LMFDB - Embedded newform 315.2.j.g.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$1.43310 - 2.48220i$ of defining polynomial
Character	$\chi$	$=$	315.46
Dual form			315.2.j.g.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933099 - 1.61618i) q^{2} +(-0.741348 + 1.28405i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.69175 + 2.03420i) q^{7} -0.965392 q^{8} +O(q^{10})$	\(q+(-0.933099 - 1.61618i) q^{2} +(-0.741348 + 1.28405i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.69175 + 2.03420i) q^{7} -0.965392 q^{8} +(0.933099 - 1.61618i) q^{10} +(2.67445 - 4.63228i) q^{11} +4.34889 q^{13} +(1.70906 - 4.63228i) q^{14} +(2.38350 + 4.12835i) q^{16} +(0.933099 - 1.61618i) q^{17} +(-2.62485 - 4.54637i) q^{19} -1.48270 q^{20} -9.98210 q^{22} +(3.45040 + 5.97627i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.05795 - 7.02857i) q^{26} +(-3.86620 + 0.664245i) q^{28} -4.38350 q^{29} +(4.71509 - 8.16678i) q^{31} +(3.48270 - 6.03221i) q^{32} -3.48270 q^{34} +(-0.915795 + 2.48220i) q^{35} +(-1.08420 - 1.87790i) q^{37} +(-4.89849 + 8.48444i) q^{38} +(-0.482696 - 0.836054i) q^{40} +0.314286 q^{41} -7.56399 q^{43} +(3.96539 + 6.86826i) q^{44} +(6.43914 - 11.1529i) q^{46} +(4.21509 + 7.30075i) q^{47} +(-1.27596 + 6.88273i) q^{49} +1.86620 q^{50} +(-3.22404 + 5.58421i) q^{52} +(-1.86620 + 3.23235i) q^{53} +5.34889 q^{55} +(-1.63320 - 1.96380i) q^{56} +(4.09024 + 7.08451i) q^{58} +(0.639839 - 1.10823i) q^{59} +(1.39245 + 2.41180i) q^{61} -17.5986 q^{62} -3.46479 q^{64} +(2.17445 + 3.76625i) q^{65} +(-1.04065 + 1.80245i) q^{67} +(1.38350 + 2.39630i) q^{68} +(4.86620 - 0.836054i) q^{70} +6.81369 q^{71} +(2.81660 - 4.87850i) q^{73} +(-2.02334 + 3.50453i) q^{74} +7.78371 q^{76} +(13.9475 - 2.39630i) q^{77} +(5.97374 + 10.3468i) q^{79} +(-2.38350 + 4.12835i) q^{80} +(-0.293260 - 0.507941i) q^{82} -3.16841 q^{83} +1.86620 q^{85} +(7.05795 + 12.2247i) q^{86} +(-2.58189 + 4.47196i) q^{88} +(-1.45935 - 2.52768i) q^{89} +(7.35725 + 8.84653i) q^{91} -10.2318 q^{92} +(7.86620 - 13.6247i) q^{94} +(2.62485 - 4.54637i) q^{95} -9.91288 q^{97} +(12.3143 - 4.36010i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8	$ 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8} - 2 q^{10} + 10 q^{11} + 14 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + q^{19} - 12 q^{20} + 4 q^{22} + 10 q^{23} - 3 q^{25} - 8 q^{28} - 8 q^{29} + q^{31} + 24 q^{32} - 24 q^{34} - q^{35} - 11 q^{37} - 28 q^{38} - 6 q^{40} - 4 q^{41} - 6 q^{43} + 30 q^{44} + 16 q^{46} - 2 q^{47} - 3 q^{49} - 4 q^{50} - 24 q^{52} + 4 q^{53} + 20 q^{55} + 42 q^{56} + 14 q^{58} + 4 q^{59} + 22 q^{61} - 60 q^{62} + 40 q^{64} + 7 q^{65} + 15 q^{67} - 10 q^{68} + 14 q^{70} - 32 q^{71} - 9 q^{73} + 6 q^{74} - 60 q^{76} + 26 q^{77} + 7 q^{79} + 4 q^{80} + 6 q^{82} - 28 q^{83} - 4 q^{85} + 18 q^{86} - 40 q^{88} - 30 q^{89} - 3 q^{91} + 36 q^{92} + 32 q^{94} - q^{95} - 8 q^{97} + 68 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8 - 2 * q^10 + 10 * q^11 + 14 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + q^19 - 12 * q^20 + 4 * q^22 + 10 * q^23 - 3 * q^25 - 8 * q^28 - 8 * q^29 + q^31 + 24 * q^32 - 24 * q^34 - q^35 - 11 * q^37 - 28 * q^38 - 6 * q^40 - 4 * q^41 - 6 * q^43 + 30 * q^44 + 16 * q^46 - 2 * q^47 - 3 * q^49 - 4 * q^50 - 24 * q^52 + 4 * q^53 + 20 * q^55 + 42 * q^56 + 14 * q^58 + 4 * q^59 + 22 * q^61 - 60 * q^62 + 40 * q^64 + 7 * q^65 + 15 * q^67 - 10 * q^68 + 14 * q^70 - 32 * q^71 - 9 * q^73 + 6 * q^74 - 60 * q^76 + 26 * q^77 + 7 * q^79 + 4 * q^80 + 6 * q^82 - 28 * q^83 - 4 * q^85 + 18 * q^86 - 40 * q^88 - 30 * q^89 - 3 * q^91 + 36 * q^92 + 32 * q^94 - q^95 - 8 * q^97 + 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.933099	−	1.61618i	−0.659801	−	1.14281i	−0.980667	−	0.195684i	$-0.937307\pi$
$2$	−0.933099	−	1.61618i	−0.659801	−	1.14281i	0.320866	−	0.947124i	$-0.396026\pi$
$3$		0			0
$3$		0			0
$4$	−0.741348	+	1.28405i	−0.370674	+	0.642026i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.69175	+	2.03420i	0.639422	+	0.768856i
$7$	1.69175	+	2.03420i	0.639422	+	0.768856i
$8$	−0.965392			−0.341318
$9$		0			0
$10$	0.933099	−	1.61618i	0.295072	−	0.511079i
$11$	2.67445	−	4.63228i	0.806376	−	1.39668i	−0.108982	−	0.994044i	$-0.534759\pi$
$11$	2.67445	−	4.63228i	0.806376	−	1.39668i	0.915358	−	0.402641i	$-0.131908\pi$
$12$		0			0
$13$	4.34889			1.20617			0.603083	−	0.797678i	$-0.293939\pi$
$13$	4.34889			1.20617			0.603083	+	0.797678i	$0.293939\pi$
$14$	1.70906	−	4.63228i	0.456764	−	1.23803i
$15$		0			0
$16$	2.38350	+	4.12835i	0.595876	+	1.03209i
$17$	0.933099	−	1.61618i	0.226310	−	0.391980i	−0.730402	−	0.683018i	$-0.760667\pi$
$17$	0.933099	−	1.61618i	0.226310	−	0.391980i	0.956712	+	0.291038i	$0.0940005\pi$
$18$		0			0
$19$	−2.62485	−	4.54637i	−0.602182	−	1.04301i	−0.992490	−	0.122325i	$-0.960965\pi$
$19$	−2.62485	−	4.54637i	−0.602182	−	1.04301i	0.390308	−	0.920684i	$-0.372368\pi$
$20$	−1.48270			−0.331541
$21$		0			0
$22$	−9.98210			−2.12819
$23$	3.45040	+	5.97627i	0.719459	+	1.24614i	0.961214	+	0.275802i	$0.0889434\pi$
$23$	3.45040	+	5.97627i	0.719459	+	1.24614i	−0.241756	+	0.970337i	$0.577723\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.05795	−	7.02857i	−0.795829	−	1.37842i
$27$		0			0
$28$	−3.86620	+	0.664245i	−0.730643	+	0.125531i
$29$	−4.38350			−0.813996			−0.406998	−	0.913429i	$-0.633424\pi$
$29$	−4.38350			−0.813996			−0.406998	+	0.913429i	$0.633424\pi$
$30$		0			0
$31$	4.71509	−	8.16678i	0.846856	−	1.46680i	−0.0371443	−	0.999310i	$-0.511826\pi$
$31$	4.71509	−	8.16678i	0.846856	−	1.46680i	0.884000	−	0.467487i	$-0.154841\pi$
$32$	3.48270	−	6.03221i	0.615659	−	1.06635i
$33$		0			0
$34$	−3.48270			−0.597277
$35$	−0.915795	+	2.48220i	−0.154798	+	0.419568i
$36$		0			0
$37$	−1.08420	−	1.87790i	−0.178242	−	0.308725i	0.763036	−	0.646356i	$-0.223708\pi$
$37$	−1.08420	−	1.87790i	−0.178242	−	0.308725i	−0.941279	+	0.337631i	$0.890374\pi$
$38$	−4.89849	+	8.48444i	−0.794640	+	1.37636i
$39$		0			0
$40$	−0.482696	−	0.836054i	−0.0763209	−	0.132192i
$41$	0.314286			0.0490832			0.0245416	−	0.999699i	$-0.492187\pi$
$41$	0.314286			0.0490832			0.0245416	+	0.999699i	$0.492187\pi$
$42$		0			0
$43$	−7.56399			−1.15350			−0.576749	−	0.816922i	$-0.695679\pi$
$43$	−7.56399			−1.15350			−0.576749	+	0.816922i	$0.695679\pi$
$44$	3.96539	+	6.86826i	0.597805	+	1.03543i
$45$		0			0
$46$	6.43914	−	11.1529i	0.949399	−	1.64441i
$47$	4.21509	+	7.30075i	0.614834	+	1.06492i	0.990414	+	0.138134i	$0.0441105\pi$
$47$	4.21509	+	7.30075i	0.614834	+	1.06492i	−0.375579	+	0.926790i	$0.622556\pi$
$48$		0			0
$49$	−1.27596	+	6.88273i	−0.182279	+	0.983247i
$50$	1.86620			0.263920
$51$		0			0
$52$	−3.22404	+	5.58421i	−0.447094	+	0.774390i
$53$	−1.86620	+	3.23235i	−0.256342	+	0.443997i	−0.965259	−	0.261294i	$-0.915851\pi$
$53$	−1.86620	+	3.23235i	−0.256342	+	0.443997i	0.708917	+	0.705292i	$0.249184\pi$
$54$		0			0
$55$	5.34889			0.721245
$56$	−1.63320	−	1.96380i	−0.218246	−	0.262424i
$57$		0			0
$58$	4.09024	+	7.08451i	0.537075	+	0.930241i
$59$	0.639839	−	1.10823i	0.0832999	−	0.144280i	−0.821366	−	0.570402i	$-0.806787\pi$
$59$	0.639839	−	1.10823i	0.0832999	−	0.144280i	0.904666	+	0.426122i	$0.140121\pi$
$60$		0			0
$61$	1.39245	+	2.41180i	0.178285	+	0.308799i	0.941293	−	0.337590i	$-0.109612\pi$
$61$	1.39245	+	2.41180i	0.178285	+	0.308799i	−0.763008	+	0.646389i	$0.776278\pi$
