LMFDB - Embedded newform 756.2.bx.a.41.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.6
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36115 - 1.07111i) q^{3} +(-2.64973 - 2.22338i) q^{5} +(0.252743 - 2.63365i) q^{7} +(0.705464 + 2.91587i) q^{9} +O(q^{10})$	\(q+(-1.36115 - 1.07111i) q^{3} +(-2.64973 - 2.22338i) q^{5} +(0.252743 - 2.63365i) q^{7} +(0.705464 + 2.91587i) q^{9} +(-2.03215 - 2.42182i) q^{11} +(-0.556467 - 0.0981201i) q^{13} +(1.22520 + 5.86450i) q^{15} +(2.06648 - 3.57924i) q^{17} +(-3.53576 + 2.04137i) q^{19} +(-3.16494 + 3.31408i) q^{21} +(-0.946495 - 2.60047i) q^{23} +(1.20937 + 6.85868i) q^{25} +(2.16297 - 4.72457i) q^{27} +(2.95261 - 0.520625i) q^{29} +(3.68626 + 10.1279i) q^{31} +(0.172035 + 5.47311i) q^{33} +(-6.52532 + 6.41651i) q^{35} +(-4.53685 + 7.85806i) q^{37} +(0.652338 + 0.729591i) q^{39} +(-1.54293 + 8.75041i) q^{41} +(6.19754 - 5.20035i) q^{43} +(4.61382 - 9.29479i) q^{45} +(-8.99408 - 3.27358i) q^{47} +(-6.87224 - 1.33128i) q^{49} +(-6.64653 + 2.65847i) q^{51} +5.85691i q^{53} +10.9354i q^{55} +(6.99922 + 1.00856i) q^{57} +(-5.73216 - 4.80985i) q^{59} +(1.66114 - 4.56395i) q^{61} +(7.85770 - 1.12098i) q^{63} +(1.25633 + 1.49723i) q^{65} +(0.725278 - 4.11326i) q^{67} +(-1.49706 + 4.55343i) q^{69} +(6.30324 + 3.63918i) q^{71} +(-5.79615 + 3.34641i) q^{73} +(5.70024 - 10.6311i) q^{75} +(-6.89184 + 4.73987i) q^{77} +(-0.410711 - 2.32926i) q^{79} +(-8.00464 + 4.11409i) q^{81} +(-2.32844 - 13.2053i) q^{83} +(-13.4336 + 4.88944i) q^{85} +(-4.57660 - 2.45391i) q^{87} +(-2.95877 - 5.12473i) q^{89} +(-0.399057 + 1.44074i) q^{91} +(5.83051 - 17.7340i) q^{93} +(13.9075 + 2.45227i) q^{95} +(6.65243 + 7.92806i) q^{97} +(5.62812 - 7.63400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.36115	−	1.07111i	−0.785861	−	0.618403i
$3$	−1.36115	−	1.07111i	−0.785861	−	0.618403i
$4$		0			0
$5$	−2.64973	−	2.22338i	−1.18499	−	0.994328i	−0.999933	−	0.0116007i	$-0.996307\pi$
$5$	−2.64973	−	2.22338i	−1.18499	−	0.994328i	−0.185061	−	0.982727i	$-0.559248\pi$
$6$		0			0
$7$	0.252743	−	2.63365i	0.0955280	−	0.995427i
$7$	0.252743	−	2.63365i	0.0955280	−	0.995427i
$8$		0			0
$9$	0.705464	+	2.91587i	0.235155	+	0.971958i
$10$		0			0
$11$	−2.03215	−	2.42182i	−0.612716	−	0.730206i	0.367084	−	0.930188i	$-0.380356\pi$
$11$	−2.03215	−	2.42182i	−0.612716	−	0.730206i	−0.979800	+	0.199982i	$0.935912\pi$
$12$		0			0
$13$	−0.556467	−	0.0981201i	−0.154336	−	0.0272136i	0.0959462	−	0.995387i	$-0.469412\pi$
$13$	−0.556467	−	0.0981201i	−0.154336	−	0.0272136i	−0.250282	+	0.968173i	$0.580523\pi$
$14$		0			0
$15$	1.22520	+	5.86450i	0.316345	+	1.51421i
$16$		0			0
$17$	2.06648	−	3.57924i	0.501194	−	0.868093i	−0.498805	−	0.866714i	$-0.666228\pi$
$17$	2.06648	−	3.57924i	0.501194	−	0.868093i	0.999999	−	0.00137926i	$-0.000439033\pi$
$18$		0			0
$19$	−3.53576	+	2.04137i	−0.811158	+	0.468322i	−0.847358	−	0.531022i	$-0.821808\pi$
$19$	−3.53576	+	2.04137i	−0.811158	+	0.468322i	0.0361996	+	0.999345i	$0.488475\pi$
$20$		0			0
$21$	−3.16494	+	3.31408i	−0.690647	+	0.723192i
$22$		0			0
$23$	−0.946495	−	2.60047i	−0.197358	−	0.542236i	0.801053	−	0.598594i	$-0.204274\pi$
$23$	−0.946495	−	2.60047i	−0.197358	−	0.542236i	−0.998411	+	0.0563575i	$0.982051\pi$
$24$		0			0
$25$	1.20937	+	6.85868i	0.241874	+	1.37174i
$26$		0			0
$27$	2.16297	−	4.72457i	0.416263	−	0.909244i
$28$		0			0
$29$	2.95261	−	0.520625i	0.548286	−	0.0966777i	0.107359	−	0.994220i	$-0.465761\pi$
$29$	2.95261	−	0.520625i	0.548286	−	0.0966777i	0.440928	+	0.897543i	$0.354650\pi$
$30$		0			0
$31$	3.68626	+	10.1279i	0.662072	+	1.81903i	0.567272	+	0.823530i	$0.307999\pi$
$31$	3.68626	+	10.1279i	0.662072	+	1.81903i	0.0947991	+	0.995496i	$0.469779\pi$
$32$		0			0
$33$	0.172035	+	5.47311i	0.0299474	+	0.952746i
$34$		0			0
$35$	−6.52532	+	6.41651i	−1.10298	+	1.08459i
$36$		0			0
$37$	−4.53685	+	7.85806i	−0.745854	+	1.29186i	0.203940	+	0.978983i	$0.434625\pi$
$37$	−4.53685	+	7.85806i	−0.745854	+	1.29186i	−0.949795	+	0.312874i	$0.898708\pi$
$38$		0			0
$39$	0.652338	+	0.729591i	0.104458	+	0.116828i
$40$		0			0
$41$	−1.54293	+	8.75041i	−0.240966	+	1.36658i	0.588713	+	0.808342i	$0.299635\pi$
$41$	−1.54293	+	8.75041i	−0.240966	+	1.36658i	−0.829678	+	0.558242i	$0.811476\pi$
$42$		0			0
$43$	6.19754	−	5.20035i	0.945116	−	0.793046i	−0.0333523	−	0.999444i	$-0.510618\pi$
$43$	6.19754	−	5.20035i	0.945116	−	0.793046i	0.978468	+	0.206397i	$0.0661739\pi$
$44$		0			0
$45$	4.61382	−	9.29479i	0.687788	−	1.38558i
$46$		0			0
$47$	−8.99408	−	3.27358i	−1.31192	−	0.477500i	−0.411060	−	0.911608i	$-0.634841\pi$
$47$	−8.99408	−	3.27358i	−1.31192	−	0.477500i	−0.900861	+	0.434108i	$0.857064\pi$
$48$		0			0
$49$	−6.87224	−	1.33128i	−0.981749	−	0.190182i
$50$		0			0
$51$	−6.64653	+	2.65847i	−0.930701	+	0.372261i
$52$		0			0
$53$			5.85691i			0.804508i	0.915528	+	0.402254i	$0.131773\pi$
$53$			5.85691i			0.804508i	−0.915528	+	0.402254i	$0.868227\pi$
$54$		0			0
$55$			10.9354i			1.47453i
$56$		0			0
$57$	6.99922	+	1.00856i	0.927070	+	0.133587i
$58$		0			0
$59$	−5.73216	−	4.80985i	−0.746263	−	0.626189i	0.188248	−	0.982121i	$-0.439719\pi$
$59$	−5.73216	−	4.80985i	−0.746263	−	0.626189i	−0.934512	+	0.355932i	$0.884163\pi$
$60$		0			0
$61$	1.66114	−	4.56395i	0.212687	−	0.584354i	−0.786772	−	0.617244i	$-0.788249\pi$
$61$	1.66114	−	4.56395i	0.212687	−	0.584354i	0.999459	+	0.0328904i	$0.0104712\pi$
$62$		0			0
$63$	7.85770	−	1.12098i	0.989977	−	0.141230i
$64$		0			0
$65$	1.25633	+	1.49723i	0.155828	+	0.185709i
$66$		0			0
$67$	0.725278	−	4.11326i	0.0886068	−	0.502514i	−0.907913	−	0.419159i	$-0.862325\pi$
$67$	0.725278	−	4.11326i	0.0886068	−	0.502514i	0.996520	−	0.0833557i	$-0.0265638\pi$
$68$		0			0
$69$	−1.49706	+	4.55343i	−0.180225	+	0.548169i
$70$		0			0
$71$	6.30324	+	3.63918i	0.748057	+	0.431891i	0.824991	−	0.565145i	$-0.191180\pi$
$71$	6.30324	+	3.63918i	0.748057	+	0.431891i	−0.0769345	+	0.997036i	$0.524513\pi$
$72$		0			0
$73$	−5.79615	+	3.34641i	−0.678388	+	0.391667i	−0.799247	−	0.601002i	$-0.794768\pi$
$73$	−5.79615	+	3.34641i	−0.678388	+	0.391667i	0.120860	+	0.992670i	$0.461435\pi$
$74$		0			0
$75$	5.70024	−	10.6311i	0.658207	−	1.22757i
$76$		0			0
$77$	−6.89184	+	4.73987i	−0.785398	+	0.540159i
$78$		0			0
$79$	−0.410711	−	2.32926i	−0.0462086	−	0.262062i	0.952948	−	0.303135i	$-0.0980334\pi$
$79$	−0.410711	−	2.32926i	−0.0462086	−	0.262062i	−0.999156	+	0.0410733i	$0.986922\pi$
$80$		0			0
$81$	−8.00464	+	4.11409i	−0.889405	+	0.457121i
$82$		0			0
$83$	−2.32844	−	13.2053i	−0.255580	−	1.44946i	−0.794580	−	0.607159i	$-0.792309\pi$
$83$	−2.32844	−	13.2053i	−0.255580	−	1.44946i	0.539000	−	0.842306i	$-0.318802\pi$
$84$		0			0
$85$	−13.4336	+	4.88944i	−1.45708	+	0.530334i
