LMFDB - Embedded newform 850.2.s.d.743.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(7,850)]

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, 11]))

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

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

chi := DirichletCharacter("850.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.s (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			743.1
Character	$\chi$	$=$	850.743
Dual form			850.2.s.d.707.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 + 0.382683i) q^{2} +(-2.85081 - 0.567062i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.41680 - 1.61486i) q^{6} +(-2.40863 + 3.60477i) q^{7} +(0.382683 + 0.923880i) q^{8} +(5.03395 + 2.08513i) q^{9} +(-0.113862 + 0.170406i) q^{11} +(-1.61486 - 2.41680i) q^{12} -3.32855i q^{13} +(-3.60477 + 2.40863i) q^{14} +1.00000i q^{16} +(0.761002 - 4.05227i) q^{17} +(3.85282 + 3.85282i) q^{18} +(-1.76021 + 0.729105i) q^{19} +(8.91069 - 8.91069i) q^{21} +(-0.170406 + 0.113862i) q^{22} +(0.153052 + 0.769445i) q^{23} +(-0.567062 - 2.85081i) q^{24} +(1.27378 - 3.07518i) q^{26} +(-5.91804 - 3.95431i) q^{27} +(-4.25212 + 0.845799i) q^{28} +(-8.95670 - 1.78160i) q^{29} +(-4.85565 - 7.26699i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(0.421230 - 0.421230i) q^{33} +(2.25381 - 3.45258i) q^{34} +(2.08513 + 5.03395i) q^{36} +(0.374777 - 1.88413i) q^{37} -1.90524 q^{38} +(-1.88750 + 9.48908i) q^{39} +(-3.42967 + 0.682203i) q^{41} +(11.6424 - 4.82243i) q^{42} +(6.29559 - 2.60772i) q^{43} +(-0.201008 + 0.0399830i) q^{44} +(-0.153052 + 0.769445i) q^{46} -11.8186 q^{47} +(0.567062 - 2.85081i) q^{48} +(-4.51409 - 10.8980i) q^{49} +(-4.46736 + 11.1207i) q^{51} +(2.35364 - 2.35364i) q^{52} +(1.97998 - 4.78009i) q^{53} +(-3.95431 - 5.91804i) q^{54} +(-4.25212 - 0.845799i) q^{56} +(5.43149 - 1.08039i) q^{57} +(-7.59313 - 5.07356i) q^{58} +(1.58062 - 3.81596i) q^{59} +(0.209544 + 1.05345i) q^{61} +(-1.70508 - 8.57200i) q^{62} +(-19.6413 + 13.1239i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(0.550364 - 0.227968i) q^{66} +(-5.49540 - 5.49540i) q^{67} +(3.40350 - 2.32728i) q^{68} -2.28034i q^{69} +(-1.33556 + 0.892391i) q^{71} +5.44870i q^{72} +(0.452947 + 0.677883i) q^{73} +(1.06727 - 1.59729i) q^{74} +(-1.76021 - 0.729105i) q^{76} +(-0.340025 - 0.820892i) q^{77} +(-5.37513 + 8.04446i) q^{78} +(10.3045 + 6.88525i) q^{79} +(3.07044 + 3.07044i) q^{81} +(-3.42967 - 0.682203i) q^{82} +(0.650559 + 0.269470i) q^{83} +12.6016 q^{84} +6.81430 q^{86} +(24.5236 + 10.1580i) q^{87} +(-0.201008 - 0.0399830i) q^{88} +(3.70552 + 3.70552i) q^{89} +(11.9987 + 8.01725i) q^{91} +(-0.435856 + 0.652304i) q^{92} +(9.72172 + 23.4703i) q^{93} +(-10.9189 - 4.52277i) q^{94} +(1.61486 - 2.41680i) q^{96} +(0.0834089 + 0.124830i) q^{97} -11.7959i 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} - 16 q^{37} + 32 q^{39} - 56 q^{41} + 8 q^{42} + 48 q^{43} - 16 q^{44} + 96 q^{47} - 16 q^{49} - 32 q^{51}+ \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 - 16 * q^37 + 32 * q^39 - 56 * q^41 + 8 * q^42 + 48 * q^43 - 16 * q^44 + 96 * q^47 - 16 * q^49 - 32 * q^51 + 16 * q^52 + 40 * q^53 + 24 * q^54 - 8 * q^56 + 8 * q^57 - 16 * q^58 + 24 * q^61 + 24 * q^62 + 24 * q^63 + 16 * q^67 - 24 * q^68 + 24 * q^71 - 16 * q^73 - 32 * q^74 - 40 * q^77 - 16 * q^78 + 104 * q^79 + 48 * q^81 - 56 * q^82 - 16 * q^83 + 96 * q^86 + 8 * q^87 - 16 * q^88 + 16 * q^89 + 48 * q^91 - 8 * q^92 - 136 * q^93 + 8 * q^94 - 144 * q^97 - 160 * q^99

Character values

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

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{16}\right)$

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 $

$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$3$	−2.85081	−	0.567062i	−1.64592	−	0.327394i	−0.716829	−	0.697249i	$-0.754407\pi$
$3$	−2.85081	−	0.567062i	−1.64592	−	0.327394i	−0.929089	+	0.369855i	$0.879407\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−2.41680	−	1.61486i	−0.986656	−	0.659263i
$7$	−2.40863	+	3.60477i	−0.910377	+	1.36248i	0.0215260	+	0.999768i	$0.493148\pi$
$7$	−2.40863	+	3.60477i	−0.910377	+	1.36248i	−0.931903	+	0.362707i	$0.881852\pi$
$8$	0.382683	+	0.923880i	0.135299	+	0.326641i
$9$	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	$0.197336\pi$
$12$	−1.61486	−	2.41680i	−0.466169	−	0.697671i
$13$		−	3.32855i		−	0.923174i	−0.887095	−	0.461587i	$-0.847280\pi$
$13$		−	3.32855i		−	0.923174i	0.887095	−	0.461587i	$-0.152720\pi$
$14$	−3.60477	+	2.40863i	−0.963416	+	0.643734i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	0.761002	−	4.05227i	0.184570	−	0.982819i
$17$	0.761002	−	4.05227i	0.184570	−	0.982819i
$18$	3.85282	+	3.85282i	0.908117	+	0.908117i
$19$	−1.76021	+	0.729105i	−0.403821	+	0.167268i	−0.575343	−	0.817912i	$-0.695131\pi$
$19$	−1.76021	+	0.729105i	−0.403821	+	0.167268i	0.171522	+	0.985180i	$0.445131\pi$
$20$		0			0
$21$	8.91069	−	8.91069i	1.94447	−	1.94447i
$22$	−0.170406	+	0.113862i	−0.0363307	+	0.0242754i
$23$	0.153052	+	0.769445i	0.0319136	+	0.160440i	0.993456	−	0.114216i	$-0.0364357\pi$
$23$	0.153052	+	0.769445i	0.0319136	+	0.160440i	−0.961542	+	0.274657i	$0.911436\pi$
$24$	−0.567062	−	2.85081i	−0.115751	−	0.581920i
$25$		0			0
$26$	1.27378	−	3.07518i	0.249809	−	0.603093i
$27$	−5.91804	−	3.95431i	−1.13893	−	0.761007i
$28$	−4.25212	+	0.845799i	−0.803575	+	0.159841i
$29$	−8.95670	−	1.78160i	−1.66322	−	0.330835i	−0.728181	−	0.685385i	$-0.759634\pi$
$29$	−8.95670	−	1.78160i	−1.66322	−	0.330835i	−0.935037	+	0.354550i	$0.884634\pi$
$30$		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	$-0.474770\pi$
$32$	−0.382683	+	0.923880i	−0.0676495	+	0.163320i
$33$	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
$37$	0.374777	−	1.88413i	0.0616129	−	0.309749i	−0.937674	−	0.347517i	$-0.887025\pi$
$37$	0.374777	−	1.88413i	0.0616129	−	0.309749i	0.999287	+	0.0377681i	$0.0120248\pi$
$38$	−1.90524			−0.309071
$39$	−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	$0.525535\pi$
$42$	11.6424	−	4.82243i	1.79646	−	0.744117i
$43$	6.29559	−	2.60772i	0.960069	−	0.397674i	0.153063	−	0.988216i	$-0.451086\pi$
$43$	6.29559	−	2.60772i	0.960069	−	0.397674i	0.807006	+	0.590543i	$0.201086\pi$
$44$	−0.201008	+	0.0399830i	−0.0303031	+	0.00602766i
$45$		0			0
$46$	−0.153052	+	0.769445i	−0.0225663	+	0.113449i
$47$	−11.8186			−1.72392			−0.861958	−	0.506979i	$-0.830762\pi$
$47$	−11.8186			−1.72392			−0.861958	+	0.506979i	$0.830762\pi$
$48$	0.567062	−	2.85081i	0.0818484	−	0.411480i
$49$	−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
$53$	1.97998	−	4.78009i	0.271971	−	0.656596i	−0.727597	−	0.686005i	$-0.759363\pi$
$53$	1.97998	−	4.78009i	0.271971	−	0.656596i	0.999567	+	0.0294096i	$0.00936271\pi$
$54$	−3.95431	−	5.91804i	−0.538113	−	0.805343i
$55$		0			0
$56$	−4.25212	−	0.845799i	−0.568213	−	0.113025i
$57$	5.43149	−	1.08039i	0.719419	−	0.143101i
$58$	−7.59313	−	5.07356i	−0.997026	−	0.666192i
$59$	1.58062	−	3.81596i	0.205779	−	0.496795i	−0.786971	−	0.616990i	$-0.788352\pi$
$59$	1.58062	−	3.81596i	0.205779	−	0.496795i	0.992750	+	0.120195i	$0.0383519\pi$
$60$		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	$0.915595\pi$
$62$	−1.70508	−	8.57200i	−0.216545	−	1.08865i
