LMFDB - Embedded newform 300.2.x.a.113.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.10
Character	$\chi$	$=$	300.113
Dual form			300.2.x.a.77.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71709 - 0.227126i) q^{3} +(-0.0496546 - 2.23552i) q^{5} +(-2.02060 + 2.02060i) q^{7} +(2.89683 - 0.779992i) q^{9} +O(q^{10})$	\(q+(1.71709 - 0.227126i) q^{3} +(-0.0496546 - 2.23552i) q^{5} +(-2.02060 + 2.02060i) q^{7} +(2.89683 - 0.779992i) q^{9} +(2.82802 - 3.89243i) q^{11} +(5.74634 + 0.910130i) q^{13} +(-0.593005 - 3.82732i) q^{15} +(-1.36348 + 0.694729i) q^{17} +(-3.53381 - 1.14820i) q^{19} +(-3.01063 + 3.92848i) q^{21} +(-2.52651 + 0.400161i) q^{23} +(-4.99507 + 0.222007i) q^{25} +(4.79697 - 1.99726i) q^{27} +(-0.0334412 - 0.102921i) q^{29} +(-3.13145 + 9.63760i) q^{31} +(3.97190 - 7.32598i) q^{33} +(4.61741 + 4.41674i) q^{35} +(-0.418876 + 2.64468i) q^{37} +(10.0737 + 0.257640i) q^{39} +(-2.26109 - 3.11213i) q^{41} +(-1.86113 - 1.86113i) q^{43} +(-1.88753 - 6.43718i) q^{45} +(-4.48724 + 8.80670i) q^{47} -1.16562i q^{49} +(-2.18344 + 1.50260i) q^{51} +(9.81020 + 4.99855i) q^{53} +(-8.84201 - 6.12880i) q^{55} +(-6.32867 - 1.16896i) q^{57} +(-0.210836 + 0.153181i) q^{59} +(-4.36920 - 3.17441i) q^{61} +(-4.27727 + 7.42937i) q^{63} +(1.74928 - 12.8912i) q^{65} +(1.74449 + 3.42375i) q^{67} +(-4.24738 + 1.26095i) q^{69} +(-14.1996 + 4.61373i) q^{71} +(-0.320861 - 2.02584i) q^{73} +(-8.52658 + 1.51572i) q^{75} +(2.15075 + 13.5793i) q^{77} +(8.17124 - 2.65500i) q^{79} +(7.78322 - 4.51901i) q^{81} +(3.16454 + 6.21076i) q^{83} +(1.62078 + 3.01359i) q^{85} +(-0.0807978 - 0.169131i) q^{87} +(-3.84520 - 2.79370i) q^{89} +(-13.4500 + 9.77202i) q^{91} +(-3.18805 + 17.2599i) q^{93} +(-2.39136 + 7.95690i) q^{95} +(14.9764 + 7.63086i) q^{97} +(5.15621 - 13.4815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{19}{20}\right)$

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
$3$	1.71709	−	0.227126i	0.991365	−	0.131131i
$3$	1.71709	−	0.227126i	0.991365	−	0.131131i
$4$		0			0
$5$	−0.0496546	−	2.23552i	−0.0222062	−	0.999753i
$5$	−0.0496546	−	2.23552i	−0.0222062	−	0.999753i
$6$		0			0
$7$	−2.02060	+	2.02060i	−0.763714	+	0.763714i	−0.976992	−	0.213278i	$-0.931586\pi$
$7$	−2.02060	+	2.02060i	−0.763714	+	0.763714i	0.213278	+	0.976992i	$0.431586\pi$
$8$		0			0
$9$	2.89683	−	0.779992i	0.965609	−	0.259997i
$10$		0			0
$11$	2.82802	−	3.89243i	0.852679	−	1.17361i	−0.130587	−	0.991437i	$-0.541686\pi$
$11$	2.82802	−	3.89243i	0.852679	−	1.17361i	0.983266	−	0.182175i	$-0.0583137\pi$
$12$		0			0
$13$	5.74634	+	0.910130i	1.59375	+	0.252425i	0.889297	−	0.457329i	$-0.151194\pi$
$13$	5.74634	+	0.910130i	1.59375	+	0.252425i	0.704450	+	0.709754i	$0.251194\pi$
$14$		0			0
$15$	−0.593005	−	3.82732i	−0.153113	−	0.988209i
$16$		0			0
$17$	−1.36348	+	0.694729i	−0.330693	+	0.168497i	−0.611451	−	0.791282i	$-0.709414\pi$
$17$	−1.36348	+	0.694729i	−0.330693	+	0.168497i	0.280758	+	0.959778i	$0.409414\pi$
$18$		0			0
$19$	−3.53381	−	1.14820i	−0.810711	−	0.263416i	−0.125812	−	0.992054i	$-0.540154\pi$
$19$	−3.53381	−	1.14820i	−0.810711	−	0.263416i	−0.684899	+	0.728638i	$0.740154\pi$
$20$		0			0
$21$	−3.01063	+	3.92848i	−0.656972	+	0.857265i
$22$		0			0
$23$	−2.52651	+	0.400161i	−0.526815	+	0.0834393i	−0.414176	−	0.910197i	$-0.635930\pi$
$23$	−2.52651	+	0.400161i	−0.526815	+	0.0834393i	−0.112639	+	0.993636i	$0.535930\pi$
$24$		0			0
$25$	−4.99507	+	0.222007i	−0.999014	+	0.0444015i
$26$		0			0
$27$	4.79697	−	1.99726i	0.923178	−	0.384374i
$28$		0			0
$29$	−0.0334412	−	0.102921i	−0.00620988	−	0.0191120i	0.947904	−	0.318557i	$-0.103198\pi$
$29$	−0.0334412	−	0.102921i	−0.00620988	−	0.0191120i	−0.954113	+	0.299445i	$0.903198\pi$
$30$		0			0
$31$	−3.13145	+	9.63760i	−0.562425	+	1.73096i	0.113058	+	0.993588i	$0.463936\pi$
$31$	−3.13145	+	9.63760i	−0.562425	+	1.73096i	−0.675482	+	0.737376i	$0.736064\pi$
$32$		0			0
$33$	3.97190	−	7.32598i	0.691419	−	1.27529i
$34$		0			0
$35$	4.61741	+	4.41674i	0.780484	+	0.746566i
$36$		0			0
$37$	−0.418876	+	2.64468i	−0.0688628	+	0.434782i	0.929036	+	0.369989i	$0.120639\pi$
$37$	−0.418876	+	2.64468i	−0.0688628	+	0.434782i	−0.997899	+	0.0647929i	$0.979361\pi$
$38$		0			0
$39$	10.0737	+	0.257640i	1.61309	+	0.0412554i
$40$		0			0
$41$	−2.26109	−	3.11213i	−0.353123	−	0.486032i	0.595093	−	0.803656i	$-0.297115\pi$
$41$	−2.26109	−	3.11213i	−0.353123	−	0.486032i	−0.948217	+	0.317624i	$0.897115\pi$
$42$		0			0
$43$	−1.86113	−	1.86113i	−0.283820	−	0.283820i	0.550810	−	0.834631i	$-0.314319\pi$
$43$	−1.86113	−	1.86113i	−0.283820	−	0.283820i	−0.834631	+	0.550810i	$0.814319\pi$
$44$		0			0
$45$	−1.88753	−	6.43718i	−0.281376	−	0.959598i
$46$		0			0
$47$	−4.48724	+	8.80670i	−0.654531	+	1.28459i	0.290271	+	0.956945i	$0.406255\pi$
$47$	−4.48724	+	8.80670i	−0.654531	+	1.28459i	−0.944801	+	0.327644i	$0.893745\pi$
$48$		0			0
$49$		−	1.16562i		−	0.166517i
$50$		0			0
$51$	−2.18344	+	1.50260i	−0.305742	+	0.210406i
$52$		0			0
$53$	9.81020	+	4.99855i	1.34754	+	0.686604i	0.970839	−	0.239733i	$-0.0770600\pi$
$53$	9.81020	+	4.99855i	1.34754	+	0.686604i	0.376696	+	0.926337i	$0.377060\pi$
$54$		0			0
$55$	−8.84201	−	6.12880i	−1.19226	−	0.826407i
$56$		0			0
$57$	−6.32867	−	1.16896i	−0.838253	−	0.154832i
$58$		0			0
$59$	−0.210836	+	0.153181i	−0.0274485	+	0.0199425i	−0.601425	−	0.798929i	$-0.705400\pi$
$59$	−0.210836	+	0.153181i	−0.0274485	+	0.0199425i	0.573976	+	0.818872i	$0.305400\pi$
$60$		0			0
$61$	−4.36920	−	3.17441i	−0.559418	−	0.406441i	0.271828	−	0.962346i	$-0.412372\pi$
$61$	−4.36920	−	3.17441i	−0.559418	−	0.406441i	−0.831246	+	0.555905i	$0.812372\pi$
$62$		0			0
$63$	−4.27727	+	7.42937i	−0.538885	+	0.936012i
$64$		0			0
$65$	1.74928	−	12.8912i	0.216971	−	1.59896i
$66$		0			0
$67$	1.74449	+	3.42375i	0.213123	+	0.418278i	0.972676	−	0.232168i	$-0.0745819\pi$
$67$	1.74449	+	3.42375i	0.213123	+	0.418278i	−0.759552	+	0.650446i	$0.774582\pi$
$68$		0			0
$69$	−4.24738	+	1.26095i	−0.511324	+	0.151801i
$70$		0			0
$71$	−14.1996	+	4.61373i	−1.68518	+	0.547549i	−0.985906	−	0.167302i	$-0.946495\pi$
$71$	−14.1996	+	4.61373i	−1.68518	+	0.547549i	−0.699277	+	0.714851i	$0.746495\pi$
$72$		0			0
$73$	−0.320861	−	2.02584i	−0.0375539	−	0.237106i	0.961771	−	0.273857i	$-0.0882993\pi$
$73$	−0.320861	−	2.02584i	−0.0375539	−	0.237106i	−0.999324	+	0.0367504i	$0.988299\pi$
$74$		0			0
$75$	−8.52658	+	1.51572i	−0.984565	+	0.175020i
$76$		0			0
$77$	2.15075	+	13.5793i	0.245101	+	1.54751i
$78$		0			0
$79$	8.17124	−	2.65500i	0.919337	−	0.298711i	0.189142	−	0.981950i	$-0.439429\pi$
$79$	8.17124	−	2.65500i	0.919337	−	0.298711i	0.730195	+	0.683239i	$0.239429\pi$
$80$		0			0
$81$	7.78322	−	4.51901i	0.864803	−	0.502112i
$82$		0			0
$83$	3.16454	+	6.21076i	0.347353	+	0.681719i	0.996906	−	0.0785968i	$-0.0250440\pi$
