LMFDB - Embedded newform 825.2.bi.h.101.19

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			101.19
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.h.776.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694544 - 2.13759i) q^{2} +(-1.37856 - 1.04861i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.19896 + 2.21848i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(-1.91228 + 1.38935i) q^{8} +(0.800839 + 2.89113i) q^{9} +O(q^{10})$	\(q+(0.694544 - 2.13759i) q^{2} +(-1.37856 - 1.04861i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.19896 + 2.21848i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(-1.91228 + 1.38935i) q^{8} +(0.800839 + 2.89113i) 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} +(6.73626 + 0.296157i) q^{18} +(2.85337 + 3.92732i) q^{19} +(6.81098 - 2.04875i) q^{21} +(7.45006 + 0.254724i) q^{22} +1.54048i q^{23} +(4.09307 + 0.0899318i) q^{24} +(-0.554855 + 0.763692i) q^{26} +(1.92767 - 4.82536i) q^{27} +(11.9179 - 3.87237i) q^{28} +(1.83926 + 1.33630i) q^{29} +(-2.13274 + 6.56391i) q^{31} -6.50454 q^{32} +(2.07896 - 5.35518i) q^{33} -3.47918 q^{34} +(3.20874 - 8.57425i) q^{36} +(-3.36663 - 2.44600i) q^{37} +(10.3768 - 3.37162i) q^{38} +(0.414554 + 0.597771i) q^{39} +(-7.86568 + 5.71475i) q^{41} +(0.351152 - 15.9820i) q^{42} +0.898807i q^{43} +(3.45473 - 9.51336i) q^{44} +(3.29291 + 1.06993i) q^{46} +(5.84743 + 8.04830i) q^{47} +(-0.451708 + 1.29286i) q^{48} +(-3.04761 - 9.37957i) q^{49} +(-0.884333 + 2.53111i) q^{51} +(0.753353 + 1.03690i) q^{52} +(-0.206545 - 0.0671104i) q^{53} +(-8.97577 - 7.47198i) q^{54} -9.70625i q^{56} +(0.184697 - 8.40611i) 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} +(-11.5377 - 4.31774i) q^{63} +(-4.02902 + 12.4000i) q^{64} +(-10.0032 - 8.16335i) q^{66} +0.651654 q^{67} +(-1.45975 + 4.49265i) q^{68} +(1.61536 - 2.12364i) q^{69} +(11.3748 - 3.69589i) q^{71} +(-5.54823 - 4.41601i) 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} +(-7.71731 + 4.63066i) q^{81} +(6.75271 + 20.7827i) q^{82} +(-2.63127 - 8.09822i) q^{83} +(-20.4901 - 7.15896i) 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} +(9.82308 - 6.81231i) q^{93} +(21.2652 - 6.90949i) q^{94} +(8.96688 + 6.82072i) q^{96} +(-3.70900 + 11.4151i) q^{97} -22.1663 q^{98} +(-8.48145 + 5.20241i) 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	$-0.607658\pi$
$2$	0.694544	−	2.13759i	0.491116	−	1.51150i	0.822923	−	0.568154i	$-0.192342\pi$
$3$	−1.37856	−	1.04861i	−0.795910	−	0.605415i
$3$	−1.37856	−	1.04861i	−0.795910	−	0.605415i
$4$	−2.46885	−	1.79372i	−1.23442	−	0.896861i
$5$		0			0
$5$		0			0
$6$	−3.19896	+	2.21848i	−1.30597	+	0.905690i
$7$	−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
$9$	0.800839	+	2.89113i	0.266946	+	0.963711i
$10$		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	0.876142	−	0.482054i	$-0.160109\pi$
$17$	−0.478346	−	1.47220i	−0.116016	−	0.357061i	−0.992158	+	0.124993i	$0.960109\pi$
$18$	6.73626	+	0.296157i	1.58775	+	0.0698050i
$19$	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	$0.0513450\pi$
$23$			1.54048i			0.321213i	−0.987019	+	0.160606i	$0.948655\pi$
$24$	4.09307	+	0.0899318i	0.835495	+	0.0183572i
$25$		0			0
$26$	−0.554855	+	0.763692i	−0.108816	+	0.149772i
$27$	1.92767	−	4.82536i	0.370980	−	0.928641i
$28$	11.9179	−	3.87237i	2.25228	−	0.731809i
$29$	1.83926	+	1.33630i	0.341542	+	0.248145i	0.745312	−	0.666716i	$-0.232300\pi$
$29$	1.83926	+	1.33630i	0.341542	+	0.248145i	−0.403770	+	0.914861i	$0.632300\pi$
$30$		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
$33$	2.07896	−	5.35518i	0.361900	−	0.932217i
$34$	−3.47918			−0.596675
$35$		0			0
$36$	3.20874	−	8.57425i	0.534791	−	1.42904i
$37$	−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
$39$	0.414554	+	0.597771i	0.0663818	+	0.0957200i
$40$		0			0
$41$	−7.86568	+	5.71475i	−1.22841	+	0.892494i	−0.996770	−	0.0803075i	$-0.974410\pi$
$41$	−7.86568	+	5.71475i	−1.22841	+	0.892494i	−0.231642	+	0.972801i	$0.574410\pi$
$42$	0.351152	−	15.9820i	0.0541839	−	2.46607i
$43$			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	$0.0584149\pi$
$47$	5.84743	+	8.04830i	0.852936	+	1.17397i	−0.130272	+	0.991478i	$0.541585\pi$
$48$	−0.451708	+	1.29286i	−0.0651984	+	0.186609i
$49$	−3.04761	−	9.37957i	−0.435372	−	1.33994i
$50$		0			0
$51$	−0.884333	+	2.53111i	−0.123831	+	0.354426i
$52$	0.753353	+	1.03690i	0.104471	+	0.143792i
$53$	−0.206545	−	0.0671104i	−0.0283711	−	0.00921833i	0.294797	−	0.955560i	$-0.404748\pi$
$53$	−0.206545	−	0.0671104i	−0.0283711	−	0.00921833i	−0.323168	+	0.946342i	$0.604748\pi$
$54$	−8.97577	−	7.47198i	−1.22145	−	1.01681i
$55$		0			0
$56$		−	9.70625i		−	1.29705i
$57$	0.184697	−	8.40611i	0.0244637	−	1.11342i
$58$	4.13391	−	3.00346i	0.542809	−	0.394373i
$59$	1.03943	−	1.43066i	0.135323	−	0.186255i	−0.735978	−	0.677006i	$-0.763277\pi$
$59$	1.03943	−	1.43066i	0.135323	−	0.186255i	0.871300	+	0.490750i	$0.163277\pi$
$60$		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
$63$	−11.5377	−	4.31774i	−1.45361	−	0.543984i
$64$	−4.02902	+	12.4000i	−0.503627	+	1.55001i
$65$		0			0
$66$	−10.0032	−	8.16335i	−1.23131	−	1.00484i
$67$	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
