LMFDB - Embedded newform 504.2.q.c.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	504.25
Dual form			504.2.q.c.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.704143 - 1.58246i) q^{3} +(-1.05220 + 1.82246i) q^{5} +(2.58382 + 0.569079i) q^{7} +(-2.00837 + 2.22856i) q^{9} +O(q^{10})$	\(q+(-0.704143 - 1.58246i) q^{3} +(-1.05220 + 1.82246i) q^{5} +(2.58382 + 0.569079i) q^{7} +(-2.00837 + 2.22856i) q^{9} +(-0.199532 - 0.345600i) q^{11} +(1.44292 + 2.49921i) q^{13} +(3.62487 + 0.381790i) q^{15} +(-0.176596 + 0.305873i) q^{17} +(2.84888 + 4.93440i) q^{19} +(-0.918837 - 4.48951i) q^{21} +(0.438682 - 0.759820i) q^{23} +(0.285756 + 0.494945i) q^{25} +(4.94078 + 1.60894i) q^{27} +(0.874997 - 1.51554i) q^{29} +9.13490 q^{31} +(-0.406399 + 0.559103i) q^{33} +(-3.75582 + 4.11014i) q^{35} +(-3.39555 - 5.88127i) q^{37} +(2.93888 - 4.04317i) q^{39} +(1.20377 + 2.08499i) q^{41} +(0.276745 - 0.479336i) q^{43} +(-1.94826 - 6.00505i) q^{45} +11.7372 q^{47} +(6.35230 + 2.94080i) q^{49} +(0.608381 + 0.0640778i) q^{51} +(-2.07821 + 3.59956i) q^{53} +0.839790 q^{55} +(5.80248 - 7.98277i) q^{57} -9.32421 q^{59} -10.0720 q^{61} +(-6.45749 + 4.61528i) q^{63} -6.07296 q^{65} +1.20241 q^{67} +(-1.51128 - 0.159176i) q^{69} -14.6826 q^{71} +(0.315636 - 0.546697i) q^{73} +(0.582017 - 0.800710i) q^{75} +(-0.318883 - 1.00652i) q^{77} -2.48729 q^{79} +(-0.932933 - 8.95152i) q^{81} +(-4.59366 + 7.95645i) q^{83} +(-0.371628 - 0.643678i) q^{85} +(-3.01440 - 0.317493i) q^{87} +(7.29358 + 12.6328i) q^{89} +(2.30601 + 7.27866i) q^{91} +(-6.43228 - 14.4556i) q^{93} -11.9903 q^{95} +(-7.84245 + 13.5835i) q^{97} +(1.17092 + 0.249422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.704143	−	1.58246i	−0.406537	−	0.913634i
$3$	−0.704143	−	1.58246i	−0.406537	−	0.913634i
$4$		0			0
$5$	−1.05220	+	1.82246i	−0.470558	+	0.815030i	−0.999433	−	0.0336699i	$-0.989281\pi$
$5$	−1.05220	+	1.82246i	−0.470558	+	0.815030i	0.528876	+	0.848699i	$0.322614\pi$
$6$		0			0
$7$	2.58382	+	0.569079i	0.976594	+	0.215092i
$7$	2.58382	+	0.569079i	0.976594	+	0.215092i
$8$		0			0
$9$	−2.00837	+	2.22856i	−0.669455	+	0.742852i
$10$		0			0
$11$	−0.199532	−	0.345600i	−0.0601612	−	0.104202i	0.834376	−	0.551195i	$-0.185828\pi$
$11$	−0.199532	−	0.345600i	−0.0601612	−	0.104202i	−0.894537	+	0.446993i	$0.852495\pi$
$12$		0			0
$13$	1.44292	+	2.49921i	0.400194	+	0.693157i	0.993749	−	0.111637i	$-0.0356093\pi$
$13$	1.44292	+	2.49921i	0.400194	+	0.693157i	−0.593555	+	0.804794i	$0.702276\pi$
$14$		0			0
$15$	3.62487	+	0.381790i	0.935938	+	0.0985778i
$16$		0			0
$17$	−0.176596	+	0.305873i	−0.0428308	+	0.0741851i	−0.886646	−	0.462449i	$-0.846971\pi$
$17$	−0.176596	+	0.305873i	−0.0428308	+	0.0741851i	0.843815	+	0.536634i	$0.180304\pi$
$18$		0			0
$19$	2.84888	+	4.93440i	0.653578	+	1.13203i	0.982248	+	0.187585i	$0.0600661\pi$
$19$	2.84888	+	4.93440i	0.653578	+	1.13203i	−0.328670	+	0.944445i	$0.606601\pi$
$20$		0			0
$21$	−0.918837	−	4.48951i	−0.200507	−	0.979692i
$22$		0			0
$23$	0.438682	−	0.759820i	0.0914716	−	0.158433i	−0.816659	−	0.577121i	$-0.804176\pi$
$23$	0.438682	−	0.759820i	0.0914716	−	0.158433i	0.908131	+	0.418687i	$0.137510\pi$
$24$		0			0
$25$	0.285756	+	0.494945i	0.0571513	+	0.0989889i
$26$		0			0
$27$	4.94078	+	1.60894i	0.950854	+	0.309640i
$28$		0			0
$29$	0.874997	−	1.51554i	0.162483	−	0.281429i	−0.773276	−	0.634070i	$-0.781383\pi$
$29$	0.874997	−	1.51554i	0.162483	−	0.281429i	0.935759	+	0.352641i	$0.114716\pi$
$30$		0			0
$31$	9.13490			1.64068			0.820339	−	0.571878i	$-0.193785\pi$
$31$	9.13490			1.64068			0.820339	+	0.571878i	$0.193785\pi$
$32$		0			0
$33$	−0.406399	+	0.559103i	−0.0707450	+	0.0973274i
$34$		0			0
$35$	−3.75582	+	4.11014i	−0.634850	+	0.694740i
$36$		0			0
$37$	−3.39555	−	5.88127i	−0.558225	−	0.966874i	−0.997645	−	0.0685922i	$-0.978149\pi$
$37$	−3.39555	−	5.88127i	−0.558225	−	0.966874i	0.439420	−	0.898282i	$-0.355184\pi$
$38$		0			0
$39$	2.93888	−	4.04317i	0.470598	−	0.647425i
$40$		0			0
$41$	1.20377	+	2.08499i	0.187997	+	0.325621i	0.944582	−	0.328274i	$-0.106467\pi$
$41$	1.20377	+	2.08499i	0.187997	+	0.325621i	−0.756585	+	0.653895i	$0.773134\pi$
$42$		0			0
$43$	0.276745	−	0.479336i	0.0422032	−	0.0730981i	−0.844152	−	0.536104i	$-0.819896\pi$
$43$	0.276745	−	0.479336i	0.0422032	−	0.0730981i	0.886355	+	0.463005i	$0.153229\pi$
$44$		0			0
$45$	−1.94826	−	6.00505i	−0.290429	−	0.895181i
$46$		0			0
$47$	11.7372			1.71205			0.856023	−	0.516939i	$-0.172928\pi$
$47$	11.7372			1.71205			0.856023	+	0.516939i	$0.172928\pi$
$48$		0			0
$49$	6.35230	+	2.94080i	0.907471	+	0.420114i
$50$		0			0
$51$	0.608381	+	0.0640778i	0.0851904	+	0.00897269i
$52$		0			0
$53$	−2.07821	+	3.59956i	−0.285464	+	0.494437i	−0.972721	−	0.231976i	$-0.925481\pi$
$53$	−2.07821	+	3.59956i	−0.285464	+	0.494437i	0.687258	+	0.726413i	$0.258814\pi$
$54$		0			0
$55$	0.839790			0.113237
$56$		0			0
$57$	5.80248	−	7.98277i	0.768558	−	1.05734i
$58$		0			0
$59$	−9.32421			−1.21391			−0.606954	−	0.794737i	$-0.707609\pi$
$59$	−9.32421			−1.21391			−0.606954	+	0.794737i	$0.707609\pi$
$60$		0			0
$61$	−10.0720			−1.28959			−0.644795	−	0.764356i	$-0.723057\pi$
$61$	−10.0720			−1.28959			−0.644795	+	0.764356i	$0.723057\pi$
$62$		0			0
$63$	−6.45749	+	4.61528i	−0.813567	+	0.581471i
$64$		0			0
$65$	−6.07296			−0.753258
$66$		0			0
$67$	1.20241			0.146898			0.0734488	−	0.997299i	$-0.476599\pi$
$67$	1.20241			0.146898			0.0734488	+	0.997299i	$0.476599\pi$
$68$		0			0
$69$	−1.51128	−	0.159176i	−0.181937	−	0.0191625i
$70$		0			0
$71$	−14.6826			−1.74250			−0.871250	−	0.490840i	$-0.836690\pi$
$71$	−14.6826			−1.74250			−0.871250	+	0.490840i	$0.836690\pi$
$72$		0			0
$73$	0.315636	−	0.546697i	0.0369423	−	0.0639860i	−0.846963	−	0.531652i	$-0.821572\pi$
$73$	0.315636	−	0.546697i	0.0369423	−	0.0639860i	0.883905	+	0.467666i	$0.154905\pi$
$74$		0			0
$75$	0.582017	−	0.800710i	0.0672056	−	0.0924580i
$76$		0			0
$77$	−0.318883	−	1.00652i	−0.0363400	−	0.114703i
$78$		0			0
$79$	−2.48729			−0.279842			−0.139921	−	0.990163i	$-0.544685\pi$
$79$	−2.48729			−0.279842			−0.139921	+	0.990163i	$0.544685\pi$
$80$		0			0
$81$	−0.932933	−	8.95152i	−0.103659	−	0.994613i
$82$		0			0
$83$	−4.59366	+	7.95645i	−0.504219	+	0.873333i	0.495769	+	0.868455i	$0.334886\pi$
$83$	−4.59366	+	7.95645i	−0.504219	+	0.873333i	−0.999988	+	0.00487885i	$0.998447\pi$
$84$		0			0
$85$	−0.371628	−	0.643678i	−0.0403087	−	0.0698167i
$86$		0			0
$87$	−3.01440	−	0.317493i	−0.323178	−	0.0340388i
$88$		0			0
$89$	7.29358	+	12.6328i	0.773118	+	1.33908i	0.935846	+	0.352408i	$0.114637\pi$