$83$	3.16454	+	6.21076i	0.347353	+	0.681719i	−0.649553	+	0.760316i	$0.725044\pi$
$84$		0			0
$85$	1.62078	+	3.01359i	0.175798	+	0.326870i
$86$		0			0
$87$	−0.0807978	−	0.169131i	−0.00866243	−	0.0181327i
$88$		0			0
$89$	−3.84520	−	2.79370i	−0.407590	−	0.296132i	0.365035	−	0.930994i	$-0.381057\pi$
$89$	−3.84520	−	2.79370i	−0.407590	−	0.296132i	−0.772625	+	0.634862i	$0.781057\pi$
$90$		0			0
$91$	−13.4500	+	9.77202i	−1.40995	+	1.02439i
$92$		0			0
$93$	−3.18805	+	17.2599i	−0.330585	+	1.78977i
$94$		0			0
$95$	−2.39136	+	7.95690i	−0.245348	+	0.816361i
$96$		0			0
$97$	14.9764	+	7.63086i	1.52062	+	0.774797i	0.997018	−	0.0771640i	$-0.0245865\pi$
$97$	14.9764	+	7.63086i	1.52062	+	0.774797i	0.523606	+	0.851961i	$0.324587\pi$
$98$		0			0
$99$	5.15621	−	13.4815i	0.518219	−	1.35494i
$100$		0			0
$101$		−	17.3569i		−	1.72707i	−0.504288	−	0.863536i	$-0.668245\pi$
$101$		−	17.3569i		−	1.72707i	0.504288	−	0.863536i	$-0.331755\pi$
$102$		0			0
$103$	−2.15137	+	4.22231i	−0.211981	+	0.416036i	−0.972374	−	0.233426i	$-0.925006\pi$
$103$	−2.15137	+	4.22231i	−0.211981	+	0.416036i	0.760393	+	0.649463i	$0.225006\pi$
$104$		0			0
$105$	8.93168	+	6.53524i	0.871643	+	0.637774i
$106$		0			0
$107$	−12.4265	−	12.4265i	−1.20132	−	1.20132i	−0.973766	−	0.227550i	$-0.926928\pi$
$107$	−12.4265	−	12.4265i	−1.20132	−	1.20132i	−0.227550	−	0.973766i	$-0.573072\pi$
$108$		0			0
$109$	−10.0321	−	13.8080i	−0.960904	−	1.32257i	−0.946510	−	0.322675i	$-0.895418\pi$
$109$	−10.0321	−	13.8080i	−0.960904	−	1.32257i	−0.0143943	−	0.999896i	$-0.504582\pi$
$110$		0			0
$111$	−0.118576	+	4.63630i	−0.0112547	+	0.440058i
$112$		0			0
$113$	0.324731	−	2.05027i	0.0305481	−	0.192873i	−0.967695	−	0.252124i	$-0.918871\pi$
$113$	0.324731	−	2.05027i	0.0305481	−	0.192873i	0.998243	+	0.0592504i	$0.0188710\pi$
$114$		0			0
$115$	1.02002	+	5.62820i	0.0951172	+	0.524832i
$116$		0			0
$117$	17.3560	−	1.84561i	1.60457	−	0.170626i
$118$		0			0
$119$	1.35128	−	4.15881i	0.123872	−	0.381238i
$120$		0			0
$121$	−3.75415	−	11.5541i	−0.341286	−	1.05037i
$122$		0			0
$123$	−4.58935	−	4.83026i	−0.413808	−	0.435530i
$124$		0			0
$125$	0.744329	+	11.1555i	0.0665748	+	0.997781i
$126$		0			0
$127$	−1.50225	+	0.237933i	−0.133303	+	0.0211132i	−0.222729	−	0.974880i	$-0.571497\pi$
$127$	−1.50225	+	0.237933i	−0.133303	+	0.0211132i	0.0894262	+	0.995993i	$0.471497\pi$
$128$		0			0
$129$	−3.61846	−	2.77303i	−0.318587	−	0.244152i
$130$		0			0
$131$	5.58648	+	1.81516i	0.488093	+	0.158591i	0.542717	−	0.839916i	$-0.317396\pi$
$131$	5.58648	+	1.81516i	0.488093	+	0.158591i	−0.0546233	+	0.998507i	$0.517396\pi$
$132$		0			0
$133$	9.46045	−	4.82034i	0.820325	−	0.417977i
$134$		0			0
$135$	−4.70311	−	10.6245i	−0.404779	−	0.914415i
$136$		0			0
$137$	−8.72702	−	1.38222i	−0.745599	−	0.118091i	−0.227936	−	0.973676i	$-0.573198\pi$
$137$	−8.72702	−	1.38222i	−0.745599	−	0.118091i	−0.517663	+	0.855585i	$0.673198\pi$
$138$		0			0
$139$	2.77543	−	3.82005i	0.235409	−	0.324012i	−0.674926	−	0.737886i	$-0.735824\pi$
$139$	2.77543	−	3.82005i	0.235409	−	0.324012i	0.910335	+	0.413873i	$0.135824\pi$
$140$		0			0
$141$	−5.70478	+	16.1411i	−0.480429	+	1.35933i
$142$		0			0
$143$	19.7933	−	19.7933i	1.65520	−	1.65520i
$144$		0			0
$145$	−0.228422	+	0.0798689i	−0.0189694	+	0.00663275i
$146$		0			0
$147$	−0.264741	−	2.00148i	−0.0218355	−	0.165079i
$148$		0			0
$149$	−1.98633			−0.162726			−0.0813632	−	0.996685i	$-0.525927\pi$
$149$	−1.98633			−0.162726			−0.0813632	+	0.996685i	$0.525927\pi$
$150$		0			0
$151$	21.4868			1.74857			0.874284	−	0.485415i	$-0.161332\pi$
$151$	21.4868			1.74857			0.874284	+	0.485415i	$0.161332\pi$
$152$		0			0
$153$	−3.40789	+	3.07602i	−0.275512	+	0.248681i
$154$		0			0
$155$	21.7005	+	6.52185i	1.74303	+	0.523848i
$156$		0			0
$157$	7.63307	−	7.63307i	0.609185	−	0.609185i	−0.333548	−	0.942733i	$-0.608246\pi$
$157$	7.63307	−	7.63307i	0.609185	−	0.609185i	0.942733	+	0.333548i	$0.108246\pi$
$158$		0			0
$159$	17.9803	+	6.35483i	1.42593	+	0.503971i
$160$		0			0
$161$	4.29650	−	5.91363i	0.338612	−	0.466059i
$162$		0			0
$163$	−4.19979	−	0.665182i	−0.328953	−	0.0521011i	−0.0102264	−	0.999948i	$-0.503255\pi$
$163$	−4.19979	−	0.665182i	−0.328953	−	0.0521011i	−0.318727	+	0.947847i	$0.603255\pi$
$164$		0			0
$165$	−16.5746	−	8.51548i	−1.29033	−	0.662929i
$166$		0			0
$167$	9.52908	−	4.85531i	0.737383	−	0.375715i	−0.0446088	−	0.999005i	$-0.514204\pi$
$167$	9.52908	−	4.85531i	0.737383	−	0.375715i	0.781991	+	0.623289i	$0.214204\pi$
$168$		0			0
$169$	19.8283	+	6.44261i	1.52525	+	0.495585i
$170$		0			0
$171$	−11.1324	−	0.569807i	−0.851318	−	0.0435742i
$172$		0			0
$173$	−2.32976	+	0.368997i	−0.177128	+	0.0280543i	−0.244368	−	0.969682i	$-0.578581\pi$
$173$	−2.32976	+	0.368997i	−0.177128	+	0.0280543i	0.0672403	+	0.997737i	$0.478581\pi$
$174$		0			0
$175$	9.64443	−	10.5416i	0.729050	−	0.796870i
$176$		0			0
$177$	−0.327234	+	0.310913i	−0.0245964	+	0.0233697i
$178$		0			0
$179$	1.36907	+	4.21356i	0.102329	+	0.314936i	0.989094	−	0.147284i	$-0.0470531\pi$
$179$	1.36907	+	4.21356i	0.102329	+	0.314936i	−0.886765	+	0.462220i	$0.847053\pi$
$180$		0			0
$181$	2.45027	−	7.54116i	0.182127	−	0.560530i	−0.817760	−	0.575559i	$-0.804784\pi$
$181$	2.45027	−	7.54116i	0.182127	−	0.560530i	0.999887	+	0.0150298i	$0.00478432\pi$
$182$		0			0
$183$	−8.22331	−	4.45840i	−0.607885	−	0.329574i
$184$		0			0
$185$	5.93302	+	0.805083i	0.436204	+	0.0591909i
$186$		0			0
$187$	−1.15177	+	7.27196i	−0.0842254	+	0.531779i
$188$		0			0
$189$	−5.65708	+	13.7284i	−0.411492	+	0.998595i
$190$		0			0
$191$	−4.93725	−	6.79554i	−0.357247	−	0.491708i	0.592132	−	0.805841i	$-0.298286\pi$
$191$	−4.93725	−	6.79554i	−0.357247	−	0.491708i	−0.949379	+	0.314133i	$0.898286\pi$
$192$		0			0
$193$	9.74578	+	9.74578i	0.701517	+	0.701517i	0.964736	−	0.263219i	$-0.0847843\pi$
$193$	9.74578	+	9.74578i	0.701517	+	0.701517i	−0.263219	+	0.964736i	$0.584784\pi$
$194$		0			0
$195$	0.0757523	−	22.5328i	0.00542473	−	1.61360i
$196$		0			0
$197$	−7.05689	+	13.8499i	−0.502783	+	0.986766i	0.490543	+	0.871417i	$0.336799\pi$
$197$	−7.05689	+	13.8499i	−0.502783	+	0.986766i	−0.993325	+	0.115349i	$0.963201\pi$
$198$		0			0
$199$			10.6381i			0.754117i	0.926189	+	0.377059i	$0.123064\pi$
$199$			10.6381i			0.754117i	−0.926189	+	0.377059i	$0.876936\pi$
$200$		0			0
$201$	3.77308	+	5.48269i	0.266132	+	0.386719i
$202$		0			0
$203$	0.275534	+	0.140392i	0.0193387	+	0.00985355i
$204$		0			0
$205$	−6.84494	+	5.20924i	−0.478071	+	0.363829i
$206$		0			0
$207$	−7.00676	+	3.12986i	−0.487003	+	0.217540i
$208$		0			0
$209$	−14.4630	+	10.5080i	−1.00042	+	0.726851i
$210$		0			0
$211$	8.87487	+	6.44797i	0.610971	+	0.443897i	0.849756	−	0.527176i	$-0.176749\pi$