$69$	1.61536	−	2.12364i	0.194467	−	0.255657i
$70$		0			0
$71$	11.3748	−	3.69589i	1.34994	−	0.438622i	0.457267	−	0.889329i	$-0.348828\pi$
$71$	11.3748	−	3.69589i	1.34994	−	0.438622i	0.892672	+	0.450708i	$0.148828\pi$
$72$	−5.54823	−	4.41601i	−0.653865	−	0.520431i
$73$	−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
$81$	−7.71731	+	4.63066i	−0.857479	+	0.514518i
$82$	6.75271	+	20.7827i	0.745712	+	2.29506i
$83$	−2.63127	−	8.09822i	−0.288820	−	0.888895i	−0.985228	−	0.171249i	$-0.945220\pi$
$83$	−2.63127	−	8.09822i	−0.288820	−	0.888895i	0.696408	−	0.717646i	$-0.254780\pi$
$84$	−20.4901	−	7.15896i	−2.23566	−	0.781107i
$85$		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	$-0.855154\pi$
$89$		−	8.29256i		−	0.879010i	0.898240	−	0.439505i	$-0.144846\pi$
$90$		0			0
$91$	1.39527	−	1.01372i	0.146264	−	0.106267i
$92$	2.76320	−	3.80322i	0.288083	−	0.396513i
$93$	9.82308	−	6.81231i	1.01861	−	0.706404i
$94$	21.2652	−	6.90949i	2.19334	−	0.712660i
$95$		0			0
$96$	8.96688	+	6.82072i	0.915178	+	0.696137i
$97$	−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
$99$	−8.48145	+	5.20241i	−0.852418	+	0.522862i
$100$		0			0
$101$	0.448958	−	1.38175i	0.0446730	−	0.137489i	−0.926232	−	0.376953i	$-0.876972\pi$
$101$	0.448958	−	1.38175i	0.0446730	−	0.137489i	0.970905	+	0.239464i	$0.0769717\pi$
$102$	4.79625	+	3.64830i	0.474900	+	0.361236i
$103$	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	−0.514427	−	0.857534i	$-0.671995\pi$
$107$	1.47062	−	1.06847i	0.142170	−	0.103292i	0.656597	+	0.754242i	$0.271995\pi$
$108$	−13.4145	+	8.45537i	−1.29081	+	0.813619i
$109$		−	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	$0.0361062\pi$
$113$	8.44236	+	11.6199i	0.794191	+	1.09311i	−0.199383	+	0.979922i	$0.563894\pi$
$114$	−17.8405	−	6.23321i	−1.67091	−	0.583794i
$115$		0			0
$116$	−2.14390	−	6.59825i	−0.199056	−	0.612632i
$117$	0.0553412	−	1.25877i	0.00511630	−	0.116373i
$118$	−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
$123$	16.8358	+	0.369912i	1.51803	+	0.0333538i
$124$	17.0392	−	12.3797i	1.53017	−	1.11173i
$125$		0			0
$126$	−17.2429	+	21.6639i	−1.53612	+	1.92997i
$127$	−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
$129$	0.942497	−	1.23906i	0.0829822	−	0.109093i
$130$		0			0
$131$	4.65863			0.407026			0.203513	−	0.979072i	$-0.434764\pi$
$131$	4.65863			0.407026			0.203513	+	0.979072i	$0.434764\pi$
$132$	−14.7383	+	9.49205i	−1.28281	+	0.826177i
$133$	−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	−0.263047	−	0.964783i	$-0.584727\pi$
$137$	1.06780	−	0.346949i	0.0912283	−	0.0296419i	0.354276	+	0.935141i	$0.384727\pi$
$138$	−3.41753	−	4.92794i	−0.290919	−	0.419494i
$139$	−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
$141$	0.378500	−	17.2267i	0.0318755	−	1.45075i
$142$		−	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
$147$	−5.63420	+	16.1260i	−0.464701	+	1.33005i
$148$	3.92425	+	12.0776i	0.322572	+	0.992774i
$149$	5.61165	+	17.2709i	0.459724	+	1.41489i	0.865498	+	0.500912i	$0.167002\pi$
$149$	5.61165	+	17.2709i	0.459724	+	1.41489i	−0.405774	+	0.913973i	$0.632998\pi$
$150$		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
$156$	0.0487640	−	2.21940i	0.00390425	−	0.177694i
$157$	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
$159$	0.214361	+	0.309100i	0.0169999	+	0.0245132i
$160$		0			0
$161$	−5.11767	−	3.71821i	−0.403329	−	0.293036i
$162$	4.53843	+	19.7126i	0.356573	+	1.54877i
$163$	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	$-0.764941\pi$
$167$	3.28802	−	10.1195i	0.254434	−	0.783069i	0.993941	−	0.109919i	$-0.0350591\pi$
$168$	−10.1781	+	13.3806i	−0.785254	+	1.03234i
$169$	−10.3745	−	7.53753i	−0.798040	−	0.579810i
$170$		0			0
$171$	−9.06933	+	11.3946i	−0.693549	+	0.871368i
$172$	1.61221	−	2.21902i	0.122930	−	0.169198i
$173$	−1.82207	+	1.32381i	−0.138529	+	0.100647i	−0.654892	−	0.755723i	$-0.727286\pi$
$173$	−1.82207	+	1.32381i	−0.138529	+	0.100647i	0.516362	+	0.856370i	$0.327286\pi$
$174$	−8.84828	−	0.194412i	−0.670786	−	0.0147383i
$175$		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	0.359320	−	0.933215i	$-0.383009\pi$
$179$	−8.55266	−	11.7717i	−0.639256	−	0.879860i	−0.998576	+	0.0533542i	$0.983009\pi$
$180$		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
$183$	−2.82528	−	0.987111i	−0.208850	−	0.0729694i
$184$	−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
$189$	11.3777	+	18.0507i	0.827606	+	1.31300i
$190$		0			0
$191$	−0.896200	+	1.23351i	−0.0648467	+	0.0892539i	−0.840209	−	0.542263i	$-0.817568\pi$
$191$	−0.896200	+	1.23351i	−0.0648467	+	0.0892539i	0.775362	+	0.631517i	$0.217568\pi$
$192$	18.5570	−	12.8693i	1.33924	−	0.928762i
$193$	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	$-0.605280\pi$
$197$	−9.11618			−0.649501			−0.324751	+	0.945800i	$0.605280\pi$
$198$	5.22986	+	21.7431i	0.371670	+	1.54522i
$199$	−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
$201$	−0.898342	−	0.683330i	−0.0633641	−	0.0481984i
$202$	−2.64179	−	1.91937i	−0.185876	−	0.135047i
$203$	−8.87871	+	2.88487i	−0.623164	+	0.202478i
$204$	6.72339	−	4.66267i	0.470731	−	0.326452i
$205$		0			0
$206$	22.9812	−	16.6968i	1.60118	−	1.16332i
