LMFDB - Embedded newform 945.2.bj.g.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(26,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("945.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bj (of order $6$, degree $2$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	945.26
Dual form			945.2.bj.g.836.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555632 - 0.320794i) q^{2} +(-0.794182 - 1.37556i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +2.30225i q^{8} +O(q^{10})$	\(q+(-0.555632 - 0.320794i) q^{2} +(-0.794182 - 1.37556i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +2.30225i q^{8} +(0.555632 - 0.320794i) q^{10} +(4.43818 - 2.56238i) q^{11} +4.67589i q^{13} +(1.43818 + 0.901718i) q^{14} +(-0.849814 + 1.47192i) q^{16} +(0.388736 + 0.673310i) q^{17} +(0.450558 + 0.260130i) q^{19} +1.58836 q^{20} -3.28799 q^{22} +(0.944368 + 0.545231i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.50000 - 2.59808i) q^{26} +(1.96727 + 3.71351i) q^{28} -9.92199i q^{29} +(3.88255 - 2.24159i) q^{31} +(4.93199 - 2.84748i) q^{32} -0.498817i q^{34} +(1.40545 - 2.24159i) q^{35} +(-1.34362 + 2.32723i) q^{37} +(-0.166896 - 0.289073i) q^{38} +(-1.99381 - 1.15113i) q^{40} +4.11126 q^{41} +6.79851 q^{43} +(-7.04944 - 4.07000i) q^{44} +(-0.349814 - 0.605896i) q^{46} +(3.55563 - 6.15854i) q^{47} +(6.98143 + 0.509538i) q^{49} +0.641589i q^{50} +(6.43199 - 3.71351i) q^{52} +(7.60507 - 4.39079i) q^{53} +5.12477i q^{55} +(0.221840 - 6.08715i) q^{56} +(-3.18292 + 5.51298i) q^{58} +(6.43199 + 11.1405i) q^{59} +(-8.71634 - 5.03238i) q^{61} -2.87636 q^{62} -0.254572 q^{64} +(-4.04944 - 2.33795i) q^{65} +(-7.66071 - 13.2687i) q^{67} +(0.617454 - 1.06946i) q^{68} +(-1.50000 + 0.794640i) q^{70} +11.1473i q^{71} +(-7.93199 + 4.57954i) q^{73} +(1.49312 - 0.862054i) q^{74} -0.826361i q^{76} +(-11.9814 + 6.34728i) q^{77} +(4.77128 - 8.26410i) q^{79} +(-0.849814 - 1.47192i) q^{80} +(-2.28435 - 1.31887i) q^{82} +9.77747 q^{83} -0.777472 q^{85} +(-3.77747 - 2.18092i) q^{86} +(5.89926 + 10.2178i) q^{88} +(6.92580 - 11.9958i) q^{89} +(0.450558 - 12.3630i) q^{91} -1.73205i q^{92} +(-3.95125 + 2.28125i) q^{94} +(-0.450558 + 0.260130i) q^{95} +3.32927i q^{97} +(-3.71565 - 2.52272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7	$ 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7} + 3 q^{10} + 9 q^{11} - 9 q^{14} + q^{16} + 3 q^{17} + 21 q^{19} - 2 q^{20} + 4 q^{22} + 6 q^{23} - 3 q^{25} + 9 q^{26} + 23 q^{28} + 6 q^{31} - 6 q^{32} + 2 q^{35} + 16 q^{37} + 6 q^{40} + 24 q^{41} - 8 q^{43} - 24 q^{44} + 4 q^{46} + 21 q^{47} - 12 q^{49} + 3 q^{52} + 27 q^{53} + 3 q^{56} - 14 q^{58} + 3 q^{59} - 33 q^{61} + 18 q^{62} + 8 q^{64} - 6 q^{65} - 27 q^{67} + 21 q^{68} - 9 q^{70} - 12 q^{73} - 6 q^{74} - 18 q^{77} + 12 q^{79} + q^{80} - 30 q^{82} + 60 q^{83} - 6 q^{85} - 24 q^{86} + 11 q^{88} - 12 q^{89} + 21 q^{91} - 39 q^{94} - 21 q^{95} - 6 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7 + 3 * q^10 + 9 * q^11 - 9 * q^14 + q^16 + 3 * q^17 + 21 * q^19 - 2 * q^20 + 4 * q^22 + 6 * q^23 - 3 * q^25 + 9 * q^26 + 23 * q^28 + 6 * q^31 - 6 * q^32 + 2 * q^35 + 16 * q^37 + 6 * q^40 + 24 * q^41 - 8 * q^43 - 24 * q^44 + 4 * q^46 + 21 * q^47 - 12 * q^49 + 3 * q^52 + 27 * q^53 + 3 * q^56 - 14 * q^58 + 3 * q^59 - 33 * q^61 + 18 * q^62 + 8 * q^64 - 6 * q^65 - 27 * q^67 + 21 * q^68 - 9 * q^70 - 12 * q^73 - 6 * q^74 - 18 * q^77 + 12 * q^79 + q^80 - 30 * q^82 + 60 * q^83 - 6 * q^85 - 24 * q^86 + 11 * q^88 - 12 * q^89 + 21 * q^91 - 39 * q^94 - 21 * q^95 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−0.555632	−	0.320794i	−0.392891	−	0.226836i	0.290521	−	0.956869i	$-0.406171\pi$
$2$	−0.555632	−	0.320794i	−0.392891	−	0.226836i	−0.683412	+	0.730033i	$0.739505\pi$
$3$		0			0
$3$		0			0
$4$	−0.794182	−	1.37556i	−0.397091	−	0.687782i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$7$	−2.64400	−	0.0963576i	−0.999337	−	0.0364197i
$8$			2.30225i			0.813970i
$9$		0			0
$10$	0.555632	−	0.320794i	0.175706	−	0.101444i
$11$	4.43818	−	2.56238i	1.33816	−	0.772588i	0.351626	−	0.936140i	$-0.385629\pi$
$11$	4.43818	−	2.56238i	1.33816	−	0.772588i	0.986535	+	0.163553i	$0.0522954\pi$
$12$		0			0
$13$			4.67589i			1.29686i	0.761275	+	0.648430i	$0.224574\pi$
$13$			4.67589i			1.29686i	−0.761275	+	0.648430i	$0.775426\pi$
$14$	1.43818	+	0.901718i	0.384369	+	0.240994i
$15$		0			0
$16$	−0.849814	+	1.47192i	−0.212454	+	0.367980i
$17$	0.388736	+	0.673310i	0.0942823	+	0.163302i	0.909309	−	0.416122i	$-0.136611\pi$
$17$	0.388736	+	0.673310i	0.0942823	+	0.163302i	−0.815027	+	0.579424i	$0.803278\pi$
$18$		0			0
$19$	0.450558	+	0.260130i	0.103365	+	0.0596778i	0.550791	−	0.834643i	$-0.314326\pi$
$19$	0.450558	+	0.260130i	0.103365	+	0.0596778i	−0.447426	+	0.894321i	$0.647659\pi$
$20$	1.58836			0.355169
$21$		0			0
$22$	−3.28799			−0.701002
$23$	0.944368	+	0.545231i	0.196914	+	0.113689i	0.595215	−	0.803566i	$-0.297067\pi$
$23$	0.944368	+	0.545231i	0.196914	+	0.113689i	−0.398301	+	0.917255i	$0.630400\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.50000	−	2.59808i	0.294174	−	0.509525i
$27$		0			0
$28$	1.96727	+	3.71351i	0.371779	+	0.701787i
$29$		−	9.92199i		−	1.84247i	−0.389010	−	0.921234i	$-0.627183\pi$
$29$		−	9.92199i		−	1.84247i	0.389010	−	0.921234i	$-0.372817\pi$
$30$		0			0
$31$	3.88255	−	2.24159i	0.697326	−	0.402601i	−0.109025	−	0.994039i	$-0.534773\pi$
$31$	3.88255	−	2.24159i	0.697326	−	0.402601i	0.806351	+	0.591438i	$0.201439\pi$
$32$	4.93199	−	2.84748i	0.871861	−	0.503369i
$33$		0			0
$34$		−	0.498817i		−	0.0855464i
$35$	1.40545	−	2.24159i	0.237564	−	0.378898i
$36$		0			0
$37$	−1.34362	+	2.32723i	−0.220890	+	0.382594i	−0.955079	−	0.296353i	$-0.904230\pi$
$37$	−1.34362	+	2.32723i	−0.220890	+	0.382594i	0.734188	+	0.678946i	$0.237563\pi$
$38$	−0.166896	−	0.289073i	−0.0270741	−	0.0468938i
$39$		0			0
$40$	−1.99381	−	1.15113i	−0.315249	−	0.182009i
$41$	4.11126			0.642072			0.321036	−	0.947067i	$-0.395969\pi$
$41$	4.11126			0.642072			0.321036	+	0.947067i	$0.395969\pi$
$42$		0			0
$43$	6.79851			1.03676			0.518382	−	0.855149i	$-0.326535\pi$
$43$	6.79851			1.03676			0.518382	+	0.855149i	$0.326535\pi$
$44$	−7.04944	−	4.07000i	−1.06274	−	0.613575i
$45$		0			0
$46$	−0.349814	−	0.605896i	−0.0515773	−	0.0893345i
$47$	3.55563	−	6.15854i	0.518642	−	0.898315i	−0.481123	−	0.876653i	$-0.659771\pi$
$47$	3.55563	−	6.15854i	0.518642	−	0.898315i	0.999765	−	0.0216617i	$-0.00689567\pi$
$48$		0			0
$49$	6.98143	+	0.509538i	0.997347	+	0.0727912i
$50$			0.641589i			0.0907343i
$51$		0			0
$52$	6.43199	−	3.71351i	0.891956	−	0.514971i
$53$	7.60507	−	4.39079i	1.04464	−	0.603122i	0.123494	−	0.992345i	$-0.460590\pi$
$53$	7.60507	−	4.39079i	1.04464	−	0.603122i	0.921143	+	0.389224i	$0.127257\pi$
$54$		0			0
$55$			5.12477i			0.691023i
$56$	0.221840	−	6.08715i	0.0296446	−	0.813430i
$57$		0			0
$58$	−3.18292	+	5.51298i	−0.417938	+	0.723889i
$59$	6.43199	+	11.1405i	0.837374	+	1.45037i	0.892083	+	0.451871i	$0.149243\pi$
$59$	6.43199	+	11.1405i	0.837374	+	1.45037i	−0.0547096	+	0.998502i	$0.517423\pi$
$60$		0			0
$61$	−8.71634	−	5.03238i	−1.11601	−	0.644330i	−0.175633	−	0.984456i	$-0.556197\pi$
$61$	−8.71634	−	5.03238i	−1.11601	−	0.644330i	−0.940380	+	0.340125i	$0.889530\pi$
$62$	−2.87636			−0.365298
$63$		0			0
$64$	−0.254572			−0.0318214
$65$	−4.04944	−	2.33795i	−0.502271	−	0.289987i
$66$		0			0
