LMFDB - Embedded newform 850.2.v.d.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			607.1
Character	$\chi$	$=$	850.607
Dual form			850.2.v.d.843.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 + 0.923880i) q^{2} +(-0.567062 + 2.85081i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-2.41680 - 1.61486i) q^{6} +(-3.60477 - 2.40863i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-5.03395 - 2.08513i) q^{9} +(-0.113862 + 0.170406i) q^{11} +(2.41680 - 1.61486i) q^{12} -3.32855 q^{13} +(3.60477 - 2.40863i) q^{14} +1.00000i q^{16} +(4.05227 + 0.761002i) q^{17} +(3.85282 - 3.85282i) q^{18} +(1.76021 - 0.729105i) q^{19} +(8.91069 - 8.91069i) q^{21} +(-0.113862 - 0.170406i) q^{22} +(0.769445 - 0.153052i) q^{23} +(0.567062 + 2.85081i) q^{24} +(1.27378 - 3.07518i) q^{26} +(3.95431 - 5.91804i) q^{27} +(0.845799 + 4.25212i) q^{28} +(8.95670 + 1.78160i) q^{29} +(-4.85565 - 7.26699i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-0.421230 - 0.421230i) q^{33} +(-2.25381 + 3.45258i) q^{34} +(2.08513 + 5.03395i) q^{36} +(1.88413 + 0.374777i) q^{37} +1.90524i q^{38} +(1.88750 - 9.48908i) q^{39} +(-3.42967 + 0.682203i) q^{41} +(4.82243 + 11.6424i) q^{42} +(-2.60772 - 6.29559i) q^{43} +(0.201008 - 0.0399830i) q^{44} +(-0.153052 + 0.769445i) q^{46} -11.8186i q^{47} +(-2.85081 - 0.567062i) q^{48} +(4.51409 + 10.8980i) q^{49} +(-4.46736 + 11.1207i) q^{51} +(2.35364 + 2.35364i) q^{52} +(-4.78009 - 1.97998i) q^{53} +(3.95431 + 5.91804i) q^{54} +(-4.25212 - 0.845799i) q^{56} +(1.08039 + 5.43149i) q^{57} +(-5.07356 + 7.59313i) q^{58} +(-1.58062 + 3.81596i) q^{59} +(0.209544 + 1.05345i) q^{61} +(8.57200 - 1.70508i) q^{62} +(13.1239 + 19.6413i) q^{63} +(0.707107 - 0.707107i) q^{64} +(0.550364 - 0.227968i) q^{66} +(5.49540 - 5.49540i) q^{67} +(-2.32728 - 3.40350i) q^{68} +2.28034i q^{69} +(-1.33556 + 0.892391i) q^{71} -5.44870 q^{72} +(0.677883 - 0.452947i) q^{73} +(-1.06727 + 1.59729i) q^{74} +(-1.76021 - 0.729105i) q^{76} +(0.820892 - 0.340025i) q^{77} +(8.04446 + 5.37513i) q^{78} +(-10.3045 - 6.88525i) q^{79} +(3.07044 + 3.07044i) q^{81} +(0.682203 - 3.42967i) q^{82} +(0.269470 - 0.650559i) q^{83} -12.6016 q^{84} +6.81430 q^{86} +(-10.1580 + 24.5236i) q^{87} +(-0.0399830 + 0.201008i) q^{88} +(-3.70552 - 3.70552i) q^{89} +(11.9987 + 8.01725i) q^{91} +(-0.652304 - 0.435856i) q^{92} +(23.4703 - 9.72172i) q^{93} +(10.9189 + 4.52277i) q^{94} +(1.61486 - 2.41680i) q^{96} +(-0.124830 + 0.0834089i) q^{97} -11.7959 q^{98} +(0.928493 - 0.620400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$3$	−0.567062	+	2.85081i	−0.327394	+	1.64592i	0.369855	+	0.929089i	$0.379407\pi$
$3$	−0.567062	+	2.85081i	−0.327394	+	1.64592i	−0.697249	+	0.716829i	$0.745593\pi$
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$		0			0
$5$		0			0
$6$	−2.41680	−	1.61486i	−0.986656	−	0.659263i
$7$	−3.60477	−	2.40863i	−1.36248	−	0.910377i	−0.362707	−	0.931903i	$-0.618148\pi$
$7$	−3.60477	−	2.40863i	−1.36248	−	0.910377i	−0.999768	+	0.0215260i	$0.993148\pi$
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−5.03395	−	2.08513i	−1.67798	−	0.695043i
$10$		0			0
$11$	−0.113862	+	0.170406i	−0.0343306	+	0.0513794i	−0.848238	−	0.529615i	$-0.822336\pi$
$11$	−0.113862	+	0.170406i	−0.0343306	+	0.0513794i	0.813907	+	0.580995i	$0.197336\pi$
$12$	2.41680	−	1.61486i	0.697671	−	0.466169i
$13$	−3.32855			−0.923174			−0.461587	−	0.887095i	$-0.652720\pi$
$13$	−3.32855			−0.923174			−0.461587	+	0.887095i	$0.652720\pi$
$14$	3.60477	−	2.40863i	0.963416	−	0.643734i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	4.05227	+	0.761002i	0.982819	+	0.184570i
$17$	4.05227	+	0.761002i	0.982819	+	0.184570i
$18$	3.85282	−	3.85282i	0.908117	−	0.908117i
$19$	1.76021	−	0.729105i	0.403821	−	0.167268i	−0.171522	−	0.985180i	$-0.554869\pi$
$19$	1.76021	−	0.729105i	0.403821	−	0.167268i	0.575343	+	0.817912i	$0.304869\pi$
$20$		0			0
$21$	8.91069	−	8.91069i	1.94447	−	1.94447i
$22$	−0.113862	−	0.170406i	−0.0242754	−	0.0363307i
$23$	0.769445	−	0.153052i	0.160440	−	0.0319136i	−0.114216	−	0.993456i	$-0.536436\pi$
$23$	0.769445	−	0.153052i	0.160440	−	0.0319136i	0.274657	+	0.961542i	$0.411436\pi$
$24$	0.567062	+	2.85081i	0.115751	+	0.581920i
$25$		0			0
$26$	1.27378	−	3.07518i	0.249809	−	0.603093i
$27$	3.95431	−	5.91804i	0.761007	−	1.13893i
$28$	0.845799	+	4.25212i	0.159841	+	0.803575i
$29$	8.95670	+	1.78160i	1.66322	+	0.330835i	0.935037	−	0.354550i	$-0.115366\pi$
$29$	8.95670	+	1.78160i	1.66322	+	0.330835i	0.728181	+	0.685385i	$0.240366\pi$
$30$		0			0
$31$	−4.85565	−	7.26699i	−0.872100	−	1.30519i	−0.951279	−	0.308330i	$-0.900230\pi$
$31$	−4.85565	−	7.26699i	−0.872100	−	1.30519i	0.0791791	−	0.996860i	$-0.474770\pi$
$32$	−0.923880	−	0.382683i	−0.163320	−	0.0676495i
$33$	−0.421230	−	0.421230i	−0.0733267	−	0.0733267i
$34$	−2.25381	+	3.45258i	−0.386525	+	0.592113i
$35$		0			0
$36$	2.08513	+	5.03395i	0.347521	+	0.838991i
$37$	1.88413	+	0.374777i	0.309749	+	0.0616129i	0.347517	−	0.937674i	$-0.387025\pi$
$37$	1.88413	+	0.374777i	0.309749	+	0.0616129i	−0.0377681	+	0.999287i	$0.512025\pi$
$38$			1.90524i			0.309071i
$39$	1.88750	−	9.48908i	0.302241	−	1.51947i
$40$		0			0
$41$	−3.42967	+	0.682203i	−0.535624	+	0.106542i	−0.455488	−	0.890242i	$-0.650535\pi$
$41$	−3.42967	+	0.682203i	−0.535624	+	0.106542i	−0.0801355	+	0.996784i	$0.525535\pi$
$42$	4.82243	+	11.6424i	0.744117	+	1.79646i
$43$	−2.60772	−	6.29559i	−0.397674	−	0.960069i	−0.988216	−	0.153063i	$-0.951086\pi$
$43$	−2.60772	−	6.29559i	−0.397674	−	0.960069i	0.590543	−	0.807006i	$-0.298914\pi$
$44$	0.201008	−	0.0399830i	0.0303031	−	0.00602766i
$45$		0			0
$46$	−0.153052	+	0.769445i	−0.0225663	+	0.113449i
$47$		−	11.8186i		−	1.72392i	−0.506979	−	0.861958i	$-0.669238\pi$
$47$		−	11.8186i		−	1.72392i	0.506979	−	0.861958i	$-0.330762\pi$
$48$	−2.85081	−	0.567062i	−0.411480	−	0.0818484i
$49$	4.51409	+	10.8980i	0.644870	+	1.55685i
$50$		0			0
$51$	−4.46736	+	11.1207i	−0.625556	+	1.55721i
$52$	2.35364	+	2.35364i	0.326391	+	0.326391i
$53$	−4.78009	−	1.97998i	−0.656596	−	0.271971i	0.0294096	−	0.999567i	$-0.490637\pi$
$53$	−4.78009	−	1.97998i	−0.656596	−	0.271971i	−0.686005	+	0.727597i	$0.740637\pi$
$54$	3.95431	+	5.91804i	0.538113	+	0.805343i
$55$		0			0
$56$	−4.25212	−	0.845799i	−0.568213	−	0.113025i
$57$	1.08039	+	5.43149i	0.143101	+	0.719419i
$58$	−5.07356	+	7.59313i	−0.666192	+	0.997026i
$59$	−1.58062	+	3.81596i	−0.205779	+	0.496795i	−0.992750	−	0.120195i	$-0.961648\pi$
$59$	−1.58062	+	3.81596i	−0.205779	+	0.496795i	0.786971	+	0.616990i	$0.211648\pi$
$60$		0			0
$61$	0.209544	+	1.05345i	0.0268294	+	0.134881i	0.991879	−	0.127188i	$-0.0405952\pi$
$61$	0.209544	+	1.05345i	0.0268294	+	0.134881i	−0.965049	+	0.262069i	$0.915595\pi$
$62$	8.57200	−	1.70508i	1.08865	−	0.216545i
$63$	13.1239	+	19.6413i	1.65346	+	2.47458i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$		0			0
$66$	0.550364	−	0.227968i	0.0677451	−	0.0280609i
$67$	5.49540	−	5.49540i	0.671369	−	0.671369i	−0.286662	−	0.958032i	$-0.592546\pi$
$67$	5.49540	−	5.49540i	0.671369	−	0.671369i	0.958032	+	0.286662i	$0.0925458\pi$
$68$	−2.32728	−	3.40350i	−0.282224	−	0.412734i
$69$			2.28034i			0.274520i
$70$		0			0
$71$	−1.33556	+	0.892391i	−0.158502	+	0.105907i	−0.632292	−	0.774730i	$-0.717886\pi$
$71$	−1.33556	+	0.892391i	−0.158502	+	0.105907i	0.473790	+	0.880638i	$0.342886\pi$
$72$	−5.44870			−0.642136
$73$	0.677883	−	0.452947i	0.0793403	−	0.0530135i	−0.515267	−	0.857029i	$-0.672307\pi$
$73$	0.677883	−	0.452947i	0.0793403	−	0.0530135i	0.594608	+	0.804016i	$0.297307\pi$
$74$	−1.06727	+	1.59729i	−0.124068	+	0.185681i
$75$		0			0
$76$	−1.76021	−	0.729105i	−0.201910	−	0.0836340i
$77$	0.820892	−	0.340025i	0.0935493	−	0.0387494i
$78$	8.04446	+	5.37513i	0.910855	+	0.608614i
$79$	−10.3045	−	6.88525i	−1.15935	−	0.774651i	−0.181380	−	0.983413i	$-0.558056\pi$
$79$	−10.3045	−	6.88525i	−1.15935	−	0.774651i	−0.977966	+	0.208762i	$0.933056\pi$
$80$		0			0
$81$	3.07044	+	3.07044i	0.341160	+	0.341160i
$82$	0.682203	−	3.42967i	0.0753367	−	0.378743i
$83$	0.269470	−	0.650559i	0.0295782	−	0.0714081i	−0.908400	−	0.418102i	$-0.862696\pi$
