074i	−0.887640	−	0.460537i	$-0.847657\pi$
$727$		−	24.8349i		−	0.921074i	0.887640	−	0.460537i	$-0.152343\pi$
$728$	0.546049	+	8.55295i	0.0202379	+	0.316994i
$729$	22.2467	+	15.2999i	0.823951	+	0.566661i
$730$	2.07550			0.0768177
$731$	35.8116			1.32454
$732$	14.0985	−	6.35003i	0.521095	−	0.234704i
$733$			4.68413i			0.173012i	0.996251	+	0.0865061i	$0.0275702\pi$
$733$			4.68413i			0.173012i	−0.996251	+	0.0865061i	$0.972430\pi$
$734$	23.8207			0.879237
$735$	2.12042	+	3.45303i	0.0782128	+	0.127367i
$736$	−1.00000			−0.0368605
$737$			3.40027i			0.125251i
$738$	11.4187	+	10.1045i	0.420329	+	0.371953i
$739$	−35.0108			−1.28789			−0.643946	−	0.765071i	$-0.722704\pi$
$739$	−35.0108			−1.28789			−0.643946	+	0.765071i	$0.722704\pi$
$740$	0.696313			0.0255970
$741$	−2.05108	−	4.55386i	−0.0753483	−	0.167290i
$742$	−0.00155091	−	0.0242925i	−5.69358e−5	−	0.000891805i
$743$			1.09183i			0.0400553i	0.999799	+	0.0200276i	$0.00637542\pi$
$743$			1.09183i			0.0400553i	−0.999799	+	0.0200276i	$0.993625\pi$
$744$	−2.11867	−	4.70391i	−0.0776741	−	0.172454i
$745$			3.74032i			0.137035i
$746$		−	36.8075i		−	1.34762i
$747$	−22.6420	+	25.5868i	−0.828427	+	0.936171i
$748$			1.94705i			0.0711914i
$749$	17.6029	−	1.12383i	0.643198	−	0.0410639i
$750$	−5.21911	+	2.35071i	−0.190575	+	0.0858359i
$751$	−17.0491			−0.622130			−0.311065	−	0.950389i	$-0.600686\pi$
$751$	−17.0491			−0.622130			−0.311065	+	0.950389i	$0.600686\pi$
$752$	2.96029			0.107951
$753$	−1.54849	−	3.43800i	−0.0564301	−	0.125288i
$754$		−	6.93624i		−	0.252603i
$755$	5.26616			0.191655
$756$	−3.23404	+	13.3619i	−0.117621	+	0.485968i
$757$	10.1936			0.370494			0.185247	−	0.982692i	$-0.440691\pi$
$757$	10.1936			0.370494			0.185247	+	0.982692i	$0.440691\pi$
$758$			0.647490i			0.0235179i
$759$	0.438482	+	0.973527i	0.0159159	+	0.0353368i
$760$	0.297508			0.0107918
$761$	−53.5953			−1.94283			−0.971414	−	0.237393i	$-0.923707\pi$
$761$	−53.5953			−1.94283			−0.971414	+	0.237393i	$0.923707\pi$
$762$	2.00978	−	0.905216i	0.0728067	−	0.0327925i
$763$	−2.47969	−	38.8402i	−0.0897706	−	1.40611i
$764$		−	11.5303i		−	0.417152i
$765$	2.09866	−	2.37160i	0.0758770	−	0.0857456i
$766$		−	23.8151i		−	0.860474i
$767$			42.5161i			1.53517i
$768$	−0.711304	−	1.57925i	−0.0256670	−	0.0569865i
$769$			38.8414i			1.40066i	0.713821	+	0.700328i	$0.246963\pi$
$769$			38.8414i			1.40066i	−0.713821	+	0.700328i	$0.753037\pi$
$770$	0.0347296	+	0.543981i	0.00125157	+	0.0196037i
$771$	8.81109	+	19.5626i	0.317324	+	0.704530i
$772$	5.65666			0.203588
$773$	15.9469			0.573570			0.286785	−	0.957995i	$-0.407414\pi$
$773$	15.9469			0.573570			0.286785	+	0.957995i	$0.407414\pi$
$774$	25.4730	+	22.5413i	0.915607	+	0.810230i
$775$		−	14.5601i		−	0.523015i
$776$	−10.2696			−0.368656
$777$	8.43780	−	4.46759i	0.302704	−	0.160274i
$778$	33.3678			1.19629
$779$		−	4.52436i		−	0.162102i
