LMFDB - Embedded newform 675.2.u.b.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.1
Character	$\chi$	$=$	675.499
Dual form			675.2.u.b.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36514 + 0.417037i) q^{2} +(-1.71926 - 0.210069i) q^{3} +(3.54056 - 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(0.198324 - 0.544891i) q^{7} +(-3.67675 + 2.12277i) q^{8} +(2.91174 + 0.722330i) q^{9} +O(q^{10})$	\(q+(-2.36514 + 0.417037i) q^{2} +(-1.71926 - 0.210069i) q^{3} +(3.54056 - 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(0.198324 - 0.544891i) q^{7} +(-3.67675 + 2.12277i) q^{8} +(2.91174 + 0.722330i) q^{9} +(-2.36944 + 1.98820i) q^{11} +(-6.35787 + 1.47178i) q^{12} +(4.13790 + 0.729623i) q^{13} +(-0.241824 + 1.37145i) q^{14} +(2.03816 - 1.71022i) q^{16} +(-1.72424 - 0.995493i) q^{17} +(-7.18790 - 0.494102i) q^{18} +(-1.92271 - 3.33023i) q^{19} +(-0.455437 + 0.895151i) q^{21} +(4.77489 - 5.69050i) q^{22} +(1.52295 + 4.18428i) q^{23} +(6.76724 - 2.87724i) q^{24} -10.0910 q^{26} +(-4.85432 - 1.85354i) q^{27} -2.18479i q^{28} +(-1.11126 - 6.30229i) q^{29} +(-1.55754 + 0.566898i) q^{31} +(1.35067 - 1.60967i) q^{32} +(4.49135 - 2.92049i) q^{33} +(4.49323 + 1.63540i) q^{34} +(11.2400 - 1.19479i) q^{36} +(3.49016 + 2.01505i) q^{37} +(5.93630 + 7.07461i) q^{38} +(-6.96087 - 2.12366i) q^{39} +(-0.190345 + 1.07950i) q^{41} +(0.703859 - 2.30709i) q^{42} +(-4.43596 - 5.28657i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(-1.22894 + 3.37650i) q^{47} +(-3.86340 + 2.51217i) q^{48} +(5.10474 + 4.28338i) q^{49} +(2.75531 + 2.07373i) q^{51} +(15.5907 - 2.74906i) q^{52} +5.40034i q^{53} +(12.2541 + 2.35945i) q^{54} +(0.427492 + 2.42443i) q^{56} +(2.60607 + 6.12946i) q^{57} +(5.25657 + 14.4423i) q^{58} +(7.87850 + 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(3.44738 - 1.99034i) q^{62} +(0.971060 - 1.44333i) q^{63} +(-5.18386 + 8.97871i) q^{64} +(-9.40470 + 8.78041i) q^{66} +(8.70304 + 1.53458i) q^{67} +(-7.38764 - 1.30264i) q^{68} +(-1.73937 - 7.51381i) q^{69} +(-0.572473 + 0.991553i) q^{71} +(-12.2391 + 3.52514i) q^{72} +(0.169284 - 0.0977361i) q^{73} +(-9.09506 - 3.31033i) q^{74} +(-11.0990 - 9.31317i) q^{76} +(0.613433 + 1.68539i) q^{77} +(17.3491 + 2.11980i) q^{78} +(1.25166 + 7.09849i) q^{79} +(7.95648 + 4.20647i) q^{81} -2.63255i q^{82} +(14.6741 - 2.58744i) q^{83} +(-0.458958 + 3.75624i) q^{84} +(12.6963 + 10.6535i) q^{86} +(0.586638 + 11.0687i) q^{87} +(4.49135 - 12.3399i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(10.7842 + 12.8521i) q^{92} +(2.79691 - 0.647457i) q^{93} +(1.49850 - 8.49839i) q^{94} +(-2.66030 + 2.48371i) q^{96} +(-3.40390 - 4.05661i) q^{97} +(-13.8597 - 8.00191i) q^{98} +(-8.33533 + 4.07760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4}+O(q^{10}) $ 24 * q + 12 * q^4	$ 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	−2.36514	+	0.417037i	−1.67240	+	0.294890i	−0.927928	−	0.372760i	$-0.878411\pi$
$2$	−2.36514	+	0.417037i	−1.67240	+	0.294890i	−0.744475	+	0.667650i	$0.767300\pi$
$3$	−1.71926	−	0.210069i	−0.992618	−	0.121284i
$3$	−1.71926	−	0.210069i	−0.992618	−	0.121284i
$4$	3.54056	−	1.28866i	1.77028	−	0.644329i
$5$		0			0
$5$		0			0
$6$	4.15390	−	0.220155i	1.69582	−	0.0898778i
$7$	0.198324	−	0.544891i	0.0749595	−	0.205950i	−0.896554	−	0.442935i	$-0.853937\pi$
$7$	0.198324	−	0.544891i	0.0749595	−	0.205950i	0.971513	+	0.236986i	$0.0761594\pi$
$8$	−3.67675	+	2.12277i	−1.29993	+	0.750514i
$9$	2.91174	+	0.722330i	0.970581	+	0.240777i
$10$		0			0
$11$	−2.36944	+	1.98820i	−0.714413	+	0.599464i	−0.925834	−	0.377932i	$-0.876635\pi$
$11$	−2.36944	+	1.98820i	−0.714413	+	0.599464i	0.211421	+	0.977395i	$0.432191\pi$
$12$	−6.35787	+	1.47178i	−1.83536	+	0.424867i
$13$	4.13790	+	0.729623i	1.14765	+	0.202361i	0.714948	−	0.699178i	$-0.246450\pi$
$13$	4.13790	+	0.729623i	1.14765	+	0.202361i	0.432699	+	0.901539i	$0.357561\pi$
$14$	−0.241824	+	1.37145i	−0.0646301	+	0.366536i
$15$		0			0
$16$	2.03816	−	1.71022i	0.509540	−	0.427555i
$17$	−1.72424	−	0.995493i	−0.418191	−	0.241443i	0.276112	−	0.961125i	$-0.410954\pi$
$17$	−1.72424	−	0.995493i	−0.418191	−	0.241443i	−0.694303	+	0.719683i	$0.744287\pi$
$18$	−7.18790	−	0.494102i	−1.69420	−	0.116461i
$19$	−1.92271	−	3.33023i	−0.441100	−	0.764008i	0.556671	−	0.830733i	$-0.312078\pi$
$19$	−1.92271	−	3.33023i	−0.441100	−	0.764008i	−0.997771	+	0.0667249i	$0.978745\pi$
$20$		0			0
$21$	−0.455437	+	0.895151i	−0.0993845	+	0.195338i
$22$	4.77489	−	5.69050i	1.01801	−	1.21322i
$23$	1.52295	+	4.18428i	0.317558	+	0.872482i	0.991074	+	0.133310i	$0.0425607\pi$
$23$	1.52295	+	4.18428i	0.317558	+	0.872482i	−0.673517	+	0.739172i	$0.735217\pi$
$24$	6.76724	−	2.87724i	1.38136	−	0.587314i
$25$		0			0
$26$	−10.0910			−1.97900
$27$	−4.85432	−	1.85354i	−0.934213	−	0.356715i
$28$		−	2.18479i		−	0.412887i
$29$	−1.11126	−	6.30229i	−0.206356	−	1.17031i	−0.895291	−	0.445482i	$-0.853032\pi$
$29$	−1.11126	−	6.30229i	−0.206356	−	1.17031i	0.688935	−	0.724823i	$-0.258079\pi$
$30$		0			0
$31$	−1.55754	+	0.566898i	−0.279743	+	0.101818i	−0.478081	−	0.878316i	$-0.658668\pi$
$31$	−1.55754	+	0.566898i	−0.279743	+	0.101818i	0.198339	+	0.980134i	$0.436445\pi$
$32$	1.35067	−	1.60967i	0.238767	−	0.284552i
$33$	4.49135	−	2.92049i	0.781844	−	0.508392i
$34$	4.49323	+	1.63540i	0.770582	+	0.280469i
$35$		0			0
$36$	11.2400	−	1.19479i	1.87334	−	0.199132i
$37$	3.49016	+	2.01505i	0.573779	+	0.331272i	0.758657	−	0.651490i	$-0.225856\pi$
$37$	3.49016	+	2.01505i	0.573779	+	0.331272i	−0.184878	+	0.982761i	$0.559189\pi$
$38$	5.93630	+	7.07461i	0.962996	+	1.14765i
$39$	−6.96087	−	2.12366i	−1.11463	−	0.340058i
$40$		0			0
$41$	−0.190345	+	1.07950i	−0.0297270	+	0.168590i	−0.996057	−	0.0887159i	$-0.971724\pi$
$41$	−0.190345	+	1.07950i	−0.0297270	+	0.168590i	0.966330	+	0.257306i	$0.0828348\pi$
$42$	0.703859	−	2.30709i	0.108608	−	0.355991i
$43$	−4.43596	−	5.28657i	−0.676477	−	0.806194i	0.313173	−	0.949696i	$-0.398608\pi$
$43$	−4.43596	−	5.28657i	−0.676477	−	0.806194i	−0.989650	+	0.143502i	$0.954164\pi$
$44$	−5.82704	+	10.0927i	−0.878459	+	1.52154i
$45$		0			0
$46$	−5.34699	−	9.26126i	−0.788370	−	1.36550i
$47$	−1.22894	+	3.37650i	−0.179260	+	0.492513i	−0.996482	−	0.0838106i	$-0.973291\pi$
$47$	−1.22894	+	3.37650i	−0.179260	+	0.492513i	0.817222	+	0.576323i	$0.195513\pi$
$48$	−3.86340	+	2.51217i	−0.557634	+	0.362600i
$49$	5.10474	+	4.28338i	0.729248	+	0.611912i
$50$		0			0
$51$	2.75531	+	2.07373i	0.385821	+	0.290380i
$52$	15.5907	−	2.74906i	2.16204	−	0.381226i
$53$			5.40034i			0.741793i	0.928674	+	0.370897i	$0.120950\pi$
$53$			5.40034i			0.741793i	−0.928674	+	0.370897i	$0.879050\pi$
$54$	12.2541	+	2.35945i	1.66757	+	0.321081i
$55$		0			0
$56$	0.427492	+	2.42443i	0.0571260	+	0.323978i
$57$	2.60607	+	6.12946i	0.345182	+	0.811866i
$58$	5.25657	+	14.4423i	0.690222	+	1.89637i
$59$	7.87850	+	6.61085i	1.02569	+	0.860659i	0.990332	−	0.138715i	$-0.0442973\pi$
$59$	7.87850	+	6.61085i	1.02569	+	0.860659i	0.0353615	+	0.999375i	$0.488742\pi$
$60$		0			0
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.976864	−	0.213860i	$-0.0686036\pi$
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.610855	+	0.791742i	$0.290826\pi$
$62$	3.44738	−	1.99034i	0.437817	−	0.252774i
$63$	0.971060	−	1.44333i	0.122342	−	0.181842i
$64$	−5.18386	+	8.97871i	−0.647982	+	1.12234i
$65$		0			0
$66$	−9.40470	+	8.78041i	−1.15764	+	1.08079i
$67$	8.70304	+	1.53458i	1.06324	+	0.187479i	0.677796	−	0.735250i	$-0.262935\pi$
$67$	8.70304	+	1.53458i	1.06324	+	0.187479i	0.385449	+	0.922729i	$0.374046\pi$
$68$	−7.38764	−	1.30264i	−0.895883	−	0.157968i
$69$	−1.73937	−	7.51381i	−0.209396	−	0.904556i
$70$		0			0
$71$	−0.572473	+	0.991553i	−0.0679401	+	0.117676i	−0.897994	−	0.440007i	$-0.854976\pi$
$71$	−0.572473	+	0.991553i	−0.0679401	+	0.117676i	0.830054	+	0.557683i	$0.188309\pi$
$72$	−12.2391	+	3.52514i	−1.44239	+	0.415442i
$73$	0.169284	−	0.0977361i	0.0198132	−	0.0114391i	−0.490061	−	0.871688i	$-0.663025\pi$
$73$	0.169284	−	0.0977361i	0.0198132	−	0.0114391i	0.509874	+	0.860249i	$0.329692\pi$
$74$	−9.09506	−	3.31033i	−1.05728	−	0.384818i
$75$		0			0
$76$	−11.0990	−	9.31317i	−1.27314	−	1.06829i
$77$	0.613433	+	1.68539i	0.0699072	+	0.192069i
$78$	17.3491	+	2.11980i	1.96439	+	0.240020i
$79$	1.25166	+	7.09849i	0.140822	+	0.798642i	0.970627	+	0.240589i	$0.0773405\pi$
$79$	1.25166	+	7.09849i	0.140822	+	0.798642i	−0.829805	+	0.558054i	$0.811548\pi$