$83$	0.269470	−	0.650559i	0.0295782	−	0.0714081i	0.937978	+	0.346693i	$0.112696\pi$
$84$	−12.6016			−1.37495
$85$		0			0
$86$	6.81430			0.734805
$87$	−10.1580	+	24.5236i	−1.08905	+	2.62921i
$88$	−0.0399830	+	0.201008i	−0.00426220	+	0.0214275i
$89$	−3.70552	−	3.70552i	−0.392784	−	0.392784i	0.482894	−	0.875679i	$-0.339585\pi$
$89$	−3.70552	−	3.70552i	−0.392784	−	0.392784i	−0.875679	+	0.482894i	$0.839585\pi$
$90$		0			0
$91$	11.9987	+	8.01725i	1.25780	+	0.840437i
$92$	−0.652304	−	0.435856i	−0.0680074	−	0.0454411i
$93$	23.4703	−	9.72172i	2.43376	−	1.00810i
$94$	10.9189	+	4.52277i	1.12620	+	0.466489i
$95$		0			0
$96$	1.61486	−	2.41680i	0.164816	−	0.246664i
$97$	−0.124830	+	0.0834089i	−0.0126746	+	0.00846889i	−0.561891	−	0.827211i	$-0.689926\pi$
$97$	−0.124830	+	0.0834089i	−0.0126746	+	0.00846889i	0.549217	+	0.835680i	$0.314926\pi$
$98$	−11.7959			−1.19156
$99$	0.928493	−	0.620400i	0.0933171	−	0.0623525i
$100$		0			0
$101$		−	15.1577i		−	1.50824i	−0.656735	−	0.754122i	$-0.728063\pi$
$101$		−	15.1577i		−	1.50824i	0.656735	−	0.754122i	$-0.271937\pi$
$102$	−8.56463	−	8.38302i	−0.848025	−	0.830043i
$103$	2.06188	−	2.06188i	0.203163	−	0.203163i	−0.598191	−	0.801354i	$-0.704113\pi$
$103$	2.06188	−	2.06188i	0.203163	−	0.203163i	0.801354	+	0.598191i	$0.204113\pi$
$104$	−3.07518	+	1.27378i	−0.301546	+	0.124905i
$105$		0			0
$106$	3.65852	−	3.65852i	0.355347	−	0.355347i
$107$	0.326739	+	0.488999i	0.0315870	+	0.0472733i	0.846927	−	0.531709i	$-0.178450\pi$
$107$	0.326739	+	0.488999i	0.0315870	+	0.0472733i	−0.815340	+	0.578982i	$0.803450\pi$
$108$	−6.98080	+	1.38857i	−0.671728	+	0.133615i
$109$	0.693887	+	3.48840i	0.0664623	+	0.334129i	0.999683	−	0.0251750i	$-0.00801429\pi$
$109$	0.693887	+	3.48840i	0.0664623	+	0.334129i	−0.933221	+	0.359304i	$0.883014\pi$
$110$		0			0
$111$	−2.13684	+	5.15878i	−0.202820	+	0.489650i
$112$	2.40863	−	3.60477i	0.227594	−	0.340619i
$113$	0.643843	+	3.23682i	0.0605677	+	0.304494i	0.999180	−	0.0404784i	$-0.0128882\pi$
$113$	0.643843	+	3.23682i	0.0605677	+	0.304494i	−0.938613	+	0.344973i	$0.887888\pi$
$114$	−5.43149	−	1.08039i	−0.508706	−	0.101188i
$115$		0			0
$116$	−5.07356	−	7.59313i	−0.471069	−	0.705004i
$117$	16.7557	+	6.94046i	1.54907	+	0.641646i
$118$	−2.92061	−	2.92061i	−0.268864	−	0.268864i
$119$	−12.7745	−	12.5037i	−1.17104	−	1.14621i
$120$		0			0
$121$	4.19344	+	10.1239i	0.381222	+	0.920352i
$122$	−1.05345	−	0.209544i	−0.0953749	−	0.0189713i
$123$		−	10.1642i		−	0.916474i
$124$	−1.70508	+	8.57200i	−0.153120	+	0.769789i
$125$		0			0
$126$	−23.1685	+	4.60851i	−2.06402	+	0.410558i
$127$	−1.97507	−	4.76825i	−0.175260	−	0.423114i	0.811702	−	0.584072i	$-0.198542\pi$
$127$	−1.97507	−	4.76825i	−0.175260	−	0.423114i	−0.986961	+	0.160958i	$0.948542\pi$
$128$	0.382683	+	0.923880i	0.0338248	+	0.0816602i
$129$	19.4263	−	3.86413i	1.71039	−	0.340218i
$130$		0			0
$131$	2.13002	−	10.7084i	0.186101	−	0.935593i	−0.768985	−	0.639266i	$-0.779238\pi$
$131$	2.13002	−	10.7084i	0.186101	−	0.935593i	0.955087	−	0.296327i	$-0.0957618\pi$
$132$			0.595709i			0.0518498i
$133$	−8.10132	−	1.61145i	−0.702473	−	0.139731i
$134$	2.97409	+	7.18008i	0.256922	+	0.620264i
$135$		0			0
$136$	4.03503	−	0.847662i	0.346001	−	0.0726864i
$137$	−12.3373	−	12.3373i	−1.05405	−	1.05405i	−0.998453	−	0.0555950i	$-0.982294\pi$
$137$	−12.3373	−	12.3373i	−1.05405	−	1.05405i	−0.0555950	−	0.998453i	$-0.517706\pi$
$138$	−2.10676	−	0.872647i	−0.179339	−	0.0742847i
$139$	−1.10884	−	1.65949i	−0.0940503	−	0.140756i	0.781461	−	0.623955i	$-0.214475\pi$
$139$	−1.10884	−	1.65949i	−0.0940503	−	0.140756i	−0.875511	+	0.483198i	$0.839475\pi$
$140$		0			0
$141$	33.6926	+	6.70187i	2.83743	+	0.564399i
$142$	−0.313366	−	1.57540i	−0.0262971	−	0.132204i
$143$	0.378995	−	0.567206i	0.0316932	−	0.0474322i
$144$	2.08513	−	5.03395i	0.173761	−	0.419496i
$145$		0			0
$146$	0.159054	+	0.799618i	0.0131634	+	0.0661769i
$147$	−33.6279	+	6.68900i	−2.77358	+	0.551699i
$148$	−1.06727	−	1.59729i	−0.0877294	−	0.131296i
$149$	6.12503	−	6.12503i	0.501782	−	0.501782i	−0.410209	−	0.911991i	$-0.634544\pi$
$149$	6.12503	−	6.12503i	0.501782	−	0.501782i	0.911991	+	0.410209i	$0.134544\pi$
$150$		0			0
$151$	−20.9830	+	8.69145i	−1.70757	+	0.707300i	−0.707573	+	0.706640i	$0.750210\pi$
$151$	−20.9830	+	8.69145i	−1.70757	+	0.707300i	−1.00000		0.000659759i	$0.999790\pi$
$152$	1.34721	−	1.34721i	0.109273	−	0.109273i
$153$	−18.8121	−	12.2803i	−1.52087	−	0.992807i
$154$			0.888527i			0.0715995i
$155$		0			0
$156$	−8.04446	+	5.37513i	−0.644072	+	0.430355i
$157$	−4.30033			−0.343204			−0.171602	−	0.985166i	$-0.554894\pi$
$157$	−4.30033			−0.343204			−0.171602	+	0.985166i	$0.554894\pi$
$158$	10.3045	−	6.88525i	0.819782	−	0.547761i
$159$	8.35516	−	12.5044i	0.662607	−	0.991661i
$160$		0			0
$161$	−3.14232	−	1.30159i	−0.247650	−	0.102580i
$162$	−4.01173	+	1.66171i	−0.315191	+	0.130556i
$163$	3.31976	+	2.21819i	0.260024	+	0.173742i	0.678748	−	0.734371i	$-0.262523\pi$
$163$	3.31976	+	2.21819i	0.260024	+	0.173742i	−0.418724	+	0.908113i	$0.637523\pi$
$164$	2.90753	+	1.94275i	0.227040	+	0.151703i
$165$		0			0
$166$	0.497916	+	0.497916i	0.0386458	+	0.0386458i
$167$	2.41993	−	12.1658i	0.187260	−	0.941419i	−0.766819	−	0.641864i	$-0.778162\pi$
$167$	2.41993	−	12.1658i	0.187260	−	0.941419i	0.954079	−	0.299556i	$-0.0968384\pi$
$168$	4.82243	−	11.6424i	0.372059	−	0.898229i
$169$	−1.92074			−0.147750
$170$		0			0
$171$	−10.3811			−0.793863
$172$	−2.60772	+	6.29559i	−0.198837	+	0.480035i
$173$	−2.69051	+	13.5261i	−0.204556	+	1.02837i	0.732919	+	0.680316i	$0.238157\pi$
$173$	−2.69051	+	13.5261i	−0.204556	+	1.02837i	−0.937474	+	0.348054i	$0.886843\pi$
$174$	−18.7696	−	18.7696i	−1.42292	−	1.42292i
$175$		0			0
$176$	−0.170406	−	0.113862i	−0.0128449	−	0.00858266i
$177$	−9.98227	−	6.66994i	−0.750314	−	0.501344i
$178$	4.84149	−	2.00541i	0.362885	−	0.150312i
$179$	−17.1204	−	7.09151i	−1.27964	−	0.530044i	−0.363758	−	0.931493i	$-0.618507\pi$
$179$	−17.1204	−	7.09151i	−1.27964	−	0.530044i	−0.915881	+	0.401449i	$0.868507\pi$
$180$		0			0
$181$	11.0377	−	16.5190i	0.820422	−	1.22785i	−0.150537	−	0.988604i	$-0.548100\pi$
$181$	11.0377	−	16.5190i	0.820422	−	1.22785i	0.970959	−	0.239244i	$-0.0768997\pi$
$182$	−11.9987	+	8.01725i	−0.889400	+	0.594278i
$183$	−3.12202			−0.230786
$184$	0.652304	−	0.435856i	0.0480885	−	0.0321317i
$185$		0			0
$186$			25.4041i			1.86272i
$187$	−0.591078	+	0.603883i	−0.0432239	+	0.0441603i
$188$	−8.35700	+	8.35700i	−0.609497	+	0.609497i
$189$	−28.5087	+	11.8087i	−2.07371	+	0.858957i
$190$		0			0
$191$	−4.91463	+	4.91463i	−0.355610	+	0.355610i	−0.862192	−	0.506582i	$-0.830909\pi$
$191$	−4.91463	+	4.91463i	−0.355610	+	0.355610i	0.506582	+	0.862192i	$0.330909\pi$
$192$	1.61486	+	2.41680i	0.116542	+	0.174418i
$193$	18.1291	−	3.60610i	1.30496	−	0.259573i	0.506825	−	0.862049i	$-0.330819\pi$
$193$	18.1291	−	3.60610i	1.30496	−	0.259573i	0.798137	+	0.602476i	$0.205819\pi$
$194$	−0.0292893	−	0.147247i	−0.00210285	−	0.0105717i
$195$		0			0
$196$	4.51409	−	10.8980i	0.322435	−	0.778427i
$197$	−6.03705	+	9.03509i	−0.430122	+	0.643723i	−0.981708	−	0.190395i	$-0.939023\pi$
$197$	−6.03705	+	9.03509i	−0.430122	+	0.643723i	0.551585	+	0.834118i	$0.314023\pi$
$198$	0.217855	+	1.09523i	0.0154823	+	0.0778348i
$199$	15.2386	+	3.03114i	1.08024	+	0.214872i	0.702960	−	0.711229i	$-0.251861\pi$
$199$	15.2386	+	3.03114i	1.08024	+	0.214872i	0.377275	+	0.926101i	$0.376861\pi$
$200$		0			0
$201$	12.5501	+	18.7826i	0.885217	+	1.32482i
$202$	14.0039	+	5.80059i	0.985308	+	0.408128i
$203$	−27.9957	−	27.9957i	−1.96491	−	1.96491i
$204$	11.0224	−	4.70464i	0.771726	−	0.329391i
$205$		0			0
$206$	1.11588	+	2.69398i	0.0777471	+	0.187698i
$207$	−4.19248	−	0.833936i	−0.291398	−	0.0579626i
$208$		−	3.32855i		−	0.230794i
$209$	−0.0761772	+	0.382969i	−0.00526929	+	0.0264905i
$210$		0			0
$211$	−17.6704	+	3.51487i	−1.21648	+	0.241973i	−0.761285	−	0.648417i	$-0.775431\pi$
$211$	−17.6704	+	3.51487i	−1.21648	+	0.241973i	−0.455197	+	0.890391i	$0.650431\pi$
$212$	1.97998	+	4.78009i	0.135985	+	0.328298i
$213$	−1.78670	−	4.31347i	−0.122422	−	0.295554i