$207$	−4.45374	+	1.23368i	−0.309556	+	0.0857466i
$208$			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
$213$	−19.5563	−	6.83270i	−1.33998	−	0.468169i
$214$	−1.26253	−	3.88566i	−0.0863047	−	0.265619i
$215$		0			0
$216$	3.01788	+	11.9056i	0.205341	+	0.810076i
$217$	−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
$222$	16.1961	+	0.355857i	1.08701	+	0.0238835i
$223$	−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	0.851565	−	0.524249i	$-0.175654\pi$
$227$	9.28284	+	6.74438i	0.616124	+	0.447640i	−0.235442	+	0.971888i	$0.575654\pi$
$228$	−15.5342	+	20.4221i	−1.02878	+	1.35249i
$229$	−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
$231$	12.7727	+	19.8321i	0.840379	+	1.30486i
$232$	−5.37377			−0.352805
$233$	−0.161672	+	0.497576i	−0.0105915	+	0.0325973i	−0.956213	−	0.292673i	$-0.905455\pi$
$233$	−0.161672	+	0.497576i	−0.0105915	+	0.0325973i	0.945621	+	0.325270i	$0.105455\pi$
$234$	−2.65229	−	0.992565i	−0.173385	−	0.0648860i
$235$		0			0
$236$	−5.13240	+	1.66762i	−0.334091	+	0.108553i
$237$	−3.77486	−	5.44320i	−0.245203	−	0.353574i
$238$	8.39757	−	11.5583i	0.544334	−	0.749211i
$239$	3.09023	−	2.24519i	0.199891	−	0.145229i	−0.483337	−	0.875434i	$-0.660576\pi$
$239$	3.09023	−	2.24519i	0.199891	−	0.145229i	0.683228	+	0.730205i	$0.260576\pi$
$240$		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
$246$	12.4839	−	35.7311i	0.795946	−	2.27813i
$247$	−0.630035	−	1.93905i	−0.0400882	−	0.123379i
$248$	−5.04118	−	15.5152i	−0.320115	−	0.985213i
$249$	−4.86451	+	13.9230i	−0.308276	+	0.882337i
$250$		0			0
$251$	−8.45794	−	2.74815i	−0.533861	−	0.173462i	0.0296658	−	0.999560i	$-0.490556\pi$
$251$	−8.45794	−	2.74815i	−0.533861	−	0.173462i	−0.563526	+	0.826098i	$0.690556\pi$
$252$	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	−0.804054	−	0.594556i	$-0.797328\pi$
$257$	0.158202	−	0.217746i	0.00986837	−	0.0135827i	0.813923	+	0.580973i	$0.197328\pi$
$258$	−1.99398	−	2.87525i	−0.124140	−	0.179005i
$259$	16.2518	−	5.28054i	1.00984	−	0.328117i
$260$		0			0
$261$	−2.39048	+	6.38771i	−0.147967	+	0.395390i
$262$	3.23562	−	9.95822i	0.199897	−	0.615221i
$263$	2.61887			0.161486			0.0807432	−	0.996735i	$-0.474271\pi$
$263$	2.61887			0.161486			0.0807432	+	0.996735i	$0.474271\pi$
$264$	3.46468	+	13.1290i	0.213236	+	0.808034i
$265$		0			0
$266$	−13.8451	+	42.6109i	−0.848898	+	2.61264i
$267$	−8.69565	+	11.4318i	−0.532165	+	0.699613i
$268$	−1.60883	−	1.16889i	−0.0982751	−	0.0714010i
$269$	10.0206	−	3.25591i	0.610970	−	0.198516i	0.0128429	−	0.999918i	$-0.495912\pi$
$269$	10.0206	−	3.25591i	0.610970	−	0.198516i	0.598127	+	0.801401i	$0.295912\pi$
$270$		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
$273$	−2.98646	−	0.0656177i	−0.180749	−	0.00397136i
$274$		−	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
$279$	−20.6851	−	0.909414i	−1.23839	−	0.0544452i
$280$		0			0
$281$	−5.94778	−	18.3054i	−0.354815	−	1.09201i	−0.956117	−	0.292985i	$-0.905351\pi$
$281$	−5.94778	−	18.3054i	−0.354815	−	1.09201i	0.601302	−	0.799022i	$-0.294649\pi$
$282$	−36.5607	−	12.7738i	−2.17716	−	0.760668i
$283$	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
$288$	−5.20909	−	18.8055i	−0.306949	−	1.10812i
$289$	11.8147	−	8.58391i	0.694984	−	0.504936i
$290$		0			0
$291$	17.0831	−	11.8471i	1.00143	−	0.694490i
$292$	39.4683	−	12.8240i	2.30971	−	0.750469i
$293$	−12.7682	−	9.27667i	−0.745929	−	0.541949i	0.148634	−	0.988892i	$-0.452512\pi$
$293$	−12.7682	−	9.27667i	−0.745929	−	0.541949i	−0.894562	+	0.446944i	$0.852512\pi$
$294$	30.5575	+	23.2438i	1.78215	+	1.35561i
$295$		0			0
$296$	9.83630			0.571723
$297$	17.1474	+	1.72191i	0.994996	+	0.0999151i
$298$	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
$303$	−2.06783	+	1.43404i	−0.118794	+	0.0823835i
$304$	2.25611	−	3.10526i	0.129397	−	0.178099i
$305$		0			0
$306$	−2.78626	−	10.0588i	−0.159280	−	0.575022i
$307$			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	$-0.919896\pi$
$311$	−15.9782	−	21.9921i	−0.906038	−	1.24705i	0.0624630	−	0.998047i	$-0.480104\pi$
$312$	−1.62326	−	0.567143i	−0.0918989	−	0.0321081i
$313$	−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	0.881798	−	0.471627i	$-0.156333\pi$
$317$	23.4658	+	7.62451i	1.31797	+	0.428235i	0.436175	+	0.899862i	$0.356333\pi$
$318$	0.809611	−	0.243531i	0.0454007	−	0.0136566i
$319$	−2.57373	+	7.08734i	−0.144101	+	0.396815i
$320$		0			0
$321$	−3.14773	−	0.0691610i	−0.175689	−	0.00386019i
$322$	−11.5024	+	8.35700i	−0.641005	+	0.465718i
$323$	4.41690	−	6.07934i	0.245763	−	0.338264i
$324$	27.3590	+	2.41032i	1.51994	+	0.133906i
$325$		0			0
$326$	−8.74180	−	6.35129i	−0.484164	−	0.351766i
$327$	−8.14061	+	10.7021i	−0.450177	+	0.591827i
$328$	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
$333$	4.37559	−	11.6922i	0.239781	−	0.640731i
$334$	−19.3476	−	14.0568i	−1.05865	−	0.769156i
$335$		0			0
$336$	−3.20478	−	4.62116i	−0.174835	−	0.252105i
$337$	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
$339$	0.546468	−	24.8714i	0.0296801	−	1.35083i
$340$		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	$0.0948681\pi$
$347$	6.61596	+	20.3618i	0.355163	+	1.09308i	−0.600751	+	0.799436i	$0.705132\pi$