$80$		0			0
$81$	7.95648	+	4.20647i	0.884053	+	0.467386i
$82$		−	2.63255i		−	0.290717i
$83$	14.6741	−	2.58744i	1.61069	−	0.284008i	0.705402	−	0.708808i	$-0.250767\pi$
$83$	14.6741	−	2.58744i	1.61069	−	0.284008i	0.905287	+	0.424800i	$0.139656\pi$
$84$	−0.458958	+	3.75624i	−0.0500764	+	0.409839i
$85$		0			0
$86$	12.6963	+	10.6535i	1.36908	+	1.14879i
$87$	0.586638	+	11.0687i	0.0628942	+	1.18669i
$88$	4.49135	−	12.3399i	0.478780	−	1.31544i
$89$	−0.776563	−	1.34505i	−0.0823155	−	0.142575i	0.821929	−	0.569590i	$-0.192898\pi$
$89$	−0.776563	−	1.34505i	−0.0823155	−	0.142575i	−0.904244	+	0.427016i	$0.859565\pi$
$90$		0			0
$91$	1.21821	−	2.11000i	0.127703	−	0.221189i
$92$	10.7842	+	12.8521i	1.12433	+	1.33993i
$93$	2.79691	−	0.647457i	0.290026	−	0.0671381i
$94$	1.49850	−	8.49839i	0.154558	−	0.876542i
$95$		0			0
$96$	−2.66030	+	2.48371i	−0.271516	+	0.253492i
$97$	−3.40390	−	4.05661i	−0.345614	−	0.411887i	0.565035	−	0.825067i	$-0.308863\pi$
$97$	−3.40390	−	4.05661i	−0.345614	−	0.411887i	−0.910649	+	0.413180i	$0.864418\pi$
$98$	−13.8597	−	8.00191i	−1.40004	−	0.808315i
$99$	−8.33533	+	4.07760i	−0.837732	+	0.409814i
$100$		0			0
$101$	6.83061	+	2.48614i	0.679671	+	0.247380i	0.658706	−	0.752400i	$-0.271104\pi$
$101$	6.83061	+	2.48614i	0.679671	+	0.247380i	0.0209647	+	0.999780i	$0.493326\pi$
$102$	−7.38150	−	3.75558i	−0.730878	−	0.371858i
$103$	−4.11472	+	4.90374i	−0.405436	+	0.483179i	−0.929669	−	0.368395i	$-0.879907\pi$
$103$	−4.11472	+	4.90374i	−0.405436	+	0.483179i	0.524234	+	0.851574i	$0.324352\pi$
$104$	−16.7629	+	6.10118i	−1.64373	+	0.598270i
$105$		0			0
$106$	−2.25214	−	12.7725i	−0.218747	−	1.24058i
$107$			5.54365i			0.535925i	0.963429	+	0.267963i	$0.0863504\pi$
$107$			5.54365i			0.535925i	−0.963429	+	0.267963i	$0.913650\pi$
$108$	−19.5756	−	0.307026i	−1.88366	−	0.0295436i
$109$	6.23137			0.596857			0.298428	−	0.954432i	$-0.403538\pi$
$109$	6.23137			0.596857			0.298428	+	0.954432i	$0.403538\pi$
$110$		0			0
$111$	−5.57722	−	4.19758i	−0.529366	−	0.398416i
$112$	−0.527668	−	1.44975i	−0.0498599	−	0.136989i
$113$	7.61316	−	9.07301i	0.716186	−	0.853517i	−0.278068	−	0.960561i	$-0.589694\pi$
$113$	7.61316	−	9.07301i	0.716186	−	0.853517i	0.994254	+	0.107044i	$0.0341385\pi$
$114$	−8.71992	−	13.4102i	−0.816695	−	1.25598i
$115$		0			0
$116$	−12.0560	−	20.8816i	−1.11937	−	1.93881i
$117$	11.5215	+	5.11340i	1.06516	+	0.472734i
$118$	−21.3907	−	12.3499i	−1.96917	−	1.13690i
$119$	−0.884395	+	0.742096i	−0.0810724	+	0.0680278i
$120$		0			0
$121$	−0.248809	+	1.41107i	−0.0226190	+	0.128279i
$122$	−31.2111	−	5.50336i	−2.82572	−	0.498250i
$123$	0.554025	−	1.81597i	0.0499547	−	0.163740i
$124$	−4.78403	+	4.01427i	−0.429618	+	0.360492i
$125$		0			0
$126$	−1.69477	+	3.81863i	−0.150982	+	0.340191i
$127$	−9.98473	+	5.76469i	−0.886002	+	0.511533i	−0.872633	−	0.488377i	$-0.837589\pi$
$127$	−9.98473	+	5.76469i	−0.886002	+	0.511533i	−0.0133693	+	0.999911i	$0.504256\pi$
$128$	7.07872	−	19.4486i	0.625676	−	1.71903i
$129$	6.51604	+	10.0209i	0.573705	+	0.882288i
$130$		0			0
$131$	8.46830	−	3.08221i	0.739879	−	0.269294i	0.0555383	−	0.998457i	$-0.482312\pi$
$131$	8.46830	−	3.08221i	0.739879	−	0.269294i	0.684340	+	0.729163i	$0.260090\pi$
$132$	12.1384	−	16.1280i	1.05651	−	1.40376i
$133$	−2.19594	+	0.387203i	−0.190412	+	0.0335747i
$134$	−21.2238			−1.83346
$135$		0			0
$136$	8.45283			0.724824
$137$	11.3452	−	2.00047i	0.969287	−	0.170911i	0.333478	−	0.942758i	$-0.391778\pi$
$137$	11.3452	−	2.00047i	0.969287	−	0.170911i	0.635809	+	0.771846i	$0.280667\pi$
$138$	7.24738	+	17.0458i	0.616938	+	1.45103i
$139$	1.60108	−	0.582746i	0.135802	−	0.0494279i	−0.273225	−	0.961950i	$-0.588090\pi$
$139$	1.60108	−	0.582746i	0.135802	−	0.0494279i	0.409027	+	0.912522i	$0.365868\pi$
$140$		0			0
$141$	2.82218	−	5.54693i	0.237670	−	0.467136i
$142$	0.940462	−	2.58390i	0.0789219	−	0.216836i
$143$	−11.2551	+	6.49816i	−0.941202	+	0.543403i
$144$	7.16994	−	3.50750i	0.597495	−	0.292291i
$145$		0			0
$146$	−0.359620	+	0.301757i	−0.0297623	+	0.0249736i
$147$	−7.87659	−	8.43662i	−0.649650	−	0.695840i
$148$	14.9538	+	2.63677i	1.22920	+	0.216741i
$149$	3.75996	−	21.3238i	0.308028	−	1.74691i	−0.300869	−	0.953666i	$-0.597277\pi$
$149$	3.75996	−	21.3238i	0.308028	−	1.74691i	0.608897	−	0.793249i	$-0.291612\pi$
$150$		0			0
$151$	−3.63222	+	3.04779i	−0.295586	+	0.248026i	−0.778504	−	0.627640i	$-0.784021\pi$
$151$	−3.63222	+	3.04779i	−0.295586	+	0.248026i	0.482918	+	0.875665i	$0.339577\pi$
$152$	14.1387	+	8.16296i	1.14680	+	0.662104i
$153$	−4.30148	−	4.14409i	−0.347754	−	0.335030i
$154$	−2.15373	−	3.73036i	−0.173552	−	0.300601i
$155$		0			0
$156$	−27.3821	+	1.45124i	−2.19232	+	0.116192i
$157$	−0.134475	+	0.160261i	−0.0107323	+	0.0127902i	−0.771384	−	0.636370i	$-0.780435\pi$
$157$	−0.134475	+	0.160261i	−0.0107323	+	0.0127902i	0.760652	+	0.649160i	$0.224880\pi$
$158$	−5.92067	−	16.2669i	−0.471023	−	1.29412i
$159$	1.13444	−	9.28461i	0.0899673	−	0.736317i
$160$		0			0
$161$	2.58202			0.203491
$162$	−20.5724	−	6.63073i	−1.61632	−	0.520960i
$163$			5.62384i			0.440493i	0.975444	+	0.220247i	$0.0706862\pi$
$163$			5.62384i			0.440493i	−0.975444	+	0.220247i	$0.929314\pi$
$164$	0.717181	+	4.06733i	0.0560024	+	0.317605i
$165$		0			0
$166$	−33.6271	+	12.2393i	−2.60997	+	0.949951i
$167$	10.7220	−	12.7780i	0.829695	−	0.988791i	−0.170300	−	0.985392i	$-0.554474\pi$
$167$	10.7220	−	12.7780i	0.829695	−	0.988791i	0.999994	−	0.00339914i	$-0.00108198\pi$
$168$	−0.225674	−	4.25804i	−0.0174111	−	0.328515i
$169$	4.37386	+	1.59195i	0.336451	+	0.122458i
$170$		0			0
$171$	−3.19291	−	11.0856i	−0.244168	−	0.847738i
$172$	−22.5183	−	13.0010i	−1.71701	−	0.991315i
$173$	12.2143	+	14.5565i	0.928639	+	1.10671i	0.994058	+	0.108851i	$0.0347172\pi$
$173$	12.2143	+	14.5565i	0.928639	+	1.10671i	−0.0654187	+	0.997858i	$0.520838\pi$
$174$	−6.00355	−	25.9344i	−0.455128	−	1.96608i
$175$		0			0
$176$	−1.42905	+	8.10453i	−0.107718	+	0.610902i
$177$	−12.1565	−	13.0208i	−0.913738	−	0.978706i
$178$	2.39761	+	2.85736i	0.179709	+	0.214168i
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	−0.385035	−	0.922902i	$-0.625811\pi$
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	0.991774	−	0.128001i	$-0.0408560\pi$
$180$		0			0
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$182$	−2.00128	+	5.49848i	−0.148345	+	0.407575i
$183$	−20.3716	−	10.3647i	−1.50591	−	0.766181i
$184$	−14.4818	−	12.1517i	−1.06761	−	0.895833i
$185$		0			0
$186$	−6.34506	+	2.69774i	−0.465242	+	0.197808i
$187$	6.06473	−	1.06938i	0.443497	−	0.0782005i
$188$			13.5384i			0.987388i
$189$	−1.97271	+	2.27747i	−0.143493	+	0.165662i
$190$		0			0
$191$	−0.391371	−	2.21958i	−0.0283186	−	0.160603i	0.967369	−	0.253371i	$-0.0815395\pi$
$191$	−0.391371	−	2.21958i	−0.0283186	−	0.160603i	−0.995688	+	0.0927685i	$0.970428\pi$
$192$	10.7986	−	14.3478i	0.779320	−	1.03546i
$193$	0.301071	+	0.827186i	0.0216716	+	0.0595422i	0.950057	−	0.312077i	$-0.101025\pi$
$193$	0.301071	+	0.827186i	0.0216716	+	0.0595422i	−0.928385	+	0.371620i	$0.878803\pi$
$194$	9.74245	+	8.17489i	0.699467	+	0.586923i
$195$		0			0
$196$	23.5934	+	8.58731i	1.68525	+	0.613379i
$197$	−17.5600	+	10.1383i	−1.25110	+	0.722322i	−0.971328	−	0.237744i	$-0.923592\pi$
$197$	−17.5600	+	10.1383i	−1.25110	+	0.722322i	−0.279771	+	0.960067i	$0.590259\pi$
$198$	18.0137	−	13.1202i	1.28018	−	0.932413i
$199$	−9.50472	+	16.4627i	−0.673772	+	1.16701i	0.303054	+	0.952973i	$0.401994\pi$
$199$	−9.50472	+	16.4627i	−0.673772	+	1.16701i	−0.976826	+	0.214034i	$0.931340\pi$
$200$		0			0
$201$	−14.6405	−	4.46659i	−1.03266	−	0.315049i
$202$	−17.1921	−	3.03144i	−1.20963	−	0.213291i
$203$	−3.65445	−	0.644379i	−0.256492	−	0.0452265i
$204$	12.4277	+	3.79150i	0.870110	+	0.265458i
$205$		0			0
$206$	7.68684	−	13.3140i	0.535567	−	0.927630i
$207$	1.41202	+	13.2836i	0.0981420	+	0.923275i
$208$	9.68152	−	5.58963i	0.671293	−	0.387571i
$209$	11.1769	+	4.06806i	0.773123	+	0.281394i
$210$		0			0
$211$	12.3977	+	10.4029i	0.853494	+	0.716166i	0.960556	−	0.278086i	$-0.0897000\pi$
$211$	12.3977	+	10.4029i	0.853494	+	0.716166i	−0.107062	+	0.994252i	$0.534144\pi$
$212$	6.95919	+	19.1202i	0.477959	+	1.31318i
$213$	1.19253	−	1.58448i	0.0817107	−	0.108567i
$214$	−2.31191	−	13.1115i	−0.158039	−	0.896283i
$215$		0			0
$216$	21.7828	−	3.48960i	1.48213	−	0.237437i
$217$			0.961120i			0.0652451i
