LMFDB - Embedded newform 850.2.v.a.143.1

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			143.1
Character	$\chi$	$=$	850.143
Dual form			850.2.v.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.382683 + 0.923880i) q^{2} +(-2.42161 + 0.481688i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-1.37173 - 2.05294i) q^{6} +(1.11717 + 1.67197i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(2.86054 - 1.18487i) q^{9} +(-0.137062 + 0.0915821i) q^{11} +(1.37173 - 2.05294i) q^{12} -5.44277 q^{13} +(-1.11717 + 1.67197i) q^{14} -1.00000i q^{16} +(-3.49559 + 2.18651i) q^{17} +(2.18936 + 2.18936i) q^{18} +(2.58575 + 1.07105i) q^{19} +(-3.51072 - 3.51072i) q^{21} +(-0.137062 - 0.0915821i) q^{22} +(0.0404931 - 0.203573i) q^{23} +(2.42161 + 0.481688i) q^{24} +(-2.08286 - 5.02846i) q^{26} +(-0.197542 + 0.131993i) q^{27} +(-1.97222 - 0.392299i) q^{28} +(-1.22686 - 6.16787i) q^{29} +(-6.37814 - 4.26174i) q^{31} +(0.923880 - 0.382683i) q^{32} +(0.287798 - 0.287798i) q^{33} +(-3.35778 - 2.39276i) q^{34} +(-1.18487 + 2.86054i) q^{36} +(0.949883 + 4.77539i) q^{37} +2.79879i q^{38} +(13.1803 - 2.62172i) q^{39} +(0.215622 - 1.08401i) q^{41} +(1.89999 - 4.58698i) q^{42} +(3.03073 - 7.31684i) q^{43} +(0.0321594 - 0.161676i) q^{44} +(0.203573 - 0.0404931i) q^{46} -4.35668i q^{47} +(0.481688 + 2.42161i) q^{48} +(1.13139 - 2.73141i) q^{49} +(7.41174 - 6.97867i) q^{51} +(3.84862 - 3.84862i) q^{52} +(0.874556 - 0.362253i) q^{53} +(-0.197542 - 0.131993i) q^{54} +(-0.392299 - 1.97222i) q^{56} +(-6.77758 - 1.34815i) q^{57} +(5.22886 - 3.49382i) q^{58} +(-3.27940 - 7.91716i) q^{59} +(3.00717 + 0.598163i) q^{61} +(1.49652 - 7.52353i) q^{62} +(5.17678 + 3.45902i) q^{63} +(0.707107 + 0.707107i) q^{64} +(0.376026 + 0.155755i) q^{66} +(-10.0369 - 10.0369i) q^{67} +(0.925658 - 4.01785i) q^{68} +0.512479i q^{69} +(1.89344 - 2.83374i) q^{71} -3.09622 q^{72} +(-2.57706 + 3.85684i) q^{73} +(-4.04838 + 2.70504i) q^{74} +(-2.58575 + 1.07105i) q^{76} +(-0.306245 - 0.126851i) q^{77} +(7.46602 + 11.1737i) q^{78} +(9.16543 + 13.7170i) q^{79} +(-6.15329 + 6.15329i) q^{81} +(1.08401 - 0.215622i) q^{82} +(-6.62511 - 15.9944i) q^{83} +4.96491 q^{84} +7.91969 q^{86} +(5.94198 + 14.3452i) q^{87} +(0.161676 - 0.0321594i) q^{88} +(-11.5405 + 11.5405i) q^{89} +(-6.08051 - 9.10013i) q^{91} +(0.115315 + 0.172580i) q^{92} +(17.4982 + 7.24799i) q^{93} +(4.02504 - 1.66723i) q^{94} +(-2.05294 + 1.37173i) q^{96} +(-3.00953 + 4.50408i) q^{97} +2.95645 q^{98} +(-0.283559 + 0.424376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 32 * q^13 - 16 * q^18 + 48 * q^27 + 16 * q^29 + 16 * q^31 - 8 * q^33 - 16 * q^34 + 16 * q^37 + 32 * q^39 + 48 * q^41 - 48 * q^42 + 16 * q^43 - 16 * q^44 + 32 * q^46 + 8 * q^48 + 16 * q^49 + 64 * q^51 + 48 * q^54 - 48 * q^57 + 16 * q^58 - 8 * q^59 + 16 * q^61 + 16 * q^62 + 80 * q^63 + 8 * q^66 - 48 * q^67 - 32 * q^71 - 24 * q^72 + 48 * q^73 + 16 * q^77 + 48 * q^78 + 16 * q^79 - 56 * q^81 - 16 * q^82 - 72 * q^83 - 32 * q^84 - 16 * q^86 + 80 * q^87 - 16 * q^88 - 48 * q^89 - 48 * q^91 - 16 * q^92 + 64 * q^93 + 32 * q^94 + 32 * q^97 - 56 * q^98 - 24 * q^99

Character values

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

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$3$	−2.42161	+	0.481688i	−1.39812	+	0.278103i	−0.835898	−	0.548885i	$-0.815053\pi$
$3$	−2.42161	+	0.481688i	−1.39812	+	0.278103i	−0.562220	+	0.826988i	$0.690053\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−1.37173	−	2.05294i	−0.560007	−	0.838110i
$7$	1.11717	+	1.67197i	0.422252	+	0.631944i	0.980218	−	0.197919i	$-0.0634184\pi$
$7$	1.11717	+	1.67197i	0.422252	+	0.631944i	−0.557967	+	0.829863i	$0.688418\pi$
$8$	−0.923880	−	0.382683i	−0.326641	−	0.135299i
$9$	2.86054	−	1.18487i	0.953513	−	0.394958i
$10$		0			0
$11$	−0.137062	+	0.0915821i	−0.0413259	+	0.0276131i	−0.576062	−	0.817406i	$-0.695411\pi$
$11$	−0.137062	+	0.0915821i	−0.0413259	+	0.0276131i	0.534736	+	0.845019i	$0.320411\pi$
$12$	1.37173	−	2.05294i	0.395985	−	0.592634i
$13$	−5.44277			−1.50955			−0.754776	−	0.655983i	$-0.772254\pi$
$13$	−5.44277			−1.50955			−0.754776	+	0.655983i	$0.772254\pi$
$14$	−1.11717	+	1.67197i	−0.298577	+	0.446852i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−3.49559	+	2.18651i	−0.847805	+	0.530307i
$17$	−3.49559	+	2.18651i	−0.847805	+	0.530307i
$18$	2.18936	+	2.18936i	0.516037	+	0.516037i
$19$	2.58575	+	1.07105i	0.593211	+	0.245716i	0.659031	−	0.752116i	$-0.270966\pi$
$19$	2.58575	+	1.07105i	0.593211	+	0.245716i	−0.0658205	+	0.997831i	$0.520966\pi$
$20$		0			0
$21$	−3.51072	−	3.51072i	−0.766103	−	0.766103i
$22$	−0.137062	−	0.0915821i	−0.0292218	−	0.0195254i
$23$	0.0404931	−	0.203573i	0.00844340	−	0.0424478i	−0.976334	−	0.216269i	$-0.930611\pi$
$23$	0.0404931	−	0.203573i	0.00844340	−	0.0424478i	0.984777	+	0.173821i	$0.0556113\pi$
$24$	2.42161	+	0.481688i	0.494309	+	0.0983242i
$25$		0			0
$26$	−2.08286	−	5.02846i	−0.408482	−	0.986162i
$27$	−0.197542	+	0.131993i	−0.0380170	+	0.0254022i
$28$	−1.97222	−	0.392299i	−0.372714	−	0.0741375i
$29$	−1.22686	−	6.16787i	−0.227823	−	1.14534i	−0.910144	−	0.414292i	$-0.864029\pi$
$29$	−1.22686	−	6.16787i	−0.227823	−	1.14534i	0.682321	−	0.731053i	$-0.260971\pi$
$30$		0			0
$31$	−6.37814	−	4.26174i	−1.14555	−	0.765430i	−0.170049	−	0.985436i	$-0.554393\pi$
$31$	−6.37814	−	4.26174i	−1.14555	−	0.765430i	−0.975499	+	0.220005i	$0.929393\pi$
$32$	0.923880	−	0.382683i	0.163320	−	0.0676495i
$33$	0.287798	−	0.287798i	0.0500991	−	0.0500991i
$34$	−3.35778	−	2.39276i	−0.575855	−	0.410355i
$35$		0			0
$36$	−1.18487	+	2.86054i	−0.197479	+	0.476756i
$37$	0.949883	+	4.77539i	0.156160	+	0.785069i	0.976888	+	0.213750i	$0.0685679\pi$
$37$	0.949883	+	4.77539i	0.156160	+	0.785069i	−0.820728	+	0.571318i	$0.806432\pi$
$38$			2.79879i			0.454024i
$39$	13.1803	−	2.62172i	2.11053	−	0.419811i
$40$		0			0
$41$	0.215622	−	1.08401i	0.0336745	−	0.169293i	−0.960288	−	0.279009i	$-0.909994\pi$
$41$	0.215622	−	1.08401i	0.0336745	−	0.169293i	0.993963	+	0.109716i	$0.0349941\pi$
$42$	1.89999	−	4.58698i	0.293175	−	0.707787i
$43$	3.03073	−	7.31684i	0.462183	−	1.11581i	−0.505317	−	0.862934i	$-0.668624\pi$
$43$	3.03073	−	7.31684i	0.462183	−	1.11581i	0.967499	−	0.252874i	$-0.0813757\pi$
$44$	0.0321594	−	0.161676i	0.00484821	−	0.0243736i
$45$		0			0
$46$	0.203573	−	0.0404931i	0.0300151	−	0.00597038i
$47$		−	4.35668i		−	0.635487i	−0.948177	−	0.317743i	$-0.897075\pi$
$47$		−	4.35668i		−	0.635487i	0.948177	−	0.317743i	$-0.102925\pi$
$48$	0.481688	+	2.42161i	0.0695257	+	0.349529i
$49$	1.13139	−	2.73141i	0.161626	−	0.390201i
$50$		0			0
$51$	7.41174	−	6.97867i	1.03785	−	0.977209i
$52$	3.84862	−	3.84862i	0.533707	−	0.533707i
$53$	0.874556	−	0.362253i	0.120130	−	0.0497593i	−0.321809	−	0.946805i	$-0.604291\pi$
$53$	0.874556	−	0.362253i	0.120130	−	0.0497593i	0.441939	+	0.897045i	$0.354291\pi$
$54$	−0.197542	−	0.131993i	−0.0268821	−	0.0179620i
$55$		0			0
$56$	−0.392299	−	1.97222i	−0.0524231	−	0.263549i
$57$	−6.77758	−	1.34815i	−0.897713	−	0.178566i
$58$	5.22886	−	3.49382i	0.686584	−	0.458760i
$59$	−3.27940	−	7.91716i	−0.426941	−	1.03073i	−0.980252	−	0.197752i	$-0.936636\pi$
$59$	−3.27940	−	7.91716i	−0.426941	−	1.03073i	0.553311	−	0.832975i	$-0.313364\pi$
$60$		0			0
$61$	3.00717	+	0.598163i	0.385029	+	0.0765870i	0.383810	−	0.923412i	$-0.374612\pi$
$61$	3.00717	+	0.598163i	0.385029	+	0.0765870i	0.00121919	+	0.999999i	$0.499612\pi$
$62$	1.49652	−	7.52353i	0.190059	−	0.955489i
$63$	5.17678	+	3.45902i	0.652213	+	0.435795i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	0.376026	+	0.155755i	0.0462856	+	0.0191721i
$67$	−10.0369	−	10.0369i	−1.22621	−	1.22621i	−0.965388	−	0.260818i	$-0.916008\pi$
$67$	−10.0369	−	10.0369i	−1.22621	−	1.22621i	−0.260818	−	0.965388i	$-0.583992\pi$
$68$	0.925658	−	4.01785i	0.112252	−	0.487236i
$69$			0.512479i			0.0616952i
$70$		0			0
$71$	1.89344	−	2.83374i	0.224710	−	0.336303i	−0.701934	−	0.712242i	$-0.747680\pi$
$71$	1.89344	−	2.83374i	0.224710	−	0.336303i	0.926644	+	0.375939i	$0.122680\pi$
$72$	−3.09622			−0.364893
$73$	−2.57706	+	3.85684i	−0.301622	+	0.451408i	−0.951060	−	0.309005i	$-0.900004\pi$
$73$	−2.57706	+	3.85684i	−0.301622	+	0.451408i	0.649439	+	0.760414i	$0.275004\pi$
$74$	−4.04838	+	2.70504i	−0.470614	+	0.314454i
$75$		0			0