$348$	−3.96349	+	11.3442i	−0.212465	+	0.608112i
$349$	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	$-0.725799\pi$
$353$		−	28.5121i		−	1.51755i	0.651354	−	0.758774i	$-0.274201\pi$
$354$	−0.151222	+	6.88257i	−0.00803735	+	0.365804i
$355$		0			0
$356$	−14.8746	+	20.4731i	−0.788350	+	1.08507i
$357$	−6.27417	−	9.04710i	−0.332064	−	0.478823i
$358$	−31.1033	+	10.1061i	−1.64386	+	0.534122i
$359$	−20.5548	−	14.9340i	−1.08484	−	0.788184i	−0.106322	−	0.994332i	$-0.533907\pi$
$359$	−20.5548	−	14.9340i	−1.08484	−	0.788184i	−0.978521	+	0.206148i	$0.933907\pi$
$360$		0			0
$361$	−1.41084	+	4.34212i	−0.0742547	+	0.228533i
$362$	−39.4582			−2.07388
$363$	18.9749	+	1.71855i	0.995924	+	0.0902006i
$364$	−5.26305			−0.275859
$365$		0			0
$366$	−4.07231	+	5.35368i	−0.212863	+	0.279841i
$367$	−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
$369$	−22.8212	−	18.1641i	−1.18803	−	0.945587i
$370$		0			0
$371$	0.721478	−	0.524185i	0.0374573	−	0.0272143i
$372$	−36.4711	−	0.801332i	−1.89094	−	0.0415471i
$373$		−	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
$378$	46.4873	−	11.7838i	2.39105	−	0.606092i
$379$	−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
$381$	19.7575	+	6.90297i	1.01221	+	0.353650i
$382$	2.01429	+	2.77243i	0.103060	+	0.141850i
$383$	17.2529	+	5.60580i	0.881581	+	0.286443i	0.714614	−	0.699519i	$-0.246602\pi$
$383$	17.2529	+	5.60580i	0.881581	+	0.286443i	0.166968	+	0.985962i	$0.446602\pi$
$384$	−8.13009	−	27.0282i	−0.414887	−	1.37928i
$385$		0			0
$386$		−	4.34023i		−	0.220912i
$387$	−2.59857	+	0.719799i	−0.132093	+	0.0365895i
$388$	29.6325	−	21.5293i	1.50436	−	1.09298i
$389$	13.4063	−	18.4522i	0.679726	−	0.935563i	−0.320204	−	0.947349i	$-0.603752\pi$
$389$	13.4063	−	18.4522i	0.679726	−	0.935563i	0.999931	+	0.0117856i	$0.00375157\pi$
$390$		0			0
$391$	2.26790	−	0.736884i	0.114692	−	0.0372658i
$392$	18.8594	+	13.7021i	0.952543	+	0.692063i
$393$	−6.42219	−	4.88508i	−0.323957	−	0.246420i
$394$	−6.33159	+	19.4866i	−0.318981	+	0.981722i
$395$		0			0
$396$	30.2711	+	2.36941i	1.52118	+	0.119068i
$397$	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
$399$	27.4803	+	20.9031i	1.37574	+	1.04646i
$400$		0			0
$401$	−8.17434	+	2.65600i	−0.408207	+	0.132635i	−0.505921	−	0.862580i	$-0.668847\pi$
$401$	−8.17434	+	2.65600i	−0.408207	+	0.132635i	0.0977135	+	0.995215i	$0.468847\pi$
$402$	−2.08461	+	1.44568i	−0.103971	+	0.0721039i
$403$	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
$411$	−1.83584	−	0.641415i	−0.0905552	−	0.0316387i
$412$	−11.9184	−	36.6810i	−0.587176	−	1.80714i
$413$	2.24397	+	6.90624i	0.110419	+	0.339834i
$414$	−0.456225	+	10.3771i	−0.0224223	+	0.510006i
$415$		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	$0.0798825\pi$
$419$			10.1665i			0.496664i	−0.968675	+	0.248332i	$0.920118\pi$
$420$		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
$423$	−18.5859	+	23.3511i	−0.903676	+	1.13537i
$424$	0.488211	−	0.158629i	0.0237096	−	0.00770372i
$425$		0			0
$426$	−28.1882	+	37.0577i	−1.36572	+	1.79545i
$427$	−2.19256	+	6.74799i	−0.106105	+	0.326558i
$428$	−5.54726			−0.268137
$429$	−1.52544	+	1.86925i	−0.0736489	+	0.0902480i
$430$		0			0
$431$	10.0425	−	30.9076i	0.483730	−	1.48877i	−0.350082	−	0.936719i	$-0.613846\pi$
$431$	10.0425	−	30.9076i	0.483730	−	1.48877i	0.833812	−	0.552049i	$-0.186154\pi$
$432$	−4.09959	−	0.270573i	−0.197241	−	0.0130180i
$433$	−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
$438$	1.16290	−	52.9272i	0.0555655	−	2.52896i
$439$			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	0.735486	−	0.677540i	$-0.236954\pi$
$443$	−2.86606	−	3.94480i	−0.136171	−	0.187423i	−0.871657	+	0.490117i	$0.836954\pi$
$444$	7.25488	−	20.7647i	0.344302	−	0.985448i
$445$		0			0
$446$	16.9969	+	52.3111i	0.804827	+	2.47700i
$447$	10.3744	−	29.6933i	0.490693	−	1.40445i
$448$	−31.4698	−	43.3144i	−1.48681	−	2.04641i
$449$	−0.710721	−	0.230927i	−0.0335410	−	0.0108981i	0.292198	−	0.956358i	$-0.405613\pi$
$449$	−0.710721	−	0.230927i	−0.0335410	−	0.0108981i	−0.325739	+	0.945460i	$0.605613\pi$
$450$		0			0
$451$	−25.4246	−	19.8340i	−1.19720	−	0.933948i
$452$		−	43.8310i		−	2.06164i
$453$	−0.200340	+	9.11807i	−0.00941277	+	0.428404i
$454$	20.8640	−	15.1586i	0.979197	−	0.711428i
$455$		0			0
$456$	11.3258	+	16.3314i	0.530381	+	0.764789i
$457$	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
$459$	−8.02598	−	0.529716i	−0.374621	−	0.0247250i
$460$		0			0
$461$	6.12820			0.285419			0.142709	−	0.989765i	$-0.454419\pi$
$461$	6.12820			0.285419			0.142709	+	0.989765i	$0.454419\pi$
$462$	51.2641	−	13.5284i	2.38502	−	0.629396i
$463$	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	−0.987349	−	0.158565i	$-0.949313\pi$
$467$	−36.5845	+	11.8870i	−1.69293	+	0.550066i	−0.705580	+	0.708631i	$0.749313\pi$
$468$	−2.39451	+	3.00844i	−0.110686	+	0.139065i
$469$	−1.57287	+	2.16487i	−0.0726285	+	0.0999645i
$470$		0			0
$471$	−1.07902	−	0.0237079i	−0.0497185	−	0.00109240i
$472$			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
$477$	0.0286163	−	0.650893i	0.00131025	−	0.0298023i
$478$	−2.65297	−	8.16502i	−0.121344	−	0.373459i
$479$	−6.94651	−	21.3792i	−0.317394	−	0.976839i	−0.974758	−	0.223265i	$-0.928328\pi$
