LMFDB - Embedded newform 976.2.bw.c.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [976,2,Mod(225,976)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(976, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 28]))

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

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

chi := DirichletCharacter("976.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, 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:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			225.1
Character	$\chi$	$=$	976.225
Dual form			976.2.bw.c.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.508502 + 1.56501i) q^{3} +(-0.0637708 + 0.606739i) q^{5} +(0.455761 - 0.506174i) q^{7} +(0.236374 + 0.171736i) q^{9} +O(q^{10})$	\(q+(-0.508502 + 1.56501i) q^{3} +(-0.0637708 + 0.606739i) q^{5} +(0.455761 - 0.506174i) q^{7} +(0.236374 + 0.171736i) q^{9} +0.856770 q^{11} +(-0.256551 - 0.444360i) q^{13} +(-0.917124 - 0.408330i) q^{15} +(0.929560 - 0.413867i) q^{17} +(2.82829 + 3.14113i) q^{19} +(0.560411 + 0.970661i) q^{21} +(6.80521 + 4.94428i) q^{23} +(4.52667 + 0.962174i) q^{25} +(-4.38279 + 3.18428i) q^{27} +(-3.37045 + 5.83778i) q^{29} +(-10.6295 - 2.25937i) q^{31} +(-0.435669 + 1.34085i) q^{33} +(0.278051 + 0.308807i) q^{35} +(-0.711916 - 2.19105i) q^{37} +(0.825883 - 0.175547i) q^{39} +(-1.10908 - 3.41340i) q^{41} +(-2.98244 - 1.32787i) q^{43} +(-0.119273 + 0.132466i) q^{45} +(1.86946 - 3.23800i) q^{47} +(0.683205 + 6.50026i) q^{49} +(0.175022 + 1.66522i) q^{51} +(-4.74398 + 3.44671i) q^{53} +(-0.0546369 + 0.519836i) q^{55} +(-6.35408 + 2.82902i) q^{57} +(8.67000 - 1.84286i) q^{59} +(-2.66773 + 7.34052i) q^{61} +(0.194659 - 0.0413760i) q^{63} +(0.285971 - 0.127322i) q^{65} +(-1.18285 + 11.2540i) q^{67} +(-11.1983 + 8.13604i) q^{69} +(-0.576283 - 5.48297i) q^{71} +(0.289912 + 2.75833i) q^{73} +(-3.80763 + 6.59501i) q^{75} +(0.390483 - 0.433675i) q^{77} +(6.78344 + 3.02018i) q^{79} +(-2.48391 - 7.64470i) q^{81} +(-10.5592 + 2.24442i) q^{83} +(0.191830 + 0.590393i) q^{85} +(-7.42230 - 8.24330i) q^{87} +(2.60821 - 8.02724i) q^{89} +(-0.341850 - 0.0726624i) q^{91} +(8.94104 - 15.4863i) q^{93} +(-2.08621 + 1.51572i) q^{95} +(10.4211 + 2.21507i) q^{97} +(0.202519 + 0.147138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39} + 11 q^{41} - 40 q^{43} + 12 q^{45} - 40 q^{47} + q^{49} + 9 q^{51} + 17 q^{53} + 60 q^{55} - 38 q^{57} + 11 q^{59} - 55 q^{61} + 58 q^{63} + 59 q^{65} + 13 q^{67} - 32 q^{69} - 63 q^{71} - 46 q^{73} - q^{75} - 31 q^{77} + 49 q^{79} + 48 q^{81} - 39 q^{83} + 21 q^{85} - 17 q^{87} + 32 q^{89} - 70 q^{91} + 67 q^{93} - 47 q^{95} + 37 q^{97} + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{14}{15}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.508502	+	1.56501i	−0.293584	+	0.903558i	0.690110	+	0.723705i	$0.257562\pi$
$3$	−0.508502	+	1.56501i	−0.293584	+	0.903558i	−0.983693	+	0.179853i	$0.942438\pi$
$4$		0			0
$5$	−0.0637708	+	0.606739i	−0.0285192	+	0.271342i	0.970965	+	0.239222i	$0.0768925\pi$
$5$	−0.0637708	+	0.606739i	−0.0285192	+	0.271342i	−0.999484	+	0.0321197i	$0.989774\pi$
$6$		0			0
$7$	0.455761	−	0.506174i	0.172262	−	0.191316i	−0.650832	−	0.759222i	$-0.725580\pi$
$7$	0.455761	−	0.506174i	0.172262	−	0.191316i	0.823093	+	0.567906i	$0.192246\pi$
$8$		0			0
$9$	0.236374	+	0.171736i	0.0787915	+	0.0572454i
$10$		0			0
$11$	0.856770			0.258326			0.129163	−	0.991623i	$-0.458771\pi$
$11$	0.856770			0.258326			0.129163	+	0.991623i	$0.458771\pi$
$12$		0			0
$13$	−0.256551	−	0.444360i	−0.0711545	−	0.123243i	0.828253	−	0.560354i	$-0.189335\pi$
$13$	−0.256551	−	0.444360i	−0.0711545	−	0.123243i	−0.899408	+	0.437111i	$0.856002\pi$
$14$		0			0
$15$	−0.917124	−	0.408330i	−0.236800	−	0.105430i
$16$		0			0
$17$	0.929560	−	0.413867i	0.225452	−	0.100377i	−0.290903	−	0.956753i	$-0.593956\pi$
$17$	0.929560	−	0.413867i	0.225452	−	0.100377i	0.516354	+	0.856375i	$0.327289\pi$
$18$		0			0
$19$	2.82829	+	3.14113i	0.648853	+	0.720625i	0.974380	−	0.224908i	$-0.0722082\pi$
$19$	2.82829	+	3.14113i	0.648853	+	0.720625i	−0.325527	+	0.945533i	$0.605542\pi$
$20$		0			0
$21$	0.560411	+	0.970661i	0.122292	+	0.211816i
$22$		0			0
$23$	6.80521	+	4.94428i	1.41899	+	1.03095i	0.991938	+	0.126724i	$0.0404461\pi$
$23$	6.80521	+	4.94428i	1.41899	+	1.03095i	0.427047	+	0.904229i	$0.359554\pi$
$24$		0			0
$25$	4.52667	+	0.962174i	0.905334	+	0.192435i
$26$		0			0
$27$	−4.38279	+	3.18428i	−0.843469	+	0.612816i
$28$		0			0
$29$	−3.37045	+	5.83778i	−0.625876	+	1.08405i	0.362495	+	0.931986i	$0.381925\pi$
$29$	−3.37045	+	5.83778i	−0.625876	+	1.08405i	−0.988371	+	0.152063i	$0.951408\pi$
$30$		0			0
$31$	−10.6295	−	2.25937i	−1.90911	−	0.405794i	−0.909168	−	0.416430i	$-0.863281\pi$
$31$	−10.6295	−	2.25937i	−1.90911	−	0.405794i	−0.999943	+	0.0106355i	$0.996615\pi$
$32$		0			0
$33$	−0.435669	+	1.34085i	−0.0758403	+	0.233412i
$34$		0			0
$35$	0.278051	+	0.308807i	0.0469993	+	0.0521980i
$36$		0			0
$37$	−0.711916	−	2.19105i	−0.117038	−	0.360207i	0.875328	−	0.483529i	$-0.160645\pi$
$37$	−0.711916	−	2.19105i	−0.117038	−	0.360207i	−0.992367	+	0.123322i	$0.960645\pi$
$38$		0			0
$39$	0.825883	−	0.175547i	0.132247	−	0.0281100i
$40$		0			0
$41$	−1.10908	−	3.41340i	−0.173209	−	0.533084i	0.826338	−	0.563175i	$-0.190420\pi$
$41$	−1.10908	−	3.41340i	−0.173209	−	0.533084i	−0.999547	+	0.0300912i	$0.990420\pi$
$42$		0			0
$43$	−2.98244	−	1.32787i	−0.454818	−	0.202498i	0.166524	−	0.986037i	$-0.446746\pi$
$43$	−2.98244	−	1.32787i	−0.454818	−	0.202498i	−0.621342	+	0.783539i	$0.713412\pi$
$44$		0			0
$45$	−0.119273	+	0.132466i	−0.0177801	+	0.0197468i
$46$		0			0
$47$	1.86946	−	3.23800i	0.272688	−	0.472310i	−0.696861	−	0.717206i	$-0.745421\pi$
$47$	1.86946	−	3.23800i	0.272688	−	0.472310i	0.969549	+	0.244896i	$0.0787538\pi$
$48$		0			0
$49$	0.683205	+	6.50026i	0.0976008	+	0.928609i
$50$		0			0
$51$	0.175022	+	1.66522i	0.0245080	+	0.233178i
$52$		0			0
$53$	−4.74398	+	3.44671i	−0.651636	+	0.473441i	−0.863828	−	0.503787i	$-0.831940\pi$
$53$	−4.74398	+	3.44671i	−0.651636	+	0.473441i	0.212192	+	0.977228i	$0.431940\pi$
$54$		0			0
$55$	−0.0546369	+	0.519836i	−0.00736724	+	0.0700947i
$56$		0			0
$57$	−6.35408	+	2.82902i	−0.841619	+	0.374713i
$58$		0			0
$59$	8.67000	−	1.84286i	1.12874	−	0.239921i	0.394555	−	0.918872i	$-0.370899\pi$
$59$	8.67000	−	1.84286i	1.12874	−	0.239921i	0.734183	+	0.678952i	$0.237566\pi$
$60$		0			0
$61$	−2.66773	+	7.34052i	−0.341568	+	0.939857i
$61$	−2.66773	+	7.34052i	−0.341568	+	0.939857i
$62$		0			0
$63$	0.194659	−	0.0413760i	0.0245247	−	0.00521289i
$64$		0			0
$65$	0.285971	−	0.127322i	0.0354703	−	0.0157924i
$66$		0			0
$67$	−1.18285	+	11.2540i	−0.144508	+	1.37490i	0.646416	+	0.762985i	$0.276267\pi$
$67$	−1.18285	+	11.2540i	−0.144508	+	1.37490i	−0.790924	+	0.611915i	$0.790400\pi$
$68$		0			0
$69$	−11.1983	+	8.13604i	−1.34812	+	0.979464i
$70$		0			0
$71$	−0.576283	−	5.48297i	−0.0683922	−	0.650709i	−0.973993	−	0.226578i	$-0.927246\pi$