$214$	−0.576814	+	0.114735i	−0.0394302	+	0.00784315i
$215$		0			0
$216$	1.38857	−	6.98080i	0.0944801	−	0.474983i
$217$			37.8913i			2.57223i
$218$	−3.48840	−	0.693887i	−0.236265	−	0.0469959i
$219$	0.906866	+	2.18937i	0.0612804	+	0.147944i
$220$		0			0
$221$	−13.4882	−	2.53303i	−0.907313	−	0.170390i
$222$	−3.94836	−	3.94836i	−0.264997	−	0.264997i
$223$	8.96939	+	3.71524i	0.600635	+	0.248791i	0.662218	−	0.749311i	$-0.269615\pi$
$223$	8.96939	+	3.71524i	0.600635	+	0.248791i	−0.0615836	+	0.998102i	$0.519615\pi$
$224$	2.40863	+	3.60477i	0.160933	+	0.240854i
$225$		0			0
$226$	−3.23682	−	0.643843i	−0.215310	−	0.0428278i
$227$	0.103244	+	0.519043i	0.00685255	+	0.0344501i	0.984060	−	0.177835i	$-0.0569094\pi$
$227$	0.103244	+	0.519043i	0.00685255	+	0.0344501i	−0.977208	+	0.212285i	$0.931909\pi$
$228$	3.07669	−	4.60460i	0.203759	−	0.304947i
$229$	11.2020	−	27.0440i	0.740249	−	1.78712i	0.135382	−	0.990793i	$-0.456774\pi$
$229$	11.2020	−	27.0440i	0.740249	−	1.78712i	0.604867	−	0.796326i	$-0.293226\pi$
$230$		0			0
$231$	0.503850	+	2.53303i	0.0331509	+	0.166661i
$232$	8.95670	−	1.78160i	0.588036	−	0.116968i
$233$	4.49587	+	6.72855i	0.294535	+	0.440802i	0.948994	−	0.315295i	$-0.102104\pi$
$233$	4.49587	+	6.72855i	0.294535	+	0.440802i	−0.654459	+	0.756097i	$0.727104\pi$
$234$	−12.8243	+	12.8243i	−0.838350	+	0.838350i
$235$		0			0
$236$	3.81596	−	1.58062i	0.248398	−	0.102890i
$237$	25.4719	−	25.4719i	1.65457	−	1.65457i
$238$	16.4405	−	7.01718i	1.06568	−	0.454856i
$239$			20.1335i			1.30233i	0.758937	+	0.651164i	$0.225719\pi$
$239$			20.1335i			1.30233i	−0.758937	+	0.651164i	$0.774281\pi$
$240$		0			0
$241$	−7.62327	+	5.09371i	−0.491058	+	0.328115i	−0.776324	−	0.630334i	$-0.782918\pi$
$241$	−7.62327	+	5.09371i	−0.491058	+	0.328115i	0.285266	+	0.958448i	$0.407918\pi$
$242$	−10.9580			−0.704407
$243$	7.25971	−	4.85079i	0.465711	−	0.311178i
$244$	0.596732	−	0.893072i	0.0382018	−	0.0571731i
$245$		0			0
$246$	9.39049	+	3.88967i	0.598716	+	0.247996i
$247$	−5.85896	+	2.42686i	−0.372797	+	0.154418i
$248$	−7.26699	−	4.85565i	−0.461454	−	0.308334i
$249$	1.70182	+	1.13712i	0.107848	+	0.0720619i
$250$		0			0
$251$	6.12489	+	6.12489i	0.386600	+	0.386600i	0.873473	−	0.486873i	$-0.161863\pi$
$251$	6.12489	+	6.12489i	0.386600	+	0.386600i	−0.486873	+	0.873473i	$0.661863\pi$
$252$	4.60851	−	23.1685i	0.290309	−	1.45948i
$253$	−0.0615294	+	0.148545i	−0.00386832	+	0.00933895i
$254$	5.16112			0.323837
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	1.52117	−	3.67244i	0.0948882	−	0.229080i	−0.869308	−	0.494271i	$-0.835435\pi$
$257$	1.52117	−	3.67244i	0.0948882	−	0.229080i	0.964196	+	0.265191i	$0.0854350\pi$
$258$	−3.86413	+	19.4263i	−0.240570	+	1.20943i
$259$	−5.88916	−	5.88916i	−0.365935	−	0.365935i
$260$		0			0
$261$	−41.3727	−	27.6444i	−2.56091	−	1.71114i
$262$	9.07811	+	6.06580i	0.560847	+	0.374746i
$263$	−28.4288	+	11.7756i	−1.75299	+	0.726113i	−0.755514	+	0.655132i	$0.772613\pi$
$263$	−28.4288	+	11.7756i	−1.75299	+	0.726113i	−0.997478	+	0.0709807i	$0.977387\pi$
$264$	−0.550364	−	0.227968i	−0.0338725	−	0.0140305i
$265$		0			0
$266$	4.58903	−	6.86796i	0.281371	−	0.421102i
$267$	12.6650	−	8.46248i	0.775086	−	0.517896i
$268$	−7.77166			−0.474730
$269$	−13.2000	+	8.81994i	−0.804817	+	0.537761i	−0.888579	−	0.458724i	$-0.848307\pi$
$269$	−13.2000	+	8.81994i	−0.804817	+	0.537761i	0.0837617	+	0.996486i	$0.473307\pi$
$270$		0			0
$271$		−	19.7242i		−	1.19816i	−0.800690	−	0.599079i	$-0.795534\pi$
$271$		−	19.7242i		−	1.19816i	0.800690	−	0.599079i	$-0.204466\pi$
$272$	−0.761002	+	4.05227i	−0.0461425	+	0.245705i
$273$	−29.6597	+	29.6597i	−1.79509	+	1.79509i
$274$	16.1195	−	6.67691i	0.973814	−	0.403367i
$275$		0			0
$276$	1.61244	−	1.61244i	0.0970576	−	0.0970576i
$277$	−7.52505	−	11.2620i	−0.452136	−	0.676670i	0.533452	−	0.845830i	$-0.320894\pi$
$277$	−7.52505	−	11.2620i	−0.452136	−	0.676670i	−0.985589	+	0.169160i	$0.945894\pi$
$278$	1.95750	−	0.389372i	0.117403	−	0.0233530i
$279$	9.29046	+	46.7063i	0.556205	+	2.79623i
$280$		0			0
$281$	6.96372	−	16.8119i	0.415421	−	1.00291i	−0.568237	−	0.822865i	$-0.692374\pi$
$281$	6.96372	−	16.8119i	0.415421	−	1.00291i	0.983658	−	0.180049i	$-0.0576258\pi$
$282$	−19.0853	+	28.5632i	−1.13651	+	1.70091i
$283$	3.51053	+	17.6486i	0.208679	+	1.04910i	0.933065	+	0.359707i	$0.117123\pi$
$283$	3.51053	+	17.6486i	0.208679	+	1.04910i	−0.724386	+	0.689394i	$0.757877\pi$
$284$	1.57540	+	0.313366i	0.0934827	+	0.0185949i
$285$		0			0
$286$	0.378995	+	0.567206i	0.0224104	+	0.0335396i
$287$	14.0063	+	5.80161i	0.826768	+	0.342458i
$288$	3.85282	+	3.85282i	0.227029	+	0.227029i
$289$	15.8418	+	6.16757i	0.931868	+	0.362798i
$290$		0			0
$291$	−0.166997	−	0.403166i	−0.00978952	−	0.0236340i
$292$	−0.799618	−	0.159054i	−0.0467941	−	0.00930793i
$293$		−	16.4811i		−	0.962835i	−0.876492	−	0.481417i	$-0.840122\pi$
$293$		−	16.4811i		−	0.962835i	0.876492	−	0.481417i	$-0.159878\pi$
$294$	6.68900	−	33.6279i	0.390110	−	1.96122i
$295$		0			0
$296$	1.88413	−	0.374777i	0.109513	−	0.0217835i
$297$	0.558226	+	1.34768i	0.0323916	+	0.0782002i
$298$	3.31484	+	8.00274i	0.192024	+	0.463586i
$299$	−2.56114	+	0.509442i	−0.148114	+	0.0294618i
$300$		0			0
$301$	−5.76353	+	28.9752i	−0.332204	+	1.67010i
$302$		−	22.7118i		−	1.30692i
$303$	43.2117	+	8.59534i	2.48245	+	0.493789i
$304$	0.729105	+	1.76021i	0.0418170	+	0.100955i
$305$		0			0
$306$	18.5446	−	12.6806i	1.06013	−	0.724904i
$307$	3.83948	+	3.83948i	0.219130	+	0.219130i	0.808132	−	0.589001i	$-0.200479\pi$
$307$	3.83948	+	3.83948i	0.219130	+	0.219130i	−0.589001	+	0.808132i	$0.700479\pi$
$308$	−0.820892	−	0.340025i	−0.0467747	−	0.0193747i
$309$	4.70882	+	7.04725i	0.267876	+	0.400904i
$310$		0			0
$311$	0.370233	+	0.0736439i	0.0209940	+	0.00417596i	0.205576	−	0.978641i	$-0.434093\pi$
$311$	0.370233	+	0.0736439i	0.0209940	+	0.00417596i	−0.184582	+	0.982817i	$0.559093\pi$
$312$	−1.88750	−	9.48908i	−0.106858	−	0.537214i
$313$	−8.62342	+	12.9059i	−0.487424	+	0.729482i	−0.990911	−	0.134521i	$-0.957050\pi$
$313$	−8.62342	+	12.9059i	−0.487424	+	0.729482i	0.503486	+	0.864003i	$0.332050\pi$
$314$	1.64567	−	3.97299i	0.0928704	−	0.224209i
$315$		0			0
$316$	2.41778	+	12.1550i	0.136011	+	0.683771i
$317$	22.8685	−	4.54883i	1.28442	−	0.255488i	0.494761	−	0.869029i	$-0.335255\pi$
$317$	22.8685	−	4.54883i	1.28442	−	0.255488i	0.789663	+	0.613541i	$0.210255\pi$
$318$	8.35516	+	12.5044i	0.468534	+	0.701211i
$319$	−1.32342	+	1.32342i	−0.0740974	+	0.0740974i
$320$		0			0
$321$	−1.57933	+	0.654179i	−0.0881495	+	0.0365127i
$322$	2.40503	−	2.40503i	0.134027	−	0.134027i
$323$	7.68771	−	1.61500i	0.427756	−	0.0898611i
$324$		−	4.34226i		−	0.241237i
$325$		0			0
$326$	−3.31976	+	2.21819i	−0.183865	+	0.122854i
$327$	−10.3383			−0.571708
$328$	−2.90753	+	1.94275i	−0.160542	+	0.107270i
$329$	−28.4666	+	42.6033i	−1.56941	+	2.34879i
$330$		0			0
$331$	−2.05592	−	0.851588i	−0.113003	−	0.0468075i	0.325465	−	0.945554i	$-0.394479\pi$
$331$	−2.05592	−	0.851588i	−0.113003	−	0.0468075i	−0.438469	+	0.898746i	$0.644479\pi$
$332$	−0.650559	+	0.269470i	−0.0357041	+	0.0147891i
$333$	−8.70315	−	5.81526i	−0.476930	−	0.318674i
$334$	10.3137	+	6.89138i	0.564340	+	0.377080i
$335$		0			0
$336$	8.91069	+	8.91069i	0.486118	+	0.486118i
$337$	−4.78384	+	24.0500i	−0.260592	+	1.31009i	0.599676	+	0.800243i	$0.295296\pi$
$337$	−4.78384	+	24.0500i	−0.260592	+	1.31009i	−0.860268	+	0.509842i	$0.829704\pi$
$338$	0.735037	−	1.77454i	0.0399808	−	0.0965221i
$339$	−9.59267			−0.521002
$340$		0			0
$341$	1.79121			0.0969997
$342$	3.97268	−	9.59089i	0.214818	−	0.518616i
$343$	4.05635	−	20.3927i	0.219022	−	1.10110i
$344$	−4.81844	−	4.81844i	−0.259793	−	0.259793i
$345$		0			0
$346$	−11.4669	−	7.66192i	−0.616463	−	0.411907i
$347$	−3.66998	−	2.45220i	−0.197015	−	0.131641i	0.453150	−	0.891434i	$-0.350300\pi$
$347$	−3.66998	−	2.45220i	−0.197015	−	0.131641i	−0.650165	+	0.759793i	$0.725300\pi$
$348$	24.5236	−	10.1580i	1.31460	−	0.544527i
$349$	2.43735	+	1.00958i	0.130468	+	0.0540418i	0.446963	−	0.894553i	$-0.352506\pi$
$349$	2.43735	+	1.00958i	0.130468	+	0.0540418i	−0.316494	+	0.948594i	$0.602506\pi$
$350$		0			0