$89$	7.29358	+	12.6328i	0.773118	+	1.33908i	−0.162729	+	0.986671i	$0.552029\pi$
$90$		0			0
$91$	2.30601	+	7.27866i	0.241735	+	0.763011i
$92$		0			0
$93$	−6.43228	−	14.4556i	−0.666996	−	1.49898i
$94$		0			0
$95$	−11.9903			−1.23018
$96$		0			0
$97$	−7.84245	+	13.5835i	−0.796280	+	1.37920i	0.125744	+	0.992063i	$0.459868\pi$
$97$	−7.84245	+	13.5835i	−0.796280	+	1.37920i	−0.922023	+	0.387134i	$0.873465\pi$
$98$		0			0
$99$	1.17092	+	0.249422i	0.117682	+	0.0250679i
$100$		0			0
$101$	0.0464285	+	0.0804166i	0.00461981	+	0.00800175i	0.868326	−	0.495994i	$-0.165196\pi$
$101$	0.0464285	+	0.0804166i	0.00461981	+	0.00800175i	−0.863706	+	0.503996i	$0.831863\pi$
$102$		0			0
$103$	9.95769	−	17.2472i	0.981161	−	1.69942i	0.323270	−	0.946307i	$-0.395218\pi$
$103$	9.95769	−	17.2472i	0.981161	−	1.69942i	0.657891	−	0.753113i	$-0.271449\pi$
$104$		0			0
$105$	9.14877	+	3.04932i	0.892828	+	0.297583i
$106$		0			0
$107$	−2.89225	−	5.00953i	−0.279605	−	0.484290i	0.691682	−	0.722202i	$-0.256870\pi$
$107$	−2.89225	−	5.00953i	−0.279605	−	0.484290i	−0.971287	+	0.237913i	$0.923537\pi$
$108$		0			0
$109$	−6.25516	+	10.8343i	−0.599136	+	1.03773i	0.393813	+	0.919191i	$0.371156\pi$
$109$	−6.25516	+	10.8343i	−0.599136	+	1.03773i	−0.992949	+	0.118543i	$0.962178\pi$
$110$		0			0
$111$	−6.91592	+	9.51458i	−0.656430	+	0.903084i
$112$		0			0
$113$	1.69411	+	2.93428i	0.159368	+	0.276034i	0.934641	−	0.355593i	$-0.115721\pi$
$113$	1.69411	+	2.93428i	0.159368	+	0.276034i	−0.775273	+	0.631627i	$0.782388\pi$
$114$		0			0
$115$	0.923161	+	1.59896i	0.0860853	+	0.149104i
$116$		0			0
$117$	−8.46755	−	1.80370i	−0.782826	−	0.166752i
$118$		0			0
$119$	−0.630359	+	0.689825i	−0.0577849	+	0.0632362i
$120$		0			0
$121$	5.42037	−	9.38836i	0.492761	−	0.853488i
$122$		0			0
$123$	2.45179	−	3.37305i	0.221071	−	0.304138i
$124$		0			0
$125$	−11.7247			−1.04869
$126$		0			0
$127$	14.7348			1.30750			0.653752	−	0.756709i	$-0.273194\pi$
$127$	14.7348			1.30750			0.653752	+	0.756709i	$0.273194\pi$
$128$		0			0
$129$	−0.953399	−	0.100417i	−0.0839421	−	0.00884122i
$130$		0			0
$131$	6.95392	−	12.0445i	0.607567	−	1.05234i	−0.384073	−	0.923303i	$-0.625479\pi$
$131$	6.95392	−	12.0445i	0.607567	−	1.05234i	0.991640	−	0.129034i	$-0.0411877\pi$
$132$		0			0
$133$	4.55294	+	14.3709i	0.394790	+	1.24611i
$134$		0			0
$135$	−8.13091	+	7.31146i	−0.699797	+	0.629270i
$136$		0			0
$137$	−7.27874	−	12.6072i	−0.621865	−	1.07710i	−0.989138	−	0.146989i	$-0.953042\pi$
$137$	−7.27874	−	12.6072i	−0.621865	−	1.07710i	0.367273	−	0.930113i	$-0.380291\pi$
$138$		0			0
$139$	−3.63996	−	6.30460i	−0.308737	−	0.534749i	0.669349	−	0.742948i	$-0.266573\pi$
$139$	−3.63996	−	6.30460i	−0.308737	−	0.534749i	−0.978086	+	0.208199i	$0.933240\pi$
$140$		0			0
$141$	−8.26466	−	18.5736i	−0.696010	−	1.56418i
$142$		0			0
$143$	0.575818	−	0.997347i	0.0481523	−	0.0834023i
$144$		0			0
$145$	1.84134	+	3.18930i	0.152915	+	0.264857i
$146$		0			0
$147$	0.180775	−	12.1230i	0.0149100	−	0.999889i
$148$		0			0
$149$	0.360832	−	0.624979i	0.0295605	−	0.0512003i	−0.850867	−	0.525382i	$-0.823923\pi$
$149$	0.360832	−	0.624979i	0.0295605	−	0.0512003i	0.880427	+	0.474181i	$0.157256\pi$
$150$		0			0
$151$	−10.9022	−	18.8831i	−0.887207	−	1.53669i	−0.843163	−	0.537657i	$-0.819309\pi$
$151$	−10.9022	−	18.8831i	−0.887207	−	1.53669i	−0.0440432	−	0.999030i	$-0.514024\pi$
$152$		0			0
$153$	−0.326986	−	1.00786i	−0.0264353	−	0.0814806i
$154$		0			0
$155$	−9.61173	+	16.6480i	−0.772033	+	1.33720i
$156$		0			0
$157$	5.17973			0.413387			0.206694	−	0.978406i	$-0.433730\pi$
$157$	5.17973			0.413387			0.206694	+	0.978406i	$0.433730\pi$
$158$		0			0
$159$	7.15951	+	0.754077i	0.567786	+	0.0598022i
$160$		0			0
$161$	1.56588	−	1.71360i	0.123408	−	0.135050i
$162$		0			0
$163$	2.63906	+	4.57098i	0.206707	+	0.358027i	0.950675	−	0.310188i	$-0.100392\pi$
$163$	2.63906	+	4.57098i	0.206707	+	0.358027i	−0.743968	+	0.668215i	$0.767059\pi$
$164$		0			0
$165$	−0.591332	−	1.32893i	−0.0460351	−	0.103457i
$166$		0			0
$167$	−6.83710	−	11.8422i	−0.529071	−	0.916378i	−0.999425	−	0.0339001i	$-0.989207\pi$
$167$	−6.83710	−	11.8422i	−0.529071	−	0.916378i	0.470354	−	0.882478i	$-0.344126\pi$
$168$		0			0
$169$	2.33596	−	4.04599i	0.179689	−	0.311230i
$170$		0			0
$171$	−16.7182	−	3.56120i	−1.27847	−	0.272332i
$172$		0			0
$173$	20.1824			1.53444			0.767218	−	0.641386i	$-0.221640\pi$
$173$	20.1824			1.53444			0.767218	+	0.641386i	$0.221640\pi$
$174$		0			0
$175$	0.456682	+	1.44147i	0.0345219	+	0.108965i
$176$		0			0
$177$	6.56557	+	14.7552i	0.493499	+	1.10907i
$178$		0			0
$179$	12.5968	−	21.8183i	0.941528	−	1.63077i	0.178971	−	0.983854i	$-0.442723\pi$
$179$	12.5968	−	21.8183i	0.941528	−	1.63077i	0.762557	−	0.646921i	$-0.223944\pi$
$180$		0			0
$181$	−17.2815			−1.28453			−0.642263	−	0.766485i	$-0.722004\pi$
$181$	−17.2815			−1.28453			−0.642263	+	0.766485i	$0.722004\pi$
$182$		0			0
$183$	7.09214	+	15.9386i	0.524266	+	1.17821i
$184$		0			0
$185$	14.2912			1.05071
$186$		0			0
$187$	0.140946			0.0103070
$188$		0			0
$189$	11.8505	+	6.96891i	0.861997	+	0.506913i
$190$		0			0
$191$	−5.01898			−0.363161			−0.181580	−	0.983376i	$-0.558121\pi$
$191$	−5.01898			−0.363161			−0.181580	+	0.983376i	$0.558121\pi$
$192$		0			0
$193$	−5.43765			−0.391411			−0.195705	−	0.980663i	$-0.562700\pi$
$193$	−5.43765			−0.391411			−0.195705	+	0.980663i	$0.562700\pi$
$194$		0			0
$195$	4.27623	+	9.61022i	0.306227	+	0.688202i
$196$		0			0
$197$	5.95839			0.424517			0.212259	−	0.977214i	$-0.431918\pi$
$197$	5.95839			0.424517			0.212259	+	0.977214i	$0.431918\pi$
$198$		0			0
$199$	5.62062	−	9.73520i	0.398435	−	0.690110i	−0.595098	−	0.803653i	$-0.702887\pi$
$199$	5.62062	−	9.73520i	0.398435	−	0.690110i	0.993533	+	0.113543i	$0.0362200\pi$
$200$		0			0
$201$	−0.846668	−	1.90277i	−0.0597193	−	0.134211i
$202$		0			0
$203$	3.12330	−	3.41795i	0.219213	−	0.239893i
$204$		0			0
$205$	−5.06643			−0.353855
$206$		0			0
$207$	0.812267	+	2.50362i	0.0564565	+	0.174014i
$208$		0			0
$209$	1.13689	−	1.96914i	0.0786401	−	0.136209i
$210$		0			0
$211$	0.381084	+	0.660057i	0.0262349	+	0.0454402i	0.878845	−	0.477108i	$-0.158315\pi$
$211$	0.381084	+	0.660057i	0.0262349	+	0.0454402i	−0.852610	+	0.522548i	$0.824982\pi$
$212$		0			0
$213$	10.3386	+	23.2346i	0.708391	+	1.59201i
$214$		0			0
$215$	0.582381	+	1.00871i	0.0397181	+	0.0687937i
$216$		0			0
$217$	23.6030	+	5.19848i	1.60228	+	0.352896i
$218$		0			0
$219$	−1.08738	−	0.114528i	−0.0734783	−	0.00773911i
$220$		0			0