$67$	−7.66071	−	13.2687i	−0.935904	−	1.62103i	−0.773013	−	0.634390i	$-0.781252\pi$
$67$	−7.66071	−	13.2687i	−0.935904	−	1.62103i	−0.162891	−	0.986644i	$-0.552082\pi$
$68$	0.617454	−	1.06946i	0.0748773	−	0.129691i
$69$		0			0
$70$	−1.50000	+	0.794640i	−0.179284	+	0.0949776i
$71$			11.1473i			1.32294i	0.749972	+	0.661469i	$0.230067\pi$
$71$			11.1473i			1.32294i	−0.749972	+	0.661469i	$0.769933\pi$
$72$		0			0
$73$	−7.93199	+	4.57954i	−0.928369	+	0.535994i	−0.886295	−	0.463120i	$-0.846730\pi$
$73$	−7.93199	+	4.57954i	−0.928369	+	0.535994i	−0.0420736	+	0.999115i	$0.513396\pi$
$74$	1.49312	−	0.862054i	0.173572	−	0.100212i
$75$		0			0
$76$		−	0.826361i		−	0.0947901i
$77$	−11.9814	+	6.34728i	−1.36541	+	0.723340i
$78$		0			0
$79$	4.77128	−	8.26410i	0.536811	−	0.929784i	−0.462262	−	0.886743i	$-0.652962\pi$
$79$	4.77128	−	8.26410i	0.536811	−	0.929784i	0.999073	−	0.0430409i	$-0.0137046\pi$
$80$	−0.849814	−	1.47192i	−0.0950121	−	0.164566i
$81$		0			0
$82$	−2.28435	−	1.31887i	−0.252264	−	0.145645i
$83$	9.77747			1.07322			0.536608	−	0.843831i	$-0.319705\pi$
$83$	9.77747			1.07322			0.536608	+	0.843831i	$0.319705\pi$
$84$		0			0
$85$	−0.777472			−0.0843286
$86$	−3.77747	−	2.18092i	−0.407335	−	0.235175i
$87$		0			0
$88$	5.89926	+	10.2178i	0.628863	+	1.08922i
$89$	6.92580	−	11.9958i	0.734133	−	1.27156i	−0.220969	−	0.975281i	$-0.570922\pi$
$89$	6.92580	−	11.9958i	0.734133	−	1.27156i	0.955103	−	0.296275i	$-0.0957446\pi$
$90$		0			0
$91$	0.450558	−	12.3630i	0.0472313	−	1.29600i
$92$		−	1.73205i		−	0.180579i
$93$		0			0
$94$	−3.95125	+	2.28125i	−0.407540	+	0.235293i
$95$	−0.450558	+	0.260130i	−0.0462263	+	0.0266887i
$96$		0			0
$97$			3.32927i			0.338036i	0.985613	+	0.169018i	$0.0540597\pi$
$97$			3.32927i			0.338036i	−0.985613	+	0.169018i	$0.945940\pi$
$98$	−3.71565	−	2.52272i	−0.375337	−	0.254833i
$99$		0			0
$100$	−0.794182	+	1.37556i	−0.0794182	+	0.137556i
$101$	3.88255	+	6.72477i	0.386328	+	0.669139i	0.991952	−	0.126611i	$-0.0404100\pi$
$101$	3.88255	+	6.72477i	0.386328	+	0.669139i	−0.605625	+	0.795750i	$0.707077\pi$
$102$		0			0
$103$	8.53087	+	4.92530i	0.840572	+	0.485304i	0.857459	−	0.514553i	$-0.172042\pi$
$103$	8.53087	+	4.92530i	0.840572	+	0.485304i	−0.0168867	+	0.999857i	$0.505375\pi$
$104$	−10.7651			−1.05560
$105$		0			0
$106$	−5.63416			−0.547238
$107$	10.5247	+	6.07643i	1.01746	+	0.587431i	0.913367	−	0.407137i	$-0.133473\pi$
$107$	10.5247	+	6.07643i	1.01746	+	0.587431i	0.104092	+	0.994568i	$0.466806\pi$
$108$		0			0
$109$	5.02654	+	8.70623i	0.481455	+	0.833905i	0.999773	−	0.0212827i	$-0.00677500\pi$
$109$	5.02654	+	8.70623i	0.481455	+	0.833905i	−0.518318	+	0.855188i	$0.673442\pi$
$110$	1.64400	−	2.84748i	0.156749	−	0.271497i
$111$		0			0
$112$	2.38874	−	3.80987i	0.225714	−	0.359999i
$113$		−	1.80344i		−	0.169653i	−0.996396	−	0.0848265i	$-0.972966\pi$
$113$		−	1.80344i		−	0.169653i	0.996396	−	0.0848265i	$-0.0270336\pi$
$114$		0			0
$115$	−0.944368	+	0.545231i	−0.0880628	+	0.0508431i
$116$	−13.6483	+	7.87987i	−1.26722	+	0.731627i
$117$		0			0
$118$		−	8.25338i		−	0.759785i
$119$	−0.962937	−	1.81769i	−0.0882723	−	0.166627i
$120$		0			0
$121$	7.63162	−	13.2183i	0.693783	−	1.20167i
$122$	3.22872	+	5.59230i	0.292314	+	0.506303i
$123$		0			0
$124$	−6.16690	−	3.56046i	−0.553804	−	0.319739i
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.21015			0.728533			0.364266	−	0.931295i	$-0.381320\pi$
$127$	8.21015			0.728533			0.364266	+	0.931295i	$0.381320\pi$
$128$	−9.72253	−	5.61330i	−0.859358	−	0.496151i
$129$		0			0
$130$	1.50000	+	2.59808i	0.131559	+	0.227866i
$131$	−2.32072	+	4.01961i	−0.202763	+	0.351195i	−0.949418	−	0.314016i	$-0.898325\pi$
$131$	−2.32072	+	4.01961i	−0.202763	+	0.351195i	0.746655	+	0.665212i	$0.231659\pi$
$132$		0			0
$133$	−1.16621	−	0.731196i	−0.101123	−	0.0634028i
$134$			9.83004i			0.849187i
$135$		0			0
$136$	−1.55013	+	0.894969i	−0.132923	+	0.0767429i
$137$	13.0858	−	7.55510i	1.11800	−	0.645476i	0.177108	−	0.984191i	$-0.443326\pi$
$137$	13.0858	−	7.55510i	1.11800	−	0.645476i	0.940889	+	0.338716i	$0.109992\pi$
$138$		0			0
$139$			4.46174i			0.378439i	0.981935	+	0.189220i	$0.0605958\pi$
$139$			4.46174i			0.378439i	−0.981935	+	0.189220i	$0.939404\pi$
$140$	−4.19963	−	0.153051i	−0.354933	−	0.0129352i
$141$		0			0
$142$	3.57598	−	6.19379i	0.300090	−	0.519771i
$143$	11.9814	+	20.7524i	1.00194	+	1.73541i
$144$		0			0
$145$	8.59269	+	4.96099i	0.713584	+	0.411988i
$146$	5.87636			0.486331
$147$		0			0
$148$	4.26833			0.350854
$149$	−1.72184	−	0.994105i	−0.141059	−	0.0814402i	0.427810	−	0.903869i	$-0.359285\pi$
$149$	−1.72184	−	0.994105i	−0.141059	−	0.0814402i	−0.568868	+	0.822429i	$0.692619\pi$
$150$		0			0
$151$	0.0327319	+	0.0566933i	0.00266369	+	0.00461364i	0.867354	−	0.497691i	$-0.165819\pi$
$151$	0.0327319	+	0.0566933i	0.00266369	+	0.00461364i	−0.864690	+	0.502305i	$0.832485\pi$
$152$	−0.598884	+	1.03730i	−0.0485759	+	0.0841360i
$153$		0			0
$154$	8.69344	+	0.316823i	0.700537	+	0.0255303i
$155$			4.48318i			0.360098i
$156$		0			0
$157$	−11.9814	+	6.91748i	−0.956222	+	0.552075i	−0.895008	−	0.446049i	$-0.852831\pi$
$157$	−11.9814	+	6.91748i	−0.956222	+	0.552075i	−0.0612140	+	0.998125i	$0.519497\pi$
$158$	−5.30215	+	3.06120i	−0.421817	+	0.243536i
$159$		0			0
$160$			5.69497i			0.450227i
$161$	−2.44437	−	1.53259i	−0.192643	−	0.120785i
$162$		0			0
$163$	−3.38255	+	5.85874i	−0.264941	+	0.458892i	−0.967548	−	0.252686i	$-0.918686\pi$
$163$	−3.38255	+	5.85874i	−0.264941	+	0.458892i	0.702607	+	0.711578i	$0.252019\pi$
$164$	−3.26509	−	5.65531i	−0.254961	−	0.441605i
$165$		0			0
$166$	−5.43268	−	3.13656i	−0.421658	−	0.243444i
$167$	−10.5549			−0.816766			−0.408383	−	0.912811i	$-0.633907\pi$
$167$	−10.5549			−0.816766			−0.408383	+	0.912811i	$0.633907\pi$
$168$		0			0
$169$	−8.86398			−0.681844
$170$	0.431988	+	0.249409i	0.0331320	+	0.0191288i
$171$		0			0
$172$	−5.39926	−	9.35179i	−0.411689	−	0.713067i
$173$	−0.105074	+	0.181994i	−0.00798865	+	0.0138367i	−0.869992	−	0.493066i	$-0.835876\pi$
$173$	−0.105074	+	0.181994i	−0.00798865	+	0.0138367i	0.862003	+	0.506902i	$0.169210\pi$
$174$		0			0
$175$	1.23855	+	2.33795i	0.0936256	+	0.176732i
$176$			8.71020i			0.656556i
$177$		0			0
$178$	−7.69639	+	4.44351i	−0.576869	+	0.333055i
$179$	−13.0426	+	7.53013i	−0.974847	+	0.562828i	−0.900710	−	0.434420i	$-0.856953\pi$
$179$	−13.0426	+	7.53013i	−0.974847	+	0.562828i	−0.0741365	+	0.997248i	$0.523620\pi$
$180$		0			0
$181$		−	17.2197i		−	1.27993i	−0.768403	−	0.639966i	$-0.778948\pi$
$181$		−	17.2197i		−	1.27993i	0.768403	−	0.639966i	$-0.221052\pi$
$182$	−4.21634	+	6.72477i	−0.312536	+	0.498473i
$183$		0			0
$184$	−1.25526	+	2.17417i	−0.0925390	+	0.160282i
$185$	−1.34362	−	2.32723i	−0.0987852	−	0.171101i
$186$		0			0
$187$	3.45056	+	1.99218i	0.252330	+	0.145683i
$188$	−11.2953			−0.823793
$189$		0			0
$190$	0.333792			0.0242159
$191$	−21.9004	−	12.6442i	−1.58465	−	0.914900i	−0.994167	−	0.107853i	$-0.965602\pi$
$191$	−21.9004	−	12.6442i	−1.58465	−	0.914900i	−0.590487	−	0.807047i	$-0.701064\pi$
$192$		0			0
$193$	7.40909	+	12.8329i	0.533318	+	0.923734i	0.999243	+	0.0389093i	$0.0123883\pi$
$193$	7.40909	+	12.8329i	0.533318	+	0.923734i	−0.465925	+	0.884824i	$0.654278\pi$
$194$	1.06801	−	1.84985i	0.0766788	−	0.132812i
$195$		0			0
$196$	−4.84362	−	10.0081i	−0.345973	−	0.714862i
$197$			6.83538i			0.487000i	0.969901	+	0.243500i	$0.0782956\pi$