$351$	−13.1621	+	19.6985i	−0.702542	+	1.05143i
$352$	0.170406	−	0.113862i	0.00908269	−	0.00606886i
$353$	7.64333			0.406813			0.203407	−	0.979094i	$-0.434799\pi$
$353$	7.64333			0.406813			0.203407	+	0.979094i	$0.434799\pi$
$354$	9.98227	−	6.66994i	0.530552	−	0.354503i
$355$		0			0
$356$			5.24039i			0.277740i
$357$	42.8896	−	29.3275i	2.26996	−	1.55217i
$358$	13.1034	−	13.1034i	0.692536	−	0.692536i
$359$	15.2351	−	6.31059i	0.804079	−	0.333060i	0.0574900	−	0.998346i	$-0.481690\pi$
$359$	15.2351	−	6.31059i	0.804079	−	0.333060i	0.746589	+	0.665286i	$0.231690\pi$
$360$		0			0
$361$	−10.8683	+	10.8683i	−0.572014	+	0.572014i
$362$	11.0377	+	16.5190i	0.580126	+	0.868220i
$363$	−31.2392	+	6.21387i	−1.63963	+	0.326143i
$364$	−2.81529	−	14.1534i	−0.147561	−	0.741839i
$365$		0			0
$366$	1.19474	−	2.88437i	0.0624503	−	0.150768i
$367$	0.510232	−	0.763616i	0.0266339	−	0.0398605i	−0.817914	−	0.575341i	$-0.804869\pi$
$367$	0.510232	−	0.763616i	0.0266339	−	0.0398605i	0.844548	+	0.535480i	$0.179869\pi$
$368$	0.153052	+	0.769445i	0.00797840	+	0.0401101i
$369$	18.6872	+	3.71712i	0.972819	+	0.193506i
$370$		0			0
$371$	12.4621	+	18.6508i	0.647000	+	0.968303i
$372$	−23.4703	−	9.72172i	−1.21688	−	0.504048i
$373$	−20.4777	−	20.4777i	−1.06030	−	1.06030i	−0.998061	−	0.0622355i	$-0.980177\pi$
$373$	−20.4777	−	20.4777i	−1.06030	−	1.06030i	−0.0622355	−	0.998061i	$-0.519823\pi$
$374$	−0.331719	−	0.777181i	−0.0171528	−	0.0401871i
$375$		0			0
$376$	−4.52277	−	10.9189i	−0.233244	−	0.563101i
$377$	−29.8128	−	5.93014i	−1.53544	−	0.305418i
$378$		−	30.8576i		−	1.58715i
$379$	−1.18087	+	5.93665i	−0.0606573	+	0.304945i	−0.999190	−	0.0402460i	$-0.987186\pi$
$379$	−1.18087	+	5.93665i	−0.0606573	+	0.304945i	0.938532	+	0.345191i	$0.112186\pi$
$380$		0			0
$381$	14.7134	−	2.92668i	0.753790	−	0.149938i
$382$	−2.65978	−	6.42127i	−0.136086	−	0.328541i
$383$	−11.1820	−	26.9957i	−0.571374	−	1.37942i	−0.900386	−	0.435092i	$-0.856716\pi$
$383$	−11.1820	−	26.9957i	−0.571374	−	1.37942i	0.329012	−	0.944326i	$-0.393284\pi$
$384$	−2.85081	+	0.567062i	−0.145480	+	0.0289378i
$385$		0			0
$386$	−3.60610	+	18.1291i	−0.183546	+	0.922747i
$387$			37.1291i			1.88738i
$388$	0.147247	+	0.0292893i	0.00747535	+	0.00148694i
$389$	−10.1663	−	24.5436i	−0.515451	−	1.24441i	−0.940672	−	0.339318i	$-0.889804\pi$
$389$	−10.1663	−	24.5436i	−0.515451	−	1.24441i	0.425221	−	0.905090i	$-0.360196\pi$
$390$		0			0
$391$	3.23447	−	0.0346593i	0.163574	−	0.00175279i
$392$	8.34095	+	8.34095i	0.421282	+	0.421282i
$393$	29.3197	+	12.1446i	1.47898	+	0.612615i
$394$	−6.03705	−	9.03509i	−0.304142	−	0.455181i
$395$		0			0
$396$	−1.09523	−	0.217855i	−0.0550375	−	0.0109476i
$397$	3.71505	+	18.6768i	0.186453	+	0.937363i	0.954782	+	0.297307i	$0.0960886\pi$
$397$	3.71505	+	18.6768i	0.186453	+	0.937363i	−0.768329	+	0.640055i	$0.778911\pi$
$398$	−8.63197	+	12.9187i	−0.432681	+	0.647554i
$399$	9.18790	−	22.1816i	0.459970	−	1.11047i
$400$		0			0
$401$	−1.47933	−	7.43709i	−0.0738742	−	0.371391i	0.926109	−	0.377257i	$-0.123133\pi$
$401$	−1.47933	−	7.43709i	−0.0738742	−	0.371391i	−0.999983	+	0.00586632i	$0.998133\pi$
$402$	−22.1556	+	4.40702i	−1.10502	+	0.219802i
$403$	16.1623	+	24.1886i	0.805100	+	1.20492i
$404$	−10.7181	+	10.7181i	−0.533245	+	0.533245i
$405$		0			0
$406$	36.5781	−	15.1511i	1.81534	−	0.751938i
$407$	−0.278395	+	0.278395i	−0.0137995	+	0.0137995i
$408$	0.128413	+	11.9838i	0.00635741	+	0.593287i
$409$		−	10.2044i		−	0.504575i	−0.967652	−	0.252287i	$-0.918817\pi$
$409$		−	10.2044i		−	0.504575i	0.967652	−	0.252287i	$-0.0811828\pi$
$410$		0			0
$411$	42.1674	−	28.1754i	2.07997	−	1.38979i
$412$	−2.91594			−0.143658
$413$	14.8890	−	9.94852i	0.732640	−	0.489535i
$414$	2.37485	−	3.55421i	0.116717	−	0.174680i
$415$		0			0
$416$	3.07518	+	1.27378i	0.150773	+	0.0624523i
$417$	5.35968	−	2.22005i	0.262465	−	0.108716i
$418$	−0.324665	−	0.216934i	−0.0158799	−	0.0106106i
$419$	−6.68327	−	4.46562i	−0.326499	−	0.218160i	0.381507	−	0.924366i	$-0.375405\pi$
$419$	−6.68327	−	4.46562i	−0.326499	−	0.218160i	−0.708006	+	0.706206i	$0.750405\pi$
$420$		0			0
$421$	8.14770	+	8.14770i	0.397094	+	0.397094i	0.877207	−	0.480113i	$-0.159404\pi$
$421$	8.14770	+	8.14770i	0.397094	+	0.397094i	−0.480113	+	0.877207i	$0.659404\pi$
$422$	3.51487	−	17.6704i	0.171101	−	0.860183i
$423$	−24.6433	+	59.4941i	−1.19820	+	2.89270i
$424$	−5.17393			−0.251268
$425$		0			0
$426$	4.66887			0.226207
$427$	1.78201	−	4.30216i	0.0862377	−	0.208196i
$428$	0.114735	−	0.576814i	0.00554595	−	0.0278814i
$429$	1.40209	+	1.40209i	0.0676933	+	0.0676933i
$430$		0			0
$431$	8.95105	+	5.98090i	0.431157	+	0.288090i	0.752150	−	0.658992i	$-0.229017\pi$
$431$	8.95105	+	5.98090i	0.431157	+	0.288090i	−0.320993	+	0.947081i	$0.604017\pi$
$432$	5.91804	+	3.95431i	0.284732	+	0.190252i
$433$	25.9274	−	10.7395i	1.24599	−	0.516107i	0.340410	−	0.940277i	$-0.389434\pi$
$433$	25.9274	−	10.7395i	1.24599	−	0.516107i	0.905582	+	0.424170i	$0.139434\pi$
$434$	−35.0070	−	14.5004i	−1.68039	−	0.696040i
$435$		0			0
$436$	1.97602	−	2.95733i	0.0946343	−	0.141630i
$437$	1.24280	−	0.830411i	0.0594511	−	0.0397239i
$438$	−2.36976			−0.113231
$439$	4.11795	−	2.75152i	0.196539	−	0.131323i	−0.453407	−	0.891304i	$-0.649792\pi$
$439$	4.11795	−	2.75152i	0.196539	−	0.131323i	0.649946	+	0.759981i	$0.274792\pi$
$440$		0			0
$441$		−	64.2723i		−	3.06058i
$442$	7.50192	−	11.4921i	0.356830	−	0.546624i
$443$	−14.5879	+	14.5879i	−0.693094	+	0.693094i	−0.962911	−	0.269818i	$-0.913037\pi$
$443$	−14.5879	+	14.5879i	−0.693094	+	0.693094i	0.269818	+	0.962911i	$0.413037\pi$
$444$	5.15878	−	2.13684i	0.244825	−	0.101410i
$445$		0			0
$446$	−6.86488	+	6.86488i	−0.325061	+	0.325061i
$447$	13.9881	+	20.9346i	0.661612	+	0.990173i
$448$	−4.25212	+	0.845799i	−0.200894	+	0.0399602i
$449$	5.09616	+	25.6201i	0.240503	+	1.20909i	0.892564	+	0.450922i	$0.148905\pi$
$449$	5.09616	+	25.6201i	0.240503	+	1.20909i	−0.652061	+	0.758166i	$0.726095\pi$
$450$		0			0
$451$	0.274256	−	0.662114i	0.0129142	−	0.0311777i
$452$	1.83351	−	2.74404i	0.0862411	−	0.129069i
$453$	−12.8790	−	64.7473i	−0.605110	−	3.04209i
$454$	−0.519043	−	0.103244i	−0.0243599	−	0.00484548i
$455$		0			0
$456$	3.07669	+	4.60460i	0.144079	+	0.215630i
$457$	−32.7813	−	13.5785i	−1.53344	−	0.635173i	−0.553215	−	0.833038i	$-0.686599\pi$
$457$	−32.7813	−	13.5785i	−1.53344	−	0.635173i	−0.980229	+	0.197865i	$0.936599\pi$
$458$	20.6986	+	20.6986i	0.967182	+	0.967182i
$459$	20.5275	−	20.9722i	0.958144	−	0.978900i
$460$		0			0
$461$	−6.81224	−	16.4462i	−0.317277	−	0.765976i	−0.999397	−	0.0347345i	$-0.988941\pi$
$461$	−6.81224	−	16.4462i	−0.317277	−	0.765976i	0.682119	−	0.731241i	$-0.261059\pi$
$462$	−2.53303	−	0.503850i	−0.117847	−	0.0234412i
$463$			33.8924i			1.57511i	0.616242	+	0.787557i	$0.288654\pi$
$463$			33.8924i			1.57511i	−0.616242	+	0.787557i	$0.711346\pi$
$464$	−1.78160	+	8.95670i	−0.0827087	+	0.415804i
$465$		0			0
$466$	−7.93687	+	1.57874i	−0.367668	+	0.0731338i
$467$	−4.98700	−	12.0397i	−0.230771	−	0.557130i	0.765498	−	0.643439i	$-0.222493\pi$
$467$	−4.98700	−	12.0397i	−0.230771	−	0.557130i	−0.996268	+	0.0863086i	$0.972493\pi$
$468$	−6.94046	−	16.7557i	−0.320823	−	0.774535i
$469$	−33.0460	+	6.57326i	−1.52592	+	0.303525i
$470$		0			0
$471$	2.43856	−	12.2595i	0.112363	−	0.564886i
$472$			4.13036i			0.190115i
$473$	1.36973	+	0.272456i	0.0629802	+	0.0125275i
$474$	13.7853	+	33.2806i	0.633178	+	1.52863i
$475$		0			0
$476$	0.191534	+	17.8744i	0.00877897	+	0.819271i
$477$	19.9342	+	19.9342i	0.912724	+	0.912724i
$478$	−18.6009	−	7.70476i	−0.850787	−	0.352407i
$479$	−0.00324632	−	0.00485846i	−0.000148328	−	0.000221989i	0.831395	−	0.555681i	$-0.187542\pi$
$479$	−0.00324632	−	0.00485846i	−0.000148328	−	0.000221989i	−0.831544	+	0.555459i	$0.812542\pi$
$480$		0			0
$481$	−6.27142	−	1.24746i	−0.285952	−	0.0568795i
$482$	−1.78867	−	8.99226i	−0.0814718	−	0.409586i
$483$	5.49249	−	8.22009i	0.249917	−	0.374027i
$484$	4.19344	−	10.1239i	0.190611	−	0.460176i
$485$		0			0
$486$	1.70337	+	8.56342i	0.0772664	+	0.388444i
$487$	28.4214	−	5.65336i	1.28790	−	0.256178i	0.496797	−	0.867867i	$-0.334509\pi$
