LMFDB - Embedded newform 504.2.t.d.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (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			193.5
Character	$\chi$	$=$	504.193
Dual form			504.2.t.d.457.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.134843 + 1.72679i) q^{3} -3.43592 q^{5} +(-1.83889 - 1.90223i) q^{7} +(-2.96363 + 0.465691i) q^{9} +O(q^{10})$	\(q+(0.134843 + 1.72679i) q^{3} -3.43592 q^{5} +(-1.83889 - 1.90223i) q^{7} +(-2.96363 + 0.465691i) q^{9} +4.40938 q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.463308 - 5.93312i) q^{15} +(0.542270 - 0.939239i) q^{17} +(-3.74273 - 6.48261i) q^{19} +(3.03680 - 3.43189i) q^{21} -4.32558 q^{23} +6.80552 q^{25} +(-1.20378 - 5.05479i) q^{27} +(1.68485 + 2.91825i) q^{29} +(-4.68734 - 8.11872i) q^{31} +(0.594572 + 7.61409i) q^{33} +(6.31828 + 6.53590i) q^{35} +(-2.50767 - 4.34341i) q^{37} +(4.66990 + 2.23092i) q^{39} +(-1.20160 + 2.08122i) q^{41} +(3.31412 + 5.74023i) q^{43} +(10.1828 - 1.60007i) q^{45} +(-1.50415 + 2.60527i) q^{47} +(-0.236948 + 6.99599i) q^{49} +(1.69499 + 0.809739i) q^{51} +(-0.530699 + 0.919198i) q^{53} -15.1502 q^{55} +(10.6894 - 7.33706i) q^{57} +(-6.20470 - 10.7468i) q^{59} +(2.71334 - 4.69965i) q^{61} +(6.33566 + 4.78116i) q^{63} +(-5.13331 + 8.89115i) q^{65} +(-1.66999 - 2.89251i) q^{67} +(-0.583272 - 7.46938i) q^{69} -12.9064 q^{71} +(-8.21382 + 14.2267i) q^{73} +(0.917674 + 11.7517i) q^{75} +(-8.10837 - 8.38764i) q^{77} +(1.17516 - 2.03543i) q^{79} +(8.56626 - 2.76028i) q^{81} +(-1.60602 - 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-4.81203 + 3.30290i) q^{87} +(5.67524 + 9.82981i) q^{89} +(-7.66974 + 1.91656i) q^{91} +(13.3873 - 9.18882i) q^{93} +(12.8597 + 22.2737i) q^{95} +(-6.40321 - 11.0907i) q^{97} +(-13.0678 + 2.05341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39} + 16 q^{41} + 22 q^{45} + 5 q^{47} - 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} - 19 q^{59} - 13 q^{61} + 21 q^{63} + 13 q^{65} + 26 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 8 q^{75} - 4 q^{77} + 10 q^{79} - 8 q^{81} - 28 q^{83} - 20 q^{85} + 9 q^{87} + 6 q^{89} - 37 q^{91} - 32 q^{93} + 12 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.134843	+	1.72679i	0.0778514	+	0.996965i
$3$	0.134843	+	1.72679i	0.0778514	+	0.996965i
$4$		0			0
$5$	−3.43592			−1.53659			−0.768294	−	0.640097i	$-0.778894\pi$
$5$	−3.43592			−1.53659			−0.768294	+	0.640097i	$0.778894\pi$
$6$		0			0
$7$	−1.83889	−	1.90223i	−0.695036	−	0.718975i
$7$	−1.83889	−	1.90223i	−0.695036	−	0.718975i
$8$		0			0
$9$	−2.96363	+	0.465691i	−0.987878	+	0.155230i
$10$		0			0
$11$	4.40938			1.32948			0.664739	−	0.747076i	$-0.268543\pi$
$11$	4.40938			1.32948			0.664739	+	0.747076i	$0.268543\pi$
$12$		0			0
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	−0.580997	−	0.813906i	$-0.697337\pi$
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	0.995362	+	0.0962048i	$0.0306704\pi$
$14$		0			0
$15$	−0.463308	−	5.93312i	−0.119626	−	1.53192i
$16$		0			0
$17$	0.542270	−	0.939239i	0.131520	−	0.227799i	−0.792743	−	0.609556i	$-0.791348\pi$
$17$	0.542270	−	0.939239i	0.131520	−	0.227799i	0.924263	+	0.381757i	$0.124681\pi$
$18$		0			0
$19$	−3.74273	−	6.48261i	−0.858642	−	1.48721i	−0.873225	−	0.487318i	$-0.837975\pi$
$19$	−3.74273	−	6.48261i	−0.858642	−	1.48721i	0.0145824	−	0.999894i	$-0.495358\pi$
$20$		0			0
$21$	3.03680	−	3.43189i	0.662683	−	0.748900i
$22$		0			0
$23$	−4.32558			−0.901945			−0.450972	−	0.892538i	$-0.648923\pi$
$23$	−4.32558			−0.901945			−0.450972	+	0.892538i	$0.648923\pi$
$24$		0			0
$25$	6.80552			1.36110
$26$		0			0
$27$	−1.20378	−	5.05479i	−0.231667	−	0.972795i
$28$		0			0
$29$	1.68485	+	2.91825i	0.312870	+	0.541906i	0.978982	−	0.203945i	$-0.0653764\pi$
$29$	1.68485	+	2.91825i	0.312870	+	0.541906i	−0.666113	+	0.745851i	$0.732043\pi$
$30$		0			0
$31$	−4.68734	−	8.11872i	−0.841872	−	1.45816i	−0.888311	−	0.459243i	$-0.848121\pi$
$31$	−4.68734	−	8.11872i	−0.841872	−	1.45816i	0.0464389	−	0.998921i	$-0.485213\pi$
$32$		0			0
$33$	0.594572	+	7.61409i	0.103502	+	1.32544i
$34$		0			0
$35$	6.31828	+	6.53590i	1.06798	+	1.10477i
$36$		0			0
$37$	−2.50767	−	4.34341i	−0.412258	−	0.714052i	0.582878	−	0.812559i	$-0.301926\pi$
$37$	−2.50767	−	4.34341i	−0.412258	−	0.714052i	−0.995136	+	0.0985079i	$0.968593\pi$
$38$		0			0
$39$	4.66990	+	2.23092i	0.747782	+	0.357233i
$40$		0			0
$41$	−1.20160	+	2.08122i	−0.187658	+	0.325033i	−0.944469	−	0.328601i	$-0.893423\pi$
$41$	−1.20160	+	2.08122i	−0.187658	+	0.325033i	0.756811	+	0.653634i	$0.226756\pi$
$42$		0			0
$43$	3.31412	+	5.74023i	0.505399	+	0.875377i	0.999980	+	0.00624563i	$0.00198806\pi$
$43$	3.31412	+	5.74023i	0.505399	+	0.875377i	−0.494581	+	0.869131i	$0.664679\pi$
$44$		0			0
$45$	10.1828	−	1.60007i	1.51796	−	0.238525i
$46$		0			0
$47$	−1.50415	+	2.60527i	−0.219403	+	0.380018i	−0.954626	−	0.297808i	$-0.903744\pi$
$47$	−1.50415	+	2.60527i	−0.219403	+	0.380018i	0.735222	+	0.677826i	$0.237078\pi$
$48$		0			0
$49$	−0.236948	+	6.99599i	−0.0338498	+	0.999427i
$50$		0			0
$51$	1.69499	+	0.809739i	0.237347	+	0.113386i
$52$		0			0
$53$	−0.530699	+	0.919198i	−0.0728971	+	0.126262i	−0.900170	−	0.435539i	$-0.856558\pi$
$53$	−0.530699	+	0.919198i	−0.0728971	+	0.126262i	0.827273	+	0.561801i	$0.189891\pi$
$54$		0			0
$55$	−15.1502			−2.04286
$56$		0			0
$57$	10.6894	−	7.33706i	1.41585	−	0.971818i
$58$		0			0
$59$	−6.20470	−	10.7468i	−0.807783	−	1.39912i	−0.914396	−	0.404820i	$-0.867334\pi$
$59$	−6.20470	−	10.7468i	−0.807783	−	1.39912i	0.106614	−	0.994301i	$-0.465999\pi$
$60$		0			0
$61$	2.71334	−	4.69965i	0.347408	−	0.601728i	−0.638380	−	0.769721i	$-0.720395\pi$
$61$	2.71334	−	4.69965i	0.347408	−	0.601728i	0.985788	+	0.167993i	$0.0537286\pi$
$62$		0			0
$63$	6.33566	+	4.78116i	0.798218	+	0.602369i
$64$		0			0
$65$	−5.13331	+	8.89115i	−0.636708	+	1.10281i
$66$		0			0
$67$	−1.66999	−	2.89251i	−0.204022	−	0.353376i	0.745799	−	0.666171i	$-0.232068\pi$
$67$	−1.66999	−	2.89251i	−0.204022	−	0.353376i	−0.949821	+	0.312795i	$0.898735\pi$
$68$		0			0
$69$	−0.583272	−	7.46938i	−0.0702177	−	0.899208i
$70$		0			0
$71$	−12.9064			−1.53171			−0.765857	−	0.643011i	$-0.777685\pi$
$71$	−12.9064			−1.53171			−0.765857	+	0.643011i	$0.777685\pi$
$72$		0			0
$73$	−8.21382	+	14.2267i	−0.961355	+	1.66511i	−0.242249	+	0.970214i	$0.577885\pi$
$73$	−8.21382	+	14.2267i	−0.961355	+	1.66511i	−0.719106	+	0.694901i	$0.755448\pi$
$74$		0			0
$75$	0.917674	+	11.7517i	0.105964	+	1.35697i
$76$		0			0
$77$	−8.10837	−	8.38764i	−0.924035	−	0.955861i
$78$		0			0
$79$	1.17516	−	2.03543i	0.132216	−	0.229004i	−0.792315	−	0.610113i	$-0.791124\pi$