$197$			6.83538i			0.487000i	−0.969901	+	0.243500i	$0.921704\pi$
$198$		0			0
$199$	−9.71565	+	5.60933i	−0.688724	+	0.397635i	−0.803134	−	0.595799i	$-0.796836\pi$
$199$	−9.71565	+	5.60933i	−0.688724	+	0.397635i	0.114410	+	0.993434i	$0.463502\pi$
$200$	1.99381	−	1.15113i	0.140984	−	0.0813970i
$201$		0			0
$202$		−	4.98199i		−	0.350532i
$203$	−0.956059	+	26.2337i	−0.0671022	+	1.84124i
$204$		0			0
$205$	−2.05563	+	3.56046i	−0.143572	+	0.248673i
$206$	−3.16002	−	5.47331i	−0.220169	−	0.381344i
$207$		0			0
$208$	−6.88255	−	3.97364i	−0.477219	−	0.275522i
$209$	2.66621			0.184425
$210$		0			0
$211$	8.81089			0.606567			0.303283	−	0.952900i	$-0.401917\pi$
$211$	8.81089			0.606567			0.303283	+	0.952900i	$0.401917\pi$
$212$	−12.0796	−	6.97418i	−0.829632	−	0.478988i
$213$		0			0
$214$	−3.89857	−	6.75252i	−0.266501	−	0.461593i
$215$	−3.39926	+	5.88768i	−0.231827	+	0.401537i
$216$		0			0
$217$	−10.4814	+	5.55264i	−0.711526	+	0.376938i
$218$		−	6.44994i		−	0.436845i
$219$		0			0
$220$	7.04944	−	4.07000i	0.475273	−	0.274399i
$221$	−3.14833	+	1.81769i	−0.211779	+	0.122271i
$222$		0			0
$223$			23.4009i			1.56704i	0.621366	+	0.783520i	$0.286578\pi$
$223$			23.4009i			1.56704i	−0.621366	+	0.783520i	$0.713422\pi$
$224$	−13.3145	+	7.05350i	−0.889615	+	0.471282i
$225$		0			0
$226$	−0.578532	+	1.00205i	−0.0384834	+	0.0666552i
$227$	1.39493	+	2.41608i	0.0925845	+	0.160361i	0.908598	−	0.417672i	$-0.137154\pi$
$227$	1.39493	+	2.41608i	0.0925845	+	0.160361i	−0.816013	+	0.578033i	$0.803821\pi$
$228$		0			0
$229$	−5.26578	−	3.04020i	−0.347973	−	0.200902i	0.315819	−	0.948819i	$-0.397721\pi$
$229$	−5.26578	−	3.04020i	−0.347973	−	0.200902i	−0.663792	+	0.747917i	$0.731054\pi$
$230$	0.699628			0.0461321
$231$		0			0
$232$	22.8429			1.49971
$233$	−19.4883	−	11.2516i	−1.27672	−	0.737116i	−0.300477	−	0.953789i	$-0.597146\pi$
$233$	−19.4883	−	11.2516i	−1.27672	−	0.737116i	−0.976244	+	0.216673i	$0.930479\pi$
$234$		0			0
$235$	3.55563	+	6.15854i	0.231944	+	0.401739i
$236$	10.2163	−	17.6952i	0.665027	−	1.15186i
$237$		0			0
$238$	−0.0480648	+	1.31887i	−0.00311558	+	0.0854897i
$239$		−	12.0030i		−	0.776411i	−0.921573	−	0.388206i	$-0.873095\pi$
$239$		−	12.0030i		−	0.776411i	0.921573	−	0.388206i	$-0.126905\pi$
$240$		0			0
$241$	18.1669	−	10.4887i	1.17023	−	0.675634i	0.216498	−	0.976283i	$-0.430537\pi$
$241$	18.1669	−	10.4887i	1.17023	−	0.675634i	0.953735	+	0.300649i	$0.0972033\pi$
$242$	−8.48074	+	4.89636i	−0.545163	+	0.314750i
$243$		0			0
$244$			15.9865i			1.02343i
$245$	−3.93199	+	5.79133i	−0.251206	+	0.369994i
$246$		0			0
$247$	−1.21634	+	2.10676i	−0.0773938	+	0.134050i
$248$	5.16071	+	8.93861i	0.327705	+	0.567602i
$249$		0			0
$250$	−0.555632	−	0.320794i	−0.0351413	−	0.0202888i
$251$	27.9876			1.76656			0.883281	−	0.468843i	$-0.155329\pi$
$251$	27.9876			1.76656			0.883281	+	0.468843i	$0.155329\pi$
$252$		0			0
$253$	5.58836			0.351337
$254$	−4.56182	−	2.63377i	−0.286234	−	0.165257i
$255$		0			0
$256$	3.85600	+	6.67879i	0.241000	+	0.417425i
$257$	5.03706	−	8.72445i	0.314203	−	0.544216i	−0.665065	−	0.746786i	$-0.731596\pi$
$257$	5.03706	−	8.72445i	0.314203	−	0.544216i	0.979268	+	0.202570i	$0.0649293\pi$
$258$		0			0
$259$	3.77678	−	6.02371i	0.234678	−	0.374295i
$260$			7.42702i			0.460604i
$261$		0			0
$262$	2.57894	−	1.48895i	0.159327	−	0.0919877i
$263$	−6.70877	+	3.87331i	−0.413681	+	0.238839i	−0.692370	−	0.721543i	$-0.743433\pi$
$263$	−6.70877	+	3.87331i	−0.413681	+	0.238839i	0.278689	+	0.960381i	$0.410100\pi$
$264$		0			0
$265$			8.78158i			0.539448i
$266$	0.413419	+	0.780389i	0.0253483	+	0.0478487i
$267$		0			0
$268$	−12.1680	+	21.0756i	−0.743278	+	1.28740i
$269$	6.88255	+	11.9209i	0.419636	+	0.726831i	0.995903	−	0.0904305i	$-0.0288243\pi$
$269$	6.88255	+	11.9209i	0.419636	+	0.726831i	−0.576267	+	0.817262i	$0.695491\pi$
$270$		0			0
$271$	−8.26578	−	4.77225i	−0.502110	−	0.289894i	0.227474	−	0.973784i	$-0.426953\pi$
$271$	−8.26578	−	4.77225i	−0.502110	−	0.289894i	−0.729585	+	0.683891i	$0.760287\pi$
$272$	−1.32141			−0.0801224
$273$		0			0
$274$	−9.69453			−0.585668
$275$	−4.43818	−	2.56238i	−0.267632	−	0.154518i
$276$		0			0
$277$	−4.09820	−	7.09828i	−0.246237	−	0.426495i	0.716242	−	0.697852i	$-0.245861\pi$
$277$	−4.09820	−	7.09828i	−0.246237	−	0.426495i	−0.962479	+	0.271358i	$0.912527\pi$
$278$	1.43130	−	2.47908i	0.0858436	−	0.148686i
$279$		0			0
$280$	5.16071	+	3.23569i	0.308411	+	0.193370i
$281$			15.5750i			0.929124i	0.885541	+	0.464562i	$0.153788\pi$
$281$			15.5750i			0.929124i	−0.885541	+	0.464562i	$0.846212\pi$
$282$		0			0
$283$	−5.38255	+	3.10761i	−0.319959	+	0.184729i	−0.651374	−	0.758757i	$-0.725807\pi$
$283$	−5.38255	+	3.10761i	−0.319959	+	0.184729i	0.331415	+	0.943485i	$0.392474\pi$
$284$	15.3338	−	8.85297i	0.909893	−	0.525327i
$285$		0			0
$286$		−	15.3743i		−	0.909101i
$287$	−10.8702	−	0.396151i	−0.641646	−	0.0233841i
$288$		0			0
$289$	8.19777	−	14.1990i	0.482222	−	0.835232i
$290$	−3.18292	−	5.51298i	−0.186907	−	0.323733i
$291$		0			0
$292$	12.5989	+	7.27397i	0.737294	+	0.425677i
$293$	−0.123644			−0.00722335			−0.00361168	−	0.999993i	$-0.501150\pi$
$293$	−0.123644			−0.00722335			−0.00361168	+	0.999993i	$0.501150\pi$
$294$		0			0
$295$	−12.8640			−0.748970
$296$	−5.35786	−	3.09336i	−0.311419	−	0.179798i
$297$		0			0
$298$	0.637806	+	1.10471i	0.0369471	+	0.0639943i
$299$	−2.54944	+	4.41576i	−0.147438	+	0.255370i
$300$		0			0
$301$	−17.9752	−	0.655088i	−1.03608	−	0.0377587i
$302$		−	0.0420008i		−	0.00241688i
$303$		0			0
$304$	−0.765781	+	0.442124i	−0.0439205	+	0.0253575i
$305$	8.71634	−	5.03238i	0.499096	−	0.288153i
$306$		0			0
$307$			3.84953i			0.219704i	0.993948	+	0.109852i	$0.0350378\pi$
$307$			3.84953i			0.219704i	−0.993948	+	0.109852i	$0.964962\pi$
$308$	18.2465	+	11.4403i	1.03969	+	0.651873i
$309$		0			0
$310$	1.43818	−	2.49100i	0.0816830	−	0.141479i
$311$	8.67309	+	15.0222i	0.491806	+	0.851832i	0.999955	−	0.00943638i	$-0.00300374\pi$
$311$	8.67309	+	15.0222i	0.491806	+	0.851832i	−0.508150	+	0.861269i	$0.669670\pi$
$312$		0			0
$313$	23.9814	+	13.8457i	1.35551	+	0.782604i	0.989015	−	0.147815i	$-0.0472241\pi$
$313$	23.9814	+	13.8457i	1.35551	+	0.782604i	0.366496	+	0.930420i	$0.380557\pi$
$314$	8.87636			0.500922
$315$		0			0
$316$	−15.1571			−0.852651
$317$	−5.35786	−	3.09336i	−0.300928	−	0.173741i	0.341932	−	0.939725i	$-0.388919\pi$
$317$	−5.35786	−	3.09336i	−0.300928	−	0.173741i	−0.642860	+	0.765984i	$0.722252\pi$
$318$		0			0
$319$	−25.4239	−	44.0356i	−1.42347	−	2.46552i
$320$	0.127286	−	0.220465i	0.00711549	−	0.0123244i
$321$		0			0
$322$	0.866524	+	1.63569i	0.0482895	+	0.0911536i
$323$			0.404487i			0.0225063i
$324$		0			0
$325$	4.04944	−	2.33795i	0.224623	−	0.129686i
$326$	3.75890	−	2.17020i	0.208186	−	0.120196i
$327$		0			0
$328$			9.46517i			0.522627i
$329$	−9.99450	+	15.9405i	−0.551015	+	0.878830i
$330$		0			0
$331$	−16.3869	+	28.3829i	−0.900704	+	1.56007i	−0.0741222	+	0.997249i	$0.523615\pi$
$331$	−16.3869	+	28.3829i	−0.900704	+	1.56007i	−0.826582	+	0.562816i	$0.809718\pi$
$332$	−7.76509	−	13.4495i	−0.426165	−	0.738139i
$333$		0			0
$334$	5.86467	+	3.38597i	0.320900	+	0.185272i
$335$	15.3214			0.837098
$336$		0			0
$337$	7.90978			0.430873			0.215436	−	0.976518i	$-0.430883\pi$
$337$	7.90978			0.430873			0.215436	+	0.976518i	$0.430883\pi$
$338$	4.92511	+	2.84351i	0.267891	+	0.154667i
$339$		0			0