$221$	−1.01926			−0.0685626
$222$		0			0
$223$	−5.80556	+	10.0555i	−0.388769	+	0.673368i	−0.992284	−	0.123984i	$-0.960433\pi$
$223$	−5.80556	+	10.0555i	−0.388769	+	0.673368i	0.603515	+	0.797352i	$0.293766\pi$
$224$		0			0
$225$	−1.67692	−	0.357205i	−0.111794	−	0.0238137i
$226$		0			0
$227$	5.16624	+	8.94818i	0.342895	+	0.593912i	0.984969	−	0.172731i	$-0.0552591\pi$
$227$	5.16624	+	8.94818i	0.342895	+	0.593912i	−0.642074	+	0.766643i	$0.721926\pi$
$228$		0			0
$229$	1.86191	−	3.22493i	0.123039	−	0.213109i	−0.797926	−	0.602756i	$-0.794069\pi$
$229$	1.86191	−	3.22493i	0.123039	−	0.213109i	0.920965	+	0.389646i	$0.127403\pi$
$230$		0			0
$231$	−1.36824	+	1.21335i	−0.0900234	+	0.0798327i
$232$		0			0
$233$	13.3649	+	23.1488i	0.875566	+	1.51653i	0.856158	+	0.516714i	$0.172845\pi$
$233$	13.3649	+	23.1488i	0.875566	+	1.51653i	0.0194083	+	0.999812i	$0.493822\pi$
$234$		0			0
$235$	−12.3499	+	21.3906i	−0.805616	+	1.39537i
$236$		0			0
$237$	1.75141	+	3.93604i	0.113766	+	0.255673i
$238$		0			0
$239$	6.94164	+	12.0233i	0.449018	+	0.777721i	0.998322	−	0.0579007i	$-0.0184407\pi$
$239$	6.94164	+	12.0233i	0.449018	+	0.777721i	−0.549305	+	0.835622i	$0.685107\pi$
$240$		0			0
$241$	−7.45280	−	12.9086i	−0.480077	−	0.831518i	0.519662	−	0.854372i	$-0.326058\pi$
$241$	−7.45280	−	12.9086i	−0.480077	−	0.831518i	−0.999739	+	0.0228542i	$0.992725\pi$
$242$		0			0
$243$	−13.5085	+	7.77948i	−0.866571	+	0.499054i
$244$		0			0
$245$	−12.0434	+	8.48251i	−0.769423	+	0.541928i
$246$		0			0
$247$	−8.22142	+	14.2399i	−0.523116	+	0.906064i
$248$		0			0
$249$	15.8254	+	1.66681i	1.00289	+	0.105630i
$250$		0			0
$251$	22.5515			1.42344			0.711720	−	0.702464i	$-0.247917\pi$
$251$	22.5515			1.42344			0.711720	+	0.702464i	$0.247917\pi$
$252$		0			0
$253$	−0.350125			−0.0220122
$254$		0			0
$255$	−0.756917	+	1.04133i	−0.0474000	+	0.0652105i
$256$		0			0
$257$	−5.94765	+	10.3016i	−0.371004	+	0.642598i	−0.989720	−	0.143017i	$-0.954320\pi$
$257$	−5.94765	+	10.3016i	−0.371004	+	0.642598i	0.618716	+	0.785615i	$0.287653\pi$
$258$		0			0
$259$	−5.42660	−	17.1285i	−0.337193	−	1.06431i
$260$		0			0
$261$	1.62015	+	4.99374i	0.100285	+	0.309105i
$262$		0			0
$263$	−12.3030	−	21.3094i	−0.758633	−	1.31399i	−0.943548	−	0.331236i	$-0.892534\pi$
$263$	−12.3030	−	21.3094i	−0.758633	−	1.31399i	0.184915	−	0.982755i	$-0.440799\pi$
$264$		0			0
$265$	−4.37337	−	7.57490i	−0.268654	−	0.465322i
$266$		0			0
$267$	14.8553	−	20.4371i	0.909128	−	1.25073i
$268$		0			0
$269$	6.75722	−	11.7039i	0.411995	−	0.713597i	−0.583113	−	0.812391i	$-0.698165\pi$
$269$	6.75722	−	11.7039i	0.411995	−	0.713597i	0.995108	+	0.0987947i	$0.0314987\pi$
$270$		0			0
$271$	−1.34195	−	2.32433i	−0.0815177	−	0.141193i	0.822384	−	0.568932i	$-0.192643\pi$
$271$	−1.34195	−	2.32433i	−0.0815177	−	0.141193i	−0.903902	+	0.427740i	$0.859310\pi$
$272$		0			0
$273$	9.89444	−	8.77438i	0.598839	−	0.531050i
$274$		0			0
$275$	0.114035	−	0.197515i	0.00687658	−	0.0119106i
$276$		0			0
$277$	−9.52618	−	16.4998i	−0.572373	−	0.991379i	−0.996322	−	0.0856928i	$-0.972690\pi$
$277$	−9.52618	−	16.4998i	−0.572373	−	0.991379i	0.423949	−	0.905686i	$-0.360644\pi$
$278$		0			0
$279$	−18.3462	+	20.3577i	−1.09836	+	1.21878i
$280$		0			0
$281$	14.2006	−	24.5962i	0.847139	−	1.46729i	−0.0366118	−	0.999330i	$-0.511657\pi$
$281$	14.2006	−	24.5962i	0.847139	−	1.46729i	0.883751	−	0.467958i	$-0.155010\pi$
$282$		0			0
$283$	−15.4221			−0.916749			−0.458374	−	0.888759i	$-0.651568\pi$
$283$	−15.4221			−0.916749			−0.458374	+	0.888759i	$0.651568\pi$
$284$		0			0
$285$	8.44292	+	18.9743i	0.500115	+	1.12394i
$286$		0			0
$287$	1.92381	+	6.07230i	0.113559	+	0.358436i
$288$		0			0
$289$	8.43763	+	14.6144i	0.496331	+	0.859671i
$290$		0			0
$291$	27.0176	+	2.84563i	1.58380	+	0.166814i
$292$		0			0
$293$	9.02253	+	15.6275i	0.527102	+	0.912967i	0.999501	+	0.0315825i	$0.0100547\pi$
$293$	9.02253	+	15.6275i	0.527102	+	0.912967i	−0.472399	+	0.881385i	$0.656612\pi$
$294$		0			0
$295$	9.81092	−	16.9930i	0.571214	−	0.989371i
$296$		0			0
$297$	−0.429796	−	2.02857i	−0.0249393	−	0.117709i
$298$		0			0
$299$	2.53194			0.146426
$300$		0			0
$301$	0.987841	−	1.08103i	0.0569382	−	0.0623096i
$302$		0			0
$303$	0.0945638	−	0.130096i	0.00543255	−	0.00747383i
$304$		0			0
$305$	10.5978	−	18.3559i	0.606826	−	1.05105i
$306$		0			0
$307$	−7.30860			−0.417124			−0.208562	−	0.978009i	$-0.566878\pi$
$307$	−7.30860			−0.417124			−0.208562	+	0.978009i	$0.566878\pi$
$308$		0			0
$309$	−34.3047	−	3.61315i	−1.95153	−	0.205545i
$310$		0			0
$311$	−23.7792			−1.34839			−0.674197	−	0.738551i	$-0.735510\pi$
$311$	−23.7792			−1.34839			−0.674197	+	0.738551i	$0.735510\pi$
$312$		0			0
$313$	−18.2907			−1.03385			−0.516925	−	0.856031i	$-0.672923\pi$
$313$	−18.2907			−1.03385			−0.516925	+	0.856031i	$0.672923\pi$
$314$		0			0
$315$	−1.61661	−	16.6247i	−0.0910858	−	0.936697i
$316$		0			0
$317$	−4.68988			−0.263410			−0.131705	−	0.991289i	$-0.542045\pi$
$317$	−4.68988			−0.263410			−0.131705	+	0.991289i	$0.542045\pi$
$318$		0			0
$319$	−0.698360			−0.0391007
$320$		0			0
$321$	−5.89083	+	8.10430i	−0.328794	+	0.452338i
$322$		0			0
$323$	−2.01240			−0.111973
$324$		0			0
$325$	−0.824648	+	1.42833i	−0.0457432	+	0.0792296i
$326$		0			0
$327$	21.5493	+	2.26969i	1.19168	+	0.125514i
$328$		0			0
$329$	30.3268	+	6.67938i	1.67197	+	0.368246i
$330$		0			0
$331$	−11.4287			−0.628176			−0.314088	−	0.949394i	$-0.601699\pi$
$331$	−11.4287			−0.628176			−0.314088	+	0.949394i	$0.601699\pi$
$332$		0			0
$333$	19.9262	+	4.24456i	1.09195	+	0.232600i
$334$		0			0
$335$	−1.26517	+	2.19134i	−0.0691238	+	0.119726i
$336$		0			0
$337$	8.74160	+	15.1409i	0.476185	+	0.824777i	0.999628	−	0.0272840i	$-0.00868584\pi$
$337$	8.74160	+	15.1409i	0.476185	+	0.824777i	−0.523442	+	0.852061i	$0.675353\pi$
$338$		0			0
$339$	3.45049	−	4.74702i	0.187405	−	0.257823i
$340$		0			0
$341$	−1.82271	−	3.15702i	−0.0987051	−	0.170962i
$342$		0			0
$343$	14.7397	+	11.2135i	0.795868	+	0.605470i
$344$		0			0
$345$	1.88026	−	2.58677i	0.101230	−	0.139267i
$346$		0			0
$347$	14.1186			0.757925			0.378962	−	0.925412i	$-0.376281\pi$
$347$	14.1186			0.757925			0.378962	+	0.925412i	$0.376281\pi$
$348$		0			0
$349$	10.7216	−	18.5704i	0.573916	−	0.994052i	−0.422242	−	0.906483i	$-0.638757\pi$
$349$	10.7216	−	18.5704i	0.573916	−	0.994052i	0.996158	−	0.0875692i	$-0.0279099\pi$
$350$		0			0
$351$	3.10808	+	14.6696i	0.165897	+	0.783007i
$352$		0			0
$353$	15.6880	+	27.1724i	0.834987	+	1.44624i	0.894041	+	0.447985i	$0.147858\pi$