$63$	−19.6413	+	13.1239i	−2.47458	+	1.65346i
$64$	−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	$-0.407454\pi$
$67$	−5.49540	−	5.49540i	−0.671369	−	0.671369i	−0.958032	+	0.286662i	$0.907454\pi$
$68$	3.40350	−	2.32728i	0.412734	−	0.282224i
$69$		−	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	$0.342886\pi$
$72$			5.44870i			0.642136i
$73$	0.452947	+	0.677883i	0.0530135	+	0.0793403i	0.857029	−	0.515267i	$-0.172307\pi$
$73$	0.452947	+	0.677883i	0.0530135	+	0.0793403i	−0.804016	+	0.594608i	$0.797307\pi$
$74$	1.06727	−	1.59729i	0.124068	−	0.185681i
$75$		0			0
$76$	−1.76021	−	0.729105i	−0.201910	−	0.0836340i
$77$	−0.340025	−	0.820892i	−0.0387494	−	0.0935493i
$78$	−5.37513	+	8.04446i	−0.608614	+	0.910855i
$79$	10.3045	+	6.88525i	1.15935	+	0.774651i	0.977966	−	0.208762i	$-0.0669435\pi$
$79$	10.3045	+	6.88525i	1.15935	+	0.774651i	0.181380	+	0.983413i	$0.441944\pi$
$80$		0			0
$81$	3.07044	+	3.07044i	0.341160	+	0.341160i
$82$	−3.42967	−	0.682203i	−0.378743	−	0.0753367i
$83$	0.650559	+	0.269470i	0.0714081	+	0.0295782i	0.418102	−	0.908400i	$-0.362696\pi$
$83$	0.650559	+	0.269470i	0.0714081	+	0.0295782i	−0.346693	+	0.937978i	$0.612696\pi$
$84$	12.6016			1.37495
$85$		0			0
$86$	6.81430			0.734805
$87$	24.5236	+	10.1580i	2.62921	+	1.08905i
$88$	−0.201008	−	0.0399830i	−0.0214275	−	0.00426220i
$89$	3.70552	+	3.70552i	0.392784	+	0.392784i	0.875679	−	0.482894i	$-0.160415\pi$
$89$	3.70552	+	3.70552i	0.392784	+	0.392784i	−0.482894	+	0.875679i	$0.660415\pi$
$90$		0			0
$91$	11.9987	+	8.01725i	1.25780	+	0.840437i
$92$	−0.435856	+	0.652304i	−0.0454411	+	0.0680074i
$93$	9.72172	+	23.4703i	1.00810	+	2.43376i
$94$	−10.9189	−	4.52277i	−1.12620	−	0.466489i
$95$		0			0
$96$	1.61486	−	2.41680i	0.164816	−	0.246664i
$97$	0.0834089	+	0.124830i	0.00846889	+	0.0126746i	0.835680	−	0.549217i	$-0.185074\pi$
$97$	0.0834089	+	0.124830i	0.00846889	+	0.0126746i	−0.827211	+	0.561891i	$0.810074\pi$
$98$		−	11.7959i		−	1.19156i
$99$	−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	$-0.271937\pi$
$102$	−8.38302	+	8.56463i	−0.830043	+	0.848025i
$103$	2.06188	+	2.06188i	0.203163	+	0.203163i	0.801354	−	0.598191i	$-0.204113\pi$
$103$	2.06188	+	2.06188i	0.203163	+	0.203163i	−0.598191	+	0.801354i	$0.704113\pi$
$104$	3.07518	−	1.27378i	0.301546	−	0.124905i
$105$		0			0
$106$	3.65852	−	3.65852i	0.355347	−	0.355347i
$107$	0.488999	−	0.326739i	0.0472733	−	0.0315870i	−0.531709	−	0.846927i	$-0.678450\pi$
$107$	0.488999	−	0.326739i	0.0472733	−	0.0315870i	0.578982	+	0.815340i	$0.303450\pi$
$108$	−1.38857	−	6.98080i	−0.133615	−	0.671728i
$109$	−0.693887	−	3.48840i	−0.0664623	−	0.334129i	0.933221	−	0.359304i	$-0.116986\pi$
$109$	−0.693887	−	3.48840i	−0.0664623	−	0.334129i	−0.999683	+	0.0251750i	$0.991986\pi$
$110$		0			0
$111$	−2.13684	+	5.15878i	−0.202820	+	0.489650i
$112$	−3.60477	−	2.40863i	−0.340619	−	0.227594i
$113$	−3.23682	+	0.643843i	−0.304494	+	0.0605677i	−0.344973	−	0.938613i	$-0.612112\pi$
$113$	−3.23682	+	0.643843i	−0.304494	+	0.0605677i	0.0404784	+	0.999180i	$0.487112\pi$
$114$	5.43149	+	1.08039i	0.508706	+	0.101188i
$115$		0			0
$116$	−5.07356	−	7.59313i	−0.471069	−	0.705004i
$117$	6.94046	−	16.7557i	0.641646	−	1.54907i
$118$	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
$122$	−0.209544	+	1.05345i	−0.0189713	+	0.0953749i
$123$	10.1642			0.916474
$124$	1.70508	−	8.57200i	0.153120	−	0.769789i
$125$		0			0
$126$	−23.1685	+	4.60851i	−2.06402	+	0.410558i
$127$	−4.76825	+	1.97507i	−0.423114	+	0.175260i	−0.584072	−	0.811702i	$-0.698542\pi$
$127$	−4.76825	+	1.97507i	−0.423114	+	0.175260i	0.160958	+	0.986961i	$0.448542\pi$
$128$	−0.923880	+	0.382683i	−0.0816602	+	0.0338248i
$129$	−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	$-0.0957618\pi$
$132$	0.595709			0.0518498
$133$	1.61145	−	8.10132i	0.139731	−	0.702473i
$134$	−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	−0.0555950	+	0.998453i	$0.517706\pi$
$137$	−12.3373	+	12.3373i	−1.05405	+	1.05405i	−0.998453	+	0.0555950i	$0.982294\pi$
$138$	0.872647	−	2.10676i	0.0742847	−	0.179339i
$139$	1.10884	+	1.65949i	0.0940503	+	0.140756i	0.875511	−	0.483198i	$-0.160525\pi$
$139$	1.10884	+	1.65949i	0.0940503	+	0.140756i	−0.781461	+	0.623955i	$0.785525\pi$
$140$		0			0
$141$	33.6926	+	6.70187i	2.83743	+	0.564399i
$142$	−1.57540	+	0.313366i	−0.132204	+	0.0262971i
$143$	0.567206	+	0.378995i	0.0474322	+	0.0316932i
$144$	−2.08513	+	5.03395i	−0.173761	+	0.419496i
$145$		0			0
$146$	0.159054	+	0.799618i	0.0131634	+	0.0661769i
$147$	6.68900	+	33.6279i	0.551699	+	2.77358i
$148$	1.59729	−	1.06727i	0.131296	−	0.0877294i
$149$	−6.12503	+	6.12503i	−0.501782	+	0.501782i	−0.911991	−	0.410209i	$-0.865456\pi$
$149$	−6.12503	+	6.12503i	−0.501782	+	0.501782i	0.410209	+	0.911991i	$0.365456\pi$
$150$		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
$153$	12.2803	−	18.8121i	0.992807	−	1.52087i
$154$		−	0.888527i		−	0.0715995i
$155$		0			0
$156$	−8.04446	+	5.37513i	−0.644072	+	0.430355i
$157$			4.30033i			0.343204i	0.985166	+	0.171602i	$0.0548943\pi$
$157$			4.30033i			0.343204i	−0.985166	+	0.171602i	$0.945106\pi$
$158$	6.88525	+	10.3045i	0.547761	+	0.819782i
$159$	−8.35516	+	12.5044i	−0.662607	+	0.991661i
$160$		0			0
$161$	−3.14232	−	1.30159i	−0.247650	−	0.102580i
$162$	1.66171	+	4.01173i	0.130556	+	0.315191i
$163$	−2.21819	+	3.31976i	−0.173742	+	0.260024i	−0.908113	−	0.418724i	$-0.862477\pi$
$163$	−2.21819	+	3.31976i	−0.173742	+	0.260024i	0.734371	+	0.678748i	$0.237477\pi$
$164$	−2.90753	−	1.94275i	−0.227040	−	0.151703i
$165$		0			0
$166$	0.497916	+	0.497916i	0.0386458	+	0.0386458i
$167$	−12.1658	−	2.41993i	−0.941419	−	0.187260i	−0.299556	−	0.954079i	$-0.596838\pi$
$167$	−12.1658	−	2.41993i	−0.941419	−	0.187260i	−0.641864	+	0.766819i	$0.721838\pi$
$168$	11.6424	+	4.82243i	0.898229	+	0.372059i
$169$	1.92074			0.147750
$170$		0			0
$171$	−10.3811			−0.793863
$172$	6.29559	+	2.60772i	0.480035	+	0.198837i
$173$	−13.5261	−	2.69051i	−1.02837	−	0.204556i	−0.348054	−	0.937474i	$-0.613157\pi$
$173$	−13.5261	−	2.69051i	−1.02837	−	0.204556i	−0.680316	+	0.732919i	$0.738157\pi$
$174$	18.7696	+	18.7696i	1.42292	+	1.42292i
$175$		0			0
$176$	−0.170406	−	0.113862i	−0.0128449	−	0.00858266i
$177$	−6.66994	+	9.98227i	−0.501344	+	0.750314i
$178$	2.00541	+	4.84149i	0.150312	+	0.362885i
$179$	17.1204	+	7.09151i	1.27964	+	0.530044i	0.915881	−	0.401449i	$-0.131493\pi$
$179$	17.1204	+	7.09151i	1.27964	+	0.530044i	0.363758	+	0.931493i	$0.381493\pi$
$180$		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	$-0.0768997\pi$
$182$	8.01725	+	11.9987i	0.594278	+	0.889400i
$183$		−	3.12202i		−	0.230786i
$184$	−0.652304	+	0.435856i	−0.0480885	+	0.0321317i
$185$		0			0
$186$			25.4041i			1.86272i
$187$	0.603883	+	0.591078i	0.0441603	+	0.0432239i
$188$	−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	$0.330909\pi$
$192$	2.41680	−	1.61486i	0.174418	−	0.116542i
$193$	3.60610	+	18.1291i	0.259573	+	1.30496i	0.862049	+	0.506825i	$0.169181\pi$
$193$	3.60610	+	18.1291i	0.259573	+	1.30496i	−0.602476	+	0.798137i	$0.705819\pi$
$194$	0.0292893	+	0.147247i	0.00210285	+	0.0105717i
$195$		0			0
$196$	4.51409	−	10.8980i	0.322435	−	0.778427i
