LMFDB - Embedded newform 598.2.h.c.277.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [598,2,Mod(231,598)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("598.231"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(598, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 598 = 2 \cdot 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	598.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.77505404087$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.1
Character	$\chi$	$=$	598.277
Dual form			598.2.h.c.231.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.46307 + 2.53412i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.30968i q^{5} +(2.53412 - 1.46307i) q^{6} +(-0.0644396 + 0.0372042i) q^{7} -1.00000i q^{8} +(-2.78116 - 4.81712i) q^{9} +(-0.654838 + 1.13421i) q^{10} +(4.89375 + 2.82541i) q^{11} -2.92615 q^{12} +(2.55264 - 2.54638i) q^{13} +0.0744085 q^{14} +(3.31887 + 1.91615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00414 - 3.47126i) q^{17} +5.56233i q^{18} +(1.93556 - 1.11750i) q^{19} +(1.13421 - 0.654838i) q^{20} -0.217730i q^{21} +(-2.82541 - 4.89375i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.53412 + 1.46307i) q^{24} +3.28475 q^{25} +(-3.48384 + 0.928907i) q^{26} +7.49774 q^{27} +(-0.0644396 - 0.0372042i) q^{28} +(-0.835909 + 1.44784i) q^{29} +(-1.91615 - 3.31887i) q^{30} +8.30032i q^{31} +(0.866025 - 0.500000i) q^{32} +(-14.3198 + 8.26755i) q^{33} +4.00827i q^{34} +(0.0487255 + 0.0843950i) q^{35} +(2.78116 - 4.81712i) q^{36} +(2.00203 + 1.15588i) q^{37} -2.23499 q^{38} +(2.71812 + 10.1942i) q^{39} -1.30968 q^{40} +(2.93043 + 1.69189i) q^{41} +(-0.108865 + 0.188560i) q^{42} +(1.98749 + 3.44244i) q^{43} +5.65081i q^{44} +(-6.30886 + 3.64242i) q^{45} +(-0.866025 + 0.500000i) q^{46} -2.02762i q^{47} +(-1.46307 - 2.53412i) q^{48} +(-3.49723 + 6.05738i) q^{49} +(-2.84468 - 1.64237i) q^{50} +11.7288 q^{51} +(3.48155 + 0.937462i) q^{52} +5.91136 q^{53} +(-6.49324 - 3.74887i) q^{54} +(3.70037 - 6.40922i) q^{55} +(0.0372042 + 0.0644396i) q^{56} +6.53992i q^{57} +(1.44784 - 0.835909i) q^{58} +(-9.23895 + 5.33411i) q^{59} +3.83230i q^{60} +(4.71589 + 8.16816i) q^{61} +(4.15016 - 7.18828i) q^{62} +(0.358434 + 0.206942i) q^{63} -1.00000 q^{64} +(-3.33493 - 3.34313i) q^{65} +16.5351 q^{66} +(7.21077 + 4.16314i) q^{67} +(2.00414 - 3.47126i) q^{68} +(1.46307 + 2.53412i) q^{69} -0.0974510i q^{70} +(5.85700 - 3.38154i) q^{71} +(-4.81712 + 2.78116i) q^{72} -2.97670i q^{73} +(-1.15588 - 2.00203i) q^{74} +(-4.80583 + 8.32394i) q^{75} +(1.93556 + 1.11750i) q^{76} -0.420468 q^{77} +(2.74315 - 10.1875i) q^{78} +0.878908 q^{79} +(1.13421 + 0.654838i) q^{80} +(-2.62625 + 4.54880i) q^{81} +(-1.69189 - 2.93043i) q^{82} -16.8277i q^{83} +(0.188560 - 0.108865i) q^{84} +(-4.54623 + 2.62477i) q^{85} -3.97499i q^{86} +(-2.44599 - 4.23658i) q^{87} +(2.82541 - 4.89375i) q^{88} +(-5.62577 - 3.24804i) q^{89} +7.28485 q^{90} +(-0.0697552 + 0.259057i) q^{91} +1.00000 q^{92} +(-21.0340 - 12.1440i) q^{93} +(-1.01381 + 1.75597i) q^{94} +(-1.46356 - 2.53496i) q^{95} +2.92615i q^{96} +(6.68283 - 3.85833i) q^{97} +(6.05738 - 3.49723i) q^{98} -31.4317i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 14 q^{4} - 6 q^{9} + 8 q^{10} - 8 q^{12} + 2 q^{13} + 4 q^{14} + 12 q^{15} - 14 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{22} + 14 q^{23} - 28 q^{25} - 10 q^{26} + 20 q^{27} - 14 q^{29} + 8 q^{30}+ \cdots + 12 q^{98}+O(q^{100}) $ 28 * q - 4 * q^3 + 14 * q^4 - 6 * q^9 + 8 * q^10 - 8 * q^12 + 2 * q^13 + 4 * q^14 + 12 * q^15 - 14 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^22 + 14 * q^23 - 28 * q^25 - 10 * q^26 + 20 * q^27 - 14 * q^29 + 8 * q^30 + 18 * q^33 + 18 * q^35 + 6 * q^36 - 12 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^40 + 24 * q^41 - 6 * q^42 + 12 * q^43 - 36 * q^45 - 4 * q^48 + 36 * q^49 - 36 * q^50 - 12 * q^51 - 2 * q^52 + 8 * q^53 - 18 * q^54 - 12 * q^55 + 2 * q^56 + 18 * q^58 - 30 * q^59 + 6 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^64 - 66 * q^65 + 44 * q^66 + 42 * q^67 + 2 * q^68 + 4 * q^69 - 60 * q^71 + 44 * q^75 - 12 * q^76 + 16 * q^77 - 48 * q^78 + 68 * q^79 + 2 * q^81 + 40 * q^82 + 42 * q^84 - 72 * q^85 + 10 * q^87 + 12 * q^88 - 6 * q^89 - 36 * q^90 + 4 * q^91 + 28 * q^92 + 60 * q^93 - 26 * q^94 + 16 * q^95 - 12 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/598\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.46307	+	2.53412i	−0.844705	+	1.46307i	0.0411713	+	0.999152i	$0.486891\pi$
$3$	−1.46307	+	2.53412i	−0.844705	+	1.46307i	−0.885877	+	0.463921i	$0.846442\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.30968i		−	0.585705i	−0.956158	−	0.292852i	$-0.905396\pi$
$5$		−	1.30968i		−	0.585705i	0.956158	−	0.292852i	$-0.0946045\pi$
$6$	2.53412	−	1.46307i	1.03455	−	0.597297i
$7$	−0.0644396	+	0.0372042i	−0.0243559	+	0.0140619i	−0.512129	−	0.858909i	$-0.671143\pi$
$7$	−0.0644396	+	0.0372042i	−0.0243559	+	0.0140619i	0.487773	+	0.872971i	$0.337810\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.78116	−	4.81712i	−0.927055	−	1.60571i
$10$	−0.654838	+	1.13421i	−0.207078	+	0.358669i
$11$	4.89375	+	2.82541i	1.47552	+	0.851892i	0.999619	−	0.0276070i	$-0.00878869\pi$
$11$	4.89375	+	2.82541i	1.47552	+	0.851892i	0.475901	+	0.879499i	$0.342122\pi$
$12$	−2.92615			−0.844705
$13$	2.55264	−	2.54638i	0.707975	−	0.706238i
$13$	2.55264	−	2.54638i	0.707975	−	0.706238i
$14$	0.0744085			0.0198865
$15$	3.31887	+	1.91615i	0.856929	+	0.494748i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00414	−	3.47126i	−0.486074	−	0.841905i	0.513798	−	0.857911i	$-0.328238\pi$
$17$	−2.00414	−	3.47126i	−0.486074	−	0.841905i	−0.999872	+	0.0160060i	$0.994905\pi$
$18$			5.56233i			1.31105i
$19$	1.93556	−	1.11750i	0.444048	−	0.256372i	−0.261265	−	0.965267i	$-0.584140\pi$
$19$	1.93556	−	1.11750i	0.444048	−	0.256372i	0.705313	+	0.708896i	$0.250806\pi$
$20$	1.13421	−	0.654838i	0.253618	−	0.146426i
$21$		−	0.217730i		−	0.0475126i
$22$	−2.82541	−	4.89375i	−0.602378	−	1.04335i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	2.53412	+	1.46307i	0.517274	+	0.298648i
$25$	3.28475			0.656950
$26$	−3.48384	+	0.928907i	−0.683237	+	0.182174i
$27$	7.49774			1.44294
$28$	−0.0644396	−	0.0372042i	−0.0121779	−	0.00703094i
$29$	−0.835909	+	1.44784i	−0.155224	+	0.268856i	−0.933141	−	0.359511i	$-0.882943\pi$
$29$	−0.835909	+	1.44784i	−0.155224	+	0.268856i	0.777916	+	0.628368i	$0.216277\pi$
$30$	−1.91615	−	3.31887i	−0.349840	−	0.605940i
$31$			8.30032i			1.49078i	0.666628	+	0.745390i	$0.267737\pi$
$31$			8.30032i			1.49078i	−0.666628	+	0.745390i	$0.732263\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−14.3198	+	8.26755i	−2.49276	+	1.43920i
$34$			4.00827i			0.687413i
$35$	0.0487255	+	0.0843950i	0.00823611	+	0.0142654i
$36$	2.78116	−	4.81712i	0.463527	−	0.802853i
$37$	2.00203	+	1.15588i	0.329132	+	0.190025i	0.655456	−	0.755233i	$-0.272477\pi$
$37$	2.00203	+	1.15588i	0.329132	+	0.190025i	−0.326323	+	0.945258i	$0.605810\pi$
$38$	−2.23499			−0.362564
$39$	2.71812	+	10.1942i	0.435247	+	1.63238i
$40$	−1.30968			−0.207078
$41$	2.93043	+	1.69189i	0.457657	+	0.264228i	0.711058	−	0.703133i	$-0.248216\pi$
$41$	2.93043	+	1.69189i	0.457657	+	0.264228i	−0.253402	+	0.967361i	$0.581549\pi$
$42$	−0.108865	+	0.188560i	−0.0167982	+	0.0290954i
$43$	1.98749	+	3.44244i	0.303090	+	0.524967i	0.976834	−	0.213997i	$-0.0686484\pi$
$43$	1.98749	+	3.44244i	0.303090	+	0.524967i	−0.673744	+	0.738965i	$0.735315\pi$
$44$			5.65081i			0.851892i
$45$	−6.30886	+	3.64242i	−0.940470	+	0.542980i
$46$	−0.866025	+	0.500000i	−0.127688	+	0.0737210i
$47$		−	2.02762i		−	0.295759i	−0.989005	−	0.147880i	$-0.952755\pi$
$47$		−	2.02762i		−	0.295759i	0.989005	−	0.147880i	$-0.0472448\pi$
$48$	−1.46307	−	2.53412i	−0.211176	−	0.365768i
$49$	−3.49723	+	6.05738i	−0.499605	+	0.865340i
$50$	−2.84468	−	1.64237i	−0.402298	−	0.232267i
$51$	11.7288			1.64236
$52$	3.48155	+	0.937462i	0.482804	+	0.130003i
$53$	5.91136			0.811988			0.405994	−	0.913876i	$-0.366925\pi$
$53$	5.91136			0.811988			0.405994	+	0.913876i	$0.366925\pi$
$54$	−6.49324	−	3.74887i	−0.883618	−	0.510157i
$55$	3.70037	−	6.40922i	0.498957	−	0.864219i
$56$	0.0372042	+	0.0644396i	0.00497163	+	0.00861111i
$57$			6.53992i			0.866234i
$58$	1.44784	−	0.835909i	0.190110	−	0.109760i
$59$	−9.23895	+	5.33411i	−1.20281	+	0.694442i	−0.961179	−	0.275927i	$-0.911015\pi$
$59$	−9.23895	+	5.33411i	−1.20281	+	0.694442i	−0.241630	+	0.970369i	$0.577682\pi$
$60$			3.83230i			0.494748i
$61$	4.71589	+	8.16816i	0.603807	+	1.04583i	0.992239	+	0.124348i	$0.0396838\pi$
$61$	4.71589	+	8.16816i	0.603807	+	1.04583i	−0.388431	+	0.921478i	$0.626983\pi$
$62$	4.15016	−	7.18828i	0.527071	−	0.912913i
$63$	0.358434	+	0.206942i	0.0451585	+	0.0260723i
