LMFDB - Embedded newform 378.2.e.d.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(37,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("378.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	378.37
Dual form			378.2.e.d.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.59097 - 2.75564i) q^{5} +(-2.56238 - 0.658939i) q^{7} +1.00000 q^{8} +(-1.59097 - 2.75564i) q^{10} +(1.59097 - 2.75564i) q^{11} +(2.85185 - 4.93955i) q^{13} +(-2.56238 - 0.658939i) q^{14} +1.00000 q^{16} +(0.760877 + 1.31788i) q^{17} +(-0.641315 + 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(1.11956 + 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(2.85185 - 4.93955i) q^{26} +(-2.56238 - 0.658939i) q^{28} +(3.54063 + 6.13255i) q^{29} -9.42107 q^{31} +1.00000 q^{32} +(0.760877 + 1.31788i) q^{34} +(2.26088 + 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-0.641315 + 1.11079i) q^{38} +(-1.59097 - 2.75564i) q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(1.59097 - 2.75564i) q^{44} +(1.11956 + 1.93914i) q^{46} +5.82846 q^{47} +(6.13160 + 3.37690i) q^{49} +(-2.56238 + 4.43818i) q^{50} +(2.85185 - 4.93955i) q^{52} +(-1.02859 - 1.78157i) q^{53} -10.1248 q^{55} +(-2.56238 - 0.658939i) q^{56} +(3.54063 + 6.13255i) q^{58} +1.12476 q^{59} +3.12476 q^{61} -9.42107 q^{62} +1.00000 q^{64} -18.1488 q^{65} +10.9669 q^{67} +(0.760877 + 1.31788i) q^{68} +(2.26088 + 8.10936i) q^{70} -8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-0.641315 + 1.11079i) q^{76} +(-5.89248 + 6.01266i) q^{77} -4.13844 q^{79} +(-1.59097 - 2.75564i) q^{80} +(2.80150 - 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(3.41423 + 5.91362i) q^{86} +(1.59097 - 2.75564i) q^{88} +(-0.112725 + 0.195246i) q^{89} +(-10.5624 + 10.7778i) q^{91} +(1.11956 + 1.93914i) q^{92} +5.82846 q^{94} +4.08126 q^{95} +(7.42107 + 12.8537i) q^{97} +(6.13160 + 3.37690i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 2 q^{7} + 6 q^{8} - q^{10} + q^{11} + 8 q^{13} + 2 q^{14} + 6 q^{16} + 4 q^{17} - 3 q^{19} - q^{20} + q^{22} + 7 q^{23} + 2 q^{25} + 8 q^{26} + 2 q^{28} + 5 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 2 * q^7 + 6 * q^8 - q^10 + q^11 + 8 * q^13 + 2 * q^14 + 6 * q^16 + 4 * q^17 - 3 * q^19 - q^20 + q^22 + 7 * q^23 + 2 * q^25 + 8 * q^26 + 2 * q^28 + 5 * q^29 - 40 * q^31 + 6 * q^32 + 4 * q^34 + 13 * q^35 + 3 * q^37 - 3 * q^38 - q^40 - 6 * q^43 + q^44 + 7 * q^46 - 18 * q^47 + 12 * q^49 + 2 * q^50 + 8 * q^52 - 15 * q^53 - 26 * q^55 + 2 * q^56 + 5 * q^58 - 28 * q^59 - 16 * q^61 - 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 + 4 * q^68 + 13 * q^70 - 14 * q^71 + 19 * q^73 + 3 * q^74 - 3 * q^76 - 10 * q^77 - 10 * q^79 - q^80 - 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 + 9 * q^89 - 46 * q^91 + 7 * q^92 - 18 * q^94 - 8 * q^95 + 28 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	−0.964292	−	0.264840i	$-0.914681\pi$
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	0.252788	−	0.967522i	$-0.418652\pi$
$6$		0			0
$7$	−2.56238	−	0.658939i	−0.968489	−	0.249055i
$7$	−2.56238	−	0.658939i	−0.968489	−	0.249055i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.59097	−	2.75564i	−0.503109	−	0.871411i
$11$	1.59097	−	2.75564i	0.479696	−	0.830858i	−0.520033	−	0.854146i	$-0.674080\pi$
$11$	1.59097	−	2.75564i	0.479696	−	0.830858i	0.999729	+	0.0232884i	$0.00741361\pi$
$12$		0			0
$13$	2.85185	−	4.93955i	0.790960	−	1.36998i	−0.134412	−	0.990925i	$-0.542915\pi$
$13$	2.85185	−	4.93955i	0.790960	−	1.36998i	0.925373	−	0.379058i	$-0.123752\pi$
$14$	−2.56238	−	0.658939i	−0.684825	−	0.176109i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	0.943421	−	0.331596i	$-0.107587\pi$
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	−0.758882	+	0.651229i	$0.774254\pi$
$18$		0			0
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	−0.930165	−	0.367142i	$-0.880336\pi$
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	0.783037	+	0.621975i	$0.213670\pi$
$20$	−1.59097	−	2.75564i	−0.355752	−	0.616181i
$21$		0			0
$22$	1.59097	−	2.75564i	0.339196	−	0.587505i
$23$	1.11956	+	1.93914i	0.233445	+	0.404338i	0.958820	−	0.284016i	$-0.0916669\pi$
$23$	1.11956	+	1.93914i	0.233445	+	0.404338i	−0.725375	+	0.688354i	$0.758334\pi$
$24$		0			0
$25$	−2.56238	+	4.43818i	−0.512476	+	0.887635i
$26$	2.85185	−	4.93955i	0.559293	−	0.968725i
$27$		0			0
$28$	−2.56238	−	0.658939i	−0.484245	−	0.124528i
$29$	3.54063	+	6.13255i	0.657478	+	1.13879i	0.981266	+	0.192656i	$0.0617101\pi$
$29$	3.54063	+	6.13255i	0.657478	+	1.13879i	−0.323788	+	0.946130i	$0.604957\pi$
$30$		0			0
$31$	−9.42107			−1.69207			−0.846037	−	0.533125i	$-0.821018\pi$
$31$	−9.42107			−1.69207			−0.846037	+	0.533125i	$0.821018\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.760877	+	1.31788i	0.130489	+	0.226014i
$35$	2.26088	+	8.10936i	0.382158	+	1.37073i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−0.641315	+	1.11079i	−0.104035	+	0.180194i
$39$		0			0
$40$	−1.59097	−	2.75564i	−0.251555	−	0.435706i
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	−0.559976	−	0.828509i	$-0.689190\pi$
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	0.997498	+	0.0706992i	$0.0225230\pi$
$42$		0			0
$43$	3.41423	+	5.91362i	0.520665	+	0.901819i	0.999711	+	0.0240288i	$0.00764935\pi$
$43$	3.41423	+	5.91362i	0.520665	+	0.901819i	−0.479046	+	0.877790i	$0.659017\pi$
$44$	1.59097	−	2.75564i	0.239848	−	0.415429i
$45$		0			0
$46$	1.11956	+	1.93914i	0.165070	+	0.285910i
$47$	5.82846			0.850168			0.425084	−	0.905154i	$-0.360245\pi$
$47$	5.82846			0.850168			0.425084	+	0.905154i	$0.360245\pi$
$48$		0			0
$49$	6.13160	+	3.37690i	0.875943	+	0.482415i
$50$	−2.56238	+	4.43818i	−0.362375	+	0.627653i
$51$		0			0
$52$	2.85185	−	4.93955i	0.395480	−	0.684992i
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	0.786694	−	0.617343i	$-0.211791\pi$
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	−0.927982	+	0.372626i	$0.878458\pi$
$54$		0			0
$55$	−10.1248			−1.36522
$56$	−2.56238	−	0.658939i	−0.342413	−	0.0880544i
$57$		0			0
$58$	3.54063	+	6.13255i	0.464907	+	0.805243i
$59$	1.12476			0.146432			0.0732159	−	0.997316i	$-0.476674\pi$
$59$	1.12476			0.146432			0.0732159	+	0.997316i	$0.476674\pi$
$60$		0			0
$61$	3.12476			0.400085			0.200042	−	0.979787i	$-0.435892\pi$
$61$	3.12476			0.400085			0.200042	+	0.979787i	$0.435892\pi$
$62$	−9.42107			−1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	−18.1488			−2.25109
$66$		0			0
$67$	10.9669			1.33982			0.669910	−	0.742442i	$-0.266333\pi$
$67$	10.9669			1.33982			0.669910	+	0.742442i	$0.266333\pi$
$68$	0.760877	+	1.31788i	0.0922699	+	0.159816i
$69$		0			0
$70$	2.26088	+	8.10936i	0.270226	+	0.969254i
$71$	−8.69002			−1.03132			−0.515658	−	0.856794i	$-0.672452\pi$
$71$	−8.69002			−1.03132			−0.515658	+	0.856794i	$0.672452\pi$
$72$		0			0
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	0.683302	−	0.730136i	$-0.260543\pi$
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	−0.973967	+	0.226689i	$0.927210\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−0.641315	+	1.11079i	−0.0735639	+	0.127416i
$77$	−5.89248	+	6.01266i	−0.671510	+	0.685206i
$78$		0			0
$79$	−4.13844			−0.465610			−0.232805	−	0.972523i	$-0.574790\pi$
$79$	−4.13844			−0.465610			−0.232805	+	0.972523i	$0.574790\pi$
$80$	−1.59097	−	2.75564i	−0.177876	−	0.308090i
$81$		0			0