$780$	1.70972	−	0.770067i	0.0612178	−	0.0275728i
$781$	−2.81930			−0.100883
$782$	3.15851			0.112948
$783$	3.30109	−	10.6254i	0.117971	−	0.379722i
$784$	−6.94317	+	0.890178i	−0.247970	+	0.0317921i
$785$			0.0442739i			0.00158020i
$786$	4.93950	−	2.22478i	0.176186	−	0.0793552i
$787$		−	1.53740i		−	0.0548025i	−0.999625	−	0.0274012i	$-0.991277\pi$
$787$		−	1.53740i		−	0.0548025i	0.999625	−	0.0274012i	$-0.00872318\pi$
$788$		−	3.68947i		−	0.131432i
$789$	−25.2356	+	11.3662i	−0.898410	+	0.404648i
$790$		−	2.46851i		−	0.0878258i
$791$	−44.6684	+	2.85178i	−1.58822	+	0.101397i
$792$	−1.22555	+	1.38495i	−0.0435482	+	0.0492120i
$793$	−28.9182			−1.02691
$794$	−6.35096			−0.225387
$795$	−0.00485602	+	0.00218718i	−0.000172225	+	7.75712e-5i
$796$			9.66592i			0.342599i
$797$	−27.4564			−0.972554			−0.486277	−	0.873805i	$-0.661645\pi$
$797$	−27.4564			−0.972554			−0.486277	+	0.873805i	$0.661645\pi$
$798$	3.60515	−	1.90883i	0.127621	−	0.0675719i
$799$	−9.35011			−0.330783
$800$		−	4.88830i		−	0.172828i
$801$	31.0402	−	35.0772i	1.09675	−	1.23939i
$802$	30.0803			1.06217
$803$	3.82821			0.135095
$804$	3.92350	+	8.71104i	0.138371	+	0.307215i
$805$	0.882446	−	0.0563383i	0.0311021	−	0.00198566i
$806$			9.64845i			0.339852i
$807$	19.8200	+	44.0049i	0.697697	+	1.54904i
$808$			11.1328i			0.391649i
$809$			26.8772i			0.944952i	0.881344	+	0.472476i	$0.156640\pi$
$809$			26.8772i			0.944952i	−0.881344	+	0.472476i	$0.843360\pi$
$810$	2.98557	−	0.365956i	0.104902	−	0.0128584i
$811$			25.2349i			0.886118i	0.896492	+	0.443059i	$0.146107\pi$
$811$			25.2349i			0.886118i	−0.896492	+	0.443059i	$0.853893\pi$
$812$	5.65379	−	0.360956i	0.198409	−	0.0126671i
$813$	−21.4452	+	9.65901i	−0.752115	+	0.338756i
$814$	1.28433			0.0450159
$815$	−0.522403			−0.0182990
$816$	2.24666	+	4.98809i	0.0786489	+	0.174618i
$817$		−	10.0930i		−	0.353108i
$818$	−7.71976			−0.269915
$819$	15.7773	−	20.3012i	0.551303	−	0.709381i
$820$	1.69864			0.0593192
$821$			48.8711i			1.70561i	0.522228	+	0.852806i	$0.325101\pi$
$821$			48.8711i			1.70561i	−0.522228	+	0.852806i	$0.674899\pi$
$822$	6.74255	+	14.9700i	0.235174	+	0.522138i
$823$	23.4785			0.818411			0.409205	−	0.912442i	$-0.365806\pi$
$823$	23.4785			0.818411			0.409205	+	0.912442i	$0.365806\pi$
$824$	4.70411			0.163876
$825$	−4.75889	+	2.14343i	−0.165683	+	0.0746247i
$826$	−34.6552	+	2.21250i	−1.20581	+	0.0769828i
$827$			14.5382i			0.505544i	0.967526	+	0.252772i	$0.0813422\pi$
$827$			14.5382i			0.505544i	−0.967526	+	0.252772i	$0.918658\pi$
$828$	2.24666	+	1.98809i	0.0780769	+	0.0690910i
$829$			21.8284i			0.758131i	0.925370	+	0.379066i	$0.123755\pi$
$829$			21.8284i			0.758131i	−0.925370	+	0.379066i	$0.876245\pi$
$830$			3.80628i			0.132118i
$831$	−19.3935	−	43.0578i	−0.672752	−	1.49366i
$832$			3.23929i			0.112302i
$833$	21.9301	−	2.81164i	0.759832	−	0.0974174i
$834$	−8.86759	−	19.6880i	−0.307059	−	0.681741i
