LMFDB - Embedded newform 912.2.ci.f.895.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} + \cdots + 1367631 $ x^18 - 6x^17 - 3x^16 + 100x^15 - 171x^14 - 471x^13 + 1537x^12 + 321x^11 - 3936x^10 - 1317x^9 + 4941x^8 + 21078x^7 - 14829x^6 - 68589x^5 - 45711x^4 + 421452x^3 - 61938x^2 - 1219779*x + 1367631
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			895.1
Root			$1.98709 + 0.839158i$ of defining polynomial
Character	$\chi$	$=$	912.895
Dual form			912.2.ci.f.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{3} +(-3.87454 + 1.41022i) q^{5} +(3.15920 - 1.82397i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{3} +(-3.87454 + 1.41022i) q^{5} +(3.15920 - 1.82397i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-3.84496 - 2.21989i) q^{11} +(-1.63837 - 1.95253i) q^{13} +(-3.87454 - 1.41022i) q^{15} +(0.911628 - 5.17010i) q^{17} +(3.02288 - 3.14041i) q^{19} +(3.59251 + 0.633457i) q^{21} +(0.131586 - 0.361530i) q^{23} +(9.19310 - 7.71393i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(1.63226 - 0.287812i) q^{29} +(3.82622 + 6.62722i) q^{31} +(-1.51849 - 4.17203i) q^{33} +(-9.66825 + 11.5222i) q^{35} +3.69658i q^{37} -2.54884i q^{39} +(6.15307 - 7.33294i) q^{41} +(-1.24774 - 3.42813i) q^{43} +(-2.06160 - 3.57079i) q^{45} +(-6.65325 + 1.17315i) q^{47} +(3.15370 - 5.46237i) q^{49} +(4.02162 - 3.37454i) q^{51} +(3.78420 - 10.3970i) q^{53} +(18.0280 + 3.17882i) q^{55} +(4.33428 - 0.462625i) q^{57} +(0.705104 - 3.99884i) q^{59} +(-8.72996 - 3.17744i) q^{61} +(2.34484 + 2.79448i) q^{63} +(9.10139 + 5.25469i) q^{65} +(-0.516231 - 2.92769i) q^{67} +(0.333188 - 0.192366i) q^{69} +(-4.17878 + 1.52095i) q^{71} +(-7.13717 - 5.98880i) q^{73} +12.0007 q^{75} -16.1960 q^{77} +(-11.3896 - 9.55699i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(8.35618 - 4.82444i) q^{83} +(3.75882 + 21.3173i) q^{85} +(1.43539 + 0.828721i) q^{87} +(8.58784 + 10.2346i) q^{89} +(-8.73727 - 3.18011i) q^{91} +(-1.32883 + 7.53619i) q^{93} +(-7.28360 + 16.4306i) q^{95} +(-4.55463 - 0.803105i) q^{97} +(1.51849 - 4.17203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) $ 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$	$1$	$-1$

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
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$		0			0
$5$	−3.87454	+	1.41022i	−1.73275	+	0.630668i	−0.998820	−	0.0485626i	$-0.984536\pi$
$5$	−3.87454	+	1.41022i	−1.73275	+	0.630668i	−0.733925	+	0.679230i	$0.762314\pi$
$6$		0			0
$7$	3.15920	−	1.82397i	1.19407	−	0.689394i	0.234840	−	0.972034i	$-0.424544\pi$
$7$	3.15920	−	1.82397i	1.19407	−	0.689394i	0.959226	+	0.282640i	$0.0912102\pi$
$8$		0			0
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$		0			0
$11$	−3.84496	−	2.21989i	−1.15930	−	0.669321i	−0.208163	−	0.978094i	$-0.566748\pi$
$11$	−3.84496	−	2.21989i	−1.15930	−	0.669321i	−0.951136	+	0.308773i	$0.900082\pi$
$12$		0			0
$13$	−1.63837	−	1.95253i	−0.454401	−	0.541534i	0.489395	−	0.872062i	$-0.337218\pi$
$13$	−1.63837	−	1.95253i	−0.454401	−	0.541534i	−0.943796	+	0.330528i	$0.892773\pi$
$14$		0			0
$15$	−3.87454	−	1.41022i	−1.00040	−	0.364116i
$16$		0			0
$17$	0.911628	−	5.17010i	0.221102	−	1.25393i	−0.648896	−	0.760877i	$-0.724769\pi$
$17$	0.911628	−	5.17010i	0.221102	−	1.25393i	0.869998	−	0.493055i	$-0.164120\pi$
$18$		0			0
$19$	3.02288	−	3.14041i	0.693497	−	0.720460i
$19$	3.02288	−	3.14041i	0.693497	−	0.720460i
$20$		0			0
$21$	3.59251	+	0.633457i	0.783950	+	0.138232i
$22$		0			0
$23$	0.131586	−	0.361530i	0.0274376	−	0.0753843i	−0.925218	−	0.379437i	$-0.876118\pi$
$23$	0.131586	−	0.361530i	0.0274376	−	0.0753843i	0.952655	+	0.304053i	$0.0983399\pi$
$24$		0			0
$25$	9.19310	−	7.71393i	1.83862	−	1.54279i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	1.63226	−	0.287812i	0.303103	−	0.0534453i	−0.0200280	−	0.999799i	$-0.506376\pi$
$29$	1.63226	−	0.287812i	0.303103	−	0.0534453i	0.323131	+	0.946354i	$0.395264\pi$
$30$		0			0
$31$	3.82622	+	6.62722i	0.687210	+	1.19028i	0.972737	+	0.231912i	$0.0744982\pi$
$31$	3.82622	+	6.62722i	0.687210	+	1.19028i	−0.285526	+	0.958371i	$0.592168\pi$
$32$		0			0
$33$	−1.51849	−	4.17203i	−0.264336	−	0.726256i
$34$		0			0
$35$	−9.66825	+	11.5222i	−1.63423	+	1.94760i
$36$		0			0
$37$			3.69658i			0.607714i	0.952718	+	0.303857i	$0.0982745\pi$
$37$			3.69658i			0.607714i	−0.952718	+	0.303857i	$0.901726\pi$
$38$		0			0
$39$		−	2.54884i		−	0.408142i
$40$		0			0
$41$	6.15307	−	7.33294i	0.960948	−	1.14521i	−0.0283936	−	0.999597i	$-0.509039\pi$
$41$	6.15307	−	7.33294i	0.960948	−	1.14521i	0.989341	−	0.145616i	$-0.0465164\pi$
$42$		0			0
$43$	−1.24774	−	3.42813i	−0.190278	−	0.522785i	0.807466	−	0.589914i	$-0.200838\pi$
$43$	−1.24774	−	3.42813i	−0.190278	−	0.522785i	−0.997744	+	0.0671287i	$0.978616\pi$
$44$		0			0
$45$	−2.06160	−	3.57079i	−0.307325	−	0.532302i
$46$		0			0
$47$	−6.65325	+	1.17315i	−0.970477	+	0.171121i	−0.636345	−	0.771405i	$-0.719554\pi$
$47$	−6.65325	+	1.17315i	−0.970477	+	0.171121i	−0.334132	+	0.942526i	$0.608443\pi$
$48$		0			0
$49$	3.15370	−	5.46237i	0.450529	−	0.780338i
$50$		0			0
$51$	4.02162	−	3.37454i	0.563140	−	0.472530i
$52$		0			0
$53$	3.78420	−	10.3970i	0.519799	−	1.42814i	−0.350943	−	0.936397i	$-0.614139\pi$
$53$	3.78420	−	10.3970i	0.519799	−	1.42814i	0.870742	−	0.491740i	$-0.163639\pi$
$54$		0			0
$55$	18.0280	+	3.17882i	2.43089	+	0.428631i
$56$		0			0
$57$	4.33428	−	0.462625i	0.574089	−	0.0612761i
$58$		0			0
$59$	0.705104	−	3.99884i	0.0917967	−	0.520605i	−0.903885	−	0.427775i	$-0.859298\pi$
$59$	0.705104	−	3.99884i	0.0917967	−	0.520605i	0.995682	−	0.0928301i	$-0.0295914\pi$
$60$		0			0
$61$	−8.72996	−	3.17744i	−1.11776	−	0.406830i	−0.283923	−	0.958847i	$-0.591636\pi$
$61$	−8.72996	−	3.17744i	−1.11776	−	0.406830i	−0.833833	+	0.552017i	$0.813858\pi$
$62$		0			0
$63$	2.34484	+	2.79448i	0.295423	+	0.352071i
$64$		0			0
$65$	9.10139	+	5.25469i	1.12889	+	0.651764i
$66$		0			0
$67$	−0.516231	−	2.92769i	−0.0630677	−	0.357675i	−0.999967	−	0.00807642i	$-0.997429\pi$
$67$	−0.516231	−	2.92769i	−0.0630677	−	0.357675i	0.936900	−	0.349598i	$-0.113682\pi$
$68$		0			0
$69$	0.333188	−	0.192366i	0.0401111	−	0.0231582i
$70$		0			0
$71$	−4.17878	+	1.52095i	−0.495930	+	0.180504i	−0.577863	−	0.816134i	$-0.696113\pi$
$71$	−4.17878	+	1.52095i	−0.495930	+	0.180504i	0.0819324	+	0.996638i	$0.473891\pi$
$72$		0			0
$73$	−7.13717	−	5.98880i	−0.835343	−	0.700936i	0.121168	−	0.992632i	$-0.461336\pi$
$73$	−7.13717	−	5.98880i	−0.835343	−	0.700936i	−0.956511	+	0.291696i	$0.905780\pi$
$74$		0			0
$75$	12.0007			1.38573
$76$		0			0
$77$	−16.1960			−1.84571
$78$		0			0
$79$	−11.3896	−	9.55699i	−1.28143	−	1.07525i	−0.993046	−	0.117730i	$-0.962438\pi$