$211$	8.87487	+	6.44797i	0.610971	+	0.443897i	−0.238785	+	0.971072i	$0.576749\pi$
$212$		0			0
$213$	−23.3342	+	11.1473i	−1.59883	+	0.763801i
$214$		0			0
$215$	−4.06818	+	4.25301i	−0.277448	+	0.290053i
$216$		0			0
$217$	−13.1463	−	25.8011i	−0.892430	−	1.75149i
$218$		0			0
$219$	−1.01107	−	3.40568i	−0.0683216	−	0.230134i
$220$		0			0
$221$	−8.46732	+	2.75120i	−0.569574	+	0.185066i
$222$		0			0
$223$	−2.83443	−	17.8959i	−0.189807	−	1.19840i	−0.880072	−	0.474840i	$-0.842506\pi$
$223$	−2.83443	−	17.8959i	−0.189807	−	1.19840i	0.690265	−	0.723557i	$-0.257494\pi$
$224$		0			0
$225$	−14.2967	+	4.53923i	−0.953113	+	0.302615i
$226$		0			0
$227$	−0.381413	−	2.40815i	−0.0253153	−	0.159834i	0.971792	−	0.235839i	$-0.0757837\pi$
$227$	−0.381413	−	2.40815i	−0.0253153	−	0.159834i	−0.997107	+	0.0760044i	$0.975784\pi$
$228$		0			0
$229$	−13.9452	+	4.53107i	−0.921524	+	0.299421i	−0.731092	−	0.682279i	$-0.760989\pi$
$229$	−13.9452	+	4.53107i	−0.921524	+	0.299421i	−0.190432	+	0.981700i	$0.560989\pi$
$230$		0			0
$231$	6.77725	+	22.8285i	0.445910	+	1.50200i
$232$		0			0
$233$	−8.99659	−	17.6568i	−0.589386	−	1.15674i	−0.972471	−	0.233022i	$-0.925139\pi$
$233$	−8.99659	−	17.6568i	−0.589386	−	1.15674i	0.383085	−	0.923713i	$-0.374861\pi$
$234$		0			0
$235$	19.9103	+	9.59400i	1.29881	+	0.625843i
$236$		0			0
$237$	13.4278	−	6.41478i	0.872228	−	0.416685i
$238$		0			0
$239$	−18.6744	−	13.5678i	−1.20795	−	0.877625i	−0.212904	−	0.977073i	$-0.568292\pi$
$239$	−18.6744	−	13.5678i	−1.20795	−	0.877625i	−0.995043	+	0.0994482i	$0.968292\pi$
$240$		0			0
$241$	7.99196	−	5.80650i	0.514807	−	0.374029i	−0.299837	−	0.953990i	$-0.596932\pi$
$241$	7.99196	−	5.80650i	0.514807	−	0.374029i	0.814644	+	0.579961i	$0.196932\pi$
$242$		0			0
$243$	12.3382	−	9.52733i	0.791493	−	0.611178i
$244$		0			0
$245$	−2.60576	+	0.0578783i	−0.166476	+	0.00369771i
$246$		0			0
$247$	−19.2614	−	9.81419i	−1.22558	−	0.624462i
$248$		0			0
$249$	6.84444	+	9.94571i	0.433749	+	0.630284i
$250$		0			0
$251$		−	16.9633i		−	1.07071i	−0.844626	−	0.535357i	$-0.820177\pi$
$251$		−	16.9633i		−	1.07071i	0.844626	−	0.535357i	$-0.179823\pi$
$252$		0			0
$253$	−5.58743	+	10.9659i	−0.351278	+	0.689423i
$254$		0			0
$255$	3.46750	+	4.80650i	0.217143	+	0.300995i
$256$		0			0
$257$	17.5417	+	17.5417i	1.09422	+	1.09422i	0.995073	+	0.0991458i	$0.0316110\pi$
$257$	17.5417	+	17.5417i	1.09422	+	1.09422i	0.0991458	+	0.995073i	$0.468389\pi$
$258$		0			0
$259$	−4.49745	−	6.19020i	−0.279458	−	0.384641i
$260$		0			0
$261$	−0.177151	−	0.272062i	−0.0109654	−	0.0168402i
$262$		0			0
$263$	−2.55900	+	16.1569i	−0.157795	+	0.996277i	0.773972	+	0.633220i	$0.218267\pi$
$263$	−2.55900	+	16.1569i	−0.157795	+	0.996277i	−0.931767	+	0.363057i	$0.881733\pi$
$264$		0			0
$265$	10.6872	−	22.1791i	0.656511	−	1.36245i
$266$		0			0
$267$	−7.23709	−	3.92370i	−0.442903	−	0.240127i
$268$		0			0
$269$	−2.50454	+	7.70819i	−0.152705	+	0.469977i	−0.997921	−	0.0644474i	$-0.979472\pi$
$269$	−2.50454	+	7.70819i	−0.152705	+	0.469977i	0.845216	+	0.534424i	$0.179472\pi$
$270$		0			0
$271$	−2.83005	−	8.70999i	−0.171913	−	0.529094i	0.827566	−	0.561368i	$-0.189725\pi$
$271$	−2.83005	−	8.70999i	−0.171913	−	0.529094i	−0.999479	+	0.0322745i	$0.989725\pi$
$272$		0			0
$273$	−20.8755	+	19.8343i	−1.26344	+	1.20043i
$274$		0			0
$275$	−13.2620	+	20.0708i	−0.799728	+	1.21031i
$276$		0			0
$277$	−3.90301	+	0.618177i	−0.234509	+	0.0371426i	−0.272583	−	0.962132i	$-0.587878\pi$
$277$	−3.90301	+	0.618177i	−0.234509	+	0.0371426i	0.0380735	+	0.999275i	$0.487878\pi$
$278$		0			0
$279$	−1.55401	+	30.3610i	−0.0930361	+	1.81766i
$280$		0			0
$281$	24.5537	+	7.97798i	1.46475	+	0.475926i	0.929517	−	0.368778i	$-0.120224\pi$
$281$	24.5537	+	7.97798i	1.46475	+	0.475926i	0.535233	+	0.844704i	$0.320224\pi$
$282$		0			0
$283$	−1.20672	+	0.614853i	−0.0717319	+	0.0365492i	−0.489489	−	0.872010i	$-0.662816\pi$
$283$	−1.20672	+	0.614853i	−0.0717319	+	0.0365492i	0.417757	+	0.908559i	$0.362816\pi$
$284$		0			0
$285$	−2.29897	+	14.2059i	−0.136179	+	0.841484i
$286$		0			0
$287$	10.8571	+	1.71960i	0.640875	+	0.101505i
$288$		0			0
$289$	−8.61591	+	11.8588i	−0.506818	+	0.697576i
$290$		0			0
$291$	27.4491	+	9.70139i	1.60909	+	0.568705i
$292$		0			0
$293$	9.43835	−	9.43835i	0.551395	−	0.551395i	−0.375449	−	0.926843i	$-0.622511\pi$
$293$	9.43835	−	9.43835i	0.551395	−	0.551395i	0.926843	+	0.375449i	$0.122511\pi$
$294$		0			0
$295$	0.352909	+	0.463722i	0.0205471	+	0.0269989i
$296$		0			0
$297$	5.79170	−	24.3202i	0.336069	−	1.41120i
$298$		0			0
$299$	−14.8824			−0.860672
$300$		0			0
$301$	7.52120			0.433515
$302$		0			0
$303$	−3.94218	−	29.8034i	−0.226473	−	1.71216i
$304$		0			0
$305$	−6.87949	+	9.92503i	−0.393918	+	0.568306i
$306$		0			0
$307$	−9.42497	+	9.42497i	−0.537911	+	0.537911i	−0.922915	−	0.385004i	$-0.874200\pi$
$307$	−9.42497	+	9.42497i	−0.537911	+	0.537911i	0.385004	+	0.922915i	$0.374200\pi$
$308$		0			0
$309$	−2.73512	+	7.73874i	−0.155595	+	0.440241i
$310$		0			0
$311$	7.79335	−	10.7266i	0.441920	−	0.608251i	−0.528717	−	0.848798i	$-0.677327\pi$
$311$	7.79335	−	10.7266i	0.441920	−	0.608251i	0.970637	+	0.240547i	$0.0773269\pi$
$312$		0			0
$313$	0.0874904	+	0.0138571i	0.00494525	+	0.000783251i	0.158907	−	0.987294i	$-0.449203\pi$
$313$	0.0874904	+	0.0138571i	0.00494525	+	0.000783251i	−0.153961	+	0.988077i	$0.549203\pi$
$314$		0			0
$315$	16.8209	+	9.19301i	0.947748	+	0.517967i
$316$		0			0
$317$	−25.7112	+	13.1005i	−1.44409	+	0.735799i	−0.988046	−	0.154160i	$-0.950733\pi$
$317$	−25.7112	+	13.1005i	−1.44409	+	0.735799i	−0.456041	+	0.889959i	$0.650733\pi$
$318$		0			0
$319$	−0.495187	−	0.160896i	−0.0277251	−	0.00900844i
$320$		0			0
$321$	−24.1599	−	18.5151i	−1.34847	−	1.03341i
$322$		0			0
$323$	5.61597	−	0.889483i	0.312481	−	0.0494922i
$324$		0			0
$325$	−28.9054	−	3.27043i	−1.60338	−	0.181411i
$326$		0			0
$327$	−20.3623	−	21.4312i	−1.12604	−	1.18515i
$328$		0			0
$329$	−8.72788	−	26.8617i	−0.481184	−	1.48093i
$330$		0			0
$331$	1.58196	−	4.86878i	0.0869525	−	0.267612i	−0.898120	−	0.439750i	$-0.855067\pi$
$331$	1.58196	−	4.86878i	0.0869525	−	0.267612i	0.985073	+	0.172137i	$0.0550672\pi$
$332$		0			0
$333$	0.849417	+	7.98790i	0.0465477	+	0.437734i
$334$		0			0
$335$	7.56724	−	4.06984i	0.413442	−	0.222359i
$336$		0			0
$337$	2.34521	−	14.8070i	0.127752	−	0.806591i	−0.837723	−	0.546095i	$-0.816114\pi$
$337$	2.34521	−	14.8070i	0.127752	−	0.806591i	0.965475	−	0.260496i	$-0.0838862\pi$
$338$		0			0
$339$	0.0919250	−	3.59426i	0.00499268	−	0.195214i
$340$		0			0
$341$	28.6579	+	39.4442i	1.55191	+	2.13602i
$342$		0			0
$343$	−11.7889	−	11.7889i	−0.636542	−	0.636542i
$344$		0			0
$345$	3.02978	+	9.43247i	0.163118	+	0.507827i
$346$		0			0
$347$	4.06670	−	7.98136i	0.218312	−	0.428462i	−0.755713	−	0.654903i	$-0.772709\pi$