$835$	3.33349			0.115360
$836$	0.548748			0.0189788
$837$	−4.59189	+	14.7802i	−0.158719	+	0.510879i
$838$			27.4462i			0.948113i
$839$	26.6696			0.920737			0.460368	−	0.887728i	$-0.347717\pi$
$839$	26.6696			0.920737			0.460368	+	0.887728i	$0.347717\pi$
$840$	0.716660	+	1.35353i	0.0247271	+	0.0467013i
$841$	24.4149			0.841894
$842$		−	1.72287i		−	0.0593742i
$843$	−16.6417	+	7.49550i	−0.573170	+	0.258159i
$844$	−9.28923			−0.319748
$845$	0.837860			0.0288233
$846$	−6.65077	−	5.88533i	−0.228658	−	0.202342i
$847$	−1.79022	−	28.0408i	−0.0615125	−	0.963492i
$848$		−	0.00920039i		−	0.000315943i
$849$	23.9565	−	10.7901i	0.822184	−	0.370316i
$850$			15.4398i			0.529579i
$851$		−	2.08345i		−	0.0714196i
$852$	−7.22268	+	3.25313i	−0.247445	+	0.111450i
$853$			3.50989i			0.120176i	0.998193	+	0.0600882i	$0.0191382\pi$
$853$			3.50989i			0.120176i	−0.998193	+	0.0600882i	$0.980862\pi$
$854$	−1.50488	−	23.5714i	−0.0514959	−	0.806598i
$855$	−0.668401	−	0.591474i	−0.0228588	−	0.0202280i
$856$	6.66683			0.227868
$857$	−32.7365			−1.11826			−0.559129	−	0.829080i	$-0.688865\pi$
$857$	−32.7365			−1.11826			−0.559129	+	0.829080i	$0.688865\pi$
$858$	3.15354	−	1.42037i	0.107660	−	0.0484907i
$859$			18.9860i			0.647794i	0.946092	+	0.323897i	$0.104993\pi$
$859$			18.9860i			0.647794i	−0.946092	+	0.323897i	$0.895007\pi$
$860$	3.78935			0.129216
$861$	20.5839	−	10.8986i	0.701496	−	0.371424i
$862$	28.3079			0.964170
$863$			22.9285i			0.780494i	0.920710	+	0.390247i	$0.127610\pi$
$863$			22.9285i			0.780494i	−0.920710	+	0.390247i	$0.872390\pi$
$864$	−1.54164	+	4.96219i	−0.0524478	+	0.168817i
$865$	4.14205			0.140834
$866$	−3.77079			−0.128137
$867$	4.99607	+	11.0924i	0.169675	+	0.376718i
$868$	−7.86453	+	0.502098i	−0.266940	+	0.0170423i
$869$		−	4.55312i		−	0.154454i
$870$	−0.509040	−	1.13018i	−0.0172581	−	0.0383167i
$871$		−	17.8677i		−	0.605424i
$872$		−	14.7101i		−	0.498147i
$873$	23.0722	+	20.4168i	0.780877	+	0.691005i
$874$		−	0.890178i		−	0.0301107i
$875$	0.557090	+	8.72589i	0.0188331	+	0.294989i
$876$	9.80737	−	4.41729i	0.331360	−	0.149246i
$877$	32.0494			1.08223			0.541116	−	0.840948i	$-0.318002\pi$
$877$	32.0494			1.08223			0.541116	+	0.840948i	$0.318002\pi$
$878$	4.15471			0.140215
$879$	−13.8571	−	30.7660i	−0.467390	−	1.03771i
$880$			0.206024i			0.00694507i
$881$	−20.8969			−0.704034			−0.352017	−	0.935994i	$-0.614504\pi$
$881$	−20.8969			−0.704034			−0.352017	+	0.935994i	$0.614504\pi$
$882$	17.3687	+	11.8037i	0.584835	+	0.397452i
$883$	−51.9603			−1.74860			−0.874302	−	0.485383i	$-0.838680\pi$
$883$	−51.9603			−1.74860			−0.874302	+	0.485383i	$0.838680\pi$
$884$		−	10.2313i		−	0.344117i
$885$	3.12019	+	6.92751i	0.104884	+	0.232866i
$886$	16.9438			0.569239
$887$	−13.1666			−0.442091			−0.221046	−	0.975263i	$-0.570947\pi$
$887$	−13.1666			−0.442091			−0.221046	+	0.975263i	$0.570947\pi$