$487$	28.4214	−	5.65336i	1.28790	−	0.256178i	0.791099	+	0.611689i	$0.209509\pi$
$488$	0.596732	+	0.893072i	0.0270128	+	0.0404275i
$489$	−8.20617	+	8.20617i	−0.371096	+	0.371096i
$490$		0			0
$491$	−28.8893	+	11.9663i	−1.30376	+	0.540034i	−0.923056	−	0.384665i	$-0.874317\pi$
$491$	−28.8893	+	11.9663i	−1.30376	+	0.540034i	−0.380700	+	0.924698i	$0.624317\pi$
$492$	−7.18717	+	7.18717i	−0.324023	+	0.324023i
$493$	34.9392	+	14.0356i	1.57358	+	0.632131i
$494$		−	6.34170i		−	0.285326i
$495$		0			0
$496$	7.26699	−	4.85565i	0.326298	−	0.218025i
$497$	6.96382			0.312370
$498$	−1.70182	+	1.13712i	−0.0762602	+	0.0509555i
$499$	3.60412	−	5.39395i	0.161343	−	0.241466i	−0.741986	−	0.670415i	$-0.766116\pi$
$499$	3.60412	−	5.39395i	0.161343	−	0.241466i	0.903329	+	0.428949i	$0.141116\pi$
$500$		0			0
$501$	33.3102	+	13.7976i	1.48819	+	0.616429i
$502$	−8.00255	+	3.31477i	−0.357171	+	0.147945i
$503$	−21.7947	−	14.5628i	−0.971779	−	0.649322i	−0.0350533	−	0.999385i	$-0.511160\pi$
$503$	−21.7947	−	14.5628i	−0.971779	−	0.649322i	−0.936726	+	0.350063i	$0.886160\pi$
$504$	19.6413	+	13.1239i	0.874895	+	0.584586i
$505$		0			0
$506$	−0.113692	−	0.113692i	−0.00505421	−	0.00505421i
$507$	1.08918	−	5.47569i	0.0483723	−	0.243184i
$508$	−1.97507	+	4.76825i	−0.0876298	+	0.211557i
$509$	37.2931			1.65299			0.826495	−	0.562944i	$-0.190331\pi$
$509$	37.2931			1.65299			0.826495	+	0.562944i	$0.190331\pi$
$510$		0			0
$511$	−3.53460			−0.156361
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	2.64556	−	13.3001i	0.116804	−	0.587215i
$514$	2.81076	+	2.81076i	0.123977	+	0.123977i
$515$		0			0
$516$	−16.4688	−	11.0041i	−0.725000	−	0.484429i
$517$	2.01396	+	1.34569i	0.0885739	+	0.0591832i
$518$	7.69456	−	3.18719i	0.338079	−	0.140037i
$519$	−37.0347	−	15.3403i	−1.62564	−	0.673364i
$520$		0			0
$521$	−3.95806	+	5.92366i	−0.173406	+	0.259520i	−0.907985	−	0.419003i	$-0.862380\pi$
$521$	−3.95806	+	5.92366i	−0.173406	+	0.259520i	0.734579	+	0.678523i	$0.237380\pi$
$522$	41.3727	−	27.6444i	1.81083	−	1.20996i
$523$	25.1852			1.10127			0.550637	−	0.834745i	$-0.314385\pi$
$523$	25.1852			1.10127			0.550637	+	0.834745i	$0.314385\pi$
$524$	−9.07811	+	6.06580i	−0.396579	+	0.264986i
$525$		0			0
$526$		−	30.7711i		−	1.34168i
$527$	−14.1462	−	33.1430i	−0.616218	−	1.44373i
$528$	0.421230	−	0.421230i	0.0183317	−	0.0183317i
$529$	−20.6806	+	8.56619i	−0.899157	+	0.372443i
$530$		0			0
$531$	15.9135	−	15.9135i	0.690588	−	0.690588i
$532$	4.58903	+	6.86796i	0.198960	+	0.297764i
$533$	11.4158	−	2.27075i	0.494474	−	0.0983570i
$534$	2.97163	+	14.9394i	0.128595	+	0.646491i
$535$		0			0
$536$	2.97409	−	7.18008i	0.128461	−	0.310132i
$537$	29.9249	−	44.7858i	1.29136	−	1.93265i
$538$	−3.09715	−	15.5704i	−0.133528	−	0.671289i
$539$	−2.37107	−	0.471634i	−0.102129	−	0.0203147i
$540$		0			0
$541$	3.83883	+	5.74521i	0.165044	+	0.247006i	0.904768	−	0.425904i	$-0.140044\pi$
$541$	3.83883	+	5.74521i	0.165044	+	0.247006i	−0.739724	+	0.672910i	$0.765044\pi$
$542$	18.2228	+	7.54811i	0.782734	+	0.324219i
$543$	40.8336	+	40.8336i	1.75234	+	1.75234i
$544$	−3.45258	−	2.25381i	−0.148028	−	0.0966313i
$545$		0			0
$546$	−16.0517	−	38.7523i	−0.686950	−	1.65844i
$547$	29.6203	+	5.89185i	1.26647	+	0.251917i	0.782215	−	0.623008i	$-0.214090\pi$
$547$	29.6203	+	5.89185i	1.26647	+	0.251917i	0.484258	+	0.874925i	$0.339090\pi$
$548$			17.4476i			0.745325i
$549$	1.14175	−	5.73994i	0.0487285	−	0.244975i
$550$		0			0
$551$	17.0647	−	3.39438i	0.726980	−	0.144605i
$552$	0.872647	+	2.10676i	0.0371423	+	0.0896695i
$553$	20.5613	+	49.6395i	0.874357	+	2.11089i
$554$	13.2845	−	2.64245i	0.564403	−	0.112267i
$555$		0			0
$556$	−0.389372	+	1.95750i	−0.0165130	+	0.0830166i
$557$			8.16499i			0.345962i	0.984925	+	0.172981i	$0.0553399\pi$
$557$			8.16499i			0.345962i	−0.984925	+	0.172981i	$0.944660\pi$
$558$	−46.7063	−	9.29046i	−1.97724	−	0.393297i
$559$	8.67993	+	20.9552i	0.367122	+	0.886311i
$560$		0			0
$561$	−1.38638	−	2.02749i	−0.0585330	−	0.0856009i
$562$	12.8673	+	12.8673i	0.542773	+	0.542773i
$563$	0.665621	+	0.275709i	0.0280526	+	0.0116198i	0.396666	−	0.917963i	$-0.370167\pi$
$563$	0.665621	+	0.275709i	0.0280526	+	0.0116198i	−0.368613	+	0.929583i	$0.620167\pi$
$564$	−19.0853	−	28.5632i	−0.803637	−	1.20273i
$565$		0			0
$566$	−17.6486	−	3.51053i	−0.741827	−	0.147559i
$567$	−3.67268	−	18.4638i	−0.154238	−	0.775407i
$568$	−0.892391	+	1.33556i	−0.0374439	+	0.0560388i
$569$	11.0704	−	26.7264i	0.464097	−	1.12043i	−0.502604	−	0.864517i	$-0.667624\pi$
$569$	11.0704	−	26.7264i	0.464097	−	1.12043i	0.966700	−	0.255911i	$-0.0823756\pi$
$570$		0			0
$571$	5.99542	+	30.1410i	0.250901	+	1.26136i	0.876570	+	0.481274i	$0.159826\pi$
$571$	5.99542	+	30.1410i	0.250901	+	1.26136i	−0.625670	+	0.780088i	$0.715174\pi$
$572$	−0.669065	+	0.133085i	−0.0279750	+	0.00556458i
$573$	−11.2238	−	16.7976i	−0.468881	−	0.701729i
$574$	−10.7200	+	10.7200i	−0.447444	+	0.447444i
$575$		0			0
$576$	−5.03395	+	2.08513i	−0.209748	+	0.0868804i
$577$	−14.2185	+	14.2185i	−0.591924	+	0.591924i	−0.938151	−	0.346227i	$-0.887463\pi$
$577$	−14.2185	+	14.2185i	−0.591924	+	0.591924i	0.346227	+	0.938151i	$0.387463\pi$
$578$	−11.7605	+	12.2756i	−0.489171	+	0.510600i
$579$			53.7276i			2.23284i
$580$		0			0
$581$	−2.53834	+	1.69606i	−0.105308	+	0.0703645i
$582$	0.436383			0.0180887
$583$	0.881670	−	0.589113i	0.0365151	−	0.0243986i
$584$	0.452947	−	0.677883i	0.0187431	−	0.0280510i
$585$		0			0
$586$	15.2265	+	6.30703i	0.629002	+	0.260541i
$587$	−11.2438	+	4.65734i	−0.464082	+	0.192229i	−0.602458	−	0.798151i	$-0.705812\pi$
$587$	−11.2438	+	4.65734i	−0.464082	+	0.192229i	0.138376	+	0.990380i	$0.455812\pi$
$588$	28.5083	+	19.0487i	1.17566	+	0.785554i
$589$	−13.8454	−	9.25119i	−0.570489	−	0.381189i
$590$		0			0
$591$	−22.3340	−	22.3340i	−0.918697	−	0.918697i
$592$	−0.374777	+	1.88413i	−0.0154032	+	0.0774373i
$593$	−3.31399	+	8.00069i	−0.136089	+	0.328549i	−0.977202	−	0.212311i	$-0.931901\pi$
$593$	−3.31399	+	8.00069i	−0.136089	+	0.328549i	0.841113	+	0.540860i	$0.181901\pi$
$594$	−1.45872			−0.0598518
$595$		0			0
$596$	−8.66210			−0.354814
$597$	−17.2825	+	41.7235i	−0.707324	+	1.70763i
$598$	0.509442	−	2.56114i	0.0208326	−	0.104733i
$599$	10.9709	+	10.9709i	0.448260	+	0.448260i	0.894776	−	0.446516i	$-0.147335\pi$
$599$	10.9709	+	10.9709i	0.448260	+	0.448260i	−0.446516	+	0.894776i	$0.647335\pi$
$600$		0			0
$601$	11.5196	+	7.69712i	0.469893	+	0.313972i	0.767876	−	0.640599i	$-0.221314\pi$
$601$	11.5196	+	7.69712i	0.469893	+	0.313972i	−0.297983	+	0.954571i	$0.596314\pi$
$602$	−24.5640	−	16.4131i	−1.00115	−	0.668950i
$603$	−39.1221	+	16.2049i	−1.59318	+	0.659915i
$604$	20.9830	+	8.69145i	0.853786	+	0.353650i
$605$		0			0
$606$	−24.4774	+	36.6331i	−0.994328	+	1.48812i
$607$	−23.3412	+	15.5961i	−0.947388	+	0.633025i	−0.930288	−	0.366829i	$-0.880443\pi$
$607$	−23.3412	+	15.5961i	−0.947388	+	0.633025i	−0.0170998	+	0.999854i	$0.505443\pi$
$608$	−1.90524			−0.0772678
$609$	95.6857	−	63.9351i	3.87738	−	2.59078i
$610$		0			0
$611$			39.3387i			1.59148i
$612$	4.61866	+	21.9857i	0.186698	+	0.888719i
$613$	−13.6504	+	13.6504i	−0.551333	+	0.551333i	−0.926826	−	0.375492i	$-0.877474\pi$
$613$	−13.6504	+	13.6504i	−0.551333	+	0.551333i	0.375492	+	0.926826i	$0.377474\pi$
$614$	−5.01652	+	2.07791i	−0.202450	+	0.0838576i
$615$		0			0
$616$	0.628283	−	0.628283i	0.0253143	−	0.0253143i
$617$	−2.86892	−	4.29364i	−0.115498	−	0.172856i	0.769216	−	0.638988i	$-0.220647\pi$
$617$	−2.86892	−	4.29364i	−0.115498	−	0.172856i	−0.884715	+	0.466133i	$0.845647\pi$
$618$	−8.31280	+	1.65352i	−0.334390	+	0.0665143i
$619$	−2.42896	−	12.2112i	−0.0976280	−	0.490809i	−0.998401	−	0.0565198i	$-0.982000\pi$
$619$	−2.42896	−	12.2112i	−0.0976280	−	0.490809i	0.900774	−	0.434289i	$-0.143000\pi$
$620$		0			0
$621$	2.13685	−	5.15882i	0.0857490	−	0.207016i
$622$	−0.209720	+	0.313868i	−0.00840900	+	0.0125850i
$623$	4.43232	+	22.2828i	0.177577	+	0.892740i
$624$	9.48908	+	1.88750i	0.379867	+	0.0755603i
$625$		0			0
$626$	−8.62342	−	12.9059i	−0.344661	−	0.515822i
$627$	−1.04858	−	0.434334i	−0.0418761	−	0.0173456i
$628$	3.04080	+	3.04080i	0.121341	+	0.121341i
