LMFDB - Embedded newform 378.2.h.c.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(289,378)]

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([4, 2]))

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

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

chi := DirichletCharacter("378.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.h (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	378.361
Dual form			378.2.h.c.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.18194 q^{5} +(0.710533 - 2.54856i) q^{7} +1.00000 q^{8} +(-1.59097 + 2.75564i) q^{10} -3.18194 q^{11} +(2.85185 - 4.93955i) q^{13} +(1.85185 + 1.88962i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.760877 - 1.31788i) q^{17} +(-0.641315 - 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} -2.23912 q^{23} +5.12476 q^{25} +(2.85185 + 4.93955i) q^{26} +(-2.56238 + 0.658939i) q^{28} +(3.54063 + 6.13255i) q^{29} +(4.71053 + 8.15888i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.760877 + 1.31788i) q^{34} +(2.26088 - 8.10936i) q^{35} +(0.500000 + 0.866025i) q^{37} +1.28263 q^{38} +3.18194 q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(1.59097 + 2.75564i) q^{44} +(1.11956 - 1.93914i) q^{46} +(-2.91423 + 5.04759i) q^{47} +(-5.99028 - 3.62167i) q^{49} +(-2.56238 + 4.43818i) q^{50} -5.70370 q^{52} +(-1.02859 + 1.78157i) q^{53} -10.1248 q^{55} +(0.710533 - 2.54856i) q^{56} -7.08126 q^{58} +(-0.562382 - 0.974074i) q^{59} +(-1.56238 + 2.70612i) q^{61} -9.42107 q^{62} +1.00000 q^{64} +(9.07442 - 15.7174i) q^{65} +(-5.48345 - 9.49761i) q^{67} -1.52175 q^{68} +(5.89248 + 6.01266i) q^{70} -8.69002 q^{71} +(-2.48345 + 4.30146i) q^{73} -1.00000 q^{74} +(-0.641315 + 1.11079i) q^{76} +(-2.26088 + 8.10936i) q^{77} +(2.06922 - 3.58399i) q^{79} +(-1.59097 + 2.75564i) q^{80} +(2.80150 + 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} -6.82846 q^{86} -3.18194 q^{88} +(-0.112725 - 0.195246i) q^{89} +(-10.5624 - 10.7778i) q^{91} +(1.11956 + 1.93914i) q^{92} +(-2.91423 - 5.04759i) q^{94} +(-2.04063 - 3.53447i) q^{95} +(7.42107 + 12.8537i) q^{97} +(6.13160 - 3.37690i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8} - q^{10} - 2 q^{11} + 8 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} - q^{20} + q^{22} - 14 q^{23} - 4 q^{25} + 8 q^{26} + 2 q^{28} + 5 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 2 * q^5 - 4 * q^7 + 6 * q^8 - q^10 - 2 * q^11 + 8 * q^13 + 2 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 - q^20 + q^22 - 14 * q^23 - 4 * q^25 + 8 * q^26 + 2 * q^28 + 5 * q^29 + 20 * q^31 - 3 * q^32 + 4 * q^34 + 13 * q^35 + 3 * q^37 + 6 * q^38 + 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 + 9 * q^47 - 12 * q^49 + 2 * q^50 - 16 * q^52 - 15 * q^53 - 26 * q^55 - 4 * q^56 - 10 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 - 8 * q^68 + 10 * q^70 - 14 * q^71 + 19 * q^73 - 6 * q^74 - 3 * q^76 - 13 * q^77 + 5 * q^79 - q^80 - 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 + 9 * q^89 - 46 * q^91 + 7 * q^92 + 9 * q^94 + 4 * q^95 + 28 * q^97 + 12 * q^98

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.18194			1.42301			0.711504	−	0.702682i	$-0.248014\pi$
$5$	3.18194			1.42301			0.711504	+	0.702682i	$0.248014\pi$
$6$		0			0
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.59097	+	2.75564i	−0.503109	+	0.871411i
$11$	−3.18194			−0.959392			−0.479696	−	0.877435i	$-0.659253\pi$
$11$	−3.18194			−0.959392			−0.479696	+	0.877435i	$0.659253\pi$
$12$		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	$-0.123752\pi$
$14$	1.85185	+	1.88962i	0.494927	+	0.505022i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.760877	−	1.31788i	0.184540	−	0.319632i	−0.758882	−	0.651229i	$-0.774254\pi$
$17$	0.760877	−	1.31788i	0.184540	−	0.319632i	0.943421	+	0.331596i	$0.107587\pi$
$18$		0			0
$19$	−0.641315	−	1.11079i	−0.147128	−	0.254833i	0.783037	−	0.621975i	$-0.213670\pi$
$19$	−0.641315	−	1.11079i	−0.147128	−	0.254833i	−0.930165	+	0.367142i	$0.880336\pi$
$20$	−1.59097	−	2.75564i	−0.355752	−	0.616181i
$21$		0			0
$22$	1.59097	−	2.75564i	0.339196	−	0.587505i
$23$	−2.23912			−0.466889			−0.233445	−	0.972370i	$-0.575000\pi$
$23$	−2.23912			−0.466889			−0.233445	+	0.972370i	$0.575000\pi$
$24$		0			0
$25$	5.12476			1.02495
$26$	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
$31$	4.71053	+	8.15888i	0.846037	+	1.46538i	0.884718	+	0.466127i	$0.154351\pi$
$31$	4.71053	+	8.15888i	0.846037	+	1.46538i	−0.0386810	+	0.999252i	$0.512316\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		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	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	1.28263			0.208070
$39$		0			0
$40$	3.18194			0.503109
$41$	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
$47$	−2.91423	+	5.04759i	−0.425084	+	0.736267i	−0.996428	−	0.0844432i	$-0.973089\pi$
$47$	−2.91423	+	5.04759i	−0.425084	+	0.736267i	0.571344	+	0.820711i	$0.306422\pi$
$48$		0			0
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$	−2.56238	+	4.43818i	−0.362375	+	0.627653i
$51$		0			0
$52$	−5.70370			−0.790960
$53$	−1.02859	+	1.78157i	−0.141288	+	0.244717i	−0.927982	−	0.372626i	$-0.878458\pi$
$53$	−1.02859	+	1.78157i	−0.141288	+	0.244717i	0.786694	+	0.617343i	$0.211791\pi$
$54$		0			0
$55$	−10.1248			−1.36522
$56$	0.710533	−	2.54856i	0.0949490	−	0.340565i
$57$		0			0
$58$	−7.08126			−0.929815
$59$	−0.562382	−	0.974074i	−0.0732159	−	0.126814i	0.827093	−	0.562065i	$-0.189993\pi$
$59$	−0.562382	−	0.974074i	−0.0732159	−	0.126814i	−0.900309	+	0.435251i	$0.856660\pi$
$60$		0			0
$61$	−1.56238	+	2.70612i	−0.200042	+	0.346484i	−0.948542	−	0.316652i	$-0.897441\pi$
$61$	−1.56238	+	2.70612i	−0.200042	+	0.346484i	0.748499	+	0.663135i	$0.230775\pi$
