LMFDB - Embedded newform 300.2.x.a.77.4

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			77.4
Character	$\chi$	$=$	300.77
Dual form			300.2.x.a.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.825534 + 1.52266i) q^{3} +(0.0496546 - 2.23552i) q^{5} +(-2.02060 - 2.02060i) q^{7} +(-1.63699 - 2.51402i) q^{9} +O(q^{10})$	\(q+(-0.825534 + 1.52266i) q^{3} +(0.0496546 - 2.23552i) q^{5} +(-2.02060 - 2.02060i) q^{7} +(-1.63699 - 2.51402i) q^{9} +(-2.82802 - 3.89243i) q^{11} +(5.74634 - 0.910130i) q^{13} +(3.36294 + 1.92110i) q^{15} +(1.36348 + 0.694729i) q^{17} +(-3.53381 + 1.14820i) q^{19} +(4.74475 - 1.40861i) q^{21} +(2.52651 + 0.400161i) q^{23} +(-4.99507 - 0.222007i) q^{25} +(5.17938 - 0.417165i) q^{27} +(0.0334412 - 0.102921i) q^{29} +(-3.13145 - 9.63760i) q^{31} +(8.26147 - 1.09277i) q^{33} +(-4.61741 + 4.41674i) q^{35} +(-0.418876 - 2.64468i) q^{37} +(-3.35798 + 9.50106i) q^{39} +(2.26109 - 3.11213i) q^{41} +(-1.86113 + 1.86113i) q^{43} +(-5.70141 + 3.53468i) q^{45} +(4.48724 + 8.80670i) q^{47} +1.16562i q^{49} +(-2.18344 + 1.50260i) q^{51} +(-9.81020 + 4.99855i) q^{53} +(-8.84201 + 6.12880i) q^{55} +(1.16896 - 6.32867i) q^{57} +(0.210836 + 0.153181i) q^{59} +(-4.36920 + 3.17441i) q^{61} +(-1.77212 + 8.38750i) q^{63} +(-1.74928 - 12.8912i) q^{65} +(1.74449 - 3.42375i) q^{67} +(-2.69503 + 3.51668i) q^{69} +(14.1996 + 4.61373i) q^{71} +(-0.320861 + 2.02584i) q^{73} +(4.46164 - 7.42252i) q^{75} +(-2.15075 + 13.5793i) q^{77} +(8.17124 + 2.65500i) q^{79} +(-3.64056 + 8.23082i) q^{81} +(-3.16454 + 6.21076i) q^{83} +(1.62078 - 3.01359i) q^{85} +(0.129107 + 0.135885i) q^{87} +(3.84520 - 2.79370i) q^{89} +(-13.4500 - 9.77202i) q^{91} +(17.2599 + 3.18805i) q^{93} +(2.39136 + 7.95690i) q^{95} +(14.9764 - 7.63086i) q^{97} +(-5.15621 + 13.4815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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
$3$	−0.825534	+	1.52266i	−0.476623	+	0.879108i
$3$	−0.825534	+	1.52266i	−0.476623	+	0.879108i
$4$		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	0.213278	−	0.976992i	$-0.431586\pi$
$7$	−2.02060	−	2.02060i	−0.763714	−	0.763714i	−0.976992	+	0.213278i	$0.931586\pi$
$8$		0			0
$9$	−1.63699	−	2.51402i	−0.545662	−	0.838005i
$10$		0			0
$11$	−2.82802	−	3.89243i	−0.852679	−	1.17361i	−0.983266	−	0.182175i	$-0.941686\pi$
$11$	−2.82802	−	3.89243i	−0.852679	−	1.17361i	0.130587	−	0.991437i	$-0.458314\pi$
$12$		0			0
$13$	5.74634	−	0.910130i	1.59375	−	0.252425i	0.704450	−	0.709754i	$-0.251194\pi$
$13$	5.74634	−	0.910130i	1.59375	−	0.252425i	0.889297	+	0.457329i	$0.151194\pi$
$14$		0			0
$15$	3.36294	+	1.92110i	0.868307	+	0.496027i
$16$		0			0
$17$	1.36348	+	0.694729i	0.330693	+	0.168497i	0.611451	−	0.791282i	$-0.290586\pi$
$17$	1.36348	+	0.694729i	0.330693	+	0.168497i	−0.280758	+	0.959778i	$0.590586\pi$
$18$		0			0
$19$	−3.53381	+	1.14820i	−0.810711	+	0.263416i	−0.684899	−	0.728638i	$-0.740154\pi$
$19$	−3.53381	+	1.14820i	−0.810711	+	0.263416i	−0.125812	+	0.992054i	$0.540154\pi$