$86$		0			0
$87$	−4.57660	−	2.45391i	−0.490663	−	0.263087i
$88$		0			0
$89$	−2.95877	−	5.12473i	−0.313629	−	0.543221i	0.665516	−	0.746383i	$-0.268211\pi$
$89$	−2.95877	−	5.12473i	−0.313629	−	0.543221i	−0.979145	+	0.203163i	$0.934878\pi$
$90$		0			0
$91$	−0.399057	+	1.44074i	−0.0418326	+	0.151031i
$92$		0			0
$93$	5.83051	−	17.7340i	0.604596	−	1.83893i
$94$		0			0
$95$	13.9075	+	2.45227i	1.42688	+	0.251598i
$96$		0			0
$97$	6.65243	+	7.92806i	0.675452	+	0.804973i	0.989515	−	0.144429i	$-0.0461347\pi$
$97$	6.65243	+	7.92806i	0.675452	+	0.804973i	−0.314063	+	0.949402i	$0.601690\pi$
$98$		0			0
$99$	5.62812	−	7.63400i	0.565647	−	0.767245i
$100$		0			0
$101$	−0.241554	−	0.0879186i	−0.0240356	−	0.00874823i	0.329974	−	0.943990i	$-0.392960\pi$
$101$	−0.241554	−	0.0879186i	−0.0240356	−	0.00874823i	−0.354010	+	0.935242i	$0.615182\pi$
$102$		0			0
$103$	8.83649	−	10.5309i	0.870685	−	1.03764i	−0.128261	−	0.991740i	$-0.540939\pi$
$103$	8.83649	−	10.5309i	0.870685	−	1.03764i	0.998946	−	0.0459019i	$-0.0146162\pi$
$104$		0			0
$105$	15.7547	−	1.74453i	1.53750	−	0.170249i
$106$		0			0
$107$		−	6.76613i		−	0.654107i	−0.945006	−	0.327053i	$-0.893944\pi$
$107$		−	6.76613i		−	0.654107i	0.945006	−	0.327053i	$-0.106056\pi$
$108$		0			0
$109$	−3.99280			−0.382441			−0.191220	−	0.981547i	$-0.561245\pi$
$109$	−3.99280			−0.382441			−0.191220	+	0.981547i	$0.561245\pi$
$110$		0			0
$111$	14.5922	−	5.83656i	1.38503	−	0.553982i
$112$		0			0
$113$	−2.90190	+	3.45835i	−0.272987	+	0.325334i	−0.885068	−	0.465462i	$-0.845888\pi$
$113$	−2.90190	+	3.45835i	−0.272987	+	0.325334i	0.612081	+	0.790795i	$0.290333\pi$
$114$		0			0
$115$	−3.27390	+	8.99497i	−0.305293	+	0.838785i
$116$		0			0
$117$	−0.106461	−	1.69181i	−0.00984235	−	0.156408i
$118$		0			0
$119$	−8.90419	−	6.34701i	−0.816245	−	0.581829i
$120$		0			0
$121$	0.174544	−	0.989888i	0.0158676	−	0.0899898i
$122$		0			0
$123$	11.4728	−	10.2580i	1.03447	−	0.924931i
$124$		0			0
$125$	3.39756	−	5.88474i	0.303887	−	0.526347i
$126$		0			0
$127$	−0.735671	−	1.27422i	−0.0652802	−	0.113069i	0.831538	−	0.555468i	$-0.187461\pi$
$127$	−0.735671	−	1.27422i	−0.0652802	−	0.113069i	−0.896818	+	0.442399i	$0.854127\pi$
$128$		0			0
$129$	−14.0059	+	0.440244i	−1.23315	+	0.0387613i
$130$		0			0
$131$	−17.9201	+	6.52237i	−1.56568	+	0.569862i	−0.972029	−	0.234859i	$-0.924537\pi$
$131$	−17.9201	+	6.52237i	−1.56568	+	0.569862i	−0.593653	+	0.804721i	$0.702315\pi$
$132$		0			0
$133$	4.48262	+	9.82790i	0.388692	+	0.852187i
$134$		0			0
$135$	−16.2358	+	7.70971i	−1.39736	+	0.663546i
$136$		0			0
$137$	2.66040	−	0.469100i	0.227293	−	0.0400779i	−0.0588415	−	0.998267i	$-0.518741\pi$
$137$	2.66040	−	0.469100i	0.227293	−	0.0400779i	0.286135	+	0.958189i	$0.407630\pi$
$138$		0			0
$139$	2.03951	+	5.60351i	0.172989	+	0.475283i	0.995642	−	0.0932608i	$-0.0297291\pi$
$139$	2.03951	+	5.60351i	0.172989	+	0.475283i	−0.822653	+	0.568544i	$0.807507\pi$
$140$		0			0
$141$	8.73595	+	14.0894i	0.735700	+	1.18655i
$142$		0			0
$143$	0.893194	+	1.54706i	0.0746926	+	0.129371i
$144$		0			0
$145$	−8.98117	−	5.18528i	−0.745845	−	0.430614i
$146$		0			0
$147$	7.92822	+	9.17297i	0.653909	+	0.756574i
$148$		0			0
$149$	20.0653	+	3.53805i	1.64381	+	0.289848i	0.917565	−	0.397587i	$-0.130152\pi$
$149$	20.0653	+	3.53805i	1.64381	+	0.289848i	0.726246	+	0.687435i	$0.241263\pi$
$150$		0			0
$151$	15.6983	−	13.1725i	1.27751	−	1.07196i	0.283931	−	0.958845i	$-0.408361\pi$
$151$	15.6983	−	13.1725i	1.27751	−	1.07196i	0.993582	−	0.113116i	$-0.0360831\pi$
$152$		0			0
$153$	11.8944	+	3.50056i	0.961608	+	0.283003i
$154$		0			0
$155$	12.7507	−	35.0322i	1.02416	−	2.81385i
$156$		0			0
$157$	−10.2635	+	12.2316i	−0.819118	+	0.976186i	−0.999973	−	0.00732329i	$-0.997669\pi$
$157$	−10.2635	+	12.2316i	−0.819118	+	0.976186i	0.180856	+	0.983510i	$0.442113\pi$
$158$		0			0
$159$	6.27337	−	7.97213i	0.497510	−	0.632231i
$160$		0			0
$161$	−7.08796	+	1.83549i	−0.558610	+	0.144657i
$162$		0			0
$163$	−23.0194			−1.80302			−0.901510	−	0.432759i	$-0.857540\pi$
$163$	−23.0194			−1.80302			−0.901510	+	0.432759i	$0.857540\pi$
$164$		0			0
$165$	11.7130	−	14.8847i	0.911854	−	1.15878i
$166$		0			0
$167$	4.35035	+	3.65038i	0.336640	+	0.282475i	0.795399	−	0.606086i	$-0.207261\pi$
$167$	4.35035	+	3.65038i	0.336640	+	0.282475i	−0.458759	+	0.888561i	$0.651706\pi$
$168$		0			0
$169$	−11.9160	−	4.33706i	−0.916614	−	0.333620i
$170$		0			0
$171$	−8.44673	−	8.86971i	−0.645937	−	0.678284i
$172$		0			0
$173$	−3.09871	+	2.60013i	−0.235591	+	0.197684i	−0.752938	−	0.658092i	$-0.771364\pi$
$173$	−3.09871	+	2.60013i	−0.235591	+	0.197684i	0.517347	+	0.855776i	$0.326920\pi$
$174$		0			0
$175$	18.3690	−	1.45158i	1.38857	−	0.109729i
$176$		0			0
$177$	2.65047	+	12.6867i	0.199222	+	0.953590i
$178$		0			0
$179$	−20.5779	−	11.8807i	−1.53807	−	0.888003i	−0.998952	−	0.0457703i	$-0.985426\pi$
$179$	−20.5779	−	11.8807i	−1.53807	−	0.888003i	−0.539114	−	0.842233i	$-0.681241\pi$
$180$		0			0
$181$	8.30621	−	4.79559i	0.617396	−	0.356453i	−0.158459	−	0.987366i	$-0.550652\pi$
$181$	8.30621	−	4.79559i	0.617396	−	0.356453i	0.775854	+	0.630912i	$0.217319\pi$
$182$		0			0
$183$	−7.14954	+	4.43297i	−0.528509	+	0.327694i
$184$		0			0
$185$	29.4929	−	10.7345i	2.16836	−	0.789219i
$186$		0			0
$187$	−12.8677	+	2.26892i	−0.940977	+	0.165920i
$188$		0			0
$189$	−11.8962	−	6.89061i	−0.865321	−	0.501218i
$190$		0			0
$191$	−14.4871	+	2.55447i	−1.04825	+	0.184835i	−0.671137	−	0.741333i	$-0.734194\pi$
$191$	−14.4871	+	2.55447i	−1.04825	+	0.184835i	−0.377112	+	0.926168i	$0.623083\pi$
$192$		0			0
$193$	8.40393	−	3.05878i	0.604928	−	0.220176i	−0.0213544	−	0.999772i	$-0.506798\pi$
$193$	8.40393	−	3.05878i	0.604928	−	0.220176i	0.626283	+	0.779596i	$0.284576\pi$
$194$		0			0
$195$	−0.106356	−	3.38361i	−0.00761632	−	0.242306i
$196$		0			0
$197$	−3.56973	+	2.06099i	−0.254333	+	0.146839i	−0.621747	−	0.783218i	$-0.713577\pi$
$197$	−3.56973	+	2.06099i	−0.254333	+	0.146839i	0.367414	+	0.930058i	$0.380243\pi$
$198$		0			0
$199$	4.45637	+	2.57289i	0.315904	+	0.182387i	0.649565	−	0.760306i	$-0.274951\pi$
$199$	4.45637	+	2.57289i	0.315904	+	0.182387i	−0.333662	+	0.942693i	$0.608284\pi$
$200$		0			0
$201$	−5.39295	+	4.82191i	−0.380389	+	0.340112i
$202$		0			0
$203$	−0.624893	−	7.90774i	−0.0438589	−	0.555014i
$204$		0			0
$205$	23.5439	−	19.7557i	1.64437	−	1.37979i
$206$		0			0
$207$	6.91493	−	4.59440i	0.480621	−	0.319333i
$208$		0			0
$209$	12.1290	+	4.41460i	0.838982	+	0.305364i
$210$		0			0
$211$	−20.1132	−	16.8770i	−1.38465	−	1.16186i	−0.967455	−	0.253043i	$-0.918568\pi$
$211$	−20.1132	−	16.8770i	−1.38465	−	1.16186i	−0.417196	−	0.908817i	$-0.636987\pi$
$212$		0			0