$62$	−9.42107			−1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	9.07442	−	15.7174i	1.12554	−	1.94950i
$66$		0			0
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	−0.977929	−	0.208938i	$-0.932999\pi$
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	0.308019	−	0.951380i	$-0.400334\pi$
$68$	−1.52175			−0.184540
$69$		0			0
$70$	5.89248	+	6.01266i	0.704286	+	0.718650i
$71$	−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	−0.973967	−	0.226689i	$-0.927210\pi$
$73$	−2.48345	+	4.30146i	−0.290666	+	0.503448i	0.683302	+	0.730136i	$0.260543\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	−0.641315	+	1.11079i	−0.0735639	+	0.127416i
$77$	−2.26088	+	8.10936i	−0.257651	+	0.924148i
$78$		0			0
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	−0.725827	−	0.687877i	$-0.758543\pi$
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	0.958633	+	0.284646i	$0.0918762\pi$
$80$	−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
$86$	−6.82846			−0.736332
$87$		0			0
$88$	−3.18194			−0.339196
$89$	−0.112725	−	0.195246i	−0.0119488	−	0.0206960i	0.859989	−	0.510312i	$-0.170470\pi$
$89$	−0.112725	−	0.195246i	−0.0119488	−	0.0206960i	−0.871938	+	0.489616i	$0.837137\pi$
$90$		0			0
$91$	−10.5624	−	10.7778i	−1.10724	−	1.12982i
$92$	1.11956	+	1.93914i	0.116722	+	0.202169i
$93$		0			0
$94$	−2.91423	−	5.04759i	−0.300580	−	0.520620i
$95$	−2.04063	−	3.53447i	−0.209364	−	0.362629i
$96$		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
$101$	−18.5893			−1.84971			−0.924854	−	0.380322i	$-0.875813\pi$
$101$	−18.5893			−1.84971			−0.924854	+	0.380322i	$0.875813\pi$
$102$		0			0
$103$	−0.282630			−0.0278484			−0.0139242	−	0.999903i	$-0.504432\pi$
$103$	−0.282630			−0.0278484			−0.0139242	+	0.999903i	$0.504432\pi$
$104$	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	−0.998277	−	0.0586780i	$-0.981311\pi$
$107$	−5.68878	−	9.85326i	−0.549955	−	0.952550i	0.448322	−	0.893872i	$-0.352022\pi$
$108$		0			0
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	−0.952256	−	0.305300i	$-0.901243\pi$
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	0.740526	+	0.672028i	$0.234577\pi$
$110$	5.06238	−	8.76830i	0.482679	−	0.836025i
$111$		0			0
$112$	1.85185	+	1.88962i	0.174983	+	0.178552i
$113$	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
$115$	−7.12476			−0.664388
$116$	3.54063	−	6.13255i	0.328739	−	0.569393i
$117$		0			0
$118$	1.12476			0.103543
$119$	−2.81806	−	2.87553i	−0.258331	−	0.263600i
$120$		0			0
$121$	−0.875237			−0.0795670
$122$	−1.56238	−	2.70612i	−0.141451	−	0.245001i
$123$		0			0
$124$	4.71053	−	8.15888i	0.423018	−	0.732689i
$125$	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	$0.149281\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	9.07442	+	15.7174i	0.795879	+	1.37850i
$131$	−6.36389			−0.556015			−0.278008	−	0.960579i	$-0.589674\pi$
$131$	−6.36389			−0.556015			−0.278008	+	0.960579i	$0.589674\pi$
$132$		0			0
$133$	−3.28659	+	0.845174i	−0.284983	+	0.0732859i
$134$	10.9669			0.947396
$135$		0			0
$136$	0.760877	−	1.31788i	0.0652446	−	0.113007i
$137$	−2.74145			−0.234218			−0.117109	−	0.993119i	$-0.537363\pi$
$137$	−2.74145			−0.234218			−0.117109	+	0.993119i	$0.537363\pi$
$138$		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	$0.276374\pi$
$140$	−8.15335	+	2.09671i	−0.689084	+	0.177204i
$141$		0			0
$142$	4.34501	−	7.52578i	0.364625	−	0.631550i
$143$	−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
$149$	23.2599			1.90553			0.952764	−	0.303712i	$-0.0982261\pi$
$149$	23.2599			1.90553			0.952764	+	0.303712i	$0.0982261\pi$
$150$		0			0
$151$	−8.12476			−0.661184			−0.330592	−	0.943774i	$-0.607248\pi$
$151$	−8.12476			−0.661184			−0.330592	+	0.943774i	$0.607248\pi$
$152$	−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
$157$	5.63160	+	9.75422i	0.449451	+	0.778471i	0.998350	−	0.0574170i	$-0.0182864\pi$
$157$	5.63160	+	9.75422i	0.449451	+	0.778471i	−0.548900	+	0.835888i	$0.684953\pi$
$158$	2.06922	+	3.58399i	0.164618	+	0.285127i
$159$		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	0.777492	−	0.628893i	$-0.216492\pi$
$163$	−1.99028	−	3.44727i	−0.155891	−	0.270011i	−0.933383	+	0.358881i	$0.883158\pi$
$164$	−5.60301			−0.437522
$165$		0			0
$166$	−8.06758			−0.626166
$167$	−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
$173$	1.27579	−	2.20974i	0.0969968	−	0.168003i	−0.813443	−	0.581644i	$-0.802410\pi$
$173$	1.27579	−	2.20974i	0.0969968	−	0.168003i	0.910440	+	0.413641i	$0.135743\pi$
$174$		0			0
$175$	3.64132	−	13.0608i	0.275258	−	0.987300i
$176$	1.59097	−	2.75564i	0.119924	−	0.207714i
$177$		0			0
$178$	0.225450			0.0168982
$179$	−3.51887	+	6.09487i	−0.263013	+	0.455552i	−0.967041	−	0.254620i	$-0.918050\pi$
$179$	−3.51887	+	6.09487i	−0.263013	+	0.455552i	0.704028	+	0.710172i	$0.251383\pi$
$180$		0			0
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$	14.6150	−	3.75839i	1.08334	−	0.278590i
$183$		0			0
$184$	−2.23912			−0.165070
$185$	1.59097	+	2.75564i	0.116971	+	0.202599i
$186$		0			0
$187$	−2.42107	+	4.19341i	−0.177046	+	0.306653i
$188$	5.82846			0.425084
$189$		0			0
$190$	4.08126			0.296085
$191$	0.990285	−	1.71522i	0.0716545	−	0.124109i	−0.827972	−	0.560769i	$-0.810505\pi$
$191$	0.990285	−	1.71522i	0.0716545	−	0.124109i	0.899627	+	0.436660i	$0.143839\pi$
$192$		0			0
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	0.936160	−	0.351574i	$-0.114353\pi$
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	−0.772552	+	0.634951i	$0.781020\pi$
$194$	−14.8421			−1.06560
$195$		0			0
$196$	−0.141315	+	6.99857i	−0.0100939	+	0.499898i
$197$	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	−0.561978	−	0.827152i	$-0.689959\pi$
$199$	6.14132	−	10.6371i	0.435346	−	0.754042i	0.997324	+	0.0731106i	$0.0232926\pi$
$200$	5.12476			0.362375
$201$		0			0
$202$	9.29467	−	16.0988i	0.653971	−	1.13271i