$888$	3.29029	−	1.48196i	0.110415	−	0.0497315i
$889$	−0.214525	−	3.36018i	−0.00719494	−	0.112697i
$890$		−	5.21807i		−	0.174910i
$891$	5.50681	−	0.674997i	0.184485	−	0.0226132i
$892$			26.0351i			0.871720i
$893$			2.63519i			0.0881831i
$894$	7.96053	+	17.6742i	0.266240	+	0.591112i
$895$		−	1.65332i		−	0.0552645i
$896$	−2.64038	+	0.168570i	−0.0882088	+	0.00563154i
$897$	−2.30412	−	5.11567i	−0.0769325	−	0.170807i
$898$	19.5254			0.651570
$899$	6.37794			0.212716
$900$	−9.71840	+	10.9824i	−0.323947	+	0.366079i
$901$			0.0290595i			0.000968113i
$902$	3.13311			0.104321
$903$	45.9186	−	24.3127i	1.52808	−	0.809076i
$904$	−16.9174			−0.562665
$905$		−	3.75744i		−	0.124901i
$906$	24.8842	−	11.2080i	0.826723	−	0.372360i
$907$	3.89982			0.129491			0.0647457	−	0.997902i	$-0.479376\pi$
$907$	3.89982			0.129491			0.0647457	+	0.997902i	$0.479376\pi$
$908$	1.73870			0.0577006
$909$	22.1329	−	25.0115i	0.734103	−	0.829580i
$910$	−0.182496	−	2.85850i	−0.00604969	−	0.0947584i
$911$		−	12.1667i		−	0.403102i	−0.979478	−	0.201551i	$-0.935402\pi$
$911$		−	12.1667i		−	0.403102i	0.979478	−	0.201551i	$-0.0645982\pi$
$912$	1.40582	−	0.633187i	0.0465513	−	0.0209669i
$913$			7.02059i			0.232348i
$914$		−	19.7471i		−	0.653175i
$915$	−4.71189	+	2.12226i	−0.155770	+	0.0701597i
$916$			5.40527i			0.178595i
$917$	−0.527244	−	8.25841i	−0.0174111	−	0.272717i
$918$	4.86930	−	15.6731i	0.160711	−	0.517290i
$919$	−30.9169			−1.01985			−0.509927	−	0.860217i	$-0.670328\pi$
$919$	−30.9169			−1.01985			−0.509927	+	0.860217i	$0.670328\pi$
$920$	0.334212			0.0110187
$921$	17.6818	−	7.96399i	0.582637	−	0.262422i
$922$		−	24.1439i		−	0.795137i
$923$	14.8148			0.487636
$924$	1.32186	+	2.49656i	0.0434861	+	0.0821309i
$925$	10.1845			0.334865
$926$		−	34.1392i		−	1.12188i
$927$	−10.5686	−	9.35221i	−0.347117	−	0.307167i
$928$	2.14128			0.0702910
$929$	9.49474			0.311512			0.155756	−	0.987796i	$-0.450219\pi$
$929$	9.49474			0.311512			0.155756	+	0.987796i	$0.450219\pi$
$930$	0.708084	+	1.57211i	0.0232190	+	0.0515514i
$931$	−0.792417	−	6.18065i	−0.0259704	−	0.202563i
$932$			13.3463i			0.437173i
$933$	7.01696	+	15.5792i	0.229725	+	0.510041i
$934$			17.3020i			0.566139i
$935$		−	0.650729i		−	0.0212811i
$936$	6.44002	−	7.27760i	0.210499	−	0.237876i
$937$		−	21.2783i		−	0.695132i	−0.937655	−	0.347566i	$-0.887008\pi$
$937$		−	21.2783i		−	0.695132i	0.937655	−	0.347566i	$-0.112992\pi$
$938$	14.5641	−	0.929820i	0.475535	−	0.0303597i
$939$	−26.1356	+	11.7716i	−0.852903	+	0.384152i
$940$	−0.989366			−0.0322695
$941$	11.8428			0.386063			0.193032	−	0.981193i	$-0.438168\pi$
$941$	11.8428			0.386063			0.193032	+	0.981193i	$0.438168\pi$
$942$	0.0942282	+	0.209208i	0.00307012	+	0.00681635i
$943$		−	5.08253i		−	0.165510i
$944$	−13.1251			−0.427186
$945$	1.08086	−	4.46572i	0.0351603	−	0.145270i
$946$	6.98937			0.227244
$947$			36.6641i			1.19142i	0.803198	+	0.595712i	$0.203130\pi$