$479$	−6.94651	−	21.3792i	−0.317394	−	0.976839i	0.657364	−	0.753573i	$-0.271672\pi$
$480$		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
$486$	14.4143	−	31.9340i	0.653848	−	1.44856i
$487$	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
$489$	−6.84255	+	4.74531i	−0.309431	+	0.214590i
$490$		0			0
$491$	−21.7780	−	15.8227i	−0.982828	−	0.714067i	−0.0244895	−	0.999700i	$-0.507796\pi$
$491$	−21.7780	−	15.8227i	−0.982828	−	0.714067i	−0.958339	+	0.285633i	$0.907796\pi$
$492$	−40.9015	−	31.1120i	−1.84398	−	1.40264i
$493$	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
$498$	26.3831	+	20.0685i	1.18225	+	0.899289i
$499$	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
$501$	−15.1441	+	10.5024i	−0.676588	+	0.469214i
$502$	−11.7488	+	16.1709i	−0.524376	+	0.721741i
$503$	−18.2128	+	13.2324i	−0.812068	+	0.590002i	−0.914429	−	0.404745i	$-0.867360\pi$
$503$	−18.2128	+	13.2324i	−0.812068	+	0.590002i	0.102362	+	0.994747i	$0.467360\pi$
$504$	28.0621	−	7.77314i	1.24998	−	0.346243i
$505$		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	0.916619	−	0.399763i	$-0.130908\pi$
$509$	5.71179	+	7.86161i	0.253171	+	0.348460i	−0.663448	+	0.748223i	$0.730908\pi$
$510$		0			0
$511$	−17.2562	−	53.1092i	−0.763371	−	2.34941i
$512$	2.74435	+	8.44624i	0.121284	+	0.373275i
$513$	24.4511	−	6.19795i	1.07954	−	0.273646i
$514$	−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
$519$	3.89998	+	0.0856892i	0.171190	+	0.00376134i
$520$		0			0
$521$	4.08412	−	5.62131i	0.178929	−	0.246274i	−0.710127	−	0.704074i	$-0.751362\pi$
$521$	4.08412	−	5.62131i	0.178929	−	0.246274i	0.889055	+	0.457800i	$0.151362\pi$
$522$	11.9940	+	9.54639i	0.524963	+	0.417834i
$523$	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
$528$	−4.53497	−	0.254887i	−0.197359	−	0.0110925i
$529$	20.6269			0.896822
$530$		0			0
$531$	4.96863	+	1.85941i	0.215620	+	0.0806917i
$532$	49.2143	+	35.7563i	2.13371	+	1.55023i
$533$	3.88354	−	1.26184i	0.168215	−	0.0546563i
$534$	18.3969	+	26.5276i	0.796111	+	1.14796i
$535$		0			0
$536$	−1.24614	+	0.905376i	−0.0538252	+	0.0391063i
$537$	−0.553608	+	25.1964i	−0.0238899	+	1.08730i
$538$		−	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
$543$	−10.0294	+	28.7059i	−0.430404	+	1.23189i
$544$	3.11142	+	9.57598i	0.133401	+	0.410567i
$545$		0			0
$546$	−2.21449	+	6.33825i	−0.0947715	+	0.271252i
$547$	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
$552$	−0.138538	+	6.30530i	−0.00589658	+	0.268372i
$553$	−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	0.646326	−	0.763061i	$-0.276305\pi$
$557$	2.84006	+	2.06343i	0.120337	+	0.0874302i	−0.525989	+	0.850492i	$0.676305\pi$
$558$	−16.3107	+	43.5846i	−0.690486	+	1.84508i
$559$	0.116652	−	0.359018i	0.00493385	−	0.0151848i
$560$		0			0
$561$	−8.87835	−	0.499006i	−0.374844	−	0.0210681i
$562$	−43.2603			−1.82483
$563$	−3.50120	+	10.7756i	−0.147558	+	0.454136i	−0.997331	−	0.0730122i	$-0.976739\pi$
$563$	−3.50120	+	10.7756i	−0.147558	+	0.454136i	0.849773	+	0.527148i	$0.176739\pi$
$564$	−31.8344	+	41.8512i	−1.34047	+	1.76225i
$565$		0			0
$566$	29.1256	−	9.46347i	1.22424	−	0.397779i
$567$	3.24336	−	36.8147i	0.136208	−	1.54607i
$568$	−16.6169	+	22.8712i	−0.697228	+	0.959652i
$569$	2.66042	−	1.93291i	0.111530	−	0.0810316i	−0.530622	−	0.847609i	$-0.678042\pi$
$569$	2.66042	−	1.93291i	0.111530	−	0.0810316i	0.642152	+	0.766577i	$0.278042\pi$
$570$		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
$576$	−39.0768	−	1.71800i	−1.62820	−	0.0715832i
$577$	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
$579$	−3.15752	−	1.10319i	−0.131222	−	0.0458471i
$580$		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	−0.930539	−	0.366193i	$-0.880661\pi$
$587$	−7.14042	+	9.82794i	−0.294717	+	0.405642i	0.635822	+	0.771835i	$0.280661\pi$
$588$	42.8356	−	29.7065i	1.76651	−	1.22507i
$589$	−31.8641	+	10.3533i	−1.31294	+	0.426599i
$590$		0			0
$591$	12.5672	+	9.55931i	0.516945	+	0.393217i
$592$	−1.01677	+	3.12930i	−0.0417890	+	0.128613i
$593$	15.9770			0.656098			0.328049	−	0.944661i	$-0.393609\pi$
$593$	15.9770			0.656098			0.328049	+	0.944661i	$0.393609\pi$
$594$	15.5904	−	35.4582i	0.639681	−	1.45487i
$595$		0			0
$596$	17.1249	−	52.7049i	0.701461	−	2.15888i
$597$	2.49526	+	1.89804i	0.102124	+	0.0776816i
$598$	−1.17645	−	0.854744i	−0.0481088	−	0.0349531i
$599$	34.7597	−	11.2941i	1.42024	−	0.461465i	0.504564	−	0.863374i	$-0.331653\pi$
$599$	34.7597	−	11.2941i	1.42024	−	0.461465i	0.915680	+	0.401909i	$0.131653\pi$
$600$		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
$603$	0.521869	+	1.88402i	0.0212522	+	0.0767231i
$604$			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
$609$	15.2649	+	5.33334i	0.618566	+	0.216118i
$610$		0			0
$611$	−1.29114	−	3.97371i	−0.0522338	−	0.160759i
$612$	−14.1579	−	0.622447i	−0.572299	−	0.0251609i
$613$	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	$-0.796996\pi$
$617$		−	29.5786i		−	1.19079i	0.803433	−	0.595395i	$-0.203004\pi$
$618$	−49.1893	−	1.08077i	−1.97869	−	0.0434751i
$619$	−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
$621$	7.43338	+	2.96954i	0.298291	+	0.119163i
$622$	−58.1074	+	18.8802i	−2.32990	+	0.757029i