$82$	2.80150	−	4.85235i	0.309374	−	0.535852i
$83$	4.03379	+	6.98673i	0.442766	+	0.766893i	0.997894	−	0.0648718i	$-0.0206639\pi$
$83$	4.03379	+	6.98673i	0.442766	+	0.766893i	−0.555127	+	0.831765i	$0.687331\pi$
$84$		0			0
$85$	2.42107	−	4.19341i	0.262602	−	0.454839i
$86$	3.41423	+	5.91362i	0.368166	+	0.637682i
$87$		0			0
$88$	1.59097	−	2.75564i	0.169598	−	0.293753i
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	−0.871938	−	0.489616i	$-0.837137\pi$
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	0.859989	+	0.510312i	$0.170470\pi$
$90$		0			0
$91$	−10.5624	+	10.7778i	−1.10724	+	1.12982i
$92$	1.11956	+	1.93914i	0.116722	+	0.202169i
$93$		0			0
$94$	5.82846			0.601160
$95$	4.08126			0.418728
$96$		0			0
$97$	7.42107	+	12.8537i	0.753495	+	1.30509i	0.946119	+	0.323819i	$0.104967\pi$
$97$	7.42107	+	12.8537i	0.753495	+	1.30509i	−0.192624	+	0.981273i	$0.561700\pi$
$98$	6.13160	+	3.37690i	0.619385	+	0.341119i
$99$		0			0
$100$	−2.56238	+	4.43818i	−0.256238	+	0.443818i
$101$	9.29467	−	16.0988i	0.924854	−	1.60189i	0.133058	−	0.991108i	$-0.457520\pi$
$101$	9.29467	−	16.0988i	0.924854	−	1.60189i	0.791796	−	0.610786i	$-0.209146\pi$
$102$		0			0
$103$	0.141315	+	0.244765i	0.0139242	+	0.0241174i	0.872904	−	0.487893i	$-0.162234\pi$
$103$	0.141315	+	0.244765i	0.0139242	+	0.0241174i	−0.858979	+	0.512010i	$0.828901\pi$
$104$	2.85185	−	4.93955i	0.279647	−	0.484362i
$105$		0			0
$106$	−1.02859	−	1.78157i	−0.0999055	−	0.173041i
$107$	−5.68878	+	9.85326i	−0.549955	+	0.952550i	0.448322	+	0.893872i	$0.352022\pi$
$107$	−5.68878	+	9.85326i	−0.549955	+	0.952550i	−0.998277	+	0.0586780i	$0.981311\pi$
$108$		0			0
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$	−10.1248			−0.965358
$111$		0			0
$112$	−2.56238	−	0.658939i	−0.242122	−	0.0622638i
$113$	1.60752	−	2.78431i	0.151223	−	0.261926i	−0.780454	−	0.625213i	$-0.785012\pi$
$113$	1.60752	−	2.78431i	0.151223	−	0.261926i	0.931677	+	0.363287i	$0.118345\pi$
$114$		0			0
$115$	3.56238	−	6.17023i	0.332194	−	0.575377i
$116$	3.54063	+	6.13255i	0.328739	+	0.569393i
$117$		0			0
$118$	1.12476			0.103543
$119$	−1.08126	−	3.87828i	−0.0991186	−	0.355521i
$120$		0			0
$121$	0.437618	+	0.757977i	0.0397835	+	0.0689070i
$122$	3.12476			0.282903
$123$		0			0
$124$	−9.42107			−0.846037
$125$	0.396990			0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−18.1488			−1.59176
$131$	3.18194	+	5.51129i	0.278008	+	0.481523i	0.970890	−	0.239528i	$-0.0769926\pi$
$131$	3.18194	+	5.51129i	0.278008	+	0.481523i	−0.692882	+	0.721051i	$0.743659\pi$
$132$		0			0
$133$	2.37524	−	2.42368i	0.205959	−	0.210160i
$134$	10.9669			0.947396
$135$		0			0
$136$	0.760877	+	1.31788i	0.0652446	+	0.113007i
$137$	1.37072	−	2.37416i	0.117109	−	0.202838i	−0.801512	−	0.597979i	$-0.795971\pi$
$137$	1.37072	−	2.37416i	0.117109	−	0.202838i	0.918621	+	0.395140i	$0.129304\pi$
$138$		0			0
$139$	−3.98345	+	6.89953i	−0.337872	+	0.585211i	−0.984032	−	0.177991i	$-0.943040\pi$
$139$	−3.98345	+	6.89953i	−0.337872	+	0.585211i	0.646161	+	0.763202i	$0.276374\pi$
$140$	2.26088	+	8.10936i	0.191079	+	0.685366i
$141$		0			0
$142$	−8.69002			−0.729251
$143$	−9.07442	−	15.7174i	−0.758841	−	1.31435i
$144$		0			0
$145$	11.2661	−	19.5134i	0.935597	−	1.62050i
$146$	−2.48345	−	4.30146i	−0.205532	−	0.355991i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−11.6300	−	20.1437i	−0.952764	−	1.65024i	−0.739404	−	0.673262i	$-0.764893\pi$
$149$	−11.6300	−	20.1437i	−0.952764	−	1.65024i	−0.213360	−	0.976974i	$-0.568441\pi$
$150$		0			0
$151$	4.06238	−	7.03625i	0.330592	−	0.572602i	−0.652036	−	0.758188i	$-0.726085\pi$
$151$	4.06238	−	7.03625i	0.330592	−	0.572602i	0.982628	+	0.185586i	$0.0594183\pi$
$152$	−0.641315	+	1.11079i	−0.0520175	+	0.0900970i
$153$		0			0
$154$	−5.89248	+	6.01266i	−0.474829	+	0.484514i
$155$	14.9887	+	25.9611i	1.20392	+	2.08525i
$156$		0			0
$157$	−11.2632			−0.898901			−0.449451	−	0.893305i	$-0.648380\pi$
$157$	−11.2632			−0.898901			−0.449451	+	0.893305i	$0.648380\pi$
$158$	−4.13844			−0.329236
$159$		0			0
$160$	−1.59097	−	2.75564i	−0.125777	−	0.217853i
$161$	−1.59097	−	5.70653i	−0.125386	−	0.449738i
$162$		0			0
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	−0.933383	−	0.358881i	$-0.883158\pi$
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	0.777492	+	0.628893i	$0.216492\pi$
$164$	2.80150	−	4.85235i	0.218761	−	0.378905i
$165$		0			0
$166$	4.03379	+	6.98673i	0.313083	+	0.542276i
$167$	−2.61956	+	4.53721i	−0.202708	+	0.351100i	−0.949400	−	0.314070i	$-0.898307\pi$
$167$	−2.61956	+	4.53721i	−0.202708	+	0.351100i	0.746692	+	0.665170i	$0.231641\pi$
$168$		0			0
$169$	−9.76608	−	16.9153i	−0.751237	−	1.30118i
$170$	2.42107	−	4.19341i	0.185687	−	0.321620i
$171$		0			0
$172$	3.41423	+	5.91362i	0.260333	+	0.450909i
$173$	−2.55159			−0.193994			−0.0969968	−	0.995285i	$-0.530924\pi$
$173$	−2.55159			−0.193994			−0.0969968	+	0.995285i	$0.530924\pi$
$174$		0			0
$175$	9.49028	−	9.68385i	0.717398	−	0.732030i
$176$	1.59097	−	2.75564i	0.119924	−	0.207714i
$177$		0			0
$178$	−0.112725	+	0.195246i	−0.00844910	+	0.0146343i
$179$	−3.51887	−	6.09487i	−0.263013	−	0.455552i	0.704028	−	0.710172i	$-0.251383\pi$
$179$	−3.51887	−	6.09487i	−0.263013	−	0.455552i	−0.967041	+	0.254620i	$0.918050\pi$
$180$		0			0
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$	−10.5624	+	10.7778i	−0.782936	+	0.798904i
$183$		0			0
$184$	1.11956	+	1.93914i	0.0825352	+	0.142955i
$185$	−3.18194			−0.233941
$186$		0			0
$187$	4.84213			0.354092
$188$	5.82846			0.425084
$189$		0			0
$190$	4.08126			0.296085
$191$	−1.98057			−0.143309			−0.0716545	−	0.997430i	$-0.522828\pi$
$191$	−1.98057			−0.143309			−0.0716545	+	0.997430i	$0.522828\pi$
$192$		0			0
$193$	−4.54583			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$193$	−4.54583			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$194$	7.42107	+	12.8537i	0.532802	+	0.922839i
$195$		0			0
$196$	6.13160	+	3.37690i	0.437971	+	0.241207i
$197$	21.8148			1.55424			0.777120	−	0.629353i	$-0.216680\pi$
$197$	21.8148			1.55424			0.777120	+	0.629353i	$0.216680\pi$
$198$		0			0
$199$	6.14132	+	10.6371i	0.435346	+	0.754042i	0.997324	−	0.0731106i	$-0.0232926\pi$
$199$	6.14132	+	10.6371i	0.435346	+	0.754042i	−0.561978	+	0.827152i	$0.689959\pi$
$200$	−2.56238	+	4.43818i	−0.181188	+	0.313826i
$201$		0			0
$202$	9.29467	−	16.0988i	0.653971	−	1.13271i
$203$	−5.03147	−	18.0470i	−0.353140	−	1.26665i
$204$		0			0
$205$	−17.8285			−1.24519
$206$	0.141315	+	0.244765i	0.00984589	+	0.0170536i
$207$		0			0
$208$	2.85185	−	4.93955i	0.197740	−	0.342496i
$209$	2.04063	+	3.53447i	0.141153	+	0.244485i
$210$		0			0
$211$	−8.32846	+	14.4253i	−0.573355	+	0.993080i	0.422863	+	0.906193i	$0.361025\pi$
$211$	−8.32846	+	14.4253i	−0.573355	+	0.993080i	−0.996218	+	0.0868863i	$0.972308\pi$
$212$	−1.02859	−	1.78157i	−0.0706438	−	0.122359i
$213$		0			0
$214$	−5.68878	+	9.85326i	−0.388877	+	0.673555i
$215$	10.8639	−	18.8168i	0.740911	−	1.28330i
$216$		0			0
$217$	24.1404	+	6.20790i	1.63876	+	0.421420i
$218$	−2.21053	−	3.82876i	−0.149716	−	0.259316i
$219$		0			0
$220$	−10.1248			−0.682611
$221$	8.67962			0.583854
$222$		0			0
$223$	−5.32846	−	9.22916i	−0.356820	−	0.618031i	0.630608	−	0.776102i	$-0.282806\pi$
$223$	−5.32846	−	9.22916i	−0.356820	−	0.618031i	−0.987428	+	0.158071i	$0.949472\pi$
$224$	−2.56238	−	0.658939i	−0.171206	−	0.0440272i