$218$	−14.7380	+	2.59871i	−0.998186	+	0.176007i
$219$	−0.311575	+	0.132473i	−0.0210543	+	0.00895168i
$220$		0			0
$221$	−6.40842	−	5.37730i	−0.431077	−	0.361716i
$222$	14.9414	+	7.60193i	1.00280	+	0.510208i
$223$	7.33883	−	20.1633i	0.491444	−	1.35023i	−0.407914	−	0.913020i	$-0.633744\pi$
$223$	7.33883	−	20.1633i	0.491444	−	1.35023i	0.899359	−	0.437212i	$-0.144034\pi$
$224$	−0.609223	−	1.05520i	−0.0407054	−	0.0705038i
$225$		0			0
$226$	−14.2224	+	24.6339i	−0.946058	+	1.63862i
$227$	12.2864	+	14.6424i	0.815477	+	0.971848i	0.999940	−	0.0109918i	$-0.00349886\pi$
$227$	12.2864	+	14.6424i	0.815477	+	0.971848i	−0.184462	+	0.982840i	$0.559054\pi$
$228$	17.1257	+	18.3434i	1.13418	+	1.21482i
$229$	−3.90190	+	22.1288i	−0.257845	+	1.46231i	0.530818	+	0.847486i	$0.321885\pi$
$229$	−3.90190	+	22.1288i	−0.257845	+	1.46231i	−0.788663	+	0.614826i	$0.789226\pi$
$230$		0			0
$231$	−0.700605	−	3.02650i	−0.0460964	−	0.199129i
$232$	17.4642	+	20.8130i	1.14658	+	1.36644i
$233$	15.3126	+	8.84074i	1.00316	+	0.579176i	0.909182	−	0.416398i	$-0.136708\pi$
$233$	15.3126	+	8.84074i	1.00316	+	0.579176i	0.0939796	+	0.995574i	$0.470041\pi$
$234$	−29.3823	−	7.28901i	−1.92078	−	0.476497i
$235$		0			0
$236$	36.4134	+	13.2534i	2.37031	+	0.862723i
$237$	−0.660752	−	12.4671i	−0.0429204	−	0.809826i
$238$	1.78223	−	2.12398i	0.115525	−	0.137677i
$239$	−14.4904	+	5.27406i	−0.937303	+	0.341151i	−0.765100	−	0.643911i	$-0.777311\pi$
$239$	−14.4904	+	5.27406i	−0.937303	+	0.341151i	−0.172203	+	0.985061i	$0.555088\pi$
$240$		0			0
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	0.965651	+	0.259844i	$0.0836711\pi$
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	−0.818543	+	0.574445i	$0.805218\pi$
$242$		−	3.44113i		−	0.221204i
$243$	−12.7956	−	8.90345i	−0.820841	−	0.571157i
$244$	49.7209			3.18305
$245$		0			0
$246$	−0.553018	+	4.52605i	−0.0352592	+	0.288571i
$247$	−5.52617	−	15.1830i	−0.351622	−	0.966073i
$248$	4.52329	−	5.39065i	0.287229	−	0.342307i
$249$	−25.7722	+	1.36591i	−1.63324	+	0.0865612i
$250$		0			0
$251$	−8.70830	−	15.0832i	−0.549663	−	0.952045i	−0.998297	−	0.0583292i	$-0.981423\pi$
$251$	−8.70830	−	15.0832i	−0.549663	−	0.952045i	0.448634	−	0.893716i	$-0.351911\pi$
$252$	1.57814	−	6.36155i	0.0994135	−	0.400740i
$253$	−11.9277	−	6.88646i	−0.749889	−	0.432948i
$254$	21.2112	−	17.7983i	1.33091	−	1.11676i
$255$		0			0
$256$	−5.03066	+	28.5303i	−0.314416	+	1.78314i
$257$	−11.0176	−	1.94270i	−0.687260	−	0.121182i	−0.180896	−	0.983502i	$-0.557900\pi$
$257$	−11.0176	−	1.94270i	−0.687260	−	0.121182i	−0.506364	+	0.862320i	$0.669011\pi$
$258$	−19.5904	−	20.9833i	−1.21964	−	1.30636i
$259$	1.79017	−	1.50213i	0.111236	−	0.0933377i
$260$		0			0
$261$	1.31662	−	19.1533i	0.0814965	−	1.18556i
$262$	−18.7433	+	10.8214i	−1.15796	+	0.668550i
$263$	−7.08354	+	19.4619i	−0.436790	+	1.20007i	0.504779	+	0.863249i	$0.331574\pi$
$263$	−7.08354	+	19.4619i	−0.436790	+	1.20007i	−0.941569	+	0.336821i	$0.890648\pi$
$264$	−10.3141	+	20.2720i	−0.634786	+	1.24766i
$265$		0			0
$266$	5.03221	−	1.83157i	0.308544	−	0.112301i
$267$	1.05256	+	2.47562i	0.0644159	+	0.151506i
$268$	32.7912	−	5.78197i	2.00304	−	0.353190i
$269$	28.2449			1.72212			0.861060	−	0.508504i	$-0.169801\pi$
$269$	28.2449			1.72212			0.861060	+	0.508504i	$0.169801\pi$
$270$		0			0
$271$	17.2626			1.04863			0.524316	−	0.851524i	$-0.324321\pi$
$271$	17.2626			1.04863			0.524316	+	0.851524i	$0.324321\pi$
$272$	−5.21680	+	0.919863i	−0.316315	+	0.0557749i
$273$	−2.53767	+	3.37175i	−0.153587	+	0.204067i
$274$	−25.9987	+	9.46275i	−1.57064	+	0.571666i
$275$		0			0
$276$	−15.8411	−	24.3616i	−0.953520	−	1.46640i
$277$	−1.76789	+	4.85725i	−0.106222	+	0.291844i	−0.981405	−	0.191949i	$-0.938519\pi$
$277$	−1.76789	+	4.85725i	−0.106222	+	0.291844i	0.875182	+	0.483793i	$0.160741\pi$
$278$	−3.54375	+	2.04598i	−0.212540	+	0.122710i
$279$	−4.94464	+	0.525604i	−0.296028	+	0.0314671i
$280$		0			0
$281$	−2.52522	+	2.11891i	−0.150642	+	0.126404i	−0.714994	−	0.699131i	$-0.753571\pi$
$281$	−2.52522	+	2.11891i	−0.150642	+	0.126404i	0.564352	+	0.825534i	$0.309126\pi$
$282$	−4.36156	+	14.2962i	−0.259727	+	0.851326i
$283$	−8.99200	−	1.58553i	−0.534519	−	0.0942501i	−0.100128	−	0.994975i	$-0.531925\pi$
$283$	−8.99200	−	1.58553i	−0.534519	−	0.0942501i	−0.434391	+	0.900724i	$0.643036\pi$
$284$	−0.749103	+	4.24837i	−0.0444511	+	0.252095i
$285$		0			0
$286$	23.9099	−	20.0628i	1.41382	−	1.18634i
$287$	0.550462	+	0.317809i	0.0324927	+	0.0187597i
$288$	5.09551	−	3.71130i	0.300256	−	0.218691i
$289$	−6.51799	−	11.2895i	−0.383411	−	0.664087i
$290$		0			0
$291$	5.00004	+	7.68945i	0.293108	+	0.450764i
$292$	0.473411	−	0.564189i	0.0277043	−	0.0330167i
$293$	0.966697	+	2.65598i	0.0564750	+	0.155164i	0.964722	−	0.263271i	$-0.0848012\pi$
$293$	0.966697	+	2.65598i	0.0564750	+	0.155164i	−0.908247	+	0.418434i	$0.862579\pi$
$294$	22.1476	+	16.6689i	1.29167	+	0.972151i
$295$		0			0
$296$	−17.1100			−0.994496
$297$	15.1872	−	5.25947i	0.881251	−	0.305185i
$298$			52.0017i			3.01238i
$299$	3.24888	+	18.4253i	0.187887	+	1.06556i
$300$		0			0
$301$	−3.76036	+	1.36866i	−0.216744	+	0.0788882i
$302$	7.31964	−	8.72321i	0.421198	−	0.501964i
$303$	−11.2214	−	5.70923i	−0.644650	−	0.327987i
$304$	−9.61423	−	3.49929i	−0.551414	−	0.200698i
$305$		0			0
$306$	11.9018	+	8.00746i	0.680382	+	0.457756i
$307$	5.45116	+	3.14723i	0.311114	+	0.179622i	0.647425	−	0.762129i	$-0.275846\pi$
$307$	5.45116	+	3.14723i	0.311114	+	0.179622i	−0.336311	+	0.941751i	$0.609179\pi$
$308$	4.34380	+	5.17673i	0.247511	+	0.294972i
$309$	8.10442	−	7.56644i	0.461045	−	0.430440i
$310$		0			0
$311$	−1.28029	+	7.26088i	−0.0725985	+	0.411727i	0.926751	+	0.375675i	$0.122589\pi$
$311$	−1.28029	+	7.26088i	−0.0725985	+	0.411727i	−0.999350	+	0.0360515i	$0.988522\pi$
$312$	30.1015	−	6.96818i	1.70416	−	0.394496i
$313$	−2.74519	−	3.27159i	−0.155167	−	0.184921i	0.682860	−	0.730549i	$-0.260736\pi$
$313$	−2.74519	−	3.27159i	−0.155167	−	0.184921i	−0.838028	+	0.545628i	$0.816291\pi$
$314$	0.251217	−	0.435120i	0.0141770	−	0.0245552i
$315$		0			0
$316$	13.5791	+	23.5197i	0.763883	+	1.32308i
$317$	−5.52279	+	15.1738i	−0.310191	+	0.852243i	0.682426	+	0.730954i	$0.260925\pi$
$317$	−5.52279	+	15.1738i	−0.310191	+	0.852243i	−0.992617	+	0.121288i	$0.961297\pi$
$318$	1.18891	+	22.4325i	0.0666708	+	1.25795i
$319$	15.1632	+	12.7235i	0.848979	+	0.712378i
$320$		0			0
$321$	1.16455	−	9.53101i	0.0649989	−	0.531969i
$322$	−6.10682	+	1.07680i	−0.340320	+	0.0600075i
$323$			7.65618i			0.426001i
$324$	33.5911	+	4.64009i	1.86617	+	0.257783i
$325$		0			0
$326$	−2.34535	−	13.3012i	−0.129897	−	0.736683i
$327$	−10.7134	−	1.30902i	−0.592451	−	0.0723890i
$328$	−1.59169	−	4.37313i	−0.0878862	−	0.241465i
$329$	1.59610	+	1.33928i	0.0879956	+	0.0738371i
$330$		0			0
$331$	−18.0686	−	6.57644i	−0.993142	−	0.361474i	−0.206206	−	0.978509i	$-0.566112\pi$
$331$	−18.0686	−	6.57644i	−0.993142	−	0.361474i	−0.786936	+	0.617035i	$0.788334\pi$
$332$	48.6201	−	28.0708i	2.66838	−	1.54059i
$333$	8.70693	+	8.38834i	0.477137	+	0.459678i
$334$	−20.0301	+	34.6932i	−1.09600	+	1.89833i
$335$		0			0
$336$	0.602651	+	2.60336i	0.0328773	+	0.142025i
$337$	29.0152	+	5.11615i	1.58056	+	0.278695i	0.893893	−	0.448281i	$-0.147964\pi$
$337$	29.0152	+	5.11615i	1.58056	+	0.278695i	0.686663	+	0.726976i	$0.259075\pi$
$338$	−11.0087	−	1.94112i	−0.598792	−	0.105583i
$339$	−14.9950	+	13.9996i	−0.814417	+	0.760355i
$340$		0			0
$341$	2.56339	−	4.43993i	0.138815	−	0.240435i
$342$	12.1748	+	24.8874i	0.658337	+	1.34576i
$343$	6.86159	−	3.96154i	0.370491	−	0.213903i
$344$	27.5321	+	10.0209i	1.48443	+	0.540289i
$345$		0			0
$346$	−34.9592	−	29.3342i	−1.87942	−	1.57702i
$347$	3.89801	+	10.7097i	0.209256	+	0.574927i	0.999272	−	0.0381600i	$-0.0121497\pi$
$347$	3.89801	+	10.7097i	0.209256	+	0.574927i	−0.790015	+	0.613087i	$0.789927\pi$
$348$	16.3408	+	38.4336i	0.875961	+	2.06025i
$349$	−4.89021	−	27.7338i	−0.261767	−	1.48456i	−0.778085	−	0.628158i	$-0.783809\pi$
$349$	−4.89021	−	27.7338i	−0.261767	−	1.48456i	0.516318	−	0.856397i	$-0.327302\pi$
$350$		0			0
$351$	−18.7343	−	11.2116i	−0.999962	−	0.598431i
$352$			6.49941i			0.346419i
$353$	−28.2188	+	4.97573i	−1.50193	+	0.264831i	−0.863305	−	0.504683i	$-0.831609\pi$
$353$	−28.2188	+	4.97573i	−1.50193	+	0.264831i	−0.638629	+	0.769515i	$0.720498\pi$
$354$	34.1819	+	25.7263i	1.81675	+	1.36734i
$355$		0			0