$76$	−2.58575	+	1.07105i	−0.296605	+	0.122858i
$77$	−0.306245	−	0.126851i	−0.0348998	−	0.0144560i
$78$	7.46602	+	11.1737i	0.845360	+	1.26517i
$79$	9.16543	+	13.7170i	1.03119	+	1.54329i	0.825285	+	0.564716i	$0.191014\pi$
$79$	9.16543	+	13.7170i	1.03119	+	1.54329i	0.205906	+	0.978572i	$0.433986\pi$
$80$		0			0
$81$	−6.15329	+	6.15329i	−0.683699	+	0.683699i
$82$	1.08401	−	0.215622i	0.119708	−	0.0238115i
$83$	−6.62511	−	15.9944i	−0.727201	−	1.75562i	−0.651706	−	0.758472i	$-0.725946\pi$
$83$	−6.62511	−	15.9944i	−0.727201	−	1.75562i	−0.0754950	−	0.997146i	$-0.524054\pi$
$84$	4.96491			0.541717
$85$		0			0
$86$	7.91969			0.854002
$87$	5.94198	+	14.3452i	0.637047	+	1.53797i
$88$	0.161676	−	0.0321594i	0.0172347	−	0.00342820i
$89$	−11.5405	+	11.5405i	−1.22329	+	1.22329i	−0.256835	+	0.966455i	$0.582680\pi$
$89$	−11.5405	+	11.5405i	−1.22329	+	1.22329i	−0.966455	+	0.256835i	$0.917320\pi$
$90$		0			0
$91$	−6.08051	−	9.10013i	−0.637411	−	0.953952i
$92$	0.115315	+	0.172580i	0.0120224	+	0.0179928i
$93$	17.4982	+	7.24799i	1.81448	+	0.751582i
$94$	4.02504	−	1.66723i	0.415152	−	0.171961i
$95$		0			0
$96$	−2.05294	+	1.37173i	−0.209528	+	0.140002i
$97$	−3.00953	+	4.50408i	−0.305571	+	0.457320i	−0.952196	−	0.305489i	$-0.901180\pi$
$97$	−3.00953	+	4.50408i	−0.305571	+	0.457320i	0.646624	+	0.762809i	$0.276180\pi$
$98$	2.95645			0.298647
$99$	−0.283559	+	0.424376i	−0.0284987	+	0.0426514i
$100$		0			0
$101$			10.9761i			1.09216i	0.837733	+	0.546081i	$0.183881\pi$
$101$			10.9761i			1.09216i	−0.837733	+	0.546081i	$0.816119\pi$
$102$	9.28380	+	4.17694i	0.919233	+	0.413578i
$103$	−4.34046	−	4.34046i	−0.427678	−	0.427678i	0.460159	−	0.887837i	$-0.347793\pi$
$103$	−4.34046	−	4.34046i	−0.427678	−	0.427678i	−0.887837	+	0.460159i	$0.847793\pi$
$104$	5.02846	+	2.08286i	0.493081	+	0.204241i
$105$		0			0
$106$	0.669356	+	0.669356i	0.0650136	+	0.0650136i
$107$	12.1460	+	8.11573i	1.17420	+	0.784577i	0.980507	−	0.196484i	$-0.0629525\pi$
$107$	12.1460	+	8.11573i	1.17420	+	0.784577i	0.193696	+	0.981062i	$0.437953\pi$
$108$	0.0463499	−	0.233017i	0.00446002	−	0.0224221i
$109$	−16.5795	−	3.29787i	−1.58803	−	0.315879i	−0.679492	−	0.733683i	$-0.737800\pi$
$109$	−16.5795	−	3.29787i	−1.58803	−	0.315879i	−0.908537	+	0.417804i	$0.862800\pi$
$110$		0			0
$111$	−4.60050	−	11.1066i	−0.436660	−	1.05419i
$112$	1.67197	−	1.11717i	0.157986	−	0.105563i
$113$	−6.34981	−	1.26306i	−0.597340	−	0.118818i	−0.112845	−	0.993613i	$-0.535997\pi$
$113$	−6.34981	−	1.26306i	−0.597340	−	0.118818i	−0.484495	+	0.874794i	$0.660997\pi$
$114$	−1.34815	−	6.77758i	−0.126265	−	0.634779i
$115$		0			0
$116$	5.22886	+	3.49382i	0.485488	+	0.324393i
$117$	−15.5692	+	6.44899i	−1.43938	+	0.596209i
$118$	6.05953	−	6.05953i	0.557825	−	0.557825i
$119$	−7.56096	−	3.40180i	−0.693112	−	0.311843i
$120$		0			0
$121$	−4.19912	+	10.1376i	−0.381738	+	0.921597i
$122$	0.598163	+	3.00717i	0.0541552	+	0.272256i
$123$			2.72890i			0.246057i
$124$	7.52353	−	1.49652i	0.675633	−	0.134392i
$125$		0			0
$126$	−1.21465	+	6.10643i	−0.108209	+	0.544004i
$127$	−3.26570	+	7.88410i	−0.289784	+	0.699601i	−0.999990	−	0.00439290i	$-0.998602\pi$
$127$	−3.26570	+	7.88410i	−0.289784	+	0.699601i	0.710206	+	0.703994i	$0.248602\pi$
$128$	−0.382683	+	0.923880i	−0.0338248	+	0.0816602i
$129$	−3.81482	+	19.1784i	−0.335876	+	1.68856i
$130$		0			0
$131$	1.48936	−	0.296253i	0.130126	−	0.0258837i	−0.129597	−	0.991567i	$-0.541368\pi$
$131$	1.48936	−	0.296253i	0.130126	−	0.0258837i	0.259724	+	0.965683i	$0.416368\pi$
$132$			0.407007i			0.0354254i
$133$	1.09796	+	5.51983i	0.0952054	+	0.478630i
$134$	5.43195	−	13.1139i	0.469249	−	1.13287i
$135$		0			0
$136$	4.06625	−	0.682370i	0.348678	−	0.0585128i
$137$	5.30209	−	5.30209i	0.452988	−	0.452988i	−0.443357	−	0.896345i	$-0.646213\pi$
$137$	5.30209	−	5.30209i	0.452988	−	0.452988i	0.896345	+	0.443357i	$0.146213\pi$
$138$	−0.473469	+	0.196117i	−0.0403043	+	0.0166946i
$139$	1.25930	+	0.841435i	0.106812	+	0.0713696i	0.607829	−	0.794068i	$-0.292041\pi$
$139$	1.25930	+	0.841435i	0.106812	+	0.0713696i	−0.501017	+	0.865437i	$0.667041\pi$
$140$		0			0
$141$	2.09856	+	10.5502i	0.176731	+	0.888485i
$142$	3.34262	+	0.664889i	0.280506	+	0.0557962i
$143$	0.745998	−	0.498460i	0.0623835	−	0.0416833i
$144$	−1.18487	−	2.86054i	−0.0987395	−	0.238378i
$145$		0			0
$146$	−4.54945	−	0.904941i	−0.376515	−	0.0748935i
$147$	−1.42409	+	7.15938i	−0.117457	+	0.590495i
$148$	−4.04838	−	2.70504i	−0.332775	−	0.222353i
$149$	−14.8597	−	14.8597i	−1.21736	−	1.21736i	−0.968554	−	0.248802i	$-0.919963\pi$
$149$	−14.8597	−	14.8597i	−1.21736	−	1.21736i	−0.248802	−	0.968554i	$-0.580037\pi$
$150$		0			0
$151$	12.6528	+	5.24097i	1.02967	+	0.426504i	0.832594	−	0.553883i	$-0.186855\pi$
$151$	12.6528	+	5.24097i	1.02967	+	0.426504i	0.197078	+	0.980388i	$0.436855\pi$
$152$	−1.97904	−	1.97904i	−0.160522	−	0.160522i
$153$	−7.40853	+	10.3964i	−0.598944	+	0.840502i
$154$		−	0.331477i		−	0.0267112i
$155$		0			0
$156$	−7.46602	+	11.1737i	−0.597760	+	0.894611i
$157$	−8.14465			−0.650014			−0.325007	−	0.945712i	$-0.605367\pi$
$157$	−8.14465			−0.650014			−0.325007	+	0.945712i	$0.605367\pi$
$158$	−9.16543	+	13.7170i	−0.729163	+	1.09127i
$159$	−1.94334	+	1.29850i	−0.154117	+	0.102978i
$160$		0			0
$161$	0.385604	−	0.159723i	0.0303899	−	0.0125879i
$162$	−8.03966	−	3.33014i	−0.631656	−	0.261640i
$163$	−7.07524	−	10.5888i	−0.554176	−	0.829382i	0.443587	−	0.896231i	$-0.353706\pi$
$163$	−7.07524	−	10.5888i	−0.554176	−	0.829382i	−0.997763	+	0.0668486i	$0.978706\pi$
$164$	0.614040	+	0.918975i	0.0479484	+	0.0717599i
$165$		0			0
$166$	12.2416	−	12.2416i	0.950134	−	0.950134i
$167$	8.79378	−	1.74919i	0.680483	−	0.135357i	0.157266	−	0.987556i	$-0.449732\pi$
$167$	8.79378	−	1.74919i	0.680483	−	0.135357i	0.523217	+	0.852200i	$0.324732\pi$
$168$	1.89999	+	4.58698i	0.146587	+	0.353893i
$169$	16.6237			1.27875
$170$		0			0
$171$	8.66568			0.662681
$172$	3.03073	+	7.31684i	0.231091	+	0.557904i
$173$	−14.6510	+	2.91426i	−1.11389	+	0.221567i	−0.717531	−	0.696527i	$-0.754728\pi$
$173$	−14.6510	+	2.91426i	−1.11389	+	0.221567i	−0.396363	+	0.918094i	$0.629728\pi$
$174$	−10.9793	+	10.9793i	−0.832342	+	0.832342i
$175$		0			0
$176$	0.0915821	+	0.137062i	0.00690326	+	0.0103315i
$177$	11.7550	+	17.5926i	0.883562	+	1.32234i
$178$	−15.0784	−	6.24567i	−1.13017	−	0.468133i
$179$	−16.8710	+	6.98820i	−1.26100	+	0.522322i	−0.910216	−	0.414135i	$-0.864084\pi$
$179$	−16.8710	+	6.98820i	−1.26100	+	0.522322i	−0.350782	+	0.936457i	$0.614084\pi$
$180$		0			0
$181$	−12.9464	+	8.65048i	−0.962296	+	0.642985i	−0.934249	−	0.356621i	$-0.883929\pi$
$181$	−12.9464	+	8.65048i	−0.962296	+	0.642985i	−0.0280465	+	0.999607i	$0.508929\pi$
$182$	6.08051	−	9.10013i	0.450717	−	0.674546i
$183$	−7.57033			−0.559615
$184$	−0.115315	+	0.172580i	−0.00850111	+	0.0127228i
$185$		0			0
$186$			18.9399i			1.38874i
$187$	0.278868	−	0.619822i	0.0203929	−	0.0453259i
$188$	3.08064	+	3.08064i	0.224678	+	0.224678i
$189$	−0.441377	−	0.182824i	−0.0321055	−	0.0132985i
$190$		0			0
$191$	−1.58915	−	1.58915i	−0.114987	−	0.114987i	0.647272	−	0.762259i	$-0.275910\pi$
$191$	−1.58915	−	1.58915i	−0.114987	−	0.114987i	−0.762259	+	0.647272i	$0.775910\pi$
$192$	−2.05294	−	1.37173i	−0.148158	−	0.0989963i
$193$	2.05947	−	10.3537i	0.148244	−	0.745274i	−0.833116	−	0.553098i	$-0.813446\pi$
$193$	2.05947	−	10.3537i	0.148244	−	0.745274i	0.981360	−	0.192176i	$-0.0615544\pi$
$194$	−5.31292	−	1.05681i	−0.381446	−	0.0758743i
$195$		0			0
$196$	1.13139	+	2.73141i	0.0808132	+	0.195100i
$197$	13.1586	−	8.79230i	0.937512	−	0.626425i	0.00989197	−	0.999951i	$-0.496851\pi$
$197$	13.1586	−	8.79230i	0.937512	−	0.626425i	0.927620	+	0.373526i	$0.121851\pi$
$198$	−0.500585	−	0.0995726i	−0.0355750	−	0.00707632i
$199$	3.55447	+	17.8695i	0.251970	+	1.26674i	0.874840	+	0.484412i	$0.160966\pi$
$199$	3.55447	+	17.8695i	0.251970	+	1.26674i	−0.622870	+	0.782325i	$0.714034\pi$
$200$		0			0
$201$	29.1402	+	19.4709i	2.05539	+	1.37337i
$202$	−10.1406	+	4.20037i	−0.713489	+	0.295537i
$203$	8.94185	−	8.94185i	0.627595	−	0.627595i
$204$	−0.306229	+	10.1756i	−0.0214403	+	0.712432i
$205$		0			0
$206$	2.34904	−	5.67108i	0.163665	−	0.395123i
$207$	−0.125376	−	0.630306i	−0.00871421	−	0.0438093i
$208$			5.44277i			0.377388i
$209$	−0.452498	+	0.0900074i	−0.0312999	+	0.00622594i
$210$		0			0
