LMFDB - Embedded newform 850.2.v.d.207.1

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			207.1
Character	$\chi$	$=$	850.207
Dual form			850.2.v.d.193.1

$q$-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} +(-2.12983 + 1.42311i) q^{3} +(0.707107 + 0.707107i) q^{4} +(2.51231 - 0.499730i) q^{6} +(-0.0411526 + 0.00818577i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(1.36290 - 3.29034i) q^{9} +(0.476069 + 2.39336i) q^{11} +(-2.51231 - 0.499730i) q^{12} +2.17043 q^{13} +(0.0411526 + 0.00818577i) q^{14} +1.00000i q^{16} +(2.37892 + 3.36760i) q^{17} +(-2.51831 + 2.51831i) q^{18} +(-1.43074 - 3.45410i) q^{19} +(0.0759990 - 0.0759990i) q^{21} +(0.476069 - 2.39336i) q^{22} +(3.96256 - 5.93039i) q^{23} +(2.12983 + 1.42311i) q^{24} +(-2.00521 - 0.830586i) q^{26} +(0.280566 + 1.41050i) q^{27} +(-0.0348875 - 0.0233111i) q^{28} +(4.73332 + 7.08392i) q^{29} +(0.226000 - 1.13618i) q^{31} +(0.382683 - 0.923880i) q^{32} +(-4.41996 - 4.41996i) q^{33} +(-0.909115 - 4.02163i) q^{34} +(3.29034 - 1.36290i) q^{36} +(4.07998 + 6.10612i) q^{37} +3.73869i q^{38} +(-4.62265 + 3.08876i) q^{39} +(0.400666 - 0.599639i) q^{41} +(-0.0992975 + 0.0411304i) q^{42} +(-8.37226 + 3.46790i) q^{43} +(-1.35573 + 2.02899i) q^{44} +(-5.93039 + 3.96256i) q^{46} +4.13811i q^{47} +(-1.42311 - 2.12983i) q^{48} +(-6.46553 + 2.67811i) q^{49} +(-9.85918 - 3.78696i) q^{51} +(1.53472 + 1.53472i) q^{52} +(-2.01791 + 4.87166i) q^{53} +(0.280566 - 1.41050i) q^{54} +(0.0233111 + 0.0348875i) q^{56} +(7.96279 + 5.32057i) q^{57} +(-1.66212 - 8.35605i) q^{58} +(-8.77968 - 3.63666i) q^{59} +(5.87005 + 3.92224i) q^{61} +(-0.643594 + 0.963206i) q^{62} +(-0.0291531 + 0.146562i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(2.39207 + 5.77496i) q^{66} +(-11.0282 + 11.0282i) q^{67} +(-0.699099 + 4.06341i) q^{68} +18.2699i q^{69} +(5.22907 + 1.04013i) q^{71} -3.56143 q^{72} +(-11.1908 - 2.22600i) q^{73} +(-1.43270 - 7.20266i) q^{74} +(1.43074 - 3.45410i) q^{76} +(-0.0391830 - 0.0945961i) q^{77} +(5.45279 - 1.08463i) q^{78} +(-7.04108 + 1.40056i) q^{79} +(4.95009 + 4.95009i) q^{81} +(-0.599639 + 0.400666i) q^{82} +(15.6168 + 6.46869i) q^{83} +0.107479 q^{84} +9.06206 q^{86} +(-20.1624 - 8.35153i) q^{87} +(2.02899 - 1.35573i) q^{88} +(11.5475 + 11.5475i) q^{89} +(-0.0893188 + 0.0177666i) q^{91} +(6.99537 - 1.39147i) q^{92} +(1.13557 + 2.74150i) q^{93} +(1.58359 - 3.82312i) q^{94} +(0.499730 + 2.51231i) q^{96} +(4.02485 + 0.800592i) q^{97} +6.99824 q^{98} +(8.52380 + 1.69549i) 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 $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

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

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
$3$	−2.12983	+	1.42311i	−1.22966	+	0.821633i	−0.988846	−	0.148939i	$-0.952414\pi$
$3$	−2.12983	+	1.42311i	−1.22966	+	0.821633i	−0.240814	+	0.970571i	$0.577414\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	2.51231	−	0.499730i	1.02565	−	0.204014i
$7$	−0.0411526	+	0.00818577i	−0.0155542	+	0.00309393i	−0.202861	−	0.979207i	$-0.565024\pi$
$7$	−0.0411526	+	0.00818577i	−0.0155542	+	0.00309393i	0.187307	+	0.982301i	$0.440024\pi$
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	1.36290	−	3.29034i	0.454301	−	1.09678i
$10$		0			0
$11$	0.476069	+	2.39336i	0.143540	+	0.721625i	0.983776	+	0.179404i	$0.0574168\pi$
$11$	0.476069	+	2.39336i	0.143540	+	0.721625i	−0.840235	+	0.542222i	$0.817583\pi$
$12$	−2.51231	−	0.499730i	−0.725242	−	0.144260i
$13$	2.17043			0.601968			0.300984	−	0.953629i	$-0.402685\pi$
$13$	2.17043			0.601968			0.300984	+	0.953629i	$0.402685\pi$
$14$	0.0411526	+	0.00818577i	0.0109985	+	0.00218774i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	2.37892	+	3.36760i	0.576974	+	0.816763i
$17$	2.37892	+	3.36760i	0.576974	+	0.816763i
$18$	−2.51831	+	2.51831i	−0.593572	+	0.593572i
$19$	−1.43074	−	3.45410i	−0.328233	−	0.792425i	−0.998724	−	0.0505070i	$-0.983916\pi$
$19$	−1.43074	−	3.45410i	−0.328233	−	0.792425i	0.670490	−	0.741918i	$-0.266084\pi$
$20$		0			0
$21$	0.0759990	−	0.0759990i	0.0165844	−	0.0165844i
$22$	0.476069	−	2.39336i	0.101498	−	0.510266i
$23$	3.96256	−	5.93039i	0.826250	−	1.23657i	−0.142811	−	0.989750i	$-0.545614\pi$
$23$	3.96256	−	5.93039i	0.826250	−	1.23657i	0.969061	−	0.246821i	$-0.0793860\pi$
$24$	2.12983	+	1.42311i	0.434751	+	0.290491i
$25$		0			0
$26$	−2.00521	−	0.830586i	−0.393255	−	0.162891i
$27$	0.280566	+	1.41050i	0.0539949	+	0.271450i
$28$	−0.0348875	−	0.0233111i	−0.00659312	−	0.00440538i
$29$	4.73332	+	7.08392i	0.878956	+	1.31545i	0.948142	+	0.317846i	$0.102960\pi$
$29$	4.73332	+	7.08392i	0.878956	+	1.31545i	−0.0691866	+	0.997604i	$0.522040\pi$
$30$		0			0
$31$	0.226000	−	1.13618i	0.0405908	−	0.204064i	−0.955168	−	0.296064i	$-0.904326\pi$
$31$	0.226000	−	1.13618i	0.0405908	−	0.204064i	0.995759	+	0.0919999i	$0.0293259\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	−4.41996	−	4.41996i	−0.769417	−	0.769417i
$34$	−0.909115	−	4.02163i	−0.155912	−	0.689704i
$35$		0			0
$36$	3.29034	−	1.36290i	0.548389	−	0.227150i
$37$	4.07998	+	6.10612i	0.670744	+	1.00384i	0.998258	+	0.0589933i	$0.0187891\pi$
$37$	4.07998	+	6.10612i	0.670744	+	1.00384i	−0.327514	+	0.944846i	$0.606211\pi$
$38$			3.73869i			0.606496i
$39$	−4.62265	+	3.08876i	−0.740216	+	0.494597i
$40$		0			0
$41$	0.400666	−	0.599639i	0.0625735	−	0.0936479i	−0.798863	−	0.601513i	$-0.794565\pi$
$41$	0.400666	−	0.599639i	0.0625735	−	0.0936479i	0.861437	+	0.507865i	$0.169565\pi$
$42$	−0.0992975	+	0.0411304i	−0.0153219	+	0.00634656i
$43$	−8.37226	+	3.46790i	−1.27676	+	0.528850i	−0.915012	−	0.403427i	$-0.867819\pi$
$43$	−8.37226	+	3.46790i	−1.27676	+	0.528850i	−0.361745	+	0.932277i	$0.617819\pi$
$44$	−1.35573	+	2.02899i	−0.204384	+	0.305882i
$45$		0			0
$46$	−5.93039	+	3.96256i	−0.874388	+	0.584247i
$47$			4.13811i			0.603605i	0.953370	+	0.301803i	$0.0975884\pi$
$47$			4.13811i			0.603605i	−0.953370	+	0.301803i	$0.902412\pi$
$48$	−1.42311	−	2.12983i	−0.205408	−	0.307415i
$49$	−6.46553	+	2.67811i	−0.923647	+	0.382587i
$50$		0			0
$51$	−9.85918	−	3.78696i	−1.38056	−	0.530280i
$52$	1.53472	+	1.53472i	0.212828	+	0.212828i
$53$	−2.01791	+	4.87166i	−0.277181	+	0.669174i	−0.999755	−	0.0221193i	$-0.992959\pi$
$53$	−2.01791	+	4.87166i	−0.277181	+	0.669174i	0.722575	+	0.691293i	$0.242959\pi$
$54$	0.280566	−	1.41050i	0.0381801	−	0.191944i
$55$		0			0
$56$	0.0233111	+	0.0348875i	0.00311508	+	0.00466204i
$57$	7.96279	+	5.32057i	1.05470	+	0.704727i
$58$	−1.66212	−	8.35605i	−0.218247	−	1.09720i
$59$	−8.77968	−	3.63666i	−1.14302	−	0.473453i	−0.270831	−	0.962627i	$-0.587298\pi$
$59$	−8.77968	−	3.63666i	−1.14302	−	0.473453i	−0.872186	+	0.489174i	$0.837298\pi$
$60$		0			0
$61$	5.87005	+	3.92224i	0.751583	+	0.502192i	0.871381	−	0.490607i	$-0.163225\pi$
$61$	5.87005	+	3.92224i	0.751583	+	0.502192i	−0.119798	+	0.992798i	$0.538225\pi$
$62$	−0.643594	+	0.963206i	−0.0817365	+	0.122327i
$63$	−0.0291531	+	0.146562i	−0.00367294	+	0.0184651i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$		0			0
$66$	2.39207	+	5.77496i	0.294443	+	0.710848i
$67$	−11.0282	+	11.0282i	−1.34731	+	1.34731i	−0.458729	+	0.888576i	$0.651695\pi$
$67$	−11.0282	+	11.0282i	−1.34731	+	1.34731i	−0.888576	+	0.458729i	$0.848305\pi$
$68$	−0.699099	+	4.06341i	−0.0847782	+	0.492760i
$69$			18.2699i			2.19944i
$70$		0			0
$71$	5.22907	+	1.04013i	0.620576	+	0.123440i	0.495358	−	0.868689i	$-0.335037\pi$
$71$	5.22907	+	1.04013i	0.620576	+	0.123440i	0.125218	+	0.992129i	$0.460037\pi$
$72$	−3.56143			−0.419719
$73$	−11.1908	−	2.22600i	−1.30979	−	0.260533i	−0.509667	−	0.860372i	$-0.670231\pi$
$73$	−11.1908	−	2.22600i	−1.30979	−	0.260533i	−0.800121	+	0.599839i	$0.795231\pi$
$74$	−1.43270	−	7.20266i	−0.166548	−	0.837292i
$75$		0			0
$76$	1.43074	−	3.45410i	0.164117	−	0.396213i
$77$	−0.0391830	−	0.0945961i	−0.00446532	−	0.0107802i
$78$	5.45279	−	1.08463i	0.617406	−	0.122810i
$79$	−7.04108	+	1.40056i	−0.792183	+	0.157575i	−0.574565	−	0.818459i	$-0.694829\pi$
$79$	−7.04108	+	1.40056i	−0.792183	+	0.157575i	−0.217618	+	0.976034i	$0.569829\pi$
$80$		0			0
$81$	4.95009	+	4.95009i	0.550010	+	0.550010i
$82$	−0.599639	+	0.400666i	−0.0662190	+	0.0442461i