$62$	−17.5986			−2.23502
$63$		0			0
$64$	−3.46479			−0.433099
$65$	2.17445	+	3.76625i	0.269707	+	0.467146i
$66$		0			0
$67$	−1.04065	+	1.80245i	−0.127135	+	0.220204i	−0.922565	−	0.385841i	$-0.873911\pi$
$67$	−1.04065	+	1.80245i	−0.127135	+	0.220204i	0.795430	+	0.606045i	$0.207245\pi$
$68$	1.38350	+	2.39630i	0.167774	+	0.290594i
$69$		0			0
$70$	4.86620	−	0.836054i	0.581622	−	0.0999276i
$71$	6.81369			0.808636			0.404318	−	0.914618i	$-0.367509\pi$
$71$	6.81369			0.808636			0.404318	+	0.914618i	$0.367509\pi$
$72$		0			0
$73$	2.81660	−	4.87850i	0.329658	−	0.570985i	−0.652786	−	0.757543i	$-0.726400\pi$
$73$	2.81660	−	4.87850i	0.329658	−	0.570985i	0.982444	+	0.186558i	$0.0597331\pi$
$74$	−2.02334	+	3.50453i	−0.235209	+	0.407393i
$75$		0			0
$76$	7.78371			0.892853
$77$	13.9475	−	2.39630i	1.58946	−	0.273083i
$78$		0			0
$79$	5.97374	+	10.3468i	0.672099	+	1.16411i	0.977308	+	0.211824i	$0.0679403\pi$
$79$	5.97374	+	10.3468i	0.672099	+	1.16411i	−0.305209	+	0.952285i	$0.598726\pi$
$80$	−2.38350	+	4.12835i	−0.266484	+	0.461563i
$81$		0			0
$82$	−0.293260	−	0.507941i	−0.0323852	−	0.0560927i
$83$	−3.16841			−0.347778			−0.173889	−	0.984765i	$-0.555633\pi$
$83$	−3.16841			−0.347778			−0.173889	+	0.984765i	$0.555633\pi$
$84$		0			0
$85$	1.86620			0.202418
$86$	7.05795	+	12.2247i	0.761078	+	1.31823i
$87$		0			0
$88$	−2.58189	+	4.47196i	−0.275230	+	0.476713i
$89$	−1.45935	−	2.52768i	−0.154691	−	0.267933i	0.778255	−	0.627948i	$-0.216105\pi$
$89$	−1.45935	−	2.52768i	−0.154691	−	0.267933i	−0.932947	+	0.360015i	$0.882772\pi$
$90$		0			0
$91$	7.35725	+	8.84653i	0.771249	+	0.927368i
$92$	−10.2318			−1.06674
$93$		0			0
$94$	7.86620	−	13.6247i	0.811336	−	1.40528i
$95$	2.62485	−	4.54637i	0.269304	−	0.466448i
$96$		0			0
$97$	−9.91288			−1.00650			−0.503250	−	0.864141i	$-0.667863\pi$
$97$	−9.91288			−1.00650			−0.503250	+	0.864141i	$0.667863\pi$
$98$	12.3143	−	4.36010i	1.24393	−	0.440436i
$99$		0			0
$100$	−0.741348	−	1.28405i	−0.0741348	−	0.128405i
$101$	−8.75574	+	15.1654i	−0.871228	+	1.50901i	−0.0105017	+	0.999945i	$0.503343\pi$
$101$	−8.75574	+	15.1654i	−0.871228	+	1.50901i	−0.860727	+	0.509067i	$0.829990\pi$
$102$		0			0
$103$	−6.26469	−	10.8508i	−0.617278	−	1.06916i	−0.989980	−	0.141206i	$-0.954902\pi$
$103$	−6.26469	−	10.8508i	−0.617278	−	1.06916i	0.372702	−	0.927951i	$-0.378431\pi$
$104$	−4.19839			−0.411686
$105$		0			0
$106$	6.96539			0.676539
$107$	4.58420	+	7.94008i	0.443172	+	0.767596i	0.997923	−	0.0644203i	$-0.0205198\pi$
$107$	4.58420	+	7.94008i	0.443172	+	0.767596i	−0.554751	+	0.832016i	$0.687186\pi$
$108$		0			0
$109$	−4.49105	+	7.77872i	−0.430164	+	0.745067i	−0.996887	−	0.0788419i	$-0.974878\pi$
$109$	−4.49105	+	7.77872i	−0.430164	+	0.745067i	0.566723	+	0.823909i	$0.308211\pi$
$110$	−4.99105	−	8.64475i	−0.475878	−	0.824245i
$111$		0			0
$112$	−4.36560	+	11.8327i	−0.412510	+	1.11808i
$113$	−8.76700			−0.824730			−0.412365	−	0.911019i	$-0.635297\pi$
$113$	−8.76700			−0.824730			−0.412365	+	0.911019i	$0.635297\pi$
$114$		0			0
$115$	−3.45040	+	5.97627i	−0.321752	+	0.557290i
$116$	3.24970	−	5.62865i	0.301727	−	0.522607i
$117$		0			0
$118$	−2.38813			−0.219845
$119$	4.86620	−	0.836054i	0.446084	−	0.0766409i
$120$		0			0
$121$	−8.80533	−	15.2513i	−0.800485	−	1.38648i
$122$	2.59859	−	4.50090i	0.235266	−	0.407492i
$123$		0			0
$124$	6.99105	+	12.1089i	0.627815	+	1.08741i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	1.11590			0.0990200			0.0495100	−	0.998774i	$-0.484234\pi$
$127$	1.11590			0.0990200			0.0495100	+	0.998774i	$0.484234\pi$
$128$	−3.73240	−	6.46470i	−0.329900	−	0.571404i
$129$		0			0
$130$	4.05795	−	7.02857i	0.355906	−	0.616447i
$131$	−10.7791	−	18.6699i	−0.941773	−	1.63120i	−0.762088	−	0.647474i	$-0.775826\pi$
$131$	−10.7791	−	18.6699i	−0.941773	−	1.63120i	−0.179685	−	0.983724i	$-0.557508\pi$
$132$		0			0
$133$	4.80765	−	13.0308i	0.416876	−	1.12991i
$134$	3.88410			0.335535
$135$		0			0
$136$	−0.900806	+	1.56024i	−0.0772435	+	0.133790i
$137$	−6.11358	+	10.5890i	−0.522319	+	0.904683i	0.477344	+	0.878716i	$0.341600\pi$
$137$	−6.11358	+	10.5890i	−0.522319	+	0.904683i	−0.999663	+	0.0259661i	$0.991734\pi$
$138$		0			0
$139$	−12.2843			−1.04194			−0.520971	−	0.853575i	$-0.674430\pi$
$139$	−12.2843			−1.04194			−0.520971	+	0.853575i	$0.674430\pi$
$140$	−2.50835	−	3.01610i	−0.211994	−	0.254907i
$141$		0			0
$142$	−6.35785	−	11.0121i	−0.533539	−	0.924116i
$143$	11.6309	−	20.1453i	0.972624	−	1.68463i
$144$		0			0
$145$	−2.19175	−	3.79622i	−0.182015	−	0.315259i
$146$	−10.5127			−0.870035
$147$		0			0
$148$	3.21509			0.264279
$149$	−1.69779	−	2.94066i	−0.139088	−	0.240908i	0.788064	−	0.615594i	$-0.211084\pi$
$149$	−1.69779	−	2.94066i	−0.139088	−	0.240908i	−0.927152	+	0.374686i	$0.877751\pi$
$150$		0			0
$151$	−0.642154	+	1.11224i	−0.0522578	+	0.0905131i	−0.890971	−	0.454060i	$-0.849975\pi$
$151$	−0.642154	+	1.11224i	−0.0522578	+	0.0905131i	0.838713	+	0.544573i	$0.183308\pi$
$152$	2.53401	+	4.38903i	0.205535	+	0.355998i
$153$		0			0
$154$	−16.8872	−	20.3056i	−1.36081	−	1.63627i
$155$	9.43018			0.757451
$156$		0			0
$157$	−7.90081	+	13.6846i	−0.630553	+	1.09215i	0.356886	+	0.934148i	$0.383839\pi$
$157$	−7.90081	+	13.6846i	−0.630553	+	1.09215i	−0.987439	+	0.158002i	$0.949495\pi$
$158$	11.1482	−	19.3092i	0.886903	−	1.53616i
$159$		0			0
$160$	6.96539			0.550663
$161$	−6.31972	+	17.1292i	−0.498064	+	1.34997i
$162$		0			0
$163$	2.65111	+	4.59185i	0.207651	+	0.359661i	0.950974	−	0.309271i	$-0.100085\pi$
$163$	2.65111	+	4.59185i	0.207651	+	0.359661i	−0.743323	+	0.668932i	$0.766752\pi$
$164$	−0.232995	+	0.403560i	−0.0181939	+	0.0315127i
$165$		0			0
$166$	2.95644	+	5.12071i	0.229464	+	0.397444i
$167$	16.6332			1.28712			0.643558	−	0.765397i	$-0.277458\pi$
$167$	16.6332			1.28712			0.643558	+	0.765397i	$0.277458\pi$
$168$		0			0
$169$	5.91288			0.454837
$170$	−1.74135	−	3.01610i	−0.133555	−	0.231325i
$171$		0			0
$172$	5.60755	−	9.71255i	0.427571	−	0.740575i
$173$	−9.24970	−	16.0210i	−0.703242	−	1.21805i	−0.967322	−	0.253550i	$-0.918402\pi$
$173$	−9.24970	−	16.0210i	−0.703242	−	1.21805i	0.264081	−	0.964501i	$-0.414931\pi$
$174$		0			0
$175$	−2.60755	+	0.447998i	−0.197112	+	0.0338655i
$176$	25.4982			1.92200
$177$		0			0
$178$	−2.72345	+	4.71715i	−0.204131	+	0.353565i
$179$	7.21509	−	12.4969i	0.539281	−	0.934063i	−0.459662	−	0.888094i	$-0.652029\pi$
$179$	7.21509	−	12.4969i	0.539281	−	0.934063i	0.998943	−	0.0459685i	$-0.0146374\pi$
$180$		0			0
$181$	−12.9129			−0.959807			−0.479903	−	0.877321i	$-0.659328\pi$
$181$	−12.9129			−0.959807			−0.479903	+	0.877321i	$0.659328\pi$
$182$	7.43250	−	20.1453i	0.550934	−	1.49327i
$183$		0			0
$184$	−3.33099	−	5.76945i	−0.245564	−	0.425329i
$185$	1.08420	−	1.87790i	0.0797123	−	0.138066i
$186$		0			0
$187$	−4.99105	−	8.64475i	−0.364982	−	0.632167i
$188$	−12.4994			−0.911613
$189$		0			0
$190$	−9.79698			−0.710748
$191$	6.24970	+	10.8248i	0.452212	+	0.783255i	0.998523	−	0.0543276i	$-0.0173015\pi$
$191$	6.24970	+	10.8248i	0.452212	+	0.783255i	−0.546311	+	0.837583i	$0.683968\pi$
$192$		0			0
$193$	−9.51439	+	16.4794i	−0.684861	+	1.18621i	0.288620	+	0.957444i	$0.406804\pi$
$193$	−9.51439	+	16.4794i	−0.684861	+	1.18621i	−0.973481	+	0.228770i	$0.926530\pi$
$194$	9.24970	+	16.0210i	0.664090	+	1.15024i
$195$		0			0
$196$	−7.89185	−	6.74089i	−0.563704	−	0.481492i
$197$	−26.6574			−1.89926			−0.949629	−	0.313377i	$-0.898540\pi$