$211$	−3.81423	+	19.1754i	−0.262583	+	1.32009i	0.594160	+	0.804347i	$0.297485\pi$
$211$	−3.81423	+	19.1754i	−0.262583	+	1.32009i	−0.856742	+	0.515745i	$0.827515\pi$
$212$	−0.362253	+	0.874556i	−0.0248796	+	0.0600648i
$213$	−3.22020	+	7.77426i	−0.220645	+	0.532683i
$214$	−2.84987	+	14.3272i	−0.194813	+	0.979390i
$215$		0			0
$216$	0.233017	−	0.0463499i	0.0158548	−	0.00315371i
$217$		−	15.4251i		−	1.04713i
$218$	−3.29787	−	16.5795i	−0.223360	−	1.12291i
$219$	4.38283	−	10.5811i	0.296164	−	0.715004i
$220$		0			0
$221$	19.0257	−	11.9007i	1.27981	−	0.800527i
$222$	8.50061	−	8.50061i	0.570524	−	0.570524i
$223$	−17.6802	+	7.32337i	−1.18395	+	0.490409i	−0.885781	−	0.464103i	$-0.846377\pi$
$223$	−17.6802	+	7.32337i	−1.18395	+	0.490409i	−0.298171	+	0.954512i	$0.596377\pi$
$224$	1.67197	+	1.11717i	0.111713	+	0.0746442i
$225$		0			0
$226$	−1.26306	−	6.34981i	−0.0840173	−	0.422383i
$227$	2.03468	+	0.404722i	0.135046	+	0.0268624i	0.262151	−	0.965027i	$-0.415568\pi$
$227$	2.03468	+	0.404722i	0.135046	+	0.0268624i	−0.127104	+	0.991889i	$0.540568\pi$
$228$	5.74576	−	3.83919i	0.380522	−	0.254257i
$229$	−6.23740	−	15.0584i	−0.412179	−	0.995088i	−0.984552	−	0.175094i	$-0.943977\pi$
$229$	−6.23740	−	15.0584i	−0.412179	−	0.995088i	0.572373	−	0.819993i	$-0.306023\pi$
$230$		0			0
$231$	0.802708	+	0.159669i	0.0528143	+	0.0105054i
$232$	−1.22686	+	6.16787i	−0.0805476	+	0.404940i
$233$	21.0482	+	14.0640i	1.37891	+	0.921361i	0.999992	−	0.00406748i	$-0.00129472\pi$
$233$	21.0482	+	14.0640i	1.37891	+	0.921361i	0.378922	+	0.925428i	$0.376295\pi$
$234$	−11.9162	−	11.9162i	−0.778985	−	0.778985i
$235$		0			0
$236$	7.91716	+	3.27940i	0.515363	+	0.213471i
$237$	−28.8025	−	28.8025i	−1.87092	−	1.87092i
$238$	0.249400	−	8.28723i	0.0161662	−	0.537181i
$239$		−	23.8158i		−	1.54051i	−0.637734	−	0.770257i	$-0.720128\pi$
$239$		−	23.8158i		−	1.54051i	0.637734	−	0.770257i	$-0.279872\pi$
$240$		0			0
$241$	−7.85749	+	11.7596i	−0.506146	+	0.757500i	−0.993269	−	0.115833i	$-0.963046\pi$
$241$	−7.85749	+	11.7596i	−0.506146	+	0.757500i	0.487123	+	0.873333i	$0.338046\pi$
$242$	−10.9728			−0.705360
$243$	12.3329	−	18.4575i	0.791155	−	1.18405i
$244$	−2.54936	+	1.70343i	−0.163206	+	0.109051i
$245$		0			0
$246$	−2.52118	+	1.04431i	−0.160744	+	0.0665825i
$247$	−14.0736	−	5.82948i	−0.895482	−	0.370921i
$248$	4.26174	+	6.37814i	0.270621	+	0.405012i
$249$	23.7478	+	35.5411i	1.50495	+	2.25232i
$250$		0			0
$251$	3.15891	−	3.15891i	0.199389	−	0.199389i	−0.600349	−	0.799738i	$-0.704972\pi$
$251$	3.15891	−	3.15891i	0.199389	−	0.199389i	0.799738	+	0.600349i	$0.204972\pi$
$252$	−6.10643	+	1.21465i	−0.384669	+	0.0765154i
$253$	0.0130935	+	0.0316106i	0.000823183	+	0.00198734i
$254$	−8.53369			−0.535451
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−9.27582	−	22.3938i	−0.578610	−	1.39689i	−0.894061	−	0.447945i	$-0.852156\pi$
$257$	−9.27582	−	22.3938i	−0.578610	−	1.39689i	0.315451	−	0.948942i	$-0.397844\pi$
$258$	−19.1784	+	3.81482i	−1.19400	+	0.237501i
$259$	−6.92310	+	6.92310i	−0.430181	+	0.430181i
$260$		0			0
$261$	−10.8176	−	16.1897i	−0.669595	−	1.00212i
$262$	0.843657	+	1.26262i	0.0521213	+	0.0780050i
$263$	10.7512	+	4.45327i	0.662944	+	0.274601i	0.688677	−	0.725068i	$-0.258192\pi$
$263$	10.7512	+	4.45327i	0.662944	+	0.274601i	−0.0257325	+	0.999669i	$0.508192\pi$
$264$	−0.376026	+	0.155755i	−0.0231428	+	0.00958606i
$265$		0			0
$266$	−4.67949	+	3.12673i	−0.286918	+	0.191712i
$267$	22.3877	−	33.5055i	1.37010	−	2.05050i
$268$	14.1944			0.867058
$269$	10.0744	−	15.0774i	0.614248	−	0.919287i	−0.385747	−	0.922605i	$-0.626056\pi$
$269$	10.0744	−	15.0774i	0.614248	−	0.919287i	0.999994	+	0.00331782i	$0.00105610\pi$
$270$		0			0
$271$			24.0357i			1.46007i	0.683412	+	0.730033i	$0.260495\pi$
$271$			24.0357i			1.46007i	−0.683412	+	0.730033i	$0.739505\pi$
$272$	2.18651	+	3.49559i	0.132577	+	0.211951i
$273$	19.1081	+	19.1081i	1.15647	+	1.15647i
$274$	6.92751	+	2.86947i	0.418506	+	0.173351i
$275$		0			0
$276$	−0.362377	−	0.362377i	−0.0218125	−	0.0218125i
$277$	13.8723	+	9.26918i	0.833507	+	0.556931i	0.897498	−	0.441019i	$-0.145383\pi$
$277$	13.8723	+	9.26918i	0.833507	+	0.556931i	−0.0639911	+	0.997950i	$0.520383\pi$
$278$	−0.295473	+	1.48544i	−0.0177213	+	0.0890909i
$279$	−23.2945	−	4.63357i	−1.39461	−	0.277405i
$280$		0			0
$281$	−4.65282	−	11.2329i	−0.277564	−	0.670098i	0.722203	−	0.691681i	$-0.243129\pi$
$281$	−4.65282	−	11.2329i	−0.277564	−	0.670098i	−0.999767	+	0.0215827i	$0.993129\pi$
$282$	−8.94401	+	5.97620i	−0.532608	+	0.355877i
$283$	0.583566	+	0.116078i	0.0346894	+	0.00690015i	0.212405	−	0.977182i	$-0.431871\pi$
$283$	0.583566	+	0.116078i	0.0346894	+	0.00690015i	−0.177715	+	0.984082i	$0.556871\pi$
$284$	0.664889	+	3.34262i	0.0394539	+	0.198348i
$285$		0			0
$286$	0.745998	+	0.498460i	0.0441118	+	0.0294746i
$287$	2.05331	−	0.850508i	0.121203	−	0.0502039i
$288$	2.18936	−	2.18936i	0.129009	−	0.129009i
$289$	7.43832	−	15.2863i	0.437548	−	0.899195i
$290$		0			0
$291$	5.11835	−	12.3568i	0.300043	−	0.724368i
$292$	−0.904941	−	4.54945i	−0.0529577	−	0.266236i
$293$			3.85089i			0.224972i	0.993653	+	0.112486i	$0.0358813\pi$
$293$			3.85089i			0.224972i	−0.993653	+	0.112486i	$0.964119\pi$
$294$	−7.15938	+	1.42409i	−0.417543	+	0.0830545i
$295$		0			0
$296$	0.949883	−	4.77539i	0.0552109	−	0.277564i
$297$	0.0149874	−	0.0361827i	0.000869654	−	0.00209953i
$298$	8.04203	−	19.4152i	0.465862	−	1.12469i
$299$	−0.220395	+	1.10800i	−0.0127457	+	0.0640772i
$300$		0			0
$301$	15.6194	−	3.10689i	0.900285	−	0.179078i
$302$			13.6953i			0.788077i
$303$	−5.28705	−	26.5798i	−0.303733	−	1.52697i
$304$	1.07105	−	2.58575i	0.0614290	−	0.148303i
$305$		0			0
$306$	−12.4402	−	2.86604i	−0.711158	−	0.163841i
$307$	3.91174	−	3.91174i	0.223255	−	0.223255i	−0.586613	−	0.809868i	$-0.699539\pi$
$307$	3.91174	−	3.91174i	0.223255	−	0.223255i	0.809868	+	0.586613i	$0.199539\pi$
$308$	0.306245	−	0.126851i	0.0174499	−	0.00722799i
$309$	12.6017	+	8.42015i	0.716883	+	0.479006i
$310$		0			0
$311$	2.90984	+	14.6288i	0.165002	+	0.829521i	0.971272	+	0.237973i	$0.0764831\pi$
$311$	2.90984	+	14.6288i	0.165002	+	0.829521i	−0.806270	+	0.591548i	$0.798517\pi$
$312$	−13.1803	−	2.62172i	−0.746186	−	0.148426i
$313$	−27.1152	+	18.1178i	−1.53264	+	1.02408i	−0.550745	+	0.834673i	$0.685657\pi$
$313$	−27.1152	+	18.1178i	−1.53264	+	1.02408i	−0.981899	+	0.189407i	$0.939343\pi$
$314$	−3.11682	−	7.52468i	−0.175893	−	0.424642i
$315$		0			0
$316$	−16.1804	−	3.21847i	−0.910216	−	0.181053i
$317$	−3.71575	+	18.6804i	−0.208698	+	1.04919i	0.724348	+	0.689435i	$0.242141\pi$
$317$	−3.71575	+	18.6804i	−0.208698	+	1.04919i	−0.933045	+	0.359759i	$0.882859\pi$
$318$	−1.94334	−	1.29850i	−0.108977	−	0.0728162i
$319$	0.733023	+	0.733023i	0.0410414	+	0.0410414i
$320$		0			0
$321$	−33.3223	−	13.8025i	−1.85987	−	0.770382i
$322$	0.295129	+	0.295129i	0.0164469	+	0.0164469i
$323$	−11.3806	+	1.90981i	−0.633232	+	0.106265i
$324$		−	8.70207i		−	0.483448i
$325$		0			0
$326$	7.07524	−	10.5888i	0.391861	−	0.586462i
$327$	41.7377			2.30810
$328$	−0.614040	+	0.918975i	−0.0339047	+	0.0507419i
$329$	7.28422	−	4.86716i	0.401592	−	0.268335i
$330$		0			0
$331$	−12.7521	+	5.28209i	−0.700919	+	0.290330i	−0.704541	−	0.709663i	$-0.748847\pi$
$331$	−12.7521	+	5.28209i	−0.700919	+	0.290330i	0.00362198	+	0.999993i	$0.498847\pi$
$332$	15.9944	+	6.62511i	0.877809	+	0.363600i
$333$	8.37541	+	12.5347i	0.458969	+	0.686896i
$334$	4.98128	+	7.45501i	0.272563	+	0.407920i
$335$		0			0
$336$	−3.51072	+	3.51072i	−0.191526	+	0.191526i
$337$	−33.4470	+	6.65302i	−1.82197	+	0.362413i	−0.983267	−	0.182170i	$-0.941688\pi$
$337$	−33.4470	+	6.65302i	−1.82197	+	0.362413i	−0.838707	+	0.544583i	$0.816688\pi$
$338$	6.36162	+	15.3583i	0.346026	+	0.835382i
$339$	15.9852			0.868196
$340$		0			0
$341$	1.26450			0.0684766
$342$	3.31621	+	8.00605i	0.179320	+	0.432918i
$343$	19.6363	−	3.90590i	1.06026	−	0.210899i
$344$	−5.60007	+	5.60007i	−0.301935	+	0.301935i
$345$		0			0
$346$	−8.29911	−	12.4205i	−0.446163	−	0.667730i
$347$	−4.65341	−	6.96432i	−0.249808	−	0.373864i	0.685280	−	0.728280i	$-0.259680\pi$
$347$	−4.65341	−	6.96432i	−0.249808	−	0.373864i	−0.935088	+	0.354416i	$0.884680\pi$
$348$	−14.3452	−	5.94198i	−0.768984	−	0.318524i
$349$	−15.2490	+	6.31633i	−0.816258	+	0.338105i	−0.751448	−	0.659792i	$-0.770644\pi$