$340$	0.617454	+	1.06946i	0.0334861	+	0.0579997i
$341$	11.4876	−	19.8971i	0.622090	−	1.07749i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$			15.6519i			0.843894i
$345$		0			0
$346$	0.116765	−	0.0674145i	0.00627734	−	0.00362422i
$347$	−5.51307	+	3.18297i	−0.295957	+	0.170871i	−0.640625	−	0.767854i	$-0.721325\pi$
$347$	−5.51307	+	3.18297i	−0.295957	+	0.170871i	0.344668	+	0.938725i	$0.387991\pi$
$348$		0			0
$349$		−	9.67933i		−	0.518123i	−0.965861	−	0.259061i	$-0.916587\pi$
$349$		−	9.67933i		−	0.518123i	0.965861	−	0.259061i	$-0.0834132\pi$
$350$	0.0618219	−	1.69636i	0.00330452	−	0.0906741i
$351$		0			0
$352$	14.5927	−	25.2753i	0.777793	−	1.34718i
$353$	−12.8640	−	22.2811i	−0.684680	−	1.18590i	−0.973537	−	0.228529i	$-0.926608\pi$
$353$	−12.8640	−	22.2811i	−0.684680	−	1.18590i	0.288857	−	0.957372i	$-0.406725\pi$
$354$		0			0
$355$	−9.65383	−	5.57364i	−0.512372	−	0.295818i
$356$	−22.0014			−1.16607
$357$		0			0
$358$	9.66249			0.510678
$359$	−9.10507	−	5.25682i	−0.480547	−	0.277444i	0.240097	−	0.970749i	$-0.422821\pi$
$359$	−9.10507	−	5.25682i	−0.480547	−	0.277444i	−0.720645	+	0.693305i	$0.756154\pi$
$360$		0			0
$361$	−9.36467	−	16.2201i	−0.492877	−	0.853688i
$362$	−5.52399	+	9.56784i	−0.290335	+	0.502874i
$363$		0			0
$364$	−17.3640	+	9.19874i	−0.910120	+	0.482145i
$365$		−	9.15907i		−	0.479408i
$366$		0			0
$367$	−1.28297	+	0.740725i	−0.0669706	+	0.0386655i	−0.533111	−	0.846045i	$-0.678977\pi$
$367$	−1.28297	+	0.740725i	−0.0669706	+	0.0386655i	0.466141	+	0.884711i	$0.345644\pi$
$368$	−1.60507	+	0.926690i	−0.0836703	+	0.0483071i
$369$		0			0
$370$			1.72411i			0.0896321i
$371$	−20.5309	+	10.8764i	−1.06591	+	0.564676i
$372$		0			0
$373$	−7.59201	+	13.1497i	−0.393099	+	0.680868i	−0.992857	−	0.119314i	$-0.961930\pi$
$373$	−7.59201	+	13.1497i	−0.393099	+	0.680868i	0.599757	+	0.800182i	$0.295264\pi$
$374$	−1.27816	−	2.21384i	−0.0660921	−	0.114475i
$375$		0			0
$376$	14.1785	+	8.18597i	0.731201	+	0.422159i
$377$	46.3942			2.38942
$378$		0			0
$379$	22.4661			1.15401			0.577003	−	0.816742i	$-0.304222\pi$
$379$	22.4661			1.15401			0.577003	+	0.816742i	$0.304222\pi$
$380$	0.715650	+	0.413181i	0.0367121	+	0.0211957i
$381$		0			0
$382$	8.11236	+	14.0510i	0.415064	+	0.718913i
$383$	6.87567	−	11.9090i	0.351330	−	0.608522i	−0.635153	−	0.772387i	$-0.719063\pi$
$383$	6.87567	−	11.9090i	0.351330	−	0.608522i	0.986483	+	0.163865i	$0.0523961\pi$
$384$		0			0
$385$	0.493810	−	13.5499i	0.0251669	−	0.690565i
$386$		−	9.50717i		−	0.483902i
$387$		0			0
$388$	4.57963	−	2.64405i	0.232495	−	0.134231i
$389$	−6.47524	+	3.73848i	−0.328308	+	0.189549i	−0.655090	−	0.755551i	$-0.727369\pi$
$389$	−6.47524	+	3.73848i	−0.328308	+	0.189549i	0.326782	+	0.945100i	$0.394036\pi$
$390$		0			0
$391$			0.847803i			0.0428753i
$392$	−1.17309	+	16.0730i	−0.0592498	+	0.811810i
$393$		0			0
$394$	2.19275	−	3.79795i	0.110469	−	0.191338i
$395$	4.77128	+	8.26410i	0.240069	+	0.415812i
$396$		0			0
$397$	−16.4629	−	9.50484i	−0.826247	−	0.477034i	0.0263187	−	0.999654i	$-0.491622\pi$
$397$	−16.4629	−	9.50484i	−0.826247	−	0.477034i	−0.852566	+	0.522619i	$0.824955\pi$
$398$	7.19777			0.360792
$399$		0			0
$400$	1.69963			0.0849814
$401$	24.1916	+	13.9670i	1.20807	+	0.697479i	0.962337	−	0.271858i	$-0.0876382\pi$
$401$	24.1916	+	13.9670i	1.20807	+	0.697479i	0.245733	+	0.969338i	$0.420972\pi$
$402$		0			0
$403$	10.4814	+	18.1544i	0.522117	+	0.904334i
$404$	6.16690	−	10.6814i	0.306815	−	0.531418i
$405$		0			0
$406$	8.94684	−	14.2696i	0.444024	−	0.708188i
$407$			13.7715i			0.682629i
$408$		0			0
$409$	24.1778	−	13.9591i	1.19552	−	0.690232i	0.235964	−	0.971762i	$-0.424175\pi$
$409$	24.1778	−	13.9591i	1.19552	−	0.690232i	0.959552	+	0.281530i	$0.0908419\pi$
$410$	2.28435	−	1.31887i	0.112816	−	0.0651344i
$411$		0			0
$412$		−	15.6463i		−	0.770840i
$413$	−15.9327	−	30.0753i	−0.783996	−	1.47991i
$414$		0			0
$415$	−4.88874	+	8.46754i	−0.239979	+	0.415655i
$416$	13.3145	+	23.0614i	0.652799	+	1.13068i
$417$		0			0
$418$	−1.48143	−	0.855304i	−0.0724591	−	0.0418343i
$419$	21.8640			1.06813			0.534063	−	0.845445i	$-0.320665\pi$
$419$	21.8640			1.06813			0.534063	+	0.845445i	$0.320665\pi$
$420$		0			0
$421$	−14.6552			−0.714251			−0.357125	−	0.934056i	$-0.616243\pi$
$421$	−14.6552			−0.714251			−0.357125	+	0.934056i	$0.616243\pi$
$422$	−4.89561	−	2.82648i	−0.238315	−	0.137591i
$423$		0			0
$424$	10.1087	+	17.5088i	0.490923	+	0.850303i
$425$	0.388736	−	0.673310i	0.0188565	−	0.0326603i
$426$		0			0
$427$	22.5611	+	14.1455i	1.09181	+	0.684548i
$428$		−	19.3032i		−	0.933053i
$429$		0			0
$430$	3.77747	−	2.18092i	0.182166	−	0.105174i
$431$	−19.0240	+	10.9835i	−0.916354	+	0.529057i	−0.882470	−	0.470369i	$-0.844121\pi$
$431$	−19.0240	+	10.9835i	−0.916354	+	0.529057i	−0.0338836	+	0.999426i	$0.510788\pi$
$432$		0			0
$433$		−	27.6120i		−	1.32695i	−0.748198	−	0.663475i	$-0.769081\pi$
$433$		−	27.6120i		−	1.32695i	0.748198	−	0.663475i	$-0.230919\pi$
$434$	7.60507	+	0.277159i	0.365055	+	0.0133040i
$435$		0			0
$436$	7.98398	−	13.8287i	0.382363	−	0.662273i
$437$	0.283662	+	0.491316i	0.0135694	+	0.0235028i
$438$		0			0
$439$	−13.2960	−	7.67643i	−0.634582	−	0.366376i	0.147943	−	0.988996i	$-0.452735\pi$
$439$	−13.2960	−	7.67643i	−0.634582	−	0.366376i	−0.782524	+	0.622620i	$0.786068\pi$
$440$	−11.7985			−0.562472
$441$		0			0
$442$	2.33242			0.110942
$443$	−5.93818	−	3.42841i	−0.282131	−	0.162889i	0.352257	−	0.935903i	$-0.385414\pi$
$443$	−5.93818	−	3.42841i	−0.282131	−	0.162889i	−0.634388	+	0.773015i	$0.718748\pi$
$444$		0			0
$445$	6.92580	+	11.9958i	0.328314	+	0.568657i
$446$	7.50688	−	13.0023i	0.355461	−	0.615677i
$447$		0			0
$448$	0.673086	+	0.0245299i	0.0318003	+	0.00115893i
$449$		−	4.55456i		−	0.214943i	−0.994208	−	0.107472i	$-0.965725\pi$
$449$		−	4.55456i		−	0.214943i	0.994208	−	0.107472i	$-0.0342755\pi$
$450$		0			0
$451$	18.2465	−	10.5346i	0.859195	−	0.496057i
$452$	−2.48074	+	1.43226i	−0.116684	+	0.0673677i
$453$		0			0
$454$		−	1.78994i		−	0.0840059i
$455$	10.4814	+	6.57172i	0.491377	+	0.308087i
$456$		0			0
$457$	−9.83124	+	17.0282i	−0.459886	+	0.796546i	−0.998954	−	0.0457158i	$-0.985443\pi$
$457$	−9.83124	+	17.0282i	−0.459886	+	0.796546i	0.539068	+	0.842262i	$0.318776\pi$
$458$	1.95056	+	3.37847i	0.0911436	+	0.157865i
$459$		0			0
$460$	1.50000	+	0.866025i	0.0699379	+	0.0403786i
$461$	−10.6552			−0.496262			−0.248131	−	0.968726i	$-0.579816\pi$
$461$	−10.6552			−0.496262			−0.248131	+	0.968726i	$0.579816\pi$
$462$		0			0
$463$	31.5919			1.46820			0.734101	−	0.679041i	$-0.237604\pi$
$463$	31.5919			1.46820			0.734101	+	0.679041i	$0.237604\pi$
$464$	14.6044	+	8.43185i	0.677992	+	0.391439i
$465$		0			0
$466$	7.21889	+	12.5035i	0.334408	+	0.579212i
$467$	19.3028	−	33.4335i	0.893229	−	1.54712i	0.0572479	−	0.998360i	$-0.481767\pi$
$467$	19.3028	−	33.4335i	0.893229	−	1.54712i	0.835981	−	0.548758i	$-0.184899\pi$
$468$		0			0
$469$	18.9763	+	35.8206i	0.876246	+	1.65404i
$470$		−	4.56251i		−	0.210453i
$471$		0			0
$472$	−25.6483	+	14.8081i	−1.18056	+	0.681597i
$473$	30.1730	−	17.4204i	1.38736	−	0.800991i
$474$		0			0
$475$		−	0.520259i		−	0.0238711i
$476$	−1.73560	+	2.76816i	−0.0795509	+	0.126878i
$477$		0			0
$478$	−3.85050	+	6.66927i	−0.176118	+	0.305045i
$479$	9.37704	+	16.2415i	0.428448	+	0.742094i	0.996736	−	0.0807362i	$-0.0257271\pi$
$479$	9.37704	+	16.2415i	0.428448	+	0.742094i	−0.568287	+	0.822830i	$0.692394\pi$