$347$	4.06670	−	7.98136i	0.218312	−	0.428462i	0.974025	+	0.226442i	$0.0727093\pi$
$348$		0			0
$349$			31.6418i			1.69375i	0.531793	+	0.846874i	$0.321518\pi$
$349$			31.6418i			1.69375i	−0.531793	+	0.846874i	$0.678482\pi$
$350$		0			0
$351$	29.3828	−	7.11108i	1.56834	−	0.379561i
$352$		0			0
$353$	16.4179	+	8.36532i	0.873834	+	0.445241i	0.832578	−	0.553908i	$-0.186864\pi$
$353$	16.4179	+	8.36532i	0.873834	+	0.445241i	0.0412563	+	0.999149i	$0.486864\pi$
$354$		0			0
$355$	11.0191	+	31.5144i	0.584836	+	1.67261i
$356$		0			0
$357$	1.37570	−	7.44799i	0.0728100	−	0.394189i
$358$		0			0
$359$	−3.85147	+	2.79826i	−0.203273	+	0.147686i	−0.684765	−	0.728764i	$-0.740095\pi$
$359$	−3.85147	+	2.79826i	−0.203273	+	0.147686i	0.481492	+	0.876450i	$0.340095\pi$
$360$		0			0
$361$	−4.20190	−	3.05286i	−0.221153	−	0.160677i
$362$		0			0
$363$	−9.07045	−	18.9868i	−0.476075	−	0.996547i
$364$		0			0
$365$	−4.51286	+	0.817882i	−0.236214	+	0.0428099i
$366$		0			0
$367$	2.16114	+	4.24147i	0.112810	+	0.221403i	0.940508	−	0.339771i	$-0.110350\pi$
$367$	2.16114	+	4.24147i	0.112810	+	0.221403i	−0.827698	+	0.561174i	$0.810350\pi$
$368$		0			0
$369$	−8.97743	−	7.25166i	−0.467346	−	0.377506i
$370$		0			0
$371$	−29.9225	+	9.72241i	−1.55350	+	0.504763i
$372$		0			0
$373$	−3.54113	−	22.3578i	−0.183353	−	1.15765i	−0.891984	−	0.452066i	$-0.850687\pi$
$373$	−3.54113	−	22.3578i	−0.183353	−	1.15765i	0.708631	−	0.705579i	$-0.249313\pi$
$374$		0			0
$375$	3.81179	+	18.9861i	0.196840	+	0.980436i
$376$		0			0
$377$	−0.0984925	−	0.621857i	−0.00507262	−	0.0320273i
$378$		0			0
$379$	−2.26244	+	0.735112i	−0.116214	+	0.0377601i	−0.366547	−	0.930400i	$-0.619460\pi$
$379$	−2.26244	+	0.735112i	−0.116214	+	0.0377601i	0.250333	+	0.968160i	$0.419460\pi$
$380$		0			0
$381$	−2.52547	+	0.749754i	−0.129384	+	0.0384110i
$382$		0			0
$383$	−13.1453	−	25.7992i	−0.671696	−	1.31828i	−0.935372	−	0.353666i	$-0.884935\pi$
$383$	−13.1453	−	25.7992i	−0.671696	−	1.31828i	0.263676	−	0.964611i	$-0.415065\pi$
$384$		0			0
$385$	30.2500	−	5.48231i	1.54168	−	0.279405i
$386$		0			0
$387$	−6.84306	−	3.93972i	−0.347852	−	0.200267i
$388$		0			0
$389$	15.3567	+	11.1573i	0.778614	+	0.565697i	0.904563	−	0.426340i	$-0.140197\pi$
$389$	15.3567	+	11.1573i	0.778614	+	0.565697i	−0.125948	+	0.992037i	$0.540197\pi$
$390$		0			0
$391$	3.16685	−	2.30085i	0.160155	−	0.116359i
$392$		0			0
$393$	10.0048	+	1.84797i	0.504675	+	0.0932175i
$394$		0			0
$395$	−6.34103	−	18.1351i	−0.319052	−	0.912477i
$396$		0			0
$397$	−1.51760	−	0.773254i	−0.0761660	−	0.0388085i	0.415493	−	0.909597i	$-0.363609\pi$
$397$	−1.51760	−	0.773254i	−0.0761660	−	0.0388085i	−0.491659	+	0.870788i	$0.663609\pi$
$398$		0			0
$399$	15.1497	−	10.4257i	0.758432	−	0.521937i
$400$		0			0
$401$		−	35.0603i		−	1.75083i	−0.483376	−	0.875413i	$-0.660589\pi$
$401$		−	35.0603i		−	1.75083i	0.483376	−	0.875413i	$-0.339411\pi$
$402$		0			0
$403$	−26.7658	+	52.5309i	−1.33330	+	2.61675i
$404$		0			0
$405$	−10.4888	−	17.1751i	−0.521192	−	0.853439i
$406$		0			0
$407$	9.10963	+	9.10963i	0.451548	+	0.451548i
$408$		0			0
$409$	18.8051	+	25.8830i	0.929853	+	1.27983i	0.959917	+	0.280285i	$0.0904291\pi$
$409$	18.8051	+	25.8830i	0.929853	+	1.27983i	−0.0300633	+	0.999548i	$0.509571\pi$
$410$		0			0
$411$	−15.2991	−	0.391281i	−0.754647	−	0.0193004i
$412$		0			0
$413$	0.116497	−	0.735533i	0.00573244	−	0.0361932i
$414$		0			0
$415$	13.7271	−	7.38277i	0.673838	−	0.362406i
$416$		0			0
$417$	3.89804	−	7.18976i	0.190888	−	0.352084i
$418$		0			0
$419$	2.91963	−	8.98569i	0.142633	−	0.438980i	−0.854066	−	0.520165i	$-0.825870\pi$
$419$	2.91963	−	8.98569i	0.142633	−	0.438980i	0.996699	+	0.0811851i	$0.0258705\pi$
$420$		0			0
$421$	−1.74189	−	5.36098i	−0.0848945	−	0.261278i	0.899594	−	0.436727i	$-0.143862\pi$
$421$	−1.74189	−	5.36098i	−0.0848945	−	0.261278i	−0.984489	+	0.175449i	$0.943862\pi$
$422$		0			0
$423$	−6.12960	+	29.0115i	−0.298031	+	1.41059i
$424$		0			0
$425$	6.65645	−	3.77292i	0.322885	−	0.183014i
$426$		0			0
$427$	15.2426	−	2.41419i	0.737640	−	0.116831i
$428$		0			0
$429$	29.4915	−	38.4826i	1.42386	−	1.85796i
$430$		0			0
$431$	−11.7037	−	3.80275i	−0.563745	−	0.183172i	0.0132603	−	0.999912i	$-0.495779\pi$
$431$	−11.7037	−	3.80275i	−0.563745	−	0.183172i	−0.577006	+	0.816740i	$0.695779\pi$
$432$		0			0
$433$	−26.3686	+	13.4355i	−1.26719	+	0.645667i	−0.952792	−	0.303624i	$-0.901803\pi$
$433$	−26.3686	+	13.4355i	−1.26719	+	0.645667i	−0.314400	+	0.949291i	$0.601803\pi$
$434$		0			0
$435$	−0.374082	+	0.189023i	−0.0179359	+	0.00906296i
$436$		0			0
$437$	9.38768	+	1.48686i	0.449074	+	0.0711263i
$438$		0			0
$439$	10.9368	−	15.0532i	0.521984	−	0.718449i	−0.463898	−	0.885888i	$-0.653550\pi$
$439$	10.9368	−	15.0532i	0.521984	−	0.718449i	0.985882	+	0.167439i	$0.0535497\pi$
$440$		0			0
$441$	−0.909172	−	3.37659i	−0.0432939	−	0.160790i
$442$		0			0
$443$	−1.48265	+	1.48265i	−0.0704427	+	0.0704427i	−0.741450	−	0.671008i	$-0.765862\pi$
$443$	−1.48265	+	1.48265i	−0.0704427	+	0.0704427i	0.671008	+	0.741450i	$0.265862\pi$
$444$		0			0
$445$	−6.05443	+	8.73472i	−0.287007	+	0.414066i
$446$		0			0
$447$	−3.41071	+	0.451146i	−0.161321	+	0.0213385i
$448$		0			0
$449$	−33.3934			−1.57593			−0.787967	−	0.615718i	$-0.788866\pi$
$449$	−33.3934			−1.57593			−0.787967	+	0.615718i	$0.788866\pi$
$450$		0			0
$451$	−18.5081			−0.871514
$452$		0			0
$453$	36.8948	−	4.88019i	1.73347	−	0.229291i
$454$		0			0
$455$	22.5134	+	29.5825i	1.05544	+	1.38685i
$456$		0			0
$457$	14.4358	−	14.4358i	0.675278	−	0.675278i	−0.283650	−	0.958928i	$-0.591545\pi$
$457$	14.4358	−	14.4358i	0.675278	−	0.675278i	0.958928	+	0.283650i	$0.0915453\pi$
$458$		0			0
$459$	−5.15303	+	6.05583i	−0.240523	+	0.282662i
$460$		0			0
$461$	−1.12640	+	1.55036i	−0.0524617	+	0.0722073i	−0.834442	−	0.551096i	$-0.814210\pi$
$461$	−1.12640	+	1.55036i	−0.0524617	+	0.0722073i	0.781980	+	0.623303i	$0.214210\pi$
$462$		0			0
$463$	−2.40651	−	0.381153i	−0.111840	−	0.0177137i	0.100264	−	0.994961i	$-0.468031\pi$
$463$	−2.40651	−	0.381153i	−0.111840	−	0.0177137i	−0.212103	+	0.977247i	$0.568031\pi$
$464$		0			0
$465$	38.7431	+	6.26989i	1.79667	+	0.290759i
$466$		0			0
$467$	13.9849	−	7.12568i	0.647146	−	0.329737i	−0.0994231	−	0.995045i	$-0.531700\pi$
$467$	13.9849	−	7.12568i	0.647146	−	0.329737i	0.746569	+	0.665308i	$0.231700\pi$
$468$		0			0
$469$	−10.4429	−	3.39312i	−0.482210	−	0.156680i
$470$		0			0
$471$	11.3730	−	14.8404i	0.524042	−	0.683808i
$472$		0			0
$473$	−12.5077	+	1.98102i	−0.575102	+	0.0910873i
$474$		0			0
$475$	17.9065	+	4.95082i	0.821607	+	0.227159i
$476$		0			0
$477$	32.3173	+	6.82805i	1.47971	+	0.312635i
$478$		0			0
$479$	3.70860	+	11.4139i	0.169450	+	0.521514i	0.999337	−	0.0364182i	$-0.0115948\pi$
