LMFDB - Embedded newform 304.2.u.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(17,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("304.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	304.289
Dual form			304.2.u.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0923963 - 0.524005i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.939693 + 1.62760i) q^{7} +(2.55303 - 0.929228i) q^{9} +O(q^{10})$	\(q+(-0.0923963 - 0.524005i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.939693 + 1.62760i) q^{7} +(2.55303 - 0.929228i) q^{9} +(1.70574 + 2.95442i) q^{11} +(-0.918748 + 5.21048i) q^{13} +(1.03209 + 0.866025i) q^{15} +(-1.55303 - 0.565258i) q^{17} +(2.52094 + 3.55596i) q^{19} +(0.939693 + 0.342020i) q^{21} +(-1.34730 - 1.13052i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-1.52094 - 2.63435i) q^{27} +(3.25877 - 1.18610i) q^{29} +(0.971782 - 1.68317i) q^{31} +(1.39053 - 1.16679i) q^{33} +(-0.826352 - 4.68647i) q^{35} -0.837496 q^{37} +2.81521 q^{39} +(-0.779715 - 4.42198i) q^{41} +(-3.67752 + 3.08580i) q^{43} +(-3.43969 + 5.95772i) q^{45} +(0.673648 - 0.245188i) q^{47} +(1.73396 + 3.00330i) q^{49} +(-0.152704 + 0.866025i) q^{51} +(-4.67752 - 3.92490i) q^{53} +(-8.11721 - 2.95442i) q^{55} +(1.63041 - 1.64955i) q^{57} +(-10.1099 - 3.67972i) q^{59} +(3.36231 + 2.82131i) q^{61} +(-0.886659 + 5.02849i) q^{63} +(-6.69846 - 11.6021i) q^{65} +(13.3550 - 4.86084i) q^{67} +(-0.467911 + 0.810446i) q^{69} +(10.5398 - 8.84397i) q^{71} +(-1.30541 - 7.40333i) q^{73} -0.751030 q^{75} -6.41147 q^{77} +(1.20914 + 6.85738i) q^{79} +(5.00387 - 4.19875i) q^{81} +(1.25624 - 2.17588i) q^{83} +(3.93242 - 1.43128i) q^{85} +(-0.922618 - 1.59802i) q^{87} +(-0.396459 + 2.24843i) q^{89} +(-7.61721 - 6.39160i) q^{91} +(-0.971782 - 0.353700i) q^{93} +(-10.6775 - 2.79439i) q^{95} +(1.71301 + 0.623485i) q^{97} +(7.10014 + 5.95772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9	$ 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{19} - 6 q^{23} - 6 q^{27} - 3 q^{29} - 9 q^{31} - 9 q^{33} - 6 q^{35} + 24 q^{39} + 21 q^{41} + 3 q^{43} - 15 q^{45} + 3 q^{47} + 15 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} + 24 q^{57} - 12 q^{59} - 12 q^{61} - 12 q^{63} - 12 q^{65} + 30 q^{67} - 12 q^{69} + 6 q^{71} - 12 q^{73} - 30 q^{75} - 18 q^{77} + 39 q^{79} + 6 q^{81} + 21 q^{87} - 12 q^{89} - 15 q^{91} + 9 q^{93} - 39 q^{95} + 18 q^{97} - 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9 - 3 * q^13 - 3 * q^15 + 3 * q^17 + 12 * q^19 - 6 * q^23 - 6 * q^27 - 3 * q^29 - 9 * q^31 - 9 * q^33 - 6 * q^35 + 24 * q^39 + 21 * q^41 + 3 * q^43 - 15 * q^45 + 3 * q^47 + 15 * q^49 - 3 * q^51 - 3 * q^53 - 18 * q^55 + 24 * q^57 - 12 * q^59 - 12 * q^61 - 12 * q^63 - 12 * q^65 + 30 * q^67 - 12 * q^69 + 6 * q^71 - 12 * q^73 - 30 * q^75 - 18 * q^77 + 39 * q^79 + 6 * q^81 + 21 * q^87 - 12 * q^89 - 15 * q^91 + 9 * q^93 - 39 * q^95 + 18 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

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
$3$	−0.0923963	−	0.524005i	−0.0533450	−	0.302535i	0.946449	−	0.322855i	$-0.104643\pi$
$3$	−0.0923963	−	0.524005i	−0.0533450	−	0.302535i	−0.999794	+	0.0203202i	$0.993531\pi$
$4$		0			0
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	−0.963561	−	0.267489i	$-0.913806\pi$
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	0.0961041	+	0.995371i	$0.469362\pi$
$6$		0			0
$7$	−0.939693	+	1.62760i	−0.355170	+	0.615173i	−0.987147	−	0.159814i	$-0.948910\pi$
$7$	−0.939693	+	1.62760i	−0.355170	+	0.615173i	0.631977	+	0.774987i	$0.282244\pi$
$8$		0			0
$9$	2.55303	−	0.929228i	0.851011	−	0.309743i
$10$		0			0
$11$	1.70574	+	2.95442i	0.514299	+	0.890792i	0.999862	+	0.0165906i	$0.00528120\pi$
$11$	1.70574	+	2.95442i	0.514299	+	0.890792i	−0.485563	+	0.874202i	$0.661385\pi$
$12$		0			0
$13$	−0.918748	+	5.21048i	−0.254815	+	1.44513i	0.541733	+	0.840551i	$0.317769\pi$
$13$	−0.918748	+	5.21048i	−0.254815	+	1.44513i	−0.796547	+	0.604576i	$0.793343\pi$
$14$		0			0
$15$	1.03209	+	0.866025i	0.266484	+	0.223607i
$16$		0			0
$17$	−1.55303	−	0.565258i	−0.376666	−	0.137095i	0.146748	−	0.989174i	$-0.453119\pi$
$17$	−1.55303	−	0.565258i	−0.376666	−	0.137095i	−0.523414	+	0.852079i	$0.675342\pi$
$18$		0			0
$19$	2.52094	+	3.55596i	0.578344	+	0.815793i
$19$	2.52094	+	3.55596i	0.578344	+	0.815793i
$20$		0			0
$21$	0.939693	+	0.342020i	0.205058	+	0.0746349i
$22$		0			0
$23$	−1.34730	−	1.13052i	−0.280931	−	0.235729i	0.491424	−	0.870921i	$-0.336477\pi$
$23$	−1.34730	−	1.13052i	−0.280931	−	0.235729i	−0.772354	+	0.635192i	$0.780921\pi$
$24$		0			0
$25$	0.245100	−	1.39003i	0.0490200	−	0.278006i
$26$		0			0
$27$	−1.52094	−	2.63435i	−0.292706	−	0.506982i
$28$		0			0
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	−0.0212363	−	0.999774i	$-0.506760\pi$
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	0.626375	+	0.779522i	$0.284538\pi$
$30$		0			0
$31$	0.971782	−	1.68317i	0.174537	−	0.302307i	−0.765464	−	0.643479i	$-0.777490\pi$
$31$	0.971782	−	1.68317i	0.174537	−	0.302307i	0.940001	+	0.341172i	$0.110824\pi$
$32$		0			0
$33$	1.39053	−	1.16679i	0.242060	−	0.203113i
$34$		0			0
$35$	−0.826352	−	4.68647i	−0.139679	−	0.792159i
$36$		0			0
$37$	−0.837496			−0.137684			−0.0688418	−	0.997628i	$-0.521930\pi$
$37$	−0.837496			−0.137684			−0.0688418	+	0.997628i	$0.521930\pi$
$38$		0			0
$39$	2.81521			0.450794
$40$		0			0
$41$	−0.779715	−	4.42198i	−0.121771	−	0.690598i	−0.983173	−	0.182675i	$-0.941524\pi$
$41$	−0.779715	−	4.42198i	−0.121771	−	0.690598i	0.861402	−	0.507923i	$-0.169587\pi$
$42$		0			0
$43$	−3.67752	+	3.08580i	−0.560816	+	0.470581i	−0.878584	−	0.477588i	$-0.841511\pi$
$43$	−3.67752	+	3.08580i	−0.560816	+	0.470581i	0.317768	+	0.948169i	$0.397067\pi$
$44$		0			0
$45$	−3.43969	+	5.95772i	−0.512759	+	0.888125i
$46$		0			0
$47$	0.673648	−	0.245188i	0.0982617	−	0.0357643i	−0.292422	−	0.956290i	$-0.594461\pi$
$47$	0.673648	−	0.245188i	0.0982617	−	0.0357643i	0.390683	+	0.920525i	$0.372239\pi$
$48$		0			0
$49$	1.73396	+	3.00330i	0.247708	+	0.429043i
$50$		0			0
$51$	−0.152704	+	0.866025i	−0.0213828	+	0.121268i
$52$		0			0
$53$	−4.67752	−	3.92490i	−0.642507	−	0.539127i	0.262280	−	0.964992i	$-0.415526\pi$
$53$	−4.67752	−	3.92490i	−0.642507	−	0.539127i	−0.904787	+	0.425865i	$0.859970\pi$
$54$		0			0
$55$	−8.11721	−	2.95442i	−1.09452	−	0.398374i
$56$		0			0
$57$	1.63041	−	1.64955i	0.215954	−	0.218488i
$58$		0			0
$59$	−10.1099	−	3.67972i	−1.31620	−	0.479058i	−0.413962	−	0.910294i	$-0.635856\pi$
$59$	−10.1099	−	3.67972i	−1.31620	−	0.479058i	−0.902239	+	0.431236i	$0.858078\pi$
$60$		0			0
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	0.832140	−	0.554565i	$-0.187115\pi$
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	−0.401640	+	0.915797i	$0.631560\pi$
$62$		0			0
$63$	−0.886659	+	5.02849i	−0.111709	+	0.633531i
$64$		0			0
$65$	−6.69846	−	11.6021i	−0.830842	−	1.43906i
$66$		0			0
$67$	13.3550	−	4.86084i	1.63158	−	0.593846i	0.646040	−	0.763304i	$-0.276424\pi$
$67$	13.3550	−	4.86084i	1.63158	−	0.593846i	0.985537	+	0.169458i	$0.0542017\pi$
$68$		0			0
$69$	−0.467911	+	0.810446i	−0.0563299	+	0.0975662i
$70$		0			0
$71$	10.5398	−	8.84397i	1.25085	−	1.04959i	0.254252	−	0.967138i	$-0.418171\pi$