$353$	15.6880	+	27.1724i	0.834987	+	1.44624i	−0.0590538	+	0.998255i	$0.518808\pi$
$354$		0			0
$355$	15.4490	−	26.7584i	0.819946	−	1.42019i
$356$		0			0
$357$	1.53548	+	0.511782i	0.0812664	+	0.0270864i
$358$		0			0
$359$	0.313156	+	0.542402i	0.0165277	+	0.0286269i	0.874171	−	0.485618i	$-0.161405\pi$
$359$	0.313156	+	0.542402i	0.0165277	+	0.0286269i	−0.857643	+	0.514245i	$0.828072\pi$
$360$		0			0
$361$	−6.73223	+	11.6606i	−0.354328	+	0.613714i
$362$		0			0
$363$	−18.6734	−	1.96678i	−0.980101	−	0.103229i
$364$		0			0
$365$	0.664223	+	1.15047i	0.0347670	+	0.0602182i
$366$		0			0
$367$	1.62199	+	2.80936i	0.0846670	+	0.146648i	0.905249	−	0.424881i	$-0.139684\pi$
$367$	1.62199	+	2.80936i	0.0846670	+	0.146648i	−0.820582	+	0.571528i	$0.806351\pi$
$368$		0			0
$369$	−7.06414	−	1.50476i	−0.367744	−	0.0783345i
$370$		0			0
$371$	−7.41815	+	8.11796i	−0.385131	+	0.421464i
$372$		0			0
$373$	13.8013	−	23.9046i	0.714606	−	1.23773i	−0.248506	−	0.968630i	$-0.579939\pi$
$373$	13.8013	−	23.9046i	0.714606	−	1.23773i	0.963111	−	0.269103i	$-0.0867272\pi$
$374$		0			0
$375$	8.25585	+	18.5538i	0.426330	+	0.958116i
$376$		0			0
$377$	5.05021			0.260099
$378$		0			0
$379$	−12.7800			−0.656463			−0.328231	−	0.944597i	$-0.606453\pi$
$379$	−12.7800			−0.656463			−0.328231	+	0.944597i	$0.606453\pi$
$380$		0			0
$381$	−10.3754	−	23.3173i	−0.531549	−	1.19458i
$382$		0			0
$383$	2.58278	−	4.47351i	0.131974	−	0.228586i	−0.792463	−	0.609919i	$-0.791202\pi$
$383$	2.58278	−	4.47351i	0.131974	−	0.228586i	0.924437	+	0.381334i	$0.124535\pi$
$384$		0			0
$385$	2.16987	+	0.477906i	0.110587	+	0.0243564i
$386$		0			0
$387$	0.512423	+	1.57943i	0.0260479	+	0.0802867i
$388$		0			0
$389$	−16.4707	−	28.5280i	−0.835095	−	1.44643i	−0.893953	−	0.448161i	$-0.852079\pi$
$389$	−16.4707	−	28.5280i	−0.835095	−	1.44643i	0.0588576	−	0.998266i	$-0.481254\pi$
$390$		0			0
$391$	0.154939	+	0.268362i	0.00783560	+	0.0135717i
$392$		0			0
$393$	−23.9566	−	2.52323i	−1.20845	−	0.127280i
$394$		0			0
$395$	2.61712	−	4.53299i	0.131682	−	0.228079i
$396$		0			0
$397$	−0.411705	−	0.713095i	−0.0206629	−	0.0357892i	0.855509	−	0.517788i	$-0.173244\pi$
$397$	−0.411705	−	0.713095i	−0.0206629	−	0.0357892i	−0.876172	+	0.481999i	$0.839911\pi$
$398$		0			0
$399$	19.5354	−	17.3240i	0.977995	−	0.867285i
$400$		0			0
$401$	9.86923	−	17.0940i	0.492846	−	0.853634i	−0.507120	−	0.861875i	$-0.669290\pi$
$401$	9.86923	−	17.0940i	0.492846	−	0.853634i	0.999966	+	0.00824153i	$0.00262339\pi$
$402$		0			0
$403$	13.1809	+	22.8301i	0.656590	+	1.13725i
$404$		0			0
$405$	17.2954	+	7.71854i	0.859416	+	0.383537i
$406$		0			0
$407$	−1.35504	+	2.34700i	−0.0671670	+	0.116337i
$408$		0			0
$409$	−25.2551			−1.24879			−0.624393	−	0.781110i	$-0.714654\pi$
$409$	−25.2551			−1.24879			−0.624393	+	0.781110i	$0.714654\pi$
$410$		0			0
$411$	−14.8251	+	20.3956i	−0.731266	+	1.00604i
$412$		0			0
$413$	−24.0921	−	5.30621i	−1.18550	−	0.261101i
$414$		0			0
$415$	−9.66688	−	16.7435i	−0.474528	−	0.821907i
$416$		0			0
$417$	−7.41372	+	10.1994i	−0.363052	+	0.499468i
$418$		0			0
$419$	0.406717	+	0.704455i	0.0198694	+	0.0344149i	0.875789	−	0.482694i	$-0.160342\pi$
$419$	0.406717	+	0.704455i	0.0198694	+	0.0344149i	−0.855920	+	0.517109i	$0.827008\pi$
$420$		0			0
$421$	5.12114	−	8.87008i	0.249589	−	0.432301i	−0.713823	−	0.700326i	$-0.753038\pi$
$421$	5.12114	−	8.87008i	0.249589	−	0.432301i	0.963412	+	0.268025i	$0.0863711\pi$
$422$		0			0
$423$	−23.5726	+	26.1570i	−1.14614	+	1.27180i
$424$		0			0
$425$	−0.201854			−0.00979134
$426$		0			0
$427$	−26.0243	−	5.73177i	−1.25941	−	0.277380i
$428$		0			0
$429$	−1.98372	−	0.208936i	−0.0957749	−	0.0100875i
$430$		0			0
$431$	16.3348	−	28.2928i	0.786822	−	1.36281i	−0.141083	−	0.989998i	$-0.545059\pi$
$431$	16.3348	−	28.2928i	0.786822	−	1.36281i	0.927905	−	0.372817i	$-0.121608\pi$
$432$		0			0
$433$	−14.3151			−0.687941			−0.343970	−	0.938980i	$-0.611772\pi$
$433$	−14.3151			−0.687941			−0.343970	+	0.938980i	$0.611772\pi$
$434$		0			0
$435$	3.75037	−	5.15957i	0.179817	−	0.247382i
$436$		0			0
$437$	4.99901			0.239135
$438$		0			0
$439$	−9.86660			−0.470907			−0.235453	−	0.971886i	$-0.575658\pi$
$439$	−9.86660			−0.470907			−0.235453	+	0.971886i	$0.575658\pi$
$440$		0			0
$441$	−19.3115	+	8.25026i	−0.919594	+	0.392870i
$442$		0			0
$443$	37.2801			1.77123			0.885615	−	0.464419i	$-0.153737\pi$
$443$	37.2801			1.77123			0.885615	+	0.464419i	$0.153737\pi$
$444$		0			0
$445$	−30.6972			−1.45519
$446$		0			0
$447$	−1.24308	−	0.130928i	−0.0587958	−	0.00619267i
$448$		0			0
$449$	−36.2926			−1.71276			−0.856378	−	0.516350i	$-0.827290\pi$
$449$	−36.2926			−1.71276			−0.856378	+	0.516350i	$0.827290\pi$
$450$		0			0
$451$	0.480382	−	0.832046i	0.0226203	−	0.0391795i
$452$		0			0
$453$	−22.2051	+	30.5487i	−1.04329	+	1.43530i
$454$		0			0
$455$	−15.6915	−	3.45599i	−0.735627	−	0.162019i
$456$		0			0
$457$	−13.1943			−0.617205			−0.308602	−	0.951191i	$-0.599861\pi$
$457$	−13.1943			−0.617205			−0.308602	+	0.951191i	$0.599861\pi$
$458$		0			0
$459$	−1.36465	+	1.22712i	−0.0636965	+	0.0572771i
$460$		0			0
$461$	10.1326	−	17.5502i	0.471924	−	0.817396i	−0.527560	−	0.849518i	$-0.676893\pi$
$461$	10.1326	−	17.5502i	0.471924	−	0.817396i	0.999484	+	0.0321215i	$0.0102263\pi$
$462$		0			0
$463$	12.7106	+	22.0154i	0.590712	+	1.02314i	0.994137	+	0.108131i	$0.0344866\pi$
$463$	12.7106	+	22.0154i	0.590712	+	1.02314i	−0.403424	+	0.915013i	$0.632180\pi$
$464$		0			0
$465$	33.1129	+	3.48762i	1.53557	+	0.161734i
$466$		0			0
$467$	−4.40661	−	7.63248i	−0.203914	−	0.353189i	0.745872	−	0.666089i	$-0.232033\pi$
$467$	−4.40661	−	7.63248i	−0.203914	−	0.353189i	−0.949786	+	0.312900i	$0.898700\pi$
$468$		0			0
$469$	3.10681	+	0.684265i	0.143459	+	0.0315964i
$470$		0			0
$471$	−3.64727	−	8.19671i	−0.168057	−	0.377685i
$472$		0			0
$473$	−0.220878			−0.0101560
$474$		0			0
$475$	−1.62817	+	2.82008i	−0.0747056	+	0.129394i
$476$		0			0
$477$	−3.84802	−	11.8606i	−0.176189	−	0.543061i
$478$		0			0
$479$	−12.1343	−	21.0173i	−0.554433	−	0.960305i	−0.997947	−	0.0640383i	$-0.979602\pi$
$479$	−12.1343	−	21.0173i	−0.554433	−	0.960305i	0.443515	−	0.896267i	$-0.353731\pi$
$480$		0			0
$481$	9.79902	−	16.9724i	0.446797	−	0.773875i
$482$		0			0
$483$	−3.81430	−	1.27132i	−0.173557	−	0.0578470i
$484$		0			0
$485$	−16.5036	−	28.5851i	−0.749391	−	1.29798i
$486$		0			0
$487$	−5.37220	+	9.30492i	−0.243438	+	0.421646i	−0.961691	−	0.274135i	$-0.911608\pi$
$487$	−5.37220	+	9.30492i	−0.243438	+	0.421646i	0.718254	+	0.695781i	$0.244942\pi$
$488$		0			0
$489$	5.37513	−	7.39483i	0.243072	−	0.334406i