$349$	−15.2490	+	6.31633i	−0.816258	+	0.338105i	−0.0648102	+	0.997898i	$0.520644\pi$
$350$		0			0
$351$	1.07518	−	0.718410i	0.0573886	−	0.0383459i
$352$	−0.0915821	+	0.137062i	−0.00488134	+	0.00730545i
$353$	21.5989			1.14960			0.574798	−	0.818295i	$-0.305081\pi$
$353$	21.5989			1.14960			0.574798	+	0.818295i	$0.305081\pi$
$354$	−11.7550	+	17.5926i	−0.624773	+	0.935038i
$355$		0			0
$356$		−	16.3207i		−	0.864997i
$357$	19.9483	+	4.59581i	1.05578	+	0.243236i
$358$	−12.9125	−	12.9125i	−0.682447	−	0.682447i
$359$	−3.06707	−	1.27042i	−0.161874	−	0.0670504i	0.300275	−	0.953853i	$-0.402922\pi$
$359$	−3.06707	−	1.27042i	−0.161874	−	0.0670504i	−0.462149	+	0.886802i	$0.652922\pi$
$360$		0			0
$361$	−7.89610	−	7.89610i	−0.415584	−	0.415584i
$362$	−12.9464	−	8.65048i	−0.680446	−	0.454659i
$363$	5.28548	−	26.5719i	0.277416	−	1.39466i
$364$	10.7343	+	2.13519i	0.562632	+	0.111914i
$365$		0			0
$366$	−2.89704	−	6.99407i	−0.151431	−	0.365586i
$367$	2.90883	−	1.94362i	0.151840	−	0.101456i	−0.477330	−	0.878724i	$-0.658395\pi$
$367$	2.90883	−	1.94362i	0.151840	−	0.101456i	0.629169	+	0.777268i	$0.283395\pi$
$368$	−0.203573	−	0.0404931i	−0.0106120	−	0.00211085i
$369$	−0.667614	−	3.35632i	−0.0347546	−	0.174723i
$370$		0			0
$371$	1.58271	+	1.05753i	0.0821700	+	0.0549042i
$372$	−17.4982	+	7.24799i	−0.907239	+	0.375791i
$373$	−6.73182	+	6.73182i	−0.348561	+	0.348561i	−0.859573	−	0.511013i	$-0.829271\pi$
$373$	−6.73182	+	6.73182i	−0.348561	+	0.348561i	0.511013	+	0.859573i	$0.329271\pi$
$374$	0.679360	+	0.0204450i	0.0351288	+	0.00105719i
$375$		0			0
$376$	−1.66723	+	4.02504i	−0.0859807	+	0.207576i
$377$	6.67754	+	33.5703i	0.343911	+	1.72896i
$378$		−	0.477743i		−	0.0245725i
$379$	37.4780	−	7.45485i	1.92512	−	0.382930i	0.925123	−	0.379667i	$-0.123962\pi$
$379$	37.4780	−	7.45485i	1.92512	−	0.382930i	0.999995	−	0.00326228i	$-0.00103842\pi$
$380$		0			0
$381$	4.11058	−	20.6653i	0.210591	−	1.05871i
$382$	0.860042	−	2.07633i	0.0440036	−	0.106234i
$383$	−5.64204	+	13.6211i	−0.288295	+	0.696005i	−0.999979	−	0.00649445i	$-0.997933\pi$
$383$	−5.64204	+	13.6211i	−0.288295	+	0.696005i	0.711684	+	0.702500i	$0.247933\pi$
$384$	0.481688	−	2.42161i	0.0245811	−	0.123577i
$385$		0			0
$386$	10.3537	−	2.05947i	0.526988	−	0.104824i
$387$		−	24.5211i		−	1.24648i
$388$	−1.05681	−	5.31292i	−0.0536512	−	0.269723i
$389$	4.95501	−	11.9624i	0.251229	−	0.606520i	−0.747075	−	0.664740i	$-0.768542\pi$
$389$	4.95501	−	11.9624i	0.251229	−	0.606520i	0.998304	+	0.0582197i	$0.0185424\pi$
$390$		0			0
$391$	0.303567	+	0.800145i	0.0153520	+	0.0404651i
$392$	−2.09053	+	2.09053i	−0.105588	+	0.105588i
$393$	−3.46396	+	1.43482i	−0.174734	+	0.0723770i
$394$	13.1586	+	8.79230i	0.662921	+	0.442950i
$395$		0			0
$396$	−0.0995726	−	0.500585i	−0.00500371	−	0.0251554i
$397$	5.88720	+	1.17104i	0.295470	+	0.0587727i	0.340600	−	0.940208i	$-0.389370\pi$
$397$	5.88720	+	1.17104i	0.295470	+	0.0587727i	−0.0451292	+	0.998981i	$0.514370\pi$
$398$	−15.1490	+	10.1223i	−0.759353	+	0.507384i
$399$	−5.31768	−	12.8380i	−0.266217	−	0.642704i
$400$		0			0
$401$	11.1376	+	2.21541i	0.556185	+	0.110632i	0.465176	−	0.885218i	$-0.345991\pi$
$401$	11.1376	+	2.21541i	0.556185	+	0.110632i	0.0910087	+	0.995850i	$0.470991\pi$
$402$	−6.83726	+	34.3732i	−0.341011	+	1.71438i
$403$	34.7147	+	23.1956i	1.72926	+	1.15546i
$404$	−7.76126	−	7.76126i	−0.386137	−	0.386137i
$405$		0			0
$406$	11.6831	+	4.83929i	0.579822	+	0.240170i
$407$	−0.567533	−	0.567533i	−0.0281316	−	0.0281316i
$408$	−9.51818	+	3.61110i	−0.471220	+	0.178776i
$409$			13.9224i			0.688419i	0.938893	+	0.344210i	$0.111853\pi$
$409$			13.9224i			0.688419i	−0.938893	+	0.344210i	$0.888147\pi$
$410$		0			0
$411$	−10.2856	+	15.3936i	−0.507353	+	0.759308i
$412$	6.13834			0.302414
$413$	9.57358	−	14.3279i	0.471085	−	0.705029i
$414$	0.534348	−	0.357040i	0.0262618	−	0.0175475i
$415$		0			0
$416$	−5.02846	+	2.08286i	−0.246541	+	0.102120i
$417$	−3.45484	−	1.43104i	−0.169184	−	0.0700783i
$418$	−0.256319	−	0.383609i	−0.0125370	−	0.0187629i
$419$	5.61700	+	8.40644i	0.274409	+	0.410682i	0.942919	−	0.333021i	$-0.108068\pi$
$419$	5.61700	+	8.40644i	0.274409	+	0.410682i	−0.668511	+	0.743702i	$0.733068\pi$
$420$		0			0
$421$	10.9505	−	10.9505i	0.533695	−	0.533695i	−0.387975	−	0.921670i	$-0.626825\pi$
$421$	10.9505	−	10.9505i	0.533695	−	0.533695i	0.921670	+	0.387975i	$0.126825\pi$
$422$	−19.1754	+	3.81423i	−0.933446	+	0.185674i
$423$	−5.16211	−	12.4624i	−0.250990	−	0.605945i
$424$	−0.946613			−0.0459716
$425$		0			0
$426$	−8.41480			−0.407698
$427$	2.35942	+	5.69614i	0.114180	+	0.275656i
$428$	−14.3272	+	2.84987i	−0.692533	+	0.137753i
$429$	−1.56642	+	1.56642i	−0.0756273	+	0.0756273i
$430$		0			0
$431$	−12.8995	−	19.3054i	−0.621345	−	0.929908i	−0.999990	−	0.00436649i	$-0.998610\pi$
$431$	−12.8995	−	19.3054i	−0.621345	−	0.929908i	0.378646	−	0.925542i	$-0.376390\pi$
$432$	0.131993	+	0.197542i	0.00635054	+	0.00950425i
$433$	5.76227	+	2.38681i	0.276917	+	0.114703i	0.516820	−	0.856094i	$-0.327116\pi$
$433$	5.76227	+	2.38681i	0.276917	+	0.114703i	−0.239903	+	0.970797i	$0.577116\pi$
$434$	14.2510	−	5.90294i	0.684068	−	0.283350i
$435$		0			0
$436$	14.0554	−	9.39154i	0.673133	−	0.449773i
$437$	0.322742	−	0.483017i	0.0154388	−	0.0231058i
$438$	11.4529			0.547240
$439$	−3.37527	+	5.05144i	−0.161093	+	0.241092i	−0.903231	−	0.429154i	$-0.858812\pi$
$439$	−3.37527	+	5.05144i	−0.161093	+	0.241092i	0.742138	+	0.670247i	$0.233812\pi$
$440$		0			0
$441$		−	9.15384i		−	0.435897i
$442$	18.2756	+	13.0232i	0.869282	+	0.619453i
$443$	7.64166	+	7.64166i	0.363066	+	0.363066i	0.864941	−	0.501874i	$-0.167356\pi$
$443$	7.64166	+	7.64166i	0.363066	+	0.363066i	−0.501874	+	0.864941i	$0.667356\pi$
$444$	11.1066	+	4.60050i	0.527095	+	0.218330i
$445$		0			0
$446$	−13.5318	−	13.5318i	−0.640750	−	0.640750i
$447$	43.1422	+	28.8267i	2.04056	+	1.36346i
$448$	−0.392299	+	1.97222i	−0.0185344	+	0.0931786i
$449$	9.62000	+	1.91354i	0.453996	+	0.0903054i	0.416791	−	0.909002i	$-0.363155\pi$
$449$	9.62000	+	1.91354i	0.453996	+	0.0903054i	0.0372048	+	0.999308i	$0.488155\pi$
$450$		0			0
$451$	0.0697218	+	0.168323i	0.00328307	+	0.00792604i
$452$	5.38311	−	3.59688i	0.253200	−	0.169183i
$453$	−33.1647	−	6.59688i	−1.55822	−	0.309948i
$454$	0.404722	+	2.03468i	0.0189946	+	0.0954921i
$455$		0			0
$456$	5.74576	+	3.83919i	0.269070	+	0.179787i
$457$	−13.5929	+	5.63037i	−0.635850	+	0.263378i	−0.677236	−	0.735766i	$-0.736822\pi$
$457$	−13.5929	+	5.63037i	−0.635850	+	0.263378i	0.0413865	+	0.999143i	$0.486822\pi$
$458$	11.5252	−	11.5252i	0.538537	−	0.538537i
$459$	0.401921	−	0.893324i	0.0187601	−	0.0416968i
$460$		0			0
$461$	14.3085	−	34.5437i	0.666411	−	1.60886i	−0.121158	−	0.992633i	$-0.538661\pi$
$461$	14.3085	−	34.5437i	0.666411	−	1.60886i	0.787569	−	0.616226i	$-0.211339\pi$
$462$	0.159669	+	0.802708i	0.00742845	+	0.0373453i
$463$			21.8622i			1.01602i	0.861351	+	0.508010i	$0.169619\pi$
$463$			21.8622i			1.01602i	−0.861351	+	0.508010i	$0.830381\pi$
$464$	−6.16787	+	1.22686i	−0.286336	+	0.0569558i
$465$		0			0
$466$	−4.93861	+	24.8281i	−0.228777	+	1.15014i
$467$	−6.22656	+	15.0322i	−0.288131	+	0.695609i	−0.999977	−	0.00672568i	$-0.997859\pi$
$467$	−6.22656	+	15.0322i	−0.288131	+	0.695609i	0.711847	+	0.702335i	$0.247859\pi$
$468$	6.44899	−	15.5692i	0.298105	−	0.719688i
$469$	5.56843	−	27.9944i	0.257126	−	1.29266i
$470$		0			0
$471$	19.7232	−	3.92319i	0.908796	−	0.180771i
$472$			8.56948i			0.394442i
$473$	0.254692	+	1.28042i	0.0117108	+	0.0588740i
$474$	15.5878	−	37.6322i	0.715970	−	1.72851i
$475$		0			0
$476$	7.75184	−	2.94097i	0.355305	−	0.134799i
$477$	2.07248	−	2.07248i	0.0948922	−	0.0948922i
$478$	22.0029	−	9.11390i	1.00639	−	0.416860i
$479$	−31.2040	−	20.8499i	−1.42575	−	0.952655i	−0.998830	−	0.0483648i	$-0.984599\pi$
$479$	−31.2040	−	20.8499i	−1.42575	−	0.952655i	−0.426919	−	0.904290i	$-0.640401\pi$
$480$		0			0
$481$	−5.16999	−	25.9913i	−0.235731	−	1.18510i
$482$	−13.8714	−	2.75918i	−0.631823	−	0.125677i
$483$	−0.856847	+	0.572527i	−0.0389879	+	0.0260509i
$484$	−4.19912	−	10.1376i	−0.190869	−	0.460799i
$485$		0			0
$486$	21.7721	+	4.33074i	0.987602	+	0.196446i
$487$	−4.25895	+	21.4112i	−0.192992	+	0.970234i	0.755913	+	0.654672i	$0.227193\pi$
$487$	−4.25895	+	21.4112i	−0.192992	+	0.970234i	−0.948905	+	0.315562i	$0.897807\pi$