$213$	−4.68172	−	11.7049i	−0.320786	−	0.802007i
$214$		0			0
$215$	−27.9842			−1.90850
$216$		0			0
$217$	27.6051	−	7.14856i	1.87395	−	0.485276i
$218$		0			0
$219$	11.4738	+	1.65332i	0.775327	+	0.111721i
$220$		0			0
$221$	−1.50112	+	1.78897i	−0.100976	+	0.120339i
$222$		0			0
$223$	−6.92889	+	19.0370i	−0.463992	+	1.27481i	0.458466	+	0.888712i	$0.348399\pi$
$223$	−6.92889	+	19.0370i	−0.463992	+	1.27481i	−0.922458	+	0.386097i	$0.873823\pi$
$224$		0			0
$225$	−19.1459	+	8.36492i	−1.27639	+	0.557662i
$226$		0			0
$227$	17.0722	−	14.3253i	1.13312	−	0.950801i	0.133928	−	0.990991i	$-0.457241\pi$
$227$	17.0722	−	14.3253i	1.13312	−	0.950801i	0.999192	+	0.0401902i	$0.0127964\pi$
$228$		0			0
$229$	−20.9328	−	3.69101i	−1.38328	−	0.243909i	−0.568022	−	0.823013i	$-0.692291\pi$
$229$	−20.9328	−	3.69101i	−1.38328	−	0.243909i	−0.815253	+	0.579104i	$0.803402\pi$
$230$		0			0
$231$	14.4577	+	0.930212i	0.951250	+	0.0612035i
$232$		0			0
$233$	−14.0977	−	8.13929i	−0.923569	−	0.533223i	−0.0387971	−	0.999247i	$-0.512353\pi$
$233$	−14.0977	−	8.13929i	−0.923569	−	0.533223i	−0.884772	+	0.466024i	$0.845686\pi$
$234$		0			0
$235$	16.5534	+	28.6714i	1.07983	+	1.87031i
$236$		0			0
$237$	−1.93584	+	3.61039i	−0.125746	+	0.234520i
$238$		0			0
$239$	−0.414141	−	1.13784i	−0.0267886	−	0.0736010i	0.925577	−	0.378558i	$-0.123580\pi$
$239$	−0.414141	−	1.13784i	−0.0267886	−	0.0736010i	−0.952366	+	0.304957i	$0.901358\pi$
$240$		0			0
$241$	1.05189	−	0.185476i	0.0677581	−	0.0119476i	−0.139666	−	0.990199i	$-0.544603\pi$
$241$	1.05189	−	0.185476i	0.0677581	−	0.0119476i	0.207424	+	0.978251i	$0.433492\pi$
$242$		0			0
$243$	15.3021	+	2.97393i	0.981633	+	0.190777i
$244$		0			0
$245$	15.2496	+	18.8072i	0.974263	+	1.20154i
$246$		0			0
$247$	2.16783	−	0.789026i	0.137936	−	0.0502045i
$248$		0			0
$249$	−10.9749	+	20.4684i	−0.695504	+	1.29713i
$250$		0			0
$251$	7.71232	+	13.3581i	0.486797	+	0.843158i	0.999885	−	0.0151785i	$-0.00483164\pi$
$251$	7.71232	+	13.3581i	0.486797	+	0.843158i	−0.513087	+	0.858336i	$0.671498\pi$
$252$		0			0
$253$	−4.37446	+	7.57679i	−0.275020	+	0.476349i
$254$		0			0
$255$	23.5223	+	7.73357i	1.47302	+	0.484295i
$256$		0			0
$257$	1.13716	−	6.44913i	0.0709338	−	0.402286i	−0.928581	−	0.371130i	$-0.878970\pi$
$257$	1.13716	−	6.44913i	0.0709338	−	0.402286i	0.999515	−	0.0311552i	$-0.00991860\pi$
$258$		0			0
$259$	19.5487	+	13.9346i	1.21470	+	0.865852i
$260$		0			0
$261$	3.60104	+	8.24217i	0.222899	+	0.510177i
$262$		0			0
$263$	−4.46619	+	12.2708i	−0.275397	+	0.756647i	0.722472	+	0.691400i	$0.243006\pi$
$263$	−4.46619	+	12.2708i	−0.275397	+	0.756647i	−0.997869	+	0.0652470i	$0.979216\pi$
$264$		0			0
$265$	13.0222	−	15.5192i	0.799945	−	0.953337i
$266$		0			0
$267$	−1.46181	+	10.1447i	−0.0894610	+	0.620845i
$268$		0			0
$269$	−30.2066			−1.84173			−0.920863	−	0.389885i	$-0.872515\pi$
$269$	−30.2066			−1.84173			−0.920863	+	0.389885i	$0.872515\pi$
$270$		0			0
$271$		−	8.96082i		−	0.544331i	−0.962250	−	0.272166i	$-0.912260\pi$
$271$		−	8.96082i		−	0.544331i	0.962250	−	0.272166i	$-0.0877398\pi$
$272$		0			0
$273$	2.08636	−	1.53363i	0.126272	−	0.0928196i
$274$		0			0
$275$	14.1529	−	16.8667i	0.853450	−	1.01710i
$276$		0			0
$277$	0.0335533	+	0.0122124i	0.00201602	+	0.000733771i	0.343028	−	0.939325i	$-0.388547\pi$
$277$	0.0335533	+	0.0122124i	0.00201602	+	0.000733771i	−0.341012	+	0.940059i	$0.610770\pi$
$278$		0			0
$279$	−26.9312	+	17.8935i	−1.61233	+	1.07126i
$280$		0			0
$281$	−14.2839	−	17.0229i	−0.852108	−	1.01550i	−0.999650	−	0.0264473i	$-0.991581\pi$
$281$	−14.2839	−	17.0229i	−0.852108	−	1.01550i	0.147542	−	0.989056i	$-0.452864\pi$
$282$		0			0
$283$	10.0879	+	1.77876i	0.599662	+	0.105737i	0.465235	−	0.885187i	$-0.345970\pi$
$283$	10.0879	+	1.77876i	0.599662	+	0.105737i	0.134426	+	0.990924i	$0.457081\pi$
$284$		0			0
$285$	−16.3036	−	18.2344i	−0.965743	−	1.08011i
$286$		0			0
$287$	22.6556	+	6.27515i	1.33732	+	0.370411i
$288$		0			0
$289$	−0.0406445	−	0.0703984i	−0.00239085	−	0.00414108i
$290$		0			0
$291$	−0.563172	−	17.9168i	−0.0330137	−	1.05030i
$292$		0			0
$293$	6.46873	−	2.35443i	0.377907	−	0.137547i	−0.146081	−	0.989273i	$-0.546666\pi$
$293$	6.46873	−	2.35443i	0.377907	−	0.137547i	0.523988	+	0.851726i	$0.324444\pi$
$294$		0			0
$295$	4.49450	+	25.4896i	0.261680	+	1.48406i
$296$		0			0
$297$	−15.8375	+	4.36271i	−0.918987	+	0.253150i
$298$		0			0
$299$	0.271534	+	1.53995i	0.0157032	+	0.0890574i
$300$		0			0
$301$	−12.1295	−	17.6365i	−0.699135	−	1.01655i
$302$		0			0
$303$	0.234622	+	0.378401i	0.0134787	+	0.0217386i
$304$		0			0
$305$	−14.5490	+	8.39986i	−0.833073	+	0.480975i
$306$		0			0
$307$	13.1510	+	7.59270i	0.750564	+	0.433339i	0.825898	−	0.563820i	$-0.190669\pi$
$307$	13.1510	+	7.59270i	0.750564	+	0.433339i	−0.0753334	+	0.997158i	$0.524002\pi$
$308$		0			0
$309$	−23.3075	+	4.86935i	−1.32592	+	0.277008i
$310$		0			0
$311$	−2.74338	+	15.5585i	−0.155563	+	0.882240i	0.802707	+	0.596374i	$0.203392\pi$
$311$	−2.74338	+	15.5585i	−0.155563	+	0.882240i	−0.958270	+	0.285866i	$0.907719\pi$
$312$		0			0
$313$	7.08530	+	8.44393i	0.400485	+	0.477279i	0.928168	−	0.372162i	$-0.121383\pi$
$313$	7.08530	+	8.44393i	0.400485	+	0.477279i	−0.527683	+	0.849441i	$0.676939\pi$
$314$		0			0
$315$	−23.3131	−	14.5004i	−1.31355	−	0.817005i
$316$		0			0
$317$	−0.695084	+	1.90973i	−0.0390398	+	0.107261i	−0.957681	−	0.287832i	$-0.907065\pi$
$317$	−0.695084	+	1.90973i	−0.0390398	+	0.107261i	0.918641	+	0.395093i	$0.129288\pi$
$318$		0			0
$319$	−7.26101	−	6.09271i	−0.406538	−	0.341126i
$320$		0			0
$321$	−7.24724	+	9.20973i	−0.404502	+	0.514037i
$322$		0			0
$323$			16.8738i			0.938882i
$324$		0			0
$325$		−	3.93529i		−	0.218291i
$326$		0			0
$327$	5.43480	+	4.27671i	0.300545	+	0.236503i
$328$		0			0
$329$	−10.8947	+	22.8599i	−0.600642	+	1.26031i
$330$		0			0
$331$	−8.15931	−	2.96974i	−0.448476	−	0.163232i	0.107901	−	0.994162i	$-0.465587\pi$
$331$	−8.15931	−	2.96974i	−0.448476	−	0.163232i	−0.556377	+	0.830930i	$0.687809\pi$
$332$		0			0
$333$	−26.1137	−	7.68532i	−1.43102	−	0.421153i
$334$		0			0
$335$	−11.0671	+	9.28643i	−0.604662	+	0.507372i
$336$		0			0
$337$	5.25724	−	29.8153i	0.286380	−	1.62414i	−0.413934	−	0.910307i	$-0.635846\pi$
$337$	5.25724	−	29.8153i	0.286380	−	1.62414i	0.700314	−	0.713835i	$-0.253043\pi$
$338$		0			0
$339$	7.65417	−	1.59909i	0.415718	−	0.0868507i
$340$		0			0
$341$	17.0370	−	29.5089i	0.922603	−	1.59800i
$342$		0			0
$343$	−5.24303	+	17.7626i	−0.283097	+	0.959091i
$344$		0			0
$345$	14.0908	−	8.73681i	0.758625	−	0.470374i
$346$		0			0
$347$	6.50551	+	17.8737i	0.349234	+	0.959513i	0.982612	+	0.185670i	$0.0594456\pi$
$347$	6.50551	+	17.8737i	0.349234	+	0.959513i	−0.633378	+	0.773843i	$0.718332\pi$