$490$		0			0
$491$	11.3934	+	19.7340i	0.514179	+	0.890584i	0.999865	+	0.0164507i	$0.00523665\pi$
$491$	11.3934	+	19.7340i	0.514179	+	0.890584i	−0.485686	+	0.874134i	$0.661430\pi$
$492$		0			0
$493$	0.309042	+	0.535276i	0.0139185	+	0.0241076i
$494$		0			0
$495$	−1.68660	+	1.87152i	−0.0758073	+	0.0841185i
$496$		0			0
$497$	−37.9372	−	8.35553i	−1.70171	−	0.374797i
$498$		0			0
$499$	−11.5755	+	20.0493i	−0.518189	+	0.897530i	0.481588	+	0.876398i	$0.340060\pi$
$499$	−11.5755	+	20.0493i	−0.518189	+	0.897530i	−0.999777	+	0.0211317i	$0.993273\pi$
$500$		0			0
$501$	−13.9255	+	19.1581i	−0.622147	+	0.855919i
$502$		0			0
$503$	9.43360			0.420623			0.210312	−	0.977634i	$-0.432552\pi$
$503$	9.43360			0.420623			0.210312	+	0.977634i	$0.432552\pi$
$504$		0			0
$505$	−0.195408			−0.00869555
$506$		0			0
$507$	−8.04747	−	0.847601i	−0.357401	−	0.0376433i
$508$		0			0
$509$	4.72981	−	8.19228i	0.209645	−	0.363116i	−0.741957	−	0.670447i	$-0.766102\pi$
$509$	4.72981	−	8.19228i	0.209645	−	0.363116i	0.951603	+	0.307331i	$0.0994357\pi$
$510$		0			0
$511$	1.12666	−	1.23295i	0.0498405	−	0.0545424i
$512$		0			0
$513$	6.13654	+	28.9635i	0.270935	+	1.27877i
$514$		0			0
$515$	20.9549	+	36.2950i	0.923385	+	1.59935i
$516$		0			0
$517$	−2.34195	−	4.05637i	−0.102999	−	0.178399i
$518$		0			0
$519$	−14.2113	−	31.9378i	−0.623805	−	1.40191i
$520$		0			0
$521$	−14.3368	+	24.8320i	−0.628105	+	1.08791i	0.359826	+	0.933019i	$0.382836\pi$
$521$	−14.3368	+	24.8320i	−0.628105	+	1.08791i	−0.987932	+	0.154891i	$0.950497\pi$
$522$		0			0
$523$	−13.5104	−	23.4006i	−0.590767	−	1.02324i	−0.994129	−	0.108198i	$-0.965492\pi$
$523$	−13.5104	−	23.4006i	−0.590767	−	1.02324i	0.403362	−	0.915040i	$-0.367841\pi$
$524$		0			0
$525$	1.95950	−	1.73768i	0.0855195	−	0.0758386i
$526$		0			0
$527$	−1.61319	+	2.79412i	−0.0702715	+	0.121714i
$528$		0			0
$529$	11.1151	+	19.2519i	0.483266	+	0.837041i
$530$		0			0
$531$	18.7264	−	20.7795i	0.812658	−	0.901755i
$532$		0			0
$533$	−3.47389	+	6.01696i	−0.150471	+	0.260624i
$534$		0			0
$535$	12.1729			0.526280
$536$		0			0
$537$	−43.3965	−	4.57075i	−1.87270	−	0.197242i
$538$		0			0
$539$	−0.251148	−	2.78214i	−0.0108177	−	0.119835i
$540$		0			0
$541$	−1.52907	−	2.64842i	−0.0657397	−	0.113864i	0.831282	−	0.555851i	$-0.187607\pi$
$541$	−1.52907	−	2.64842i	−0.0657397	−	0.113864i	−0.897022	+	0.441986i	$0.854274\pi$
$542$		0			0
$543$	12.1687	+	27.3473i	0.522207	+	1.17359i
$544$		0			0
$545$	−13.1633	−	22.7996i	−0.563856	−	0.976627i
$546$		0			0
$547$	3.58144	−	6.20323i	0.153131	−	0.265231i	−0.779246	−	0.626719i	$-0.784398\pi$
$547$	3.58144	−	6.20323i	0.153131	−	0.265231i	0.932377	+	0.361487i	$0.117731\pi$
$548$		0			0
$549$	20.2283	−	22.4461i	0.863322	−	0.957974i
$550$		0			0
$551$	9.97105			0.424781
$552$		0			0
$553$	−6.42672	−	1.41546i	−0.273292	−	0.0601916i
$554$		0			0
$555$	−10.0630	−	22.6152i	−0.427152	−	0.959963i
$556$		0			0
$557$	−14.3518	+	24.8580i	−0.608104	+	1.05327i	0.383449	+	0.923562i	$0.374736\pi$
$557$	−14.3518	+	24.8580i	−0.608104	+	1.05327i	−0.991553	+	0.129704i	$0.958597\pi$
$558$		0			0
$559$	1.59729			0.0675580
$560$		0			0
$561$	−0.0992463	−	0.223042i	−0.00419018	−	0.00941684i
$562$		0			0
$563$	35.7719			1.50761			0.753803	−	0.657101i	$-0.228218\pi$
$563$	35.7719			1.50761			0.753803	+	0.657101i	$0.228218\pi$
$564$		0			0
$565$	−7.13016			−0.299968
$566$		0			0
$567$	2.68358	−	23.6601i	0.112700	−	0.993629i
$568$		0			0
$569$	−25.2002			−1.05645			−0.528223	−	0.849106i	$-0.677142\pi$
$569$	−25.2002			−1.05645			−0.528223	+	0.849106i	$0.677142\pi$
$570$		0			0
$571$	−6.04938			−0.253159			−0.126579	−	0.991956i	$-0.540400\pi$
$571$	−6.04938			−0.253159			−0.126579	+	0.991956i	$0.540400\pi$
$572$		0			0
$573$	3.53408	+	7.94234i	0.147638	+	0.331796i
$574$		0			0
$575$	0.501425			0.0209109
$576$		0			0
$577$	9.57977	−	16.5926i	0.398811	−	0.690761i	−0.594768	−	0.803897i	$-0.702756\pi$
$577$	9.57977	−	16.5926i	0.398811	−	0.690761i	0.993580	+	0.113136i	$0.0360896\pi$
$578$		0			0
$579$	3.82888	+	8.60487i	0.159123	+	0.357606i
$580$		0			0
$581$	−16.3970	+	17.9439i	−0.680264	+	0.744439i
$582$		0			0
$583$	1.65868			0.0686953
$584$		0			0
$585$	12.1967	−	13.5339i	0.504272	−	0.559559i
$586$		0			0
$587$	18.4147	−	31.8953i	0.760058	−	1.31646i	−0.182763	−	0.983157i	$-0.558504\pi$
$587$	18.4147	−	31.8953i	0.760058	−	1.31646i	0.942820	−	0.333301i	$-0.108163\pi$
$588$		0			0
$589$	26.0242	+	45.0753i	1.07231	+	1.85730i
$590$		0			0
$591$	−4.19555	−	9.42891i	−0.172582	−	0.387854i
$592$		0			0
$593$	8.97285	+	15.5414i	0.368471	+	0.638210i	0.989327	−	0.145715i	$-0.0465481\pi$
$593$	8.97285	+	15.5414i	0.368471	+	0.638210i	−0.620856	+	0.783925i	$0.713215\pi$
$594$		0			0
$595$	−0.593918	−	1.87464i	−0.0243482	−	0.0768526i
$596$		0			0
$597$	−19.3633	−	2.03944i	−0.792487	−	0.0834688i
$598$		0			0
$599$	−40.4913			−1.65443			−0.827215	−	0.561885i	$-0.810076\pi$
$599$	−40.4913			−1.65443			−0.827215	+	0.561885i	$0.810076\pi$
$600$		0			0
$601$	13.2589	−	22.9651i	0.540841	−	0.936765i	−0.458015	−	0.888945i	$-0.651439\pi$
$601$	13.2589	−	22.9651i	0.540841	−	0.936765i	0.998856	−	0.0478200i	$-0.0152274\pi$
$602$		0			0
$603$	−2.41488	+	2.67964i	−0.0983414	+	0.109123i
$604$		0			0
$605$	11.4066	+	19.7568i	0.463745	+	0.803230i
$606$		0			0
$607$	21.0848	−	36.5200i	0.855806	−	1.48230i	−0.0200897	−	0.999798i	$-0.506395\pi$
$607$	21.0848	−	36.5200i	0.855806	−	1.48230i	0.875895	−	0.482501i	$-0.160271\pi$
$608$		0			0
$609$	−7.60802	−	2.53578i	−0.308292	−	0.102755i
$610$		0			0
$611$	16.9358	+	29.3337i	0.685151	+	1.18672i
$612$		0			0
$613$	−0.700827	+	1.21387i	−0.0283061	+	0.0490277i	−0.879831	−	0.475286i	$-0.842345\pi$
$613$	−0.700827	+	1.21387i	−0.0283061	+	0.0490277i	0.851525	+	0.524313i	$0.175678\pi$
$614$		0			0
$615$	3.56749	+	8.01742i	0.143855	+	0.323294i
$616$		0			0
$617$	−6.76787	−	11.7223i	−0.272464	−	0.471922i	0.697028	−	0.717044i	$-0.254505\pi$
$617$	−6.76787	−	11.7223i	−0.272464	−	0.471922i	−0.969492	+	0.245122i	$0.921172\pi$
$618$		0			0
$619$	14.9122	+	25.8288i	0.599374	+	1.03815i	0.992914	+	0.118838i	$0.0379171\pi$
$619$	14.9122	+	25.8288i	0.599374	+	1.03815i	−0.393540	+	0.919308i	$0.628750\pi$
$620$		0			0
$621$	3.38994	−	3.04829i	0.136033	−	0.122324i
$622$		0			0
$623$	11.6562	+	36.7917i	0.466997	+	1.47403i
$624$		0			0
$625$	10.9079	−	18.8930i	0.436316	−	0.755722i
$626$		0			0
$627$	−3.91662	−	0.412519i	−0.156415	−	0.0164744i
$628$		0			0
$629$	2.39856			0.0956369
$630$		0			0