$480$		0			0
$481$	−10.8819	−	6.28264i	−0.496170	−	0.286464i
$482$	−13.4588			−0.613032
$483$		0			0
$484$	−24.2436			−1.10198
$485$	−2.88323	−	1.66464i	−0.130921	−	0.0755872i
$486$		0			0
$487$	−7.29349	−	12.6327i	−0.330500	−	0.572442i	0.652110	−	0.758124i	$-0.273884\pi$
$487$	−7.29349	−	12.6327i	−0.330500	−	0.572442i	−0.982610	+	0.185682i	$0.940551\pi$
$488$	11.5858	−	20.0672i	0.524465	−	0.908400i
$489$		0			0
$490$	4.04256	−	1.95649i	0.182624	−	0.0883851i
$491$		−	42.2314i		−	1.90587i	−0.303167	−	0.952937i	$-0.598044\pi$
$491$		−	42.2314i		−	1.90587i	0.303167	−	0.952937i	$-0.401956\pi$
$492$		0			0
$493$	6.68058	−	3.85703i	0.300878	−	0.173712i
$494$	1.35167	−	0.780389i	0.0608147	−	0.0351114i
$495$		0			0
$496$			7.61974i			0.342136i
$497$	1.07413	−	29.4734i	0.0481811	−	1.32206i
$498$		0			0
$499$	4.40909	−	7.63676i	0.197378	−	0.341869i	−0.750300	−	0.661098i	$-0.770091\pi$
$499$	4.40909	−	7.63676i	0.197378	−	0.341869i	0.947677	+	0.319229i	$0.103424\pi$
$500$	−0.794182	−	1.37556i	−0.0355169	−	0.0615171i
$501$		0			0
$502$	−15.5508	−	8.97827i	−0.694067	−	0.400720i
$503$	33.5068			1.49399			0.746997	−	0.664827i	$-0.231495\pi$
$503$	33.5068			1.49399			0.746997	+	0.664827i	$0.231495\pi$
$504$		0			0
$505$	−7.76509			−0.345542
$506$	−3.10507	−	1.79272i	−0.138037	−	0.0796959i
$507$		0			0
$508$	−6.52035	−	11.2936i	−0.289294	−	0.501072i
$509$	14.3825	−	24.9113i	0.637495	−	1.10417i	−0.348485	−	0.937314i	$-0.613304\pi$
$509$	14.3825	−	24.9113i	0.637495	−	1.10417i	0.985981	−	0.166860i	$-0.0533627\pi$
$510$		0			0
$511$	21.4134	−	11.3440i	0.947274	−	0.501828i
$512$			17.5053i			0.773631i
$513$		0			0
$514$	−5.59751	+	3.23172i	−0.246895	+	0.142545i
$515$	−8.53087	+	4.92530i	−0.375915	+	0.217035i
$516$		0			0
$517$		−	36.4436i		−	1.60279i
$518$	−4.03087	+	2.13539i	−0.177106	+	0.0938238i
$519$		0			0
$520$	5.38255	−	9.32284i	0.236040	−	0.408834i
$521$	−11.6359	−	20.1541i	−0.509780	−	0.882965i	−0.999936	−	0.0113301i	$-0.996393\pi$
$521$	−11.6359	−	20.1541i	−0.509780	−	0.882965i	0.490156	−	0.871635i	$-0.336940\pi$
$522$		0			0
$523$	−19.9134	−	11.4970i	−0.870753	−	0.502729i	−0.00315460	−	0.999995i	$-0.501004\pi$
$523$	−19.9134	−	11.4970i	−0.870753	−	0.502729i	−0.867598	+	0.497266i	$0.834337\pi$
$524$	7.37231			0.322061
$525$		0			0
$526$	4.97014			0.216709
$527$	3.01857	+	1.74277i	0.131491	+	0.0759163i
$528$		0			0
$529$	−10.9054	−	18.8888i	−0.474150	−	0.821252i
$530$	2.81708	−	4.87933i	0.122366	−	0.211945i
$531$		0			0
$532$	−0.0796262	+	2.18490i	−0.00345223	+	0.0947272i
$533$			19.2238i			0.832677i
$534$		0			0
$535$	−10.5247	+	6.07643i	−0.455022	+	0.262707i
$536$	30.5480	−	17.6369i	1.31947	−	0.761798i
$537$		0			0
$538$		−	8.83153i		−	0.380754i
$539$	32.2905	−	15.6277i	1.39085	−	0.673132i
$540$		0			0
$541$	−6.63595	+	11.4938i	−0.285302	+	0.494157i	−0.972682	−	0.232140i	$-0.925427\pi$
$541$	−6.63595	+	11.4938i	−0.285302	+	0.494157i	0.687381	+	0.726297i	$0.258760\pi$
$542$	3.06182	+	5.30323i	0.131517	+	0.227793i
$543$		0			0
$544$	3.83448	+	2.21384i	0.164402	+	0.0949176i
$545$	−10.0531			−0.430627
$546$		0			0
$547$	−29.2843			−1.25211			−0.626053	−	0.779781i	$-0.715330\pi$
$547$	−29.2843			−1.25211			−0.626053	+	0.779781i	$0.715330\pi$
$548$	−20.7850	−	12.0002i	−0.887893	−	0.512625i
$549$		0			0
$550$	1.64400	+	2.84748i	0.0701002	+	0.121417i
$551$	2.58100	−	4.47043i	0.109954	−	0.190447i
$552$		0			0
$553$	−13.4116	+	21.3905i	−0.570318	+	0.909617i
$554$			5.25871i			0.223421i
$555$		0			0
$556$	6.13740	−	3.54343i	0.260284	−	0.150275i
$557$	1.93680	−	1.11821i	0.0820649	−	0.0473802i	−0.458406	−	0.888743i	$-0.651579\pi$
$557$	1.93680	−	1.11821i	0.0820649	−	0.0473802i	0.540471	+	0.841363i	$0.318246\pi$
$558$		0			0
$559$			31.7891i			1.34454i
$560$	2.10507	+	3.97364i	0.0889556	+	0.167917i
$561$		0			0
$562$	4.99636	−	8.65395i	0.210759	−	0.365045i
$563$	−12.7040	−	22.0039i	−0.535408	−	0.927354i	−0.999143	−	0.0413802i	$-0.986825\pi$
$563$	−12.7040	−	22.0039i	−0.535408	−	0.927354i	0.463735	−	0.885974i	$-0.346509\pi$
$564$		0			0
$565$	1.56182	+	0.901718i	0.0657063	+	0.0379356i
$566$	3.98762			0.167612
$567$		0			0
$568$	−25.6639			−1.07683
$569$	−13.1044	−	7.56582i	−0.549364	−	0.317176i	0.199501	−	0.979898i	$-0.436068\pi$
$569$	−13.1044	−	7.56582i	−0.549364	−	0.317176i	−0.748866	+	0.662722i	$0.769401\pi$
$570$		0			0
$571$	23.0796	+	39.9751i	0.965852	+	1.67291i	0.707308	+	0.706906i	$0.249910\pi$
$571$	23.0796	+	39.9751i	0.965852	+	1.67291i	0.258545	+	0.965999i	$0.416757\pi$
$572$	19.0309	−	32.9624i	0.795721	−	1.37823i
$573$		0			0
$574$	5.91273	+	3.70720i	0.246793	+	0.154736i
$575$		−	1.09046i		−	0.0454754i
$576$		0			0
$577$	−36.0611	+	20.8199i	−1.50124	+	0.866742i	−0.501242	+	0.865307i	$0.667124\pi$
$577$	−36.0611	+	20.8199i	−1.50124	+	0.866742i	−0.999999	+	0.00143526i	$0.999543\pi$
$578$	−9.10989	+	5.25960i	−0.378921	+	0.218770i
$579$		0			0
$580$		−	15.7597i		−	0.654387i
$581$	−25.8516	−	0.942134i	−1.07250	−	0.0390863i
$582$		0			0
$583$	22.5018	−	38.9742i	0.931929	−	1.61415i
$584$	−10.5433	−	18.2614i	−0.436283	−	0.755664i
$585$		0			0
$586$	0.0687005	+	0.0396643i	0.00283799	+	0.00163852i
$587$	15.3338			0.632893			0.316447	−	0.948610i	$-0.397510\pi$
$587$	15.3338			0.632893			0.316447	+	0.948610i	$0.397510\pi$
$588$		0			0
$589$	2.33242			0.0961055
$590$	7.14764	+	4.12669i	0.294264	+	0.169893i
$591$		0			0
$592$	−2.28366	−	3.95542i	−0.0938579	−	0.162567i
$593$	−21.4821	+	37.2081i	−0.882165	+	1.52795i	−0.0332359	+	0.999448i	$0.510581\pi$
$593$	−21.4821	+	37.2081i	−0.882165	+	1.52795i	−0.848929	+	0.528507i	$0.822752\pi$
$594$		0			0
$595$	2.05563	+	0.0749153i	0.0842727	+	0.00307123i
$596$			3.15800i			0.129357i
$597$		0			0
$598$	2.83310	−	1.63569i	0.115854	−	0.0668885i
$599$	−14.7410	+	8.51073i	−0.602302	+	0.347739i	−0.769947	−	0.638108i	$-0.779717\pi$
$599$	−14.7410	+	8.51073i	−0.602302	+	0.347739i	0.167645	+	0.985847i	$0.446384\pi$
$600$		0			0
$601$			14.1840i			0.578575i	0.957242	+	0.289288i	$0.0934184\pi$
$601$			14.1840i			0.578575i	−0.957242	+	0.289288i	$0.906582\pi$
$602$	9.77747	+	6.13034i	0.398500	+	0.249854i
$603$		0			0
$604$	0.0519902	−	0.0900497i	0.00211545	−	0.00366407i
$605$	7.63162	+	13.2183i	0.310269	+	0.537402i
$606$		0			0
$607$	7.00138	+	4.04225i	0.284177	+	0.164070i	0.635313	−	0.772255i	$-0.280871\pi$
$607$	7.00138	+	4.04225i	0.284177	+	0.164070i	−0.351136	+	0.936325i	$0.614204\pi$
$608$	2.96286			0.120160
$609$		0			0
$610$	−6.45744			−0.261454
$611$	28.7967	+	16.6258i	1.16499	+	0.672606i
$612$		0			0
$613$	−10.8090	−	18.7218i	−0.436573	−	0.756166i	0.560850	−	0.827918i	$-0.310475\pi$
$613$	−10.8090	−	18.7218i	−0.436573	−	0.756166i	−0.997423	+	0.0717514i	$0.977141\pi$
$614$	1.23491	−	2.13892i	0.0498368	−	0.0863199i
$615$		0			0
$616$	−14.6130	−	27.5843i	−0.588776	−	1.11140i
$617$		−	37.0352i		−	1.49098i	−0.666516	−	0.745491i	$-0.732215\pi$
$617$		−	37.0352i		−	1.49098i	0.666516	−	0.745491i	$-0.267785\pi$
$618$		0			0
$619$	7.09957	−	4.09894i	0.285356	−	0.164750i	−0.350490	−	0.936567i	$-0.613985\pi$
$619$	7.09957	−	4.09894i	0.285356	−	0.164750i	0.635846	+	0.771816i	$0.280651\pi$
$620$	6.16690	−	3.56046i	0.247669	−	0.142991i
$621$		0			0
$622$		−	11.1291i		−	0.446237i
$623$	−19.4677	+	31.0496i	−0.779956	+	1.24398i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−8.88323	−	15.3862i	−0.355045	−	0.614957i