$197$	9.03509	+	6.03705i	0.643723	+	0.430122i	0.834118	−	0.551585i	$-0.185977\pi$
$197$	9.03509	+	6.03705i	0.643723	+	0.430122i	−0.190395	+	0.981708i	$0.560977\pi$
$198$	−1.09523	+	0.217855i	−0.0778348	+	0.0154823i
$199$	−15.2386	−	3.03114i	−1.08024	−	0.214872i	−0.377275	−	0.926101i	$-0.623139\pi$
$199$	−15.2386	−	3.03114i	−1.08024	−	0.214872i	−0.702960	+	0.711229i	$0.748139\pi$
$200$		0			0
$201$	12.5501	+	18.7826i	0.885217	+	1.32482i
$202$	5.80059	−	14.0039i	0.408128	−	0.985308i
$203$	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
$207$	−0.833936	+	4.19248i	−0.0579626	+	0.291398i
$208$	3.32855			0.230794
$209$	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	$0.650431\pi$
$212$	4.78009	−	1.97998i	0.328298	−	0.135985i
$213$	4.31347	−	1.78670i	0.295554	−	0.122422i
$214$	0.576814	−	0.114735i	0.0394302	−	0.00784315i
$215$		0			0
$216$	1.38857	−	6.98080i	0.0944801	−	0.474983i
$217$	37.8913			2.57223
$218$	0.693887	−	3.48840i	0.0469959	−	0.236265i
$219$	−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
$223$	−3.71524	+	8.96939i	−0.248791	+	0.600635i	−0.998102	−	0.0615836i	$-0.980385\pi$
$223$	−3.71524	+	8.96939i	−0.248791	+	0.600635i	0.749311	+	0.662218i	$0.230385\pi$
$224$	−2.40863	−	3.60477i	−0.160933	−	0.240854i
$225$		0			0
$226$	−3.23682	−	0.643843i	−0.215310	−	0.0428278i
$227$	0.519043	−	0.103244i	0.0344501	−	0.00685255i	−0.177835	−	0.984060i	$-0.556909\pi$
$227$	0.519043	−	0.103244i	0.0344501	−	0.00685255i	0.212285	+	0.977208i	$0.431909\pi$
$228$	4.60460	+	3.07669i	0.304947	+	0.203759i
$229$	−11.2020	+	27.0440i	−0.740249	+	1.78712i	−0.135382	+	0.990793i	$0.543226\pi$
$229$	−11.2020	+	27.0440i	−0.740249	+	1.78712i	−0.604867	+	0.796326i	$0.706774\pi$
$230$		0			0
$231$	0.503850	+	2.53303i	0.0331509	+	0.166661i
$232$	−1.78160	−	8.95670i	−0.116968	−	0.588036i
$233$	−6.72855	+	4.49587i	−0.440802	+	0.294535i	−0.756097	−	0.654459i	$-0.772896\pi$
$233$	−6.72855	+	4.49587i	−0.440802	+	0.294535i	0.315295	+	0.948994i	$0.397896\pi$
$234$	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
$238$	7.01718	+	16.4405i	0.454856	+	1.06568i
$239$		−	20.1335i		−	1.30233i	−0.758937	−	0.651164i	$-0.774281\pi$
$239$		−	20.1335i		−	1.30233i	0.758937	−	0.651164i	$-0.225719\pi$
$240$		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	$0.407918\pi$
$242$			10.9580i			0.704407i
$243$	4.85079	+	7.25971i	0.311178	+	0.465711i
$244$	−0.596732	+	0.893072i	−0.0382018	+	0.0571731i
$245$		0			0
$246$	9.39049	+	3.88967i	0.598716	+	0.247996i
$247$	2.42686	+	5.85896i	0.154418	+	0.372797i
$248$	4.85565	−	7.26699i	0.308334	−	0.461454i
$249$	−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	$0.661863\pi$
$252$	−23.1685	−	4.60851i	−1.45948	−	0.290309i
$253$	−0.148545	−	0.0615294i	−0.00933895	−	0.00386832i
$254$	−5.16112			−0.323837
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−3.67244	−	1.52117i	−0.229080	−	0.0948882i	0.265191	−	0.964196i	$-0.414565\pi$
$257$	−3.67244	−	1.52117i	−0.229080	−	0.0948882i	−0.494271	+	0.869308i	$0.664565\pi$
$258$	−19.4263	−	3.86413i	−1.20943	−	0.240570i
$259$	5.88916	+	5.88916i	0.365935	+	0.365935i
$260$		0			0
$261$	−41.3727	−	27.6444i	−2.56091	−	1.71114i
$262$	6.06580	−	9.07811i	0.374746	−	0.560847i
$263$	−11.7756	−	28.4288i	−0.726113	−	1.75299i	−0.655132	−	0.755514i	$-0.727387\pi$
$263$	−11.7756	−	28.4288i	−0.726113	−	1.75299i	−0.0709807	−	0.997478i	$-0.522613\pi$
$264$	0.550364	+	0.227968i	0.0338725	+	0.0140305i
$265$		0			0
$266$	4.58903	−	6.86796i	0.281371	−	0.421102i
$267$	−8.46248	−	12.6650i	−0.517896	−	0.775086i
$268$		−	7.77166i		−	0.474730i
$269$	13.2000	−	8.81994i	0.804817	−	0.537761i	−0.0837617	−	0.996486i	$-0.526693\pi$
$269$	13.2000	−	8.81994i	0.804817	−	0.537761i	0.888579	+	0.458724i	$0.151693\pi$
$270$		0			0
$271$		−	19.7242i		−	1.19816i	−0.800690	−	0.599079i	$-0.795534\pi$
$271$		−	19.7242i		−	1.19816i	0.800690	−	0.599079i	$-0.204466\pi$
$272$	4.05227	+	0.761002i	0.245705	+	0.0461425i
$273$	−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
$277$	−11.2620	+	7.52505i	−0.676670	+	0.452136i	−0.845830	−	0.533452i	$-0.820894\pi$
$277$	−11.2620	+	7.52505i	−0.676670	+	0.452136i	0.169160	+	0.985589i	$0.445894\pi$
$278$	0.389372	+	1.95750i	0.0233530	+	0.117403i
$279$	−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	$-0.0576258\pi$
$282$	28.5632	+	19.0853i	1.70091	+	1.13651i
$283$	−17.6486	+	3.51053i	−1.04910	+	0.208679i	−0.689394	−	0.724386i	$-0.742123\pi$
$283$	−17.6486	+	3.51053i	−1.04910	+	0.208679i	−0.359707	+	0.933065i	$0.617123\pi$
$284$	−1.57540	−	0.313366i	−0.0934827	−	0.0185949i
$285$		0			0
$286$	0.378995	+	0.567206i	0.0224104	+	0.0335396i
$287$	5.80161	−	14.0063i	0.342458	−	0.826768i
$288$	−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
$292$	−0.159054	+	0.799618i	−0.00930793	+	0.0467941i
$293$	16.4811			0.962835			0.481417	−	0.876492i	$-0.340122\pi$
$293$	16.4811			0.962835			0.481417	+	0.876492i	$0.340122\pi$
$294$	−6.68900	+	33.6279i	−0.390110	+	1.96122i
$295$		0			0
$296$	1.88413	−	0.374777i	0.109513	−	0.0217835i
$297$	1.34768	−	0.558226i	0.0782002	−	0.0323916i
$298$	−8.00274	+	3.31484i	−0.463586	+	0.192024i
$299$	2.56114	−	0.509442i	0.148114	−	0.0294618i
$300$		0			0
$301$	−5.76353	+	28.9752i	−0.332204	+	1.67010i
$302$	−22.7118			−1.30692
$303$	−8.59534	+	43.2117i	−0.493789	+	2.48245i
$304$	−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	−0.589001	−	0.808132i	$-0.700479\pi$
$307$	3.83948	−	3.83948i	0.219130	−	0.219130i	0.808132	+	0.589001i	$0.200479\pi$
$308$	0.340025	−	0.820892i	0.0193747	−	0.0467747i
$309$	−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	$0.559093\pi$
$312$	−9.48908	+	1.88750i	−0.537214	+	0.106858i
$313$	−12.9059	−	8.62342i	−0.729482	−	0.487424i	0.134521	−	0.990911i	$-0.457050\pi$
$313$	−12.9059	−	8.62342i	−0.729482	−	0.487424i	−0.864003	+	0.503486i	$0.832050\pi$
$314$	−1.64567	+	3.97299i	−0.0928704	+	0.224209i
$315$		0			0
$316$	2.41778	+	12.1550i	0.136011	+	0.683771i
$317$	−4.54883	−	22.8685i	−0.255488	−	1.28442i	−0.869029	−	0.494761i	$-0.835255\pi$
$317$	−4.54883	−	22.8685i	−0.255488	−	1.28442i	0.613541	−	0.789663i	$-0.289745\pi$
$318$	−12.5044	+	8.35516i	−0.701211	+	0.468534i
$319$	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
$323$	1.61500	+	7.68771i	0.0898611	+	0.427756i
$324$			4.34226i			0.241237i
$325$		0			0
$326$	−3.31976	+	2.21819i	−0.183865	+	0.122854i
$327$			10.3383i			0.571708i
$328$	−1.94275	−	2.90753i	−0.107270	−	0.160542i
$329$	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	$0.644479\pi$
$332$	0.269470	+	0.650559i	0.0147891	+	0.0357041i
$333$	5.81526	−	8.70315i	0.318674	−	0.476930i
$334$	−10.3137	−	6.89138i	−0.564340	−	0.377080i
$335$		0			0
$336$	8.91069	+	8.91069i	0.486118	+	0.486118i
$337$	24.0500	+	4.78384i	1.31009	+	0.260592i	0.800243	−	0.599676i	$-0.204704\pi$
$337$	24.0500	+	4.78384i	1.31009	+	0.260592i	0.509842	+	0.860268i	$0.329704\pi$
$338$	1.77454	+	0.735037i	0.0965221	+	0.0399808i
$339$	9.59267			0.521002
$340$		0			0
$341$	1.79121			0.0969997
$342$	−9.59089	−	3.97268i	−0.518616	−	0.214818i
$343$	20.3927	+	4.05635i	1.10110	+	0.219022i
$344$	4.81844	+	4.81844i	0.259793	+	0.259793i
$345$		0			0
$346$	−11.4669	−	7.66192i	−0.616463	−	0.411907i