$356$	−4.48277	−	3.76149i	−0.237586	−	0.199359i
$357$	1.67640	−	1.09007i	0.0887245	−	0.0576929i
$358$	−13.3357	+	36.6394i	−0.704812	+	1.93645i
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	−0.906486	−	0.422235i	$-0.861246\pi$
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	0.0875770	−	0.996158i	$-0.472088\pi$
$360$		0			0
$361$	2.10636	−	3.64833i	0.110861	−	0.192017i
$362$	−4.61820	−	5.50376i	−0.242727	−	0.289271i
$363$	0.724191	−	2.37373i	0.0380102	−	0.124589i
$364$	1.59408	−	9.04045i	0.0835523	−	0.473848i
$365$		0			0
$366$	52.5040	+	16.0182i	2.74443	+	0.837286i
$367$	−15.5067	−	18.4802i	−0.809446	−	0.964660i	0.190409	−	0.981705i	$-0.439019\pi$
$367$	−15.5067	−	18.4802i	−0.809446	−	0.964660i	−0.999855	+	0.0170450i	$0.994574\pi$
$368$	10.2601	+	5.92365i	0.534843	+	0.308791i
$369$	−1.33399	+	3.00574i	−0.0694449	+	0.156473i
$370$		0			0
$371$	2.94260	+	1.07102i	0.152772	+	0.0556045i
$372$	9.06828	−	5.89662i	0.470169	−	0.305726i
$373$	8.08988	−	9.64114i	0.418878	−	0.499199i	−0.514801	−	0.857309i	$-0.672134\pi$
$373$	8.08988	−	9.64114i	0.418878	−	0.499199i	0.933679	+	0.358110i	$0.116579\pi$
$374$	−13.8979	+	5.05843i	−0.718645	+	0.261565i
$375$		0			0
$376$	−2.64902	−	15.0233i	−0.136613	−	0.774769i
$377$		−	26.8890i		−	1.38486i
$378$	3.71593	−	6.20922i	0.191127	−	0.319368i
$379$	7.70522			0.395790			0.197895	−	0.980223i	$-0.436589\pi$
$379$	7.70522			0.395790			0.197895	+	0.980223i	$0.436589\pi$
$380$		0			0
$381$	18.3774	−	7.81354i	0.941502	−	0.400300i
$382$	1.85129	+	5.08638i	0.0947203	+	0.260242i
$383$	11.4812	−	13.6828i	0.586664	−	0.699159i	−0.388297	−	0.921534i	$-0.626937\pi$
$383$	11.4812	−	13.6828i	0.586664	−	0.699159i	0.974961	+	0.222376i	$0.0713811\pi$
$384$	−16.2557	+	31.9503i	−0.829548	+	1.63046i
$385$		0			0
$386$	−1.05704	−	1.83085i	−0.0538020	−	0.0931878i
$387$	−9.09771	−	18.5973i	−0.462463	−	0.945356i
$388$	−17.2793	−	9.97622i	−0.877224	−	0.506466i
$389$	−20.9808	+	17.6050i	−1.06377	+	0.892607i	−0.994473	−	0.104989i	$-0.966519\pi$
$389$	−20.9808	+	17.6050i	−1.06377	+	0.892607i	−0.0692941	+	0.997596i	$0.522075\pi$
$390$		0			0
$391$	1.53948	−	8.73081i	0.0778547	−	0.441536i
$392$	−27.8615	−	4.91274i	−1.40722	−	0.248131i
$393$	−15.2067	+	3.52020i	−0.767078	+	0.177571i
$394$	37.3038	−	31.3016i	1.87934	−	1.57695i
$395$		0			0
$396$	−24.2571	+	25.1784i	−1.21896	+	1.26526i
$397$	−3.65115	+	2.10799i	−0.183246	+	0.105797i	−0.588817	−	0.808266i	$-0.700406\pi$
$397$	−3.65115	+	2.10799i	−0.183246	+	0.105797i	0.405571	+	0.914064i	$0.367073\pi$
$398$	15.6144	−	42.9002i	0.782680	−	2.15039i
$399$	3.85673	−	0.204405i	0.193078	−	0.0102331i
$400$		0			0
$401$	−14.2575	+	5.18930i	−0.711985	+	0.259141i	−0.672519	−	0.740080i	$-0.734788\pi$
$401$	−14.2575	+	5.18930i	−0.711985	+	0.259141i	−0.0394656	+	0.999221i	$0.512566\pi$
$402$	36.4894	+	4.45848i	1.81993	+	0.222369i
$403$	−6.85857	+	1.20935i	−0.341650	+	0.0602420i
$404$	27.3880			1.36260
$405$		0			0
$406$	8.91200			0.442295
$407$	−12.2760	+	2.16460i	−0.608501	+	0.107295i
$408$	−14.5326	−	1.77568i	−0.719473	−	0.0879093i
$409$	4.42559	−	1.61078i	0.218831	−	0.0796481i	−0.230278	−	0.973125i	$-0.573964\pi$
$409$	4.42559	−	1.61078i	0.218831	−	0.0796481i	0.449109	+	0.893477i	$0.351741\pi$
$410$		0			0
$411$	−19.9257	+	1.05605i	−0.982860	+	0.0520912i
$412$	−8.24918	+	22.6644i	−0.406408	+	1.11660i
$413$	5.16469	−	2.98184i	0.254138	−	0.146727i
$414$	−8.87937	−	30.8287i	−0.436397	−	1.51515i
$415$		0			0
$416$	6.76339	−	5.67516i	0.331602	−	0.278248i
$417$	−2.87510	+	0.665556i	−0.140794	+	0.0325924i
$418$	−28.1314	−	4.96033i	−1.37595	−	0.242618i
$419$	−3.43669	+	19.4905i	−0.167894	+	0.952171i	0.778137	+	0.628094i	$0.216165\pi$
$419$	−3.43669	+	19.4905i	−0.167894	+	0.952171i	−0.946031	+	0.324077i	$0.894946\pi$
$420$		0			0
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.0589715	−	0.998260i	$-0.481218\pi$
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.993334	+	0.115270i	$0.0367734\pi$
$422$	−33.6607	−	19.4340i	−1.63858	−	0.946032i
$423$	−6.01731	+	8.94379i	−0.292572	+	0.434862i
$424$	−11.4637	−	19.8557i	−0.556726	−	0.964278i
$425$		0			0
$426$	−2.15970	+	4.24484i	−0.104638	+	0.205663i
$427$	4.91863	−	5.86180i	0.238029	−	0.283672i
$428$	7.14387	+	19.6276i	0.345312	+	0.948737i
$429$	20.7156	−	8.80769i	1.00016	−	0.425239i
$430$		0			0
$431$	−5.19681			−0.250321			−0.125161	−	0.992136i	$-0.539945\pi$
$431$	−5.19681			−0.250321			−0.125161	+	0.992136i	$0.539945\pi$
$432$	−13.0638	+	4.52413i	−0.628534	+	0.217667i
$433$			25.3285i			1.21721i	0.793473	+	0.608605i	$0.208270\pi$
$433$			25.3285i			1.21721i	−0.793473	+	0.608605i	$0.791730\pi$
$434$	−0.400823	−	2.27318i	−0.0192401	−	0.109116i
$435$		0			0
$436$	22.0625	−	8.03011i	1.05660	−	0.384572i
$437$	11.0064	−	13.1169i	0.526509	−	0.627469i
$438$	0.681671	−	0.443254i	0.0325715	−	0.0211795i
$439$	−14.7167	−	5.35646i	−0.702392	−	0.255650i	−0.0339602	−	0.999423i	$-0.510812\pi$
$439$	−14.7167	−	5.35646i	−0.702392	−	0.255650i	−0.668432	+	0.743773i	$0.733034\pi$
$440$		0			0
$441$	11.7697	+	16.1594i	0.560460	+	0.769496i
$442$	17.3993	+	10.0455i	0.827600	+	0.477815i
$443$	−11.7333	−	13.9833i	−0.557468	−	0.664365i	0.411541	−	0.911391i	$-0.364991\pi$
$443$	−11.7333	−	13.9833i	−0.557468	−	0.664365i	−0.969009	+	0.247027i	$0.920546\pi$
$444$	−25.1557	−	7.67464i	−1.19384	−	0.364222i
$445$		0			0
$446$	−8.94849	+	50.7494i	−0.423723	+	2.40305i
$447$	−10.9439	+	35.8714i	−0.517626	+	1.69666i
$448$	3.86434	+	4.60534i	0.182573	+	0.217582i
$449$	14.3608	−	24.8737i	0.677729	−	1.17386i	−0.297934	−	0.954586i	$-0.596298\pi$
$449$	14.3608	−	24.8737i	0.677729	−	1.17386i	0.975663	−	0.219274i	$-0.0703690\pi$
$450$		0			0
$451$	−1.69525	−	2.93626i	−0.0798262	−	0.138263i
$452$	15.2628	−	41.9343i	0.717904	−	1.97242i
$453$	6.88499	−	4.47694i	0.323485	−	0.210345i
$454$	−35.1654	−	29.5073i	−1.65039	−	1.38485i
$455$		0			0
$456$	−22.5933	−	17.0044i	−1.05803	−	0.796304i
$457$	−34.8503	+	6.14505i	−1.63023	+	0.287453i	−0.912563	−	0.408936i	$-0.865900\pi$
$457$	−34.8503	+	6.14505i	−1.63023	+	0.287453i	−0.717665	+	0.696389i	$0.754789\pi$
$458$		−	53.9648i		−	2.52161i
$459$	6.52484	+	8.02840i	0.304553	+	0.374734i
$460$		0			0
$461$	0.395350	+	2.24214i	0.0184133	+	0.104427i	0.992629	−	0.121190i	$-0.0386712\pi$
$461$	0.395350	+	2.24214i	0.0184133	+	0.104427i	−0.974216	+	0.225617i	$0.927560\pi$
$462$	2.91919	+	6.86591i	0.135813	+	0.319431i
$463$	−6.28446	−	17.2664i	−0.292064	−	0.802438i	−0.995764	−	0.0919417i	$-0.970693\pi$
$463$	−6.28446	−	17.2664i	−0.292064	−	0.802438i	0.703701	−	0.710496i	$-0.251530\pi$
$464$	−13.0432	−	10.9446i	−0.605517	−	0.508089i
$465$		0			0
$466$	−39.9033	−	14.5236i	−1.84848	−	0.672793i
$467$	−4.03455	+	2.32935i	−0.186697	+	0.107789i	−0.590435	−	0.807085i	$-0.701044\pi$
$467$	−4.03455	+	2.32935i	−0.186697	+	0.107789i	0.403738	+	0.914874i	$0.367711\pi$
$468$	47.3819	+	3.25707i	2.19023	+	0.150558i
$469$	2.56220	−	4.43786i	0.118312	−	0.204922i
$470$		0			0
$471$	0.264864	−	0.247282i	0.0122043	−	0.0113941i
$472$	−43.0007	−	7.58218i	−1.97927	−	0.348998i
$473$	21.0215	+	3.70665i	0.966568	+	0.170432i
$474$	6.76202	+	29.2109i	0.310590	+	1.34170i
$475$		0			0
$476$	−2.17495	+	3.76712i	−0.0996885	+	0.172666i
$477$	−3.90082	+	15.7244i	−0.178606	+	0.719970i
$478$	32.0722	−	18.5169i	1.46695	−	0.846942i
$479$	−13.3210	−	4.84844i	−0.608651	−	0.221531i	0.0192617	−	0.999814i	$-0.493868\pi$
$479$	−13.3210	−	4.84844i	−0.608651	−	0.221531i	−0.627913	+	0.778283i	$0.716091\pi$
$480$		0			0
$481$	12.9717	+	10.8846i	0.591460	+	0.496294i
$482$	−10.8026	−	29.6800i	−0.492047	−	1.35189i
$483$	−4.43917	−	0.542402i	−0.201989	−	0.0246802i
$484$	0.937459	+	5.31660i	0.0426118	+	0.241663i
$485$		0			0
$486$	33.9765	+	15.7216i	1.54121	+	0.713147i
$487$			21.4338i			0.971258i	0.874165	+	0.485629i	$0.161409\pi$
$487$			21.4338i			0.971258i	−0.874165	+	0.485629i	$0.838591\pi$
$488$	−55.1745	+	9.72875i	−2.49763	+	0.440400i
$489$	1.18140	−	9.66888i	0.0534246	−	0.437242i
$490$		0			0
$491$	−10.7919	−	9.05550i	−0.487033	−	0.408669i	0.365929	−	0.930643i	$-0.380751\pi$
$491$	−10.7919	−	9.05550i	−0.487033	−	0.408669i	−0.852961	+	0.521974i	$0.825196\pi$
$492$	−0.378601	−	7.14348i	−0.0170687	−	0.322053i
$493$	−4.35779	+	11.9729i	−0.196265	+	0.539234i
$494$	19.4020	+	33.6053i	0.872938	+	1.51197i
$495$		0			0
$496$	−2.20500	+	3.81917i	−0.0990073	+	0.171486i