$20$		0			0
$21$	4.74475	−	1.40861i	1.03539	−	0.307384i
$22$		0			0
$23$	2.52651	+	0.400161i	0.526815	+	0.0834393i	0.414176	−	0.910197i	$-0.364070\pi$
$23$	2.52651	+	0.400161i	0.526815	+	0.0834393i	0.112639	+	0.993636i	$0.464070\pi$
$24$		0			0
$25$	−4.99507	−	0.222007i	−0.999014	−	0.0444015i
$26$		0			0
$27$	5.17938	−	0.417165i	0.996772	−	0.0802834i
$28$		0			0
$29$	0.0334412	−	0.102921i	0.00620988	−	0.0191120i	−0.947904	−	0.318557i	$-0.896802\pi$
$29$	0.0334412	−	0.102921i	0.00620988	−	0.0191120i	0.954113	+	0.299445i	$0.0968016\pi$
$30$		0			0
$31$	−3.13145	−	9.63760i	−0.562425	−	1.73096i	−0.675482	−	0.737376i	$-0.736064\pi$
$31$	−3.13145	−	9.63760i	−0.562425	−	1.73096i	0.113058	−	0.993588i	$-0.463936\pi$
$32$		0			0
$33$	8.26147	−	1.09277i	1.43814	−	0.190227i
$34$		0			0
$35$	−4.61741	+	4.41674i	−0.780484	+	0.746566i
$36$		0			0
$37$	−0.418876	−	2.64468i	−0.0688628	−	0.434782i	−0.997899	−	0.0647929i	$-0.979361\pi$
$37$	−0.418876	−	2.64468i	−0.0688628	−	0.434782i	0.929036	−	0.369989i	$-0.120639\pi$
$38$		0			0
$39$	−3.35798	+	9.50106i	−0.537707	+	1.52139i
$40$		0			0
$41$	2.26109	−	3.11213i	0.353123	−	0.486032i	−0.595093	−	0.803656i	$-0.702885\pi$
$41$	2.26109	−	3.11213i	0.353123	−	0.486032i	0.948217	+	0.317624i	$0.102885\pi$
$42$		0			0
$43$	−1.86113	+	1.86113i	−0.283820	+	0.283820i	−0.834631	−	0.550810i	$-0.814319\pi$
$43$	−1.86113	+	1.86113i	−0.283820	+	0.283820i	0.550810	+	0.834631i	$0.314319\pi$
$44$		0			0
$45$	−5.70141	+	3.53468i	−0.849916	+	0.526918i
$46$		0			0
$47$	4.48724	+	8.80670i	0.654531	+	1.28459i	0.944801	+	0.327644i	$0.106255\pi$
$47$	4.48724	+	8.80670i	0.654531	+	1.28459i	−0.290271	+	0.956945i	$0.593745\pi$
$48$		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	$-0.922940\pi$
$53$	−9.81020	+	4.99855i	−1.34754	+	0.686604i	−0.376696	+	0.926337i	$0.622940\pi$
$54$		0			0
$55$	−8.84201	+	6.12880i	−1.19226	+	0.826407i
$56$		0			0
$57$	1.16896	−	6.32867i	0.154832	−	0.838253i
$58$		0			0
$59$	0.210836	+	0.153181i	0.0274485	+	0.0199425i	0.601425	−	0.798929i	$-0.294600\pi$
$59$	0.210836	+	0.153181i	0.0274485	+	0.0199425i	−0.573976	+	0.818872i	$0.694600\pi$
$60$		0			0
$61$	−4.36920	+	3.17441i	−0.559418	+	0.406441i	−0.831246	−	0.555905i	$-0.812372\pi$
$61$	−4.36920	+	3.17441i	−0.559418	+	0.406441i	0.271828	+	0.962346i	$0.412372\pi$
$62$		0			0
$63$	−1.77212	+	8.38750i	−0.223267	+	1.05673i
$64$		0			0
$65$	−1.74928	−	12.8912i	−0.216971	−	1.59896i
$66$		0			0
$67$	1.74449	−	3.42375i	0.213123	−	0.418278i	−0.759552	−	0.650446i	$-0.774582\pi$
$67$	1.74449	−	3.42375i	0.213123	−	0.418278i	0.972676	+	0.232168i	$0.0745819\pi$
$68$		0			0
$69$	−2.69503	+	3.51668i	−0.324444	+	0.423358i
$70$		0			0
$71$	14.1996	+	4.61373i	1.68518	+	0.547549i	0.985906	−	0.167302i	$-0.0535055\pi$
$71$	14.1996	+	4.61373i	1.68518	+	0.547549i	0.699277	+	0.714851i	$0.253505\pi$
$72$		0			0
$73$	−0.320861	+	2.02584i	−0.0375539	+	0.237106i	−0.999324	−	0.0367504i	$-0.988299\pi$