$627$		0			0
$628$	19.0309	+	10.9875i	0.759414	+	0.438448i
$629$	−2.08926			−0.0833042
$630$		0			0
$631$	−20.1978			−0.804060			−0.402030	−	0.915626i	$-0.631695\pi$
$631$	−20.1978			−0.804060			−0.402030	+	0.915626i	$0.631695\pi$
$632$	19.0261	+	10.9847i	0.756816	+	0.436948i
$633$		0			0
$634$	1.98467	+	3.43754i	0.0788212	+	0.136522i
$635$	−4.10507	+	7.11020i	−0.162905	+	0.282160i
$636$		0			0
$637$	−2.38255	+	32.6444i	−0.0943999	+	1.29342i
$638$			32.6234i			1.29157i
$639$		0			0
$640$	9.72253	−	5.61330i	0.384317	−	0.221885i
$641$	1.03569	−	0.597953i	0.0409071	−	0.0236177i	−0.479407	−	0.877593i	$-0.659148\pi$
$641$	1.03569	−	0.597953i	0.0409071	−	0.0236177i	0.520314	+	0.853975i	$0.325815\pi$
$642$		0			0
$643$		−	22.9726i		−	0.905951i	−0.891523	−	0.452975i	$-0.850363\pi$
$643$		−	22.9726i		−	0.905951i	0.891523	−	0.452975i	$-0.149637\pi$
$644$	−0.166896	+	4.57954i	−0.00657663	+	0.180459i
$645$		0			0
$646$	0.129757	−	0.224746i	0.00510522	−	0.00884251i
$647$	15.4567	+	26.7717i	0.607664	+	1.05251i	0.991624	+	0.129156i	$0.0412268\pi$
$647$	15.4567	+	26.7717i	0.607664	+	1.05251i	−0.383960	+	0.923350i	$0.625440\pi$
$648$		0			0
$649$	57.0926	+	32.9624i	2.24108	+	1.29389i
$650$	−3.00000			−0.117670
$651$		0			0
$652$	10.7454			0.420823
$653$	−25.0693	−	14.4738i	−0.981038	−	0.566403i	−0.0784546	−	0.996918i	$-0.524999\pi$
$653$	−25.0693	−	14.4738i	−0.981038	−	0.566403i	−0.902583	+	0.430515i	$0.858332\pi$
$654$		0			0
$655$	−2.32072	−	4.01961i	−0.0906782	−	0.157059i
$656$	−3.49381	+	6.05146i	−0.136410	+	0.236270i
$657$		0			0
$658$	10.6669	−	5.65089i	0.415839	−	0.220295i
$659$			15.1102i			0.588610i	0.955712	+	0.294305i	$0.0950881\pi$
$659$			15.1102i			0.588610i	−0.955712	+	0.294305i	$0.904912\pi$
$660$		0			0
$661$	20.2658	−	11.7005i	0.788248	−	0.455095i	−0.0510977	−	0.998694i	$-0.516272\pi$
$661$	20.2658	−	11.7005i	0.788248	−	0.455095i	0.839345	+	0.543599i	$0.182939\pi$
$662$	18.2101	−	10.5136i	0.707758	−	0.408624i
$663$		0			0
$664$			22.5102i			0.873566i
$665$	1.21634	−	0.644367i	0.0471676	−	0.0249875i
$666$		0			0
$667$	5.40978	−	9.37001i	0.209467	−	0.362808i
$668$	8.38255	+	14.5190i	0.324330	+	0.561757i
$669$		0			0
$670$	−8.51307	−	4.91502i	−0.328889	−	0.189884i
$671$	−51.5795			−1.99121
$672$		0			0
$673$	−10.4871			−0.404249			−0.202125	−	0.979360i	$-0.564785\pi$
$673$	−10.4871			−0.404249			−0.202125	+	0.979360i	$0.564785\pi$
$674$	−4.39493	−	2.53741i	−0.169286	−	0.0977374i
$675$		0			0
$676$	7.03961	+	12.1930i	0.270754	+	0.468960i
$677$	−23.4141	+	40.5544i	−0.899877	+	1.55863i	−0.0722275	+	0.997388i	$0.523011\pi$
$677$	−23.4141	+	40.5544i	−0.899877	+	1.55863i	−0.827650	+	0.561245i	$0.810323\pi$
$678$		0			0
$679$	0.320801	−	8.80258i	0.0123112	−	0.337812i
$680$		−	1.78994i		−	0.0686410i
$681$		0			0
$682$	−12.7658	+	7.37033i	−0.488827	+	0.282224i
$683$	29.0795	−	16.7891i	1.11270	−	0.642417i	0.173171	−	0.984892i	$-0.444599\pi$
$683$	29.0795	−	16.7891i	1.11270	−	0.642417i	0.939527	+	0.342475i	$0.111265\pi$
$684$		0			0
$685$			15.1102i			0.577331i
$686$	9.58108	+	7.02809i	0.365807	+	0.268334i
$687$		0			0
$688$	−5.77747	+	10.0069i	−0.220264	+	0.381509i
$689$	20.5309	+	35.5605i	0.782164	+	1.35475i
$690$		0			0
$691$	−7.21427	−	4.16516i	−0.274444	−	0.158450i	0.356462	−	0.934310i	$-0.383983\pi$
$691$	−7.21427	−	4.16516i	−0.274444	−	0.158450i	−0.630905	+	0.775860i	$0.717316\pi$
$692$	0.333792			0.0126889
$693$		0			0
$694$	4.08432			0.155039
$695$	−3.86398	−	2.23087i	−0.146569	−	0.0846216i
$696$		0			0
$697$	1.59820	+	2.76816i	0.0605360	+	0.104851i
$698$	−3.10507	+	5.37815i	−0.117529	+	0.203566i
$699$		0			0
$700$	2.23236	−	3.56046i	0.0843753	−	0.134573i
$701$		−	3.53549i		−	0.133534i	−0.997769	−	0.0667668i	$-0.978732\pi$
$701$		−	3.53549i		−	0.133534i	0.997769	−	0.0667668i	$-0.0212683\pi$
$702$		0			0
$703$	−1.21076	+	0.699033i	−0.0456647	+	0.0263645i
$704$	−1.12983	+	0.652310i	−0.0425822	+	0.0245849i
$705$		0			0
$706$			16.5068i			0.621240i
$707$	−9.61745	−	18.1544i	−0.361702	−	0.682765i
$708$		0			0
$709$	1.52585	−	2.64286i	0.0573046	−	0.0992545i	−0.835950	−	0.548806i	$-0.815083\pi$
$709$	1.52585	−	2.64286i	0.0573046	−	0.0992545i	0.893255	+	0.449551i	$0.148416\pi$
$710$	3.57598	+	6.19379i	0.134204	+	0.232449i
$711$		0			0
$712$	27.6175	+	15.9449i	1.03501	+	0.597562i
$713$	4.88874			0.183085
$714$		0			0
$715$	−23.9629			−0.896160
$716$	20.7163	+	11.9606i	0.774206	+	0.446988i
$717$		0			0
$718$	3.37271	+	5.84171i	0.125869	+	0.218011i
$719$	−8.80766	+	15.2553i	−0.328470	+	0.568927i	−0.982208	−	0.187794i	$-0.939866\pi$
$719$	−8.80766	+	15.2553i	−0.328470	+	0.568927i	0.653738	+	0.756721i	$0.273200\pi$
$720$		0			0
$721$	−22.0810	−	13.8445i	−0.822340	−	0.515596i
$722$			12.0165i			0.447209i
$723$		0			0
$724$	−23.6868	+	13.6756i	−0.880315	+	0.508250i
$725$	−8.59269	+	4.96099i	−0.319125	+	0.184247i
$726$		0			0
$727$			8.94491i			0.331748i	0.986147	+	0.165874i	$0.0530446\pi$
$727$			8.94491i			0.331748i	−0.986147	+	0.165874i	$0.946955\pi$
$728$	28.4629	+	1.03730i	1.05490	+	0.0384448i
$729$		0			0
$730$	−2.93818	+	5.08907i	−0.108747	+	0.188355i
$731$	2.64283	+	4.57751i	0.0977484	+	0.169305i
$732$		0			0
$733$	3.74721	+	2.16345i	0.138406	+	0.0799090i	0.567604	−	0.823302i	$-0.307870\pi$
$733$	3.74721	+	2.16345i	0.138406	+	0.0799090i	−0.429198	+	0.903210i	$0.641204\pi$
$734$	0.950481			0.0350829
$735$		0			0
$736$	6.21015			0.228909
$737$	−67.9992	−	39.2593i	−2.50478	−	1.44614i
$738$		0			0
$739$	8.20327	+	14.2085i	0.301762	+	0.522667i	0.976535	−	0.215358i	$-0.0690918\pi$
$739$	8.20327	+	14.2085i	0.301762	+	0.522667i	−0.674773	+	0.738025i	$0.735758\pi$
$740$	−2.13416	+	3.69648i	−0.0784534	+	0.135885i
$741$		0			0
$742$	14.8967	+	0.542894i	0.546875	+	0.0199303i
$743$		−	23.7420i		−	0.871008i	−0.900187	−	0.435504i	$-0.856570\pi$
$743$		−	23.7420i		−	0.871008i	0.900187	−	0.435504i	$-0.143430\pi$
$744$		0			0
$745$	1.72184	−	0.994105i	0.0630833	−	0.0364212i
$746$	8.43672	−	4.87094i	0.308890	−	0.178338i
$747$		0			0
$748$		−	6.32862i		−	0.231397i
$749$	−27.2417	−	17.0802i	−0.995390	−	0.624096i
$750$		0			0
$751$	−23.8182	+	41.2543i	−0.869138	+	1.50539i	−0.00625829	+	0.999980i	$0.501992\pi$
$751$	−23.8182	+	41.2543i	−0.869138	+	1.50539i	−0.862879	+	0.505410i	$0.831341\pi$
$752$	6.04325	+	10.4672i	0.220375	+	0.381700i
$753$		0			0
$754$	−25.7781	−	14.8830i	−0.938782	−	0.542006i
$755$	−0.0654638			−0.00238247
$756$		0			0
$757$	19.0458			0.692231			0.346116	−	0.938192i	$-0.387500\pi$
$757$	19.0458			0.692231			0.346116	+	0.938192i	$0.387500\pi$
$758$	−12.4829	−	7.20700i	−0.453399	−	0.261770i
$759$		0			0
$760$	−0.598884	−	1.03730i	−0.0217238	−	0.0376268i
$761$	1.95056	−	3.37847i	0.0707077	−	0.122469i	−0.828504	−	0.559983i	$-0.810808\pi$
$761$	1.95056	−	3.37847i	0.0707077	−	0.122469i	0.899212	+	0.437514i	$0.144141\pi$
$762$		0			0
$763$	−12.4512	−	23.5036i	−0.450765	−	0.850886i
$764$			40.1671i			1.45319i
$765$		0			0
$766$	−7.64068	+	4.41135i	−0.276069	+	0.159389i
$767$	−52.0919	+	30.0753i	−1.88093	+	1.08596i
$768$		0			0
$769$			3.19206i			0.115109i	0.998342	+	0.0575543i	$0.0183302\pi$
$769$			3.19206i			0.115109i	−0.998342	+	0.0575543i	$0.981670\pi$
$770$	−4.62110	+	7.37033i	−0.166533	+	0.265608i
$771$		0			0
$772$	11.7683	−	20.3833i	0.423551	−	0.733613i
$773$	−10.7465	−	18.6135i	−0.386526	−	0.669482i	0.605454	−	0.795880i	$-0.292992\pi$