$203$	18.1449	−	4.66611i	1.27352	−	0.327497i
$204$		0			0
$205$	8.91423	−	15.4399i	0.622597	−	1.07837i
$206$	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	$0.972308\pi$
$212$	2.05718			0.141288
$213$		0			0
$214$	11.3776			0.777754
$215$	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
$220$	5.06238	+	8.76830i	0.341306	+	0.591159i
$221$	−4.33981	−	7.51677i	−0.291927	−	0.505633i
$222$		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
$227$	14.5081			0.962935			0.481468	−	0.876464i	$-0.340104\pi$
$227$	14.5081			0.962935			0.481468	+	0.876464i	$0.340104\pi$
$228$		0			0
$229$	10.2495			0.677308			0.338654	−	0.940911i	$-0.390028\pi$
$229$	10.2495			0.677308			0.338654	+	0.940911i	$0.390028\pi$
$230$	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	0.847773	−	0.530359i	$-0.177943\pi$
$233$	−0.540628	−	0.936396i	−0.0354177	−	0.0613453i	−0.883191	+	0.469014i	$0.844610\pi$
$234$		0			0
$235$	−9.27292	+	16.0612i	−0.604898	+	1.04771i
$236$	−0.562382	+	0.974074i	−0.0366079	+	0.0634068i
$237$		0			0
$238$	3.89931	−	1.00274i	0.252755	−	0.0649981i
$239$	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
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$	0.437618	−	0.757977i	0.0281312	−	0.0487246i
$243$		0			0
$244$	3.12476			0.200042
$245$	−19.0607	−	11.5239i	−1.21775	−	0.736238i
$246$		0			0
$247$	−7.31573			−0.465489
$248$	4.71053	+	8.15888i	0.299119	+	0.518090i
$249$		0			0
$250$	−0.198495	+	0.343803i	−0.0125539	+	0.0217440i
$251$	−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
$254$	−10.0527	+	17.4117i	−0.630760	+	1.09251i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.66019			−0.477830			−0.238915	−	0.971041i	$-0.576792\pi$
$257$	−7.66019			−0.477830			−0.238915	+	0.971041i	$0.576792\pi$
$258$		0			0
$259$	2.56238	−	0.658939i	0.159219	−	0.0409445i
$260$	−18.1488			−1.12554
$261$		0			0
$262$	3.18194	−	5.51129i	0.196581	−	0.340488i
$263$	3.09493			0.190842			0.0954208	−	0.995437i	$-0.469580\pi$
$263$	3.09493			0.190842			0.0954208	+	0.995437i	$0.469580\pi$
$264$		0			0
$265$	−3.27292	+	5.66886i	−0.201054	+	0.348235i
$266$	0.911351	−	3.26886i	0.0558785	−	0.200426i
$267$		0			0
$268$	−5.48345	+	9.49761i	−0.334955	+	0.580159i
$269$	13.4451	−	23.2877i	0.819765	−	1.41987i	−0.0860906	−	0.996287i	$-0.527437\pi$
$269$	13.4451	−	23.2877i	0.819765	−	1.41987i	0.905855	−	0.423587i	$-0.139229\pi$
$270$		0			0
$271$	−11.1082	−	19.2400i	−0.674776	−	1.16875i	−0.976534	−	0.215362i	$-0.930907\pi$
$271$	−11.1082	−	19.2400i	−0.674776	−	1.16875i	0.301759	−	0.953384i	$-0.402426\pi$
$272$	0.760877	+	1.31788i	0.0461349	+	0.0799080i
$273$		0			0
$274$	1.37072	−	2.37416i	0.0828084	−	0.143428i
$275$	−16.3067			−0.983331
$276$		0			0
$277$	−14.6375			−0.879482			−0.439741	−	0.898125i	$-0.644930\pi$
$277$	−14.6375			−0.879482			−0.439741	+	0.898125i	$0.644930\pi$
$278$	−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
$283$	13.0624	+	22.6247i	0.776478	+	1.34490i	0.933960	+	0.357377i	$0.116329\pi$
$283$	13.0624	+	22.6247i	0.776478	+	1.34490i	−0.157482	+	0.987522i	$0.550338\pi$
$284$	4.34501	+	7.52578i	0.257829	+	0.446573i
$285$		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
$290$	−22.5322			−1.32313
$291$		0			0
$292$	4.96690			0.290666
$293$	−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
$299$	−6.38564	+	11.0603i	−0.369291	+	0.639631i
$300$		0			0
$301$	17.4971	−	4.49954i	1.00852	−	0.259349i
$302$	4.06238	−	7.03625i	0.233764	−	0.404891i
$303$		0			0
$304$	1.28263			0.0735639
$305$	−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	$0.467861\pi$
$308$	8.15335	−	2.09671i	0.464580	−	0.119471i
$309$		0			0
$310$	−29.9773			−1.70260
$311$	0.851848	+	1.47544i	0.0483039	+	0.0836648i	0.889166	−	0.457584i	$-0.151285\pi$
$311$	0.851848	+	1.47544i	0.0483039	+	0.0836648i	−0.840863	+	0.541249i	$0.817952\pi$
$312$		0			0
$313$	1.42107	−	2.46136i	0.0803234	−	0.139124i	−0.823065	−	0.567947i	$-0.807738\pi$
$313$	1.42107	−	2.46136i	0.0803234	−	0.139124i	0.903389	+	0.428822i	$0.141071\pi$
$314$	−11.2632			−0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	−12.4601	+	21.5815i	−0.699827	+	1.21214i	0.268700	+	0.963224i	$0.413406\pi$
$317$	−12.4601	+	21.5815i	−0.699827	+	1.21214i	−0.968526	+	0.248911i	$0.919927\pi$
$318$		0			0
$319$	−11.2661	−	19.5134i	−0.630779	−	1.09254i
$320$	3.18194			0.177876
$321$		0			0
$322$	−4.14652	−	4.23109i	−0.231076	−	0.235789i
$323$	−1.95185			−0.108604
$324$		0			0
$325$	14.6150	−	25.3140i	0.810697	−	1.40417i
$326$	3.98057			0.220463
$327$		0			0
$328$	2.80150	−	4.85235i	0.154687	−	0.267926i
$329$	10.7934	+	11.0136i	0.595061	+	0.607198i
$330$		0			0
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	−0.750492	−	0.660879i	$-0.770184\pi$
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	0.947584	+	0.319506i	$0.103517\pi$
$332$	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	$0.963855\pi$
$338$	19.5322			1.06241
$339$		0			0
$340$	−4.84213			−0.262602
$341$	−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
$346$	1.27579	+	2.20974i	0.0685871	+	0.118796i
$347$	−1.05555	−	1.82826i	−0.0566646	−	0.0981460i	0.836302	−	0.548270i	$-0.184713\pi$
$347$	−1.05555	−	1.82826i	−0.0566646	−	0.0981460i	−0.892966	+	0.450124i	$0.851380\pi$
$348$		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
$353$	10.4887			0.558255			0.279127	−	0.960254i	$-0.409955\pi$
$353$	10.4887			0.558255			0.279127	+	0.960254i	$0.409955\pi$
$354$		0			0
$355$	−27.6512			−1.46757
$356$	−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	−0.875613	−	0.483013i	$-0.839542\pi$
$359$	−16.2209	−	28.0955i	−0.856108	−	1.48282i	0.0195047	−	0.999810i	$-0.493791\pi$
$360$		0			0
$361$	8.67743	−	15.0297i	0.456707	−	0.791039i
$362$	6.48345	−	11.2297i	0.340762	−	0.590218i