$479$	3.70860	+	11.4139i	0.169450	+	0.521514i	−0.829886	+	0.557932i	$0.811595\pi$
$480$		0			0
$481$	−4.81400	+	14.8160i	−0.219500	+	0.675550i
$482$		0			0
$483$	6.03437	−	11.1301i	0.274573	−	0.506437i
$484$		0			0
$485$	16.3153	−	33.8589i	0.740838	−	1.53745i
$486$		0			0
$487$	0.279897	−	1.76720i	0.0126833	−	0.0800794i	−0.980535	−	0.196346i	$-0.937093\pi$
$487$	0.279897	−	1.76720i	0.0126833	−	0.0800794i	0.993218	+	0.116266i	$0.0370926\pi$
$488$		0			0
$489$	−7.36252	−	0.188300i	−0.332945	−	0.00851522i
$490$		0			0
$491$	3.20544	+	4.41191i	0.144660	+	0.199107i	0.875198	−	0.483765i	$-0.160731\pi$
$491$	3.20544	+	4.41191i	0.144660	+	0.199107i	−0.730539	+	0.682871i	$0.760731\pi$
$492$		0			0
$493$	0.117099	+	0.117099i	0.00527387	+	0.00527387i
$494$		0			0
$495$	−30.3942	−	10.8574i	−1.36612	−	0.488003i
$496$		0			0
$497$	19.3692	−	38.0141i	0.868826	−	1.70517i
$498$		0			0
$499$		−	15.8865i		−	0.711177i	−0.934643	−	0.355588i	$-0.884281\pi$
$499$		−	15.8865i		−	0.711177i	0.934643	−	0.355588i	$-0.115719\pi$
$500$		0			0
$501$	15.2596	−	10.5013i	0.681747	−	0.469165i
$502$		0			0
$503$	12.2021	+	6.21728i	0.544065	+	0.277215i	0.704346	−	0.709857i	$-0.251240\pi$
$503$	12.2021	+	6.21728i	0.544065	+	0.277215i	−0.160282	+	0.987071i	$0.551240\pi$
$504$		0			0
$505$	−38.8015	+	0.861848i	−1.72665	+	0.0383517i
$506$		0			0
$507$	35.5104	+	6.55905i	1.57707	+	0.291298i
$508$		0			0
$509$	14.7649	−	10.7273i	0.654441	−	0.475479i	−0.210340	−	0.977628i	$-0.567457\pi$
$509$	14.7649	−	10.7273i	0.654441	−	0.475479i	0.864781	+	0.502149i	$0.167457\pi$
$510$		0			0
$511$	4.74173	+	3.44507i	0.209762	+	0.152401i
$512$		0			0
$513$	−19.2448	+	1.55005i	−0.849680	+	0.0684362i
$514$		0			0
$515$	9.54587	+	4.59978i	0.420641	+	0.202690i
$516$		0			0
$517$	21.5895	+	42.3717i	0.949504	+	1.86351i
$518$		0			0
$519$	−3.91660	+	1.16275i	−0.171920	+	0.0510391i
$520$		0			0
$521$	34.6323	−	11.2527i	1.51727	−	0.492991i	0.572272	−	0.820064i	$-0.306062\pi$
$521$	34.6323	−	11.2527i	1.51727	−	0.492991i	0.944999	+	0.327073i	$0.106062\pi$
$522$		0			0
$523$	−3.57185	−	22.5518i	−0.156186	−	0.986120i	−0.933908	−	0.357512i	$-0.883625\pi$
$523$	−3.57185	−	22.5518i	−0.156186	−	0.986120i	0.777722	−	0.628608i	$-0.216375\pi$
$524$		0			0
$525$	14.1661	−	20.2914i	0.618261	−	0.885591i
$526$		0			0
$527$	−2.42585	−	15.3162i	−0.105672	−	0.667185i
$528$		0			0
$529$	−15.6512	+	5.08537i	−0.680485	+	0.221103i
$530$		0			0
$531$	−0.491276	+	0.608191i	−0.0213196	+	0.0263932i
$532$		0			0
$533$	−10.1606	−	19.9412i	−0.440103	−	0.863750i
$534$		0			0
$535$	−27.1626	+	28.3967i	−1.17434	+	1.22770i
$536$		0			0
$537$	3.30782	+	6.92412i	0.142743	+	0.298798i
$538$		0			0
$539$	−4.53708	−	3.29638i	−0.195426	−	0.141985i
$540$		0			0
$541$	−14.4743	+	10.5162i	−0.622299	+	0.452126i	−0.853724	−	0.520726i	$-0.825661\pi$
$541$	−14.4743	+	10.5162i	−0.622299	+	0.452126i	0.231425	+	0.972853i	$0.425661\pi$
$542$		0			0
$543$	2.49456	−	13.5054i	0.107052	−	0.579572i
$544$		0			0
$545$	−30.3700	+	23.1126i	−1.30091	+	0.990037i
$546$		0			0
$547$	−13.1268	−	6.68845i	−0.561263	−	0.285978i	0.150253	−	0.988648i	$-0.451991\pi$
$547$	−13.1268	−	6.68845i	−0.561263	−	0.285978i	−0.711516	+	0.702670i	$0.751991\pi$
$548$		0			0
$549$	−15.1328	−	5.78777i	−0.645853	−	0.247016i
$550$		0			0
$551$			0.402102i			0.0171301i
$552$		0			0
$553$	−11.1461	+	21.8755i	−0.473981	+	0.930239i
$554$		0			0
$555$	10.3704	+	0.0348640i	0.440199	+	0.00147989i
$556$		0			0
$557$	−15.7568	−	15.7568i	−0.667638	−	0.667638i	0.289531	−	0.957169i	$-0.406501\pi$
$557$	−15.7568	−	15.7568i	−0.667638	−	0.667638i	−0.957169	+	0.289531i	$0.906501\pi$
$558$		0			0
$559$	−9.00083	−	12.3886i	−0.380695	−	0.523981i
$560$		0			0
$561$	−0.326042	+	12.7482i	−0.0137655	+	0.538231i
$562$		0			0
$563$	−3.16190	+	19.9634i	−0.133258	+	0.841358i	0.826991	+	0.562215i	$0.190050\pi$
$563$	−3.16190	+	19.9634i	−0.133258	+	0.841358i	−0.960249	+	0.279143i	$0.909950\pi$
$564$		0			0
$565$	−4.59954	−	0.624136i	−0.193504	−	0.0262576i
$566$		0			0
$567$	−6.59567	+	24.8578i	−0.276992	+	1.04393i
$568$		0			0
$569$	−10.5620	+	32.5066i	−0.442783	+	1.36275i	0.442113	+	0.896959i	$0.354229\pi$
$569$	−10.5620	+	32.5066i	−0.442783	+	1.36275i	−0.884896	+	0.465788i	$0.845771\pi$
$570$		0			0
$571$	−4.84382	−	14.9078i	−0.202708	−	0.623870i	−0.999800	−	0.0200122i	$-0.993629\pi$
$571$	−4.84382	−	14.9078i	−0.202708	−	0.623870i	0.797092	−	0.603858i	$-0.206371\pi$
$572$		0			0
$573$	−10.0212	−	10.5472i	−0.418640	−	0.440616i
$574$		0			0
$575$	12.5313	−	2.55973i	0.522590	−	0.106748i
$576$		0			0
$577$	−34.5289	+	5.46884i	−1.43746	+	0.227671i	−0.826028	−	0.563629i	$-0.809405\pi$
$577$	−34.5289	+	5.46884i	−1.43746	+	0.227671i	−0.611428	+	0.791300i	$0.709405\pi$
$578$		0			0
$579$	18.9479	+	14.5209i	0.787450	+	0.603468i
$580$		0			0
$581$	−18.9437	−	6.15518i	−0.785917	−	0.255360i
$582$		0			0
$583$	47.1999	−	24.0496i	1.95482	−	0.996031i
$584$		0			0
$585$	−4.98769	−	38.7081i	−0.206216	−	1.60038i
$586$		0			0
$587$	−38.6761	−	6.12569i	−1.59633	−	0.252834i	−0.706023	−	0.708189i	$-0.749512\pi$
$587$	−38.6761	−	6.12569i	−1.59633	−	0.252834i	−0.890310	+	0.455355i	$0.849512\pi$
$588$		0			0
$589$	22.1319	−	30.4619i	0.911927	−	1.25516i
$590$		0			0
$591$	−8.97167	+	25.3844i	−0.369045	+	1.04418i
$592$		0			0
$593$	−18.8322	+	18.8322i	−0.773348	+	0.773348i	−0.978690	−	0.205343i	$-0.934169\pi$
$593$	−18.8322	+	18.8322i	−0.773348	+	0.773348i	0.205343	+	0.978690i	$0.434169\pi$
$594$		0			0
$595$	−9.36419	−	2.81431i	−0.383895	−	0.115375i
$596$		0			0
$597$	2.41619	+	18.2667i	0.0988881	+	0.747605i
$598$		0			0
$599$	29.8132			1.21813			0.609066	−	0.793119i	$-0.291544\pi$
$599$	29.8132			1.21813			0.609066	+	0.793119i	$0.291544\pi$
$600$		0			0
$601$	12.3924			0.505498			0.252749	−	0.967532i	$-0.418665\pi$
$601$	12.3924			0.505498			0.252749	+	0.967532i	$0.418665\pi$
$602$		0			0
$603$	7.72399	+	8.55734i	0.314545	+	0.348482i
$604$		0			0
$605$	−25.6429	+	8.96617i	−1.04253	+	0.364527i
$606$		0			0
$607$	−16.4938	+	16.4938i	−0.669464	+	0.669464i	−0.957592	−	0.288128i	$-0.906967\pi$
$607$	−16.4938	+	16.4938i	−0.669464	+	0.669464i	0.288128	+	0.957592i	$0.406967\pi$
$608$		0			0
$609$	0.505004	+	0.178485i	0.0204638	+	0.00723257i
$610$		0			0
$611$	−33.8004	+	46.5223i	−1.36742	+	1.88209i
$612$		0			0
$613$	34.2415	+	5.42333i	1.38300	+	0.219046i	0.803199	−	0.595710i	$-0.203129\pi$
$613$	34.2415	+	5.42333i	1.38300	+	0.219046i	0.579803	+	0.814756i	$0.303129\pi$
$614$		0			0
$615$	−10.5703	+	10.4994i	−0.426234	+	0.423377i
$616$		0			0
$617$	−24.8462	+	12.6598i	−1.00027	+	0.509662i	−0.875858	−	0.482568i	$-0.839704\pi$
$617$	−24.8462	+	12.6598i	−1.00027	+	0.509662i	−0.124410	+	0.992231i	$0.539704\pi$
$618$		0			0