$71$	−0.576283	−	5.48297i	−0.0683922	−	0.650709i	0.905601	−	0.424131i	$-0.139420\pi$
$72$		0			0
$73$	0.289912	+	2.75833i	0.0339317	+	0.322838i	0.998300	+	0.0582767i	$0.0185606\pi$
$73$	0.289912	+	2.75833i	0.0339317	+	0.322838i	−0.964369	+	0.264562i	$0.914773\pi$
$74$		0			0
$75$	−3.80763	+	6.59501i	−0.439667	+	0.761526i
$76$		0			0
$77$	0.390483	−	0.433675i	0.0444996	−	0.0494219i
$78$		0			0
$79$	6.78344	+	3.02018i	0.763197	+	0.339797i	0.751151	−	0.660130i	$-0.229499\pi$
$79$	6.78344	+	3.02018i	0.763197	+	0.339797i	0.0120456	+	0.999927i	$0.496166\pi$
$80$		0			0
$81$	−2.48391	−	7.64470i	−0.275990	−	0.849411i
$82$		0			0
$83$	−10.5592	+	2.24442i	−1.15902	+	0.246357i	−0.747004	−	0.664819i	$-0.768509\pi$
$83$	−10.5592	+	2.24442i	−1.15902	+	0.246357i	−0.412016	+	0.911177i	$0.635175\pi$
$84$		0			0
$85$	0.191830	+	0.590393i	0.0208069	+	0.0640371i
$86$		0			0
$87$	−7.42230	−	8.24330i	−0.795754	−	0.883774i
$88$		0			0
$89$	2.60821	−	8.02724i	0.276469	−	0.850885i	−0.712357	−	0.701817i	$-0.752372\pi$
$89$	2.60821	−	8.02724i	0.276469	−	0.850885i	0.988827	−	0.149069i	$-0.0476275\pi$
$90$		0			0
$91$	−0.341850	−	0.0726624i	−0.0358356	−	0.00761709i
$92$		0			0
$93$	8.94104	−	15.4863i	0.927143	−	1.60586i
$94$		0			0
$95$	−2.08621	+	1.51572i	−0.214040	+	0.155510i
$96$		0			0
$97$	10.4211	+	2.21507i	1.05810	+	0.224907i	0.703927	−	0.710272i	$-0.251428\pi$
$97$	10.4211	+	2.21507i	1.05810	+	0.224907i	0.354176	+	0.935179i	$0.384761\pi$
$98$		0			0
$99$	0.202519	+	0.147138i	0.0203539	+	0.0147880i
$100$		0			0
$101$	6.47112	+	11.2083i	0.643901	+	1.11527i	0.984554	+	0.175080i	$0.0560184\pi$
$101$	6.47112	+	11.2083i	0.643901	+	1.11527i	−0.340654	+	0.940189i	$0.610648\pi$
$102$		0			0
$103$	−8.70997	−	9.67341i	−0.858219	−	0.953149i	0.141102	−	0.989995i	$-0.454936\pi$
$103$	−8.70997	−	9.67341i	−0.858219	−	0.953149i	−0.999321	+	0.0368460i	$0.988269\pi$
$104$		0			0
$105$	−0.624676	+	0.278124i	−0.0609621	+	0.0271421i
$106$		0			0
$107$	7.93227	+	3.53168i	0.766842	+	0.341420i	0.752599	−	0.658479i	$-0.228800\pi$
$107$	7.93227	+	3.53168i	0.766842	+	0.341420i	0.0142424	+	0.999899i	$0.495466\pi$
$108$		0			0
$109$	−6.76643	−	11.7198i	−0.648106	−	1.12255i	−0.983575	−	0.180501i	$-0.942228\pi$
$109$	−6.76643	−	11.7198i	−0.648106	−	1.12255i	0.335469	−	0.942051i	$-0.391105\pi$
$110$		0			0
$111$	3.79103			0.359828
$112$		0			0
$113$	1.52061	+	1.10479i	0.143047	+	0.103930i	0.657007	−	0.753884i	$-0.271822\pi$
$113$	1.52061	+	1.10479i	0.143047	+	0.103930i	−0.513960	+	0.857814i	$0.671822\pi$
$114$		0			0
$115$	−3.43386	+	3.81369i	−0.320209	+	0.355628i
$116$		0			0
$117$	0.0156704	−	0.149094i	0.00144873	−	0.0137838i
$118$		0			0
$119$	0.214169	−	0.659144i	0.0196328	−	0.0604237i
$120$		0			0
$121$	−10.2659			−0.933268
$122$		0			0
$123$	5.90597			0.532523
$124$		0			0
$125$	−1.81509	+	5.58626i	−0.162346	+	0.499650i
$126$		0			0
$127$	−1.19079	+	11.3296i	−0.105665	+	1.00534i	0.805303	+	0.592863i	$0.202002\pi$
$127$	−1.19079	+	11.3296i	−0.105665	+	1.00534i	−0.910969	+	0.412475i	$0.864664\pi$
$128$		0			0
$129$	3.59470	−	3.99232i	0.316496	−	0.351504i
$130$		0			0
$131$	5.10091	+	3.70603i	0.445669	+	0.323797i	0.787883	−	0.615824i	$-0.211177\pi$
$131$	5.10091	+	3.70603i	0.445669	+	0.323797i	−0.342215	+	0.939622i	$0.611177\pi$
$132$		0			0
$133$	2.87898			0.249640
$134$		0			0
$135$	−1.65254	−	2.86228i	−0.142228	−	0.246345i
$136$		0			0
$137$	9.49245	+	4.22631i	0.810995	+	0.361078i	0.769970	−	0.638080i	$-0.220271\pi$
$137$	9.49245	+	4.22631i	0.810995	+	0.361078i	0.0410247	+	0.999158i	$0.486938\pi$
$138$		0			0
$139$	8.44765	−	3.76114i	0.716521	−	0.319015i	−0.0158948	−	0.999874i	$-0.505060\pi$
$139$	8.44765	−	3.76114i	0.716521	−	0.319015i	0.732415	+	0.680858i	$0.238393\pi$
$140$		0			0
$141$	4.11687	+	4.57224i	0.346703	+	0.385052i
$142$		0			0
$143$	−0.219805	−	0.380714i	−0.0183810	−	0.0318369i
$144$		0			0
$145$	−3.32707	−	2.41726i	−0.276299	−	0.200743i
$146$		0			0
$147$	−10.5204	−	2.23618i	−0.867706	−	0.184437i
$148$		0			0
$149$	14.9673	−	10.8744i	1.22617	−	0.890865i	0.229574	−	0.973291i	$-0.426267\pi$
$149$	14.9673	−	10.8744i	1.22617	−	0.890865i	0.996597	+	0.0824257i	$0.0262667\pi$
$150$		0			0
$151$	6.52368	−	11.2993i	0.530889	−	0.919527i	−0.468461	−	0.883484i	$-0.655191\pi$
$151$	6.52368	−	11.2993i	0.530889	−	0.919527i	0.999350	−	0.0360429i	$-0.0114753\pi$
$152$		0			0
$153$	0.290800	+	0.0618115i	0.0235098	+	0.00499716i
$154$		0			0
$155$	2.04870	−	6.30524i	0.164555	−	0.506449i
$156$		0			0
$157$	−7.02158	−	7.79826i	−0.560383	−	0.622369i	0.394663	−	0.918826i	$-0.370861\pi$
$157$	−7.02158	−	7.79826i	−0.560383	−	0.622369i	−0.955046	+	0.296457i	$0.904195\pi$
$158$		0			0
$159$	−2.98180	−	9.17703i	−0.236472	−	0.727786i
$160$		0			0
$161$	5.60422	−	1.19121i	0.441674	−	0.0938808i
$162$		0			0
$163$	5.00516	+	15.4043i	0.392035	+	1.20656i	0.931247	+	0.364389i	$0.118722\pi$
$163$	5.00516	+	15.4043i	0.392035	+	1.20656i	−0.539212	+	0.842170i	$0.681278\pi$
$164$		0			0
$165$	−0.785764	−	0.349845i	−0.0611717	−	0.0272354i
$166$		0			0
$167$	5.76635	−	6.40418i	0.446214	−	0.495570i	−0.477512	−	0.878625i	$-0.658461\pi$
$167$	5.76635	−	6.40418i	0.446214	−	0.495570i	0.923726	+	0.383055i	$0.125128\pi$
$168$		0			0
$169$	6.36836	−	11.0303i	0.489874	−	0.848487i
$170$		0			0
$171$	0.129089	+	1.22820i	0.00987170	+	0.0939229i
$172$		0			0
$173$	−2.32613	−	22.1317i	−0.176853	−	1.68264i	−0.618760	−	0.785580i	$-0.712365\pi$
$173$	−2.32613	−	22.1317i	−0.176853	−	1.68264i	0.441907	−	0.897061i	$-0.354302\pi$
$174$		0			0
$175$	2.55011	−	1.85276i	0.192770	−	0.140056i
$176$		0			0
$177$	−1.52461	+	14.5057i	−0.114597	+	1.09032i
$178$		0			0
$179$	9.05857	−	4.03313i	0.677069	−	0.301451i	−0.0392439	−	0.999230i	$-0.512495\pi$
$179$	9.05857	−	4.03313i	0.677069	−	0.301451i	0.716313	+	0.697779i	$0.245828\pi$
$180$		0			0
$181$	−4.92584	+	1.04702i	−0.366135	+	0.0778243i	−0.387305	−	0.921952i	$-0.626594\pi$
$181$	−4.92584	+	1.04702i	−0.366135	+	0.0778243i	0.0211705	+	0.999776i	$0.493261\pi$
$182$		0			0
$183$	−10.1314	−	7.90769i	−0.748937	−	0.584553i
$184$		0			0
$185$	1.37480	−	0.292222i	0.101077	−	0.0214846i
$186$		0			0
$187$	0.796419	−	0.354589i	0.0582400	−	0.0259301i
$188$		0			0
$189$	−0.385704	+	3.66973i	−0.0280559	+	0.266934i
$190$		0			0
$191$	2.13177	−	1.54882i	0.154249	−	0.112069i	−0.507984	−	0.861367i	$-0.669609\pi$
$191$	2.13177	−	1.54882i	0.154249	−	0.112069i	0.662233	+	0.749298i	$0.269609\pi$
$192$		0			0
$193$	1.03878	+	9.88329i	0.0747727	+	0.711415i	0.966120	+	0.258093i	$0.0830943\pi$
$193$	1.03878	+	9.88329i	0.0747727	+	0.711415i	−0.891347	+	0.453321i	$0.850239\pi$
$194$		0			0
$195$	0.0538439	+	0.512290i	0.00385584	+	0.0366859i
$196$		0			0
$197$	5.33067	−	9.23300i	0.379795	−	0.657824i	−0.611237	−	0.791447i	$-0.709328\pi$
$197$	5.33067	−	9.23300i	0.379795	−	0.657824i	0.991032	+	0.133623i	$0.0426613\pi$
$198$		0			0
$199$	7.12127	−	7.90897i	0.504813	−	0.560652i	−0.435839	−	0.900025i	$-0.643548\pi$