$197$	−26.6574			−1.89926			−0.949629	+	0.313377i	$0.898540\pi$
$198$		0			0
$199$	−3.78803	+	6.56106i	−0.268526	+	0.465101i	−0.968481	−	0.249086i	$-0.919870\pi$
$199$	−3.78803	+	6.56106i	−0.268526	+	0.465101i	0.699955	+	0.714187i	$0.253203\pi$
$200$	0.482696	−	0.836054i	0.0341318	−	0.0591179i
$201$		0			0
$202$	32.6799			2.29935
$203$	−7.41580	−	8.91693i	−0.520487	−	0.625846i
$204$		0			0
$205$	0.157143	+	0.272180i	0.0109753	+	0.0190099i
$206$	−11.6912	+	20.2497i	−0.814561	+	1.41086i
$207$		0			0
$208$	10.3656	+	17.9537i	0.718725	+	1.24487i
$209$	−28.0801			−1.94234
$210$		0			0
$211$	14.4123			0.992182			0.496091	−	0.868270i	$-0.334768\pi$
$211$	14.4123			0.992182			0.496091	+	0.868270i	$0.334768\pi$
$212$	−2.76700	−	4.79259i	−0.190039	−	0.329157i
$213$		0			0
$214$	8.55504	−	14.8178i	0.584810	−	1.01292i
$215$	−3.78199	−	6.55060i	−0.257930	−	0.446748i
$216$		0			0
$217$	24.5896	−	4.22471i	1.66925	−	0.286792i
$218$	16.7624			1.13529
$219$		0			0
$220$	−3.96539	+	6.86826i	−0.267347	+	0.463058i
$221$	4.05795	−	7.02857i	0.272967	−	0.472793i
$222$		0			0
$223$	−1.39558			−0.0934547			−0.0467274	−	0.998908i	$-0.514879\pi$
$223$	−1.39558			−0.0934547			−0.0467274	+	0.998908i	$0.514879\pi$
$224$	18.1626	−	3.12048i	1.21354	−	0.208496i
$225$		0			0
$226$	8.18048	+	14.1690i	0.544158	+	0.942509i
$227$	4.18280	−	7.24482i	0.277622	−	0.480856i	−0.693171	−	0.720773i	$-0.743787\pi$
$227$	4.18280	−	7.24482i	0.277622	−	0.480856i	0.970793	+	0.239917i	$0.0771203\pi$
$228$		0			0
$229$	8.19779	+	14.1990i	0.541725	+	0.938295i	0.998805	+	0.0488698i	$0.0155620\pi$
$229$	8.19779	+	14.1990i	0.541725	+	0.938295i	−0.457080	+	0.889426i	$0.651105\pi$
$230$	12.8783			0.849168
$231$		0			0
$232$	4.23180			0.277831
$233$	3.31429	+	5.74051i	0.217126	+	0.376073i	0.953928	−	0.300035i	$-0.0969984\pi$
$233$	3.31429	+	5.74051i	0.217126	+	0.376073i	−0.736802	+	0.676109i	$0.763665\pi$
$234$		0			0
$235$	−4.21509	+	7.30075i	−0.274962	+	0.476249i
$236$	0.948687	+	1.64317i	0.0617542	+	0.106961i
$237$		0			0
$238$	−5.89185	−	7.08451i	−0.381912	−	0.459220i
$239$	−27.3956			−1.77207			−0.886036	−	0.463616i	$-0.846552\pi$
$239$	−27.3956			−1.77207			−0.886036	+	0.463616i	$0.846552\pi$
$240$		0			0
$241$	1.07817	−	1.86744i	0.0694509	−	0.120292i	−0.829209	−	0.558939i	$-0.811209\pi$
$241$	1.07817	−	1.86744i	0.0694509	−	0.120292i	0.898660	+	0.438646i	$0.144542\pi$
$242$	−16.4325	+	28.4619i	−1.05632	+	1.82960i
$243$		0			0
$244$	−4.12917			−0.264343
$245$	−6.59859	+	2.33635i	−0.421569	+	0.149264i
$246$		0			0
$247$	−11.4152	−	19.7717i	−0.726332	−	1.25804i
$248$	−4.55191	+	7.88414i	−0.289047	+	0.500644i
$249$		0			0
$250$	0.933099	+	1.61618i	0.0590144	+	0.102216i
$251$	17.8483			1.12657			0.563287	−	0.826261i	$-0.309536\pi$
$251$	17.8483			1.12657			0.563287	+	0.826261i	$0.309536\pi$
$252$		0			0
$253$	36.9117			2.32062
$254$	−1.04124	−	1.80349i	−0.0653335	−	0.113161i
$255$		0			0
$256$	−10.4302	+	18.0656i	−0.651887	+	1.12910i
$257$	10.8114	+	18.7258i	0.674395	+	1.16809i	0.976645	+	0.214858i	$0.0689287\pi$
$257$	10.8114	+	18.7258i	0.674395	+	1.16809i	−0.302251	+	0.953229i	$0.597738\pi$
$258$		0			0
$259$	1.98582	−	5.38243i	0.123393	−	0.334448i
$260$	−6.44809			−0.399893
$261$		0			0
$262$	−20.1159	+	34.8418i	−1.24276	+	2.15253i
$263$	−0.732397	+	1.26855i	−0.0451615	+	0.0782220i	−0.887723	−	0.460379i	$-0.847714\pi$
$263$	−0.732397	+	1.26855i	−0.0451615	+	0.0782220i	0.842561	+	0.538601i	$0.181047\pi$
$264$		0			0
$265$	−3.73240			−0.229279
$266$	−25.5461	+	4.38903i	−1.56633	+	0.269109i
$267$		0			0
$268$	−1.54296	−	2.67249i	−0.0942513	−	0.163248i
$269$	8.93541	−	15.4766i	0.544802	−	0.943624i	−0.453818	−	0.891095i	$-0.649938\pi$
$269$	8.93541	−	15.4766i	0.544802	−	0.943624i	0.998619	−	0.0525298i	$-0.0167285\pi$
$270$		0			0
$271$	1.22404	+	2.12011i	0.0743554	+	0.128787i	0.900806	−	0.434222i	$-0.142977\pi$
$271$	1.22404	+	2.12011i	0.0743554	+	0.128787i	−0.826450	+	0.563010i	$0.809643\pi$
$272$	8.89618			0.539410
$273$		0			0
$274$	22.8183			1.37850
$275$	2.67445	+	4.63228i	0.161275	+	0.279337i
$276$		0			0
$277$	7.26469	−	12.5828i	0.436493	−	0.756028i	−0.560923	−	0.827868i	$-0.689554\pi$
$277$	7.26469	−	12.5828i	0.436493	−	0.756028i	0.997416	+	0.0718399i	$0.0228871\pi$
$278$	11.4625	+	19.8536i	0.687474	+	1.19074i
$279$		0			0
$280$	0.884101	−	2.39630i	0.0528352	−	0.143206i
$281$	−1.63903			−0.0977764			−0.0488882	−	0.998804i	$-0.515568\pi$
$281$	−1.63903			−0.0977764			−0.0488882	+	0.998804i	$0.515568\pi$
$282$		0			0
$283$	6.29930	−	10.9107i	0.374454	−	0.648574i	−0.615791	−	0.787910i	$-0.711163\pi$
$283$	6.29930	−	10.9107i	0.374454	−	0.648574i	0.990245	+	0.139336i	$0.0444967\pi$
$284$	−5.05131	+	8.74913i	−0.299740	+	0.519165i
$285$		0			0
$286$	−43.4111			−2.56695
$287$	0.531694	+	0.639321i	0.0313849	+	0.0377380i
$288$		0			0
$289$	6.75865	+	11.7063i	0.397568	+	0.688608i
$290$	−4.09024	+	7.08451i	−0.240187	+	0.416017i
$291$		0			0
$292$	4.17616	+	7.23333i	0.244391	+	0.423298i
$293$	5.87083			0.342977			0.171489	−	0.985186i	$-0.445142\pi$
$293$	5.87083			0.342977			0.171489	+	0.985186i	$0.445142\pi$
$294$		0			0
$295$	1.27968			0.0745057
$296$	1.04668	+	1.81291i	0.0608372	+	0.105373i
$297$		0			0
$298$	−3.16841	+	5.48785i	−0.183541	+	0.317902i
$299$	15.0054	+	25.9902i	0.867787	+	1.50305i
$300$		0			0
$301$	−12.7964	−	15.3867i	−0.737571	−	0.886873i
$302$	2.39677			0.137919
$303$		0			0
$304$	12.5127	−	21.6726i	0.717651	−	1.24301i
$305$	−1.39245	+	2.41180i	−0.0797317	+	0.138099i
$306$		0			0
$307$	9.72032			0.554768			0.277384	−	0.960759i	$-0.410533\pi$
$307$	9.72032			0.554768			0.277384	+	0.960759i	$0.410533\pi$
$308$	−7.26297	+	19.6858i	−0.413846	+	1.12170i
$309$		0			0
$310$	−8.79930	−	15.2408i	−0.499767	−	0.865621i
$311$	−0.889540	+	1.54073i	−0.0504412	+	0.0873667i	−0.890144	−	0.455680i	$-0.849396\pi$
$311$	−0.889540	+	1.54073i	−0.0504412	+	0.0873667i	0.839702	+	0.543047i	$0.182729\pi$
$312$		0			0
$313$	−15.7641	−	27.3042i	−0.891039	−	1.54332i	−0.838632	−	0.544699i	$-0.816644\pi$
$313$	−15.7641	−	27.3042i	−0.891039	−	1.54332i	−0.0524076	−	0.998626i	$-0.516689\pi$
$314$	29.4889			1.66416
$315$		0			0
$316$	−17.7145			−0.996518
$317$	−5.31660	−	9.20862i	−0.298610	−	0.517208i	0.677208	−	0.735792i	$-0.263190\pi$
$317$	−5.31660	−	9.20862i	−0.298610	−	0.517208i	−0.975818	+	0.218584i	$0.929856\pi$
$318$		0			0
$319$	−11.7234	+	20.3056i	−0.656387	+	1.13690i
$320$	−1.73240	−	3.00060i	−0.0968439	−	0.167739i
$321$		0			0
$322$	33.5807	−	5.76945i	1.87138	−	0.321519i
$323$	−9.79698			−0.545119
$324$		0			0
$325$	−2.17445	+	3.76625i	−0.120617	+	0.208914i
$326$	4.94749	−	8.56930i	0.274016	−	0.474610i
$327$		0			0
$328$	−0.303409			−0.0167530
$329$	−7.72032	+	20.9254i	−0.425635	+	1.15366i
$330$		0			0
$331$	1.71509	+	2.97063i	0.0942700	+	0.163280i	0.909304	−	0.416133i	$-0.136615\pi$
$331$	1.71509	+	2.97063i	0.0942700	+	0.163280i	−0.815034	+	0.579414i	$0.803282\pi$
$332$	2.34889	−	4.06840i	0.128912	−	0.223283i
$333$		0			0
$334$	−15.5204	−	26.8822i	−0.849240	−	1.47093i
$335$	−2.08129			−0.113713
$336$		0			0
$337$	3.67525			0.200204			0.100102	−	0.994977i	$-0.468083\pi$
$337$	3.67525			0.200204			0.100102	+	0.994977i	$0.468083\pi$
$338$	−5.51730	−	9.55625i	−0.300102	−	0.519792i
$339$		0			0
$340$	−1.38350	+	2.39630i	−0.0750309	+	0.129957i