$71$	10.5398	−	8.84397i	1.25085	−	1.04959i	0.996595	−	0.0824479i	$-0.0262738\pi$
$72$		0			0
$73$	−1.30541	−	7.40333i	−0.152786	−	0.866495i	−0.960782	−	0.277306i	$-0.910559\pi$
$73$	−1.30541	−	7.40333i	−0.152786	−	0.866495i	0.807995	−	0.589189i	$-0.200553\pi$
$74$		0			0
$75$	−0.751030			−0.0867214
$76$		0			0
$77$	−6.41147			−0.730655
$78$		0			0
$79$	1.20914	+	6.85738i	0.136039	+	0.771515i	0.974131	+	0.225986i	$0.0725603\pi$
$79$	1.20914	+	6.85738i	0.136039	+	0.771515i	−0.838092	+	0.545529i	$0.816329\pi$
$80$		0			0
$81$	5.00387	−	4.19875i	0.555986	−	0.466527i
$82$		0			0
$83$	1.25624	−	2.17588i	0.137891	−	0.238834i	−0.788807	−	0.614641i	$-0.789301\pi$
$83$	1.25624	−	2.17588i	0.137891	−	0.238834i	0.926698	+	0.375807i	$0.122634\pi$
$84$		0			0
$85$	3.93242	−	1.43128i	0.426531	−	0.155244i
$86$		0			0
$87$	−0.922618	−	1.59802i	−0.0989151	−	0.171326i
$88$		0			0
$89$	−0.396459	+	2.24843i	−0.0420246	+	0.238333i	−0.998584	−	0.0532055i	$-0.983056\pi$
$89$	−0.396459	+	2.24843i	−0.0420246	+	0.238333i	0.956559	+	0.291539i	$0.0941673\pi$
$90$		0			0
$91$	−7.61721	−	6.39160i	−0.798501	−	0.670022i
$92$		0			0
$93$	−0.971782	−	0.353700i	−0.100769	−	0.0366769i
$94$		0			0
$95$	−10.6775	−	2.79439i	−1.09549	−	0.286698i
$96$		0			0
$97$	1.71301	+	0.623485i	0.173930	+	0.0633053i	0.427517	−	0.904007i	$-0.359388\pi$
$97$	1.71301	+	0.623485i	0.173930	+	0.0633053i	−0.253587	+	0.967312i	$0.581611\pi$
$98$		0			0
$99$	7.10014	+	5.95772i	0.713591	+	0.598774i
$100$		0			0
$101$	−1.37551	+	7.80093i	−0.136869	+	0.776222i	0.836671	+	0.547705i	$0.184499\pi$
$101$	−1.37551	+	7.80093i	−0.136869	+	0.776222i	−0.973540	+	0.228516i	$0.926613\pi$
$102$		0			0
$103$	−0.00727396	−	0.0125989i	−0.000716725	−	0.00124140i	0.865667	−	0.500621i	$-0.166895\pi$
$103$	−0.00727396	−	0.0125989i	−0.000716725	−	0.00124140i	−0.866384	+	0.499379i	$0.833561\pi$
$104$		0			0
$105$	−2.37939	+	0.866025i	−0.232204	+	0.0845154i
$106$		0			0
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	−0.939052	−	0.343776i	$-0.888294\pi$
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	0.767244	+	0.641355i	$0.221627\pi$
$108$		0			0
$109$	5.64543	−	4.73708i	0.540734	−	0.453730i	−0.331055	−	0.943612i	$-0.607404\pi$
$109$	5.64543	−	4.73708i	0.540734	−	0.453730i	0.871789	+	0.489882i	$0.162960\pi$
$110$		0			0
$111$	0.0773815	+	0.438852i	0.00734473	+	0.0416540i
$112$		0			0
$113$	7.37733			0.694000			0.347000	−	0.937865i	$-0.387200\pi$
$113$	7.37733			0.694000			0.347000	+	0.937865i	$0.387200\pi$
$114$		0			0
$115$	4.45336			0.415278
$116$		0			0
$117$	2.49613	+	14.1563i	0.230767	+	1.30875i
$118$		0			0
$119$	2.37939	−	1.99654i	0.218118	−	0.183023i
$120$		0			0
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$		0			0
$123$	−2.24510	+	0.817150i	−0.202434	+	0.0736799i
$124$		0			0
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$		0			0
$127$	0.0175410	−	0.0994798i	0.00155651	−	0.00882740i	−0.984020	−	0.178060i	$-0.943018\pi$
$127$	0.0175410	−	0.0994798i	0.00155651	−	0.00882740i	0.985576	+	0.169233i	$0.0541290\pi$
$128$		0			0
$129$	1.95677	+	1.64192i	0.172284	+	0.144563i
$130$		0			0
$131$	−2.85369	−	1.03866i	−0.249328	−	0.0907481i	0.214333	−	0.976761i	$-0.431242\pi$
$131$	−2.85369	−	1.03866i	−0.249328	−	0.0907481i	−0.463661	+	0.886013i	$0.653464\pi$
$132$		0			0
$133$	−8.15657	+	0.761570i	−0.707265	+	0.0660365i
$134$		0			0
$135$	7.23783	+	2.63435i	0.622933	+	0.226729i
$136$		0			0
$137$	14.9684	+	12.5600i	1.27883	+	1.07307i	0.993404	+	0.114671i	$0.0365813\pi$
$137$	14.9684	+	12.5600i	1.27883	+	1.07307i	0.285431	+	0.958399i	$0.407863\pi$
$138$		0			0
$139$	−2.67365	+	15.1630i	−0.226776	+	1.28611i	0.632485	+	0.774573i	$0.282035\pi$
$139$	−2.67365	+	15.1630i	−0.226776	+	1.28611i	−0.859261	+	0.511537i	$0.829076\pi$
$140$		0			0
$141$	−0.190722	−	0.330341i	−0.0160617	−	0.0278197i
$142$		0			0
$143$	−16.9611	+	6.17334i	−1.41836	+	0.516240i
$144$		0			0
$145$	−4.39053	+	7.60462i	−0.364614	+	0.631529i
$146$		0			0
$147$	1.41353	−	1.18610i	0.116586	−	0.0978275i
$148$		0			0
$149$	−0.654048	−	3.70929i	−0.0535817	−	0.303877i	0.946226	−	0.323507i	$-0.104862\pi$
$149$	−0.654048	−	3.70929i	−0.0535817	−	0.303877i	−0.999807	+	0.0196306i	$0.993751\pi$
$150$		0			0
$151$	14.5963			1.18783			0.593914	−	0.804529i	$-0.297582\pi$
$151$	14.5963			1.18783			0.593914	+	0.804529i	$0.297582\pi$
$152$		0			0
$153$	−4.49020			−0.363011
$154$		0			0
$155$	0.854570	+	4.84651i	0.0686407	+	0.389281i
$156$		0			0
$157$	−7.94743	+	6.66869i	−0.634274	+	0.532219i	−0.902254	−	0.431205i	$-0.858088\pi$
$157$	−7.94743	+	6.66869i	−0.634274	+	0.532219i	0.267980	+	0.963425i	$0.413644\pi$
$158$		0			0
$159$	−1.62449	+	2.81369i	−0.128830	+	0.223140i
$160$		0			0
$161$	3.10607	−	1.13052i	0.244792	−	0.0890971i
$162$		0			0
$163$	−1.01114	−	1.75135i	−0.0791989	−	0.137177i	0.823706	−	0.567018i	$-0.191903\pi$
$163$	−1.01114	−	1.75135i	−0.0791989	−	0.137177i	−0.902905	+	0.429841i	$0.858570\pi$
$164$		0			0
$165$	−0.798133	+	4.52644i	−0.0621346	+	0.352383i
$166$		0			0
$167$	17.8157	+	14.9491i	1.37862	+	1.15680i	0.969720	+	0.244218i	$0.0785312\pi$
$167$	17.8157	+	14.9491i	1.37862	+	1.15680i	0.408898	+	0.912580i	$0.365913\pi$
$168$		0			0
$169$	−14.0890	−	5.12797i	−1.08377	−	0.394460i
$170$		0			0
$171$	9.74035	+	6.73595i	0.744863	+	0.515111i
$172$		0			0
$173$	−0.842549	−	0.306663i	−0.0640578	−	0.0233151i	0.309793	−	0.950804i	$-0.399740\pi$
$173$	−0.842549	−	0.306663i	−0.0640578	−	0.0233151i	−0.373850	+	0.927489i	$0.621963\pi$
$174$		0			0
$175$	2.03209	+	1.70513i	0.153611	+	0.128895i
$176$		0			0
$177$	−0.994070	+	5.63765i	−0.0747189	+	0.423752i
$178$		0			0
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	−0.921755	−	0.387773i	$-0.873245\pi$
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	0.125056	−	0.992150i	$-0.460089\pi$
$180$		0			0
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.288196	−	0.957571i	$-0.406945\pi$
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.836286	+	0.548294i	$0.184722\pi$
$182$		0			0
$183$	1.16772	−	2.02255i	0.0863202	−	0.149511i
$184$		0			0
$185$	1.62449	−	1.36310i	0.119435	−	0.100217i
$186$		0			0
$187$	−0.979055	−	5.55250i	−0.0715956	−	0.406039i
$188$		0			0
$189$	5.71688			0.415842
$190$		0			0
$191$	−18.9486			−1.37107			−0.685537	−	0.728038i	$-0.740432\pi$
$191$	−18.9486			−1.37107			−0.685537	+	0.728038i	$0.740432\pi$
$192$		0			0
$193$	2.24035	+	12.7057i	0.161264	+	0.914574i	0.952833	+	0.303494i	$0.0981534\pi$
$193$	2.24035	+	12.7057i	0.161264	+	0.914574i	−0.791569	+	0.611080i	$0.790736\pi$
$194$		0			0
$195$	−5.46064	+	4.58202i	−0.391044	+	0.328125i
$196$		0			0
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	−0.0743108	−	0.997235i	$-0.523676\pi$
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	0.900786	−	0.434263i	$-0.142991\pi$
$198$		0			0
$199$	8.66550	−	3.15398i	0.614281	−	0.223580i	−0.0160945	−	0.999870i	$-0.505123\pi$
$199$	8.66550	−	3.15398i	0.614281	−	0.223580i	0.630375	+	0.776291i	$0.282901\pi$
$200$		0			0
$201$	−3.78106	−	6.54899i	−0.266695	−	0.461930i
$202$		0			0
$203$	−1.13176	+	6.41852i	−0.0794339	+	0.450492i
$204$		0			0
$205$	8.70961	+	7.30823i	0.608305	+	0.510429i
$206$		0			0
$207$	−4.49020	−	1.63430i	−0.312090	−	0.113592i