$79$	−11.3896	−	9.55699i	−1.28143	−	1.07525i	−0.288382	−	0.957516i	$-0.593117\pi$
$80$		0			0
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$		0			0
$83$	8.35618	−	4.82444i	0.917210	−	0.529551i	0.0344658	−	0.999406i	$-0.489027\pi$
$83$	8.35618	−	4.82444i	0.917210	−	0.529551i	0.882744	+	0.469855i	$0.155694\pi$
$84$		0			0
$85$	3.75882	+	21.3173i	0.407701	+	2.31219i
$86$		0			0
$87$	1.43539	+	0.828721i	0.153890	+	0.0888482i
$88$		0			0
$89$	8.58784	+	10.2346i	0.910309	+	1.08486i	0.996072	+	0.0885482i	$0.0282227\pi$
$89$	8.58784	+	10.2346i	0.910309	+	1.08486i	−0.0857631	+	0.996316i	$0.527333\pi$
$90$		0			0
$91$	−8.73727	−	3.18011i	−0.915915	−	0.333366i
$92$		0			0
$93$	−1.32883	+	7.53619i	−0.137794	+	0.781467i
$94$		0			0
$95$	−7.28360	+	16.4306i	−0.747282	+	1.68574i
$96$		0			0
$97$	−4.55463	−	0.803105i	−0.462453	−	0.0815429i	−0.0624326	−	0.998049i	$-0.519886\pi$
$97$	−4.55463	−	0.803105i	−0.462453	−	0.0815429i	−0.400020	+	0.916506i	$0.630997\pi$
$98$		0			0
$99$	1.51849	−	4.17203i	0.152614	−	0.419304i
$100$		0			0
$101$	6.37200	−	5.34675i	0.634038	−	0.532021i	−0.268143	−	0.963379i	$-0.586410\pi$
$101$	6.37200	−	5.34675i	0.634038	−	0.532021i	0.902181	+	0.431358i	$0.141965\pi$
$102$		0			0
$103$	−4.14170	+	7.17364i	−0.408094	+	0.706839i	−0.994676	−	0.103050i	$-0.967140\pi$
$103$	−4.14170	+	7.17364i	−0.408094	+	0.706839i	0.586582	+	0.809890i	$0.300473\pi$
$104$		0			0
$105$	−14.8126	+	2.61187i	−1.44556	+	0.254892i
$106$		0			0
$107$	8.41036	+	14.5672i	0.813060	+	1.40826i	0.910713	+	0.413041i	$0.135533\pi$
$107$	8.41036	+	14.5672i	0.813060	+	1.40826i	−0.0976527	+	0.995221i	$0.531133\pi$
$108$		0			0
$109$	−1.41232	−	3.88031i	−0.135276	−	0.371666i	0.853496	−	0.521099i	$-0.174478\pi$
$109$	−1.41232	−	3.88031i	−0.135276	−	0.371666i	−0.988772	+	0.149432i	$0.952255\pi$
$110$		0			0
$111$	−2.37611	+	2.83174i	−0.225531	+	0.268777i
$112$		0			0
$113$		−	1.66826i		−	0.156936i	−0.996917	−	0.0784681i	$-0.974997\pi$
$113$		−	1.66826i		−	0.156936i	0.996917	−	0.0784681i	$-0.0250029\pi$
$114$		0			0
$115$			1.58633i			0.147926i
$116$		0			0
$117$	1.63837	−	1.95253i	0.151467	−	0.180511i
$118$		0			0
$119$	−6.55006	−	17.9962i	−0.600443	−	1.64970i
$120$		0			0
$121$	4.35581	+	7.54448i	0.395982	+	0.685862i
$122$		0			0
$123$	9.42705	−	1.66224i	0.850008	−	0.149879i
$124$		0			0
$125$	−14.4327	+	24.9982i	−1.29090	+	2.23591i
$126$		0			0
$127$	−16.3441	+	13.7143i	−1.45030	+	1.21695i	−0.517943	+	0.855415i	$0.673302\pi$
$127$	−16.3441	+	13.7143i	−1.45030	+	1.21695i	−0.932359	+	0.361533i	$0.882253\pi$
$128$		0			0
$129$	1.24774	−	3.42813i	0.109857	−	0.301830i
$130$		0			0
$131$	−5.51003	−	0.971566i	−0.481413	−	0.0848861i	−0.0723252	−	0.997381i	$-0.523042\pi$
$131$	−5.51003	−	0.971566i	−0.481413	−	0.0848861i	−0.409088	+	0.912495i	$0.634153\pi$
$132$		0			0
$133$	3.82189	−	15.4348i	0.331400	−	1.33837i
$134$		0			0
$135$	0.715985	−	4.06055i	0.0616222	−	0.349477i
$136$		0			0
$137$	−4.34304	−	1.58074i	−0.371051	−	0.135052i	0.149762	−	0.988722i	$-0.452149\pi$
$137$	−4.34304	−	1.58074i	−0.371051	−	0.135052i	−0.520814	+	0.853670i	$0.674371\pi$
$138$		0			0
$139$	−8.70246	−	10.3712i	−0.738133	−	0.879673i	0.258124	−	0.966112i	$-0.416896\pi$
$139$	−8.70246	−	10.3712i	−0.738133	−	0.879673i	−0.996257	+	0.0864387i	$0.972451\pi$
$140$		0			0
$141$	−5.85077	−	3.37795i	−0.492724	−	0.284474i
$142$		0			0
$143$	1.96505	+	11.1444i	0.164326	+	0.931940i
$144$		0			0
$145$	−5.91838	+	3.41698i	−0.491495	+	0.283765i
$146$		0			0
$147$	5.92702	−	2.15726i	0.488852	−	0.177928i
$148$		0			0
$149$	5.45615	+	4.57825i	0.446985	+	0.375065i	0.838316	−	0.545185i	$-0.183541\pi$
$149$	5.45615	+	4.57825i	0.446985	+	0.375065i	−0.391331	+	0.920250i	$0.627985\pi$
$150$		0			0
$151$	15.1792			1.23527			0.617633	−	0.786466i	$-0.288092\pi$
$151$	15.1792			1.23527			0.617633	+	0.786466i	$0.288092\pi$
$152$		0			0
$153$	5.24985			0.424426
$154$		0			0
$155$	−24.1707	−	20.2816i	−1.94143	−	1.62906i
$156$		0			0
$157$	1.41375	−	0.514563i	0.112830	−	0.0410666i	−0.284988	−	0.958531i	$-0.591990\pi$
$157$	1.41375	−	0.514563i	0.112830	−	0.0410666i	0.397818	+	0.917464i	$0.369768\pi$
$158$		0			0
$159$	9.58192	−	5.53212i	0.759896	−	0.438726i
$160$		0			0
$161$	−0.243711	−	1.38216i	−0.0192071	−	0.108929i
$162$		0			0
$163$	18.7417	+	10.8205i	1.46796	+	0.847530i	0.999356	−	0.0358762i	$-0.0114222\pi$
$163$	18.7417	+	10.8205i	1.46796	+	0.847530i	0.468608	+	0.883406i	$0.344756\pi$
$164$		0			0
$165$	11.7669	+	14.0233i	0.916053	+	1.09171i
$166$		0			0
$167$	−2.52768	−	0.919999i	−0.195598	−	0.0711917i	0.242364	−	0.970185i	$-0.422077\pi$
$167$	−2.52768	−	0.919999i	−0.195598	−	0.0711917i	−0.437962	+	0.898994i	$0.644299\pi$
$168$		0			0
$169$	1.12930	−	6.40459i	0.0868694	−	0.492661i
$170$		0			0
$171$	3.61762	+	2.43163i	0.276646	+	0.185951i
$172$		0			0
$173$	7.34502	+	1.29512i	0.558431	+	0.0984665i	0.445738	−	0.895163i	$-0.352941\pi$
$173$	7.34502	+	1.29512i	0.558431	+	0.0984665i	0.112693	+	0.993630i	$0.464052\pi$
$174$		0			0
$175$	14.9729	−	41.1377i	1.13185	−	3.10972i
$176$		0			0
$177$	3.11055	−	2.61006i	0.233803	−	0.196184i
$178$		0			0
$179$	−11.0361	+	19.1151i	−0.824877	+	1.42873i	0.0771355	+	0.997021i	$0.475423\pi$
$179$	−11.0361	+	19.1151i	−0.824877	+	1.42873i	−0.902013	+	0.431709i	$0.857911\pi$
$180$		0			0
$181$	16.3128	−	2.87638i	1.21252	−	0.213800i	0.469417	−	0.882977i	$-0.344464\pi$
$181$	16.3128	−	2.87638i	1.21252	−	0.213800i	0.743103	+	0.669177i	$0.233353\pi$
$182$		0			0
$183$	−4.64511	−	8.04557i	−0.343377	−	0.594746i
$184$		0			0
$185$	−5.21297	−	14.3225i	−0.383265	−	1.05301i
$186$		0			0
$187$	−14.9822	+	17.8551i	−1.09561	+	1.30569i
$188$		0			0
$189$			3.64793i			0.265348i
$190$		0			0
$191$		−	13.5168i		−	0.978040i	−0.872273	−	0.489020i	$-0.837354\pi$
$191$		−	13.5168i		−	0.978040i	0.872273	−	0.489020i	$-0.162646\pi$
$192$		0			0
$193$	−8.59363	+	10.2415i	−0.618583	+	0.737198i	−0.980826	−	0.194885i	$-0.937567\pi$
$193$	−8.59363	+	10.2415i	−0.618583	+	0.737198i	0.362243	+	0.932084i	$0.382011\pi$
$194$		0			0
$195$	3.59442	+	9.87559i	0.257402	+	0.707206i
$196$		0			0
$197$	−3.62512	−	6.27888i	−0.258279	−	0.447352i	0.707502	−	0.706711i	$-0.249822\pi$
$197$	−3.62512	−	6.27888i	−0.258279	−	0.447352i	−0.965781	+	0.259359i	$0.916489\pi$
$198$		0			0
$199$	−3.88575	+	0.685162i	−0.275453	+	0.0485698i	−0.309668	−	0.950845i	$-0.600218\pi$
$199$	−3.88575	+	0.685162i	−0.275453	+	0.0485698i	0.0342150	+	0.999414i	$0.489107\pi$
$200$		0			0
$201$	1.48643	−	2.57457i	0.104845	−	0.181596i
$202$		0			0
$203$	4.63168	−	3.88644i	0.325080	−	0.272775i
$204$		0			0
$205$	−13.4993	+	37.0889i	−0.942829	+	2.59040i
$206$		0			0