$347$	−2.45220	+	3.66998i	−0.131641	+	0.197015i	−0.891434	−	0.453150i	$-0.850300\pi$
$347$	−2.45220	+	3.66998i	−0.131641	+	0.197015i	0.759793	+	0.650165i	$0.225300\pi$
$348$	10.1580	+	24.5236i	0.544527	+	1.31460i
$349$	−2.43735	−	1.00958i	−0.130468	−	0.0540418i	0.316494	−	0.948594i	$-0.397494\pi$
$349$	−2.43735	−	1.00958i	−0.130468	−	0.0540418i	−0.446963	+	0.894553i	$0.647494\pi$
$350$		0			0
$351$	−13.1621	+	19.6985i	−0.702542	+	1.05143i
$352$	−0.113862	−	0.170406i	−0.00606886	−	0.00908269i
$353$			7.64333i			0.406813i	0.979094	+	0.203407i	$0.0652014\pi$
$353$			7.64333i			0.406813i	−0.979094	+	0.203407i	$0.934799\pi$
$354$	−9.98227	+	6.66994i	−0.530552	+	0.354503i
$355$		0			0
$356$			5.24039i			0.277740i
$357$	−29.3275	−	42.8896i	−1.55217	−	2.26996i
$358$	13.1034	+	13.1034i	0.692536	+	0.692536i
$359$	−15.2351	+	6.31059i	−0.804079	+	0.333060i	−0.746589	−	0.665286i	$-0.768310\pi$
$359$	−15.2351	+	6.31059i	−0.804079	+	0.333060i	−0.0574900	+	0.998346i	$0.518310\pi$
$360$		0			0
$361$	−10.8683	+	10.8683i	−0.572014	+	0.572014i
$362$	16.5190	−	11.0377i	0.868220	−	0.580126i
$363$	−6.21387	−	31.2392i	−0.326143	−	1.63963i
$364$	2.81529	+	14.1534i	0.147561	+	0.741839i
$365$		0			0
$366$	1.19474	−	2.88437i	0.0624503	−	0.150768i
$367$	−0.763616	−	0.510232i	−0.0398605	−	0.0266339i	0.535480	−	0.844548i	$-0.320131\pi$
$367$	−0.763616	−	0.510232i	−0.0398605	−	0.0266339i	−0.575341	+	0.817914i	$0.695131\pi$
$368$	−0.769445	+	0.153052i	−0.0401101	+	0.00797840i
$369$	−18.6872	−	3.71712i	−0.972819	−	0.193506i
$370$		0			0
$371$	12.4621	+	18.6508i	0.647000	+	0.968303i
$372$	−9.72172	+	23.4703i	−0.504048	+	1.21688i
$373$	20.4777	−	20.4777i	1.06030	−	1.06030i	0.0622355	−	0.998061i	$-0.480177\pi$
$373$	20.4777	−	20.4777i	1.06030	−	1.06030i	0.998061	−	0.0622355i	$-0.0198230\pi$
$374$	0.331719	+	0.777181i	0.0171528	+	0.0401871i
$375$		0			0
$376$	−4.52277	−	10.9189i	−0.233244	−	0.563101i
$377$	−5.93014	+	29.8128i	−0.305418	+	1.53544i
$378$	30.8576			1.58715
$379$	1.18087	−	5.93665i	0.0606573	−	0.304945i	−0.938532	−	0.345191i	$-0.887814\pi$
$379$	1.18087	−	5.93665i	0.0606573	−	0.304945i	0.999190	+	0.0402460i	$0.0128141\pi$
$380$		0			0
$381$	14.7134	−	2.92668i	0.753790	−	0.149938i
$382$	−6.42127	+	2.65978i	−0.328541	+	0.136086i
$383$	26.9957	−	11.1820i	1.37942	−	0.571374i	0.435092	−	0.900386i	$-0.356716\pi$
$383$	26.9957	−	11.1820i	1.37942	−	0.571374i	0.944326	+	0.329012i	$0.106716\pi$
$384$	2.85081	−	0.567062i	0.145480	−	0.0289378i
$385$		0			0
$386$	−3.60610	+	18.1291i	−0.183546	+	0.922747i
$387$	37.1291			1.88738
$388$	−0.0292893	+	0.147247i	−0.00148694	+	0.00747535i
$389$	10.1663	+	24.5436i	0.515451	+	1.24441i	0.940672	+	0.339318i	$0.110196\pi$
$389$	10.1663	+	24.5436i	0.515451	+	1.24441i	−0.425221	+	0.905090i	$0.639804\pi$
$390$		0			0
$391$	3.23447	−	0.0346593i	0.163574	−	0.00175279i
$392$	8.34095	−	8.34095i	0.421282	−	0.421282i
$393$	−12.1446	+	29.3197i	−0.612615	+	1.47898i
$394$	6.03705	+	9.03509i	0.304142	+	0.455181i
$395$		0			0
$396$	−1.09523	−	0.217855i	−0.0550375	−	0.0109476i
$397$	18.6768	−	3.71505i	0.937363	−	0.186453i	0.297307	−	0.954782i	$-0.403911\pi$
$397$	18.6768	−	3.71505i	0.937363	−	0.186453i	0.640055	+	0.768329i	$0.278911\pi$
$398$	−12.9187	−	8.63197i	−0.647554	−	0.432681i
$399$	−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	$0.998133\pi$
$402$	4.40702	+	22.1556i	0.219802	+	1.10502i
$403$	−24.1886	+	16.1623i	−1.20492	+	0.805100i
$404$	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
$408$	−11.9838	+	0.128413i	−0.593287	+	0.00635741i
$409$			10.2044i			0.504575i	0.967652	+	0.252287i	$0.0811828\pi$
$409$			10.2044i			0.504575i	−0.967652	+	0.252287i	$0.918817\pi$
$410$		0			0
$411$	42.1674	−	28.1754i	2.07997	−	1.38979i
$412$			2.91594i			0.143658i
$413$	9.94852	+	14.8890i	0.489535	+	0.732640i
$414$	−2.37485	+	3.55421i	−0.116717	+	0.174680i
$415$		0			0
$416$	3.07518	+	1.27378i	0.150773	+	0.0624523i
$417$	−2.22005	−	5.35968i	−0.108716	−	0.262465i
$418$	0.216934	−	0.324665i	0.0106106	−	0.0158799i
$419$	6.68327	+	4.46562i	0.326499	+	0.218160i	0.708006	−	0.706206i	$-0.249595\pi$
$419$	6.68327	+	4.46562i	0.326499	+	0.218160i	−0.381507	+	0.924366i	$0.624595\pi$
$420$		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	$0.659404\pi$
$422$	−17.6704	−	3.51487i	−0.860183	−	0.171101i
$423$	−59.4941	−	24.6433i	−2.89270	−	1.19820i
$424$	5.17393			0.251268
$425$		0			0
$426$	4.66887			0.226207
$427$	−4.30216	−	1.78201i	−0.208196	−	0.0862377i
$428$	0.576814	+	0.114735i	0.0278814	+	0.00554595i
$429$	−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	$0.604017\pi$
$432$	3.95431	−	5.91804i	0.190252	−	0.284732i
$433$	10.7395	+	25.9274i	0.516107	+	1.24599i	0.940277	+	0.340410i	$0.110566\pi$
$433$	10.7395	+	25.9274i	0.516107	+	1.24599i	−0.424170	+	0.905582i	$0.639434\pi$
$434$	35.0070	+	14.5004i	1.68039	+	0.696040i
$435$		0			0
$436$	1.97602	−	2.95733i	0.0946343	−	0.141630i
$437$	−0.830411	−	1.24280i	−0.0397239	−	0.0594511i
$438$		−	2.36976i		−	0.113231i
$439$	−4.11795	+	2.75152i	−0.196539	+	0.131323i	−0.649946	−	0.759981i	$-0.725208\pi$
$439$	−4.11795	+	2.75152i	−0.196539	+	0.131323i	0.453407	+	0.891304i	$0.350208\pi$
$440$		0			0
$441$		−	64.2723i		−	3.06058i
$442$	−11.4921	−	7.50192i	−0.546624	−	0.356830i
$443$	−14.5879	−	14.5879i	−0.693094	−	0.693094i	0.269818	−	0.962911i	$-0.413037\pi$
$443$	−14.5879	−	14.5879i	−0.693094	−	0.693094i	−0.962911	+	0.269818i	$0.913037\pi$
$444$	−5.15878	+	2.13684i	−0.244825	+	0.101410i
$445$		0			0
$446$	−6.86488	+	6.86488i	−0.325061	+	0.325061i
$447$	20.9346	−	13.9881i	0.990173	−	0.661612i
$448$	−0.845799	−	4.25212i	−0.0399602	−	0.200894i
$449$	−5.09616	−	25.6201i	−0.240503	−	1.20909i	−0.892564	−	0.450922i	$-0.851095\pi$
$449$	−5.09616	−	25.6201i	−0.240503	−	1.20909i	0.652061	−	0.758166i	$-0.273905\pi$
$450$		0			0
$451$	0.274256	−	0.662114i	0.0129142	−	0.0311777i
$452$	−2.74404	−	1.83351i	−0.129069	−	0.0862411i
$453$	64.7473	−	12.8790i	3.04209	−	0.605110i
$454$	0.519043	+	0.103244i	0.0243599	+	0.00484548i
$455$		0			0
$456$	3.07669	+	4.60460i	0.144079	+	0.215630i
$457$	−13.5785	+	32.7813i	−0.635173	+	1.53344i	0.197865	+	0.980229i	$0.436599\pi$
$457$	−13.5785	+	32.7813i	−0.635173	+	1.53344i	−0.833038	+	0.553215i	$0.813401\pi$
$458$	−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	$-0.261059\pi$
$462$	−0.503850	+	2.53303i	−0.0234412	+	0.117847i
$463$	−33.8924			−1.57511			−0.787557	−	0.616242i	$-0.788654\pi$
$463$	−33.8924			−1.57511			−0.787557	+	0.616242i	$0.788654\pi$
$464$	1.78160	−	8.95670i	0.0827087	−	0.415804i
$465$		0			0
$466$	−7.93687	+	1.57874i	−0.367668	+	0.0731338i
$467$	−12.0397	+	4.98700i	−0.557130	+	0.230771i	−0.643439	−	0.765498i	$-0.722493\pi$
$467$	−12.0397	+	4.98700i	−0.557130	+	0.230771i	0.0863086	+	0.996268i	$0.472493\pi$
$468$	16.7557	−	6.94046i	0.774535	−	0.320823i
$469$	33.0460	−	6.57326i	1.52592	−	0.303525i
$470$		0			0
$471$	2.43856	−	12.2595i	0.112363	−	0.564886i
$472$	4.13036			0.190115
$473$	−0.272456	+	1.36973i	−0.0125275	+	0.0629802i
$474$	−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
$478$	7.70476	−	18.6009i	0.352407	−	0.850787i
$479$	0.00324632	+	0.00485846i	0.000148328	+	0.000221989i	0.831544	−	0.555459i	$-0.187458\pi$