$341$	−25.2205	−	43.6832i	−1.36577	−	2.36558i
$342$		0			0
$343$	−16.1595	+	9.04831i	−0.872529	+	0.488563i
$344$	7.30221			0.393709
$345$		0			0
$346$	−17.2618	+	29.8983i	−0.927999	+	1.60734i
$347$	9.48270	−	16.4245i	0.509058	−	0.881714i	−0.490887	−	0.871223i	$-0.663327\pi$
$347$	9.48270	−	16.4245i	0.509058	−	0.881714i	0.999945	−	0.0104908i	$-0.00333939\pi$
$348$		0			0
$349$	−0.475252			−0.0254397			−0.0127198	−	0.999919i	$-0.504049\pi$
$349$	−0.475252			−0.0254397			−0.0127198	+	0.999919i	$0.504049\pi$
$350$	3.15714	+	3.79622i	0.168756	+	0.202917i
$351$		0			0
$352$	−18.6286	−	32.2656i	−0.992906	−	1.71976i
$353$	−7.91520	+	13.7095i	−0.421283	+	0.729684i	−0.996065	−	0.0886224i	$-0.971754\pi$
$353$	−7.91520	+	13.7095i	−0.421283	+	0.729684i	0.574782	+	0.818307i	$0.305087\pi$
$354$		0			0
$355$	3.40684	+	5.90083i	0.180816	+	0.313183i
$356$	4.32756			0.229360
$357$		0			0
$358$	−26.9296			−1.42327
$359$	−15.0054	−	25.9902i	−0.791957	−	1.37171i	−0.924754	−	0.380566i	$-0.875729\pi$
$359$	−15.0054	−	25.9902i	−0.791957	−	1.37171i	0.132797	−	0.991143i	$-0.457604\pi$
$360$		0			0
$361$	−4.27968	+	7.41262i	−0.225246	+	0.390138i
$362$	12.0490	+	20.8695i	0.633281	+	1.09688i
$363$		0			0
$364$	−16.8137	+	2.88873i	−0.881277	+	0.151411i
$365$	5.63320			0.294855
$366$		0			0
$367$	5.12194	−	8.87145i	0.267363	−	0.463086i	−0.700817	−	0.713341i	$-0.747181\pi$
$367$	5.12194	−	8.87145i	0.267363	−	0.463086i	0.968180	+	0.250255i	$0.0805144\pi$
$368$	−16.4481	+	28.4889i	−0.857416	+	1.48509i
$369$		0			0
$370$	−4.04668			−0.210377
$371$	−9.73240	+	1.67211i	−0.505281	+	0.0868115i
$372$		0			0
$373$	−8.57002	−	14.8437i	−0.443739	−	0.768579i	0.554224	−	0.832367i	$-0.313015\pi$
$373$	−8.57002	−	14.8437i	−0.443739	−	0.768579i	−0.997963	+	0.0637888i	$0.979682\pi$
$374$	−9.31429	+	16.1328i	−0.481630	+	0.834208i
$375$		0			0
$376$	−4.06922	−	7.04809i	−0.209854	−	0.363477i
$377$	−19.0634			−0.981814
$378$		0			0
$379$	21.6978			1.11454			0.557270	−	0.830331i	$-0.311849\pi$
$379$	21.6978			1.11454			0.557270	+	0.830331i	$0.311849\pi$
$380$	3.89185	+	6.74089i	0.199648	+	0.345800i
$381$		0			0
$382$	11.6632	−	20.2012i	0.596740	−	1.03358i
$383$	12.9008	+	22.3449i	0.659200	+	1.14177i	0.980823	+	0.194901i	$0.0624384\pi$
$383$	12.9008	+	22.3449i	0.659200	+	1.14177i	−0.321623	+	0.946868i	$0.604228\pi$
$384$		0			0
$385$	9.04900	+	10.8807i	0.461180	+	0.554533i
$386$	35.5115			1.80749
$387$		0			0
$388$	7.34889	−	12.7287i	0.373084	−	0.646200i
$389$	−1.94205	+	3.36373i	−0.0984659	+	0.170548i	−0.911050	−	0.412296i	$-0.864727\pi$
$389$	−1.94205	+	3.36373i	−0.0984659	+	0.170548i	0.812584	+	0.582844i	$0.198060\pi$
$390$		0			0
$391$	12.8783			0.651282
$392$	1.23180	−	6.64453i	0.0622152	−	0.335599i
$393$		0			0
$394$	24.8740	+	43.0829i	1.25313	+	2.17049i
$395$	−5.97374	+	10.3468i	−0.300572	+	0.520605i
$396$		0			0
$397$	9.95040	+	17.2346i	0.499396	+	0.864980i	1.00000		0.000696814i	$-0.000221803\pi$
$397$	9.95040	+	17.2346i	0.499396	+	0.864980i	−0.500603	+	0.865677i	$0.666888\pi$
$398$	14.1384			0.708696
$399$		0			0
$400$	−4.76700			−0.238350
$401$	−2.20302	−	3.81574i	−0.110013	−	0.190549i	0.805762	−	0.592240i	$-0.201756\pi$
$401$	−2.20302	−	3.81574i	−0.110013	−	0.190549i	−0.915775	+	0.401691i	$0.868423\pi$
$402$		0			0
$403$	20.5054	−	35.5165i	1.02145	−	1.76920i
$404$	−12.9821	−	22.4857i	−0.645883	−	1.11870i
$405$		0			0
$406$	−7.49165	+	20.3056i	−0.371804	+	1.00775i
$407$	−11.5986			−0.574921
$408$		0			0
$409$	16.0640	−	27.8236i	0.794313	−	1.37579i	−0.128961	−	0.991650i	$-0.541164\pi$
$409$	16.0640	−	27.8236i	0.794313	−	1.37579i	0.923274	−	0.384141i	$-0.125502\pi$
$410$	0.293260	−	0.507941i	0.0144831	−	0.0250854i
$411$		0			0
$412$	18.5773			0.915236
$413$	3.33682	−	0.573294i	0.164194	−	0.0282099i
$414$		0			0
$415$	−1.58420	−	2.74392i	−0.0777656	−	0.134694i
$416$	15.1459	−	26.2334i	0.742588	−	1.28620i
$417$		0			0
$418$	26.2015	+	45.3823i	1.28156	+	2.21972i
$419$	10.8720			0.531133			0.265567	−	0.964093i	$-0.414441\pi$
$419$	10.8720			0.531133			0.265567	+	0.964093i	$0.414441\pi$
$420$		0			0
$421$	−36.7386			−1.79053			−0.895266	−	0.445532i	$-0.853014\pi$
$421$	−36.7386			−1.79053			−0.895266	+	0.445532i	$0.853014\pi$
$422$	−13.4481	−	23.2928i	−0.654643	−	1.13387i
$423$		0			0
$424$	1.80161	−	3.12048i	0.0874940	−	0.151544i
$425$	0.933099	+	1.61618i	0.0452620	+	0.0783960i
$426$		0			0
$427$	−2.55040	+	6.91270i	−0.123423	+	0.334529i
$428$	−13.5940			−0.657089
$429$		0			0
$430$	−7.05795	+	12.2247i	−0.340365	+	0.589529i
$431$	0.796982	−	1.38041i	0.0383893	−	0.0664922i	−0.846192	−	0.532878i	$-0.821111\pi$
$431$	0.796982	−	1.38041i	0.0383893	−	0.0664922i	0.884582	+	0.466385i	$0.154444\pi$
$432$		0			0
$433$	−12.3489			−0.593450			−0.296725	−	0.954963i	$-0.595894\pi$
$433$	−12.3489			−0.593450			−0.296725	+	0.954963i	$0.595894\pi$
$434$	−29.7724	−	35.7991i	−1.42912	−	1.71841i
$435$		0			0
$436$	−6.65886	−	11.5335i	−0.318902	−	0.552354i
$437$	18.1136	−	31.3736i	0.866490	−	1.50081i
$438$		0			0
$439$	9.99105	+	17.3050i	0.476847	+	0.825923i	0.999648	−	0.0265318i	$-0.00844634\pi$
$439$	9.99105	+	17.3050i	0.476847	+	0.825923i	−0.522801	+	0.852455i	$0.675113\pi$
$440$	−5.16378			−0.246174
$441$		0			0
$442$	−15.1459			−0.720416
$443$	3.00000	+	5.19615i	0.142534	+	0.246877i	0.928450	−	0.371457i	$-0.121142\pi$
$443$	3.00000	+	5.19615i	0.142534	+	0.246877i	−0.785916	+	0.618333i	$0.787808\pi$
$444$		0			0
$445$	1.45935	−	2.52768i	0.0691800	−	0.119823i
$446$	1.30221	+	2.25550i	0.0616615	+	0.106801i
$447$		0			0
$448$	−5.86157	−	7.04809i	−0.276933	−	0.332991i
$449$	24.4994			1.15620			0.578099	−	0.815967i	$-0.303795\pi$
$449$	24.4994			1.15620			0.578099	+	0.815967i	$0.303795\pi$
$450$		0			0
$451$	0.840542	−	1.45586i	0.0395796	−	0.0685538i
$452$	6.49940	−	11.2573i	0.305706	−	0.529499i
$453$		0			0
$454$	−15.6119			−0.732701
$455$	−3.98270	+	10.7948i	−0.186712	+	0.506069i
$456$		0			0
$457$	11.2032	+	19.4046i	0.524065	+	0.907707i	0.999608	+	0.0280143i	$0.00891839\pi$
$457$	11.2032	+	19.4046i	0.524065	+	0.907707i	−0.475543	+	0.879693i	$0.657748\pi$
$458$	15.2987	−	26.4981i	0.714861	−	1.23818i
$459$		0			0
$460$	−5.11590	−	8.86100i	−0.238530	−	0.413146i
$461$	28.4169			1.32351			0.661754	−	0.749721i	$-0.269812\pi$
$461$	28.4169			1.32351			0.661754	+	0.749721i	$0.269812\pi$
$462$		0			0
$463$	11.0225			0.512261			0.256130	−	0.966642i	$-0.417552\pi$
$463$	11.0225			0.512261			0.256130	+	0.966642i	$0.417552\pi$
$464$	−10.4481	−	18.0966i	−0.485040	−	0.840114i
$465$		0			0
$466$	6.18512	−	10.7129i	0.286520	−	0.496267i
$467$	−9.79698	−	16.9689i	−0.453350	−	0.785226i	0.545241	−	0.838279i	$-0.316438\pi$
$467$	−9.79698	−	16.9689i	−0.453350	−	0.785226i	−0.998592	+	0.0530534i	$0.983105\pi$
$468$		0			0
$469$	−5.42706	+	0.932415i	−0.250598	+	0.0430549i
$470$	15.7324			0.725681
$471$		0			0
$472$	−0.617695	+	1.06988i	−0.0284317	+	0.0492452i
$473$	−20.2295	+	35.0385i	−0.930153	+	1.61107i
$474$		0			0
$475$	5.24970			0.240873
$476$	−2.53401	+	6.86826i	−0.116146	+	0.314806i
$477$		0			0
$478$	25.5628	+	44.2760i	1.16921	+	2.02514i
$479$	15.1626	−	26.2624i	0.692796	−	1.19996i	−0.278122	−	0.960546i	$-0.589712\pi$
$479$	15.1626	−	26.2624i	0.692796	−	1.19996i	0.970918	−	0.239412i	$-0.0769547\pi$
$480$		0			0
$481$	−4.71509	−	8.16678i	−0.214990	−	0.372373i
$482$	−4.02415			−0.183295
$483$		0			0
$484$	26.1113			1.18688