$83$	15.6168	+	6.46869i	1.71417	+	0.710031i	0.999949	+	0.0101067i	$0.00321713\pi$
$83$	15.6168	+	6.46869i	1.71417	+	0.710031i	0.714217	+	0.699924i	$0.246783\pi$
$84$	0.107479			0.0117269
$85$		0			0
$86$	9.06206			0.977188
$87$	−20.1624	−	8.35153i	−2.16163	−	0.895378i
$88$	2.02899	−	1.35573i	0.216291	−	0.144521i
$89$	11.5475	+	11.5475i	1.22403	+	1.22403i	0.966187	+	0.257842i	$0.0830116\pi$
$89$	11.5475	+	11.5475i	1.22403	+	1.22403i	0.257842	+	0.966187i	$0.416988\pi$
$90$		0			0
$91$	−0.0893188	+	0.0177666i	−0.00936315	+	0.00186245i
$92$	6.99537	−	1.39147i	0.729317	−	0.145070i
$93$	1.13557	+	2.74150i	0.117753	+	0.284280i
$94$	1.58359	−	3.82312i	0.163334	−	0.394324i
$95$		0			0
$96$	0.499730	+	2.51231i	0.0510034	+	0.256412i
$97$	4.02485	+	0.800592i	0.408661	+	0.0812878i	0.395140	−	0.918621i	$-0.370696\pi$
$97$	4.02485	+	0.800592i	0.408661	+	0.0812878i	0.0135211	+	0.999909i	$0.495696\pi$
$98$	6.99824			0.706929
$99$	8.52380	+	1.69549i	0.856674	+	0.170403i
$100$		0			0
$101$			1.24630i			0.124011i	0.998076	+	0.0620057i	$0.0197497\pi$
$101$			1.24630i			0.124011i	−0.998076	+	0.0620057i	$0.980250\pi$
$102$	7.65948	+	7.27164i	0.758402	+	0.719999i
$103$	−6.84328	+	6.84328i	−0.674288	+	0.674288i	−0.958702	−	0.284414i	$-0.908201\pi$
$103$	−6.84328	+	6.84328i	−0.674288	+	0.674288i	0.284414	+	0.958702i	$0.408201\pi$
$104$	−0.830586	−	2.00521i	−0.0814457	−	0.196627i
$105$		0			0
$106$	3.72861	−	3.72861i	0.362154	−	0.362154i
$107$	0.149174	−	0.749949i	0.0144212	−	0.0725003i	−0.972905	−	0.231207i	$-0.925732\pi$
$107$	0.149174	−	0.749949i	0.0144212	−	0.0725003i	0.987326	+	0.158707i	$0.0507325\pi$
$108$	−0.798983	+	1.19576i	−0.0768822	+	0.115062i
$109$	−8.79925	−	5.87947i	−0.842815	−	0.563151i	0.0575218	−	0.998344i	$-0.481680\pi$
$109$	−8.79925	−	5.87947i	−0.842815	−	0.563151i	−0.900337	+	0.435193i	$0.856680\pi$
$110$		0			0
$111$	−17.3794	−	7.19876i	−1.64957	−	0.683276i
$112$	−0.00818577	−	0.0411526i	−0.000773482	−	0.00388856i
$113$	−5.06378	−	3.38351i	−0.476360	−	0.318294i	0.294108	−	0.955772i	$-0.404978\pi$
$113$	−5.06378	−	3.38351i	−0.476360	−	0.318294i	−0.770468	+	0.637478i	$0.779978\pi$
$114$	−5.32057	−	7.96279i	−0.498317	−	0.745784i
$115$		0			0
$116$	−1.66212	+	8.35605i	−0.154324	+	0.775840i
$117$	2.95808	−	7.14143i	0.273474	−	0.660226i
$118$	6.71968	+	6.71968i	0.618596	+	0.618596i
$119$	−0.125465	−	0.119112i	−0.0115014	−	0.0109190i
$120$		0			0
$121$	4.66114	−	1.93071i	0.423740	−	0.175519i
$122$	−3.92224	−	5.87005i	−0.355103	−	0.531449i
$123$			1.84732i			0.166567i
$124$	0.963206	−	0.643594i	0.0864985	−	0.0577964i
$125$		0			0
$126$	0.0830209	−	0.124250i	0.00739609	−	0.0110690i
$127$	12.3297	−	5.10715i	1.09409	−	0.453186i	0.238657	−	0.971104i	$-0.423293\pi$
$127$	12.3297	−	5.10715i	1.09409	−	0.453186i	0.855430	+	0.517918i	$0.173293\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	12.8963	−	19.3007i	1.13546	−	1.69933i
$130$		0			0
$131$	−2.94740	+	1.96939i	−0.257516	+	0.172066i	−0.677626	−	0.735406i	$-0.736991\pi$
$131$	−2.94740	+	1.96939i	−0.257516	+	0.172066i	0.420111	+	0.907473i	$0.361991\pi$
$132$		−	6.25077i		−	0.544060i
$133$	0.0871530	+	0.130434i	0.00755712	+	0.0113100i
$134$	14.4090	−	5.96840i	1.24475	−	0.515591i
$135$		0			0
$136$	2.20088	−	3.48656i	0.188724	−	0.298970i
$137$	−9.91781	−	9.91781i	−0.847336	−	0.847336i	0.142464	−	0.989800i	$-0.454497\pi$
$137$	−9.91781	−	9.91781i	−0.847336	−	0.847336i	−0.989800	+	0.142464i	$0.954497\pi$
$138$	6.99159	−	16.8792i	0.595163	−	1.43685i
$139$	−0.822930	+	4.13715i	−0.0698001	+	0.350909i	−0.999864	−	0.0164890i	$-0.994751\pi$
$139$	−0.822930	+	4.13715i	−0.0698001	+	0.350909i	0.930064	+	0.367398i	$0.119751\pi$
$140$		0			0
$141$	−5.88898	−	8.81349i	−0.495942	−	0.742230i
$142$	−4.43299	−	2.96203i	−0.372008	−	0.248568i
$143$	1.03327	+	5.19461i	0.0864066	+	0.434395i
$144$	3.29034	+	1.36290i	0.274195	+	0.113575i
$145$		0			0
$146$	9.48713	+	6.33910i	0.785161	+	0.524628i
$147$	9.95926	−	14.9051i	0.821426	−	1.22935i
$148$	−1.43270	+	7.20266i	−0.117767	+	0.592055i
$149$	−0.764298	+	0.764298i	−0.0626137	+	0.0626137i	−0.737720	−	0.675107i	$-0.764098\pi$
$149$	−0.764298	+	0.764298i	−0.0626137	+	0.0626137i	0.675107	+	0.737720i	$0.264098\pi$
$150$		0			0
$151$	4.97432	+	12.0091i	0.404804	+	0.977284i	0.986483	+	0.163865i	$0.0523961\pi$
$151$	4.97432	+	12.0091i	0.404804	+	0.977284i	−0.581679	+	0.813419i	$0.697604\pi$
$152$	−2.64365	+	2.64365i	−0.214429	+	0.214429i
$153$	14.3228	−	3.23775i	1.15793	−	0.261757i
$154$			0.102390i			0.00825083i
$155$		0			0
$156$	−5.45279	−	1.08463i	−0.436572	−	0.0868396i
$157$	−6.98767			−0.557677			−0.278838	−	0.960338i	$-0.589949\pi$
$157$	−6.98767			−0.557677			−0.278838	+	0.960338i	$0.589949\pi$
$158$	7.04108	+	1.40056i	0.560158	+	0.111422i
$159$	−2.63510	−	13.2475i	−0.208977	−	1.05060i
$160$		0			0
$161$	−0.114525	+	0.276488i	−0.00902583	+	0.0217903i
$162$	−2.67897	−	6.46761i	−0.210480	−	0.508143i
$163$	10.6693	−	2.12225i	0.835683	−	0.166228i	0.241341	−	0.970440i	$-0.422413\pi$
$163$	10.6693	−	2.12225i	0.835683	−	0.166228i	0.594342	+	0.804213i	$0.297413\pi$
$164$	0.707322	−	0.140695i	0.0552326	−	0.0109864i
$165$		0			0
$166$	−11.9526	−	11.9526i	−0.927700	−	0.927700i
$167$	2.75591	−	1.84144i	0.213258	−	0.142495i	−0.444354	−	0.895851i	$-0.646567\pi$
$167$	2.75591	−	1.84144i	0.213258	−	0.142495i	0.657612	+	0.753357i	$0.271567\pi$
$168$	−0.0992975	−	0.0411304i	−0.00766097	−	0.00317328i
$169$	−8.28925			−0.637634
$170$		0			0
$171$	−13.3151			−1.01823
$172$	−8.37226	−	3.46790i	−0.638379	−	0.264425i
$173$	19.7194	−	13.1760i	1.49923	−	1.00176i	0.509244	−	0.860622i	$-0.329925\pi$
$173$	19.7194	−	13.1760i	1.49923	−	1.00176i	0.989990	−	0.141134i	$-0.0450749\pi$
$174$	15.4316	+	15.4316i	1.16987	+	1.16987i
$175$		0			0
$176$	−2.39336	+	0.476069i	−0.180406	+	0.0358851i
$177$	23.8746	−	4.74896i	1.79453	−	0.356954i
$178$	−6.24945	−	15.0875i	−0.468416	−	1.13086i
$179$	−1.07522	+	2.59580i	−0.0803654	+	0.194019i	−0.958955	−	0.283558i	$-0.908485\pi$
$179$	−1.07522	+	2.59580i	−0.0803654	+	0.194019i	0.878590	+	0.477578i	$0.158485\pi$
$180$		0			0
$181$	−2.12484	−	10.6823i	−0.157938	−	0.794008i	−0.975812	−	0.218611i	$-0.929847\pi$
$181$	−2.12484	−	10.6823i	−0.157938	−	0.794008i	0.817874	−	0.575397i	$-0.195153\pi$
$182$	0.0893188	+	0.0177666i	0.00662075	+	0.00131695i
$183$	−18.0840			−1.33681
$184$	−6.99537	−	1.39147i	−0.515705	−	0.102580i
$185$		0			0
$186$		−	2.96737i		−	0.217578i
$187$	−6.92735	+	7.29683i	−0.506578	+	0.533597i
$188$	−2.92609	+	2.92609i	−0.213407	+	0.213407i
$189$	−0.0230920	−	0.0557491i	−0.00167970	−	0.00405515i
$190$		0			0
$191$	−13.5289	+	13.5289i	−0.978916	+	0.978916i	−0.999782	−	0.0208667i	$-0.993357\pi$
$191$	−13.5289	+	13.5289i	−0.978916	+	0.978916i	0.0208667	+	0.999782i	$0.493357\pi$
$192$	0.499730	−	2.51231i	0.0360649	−	0.181310i
$193$	0.490150	−	0.733561i	0.0352817	−	0.0528029i	−0.813409	−	0.581692i	$-0.802391\pi$
$193$	0.490150	−	0.733561i	0.0352817	−	0.0528029i	0.848691	+	0.528889i	$0.177391\pi$
$194$	−3.41210	−	2.27989i	−0.244975	−	0.163687i
$195$		0			0
$196$	−6.46553	−	2.67811i	−0.461824	−	0.191294i
$197$	1.96862	+	9.89694i	0.140259	+	0.705128i	0.985355	+	0.170514i	$0.0545428\pi$
$197$	1.96862	+	9.89694i	0.140259	+	0.705128i	−0.845097	+	0.534614i	$0.820457\pi$
$198$	−7.22613	−	4.82834i	−0.513538	−	0.343135i
$199$	−0.122729	−	0.183676i	−0.00870000	−	0.0130205i	0.827094	−	0.562063i	$-0.189992\pi$
$199$	−0.122729	−	0.183676i	−0.00870000	−	0.0130205i	−0.835794	+	0.549043i	$0.814992\pi$
$200$		0			0
$201$	7.79388	−	39.1825i	0.549738	−	2.76372i
$202$	0.476938	−	1.15143i	0.0335573	−	0.0810144i
$203$	−0.252776	−	0.252776i	−0.0177414	−	0.0177414i
$204$	−4.29371	−	9.64927i	−0.300620	−	0.675584i
$205$		0			0
$206$	8.94117	−	3.70355i	0.622961	−	0.258039i
$207$	−14.1124	−	21.1207i	−0.980879	−	1.46799i
$208$			2.17043i			0.150492i
$209$	7.58578	−	5.06866i	0.524719	−	0.350606i
$210$		0			0
$211$	−7.37496	+	11.0374i	−0.507713	+	0.759846i	−0.993451	−	0.114258i	$-0.963551\pi$
$211$	−7.37496	+	11.0374i	−0.507713	+	0.759846i	0.485738	+	0.874104i	$0.338551\pi$
$212$	−4.87166	+	2.01791i	−0.334587	+	0.138590i