$623$	27.5489	+	20.0154i	1.10372	+	0.801902i
$624$	0.348224	−	0.457794i	0.0139401	−	0.0183264i
$625$		0			0
$626$	−23.4047			−0.935439
$627$	26.9635	−	7.11556i	1.07682	−	0.284168i
$628$	−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
$633$	−24.6516	−	35.5466i	−0.979811	−	1.41285i
$634$	32.5961	−	44.8647i	1.29456	−	1.78180i
$635$		0			0
$636$	0.0252153	−	1.14763i	0.000999851	−	0.0455063i
$637$			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	0.773787	−	0.633445i	$-0.218360\pi$
$641$	−1.71576	−	2.36154i	−0.0677684	−	0.0932752i	−0.841556	+	0.540170i	$0.818360\pi$
$642$	−2.33407	+	6.68051i	−0.0921186	+	0.263659i
$643$	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	−0.167409	−	0.985888i	$-0.553540\pi$
$647$	−22.4433	−	7.29226i	−0.882336	−	0.286688i	−0.714927	+	0.699199i	$0.753540\pi$
$648$	8.32403	−	19.5772i	0.326999	−	0.769064i
$649$	5.51283	+	2.00196i	0.216398	+	0.0785837i
$650$		0			0
$651$	−1.07829	+	49.0761i	−0.0422614	+	1.92344i
$652$	−11.8692	+	8.62346i	−0.464833	+	0.337721i
$653$	16.6547	−	22.9233i	0.651751	−	0.897058i	−0.347423	−	0.937709i	$-0.612943\pi$
$653$	16.6547	−	22.9233i	0.651751	−	0.897058i	0.999173	+	0.0406508i	$0.0129431\pi$
$654$	17.2226	+	24.8343i	0.673457	+	0.971099i
$655$		0			0
$656$	6.21925	+	4.51855i	0.242821	+	0.176420i
$657$	−38.2090	−	14.2989i	−1.49067	−	0.557855i
$658$	−28.3729	+	87.3229i	−1.10609	+	3.40420i
$659$	24.7031			0.962295			0.481148	−	0.876640i	$-0.340220\pi$
$659$	24.7031			0.962295			0.481148	+	0.876640i	$0.340220\pi$
$660$		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
$663$	0.681737	−	0.896248i	0.0264765	−	0.0348074i
$664$	16.2830	+	11.8303i	0.631903	+	0.459104i
$665$		0			0
$666$	−21.9541	−	17.4740i	−0.850705	−	0.677103i
$667$	−2.05855	+	2.83335i	−0.0797074	+	0.109708i
$668$	−26.2691	+	19.0856i	−1.01638	+	0.738446i
$669$	42.3766	+	0.931087i	1.63838	+	0.0359979i
$670$		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	0.901608	−	0.432553i	$-0.142387\pi$
$677$	−2.13505	−	6.57101i	−0.0820566	−	0.252544i	−0.983665	+	0.180009i	$0.942387\pi$
$678$	−52.7853	−	18.4424i	−2.02721	−	0.708277i
$679$	−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	$0.0548097\pi$
$683$			8.95570i			0.342680i	−0.985212	+	0.171340i	$0.945190\pi$
$684$	42.8296	−	11.8637i	1.63763	−	0.453620i
$685$		0			0
$686$	15.5276	−	21.3718i	0.592845	−	0.815981i
$687$	14.0427	−	9.73861i	0.535762	−	0.371551i
$688$	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
$693$	3.18832	−	40.7333i	0.121114	−	1.54733i
$694$	48.1202			1.82662
$695$		0			0
$696$	7.40805	+	5.63499i	0.280801	+	0.213594i
$697$	12.1758	+	8.84621i	0.461190	+	0.335074i
$698$	21.8579	−	7.10206i	0.827333	−	0.268817i
$699$	0.744637	−	0.516406i	0.0281648	−	0.0195323i
$700$		0			0
$701$	13.2606	−	9.63436i	0.500844	−	0.363885i	−0.308495	−	0.951226i	$-0.599825\pi$
$701$	13.2606	−	9.63436i	0.500844	−	0.363885i	0.809339	+	0.587341i	$0.199825\pi$
$702$	2.61551	+	4.14952i	0.0987162	+	0.156613i
$703$		−	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
$708$	8.82398	+	3.08297i	0.331625	+	0.115865i
$709$	−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
$711$	−0.503928	+	11.4621i	−0.0188988	+	0.429863i
$712$	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
$717$	−6.61438	−	0.145329i	−0.247019	−	0.00542742i
$718$	−46.1988	+	33.5654i	−1.72413	+	1.25265i
$719$	−27.2462	+	37.5012i	−1.01611	+	1.39856i	−0.101218	+	0.994864i	$0.532274\pi$
$719$	−27.2462	+	37.5012i	−1.01611	+	1.39856i	−0.914894	+	0.403694i	$0.867726\pi$
$720$		0			0
$721$	−49.3585	+	16.0376i	−1.83821	+	0.597270i
$722$	8.30176	+	6.03158i	0.308960	+	0.224472i
$723$	20.8041	−	27.3502i	0.773713	−	1.01716i
$724$	−16.5554	+	50.9522i	−0.615276	+	1.89362i
$725$		0			0
$726$	16.8524	−	39.3668i	0.625453	−	1.46104i
$727$	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
$729$	−19.5682	−	18.6034i	−0.724748	−	0.689014i
$730$		0			0
$731$	1.32322	−	0.429941i	0.0489411	−	0.0159019i
$732$	5.20457	+	7.50479i	0.192367	+	0.277385i
$733$	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
$741$	−1.16476	+	3.33375i	−0.0427887	+	0.122468i
$742$	−0.619391	−	1.90629i	−0.0227386	−	0.0699821i
$743$	12.6813	+	39.0290i	0.465232	+	1.43184i	0.858691	+	0.512494i	$0.171278\pi$
$743$	12.6813	+	39.0290i	0.465232	+	1.43184i	−0.393459	+	0.919342i	$0.628722\pi$
$744$	−9.31977	+	26.6747i	−0.341679	+	0.977944i
$745$		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
$753$	8.77802	+	12.6576i	0.319889	+	0.461267i
$754$	−2.04105	+	0.663176i	−0.0743305	+	0.0241514i
$755$		0			0
$756$	4.28822	−	64.9729i	0.155961	−	2.36304i
$757$	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
$759$	8.24956	+	3.20260i	0.299440	+	0.116247i
$760$		0			0
$761$	−15.1277	+	46.5582i	−0.548378	+	1.68773i	0.164441	+	0.986387i	$0.447418\pi$
$761$	−15.1277	+	46.5582i	−0.548378	+	1.68773i	−0.712819	+	0.701348i	$0.752582\pi$
$762$	28.4781	−	37.4388i	1.03165	−	1.35627i
$763$	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
$768$	−18.2671	−	0.401358i	−0.659155	−	0.0144828i
$769$		−	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	0.712390	−	0.701784i	$-0.247613\pi$