$199$	7.12127	−	7.90897i	0.504813	−	0.560652i	0.940652	+	0.339373i	$0.110215\pi$
$200$		0			0
$201$	−17.0112	−	7.57387i	−1.19988	−	0.534220i
$202$		0			0
$203$	1.41882	+	4.36667i	0.0995814	+	0.306480i
$204$		0			0
$205$	2.14177	−	0.455247i	0.149588	−	0.0317959i
$206$		0			0
$207$	0.759468	+	2.33740i	0.0527867	+	0.162461i
$208$		0			0
$209$	2.42319	+	2.69123i	0.167616	+	0.186156i
$210$		0			0
$211$	0.332420	−	1.02308i	0.0228848	−	0.0704321i	−0.938962	−	0.344021i	$-0.888211\pi$
$211$	0.332420	−	1.02308i	0.0228848	−	0.0704321i	0.961847	+	0.273589i	$0.0882108\pi$
$212$		0			0
$213$	8.87393	+	1.88621i	0.608032	+	0.129241i
$214$		0			0
$215$	0.995862	−	1.72488i	0.0679172	−	0.117636i
$216$		0			0
$217$	−5.98814	+	4.35064i	−0.406502	+	0.295341i
$218$		0			0
$219$	−4.46423	−	0.948902i	−0.301665	−	0.0641208i
$220$		0			0
$221$	−0.422386	−	0.306881i	−0.0284127	−	0.0206431i
$222$		0			0
$223$	−7.42735	−	12.8646i	−0.497372	−	0.861474i	0.502623	−	0.864506i	$-0.332368\pi$
$223$	−7.42735	−	12.8646i	−0.497372	−	0.861474i	−0.999995	+	0.00303151i	$0.999035\pi$
$224$		0			0
$225$	0.904750	+	1.00483i	0.0603166	+	0.0669884i
$226$		0			0
$227$	6.07055	−	2.70278i	0.402917	−	0.179390i	−0.195265	−	0.980751i	$-0.562557\pi$
$227$	6.07055	−	2.70278i	0.402917	−	0.179390i	0.598182	+	0.801360i	$0.295890\pi$
$228$		0			0
$229$	15.3238	+	6.82260i	1.01263	+	0.450850i	0.844866	−	0.534978i	$-0.179680\pi$
$229$	15.3238	+	6.82260i	1.01263	+	0.450850i	0.167760	+	0.985828i	$0.446347\pi$
$230$		0			0
$231$	0.480144	+	0.831633i	0.0315911	+	0.0547175i
$232$		0			0
$233$	−20.8372			−1.36509			−0.682545	−	0.730844i	$-0.739127\pi$
$233$	−20.8372			−1.36509			−0.682545	+	0.730844i	$0.739127\pi$
$234$		0			0
$235$	1.84540	+	1.34076i	0.120381	+	0.0874617i
$236$		0			0
$237$	−8.17600	+	9.08037i	−0.531088	+	0.589833i
$238$		0			0
$239$	2.73583	−	26.0297i	0.176966	−	1.68372i	−0.440992	−	0.897511i	$-0.645373\pi$
$239$	2.73583	−	26.0297i	0.176966	−	1.68372i	0.617958	−	0.786211i	$-0.287960\pi$
$240$		0			0
$241$	6.19510	−	19.0666i	0.399062	−	1.22819i	−0.526691	−	0.850057i	$-0.676568\pi$
$241$	6.19510	−	19.0666i	0.399062	−	1.22819i	0.925753	−	0.378129i	$-0.123432\pi$
$242$		0			0
$243$	−3.02520			−0.194067
$244$		0			0
$245$	−3.98753			−0.254754
$246$		0			0
$247$	0.670191	−	2.06264i	0.0426433	−	0.131242i
$248$		0			0
$249$	1.85682	−	17.6665i	0.117671	−	1.11957i
$250$		0			0
$251$	10.0924	−	11.2088i	0.637027	−	0.707490i	−0.335037	−	0.942205i	$-0.608749\pi$
$251$	10.0924	−	11.2088i	0.637027	−	0.707490i	0.972064	+	0.234715i	$0.0754156\pi$
$252$		0			0
$253$	5.83050	+	4.23611i	0.366561	+	0.266322i
$254$		0			0
$255$	−1.02152			−0.0639698
$256$		0			0
$257$	−6.74852	−	11.6888i	−0.420961	−	0.729126i	0.575073	−	0.818102i	$-0.304974\pi$
$257$	−6.74852	−	11.6888i	−0.420961	−	0.729126i	−0.996034	+	0.0889763i	$0.971640\pi$
$258$		0			0
$259$	−1.43352	−	0.638244i	−0.0890745	−	0.0396585i
$260$		0			0
$261$	−1.79925	+	0.801076i	−0.111370	+	0.0495853i
$262$		0			0
$263$	3.50888	+	3.89701i	0.216367	+	0.240300i	0.841551	−	0.540177i	$-0.181643\pi$
$263$	3.50888	+	3.89701i	0.216367	+	0.240300i	−0.625184	+	0.780477i	$0.714976\pi$
$264$		0			0
$265$	−1.78872	−	3.09816i	−0.109880	−	0.190318i
$266$		0			0
$267$	11.2364	+	8.16373i	0.687657	+	0.499612i
$268$		0			0
$269$	16.3147	+	3.46780i	0.994727	+	0.211436i	0.676391	−	0.736542i	$-0.263543\pi$
$269$	16.3147	+	3.46780i	0.994727	+	0.211436i	0.318336	+	0.947978i	$0.396876\pi$
$270$		0			0
$271$	−2.08049	+	1.51156i	−0.126381	+	0.0918208i	−0.649180	−	0.760635i	$-0.724888\pi$
$271$	−2.08049	+	1.51156i	−0.126381	+	0.0918208i	0.522799	+	0.852456i	$0.324888\pi$
$272$		0			0
$273$	0.287548	−	0.498048i	0.0174032	−	0.0301433i
$274$		0			0
$275$	3.87832	+	0.824362i	0.233871	+	0.0497109i
$276$		0			0
$277$	−8.36496	+	25.7447i	−0.502602	+	1.54685i	0.302164	+	0.953256i	$0.402291\pi$
$277$	−8.36496	+	25.7447i	−0.502602	+	1.54685i	−0.804765	+	0.593593i	$0.797709\pi$
$278$		0			0
$279$	−2.12452	−	2.35952i	−0.127192	−	0.141261i
$280$		0			0
$281$	5.33849	+	16.4302i	0.318467	+	0.980142i	0.974304	+	0.225239i	$0.0723162\pi$
$281$	5.33849	+	16.4302i	0.318467	+	0.980142i	−0.655836	+	0.754903i	$0.727684\pi$
$282$		0			0
$283$	−26.1003	+	5.54779i	−1.55150	+	0.329782i	−0.902393	−	0.430915i	$-0.858191\pi$
$283$	−26.1003	+	5.54779i	−1.55150	+	0.329782i	−0.649108	+	0.760696i	$0.724858\pi$
$284$		0			0
$285$	−1.31127	−	4.03568i	−0.0776730	−	0.239053i
$286$		0			0
$287$	−2.23325	−	0.994308i	−0.131825	−	0.0586921i
$288$		0			0
$289$	−10.6824	+	11.8640i	−0.628378	+	0.697884i
$290$		0			0
$291$	−8.76576	+	15.1827i	−0.513858	+	0.890029i
$292$		0			0
$293$	−2.80776	−	26.7141i	−0.164031	−	1.56065i	−0.698591	−	0.715521i	$-0.746189\pi$
$293$	−2.80776	−	26.7141i	−0.164031	−	1.56065i	0.534560	−	0.845130i	$-0.320477\pi$
$294$		0			0
$295$	0.565245	+	5.37795i	0.0329098	+	0.313116i
$296$		0			0
$297$	−3.75504	+	2.72820i	−0.217890	+	0.158306i
$298$		0			0
$299$	0.451152	−	4.29242i	0.0260908	−	0.248237i
$300$		0			0
$301$	−2.03141	+	0.904444i	−0.117089	+	0.0521313i
$302$		0			0
$303$	−20.8317	+	4.42791i	−1.19675	+	0.254377i
$304$		0			0
$305$	−4.28366	−	2.08673i	−0.245281	−	0.119486i
$306$		0			0
$307$	−2.72903	+	0.580073i	−0.155754	+	0.0331065i	−0.285129	−	0.958489i	$-0.592036\pi$
$307$	−2.72903	+	0.580073i	−0.155754	+	0.0331065i	0.129375	+	0.991596i	$0.458703\pi$
$308$		0			0
$309$	19.5680	−	8.71224i	1.11318	−	0.495622i
$310$		0			0
$311$	−0.384323	+	3.65659i	−0.0217930	+	0.207346i	−1.00000		0.000285872i	$-0.999909\pi$
$311$	−0.384323	+	3.65659i	−0.0217930	+	0.207346i	0.978207	+	0.207632i	$0.0665757\pi$
$312$		0			0
$313$	22.0161	−	15.9956i	1.24442	−	0.904126i	0.246538	−	0.969133i	$-0.420707\pi$
$313$	22.0161	−	15.9956i	1.24442	−	0.904126i	0.997885	+	0.0650072i	$0.0207070\pi$
$314$		0			0
$315$	0.0126909	+	0.120746i	0.000715050	+	0.00680325i
$316$		0			0
$317$	−3.02393	−	28.7708i	−0.169841	−	1.61593i	−0.664807	−	0.747015i	$-0.731486\pi$
$317$	−3.02393	−	28.7708i	−0.169841	−	1.61593i	0.494966	−	0.868912i	$-0.335180\pi$
$318$		0			0
$319$	−2.88770	+	5.00164i	−0.161680	+	0.280038i
$320$		0			0
$321$	−9.56068	+	10.6182i	−0.533625	+	0.592651i
$322$		0			0
$323$	3.92907	+	1.74934i	0.218619	+	0.0973357i
$324$		0			0
$325$	−0.733772	−	2.25832i	−0.0407023	−	0.125269i
$326$		0			0
$327$	21.7823	−	4.62997i	1.20456	−	0.256038i
$328$		0			0
$329$	−0.786964	−	2.42203i	−0.0433867	−	0.133531i
$330$		0			0
$331$	−7.80996	−	8.67384i	−0.429274	−	0.476757i	0.489238	−	0.872150i	$-0.337275\pi$
$331$	−7.80996	−	8.67384i	−0.429274	−	0.476757i	−0.918512	+	0.395393i	$0.870608\pi$
$332$		0			0
$333$	0.208004	−	0.640171i	0.0113986	−	0.0350811i
$334$		0			0
$335$	−6.75284	−	1.43536i	−0.368947	−	0.0784221i
$336$		0			0
$337$	−12.1650	+	21.0703i	−0.662668	+	1.14777i	0.317244	+	0.948344i	$0.397242\pi$
$337$	−12.1650	+	21.0703i	−0.662668	+	1.14777i	−0.979912	+	0.199430i	$0.936091\pi$
$338$		0			0
