LMFDB - Embedded newform 825.2.bi.h.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(101,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("825.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bi (of order $10$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.694544 + 2.13759i) q^{2} +(0.571289 + 1.63512i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.89200 + 0.0855139i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(1.91228 - 1.38935i) q^{8} +(-2.34726 + 1.86826i) q^{9} +O(q^{10})$	\(q+(-0.694544 + 2.13759i) q^{2} +(0.571289 + 1.63512i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.89200 + 0.0855139i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(1.91228 - 1.38935i) q^{8} +(-2.34726 + 1.86826i) q^{9} +(-0.916510 - 3.18748i) q^{11} +(1.52253 - 5.06160i) q^{12} +(-0.399438 - 0.129785i) q^{13} +(-5.42493 - 7.46677i) q^{14} +(-0.244334 - 0.751983i) q^{16} +(0.478346 + 1.47220i) q^{17} +(-2.36328 - 6.31505i) q^{18} +(2.85337 + 3.92732i) q^{19} +(-6.81098 - 2.04875i) q^{21} +(7.45006 + 0.254724i) q^{22} -1.54048i q^{23} +(3.36422 + 2.33309i) q^{24} +(0.554855 - 0.763692i) q^{26} +(-4.39579 - 2.77074i) q^{27} +(11.9179 - 3.87237i) q^{28} +(-1.83926 - 1.33630i) q^{29} +(-2.13274 + 6.56391i) q^{31} +6.50454 q^{32} +(4.68833 - 3.31958i) q^{33} -3.47918 q^{34} +(9.14615 - 0.402107i) q^{36} +(-3.36663 - 2.44600i) q^{37} +(-10.3768 + 3.37162i) q^{38} +(-0.0159795 - 0.727276i) q^{39} +(7.86568 - 5.71475i) q^{41} +(9.10989 - 13.1361i) q^{42} +0.898807i q^{43} +(-3.45473 + 9.51336i) q^{44} +(3.29291 + 1.06993i) q^{46} +(-5.84743 - 8.04830i) q^{47} +(1.09000 - 0.829116i) q^{48} +(-3.04761 - 9.37957i) q^{49} +(-2.13395 + 1.62321i) q^{51} +(0.753353 + 1.03690i) q^{52} +(0.206545 + 0.0671104i) q^{53} +(8.97577 - 7.47198i) q^{54} +9.70625i q^{56} +(-4.79156 + 6.90924i) q^{57} +(4.13391 - 3.00346i) q^{58} +(-1.03943 + 1.43066i) q^{59} +(1.64330 - 0.533940i) q^{61} +(-12.5496 - 9.11784i) q^{62} +(-0.541082 - 12.3072i) q^{63} +(-4.02902 + 12.4000i) q^{64} +(3.83963 + 12.3273i) q^{66} +0.651654 q^{67} +(1.45975 - 4.49265i) q^{68} +(2.51888 - 0.880060i) q^{69} +(-11.3748 + 3.69589i) q^{71} +(-1.89295 + 6.83379i) q^{72} +(-7.99327 + 11.0018i) q^{73} +(7.56681 - 5.49761i) q^{74} -14.8141i q^{76} +(12.8013 + 4.64874i) q^{77} +(1.56571 + 0.470967i) q^{78} +(3.63722 + 1.18180i) q^{79} +(2.01924 - 8.77056i) q^{81} +(6.75271 + 20.7827i) q^{82} +(2.63127 + 8.09822i) q^{83} +(13.1404 + 17.2750i) q^{84} +(-1.92128 - 0.624261i) q^{86} +(1.13427 - 3.77083i) q^{87} +(-6.18115 - 4.82199i) q^{88} +8.29256i q^{89} +(1.39527 - 1.01372i) q^{91} +(-2.76320 + 3.80322i) q^{92} +(-11.9512 + 0.262589i) q^{93} +(21.2652 - 6.90949i) q^{94} +(3.71597 + 10.6357i) q^{96} +(-3.70900 + 11.4151i) q^{97} +22.1663 q^{98} +(8.10631 + 5.76956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.694544	+	2.13759i	−0.491116	+	1.51150i	0.331806	+	0.943348i	$0.392342\pi$
$2$	−0.694544	+	2.13759i	−0.491116	+	1.51150i	−0.822923	+	0.568154i	$0.807658\pi$
$3$	0.571289	+	1.63512i	0.329834	+	0.944039i
$3$	0.571289	+	1.63512i	0.329834	+	0.944039i
$4$	−2.46885	−	1.79372i	−1.23442	−	0.896861i
$5$		0			0
$5$		0			0
$6$	−3.89200	+	0.0855139i	−1.58890	+	0.0349109i
$7$	−2.41366	+	3.32212i	−0.912279	+	1.25564i	0.0541037	+	0.998535i	$0.482770\pi$
$7$	−2.41366	+	3.32212i	−0.912279	+	1.25564i	−0.966382	+	0.257109i	$0.917230\pi$
$8$	1.91228	−	1.38935i	0.676092	−	0.491210i
$9$	−2.34726	+	1.86826i	−0.782419	+	0.622752i
$10$		0			0
$11$	−0.916510	−	3.18748i	−0.276338	−	0.961061i
$11$	−0.916510	−	3.18748i	−0.276338	−	0.961061i
$12$	1.52253	−	5.06160i	0.439517	−	1.46116i
$13$	−0.399438	−	0.129785i	−0.110784	−	0.0359960i	0.253100	−	0.967440i	$-0.418550\pi$
$13$	−0.399438	−	0.129785i	−0.110784	−	0.0359960i	−0.363885	+	0.931444i	$0.618550\pi$
$14$	−5.42493	−	7.46677i	−1.44987	−	1.99558i
$15$		0			0
$16$	−0.244334	−	0.751983i	−0.0610836	−	0.187996i
$17$	0.478346	+	1.47220i	0.116016	+	0.357061i	0.992158	−	0.124993i	$-0.0398909\pi$
$17$	0.478346	+	1.47220i	0.116016	+	0.357061i	−0.876142	+	0.482054i	$0.839891\pi$
$18$	−2.36328	−	6.31505i	−0.557031	−	1.48847i
$19$	2.85337	+	3.92732i	0.654607	+	0.900990i	0.999288	−	0.0377303i	$-0.0120128\pi$
$19$	2.85337	+	3.92732i	0.654607	+	0.900990i	−0.344681	+	0.938720i	$0.612013\pi$
$20$		0			0
$21$	−6.81098	−	2.04875i	−1.48628	−	0.447073i
$22$	7.45006	+	0.254724i	1.58836	+	0.0543074i
$23$		−	1.54048i		−	0.321213i	−0.987019	−	0.160606i	$-0.948655\pi$
$23$		−	1.54048i		−	0.321213i	0.987019	−	0.160606i	$-0.0513450\pi$
$24$	3.36422	+	2.33309i	0.686719	+	0.476240i
$25$		0			0
$26$	0.554855	−	0.763692i	0.108816	−	0.149772i
$27$	−4.39579	−	2.77074i	−0.845970	−	0.533230i
$28$	11.9179	−	3.87237i	2.25228	−	0.731809i
$29$	−1.83926	−	1.33630i	−0.341542	−	0.248145i	0.403770	−	0.914861i	$-0.367700\pi$
$29$	−1.83926	−	1.33630i	−0.341542	−	0.248145i	−0.745312	+	0.666716i	$0.767700\pi$
$30$		0			0
$31$	−2.13274	+	6.56391i	−0.383052	+	1.17891i	0.554831	+	0.831963i	$0.312783\pi$
$31$	−2.13274	+	6.56391i	−0.383052	+	1.17891i	−0.937884	+	0.346950i	$0.887217\pi$
$32$	6.50454			1.14985
$33$	4.68833	−	3.31958i	0.816133	−	0.577864i
$34$	−3.47918			−0.596675
$35$		0			0
$36$	9.14615	−	0.402107i	1.52436	−	0.0670179i
$37$	−3.36663	−	2.44600i	−0.553471	−	0.402120i	0.275592	−	0.961275i	$-0.411126\pi$
$37$	−3.36663	−	2.44600i	−0.553471	−	0.402120i	−0.829064	+	0.559154i	$0.811126\pi$
$38$	−10.3768	+	3.37162i	−1.68334	+	0.546949i
$39$	−0.0159795	−	0.727276i	−0.00255877	−	0.116457i
$40$		0			0
$41$	7.86568	−	5.71475i	1.22841	−	0.892494i	0.231642	−	0.972801i	$-0.425590\pi$
$41$	7.86568	−	5.71475i	1.22841	−	0.892494i	0.996770	+	0.0803075i	$0.0255902\pi$
$42$	9.10989	−	13.1361i	1.40569	−	2.02694i
$43$			0.898807i			0.137067i	0.997649	+	0.0685334i	$0.0218320\pi$
$43$			0.898807i			0.137067i	−0.997649	+	0.0685334i	$0.978168\pi$
$44$	−3.45473	+	9.51336i	−0.520820	+	1.43419i
$45$		0			0
$46$	3.29291	+	1.06993i	0.485514	+	0.157753i
$47$	−5.84743	−	8.04830i	−0.852936	−	1.17397i	−0.983208	−	0.182487i	$-0.941585\pi$
$47$	−5.84743	−	8.04830i	−0.852936	−	1.17397i	0.130272	−	0.991478i	$-0.458415\pi$
$48$	1.09000	−	0.829116i	0.157328	−	0.119673i
$49$	−3.04761	−	9.37957i	−0.435372	−	1.33994i
$50$		0			0
$51$	−2.13395	+	1.62321i	−0.298813	+	0.227294i
$52$	0.753353	+	1.03690i	0.104471	+	0.143792i
$53$	0.206545	+	0.0671104i	0.0283711	+	0.00921833i	0.323168	−	0.946342i	$-0.395252\pi$
$53$	0.206545	+	0.0671104i	0.0283711	+	0.00921833i	−0.294797	+	0.955560i	$0.595252\pi$
$54$	8.97577	−	7.47198i	1.22145	−	1.01681i
$55$		0			0
$56$			9.70625i			1.29705i
$57$	−4.79156	+	6.90924i	−0.634658	+	0.915152i
$58$	4.13391	−	3.00346i	0.542809	−	0.394373i
$59$	−1.03943	+	1.43066i	−0.135323	+	0.186255i	−0.871300	−	0.490750i	$-0.836723\pi$
$59$	−1.03943	+	1.43066i	−0.135323	+	0.186255i	0.735978	+	0.677006i	$0.236723\pi$
$60$		0			0
$61$	1.64330	−	0.533940i	0.210403	−	0.0683641i	−0.201919	−	0.979402i	$-0.564718\pi$
$61$	1.64330	−	0.533940i	0.210403	−	0.0683641i	0.412322	+	0.911038i	$0.364718\pi$
$62$	−12.5496	−	9.11784i	−1.59381	−	1.15797i
$63$	−0.541082	−	12.3072i	−0.0681700	−	1.55056i
$64$	−4.02902	+	12.4000i	−0.503627	+	1.55001i
$65$		0			0
$66$	3.83963	+	12.3273i	0.472626	+	1.51738i
$67$	0.651654			0.0796121			0.0398061	−	0.999207i	$-0.487326\pi$
$67$	0.651654			0.0796121			0.0398061	+	0.999207i	$0.487326\pi$
$68$	1.45975	−	4.49265i	0.177021	−	0.544814i
$69$	2.51888	−	0.880060i	0.303237	−	0.105947i
$70$		0			0
$71$	−11.3748	+	3.69589i	−1.34994	+	0.438622i	−0.892672	−	0.450708i	$-0.851172\pi$
$71$	−11.3748	+	3.69589i	−1.34994	+	0.438622i	−0.457267	+	0.889329i	$0.651172\pi$
$72$	−1.89295	+	6.83379i	−0.223086	+	0.805370i
$73$	−7.99327	+	11.0018i	−0.935541	+	1.28766i	0.0221175	+	0.999755i	$0.492959\pi$
$73$	−7.99327	+	11.0018i	−0.935541	+	1.28766i	−0.957659	+	0.287906i	$0.907041\pi$
$74$	7.56681	−	5.49761i	0.879624	−	0.639085i
$75$		0			0
$76$		−	14.8141i		−	1.69929i
$77$	12.8013	+	4.64874i	1.45885	+	0.529773i
$78$	1.56571	+	0.470967i	0.177282	+	0.0533265i
$79$	3.63722	+	1.18180i	0.409219	+	0.132963i	0.506390	−	0.862304i	$-0.330980\pi$
$79$	3.63722	+	1.18180i	0.409219	+	0.132963i	−0.0971715	+	0.995268i	$0.530980\pi$