$479$	0.00324632	+	0.00485846i	0.000148328	+	0.000221989i	−0.831395	+	0.555681i	$0.812458\pi$
$480$		0			0
$481$	−6.27142	−	1.24746i	−0.285952	−	0.0568795i
$482$	−8.99226	+	1.78867i	−0.409586	+	0.0814718i
$483$	8.22009	+	5.49249i	0.374027	+	0.249917i
$484$	−4.19344	+	10.1239i	−0.190611	+	0.460176i
$485$		0			0
$486$	1.70337	+	8.56342i	0.0772664	+	0.388444i
$487$	−5.65336	−	28.4214i	−0.256178	−	1.28790i	−0.867867	−	0.496797i	$-0.834509\pi$
$487$	−5.65336	−	28.4214i	−0.256178	−	1.28790i	0.611689	−	0.791099i	$-0.290491\pi$
$488$	−0.893072	+	0.596732i	−0.0404275	+	0.0270128i
$489$	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
$493$	−14.0356	+	34.9392i	−0.632131	+	1.57358i
$494$			6.34170i			0.285326i
$495$		0			0
$496$	7.26699	−	4.85565i	0.326298	−	0.218025i
$497$		−	6.96382i		−	0.312370i
$498$	−1.13712	−	1.70182i	−0.0509555	−	0.0762602i
$499$	−3.60412	+	5.39395i	−0.161343	+	0.241466i	−0.903329	−	0.428949i	$-0.858884\pi$
$499$	−3.60412	+	5.39395i	−0.161343	+	0.241466i	0.741986	+	0.670415i	$0.233884\pi$
$500$		0			0
$501$	33.3102	+	13.7976i	1.48819	+	0.616429i
$502$	3.31477	+	8.00255i	0.147945	+	0.357171i
$503$	14.5628	−	21.7947i	0.649322	−	0.971779i	−0.350063	−	0.936726i	$-0.613840\pi$
$503$	14.5628	−	21.7947i	0.649322	−	0.971779i	0.999385	−	0.0350533i	$-0.0111601\pi$
$504$	−19.6413	−	13.1239i	−0.874895	−	0.584586i
$505$		0			0
$506$	−0.113692	−	0.113692i	−0.00505421	−	0.00505421i
$507$	−5.47569	−	1.08918i	−0.243184	−	0.0483723i
$508$	−4.76825	−	1.97507i	−0.211557	−	0.0876298i
$509$	−37.2931			−1.65299			−0.826495	−	0.562944i	$-0.809669\pi$
$509$	−37.2931			−1.65299			−0.826495	+	0.562944i	$0.809669\pi$
$510$		0			0
$511$	−3.53460			−0.156361
$512$	−0.923880	−	0.382683i	−0.0408301	−	0.0169124i
$513$	13.3001	+	2.64556i	0.587215	+	0.116804i
$514$	−2.81076	−	2.81076i	−0.123977	−	0.123977i
$515$		0			0
$516$	−16.4688	−	11.0041i	−0.725000	−	0.484429i
$517$	1.34569	−	2.01396i	0.0591832	−	0.0885739i
$518$	3.18719	+	7.69456i	0.140037	+	0.338079i
$519$	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	$0.237380\pi$
$522$	−27.6444	−	41.3727i	−1.20996	−	1.81083i
$523$			25.1852i			1.10127i	0.834745	+	0.550637i	$0.185615\pi$
$523$			25.1852i			1.10127i	−0.834745	+	0.550637i	$0.814385\pi$
$524$	9.07811	−	6.06580i	0.396579	−	0.264986i
$525$		0			0
$526$		−	30.7711i		−	1.34168i
$527$	−33.1430	+	14.1462i	−1.44373	+	0.616218i
$528$	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
$532$	6.86796	−	4.58903i	0.297764	−	0.198960i
$533$	2.27075	+	11.4158i	0.0983570	+	0.494474i
$534$	−2.97163	−	14.9394i	−0.128595	−	0.646491i
$535$		0			0
$536$	2.97409	−	7.18008i	0.128461	−	0.310132i
$537$	−44.7858	−	29.9249i	−1.93265	−	1.29136i
$538$	15.5704	−	3.09715i	0.671289	−	0.133528i
$539$	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	$0.765044\pi$
$542$	7.54811	−	18.2228i	0.324219	−	0.782734i
$543$	−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
$547$	5.89185	−	29.6203i	0.251917	−	1.26647i	−0.623008	−	0.782215i	$-0.714090\pi$
$547$	5.89185	−	29.6203i	0.251917	−	1.26647i	0.874925	−	0.484258i	$-0.160910\pi$
$548$	−17.4476			−0.745325
$549$	−1.14175	+	5.73994i	−0.0487285	+	0.244975i
$550$		0			0
$551$	17.0647	−	3.39438i	0.726980	−	0.144605i
$552$	2.10676	−	0.872647i	0.0896695	−	0.0371423i
$553$	−49.6395	+	20.5613i	−2.11089	+	0.874357i
$554$	−13.2845	+	2.64245i	−0.564403	+	0.112267i
$555$		0			0
$556$	−0.389372	+	1.95750i	−0.0165130	+	0.0830166i
$557$	8.16499			0.345962			0.172981	−	0.984925i	$-0.444660\pi$
$557$	8.16499			0.345962			0.172981	+	0.984925i	$0.444660\pi$
$558$	9.29046	−	46.7063i	0.393297	−	1.97724i
$559$	−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
$563$	−0.275709	+	0.665621i	−0.0116198	+	0.0280526i	−0.929583	−	0.368613i	$-0.879833\pi$
$563$	−0.275709	+	0.665621i	−0.0116198	+	0.0280526i	0.917963	+	0.396666i	$0.129833\pi$
$564$	19.0853	+	28.5632i	0.803637	+	1.20273i
$565$		0			0
$566$	−17.6486	−	3.51053i	−0.741827	−	0.147559i
$567$	−18.4638	+	3.67268i	−0.775407	+	0.154238i
$568$	−1.33556	−	0.892391i	−0.0560388	−	0.0374439i
$569$	−11.0704	+	26.7264i	−0.464097	+	1.12043i	0.502604	+	0.864517i	$0.332376\pi$
$569$	−11.0704	+	26.7264i	−0.464097	+	1.12043i	−0.966700	+	0.255911i	$0.917624\pi$
$570$		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	$0.715174\pi$
$572$	0.133085	+	0.669065i	0.00556458	+	0.0279750i
$573$	16.7976	−	11.2238i	0.701729	−	0.468881i
$574$	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	$-0.112537\pi$
$577$	14.2185	+	14.2185i	0.591924	+	0.591924i	−0.346227	+	0.938151i	$0.612537\pi$
$578$	−12.2756	−	11.7605i	−0.510600	−	0.489171i
$579$		−	53.7276i		−	2.23284i
$580$		0			0
$581$	−2.53834	+	1.69606i	−0.105308	+	0.0703645i
$582$		−	0.436383i		−	0.0180887i
$583$	0.589113	+	0.881670i	0.0243986	+	0.0365151i
$584$	−0.452947	+	0.677883i	−0.0187431	+	0.0280510i
$585$		0			0
$586$	15.2265	+	6.30703i	0.629002	+	0.260541i
$587$	4.65734	+	11.2438i	0.192229	+	0.464082i	0.990380	−	0.138376i	$-0.0441881\pi$
$587$	4.65734	+	11.2438i	0.192229	+	0.464082i	−0.798151	+	0.602458i	$0.794188\pi$
$588$	−19.0487	+	28.5083i	−0.785554	+	1.17566i
$589$	13.8454	+	9.25119i	0.570489	+	0.381189i
$590$		0			0
$591$	−22.3340	−	22.3340i	−0.918697	−	0.918697i
$592$	1.88413	+	0.374777i	0.0774373	+	0.0154032i
$593$	−8.00069	−	3.31399i	−0.328549	−	0.136089i	0.212311	−	0.977202i	$-0.431901\pi$
$593$	−8.00069	−	3.31399i	−0.328549	−	0.136089i	−0.540860	+	0.841113i	$0.681901\pi$
$594$	1.45872			0.0598518
$595$		0			0
$596$	−8.66210			−0.354814
$597$	41.7235	+	17.2825i	1.70763	+	0.707324i
$598$	2.56114	+	0.509442i	0.104733	+	0.0208326i
$599$	−10.9709	−	10.9709i	−0.448260	−	0.448260i	0.446516	−	0.894776i	$-0.352665\pi$
$599$	−10.9709	−	10.9709i	−0.448260	−	0.448260i	−0.894776	+	0.446516i	$0.852665\pi$
$600$		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	$0.596314\pi$
$602$	−16.4131	+	24.5640i	−0.668950	+	1.00115i
$603$	−16.2049	−	39.1221i	−0.659915	−	1.59318i
$604$	−20.9830	−	8.69145i	−0.853786	−	0.353650i
$605$		0			0
$606$	−24.4774	+	36.6331i	−0.994328	+	1.48812i
$607$	15.5961	+	23.3412i	0.633025	+	0.947388i	0.999854	+	0.0170998i	$0.00544332\pi$
$607$	15.5961	+	23.3412i	0.633025	+	0.947388i	−0.366829	+	0.930288i	$0.619557\pi$
$608$		−	1.90524i		−	0.0772678i
$609$	−95.6857	+	63.9351i	−3.87738	+	2.59078i
$610$		0			0
$611$			39.3387i			1.59148i
$612$	21.9857	−	4.61866i	0.888719	−	0.186698i
$613$	−13.6504	−	13.6504i	−0.551333	−	0.551333i	0.375492	−	0.926826i	$-0.377474\pi$
$613$	−13.6504	−	13.6504i	−0.551333	−	0.551333i	−0.926826	+	0.375492i	$0.877474\pi$
$614$	5.01652	−	2.07791i	0.202450	−	0.0838576i
$615$		0			0
$616$	0.628283	−	0.628283i	0.0253143	−	0.0253143i
$617$	−4.29364	+	2.86892i	−0.172856	+	0.115498i	−0.638988	−	0.769216i	$-0.720647\pi$
$617$	−4.29364	+	2.86892i	−0.172856	+	0.115498i	0.466133	+	0.884715i	$0.345647\pi$
$618$	−1.65352	−	8.31280i	−0.0665143	−	0.334390i
$619$	2.42896	+	12.2112i	0.0976280	+	0.490809i	0.998401	+	0.0565198i	$0.0180004\pi$
$619$	2.42896	+	12.2112i	0.0976280	+	0.490809i	−0.900774	+	0.434289i	$0.857000\pi$
$620$		0			0
$621$	2.13685	−	5.15882i	0.0857490	−	0.207016i
$622$	0.313868	+	0.209720i	0.0125850	+	0.00840900i