$363$		0			0
$364$	−4.05267	+	14.5362i	−0.212417	+	0.761904i
$365$	−7.90219	+	13.6870i	−0.413620	+	0.716410i
$366$		0			0
$367$	−18.1111			−0.945391			−0.472696	−	0.881226i	$-0.656719\pi$
$367$	−18.1111			−0.945391			−0.472696	+	0.881226i	$0.656719\pi$
$368$	1.11956	−	1.93914i	0.0583612	−	0.101085i
$369$		0			0
$370$	−3.18194			−0.165421
$371$	3.80959	+	3.88728i	0.197784	+	0.201818i
$372$		0			0
$373$	−11.6706			−0.604280			−0.302140	−	0.953263i	$-0.597701\pi$
$373$	−11.6706			−0.604280			−0.302140	+	0.953263i	$0.597701\pi$
$374$	−2.42107	−	4.19341i	−0.125190	−	0.216836i
$375$		0			0
$376$	−2.91423	+	5.04759i	−0.150290	+	0.260310i
$377$	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	$0.380565\pi$
$380$	−2.04063	+	3.53447i	−0.104682	+	0.181315i
$381$		0			0
$382$	0.990285	+	1.71522i	0.0506674	+	0.0877585i
$383$	1.64979			0.0843001			0.0421501	−	0.999111i	$-0.486579\pi$
$383$	1.64979			0.0843001			0.0421501	+	0.999111i	$0.486579\pi$
$384$		0			0
$385$	−7.19398	+	25.8035i	−0.366639	+	1.31507i
$386$	−4.54583			−0.231377
$387$		0			0
$388$	7.42107	−	12.8537i	0.376748	−	0.652546i
$389$	32.0676			1.62589			0.812946	−	0.582340i	$-0.197863\pi$
$389$	32.0676			1.62589			0.812946	+	0.582340i	$0.197863\pi$
$390$		0			0
$391$	−1.70370	+	2.95089i	−0.0861596	+	0.149233i
$392$	−5.99028	−	3.62167i	−0.302555	−	0.182922i
$393$		0			0
$394$	−10.9074	+	18.8922i	−0.549507	+	0.951773i
$395$	6.58414	−	11.4041i	0.331284	−	0.573800i
$396$		0			0
$397$	−18.9669	−	32.8516i	−0.951921	−	1.64878i	−0.741261	−	0.671217i	$-0.765772\pi$
$397$	−18.9669	−	32.8516i	−0.951921	−	1.64878i	−0.210660	−	0.977559i	$-0.567561\pi$
$398$	6.14132	+	10.6371i	0.307836	+	0.533188i
$399$		0			0
$400$	−2.56238	+	4.43818i	−0.128119	+	0.221909i
$401$	−10.6192			−0.530296			−0.265148	−	0.964208i	$-0.585421\pi$
$401$	−10.6192			−0.530296			−0.265148	+	0.964208i	$0.585421\pi$
$402$		0			0
$403$	53.7349			2.67673
$404$	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
$409$	−2.77292	−	4.80283i	−0.137112	−	0.237485i	0.789290	−	0.614020i	$-0.210449\pi$
$409$	−2.77292	−	4.80283i	−0.137112	−	0.237485i	−0.926402	+	0.376535i	$0.877115\pi$
$410$	8.91423	+	15.4399i	0.440242	+	0.762522i
$411$		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
$416$	−5.70370			−0.279647
$417$		0			0
$418$	−4.08126			−0.199621
$419$	−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
$425$	3.89931	−	6.75381i	0.189144	−	0.327608i
$426$		0			0
$427$	5.78659	+	5.90461i	0.280033	+	0.285744i
$428$	−5.68878	+	9.85326i	−0.274978	+	0.476275i
$429$		0			0
$430$	−21.7278			−1.04781
$431$	−16.5539	+	28.6722i	−0.797374	+	1.38109i	0.123947	+	0.992289i	$0.460445\pi$
$431$	−16.5539	+	28.6722i	−0.797374	+	1.38109i	−0.921321	+	0.388803i	$0.872889\pi$
$432$		0			0
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$	−6.69398	+	24.0101i	−0.321321	+	1.15252i
$435$		0			0
$436$	4.42107			0.211731
$437$	1.43598	+	2.48720i	0.0686924	+	0.118979i
$438$		0			0
$439$	4.41711	−	7.65066i	0.210817	−	0.365146i	−0.741153	−	0.671336i	$-0.765721\pi$
$439$	4.41711	−	7.65066i	0.210817	−	0.365146i	0.951970	+	0.306190i	$0.0990542\pi$
$440$	−10.1248			−0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	8.75924	−	15.1715i	0.416164	−	0.720817i	−0.579386	−	0.815053i	$-0.696708\pi$
$443$	8.75924	−	15.1715i	0.416164	−	0.720817i	0.995550	+	0.0942360i	$0.0300408\pi$
$444$		0			0
$445$	−0.358685	−	0.621261i	−0.0170033	−	0.0294506i
$446$	10.6569			0.504620
$447$		0			0
$448$	0.710533	−	2.54856i	0.0335695	−	0.120408i
$449$	−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
$452$	−3.21505			−0.151223
$453$		0			0
$454$	−7.25404	+	12.5644i	−0.340449	+	0.589675i
$455$	−33.6089	−	34.2944i	−1.57561	−	1.60775i
$456$		0			0
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	−0.195794	−	0.980645i	$-0.562728\pi$
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	0.947161	−	0.320760i	$-0.103938\pi$
$458$	−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	$-0.0824631\pi$
$464$	−7.08126			−0.328739
$465$		0			0
$466$	1.08126			0.0500882
$467$	7.98181	+	13.8249i	0.369354	+	0.639740i	0.989465	−	0.144774i	$-0.0462456\pi$
$467$	7.98181	+	13.8249i	0.369354	+	0.639740i	−0.620110	+	0.784515i	$0.712912\pi$
$468$		0			0
$469$	−28.1014	+	7.22651i	−1.29760	+	0.333689i
$470$	−9.27292	−	16.0612i	−0.427728	−	0.740846i
$471$		0			0
$472$	−0.562382	−	0.974074i	−0.0258857	−	0.0448354i
$473$	−10.8639	−	18.8168i	−0.499522	−	0.865198i
$474$		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
$479$	23.1729			1.05880			0.529399	−	0.848373i	$-0.322418\pi$
$479$	23.1729			1.05880			0.529399	+	0.848373i	$0.322418\pi$
$480$		0			0
$481$	5.70370			0.260066
$482$	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	−0.824766	−	0.565474i	$-0.808693\pi$
$487$	1.70658	−	2.95588i	0.0773323	−	0.133943i	0.902098	+	0.431531i	$0.142026\pi$
$488$	−1.56238	+	2.70612i	−0.0707257	+	0.122500i
$489$		0			0
$490$	19.5104	−	10.7451i	0.881390	−	0.485415i
$491$	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
$493$	10.7759			0.485323
$494$	3.65787	−	6.33561i	0.164575	−	0.285053i
$495$		0			0
$496$	−9.42107			−0.423018
$497$	−6.17455	+	22.1470i	−0.276966	+	0.993430i
$498$		0			0
$499$	41.1696			1.84301			0.921503	−	0.388371i	$-0.126962\pi$
$499$	41.1696			1.84301			0.921503	+	0.388371i	$0.126962\pi$
$500$	−0.198495	−	0.343803i	−0.00887697	−	0.0153754i
$501$		0			0
$502$	2.55555	−	4.42633i	0.114060	−	0.197557i
$503$	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
$506$	−3.56238	+	6.17023i	−0.158367	+	0.274300i
$507$		0			0
$508$	−10.0527	−	17.4117i	−0.446015	−	0.772521i
$509$	−12.7713			−0.566077			−0.283039	−	0.959109i	$-0.591342\pi$
$509$	−12.7713			−0.566077			−0.283039	+	0.959109i	$0.591342\pi$
$510$		0			0