$225$		0			0
$226$	1.60752	−	2.78431i	0.106931	−	0.185210i
$227$	−7.25404	+	12.5644i	−0.481468	+	0.833926i	−0.999774	−	0.0212688i	$-0.993229\pi$
$227$	−7.25404	+	12.5644i	−0.481468	+	0.833926i	0.518306	+	0.855195i	$0.326563\pi$
$228$		0			0
$229$	−5.12476	−	8.87635i	−0.338654	−	0.586566i	0.645526	−	0.763738i	$-0.276638\pi$
$229$	−5.12476	−	8.87635i	−0.338654	−	0.586566i	−0.984180	+	0.177173i	$0.943305\pi$
$230$	3.56238	−	6.17023i	0.234896	−	0.406853i
$231$		0			0
$232$	3.54063	+	6.13255i	0.232454	+	0.402622i
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	−0.883191	−	0.469014i	$-0.844610\pi$
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	0.847773	+	0.530359i	$0.177943\pi$
$234$		0			0
$235$	−9.27292	−	16.0612i	−0.604898	−	1.04771i
$236$	1.12476			0.0732159
$237$		0			0
$238$	−1.08126	−	3.87828i	−0.0700874	−	0.251391i
$239$	6.16019	−	10.6698i	0.398470	−	0.690170i	−0.595068	−	0.803676i	$-0.702875\pi$
$239$	6.16019	−	10.6698i	0.398470	−	0.690170i	0.993537	+	0.113506i	$0.0362081\pi$
$240$		0			0
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	−0.577107	−	0.816668i	$-0.695819\pi$
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	0.995809	+	0.0914555i	$0.0291519\pi$
$242$	0.437618	+	0.757977i	0.0281312	+	0.0487246i
$243$		0			0
$244$	3.12476			0.200042
$245$	−0.449657	−	22.2691i	−0.0287275	−	1.42272i
$246$		0			0
$247$	3.65787	+	6.33561i	0.232744	+	0.403125i
$248$	−9.42107			−0.598238
$249$		0			0
$250$	0.396990			0.0251079
$251$	−5.11109			−0.322609			−0.161305	−	0.986905i	$-0.551570\pi$
$251$	−5.11109			−0.322609			−0.161305	+	0.986905i	$0.551570\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$	20.1053			1.26152
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.83009	+	6.63392i	0.238915	+	0.413813i	0.960403	−	0.278614i	$-0.0898750\pi$
$257$	3.83009	+	6.63392i	0.238915	+	0.413813i	−0.721488	+	0.692427i	$0.756542\pi$
$258$		0			0
$259$	−1.85185	+	1.88962i	−0.115068	+	0.117415i
$260$	−18.1488			−1.12554
$261$		0			0
$262$	3.18194	+	5.51129i	0.196581	+	0.340488i
$263$	−1.54746	+	2.68029i	−0.0954208	+	0.165274i	−0.909784	−	0.415082i	$-0.863753\pi$
$263$	−1.54746	+	2.68029i	−0.0954208	+	0.165274i	0.814363	+	0.580355i	$0.197086\pi$
$264$		0			0
$265$	−3.27292	+	5.66886i	−0.201054	+	0.348235i
$266$	2.37524	−	2.42368i	0.145635	−	0.148605i
$267$		0			0
$268$	10.9669			0.669910
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	0.905855	+	0.423587i	$0.139229\pi$
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	−0.0860906	+	0.996287i	$0.527437\pi$
$270$		0			0
$271$	−11.1082	+	19.2400i	−0.674776	+	1.16875i	0.301759	+	0.953384i	$0.402426\pi$
$271$	−11.1082	+	19.2400i	−0.674776	+	1.16875i	−0.976534	+	0.215362i	$0.930907\pi$
$272$	0.760877	+	1.31788i	0.0461349	+	0.0799080i
$273$		0			0
$274$	1.37072	−	2.37416i	0.0828084	−	0.143428i
$275$	8.15335	+	14.1220i	0.491666	+	0.851590i
$276$		0			0
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	−0.557928	−	0.829889i	$-0.688404\pi$
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	0.997669	+	0.0682357i	$0.0217370\pi$
$278$	−3.98345	+	6.89953i	−0.238911	+	0.413807i
$279$		0			0
$280$	2.26088	+	8.10936i	0.135113	+	0.484627i
$281$	−11.6992	−	20.2636i	−0.697915	−	1.20882i	−0.969188	−	0.246322i	$-0.920778\pi$
$281$	−11.6992	−	20.2636i	−0.697915	−	1.20882i	0.271273	−	0.962502i	$-0.412555\pi$
$282$		0			0
$283$	−26.1248			−1.55296			−0.776478	−	0.630144i	$-0.782996\pi$
$283$	−26.1248			−1.55296			−0.776478	+	0.630144i	$0.782996\pi$
$284$	−8.69002			−0.515658
$285$		0			0
$286$	−9.07442	−	15.7174i	−0.536582	−	0.929387i
$287$	−10.3759	+	10.5876i	−0.612471	+	0.624963i
$288$		0			0
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$	11.2661	−	19.5134i	0.661567	−	1.14587i
$291$		0			0
$292$	−2.48345	−	4.30146i	−0.145333	−	0.251724i
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	0.189678	+	0.981846i	$0.439255\pi$
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	−0.945143	+	0.326657i	$0.894078\pi$
$294$		0			0
$295$	−1.78947	−	3.09945i	−0.104187	−	0.180457i
$296$	0.500000	−	0.866025i	0.0290619	−	0.0503367i
$297$		0			0
$298$	−11.6300	−	20.1437i	−0.673706	−	1.16689i
$299$	12.7713			0.738582
$300$		0			0
$301$	−4.85185	−	17.4027i	−0.279656	−	1.00308i
$302$	4.06238	−	7.03625i	0.233764	−	0.404891i
$303$		0			0
$304$	−0.641315	+	1.11079i	−0.0367819	+	0.0637082i
$305$	−4.97141	−	8.61073i	−0.284662	−	0.493049i
$306$		0			0
$307$	3.53216			0.201591			0.100795	−	0.994907i	$-0.467861\pi$
$307$	3.53216			0.201591			0.100795	+	0.994907i	$0.467861\pi$
$308$	−5.89248	+	6.01266i	−0.335755	+	0.342603i
$309$		0			0
$310$	14.9887	+	25.9611i	0.851298	+	1.47449i
$311$	−1.70370			−0.0966078			−0.0483039	−	0.998833i	$-0.515382\pi$
$311$	−1.70370			−0.0966078			−0.0483039	+	0.998833i	$0.515382\pi$
$312$		0			0
$313$	−2.84213			−0.160647			−0.0803234	−	0.996769i	$-0.525595\pi$
$313$	−2.84213			−0.160647			−0.0803234	+	0.996769i	$0.525595\pi$
$314$	−11.2632			−0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	24.9201			1.39965			0.699827	−	0.714313i	$-0.253261\pi$
$317$	24.9201			1.39965			0.699827	+	0.714313i	$0.253261\pi$
$318$		0			0
$319$	22.5322			1.26156
$320$	−1.59097	−	2.75564i	−0.0889380	−	0.154045i
$321$		0			0
$322$	−1.59097	−	5.70653i	−0.0886614	−	0.318013i
$323$	−1.95185			−0.108604
$324$		0			0
$325$	14.6150	+	25.3140i	0.810697	+	1.40417i
$326$	−1.99028	+	3.44727i	−0.110232	+	0.190927i
$327$		0			0
$328$	2.80150	−	4.85235i	0.154687	−	0.267926i
$329$	−14.9347	−	3.84060i	−0.823379	−	0.211739i
$330$		0			0
$331$	−7.17154			−0.394183			−0.197092	−	0.980385i	$-0.563150\pi$
$331$	−7.17154			−0.394183			−0.197092	+	0.980385i	$0.563150\pi$
$332$	4.03379	+	6.98673i	0.221383	+	0.383447i
$333$		0			0
$334$	−2.61956	+	4.53721i	−0.143336	+	0.248265i
$335$	−17.4480	−	30.2209i	−0.953287	−	1.65114i
$336$		0			0
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	0.398651	+	0.917103i	$0.369478\pi$
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	−0.993560	+	0.113309i	$0.963855\pi$
$338$	−9.76608	−	16.9153i	−0.531205	−	0.920073i
$339$		0			0
$340$	2.42107	−	4.19341i	0.131301	−	0.227420i
$341$	−14.9887	+	25.9611i	−0.811681	+	1.40587i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	3.41423	+	5.91362i	0.184083	+	0.318841i
$345$		0			0
$346$	−2.55159			−0.137174
$347$	2.11109			0.113329			0.0566646	−	0.998393i	$-0.481953\pi$
$347$	2.11109			0.113329			0.0566646	+	0.998393i	$0.481953\pi$
$348$		0			0
$349$	18.1082	+	31.3643i	0.969310	+	1.67889i	0.697559	+	0.716527i	$0.254269\pi$
$349$	18.1082	+	31.3643i	0.969310	+	1.67889i	0.271751	+	0.962368i	$0.412397\pi$
$350$	9.49028	−	9.68385i	0.507277	−	0.517623i
$351$		0			0
$352$	1.59097	−	2.75564i	0.0847991	−	0.146876i
$353$	−5.24433	+	9.08344i	−0.279127	+	0.483463i	−0.971168	−	0.238396i	$-0.923378\pi$
$353$	−5.24433	+	9.08344i	−0.279127	+	0.483463i	0.692041	+	0.721858i	$0.256712\pi$
$354$		0			0
$355$	13.8256	+	23.9466i	0.733786	+	1.27095i
$356$	−0.112725	+	0.195246i	−0.00597442	+	0.0103480i
$357$		0			0
$358$	−3.51887	−	6.09487i	−0.185978	−	0.322124i
$359$	−16.2209	+	28.0955i	−0.856108	+	1.48282i	0.0195047	+	0.999810i	$0.493791\pi$
$359$	−16.2209	+	28.0955i	−0.856108	+	1.48282i	−0.875613	+	0.483013i	$0.839542\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$	−12.9669			−0.681525