$623$	−22.2828	+	4.43232i	−0.892740	+	0.177577i
$624$	−9.48908	−	1.88750i	−0.379867	−	0.0755603i
$625$		0			0
$626$	−8.62342	−	12.9059i	−0.344661	−	0.515822i
$627$	−0.434334	+	1.04858i	−0.0173456	+	0.0418761i
$628$	−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	$0.763133\pi$
$632$	−2.41778	+	12.1550i	−0.0961740	+	0.483499i
$633$	52.3683			2.08145
$634$	4.54883	−	22.8685i	0.180657	−	0.908225i
$635$		0			0
$636$	−14.7499	+	2.93394i	−0.584872	+	0.116338i
$637$	−36.2745	+	15.0254i	−1.43725	+	0.595327i
$638$	1.72913	−	0.716231i	0.0684571	−	0.0283559i
$639$	−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	$0.956076\pi$
$642$	−1.70945			−0.0674667
$643$	5.69028	−	28.6070i	0.224403	−	1.12815i	−0.690145	−	0.723671i	$-0.742453\pi$
$643$	5.69028	−	28.6070i	0.224403	−	1.12815i	0.914548	−	0.404478i	$-0.132547\pi$
$644$	−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	−0.0269187	−	0.999638i	$-0.508570\pi$
$647$	24.7423	−	24.7423i	0.972719	−	0.972719i	0.999638	+	0.0269187i	$0.00856952\pi$
$648$	−1.66171	+	4.01173i	−0.0652782	+	0.157596i
$649$	0.470291	+	0.703840i	0.0184605	+	0.0276281i
$650$		0			0
$651$	−108.021	−	21.4867i	−4.23368	−	0.842132i
$652$	−3.91593	+	0.778926i	−0.153360	+	0.0305051i
$653$	2.05543	+	1.37339i	0.0804352	+	0.0537451i	0.595138	−	0.803624i	$-0.297098\pi$
$653$	2.05543	+	1.37339i	0.0804352	+	0.0537451i	−0.514702	+	0.857369i	$0.672098\pi$
$654$	−3.95629	+	9.55132i	−0.154703	+	0.373486i
$655$		0			0
$656$	−0.682203	−	3.42967i	−0.0266355	−	0.133906i
$657$	0.866638	+	4.35688i	0.0338108	+	0.169978i
$658$	42.6033	−	28.4666i	1.66085	−	1.10974i
$659$	6.38040	−	6.38040i	0.248545	−	0.248545i	−0.571828	−	0.820373i	$-0.693766\pi$
$659$	6.38040	−	6.38040i	0.248545	−	0.248545i	0.820373	+	0.571828i	$0.193766\pi$
$660$		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
$663$	37.0159	+	14.8698i	1.43758	+	0.577497i
$664$			0.704160i			0.0273267i
$665$		0			0
$666$	8.70315	−	5.81526i	0.337240	−	0.225337i
$667$		−	7.16437i		−	0.277406i
$668$	−6.89138	−	10.3137i	−0.266636	−	0.399048i
$669$	15.6777	−	23.4633i	0.606134	−	0.907144i
$670$		0			0
$671$	−0.203374	−	0.0842402i	−0.00785116	−	0.00325206i
$672$	4.82243	+	11.6424i	0.186029	+	0.449115i
$673$	16.3970	−	24.5399i	0.632059	−	0.945944i	−0.367812	−	0.929900i	$-0.619893\pi$
$673$	16.3970	−	24.5399i	0.632059	−	0.945944i	0.999871	−	0.0160435i	$-0.00510703\pi$
$674$	20.3886	+	13.6232i	0.785339	+	0.524747i
$675$		0			0
$676$	1.35817	+	1.35817i	0.0522374	+	0.0522374i
$677$	−19.6946	−	3.91750i	−0.756925	−	0.150562i	−0.198482	−	0.980105i	$-0.563601\pi$
$677$	−19.6946	−	3.91750i	−0.756925	−	0.150562i	−0.558443	+	0.829543i	$0.688601\pi$
$678$	8.86247	+	3.67095i	0.340361	+	0.140982i
$679$	−0.650886			−0.0249787
$680$		0			0
$681$	−1.53824			−0.0589455
$682$	1.65487	+	0.685468i	0.0633681	+	0.0262479i
$683$	−16.7376	−	3.32933i	−0.640448	−	0.127393i	−0.135825	−	0.990733i	$-0.543369\pi$
$683$	−16.7376	−	3.32933i	−0.640448	−	0.127393i	−0.504623	+	0.863340i	$0.668369\pi$
$684$	−7.34055	−	7.34055i	−0.280673	−	0.280673i
$685$		0			0
$686$	17.2881	+	11.5515i	0.660061	+	0.441039i
$687$	47.2705	−	70.7453i	1.80348	−	2.69910i
$688$	2.60772	+	6.29559i	0.0994184	+	0.240017i
$689$	−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	$0.113509\pi$
$692$	−7.66192	−	11.4669i	−0.291262	−	0.435905i
$693$		−	4.84132i		−	0.183907i
$694$	−3.66998	+	2.45220i	−0.139311	+	0.0930843i
$695$		0			0
$696$			26.5442i			1.00615i
$697$	0.154488	+	14.4171i	0.00585163	+	0.546086i
$698$	−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	$0.125303\pi$
$702$	−19.6985	+	13.1621i	−0.743472	+	0.496772i
$703$	0.714041	+	3.58972i	0.0269305	+	0.135389i
$704$	−0.0399830	−	0.201008i	−0.00150691	−	0.00757577i
$705$		0			0
$706$	−2.92498	+	7.06152i	−0.110083	+	0.265764i
$707$	54.6399	+	36.5092i	2.05494	+	1.37307i
$708$	−11.7749	+	2.34217i	−0.442528	+	0.0880242i
$709$	23.2275	+	4.62024i	0.872327	+	0.173517i	0.610901	−	0.791707i	$-0.290807\pi$
$709$	23.2275	+	4.62024i	0.872327	+	0.173517i	0.261426	+	0.965224i	$0.415807\pi$
$710$		0			0
$711$	37.5157	+	56.1462i	1.40695	+	2.10565i
$712$	−2.00541	+	4.84149i	−0.0751560	+	0.181443i
$713$	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
$717$	−11.4169	+	57.3969i	−0.426374	+	2.14353i
$718$	−16.4904			−0.615415
$719$	4.20295	−	21.1297i	0.156744	−	0.788003i	−0.819794	−	0.572658i	$-0.805912\pi$
$719$	4.20295	−	21.1297i	0.156744	−	0.788003i	0.976538	−	0.215345i	$-0.0690877\pi$
$720$		0			0
$721$	−12.3989	+	2.46630i	−0.461760	+	0.0918497i
$722$	−14.2001	+	5.88186i	−0.528472	+	0.218900i
$723$	24.6210	−	10.1983i	0.915664	−	0.379281i
$724$	19.4855	−	3.87591i	0.724173	−	0.144047i
$725$		0			0
$726$	6.21387	−	31.2392i	0.230618	−	1.15940i
$727$	−16.4509			−0.610131			−0.305065	−	0.952331i	$-0.598678\pi$
$727$	−16.4509			−0.610131			−0.305065	+	0.952331i	$0.598678\pi$
$728$	−2.81529	+	14.1534i	−0.104341	+	0.524560i
$729$	−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
$733$	14.9219	−	36.0246i	0.551152	−	1.33060i	−0.365462	−	0.930826i	$-0.619089\pi$
$733$	14.9219	−	36.0246i	0.551152	−	1.33060i	0.916614	−	0.399773i	$-0.130911\pi$
$734$	−0.510232	−	0.763616i	−0.0188330	−	0.0281856i
$735$		0			0
$736$	−0.769445	−	0.153052i	−0.0283621	−	0.00564158i
$737$	1.56217	−	0.310734i	0.0575431	−	0.0114460i
$738$	−15.8423	−	10.5855i	−0.583162	−	0.389656i
$739$	12.2812	−	29.6494i	0.451771	−	1.09067i	−0.519877	−	0.854241i	$-0.674022\pi$
$739$	12.2812	−	29.6494i	0.451771	−	1.09067i	0.971648	−	0.236431i	$-0.0759778\pi$
$740$		0			0
$741$	−3.59614	−	18.0790i	−0.132107	−	0.664149i
$742$	4.37610	+	22.0002i	0.160652	+	0.807651i
$743$	42.5782	−	28.4498i	1.56204	−	1.04372i	0.590445	−	0.807078i	$-0.298952\pi$
$743$	42.5782	−	28.4498i	1.56204	−	1.04372i	0.971596	−	0.236645i	$-0.0760478\pi$
$744$	−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
$748$	0.00905430	+	0.844965i	0.000331058	+	0.0308950i
$749$			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	$0.144174\pi$
$752$		−	11.8186i		−	0.430979i
$753$	−13.9877	−	20.9341i	−0.509741	−	0.762882i
$754$	−16.8876	+	25.2741i	−0.615011	+	0.920429i
$755$		0			0
$756$	28.5087	+	11.8087i	1.03685	+	0.429479i
$757$	11.9275	+	28.7956i	0.433513	+	1.04659i	0.978146	+	0.207919i	$0.0666691\pi$
$757$	11.9275	+	28.7956i	0.433513	+	1.04659i	−0.544633	+	0.838675i	$0.683331\pi$
$758$	3.36284	−	5.03285i	0.122144	−	0.182801i
$759$	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	$0.997854\pi$
$762$	14.7134	+	2.92668i	0.533010	+	0.106022i
$763$	14.2462	+	5.90098i	0.515748	+	0.213630i
$764$	−6.95033			−0.251454
$765$		0			0
$766$	29.2200			1.05576
$767$	−12.7016	−	5.26118i	−0.458629	−	0.189970i
$768$	2.85081	+	0.567062i	0.102870	+	0.0204621i
$769$	16.7358	+	16.7358i	0.603507	+	0.603507i	0.941241	−	0.337735i	$-0.109661\pi$
$769$	16.7358	+	16.7358i	0.603507	+	0.603507i	−0.337735	+	0.941241i	$0.609661\pi$
$770$		0			0
$771$	9.60684	+	6.41909i	0.345982	+	0.231178i
$772$	−10.2693	+	15.3691i	−0.369601	+	0.553146i
$773$	−1.38145	−	3.33513i	−0.0496875	−	0.119956i	0.897087	−	0.441854i	$-0.145679\pi$
$773$	−1.38145	−	3.33513i	−0.0496875	−	0.119956i	−0.946774	+	0.321898i	$0.895679\pi$
$774$	34.3028	+	14.2087i	1.23299	+	0.510721i
$775$		0			0