$64$	−1.00000			−0.125000
$65$	−3.33493	−	3.34313i	−0.413647	−	0.414664i
$66$	16.5351			2.03533
$67$	7.21077	+	4.16314i	0.880936	+	0.508608i	0.870967	−	0.491342i	$-0.163493\pi$
$67$	7.21077	+	4.16314i	0.880936	+	0.508608i	0.00996886	+	0.999950i	$0.496827\pi$
$68$	2.00414	−	3.47126i	0.243037	−	0.420953i
$69$	1.46307	+	2.53412i	0.176133	+	0.305072i
$70$		−	0.0974510i		−	0.0116476i
$71$	5.85700	−	3.38154i	0.695098	−	0.401315i	−0.110421	−	0.993885i	$-0.535220\pi$
$71$	5.85700	−	3.38154i	0.695098	−	0.401315i	0.805519	+	0.592570i	$0.201887\pi$
$72$	−4.81712	+	2.78116i	−0.567703	+	0.327763i
$73$		−	2.97670i		−	0.348397i	−0.984711	−	0.174198i	$-0.944267\pi$
$73$		−	2.97670i		−	0.348397i	0.984711	−	0.174198i	$-0.0557334\pi$
$74$	−1.15588	−	2.00203i	−0.134368	−	0.232732i
$75$	−4.80583	+	8.32394i	−0.554929	+	0.961165i
$76$	1.93556	+	1.11750i	0.222024	+	0.128186i
$77$	−0.420468			−0.0479168
$78$	2.74315	−	10.1875i	0.310601	−	1.15351i
$79$	0.878908			0.0988849			0.0494424	−	0.998777i	$-0.484256\pi$
$79$	0.878908			0.0988849			0.0494424	+	0.998777i	$0.484256\pi$
$80$	1.13421	+	0.654838i	0.126809	+	0.0732131i
$81$	−2.62625	+	4.54880i	−0.291806	+	0.505423i
$82$	−1.69189	−	2.93043i	−0.186838	−	0.323612i
$83$		−	16.8277i		−	1.84708i	−0.383500	−	0.923541i	$-0.625281\pi$
$83$		−	16.8277i		−	1.84708i	0.383500	−	0.923541i	$-0.374719\pi$
$84$	0.188560	−	0.108865i	0.0205736	−	0.0118781i
$85$	−4.54623	+	2.62477i	−0.493108	+	0.284696i
$86$		−	3.97499i		−	0.428634i
$87$	−2.44599	−	4.23658i	−0.262238	−	0.454209i
$88$	2.82541	−	4.89375i	0.301189	−	0.521675i
$89$	−5.62577	−	3.24804i	−0.596330	−	0.344291i	0.171266	−	0.985225i	$-0.445214\pi$
$89$	−5.62577	−	3.24804i	−0.596330	−	0.344291i	−0.767597	+	0.640933i	$0.778548\pi$
$90$	7.28485			0.767890
$91$	−0.0697552	+	0.259057i	−0.00731233	+	0.0271565i
$92$	1.00000			0.104257
$93$	−21.0340	−	12.1440i	−2.18112	−	1.25927i
$94$	−1.01381	+	1.75597i	−0.104567	+	0.181115i
$95$	−1.46356	−	2.53496i	−0.150158	−	0.260081i
$96$			2.92615i			0.298648i
$97$	6.68283	−	3.85833i	0.678539	−	0.391754i	−0.120766	−	0.992681i	$-0.538535\pi$
$97$	6.68283	−	3.85833i	0.678539	−	0.391754i	0.799304	+	0.600927i	$0.205202\pi$
$98$	6.05738	−	3.49723i	0.611888	−	0.353274i
$99$		−	31.4317i		−	3.15900i
$100$	1.64237	+	2.84468i	0.164237	+	0.284468i
$101$	−0.568427	+	0.984544i	−0.0565606	+	0.0979658i	−0.892919	−	0.450217i	$-0.851347\pi$
$101$	−0.568427	+	0.984544i	−0.0565606	+	0.0979658i	0.836359	+	0.548182i	$0.184680\pi$
$102$	−10.1574	−	5.86439i	−1.00574	−	0.580661i
$103$	−0.430376			−0.0424062			−0.0212031	−	0.999775i	$-0.506750\pi$
$103$	−0.430376			−0.0424062			−0.0212031	+	0.999775i	$0.506750\pi$
$104$	−2.54638	−	2.55264i	−0.249693	−	0.250307i
$105$	−0.285156			−0.0278284
$106$	−5.11939	−	2.95568i	−0.497239	−	0.287081i
$107$	8.15984	−	14.1333i	0.788841	−	1.36631i	−0.137836	−	0.990455i	$-0.544015\pi$
$107$	8.15984	−	14.1333i	0.788841	−	1.36631i	0.926677	−	0.375858i	$-0.122652\pi$
$108$	3.74887	+	6.49324i	0.360735	+	0.624812i
$109$			5.27587i			0.505337i	0.967553	+	0.252668i	$0.0813082\pi$
$109$			5.27587i			0.505337i	−0.967553	+	0.252668i	$0.918692\pi$
$110$	−6.40922	+	3.70037i	−0.611095	+	0.352816i
$111$	−5.85824	+	3.38226i	−0.556040	+	0.321030i
$112$		−	0.0744085i		−	0.00703094i
$113$	3.21810	+	5.57392i	0.302734	+	0.524350i	0.976754	−	0.214363i	$-0.0687674\pi$
$113$	3.21810	+	5.57392i	0.302734	+	0.524350i	−0.674021	+	0.738713i	$0.735434\pi$
$114$	3.26996	−	5.66374i	0.306260	−	0.530458i
$115$	−1.13421	−	0.654838i	−0.105766	−	0.0610639i
$116$	−1.67182			−0.155224
$117$	−19.3655	−	5.21447i	−1.79034	−	0.482078i
$118$	10.6682			0.982089
$119$	0.258292	+	0.149125i	0.0236775	+	0.0136702i
$120$	1.91615	−	3.31887i	0.174920	−	0.302970i
$121$	10.4658	+	18.1274i	0.951439	+	1.64794i
$122$		−	9.43177i		−	0.853913i
$123$	−8.57487	+	4.95071i	−0.773170	+	0.446390i
$124$	−7.18828	+	4.15016i	−0.645527	+	0.372695i
$125$		−	10.8503i		−	0.970484i
$126$	−0.206942	−	0.358434i	−0.0184359	−	0.0319319i
$127$	−6.42196	+	11.1232i	−0.569857	+	0.987021i	0.426723	+	0.904383i	$0.359668\pi$
$127$	−6.42196	+	11.1232i	−0.569857	+	0.987021i	−0.996580	+	0.0826387i	$0.973665\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−11.6314			−1.02409
$130$	1.21657	+	4.56270i	0.106700	+	0.400175i
$131$	16.5236			1.44367			0.721837	−	0.692063i	$-0.243298\pi$
$131$	16.5236			1.44367			0.721837	+	0.692063i	$0.243298\pi$
$132$	−14.3198	−	8.26755i	−1.24638	−	0.719598i
$133$	−0.0831513	+	0.144022i	−0.00721013	+	0.0124883i
$134$	−4.16314	−	7.21077i	−0.359640	−	0.622916i
$135$		−	9.81961i		−	0.845138i
$136$	−3.47126	+	2.00414i	−0.297659	+	0.171853i
$137$	−13.0238	+	7.51928i	−1.11270	+	0.642415i	−0.939526	−	0.342476i	$-0.888734\pi$
$137$	−13.0238	+	7.51928i	−1.11270	+	0.642415i	−0.173170	+	0.984892i	$0.555401\pi$
$138$		−	2.92615i		−	0.249090i
$139$	−8.23372	−	14.2612i	−0.698375	−	1.20962i	−0.969030	−	0.246944i	$-0.920574\pi$
$139$	−8.23372	−	14.2612i	−0.698375	−	1.20962i	0.270655	−	0.962676i	$-0.412760\pi$
$140$	−0.0487255	+	0.0843950i	−0.00411806	+	0.00713268i
$141$	5.13823	+	2.96656i	0.432717	+	0.249829i
$142$	−6.76308			−0.567545
$143$	19.6865	−	5.24908i	1.64627	−	0.438950i
$144$	5.56233			0.463527
$145$	1.89620	+	1.09477i	0.157471	+	0.0909156i
$146$	−1.48835	+	2.57790i	−0.123177	+	0.213349i
$147$	−10.2334	−	17.7248i	−0.844037	−	1.46192i
$148$			2.31175i			0.190025i
$149$	−4.78222	+	2.76102i	−0.391775	+	0.226191i	−0.682929	−	0.730485i	$-0.739294\pi$
$149$	−4.78222	+	2.76102i	−0.391775	+	0.226191i	0.291154	+	0.956676i	$0.405961\pi$
$150$	8.32394	−	4.80583i	0.679647	−	0.392394i
$151$			8.32918i			0.677819i	0.940819	+	0.338910i	$0.110058\pi$
$151$			8.32918i			0.677819i	−0.940819	+	0.338910i	$0.889942\pi$
$152$	−1.11750	−	1.93556i	−0.0906410	−	0.156995i
$153$	−11.1477	+	19.3083i	−0.901235	+	1.56098i
$154$	0.364136	+	0.210234i	0.0293429	+	0.0169412i
$155$	10.8707			0.873157
$156$	−7.46939	+	7.45107i	−0.598030	+	0.596563i
$157$	22.7900			1.81884			0.909420	−	0.415880i	$-0.136526\pi$
$157$	22.7900			1.81884			0.909420	+	0.415880i	$0.136526\pi$
$158$	−0.761157	−	0.439454i	−0.0605544	−	0.0349611i
$159$	−8.64875	+	14.9801i	−0.685891	+	1.18800i
$160$	−0.654838	−	1.13421i	−0.0517695	−	0.0896674i
$161$			0.0744085i			0.00586421i
$162$	4.54880	−	2.62625i	0.357388	−	0.206338i
$163$	−14.8938	+	8.59895i	−1.16657	+	0.673522i	−0.952871	−	0.303376i	$-0.901886\pi$
$163$	−14.8938	+	8.59895i	−1.16657	+	0.673522i	−0.213704	+	0.976899i	$0.568553\pi$
$164$			3.38377i			0.264228i
$165$	10.8278	+	18.7543i	0.842944	+	1.46002i
$166$	−8.41386	+	14.5732i	−0.653042	+	1.13110i
$167$	19.8200	+	11.4431i	1.53372	+	0.885494i	0.999186	+	0.0403476i	$0.0128465\pi$
$167$	19.8200	+	11.4431i	1.53372	+	0.885494i	0.534535	+	0.845146i	$0.320487\pi$
$168$	−0.217730			−0.0167982
$169$	0.0319355	−	13.0000i	0.00245658	−	0.999997i
$170$	5.24954			0.402621
$171$	−10.7662	−	6.21589i	−0.823314	−	0.475341i
$172$	−1.98749	+	3.44244i	−0.151545	+	0.262484i
$173$	−11.8868	−	20.5885i	−0.903736	−	1.56532i	−0.822605	−	0.568613i	$-0.807480\pi$
$173$	−11.8868	−	20.5885i	−0.903736	−	1.56532i	−0.0811303	−	0.996704i	$-0.525853\pi$
$174$			4.89198i			0.370860i
$175$	−0.211668	+	0.122207i	−0.0160006	+	0.00923795i
$176$	−4.89375	+	2.82541i	−0.368880	+	0.212973i
$177$		−	31.2168i		−	2.34639i
$178$	3.24804	+	5.62577i	0.243451	+	0.421669i
$179$	0.789029	−	1.36664i	0.0589748	−	0.102147i	−0.835031	−	0.550203i	$-0.814550\pi$
$179$	0.789029	−	1.36664i	0.0589748	−	0.102147i	0.894005	+	0.448056i	$0.147884\pi$
$180$	−6.30886	−	3.64242i	−0.470235	−	0.271490i
$181$	−8.07194			−0.599982			−0.299991	−	0.953942i	$-0.596984\pi$
$181$	−8.07194			−0.599982			−0.299991	+	0.953942i	$0.596984\pi$
$182$	0.189938	−	0.189472i	0.0140791	−	0.0140446i
$183$	−27.5987			−2.04016
$184$	−0.866025	−	0.500000i	−0.0638442	−	0.0368605i
$185$	1.51382	−	2.62202i	0.111298	−	0.192774i
$186$	12.1440	+	21.0340i	0.890439	+	1.54229i
$187$		−	22.6500i		−	1.65633i
$188$	1.75597	−	1.01381i	0.128067	−	0.0739398i
$189$	−0.483152	+	0.278948i	−0.0351441	+	0.0202905i
$190$			2.92712i			0.212356i
$191$	8.56336	+	14.8322i	0.619623	+	1.07322i	0.989555	+	0.144159i	$0.0460477\pi$
$191$	8.56336	+	14.8322i	0.619623	+	1.07322i	−0.369932	+	0.929059i	$0.620619\pi$
$192$	1.46307	−	2.53412i	0.105588	−	0.182884i
$193$	−9.41831	−	5.43766i	−0.677944	−	0.391411i	0.121136	−	0.992636i	$-0.461346\pi$
$193$	−9.41831	−	5.43766i	−0.677944	−	0.391411i	−0.799080	+	0.601225i	$0.794680\pi$
$194$	−7.71667			−0.554024
$195$	13.3511	−	3.55985i	0.956094	−	0.254926i
$196$	−6.99446			−0.499605
$197$	−15.5783	−	8.99412i	−1.10991	−	0.640805i	−0.171101	−	0.985254i	$-0.554732\pi$
$197$	−15.5783	−	8.99412i	−1.10991	−	0.640805i	−0.938805	+	0.344449i	$0.888066\pi$