$79$	1.17516	−	2.03543i	0.132216	−	0.229004i	0.924530	+	0.381108i	$0.124458\pi$
$80$		0			0
$81$	8.56626	−	2.76028i	0.951807	−	0.306697i
$82$		0			0
$83$	−1.60602	−	2.78171i	−0.176283	−	0.305332i	0.764321	−	0.644836i	$-0.223074\pi$
$83$	−1.60602	−	2.78171i	−0.176283	−	0.305332i	−0.940605	+	0.339504i	$0.889741\pi$
$84$		0			0
$85$	−1.86319	+	3.22715i	−0.202092	+	0.350033i
$86$		0			0
$87$	−4.81203	+	3.30290i	−0.515904	+	0.354108i
$88$		0			0
$89$	5.67524	+	9.82981i	0.601575	+	1.04196i	0.992583	+	0.121570i	$0.0387930\pi$
$89$	5.67524	+	9.82981i	0.601575	+	1.04196i	−0.391008	+	0.920387i	$0.627874\pi$
$90$		0			0
$91$	−7.66974	+	1.91656i	−0.804008	+	0.200910i
$92$		0			0
$93$	13.3873	−	9.18882i	1.38820	−	0.952837i
$94$		0			0
$95$	12.8597	+	22.2737i	1.31938	+	2.28523i
$96$		0			0
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	−0.983087	−	0.183140i	$-0.941374\pi$
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	0.332939	−	0.942948i	$-0.391960\pi$
$98$		0			0
$99$	−13.0678	+	2.05341i	−1.31336	+	0.206375i
$100$		0			0
$101$	−0.776221			−0.0772369			−0.0386184	−	0.999254i	$-0.512296\pi$
$101$	−0.776221			−0.0772369			−0.0386184	+	0.999254i	$0.512296\pi$
$102$		0			0
$103$	2.28262			0.224913			0.112457	−	0.993657i	$-0.464128\pi$
$103$	2.28262			0.224913			0.112457	+	0.993657i	$0.464128\pi$
$104$		0			0
$105$	−10.4342	+	11.7917i	−1.01827	+	1.15075i
$106$		0			0
$107$	−2.27468	−	3.93986i	−0.219901	−	0.380880i	0.734876	−	0.678201i	$-0.237240\pi$
$107$	−2.27468	−	3.93986i	−0.219901	−	0.380880i	−0.954778	+	0.297321i	$0.903907\pi$
$108$		0			0
$109$	2.36710	−	4.09994i	0.226727	−	0.392703i	−0.730109	−	0.683331i	$-0.760531\pi$
$109$	2.36710	−	4.09994i	0.226727	−	0.392703i	0.956836	+	0.290627i	$0.0938640\pi$
$110$		0			0
$111$	7.16203	−	4.91590i	0.679789	−	0.466597i
$112$		0			0
$113$	0.175367	−	0.303745i	0.0164972	−	0.0285740i	−0.857659	−	0.514219i	$-0.828082\pi$
$113$	0.175367	−	0.303745i	0.0164972	−	0.0285740i	0.874156	+	0.485645i	$0.161415\pi$
$114$		0			0
$115$	14.8623			1.38592
$116$		0			0
$117$	−3.22264	+	8.36477i	−0.297933	+	0.773323i
$118$		0			0
$119$	−2.78382	+	0.695638i	−0.255193	+	0.0637691i
$120$		0			0
$121$	8.44261			0.767510
$122$		0			0
$123$	−3.75587	−	1.79427i	−0.338655	−	0.161784i
$124$		0			0
$125$	−6.20360			−0.554867
$126$		0			0
$127$	12.4175			1.10187			0.550935	−	0.834548i	$-0.314271\pi$
$127$	12.4175			1.10187			0.550935	+	0.834548i	$0.314271\pi$
$128$		0			0
$129$	−9.46531	+	6.49684i	−0.833374	+	0.572015i
$130$		0			0
$131$	15.7430			1.37548			0.687738	−	0.725959i	$-0.258604\pi$
$131$	15.7430			1.37548			0.687738	+	0.725959i	$0.258604\pi$
$132$		0			0
$133$	−5.44891	+	19.0404i	−0.472481	+	1.65101i
$134$		0			0
$135$	4.13607	+	17.3678i	0.355977	+	1.49479i
$136$		0			0
$137$	−4.23020			−0.361410			−0.180705	−	0.983537i	$-0.557838\pi$
$137$	−4.23020			−0.361410			−0.180705	+	0.983537i	$0.557838\pi$
$138$		0			0
$139$	9.80367	−	16.9805i	0.831537	−	1.44026i	−0.0652824	−	0.997867i	$-0.520795\pi$
$139$	9.80367	−	16.9805i	0.831537	−	1.44026i	0.896819	−	0.442397i	$-0.145872\pi$
$140$		0			0
$141$	−4.70159	−	2.24606i	−0.395945	−	0.189152i
$142$		0			0
$143$	6.58767	−	11.4102i	0.550889	−	0.954167i
$144$		0			0
$145$	−5.78902	−	10.0269i	−0.480752	−	0.832686i
$146$		0			0
$147$	−12.1126	+	0.534197i	−0.999029	+	0.0440598i
$148$		0			0
$149$	−9.72651			−0.796827			−0.398414	−	0.917206i	$-0.630439\pi$
$149$	−9.72651			−0.796827			−0.398414	+	0.917206i	$0.630439\pi$
$150$		0			0
$151$	−9.82148			−0.799261			−0.399630	−	0.916676i	$-0.630862\pi$
$151$	−9.82148			−0.799261			−0.399630	+	0.916676i	$0.630862\pi$
$152$		0			0
$153$	−1.16969	+	3.03609i	−0.0945642	+	0.245453i
$154$		0			0
$155$	16.1053	+	27.8952i	1.29361	+	2.24060i
$156$		0			0
$157$	6.02041	+	10.4277i	0.480481	+	0.832218i	0.999749	−	0.0223936i	$-0.00712870\pi$
$157$	6.02041	+	10.4277i	0.480481	+	0.832218i	−0.519268	+	0.854611i	$0.673795\pi$
$158$		0			0
$159$	−1.65883	−	0.792461i	−0.131553	−	0.0628462i
$160$		0			0
$161$	7.95427	+	8.22824i	0.626884	+	0.648476i
$162$		0			0
$163$	0.885601	+	1.53391i	0.0693656	+	0.120145i	0.898622	−	0.438723i	$-0.144569\pi$
$163$	0.885601	+	1.53391i	0.0693656	+	0.120145i	−0.829257	+	0.558868i	$0.811236\pi$
$164$		0			0
$165$	−2.04290	−	26.1614i	−0.159039	−	2.03666i
$166$		0			0
$167$	−7.86350	+	13.6200i	−0.608496	+	1.05395i	0.382993	+	0.923751i	$0.374893\pi$
$167$	−7.86350	+	13.6200i	−0.608496	+	1.05395i	−0.991489	+	0.130194i	$0.958440\pi$
$168$		0			0
$169$	2.03584	+	3.52618i	0.156603	+	0.271245i
$170$		0			0
$171$	14.1110	+	17.4691i	1.07909	+	1.33590i
$172$		0			0
$173$	−9.40313	+	16.2867i	−0.714907	+	1.23825i	0.248089	+	0.968737i	$0.420198\pi$
$173$	−9.40313	+	16.2867i	−0.714907	+	1.23825i	−0.962996	+	0.269517i	$0.913136\pi$
$174$		0			0
$175$	−12.5146	−	12.9456i	−0.946016	−	0.978599i
$176$		0			0
$177$	17.7209	−	12.1634i	1.33199	−	0.914255i
$178$		0			0
$179$	3.34201	−	5.78853i	0.249794	−	0.432655i	−0.713675	−	0.700477i	$-0.752971\pi$
$179$	3.34201	−	5.78853i	0.249794	−	0.432655i	0.963468	+	0.267822i	$0.0863039\pi$
$180$		0			0
$181$	4.73726			0.352117			0.176059	−	0.984380i	$-0.443665\pi$
$181$	4.73726			0.352117			0.176059	+	0.984380i	$0.443665\pi$
$182$		0			0
$183$	8.48119	+	4.05167i	0.626948	+	0.299508i
$184$		0			0
$185$	8.61613	+	14.9236i	0.633471	+	1.09720i
$186$		0			0
$187$	2.39107	−	4.14146i	0.174853	−	0.302853i
$188$		0			0
$189$	−7.40175	+	11.5851i	−0.538398	+	0.842690i
$190$		0			0
$191$	11.5347	−	19.9786i	0.834618	−	1.44560i	−0.0597224	−	0.998215i	$-0.519022\pi$
$191$	11.5347	−	19.9786i	0.834618	−	1.44560i	0.894341	−	0.447386i	$-0.147645\pi$
$192$		0			0
$193$	−9.15352	−	15.8544i	−0.658885	−	1.14122i	−0.980905	−	0.194489i	$-0.937695\pi$
$193$	−9.15352	−	15.8544i	−0.658885	−	1.14122i	0.322020	−	0.946733i	$-0.395638\pi$
$194$		0			0
$195$	−16.0454	−	7.66526i	−1.14903	−	0.548920i
$196$		0			0
$197$	14.5866			1.03925			0.519625	−	0.854395i	$-0.326072\pi$
$197$	14.5866			1.03925			0.519625	+	0.854395i	$0.326072\pi$
$198$		0			0
$199$	−0.912102	+	1.57981i	−0.0646572	+	0.111990i	−0.896542	−	0.442959i	$-0.853929\pi$
$199$	−0.912102	+	1.57981i	−0.0646572	+	0.111990i	0.831885	+	0.554949i	$0.187262\pi$
$200$		0			0
$201$	4.76958	−	3.27376i	0.336420	−	0.230913i
$202$		0			0
$203$	2.45292	−	8.57133i	0.172161	−	0.601590i
$204$		0			0
$205$	4.12858	−	7.15091i	0.288352	−	0.499441i
$206$		0			0
$207$	12.8194	−	2.01438i	0.891012	−	0.140009i
$208$		0			0
$209$	−16.5031	−	28.5843i	−1.14155	−	1.97721i
$210$		0			0
$211$	−2.77359	+	4.80400i	−0.190942	+	0.330721i	−0.945563	−	0.325440i	$-0.894488\pi$