$488$	−2.54936	−	1.70343i	−0.115404	−	0.0771104i
$489$	22.2340	+	22.2340i	1.00546	+	1.00546i
$490$		0			0
$491$	−18.4719	−	7.65130i	−0.833624	−	0.345299i	−0.0752879	−	0.997162i	$-0.523988\pi$
$491$	−18.4719	−	7.65130i	−0.833624	−	0.345299i	−0.758336	+	0.651863i	$0.773988\pi$
$492$	−1.92962	−	1.92962i	−0.0869942	−	0.0869942i
$493$	17.7747	+	18.8778i	0.800534	+	0.850213i
$494$		−	15.2332i		−	0.685373i
$495$		0			0
$496$	−4.26174	+	6.37814i	−0.191358	+	0.286387i
$497$	6.85322			0.307409
$498$	−23.7478	+	35.5411i	−1.06416	+	1.59263i
$499$	−11.6751	+	7.80106i	−0.522650	+	0.349223i	−0.788742	−	0.614724i	$-0.789267\pi$
$499$	−11.6751	+	7.80106i	−0.522650	+	0.349223i	0.266092	+	0.963948i	$0.414267\pi$
$500$		0			0
$501$	−20.4526	+	8.47172i	−0.913753	+	0.378489i
$502$	4.12732	+	1.70959i	0.184211	+	0.0763028i
$503$	−14.2657	−	21.3502i	−0.636077	−	0.951957i	−0.999791	−	0.0204461i	$-0.993491\pi$
$503$	−14.2657	−	21.3502i	−0.636077	−	0.951957i	0.363714	−	0.931511i	$-0.381509\pi$
$504$	−3.45902	−	5.17678i	−0.154077	−	0.230592i
$505$		0			0
$506$	−0.0241937	+	0.0241937i	−0.00107554	+	0.00107554i
$507$	−40.2562	+	8.00745i	−1.78784	+	0.355623i
$508$	−3.26570	−	7.88410i	−0.144892	−	0.349800i
$509$	−41.1631			−1.82452			−0.912261	−	0.409609i	$-0.865665\pi$
$509$	−41.1631			−1.82452			−0.912261	+	0.409609i	$0.865665\pi$
$510$		0			0
$511$	−9.32752			−0.412625
$512$	−0.382683	−	0.923880i	−0.0169124	−	0.0408301i
$513$	−0.652166	+	0.129724i	−0.0287938	+	0.00572745i
$514$	17.1395	−	17.1395i	0.755990	−	0.755990i
$515$		0			0
$516$	−10.8637	−	16.2587i	−0.478248	−	0.715748i
$517$	0.398994	+	0.597136i	0.0175477	+	0.0262620i
$518$	−9.04547	−	3.74676i	−0.397435	−	0.164623i
$519$	34.0752	−	14.1144i	1.49574	−	0.619554i
$520$		0			0
$521$	−10.6546	+	7.11916i	−0.466786	+	0.311896i	−0.766627	−	0.642093i	$-0.778066\pi$
$521$	−10.6546	+	7.11916i	−0.466786	+	0.311896i	0.299841	+	0.953989i	$0.403066\pi$
$522$	10.8176	−	16.1897i	0.473475	−	0.708606i
$523$	−7.84295			−0.342948			−0.171474	−	0.985189i	$-0.554853\pi$
$523$	−7.84295			−0.342948			−0.171474	+	0.985189i	$0.554853\pi$
$524$	−0.843657	+	1.26262i	−0.0368553	+	0.0551579i
$525$		0			0
$526$			11.6370i			0.507396i
$527$	31.6137	+	0.951401i	1.37711	+	0.0414437i
$528$	−0.287798	−	0.287798i	−0.0125248	−	0.0125248i
$529$	21.2094	+	8.78523i	0.922149	+	0.381967i
$530$		0			0
$531$	−18.7617	−	18.7617i	−0.814187	−	0.814187i
$532$	−4.67949	−	3.12673i	−0.202881	−	0.135561i
$533$	−1.17358	+	5.89999i	−0.0508334	+	0.255557i
$534$	39.5224	+	7.86150i	1.71030	+	0.340201i
$535$		0			0
$536$	5.43195	+	13.1139i	0.234624	+	0.566433i
$537$	37.4889	−	25.0493i	1.61776	−	1.08096i
$538$	17.7850	+	3.53766i	0.766767	+	0.152520i
$539$	0.0950776	+	0.477988i	0.00409528	+	0.0205884i
$540$		0			0
$541$	−17.2632	−	11.5349i	−0.742204	−	0.495925i	0.126063	−	0.992022i	$-0.459766\pi$
$541$	−17.2632	−	11.5349i	−0.742204	−	0.495925i	−0.868267	+	0.496098i	$0.834766\pi$
$542$	−22.2061	+	9.19807i	−0.953833	+	0.395091i
$543$	27.1842	−	27.1842i	1.16659	−	1.16659i
$544$	−2.39276	+	3.35778i	−0.102589	+	0.143964i
$545$		0			0
$546$	−10.3412	+	24.9659i	−0.442563	+	1.06844i
$547$	−6.33596	−	31.8530i	−0.270906	−	1.36194i	−0.841301	−	0.540567i	$-0.818210\pi$
$547$	−6.33596	−	31.8530i	−0.270906	−	1.36194i	0.570395	−	0.821371i	$-0.306790\pi$
$548$			7.49829i			0.320311i
$549$	9.31087	−	1.85205i	0.397378	−	0.0790435i
$550$		0			0
$551$	3.43374	−	17.2626i	0.146282	−	0.735410i
$552$	0.196117	−	0.473469i	0.00834730	−	0.0201522i
$553$	−12.6951	+	30.6486i	−0.539849	+	1.30331i
$554$	−3.25490	+	16.3635i	−0.138288	+	0.695219i
$555$		0			0
$556$	−1.48544	+	0.295473i	−0.0629967	+	0.0125308i
$557$		−	25.6718i		−	1.08775i	−0.839166	−	0.543875i	$-0.816956\pi$
$557$		−	25.6718i		−	1.08775i	0.839166	−	0.543875i	$-0.183044\pi$
$558$	−4.63357	−	23.2945i	−0.196155	−	0.986136i
$559$	−16.4956	+	39.8239i	−0.697689	+	1.68437i
$560$		0			0
$561$	−0.376750	+	1.63530i	−0.0159064	+	0.0690423i
$562$	8.59728	−	8.59728i	0.362654	−	0.362654i
$563$	5.64617	−	2.33872i	0.237958	−	0.0985653i	−0.260518	−	0.965469i	$-0.583893\pi$
$563$	5.64617	−	2.33872i	0.237958	−	0.0985653i	0.498476	+	0.866904i	$0.333893\pi$
$564$	−8.94401	−	5.97620i	−0.376611	−	0.251643i
$565$		0			0
$566$	0.116078	+	0.583566i	0.00487914	+	0.0245291i
$567$	−17.1624	−	3.41381i	−0.720753	−	0.143367i
$568$	−2.83374	+	1.89344i	−0.118901	+	0.0794471i
$569$	−5.27812	−	12.7425i	−0.221270	−	0.534194i	0.773793	−	0.633439i	$-0.218357\pi$
$569$	−5.27812	−	12.7425i	−0.221270	−	0.534194i	−0.995063	+	0.0992449i	$0.968357\pi$
$570$		0			0
$571$	−9.46693	−	1.88309i	−0.396179	−	0.0788048i	−0.00701944	−	0.999975i	$-0.502234\pi$
$571$	−9.46693	−	1.88309i	−0.396179	−	0.0788048i	−0.389159	+	0.921171i	$0.627234\pi$
$572$	−0.175036	+	0.879965i	−0.00731862	+	0.0367932i
$573$	4.61378	+	3.08283i	0.192743	+	0.128787i
$574$	1.57153	+	1.57153i	0.0655946	+	0.0655946i
$575$		0			0
$576$	2.86054	+	1.18487i	0.119189	+	0.0493697i
$577$	−12.7416	−	12.7416i	−0.530440	−	0.530440i	0.390263	−	0.920703i	$-0.372384\pi$
$577$	−12.7416	−	12.7416i	−0.530440	−	0.530440i	−0.920703	+	0.390263i	$0.872384\pi$
$578$	16.9692	+	1.02229i	0.705827	+	0.0425216i
$579$			26.0646i			1.08321i
$580$		0			0
$581$	19.3408	−	28.9455i	0.802391	−	1.20086i
$582$	13.3749			0.554407
$583$	−0.0866928	+	0.129745i	−0.00359045	+	0.00537349i
$584$	3.85684	−	2.57706i	0.159597	−	0.106639i
$585$		0			0
$586$	−3.55776	+	1.47367i	−0.146970	+	0.0608769i
$587$	−32.9315	−	13.6407i	−1.35923	−	0.563011i	−0.420383	−	0.907347i	$-0.638104\pi$
$587$	−32.9315	−	13.6407i	−1.35923	−	0.563011i	−0.938847	+	0.344335i	$0.888104\pi$
$588$	−4.05546	−	6.06943i	−0.167244	−	0.250299i
$589$	−11.9277	−	17.8511i	−0.491473	−	0.735541i
$590$		0			0
$591$	−27.6299	+	27.6299i	−1.13654	+	1.13654i
$592$	4.77539	−	0.949883i	0.196267	−	0.0390400i
$593$	−11.5991	−	28.0028i	−0.476320	−	1.14994i	−0.961323	−	0.275425i	$-0.911182\pi$
$593$	−11.5991	−	28.0028i	−0.476320	−	1.14994i	0.485003	−	0.874512i	$-0.338818\pi$
$594$	0.0391638			0.00160691
$595$		0			0
$596$	21.0148			0.860801
$597$	−17.2151	−	41.5609i	−0.704566	−	1.70097i
$598$	−1.10800	+	0.220395i	−0.0453094	+	0.00901260i
$599$	−4.21720	+	4.21720i	−0.172310	+	0.172310i	−0.787994	−	0.615683i	$-0.788880\pi$
$599$	−4.21720	+	4.21720i	−0.172310	+	0.172310i	0.615683	+	0.787994i	$0.288880\pi$
$600$		0			0
$601$	3.08621	+	4.61884i	0.125889	+	0.188407i	0.889060	−	0.457790i	$-0.151359\pi$
$601$	3.08621	+	4.61884i	0.125889	+	0.188407i	−0.763171	+	0.646196i	$0.776359\pi$
$602$	8.84766	+	13.2415i	0.360604	+	0.539682i
$603$	−40.6035	−	16.8185i	−1.65350	−	0.684903i
$604$	−12.6528	+	5.24097i	−0.514836	+	0.213252i
$605$		0			0
$606$	22.5333	−	15.0563i	0.915352	−	0.611618i
$607$	26.4193	−	39.5393i	1.07233	−	1.60485i	0.318322	−	0.947983i	$-0.396881\pi$
$607$	26.4193	−	39.5393i	1.07233	−	1.60485i	0.754005	−	0.656869i	$-0.228119\pi$
$608$	2.79879			0.113506
$609$	−17.3465	+	25.9609i	−0.702916	+	1.05199i
$610$		0			0
$611$			23.7124i			0.959300i
$612$	−2.11277	−	12.5900i	−0.0854037	−	0.508921i
$613$	29.8715	+	29.8715i	1.20650	+	1.20650i	0.972154	+	0.234343i	$0.0752940\pi$
$613$	29.8715	+	29.8715i	1.20650	+	1.20650i	0.234343	+	0.972154i	$0.424706\pi$
$614$	5.11094	+	2.11702i	0.206261	+	0.0854360i
$615$		0			0
$616$	0.234389	+	0.234389i	0.00944382	+	0.00944382i
$617$	−22.4565	−	15.0049i	−0.904063	−	0.604076i	0.0142639	−	0.999898i	$-0.495460\pi$
$617$	−22.4565	−	15.0049i	−0.904063	−	0.604076i	−0.918327	+	0.395823i	$0.870460\pi$
$618$	−2.95677	+	14.8647i	−0.118939	+	0.597944i
$619$	−14.8962	−	2.96304i	−0.598729	−	0.119095i	−0.113584	−	0.993528i	$-0.536233\pi$
$619$	−14.8962	−	2.96304i	−0.598729	−	0.119095i	−0.485145	+	0.874434i	$0.661233\pi$
$620$		0			0
$621$	0.0188712	+	0.0455590i	0.000757273	+	0.00182822i
$622$	−12.4017	+	8.28653i	−0.497262	+	0.332260i
$623$	−32.1881	−	6.40260i	−1.28959	−	0.256515i
$624$	−2.62172	−	13.1803i	−0.104953	−	0.527633i
$625$		0			0
$626$	−27.1152	−	18.1178i	−1.08374	−	0.724134i
$627$	1.05242	−	0.435926i	0.0420295	−	0.0174092i
$628$	5.75914	−	5.75914i	0.229815	−	0.229815i
$629$	−13.7619	−	14.6159i	−0.548721	−	0.582773i
$630$		0			0
$631$	1.73514	−	4.18901i	0.0690750	−	0.166762i	−0.885572	−	0.464503i	$-0.846233\pi$
$631$	1.73514	−	4.18901i	0.0690750	−	0.166762i	0.954647	+	0.297741i	$0.0962331\pi$