$198$	−15.7158	+	27.2206i	−1.11688	+	1.93449i
$199$	5.98186	+	10.3609i	0.424043	+	0.734464i	0.996331	−	0.0855892i	$-0.0272773\pi$
$199$	5.98186	+	10.3609i	0.424043	+	0.734464i	−0.572288	+	0.820053i	$0.693944\pi$
$200$		−	3.28475i		−	0.232267i
$201$	−21.0998	+	12.1820i	−1.48826	+	0.859249i
$202$	0.984544	−	0.568427i	0.0692723	−	0.0399944i
$203$		−	0.124397i		−	0.00873098i
$204$	5.86439	+	10.1574i	0.410590	+	0.711162i
$205$	2.21582	−	3.83792i	0.154760	−	0.268052i
$206$	0.372717	+	0.215188i	0.0259684	+	0.0149929i
$207$	−5.56233			−0.386609
$208$	0.928907	+	3.48384i	0.0644081	+	0.241561i
$209$	12.6295			0.873603
$210$	0.246952	+	0.142578i	0.0170413	+	0.00983881i
$211$	6.85611	−	11.8751i	0.471994	−	0.817518i	−0.527492	−	0.849560i	$-0.676868\pi$
$211$	6.85611	−	11.8751i	0.471994	−	0.817518i	0.999487	+	0.0320420i	$0.0102010\pi$
$212$	2.95568	+	5.11939i	0.202997	+	0.351601i
$213$			19.7897i			1.35597i
$214$	−14.1333	+	8.15984i	−0.966129	+	0.557795i
$215$	4.50848	−	2.60297i	0.307476	−	0.177521i
$216$		−	7.49774i		−	0.510157i
$217$	−0.308807	−	0.534869i	−0.0209632	−	0.0363093i
$218$	2.63794	−	4.56904i	0.178664	−	0.309454i
$219$	7.54331	+	4.35513i	0.509730	+	0.294293i
$220$	7.40073			0.498957
$221$	−13.9550	−	3.75760i	−0.938714	−	0.252764i
$222$	6.76452			0.454005
$223$	6.48527	+	3.74427i	0.434286	+	0.250735i	0.701171	−	0.712993i	$-0.252661\pi$
$223$	6.48527	+	3.74427i	0.434286	+	0.250735i	−0.266885	+	0.963728i	$0.585994\pi$
$224$	−0.0372042	+	0.0644396i	−0.00248581	+	0.00430555i
$225$	−9.13543	−	15.8230i	−0.609028	−	1.05487i
$226$		−	6.43620i		−	0.428130i
$227$	−19.7333	+	11.3930i	−1.30974	+	0.756182i	−0.982053	−	0.188603i	$-0.939604\pi$
$227$	−19.7333	+	11.3930i	−1.30974	+	0.756182i	−0.327692	+	0.944785i	$0.606271\pi$
$228$	−5.66374	+	3.26996i	−0.375090	+	0.216558i
$229$			5.74896i			0.379902i	0.981794	+	0.189951i	$0.0608329\pi$
$229$			5.74896i			0.379902i	−0.981794	+	0.189951i	$0.939167\pi$
$230$	0.654838	+	1.13421i	0.0431787	+	0.0747878i
$231$	0.615176	−	1.06552i	0.0404756	−	0.0701058i
$232$	1.44784	+	0.835909i	0.0950551	+	0.0548801i
$233$	22.6891			1.48641			0.743206	−	0.669063i	$-0.233304\pi$
$233$	22.6891			1.48641			0.743206	+	0.669063i	$0.233304\pi$
$234$	14.1638	+	14.1986i	0.925915	+	0.928193i
$235$	−2.65553			−0.173228
$236$	−9.23895	−	5.33411i	−0.601404	−	0.347221i
$237$	−1.28591	+	2.22726i	−0.0835286	+	0.144676i
$238$	−0.149125	−	0.258292i	−0.00966632	−	0.0167426i
$239$		−	2.91464i		−	0.188532i	−0.995547	−	0.0942661i	$-0.969950\pi$
$239$		−	2.91464i		−	0.188532i	0.995547	−	0.0942661i	$-0.0300505\pi$
$240$	−3.31887	+	1.91615i	−0.214232	+	0.123687i
$241$	25.3699	−	14.6473i	1.63422	−	0.943517i	0.651447	−	0.758694i	$-0.274162\pi$
$241$	25.3699	−	14.6473i	1.63422	−	0.943517i	0.982772	−	0.184823i	$-0.0591712\pi$
$242$		−	20.9317i		−	1.34554i
$243$	3.56182	+	6.16925i	0.228491	+	0.395757i
$244$	−4.71589	+	8.16816i	−0.301904	+	0.522913i
$245$	7.93321	+	4.58024i	0.506834	+	0.292621i
$246$	9.90141			0.631291
$247$	2.09522	−	7.78124i	0.133316	−	0.495108i
$248$	8.30032			0.527071
$249$	42.6434	+	24.6202i	2.70242	+	1.56024i
$250$	−5.42517	+	9.39667i	−0.343118	+	0.594297i
$251$	−12.0127	−	20.8066i	−0.758235	−	1.31330i	−0.943750	−	0.330661i	$-0.892728\pi$
$251$	−12.0127	−	20.8066i	−0.758235	−	1.31330i	0.185514	−	0.982642i	$-0.440605\pi$
$252$			0.413884i			0.0260723i
$253$	4.89375	−	2.82541i	0.307667	−	0.177632i
$254$	11.1232	−	6.42196i	0.697929	−	0.402950i
$255$		−	15.3609i		−	0.961937i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.2009	−	21.1326i	0.761071	−	1.31821i	−0.181229	−	0.983441i	$-0.558007\pi$
$257$	12.2009	−	21.1326i	0.761071	−	1.31821i	0.942299	−	0.334772i	$-0.108659\pi$
$258$	10.0731	+	5.81570i	0.627123	+	0.362070i
$259$	−0.172014			−0.0106884
$260$	1.22777	−	4.55970i	0.0761432	−	0.282780i
$261$	9.29919			0.575606
$262$	−14.3099	−	8.26180i	−0.884066	−	0.510416i
$263$	1.05184	−	1.82184i	0.0648592	−	0.112340i	−0.831772	−	0.555117i	$-0.812673\pi$
$263$	1.05184	−	1.82184i	0.0648592	−	0.112340i	0.896632	+	0.442777i	$0.146007\pi$
$264$	8.26755	+	14.3198i	0.508832	+	0.881324i
$265$		−	7.74197i		−	0.475585i
$266$	0.144022	−	0.0831513i	0.00883057	−	0.00509833i
$267$	16.4618	−	9.50424i	1.00745	−	0.581650i
$268$			8.32628i			0.508608i
$269$	5.21969	+	9.04076i	0.318250	+	0.551225i	0.980123	−	0.198391i	$-0.0635716\pi$
$269$	5.21969	+	9.04076i	0.318250	+	0.551225i	−0.661873	+	0.749616i	$0.730238\pi$
$270$	−4.90981	+	8.50403i	−0.298801	+	0.517539i
$271$	−12.4630	−	7.19550i	−0.757071	−	0.437095i	0.0711720	−	0.997464i	$-0.477326\pi$
$271$	−12.4630	−	7.19550i	−0.757071	−	0.437095i	−0.828243	+	0.560369i	$0.810659\pi$
$272$	4.00827			0.243037
$273$	−0.554423	−	0.555786i	−0.0335552	−	0.0336377i
$274$	15.0386			0.908513
$275$	16.0747	+	9.28075i	0.969343	+	0.559650i
$276$	−1.46307	+	2.53412i	−0.0880666	+	0.152536i
$277$	−11.2085	−	19.4137i	−0.673453	−	1.16646i	−0.976918	−	0.213613i	$-0.931477\pi$
$277$	−11.2085	−	19.4137i	−0.673453	−	1.16646i	0.303465	−	0.952843i	$-0.401856\pi$
$278$			16.4674i			0.987651i
$279$	39.9836	−	23.0845i	2.39376	−	1.38204i
$280$	0.0843950	−	0.0487255i	0.00504357	−	0.00291191i
$281$		−	5.12400i		−	0.305672i	−0.988252	−	0.152836i	$-0.951159\pi$
$281$		−	5.12400i		−	0.305672i	0.988252	−	0.152836i	$-0.0488407\pi$
$282$	−2.96656	−	5.13823i	−0.176656	−	0.305977i
$283$	0.346987	−	0.600999i	0.0206262	−	0.0357257i	−0.855528	−	0.517756i	$-0.826767\pi$
$283$	0.346987	−	0.600999i	0.0206262	−	0.0357257i	0.876154	+	0.482031i	$0.160101\pi$
$284$	5.85700	+	3.38154i	0.347549	+	0.200657i
$285$	8.56518			0.507357
$286$	−19.6736	−	5.29742i	−1.16332	−	0.313243i
$287$	−0.251781			−0.0148622
$288$	−4.81712	−	2.78116i	−0.283851	−	0.163882i
$289$	0.466880	−	0.808660i	0.0274635	−	0.0475682i
$290$	−1.09477	−	1.89620i	−0.0642871	−	0.111348i
$291$			22.5801i			1.32367i
$292$	2.57790	−	1.48835i	0.150860	−	0.0870992i
$293$	−26.2779	+	15.1715i	−1.53517	+	0.886331i	−0.536059	+	0.844180i	$0.680088\pi$
$293$	−26.2779	+	15.1715i	−1.53517	+	0.886331i	−0.999111	+	0.0421509i	$0.986579\pi$
$294$			20.4668i			1.19365i
$295$	6.98595	+	12.1000i	0.406738	+	0.704491i
$296$	1.15588	−	2.00203i	0.0671839	−	0.116366i
$297$	36.6921	+	21.1842i	2.12909	+	1.22923i
$298$	5.52203			0.319883
$299$	−0.928907	−	3.48384i	−0.0537201	−	0.201476i
$300$	−9.61165			−0.554929
$301$	−0.256147	−	0.147886i	−0.0147641	−	0.00852403i
$302$	4.16459	−	7.21328i	0.239645	−	0.415078i
$303$	−1.66330	−	2.88092i	−0.0955540	−	0.165504i
$304$			2.23499i			0.128186i
$305$	10.6976	−	6.17628i	0.612545	−	0.353653i
$306$	19.3083	−	11.1477i	1.10378	−	0.637269i
$307$			29.9173i			1.70747i	0.520707	+	0.853735i	$0.325668\pi$
$307$			29.9173i			1.70747i	−0.520707	+	0.853735i	$0.674332\pi$
$308$	−0.210234	−	0.364136i	−0.0119792	−	0.0207486i
$309$	0.629672	−	1.09062i	0.0358208	−	0.0620434i
$310$	−9.41432	−	5.43536i	−0.534698	−	0.308708i
$311$	−15.6226			−0.885878			−0.442939	−	0.896552i	$-0.646064\pi$
$311$	−15.6226			−0.885878			−0.442939	+	0.896552i	$0.646064\pi$
$312$	10.1942	−	2.71812i	0.577134	−	0.153883i
$313$	−14.4709			−0.817942			−0.408971	−	0.912547i	$-0.634112\pi$
$313$	−14.4709			−0.817942			−0.408971	+	0.912547i	$0.634112\pi$
$314$	−19.7367	−	11.3950i	−1.11381	−	0.643057i
$315$	0.271027	−	0.469433i	0.0152707	−	0.0264495i
$316$	0.439454	+	0.761157i	0.0247212	+	0.0428184i
$317$			19.2184i			1.07941i	0.841854	+	0.539706i	$0.181465\pi$
$317$			19.2184i			1.07941i	−0.841854	+	0.539706i	$0.818535\pi$
$318$	14.9801	−	8.64875i	0.840041	−	0.484998i
$319$	−8.18145	+	4.72356i	−0.458073	+	0.264469i
$320$			1.30968i			0.0732131i
$321$	23.8769	+	41.3560i	1.33268	+	2.30826i
$322$	0.0372042	−	0.0644396i	0.00207331	−	0.00359108i
$323$	−7.75826	−	4.47923i	−0.431681	−	0.249231i
$324$	−5.25251			−0.291806
$325$	8.38478	−	8.36421i	0.465104	−	0.463963i
$326$	17.1979			0.952504
$327$	−13.3697	−	7.71898i	−0.739345	−	0.426861i
$328$	1.69189	−	2.93043i	0.0934188	−	0.161806i
$329$	0.0754361	+	0.130659i	0.00415893	+	0.00720348i
$330$		−	21.6556i		−	1.19210i
$331$	12.0838	−	6.97656i	0.664183	−	0.383466i	−0.129686	−	0.991555i	$-0.541397\pi$
$331$	12.0838	−	6.97656i	0.664183	−	0.383466i	0.793869	+	0.608089i	$0.208063\pi$
$332$	14.5732	−	8.41386i	0.799810	−	0.461770i
$333$		−	12.8587i		−	0.704653i
$334$	−11.4431	−	19.8200i	−0.626139	−	1.08450i
$335$	5.45236	−	9.44377i	0.297894	−	0.515968i
$336$	0.188560	+	0.108865i	0.0102868	+	0.00593907i
$337$	−20.3538			−1.10874			−0.554372	−	0.832269i	$-0.687041\pi$
$337$	−20.3538			−1.10874			−0.554372	+	0.832269i	$0.687041\pi$
$338$	−6.52764	+	11.2423i	−0.355057	+	0.611502i
$339$	−18.8333			−1.02288
$340$	−4.54623	−	2.62477i	−0.246554	−	0.142348i
$341$	−23.4518	+	40.6196i	−1.26998	+	2.19968i