$213$	−12.6173	+	5.22624i	−0.864520	+	0.358096i
$214$	−0.424812	+	0.635776i	−0.0290395	+	0.0434608i
$215$		0			0
$216$	1.19576	−	0.798983i	0.0813613	−	0.0543639i
$217$			0.0486068i			0.00329964i
$218$	5.87947	+	8.79925i	0.398208	+	0.595960i
$219$	27.0025	−	11.1848i	1.82466	−	0.755798i
$220$		0			0
$221$	5.16328	+	7.30913i	0.347320	+	0.491665i
$222$	13.3016	+	13.3016i	0.892744	+	0.892744i
$223$	5.54308	−	13.3822i	0.371192	−	0.896138i	−0.622357	−	0.782734i	$-0.713825\pi$
$223$	5.54308	−	13.3822i	0.371192	−	0.896138i	0.993549	−	0.113404i	$-0.0361754\pi$
$224$	−0.00818577	+	0.0411526i	−0.000546935	+	0.00274963i
$225$		0			0
$226$	3.38351	+	5.06378i	0.225068	+	0.336838i
$227$	24.2962	+	16.2342i	1.61260	+	1.07750i	0.941965	+	0.335711i	$0.108977\pi$
$227$	24.2962	+	16.2342i	1.61260	+	1.07750i	0.670631	+	0.741791i	$0.266023\pi$
$228$	1.86834	+	9.39276i	0.123734	+	0.622050i
$229$	8.84241	+	3.66265i	0.584323	+	0.242035i	0.655206	−	0.755450i	$-0.272582\pi$
$229$	8.84241	+	3.66265i	0.584323	+	0.242035i	−0.0708832	+	0.997485i	$0.522582\pi$
$230$		0			0
$231$	0.218074	+	0.145712i	0.0143482	+	0.00958717i
$232$	4.73332	−	7.08392i	0.310758	−	0.465082i
$233$	−0.644021	+	3.23771i	−0.0421912	+	0.212110i	−0.996130	−	0.0878915i	$-0.971987\pi$
$233$	−0.644021	+	3.23771i	−0.0421912	+	0.212110i	0.953939	+	0.300001i	$0.0969871\pi$
$234$	−5.46582	+	5.46582i	−0.357312	+	0.357312i
$235$		0			0
$236$	−3.63666	−	8.77968i	−0.236727	−	0.571509i
$237$	13.0032	−	13.0032i	0.844648	−	0.844648i
$238$	0.0703326	+	0.158059i	0.00455899	+	0.0102454i
$239$		−	3.25093i		−	0.210285i	−0.994457	−	0.105142i	$-0.966470\pi$
$239$		−	3.25093i		−	0.210285i	0.994457	−	0.105142i	$-0.0335299\pi$
$240$		0			0
$241$	6.53894	+	1.30068i	0.421210	+	0.0837839i	0.401145	−	0.916015i	$-0.368612\pi$
$241$	6.53894	+	1.30068i	0.421210	+	0.0837839i	0.0200657	+	0.999799i	$0.493612\pi$
$242$	−5.04518			−0.324317
$243$	−21.8189	−	4.34005i	−1.39968	−	0.278414i
$244$	1.37731	+	6.92420i	0.0881731	+	0.443276i
$245$		0			0
$246$	0.706940	−	1.70670i	0.0450728	−	0.108815i
$247$	−3.10531	−	7.49687i	−0.197586	−	0.477015i
$248$	−1.13618	+	0.226000i	−0.0721475	+	0.0143510i
$249$	−42.4668	+	8.44718i	−2.69123	+	0.535318i
$250$		0			0
$251$	−3.57690	−	3.57690i	−0.225772	−	0.225772i	0.585152	−	0.810924i	$-0.301035\pi$
$251$	−3.57690	−	3.57690i	−0.225772	−	0.225772i	−0.810924	+	0.585152i	$0.801035\pi$
$252$	−0.124250	+	0.0830209i	−0.00782699	+	0.00522983i
$253$	16.0800	+	6.66056i	1.01094	+	0.418746i
$254$	−13.3456			−0.837378
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−12.9376	−	5.35892i	−0.807025	−	0.334281i	−0.0592584	−	0.998243i	$-0.518874\pi$
$257$	−12.9376	−	5.35892i	−0.807025	−	0.334281i	−0.747766	+	0.663962i	$0.768874\pi$
$258$	−19.3007	+	12.8963i	−1.20161	+	0.802889i
$259$	−0.217885	−	0.217885i	−0.0135387	−	0.0135387i
$260$		0			0
$261$	29.7595	−	5.91954i	1.84207	−	0.366410i
$262$	3.47670	−	0.691558i	0.214791	−	0.0427246i
$263$	0.832416	+	2.00963i	0.0513289	+	0.123919i	0.947464	−	0.319862i	$-0.103637\pi$
$263$	0.832416	+	2.00963i	0.0513289	+	0.123919i	−0.896135	+	0.443781i	$0.853637\pi$
$264$	−2.39207	+	5.77496i	−0.147222	+	0.355424i
$265$		0			0
$266$	−0.0306041	−	0.153857i	−0.00187646	−	0.00943358i
$267$	−41.0275	−	8.16088i	−2.51084	−	0.499438i
$268$	−15.5962			−0.952689
$269$	26.3314	+	5.23765i	1.60546	+	0.319345i	0.914822	−	0.403858i	$-0.132331\pi$
$269$	26.3314	+	5.23765i	1.60546	+	0.319345i	0.690635	+	0.723203i	$0.257331\pi$
$270$		0			0
$271$		−	23.7642i		−	1.44358i	−0.692115	−	0.721788i	$-0.743321\pi$
$271$		−	23.7642i		−	1.44358i	0.692115	−	0.721788i	$-0.256679\pi$
$272$	−3.36760	+	2.37892i	−0.204191	+	0.144243i
$273$	0.164950	−	0.164950i	0.00998325	−	0.00998325i
$274$	5.36748	+	12.9582i	0.324261	+	0.782836i
$275$		0			0
$276$	−12.9188	+	12.9188i	−0.777618	+	0.777618i
$277$	−1.98592	+	9.98392i	−0.119323	+	0.599876i	0.874136	+	0.485682i	$0.161429\pi$
$277$	−1.98592	+	9.98392i	−0.119323	+	0.599876i	−0.993458	+	0.114194i	$0.963571\pi$
$278$	2.34351	−	3.50731i	0.140554	−	0.210354i
$279$	−3.43040	−	2.29212i	−0.205372	−	0.137225i
$280$		0			0
$281$	−7.97842	−	3.30477i	−0.475953	−	0.197146i	0.131794	−	0.991277i	$-0.457926\pi$
$281$	−7.97842	−	3.30477i	−0.475953	−	0.197146i	−0.607747	+	0.794131i	$0.707926\pi$
$282$	2.06794	+	10.3962i	0.123144	+	0.619086i
$283$	5.81872	+	3.88795i	0.345887	+	0.231114i	0.716363	−	0.697728i	$-0.245805\pi$
$283$	5.81872	+	3.88795i	0.345887	+	0.231114i	−0.370476	+	0.928842i	$0.620805\pi$
$284$	2.96203	+	4.43299i	0.175764	+	0.263050i
$285$		0			0
$286$	1.03327	−	5.19461i	0.0610987	−	0.307164i
$287$	−0.0115800	+	0.0279565i	−0.000683543	+	0.00165022i
$288$	−2.51831	−	2.51831i	−0.148393	−	0.148393i
$289$	−5.68144	+	16.0225i	−0.334202	+	0.942501i
$290$		0			0
$291$	−9.71159	+	4.02267i	−0.569303	+	0.235813i
$292$	−6.33910	−	9.48713i	−0.370968	−	0.555192i
$293$			33.0521i			1.93092i	0.260542	+	0.965462i	$0.416099\pi$
$293$			33.0521i			1.93092i	−0.260542	+	0.965462i	$0.583901\pi$
$294$	−14.9051	+	9.95926i	−0.869282	+	0.580836i
$295$		0			0
$296$	4.07998	−	6.10612i	0.237144	−	0.354911i
$297$	−3.24226	+	1.34299i	−0.188135	+	0.0779281i
$298$	0.998603	−	0.413635i	0.0578475	−	0.0239612i
$299$	8.60044	−	12.8715i	0.497376	−	0.744376i
$300$		0			0
$301$	0.316153	−	0.211247i	0.0182228	−	0.0121761i
$302$		−	12.9985i		−	0.747980i
$303$	−1.77362	−	2.65441i	−0.101892	−	0.152492i
$304$	3.45410	−	1.43074i	0.198106	−	0.0820583i
$305$		0			0
$306$	−14.4716	−	2.48979i	−0.827284	−	0.142332i
$307$	2.40170	+	2.40170i	0.137072	+	0.137072i	0.772314	−	0.635241i	$-0.219099\pi$
$307$	2.40170	+	2.40170i	0.137072	+	0.137072i	−0.635241	+	0.772314i	$0.719099\pi$
$308$	0.0391830	−	0.0945961i	0.00223266	−	0.00539011i
$309$	4.83631	−	24.3138i	0.275128	−	1.38316i
$310$		0			0
$311$	11.7323	+	17.5586i	0.665276	+	0.995655i	0.998603	+	0.0528442i	$0.0168287\pi$
$311$	11.7323	+	17.5586i	0.665276	+	0.995655i	−0.333327	+	0.942811i	$0.608171\pi$
$312$	4.62265	+	3.08876i	0.261706	+	0.174866i
$313$	−6.40363	−	32.1932i	−0.361954	−	1.81967i	−0.547231	−	0.836981i	$-0.684318\pi$
$313$	−6.40363	−	32.1932i	−0.361954	−	1.81967i	0.185277	−	0.982686i	$-0.440682\pi$
$314$	6.45576	+	2.67407i	0.364320	+	0.150906i
$315$		0			0
$316$	−5.96914	−	3.98845i	−0.335790	−	0.224368i
$317$	−17.3586	+	25.9790i	−0.974957	+	1.45913i	−0.0886306	+	0.996065i	$0.528249\pi$
$317$	−17.3586	+	25.9790i	−0.974957	+	1.45913i	−0.886326	+	0.463061i	$0.846751\pi$
$318$	−2.63510	+	13.2475i	−0.147769	+	0.742884i
$319$	−14.7010	+	14.7010i	−0.823097	+	0.823097i
$320$		0			0
$321$	0.749543	+	1.80956i	0.0418354	+	0.101000i
$322$	0.211614	−	0.211614i	0.0117928	−	0.0117928i
$323$	8.22842	−	13.0352i	0.457841	−	0.725297i
$324$			7.00049i			0.388916i
$325$		0			0
$326$	−10.6693	−	2.12225i	−0.590917	−	0.117541i
$327$	27.1081			1.49908
$328$	−0.707322	−	0.140695i	−0.0390553	−	0.00776859i
$329$	−0.0338736	−	0.170294i	−0.00186751	−	0.00938862i
$330$		0			0
$331$	−3.75693	+	9.07002i	−0.206499	+	0.498533i	−0.992867	−	0.119225i	$-0.961959\pi$
$331$	−3.75693	+	9.07002i	−0.206499	+	0.498533i	0.786368	+	0.617758i	$0.211959\pi$
$332$	6.46869	+	15.6168i	0.355015	+	0.857083i
$333$	25.6518	−	5.10246i	1.40571	−	0.279613i
$334$	−3.25081	+	0.646627i	−0.177877	+	0.0353818i
$335$		0			0
$336$	0.0759990	+	0.0759990i	0.00414609	+	0.00414609i
$337$	12.5920	−	8.41370i	0.685929	−	0.458323i	−0.163141	−	0.986603i	$-0.552163\pi$
$337$	12.5920	−	8.41370i	0.685929	−	0.458323i	0.849071	+	0.528279i	$0.177163\pi$
$338$	7.65827	+	3.17216i	0.416555	+	0.172543i
$339$	15.6001			0.847282
$340$		0			0
$341$	2.82688			0.153084
$342$	12.3016	+	5.09547i	0.665192	+	0.275531i
$343$	0.488364	−	0.326314i	0.0263692	−	0.0176193i
$344$	6.40785	+	6.40785i	0.345488	+	0.345488i
$345$		0			0
$346$	−23.2606	+	4.62681i	−1.25050	+	0.248739i
$347$	3.17804	−	0.632152i	0.170606	−	0.0339357i	−0.109048	−	0.994036i	$-0.534780\pi$
$347$	3.17804	−	0.632152i	0.170606	−	0.0339357i	0.279654	+	0.960101i	$0.409780\pi$
$348$	−8.35153	−	20.1624i	−0.447689	−	1.08082i
$349$	1.97926	−	4.77837i	0.105948	−	0.255780i	−0.862011	−	0.506889i	$-0.830795\pi$
$349$	1.97926	−	4.77837i	0.105948	−	0.255780i	0.967959	+	0.251109i	$0.0807953\pi$