$485$	−4.95644	−	8.58481i	−0.225060	−	0.389816i
$486$		0			0
$487$	−7.10523	+	12.3066i	−0.321969	+	0.557666i	−0.980894	−	0.194542i	$-0.937678\pi$
$487$	−7.10523	+	12.3066i	−0.321969	+	0.557666i	0.658925	+	0.752208i	$0.271011\pi$
$488$	−1.34426	−	2.32833i	−0.0608520	−	0.105399i
$489$		0			0
$490$	9.93310	+	8.48444i	0.448732	+	0.383288i
$491$	−19.8016			−0.893634			−0.446817	−	0.894625i	$-0.647443\pi$
$491$	−19.8016			−0.893634			−0.446817	+	0.894625i	$0.647443\pi$
$492$		0			0
$493$	−4.09024	+	7.08451i	−0.184215	+	0.319070i
$494$	−21.3030	+	36.8979i	−0.958468	+	1.66012i
$495$		0			0
$496$	44.9537			2.01848
$497$	11.5271	+	13.8604i	0.517059	+	0.621725i
$498$		0			0
$499$	−5.58129	−	9.66708i	−0.249853	−	0.432758i	0.713632	−	0.700521i	$-0.247049\pi$
$499$	−5.58129	−	9.66708i	−0.249853	−	0.432758i	−0.963485	+	0.267763i	$0.913716\pi$
$500$	0.741348	−	1.28405i	0.0331541	−	0.0574246i
$501$		0			0
$502$	−16.6542	−	28.8460i	−0.743315	−	1.28746i
$503$	26.9296			1.20073			0.600365	−	0.799726i	$-0.295022\pi$
$503$	26.9296			1.20073			0.600365	+	0.799726i	$0.295022\pi$
$504$		0			0
$505$	−17.5115			−0.779250
$506$	−34.4423	−	59.6557i	−1.53115	−	2.65202i
$507$		0			0
$508$	−0.827269	+	1.43287i	−0.0367041	+	0.0635734i
$509$	−5.09919	−	8.83206i	−0.226018	−	0.391474i	0.730607	−	0.682799i	$-0.239237\pi$
$509$	−5.09919	−	8.83206i	−0.226018	−	0.391474i	−0.956624	+	0.291324i	$0.905904\pi$
$510$		0			0
$511$	14.6888	−	2.52367i	0.649796	−	0.111640i
$512$	24.0000			1.06066
$513$		0			0
$514$	20.1762	−	34.9461i	0.889932	−	1.54141i
$515$	6.26469	−	10.8508i	0.276055	−	0.478142i
$516$		0			0
$517$	45.0922			1.98315
$518$	−10.5519	+	1.81291i	−0.463624	+	0.0796546i
$519$		0			0
$520$	−2.09919	−	3.63591i	−0.0920557	−	0.159445i
$521$	10.3835	−	17.9848i	0.454909	−	0.787926i	−0.543774	−	0.839232i	$-0.683005\pi$
$521$	10.3835	−	17.9848i	0.454909	−	0.787926i	0.998683	+	0.0513057i	$0.0163383\pi$
$522$		0			0
$523$	−0.790945	−	1.36996i	−0.0345856	−	0.0599040i	0.848214	−	0.529653i	$-0.177678\pi$
$523$	−0.790945	−	1.36996i	−0.0345856	−	0.0599040i	−0.882800	+	0.469749i	$0.844344\pi$
$524$	31.9642			1.39636
$525$		0			0
$526$	2.73359			0.119190
$527$	−8.79930	−	15.2408i	−0.383303	−	0.663901i
$528$		0			0
$529$	−12.3106	+	21.3225i	−0.535242	+	0.927066i
$530$	3.48270	+	6.03221i	0.151279	+	0.262022i
$531$		0			0
$532$	13.1681	+	15.8336i	0.570910	+	0.686475i
$533$	1.36680			0.0592026
$534$		0			0
$535$	−4.58420	+	7.94008i	−0.198192	+	0.343279i
$536$	1.00463	−	1.74007i	0.0433934	−	0.0751596i
$537$		0			0
$538$	−33.3505			−1.43784
$539$	28.4702	+	24.3181i	1.22630	+	1.04745i
$540$		0			0
$541$	3.81429	+	6.60654i	0.163989	+	0.284037i	0.936296	−	0.351212i	$-0.114231\pi$
$541$	3.81429	+	6.60654i	0.163989	+	0.284037i	−0.772307	+	0.635250i	$0.780897\pi$
$542$	2.28431	−	3.95654i	0.0981195	−	0.169948i
$543$		0			0
$544$	−6.49940	−	11.2573i	−0.278660	−	0.482652i
$545$	−8.98210			−0.384751
$546$		0			0
$547$	−42.7553			−1.82809			−0.914043	−	0.405617i	$-0.867057\pi$
$547$	−42.7553			−1.82809			−0.914043	+	0.405617i	$0.867057\pi$
$548$	−9.06459	−	15.7003i	−0.387220	−	0.670685i
$549$		0			0
$550$	4.99105	−	8.64475i	0.212819	−	0.368613i
$551$	11.5060	+	19.9290i	0.490174	+	0.849006i
$552$		0			0
$553$	−10.9415	+	29.6561i	−0.465278	+	1.26110i
$554$	−27.1147			−1.15199
$555$		0			0
$556$	9.10695	−	15.7737i	0.386221	−	0.668954i
$557$	−14.0346	+	24.3087i	−0.594665	+	1.02999i	0.398929	+	0.916982i	$0.369382\pi$
$557$	−14.0346	+	24.3087i	−0.594665	+	1.02999i	−0.993594	+	0.113009i	$0.963951\pi$
$558$		0			0
$559$	−32.8950			−1.39131
$560$	−12.4302	+	2.13561i	−0.525271	+	0.0902460i
$561$		0			0
$562$	1.52938	+	2.64896i	0.0645129	+	0.111740i
$563$	−1.27968	+	2.21647i	−0.0539320	+	0.0934130i	−0.891731	−	0.452566i	$-0.850509\pi$
$563$	−1.27968	+	2.21647i	−0.0539320	+	0.0934130i	0.837799	+	0.545979i	$0.183842\pi$
$564$		0			0
$565$	−4.38350	−	7.59245i	−0.184415	−	0.319417i
$566$	−23.5115			−0.988261
$567$		0			0
$568$	−6.57788			−0.276002
$569$	22.7678	+	39.4350i	0.954476	+	1.65320i	0.735562	+	0.677457i	$0.236918\pi$
$569$	22.7678	+	39.4350i	0.954476	+	1.65320i	0.218914	+	0.975744i	$0.429748\pi$
$570$		0			0
$571$	−12.6941	+	21.9868i	−0.531230	+	0.920118i	0.468106	+	0.883673i	$0.344937\pi$
$571$	−12.6941	+	21.9868i	−0.531230	+	0.920118i	−0.999336	+	0.0364450i	$0.988397\pi$
$572$	17.2451	+	29.8693i	0.721053	+	1.24890i
$573$		0			0
$574$	0.537132	−	1.45586i	0.0224195	−	0.0607665i
$575$	−6.90081			−0.287784
$576$		0			0
$577$	2.41952	−	4.19073i	0.100726	−	0.174462i	−0.811258	−	0.584688i	$-0.801217\pi$
$577$	2.41952	−	4.19073i	0.100726	−	0.174462i	0.911984	+	0.410226i	$0.134550\pi$
$578$	12.6130	−	21.8463i	0.524631	−	0.908688i
$579$		0			0
$580$	6.49940			0.269873
$581$	−5.36016	−	6.44519i	−0.222377	−	0.267391i
$582$		0			0
$583$	9.98210	+	17.2895i	0.413416	+	0.716058i
$584$	−2.71912	+	4.70966i	−0.112518	+	0.194887i
$585$		0			0
$586$	−5.47807	−	9.48829i	−0.226297	−	0.391958i
$587$	1.52938			0.0631242			0.0315621	−	0.999502i	$-0.489952\pi$
$587$	1.52938			0.0631242			0.0315621	+	0.999502i	$0.489952\pi$
$588$		0			0
$589$	−49.5056			−2.03984
$590$	−1.19407	−	2.06818i	−0.0491589	−	0.0851458i
$591$		0			0
$592$	5.16841	−	8.95195i	0.212420	−	0.367923i
$593$	−14.3166	−	24.7971i	−0.587912	−	1.01829i	−0.994505	−	0.104685i	$-0.966617\pi$
$593$	−14.3166	−	24.7971i	−0.587912	−	1.01829i	0.406593	−	0.913609i	$-0.366717\pi$
$594$		0			0
$595$	3.15714	+	3.79622i	0.129430	+	0.155630i
$596$	5.03461			0.206226
$597$		0			0
$598$	28.0031	−	48.5028i	1.14513	−	1.98343i
$599$	6.66781	−	11.5490i	0.272439	−	0.471879i	−0.697047	−	0.717026i	$-0.745503\pi$
$599$	6.66781	−	11.5490i	0.272439	−	0.471879i	0.969486	+	0.245147i	$0.0788362\pi$
$600$		0			0
$601$	−1.37887			−0.0562453			−0.0281227	−	0.999604i	$-0.508953\pi$
$601$	−1.37887			−0.0562453			−0.0281227	+	0.999604i	$0.508953\pi$
$602$	−12.9273	+	35.0385i	−0.526876	+	1.42806i
$603$		0			0
$604$	−0.952120	−	1.64912i	−0.0387412	−	0.0671017i
$605$	8.80533	−	15.2513i	0.357988	−	0.620053i
$606$		0			0
$607$	−23.6738	−	41.0043i	−0.960892	−	1.66431i	−0.720269	−	0.693695i	$-0.755982\pi$
$607$	−23.6738	−	41.0043i	−0.960892	−	1.66431i	−0.240623	−	0.970619i	$-0.577352\pi$
$608$	−36.5662			−1.48296
$609$		0			0
$610$	5.19719			0.210428
$611$	18.3310	+	31.7502i	0.741593	+	1.28448i
$612$		0			0
$613$	14.1023	−	24.4259i	0.569587	−	0.986554i	−0.427019	−	0.904242i	$-0.640436\pi$
$613$	14.1023	−	24.4259i	0.569587	−	0.986554i	0.996607	−	0.0823115i	$-0.0262303\pi$
$614$	−9.07002	−	15.7097i	−0.366036	−	0.633994i
$615$		0			0
$616$	−13.4648	+	2.31337i	−0.542512	+	0.0932081i
$617$	−8.13843			−0.327641			−0.163820	−	0.986490i	$-0.552382\pi$
$617$	−8.13843			−0.327641			−0.163820	+	0.986490i	$0.552382\pi$
$618$		0			0
$619$	0.435414	−	0.754160i	0.0175008	−	0.0303122i	−0.857142	−	0.515080i	$-0.827762\pi$
$619$	0.435414	−	0.754160i	0.0175008	−	0.0303122i	0.874643	+	0.484767i	$0.161096\pi$
$620$	−6.99105	+	12.1089i	−0.280767	+	0.486303i
$621$		0			0
$622$	3.32011			0.133124
$623$	2.67294	−	7.24482i	0.107089	−	0.290258i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−29.4189	+	50.9551i	−1.17582	+	2.03657i
$627$		0			0
$628$	−11.7145	−	20.2901i	−0.467459	−	0.809663i
$629$	−4.04668			−0.161352
$630$		0			0
$631$	−5.30221			−0.211078			−0.105539	−	0.994415i	$-0.533657\pi$