$631$	6.84708			0.272578			0.136289	−	0.990669i	$-0.456482\pi$
$631$	6.84708			0.272578			0.136289	+	0.990669i	$0.456482\pi$
$632$		0			0
$633$	0.776177	−	1.06782i	0.0308503	−	0.0424422i
$634$		0			0
$635$	−15.5040	+	26.8536i	−0.615256	+	1.06565i
$636$		0			0
$637$	1.81618	+	20.1191i	0.0719598	+	0.797147i
$638$		0			0
$639$	29.4880	−	32.7209i	1.16653	−	1.29442i
$640$		0			0
$641$	−16.1209	−	27.9221i	−0.636735	−	1.10286i	−0.986145	−	0.165888i	$-0.946951\pi$
$641$	−16.1209	−	27.9221i	−0.636735	−	1.10286i	0.349409	−	0.936970i	$-0.386382\pi$
$642$		0			0
$643$	1.16002	+	2.00921i	0.0457465	+	0.0792353i	0.887992	−	0.459859i	$-0.152100\pi$
$643$	1.16002	+	2.00921i	0.0457465	+	0.0792353i	−0.842245	+	0.539094i	$0.818767\pi$
$644$		0			0
$645$	1.18617	−	1.63187i	0.0467055	−	0.0642550i
$646$		0			0
$647$	1.06813	−	1.85005i	0.0419924	−	0.0727329i	−0.844265	−	0.535925i	$-0.819963\pi$
$647$	1.06813	−	1.85005i	0.0419924	−	0.0727329i	0.886258	+	0.463193i	$0.153296\pi$
$648$		0			0
$649$	1.86048	+	3.22244i	0.0730302	+	0.126492i
$650$		0			0
$651$	−8.39348	−	41.0113i	−0.328967	−	1.60736i
$652$		0			0
$653$	−1.51932	+	2.63155i	−0.0594558	+	0.102980i	−0.894221	−	0.447625i	$-0.852270\pi$
$653$	−1.51932	+	2.63155i	−0.0594558	+	0.102980i	0.834765	+	0.550606i	$0.185603\pi$
$654$		0			0
$655$	14.6338	+	25.3465i	0.571790	+	0.990370i
$656$		0			0
$657$	0.584433	+	1.80138i	0.0228009	+	0.0702785i
$658$		0			0
$659$	−19.8000	+	34.2946i	−0.771298	+	1.33593i	0.165554	+	0.986201i	$0.447059\pi$
$659$	−19.8000	+	34.2946i	−0.771298	+	1.33593i	−0.936852	+	0.349726i	$0.886275\pi$
$660$		0			0
$661$	6.12398			0.238195			0.119098	−	0.992883i	$-0.462000\pi$
$661$	6.12398			0.238195			0.119098	+	0.992883i	$0.462000\pi$
$662$		0			0
$663$	0.717702	+	1.61293i	0.0278732	+	0.0626411i
$664$		0			0
$665$	−30.9810	−	6.82345i	−1.20139	−	0.264602i
$666$		0			0
$667$	−0.767691	−	1.32968i	−0.0297251	−	0.0514854i
$668$		0			0
$669$	20.0004	+	2.10655i	0.773261	+	0.0814439i
$670$		0			0
$671$	2.00969	+	3.48089i	0.0775832	+	0.134378i
$672$		0			0
$673$	−4.36248	+	7.55603i	−0.168161	+	0.291264i	−0.937773	−	0.347248i	$-0.887116\pi$
$673$	−4.36248	+	7.55603i	−0.168161	+	0.291264i	0.769612	+	0.638512i	$0.220450\pi$
$674$		0			0
$675$	0.615524	+	2.90518i	0.0236915	+	0.111820i
$676$		0			0
$677$	14.9601			0.574965			0.287482	−	0.957786i	$-0.407182\pi$
$677$	14.9601			0.574965			0.287482	+	0.957786i	$0.407182\pi$
$678$		0			0
$679$	−27.9936	+	30.6345i	−1.07430	+	1.17564i
$680$		0			0
$681$	10.5224	−	14.4762i	0.403219	−	0.554728i
$682$		0			0
$683$	−8.89558	+	15.4076i	−0.340380	+	0.589555i	−0.984503	−	0.175366i	$-0.943889\pi$
$683$	−8.89558	+	15.4076i	−0.340380	+	0.589555i	0.644123	+	0.764922i	$0.277222\pi$
$684$		0			0
$685$	30.6347			1.17049
$686$		0			0
$687$	−6.41437	−	0.675595i	−0.244724	−	0.0257756i
$688$		0			0
$689$	−11.9948			−0.456964
$690$		0			0
$691$	−29.5389			−1.12371			−0.561856	−	0.827235i	$-0.689913\pi$
$691$	−29.5389			−1.12371			−0.561856	+	0.827235i	$0.689913\pi$
$692$		0			0
$693$	2.88352	+	1.31081i	0.109536	+	0.0497935i
$694$		0			0
$695$	15.3198			0.581115
$696$		0			0
$697$	−0.850324			−0.0322083
$698$		0			0
$699$	27.2212	−	37.4495i	1.02960	−	1.41647i
$700$		0			0
$701$	27.7740			1.04901			0.524504	−	0.851408i	$-0.324251\pi$
$701$	27.7740			1.04901			0.524504	+	0.851408i	$0.324251\pi$
$702$		0			0
$703$	19.3470	−	33.5100i	0.729687	−	1.26385i
$704$		0			0
$705$	42.5458	+	4.48114i	1.60237	+	0.168770i
$706$		0			0
$707$	0.0741998	+	0.234204i	0.00279057	+	0.00880814i
$708$		0			0
$709$	47.0984			1.76882			0.884409	−	0.466712i	$-0.154562\pi$
$709$	47.0984			1.76882			0.884409	+	0.466712i	$0.154562\pi$
$710$		0			0
$711$	4.99539	−	5.54307i	0.187342	−	0.207881i
$712$		0			0
$713$	4.00732	−	6.94088i	0.150075	−	0.259938i
$714$		0			0
$715$	1.21175	+	2.09881i	0.0453169	+	0.0784912i
$716$		0			0
$717$	14.1385	−	19.4510i	0.528011	−	0.726411i
$718$		0			0
$719$	1.63394	+	2.83007i	0.0609357	+	0.105544i	0.894884	−	0.446299i	$-0.147258\pi$
$719$	1.63394	+	2.83007i	0.0609357	+	0.105544i	−0.833948	+	0.551843i	$0.813925\pi$
$720$		0			0
$721$	35.5440	−	38.8971i	1.32373	−	1.44860i
$722$		0			0
$723$	−15.1796	+	20.8833i	−0.564534	+	0.776658i
$724$		0			0
$725$	1.00014			0.0371444
$726$		0			0
$727$	−6.37047	+	11.0340i	−0.236268	+	0.409228i	−0.959640	−	0.281230i	$-0.909258\pi$
$727$	−6.37047	+	11.0340i	−0.236268	+	0.409228i	0.723373	+	0.690458i	$0.242591\pi$
$728$		0			0
$729$	21.8226	+	15.8988i	0.808246	+	0.588845i
$730$		0			0
$731$	0.0977441	+	0.169298i	0.00361520	+	0.00626170i
$732$		0			0
$733$	−4.58858	+	7.94765i	−0.169483	+	0.293553i	−0.938238	−	0.345990i	$-0.887543\pi$
$733$	−4.58858	+	7.94765i	−0.169483	+	0.293553i	0.768755	+	0.639543i	$0.220876\pi$
$734$		0			0
$735$	21.9035	+	13.0853i	0.807923	+	0.482657i
$736$		0			0
$737$	−0.239919	−	0.415552i	−0.00883754	−	0.0153071i
$738$		0			0
$739$	−23.3467	+	40.4377i	−0.858823	+	1.48752i	0.0142303	+	0.999899i	$0.495470\pi$
$739$	−23.3467	+	40.4377i	−0.858823	+	1.48752i	−0.873053	+	0.487626i	$0.837863\pi$
$740$		0			0
$741$	28.3232	+	2.98314i	1.04048	+	0.109588i
$742$		0			0
$743$	−7.62654	−	13.2095i	−0.279790	−	0.484611i	0.691542	−	0.722336i	$-0.256932\pi$
$743$	−7.62654	−	13.2095i	−0.279790	−	0.484611i	−0.971333	+	0.237725i	$0.923598\pi$
$744$		0			0
$745$	0.759333	+	1.31520i	0.0278198	+	0.0481853i
$746$		0			0
$747$	−8.50565	−	26.2167i	−0.311205	−	0.959218i
$748$		0			0
$749$	−4.62226	−	14.5897i	−0.168894	−	0.533095i
$750$		0			0
$751$	−3.17443	+	5.49828i	−0.115837	+	0.200635i	−0.918114	−	0.396317i	$-0.870288\pi$
$751$	−3.17443	+	5.49828i	−0.115837	+	0.200635i	0.802277	+	0.596952i	$0.203622\pi$
$752$		0			0
$753$	−15.8795	−	35.6869i	−0.578681	−	1.30050i
$754$		0			0
$755$	45.8850			1.66993
$756$		0			0
$757$	28.4278			1.03323			0.516614	−	0.856219i	$-0.327192\pi$
$757$	28.4278			1.03323			0.516614	+	0.856219i	$0.327192\pi$
$758$		0			0
$759$	0.246538	+	0.554059i	0.00894876	+	0.0201111i
$760$		0			0
$761$	9.03437	−	15.6480i	0.327496	−	0.567239i	−0.654519	−	0.756046i	$-0.727129\pi$
$761$	9.03437	−	15.6480i	0.327496	−	0.567239i	0.982014	+	0.188807i	$0.0604620\pi$
$762$		0			0
$763$	−22.3278	+	24.4341i	−0.808320	+	0.884575i
$764$		0			0
$765$	2.18084	+	0.464548i	0.0788484	+	0.0167958i
$766$		0			0
$767$	−13.4541	−	23.3032i	−0.485799	−	0.841429i
$768$		0			0
$769$	−1.72471	−	2.98728i	−0.0621946	−	0.107724i	0.833252	−	0.552894i	$-0.186477\pi$
$769$	−1.72471	−	2.98728i	−0.0621946	−	0.107724i	−0.895446	+	0.445170i	$0.853143\pi$
$770$		0			0