$629$	7.34979	+	2.95252i	0.293055	+	0.117725i
$630$		0			0
$631$	6.61850	+	15.9785i	0.263478	+	0.636093i	0.999149	−	0.0412464i	$-0.0131329\pi$
$631$	6.61850	+	15.9785i	0.263478	+	0.636093i	−0.735671	+	0.677339i	$0.763133\pi$
$632$	−12.1550	−	2.41778i	−0.483499	−	0.0961740i
$633$		−	52.3683i		−	2.08145i
$634$	−4.54883	+	22.8685i	−0.180657	+	0.908225i
$635$		0			0
$636$	−14.7499	+	2.93394i	−0.584872	+	0.116338i
$637$	−15.0254	−	36.2745i	−0.595327	−	1.43725i
$638$	−0.716231	−	1.72913i	−0.0283559	−	0.0684571i
$639$	8.58388	−	1.70744i	0.339573	−	0.0675452i
$640$		0			0
$641$	−3.24162	+	16.2967i	−0.128036	+	0.643683i	0.862458	+	0.506129i	$0.168924\pi$
$641$	−3.24162	+	16.2967i	−0.128036	+	0.643683i	−0.990494	+	0.137554i	$0.956076\pi$
$642$		−	1.70945i		−	0.0674667i
$643$	−28.6070	−	5.69028i	−1.12815	−	0.224403i	−0.404478	−	0.914548i	$-0.632547\pi$
$643$	−28.6070	−	5.69028i	−1.12815	−	0.224403i	−0.723671	+	0.690145i	$0.757547\pi$
$644$	1.30159	+	3.14232i	0.0512899	+	0.123825i
$645$		0			0
$646$	−1.44989	+	7.72055i	−0.0570453	+	0.303761i
$647$	24.7423	+	24.7423i	0.972719	+	0.972719i	0.999638	−	0.0269187i	$-0.00856952\pi$
$647$	24.7423	+	24.7423i	0.972719	+	0.972719i	−0.0269187	+	0.999638i	$0.508570\pi$
$648$	4.01173	+	1.66171i	0.157596	+	0.0652782i
$649$	−0.470291	−	0.703840i	−0.0184605	−	0.0276281i
$650$		0			0
$651$	−108.021	−	21.4867i	−4.23368	−	0.842132i
$652$	−0.778926	−	3.91593i	−0.0305051	−	0.153360i
$653$	1.37339	−	2.05543i	0.0537451	−	0.0804352i	−0.803624	−	0.595138i	$-0.797098\pi$
$653$	1.37339	−	2.05543i	0.0537451	−	0.0804352i	0.857369	+	0.514702i	$0.172098\pi$
$654$	3.95629	−	9.55132i	0.154703	−	0.373486i
$655$		0			0
$656$	−0.682203	−	3.42967i	−0.0266355	−	0.133906i
$657$	−4.35688	+	0.866638i	−0.169978	+	0.0338108i
$658$	−28.4666	−	42.6033i	−1.10974	−	1.66085i
$659$	−6.38040	+	6.38040i	−0.248545	+	0.248545i	−0.820373	−	0.571828i	$-0.806234\pi$
$659$	−6.38040	+	6.38040i	−0.248545	+	0.248545i	0.571828	+	0.820373i	$0.306234\pi$
$660$		0			0
$661$	−36.7694	+	15.2304i	−1.43016	+	0.592394i	−0.957392	−	0.288791i	$-0.906747\pi$
$661$	−36.7694	+	15.2304i	−1.43016	+	0.592394i	−0.472772	+	0.881185i	$0.656747\pi$
$662$	1.57353	−	1.57353i	0.0611570	−	0.0611570i
$663$	14.8698	−	37.0159i	0.577497	−	1.43758i
$664$		−	0.704160i		−	0.0273267i
$665$		0			0
$666$	8.70315	−	5.81526i	0.337240	−	0.225337i
$667$	7.16437			0.277406
$668$	−10.3137	+	6.89138i	−0.399048	+	0.266636i
$669$	−15.6777	+	23.4633i	−0.606134	+	0.907144i
$670$		0			0
$671$	−0.203374	−	0.0842402i	−0.00785116	−	0.00325206i
$672$	−11.6424	+	4.82243i	−0.449115	+	0.186029i
$673$	−24.5399	−	16.3970i	−0.945944	−	0.632059i	−0.0160435	−	0.999871i	$-0.505107\pi$
$673$	−24.5399	−	16.3970i	−0.945944	−	0.632059i	−0.929900	+	0.367812i	$0.880107\pi$
$674$	−20.3886	−	13.6232i	−0.785339	−	0.524747i
$675$		0			0
$676$	1.35817	+	1.35817i	0.0522374	+	0.0522374i
$677$	3.91750	−	19.6946i	0.150562	−	0.756925i	−0.829543	−	0.558443i	$-0.811399\pi$
$677$	3.91750	−	19.6946i	0.150562	−	0.756925i	0.980105	−	0.198482i	$-0.0636010\pi$
$678$	3.67095	−	8.86247i	0.140982	−	0.340361i
$679$	0.650886			0.0249787
$680$		0			0
$681$	−1.53824			−0.0589455
$682$	−0.685468	+	1.65487i	−0.0262479	+	0.0633681i
$683$	−3.32933	+	16.7376i	−0.127393	+	0.640448i	0.863340	+	0.504623i	$0.168369\pi$
$683$	−3.32933	+	16.7376i	−0.127393	+	0.640448i	−0.990733	+	0.135825i	$0.956631\pi$
$684$	7.34055	+	7.34055i	0.280673	+	0.280673i
$685$		0			0
$686$	17.2881	+	11.5515i	0.660061	+	0.441039i
$687$	70.7453	+	47.2705i	2.69910	+	1.80348i
$688$	6.29559	−	2.60772i	0.240017	−	0.0994184i
$689$	15.9108	+	6.59046i	0.606152	+	0.251076i
$690$		0			0
$691$	6.72848	−	10.0699i	0.255963	−	0.383076i	−0.681126	−	0.732166i	$-0.738509\pi$
$691$	6.72848	−	10.0699i	0.255963	−	0.383076i	0.937089	+	0.349090i	$0.113509\pi$
$692$	11.4669	−	7.66192i	0.435905	−	0.291262i
$693$	−4.84132			−0.183907
$694$	3.66998	−	2.45220i	0.139311	−	0.0930843i
$695$		0			0
$696$			26.5442i			1.00615i
$697$	−14.4171	+	0.154488i	−0.546086	+	0.00585163i
$698$	−1.86547	+	1.86547i	−0.0706090	+	0.0706090i
$699$	−21.7313	+	9.00140i	−0.821953	+	0.340464i
$700$		0			0
$701$	14.2960	−	14.2960i	0.539954	−	0.539954i	−0.383561	−	0.923515i	$-0.625303\pi$
$701$	14.2960	−	14.2960i	0.539954	−	0.539954i	0.923515	+	0.383561i	$0.125303\pi$
$702$	−13.1621	−	19.6985i	−0.496772	−	0.743472i
$703$	3.58972	−	0.714041i	0.135389	−	0.0269305i
$704$	0.0399830	+	0.201008i	0.00150691	+	0.00757577i
$705$		0			0
$706$	−2.92498	+	7.06152i	−0.110083	+	0.265764i
$707$	−36.5092	+	54.6399i	−1.37307	+	2.05494i
$708$	2.34217	+	11.7749i	0.0880242	+	0.442528i
$709$	−23.2275	−	4.62024i	−0.872327	−	0.173517i	−0.261426	−	0.965224i	$-0.584193\pi$
$709$	−23.2275	−	4.62024i	−0.872327	−	0.173517i	−0.610901	+	0.791707i	$0.709193\pi$
$710$		0			0
$711$	37.5157	+	56.1462i	1.40695	+	2.10565i
$712$	−4.84149	−	2.00541i	−0.181443	−	0.0751560i
$713$	−4.84839	−	4.84839i	−0.181574	−	0.181574i
$714$	10.6819	+	50.8479i	0.399761	+	1.90294i
$715$		0			0
$716$	7.09151	+	17.1204i	0.265022	+	0.639820i
$717$	−57.3969	−	11.4169i	−2.14353	−	0.426374i
$718$			16.4904i			0.615415i
$719$	−4.20295	+	21.1297i	−0.156744	+	0.788003i	0.819794	+	0.572658i	$0.194088\pi$
$719$	−4.20295	+	21.1297i	−0.156744	+	0.788003i	−0.976538	+	0.215345i	$0.930912\pi$
$720$		0			0
$721$	−12.3989	+	2.46630i	−0.461760	+	0.0918497i
$722$	−5.88186	−	14.2001i	−0.218900	−	0.528472i
$723$	−10.1983	−	24.6210i	−0.379281	−	0.915664i
$724$	−19.4855	+	3.87591i	−0.724173	+	0.144047i
$725$		0			0
$726$	6.21387	−	31.2392i	0.230618	−	1.15940i
$727$		−	16.4509i		−	0.610131i	−0.952331	−	0.305065i	$-0.901322\pi$
$727$		−	16.4509i		−	0.610131i	0.952331	−	0.305065i	$-0.0986783\pi$
$728$	14.1534	+	2.81529i	0.524560	+	0.104341i
$729$	14.6971	+	35.4820i	0.544338	+	1.31415i
$730$		0			0
$731$	−5.77622	−	27.4959i	−0.213641	−	1.01697i
$732$	2.20760	+	2.20760i	0.0815952	+	0.0815952i
$733$	−36.0246	−	14.9219i	−1.33060	−	0.551152i	−0.399773	−	0.916614i	$-0.630911\pi$
$733$	−36.0246	−	14.9219i	−1.33060	−	0.551152i	−0.930826	+	0.365462i	$0.880911\pi$
$734$	0.510232	+	0.763616i	0.0188330	+	0.0281856i
$735$		0			0
$736$	−0.769445	−	0.153052i	−0.0283621	−	0.00564158i
$737$	0.310734	+	1.56217i	0.0114460	+	0.0575431i
$738$	−10.5855	+	15.8423i	−0.389656	+	0.583162i
$739$	−12.2812	+	29.6494i	−0.451771	+	1.09067i	0.519877	+	0.854241i	$0.325978\pi$
$739$	−12.2812	+	29.6494i	−0.451771	+	1.09067i	−0.971648	+	0.236431i	$0.924022\pi$
$740$		0			0
$741$	−3.59614	−	18.0790i	−0.132107	−	0.664149i
$742$	−22.0002	+	4.37610i	−0.807651	+	0.160652i
$743$	−28.4498	−	42.5782i	−1.04372	−	1.56204i	−0.807078	−	0.590445i	$-0.798952\pi$
$743$	−28.4498	−	42.5782i	−1.04372	−	1.56204i	−0.236645	−	0.971596i	$-0.576048\pi$
$744$	17.9634	−	17.9634i	0.658570	−	0.658570i
$745$		0			0
$746$	26.7555	−	11.0825i	0.979587	−	0.405758i
$747$	−2.71300	+	2.71300i	−0.0992634	+	0.0992634i
$748$	0.844965	−	0.00905430i	0.0308950	−	0.000331058i
$749$		−	2.54972i		−	0.0931649i
$750$		0			0
$751$	22.9913	−	15.3623i	0.838965	−	0.560578i	−0.0602011	−	0.998186i	$-0.519174\pi$
$751$	22.9913	−	15.3623i	0.838965	−	0.560578i	0.899166	+	0.437608i	$0.144174\pi$
$752$	11.8186			0.430979
$753$	−20.9341	+	13.9877i	−0.762882	+	0.509741i
$754$	16.8876	−	25.2741i	0.615011	−	0.920429i
$755$		0			0
$756$	28.5087	+	11.8087i	1.03685	+	0.429479i
$757$	−28.7956	+	11.9275i	−1.04659	+	0.433513i	−0.838675	−	0.544633i	$-0.816669\pi$
$757$	−28.7956	+	11.9275i	−1.04659	+	0.433513i	−0.207919	+	0.978146i	$0.566669\pi$
$758$	−5.03285	−	3.36284i	−0.182801	−	0.122144i
$759$	−0.388584	−	0.259643i	−0.0141047	−	0.00942446i
$760$		0			0
$761$	−27.3997	−	27.3997i	−0.993237	−	0.993237i	0.00674063	−	0.999977i	$-0.497854\pi$
$761$	−27.3997	−	27.3997i	−0.993237	−	0.993237i	−0.999977	+	0.00674063i	$0.997854\pi$
$762$	−2.92668	+	14.7134i	−0.106022	+	0.533010i
$763$	5.90098	−	14.2462i	0.213630	−	0.515748i
$764$	6.95033			0.251454
$765$		0			0
$766$	29.2200			1.05576
$767$	5.26118	−	12.7016i	0.189970	−	0.458629i
$768$	0.567062	−	2.85081i	0.0204621	−	0.102870i