$342$	6.21589	+	10.7662i	0.336117	+	0.582171i
$343$		−	1.04131i		−	0.0562253i
$344$	3.44244	−	1.98749i	0.185604	−	0.107159i
$345$	3.31887	−	1.91615i	0.178682	−	0.103162i
$346$			23.7736i			1.27808i
$347$	−6.83711	−	11.8422i	−0.367035	−	0.635724i	0.622065	−	0.782965i	$-0.286294\pi$
$347$	−6.83711	−	11.8422i	−0.367035	−	0.635724i	−0.989101	+	0.147242i	$0.952961\pi$
$348$	2.44599	−	4.23658i	0.131119	−	0.227104i
$349$	−13.8437	−	7.99268i	−0.741038	−	0.427838i	0.0814089	−	0.996681i	$-0.474058\pi$
$349$	−13.8437	−	7.99268i	−0.741038	−	0.427838i	−0.822446	+	0.568843i	$0.807391\pi$
$350$	0.244413			0.0130644
$351$	19.1390	−	19.0921i	1.02157	−	1.01906i
$352$	5.65081			0.301189
$353$	−10.6195	−	6.13117i	−0.565219	−	0.326329i	0.190019	−	0.981780i	$-0.439145\pi$
$353$	−10.6195	−	6.13117i	−0.565219	−	0.326329i	−0.755238	+	0.655451i	$0.772478\pi$
$354$	−15.6084	+	27.0345i	−0.829576	+	1.43687i
$355$	−4.42872	−	7.67077i	−0.235052	−	0.407122i
$356$		−	6.49608i		−	0.344291i
$357$	−0.755799	+	0.436361i	−0.0400011	+	0.0230947i
$358$	−1.36664	+	0.789029i	−0.0722291	+	0.0417015i
$359$			22.2390i			1.17373i	0.809685	+	0.586865i	$0.199638\pi$
$359$			22.2390i			1.17373i	−0.809685	+	0.586865i	$0.800362\pi$
$360$	3.64242	+	6.30886i	0.191973	+	0.332506i
$361$	−7.00240	+	12.1285i	−0.368547	+	0.638343i
$362$	6.99050	+	4.03597i	0.367413	+	0.212126i
$363$	−61.2491			−3.21474
$364$	−0.259227	+	0.0691186i	−0.0135872	+	0.00362280i
$365$	−3.89852			−0.204058
$366$	23.9012	+	13.7994i	1.24934	+	0.721305i
$367$	−11.6235	+	20.1326i	−0.606744	+	1.05091i	0.385029	+	0.922904i	$0.374191\pi$
$367$	−11.6235	+	20.1326i	−0.606744	+	1.05091i	−0.991773	+	0.128007i	$0.959142\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$		−	18.8217i		−	0.979816i
$370$	−2.62202	+	1.51382i	−0.136312	+	0.0786998i
$371$	−0.380926	+	0.219928i	−0.0197767	+	0.0114181i
$372$		−	24.2879i		−	1.25927i
$373$	5.00155	+	8.66294i	0.258970	+	0.448550i	0.965966	−	0.258668i	$-0.0832834\pi$
$373$	5.00155	+	8.66294i	0.258970	+	0.448550i	−0.706996	+	0.707218i	$0.749950\pi$
$374$	−11.3250	+	19.6155i	−0.585601	+	1.01429i
$375$	27.4960	+	15.8748i	1.41989	+	0.819773i
$376$	−2.02762			−0.104567
$377$	1.55296	+	5.82434i	0.0799816	+	0.299969i
$378$	0.557896			0.0286951
$379$	−11.0204	−	6.36264i	−0.566081	−	0.326827i	0.189502	−	0.981880i	$-0.439313\pi$
$379$	−11.0204	−	6.36264i	−0.566081	−	0.326827i	−0.755583	+	0.655053i	$0.772646\pi$
$380$	1.46356	−	2.53496i	0.0750790	−	0.130041i
$381$	−18.7916	−	32.5480i	−0.962723	−	1.66748i
$382$		−	17.1267i		−	0.876279i
$383$	−0.810252	+	0.467799i	−0.0414019	+	0.0239034i	−0.520558	−	0.853826i	$-0.674276\pi$
$383$	−0.810252	+	0.467799i	−0.0414019	+	0.0239034i	0.479156	+	0.877730i	$0.340943\pi$
$384$	−2.53412	+	1.46307i	−0.129319	+	0.0746621i
$385$			0.550677i			0.0280651i
$386$	5.43766	+	9.41831i	0.276770	+	0.479379i
$387$	11.0551	−	19.1480i	0.561962	−	0.973347i
$388$	6.68283	+	3.85833i	0.339269	+	0.195877i
$389$	18.1087			0.918148			0.459074	−	0.888398i	$-0.348181\pi$
$389$	18.1087			0.918148			0.459074	+	0.888398i	$0.348181\pi$
$390$	−13.3423	−	3.59264i	−0.675615	−	0.181920i
$391$	−4.00827			−0.202707
$392$	6.05738	+	3.49723i	0.305944	+	0.176637i
$393$	−24.1752	+	41.8727i	−1.21948	+	2.11220i
$394$	8.99412	+	15.5783i	0.453117	+	0.784822i
$395$		−	1.15108i		−	0.0579174i
$396$	27.2206	−	15.7158i	1.36789	−	0.789750i
$397$	4.91414	−	2.83718i	0.246633	−	0.142394i	−0.371588	−	0.928398i	$-0.621187\pi$
$397$	4.91414	−	2.83718i	0.246633	−	0.142394i	0.618222	+	0.786004i	$0.287853\pi$
$398$		−	11.9637i		−	0.599687i
$399$	−0.243313	−	0.421430i	−0.0121809	−	0.0210979i
$400$	−1.64237	+	2.84468i	−0.0821187	+	0.142234i
$401$	−26.1659	−	15.1069i	−1.30666	−	0.754403i	−0.325127	−	0.945670i	$-0.605407\pi$
$401$	−26.1659	−	15.1069i	−1.30666	−	0.754403i	−0.981538	+	0.191267i	$0.938740\pi$
$402$	24.3639			1.21516
$403$	21.1357	+	21.1877i	1.05285	+	1.05544i
$404$	−1.13685			−0.0565606
$405$	5.95746	+	3.43954i	0.296029	+	0.170912i
$406$	−0.0621987	+	0.107731i	−0.00308687	+	0.00534661i
$407$	6.53163	+	11.3131i	0.323761	+	0.560770i
$408$		−	11.7288i		−	0.580661i
$409$	20.0266	−	11.5624i	0.990252	−	0.571722i	0.0849025	−	0.996389i	$-0.472942\pi$
$409$	20.0266	−	11.5624i	0.990252	−	0.571722i	0.905350	+	0.424667i	$0.139609\pi$
$410$	−3.83792	+	2.21582i	−0.189541	+	0.109432i
$411$		−	44.0050i		−	2.17061i
$412$	−0.215188	−	0.372717i	−0.0106016	−	0.0183624i
$413$	0.396903	−	0.687456i	0.0195303	−	0.0338275i
$414$	4.81712	+	2.78116i	0.236748	+	0.136687i
$415$	−22.0389			−1.08184
$416$	0.937462	−	3.48155i	0.0459629	−	0.170697i
$417$	48.1861			2.35968
$418$	−10.9375	−	6.31477i	−0.534971	−	0.308865i
$419$	5.08784	−	8.81239i	0.248557	−	0.430513i	−0.714569	−	0.699565i	$-0.753377\pi$
$419$	5.08784	−	8.81239i	0.248557	−	0.430513i	0.963126	+	0.269052i	$0.0867103\pi$
$420$	−0.142578	−	0.246952i	−0.00695709	−	0.0120500i
$421$			16.7171i			0.814740i	0.913263	+	0.407370i	$0.133554\pi$
$421$			16.7171i			0.814740i	−0.913263	+	0.407370i	$0.866446\pi$
$422$	−11.8751	+	6.85611i	−0.578072	+	0.333750i
$423$	−9.76729	+	5.63915i	−0.474902	+	0.274185i
$424$		−	5.91136i		−	0.287081i
$425$	−6.58308	−	11.4022i	−0.319326	−	0.553090i
$426$	9.89487	−	17.1384i	0.479408	−	0.830359i
$427$	−0.607780	−	0.350902i	−0.0294125	−	0.0169813i
$428$	16.3197			0.788841
$429$	−15.5010	+	57.5677i	−0.748397	+	2.77939i
$430$	−5.20595			−0.251053
$431$	21.5395	+	12.4358i	1.03752	+	0.599012i	0.919130	−	0.393955i	$-0.128894\pi$
$431$	21.5395	+	12.4358i	1.03752	+	0.599012i	0.118389	+	0.992967i	$0.462227\pi$
$432$	−3.74887	+	6.49324i	−0.180368	+	0.312406i
$433$	1.74165	+	3.01662i	0.0836983	+	0.144970i	0.904836	−	0.425761i	$-0.139993\pi$
$433$	1.74165	+	3.01662i	0.0836983	+	0.144970i	−0.821138	+	0.570730i	$0.806660\pi$
$434$			0.617614i			0.0296464i
$435$	−5.54855	+	3.20345i	−0.266032	+	0.153594i
$436$	−4.56904	+	2.63794i	−0.218817	+	0.126334i
$437$		−	2.23499i		−	0.106914i
$438$	−4.35513	−	7.54331i	−0.208096	−	0.360433i
$439$	9.14734	−	15.8437i	0.436579	−	0.756177i	−0.560844	−	0.827921i	$-0.689523\pi$
$439$	9.14734	−	15.8437i	0.436579	−	0.756177i	0.997423	+	0.0717448i	$0.0228567\pi$
$440$	−6.40922	−	3.70037i	−0.305548	−	0.176408i
$441$	38.9055			1.85264
$442$	10.2066	+	10.2317i	0.485477	+	0.486671i
$443$	−20.6078			−0.979107			−0.489553	−	0.871973i	$-0.662840\pi$
$443$	−20.6078			−0.979107			−0.489553	+	0.871973i	$0.662840\pi$
$444$	−5.85824	−	3.38226i	−0.278020	−	0.160515i
$445$	−4.25388	+	7.36793i	−0.201653	+	0.349274i
$446$	−3.74427	−	6.48527i	−0.177296	−	0.307086i
$447$		−	16.1583i		−	0.764260i
$448$	0.0644396	−	0.0372042i	0.00304449	−	0.00175774i
$449$	−10.9965	+	6.34885i	−0.518958	+	0.299621i	−0.736508	−	0.676428i	$-0.763527\pi$
$449$	−10.9965	+	6.34885i	−0.518958	+	0.299621i	0.217550	+	0.976049i	$0.430193\pi$
$450$			18.2709i			0.861296i
$451$	9.56053	+	16.5593i	0.450188	+	0.779748i
$452$	−3.21810	+	5.57392i	−0.151367	+	0.262175i
$453$	−21.1071	−	12.1862i	−0.991699	−	0.572558i
$454$	22.7860			1.06940
$455$	0.339280	+	0.0913566i	0.0159057	+	0.00428287i
$456$	6.53992			0.306260
$457$	20.7974	+	12.0074i	0.972861	+	0.561682i	0.900107	−	0.435668i	$-0.143488\pi$
$457$	20.7974	+	12.0074i	0.972861	+	0.561682i	0.0727538	+	0.997350i	$0.476821\pi$
$458$	2.87448	−	4.97874i	0.134316	−	0.232641i
$459$	−15.0265	−	26.0267i	−0.701377	−	1.21482i
$460$		−	1.30968i		−	0.0610639i
$461$	16.6571	−	9.61700i	0.775800	−	0.447908i	−0.0591399	−	0.998250i	$-0.518836\pi$
$461$	16.6571	−	9.61700i	0.775800	−	0.447908i	0.834940	+	0.550342i	$0.185502\pi$
$462$	−1.06552	+	0.615176i	−0.0495723	+	0.0286206i
$463$			25.9863i			1.20768i	0.797104	+	0.603842i	$0.206364\pi$
$463$			25.9863i			1.20768i	−0.797104	+	0.603842i	$0.793636\pi$
$464$	−0.835909	−	1.44784i	−0.0388061	−	0.0672141i
$465$	−15.9047	+	27.5477i	−0.737561	+	1.27749i
$466$	−19.6493	−	11.3445i	−0.910237	−	0.525526i
$467$	−34.7405			−1.60760			−0.803798	−	0.594902i	$-0.797191\pi$
$467$	−34.7405			−1.60760			−0.803798	+	0.594902i	$0.797191\pi$
$468$	−5.16688	−	19.3783i	−0.238839	−	0.895760i
$469$	−0.619546			−0.0286080
$470$	2.29975	+	1.32776i	0.106080	+	0.0612452i
$471$	−33.3434	+	57.7525i	−1.53638	+	2.66109i
$472$	5.33411	+	9.23895i	0.245522	+	0.425257i
$473$			22.4619i			1.03280i
$474$	2.22726	−	1.28591i	0.102301	−	0.0590636i
$475$	6.35784	−	3.67070i	0.291718	−	0.168423i
$476$			0.298249i			0.0136702i
$477$	−16.4405	−	28.4757i	−0.752757	−	1.30381i
$478$	−1.45732	+	2.52415i	−0.0666562	+	0.115452i
$479$	−29.3104	−	16.9224i	−1.33923	−	0.773204i	−0.352535	−	0.935799i	$-0.614680\pi$
$479$	−29.3104	−	16.9224i	−1.33923	−	0.773204i	−0.986693	+	0.162595i	$0.948014\pi$
$480$	3.83230			0.174920
$481$	8.05377	−	2.14740i	0.367220	−	0.0979130i
$482$	−29.2946			−1.33433