$511$	9.19794	+	9.38554i	0.406893	+	0.415192i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.83009	−	6.63392i	0.168938	−	0.292610i
$515$	−0.899313			−0.0396285
$516$		0			0
$517$	9.27292	−	16.0612i	0.407822	−	0.706369i
$518$	−0.710533	+	2.54856i	−0.0312190	+	0.111977i
$519$		0			0
$520$	9.07442	−	15.7174i	0.397940	−	0.689252i
$521$	3.40615	−	5.89962i	0.149226	−	0.258467i	−0.781716	−	0.623635i	$-0.785655\pi$
$521$	3.40615	−	5.89962i	0.149226	−	0.258467i	0.930942	+	0.365168i	$0.118988\pi$
$522$		0			0
$523$	14.7535	+	25.5538i	0.645125	+	1.11739i	0.984273	+	0.176656i	$0.0565280\pi$
$523$	14.7535	+	25.5538i	0.645125	+	1.11739i	−0.339148	+	0.940733i	$0.610139\pi$
$524$	3.18194	+	5.51129i	0.139004	+	0.240762i
$525$		0			0
$526$	−1.54746	+	2.68029i	−0.0674727	+	0.116866i
$527$	14.3365			0.624510
$528$		0			0
$529$	−17.9863			−0.782014
$530$	−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
$535$	−18.1014	−	31.3525i	−0.782591	−	1.35549i
$536$	−5.48345	−	9.49761i	−0.236849	−	0.410234i
$537$		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	0.987135	+	0.159892i	$0.0511145\pi$
$541$	14.7008	+	25.4626i	0.632038	+	1.09472i	−0.355097	+	0.934829i	$0.615552\pi$
$542$	22.2164			0.954277
$543$		0			0
$544$	−1.52175			−0.0652446
$545$	−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
$551$	4.54132	−	7.86579i	0.193467	−	0.335094i
$552$		0			0
$553$	−7.66376	−	7.82007i	−0.325896	−	0.332543i
$554$	7.31875	−	12.6764i	0.310944	−	0.538570i
$555$		0			0
$556$	7.96690			0.337872
$557$	3.36909	−	5.83543i	0.142753	−	0.247255i	−0.785779	−	0.618507i	$-0.787738\pi$
$557$	3.36909	−	5.83543i	0.142753	−	0.247255i	0.928532	+	0.371252i	$0.121071\pi$
$558$		0			0
$559$	38.9475			1.64730
$560$	5.89248	+	6.01266i	0.249003	+	0.254081i
$561$		0			0
$562$	23.3984			0.987001
$563$	−0.729964	−	1.26433i	−0.0307643	−	0.0532853i	0.850233	−	0.526406i	$-0.176461\pi$
$563$	−0.729964	−	1.26433i	−0.0307643	−	0.0532853i	−0.880998	+	0.473121i	$0.843127\pi$
$564$		0			0
$565$	5.11505	−	8.85952i	0.215192	−	0.372723i
$566$	−26.1248			−1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	9.78263	−	16.9440i	0.410109	−	0.710330i	−0.584792	−	0.811183i	$-0.698824\pi$
$569$	9.78263	−	16.9440i	0.410109	−	0.710330i	0.994901	+	0.100853i	$0.0321573\pi$
$570$		0			0
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	0.998897	−	0.0469545i	$-0.0149516\pi$
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	−0.540112	+	0.841593i	$0.681618\pi$
$572$	18.1488			0.758841
$573$		0			0
$574$	14.3571	−	3.69204i	0.599252	−	0.154103i
$575$	−11.4750			−0.478540
$576$		0			0
$577$	12.3655	−	21.4177i	0.514783	−	0.891631i	−0.485069	−	0.874476i	$-0.661206\pi$
$577$	12.3655	−	21.4177i	0.514783	−	0.891631i	0.999853	−	0.0171554i	$-0.00546099\pi$
$578$	−14.6843			−0.610785
$579$		0			0
$580$	11.2661	−	19.5134i	0.467798	−	0.810251i
$581$	20.6722	−	5.31604i	0.857629	−	0.220547i
$582$		0			0
$583$	3.27292	−	5.66886i	0.135550	−	0.234780i
$584$	−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
$590$	3.57893			0.147342
$591$		0			0
$592$	−1.00000			−0.0410997
$593$	7.55391	+	13.0838i	0.310202	+	0.537285i	0.978406	−	0.206693i	$-0.0662700\pi$
$593$	7.55391	+	13.0838i	0.310202	+	0.537285i	−0.668204	+	0.743978i	$0.732937\pi$
$594$		0			0
$595$	−8.96690	−	9.14978i	−0.367607	−	0.375105i
$596$	−11.6300	−	20.1437i	−0.476382	−	0.825118i
$597$		0			0
$598$	−6.38564	−	11.0603i	−0.261128	−	0.452287i
$599$	−2.72708	−	4.72345i	−0.111426	−	0.192995i	0.804920	−	0.593384i	$-0.202208\pi$
$599$	−2.72708	−	4.72345i	−0.111426	−	0.192995i	−0.916345	+	0.400389i	$0.868875\pi$
$600$		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
$605$	−2.78495			−0.113224
$606$		0			0
$607$	6.67059			0.270751			0.135376	−	0.990794i	$-0.456776\pi$
$607$	6.67059			0.270751			0.135376	+	0.990794i	$0.456776\pi$
$608$	−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	−0.852495	−	0.522735i	$-0.824912\pi$
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	0.878950	+	0.476915i	$0.158245\pi$
$614$	−1.76608	+	3.05894i	−0.0712731	+	0.123449i
$615$		0			0
$616$	−2.26088	+	8.10936i	−0.0910933	+	0.326736i
$617$	−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
$619$	−16.4484			−0.661118			−0.330559	−	0.943785i	$-0.607237\pi$
$619$	−16.4484			−0.661118			−0.330559	+	0.943785i	$0.607237\pi$
$620$	14.9887	−	25.9611i	0.601959	−	1.04262i
$621$		0			0
$622$	−1.70370			−0.0683120
$623$	−0.577690	+	0.148558i	−0.0231446	+	0.00595184i
$624$		0			0
$625$	−24.3606			−0.974425
$626$	1.42107	+	2.46136i	0.0567972	+	0.0983757i
$627$		0			0
$628$	5.63160	−	9.75422i	0.224725	−	0.389236i
$629$	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	$0.703790\pi$
$632$	2.06922	−	3.58399i	0.0823091	−	0.142564i
$633$		0			0
$634$	−12.4601	−	21.5815i	−0.494852	−	0.857109i
$635$	63.9740			2.53873
$636$		0			0
$637$	−34.9728	+	19.2608i	−1.38567	+	0.763142i
$638$	22.5322			0.892057
$639$		0			0
$640$	−1.59097	+	2.75564i	−0.0628887	+	0.108926i
$641$	−27.8993			−1.10196			−0.550978	−	0.834520i	$-0.685745\pi$
$641$	−27.8993			−1.10196			−0.550978	+	0.834520i	$0.685745\pi$
$642$		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	$-0.0233243\pi$
$644$	5.73749	−	1.47544i	0.226089	−	0.0581407i
$645$		0			0
$646$	0.975923	−	1.69035i	0.0383972	−	0.0665059i
$647$	−8.35705	+	14.4748i	−0.328550	+	0.569065i	−0.982224	−	0.187711i	$-0.939893\pi$
$647$	−8.35705	+	14.4748i	−0.328550	+	0.569065i	0.653675	+	0.756776i	$0.273226\pi$
$648$		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
$653$	−38.1650			−1.49351			−0.746756	−	0.665098i	$-0.768390\pi$
$653$	−38.1650			−1.49351			−0.746756	+	0.665098i	$0.768390\pi$
$654$		0			0
$655$	−20.2495			−0.791214
$656$	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
$661$	10.0419	+	17.3930i	0.390584	+	0.676511i	0.992527	−	0.122028i	$-0.0389399\pi$