$207$	0.378888	+	0.0668081i	0.0263345	+	0.00464348i
$208$		0			0
$209$	−18.5942	+	5.36430i	−1.28619	+	0.371056i
$210$		0			0
$211$	1.42733	−	8.09478i	0.0982613	−	0.557267i	−0.895438	−	0.445187i	$-0.853137\pi$
$211$	1.42733	−	8.09478i	0.0982613	−	0.557267i	0.993699	−	0.112081i	$-0.0357515\pi$
$212$		0			0
$213$	−4.17878	−	1.52095i	−0.286325	−	0.104214i
$214$		0			0
$215$	9.66882	+	11.5228i	0.659408	+	0.785852i
$216$		0			0
$217$	24.1756	+	13.9578i	1.64115	+	0.947517i
$218$		0			0
$219$	−1.61787	−	9.17537i	−0.109325	−	0.620014i
$220$		0			0
$221$	−11.5883	+	6.69053i	−0.779516	+	0.450054i
$222$		0			0
$223$	9.24001	−	3.36309i	0.618757	−	0.225209i	−0.0135737	−	0.999908i	$-0.504321\pi$
$223$	9.24001	−	3.36309i	0.618757	−	0.225209i	0.632330	+	0.774699i	$0.282099\pi$
$224$		0			0
$225$	9.19310	+	7.71393i	0.612873	+	0.514262i
$226$		0			0
$227$	−1.40070			−0.0929678			−0.0464839	−	0.998919i	$-0.514802\pi$
$227$	−1.40070			−0.0929678			−0.0464839	+	0.998919i	$0.514802\pi$
$228$		0			0
$229$	−9.69448			−0.640630			−0.320315	−	0.947311i	$-0.603789\pi$
$229$	−9.69448			−0.640630			−0.320315	+	0.947311i	$0.603789\pi$
$230$		0			0
$231$	−12.4069	−	10.4106i	−0.816311	−	0.684966i
$232$		0			0
$233$	−12.6643	+	4.60943i	−0.829665	+	0.301974i	−0.721722	−	0.692183i	$-0.756649\pi$
$233$	−12.6643	+	4.60943i	−0.829665	+	0.301974i	−0.107944	+	0.994157i	$0.534427\pi$
$234$		0			0
$235$	24.1239	−	13.9279i	1.57367	−	0.908558i
$236$		0			0
$237$	−2.58181	−	14.6422i	−0.167706	−	0.951110i
$238$		0			0
$239$	24.7614	+	14.2960i	1.60168	+	0.924732i	0.991151	+	0.132740i	$0.0423774\pi$
$239$	24.7614	+	14.2960i	1.60168	+	0.924732i	0.610531	+	0.791992i	$0.290956\pi$
$240$		0			0
$241$	−14.7002	−	17.5190i	−0.946920	−	1.12850i	−0.991580	−	0.129494i	$-0.958665\pi$
$241$	−14.7002	−	17.5190i	−0.946920	−	1.12850i	0.0446598	−	0.999002i	$-0.485780\pi$
$242$		0			0
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$		0			0
$245$	−4.51601	+	25.6115i	−0.288517	+	1.63626i
$246$		0			0
$247$	−11.0843	−	0.757117i	−0.705279	−	0.0481742i
$248$		0			0
$249$	9.50229	+	1.67551i	0.602183	+	0.106181i
$250$		0			0
$251$	−6.60246	+	18.1401i	−0.416744	+	1.14499i	0.536792	+	0.843714i	$0.319636\pi$
$251$	−6.60246	+	18.1401i	−0.416744	+	1.14499i	−0.953536	+	0.301279i	$0.902586\pi$
$252$		0			0
$253$	−1.30850	+	1.09796i	−0.0822647	+	0.0690283i
$254$		0			0
$255$	−10.8231	+	18.7461i	−0.677768	+	1.17393i
$256$		0			0
$257$	3.48437	−	0.614389i	0.217349	−	0.0383245i	−0.0639130	−	0.997955i	$-0.520358\pi$
$257$	3.48437	−	0.614389i	0.217349	−	0.0383245i	0.281262	+	0.959631i	$0.409247\pi$
$258$		0			0
$259$	6.74243	+	11.6782i	0.418954	+	0.725650i
$260$		0			0
$261$	0.566878	+	1.55749i	0.0350889	+	0.0964059i
$262$		0			0
$263$	−9.44534	+	11.2565i	−0.582425	+	0.694107i	−0.974131	−	0.225983i	$-0.927440\pi$
$263$	−9.44534	+	11.2565i	−0.582425	+	0.694107i	0.391706	+	0.920090i	$0.371885\pi$
$264$		0			0
$265$			45.6201i			2.80242i
$266$		0			0
$267$			13.3603i			0.817637i
$268$		0			0
$269$	−5.93473	+	7.07273i	−0.361847	+	0.431232i	−0.915997	−	0.401184i	$-0.868599\pi$
$269$	−5.93473	+	7.07273i	−0.361847	+	0.431232i	0.554151	+	0.832416i	$0.313043\pi$
$270$		0			0
$271$	3.95984	+	10.8796i	0.240543	+	0.660887i	0.999947	+	0.0102675i	$0.00326830\pi$
$271$	3.95984	+	10.8796i	0.240543	+	0.660887i	−0.759404	+	0.650619i	$0.774509\pi$
$272$		0			0
$273$	−4.64900	−	8.05231i	−0.281370	−	0.487348i
$274$		0			0
$275$	−52.4712	+	9.25208i	−3.16413	+	0.557921i
$276$		0			0
$277$	1.38165	−	2.39308i	0.0830151	−	0.143786i	−0.821529	−	0.570167i	$-0.806878\pi$
$277$	1.38165	−	2.39308i	0.0830151	−	0.143786i	0.904544	+	0.426381i	$0.140212\pi$
$278$		0			0
$279$	−5.86212	+	4.91890i	−0.350956	+	0.294487i
$280$		0			0
$281$	0.578584	−	1.58965i	0.0345154	−	0.0948304i	−0.921238	−	0.389000i	$-0.872821\pi$
$281$	0.578584	−	1.58965i	0.0345154	−	0.0948304i	0.955753	+	0.294169i	$0.0950429\pi$
$282$		0			0
$283$	0.165519	+	0.0291855i	0.00983910	+	0.00173490i	0.178566	−	0.983928i	$-0.442854\pi$
$283$	0.165519	+	0.0291855i	0.00983910	+	0.00173490i	−0.168726	+	0.985663i	$0.553965\pi$
$284$		0			0
$285$	−16.1409	+	7.90473i	−0.956106	+	0.468236i
$286$		0			0
$287$	6.06375	−	34.3892i	0.357932	−	2.02993i
$288$		0			0
$289$	−9.92406	−	3.61206i	−0.583768	−	0.212474i
$290$		0			0
$291$	−2.97283	−	3.54288i	−0.174270	−	0.207687i
$292$		0			0
$293$	0.682160	+	0.393845i	0.0398522	+	0.0230087i	0.519794	−	0.854292i	$-0.326009\pi$
$293$	0.682160	+	0.393845i	0.0398522	+	0.0230087i	−0.479942	+	0.877300i	$0.659342\pi$
$294$		0			0
$295$	2.90728	+	16.4880i	0.169269	+	0.959969i
$296$		0			0
$297$	3.84496	−	2.21989i	0.223107	−	0.128811i
$298$		0			0
$299$	−0.921484	+	0.335393i	−0.0532908	+	0.0193963i
$300$		0			0
$301$	−10.1947	−	8.55433i	−0.587610	−	0.493063i
$302$		0			0
$303$	8.31806			0.477860
$304$		0			0
$305$	38.3054			2.19336
$306$		0			0
$307$	22.9191	+	19.2314i	1.30806	+	1.09759i	0.988692	+	0.149961i	$0.0479150\pi$
$307$	22.9191	+	19.2314i	1.30806	+	1.09759i	0.319368	+	0.947631i	$0.396529\pi$
$308$		0			0
$309$	−7.78385	+	2.83309i	−0.442808	+	0.161169i
$310$		0			0
$311$	9.60316	−	5.54439i	0.544545	−	0.314393i	−0.202374	−	0.979308i	$-0.564866\pi$
$311$	9.60316	−	5.54439i	0.544545	−	0.314393i	0.746919	+	0.664915i	$0.231532\pi$
$312$		0			0
$313$	−5.00657	−	28.3937i	−0.282988	−	1.60490i	−0.712385	−	0.701789i	$-0.752385\pi$
$313$	−5.00657	−	28.3937i	−0.282988	−	1.60490i	0.429397	−	0.903116i	$-0.358726\pi$
$314$		0			0
$315$	−13.0260	−	7.52057i	−0.733932	−	0.423736i
$316$		0			0
$317$	2.34077	+	2.78962i	0.131471	+	0.156681i	0.827763	−	0.561077i	$-0.189613\pi$
$317$	2.34077	+	2.78962i	0.131471	+	0.156681i	−0.696293	+	0.717758i	$0.745168\pi$
$318$		0			0
$319$	−6.91489	−	2.51681i	−0.387159	−	0.140914i
$320$		0			0
$321$	−2.92089	+	16.5652i	−0.163028	+	0.924578i
$322$		0			0
$323$	−13.4805	−	18.4915i	−0.750075	−	1.02889i
$324$		0			0
$325$	−30.1233	−	5.31155i	−1.67094	−	0.294632i
$326$		0			0
$327$	1.41232	−	3.88031i	0.0781014	−	0.214582i
$328$		0			0
$329$	−18.8792	+	15.8415i	−1.04084	+	0.873371i
$330$		0			0
$331$	4.51375	−	7.81805i	0.248098	−	0.429719i	−0.714900	−	0.699227i	$-0.753528\pi$
$331$	4.51375	−	7.81805i	0.248098	−	0.429719i	0.962998	+	0.269508i	$0.0868610\pi$
$332$		0			0
$333$	−3.64042	+	0.641904i	−0.199494	+	0.0351761i
$334$		0			0
$335$	6.12884	+	10.6155i	0.334854	+	0.579985i
$336$		0			0
$337$	−0.984403	−	2.70463i	−0.0536239	−	0.147330i	0.909989	−	0.414633i	$-0.136090\pi$
$337$	−0.984403	−	2.70463i	−0.0536239	−	0.147330i	−0.963613	+	0.267302i	$0.913868\pi$
$338$		0			0
$339$	1.07233	−	1.27796i	0.0582412	−	0.0694091i
$340$		0			0
$341$		−	33.9752i		−	1.83986i
$342$		0			0