$631$	−5.30221			−0.211078			−0.105539	+	0.994415i	$0.533657\pi$
$632$	−5.76700	−	9.98875i	−0.229399	−	0.397331i
$633$		0			0
$634$	−9.92183	+	17.1851i	−0.394046	+	0.682508i
$635$	0.557949	+	0.966397i	0.0221415	+	0.0383503i
$636$		0			0
$637$	−5.54900	+	29.9323i	−0.219859	+	1.18596i
$638$	43.7565			1.73234
$639$		0			0
$640$	3.73240	−	6.46470i	0.147536	−	0.255540i
$641$	−19.5574	+	33.8743i	−0.772469	+	1.33796i	0.163737	+	0.986504i	$0.447645\pi$
$641$	−19.5574	+	33.8743i	−0.772469	+	1.33796i	−0.936206	+	0.351451i	$0.885688\pi$
$642$		0			0
$643$	−13.4885			−0.531935			−0.265968	−	0.963982i	$-0.585691\pi$
$643$	−13.4885			−0.531935			−0.265968	+	0.963982i	$0.585691\pi$
$644$	−17.3097	−	20.8135i	−0.682096	−	0.820169i
$645$		0			0
$646$	9.14156	+	15.8336i	0.359670	+	0.622966i
$647$	−6.70010	+	11.6049i	−0.263408	+	0.456236i	−0.967145	−	0.254224i	$-0.918180\pi$
$647$	−6.70010	+	11.6049i	−0.263408	+	0.456236i	0.703737	+	0.710460i	$0.251513\pi$
$648$		0			0
$649$	−3.42243	−	5.92782i	−0.134342	−	0.232687i
$650$	8.11590			0.318332
$651$		0			0
$652$	−7.86157			−0.307883
$653$	2.08361	+	3.60891i	0.0815378	+	0.141228i	0.903911	−	0.427721i	$-0.140684\pi$
$653$	2.08361	+	3.60891i	0.0815378	+	0.141228i	−0.822373	+	0.568949i	$0.807350\pi$
$654$		0			0
$655$	10.7791	−	18.6699i	0.421173	−	0.729494i
$656$	0.749102	+	1.29748i	0.0292475	+	0.0506582i
$657$		0			0
$658$	41.0230	−	7.04809i	1.59924	−	0.274763i
$659$	0.325163			0.0126666			0.00633328	−	0.999980i	$-0.497984\pi$
$659$	0.325163			0.0126666			0.00633328	+	0.999980i	$0.497984\pi$
$660$		0			0
$661$	15.9558	−	27.6363i	0.620610	−	1.07493i	−0.368762	−	0.929524i	$-0.620218\pi$
$661$	15.9558	−	27.6363i	0.620610	−	1.07493i	0.989372	−	0.145405i	$-0.0464484\pi$
$662$	3.20070	−	5.54378i	0.124399	−	0.215465i
$663$		0			0
$664$	3.05876			0.118703
$665$	13.6888	−	2.35186i	0.530830	−	0.0912011i
$666$		0			0
$667$	−15.1249	−	26.1970i	−0.585637	−	1.01435i
$668$	−12.3310	+	21.3579i	−0.477100	+	0.826362i
$669$		0			0
$670$	1.94205	+	3.36373i	0.0750280	+	0.129952i
$671$	14.8962			0.575060
$672$		0			0
$673$	−5.70867			−0.220053			−0.110026	−	0.993929i	$-0.535094\pi$
$673$	−5.70867			−0.220053			−0.110026	+	0.993929i	$0.535094\pi$
$674$	−3.42938	−	5.93986i	−0.132095	−	0.228795i
$675$		0			0
$676$	−4.38350	+	7.59245i	−0.168596	+	0.292017i
$677$	−0.346579	−	0.600292i	−0.0133201	−	0.0230711i	0.859289	−	0.511491i	$-0.170907\pi$
$677$	−0.346579	−	0.600292i	−0.0133201	−	0.0230711i	−0.872609	+	0.488420i	$0.837573\pi$
$678$		0			0
$679$	−16.7701	−	20.1648i	−0.643578	−	0.773854i
$680$	−1.80161			−0.0690887
$681$		0			0
$682$	−47.0665	+	81.5216i	−1.80227	+	3.12162i
$683$	4.64879	−	8.05194i	0.177881	−	0.308099i	−0.763274	−	0.646075i	$-0.776409\pi$
$683$	4.64879	−	8.05194i	0.177881	−	0.308099i	0.941155	+	0.337977i	$0.109742\pi$
$684$		0			0
$685$	−12.2272			−0.467176
$686$	29.7020	+	17.6735i	1.13403	+	0.674779i
$687$		0			0
$688$	−18.0288	−	31.2268i	−0.687341	−	1.19051i
$689$	−8.11590	+	14.0571i	−0.309191	+	0.535535i
$690$		0			0
$691$	5.87143	+	10.1696i	0.223360	+	0.386870i	0.955826	−	0.293933i	$-0.0949642\pi$
$691$	5.87143	+	10.1696i	0.223360	+	0.386870i	−0.732466	+	0.680803i	$0.761631\pi$
$692$	27.4290			1.04269
$693$		0			0
$694$	−35.3932			−1.34351
$695$	−6.14215	−	10.6385i	−0.232985	−	0.403542i
$696$		0			0
$697$	0.293260	−	0.507941i	0.0111080	−	0.0192397i
$698$	0.443457	+	0.768090i	0.0167851	+	0.0290727i
$699$		0			0
$700$	1.35785	−	3.68035i	0.0513217	−	0.139104i
$701$	23.5565			0.889718			0.444859	−	0.895601i	$-0.353254\pi$
$701$	23.5565			0.889718			0.444859	+	0.895601i	$0.353254\pi$
$702$		0			0
$703$	−5.69175	+	9.85840i	−0.214668	+	0.371817i
$704$	−9.26641	+	16.0499i	−0.349241	+	0.604903i
$705$		0			0
$706$	29.5427			1.11185
$707$	−45.6620	+	7.84511i	−1.71730	+	0.295046i
$708$		0			0
$709$	25.1536	+	43.5674i	0.944664	+	1.63621i	0.756422	+	0.654084i	$0.226946\pi$
$709$	25.1536	+	43.5674i	0.944664	+	1.63621i	0.188243	+	0.982123i	$0.439721\pi$
$710$	6.35785	−	11.0121i	0.238606	−	0.413277i
$711$		0			0
$712$	1.40885	+	2.44020i	0.0527989	+	0.0914503i
$713$	65.0759			2.43711
$714$		0			0
$715$	23.2618			0.869941
$716$	10.6978	+	18.5291i	0.399795	+	0.692465i
$717$		0			0
$718$	−28.0031	+	48.5028i	−1.04507	+	1.81011i
$719$	23.7445	+	41.1266i	0.885519	+	1.53376i	0.845117	+	0.534581i	$0.179531\pi$
$719$	23.7445	+	41.1266i	0.885519	+	1.53376i	0.0404021	+	0.999184i	$0.487136\pi$
$720$		0			0
$721$	11.4743	−	31.1004i	0.427327	−	1.15824i
$722$	15.9735			0.594470
$723$		0			0
$724$	9.57294	−	16.5808i	0.355775	−	0.616221i
$725$	2.19175	−	3.79622i	0.0813996	−	0.140988i
$726$		0			0
$727$	1.04044			0.0385877			0.0192938	−	0.999814i	$-0.493858\pi$
$727$	1.04044			0.0385877			0.0192938	+	0.999814i	$0.493858\pi$
$728$	−7.10263	−	8.54037i	−0.263241	−	0.316527i
$729$		0			0
$730$	−5.25634	−	9.10424i	−0.194546	−	0.336963i
$731$	−7.05795	+	12.2247i	−0.261048	+	0.452148i
$732$		0			0
$733$	13.7205	+	23.7647i	0.506779	+	0.877768i	0.999969	+	0.00784592i	$0.00249746\pi$
$733$	13.7205	+	23.7647i	0.506779	+	0.877768i	−0.493190	+	0.869922i	$0.664169\pi$
$734$	−19.1171			−0.705625
$735$		0			0
$736$	48.0668			1.77177
$737$	5.56630	+	9.64112i	0.205037	+	0.355135i
$738$		0			0
$739$	17.7407	−	30.7279i	0.652604	−	1.13034i	−0.329885	−	0.944021i	$-0.607010\pi$
$739$	17.7407	−	30.7279i	0.652604	−	1.13034i	0.982489	−	0.186322i	$-0.0596568\pi$
$740$	1.60755	+	2.78435i	0.0590946	+	0.102355i
$741$		0			0
$742$	11.7837	+	14.1690i	0.432594	+	0.520161i
$743$	−30.5640			−1.12128			−0.560642	−	0.828058i	$-0.689446\pi$
$743$	−30.5640			−1.12128			−0.560642	+	0.828058i	$0.689446\pi$
$744$		0			0
$745$	1.69779	−	2.94066i	0.0622022	−	0.107737i
$746$	−15.9934	+	27.7013i	−0.585559	+	1.01422i
$747$		0			0
$748$	14.8004			0.541157
$749$	−8.39638	+	22.7578i	−0.306797	+	0.831553i
$750$		0			0
$751$	26.3829	+	45.6965i	0.962726	+	1.66749i	0.715605	+	0.698505i	$0.246151\pi$
$751$	26.3829	+	45.6965i	0.962726	+	1.66749i	0.247121	+	0.968985i	$0.420515\pi$
$752$	−20.0934	+	34.8027i	−0.732730	+	1.26912i
$753$		0			0
$754$	17.7880	+	30.8098i	0.647802	+	1.12203i
$755$	−1.28431			−0.0467408
$756$		0			0
$757$	−16.3368			−0.593772			−0.296886	−	0.954913i	$-0.595948\pi$
$757$	−16.3368			−0.593772			−0.296886	+	0.954913i	$0.595948\pi$
$758$	−20.2462	−	35.0674i	−0.735375	−	1.27371i
$759$		0			0
$760$	−2.53401	+	4.38903i	−0.0919182	+	0.159207i
$761$	23.1213	+	40.0473i	0.838148	+	1.45171i	0.891442	+	0.453136i	$0.149695\pi$
$761$	23.1213	+	40.0473i	0.838148	+	1.45171i	−0.0532937	+	0.998579i	$0.516972\pi$
$762$		0			0
$763$	−23.4212	+	4.02397i	−0.847906	+	0.145677i
$764$	−18.5328			−0.670494
$765$		0			0
$766$	24.0755	−	41.6999i	0.869882	−	1.50668i
$767$	2.78259	−	4.81959i	0.100474	−	0.174025i
$768$		0			0
$769$	51.3073			1.85019			0.925094	−	0.379739i	$-0.123986\pi$
$769$	51.3073			1.85019			0.925094	+	0.379739i	$0.123986\pi$
$770$	9.14156	−	24.7776i	0.329439	−	0.892922i
$771$		0			0
$772$	−14.1069	−	24.4339i	−0.507720	−	0.879397i
$773$	10.9152	−	18.9057i	0.392592	−	0.679990i	−0.600198	−	0.799851i	$-0.704912\pi$
$773$	10.9152	−	18.9057i	0.392592	−	0.679990i	0.992791	+	0.119861i	$0.0382450\pi$
$774$		0			0
$775$	4.71509	+	8.16678i	0.169371	+	0.293359i
$776$	9.56982			0.343536
$777$		0			0
$778$	7.24850			0.259871
$779$	−0.824954	−	1.42886i	−0.0295570	−	0.0511943i
$780$		0			0