$947$			36.6641i			1.19142i	−0.803198	+	0.595712i	$0.796870\pi$
$948$	−5.25374	−	11.6645i	−0.170634	−	0.378845i
$949$	−20.1164			−0.653007
$950$	4.35146			0.141180
$951$	−19.9568	+	8.98866i	−0.647145	+	0.291477i
$952$	8.33965	−	0.532431i	0.270290	−	0.0172562i
$953$		−	8.27408i		−	0.268024i	−0.990980	−	0.134012i	$-0.957214\pi$
$953$		−	8.27408i		−	0.268024i	0.990980	−	0.134012i	$-0.0427860\pi$
$954$	−0.0182912	+	0.0206702i	−0.000592200	+	0.000669221i
$955$			3.85357i			0.124699i
$956$		−	29.0538i		−	0.939666i
$957$	−0.938912	−	2.08459i	−0.0303507	−	0.0673854i
$958$		−	6.66557i		−	0.215355i
$959$	25.0285	−	1.59790i	0.808212	−	0.0515989i
$960$	0.237727	+	0.527806i	0.00767259	+	0.0170349i
$961$	22.1282			0.713811
$962$	−6.74890			−0.217593
$963$	−14.9781	−	13.2543i	−0.482663	−	0.427113i
$964$		−	16.1968i		−	0.521664i
$965$	−1.89052			−0.0608581
$966$	4.04992	−	2.14433i	0.130304	−	0.0689926i
$967$	33.8380			1.08816			0.544078	−	0.839034i	$-0.316879\pi$
$967$	33.8380			1.08816			0.544078	+	0.839034i	$0.316879\pi$
$968$		−	10.6200i		−	0.341340i
$969$	−4.44029	+	1.99993i	−0.142643	+	0.0642470i
$970$	3.43221			0.110202
$971$	6.44381			0.206792			0.103396	−	0.994640i	$-0.467029\pi$
$971$	6.44381			0.206792			0.103396	+	0.994640i	$0.467029\pi$
$972$	13.3288	−	8.08343i	0.427523	−	0.259276i
$973$	−32.9167	+	2.10151i	−1.05526	+	0.0673713i
$974$			16.2562i			0.520881i
$975$	25.0069	−	11.2633i	0.800863	−	0.360713i
$976$		−	8.92731i		−	0.285756i
$977$		−	30.1308i		−	0.963970i	−0.876179	−	0.481985i	$-0.839916\pi$
$977$		−	30.1308i		−	0.963970i	0.876179	−	0.481985i	$-0.160084\pi$
$978$	−2.46851	+	1.11183i	−0.0789344	+	0.0355524i
$979$		−	9.62462i		−	0.307604i
$980$	2.32049	−	0.297508i	0.0741254	−	0.00950356i
$981$	−29.2450	+	33.0486i	−0.933722	+	1.05516i
$982$	−24.7150			−0.788689
$983$	14.5978			0.465597			0.232798	−	0.972525i	$-0.425212\pi$
$983$	14.5978			0.465597			0.232798	+	0.972525i	$0.425212\pi$
$984$	8.02661	−	3.61523i	0.255879	−	0.115249i
$985$			1.23307i			0.0392888i
$986$	−6.76326			−0.215386
$987$	−11.9889	+	6.34783i	−0.381612	+	0.202054i
$988$	−2.88355			−0.0917379
$989$		−	11.3381i		−	0.360532i
$990$	0.409595	−	0.462867i	0.0130178	−	0.0147109i
$991$	25.0380			0.795358			0.397679	−	0.917525i	$-0.369816\pi$
$991$	25.0380			0.795358			0.397679	+	0.917525i	$0.369816\pi$
$992$	−2.97856			−0.0945695
$993$	13.9194	+	30.9041i	0.441717	+	0.980711i
$994$	0.770951	+	12.0757i	0.0244531	+	0.383017i
$995$		−	3.23047i		−	0.102413i
$996$	8.10090	+	17.9858i	0.256687	+	0.569902i
$997$		−	45.0748i		−	1.42753i	−0.700384	−	0.713766i	$-0.746988\pi$
$997$		−	45.0748i		−	1.42753i	0.700384	−	0.713766i	$-0.253012\pi$
$998$			14.1996i			0.449481i
$999$	−10.3385	−	3.21193i	−0.327094	−	0.101621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.c.461.20	yes	28
3.2	odd	2	inner	966.2.f.c.461.9	yes	28