$73$	−0.320861	+	2.02584i	−0.0375539	+	0.237106i	0.961771	+	0.273857i	$0.0882993\pi$
$74$		0			0
$75$	4.46164	−	7.42252i	0.515186	−	0.857078i
$76$		0			0
$77$	−2.15075	+	13.5793i	−0.245101	+	1.54751i
$78$		0			0
$79$	8.17124	+	2.65500i	0.919337	+	0.298711i	0.730195	−	0.683239i	$-0.239429\pi$
$79$	8.17124	+	2.65500i	0.919337	+	0.298711i	0.189142	+	0.981950i	$0.439429\pi$
$80$		0			0
$81$	−3.64056	+	8.23082i	−0.404506	+	0.914535i
$82$		0			0
$83$	−3.16454	+	6.21076i	−0.347353	+	0.681719i	−0.996906	−	0.0785968i	$-0.974956\pi$
$83$	−3.16454	+	6.21076i	−0.347353	+	0.681719i	0.649553	+	0.760316i	$0.274956\pi$
$84$		0			0
$85$	1.62078	−	3.01359i	0.175798	−	0.326870i
$86$		0			0
$87$	0.129107	+	0.135885i	0.0138418	+	0.0145684i
$88$		0			0
$89$	3.84520	−	2.79370i	0.407590	−	0.296132i	−0.365035	−	0.930994i	$-0.618943\pi$
$89$	3.84520	−	2.79370i	0.407590	−	0.296132i	0.772625	+	0.634862i	$0.218943\pi$
$90$		0			0
$91$	−13.4500	−	9.77202i	−1.40995	−	1.02439i
$92$		0			0
$93$	17.2599	+	3.18805i	1.78977	+	0.330585i
$94$		0			0
$95$	2.39136	+	7.95690i	0.245348	+	0.816361i
$96$		0			0
$97$	14.9764	−	7.63086i	1.52062	−	0.774797i	0.523606	−	0.851961i	$-0.324587\pi$
$97$	14.9764	−	7.63086i	1.52062	−	0.774797i	0.997018	+	0.0771640i	$0.0245865\pi$
$98$		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	0.760393	−	0.649463i	$-0.225006\pi$
$103$	−2.15137	−	4.22231i	−0.211981	−	0.416036i	−0.972374	+	0.233426i	$0.925006\pi$
$104$		0			0
$105$	−2.91337	−	10.6769i	−0.284316	−	1.04196i
$106$		0			0
$107$	12.4265	−	12.4265i	1.20132	−	1.20132i	0.227550	−	0.973766i	$-0.426928\pi$
$107$	12.4265	−	12.4265i	1.20132	−	1.20132i	0.973766	−	0.227550i	$-0.0730716\pi$
$108$		0			0
$109$	−10.0321	+	13.8080i	−0.960904	+	1.32257i	−0.0143943	+	0.999896i	$0.504582\pi$
$109$	−10.0321	+	13.8080i	−0.960904	+	1.32257i	−0.946510	+	0.322675i	$0.895418\pi$
$110$		0			0
$111$	4.37274	+	1.54547i	0.415042	+	0.146689i
$112$		0			0
$113$	−0.324731	−	2.05027i	−0.0305481	−	0.192873i	0.967695	−	0.252124i	$-0.0811290\pi$
$113$	−0.324731	−	2.05027i	−0.0305481	−	0.192873i	−0.998243	+	0.0592504i	$0.981129\pi$
$114$		0			0
$115$	1.02002	−	5.62820i	0.0951172	−	0.524832i
$116$		0			0
$117$	−11.6948	−	12.9565i	−1.08118	−	1.19783i
$118$		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
$123$	2.87210	+	6.01204i	0.258969	+	0.542088i
$124$		0			0
$125$	−0.744329	+	11.1555i	−0.0665748	+	0.997781i
$126$		0			0
$127$	−1.50225	−	0.237933i	−0.133303	−	0.0211132i	0.0894262	−	0.995993i	$-0.471497\pi$
$127$	−1.50225	−	0.237933i	−0.133303	−	0.0211132i	−0.222729	+	0.974880i	$0.571497\pi$
$128$		0			0
$129$	−1.29744	−	4.37031i	−0.114234	−	0.384784i
$130$		0			0
$131$	−5.58648	+	1.81516i	−0.488093	+	0.158591i	−0.542717	−	0.839916i	$-0.682604\pi$
$131$	−5.58648	+	1.81516i	−0.488093	+	0.158591i	0.0546233	+	0.998507i	$0.482604\pi$
$132$		0			0
$133$	9.46045	+	4.82034i	0.820325	+	0.417977i
$134$		0			0
$135$	−0.675399	−	11.5993i	−0.0581291	−	0.998309i