$773$	−4.87069	−	6.70392i	−0.175186	−	0.241123i	−0.887577	+	0.460660i	$0.847613\pi$
$774$	−0.266188	+	6.05460i	−0.00956794	+	0.217628i
$775$		0			0
$776$	−8.76698	−	26.9820i	−0.314716	−	0.968597i
$777$	−27.9413	−	9.76229i	−1.00239	−	0.350220i
$778$	−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
$783$	9.99362	−	6.29915i	0.357143	−	0.225113i
$784$	−6.30865	+	4.58350i	−0.225309	+	0.163696i
$785$		0			0
$786$	−14.9028	+	10.3351i	−0.531564	+	0.368640i
$787$	−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
$789$	−3.61026	−	2.74617i	−0.128529	−	0.0977663i
$790$		0			0
$791$	−58.9798			−2.09708
$792$	8.99091	−	21.7322i	0.319478	−	0.772219i
$793$	−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	0.563586	−	0.826057i	$-0.309421\pi$
$797$	42.4902	−	13.8059i	1.50508	−	0.489030i	0.941495	+	0.337027i	$0.109421\pi$
$798$	63.7684	−	44.2234i	2.25738	−	1.56549i
$799$	9.05160	−	12.4585i	0.320223	−	0.440749i
$800$		0			0
$801$	23.9749	−	6.64101i	0.847112	−	0.234648i
$802$			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
$807$	−17.2282	−	6.01929i	−0.606462	−	0.211889i
$808$	1.06120	+	3.26605i	0.0373331	+	0.114899i
$809$	6.35086	+	19.5459i	0.223284	+	0.687198i	0.998461	+	0.0554542i	$0.0176607\pi$
$809$	6.35086	+	19.5459i	0.223284	+	0.687198i	−0.775177	+	0.631744i	$0.782339\pi$
$810$		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
$816$	2.11942	+	0.0465674i	0.0741947	+	0.00163018i
$817$	−3.52991	+	2.56463i	−0.123496	+	0.0897249i
$818$	13.6970	−	18.8524i	0.478906	−	0.659158i
$819$	4.04820	+	3.22209i	0.141456	+	0.112589i
$820$		0			0
$821$	19.3665	+	14.0706i	0.675895	+	0.491066i	0.871993	−	0.489518i	$-0.162827\pi$
$821$	19.3665	+	14.0706i	0.675895	+	0.491066i	−0.196099	+	0.980584i	$0.562827\pi$
$822$	−2.64615	+	3.47877i	−0.0922951	+	0.121336i
$823$	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	−0.983507	−	0.180872i	$-0.942108\pi$
$827$	−2.34430	+	7.21501i	−0.0815193	+	0.250891i	0.901987	+	0.431762i	$0.142108\pi$
$828$	13.2085	+	4.94301i	0.459026	+	0.171782i
$829$	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
$831$	17.7396	+	25.5799i	0.615381	+	0.887355i
$832$	3.21869	−	4.43015i	0.111588	−	0.153588i
$833$	−12.3508	+	8.97336i	−0.427929	+	0.310909i
$834$	1.46820	−	66.8221i	0.0508395	−	2.31386i
$835$		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	0.436883	−	0.899518i	$-0.356082\pi$
$839$	−16.0357	−	22.0712i	−0.553614	−	0.761984i	−0.990497	+	0.137534i	$0.956082\pi$
$840$		0			0
$841$	−7.36431	−	22.6650i	−0.253942	−	0.781552i
$842$	−8.62048	−	26.5311i	−0.297081	−	0.914322i
$843$	−10.9958	+	31.4719i	−0.378716	+	1.08395i
$844$	−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
$849$	0.518407	−	23.5943i	0.0177917	−	0.809754i
$850$		0			0
$851$	3.76803	−	5.18624i	0.129166	−	0.177782i
$852$	36.0256	+	51.9475i	1.23422	+	1.77969i
$853$	−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	$-0.376668\pi$
$857$	22.1220			0.755673			0.377837	+	0.925872i	$0.376668\pi$
$858$	2.93619	+	4.55903i	0.100240	+	0.155643i
$859$	−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
$861$	−41.8649	+	55.0378i	−1.42675	+	1.87568i
$862$	−59.0927	−	42.9334i	−2.01271	−	1.46232i
$863$	17.5560	−	5.70429i	0.597613	−	0.194176i	0.00543755	−	0.999985i	$-0.498269\pi$
$863$	17.5560	−	5.70429i	0.597613	−	0.194176i	0.592176	+	0.805809i	$0.298269\pi$
$864$	−12.5386	+	31.3868i	−0.426572	+	1.06780i
$865$		0			0
$866$	−50.8095	+	36.9153i	−1.72658	+	1.25443i
$867$	−25.2884	−	0.555631i	−0.858841	−	0.0188702i
$868$			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
$873$	−35.9730	−	1.58154i	−1.21750	−	0.0535270i
$874$	5.19392	+	15.9852i	0.175687	+	0.540709i
$875$		0			0
$876$	−67.8567	−	23.7082i	−2.29266	−	0.801024i
$877$	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	$-0.990459\pi$
$881$		−	1.77914i		−	0.0599409i	0.999551	−	0.0299704i	$-0.00954131\pi$
$882$	−17.7517	−	64.0858i	−0.597729	−	2.15788i
$883$	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	0.976064	−	0.217481i	$-0.0697841\pi$
$887$	31.8926	+	23.1713i	1.07085	+	0.778017i	0.0947835	+	0.995498i	$0.469784\pi$
$888$	−13.5599	−	10.3144i	−0.455040	−	0.346130i
$889$	15.3328	−	47.1894i	0.514245	−	1.58268i
$890$		0			0
$891$	−21.8331	−	20.3547i	−0.731437	−	0.681909i
$892$	74.6805			2.50049
$893$	−14.9234	+	45.9295i	−0.499393	+	1.53697i
$894$	−56.2665	−	42.7995i	−1.88183	−	1.43143i
$895$		0			0
$896$	−63.6399	+	20.6779i	−2.12606	+	0.690798i
$897$	−0.920856	+	0.638614i	−0.0307465	+	0.0213227i
$898$	−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
$906$	19.3515	+	6.76114i	0.642911	+	0.224624i
$907$	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
$909$	4.35437	+	0.191438i	0.144425	+	0.00634961i
$910$		0			0
$911$	4.06381	+	1.32041i	0.134640	+	0.0437471i	0.375562	−	0.926797i	$-0.377450\pi$
$911$	4.06381	+	1.32041i	0.134640	+	0.0437471i	−0.240922	+	0.970544i	$0.577450\pi$
$912$	−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
$918$	−6.70671	+	16.7883i	−0.221354	+	0.554097i
$919$	−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
$921$	31.2760	−	41.1170i	1.03058	−	1.35485i
$922$	4.25630	−	13.0996i	0.140174	−	0.431411i
$923$	−5.02320			−0.165341
$924$	4.03962	−	71.8731i	0.132894	−	2.36445i