$80$		0			0
$81$	2.01924	−	8.77056i	0.224360	−	0.974506i
$82$	6.75271	+	20.7827i	0.745712	+	2.29506i
$83$	2.63127	+	8.09822i	0.288820	+	0.888895i	0.985228	+	0.171249i	$0.0547804\pi$
$83$	2.63127	+	8.09822i	0.288820	+	0.888895i	−0.696408	+	0.717646i	$0.745220\pi$
$84$	13.1404	+	17.2750i	1.43373	+	1.88486i
$85$		0			0
$86$	−1.92128	−	0.624261i	−0.207177	−	0.0673158i
$87$	1.13427	−	3.77083i	0.121606	−	0.404276i
$88$	−6.18115	−	4.82199i	−0.658912	−	0.514026i
$89$			8.29256i			0.879010i	0.898240	+	0.439505i	$0.144846\pi$
$89$			8.29256i			0.879010i	−0.898240	+	0.439505i	$0.855154\pi$
$90$		0			0
$91$	1.39527	−	1.01372i	0.146264	−	0.106267i
$92$	−2.76320	+	3.80322i	−0.288083	+	0.396513i
$93$	−11.9512	+	0.262589i	−1.23928	+	0.0272292i
$94$	21.2652	−	6.90949i	2.19334	−	0.712660i
$95$		0			0
$96$	3.71597	+	10.6357i	0.379260	+	1.08550i
$97$	−3.70900	+	11.4151i	−0.376592	+	1.15903i	0.565807	+	0.824538i	$0.308565\pi$
$97$	−3.70900	+	11.4151i	−0.376592	+	1.15903i	−0.942399	+	0.334492i	$0.891435\pi$
$98$	22.1663			2.23914
$99$	8.10631	+	5.76956i	0.814714	+	0.579862i
$100$		0			0
$101$	−0.448958	+	1.38175i	−0.0446730	+	0.137489i	−0.970905	−	0.239464i	$-0.923028\pi$
$101$	−0.448958	+	1.38175i	−0.0446730	+	0.137489i	0.926232	+	0.376953i	$0.123028\pi$
$102$	−1.98762	−	5.68889i	−0.196803	−	0.563284i
$103$	10.2248	+	7.42877i	1.00748	+	0.731978i	0.963679	−	0.267062i	$-0.0860529\pi$
$103$	10.2248	+	7.42877i	1.00748	+	0.731978i	0.0438022	+	0.999040i	$0.486053\pi$
$104$	−0.944155	+	0.306774i	−0.0925820	+	0.0300817i
$105$		0			0
$106$	−0.286909	+	0.394896i	−0.0278670	+	0.0383557i
$107$	−1.47062	+	1.06847i	−0.142170	+	0.103292i	−0.656597	−	0.754242i	$-0.728005\pi$
$107$	−1.47062	+	1.06847i	−0.142170	+	0.103292i	0.514427	+	0.857534i	$0.328005\pi$
$108$	5.88259	+	14.7254i	0.566052	+	1.41695i
$109$		−	7.76325i		−	0.743585i	−0.928316	−	0.371792i	$-0.878743\pi$
$109$		−	7.76325i		−	0.743585i	0.928316	−	0.371792i	$-0.121257\pi$
$110$		0			0
$111$	2.07620	−	6.90224i	0.197064	−	0.655131i
$112$	3.08792	+	1.00333i	0.291781	+	0.0948054i
$113$	−8.44236	−	11.6199i	−0.794191	−	1.09311i	−0.993574	−	0.113188i	$-0.963894\pi$
$113$	−8.44236	−	11.6199i	−0.794191	−	1.09311i	0.199383	−	0.979922i	$-0.436106\pi$
$114$	−11.4412	−	15.0411i	−1.07156	−	1.40873i
$115$		0			0
$116$	2.14390	+	6.59825i	0.199056	+	0.612632i
$117$	1.18006	−	0.441613i	0.109096	−	0.0408271i
$118$	−2.33622	−	3.21553i	−0.215066	−	0.296013i
$119$	−6.04539	−	1.96427i	−0.554180	−	0.180064i
$120$		0			0
$121$	−9.32002	+	5.84271i	−0.847275	+	0.531155i
$122$			3.88354i			0.351599i
$123$	13.8379	+	9.59658i	1.24772	+	0.865294i
$124$	17.0392	−	12.3797i	1.53017	−	1.11173i
$125$		0			0
$126$	26.6835	+	7.39129i	2.37716	+	0.658468i
$127$	−11.4918	+	3.73390i	−1.01973	+	0.331330i	−0.770722	−	0.637171i	$-0.780104\pi$
$127$	−11.4918	+	3.73390i	−1.01973	+	0.331330i	−0.249007	+	0.968502i	$0.580104\pi$
$128$	−13.1833	−	9.57820i	−1.16525	−	0.846601i
$129$	−1.46966	+	0.513478i	−0.129396	+	0.0452092i
$130$		0			0
$131$	−4.65863			−0.407026			−0.203513	−	0.979072i	$-0.565236\pi$
$131$	−4.65863			−0.407026			−0.203513	+	0.979072i	$0.565236\pi$
$132$	−17.5292	−	0.214031i	−1.52572	−	0.0186290i
$133$	−19.9341			−1.72851
$134$	−0.452602	+	1.39297i	−0.0390988	+	0.120334i
$135$		0			0
$136$	2.96013	+	2.15066i	0.253829	+	0.184418i
$137$	−1.06780	+	0.346949i	−0.0912283	+	0.0296419i	−0.354276	−	0.935141i	$-0.615273\pi$
$137$	−1.06780	+	0.346949i	−0.0912283	+	0.0296419i	0.263047	+	0.964783i	$0.415273\pi$
$138$	0.131733	+	5.99556i	0.0112138	+	0.510376i
$139$	−10.0917	+	13.8901i	−0.855970	+	1.17814i	0.126546	+	0.991961i	$0.459611\pi$
$139$	−10.0917	+	13.8901i	−0.855970	+	1.17814i	−0.982516	+	0.186180i	$0.940389\pi$
$140$		0			0
$141$	9.81940	−	14.1592i	0.826942	−	1.19242i
$142$		−	26.8815i		−	2.25585i
$143$	−0.0475989	+	1.39215i	−0.00398042	+	0.116417i
$144$	1.97841	+	1.30862i	0.164868	+	0.109052i
$145$		0			0
$146$	−17.9656	−	24.7275i	−1.48684	−	2.04646i
$147$	13.5957	−	10.3417i	1.12135	−	0.852965i
$148$	3.92425	+	12.0776i	0.322572	+	0.992774i
$149$	−5.61165	−	17.2709i	−0.459724	−	1.41489i	−0.865498	−	0.500912i	$-0.832998\pi$
$149$	−5.61165	−	17.2709i	−0.459724	−	1.41489i	0.405774	−	0.913973i	$-0.367002\pi$
$150$		0			0
$151$	−3.09504	−	4.25995i	−0.251870	−	0.346670i	0.664295	−	0.747471i	$-0.268732\pi$
$151$	−3.09504	−	4.25995i	−0.251870	−	0.346670i	−0.916165	+	0.400801i	$0.868732\pi$
$152$	10.9129	+	3.54580i	0.885150	+	0.287603i
$153$	−3.87325	−	2.56196i	−0.313133	−	0.207122i
$154$	−18.8282	+	24.1352i	−1.51722	+	1.94487i
$155$		0			0
$156$	−1.26508	+	1.82420i	−0.101287	+	0.146053i
$157$	0.504116	−	0.366262i	0.0402328	−	0.0292309i	−0.567487	−	0.823382i	$-0.692084\pi$
$157$	0.504116	−	0.366262i	0.0402328	−	0.0292309i	0.607720	+	0.794151i	$0.292084\pi$
$158$	−5.05241	+	6.95404i	−0.401948	+	0.553234i
$159$	0.00826280	+	0.376066i	0.000655283	+	0.0298239i
$160$		0			0
$161$	5.11767	+	3.71821i	0.403329	+	0.293036i
$162$	17.3454	+	10.4078i	1.36278	+	0.817717i
$163$	1.48562	−	4.57228i	0.116363	−	0.358128i	−0.875866	−	0.482555i	$-0.839709\pi$
$163$	1.48562	−	4.57228i	0.116363	−	0.358128i	0.992229	+	0.124426i	$0.0397090\pi$
$164$	−29.6698			−2.31682
$165$		0			0
$166$	−19.1382			−1.48541
$167$	−3.28802	+	10.1195i	−0.254434	+	0.783069i	0.739506	+	0.673150i	$0.235059\pi$
$167$	−3.28802	+	10.1195i	−0.254434	+	0.783069i	−0.993941	+	0.109919i	$0.964941\pi$
$168$	−15.8709	+	5.54507i	−1.22447	+	0.427811i
$169$	−10.3745	−	7.53753i	−0.798040	−	0.579810i
$170$		0			0
$171$	−14.0348	−	3.88762i	−1.07327	−	0.297294i
$172$	1.61221	−	2.21902i	0.122930	−	0.169198i
$173$	1.82207	−	1.32381i	0.138529	−	0.100647i	−0.516362	−	0.856370i	$-0.672714\pi$
$173$	1.82207	−	1.32381i	0.138529	−	0.100647i	0.654892	+	0.755723i	$0.272714\pi$
$174$	7.27268	+	5.04361i	0.551341	+	0.382355i
$175$		0			0
$176$	−2.17300	+	1.46801i	−0.163796	+	0.110655i
$177$	−2.93311	−	0.882282i	−0.220466	−	0.0663164i
$178$	−17.7261	−	5.75955i	−1.32862	−	0.431696i
$179$	8.55266	+	11.7717i	0.639256	+	0.879860i	0.998576	−	0.0533542i	$-0.0169912\pi$
$179$	8.55266	+	11.7717i	0.639256	+	0.879860i	−0.359320	+	0.933215i	$0.616991\pi$
$180$		0			0
$181$	−5.42504	−	16.6965i	−0.403240	−	1.24104i	−0.922356	−	0.386341i	$-0.873739\pi$
$181$	−5.42504	−	16.6965i	−0.403240	−	1.24104i	0.519116	−	0.854704i	$-0.326261\pi$
$182$	1.19785	+	3.68659i	0.0887902	+	0.273268i
$183$	1.81186	+	2.38196i	0.133936	+	0.176080i
$184$	−2.14027	−	2.94583i	−0.157783	−	0.217170i
$185$		0			0
$186$	7.73933	−	25.7291i	0.567476	−	1.88655i
$187$	4.25419	−	2.87400i	0.311097	−	0.210168i
$188$			30.3587i			2.21414i
$189$	19.8147	−	7.91571i	1.44131	−	0.575783i
$190$		0			0
$191$	0.896200	−	1.23351i	0.0648467	−	0.0892539i	−0.775362	−	0.631517i	$-0.782432\pi$
$191$	0.896200	−	1.23351i	0.0648467	−	0.0892539i	0.840209	+	0.542263i	$0.182432\pi$
$192$	−22.5773	+	0.496063i	−1.62938	+	0.0358003i
$193$	1.83654	−	0.596730i	0.132197	−	0.0429535i	−0.242171	−	0.970234i	$-0.577860\pi$
$193$	1.83654	−	0.596730i	0.132197	−	0.0429535i	0.374368	+	0.927280i	$0.377860\pi$
$194$	−21.8247	−	15.8566i	−1.56692	−	1.13844i
$195$		0			0
$196$	−9.30027	+	28.6233i	−0.664305	+	2.04452i
$197$	9.11618			0.649501			0.324751	−	0.945800i	$-0.394720\pi$
$197$	9.11618			0.649501			0.324751	+	0.945800i	$0.394720\pi$
$198$	−17.9631	+	13.3207i	−1.27658	+	0.946662i
$199$	−1.81006			−0.128311			−0.0641557	−	0.997940i	$-0.520435\pi$
$199$	−1.81006			−0.128311			−0.0641557	+	0.997940i	$0.520435\pi$
$200$		0			0
$201$	0.372282	+	1.06553i	0.0262588	+	0.0751570i
$202$	−2.64179	−	1.91937i	−0.185876	−	0.135047i
$203$	8.87871	−	2.88487i	0.623164	−	0.202478i
$204$	8.17998	−	0.179728i	0.572713	−	0.0125835i
$205$		0			0
$206$	−22.9812	+	16.6968i	−1.60118	+	1.16332i
$207$	2.87801	+	3.61591i	0.200036	+	0.251323i
$208$			0.332082i			0.0230257i
$209$	9.90311	−	12.6945i	0.685013	−	0.878095i
$210$		0			0
$211$	23.7527	+	7.71771i	1.63520	+	0.531309i	0.975459	−	0.220182i	$-0.0706652\pi$
$211$	23.7527	+	7.71771i	1.63520	+	0.531309i	0.659743	+	0.751491i	$0.270665\pi$
$212$	−0.389550	−	0.536169i	−0.0267544	−	0.0368242i