$781$	18.2228	−	31.5629i	0.652065	−	1.12941i
$782$	−12.0167	−	20.8135i	−0.429717	−	0.744291i
$783$		0			0
$784$	−31.4555	+	11.1374i	−1.12341	+	0.397765i
$785$	−15.8016			−0.563984
$786$		0			0
$787$	−26.2093	+	45.3958i	−0.934259	+	1.61818i	−0.158310	+	0.987389i	$0.550605\pi$
$787$	−26.2093	+	45.3958i	−0.934259	+	1.61818i	−0.775949	+	0.630795i	$0.782729\pi$
$788$	19.7624	−	34.2294i	0.704005	−	1.21937i
$789$		0			0
$790$	22.2964			0.793270
$791$	−14.8316	−	17.8339i	−0.527351	−	0.634099i
$792$		0			0
$793$	6.05563	+	10.4887i	0.215042	+	0.372463i
$794$	18.5694	−	32.1632i	0.659004	−	1.14143i
$795$		0			0
$796$	−5.61650	−	9.72806i	−0.199071	−	0.344802i
$797$	−6.06459			−0.214819			−0.107409	−	0.994215i	$-0.534256\pi$
$797$	−6.06459			−0.214819			−0.107409	+	0.994215i	$0.534256\pi$
$798$		0			0
$799$	15.7324			0.556572
$800$	3.48270	+	6.03221i	0.123132	+	0.213271i
$801$		0			0
$802$	−4.11127	+	7.12093i	−0.145174	+	0.251449i
$803$	−15.0657	−	26.0946i	−0.531657	−	0.920857i
$804$		0			0
$805$	−17.9942	+	3.09155i	−0.634211	+	0.108963i
$806$	−76.5344			−2.69581
$807$		0			0
$808$	8.45272	−	14.6405i	0.297366	−	0.515052i
$809$	14.1101	−	24.4394i	0.496084	−	0.859242i	−0.503906	−	0.863758i	$-0.668104\pi$
$809$	14.1101	−	24.4394i	0.496084	−	0.859242i	0.999990	+	0.00451631i	$0.00143759\pi$
$810$		0			0
$811$	4.47224			0.157041			0.0785207	−	0.996912i	$-0.474980\pi$
$811$	4.47224			0.157041			0.0785207	+	0.996912i	$0.474980\pi$
$812$	16.9475	−	2.91172i	0.594740	−	0.102181i
$813$		0			0
$814$	10.8226	+	18.7454i	0.379333	+	0.657025i
$815$	−2.65111	+	4.59185i	−0.0928642	+	0.160845i
$816$		0			0
$817$	19.8543	+	34.3887i	0.694615	+	1.20311i
$818$	−59.9572			−2.09635
$819$		0			0
$820$	−0.465991			−0.0162731
$821$	7.14507	+	12.3756i	0.249365	+	0.431912i	0.963350	−	0.268249i	$-0.0864449\pi$
$821$	7.14507	+	12.3756i	0.249365	+	0.431912i	−0.713985	+	0.700161i	$0.753112\pi$
$822$		0			0
$823$	9.19407	−	15.9246i	0.320485	−	0.555096i	−0.660103	−	0.751175i	$-0.729487\pi$
$823$	9.19407	−	15.9246i	0.320485	−	0.555096i	0.980588	+	0.196079i	$0.0628208\pi$
$824$	6.04788	+	10.4752i	0.210688	+	0.364922i
$825$		0			0
$826$	−4.04013	−	4.85794i	−0.140574	−	0.169030i
$827$	16.5236			0.574580			0.287290	−	0.957844i	$-0.407246\pi$
$827$	16.5236			0.574580			0.287290	+	0.957844i	$0.407246\pi$
$828$		0			0
$829$	−6.27013	+	10.8602i	−0.217771	+	0.377190i	−0.954126	−	0.299405i	$-0.903212\pi$
$829$	−6.27013	+	10.8602i	−0.217771	+	0.377190i	0.736356	+	0.676595i	$0.236545\pi$
$830$	−2.95644	+	5.12071i	−0.102620	+	0.177742i
$831$		0			0
$832$	−15.0680			−0.522390
$833$	9.93310	+	8.48444i	0.344161	+	0.293968i
$834$		0			0
$835$	8.31660	+	14.4048i	0.287808	+	0.498498i
$836$	20.8171	−	36.0563i	0.719975	−	1.24703i
$837$		0			0
$838$	−10.1447	−	17.5711i	−0.350442	−	0.606984i
$839$	−38.6036			−1.33275			−0.666373	−	0.745619i	$-0.732154\pi$
$839$	−38.6036			−1.33275			−0.666373	+	0.745619i	$0.732154\pi$
$840$		0			0
$841$	−9.78491			−0.337411
$842$	34.2808	+	59.3761i	1.18139	+	2.04623i
$843$		0			0
$844$	−10.6845	+	18.5061i	−0.367776	+	0.637007i
$845$	2.95644	+	5.12071i	0.101705	+	0.176158i
$846$		0			0
$847$	16.1278	−	43.7132i	0.554157	−	1.50200i
$848$	−17.7924			−0.610992
$849$		0			0
$850$	1.74135	−	3.01610i	0.0597277	−	0.103451i
$851$	7.48189	−	12.9590i	0.256476	−	0.444229i
$852$		0			0
$853$	−11.4590			−0.392347			−0.196174	−	0.980569i	$-0.562852\pi$
$853$	−11.4590			−0.392347			−0.196174	+	0.980569i	$0.562852\pi$
$854$	13.5519	−	2.32833i	0.463737	−	0.0796739i
$855$		0			0
$856$	−4.42555	−	7.66528i	−0.151262	−	0.261994i
$857$	−4.43250	+	7.67732i	−0.151411	+	0.262252i	−0.931747	−	0.363109i	$-0.881715\pi$
$857$	−4.43250	+	7.67732i	−0.151411	+	0.262252i	0.780335	+	0.625361i	$0.215048\pi$
$858$		0			0
$859$	10.3699	+	17.9612i	0.353817	+	0.612829i	0.986915	−	0.161243i	$-0.0515502\pi$
$859$	10.3699	+	17.9612i	0.353817	+	0.612829i	−0.633098	+	0.774072i	$0.718217\pi$
$860$	11.2151			0.382431
$861$		0			0
$862$	−2.97465			−0.101317
$863$	6.33099	+	10.9656i	0.215509	+	0.373273i	0.953430	−	0.301614i	$-0.0975255\pi$
$863$	6.33099	+	10.9656i	0.215509	+	0.373273i	−0.737921	+	0.674888i	$0.764192\pi$
$864$		0			0
$865$	9.24970	−	16.0210i	0.314499	−	0.544729i
$866$	11.5227	+	19.9580i	0.391559	+	0.678200i
$867$		0			0
$868$	−12.8047	+	34.7064i	−0.434621	+	1.17801i
$869$	63.9059			2.16786
$870$		0			0
$871$	−4.52566	+	7.83867i	−0.153346	+	0.265603i
$872$	4.33562	−	7.50952i	0.146823	−	0.254304i
$873$		0			0
$874$	−67.6071			−2.28684
$875$	−1.69175	−	2.03420i	−0.0571916	−	0.0687686i
$876$		0			0
$877$	−18.8483	−	32.6462i	−0.636462	−	1.10238i	−0.986203	−	0.165538i	$-0.947064\pi$
$877$	−18.8483	−	32.6462i	−0.636462	−	1.10238i	0.349742	−	0.936846i	$-0.386269\pi$
$878$	18.6453	−	32.2946i	0.629248	−	1.08989i
$879$		0			0
$880$	12.7491	+	22.0821i	0.429772	+	0.744387i
$881$	−49.4648			−1.66651			−0.833256	−	0.552888i	$-0.813526\pi$
$881$	−49.4648			−1.66651			−0.833256	+	0.552888i	$0.813526\pi$
$882$		0			0
$883$	15.4256			0.519111			0.259556	−	0.965728i	$-0.416424\pi$
$883$	15.4256			0.519111			0.259556	+	0.965728i	$0.416424\pi$
$884$	6.01671	+	10.4212i	0.202364	+	0.350504i
$885$		0			0
$886$	5.59859	−	9.69705i	0.188088	−	0.325779i
$887$	−24.7756	−	42.9125i	−0.831882	−	1.44086i	−0.896544	−	0.442955i	$-0.853930\pi$
$887$	−24.7756	−	42.9125i	−0.831882	−	1.44086i	0.0646618	−	0.997907i	$-0.479403\pi$
$888$		0			0
$889$	1.88782	+	2.26996i	0.0633156	+	0.0761321i
$890$	−5.44689			−0.182580
$891$		0			0
$892$	1.03461	−	1.79199i	0.0346412	−	0.0600004i
$893$	22.1280	−	38.3268i	0.740484	−	1.28256i
$894$		0			0
$895$	14.4302			0.482348
$896$	6.83622	−	18.5291i	0.228382	−	0.619014i
$897$		0			0
$898$	−22.8604	−	39.5953i	−0.762860	−	1.32131i
$899$	−20.6686	+	35.7991i	−0.689337	+	1.19397i
$900$		0			0
$901$	3.48270	+	6.03221i	0.116025	+	0.200962i
$902$	−3.13723			−0.104458
$903$		0			0
$904$	8.46360			0.281495
$905$	−6.45644	−	11.1829i	−0.214619	−	0.371732i
$906$		0			0
$907$	−2.36388	+	4.09437i	−0.0784914	+	0.135951i	−0.902599	−	0.430482i	$-0.858344\pi$
$907$	−2.36388	+	4.09437i	−0.0784914	+	0.135951i	0.824108	+	0.566433i	$0.191677\pi$
$908$	6.20182	+	10.7419i	0.205815	+	0.356481i
$909$		0			0
$910$	21.1626	−	3.63591i	0.701533	−	0.120529i
$911$	−37.2680			−1.23474			−0.617372	−	0.786671i	$-0.711803\pi$
$911$	−37.2680			−1.23474			−0.617372	+	0.786671i	$0.711803\pi$
$912$		0			0
$913$	−8.47374	+	14.6770i	−0.280440	+	0.485736i
$914$	20.9074	−	36.2128i	0.691557	−	1.19781i
$915$		0			0
$916$	−24.3097			−0.803214
$917$	19.7429	−	53.5117i	0.651967	−	1.76711i
$918$		0			0
$919$	−24.9423	−	43.2013i	−0.822769	−	1.42508i	−0.903612	−	0.428351i	$-0.859095\pi$
$919$	−24.9423	−	43.2013i	−0.822769	−	1.42508i	0.0808431	−	0.996727i	$-0.474239\pi$
$920$	3.33099	−	5.76945i	0.109820	−	0.190213i
$921$		0			0
$922$	−26.5158	−	45.9267i	−0.873251	−	1.51252i
$923$	29.6320			0.975349
$924$		0			0
$925$	2.16841			0.0712969
$926$	−10.2851	−	17.8143i	−0.337990	−	0.585416i
$927$		0			0
$928$	−15.2664	+	26.4422i	−0.501144	+	0.868007i
$929$	−8.42475	−	14.5921i	−0.276407	−	0.478751i	0.694082	−	0.719896i	$-0.255810\pi$
$929$	−8.42475	−	14.5921i	−0.276407	−	0.478751i	−0.970489	+	0.241145i	$0.922477\pi$
$930$		0			0
$931$	34.6406	−	12.2652i	1.13530	−	0.401974i
$932$	−9.82816			−0.321932
$933$		0			0
$934$	−18.2831	+	31.6673i	−0.598242	+	1.03618i