$136$		0			0
$137$	8.72702	−	1.38222i	0.745599	−	0.118091i	0.227936	−	0.973676i	$-0.426802\pi$
$137$	8.72702	−	1.38222i	0.745599	−	0.118091i	0.517663	+	0.855585i	$0.326802\pi$
$138$		0			0
$139$	2.77543	+	3.82005i	0.235409	+	0.324012i	0.910335	−	0.413873i	$-0.135824\pi$
$139$	2.77543	+	3.82005i	0.235409	+	0.324012i	−0.674926	+	0.737886i	$0.735824\pi$
$140$		0			0
$141$	−17.1140	−	0.437698i	−1.44126	−	0.0368608i
$142$		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
$147$	−1.77484	−	0.962257i	−0.146386	−	0.0793656i
$148$		0			0
$149$	1.98633			0.162726			0.0813632	−	0.996685i	$-0.474073\pi$
$149$	1.98633			0.162726			0.0813632	+	0.996685i	$0.474073\pi$
$150$		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
$153$	−0.485441	−	4.56508i	−0.0392456	−	0.369065i
$154$		0			0
$155$	−21.7005	+	6.52185i	−1.74303	+	0.523848i
$156$		0			0
$157$	7.63307	+	7.63307i	0.609185	+	0.609185i	0.942733	−	0.333548i	$-0.108246\pi$
$157$	7.63307	+	7.63307i	0.609185	+	0.609185i	−0.333548	+	0.942733i	$0.608246\pi$
$158$		0			0
$159$	0.487573	−	19.0641i	0.0386670	−	1.51188i
$160$		0			0
$161$	−4.29650	−	5.91363i	−0.338612	−	0.466059i
$162$		0			0
$163$	−4.19979	+	0.665182i	−0.328953	+	0.0521011i	−0.318727	−	0.947847i	$-0.603255\pi$
$163$	−4.19979	+	0.665182i	−0.328953	+	0.0521011i	−0.0102264	+	0.999948i	$0.503255\pi$
$164$		0			0
$165$	−2.03269	−	18.5229i	−0.158244	−	1.44201i
$166$		0			0
$167$	−9.52908	−	4.85531i	−0.737383	−	0.375715i	0.0446088	−	0.999005i	$-0.485796\pi$
$167$	−9.52908	−	4.85531i	−0.737383	−	0.375715i	−0.781991	+	0.623289i	$0.785796\pi$
$168$		0			0
$169$	19.8283	−	6.44261i	1.52525	−	0.495585i
$170$		0			0
$171$	8.67139	+	7.00446i	0.663118	+	0.535644i
$172$		0			0
$173$	2.32976	+	0.368997i	0.177128	+	0.0280543i	0.244368	−	0.969682i	$-0.421419\pi$
$173$	2.32976	+	0.368997i	0.177128	+	0.0280543i	−0.0672403	+	0.997737i	$0.521419\pi$
$174$		0			0
$175$	9.64443	+	10.5416i	0.729050	+	0.796870i
$176$		0			0
$177$	−0.407296	+	0.194575i	−0.0306142	+	0.0146252i
$178$		0			0
$179$	−1.36907	+	4.21356i	−0.102329	+	0.314936i	−0.989094	−	0.147284i	$-0.952947\pi$
$179$	−1.36907	+	4.21356i	−0.102329	+	0.314936i	0.886765	+	0.462220i	$0.152947\pi$
$180$		0			0
$181$	2.45027	+	7.54116i	0.182127	+	0.560530i	0.999887	−	0.0150298i	$-0.00478432\pi$
$181$	2.45027	+	7.54116i	0.182127	+	0.560530i	−0.817760	+	0.575559i	$0.804784\pi$
$182$		0			0
$183$	−1.22662	−	9.27338i	−0.0906743	−	0.685508i
$184$		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
$189$	−11.3084	−	9.62251i	−0.822562	−	0.699935i
$190$		0			0
$191$	4.93725	−	6.79554i	0.357247	−	0.491708i	−0.592132	−	0.805841i	$-0.701714\pi$
$191$	4.93725	−	6.79554i	0.357247	−	0.491708i	0.949379	+	0.314133i	$0.101714\pi$
$192$		0			0
$193$	9.74578	−	9.74578i	0.701517	−	0.701517i	−0.263219	−	0.964736i	$-0.584784\pi$
$193$	9.74578	−	9.74578i	0.701517	−	0.701517i	0.964736	+	0.263219i	$0.0847843\pi$
$194$		0			0