$343$			2.52656i			0.136421i
$344$		0			0
$345$	−1.01967	+	1.21520i	−0.0548973	+	0.0654240i
$346$		0			0
$347$	2.82775	+	7.76919i	0.151802	+	0.417072i	0.992162	−	0.124956i	$-0.0398790\pi$
$347$	2.82775	+	7.76919i	0.151802	+	0.417072i	−0.840361	+	0.542028i	$0.817657\pi$
$348$		0			0
$349$	13.8793	+	24.0396i	0.742939	+	1.28681i	0.951151	+	0.308725i	$0.0999023\pi$
$349$	13.8793	+	24.0396i	0.742939	+	1.28681i	−0.208212	+	0.978084i	$0.566764\pi$
$350$		0			0
$351$	2.51012	−	0.442602i	0.133980	−	0.0236244i
$352$		0			0
$353$	15.7543	−	27.2872i	0.838514	−	1.45235i	−0.0526222	−	0.998614i	$-0.516758\pi$
$353$	15.7543	−	27.2872i	0.838514	−	1.45235i	0.891137	−	0.453735i	$-0.149909\pi$
$354$		0			0
$355$	14.0460	−	11.7860i	0.745483	−	0.625534i
$356$		0			0
$357$	6.55006	−	17.9962i	0.346666	−	0.952457i
$358$		0			0
$359$	18.4789	+	3.25833i	0.975278	+	0.171968i	0.638505	−	0.769618i	$-0.279553\pi$
$359$	18.4789	+	3.25833i	0.975278	+	0.171968i	0.336773	+	0.941586i	$0.390664\pi$
$360$		0			0
$361$	−0.724378	−	18.9862i	−0.0381251	−	0.999273i
$362$		0			0
$363$	−1.51276	+	8.57927i	−0.0793991	+	0.450295i
$364$		0			0
$365$	36.0987	+	13.1389i	1.88949	+	0.687720i
$366$		0			0
$367$	−7.72621	−	9.20774i	−0.403305	−	0.480640i	0.525720	−	0.850658i	$-0.323796\pi$
$367$	−7.72621	−	9.20774i	−0.403305	−	0.480640i	−0.929025	+	0.370018i	$0.879352\pi$
$368$		0			0
$369$	8.29000	+	4.78624i	0.431560	+	0.249162i
$370$		0			0
$371$	−7.00872	−	39.7484i	−0.363875	−	2.06364i
$372$		0			0
$373$	23.0578	−	13.3124i	1.19389	−	0.689291i	0.234701	−	0.972068i	$-0.424589\pi$
$373$	23.0578	−	13.3124i	1.19389	−	0.689291i	0.959186	+	0.282777i	$0.0912556\pi$
$374$		0			0
$375$	−27.1246	+	9.87256i	−1.40071	+	0.509817i
$376$		0			0
$377$	−3.23620	−	2.71549i	−0.166673	−	0.139855i
$378$		0			0
$379$	17.9652			0.922808			0.461404	−	0.887190i	$-0.347346\pi$
$379$	17.9652			0.922808			0.461404	+	0.887190i	$0.347346\pi$
$380$		0			0
$381$	−21.3357			−1.09306
$382$		0			0
$383$	−12.5580	−	10.5374i	−0.641682	−	0.538435i	0.262852	−	0.964836i	$-0.415337\pi$
$383$	−12.5580	−	10.5374i	−0.641682	−	0.538435i	−0.904534	+	0.426401i	$0.859781\pi$
$384$		0			0
$385$	62.7520	−	22.8399i	3.19814	−	1.16403i
$386$		0			0
$387$	3.15938	−	1.82407i	0.160601	−	0.0927228i
$388$		0			0
$389$	2.33388	+	13.2361i	0.118332	+	0.671095i	0.985046	+	0.172290i	$0.0551166\pi$
$389$	2.33388	+	13.2361i	0.118332	+	0.671095i	−0.866714	+	0.498805i	$0.833772\pi$
$390$		0			0
$391$	−1.74919	−	1.00989i	−0.0884603	−	0.0510726i
$392$		0			0
$393$	−3.59641	−	4.28604i	−0.181415	−	0.216202i
$394$		0			0
$395$	57.6067	+	20.9671i	2.89851	+	1.05497i
$396$		0			0
$397$	4.75521	−	26.9682i	0.238657	−	1.35349i	−0.596115	−	0.802899i	$-0.703290\pi$
$397$	4.75521	−	26.9682i	0.238657	−	1.35349i	0.834773	−	0.550594i	$-0.185599\pi$
$398$		0			0
$399$	12.8490	−	9.36710i	0.643257	−	0.468942i
$400$		0			0
$401$	35.6930	+	6.29365i	1.78243	+	0.314290i	0.965099	−	0.261885i	$-0.0843442\pi$
$401$	35.6930	+	6.29365i	1.78243	+	0.314290i	0.817326	+	0.576175i	$0.195455\pi$
$402$		0			0
$403$	6.67107	−	18.3286i	0.332310	−	0.913013i
$404$		0			0
$405$	3.15855	−	2.65034i	0.156950	−	0.131696i
$406$		0			0
$407$	8.20599	−	14.2132i	0.406756	−	0.704522i
$408$		0			0
$409$	34.9323	−	6.15951i	1.72729	−	0.304568i	0.780200	−	0.625531i	$-0.215117\pi$
$409$	34.9323	−	6.15951i	1.72729	−	0.304568i	0.947092	+	0.320962i	$0.104006\pi$
$410$		0			0
$411$	−2.31088	−	4.00257i	−0.113988	−	0.197432i
$412$		0			0
$413$	−5.06619	−	13.9192i	−0.249291	−	0.684921i
$414$		0			0
$415$	−25.5728	+	30.4765i	−1.25532	+	1.49603i
$416$		0			0
$417$		−	13.5386i		−	0.662990i
$418$		0			0
$419$			12.1067i			0.591452i	0.955273	+	0.295726i	$0.0955616\pi$
$419$			12.1067i			0.591452i	−0.955273	+	0.295726i	$0.904438\pi$
$420$		0			0
$421$	−13.3314	+	15.8877i	−0.649733	+	0.774321i	−0.985874	−	0.167490i	$-0.946434\pi$
$421$	−13.3314	+	15.8877i	−0.649733	+	0.774321i	0.336141	+	0.941812i	$0.390878\pi$
$422$		0			0
$423$	−2.31065	−	6.34846i	−0.112348	−	0.308673i
$424$		0			0
$425$	−31.5011	−	54.5615i	−1.52803	−	2.64662i
$426$		0			0
$427$	−33.3752	+	5.88495i	−1.61514	+	0.284793i
$428$		0			0
$429$	−5.65815	+	9.80020i	−0.273178	+	0.473158i
$430$		0			0
$431$	6.78641	−	5.69447i	0.326890	−	0.274293i	−0.464541	−	0.885551i	$-0.653781\pi$
$431$	6.78641	−	5.69447i	0.326890	−	0.274293i	0.791431	+	0.611258i	$0.209336\pi$
$432$		0			0
$433$	2.14150	−	5.88372i	0.102914	−	0.282754i	−0.877540	−	0.479504i	$-0.840817\pi$
$433$	2.14150	−	5.88372i	0.102914	−	0.282754i	0.980454	+	0.196750i	$0.0630388\pi$
$434$		0			0
$435$	−6.73013	−	1.18670i	−0.322685	−	0.0568981i
$436$		0			0
$437$	−0.737585	−	1.50610i	−0.0352835	−	0.0720465i
$438$		0			0
$439$	1.17328	−	6.65398i	0.0559974	−	0.317577i	−0.943923	−	0.330165i	$-0.892896\pi$
$439$	1.17328	−	6.65398i	0.0559974	−	0.317577i	0.999921	+	0.0125876i	$0.00400686\pi$
$440$		0			0
$441$	5.92702	+	2.15726i	0.282239	+	0.102727i
$442$		0			0
$443$	13.5778	+	16.1814i	0.645101	+	0.768802i	0.985167	−	0.171600i	$-0.0548936\pi$
$443$	13.5778	+	16.1814i	0.645101	+	0.768802i	−0.340065	+	0.940402i	$0.610449\pi$
$444$		0			0
$445$	−47.7069	−	27.5436i	−2.26152	−	1.30569i
$446$		0			0
$447$	1.23681	+	7.01429i	0.0584990	+	0.331764i
$448$		0			0
$449$	4.36515	−	2.52022i	0.206004	−	0.118937i	−0.393449	−	0.919347i	$-0.628718\pi$
$449$	4.36515	−	2.52022i	0.206004	−	0.118937i	0.599453	+	0.800410i	$0.295385\pi$
$450$		0			0
$451$	−39.9366	+	14.5357i	−1.88054	+	0.684461i
$452$		0			0
$453$	11.6279	+	9.75701i	0.546329	+	0.458424i
$454$		0			0
$455$	38.3375			1.79729
$456$		0			0
$457$	−16.8633			−0.788833			−0.394417	−	0.918932i	$-0.629053\pi$
$457$	−16.8633			−0.788833			−0.394417	+	0.918932i	$0.629053\pi$
$458$		0			0
$459$	4.02162	+	3.37454i	0.187713	+	0.157510i
$460$		0			0
$461$	17.4279	−	6.34325i	0.811699	−	0.295434i	0.0973738	−	0.995248i	$-0.468956\pi$
$461$	17.4279	−	6.34325i	0.811699	−	0.295434i	0.714326	+	0.699813i	$0.246734\pi$
$462$		0			0
$463$	−36.4641	+	21.0525i	−1.69463	+	0.978394i	−0.743941	+	0.668245i	$0.767046\pi$
$463$	−36.4641	+	21.0525i	−1.69463	+	0.978394i	−0.950688	+	0.310149i	$0.899621\pi$
$464$		0			0
$465$	−5.47904	−	31.0732i	−0.254084	−	1.44098i
$466$		0			0
$467$	−12.6239	−	7.28839i	−0.584162	−	0.337266i	0.178624	−	0.983917i	$-0.442836\pi$
$467$	−12.6239	−	7.28839i	−0.584162	−	0.337266i	−0.762786	+	0.646651i	$0.776169\pi$
$468$		0			0
$469$	−6.97089	−	8.30759i	−0.321886	−	0.383609i
$470$		0			0
$471$	1.41375	+	0.514563i	0.0651422	+	0.0237098i
$472$		0			0
$473$	−2.81257	+	15.9509i	−0.129322	+	0.733422i
$474$		0			0
$475$	3.56474	−	52.1884i	0.163562	−	2.39457i
$476$		0			0
$477$	10.8962	+	1.92129i	0.498901	+	0.0879697i