$661$	10.0419	+	17.3930i	0.390584	+	0.676511i	−0.601943	+	0.798539i	$0.705607\pi$
$662$	3.58577	+	6.21074i	0.139365	+	0.241387i
$663$		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
$668$	5.23912			0.202708
$669$		0			0
$670$	34.8960			1.34815
$671$	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
$677$	−0.358685	+	0.621261i	−0.0137854	+	0.0238770i	−0.872836	−	0.488014i	$-0.837721\pi$
$677$	−0.358685	+	0.621261i	−0.0137854	+	0.0238770i	0.859050	+	0.511891i	$0.171055\pi$
$678$		0			0
$679$	38.0312	−	9.78005i	1.45950	−	0.375324i
$680$	2.42107	−	4.19341i	0.0928437	−	0.160810i
$681$		0			0
$682$	29.9773			1.14789
$683$	10.5270	−	18.2332i	0.402803	−	0.697675i	−0.591260	−	0.806481i	$-0.701369\pi$
$683$	10.5270	−	18.2332i	0.402803	−	0.697675i	0.994063	+	0.108806i	$0.0347027\pi$
$684$		0			0
$685$	−8.72313			−0.333294
$686$	−4.24953	−	18.0261i	−0.162248	−	0.688241i
$687$		0			0
$688$	−6.82846			−0.260333
$689$	5.86677	+	10.1615i	0.223506	+	0.387124i
$690$		0			0
$691$	−2.92395	+	5.06442i	−0.111232	+	0.192660i	−0.916267	−	0.400567i	$-0.868813\pi$
$691$	−2.92395	+	5.06442i	−0.111232	+	0.192660i	0.805035	+	0.593227i	$0.202146\pi$
$692$	−2.55159			−0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	−12.6751	+	21.9539i	−0.480794	+	0.832760i
$696$		0			0
$697$	−4.26320	−	7.38408i	−0.161480	−	0.279692i
$698$	−36.2164			−1.37081
$699$		0			0
$700$	−13.1316	+	3.37690i	−0.496328	+	0.127635i
$701$	−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
$704$	−3.18194			−0.119924
$705$		0			0
$706$	−5.24433	+	9.08344i	−0.197373	+	0.341860i
$707$	−13.2083	+	47.3760i	−0.496751	+	1.78176i
$708$		0			0
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	0.0916356	+	0.995793i	$0.470790\pi$
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	−0.908200	+	0.418538i	$0.862543\pi$
$710$	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
$716$	7.03775			0.263013
$717$		0			0
$718$	32.4419			1.21072
$719$	−25.4412	−	44.0654i	−0.948796	−	1.64336i	−0.747966	−	0.663737i	$-0.768969\pi$
$719$	−25.4412	−	44.0654i	−0.948796	−	1.64336i	−0.200830	−	0.979626i	$-0.564364\pi$
$720$		0			0
$721$	−0.200818	+	0.720299i	−0.00747886	+	0.0268253i
$722$	8.67743	+	15.0297i	0.322941	+	0.559349i
$723$		0			0
$724$	6.48345	+	11.2297i	0.240955	+	0.417347i
$725$	18.1449	+	31.4279i	0.673884	+	1.16720i
$726$		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
$731$	10.3912			0.384334
$732$		0			0
$733$	−46.1696			−1.70531			−0.852657	−	0.522470i	$-0.825011\pi$
$733$	−46.1696			−1.70531			−0.852657	+	0.522470i	$0.825011\pi$
$734$	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	−0.908276	−	0.418371i	$-0.862601\pi$
$739$	−2.49604	+	4.32327i	−0.0918184	+	0.159034i	0.816458	+	0.577405i	$0.195935\pi$
$740$	1.59097	−	2.75564i	0.0584853	−	0.101299i
$741$		0			0
$742$	−5.27128	+	1.35556i	−0.193515	+	0.0497640i
$743$	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
$745$	74.0118			2.71158
$746$	5.83530	−	10.1070i	0.213645	−	0.370045i
$747$		0			0
$748$	4.84213			0.177046
$749$	−29.1537	+	7.49711i	−1.06525	+	0.273939i
$750$		0			0
$751$	3.29630			0.120284			0.0601419	−	0.998190i	$-0.480845\pi$
$751$	3.29630			0.120284			0.0601419	+	0.998190i	$0.480845\pi$
$752$	−2.91423	−	5.04759i	−0.106271	−	0.184067i
$753$		0			0
$754$	−20.1947	+	34.9782i	−0.735447	+	1.27383i
$755$	−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	$0.558984\pi$
$758$	−7.13448	+	12.3573i	−0.259136	+	0.448837i
$759$		0			0
$760$	−2.04063	−	3.53447i	−0.0740214	−	0.128209i
$761$	−14.0676			−0.509950			−0.254975	−	0.966948i	$-0.582067\pi$
$761$	−14.0676			−0.509950			−0.254975	+	0.966948i	$0.582067\pi$
$762$		0			0
$763$	8.18715	+	8.35413i	0.296395	+	0.302440i
$764$	−1.98057			−0.0716545
$765$		0			0
$766$	−0.824893	+	1.42876i	−0.0298046	+	0.0516231i
$767$	−6.41531			−0.231643
$768$		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	$0.0324918\pi$
$770$	−18.7495	−	19.1319i	−0.675686	−	0.689467i
$771$		0			0
$772$	2.27292	−	3.93680i	0.0818040	−	0.141689i
$773$	−0.327772	+	0.567717i	−0.0117891	+	0.0204194i	−0.871860	−	0.489756i	$-0.837086\pi$
$773$	−0.327772	+	0.567717i	−0.0117891	+	0.0204194i	0.860071	+	0.510175i	$0.170419\pi$
$774$		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
$779$	−7.18659			−0.257486
$780$		0			0
$781$	27.6512			0.989436
$782$	−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
$787$	−0.270036	−	0.467717i	−0.00962576	−	0.0166723i	0.861172	−	0.508313i	$-0.169731\pi$
$787$	−0.270036	−	0.467717i	−0.00962576	−	0.0166723i	−0.870798	+	0.491641i	$0.836397\pi$
$788$	−10.9074	−	18.8922i	−0.388560	−	0.673005i
$789$		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
$794$	37.9338			1.34622
$795$		0			0
$796$	−12.2826			−0.435346
$797$	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
$803$	7.90219	−	13.6870i	0.278862	−	0.483004i
$804$		0			0
$805$	−5.06238	+	18.1579i	−0.178426	+	0.639981i
$806$	−26.8675	+	46.5358i	−0.946366	+	1.63915i
$807$		0			0
$808$	−18.5893			−0.653971
$809$	14.5865	−	25.2645i	0.512833	−	0.888252i	−0.487057	−	0.873370i	$-0.661929\pi$
$809$	14.5865	−	25.2645i	0.512833	−	0.888252i	0.999889	−	0.0148817i	$-0.00473717\pi$
$810$		0			0
$811$	−15.4290			−0.541785			−0.270892	−	0.962610i	$-0.587319\pi$
$811$	−15.4290			−0.541785			−0.270892	+	0.962610i	$0.587319\pi$
$812$	−13.1134	−	13.3809i	−0.460191	−	0.469577i
$813$		0			0
$814$	3.18194			0.111527
$815$	−6.33297	−	10.9690i	−0.221834	−	0.384228i
$816$		0			0
$817$	4.37919	−	7.58499i	0.153209	−	0.265365i
$818$	5.54583			0.193905
$819$		0			0
$820$	−17.8285			−0.622597
$821$	4.24364	−	7.35019i	0.148104	−	0.256524i	−0.782423	−	0.622748i	$-0.786016\pi$
$821$	4.24364	−	7.35019i	0.148104	−	0.256524i	0.930527	+	0.366224i	$0.119350\pi$
$822$		0			0