$195$	21.0730	+	7.97859i	1.50907	+	0.571359i
$196$		0			0
$197$	7.05689	+	13.8499i	0.502783	+	0.986766i	0.993325	+	0.115349i	$0.0367986\pi$
$197$	7.05689	+	13.8499i	0.502783	+	0.986766i	−0.490543	+	0.871417i	$0.663201\pi$
$198$		0			0
$199$		−	10.6381i		−	0.754117i	−0.926189	−	0.377059i	$-0.876936\pi$
$199$		−	10.6381i		−	0.754117i	0.926189	−	0.377059i	$-0.123064\pi$
$200$		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
$207$	−3.12986	−	7.00676i	−0.217540	−	0.487003i
$208$		0			0
$209$	14.4630	+	10.5080i	1.00042	+	0.726851i
$210$		0			0
$211$	8.87487	−	6.44797i	0.610971	−	0.443897i	−0.238785	−	0.971072i	$-0.576749\pi$
$211$	8.87487	−	6.44797i	0.610971	−	0.443897i	0.849756	+	0.527176i	$0.176749\pi$
$212$		0			0
$213$	−18.7474	+	17.8124i	−1.28455	+	1.22048i
$214$		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
$219$	−2.81978	−	2.16096i	−0.190543	−	0.146024i
$220$		0			0
$221$	8.46732	+	2.75120i	0.569574	+	0.185066i
$222$		0			0
$223$	−2.83443	+	17.8959i	−0.189807	+	1.19840i	0.690265	+	0.723557i	$0.257494\pi$
$223$	−2.83443	+	17.8959i	−0.189807	+	1.19840i	−0.880072	+	0.474840i	$0.842506\pi$
$224$		0			0
$225$	7.61873	+	12.9211i	0.507915	+	0.861407i
$226$		0			0
$227$	0.381413	−	2.40815i	0.0253153	−	0.159834i	−0.971792	−	0.235839i	$-0.924216\pi$
$227$	0.381413	−	2.40815i	0.0253153	−	0.159834i	0.997107	+	0.0760044i	$0.0242163\pi$
$228$		0			0
$229$	−13.9452	−	4.53107i	−0.921524	−	0.299421i	−0.190432	−	0.981700i	$-0.560989\pi$
$229$	−13.9452	−	4.53107i	−0.921524	−	0.299421i	−0.731092	+	0.682279i	$0.760989\pi$
$230$		0			0
$231$	−18.9011	−	14.4850i	−1.24360	−	0.953046i
$232$		0			0
$233$	8.99659	−	17.6568i	0.589386	−	1.15674i	−0.383085	−	0.923713i	$-0.625139\pi$
$233$	8.99659	−	17.6568i	0.589386	−	1.15674i	0.972471	−	0.233022i	$-0.0748615\pi$
$234$		0			0
$235$	19.9103	−	9.59400i	1.29881	−	0.625843i
$236$		0			0
$237$	−10.7883	+	10.2502i	−0.700776	+	0.665824i
$238$		0			0
$239$	18.6744	−	13.5678i	1.20795	−	0.877625i	0.212904	−	0.977073i	$-0.431708\pi$
$239$	18.6744	−	13.5678i	1.20795	−	0.877625i	0.995043	+	0.0994482i	$0.0317078\pi$
$240$		0			0
$241$	7.99196	+	5.80650i	0.514807	+	0.374029i	0.814644	−	0.579961i	$-0.196932\pi$
$241$	7.99196	+	5.80650i	0.514807	+	0.374029i	−0.299837	+	0.953990i	$0.596932\pi$
$242$		0			0
$243$	−9.52733	−	12.3382i	−0.611178	−	0.791493i
$244$		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
$255$	3.25066	+	4.95572i	0.203564	+	0.310339i
$256$		0			0
$257$	−17.5417	+	17.5417i	−1.09422	+	1.09422i	−0.0991458	+	0.995073i	$0.531611\pi$
$257$	−17.5417	+	17.5417i	−1.09422	+	1.09422i	−0.995073	+	0.0991458i	$0.968389\pi$
$258$		0			0
$259$	−4.49745	+	6.19020i	−0.279458	+	0.384641i
$260$		0			0
$261$	−0.313489	+	0.0844092i	−0.0194045	+	0.00522480i
$262$		0			0
$263$	2.55900	+	16.1569i	0.157795	+	0.996277i	0.931767	+	0.363057i	$0.118267\pi$
$263$	2.55900	+	16.1569i	0.157795	+	0.996277i	−0.773972	+	0.633220i	$0.781733\pi$
$264$		0			0
$265$	10.6872	+	22.1791i	0.656511	+	1.36245i