$339$	−2.50224	+	1.81798i	−0.135903	+	0.0987393i
$340$		0			0
$341$	−9.10702	−	1.93576i	−0.493173	−	0.104827i
$342$		0			0
$343$	7.45894	+	5.41923i	0.402745	+	0.292611i
$344$		0			0
$345$	−4.22233	−	7.31329i	−0.227323	−	0.393734i
$346$		0			0
$347$	−2.71729	−	3.01786i	−0.145872	−	0.162007i	0.665781	−	0.746147i	$-0.268099\pi$
$347$	−2.71729	−	3.01786i	−0.145872	−	0.162007i	−0.811653	+	0.584140i	$0.801432\pi$
$348$		0			0
$349$	−0.804572	+	0.358219i	−0.0430678	+	0.0191750i	−0.428158	−	0.903704i	$-0.640837\pi$
$349$	−0.804572	+	0.358219i	−0.0430678	+	0.0191750i	0.385090	+	0.922879i	$0.374170\pi$
$350$		0			0
$351$	2.53938	+	1.13060i	0.135542	+	0.0603472i
$352$		0			0
$353$	9.77716	+	16.9345i	0.520385	+	0.901334i	0.999719	+	0.0237013i	$0.00754506\pi$
$353$	9.77716	+	16.9345i	0.520385	+	0.901334i	−0.479334	+	0.877633i	$0.659122\pi$
$354$		0			0
$355$	3.36348			0.178515
$356$		0			0
$357$	0.922661	+	0.670352i	0.0488324	+	0.0354788i
$358$		0			0
$359$	−0.484832	+	0.538460i	−0.0255884	+	0.0284188i	−0.755803	−	0.654799i	$-0.772753\pi$
$359$	−0.484832	+	0.538460i	−0.0255884	+	0.0284188i	0.730215	+	0.683218i	$0.239420\pi$
$360$		0			0
$361$	0.118546	−	1.12789i	0.00623925	−	0.0593625i
$362$		0			0
$363$	5.22025	−	16.0663i	0.273992	−	0.843261i
$364$		0			0
$365$	−1.69208			−0.0885673
$366$		0			0
$367$	0.914369			0.0477297			0.0238648	−	0.999715i	$-0.492403\pi$
$367$	0.914369			0.0477297			0.0238648	+	0.999715i	$0.492403\pi$
$368$		0			0
$369$	0.324046	−	0.997310i	0.0168691	−	0.0519179i
$370$		0			0
$371$	−0.417491	+	3.97216i	−0.0216750	+	0.206224i
$372$		0			0
$373$	−10.4956	+	11.6566i	−0.543443	+	0.603554i	−0.950835	−	0.309699i	$-0.899772\pi$
$373$	−10.4956	+	11.6566i	−0.543443	+	0.603554i	0.407392	+	0.913253i	$0.366438\pi$
$374$		0			0
$375$	−7.81957	−	5.68125i	−0.403801	−	0.293378i
$376$		0			0
$377$	3.45877			0.178136
$378$		0			0
$379$	11.4376	+	19.8105i	0.587509	+	1.01760i	0.994557	+	0.104189i	$0.0332248\pi$
$379$	11.4376	+	19.8105i	0.587509	+	1.01760i	−0.407048	+	0.913407i	$0.633442\pi$
$380$		0			0
$381$	−17.1254	−	7.62471i	−0.877360	−	0.390626i
$382$		0			0
$383$	−5.04189	+	2.24479i	−0.257629	+	0.114704i	−0.531487	−	0.847066i	$-0.678367\pi$
$383$	−5.04189	+	2.24479i	−0.257629	+	0.114704i	0.273859	+	0.961770i	$0.411700\pi$
$384$		0			0
$385$	0.238226	+	0.264577i	0.0121411	+	0.0134841i
$386$		0			0
$387$	−0.476930	−	0.826066i	−0.0242437	−	0.0419913i
$388$		0			0
$389$	10.0616	+	7.31021i	0.510146	+	0.370643i	0.812879	−	0.582433i	$-0.197899\pi$
$389$	10.0616	+	7.31021i	0.510146	+	0.370643i	−0.302733	+	0.953075i	$0.597899\pi$
$390$		0			0
$391$	8.37213	+	1.77955i	0.423397	+	0.0899958i
$392$		0			0
$393$	−8.39379	+	6.09845i	−0.423411	+	0.307626i
$394$		0			0
$395$	−2.26505	+	3.92318i	−0.113967	+	0.197397i
$396$		0			0
$397$	−9.26093	−	1.96847i	−0.464793	−	0.0987947i	−0.0304380	−	0.999537i	$-0.509690\pi$
$397$	−9.26093	−	1.96847i	−0.464793	−	0.0987947i	−0.434355	+	0.900742i	$0.643024\pi$
$398$		0			0
$399$	−1.46397	+	4.50563i	−0.0732901	+	0.225564i
$400$		0			0
$401$	14.6456	+	16.2656i	0.731367	+	0.812265i	0.988034	−	0.154234i	$-0.0492911\pi$
$401$	14.6456	+	16.2656i	0.731367	+	0.812265i	−0.256667	+	0.966500i	$0.582624\pi$
$402$		0			0
$403$	1.72303	+	5.30296i	0.0858305	+	0.264159i
$404$		0			0
$405$	4.79674	−	1.01958i	0.238352	−	0.0506632i
$406$		0			0
$407$	−0.609948	−	1.87723i	−0.0302340	−	0.0930508i
$408$		0			0
$409$	−4.39611	−	1.95728i	−0.217374	−	0.0967811i	0.295161	−	0.955448i	$-0.404627\pi$
$409$	−4.39611	−	1.95728i	−0.217374	−	0.0967811i	−0.512535	+	0.858666i	$0.671293\pi$
$410$		0			0
$411$	−11.4411	+	12.7067i	−0.564350	+	0.626774i
$412$		0			0
$413$	3.01864	−	5.22844i	0.148538	−	0.257275i
$414$		0			0
$415$	−0.688411	−	6.54979i	−0.0337928	−	0.321517i
$416$		0			0
$417$	1.59056	+	15.1332i	0.0778902	+	0.741076i
$418$		0			0
$419$	−26.7785	+	19.4557i	−1.30822	+	0.950474i	−1.00000		0.000842259i	$-0.999732\pi$
$419$	−26.7785	+	19.4557i	−1.30822	+	0.950474i	−0.308216	+	0.951316i	$0.599732\pi$
$420$		0			0
$421$	0.0752115	−	0.715590i	0.00366558	−	0.0348757i	−0.992536	−	0.121950i	$-0.961085\pi$
$421$	0.0752115	−	0.715590i	0.00366558	−	0.0348757i	0.996202	+	0.0870745i	$0.0277518\pi$
$422$		0			0
$423$	0.997973	−	0.444326i	0.0485231	−	0.0216039i
$424$		0			0
$425$	4.60603	−	0.979041i	0.223425	−	0.0474905i
$426$		0			0
$427$	2.49973	+	4.69586i	0.120971	+	0.227249i
$428$		0			0
$429$	0.707592	−	0.150403i	0.0341629	−	0.00726154i
$430$		0			0
$431$	−18.9160	+	8.42194i	−0.911151	+	0.405671i	−0.808127	−	0.589008i	$-0.799519\pi$
$431$	−18.9160	+	8.42194i	−0.911151	+	0.405671i	−0.103024	+	0.994679i	$0.532852\pi$
$432$		0			0
$433$	3.26231	−	31.0388i	0.156777	−	1.49163i	−0.579512	−	0.814964i	$-0.696757\pi$
$433$	3.26231	−	31.0388i	0.156777	−	1.49163i	0.736289	−	0.676667i	$-0.236576\pi$
$434$		0			0
$435$	5.47486	−	3.97772i	0.262499	−	0.190717i
$436$		0			0
$437$	3.71647	+	35.3599i	0.177783	+	1.69149i
$438$		0			0
$439$	−0.700537	−	6.66517i	−0.0334348	−	0.318111i	−0.998438	−	0.0558725i	$-0.982206\pi$
$439$	−0.700537	−	6.66517i	−0.0334348	−	0.318111i	0.965003	−	0.262238i	$-0.0844607\pi$
$440$		0			0
$441$	−0.954838	+	1.65383i	−0.0454685	+	0.0787537i
$442$		0			0
$443$	−2.91815	+	3.24094i	−0.138646	+	0.153982i	−0.808469	−	0.588539i	$-0.799703\pi$
$443$	−2.91815	+	3.24094i	−0.138646	+	0.153982i	0.669823	+	0.742521i	$0.266370\pi$
$444$		0			0
$445$	4.70411	+	2.09441i	0.222996	+	0.0992843i
$446$		0			0
$447$	9.40761	+	28.9536i	0.444965	+	1.36946i
$448$		0			0
$449$	34.5074	−	7.33476i	1.62850	−	0.346149i	0.699045	−	0.715078i	$-0.253609\pi$
$449$	34.5074	−	7.33476i	1.62850	−	0.346149i	0.929458	+	0.368929i	$0.120275\pi$
$450$		0			0
$451$	−0.950227	−	2.92450i	−0.0447445	−	0.137709i
$452$		0			0
$453$	14.3663	+	15.9553i	0.674985	+	0.749647i
$454$		0			0
$455$	0.0658871	−	0.202780i	0.00308884	−	0.00950646i
$456$		0			0
$457$	−37.3323	−	7.93522i	−1.74633	−	0.371194i	−0.779457	−	0.626455i	$-0.784505\pi$
$457$	−37.3323	−	7.93522i	−1.74633	−	0.371194i	−0.966872	+	0.255262i	$0.917838\pi$
$458$		0			0
$459$	−2.75620	+	4.77388i	−0.128648	+	0.222826i
$460$		0			0
$461$	13.7355	−	9.97940i	0.639725	−	0.464787i	−0.220031	−	0.975493i	$-0.570616\pi$
$461$	13.7355	−	9.97940i	0.639725	−	0.464787i	0.859756	+	0.510706i	$0.170616\pi$
$462$		0			0
$463$	−10.2726	−	2.18351i	−0.477409	−	0.101476i	−0.0370789	−	0.999312i	$-0.511805\pi$
$463$	−10.2726	−	2.18351i	−0.477409	−	0.101476i	−0.440330	+	0.897836i	$0.645139\pi$
$464$		0			0
$465$	8.82599	+	6.41245i	0.409295	+	0.297370i
$466$		0			0
$467$	−15.4407	−	26.7441i	−0.714512	−	1.23757i	−0.963147	−	0.268974i	$-0.913315\pi$
$467$	−15.4407	−	26.7441i	−0.714512	−	1.23757i	0.248635	−	0.968597i	$-0.420018\pi$
$468$		0			0
$469$	5.15741	+	5.72789i	0.238147	+	0.264489i
$470$		0			0
$471$	15.7748	−	7.02340i	0.726865	−	0.323621i
$472$		0			0
$473$	−2.55526	−	1.13768i	−0.117491	−	0.0523105i
$474$		0			0
$475$	9.78041	+	16.9402i	0.448756	+	0.777268i