$211$	−2.77359	+	4.80400i	−0.190942	+	0.330721i	0.754621	+	0.656161i	$0.227821\pi$
$212$		0			0
$213$	−1.74034	−	22.2868i	−0.119246	−	1.52706i
$214$		0			0
$215$	−11.3870	−	19.7229i	−0.776590	−	1.34509i
$216$		0			0
$217$	−6.82413	+	23.8458i	−0.463252	+	1.61876i
$218$		0			0
$219$	−25.6742	−	12.2652i	−1.73490	−	0.828805i
$220$		0			0
$221$	−1.62032	−	2.80647i	−0.108994	−	0.188784i
$222$		0			0
$223$	6.01726	+	10.4222i	0.402946	+	0.697922i	0.994080	−	0.108651i	$-0.0346530\pi$
$223$	6.01726	+	10.4222i	0.402946	+	0.697922i	−0.591134	+	0.806573i	$0.701320\pi$
$224$		0			0
$225$	−20.1691	+	3.16927i	−1.34460	+	0.211284i
$226$		0			0
$227$	−13.1567			−0.873240			−0.436620	−	0.899646i	$-0.643825\pi$
$227$	−13.1567			−0.873240			−0.436620	+	0.899646i	$0.643825\pi$
$228$		0			0
$229$	12.4832			0.824912			0.412456	−	0.910978i	$-0.364671\pi$
$229$	12.4832			0.824912			0.412456	+	0.910978i	$0.364671\pi$
$230$		0			0
$231$	13.3904	−	15.1325i	0.881022	−	0.995645i
$232$		0			0
$233$	−2.01687	−	3.49332i	−0.132130	−	0.228855i	0.792368	−	0.610044i	$-0.208848\pi$
$233$	−2.01687	−	3.49332i	−0.132130	−	0.228855i	−0.924497	+	0.381189i	$0.875515\pi$
$234$		0			0
$235$	5.16814	−	8.95149i	0.337133	−	0.583931i
$236$		0			0
$237$	3.67323	+	1.75479i	0.238602	+	0.113986i
$238$		0			0
$239$	13.8679	−	24.0200i	0.897043	−	1.55372i	0.0657873	−	0.997834i	$-0.479044\pi$
$239$	13.8679	−	24.0200i	0.897043	−	1.55372i	0.831256	−	0.555890i	$-0.187623\pi$
$240$		0			0
$241$	23.9134			1.54040			0.770199	−	0.637803i	$-0.220157\pi$
$241$	23.9134			1.54040			0.770199	+	0.637803i	$0.220157\pi$
$242$		0			0
$243$	5.92152	+	14.4200i	0.379866	+	0.925042i
$244$		0			0
$245$	0.814135	−	24.0376i	0.0520131	−	1.53571i
$246$		0			0
$247$	−22.3668			−1.42316
$248$		0			0
$249$	4.58687	−	3.14836i	0.290681	−	0.199519i
$250$		0			0
$251$	−3.33510			−0.210509			−0.105255	−	0.994445i	$-0.533566\pi$
$251$	−3.33510			−0.210509			−0.105255	+	0.994445i	$0.533566\pi$
$252$		0			0
$253$	−19.0731			−1.19912
$254$		0			0
$255$	−5.82385	−	2.78219i	−0.364704	−	0.174228i
$256$		0			0
$257$	−21.8691			−1.36416			−0.682078	−	0.731280i	$-0.738923\pi$
$257$	−21.8691			−1.36416			−0.682078	+	0.731280i	$0.738923\pi$
$258$		0			0
$259$	−3.65082	+	12.7572i	−0.226851	+	0.792695i
$260$		0			0
$261$	−6.35230	−	7.86402i	−0.393197	−	0.486770i
$262$		0			0
$263$	5.51044			0.339788			0.169894	−	0.985462i	$-0.445657\pi$
$263$	5.51044			0.339788			0.169894	+	0.985462i	$0.445657\pi$
$264$		0			0
$265$	1.82344	−	3.15829i	0.112013	−	0.194012i
$266$		0			0
$267$	−16.2088	+	11.1255i	−0.991962	+	0.680867i
$268$		0			0
$269$	3.37393	−	5.84382i	0.205712	−	0.356304i	−0.744647	−	0.667458i	$-0.767382\pi$
$269$	3.37393	−	5.84382i	0.205712	−	0.356304i	0.950359	+	0.311154i	$0.100716\pi$
$270$		0			0
$271$	6.21944	+	10.7724i	0.377804	+	0.654376i	0.990742	−	0.135755i	$-0.0433459\pi$
$271$	6.21944	+	10.7724i	0.377804	+	0.654376i	−0.612938	+	0.790131i	$0.710013\pi$
$272$		0			0
$273$	−4.34371	−	12.9856i	−0.262894	−	0.785926i
$274$		0			0
$275$	30.0081			1.80956
$276$		0			0
$277$	−9.71890			−0.583952			−0.291976	−	0.956426i	$-0.594313\pi$
$277$	−9.71890			−0.583952			−0.291976	+	0.956426i	$0.594313\pi$
$278$		0			0
$279$	17.6724	+	21.8781i	1.05802	+	1.30981i
$280$		0			0
$281$	−9.66772	−	16.7450i	−0.576728	−	0.998922i	−0.995852	−	0.0909928i	$-0.970996\pi$
$281$	−9.66772	−	16.7450i	−0.576728	−	0.998922i	0.419124	−	0.907929i	$-0.362337\pi$
$282$		0			0
$283$	−4.15450	−	7.19581i	−0.246959	−	0.427746i	0.715721	−	0.698386i	$-0.246098\pi$
$283$	−4.15450	−	7.19581i	−0.246959	−	0.427746i	−0.962681	+	0.270640i	$0.912765\pi$
$284$		0			0
$285$	−36.7280	+	25.2095i	−2.17558	+	1.49328i
$286$		0			0
$287$	6.16857	−	1.54144i	0.364119	−	0.0909882i
$288$		0			0
$289$	7.91189	+	13.7038i	0.465405	+	0.806105i
$290$		0			0
$291$	18.2879	−	12.5525i	1.07206	−	0.735842i
$292$		0			0
$293$	−3.97318	+	6.88175i	−0.232116	+	0.402036i	−0.958430	−	0.285326i	$-0.907898\pi$
$293$	−3.97318	+	6.88175i	−0.232116	+	0.402036i	0.726315	+	0.687362i	$0.241231\pi$
$294$		0			0
$295$	21.3188	+	36.9253i	1.24123	+	2.14987i
$296$		0			0
$297$	−5.30790	−	22.2885i	−0.307996	−	1.29331i
$298$		0			0
$299$	−6.46247	+	11.1933i	−0.373734	+	0.647327i
$300$		0			0
$301$	4.82491	−	16.8599i	0.278103	−	0.971788i
$302$		0			0
$303$	−0.104668	−	1.34037i	−0.00601300	−	0.0770024i
$304$		0			0
$305$	−9.32281	+	16.1476i	−0.533823	+	0.924608i
$306$		0			0
$307$	−26.9180			−1.53629			−0.768145	−	0.640276i	$-0.778820\pi$
$307$	−26.9180			−1.53629			−0.768145	+	0.640276i	$0.778820\pi$
$308$		0			0
$309$	0.307795	+	3.94162i	0.0175098	+	0.224231i
$310$		0			0
$311$	−4.67458	−	8.09662i	−0.265071	−	0.459117i	0.702511	−	0.711673i	$-0.252062\pi$
$311$	−4.67458	−	8.09662i	−0.265071	−	0.459117i	−0.967582	+	0.252556i	$0.918729\pi$
$312$		0			0
$313$	−7.91902	+	13.7161i	−0.447610	+	0.775282i	−0.998230	−	0.0594734i	$-0.981058\pi$
$313$	−7.91902	+	13.7161i	−0.447610	+	0.775282i	0.550620	+	0.834756i	$0.314391\pi$
$314$		0			0
$315$	−21.7688	−	16.4276i	−1.22653	−	0.925593i
$316$		0			0
$317$	14.2296	−	24.6463i	0.799213	−	1.38428i	−0.120917	−	0.992663i	$-0.538583\pi$
$317$	14.2296	−	24.6463i	0.799213	−	1.38428i	0.920130	−	0.391614i	$-0.128083\pi$
$318$		0			0
$319$	7.42916	+	12.8677i	0.415953	+	0.720452i
$320$		0			0
$321$	6.49660	−	4.45916i	0.362605	−	0.248886i
$322$		0			0
$323$	−8.11829			−0.451714
$324$		0			0
$325$	10.1675	−	17.6107i	0.563994	−	0.976865i
$326$		0			0
$327$	7.39894	+	3.53465i	0.409162	+	0.195467i
$328$		0			0
$329$	7.72180	−	1.92957i	0.425716	−	0.106381i
$330$		0			0
$331$	9.79521	−	16.9658i	0.538393	−	0.932524i	−0.460598	−	0.887609i	$-0.652365\pi$
$331$	9.79521	−	16.9658i	0.538393	−	0.932524i	0.998991	−	0.0449153i	$-0.0143018\pi$
$332$		0			0
$333$	9.45449	+	11.7045i	0.518103	+	0.641401i
$334$		0			0
$335$	5.73794	+	9.93841i	0.313497	+	0.542993i
$336$		0			0
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	−0.524023	−	0.851704i	$-0.675569\pi$
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	0.999609	+	0.0279654i	$0.00890283\pi$
$338$		0			0
$339$	0.548153	+	0.261866i	0.0297716	+	0.0142226i
$340$		0			0
$341$	−20.6683	−	35.7985i	−1.11925	−	1.93860i
$342$		0			0
$343$	13.7437	−	12.4141i	0.742090	−	0.670301i
$344$		0			0
$345$	2.00407	+	25.6642i	0.107896	+	1.38171i
$346$		0			0
$347$	9.72509	+	16.8443i	0.522070	+	0.904252i	0.999670	+	0.0256747i	$0.00817340\pi$
$347$	9.72509	+	16.8443i	0.522070	+	0.904252i	−0.477600	+	0.878577i	$0.658493\pi$
$348$		0			0
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	0.989582	−	0.143971i	$-0.0459872\pi$