$213$	−12.5415	−	16.4878i	−0.859331	−	1.12972i
$214$	−1.26253	−	3.88566i	−0.0863047	−	0.265619i
$215$		0			0
$216$	−12.2555	+	0.808865i	−0.833882	+	0.0550363i
$217$	−16.6584	−	22.9283i	−1.13084	−	1.55647i
$218$	16.5946	+	5.39192i	1.12393	+	0.365187i
$219$	−22.5557	−	6.78478i	−1.52418	−	0.458473i
$220$		0			0
$221$		−	0.650135i		−	0.0437328i
$222$	13.3121	+	9.23195i	0.893451	+	0.619608i
$223$	−19.7983	+	14.3843i	−1.32579	+	0.963245i	−0.325953	+	0.945386i	$0.605685\pi$
$223$	−19.7983	+	14.3843i	−1.32579	+	0.963245i	−0.999841	+	0.0178594i	$0.994315\pi$
$224$	−15.6998	+	21.6089i	−1.04898	+	1.44380i
$225$		0			0
$226$	30.7021	−	9.97573i	2.04228	−	0.663576i
$227$	−9.28284	−	6.74438i	−0.616124	−	0.447640i	0.235442	−	0.971888i	$-0.424346\pi$
$227$	−9.28284	−	6.74438i	−0.616124	−	0.447640i	−0.851565	+	0.524249i	$0.824346\pi$
$228$	24.2229	−	8.46313i	1.60420	−	0.560485i
$229$	−3.04889	+	9.38351i	−0.201476	+	0.620080i	0.798364	+	0.602176i	$0.205699\pi$
$229$	−3.04889	+	9.38351i	−0.201476	+	0.620080i	−0.999840	+	0.0179041i	$0.994301\pi$
$230$		0			0
$231$	−0.288004	+	23.5875i	−0.0189493	+	1.55195i
$232$	−5.37377			−0.352805
$233$	0.161672	−	0.497576i	0.0105915	−	0.0325973i	−0.945621	−	0.325270i	$-0.894545\pi$
$233$	0.161672	−	0.497576i	0.0105915	−	0.0325973i	0.956213	+	0.292673i	$0.0945447\pi$
$234$	0.124384	+	2.82919i	0.00813127	+	0.184950i
$235$		0			0
$236$	5.13240	−	1.66762i	0.334091	−	0.108553i
$237$	0.145506	+	6.62245i	0.00945166	+	0.430174i
$238$	8.39757	−	11.5583i	0.544334	−	0.749211i
$239$	−3.09023	+	2.24519i	−0.199891	+	0.145229i	−0.683228	−	0.730205i	$-0.739424\pi$
$239$	−3.09023	+	2.24519i	−0.199891	+	0.145229i	0.483337	+	0.875434i	$0.339424\pi$
$240$		0			0
$241$			19.8397i			1.27799i	0.769212	+	0.638994i	$0.220649\pi$
$241$			19.8397i			1.27799i	−0.769212	+	0.638994i	$0.779351\pi$
$242$	−6.01612	−	23.9804i	−0.386731	−	1.54152i
$243$	15.4945	−	1.70881i	0.993974	−	0.109620i
$244$	−5.01480	−	1.62941i	−0.321039	−	0.104312i
$245$		0			0
$246$	−30.1245	+	22.9144i	−1.92067	+	1.46097i
$247$	−0.630035	−	1.93905i	−0.0400882	−	0.123379i
$248$	5.04118	+	15.5152i	0.320115	+	0.985213i
$249$	−11.7384	+	8.92888i	−0.743889	+	0.565845i
$250$		0			0
$251$	8.45794	+	2.74815i	0.533861	+	0.173462i	0.563526	−	0.826098i	$-0.309444\pi$
$251$	8.45794	+	2.74815i	0.533861	+	0.173462i	−0.0296658	+	0.999560i	$0.509444\pi$
$252$	−20.7399	+	31.3552i	−1.30649	+	1.97519i
$253$	−4.91025	+	1.41187i	−0.308705	+	0.0887633i
$254$		−	27.1580i		−	1.70404i
$255$		0			0
$256$	8.53435	−	6.20057i	0.533397	−	0.387535i
$257$	−0.158202	+	0.217746i	−0.00986837	+	0.0135827i	−0.813923	−	0.580973i	$-0.802672\pi$
$257$	−0.158202	+	0.217746i	−0.00986837	+	0.0135827i	0.804054	+	0.594556i	$0.202672\pi$
$258$	−0.0768605	−	3.49816i	−0.00478513	−	0.217786i
$259$	16.2518	−	5.28054i	1.00984	−	0.328117i
$260$		0			0
$261$	6.81378	−	0.299565i	0.421762	−	0.0185426i
$262$	3.23562	−	9.95822i	0.199897	−	0.615221i
$263$	−2.61887			−0.161486			−0.0807432	−	0.996735i	$-0.525729\pi$
$263$	−2.61887			−0.161486			−0.0807432	+	0.996735i	$0.525729\pi$
$264$	4.35333	−	12.8617i	0.267929	−	0.791582i
$265$		0			0
$266$	13.8451	−	42.6109i	0.848898	−	2.61264i
$267$	−13.5594	+	4.73745i	−0.829820	+	0.289927i
$268$	−1.60883	−	1.16889i	−0.0982751	−	0.0714010i
$269$	−10.0206	+	3.25591i	−0.610970	+	0.198516i	−0.598127	−	0.801401i	$-0.704088\pi$
$269$	−10.0206	+	3.25591i	−0.610970	+	0.198516i	−0.0128429	+	0.999918i	$0.504088\pi$
$270$		0			0
$271$	8.73559	−	12.0235i	0.530649	−	0.730376i	−0.456580	−	0.889682i	$-0.650926\pi$
$271$	8.73559	−	12.0235i	0.530649	−	0.730376i	0.987229	+	0.159306i	$0.0509257\pi$
$272$	0.990193	−	0.719417i	0.0600392	−	0.0436211i
$273$	2.45467	+	1.70231i	0.148563	+	0.103029i
$274$		−	2.52349i		−	0.152449i
$275$		0			0
$276$	−7.79731	−	2.34544i	−0.469343	−	0.141179i
$277$	−17.0928	−	5.55378i	−1.02701	−	0.333694i	−0.253400	−	0.967362i	$-0.581549\pi$
$277$	−17.0928	−	5.55378i	−1.02701	−	0.333694i	−0.773606	+	0.633667i	$0.781549\pi$
$278$	−22.6821	−	31.2192i	−1.36038	−	1.87240i
$279$	−7.25696	−	19.3917i	−0.434463	−	1.16095i
$280$		0			0
$281$	5.94778	+	18.3054i	0.354815	+	1.09201i	0.956117	+	0.292985i	$0.0946487\pi$
$281$	5.94778	+	18.3054i	0.354815	+	1.09201i	−0.601302	+	0.799022i	$0.705351\pi$
$282$	23.4465	+	30.8240i	1.39622	+	1.83554i
$283$	8.00884	+	11.0232i	0.476076	+	0.655263i	0.977745	−	0.209797i	$-0.0672804\pi$
$283$	8.00884	+	11.0232i	0.476076	+	0.655263i	−0.501669	+	0.865060i	$0.667280\pi$
$284$	34.7120	+	11.2786i	2.05978	+	0.669263i
$285$		0			0
$286$	−2.94278	−	1.06866i	−0.174010	−	0.0631909i
$287$			39.9242i			2.35665i
$288$	−15.2678	+	12.1521i	−0.899666	+	0.716072i
$289$	11.8147	−	8.58391i	0.694984	−	0.504936i
$290$		0			0
$291$	−20.7840	+	0.456661i	−1.21838	+	0.0267699i
$292$	39.4683	−	12.8240i	2.30971	−	0.750469i
$293$	12.7682	+	9.27667i	0.745929	+	0.541949i	0.894562	−	0.446944i	$-0.147488\pi$
$293$	12.7682	+	9.27667i	0.745929	+	0.541949i	−0.148634	+	0.988892i	$0.547488\pi$
$294$	12.6634	+	36.2447i	0.738543	+	2.11383i
$295$		0			0
$296$	−9.83630			−0.571723
$297$	−4.80290	+	16.5509i	−0.278692	+	0.960380i
$298$	40.8155			2.36438
$299$	−0.199932	+	0.615328i	−0.0115624	+	0.0355853i
$300$		0			0
$301$	−2.98595	−	2.16942i	−0.172107	−	0.125043i
$302$	11.2556	−	3.65718i	0.647690	−	0.210447i
$303$	−2.51582	+	0.0552768i	−0.144530	+	0.00317557i
$304$	2.25611	−	3.10526i	0.129397	−	0.178099i
$305$		0			0
$306$	8.16654	−	6.50000i	0.466850	−	0.371580i
$307$			29.8261i			1.70227i	0.524948	+	0.851134i	$0.324085\pi$
$307$			29.8261i			1.70227i	−0.524948	+	0.851134i	$0.675915\pi$
$308$	−23.2660	−	34.4391i	−1.32570	−	1.96235i
$309$	−6.30563	+	20.9628i	−0.358715	+	1.19253i
$310$		0			0
$311$	15.9782	+	21.9921i	0.906038	+	1.24705i	0.968502	+	0.249008i	$0.0801045\pi$
$311$	15.9782	+	21.9921i	0.906038	+	1.24705i	−0.0624630	+	0.998047i	$0.519896\pi$
$312$	−1.04100	−	1.36855i	−0.0589350	−	0.0774790i
$313$	−3.21787	−	9.90357i	−0.181885	−	0.559783i	0.817996	−	0.575224i	$-0.195085\pi$
$313$	−3.21787	−	9.90357i	−0.181885	−	0.559783i	−0.999881	+	0.0154405i	$0.995085\pi$
$314$	0.432785	+	1.33198i	0.0244235	+	0.0751678i
$315$		0			0
$316$	−6.85990	−	9.44184i	−0.385900	−	0.531145i
$317$	−23.4658	−	7.62451i	−1.31797	−	0.428235i	−0.436175	−	0.899862i	$-0.643667\pi$
$317$	−23.4658	−	7.62451i	−1.31797	−	0.428235i	−0.881798	+	0.471627i	$0.843667\pi$
$318$	−0.809611	−	0.243531i	−0.0454007	−	0.0136566i
$319$	−2.57373	+	7.08734i	−0.144101	+	0.396815i
$320$		0			0
$321$	−2.58722	−	1.79424i	−0.144405	−	0.100145i
$322$	−11.5024	+	8.35700i	−0.641005	+	0.465718i
$323$	−4.41690	+	6.07934i	−0.245763	+	0.338264i
$324$	−20.7171	+	18.0312i	−1.15095	+	1.00173i
$325$		0			0
$326$	8.74180	+	6.35129i	0.484164	+	0.351766i
$327$	12.6939	−	4.43506i	0.701973	−	0.245259i
$328$	7.10157	−	21.8564i	0.392118	−	1.20682i
$329$	40.8512			2.25220
$330$		0			0
$331$	−4.51243			−0.248025			−0.124013	−	0.992281i	$-0.539576\pi$
$331$	−4.51243			−0.248025			−0.124013	+	0.992281i	$0.539576\pi$
$332$	8.02975	−	24.7130i	0.440690	−	1.35630i
$333$	12.4721	−	0.548332i	0.683468	−	0.0300484i
$334$	−19.3476	−	14.0568i	−1.05865	−	0.769156i
$335$		0			0
$336$	0.123532	+	5.62232i	0.00673923	+	0.306723i
$337$	4.26628	−	5.87203i	0.232399	−	0.319870i	−0.676851	−	0.736120i	$-0.736656\pi$
$337$	4.26628	−	5.87203i	0.232399	−	0.319870i	0.909250	+	0.416250i	$0.136656\pi$
$338$	23.3177	−	16.9413i	1.26831	−	0.921484i
$339$	14.1770	−	20.4426i	0.769987	−	1.11029i
$340$		0			0
$341$	22.8770	+	0.782185i	1.23886	+	0.0423577i
$342$	18.0579	−	27.3005i	0.976461	−	1.47624i
$343$	11.1782	+	3.63203i	0.603568	+	0.196111i
$344$	1.24876	+	1.71877i	0.0673286	+	0.0926698i
$345$		0			0
$346$	1.56425	+	4.81426i	0.0840946	+	0.258816i
$347$	−6.61596	−	20.3618i	−0.355163	−	1.09308i	−0.955915	−	0.293644i	$-0.905132\pi$
$347$	−6.61596	−	20.3618i	−0.355163	−	1.09308i	0.600751	−	0.799436i	$-0.294868\pi$
$348$	−9.56416	+	7.27505i	−0.512693	+	0.389984i
$349$	6.01040	+	8.27261i	0.321729	+	0.442822i	0.938994	−	0.343933i	$-0.111759\pi$
$349$	6.01040	+	8.27261i	0.321729	+	0.442822i	−0.617265	+	0.786755i	$0.711759\pi$
$350$		0			0
$351$	1.39625	+	1.67725i	0.0745261	+	0.0895250i