$208$		0			0
$209$	−6.20574	+	13.5135i	−0.429260	+	0.934746i
$210$		0			0
$211$	13.7417	+	5.00157i	0.946017	+	0.344322i	0.768539	−	0.639803i	$-0.220984\pi$
$211$	13.7417	+	5.00157i	0.946017	+	0.344322i	0.177478	+	0.984125i	$0.443206\pi$
$212$		0			0
$213$	−5.60813	−	4.70578i	−0.384262	−	0.322435i
$214$		0			0
$215$	2.11081	−	11.9710i	0.143956	−	0.816417i
$216$		0			0
$217$	1.82635	+	3.16333i	0.123981	+	0.214741i
$218$		0			0
$219$	−3.75877	+	1.36808i	−0.253994	+	0.0924463i
$220$		0			0
$221$	4.37211	−	7.57272i	0.294100	−	0.509396i
$222$		0			0
$223$	2.30928	−	1.93771i	0.154641	−	0.129759i	−0.562185	−	0.827012i	$-0.690039\pi$
$223$	2.30928	−	1.93771i	0.154641	−	0.129759i	0.716825	+	0.697253i	$0.245595\pi$
$224$		0			0
$225$	−0.665907	−	3.77655i	−0.0443938	−	0.251770i
$226$		0			0
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$		0			0
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$		0			0
$231$	0.592396	+	3.35965i	0.0389768	+	0.221048i
$232$		0			0
$233$	−18.5273	+	15.5463i	−1.21377	+	1.01847i	−0.214640	+	0.976693i	$0.568858\pi$
$233$	−18.5273	+	15.5463i	−1.21377	+	1.01847i	−0.999127	+	0.0417777i	$0.986698\pi$
$234$		0			0
$235$	−0.907604	+	1.57202i	−0.0592055	+	0.102547i
$236$		0			0
$237$	3.48158	−	1.26719i	0.226153	−	0.0823130i
$238$		0			0
$239$	−11.6630	−	20.2009i	−0.754415	−	1.30668i	−0.945665	−	0.325143i	$-0.894587\pi$
$239$	−11.6630	−	20.2009i	−0.754415	−	1.30668i	0.191250	−	0.981541i	$-0.438746\pi$
$240$		0			0
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	−0.983098	−	0.183082i	$-0.941393\pi$
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	0.986427	+	0.164199i	$0.0525038\pi$
$242$		0			0
$243$	−9.65317	−	8.09997i	−0.619251	−	0.519613i
$244$		0			0
$245$	−8.25150	−	3.00330i	−0.527169	−	0.191874i
$246$		0			0
$247$	−20.8444	+	9.86830i	−1.32629	+	0.627905i
$248$		0			0
$249$	−1.25624	−	0.457236i	−0.0796112	−	0.0289761i
$250$		0			0
$251$	12.4081	+	10.4116i	0.783190	+	0.657175i	0.944050	−	0.329802i	$-0.106982\pi$
$251$	12.4081	+	10.4116i	0.783190	+	0.657175i	−0.160859	+	0.986977i	$0.551427\pi$
$252$		0			0
$253$	1.04189	−	5.90885i	0.0655030	−	0.371486i
$254$		0			0
$255$	−1.11334	−	1.92836i	−0.0697201	−	0.120759i
$256$		0			0
$257$	−14.4290	+	5.25173i	−0.900057	+	0.327594i	−0.750276	−	0.661125i	$-0.770079\pi$
$257$	−14.4290	+	5.25173i	−0.900057	+	0.327594i	−0.149782	+	0.988719i	$0.547857\pi$
$258$		0			0
$259$	0.786989	−	1.36310i	0.0489011	−	0.0846992i
$260$		0			0
$261$	7.21760	−	6.05628i	0.446758	−	0.374874i
$262$		0			0
$263$	−1.67453	−	9.49671i	−0.103256	−	0.585592i	−0.991903	−	0.127000i	$-0.959465\pi$
$263$	−1.67453	−	9.49671i	−0.103256	−	0.585592i	0.888647	−	0.458592i	$-0.151646\pi$
$264$		0			0
$265$	15.4611			0.949768
$266$		0			0
$267$	1.21482			0.0743459
$268$		0			0
$269$	−3.17412	−	18.0013i	−0.193529	−	1.09756i	−0.914498	−	0.404591i	$-0.867414\pi$
$269$	−3.17412	−	18.0013i	−0.193529	−	1.09756i	0.720969	−	0.692968i	$-0.243697\pi$
$270$		0			0
$271$	−14.5273	+	12.1899i	−0.882473	+	0.740483i	−0.966686	−	0.255965i	$-0.917607\pi$
$271$	−14.5273	+	12.1899i	−0.882473	+	0.740483i	0.0842129	+	0.996448i	$0.473162\pi$
$272$		0			0
$273$	−2.64543	+	4.58202i	−0.160109	+	0.277316i
$274$		0			0
$275$	4.52481	−	1.64690i	0.272857	−	0.0993117i
$276$		0			0
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	0.581775	−	0.813350i	$-0.302358\pi$
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	−0.995269	+	0.0971571i	$0.969025\pi$
$278$		0			0
$279$	0.916937	−	5.20021i	0.0548956	−	0.311328i
$280$		0			0
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	0.891175	−	0.453661i	$-0.149882\pi$
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	−0.292018	+	0.956413i	$0.594327\pi$
$282$		0			0
$283$	−16.3293	−	5.94340i	−0.970679	−	0.353298i	−0.192469	−	0.981303i	$-0.561650\pi$
$283$	−16.3293	−	5.94340i	−0.970679	−	0.353298i	−0.778209	+	0.628005i	$0.783872\pi$
$284$		0			0
$285$	−0.477711	+	5.85327i	−0.0282972	+	0.346718i
$286$		0			0
$287$	7.92989	+	2.88624i	0.468087	+	0.170370i
$288$		0			0
$289$	−10.9304	−	9.17166i	−0.642962	−	0.539509i
$290$		0			0
$291$	0.168434	−	0.955234i	0.00987375	−	0.0559968i
$292$		0			0
$293$	−7.80200	−	13.5135i	−0.455798	−	0.789465i	0.542936	−	0.839774i	$-0.317313\pi$
$293$	−7.80200	−	13.5135i	−0.455798	−	0.789465i	−0.998734	+	0.0503091i	$0.983979\pi$
$294$		0			0
$295$	25.5993	−	9.31737i	1.49045	−	0.542478i
$296$		0			0
$297$	5.18866	−	8.98703i	0.301077	−	0.521480i
$298$		0			0
$299$	7.12836	−	5.98140i	0.412243	−	0.345913i
$300$		0			0
$301$	−1.56670	−	8.88522i	−0.0903033	−	0.512136i
$302$		0			0
$303$	4.21482			0.242135
$304$		0			0
$305$	−11.1138			−0.636375
$306$		0			0
$307$	−3.73695	−	21.1933i	−0.213279	−	1.20956i	−0.883868	−	0.467736i	$-0.845070\pi$
$307$	−3.73695	−	21.1933i	−0.213279	−	1.20956i	0.670589	−	0.741829i	$-0.266041\pi$
$308$		0			0
$309$	−0.00592979	+	0.00497568i	−0.000337334	+	0.000283057i
$310$		0			0
$311$	7.24763	−	12.5533i	0.410975	−	0.711830i	−0.584021	−	0.811738i	$-0.698522\pi$
$311$	7.24763	−	12.5533i	0.410975	−	0.711830i	0.994997	+	0.0999083i	$0.0318550\pi$
$312$		0			0
$313$	−18.3414	+	6.67571i	−1.03672	+	0.377334i	−0.803634	−	0.595124i	$-0.797103\pi$
$313$	−18.3414	+	6.67571i	−1.03672	+	0.377334i	−0.233081	+	0.972457i	$0.574881\pi$
$314$		0			0
$315$	−6.46451	−	11.1969i	−0.364234	−	0.630871i
$316$		0			0
$317$	4.92246	−	27.9166i	0.276473	−	1.56795i	−0.457772	−	0.889070i	$-0.651352\pi$
$317$	4.92246	−	27.9166i	0.276473	−	1.56795i	0.734245	−	0.678885i	$-0.237536\pi$
$318$		0			0
$319$	9.06283	+	7.60462i	0.507421	+	0.425777i
$320$		0			0
$321$	1.77719	+	0.646844i	0.0991930	+	0.0361033i
$322$		0			0
$323$	−1.90508	−	6.94751i	−0.106001	−	0.386570i
$324$		0			0
$325$	7.01754	+	2.55418i	0.389263	+	0.141680i
$326$		0			0
$327$	−3.00387	−	2.52055i	−0.166114	−	0.139387i
$328$		0			0
$329$	−0.233956	+	1.32683i	−0.0128984	+	0.0731504i
$330$		0			0
$331$	−0.855037	−	1.48097i	−0.0469971	−	0.0814014i	0.841570	−	0.540148i	$-0.181632\pi$
$331$	−0.855037	−	1.48097i	−0.0469971	−	0.0814014i	−0.888567	+	0.458747i	$0.848298\pi$
$332$		0			0
$333$	−2.13816	+	0.778225i	−0.117170	+	0.0426465i
$334$		0			0
$335$	−17.9932	+	31.1651i	−0.983073	+	1.70273i
$336$		0			0
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.0672796	−	0.997734i	$-0.478568\pi$
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.994259	+	0.106997i	$0.0341236\pi$
$338$		0			0
$339$	−0.681637	−	3.86576i	−0.0370215	−	0.209959i
$340$		0			0
$341$	6.63041			0.359057
$342$		0			0
$343$	−19.6732			−1.06225
$344$		0			0
$345$	−0.411474	−	2.33359i	−0.0221530	−	0.125636i
$346$		0			0
$347$	−5.90033	+	4.95096i	−0.316746	+	0.265782i	−0.787274	−	0.616604i	$-0.788508\pi$
$347$	−5.90033	+	4.95096i	−0.316746	+	0.265782i	0.470527	+	0.882385i	$0.344064\pi$
$348$		0			0
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	0.382315	+	0.924032i	$0.375127\pi$
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	−0.991393	+	0.130921i	$0.958206\pi$
$350$		0			0
$351$	15.1236	−	5.50454i	0.807238	−	0.293811i
$352$		0			0
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	0.977171	−	0.212454i	$-0.0681457\pi$
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	−0.672576	+	0.740028i	$0.734812\pi$