$773$	−10.7465	−	18.6135i	−0.386526	−	0.669482i	−0.991980	+	0.126398i	$0.959658\pi$
$774$		0			0
$775$	−3.88255	−	2.24159i	−0.139465	−	0.0805203i
$776$	−7.66483			−0.275151
$777$		0			0
$778$	4.79714			0.171986
$779$	1.85236	+	1.06946i	0.0663678	+	0.0383174i
$780$		0			0
$781$	28.5636	+	49.4736i	1.02209	+	1.77031i
$782$	0.271971	−	0.471067i	0.00972565	−	0.0168453i
$783$		0			0
$784$	−6.68292	+	9.84310i	−0.238676	+	0.351539i
$785$		−	13.8350i		−	0.493791i
$786$		0			0
$787$	−39.7080	+	22.9254i	−1.41544	+	0.817203i	−0.995894	−	0.0905318i	$-0.971143\pi$
$787$	−39.7080	+	22.9254i	−1.41544	+	0.817203i	−0.419544	+	0.907735i	$0.637810\pi$
$788$	9.40249	−	5.42853i	0.334950	−	0.193383i
$789$		0			0
$790$		−	6.12240i		−	0.217825i
$791$	−0.173775	+	4.76828i	−0.00617872	+	0.169540i
$792$		0			0
$793$	23.5309	−	40.7567i	0.835606	−	1.44731i
$794$	6.09820	+	10.5624i	0.216417	+	0.374845i
$795$		0			0
$796$	15.4320	+	8.90966i	0.546972	+	0.315795i
$797$	−13.0975			−0.463938			−0.231969	−	0.972723i	$-0.574517\pi$
$797$	−13.0975			−0.463938			−0.231969	+	0.972723i	$0.574517\pi$
$798$		0			0
$799$	5.52881			0.195595
$800$	−4.93199	−	2.84748i	−0.174372	−	0.100674i
$801$		0			0
$802$	−8.96108	−	15.5210i	−0.316427	−	0.548067i
$803$	−23.4691	+	40.6496i	−0.828205	+	1.43449i
$804$		0			0
$805$	2.54944	−	1.35059i	0.0898560	−	0.0476021i
$806$		−	13.4495i		−	0.473740i
$807$		0			0
$808$	−15.4821	+	8.93861i	−0.544659	+	0.314459i
$809$	19.0988	−	11.0267i	0.671478	−	0.387678i	−0.125158	−	0.992137i	$-0.539944\pi$
$809$	19.0988	−	11.0267i	0.671478	−	0.387678i	0.796637	+	0.604459i	$0.206611\pi$
$810$		0			0
$811$		−	0.963576i		−	0.0338357i	−0.999857	−	0.0169179i	$-0.994615\pi$
$811$		−	0.963576i		−	0.0338357i	0.999857	−	0.0169179i	$-0.00538538\pi$
$812$	36.8454	−	19.5192i	1.29302	−	0.684990i
$813$		0			0
$814$	4.41783	−	7.65190i	0.154845	−	0.268199i
$815$	−3.38255	−	5.85874i	−0.118485	−	0.205223i
$816$		0			0
$817$	3.06312	+	1.76849i	0.107165	+	0.0618718i
$818$	−17.9120			−0.626277
$819$		0			0
$820$	6.53018			0.228044
$821$	10.2301	+	5.90635i	0.357033	+	0.206133i	0.667778	−	0.744360i	$-0.267245\pi$
$821$	10.2301	+	5.90635i	0.357033	+	0.206133i	−0.310746	+	0.950493i	$0.600579\pi$
$822$		0			0
$823$	−26.9134	−	46.6154i	−0.938143	−	1.62491i	−0.768931	−	0.639331i	$-0.779211\pi$
$823$	−26.9134	−	46.6154i	−0.938143	−	1.62491i	−0.169211	−	0.985580i	$-0.554122\pi$
$824$	−11.3393	+	19.6402i	−0.395023	+	0.684200i
$825$		0			0
$826$	−0.795276	+	21.8219i	−0.0276712	+	0.759281i
$827$			22.6380i			0.787200i	0.919282	+	0.393600i	$0.128770\pi$
$827$			22.6380i			0.787200i	−0.919282	+	0.393600i	$0.871230\pi$
$828$		0			0
$829$	29.9649	−	17.3003i	1.04072	−	0.600863i	0.120686	−	0.992691i	$-0.461490\pi$
$829$	29.9649	−	17.3003i	1.04072	−	0.600863i	0.920039	+	0.391828i	$0.128157\pi$
$830$	5.43268	−	3.13656i	0.188571	−	0.108871i
$831$		0			0
$832$		−	1.19035i		−	0.0412679i
$833$	2.37085	+	4.89874i	0.0821453	+	0.169731i
$834$		0			0
$835$	5.27747	−	9.14085i	0.182634	−	0.316332i
$836$	−2.11745	−	3.66754i	−0.0732337	−	0.126844i
$837$		0			0
$838$	−12.1483	−	7.01384i	−0.419657	−	0.242289i
$839$	9.10026			0.314176			0.157088	−	0.987585i	$-0.449789\pi$
$839$	9.10026			0.314176			0.157088	+	0.987585i	$0.449789\pi$
$840$		0			0
$841$	−69.4459			−2.39469
$842$	8.14290	+	4.70131i	0.280623	+	0.162018i
$843$		0			0
$844$	−6.99745	−	12.1199i	−0.240862	−	0.417186i
$845$	4.43199	−	7.67643i	0.152465	−	0.264077i
$846$		0			0
$847$	−21.4517	+	34.2139i	−0.737087	+	1.17560i
$848$			14.9254i			0.512541i
$849$		0			0
$850$	−0.431988	+	0.249409i	−0.0148171	+	0.00855464i
$851$	−2.53775	+	1.46517i	−0.0869930	+	0.0502254i
$852$		0			0
$853$			1.98027i			0.0678030i	0.999425	+	0.0339015i	$0.0107933\pi$
$853$			1.98027i			0.0678030i	−0.999425	+	0.0339015i	$0.989207\pi$
$854$	−7.99786	−	15.0971i	−0.273681	−	0.516614i
$855$		0			0
$856$	−13.9895	+	24.2305i	−0.478151	+	0.828181i
$857$	−11.8331	−	20.4955i	−0.404211	−	0.700114i	0.590018	−	0.807390i	$-0.299121\pi$
$857$	−11.8331	−	20.4955i	−0.404211	−	0.700114i	−0.994229	+	0.107276i	$0.965787\pi$
$858$		0			0
$859$	33.7767	+	19.5010i	1.15245	+	0.665365i	0.949482	−	0.313821i	$-0.101609\pi$
$859$	33.7767	+	19.5010i	1.15245	+	0.665365i	0.202964	+	0.979186i	$0.434943\pi$
$860$	10.7985			0.368226
$861$		0			0
$862$	14.0938			0.480036
$863$	11.5446	+	6.66530i	0.392984	+	0.226889i	0.683452	−	0.729995i	$-0.260478\pi$
$863$	11.5446	+	6.66530i	0.392984	+	0.226889i	−0.290468	+	0.956885i	$0.593811\pi$
$864$		0			0
$865$	−0.105074	−	0.181994i	−0.00357263	−	0.00618798i
$866$	−8.85779	+	15.3421i	−0.301000	+	0.521347i
$867$		0			0
$868$	15.9622	+	10.0081i	0.541791	+	0.339696i
$869$		−	48.9034i		−	1.65893i
$870$		0			0
$871$	62.0432	−	35.8206i	2.10225	−	1.21374i
$872$	−20.0439	+	11.5724i	−0.678773	+	0.391890i
$873$		0			0
$874$		−	0.363988i		−	0.0123121i
$875$	−2.64400	−	0.0963576i	−0.0893834	−	0.00325748i
$876$		0			0
$877$	10.4622	−	18.1210i	0.353282	−	0.611903i	−0.633540	−	0.773710i	$-0.718399\pi$
$877$	10.4622	−	18.1210i	0.353282	−	0.611903i	0.986822	+	0.161807i	$0.0517321\pi$
$878$	4.92511	+	8.53054i	0.166214	+	0.287892i
$879$		0			0
$880$	−7.54325	−	4.35510i	−0.254283	−	0.146810i
$881$	−11.0617			−0.372680			−0.186340	−	0.982485i	$-0.559663\pi$
$881$	−11.0617			−0.372680			−0.186340	+	0.982485i	$0.559663\pi$
$882$		0			0
$883$	−8.17811			−0.275215			−0.137608	−	0.990487i	$-0.543941\pi$
$883$	−8.17811			−0.275215			−0.137608	+	0.990487i	$0.543941\pi$
$884$	5.00069	+	2.88715i	0.168191	+	0.0971053i
$885$		0			0
$886$	2.19963	+	3.80987i	0.0738980	+	0.127995i
$887$	−19.5247	+	33.8177i	−0.655575	+	1.13549i	0.326175	+	0.945310i	$0.394240\pi$
$887$	−19.5247	+	33.8177i	−0.655575	+	1.13549i	−0.981749	+	0.190179i	$0.939093\pi$
$888$		0			0
$889$	−21.7076	−	0.791110i	−0.728050	−	0.0265330i
$890$		−	8.88703i		−	0.297894i
$891$		0			0
$892$	32.1894	−	18.5846i	1.07778	−	0.622258i
$893$	3.20404	−	1.84985i	0.107219	−	0.0619029i
$894$		0			0
$895$		−	15.0603i		−	0.503409i
$896$	25.1654	+	15.7784i	0.840718	+	0.527119i
$897$		0			0
$898$	−1.46108	+	2.53066i	−0.0487568	+	0.0844493i
$899$	−22.2410	−	38.5226i	−0.741780	−	1.28480i
$900$		0			0
$901$	5.91273	+	3.41372i	0.196982	+	0.113727i
$902$	−13.5178			−0.450094
$903$		0			0
$904$	4.15197			0.138092
$905$	14.9127	+	8.60987i	0.495716	+	0.286202i
$906$		0			0
$907$	−4.25712	−	7.37355i	−0.141355	−	0.244835i	0.786652	−	0.617397i	$-0.211813\pi$
$907$	−4.25712	−	7.37355i	−0.141355	−	0.244835i	−0.928007	+	0.372562i	$0.878479\pi$
$908$	2.21565	−	3.83762i	0.0735289	−	0.127356i
$909$		0			0
$910$	−3.71565	−	7.01384i	−0.123173	−	0.232507i
$911$			25.9244i			0.858913i	0.903088	+	0.429456i	$0.141295\pi$
$911$			25.9244i			0.858913i	−0.903088	+	0.429456i	$0.858705\pi$
$912$		0			0
$913$	43.3942	−	25.0536i	1.43614	−	0.829154i
$914$	10.9251	−	6.30761i	0.361371	−	0.208637i
$915$		0			0
$916$			9.65789i			0.319106i
$917$	6.52331	−	10.4042i	0.215419	−	0.343578i
$918$		0			0
$919$	−10.8738	+	18.8340i	−0.358694	+	0.621276i	−0.987743	−	0.156090i	$-0.950111\pi$
$919$	−10.8738	+	18.8340i	−0.358694	+	0.621276i	0.629049	+	0.777366i	$0.283444\pi$
$920$	−1.25526	−	2.17417i	−0.0413847	−	0.0716804i
$921$		0			0
$922$	5.92037	+	3.41813i	0.194977	+	0.112570i
$923$	−52.1235			−1.71567
$924$		0			0
$925$	2.68725			0.0883562