$352$	−5.96147	−	20.7331i	−0.317748	−	1.10508i
$353$			28.5121i			1.51755i	0.651354	+	0.758774i	$0.274201\pi$
$353$			28.5121i			1.51755i	−0.651354	+	0.758774i	$0.725799\pi$
$354$	3.92313	−	5.65700i	0.208512	−	0.300666i
$355$		0			0
$356$	14.8746	−	20.4731i	0.788350	−	1.08507i
$357$	−0.241845	−	11.0071i	−0.0127998	−	0.582559i
$358$	−31.1033	+	10.1061i	−1.64386	+	0.534122i
$359$	20.5548	+	14.9340i	1.08484	+	0.788184i	0.978521	−	0.206148i	$-0.0660927\pi$
$359$	20.5548	+	14.9340i	1.08484	+	0.788184i	0.106322	+	0.994332i	$0.466093\pi$
$360$		0			0
$361$	−1.41084	+	4.34212i	−0.0742547	+	0.228533i
$362$	39.4582			2.07388
$363$	−14.8780	−	11.9015i	−0.780891	−	0.624667i
$364$	−5.26305			−0.275859
$365$		0			0
$366$	−6.35006	+	2.21862i	−0.331923	+	0.115969i
$367$	−6.22460	−	4.52244i	−0.324922	−	0.236069i	0.413351	−	0.910572i	$-0.364358\pi$
$367$	−6.22460	−	4.52244i	−0.324922	−	0.236069i	−0.738273	+	0.674502i	$0.764358\pi$
$368$	−1.15842	+	0.376393i	−0.0603867	+	0.0196208i
$369$	−7.78616	+	28.1091i	−0.405331	+	1.46330i
$370$		0			0
$371$	−0.721478	+	0.524185i	−0.0374573	+	0.0272143i
$372$	29.9767	+	20.7889i	1.55422	+	1.07785i
$373$		−	8.41462i		−	0.435692i	−0.975983	−	0.217846i	$-0.930097\pi$
$373$		−	8.41462i		−	0.435692i	0.975983	−	0.217846i	$-0.0699031\pi$
$374$	3.18870	+	11.0898i	0.164884	+	0.573441i
$375$		0			0
$376$	−22.3638	−	7.26645i	−1.15333	−	0.374739i
$377$	0.561239	+	0.772479i	0.0289053	+	0.0397847i
$378$	3.15833	+	47.8534i	0.162447	+	2.46132i
$379$	−9.75366	−	30.0187i	−0.501012	−	1.54196i	−0.807374	−	0.590040i	$-0.799112\pi$
$379$	−9.75366	−	30.0187i	−0.501012	−	1.54196i	0.306362	−	0.951915i	$-0.400888\pi$
$380$		0			0
$381$	−12.6705	−	16.6573i	−0.649130	−	0.853381i
$382$	2.01429	+	2.77243i	0.103060	+	0.141850i
$383$	−17.2529	−	5.60580i	−0.881581	−	0.286443i	−0.166968	−	0.985962i	$-0.553398\pi$
$383$	−17.2529	−	5.60580i	−0.881581	−	0.286443i	−0.714614	+	0.699519i	$0.753398\pi$
$384$	8.13009	−	27.0282i	0.414887	−	1.37928i
$385$		0			0
$386$			4.34023i			0.220912i
$387$	−1.67920	−	2.10973i	−0.0853586	−	0.107244i
$388$	29.6325	−	21.5293i	1.50436	−	1.09298i
$389$	−13.4063	+	18.4522i	−0.679726	+	0.935563i	−0.999931	−	0.0117856i	$-0.996248\pi$
$389$	−13.4063	+	18.4522i	−0.679726	+	0.935563i	0.320204	+	0.947349i	$0.396248\pi$
$390$		0			0
$391$	2.26790	−	0.736884i	0.114692	−	0.0372658i
$392$	−18.8594	−	13.7021i	−0.952543	−	0.692063i
$393$	−2.66142	−	7.61744i	−0.134251	−	0.384249i
$394$	−6.33159	+	19.4866i	−0.318981	+	0.981722i
$395$		0			0
$396$	−9.66424	−	28.7846i	−0.485647	−	1.44648i
$397$	16.7511			0.840711			0.420356	−	0.907359i	$-0.361905\pi$
$397$	16.7511			0.840711			0.420356	+	0.907359i	$0.361905\pi$
$398$	1.25716	−	3.86915i	0.0630159	−	0.193943i
$399$	−11.3881	−	32.5947i	−0.570120	−	1.63178i
$400$		0			0
$401$	8.17434	−	2.65600i	0.408207	−	0.132635i	−0.0977135	−	0.995215i	$-0.531153\pi$
$401$	8.17434	−	2.65600i	0.408207	−	0.132635i	0.505921	+	0.862580i	$0.331153\pi$
$402$	−2.53624	+	0.0557255i	−0.126496	+	0.00277933i
$403$	1.70380	−	2.34508i	0.0848723	−	0.116817i
$404$	3.58689	−	2.60603i	0.178454	−	0.129655i
$405$		0			0
$406$			20.9827i			1.04135i
$407$	−4.71103	+	12.9729i	−0.233517	+	0.643041i
$408$	−1.82551	+	6.06883i	−0.0903761	+	0.300452i
$409$	9.86047	+	3.20386i	0.487569	+	0.158421i	0.542477	−	0.840071i	$-0.317487\pi$
$409$	9.86047	+	3.20386i	0.487569	+	0.158421i	−0.0549082	+	0.998491i	$0.517487\pi$
$410$		0			0
$411$	−1.17733	−	1.54778i	−0.0580733	−	0.0763462i
$412$	−11.9184	−	36.6810i	−0.587176	−	1.80714i
$413$	−2.24397	−	6.90624i	−0.110419	−	0.339834i
$414$	−9.72822	+	3.64060i	−0.478116	+	0.178926i
$415$		0			0
$416$	−2.59816	−	0.844194i	−0.127385	−	0.0413900i
$417$	−28.4773	−	8.56598i	−1.39454	−	0.419478i
$418$	20.2574	+	29.9856i	0.990821	+	1.46664i
$419$		−	10.1665i		−	0.496664i	−0.968675	−	0.248332i	$-0.920118\pi$
$419$		−	10.1665i		−	0.496664i	0.968675	−	0.248332i	$-0.0798825\pi$
$420$		0			0
$421$	10.0413	−	7.29542i	0.489382	−	0.355557i	−0.315564	−	0.948904i	$-0.602194\pi$
$421$	10.0413	−	7.29542i	0.489382	−	0.355557i	0.804947	+	0.593347i	$0.202194\pi$
$422$	−32.9945	+	45.4131i	−1.60615	+	2.21067i
$423$	28.7617	+	7.96694i	1.39844	+	0.387366i
$424$	0.488211	−	0.158629i	0.0237096	−	0.00770372i
$425$		0			0
$426$	43.9546	−	15.3571i	2.12961	−	0.744055i
$427$	−2.19256	+	6.74799i	−0.106105	+	0.326558i
$428$	5.54726			0.268137
$429$	−2.30353	+	0.717490i	−0.111215	+	0.0346407i
$430$		0			0
$431$	−10.0425	+	30.9076i	−0.483730	+	1.48877i	0.350082	+	0.936719i	$0.386154\pi$
$431$	−10.0425	+	30.9076i	−0.483730	+	1.48877i	−0.833812	+	0.552049i	$0.813846\pi$
$432$	−1.00951	+	3.98255i	−0.0485701	+	0.191611i
$433$	−22.6062	−	16.4244i	−1.08639	−	0.789305i	−0.107600	−	0.994194i	$-0.534317\pi$
$433$	−22.6062	−	16.4244i	−1.08639	−	0.789305i	−0.978785	+	0.204889i	$0.934317\pi$
$434$	60.5812	−	19.6840i	2.90799	−	0.944863i
$435$		0			0
$436$	−13.9251	+	19.1663i	−0.666892	+	0.917898i
$437$	6.04997	−	4.39556i	0.289409	−	0.210268i
$438$	30.1690	−	43.5025i	1.44153	−	2.07863i
$439$			24.3322i			1.16131i	0.814148	+	0.580657i	$0.197204\pi$
$439$			24.3322i			1.16131i	−0.814148	+	0.580657i	$0.802796\pi$
$440$		0			0
$441$	24.6769	+	16.3226i	1.17509	+	0.777265i
$442$	1.38972	+	0.451547i	0.0661022	+	0.0214779i
$443$	2.86606	+	3.94480i	0.136171	+	0.187423i	0.871657	−	0.490117i	$-0.163046\pi$
$443$	2.86606	+	3.94480i	0.136171	+	0.187423i	−0.735486	+	0.677540i	$0.763046\pi$
$444$	−17.5065	+	13.3164i	−0.830822	+	0.631971i
$445$		0			0
$446$	−16.9969	−	52.3111i	−0.804827	−	2.47700i
$447$	25.0341	−	19.0424i	1.18407	−	0.900674i
$448$	−31.4698	−	43.3144i	−1.48681	−	2.04641i
$449$	0.710721	+	0.230927i	0.0335410	+	0.0108981i	0.325739	−	0.945460i	$-0.394387\pi$
$449$	0.710721	+	0.230927i	0.0335410	+	0.0108981i	−0.292198	+	0.956358i	$0.594387\pi$
$450$		0			0
$451$	−25.4246	−	19.8340i	−1.19720	−	0.933948i
$452$			43.8310i			2.06164i
$453$	5.19739	−	7.49443i	0.244195	−	0.352119i
$454$	20.8640	−	15.1586i	0.979197	−	0.711428i
$455$		0			0
$456$	0.436568	+	19.8696i	0.0204442	+	0.930477i
$457$	21.2899	−	6.91750i	0.995899	−	0.323587i	0.234673	−	0.972074i	$-0.424598\pi$
$457$	21.2899	−	6.91750i	0.995899	−	0.323587i	0.761226	+	0.648487i	$0.224598\pi$
$458$	−17.9405	−	13.0345i	−0.838303	−	0.609063i
$459$	1.97637	−	7.79685i	0.0922493	−	0.363926i
$460$		0			0
$461$	−6.12820			−0.285419			−0.142709	−	0.989765i	$-0.545581\pi$
$461$	−6.12820			−0.285419			−0.142709	+	0.989765i	$0.545581\pi$
$462$	−50.2203	−	16.9982i	−2.33646	−	0.790828i
$463$	11.6529			0.541555			0.270777	−	0.962642i	$-0.412719\pi$
$463$	11.6529			0.541555			0.270777	+	0.962642i	$0.412719\pi$
$464$	−0.555482	+	1.70960i	−0.0257876	+	0.0793661i
$465$		0			0
$466$	0.951323	+	0.691177i	0.0440692	+	0.0320181i
$467$	36.5845	−	11.8870i	1.69293	−	0.550066i	0.705580	−	0.708631i	$-0.250687\pi$
$467$	36.5845	−	11.8870i	1.69293	−	0.550066i	0.987349	+	0.158565i	$0.0506867\pi$
$468$	−3.70551	−	1.02642i	−0.171287	−	0.0474463i
$469$	−1.57287	+	2.16487i	−0.0726285	+	0.0999645i
$470$		0			0
$471$	0.886879	+	0.615051i	0.0408652	+	0.0283401i
$472$			4.17995i			0.192398i
$473$	2.86493	−	0.823765i	0.131729	−	0.0378768i
$474$	−14.2571	−	4.28855i	−0.654851	−	0.196979i
$475$		0			0
$476$	11.4018	+	15.6932i	0.522600	+	0.719298i
$477$	−0.610193	+	0.228353i	−0.0279388	+	0.0104556i
$478$	−2.65297	−	8.16502i	−0.121344	−	0.373459i
$479$	6.94651	+	21.3792i	0.317394	+	0.976839i	0.974758	+	0.223265i	$0.0716715\pi$
$479$	6.94651	+	21.3792i	0.317394	+	0.976839i	−0.657364	+	0.753573i	$0.728328\pi$
$480$		0			0
$481$	1.02731	+	1.41397i	0.0468412	+	0.0644714i
$482$	−42.4091	−	13.7795i	−1.93168	−	0.627641i
$483$	−3.15606	+	10.4922i	−0.143606	+	0.477411i
$484$	33.4899	+	2.29278i	1.52227	+	0.104217i
$485$		0			0
$486$	−7.10889	+	34.3077i	−0.322466	+	1.55623i
$487$	30.0136	−	21.8062i	1.36005	−	0.988131i	0.361604	−	0.932332i	$-0.382229\pi$
$487$	30.0136	−	21.8062i	1.36005	−	0.988131i	0.998442	−	0.0557991i	$-0.0177706\pi$
$488$	2.40061	−	3.30416i	0.108671	−	0.149572i
$489$	8.32496	−	0.182914i	0.376468	−	0.00827164i
$490$		0			0
$491$	21.7780	+	15.8227i	0.982828	+	0.714067i	0.958339	−	0.285633i	$-0.0922040\pi$