$776$	−0.0834089	+	0.124830i	−0.00299420	+	0.00448114i
$777$	−13.4494	−	20.1284i	−0.482494	−	0.722103i
$778$			26.5658i			0.952429i
$779$	5.53955	−	3.70141i	0.198475	−	0.132617i
$780$		0			0
$781$		−	0.329197i		−	0.0117796i
$782$	3.00153	+	1.20576i	0.107334	+	0.0431178i
$783$	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
$787$	−37.2222	+	24.8711i	−1.32683	+	0.886557i	−0.998320	−	0.0579442i	$-0.981545\pi$
$787$	−37.2222	+	24.8711i	−1.32683	+	0.886557i	−0.328507	+	0.944502i	$0.606545\pi$
$788$	2.11993	+	10.6576i	0.0755194	+	0.379662i
$789$	17.4491	+	87.7226i	0.621205	+	3.12301i
$790$		0			0
$791$	5.47539	−	13.2188i	0.194683	−	0.470005i
$792$	−0.928493	−	0.620400i	−0.0329926	−	0.0220449i
$793$	3.50646	−	0.697479i	0.124518	−	0.0247682i
$794$	18.6768	+	3.71505i	0.662816	+	0.131842i
$795$		0			0
$796$	−8.63197	−	12.9187i	−0.305952	−	0.457890i
$797$	6.32428	−	15.2682i	0.224017	−	0.540826i	−0.771411	−	0.636337i	$-0.780449\pi$
$797$	6.32428	−	15.2682i	0.224017	−	0.540826i	0.995428	+	0.0955114i	$0.0304486\pi$
$798$	−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
$802$	1.47933	−	7.43709i	0.0522370	−	0.262613i
$803$	−0.167089			−0.00589644
$804$	−4.40702	+	22.1556i	−0.155424	+	0.781367i
$805$		0			0
$806$	−28.5324	+	5.67544i	−1.00501	+	0.199909i
$807$	−42.6321	+	17.6588i	−1.50072	+	0.621620i
$808$	14.0039	−	5.80059i	0.492654	−	0.204064i
$809$	−13.8880	+	2.76250i	−0.488276	+	0.0971242i	−0.433088	−	0.901352i	$-0.642576\pi$
$809$	−13.8880	+	2.76250i	−0.488276	+	0.0971242i	−0.0551885	+	0.998476i	$0.517576\pi$
$810$		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	$-0.0126133\pi$
$812$	39.5918			1.38940
$813$	−11.1848	+	56.2299i	−0.392269	+	1.97207i
$814$	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
$818$	−3.90505	+	9.42763i	−0.136537	+	0.329629i
$819$	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	$0.354783\pi$
$822$	49.7399	−	9.89388i	1.73488	−	0.345089i
$823$	17.2766	+	11.5439i	0.602226	+	0.402394i	0.818972	−	0.573834i	$-0.194544\pi$
$823$	17.2766	+	11.5439i	0.602226	+	0.402394i	−0.216746	+	0.976228i	$0.569544\pi$
$824$	−1.11588	+	2.69398i	−0.0388736	+	0.0938491i
$825$		0			0
$826$	3.49346	+	17.5628i	0.121553	+	0.611087i
$827$	−3.28843	−	16.5320i	−0.114350	−	0.574875i	−0.994895	−	0.100914i	$-0.967823\pi$
$827$	−3.28843	−	16.5320i	−0.114350	−	0.574875i	0.880545	−	0.473962i	$-0.157177\pi$
$828$	−3.55421	+	2.37485i	−0.123517	+	0.0825317i
$829$	−6.04684	+	6.04684i	−0.210015	+	0.210015i	−0.804274	−	0.594259i	$-0.797446\pi$
$829$	−6.04684	+	6.04684i	−0.210015	+	0.210015i	0.594259	+	0.804274i	$0.297446\pi$
$830$		0			0
$831$	36.3731	−	15.0662i	1.26177	−	0.522642i
$832$	2.35364	+	2.35364i	0.0815978	+	0.0815978i
$833$	−47.5967	+	9.99892i	−1.64913	+	0.346442i
$834$		−	5.80128i		−	0.200882i
$835$		0			0
$836$	0.324665	−	0.216934i	0.0112288	−	0.00750283i
$837$			62.2071i			2.15019i
$838$	4.46562	+	6.68327i	0.154262	+	0.230870i
$839$	7.84414	−	11.7396i	0.270810	−	0.405295i	−0.670992	−	0.741465i	$-0.734131\pi$
$839$	7.84414	−	11.7396i	0.270810	−	0.405295i	0.941802	+	0.336169i	$0.109131\pi$
$840$		0			0
$841$	50.2559	+	20.8167i	1.73296	+	0.717817i
$842$	4.40950	+	10.6455i	0.151961	+	0.366867i
$843$	−29.3857	+	43.9788i	−1.01210	+	1.51471i
$844$	−14.9803	−	10.0095i	−0.515642	−	0.344541i
$845$		0			0
$846$	−45.5348	−	45.5348i	−1.56552	−	1.56552i
$847$	−46.5947	−	9.26826i	−1.60101	−	0.318461i
$848$	4.78009	+	1.97998i	0.164149	+	0.0679927i
$849$	52.3036			1.79506
$850$		0			0
$851$	1.50710			0.0516626
$852$	4.31347	+	1.78670i	0.147777	+	0.0612112i
$853$	5.45336	+	1.08474i	0.186720	+	0.0371408i	0.287564	−	0.957761i	$-0.407155\pi$
$853$	5.45336	+	1.08474i	0.186720	+	0.0371408i	−0.100845	+	0.994902i	$0.532155\pi$
$854$	−3.29273	−	3.29273i	−0.112675	−	0.112675i
$855$		0			0
$856$	0.488999	+	0.326739i	0.0167136	+	0.0111677i
$857$	−4.63849	+	6.94199i	−0.158448	+	0.237134i	−0.902196	−	0.431326i	$-0.858046\pi$
$857$	−4.63849	+	6.94199i	−0.158448	+	0.237134i	0.743748	+	0.668460i	$0.233046\pi$
$858$	−0.758803	−	1.83191i	−0.0259051	−	0.0625405i
$859$	25.9674	+	10.7561i	0.885997	+	0.366992i	0.778819	−	0.627248i	$-0.215819\pi$
$859$	25.9674	+	10.7561i	0.885997	+	0.366992i	0.107177	+	0.994240i	$0.465819\pi$
$860$		0			0
$861$	−24.4818	+	36.6396i	−0.834337	+	1.24867i
$862$	5.98090	+	8.95105i	0.203710	+	0.304874i
$863$		−	6.00314i		−	0.204349i	−0.994766	−	0.102175i	$-0.967420\pi$
$863$		−	6.00314i		−	0.204349i	0.994766	−	0.102175i	$-0.0325800\pi$
$864$	5.91804	−	3.95431i	0.201336	−	0.134528i
$865$		0			0
$866$			28.0636i			0.953641i
$867$	41.6645	+	26.5658i	1.41500	+	0.902224i
$868$	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
$872$	2.95733	−	1.97602i	0.100148	−	0.0669166i
$873$	0.159589	+	0.802307i	0.00540126	+	0.0271540i
$874$	−0.291602	−	1.46598i	−0.00986357	−	0.0495875i
$875$		0			0
$876$	0.906866	−	2.18937i	0.0306402	−	0.0739719i
$877$	−11.5066	−	7.68846i	−0.388550	−	0.259621i	0.345917	−	0.938265i	$-0.387568\pi$
$877$	−11.5066	−	7.68846i	−0.388550	−	0.259621i	−0.734467	+	0.678644i	$0.762568\pi$
$878$	−4.85745	+	0.966207i	−0.163931	+	0.0326079i
$879$	−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	$0.728400\pi$
$882$	24.5959	−	59.3798i	0.828188	−	1.99942i
$883$	−15.7079	+	15.7079i	−0.528614	+	0.528614i	−0.920159	−	0.391545i	$-0.871941\pi$
$883$	−15.7079	+	15.7079i	−0.528614	+	0.528614i	0.391545	+	0.920159i	$0.371941\pi$
$884$	−7.74646	−	11.3287i	−0.260542	−	0.381026i
$885$		0			0
$886$	−7.89494	−	19.0601i	−0.265236	−	0.640335i
$887$	3.84511	−	19.3307i	0.129106	−	0.649061i	−0.860984	−	0.508631i	$-0.830152\pi$
$887$	3.84511	−	19.3307i	0.129106	−	0.649061i	0.990091	−	0.140430i	$-0.0448484\pi$
$888$	−5.58383			−0.187381
$889$	4.36527	−	21.9457i	0.146406	−	0.736035i
$890$		0			0
$891$	−0.872829	+	0.173617i	−0.0292409	+	0.00581637i
$892$	−8.96939	+	3.71524i	−0.300317	+	0.124396i
$893$	20.8032	−	8.61698i	0.696154	−	0.288356i
$894$	24.6941	−	4.91195i	0.825893	−	0.164280i
$895$		0			0
$896$	0.845799	−	4.25212i	0.0282562	−	0.142053i
$897$	−7.59022			−0.253430
$898$	5.09616	−	25.6201i	0.170061	−	0.854954i
$899$	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
$903$	32.8615	−	79.3347i	1.09356	−	2.64009i
$904$	−1.83351	−	2.74404i	−0.0609816	−	0.0912655i
$905$		0			0
$906$	64.7473	+	12.8790i	2.15108	+	0.427877i
$907$	33.2225	−	6.60837i	1.10314	−	0.219427i	0.390251	−	0.920708i	$-0.372388\pi$
$907$	33.2225	−	6.60837i	1.10314	−	0.219427i	0.712885	+	0.701281i	$0.247388\pi$
$908$	0.440023	+	0.294014i	0.0146027	+	0.00975721i
$909$	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	$-0.462859\pi$
$912$	1.08039	+	5.43149i	0.0357753	+	0.179855i
$913$	−0.119993	+	0.0801770i	−0.00397120	+	0.00265347i
$914$	−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
$918$	−26.9907	+	11.5203i	−0.890826	+	0.380226i
$919$			52.4129i			1.72894i	0.502682	+	0.864472i	$0.332347\pi$
$919$			52.4129i			1.72894i	−0.502682	+	0.864472i	$0.667653\pi$
$920$		0			0
$921$	−13.1229	+	8.76841i	−0.432413	+	0.288929i
$922$		−	17.8012i		−	0.586252i
$923$	2.97037	+	4.44547i	0.0977709	+	0.146325i
$924$	−1.43484	+	2.14740i	−0.0472029	+	0.0706441i
$925$		0			0
$926$	−31.3125	−	12.9701i	−1.02899	−	0.426223i