$266$		0			0
$267$	1.07951	+	8.16122i	0.0660650	+	0.499459i
$268$		0			0
$269$	2.50454	+	7.70819i	0.152705	+	0.469977i	0.997921	−	0.0644474i	$-0.0205285\pi$
$269$	2.50454	+	7.70819i	0.152705	+	0.469977i	−0.845216	+	0.534424i	$0.820528\pi$
$270$		0			0
$271$	−2.83005	+	8.70999i	−0.171913	+	0.529094i	−0.999479	−	0.0322745i	$-0.989725\pi$
$271$	−2.83005	+	8.70999i	−0.171913	+	0.529094i	0.827566	+	0.561368i	$0.189725\pi$
$272$		0			0
$273$	25.9829	−	12.4127i	1.57256	−	0.751250i
$274$		0			0
$275$	13.2620	+	20.0708i	0.799728	+	1.21031i
$276$		0			0
$277$	−3.90301	−	0.618177i	−0.234509	−	0.0371426i	0.0380735	−	0.999275i	$-0.487878\pi$
$277$	−3.90301	−	0.618177i	−0.234509	−	0.0371426i	−0.272583	+	0.962132i	$0.587878\pi$
$278$		0			0
$279$	−19.1030	+	23.6491i	−1.14366	+	1.41584i
$280$		0			0
$281$	−24.5537	+	7.97798i	−1.46475	+	0.475926i	−0.929517	−	0.368778i	$-0.879776\pi$
$281$	−24.5537	+	7.97798i	−1.46475	+	0.475926i	−0.535233	+	0.844704i	$0.679776\pi$
$282$		0			0
$283$	−1.20672	−	0.614853i	−0.0717319	−	0.0365492i	0.417757	−	0.908559i	$-0.362816\pi$
$283$	−1.20672	−	0.614853i	−0.0717319	−	0.0365492i	−0.489489	+	0.872010i	$0.662816\pi$
$284$		0			0
$285$	−14.0898	−	2.92747i	−0.834608	−	0.173408i
$286$		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
$291$	−0.744336	+	29.1035i	−0.0436338	+	1.70608i
$292$		0			0
$293$	−9.43835	−	9.43835i	−0.551395	−	0.551395i	0.375449	−	0.926843i	$-0.377489\pi$
$293$	−9.43835	−	9.43835i	−0.551395	−	0.551395i	−0.926843	+	0.375449i	$0.877489\pi$
$294$		0			0
$295$	0.352909	−	0.463722i	0.0205471	−	0.0269989i
$296$		0			0
$297$	−16.2711	−	18.9806i	−0.944148	−	1.10137i
$298$		0			0
$299$	14.8824			0.860672
$300$		0			0
$301$	7.52120			0.433515
$302$		0			0
$303$	26.4286	+	14.3287i	1.51828	+	0.823161i
$304$		0			0
$305$	6.87949	+	9.92503i	0.393918	+	0.568306i
$306$		0			0
$307$	−9.42497	−	9.42497i	−0.537911	−	0.537911i	0.385004	−	0.922915i	$-0.374200\pi$
$307$	−9.42497	−	9.42497i	−0.537911	−	0.537911i	−0.922915	+	0.385004i	$0.874200\pi$
$308$		0			0
$309$	8.20517	+	0.209851i	0.466776	+	0.0119380i
$310$		0			0
$311$	−7.79335	−	10.7266i	−0.441920	−	0.608251i	0.528717	−	0.848798i	$-0.322673\pi$
$311$	−7.79335	−	10.7266i	−0.441920	−	0.608251i	−0.970637	+	0.240547i	$0.922673\pi$
$312$		0			0
$313$	0.0874904	−	0.0138571i	0.00494525	−	0.000783251i	−0.153961	−	0.988077i	$-0.549203\pi$
$313$	0.0874904	−	0.0138571i	0.00494525	−	0.000783251i	0.158907	+	0.987294i	$0.449203\pi$
$314$		0			0
$315$	18.6624	+	4.37809i	1.05151	+	0.246678i
$316$		0			0
$317$	25.7112	+	13.1005i	1.44409	+	0.735799i	0.988046	−	0.154160i	$-0.0492672\pi$
$317$	25.7112	+	13.1005i	1.44409	+	0.735799i	0.456041	+	0.889959i	$0.349267\pi$
$318$		0			0
$319$	−0.495187	+	0.160896i	−0.0277251	+	0.00900844i
$320$		0			0
$321$	8.66284	+	29.1799i	0.483512	+	1.62866i
$322$		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
$327$	−12.7431	−	26.6745i	−0.704694	−	1.47511i
$328$		0			0