$483$	−0.188560	−	0.108865i	−0.00857977	−	0.00495353i
$484$	−10.4658	+	18.1274i	−0.475720	+	0.823971i
$485$	−5.05317	−	8.75234i	−0.229452	−	0.397423i
$486$		−	7.12363i		−	0.323135i
$487$	−19.7721	+	11.4154i	−0.895960	+	0.517283i	−0.875887	−	0.482516i	$-0.839723\pi$
$487$	−19.7721	+	11.4154i	−0.895960	+	0.517283i	−0.0200730	+	0.999799i	$0.506390\pi$
$488$	8.16816	−	4.71589i	0.369755	−	0.213478i
$489$		−	50.3236i		−	2.27571i
$490$	−4.58024	−	7.93321i	−0.206914	−	0.358386i
$491$	5.59970	−	9.69897i	0.252711	−	0.437708i	−0.711560	−	0.702625i	$-0.752011\pi$
$491$	5.59970	−	9.69897i	0.252711	−	0.437708i	0.964271	+	0.264917i	$0.0853444\pi$
$492$	−8.57487	−	4.95071i	−0.386585	−	0.223195i
$493$	6.70110			0.301802
$494$	−5.70514	+	5.69114i	−0.256686	+	0.256056i
$495$	−41.1653			−1.85024
$496$	−7.18828	−	4.15016i	−0.322764	−	0.186348i
$497$	−0.251615	+	0.435810i	−0.0112865	+	0.0195488i
$498$	−24.6202	−	42.6434i	−1.10326	−	1.91090i
$499$		−	26.0634i		−	1.16676i	−0.812200	−	0.583378i	$-0.801730\pi$
$499$		−	26.0634i		−	1.16676i	0.812200	−	0.583378i	$-0.198270\pi$
$500$	9.39667	−	5.42517i	0.420232	−	0.242621i
$501$	−57.9963	+	33.4842i	−2.59108	+	1.49596i
$502$			24.0254i			1.07231i
$503$	−3.43953	−	5.95743i	−0.153361	−	0.265629i	0.779100	−	0.626900i	$-0.215676\pi$
$503$	−3.43953	−	5.95743i	−0.153361	−	0.265629i	−0.932461	+	0.361271i	$0.882343\pi$
$504$	0.206942	−	0.358434i	0.00921794	−	0.0159659i
$505$	1.28943	+	0.744455i	0.0573790	+	0.0331278i
$506$	−5.65081			−0.251209
$507$	32.8967	+	19.1008i	1.46099	+	0.848297i
$508$	−12.8439			−0.569857
$509$	−4.64420	−	2.68133i	−0.205850	−	0.118848i	0.393531	−	0.919311i	$-0.371253\pi$
$509$	−4.64420	−	2.68133i	−0.205850	−	0.118848i	−0.599381	+	0.800464i	$0.704587\pi$
$510$	−7.68045	+	13.3029i	−0.340096	+	0.589064i
$511$	0.110746	+	0.191818i	0.00489911	+	0.00848552i
$512$			1.00000i			0.0441942i
$513$	14.5124	−	8.37871i	0.640736	−	0.369929i
$514$	−21.1326	+	12.2009i	−0.932117	+	0.538158i
$515$			0.563653i			0.0248375i
$516$	−5.81570	−	10.0731i	−0.256022	−	0.443443i
$517$	5.72885	−	9.92267i	0.251955	−	0.436398i
$518$	0.148968	+	0.0860069i	0.00654529	+	0.00377893i
$519$	69.5649			3.05356
$520$	−3.34313	+	3.33493i	−0.146606	+	0.146246i
$521$	−13.4857			−0.590819			−0.295409	−	0.955371i	$-0.595456\pi$
$521$	−13.4857			−0.590819			−0.295409	+	0.955371i	$0.595456\pi$
$522$	−8.05334	−	4.64960i	−0.352485	−	0.203507i
$523$	2.95781	−	5.12309i	0.129336	−	0.224017i	−0.794083	−	0.607809i	$-0.792049\pi$
$523$	2.95781	−	5.12309i	0.129336	−	0.224017i	0.923420	+	0.383792i	$0.125382\pi$
$524$	8.26180	+	14.3099i	0.360919	+	0.625129i
$525$		−	0.715189i		−	0.0312134i
$526$	−1.82184	+	1.05184i	−0.0794360	+	0.0458624i
$527$	28.8126	−	16.6350i	1.25510	−	0.724630i
$528$		−	16.5351i		−	0.719598i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−3.87098	+	6.70474i	−0.168145	+	0.291235i
$531$	51.3900	+	29.6701i	2.23014	+	1.28757i
$532$	−0.166303			−0.00721013
$533$	11.7885	−	3.14321i	0.510617	−	0.136148i
$534$	−19.0085			−0.822577
$535$	−18.5100	−	10.6867i	−0.800256	−	0.462028i
$536$	4.16314	−	7.21077i	0.179820	−	0.311458i
$537$	2.30881	+	3.99898i	0.0996327	+	0.172569i
$538$		−	10.4394i		−	0.450073i
$539$	−34.2291	+	19.7622i	−1.47435	+	0.851218i
$540$	8.50403	−	4.90981i	0.365955	−	0.211284i
$541$		−	7.51020i		−	0.322889i	−0.986882	−	0.161444i	$-0.948385\pi$
$541$		−	7.51020i		−	0.322889i	0.986882	−	0.161444i	$-0.0516152\pi$
$542$	7.19550	+	12.4630i	0.309073	+	0.535330i
$543$	11.8098	−	20.4552i	0.506808	−	0.877818i
$544$	−3.47126	−	2.00414i	−0.148829	−	0.0859266i
$545$	6.90968			0.295978
$546$	0.202251	+	0.758536i	0.00865554	+	0.0324624i
$547$	−15.1890			−0.649433			−0.324717	−	0.945811i	$-0.605269\pi$
$547$	−15.1890			−0.649433			−0.324717	+	0.945811i	$0.605269\pi$
$548$	−13.0238	−	7.51928i	−0.556348	−	0.321208i
$549$	26.2313	−	45.4340i	1.11953	−	1.93907i
$550$	−9.28075	−	16.0747i	−0.395732	−	0.685429i
$551$			3.73650i			0.159180i
$552$	2.53412	−	1.46307i	0.107859	−	0.0622725i
$553$	−0.0566365	+	0.0326991i	−0.00240843	+	0.00139051i
$554$			22.4170i			0.952407i
$555$	4.42966	+	7.67240i	0.188029	+	0.325675i
$556$	8.23372	−	14.2612i	0.349187	−	0.604810i
$557$	−17.7880	−	10.2699i	−0.753703	−	0.435151i	0.0733272	−	0.997308i	$-0.476638\pi$
$557$	−17.7880	−	10.2699i	−0.753703	−	0.435151i	−0.827030	+	0.562157i	$0.809972\pi$
$558$	−46.1691			−1.95449
$559$	13.8391	+	3.72640i	0.585332	+	0.157610i
$560$	−0.0974510			−0.00411806
$561$	57.3977	+	33.1386i	2.42333	+	1.39911i
$562$	−2.56200	+	4.43751i	−0.108071	+	0.187185i
$563$	−7.34536	−	12.7225i	−0.309570	−	0.536191i	0.668698	−	0.743534i	$-0.266852\pi$
$563$	−7.34536	−	12.7225i	−0.309570	−	0.536191i	−0.978268	+	0.207343i	$0.933518\pi$
$564$			5.93312i			0.249829i
$565$	7.30002	−	4.21467i	0.307114	−	0.177312i
$566$	−0.600999	+	0.346987i	−0.0252619	+	0.0145849i
$567$		−	0.390831i		−	0.0164134i
$568$	−3.38154	−	5.85700i	−0.141886	−	0.245754i
$569$	7.30417	−	12.6512i	0.306207	−	0.530366i	−0.671322	−	0.741165i	$-0.734273\pi$
$569$	7.30417	−	12.6512i	0.306207	−	0.530366i	0.977529	+	0.210800i	$0.0676067\pi$
$570$	−7.41766	−	4.28259i	−0.310692	−	0.179378i
$571$	32.1199			1.34418			0.672088	−	0.740471i	$-0.265398\pi$
$571$	32.1199			1.34418			0.672088	+	0.740471i	$0.265398\pi$
$572$	14.3891	+	14.4245i	0.601638	+	0.603118i
$573$	−50.1153			−2.09360
$574$	0.218049	+	0.125891i	0.00910119	+	0.00525458i
$575$	1.64237	−	2.84468i	0.0684918	−	0.118631i
$576$	2.78116	+	4.81712i	0.115882	+	0.200713i
$577$		−	27.3646i		−	1.13920i	−0.821921	−	0.569601i	$-0.807098\pi$
$577$		−	27.3646i		−	1.13920i	0.821921	−	0.569601i	$-0.192902\pi$
$578$	−0.808660	+	0.466880i	−0.0336358	+	0.0194197i
$579$	27.5593	−	15.9114i	1.14533	−	0.661255i
$580$			2.18954i			0.0909156i
$581$	0.626062	+	1.08437i	0.0259734	+	0.0449873i
$582$	11.2900	−	19.5549i	0.467987	−	0.810578i
$583$	28.9287	+	16.7020i	1.19810	+	0.691726i
$584$	−2.97670			−0.123177
$585$	−6.82927	+	25.3625i	−0.282356	+	1.04861i
$586$	30.3431			1.25346
$587$	−37.8248	−	21.8381i	−1.56119	−	0.901356i	−0.997137	−	0.0756211i	$-0.975906\pi$
$587$	−37.8248	−	21.8381i	−1.56119	−	0.901356i	−0.564058	−	0.825735i	$-0.690761\pi$
$588$	10.2334	−	17.7248i	0.422019	−	0.730958i
$589$	9.27558	+	16.0658i	0.382194	+	0.661979i
$590$		−	13.9719i		−	0.575214i
$591$	45.5843	−	26.3181i	1.87509	−	1.08258i
$592$	−2.00203	+	1.15588i	−0.0822831	+	0.0475062i
$593$		−	5.91730i		−	0.242994i	−0.992592	−	0.121497i	$-0.961230\pi$
$593$		−	5.91730i		−	0.242994i	0.992592	−	0.121497i	$-0.0387696\pi$
$594$	−21.1842	−	36.6921i	−0.869197	−	1.50549i
$595$	0.195305	−	0.338278i	0.00800673	−	0.0138681i
$596$	−4.78222	−	2.76102i	−0.195887	−	0.113096i
$597$	−35.0076			−1.43277
$598$	−0.937462	+	3.48155i	−0.0383357	+	0.142371i
$599$	19.2853			0.787974			0.393987	−	0.919116i	$-0.371096\pi$
$599$	19.2853			0.787974			0.393987	+	0.919116i	$0.371096\pi$
$600$	8.32394	+	4.80583i	0.339823	+	0.196197i
$601$	4.67769	−	8.10199i	0.190807	−	0.330487i	−0.754711	−	0.656057i	$-0.772223\pi$
$601$	4.67769	−	8.10199i	0.190807	−	0.330487i	0.945518	+	0.325570i	$0.105556\pi$
$602$	0.147886	+	0.256147i	0.00602740	+	0.0104398i
$603$		−	46.3135i		−	1.88603i
$604$	−7.21328	+	4.16459i	−0.293504	+	0.169455i
$605$	23.7410	−	13.7068i	0.965207	−	0.557263i
$606$			3.32660i			0.135134i
$607$	−23.5816	−	40.8446i	−0.957150	−	1.65783i	−0.729371	−	0.684119i	$-0.760187\pi$
$607$	−23.5816	−	40.8446i	−0.957150	−	1.65783i	−0.227779	−	0.973713i	$-0.573146\pi$
$608$	1.11750	−	1.93556i	0.0453205	−	0.0784974i
$609$	0.315237	+	0.182002i	0.0127741	+	0.00737511i
$610$	−12.3526			−0.500141
$611$	−5.16309	−	5.17579i	−0.208876	−	0.209390i
$612$	−22.2953			−0.901235
$613$	−30.8166	−	17.7920i	−1.24467	−	0.718611i	−0.274629	−	0.961550i	$-0.588555\pi$
$613$	−30.8166	−	17.7920i	−1.24467	−	0.718611i	−0.970041	+	0.242940i	$0.921888\pi$
$614$	14.9587	−	25.9091i	0.603682	−	1.04561i
$615$	6.48382	+	11.2303i	0.261453	+	0.452850i
$616$			0.420468i			0.0169412i
$617$	3.67692	−	2.12287i	0.148027	−	0.0854635i	−0.424157	−	0.905589i	$-0.639430\pi$
$617$	3.67692	−	2.12287i	0.148027	−	0.0854635i	0.572184	+	0.820125i	$0.306096\pi$
$618$	−1.09062	+	0.629672i	−0.0438713	+	0.0253291i
$619$		−	15.1830i		−	0.610255i	−0.952312	−	0.305127i	$-0.901301\pi$
$619$		−	15.1830i		−	0.610255i	0.952312	−	0.305127i	$-0.0986991\pi$
$620$	5.43536	+	9.41432i	0.218289	+	0.378088i
$621$	3.74887	−	6.49324i	0.150437	−	0.260565i
$622$	13.5296	+	7.81132i	0.542487	+	0.313205i
$623$	0.483363			0.0193655
$624$	−10.1875	−	2.74315i	−0.407827	−	0.109814i
$625$	2.21332			0.0885330
$626$	12.5321	+	7.23543i	0.500885	+	0.289186i
$627$	−18.4779	+	32.0047i	−0.737937	+	1.27815i
$628$	11.3950	+	19.7367i	0.454710	+	0.787580i
$629$		−	9.26612i		−	0.369464i