$363$		0			0
$364$	−10.5624	+	10.7778i	−0.553619	+	0.564911i
$365$	−7.90219	+	13.6870i	−0.413620	+	0.716410i
$366$		0			0
$367$	9.05555	−	15.6847i	0.472696	−	0.818733i	−0.526816	−	0.849979i	$-0.676614\pi$
$367$	9.05555	−	15.6847i	0.472696	−	0.818733i	0.999512	+	0.0312465i	$0.00994768\pi$
$368$	1.11956	+	1.93914i	0.0583612	+	0.101085i
$369$		0			0
$370$	−3.18194			−0.165421
$371$	1.46169	+	5.24284i	0.0758874	+	0.272195i
$372$		0			0
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	0.976621	−	0.214971i	$-0.0689656\pi$
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	−0.674480	+	0.738293i	$0.735632\pi$
$374$	4.84213			0.250381
$375$		0			0
$376$	5.82846			0.300580
$377$	40.3893			2.08016
$378$		0			0
$379$	14.2690			0.732947			0.366474	−	0.930428i	$-0.380565\pi$
$379$	14.2690			0.732947			0.366474	+	0.930428i	$0.380565\pi$
$380$	4.08126			0.209364
$381$		0			0
$382$	−1.98057			−0.101335
$383$	−0.824893	−	1.42876i	−0.0421501	−	0.0730061i	0.844181	−	0.536059i	$-0.180087\pi$
$383$	−0.824893	−	1.42876i	−0.0421501	−	0.0730061i	−0.886331	+	0.463053i	$0.846754\pi$
$384$		0			0
$385$	25.9435	+	6.67160i	1.32220	+	0.340016i
$386$	−4.54583			−0.231377
$387$		0			0
$388$	7.42107	+	12.8537i	0.376748	+	0.652546i
$389$	−16.0338	+	27.7713i	−0.812946	+	1.40806i	0.0978483	+	0.995201i	$0.468804\pi$
$389$	−16.0338	+	27.7713i	−0.812946	+	1.40806i	−0.910794	+	0.412862i	$0.864529\pi$
$390$		0			0
$391$	−1.70370	+	2.95089i	−0.0861596	+	0.149233i
$392$	6.13160	+	3.37690i	0.309693	+	0.170559i
$393$		0			0
$394$	21.8148			1.09901
$395$	6.58414	+	11.4041i	0.331284	+	0.573800i
$396$		0			0
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.210660	+	0.977559i	$0.567561\pi$
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.741261	+	0.671217i	$0.765772\pi$
$398$	6.14132	+	10.6371i	0.307836	+	0.533188i
$399$		0			0
$400$	−2.56238	+	4.43818i	−0.128119	+	0.221909i
$401$	5.30959	+	9.19647i	0.265148	+	0.459250i	0.967602	−	0.252479i	$-0.0812458\pi$
$401$	5.30959	+	9.19647i	0.265148	+	0.459250i	−0.702454	+	0.711729i	$0.747913\pi$
$402$		0			0
$403$	−26.8675	+	46.5358i	−1.33836	+	2.31811i
$404$	9.29467	−	16.0988i	0.462427	−	0.800947i
$405$		0			0
$406$	−5.03147	−	18.0470i	−0.249708	−	0.895657i
$407$	−1.59097	−	2.75564i	−0.0788615	−	0.136592i
$408$		0			0
$409$	5.54583			0.274224			0.137112	−	0.990556i	$-0.456218\pi$
$409$	5.54583			0.274224			0.137112	+	0.990556i	$0.456218\pi$
$410$	−17.8285			−0.880485
$411$		0			0
$412$	0.141315	+	0.244765i	0.00696209	+	0.0120587i
$413$	−2.88207	−	0.741150i	−0.141818	−	0.0364696i
$414$		0			0
$415$	12.8353	−	22.2314i	0.630060	−	1.09130i
$416$	2.85185	−	4.93955i	0.139823	−	0.242181i
$417$		0			0
$418$	2.04063	+	3.53447i	0.0998104	+	0.172877i
$419$	−2.77455	+	4.80566i	−0.135546	+	0.234772i	−0.925806	−	0.378000i	$-0.876612\pi$
$419$	−2.77455	+	4.80566i	−0.135546	+	0.234772i	0.790260	+	0.612772i	$0.209945\pi$
$420$		0			0
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	0.770537	−	0.637396i	$-0.219988\pi$
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	−0.937269	+	0.348606i	$0.886655\pi$
$422$	−8.32846	+	14.4253i	−0.405423	+	0.702213i
$423$		0			0
$424$	−1.02859	−	1.78157i	−0.0499527	−	0.0865207i
$425$	−7.79863			−0.378289
$426$		0			0
$427$	−8.00684	−	2.05903i	−0.387478	−	0.0996433i
$428$	−5.68878	+	9.85326i	−0.274978	+	0.476275i
$429$		0			0
$430$	10.8639	−	18.8168i	0.523903	−	0.907427i
$431$	−16.5539	−	28.6722i	−0.797374	−	1.38109i	−0.921321	−	0.388803i	$-0.872889\pi$
$431$	−16.5539	−	28.6722i	−0.797374	−	1.38109i	0.123947	−	0.992289i	$-0.460445\pi$
$432$		0			0
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$	24.1404	+	6.20790i	1.15877	+	0.297989i
$435$		0			0
$436$	−2.21053	−	3.82876i	−0.105865	−	0.183364i
$437$	−2.87197			−0.137385
$438$		0			0
$439$	−8.83422			−0.421634			−0.210817	−	0.977526i	$-0.567612\pi$
$439$	−8.83422			−0.421634			−0.210817	+	0.977526i	$0.567612\pi$
$440$	−10.1248			−0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	−17.5185			−0.832328			−0.416164	−	0.909290i	$-0.636626\pi$
$443$	−17.5185			−0.832328			−0.416164	+	0.909290i	$0.636626\pi$
$444$		0			0
$445$	0.717370			0.0340066
$446$	−5.32846	−	9.22916i	−0.252310	−	0.437014i
$447$		0			0
$448$	−2.56238	−	0.658939i	−0.121061	−	0.0311319i
$449$	−31.2301			−1.47384			−0.736920	−	0.675980i	$-0.763720\pi$
$449$	−31.2301			−1.47384			−0.736920	+	0.675980i	$0.763720\pi$
$450$		0			0
$451$	−8.91423	−	15.4399i	−0.419755	−	0.727036i
$452$	1.60752	−	2.78431i	0.0756115	−	0.130963i
$453$		0			0
$454$	−7.25404	+	12.5644i	−0.340449	+	0.589675i
$455$	46.5043	+	11.9590i	2.18015	+	0.560645i
$456$		0			0
$457$	−32.1248			−1.50273			−0.751367	−	0.659885i	$-0.770605\pi$
$457$	−32.1248			−1.50273			−0.751367	+	0.659885i	$0.770605\pi$
$458$	−5.12476	−	8.87635i	−0.239464	−	0.414765i
$459$		0			0
$460$	3.56238	−	6.17023i	0.166097	−	0.287688i
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	0.835901	−	0.548880i	$-0.184946\pi$
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	−0.893295	+	0.449472i	$0.851612\pi$
$462$		0			0
$463$	15.1735	−	26.2812i	0.705171	−	1.22139i	−0.261459	−	0.965215i	$-0.584204\pi$
$463$	15.1735	−	26.2812i	0.705171	−	1.22139i	0.966630	−	0.256177i	$-0.0824631\pi$
$464$	3.54063	+	6.13255i	0.164370	+	0.284696i
$465$		0			0
$466$	−0.540628	+	0.936396i	−0.0250441	+	0.0433777i
$467$	7.98181	−	13.8249i	0.369354	−	0.639740i	−0.620110	−	0.784515i	$-0.712912\pi$
$467$	7.98181	−	13.8249i	0.369354	−	0.639740i	0.989465	+	0.144774i	$0.0462456\pi$
$468$		0			0
$469$	−28.1014	−	7.22651i	−1.29760	−	0.333689i
$470$	−9.27292	−	16.0612i	−0.427728	−	0.740846i
$471$		0			0
$472$	1.12476			0.0517714
$473$	21.7278			0.999044
$474$		0			0
$475$	−3.28659	−	5.69254i	−0.150799	−	0.261192i
$476$	−1.08126	−	3.87828i	−0.0495593	−	0.177760i
$477$		0			0
$478$	6.16019	−	10.6698i	0.281761	−	0.488024i
$479$	−11.5865	+	20.0683i	−0.529399	+	0.916946i	0.470013	+	0.882659i	$0.344249\pi$
$479$	−11.5865	+	20.0683i	−0.529399	+	0.916946i	−0.999412	+	0.0342863i	$0.989084\pi$
$480$		0			0
$481$	−2.85185	−	4.93955i	−0.130033	−	0.225224i
$482$	6.50000	−	11.2583i	0.296067	−	0.512803i
$483$		0			0
$484$	0.437618	+	0.757977i	0.0198917	+	0.0344535i
$485$	23.6134	−	40.8996i	1.07223	−	1.85716i
$486$		0			0
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	0.902098	−	0.431531i	$-0.142026\pi$
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	−0.824766	+	0.565474i	$0.808693\pi$
$488$	3.12476			0.141451
$489$		0			0
$490$	−0.449657	−	22.2691i	−0.0203134	−	1.00601i
$491$	9.58414	−	16.6002i	0.432526	−	0.749157i	−0.564564	−	0.825389i	$-0.690956\pi$
$491$	9.58414	−	16.6002i	0.432526	−	0.749157i	0.997090	+	0.0762323i	$0.0242890\pi$
$492$		0			0
$493$	−5.38796	+	9.33223i	−0.242662	+	0.420302i
$494$	3.65787	+	6.33561i	0.164575	+	0.285053i
$495$		0			0
$496$	−9.42107			−0.423018
$497$	22.2672	+	5.72619i	0.998819	+	0.256855i
$498$		0			0
$499$	−20.5848	−	35.6540i	−0.921503	−	1.59609i	−0.797090	−	0.603860i	$-0.793629\pi$
$499$	−20.5848	−	35.6540i	−0.921503	−	1.59609i	−0.124413	−	0.992231i	$-0.539705\pi$
$500$	0.396990			0.0177539
$501$		0			0
$502$	−5.11109			−0.228119
$503$	26.4542			1.17953			0.589767	−	0.807574i	$-0.299220\pi$
$503$	26.4542			1.17953			0.589767	+	0.807574i	$0.299220\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$	7.12476			0.316734