$329$	8.72788	−	26.8617i	0.481184	−	1.48093i
$330$		0			0
$331$	1.58196	+	4.86878i	0.0869525	+	0.267612i	0.985073	−	0.172137i	$-0.0550672\pi$
$331$	1.58196	+	4.86878i	0.0869525	+	0.267612i	−0.898120	+	0.439750i	$0.855067\pi$
$332$		0			0
$333$	−5.96307	+	5.38236i	−0.326774	+	0.294952i
$334$		0			0
$335$	−7.56724	−	4.06984i	−0.413442	−	0.222359i
$336$		0			0
$337$	2.34521	+	14.8070i	0.127752	+	0.806591i	0.965475	+	0.260496i	$0.0838862\pi$
$337$	2.34521	+	14.8070i	0.127752	+	0.806591i	−0.837723	+	0.546095i	$0.816114\pi$
$338$		0			0
$339$	3.38994	+	1.19811i	0.184116	+	0.0650726i
$340$		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
$345$	7.72777	+	6.19941i	0.416049	+	0.333765i
$346$		0			0
$347$	−4.06670	−	7.98136i	−0.218312	−	0.428462i	0.755713	−	0.654903i	$-0.227291\pi$
$347$	−4.06670	−	7.98136i	−0.218312	−	0.428462i	−0.974025	+	0.226442i	$0.927291\pi$
$348$		0			0
$349$		−	31.6418i		−	1.69375i	−0.531793	−	0.846874i	$-0.678482\pi$
$349$		−	31.6418i		−	1.69375i	0.531793	−	0.846874i	$-0.321518\pi$
$350$		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	$-0.813136\pi$
$353$	−16.4179	+	8.36532i	−0.873834	+	0.445241i	−0.0412563	+	0.999149i	$0.513136\pi$
$354$		0			0
$355$	11.0191	−	31.5144i	0.584836	−	1.67261i
$356$		0			0
$357$	7.44799	+	1.37570i	0.394189	+	0.0728100i
$358$		0			0
$359$	3.85147	+	2.79826i	0.203273	+	0.147686i	0.684765	−	0.728764i	$-0.259905\pi$
$359$	3.85147	+	2.79826i	0.203273	+	0.147686i	−0.481492	+	0.876450i	$0.659905\pi$
$360$		0			0
$361$	−4.20190	+	3.05286i	−0.221153	+	0.160677i
$362$		0			0
$363$	−14.4937	−	15.2546i	−0.760725	−	0.800658i
$364$		0			0
$365$	4.51286	+	0.817882i	0.236214	+	0.0428099i
$366$		0			0
$367$	2.16114	−	4.24147i	0.112810	−	0.221403i	−0.827698	−	0.561174i	$-0.810350\pi$
$367$	2.16114	−	4.24147i	0.112810	−	0.221403i	0.940508	+	0.339771i	$0.110350\pi$
$368$		0			0
$369$	−11.5253	−	0.589917i	−0.599984	−	0.0307098i
$370$		0			0
$371$	29.9225	+	9.72241i	1.55350	+	0.504763i
$372$		0			0
$373$	−3.54113	+	22.3578i	−0.183353	+	1.15765i	0.708631	+	0.705579i	$0.249313\pi$
$373$	−3.54113	+	22.3578i	−0.183353	+	1.15765i	−0.891984	+	0.452066i	$0.850687\pi$
$374$		0			0
$375$	−16.3716	−	10.3426i	−0.845427	−	0.534092i
$376$		0			0
$377$	0.0984925	−	0.621857i	0.00507262	−	0.0320273i
$378$		0			0
$379$	−2.26244	−	0.735112i	−0.116214	−	0.0377601i	0.250333	−	0.968160i	$-0.419460\pi$
$379$	−2.26244	−	0.735112i	−0.116214	−	0.0377601i	−0.366547	+	0.930400i	$0.619460\pi$
$380$		0			0
$381$	1.60245	−	2.09100i	0.0820961	−	0.107125i
$382$		0			0
$383$	13.1453	−	25.7992i	0.671696	−	1.31828i	−0.263676	−	0.964611i	$-0.584935\pi$
$383$	13.1453	−	25.7992i	0.671696	−	1.31828i	0.935372	−	0.353666i	$-0.115065\pi$
$384$		0			0
$385$	30.2500	+	5.48231i	1.54168	+	0.279405i
$386$		0			0
$387$	7.72557	+	1.63227i	0.392713	+	0.0829731i
$388$		0			0
$389$	−15.3567	+	11.1573i	−0.778614	+	0.565697i	−0.904563	−	0.426340i	$-0.859803\pi$