$769$	−16.7358	−	16.7358i	−0.603507	−	0.603507i	0.337735	−	0.941241i	$-0.390339\pi$
$769$	−16.7358	−	16.7358i	−0.603507	−	0.603507i	−0.941241	+	0.337735i	$0.890339\pi$
$770$		0			0
$771$	9.60684	+	6.41909i	0.345982	+	0.231178i
$772$	−15.3691	−	10.2693i	−0.553146	−	0.369601i
$773$	−3.33513	+	1.38145i	−0.119956	+	0.0496875i	−0.441854	−	0.897087i	$-0.645679\pi$
$773$	−3.33513	+	1.38145i	−0.119956	+	0.0496875i	0.321898	+	0.946774i	$0.395679\pi$
$774$	−34.3028	−	14.2087i	−1.23299	−	0.510721i
$775$		0			0
$776$	−0.0834089	+	0.124830i	−0.00299420	+	0.00448114i
$777$	20.1284	−	13.4494i	0.722103	−	0.482494i
$778$	26.5658			0.952429
$779$	−5.53955	+	3.70141i	−0.198475	+	0.132617i
$780$		0			0
$781$		−	0.329197i		−	0.0117796i
$782$	−1.20576	+	3.00153i	−0.0431178	+	0.107334i
$783$	45.9611	−	45.9611i	1.64252	−	1.64252i
$784$	−10.8980	+	4.51409i	−0.389213	+	0.161217i
$785$		0			0
$786$	−22.4403	+	22.4403i	−0.800419	+	0.800419i
$787$	−24.8711	−	37.2222i	−0.886557	−	1.32683i	−0.944502	−	0.328507i	$-0.893455\pi$
$787$	−24.8711	−	37.2222i	−0.886557	−	1.32683i	0.0579442	−	0.998320i	$-0.481545\pi$
$788$	10.6576	−	2.11993i	0.379662	−	0.0755194i
$789$	−17.4491	−	87.7226i	−0.621205	−	3.12301i
$790$		0			0
$791$	5.47539	−	13.2188i	0.194683	−	0.470005i
$792$	0.620400	−	0.928493i	0.0220449	−	0.0329926i
$793$	−0.697479	−	3.50646i	−0.0247682	−	0.124518i
$794$	−18.6768	−	3.71505i	−0.662816	−	0.131842i
$795$		0			0
$796$	−8.63197	−	12.9187i	−0.305952	−	0.457890i
$797$	15.2682	+	6.32428i	0.540826	+	0.224017i	0.636337	−	0.771411i	$-0.280449\pi$
$797$	15.2682	+	6.32428i	0.540826	+	0.224017i	−0.0955114	+	0.995428i	$0.530449\pi$
$798$	16.9770	+	16.9770i	0.600980	+	0.600980i
$799$	8.99396	−	47.8920i	0.318183	−	1.69430i
$800$		0			0
$801$	10.9269	+	26.3799i	0.386083	+	0.932086i
$802$	7.43709	+	1.47933i	0.262613	+	0.0522370i
$803$			0.167089i			0.00589644i
$804$	4.40702	−	22.1556i	0.155424	−	0.781367i
$805$		0			0
$806$	−28.5324	+	5.67544i	−1.00501	+	0.199909i
$807$	−17.6588	−	42.6321i	−0.621620	−	1.50072i
$808$	−5.80059	−	14.0039i	−0.204064	−	0.492654i
$809$	13.8880	−	2.76250i	0.488276	−	0.0971242i	0.0551885	−	0.998476i	$-0.482424\pi$
$809$	13.8880	−	2.76250i	0.488276	−	0.0971242i	0.433088	+	0.901352i	$0.357424\pi$
$810$		0			0
$811$	2.59779	−	13.0600i	0.0912209	−	0.458598i	−0.907994	−	0.418983i	$-0.862387\pi$
$811$	2.59779	−	13.0600i	0.0912209	−	0.458598i	0.999215	−	0.0396154i	$-0.0126133\pi$
$812$			39.5918i			1.38940i
$813$	56.2299	+	11.1848i	1.97207	+	0.392269i
$814$	−0.150666	−	0.363740i	−0.00528085	−	0.0127491i
$815$		0			0
$816$	−11.1207	−	4.46736i	−0.389303	−	0.156389i
$817$	−9.18029	−	9.18029i	−0.321178	−	0.321178i
$818$	9.42763	+	3.90505i	0.329629	+	0.136537i
$819$	−43.6836	−	65.3772i	−1.52643	−	2.28446i
$820$		0			0
$821$	34.1291	+	6.78870i	1.19111	+	0.236927i	0.750562	−	0.660800i	$-0.229783\pi$
$821$	34.1291	+	6.78870i	1.19111	+	0.236927i	0.440552	+	0.897727i	$0.354783\pi$
$822$	9.89388	+	49.7399i	0.345089	+	1.73488i
$823$	11.5439	−	17.2766i	0.402394	−	0.602226i	−0.573834	−	0.818972i	$-0.694544\pi$
$823$	11.5439	−	17.2766i	0.402394	−	0.602226i	0.976228	+	0.216746i	$0.0695444\pi$
$824$	1.11588	−	2.69398i	0.0388736	−	0.0938491i
$825$		0			0
$826$	3.49346	+	17.5628i	0.121553	+	0.611087i
$827$	16.5320	−	3.28843i	0.574875	−	0.114350i	0.100914	−	0.994895i	$-0.467823\pi$
$827$	16.5320	−	3.28843i	0.574875	−	0.114350i	0.473962	+	0.880545i	$0.342823\pi$
$828$	2.37485	+	3.55421i	0.0825317	+	0.123517i
$829$	6.04684	−	6.04684i	0.210015	−	0.210015i	−0.594259	−	0.804274i	$-0.702554\pi$
$829$	6.04684	−	6.04684i	0.210015	−	0.210015i	0.804274	+	0.594259i	$0.202554\pi$
$830$		0			0
$831$	36.3731	−	15.0662i	1.26177	−	0.522642i
$832$	−2.35364	+	2.35364i	−0.0815978	+	0.0815978i
$833$	9.99892	+	47.5967i	0.346442	+	1.64913i
$834$			5.80128i			0.200882i
$835$		0			0
$836$	0.324665	−	0.216934i	0.0112288	−	0.00750283i
$837$	−62.2071			−2.15019
$838$	6.68327	−	4.46562i	0.230870	−	0.154262i
$839$	−7.84414	+	11.7396i	−0.270810	+	0.405295i	−0.941802	−	0.336169i	$-0.890869\pi$
$839$	−7.84414	+	11.7396i	−0.270810	+	0.405295i	0.670992	+	0.741465i	$0.265869\pi$
$840$		0			0
$841$	50.2559	+	20.8167i	1.73296	+	0.717817i
$842$	−10.6455	+	4.40950i	−0.366867	+	0.151961i
$843$	43.9788	+	29.3857i	1.51471	+	1.01210i
$844$	14.9803	+	10.0095i	0.515642	+	0.344541i
$845$		0			0
$846$	−45.5348	−	45.5348i	−1.56552	−	1.56552i
$847$	9.26826	−	46.5947i	0.318461	−	1.60101i
$848$	1.97998	−	4.78009i	0.0679927	−	0.164149i
$849$	−52.3036			−1.79506
$850$		0			0
$851$	1.50710			0.0516626
$852$	−1.78670	+	4.31347i	−0.0612112	+	0.147777i
$853$	1.08474	−	5.45336i	0.0371408	−	0.186720i	−0.957761	−	0.287564i	$-0.907155\pi$
$853$	1.08474	−	5.45336i	0.0371408	−	0.186720i	0.994902	+	0.100845i	$0.0321545\pi$
$854$	3.29273	+	3.29273i	0.112675	+	0.112675i
$855$		0			0
$856$	0.488999	+	0.326739i	0.0167136	+	0.0111677i
$857$	−6.94199	−	4.63849i	−0.237134	−	0.158448i	0.431326	−	0.902196i	$-0.358046\pi$
$857$	−6.94199	−	4.63849i	−0.237134	−	0.158448i	−0.668460	+	0.743748i	$0.733046\pi$
$858$	−1.83191	+	0.758803i	−0.0625405	+	0.0259051i
$859$	−25.9674	−	10.7561i	−0.885997	−	0.366992i	−0.107177	−	0.994240i	$-0.534181\pi$
$859$	−25.9674	−	10.7561i	−0.885997	−	0.366992i	−0.778819	+	0.627248i	$0.784181\pi$
$860$		0			0
$861$	−24.4818	+	36.6396i	−0.834337	+	1.24867i
$862$	−8.95105	+	5.98090i	−0.304874	+	0.203710i
$863$	−6.00314			−0.204349			−0.102175	−	0.994766i	$-0.532580\pi$
$863$	−6.00314			−0.204349			−0.102175	+	0.994766i	$0.532580\pi$
$864$	−5.91804	+	3.95431i	−0.201336	+	0.134528i
$865$		0			0
$866$			28.0636i			0.953641i
$867$	−26.5658	+	41.6645i	−0.902224	+	1.41500i
$868$	26.7932	−	26.7932i	0.909421	−	0.909421i
$869$	2.34658	−	0.971985i	0.0796022	−	0.0329723i
$870$		0			0
$871$	−18.2917	+	18.2917i	−0.619791	+	0.619791i
$872$	1.97602	+	2.95733i	0.0669166	+	0.100148i
$873$	0.802307	−	0.159589i	0.0271540	−	0.00540126i
$874$	0.291602	+	1.46598i	0.00986357	+	0.0495875i
$875$		0			0
$876$	0.906866	−	2.18937i	0.0306402	−	0.0739719i
$877$	7.68846	−	11.5066i	0.259621	−	0.388550i	−0.678644	−	0.734467i	$-0.737432\pi$
$877$	7.68846	−	11.5066i	0.259621	−	0.388550i	0.938265	+	0.345917i	$0.112432\pi$
$878$	0.966207	+	4.85745i	0.0326079	+	0.163931i
$879$	46.9845	+	9.34579i	1.58475	+	0.315226i
$880$		0			0
$881$	8.61265	+	12.8897i	0.290168	+	0.434267i	0.947701	−	0.319159i	$-0.103400\pi$
$881$	8.61265	+	12.8897i	0.290168	+	0.434267i	−0.657534	+	0.753425i	$0.728400\pi$
$882$	59.3798	+	24.5959i	1.99942	+	0.828188i
$883$	15.7079	+	15.7079i	0.528614	+	0.528614i	0.920159	−	0.391545i	$-0.128059\pi$
$883$	15.7079	+	15.7079i	0.528614	+	0.528614i	−0.391545	+	0.920159i	$0.628059\pi$
$884$	7.74646	+	11.3287i	0.260542	+	0.381026i
$885$		0			0
$886$	−7.89494	−	19.0601i	−0.265236	−	0.640335i
$887$	19.3307	+	3.84511i	0.649061	+	0.129106i	0.508631	−	0.860984i	$-0.330152\pi$
$887$	19.3307	+	3.84511i	0.649061	+	0.129106i	0.140430	+	0.990091i	$0.455152\pi$
$888$			5.58383i			0.187381i
$889$	−4.36527	+	21.9457i	−0.146406	+	0.736035i
$890$		0			0
$891$	−0.872829	+	0.173617i	−0.0292409	+	0.00581637i
$892$	−3.71524	−	8.96939i	−0.124396	−	0.300317i
$893$	−8.61698	−	20.8032i	−0.288356	−	0.696154i
$894$	−24.6941	+	4.91195i	−0.825893	+	0.164280i
$895$		0			0
$896$	0.845799	−	4.25212i	0.0282562	−	0.142053i
$897$		−	7.59022i		−	0.253430i
$898$	−25.6201	−	5.09616i	−0.854954	−	0.170061i
$899$	−30.5437	−	73.7391i	−1.01869	−	2.45934i
$900$		0			0
$901$	−17.8634	−	11.6611i	−0.595117	−	0.388486i
$902$	0.506760	+	0.506760i	0.0168733	+	0.0168733i
$903$	−79.3347	−	32.8615i	−2.64009	−	1.09356i
$904$	1.83351	+	2.74404i	0.0609816	+	0.0912655i
$905$		0			0
$906$	64.7473	+	12.8790i	2.15108	+	0.427877i
$907$	6.60837	+	33.2225i	0.219427	+	1.10314i	0.920708	+	0.390251i	$0.127612\pi$
$907$	6.60837	+	33.2225i	0.219427	+	1.10314i	−0.701281	+	0.712885i	$0.747388\pi$
$908$	0.294014	−	0.440023i	0.00975721	−	0.0146027i
$909$	−31.6057	+	76.3028i	−1.04829	+	2.53081i
$910$		0			0
$911$	−11.2044	−	56.3285i	−0.371220	−	1.86625i	−0.487636	−	0.873047i	$-0.662141\pi$