$476$		0			0
$477$	−1.71328			−0.0784457
$478$		0			0
$479$	31.1947	+	22.6642i	1.42532	+	1.03556i	0.990864	+	0.134863i	$0.0430593\pi$
$479$	31.1947	+	22.6642i	1.42532	+	1.03556i	0.434456	+	0.900693i	$0.356941\pi$
$480$		0			0
$481$	−0.790973	+	0.878464i	−0.0360652	+	0.0400545i
$482$		0			0
$483$	−0.985498	+	9.37639i	−0.0448417	+	0.426640i
$484$		0			0
$485$	−2.00854	+	6.18164i	−0.0912029	+	0.280694i
$486$		0			0
$487$	−26.4637			−1.19918			−0.599592	−	0.800306i	$-0.704670\pi$
$487$	−26.4637			−1.19918			−0.599592	+	0.800306i	$0.704670\pi$
$488$		0			0
$489$	−26.6530			−1.20529
$490$		0			0
$491$	12.3809	−	38.1046i	0.558744	−	1.71964i	−0.127101	−	0.991890i	$-0.540567\pi$
$491$	12.3809	−	38.1046i	0.558744	−	1.71964i	0.685845	−	0.727748i	$-0.259433\pi$
$492$		0			0
$493$	−0.716967	+	6.82149i	−0.0322906	+	0.307224i
$494$		0			0
$495$	−0.102189	+	0.113493i	−0.00459307	+	0.00510112i
$496$		0			0
$497$	−3.03799	−	2.20723i	−0.136272	−	0.0990076i
$498$		0			0
$499$	24.8592			1.11285			0.556425	−	0.830898i	$-0.312173\pi$
$499$	24.8592			1.11285			0.556425	+	0.830898i	$0.312173\pi$
$500$		0			0
$501$	7.09039	+	12.2809i	0.316775	+	0.548671i
$502$		0			0
$503$	13.4579	+	5.99185i	0.600059	+	0.267163i	0.684205	−	0.729290i	$-0.260149\pi$
$503$	13.4579	+	5.99185i	0.600059	+	0.267163i	−0.0841457	+	0.996453i	$0.526816\pi$
$504$		0			0
$505$	−7.21319	+	3.21152i	−0.320983	+	0.142911i
$506$		0			0
$507$	14.0242	+	15.5755i	0.622838	+	0.691732i
$508$		0			0
$509$	−0.405541	−	0.702418i	−0.0179753	−	0.0311341i	0.856898	−	0.515486i	$-0.172389\pi$
$509$	−0.405541	−	0.702418i	−0.0179753	−	0.0311341i	−0.874873	+	0.484352i	$0.839055\pi$
$510$		0			0
$511$	1.52833	+	1.11039i	0.0676092	+	0.0491210i
$512$		0			0
$513$	−22.3980	−	4.76085i	−0.988898	−	0.210197i
$514$		0			0
$515$	6.42468	−	4.66780i	0.283105	−	0.205688i
$516$		0			0
$517$	1.60170	−	2.77422i	0.0704425	−	0.122010i
$518$		0			0
$519$	35.8191	+	7.61359i	1.57228	+	0.334199i
$520$		0			0
$521$	9.67741	−	29.7840i	0.423975	−	1.30486i	−0.479998	−	0.877270i	$-0.659362\pi$
$521$	9.67741	−	29.7840i	0.423975	−	1.30486i	0.903972	−	0.427591i	$-0.140638\pi$
$522$		0			0
$523$	−12.8481	−	14.2692i	−0.561807	−	0.623949i	0.393586	−	0.919288i	$-0.371234\pi$
$523$	−12.8481	−	14.2692i	−0.561807	−	0.623949i	−0.955393	+	0.295338i	$0.904568\pi$
$524$		0			0
$525$	1.60285	+	4.93308i	0.0699543	+	0.215297i
$526$		0			0
$527$	−10.8158	+	2.29897i	−0.471145	+	0.100145i
$528$		0			0
$529$	14.7577	+	45.4194i	0.641638	+	1.97476i
$530$		0			0
$531$	2.36585	+	1.05335i	0.102669	+	0.0457113i
$532$		0			0
$533$	−1.23224	+	1.36854i	−0.0533743	+	0.0592782i
$534$		0			0
$535$	−2.64865	+	4.58760i	−0.114511	+	0.198339i
$536$		0			0
$537$	1.70559	+	16.2276i	0.0736016	+	0.700272i
$538$		0			0
$539$	0.585350	+	5.56923i	0.0252128	+	0.239884i
$540$		0			0
$541$	−18.5587	+	13.4837i	−0.797899	+	0.579708i	−0.910297	−	0.413955i	$-0.864147\pi$
$541$	−18.5587	+	13.4837i	−0.797899	+	0.579708i	0.112398	+	0.993663i	$0.464147\pi$
$542$		0			0
$543$	0.866205	−	8.24139i	0.0371724	−	0.353672i
$544$		0			0
$545$	7.54236	−	3.35807i	0.323079	−	0.143844i
$546$		0			0
$547$	−22.4075	+	4.76286i	−0.958076	+	0.203645i	−0.660310	−	0.750993i	$-0.729575\pi$
$547$	−22.4075	+	4.76286i	−0.958076	+	0.203645i	−0.297766	+	0.954639i	$0.596242\pi$
$548$		0			0
$549$	−1.89121	+	1.27697i	−0.0807151	+	0.0544996i
$550$		0			0
$551$	−27.8698	+	5.92391i	−1.18729	+	0.252367i
$552$		0			0
$553$	4.62037	−	2.05712i	0.196478	−	0.0874777i
$554$		0			0
$555$	−0.241757	+	2.30016i	−0.0102620	+	0.0976365i
$556$		0			0
$557$	−6.96052	+	5.05712i	−0.294927	+	0.214277i	−0.725402	−	0.688326i	$-0.758346\pi$
$557$	−6.96052	+	5.05712i	−0.294927	+	0.214277i	0.430475	+	0.902602i	$0.358346\pi$
$558$		0			0
$559$	0.175098	+	1.66594i	0.00740584	+	0.0704618i
$560$		0			0
$561$	0.149953	+	1.42671i	0.00633104	+	0.0602358i
$562$		0			0
$563$	18.9951	−	32.9004i	0.800546	−	1.38659i	−0.118711	−	0.992929i	$-0.537876\pi$
$563$	18.9951	−	32.9004i	0.800546	−	1.38659i	0.919257	−	0.393658i	$-0.128791\pi$
$564$		0			0
$565$	−0.767290	+	0.852161i	−0.0322801	+	0.0358507i
$566$		0			0
$567$	−5.00162	−	2.22686i	−0.210048	−	0.0935195i
$568$		0			0
$569$	5.59899	+	17.2319i	0.234722	+	0.722399i	0.997158	+	0.0753362i	$0.0240030\pi$
$569$	5.59899	+	17.2319i	0.234722	+	0.722399i	−0.762436	+	0.647063i	$0.775997\pi$
$570$		0			0
$571$	32.8120	−	6.97440i	1.37314	−	0.291869i	0.538480	−	0.842638i	$-0.318999\pi$
$571$	32.8120	−	6.97440i	1.37314	−	0.291869i	0.834658	+	0.550769i	$0.185665\pi$
$572$		0			0
$573$	1.33991	+	4.12381i	0.0559755	+	0.172275i
$574$		0			0
$575$	26.0477	+	28.9289i	1.08626	+	1.20642i
$576$		0			0
$577$	−6.40990	+	19.7276i	−0.266848	+	0.821273i	0.724414	+	0.689365i	$0.242110\pi$
$577$	−6.40990	+	19.7276i	−0.266848	+	0.821273i	−0.991262	+	0.131908i	$0.957890\pi$
$578$		0			0
$579$	−15.9956	−	3.39998i	−0.664756	−	0.141298i
$580$		0			0
$581$	−3.67640	+	6.36771i	−0.152523	+	0.264177i
$582$		0			0
$583$	−4.06450	+	2.95303i	−0.168335	+	0.122302i
$584$		0			0
$585$	0.0894621	+	0.0190157i	0.00369880	+	0.000786204i
$586$		0			0
$587$	9.40173	+	6.83076i	0.388051	+	0.281935i	0.764656	−	0.644438i	$-0.222909\pi$
$587$	9.40173	+	6.83076i	0.388051	+	0.281935i	−0.376605	+	0.926374i	$0.622909\pi$
$588$		0			0
$589$	−22.9663	−	39.7787i	−0.946308	−	1.63905i
$590$		0			0
$591$	11.7391	+	13.0375i	0.482880	+	0.536293i
$592$		0			0
$593$	3.86178	−	1.71938i	0.158584	−	0.0706063i	−0.325909	−	0.945401i	$-0.605670\pi$
$593$	3.86178	−	1.71938i	0.158584	−	0.0706063i	0.484494	+	0.874795i	$0.339004\pi$
$594$		0			0
$595$	0.386271	+	0.171979i	0.0158356	+	0.00705045i
$596$		0			0
$597$	8.75642	+	15.1666i	0.358377	+	0.620726i
$598$		0			0
$599$	−37.2796			−1.52321			−0.761603	−	0.648044i	$-0.775587\pi$
$599$	−37.2796			−1.52321			−0.761603	+	0.648044i	$0.775587\pi$
$600$		0			0
$601$	17.5422	+	12.7452i	0.715563	+	0.519887i	0.884964	−	0.465660i	$-0.154183\pi$
$601$	17.5422	+	12.7452i	0.715563	+	0.519887i	−0.169400	+	0.985547i	$0.554183\pi$
$602$		0			0
$603$	−2.21232	+	2.45703i	−0.0900926	+	0.100058i
$604$		0			0
$605$	0.654668	−	6.22875i	0.0266160	−	0.253235i
$606$		0			0
$607$	4.82134	−	14.8386i	0.195692	−	0.602278i	−0.804276	−	0.594256i	$-0.797446\pi$
$607$	4.82134	−	14.8386i	0.195692	−	0.602278i	0.999968	−	0.00802202i	$-0.00255351\pi$
$608$		0			0
$609$	−7.55534			−0.306158
$610$		0			0
$611$	−1.91845			−0.0776120
$612$		0			0
$613$	−3.33088	+	10.2514i	−0.134533	+	0.414050i	−0.995517	−	0.0945818i	$-0.969849\pi$
$613$	−3.33088	+	10.2514i	−0.134533	+	0.414050i	0.860984	+	0.508632i	$0.169849\pi$
$614$		0			0
$615$	−0.376629	+	3.58338i	−0.0151871	+	0.144496i
$616$		0			0
$617$	22.8097	−	25.3327i	0.918284	−	1.01986i	−0.0814478	−	0.996678i	$-0.525954\pi$
$617$	22.8097	−	25.3327i	0.918284	−	1.01986i	0.999731	−	0.0231796i	$-0.00737894\pi$
$618$		0			0
$619$	−13.5486	−	9.84363i	−0.544564	−	0.395649i	0.281213	−	0.959645i	$-0.409263\pi$