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	−0.619474	+	0.785018i	$0.712654\pi$
$350$		0			0
$351$	−14.8788	−	4.43691i	−0.794171	−	0.236825i
$352$		0			0
$353$	11.8459			0.630493			0.315247	−	0.949010i	$-0.397913\pi$
$353$	11.8459			0.630493			0.315247	+	0.949010i	$0.397913\pi$
$354$		0			0
$355$	44.3455			2.35361
$356$		0			0
$357$	−1.57660	−	4.71329i	−0.0834426	−	0.249454i
$358$		0			0
$359$	−0.628489	−	1.08858i	−0.0331704	−	0.0574528i	0.848964	−	0.528451i	$-0.177227\pi$
$359$	−0.628489	−	1.08858i	−0.0331704	−	0.0574528i	−0.882134	+	0.470998i	$0.843894\pi$
$360$		0			0
$361$	−18.5161	+	32.0709i	−0.974533	+	1.68794i
$362$		0			0
$363$	1.13842	+	14.5786i	0.0597517	+	0.765180i
$364$		0			0
$365$	28.2220	−	48.8819i	1.47721	−	2.55860i
$366$		0			0
$367$	−15.2386			−0.795446			−0.397723	−	0.917505i	$-0.630200\pi$
$367$	−15.2386			−0.795446			−0.397723	+	0.917505i	$0.630200\pi$
$368$		0			0
$369$	2.59188	−	6.72756i	0.134928	−	0.350223i
$370$		0			0
$371$	2.72442	−	0.680795i	0.141445	−	0.0353451i
$372$		0			0
$373$	17.3351			0.897579			0.448789	−	0.893638i	$-0.351855\pi$
$373$	17.3351			0.897579			0.448789	+	0.893638i	$0.351855\pi$
$374$		0			0
$375$	−0.836510	−	10.7123i	−0.0431972	−	0.553183i
$376$		0			0
$377$	10.0688			0.518569
$378$		0			0
$379$	15.6319			0.802955			0.401478	−	0.915869i	$-0.368497\pi$
$379$	15.6319			0.802955			0.401478	+	0.915869i	$0.368497\pi$
$380$		0			0
$381$	1.67440	+	21.4424i	0.0857822	+	1.09853i
$382$		0			0
$383$	−17.8123			−0.910166			−0.455083	−	0.890449i	$-0.650390\pi$
$383$	−17.8123			−0.910166			−0.455083	+	0.890449i	$0.650390\pi$
$384$		0			0
$385$	27.8597	+	28.8192i	1.41986	+	1.46876i
$386$		0			0
$387$	−12.4950	−	15.4686i	−0.635158	−	0.786313i
$388$		0			0
$389$	29.4148			1.49139			0.745695	−	0.666288i	$-0.232118\pi$
$389$	29.4148			1.49139			0.745695	+	0.666288i	$0.232118\pi$
$390$		0			0
$391$	−2.34563	+	4.06275i	−0.118624	+	0.205462i
$392$		0			0
$393$	2.12283	+	27.1850i	0.107083	+	1.37130i
$394$		0			0
$395$	−4.03774	+	6.99357i	−0.203161	+	0.351885i
$396$		0			0
$397$	−1.55930	−	2.70079i	−0.0782592	−	0.135549i	0.824240	−	0.566241i	$-0.191603\pi$
$397$	−1.55930	−	2.70079i	−0.0782592	−	0.135549i	−0.902499	+	0.430692i	$0.858270\pi$
$398$		0			0
$399$	−33.6135	−	6.84170i	−1.68278	−	0.342513i
$400$		0			0
$401$	−35.7226			−1.78390			−0.891950	−	0.452134i	$-0.850663\pi$
$401$	−35.7226			−1.78390			−0.891950	+	0.452134i	$0.850663\pi$
$402$		0			0
$403$	−28.0118			−1.39537
$404$		0			0
$405$	−29.4330	+	9.48407i	−1.46254	+	0.471267i
$406$		0			0
$407$	−11.0572	−	19.1517i	−0.548087	−	0.949315i
$408$		0			0
$409$	−4.90826	−	8.50135i	−0.242698	−	0.420365i	0.718784	−	0.695233i	$-0.244699\pi$
$409$	−4.90826	−	8.50135i	−0.242698	−	0.420365i	−0.961482	+	0.274869i	$0.911366\pi$
$410$		0			0
$411$	−0.570411	−	7.30468i	−0.0281363	−	0.360313i
$412$		0			0
$413$	−9.03320	+	31.5651i	−0.444494	+	1.55321i
$414$		0			0
$415$	5.51814	+	9.55771i	0.270875	+	0.469169i
$416$		0			0
$417$	30.6437	+	14.6392i	1.50063	+	0.716886i
$418$		0			0
$419$	6.09812	−	10.5623i	0.297913	−	0.516000i	−0.677746	−	0.735297i	$-0.737043\pi$
$419$	6.09812	−	10.5623i	0.297913	−	0.516000i	0.975658	+	0.219297i	$0.0703762\pi$
$420$		0			0
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	0.714562	−	0.699572i	$-0.246626\pi$
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	−0.963128	+	0.269043i	$0.913293\pi$
$422$		0			0
$423$	3.24451	−	8.42154i	0.157754	−	0.409469i
$424$		0			0
$425$	3.69043	−	6.39201i	0.179012	−	0.310058i
$426$		0			0
$427$	−13.9293	+	3.48075i	−0.674088	+	0.168445i
$428$		0			0
$429$	20.5913	+	9.83697i	0.994159	+	0.474934i
$430$		0			0
$431$	−5.70254	+	9.87710i	−0.274682	+	0.475763i	−0.970055	−	0.242886i	$-0.921906\pi$
$431$	−5.70254	+	9.87710i	−0.274682	+	0.475763i	0.695373	+	0.718649i	$0.255239\pi$
$432$		0			0
$433$	26.2391			1.26097			0.630486	−	0.776201i	$-0.282856\pi$
$433$	26.2391			1.26097			0.630486	+	0.776201i	$0.282856\pi$
$434$		0			0
$435$	16.5337	−	11.3485i	0.792732	−	0.544118i
$436$		0			0
$437$	16.1895	+	28.0410i	0.774448	+	1.34138i
$438$		0			0
$439$	−11.4777	+	19.8800i	−0.547801	+	0.948819i	0.450624	+	0.892714i	$0.351202\pi$
$439$	−11.4777	+	19.8800i	−0.547801	+	0.948819i	−0.998425	+	0.0561054i	$0.982132\pi$
$440$		0			0
$441$	−2.55574	−	20.8439i	−0.121702	−	0.992567i
$442$		0			0
$443$	−11.2013	+	19.4012i	−0.532188	+	0.921777i	0.467105	+	0.884202i	$0.345297\pi$
$443$	−11.2013	+	19.4012i	−0.532188	+	0.921777i	−0.999294	+	0.0375758i	$0.988036\pi$
$444$		0			0
$445$	−19.4997	−	33.7744i	−0.924372	−	1.60106i
$446$		0			0
$447$	−1.31155	−	16.7957i	−0.0620341	−	0.794409i
$448$		0			0
$449$	17.0576			0.805000			0.402500	−	0.915420i	$-0.368141\pi$
$449$	17.0576			0.805000			0.402500	+	0.915420i	$0.368141\pi$
$450$		0			0
$451$	−5.29829	+	9.17690i	−0.249487	+	0.432123i
$452$		0			0
$453$	−1.32435	−	16.9597i	−0.0622236	−	0.796835i
$454$		0			0
$455$	26.3526	−	6.58514i	1.23543	−	0.308716i
$456$		0			0
$457$	−4.77365	+	8.26820i	−0.223302	+	0.386770i	−0.955809	−	0.293990i	$-0.905017\pi$
$457$	−4.77365	+	8.26820i	−0.223302	+	0.386770i	0.732507	+	0.680760i	$0.238350\pi$
$458$		0			0
$459$	−5.40043	−	1.61043i	−0.252070	−	0.0751683i
$460$		0			0
$461$	10.1213	+	17.5305i	0.471394	+	0.816478i	0.999464	−	0.0327222i	$-0.0104177\pi$
$461$	10.1213	+	17.5305i	0.471394	+	0.816478i	−0.528070	+	0.849201i	$0.677084\pi$
$462$		0			0
$463$	−7.81948	+	13.5437i	−0.363402	+	0.629431i	−0.988518	−	0.151101i	$-0.951718\pi$
$463$	−7.81948	+	13.5437i	−0.363402	+	0.629431i	0.625116	+	0.780532i	$0.285052\pi$
$464$		0			0
$465$	−45.9976	+	31.5720i	−2.13309	+	1.46412i
$466$		0			0
$467$	−2.96638	−	5.13793i	−0.137268	−	0.237755i	0.789194	−	0.614144i	$-0.210499\pi$
$467$	−2.96638	−	5.13793i	−0.137268	−	0.237755i	−0.926461	+	0.376390i	$0.877165\pi$
$468$		0			0
$469$	−2.43128	+	8.49571i	−0.112266	+	0.392295i
$470$		0			0
$471$	−17.1946	+	11.8021i	−0.792286	+	0.543812i
$472$		0			0
$473$	14.6132	+	25.3108i	0.671917	+	1.16379i
$474$		0			0
$475$	−25.4712	−	44.1175i	−1.16870	−	2.02425i
$476$		0			0
$477$	1.14474	−	2.97131i	0.0524139	−	0.136047i
$478$		0			0
$479$	−17.3942			−0.794760			−0.397380	−	0.917654i	$-0.630080\pi$
$479$	−17.3942			−0.794760			−0.397380	+	0.917654i	$0.630080\pi$
$480$		0			0
$481$	−14.9860			−0.683301
$482$		0			0
$483$	−13.1359	+	14.8449i	−0.597704	+	0.675466i
$484$		0			0
$485$	22.0009	+	38.1067i	0.999009	+	1.73033i
$486$		0			0
$487$	−9.76967	+	16.9216i	−0.442706	+	0.766790i	−0.997889	−	0.0649386i	$-0.979315\pi$
$487$	−9.76967	+	16.9216i	−0.442706	+	0.766790i	0.555183	+	0.831728i	$0.312648\pi$
$488$		0			0