$632$	−3.21847	−	16.1804i	−0.128024	−	0.643620i
$633$		−	48.2727i		−	1.91867i
$634$	−18.6804	+	3.71575i	−0.741892	+	0.147571i
$635$		0			0
$636$	0.455972	−	2.29233i	0.0180805	−	0.0908967i
$637$	−6.15787	+	14.8664i	−0.243983	+	0.589028i
$638$	−0.396709	+	0.957741i	−0.0157059	+	0.0379173i
$639$	2.05864	−	10.3495i	0.0814387	−	0.409420i
$640$		0			0
$641$	−16.8378	+	3.34924i	−0.665052	+	0.132287i	−0.516061	−	0.856552i	$-0.672602\pi$
$641$	−16.8378	+	3.34924i	−0.665052	+	0.132287i	−0.148990	+	0.988839i	$0.547602\pi$
$642$		−	36.0677i		−	1.42348i
$643$	2.62592	+	13.2014i	0.103556	+	0.520611i	0.997389	+	0.0722118i	$0.0230058\pi$
$643$	2.62592	+	13.2014i	0.103556	+	0.520611i	−0.893833	+	0.448399i	$0.851994\pi$
$644$	−0.159723	+	0.385604i	−0.00629395	+	0.0151949i
$645$		0			0
$646$	−6.11960	−	9.78343i	−0.240772	−	0.384924i
$647$	15.2155	−	15.2155i	0.598183	−	0.598183i	−0.341646	−	0.939829i	$-0.610984\pi$
$647$	15.2155	−	15.2155i	0.598183	−	0.598183i	0.939829	+	0.341646i	$0.110984\pi$
$648$	8.03966	−	3.33014i	0.315828	−	0.130820i
$649$	1.17455	+	0.784811i	0.0461052	+	0.0308065i
$650$		0			0
$651$	7.43011	+	37.3537i	0.291209	+	1.46401i
$652$	12.4904	+	2.48449i	0.489162	+	0.0973003i
$653$	−0.904045	+	0.604064i	−0.0353780	+	0.0236388i	−0.573134	−	0.819462i	$-0.694272\pi$
$653$	−0.904045	+	0.604064i	−0.0353780	+	0.0236388i	0.537755	+	0.843101i	$0.319272\pi$
$654$	15.9723	+	38.5606i	0.624567	+	1.50784i
$655$		0			0
$656$	−1.08401	−	0.215622i	−0.0423233	−	0.00841863i
$657$	−2.80190	+	14.0861i	−0.109313	+	0.549551i
$658$	7.28422	+	4.86716i	0.283968	+	0.189742i
$659$	26.3191	+	26.3191i	1.02525	+	1.02525i	0.999673	+	0.0255752i	$0.00814173\pi$
$659$	26.3191	+	26.3191i	1.02525	+	1.02525i	0.0255752	+	0.999673i	$0.491858\pi$
$660$		0			0
$661$	23.3798	+	9.68424i	0.909370	+	0.376673i	0.787815	−	0.615911i	$-0.211212\pi$
$661$	23.3798	+	9.68424i	0.909370	+	0.376673i	0.121554	+	0.992585i	$0.461212\pi$
$662$	−9.76004	−	9.76004i	−0.379335	−	0.379335i
$663$	−40.3404	+	37.9833i	−1.56669	+	1.47515i
$664$			17.3123i			0.671846i
$665$		0			0
$666$	−8.37541	+	12.5347i	−0.324540	+	0.485709i
$667$	−1.30529			−0.0505410
$668$	−4.98128	+	7.45501i	−0.192731	+	0.288443i
$669$	39.2869	−	26.2507i	1.51892	−	1.01491i
$670$		0			0
$671$	−0.466951	+	0.193417i	−0.0180264	+	0.00746680i
$672$	−4.58698	−	1.89999i	−0.176947	−	0.0732937i
$673$	2.52990	+	3.78626i	0.0975204	+	0.145950i	0.877021	−	0.480452i	$-0.159527\pi$
$673$	2.52990	+	3.78626i	0.0975204	+	0.145950i	−0.779501	+	0.626401i	$0.784527\pi$
$674$	−18.9462	−	28.3550i	−0.729780	−	1.09219i
$675$		0			0
$676$	−11.7547	+	11.7547i	−0.452105	+	0.452105i
$677$	−37.0395	+	7.36762i	−1.42354	+	0.283161i	−0.845993	−	0.533194i	$-0.820992\pi$
$677$	−37.0395	+	7.36762i	−1.42354	+	0.283161i	−0.577551	+	0.816355i	$0.695992\pi$
$678$	6.11726	+	14.7684i	0.234932	+	0.567176i
$679$	−10.8928			−0.418029
$680$		0			0
$681$	−5.12214			−0.196281
$682$	0.483904	+	1.16825i	0.0185296	+	0.0447345i
$683$	45.8439	−	9.11892i	1.75417	−	0.348926i	0.789775	−	0.613397i	$-0.210197\pi$
$683$	45.8439	−	9.11892i	1.75417	−	0.348926i	0.964394	+	0.264471i	$0.0851973\pi$
$684$	−6.12756	+	6.12756i	−0.234293	+	0.234293i
$685$		0			0
$686$	11.1231	+	16.6469i	0.424681	+	0.635580i
$687$	22.3580	+	33.4611i	0.853011	+	1.27662i
$688$	−7.31684	−	3.03073i	−0.278952	−	0.115546i
$689$	−4.76000	+	1.97166i	−0.181342	+	0.0751142i
$690$		0			0
$691$	29.7443	−	19.8745i	1.13153	−	0.756061i	0.158638	−	0.987337i	$-0.449290\pi$
$691$	29.7443	−	19.8745i	1.13153	−	0.756061i	0.972888	+	0.231275i	$0.0742899\pi$
$692$	8.29911	−	12.4205i	0.315485	−	0.472157i
$693$	−1.02633			−0.0389869
$694$	4.65341	−	6.96432i	0.176641	−	0.264362i
$695$		0			0
$696$		−	15.5271i		−	0.588555i
$697$	1.61647	+	4.26070i	0.0612280	+	0.161386i
$698$	−11.6710	−	11.6710i	−0.441756	−	0.441756i
$699$	−57.7450	−	23.9188i	−2.18412	−	0.904691i
$700$		0			0
$701$	30.0666	+	30.0666i	1.13560	+	1.13560i	0.989230	+	0.146368i	$0.0467585\pi$
$701$	30.0666	+	30.0666i	1.13560	+	1.13560i	0.146368	+	0.989230i	$0.453242\pi$
$702$	1.07518	+	0.718410i	0.0405799	+	0.0271146i
$703$	−2.65853	+	13.3653i	−0.100268	+	0.504082i
$704$	−0.161676	−	0.0321594i	−0.00609340	−	0.00121205i
$705$		0			0
$706$	8.26556	+	19.9548i	0.311078	+	0.751010i
$707$	−18.3517	+	12.2622i	−0.690185	+	0.461167i
$708$	−20.7519	−	4.12782i	−0.779905	−	0.155133i
$709$	6.59379	+	33.1492i	0.247635	+	1.24494i	0.881754	+	0.471709i	$0.156363\pi$
$709$	6.59379	+	33.1492i	0.247635	+	1.24494i	−0.634119	+	0.773235i	$0.718637\pi$
$710$		0			0
$711$	42.4710	+	28.3782i	1.59279	+	1.06427i
$712$	15.0784	−	6.24567i	0.565086	−	0.234066i
$713$	−1.12584	+	1.12584i	−0.0421632	+	0.0421632i
$714$	3.38791	+	20.1886i	0.126789	+	0.755538i
$715$		0			0
$716$	6.98820	−	16.8710i	0.261161	−	0.630499i
$717$	11.4718	+	57.6725i	0.428421	+	2.15382i
$718$		−	3.31978i		−	0.123893i
$719$	−3.48652	+	0.693512i	−0.130025	+	0.0258636i	−0.259674	−	0.965696i	$-0.583615\pi$
$719$	−3.48652	+	0.693512i	−0.130025	+	0.0258636i	0.129649	+	0.991560i	$0.458615\pi$
$720$		0			0
$721$	2.40806	−	12.1061i	0.0896809	−	0.450856i
$722$	4.27334	−	10.3167i	0.159037	−	0.383950i
$723$	13.3633	−	32.2620i	0.496988	−	1.19984i
$724$	3.03765	−	15.2713i	0.112893	−	0.567552i
$725$		0			0
$726$	26.5719	−	5.28548i	0.986176	−	0.196163i
$727$			4.30155i			0.159536i	0.996813	+	0.0797678i	$0.0254179\pi$
$727$			4.30155i			0.159536i	−0.996813	+	0.0797678i	$0.974582\pi$
$728$	2.13519	+	10.7343i	0.0791354	+	0.397841i
$729$	−10.9843	+	26.5184i	−0.406826	+	0.982165i
$730$		0			0
$731$	5.40416	+	32.2034i	0.199880	+	1.19109i
$732$	5.35303	−	5.35303i	0.197854	−	0.197854i
$733$	−4.70359	+	1.94829i	−0.173731	+	0.0719618i	−0.467854	−	0.883806i	$-0.654973\pi$
$733$	−4.70359	+	1.94829i	−0.173731	+	0.0719618i	0.294123	+	0.955768i	$0.404973\pi$
$734$	2.90883	+	1.94362i	0.107367	+	0.0717403i
$735$		0			0
$736$	−0.0404931	−	0.203573i	−0.00149260	−	0.00750378i
$737$	2.29489	+	0.456482i	0.0845333	+	0.0168147i
$738$	2.84535	−	1.90120i	0.104739	−	0.0699843i
$739$	−7.13655	−	17.2291i	−0.262522	−	0.633784i	0.736571	−	0.676360i	$-0.236444\pi$
$739$	−7.13655	−	17.2291i	−0.262522	−	0.633784i	−0.999093	+	0.0425757i	$0.986444\pi$
$740$		0			0
$741$	36.8888	+	7.33764i	1.35514	+	0.269555i
$742$	−0.371355	+	1.86693i	−0.0136329	+	0.0685371i
$743$	−7.11960	−	4.75716i	−0.261193	−	0.174523i	0.418078	−	0.908411i	$-0.362704\pi$
$743$	−7.11960	−	4.75716i	−0.261193	−	0.174523i	−0.679271	+	0.733888i	$0.737704\pi$
$744$	−13.3925	−	13.3925i	−0.490994	−	0.490994i
$745$		0			0
$746$	−8.79555	−	3.64324i	−0.322028	−	0.133388i
$747$	−37.9028	−	37.9028i	−1.38679	−	1.38679i
$748$	0.241091	+	0.635470i	0.00881516	+	0.0232351i
$749$			29.3745i			1.07332i
$750$		0			0
$751$	0.952209	−	1.42508i	0.0347466	−	0.0520020i	−0.813690	−	0.581300i	$-0.802544\pi$
$751$	0.952209	−	1.42508i	0.0347466	−	0.0520020i	0.848436	+	0.529298i	$0.177544\pi$
$752$	−4.35668			−0.158872
$753$	−6.12805	+	9.17127i	−0.223319	+	0.334220i
$754$	−28.4595	+	19.0160i	−1.03643	+	0.692523i
$755$		0			0
$756$	0.441377	−	0.182824i	0.0160527	−	0.00664926i
$757$	26.8469	+	11.1203i	0.975766	+	0.404176i	0.812856	−	0.582465i	$-0.197912\pi$
$757$	26.8469	+	11.1203i	0.975766	+	0.404176i	0.162911	+	0.986641i	$0.447912\pi$
$758$	21.2296	+	31.7723i	0.771094	+	1.15402i
$759$	−0.0469339	−	0.0702415i	−0.00170359	−	0.00254961i
$760$		0			0
$761$	−8.96625	+	8.96625i	−0.325026	+	0.325026i	−0.850692	−	0.525665i	$-0.823816\pi$
$761$	−8.96625	+	8.96625i	−0.325026	+	0.325026i	0.525665	+	0.850692i	$0.323816\pi$
$762$	20.6653	−	4.11058i	0.748624	−	0.148911i
$763$	−13.0082	−	31.4047i	−0.470930	−	1.13693i
$764$	2.24740			0.0813080
$765$		0			0
$766$	−14.7434			−0.532699
$767$	17.8490	+	43.0913i	0.644490	+	1.55594i
$768$	2.42161	−	0.481688i	0.0873824	−	0.0173814i
$769$	27.2036	−	27.2036i	0.980987	−	0.980987i	−0.0188354	−	0.999823i	$-0.505996\pi$
$769$	27.2036	−	27.2036i	0.980987	−	0.980987i	0.999823	+	0.0188354i	$0.00599584\pi$
$770$		0			0
$771$	33.2493	+	49.7610i	1.19744	+	1.79210i
$772$	5.86489	+	8.77742i	0.211082	+	0.315906i
$773$	31.8409	+	13.1889i	1.14524	+	0.474373i	0.872934	−	0.487838i	$-0.162214\pi$
$773$	31.8409	+	13.1889i	1.14524	+	0.474373i	0.272304	+	0.962211i	$0.412214\pi$
$774$	22.6546	−	9.38383i	0.814302	−	0.337295i