$348$		0			0
$349$	−9.55852	+	1.68542i	−0.511656	+	0.0902187i	−0.423515	−	0.905889i	$-0.639204\pi$
$349$	−9.55852	+	1.68542i	−0.511656	+	0.0902187i	−0.0881412	+	0.996108i	$0.528093\pi$
$350$		0			0
$351$	−1.66719	+	2.41684i	−0.0889882	+	0.129001i
$352$		0			0
$353$	−0.359374	−	2.03811i	−0.0191275	−	0.108478i	0.973749	−	0.227623i	$-0.0730955\pi$
$353$	−0.359374	−	2.03811i	−0.0191275	−	0.108478i	−0.992877	+	0.119146i	$0.961984\pi$
$354$		0			0
$355$	−8.61057	−	23.6573i	−0.457002	−	1.25560i
$356$		0			0
$357$	5.32162	+	18.1766i	0.281650	+	0.962006i
$358$		0			0
$359$	−25.6881	+	14.8310i	−1.35576	+	0.782751i	−0.989050	−	0.147583i	$-0.952851\pi$
$359$	−25.6881	+	14.8310i	−1.35576	+	0.782751i	−0.366714	+	0.930334i	$0.619517\pi$
$360$		0			0
$361$	−1.16561	+	2.01890i	−0.0613481	+	0.106258i
$362$		0			0
$363$	−1.29786	+	1.16043i	−0.0681197	+	0.0609069i
$364$		0			0
$365$	22.7986	+	4.02000i	1.19333	+	0.210416i
$366$		0			0
$367$	−13.4246	−	15.9988i	−0.700757	−	0.835130i	0.291854	−	0.956463i	$-0.405728\pi$
$367$	−13.4246	−	15.9988i	−0.700757	−	0.835130i	−0.992612	+	0.121333i	$0.961283\pi$
$368$		0			0
$369$	−26.6036	+	1.67410i	−1.38493	+	0.0871500i
$370$		0			0
$371$	15.4251	+	1.48029i	0.800829	+	0.0768530i
$372$		0			0
$373$	9.60185	+	8.05691i	0.497165	+	0.417171i	0.856586	−	0.516005i	$-0.172581\pi$
$373$	9.60185	+	8.05691i	0.497165	+	0.417171i	−0.359421	+	0.933176i	$0.617026\pi$
$374$		0			0
$375$	−10.9278	+	4.37088i	−0.564307	+	0.225711i
$376$		0			0
$377$	−1.69411			−0.0872513
$378$		0			0
$379$	−21.0853			−1.08308			−0.541540	−	0.840675i	$-0.682159\pi$
$379$	−21.0853			−1.08308			−0.541540	+	0.840675i	$0.682159\pi$
$380$		0			0
$381$	−0.363465	+	2.52239i	−0.0186209	+	0.129226i
$382$		0			0
$383$	−5.67957	−	4.76572i	−0.290212	−	0.243517i	0.486044	−	0.873934i	$-0.338439\pi$
$383$	−5.67957	−	4.76572i	−0.290212	−	0.243517i	−0.776257	+	0.630417i	$0.782884\pi$
$384$		0			0
$385$	28.8001	+	2.76385i	1.46779	+	0.140859i
$386$		0			0
$387$	19.5357	+	14.4026i	0.993056	+	0.732124i
$388$		0			0
$389$	−4.56707	−	5.44282i	−0.231560	−	0.275962i	0.637735	−	0.770255i	$-0.279871\pi$
$389$	−4.56707	−	5.44282i	−0.231560	−	0.275962i	−0.869295	+	0.494293i	$0.835427\pi$
$390$		0			0
$391$	−11.2636	−	1.98608i	−0.569626	−	0.100440i
$392$		0			0
$393$	31.3780	+	10.3164i	1.58281	+	0.520391i
$394$		0			0
$395$	−4.09056	+	7.08506i	−0.205819	+	0.356488i
$396$		0			0
$397$	4.72424	−	2.72754i	0.237103	−	0.136891i	−0.376742	−	0.926318i	$-0.622956\pi$
$397$	4.72424	−	2.72754i	0.237103	−	0.136891i	0.613844	+	0.789427i	$0.289622\pi$
$398$		0			0
$399$	4.42520	−	18.1786i	0.221537	−	0.910069i
$400$		0			0
$401$	13.3624	+	36.7130i	0.667288	+	1.83336i	0.540337	+	0.841449i	$0.318297\pi$
$401$	13.3624	+	36.7130i	0.667288	+	1.83336i	0.126951	+	0.991909i	$0.459481\pi$
$402$		0			0
$403$	−1.05753	−	5.99754i	−0.0526792	−	0.298759i
$404$		0			0
$405$	30.3573	+	6.89619i	1.50847	+	0.342674i
$406$		0			0
$407$	28.2504	−	4.98130i	1.40032	−	0.246914i
$408$		0			0
$409$	−11.1247	−	30.5648i	−0.550080	−	1.51133i	−0.833602	−	0.552366i	$-0.813725\pi$
$409$	−11.1247	−	30.5648i	−0.550080	−	1.51133i	0.283522	−	0.958966i	$-0.408497\pi$
$410$		0			0
$411$	−4.12366	−	2.21105i	−0.203405	−	0.109063i
$412$		0			0
$413$	−14.1162	+	13.8808i	−0.694615	+	0.683032i
$414$		0			0
$415$	−23.1906	+	40.1673i	−1.13838	+	1.97174i
$416$		0			0
$417$	3.22587	−	9.81175i	0.157972	−	0.480484i
$418$		0			0
$419$	0.915621	−	5.19274i	0.0447310	−	0.253682i	−0.954240	−	0.299043i	$-0.903333\pi$
$419$	0.915621	−	5.19274i	0.0447310	−	0.253682i	0.998971	+	0.0453608i	$0.0144437\pi$
$420$		0			0
$421$	−17.9009	+	15.0206i	−0.872437	+	0.732061i	−0.964610	−	0.263682i	$-0.915063\pi$
$421$	−17.9009	+	15.0206i	−0.872437	+	0.732061i	0.0921731	+	0.995743i	$0.470619\pi$
$422$		0			0
$423$	3.20034	−	28.5350i	0.155606	−	1.38742i
$424$		0			0
$425$	27.0480	+	9.84467i	1.31202	+	0.477537i
$426$		0			0
$427$	−11.6000	−	5.52838i	−0.561364	−	0.267537i
$428$		0			0
$429$	0.441290	−	3.06248i	0.0213057	−	0.147858i
$430$		0			0
$431$			23.4485i			1.12948i	0.825270	+	0.564738i	$0.191023\pi$
$431$			23.4485i			1.12948i	−0.825270	+	0.564738i	$0.808977\pi$
$432$		0			0
$433$		−	22.9553i		−	1.10316i	−0.834122	−	0.551580i	$-0.814025\pi$
$433$		−	22.9553i		−	1.10316i	0.834122	−	0.551580i	$-0.185975\pi$
$434$		0			0
$435$	6.67074	+	16.6777i	0.319838	+	0.799636i
$436$		0			0
$437$	8.65511	+	7.26250i	0.414030	+	0.347412i
$438$		0			0
$439$	2.72959	−	7.49950i	0.130276	−	0.357932i	−0.857355	−	0.514726i	$-0.827894\pi$
$439$	2.72959	−	7.49950i	0.130276	−	0.357932i	0.987631	+	0.156794i	$0.0501160\pi$
$440$		0			0
$441$	−0.966286	−	20.9778i	−0.0460136	−	0.998941i
$442$		0			0
$443$	4.87479	+	5.80954i	0.231608	+	0.276020i	0.869314	−	0.494260i	$-0.164561\pi$
$443$	4.87479	+	5.80954i	0.231608	+	0.276020i	−0.637706	+	0.770280i	$0.720117\pi$
$444$		0			0
$445$	−3.55433	+	20.1576i	−0.168491	+	0.955563i
$446$		0			0
$447$	−23.5222	−	26.3078i	−1.11256	−	1.24432i
$448$		0			0
$449$	11.6527	+	6.72770i	0.549926	+	0.317500i	0.749092	−	0.662466i	$-0.230490\pi$
$449$	11.6527	+	6.72770i	0.549926	+	0.317500i	−0.199166	+	0.979966i	$0.563823\pi$
$450$		0			0
$451$	24.3274	−	14.0454i	1.14553	−	0.661373i
$452$		0			0
$453$	−35.4769	+	1.11514i	−1.66685	+	0.0523936i
$454$		0			0
$455$	4.26071	−	2.93031i	0.199745	−	0.137375i
$456$		0			0
$457$	−5.48298	−	31.0955i	−0.256483	−	1.45459i	−0.792237	−	0.610213i	$-0.791084\pi$
$457$	−5.48298	−	31.0955i	−0.256483	−	1.45459i	0.535754	−	0.844374i	$-0.320027\pi$
$458$		0			0
$459$	−12.4407	−	17.5050i	−0.580680	−	0.817063i
$460$		0			0
$461$	4.03993	+	22.9116i	0.188159	+	1.06710i	0.921830	+	0.387595i	$0.126694\pi$
$461$	4.03993	+	22.9116i	0.188159	+	1.06710i	−0.733671	+	0.679505i	$0.762195\pi$
$462$		0			0
$463$	−24.4605	+	8.90290i	−1.13678	+	0.413753i	−0.840748	−	0.541427i	$-0.817884\pi$
$463$	−24.4605	+	8.90290i	−1.13678	+	0.413753i	−0.296028	+	0.955179i	$0.595662\pi$
$464$		0			0
$465$	−54.8787	+	34.0267i	−2.54494	+	1.57795i
$466$		0			0
$467$	10.2317	+	17.7218i	0.473465	+	0.820065i	0.999539	−	0.0303736i	$-0.00966970\pi$
$467$	10.2317	+	17.7218i	0.473465	+	0.820065i	−0.526074	+	0.850439i	$0.676336\pi$
$468$		0			0
$469$	−10.6496	−	2.94973i	−0.491752	−	0.136206i
$470$		0			0
$471$	27.0715	−	5.65571i	1.24739	−	0.260602i
$472$		0			0
$473$	−25.1886	−	4.44144i	−1.15818	−	0.204218i
$474$		0			0
$475$	−18.2772	−	21.7819i	−0.838613	−	0.999420i
$476$		0			0
$477$	−17.0780	+	4.13184i	−0.781948	+	0.189184i
$478$		0			0
$479$	−13.7467	−	5.00339i	−0.628103	−	0.228611i	0.00830225	−	0.999966i	$-0.497357\pi$
$479$	−13.7467	−	5.00339i	−0.628103	−	0.228611i	−0.636406	+	0.771355i	$0.719580\pi$