$354$		0			0
$355$	−6.04963	+	34.3092i	−0.321081	+	1.82094i
$356$		0			0
$357$	−1.26604	−	1.06234i	−0.0670062	−	0.0562249i
$358$		0			0
$359$	9.75789	+	3.55158i	0.515002	+	0.187445i	0.586429	−	0.810000i	$-0.300533\pi$
$359$	9.75789	+	3.55158i	0.515002	+	0.187445i	−0.0714274	+	0.997446i	$0.522755\pi$
$360$		0			0
$361$	−6.28968	+	17.9287i	−0.331036	+	0.943618i
$362$		0			0
$363$	0.319078	+	0.116135i	0.0167472	+	0.00609550i
$364$		0			0
$365$	14.5817	+	12.2355i	0.763242	+	0.640436i
$366$		0			0
$367$	5.64930	−	32.0388i	0.294891	−	1.67241i	−0.372754	−	0.927930i	$-0.621586\pi$
$367$	5.64930	−	32.0388i	0.294891	−	1.67241i	0.667645	−	0.744480i	$-0.267303\pi$
$368$		0			0
$369$	−6.09967	−	10.5649i	−0.317536	−	0.549989i
$370$		0			0
$371$	10.7836	−	3.92490i	0.559856	−	0.203771i
$372$		0			0
$373$	−15.2429	+	26.4014i	−0.789246	+	1.36701i	0.137183	+	0.990546i	$0.456195\pi$
$373$	−15.2429	+	26.4014i	−0.789246	+	1.36701i	−0.926429	+	0.376469i	$0.877138\pi$
$374$		0			0
$375$	−3.70368	+	3.10775i	−0.191257	+	0.160484i
$376$		0			0
$377$	3.18614	+	18.0695i	0.164094	+	0.930626i
$378$		0			0
$379$	−17.8598			−0.917396			−0.458698	−	0.888592i	$-0.651684\pi$
$379$	−17.8598			−0.917396			−0.458698	+	0.888592i	$0.651684\pi$
$380$		0			0
$381$	−0.0537486			−0.00275363
$382$		0			0
$383$	4.07310	+	23.0997i	0.208126	+	1.18034i	0.892445	+	0.451157i	$0.148988\pi$
$383$	4.07310	+	23.0997i	0.208126	+	1.18034i	−0.684319	+	0.729183i	$0.739900\pi$
$384$		0			0
$385$	12.4363	−	10.4353i	0.633812	−	0.531831i
$386$		0			0
$387$	−6.52141	+	11.2954i	−0.331502	+	0.574178i
$388$		0			0
$389$	−3.67365	+	1.33710i	−0.186261	+	0.0677936i	−0.433467	−	0.901169i	$-0.642710\pi$
$389$	−3.67365	+	1.33710i	−0.186261	+	0.0677936i	0.247206	+	0.968963i	$0.420488\pi$
$390$		0			0
$391$	1.45336	+	2.51730i	0.0734997	+	0.127305i
$392$		0			0
$393$	−0.280592	+	1.59132i	−0.0141540	+	0.0802714i
$394$		0			0
$395$	−13.5064	−	11.3332i	−0.679581	−	0.570236i
$396$		0			0
$397$	−8.41875	−	3.06417i	−0.422525	−	0.153786i	0.122002	−	0.992530i	$-0.461069\pi$
$397$	−8.41875	−	3.06417i	−0.422525	−	0.153786i	−0.544527	+	0.838743i	$0.683291\pi$
$398$		0			0
$399$	1.15270	+	4.20372i	0.0577074	+	0.210449i
$400$		0			0
$401$	1.90508	+	0.693392i	0.0951350	+	0.0346263i	0.389149	−	0.921175i	$-0.372769\pi$
$401$	1.90508	+	0.693392i	0.0951350	+	0.0346263i	−0.294014	+	0.955801i	$0.594991\pi$
$402$		0			0
$403$	7.87733	+	6.60986i	0.392398	+	0.329261i
$404$		0			0
$405$	−2.87211	+	16.2886i	−0.142716	+	0.809385i
$406$		0			0
$407$	−1.42855	−	2.47432i	−0.0708105	−	0.122647i
$408$		0			0
$409$	30.2656	−	11.0158i	1.49654	−	0.544696i	0.541377	−	0.840780i	$-0.317903\pi$
$409$	30.2656	−	11.0158i	1.49654	−	0.544696i	0.955162	+	0.296084i	$0.0956808\pi$
$410$		0			0
$411$	5.19846	−	9.00400i	0.256421	−	0.444135i
$412$		0			0
$413$	15.4893	−	12.9971i	0.762180	−	0.639545i
$414$		0			0
$415$	1.10472	+	6.26519i	0.0542287	+	0.307546i
$416$		0			0
$417$	8.19253			0.401190
$418$		0			0
$419$	23.2499			1.13583			0.567916	−	0.823086i	$-0.307750\pi$
$419$	23.2499			1.13583			0.567916	+	0.823086i	$0.307750\pi$
$420$		0			0
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	0.999862	−	0.0166178i	$-0.00528986\pi$
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	−0.945246	+	0.326357i	$0.894179\pi$
$422$		0			0
$423$	1.49201	−	1.25195i	0.0725440	−	0.0608717i
$424$		0			0
$425$	−1.16637	+	2.02022i	−0.0565775	+	0.0979950i
$426$		0			0
$427$	−7.75150	+	2.82131i	−0.375121	+	0.136533i
$428$		0			0
$429$	4.80200	+	8.31731i	0.231843	+	0.401564i
$430$		0			0
$431$	2.43061	−	13.7847i	0.117078	−	0.663984i	−0.868622	−	0.495475i	$-0.834994\pi$
$431$	2.43061	−	13.7847i	0.117078	−	0.663984i	0.985700	−	0.168508i	$-0.0538950\pi$
$432$		0			0
$433$	−21.9800	−	18.4434i	−1.05629	−	0.886333i	−0.0625499	−	0.998042i	$-0.519923\pi$
$433$	−21.9800	−	18.4434i	−1.05629	−	0.886333i	−0.993741	+	0.111709i	$0.964368\pi$
$434$		0			0
$435$	4.39053	+	1.59802i	0.210510	+	0.0766193i
$436$		0			0
$437$	0.623608	−	7.64090i	0.0298312	−	0.365514i
$438$		0			0
$439$	−12.5376	−	4.56332i	−0.598387	−	0.217795i	0.0250271	−	0.999687i	$-0.492033\pi$
$439$	−12.5376	−	4.56332i	−0.598387	−	0.217795i	−0.623414	+	0.781892i	$0.714255\pi$
$440$		0			0
$441$	7.21760	+	6.05628i	0.343695	+	0.288394i
$442$		0			0
$443$	−5.88372	+	33.3682i	−0.279544	+	1.58537i	0.444603	+	0.895728i	$0.353345\pi$
$443$	−5.88372	+	33.3682i	−0.279544	+	1.58537i	−0.724147	+	0.689646i	$0.757766\pi$
$444$		0			0
$445$	−2.89053	−	5.00654i	−0.137024	−	0.237333i
$446$		0			0
$447$	−1.88326	+	0.685449i	−0.0890749	+	0.0324206i
$448$		0			0
$449$	−9.42009	+	16.3161i	−0.444562	+	0.770003i	−0.998022	−	0.0628725i	$-0.979974\pi$
$449$	−9.42009	+	16.3161i	−0.444562	+	0.770003i	0.553460	+	0.832876i	$0.313307\pi$
$450$		0			0
$451$	11.7344	−	9.84635i	0.552552	−	0.463646i
$452$		0			0
$453$	−1.34864	−	7.64852i	−0.0633647	−	0.359359i
$454$		0			0
$455$	25.1780			1.18036
$456$		0			0
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$		0			0
$459$	0.872989	+	4.95096i	0.0407476	+	0.231091i
$460$		0			0
$461$	−10.6695	+	8.95280i	−0.496930	+	0.416973i	−0.856502	−	0.516144i	$-0.827367\pi$
$461$	−10.6695	+	8.95280i	−0.496930	+	0.416973i	0.359572	+	0.933117i	$0.382923\pi$
$462$		0			0
$463$	−0.881445	+	1.52671i	−0.0409642	+	0.0709521i	−0.885781	−	0.464104i	$-0.846376\pi$
$463$	−0.881445	+	1.52671i	−0.0409642	+	0.0709521i	0.844816	+	0.535056i	$0.179710\pi$
$464$		0			0
$465$	2.46064	−	0.895599i	0.114109	−	0.0415324i
$466$		0			0
$467$	11.0209	+	19.0888i	0.509988	+	0.883326i	0.999933	+	0.0115724i	$0.00368368\pi$
$467$	11.0209	+	19.0888i	0.509988	+	0.883326i	−0.489945	+	0.871754i	$0.662983\pi$
$468$		0			0
$469$	−4.63816	+	26.3043i	−0.214170	+	1.21462i
$470$		0			0
$471$	4.22874	+	3.54834i	0.194850	+	0.163499i
$472$		0			0
$473$	−15.3897	−	5.60138i	−0.707617	−	0.257552i
$474$		0			0
$475$	5.56077	−	2.63263i	0.255146	−	0.120793i
$476$		0			0
$477$	−15.5890	−	5.67393i	−0.713771	−	0.259791i
$478$		0			0
$479$	19.5012	+	16.3634i	0.891032	+	0.747664i	0.968417	−	0.249337i	$-0.0802126\pi$
$479$	19.5012	+	16.3634i	0.891032	+	0.747664i	−0.0773851	+	0.997001i	$0.524657\pi$
$480$		0			0
$481$	0.769448	−	4.36376i	0.0350838	−	0.198970i
$482$		0			0
$483$	−0.879385	−	1.52314i	−0.0400134	−	0.0693053i
$484$		0			0
$485$	−4.33750	+	1.57872i	−0.196956	+	0.0716860i
$486$		0			0
$487$	−11.2554	+	19.4949i	−0.510029	+	0.883397i	0.489903	+	0.871777i	$0.337032\pi$
$487$	−11.2554	+	19.4949i	−0.510029	+	0.883397i	−0.999932	+	0.0116199i	$0.996301\pi$
$488$		0			0
$489$	−0.824292	+	0.691663i	−0.0372758	+	0.0312781i
$490$		0			0
$491$	−2.71482	−	15.3965i	−0.122518	−	0.694835i	−0.982751	−	0.184934i	$-0.940793\pi$
$491$	−2.71482	−	15.3965i	−0.122518	−	0.694835i	0.860233	−	0.509902i	$-0.170318\pi$
$492$		0			0
$493$	−5.73143			−0.258131
$494$		0			0
$495$	−23.4688			−1.05485
$496$		0			0
$497$	4.49020	+	25.4652i	0.201413	+	1.14227i
$498$		0			0
$499$	21.9217	−	18.3945i	0.981352	−	0.823452i	−0.00294090	−	0.999996i	$-0.500936\pi$
$499$	21.9217	−	18.3945i	0.981352	−	0.823452i	0.984293	+	0.176544i	$0.0564917\pi$
$500$		0			0
$501$	6.18732	−	10.7168i	0.276429	−	0.478789i
$502$		0			0
$503$	−23.5351	+	8.56607i	−1.04938	+	0.381942i	−0.808428	−	0.588595i	$-0.799681\pi$