$489$	−2.52932	+	1.73609i	−0.114380	+	0.0785086i
$490$		0			0
$491$	−6.16702	+	10.6816i	−0.278314	+	0.482054i	−0.970966	−	0.239218i	$-0.923109\pi$
$491$	−6.16702	+	10.6816i	−0.278314	+	0.482054i	0.692652	+	0.721272i	$0.256442\pi$
$492$		0			0
$493$	3.65458			0.164594
$494$		0			0
$495$	44.8998	−	7.05533i	2.01810	−	0.317114i
$496$		0			0
$497$	23.7336	+	24.5510i	1.06460	+	1.10126i
$498$		0			0
$499$	18.5462			0.830240			0.415120	−	0.909767i	$-0.363740\pi$
$499$	18.5462			0.830240			0.415120	+	0.909767i	$0.363740\pi$
$500$		0			0
$501$	−24.5792	−	11.7421i	−1.09812	−	0.524598i
$502$		0			0
$503$	−14.3264			−0.638782			−0.319391	−	0.947623i	$-0.603478\pi$
$503$	−14.3264			−0.638782			−0.319391	+	0.947623i	$0.603478\pi$
$504$		0			0
$505$	2.66703			0.118681
$506$		0			0
$507$	−5.81448	+	3.99096i	−0.258230	+	0.177245i
$508$		0			0
$509$	−16.8611			−0.747356			−0.373678	−	0.927559i	$-0.621903\pi$
$509$	−16.8611			−0.747356			−0.373678	+	0.927559i	$0.621903\pi$
$510$		0			0
$511$	42.1669	−	10.5369i	1.86535	−	0.466125i
$512$		0			0
$513$	−28.2628	+	26.7224i	−1.24783	+	1.17982i
$514$		0			0
$515$	−7.84290			−0.345599
$516$		0			0
$517$	−6.63238	+	11.4876i	−0.291692	+	0.505225i
$518$		0			0
$519$	−29.3917	−	14.0411i	−1.29015	−	0.616337i
$520$		0			0
$521$	10.8132	−	18.7291i	0.473737	−	0.820536i	−0.525811	−	0.850601i	$-0.676238\pi$
$521$	10.8132	−	18.7291i	0.473737	−	0.820536i	0.999548	+	0.0300652i	$0.00957151\pi$
$522$		0			0
$523$	8.27472	+	14.3322i	0.361828	+	0.626705i	0.988262	−	0.152770i	$-0.0488193\pi$
$523$	8.27472	+	14.3322i	0.361828	+	0.626705i	−0.626433	+	0.779475i	$0.715486\pi$
$524$		0			0
$525$	20.6670	−	23.3558i	0.901980	−	1.01933i
$526$		0			0
$527$	−10.1672			−0.442891
$528$		0			0
$529$	−4.28939			−0.186495
$530$		0			0
$531$	23.3932	+	28.9603i	1.01518	+	1.25677i
$532$		0			0
$533$	3.59040	+	6.21876i	0.155517	+	0.269364i
$534$		0			0
$535$	7.81560	+	13.5370i	0.337898	+	0.585256i
$536$		0			0
$537$	10.4462	+	4.99042i	0.450789	+	0.215353i
$538$		0			0
$539$	−1.04479	+	30.8480i	−0.0450025	+	1.32872i
$540$		0			0
$541$	−11.9542	−	20.7053i	−0.513952	−	0.890191i	−0.999869	−	0.0161861i	$-0.994848\pi$
$541$	−11.9542	−	20.7053i	−0.513952	−	0.890191i	0.485917	−	0.874005i	$-0.338486\pi$
$542$		0			0
$543$	0.638784	+	8.18027i	0.0274128	+	0.351049i
$544$		0			0
$545$	−8.13317	+	14.0871i	−0.348387	+	0.603423i
$546$		0			0
$547$	−14.8193	−	25.6678i	−0.633627	−	1.09747i	−0.986804	−	0.161918i	$-0.948232\pi$
$547$	−14.8193	−	25.6678i	−0.633627	−	1.09747i	0.353177	−	0.935556i	$-0.385101\pi$
$548$		0			0
$549$	−5.85277	+	15.1916i	−0.249790	+	0.648362i
$550$		0			0
$551$	12.6119	−	21.8445i	0.537286	−	0.930607i
$552$		0			0
$553$	−6.03285	+	1.50752i	−0.256543	+	0.0641064i
$554$		0			0
$555$	−24.6081	+	16.8906i	−1.04456	+	0.716967i
$556$		0			0
$557$	−10.8366	+	18.7695i	−0.459160	+	0.795288i	−0.998917	−	0.0465330i	$-0.985183\pi$
$557$	−10.8366	+	18.7695i	−0.459160	+	0.795288i	0.539757	+	0.841821i	$0.318516\pi$
$558$		0			0
$559$	19.8054			0.837679
$560$		0			0
$561$	7.47387	+	3.57044i	0.315547	+	0.150744i
$562$		0			0
$563$	−7.07782	−	12.2591i	−0.298294	−	0.516661i	0.677451	−	0.735567i	$-0.263084\pi$
$563$	−7.07782	−	12.2591i	−0.298294	−	0.516661i	−0.975746	+	0.218906i	$0.929751\pi$
$564$		0			0
$565$	−0.602548	+	1.04364i	−0.0253494	+	0.0439064i
$566$		0			0
$567$	−21.0031	−	11.2191i	−0.882048	−	0.471160i
$568$		0			0
$569$	17.0178	−	29.4757i	0.713422	−	1.23568i	−0.250143	−	0.968209i	$-0.580478\pi$
$569$	17.0178	−	29.4757i	0.713422	−	1.23568i	0.963565	−	0.267475i	$-0.0861891\pi$
$570$		0			0
$571$	2.67485	+	4.63298i	0.111939	+	0.193884i	0.916552	−	0.399915i	$-0.130961\pi$
$571$	2.67485	+	4.63298i	0.111939	+	0.193884i	−0.804613	+	0.593800i	$0.797627\pi$
$572$		0			0
$573$	36.0543	+	17.2240i	1.50619	+	0.719543i
$574$		0			0
$575$	−29.4378			−1.22764
$576$		0			0
$577$	11.1865	−	19.3756i	0.465699	−	0.806615i	−0.533533	−	0.845779i	$-0.679136\pi$
$577$	11.1865	−	19.3756i	0.465699	−	0.806615i	0.999233	+	0.0391640i	$0.0124695\pi$
$578$		0			0
$579$	26.1429	−	17.9441i	1.08646	−	0.745731i
$580$		0			0
$581$	−2.33814	+	8.17027i	−0.0970026	+	0.338960i
$582$		0			0
$583$	−2.34005	+	4.05309i	−0.0969151	+	0.167862i
$584$		0			0
$585$	11.0727	−	28.7407i	0.457801	−	1.18828i
$586$		0			0
$587$	−2.49899	−	4.32839i	−0.103145	−	0.178652i	0.809834	−	0.586659i	$-0.199557\pi$
$587$	−2.49899	−	4.32839i	−0.103145	−	0.178652i	−0.912979	+	0.408007i	$0.866224\pi$
$588$		0			0
$589$	−35.0870	+	60.7724i	−1.44573	+	2.50408i
$590$		0			0
$591$	1.96689	+	25.1880i	0.0809071	+	1.03610i
$592$		0			0
$593$	12.1698	+	21.0788i	0.499755	+	0.865601i	1.00000		0.000282582i	$-8.99487e-5\pi$
$593$	12.1698	+	21.0788i	0.499755	+	0.865601i	−0.500245	+	0.865884i	$0.666757\pi$
$594$		0			0
$595$	9.56498	−	2.39015i	0.392126	−	0.0979868i
$596$		0			0
$597$	−2.85099	−	1.36199i	−0.116683	−	0.0557424i
$598$		0			0
$599$	−23.1073	−	40.0230i	−0.944137	−	1.63529i	−0.757469	−	0.652871i	$-0.773564\pi$
$599$	−23.1073	−	40.0230i	−0.944137	−	1.63529i	−0.186668	−	0.982423i	$-0.559769\pi$
$600$		0			0
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	−0.975644	−	0.219359i	$-0.929603\pi$
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	0.297852	−	0.954612i	$-0.403730\pi$
$602$		0			0
$603$	6.29625	+	7.79463i	0.256403	+	0.317422i
$604$		0			0
$605$	−29.0081			−1.17935
$606$		0			0
$607$	43.8635			1.78036			0.890182	−	0.455604i	$-0.150577\pi$
$607$	43.8635			1.78036			0.890182	+	0.455604i	$0.150577\pi$
$608$		0			0
$609$	15.1317	+	3.07990i	0.613167	+	0.124804i
$610$		0			0
$611$	4.49445	+	7.78462i	0.181826	+	0.314932i
$612$		0			0
$613$	1.81569	−	3.14487i	0.0733351	−	0.127020i	−0.827026	−	0.562164i	$-0.809969\pi$
$613$	1.81569	−	3.14487i	0.0733351	−	0.127020i	0.900361	+	0.435144i	$0.143302\pi$
$614$		0			0
$615$	12.9049	+	6.16496i	0.520374	+	0.248595i
$616$		0			0
$617$	10.4542	−	18.1073i	0.420872	−	0.728971i	−0.575153	−	0.818046i	$-0.695058\pi$
$617$	10.4542	−	18.1073i	0.420872	−	0.728971i	0.996025	+	0.0890744i	$0.0283909\pi$
$618$		0			0
$619$	23.9490			0.962592			0.481296	−	0.876558i	$-0.340166\pi$
$619$	23.9490			0.962592			0.481296	+	0.876558i	$0.340166\pi$
$620$		0			0
$621$	5.20703	+	21.8649i	0.208951	+	0.877408i
$622$		0			0
$623$	8.26238	−	28.8716i	0.331025	−	1.15672i
$624$		0			0
$625$	−12.7125			−0.508501
$626$		0			0
$627$	47.1338	−	32.3519i	1.88234	−	1.29201i
$628$		0			0
$629$	−5.43933			−0.216880
$630$		0			0
$631$	−6.06918			−0.241610			−0.120805	−	0.992676i	$-0.538548\pi$
$631$	−6.06918			−0.241610			−0.120805	+	0.992676i	$0.538548\pi$
$632$		0			0