$350$		0			0
$351$	0.608947	+	3.06138i	0.0325032	+	0.163405i
$352$	2.39336	+	0.476069i	0.127567	+	0.0253746i
$353$	22.4791			1.19644			0.598220	−	0.801332i	$-0.295875\pi$
$353$	22.4791			1.19644			0.598220	+	0.801332i	$0.295875\pi$
$354$	−23.8746	−	4.74896i	−1.26892	−	0.252404i
$355$		0			0
$356$			16.3306i			0.865520i
$357$	0.436730	+	0.0751383i	0.0231142	+	0.00397674i
$358$	1.98674	−	1.98674i	0.105002	−	0.105002i
$359$	−12.8019	−	30.9065i	−0.675658	−	1.63118i	−0.771839	−	0.635818i	$-0.780663\pi$
$359$	−12.8019	−	30.9065i	−0.675658	−	1.63118i	0.0961812	−	0.995364i	$-0.469337\pi$
$360$		0			0
$361$	3.55122	−	3.55122i	0.186906	−	0.186906i
$362$	−2.12484	+	10.6823i	−0.111679	+	0.561449i
$363$	−7.17985	+	10.7454i	−0.376844	+	0.563987i
$364$	−0.0757208	−	0.0505950i	−0.00396885	−	0.00265190i
$365$		0			0
$366$	16.7075	+	6.92045i	0.873312	+	0.361738i
$367$	−1.86891	−	9.39563i	−0.0975562	−	0.490448i	−0.998412	−	0.0563300i	$-0.982060\pi$
$367$	−1.86891	−	9.39563i	−0.0975562	−	0.490448i	0.900856	−	0.434118i	$-0.142940\pi$
$368$	5.93039	+	3.96256i	0.309143	+	0.206563i
$369$	−1.42695	−	2.13557i	−0.0742838	−	0.111174i
$370$		0			0
$371$	0.0431639	−	0.217000i	0.00224096	−	0.0112661i
$372$	−1.13557	+	2.74150i	−0.0588763	+	0.142140i
$373$	−4.49749	−	4.49749i	−0.232871	−	0.232871i	0.581019	−	0.813890i	$-0.302654\pi$
$373$	−4.49749	−	4.49749i	−0.232871	−	0.232871i	−0.813890	+	0.581019i	$0.802654\pi$
$374$	9.19241	−	4.09041i	0.475328	−	0.211510i
$375$		0			0
$376$	3.82312	−	1.58359i	0.197162	−	0.0816672i
$377$	10.2733	+	15.3751i	0.529103	+	0.791859i
$378$			0.0603424i			0.00310368i
$379$	−8.45523	+	5.64960i	−0.434316	+	0.290201i	−0.753445	−	0.657511i	$-0.771610\pi$
$379$	−8.45523	+	5.64960i	−0.434316	+	0.290201i	0.319129	+	0.947711i	$0.396610\pi$
$380$		0			0
$381$	−18.9923	+	28.4239i	−0.973004	+	1.45620i
$382$	17.6763	−	7.32178i	0.904400	−	0.374615i
$383$	−1.74137	+	0.721299i	−0.0889799	+	0.0368567i	−0.426729	−	0.904379i	$-0.640334\pi$
$383$	−1.74137	+	0.721299i	−0.0889799	+	0.0368567i	0.337750	+	0.941236i	$0.390334\pi$
$384$	−1.42311	+	2.12983i	−0.0726228	+	0.108688i
$385$		0			0
$386$	−0.733561	+	0.490150i	−0.0373373	+	0.0249480i
$387$			32.2740i			1.64058i
$388$	2.27989	+	3.41210i	0.115744	+	0.173223i
$389$	7.74116	−	3.20649i	0.392492	−	0.162576i	−0.177704	−	0.984084i	$-0.556867\pi$
$389$	7.74116	−	3.20649i	0.392492	−	0.162576i	0.570197	+	0.821508i	$0.306867\pi$
$390$		0			0
$391$	29.3978	−	0.763634i	1.48671	−	0.0386186i
$392$	4.94850	+	4.94850i	0.249937	+	0.249937i
$393$	3.47482	−	8.38895i	0.175281	−	0.423167i
$394$	1.96862	−	9.89694i	0.0991778	−	0.498600i
$395$		0			0
$396$	4.82834	+	7.22613i	0.242633	+	0.363127i
$397$	−13.9557	−	9.32491i	−0.700417	−	0.468004i	0.153678	−	0.988121i	$-0.450888\pi$
$397$	−13.9557	−	9.32491i	−0.700417	−	0.468004i	−0.854095	+	0.520117i	$0.825888\pi$
$398$	0.0430965	+	0.216661i	0.00216023	+	0.0108602i
$399$	−0.371243	−	0.153774i	−0.0185854	−	0.00769832i
$400$		0			0
$401$	27.0871	+	18.0990i	1.35267	+	0.903822i	0.999496	−	0.0317369i	$-0.0101039\pi$
$401$	27.0871	+	18.0990i	1.35267	+	0.903822i	0.353170	+	0.935559i	$0.385104\pi$
$402$	−22.1951	+	33.2173i	−1.10699	+	1.65673i
$403$	0.490517	−	2.46599i	0.0244344	−	0.122840i
$404$	−0.881267	+	0.881267i	−0.0438447	+	0.0438447i
$405$		0			0
$406$	0.136801	+	0.330268i	0.00678934	+	0.0163909i
$407$	−12.6718	+	12.6718i	−0.628117	+	0.628117i
$408$	0.274251	+	10.5579i	0.0135774	+	0.522694i
$409$			25.7330i			1.27241i	0.771519	+	0.636207i	$0.219497\pi$
$409$			25.7330i			1.27241i	−0.771519	+	0.636207i	$0.780503\pi$
$410$		0			0
$411$	35.2374	+	7.00916i	1.73813	+	0.345736i
$412$	−9.67785			−0.476794
$413$	0.391076	+	0.0777898i	0.0192436	+	0.00382779i
$414$	4.95561	+	24.9135i	0.243555	+	1.22443i
$415$		0			0
$416$	0.830586	−	2.00521i	0.0407228	−	0.0983136i
$417$	−4.13491	−	9.98257i	−0.202488	−	0.488848i
$418$	−8.94804	+	1.77988i	−0.437663	+	0.0870566i
$419$	23.5187	−	4.67816i	1.14896	−	0.228543i	0.416361	−	0.909199i	$-0.363305\pi$
$419$	23.5187	−	4.67816i	1.14896	−	0.228543i	0.732603	+	0.680656i	$0.238305\pi$
$420$		0			0
$421$	7.63147	+	7.63147i	0.371935	+	0.371935i	0.868182	−	0.496246i	$-0.165289\pi$
$421$	7.63147	+	7.63147i	0.371935	+	0.371935i	−0.496246	+	0.868182i	$0.665289\pi$
$422$	11.0374	−	7.37496i	0.537292	−	0.359007i
$423$	13.6158	+	5.63984i	0.662022	+	0.274218i
$424$	5.27304			0.256082
$425$		0			0
$426$	13.6568			0.661675
$427$	−0.273675	−	0.113360i	−0.0132440	−	0.00548586i
$428$	0.635776	−	0.424812i	0.0307314	−	0.0205341i
$429$	−9.59320	−	9.59320i	−0.463164	−	0.463164i
$430$		0			0
$431$	−9.64284	+	1.91808i	−0.464479	+	0.0923906i	−0.421782	−	0.906697i	$-0.638595\pi$
$431$	−9.64284	+	1.91808i	−0.464479	+	0.0923906i	−0.0426974	+	0.999088i	$0.513595\pi$
$432$	−1.41050	+	0.280566i	−0.0678626	+	0.0134987i
$433$	−0.404025	−	0.975402i	−0.0194162	−	0.0468748i	0.913874	−	0.405998i	$-0.133076\pi$
$433$	−0.404025	−	0.975402i	−0.0194162	−	0.0468748i	−0.933290	+	0.359123i	$0.883076\pi$
$434$	0.0186010	−	0.0449068i	0.000892877	−	0.00215559i
$435$		0			0
$436$	−2.06460	−	10.3794i	−0.0988762	−	0.497084i
$437$	−26.1535	−	5.20226i	−1.25109	−	0.248858i
$438$	−29.2273			−1.39653
$439$	−1.72130	−	0.342388i	−0.0821533	−	0.0163413i	0.153842	−	0.988095i	$-0.450835\pi$
$439$	−1.72130	−	0.342388i	−0.0821533	−	0.0163413i	−0.235996	+	0.971754i	$0.575835\pi$
$440$		0			0
$441$			24.9238i			1.18685i
$442$	−1.97317	−	8.72865i	−0.0938540	−	0.415180i
$443$	−17.4487	+	17.4487i	−0.829013	+	0.829013i	−0.987380	−	0.158367i	$-0.949377\pi$
$443$	−17.4487	+	17.4487i	−0.829013	+	0.829013i	0.158367	+	0.987380i	$0.449377\pi$
$444$	−7.19876	−	17.3794i	−0.341638	−	0.824787i
$445$		0			0
$446$	−10.2423	+	10.2423i	−0.484986	+	0.484986i
$447$	0.540148	−	2.71551i	0.0255481	−	0.128439i
$448$	0.0233111	−	0.0348875i	0.00110135	−	0.00164828i
$449$	−3.28010	−	2.19169i	−0.154797	−	0.103432i	0.475759	−	0.879576i	$-0.342173\pi$
$449$	−3.28010	−	2.19169i	−0.154797	−	0.103432i	−0.630557	+	0.776143i	$0.717173\pi$
$450$		0			0
$451$	1.62590	+	0.673468i	0.0765605	+	0.0317124i
$452$	−1.18813	−	5.97314i	−0.0558850	−	0.280953i
$453$	−27.6847	−	18.4983i	−1.30074	−	0.869127i
$454$	−16.2342	−	24.2962i	−0.761909	−	1.14028i
$455$		0			0
$456$	1.86834	−	9.39276i	0.0874928	−	0.439856i
$457$	7.70665	−	18.6055i	0.360502	−	0.870328i	−0.634725	−	0.772738i	$-0.718887\pi$
$457$	7.70665	−	18.6055i	0.360502	−	0.870328i	0.995227	−	0.0975901i	$-0.0311134\pi$
$458$	−6.76769	−	6.76769i	−0.316233	−	0.316233i
$459$	−4.08255	+	4.30030i	−0.190557	+	0.200721i
$460$		0			0
$461$	−14.0354	+	5.81365i	−0.653693	+	0.270769i	−0.684782	−	0.728748i	$-0.740103\pi$
$461$	−14.0354	+	5.81365i	−0.653693	+	0.270769i	0.0310887	+	0.999517i	$0.490103\pi$
$462$	−0.145712	−	0.218074i	−0.00677915	−	0.0101457i
$463$			4.79079i			0.222647i	0.993784	+	0.111323i	$0.0355090\pi$
$463$			4.79079i			0.222647i	−0.993784	+	0.111323i	$0.964491\pi$
$464$	−7.08392	+	4.73332i	−0.328863	+	0.219739i
$465$		0			0
$466$	1.83402	−	2.74480i	0.0849592	−	0.127150i
$467$	14.1041	−	5.84209i	0.652658	−	0.270340i	−0.0316875	−	0.999498i	$-0.510088\pi$
$467$	14.1041	−	5.84209i	0.652658	−	0.270340i	0.684345	+	0.729158i	$0.260088\pi$
$468$	7.14143	−	2.95808i	0.330113	−	0.136737i
$469$	0.363564	−	0.544112i	0.0167878	−	0.0251248i
$470$		0			0
$471$	14.8826	−	9.94422i	0.685753	−	0.458205i
$472$			9.50306i			0.437414i
$473$	−12.2857	−	18.3869i	−0.564898	−	0.845429i
$474$	−16.9895	+	7.03727i	−0.780353	+	0.323233i
$475$		0			0
$476$	−0.00449234	−	0.172942i	−0.000205906	−	0.00792681i
$477$	13.2792	+	13.2792i	0.608012	+	0.608012i
$478$	−1.24408	+	3.00347i	−0.0569027	+	0.137375i
$479$	4.20902	−	21.1602i	0.192315	−	0.966834i	−0.757217	−	0.653164i	$-0.773441\pi$
$479$	4.20902	−	21.1602i	0.192315	−	0.966834i	0.949532	−	0.313670i	$-0.101559\pi$
$480$		0			0
$481$	8.85529	+	13.2529i	0.403767	+	0.604279i
$482$	−5.54345	−	3.70401i	−0.252497	−	0.168713i
$483$	−0.149553	−	0.751854i	−0.00680490	−	0.0342106i
$484$	4.66114	+	1.93071i	0.211870	+	0.0877595i
$485$		0			0
$486$	18.4972	+	12.3594i	0.839048	+	0.560634i