$503$	−23.5351	+	8.56607i	−1.04938	+	0.381942i	−0.240950	+	0.970538i	$0.577459\pi$
$504$		0			0
$505$	−10.0287	−	17.3702i	−0.446271	−	0.772963i
$506$		0			0
$507$	−1.38532	+	7.85651i	−0.0615240	+	0.348920i
$508$		0			0
$509$	25.6787	+	21.5470i	1.13819	+	0.955053i	0.999378	−	0.0352655i	$-0.0112277\pi$
$509$	25.6787	+	21.5470i	1.13819	+	0.955053i	0.138810	+	0.990319i	$0.455672\pi$
$510$		0			0
$511$	13.2763	+	4.83218i	0.587309	+	0.213763i
$512$		0			0
$513$	5.53343	−	12.0495i	0.244307	−	0.531997i
$514$		0			0
$515$	0.0346151	+	0.0125989i	0.00152532	+	0.000555172i
$516$		0			0
$517$	1.87346	+	1.57202i	0.0823945	+	0.0691372i
$518$		0			0
$519$	−0.0828445	+	0.469834i	−0.00363647	+	0.0206234i
$520$		0			0
$521$	13.7392	+	23.7969i	0.601924	+	1.04256i	0.992530	+	0.122005i	$0.0389323\pi$
$521$	13.7392	+	23.7969i	0.601924	+	1.04256i	−0.390606	+	0.920558i	$0.627734\pi$
$522$		0			0
$523$	−9.73277	+	3.54244i	−0.425584	+	0.154900i	−0.545928	−	0.837832i	$-0.683823\pi$
$523$	−9.73277	+	3.54244i	−0.425584	+	0.154900i	0.120343	+	0.992732i	$0.461600\pi$
$524$		0			0
$525$	0.705737	−	1.22237i	0.0308009	−	0.0533487i
$526$		0			0
$527$	−2.46064	+	2.06472i	−0.107187	+	0.0899406i
$528$		0			0
$529$	−3.45677	−	19.6043i	−0.150294	−	0.852361i
$530$		0			0
$531$	−29.2303			−1.26849
$532$		0			0
$533$	23.7570			1.02903
$534$		0			0
$535$	−1.56283	−	8.86327i	−0.0675672	−	0.383193i
$536$		0			0
$537$	−8.68938	+	7.29125i	−0.374974	+	0.314641i
$538$		0			0
$539$	−5.91534	+	10.2457i	−0.254792	+	0.441313i
$540$		0			0
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	−0.392509	−	0.919748i	$-0.628393\pi$
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	0.290524	+	0.956868i	$0.406170\pi$
$542$		0			0
$543$	−4.28312	−	7.41858i	−0.183806	−	0.318362i
$544$		0			0
$545$	−3.24035	+	18.3770i	−0.138801	+	0.787182i
$546$		0			0
$547$	−5.87939	−	4.93339i	−0.251384	−	0.210937i	0.508384	−	0.861131i	$-0.330243\pi$
$547$	−5.87939	−	4.93339i	−0.251384	−	0.210937i	−0.759768	+	0.650194i	$0.774688\pi$
$548$		0			0
$549$	11.2057	+	4.07855i	0.478249	+	0.174068i
$550$		0			0
$551$	12.4329	+	8.59797i	0.529659	+	0.366286i
$552$		0			0
$553$	−12.2973	−	4.47584i	−0.522933	−	0.190332i
$554$		0			0
$555$	−0.864370	−	0.725293i	−0.0366905	−	0.0307870i
$556$		0			0
$557$	0.565360	−	3.20631i	0.0239551	−	0.135856i	−0.970485	−	0.241163i	$-0.922471\pi$
$557$	0.565360	−	3.20631i	0.0239551	−	0.135856i	0.994440	+	0.105307i	$0.0335824\pi$
$558$		0			0
$559$	−12.6998	−	21.9967i	−0.537145	−	0.930362i
$560$		0			0
$561$	−2.81908	+	1.02606i	−0.119022	+	0.0433203i
$562$		0			0
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	−0.805280	−	0.592895i	$-0.797985\pi$
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	0.916102	+	0.400946i	$0.131318\pi$
$564$		0			0
$565$	−14.3097	+	12.0073i	−0.602015	+	0.505151i
$566$		0			0
$567$	2.13176	+	12.0898i	0.0895255	+	0.507724i
$568$		0			0
$569$	−29.9564			−1.25584			−0.627918	−	0.778280i	$-0.716093\pi$
$569$	−29.9564			−1.25584			−0.627918	+	0.778280i	$0.716093\pi$
$570$		0			0
$571$	16.7101			0.699295			0.349647	−	0.936881i	$-0.386301\pi$
$571$	16.7101			0.699295			0.349647	+	0.936881i	$0.386301\pi$
$572$		0			0
$573$	1.75078	+	9.92917i	0.0731399	+	0.414797i
$574$		0			0
$575$	−1.90167	+	1.59569i	−0.0793053	+	0.0665450i
$576$		0			0
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$578$		0			0
$579$	6.45084	−	2.34791i	0.268088	−	0.0975759i
$580$		0			0
$581$	2.36097	+	4.08931i	0.0979494	+	0.169653i
$582$		0			0
$583$	3.61721	−	20.5142i	0.149810	−	0.849612i
$584$		0			0
$585$	−27.8824	−	23.3961i	−1.15279	−	0.967309i
$586$		0			0
$587$	−22.5872	−	8.22108i	−0.932275	−	0.339320i	−0.169164	−	0.985588i	$-0.554107\pi$
$587$	−22.5872	−	8.22108i	−0.932275	−	0.339320i	−0.763111	+	0.646268i	$0.776329\pi$
$588$		0			0
$589$	8.43511	−	0.787576i	0.347563	−	0.0324515i
$590$		0			0
$591$	−11.6001	−	4.22210i	−0.477166	−	0.173674i
$592$		0			0
$593$	−3.24897	−	2.72621i	−0.133419	−	0.111952i	0.573636	−	0.819110i	$-0.305532\pi$
$593$	−3.24897	−	2.72621i	−0.133419	−	0.111952i	−0.707055	+	0.707158i	$0.749977\pi$
$594$		0			0
$595$	−1.36571	+	7.74535i	−0.0559888	+	0.317529i
$596$		0			0
$597$	−2.45336	−	4.24935i	−0.100409	−	0.173914i
$598$		0			0
$599$	−24.6894	+	8.98622i	−1.00878	+	0.367167i	−0.792965	−	0.609267i	$-0.791464\pi$
$599$	−24.6894	+	8.98622i	−1.00878	+	0.367167i	−0.215818	+	0.976434i	$0.569242\pi$
$600$		0			0
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	−0.00899659	−	0.999960i	$-0.502864\pi$
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	0.870489	−	0.492188i	$-0.163803\pi$
$602$		0			0
$603$	29.5790	−	24.8198i	1.20455	−	1.01074i
$604$		0			0
$605$	−0.280592	−	1.59132i	−0.0114077	−	0.0646963i
$606$		0			0
$607$	22.0969			0.896885			0.448443	−	0.893812i	$-0.351979\pi$
$607$	22.0969			0.896885			0.448443	+	0.893812i	$0.351979\pi$
$608$		0			0
$609$	3.46791			0.140527
$610$		0			0
$611$	0.658633	+	3.73530i	0.0266455	+	0.151114i
$612$		0			0
$613$	5.49794	−	4.61332i	0.222060	−	0.186330i	−0.524970	−	0.851121i	$-0.675924\pi$
$613$	5.49794	−	4.61332i	0.222060	−	0.186330i	0.747030	+	0.664790i	$0.231479\pi$
$614$		0			0
$615$	3.02481	−	5.23913i	0.121972	−	0.211262i
$616$		0			0
$617$	46.3953	−	16.8865i	1.86781	−	0.679826i	0.895995	−	0.444065i	$-0.146464\pi$
$617$	46.3953	−	16.8865i	1.86781	−	0.679826i	0.971811	−	0.235761i	$-0.0757583\pi$
$618$		0			0
$619$	13.2490	+	22.9479i	0.532521	+	0.922354i	0.999279	+	0.0379684i	$0.0120886\pi$
$619$	13.2490	+	22.9479i	0.532521	+	0.922354i	−0.466758	+	0.884385i	$0.654578\pi$
$620$		0			0
$621$	−0.929015	+	5.26871i	−0.0372801	+	0.211426i
$622$		0			0
$623$	−3.28699	−	2.75811i	−0.131690	−	0.110501i
$624$		0			0
$625$	28.2520	+	10.2829i	1.13008	+	0.411315i
$626$		0			0
$627$	7.65451	+	2.00324i	0.305692	+	0.0800019i
$628$		0			0
$629$	1.30066	+	0.473401i	0.0518607	+	0.0188757i
$630$		0			0
$631$	−25.5253	−	21.4183i	−1.01615	−	0.852647i	−0.0270071	−	0.999635i	$-0.508598\pi$
$631$	−25.5253	−	21.4183i	−1.01615	−	0.852647i	−0.989138	+	0.146988i	$0.953042\pi$
$632$		0			0
$633$	1.35117	−	7.66285i	0.0537041	−	0.304571i
$634$		0			0
$635$	0.127889	+	0.221510i	0.00507511	+	0.00879035i
$636$		0			0
$637$	−17.2417	+	6.27546i	−0.683141	+	0.248643i
$638$		0			0
$639$	18.6905	−	32.3729i	0.739384	−	1.28065i
$640$		0			0
$641$	−0.104256	+	0.0874810i	−0.00411786	+	0.00345529i	−0.644844	−	0.764314i	$-0.723078\pi$
$641$	−0.104256	+	0.0874810i	−0.00411786	+	0.00345529i	0.640726	+	0.767769i	$0.278633\pi$
$642$		0			0
$643$	−8.36602	−	47.4461i	−0.329924	−	1.87109i	−0.472536	−	0.881311i	$-0.656661\pi$
$643$	−8.36602	−	47.4461i	−0.329924	−	1.87109i	0.142613	−	0.989779i	$-0.454450\pi$
$644$		0			0
$645$	−6.46791			−0.254674
$646$		0			0
$647$	36.9718			1.45351			0.726756	−	0.686895i	$-0.241027\pi$
$647$	36.9718			1.45351			0.726756	+	0.686895i	$0.241027\pi$
$648$		0			0
$649$	−6.37346	−	36.1457i	−0.250180	−	1.41884i
$650$		0			0
$651$	1.48886	−	1.24930i	0.0583529	−	0.0489639i
$652$		0			0
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$		0			0
$655$	7.22580	−	2.62998i	0.282336	−	0.102762i
$656$		0			0
$657$	−10.2121	−	17.6879i	−0.398413	−	0.690072i
$658$		0			0