$619$	−13.5486	−	9.84363i	−0.544564	−	0.395649i	−0.825777	+	0.563996i	$0.809263\pi$
$620$		0			0
$621$	−45.5698			−1.82865
$622$		0			0
$623$	−2.87446	−	4.97871i	−0.115163	−	0.199468i
$624$		0			0
$625$	17.8649	+	7.95396i	0.714595	+	0.318158i
$626$		0			0
$627$	−5.44399	+	2.42382i	−0.217412	+	0.0967980i
$628$		0			0
$629$	−1.56857	−	1.74208i	−0.0625431	−	0.0694612i
$630$		0			0
$631$	6.34192	+	10.9845i	0.252468	+	0.437287i	0.964205	−	0.265159i	$-0.0854245\pi$
$631$	6.34192	+	10.9845i	0.252468	+	0.437287i	−0.711737	+	0.702446i	$0.752091\pi$
$632$		0			0
$633$	1.43210	+	1.04048i	0.0569209	+	0.0413554i
$634$		0			0
$635$	−6.79817	−	1.44499i	−0.269777	−	0.0573429i
$636$		0			0
$637$	2.71318	−	1.97124i	0.107500	−	0.0781033i
$638$		0			0
$639$	0.805405	−	1.39500i	0.0318613	−	0.0551854i
$640$		0			0
$641$	18.6608	+	3.96648i	0.737059	+	0.156667i	0.561120	−	0.827734i	$-0.310371\pi$
$641$	18.6608	+	3.96648i	0.737059	+	0.156667i	0.175939	+	0.984401i	$0.443704\pi$
$642$		0			0
$643$	−7.77790	+	23.9379i	−0.306730	+	0.944019i	0.672296	+	0.740283i	$0.265308\pi$
$643$	−7.77790	+	23.9379i	−0.306730	+	0.944019i	−0.979026	+	0.203736i	$0.934692\pi$
$644$		0			0
$645$	2.19306	+	2.43564i	0.0863516	+	0.0959032i
$646$		0			0
$647$	4.98079	+	15.3293i	0.195815	+	0.602657i	0.999966	+	0.00823206i	$0.00262038\pi$
$647$	4.98079	+	15.3293i	0.195815	+	0.602657i	−0.804151	+	0.594425i	$0.797380\pi$
$648$		0			0
$649$	7.42819	−	1.57891i	0.291582	−	0.0619777i
$650$		0			0
$651$	−3.76380	−	11.5838i	−0.147515	−	0.454005i
$652$		0			0
$653$	−17.5919	−	7.83243i	−0.688425	−	0.306507i	0.0325474	−	0.999470i	$-0.489638\pi$
$653$	−17.5919	−	7.83243i	−0.688425	−	0.306507i	−0.720973	+	0.692964i	$0.756305\pi$
$654$		0			0
$655$	−2.57388	+	2.85859i	−0.100570	+	0.111694i
$656$		0			0
$657$	−0.405177	+	0.701787i	−0.0158075	+	0.0273793i
$658$		0			0
$659$	−3.60363	−	34.2863i	−0.140378	−	1.33560i	−0.807152	−	0.590344i	$-0.798992\pi$
$659$	−3.60363	−	34.2863i	−0.140378	−	1.33560i	0.666774	−	0.745260i	$-0.267675\pi$
$660$		0			0
$661$	−3.15633	−	30.0305i	−0.122767	−	1.16805i	−0.866361	−	0.499419i	$-0.833547\pi$
$661$	−3.15633	−	30.0305i	−0.122767	−	1.16805i	0.743594	−	0.668632i	$-0.233120\pi$
$662$		0			0
$663$	0.695055	−	0.504987i	0.0269937	−	0.0196121i
$664$		0			0
$665$	−0.183595	+	1.74679i	−0.00711952	+	0.0677377i
$666$		0			0
$667$	−51.8002	+	23.0629i	−2.00571	+	0.893001i
$668$		0			0
$669$	23.9100	−	5.08222i	0.924412	−	0.196490i
$670$		0			0
$671$	−2.28563	+	6.28914i	−0.0882358	+	0.242789i
$672$		0			0
$673$	7.82105	−	1.66241i	0.301479	−	0.0640814i	−0.0546884	−	0.998503i	$-0.517417\pi$
$673$	7.82105	−	1.66241i	0.301479	−	0.0640814i	0.356168	+	0.934422i	$0.384083\pi$
$674$		0			0
$675$	−22.9033	+	10.1972i	−0.881548	+	0.392491i
$676$		0			0
$677$	−0.553332	+	5.26460i	−0.0212663	+	0.202335i	−0.999996	−	0.00281869i	$-0.999103\pi$
$677$	−0.553332	+	5.26460i	−0.0212663	+	0.202335i	0.978730	+	0.205154i	$0.0657694\pi$
$678$		0			0
$679$	5.87075	−	4.26535i	0.225299	−	0.163689i
$680$		0			0
$681$	1.14299	+	10.8748i	0.0437995	+	0.416725i
$682$		0			0
$683$	−0.472716	−	4.49759i	−0.0180880	−	0.172096i	0.981748	−	0.190184i	$-0.0609085\pi$
$683$	−0.472716	−	4.49759i	−0.0180880	−	0.172096i	−0.999836	+	0.0180887i	$0.994242\pi$
$684$		0			0
$685$	−3.16961	+	5.48993i	−0.121105	+	0.209759i
$686$		0			0
$687$	−18.4696	+	20.5126i	−0.704660	+	0.782604i
$688$		0			0
$689$	2.74865	+	1.22378i	0.104715	+	0.0466222i
$690$		0			0
$691$	−5.37993	−	16.5577i	−0.204662	−	0.629885i	−0.999727	−	0.0233610i	$-0.992563\pi$
$691$	−5.37993	−	16.5577i	−0.204662	−	0.629885i	0.795065	−	0.606524i	$-0.207437\pi$
$692$		0			0
$693$	0.166778	−	0.0354497i	0.00633536	−	0.00134662i
$694$		0			0
$695$	1.74331	+	5.36537i	0.0661277	+	0.203520i
$696$		0			0
$697$	−2.44365	−	2.71395i	−0.0925599	−	0.102798i
$698$		0			0
$699$	10.5958	−	32.6104i	0.400768	−	1.23344i
$700$		0			0
$701$	−33.6865	−	7.16028i	−1.27232	−	0.270440i	−0.478227	−	0.878236i	$-0.658720\pi$
$701$	−33.6865	−	7.16028i	−1.27232	−	0.270440i	−0.794093	+	0.607796i	$0.792054\pi$
$702$		0			0
$703$	4.86888	−	8.43315i	0.183633	−	0.318062i
$704$		0			0
$705$	−3.03670	+	2.20629i	−0.114369	+	0.0830936i
$706$		0			0
$707$	8.62265	+	1.83280i	0.324288	+	0.0689296i
$708$		0			0
$709$	−10.4725	−	7.60873i	−0.393304	−	0.285752i	0.373504	−	0.927628i	$-0.378156\pi$
$709$	−10.4725	−	7.60873i	−0.393304	−	0.285752i	−0.766808	+	0.641877i	$0.778156\pi$
$710$		0			0
$711$	1.08476	+	1.87885i	0.0406816	+	0.0704626i
$712$		0			0
$713$	−61.1650	−	67.9306i	−2.29065	−	2.54402i
$714$		0			0
$715$	0.245011	−	0.109086i	0.00916290	−	0.00407959i
$716$		0			0
$717$	39.3455	+	17.5178i	1.46939	+	0.654213i
$718$		0			0
$719$	0.0146839	+	0.0254333i	0.000547618	+	0.000948502i	0.866299	−	0.499526i	$-0.166492\pi$
$719$	0.0146839	+	0.0254333i	0.000547618	+	0.000948502i	−0.865751	+	0.500474i	$0.833159\pi$
$720$		0			0
$721$	−8.86610			−0.330191
$722$		0			0
$723$	26.6891	+	19.3908i	0.992579	+	0.721151i
$724$		0			0
$725$	−20.8739	+	23.1828i	−0.775236	+	0.860987i
$726$		0			0
$727$	−3.52859	+	33.5723i	−0.130868	+	1.24513i	0.710123	+	0.704078i	$0.248639\pi$
$727$	−3.52859	+	33.5723i	−0.130868	+	1.24513i	−0.840991	+	0.541049i	$0.818027\pi$
$728$		0			0
$729$	8.99006	−	27.6685i	0.332965	−	1.02476i
$730$		0			0
$731$	−3.32192			−0.122866
$732$		0			0
$733$	−27.0169			−0.997891			−0.498945	−	0.866633i	$-0.666279\pi$
$733$	−27.0169			−0.997891			−0.498945	+	0.866633i	$0.666279\pi$
$734$		0			0
$735$	2.02767	−	6.24052i	0.0747917	−	0.230185i
$736$		0			0
$737$	−1.01343	+	9.64213i	−0.0373301	+	0.355172i
$738$		0			0
$739$	10.2104	−	11.3398i	0.375595	−	0.417141i	−0.525478	−	0.850807i	$-0.676114\pi$
$739$	10.2104	−	11.3398i	0.375595	−	0.417141i	0.901074	+	0.433666i	$0.142780\pi$
$740$		0			0
$741$	2.88725	+	2.09771i	0.106066	+	0.0770613i
$742$		0			0
$743$	8.97804			0.329372			0.164686	−	0.986346i	$-0.447339\pi$
$743$	8.97804			0.329372			0.164686	+	0.986346i	$0.447339\pi$
$744$		0			0
$745$	5.64344	+	9.77473i	0.206760	+	0.358118i
$746$		0			0
$747$	−2.88137	−	1.28287i	−0.105424	−	0.0469377i
$748$		0			0
$749$	5.40287	−	2.40551i	0.197417	−	0.0878955i
$750$		0			0
$751$	23.2508	+	25.8227i	0.848435	+	0.942283i	0.998926	−	0.0463287i	$-0.0147522\pi$
$751$	23.2508	+	25.8227i	0.848435	+	0.942283i	−0.150491	+	0.988611i	$0.548085\pi$
$752$		0			0
$753$	12.4098	+	21.4944i	0.452238	+	0.783298i
$754$		0			0
$755$	6.43973	+	4.67874i	0.234366	+	0.170277i
$756$		0			0
$757$	10.1259	+	2.15233i	0.368033	+	0.0782278i	0.388216	−	0.921569i	$-0.373092\pi$
$757$	10.1259	+	2.15233i	0.368033	+	0.0782278i	−0.0201829	+	0.999796i	$0.506425\pi$
$758$		0			0
$759$	−9.59437	+	6.97072i	−0.348253	+	0.253021i
$760$		0			0
$761$	11.8893	−	20.5929i	0.430988	−	0.746494i	−0.565970	−	0.824426i	$-0.691498\pi$
$761$	11.8893	−	20.5929i	0.430988	−	0.746494i	0.996959	+	0.0779319i	$0.0248317\pi$
$762$		0			0
$763$	−9.01613	−	1.91644i	−0.326406	−	0.0693797i
$764$		0			0