$478$		0			0
$479$	2.56822	−	7.05614i	0.117345	−	0.322403i	−0.867090	−	0.498152i	$-0.834012\pi$
$479$	2.56822	−	7.05614i	0.117345	−	0.322403i	0.984435	+	0.175748i	$0.0562345\pi$
$480$		0			0
$481$	7.21767	−	6.05635i	0.329098	−	0.276146i
$482$		0			0
$483$	0.701739	−	1.21545i	0.0319302	−	0.0553048i
$484$		0			0
$485$	18.7796	−	3.31136i	0.852740	−	0.150361i
$486$		0			0
$487$	−16.1563	−	27.9835i	−0.732112	−	1.26805i	−0.955979	−	0.293435i	$-0.905201\pi$
$487$	−16.1563	−	27.9835i	−0.732112	−	1.26805i	0.223867	−	0.974620i	$-0.428132\pi$
$488$		0			0
$489$	7.40168	+	20.3360i	0.334716	+	0.919624i
$490$		0			0
$491$	−9.83722	+	11.7235i	−0.443948	+	0.529076i	−0.940892	−	0.338706i	$-0.890011\pi$
$491$	−9.83722	+	11.7235i	−0.443948	+	0.529076i	0.496945	+	0.867782i	$0.334455\pi$
$492$		0			0
$493$		−	8.70133i		−	0.391888i
$494$		0			0
$495$			18.3061i			0.822796i
$496$		0			0
$497$	−10.4274	+	12.4269i	−0.467735	+	0.557425i
$498$		0			0
$499$	11.2552	+	30.9233i	0.503850	+	1.38432i	0.887487	+	0.460833i	$0.152449\pi$
$499$	11.2552	+	30.9233i	0.503850	+	1.38432i	−0.383637	+	0.923484i	$0.625329\pi$
$500$		0			0
$501$	−1.34495	−	2.32952i	−0.0600879	−	0.104075i
$502$		0			0
$503$	21.5742	−	3.80411i	0.961946	−	0.169617i	0.329443	−	0.944175i	$-0.393139\pi$
$503$	21.5742	−	3.80411i	0.961946	−	0.169617i	0.632502	+	0.774558i	$0.282028\pi$
$504$		0			0
$505$	−17.1485	+	29.7021i	−0.763098	+	1.32172i
$506$		0			0
$507$	4.98189	−	4.18030i	0.221253	−	0.185654i
$508$		0			0
$509$	6.38080	−	17.5311i	0.282824	−	0.777052i	−0.714199	−	0.699943i	$-0.753209\pi$
$509$	6.38080	−	17.5311i	0.282824	−	0.777052i	0.997023	−	0.0771091i	$-0.0245690\pi$
$510$		0			0
$511$	−33.4711	−	5.90186i	−1.48068	−	0.261083i
$512$		0			0
$513$	1.20824	+	4.18810i	0.0533449	+	0.184909i
$514$		0			0
$515$	5.93079	−	33.6352i	0.261342	−	1.48214i
$516$		0			0
$517$	28.1858	+	10.2588i	1.23961	+	0.451180i
$518$		0			0
$519$	4.79412	+	5.71341i	0.210438	+	0.250791i
$520$		0			0
$521$	−36.2200	−	20.9116i	−1.58683	−	0.916155i	−0.993826	−	0.110953i	$-0.964610\pi$
$521$	−36.2200	−	20.9116i	−1.58683	−	0.916155i	−0.593001	−	0.805202i	$-0.702057\pi$
$522$		0			0
$523$	1.71274	+	9.71345i	0.0748931	+	0.424740i	0.999083	+	0.0428073i	$0.0136302\pi$
$523$	1.71274	+	9.71345i	0.0748931	+	0.424740i	−0.924190	+	0.381932i	$0.875259\pi$
$524$		0			0
$525$	37.9128	−	21.8889i	1.65465	−	0.955312i
$526$		0			0
$527$	37.7514	−	13.7404i	1.64448	−	0.598541i
$528$		0			0
$529$	17.5056	+	14.6890i	0.761114	+	0.638651i
$530$		0			0
$531$	4.06053			0.176212
$532$		0			0
$533$	−24.3987			−1.05683
$534$		0			0
$535$	−53.1291	−	44.5806i	−2.29697	−	1.92739i
$536$		0			0
$537$	−20.7411	+	7.54914i	−0.895044	+	0.325770i
$538$		0			0
$539$	−24.2517	+	14.0017i	−1.04459	+	0.603097i
$540$		0			0
$541$	2.63537	+	14.9459i	0.113304	+	0.642577i	0.987576	+	0.157141i	$0.0502278\pi$
$541$	2.63537	+	14.9459i	0.113304	+	0.642577i	−0.874273	+	0.485435i	$0.838661\pi$
$542$		0			0
$543$	14.3452	+	8.28222i	0.615613	+	0.355424i
$544$		0			0
$545$	10.9442	+	13.0427i	0.468796	+	0.558689i
$546$		0			0
$547$	18.1236	+	6.59645i	0.774909	+	0.282044i	0.699048	−	0.715074i	$-0.253607\pi$
$547$	18.1236	+	6.59645i	0.774909	+	0.282044i	0.0758611	+	0.997118i	$0.475829\pi$
$548$		0			0
$549$	1.61323	−	9.14909i	0.0688510	−	0.390473i
$550$		0			0
$551$	4.03028	−	5.99599i	0.171696	−	0.255438i
$552$		0			0
$553$	−53.4136	−	9.41825i	−2.27138	−	0.400505i
$554$		0			0
$555$	5.21297	−	14.3225i	0.221278	−	0.607957i
$556$		0			0
$557$	−16.2789	+	13.6596i	−0.689759	+	0.578777i	−0.918840	−	0.394631i	$-0.870872\pi$
$557$	−16.2789	+	13.6596i	−0.689759	+	0.578777i	0.229081	+	0.973407i	$0.426428\pi$
$558$		0			0
$559$	−4.64927	+	8.05278i	−0.196643	+	0.340596i
$560$		0			0
$561$	−22.9541	+	4.04742i	−0.969122	+	0.170882i
$562$		0			0
$563$	−13.2679	−	22.9807i	−0.559175	−	0.968519i	−0.997566	−	0.0697347i	$-0.977785\pi$
$563$	−13.2679	−	22.9807i	−0.559175	−	0.968519i	0.438391	−	0.898784i	$-0.355549\pi$
$564$		0			0
$565$	2.35260	+	6.46372i	0.0989746	+	0.271931i
$566$		0			0
$567$	−2.34484	+	2.79448i	−0.0984742	+	0.117357i
$568$		0			0
$569$			22.9845i			0.963562i	0.876292	+	0.481781i	$0.160010\pi$
$569$			22.9845i			0.963562i	−0.876292	+	0.481781i	$0.839990\pi$
$570$		0			0
$571$			22.1531i			0.927077i	0.886077	+	0.463538i	$0.153420\pi$
$571$			22.1531i			0.927077i	−0.886077	+	0.463538i	$0.846580\pi$
$572$		0			0
$573$	8.68842	−	10.3545i	0.362964	−	0.432564i
$574$		0			0
$575$	−1.57913	−	4.33863i	−0.0658544	−	0.180933i
$576$		0			0
$577$	12.0619	+	20.8917i	0.502141	+	0.869735i	0.999997	+	0.00247452i	$0.000787664\pi$
$577$	12.0619	+	20.8917i	0.502141	+	0.869735i	−0.497855	+	0.867260i	$0.665879\pi$
$578$		0			0
$579$	−13.1662	+	2.32156i	−0.547169	+	0.0964806i
$580$		0			0
$581$	17.5992	−	30.4828i	0.730139	−	1.26464i
$582$		0			0
$583$	−37.6302	+	31.5755i	−1.55849	+	1.30772i
$584$		0			0
$585$	−3.59442	+	9.87559i	−0.148611	+	0.408305i
$586$		0			0
$587$	0.961681	+	0.169570i	0.0396928	+	0.00699892i	0.193459	−	0.981108i	$-0.438029\pi$
$587$	0.961681	+	0.169570i	0.0396928	+	0.00699892i	−0.153766	+	0.988107i	$0.549140\pi$
$588$		0			0
$589$	32.3784	+	8.01736i	1.33413	+	0.330350i
$590$		0			0
$591$	1.25899	−	7.14008i	0.0517879	−	0.293704i
$592$		0			0
$593$	−1.90105	−	0.691926i	−0.0780668	−	0.0284140i	0.302692	−	0.953089i	$-0.402115\pi$
$593$	−1.90105	−	0.691926i	−0.0780668	−	0.0284140i	−0.380758	+	0.924675i	$0.624337\pi$
$594$		0			0
$595$	50.7569	+	60.4897i	2.08083	+	2.47984i
$596$		0			0
$597$	−3.41707	−	1.97284i	−0.139851	−	0.0807432i
$598$		0			0
$599$	7.06708	+	40.0794i	0.288753	+	1.63760i	0.691563	+	0.722316i	$0.256923\pi$
$599$	7.06708	+	40.0794i	0.288753	+	1.63760i	−0.402810	+	0.915284i	$0.631966\pi$
$600$		0			0
$601$	−36.3468	+	20.9848i	−1.48262	+	0.855988i	−0.999805	−	0.0197369i	$-0.993717\pi$
$601$	−36.3468	+	20.9848i	−1.48262	+	0.855988i	−0.482810	+	0.875725i	$0.660384\pi$
$602$		0			0
$603$	2.79357	−	1.01678i	0.113763	−	0.0414064i
$604$		0			0
$605$	−27.5161	−	23.0887i	−1.11869	−	0.938690i
$606$		0			0
$607$	5.71191			0.231839			0.115920	−	0.993259i	$-0.463019\pi$
$607$	5.71191			0.231839			0.115920	+	0.993259i	$0.463019\pi$
$608$		0			0
$609$	6.04623			0.245006
$610$		0			0
$611$	13.1911	+	11.0686i	0.533653	+	0.447788i
$612$		0			0
$613$	40.8719	−	14.8761i	1.65080	−	0.600842i	0.661921	−	0.749573i	$-0.269741\pi$
$613$	40.8719	−	14.8761i	1.65080	−	0.600842i	0.988878	+	0.148731i	$0.0475190\pi$
$614$		0			0
$615$	−34.1813	+	19.7346i	−1.37832	+	0.795775i
$616$		0			0
$617$	0.259118	+	1.46953i	0.0104317	+	0.0591610i	0.989579	−	0.143989i	$-0.0459931\pi$