$491$	21.7780	+	15.8227i	0.982828	+	0.714067i	0.0244895	+	0.999700i	$0.492204\pi$
$492$	−16.9500	−	48.5138i	−0.764166	−	2.18717i
$493$	1.08750	−	3.34697i	0.0489784	−	0.150740i
$494$	4.58247			0.206175
$495$		0			0
$496$	5.45705			0.245029
$497$	15.1767	−	46.7091i	0.680768	−	2.09519i
$498$	−10.9334	−	31.2933i	−0.489938	−	1.40229i
$499$	24.1604	+	17.5535i	1.08157	+	0.785804i	0.977955	−	0.208814i	$-0.0669603\pi$
$499$	24.1604	+	17.5535i	1.08157	+	0.785804i	0.103611	+	0.994618i	$0.466960\pi$
$500$		0			0
$501$	−18.4250	+	0.404829i	−0.823169	+	0.0180864i
$502$	−11.7488	+	16.1709i	−0.524376	+	0.721741i
$503$	18.2128	−	13.2324i	0.812068	−	0.590002i	−0.102362	−	0.994747i	$-0.532640\pi$
$503$	18.2128	−	13.2324i	0.812068	−	0.590002i	0.914429	+	0.404745i	$0.132640\pi$
$504$	−18.1337	−	22.7831i	−0.807741	−	1.01484i
$505$		0			0
$506$	0.392398	−	11.4767i	0.0174442	−	0.510201i
$507$	6.39794	−	21.2697i	0.284143	−	0.944621i
$508$	35.0690	+	11.3946i	1.55594	+	0.505554i
$509$	−5.71179	−	7.86161i	−0.253171	−	0.348460i	0.663448	−	0.748223i	$-0.269092\pi$
$509$	−5.71179	−	7.86161i	−0.253171	−	0.348460i	−0.916619	+	0.399763i	$0.869092\pi$
$510$		0			0
$511$	−17.2562	−	53.1092i	−0.763371	−	2.34941i
$512$	−2.74435	−	8.44624i	−0.121284	−	0.373275i
$513$	−1.66120	−	25.1696i	−0.0733437	−	1.11127i
$514$	−0.355573	−	0.489405i	−0.0156837	−	0.0215867i
$515$		0			0
$516$	4.54940	+	1.36846i	0.200276	+	0.0602432i
$517$	−20.2946	+	26.0149i	−0.892553	+	1.14413i
$518$			38.4073i			1.68752i
$519$	3.20552	+	2.22303i	0.140707	+	0.0975800i
$520$		0			0
$521$	−4.08412	+	5.62131i	−0.178929	+	0.246274i	−0.889055	−	0.457800i	$-0.848638\pi$
$521$	−4.08412	+	5.62131i	−0.178929	+	0.246274i	0.710127	+	0.704074i	$0.248638\pi$
$522$	−4.09212	+	14.7731i	−0.179107	+	0.646600i
$523$	24.2067	−	7.86524i	1.05849	−	0.343923i	0.272493	−	0.962158i	$-0.412152\pi$
$523$	24.2067	−	7.86524i	1.05849	−	0.343923i	0.785993	+	0.618235i	$0.212152\pi$
$524$	11.5014	+	8.35629i	0.502443	+	0.365046i
$525$		0			0
$526$	1.81892	−	5.59806i	0.0793087	−	0.244087i
$527$	−10.6836			−0.465384
$528$	−3.64179	−	2.71446i	−0.158488	−	0.118132i
$529$	20.6269			0.896822
$530$		0			0
$531$	−0.233015	−	5.30004i	−0.0101120	−	0.230002i
$532$	49.2143	+	35.7563i	2.13371	+	1.55023i
$533$	−3.88354	+	1.26184i	−0.168215	+	0.0546563i
$534$	−0.709130	−	32.2747i	−0.0306870	−	1.39666i
$535$		0			0
$536$	1.24614	−	0.905376i	0.0538252	−	0.0391063i
$537$	−14.3622	+	20.7097i	−0.619774	+	0.893690i
$538$		−	23.6814i		−	1.02098i
$539$	−27.1040	+	18.3106i	−1.16745	+	0.788695i
$540$		0			0
$541$	5.71606	+	1.85726i	0.245753	+	0.0798499i	0.429303	−	0.903160i	$-0.358759\pi$
$541$	5.71606	+	1.85726i	0.245753	+	0.0798499i	−0.183551	+	0.983010i	$0.558759\pi$
$542$	19.6340	+	27.0239i	0.843354	+	1.16078i
$543$	24.2017	−	18.4092i	1.03859	−	0.790012i
$544$	3.11142	+	9.57598i	0.133401	+	0.410567i
$545$		0			0
$546$	−5.34371	+	4.06473i	−0.228690	+	0.173955i
$547$	16.2074	+	22.3075i	0.692977	+	0.953801i	0.999998	+	0.00209794i	$0.000667795\pi$
$547$	16.2074	+	22.3075i	0.692977	+	0.953801i	−0.307021	+	0.951703i	$0.599332\pi$
$548$	3.25857	+	1.05877i	0.139199	+	0.0452285i
$549$	−2.85971	+	4.32340i	−0.122050	+	0.184518i
$550$		0			0
$551$		−	11.0363i		−	0.470164i
$552$	3.59408	−	5.18253i	0.152974	−	0.220583i
$553$	−12.7051	+	9.23080i	−0.540276	+	0.392533i
$554$	23.7434	−	32.6799i	1.00876	−	1.38844i
$555$		0			0
$556$	49.8299	−	16.1907i	2.11326	−	0.686639i
$557$	−2.84006	−	2.06343i	−0.120337	−	0.0874302i	0.525989	−	0.850492i	$-0.323695\pi$
$557$	−2.84006	−	2.06343i	−0.120337	−	0.0874302i	−0.646326	+	0.763061i	$0.723695\pi$
$558$	46.4917	−	2.04399i	1.96815	−	0.0865290i
$559$	0.116652	−	0.359018i	0.00493385	−	0.0151848i
$560$		0			0
$561$	7.12972	+	5.31424i	0.301017	+	0.224367i
$562$	−43.2603			−1.82483
$563$	3.50120	−	10.7756i	0.147558	−	0.454136i	−0.849773	−	0.527148i	$-0.823261\pi$
$563$	3.50120	−	10.7756i	0.147558	−	0.454136i	0.997331	+	0.0730122i	$0.0232612\pi$
$564$	−49.6402	+	17.3436i	−2.09023	+	0.730297i
$565$		0			0
$566$	−29.1256	+	9.46347i	−1.22424	+	0.397779i
$567$	24.2631	+	27.8773i	1.01895	+	1.17074i
$568$	−16.6169	+	22.8712i	−0.697228	+	0.959652i
$569$	−2.66042	+	1.93291i	−0.111530	+	0.0810316i	−0.642152	−	0.766577i	$-0.721958\pi$
$569$	−2.66042	+	1.93291i	−0.111530	+	0.0810316i	0.530622	+	0.847609i	$0.321958\pi$
$570$		0			0
$571$			30.6612i			1.28313i	0.767068	+	0.641566i	$0.221715\pi$
$571$			30.6612i			1.28313i	−0.767068	+	0.641566i	$0.778285\pi$
$572$	2.61464	−	3.35163i	0.109324	−	0.140139i
$573$	2.52893	+	0.760705i	0.105648	+	0.0317789i
$574$	−85.3414	−	27.7291i	−3.56208	−	1.15739i
$575$		0			0
$576$	−13.7093	−	36.6333i	−0.571221	−	1.52639i
$577$	2.84802	+	8.76530i	0.118565	+	0.364904i	0.992674	−	0.120825i	$-0.0385541\pi$
$577$	2.84802	+	8.76530i	0.118565	+	0.364904i	−0.874109	+	0.485729i	$0.838554\pi$
$578$	10.1430	+	31.2169i	0.421893	+	1.29845i
$579$	2.02492	+	2.66207i	0.0841530	+	0.110632i
$580$		0			0
$581$	−33.2543	−	10.8050i	−1.37962	−	0.448266i
$582$	13.4593	−	44.7448i	0.557905	−	1.85473i
$583$	0.0246128	−	0.719864i	0.00101936	−	0.0298137i
$584$			32.1439i			1.33013i
$585$		0			0
$586$	−28.6978	+	20.8502i	−1.18549	+	0.861312i
$587$	7.14042	−	9.82794i	0.294717	−	0.405642i	−0.635822	−	0.771835i	$-0.719339\pi$
$587$	7.14042	−	9.82794i	0.294717	−	0.405642i	0.930539	+	0.366193i	$0.119339\pi$
$588$	−52.1157	+	1.14507i	−2.14922	+	0.0472220i
$589$	−31.8641	+	10.3533i	−1.31294	+	0.426599i
$590$		0			0
$591$	5.20797	+	14.9061i	0.214227	+	0.613154i
$592$	−1.01677	+	3.12930i	−0.0417890	+	0.128613i
$593$	−15.9770			−0.656098			−0.328049	−	0.944661i	$-0.606391\pi$
$593$	−15.9770			−0.656098			−0.328049	+	0.944661i	$0.606391\pi$
$594$	−32.0431	−	21.7619i	−1.31475	−	0.892903i
$595$		0			0
$596$	−17.1249	+	52.7049i	−0.701461	+	2.15888i
$597$	−1.03406	−	2.95966i	−0.0423214	−	0.121131i
$598$	−1.17645	−	0.854744i	−0.0481088	−	0.0349531i
$599$	−34.7597	+	11.2941i	−1.42024	+	0.461465i	−0.915680	−	0.401909i	$-0.868347\pi$
$599$	−34.7597	+	11.2941i	−1.42024	+	0.461465i	−0.504564	+	0.863374i	$0.668347\pi$
$600$		0			0
$601$	−13.2813	+	18.2801i	−0.541755	+	0.745662i	−0.988865	−	0.148817i	$-0.952453\pi$
$601$	−13.2813	+	18.2801i	−0.541755	+	0.745662i	0.447109	+	0.894479i	$0.352453\pi$
$602$	6.71118	−	4.87596i	0.273527	−	0.198729i
$603$	−1.52960	+	1.21746i	−0.0622901	+	0.0495786i
$604$			16.0688i			0.653830i
$605$		0			0
$606$	1.62919	−	5.41617i	0.0661812	−	0.220017i
$607$	17.9973	+	5.84767i	0.730488	+	0.237350i	0.650564	−	0.759451i	$-0.274532\pi$
$607$	17.9973	+	5.84767i	0.730488	+	0.237350i	0.0799233	+	0.996801i	$0.474532\pi$
$608$	18.5598	+	25.5454i	0.752701	+	1.03600i
$609$	9.78943	+	12.8697i	0.396688	+	0.521507i
$610$		0			0
$611$	1.29114	+	3.97371i	0.0522338	+	0.160759i
$612$	4.96701	+	13.2726i	0.200779	+	0.536513i
$613$	21.7426	+	29.9261i	0.878175	+	1.20870i	0.976923	+	0.213592i	$0.0685162\pi$
$613$	21.7426	+	29.9261i	0.878175	+	1.20870i	−0.0987480	+	0.995112i	$0.531484\pi$
$614$	−63.7559	−	20.7156i	−2.57298	−	0.836012i
$615$		0			0
$616$	30.9384	−	8.89587i	1.24655	−	0.358425i
$617$			29.5786i			1.19079i	0.803433	+	0.595395i	$0.203004\pi$
$617$			29.5786i			1.19079i	−0.803433	+	0.595395i	$0.796996\pi$
$618$	−40.4303	−	28.0384i	−1.62634	−	1.12787i
$619$	−32.8748	+	23.8849i	−1.32135	+	0.960017i	−0.321435	+	0.946932i	$0.604165\pi$
$619$	−32.8748	+	23.8849i	−1.32135	+	0.960017i	−0.999914	+	0.0130852i	$0.995835\pi$
$620$		0			0
$621$	−4.26828	+	6.77164i	−0.171280	+	0.271737i
$622$	−58.1074	+	18.8802i	−2.32990	+	0.757029i
$623$	−27.5489	−	20.0154i	−1.10372	−	0.801902i
$624$	−0.542995	+	0.189715i	−0.0217372	+	0.00759467i
$625$		0			0
$626$	23.4047			0.935439
$627$	26.4146	+	8.94061i	1.05490	+	0.357053i
$628$	−1.90156			−0.0758804
$629$	1.99059	−	6.12639i	0.0793698	−	0.244275i
$630$		0			0
$631$	20.9393	+	15.2133i	0.833581	+	0.605632i	0.920570	−	0.390578i	$-0.127725\pi$
$631$	20.9393	+	15.2133i	0.833581	+	0.605632i	−0.0869895	+	0.996209i	$0.527725\pi$
$632$	8.59731	−	2.79343i	0.341982	−	0.111117i
$633$	0.950224	+	43.2476i	0.0377680	+	1.71894i
$634$	32.5961	−	44.8647i	1.29456	−	1.78180i
$635$		0			0