$633$	−8.66951	−	4.14163i	−0.344582	−	0.164615i
$634$		0			0
$635$	−42.6653			−1.69312
$636$		0			0
$637$	17.7496	+	11.0653i	0.703264	+	0.438422i
$638$		0			0
$639$	38.2500	−	6.01042i	1.51315	−	0.237768i
$640$		0			0
$641$	−17.3881			−0.686790			−0.343395	−	0.939191i	$-0.611577\pi$
$641$	−17.3881			−0.686790			−0.343395	+	0.939191i	$0.611577\pi$
$642$		0			0
$643$	9.66411	−	16.7387i	0.381115	−	0.660111i	−0.610107	−	0.792319i	$-0.708873\pi$
$643$	9.66411	−	16.7387i	0.381115	−	0.660111i	0.991222	+	0.132208i	$0.0422068\pi$
$644$		0			0
$645$	32.5220	−	22.3226i	1.28055	−	0.878951i
$646$		0			0
$647$	12.7041	−	22.0042i	0.499451	−	0.865075i	−0.500549	−	0.865708i	$-0.666868\pi$
$647$	12.7041	−	22.0042i	0.499451	−	0.865075i	1.00000		0.000633482i	$0.000201644\pi$
$648$		0			0
$649$	−27.3588	−	47.3869i	−1.07393	−	1.86010i
$650$		0			0
$651$	−42.0970	−	8.56844i	−1.64991	−	0.335824i
$652$		0			0
$653$	−25.8127			−1.01013			−0.505065	−	0.863081i	$-0.668532\pi$
$653$	−25.8127			−1.01013			−0.505065	+	0.863081i	$0.668532\pi$
$654$		0			0
$655$	−54.0918			−2.11354
$656$		0			0
$657$	17.7175	−	45.9880i	0.691225	−	1.79416i
$658$		0			0
$659$	8.62598	+	14.9406i	0.336020	+	0.582004i	0.983680	−	0.179925i	$-0.0575856\pi$
$659$	8.62598	+	14.9406i	0.336020	+	0.582004i	−0.647660	+	0.761930i	$0.724252\pi$
$660$		0			0
$661$	−6.48175	−	11.2267i	−0.252111	−	0.436669i	0.711996	−	0.702184i	$-0.247791\pi$
$661$	−6.48175	−	11.2267i	−0.252111	−	0.436669i	−0.964107	+	0.265515i	$0.914458\pi$
$662$		0			0
$663$	4.62771	−	3.17639i	0.179725	−	0.123361i
$664$		0			0
$665$	18.7220	−	65.4210i	0.726008	−	2.53692i
$666$		0			0
$667$	−7.28797	−	12.6231i	−0.282191	−	0.488769i
$668$		0			0
$669$	−17.1856	+	11.7959i	−0.664434	+	0.456057i
$670$		0			0
$671$	11.9641	−	20.7225i	0.461871	−	0.799984i
$672$		0			0
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	−0.918289	−	0.395910i	$-0.870429\pi$
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	0.116277	−	0.993217i	$-0.462904\pi$
$674$		0			0
$675$	−8.19232	−	34.4005i	−0.315323	−	1.32407i
$676$		0			0
$677$	11.0999	−	19.2256i	0.426605	−	0.738901i	−0.569964	−	0.821669i	$-0.693043\pi$
$677$	11.0999	−	19.2256i	0.426605	−	0.738901i	0.996569	+	0.0827688i	$0.0263763\pi$
$678$		0			0
$679$	−9.32221	+	32.5750i	−0.357753	+	1.25011i
$680$		0			0
$681$	−1.77408	−	22.7189i	−0.0679830	−	0.870590i
$682$		0			0
$683$	−4.60315	+	7.97289i	−0.176135	+	0.305074i	−0.940553	−	0.339646i	$-0.889693\pi$
$683$	−4.60315	+	7.97289i	−0.176135	+	0.305074i	0.764419	+	0.644720i	$0.223026\pi$
$684$		0			0
$685$	14.5346			0.555338
$686$		0			0
$687$	1.68326	+	21.5559i	0.0642206	+	0.822408i
$688$		0			0
$689$	1.58574	+	2.74659i	0.0604120	+	0.104637i
$690$		0			0
$691$	20.0293	−	34.6917i	0.761949	−	1.31974i	−0.179895	−	0.983686i	$-0.557576\pi$
$691$	20.0293	−	34.6917i	0.761949	−	1.31974i	0.941844	−	0.336049i	$-0.109091\pi$
$692$		0			0
$693$	27.9363	+	21.0819i	1.06121	+	0.800836i
$694$		0			0
$695$	−33.6846	+	58.3434i	−1.27773	+	2.21309i
$696$		0			0
$697$	1.30318	+	2.25717i	0.0493614	+	0.0854964i
$698$		0			0
$699$	5.76029	−	3.95377i	0.217874	−	0.149545i
$700$		0			0
$701$	34.3868			1.29877			0.649385	−	0.760459i	$-0.275026\pi$
$701$	34.3868			1.29877			0.649385	+	0.760459i	$0.275026\pi$
$702$		0			0
$703$	−18.7711	+	32.5124i	−0.707964	+	1.22623i
$704$		0			0
$705$	16.1543	+	7.71728i	0.608405	+	0.290649i
$706$		0			0
$707$	1.42739	+	1.47655i	0.0536824	+	0.0555314i
$708$		0			0
$709$	−10.5920	+	18.3459i	−0.397791	+	0.688994i	−0.993453	−	0.114241i	$-0.963556\pi$
$709$	−10.5920	+	18.3459i	−0.397791	+	0.688994i	0.595662	+	0.803235i	$0.296890\pi$
$710$		0			0
$711$	−2.53486	+	6.57954i	−0.0950645	+	0.246752i
$712$		0			0
$713$	20.2755	+	35.1181i	0.759322	+	1.31518i
$714$		0			0
$715$	−22.6347	+	39.2044i	−0.846489	+	1.46616i
$716$		0			0
$717$	43.3476	+	20.7082i	1.61884	+	0.773361i
$718$		0			0
$719$	−21.5994	−	37.4113i	−0.805523	−	1.39521i	−0.915937	−	0.401321i	$-0.868551\pi$
$719$	−21.5994	−	37.4113i	−0.805523	−	1.39521i	0.110414	−	0.993886i	$-0.464782\pi$
$720$		0			0
$721$	−4.19750	−	4.34207i	−0.156323	−	0.161707i
$722$		0			0
$723$	3.22455	+	41.2936i	0.119922	+	1.53572i
$724$		0			0
$725$	11.4663	+	19.8602i	0.425848	+	0.737590i
$726$		0			0
$727$	20.5571	+	35.6059i	0.762420	+	1.32055i	0.941600	+	0.336734i	$0.109322\pi$
$727$	20.5571	+	35.6059i	0.762420	+	1.32055i	−0.179180	+	0.983816i	$0.557344\pi$
$728$		0			0
$729$	−24.1018	+	12.1697i	−0.892661	+	0.450729i
$730$		0			0
$731$	7.18860			0.265880
$732$		0			0
$733$	52.0851			1.92381			0.961903	−	0.273390i	$-0.0881451\pi$
$733$	52.0851			1.92381			0.961903	+	0.273390i	$0.0881451\pi$
$734$		0			0
$735$	41.6178	−	1.83545i	1.53510	−	0.0677018i
$736$		0			0
$737$	−7.36361	−	12.7541i	−0.271242	−	0.469805i
$738$		0			0
$739$	7.18624	−	12.4469i	0.264350	−	0.457868i	−0.703043	−	0.711147i	$-0.748176\pi$
$739$	7.18624	−	12.4469i	0.264350	−	0.457868i	0.967393	+	0.253279i	$0.0815092\pi$
$740$		0			0
$741$	−3.01600	−	38.6228i	−0.110795	−	1.41885i
$742$		0			0
$743$	−21.3167	+	36.9216i	−0.782034	+	1.35452i	0.148721	+	0.988879i	$0.452484\pi$
$743$	−21.3167	+	36.9216i	−0.782034	+	1.35452i	−0.930755	+	0.365643i	$0.880849\pi$
$744$		0			0
$745$	33.4195			1.22440
$746$		0			0
$747$	6.05507	+	7.49605i	0.221543	+	0.274266i
$748$		0			0
$749$	−3.31162	+	11.5719i	−0.121004	+	0.422829i
$750$		0			0
$751$	−37.9692			−1.38552			−0.692758	−	0.721171i	$-0.743604\pi$
$751$	−37.9692			−1.38552			−0.692758	+	0.721171i	$0.743604\pi$
$752$		0			0
$753$	−0.449713	−	5.75902i	−0.0163885	−	0.209870i
$754$		0			0
$755$	33.7458			1.22813
$756$		0			0
$757$	27.6692			1.00565			0.502827	−	0.864387i	$-0.332293\pi$
$757$	27.6692			1.00565			0.502827	+	0.864387i	$0.332293\pi$
$758$		0			0
$759$	−2.57187	−	32.9353i	−0.0933528	−	1.19548i
$760$		0			0
$761$	11.9442			0.432977			0.216488	−	0.976285i	$-0.430540\pi$
$761$	11.9442			0.432977			0.216488	+	0.976285i	$0.430540\pi$
$762$		0			0
$763$	−12.1519	+	3.03658i	−0.439927	+	0.109932i
$764$		0			0
$765$	4.01897	−	10.4318i	0.145306	−	0.377161i
$766$		0			0
$767$	−37.0796			−1.33887
$768$		0			0
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	0.360487	+	0.932764i	$0.382610\pi$
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	−0.988041	+	0.154191i	$0.950723\pi$
$770$		0			0
$771$	−2.94888	−	37.7634i	−0.106201	−	1.36002i
$772$		0			0
$773$	−13.5014	+	23.3851i	−0.485611	+	0.841103i	−0.999863	−	0.0165363i	$-0.994736\pi$
$773$	−13.5014	+	23.3851i	−0.485611	+	0.841103i	0.514253	+	0.857639i	$0.328069\pi$
$774$		0			0
$775$	−31.8998	−	55.2521i	−1.14587	−	1.98471i
$776$		0			0