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	−0.999966	−	0.00825976i	$-0.997371\pi$
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	0.492830	−	0.870126i	$-0.335963\pi$
$824$	−0.282630			−0.00984589
$825$		0			0
$826$	0.799182	−	2.86652i	0.0278071	−	0.0997391i
$827$	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	−0.806988	−	0.590568i	$-0.798904\pi$
$829$	3.10821	−	5.38358i	0.107953	−	0.186979i	0.914941	+	0.403588i	$0.132237\pi$
$830$	−25.6706			−0.891039
$831$		0			0
$832$	2.85185	−	4.93955i	0.0988701	−	0.171248i
$833$	−9.33078	+	5.13882i	−0.323292	+	0.178049i
$834$		0			0
$835$	−8.33530	+	14.4372i	−0.288455	+	0.499618i
$836$	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
$842$	6.84213			0.235795
$843$		0			0
$844$	16.6569			0.573355
$845$	−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
$850$	3.89931	+	6.75381i	0.133745	+	0.231654i
$851$	−1.11956	−	1.93914i	−0.0383781	−	0.0664728i
$852$		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
$857$	36.8435			1.25855			0.629275	−	0.777183i	$-0.283352\pi$
$857$	36.8435			1.25855			0.629275	+	0.777183i	$0.283352\pi$
$858$		0			0
$859$	−17.6375			−0.601783			−0.300892	−	0.953658i	$-0.597284\pi$
$859$	−17.6375			−0.601783			−0.300892	+	0.953658i	$0.597284\pi$
$860$	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	0.872428	−	0.488743i	$-0.162544\pi$
$863$	0.380438	+	0.658939i	0.0129503	+	0.0224305i	−0.859478	+	0.511173i	$0.829211\pi$
$864$		0			0
$865$	4.05950	−	7.03127i	0.138027	−	0.239070i
$866$	6.05555	−	10.4885i	0.205776	−	0.356414i
$867$		0			0
$868$	−17.4464	−	17.8022i	−0.592169	−	0.604247i
$869$	−6.58414	+	11.4041i	−0.223351	+	0.386856i
$870$		0			0
$871$	−62.5519			−2.11949
$872$	−2.21053	+	3.82876i	−0.0748581	+	0.129658i
$873$		0			0
$874$	−2.87197			−0.0971457
$875$	0.282075	−	1.01175i	0.00953586	−	0.0342035i
$876$		0			0
$877$	−41.4991			−1.40132			−0.700662	−	0.713494i	$-0.747112\pi$
$877$	−41.4991			−1.40132			−0.700662	+	0.713494i	$0.747112\pi$
$878$	4.41711	+	7.65066i	0.149070	+	0.258197i
$879$		0			0
$880$	5.06238	−	8.76830i	0.170653	−	0.295579i
$881$	−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	$0.295437\pi$
$884$	−4.33981	+	7.51677i	−0.145964	+	0.252816i
$885$		0			0
$886$	8.75924	+	15.1715i	0.294272	+	0.509695i
$887$	37.1100			1.24603			0.623016	−	0.782209i	$-0.285907\pi$
$887$	37.1100			1.24603			0.623016	+	0.782209i	$0.285907\pi$
$888$		0			0
$889$	14.2855	−	51.2396i	0.479121	−	1.71852i
$890$	0.717370			0.0240463
$891$		0			0
$892$	−5.32846	+	9.22916i	−0.178410	+	0.309015i
$893$	7.47576			0.250167
$894$		0			0
$895$	−11.1969	+	19.3935i	−0.374270	+	0.648254i
$896$	1.85185	+	1.88962i	0.0618659	+	0.0631277i
$897$		0			0
$898$	15.6150	−	27.0461i	0.521081	−	0.902539i
$899$	−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
$905$	−41.2599			−1.37153
$906$		0			0
$907$	−48.1502			−1.59880			−0.799401	−	0.600798i	$-0.794850\pi$
$907$	−48.1502			−1.59880			−0.799401	+	0.600798i	$0.794850\pi$
$908$	−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
$913$	−12.8353	−	22.2314i	−0.424786	−	0.735751i
$914$	16.0624	+	27.8209i	0.531296	+	0.920232i
$915$		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	−0.878224	−	0.478250i	$-0.841271\pi$
$919$	−25.8675	−	44.8037i	−0.853289	−	1.47794i	0.0249351	−	0.999689i	$-0.492062\pi$
$920$	−7.12476			−0.234896
$921$		0			0
$922$	2.46457			0.0811664
$923$	−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
$929$	−25.4142	+	44.0187i	−0.833814	+	1.44421i	0.0611787	+	0.998127i	$0.480514\pi$
$929$	−25.4142	+	44.0187i	−0.833814	+	1.44421i	−0.894993	+	0.446081i	$0.852819\pi$
$930$		0			0
$931$	−0.181255	+	8.97658i	−0.00594039	+	0.294196i
$932$	−0.540628	+	0.936396i	−0.0177089	+	0.0306727i
$933$		0			0
$934$	−15.9636			−0.522346
$935$	−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	$0.486759\pi$
$938$	7.79235	−	27.9498i	0.254429	−	0.912592i
$939$		0			0
$940$	18.5458			0.604898
$941$	0.578933	+	1.00274i	0.0188727	+	0.0326885i	0.875308	−	0.483567i	$-0.160659\pi$
$941$	0.578933	+	1.00274i	0.0188727	+	0.0326885i	−0.856435	+	0.516255i	$0.827326\pi$
$942$		0			0
$943$	−6.27292	+	10.8650i	−0.204274	+	0.353813i
$944$	1.12476			0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	4.90739	−	8.49985i	0.159469	−	0.276208i	−0.775208	−	0.631706i	$-0.782355\pi$
$947$	4.90739	−	8.49985i	0.159469	−	0.276208i	0.934677	+	0.355497i	$0.115689\pi$
$948$		0			0
$949$	14.1648	+	24.5342i	0.459810	+	0.796414i
$950$	6.57318			0.213262
$951$		0			0
$952$	−2.81806	−	2.87553i	−0.0913337	−	0.0931966i
$953$	−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
$956$	−12.3204			−0.398470
$957$		0			0
$958$	−11.5865	+	20.0683i	−0.374341	+	0.648378i
$959$	−1.94789	+	6.98673i	−0.0629006	+	0.225613i
$960$		0			0
$961$	−28.8782	+	50.0186i	−0.931556	+	1.61350i
$962$	−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	$0.0128999\pi$
$968$	−0.875237			−0.0281312
$969$		0			0
$970$	−47.2268			−1.51636
$971$	−2.66827	−	4.62158i	−0.0856289	−	0.148314i	0.820030	−	0.572320i	$-0.193957\pi$
$971$	−2.66827	−	4.62158i	−0.0856289	−	0.148314i	−0.905659	+	0.424007i	$0.860623\pi$
$972$		0			0
$973$	14.7535	+	15.0544i	0.472975	+	0.482622i
$974$	1.70658	+	2.95588i	0.0546822	+	0.0947124i
$975$		0			0
$976$	−1.56238	−	2.70612i	−0.0500106	−	0.0866209i
$977$	−24.0361	−	41.6318i	−0.768983	−	1.33192i	−0.938115	−	0.346325i	$-0.887429\pi$
$977$	−24.0361	−	41.6318i	−0.768983	−	1.33192i	0.169131	−	0.985594i	$-0.445904\pi$
$978$		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
$983$	−29.4627			−0.939714			−0.469857	−	0.882743i	$-0.655694\pi$
$983$	−29.4627			−0.939714			−0.469857	+	0.882743i	$0.655694\pi$
$984$		0			0
$985$	69.4134			2.21170
$986$	−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	−0.510280	−	0.860008i	$-0.670458\pi$