$765$	−0.0560480	+	0.172498i	−0.00202642	+	0.00623668i
$766$		0			0
$767$	−3.04319	−	3.37981i	−0.109883	−	0.122038i
$768$		0			0
$769$	−8.42000	−	25.9141i	−0.303633	−	0.934486i	−0.980184	−	0.198090i	$-0.936526\pi$
$769$	−8.42000	−	25.9141i	−0.303633	−	0.934486i	0.676551	−	0.736396i	$-0.263474\pi$
$770$		0			0
$771$	21.7247	−	4.61772i	0.782395	−	0.166303i
$772$		0			0
$773$	10.4836	+	32.2651i	0.377068	+	1.16050i	0.942073	+	0.335409i	$0.108874\pi$
$773$	10.4836	+	32.2651i	0.377068	+	1.16050i	−0.565005	+	0.825088i	$0.691126\pi$
$774$		0			0
$775$	−45.9423	−	20.4548i	−1.65030	−	0.734759i
$776$		0			0
$777$	1.72780	−	1.91892i	0.0619846	−	0.0688409i
$778$		0			0
$779$	7.58514	−	13.1378i	0.271766	−	0.470712i
$780$		0			0
$781$	−0.493742	−	4.69764i	−0.0176675	−	0.168095i
$782$		0			0
$783$	−3.81720	−	36.3182i	−0.136416	−	1.29791i
$784$		0			0
$785$	5.17928	−	3.76297i	0.184856	−	0.134306i
$786$		0			0
$787$	0.814123	−	7.74586i	0.0290203	−	0.276110i	−0.970383	−	0.241571i	$-0.922337\pi$
$787$	0.814123	−	7.74586i	0.0290203	−	0.276110i	0.999403	−	0.0345386i	$-0.0109962\pi$
$788$		0			0
$789$	−7.88312	+	3.50979i	−0.280647	+	0.124952i
$790$		0			0
$791$	1.25225	−	0.266174i	0.0445250	−	0.00946407i
$792$		0			0
$793$	3.94624	−	0.697788i	0.140135	−	0.0247792i
$794$		0			0
$795$	5.75821	−	1.22395i	0.204223	−	0.0434089i
$796$		0			0
$797$	−12.4460	+	5.54130i	−0.440859	+	0.196283i	−0.615148	−	0.788412i	$-0.710904\pi$
$797$	−12.4460	+	5.54130i	−0.440859	+	0.196283i	0.174289	+	0.984694i	$0.444237\pi$
$798$		0			0
$799$	0.397674	−	3.78362i	0.0140687	−	0.133855i
$800$		0			0
$801$	1.99508	−	1.44951i	0.0704927	−	0.0512159i
$802$		0			0
$803$	0.248388	+	2.36326i	0.00876543	+	0.0833975i
$804$		0			0
$805$	0.365370	+	3.47626i	0.0128776	+	0.122522i
$806$		0			0
$807$	−13.7232	+	23.7693i	−0.483080	+	0.836719i
$808$		0			0
$809$	25.3258	−	28.1272i	0.890408	−	0.988898i	−0.109579	−	0.993978i	$-0.534950\pi$
$809$	25.3258	−	28.1272i	0.890408	−	0.988898i	0.999987	+	0.00507987i	$0.00161698\pi$
$810$		0			0
$811$	−22.4740	−	10.0061i	−0.789168	−	0.351360i	−0.0277447	−	0.999615i	$-0.508833\pi$
$811$	−22.4740	−	10.0061i	−0.789168	−	0.351360i	−0.761424	+	0.648255i	$0.775499\pi$
$812$		0			0
$813$	−1.30768	−	4.02461i	−0.0458622	−	0.141149i
$814$		0			0
$815$	−9.66558	+	2.05448i	−0.338570	+	0.0719654i
$816$		0			0
$817$	−4.26419	−	13.1238i	−0.149185	−	0.459144i
$818$		0			0
$819$	−0.0683258	−	0.0758834i	−0.00238750	−	0.00265158i
$820$		0			0
$821$	8.45452	−	26.0203i	0.295065	−	0.908116i	−0.688135	−	0.725583i	$-0.741570\pi$
$821$	8.45452	−	26.0203i	0.295065	−	0.908116i	0.983200	−	0.182533i	$-0.0584297\pi$
$822$		0			0
$823$	24.7330	+	5.25717i	0.862140	+	0.183253i	0.617703	−	0.786412i	$-0.288064\pi$
$823$	24.7330	+	5.25717i	0.862140	+	0.183253i	0.244437	+	0.969665i	$0.421397\pi$
$824$		0			0
$825$	−3.26227	+	5.65041i	−0.113577	+	0.196722i
$826$		0			0
$827$	−4.74882	+	3.45022i	−0.165133	+	0.119976i	−0.667282	−	0.744805i	$-0.732543\pi$
$827$	−4.74882	+	3.45022i	−0.165133	+	0.119976i	0.502150	+	0.864781i	$0.332543\pi$
$828$		0			0
$829$	−0.515894	−	0.109657i	−0.0179177	−	0.00380853i	0.198944	−	0.980011i	$-0.436249\pi$
$829$	−0.515894	−	0.109657i	−0.0179177	−	0.00380853i	−0.216862	+	0.976202i	$0.569582\pi$
$830$		0			0
$831$	−36.0371	−	26.1825i	−1.25011	−	0.908260i
$832$		0			0
$833$	3.32532	+	5.75963i	0.115216	+	0.199559i
$834$		0			0
$835$	3.51794	+	3.90707i	0.121743	+	0.135210i
$836$		0			0
$837$	53.7813	−	23.9450i	1.85895	−	0.827659i
$838$		0			0
$839$	−14.3582	−	6.39269i	−0.495700	−	0.220700i	0.143631	−	0.989631i	$-0.454122\pi$
$839$	−14.3582	−	6.39269i	−0.495700	−	0.220700i	−0.639331	+	0.768931i	$0.720789\pi$
$840$		0			0
$841$	−8.21980	−	14.2371i	−0.283441	−	0.490935i
$842$		0			0
$843$	−28.4280			−0.979112
$844$		0			0
$845$	6.28642	+	4.56735i	0.216259	+	0.157122i
$846$		0			0
$847$	−4.67882	+	5.19636i	−0.160766	+	0.178549i
$848$		0			0
$849$	4.58971	−	43.6682i	0.157519	−	1.49869i
$850$		0			0
$851$	5.98843	−	18.4305i	0.205281	−	0.631789i
$852$		0			0
$853$	0.923533			0.0316212			0.0158106	−	0.999875i	$-0.494967\pi$
$853$	0.923533			0.0316212			0.0158106	+	0.999875i	$0.494967\pi$
$854$		0			0
$855$	−0.753430			−0.0257668
$856$		0			0
$857$	−1.21293	+	3.73303i	−0.0414330	+	0.127518i	−0.969633	−	0.244563i	$-0.921356\pi$
$857$	−1.21293	+	3.73303i	−0.0414330	+	0.127518i	0.928200	+	0.372081i	$0.121356\pi$
$858$		0			0
$859$	5.16551	−	49.1465i	0.176245	−	1.67686i	−0.446771	−	0.894648i	$-0.647426\pi$
$859$	5.16551	−	49.1465i	0.176245	−	1.67686i	0.623016	−	0.782209i	$-0.285907\pi$
$860$		0			0
$861$	2.69171	−	2.98945i	0.0917333	−	0.101880i
$862$		0			0
$863$	37.7613	+	27.4352i	1.28541	+	0.933904i	0.999702	−	0.0244125i	$-0.00777152\pi$
$863$	37.7613	+	27.4352i	1.28541	+	0.933904i	0.285707	+	0.958317i	$0.407772\pi$
$864$		0			0
$865$	13.5765			0.461615
$866$		0			0
$867$	−13.1353	−	22.7510i	−0.446097	−	0.772663i
$868$		0			0
$869$	5.81185	+	2.58760i	0.197153	+	0.0877784i
$870$		0			0
$871$	5.30430	−	2.36163i	0.179729	−	0.0800207i
$872$		0			0
$873$	2.08288	+	2.31327i	0.0704946	+	0.0782922i
$874$		0			0
$875$	2.00037	+	3.46475i	0.0676250	+	0.117130i
$876$		0			0
$877$	2.15616	+	1.56654i	0.0728084	+	0.0528984i	0.623594	−	0.781748i	$-0.285672\pi$
$877$	2.15616	+	1.56654i	0.0728084	+	0.0528984i	−0.550786	+	0.834647i	$0.685672\pi$
$878$		0			0
$879$	43.2355	+	9.18998i	1.45830	+	0.309970i
$880$		0			0
$881$	−33.3532	+	24.2325i	−1.12370	+	0.816414i	−0.984765	−	0.173888i	$-0.944367\pi$
$881$	−33.3532	+	24.2325i	−1.12370	+	0.816414i	−0.138932	+	0.990302i	$0.544367\pi$
$882$		0			0
$883$	9.76186	−	16.9080i	0.328513	−	0.569001i	−0.653704	−	0.756750i	$-0.726786\pi$
$883$	9.76186	−	16.9080i	0.328513	−	0.569001i	0.982217	+	0.187749i	$0.0601192\pi$
$884$		0			0
$885$	−8.70396	−	1.85008i	−0.292580	−	0.0621899i
$886$		0			0
$887$	−12.8834	+	39.6511i	−0.432583	+	1.33135i	0.462960	+	0.886379i	$0.346787\pi$
$887$	−12.8834	+	39.6511i	−0.432583	+	1.33135i	−0.895543	+	0.444975i	$0.853213\pi$
$888$		0			0
$889$	5.19203	+	5.76634i	0.174135	+	0.193397i
$890$		0			0
$891$	−2.12814	−	6.54975i	−0.0712954	−	0.219425i
$892$		0			0
$893$	15.4583	−	3.28577i	0.517293	−	0.109954i
$894$		0			0
$895$	1.86939	+	5.75338i	0.0624867	+	0.192314i
$896$		0			0
$897$	6.48827	+	2.88876i	0.216637	+	0.0964529i
$898$		0			0
$899$	49.0158	−	54.4375i	1.63477	−	1.81559i
$900$		0			0
$901$	−2.98334	+	5.16730i	−0.0993895	+	0.172148i
$902$		0			0
$903$	−0.382484	−	3.63909i	−0.0127283	−	0.121101i
$904$		0			0
$905$	−0.321143	−	3.05547i	−0.0106751	−	0.101567i
$906$		0			0
$907$	12.8215	−	9.31537i	0.425731	−	0.309312i	−0.354209	−	0.935166i	$-0.615250\pi$
$907$	12.8215	−	9.31537i	0.425731	−	0.309312i	0.779940	+	0.625855i	$0.215250\pi$
$908$		0			0
$909$	−0.395264	+	3.76068i	−0.0131101	+	0.124734i
$910$		0			0
$911$	14.1433	−	6.29700i	0.468588	−	0.208629i	−0.158838	−	0.987305i	$-0.550775\pi$
$911$	14.1433	−	6.29700i	0.468588	−	0.208629i	0.627427	+	0.778676i	$0.284108\pi$