$935$	4.99105	−	8.64475i	0.163225	−	0.282714i
$936$		0			0
$937$	−9.87666			−0.322656			−0.161328	−	0.986901i	$-0.551578\pi$
$937$	−9.87666			−0.322656			−0.161328	+	0.986901i	$0.551578\pi$
$938$	6.57093	+	7.90105i	0.214549	+	0.257978i
$939$		0			0
$940$	−6.24970	−	10.8248i	−0.203843	−	0.353066i
$941$	28.1980	−	48.8404i	0.919228	−	1.59215i	0.118639	−	0.992937i	$-0.462147\pi$
$941$	28.1980	−	48.8404i	0.919228	−	1.59215i	0.800590	−	0.599213i	$-0.204520\pi$
$942$		0			0
$943$	1.08441	+	1.87826i	0.0353134	+	0.0611646i
$944$	6.10023			0.198546
$945$		0			0
$946$	75.5044			2.45486
$947$	20.6309	+	35.7337i	0.670414	+	1.16119i	0.977787	+	0.209602i	$0.0672167\pi$
$947$	20.6309	+	35.7337i	0.670414	+	1.16119i	−0.307373	+	0.951589i	$0.599450\pi$
$948$		0			0
$949$	12.2491	−	21.2161i	0.397623	−	0.688703i
$950$	−4.89849	−	8.48444i	−0.158928	−	0.275271i
$951$		0			0
$952$	−4.69779	+	0.807120i	−0.152256	+	0.0261589i
$953$	13.3022			0.430901			0.215450	−	0.976515i	$-0.430878\pi$
$953$	13.3022			0.430901			0.215450	+	0.976515i	$0.430878\pi$
$954$		0			0
$955$	−6.24970	+	10.8248i	−0.202236	+	0.350282i
$956$	20.3097	−	35.1774i	0.656861	−	1.13772i
$957$		0			0
$958$	−56.5928			−1.82843
$959$	−31.8829	+	5.47775i	−1.02955	+	0.176886i
$960$		0			0
$961$	−28.9642	−	50.1675i	−0.934329	−	1.61831i
$962$	−8.79930	+	15.2408i	−0.283701	+	0.491384i
$963$		0			0
$964$	1.59859	+	2.76885i	0.0514873	+	0.0891786i
$965$	−19.0288			−0.612558
$966$		0			0
$967$	−16.6678			−0.536001			−0.268000	−	0.963419i	$-0.586363\pi$
$967$	−16.6678			−0.536001			−0.268000	+	0.963419i	$0.586363\pi$
$968$	8.50060	+	14.7235i	0.273220	+	0.473230i
$969$		0			0
$970$	−9.24970	+	16.0210i	−0.296990	+	0.514402i
$971$	17.0934	+	29.6066i	0.548552	+	0.950120i	0.998374	+	0.0570020i	$0.0181541\pi$
$971$	17.0934	+	29.6066i	0.548552	+	0.950120i	−0.449822	+	0.893118i	$0.648513\pi$
$972$		0			0
$973$	−20.7820	−	24.9888i	−0.666240	−	0.801103i
$974$	26.5195			0.849741
$975$		0			0
$976$	−6.63783	+	11.4971i	−0.212472	+	0.368012i
$977$	7.16027	−	12.4019i	0.229077	−	0.396773i	−0.728458	−	0.685091i	$-0.759763\pi$
$977$	7.16027	−	12.4019i	0.229077	−	0.396773i	0.957535	+	0.288317i	$0.0930958\pi$
$978$		0			0
$979$	−15.6119			−0.498957
$980$	1.89185	−	10.2050i	0.0604331	−	0.325987i
$981$		0			0
$982$	18.4769	+	32.0029i	0.589621	+	1.02125i
$983$	−28.6597	+	49.6400i	−0.914101	+	1.58327i	−0.105890	+	0.994378i	$0.533769\pi$
$983$	−28.6597	+	49.6400i	−0.914101	+	1.58327i	−0.808212	+	0.588892i	$0.799564\pi$
$984$		0			0
$985$	−13.3287	−	23.0859i	−0.424687	−	0.735579i
$986$	15.2664			0.486181
$987$		0			0
$988$	33.8505			1.07693
$989$	−26.0988	−	45.2045i	−0.829894	−	1.43742i
$990$		0			0
$991$	1.73612	−	3.00705i	0.0551496	−	0.0955219i	−0.837133	−	0.547000i	$-0.815770\pi$
$991$	1.73612	−	3.00705i	0.0551496	−	0.0955219i	0.892282	+	0.451478i	$0.149103\pi$
$992$	−32.8425	−	56.8848i	−1.04275	−	1.80609i
$993$		0			0
$994$	11.6450	−	31.5629i	0.369356	−	1.00111i
$995$	−7.57606			−0.240177
$996$		0			0
$997$	9.29930	−	16.1069i	0.294512	−	0.510109i	−0.680359	−	0.732879i	$-0.738176\pi$
$997$	9.29930	−	16.1069i	0.294512	−	0.510109i	0.974871	+	0.222769i	$0.0715097\pi$
$998$	−10.4158	+	18.0407i	−0.329706	+	0.571068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.g.46.1	yes	6
3.2	odd	2		315.2.j.f.46.3	✓	6
7.2	even	3	inner	315.2.j.g.226.1	yes	6
7.3	odd	6		2205.2.a.bc.1.3		3
7.4	even	3		2205.2.a.bb.1.3		3
21.2	odd	6		315.2.j.f.226.3	yes	6
21.11	odd	6		2205.2.a.be.1.1		3
21.17	even	6		2205.2.a.bd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.j.f.46.3	✓	6	3.2	odd	2
315.2.j.f.226.3	yes	6	21.2	odd	6
315.2.j.g.46.1	yes	6	1.1	even	1	trivial
315.2.j.g.226.1	yes	6	7.2	even	3	inner
2205.2.a.bb.1.3		3	7.4	even	3
2205.2.a.bc.1.3		3	7.3	odd	6
2205.2.a.bd.1.1		3	21.17	even	6
2205.2.a.be.1.1		3	21.11	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933099 - 1.61618i) q^{2} +(-0.741348 + 1.28405i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.69175 + 2.03420i) q^{7} -0.965392 q^{8} +O(q^{10})\)	\(q+(-0.933099 - 1.61618i) q^{2} +(-0.741348 + 1.28405i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.69175 + 2.03420i) q^{7} -0.965392 q^{8} +(0.933099 - 1.61618i) q^{10} +(2.67445 - 4.63228i) q^{11} +4.34889 q^{13} +(1.70906 - 4.63228i) q^{14} +(2.38350 + 4.12835i) q^{16} +(0.933099 - 1.61618i) q^{17} +(-2.62485 - 4.54637i) q^{19} -1.48270 q^{20} -9.98210 q^{22} +(3.45040 + 5.97627i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.05795 - 7.02857i) q^{26} +(-3.86620 + 0.664245i) q^{28} -4.38350 q^{29} +(4.71509 - 8.16678i) q^{31} +(3.48270 - 6.03221i) q^{32} -3.48270 q^{34} +(-0.915795 + 2.48220i) q^{35} +(-1.08420 - 1.87790i) q^{37} +(-4.89849 + 8.48444i) q^{38} +(-0.482696 - 0.836054i) q^{40} +0.314286 q^{41} -7.56399 q^{43} +(3.96539 + 6.86826i) q^{44} +(6.43914 - 11.1529i) q^{46} +(4.21509 + 7.30075i) q^{47} +(-1.27596 + 6.88273i) q^{49} +1.86620 q^{50} +(-3.22404 + 5.58421i) q^{52} +(-1.86620 + 3.23235i) q^{53} +5.34889 q^{55} +(-1.63320 - 1.96380i) q^{56} +(4.09024 + 7.08451i) q^{58} +(0.639839 - 1.10823i) q^{59} +(1.39245 + 2.41180i) q^{61} -17.5986 q^{62} -3.46479 q^{64} +(2.17445 + 3.76625i) q^{65} +(-1.04065 + 1.80245i) q^{67} +(1.38350 + 2.39630i) q^{68} +(4.86620 - 0.836054i) q^{70} +6.81369 q^{71} +(2.81660 - 4.87850i) q^{73} +(-2.02334 + 3.50453i) q^{74} +7.78371 q^{76} +(13.9475 - 2.39630i) q^{77} +(5.97374 + 10.3468i) q^{79} +(-2.38350 + 4.12835i) q^{80} +(-0.293260 - 0.507941i) q^{82} -3.16841 q^{83} +1.86620 q^{85} +(7.05795 + 12.2247i) q^{86} +(-2.58189 + 4.47196i) q^{88} +(-1.45935 - 2.52768i) q^{89} +(7.35725 + 8.84653i) q^{91} -10.2318 q^{92} +(7.86620 - 13.6247i) q^{94} +(2.62485 - 4.54637i) q^{95} -9.91288 q^{97} +(12.3143 - 4.36010i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8	\( 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8} - 2 q^{10} + 10 q^{11} + 14 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + q^{19} - 12 q^{20} + 4 q^{22} + 10 q^{23} - 3 q^{25} - 8 q^{28} - 8 q^{29} + q^{31} + 24 q^{32} - 24 q^{34} - q^{35} - 11 q^{37} - 28 q^{38} - 6 q^{40} - 4 q^{41} - 6 q^{43} + 30 q^{44} + 16 q^{46} - 2 q^{47} - 3 q^{49} - 4 q^{50} - 24 q^{52} + 4 q^{53} + 20 q^{55} + 42 q^{56} + 14 q^{58} + 4 q^{59} + 22 q^{61} - 60 q^{62} + 40 q^{64} + 7 q^{65} + 15 q^{67} - 10 q^{68} + 14 q^{70} - 32 q^{71} - 9 q^{73} + 6 q^{74} - 60 q^{76} + 26 q^{77} + 7 q^{79} + 4 q^{80} + 6 q^{82} - 28 q^{83} - 4 q^{85} + 18 q^{86} - 40 q^{88} - 30 q^{89} - 3 q^{91} + 36 q^{92} + 32 q^{94} - q^{95} - 8 q^{97} + 68 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8 - 2 * q^10 + 10 * q^11 + 14 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + q^19 - 12 * q^20 + 4 * q^22 + 10 * q^23 - 3 * q^25 - 8 * q^28 - 8 * q^29 + q^31 + 24 * q^32 - 24 * q^34 - q^35 - 11 * q^37 - 28 * q^38 - 6 * q^40 - 4 * q^41 - 6 * q^43 + 30 * q^44 + 16 * q^46 - 2 * q^47 - 3 * q^49 - 4 * q^50 - 24 * q^52 + 4 * q^53 + 20 * q^55 + 42 * q^56 + 14 * q^58 + 4 * q^59 + 22 * q^61 - 60 * q^62 + 40 * q^64 + 7 * q^65 + 15 * q^67 - 10 * q^68 + 14 * q^70 - 32 * q^71 - 9 * q^73 + 6 * q^74 - 60 * q^76 + 26 * q^77 + 7 * q^79 + 4 * q^80 + 6 * q^82 - 28 * q^83 - 4 * q^85 + 18 * q^86 - 40 * q^88 - 30 * q^89 - 3 * q^91 + 36 * q^92 + 32 * q^94 - q^95 - 8 * q^97 + 68 * q^98

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