$497$	0.426753	+	0.508585i	0.0191425	+	0.0228131i
$498$	60.3850	−	13.9785i	2.70592	−	0.626392i
$499$	−2.58898	+	14.6828i	−0.115899	+	0.657294i	0.870403	+	0.492340i	$0.163858\pi$
$499$	−2.58898	+	14.6828i	−0.115899	+	0.657294i	−0.986301	+	0.164953i	$0.947253\pi$
$500$		0			0
$501$	−21.1182	+	19.7164i	−0.943494	+	0.880864i
$502$	26.8866	+	32.0422i	1.20001	+	1.43011i
$503$	13.7378	+	7.93153i	0.612539	+	0.353650i	0.773958	−	0.633236i	$-0.218274\pi$
$503$	13.7378	+	7.93153i	0.612539	+	0.353650i	−0.161420	+	0.986886i	$0.551607\pi$
$504$	−0.506490	+	7.36810i	−0.0225608	+	0.328201i
$505$		0			0
$506$	31.0826	+	11.3131i	1.38179	+	0.502930i
$507$	−7.18540	−	3.65580i	−0.319115	−	0.162360i
$508$	−27.9228	+	33.2771i	−1.23888	+	1.47643i
$509$	31.8807	−	11.6036i	1.41309	−	0.514321i	0.481052	−	0.876692i	$-0.340255\pi$
$509$	31.8807	−	11.6036i	1.41309	−	0.514321i	0.932034	+	0.362371i	$0.118033\pi$
$510$		0			0
$511$	−0.0196825	−	0.111625i	−0.000870700	−	0.00493799i
$512$		−	28.1824i		−	1.24550i
$513$	3.16072	+	19.7298i	0.139549	+	0.871093i
$514$	26.8683			1.18511
$515$		0			0
$516$	35.9839	+	27.0825i	1.58410	+	1.19224i
$517$	−3.80123	−	10.4438i	−0.167178	−	0.459317i
$518$	−3.60754	+	4.29930i	−0.158506	+	0.188900i
$519$	−17.9418	−	27.5923i	−0.787558	−	1.21117i
$520$		0			0
$521$	21.3899	+	37.0484i	0.937108	+	1.62312i	0.770831	+	0.637040i	$0.219841\pi$
$521$	21.3899	+	37.0484i	0.937108	+	1.62312i	0.166277	+	0.986079i	$0.446825\pi$
$522$	4.87367	+	45.8493i	0.213315	+	2.00677i
$523$	2.40569	+	1.38893i	0.105193	+	0.0607335i	0.551674	−	0.834060i	$-0.313989\pi$
$523$	2.40569	+	1.38893i	0.105193	+	0.0607335i	−0.446480	+	0.894793i	$0.647323\pi$
$524$	26.0106	−	21.8255i	1.13628	−	0.953451i
$525$		0			0
$526$	8.63721	−	48.9840i	0.376600	−	2.13581i
$527$	3.24992	+	0.573049i	0.141569	+	0.0249624i
$528$	4.15942	−	13.6336i	0.181016	−	0.593327i
$529$	2.43023	−	2.03920i	0.105662	−	0.0886609i
$530$		0			0
$531$	18.1650	+	24.9400i	0.788292	+	1.08230i
$532$	−7.27587	+	4.20073i	−0.315449	+	0.182125i
$533$	−1.57526	+	4.32799i	−0.0682321	+	0.187466i
$534$	−3.52188	−	5.41622i	−0.152407	−	0.234383i
$535$		0			0
$536$	−35.2565	+	12.8323i	−1.52285	+	0.554271i
$537$	−16.9099	+	22.4678i	−0.729717	+	0.969557i
$538$	−66.8029	+	11.7792i	−2.88008	+	0.507835i
$539$	−20.6116			−0.887803
$540$		0			0
$541$	−3.59390			−0.154514			−0.0772570	−	0.997011i	$-0.524616\pi$
$541$	−3.59390			−0.154514			−0.0772570	+	0.997011i	$0.524616\pi$
$542$	−40.8285	+	7.19917i	−1.75373	+	0.309231i
$543$	−2.02741	−	4.76846i	−0.0870047	−	0.204634i
$544$	−3.93130	+	1.43088i	−0.168553	+	0.0613483i
$545$		0			0
$546$	4.59580	−	9.03294i	0.196682	−	0.386574i
$547$	13.5392	−	37.1985i	0.578892	−	1.59049i	−0.211158	−	0.977452i	$-0.567724\pi$
$547$	13.5392	−	37.1985i	0.578892	−	1.59049i	0.790051	−	0.613042i	$-0.210054\pi$
$548$	37.5905	−	21.7029i	1.60579	−	0.927101i
$549$	32.8468	+	22.0991i	1.40187	+	0.943167i
$550$		0			0
$551$	−18.8514	+	15.8182i	−0.803099	+	0.673880i
$552$	22.3453	+	23.9341i	0.951081	+	1.01870i
$553$	4.11614	+	0.725786i	0.175036	+	0.0308636i
$554$	2.15566	−	12.2253i	0.0915850	−	0.519405i
$555$		0			0
$556$	4.91776	−	4.12649i	0.208560	−	0.175002i
$557$	−9.90267	−	5.71731i	−0.419590	−	0.242250i	0.275312	−	0.961355i	$-0.411219\pi$
$557$	−9.90267	−	5.71731i	−0.419590	−	0.242250i	−0.694902	+	0.719105i	$0.744552\pi$
$558$	11.4756	−	3.30522i	0.485799	−	0.139921i
$559$	−14.4983	−	25.1119i	−0.613214	−	1.06212i
$560$		0			0
$561$	−10.6515	+	0.564526i	−0.449707	+	0.0238343i
$562$	5.08882	−	6.06462i	0.214659	−	0.255821i
$563$	−4.96298	−	13.6357i	−0.209165	−	0.574676i	0.790101	−	0.612976i	$-0.210028\pi$
$563$	−4.96298	−	13.6357i	−0.209165	−	0.574676i	−0.999266	+	0.0383005i	$0.987806\pi$
$564$	2.84400	−	23.2761i	0.119754	−	0.980099i
$565$		0			0
$566$	21.9285			0.921725
$567$	3.87003	−	3.50117i	0.162526	−	0.147035i
$568$		−	4.86093i		−	0.203960i
$569$	0.225601	+	1.27945i	0.00945767	+	0.0536371i	0.989171	−	0.146765i	$-0.0468862\pi$
$569$	0.225601	+	1.27945i	0.00945767	+	0.0536371i	−0.979714	+	0.200402i	$0.935775\pi$
$570$		0			0
$571$	−15.0890	+	5.49193i	−0.631453	+	0.229830i	−0.637864	−	0.770149i	$-0.720182\pi$
$571$	−15.0890	+	5.49193i	−0.631453	+	0.229830i	0.00641065	+	0.999979i	$0.497959\pi$
$572$	−31.4756	+	37.5111i	−1.31606	+	1.56842i
$573$	0.206606	+	3.89825i	0.00863108	+	0.162852i
$574$	−1.43445	−	0.522099i	−0.0598730	−	0.0217920i
$575$		0			0
$576$	−21.5796	+	22.3992i	−0.899152	+	0.933301i
$577$	−7.32686	−	4.23017i	−0.305021	−	0.176104i	0.339675	−	0.940543i	$-0.389683\pi$
$577$	−7.32686	−	4.23017i	−0.305021	−	0.176104i	−0.644696	+	0.764439i	$0.723016\pi$
$578$	20.1241	+	23.9829i	0.837050	+	0.997558i
$579$	−0.343854	−	1.48540i	−0.0142901	−	0.0617310i
$580$		0			0
$581$	1.50035	−	8.50893i	0.0622452	−	0.353010i
$582$	−15.0326	−	16.1014i	−0.623120	−	0.667424i
$583$	−10.7369	−	12.7958i	−0.444678	−	0.529947i
$584$	−0.414943	+	0.718703i	−0.0171705	+	0.0297401i
$585$		0			0
$586$	−3.39401	−	5.87860i	−0.140205	−	0.242843i
$587$	6.28811	−	17.2764i	0.259538	−	0.713075i	−0.739658	−	0.672983i	$-0.765013\pi$
$587$	6.28811	−	17.2764i	0.259538	−	0.713075i	0.999196	−	0.0400919i	$-0.0127651\pi$
$588$	−38.7594	−	19.7201i	−1.59841	−	0.813244i
$589$	4.88260	+	4.09699i	0.201184	+	0.168814i
$590$		0			0
$591$	32.3200	−	13.7416i	1.32947	−	0.565252i
$592$	10.5597	−	1.86196i	0.434001	−	0.0765260i
$593$			13.5128i			0.554905i	0.960739	+	0.277452i	$0.0894901\pi$
$593$			13.5128i			0.554905i	−0.960739	+	0.277452i	$0.910510\pi$
$594$	−33.7264	+	18.7730i	−1.38381	+	0.770265i
$595$		0			0
$596$	−14.1667	−	80.3435i	−0.580292	−	3.29100i
$597$	19.7994	−	26.3070i	0.810337	−	1.07667i
$598$	−15.3681	−	42.2234i	−0.628447	−	1.72664i
$599$	−8.44772	−	7.08848i	−0.345165	−	0.289627i	0.453680	−	0.891164i	$-0.350111\pi$
$599$	−8.44772	−	7.08848i	−0.345165	−	0.289627i	−0.798845	+	0.601537i	$0.794555\pi$
$600$		0			0
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.203579	−	0.979058i	$-0.565257\pi$
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.785277	+	0.619144i	$0.787480\pi$
$602$	8.32298	−	4.80528i	0.339219	−	0.195848i
$603$	24.2325	+	10.7548i	0.986824	+	0.437968i
$604$	−8.93252	+	15.4716i	−0.363459	+	0.629529i
$605$		0			0
$606$	28.9210	+	8.82338i	1.17484	+	0.358425i
$607$	14.5652	+	2.56823i	0.591182	+	0.104241i	0.461233	−	0.887279i	$-0.347407\pi$
$607$	14.5652	+	2.56823i	0.591182	+	0.104241i	0.129950	+	0.991521i	$0.458518\pi$
$608$	−7.95752	−	1.40312i	−0.322720	−	0.0569042i
$609$	6.14761	+	1.87555i	0.249114	+	0.0760009i
$610$		0			0
$611$	−7.54882	+	13.0749i	−0.305393	+	0.528956i
$612$	−20.5700	−	9.12926i	−0.831492	−	0.369029i
$613$	31.4141	−	18.1370i	1.26880	−	0.732545i	0.294043	−	0.955792i	$-0.404999\pi$
$613$	31.4141	−	18.1370i	1.26880	−	0.732545i	0.974762	+	0.223248i	$0.0716658\pi$
$614$	−14.2053	−	5.17029i	−0.573277	−	0.208656i
$615$		0			0
$616$	−5.83316	−	4.89460i	−0.235025	−	0.197209i
$617$	−13.8086	−	37.9387i	−0.555912	−	1.52736i	−0.825513	−	0.564383i	$-0.809114\pi$
$617$	−13.8086	−	37.9387i	−0.555912	−	1.52736i	0.269601	−	0.962972i	$-0.413108\pi$
$618$	−16.0126	+	21.2755i	−0.644120	+	0.855826i
$619$	1.19701	+	6.78858i	0.0481119	+	0.272856i	0.999368	−	0.0355458i	$-0.0113170\pi$
$619$	1.19701	+	6.78858i	0.0481119	+	0.272856i	−0.951256	+	0.308402i	$0.900206\pi$
$620$		0			0
$621$	0.362848	−	23.1347i	0.0145606	−	0.928362i
$622$		−	17.7069i		−	0.709981i
$623$	−0.886916	+	0.156387i	−0.0355335	+	0.00626552i
$624$	−17.8193	+	7.57626i	−0.713343	+	0.303293i
$625$		0			0
$626$	7.85711	+	6.59290i	0.314033	+	0.263505i
$627$	−18.3615	−	9.34200i	−0.733287	−	0.373083i
$628$	−0.269595	+	0.740705i	−0.0107580	+	0.0295574i
$629$	−4.01193	−	6.94887i	−0.159966	−	0.277070i
$630$		0			0
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	0.400212	+	0.916423i	$0.368936\pi$
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	−0.993751	+	0.111617i	$0.964397\pi$
$632$	−19.6705	−	23.4424i	−0.782451	−	0.932489i
$633$	−19.1296	−	20.4897i	−0.760334	−	0.814394i
$634$	6.73414	−	38.1912i	0.267447	−	1.51677i
$635$		0			0
$636$	−7.94811	−	34.3346i	−0.315163	−	1.36146i
$637$	17.9976	+	21.4487i	0.713092	+	0.849830i
$638$	−41.1693	−	23.7691i	−1.62991	−	0.941028i
$639$	−2.38312	+	2.47363i	−0.0942749	+	0.0978554i
$640$		0			0
$641$	−40.2947	−	14.6661i	−1.59155	−	0.579275i	−0.613872	−	0.789406i	$-0.710389\pi$