$636$	0.654157	−	0.943269i	0.0259390	−	0.0374031i
$637$			4.14209i			0.164116i
$638$	−13.3622	−	10.4240i	−0.529015	−	0.412691i
$639$	19.7947	−	29.9262i	0.783066	−	1.18386i
$640$		0			0
$641$	1.71576	+	2.36154i	0.0677684	+	0.0932752i	0.841556	−	0.540170i	$-0.181640\pi$
$641$	1.71576	+	2.36154i	0.0677684	+	0.0932752i	−0.773787	+	0.633445i	$0.781640\pi$
$642$	5.63227	−	4.28423i	0.222288	−	0.169085i
$643$	14.4945	+	44.6095i	0.571607	+	1.75923i	0.647452	+	0.762106i	$0.275834\pi$
$643$	14.4945	+	44.6095i	0.571607	+	1.75923i	−0.0758453	+	0.997120i	$0.524166\pi$
$644$	−5.96532	−	18.3594i	−0.235066	−	0.723460i
$645$		0			0
$646$	−9.92739	−	13.6639i	−0.390588	−	0.537598i
$647$	22.4433	+	7.29226i	0.882336	+	0.286688i	0.714927	−	0.699199i	$-0.246460\pi$
$647$	22.4433	+	7.29226i	0.882336	+	0.286688i	0.167409	+	0.985888i	$0.446460\pi$
$648$	−8.32403	−	19.5772i	−0.326999	−	0.769064i
$649$	5.51283	+	2.00196i	0.216398	+	0.0785837i
$650$		0			0
$651$	27.9739	−	40.3372i	1.09638	−	1.58094i
$652$	−11.8692	+	8.62346i	−0.464833	+	0.337721i
$653$	−16.6547	+	22.9233i	−0.651751	+	0.897058i	−0.999173	−	0.0406508i	$-0.987057\pi$
$653$	−16.6547	+	22.9233i	−0.651751	+	0.897058i	0.347423	+	0.937709i	$0.387057\pi$
$654$	0.663866	+	30.2146i	0.0259592	+	1.18148i
$655$		0			0
$656$	−6.21925	−	4.51855i	−0.242821	−	0.176420i
$657$	−1.79189	−	40.7575i	−0.0699083	−	1.59010i
$658$	−28.3729	+	87.3229i	−1.10609	+	3.40420i
$659$	−24.7031			−0.962295			−0.481148	−	0.876640i	$-0.659780\pi$
$659$	−24.7031			−0.962295			−0.481148	+	0.876640i	$0.659780\pi$
$660$		0			0
$661$	39.9917			1.55550			0.777749	−	0.628575i	$-0.216361\pi$
$661$	39.9917			1.55550			0.777749	+	0.628575i	$0.216361\pi$
$662$	3.13408	−	9.64570i	0.121809	−	0.374891i
$663$	1.06305	−	0.371415i	0.0412855	−	0.0144246i
$664$	16.2830	+	11.8303i	0.631903	+	0.459104i
$665$		0			0
$666$	−7.49032	+	27.0411i	−0.290244	+	1.04782i
$667$	−2.05855	+	2.83335i	−0.0797074	+	0.109708i
$668$	26.2691	−	19.0856i	1.01638	−	0.738446i
$669$	−34.8307	−	24.1551i	−1.34663	−	0.933890i
$670$		0			0
$671$	−3.20802	−	4.74862i	−0.123844	−	0.183318i
$672$	−44.3023	−	13.3262i	−1.70900	−	0.514068i
$673$	−37.0371	−	12.0341i	−1.42768	−	0.463880i	−0.509644	−	0.860385i	$-0.670223\pi$
$673$	−37.0371	−	12.0341i	−1.42768	−	0.463880i	−0.918032	+	0.396505i	$0.870223\pi$
$674$	9.58884	+	13.1979i	0.369348	+	0.508364i
$675$		0			0
$676$	12.0929	+	37.2180i	0.465110	+	1.43146i
$677$	2.13505	+	6.57101i	0.0820566	+	0.252544i	0.983665	−	0.180009i	$-0.0576127\pi$
$677$	2.13505	+	6.57101i	0.0820566	+	0.252544i	−0.901608	+	0.432553i	$0.857613\pi$
$678$	33.8513	+	44.5028i	1.30005	+	1.70912i
$679$	−28.9702	−	39.8740i	−1.11177	−	1.53022i
$680$		0			0
$681$	5.72471	−	19.0316i	0.219371	−	0.729291i
$682$	−17.5611	+	48.3583i	−0.672448	+	1.85173i
$683$		−	8.95570i		−	0.342680i	−0.985212	−	0.171340i	$-0.945190\pi$
$683$		−	8.95570i		−	0.342680i	0.985212	−	0.171340i	$-0.0548097\pi$
$684$	27.6765	+	34.7725i	1.05824	+	1.32956i
$685$		0			0
$686$	−15.5276	+	21.3718i	−0.592845	+	0.815981i
$687$	−17.0850	+	0.375387i	−0.651833	+	0.0143219i
$688$	0.675888	−	0.219609i	0.0257680	−	0.00837253i
$689$	−0.0737919	−	0.0536130i	−0.00281125	−	0.00204249i
$690$		0			0
$691$	3.93150	−	12.0999i	0.149561	−	0.460303i	−0.848008	−	0.529984i	$-0.822198\pi$
$691$	3.93150	−	12.0999i	0.149561	−	0.460303i	0.997569	+	0.0696809i	$0.0221981\pi$
$692$	−6.87295			−0.261270
$693$	−38.7331	+	13.0044i	−1.47135	+	0.493995i
$694$	48.1202			1.82662
$695$		0			0
$696$	−3.06998	−	8.78678i	−0.116367	−	0.333062i
$697$	12.1758	+	8.84621i	0.461190	+	0.335074i
$698$	−21.8579	+	7.10206i	−0.827333	+	0.268817i
$699$	0.905960	−	0.0199055i	0.0342666	−	0.000752895i
$700$		0			0
$701$	−13.2606	+	9.63436i	−0.500844	+	0.363885i	−0.809339	−	0.587341i	$-0.800175\pi$
$701$	−13.2606	+	9.63436i	−0.500844	+	0.363885i	0.308495	+	0.951226i	$0.400175\pi$
$702$	−4.55502	+	1.81967i	−0.171918	+	0.0686790i
$703$		−	20.2012i		−	0.761903i
$704$	43.2175	+	1.47765i	1.62882	+	0.0556908i
$705$		0			0
$706$	−60.9471	−	19.8029i	−2.29378	−	0.745293i
$707$	−3.50671	−	4.82657i	−0.131883	−	0.181522i
$708$	5.65884	+	7.43941i	0.212672	+	0.279590i
$709$	−1.31727	−	4.05414i	−0.0494711	−	0.152256i	0.923269	−	0.384154i	$-0.125507\pi$
$709$	−1.31727	−	4.05414i	−0.0494711	−	0.152256i	−0.972740	+	0.231897i	$0.925507\pi$
$710$		0			0
$711$	−10.7454	+	4.02125i	−0.402984	+	0.150809i
$712$	11.5213	+	15.8577i	0.431778	+	0.594292i
$713$	10.1116	+	3.28545i	0.378682	+	0.123041i
$714$	23.6966	+	7.12796i	0.886824	+	0.266757i
$715$		0			0
$716$		−	44.4037i		−	1.65944i
$717$	−5.43657	−	3.77026i	−0.203032	−	0.140803i
$718$	−46.1988	+	33.5654i	−1.72413	+	1.25265i
$719$	27.2462	−	37.5012i	1.01611	−	1.39856i	0.101218	−	0.994864i	$-0.467726\pi$
$719$	27.2462	−	37.5012i	1.01611	−	1.39856i	0.914894	−	0.403694i	$-0.132274\pi$
$720$		0			0
$721$	−49.3585	+	16.0376i	−1.83821	+	0.597270i
$722$	−8.30176	−	6.03158i	−0.308960	−	0.224472i
$723$	−32.4404	+	11.3342i	−1.20647	+	0.421524i
$724$	−16.5554	+	50.9522i	−0.615276	+	1.89362i
$725$		0			0
$726$	35.7739	−	23.5368i	1.32769	−	0.873533i
$727$	4.89596			0.181581			0.0907906	−	0.995870i	$-0.471061\pi$
$727$	4.89596			0.181581			0.0907906	+	0.995870i	$0.471061\pi$
$728$	1.25973	−	3.87705i	0.0466887	−	0.143693i
$729$	11.6460	+	24.3592i	0.431332	+	0.902193i
$730$		0			0
$731$	−1.32322	+	0.429941i	−0.0489411	+	0.0159019i
$732$	−0.200616	−	9.13067i	−0.00741500	−	0.337479i
$733$	18.8805	−	25.9868i	0.697368	−	0.959844i	−0.302610	−	0.953115i	$-0.597858\pi$
$733$	18.8805	−	25.9868i	0.697368	−	0.959844i	0.999977	−	0.00672965i	$-0.00214213\pi$
$734$	13.9904	−	10.1646i	0.516394	−	0.375182i
$735$		0			0
$736$		−	10.0201i		−	0.369347i
$737$	−0.597247	−	2.07713i	−0.0219999	−	0.0765121i
$738$	−54.6777	−	36.1666i	−2.01272	−	1.33131i
$739$	31.9298	+	10.3746i	1.17456	+	0.381637i	0.830342	−	0.557254i	$-0.188145\pi$
$739$	31.9298	+	10.3746i	1.17456	+	0.381637i	0.344215	+	0.938891i	$0.388145\pi$
$740$		0			0
$741$	2.81065	−	2.13794i	0.103252	−	0.0785393i
$742$	−0.619391	−	1.90629i	−0.0227386	−	0.0699821i
$743$	−12.6813	−	39.0290i	−0.465232	−	1.43184i	−0.858691	−	0.512494i	$-0.828722\pi$
$743$	−12.6813	−	39.0290i	−0.465232	−	1.43184i	0.393459	−	0.919342i	$-0.371278\pi$
$744$	−22.4892	+	17.1066i	−0.824495	+	0.627158i
$745$		0			0
$746$	17.9870	+	5.84432i	0.658549	+	0.213976i
$747$	−21.3058	−	14.0927i	−0.779539	−	0.515626i
$748$	−15.6581	−	0.535365i	−0.572517	−	0.0195749i
$749$		−	7.46448i		−	0.272746i
$750$		0			0
$751$	−14.2284	+	10.3375i	−0.519202	+	0.377222i	−0.816303	−	0.577624i	$-0.803980\pi$
$751$	−14.2284	+	10.3375i	−0.519202	+	0.377222i	0.297101	+	0.954846i	$0.403980\pi$
$752$	−4.62346	+	6.36365i	−0.168600	+	0.232058i
$753$	0.338359	+	15.3998i	0.0123305	+	0.561199i
$754$	−2.04105	+	0.663176i	−0.0743305	+	0.0241514i
$755$		0			0
$756$	−63.1181	−	15.9994i	−2.29558	−	0.581892i
$757$	13.5175	−	41.6026i	0.491302	−	1.51207i	−0.331340	−	0.943511i	$-0.607501\pi$
$757$	13.5175	−	41.6026i	0.491302	−	1.51207i	0.822642	−	0.568560i	$-0.192499\pi$
$758$	70.9418			2.57672
$759$	−5.11375	−	7.22229i	−0.185617	−	0.262152i
$760$		0			0
$761$	15.1277	−	46.5582i	0.548378	−	1.68773i	−0.164441	−	0.986387i	$-0.552582\pi$
$761$	15.1277	−	46.5582i	0.548378	−	1.68773i	0.712819	−	0.701348i	$-0.247418\pi$
$762$	44.4067	−	15.5151i	1.60868	−	0.562051i
$763$	25.7905	+	18.7379i	0.933678	+	0.678356i
$764$	−4.42516	+	1.43782i	−0.160097	+	0.0520185i
$765$		0			0
$766$	23.9658	−	32.9860i	0.865918	−	1.19183i
$767$	0.600867	−	0.436556i	0.0216961	−	0.0157631i
$768$	15.0143	+	10.4124i	0.541781	+	0.375725i
$769$		−	12.5601i		−	0.452930i	−0.974019	−	0.226465i	$-0.927283\pi$
$769$		−	12.5601i		−	0.452930i	0.974019	−	0.226465i	$-0.0727169\pi$
$770$		0			0
$771$	−0.446421	−	0.134284i	−0.0160775	−	0.00483611i
$772$	−5.60451	−	1.82102i	−0.201711	−	0.0655398i
$773$	4.87069	+	6.70392i	0.175186	+	0.241123i	0.887577	−	0.460660i	$-0.152387\pi$
$773$	4.87069	+	6.70392i	0.175186	+	0.241123i	−0.712390	+	0.701784i	$0.752387\pi$
$774$	5.67601	−	2.12413i	0.204020	−	0.0763504i
$775$		0			0
$776$	8.76698	+	26.9820i	0.314716	+	0.968597i
$777$	17.9188	+	23.5571i	0.642835	+	0.845105i