$771$	20.4899	+	2.15810i	0.737926	+	0.0777222i
$772$		0			0
$773$	−20.1837	+	34.9592i	−0.725957	+	1.25740i	0.232621	+	0.972567i	$0.425270\pi$
$773$	−20.1837	+	34.9592i	−0.725957	+	1.25740i	−0.958579	+	0.284828i	$0.908064\pi$
$774$		0			0
$775$	2.61036	+	4.52127i	0.0937668	+	0.162409i
$776$		0			0
$777$	−23.2841	+	20.6483i	−0.835311	+	0.740753i
$778$		0			0
$779$	−6.85880	+	11.8798i	−0.245742	+	0.425638i
$780$		0			0
$781$	2.92964	+	5.07429i	0.104831	+	0.181572i
$782$		0			0
$783$	6.76158	−	6.08013i	0.241639	−	0.217286i
$784$		0			0
$785$	−5.45010	+	9.43985i	−0.194522	+	0.336923i
$786$		0			0
$787$	18.3206			0.653060			0.326530	−	0.945187i	$-0.394121\pi$
$787$	18.3206			0.653060			0.326530	+	0.945187i	$0.394121\pi$
$788$		0			0
$789$	−25.0582	+	34.4738i	−0.892095	+	1.22730i
$790$		0			0
$791$	2.70744	+	8.54575i	0.0962656	+	0.303852i
$792$		0			0
$793$	−14.5331	−	25.1721i	−0.516086	−	0.893888i
$794$		0			0
$795$	−8.90751	+	12.2545i	−0.315917	+	0.434622i
$796$		0			0
$797$	−4.86884	−	8.43307i	−0.172463	−	0.298715i	0.766817	−	0.641865i	$-0.221839\pi$
$797$	−4.86884	−	8.43307i	−0.172463	−	0.298715i	−0.939280	+	0.343151i	$0.888506\pi$
$798$		0			0
$799$	−2.07274	+	3.59009i	−0.0733283	+	0.127008i
$800$		0			0
$801$	−42.8012	−	9.11723i	−1.51231	−	0.322141i
$802$		0			0
$803$	−0.251918			−0.00888998
$804$		0			0
$805$	1.47535	+	4.65679i	0.0519993	+	0.164130i
$806$		0			0
$807$	−23.2789	−	2.45186i	−0.819458	−	0.0863095i
$808$		0			0
$809$	−5.98714	+	10.3700i	−0.210497	+	0.364591i	−0.951870	−	0.306502i	$-0.900841\pi$
$809$	−5.98714	+	10.3700i	−0.210497	+	0.364591i	0.741373	+	0.671093i	$0.234175\pi$
$810$		0			0
$811$	4.05517			0.142396			0.0711982	−	0.997462i	$-0.477318\pi$
$811$	4.05517			0.142396			0.0711982	+	0.997462i	$0.477318\pi$
$812$		0			0
$813$	−2.73323	+	3.76024i	−0.0958586	+	0.131877i
$814$		0			0
$815$	−11.1072			−0.389070
$816$		0			0
$817$	3.15365			0.110332
$818$		0			0
$819$	−20.8522	−	9.47915i	−0.728636	−	0.331228i
$820$		0			0
$821$	7.98513			0.278683			0.139341	−	0.990244i	$-0.455501\pi$
$821$	7.98513			0.278683			0.139341	+	0.990244i	$0.455501\pi$
$822$		0			0
$823$	47.5802			1.65854			0.829270	−	0.558847i	$-0.188756\pi$
$823$	47.5802			1.65854			0.829270	+	0.558847i	$0.188756\pi$
$824$		0			0
$825$	−0.392856	−	0.0413776i	−0.0136775	−	0.00144058i
$826$		0			0
$827$	−29.2725			−1.01790			−0.508952	−	0.860795i	$-0.669967\pi$
$827$	−29.2725			−1.01790			−0.508952	+	0.860795i	$0.669967\pi$
$828$		0			0
$829$	3.15249	−	5.46028i	0.109491	−	0.189643i	−0.806073	−	0.591816i	$-0.798411\pi$
$829$	3.15249	−	5.46028i	0.109491	−	0.189643i	0.915564	+	0.402172i	$0.131745\pi$
$830$		0			0
$831$	−19.4026	+	26.6931i	−0.673067	+	0.925972i
$832$		0			0
$833$	−2.02130	+	1.42366i	−0.0700339	+	0.0493270i
$834$		0			0
$835$	28.7760			0.995833
$836$		0			0
$837$	45.1336	+	14.6975i	1.56004	+	0.508020i
$838$		0			0
$839$	−0.501711	+	0.868989i	−0.0173210	+	0.0300008i	−0.874556	−	0.484925i	$-0.838847\pi$
$839$	−0.501711	+	0.868989i	−0.0173210	+	0.0300008i	0.857235	+	0.514925i	$0.172180\pi$
$840$		0			0
$841$	12.9688	+	22.4626i	0.447199	+	0.774571i
$842$		0			0
$843$	−48.9218	−	5.15270i	−1.68496	−	0.177468i
$844$		0			0
$845$	4.91578	+	8.51438i	0.169108	+	0.292904i
$846$		0			0
$847$	19.3480	−	21.1733i	0.664806	−	0.727522i
$848$		0			0
$849$	10.8594	+	24.4049i	0.372692	+	0.837573i
$850$		0			0
$851$	−5.95827			−0.204247
$852$		0			0
$853$	20.0519	−	34.7309i	0.686565	−	1.18916i	−0.286378	−	0.958117i	$-0.592451\pi$
$853$	20.0519	−	34.7309i	0.686565	−	1.18916i	0.972942	−	0.231048i	$-0.0742154\pi$
$854$		0			0
$855$	24.0810	−	26.7212i	0.823553	−	0.913845i
$856$		0			0
$857$	18.7388	+	32.4566i	0.640106	+	1.10870i	0.985409	+	0.170205i	$0.0544428\pi$
$857$	18.7388	+	32.4566i	0.640106	+	1.10870i	−0.345303	+	0.938491i	$0.612224\pi$
$858$		0			0
$859$	−12.2516	+	21.2204i	−0.418019	+	0.724031i	−0.995740	−	0.0922036i	$-0.970609\pi$
$859$	−12.2516	+	21.2204i	−0.418019	+	0.724031i	0.577721	+	0.816234i	$0.303942\pi$
$860$		0			0
$861$	8.25454	−	7.32012i	0.281314	−	0.249469i
$862$		0			0
$863$	9.79806	+	16.9707i	0.333530	+	0.577691i	0.983201	−	0.182524i	$-0.0584269\pi$
$863$	9.79806	+	16.9707i	0.333530	+	0.577691i	−0.649671	+	0.760215i	$0.725094\pi$
$864$		0			0
$865$	−21.2359	+	36.7816i	−0.722041	+	1.25061i
$866$		0			0
$867$	17.1854	−	23.6428i	0.583648	−	0.802953i
$868$		0			0
$869$	0.496294	+	0.859607i	0.0168356	+	0.0291602i
$870$		0			0
$871$	1.73498	+	3.00508i	0.0587876	+	0.101823i
$872$		0			0
$873$	−14.5211	−	44.7580i	−0.491466	−	1.51483i
$874$		0			0
$875$	−30.2945	−	6.67226i	−1.02414	−	0.225564i
$876$		0			0
$877$	−17.1134	+	29.6414i	−0.577880	+	1.00092i	0.417842	+	0.908520i	$0.362786\pi$
$877$	−17.1134	+	29.6414i	−0.577880	+	1.00092i	−0.995722	+	0.0923977i	$0.970547\pi$
$878$		0			0
$879$	18.3767	−	25.2818i	0.619832	−	0.852733i
$880$		0			0
$881$	−25.2818			−0.851764			−0.425882	−	0.904779i	$-0.640036\pi$
$881$	−25.2818			−0.851764			−0.425882	+	0.904779i	$0.640036\pi$
$882$		0			0
$883$	−45.4688			−1.53015			−0.765073	−	0.643943i	$-0.777297\pi$
$883$	−45.4688			−1.53015			−0.765073	+	0.643943i	$0.777297\pi$
$884$		0			0
$885$	−33.7991	−	3.55989i	−1.13614	−	0.119664i
$886$		0			0
$887$	−5.41504	+	9.37912i	−0.181819	+	0.314920i	−0.942500	−	0.334206i	$-0.891532\pi$
$887$	−5.41504	+	9.37912i	−0.181819	+	0.314920i	0.760681	+	0.649126i	$0.224865\pi$
$888$		0			0
$889$	38.0722	+	8.38527i	1.27690	+	0.281233i
$890$		0			0
$891$	−2.90749	+	2.10854i	−0.0974046	+	0.0706386i
$892$		0			0
$893$	33.4378	+	57.9160i	1.11895	+	1.93809i
$894$		0			0
$895$	26.5087	+	45.9143i	0.886086	+	1.53475i
$896$		0			0
$897$	−1.78284	−	4.00669i	−0.0595274	−	0.133779i
$898$		0			0
$899$	7.99301	−	13.8443i	0.266582	−	0.461733i
$900$		0			0
$901$	−0.734005	−	1.27133i	−0.0244533	−	0.0423543i
$902$		0			0
$903$	−2.40627	−	0.802019i	−0.0800757	−	0.0266895i
$904$		0			0
$905$	18.1836	−	31.4949i	0.604443	−	1.04693i
$906$		0			0
$907$	−2.00841	−	3.47868i	−0.0666883	−	0.115508i	0.830753	−	0.556641i	$-0.187910\pi$
$907$	−2.00841	−	3.47868i	−0.0666883	−	0.115508i	−0.897442	+	0.441133i	$0.854577\pi$
$908$		0			0
$909$	−0.272458	−	0.0580373i	−0.00903688	−	0.00192498i
$910$		0			0
$911$	−8.43681	+	14.6130i	−0.279524	+	0.484150i	−0.971266	−	0.237995i	$-0.923510\pi$
$911$	−8.43681	+	14.6130i	−0.279524	+	0.484150i	0.691743	+	0.722144i	$0.256843\pi$
$912$		0			0
$913$	3.66633			0.121338
$914$		0			0
$915$	−36.5098	−	3.84540i	−1.20698	−	0.127125i
$916$		0			0