$487$	−10.9420	+	16.3758i	−0.495829	+	0.742060i	−0.992010	−	0.126159i	$-0.959735\pi$
$487$	−10.9420	+	16.3758i	−0.495829	+	0.742060i	0.496181	+	0.868219i	$0.334735\pi$
$488$	1.37731	−	6.92420i	0.0623478	−	0.313444i
$489$	−19.7036	+	19.7036i	−0.891028	+	0.891028i
$490$		0			0
$491$	−4.17779	−	10.0861i	−0.188541	−	0.455179i	0.801138	−	0.598480i	$-0.204228\pi$
$491$	−4.17779	−	10.0861i	−0.188541	−	0.455179i	−0.989679	+	0.143301i	$0.954228\pi$
$492$	−1.30625	+	1.30625i	−0.0588905	+	0.0588905i
$493$	−12.5956	+	32.7920i	−0.567276	+	1.47688i
$494$			8.11456i			0.365091i
$495$		0			0
$496$	1.13618	+	0.226000i	0.0510160	+	0.0101477i
$497$	−0.223704			−0.0100345
$498$	42.4668	+	8.44718i	1.90298	+	0.378527i
$499$	−2.05219	−	10.3170i	−0.0918685	−	0.461854i	−0.999146	−	0.0413215i	$-0.986843\pi$
$499$	−2.05219	−	10.3170i	−0.0918685	−	0.461854i	0.907277	−	0.420533i	$-0.138157\pi$
$500$		0			0
$501$	−3.24905	+	7.84391i	−0.145157	+	0.350440i
$502$	1.93580	+	4.67345i	0.0863992	+	0.208586i
$503$	−23.5465	+	4.68369i	−1.04989	+	0.208836i	−0.689738	−	0.724059i	$-0.742274\pi$
$503$	−23.5465	+	4.68369i	−1.04989	+	0.208836i	−0.360149	+	0.932895i	$0.617274\pi$
$504$	0.146562	−	0.0291531i	0.00652841	−	0.00129858i
$505$		0			0
$506$	−12.3071	−	12.3071i	−0.547117	−	0.547117i
$507$	17.6547	−	11.7965i	0.784074	−	0.523901i
$508$	12.3297	+	5.10715i	0.547044	+	0.226593i
$509$	25.3539			1.12379			0.561895	−	0.827209i	$-0.310072\pi$
$509$	25.3539			1.12379			0.561895	+	0.827209i	$0.310072\pi$
$510$		0			0
$511$	0.478754			0.0211788
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	4.47059	−	2.98715i	0.197381	−	0.131886i
$514$	9.90200	+	9.90200i	0.436759	+	0.436759i
$515$		0			0
$516$	22.7667	−	4.52858i	1.00225	−	0.199360i
$517$	−9.90399	+	1.97003i	−0.435577	+	0.0866416i
$518$	0.117919	+	0.284681i	0.00518104	+	0.0125081i
$519$	−23.2480	+	56.1256i	−1.02047	+	2.46364i
$520$		0			0
$521$	−7.91442	−	39.7885i	−0.346737	−	1.74316i	−0.623128	−	0.782120i	$-0.714139\pi$
$521$	−7.91442	−	39.7885i	−0.346737	−	1.74316i	0.276391	−	0.961045i	$-0.410861\pi$
$522$	−29.7595	−	5.91954i	−1.30254	−	0.259091i
$523$	−6.98382			−0.305381			−0.152690	−	0.988274i	$-0.548794\pi$
$523$	−6.98382			−0.305381			−0.152690	+	0.988274i	$0.548794\pi$
$524$	−3.47670	−	0.691558i	−0.151880	−	0.0302109i
$525$		0			0
$526$		−	2.17521i		−	0.0948435i
$527$	4.36383	−	1.94181i	0.190092	−	0.0845864i
$528$	4.41996	−	4.41996i	0.192354	−	0.192354i
$529$	−10.6659	−	25.7498i	−0.463735	−	1.11955i
$530$		0			0
$531$	−23.9317	+	23.9317i	−1.03855	+	1.03855i
$532$	−0.0306041	+	0.153857i	−0.00132685	+	0.00667055i
$533$	0.869616	−	1.30147i	0.0376672	−	0.0563730i
$534$	34.7814	+	23.2402i	1.50514	+	1.00570i
$535$		0			0
$536$	14.4090	+	5.96840i	0.622374	+	0.257796i
$537$	−1.40408	−	7.05878i	−0.0605904	−	0.304609i
$538$	−22.3227	−	14.9156i	−0.962401	−	0.643056i
$539$	−9.48772	−	14.1994i	−0.408665	−	0.611611i
$540$		0			0
$541$	−2.94451	+	14.8030i	−0.126594	+	0.636432i	0.864430	+	0.502753i	$0.167679\pi$
$541$	−2.94451	+	14.8030i	−0.126594	+	0.636432i	−0.991025	+	0.133680i	$0.957321\pi$
$542$	−9.09418	+	21.9553i	−0.390629	+	0.943061i
$543$	19.7276	+	19.7276i	0.846593	+	0.846593i
$544$	4.02163	−	0.909115i	0.172426	−	0.0389780i
$545$		0			0
$546$	−0.215518	+	0.0892705i	−0.00922332	+	0.00382042i
$547$	2.34789	+	3.51387i	0.100389	+	0.150242i	0.878263	−	0.478177i	$-0.158702\pi$
$547$	2.34789	+	3.51387i	0.100389	+	0.150242i	−0.777875	+	0.628419i	$0.783702\pi$
$548$		−	14.0259i		−	0.599157i
$549$	20.9058	−	13.9688i	0.892238	−	0.596174i
$550$		0			0
$551$	17.6964	−	26.4846i	0.753893	−	1.12828i
$552$	16.8792	−	6.99159i	0.718426	−	0.297582i
$553$	0.278294	−	0.115273i	0.0118343	−	0.00490192i
$554$	5.65544	−	8.46396i	0.240276	−	0.359599i
$555$		0			0
$556$	−3.50731	+	2.34351i	−0.148743	+	0.0993869i
$557$			11.6947i			0.495521i	0.968821	+	0.247761i	$0.0796947\pi$
$557$			11.6947i			0.495521i	−0.968821	+	0.247761i	$0.920305\pi$
$558$	2.29212	+	3.43040i	0.0970331	+	0.145220i
$559$	−18.1714	+	7.52683i	−0.768567	+	0.318351i
$560$		0			0
$561$	4.36991	−	25.3994i	0.184498	−	1.07236i
$562$	6.10642	+	6.10642i	0.257584	+	0.257584i
$563$	−14.0670	+	33.9608i	−0.592854	+	1.43128i	0.287880	+	0.957666i	$0.407050\pi$
$563$	−14.0670	+	33.9608i	−0.592854	+	1.43128i	−0.880734	+	0.473611i	$0.842950\pi$
$564$	2.06794	−	10.3962i	0.0870758	−	0.437760i
$565$		0			0
$566$	−3.88795	−	5.81872i	−0.163423	−	0.244579i
$567$	−0.244230	−	0.163189i	−0.0102567	−	0.00685330i
$568$	−1.04013	−	5.22907i	−0.0436427	−	0.219407i
$569$	−12.1903	−	5.04937i	−0.511043	−	0.211681i	0.112235	−	0.993682i	$-0.464199\pi$
$569$	−12.1903	−	5.04937i	−0.511043	−	0.211681i	−0.623277	+	0.782001i	$0.714199\pi$
$570$		0			0
$571$	−19.7618	−	13.2044i	−0.827008	−	0.552589i	0.0684917	−	0.997652i	$-0.478181\pi$
$571$	−19.7618	−	13.2044i	−0.827008	−	0.552589i	−0.895499	+	0.445063i	$0.853181\pi$
$572$	−2.94251	+	4.40378i	−0.123033	+	0.184131i
$573$	9.56119	−	48.0674i	0.399425	−	2.00804i
$574$	0.0213970	−	0.0213970i	0.000893092	−	0.000893092i
$575$		0			0
$576$	1.36290	+	3.29034i	0.0567876	+	0.137097i
$577$	6.38096	−	6.38096i	0.265643	−	0.265643i	−0.561699	−	0.827342i	$-0.689852\pi$
$577$	6.38096	−	6.38096i	0.265643	−	0.265643i	0.827342	+	0.561699i	$0.189852\pi$
$578$	11.3805	−	12.6287i	0.473367	−	0.525284i
$579$			2.25990i			0.0939182i
$580$		0			0
$581$	−0.695624	−	0.138368i	−0.0288593	−	0.00574048i
$582$	10.5117			0.435726
$583$	−12.6203	−	2.51033i	−0.522679	−	0.103967i
$584$	2.22600	+	11.1908i	0.0921124	+	0.463080i
$585$		0			0
$586$	12.6485	−	30.5362i	0.522505	−	1.26144i
$587$	−8.31106	−	20.0647i	−0.343034	−	0.828158i	−0.997406	−	0.0719847i	$-0.977067\pi$
$587$	−8.31106	−	20.0647i	−0.343034	−	0.828158i	0.654371	−	0.756173i	$-0.272933\pi$
$588$	17.5818	−	3.49723i	0.725059	−	0.144223i
$589$	−4.24782	+	0.844945i	−0.175029	+	0.0348153i
$590$		0			0
$591$	−18.2773	−	18.2773i	−0.751826	−	0.751826i
$592$	−6.10612	+	4.07998i	−0.250960	+	0.167686i
$593$	−25.9568	−	10.7516i	−1.06592	−	0.441517i	−0.220368	−	0.975417i	$-0.570726\pi$
$593$	−25.9568	−	10.7516i	−1.06592	−	0.441517i	−0.845548	+	0.533900i	$0.820726\pi$
$594$	3.50940			0.143992
$595$		0			0
$596$	−1.08088			−0.0442746
$597$	0.522783	+	0.216544i	0.0213961	+	0.00886255i
$598$	−12.8715	+	8.60044i	−0.526353	+	0.351698i
$599$	−3.04934	−	3.04934i	−0.124593	−	0.124593i	0.642061	−	0.766654i	$-0.278080\pi$
$599$	−3.04934	−	3.04934i	−0.124593	−	0.124593i	−0.766654	+	0.642061i	$0.778080\pi$
$600$		0			0
$601$	−12.0448	+	2.39585i	−0.491317	+	0.0977289i	−0.434530	−	0.900657i	$-0.643085\pi$
$601$	−12.0448	+	2.39585i	−0.491317	+	0.0977289i	−0.0567866	+	0.998386i	$0.518085\pi$
$602$	−0.372928	+	0.0741800i	−0.0151994	+	0.00302335i
$603$	21.2561	+	51.3167i	0.865614	+	2.08978i
$604$	−4.97432	+	12.0091i	−0.202402	+	0.488642i
$605$		0			0
$606$	0.622813	+	3.13109i	0.0253000	+	0.127192i
$607$	14.1007	+	2.80480i	0.572328	+	0.113843i	0.472766	−	0.881188i	$-0.343256\pi$
$607$	14.1007	+	2.80480i	0.572328	+	0.113843i	0.0995626	+	0.995031i	$0.468256\pi$
$608$	−3.73869			−0.151624
$609$	0.898099	+	0.178643i	0.0363928	+	0.00723898i
$610$		0			0
$611$			8.98146i			0.363351i
$612$	12.4172	+	7.83829i	0.501934	+	0.316844i
$613$	−2.17490	+	2.17490i	−0.0878433	+	0.0878433i	−0.749663	−	0.661820i	$-0.769784\pi$
$613$	−2.17490	+	2.17490i	−0.0878433	+	0.0878433i	0.661820	+	0.749663i	$0.269784\pi$
$614$	−1.29979	−	3.13798i	−0.0524554	−	0.126638i
$615$		0			0
$616$	−0.0724007	+	0.0724007i	−0.00291711	+	0.00291711i
$617$	2.42495	−	12.1910i	0.0976247	−	0.490793i	−0.900777	−	0.434281i	$-0.857002\pi$
$617$	2.42495	−	12.1910i	0.0976247	−	0.490793i	0.998402	−	0.0565112i	$-0.0179977\pi$
$618$	−13.7726	+	20.6122i	−0.554017	+	0.829145i
$619$	38.7236	+	25.8743i	1.55643	+	1.03998i	0.973846	+	0.227208i	$0.0729597\pi$
$619$	38.7236	+	25.8743i	1.55643	+	1.03998i	0.582588	+	0.812768i	$0.302040\pi$
$620$		0			0
$621$	9.47656	+	3.92532i	0.380281	+	0.157518i
$622$	−4.11982	−	20.7118i	−0.165190	−	0.830466i
$623$	−0.569734	−	0.380684i	−0.0228259	−	0.0152518i
$624$	−3.08876	−	4.62265i	−0.123649	−	0.185054i
$625$		0			0
$626$	−6.40363	+	32.1932i	−0.255940	+	1.28670i