$480$		0			0
$481$	3.29564	−	3.92759i	0.150268	−	0.179083i
$482$		0			0
$483$	11.6138	+	5.09358i	0.528446	+	0.231766i
$484$		0			0
$485$		−	35.7981i		−	1.62551i
$486$		0			0
$487$	−17.8117			−0.807124			−0.403562	−	0.914952i	$-0.632228\pi$
$487$	−17.8117			−0.807124			−0.403562	+	0.914952i	$0.632228\pi$
$488$		0			0
$489$	31.3329	+	24.6562i	1.41692	+	1.11499i
$490$		0			0
$491$	23.4589	−	27.9572i	1.05868	−	1.26169i	0.0947642	−	0.995500i	$-0.469790\pi$
$491$	23.4589	−	27.9572i	1.05868	−	1.26169i	0.963920	−	0.266191i	$-0.0857653\pi$
$492$		0			0
$493$	4.23806	−	11.6440i	0.190873	−	0.524418i
$494$		0			0
$495$	−31.8863	+	7.71454i	−1.43318	+	0.346743i
$496$		0			0
$497$	11.1774	−	15.6808i	0.501376	−	0.703378i
$498$		0			0
$499$	0.557450	−	3.16146i	0.0249549	−	0.141526i	−0.969785	−	0.243962i	$-0.921553\pi$
$499$	0.557450	−	3.16146i	0.0249549	−	0.141526i	0.994740	+	0.102436i	$0.0326637\pi$
$500$		0			0
$501$	−2.01154	−	9.62841i	−0.0898691	−	0.430165i
$502$		0			0
$503$	13.5453	−	23.4612i	0.603955	−	1.04608i	−0.388260	−	0.921550i	$-0.626924\pi$
$503$	13.5453	−	23.4612i	0.603955	−	1.04608i	0.992216	−	0.124531i	$-0.0397428\pi$
$504$		0			0
$505$	0.444576	+	0.770029i	0.0197834	+	0.0342658i
$506$		0			0
$507$	11.5740	+	18.6667i	0.514019	+	0.829016i
$508$		0			0
$509$	4.83242	−	1.75886i	0.214193	−	0.0779599i	−0.232695	−	0.972550i	$-0.574754\pi$
$509$	4.83242	−	1.75886i	0.214193	−	0.0779599i	0.446888	+	0.894590i	$0.352532\pi$
$510$		0			0
$511$	7.34833	+	16.1108i	0.325071	+	0.712700i
$512$		0			0
$513$	1.99687	+	21.1204i	0.0881640	+	0.932486i
$514$		0			0
$515$	−46.8286	+	8.25714i	−2.06351	+	0.363853i
$516$		0			0
$517$	10.3493	+	28.4344i	0.455161	+	1.25054i
$518$		0			0
$519$	7.00282	−	0.220118i	0.307390	−	0.00966209i
$520$		0			0
$521$	15.4785	+	26.8095i	0.678125	+	1.17455i	0.975545	+	0.219800i	$0.0705405\pi$
$521$	15.4785	+	26.8095i	0.678125	+	1.17455i	−0.297420	+	0.954747i	$0.596126\pi$
$522$		0			0
$523$	−15.8993	−	9.17944i	−0.695226	−	0.401389i	0.110341	−	0.993894i	$-0.464806\pi$
$523$	−15.8993	−	9.17944i	−0.695226	−	0.401389i	−0.805567	+	0.592505i	$0.798139\pi$
$524$		0			0
$525$	−26.5578	−	17.6994i	−1.15908	−	0.772464i
$526$		0			0
$527$	43.8678	+	7.73508i	1.91091	+	0.336945i
$528$		0			0
$529$	11.7524	−	9.86145i	0.510974	−	0.428758i
$530$		0			0
$531$	9.98109	−	20.1074i	0.433142	−	0.872588i
$532$		0			0
$533$	1.71718	−	4.71792i	0.0743794	−	0.204356i
$534$		0			0
$535$	−15.0437	+	17.9284i	−0.650396	+	0.775112i
$536$		0			0
$537$	15.2842	+	38.2125i	0.659562	+	1.64899i
$538$		0			0
$539$	10.7413	+	19.3487i	0.462661	+	0.833407i
$540$		0			0
$541$	18.9614			0.815216			0.407608	−	0.913157i	$-0.366363\pi$
$541$	18.9614			0.815216			0.407608	+	0.913157i	$0.366363\pi$
$542$		0			0
$543$	−16.4426	−	2.36931i	−0.705619	−	0.101677i
$544$		0			0
$545$	10.5798	+	8.87752i	0.453190	+	0.380271i
$546$		0			0
$547$	24.6262	+	8.96322i	1.05294	+	0.383240i	0.809772	−	0.586744i	$-0.199591\pi$
$547$	24.6262	+	8.96322i	1.05294	+	0.383240i	0.243170	+	0.969984i	$0.421813\pi$
$548$		0			0
$549$	14.4798	+	1.62398i	0.617982	+	0.0693097i
$550$		0			0
$551$	−9.37693	+	7.86818i	−0.399471	+	0.335196i
$552$		0			0
$553$	−6.23826	+	0.492965i	−0.265278	+	0.0209630i
$554$		0			0
$555$	−51.6421	−	16.9787i	−2.19209	−	0.720706i
$556$		0			0
$557$	3.88481	+	2.24289i	0.164604	+	0.0950344i	0.580039	−	0.814589i	$-0.303037\pi$
$557$	3.88481	+	2.24289i	0.164604	+	0.0950344i	−0.415435	+	0.909623i	$0.636371\pi$
$558$		0			0
$559$	−3.95898	+	2.28572i	−0.167447	+	0.0966756i
$560$		0			0
$561$	19.9451	+	10.6943i	0.842082	+	0.451514i
$562$		0			0
$563$	−27.5579	+	10.0303i	−1.16143	+	0.422725i	−0.849608	−	0.527415i	$-0.823161\pi$
$563$	−27.5579	+	10.0303i	−1.16143	+	0.422725i	−0.311821	+	0.950141i	$0.600939\pi$
$564$		0			0
$565$	15.3785	−	2.71164i	0.646977	−	0.114079i
$566$		0			0
$567$	8.81195	+	22.1212i	0.370067	+	0.929005i
$568$		0			0
$569$	−8.40534	+	1.48209i	−0.352370	+	0.0621324i	−0.347032	−	0.937853i	$-0.612810\pi$
$569$	−8.40534	+	1.48209i	−0.352370	+	0.0621324i	−0.00533844	+	0.999986i	$0.501699\pi$
$570$		0			0
$571$	6.26386	−	2.27986i	0.262135	−	0.0954092i	−0.207610	−	0.978212i	$-0.566568\pi$
$571$	6.26386	−	2.27986i	0.262135	−	0.0954092i	0.469744	+	0.882803i	$0.344346\pi$
$572$		0			0
$573$	22.4552	+	12.0402i	0.938081	+	0.502987i
$574$		0			0
$575$	16.6912	−	9.63664i	0.696069	−	0.401876i
$576$		0			0
$577$	−17.4205	−	10.0577i	−0.725223	−	0.418708i	0.0914490	−	0.995810i	$-0.470850\pi$
$577$	−17.4205	−	10.0577i	−0.725223	−	0.418708i	−0.816672	+	0.577102i	$0.804183\pi$
$578$		0			0
$579$	−14.7153	−	4.83804i	−0.611547	−	0.201062i
$580$		0			0
$581$	−35.3665	+	2.79477i	−1.46725	+	0.115946i
$582$		0			0
$583$	14.1844	−	11.9021i	0.587457	−	0.492935i
$584$		0			0
$585$	−3.47944	+	4.71953i	−0.143857	+	0.195128i
$586$		0			0
$587$	3.86800	+	1.40784i	0.159650	+	0.0581077i	0.420609	−	0.907242i	$-0.361817\pi$
$587$	3.86800	+	1.40784i	0.159650	+	0.0581077i	−0.260959	+	0.965350i	$0.584039\pi$
$588$		0			0
$589$	−33.7085	−	28.2848i	−1.38894	−	1.16546i
$590$		0			0
$591$	7.06648	+	1.01825i	0.290676	+	0.0418852i
$592$		0			0
$593$	44.5370			1.82892			0.914458	−	0.404682i	$-0.132618\pi$
$593$	44.5370			1.82892			0.914458	+	0.404682i	$0.132618\pi$
$594$		0			0
$595$	9.48182	+	36.6153i	0.388717	+	1.50108i
$596$		0			0
$597$	−3.30996	−	8.27533i	−0.135468	−	0.338687i
$598$		0			0
$599$	−9.80148	+	11.6809i	−0.400478	+	0.477271i	−0.928165	−	0.372168i	$-0.878615\pi$
$599$	−9.80148	+	11.6809i	−0.400478	+	0.477271i	0.527688	+	0.849438i	$0.323059\pi$
$600$		0			0
$601$	14.6792	−	40.3307i	0.598776	−	1.64512i	−0.154940	−	0.987924i	$-0.549518\pi$
$601$	14.6792	−	40.3307i	0.598776	−	1.64512i	0.753716	−	0.657200i	$-0.228260\pi$
$602$		0			0
$603$	12.5054	−	0.786934i	0.509259	−	0.0320464i
$604$		0			0
$605$	−2.66339	+	2.23485i	−0.108282	+	0.0908597i
$606$		0			0
$607$	16.3861	+	2.88931i	0.665091	+	0.117273i	0.495994	−	0.868326i	$-0.334804\pi$
$607$	16.3861	+	2.88931i	0.665091	+	0.117273i	0.169097	+	0.985599i	$0.445915\pi$
$608$		0			0
$609$	−7.61945	+	11.4330i	−0.308756	+	0.463287i
$610$		0			0
$611$	4.68370	+	2.70414i	0.189482	+	0.109398i
$612$		0			0
$613$	−1.01350	−	1.75543i	−0.0409347	−	0.0709010i	0.844832	−	0.535031i	$-0.179700\pi$
$613$	−1.01350	−	1.75543i	−0.0409347	−	0.0709010i	−0.885767	+	0.464130i	$0.846367\pi$
$614$		0			0
$615$	−53.2072	+	1.67244i	−2.14552	+	0.0674395i
$616$		0			0
$617$	−1.97591	−	5.42876i	−0.0795470	−	0.218554i	0.893544	−	0.448976i	$-0.148211\pi$
$617$	−1.97591	−	5.42876i	−0.0795470	−	0.218554i	−0.973091	+	0.230423i	$0.925989\pi$
$618$		0			0