$641$	−40.2947	−	14.6661i	−1.59155	−	0.579275i	−0.977673	+	0.210131i	$0.932611\pi$
$642$	1.22046	+	23.0278i	0.0481678	+	0.908834i
$643$	17.6209	−	20.9998i	0.694901	−	0.828150i	−0.297038	−	0.954866i	$-0.595999\pi$
$643$	17.6209	−	20.9998i	0.694901	−	0.828150i	0.991939	+	0.126715i	$0.0404434\pi$
$644$	9.14178	−	3.32734i	0.360237	−	0.131115i
$645$		0			0
$646$	−3.19291	−	18.1079i	−0.125623	−	0.712446i
$647$			16.1623i			0.635407i	0.948190	+	0.317703i	$0.102912\pi$
$647$			16.1623i			0.635407i	−0.948190	+	0.317703i	$0.897088\pi$
$648$	−38.1834	+	1.42365i	−1.49999	+	0.0559261i
$649$	−31.8113			−1.24870
$650$		0			0
$651$	0.201902	−	1.65242i	0.00791316	−	0.0647634i
$652$	7.24721	+	19.9116i	0.283823	+	0.779797i
$653$	−20.7275	+	24.7021i	−0.811130	+	0.966668i	−0.999882	−	0.0153573i	$-0.995111\pi$
$653$	−20.7275	+	24.7021i	−0.811130	+	0.966668i	0.188752	+	0.982025i	$0.439556\pi$
$654$	25.8845	−	1.37187i	1.01216	−	0.0536442i
$655$		0			0
$656$	1.45823	+	2.52573i	0.0569344	+	0.0986133i
$657$	0.563508	−	0.162303i	0.0219846	−	0.00633206i
$658$	−4.33351	−	2.50195i	−0.168938	−	0.0975363i
$659$	−21.3103	+	17.8814i	−0.830130	+	0.696562i	−0.955321	−	0.295571i	$-0.904490\pi$
$659$	−21.3103	+	17.8814i	−0.830130	+	0.696562i	0.125191	+	0.992133i	$0.460046\pi$
$660$		0			0
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	−0.684779	−	0.728751i	$-0.740101\pi$
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	0.892729	−	0.450594i	$-0.148788\pi$
$662$	45.4774	+	8.01889i	1.76753	+	0.311663i
$663$	9.88816	+	10.5912i	0.384024	+	0.411329i
$664$	−48.4604	+	40.6631i	−1.88063	+	1.57803i
$665$		0			0
$666$	−24.0913	−	16.2085i	−0.933519	−	0.628065i
$667$	24.6781	−	14.2479i	0.955540	−	0.551682i
$668$	21.4955	−	59.0583i	0.831684	−	2.28503i
$669$	−16.8531	+	33.1243i	−0.651577	+	1.28066i
$670$		0			0
$671$	−38.3557	+	13.9603i	−1.48071	+	0.538933i
$672$	0.825749	+	1.94216i	0.0318540	+	0.0749203i
$673$	25.7336	−	4.53753i	0.991959	−	0.174909i	0.345961	−	0.938249i	$-0.387553\pi$
$673$	25.7336	−	4.53753i	0.991959	−	0.174909i	0.645997	+	0.763340i	$0.276442\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	17.9181	−	3.15944i	0.688648	−	0.121427i	0.181635	−	0.983366i	$-0.441861\pi$
$677$	17.9181	−	3.15944i	0.688648	−	0.121427i	0.507012	+	0.861939i	$0.330750\pi$
$678$	29.6269	−	39.3645i	1.13781	−	1.51178i
$679$	−2.88549	+	1.05023i	−0.110735	+	0.0403042i
$680$		0			0
$681$	−18.0477	−	27.7551i	−0.691588	−	1.06358i
$682$	−4.21116	+	11.5701i	−0.161253	+	0.443040i
$683$	20.3491	−	11.7486i	0.778636	−	0.449546i	−0.0573104	−	0.998356i	$-0.518252\pi$
$683$	20.3491	−	11.7486i	0.778636	−	0.449546i	0.835947	+	0.548811i	$0.184919\pi$
$684$	−25.5903	−	35.1347i	−0.978468	−	1.34341i
$685$		0			0
$686$	−14.5765	+	12.2311i	−0.556533	+	0.466987i
$687$	11.3570	−	37.2256i	0.433296	−	1.42024i
$688$	−18.0824	−	3.18841i	−0.689384	−	0.121557i
$689$	−3.94021	+	22.3460i	−0.150110	+	0.851317i
$690$		0			0
$691$	−34.1180	+	28.6284i	−1.29791	+	1.08908i	−0.307409	+	0.951577i	$0.599462\pi$
$691$	−34.1180	+	28.6284i	−1.29791	+	1.08908i	−0.990502	+	0.137499i	$0.956094\pi$
$692$	62.0039	+	35.7980i	2.35704	+	1.36084i
$693$	0.568750	+	5.35054i	0.0216050	+	0.203250i
$694$	−13.6857	−	23.7043i	−0.519501	−	0.899802i
$695$		0			0
$696$	−25.6534	−	39.4517i	−0.972388	−	1.49541i
$697$	1.40284	−	1.67184i	0.0531363	−	0.0633254i
$698$	23.1320	+	63.5547i	0.875560	+	2.40558i
$699$	−24.4692	−	18.4163i	−0.925512	−	0.696567i
$700$		0			0
$701$	−25.2567			−0.953934			−0.476967	−	0.878921i	$-0.658264\pi$
$701$	−25.2567			−0.953934			−0.476967	+	0.878921i	$0.658264\pi$
$702$	48.9848	+	18.7041i	1.84881	+	0.705939i
$703$		−	15.4974i		−	0.584496i
$704$	−5.56859	−	31.5810i	−0.209874	−	1.19025i
$705$		0			0
$706$	64.6662	−	23.5366i	2.43374	−	0.885810i
$707$	2.70935	−	3.22888i	0.101896	−	0.121434i
$708$	−59.8202	−	30.4355i	−2.24818	−	1.14383i
$709$	−14.7382	−	5.36425i	−0.553503	−	0.201459i	0.0500991	−	0.998744i	$-0.484046\pi$
$709$	−14.7382	−	5.36425i	−0.553503	−	0.201459i	−0.603602	+	0.797286i	$0.706269\pi$
$710$		0			0
$711$	−1.48295	+	21.5731i	−0.0556150	+	0.809053i
$712$	5.71046	+	3.29694i	0.214009	+	0.123558i
$713$	−4.74412	−	5.65382i	−0.177669	−	0.211737i
$714$	−3.51031	+	3.27730i	−0.131370	+	0.122650i
$715$		0			0
$716$	10.6222	−	60.2415i	0.396970	−	2.25133i
$717$	26.0207	−	6.02352i	0.971760	−	0.224953i
$718$	47.9055	+	57.0915i	1.78782	+	2.13064i
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.381523	+	0.924359i	$0.624600\pi$
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.609757	+	0.792588i	$0.708733\pi$
$720$		0			0
$721$	1.85595	+	3.21461i	0.0691194	+	0.119718i
$722$	−3.46034	+	9.50721i	−0.128781	+	0.353822i
$723$	−1.20558	−	22.7471i	−0.0448361	−	0.845972i
$724$	8.63457	+	7.24526i	0.320901	+	0.269268i
$725$		0			0
$726$	−0.722875	+	5.91621i	−0.0268284	+	0.219571i
$727$	0.462044	−	0.0814709i	0.0171363	−	0.00302159i	−0.165073	−	0.986281i	$-0.552786\pi$
$727$	0.462044	−	0.0814709i	0.0171363	−	0.00302159i	0.182210	+	0.983260i	$0.441675\pi$
$728$			10.3440i			0.383372i
$729$	20.1288	+	17.9954i	0.745509	+	0.666495i
$730$		0			0
$731$	2.38593	+	13.5313i	0.0882469	+	0.500473i
$732$	−85.4834	−	10.4448i	−3.15956	−	0.386052i
$733$	15.8719	+	43.6076i	0.586241	+	1.61068i	0.777317	+	0.629109i	$0.216580\pi$
$733$	15.8719	+	43.6076i	0.586241	+	1.61068i	−0.191075	+	0.981575i	$0.561197\pi$
$734$	44.3825	+	37.2413i	1.63819	+	1.37460i
$735$		0			0
$736$	8.79230	+	3.20014i	0.324088	+	0.117959i
$737$	−23.6724	+	13.6672i	−0.871983	+	0.503439i
$738$	1.90157	−	7.66531i	0.0699977	−	0.282164i
$739$	12.9047	−	22.3515i	0.474706	−	0.822214i	−0.524875	−	0.851179i	$-0.675888\pi$
$739$	12.9047	−	22.3515i	0.474706	−	0.822214i	0.999580	+	0.0289653i	$0.00922124\pi$
$740$		0			0
$741$	6.31146	+	27.2645i	0.231857	+	1.00159i
$742$	−7.40629	−	1.30593i	−0.271894	−	0.0479422i
$743$	34.1823	+	6.02726i	1.25403	+	0.221119i	0.760918	−	0.648848i	$-0.224749\pi$
$743$	34.1823	+	6.02726i	1.25403	+	0.221119i	0.493110	+	0.869967i	$0.335860\pi$
$744$	−8.90915	+	8.31775i	−0.326625	+	0.304944i
$745$		0			0
$746$	−15.1129	+	26.1764i	−0.553324	+	0.958385i
$747$	44.5961	+	3.06557i	1.63169	+	0.112163i
$748$	20.0945	−	11.6015i	0.734727	−	0.424195i
$749$	3.02069	+	1.09944i	0.110374	+	0.0401727i
$750$		0			0
$751$	18.3742	+	15.4178i	0.670485	+	0.562604i	0.913209	−	0.407492i	$-0.133596\pi$
$751$	18.3742	+	15.4178i	0.670485	+	0.562604i	−0.242724	+	0.970095i	$0.578041\pi$
$752$	3.26977	+	8.98361i	0.119236	+	0.327599i
$753$	11.8034	+	27.7614i	0.430138	+	1.01168i
$754$	11.2137	+	63.5962i	0.408380	+	2.31604i
$755$		0			0
$756$	−4.04961	+	10.6057i	−0.147283	+	0.385725i
$757$			8.78780i			0.319398i	0.987166	+	0.159699i	$0.0510524\pi$
$757$			8.78780i			0.319398i	−0.987166	+	0.159699i	$0.948948\pi$
$758$	−18.2239	+	3.21336i	−0.661921	+	0.116715i
$759$	19.0603	+	14.3453i	0.691843	+	0.520701i
$760$		0			0
$761$	10.5361	+	8.84082i	0.381933	+	0.320479i	0.813461	−	0.581620i	$-0.197581\pi$
$761$	10.5361	+	8.84082i	0.381933	+	0.320479i	−0.431528	+	0.902100i	$0.642025\pi$
$762$	−40.2065	+	26.1441i	−1.45653	+	0.947102i
$763$	1.23583	−	3.39542i	0.0447401	−	0.122922i
$764$	−4.24595	−	7.35420i	−0.153613	−	0.266066i
$765$		0			0
$766$	−21.4484	+	37.1498i	−0.774963	+	1.34228i
$767$	27.7770	+	33.1034i	1.00297	+	1.19529i
$768$	14.6424	−	47.9943i	0.528361	−	1.73185i
$769$	5.44525	−	30.8815i	0.196361	−	1.11362i	−0.714107	−	0.700036i	$-0.753167\pi$
$769$	5.44525	−	30.8815i	0.196361	−	1.11362i	0.910468	−	0.413580i	$-0.135722\pi$
$770$		0			0
$771$	18.5341	+	5.65448i	0.667489	+	0.203641i
$772$	2.13192	+	2.54072i	0.0767295	+	0.0914426i
$773$	−24.3539	−	14.0607i	−0.875948	−	0.505729i	−0.00662776	−	0.999978i	$-0.502110\pi$
$773$	−24.3539	−	14.0607i	−0.875948	−	0.505729i	−0.869320	+	0.494249i	$0.835443\pi$
$774$	29.2731	+	40.1911i	1.05220	+	1.44464i
$775$		0			0
$776$	21.1266	+	7.68945i	0.758400	+	0.276035i
$777$	−3.39332	+	2.20650i	−0.121735	+	0.0791576i
$778$	42.2804	−	50.3879i	1.51583	−	1.80649i
$779$	3.96098	−	1.44168i	0.141917	−	0.0516535i
$780$		0			0
$781$	−0.614960	−	3.48761i	−0.0220050	−	0.124797i
$782$			21.2916i			0.761385i
$783$	−6.28714	+	32.6531i	−0.224684	+	1.16693i
$784$	17.7298			0.633207
$785$		0			0
$786$	34.4979	−	14.6675i	1.23050	−	0.523173i
$787$	−12.3812	−	34.0170i	−0.441342	−	1.21258i	−0.938610	−	0.344979i	$-0.887886\pi$