$778$	−30.1319	−	41.4730i	−1.08028	−	1.48688i
$779$	44.8873	+	14.5848i	1.60826	+	0.522554i
$780$		0			0
$781$	22.2057	+	32.8696i	0.794581	+	1.17617i
$782$			5.35962i			0.191660i
$783$	4.38246	+	10.9702i	0.156616	+	0.392044i
$784$	−6.30865	+	4.58350i	−0.225309	+	0.163696i
$785$		0			0
$786$	18.1314	−	0.398378i	0.646726	−	0.0142097i
$787$	−5.62071	+	1.82628i	−0.200356	+	0.0650998i	−0.407476	−	0.913216i	$-0.633591\pi$
$787$	−5.62071	+	1.82628i	−0.200356	+	0.0650998i	0.207120	+	0.978316i	$0.433591\pi$
$788$	−22.5065	−	16.3519i	−0.801759	−	0.582512i
$789$	−1.49613	−	4.28218i	−0.0532637	−	0.152450i
$790$		0			0
$791$	58.9798			2.09708
$792$	23.5175	−	0.229509i	0.835656	−	0.00815523i
$793$	−0.725694			−0.0257702
$794$	−11.6343	+	35.8068i	−0.412887	+	1.27074i
$795$		0			0
$796$	4.46875	+	3.24674i	0.158391	+	0.115078i
$797$	−42.4902	+	13.8059i	−1.50508	+	0.489030i	−0.941495	−	0.337027i	$-0.890579\pi$
$797$	−42.4902	+	13.8059i	−1.50508	+	0.489030i	−0.563586	+	0.826057i	$0.690579\pi$
$798$	77.5836	−	1.70464i	2.74643	−	0.0603438i
$799$	9.05160	−	12.4585i	0.320223	−	0.440749i
$800$		0			0
$801$	−15.4926	−	19.4648i	−0.547405	−	0.687754i
$802$			19.3181i			0.682145i
$803$	42.3939	+	15.3951i	1.49605	+	0.543282i
$804$	0.992164	−	3.29841i	0.0349909	−	0.116326i
$805$		0			0
$806$	3.82944	+	5.27077i	0.134886	+	0.185655i
$807$	−11.0485	−	14.5249i	−0.388925	−	0.511302i
$808$	1.06120	+	3.26605i	0.0373331	+	0.114899i
$809$	−6.35086	−	19.5459i	−0.223284	−	0.687198i	−0.998461	−	0.0554542i	$-0.982339\pi$
$809$	−6.35086	−	19.5459i	−0.223284	−	0.687198i	0.775177	−	0.631744i	$-0.217661\pi$
$810$		0			0
$811$	14.2447	+	19.6061i	0.500199	+	0.688465i	0.982228	−	0.187690i	$-0.0601001\pi$
$811$	14.2447	+	19.6061i	0.500199	+	0.688465i	−0.482029	+	0.876155i	$0.660100\pi$
$812$	−27.0948	−	8.80365i	−0.950842	−	0.308947i
$813$	24.6505	+	7.41487i	0.864530	+	0.260051i
$814$	−24.4586	−	19.0804i	−0.857273	−	0.668769i
$815$		0			0
$816$	1.74202	+	1.20809i	0.0609830	+	0.0422917i
$817$	−3.52991	+	2.56463i	−0.123496	+	0.0897249i
$818$	−13.6970	+	18.8524i	−0.478906	+	0.659158i
$819$	−1.38117	+	4.98620i	−0.0482619	+	0.174232i
$820$		0			0
$821$	−19.3665	−	14.0706i	−0.675895	−	0.491066i	0.196099	−	0.980584i	$-0.437173\pi$
$821$	−19.3665	−	14.0706i	−0.675895	−	0.491066i	−0.871993	+	0.489518i	$0.837173\pi$
$822$	4.12621	−	1.44164i	0.143918	−	0.0502829i
$823$	10.6897	−	32.8996i	0.372620	−	1.14681i	−0.572450	−	0.819940i	$-0.694007\pi$
$823$	10.6897	−	32.8996i	0.372620	−	1.14681i	0.945070	−	0.326868i	$-0.105993\pi$
$824$	29.8739			1.04071
$825$		0			0
$826$	16.3212			0.567888
$827$	2.34430	−	7.21501i	0.0815193	−	0.250891i	−0.901987	−	0.431762i	$-0.857892\pi$
$827$	2.34430	−	7.21501i	0.0815193	−	0.250891i	0.983507	+	0.180872i	$0.0578919\pi$
$828$	−0.619439	−	14.0895i	−0.0215270	−	0.489644i
$829$	23.2437	+	16.8875i	0.807286	+	0.586528i	0.913042	−	0.407865i	$-0.133726\pi$
$829$	23.2437	+	16.8875i	0.807286	+	0.586528i	−0.105757	+	0.994392i	$0.533726\pi$
$830$		0			0
$831$	−0.683796	−	31.1216i	−0.0237206	−	1.07960i
$832$	3.21869	−	4.43015i	0.111588	−	0.153588i
$833$	12.3508	−	8.97336i	0.427929	−	0.310909i
$834$	38.0892	−	54.9232i	1.31892	−	1.90183i
$835$		0			0
$836$	−47.2196	+	13.5773i	−1.63312	+	0.469580i
$837$	27.5620	−	22.9443i	0.952682	−	0.793071i
$838$	21.7317	+	7.06106i	0.750709	+	0.243920i
$839$	16.0357	+	22.0712i	0.553614	+	0.761984i	0.990497	−	0.137534i	$-0.0439178\pi$
$839$	16.0357	+	22.0712i	0.553614	+	0.761984i	−0.436883	+	0.899518i	$0.643918\pi$
$840$		0			0
$841$	−7.36431	−	22.6650i	−0.253942	−	0.781552i
$842$	8.62048	+	26.5311i	0.297081	+	0.914322i
$843$	−26.5336	+	20.1830i	−0.913867	+	0.695140i
$844$	−44.7983	−	61.6595i	−1.54202	−	2.12241i
$845$		0			0
$846$	−37.0063	+	55.9473i	−1.27230	+	1.92351i
$847$	3.08520	−	45.0646i	0.106009	−	1.54844i
$848$		−	0.171716i		−	0.00589674i
$849$	−13.4490	+	19.3929i	−0.461568	+	0.665562i
$850$		0			0
$851$	−3.76803	+	5.18624i	−0.129166	+	0.177782i
$852$	1.38865	+	63.2018i	0.0475744	+	2.16526i
$853$	−20.5047	+	6.66237i	−0.702066	+	0.228115i	−0.638231	−	0.769845i	$-0.720333\pi$
$853$	−20.5047	+	6.66237i	−0.702066	+	0.228115i	−0.0638357	+	0.997960i	$0.520333\pi$
$854$	−12.9016	−	9.37355i	−0.441483	−	0.320756i
$855$		0			0
$856$	−1.32775	+	4.08641i	−0.0453817	+	0.139671i
$857$	−22.1220			−0.755673			−0.377837	−	0.925872i	$-0.623332\pi$
$857$	−22.1220			−0.755673			−0.377837	+	0.925872i	$0.623332\pi$
$858$	0.0662066	−	5.42232i	0.00226026	−	0.185115i
$859$	−46.0605			−1.57156			−0.785782	−	0.618504i	$-0.787739\pi$
$859$	−46.0605			−1.57156			−0.785782	+	0.618504i	$0.787739\pi$
$860$		0			0
$861$	−65.2810	+	22.8083i	−2.22477	+	0.777303i
$862$	−59.0927	−	42.9334i	−2.01271	−	1.46232i
$863$	−17.5560	+	5.70429i	−0.597613	+	0.194176i	−0.592176	−	0.805809i	$-0.701731\pi$
$863$	−17.5560	+	5.70429i	−0.597613	+	0.194176i	−0.00543755	+	0.999985i	$0.501731\pi$
$864$	−28.5926	−	18.0224i	−0.972740	−	0.613135i
$865$		0			0
$866$	50.8095	−	36.9153i	1.72658	−	1.25443i
$867$	20.7854	+	14.4147i	0.705908	+	0.489548i
$868$			86.4870i			2.93556i
$869$	0.433427	−	12.6767i	0.0147030	−	0.430027i
$870$		0			0
$871$	−0.260295	−	0.0845751i	−0.00881977	−	0.00286572i
$872$	−10.7859	−	14.8455i	−0.365256	−	0.502732i
$873$	−12.6204	−	33.7236i	−0.427135	−	1.14137i
$874$	5.19392	+	15.9852i	0.175687	+	0.540709i
$875$		0			0
$876$	43.5167	+	57.2093i	1.47029	+	1.93292i
$877$	8.76894	+	12.0694i	0.296106	+	0.407555i	0.930985	−	0.365056i	$-0.118950\pi$
$877$	8.76894	+	12.0694i	0.296106	+	0.407555i	−0.634879	+	0.772611i	$0.718950\pi$
$878$	−52.0122	−	16.8998i	−1.75533	−	0.570340i
$879$	−7.87415	+	26.1773i	−0.265588	+	0.882939i
$880$		0			0
$881$			1.77914i			0.0599409i	0.999551	+	0.0299704i	$0.00954131\pi$
$881$			1.77914i			0.0599409i	−0.999551	+	0.0299704i	$0.990459\pi$
$882$	−52.0301	+	41.4124i	−1.75194	+	1.39443i
$883$	15.1704	−	11.0220i	0.510526	−	0.370919i	−0.302497	−	0.953150i	$-0.597820\pi$
$883$	15.1704	−	11.0220i	0.510526	−	0.370919i	0.813023	+	0.582231i	$0.197820\pi$
$884$	−1.16616	+	1.60508i	−0.0392222	+	0.0539848i
$885$		0			0
$886$	−10.4229	+	3.38662i	−0.350166	+	0.113776i
$887$	−31.8926	−	23.1713i	−1.07085	−	0.778017i	−0.0947835	−	0.995498i	$-0.530216\pi$
$887$	−31.8926	−	23.1713i	−1.07085	−	0.778017i	−0.976064	+	0.217481i	$0.930216\pi$
$888$	−5.61937	−	16.0836i	−0.188574	−	0.539729i
$889$	15.3328	−	47.1894i	0.514245	−	1.58268i
$890$		0			0
$891$	−29.8066	+	1.60201i	−0.998559	+	0.0536693i
$892$	74.6805			2.50049
$893$	14.9234	−	45.9295i	0.499393	−	1.53697i
$894$	23.3174	+	66.7384i	0.779852	+	2.23207i
$895$		0			0
$896$	63.6399	−	20.6779i	2.12606	−	0.690798i
$897$	−1.12036	+	0.0246161i	−0.0374076	+	0.000821909i
$898$	−0.987254	+	1.35884i	−0.0329451	+	0.0453450i
$899$	12.6940	−	9.22276i	0.423370	−	0.307596i
$900$		0			0
$901$			0.336177i			0.0111997i
$902$	60.0554	−	40.5716i	1.99963	−	1.35089i
$903$	1.84143	−	6.12175i	0.0612789	−	0.203719i
$904$	−32.2883	−	10.4911i	−1.07389	−	0.348929i
$905$		0			0
$906$	12.4102	+	16.3151i	0.412300	+	0.542032i
$907$	6.37992	+	19.6354i	0.211842	+	0.651982i	0.999363	+	0.0356942i	$0.0113642\pi$
$907$	6.37992	+	19.6354i	0.211842	+	0.651982i	−0.787521	+	0.616288i	$0.788636\pi$
$908$	10.8204	+	33.3017i	0.359086	+	1.10515i
$909$	−1.52764	−	4.08209i	−0.0506687	−	0.135395i
$910$		0			0
$911$	−4.06381	−	1.32041i	−0.134640	−	0.0437471i	0.240922	−	0.970544i	$-0.422550\pi$
$911$	−4.06381	−	1.32041i	−0.134640	−	0.0437471i	−0.375562	+	0.926797i	$0.622550\pi$
$912$	6.36638	+	1.91501i	0.210812	+	0.0634123i
$913$	23.4013	−	15.8092i	0.774470	−	0.523209i
$914$			50.3135i			1.66422i
$915$		0			0
$916$	24.3586	−	17.6976i	0.804832	−	0.584745i
$917$	11.2444	−	15.4765i	0.371322	−	0.511080i
$918$	15.2938	+	9.63992i	0.504769	+	0.318165i
$919$	−25.1872	+	8.18381i	−0.830849	+	0.269959i	−0.693403	−	0.720550i	$-0.743889\pi$
$919$	−25.1872	+	8.18381i	−0.830849	+	0.269959i	−0.137446	+	0.990509i	$0.543889\pi$
$920$		0			0
$921$	−48.7694	+	17.0393i	−1.60701	+	0.561465i
$922$	4.25630	−	13.0996i	0.140174	−	0.431411i
$923$	5.02320			0.165341
$924$	43.0205	−	57.7174i	1.41527	−	1.89876i
$925$		0			0
$926$	−8.09343	+	24.9090i	−0.265966	+	0.818561i