$619$	9.32392	−	1.64406i	0.374760	−	0.0660803i	0.0169040	−	0.999857i	$-0.494619\pi$
$619$	9.32392	−	1.64406i	0.374760	−	0.0660803i	0.357856	+	0.933777i	$0.383508\pi$
$620$		0			0
$621$	−14.3334	−	1.15296i	−0.575178	−	0.0462666i
$622$		0			0
$623$	−14.2446	+	6.49712i	−0.570697	+	0.260302i
$624$		0			0
$625$	10.6358	−	3.87110i	0.425430	−	0.154844i
$626$		0			0
$627$	−11.7809	−	19.0004i	−0.470484	−	0.758803i
$628$		0			0
$629$	18.7506	+	32.4770i	0.747635	+	1.29494i
$630$		0			0
$631$	14.6856	−	25.4362i	0.584625	−	1.01260i	−0.410297	−	0.911952i	$-0.634575\pi$
$631$	14.6856	−	25.4362i	0.584625	−	1.01260i	0.994922	−	0.100648i	$-0.0320916\pi$
$632$		0			0
$633$	9.30007	+	44.5155i	0.369645	+	1.76933i
$634$		0			0
$635$	−0.883753	+	5.01201i	−0.0350707	+	0.198896i
$636$		0			0
$637$	3.69355	+	1.41512i	0.146344	+	0.0560689i
$638$		0			0
$639$	−6.16467	+	20.9468i	−0.243871	+	0.828641i
$640$		0			0
$641$	8.08704	−	22.2190i	0.319419	−	0.877596i	−0.671241	−	0.741239i	$-0.734238\pi$
$641$	8.08704	−	22.2190i	0.319419	−	0.877596i	0.990660	−	0.136357i	$-0.0435394\pi$
$642$		0			0
$643$	14.6050	−	17.4055i	0.575963	−	0.686406i	−0.396880	−	0.917870i	$-0.629907\pi$
$643$	14.6050	−	17.4055i	0.575963	−	0.686406i	0.972843	+	0.231464i	$0.0743516\pi$
$644$		0			0
$645$	38.0907	+	29.9740i	1.49982	+	1.18023i
$646$		0			0
$647$	−22.5032			−0.884690			−0.442345	−	0.896845i	$-0.645853\pi$
$647$	−22.5032			−0.884690			−0.442345	+	0.896845i	$0.645853\pi$
$648$		0			0
$649$			23.6566i			0.928602i
$650$		0			0
$651$	−45.2315	−	19.8377i	−1.77276	−	0.777500i
$652$		0			0
$653$	19.8057	−	23.6036i	0.775059	−	0.923679i	−0.223640	−	0.974672i	$-0.571794\pi$
$653$	19.8057	−	23.6036i	0.775059	−	0.923679i	0.998699	+	0.0509929i	$0.0162386\pi$
$654$		0			0
$655$	61.9850	+	22.5607i	2.42195	+	0.881519i
$656$		0			0
$657$	−13.8467	−	14.5401i	−0.540210	−	0.567262i
$658$		0			0
$659$	−4.25357	−	5.06921i	−0.165696	−	0.197468i	0.676807	−	0.736160i	$-0.263363\pi$
$659$	−4.25357	−	5.06921i	−0.165696	−	0.197468i	−0.842503	+	0.538692i	$0.818919\pi$
$660$		0			0
$661$	48.2694	+	8.51119i	1.87746	+	0.331047i	0.991225	−	0.132188i	$-0.0422002\pi$
$661$	48.2694	+	8.51119i	1.87746	+	0.331047i	0.886236	+	0.463235i	$0.153311\pi$
$662$		0			0
$663$	3.95942	−	0.827193i	0.153771	−	0.0321255i
$664$		0			0
$665$	9.97347	−	36.0078i	0.386755	−	1.39632i
$666$		0			0
$667$	−4.14851	−	7.18542i	−0.160631	−	0.278221i
$668$		0			0
$669$	29.8219	−	18.4906i	1.15298	−	0.714888i
$670$		0			0
$671$	−14.4288	+	5.25164i	−0.557016	+	0.202737i
$672$		0			0
$673$	−5.87854	−	33.3388i	−0.226601	−	1.28512i	−0.859601	−	0.510966i	$-0.829288\pi$
$673$	−5.87854	−	33.3388i	−0.226601	−	1.28512i	0.633000	−	0.774152i	$-0.281823\pi$
$674$		0			0
$675$	35.0202	+	9.12135i	1.34793	+	0.351081i
$676$		0			0
$677$	−1.39731	−	7.92456i	−0.0537032	−	0.304566i	0.946111	−	0.323842i	$-0.104975\pi$
$677$	−1.39731	−	7.92456i	−0.0537032	−	0.304566i	−0.999814	+	0.0192767i	$0.993864\pi$
$678$		0			0
$679$	22.5611	−	15.5164i	0.865816	−	0.595466i
$680$		0			0
$681$	−38.5817	+	1.21273i	−1.47845	+	0.0464718i
$682$		0			0
$683$	−25.8010	+	14.8962i	−0.987246	+	0.569987i	−0.904450	−	0.426580i	$-0.859718\pi$
$683$	−25.8010	+	14.8962i	−0.987246	+	0.569987i	−0.0827963	+	0.996566i	$0.526385\pi$
$684$		0			0
$685$	−8.09232	−	4.67210i	−0.309192	−	0.178512i
$686$		0			0
$687$	24.5392	+	27.4452i	0.936228	+	1.04710i
$688$		0			0
$689$	0.574680	−	3.25917i	0.0218936	−	0.124165i
$690$		0			0
$691$	20.1697	+	24.0373i	0.767290	+	0.914421i	0.998285	−	0.0585343i	$-0.0186427\pi$
$691$	20.1697	+	24.0373i	0.767290	+	0.914421i	−0.230995	+	0.972955i	$0.574198\pi$
$692$		0			0
$693$	−18.6828	−	16.7519i	−0.709702	−	0.636353i
$694$		0			0
$695$	7.05461	−	19.3824i	0.267597	−	0.735216i
$696$		0			0
$697$	28.1314	+	23.6050i	1.06555	+	0.894104i
$698$		0			0
$699$	10.4710	+	26.1789i	0.396050	+	0.990177i
$700$		0			0
$701$		−	37.7812i		−	1.42698i	−0.700667	−	0.713488i	$-0.747114\pi$
$701$		−	37.7812i		−	1.42698i	0.700667	−	0.713488i	$-0.252886\pi$
$702$		0			0
$703$		−	37.0456i		−	1.39720i
$704$		0			0
$705$	8.17837	−	56.7565i	0.308015	−	2.13758i
$706$		0			0
$707$	−0.292598	+	0.613949i	−0.0110043	+	0.0230899i
$708$		0			0
$709$	−5.34897	−	1.94686i	−0.200885	−	0.0731160i	0.239618	−	0.970867i	$-0.422978\pi$
$709$	−5.34897	−	1.94686i	−0.200885	−	0.0731160i	−0.440503	+	0.897751i	$0.645200\pi$
$710$		0			0
$711$	6.50208	−	2.84079i	0.243847	−	0.106538i
$712$		0			0
$713$	22.8483	−	19.1720i	0.855677	−	0.717998i
$714$		0			0
$715$	1.07298	−	6.08519i	0.0401273	−	0.227573i
$716$		0			0
$717$	−0.655042	+	1.99237i	−0.0244630	+	0.0744062i
$718$		0			0
$719$	20.1776	−	34.9486i	0.752496	−	1.30336i	−0.194114	−	0.980979i	$-0.562183\pi$
$719$	20.1776	−	34.9486i	0.752496	−	1.30336i	0.946610	−	0.322382i	$-0.104484\pi$
$720$		0			0
$721$	−25.5014	−	25.9339i	−0.949722	−	0.965827i
$722$		0			0
$723$	−1.63044	−	0.874223i	−0.0606369	−	0.0325127i
$724$		0			0
$725$	7.14161	+	19.6214i	0.265233	+	0.728721i
$726$		0			0
$727$	23.4856	−	4.14114i	0.871032	−	0.153586i	0.279771	−	0.960067i	$-0.409741\pi$
$727$	23.4856	−	4.14114i	0.871032	−	0.153586i	0.591261	+	0.806480i	$0.298630\pi$
$728$		0			0
$729$	−17.6431	−	20.4382i	−0.653450	−	0.756970i
$730$		0			0
$731$	−5.80625	−	32.9289i	−0.214752	−	1.21792i
$732$		0			0
$733$	8.64830	+	23.7610i	0.319432	+	0.877633i	0.990657	+	0.136379i	$0.0435465\pi$
$733$	8.64830	+	23.7610i	0.319432	+	0.877633i	−0.671224	+	0.741254i	$0.734231\pi$
$734$		0			0
$735$	−0.612586	−	41.9333i	−0.0225956	−	1.54673i
$736$		0			0
$737$	−11.4354	+	6.60226i	−0.421230	+	0.243197i
$738$		0			0
$739$	8.73389	−	15.1275i	0.321281	−	0.556476i	−0.659471	−	0.751730i	$-0.729220\pi$
$739$	8.73389	−	15.1275i	0.321281	−	0.556476i	0.980753	+	0.195254i	$0.0625531\pi$
$740$		0			0
$741$	−3.79587	−	1.24799i	−0.139445	−	0.0458462i
$742$		0			0
$743$	−47.9734	−	8.45901i	−1.75997	−	0.310331i	−0.802029	−	0.597285i	$-0.796246\pi$
$743$	−47.9734	−	8.45901i	−1.75997	−	0.310331i	−0.957944	+	0.286954i	$0.907357\pi$
$744$		0			0
$745$	−45.3010	−	53.9877i	−1.65970	−	1.97796i
$746$		0			0
$747$	36.8622	−	16.1053i	1.34872	−	0.589261i
$748$		0			0
$749$	−17.8196	−	1.71009i	−0.651115	−	0.0624855i
$750$		0			0
$751$	5.39799	+	4.52945i	0.196975	+	0.165282i	0.735941	−	0.677046i	$-0.236740\pi$
$751$	5.39799	+	4.52945i	0.196975	+	0.165282i	−0.538965	+	0.842328i	$0.681185\pi$
$752$		0			0
$753$	3.81034	−	26.4432i	0.138857	−	0.963642i
$754$		0			0
$755$	−70.8838			−2.57972
$756$		0			0
$757$	30.6016			1.11223			0.556117	−	0.831104i	$-0.312291\pi$
$757$	30.6016			1.11223			0.556117	+	0.831104i	$0.312291\pi$
$758$		0			0
$759$	14.0698	−	5.62764i	0.510703	−	0.204270i
$760$		0			0