$659$	−3.27760	+	18.5882i	−0.127677	+	0.724093i	0.852005	+	0.523534i	$0.175387\pi$
$659$	−3.27760	+	18.5882i	−0.127677	+	0.724093i	−0.979682	+	0.200559i	$0.935724\pi$
$660$		0			0
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	0.0604192	−	0.998173i	$-0.480756\pi$
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	−0.972517	+	0.232832i	$0.925201\pi$
$662$		0			0
$663$	−4.37211	−	1.59132i	−0.169799	−	0.0618017i
$664$		0			0
$665$	14.5817	−	14.7528i	0.565455	−	0.572090i
$666$		0			0
$667$	−5.73143	−	2.08607i	−0.221922	−	0.0807729i
$668$		0			0
$669$	−1.22874	−	1.03104i	−0.0475059	−	0.0398622i
$670$		0			0
$671$	−2.60014	+	14.7461i	−0.100377	+	0.569267i
$672$		0			0
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	0.728134	−	0.685435i	$-0.240388\pi$
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	−0.957671	+	0.287865i	$0.907055\pi$
$674$		0			0
$675$	−4.03462	+	1.46848i	−0.155292	+	0.0565218i
$676$		0			0
$677$	−2.89053	+	5.00654i	−0.111092	+	0.192417i	−0.916211	−	0.400696i	$-0.868768\pi$
$677$	−2.89053	+	5.00654i	−0.111092	+	0.192417i	0.805119	+	0.593114i	$0.202102\pi$
$678$		0			0
$679$	−2.62449	+	2.20220i	−0.100718	+	0.0845129i
$680$		0			0
$681$	−1.26786	−	7.19037i	−0.0485843	−	0.275535i
$682$		0			0
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$		0			0
$685$	−49.4766			−1.89040
$686$		0			0
$687$	−0.869833	−	4.93307i	−0.0331862	−	0.188208i
$688$		0			0
$689$	24.7481	−	20.7661i	0.942827	−	0.791126i
$690$		0			0
$691$	−16.4688	+	28.5249i	−0.626504	+	1.08514i	0.361744	+	0.932278i	$0.382182\pi$
$691$	−16.4688	+	28.5249i	−0.626504	+	1.08514i	−0.988248	+	0.152860i	$0.951152\pi$
$692$		0			0
$693$	−16.3687	+	5.95772i	−0.621796	+	0.226315i
$694$		0			0
$695$	−19.4932	−	33.7632i	−0.739419	−	1.28071i
$696$		0			0
$697$	−1.28864	+	7.30823i	−0.0488106	+	0.276819i
$698$		0			0
$699$	9.85819	+	8.27201i	0.372871	+	0.312876i
$700$		0			0
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.0660380	−	0.997817i	$-0.521036\pi$
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.691973	+	0.721924i	$0.743258\pi$
$702$		0			0
$703$	−2.11128	−	2.97810i	−0.0796285	−	0.112321i
$704$		0			0
$705$	0.907604	+	0.330341i	0.0341823	+	0.0124414i
$706$		0			0
$707$	−11.4042	−	9.56926i	−0.428899	−	0.359889i
$708$		0			0
$709$	−2.73854	+	15.5310i	−0.102848	+	0.583280i	0.889210	+	0.457499i	$0.151255\pi$
$709$	−2.73854	+	15.5310i	−0.102848	+	0.583280i	−0.992058	+	0.125781i	$0.959856\pi$
$710$		0			0
$711$	9.45904	+	16.3835i	0.354742	+	0.614431i
$712$		0			0
$713$	−3.21213	+	1.16912i	−0.120295	+	0.0437839i
$714$		0			0
$715$	22.8516	−	39.5802i	0.854603	−	1.48022i
$716$		0			0
$717$	−9.50774	+	7.97794i	−0.355073	+	0.297942i
$718$		0			0
$719$	6.13470	+	34.7916i	0.228786	+	1.29751i	0.855314	+	0.518109i	$0.173364\pi$
$719$	6.13470	+	34.7916i	0.228786	+	1.29751i	−0.626529	+	0.779398i	$0.715525\pi$
$720$		0			0
$721$	0.0273411			0.00101824
$722$		0			0
$723$	−0.158385			−0.00589040
$724$		0			0
$725$	−0.849985	−	4.82050i	−0.0315676	−	0.179029i
$726$		0			0
$727$	−30.9647	+	25.9825i	−1.14842	+	0.963637i	−0.999681	−	0.0252396i	$-0.991965\pi$
$727$	−30.9647	+	25.9825i	−1.14842	+	0.963637i	−0.148737	+	0.988877i	$0.547521\pi$
$728$		0			0
$729$	6.44562	−	11.1641i	0.238727	−	0.413487i
$730$		0			0
$731$	7.45558	−	2.71361i	0.275755	−	0.100367i
$732$		0			0
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	0.977918	+	0.208988i	$0.0670170\pi$
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	−0.307970	+	0.951396i	$0.599650\pi$
$734$		0			0
$735$	−0.811337	+	4.60132i	−0.0299266	+	0.169722i
$736$		0			0
$737$	37.1411	+	31.1651i	1.36811	+	1.14798i
$738$		0			0
$739$	−19.4290	−	7.07158i	−0.714708	−	0.260132i	−0.0410304	−	0.999158i	$-0.513064\pi$
$739$	−19.4290	−	7.07158i	−0.714708	−	0.260132i	−0.673677	+	0.739026i	$0.735286\pi$
$740$		0			0
$741$	7.09698	+	10.0108i	0.260714	+	0.367754i
$742$		0			0
$743$	6.29978	+	2.29293i	0.231117	+	0.0841196i	0.454982	−	0.890500i	$-0.349646\pi$
$743$	6.29978	+	2.29293i	0.231117	+	0.0841196i	−0.223866	+	0.974620i	$0.571868\pi$
$744$		0			0
$745$	7.30587	+	6.13036i	0.267667	+	0.224599i
$746$		0			0
$747$	1.18535	−	6.72243i	0.0433695	−	0.245961i
$748$		0			0
$749$	−3.34002	−	5.78509i	−0.122042	−	0.211383i
$750$		0			0
$751$	10.0617	−	3.66214i	0.367155	−	0.133633i	−0.151853	−	0.988403i	$-0.548524\pi$
$751$	10.0617	−	3.66214i	0.367155	−	0.133633i	0.519007	+	0.854770i	$0.326302\pi$
$752$		0			0
$753$	4.30928	−	7.46389i	0.157039	−	0.271999i
$754$		0			0
$755$	−28.3123	+	23.7568i	−1.03039	+	0.864599i
$756$		0			0
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	0.969301	−	0.245878i	$-0.0790764\pi$
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	−0.994940	+	0.100470i	$0.967965\pi$
$758$		0			0
$759$	−3.19253			−0.115882
$760$		0			0
$761$	−11.0077			−0.399030			−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077			−0.399030			−0.199515	+	0.979895i	$0.563937\pi$
$762$		0			0
$763$	2.40508	+	13.6399i	0.0870697	+	0.493797i
$764$		0			0
$765$	8.70961	−	7.30823i	0.314897	−	0.264230i
$766$		0			0
$767$	28.4616	−	49.2969i	1.02769	−	1.78001i
$768$		0			0
$769$	−20.0599	+	7.30121i	−0.723378	+	0.263288i	−0.677359	−	0.735652i	$-0.736876\pi$
$769$	−20.0599	+	7.30121i	−0.723378	+	0.263288i	−0.0460191	+	0.998941i	$0.514654\pi$
$770$		0			0
$771$	4.08512	+	7.07564i	0.147122	+	0.254823i
$772$		0			0
$773$	3.11128	−	17.6450i	0.111905	−	0.634645i	−0.876331	−	0.481709i	$-0.840016\pi$
$773$	3.11128	−	17.6450i	0.111905	−	0.634645i	0.988236	−	0.152936i	$-0.0488727\pi$
$774$		0			0
$775$	−2.10148	−	1.76335i	−0.0754874	−	0.0633415i
$776$		0			0
$777$	−0.786989	−	0.286441i	−0.0282331	−	0.0102760i
$778$		0			0
$779$	13.7588	−	13.9202i	0.492959	−	0.498743i
$780$		0			0
$781$	44.1070	+	16.0536i	1.57827	+	0.574444i
$782$		0			0
$783$	−8.08100	−	6.78077i	−0.288792	−	0.242325i
$784$		0			0
$785$	4.56165	−	25.8704i	0.162812	−	0.923355i
$786$		0			0
$787$	24.4158	+	42.2894i	0.870330	+	1.50746i	0.861656	+	0.507493i	$0.169428\pi$
$787$	24.4158	+	42.2894i	0.870330	+	1.50746i	0.00867371	+	0.999962i	$0.497239\pi$
$788$		0			0
$789$	−4.82160	+	1.75492i	−0.171654	+	0.0624768i
$790$		0			0
$791$	−6.93242	+	12.0073i	−0.246488	+	0.426930i
$792$		0			0
$793$	−17.7895	+	14.9272i	−0.631724	+	0.530080i
$794$		0			0
$795$	−1.42855	−	8.10170i	−0.0506654	−	0.287338i
$796$		0			0
$797$	−28.5262			−1.01045			−0.505225	−	0.862988i	$-0.668591\pi$
$797$	−28.5262			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$798$		0			0
$799$	−1.18479			−0.0419149
$800$		0			0
$801$	1.07713	+	6.10873i	0.0380586	+	0.215841i
$802$		0			0
$803$	19.6459	−	16.4849i	0.693289	−	0.581738i
$804$		0			0
$805$	−4.18479	+	7.24827i	−0.147495	+	0.255468i
$806$		0			0
$807$	−9.13950	+	3.32651i	−0.321726	+	0.117099i
$808$		0			0
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	0.966459	−	0.256822i	$-0.0826755\pi$
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	−0.705644	+	0.708567i	$0.749342\pi$
$810$		0			0
$811$	1.45471	−	8.25006i	0.0510817	−	0.289699i	−0.948556	−	0.316609i	$-0.897456\pi$
$811$	1.45471	−	8.25006i	0.0510817	−	0.289699i	0.999638	+	0.0269103i	$0.00856684\pi$
$812$		0			0
$813$	7.72984	+	6.48610i	0.271097	+	0.227478i