$787$	−12.3812	−	34.0170i	−0.441342	−	1.21258i	0.497269	−	0.867597i	$-0.334336\pi$
$788$	−49.1075	+	58.5240i	−1.74938	+	2.08483i
$789$	16.2668	−	31.9721i	0.579114	−	1.13824i
$790$		0			0
$791$	−3.43393	−	5.94775i	−0.122097	−	0.211478i
$792$	21.9911	−	32.6863i	0.781421	−	1.16146i
$793$	48.0189	+	27.7237i	1.70520	+	0.984498i
$794$	7.75636	−	6.50836i	0.275263	−	0.230973i
$795$		0			0
$796$	−12.4373	+	70.5354i	−0.440828	+	2.50006i
$797$	29.1504	+	5.14000i	1.03256	+	0.182068i	0.664153	−	0.747596i	$-0.268792\pi$
$797$	29.1504	+	5.14000i	1.03256	+	0.182068i	0.368407	+	0.929665i	$0.379903\pi$
$798$	−9.03645	+	2.09185i	−0.319887	+	0.0740506i
$799$	5.48028	−	4.59850i	0.193878	−	0.162683i
$800$		0			0
$801$	−1.28958	−	4.47736i	−0.0455652	−	0.158200i
$802$	31.5568	−	18.2193i	1.11431	−	0.643346i
$803$	−0.206789	+	0.568149i	−0.00729744	+	0.0200495i
$804$	−57.5913	+	3.05231i	−2.03109	+	0.107647i
$805$		0			0
$806$	15.7171	−	5.72055i	0.553611	−	0.201498i
$807$	−48.5604	−	5.93338i	−1.70941	−	0.208865i
$808$	−30.3920	+	5.35892i	−1.06919	+	0.188526i
$809$	5.75943			0.202491			0.101245	−	0.994861i	$-0.467717\pi$
$809$	5.75943			0.202491			0.101245	+	0.994861i	$0.467717\pi$
$810$		0			0
$811$	12.4896			0.438569			0.219284	−	0.975661i	$-0.429628\pi$
$811$	12.4896			0.438569			0.219284	+	0.975661i	$0.429628\pi$
$812$	−13.7692	+	2.42788i	−0.483204	+	0.0852019i
$813$	−29.6791	−	3.62635i	−1.04089	−	0.127182i
$814$	28.1318	−	10.2391i	0.986018	−	0.358881i
$815$		0			0
$816$	9.16230	−	0.485598i	0.320744	−	0.0169993i
$817$	−9.07644	+	24.9373i	−0.317544	+	0.872446i
$818$	−9.79536	+	5.65535i	−0.342487	+	0.197735i
$819$	5.07123	−	5.26384i	0.177203	−	0.183933i
$820$		0			0
$821$	32.9911	−	27.6828i	1.15140	−	0.966136i	0.151644	−	0.988435i	$-0.451543\pi$
$821$	32.9911	−	27.6828i	1.15140	−	0.966136i	0.999751	+	0.0222995i	$0.00709873\pi$
$822$	46.6865	−	10.8074i	1.62838	−	0.376953i
$823$	10.1279	+	1.78581i	0.353035	+	0.0622496i	0.347353	−	0.937734i	$-0.387080\pi$
$823$	10.1279	+	1.78581i	0.353035	+	0.0622496i	0.00568141	+	0.999984i	$0.498192\pi$
$824$	4.71930	−	26.7645i	0.164404	−	0.932384i
$825$		0			0
$826$	−10.9717	+	9.20632i	−0.381753	+	0.320329i
$827$	5.27810	+	3.04731i	0.183538	+	0.105965i	0.588954	−	0.808167i	$-0.299540\pi$
$827$	5.27810	+	3.04731i	0.183538	+	0.105965i	−0.405416	+	0.914132i	$0.632873\pi$
$828$	22.1174	+	45.2118i	0.768632	+	1.57122i
$829$	−16.8489	−	29.1832i	−0.585188	−	1.01358i	−0.994852	−	0.101339i	$-0.967687\pi$
$829$	−16.8489	−	29.1832i	−0.585188	−	1.01358i	0.409664	−	0.912236i	$-0.365646\pi$
$830$		0			0
$831$	4.05984	−	7.97952i	0.140834	−	0.276806i
$832$	−28.0014	+	33.3707i	−0.970772	+	1.15692i
$833$	−4.53774	−	12.4673i	−0.157223	−	0.431967i
$834$	6.52244	−	2.77315i	0.225853	−	0.0960264i
$835$		0			0
$836$	44.8148			1.54995
$837$	8.61156	+	0.135065i	0.297659	+	0.00466853i
$838$		−	47.5308i		−	1.64192i
$839$	7.33250	+	41.5847i	0.253146	+	1.43566i	0.800787	+	0.598950i	$0.204415\pi$
$839$	7.33250	+	41.5847i	0.253146	+	1.43566i	−0.547641	+	0.836714i	$0.684474\pi$
$840$		0			0
$841$	−11.2328	+	4.08841i	−0.387339	+	0.140980i
$842$	−43.5112	+	51.8546i	−1.49949	+	1.78703i
$843$	4.78664	−	3.11250i	0.164861	−	0.107200i
$844$	57.3007	+	20.8557i	1.97237	+	0.717884i
$845$		0			0
$846$	10.5019	−	23.6627i	0.361062	−	0.813541i
$847$	0.719533	+	0.415423i	0.0247235	+	0.0142741i
$848$	9.23576	+	11.0068i	0.317157	+	0.377973i
$849$	15.1266	+	4.61489i	0.519142	+	0.158383i
$850$		0			0
$851$	−3.11616	+	17.6726i	−0.106821	+	0.605810i
$852$	2.18036	−	7.14672i	0.0746979	−	0.244842i
$853$	−22.9665	−	27.3705i	−0.786359	−	0.937147i	0.212843	−	0.977086i	$-0.431728\pi$
$853$	−22.9665	−	27.3705i	−0.786359	−	0.937147i	−0.999202	+	0.0399399i	$0.987283\pi$
$854$	−9.18865	+	15.9152i	−0.314429	+	0.544607i
$855$		0			0
$856$	−11.7679	−	20.3826i	−0.402219	−	0.696664i
$857$	−2.70492	+	7.43170i	−0.0923983	+	0.253862i	−0.977280	−	0.211954i	$-0.932017\pi$
$857$	−2.70492	+	7.43170i	−0.0923983	+	0.253862i	0.884881	+	0.465817i	$0.154239\pi$
$858$	−45.3221	+	29.4706i	−1.54727	+	1.00611i
$859$	34.2569	+	28.7449i	1.16883	+	0.980764i	0.999988	−	0.00487963i	$-0.00155324\pi$
$859$	34.2569	+	28.7449i	1.16883	+	0.980764i	0.168841	+	0.985643i	$0.445998\pi$
$860$		0			0
$861$	−0.879627	−	0.662033i	−0.0299776	−	0.0225620i
$862$	12.2911	−	2.16726i	0.418638	−	0.0738172i
$863$		−	22.9170i		−	0.780103i	−0.920793	−	0.390052i	$-0.872457\pi$
$863$		−	22.9170i		−	0.780103i	0.920793	−	0.390052i	$-0.127543\pi$
$864$	−9.54017	+	5.31030i	−0.324563	+	0.180660i
$865$		0			0
$866$	−10.5629	−	59.9053i	−0.358943	−	2.03567i
$867$	8.83457	+	20.7788i	0.300038	+	0.705686i
$868$	1.23856	+	3.40290i	0.0420393	+	0.115502i
$869$	−17.0789	−	14.3309i	−0.579362	−	0.486143i
$870$		0			0
$871$	34.8926	+	12.6999i	1.18229	+	0.430319i
$872$	−22.9112	+	13.2278i	−0.775871	+	0.447950i
$873$	−6.98108	−	14.2706i	−0.236274	−	0.482985i
$874$	−20.5614	+	35.6134i	−0.695501	+	1.20464i
$875$		0			0
$876$	−0.932438	+	0.870542i	−0.0315041	+	0.0294129i
$877$	21.8013	+	3.84416i	0.736178	+	0.129808i	0.529152	−	0.848527i	$-0.322510\pi$
$877$	21.8013	+	3.84416i	0.736178	+	0.129808i	0.207026	+	0.978335i	$0.433621\pi$
$878$	37.0409	+	6.53132i	1.25007	+	0.220421i
$879$	−1.10407	−	4.76940i	−0.0372393	−	0.160868i
$880$		0			0
$881$	−4.93202	+	8.54251i	−0.166164	+	0.287804i	−0.937068	−	0.349147i	$-0.886471\pi$
$881$	−4.93202	+	8.54251i	−0.166164	+	0.287804i	0.770904	+	0.636951i	$0.219805\pi$
$882$	−34.5759	−	33.3108i	−1.16423	−	1.12163i
$883$	41.1995	−	23.7865i	1.38647	−	0.800481i	0.393558	−	0.919300i	$-0.371244\pi$
$883$	41.1995	−	23.7865i	1.38647	−	0.800481i	0.992916	+	0.118819i	$0.0379109\pi$
$884$	−29.6189	−	10.7804i	−0.996191	−	0.362584i
$885$		0			0
$886$	33.5825	+	28.1791i	1.12823	+	0.946694i
$887$	4.56846	+	12.5517i	0.153394	+	0.421446i	0.992458	−	0.122587i	$-0.0391189\pi$
$887$	4.56846	+	12.5517i	0.153394	+	0.421446i	−0.839064	+	0.544033i	$0.816897\pi$
$888$	29.4165	+	3.59428i	0.987155	+	0.120616i
$889$	1.16091	+	6.58387i	0.0389358	+	0.220816i
$890$		0			0
$891$	−27.2157	+	5.85205i	−0.911760	+	0.196051i
$892$		−	80.8465i		−	2.70694i
$893$	13.6074	−	2.39936i	0.455355	−	0.0802914i
$894$	10.9240	−	89.4048i	0.365352	−	2.99014i
$895$		0			0
$896$	−9.19350	−	7.71427i	−0.307133	−	0.257716i
$897$	−1.71509	−	32.3605i	−0.0572652	−	1.08048i
$898$	−23.5920	+	64.8186i	−0.787276	+	2.16302i
$899$	5.30359	+	9.18609i	0.176885	+	0.306373i
$900$		0			0
$901$	5.37600	−	9.31150i	0.179100	−	0.310211i
$902$	5.23403	+	6.23767i	0.174274	+	0.207692i
$903$	6.75257	−	1.56315i	0.224712	−	0.0520184i
$904$	−8.73176	+	49.5203i	−0.290414	+	1.64702i
$905$		0			0
$906$	−14.4169	+	13.4599i	−0.478969	+	0.447174i
$907$	−23.7578	−	28.3135i	−0.788866	−	0.940134i	0.210431	−	0.977609i	$-0.432513\pi$
$907$	−23.7578	−	28.3135i	−0.788866	−	0.940134i	−0.999298	+	0.0374746i	$0.988069\pi$
$908$	62.3697	+	36.0092i	2.06981	+	1.19501i
$909$	18.0932	+	12.1729i	0.600112	+	0.403751i
$910$		0			0
$911$	45.4916	+	16.5576i	1.50720	+	0.548577i	0.957914	−	0.287056i	$-0.0926766\pi$
$911$	45.4916	+	16.5576i	1.50720	+	0.548577i	0.549288	+	0.835633i	$0.314899\pi$
$912$	15.7943	+	8.03587i	0.523002	+	0.266094i
$913$	−29.6250	+	35.3057i	−0.980445	+	1.16845i
$914$	79.8629	−	29.0677i	2.64163	−	0.961475i
$915$		0			0
$916$	14.7015	+	83.3765i	0.485752	+	2.75484i
$917$		−	5.22558i		−	0.172564i
$918$	−18.7803	−	16.2671i	−0.619841	−	0.536896i
$919$	−8.93459			−0.294725			−0.147363	−	0.989083i	$-0.547078\pi$
$919$	−8.93459			−0.294725			−0.147363	+	0.989083i	$0.547078\pi$
$920$		0			0
$921$	−8.71086	−	6.55604i	−0.287032	−	0.216029i
$922$	−1.87011	−	5.13809i	−0.0615889	−	0.169214i
$923$	−3.09230	+	3.68526i	−0.101784	+	0.121302i
$924$	−6.38066	−	9.81267i	−0.209908	−	0.322813i
$925$		0			0
$926$	22.0643	+	38.2165i	0.725079	+	1.25587i
$927$	−15.5231	+	11.3062i	−0.509846	+	0.371345i
$928$	−11.6455	−	6.72355i	−0.382283	−	0.220711i
$929$	4.78330	−	4.01366i	0.156935	−	0.131684i	−0.560939	−	0.827857i	$-0.689560\pi$
$929$	4.78330	−	4.01366i	0.156935	−	0.131684i	0.717874	+	0.696173i	$0.245115\pi$
$930$		0			0
$931$	4.44973	−	25.2357i	0.145834	−	0.827066i
$932$	65.6079	+	11.5684i	2.14906	+	0.378937i
$933$	3.72644	−	12.2144i	0.121998	−	0.399882i
$934$	8.57084	−	7.19179i	0.280446	−	0.235322i
$935$		0			0
$936$	−53.2162	+	5.65676i	−1.73943	+	0.184897i