$507$		0			0
$508$	20.1053			0.892030
$509$	6.38564	+	11.0603i	0.283039	+	0.490237i	0.972132	−	0.234436i	$-0.0753242\pi$
$509$	6.38564	+	11.0603i	0.283039	+	0.490237i	−0.689093	+	0.724673i	$0.741991\pi$
$510$		0			0
$511$	3.52915	+	12.6584i	0.156120	+	0.559975i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.83009	+	6.63392i	0.168938	+	0.292610i
$515$	0.449657	−	0.778828i	0.0198142	−	0.0343193i
$516$		0			0
$517$	9.27292	−	16.0612i	0.407822	−	0.706369i
$518$	−1.85185	+	1.88962i	−0.0813655	+	0.0830251i
$519$		0			0
$520$	−18.1488			−0.795879
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	0.930942	−	0.365168i	$-0.118988\pi$
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	−0.781716	+	0.623635i	$0.785655\pi$
$522$		0			0
$523$	14.7535	−	25.5538i	0.645125	−	1.11739i	−0.339148	−	0.940733i	$-0.610139\pi$
$523$	14.7535	−	25.5538i	0.645125	−	1.11739i	0.984273	−	0.176656i	$-0.0565280\pi$
$524$	3.18194	+	5.51129i	0.139004	+	0.240762i
$525$		0			0
$526$	−1.54746	+	2.68029i	−0.0674727	+	0.116866i
$527$	−7.16827	−	12.4158i	−0.312255	−	0.540841i
$528$		0			0
$529$	8.99316	−	15.5766i	0.391007	−	0.677244i
$530$	−3.27292	+	5.66886i	−0.142166	+	0.246239i
$531$		0			0
$532$	2.37524	−	2.42368i	0.102980	−	0.105080i
$533$	−15.9789	−	27.6763i	−0.692125	−	1.19879i
$534$		0			0
$535$	36.2028			1.56518
$536$	10.9669			0.473698
$537$		0			0
$538$	13.4451	+	23.2877i	0.579661	+	1.00400i
$539$	19.0607	−	11.5239i	0.821004	−	0.496371i
$540$		0			0
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$	−11.1082	+	19.2400i	−0.477139	+	0.826428i
$543$		0			0
$544$	0.760877	+	1.31788i	0.0326223	+	0.0565035i
$545$	−7.03379	+	12.1829i	−0.301295	+	0.521857i
$546$		0			0
$547$	17.6150	+	30.5102i	0.753165	+	1.30452i	0.946281	+	0.323344i	$0.104807\pi$
$547$	17.6150	+	30.5102i	0.753165	+	1.30452i	−0.193116	+	0.981176i	$0.561859\pi$
$548$	1.37072	−	2.37416i	0.0585544	−	0.101419i
$549$		0			0
$550$	8.15335	+	14.1220i	0.347660	+	0.602165i
$551$	−9.08263			−0.386933
$552$		0			0
$553$	10.6043	+	2.72698i	0.450939	+	0.115963i
$554$	7.31875	−	12.6764i	0.310944	−	0.538570i
$555$		0			0
$556$	−3.98345	+	6.89953i	−0.168936	+	0.292605i
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	0.928532	−	0.371252i	$-0.121071\pi$
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	−0.785779	+	0.618507i	$0.787738\pi$
$558$		0			0
$559$	38.9475			1.64730
$560$	2.26088	+	8.10936i	0.0955395	+	0.342683i
$561$		0			0
$562$	−11.6992	−	20.2636i	−0.493500	−	0.854768i
$563$	1.45993			0.0615286			0.0307643	−	0.999527i	$-0.490206\pi$
$563$	1.45993			0.0615286			0.0307643	+	0.999527i	$0.490206\pi$
$564$		0			0
$565$	−10.2301			−0.430383
$566$	−26.1248			−1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	−19.5653			−0.820218			−0.410109	−	0.912036i	$-0.634509\pi$
$569$	−19.5653			−0.820218			−0.410109	+	0.912036i	$0.634509\pi$
$570$		0			0
$571$	−21.9259			−0.917569			−0.458785	−	0.888547i	$-0.651715\pi$
$571$	−21.9259			−0.917569			−0.458785	+	0.888547i	$0.651715\pi$
$572$	−9.07442	−	15.7174i	−0.379421	−	0.657176i
$573$		0			0
$574$	−10.3759	+	10.5876i	−0.433083	+	0.441916i
$575$	−11.4750			−0.478540
$576$		0			0
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	0.999853	+	0.0171554i	$0.00546099\pi$
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	−0.485069	+	0.874476i	$0.661206\pi$
$578$	7.34213	−	12.7169i	0.305392	−	0.528955i
$579$		0			0
$580$	11.2661	−	19.5134i	0.467798	−	0.810251i
$581$	−5.73229	−	20.5607i	−0.237815	−	0.853001i
$582$		0			0
$583$	−6.54583			−0.271101
$584$	−2.48345	−	4.30146i	−0.102766	−	0.177996i
$585$		0			0
$586$	−12.9315	+	22.3980i	−0.534194	+	0.925251i
$587$	18.0796	+	31.3148i	0.746226	+	1.29250i	0.949620	+	0.313404i	$0.101469\pi$
$587$	18.0796	+	31.3148i	0.746226	+	1.29250i	−0.203394	+	0.979097i	$0.565197\pi$
$588$		0			0
$589$	6.04187	−	10.4648i	0.248951	−	0.431196i
$590$	−1.78947	−	3.09945i	−0.0736712	−	0.127602i
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	−0.668204	−	0.743978i	$-0.732937\pi$
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	0.978406	+	0.206693i	$0.0662700\pi$
$594$		0			0
$595$	−8.96690	+	9.14978i	−0.367607	+	0.375105i
$596$	−11.6300	−	20.1437i	−0.476382	−	0.825118i
$597$		0			0
$598$	12.7713			0.522256
$599$	5.45417			0.222851			0.111426	−	0.993773i	$-0.464458\pi$
$599$	5.45417			0.222851			0.111426	+	0.993773i	$0.464458\pi$
$600$		0			0
$601$	−3.36840	−	5.83424i	−0.137400	−	0.237984i	0.789112	−	0.614250i	$-0.210541\pi$
$601$	−3.36840	−	5.83424i	−0.137400	−	0.237984i	−0.926512	+	0.376266i	$0.877208\pi$
$602$	−4.85185	−	17.4027i	−0.197747	−	0.709282i
$603$		0			0
$604$	4.06238	−	7.03625i	0.165296	−	0.286301i
$605$	1.39248	−	2.41184i	0.0566122	−	0.0980553i
$606$		0			0
$607$	−3.33530	−	5.77690i	−0.135376	−	0.234477i	0.790365	−	0.612636i	$-0.209891\pi$
$607$	−3.33530	−	5.77690i	−0.135376	−	0.234477i	−0.925741	+	0.378159i	$0.876557\pi$
$608$	−0.641315	+	1.11079i	−0.0260088	+	0.0450485i
$609$		0			0
$610$	−4.97141	−	8.61073i	−0.201287	−	0.348638i
$611$	16.6219	−	28.7899i	0.672449	−	1.16472i
$612$		0			0
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$	3.53216			0.142546
$615$		0			0
$616$	−5.89248	+	6.01266i	−0.237415	+	0.242257i
$617$	−17.2483	+	29.8749i	−0.694390	+	1.20272i	0.275996	+	0.961159i	$0.410992\pi$
$617$	−17.2483	+	29.8749i	−0.694390	+	1.20272i	−0.970386	+	0.241560i	$0.922341\pi$
$618$		0			0
$619$	8.22421	−	14.2447i	0.330559	−	0.572545i	−0.652063	−	0.758165i	$-0.726096\pi$
$619$	8.22421	−	14.2447i	0.330559	−	0.572545i	0.982622	+	0.185620i	$0.0594295\pi$
$620$	14.9887	+	25.9611i	0.601959	+	1.04262i
$621$		0			0
$622$	−1.70370			−0.0683120
$623$	0.417500	−	0.426015i	0.0167268	−	0.0170679i
$624$		0			0
$625$	12.1803	+	21.0969i	0.487212	+	0.843877i
$626$	−2.84213			−0.113594
$627$		0			0
$628$	−11.2632			−0.449451
$629$	1.52175			0.0606763
$630$		0			0
$631$	−30.0118			−1.19475			−0.597375	−	0.801962i	$-0.703790\pi$
$631$	−30.0118			−1.19475			−0.597375	+	0.801962i	$0.703790\pi$
$632$	−4.13844			−0.164618
$633$		0			0
$634$	24.9201			0.989704
$635$	−31.9870	−	55.4031i	−1.26937	−	2.19861i
$636$		0			0
$637$	34.1668	−	20.6569i	1.35374	−	0.818456i
$638$	22.5322			0.892057
$639$		0			0
$640$	−1.59097	−	2.75564i	−0.0628887	−	0.108926i
$641$	13.9497	−	24.1615i	0.550978	−	0.954322i	−0.447226	−	0.894421i	$-0.647588\pi$
$641$	13.9497	−	24.1615i	0.550978	−	0.954322i	0.998204	−	0.0599014i	$-0.0190786\pi$
$642$		0			0
$643$	14.2524	−	24.6859i	0.562060	−	0.973516i	−0.435257	−	0.900306i	$-0.643342\pi$
$643$	14.2524	−	24.6859i	0.562060	−	0.973516i	0.997317	−	0.0732100i	$-0.0233243\pi$
$644$	−1.59097	−	5.70653i	−0.0626931	−	0.224869i
$645$		0			0
$646$	−1.95185			−0.0767944
$647$	−8.35705	−	14.4748i	−0.328550	−	0.569065i	0.653675	−	0.756776i	$-0.273226\pi$
$647$	−8.35705	−	14.4748i	−0.328550	−	0.569065i	−0.982224	+	0.187711i	$0.939893\pi$
$648$		0			0
$649$	1.78947	−	3.09945i	0.0702427	−	0.121664i
$650$	14.6150	+	25.3140i	0.573249	+	0.992897i
$651$		0			0
$652$	−1.99028	+	3.44727i	−0.0779456	+	0.135006i
$653$	19.0825	+	33.0519i	0.746756	+	1.29342i	0.949370	+	0.314161i	$0.101723\pi$
$653$	19.0825	+	33.0519i	0.746756	+	1.29342i	−0.202614	+	0.979259i	$0.564944\pi$
$654$		0			0
$655$	10.1248	−	17.5366i	0.395607	−	0.685212i
$656$	2.80150	−	4.85235i	0.109380	−	0.189452i