$617$	0.259118	+	1.46953i	0.0104317	+	0.0591610i	−0.979148	+	0.203150i	$0.934882\pi$
$618$		0			0
$619$	−1.07451	−	0.620369i	−0.0431882	−	0.0249347i	0.478250	−	0.878224i	$-0.341271\pi$
$619$	−1.07451	−	0.620369i	−0.0431882	−	0.0249347i	−0.521439	+	0.853289i	$0.674604\pi$
$620$		0			0
$621$	0.247301	+	0.294722i	0.00992386	+	0.0118268i
$622$		0			0
$623$	45.7982	+	16.6692i	1.83487	+	0.667837i
$624$		0			0
$625$	10.2477	−	58.1175i	0.409908	−	2.32470i
$626$		0			0
$627$	−17.6921	−	7.84284i	−0.706555	−	0.313213i
$628$		0			0
$629$	19.1117	+	3.36990i	0.762032	+	0.134367i
$630$		0			0
$631$	−3.62075	+	9.94792i	−0.144140	+	0.396020i	−0.990663	−	0.136331i	$-0.956469\pi$
$631$	−3.62075	+	9.94792i	−0.144140	+	0.396020i	0.846524	+	0.532351i	$0.178691\pi$
$632$		0			0
$633$	6.29662	−	5.28349i	0.250268	−	0.210000i
$634$		0			0
$635$	43.9856	−	76.1853i	1.74551	−	3.02332i
$636$		0			0
$637$	−15.8323	+	2.79167i	−0.627300	+	0.110610i
$638$		0			0
$639$	−2.22348	−	3.85119i	−0.0879597	−	0.152351i
$640$		0			0
$641$	−3.80723	−	10.4603i	−0.150377	−	0.413157i	0.841516	−	0.540232i	$-0.181663\pi$
$641$	−3.80723	−	10.4603i	−0.150377	−	0.413157i	−0.991893	+	0.127075i	$0.959441\pi$
$642$		0			0
$643$	16.7207	−	19.9270i	0.659400	−	0.785842i	−0.327899	−	0.944713i	$-0.606341\pi$
$643$	16.7207	−	19.9270i	0.659400	−	0.785842i	0.987299	+	0.158870i	$0.0507852\pi$
$644$		0			0
$645$			15.0420i			0.592278i
$646$		0			0
$647$		−	43.6097i		−	1.71448i	−0.514921	−	0.857238i	$-0.672179\pi$
$647$		−	43.6097i		−	1.71448i	0.514921	−	0.857238i	$-0.327821\pi$
$648$		0			0
$649$	−11.5881	+	13.8101i	−0.454872	+	0.542095i
$650$		0			0
$651$	9.54770	+	26.2321i	0.374204	+	1.02812i
$652$		0			0
$653$	−14.7066	−	25.4727i	−0.575516	−	0.996822i	−0.995985	−	0.0895157i	$-0.971468\pi$
$653$	−14.7066	−	25.4727i	−0.575516	−	0.996822i	0.420470	−	0.907307i	$-0.361865\pi$
$654$		0			0
$655$	22.7189	−	4.00596i	0.887701	−	0.156526i
$656$		0			0
$657$	4.65846	−	8.06869i	0.181744	−	0.314790i
$658$		0			0
$659$	−8.81757	+	7.39882i	−0.343484	+	0.288217i	−0.798167	−	0.602436i	$-0.794197\pi$
$659$	−8.81757	+	7.39882i	−0.343484	+	0.288217i	0.454684	+	0.890653i	$0.349752\pi$
$660$		0			0
$661$	11.9148	−	32.7356i	0.463431	−	1.27327i	−0.459458	−	0.888199i	$-0.651956\pi$
$661$	11.9148	−	32.7356i	0.463431	−	1.27327i	0.922889	−	0.385066i	$-0.125821\pi$
$662$		0			0
$663$	−13.1778	−	2.32360i	−0.511782	−	0.0902410i
$664$		0			0
$665$	6.95840	+	65.1925i	0.269835	+	2.52806i
$666$		0			0
$667$	0.110731	−	0.627984i	0.00428750	−	0.0243156i
$668$		0			0
$669$	9.24001	+	3.36309i	0.357239	+	0.130024i
$670$		0			0
$671$	26.5128	+	31.5967i	1.02351	+	1.21978i
$672$		0			0
$673$	27.7642	+	16.0297i	1.07023	+	0.617898i	0.928244	−	0.371971i	$-0.121318\pi$
$673$	27.7642	+	16.0297i	1.07023	+	0.617898i	0.141986	+	0.989869i	$0.454651\pi$
$674$		0			0
$675$	2.08391	+	11.8184i	0.0802096	+	0.454891i
$676$		0			0
$677$	−2.00392	+	1.15696i	−0.0770170	+	0.0444658i	−0.538014	−	0.842936i	$-0.680825\pi$
$677$	−2.00392	+	1.15696i	−0.0770170	+	0.0444658i	0.460997	+	0.887402i	$0.347492\pi$
$678$		0			0
$679$	−15.8538	+	5.77033i	−0.608415	+	0.221445i
$680$		0			0
$681$	−1.07300	−	0.900353i	−0.0411174	−	0.0345016i
$682$		0			0
$683$	−10.3583			−0.396351			−0.198175	−	0.980167i	$-0.563502\pi$
$683$	−10.3583			−0.396351			−0.198175	+	0.980167i	$0.563502\pi$
$684$		0			0
$685$	19.0565			0.728110
$686$		0			0
$687$	−7.42641	−	6.23149i	−0.283335	−	0.237746i
$688$		0			0
$689$	−26.5003	+	9.64532i	−1.00958	+	0.367458i
$690$		0			0
$691$	−16.8796	+	9.74547i	−0.642132	+	0.370735i	−0.785435	−	0.618944i	$-0.787561\pi$
$691$	−16.8796	+	9.74547i	−0.642132	+	0.370735i	0.143303	+	0.989679i	$0.454228\pi$
$692$		0			0
$693$	−2.81241	−	15.9499i	−0.106834	−	0.605888i
$694$		0			0
$695$	48.3436	+	27.9112i	1.83378	+	1.05873i
$696$		0			0
$697$	−32.3027	−	38.4969i	−1.22355	−	1.45817i
$698$		0			0
$699$	−12.6643	−	4.60943i	−0.479008	−	0.174345i
$700$		0			0
$701$	0.475853	−	2.69870i	0.0179727	−	0.101928i	−0.974502	−	0.224380i	$-0.927964\pi$
$701$	0.475853	−	2.69870i	0.0179727	−	0.101928i	0.992475	+	0.122451i	$0.0390755\pi$
$702$		0			0
$703$	11.6088	+	11.1743i	0.437833	+	0.421447i
$704$		0			0
$705$	27.4327	+	4.83712i	1.03317	+	0.182176i
$706$		0			0
$707$	10.3782	−	28.5138i	0.390311	−	1.07237i
$708$		0			0
$709$	−7.74843	+	6.50171i	−0.290998	+	0.244177i	−0.776586	−	0.630011i	$-0.783050\pi$
$709$	−7.74843	+	6.50171i	−0.290998	+	0.244177i	0.485587	+	0.874188i	$0.338606\pi$
$710$		0			0
$711$	7.43402	−	12.8761i	0.278797	−	0.482891i
$712$		0			0
$713$	2.89942	−	0.511246i	0.108584	−	0.0191463i
$714$		0			0
$715$	−23.3297	−	40.4081i	−0.872480	−	1.51118i
$716$		0			0
$717$	9.77904	+	26.8677i	0.365205	+	1.00339i
$718$		0			0
$719$	−2.81250	+	3.35181i	−0.104889	+	0.125001i	−0.815935	−	0.578144i	$-0.803777\pi$
$719$	−2.81250	+	3.35181i	−0.104889	+	0.125001i	0.711046	+	0.703145i	$0.248222\pi$
$720$		0			0
$721$			30.2173i			1.12535i
$722$		0			0
$723$		−	22.8694i		−	0.850522i
$724$		0			0
$725$	12.7854	−	15.2370i	0.474837	−	0.565889i
$726$		0			0
$727$	−0.718106	−	1.97298i	−0.0266331	−	0.0731738i	0.925664	−	0.378348i	$-0.123508\pi$
$727$	−0.718106	−	1.97298i	−0.0266331	−	0.0731738i	−0.952297	+	0.305174i	$0.901285\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−18.8613	+	3.32575i	−0.697609	+	0.123007i
$732$		0			0
$733$	16.9310	−	29.3254i	0.625362	−	1.08316i	−0.363109	−	0.931747i	$-0.618285\pi$
$733$	16.9310	−	29.3254i	0.625362	−	1.08316i	0.988471	−	0.151412i	$-0.0483821\pi$
$734$		0			0
$735$	−19.9222	+	16.7167i	−0.734843	+	0.616607i
$736$		0			0
$737$	−4.51426	+	12.4028i	−0.166285	+	0.456864i
$738$		0			0
$739$	−12.9275	−	2.27947i	−0.475547	−	0.0838518i	−0.0692626	−	0.997598i	$-0.522065\pi$
$739$	−12.9275	−	2.27947i	−0.475547	−	0.0838518i	−0.406284	+	0.913747i	$0.633176\pi$
$740$		0			0
$741$	−8.00442	−	7.70485i	−0.294050	−	0.283045i
$742$		0			0
$743$	−1.22362	+	6.93950i	−0.0448903	+	0.254586i	−0.998992	−	0.0448986i	$-0.985704\pi$
$743$	−1.22362	+	6.93950i	−0.0448903	+	0.254586i	0.954101	+	0.299484i	$0.0968146\pi$
$744$		0			0
$745$	−27.5964	−	10.0443i	−1.01105	−	0.367993i
$746$		0			0
$747$	6.20218	+	7.39147i	0.226926	+	0.270440i
$748$		0			0
$749$	53.1400	+	30.6804i	1.94169	+	1.12104i
$750$		0			0
$751$	−7.29297	−	41.3605i	−0.266124	−	1.50927i	−0.765815	−	0.643061i	$-0.777664\pi$
$751$	−7.29297	−	41.3605i	−0.266124	−	1.50927i	0.499690	−	0.866204i	$-0.333447\pi$
$752$		0			0
$753$	−16.7180	+	9.65215i	−0.609238	+	0.351744i
$754$		0			0
$755$	−58.8124	+	21.4060i	−2.14040	+	0.779043i
$756$		0			0
$757$	19.1403	+	16.0607i	0.695667	+	0.583734i	0.920537	−	0.390654i	$-0.127751\pi$