$927$	−37.8791	+	1.66534i	−1.24411	+	0.0546970i
$928$	−11.9636	−	8.69203i	−0.392723	−	0.285330i
$929$	7.40448	−	2.40586i	0.242933	−	0.0789337i	−0.185020	−	0.982735i	$-0.559235\pi$
$929$	7.40448	−	2.40586i	0.242933	−	0.0789337i	0.427953	+	0.903801i	$0.359235\pi$
$930$		0			0
$931$	28.1407	−	38.7323i	0.922273	−	1.26940i
$932$	−1.29166	+	0.938444i	−0.0423096	+	0.0307398i
$933$	−26.8316	+	38.6901i	−0.878427	+	1.26666i
$934$			86.4585i			2.82901i
$935$		0			0
$936$	1.64304	−	2.48400i	0.0537045	−	0.0811921i
$937$	−36.0757	−	11.7217i	−1.17854	−	0.382931i	−0.346717	−	0.937970i	$-0.612704\pi$
$937$	−36.0757	−	11.7217i	−1.17854	−	0.382931i	−0.831825	+	0.555038i	$0.812704\pi$
$938$	−3.53517	−	4.86575i	−0.115427	−	0.158872i
$939$	14.3552	−	10.9194i	0.468465	−	0.356341i
$940$		0			0
$941$	6.90820	+	21.2613i	0.225201	+	0.693097i	0.998271	+	0.0587768i	$0.0187200\pi$
$941$	6.90820	+	21.2613i	0.225201	+	0.693097i	−0.773070	+	0.634320i	$0.781280\pi$
$942$	−1.93070	+	1.46860i	−0.0629056	+	0.0478496i
$943$	−8.80347	−	12.1169i	−0.286680	−	0.394582i
$944$	1.32980	+	0.432078i	0.0432812	+	0.0140629i
$945$		0			0
$946$	−0.228948	+	6.69617i	−0.00744374	+	0.217711i
$947$		−	4.51042i		−	0.146569i	−0.997311	−	0.0732844i	$-0.976652\pi$
$947$		−	4.51042i		−	0.146569i	0.997311	−	0.0732844i	$-0.0233481\pi$
$948$	11.5196	−	16.6108i	0.374139	−	0.539494i
$949$	4.62069	−	3.35713i	0.149994	−	0.108977i
$950$		0			0
$951$	−0.938749	−	42.7253i	−0.0304410	−	1.38546i
$952$	−14.2895	+	4.64295i	−0.463126	+	0.150479i
$953$	14.7032	+	10.6825i	0.476284	+	0.346041i	0.799885	−	0.600153i	$-0.204894\pi$
$953$	14.7032	+	10.6825i	0.476284	+	0.346041i	−0.323601	+	0.946194i	$0.604894\pi$
$954$	−0.0643177	−	1.46294i	−0.00208236	−	0.0473645i
$955$		0			0
$956$	11.6565			0.377000
$957$	−13.0590	−	0.159451i	−0.422138	−	0.00515431i
$958$	−50.5244			−1.63237
$959$	1.42470	−	4.38478i	0.0460060	−	0.141592i
$960$		0			0
$961$	−13.4568	−	9.77693i	−0.434090	−	0.315385i
$962$	−3.73599	+	1.21390i	−0.120453	+	0.0391376i
$963$	1.45575	−	5.25545i	0.0469109	−	0.169355i
$964$	35.5869	−	48.9812i	1.14618	−	1.57758i
$965$		0			0
$966$	−20.2359	−	14.0336i	−0.651081	−	0.451525i
$967$			7.36207i			0.236748i	0.992969	+	0.118374i	$0.0377682\pi$
$967$			7.36207i			0.236748i	−0.992969	+	0.118374i	$0.962232\pi$
$968$	−9.70490	+	24.1217i	−0.311927	+	0.775300i
$969$	−12.4638	−	3.74912i	−0.400395	−	0.120439i
$970$		0			0
$971$	−31.4990	−	43.3547i	−1.01085	−	1.39132i	−0.918423	−	0.395600i	$-0.870537\pi$
$971$	−31.4990	−	43.3547i	−1.01085	−	1.39132i	−0.0924296	−	0.995719i	$-0.529463\pi$
$972$	−41.3187	−	23.5741i	−1.32530	−	0.756138i
$973$	−21.7865	−	67.0519i	−0.698443	−	2.14959i
$974$	25.7668	+	79.3019i	0.825620	+	2.54100i
$975$		0			0
$976$	−0.803029	−	1.10527i	−0.0257043	−	0.0353790i
$977$	34.6954	+	11.2732i	1.11000	+	0.360662i	0.805944	−	0.591991i	$-0.201658\pi$
$977$	34.6954	+	11.2732i	1.11000	+	0.360662i	0.304059	+	0.952653i	$0.401658\pi$
$978$	−5.39105	+	17.9224i	−0.172387	+	0.573094i
$979$	26.4324	−	7.60021i	0.844782	−	0.242904i
$980$		0			0
$981$	14.5037	+	18.2224i	0.463069	+	0.581795i
$982$	−48.9481	+	35.5629i	−1.56200	+	1.13486i
$983$	−10.6166	+	14.6125i	−0.338618	+	0.466067i	−0.944037	−	0.329839i	$-0.893005\pi$
$983$	−10.6166	+	14.6125i	−0.338618	+	0.466067i	0.605419	+	0.795907i	$0.293005\pi$
$984$	39.7949	−	0.874363i	1.26862	−	0.0278737i
$985$		0			0
$986$	6.39913	+	4.64924i	0.203790	+	0.148062i
$987$	23.3378	+	66.7967i	0.742851	+	2.12616i
$988$	−1.92265	+	5.91732i	−0.0611678	+	0.188255i
$989$	1.38460			0.0440276
$990$		0			0
$991$	−25.3541			−0.805398			−0.402699	−	0.915332i	$-0.631928\pi$
$991$	−25.3541			−0.805398			−0.402699	+	0.915332i	$0.631928\pi$
$992$	−13.8725	+	42.6952i	−0.440453	+	1.35557i
$993$	−2.57790	−	7.37837i	−0.0818071	−	0.234146i
$994$	89.3037	+	64.8830i	2.83254	+	2.05796i
$995$		0			0
$996$	44.9962	−	0.988643i	1.42576	−	0.0313264i
$997$	−3.14457	+	4.32813i	−0.0995897	+	0.137073i	−0.855904	−	0.517136i	$-0.826998\pi$
$997$	−3.14457	+	4.32813i	−0.0995897	+	0.137073i	0.756314	+	0.654209i	$0.226998\pi$
$998$	−54.3026	+	39.4532i	−1.71892	+	1.24887i
$999$	8.02177	+	20.0802i	0.253798	+	0.635309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bi.h.101.1		80
3.2	odd	2	inner	825.2.bi.h.101.19		80
5.2	odd	4		165.2.r.a.134.2	yes	80
5.3	odd	4		165.2.r.a.134.19	yes	80
5.4	even	2	inner	825.2.bi.h.101.20		80
11.6	odd	10	inner	825.2.bi.h.776.19		80
15.2	even	4		165.2.r.a.134.20	yes	80
15.8	even	4		165.2.r.a.134.1	✓	80
15.14	odd	2	inner	825.2.bi.h.101.2		80
33.17	even	10	inner	825.2.bi.h.776.1		80
55.17	even	20		165.2.r.a.149.1	yes	80
55.28	even	20		165.2.r.a.149.20	yes	80
55.39	odd	10	inner	825.2.bi.h.776.2		80
165.17	odd	20		165.2.r.a.149.19	yes	80
165.83	odd	20		165.2.r.a.149.2	yes	80
165.149	even	10	inner	825.2.bi.h.776.20		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.r.a.134.1	✓	80	15.8	even	4
165.2.r.a.134.2	yes	80	5.2	odd	4
165.2.r.a.134.19	yes	80	5.3	odd	4
165.2.r.a.134.20	yes	80	15.2	even	4
165.2.r.a.149.1	yes	80	55.17	even	20
165.2.r.a.149.2	yes	80	165.83	odd	20
165.2.r.a.149.19	yes	80	165.17	odd	20
165.2.r.a.149.20	yes	80	55.28	even	20
825.2.bi.h.101.1		80	1.1	even	1	trivial
825.2.bi.h.101.2		80	15.14	odd	2	inner
825.2.bi.h.101.19		80	3.2	odd	2	inner
825.2.bi.h.101.20		80	5.4	even	2	inner
825.2.bi.h.776.1		80	33.17	even	10	inner
825.2.bi.h.776.2		80	55.39	odd	10	inner
825.2.bi.h.776.19		80	11.6	odd	10	inner
825.2.bi.h.776.20		80	165.149	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.694544 + 2.13759i) q^{2} +(0.571289 + 1.63512i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.89200 + 0.0855139i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(1.91228 - 1.38935i) q^{8} +(-2.34726 + 1.86826i) q^{9} +O(q^{10})\)	\(q+(-0.694544 + 2.13759i) q^{2} +(0.571289 + 1.63512i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.89200 + 0.0855139i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(1.91228 - 1.38935i) q^{8} +(-2.34726 + 1.86826i) q^{9} +(-0.916510 - 3.18748i) q^{11} +(1.52253 - 5.06160i) q^{12} +(-0.399438 - 0.129785i) q^{13} +(-5.42493 - 7.46677i) q^{14} +(-0.244334 - 0.751983i) q^{16} +(0.478346 + 1.47220i) q^{17} +(-2.36328 - 6.31505i) q^{18} +(2.85337 + 3.92732i) q^{19} +(-6.81098 - 2.04875i) q^{21} +(7.45006 + 0.254724i) q^{22} -1.54048i q^{23} +(3.36422 + 2.33309i) q^{24} +(0.554855 - 0.763692i) q^{26} +(-4.39579 - 2.77074i) q^{27} +(11.9179 - 3.87237i) q^{28} +(-1.83926 - 1.33630i) q^{29} +(-2.13274 + 6.56391i) q^{31} +6.50454 q^{32} +(4.68833 - 3.31958i) q^{33} -3.47918 q^{34} +(9.14615 - 0.402107i) q^{36} +(-3.36663 - 2.44600i) q^{37} +(-10.3768 + 3.37162i) q^{38} +(-0.0159795 - 0.727276i) q^{39} +(7.86568 - 5.71475i) q^{41} +(9.10989 - 13.1361i) q^{42} +0.898807i q^{43} +(-3.45473 + 9.51336i) q^{44} +(3.29291 + 1.06993i) q^{46} +(-5.84743 - 8.04830i) q^{47} +(1.09000 - 0.829116i) q^{48} +(-3.04761 - 9.37957i) q^{49} +(-2.13395 + 1.62321i) q^{51} +(0.753353 + 1.03690i) q^{52} +(0.206545 + 0.0671104i) q^{53} +(8.97577 - 7.47198i) q^{54} +9.70625i q^{56} +(-4.79156 + 6.90924i) q^{57} +(4.13391 - 3.00346i) q^{58} +(-1.03943 + 1.43066i) q^{59} +(1.64330 - 0.533940i) q^{61} +(-12.5496 - 9.11784i) q^{62} +(-0.541082 - 12.3072i) q^{63} +(-4.02902 + 12.4000i) q^{64} +(3.83963 + 12.3273i) q^{66} +0.651654 q^{67} +(1.45975 - 4.49265i) q^{68} +(2.51888 - 0.880060i) q^{69} +(-11.3748 + 3.69589i) q^{71} +(-1.89295 + 6.83379i) q^{72} +(-7.99327 + 11.0018i) q^{73} +(7.56681 - 5.49761i) q^{74} -14.8141i q^{76} +(12.8013 + 4.64874i) q^{77} +(1.56571 + 0.470967i) q^{78} +(3.63722 + 1.18180i) q^{79} +(2.01924 - 8.77056i) q^{81} +(6.75271 + 20.7827i) q^{82} +(2.63127 + 8.09822i) q^{83} +(13.1404 + 17.2750i) q^{84} +(-1.92128 - 0.624261i) q^{86} +(1.13427 - 3.77083i) q^{87} +(-6.18115 - 4.82199i) q^{88} +8.29256i q^{89} +(1.39527 - 1.01372i) q^{91} +(-2.76320 + 3.80322i) q^{92} +(-11.9512 + 0.262589i) q^{93} +(21.2652 - 6.90949i) q^{94} +(3.71597 + 10.6357i) q^{96} +(-3.70900 + 11.4151i) q^{97} +22.1663 q^{98} +(8.10631 + 5.76956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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