$657$		0			0
$658$	−14.9347	−	3.84060i	−0.582217	−	0.149722i
$659$	−4.37072	−	7.57031i	−0.170259	−	0.294898i	0.768251	−	0.640148i	$-0.221127\pi$
$659$	−4.37072	−	7.57031i	−0.170259	−	0.294898i	−0.938510	+	0.345251i	$0.887794\pi$
$660$		0			0
$661$	−20.0837			−0.781167			−0.390584	−	0.920567i	$-0.627727\pi$
$661$	−20.0837			−0.781167			−0.390584	+	0.920567i	$0.627727\pi$
$662$	−7.17154			−0.278730
$663$		0			0
$664$	4.03379	+	6.98673i	0.156541	+	0.271138i
$665$	−10.4577	−	2.68930i	−0.405534	−	0.104286i
$666$		0			0
$667$	−7.92790	+	13.7315i	−0.306970	+	0.531687i
$668$	−2.61956	+	4.53721i	−0.101354	+	0.175550i
$669$		0			0
$670$	−17.4480	−	30.2209i	−0.674076	−	1.16753i
$671$	4.97141	−	8.61073i	0.191919	−	0.332414i
$672$		0			0
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	−0.981561	−	0.191148i	$-0.938779\pi$
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	0.325242	−	0.945631i	$-0.394554\pi$
$674$	−10.9211	+	18.9158i	−0.420664	+	0.728611i
$675$		0			0
$676$	−9.76608	−	16.9153i	−0.375618	−	0.650590i
$677$	0.717370			0.0275708			0.0137854	−	0.999905i	$-0.495612\pi$
$677$	0.717370			0.0275708			0.0137854	+	0.999905i	$0.495612\pi$
$678$		0			0
$679$	−10.5458	−	37.8260i	−0.404712	−	1.45163i
$680$	2.42107	−	4.19341i	0.0928437	−	0.160810i
$681$		0			0
$682$	−14.9887	+	25.9611i	−0.573945	+	0.994102i
$683$	10.5270	+	18.2332i	0.402803	+	0.697675i	0.994063	−	0.108806i	$-0.0347027\pi$
$683$	10.5270	+	18.2332i	0.402803	+	0.697675i	−0.591260	+	0.806481i	$0.701369\pi$
$684$		0			0
$685$	−8.72313			−0.333294
$686$	−13.4863	−	12.6933i	−0.514910	−	0.484631i
$687$		0			0
$688$	3.41423	+	5.91362i	0.130166	+	0.225455i
$689$	−11.7335			−0.447012
$690$		0			0
$691$	5.84789			0.222464			0.111232	−	0.993794i	$-0.464520\pi$
$691$	5.84789			0.222464			0.111232	+	0.993794i	$0.464520\pi$
$692$	−2.55159			−0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	25.3502			0.961588
$696$		0			0
$697$	8.52640			0.322960
$698$	18.1082	+	31.3643i	0.685406	+	1.18716i
$699$		0			0
$700$	9.49028	−	9.68385i	0.358699	−	0.366015i
$701$	−10.2711			−0.387935			−0.193967	−	0.981008i	$-0.562136\pi$
$701$	−10.2711			−0.387935			−0.193967	+	0.981008i	$0.562136\pi$
$702$		0			0
$703$	0.641315	+	1.11079i	0.0241877	+	0.0418942i
$704$	1.59097	−	2.75564i	0.0599620	−	0.103857i
$705$		0			0
$706$	−5.24433	+	9.08344i	−0.197373	+	0.341860i
$707$	−34.4246	+	35.1268i	−1.29467	+	1.32108i
$708$		0			0
$709$	43.4854			1.63313			0.816564	−	0.577255i	$-0.195876\pi$
$709$	43.4854			1.63313			0.816564	+	0.577255i	$0.195876\pi$
$710$	13.8256	+	23.9466i	0.518865	+	0.898700i
$711$		0			0
$712$	−0.112725	+	0.195246i	−0.00422455	+	0.00731714i
$713$	−10.5475	−	18.2687i	−0.395006	−	0.684170i
$714$		0			0
$715$	−28.8743	+	50.0117i	−1.07984	+	1.87033i
$716$	−3.51887	−	6.09487i	−0.131507	−	0.227776i
$717$		0			0
$718$	−16.2209	+	28.0955i	−0.605360	+	1.04851i
$719$	−25.4412	+	44.0654i	−0.948796	+	1.64336i	−0.200830	+	0.979626i	$0.564364\pi$
$719$	−25.4412	+	44.0654i	−0.948796	+	1.64336i	−0.747966	+	0.663737i	$0.768969\pi$
$720$		0			0
$721$	−0.200818	−	0.720299i	−0.00747886	−	0.0268253i
$722$	8.67743	+	15.0297i	0.322941	+	0.559349i
$723$		0			0
$724$	−12.9669			−0.481911
$725$	−36.2898			−1.34777
$726$		0			0
$727$	6.07210	+	10.5172i	0.225202	+	0.390061i	0.956380	−	0.292126i	$-0.0943626\pi$
$727$	6.07210	+	10.5172i	0.225202	+	0.390061i	−0.731178	+	0.682186i	$0.761029\pi$
$728$	−10.5624	+	10.7778i	−0.391468	+	0.399452i
$729$		0			0
$730$	−7.90219	+	13.6870i	−0.292473	+	0.506579i
$731$	−5.19562	+	8.99907i	−0.192167	+	0.332843i
$732$		0			0
$733$	23.0848	+	39.9841i	0.852657	+	1.47685i	0.878801	+	0.477188i	$0.158344\pi$
$733$	23.0848	+	39.9841i	0.852657	+	1.47685i	−0.0261440	+	0.999658i	$0.508323\pi$
$734$	9.05555	−	15.6847i	0.334246	−	0.578932i
$735$		0			0
$736$	1.11956	+	1.93914i	0.0412676	+	0.0714776i
$737$	17.4480	−	30.2209i	0.642706	−	1.11320i
$738$		0			0
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	0.816458	−	0.577405i	$-0.195935\pi$
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	−0.908276	+	0.418371i	$0.862601\pi$
$740$	−3.18194			−0.116971
$741$		0			0
$742$	1.46169	+	5.24284i	0.0536605	+	0.192471i
$743$	15.7060	−	27.2036i	0.576198	−	0.998004i	−0.419712	−	0.907657i	$-0.637869\pi$
$743$	15.7060	−	27.2036i	0.576198	−	0.998004i	0.995910	−	0.0903470i	$-0.0287976\pi$
$744$		0			0
$745$	−37.0059	+	64.0961i	−1.35579	+	2.34830i
$746$	5.83530	+	10.1070i	0.213645	+	0.370045i
$747$		0			0
$748$	4.84213			0.177046
$749$	21.0695	−	21.4992i	0.769863	−	0.785565i
$750$		0			0
$751$	−1.64815	−	2.85468i	−0.0601419	−	0.104169i	0.834387	−	0.551179i	$-0.185822\pi$
$751$	−1.64815	−	2.85468i	−0.0601419	−	0.104169i	−0.894529	+	0.447010i	$0.852489\pi$
$752$	5.82846			0.212542
$753$		0			0
$754$	40.3893			1.47089
$755$	−25.8525			−0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$	14.2690			0.518272
$759$		0			0
$760$	4.08126			0.148043
$761$	7.03379	+	12.1829i	0.254975	+	0.441629i	0.964889	−	0.262659i	$-0.0845995\pi$
$761$	7.03379	+	12.1829i	0.254975	+	0.441629i	−0.709914	+	0.704288i	$0.751266\pi$
$762$		0			0
$763$	3.14132	+	11.2673i	0.113723	+	0.407905i
$764$	−1.98057			−0.0716545
$765$		0			0
$766$	−0.824893	−	1.42876i	−0.0298046	−	0.0516231i
$767$	3.20765	−	5.55582i	0.115822	−	0.200609i
$768$		0			0
$769$	11.3461	−	19.6520i	0.409151	−	0.708669i	−0.585644	−	0.810568i	$-0.699158\pi$
$769$	11.3461	−	19.6520i	0.409151	−	0.708669i	0.994795	+	0.101899i	$0.0324918\pi$
$770$	25.9435	+	6.67160i	0.934939	+	0.240428i
$771$		0			0
$772$	−4.54583			−0.163608
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	0.860071	−	0.510175i	$-0.170419\pi$
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	−0.871860	+	0.489756i	$0.837086\pi$
$774$		0			0
$775$	24.1404	−	41.8123i	0.867148	−	1.50194i
$776$	7.42107	+	12.8537i	0.266401	+	0.461420i
$777$		0			0
$778$	−16.0338	+	27.7713i	−0.574839	+	0.995651i
$779$	3.59329	+	6.22377i	0.128743	+	0.222990i
$780$		0			0
$781$	−13.8256	+	23.9466i	−0.494718	+	0.856877i
$782$	−1.70370	+	2.95089i	−0.0609241	+	0.105524i
$783$		0			0
$784$	6.13160	+	3.37690i	0.218986	+	0.120604i
$785$	17.9194	+	31.0374i	0.639572	+	1.10777i
$786$		0			0
$787$	0.540073			0.0192515			0.00962576	−	0.999954i	$-0.496936\pi$
$787$	0.540073			0.0192515			0.00962576	+	0.999954i	$0.496936\pi$
$788$	21.8148			0.777120
$789$		0			0
$790$	6.58414	+	11.4041i	0.234253	+	0.405738i
$791$	−5.95378	+	6.07521i	−0.211692	+	0.216010i
$792$		0			0
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$	−18.9669	+	32.8516i	−0.673110	+	1.16586i
$795$		0			0
$796$	6.14132	+	10.6371i	0.217673	+	0.377021i
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	−0.553312	−	0.832974i	$-0.686636\pi$
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	0.998033	+	0.0626954i	$0.0199697\pi$
$798$		0			0
$799$	4.43474	+	7.68119i	0.156890	+	0.271741i
$800$	−2.56238	+	4.43818i	−0.0905939	+	0.156913i
$801$		0			0
$802$	5.30959	+	9.19647i	0.187488	+	0.324739i
$803$	−15.8044			−0.557725
$804$		0			0
$805$	−13.1940	+	13.4631i	−0.465027	+	0.474511i
$806$	−26.8675	+	46.5358i	−0.946366	+	1.63915i
$807$		0			0
$808$	9.29467	−	16.0988i	0.326985	−	0.566355i
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	0.999889	+	0.0148817i	$0.00473717\pi$