$757$	19.1403	+	16.0607i	0.695667	+	0.583734i	−0.224870	+	0.974389i	$0.572196\pi$
$758$		0			0
$759$	−1.70813			−0.0620011
$760$		0			0
$761$	16.2041			0.587396			0.293698	−	0.955898i	$-0.405114\pi$
$761$	16.2041			0.587396			0.293698	+	0.955898i	$0.405114\pi$
$762$		0			0
$763$	−11.5393	−	9.68266i	−0.417752	−	0.350536i
$764$		0			0
$765$	−20.3408	+	7.40343i	−0.735421	+	0.267671i
$766$		0			0
$767$	−8.96307	+	5.17483i	−0.323638	+	0.186852i
$768$		0			0
$769$	4.81140	+	27.2868i	0.173504	+	0.983987i	0.939857	+	0.341568i	$0.110958\pi$
$769$	4.81140	+	27.2868i	0.173504	+	0.983987i	−0.766353	+	0.642419i	$0.777931\pi$
$770$		0			0
$771$	3.06411	+	1.76906i	0.110351	+	0.0637113i
$772$		0			0
$773$	−21.6186	−	25.7640i	−0.777566	−	0.926667i	0.221255	−	0.975216i	$-0.428985\pi$
$773$	−21.6186	−	25.7640i	−0.777566	−	0.926667i	−0.998821	+	0.0485493i	$0.984540\pi$
$774$		0			0
$775$	86.2967	+	31.4094i	3.09987	+	1.12826i
$776$		0			0
$777$	−2.34162	+	13.2800i	−0.0840052	+	0.476417i
$778$		0			0
$779$	−4.42846	−	41.4898i	−0.158666	−	1.48653i
$780$		0			0
$781$	19.4436	+	3.42843i	0.695746	+	0.122679i
$782$		0			0
$783$	−0.566878	+	1.55749i	−0.0202586	+	0.0556600i
$784$		0			0
$785$	−4.75199	+	3.98739i	−0.169606	+	0.142316i
$786$		0			0
$787$	12.0588	−	20.8864i	0.429848	−	0.744519i	−0.567011	−	0.823710i	$-0.691900\pi$
$787$	12.0588	−	20.8864i	0.429848	−	0.744519i	0.996859	+	0.0791912i	$0.0252338\pi$
$788$		0			0
$789$	−14.4711	+	2.55165i	−0.515185	+	0.0908410i
$790$		0			0
$791$	−3.04284	−	5.27035i	−0.108191	−	0.187392i
$792$		0			0
$793$	8.09881	+	22.2513i	0.287597	+	0.790167i
$794$		0			0
$795$	−29.3240	+	34.9470i	−1.04002	+	1.23944i
$796$		0			0
$797$		−	16.6476i		−	0.589687i	−0.955546	−	0.294843i	$-0.904733\pi$
$797$		−	16.6476i		−	0.589687i	0.955546	−	0.294843i	$-0.0952675\pi$
$798$		0			0
$799$			35.4674i			1.25475i
$800$		0			0
$801$	−8.58784	+	10.2346i	−0.303436	+	0.361621i
$802$		0			0
$803$	14.1477	+	38.8704i	0.499261	+	1.37171i
$804$		0			0
$805$	2.89341	+	5.01153i	0.101979	+	0.176633i
$806$		0			0
$807$	−9.09253	+	1.60326i	−0.320072	+	0.0564373i
$808$		0			0
$809$	−10.0577	+	17.4204i	−0.353609	+	0.612470i	−0.986879	−	0.161462i	$-0.948379\pi$
$809$	−10.0577	+	17.4204i	−0.353609	+	0.612470i	0.633270	+	0.773931i	$0.281712\pi$
$810$		0			0
$811$	13.4358	−	11.2740i	0.471796	−	0.395884i	−0.375653	−	0.926760i	$-0.622582\pi$
$811$	13.4358	−	11.2740i	0.471796	−	0.395884i	0.847449	+	0.530877i	$0.178137\pi$
$812$		0			0
$813$	−3.95984	+	10.8796i	−0.138878	+	0.381563i
$814$		0			0
$815$	−87.8748	−	15.4947i	−3.07812	−	0.542755i
$816$		0			0
$817$	−14.5375	−	6.44443i	−0.508603	−	0.225462i
$818$		0			0
$819$	1.61458	−	9.15675i	0.0564181	−	0.319963i
$820$		0			0
$821$	3.95505	+	1.43952i	0.138032	+	0.0502396i	0.410112	−	0.912035i	$-0.365489\pi$
$821$	3.95505	+	1.43952i	0.138032	+	0.0502396i	−0.272080	+	0.962275i	$0.587712\pi$
$822$		0			0
$823$	12.6005	+	15.0167i	0.439225	+	0.523448i	0.939560	−	0.342384i	$-0.111234\pi$
$823$	12.6005	+	15.0167i	0.439225	+	0.523448i	−0.500335	+	0.865832i	$0.666790\pi$
$824$		0			0
$825$	−46.1424	−	26.6403i	−1.60647	−	0.927496i
$826$		0			0
$827$	−2.77465	−	15.7358i	−0.0964841	−	0.547189i	−0.994282	−	0.106782i	$-0.965945\pi$
$827$	−2.77465	−	15.7358i	−0.0964841	−	0.547189i	0.897798	−	0.440407i	$-0.145166\pi$
$828$		0			0
$829$	−14.2705	+	8.23907i	−0.495634	+	0.286155i	−0.726909	−	0.686734i	$-0.759044\pi$
$829$	−14.2705	+	8.23907i	−0.495634	+	0.286155i	0.231275	+	0.972889i	$0.425710\pi$
$830$		0			0
$831$	2.59665	−	0.945102i	0.0900767	−	0.0327852i
$832$		0			0
$833$	−25.3660	−	21.2846i	−0.878879	−	0.737467i
$834$		0			0
$835$	11.0910			0.383819
$836$		0			0
$837$	−7.65245			−0.264507
$838$		0			0
$839$	−7.14174	−	5.99263i	−0.246560	−	0.206889i	0.511129	−	0.859504i	$-0.329227\pi$
$839$	−7.14174	−	5.99263i	−0.246560	−	0.206889i	−0.757689	+	0.652615i	$0.773672\pi$
$840$		0			0
$841$	−24.6696	+	8.97902i	−0.850677	+	0.309621i
$842$		0			0
$843$	1.46503	−	0.845834i	0.0504582	−	0.0291321i
$844$		0			0
$845$	4.65634	+	26.4074i	0.160183	+	0.908442i
$846$		0			0
$847$	27.5217	+	15.8897i	0.945658	+	0.545976i
$848$		0			0
$849$	0.108035	+	0.128751i	0.00370775	+	0.00441873i
$850$		0			0
$851$	1.33643	+	0.486419i	0.0458121	+	0.0166742i
$852$		0			0
$853$	1.25287	−	7.10537i	0.0428974	−	0.243283i	−0.955818	−	0.293960i	$-0.905027\pi$
$853$	1.25287	−	7.10537i	0.0428974	−	0.243283i	0.998715	+	0.0506769i	$0.0161379\pi$
$854$		0			0
$855$	−17.4457	−	4.31981i	−0.596631	−	0.147735i
$856$		0			0
$857$	7.48907	+	1.32053i	0.255822	+	0.0451083i	0.300088	−	0.953911i	$-0.402984\pi$
$857$	7.48907	+	1.32053i	0.255822	+	0.0451083i	−0.0442663	+	0.999020i	$0.514095\pi$
$858$		0			0
$859$	−6.56106	+	18.0264i	−0.223861	+	0.615052i	−0.999877	−	0.0156603i	$-0.995015\pi$
$859$	−6.56106	+	18.0264i	−0.223861	+	0.615052i	0.776017	+	0.630712i	$0.217237\pi$
$860$		0			0
$861$	26.7501	−	22.4460i	0.911640	−	0.764956i
$862$		0			0
$863$	1.17771	−	2.03986i	0.0400897	−	0.0694375i	−0.845284	−	0.534317i	$-0.820569\pi$
$863$	1.17771	−	2.03986i	0.0400897	−	0.0694375i	0.885374	+	0.464879i	$0.153902\pi$
$864$		0			0
$865$	−30.2849	+	5.34005i	−1.02972	+	0.181567i
$866$		0			0
$867$	−5.28048	−	9.14607i	−0.179335	−	0.310617i
$868$		0			0
$869$	22.5770	+	62.0298i	0.765872	+	2.10422i
$870$		0			0
$871$	−4.87063	+	5.80459i	−0.165035	+	0.196681i
$872$		0			0
$873$		−	4.62490i		−	0.156529i
$874$		0			0
$875$			105.299i			3.55976i
$876$		0			0
$877$	−15.8012	+	18.8312i	−0.533570	+	0.635884i	−0.963733	−	0.266867i	$-0.914012\pi$
$877$	−15.8012	+	18.8312i	−0.533570	+	0.635884i	0.430163	+	0.902751i	$0.358456\pi$
$878$		0			0
$879$	0.269406	+	0.740187i	0.00908684	+	0.0249659i
$880$		0			0
$881$	25.9820	+	45.0022i	0.875357	+	1.51616i	0.856382	+	0.516343i	$0.172707\pi$
$881$	25.9820	+	45.0022i	0.875357	+	1.51616i	0.0189751	+	0.999820i	$0.493960\pi$
$882$		0			0
$883$	−27.6188	+	4.86994i	−0.929446	+	0.163886i	−0.617821	−	0.786319i	$-0.711984\pi$
$883$	−27.6188	+	4.86994i	−0.929446	+	0.163886i	−0.311625	+	0.950205i	$0.600873\pi$
$884$		0			0
$885$	−8.37119	+	14.4993i	−0.281394	+	0.487389i
$886$		0			0
$887$	13.9020	−	11.6651i	0.466783	−	0.391677i	−0.378837	−	0.925464i	$-0.623676\pi$
$887$	13.9020	−	11.6651i	0.466783	−	0.391677i	0.845619	+	0.533786i	$0.179231\pi$
$888$		0			0
$889$	−26.6198	+	73.1373i	−0.892799	+	2.45295i
$890$		0			0
$891$	4.37233	+	0.770959i	0.146478	+	0.0258281i
$892$		0			0
$893$	−16.4278	+	24.4403i	−0.549736	+	0.817862i
$894$		0			0
$895$	15.8034	−	89.6254i	0.528249	−	2.99585i
$896$		0			0
$897$	−0.921484	−	0.335393i	−0.0307675	−	0.0111984i
$898$		0			0
$899$	8.15279	+	9.71612i	0.271911	+	0.324051i
$900$		0			0