$619$	11.8893	+	3.86308i	0.477872	+	0.155270i	0.538042	−	0.842918i	$-0.319164\pi$
$619$	11.8893	+	3.86308i	0.477872	+	0.155270i	−0.0601697	+	0.998188i	$0.519164\pi$
$620$		0			0
$621$	−11.3204	+	6.96568i	−0.454272	+	0.279523i
$622$		0			0
$623$	13.4145	−	2.12465i	0.537442	−	0.0851224i
$624$		0			0
$625$	24.9014	−	2.21788i	0.996057	−	0.0887154i
$626$		0			0
$627$	−22.4476	+	21.3281i	−0.896473	+	0.851761i
$628$		0			0
$629$	−1.26620	−	3.89698i	−0.0504869	−	0.155383i
$630$		0			0
$631$	5.26220	−	16.1954i	0.209485	−	0.644728i	−0.790014	−	0.613088i	$-0.789927\pi$
$631$	5.26220	−	16.1954i	0.209485	−	0.644728i	0.999499	−	0.0316401i	$-0.0100730\pi$
$632$		0			0
$633$	16.7035	+	9.05607i	0.663904	+	0.359946i
$634$		0			0
$635$	0.606497	+	3.34649i	0.0240681	+	0.132802i
$636$		0			0
$637$	1.06086	−	6.69803i	0.0420329	−	0.265386i
$638$		0			0
$639$	−37.5351	+	24.4408i	−1.48487	+	0.966861i
$640$		0			0
$641$	2.68121	+	3.69037i	0.105901	+	0.145761i	0.858678	−	0.512515i	$-0.171286\pi$
$641$	2.68121	+	3.69037i	0.105901	+	0.145761i	−0.752777	+	0.658276i	$0.771286\pi$
$642$		0			0
$643$	1.57617	+	1.57617i	0.0621582	+	0.0621582i	0.737503	−	0.675344i	$-0.236005\pi$
$643$	1.57617	+	1.57617i	0.0621582	+	0.0621582i	−0.675344	+	0.737503i	$0.736005\pi$
$644$		0			0
$645$	−6.01949	+	8.22681i	−0.237017	+	0.323930i
$646$		0			0
$647$	−10.6313	+	20.8650i	−0.417958	+	0.820289i	0.582017	+	0.813177i	$0.302264\pi$
$647$	−10.6313	+	20.8650i	−0.417958	+	0.820289i	−0.999975	+	0.00711204i	$0.997736\pi$
$648$		0			0
$649$			1.25386i			0.0492185i
$650$		0			0
$651$	−28.4336	−	41.3171i	−1.11440	−	1.61934i
$652$		0			0
$653$	−1.68056	−	0.856287i	−0.0657653	−	0.0335091i	0.420799	−	0.907154i	$-0.361750\pi$
$653$	−1.68056	−	0.856287i	−0.0657653	−	0.0335091i	−0.486564	+	0.873645i	$0.661750\pi$
$654$		0			0
$655$	3.78042	−	12.5788i	0.147713	−	0.491495i
$656$		0			0
$657$	−2.50961	−	5.61823i	−0.0979094	−	0.219188i
$658$		0			0
$659$	39.3347	−	28.5783i	1.53226	−	1.11325i	0.577297	−	0.816534i	$-0.304107\pi$
$659$	39.3347	−	28.5783i	1.53226	−	1.11325i	0.954965	−	0.296719i	$-0.0958925\pi$
$660$		0			0
$661$	10.8497	+	7.88279i	0.422006	+	0.306605i	0.778444	−	0.627714i	$-0.216009\pi$
$661$	10.8497	+	7.88279i	0.422006	+	0.306605i	−0.356439	+	0.934319i	$0.616009\pi$
$662$		0			0
$663$	−13.9143	+	6.64722i	−0.540388	+	0.258156i
$664$		0			0
$665$	−11.2457	−	20.9096i	−0.436090	−	0.810841i
$666$		0			0
$667$	0.125675	+	0.246651i	0.00486615	+	0.00955035i
$668$		0			0
$669$	−8.93159	−	30.0851i	−0.345315	−	1.16316i
$670$		0			0
$671$	−24.7123	+	8.02951i	−0.954008	+	0.309976i
$672$		0			0
$673$	1.34636	+	8.50057i	0.0518983	+	0.327673i	0.999954	+	0.00956929i	$0.00304604\pi$
$673$	1.34636	+	8.50057i	0.0518983	+	0.327673i	−0.948056	+	0.318104i	$0.896954\pi$
$674$		0			0
$675$	−23.5178	+	11.0414i	−0.905200	+	0.424985i
$676$		0			0
$677$	0.116734	+	0.737029i	0.00448645	+	0.0283263i	0.989830	−	0.142255i	$-0.0454354\pi$
$677$	0.116734	+	0.737029i	0.00448645	+	0.0283263i	−0.985344	+	0.170582i	$0.945435\pi$
$678$		0			0
$679$	−45.6802	+	14.8424i	−1.75304	+	0.569599i
$680$		0			0
$681$	−1.20187	−	4.04839i	−0.0460559	−	0.155134i
$682$		0			0
$683$	16.4590	+	32.3026i	0.629785	+	1.23602i	0.956729	+	0.290980i	$0.0939812\pi$
$683$	16.4590	+	32.3026i	0.629785	+	1.23602i	−0.326944	+	0.945044i	$0.606019\pi$
$684$		0			0
$685$	−2.65665	+	19.5780i	−0.101505	+	0.748038i
$686$		0			0
$687$	−22.9161	+	10.9476i	−0.874303	+	0.417676i
$688$		0			0
$689$	51.8234	+	37.6519i	1.97431	+	1.43442i
$690$		0			0
$691$	−25.1665	+	18.2845i	−0.957378	+	0.695576i	−0.952540	−	0.304412i	$-0.901540\pi$
$691$	−25.1665	+	18.2845i	−0.957378	+	0.695576i	−0.00483787	+	0.999988i	$0.501540\pi$
$692$		0			0
$693$	16.8221	+	37.6593i	0.639019	+	1.43056i
$694$		0			0
$695$	−8.67760	−	6.01484i	−0.329160	−	0.228156i
$696$		0			0
$697$	5.24504	+	2.67248i	0.198670	+	0.101228i
$698$		0			0
$699$	−19.4583	−	28.2750i	−0.735981	−	1.06946i
$700$		0			0
$701$			0.173863i			0.00656672i	0.999995	+	0.00328336i	$0.00104513\pi$
$701$			0.173863i			0.00656672i	−0.999995	+	0.00328336i	$0.998955\pi$
$702$		0			0
$703$	4.51685	−	8.86483i	0.170356	−	0.334343i
$704$		0			0
$705$	36.3670	+	11.9517i	1.36966	+	0.450125i
$706$		0			0
$707$	35.0712	+	35.0712i	1.31899	+	1.31899i
$708$		0			0
$709$	−27.9112	−	38.4165i	−1.04823	−	1.44276i	−0.890336	−	0.455304i	$-0.849531\pi$
$709$	−27.9112	−	38.4165i	−1.04823	−	1.44276i	−0.157891	−	0.987457i	$-0.550469\pi$
$710$		0			0
$711$	21.5998	−	14.0646i	0.810056	−	0.527463i
$712$		0			0
$713$	4.05506	−	25.6026i	0.151863	−	0.958826i
$714$		0			0
$715$	−45.2312	−	43.2655i	−1.69155	−	1.61804i
$716$		0			0
$717$	−35.1473	−	19.0557i	−1.31260	−	0.711647i
$718$		0			0
$719$	1.22324	−	3.76475i	0.0456192	−	0.140401i	−0.925653	−	0.378375i	$-0.876483\pi$
$719$	1.22324	−	3.76475i	0.0456192	−	0.140401i	0.971272	+	0.237973i	$0.0764831\pi$
$720$		0			0
$721$	−4.18452	−	12.8786i	−0.155840	−	0.479626i
$722$		0			0
$723$	12.4041	−	11.7855i	0.461315	−	0.438307i
$724$		0			0
$725$	0.189890	+	0.506676i	0.00705235	+	0.0188175i
$726$		0			0
$727$	8.95795	−	1.41880i	0.332232	−	0.0526204i	0.0119099	−	0.999929i	$-0.496209\pi$
$727$	8.95795	−	1.41880i	0.332232	−	0.0526204i	0.320322	+	0.947309i	$0.396209\pi$
$728$		0			0
$729$	19.0219	−	19.1616i	0.704514	−	0.709690i
$730$		0			0
$731$	3.83061	+	1.24464i	0.141680	+	0.0460347i
$732$		0			0
$733$	20.9011	−	10.6496i	0.772000	−	0.393353i	−0.0231770	−	0.999731i	$-0.507378\pi$
$733$	20.9011	−	10.6496i	0.772000	−	0.393353i	0.795177	+	0.606378i	$0.207378\pi$
$734$		0			0
$735$	−4.46119	+	0.691216i	−0.164553	+	0.0254959i
$736$		0			0
$737$	18.2602	+	2.89213i	0.672622	+	0.106533i
$738$		0			0
$739$	6.02439	−	8.29186i	0.221611	−	0.305021i	−0.683706	−	0.729757i	$-0.739633\pi$
$739$	6.02439	−	8.29186i	0.221611	−	0.305021i	0.905317	+	0.424736i	$0.139633\pi$
$740$		0			0
$741$	−35.3028	−	12.4771i	−1.29688	−	0.458359i
$742$		0			0
$743$	−21.7690	+	21.7690i	−0.798626	+	0.798626i	−0.982879	−	0.184253i	$-0.941013\pi$
$743$	−21.7690	+	21.7690i	−0.798626	+	0.798626i	0.184253	+	0.982879i	$0.441013\pi$
$744$		0			0
$745$	0.0986303	+	4.44047i	0.00361354	+	0.162686i
$746$		0			0
$747$	14.0115	+	15.5232i	0.512653	+	0.567964i
$748$		0			0
$749$	50.2179			1.83492
$750$		0			0
$751$	7.73768			0.282352			0.141176	−	0.989985i	$-0.454912\pi$
$751$	7.73768			0.282352			0.141176	+	0.989985i	$0.454912\pi$
$752$		0			0
$753$	−3.85280	−	29.1276i	−0.140404	−	1.06147i
$754$		0			0
$755$	−1.06692	−	48.0340i	−0.0388291	−	1.74814i
$756$		0			0
$757$	4.50352	−	4.50352i	0.163683	−	0.163683i	−0.620513	−	0.784196i	$-0.713076\pi$
$757$	4.50352	−	4.50352i	0.163683	−	0.163683i	0.784196	+	0.620513i	$0.213076\pi$
$758$		0			0
$759$	−7.10349	+	20.0986i	−0.257840	+	0.729533i