$630$	−0.469433	+	0.271027i	−0.0187027	+	0.0107980i
$631$	−13.7568	+	7.94248i	−0.547648	+	0.316185i	−0.748173	−	0.663504i	$-0.769069\pi$
$631$	−13.7568	+	7.94248i	−0.547648	+	0.316185i	0.200525	+	0.979689i	$0.435735\pi$
$632$		−	0.878908i		−	0.0349611i
$633$	20.0620	+	34.7484i	0.797392	+	1.38112i
$634$	9.60919	−	16.6436i	0.381630	−	0.661002i
$635$	14.5677	+	8.41069i	0.578103	+	0.333768i
$636$	−17.2975			−0.685891
$637$	6.49721	+	24.3676i	0.257429	+	0.965479i
$638$	9.44712			0.374015
$639$	−32.5785	−	18.8092i	−1.28879	−	0.744081i
$640$	0.654838	−	1.13421i	0.0258847	−	0.0448337i
$641$	−5.34441	−	9.25679i	−0.211092	−	0.365621i	0.740965	−	0.671544i	$-0.234369\pi$
$641$	−5.34441	−	9.25679i	−0.211092	−	0.365621i	−0.952056	+	0.305922i	$0.901035\pi$
$642$		−	47.7537i		−	1.88469i
$643$	−22.1136	+	12.7673i	−0.872075	+	0.503493i	−0.868037	−	0.496499i	$-0.834619\pi$
$643$	−22.1136	+	12.7673i	−0.872075	+	0.503493i	−0.00403793	+	0.999992i	$0.501285\pi$
$644$	−0.0644396	+	0.0372042i	−0.00253928	+	0.00146605i
$645$			15.2334i			0.599813i
$646$	4.47923	+	7.75826i	0.176233	+	0.305245i
$647$	−22.8774	+	39.6248i	−0.899404	+	1.55781i	−0.0711455	+	0.997466i	$0.522665\pi$
$647$	−22.8774	+	39.6248i	−0.899404	+	1.55781i	−0.828258	+	0.560347i	$0.810668\pi$
$648$	4.54880	+	2.62625i	0.178694	+	0.103169i
$649$	−60.2841			−2.36636
$650$	−11.4435	+	3.05123i	−0.448852	+	0.119679i
$651$	1.80723			0.0708309
$652$	−14.8938	−	8.59895i	−0.583287	−	0.336761i
$653$	13.5632	−	23.4922i	0.530769	−	0.919320i	−0.468586	−	0.883418i	$-0.655236\pi$
$653$	13.5632	−	23.4922i	0.530769	−	0.919320i	0.999355	−	0.0359017i	$-0.0114303\pi$
$654$	7.71898	+	13.3697i	0.301836	+	0.522796i
$655$		−	21.6406i		−	0.845567i
$656$	−2.93043	+	1.69189i	−0.114414	+	0.0660571i
$657$	−14.3391	+	8.27870i	−0.559423	+	0.322983i
$658$		−	0.150872i		−	0.00588161i
$659$	1.04407	+	1.80839i	0.0406713	+	0.0704447i	0.885644	−	0.464364i	$-0.153717\pi$
$659$	1.04407	+	1.80839i	0.0406713	+	0.0704447i	−0.844973	+	0.534809i	$0.820384\pi$
$660$	−10.8278	+	18.7543i	−0.421472	+	0.730011i
$661$	−32.5732	−	18.8061i	−1.26695	−	0.731474i	−0.292540	−	0.956253i	$-0.594501\pi$
$661$	−32.5732	−	18.8061i	−1.26695	−	0.731474i	−0.974410	+	0.224779i	$0.927834\pi$
$662$	−13.9531			−0.542304
$663$	29.9394	−	29.8659i	1.16275	−	1.15990i
$664$	−16.8277			−0.653042
$665$	0.188622	+	0.108901i	0.00731447	+	0.00422301i
$666$	−6.42936	+	11.1360i	−0.249132	+	0.431510i
$667$	0.835909	+	1.44784i	0.0323665	+	0.0560604i
$668$			22.8862i			0.885494i
$669$	−18.9768	+	10.9563i	−0.733687	+	0.423594i
$670$	−9.44377	+	5.45236i	−0.364845	+	0.210643i
$671$			53.2972i			2.05751i
$672$	−0.108865	−	0.188560i	−0.00419956	−	0.00727385i
$673$	9.17398	−	15.8898i	0.353631	−	0.612506i	−0.633252	−	0.773946i	$-0.718280\pi$
$673$	9.17398	−	15.8898i	0.353631	−	0.612506i	0.986883	+	0.161439i	$0.0516136\pi$
$674$	17.6269	+	10.1769i	0.678964	+	0.392000i
$675$	24.6282			0.947940
$676$	11.2743	−	6.47232i	0.433626	−	0.248936i
$677$	20.0899			0.772116			0.386058	−	0.922474i	$-0.373836\pi$
$677$	20.0899			0.772116			0.386058	+	0.922474i	$0.373836\pi$
$678$	16.3101	+	9.41663i	0.626385	+	0.361644i
$679$	−0.287093	+	0.497259i	−0.0110176	+	0.0190831i
$680$	2.62477	+	4.54623i	0.100655	+	0.174340i
$681$		−	66.6753i		−	2.55500i
$682$	40.6196	−	23.4518i	1.55541	−	0.898014i
$683$	22.5558	−	13.0226i	0.863074	−	0.498296i	−0.00196644	−	0.999998i	$-0.500626\pi$
$683$	22.5558	−	13.0226i	0.863074	−	0.498296i	0.865041	+	0.501702i	$0.167293\pi$
$684$		−	12.4318i		−	0.475341i
$685$	9.84782	+	17.0569i	0.376266	+	0.651712i
$686$	−0.520653	+	0.901798i	−0.0198786	+	0.0344308i
$687$	−14.5685	−	8.41114i	−0.555824	−	0.320905i
$688$	−3.97499			−0.151545
$689$	15.0896	−	15.0526i	0.574867	−	0.573457i
$690$	−3.83230			−0.145893
$691$	4.76353	+	2.75023i	0.181213	+	0.104623i	0.587863	−	0.808961i	$-0.299970\pi$
$691$	4.76353	+	2.75023i	0.181213	+	0.104623i	−0.406649	+	0.913584i	$0.633303\pi$
$692$	11.8868	−	20.5885i	0.451868	−	0.782658i
$693$	1.16939	+	2.02545i	0.0444215	+	0.0769403i
$694$			13.6742i			0.519066i
$695$	−18.6776	+	10.7835i	−0.708481	+	0.409042i
$696$	−4.23658	+	2.44599i	−0.160587	+	0.0927150i
$697$		−	13.5631i		−	0.513738i
$698$	7.99268	+	13.8437i	0.302527	+	0.523993i
$699$	−33.1958	+	57.4968i	−1.25558	+	2.17473i
$700$	−0.211668	−	0.122207i	−0.00800030	−	0.00461898i
$701$	−17.4558			−0.659298			−0.329649	−	0.944104i	$-0.606930\pi$
$701$	−17.4558			−0.659298			−0.329649	+	0.944104i	$0.606930\pi$
$702$	−26.1209	+	6.96471i	−0.985871	+	0.262866i
$703$	5.16675			0.194868
$704$	−4.89375	−	2.82541i	−0.184440	−	0.106486i
$705$	3.88523	−	6.72942i	0.146326	−	0.253444i
$706$	6.13117	+	10.6195i	0.230750	+	0.399670i
$707$		−	0.0845915i		−	0.00318139i
$708$	27.0345	−	15.6084i	1.01602	−	0.586599i
$709$	24.1782	−	13.9593i	0.908031	−	0.524252i	0.0282338	−	0.999601i	$-0.491012\pi$
$709$	24.1782	−	13.9593i	0.908031	−	0.524252i	0.879797	+	0.475350i	$0.157678\pi$
$710$			8.85744i			0.332414i
$711$	−2.44439	−	4.23380i	−0.0916717	−	0.158780i
$712$	−3.24804	+	5.62577i	−0.121725	+	0.210835i
$713$	7.18828	+	4.15016i	0.269203	+	0.155425i
$714$	0.872721			0.0326608
$715$	−6.87459	−	25.7830i	−0.257095	−	0.964228i
$716$	1.57806			0.0589748
$717$	7.38603	+	4.26433i	0.275836	+	0.159254i
$718$	11.1195	−	19.2596i	0.414976	−	0.718760i
$719$	17.1888	+	29.7719i	0.641034	+	1.11030i	0.985202	+	0.171396i	$0.0548278\pi$
$719$	17.1888	+	29.7719i	0.641034	+	1.11030i	−0.344168	+	0.938908i	$0.611839\pi$
$720$		−	7.28485i		−	0.271490i
$721$	0.0277333	−	0.0160118i	0.00103284	−	0.000596311i
$722$	12.1285	−	7.00240i	0.451376	−	0.260602i
$723$			85.7204i			3.18798i
$724$	−4.03597	−	6.99050i	−0.149996	−	0.259800i
$725$	−2.74575	+	4.75578i	−0.101975	+	0.176625i
$726$	53.0433	+	30.6246i	1.96862	+	1.13658i
$727$	8.20448			0.304287			0.152144	−	0.988358i	$-0.451382\pi$
$727$	8.20448			0.304287			0.152144	+	0.988358i	$0.451382\pi$
$728$	0.259057	+	0.0697552i	0.00960128	+	0.00258530i
$729$	−36.6023			−1.35564
$730$	3.37621	+	1.94926i	0.124959	+	0.0721453i
$731$	7.96642	−	13.7982i	0.294649	−	0.510346i
$732$	−13.7994	−	23.9012i	−0.510039	−	0.883414i
$733$		−	18.0318i		−	0.666020i	−0.942923	−	0.333010i	$-0.891936\pi$
$733$		−	18.0318i		−	0.666020i	0.942923	−	0.333010i	$-0.108064\pi$
$734$	20.1326	−	11.6235i	0.743107	−	0.429033i
$735$	−23.2137	+	13.4024i	−0.856251	+	0.494357i
$736$		−	1.00000i		−	0.0368605i
$737$	23.5251	+	40.7467i	0.866559	+	1.50092i
$738$	−9.41083	+	16.3000i	−0.346417	+	0.600012i
$739$	−15.8628	−	9.15837i	−0.583521	−	0.336896i	0.179010	−	0.983847i	$-0.442710\pi$
$739$	−15.8628	−	9.15837i	−0.583521	−	0.336896i	−0.762532	+	0.646951i	$0.776044\pi$
$740$	3.02764			0.111298
$741$	16.6531	+	16.6941i	0.611767	+	0.613272i
$742$	0.439855			0.0161476
$743$	26.3111	+	15.1907i	0.965260	+	0.557293i	0.897788	−	0.440428i	$-0.145173\pi$
$743$	26.3111	+	15.1907i	0.965260	+	0.557293i	0.0674719	+	0.997721i	$0.478507\pi$
$744$	−12.1440	+	21.0340i	−0.445219	+	0.771143i
$745$	3.61604	+	6.26316i	0.132481	+	0.229464i
$746$		−	10.0031i		−	0.366240i
$747$	−81.0611	+	46.8006i	−2.96587	+	1.71235i
$748$	19.6155	−	11.3250i	0.717212	−	0.414083i
$749$			1.21432i			0.0443704i
$750$	−15.8748	−	27.4960i	−0.579667	−	1.00401i
$751$	16.1298	−	27.9376i	0.588583	−	1.01946i	−0.405835	−	0.913946i	$-0.633019\pi$
$751$	16.1298	−	27.9376i	0.588583	−	1.01946i	0.994418	−	0.105510i	$-0.0336473\pi$
$752$	1.75597	+	1.01381i	0.0640337	+	0.0369699i
$753$	70.3019			2.56194
$754$	1.56727	−	5.82051i	0.0570765	−	0.211970i
$755$	10.9085			0.397002
$756$	−0.483152	−	0.278948i	−0.0175721	−	0.0101452i
$757$	−1.45951	+	2.52794i	−0.0530467	+	0.0918795i	−0.891329	−	0.453356i	$-0.850227\pi$
$757$	−1.45951	+	2.52794i	−0.0530467	+	0.0918795i	0.838283	+	0.545236i	$0.183560\pi$
$758$	6.36264	+	11.0204i	0.231102	+	0.400280i
$759$			16.5351i			0.600186i
$760$	−2.53496	+	1.46356i	−0.0919526	+	0.0530889i
$761$	−14.2481	+	8.22614i	−0.516493	+	0.298197i	−0.735498	−	0.677526i	$-0.763052\pi$
$761$	−14.2481	+	8.22614i	−0.516493	+	0.298197i	0.219006	+	0.975724i	$0.429719\pi$
$762$			37.5832i			1.36150i
$763$	−0.196285	−	0.339975i	−0.00710599	−	0.0123079i
$764$	−8.56336	+	14.8322i	−0.309811	+	0.536609i
$765$	25.2876	+	14.5998i	0.914276	+	0.527858i
$766$	0.935598			0.0338045
$767$	−10.0011	+	37.1419i	−0.361117	+	1.34112i
$768$	2.92615			0.105588
$769$	−22.6016	−	13.0491i	−0.815036	−	0.470561i	0.0336657	−	0.999433i	$-0.489282\pi$
$769$	−22.6016	−	13.0491i	−0.815036	−	0.470561i	−0.848702	+	0.528872i	$0.822615\pi$
$770$	0.275339	−	0.476900i	0.00992251	−	0.0171863i
$771$	35.7016	+	61.8370i	1.28576	+	2.22700i
$772$		−	10.8753i		−	0.391411i
$773$	−24.8921	+	14.3715i	−0.895307	+	0.516906i	−0.875675	−	0.482901i	$-0.839583\pi$