$901$	−50.3037	−	29.0428i	−1.67586	−	0.967557i
$902$		0			0
$903$	−2.31094	−	13.1060i	−0.0769033	−	0.436140i
$904$		0			0
$905$	−59.1482	+	34.1492i	−1.96615	+	1.13516i
$906$		0			0
$907$	2.12954	−	0.775090i	0.0707103	−	0.0257364i	−0.306423	−	0.951896i	$-0.599132\pi$
$907$	2.12954	−	0.775090i	0.0707103	−	0.0257364i	0.377133	+	0.926159i	$0.376910\pi$
$908$		0			0
$909$	6.37200	+	5.34675i	0.211346	+	0.177340i
$910$		0			0
$911$	9.96129			0.330032			0.165016	−	0.986291i	$-0.447232\pi$
$911$	9.96129			0.330032			0.165016	+	0.986291i	$0.447232\pi$
$912$		0			0
$913$	−42.8389			−1.41776
$914$		0			0
$915$	29.3437	+	24.6222i	0.970071	+	0.813986i
$916$		0			0
$917$	−19.1794	+	6.98072i	−0.633359	+	0.230524i
$918$		0			0
$919$	3.83866	−	2.21625i	0.126626	−	0.0731073i	−0.435349	−	0.900262i	$-0.643375\pi$
$919$	3.83866	−	2.21625i	0.126626	−	0.0731073i	0.561975	+	0.827154i	$0.310042\pi$
$920$		0			0
$921$	5.19533	+	29.4642i	0.171192	+	0.970877i
$922$		0			0
$923$	9.81607	+	5.66731i	0.323100	+	0.186542i
$924$		0			0
$925$	28.5151	+	33.9830i	0.937572	+	1.11735i
$926$		0			0
$927$	−7.78385	−	2.83309i	−0.255655	−	0.0930509i
$928$		0			0
$929$	−3.29313	+	18.6763i	−0.108044	+	0.612749i	0.881916	+	0.471406i	$0.156253\pi$
$929$	−3.29313	+	18.6763i	−0.108044	+	0.612749i	−0.989961	+	0.141343i	$0.954858\pi$
$930$		0			0
$931$	−7.62083	−	26.4160i	−0.249763	−	0.865750i
$932$		0			0
$933$	10.9203	+	1.92555i	0.357515	+	0.0630395i
$934$		0			0
$935$	32.8696	−	90.3084i	1.07495	−	2.95340i
$936$		0			0
$937$	2.28193	−	1.91477i	0.0745474	−	0.0625527i	−0.604753	−	0.796413i	$-0.706728\pi$
$937$	2.28193	−	1.91477i	0.0745474	−	0.0625527i	0.679300	+	0.733861i	$0.262284\pi$
$938$		0			0
$939$	14.4158	−	24.9690i	0.470443	−	0.814832i
$940$		0			0
$941$	18.6430	−	3.28726i	0.607743	−	0.107162i	0.138697	−	0.990335i	$-0.455709\pi$
$941$	18.6430	−	3.28726i	0.607743	−	0.107162i	0.469047	+	0.883173i	$0.344598\pi$
$942$		0			0
$943$	−1.84142	−	3.18943i	−0.0599649	−	0.103862i
$944$		0			0
$945$	−5.14437	−	14.1340i	−0.167346	−	0.459780i
$946$		0			0
$947$	20.6598	−	24.6214i	0.671352	−	0.800086i	−0.317615	−	0.948220i	$-0.602882\pi$
$947$	20.6598	−	24.6214i	0.671352	−	0.800086i	0.988967	+	0.148133i	$0.0473264\pi$
$948$		0			0
$949$			23.7474i			0.770872i
$950$		0			0
$951$			3.64159i			0.118087i
$952$		0			0
$953$	34.2737	−	40.8459i	1.11024	−	1.32313i	0.168908	−	0.985632i	$-0.445976\pi$
$953$	34.2737	−	40.8459i	1.11024	−	1.32313i	0.941327	−	0.337495i	$-0.109580\pi$
$954$		0			0
$955$	19.0616	+	52.3713i	0.616818	+	1.69469i
$956$		0			0
$957$	−3.67933	−	6.37280i	−0.118936	−	0.206003i
$958$		0			0
$959$	−16.6038	+	2.92769i	−0.536163	+	0.0945400i
$960$		0			0
$961$	−13.7800	+	23.8676i	−0.444516	+	0.769924i
$962$		0			0
$963$	−12.8854	+	10.8121i	−0.415227	+	0.348417i
$964$		0			0
$965$	18.8536	−	51.7999i	0.606919	−	1.66750i
$966$		0			0
$967$	17.4641	+	3.07940i	0.561609	+	0.0990267i	0.447244	−	0.894412i	$-0.352406\pi$
$967$	17.4641	+	3.07940i	0.561609	+	0.0990267i	0.114365	+	0.993439i	$0.463517\pi$
$968$		0			0
$969$	1.55943	−	22.8304i	0.0500962	−	0.733418i
$970$		0			0
$971$	8.07418	−	45.7910i	0.259113	−	1.46950i	−0.526178	−	0.850375i	$-0.676375\pi$
$971$	8.07418	−	45.7910i	0.259113	−	1.46950i	0.785291	−	0.619127i	$-0.212514\pi$
$972$		0			0
$973$	−46.4095	−	16.8917i	−1.48782	−	0.541523i
$974$		0			0
$975$	−19.6616	−	23.4318i	−0.629675	−	0.750418i
$976$		0			0
$977$	48.7012	+	28.1177i	1.55809	+	0.899564i	0.997440	+	0.0715107i	$0.0227820\pi$
$977$	48.7012	+	28.1177i	1.55809	+	0.899564i	0.560650	+	0.828053i	$0.310551\pi$
$978$		0			0
$979$	−10.3002	−	58.4156i	−0.329197	−	1.86697i
$980$		0			0
$981$	3.57611	−	2.06467i	0.114177	−	0.0659199i
$982$		0			0
$983$	−40.6494	+	14.7952i	−1.29652	+	0.471893i	−0.895860	−	0.444336i	$-0.853440\pi$
$983$	−40.6494	+	14.7952i	−1.29652	+	0.471893i	−0.400656	+	0.916229i	$0.631218\pi$
$984$		0			0
$985$	22.9002	+	19.2156i	0.729662	+	0.612259i
$986$		0			0
$987$	−24.6450			−0.784460
$988$		0			0
$989$	−1.40356			−0.0446306
$990$		0			0
$991$	−2.62960	−	2.20650i	−0.0835321	−	0.0700918i	0.600065	−	0.799951i	$-0.295141\pi$
$991$	−2.62960	−	2.20650i	−0.0835321	−	0.0700918i	−0.683598	+	0.729859i	$0.739586\pi$
$992$		0			0
$993$	8.48308	−	3.08759i	0.269203	−	0.0979817i
$994$		0			0
$995$	14.0892	−	8.13442i	0.446659	−	0.257879i
$996$		0			0
$997$	0.746392	+	4.23300i	0.0236385	+	0.134060i	0.994343	−	0.106215i	$-0.0338733\pi$
$997$	0.746392	+	4.23300i	0.0236385	+	0.134060i	−0.970705	+	0.240276i	$0.922762\pi$
$998$		0			0
$999$	−3.20133	−	1.84829i	−0.101286	−	0.0584773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.f.895.1	yes	18
4.3	odd	2		912.2.ci.e.895.1	yes	18
19.10	odd	18		912.2.ci.e.751.1	✓	18
76.67	even	18	inner	912.2.ci.f.751.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.e.751.1	✓	18	19.10	odd	18
912.2.ci.e.895.1	yes	18	4.3	odd	2
912.2.ci.f.751.1	yes	18	76.67	even	18	inner
912.2.ci.f.895.1	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{3} +(-3.87454 + 1.41022i) q^{5} +(3.15920 - 1.82397i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{3} +(-3.87454 + 1.41022i) q^{5} +(3.15920 - 1.82397i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-3.84496 - 2.21989i) q^{11} +(-1.63837 - 1.95253i) q^{13} +(-3.87454 - 1.41022i) q^{15} +(0.911628 - 5.17010i) q^{17} +(3.02288 - 3.14041i) q^{19} +(3.59251 + 0.633457i) q^{21} +(0.131586 - 0.361530i) q^{23} +(9.19310 - 7.71393i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(1.63226 - 0.287812i) q^{29} +(3.82622 + 6.62722i) q^{31} +(-1.51849 - 4.17203i) q^{33} +(-9.66825 + 11.5222i) q^{35} +3.69658i q^{37} -2.54884i q^{39} +(6.15307 - 7.33294i) q^{41} +(-1.24774 - 3.42813i) q^{43} +(-2.06160 - 3.57079i) q^{45} +(-6.65325 + 1.17315i) q^{47} +(3.15370 - 5.46237i) q^{49} +(4.02162 - 3.37454i) q^{51} +(3.78420 - 10.3970i) q^{53} +(18.0280 + 3.17882i) q^{55} +(4.33428 - 0.462625i) q^{57} +(0.705104 - 3.99884i) q^{59} +(-8.72996 - 3.17744i) q^{61} +(2.34484 + 2.79448i) q^{63} +(9.10139 + 5.25469i) q^{65} +(-0.516231 - 2.92769i) q^{67} +(0.333188 - 0.192366i) q^{69} +(-4.17878 + 1.52095i) q^{71} +(-7.13717 - 5.98880i) q^{73} +12.0007 q^{75} -16.1960 q^{77} +(-11.3896 - 9.55699i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(8.35618 - 4.82444i) q^{83} +(3.75882 + 21.3173i) q^{85} +(1.43539 + 0.828721i) q^{87} +(8.58784 + 10.2346i) q^{89} +(-8.73727 - 3.18011i) q^{91} +(-1.32883 + 7.53619i) q^{93} +(-7.28360 + 16.4306i) q^{95} +(-4.55463 - 0.803105i) q^{97} +(1.51849 - 4.17203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) \) 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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