$761$	−12.0773	−	10.1340i	−0.437801	−	0.367359i	0.397085	−	0.917782i	$-0.370022\pi$
$761$	−12.0773	−	10.1340i	−0.437801	−	0.367359i	−0.834886	+	0.550423i	$0.814466\pi$
$762$		0			0
$763$	−1.00915	+	10.5156i	−0.0365338	+	0.380692i
$764$		0			0
$765$	−23.7339	−	35.7214i	−0.858102	−	1.29151i
$766$		0			0
$767$	2.71781	+	3.23896i	0.0981345	+	0.116952i
$768$		0			0
$769$	−47.9808	−	8.46030i	−1.73023	−	0.305086i	−0.782144	−	0.623098i	$-0.785874\pi$
$769$	−47.9808	−	8.46030i	−1.73023	−	0.305086i	−0.948087	+	0.318011i	$0.896985\pi$
$770$		0			0
$771$	−8.45554	+	7.56022i	−0.304519	+	0.272275i
$772$		0			0
$773$	3.84584	−	6.66120i	0.138325	−	0.239587i	−0.788537	−	0.614987i	$-0.789161\pi$
$773$	3.84584	−	6.66120i	0.138325	−	0.239587i	0.926863	+	0.375400i	$0.122495\pi$
$774$		0			0
$775$	−65.0061	+	37.5313i	−2.33509	+	1.34816i
$776$		0			0
$777$	−11.6834	−	39.9058i	−0.419139	−	1.43161i
$778$		0			0
$779$	−12.4074	−	34.0890i	−0.444541	−	1.22137i
$780$		0			0
$781$	−3.99569	−	22.6607i	−0.142977	−	0.810862i
$782$		0			0
$783$	3.92667	−	15.0759i	0.140328	−	0.538770i
$784$		0			0
$785$	54.3910	−	9.59060i	1.94130	−	0.342303i
$786$		0			0
$787$	−3.43997	−	9.45124i	−0.122622	−	0.336900i	0.863160	−	0.504930i	$-0.168482\pi$
$787$	−3.43997	−	9.45124i	−0.122622	−	0.336900i	−0.985782	+	0.168030i	$0.946259\pi$
$788$		0			0
$789$	19.2224	−	11.9186i	0.684337	−	0.424313i
$790$		0			0
$791$	8.37464	+	8.51666i	0.297768	+	0.302818i
$792$		0			0
$793$	−1.37218	+	2.37669i	−0.0487277	+	0.0843989i
$794$		0			0
$795$	−34.3478	+	7.17587i	−1.21819	+	0.254502i
$796$		0			0
$797$	−1.17215	+	6.64759i	−0.0415197	+	0.235470i	−0.998505	−	0.0546679i	$-0.982590\pi$
$797$	−1.17215	+	6.64759i	−0.0415197	+	0.235470i	0.956985	+	0.290138i	$0.0937011\pi$
$798$		0			0
$799$	−30.3030	+	25.4272i	−1.07204	+	0.899550i
$800$		0			0
$801$	12.8558	−	12.2427i	0.454236	−	0.432575i
$802$		0			0
$803$	19.8830	+	7.23683i	0.701657	+	0.255382i
$804$		0			0
$805$	22.8621	+	10.8957i	0.805785	+	0.384024i
$806$		0			0
$807$	41.1157	+	32.3544i	1.44734	+	1.13893i
$808$		0			0
$809$		−	29.6074i		−	1.04094i	−0.853879	−	0.520471i	$-0.825756\pi$
$809$		−	29.6074i		−	1.04094i	0.853879	−	0.520471i	$-0.174244\pi$
$810$		0			0
$811$		−	14.3243i		−	0.502993i	−0.967858	−	0.251497i	$-0.919077\pi$
$811$		−	14.3243i		−	0.502993i	0.967858	−	0.251497i	$-0.0809227\pi$
$812$		0			0
$813$	−9.59799	+	12.1970i	−0.336616	+	0.427768i
$814$		0			0
$815$	60.9951	+	51.1810i	2.13657	+	1.79279i
$816$		0			0
$817$	−11.2971	+	31.0387i	−0.395237	+	1.08591i
$818$		0			0
$819$	−4.48254	−	0.147211i	−0.156632	−	0.00514396i
$820$		0			0
$821$	20.0329	+	23.8743i	0.699153	+	0.833219i	0.992430	−	0.122809i	$-0.0391903\pi$
$821$	20.0329	+	23.8743i	0.699153	+	0.833219i	−0.293277	+	0.956028i	$0.594746\pi$
$822$		0			0
$823$	5.57871	−	31.6384i	0.194462	−	1.10285i	−0.718722	−	0.695298i	$-0.755273\pi$
$823$	5.57871	−	31.6384i	0.194462	−	1.10285i	0.913183	−	0.407549i	$-0.133616\pi$
$824$		0			0
$825$	−37.3303	+	7.79895i	−1.29967	+	0.271525i
$826$		0			0
$827$	12.6923	+	7.32789i	0.441354	+	0.254816i	0.704172	−	0.710030i	$-0.251318\pi$
$827$	12.6923	+	7.32789i	0.441354	+	0.254816i	−0.262818	+	0.964845i	$0.584652\pi$
$828$		0			0
$829$	42.4657	−	24.5176i	1.47490	−	0.851532i	0.475296	−	0.879826i	$-0.342341\pi$
$829$	42.4657	−	24.5176i	1.47490	−	0.851532i	0.999600	+	0.0282942i	$0.00900754\pi$
$830$		0			0
$831$	−0.0325903	−	0.0525620i	−0.00113054	−	0.00182336i
$832$		0			0
$833$	−18.9663	+	21.8464i	−0.657143	+	0.756932i
$834$		0			0
$835$	−3.41105	−	19.3450i	−0.118044	−	0.669462i
$836$		0			0
$837$	55.8233	+	4.49035i	1.92954	+	0.155209i
$838$		0			0
$839$	−8.34845	−	47.3464i	−0.288221	−	1.63458i	−0.693549	−	0.720409i	$-0.743954\pi$
$839$	−8.34845	−	47.3464i	−0.288221	−	1.63458i	0.405329	−	0.914171i	$-0.367157\pi$
$840$		0			0
$841$	−18.8042	+	6.84417i	−0.648421	+	0.236006i
$842$		0			0
$843$	1.20923	+	38.4704i	0.0416480	+	1.32499i
$844$		0			0
$845$	21.9311	+	37.9858i	0.754454	+	1.30675i
$846$		0			0
$847$	−2.56290	−	0.709875i	−0.0880625	−	0.0243916i
$848$		0			0
$849$	−11.8259	−	13.2263i	−0.405863	−	0.453927i
$850$		0			0
$851$	24.7288	+	4.36035i	0.847692	+	0.149471i
$852$		0			0
$853$	−0.320587	−	0.382060i	−0.0109767	−	0.0130815i	0.760528	−	0.649305i	$-0.224940\pi$
$853$	−0.320587	−	0.382060i	−0.0109767	−	0.0130815i	−0.771505	+	0.636223i	$0.780496\pi$
$854$		0			0
$855$	2.66074	+	42.2826i	0.0909955	+	1.44604i
$856$		0			0
$857$	−40.1969	−	14.6305i	−1.37310	−	0.499767i	−0.453020	−	0.891500i	$-0.649653\pi$
$857$	−40.1969	−	14.6305i	−1.37310	−	0.499767i	−0.920079	+	0.391733i	$0.871876\pi$
$858$		0			0
$859$	13.8583	−	16.5157i	0.472839	−	0.563508i	−0.475928	−	0.879484i	$-0.657888\pi$
$859$	13.8583	−	16.5157i	0.472839	−	0.563508i	0.948767	+	0.315977i	$0.102332\pi$
$860$		0			0
$861$	−24.1163	−	32.8079i	−0.821880	−	1.11809i
$862$		0			0
$863$		−	16.8920i		−	0.575012i	−0.957779	−	0.287506i	$-0.907174\pi$
$863$		−	16.8920i		−	0.575012i	0.957779	−	0.287506i	$-0.0928261\pi$
$864$		0			0
$865$	13.9918			0.475736
$866$		0			0
$867$	−0.0200808	+	0.139357i	−0.000681980	+	0.00473283i
$868$		0			0
$869$	−4.80642	+	5.72807i	−0.163047	+	0.194311i
$870$		0			0
$871$	−0.807186	+	2.21773i	−0.0273505	+	0.0751448i
$872$		0			0
$873$	−18.4242	+	24.9906i	−0.623564	+	0.845804i
$874$		0			0
$875$	−14.6396	−	10.4353i	−0.494910	−	0.352778i
$876$		0			0
$877$	−8.39799	+	47.6274i	−0.283580	+	1.60826i	0.426734	+	0.904377i	$0.359664\pi$
$877$	−8.39799	+	47.6274i	−0.283580	+	1.60826i	−0.710314	+	0.703885i	$0.751447\pi$
$878$		0			0
$879$	−11.3268	−	3.72397i	−0.382042	−	0.125606i
$880$		0			0
$881$	−6.10689	+	10.5774i	−0.205746	+	0.356363i	−0.950370	−	0.311121i	$-0.899296\pi$
$881$	−6.10689	+	10.5774i	−0.205746	+	0.356363i	0.744624	+	0.667484i	$0.232629\pi$
$882$		0			0
$883$	−6.58997	−	11.4142i	−0.221770	−	0.384117i	0.733575	−	0.679608i	$-0.237850\pi$
$883$	−6.58997	−	11.4142i	−0.221770	−	0.384117i	−0.955346	+	0.295491i	$0.904517\pi$
$884$		0			0
$885$	21.1844	−	39.5093i	0.712104	−	1.32809i
$886$		0			0
$887$	1.30180	−	0.473817i	0.0437103	−	0.0159092i	−0.320072	−	0.947393i	$-0.603707\pi$
$887$	1.30180	−	0.473817i	0.0437103	−	0.0159092i	0.363783	+	0.931484i	$0.381485\pi$
$888$		0			0
$889$	−3.54179	+	1.61545i	−0.118788	+	0.0541805i
$890$		0			0
$891$	26.2302	+	11.0254i	0.878745	+	0.369364i
$892$		0			0
$893$	38.4835	−	6.78567i	1.28780	−	0.227074i
$894$		0			0
$895$	28.1106	+	77.2332i	0.939633	+	2.58162i
$896$		0			0
$897$	1.27985	−	2.38694i	0.0427329	−	0.0796977i
$898$		0			0
$899$	16.1569	+	27.9846i	0.538864	+	0.933340i
$900$		0			0
$901$	20.9633	+	12.1032i	0.698388	+	0.403215i
$902$		0			0
$903$	−2.38045	+	36.9980i	−0.0792165	+	1.23122i