$760$		0			0
$761$	7.27565	−	10.0141i	0.263742	−	0.363010i	−0.656523	−	0.754306i	$-0.727973\pi$
$761$	7.27565	−	10.0141i	0.263742	−	0.363010i	0.920265	+	0.391297i	$0.127973\pi$
$762$		0			0
$763$	48.1714	+	7.62960i	1.74392	+	0.276210i
$764$		0			0
$765$	7.04570	+	7.46566i	0.254738	+	0.269921i
$766$		0			0
$767$	−1.35095	+	0.688344i	−0.0487800	+	0.0248547i
$768$		0			0
$769$	28.2227	+	9.17010i	1.01774	+	0.330682i	0.769931	−	0.638128i	$-0.220291\pi$
$769$	28.2227	+	9.17010i	1.01774	+	0.330682i	0.247805	+	0.968810i	$0.420291\pi$
$770$		0			0
$771$	34.1049	+	26.1365i	1.22826	+	0.941284i
$772$		0			0
$773$	−0.378278	+	0.0599133i	−0.0136057	+	0.00215493i	−0.163234	−	0.986587i	$-0.552192\pi$
$773$	−0.378278	+	0.0599133i	−0.0136057	+	0.00215493i	0.149628	+	0.988742i	$0.452192\pi$
$774$		0			0
$775$	13.5022	−	48.8357i	0.485012	−	1.75423i
$776$		0			0
$777$	−9.12850	−	9.60768i	−0.327483	−	0.344674i
$778$		0			0
$779$	4.41691	+	13.5938i	0.158252	+	0.487050i
$780$		0			0
$781$	−22.1981	+	68.3186i	−0.794309	+	2.44463i
$782$		0			0
$783$	−0.365978	−	0.426920i	−0.0130790	−	0.0152569i
$784$		0			0
$785$	−17.4429	−	16.6848i	−0.622563	−	0.595507i
$786$		0			0
$787$	−0.702867	+	4.43773i	−0.0250545	+	0.158188i	−0.997044	−	0.0768381i	$-0.975518\pi$
$787$	−0.702867	+	4.43773i	−0.0250545	+	0.158188i	0.971989	+	0.235026i	$0.0755175\pi$
$788$		0			0
$789$	−0.724403	+	28.3241i	−0.0257894	+	1.00837i
$790$		0			0
$791$	3.48662	+	4.79892i	0.123970	+	0.170630i
$792$		0			0
$793$	−22.2177	−	22.2177i	−0.788975	−	0.788975i
$794$		0			0
$795$	13.3135	−	40.5109i	0.472182	−	1.43677i
$796$		0			0
$797$	1.40159	−	2.75078i	0.0496469	−	0.0974376i	−0.864850	−	0.502030i	$-0.832587\pi$
$797$	1.40159	−	2.75078i	0.0496469	−	0.0974376i	0.914497	+	0.404593i	$0.132587\pi$
$798$		0			0
$799$		−	15.1252i		−	0.535091i
$800$		0			0
$801$	−13.3179	−	5.09364i	−0.470566	−	0.179975i
$802$		0			0
$803$	−8.79282	−	4.48017i	−0.310292	−	0.158102i
$804$		0			0
$805$	−13.4334	−	9.31126i	−0.473464	−	0.328179i
$806$		0			0
$807$	−2.54981	+	13.8045i	−0.0897576	+	0.485943i
$808$		0			0
$809$	−30.0466	+	21.8301i	−1.05638	+	0.767506i	−0.973415	−	0.229047i	$-0.926439\pi$
$809$	−30.0466	+	21.8301i	−1.05638	+	0.767506i	−0.0829655	+	0.996552i	$0.526439\pi$
$810$		0			0
$811$	28.0735	+	20.3966i	0.985793	+	0.716221i	0.958996	−	0.283420i	$-0.0914692\pi$
$811$	28.0735	+	20.3966i	0.985793	+	0.716221i	0.0267972	+	0.999641i	$0.491469\pi$
$812$		0			0
$813$	−6.83772	−	14.3131i	−0.239809	−	0.501982i
$814$		0			0
$815$	−1.27849	+	9.42173i	−0.0447834	+	0.330029i
$816$		0			0
$817$	4.43993	+	8.71385i	0.155333	+	0.304859i
$818$		0			0
$819$	−31.3403	+	38.7988i	−1.09512	+	1.35574i
$820$		0			0
$821$	−22.2902	+	7.24251i	−0.777932	+	0.252765i	−0.670957	−	0.741496i	$-0.734116\pi$
$821$	−22.2902	+	7.24251i	−0.777932	+	0.252765i	−0.106975	+	0.994262i	$0.534116\pi$
$822$		0			0
$823$	−4.56451	−	28.8192i	−0.159109	−	1.00457i	−0.929988	−	0.367591i	$-0.880183\pi$
$823$	−4.56451	−	28.8192i	−0.159109	−	1.00457i	0.770879	−	0.636982i	$-0.219817\pi$
$824$		0			0
$825$	−18.2135	+	37.4756i	−0.634112	+	1.30473i
$826$		0			0
$827$	−5.14586	−	32.4897i	−0.178939	−	1.12978i	−0.899673	−	0.436565i	$-0.856195\pi$
$827$	−5.14586	−	32.4897i	−0.178939	−	1.12978i	0.720733	−	0.693212i	$-0.243805\pi$
$828$		0			0
$829$	22.5304	−	7.32056i	0.782512	−	0.254254i	0.109600	−	0.993976i	$-0.465043\pi$
$829$	22.5304	−	7.32056i	0.782512	−	0.254254i	0.672912	+	0.739722i	$0.265043\pi$
$830$		0			0
$831$	−6.56144	+	1.94794i	−0.227614	+	0.0675733i
$832$		0			0
$833$	0.809788	+	1.58930i	0.0280575	+	0.0550659i
$834$		0			0
$835$	−11.3273	−	21.0613i	−0.391997	−	0.728857i
$836$		0			0
$837$	4.22737	+	52.4856i	0.146119	+	1.81417i
$838$		0			0
$839$	−35.6364	−	25.8914i	−1.23031	−	0.893869i	−0.233393	−	0.972383i	$-0.574983\pi$
$839$	−35.6364	−	25.8914i	−1.23031	−	0.893869i	−0.996913	+	0.0785132i	$0.974983\pi$
$840$		0			0
$841$	23.4520	−	17.0389i	0.808690	−	0.587548i
$842$		0			0
$843$	43.9730	+	8.12217i	1.51451	+	0.279742i
$844$		0			0
$845$	13.4180	−	44.6464i	0.461593	−	1.53588i
$846$		0			0
$847$	30.9317	+	15.7605i	1.06283	+	0.541537i
$848$		0			0
$849$	−1.93240	+	1.32984i	−0.0663198	+	0.0456399i
$850$		0			0
$851$		−	6.84944i		−	0.234796i
$852$		0			0
$853$	11.7145	−	22.9910i	0.401097	−	0.787197i	−0.598809	−	0.800892i	$-0.704359\pi$
$853$	11.7145	−	22.9910i	0.401097	−	0.787197i	0.999906	+	0.0136947i	$0.00435930\pi$
$854$		0			0
$855$	−0.721036	+	24.9150i	−0.0246589	+	0.852075i
$856$		0			0
$857$	−11.3014	−	11.3014i	−0.386047	−	0.386047i	0.487228	−	0.873275i	$-0.338008\pi$
$857$	−11.3014	−	11.3014i	−0.386047	−	0.386047i	−0.873275	+	0.487228i	$0.838008\pi$
$858$		0			0
$859$	22.0585	+	30.3610i	0.752627	+	1.03590i	0.997792	+	0.0664210i	$0.0211580\pi$
$859$	22.0585	+	30.3610i	0.752627	+	1.03590i	−0.245164	+	0.969482i	$0.578842\pi$
$860$		0			0
$861$	19.0332	+	0.486784i	0.648651	+	0.0165896i
$862$		0			0
$863$	−6.11502	+	38.6087i	−0.208158	+	1.31426i	0.633289	+	0.773915i	$0.281704\pi$
$863$	−6.11502	+	38.6087i	−0.208158	+	1.31426i	−0.841447	+	0.540340i	$0.818296\pi$
$864$		0			0
$865$	0.940582	+	5.18989i	0.0319808	+	0.176461i
$866$		0			0
$867$	−12.1009	+	22.3196i	−0.410968	+	0.758012i
$868$		0			0
$869$	12.7740	−	39.3144i	0.433329	−	1.33365i
$870$		0			0
$871$	6.90837	+	21.2618i	0.234081	+	0.720427i
$872$		0			0
$873$	49.3361	+	10.4238i	1.66977	+	0.352793i
$874$		0			0
$875$	−24.0448	−	21.0368i	−0.812863	−	0.711175i
$876$		0			0
$877$	41.1085	−	6.51094i	1.38813	−	0.219859i	0.582769	−	0.812638i	$-0.301969\pi$
$877$	41.1085	−	6.51094i	1.38813	−	0.219859i	0.805365	+	0.592779i	$0.201969\pi$
$878$		0			0
$879$	14.0629	−	18.3502i	0.474328	−	0.618938i
$880$		0			0
$881$	31.4946	+	10.2332i	1.06108	+	0.344766i	0.787008	−	0.616943i	$-0.211629\pi$
$881$	31.4946	+	10.2332i	1.06108	+	0.344766i	0.274072	+	0.961709i	$0.411629\pi$
$882$		0			0
$883$	−18.6577	+	9.50655i	−0.627880	+	0.319921i	−0.738817	−	0.673907i	$-0.764615\pi$
$883$	−18.6577	+	9.50655i	−0.627880	+	0.319921i	0.110936	+	0.993828i	$0.464615\pi$
$884$		0			0
$885$	0.711301	+	0.716100i	0.0239101	+	0.0240714i
$886$		0			0
$887$	20.2617	+	3.20914i	0.680321	+	0.107752i	0.487025	−	0.873388i	$-0.338082\pi$
$887$	20.2617	+	3.20914i	0.680321	+	0.107752i	0.193296	+	0.981140i	$0.438082\pi$
$888$		0			0
$889$	2.55468	−	3.51621i	0.0856811	−	0.117930i
$890$		0			0
$891$	4.42117	−	43.0755i	0.148115	−	1.44308i
$892$		0			0
$893$	25.9689	−	25.9689i	0.869016	−	0.869016i
$894$		0			0
$895$	9.35149	−	3.26980i	0.312586	−	0.109297i
$896$		0			0
$897$	−25.5545	+	3.38017i	−0.853240	+	0.112861i
$898$		0			0
$899$	1.09664			0.0365748
$900$		0			0
$901$	−16.8487			−0.561311
$902$		0			0
$903$	12.9146	−	1.70826i	0.429772	−	0.0568472i