$911$	−11.2044	−	56.3285i	−0.371220	−	1.86625i	0.116416	−	0.993200i	$-0.462859\pi$
$912$	−5.43149	+	1.08039i	−0.179855	+	0.0357753i
$913$	0.0801770	+	0.119993i	0.00265347	+	0.00397120i
$914$	25.0897	−	25.0897i	0.829894	−	0.829894i
$915$		0			0
$916$	−27.0440	+	11.2020i	−0.893560	+	0.370125i
$917$	−33.4707	+	33.4707i	−1.10530	+	1.10530i
$918$	11.5203	+	26.9907i	0.380226	+	0.890826i
$919$		−	52.4129i		−	1.72894i	−0.502682	−	0.864472i	$-0.667653\pi$
$919$		−	52.4129i		−	1.72894i	0.502682	−	0.864472i	$-0.332347\pi$
$920$		0			0
$921$	−13.1229	+	8.76841i	−0.432413	+	0.288929i
$922$	17.8012			0.586252
$923$	4.44547	−	2.97037i	0.146325	−	0.0977709i
$924$	1.43484	−	2.14740i	0.0472029	−	0.0706441i
$925$		0			0
$926$	−31.3125	−	12.9701i	−1.02899	−	0.426223i
$927$	−14.6787	+	6.08011i	−0.482111	+	0.199697i
$928$	−7.59313	−	5.07356i	−0.249257	−	0.166548i
$929$	2.80819	+	1.87637i	0.0921337	+	0.0615617i	0.600784	−	0.799412i	$-0.294855\pi$
$929$	2.80819	+	1.87637i	0.0921337	+	0.0615617i	−0.508650	+	0.860973i	$0.669855\pi$
$930$		0			0
$931$	15.8915	+	15.8915i	0.520824	+	0.520824i
$932$	1.57874	−	7.93687i	0.0517134	−	0.259981i
$933$	−0.419890	+	1.01370i	−0.0137466	+	0.0331872i
$934$	13.0317			0.426409
$935$		0			0
$936$	18.1363			0.592803
$937$	3.23192	−	7.80256i	0.105582	−	0.254898i	−0.862255	−	0.506474i	$-0.830949\pi$
$937$	3.23192	−	7.80256i	0.105582	−	0.254898i	0.967838	+	0.251575i	$0.0809487\pi$
$938$	6.57326	−	33.0460i	0.214625	−	1.07899i
$939$	−31.9022	−	31.9022i	−1.04109	−	1.04109i
$940$		0			0
$941$	7.93491	+	5.30194i	0.258671	+	0.172838i	0.678143	−	0.734930i	$-0.262785\pi$
$941$	7.93491	+	5.30194i	0.258671	+	0.172838i	−0.419472	+	0.907768i	$0.637785\pi$
$942$	10.3931	+	6.94442i	0.338624	+	0.226262i
$943$	−2.53453	+	1.04984i	−0.0825356	+	0.0341874i
$944$	−3.81596	−	1.58062i	−0.124199	−	0.0514448i
$945$		0			0
$946$	−0.775889	+	1.16120i	−0.0252263	+	0.0377539i
$947$	19.5020	−	13.0308i	0.633730	−	0.423445i	−0.196781	−	0.980448i	$-0.563049\pi$
$947$	19.5020	−	13.0308i	0.633730	−	0.423445i	0.830511	+	0.557003i	$0.188049\pi$
$948$	−36.0226			−1.16996
$949$	−2.25637	+	1.50766i	−0.0732449	+	0.0489407i
$950$		0			0
$951$			67.7734i			2.19770i
$952$	−16.5871	−	6.66327i	−0.537590	−	0.215958i
$953$	−14.9101	+	14.9101i	−0.482986	+	0.482986i	−0.906084	−	0.423098i	$-0.860943\pi$
$953$	−14.9101	+	14.9101i	−0.482986	+	0.482986i	0.423098	+	0.906084i	$0.360943\pi$
$954$	−26.0453	+	10.7883i	−0.843247	+	0.349284i
$955$		0			0
$956$	14.2365	−	14.2365i	0.460442	−	0.460442i
$957$	−3.02237	−	4.52330i	−0.0976993	−	0.146217i
$958$	0.00573095	−	0.00113996i	0.000185158	−	3.68303e-5i
$959$	14.7572	+	74.1893i	0.476534	+	2.39570i
$960$		0			0
$961$	−17.3687	+	41.9317i	−0.560279	+	1.35263i
$962$	3.55248	−	5.31666i	0.114536	−	0.171416i
$963$	−0.625159	−	3.14289i	−0.0201455	−	0.101278i
$964$	8.99226	+	1.78867i	0.289621	+	0.0576093i
$965$		0			0
$966$	5.49249	+	8.22009i	0.176718	+	0.264477i
$967$	−21.6193	−	8.95502i	−0.695231	−	0.287974i	0.00694687	−	0.999976i	$-0.497789\pi$
$967$	−21.6193	−	8.95502i	−0.695231	−	0.287974i	−0.702178	+	0.712002i	$0.747789\pi$
$968$	7.74847	+	7.74847i	0.249045	+	0.249045i
$969$	0.244659	+	22.8320i	0.00785957	+	0.733471i
$970$		0			0
$971$	−15.8385	−	38.2375i	−0.508281	−	1.22710i	−0.944872	−	0.327439i	$-0.893814\pi$
$971$	−15.8385	−	38.2375i	−0.508281	−	1.22710i	0.436591	−	0.899660i	$-0.356186\pi$
$972$	−8.56342	−	1.70337i	−0.274672	−	0.0546356i
$973$			8.65286i			0.277398i
$974$	−5.65336	+	28.4214i	−0.181145	+	0.910680i
$975$		0			0
$976$	−1.05345	+	0.209544i	−0.0337201	+	0.00670735i
$977$	17.9798	+	43.4070i	0.575223	+	1.38871i	0.897057	+	0.441916i	$0.145701\pi$
$977$	17.9798	+	43.4070i	0.575223	+	1.38871i	−0.321833	+	0.946796i	$0.604299\pi$
$978$	−4.44115	−	10.7219i	−0.142012	−	0.342848i
$979$	1.05336	−	0.209526i	0.0336655	−	0.00669649i
$980$		0			0
$981$	3.78078	−	19.0073i	0.120711	−	0.606856i
$982$		−	31.2696i		−	0.997852i
$983$	46.5284	+	9.25506i	1.48402	+	0.295191i	0.869589	−	0.493777i	$-0.164384\pi$
$983$	46.5284	+	9.25506i	1.48402	+	0.295191i	0.614435	+	0.788967i	$0.289384\pi$
$984$	−3.88967	−	9.39049i	−0.123998	−	0.299358i
$985$		0			0
$986$	−26.3378	+	26.9084i	−0.838767	+	0.856938i
$987$	−105.312	−	105.312i	−3.35211	−	3.35211i
$988$	5.85896	+	2.42686i	0.186398	+	0.0772088i
$989$	−2.97005	−	4.44500i	−0.0944422	−	0.141343i
$990$		0			0
$991$	44.9876	+	8.94859i	1.42908	+	0.284261i	0.848177	−	0.529712i	$-0.177700\pi$
$991$	44.9876	+	8.94859i	1.42908	+	0.284261i	0.580902	+	0.813974i	$0.302700\pi$
$992$	1.70508	+	8.57200i	0.0541363	+	0.272161i
$993$	3.59355	−	5.37813i	0.114038	−	0.170670i
$994$	−2.66494	+	6.43373i	−0.0845267	+	0.204066i
$995$		0			0
$996$	−0.399303	−	2.00743i	−0.0126524	−	0.0636078i
$997$	−39.4467	+	7.84644i	−1.24929	+	0.248499i	−0.775052	−	0.631897i	$-0.782276\pi$
$997$	−39.4467	+	7.84644i	−1.24929	+	0.248499i	−0.474238	+	0.880397i	$0.657276\pi$
$998$	3.60412	+	5.39395i	0.114087	+	0.170743i
$999$	9.66837	−	9.66837i	0.305894	−	0.305894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.607.1		40
5.2	odd	4		170.2.o.b.63.5	yes	40
5.3	odd	4		850.2.s.d.743.1		40
5.4	even	2		170.2.r.b.97.5	yes	40
17.10	odd	16		850.2.s.d.707.1		40
85.27	even	16		170.2.r.b.163.5	yes	40
85.44	odd	16		170.2.o.b.27.5	✓	40
85.78	even	16	inner	850.2.v.d.843.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.27.5	✓	40	85.44	odd	16
170.2.o.b.63.5	yes	40	5.2	odd	4
170.2.r.b.97.5	yes	40	5.4	even	2
170.2.r.b.163.5	yes	40	85.27	even	16
850.2.s.d.707.1		40	17.10	odd	16
850.2.s.d.743.1		40	5.3	odd	4
850.2.v.d.607.1		40	1.1	even	1	trivial
850.2.v.d.843.1		40	85.78	even	16	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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(-0.567062 + 2.85081i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-2.41680 - 1.61486i) q^{6} +(-3.60477 - 2.40863i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-5.03395 - 2.08513i) q^{9} +(-0.113862 + 0.170406i) q^{11} +(2.41680 - 1.61486i) q^{12} -3.32855 q^{13} +(3.60477 - 2.40863i) q^{14} +1.00000i q^{16} +(4.05227 + 0.761002i) q^{17} +(3.85282 - 3.85282i) q^{18} +(1.76021 - 0.729105i) q^{19} +(8.91069 - 8.91069i) q^{21} +(-0.113862 - 0.170406i) q^{22} +(0.769445 - 0.153052i) q^{23} +(0.567062 + 2.85081i) q^{24} +(1.27378 - 3.07518i) q^{26} +(3.95431 - 5.91804i) q^{27} +(0.845799 + 4.25212i) q^{28} +(8.95670 + 1.78160i) q^{29} +(-4.85565 - 7.26699i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-0.421230 - 0.421230i) q^{33} +(-2.25381 + 3.45258i) q^{34} +(2.08513 + 5.03395i) q^{36} +(1.88413 + 0.374777i) q^{37} +1.90524i q^{38} +(1.88750 - 9.48908i) q^{39} +(-3.42967 + 0.682203i) q^{41} +(4.82243 + 11.6424i) q^{42} +(-2.60772 - 6.29559i) q^{43} +(0.201008 - 0.0399830i) q^{44} +(-0.153052 + 0.769445i) q^{46} -11.8186i q^{47} +(-2.85081 - 0.567062i) q^{48} +(4.51409 + 10.8980i) q^{49} +(-4.46736 + 11.1207i) q^{51} +(2.35364 + 2.35364i) q^{52} +(-4.78009 - 1.97998i) q^{53} +(3.95431 + 5.91804i) q^{54} +(-4.25212 - 0.845799i) q^{56} +(1.08039 + 5.43149i) q^{57} +(-5.07356 + 7.59313i) q^{58} +(-1.58062 + 3.81596i) q^{59} +(0.209544 + 1.05345i) q^{61} +(8.57200 - 1.70508i) q^{62} +(13.1239 + 19.6413i) q^{63} +(0.707107 - 0.707107i) q^{64} +(0.550364 - 0.227968i) q^{66} +(5.49540 - 5.49540i) q^{67} +(-2.32728 - 3.40350i) q^{68} +2.28034i q^{69} +(-1.33556 + 0.892391i) q^{71} -5.44870 q^{72} +(0.677883 - 0.452947i) q^{73} +(-1.06727 + 1.59729i) q^{74} +(-1.76021 - 0.729105i) q^{76} +(0.820892 - 0.340025i) q^{77} +(8.04446 + 5.37513i) q^{78} +(-10.3045 - 6.88525i) q^{79} +(3.07044 + 3.07044i) q^{81} +(0.682203 - 3.42967i) q^{82} +(0.269470 - 0.650559i) q^{83} -12.6016 q^{84} +6.81430 q^{86} +(-10.1580 + 24.5236i) q^{87} +(-0.0399830 + 0.201008i) q^{88} +(-3.70552 - 3.70552i) q^{89} +(11.9987 + 8.01725i) q^{91} +(-0.652304 - 0.435856i) q^{92} +(23.4703 - 9.72172i) q^{93} +(10.9189 + 4.52277i) q^{94} +(1.61486 - 2.41680i) q^{96} +(-0.124830 + 0.0834089i) q^{97} -11.7959 q^{98} +(0.928493 - 0.620400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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