$814$		0			0
$815$	4.81180	+	1.75135i	0.168550	+	0.0613472i
$816$		0			0
$817$	−20.2438	−	5.29796i	−0.708241	−	0.185352i
$818$		0			0
$819$	−25.3862	−	9.23984i	−0.887067	−	0.322866i
$820$		0			0
$821$	4.80999	+	4.03606i	0.167870	+	0.140860i	0.722852	−	0.691002i	$-0.242831\pi$
$821$	4.80999	+	4.03606i	0.167870	+	0.140860i	−0.554983	+	0.831862i	$0.687275\pi$
$822$		0			0
$823$	−1.91472	+	10.8589i	−0.0667428	+	0.378517i	0.933080	+	0.359670i	$0.117111\pi$
$823$	−1.91472	+	10.8589i	−0.0667428	+	0.378517i	−0.999822	+	0.0188472i	$0.994000\pi$
$824$		0			0
$825$	−1.28106	−	2.21886i	−0.0446008	−	0.0772508i
$826$		0			0
$827$	31.8892	−	11.6067i	1.10890	−	0.403606i	0.278309	−	0.960492i	$-0.410226\pi$
$827$	31.8892	−	11.6067i	1.10890	−	0.403606i	0.830589	+	0.556886i	$0.188004\pi$
$828$		0			0
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	−0.633206	−	0.773983i	$-0.718262\pi$
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	0.986892	+	0.161381i	$0.0515949\pi$
$830$		0			0
$831$	−5.61019	+	4.70750i	−0.194615	+	0.163302i
$832$		0			0
$833$	−0.995252	−	5.64436i	−0.0344834	−	0.195565i
$834$		0			0
$835$	−58.8881			−2.03791
$836$		0			0
$837$	−5.91210			−0.204352
$838$		0			0
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	−0.994815	−	0.101697i	$-0.967573\pi$
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	0.900038	−	0.435810i	$-0.143538\pi$
$840$		0			0
$841$	−13.0025	+	10.9104i	−0.448363	+	0.376221i
$842$		0			0
$843$	3.48814	−	6.04164i	0.120138	−	0.208085i
$844$		0			0
$845$	35.6746	−	12.9845i	1.22724	−	0.446680i
$846$		0			0
$847$	−0.599670	−	1.03866i	−0.0206049	−	0.0356888i
$848$		0			0
$849$	−1.60560	+	9.10581i	−0.0551040	+	0.312511i
$850$		0			0
$851$	1.12836	+	0.946803i	0.0386795	+	0.0324560i
$852$		0			0
$853$	49.4741	+	18.0071i	1.69396	+	0.616551i	0.995115	−	0.0987227i	$-0.0314757\pi$
$853$	49.4741	+	18.0071i	1.69396	+	0.616551i	0.698845	+	0.715274i	$0.253698\pi$
$854$		0			0
$855$	−29.8567	+	2.78768i	−1.02108	+	0.0953368i
$856$		0			0
$857$	21.6386	+	7.87581i	0.739161	+	0.269033i	0.684038	−	0.729447i	$-0.260222\pi$
$857$	21.6386	+	7.87581i	0.739161	+	0.269033i	0.0551238	+	0.998480i	$0.482445\pi$
$858$		0			0
$859$	−6.82501	−	5.72686i	−0.232866	−	0.195398i	0.518886	−	0.854843i	$-0.326347\pi$
$859$	−6.82501	−	5.72686i	−0.232866	−	0.195398i	−0.751753	+	0.659445i	$0.770791\pi$
$860$		0			0
$861$	0.779715	−	4.42198i	0.0265726	−	0.150701i
$862$		0			0
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	0.999970	+	0.00773998i	$0.00246374\pi$
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	−0.493282	+	0.869869i	$0.664203\pi$
$864$		0			0
$865$	2.13341	−	0.776497i	0.0725380	−	0.0264017i
$866$		0			0
$867$	−3.79607	+	6.57499i	−0.128921	+	0.223298i
$868$		0			0
$869$	−18.1971	+	15.2692i	−0.617295	+	0.517972i
$870$		0			0
$871$	13.0574	+	74.0520i	0.442432	+	2.50916i
$872$		0			0
$873$	4.95273			0.167625
$874$		0			0
$875$	17.0770			0.577307
$876$		0			0
$877$	−4.34642	−	24.6498i	−0.146768	−	0.832363i	−0.965930	−	0.258802i	$-0.916672\pi$
$877$	−4.34642	−	24.6498i	−0.146768	−	0.832363i	0.819162	−	0.573562i	$-0.194439\pi$
$878$		0			0
$879$	−6.36025	+	5.33688i	−0.214526	+	0.180009i
$880$		0			0
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	−0.985095	−	0.172014i	$-0.944973\pi$
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	0.641515	+	0.767110i	$0.278306\pi$
$882$		0			0
$883$	−9.98710	+	3.63501i	−0.336093	+	0.122328i	−0.504553	−	0.863381i	$-0.668343\pi$
$883$	−9.98710	+	3.63501i	−0.336093	+	0.122328i	0.168460	+	0.985708i	$0.446120\pi$
$884$		0			0
$885$	−7.24763	−	12.5533i	−0.243626	−	0.421973i
$886$		0			0
$887$	9.78312	−	55.4828i	0.328485	−	1.86293i	−0.155474	−	0.987840i	$-0.549690\pi$
$887$	9.78312	−	55.4828i	0.328485	−	1.86293i	0.483959	−	0.875091i	$-0.339198\pi$
$888$		0			0
$889$	0.145430	+	0.122030i	0.00487756	+	0.00409275i
$890$		0			0
$891$	20.9402	+	7.62159i	0.701522	+	0.255333i
$892$		0			0
$893$	2.57011	+	1.77736i	0.0860054	+	0.0594771i
$894$		0			0
$895$	50.7242	+	18.4621i	1.69552	+	0.617120i
$896$		0			0
$897$	−3.79292	−	3.18264i	−0.126642	−	0.106265i
$898$		0			0
$899$	1.17041	−	6.63771i	0.0390353	−	0.221380i
$900$		0			0
$901$	5.04576	+	8.73951i	0.168099	+	0.291155i
$902$		0			0
$903$	−4.51114	+	1.64192i	−0.150121	+	0.0546398i
$904$		0			0
$905$	−20.3824	+	35.3033i	−0.677533	+	1.17352i
$906$		0			0
$907$	4.53777	−	3.80764i	0.150674	−	0.126431i	−0.564334	−	0.825546i	$-0.690867\pi$
$907$	4.53777	−	3.80764i	0.150674	−	0.126431i	0.715009	+	0.699116i	$0.246423\pi$
$908$		0			0
$909$	3.73711	+	21.1942i	0.123952	+	0.702968i
$910$		0			0
$911$	34.0591			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$912$		0			0
$913$	8.57129			0.283668
$914$		0			0
$915$	1.02687	+	5.82369i	0.0339474	+	0.192525i
$916$		0			0
$917$	4.37211	−	3.66864i	0.144380	−	0.121149i
$918$		0			0
$919$	−3.13697	+	5.43340i	−0.103479	+	0.179231i	−0.913116	−	0.407700i	$-0.866331\pi$
$919$	−3.13697	+	5.43340i	−0.103479	+	0.179231i	0.809637	+	0.586931i	$0.199664\pi$
$920$		0			0
$921$	−10.7601	+	3.91636i	−0.354558	+	0.129048i
$922$		0			0
$923$	36.3979	+	63.0429i	1.19805	+	2.07508i
$924$		0			0
$925$	−0.205270	+	1.16415i	−0.00674924	+	0.0382769i
$926$		0			0
$927$	−0.0302779	−	0.0254062i	−0.000994456	−	0.000834448i
$928$		0			0
$929$	−26.6152	−	9.68712i	−0.873215	−	0.317824i	−0.133747	−	0.991016i	$-0.542701\pi$
$929$	−26.6152	−	9.68712i	−0.873215	−	0.317824i	−0.739468	+	0.673191i	$0.764923\pi$
$930$		0			0
$931$	−6.30840	+	13.7370i	−0.206749	+	0.450213i
$932$		0			0
$933$	−7.24763	−	2.63792i	−0.237277	−	0.0863616i
$934$		0			0
$935$	10.9363	+	9.17664i	0.357655	+	0.300108i
$936$		0			0
$937$	−3.48545	+	19.7670i	−0.113865	+	0.645759i	0.873441	+	0.486930i	$0.161883\pi$
$937$	−3.48545	+	19.7670i	−0.113865	+	0.645759i	−0.987306	+	0.158830i	$0.949228\pi$
$938$		0			0
$939$	5.19278	+	8.99416i	0.169460	+	0.293513i
$940$		0			0
$941$	−5.06980	+	1.84526i	−0.165271	+	0.0601537i	−0.423331	−	0.905975i	$-0.639139\pi$
$941$	−5.06980	+	1.84526i	−0.165271	+	0.0601537i	0.258060	+	0.966129i	$0.416917\pi$
$942$		0			0
$943$	−3.94862	+	6.83920i	−0.128585	+	0.222715i
$944$		0			0
$945$	−11.0890	+	9.30477i	−0.360725	+	0.302684i
$946$		0			0
$947$	−1.15358	−	6.54228i	−0.0374863	−	0.212596i	0.960311	−	0.278931i	$-0.0899802\pi$
$947$	−1.15358	−	6.54228i	−0.0374863	−	0.212596i	−0.997797	+	0.0663359i	$0.978869\pi$
$948$		0			0
$949$	39.7743			1.29113
$950$		0			0
$951$	−15.0833			−0.489109
$952$		0			0
$953$	−2.57414	−	14.5987i	−0.0833846	−	0.472897i	−0.997693	−	0.0678799i	$-0.978377\pi$
$953$	−2.57414	−	14.5987i	−0.0833846	−	0.472897i	0.914309	−	0.405018i	$-0.132735\pi$
$954$		0			0
$955$	36.7545	−	30.8407i	1.18935	−	0.997981i
$956$		0			0
$957$	3.14749	−	5.45161i	0.101744	−	0.176226i
$958$		0			0
$959$	−34.5082	+	12.5600i	−1.11433	+	0.405582i
$960$		0			0
$961$	13.6113	+	23.5754i	0.439074	+	0.760498i
$962$		0			0
$963$	−1.67689	+	9.51011i	−0.0540370	+	0.306459i
$964$		0			0
$965$	−25.0253	−	20.9987i	−0.805592	−	0.675972i
$966$		0			0
$967$	19.9418	+	7.25822i	0.641285	+	0.233409i	0.642136	−	0.766591i	$-0.278049\pi$
$967$	19.9418	+	7.25822i	0.641285	+	0.233409i	−0.000850519		1.00000i	$0.500271\pi$
$968$		0			0