$627$	−8.94320	+	21.5908i	−0.357157	+	0.862253i
$628$	−4.94103	−	4.94103i	−0.197168	−	0.197168i
$629$	−10.8570	+	28.2657i	−0.432897	+	1.12703i
$630$		0			0
$631$	−25.1686	+	10.4252i	−1.00195	+	0.415020i	−0.822511	−	0.568749i	$-0.807427\pi$
$631$	−25.1686	+	10.4252i	−1.00195	+	0.415020i	−0.179436	+	0.983770i	$0.557427\pi$
$632$	3.98845	+	5.96914i	0.158652	+	0.237440i
$633$		−	34.0032i		−	1.35151i
$634$	25.9790	−	17.3586i	1.03176	−	0.689399i
$635$		0			0
$636$	7.50412	−	11.2307i	0.297558	−	0.445327i
$637$	−14.0330	+	5.81264i	−0.556006	+	0.230305i
$638$	19.2078	−	7.95611i	0.760442	−	0.314985i
$639$	10.5491	−	15.7878i	0.417315	−	0.624556i
$640$		0			0
$641$	4.62681	−	3.09154i	0.182748	−	0.122108i	−0.460831	−	0.887488i	$-0.652449\pi$
$641$	4.62681	−	3.09154i	0.182748	−	0.122108i	0.643579	+	0.765379i	$0.277449\pi$
$642$		−	1.95865i		−	0.0773018i
$643$	1.30468	+	1.95259i	0.0514515	+	0.0770025i	0.856303	−	0.516473i	$-0.172755\pi$
$643$	1.30468	+	1.95259i	0.0514515	+	0.0770025i	−0.804852	+	0.593476i	$0.797755\pi$
$644$	−0.276488	+	0.114525i	−0.0108951	+	0.00451291i
$645$		0			0
$646$	−12.5904	+	8.89406i	−0.495363	+	0.349932i
$647$	−2.50204	−	2.50204i	−0.0983654	−	0.0983654i	0.656212	−	0.754577i	$-0.272158\pi$
$647$	−2.50204	−	2.50204i	−0.0983654	−	0.0983654i	−0.754577	+	0.656212i	$0.772158\pi$
$648$	2.67897	−	6.46761i	0.105240	−	0.254072i
$649$	4.52411	−	22.7442i	0.177587	−	0.892790i
$650$		0			0
$651$	−0.0691728	−	0.103524i	−0.00271109	−	0.00405744i
$652$	9.04498	+	6.04366i	0.354229	+	0.236688i
$653$	6.07974	+	30.5649i	0.237919	+	1.19610i	0.896312	+	0.443424i	$0.146236\pi$
$653$	6.07974	+	30.5649i	0.237919	+	1.19610i	−0.658393	+	0.752674i	$0.728764\pi$
$654$	−25.0446	−	10.3738i	−0.979321	−	0.405648i
$655$		0			0
$656$	0.599639	+	0.400666i	0.0234120	+	0.0156434i
$657$	−22.5763	+	33.7878i	−0.880785	+	1.31819i
$658$	−0.0338736	+	0.170294i	−0.00132053	+	0.00663876i
$659$	−21.8155	+	21.8155i	−0.849813	+	0.849813i	−0.990110	−	0.140296i	$-0.955194\pi$
$659$	−21.8155	+	21.8155i	−0.849813	+	0.849813i	0.140296	+	0.990110i	$0.455194\pi$
$660$		0			0
$661$	−6.74921	−	16.2940i	−0.262514	−	0.633765i	0.736579	−	0.676352i	$-0.236440\pi$
$661$	−6.74921	−	16.2940i	−0.262514	−	0.633765i	−0.999093	+	0.0425871i	$0.986440\pi$
$662$	6.94189	−	6.94189i	0.269804	−	0.269804i
$663$	−21.3986	−	8.21931i	−0.831053	−	0.319212i
$664$		−	16.9035i		−	0.655983i
$665$		0			0
$666$	−25.6518	−	5.10246i	−0.993987	−	0.197716i
$667$	60.7664			2.35288
$668$	3.25081	+	0.646627i	0.125778	+	0.0250187i
$669$	7.23847	+	36.3903i	0.279856	+	1.40693i
$670$		0			0
$671$	−6.59279	+	15.9164i	−0.254512	+	0.614446i
$672$	−0.0411304	−	0.0992975i	−0.00158664	−	0.00383049i
$673$	−26.3089	+	5.23317i	−1.01413	+	0.201724i	−0.674061	−	0.738675i	$-0.735452\pi$
$673$	−26.3089	+	5.23317i	−1.01413	+	0.201724i	−0.340072	+	0.940399i	$0.610452\pi$
$674$	−14.8533	+	2.95450i	−0.572126	+	0.113803i
$675$		0			0
$676$	−5.86138	−	5.86138i	−0.225438	−	0.225438i
$677$	−4.36912	+	2.91935i	−0.167919	+	0.112200i	−0.636690	−	0.771120i	$-0.719697\pi$
$677$	−4.36912	+	2.91935i	−0.167919	+	0.112200i	0.468771	+	0.883320i	$0.344697\pi$
$678$	−14.4126	−	5.96991i	−0.553514	−	0.229273i
$679$	−0.172187			−0.00660791
$680$		0			0
$681$	−74.8500			−2.86826
$682$	−2.61170	−	1.08180i	−0.100007	−	0.0414242i
$683$	32.9122	−	21.9912i	1.25935	−	0.841470i	0.266851	−	0.963738i	$-0.414017\pi$
$683$	32.9122	−	21.9912i	1.25935	−	0.841470i	0.992497	+	0.122268i	$0.0390167\pi$
$684$	−9.41520	−	9.41520i	−0.359999	−	0.359999i
$685$		0			0
$686$	−0.576064	+	0.114586i	−0.0219942	+	0.00437493i
$687$	−24.0452	+	4.78289i	−0.917382	+	0.182479i
$688$	−3.46790	−	8.37226i	−0.132213	−	0.319189i
$689$	−4.37972	+	10.5736i	−0.166854	+	0.402821i
$690$		0			0
$691$	−5.45405	−	27.4193i	−0.207482	−	1.04308i	−0.934364	−	0.356319i	$-0.884032\pi$
$691$	−5.45405	−	27.4193i	−0.207482	−	1.04308i	0.726883	−	0.686762i	$-0.240968\pi$
$692$	23.2606	+	4.62681i	0.884234	+	0.175885i
$693$	−0.364656			−0.0138521
$694$	−3.17804	−	0.632152i	−0.120637	−	0.0239962i
$695$		0			0
$696$			21.8236i			0.827221i
$697$	2.97250	−	0.0772133i	0.112591	−	0.00292466i
$698$	−3.65720	+	3.65720i	−0.138427	+	0.138427i
$699$	−3.23596	−	7.81231i	−0.122395	−	0.295489i
$700$		0			0
$701$	31.7560	−	31.7560i	1.19941	−	1.19941i	0.225063	−	0.974344i	$-0.427741\pi$
$701$	31.7560	−	31.7560i	1.19941	−	1.19941i	0.974344	−	0.225063i	$-0.0722588\pi$
$702$	0.608947	−	3.06138i	0.0229832	−	0.115544i
$703$	15.2538	−	22.8289i	0.575307	−	0.861008i
$704$	−2.02899	−	1.35573i	−0.0764706	−	0.0510960i
$705$		0			0
$706$	−20.7680	−	8.60237i	−0.781612	−	0.323754i
$707$	−0.0102019	−	0.0512885i	−0.000383683	−	0.00192890i
$708$	20.2399	+	13.5239i	0.760663	+	0.508259i
$709$	3.74297	+	5.60175i	0.140570	+	0.210378i	0.895074	−	0.445917i	$-0.147122\pi$
$709$	3.74297	+	5.60175i	0.140570	+	0.210378i	−0.754504	+	0.656295i	$0.772122\pi$
$710$		0			0
$711$	−4.98799	+	25.0763i	−0.187064	+	0.940436i
$712$	6.24945	−	15.0875i	0.234208	−	0.565428i
$713$	−5.84244	−	5.84244i	−0.218801	−	0.218801i
$714$	−0.374732	−	0.236548i	−0.0140240	−	0.00885259i
$715$		0			0
$716$	−2.59580	+	1.07522i	−0.0970096	+	0.0401827i
$717$	4.62643	+	6.92394i	0.172777	+	0.258579i
$718$			33.4529i			1.24845i
$719$	9.66147	−	6.45559i	0.360312	−	0.240753i	−0.362216	−	0.932094i	$-0.617980\pi$
$719$	9.66147	−	6.45559i	0.360312	−	0.240753i	0.722528	+	0.691341i	$0.242980\pi$
$720$		0			0
$721$	0.225601	−	0.337636i	0.00840184	−	0.0125742i
$722$	−4.63989	+	1.92191i	−0.172679	+	0.0715259i
$723$	−15.7779	+	6.53541i	−0.586785	+	0.243054i
$724$	6.05103	−	9.05601i	0.224885	−	0.336564i
$725$		0			0
$726$	10.7454	−	7.17985i	0.398799	−	0.266469i
$727$			4.11908i			0.152768i	0.997078	+	0.0763841i	$0.0243375\pi$
$727$			4.11908i			0.152768i	−0.997078	+	0.0763841i	$0.975662\pi$
$728$	0.0505950	+	0.0757208i	0.00187518	+	0.00280640i
$729$	33.2442	−	13.7702i	1.23127	−	0.510007i
$730$		0			0
$731$	−31.5955	−	19.9445i	−1.16860	−	0.737675i
$732$	−12.7873	−	12.7873i	−0.472633	−	0.472633i
$733$	14.9048	−	35.9833i	0.550520	−	1.32907i	−0.366568	−	0.930391i	$-0.619467\pi$
$733$	14.9048	−	35.9833i	0.550520	−	1.32907i	0.917089	−	0.398683i	$-0.130533\pi$
$734$	−1.86891	+	9.39563i	−0.0689826	+	0.346799i
$735$		0			0
$736$	−3.96256	−	5.93039i	−0.146062	−	0.218597i
$737$	−31.6446	−	21.1442i	−1.16564	−	0.778857i
$738$	0.501077	+	2.51908i	0.0184449	+	0.0927287i
$739$	45.9741	+	19.0431i	1.69119	+	0.700512i	0.999759	−	0.0219357i	$-0.00698290\pi$
$739$	45.9741	+	19.0431i	1.69119	+	0.700512i	0.691426	+	0.722448i	$0.256983\pi$
$740$		0			0
$741$	17.2827	+	11.5479i	0.634894	+	0.424223i
$742$	−0.122920	+	0.183963i	−0.00451255	+	0.00675351i
$743$	6.96374	−	35.0091i	0.255475	−	1.28436i	−0.613576	−	0.789636i	$-0.710270\pi$
$743$	6.96374	−	35.0091i	0.255475	−	1.28436i	0.869051	−	0.494723i	$-0.164730\pi$
$744$	2.09825	−	2.09825i	0.0769256	−	0.0769256i
$745$		0			0
$746$	2.43402	+	5.87625i	0.0891159	+	0.215145i
$747$	42.5683	−	42.5683i	1.55749	−	1.55749i
$748$	−10.0580	+	0.261266i	−0.367757	+	0.00955283i
$749$			0.0320835i			0.00117230i
$750$		0			0
$751$	33.2936	+	6.62250i	1.21490	+	0.241659i	0.760618	−	0.649199i	$-0.224896\pi$
$751$	33.2936	+	6.62250i	1.21490	+	0.241659i	0.454282	+	0.890858i	$0.349896\pi$
$752$	−4.13811			−0.150901
$753$	12.7085	+	2.52788i	0.463124	+	0.0921212i
$754$	−3.60751	−	18.1362i	−0.131378	−	0.660481i
$755$		0			0
$756$	0.0230920	−	0.0557491i	0.000839849	−	0.00202757i
$757$	−8.59092	−	20.7403i	−0.312242	−	0.753820i	−0.999621	−	0.0275207i	$-0.991239\pi$
$757$	−8.59092	−	20.7403i	−0.312242	−	0.753820i	0.687379	−	0.726299i	$-0.258761\pi$
$758$	9.97362	−	1.98388i	0.362258	−	0.0720577i
$759$	−43.7264	+	8.69773i	−1.58717	+	0.315708i
$760$		0			0
$761$	−13.1115	−	13.1115i	−0.475292	−	0.475292i	0.428330	−	0.903622i	$-0.359102\pi$
$761$	−13.1115	−	13.1115i	−0.475292	−	0.475292i	−0.903622	+	0.428330i	$0.859102\pi$
$762$	28.4239	−	18.9923i	1.02969	−	0.688017i
$763$	0.410240	+	0.169927i	0.0148517	+	0.00615177i
$764$	−19.1327			−0.692198
$765$		0			0
$766$	1.88485			0.0681022
$767$	−19.0557	−	7.89311i	−0.688060	−	0.285004i
$768$	2.12983	−	1.42311i	0.0768538	−	0.0513520i