$773$	−24.8921	+	14.3715i	−0.895307	+	0.516906i	−0.0196326	+	0.999807i	$0.506250\pi$
$774$	−19.1480	+	11.0551i	−0.688260	+	0.397367i
$775$			27.2645i			0.979368i
$776$	−3.85833	−	6.68283i	−0.138506	−	0.239900i
$777$	0.251669	−	0.435903i	0.00902857	−	0.0156379i
$778$	−15.6826	−	9.05436i	−0.562249	−	0.324614i
$779$	7.56272			0.270962
$780$	9.75848	+	9.78248i	0.349410	+	0.350269i
$781$	38.2169			1.36751
$782$	3.47126	+	2.00414i	0.124132	+	0.0716677i
$783$	−6.26743	+	10.8555i	−0.223980	+	0.387944i
$784$	−3.49723	−	6.05738i	−0.124901	−	0.216335i
$785$		−	29.8475i		−	1.06530i
$786$	41.8727	−	24.1752i	1.49355	−	0.862302i
$787$	35.9004	−	20.7271i	1.27971	−	0.738842i	0.302917	−	0.953017i	$-0.402040\pi$
$787$	35.9004	−	20.7271i	1.27971	−	0.738842i	0.976795	+	0.214175i	$0.0687063\pi$
$788$		−	17.9882i		−	0.640805i
$789$	3.07784	+	5.33097i	0.109574	+	0.189788i
$790$	−0.575542	+	0.996868i	−0.0204769	+	0.0354670i
$791$	−0.414747	−	0.239454i	−0.0147467	−	0.00851401i
$792$	−31.4317			−1.11688
$793$	32.8372	+	8.84193i	1.16608	+	0.313986i
$794$	−5.67436			−0.201375
$795$	19.6190	+	11.3271i	0.695816	+	0.401729i
$796$	−5.98186	+	10.3609i	−0.212021	+	0.367232i
$797$	−22.2752	−	38.5818i	−0.789028	−	1.36664i	−0.926563	−	0.376139i	$-0.877251\pi$
$797$	−22.2752	−	38.5818i	−0.789028	−	1.36664i	0.137535	−	0.990497i	$-0.456082\pi$
$798$			0.486626i			0.0172264i
$799$	−7.03841	+	4.06363i	−0.249001	+	0.143761i
$800$	2.84468	−	1.64237i	0.100574	−	0.0580667i
$801$			36.1333i			1.27671i
$802$	15.1069	+	26.1659i	0.533444	+	0.923952i
$803$	8.41040	−	14.5672i	0.296796	−	0.514066i
$804$	−21.0998	−	12.1820i	−0.744131	−	0.429624i
$805$	0.0974510			0.00343470
$806$	−7.71022	−	28.9170i	−0.271581	−	1.01856i
$807$	−30.5471			−1.07531
$808$	0.984544	+	0.568427i	0.0346361	+	0.0199972i
$809$	−2.75230	+	4.76713i	−0.0967658	+	0.167603i	−0.910344	−	0.413852i	$-0.864183\pi$
$809$	−2.75230	+	4.76713i	−0.0967658	+	0.167603i	0.813578	+	0.581455i	$0.197516\pi$
$810$	−3.43954	−	5.95746i	−0.120853	−	0.209324i
$811$		−	2.30485i		−	0.0809341i	−0.999181	−	0.0404670i	$-0.987115\pi$
$811$		−	2.30485i		−	0.0809341i	0.999181	−	0.0404670i	$-0.0128846\pi$
$812$	0.107731	−	0.0621987i	0.00378063	−	0.00218275i
$813$	36.4684	−	21.0551i	1.27900	−	0.738433i
$814$		−	13.0633i		−	0.457867i
$815$	11.2618	+	19.5061i	0.394485	+	0.683268i
$816$	−5.86439	+	10.1574i	−0.205295	+	0.355581i
$817$	7.69384	+	4.44204i	0.269173	+	0.155407i
$818$	−23.1247			−0.808537
$819$	1.44191	−	0.384460i	0.0503843	−	0.0134341i
$820$	4.43165			0.154760
$821$	−42.1461	−	24.3331i	−1.47091	−	0.849230i	−0.471444	−	0.881896i	$-0.656267\pi$
$821$	−42.1461	−	24.3331i	−1.47091	−	0.849230i	−0.999466	+	0.0326655i	$0.989600\pi$
$822$	−22.0025	+	38.1095i	−0.767426	+	1.32922i
$823$	−16.8908	−	29.2556i	−0.588775	−	1.01979i	−0.994393	−	0.105745i	$-0.966277\pi$
$823$	−16.8908	−	29.2556i	−0.588775	−	1.01979i	0.405619	−	0.914042i	$-0.367056\pi$
$824$			0.430376i			0.0149929i
$825$	−47.0370	+	27.1568i	−1.63762	+	0.945479i
$826$	−0.687456	+	0.396903i	−0.0239197	+	0.0138100i
$827$			48.8546i			1.69884i	0.527716	+	0.849421i	$0.323048\pi$
$827$			48.8546i			1.69884i	−0.527716	+	0.849421i	$0.676952\pi$
$828$	−2.78116	−	4.81712i	−0.0966521	−	0.167406i
$829$	25.5499	−	44.2537i	0.887384	−	1.53699i	0.0444265	−	0.999013i	$-0.485854\pi$
$829$	25.5499	−	44.2537i	0.887384	−	1.53699i	0.842957	−	0.537981i	$-0.180813\pi$
$830$	19.0862	+	11.0194i	0.662492	+	0.382490i
$831$	65.5954			2.27548
$832$	−2.55264	+	2.54638i	−0.0884968	+	0.0882797i
$833$	28.0357			0.971380
$834$	−41.7304	−	24.0931i	−1.44501	−	0.834274i
$835$	14.9868	−	25.9578i	0.518638	−	0.898308i
$836$	6.31477	+	10.9375i	0.218401	+	0.378281i
$837$			62.2336i			2.15111i
$838$	−8.81239	+	5.08784i	−0.304419	+	0.175756i
$839$	−31.2432	+	18.0383i	−1.07864	+	0.622751i	−0.930528	−	0.366220i	$-0.880652\pi$
$839$	−31.2432	+	18.0383i	−1.07864	+	0.622751i	−0.148108	+	0.988971i	$0.547318\pi$
$840$			0.285156i			0.00983881i
$841$	13.1025	+	22.6942i	0.451811	+	0.782559i
$842$	8.35854	−	14.4774i	0.288054	−	0.498925i
$843$	12.9848	+	7.49678i	0.447221	+	0.258203i
$844$	13.7122			0.471994
$845$	−17.0257	−	0.0418252i	−0.585703	−	0.00143883i
$846$	11.2783			0.387756
$847$	−1.34883	−	0.778747i	−0.0463463	−	0.0267581i
$848$	−2.95568	+	5.11939i	−0.101498	+	0.175801i
$849$	1.01533	+	1.75861i	0.0348462	+	0.0603553i
$850$			13.1662i			0.451596i
$851$	2.00203	−	1.15588i	0.0686289	−	0.0396229i
$852$	−17.1384	+	9.89487i	−0.587153	+	0.338993i
$853$			10.0032i			0.342504i	0.985227	+	0.171252i	$0.0547812\pi$
$853$			10.0032i			0.342504i	−0.985227	+	0.171252i	$0.945219\pi$
$854$	0.350902	+	0.607780i	0.0120076	+	0.0207978i
$855$	−8.14080	+	14.1003i	−0.278409	+	0.482219i
$856$	−14.1333	−	8.15984i	−0.483065	−	0.278898i
$857$	−40.9989			−1.40050			−0.700248	−	0.713899i	$-0.746927\pi$
$857$	−40.9989			−1.40050			−0.700248	+	0.713899i	$0.746927\pi$
$858$	42.2081	−	42.1046i	1.44096	−	1.43743i
$859$	−14.9069			−0.508616			−0.254308	−	0.967123i	$-0.581848\pi$
$859$	−14.9069			−0.508616			−0.254308	+	0.967123i	$0.581848\pi$
$860$	4.50848	+	2.60297i	0.153738	+	0.0887606i
$861$	0.368375	−	0.638043i	0.0125542	−	0.0217445i
$862$	−12.4358	−	21.5395i	−0.423565	−	0.733637i
$863$			44.8274i			1.52594i	0.646432	+	0.762972i	$0.276260\pi$
$863$			44.8274i			1.52594i	−0.646432	+	0.762972i	$0.723740\pi$
$864$	6.49324	−	3.74887i	0.220904	−	0.127539i
$865$	−26.9643	+	15.5678i	−0.916813	+	0.529322i
$866$		−	3.48330i		−	0.118367i
$867$	1.36616	+	2.36626i	0.0463972	+	0.0803623i
$868$	0.308807	−	0.534869i	0.0104816	−	0.0181546i
$869$	4.30115	+	2.48327i	0.145907	+	0.0842392i
$870$	6.40691			0.217215
$871$	29.0074	−	7.73434i	0.982879	−	0.262068i
$872$	5.27587			0.178664
$873$	−37.1721	−	21.4613i	−1.25808	−	0.726355i
$874$	−1.11750	+	1.93556i	−0.0377999	+	0.0654714i
$875$	0.403679	+	0.699192i	0.0136468	+	0.0236370i
$876$			8.71027i			0.294293i
$877$	−8.54526	+	4.93361i	−0.288553	+	0.166596i	−0.637289	−	0.770625i	$-0.719944\pi$
$877$	−8.54526	+	4.93361i	−0.288553	+	0.166596i	0.348736	+	0.937221i	$0.386611\pi$
$878$	−15.8437	+	9.14734i	−0.534698	+	0.308708i
$879$		−	88.7883i		−	2.99476i
$880$	3.70037	+	6.40922i	0.124739	+	0.216055i
$881$	−16.0498	+	27.7991i	−0.540732	+	0.936575i	0.458130	+	0.888885i	$0.348519\pi$
$881$	−16.0498	+	27.7991i	−0.540732	+	0.936575i	−0.998862	+	0.0476902i	$0.984814\pi$
$882$	−33.6931	−	19.4527i	−1.13451	−	0.655008i
$883$	37.8928			1.27519			0.637596	−	0.770371i	$-0.279929\pi$
$883$	37.8928			1.27519			0.637596	+	0.770371i	$0.279929\pi$
$884$	−3.72331	−	13.9642i	−0.125228	−	0.469666i
$885$	−40.8838			−1.37429
$886$	17.8469	+	10.3039i	0.599578	+	0.346166i
$887$	6.40491	−	11.0936i	0.215056	−	0.372487i	−0.738234	−	0.674545i	$-0.764340\pi$
$887$	6.40491	−	11.0936i	0.215056	−	0.372487i	0.953290	+	0.302057i	$0.0976734\pi$
$888$	3.38226	+	5.85824i	0.113501	+	0.196590i
$889$		−	0.955697i		−	0.0320530i
$890$	7.36793	−	4.25388i	0.246974	−	0.142590i
$891$	−25.7044	+	14.8405i	−0.861131	+	0.497174i
$892$			7.48854i			0.250735i
$893$	−2.26586	−	3.92459i	−0.0758242	−	0.131331i
$894$	−8.07914	+	13.9935i	−0.270207	+	0.468012i
$895$	−1.78985	−	1.03337i	−0.0598282	−	0.0345418i
$896$	−0.0744085			−0.00248581
$897$	10.1875	+	2.74315i	0.340151	+	0.0915912i
$898$	12.6977			0.423728
$899$	−12.0175	−	6.93831i	−0.400806	−	0.231405i
$900$	9.13543	−	15.8230i	0.304514	−	0.527434i
$901$	−11.8472	−	20.5199i	−0.394686	−	0.683617i
$902$		−	19.1211i		−	0.636662i
$903$	0.749523	−	0.432737i	0.0249426	−	0.0144006i
$904$	5.57392	−	3.21810i	0.185386	−	0.107032i
$905$			10.5716i			0.351412i
$906$	12.1862	+	21.1071i	0.404859	+	0.701237i
$907$	−28.3035	+	49.0231i	−0.939802	+	1.62778i	−0.173962	+	0.984752i	$0.555657\pi$
$907$	−28.3035	+	49.0231i	−0.939802	+	1.62778i	−0.765839	+	0.643032i	$0.777676\pi$
$908$	−19.7333	−	11.3930i	−0.654872	−	0.378091i
$909$	6.32355			0.209739
$910$	−0.248147	−	0.248757i	−0.00822599	−	0.00824622i
$911$	10.2317			0.338991			0.169495	−	0.985531i	$-0.445786\pi$
$911$	10.2317			0.338991			0.169495	+	0.985531i	$0.445786\pi$
$912$	−5.66374	−	3.26996i	−0.187545	−	0.108279i
$913$	47.5451	−	82.3506i	1.57351	−	2.72541i
$914$	−12.0074	−	20.7974i	−0.397169	−	0.687917i
$915$			36.1454i			1.19493i
$916$	−4.97874	+	2.87448i	−0.164502	+	0.0949755i
$917$	−1.06478	+	0.614748i	−0.0351620	+	0.0203008i
$918$			30.0530i			0.991897i
$919$	−15.3188	−	26.5329i	−0.505320	−	0.875240i	−0.999981	−	0.00615373i	$-0.998041\pi$
$919$	−15.3188	−	26.5329i	−0.505320	−	0.875240i	0.494661	−	0.869086i	$-0.335292\pi$
$920$	−0.654838	+	1.13421i	−0.0215894	+	0.0373939i
$921$	−75.8139	−	43.7712i	−2.49815	−	1.44231i
$922$	−19.2340			−0.633438
$923$	6.34013	−	23.5460i	0.208688	−	0.775025i
$924$	1.23035			0.0404756
$925$	6.57618	+	3.79676i	0.216224	+	0.124837i