$917$	24.8220	−	27.1637i	0.819695	−	0.897023i
$918$		0			0
$919$	−16.9485	−	29.3557i	−0.559081	−	0.968356i	−0.997573	−	0.0696214i	$-0.977821\pi$
$919$	−16.9485	−	29.3557i	−0.559081	−	0.968356i	0.438493	−	0.898735i	$-0.355512\pi$
$920$		0			0
$921$	5.14630	+	11.5656i	0.169576	+	0.381099i
$922$		0			0
$923$	−21.1858	−	36.6949i	−0.697339	−	1.20783i
$924$		0			0
$925$	1.94060	−	3.36122i	0.0638065	−	0.110516i
$926$		0			0
$927$	18.4377	+	56.8300i	0.605575	+	1.86654i
$928$		0			0
$929$	−38.6100			−1.26675			−0.633377	−	0.773843i	$-0.718332\pi$
$929$	−38.6100			−1.26675			−0.633377	+	0.773843i	$0.718332\pi$
$930$		0			0
$931$	3.58584	+	39.7228i	0.117521	+	1.30186i
$932$		0			0
$933$	16.7440	+	37.6297i	0.548172	+	1.23194i
$934$		0			0
$935$	−0.148303	+	0.256869i	−0.00485004	+	0.00840052i
$936$		0			0
$937$	−45.4955			−1.48627			−0.743136	−	0.669140i	$-0.766663\pi$
$937$	−45.4955			−1.48627			−0.743136	+	0.669140i	$0.766663\pi$
$938$		0			0
$939$	12.8793	+	28.9443i	0.420298	+	0.944561i
$940$		0			0
$941$	−17.9892			−0.586431			−0.293216	−	0.956046i	$-0.594725\pi$
$941$	−17.9892			−0.586431			−0.293216	+	0.956046i	$0.594725\pi$
$942$		0			0
$943$	2.11229			0.0687857
$944$		0			0
$945$	−25.1696	+	14.2644i	−0.818769	+	0.464021i
$946$		0			0
$947$	16.5224			0.536906			0.268453	−	0.963293i	$-0.413488\pi$
$947$	16.5224			0.536906			0.268453	+	0.963293i	$0.413488\pi$
$948$		0			0
$949$	1.82175			0.0591365
$950$		0			0
$951$	3.30234	+	7.42155i	0.107086	+	0.240660i
$952$		0			0
$953$	−15.6799			−0.507922			−0.253961	−	0.967214i	$-0.581734\pi$
$953$	−15.6799			−0.507922			−0.253961	+	0.967214i	$0.581734\pi$
$954$		0			0
$955$	5.28096	−	9.14690i	0.170888	−	0.295987i
$956$		0			0
$957$	0.491745	+	1.10513i	0.0158959	+	0.0357237i
$958$		0			0
$959$	−11.6325	−	36.7168i	−0.375634	−	1.18565i
$960$		0			0
$961$	52.4465			1.69182
$962$		0			0
$963$	16.9727	+	3.61542i	0.546938	+	0.116505i
$964$		0			0
$965$	5.72149	−	9.90991i	0.184181	−	0.319011i
$966$		0			0
$967$	−25.3908	−	43.9782i	−0.816513	−	1.41424i	−0.908236	−	0.418458i	$-0.862571\pi$
$967$	−25.3908	−	43.9782i	−0.816513	−	1.41424i	0.0917230	−	0.995785i	$-0.470763\pi$
$968$		0			0
$969$	1.41702	+	3.18455i	0.0455212	+	0.102302i
$970$		0			0
$971$	−9.23027	−	15.9873i	−0.296214	−	0.513057i	0.679053	−	0.734089i	$-0.262391\pi$
$971$	−9.23027	−	15.9873i	−0.296214	−	0.513057i	−0.975266	+	0.221032i	$0.929057\pi$
$972$		0			0
$973$	−5.81721	−	18.3614i	−0.186491	−	0.588639i
$974$		0			0
$975$	2.84095	+	0.299223i	0.0909832	+	0.00958282i
$976$		0			0
$977$	31.6302			1.01194			0.505970	−	0.862551i	$-0.331135\pi$
$977$	31.6302			1.01194			0.505970	+	0.862551i	$0.331135\pi$
$978$		0			0
$979$	2.91061	−	5.04132i	0.0930234	−	0.161121i
$980$		0			0
$981$	−11.5821	−	35.6991i	−0.369788	−	1.13979i
$982$		0			0
$983$	−20.2066	−	34.9988i	−0.644490	−	1.11629i	−0.984419	−	0.175838i	$-0.943737\pi$
$983$	−20.2066	−	34.9988i	−0.644490	−	1.11629i	0.339929	−	0.940451i	$-0.389597\pi$
$984$		0			0
$985$	−6.26940	+	10.8589i	−0.199760	+	0.345994i
$986$		0			0
$987$	−10.7846	−	52.6943i	−0.343276	−	1.67728i
$988$		0			0
$989$	−0.242806	−	0.420553i	−0.00772079	−	0.0133728i
$990$		0			0
$991$	16.6187	−	28.7845i	0.527911	−	0.914368i	−0.471560	−	0.881834i	$-0.656309\pi$
$991$	16.6187	−	28.7845i	0.527911	−	0.914368i	0.999471	−	0.0325343i	$-0.0103578\pi$
$992$		0			0
$993$	8.04741	+	18.0854i	0.255377	+	0.573923i
$994$		0			0
$995$	11.8280	+	20.4867i	0.374973	+	0.649473i
$996$		0			0
$997$	20.5592	+	35.6096i	0.651117	+	1.12777i	0.982852	+	0.184396i	$0.0590328\pi$
$997$	20.5592	+	35.6096i	0.651117	+	1.12777i	−0.331735	+	0.943373i	$0.607634\pi$
$998$		0			0
$999$	−7.31408	−	34.5213i	−0.231407	−	1.09220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.25.5	✓	22
3.2	odd	2		1512.2.q.d.1369.8		22
4.3	odd	2		1008.2.q.l.529.7		22
7.2	even	3		504.2.t.c.457.11	yes	22
9.4	even	3		504.2.t.c.193.11	yes	22
9.5	odd	6		1512.2.t.c.361.4		22
12.11	even	2		3024.2.q.l.2881.8		22
21.2	odd	6		1512.2.t.c.289.4		22
28.23	odd	6		1008.2.t.l.961.1		22
36.23	even	6		3024.2.t.k.1873.4		22
36.31	odd	6		1008.2.t.l.193.1		22
63.23	odd	6		1512.2.q.d.793.8		22
63.58	even	3	inner	504.2.q.c.121.5	yes	22
84.23	even	6		3024.2.t.k.289.4		22
252.23	even	6		3024.2.q.l.2305.8		22
252.247	odd	6		1008.2.q.l.625.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.5	✓	22	1.1	even	1	trivial
504.2.q.c.121.5	yes	22	63.58	even	3	inner
504.2.t.c.193.11	yes	22	9.4	even	3
504.2.t.c.457.11	yes	22	7.2	even	3
1008.2.q.l.529.7		22	4.3	odd	2
1008.2.q.l.625.7		22	252.247	odd	6
1008.2.t.l.193.1		22	36.31	odd	6
1008.2.t.l.961.1		22	28.23	odd	6
1512.2.q.d.793.8		22	63.23	odd	6
1512.2.q.d.1369.8		22	3.2	odd	2
1512.2.t.c.289.4		22	21.2	odd	6
1512.2.t.c.361.4		22	9.5	odd	6
3024.2.q.l.2305.8		22	252.23	even	6
3024.2.q.l.2881.8		22	12.11	even	2
3024.2.t.k.289.4		22	84.23	even	6
3024.2.t.k.1873.4		22	36.23	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.704143 - 1.58246i) q^{3} +(-1.05220 + 1.82246i) q^{5} +(2.58382 + 0.569079i) q^{7} +(-2.00837 + 2.22856i) q^{9} +O(q^{10})\)	\(q+(-0.704143 - 1.58246i) q^{3} +(-1.05220 + 1.82246i) q^{5} +(2.58382 + 0.569079i) q^{7} +(-2.00837 + 2.22856i) q^{9} +(-0.199532 - 0.345600i) q^{11} +(1.44292 + 2.49921i) q^{13} +(3.62487 + 0.381790i) q^{15} +(-0.176596 + 0.305873i) q^{17} +(2.84888 + 4.93440i) q^{19} +(-0.918837 - 4.48951i) q^{21} +(0.438682 - 0.759820i) q^{23} +(0.285756 + 0.494945i) q^{25} +(4.94078 + 1.60894i) q^{27} +(0.874997 - 1.51554i) q^{29} +9.13490 q^{31} +(-0.406399 + 0.559103i) q^{33} +(-3.75582 + 4.11014i) q^{35} +(-3.39555 - 5.88127i) q^{37} +(2.93888 - 4.04317i) q^{39} +(1.20377 + 2.08499i) q^{41} +(0.276745 - 0.479336i) q^{43} +(-1.94826 - 6.00505i) q^{45} +11.7372 q^{47} +(6.35230 + 2.94080i) q^{49} +(0.608381 + 0.0640778i) q^{51} +(-2.07821 + 3.59956i) q^{53} +0.839790 q^{55} +(5.80248 - 7.98277i) q^{57} -9.32421 q^{59} -10.0720 q^{61} +(-6.45749 + 4.61528i) q^{63} -6.07296 q^{65} +1.20241 q^{67} +(-1.51128 - 0.159176i) q^{69} -14.6826 q^{71} +(0.315636 - 0.546697i) q^{73} +(0.582017 - 0.800710i) q^{75} +(-0.318883 - 1.00652i) q^{77} -2.48729 q^{79} +(-0.932933 - 8.95152i) q^{81} +(-4.59366 + 7.95645i) q^{83} +(-0.371628 - 0.643678i) q^{85} +(-3.01440 - 0.317493i) q^{87} +(7.29358 + 12.6328i) q^{89} +(2.30601 + 7.27866i) q^{91} +(-6.43228 - 14.4556i) q^{93} -11.9903 q^{95} +(-7.84245 + 13.5835i) q^{97} +(1.17092 + 0.249422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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