$912$		0			0
$913$	−9.04679	+	1.92295i	−0.299405	+	0.0636405i
$914$		0			0
$915$	5.44399	−	5.64285i	0.179973	−	0.186547i
$916$		0			0
$917$	4.20070	−	0.892886i	0.138719	−	0.0294857i
$918$		0			0
$919$	7.32380	−	3.26076i	0.241590	−	0.107563i	−0.282370	−	0.959305i	$-0.591121\pi$
$919$	7.32380	−	3.26076i	0.241590	−	0.107563i	0.523960	+	0.851743i	$0.324454\pi$
$920$		0			0
$921$	0.479897	−	4.56592i	0.0158132	−	0.150452i
$922$		0			0
$923$	−2.28856	+	1.66274i	−0.0753290	+	0.0547297i
$924$		0			0
$925$	−1.11444	−	10.6032i	−0.0366425	−	0.348630i
$926$		0			0
$927$	−0.397542	−	3.78236i	−0.0130570	−	0.124229i
$928$		0			0
$929$	−17.2949	+	29.9557i	−0.567428	+	0.982814i	0.429391	+	0.903119i	$0.358728\pi$
$929$	−17.2949	+	29.9557i	−0.567428	+	0.982814i	−0.996819	+	0.0796955i	$0.974605\pi$
$930$		0			0
$931$	−18.4859	+	20.5306i	−0.605850	+	0.672865i
$932$		0			0
$933$	−5.52716	−	2.46085i	−0.180951	−	0.0805647i
$934$		0			0
$935$	0.164355	+	0.505831i	0.00537497	+	0.0165425i
$936$		0			0
$937$	−39.7485	+	8.44881i	−1.29853	+	0.276010i	−0.804769	−	0.593589i	$-0.797711\pi$
$937$	−39.7485	+	8.44881i	−1.29853	+	0.276010i	−0.493758	+	0.869599i	$0.664377\pi$
$938$		0			0
$939$	13.8381	+	42.5892i	0.451588	+	1.38984i
$940$		0			0
$941$	−5.38810	−	5.98409i	−0.175647	−	0.195076i	0.648893	−	0.760880i	$-0.275232\pi$
$941$	−5.38810	−	5.98409i	−0.175647	−	0.195076i	−0.824540	+	0.565804i	$0.808566\pi$
$942$		0			0
$943$	9.32926	−	28.7125i	0.303803	−	0.935008i
$944$		0			0
$945$	−2.20197	−	0.468044i	−0.0716302	−	0.0152255i
$946$		0			0
$947$	29.5744	−	51.2244i	0.961040	−	1.66457i	0.241144	−	0.970489i	$-0.422477\pi$
$947$	29.5744	−	51.2244i	0.961040	−	1.66457i	0.719896	−	0.694082i	$-0.244189\pi$
$948$		0			0
$949$	1.15131	−	0.836478i	0.0373732	−	0.0271532i
$950$		0			0
$951$	46.5642	+	9.89752i	1.50995	+	0.320949i
$952$		0			0
$953$	31.1420	+	22.6260i	1.00879	+	0.732926i	0.963954	−	0.266068i	$-0.0857246\pi$
$953$	31.1420	+	22.6260i	1.00879	+	0.732926i	0.0448325	+	0.998995i	$0.485725\pi$
$954$		0			0
$955$	0.803785	+	1.39220i	0.0260099	+	0.0450504i
$956$		0			0
$957$	−6.35920	−	7.06261i	−0.205564	−	0.228302i
$958$		0			0
$959$	6.46554	−	2.87865i	0.208783	−	0.0929563i
$960$		0			0
$961$	79.5612	+	35.4229i	2.56649	+	1.14268i
$962$		0			0
$963$	1.26847	+	2.19706i	0.0408759	+	0.0707991i
$964$		0			0
$965$	−6.06282			−0.195169
$966$		0			0
$967$	17.8887	+	12.9969i	0.575261	+	0.417952i	0.837013	−	0.547184i	$-0.184300\pi$
$967$	17.8887	+	12.9969i	0.575261	+	0.417952i	−0.261751	+	0.965135i	$0.584300\pi$
$968$		0			0
$969$	−4.73567	+	5.25949i	−0.152132	+	0.168959i
$970$		0			0
$971$	1.49997	−	14.2713i	0.0481364	−	0.457988i	−0.943731	−	0.330714i	$-0.892711\pi$
$971$	1.49997	−	14.2713i	0.0481364	−	0.457988i	0.991868	−	0.127274i	$-0.0406227\pi$
$972$		0			0
$973$	1.94632	−	5.99017i	0.0623962	−	0.192036i
$974$		0			0
$975$	3.90741			0.125137
$976$		0			0
$977$	−44.1463			−1.41236			−0.706182	−	0.708030i	$-0.749584\pi$
$977$	−44.1463			−1.41236			−0.706182	+	0.708030i	$0.749584\pi$
$978$		0			0
$979$	2.23463	−	6.87750i	0.0714192	−	0.219806i
$980$		0			0
$981$	0.413301	−	3.93230i	0.0131957	−	0.125549i
$982$		0			0
$983$	20.0742	−	22.2947i	0.640268	−	0.711090i	−0.332439	−	0.943125i	$-0.607872\pi$
$983$	20.0742	−	22.2947i	0.640268	−	0.711090i	0.972708	+	0.232035i	$0.0745383\pi$
$984$		0			0
$985$	5.26208	+	3.82312i	0.167664	+	0.121815i
$986$		0			0
$987$	4.19066			0.133390
$988$		0			0
$989$	−13.7308	−	23.7824i	−0.436614	−	0.756237i
$990$		0			0
$991$	−3.83891	−	1.70919i	−0.121947	−	0.0542943i	0.344856	−	0.938656i	$-0.387928\pi$
$991$	−3.83891	−	1.70919i	−0.121947	−	0.0542943i	−0.466803	+	0.884361i	$0.654594\pi$
$992$		0			0
$993$	17.5460	−	7.81199i	0.556806	−	0.247906i
$994$		0			0
$995$	4.34455	+	4.82511i	0.137732	+	0.152966i
$996$		0			0
$997$	−15.3292	−	26.5510i	−0.485482	−	0.840879i	0.514379	−	0.857563i	$-0.328022\pi$
$997$	−15.3292	−	26.5510i	−0.485482	−	0.840879i	−0.999861	+	0.0166839i	$0.994689\pi$
$998$		0			0
$999$	10.0971	+	7.33598i	0.319459	+	0.232100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.225.1		32
4.3	odd	2		61.2.i.a.42.3	yes	32
12.11	even	2		549.2.bl.b.469.2		32
61.16	even	15	inner	976.2.bw.c.321.1		32
244.179	odd	30		3721.2.a.j.1.7		16
244.187	odd	30		3721.2.a.l.1.10		16
244.199	odd	30		61.2.i.a.16.3	✓	32
732.443	even	30		549.2.bl.b.199.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.16.3	✓	32	244.199	odd	30
61.2.i.a.42.3	yes	32	4.3	odd	2
549.2.bl.b.199.2		32	732.443	even	30
549.2.bl.b.469.2		32	12.11	even	2
976.2.bw.c.225.1		32	1.1	even	1	trivial
976.2.bw.c.321.1		32	61.16	even	15	inner
3721.2.a.j.1.7		16	244.179	odd	30
3721.2.a.l.1.10		16	244.187	odd	30

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:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.508502 + 1.56501i) q^{3} +(-0.0637708 + 0.606739i) q^{5} +(0.455761 - 0.506174i) q^{7} +(0.236374 + 0.171736i) q^{9} +O(q^{10})\)	\(q+(-0.508502 + 1.56501i) q^{3} +(-0.0637708 + 0.606739i) q^{5} +(0.455761 - 0.506174i) q^{7} +(0.236374 + 0.171736i) q^{9} +0.856770 q^{11} +(-0.256551 - 0.444360i) q^{13} +(-0.917124 - 0.408330i) q^{15} +(0.929560 - 0.413867i) q^{17} +(2.82829 + 3.14113i) q^{19} +(0.560411 + 0.970661i) q^{21} +(6.80521 + 4.94428i) q^{23} +(4.52667 + 0.962174i) q^{25} +(-4.38279 + 3.18428i) q^{27} +(-3.37045 + 5.83778i) q^{29} +(-10.6295 - 2.25937i) q^{31} +(-0.435669 + 1.34085i) q^{33} +(0.278051 + 0.308807i) q^{35} +(-0.711916 - 2.19105i) q^{37} +(0.825883 - 0.175547i) q^{39} +(-1.10908 - 3.41340i) q^{41} +(-2.98244 - 1.32787i) q^{43} +(-0.119273 + 0.132466i) q^{45} +(1.86946 - 3.23800i) q^{47} +(0.683205 + 6.50026i) q^{49} +(0.175022 + 1.66522i) q^{51} +(-4.74398 + 3.44671i) q^{53} +(-0.0546369 + 0.519836i) q^{55} +(-6.35408 + 2.82902i) q^{57} +(8.67000 - 1.84286i) q^{59} +(-2.66773 + 7.34052i) q^{61} +(0.194659 - 0.0413760i) q^{63} +(0.285971 - 0.127322i) q^{65} +(-1.18285 + 11.2540i) q^{67} +(-11.1983 + 8.13604i) q^{69} +(-0.576283 - 5.48297i) q^{71} +(0.289912 + 2.75833i) q^{73} +(-3.80763 + 6.59501i) q^{75} +(0.390483 - 0.433675i) q^{77} +(6.78344 + 3.02018i) q^{79} +(-2.48391 - 7.64470i) q^{81} +(-10.5592 + 2.24442i) q^{83} +(0.191830 + 0.590393i) q^{85} +(-7.42230 - 8.24330i) q^{87} +(2.60821 - 8.02724i) q^{89} +(-0.341850 - 0.0726624i) q^{91} +(8.94104 - 15.4863i) q^{93} +(-2.08621 + 1.51572i) q^{95} +(10.4211 + 2.21507i) q^{97} +(0.202519 + 0.147138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39} + 11 q^{41} - 40 q^{43} + 12 q^{45} - 40 q^{47} + q^{49} + 9 q^{51} + 17 q^{53} + 60 q^{55} - 38 q^{57} + 11 q^{59} - 55 q^{61} + 58 q^{63} + 59 q^{65} + 13 q^{67} - 32 q^{69} - 63 q^{71} - 46 q^{73} - q^{75} - 31 q^{77} + 49 q^{79} + 48 q^{81} - 39 q^{83} + 21 q^{85} - 17 q^{87} + 32 q^{89} - 70 q^{91} + 67 q^{93} - 47 q^{95} + 37 q^{97} + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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