$769$	−0.316255	−	0.316255i	−0.0114044	−	0.0114044i	0.701382	−	0.712786i	$-0.252567\pi$
$769$	−0.316255	−	0.316255i	−0.0114044	−	0.0114044i	−0.712786	+	0.701382i	$0.752567\pi$
$770$		0			0
$771$	35.1813	−	6.99799i	1.26702	−	0.252026i
$772$	0.865294	−	0.172118i	0.0311426	−	0.00619465i
$773$	11.9989	+	28.9680i	0.431572	+	1.04191i	0.978781	+	0.204911i	$0.0656905\pi$
$773$	11.9989	+	28.9680i	0.431572	+	1.04191i	−0.547209	+	0.836996i	$0.684310\pi$
$774$	12.3507	−	29.8172i	0.443937	−	1.07176i
$775$		0			0
$776$	−0.800592	−	4.02485i	−0.0287396	−	0.144484i
$777$	0.774133	+	0.153985i	0.0277719	+	0.00552417i
$778$	−8.37897			−0.300401
$779$	−2.64446	−	0.526016i	−0.0947476	−	0.0188465i
$780$		0			0
$781$			13.0102i			0.465542i
$782$	−27.4522	−	10.5445i	−0.981690	−	0.377072i
$783$	−8.66384	+	8.66384i	−0.309620	+	0.309620i
$784$	−2.67811	−	6.46553i	−0.0956468	−	0.230912i
$785$		0			0
$786$	−6.42063	+	6.42063i	−0.229016	+	0.229016i
$787$	−0.528742	+	2.65816i	−0.0188476	+	0.0947533i	−0.989064	−	0.147486i	$-0.952882\pi$
$787$	−0.528742	+	2.65816i	−0.0188476	+	0.0947533i	0.970217	+	0.242239i	$0.0778819\pi$
$788$	−5.60616	+	8.39022i	−0.199711	+	0.298889i
$789$	−4.63283	−	3.09556i	−0.164933	−	0.110205i
$790$		0			0
$791$	0.236085	+	0.0977894i	0.00839420	+	0.00347699i
$792$	−1.69549	−	8.52380i	−0.0602466	−	0.302880i
$793$	12.7405	+	8.51294i	0.452429	+	0.302303i
$794$	9.32491	+	13.9557i	0.330929	+	0.495270i
$795$		0			0
$796$	0.0430965	−	0.216661i	0.00152752	−	0.00767934i
$797$	11.5058	−	27.7775i	0.407556	−	0.983928i	−0.578222	−	0.815879i	$-0.696253\pi$
$797$	11.5058	−	27.7775i	0.407556	−	0.983928i	0.985779	−	0.168049i	$-0.0537466\pi$
$798$	0.284137	+	0.284137i	0.0100583	+	0.0100583i
$799$	−13.9355	+	9.84425i	−0.493002	+	0.348264i
$800$		0			0
$801$	53.7331	−	22.2570i	1.89857	−	0.786412i
$802$	−18.0990	−	27.0871i	−0.639099	−	0.956479i
$803$		−	27.8434i		−	0.982573i
$804$	33.2173	−	22.1951i	1.17148	−	0.782760i
$805$		0			0
$806$	−1.39687	+	2.09057i	−0.0492028	+	0.0736371i
$807$	−63.5354	+	26.3172i	−2.23655	+	0.926410i
$808$	1.15143	−	0.476938i	0.0405072	−	0.0167786i
$809$	8.27844	−	12.3896i	0.291054	−	0.435594i	−0.656911	−	0.753969i	$-0.728137\pi$
$809$	8.27844	−	12.3896i	0.291054	−	0.435594i	0.947965	+	0.318375i	$0.103137\pi$
$810$		0			0
$811$	27.9751	−	18.6924i	0.982339	−	0.656378i	0.0428949	−	0.999080i	$-0.486342\pi$
$811$	27.9751	−	18.6924i	0.982339	−	0.656378i	0.939444	+	0.342701i	$0.111342\pi$
$812$		−	0.357479i		−	0.0125451i
$813$	33.8191	+	50.6139i	1.18609	+	1.77511i
$814$	16.5565	−	6.85792i	0.580305	−	0.240370i
$815$		0			0
$816$	3.78696	−	9.85918i	0.132570	−	0.345140i
$817$	23.9570	+	23.9570i	0.838148	+	0.838148i
$818$	9.84758	−	23.7742i	0.344313	−	0.831244i
$819$	−0.0632746	+	0.318103i	−0.00221099	+	0.0111154i
$820$		0			0
$821$	−10.2814	−	15.3873i	−0.358825	−	0.537019i	0.607508	−	0.794313i	$-0.292169\pi$
$821$	−10.2814	−	15.3873i	−0.358825	−	0.537019i	−0.966333	+	0.257294i	$0.917169\pi$
$822$	−29.8728	−	19.9604i	−1.04194	−	0.696199i
$823$	10.5422	+	52.9993i	0.367479	+	1.84744i	0.513409	+	0.858144i	$0.328383\pi$
$823$	10.5422	+	52.9993i	0.367479	+	1.84744i	−0.145930	+	0.989295i	$0.546617\pi$
$824$	8.94117	+	3.70355i	0.311480	+	0.129019i
$825$		0			0
$826$	−0.331538	−	0.221527i	−0.0115357	−	0.00770790i
$827$	20.4299	−	30.5755i	0.710417	−	1.06321i	−0.284116	−	0.958790i	$-0.591700\pi$
$827$	20.4299	−	30.5755i	0.710417	−	1.06321i	0.994533	−	0.104424i	$-0.0333000\pi$
$828$	4.95561	−	24.9135i	0.172219	−	0.865805i
$829$	28.6987	−	28.6987i	0.996748	−	0.996748i	−0.00324645	−	0.999995i	$-0.501033\pi$
$829$	28.6987	−	28.6987i	0.996748	−	0.996748i	0.999995	+	0.00324645i	$0.00103338\pi$
$830$		0			0
$831$	−9.97852	−	24.0903i	−0.346151	−	0.835683i
$832$	−1.53472	+	1.53472i	−0.0532070	+	0.0532070i
$833$	−24.3998	−	15.4023i	−0.845403	−	0.533658i
$834$			10.8051i			0.374148i
$835$		0			0
$836$	8.94804	+	1.77988i	0.309474	+	0.0615583i
$837$	1.66599			0.0575849
$838$	−23.5187	−	4.67816i	−0.812441	−	0.161604i
$839$	0.974657	+	4.89993i	0.0336489	+	0.169164i	0.993956	−	0.109781i	$-0.0350150\pi$
$839$	0.974657	+	4.89993i	0.0336489	+	0.169164i	−0.960307	+	0.278946i	$0.910015\pi$
$840$		0			0
$841$	−16.6797	+	40.2684i	−0.575162	+	1.38857i
$842$	−4.13012	−	9.97100i	−0.142333	−	0.343623i
$843$	21.6958	−	4.31556i	0.747242	−	0.148636i
$844$	−13.0195	+	2.58974i	−0.448150	+	0.0891425i
$845$		0			0
$846$	−10.4211	−	10.4211i	−0.358284	−	0.358284i
$847$	−0.176014	+	0.117609i	−0.00604791	+	0.00404108i
$848$	−4.87166	−	2.01791i	−0.167293	−	0.0692952i
$849$	−17.9259			−0.615215
$850$		0			0
$851$	52.3788			1.79552
$852$	−12.6173	−	5.22624i	−0.432260	−	0.179048i
$853$	34.6305	−	23.1394i	1.18573	−	0.792276i	0.203334	−	0.979109i	$-0.434822\pi$
$853$	34.6305	−	23.1394i	1.18573	−	0.792276i	0.982392	+	0.186833i	$0.0598223\pi$
$854$	0.209461	+	0.209461i	0.00716762	+	0.00716762i
$855$		0			0
$856$	−0.749949	+	0.149174i	−0.0256327	+	0.00509867i
$857$	44.5654	−	8.86461i	1.52233	−	0.302809i	0.638131	−	0.769928i	$-0.279708\pi$
$857$	44.5654	−	8.86461i	1.52233	−	0.302809i	0.884195	+	0.467119i	$0.154708\pi$
$858$	5.19181	+	12.5341i	0.177245	+	0.427908i
$859$	14.4334	−	34.8453i	0.492461	−	1.18891i	−0.461003	−	0.887399i	$-0.652510\pi$
$859$	14.4334	−	34.8453i	0.492461	−	1.18891i	0.953464	−	0.301507i	$-0.0974897\pi$
$860$		0			0
$861$	−0.0151218	−	0.0760222i	−0.000515348	−	0.00259083i
$862$	9.64284	+	1.91808i	0.328436	+	0.0653300i
$863$	38.0573			1.29548			0.647742	−	0.761860i	$-0.275713\pi$
$863$	38.0573			1.29548			0.647742	+	0.761860i	$0.275713\pi$
$864$	1.41050	+	0.280566i	0.0479861	+	0.00954503i
$865$		0			0
$866$			1.05577i			0.0358764i
$867$	−10.7013	−	42.2106i	−0.363434	−	1.43355i
$868$	−0.0343702	+	0.0343702i	−0.00116660	+	0.00116660i
$869$	−6.70408	−	16.1851i	−0.227420	−	0.549041i
$870$		0			0
$871$	−23.9358	+	23.9358i	−0.811035	+	0.811035i
$872$	−2.06460	+	10.3794i	−0.0699160	+	0.351492i
$873$	8.11969	−	12.1520i	0.274810	−	0.411282i
$874$	22.1719	+	14.8148i	0.749975	+	0.501117i
$875$		0			0
$876$	27.0025	+	11.1848i	0.912329	+	0.377899i
$877$	−8.72656	−	43.8714i	−0.294675	−	1.48143i	−0.790206	−	0.612841i	$-0.790026\pi$
$877$	−8.72656	−	43.8714i	−0.294675	−	1.48143i	0.495531	−	0.868590i	$-0.334974\pi$
$878$	1.45925	+	0.975040i	0.0492473	+	0.0329060i
$879$	−47.0368	−	70.3955i	−1.58651	−	2.37438i
$880$		0			0
$881$	−4.31320	+	21.6839i	−0.145315	+	0.730549i	0.837570	+	0.546330i	$0.183976\pi$
$881$	−4.31320	+	21.6839i	−0.145315	+	0.730549i	−0.982885	+	0.184219i	$0.941024\pi$
$882$	9.53791	−	23.0266i	0.321158	−	0.775345i
$883$	−0.609859	−	0.609859i	−0.0205234	−	0.0205234i	0.696771	−	0.717294i	$-0.254620\pi$
$883$	−0.609859	−	0.609859i	−0.0205234	−	0.0205234i	−0.717294	+	0.696771i	$0.754620\pi$
$884$	−1.51734	+	8.81932i	−0.0510337	+	0.296626i
$885$		0			0
$886$	22.7978	−	9.44317i	0.765908	−	0.317250i
$887$	1.78400	+	2.66994i	0.0599008	+	0.0896479i	0.860211	−	0.509938i	$-0.170332\pi$
$887$	1.78400	+	2.66994i	0.0599008	+	0.0896479i	−0.800310	+	0.599586i	$0.795332\pi$
$888$			18.8113i			0.631265i
$889$	−0.465595	+	0.311101i	−0.0156156	+	0.0104340i
$890$		0			0
$891$	−9.49077	+	14.2039i	−0.317953	+	0.475850i
$892$	13.3822	−	5.54308i	0.448069	−	0.185596i
$893$	14.2934	−	5.92054i	0.478312	−	0.198123i
$894$	−1.53821	+	2.30210i	−0.0514455	+	0.0769936i
$895$		0			0
$896$	−0.0348875	+	0.0233111i	−0.00116551	+	0.000778769i
$897$			39.6535i			1.32399i
$898$	2.19169	+	3.28010i	0.0731376	+	0.109458i
$899$	9.11833	−	3.77694i	0.304113	−	0.125968i
$900$		0			0
$901$	−21.2062	+	4.79380i	−0.706482	+	0.159705i
$902$	−1.24441	−	1.24441i	−0.0414342	−	0.0414342i
$903$	−0.372726	+	0.899841i	−0.0124036	+	0.0299448i
$904$	−1.18813	+	5.97314i	−0.0395166	+	0.198664i
$905$		0			0
$906$	18.4983	+	27.6847i	0.614565	+	0.919762i
$907$	−7.64783	−	5.11012i	−0.253942	−	0.169679i	0.422083	−	0.906557i	$-0.361299\pi$
$907$	−7.64783	−	5.11012i	−0.253942	−	0.169679i	−0.676025	+	0.736878i	$0.736299\pi$
$908$	5.70070	+	28.6593i	0.189184	+	0.951093i
$909$	4.10075	+	1.69858i	0.136013	+	0.0563385i
$910$		0			0
$911$	−4.16596	−	2.78361i	−0.138025	−	0.0922250i	0.484641	−	0.874713i	$-0.338950\pi$