$969$	−3.46451	+	1.64019i	−0.111296	+	0.0526906i
$970$		0			0
$971$	−35.3387	−	12.8622i	−1.13407	−	0.412769i	−0.294304	−	0.955712i	$-0.595088\pi$
$971$	−35.3387	−	12.8622i	−1.13407	−	0.412769i	−0.839770	+	0.542943i	$0.817310\pi$
$972$		0			0
$973$	−22.1668	−	18.6002i	−0.710636	−	0.596295i
$974$		0			0
$975$	0.690007	−	3.91322i	0.0220979	−	0.125323i
$976$		0			0
$977$	23.0107	+	39.8558i	0.736179	+	1.27510i	0.954204	+	0.299156i	$0.0967050\pi$
$977$	23.0107	+	39.8558i	0.736179	+	1.27510i	−0.218026	+	0.975943i	$0.569962\pi$
$978$		0			0
$979$	−7.31908	+	2.66393i	−0.233919	+	0.0851395i
$980$		0			0
$981$	10.0111	−	17.3398i	0.319631	−	0.553618i
$982$		0			0
$983$	−46.4195	+	38.9506i	−1.48055	+	1.24233i	−0.574961	+	0.818181i	$0.694983\pi$
$983$	−46.4195	+	38.9506i	−1.48055	+	1.24233i	−0.905592	+	0.424150i	$0.860573\pi$
$984$		0			0
$985$	10.2010	+	57.8527i	0.325031	+	1.84334i
$986$		0			0
$987$	0.716881			0.0228186
$988$		0			0
$989$	8.44326			0.268480
$990$		0			0
$991$	−7.27554	−	41.2616i	−0.231115	−	1.31072i	−0.850643	−	0.525744i	$-0.823787\pi$
$991$	−7.27554	−	41.2616i	−0.231115	−	1.31072i	0.619528	−	0.784975i	$-0.287324\pi$
$992$		0			0
$993$	−0.697033	+	0.584880i	−0.0221197	+	0.0185606i
$994$		0			0
$995$	−11.6750	+	20.2217i	−0.370122	+	0.641070i
$996$		0			0
$997$	−31.6819	+	11.5313i	−1.00337	+	0.365198i	−0.790885	−	0.611965i	$-0.790379\pi$
$997$	−31.6819	+	11.5313i	−1.00337	+	0.365198i	−0.212490	+	0.977163i	$0.568157\pi$
$998$		0			0
$999$	1.27379	+	2.20626i	0.0403008	+	0.0698030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.b.289.1		6
4.3	odd	2		19.2.e.a.4.1	✓	6
12.11	even	2		171.2.u.c.118.1		6
19.5	even	9	inner	304.2.u.b.81.1		6
19.9	even	9		5776.2.a.br.1.1		3
19.10	odd	18		5776.2.a.bi.1.3		3
20.3	even	4		475.2.u.a.99.1		12
20.7	even	4		475.2.u.a.99.2		12
20.19	odd	2		475.2.l.a.251.1		6
28.3	even	6		931.2.v.a.422.1		6
28.11	odd	6		931.2.v.b.422.1		6
28.19	even	6		931.2.x.b.802.1		6
28.23	odd	6		931.2.x.a.802.1		6
28.27	even	2		931.2.w.a.99.1		6
76.3	even	18		361.2.e.a.245.1		6
76.7	odd	6		361.2.e.f.234.1		6
76.11	odd	6		361.2.e.g.28.1		6
76.15	even	18		361.2.c.h.292.3		6
76.23	odd	18		361.2.c.i.292.1		6
76.27	even	6		361.2.e.a.28.1		6
76.31	even	6		361.2.e.b.234.1		6
76.35	odd	18		361.2.e.g.245.1		6
76.43	odd	18		19.2.e.a.5.1	yes	6
76.47	odd	18		361.2.a.g.1.3		3
76.51	even	18		361.2.c.h.68.3		6
76.55	odd	18		361.2.e.f.54.1		6
76.59	even	18		361.2.e.b.54.1		6
76.63	odd	18		361.2.c.i.68.1		6
76.67	even	18		361.2.a.h.1.1		3
76.71	even	18		361.2.e.h.62.1		6
76.75	even	2		361.2.e.h.99.1		6
228.47	even	18		3249.2.a.z.1.1		3
228.119	even	18		171.2.u.c.100.1		6
228.143	odd	18		3249.2.a.s.1.3		3
380.43	even	36		475.2.u.a.24.2		12
380.119	odd	18		475.2.l.a.176.1		6
380.199	odd	18		9025.2.a.bd.1.1		3
380.219	even	18		9025.2.a.x.1.3		3
380.347	even	36		475.2.u.a.24.1		12
532.195	even	18		931.2.w.a.442.1		6
532.271	even	18		931.2.v.a.214.1		6
532.347	odd	18		931.2.x.a.765.1		6
532.423	even	18		931.2.x.b.765.1		6
532.499	odd	18		931.2.v.b.214.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	4.3	odd	2
19.2.e.a.5.1	yes	6	76.43	odd	18
171.2.u.c.100.1		6	228.119	even	18
171.2.u.c.118.1		6	12.11	even	2
304.2.u.b.81.1		6	19.5	even	9	inner
304.2.u.b.289.1		6	1.1	even	1	trivial
361.2.a.g.1.3		3	76.47	odd	18
361.2.a.h.1.1		3	76.67	even	18
361.2.c.h.68.3		6	76.51	even	18
361.2.c.h.292.3		6	76.15	even	18
361.2.c.i.68.1		6	76.63	odd	18
361.2.c.i.292.1		6	76.23	odd	18
361.2.e.a.28.1		6	76.27	even	6
361.2.e.a.245.1		6	76.3	even	18
361.2.e.b.54.1		6	76.59	even	18
361.2.e.b.234.1		6	76.31	even	6
361.2.e.f.54.1		6	76.55	odd	18
361.2.e.f.234.1		6	76.7	odd	6
361.2.e.g.28.1		6	76.11	odd	6
361.2.e.g.245.1		6	76.35	odd	18
361.2.e.h.62.1		6	76.71	even	18
361.2.e.h.99.1		6	76.75	even	2
475.2.l.a.176.1		6	380.119	odd	18
475.2.l.a.251.1		6	20.19	odd	2
475.2.u.a.24.1		12	380.347	even	36
475.2.u.a.24.2		12	380.43	even	36
475.2.u.a.99.1		12	20.3	even	4
475.2.u.a.99.2		12	20.7	even	4
931.2.v.a.214.1		6	532.271	even	18
931.2.v.a.422.1		6	28.3	even	6
931.2.v.b.214.1		6	532.499	odd	18
931.2.v.b.422.1		6	28.11	odd	6
931.2.w.a.99.1		6	28.27	even	2
931.2.w.a.442.1		6	532.195	even	18
931.2.x.a.765.1		6	532.347	odd	18
931.2.x.a.802.1		6	28.23	odd	6
931.2.x.b.765.1		6	532.423	even	18
931.2.x.b.802.1		6	28.19	even	6
3249.2.a.s.1.3		3	228.143	odd	18
3249.2.a.z.1.1		3	228.47	even	18
5776.2.a.bi.1.3		3	19.10	odd	18
5776.2.a.br.1.1		3	19.9	even	9
9025.2.a.x.1.3		3	380.219	even	18
9025.2.a.bd.1.1		3	380.199	odd	18

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0923963 - 0.524005i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.939693 + 1.62760i) q^{7} +(2.55303 - 0.929228i) q^{9} +O(q^{10})\)	\(q+(-0.0923963 - 0.524005i) q^{3} +(-1.93969 + 1.62760i) q^{5} +(-0.939693 + 1.62760i) q^{7} +(2.55303 - 0.929228i) q^{9} +(1.70574 + 2.95442i) q^{11} +(-0.918748 + 5.21048i) q^{13} +(1.03209 + 0.866025i) q^{15} +(-1.55303 - 0.565258i) q^{17} +(2.52094 + 3.55596i) q^{19} +(0.939693 + 0.342020i) q^{21} +(-1.34730 - 1.13052i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-1.52094 - 2.63435i) q^{27} +(3.25877 - 1.18610i) q^{29} +(0.971782 - 1.68317i) q^{31} +(1.39053 - 1.16679i) q^{33} +(-0.826352 - 4.68647i) q^{35} -0.837496 q^{37} +2.81521 q^{39} +(-0.779715 - 4.42198i) q^{41} +(-3.67752 + 3.08580i) q^{43} +(-3.43969 + 5.95772i) q^{45} +(0.673648 - 0.245188i) q^{47} +(1.73396 + 3.00330i) q^{49} +(-0.152704 + 0.866025i) q^{51} +(-4.67752 - 3.92490i) q^{53} +(-8.11721 - 2.95442i) q^{55} +(1.63041 - 1.64955i) q^{57} +(-10.1099 - 3.67972i) q^{59} +(3.36231 + 2.82131i) q^{61} +(-0.886659 + 5.02849i) q^{63} +(-6.69846 - 11.6021i) q^{65} +(13.3550 - 4.86084i) q^{67} +(-0.467911 + 0.810446i) q^{69} +(10.5398 - 8.84397i) q^{71} +(-1.30541 - 7.40333i) q^{73} -0.751030 q^{75} -6.41147 q^{77} +(1.20914 + 6.85738i) q^{79} +(5.00387 - 4.19875i) q^{81} +(1.25624 - 2.17588i) q^{83} +(3.93242 - 1.43128i) q^{85} +(-0.922618 - 1.59802i) q^{87} +(-0.396459 + 2.24843i) q^{89} +(-7.61721 - 6.39160i) q^{91} +(-0.971782 - 0.353700i) q^{93} +(-10.6775 - 2.79439i) q^{95} +(1.71301 + 0.623485i) q^{97} +(7.10014 + 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9	\( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{19} - 6 q^{23} - 6 q^{27} - 3 q^{29} - 9 q^{31} - 9 q^{33} - 6 q^{35} + 24 q^{39} + 21 q^{41} + 3 q^{43} - 15 q^{45} + 3 q^{47} + 15 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} + 24 q^{57} - 12 q^{59} - 12 q^{61} - 12 q^{63} - 12 q^{65} + 30 q^{67} - 12 q^{69} + 6 q^{71} - 12 q^{73} - 30 q^{75} - 18 q^{77} + 39 q^{79} + 6 q^{81} + 21 q^{87} - 12 q^{89} - 15 q^{91} + 9 q^{93} - 39 q^{95} + 18 q^{97} - 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9 - 3 * q^13 - 3 * q^15 + 3 * q^17 + 12 * q^19 - 6 * q^23 - 6 * q^27 - 3 * q^29 - 9 * q^31 - 9 * q^33 - 6 * q^35 + 24 * q^39 + 21 * q^41 + 3 * q^43 - 15 * q^45 + 3 * q^47 + 15 * q^49 - 3 * q^51 - 3 * q^53 - 18 * q^55 + 24 * q^57 - 12 * q^59 - 12 * q^61 - 12 * q^63 - 12 * q^65 + 30 * q^67 - 12 * q^69 + 6 * q^71 - 12 * q^73 - 30 * q^75 - 18 * q^77 + 39 * q^79 + 6 * q^81 + 21 * q^87 - 12 * q^89 - 15 * q^91 + 9 * q^93 - 39 * q^95 + 18 * q^97 - 9 * q^99

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