$991$	15.4142	−	26.6982i	0.489649	−	0.848097i	0.999929	+	0.0119112i	$0.00379153\pi$
$992$	4.71053	−	8.15888i	0.149560	−	0.259045i
$993$		0			0
$994$	−16.0926	−	16.4208i	−0.510426	−	0.520837i
$995$	19.5413	−	33.8466i	0.619501	−	1.07301i
$996$		0			0
$997$	5.54583			0.175638			0.0878191	−	0.996136i	$-0.472010\pi$
$997$	5.54583			0.175638			0.0878191	+	0.996136i	$0.472010\pi$
$998$	−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.h.c.361.3		6
3.2	odd	2		126.2.h.d.67.1	yes	6
4.3	odd	2		3024.2.t.h.1873.3		6
7.2	even	3		378.2.e.d.37.1		6
7.3	odd	6		2646.2.f.m.1765.3		6
7.4	even	3		2646.2.f.l.1765.1		6
7.5	odd	6		2646.2.e.p.1549.3		6
7.6	odd	2		2646.2.h.o.361.1		6
9.2	odd	6		126.2.e.c.25.3	✓	6
9.4	even	3		1134.2.g.l.487.1		6
9.5	odd	6		1134.2.g.m.487.3		6
9.7	even	3		378.2.e.d.235.1		6
12.11	even	2		1008.2.t.h.193.3		6
21.2	odd	6		126.2.e.c.121.3	yes	6
21.5	even	6		882.2.e.o.373.1		6
21.11	odd	6		882.2.f.n.589.2		6
21.17	even	6		882.2.f.o.589.2		6
21.20	even	2		882.2.h.p.67.3		6
28.23	odd	6		3024.2.q.g.2305.1		6
36.7	odd	6		3024.2.q.g.2881.1		6
36.11	even	6		1008.2.q.g.529.1		6
63.2	odd	6		126.2.h.d.79.1	yes	6
63.4	even	3		7938.2.a.ca.1.3		3
63.11	odd	6		882.2.f.n.295.2		6
63.16	even	3	inner	378.2.h.c.289.3		6
63.20	even	6		882.2.e.o.655.1		6
63.23	odd	6		1134.2.g.m.163.3		6
63.25	even	3		2646.2.f.l.883.1		6
63.31	odd	6		7938.2.a.bz.1.1		3
63.32	odd	6		7938.2.a.bv.1.1		3
63.34	odd	6		2646.2.e.p.2125.3		6
63.38	even	6		882.2.f.o.295.2		6
63.47	even	6		882.2.h.p.79.3		6
63.52	odd	6		2646.2.f.m.883.3		6
63.58	even	3		1134.2.g.l.163.1		6
63.59	even	6		7938.2.a.bw.1.3		3
63.61	odd	6		2646.2.h.o.667.1		6
84.23	even	6		1008.2.q.g.625.1		6
252.79	odd	6		3024.2.t.h.289.3		6
252.191	even	6		1008.2.t.h.961.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	9.2	odd	6
126.2.e.c.121.3	yes	6	21.2	odd	6
126.2.h.d.67.1	yes	6	3.2	odd	2
126.2.h.d.79.1	yes	6	63.2	odd	6
378.2.e.d.37.1		6	7.2	even	3
378.2.e.d.235.1		6	9.7	even	3
378.2.h.c.289.3		6	63.16	even	3	inner
378.2.h.c.361.3		6	1.1	even	1	trivial
882.2.e.o.373.1		6	21.5	even	6
882.2.e.o.655.1		6	63.20	even	6
882.2.f.n.295.2		6	63.11	odd	6
882.2.f.n.589.2		6	21.11	odd	6
882.2.f.o.295.2		6	63.38	even	6
882.2.f.o.589.2		6	21.17	even	6
882.2.h.p.67.3		6	21.20	even	2
882.2.h.p.79.3		6	63.47	even	6
1008.2.q.g.529.1		6	36.11	even	6
1008.2.q.g.625.1		6	84.23	even	6
1008.2.t.h.193.3		6	12.11	even	2
1008.2.t.h.961.3		6	252.191	even	6
1134.2.g.l.163.1		6	63.58	even	3
1134.2.g.l.487.1		6	9.4	even	3
1134.2.g.m.163.3		6	63.23	odd	6
1134.2.g.m.487.3		6	9.5	odd	6
2646.2.e.p.1549.3		6	7.5	odd	6
2646.2.e.p.2125.3		6	63.34	odd	6
2646.2.f.l.883.1		6	63.25	even	3
2646.2.f.l.1765.1		6	7.4	even	3
2646.2.f.m.883.3		6	63.52	odd	6
2646.2.f.m.1765.3		6	7.3	odd	6
2646.2.h.o.361.1		6	7.6	odd	2
2646.2.h.o.667.1		6	63.61	odd	6
3024.2.q.g.2305.1		6	28.23	odd	6
3024.2.q.g.2881.1		6	36.7	odd	6
3024.2.t.h.289.3		6	252.79	odd	6
3024.2.t.h.1873.3		6	4.3	odd	2
7938.2.a.bv.1.1		3	63.32	odd	6
7938.2.a.bw.1.3		3	63.59	even	6
7938.2.a.bz.1.1		3	63.31	odd	6
7938.2.a.ca.1.3		3	63.4	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.18194 q^{5} +(0.710533 - 2.54856i) q^{7} +1.00000 q^{8} +(-1.59097 + 2.75564i) q^{10} -3.18194 q^{11} +(2.85185 - 4.93955i) q^{13} +(1.85185 + 1.88962i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.760877 - 1.31788i) q^{17} +(-0.641315 - 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} -2.23912 q^{23} +5.12476 q^{25} +(2.85185 + 4.93955i) q^{26} +(-2.56238 + 0.658939i) q^{28} +(3.54063 + 6.13255i) q^{29} +(4.71053 + 8.15888i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.760877 + 1.31788i) q^{34} +(2.26088 - 8.10936i) q^{35} +(0.500000 + 0.866025i) q^{37} +1.28263 q^{38} +3.18194 q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(1.59097 + 2.75564i) q^{44} +(1.11956 - 1.93914i) q^{46} +(-2.91423 + 5.04759i) q^{47} +(-5.99028 - 3.62167i) q^{49} +(-2.56238 + 4.43818i) q^{50} -5.70370 q^{52} +(-1.02859 + 1.78157i) q^{53} -10.1248 q^{55} +(0.710533 - 2.54856i) q^{56} -7.08126 q^{58} +(-0.562382 - 0.974074i) q^{59} +(-1.56238 + 2.70612i) q^{61} -9.42107 q^{62} +1.00000 q^{64} +(9.07442 - 15.7174i) q^{65} +(-5.48345 - 9.49761i) q^{67} -1.52175 q^{68} +(5.89248 + 6.01266i) q^{70} -8.69002 q^{71} +(-2.48345 + 4.30146i) q^{73} -1.00000 q^{74} +(-0.641315 + 1.11079i) q^{76} +(-2.26088 + 8.10936i) q^{77} +(2.06922 - 3.58399i) q^{79} +(-1.59097 + 2.75564i) q^{80} +(2.80150 + 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} -6.82846 q^{86} -3.18194 q^{88} +(-0.112725 - 0.195246i) q^{89} +(-10.5624 - 10.7778i) q^{91} +(1.11956 + 1.93914i) q^{92} +(-2.91423 - 5.04759i) q^{94} +(-2.04063 - 3.53447i) q^{95} +(7.42107 + 12.8537i) q^{97} +(6.13160 - 3.37690i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 2 q^{5} - 4 q^{7} + 6 q^{8} - q^{10} - 2 q^{11} + 8 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} - q^{20} + q^{22} - 14 q^{23} - 4 q^{25} + 8 q^{26} + 2 q^{28} + 5 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 2 * q^5 - 4 * q^7 + 6 * q^8 - q^10 - 2 * q^11 + 8 * q^13 + 2 * q^14 - 3 * q^16 + 4 * q^17 - 3 * q^19 - q^20 + q^22 - 14 * q^23 - 4 * q^25 + 8 * q^26 + 2 * q^28 + 5 * q^29 + 20 * q^31 - 3 * q^32 + 4 * q^34 + 13 * q^35 + 3 * q^37 + 6 * q^38 + 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 + 9 * q^47 - 12 * q^49 + 2 * q^50 - 16 * q^52 - 15 * q^53 - 26 * q^55 - 4 * q^56 - 10 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 - 8 * q^68 + 10 * q^70 - 14 * q^71 + 19 * q^73 - 6 * q^74 - 3 * q^76 - 13 * q^77 + 5 * q^79 - q^80 - 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 + 9 * q^89 - 46 * q^91 + 7 * q^92 + 9 * q^94 + 4 * q^95 + 28 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more