$777$	−22.5214	−	4.58400i	−0.807949	−	0.164450i
$778$		0			0
$779$	17.9890			0.644523
$780$		0			0
$781$	−56.9094			−2.03638
$782$		0			0
$783$	12.7230	−	12.0295i	0.454682	−	0.429900i
$784$		0			0
$785$	−20.6856	−	35.8286i	−0.738302	−	1.27878i
$786$		0			0
$787$	−10.6420	−	18.4325i	−0.379347	−	0.657048i	0.611621	−	0.791151i	$-0.290518\pi$
$787$	−10.6420	−	18.4325i	−0.379347	−	0.657048i	−0.990967	+	0.134104i	$0.957185\pi$
$788$		0			0
$789$	0.743042	+	9.51539i	0.0264530	+	0.338757i
$790$		0			0
$791$	−0.900275	+	0.224966i	−0.0320101	+	0.00799887i
$792$		0			0
$793$	−8.10754	−	14.0427i	−0.287907	−	0.498670i
$794$		0			0
$795$	5.69959	+	2.72283i	0.202144	+	0.0965688i
$796$		0			0
$797$	−10.3062	+	17.8508i	−0.365064	+	0.632309i	−0.988786	−	0.149337i	$-0.952286\pi$
$797$	−10.3062	+	17.8508i	−0.365064	+	0.632309i	0.623723	+	0.781646i	$0.285619\pi$
$798$		0			0
$799$	1.63131	+	2.82552i	0.0577117	+	0.0999597i
$800$		0			0
$801$	−21.3970	−	26.4891i	−0.756026	−	0.935945i
$802$		0			0
$803$	−36.2178	+	62.7311i	−1.27810	+	2.21373i
$804$		0			0
$805$	−27.3302	−	28.2715i	−0.963263	−	0.996440i
$806$		0			0
$807$	10.5460	+	5.03809i	0.371238	+	0.177349i
$808$		0			0
$809$	2.54223	−	4.40328i	0.0893802	−	0.154811i	−0.817869	−	0.575404i	$-0.804845\pi$
$809$	2.54223	−	4.40328i	0.0893802	−	0.154811i	0.907249	+	0.420593i	$0.138178\pi$
$810$		0			0
$811$	−7.58775			−0.266442			−0.133221	−	0.991086i	$-0.542532\pi$
$811$	−7.58775			−0.266442			−0.133221	+	0.991086i	$0.542532\pi$
$812$		0			0
$813$	−17.7631	+	12.1923i	−0.622977	+	0.427602i
$814$		0			0
$815$	−3.04285	−	5.27037i	−0.106586	−	0.184613i
$816$		0			0
$817$	24.8078	−	42.9683i	0.867914	−	1.50327i
$818$		0			0
$819$	21.8378	−	9.25172i	0.763074	−	0.323281i
$820$		0			0
$821$	−10.1348	+	17.5540i	−0.353706	+	0.612637i	−0.986896	−	0.161360i	$-0.948412\pi$
$821$	−10.1348	+	17.5540i	−0.353706	+	0.612637i	0.633189	+	0.773997i	$0.281745\pi$
$822$		0			0
$823$	−10.8955	−	18.8716i	−0.379794	−	0.657823i	0.611238	−	0.791447i	$-0.290672\pi$
$823$	−10.8955	−	18.8716i	−0.379794	−	0.657823i	−0.991032	+	0.133624i	$0.957339\pi$
$824$		0			0
$825$	4.04637	+	51.8178i	0.140877	+	1.80406i
$826$		0			0
$827$	26.3796			0.917307			0.458654	−	0.888615i	$-0.348332\pi$
$827$	26.3796			0.917307			0.458654	+	0.888615i	$0.348332\pi$
$828$		0			0
$829$	9.33400	−	16.1670i	0.324183	−	0.561502i	−0.657164	−	0.753748i	$-0.728244\pi$
$829$	9.33400	−	16.1670i	0.324183	−	0.561502i	0.981347	+	0.192246i	$0.0615773\pi$
$830$		0			0
$831$	−1.31052	−	16.7825i	−0.0454615	−	0.582180i
$832$		0			0
$833$	6.44242	+	4.01627i	0.223216	+	0.139155i
$834$		0			0
$835$	27.0183	−	46.7971i	0.935007	−	1.61948i
$836$		0			0
$837$	−35.3959	+	33.4667i	−1.22346	+	1.15678i
$838$		0			0
$839$	12.5265	+	21.6966i	0.432464	+	0.749050i	0.997085	−	0.0763004i	$-0.0243108\pi$
$839$	12.5265	+	21.6966i	0.432464	+	0.749050i	−0.564621	+	0.825351i	$0.690977\pi$
$840$		0			0
$841$	8.82253	−	15.2811i	0.304225	−	0.526934i
$842$		0			0
$843$	27.6115	−	18.9521i	0.950991	−	0.652745i
$844$		0			0
$845$	−6.99499	−	12.1157i	−0.240635	−	0.416792i
$846$		0			0
$847$	−15.5250	−	16.0598i	−0.533447	−	0.551820i
$848$		0			0
$849$	11.8655	−	8.14427i	0.407222	−	0.279511i
$850$		0			0
$851$	10.8471	+	18.7877i	0.371834	+	0.644035i
$852$		0			0
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	−0.981095	−	0.193526i	$-0.938008\pi$
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	0.322949	−	0.946416i	$-0.395326\pi$
$854$		0			0
$855$	−48.4842	−	60.0224i	−1.65812	−	2.05272i
$856$		0			0
$857$	−12.0060			−0.410117			−0.205058	−	0.978750i	$-0.565738\pi$
$857$	−12.0060			−0.410117			−0.205058	+	0.978750i	$0.565738\pi$
$858$		0			0
$859$	−12.6031			−0.430012			−0.215006	−	0.976613i	$-0.568977\pi$
$859$	−12.6031			−0.430012			−0.215006	+	0.976613i	$0.568977\pi$
$860$		0			0
$861$	3.49353	+	10.4440i	0.119059	+	0.355930i
$862$		0			0
$863$	−0.210643	−	0.364845i	−0.00717038	−	0.0124195i	0.862418	−	0.506197i	$-0.168949\pi$
$863$	−0.210643	−	0.364845i	−0.00717038	−	0.0124195i	−0.869588	+	0.493777i	$0.835616\pi$
$864$		0			0
$865$	32.3084	−	55.9597i	1.09852	−	1.90269i
$866$		0			0
$867$	−22.5968	+	15.5101i	−0.767426	+	0.526749i
$868$		0			0
$869$	5.18171	−	8.97499i	0.175778	−	0.304456i
$870$		0			0
$871$	−9.97995			−0.338158
$872$		0			0
$873$	24.1416	+	29.8868i	0.817070	+	1.01152i
$874$		0			0
$875$	11.4078	+	11.8007i	0.385653	+	0.398936i
$876$		0			0
$877$	1.78685			0.0603376			0.0301688	−	0.999545i	$-0.490396\pi$
$877$	1.78685			0.0603376			0.0301688	+	0.999545i	$0.490396\pi$
$878$		0			0
$879$	−12.4191	−	5.93291i	−0.418886	−	0.200112i
$880$		0			0
$881$	−49.8891			−1.68081			−0.840403	−	0.541962i	$-0.817682\pi$
$881$	−49.8891			−1.68081			−0.840403	+	0.541962i	$0.817682\pi$
$882$		0			0
$883$	34.7935			1.17090			0.585448	−	0.810710i	$-0.300919\pi$
$883$	34.7935			1.17090			0.585448	+	0.810710i	$0.300919\pi$
$884$		0			0
$885$	−60.8876	+	41.7923i	−2.04672	+	1.40483i
$886$		0			0
$887$	23.8080			0.799396			0.399698	−	0.916647i	$-0.369115\pi$
$887$	23.8080			0.799396			0.399698	+	0.916647i	$0.369115\pi$
$888$		0			0
$889$	−22.8344	−	23.6208i	−0.765840	−	0.792217i
$890$		0			0
$891$	37.7719	−	12.1711i	1.26541	−	0.407747i
$892$		0			0
$893$	22.5186			0.753556
$894$		0			0
$895$	−11.4829	+	19.8889i	−0.383830	+	0.664813i
$896$		0			0
$897$	−20.2000	−	9.65002i	−0.674458	−	0.322205i
$898$		0			0
$899$	15.7950	−	27.3577i	0.526792	−	0.912431i
$900$		0			0
$901$	0.575564	+	0.996907i	0.0191748	+	0.0332118i
$902$		0			0
$903$	29.7642	+	6.05820i	0.990489	+	0.201604i
$904$		0			0
$905$	−16.2768			−0.541060
$906$		0			0
$907$	34.2813			1.13829			0.569146	−	0.822237i	$-0.307274\pi$
$907$	34.2813			1.13829			0.569146	+	0.822237i	$0.307274\pi$
$908$		0			0
$909$	2.30044	−	0.361479i	0.0763006	−	0.0119895i
$910$		0			0
$911$	14.9839	+	25.9529i	0.496438	+	0.859857i	0.999992	−	0.00410771i	$-0.00130753\pi$
$911$	14.9839	+	25.9529i	0.496438	+	0.859857i	−0.503553	+	0.863964i	$0.667974\pi$
$912$		0			0
$913$	−7.08154	−	12.2656i	−0.234365	−	0.405932i
$914$		0			0
$915$	−29.1407	−	13.9212i	−0.963361	−	0.460221i
$916$		0			0
$917$	−28.9498	−	29.9469i	−0.956006	−	0.988933i
$918$		0			0
$919$	−0.391037	−	0.677296i	−0.0128991	−	0.0223419i	0.859504	−	0.511129i	$-0.170773\pi$
$919$	−0.391037	−	0.677296i	−0.0128991	−	0.0223419i	−0.872403	+	0.488787i	$0.837439\pi$
$920$		0			0
$921$	−3.62969	−	46.4818i	−0.119602	−	1.53163i
$922$		0			0
$923$	−19.2824	+	33.3981i	−0.634688	+	1.09931i
$924$		0			0
$925$	−17.0660	−	29.5591i	−0.561126	−	0.971898i
$926$		0			0
$927$	−6.76486	+	1.06300i	−0.222187	+	0.0349134i
$928$		0			0