$926$	−17.5535	−	10.1345i	−0.576843	−	0.333041i
$927$		0			0
$928$	−28.2527	−	48.9351i	−0.927441	−	1.60637i
$929$	−20.5996	+	35.6795i	−0.675850	+	1.17061i	0.300370	+	0.953823i	$0.402890\pi$
$929$	−20.5996	+	35.6795i	−0.675850	+	1.17061i	−0.976220	+	0.216784i	$0.930443\pi$
$930$		0			0
$931$	3.01299	+	2.04565i	0.0987468	+	0.0670436i
$932$			35.7432i			1.17081i
$933$		0			0
$934$	−21.4506	+	12.3845i	−0.701884	+	0.405233i
$935$	−3.45056	+	1.99218i	−0.112845	+	0.0651513i
$936$		0			0
$937$			47.7780i			1.56084i	0.625256	+	0.780420i	$0.284995\pi$
$937$			47.7780i			1.56084i	−0.625256	+	0.780420i	$0.715005\pi$
$938$	0.947199	−	25.9906i	0.0309272	−	0.848623i
$939$		0			0
$940$	5.64764	−	9.78200i	0.184206	−	0.319054i
$941$	17.2658	+	29.9052i	0.562848	+	0.974882i	0.997246	+	0.0741609i	$0.0236278\pi$
$941$	17.2658	+	29.9052i	0.562848	+	0.974882i	−0.434398	+	0.900721i	$0.643039\pi$
$942$		0			0
$943$	3.88255	+	2.24159i	0.126433	+	0.0729962i
$944$	−21.8640			−0.711612
$945$		0			0
$946$	−22.3535			−0.726774
$947$	3.85710	+	2.22690i	0.125339	+	0.0723644i	0.561359	−	0.827573i	$-0.310279\pi$
$947$	3.85710	+	2.22690i	0.125339	+	0.0723644i	−0.436020	+	0.899937i	$0.643612\pi$
$948$		0			0
$949$	−21.4134	−	37.0891i	−0.695109	−	1.20396i
$950$	−0.166896	+	0.289073i	−0.00541483	+	0.00937876i
$951$		0			0
$952$	4.18478	−	2.21693i	0.135629	−	0.0718510i
$953$		−	60.3227i		−	1.95405i	−0.213136	−	0.977023i	$-0.568368\pi$
$953$		−	60.3227i		−	1.95405i	0.213136	−	0.977023i	$-0.431632\pi$
$954$		0			0
$955$	21.9004	−	12.6442i	0.708679	−	0.409156i
$956$	−16.5109	+	9.53259i	−0.534001	+	0.308306i
$957$		0			0
$958$		−	12.0324i		−	0.388750i
$959$	−35.3268	+	18.7147i	−1.14076	+	0.604330i
$960$		0			0
$961$	−5.45056	+	9.44064i	−0.175824	+	0.304537i
$962$	4.03087	+	6.98168i	0.129961	+	0.225098i
$963$		0			0
$964$	−28.8556	−	16.6598i	−0.929378	−	0.536576i
$965$	−14.8182			−0.477014
$966$		0			0
$967$	10.3696			0.333462			0.166731	−	0.986002i	$-0.446679\pi$
$967$	10.3696			0.333462			0.166731	+	0.986002i	$0.446679\pi$
$968$	30.4320	+	17.5699i	0.978121	+	0.564719i
$969$		0			0
$970$	1.06801	+	1.84985i	0.0342918	+	0.0593951i
$971$	−16.9684	+	29.3901i	−0.544541	+	0.943172i	0.454095	+	0.890953i	$0.349963\pi$
$971$	−16.9684	+	29.3901i	−0.544541	+	0.943172i	−0.998636	+	0.0522188i	$0.983371\pi$
$972$		0			0
$973$	0.429922	−	11.7968i	0.0137827	−	0.378188i
$974$			9.35885i			0.299877i
$975$		0			0
$976$	14.8145	−	8.55318i	0.474202	−	0.273780i
$977$	−6.79046	+	3.92048i	−0.217246	+	0.125427i	−0.604675	−	0.796473i	$-0.706697\pi$
$977$	−6.79046	+	3.92048i	−0.217246	+	0.125427i	0.387428	+	0.921900i	$0.373363\pi$
$978$		0			0
$979$		−	70.9862i		−	2.26873i
$980$	11.0891	+	0.809332i	0.354227	+	0.0258532i
$981$		0			0
$982$	−13.5476	+	23.4651i	−0.432321	+	0.748801i
$983$	−3.24729	−	5.62447i	−0.103572	−	0.179393i	0.809582	−	0.587007i	$-0.199694\pi$
$983$	−3.24729	−	5.62447i	−0.103572	−	0.179393i	−0.913154	+	0.407615i	$0.866361\pi$
$984$		0			0
$985$	−5.91961	−	3.41769i	−0.188614	−	0.108897i
$986$	−4.94926			−0.157616
$987$		0			0
$988$	3.86398			0.122929
$989$	6.42030	+	3.70676i	0.204154	+	0.117868i
$990$		0			0
$991$	28.1501	+	48.7574i	0.894218	+	1.54883i	0.834770	+	0.550599i	$0.185601\pi$
$991$	28.1501	+	48.7574i	0.894218	+	1.54883i	0.0594479	+	0.998231i	$0.481066\pi$
$992$	12.7658	−	22.1110i	0.405314	−	0.702024i
$993$		0			0
$994$	−10.0517	+	16.0318i	−0.318821	+	0.508497i
$995$		−	11.2187i		−	0.355656i
$996$		0			0
$997$	−14.8331	+	8.56390i	−0.469769	+	0.271221i	−0.716143	−	0.697954i	$-0.754094\pi$
$997$	−14.8331	+	8.56390i	−0.469769	+	0.271221i	0.246374	+	0.969175i	$0.420761\pi$
$998$	−4.89966	+	2.82882i	−0.155096	+	0.0895448i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bj.g.26.2	✓	6
3.2	odd	2		945.2.bj.h.26.2	yes	6
7.3	odd	6		945.2.bj.h.836.2	yes	6
21.17	even	6	inner	945.2.bj.g.836.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bj.g.26.2	✓	6	1.1	even	1	trivial
945.2.bj.g.836.2	yes	6	21.17	even	6	inner
945.2.bj.h.26.2	yes	6	3.2	odd	2
945.2.bj.h.836.2	yes	6	7.3	odd	6

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.555632 - 0.320794i) q^{2} +(-0.794182 - 1.37556i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +2.30225i q^{8} +O(q^{10})\)	\(q+(-0.555632 - 0.320794i) q^{2} +(-0.794182 - 1.37556i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.64400 - 0.0963576i) q^{7} +2.30225i q^{8} +(0.555632 - 0.320794i) q^{10} +(4.43818 - 2.56238i) q^{11} +4.67589i q^{13} +(1.43818 + 0.901718i) q^{14} +(-0.849814 + 1.47192i) q^{16} +(0.388736 + 0.673310i) q^{17} +(0.450558 + 0.260130i) q^{19} +1.58836 q^{20} -3.28799 q^{22} +(0.944368 + 0.545231i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.50000 - 2.59808i) q^{26} +(1.96727 + 3.71351i) q^{28} -9.92199i q^{29} +(3.88255 - 2.24159i) q^{31} +(4.93199 - 2.84748i) q^{32} -0.498817i q^{34} +(1.40545 - 2.24159i) q^{35} +(-1.34362 + 2.32723i) q^{37} +(-0.166896 - 0.289073i) q^{38} +(-1.99381 - 1.15113i) q^{40} +4.11126 q^{41} +6.79851 q^{43} +(-7.04944 - 4.07000i) q^{44} +(-0.349814 - 0.605896i) q^{46} +(3.55563 - 6.15854i) q^{47} +(6.98143 + 0.509538i) q^{49} +0.641589i q^{50} +(6.43199 - 3.71351i) q^{52} +(7.60507 - 4.39079i) q^{53} +5.12477i q^{55} +(0.221840 - 6.08715i) q^{56} +(-3.18292 + 5.51298i) q^{58} +(6.43199 + 11.1405i) q^{59} +(-8.71634 - 5.03238i) q^{61} -2.87636 q^{62} -0.254572 q^{64} +(-4.04944 - 2.33795i) q^{65} +(-7.66071 - 13.2687i) q^{67} +(0.617454 - 1.06946i) q^{68} +(-1.50000 + 0.794640i) q^{70} +11.1473i q^{71} +(-7.93199 + 4.57954i) q^{73} +(1.49312 - 0.862054i) q^{74} -0.826361i q^{76} +(-11.9814 + 6.34728i) q^{77} +(4.77128 - 8.26410i) q^{79} +(-0.849814 - 1.47192i) q^{80} +(-2.28435 - 1.31887i) q^{82} +9.77747 q^{83} -0.777472 q^{85} +(-3.77747 - 2.18092i) q^{86} +(5.89926 + 10.2178i) q^{88} +(6.92580 - 11.9958i) q^{89} +(0.450558 - 12.3630i) q^{91} -1.73205i q^{92} +(-3.95125 + 2.28125i) q^{94} +(-0.450558 + 0.260130i) q^{95} +3.32927i q^{97} +(-3.71565 - 2.52272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7	\( 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7} + 3 q^{10} + 9 q^{11} - 9 q^{14} + q^{16} + 3 q^{17} + 21 q^{19} - 2 q^{20} + 4 q^{22} + 6 q^{23} - 3 q^{25} + 9 q^{26} + 23 q^{28} + 6 q^{31} - 6 q^{32} + 2 q^{35} + 16 q^{37} + 6 q^{40} + 24 q^{41} - 8 q^{43} - 24 q^{44} + 4 q^{46} + 21 q^{47} - 12 q^{49} + 3 q^{52} + 27 q^{53} + 3 q^{56} - 14 q^{58} + 3 q^{59} - 33 q^{61} + 18 q^{62} + 8 q^{64} - 6 q^{65} - 27 q^{67} + 21 q^{68} - 9 q^{70} - 12 q^{73} - 6 q^{74} - 18 q^{77} + 12 q^{79} + q^{80} - 30 q^{82} + 60 q^{83} - 6 q^{85} - 24 q^{86} + 11 q^{88} - 12 q^{89} + 21 q^{91} - 39 q^{94} - 21 q^{95} - 6 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7 + 3 * q^10 + 9 * q^11 - 9 * q^14 + q^16 + 3 * q^17 + 21 * q^19 - 2 * q^20 + 4 * q^22 + 6 * q^23 - 3 * q^25 + 9 * q^26 + 23 * q^28 + 6 * q^31 - 6 * q^32 + 2 * q^35 + 16 * q^37 + 6 * q^40 + 24 * q^41 - 8 * q^43 - 24 * q^44 + 4 * q^46 + 21 * q^47 - 12 * q^49 + 3 * q^52 + 27 * q^53 + 3 * q^56 - 14 * q^58 + 3 * q^59 - 33 * q^61 + 18 * q^62 + 8 * q^64 - 6 * q^65 - 27 * q^67 + 21 * q^68 - 9 * q^70 - 12 * q^73 - 6 * q^74 - 18 * q^77 + 12 * q^79 + q^80 - 30 * q^82 + 60 * q^83 - 6 * q^85 - 24 * q^86 + 11 * q^88 - 12 * q^89 + 21 * q^91 - 39 * q^94 - 21 * q^95 - 6 * q^98

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