$937$	−39.7006	+	22.9212i	−1.29696	+	0.748802i	−0.979878	−	0.199595i	$-0.936037\pi$
$937$	−39.7006	+	22.9212i	−1.29696	+	0.748802i	−0.317085	+	0.948397i	$0.602704\pi$
$938$	−4.20920	+	11.5647i	−0.137435	+	0.377600i
$939$	4.03244	+	6.20140i	0.131594	+	0.202375i
$940$		0			0
$941$	4.09014	−	1.48869i	0.133335	−	0.0485298i	−0.274491	−	0.961590i	$-0.588509\pi$
$941$	4.09014	−	1.48869i	0.133335	−	0.0485298i	0.407826	+	0.913060i	$0.366287\pi$
$942$	−0.523313	+	0.695313i	−0.0170505	+	0.0226545i
$943$	−4.80683	+	0.847573i	−0.156532	+	0.0276008i
$944$	27.3637			0.890612
$945$		0			0
$946$	−51.2644			−1.66675
$947$	1.98610	−	0.350202i	0.0645395	−	0.0113800i	−0.141285	−	0.989969i	$-0.545123\pi$
$947$	1.98610	−	0.350202i	0.0645395	−	0.0113800i	0.205825	+	0.978589i	$0.434012\pi$
$948$	−18.4053	−	43.2891i	−0.597776	−	1.40596i
$949$	0.771790	−	0.280909i	0.0250534	−	0.00911868i
$950$		0			0
$951$	12.6827	−	24.9275i	0.411264	−	0.808331i
$952$	1.67640	−	4.60587i	0.0543325	−	0.149277i
$953$	−30.9420	+	17.8644i	−1.00231	+	0.578684i	−0.908931	−	0.416947i	$-0.863100\pi$
$953$	−30.9420	+	17.8644i	−1.00231	+	0.578684i	−0.0933786	+	0.995631i	$0.529767\pi$
$954$	2.66832	−	38.8171i	0.0863900	−	1.25675i
$955$		0			0
$956$	−44.5075	+	37.3462i	−1.43948	+	1.20786i
$957$	−23.3968	−	25.0604i	−0.756312	−	0.810086i
$958$	33.5279	+	5.91188i	1.08324	+	0.191004i
$959$	1.15999	−	6.57865i	0.0374581	−	0.212436i
$960$		0			0
$961$	−21.6428	+	18.1605i	−0.698155	+	0.585822i
$962$	−35.2191	−	20.3338i	−1.13551	−	0.655587i
$963$	−4.00434	+	16.1417i	−0.129038	+	0.520159i
$964$	24.7759	+	42.9131i	0.797978	+	1.38214i
$965$		0			0
$966$	10.7254	−	0.568443i	0.345085	−	0.0182894i
$967$	−0.445656	+	0.531112i	−0.0143313	+	0.0170794i	−0.773163	−	0.634208i	$-0.781326\pi$
$967$	−0.445656	+	0.531112i	−0.0143313	+	0.0170794i	0.758831	+	0.651287i	$0.225771\pi$
$968$	−2.08057	−	5.71631i	−0.0668719	−	0.183729i
$969$	1.60833	−	13.1630i	0.0516670	−	0.422857i
$970$		0			0
$971$	47.4942			1.52416			0.762081	−	0.647482i	$-0.224178\pi$
$971$	47.4942			1.52416			0.762081	+	0.647482i	$0.224178\pi$
$972$	−56.7772	−	15.0340i	−1.82113	−	0.482216i
$973$		−	0.987988i		−	0.0316734i
$974$	−8.93869	−	50.6938i	−0.286414	−	1.62434i
$975$		0			0
$976$	32.9931	−	12.0085i	1.05608	−	0.384383i
$977$	−8.10126	+	9.65470i	−0.259182	+	0.308881i	−0.879906	−	0.475148i	$-0.842394\pi$
$977$	−8.10126	+	9.65470i	−0.259182	+	0.308881i	0.620724	+	0.784029i	$0.286839\pi$
$978$	1.23812	+	23.3609i	0.0395906	+	0.746999i
$979$	4.51423	+	1.64305i	0.144276	+	0.0525120i
$980$		0			0
$981$	18.1441	+	4.50110i	0.579298	+	0.143709i
$982$	29.3008	+	16.9168i	0.935027	+	0.539838i
$983$	7.42100	+	8.84400i	0.236693	+	0.282080i	0.871295	−	0.490759i	$-0.163280\pi$
$983$	7.42100	+	8.84400i	0.236693	+	0.282080i	−0.634602	+	0.772839i	$0.718836\pi$
$984$	1.81787	+	7.85292i	0.0579517	+	0.250342i
$985$		0			0
$986$	5.31361	−	30.1350i	0.169220	−	0.959693i
$987$	−2.46277	−	2.63787i	−0.0783908	−	0.0839644i
$988$	−39.1315	−	46.6351i	−1.24494	−	1.48366i
$989$	15.3647	−	26.6125i	0.488569	−	0.846227i
$990$		0			0
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	0.678518	−	0.734584i	$-0.262623\pi$
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	−0.975427	+	0.220322i	$0.929289\pi$
$992$	−1.19121	+	3.27281i	−0.0378209	+	0.103912i
$993$	29.6832	+	15.1023i	0.941969	+	0.479257i
$994$	−1.22143	−	1.02490i	−0.0387413	−	0.0325079i
$995$		0			0
$996$	−89.4877	+	38.0476i	−2.83553	+	1.20558i
$997$	3.30778	−	0.583250i	0.104758	−	0.0184717i	−0.121023	−	0.992650i	$-0.538618\pi$
$997$	3.30778	−	0.583250i	0.104758	−	0.0184717i	0.225782	+	0.974178i	$0.427506\pi$
$998$		−	35.8066i		−	1.13344i
$999$	−13.2074	−	16.2508i	−0.417863	−	0.514154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.b.499.1		24
5.2	odd	4		27.2.e.a.13.1	✓	12
5.3	odd	4		675.2.l.c.526.2		12
5.4	even	2	inner	675.2.u.b.499.4		24
15.2	even	4		81.2.e.a.10.2		12
20.7	even	4		432.2.u.c.337.1		12
27.25	even	9	inner	675.2.u.b.349.4		24
45.2	even	12		243.2.e.b.109.2		12
45.7	odd	12		243.2.e.c.109.1		12
45.22	odd	12		243.2.e.d.190.2		12
45.32	even	12		243.2.e.a.190.1		12
135.2	even	36		81.2.e.a.73.2		12
135.7	odd	36		243.2.e.c.136.1		12
135.22	odd	36		729.2.a.a.1.1		6
135.32	even	36		729.2.a.d.1.6		6
135.47	even	36		243.2.e.b.136.2		12
135.52	odd	36		27.2.e.a.25.1	yes	12
135.67	odd	36		729.2.c.e.244.6		12
135.77	even	36		729.2.c.b.487.1		12
135.79	even	18	inner	675.2.u.b.349.1		24
135.92	even	36		243.2.e.a.55.1		12
135.97	odd	36		243.2.e.d.55.2		12
135.112	odd	36		729.2.c.e.487.6		12
135.122	even	36		729.2.c.b.244.1		12
135.133	odd	36		675.2.l.c.376.2		12
540.187	even	36		432.2.u.c.241.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	5.2	odd	4
27.2.e.a.25.1	yes	12	135.52	odd	36
81.2.e.a.10.2		12	15.2	even	4
81.2.e.a.73.2		12	135.2	even	36
243.2.e.a.55.1		12	135.92	even	36
243.2.e.a.190.1		12	45.32	even	12
243.2.e.b.109.2		12	45.2	even	12
243.2.e.b.136.2		12	135.47	even	36
243.2.e.c.109.1		12	45.7	odd	12
243.2.e.c.136.1		12	135.7	odd	36
243.2.e.d.55.2		12	135.97	odd	36
243.2.e.d.190.2		12	45.22	odd	12
432.2.u.c.241.1		12	540.187	even	36
432.2.u.c.337.1		12	20.7	even	4
675.2.l.c.376.2		12	135.133	odd	36
675.2.l.c.526.2		12	5.3	odd	4
675.2.u.b.349.1		24	135.79	even	18	inner
675.2.u.b.349.4		24	27.25	even	9	inner
675.2.u.b.499.1		24	1.1	even	1	trivial
675.2.u.b.499.4		24	5.4	even	2	inner
729.2.a.a.1.1		6	135.22	odd	36
729.2.a.d.1.6		6	135.32	even	36
729.2.c.b.244.1		12	135.122	even	36
729.2.c.b.487.1		12	135.77	even	36
729.2.c.e.244.6		12	135.67	odd	36
729.2.c.e.487.6		12	135.112	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.36514 + 0.417037i) q^{2} +(-1.71926 - 0.210069i) q^{3} +(3.54056 - 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(0.198324 - 0.544891i) q^{7} +(-3.67675 + 2.12277i) q^{8} +(2.91174 + 0.722330i) q^{9} +O(q^{10})\)	\(q+(-2.36514 + 0.417037i) q^{2} +(-1.71926 - 0.210069i) q^{3} +(3.54056 - 1.28866i) q^{4} +(4.15390 - 0.220155i) q^{6} +(0.198324 - 0.544891i) q^{7} +(-3.67675 + 2.12277i) q^{8} +(2.91174 + 0.722330i) q^{9} +(-2.36944 + 1.98820i) q^{11} +(-6.35787 + 1.47178i) q^{12} +(4.13790 + 0.729623i) q^{13} +(-0.241824 + 1.37145i) q^{14} +(2.03816 - 1.71022i) q^{16} +(-1.72424 - 0.995493i) q^{17} +(-7.18790 - 0.494102i) q^{18} +(-1.92271 - 3.33023i) q^{19} +(-0.455437 + 0.895151i) q^{21} +(4.77489 - 5.69050i) q^{22} +(1.52295 + 4.18428i) q^{23} +(6.76724 - 2.87724i) q^{24} -10.0910 q^{26} +(-4.85432 - 1.85354i) q^{27} -2.18479i q^{28} +(-1.11126 - 6.30229i) q^{29} +(-1.55754 + 0.566898i) q^{31} +(1.35067 - 1.60967i) q^{32} +(4.49135 - 2.92049i) q^{33} +(4.49323 + 1.63540i) q^{34} +(11.2400 - 1.19479i) q^{36} +(3.49016 + 2.01505i) q^{37} +(5.93630 + 7.07461i) q^{38} +(-6.96087 - 2.12366i) q^{39} +(-0.190345 + 1.07950i) q^{41} +(0.703859 - 2.30709i) q^{42} +(-4.43596 - 5.28657i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(-1.22894 + 3.37650i) q^{47} +(-3.86340 + 2.51217i) q^{48} +(5.10474 + 4.28338i) q^{49} +(2.75531 + 2.07373i) q^{51} +(15.5907 - 2.74906i) q^{52} +5.40034i q^{53} +(12.2541 + 2.35945i) q^{54} +(0.427492 + 2.42443i) q^{56} +(2.60607 + 6.12946i) q^{57} +(5.25657 + 14.4423i) q^{58} +(7.87850 + 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(3.44738 - 1.99034i) q^{62} +(0.971060 - 1.44333i) q^{63} +(-5.18386 + 8.97871i) q^{64} +(-9.40470 + 8.78041i) q^{66} +(8.70304 + 1.53458i) q^{67} +(-7.38764 - 1.30264i) q^{68} +(-1.73937 - 7.51381i) q^{69} +(-0.572473 + 0.991553i) q^{71} +(-12.2391 + 3.52514i) q^{72} +(0.169284 - 0.0977361i) q^{73} +(-9.09506 - 3.31033i) q^{74} +(-11.0990 - 9.31317i) q^{76} +(0.613433 + 1.68539i) q^{77} +(17.3491 + 2.11980i) q^{78} +(1.25166 + 7.09849i) q^{79} +(7.95648 + 4.20647i) q^{81} -2.63255i q^{82} +(14.6741 - 2.58744i) q^{83} +(-0.458958 + 3.75624i) q^{84} +(12.6963 + 10.6535i) q^{86} +(0.586638 + 11.0687i) q^{87} +(4.49135 - 12.3399i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(10.7842 + 12.8521i) q^{92} +(2.79691 - 0.647457i) q^{93} +(1.49850 - 8.49839i) q^{94} +(-2.66030 + 2.48371i) q^{96} +(-3.40390 - 4.05661i) q^{97} +(-13.8597 - 8.00191i) q^{98} +(-8.33533 + 4.07760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4}+O(q^{10}) \) 24 * q + 12 * q^4	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Introduction

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