$927$	6.08011	+	14.6787i	0.199697	+	0.482111i
$928$	5.07356	−	7.59313i	0.166548	−	0.249257i
$929$	−2.80819	−	1.87637i	−0.0921337	−	0.0615617i	0.508650	−	0.860973i	$-0.330145\pi$
$929$	−2.80819	−	1.87637i	−0.0921337	−	0.0615617i	−0.600784	+	0.799412i	$0.705145\pi$
$930$		0			0
$931$	15.8915	+	15.8915i	0.520824	+	0.520824i
$932$	−7.93687	−	1.57874i	−0.259981	−	0.0517134i
$933$	−1.01370	−	0.419890i	−0.0331872	−	0.0137466i
$934$	−13.0317			−0.426409
$935$		0			0
$936$	18.1363			0.592803
$937$	−7.80256	−	3.23192i	−0.254898	−	0.105582i	0.251575	−	0.967838i	$-0.419051\pi$
$937$	−7.80256	−	3.23192i	−0.254898	−	0.105582i	−0.506474	+	0.862255i	$0.669051\pi$
$938$	33.0460	+	6.57326i	1.07899	+	0.214625i
$939$	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	$0.637785\pi$
$942$	6.94442	−	10.3931i	0.226262	−	0.338624i
$943$	−1.04984	−	2.53453i	−0.0341874	−	0.0825356i
$944$	3.81596	+	1.58062i	0.124199	+	0.0514448i
$945$		0			0
$946$	−0.775889	+	1.16120i	−0.0252263	+	0.0377539i
$947$	−13.0308	−	19.5020i	−0.423445	−	0.633730i	0.557003	−	0.830511i	$-0.311951\pi$
$947$	−13.0308	−	19.5020i	−0.423445	−	0.633730i	−0.980448	+	0.196781i	$0.936951\pi$
$948$		−	36.0226i		−	1.16996i
$949$	2.25637	−	1.50766i	0.0732449	−	0.0489407i
$950$		0			0
$951$			67.7734i			2.19770i
$952$	−6.66327	+	16.5871i	−0.215958	+	0.537590i
$953$	−14.9101	−	14.9101i	−0.482986	−	0.482986i	0.423098	−	0.906084i	$-0.360943\pi$
$953$	−14.9101	−	14.9101i	−0.482986	−	0.482986i	−0.906084	+	0.423098i	$0.860943\pi$
$954$	26.0453	−	10.7883i	0.843247	−	0.349284i
$955$		0			0
$956$	14.2365	−	14.2365i	0.460442	−	0.460442i
$957$	−4.52330	+	3.02237i	−0.146217	+	0.0976993i
$958$	0.00113996	+	0.00573095i	3.68303e−5	+	0.000185158i
$959$	−14.7572	−	74.1893i	−0.476534	−	2.39570i
$960$		0			0
$961$	−17.3687	+	41.9317i	−0.560279	+	1.35263i
$962$	−5.31666	−	3.55248i	−0.171416	−	0.114536i
$963$	3.14289	−	0.625159i	0.101278	−	0.0201455i
$964$	−8.99226	−	1.78867i	−0.289621	−	0.0576093i
$965$		0			0
$966$	5.49249	+	8.22009i	0.176718	+	0.264477i
$967$	−8.95502	+	21.6193i	−0.287974	+	0.695231i	−0.999976	−	0.00694687i	$-0.997789\pi$
$967$	−8.95502	+	21.6193i	−0.287974	+	0.695231i	0.712002	+	0.702178i	$0.247789\pi$
$968$	−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	$-0.356186\pi$
$972$	−1.70337	+	8.56342i	−0.0546356	+	0.274672i
$973$	−8.65286			−0.277398
$974$	5.65336	−	28.4214i	0.181145	−	0.910680i
$975$		0			0
$976$	−1.05345	+	0.209544i	−0.0337201	+	0.00670735i
$977$	43.4070	−	17.9798i	1.38871	−	0.575223i	0.441916	−	0.897057i	$-0.354299\pi$
$977$	43.4070	−	17.9798i	1.38871	−	0.575223i	0.946796	+	0.321833i	$0.104299\pi$
$978$	10.7219	−	4.44115i	0.342848	−	0.142012i
$979$	−1.05336	+	0.209526i	−0.0336655	+	0.00669649i
$980$		0			0
$981$	3.78078	−	19.0073i	0.120711	−	0.606856i
$982$	−31.2696			−0.997852
$983$	−9.25506	+	46.5284i	−0.295191	+	1.48402i	0.493777	+	0.869589i	$0.335616\pi$
$983$	−9.25506	+	46.5284i	−0.295191	+	1.48402i	−0.788967	+	0.614435i	$0.789384\pi$
$984$	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
$988$	−2.42686	+	5.85896i	−0.0772088	+	0.186398i
$989$	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	$0.302700\pi$
$992$	8.57200	−	1.70508i	0.272161	−	0.0541363i
$993$	5.37813	+	3.59355i	0.170670	+	0.114038i
$994$	2.66494	−	6.43373i	0.0845267	−	0.204066i
$995$		0			0
$996$	−0.399303	−	2.00743i	−0.0126524	−	0.0636078i
$997$	7.84644	+	39.4467i	0.248499	+	1.24929i	0.880397	+	0.474238i	$0.157276\pi$
$997$	7.84644	+	39.4467i	0.248499	+	1.24929i	−0.631897	+	0.775052i	$0.717724\pi$
$998$	−5.39395	+	3.60412i	−0.170743	+	0.114087i
$999$	−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.s.d.743.1		40
5.2	odd	4		850.2.v.d.607.1		40
5.3	odd	4		170.2.r.b.97.5	yes	40
5.4	even	2		170.2.o.b.63.5	yes	40
17.10	odd	16		850.2.v.d.843.1		40
85.27	even	16	inner	850.2.s.d.707.1		40
85.44	odd	16		170.2.r.b.163.5	yes	40
85.78	even	16		170.2.o.b.27.5	✓	40

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

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.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{2} +(-2.85081 - 0.567062i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.41680 - 1.61486i) q^{6} +(-2.40863 + 3.60477i) q^{7} +(0.382683 + 0.923880i) q^{8} +(5.03395 + 2.08513i) q^{9} +(-0.113862 + 0.170406i) q^{11} +(-1.61486 - 2.41680i) q^{12} -3.32855i q^{13} +(-3.60477 + 2.40863i) q^{14} +1.00000i q^{16} +(0.761002 - 4.05227i) q^{17} +(3.85282 + 3.85282i) q^{18} +(-1.76021 + 0.729105i) q^{19} +(8.91069 - 8.91069i) q^{21} +(-0.170406 + 0.113862i) q^{22} +(0.153052 + 0.769445i) q^{23} +(-0.567062 - 2.85081i) q^{24} +(1.27378 - 3.07518i) q^{26} +(-5.91804 - 3.95431i) q^{27} +(-4.25212 + 0.845799i) q^{28} +(-8.95670 - 1.78160i) q^{29} +(-4.85565 - 7.26699i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(0.421230 - 0.421230i) q^{33} +(2.25381 - 3.45258i) q^{34} +(2.08513 + 5.03395i) q^{36} +(0.374777 - 1.88413i) q^{37} -1.90524 q^{38} +(-1.88750 + 9.48908i) q^{39} +(-3.42967 + 0.682203i) q^{41} +(11.6424 - 4.82243i) q^{42} +(6.29559 - 2.60772i) q^{43} +(-0.201008 + 0.0399830i) q^{44} +(-0.153052 + 0.769445i) q^{46} -11.8186 q^{47} +(0.567062 - 2.85081i) q^{48} +(-4.51409 - 10.8980i) q^{49} +(-4.46736 + 11.1207i) q^{51} +(2.35364 - 2.35364i) q^{52} +(1.97998 - 4.78009i) q^{53} +(-3.95431 - 5.91804i) q^{54} +(-4.25212 - 0.845799i) q^{56} +(5.43149 - 1.08039i) q^{57} +(-7.59313 - 5.07356i) q^{58} +(1.58062 - 3.81596i) q^{59} +(0.209544 + 1.05345i) q^{61} +(-1.70508 - 8.57200i) q^{62} +(-19.6413 + 13.1239i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(0.550364 - 0.227968i) q^{66} +(-5.49540 - 5.49540i) q^{67} +(3.40350 - 2.32728i) q^{68} -2.28034i q^{69} +(-1.33556 + 0.892391i) q^{71} +5.44870i q^{72} +(0.452947 + 0.677883i) q^{73} +(1.06727 - 1.59729i) q^{74} +(-1.76021 - 0.729105i) q^{76} +(-0.340025 - 0.820892i) q^{77} +(-5.37513 + 8.04446i) q^{78} +(10.3045 + 6.88525i) q^{79} +(3.07044 + 3.07044i) q^{81} +(-3.42967 - 0.682203i) q^{82} +(0.650559 + 0.269470i) q^{83} +12.6016 q^{84} +6.81430 q^{86} +(24.5236 + 10.1580i) q^{87} +(-0.201008 - 0.0399830i) q^{88} +(3.70552 + 3.70552i) q^{89} +(11.9987 + 8.01725i) q^{91} +(-0.435856 + 0.652304i) q^{92} +(9.72172 + 23.4703i) q^{93} +(-10.9189 - 4.52277i) q^{94} +(1.61486 - 2.41680i) q^{96} +(0.0834089 + 0.124830i) q^{97} -11.7959i q^{98} +(-0.928493 + 0.620400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{31} - 32 q^{33} - 8 q^{34} - 16 q^{37} + 32 q^{39} - 56 q^{41} + 8 q^{42} + 48 q^{43} - 16 q^{44} + 96 q^{47} - 16 q^{49} - 32 q^{51}+ \cdots - 160 q^{99}+O(q^{100}) \) 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 - 16 * q^37 + 32 * q^39 - 56 * q^41 + 8 * q^42 + 48 * q^43 - 16 * q^44 + 96 * q^47 - 16 * q^49 - 32 * q^51 + 16 * q^52 + 40 * q^53 + 24 * q^54 - 8 * q^56 + 8 * q^57 - 16 * q^58 + 24 * q^61 + 24 * q^62 + 24 * q^63 + 16 * q^67 - 24 * q^68 + 24 * q^71 - 16 * q^73 - 32 * q^74 - 40 * q^77 - 16 * q^78 + 104 * q^79 + 48 * q^81 - 56 * q^82 - 16 * q^83 + 96 * q^86 + 8 * q^87 - 16 * q^88 + 16 * q^89 + 48 * q^91 - 8 * q^92 - 136 * q^93 + 8 * q^94 - 144 * q^97 - 160 * q^99

Introduction

L-functions

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