$929$	6.76620	−	11.7194i	0.221992	−	0.384501i	−0.733421	−	0.679775i	$-0.762078\pi$
$929$	6.76620	−	11.7194i	0.221992	−	0.384501i	0.955413	+	0.295274i	$0.0954109\pi$
$930$		0			0
$931$	46.2391	−	24.6481i	1.51542	−	0.807808i
$932$		0			0
$933$	13.3509	−	9.16381i	0.437087	−	0.300010i
$934$		0			0
$935$	−8.21552	+	14.2297i	−0.268676	+	0.465361i
$936$		0			0
$937$	−2.27674			−0.0743777			−0.0371889	−	0.999308i	$-0.511840\pi$
$937$	−2.27674			−0.0743777			−0.0371889	+	0.999308i	$0.511840\pi$
$938$		0			0
$939$	−24.7528	−	11.8250i	−0.807776	−	0.385894i
$940$		0			0
$941$	4.07720	+	7.06192i	0.132913	+	0.230212i	0.924798	−	0.380458i	$-0.124234\pi$
$941$	4.07720	+	7.06192i	0.132913	+	0.230212i	−0.791885	+	0.610670i	$0.790900\pi$
$942$		0			0
$943$	5.19759	−	9.00249i	0.169257	−	0.293161i
$944$		0			0
$945$	25.4318	−	39.8054i	0.827297	−	1.29487i
$946$		0			0
$947$	−3.93553	+	6.81654i	−0.127888	+	0.221508i	−0.922858	−	0.385140i	$-0.874153\pi$
$947$	−3.93553	+	6.81654i	−0.127888	+	0.221508i	0.794970	+	0.606648i	$0.207486\pi$
$948$		0			0
$949$	24.5431	+	42.5099i	0.796703	+	1.37993i
$950$		0			0
$951$	44.4779	+	21.2482i	1.44230	+	0.689019i
$952$		0			0
$953$	43.1097			1.39646			0.698230	−	0.715873i	$-0.253971\pi$
$953$	43.1097			1.39646			0.698230	+	0.715873i	$0.253971\pi$
$954$		0			0
$955$	−39.6321	+	68.6448i	−1.28246	+	2.22129i
$956$		0			0
$957$	−21.2181	+	14.5637i	−0.685883	+	0.470779i
$958$		0			0
$959$	7.77888	+	8.04680i	0.251193	+	0.259845i
$960$		0			0
$961$	−28.4424	+	49.2636i	−0.917496	+	1.58915i
$962$		0			0
$963$	8.57607	+	10.6170i	0.276360	+	0.342128i
$964$		0			0
$965$	31.4507	+	54.4742i	1.01243	+	1.75359i
$966$		0			0
$967$	13.9537	−	24.1684i	0.448719	−	0.777205i	−0.549584	−	0.835439i	$-0.685214\pi$
$967$	13.9537	−	24.1684i	0.448719	−	0.777205i	0.998303	+	0.0582340i	$0.0185470\pi$
$968$		0			0
$969$	−1.09469	−	14.0186i	−0.0351666	−	0.450343i
$970$		0			0
$971$	21.0705	+	36.4952i	0.676185	+	1.17119i	0.976121	+	0.217228i	$0.0697015\pi$
$971$	21.0705	+	36.4952i	0.676185	+	1.17119i	−0.299936	+	0.953959i	$0.596965\pi$
$972$		0			0
$973$	−50.3286	+	12.5764i	−1.61346	+	0.403181i
$974$		0			0
$975$	31.7811	+	15.1826i	1.01781	+	0.486231i
$976$		0			0
$977$	6.92747	+	11.9987i	0.221629	+	0.383873i	0.955303	−	0.295629i	$-0.0955292\pi$
$977$	6.92747	+	11.9987i	0.221629	+	0.383873i	−0.733674	+	0.679502i	$0.762196\pi$
$978$		0			0
$979$	25.0243	+	43.3433i	0.799780	+	1.38526i
$980$		0			0
$981$	−5.10592	+	13.2531i	−0.163020	+	0.423138i
$982$		0			0
$983$	7.95876			0.253845			0.126923	−	0.991913i	$-0.459490\pi$
$983$	7.95876			0.253845			0.126923	+	0.991913i	$0.459490\pi$
$984$		0			0
$985$	−50.1182			−1.59690
$986$		0			0
$987$	4.37319	+	13.0738i	0.139200	+	0.416142i
$988$		0			0
$989$	−14.3355	−	24.8298i	−0.455842	−	0.789542i
$990$		0			0
$991$	4.36428	−	7.55916i	0.138636	−	0.240125i	−0.788345	−	0.615234i	$-0.789062\pi$
$991$	4.36428	−	7.55916i	0.138636	−	0.240125i	0.926981	+	0.375109i	$0.122395\pi$
$992$		0			0
$993$	30.6172	+	14.6266i	0.971609	+	0.464161i
$994$		0			0
$995$	3.13391	−	5.42809i	0.0993515	−	0.172082i
$996$		0			0
$997$	−2.30379			−0.0729619			−0.0364810	−	0.999334i	$-0.511615\pi$
$997$	−2.30379			−0.0729619			−0.0364810	+	0.999334i	$0.511615\pi$
$998$		0			0
$999$	−18.9363	+	17.9042i	−0.599119	+	0.566465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.d.193.5	yes	22
3.2	odd	2		1512.2.t.d.361.10		22
4.3	odd	2		1008.2.t.k.193.7		22
7.2	even	3		504.2.q.d.121.2	yes	22
9.2	odd	6		1512.2.q.c.1369.2		22
9.7	even	3		504.2.q.d.25.2	✓	22
12.11	even	2		3024.2.t.l.1873.10		22
21.2	odd	6		1512.2.q.c.793.2		22
28.23	odd	6		1008.2.q.k.625.10		22
36.7	odd	6		1008.2.q.k.529.10		22
36.11	even	6		3024.2.q.k.2881.2		22
63.2	odd	6		1512.2.t.d.289.10		22
63.16	even	3	inner	504.2.t.d.457.5	yes	22
84.23	even	6		3024.2.q.k.2305.2		22
252.79	odd	6		1008.2.t.k.961.7		22
252.191	even	6		3024.2.t.l.289.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.2	✓	22	9.7	even	3
504.2.q.d.121.2	yes	22	7.2	even	3
504.2.t.d.193.5	yes	22	1.1	even	1	trivial
504.2.t.d.457.5	yes	22	63.16	even	3	inner
1008.2.q.k.529.10		22	36.7	odd	6
1008.2.q.k.625.10		22	28.23	odd	6
1008.2.t.k.193.7		22	4.3	odd	2
1008.2.t.k.961.7		22	252.79	odd	6
1512.2.q.c.793.2		22	21.2	odd	6
1512.2.q.c.1369.2		22	9.2	odd	6
1512.2.t.d.289.10		22	63.2	odd	6
1512.2.t.d.361.10		22	3.2	odd	2
3024.2.q.k.2305.2		22	84.23	even	6
3024.2.q.k.2881.2		22	36.11	even	6
3024.2.t.l.289.10		22	252.191	even	6
3024.2.t.l.1873.10		22	12.11	even	2

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.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134843 + 1.72679i) q^{3} -3.43592 q^{5} +(-1.83889 - 1.90223i) q^{7} +(-2.96363 + 0.465691i) q^{9} +O(q^{10})\)	\(q+(0.134843 + 1.72679i) q^{3} -3.43592 q^{5} +(-1.83889 - 1.90223i) q^{7} +(-2.96363 + 0.465691i) q^{9} +4.40938 q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.463308 - 5.93312i) q^{15} +(0.542270 - 0.939239i) q^{17} +(-3.74273 - 6.48261i) q^{19} +(3.03680 - 3.43189i) q^{21} -4.32558 q^{23} +6.80552 q^{25} +(-1.20378 - 5.05479i) q^{27} +(1.68485 + 2.91825i) q^{29} +(-4.68734 - 8.11872i) q^{31} +(0.594572 + 7.61409i) q^{33} +(6.31828 + 6.53590i) q^{35} +(-2.50767 - 4.34341i) q^{37} +(4.66990 + 2.23092i) q^{39} +(-1.20160 + 2.08122i) q^{41} +(3.31412 + 5.74023i) q^{43} +(10.1828 - 1.60007i) q^{45} +(-1.50415 + 2.60527i) q^{47} +(-0.236948 + 6.99599i) q^{49} +(1.69499 + 0.809739i) q^{51} +(-0.530699 + 0.919198i) q^{53} -15.1502 q^{55} +(10.6894 - 7.33706i) q^{57} +(-6.20470 - 10.7468i) q^{59} +(2.71334 - 4.69965i) q^{61} +(6.33566 + 4.78116i) q^{63} +(-5.13331 + 8.89115i) q^{65} +(-1.66999 - 2.89251i) q^{67} +(-0.583272 - 7.46938i) q^{69} -12.9064 q^{71} +(-8.21382 + 14.2267i) q^{73} +(0.917674 + 11.7517i) q^{75} +(-8.10837 - 8.38764i) q^{77} +(1.17516 - 2.03543i) q^{79} +(8.56626 - 2.76028i) q^{81} +(-1.60602 - 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-4.81203 + 3.30290i) q^{87} +(5.67524 + 9.82981i) q^{89} +(-7.66974 + 1.91656i) q^{91} +(13.3873 - 9.18882i) q^{93} +(12.8597 + 22.2737i) q^{95} +(-6.40321 - 11.0907i) q^{97} +(-13.0678 + 2.05341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39} + 16 q^{41} + 22 q^{45} + 5 q^{47} - 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} - 19 q^{59} - 13 q^{61} + 21 q^{63} + 13 q^{65} + 26 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 8 q^{75} - 4 q^{77} + 10 q^{79} - 8 q^{81} - 28 q^{83} - 20 q^{85} + 9 q^{87} + 6 q^{89} - 37 q^{91} - 32 q^{93} + 12 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

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