7.6	odd	2	inner	966.2.f.c.461.23	yes	28
21.20	even	2	inner	966.2.f.c.461.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.c.461.6	✓	28	21.20	even	2	inner
966.2.f.c.461.9	yes	28	3.2	odd	2	inner
966.2.f.c.461.20	yes	28	1.1	even	1	trivial
966.2.f.c.461.23	yes	28	7.6	odd	2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.711304 - 1.57925i) q^{3} -1.00000 q^{4} +0.334212 q^{5} +(1.57925 - 0.711304i) q^{6} +(-0.168570 - 2.64038i) q^{7} -1.00000i q^{8} +(-1.98809 + 2.24666i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.711304 - 1.57925i) q^{3} -1.00000 q^{4} +0.334212 q^{5} +(1.57925 - 0.711304i) q^{6} +(-0.168570 - 2.64038i) q^{7} -1.00000i q^{8} +(-1.98809 + 2.24666i) q^{9} +0.334212i q^{10} +0.616447i q^{11} +(0.711304 + 1.57925i) q^{12} -3.23929i q^{13} +(2.64038 - 0.168570i) q^{14} +(-0.237727 - 0.527806i) q^{15} +1.00000 q^{16} -3.15851 q^{17} +(-2.24666 - 1.98809i) q^{18} +0.890178i q^{19} -0.334212 q^{20} +(-4.04992 + 2.14433i) q^{21} -0.616447 q^{22} +1.00000i q^{23} +(-1.57925 + 0.711304i) q^{24} -4.88830 q^{25} +3.23929 q^{26} +(4.96219 + 1.54164i) q^{27} +(0.168570 + 2.64038i) q^{28} -2.14128i q^{29} +(0.527806 - 0.237727i) q^{30} +2.97856i q^{31} +1.00000i q^{32} +(0.973527 - 0.438482i) q^{33} -3.15851i q^{34} +(-0.0563383 - 0.882446i) q^{35} +(1.98809 - 2.24666i) q^{36} -2.08345 q^{37} -0.890178 q^{38} +(-5.11567 + 2.30412i) q^{39} -0.334212i q^{40} -5.08253 q^{41} +(-2.14433 - 4.04992i) q^{42} -11.3381 q^{43} -0.616447i q^{44} +(-0.664445 + 0.750862i) q^{45} -1.00000 q^{46} +2.96029 q^{47} +(-0.711304 - 1.57925i) q^{48} +(-6.94317 + 0.890178i) q^{49} -4.88830i q^{50} +(2.24666 + 4.98809i) q^{51} +3.23929i q^{52} -0.00920039i q^{53} +(-1.54164 + 4.96219i) q^{54} +0.206024i q^{55} +(-2.64038 + 0.168570i) q^{56} +(1.40582 - 0.633187i) q^{57} +2.14128 q^{58} -13.1251 q^{59} +(0.237727 + 0.527806i) q^{60} -8.92731i q^{61} -2.97856 q^{62} +(6.26716 + 4.87059i) q^{63} -1.00000 q^{64} -1.08261i q^{65} +(0.438482 + 0.973527i) q^{66} +5.51592 q^{67} +3.15851 q^{68} +(1.57925 - 0.711304i) q^{69} +(0.882446 - 0.0563383i) q^{70} +4.57347i q^{71} +(2.24666 + 1.98809i) q^{72} -6.21012i q^{73} -2.08345i q^{74} +(3.47707 + 7.71988i) q^{75} -0.890178i q^{76} +(1.62765 - 0.103915i) q^{77} +(-2.30412 - 5.11567i) q^{78} -7.38606 q^{79} +0.334212 q^{80} +(-1.09498 - 8.93314i) q^{81} -5.08253i q^{82} +11.3888 q^{83} +(4.04992 - 2.14433i) q^{84} -1.05561 q^{85} -11.3381i q^{86} +(-3.38163 + 1.52310i) q^{87} +0.616447 q^{88} -15.6130 q^{89} +(-0.750862 - 0.664445i) q^{90} +(-8.55295 + 0.546049i) q^{91} -1.00000i q^{92} +(4.70391 - 2.11867i) q^{93} +2.96029i q^{94} +0.297508i q^{95} +(1.57925 - 0.711304i) q^{96} -10.2696i q^{97} +(-0.890178 - 6.94317i) q^{98} +(-1.38495 - 1.22555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

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