$925$		0			0
$926$	8.09343	−	24.9090i	0.265966	−	0.818561i
$927$	−13.2891	+	35.5106i	−0.436472	+	1.16632i
$928$	−11.9636	−	8.69203i	−0.392723	−	0.285330i
$929$	−7.40448	+	2.40586i	−0.242933	+	0.0789337i	−0.427953	−	0.903801i	$-0.640765\pi$
$929$	−7.40448	+	2.40586i	−0.242933	+	0.0789337i	0.185020	+	0.982735i	$0.440765\pi$
$930$		0			0
$931$	28.1407	−	38.7323i	0.922273	−	1.26940i
$932$	1.29166	−	0.938444i	0.0423096	−	0.0307398i
$933$	−1.03426	+	47.0721i	−0.0338600	+	1.54107i
$934$			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
$939$	−5.94896	+	17.0269i	−0.194137	+	0.555653i
$940$		0			0
$941$	−6.90820	−	21.2613i	−0.225201	−	0.693097i	−0.998271	−	0.0587768i	$-0.981280\pi$
$941$	−6.90820	−	21.2613i	−0.225201	−	0.693097i	0.773070	−	0.634320i	$-0.218720\pi$
$942$	−0.800103	+	2.29003i	−0.0260688	+	0.0746131i
$943$	−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	$0.0233481\pi$
$947$			4.51042i			0.146569i	−0.997311	+	0.0732844i	$0.976652\pi$
$948$	−0.444037	+	20.2095i	−0.0144216	+	0.656373i
$949$	4.62069	−	3.35713i	0.149994	−	0.108977i
$950$		0			0
$951$	−24.3539	−	35.1173i	−0.789728	−	1.13876i
$952$	−14.2895	+	4.64295i	−0.463126	+	0.150479i
$953$	−14.7032	−	10.6825i	−0.476284	−	0.346041i	0.323601	−	0.946194i	$-0.395106\pi$
$953$	−14.7032	−	10.6825i	−0.476284	−	0.346041i	−0.799885	+	0.600153i	$0.795106\pi$
$954$	−1.37146	−	0.513243i	−0.0444028	−	0.0166169i
$955$		0			0
$956$	−11.6565			−0.377000
$957$	10.9799	−	7.07146i	0.354929	−	0.228588i
$958$	−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
$963$	4.26680	+	3.39608i	0.137496	+	0.109437i
$964$	35.5869	−	48.9812i	1.14618	−	1.57758i
$965$		0			0
$966$	24.6200	+	0.540943i	0.792135	+	0.0174046i
$967$			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	$0.129463\pi$
$971$	31.4990	+	43.3547i	1.01085	+	1.39132i	0.0924296	+	0.995719i	$0.470537\pi$
$972$	−35.1885	−	32.0116i	−1.12867	−	1.02677i
$973$	−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	−0.304059	−	0.952653i	$-0.598342\pi$
$977$	−34.6954	−	11.2732i	−1.11000	−	0.360662i	−0.805944	+	0.591991i	$0.798342\pi$
$978$	5.39105	+	17.9224i	0.172387	+	0.573094i
$979$	26.4324	−	7.60021i	0.844782	−	0.242904i
$980$		0			0
$981$	22.4446	−	6.21711i	0.716601	−	0.198497i
$982$	−48.9481	+	35.5629i	−1.56200	+	1.13486i
$983$	10.6166	−	14.6125i	0.338618	−	0.466067i	−0.605419	−	0.795907i	$-0.706995\pi$
$983$	10.6166	−	14.6125i	0.338618	−	0.466067i	0.944037	+	0.329839i	$0.106995\pi$
$984$	−32.7087	+	22.6835i	−1.04272	+	0.723123i
$985$		0			0
$986$	−6.39913	−	4.64924i	−0.203790	−	0.148062i
$987$	56.3157	+	42.8369i	1.79255	+	1.36351i
$988$	−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
$993$	6.22064	+	4.73177i	0.197406	+	0.150158i
$994$	89.3037	+	64.8830i	2.83254	+	2.05796i
$995$		0			0
$996$	36.9838	−	25.6483i	1.17188	−	0.812696i
$997$	−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
$999$	−18.2926	+	11.5301i	−0.578752	+	0.364798i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.694544 - 2.13759i) q^{2} +(-1.37856 - 1.04861i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.19896 + 2.21848i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(-1.91228 + 1.38935i) q^{8} +(0.800839 + 2.89113i) q^{9} +O(q^{10})\)	\(q+(0.694544 - 2.13759i) q^{2} +(-1.37856 - 1.04861i) q^{3} +(-2.46885 - 1.79372i) q^{4} +(-3.19896 + 2.21848i) q^{6} +(-2.41366 + 3.32212i) q^{7} +(-1.91228 + 1.38935i) q^{8} +(0.800839 + 2.89113i) 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} +(6.73626 + 0.296157i) q^{18} +(2.85337 + 3.92732i) q^{19} +(6.81098 - 2.04875i) q^{21} +(7.45006 + 0.254724i) q^{22} +1.54048i q^{23} +(4.09307 + 0.0899318i) q^{24} +(-0.554855 + 0.763692i) q^{26} +(1.92767 - 4.82536i) q^{27} +(11.9179 - 3.87237i) q^{28} +(1.83926 + 1.33630i) q^{29} +(-2.13274 + 6.56391i) q^{31} -6.50454 q^{32} +(2.07896 - 5.35518i) q^{33} -3.47918 q^{34} +(3.20874 - 8.57425i) q^{36} +(-3.36663 - 2.44600i) q^{37} +(10.3768 - 3.37162i) q^{38} +(0.414554 + 0.597771i) q^{39} +(-7.86568 + 5.71475i) q^{41} +(0.351152 - 15.9820i) q^{42} +0.898807i q^{43} +(3.45473 - 9.51336i) q^{44} +(3.29291 + 1.06993i) q^{46} +(5.84743 + 8.04830i) q^{47} +(-0.451708 + 1.29286i) q^{48} +(-3.04761 - 9.37957i) q^{49} +(-0.884333 + 2.53111i) q^{51} +(0.753353 + 1.03690i) q^{52} +(-0.206545 - 0.0671104i) q^{53} +(-8.97577 - 7.47198i) q^{54} -9.70625i q^{56} +(0.184697 - 8.40611i) 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} +(-11.5377 - 4.31774i) q^{63} +(-4.02902 + 12.4000i) q^{64} +(-10.0032 - 8.16335i) q^{66} +0.651654 q^{67} +(-1.45975 + 4.49265i) q^{68} +(1.61536 - 2.12364i) q^{69} +(11.3748 - 3.69589i) q^{71} +(-5.54823 - 4.41601i) 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} +(-7.71731 + 4.63066i) q^{81} +(6.75271 + 20.7827i) q^{82} +(-2.63127 - 8.09822i) q^{83} +(-20.4901 - 7.15896i) 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} +(9.82308 - 6.81231i) q^{93} +(21.2652 - 6.90949i) q^{94} +(8.96688 + 6.82072i) q^{96} +(-3.70900 + 11.4151i) q^{97} -22.1663 q^{98} +(-8.48145 + 5.20241i) 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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