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	−0.487057	+	0.873370i	$0.661929\pi$
$810$		0			0
$811$	−15.4290			−0.541785			−0.270892	−	0.962610i	$-0.587319\pi$
$811$	−15.4290			−0.541785			−0.270892	+	0.962610i	$0.587319\pi$
$812$	−5.03147	−	18.0470i	−0.176570	−	0.633325i
$813$		0			0
$814$	−1.59097	−	2.75564i	−0.0557635	−	0.0965853i
$815$	12.6659			0.443669
$816$		0			0
$817$	−8.75839			−0.306417
$818$	5.54583			0.193905
$819$		0			0
$820$	−17.8285			−0.622597
$821$	−8.48727			−0.296208			−0.148104	−	0.988972i	$-0.547317\pi$
$821$	−8.48727			−0.296208			−0.148104	+	0.988972i	$0.547317\pi$
$822$		0			0
$823$	29.0974			1.01427			0.507136	−	0.861866i	$-0.330704\pi$
$823$	29.0974			1.01427			0.507136	+	0.861866i	$0.330704\pi$
$824$	0.141315	+	0.244765i	0.00492294	+	0.00852679i
$825$		0			0
$826$	−2.88207	−	0.741150i	−0.100280	−	0.0257879i
$827$	25.9396			0.902007			0.451003	−	0.892522i	$-0.351066\pi$
$827$	25.9396			0.902007			0.451003	+	0.892522i	$0.351066\pi$
$828$		0			0
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	0.914941	−	0.403588i	$-0.132237\pi$
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	−0.806988	+	0.590568i	$0.798904\pi$
$830$	12.8353	−	22.2314i	0.445520	−	0.771663i
$831$		0			0
$832$	2.85185	−	4.93955i	0.0988701	−	0.171248i
$833$	0.215047	+	10.6501i	0.00745093	+	0.369004i
$834$		0			0
$835$	16.6706			0.576910
$836$	2.04063	+	3.53447i	0.0705766	+	0.122242i
$837$		0			0
$838$	−2.77455	+	4.80566i	−0.0958452	+	0.166009i
$839$	−21.2947	−	36.8834i	−0.735174	−	1.27336i	−0.954647	−	0.297740i	$-0.903767\pi$
$839$	−21.2947	−	36.8834i	−0.735174	−	1.27336i	0.219474	−	0.975618i	$-0.429566\pi$
$840$		0			0
$841$	−10.5721	+	18.3114i	−0.364555	+	0.631428i
$842$	−3.42107	−	5.92546i	−0.117898	−	0.204205i
$843$		0			0
$844$	−8.32846	+	14.4253i	−0.286677	+	0.496540i
$845$	−31.0751	+	53.8237i	−1.06902	+	1.85159i
$846$		0			0
$847$	−0.621885	−	2.23059i	−0.0213682	−	0.0766440i
$848$	−1.02859	−	1.78157i	−0.0353219	−	0.0611794i
$849$		0			0
$850$	−7.79863			−0.267491
$851$	2.23912			0.0767562
$852$		0			0
$853$	−10.6969	−	18.5275i	−0.366254	−	0.634370i	0.622723	−	0.782442i	$-0.286026\pi$
$853$	−10.6969	−	18.5275i	−0.366254	−	0.634370i	−0.988976	+	0.148073i	$0.952693\pi$
$854$	−8.00684	−	2.05903i	−0.273988	−	0.0704585i
$855$		0			0
$856$	−5.68878	+	9.85326i	−0.194438	+	0.336777i
$857$	−18.4218	+	31.9074i	−0.629275	+	1.08994i	0.358422	+	0.933560i	$0.383315\pi$
$857$	−18.4218	+	31.9074i	−0.629275	+	1.08994i	−0.987697	+	0.156377i	$0.950019\pi$
$858$		0			0
$859$	8.81875	+	15.2745i	0.300892	+	0.521160i	0.976338	−	0.216249i	$-0.0693824\pi$
$859$	8.81875	+	15.2745i	0.300892	+	0.521160i	−0.675446	+	0.737409i	$0.736049\pi$
$860$	10.8639	−	18.8168i	0.370455	−	0.641648i
$861$		0			0
$862$	−16.5539	−	28.6722i	−0.563828	−	0.976579i
$863$	0.380438	−	0.658939i	0.0129503	−	0.0224305i	−0.859478	−	0.511173i	$-0.829211\pi$
$863$	0.380438	−	0.658939i	0.0129503	−	0.0224305i	0.872428	+	0.488743i	$0.162544\pi$
$864$		0			0
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$	−12.1111			−0.411552
$867$		0			0
$868$	24.1404	+	6.20790i	0.819378	+	0.210710i
$869$	−6.58414	+	11.4041i	−0.223351	+	0.386856i
$870$		0			0
$871$	31.2759	−	54.1715i	1.05974	−	1.83553i
$872$	−2.21053	−	3.82876i	−0.0748581	−	0.129658i
$873$		0			0
$874$	−2.87197			−0.0971457
$875$	−1.01724	−	0.261592i	−0.0343890	−	0.00884343i
$876$		0			0
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	0.968234	+	0.250044i	$0.0804451\pi$
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	−0.267573	+	0.963538i	$0.586222\pi$
$878$	−8.83422			−0.298140
$879$		0			0
$880$	−10.1248			−0.341306
$881$	−8.35486			−0.281482			−0.140741	−	0.990046i	$-0.544949\pi$
$881$	−8.35486			−0.281482			−0.140741	+	0.990046i	$0.544949\pi$
$882$		0			0
$883$	35.6181			1.19864			0.599322	−	0.800508i	$-0.295437\pi$
$883$	35.6181			1.19864			0.599322	+	0.800508i	$0.295437\pi$
$884$	8.67962			0.291927
$885$		0			0
$886$	−17.5185			−0.588545
$887$	−18.5550	−	32.1382i	−0.623016	−	1.07909i	−0.988921	−	0.148443i	$-0.952574\pi$
$887$	−18.5550	−	32.1382i	−0.623016	−	1.07909i	0.365905	−	0.930652i	$-0.380759\pi$
$888$		0			0
$889$	−51.5175	−	13.2482i	−1.72784	−	0.444330i
$890$	0.717370			0.0240463
$891$		0			0
$892$	−5.32846	−	9.22916i	−0.178410	−	0.309015i
$893$	−3.73788	+	6.47420i	−0.125083	+	0.216651i
$894$		0			0
$895$	−11.1969	+	19.3935i	−0.374270	+	0.648254i
$896$	−2.56238	−	0.658939i	−0.0856032	−	0.0220136i
$897$		0			0
$898$	−31.2301			−1.04216
$899$	−33.3565	−	57.7751i	−1.11250	−	1.92691i
$900$		0			0
$901$	1.56526	−	2.71111i	0.0521464	−	0.0903202i
$902$	−8.91423	−	15.4399i	−0.296811	−	0.514092i
$903$		0			0
$904$	1.60752	−	2.78431i	0.0534654	−	0.0926048i
$905$	20.6300	+	35.7321i	0.685763	+	1.18778i
$906$		0			0
$907$	24.0751	−	41.6993i	0.799401	−	1.38460i	−0.120606	−	0.992700i	$-0.538484\pi$
$907$	24.0751	−	41.6993i	0.799401	−	1.38460i	0.920007	−	0.391902i	$-0.128183\pi$
$908$	−7.25404	+	12.5644i	−0.240734	+	0.416963i
$909$		0			0
$910$	46.5043	+	11.9590i	1.54160	+	0.396436i
$911$	−17.4428	−	30.2119i	−0.577906	−	1.00096i	−0.995719	−	0.0924301i	$-0.970537\pi$
$911$	−17.4428	−	30.2119i	−0.577906	−	1.00096i	0.417813	−	0.908533i	$-0.362797\pi$
$912$		0			0
$913$	25.6706			0.849573
$914$	−32.1248			−1.06259
$915$		0			0
$916$	−5.12476	−	8.87635i	−0.169327	−	0.293283i
$917$	−4.52175	−	16.2187i	−0.149321	−	0.535590i
$918$		0			0
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	0.0249351	+	0.999689i	$0.492062\pi$
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	−0.878224	+	0.478250i	$0.841271\pi$
$920$	3.56238	−	6.17023i	0.117448	−	0.203426i
$921$		0			0
$922$	−1.23229	−	2.13438i	−0.0405832	−	0.0702922i
$923$	−24.7826	+	42.9248i	−0.815730	+	1.41289i
$924$		0			0
$925$	2.56238	+	4.43818i	0.0842506	+	0.145926i
$926$	15.1735	−	26.2812i	0.498631	−	0.863655i
$927$		0			0
$928$	3.54063	+	6.13255i	0.116227	+	0.201311i
$929$	50.8285			1.66763			0.833814	−	0.552046i	$-0.186153\pi$
$929$	50.8285			1.66763			0.833814	+	0.552046i	$0.186153\pi$
$930$		0			0
$931$	−7.68332	+	4.64526i	−0.251811	+	0.152242i
$932$	−0.540628	+	0.936396i	−0.0177089	+	0.0306727i
$933$		0			0
$934$	7.98181	−	13.8249i	0.261173	−	0.452365i
$935$	−7.70370	−	13.3432i	−0.251938	−	0.436369i
$936$		0			0
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$	−28.1014	−	7.22651i	−0.917542	−	0.235954i
$939$		0			0
$940$	−9.27292	−	16.0612i	−0.302449	−	0.523857i
$941$	−1.15787			−0.0377454			−0.0188727	−	0.999822i	$-0.506008\pi$
$941$	−1.15787			−0.0377454			−0.0188727	+	0.999822i	$0.506008\pi$
$942$		0			0
$943$	12.5458			0.408548
$944$	1.12476			0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	−9.81479			−0.318938			−0.159469	−	0.987203i	$-0.550978\pi$
$947$	−9.81479			−0.318938			−0.159469	+	0.987203i	$0.550978\pi$
$948$		0			0
$949$	−28.3297			−0.919620
$950$	−3.28659	−	5.69254i	−0.106631	−	0.184690i
$951$		0			0
$952$	−1.08126	−	3.87828i	−0.0350437	−	0.125696i
$953$	−6.53791			−0.211784			−0.105892	−	0.994378i	$-0.533770\pi$
$953$	−6.53791			−0.211784			−0.105892	+	0.994378i	$0.533770\pi$
$954$		0			0
$955$	3.15103	+	5.45774i	0.101965	+	0.176608i
$956$	6.16019	−	10.6698i	0.199235	−	0.345085i
$957$		0			0
$958$	−11.5865	+	20.0683i	−0.374341	+	0.648378i
$959$	−5.07674	+	5.18029i	−0.163937	+	0.167280i
$960$		0			0
$961$	57.7565			1.86311