$904$		0			0
$905$	−16.9800	−	5.10317i	−0.564436	−	0.169635i
$906$		0			0
$907$	18.9719	−	18.9719i	0.629953	−	0.629953i	−0.318103	−	0.948056i	$-0.603046\pi$
$907$	18.9719	−	18.9719i	0.629953	−	0.629953i	0.948056	+	0.318103i	$0.103046\pi$
$908$		0			0
$909$	−13.5382	−	50.2798i	−0.449034	−	1.66768i
$910$		0			0
$911$	11.4564	−	15.7683i	0.379567	−	0.522428i	−0.575903	−	0.817518i	$-0.695349\pi$
$911$	11.4564	−	15.7683i	0.379567	−	0.522428i	0.955470	+	0.295089i	$0.0953495\pi$
$912$		0			0
$913$	33.1243	+	5.24638i	1.09625	+	0.173630i
$914$		0			0
$915$	−9.55850	+	18.6047i	−0.315994	+	0.615053i
$916$		0			0
$917$	−14.9557	+	7.62032i	−0.493882	+	0.251645i
$918$		0			0
$919$	39.3312	+	12.7795i	1.29742	+	0.421556i	0.874682	−	0.484698i	$-0.161070\pi$
$919$	39.3312	+	12.7795i	1.29742	+	0.421556i	0.422734	+	0.906254i	$0.361070\pi$
$920$		0			0
$921$	−14.0429	+	18.3242i	−0.462730	+	0.603803i
$922$		0			0
$923$	−85.7948	+	13.5886i	−2.82397	+	0.447273i
$924$		0			0
$925$	1.50518	−	13.3033i	0.0494899	−	0.437411i
$926$		0			0
$927$	−2.93879	+	13.9094i	−0.0965226	+	0.456843i
$928$		0			0
$929$	6.58580	+	20.2690i	0.216073	+	0.665004i	0.999076	+	0.0429861i	$0.0136871\pi$
$929$	6.58580	+	20.2690i	0.216073	+	0.665004i	−0.783003	+	0.622018i	$0.786313\pi$
$930$		0			0
$931$	−1.33837	+	4.11907i	−0.0438632	+	0.134997i
$932$		0			0
$933$	10.9456	−	20.1887i	0.358344	−	0.660948i
$934$		0			0
$935$	16.3138	+	2.21370i	0.533518	+	0.0723959i
$936$		0			0
$937$	−6.55487	+	41.3858i	−0.214138	+	1.35202i	0.613029	+	0.790060i	$0.289951\pi$
$937$	−6.55487	+	41.3858i	−0.214138	+	1.35202i	−0.827167	+	0.561955i	$0.810049\pi$
$938$		0			0
$939$	0.153377	+	0.00392268i	0.00500526	+	0.000128012i
$940$		0			0
$941$	−26.9763	−	37.1297i	−0.879402	−	1.21039i	−0.976586	−	0.215126i	$-0.930984\pi$
$941$	−26.9763	−	37.1297i	−0.879402	−	1.21039i	0.0971843	−	0.995266i	$-0.469016\pi$
$942$		0			0
$943$	6.95803	+	6.95803i	0.226585	+	0.226585i
$944$		0			0
$945$	30.9710	+	11.9648i	1.00749	+	0.389215i
$946$		0			0
$947$	20.9146	−	41.0473i	0.679634	−	1.33386i	−0.251029	−	0.967980i	$-0.580769\pi$
$947$	20.9146	−	41.0473i	0.679634	−	1.33386i	0.930663	−	0.365878i	$-0.119231\pi$
$948$		0			0
$949$		−	11.9332i		−	0.387367i
$950$		0			0
$951$	−41.1731	+	28.3345i	−1.33513	+	0.918810i
$952$		0			0
$953$	−9.89306	−	5.04077i	−0.320468	−	0.163286i	0.286355	−	0.958124i	$-0.407556\pi$
$953$	−9.89306	−	5.04077i	−0.320468	−	0.163286i	−0.606823	+	0.794837i	$0.707556\pi$
$954$		0			0
$955$	−14.9464	+	11.3747i	−0.483654	+	0.368078i
$956$		0			0
$957$	−0.886826	−	0.163804i	−0.0286670	−	0.00529503i
$958$		0			0
$959$	20.4267	−	14.8409i	0.659612	−	0.479236i
$960$		0			0
$961$	−57.9979	−	42.1380i	−1.87090	−	1.35929i
$962$		0			0
$963$	−45.6901	−	26.3049i	−1.47234	−	0.847663i
$964$		0			0
$965$	21.3029	−	22.2708i	0.685766	−	0.716922i
$966$		0			0
$967$	−11.6265	−	22.8184i	−0.373885	−	0.733790i	0.625019	−	0.780610i	$-0.285091\pi$
$967$	−11.6265	−	22.8184i	−0.373885	−	0.733790i	−0.998903	+	0.0468200i	$0.985091\pi$
$968$		0			0
$969$	9.44113	−	2.80286i	0.303293	−	0.0900407i
$970$		0			0
$971$	32.8712	−	10.6805i	1.05489	−	0.342753i	0.270302	−	0.962776i	$-0.412876\pi$
$971$	32.8712	−	10.6805i	1.05489	−	0.342753i	0.784584	+	0.620022i	$0.212876\pi$
$972$		0			0
$973$	2.11076	+	13.3268i	0.0676678	+	0.427238i
$974$		0			0
$975$	−50.3761	+	0.949510i	−1.61333	+	0.0304086i
$976$		0			0
$977$	2.56693	+	16.2070i	0.0821234	+	0.518507i	0.994118	+	0.108304i	$0.0345420\pi$
$977$	2.56693	+	16.2070i	0.0821234	+	0.518507i	−0.911994	+	0.410203i	$0.865458\pi$
$978$		0			0
$979$	−21.7486	+	7.06653i	−0.695087	+	0.225847i
$980$		0			0
$981$	−39.8315	−	32.1746i	−1.27172	−	1.02725i
$982$		0			0
$983$	17.5734	+	34.4898i	0.560505	+	1.10005i	0.981226	+	0.192863i	$0.0617771\pi$
$983$	17.5734	+	34.4898i	0.560505	+	1.10005i	−0.420721	+	0.907190i	$0.638223\pi$
$984$		0			0
$985$	31.3121	+	15.0881i	0.997688	+	0.480746i
$986$		0			0
$987$	−21.0876	−	44.1417i	−0.671225	−	1.40505i
$988$		0			0
$989$	5.44694	+	3.95743i	0.173203	+	0.125839i
$990$		0			0
$991$	5.23172	−	3.80107i	0.166191	−	0.120745i	−0.501581	−	0.865111i	$-0.667248\pi$
$991$	5.23172	−	3.80107i	0.166191	−	0.120745i	0.667772	+	0.744366i	$0.267248\pi$
$992$		0			0
$993$	1.61056	−	8.71946i	0.0511094	−	0.276704i
$994$		0			0
$995$	23.7817	−	0.528232i	0.753931	−	0.0167461i
$996$		0			0
$997$	1.68687	+	0.859502i	0.0534236	+	0.0272207i	0.480498	−	0.876996i	$-0.340456\pi$
$997$	1.68687	+	0.859502i	0.0534236	+	0.0272207i	−0.427075	+	0.904216i	$0.640456\pi$
$998$		0			0
$999$	3.27278	+	13.5231i	0.103546	+	0.427850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.113.10	yes	80
3.2	odd	2	inner	300.2.x.a.113.4	yes	80
25.2	odd	20	inner	300.2.x.a.77.4	✓	80
75.2	even	20	inner	300.2.x.a.77.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.77.4	✓	80	25.2	odd	20	inner
300.2.x.a.77.10	yes	80	75.2	even	20	inner
300.2.x.a.113.4	yes	80	3.2	odd	2	inner
300.2.x.a.113.10	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71709 - 0.227126i) q^{3} +(-0.0496546 - 2.23552i) q^{5} +(-2.02060 + 2.02060i) q^{7} +(2.89683 - 0.779992i) q^{9} +O(q^{10})\)	\(q+(1.71709 - 0.227126i) q^{3} +(-0.0496546 - 2.23552i) q^{5} +(-2.02060 + 2.02060i) q^{7} +(2.89683 - 0.779992i) q^{9} +(2.82802 - 3.89243i) q^{11} +(5.74634 + 0.910130i) q^{13} +(-0.593005 - 3.82732i) q^{15} +(-1.36348 + 0.694729i) q^{17} +(-3.53381 - 1.14820i) q^{19} +(-3.01063 + 3.92848i) q^{21} +(-2.52651 + 0.400161i) q^{23} +(-4.99507 + 0.222007i) q^{25} +(4.79697 - 1.99726i) q^{27} +(-0.0334412 - 0.102921i) q^{29} +(-3.13145 + 9.63760i) q^{31} +(3.97190 - 7.32598i) q^{33} +(4.61741 + 4.41674i) q^{35} +(-0.418876 + 2.64468i) q^{37} +(10.0737 + 0.257640i) q^{39} +(-2.26109 - 3.11213i) q^{41} +(-1.86113 - 1.86113i) q^{43} +(-1.88753 - 6.43718i) q^{45} +(-4.48724 + 8.80670i) q^{47} -1.16562i q^{49} +(-2.18344 + 1.50260i) q^{51} +(9.81020 + 4.99855i) q^{53} +(-8.84201 - 6.12880i) q^{55} +(-6.32867 - 1.16896i) q^{57} +(-0.210836 + 0.153181i) q^{59} +(-4.36920 - 3.17441i) q^{61} +(-4.27727 + 7.42937i) q^{63} +(1.74928 - 12.8912i) q^{65} +(1.74449 + 3.42375i) q^{67} +(-4.24738 + 1.26095i) q^{69} +(-14.1996 + 4.61373i) q^{71} +(-0.320861 - 2.02584i) q^{73} +(-8.52658 + 1.51572i) q^{75} +(2.15075 + 13.5793i) q^{77} +(8.17124 - 2.65500i) q^{79} +(7.78322 - 4.51901i) q^{81} +(3.16454 + 6.21076i) q^{83} +(1.62078 + 3.01359i) q^{85} +(-0.0807978 - 0.169131i) q^{87} +(-3.84520 - 2.79370i) q^{89} +(-13.4500 + 9.77202i) q^{91} +(-3.18805 + 17.2599i) q^{93} +(-2.39136 + 7.95690i) q^{95} +(14.9764 + 7.63086i) q^{97} +(5.15621 - 13.4815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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