$911$	−4.16596	−	2.78361i	−0.138025	−	0.0922250i	−0.622666	+	0.782488i	$0.713950\pi$
$912$	−5.32057	+	7.96279i	−0.176182	+	0.263674i
$913$	−8.04723	+	40.4562i	−0.266325	+	1.33890i
$914$	−14.2400	+	14.2400i	−0.471018	+	0.471018i
$915$		0			0
$916$	3.66265	+	8.84241i	0.121017	+	0.292162i
$917$	0.105172	−	0.105172i	0.00347310	−	0.00347310i
$918$	5.41744	−	2.41064i	0.178802	−	0.0795628i
$919$		−	51.6686i		−	1.70439i	−0.523223	−	0.852196i	$-0.675271\pi$
$919$		−	51.6686i		−	1.70439i	0.523223	−	0.852196i	$-0.324729\pi$
$920$		0			0
$921$	−8.53312	−	1.69734i	−0.281176	−	0.0559293i
$922$	15.1918			0.500315
$923$	11.3493	+	2.25752i	0.373567	+	0.0743071i
$924$	0.0511674	+	0.257236i	0.00168328	+	0.00846243i
$925$		0			0
$926$	1.83336	−	4.42611i	0.0602478	−	0.145451i
$927$	13.1900	+	31.8434i	0.433215	+	1.04587i
$928$	8.35605	−	1.66212i	0.274301	−	0.0545618i
$929$	13.5019	−	2.68570i	0.442984	−	0.0881151i	0.0314417	−	0.999506i	$-0.489990\pi$
$929$	13.5019	−	2.68570i	0.442984	−	0.0881151i	0.411543	+	0.911391i	$0.364990\pi$
$930$		0			0
$931$	18.5009	+	18.5009i	0.606343	+	0.606343i
$932$	−2.74480	+	1.83402i	−0.0899090	+	0.0600753i
$933$	−49.9756	−	20.7006i	−1.63613	−	0.677706i
$934$	−15.2661			−0.499523
$935$		0			0
$936$	−7.72983			−0.252657
$937$	10.0223	+	4.15139i	0.327415	+	0.135620i	0.540335	−	0.841450i	$-0.318297\pi$
$937$	10.0223	+	4.15139i	0.327415	+	0.135620i	−0.212920	+	0.977070i	$0.568297\pi$
$938$	−0.544112	+	0.363564i	−0.0177659	+	0.0118708i
$939$	59.4531	+	59.4531i	1.94018	+	1.94018i
$940$		0			0
$941$	−40.0808	+	7.97257i	−1.30660	+	0.259898i	−0.798809	−	0.601584i	$-0.794536\pi$
$941$	−40.0808	+	7.97257i	−1.30660	+	0.259898i	−0.507787	+	0.861482i	$0.669536\pi$
$942$	−17.5552	+	3.49195i	−0.571979	+	0.113774i
$943$	−1.96843	−	4.75221i	−0.0641009	−	0.154753i
$944$	3.63666	−	8.77968i	0.118363	−	0.285754i
$945$		0			0
$946$	4.31417	+	21.6888i	0.140266	+	0.705163i
$947$	18.0851	+	3.59735i	0.587686	+	0.116898i	0.479972	−	0.877284i	$-0.340647\pi$
$947$	18.0851	+	3.59735i	0.587686	+	0.116898i	0.107714	+	0.994182i	$0.465647\pi$
$948$	18.3893			0.597256
$949$	−24.2889	−	4.83136i	−0.788451	−	0.156833i
$950$		0			0
$951$		−	80.0342i		−	2.59529i
$952$	−0.0620318	+	0.161497i	−0.00201046	+	0.00523415i
$953$	−19.5626	+	19.5626i	−0.633696	+	0.633696i	−0.948993	−	0.315297i	$-0.897896\pi$
$953$	−19.5626	+	19.5626i	−0.633696	+	0.633696i	0.315297	+	0.948993i	$0.397896\pi$
$954$	−7.18664	−	17.3501i	−0.232676	−	0.561730i
$955$		0			0
$956$	2.29875	−	2.29875i	0.0743470	−	0.0743470i
$957$	10.3895	−	52.2317i	0.335846	−	1.68841i
$958$	−11.9863	+	17.9387i	−0.387259	+	0.579575i
$959$	0.489329	+	0.326959i	0.0158013	+	0.0105581i
$960$		0			0
$961$	27.4004	+	11.3496i	0.883885	+	0.366117i
$962$	−3.10957	−	15.6328i	−0.100256	−	0.504023i
$963$	−2.26427	−	1.51294i	−0.0729652	−	0.0487538i
$964$	3.70401	+	5.54345i	0.119298	+	0.178542i
$965$		0			0
$966$	−0.149553	+	0.751854i	−0.00481179	+	0.0241905i
$967$	−16.6678	+	40.2397i	−0.536001	+	1.29402i	0.391492	+	0.920181i	$0.371959\pi$
$967$	−16.6678	+	40.2397i	−0.536001	+	1.29402i	−0.927493	+	0.373840i	$0.878041\pi$
$968$	−3.56748	−	3.56748i	−0.114663	−	0.114663i
$969$	1.02534	+	39.4727i	0.0329387	+	1.26805i
$970$		0			0
$971$	−29.2585	+	12.1193i	−0.938949	+	0.388925i	−0.799066	−	0.601243i	$-0.794672\pi$
$971$	−29.2585	+	12.1193i	−0.938949	+	0.388925i	−0.139882	+	0.990168i	$0.544672\pi$
$972$	−12.3594	−	18.4972i	−0.396428	−	0.593297i
$973$		−	0.176991i		−	0.00567407i
$974$	16.3758	−	10.9420i	0.524716	−	0.350604i
$975$		0			0
$976$	−3.92224	+	5.87005i	−0.125548	+	0.187896i
$977$	−13.9175	+	5.76484i	−0.445262	+	0.184433i	−0.594037	−	0.804438i	$-0.702467\pi$
$977$	−13.9175	+	5.76484i	−0.445262	+	0.184433i	0.148775	+	0.988871i	$0.452467\pi$
$978$	25.7440	−	10.6635i	0.823202	−	0.340982i
$979$	−22.1399	+	33.1347i	−0.707593	+	1.05899i
$980$		0			0
$981$	−31.3380	+	20.9394i	−1.00054	+	0.668542i
$982$			10.9171i			0.348379i
$983$	−2.65830	−	3.97842i	−0.0847865	−	0.126892i	0.786652	−	0.617396i	$-0.211813\pi$
$983$	−2.65830	−	3.97842i	−0.0847865	−	0.126892i	−0.871439	+	0.490504i	$0.836813\pi$
$984$	1.70670	−	0.706940i	0.0544077	−	0.0225364i
$985$		0			0
$986$	24.1858	−	25.4758i	0.770231	−	0.811313i
$987$	0.314492	+	0.314492i	0.0100104	+	0.0100104i
$988$	3.10531	−	7.49687i	0.0987930	−	0.238507i
$989$	−12.6095	+	63.3925i	−0.400960	+	2.01576i
$990$		0			0
$991$	−28.3664	−	42.4533i	−0.901089	−	1.34857i	−0.937040	−	0.349221i	$-0.886446\pi$
$991$	−28.3664	−	42.4533i	−0.901089	−	1.34857i	0.0359517	−	0.999354i	$-0.488554\pi$
$992$	−0.963206	−	0.643594i	−0.0305818	−	0.0204341i
$993$	−4.90601	−	24.6642i	−0.155687	−	0.782693i
$994$	0.206676	+	0.0856079i	0.00655535	+	0.00271532i
$995$		0			0
$996$	−36.0016	−	24.0555i	−1.14076	−	0.762229i
$997$	−19.9191	+	29.8110i	−0.630843	+	0.944124i	0.369048	+	0.929410i	$0.379684\pi$
$997$	−19.9191	+	29.8110i	−0.630843	+	0.944124i	−0.999892	+	0.0147136i	$0.995316\pi$
$998$	−2.05219	+	10.3170i	−0.0649608	+	0.326580i
$999$	−7.46797	+	7.46797i	−0.236276	+	0.236276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.207.1		40
5.2	odd	4		170.2.o.b.3.5	✓	40
5.3	odd	4		850.2.s.d.343.1		40
5.4	even	2		170.2.r.b.37.5	yes	40
17.6	odd	16		850.2.s.d.57.1		40
85.23	even	16	inner	850.2.v.d.193.1		40
85.57	even	16		170.2.r.b.23.5	yes	40
85.74	odd	16		170.2.o.b.57.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.3.5	✓	40	5.2	odd	4
170.2.o.b.57.5	yes	40	85.74	odd	16
170.2.r.b.23.5	yes	40	85.57	even	16
170.2.r.b.37.5	yes	40	5.4	even	2
850.2.s.d.57.1		40	17.6	odd	16
850.2.s.d.343.1		40	5.3	odd	4
850.2.v.d.193.1		40	85.23	even	16	inner
850.2.v.d.207.1		40	1.1	even	1	trivial

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+(-0.923880 - 0.382683i) q^{2} +(-2.12983 + 1.42311i) q^{3} +(0.707107 + 0.707107i) q^{4} +(2.51231 - 0.499730i) q^{6} +(-0.0411526 + 0.00818577i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(1.36290 - 3.29034i) q^{9} +(0.476069 + 2.39336i) q^{11} +(-2.51231 - 0.499730i) q^{12} +2.17043 q^{13} +(0.0411526 + 0.00818577i) q^{14} +1.00000i q^{16} +(2.37892 + 3.36760i) q^{17} +(-2.51831 + 2.51831i) q^{18} +(-1.43074 - 3.45410i) q^{19} +(0.0759990 - 0.0759990i) q^{21} +(0.476069 - 2.39336i) q^{22} +(3.96256 - 5.93039i) q^{23} +(2.12983 + 1.42311i) q^{24} +(-2.00521 - 0.830586i) q^{26} +(0.280566 + 1.41050i) q^{27} +(-0.0348875 - 0.0233111i) q^{28} +(4.73332 + 7.08392i) q^{29} +(0.226000 - 1.13618i) q^{31} +(0.382683 - 0.923880i) q^{32} +(-4.41996 - 4.41996i) q^{33} +(-0.909115 - 4.02163i) q^{34} +(3.29034 - 1.36290i) q^{36} +(4.07998 + 6.10612i) q^{37} +3.73869i q^{38} +(-4.62265 + 3.08876i) q^{39} +(0.400666 - 0.599639i) q^{41} +(-0.0992975 + 0.0411304i) q^{42} +(-8.37226 + 3.46790i) q^{43} +(-1.35573 + 2.02899i) q^{44} +(-5.93039 + 3.96256i) q^{46} +4.13811i q^{47} +(-1.42311 - 2.12983i) q^{48} +(-6.46553 + 2.67811i) q^{49} +(-9.85918 - 3.78696i) q^{51} +(1.53472 + 1.53472i) q^{52} +(-2.01791 + 4.87166i) q^{53} +(0.280566 - 1.41050i) q^{54} +(0.0233111 + 0.0348875i) q^{56} +(7.96279 + 5.32057i) q^{57} +(-1.66212 - 8.35605i) q^{58} +(-8.77968 - 3.63666i) q^{59} +(5.87005 + 3.92224i) q^{61} +(-0.643594 + 0.963206i) q^{62} +(-0.0291531 + 0.146562i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(2.39207 + 5.77496i) q^{66} +(-11.0282 + 11.0282i) q^{67} +(-0.699099 + 4.06341i) q^{68} +18.2699i q^{69} +(5.22907 + 1.04013i) q^{71} -3.56143 q^{72} +(-11.1908 - 2.22600i) q^{73} +(-1.43270 - 7.20266i) q^{74} +(1.43074 - 3.45410i) q^{76} +(-0.0391830 - 0.0945961i) q^{77} +(5.45279 - 1.08463i) q^{78} +(-7.04108 + 1.40056i) q^{79} +(4.95009 + 4.95009i) q^{81} +(-0.599639 + 0.400666i) q^{82} +(15.6168 + 6.46869i) q^{83} +0.107479 q^{84} +9.06206 q^{86} +(-20.1624 - 8.35153i) q^{87} +(2.02899 - 1.35573i) q^{88} +(11.5475 + 11.5475i) q^{89} +(-0.0893188 + 0.0177666i) q^{91} +(6.99537 - 1.39147i) q^{92} +(1.13557 + 2.74150i) q^{93} +(1.58359 - 3.82312i) q^{94} +(0.499730 + 2.51231i) q^{96} +(4.02485 + 0.800592i) q^{97} +6.99824 q^{98} +(8.52380 + 1.69549i) 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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