$962$	−2.85185	−	4.93955i	−0.0919473	−	0.159257i
$963$		0			0
$964$	6.50000	−	11.2583i	0.209351	−	0.362606i
$965$	7.23229	+	12.5267i	0.232816	+	0.403248i
$966$		0			0
$967$	14.4445	−	25.0185i	0.464502	−	0.804542i	−0.534677	−	0.845057i	$-0.679567\pi$
$967$	14.4445	−	25.0185i	0.464502	−	0.804542i	0.999179	+	0.0405151i	$0.0128999\pi$
$968$	0.437618	+	0.757977i	0.0140656	+	0.0243623i
$969$		0			0
$970$	23.6134	−	40.8996i	0.758181	−	1.31321i
$971$	−2.66827	+	4.62158i	−0.0856289	+	0.148314i	−0.905659	−	0.424007i	$-0.860623\pi$
$971$	−2.66827	+	4.62158i	−0.0856289	+	0.148314i	0.820030	+	0.572320i	$0.193957\pi$
$972$		0			0
$973$	14.7535	−	15.0544i	0.472975	−	0.482622i
$974$	1.70658	+	2.95588i	0.0546822	+	0.0947124i
$975$		0			0
$976$	3.12476			0.100021
$977$	48.0722			1.53797			0.768983	−	0.639269i	$-0.220763\pi$
$977$	48.0722			1.53797			0.768983	+	0.639269i	$0.220763\pi$
$978$		0			0
$979$	0.358685	+	0.621261i	0.0114636	+	0.0198556i
$980$	−0.449657	−	22.2691i	−0.0143638	−	0.711359i
$981$		0			0
$982$	9.58414	−	16.6002i	0.305842	−	0.529734i
$983$	14.7313	−	25.5154i	0.469857	−	0.813816i	−0.529549	−	0.848279i	$-0.677639\pi$
$983$	14.7313	−	25.5154i	0.469857	−	0.813816i	0.999406	+	0.0344634i	$0.0109722\pi$
$984$		0			0
$985$	−34.7067	−	60.1138i	−1.10585	−	1.91538i
$986$	−5.38796	+	9.33223i	−0.171588	+	0.297199i
$987$		0			0
$988$	3.65787	+	6.33561i	0.116372	+	0.201563i
$989$	−7.64488	+	13.2413i	−0.243093	+	0.421050i
$990$		0			0
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	0.999929	−	0.0119112i	$-0.00379153\pi$
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	−0.510280	+	0.860008i	$0.670458\pi$
$992$	−9.42107			−0.299119
$993$		0			0
$994$	22.2672	+	5.72619i	0.706271	+	0.181624i
$995$	19.5413	−	33.8466i	0.619501	−	1.07301i
$996$		0			0
$997$	−2.77292	+	4.80283i	−0.0878191	+	0.152107i	−0.906589	−	0.422015i	$-0.861323\pi$
$997$	−2.77292	+	4.80283i	−0.0878191	+	0.152107i	0.818770	+	0.574122i	$0.194656\pi$
$998$	−20.5848	−	35.6540i	−0.651601	−	1.12861i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.e.d.37.1		6
3.2	odd	2		126.2.e.c.121.3	yes	6
4.3	odd	2		3024.2.q.g.2305.1		6
7.2	even	3		2646.2.f.l.1765.1		6
7.3	odd	6		2646.2.h.o.361.1		6
7.4	even	3		378.2.h.c.361.3		6
7.5	odd	6		2646.2.f.m.1765.3		6
7.6	odd	2		2646.2.e.p.1549.3		6
9.2	odd	6		126.2.h.d.79.1	yes	6
9.4	even	3		1134.2.g.l.163.1		6
9.5	odd	6		1134.2.g.m.163.3		6
9.7	even	3		378.2.h.c.289.3		6
12.11	even	2		1008.2.q.g.625.1		6
21.2	odd	6		882.2.f.n.589.2		6
21.5	even	6		882.2.f.o.589.2		6
21.11	odd	6		126.2.h.d.67.1	yes	6
21.17	even	6		882.2.h.p.67.3		6
21.20	even	2		882.2.e.o.373.1		6
28.11	odd	6		3024.2.t.h.1873.3		6
36.7	odd	6		3024.2.t.h.289.3		6
36.11	even	6		1008.2.t.h.961.3		6
63.2	odd	6		882.2.f.n.295.2		6
63.4	even	3		1134.2.g.l.487.1		6
63.5	even	6		7938.2.a.bw.1.3		3
63.11	odd	6		126.2.e.c.25.3	✓	6
63.16	even	3		2646.2.f.l.883.1		6
63.20	even	6		882.2.h.p.79.3		6
63.23	odd	6		7938.2.a.bv.1.1		3
63.25	even	3	inner	378.2.e.d.235.1		6
63.32	odd	6		1134.2.g.m.487.3		6
63.34	odd	6		2646.2.h.o.667.1		6
63.38	even	6		882.2.e.o.655.1		6
63.40	odd	6		7938.2.a.bz.1.1		3
63.47	even	6		882.2.f.o.295.2		6
63.52	odd	6		2646.2.e.p.2125.3		6
63.58	even	3		7938.2.a.ca.1.3		3
63.61	odd	6		2646.2.f.m.883.3		6
84.11	even	6		1008.2.t.h.193.3		6
252.11	even	6		1008.2.q.g.529.1		6
252.151	odd	6		3024.2.q.g.2881.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	63.11	odd	6
126.2.e.c.121.3	yes	6	3.2	odd	2
126.2.h.d.67.1	yes	6	21.11	odd	6
126.2.h.d.79.1	yes	6	9.2	odd	6
378.2.e.d.37.1		6	1.1	even	1	trivial
378.2.e.d.235.1		6	63.25	even	3	inner
378.2.h.c.289.3		6	9.7	even	3
378.2.h.c.361.3		6	7.4	even	3
882.2.e.o.373.1		6	21.20	even	2
882.2.e.o.655.1		6	63.38	even	6
882.2.f.n.295.2		6	63.2	odd	6
882.2.f.n.589.2		6	21.2	odd	6
882.2.f.o.295.2		6	63.47	even	6
882.2.f.o.589.2		6	21.5	even	6
882.2.h.p.67.3		6	21.17	even	6
882.2.h.p.79.3		6	63.20	even	6
1008.2.q.g.529.1		6	252.11	even	6
1008.2.q.g.625.1		6	12.11	even	2
1008.2.t.h.193.3		6	84.11	even	6
1008.2.t.h.961.3		6	36.11	even	6
1134.2.g.l.163.1		6	9.4	even	3
1134.2.g.l.487.1		6	63.4	even	3
1134.2.g.m.163.3		6	9.5	odd	6
1134.2.g.m.487.3		6	63.32	odd	6
2646.2.e.p.1549.3		6	7.6	odd	2
2646.2.e.p.2125.3		6	63.52	odd	6
2646.2.f.l.883.1		6	63.16	even	3
2646.2.f.l.1765.1		6	7.2	even	3
2646.2.f.m.883.3		6	63.61	odd	6
2646.2.f.m.1765.3		6	7.5	odd	6
2646.2.h.o.361.1		6	7.3	odd	6
2646.2.h.o.667.1		6	63.34	odd	6
3024.2.q.g.2305.1		6	4.3	odd	2
3024.2.q.g.2881.1		6	252.151	odd	6
3024.2.t.h.289.3		6	36.7	odd	6
3024.2.t.h.1873.3		6	28.11	odd	6
7938.2.a.bv.1.1		3	63.23	odd	6
7938.2.a.bw.1.3		3	63.5	even	6
7938.2.a.bz.1.1		3	63.40	odd	6
7938.2.a.ca.1.3		3	63.58	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.59097 - 2.75564i) q^{5} +(-2.56238 - 0.658939i) q^{7} +1.00000 q^{8} +(-1.59097 - 2.75564i) q^{10} +(1.59097 - 2.75564i) q^{11} +(2.85185 - 4.93955i) q^{13} +(-2.56238 - 0.658939i) q^{14} +1.00000 q^{16} +(0.760877 + 1.31788i) q^{17} +(-0.641315 + 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(1.11956 + 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(2.85185 - 4.93955i) q^{26} +(-2.56238 - 0.658939i) q^{28} +(3.54063 + 6.13255i) q^{29} -9.42107 q^{31} +1.00000 q^{32} +(0.760877 + 1.31788i) q^{34} +(2.26088 + 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-0.641315 + 1.11079i) q^{38} +(-1.59097 - 2.75564i) q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(1.59097 - 2.75564i) q^{44} +(1.11956 + 1.93914i) q^{46} +5.82846 q^{47} +(6.13160 + 3.37690i) q^{49} +(-2.56238 + 4.43818i) q^{50} +(2.85185 - 4.93955i) q^{52} +(-1.02859 - 1.78157i) q^{53} -10.1248 q^{55} +(-2.56238 - 0.658939i) q^{56} +(3.54063 + 6.13255i) q^{58} +1.12476 q^{59} +3.12476 q^{61} -9.42107 q^{62} +1.00000 q^{64} -18.1488 q^{65} +10.9669 q^{67} +(0.760877 + 1.31788i) q^{68} +(2.26088 + 8.10936i) q^{70} -8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-0.641315 + 1.11079i) q^{76} +(-5.89248 + 6.01266i) q^{77} -4.13844 q^{79} +(-1.59097 - 2.75564i) q^{80} +(2.80150 - 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(3.41423 + 5.91362i) q^{86} +(1.59097 - 2.75564i) q^{88} +(-0.112725 + 0.195246i) q^{89} +(-10.5624 + 10.7778i) q^{91} +(1.11956 + 1.93914i) q^{92} +5.82846 q^{94} +4.08126 q^{95} +(7.42107 + 12.8537i) q^{97} +(6.13160 + 3.37690i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 2 q^{7} + 6 q^{8} - q^{10} + q^{11} + 8 q^{13} + 2 q^{14} + 6 q^{16} + 4 q^{17} - 3 q^{19} - q^{20} + q^{22} + 7 q^{23} + 2 q^{25} + 8 q^{26} + 2 q^{28} + 5 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 2 * q^7 + 6 * q^8 - q^10 + q^11 + 8 * q^13 + 2 * q^14 + 6 * q^16 + 4 * q^17 - 3 * q^19 - q^20 + q^22 + 7 * q^23 + 2 * q^25 + 8 * q^26 + 2 * q^28 + 5 * q^29 - 40 * q^31 + 6 * q^32 + 4 * q^34 + 13 * q^35 + 3 * q^37 - 3 * q^38 - q^40 - 6 * q^43 + q^44 + 7 * q^46 - 18 * q^47 + 12 * q^49 + 2 * q^50 + 8 * q^52 - 15 * q^53 - 26 * q^55 + 2 * q^56 + 5 * q^58 - 28 * q^59 - 16 * q^61 - 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 + 4 * q^68 + 13 * q^70 - 14 * q^71 + 19 * q^73 + 3 * q^74 - 3 * q^76 - 10 * q^77 - 10 * q^79 - q^80 - 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 + 9 * q^89 - 46 * q^91 + 7 * q^92 - 18 * q^94 - 8 * q^95 + 28 * q^97 + 12 * q^98

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