$775$		0			0
$776$	4.50408	−	3.00953i	0.161687	−	0.108036i
$777$	13.4303	−	20.0998i	0.481809	−	0.721078i
$778$	12.9481			0.464210
$779$	1.71857	−	2.57202i	0.0615741	−	0.0921522i
$780$		0			0
$781$			0.561804i			0.0201029i
$782$	−0.623068	+	0.586662i	−0.0222809	+	0.0209790i
$783$	1.05648	+	1.05648i	0.0377554	+	0.0377554i
$784$	−2.73141	−	1.13139i	−0.0975502	−	0.0404066i
$785$		0			0
$786$	−2.65120	−	2.65120i	−0.0945651	−	0.0945651i
$787$	11.1164	+	7.42775i	0.396257	+	0.264771i	0.737696	−	0.675133i	$-0.235914\pi$
$787$	11.1164	+	7.42775i	0.396257	+	0.264771i	−0.341438	+	0.939904i	$0.610914\pi$
$788$	−3.08744	+	15.5216i	−0.109986	+	0.552935i
$789$	−28.1802	−	5.60539i	−1.00324	−	0.199557i
$790$		0			0
$791$	−4.98205	−	12.0277i	−0.177141	−	0.427657i
$792$	0.424376	−	0.283559i	0.0150795	−	0.0100758i
$793$	−16.3673	−	3.25566i	−0.581221	−	0.115612i
$794$	1.17104	+	5.88720i	0.0415586	+	0.208929i
$795$		0			0
$796$	−15.1490	−	10.1223i	−0.536944	−	0.358774i
$797$	−21.9111	+	9.07586i	−0.776130	+	0.321484i	−0.735353	−	0.677685i	$-0.762983\pi$
$797$	−21.9111	+	9.07586i	−0.776130	+	0.321484i	−0.0407774	+	0.999168i	$0.512983\pi$
$798$	9.82579	−	9.82579i	0.347829	−	0.347829i
$799$	9.52593	+	15.2292i	0.337003	+	0.538769i
$800$		0			0
$801$	−19.3380	+	46.6861i	−0.683274	+	1.64957i
$802$	2.21541	+	11.1376i	0.0782287	+	0.393282i
$803$		−	0.764639i		−	0.0269835i
$804$	−34.3732	+	6.83726i	−1.21225	+	0.241131i
$805$		0			0
$806$	−8.14522	+	40.9488i	−0.286903	+	1.44236i
$807$	−17.1337	+	41.3644i	−0.603135	+	1.45610i
$808$	4.20037	−	10.1406i	0.147768	−	0.356744i
$809$	3.50946	−	17.6432i	0.123386	−	0.620303i	−0.868762	−	0.495231i	$-0.835084\pi$
$809$	3.50946	−	17.6432i	0.123386	−	0.620303i	0.992148	−	0.125073i	$-0.0399164\pi$
$810$		0			0
$811$	−28.5352	+	5.67600i	−1.00201	+	0.199311i	−0.668720	−	0.743514i	$-0.733158\pi$
$811$	−28.5352	+	5.67600i	−1.00201	+	0.199311i	−0.333286	+	0.942826i	$0.608158\pi$
$812$			12.6457i			0.443777i
$813$	−11.5777	−	58.2051i	−0.406048	−	2.04134i
$814$	0.307147	−	0.741518i	0.0107655	−	0.0259902i
$815$		0			0
$816$	−6.97867	−	7.41174i	−0.244302	−	0.259463i
$817$	15.6734	−	15.6734i	0.548344	−	0.548344i
$818$	−12.8626	+	5.32788i	−0.449732	+	0.186285i
$819$	−28.1760	−	18.8266i	−0.984550	−	0.657855i
$820$		0			0
$821$	−5.66111	−	28.4603i	−0.197574	−	0.993272i	−0.944537	−	0.328406i	$-0.893489\pi$
$821$	−5.66111	−	28.4603i	−0.197574	−	0.993272i	0.746962	−	0.664866i	$-0.231511\pi$
$822$	−18.1579	−	3.61184i	−0.633331	−	0.125977i
$823$	−11.7845	+	7.87417i	−0.410783	+	0.274476i	−0.743744	−	0.668464i	$-0.766952\pi$
$823$	−11.7845	+	7.87417i	−0.410783	+	0.274476i	0.332962	+	0.942940i	$0.391952\pi$
$824$	2.34904	+	5.67108i	0.0818327	+	0.197562i
$825$		0			0
$826$	16.9009	+	3.36180i	0.588057	+	0.116972i
$827$	−5.13619	+	25.8214i	−0.178603	+	0.897897i	0.782699	+	0.622400i	$0.213842\pi$
$827$	−5.13619	+	25.8214i	−0.178603	+	0.897897i	−0.961302	+	0.275497i	$0.911158\pi$
$828$	0.534348	+	0.357040i	0.0185699	+	0.0124080i
$829$	13.7669	+	13.7669i	0.478144	+	0.478144i	0.904538	−	0.426393i	$-0.140216\pi$
$829$	13.7669	+	13.7669i	0.478144	+	0.478144i	−0.426393	+	0.904538i	$0.640216\pi$
$830$		0			0
$831$	−38.0582	−	15.7642i	−1.32022	−	0.546855i
$832$	−3.84862	−	3.84862i	−0.133427	−	0.133427i
$833$	2.01739	+	12.0217i	0.0698986	+	0.416526i
$834$		−	3.73949i		−	0.129488i
$835$		0			0
$836$	0.256319	−	0.383609i	0.00886499	−	0.0132674i
$837$	1.82247			0.0629939
$838$	−5.61700	+	8.40644i	−0.194036	+	0.290396i
$839$	22.0867	−	14.7579i	0.762519	−	0.509499i	−0.112462	−	0.993656i	$-0.535874\pi$
$839$	22.0867	−	14.7579i	0.762519	−	0.509499i	0.874981	+	0.484157i	$0.160874\pi$
$840$		0			0
$841$	−9.74488	+	4.03646i	−0.336030	+	0.139188i
$842$	14.3075	+	5.92637i	0.493070	+	0.204236i
$843$	16.6781	+	24.9605i	0.574423	+	0.859685i
$844$	−10.8620	−	16.2562i	−0.373886	−	0.559560i
$845$		0			0
$846$	9.53834	−	9.53834i	0.327935	−	0.327935i
$847$	−21.6408	+	4.30463i	−0.743587	+	0.147909i
$848$	−0.362253	−	0.874556i	−0.0124398	−	0.0300324i
$849$	−1.46908			−0.0504188
$850$		0			0
$851$	1.01060			0.0346430
$852$	−3.22020	−	7.77426i	−0.110322	−	0.266342i
$853$	−38.3300	+	7.62430i	−1.31239	+	0.261051i	−0.801191	−	0.598409i	$-0.795800\pi$
$853$	−38.3300	+	7.62430i	−1.31239	+	0.261051i	−0.511202	+	0.859460i	$0.670800\pi$
$854$	−4.35964	+	4.35964i	−0.149184	+	0.149184i
$855$		0			0
$856$	−8.11573	−	12.1460i	−0.277390	−	0.415143i
$857$	16.1026	+	24.0993i	0.550056	+	0.823217i	0.997468	−	0.0711109i	$-0.0226544\pi$
$857$	16.1026	+	24.0993i	0.550056	+	0.823217i	−0.447413	+	0.894328i	$0.647654\pi$
$858$	−2.04662	−	0.847738i	−0.0698705	−	0.0289413i
$859$	9.00118	−	3.72841i	0.307116	−	0.127212i	−0.223802	−	0.974635i	$-0.571847\pi$
$859$	9.00118	−	3.72841i	0.307116	−	0.127212i	0.530919	+	0.847423i	$0.321847\pi$
$860$		0			0
$861$	−4.56263	+	3.04865i	−0.155494	+	0.103898i
$862$	12.8995	−	19.3054i	0.439357	−	0.657544i
$863$	−4.39089			−0.149468			−0.0747338	−	0.997204i	$-0.523811\pi$
$863$	−4.39089			−0.149468			−0.0747338	+	0.997204i	$0.523811\pi$
$864$	−0.131993	+	0.197542i	−0.00449051	+	0.00672052i
$865$		0			0
$866$			6.23703i			0.211943i
$867$	−10.6495	+	40.6005i	−0.361675	+	1.37886i
$868$	10.9072	+	10.9072i	0.370215	+	0.370215i
$869$	−2.51247	−	1.04070i	−0.0852298	−	0.0353033i
$870$		0			0
$871$	54.6287	+	54.6287i	1.85102	+	1.85102i
$872$	14.0554	+	9.39154i	0.475977	+	0.318038i
$873$	−3.27211	+	16.4500i	−0.110744	+	0.556748i
$874$	0.569757	+	0.113332i	0.0192723	+	0.00383350i
$875$		0			0
$876$	4.38283	+	10.5811i	0.148082	+	0.357502i
$877$	−9.58247	+	6.40280i	−0.323577	+	0.216207i	−0.706740	−	0.707474i	$-0.749835\pi$
$877$	−9.58247	+	6.40280i	−0.323577	+	0.216207i	0.383163	+	0.923681i	$0.374835\pi$
$878$	−5.95858	−	1.18524i	−0.201092	−	0.0399998i
$879$	−1.85493	−	9.32536i	−0.0625652	−	0.314537i
$880$		0			0
$881$	11.1892	+	7.47638i	0.376974	+	0.251886i	0.729594	−	0.683881i	$-0.239709\pi$
$881$	11.1892	+	7.47638i	0.376974	+	0.251886i	−0.352620	+	0.935767i	$0.614709\pi$
$882$	8.45704	−	3.50302i	0.284763	−	0.117953i
$883$	−2.99595	+	2.99595i	−0.100822	+	0.100822i	−0.755718	−	0.654897i	$-0.772712\pi$
$883$	−2.99595	+	2.99595i	−0.100822	+	0.100822i	0.654897	+	0.755718i	$0.272712\pi$
$884$	−5.03814	+	21.8682i	−0.169451	+	0.735509i
$885$		0			0
$886$	−4.13564	+	9.98431i	−0.138939	+	0.335430i
$887$	5.86156	+	29.4681i	0.196812	+	0.989441i	0.945278	+	0.326267i	$0.105791\pi$
$887$	5.86156	+	29.4681i	0.196812	+	0.989441i	−0.748465	+	0.663174i	$0.769209\pi$
$888$			12.0217i			0.403421i
$889$	−16.8303	+	3.34776i	−0.564470	+	0.112280i
$890$		0			0
$891$	0.279853	−	1.40692i	0.00937543	−	0.0471335i
$892$	7.32337	−	17.6802i	0.245205	−	0.591976i
$893$	4.66622	−	11.2653i	0.156149	−	0.376978i
$894$	−10.1226	+	50.8897i	−0.338550	+	1.70201i
$895$		0			0
$896$	−1.97222	+	0.392299i	−0.0658872	+	0.0131058i
$897$		−	2.78930i		−	0.0931321i
$898$	1.91354	+	9.62000i	0.0638556	+	0.321024i
$899$	−18.4607	+	44.5681i	−0.615699	+	1.48643i
$900$		0			0
$901$	−2.26502	+	3.17852i	−0.0754587	+	0.105892i
$902$	−0.128829	+	0.128829i	−0.00428954	+	0.00428954i
$903$	−36.3275	+	15.0473i	−1.20890	+	0.500744i
$904$	5.38311	+	3.59688i	0.179040	+	0.119630i
$905$		0			0
$906$	−6.59688	−	33.1647i	−0.219167	−	1.10182i
$907$	−37.5419	−	7.46755i	−1.24656	−	0.247956i	−0.472648	−	0.881251i	$-0.656702\pi$
$907$	−37.5419	−	7.46755i	−1.24656	−	0.247956i	−0.773910	+	0.633296i	$0.781702\pi$
$908$	−1.72492	+	1.15255i	−0.0572433	+	0.0382488i
$909$	13.0053	+	31.3975i	0.431358	+	1.04139i
$910$		0			0
$911$	−12.9269	−	2.57131i	−0.428286	−	0.0851914i	−0.0237597	−	0.999718i	$-0.507564\pi$
$911$	−12.9269	−	2.57131i	−0.428286	−	0.0851914i	−0.404527	+	0.914526i	$0.632564\pi$
$912$	−1.34815	+	6.77758i	−0.0446416	+	0.224428i
$913$	2.37286	+	1.58549i	0.0785302	+	0.0524722i
$914$	−10.4036	−	10.4036i	−0.344119	−	0.344119i
$915$		0			0
$916$	15.0584	+	6.23740i	0.497544	+	0.206089i
$917$	2.15920	+	2.15920i	0.0713031	+	0.0713031i
$918$	0.979132	+	0.0294666i	0.0323162	+	0.000972541i
$919$		−	16.4986i		−	0.544239i	−0.962263	−	0.272120i	$-0.912275\pi$
$919$		−	16.4986i		−	0.544239i	0.962263	−	0.272120i	$-0.0877246\pi$
$920$		0			0
$921$	−7.58848	+	11.3570i	−0.250049	+	0.374225i
$922$	37.3898			1.23137
$923$	−10.3056	+	15.4234i	−0.339212	+	0.507666i