$926$	12.9931	−	22.5048i	0.426981	−	0.739552i
$927$	1.19695	+	2.07317i	0.0393129	+	0.0680919i
$928$			1.67182i			0.0548801i
$929$	−7.48871	+	4.32361i	−0.245697	+	0.141853i	−0.617792	−	0.786341i	$-0.711973\pi$
$929$	−7.48871	+	4.32361i	−0.245697	+	0.141853i	0.372096	+	0.928194i	$0.378639\pi$
$930$	27.5477	−	15.9047i	0.903324	−	0.521534i
$931$			15.6326i			0.512337i
$932$	11.3445	+	19.6493i	0.371603	+	0.643635i
$933$	22.8570	−	39.5896i	0.748306	−	1.29610i
$934$	30.0861	+	17.3702i	0.984448	+	0.568371i
$935$	−29.6641			−0.970121
$936$	−5.21447	+	19.3655i	−0.170440	+	0.632981i
$937$	−14.5176			−0.474269			−0.237135	−	0.971477i	$-0.576208\pi$
$937$	−14.5176			−0.474269			−0.237135	+	0.971477i	$0.576208\pi$
$938$	0.536542	+	0.309773i	0.0175187	+	0.0101144i
$939$	21.1719	−	36.6709i	0.690920	−	1.19671i
$940$	−1.32776	−	2.29975i	−0.0433069	−	0.0750097i
$941$		−	4.02428i		−	0.131188i	−0.997846	−	0.0655939i	$-0.979106\pi$
$941$		−	4.02428i		−	0.131188i	0.997846	−	0.0655939i	$-0.0208942\pi$
$942$	57.7525	−	33.3434i	1.88168	−	1.08639i
$943$	2.93043	−	1.69189i	0.0954280	−	0.0550954i
$944$		−	10.6682i		−	0.347221i
$945$	0.365331	+	0.632772i	0.0118842	+	0.0205841i
$946$	11.2310	−	19.4526i	0.365150	−	0.632458i
$947$	11.9542	+	6.90174i	0.388458	+	0.224277i	0.681492	−	0.731826i	$-0.261331\pi$
$947$	11.9542	+	6.90174i	0.388458	+	0.224277i	−0.293034	+	0.956102i	$0.594665\pi$
$948$	−2.57181			−0.0835286
$949$	−7.57981	−	7.59845i	−0.246051	−	0.246656i
$950$	−7.34140			−0.238186
$951$	−48.7016	−	28.1179i	−1.57926	−	0.911785i
$952$	0.149125	−	0.258292i	0.00483316	−	0.00837128i
$953$	2.82416	+	4.89158i	0.0914834	+	0.158454i	0.908136	−	0.418676i	$-0.137506\pi$
$953$	2.82416	+	4.89158i	0.0914834	+	0.158454i	−0.816652	+	0.577130i	$0.804172\pi$
$954$			32.8809i			1.06456i
$955$	19.4253	−	11.2152i	0.628589	−	0.362916i
$956$	2.52415	−	1.45732i	0.0816368	−	0.0471331i
$957$		−	27.6437i		−	0.893593i
$958$	16.9224	+	29.3104i	0.546738	+	0.946977i
$959$	0.559498	−	0.969079i	0.0180671	−	0.0312932i
$960$	−3.31887	−	1.91615i	−0.107116	−	0.0618435i
$961$	−37.8952			−1.22243
$962$	−8.04847	−	2.16718i	−0.259493	−	0.0698727i
$963$	−90.7754			−2.92520
$964$	25.3699	+	14.6473i	0.817110	+	0.471758i
$965$	−7.12157	+	12.3349i	−0.229252	+	0.397075i
$966$	0.108865	+	0.188560i	0.00350267	+	0.00606681i
$967$			59.0748i			1.89972i	0.312677	+	0.949859i	$0.398774\pi$
$967$			59.0748i			1.89972i	−0.312677	+	0.949859i	$0.601226\pi$
$968$	18.1274	−	10.4658i	0.582635	−	0.336385i
$969$	22.7018	−	13.1069i	0.729287	−	0.421054i
$970$			10.1063i			0.324495i
$971$	11.6517	+	20.1813i	0.373920	+	0.647648i	0.990165	−	0.139907i	$-0.0446803\pi$
$971$	11.6517	+	20.1813i	0.373920	+	0.647648i	−0.616245	+	0.787554i	$0.711347\pi$
$972$	−3.56182	+	6.16925i	−0.114245	+	0.197879i
$973$	1.06116	+	0.612659i	0.0340191	+	0.0196409i
$974$	22.8309			0.731549
$975$	8.92833	+	33.4855i	0.285935	+	1.07239i
$976$	−9.43177			−0.301904
$977$	10.8377	+	6.25712i	0.346727	+	0.200183i	0.663243	−	0.748404i	$-0.269180\pi$
$977$	10.8377	+	6.25712i	0.346727	+	0.200183i	−0.316516	+	0.948587i	$0.602513\pi$
$978$	−25.1618	+	43.5815i	−0.804585	+	1.39358i
$979$	−18.3541	−	31.7902i	−0.586598	−	1.01602i
$980$			9.16048i			0.292621i
$981$	25.4145	−	14.6731i	0.811422	−	0.468475i
$982$	−9.69897	+	5.59970i	−0.309507	+	0.178694i
$983$		−	22.6668i		−	0.722960i	−0.932380	−	0.361480i	$-0.882272\pi$
$983$		−	22.6668i		−	0.722960i	0.932380	−	0.361480i	$-0.117728\pi$
$984$	4.95071	+	8.57487i	0.157823	+	0.273357i
$985$	−11.7794	+	20.4025i	−0.375322	+	0.650077i
$986$	−5.80332	−	3.35055i	−0.184815	−	0.106703i
$987$	−0.441474			−0.0140523
$988$	7.78636	−	2.07610i	0.247717	−	0.0660496i
$989$	3.97499			0.126397
$990$	35.6502	+	20.5826i	1.13304	+	0.654159i
$991$	13.1428	−	22.7641i	0.417496	−	0.723124i	−0.578191	−	0.815902i	$-0.696241\pi$
$991$	13.1428	−	22.7641i	0.417496	−	0.723124i	0.995687	+	0.0927771i	$0.0295744\pi$
$992$	4.15016	+	7.18828i	0.131768	+	0.228228i
$993$			40.8289i			1.29566i
$994$	0.435810	−	0.251615i	0.0138231	−	0.00798075i
$995$	13.5694	−	7.83430i	0.430179	−	0.248364i
$996$			49.2403i			1.56024i
$997$	16.6433	+	28.8270i	0.527098	+	0.912960i	0.999501	+	0.0315779i	$0.0100532\pi$
$997$	16.6433	+	28.8270i	0.527098	+	0.912960i	−0.472403	+	0.881382i	$0.656613\pi$
$998$	−13.0317	+	22.5715i	−0.412511	+	0.714490i
$999$	15.0107	+	8.66646i	0.474919	+	0.274195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	598.2.h.c.277.1	yes	28
13.6	odd	12		7774.2.a.bm.1.14		14
13.7	odd	12		7774.2.a.bl.1.14		14
13.10	even	6	inner	598.2.h.c.231.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
598.2.h.c.231.1	✓	28	13.10	even	6	inner
598.2.h.c.277.1	yes	28	1.1	even	1	trivial
7774.2.a.bl.1.14		14	13.7	odd	12
7774.2.a.bm.1.14		14	13.6	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 598 = 2 \cdot 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	598.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.46307 + 2.53412i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.30968i q^{5} +(2.53412 - 1.46307i) q^{6} +(-0.0644396 + 0.0372042i) q^{7} -1.00000i q^{8} +(-2.78116 - 4.81712i) q^{9} +(-0.654838 + 1.13421i) q^{10} +(4.89375 + 2.82541i) q^{11} -2.92615 q^{12} +(2.55264 - 2.54638i) q^{13} +0.0744085 q^{14} +(3.31887 + 1.91615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00414 - 3.47126i) q^{17} +5.56233i q^{18} +(1.93556 - 1.11750i) q^{19} +(1.13421 - 0.654838i) q^{20} -0.217730i q^{21} +(-2.82541 - 4.89375i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.53412 + 1.46307i) q^{24} +3.28475 q^{25} +(-3.48384 + 0.928907i) q^{26} +7.49774 q^{27} +(-0.0644396 - 0.0372042i) q^{28} +(-0.835909 + 1.44784i) q^{29} +(-1.91615 - 3.31887i) q^{30} +8.30032i q^{31} +(0.866025 - 0.500000i) q^{32} +(-14.3198 + 8.26755i) q^{33} +4.00827i q^{34} +(0.0487255 + 0.0843950i) q^{35} +(2.78116 - 4.81712i) q^{36} +(2.00203 + 1.15588i) q^{37} -2.23499 q^{38} +(2.71812 + 10.1942i) q^{39} -1.30968 q^{40} +(2.93043 + 1.69189i) q^{41} +(-0.108865 + 0.188560i) q^{42} +(1.98749 + 3.44244i) q^{43} +5.65081i q^{44} +(-6.30886 + 3.64242i) q^{45} +(-0.866025 + 0.500000i) q^{46} -2.02762i q^{47} +(-1.46307 - 2.53412i) q^{48} +(-3.49723 + 6.05738i) q^{49} +(-2.84468 - 1.64237i) q^{50} +11.7288 q^{51} +(3.48155 + 0.937462i) q^{52} +5.91136 q^{53} +(-6.49324 - 3.74887i) q^{54} +(3.70037 - 6.40922i) q^{55} +(0.0372042 + 0.0644396i) q^{56} +6.53992i q^{57} +(1.44784 - 0.835909i) q^{58} +(-9.23895 + 5.33411i) q^{59} +3.83230i q^{60} +(4.71589 + 8.16816i) q^{61} +(4.15016 - 7.18828i) q^{62} +(0.358434 + 0.206942i) q^{63} -1.00000 q^{64} +(-3.33493 - 3.34313i) q^{65} +16.5351 q^{66} +(7.21077 + 4.16314i) q^{67} +(2.00414 - 3.47126i) q^{68} +(1.46307 + 2.53412i) q^{69} -0.0974510i q^{70} +(5.85700 - 3.38154i) q^{71} +(-4.81712 + 2.78116i) q^{72} -2.97670i q^{73} +(-1.15588 - 2.00203i) q^{74} +(-4.80583 + 8.32394i) q^{75} +(1.93556 + 1.11750i) q^{76} -0.420468 q^{77} +(2.74315 - 10.1875i) q^{78} +0.878908 q^{79} +(1.13421 + 0.654838i) q^{80} +(-2.62625 + 4.54880i) q^{81} +(-1.69189 - 2.93043i) q^{82} -16.8277i q^{83} +(0.188560 - 0.108865i) q^{84} +(-4.54623 + 2.62477i) q^{85} -3.97499i q^{86} +(-2.44599 - 4.23658i) q^{87} +(2.82541 - 4.89375i) q^{88} +(-5.62577 - 3.24804i) q^{89} +7.28485 q^{90} +(-0.0697552 + 0.259057i) q^{91} +1.00000 q^{92} +(-21.0340 - 12.1440i) q^{93} +(-1.01381 + 1.75597i) q^{94} +(-1.46356 - 2.53496i) q^{95} +2.92615i q^{96} +(6.68283 - 3.85833i) q^{97} +(6.05738 - 3.49723i) q^{98} -31.4317i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 14 q^{4} - 6 q^{9} + 8 q^{10} - 8 q^{12} + 2 q^{13} + 4 q^{14} + 12 q^{15} - 14 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{22} + 14 q^{23} - 28 q^{25} - 10 q^{26} + 20 q^{27} - 14 q^{29} + 8 q^{30}+ \cdots + 12 q^{98}+O(q^{100}) \) 28 * q - 4 * q^3 + 14 * q^4 - 6 * q^9 + 8 * q^10 - 8 * q^12 + 2 * q^13 + 4 * q^14 + 12 * q^15 - 14 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^22 + 14 * q^23 - 28 * q^25 - 10 * q^26 + 20 * q^27 - 14 * q^29 + 8 * q^30 + 18 * q^33 + 18 * q^35 + 6 * q^36 - 12 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^40 + 24 * q^41 - 6 * q^42 + 12 * q^43 - 36 * q^45 - 4 * q^48 + 36 * q^49 - 36 * q^50 - 12 * q^51 - 2 * q^52 + 8 * q^53 - 18 * q^54 - 12 * q^55 + 2 * q^56 + 18 * q^58 - 30 * q^59 + 6 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^64 - 66 * q^65 + 44 * q^66 + 42 * q^67 + 2 * q^68 + 4 * q^69 - 60 * q^71 + 44 * q^75 - 12 * q^76 + 16 * q^77 - 48 * q^78 + 68 * q^79 + 2 * q^81 + 40 * q^82 + 42 * q^84 - 72 * q^85 + 10 * q^87 + 12 * q^88 - 6 * q^89 - 36 * q^90 + 4 * q^91 + 28 * q^92 + 60 * q^93 - 26 * q^94 + 16 * q^95 - 12 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more