$904$		0			0
$905$	−32.6716	−	5.76089i	−1.08604	−	0.191498i
$906$		0			0
$907$	−22.9220	+	19.2338i	−0.761112	+	0.638649i	−0.938416	−	0.345507i	$-0.887707\pi$
$907$	−22.9220	+	19.2338i	−0.761112	+	0.638649i	0.177304	+	0.984156i	$0.443262\pi$
$908$		0			0
$909$	0.0859517	−	0.766366i	0.00285084	−	0.0254187i
$910$		0			0
$911$	−13.9440	+	38.3107i	−0.461984	+	1.26929i	0.462006	+	0.886877i	$0.347130\pi$
$911$	−13.9440	+	38.3107i	−0.461984	+	1.26929i	−0.923991	+	0.382415i	$0.875093\pi$
$912$		0			0
$913$	−27.2490	+	32.4741i	−0.901811	+	1.07474i
$914$		0			0
$915$	28.8005	+	4.15003i	0.952115	+	0.137196i
$916$		0			0
$917$	12.6485	+	48.8437i	0.417689	+	1.61296i
$918$		0			0
$919$	−35.5177			−1.17162			−0.585811	−	0.810448i	$-0.699224\pi$
$919$	−35.5177			−1.17162			−0.585811	+	0.810448i	$0.699224\pi$
$920$		0			0
$921$	−9.76784	−	24.4209i	−0.321861	−	0.804695i
$922$		0			0
$923$	−3.15047	−	2.64355i	−0.103699	−	0.0870136i
$924$		0			0
$925$	−59.3827	−	21.6135i	−1.95249	−	0.710649i
$926$		0			0
$927$	36.9407	+	18.3369i	1.21329	+	0.602263i
$928$		0			0
$929$	8.06709	−	6.76910i	0.264673	−	0.222087i	−0.500787	−	0.865571i	$-0.666956\pi$
$929$	8.06709	−	6.76910i	0.264673	−	0.222087i	0.765460	+	0.643484i	$0.222512\pi$
$930$		0			0
$931$	27.0162	−	9.32172i	0.885420	−	0.305507i
$932$		0			0
$933$	20.3989	−	18.2390i	0.667831	−	0.597117i
$934$		0			0
$935$	39.1405	+	22.5978i	1.28003	+	0.739026i
$936$		0			0
$937$	−22.8918	+	13.2166i	−0.747843	+	0.431767i	−0.824914	−	0.565258i	$-0.808777\pi$
$937$	−22.8918	+	13.2166i	−0.747843	+	0.431767i	0.0770710	+	0.997026i	$0.475443\pi$
$938$		0			0
$939$	−0.599817	−	19.0826i	−0.0195743	−	0.622736i
$940$		0			0
$941$	−3.31787	+	1.20761i	−0.108160	+	0.0393668i	−0.395533	−	0.918452i	$-0.629440\pi$
$941$	−3.31787	+	1.20761i	−0.108160	+	0.0393668i	0.287374	+	0.957819i	$0.407218\pi$
$942$		0			0
$943$	24.2156	−	4.26986i	0.788568	−	0.139046i
$944$		0			0
$945$	16.2012	+	44.7080i	0.527025	+	1.45435i
$946$		0			0
$947$	−11.9452	+	2.10627i	−0.388168	+	0.0684445i	−0.364327	−	0.931271i	$-0.618701\pi$
$947$	−11.9452	+	2.10627i	−0.388168	+	0.0684445i	−0.0238416	+	0.999716i	$0.507590\pi$
$948$		0			0
$949$	3.55371	−	1.29345i	0.115358	−	0.0419870i
$950$		0			0
$951$	2.99163	−	1.85492i	0.0970104	−	0.0601499i
$952$		0			0
$953$	38.2620	−	22.0906i	1.23943	−	0.715583i	0.270449	−	0.962734i	$-0.412828\pi$
$953$	38.2620	−	22.0906i	1.23943	−	0.715583i	0.968977	+	0.247151i	$0.0794944\pi$
$954$		0			0
$955$	44.0664	+	25.4418i	1.42596	+	0.823276i
$956$		0			0
$957$	3.35739	+	16.0704i	0.108529	+	0.519483i
$958$		0			0
$959$	−0.563048	−	7.12512i	−0.0181818	−	0.230082i
$960$		0			0
$961$	−65.2387	+	54.7418i	−2.10447	+	1.76586i
$962$		0			0
$963$	19.7292	−	4.77326i	0.635764	−	0.153816i
$964$		0			0
$965$	−29.0690	−	10.5802i	−0.935763	−	0.340590i
$966$		0			0
$967$	−18.9904	−	15.9348i	−0.610689	−	0.512429i	0.284172	−	0.958773i	$-0.408281\pi$
$967$	−18.9904	−	15.9348i	−0.610689	−	0.512429i	−0.894861	+	0.446344i	$0.852726\pi$
$968$		0			0
$969$	18.0736	−	22.9677i	0.580608	−	0.737830i
$970$		0			0
$971$	−38.0070			−1.21970			−0.609852	−	0.792515i	$-0.708771\pi$
$971$	−38.0070			−1.21970			−0.609852	+	0.792515i	$0.708771\pi$
$972$		0			0
$973$	15.2732	−	3.95511i	0.489635	−	0.126795i
$974$		0			0
$975$	−4.21511	+	5.35652i	−0.134992	+	0.171546i
$976$		0			0
$977$	5.98193	−	7.12898i	0.191379	−	0.228076i	−0.661819	−	0.749663i	$-0.730215\pi$
$977$	5.98193	−	7.12898i	0.191379	−	0.228076i	0.853198	+	0.521587i	$0.174660\pi$
$978$		0			0
$979$	−6.39853	+	17.5798i	−0.204498	+	0.561854i
$980$		0			0
$981$	−2.81677	−	11.6425i	−0.0899327	−	0.371716i
$982$		0			0
$983$	−17.4540	+	14.6456i	−0.556695	+	0.467122i	−0.877200	−	0.480124i	$-0.840592\pi$
$983$	−17.4540	+	14.6456i	−0.556695	+	0.467122i	0.320506	+	0.947247i	$0.396147\pi$
$984$		0			0
$985$	14.0412	+	2.47584i	0.447389	+	0.0788868i
$986$		0			0
$987$	39.3146	−	19.4464i	1.25140	−	0.618987i
$988$		0			0
$989$	−19.3893	−	11.1944i	−0.616545	−	0.355962i
$990$		0			0
$991$	23.6289	+	40.9265i	0.750597	+	1.30007i	0.947533	+	0.319656i	$0.103568\pi$
$991$	23.6289	+	40.9265i	0.750597	+	1.30007i	−0.196936	+	0.980416i	$0.563099\pi$
$992$		0			0
$993$	7.92514	+	12.7818i	0.251497	+	0.405617i
$994$		0			0
$995$	−6.08764	−	16.7257i	−0.192991	−	0.530239i
$996$		0			0
$997$	−57.6137	+	10.1589i	−1.82465	+	0.321734i	−0.977710	−	0.209961i	$-0.932666\pi$
$997$	−57.6137	+	10.1589i	−1.82465	+	0.321734i	−0.846936	+	0.531695i	$0.821555\pi$
$998$		0			0
$999$	27.3129	+	38.4314i	0.864142	+	1.21592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.6	✓	144
7.6	odd	2	inner	756.2.bx.a.41.19	yes	144
27.2	odd	18	inner	756.2.bx.a.461.19	yes	144
189.83	even	18	inner	756.2.bx.a.461.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.6	✓	144	1.1	even	1	trivial
756.2.bx.a.41.19	yes	144	7.6	odd	2	inner
756.2.bx.a.461.6	yes	144	189.83	even	18	inner
756.2.bx.a.461.19	yes	144	27.2	odd	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36115 - 1.07111i) q^{3} +(-2.64973 - 2.22338i) q^{5} +(0.252743 - 2.63365i) q^{7} +(0.705464 + 2.91587i) q^{9} +O(q^{10})\)	\(q+(-1.36115 - 1.07111i) q^{3} +(-2.64973 - 2.22338i) q^{5} +(0.252743 - 2.63365i) q^{7} +(0.705464 + 2.91587i) q^{9} +(-2.03215 - 2.42182i) q^{11} +(-0.556467 - 0.0981201i) q^{13} +(1.22520 + 5.86450i) q^{15} +(2.06648 - 3.57924i) q^{17} +(-3.53576 + 2.04137i) q^{19} +(-3.16494 + 3.31408i) q^{21} +(-0.946495 - 2.60047i) q^{23} +(1.20937 + 6.85868i) q^{25} +(2.16297 - 4.72457i) q^{27} +(2.95261 - 0.520625i) q^{29} +(3.68626 + 10.1279i) q^{31} +(0.172035 + 5.47311i) q^{33} +(-6.52532 + 6.41651i) q^{35} +(-4.53685 + 7.85806i) q^{37} +(0.652338 + 0.729591i) q^{39} +(-1.54293 + 8.75041i) q^{41} +(6.19754 - 5.20035i) q^{43} +(4.61382 - 9.29479i) q^{45} +(-8.99408 - 3.27358i) q^{47} +(-6.87224 - 1.33128i) q^{49} +(-6.64653 + 2.65847i) q^{51} +5.85691i q^{53} +10.9354i q^{55} +(6.99922 + 1.00856i) q^{57} +(-5.73216 - 4.80985i) q^{59} +(1.66114 - 4.56395i) q^{61} +(7.85770 - 1.12098i) q^{63} +(1.25633 + 1.49723i) q^{65} +(0.725278 - 4.11326i) q^{67} +(-1.49706 + 4.55343i) q^{69} +(6.30324 + 3.63918i) q^{71} +(-5.79615 + 3.34641i) q^{73} +(5.70024 - 10.6311i) q^{75} +(-6.89184 + 4.73987i) q^{77} +(-0.410711 - 2.32926i) q^{79} +(-8.00464 + 4.11409i) q^{81} +(-2.32844 - 13.2053i) q^{83} +(-13.4336 + 4.88944i) q^{85} +(-4.57660 - 2.45391i) q^{87} +(-2.95877 - 5.12473i) q^{89} +(-0.399057 + 1.44074i) q^{91} +(5.83051 - 17.7340i) q^{93} +(13.9075 + 2.45227i) q^{95} +(6.65243 + 7.92806i) q^{97} +(5.62812 - 7.63400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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