$924$	−0.680503	+	0.454697i	−0.0223869	+	0.0149584i
$925$		0			0
$926$	−20.1980	+	8.36628i	−0.663747	+	0.274933i
$927$	−17.5589	−	7.27315i	−0.576711	−	0.238882i
$928$	−3.49382	−	5.22886i	−0.114690	−	0.171646i
$929$	−25.1870	−	37.6951i	−0.826360	−	1.23673i	−0.969025	−	0.246964i	$-0.920567\pi$
$929$	−25.1870	−	37.6951i	−0.826360	−	1.23673i	0.142665	−	0.989771i	$-0.454433\pi$
$930$		0			0
$931$	5.85095	−	5.85095i	0.191757	−	0.191757i
$932$	−24.8281	+	4.93861i	−0.813270	+	0.161769i
$933$	−14.0930	−	34.0236i	−0.461385	−	1.11388i
$934$	−16.2708			−0.532396
$935$		0			0
$936$	16.8520			0.550826
$937$	19.3123	+	46.6240i	0.630905	+	1.52314i	0.838487	+	0.544922i	$0.183441\pi$
$937$	19.3123	+	46.6240i	0.630905	+	1.52314i	−0.207581	+	0.978218i	$0.566559\pi$
$938$	27.9944	−	5.56843i	0.914049	−	0.181816i
$939$	56.9354	−	56.9354i	1.85802	−	1.85802i
$940$		0			0
$941$	30.3739	+	45.4577i	0.990160	+	1.48188i	0.872374	+	0.488840i	$0.162580\pi$
$941$	30.3739	+	45.4577i	0.990160	+	1.48188i	0.117786	+	0.993039i	$0.462420\pi$
$942$	11.1723	+	16.7205i	0.364013	+	0.544784i
$943$	−0.211943	−	0.0877895i	−0.00690180	−	0.00285882i
$944$	−7.91716	+	3.27940i	−0.257682	+	0.106735i
$945$		0			0
$946$	−1.08549	+	0.725302i	−0.0352924	+	0.0235816i
$947$	0.588918	−	0.881378i	0.0191373	−	0.0286409i	−0.821778	−	0.569808i	$-0.807017\pi$
$947$	0.588918	−	0.881378i	0.0191373	−	0.0286409i	0.840915	+	0.541167i	$0.182017\pi$
$948$	40.7328			1.32294
$949$	14.0263	−	20.9919i	0.455313	−	0.681425i
$950$		0			0
$951$		−	47.0264i		−	1.52494i
$952$	5.68360	+	6.03631i	0.184207	+	0.195638i
$953$	−18.8018	−	18.8018i	−0.609049	−	0.609049i	0.333648	−	0.942698i	$-0.391720\pi$
$953$	−18.8018	−	18.8018i	−0.609049	−	0.609049i	−0.942698	+	0.333648i	$0.891720\pi$
$954$	2.70782	+	1.12162i	0.0876690	+	0.0363137i
$955$		0			0
$956$	16.8403	+	16.8403i	0.544654	+	0.544654i
$957$	−2.12819	−	1.42201i	−0.0687945	−	0.0459670i
$958$	7.32150	−	36.8077i	0.236547	−	1.18920i
$959$	14.7883	+	2.94157i	0.477538	+	0.0949882i
$960$		0			0
$961$	10.6551	+	25.7236i	0.343712	+	0.829794i
$962$	22.0344	−	14.7229i	0.710417	−	0.474685i
$963$	44.3603	+	8.82382i	1.42949	+	0.284344i
$964$	−2.75918	−	13.8714i	−0.0888674	−	0.446766i
$965$		0			0
$966$	−0.856847	−	0.572527i	−0.0275686	−	0.0184208i
$967$	24.7844	−	10.2660i	0.797013	−	0.330134i	0.0532536	−	0.998581i	$-0.483041\pi$
$967$	24.7844	−	10.2660i	0.797013	−	0.330134i	0.743759	+	0.668447i	$0.233041\pi$
$968$	7.75896	−	7.75896i	0.249382	−	0.249382i
$969$	26.6394	−	10.1067i	0.855781	−	0.324674i
$970$		0			0
$971$	13.9908	−	33.7768i	0.448986	−	1.08395i	−0.523717	−	0.851892i	$-0.675455\pi$
$971$	13.9908	−	33.7768i	0.448986	−	1.08395i	0.972703	−	0.232055i	$-0.0745450\pi$
$972$	4.33074	+	21.7721i	0.138908	+	0.698340i
$973$			3.04553i			0.0976352i
$974$	−21.4112	+	4.25895i	−0.686059	+	0.136466i
$975$		0			0
$976$	0.598163	−	3.00717i	0.0191467	−	0.0962572i
$977$	6.74211	−	16.2769i	0.215699	−	0.520744i	−0.778581	−	0.627544i	$-0.784060\pi$
$977$	6.74211	−	16.2769i	0.215699	−	0.520744i	0.994281	+	0.106800i	$0.0340604\pi$
$978$	−12.0330	+	29.0501i	−0.384772	+	0.928921i
$979$	0.524864	−	2.63867i	0.0167747	−	0.0843323i
$980$		0			0
$981$	−51.3339	+	10.2109i	−1.63896	+	0.326010i
$982$		−	19.9938i		−	0.638028i
$983$	4.41995	+	22.2206i	0.140974	+	0.708726i	0.985018	+	0.172452i	$0.0551688\pi$
$983$	4.41995	+	22.2206i	0.140974	+	0.708726i	−0.844044	+	0.536275i	$0.819831\pi$
$984$	1.04431	−	2.52118i	0.0332912	−	0.0803722i
$985$		0			0
$986$	−10.6387	+	23.6459i	−0.338805	+	0.753040i
$987$	−15.2951	+	15.2951i	−0.486848	+	0.486848i
$988$	14.0736	−	5.82948i	0.447741	−	0.185460i
$989$	−1.36678	−	0.913256i	−0.0434612	−	0.0290398i
$990$		0			0
$991$	−5.99310	−	30.1293i	−0.190377	−	0.957090i	−0.951304	−	0.308253i	$-0.900256\pi$
$991$	−5.99310	−	30.1293i	−0.190377	−	0.957090i	0.760927	−	0.648837i	$-0.224744\pi$
$992$	−7.52353	−	1.49652i	−0.238872	−	0.0475146i
$993$	28.3363	−	18.9337i	0.899226	−	0.600843i
$994$	2.62261	+	6.33155i	0.0831842	+	0.200824i
$995$		0			0
$996$	−41.9236	−	8.33911i	−1.32840	−	0.264235i
$997$	3.04388	−	15.3026i	0.0964008	−	0.484639i	−0.902179	−	0.431362i	$-0.858033\pi$
$997$	3.04388	−	15.3026i	0.0964008	−	0.484639i	0.998580	−	0.0532774i	$-0.0169668\pi$
$998$	−11.6751	−	7.80106i	−0.369569	−	0.246938i
$999$	−0.817962	−	0.817962i	−0.0258792	−	0.0258792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.a.143.1	yes	24
5.2	odd	4		850.2.s.b.7.3	yes	24
5.3	odd	4		850.2.s.a.7.1	✓	24
5.4	even	2		850.2.v.b.143.3	yes	24
17.5	odd	16		850.2.s.b.243.3	yes	24
85.22	even	16	inner	850.2.v.a.107.1	yes	24
85.39	odd	16		850.2.s.a.243.1	yes	24
85.73	even	16		850.2.v.b.107.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.s.a.7.1	✓	24	5.3	odd	4
850.2.s.a.243.1	yes	24	85.39	odd	16
850.2.s.b.7.3	yes	24	5.2	odd	4
850.2.s.b.243.3	yes	24	17.5	odd	16
850.2.v.a.107.1	yes	24	85.22	even	16	inner
850.2.v.a.143.1	yes	24	1.1	even	1	trivial
850.2.v.b.107.3	yes	24	85.73	even	16
850.2.v.b.143.3	yes	24	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{2} +(-2.42161 + 0.481688i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-1.37173 - 2.05294i) q^{6} +(1.11717 + 1.67197i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(2.86054 - 1.18487i) q^{9} +(-0.137062 + 0.0915821i) q^{11} +(1.37173 - 2.05294i) q^{12} -5.44277 q^{13} +(-1.11717 + 1.67197i) q^{14} -1.00000i q^{16} +(-3.49559 + 2.18651i) q^{17} +(2.18936 + 2.18936i) q^{18} +(2.58575 + 1.07105i) q^{19} +(-3.51072 - 3.51072i) q^{21} +(-0.137062 - 0.0915821i) q^{22} +(0.0404931 - 0.203573i) q^{23} +(2.42161 + 0.481688i) q^{24} +(-2.08286 - 5.02846i) q^{26} +(-0.197542 + 0.131993i) q^{27} +(-1.97222 - 0.392299i) q^{28} +(-1.22686 - 6.16787i) q^{29} +(-6.37814 - 4.26174i) q^{31} +(0.923880 - 0.382683i) q^{32} +(0.287798 - 0.287798i) q^{33} +(-3.35778 - 2.39276i) q^{34} +(-1.18487 + 2.86054i) q^{36} +(0.949883 + 4.77539i) q^{37} +2.79879i q^{38} +(13.1803 - 2.62172i) q^{39} +(0.215622 - 1.08401i) q^{41} +(1.89999 - 4.58698i) q^{42} +(3.03073 - 7.31684i) q^{43} +(0.0321594 - 0.161676i) q^{44} +(0.203573 - 0.0404931i) q^{46} -4.35668i q^{47} +(0.481688 + 2.42161i) q^{48} +(1.13139 - 2.73141i) q^{49} +(7.41174 - 6.97867i) q^{51} +(3.84862 - 3.84862i) q^{52} +(0.874556 - 0.362253i) q^{53} +(-0.197542 - 0.131993i) q^{54} +(-0.392299 - 1.97222i) q^{56} +(-6.77758 - 1.34815i) q^{57} +(5.22886 - 3.49382i) q^{58} +(-3.27940 - 7.91716i) q^{59} +(3.00717 + 0.598163i) q^{61} +(1.49652 - 7.52353i) q^{62} +(5.17678 + 3.45902i) q^{63} +(0.707107 + 0.707107i) q^{64} +(0.376026 + 0.155755i) q^{66} +(-10.0369 - 10.0369i) q^{67} +(0.925658 - 4.01785i) q^{68} +0.512479i q^{69} +(1.89344 - 2.83374i) q^{71} -3.09622 q^{72} +(-2.57706 + 3.85684i) q^{73} +(-4.04838 + 2.70504i) q^{74} +(-2.58575 + 1.07105i) q^{76} +(-0.306245 - 0.126851i) q^{77} +(7.46602 + 11.1737i) q^{78} +(9.16543 + 13.7170i) q^{79} +(-6.15329 + 6.15329i) q^{81} +(1.08401 - 0.215622i) q^{82} +(-6.62511 - 15.9944i) q^{83} +4.96491 q^{84} +7.91969 q^{86} +(5.94198 + 14.3452i) q^{87} +(0.161676 - 0.0321594i) q^{88} +(-11.5405 + 11.5405i) q^{89} +(-6.08051 - 9.10013i) q^{91} +(0.115315 + 0.172580i) q^{92} +(17.4982 + 7.24799i) q^{93} +(4.02504 - 1.66723i) q^{94} +(-2.05294 + 1.37173i) q^{96} +(-3.00953 + 4.50408i) q^{97} +2.95645 q^{98} +(-0.283559 + 0.424376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} - 32 q^{13} - 16 q^{18} + 48 q^{27} + 16 q^{29} + 16 q^{31} - 8 q^{33} - 16 q^{34} + 16 q^{37} + 32 q^{39} + 48 q^{41} - 48 q^{42} + 16 q^{43} - 16 q^{44} + 32 q^{46} + 8 q^{48} + 16 q^{49}+ \cdots - 24 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 32 * q^13 - 16 * q^18 + 48 * q^27 + 16 * q^29 + 16 * q^31 - 8 * q^33 - 16 * q^34 + 16 * q^37 + 32 * q^39 + 48 * q^41 - 48 * q^42 + 16 * q^43 - 16 * q^44 + 32 * q^46 + 8 * q^48 + 16 * q^49 + 64 * q^51 + 48 * q^54 - 48 * q^57 + 16 * q^58 - 8 * q^59 + 16 * q^61 + 16 * q^62 + 80 * q^63 + 8 * q^66 - 48 * q^67 - 32 * q^71 - 24 * q^72 + 48 * q^73 + 16 * q^77 + 48 * q^78 + 16 * q^79 - 56 * q^81 - 16 * q^82 - 72 * q^83 - 32 * q^84 - 16 * q^86 + 80 * q^87 - 16 * q^88 - 48 * q^89 - 48 * q^91 - 16 * q^92 + 64 * q^93 + 32 * q^94 + 32 * q^97 - 56 * q^98 - 24 * q^99

Introduction

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