$389$	−15.3567	+	11.1573i	−0.778614	+	0.565697i	0.125948	+	0.992037i	$0.459803\pi$
$390$		0			0
$391$	3.16685	+	2.30085i	0.160155	+	0.116359i
$392$		0			0
$393$	1.84797	−	10.0048i	0.0932175	−	0.504675i
$394$		0			0
$395$	6.34103	−	18.1351i	0.319052	−	0.912477i
$396$		0			0
$397$	−1.51760	+	0.773254i	−0.0761660	+	0.0388085i	−0.491659	−	0.870788i	$-0.663609\pi$
$397$	−1.51760	+	0.773254i	−0.0761660	+	0.0388085i	0.415493	+	0.909597i	$0.363609\pi$
$398$		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
$405$	18.2194	+	8.54722i	0.905327	+	0.424715i
$406$		0			0
$407$	−9.10963	+	9.10963i	−0.451548	+	0.451548i
$408$		0			0
$409$	18.8051	−	25.8830i	0.929853	−	1.27983i	−0.0300633	−	0.999548i	$-0.509571\pi$
$409$	18.8051	−	25.8830i	0.929853	−	1.27983i	0.959917	−	0.280285i	$-0.0904291\pi$
$410$		0			0
$411$	−5.09980	+	14.4294i	−0.251554	+	0.711747i
$412$		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
$417$	−8.10785	+	1.07245i	−0.397043	+	0.0525182i
$418$		0			0
$419$	−2.91963	−	8.98569i	−0.142633	−	0.438980i	0.854066	−	0.520165i	$-0.174130\pi$
$419$	−2.91963	−	8.98569i	−0.142633	−	0.438980i	−0.996699	+	0.0811851i	$0.974130\pi$
$420$		0			0
$421$	−1.74189	+	5.36098i	−0.0848945	+	0.261278i	−0.984489	−	0.175449i	$-0.943862\pi$
$421$	−1.74189	+	5.36098i	−0.0848945	+	0.261278i	0.899594	+	0.436727i	$0.143862\pi$
$422$		0			0
$423$	14.7946	−	25.6974i	0.719340	−	1.24945i
$424$		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
$429$	46.4786	−	13.7984i	2.24401	−	0.666195i
$430$		0			0
$431$	11.7037	−	3.80275i	0.563745	−	0.183172i	−0.0132603	−	0.999912i	$-0.504221\pi$
$431$	11.7037	−	3.80275i	0.563745	−	0.183172i	0.577006	+	0.816740i	$0.304221\pi$
$432$		0			0
$433$	−26.3686	−	13.4355i	−1.26719	−	0.645667i	−0.314400	−	0.949291i	$-0.601803\pi$
$433$	−26.3686	−	13.4355i	−1.26719	−	0.645667i	−0.952792	+	0.303624i	$0.901803\pi$
$434$		0			0
$435$	0.310183	−	0.281875i	0.0148722	−	0.0135149i
$436$		0			0
$437$	−9.38768	+	1.48686i	−0.449074	+	0.0711263i
$438$		0			0
$439$	10.9368	+	15.0532i	0.521984	+	0.718449i	0.985882	−	0.167439i	$-0.0535497\pi$
$439$	10.9368	+	15.0532i	0.521984	+	0.718449i	−0.463898	+	0.885888i	$0.653550\pi$
$440$		0			0
$441$	2.93038	−	1.90810i	0.139542	−	0.0908618i
$442$		0			0
$443$	1.48265	+	1.48265i	0.0704427	+	0.0704427i	0.741450	−	0.671008i	$-0.234138\pi$
$443$	1.48265	+	1.48265i	0.0704427	+	0.0704427i	−0.671008	+	0.741450i	$0.734138\pi$
$444$		0			0
$445$	−6.05443	−	8.73472i	−0.287007	−	0.414066i
$446$		0			0
$447$	−1.63978	+	3.02450i	−0.0775590	+	0.143054i
$448$		0			0
$449$	33.3934			1.57593			0.787967	−	0.615718i	$-0.211134\pi$
$449$	33.3934			1.57593			0.787967	+	0.615718i	$0.211134\pi$
$450$		0			0
$451$	−18.5081			−0.871514
$452$		0			0
$453$	−17.7381	+	32.7170i	−0.833407	+	1.53718i
$454$		0			0
$455$	−22.5134	+	29.5825i	−1.05544	+	1.38685i
$456$		0			0
$457$	14.4358	+	14.4358i	0.675278	+	0.675278i	0.958928	−	0.283650i	$-0.0915453\pi$
$457$	14.4358	+	14.4358i	0.675278	+	0.675278i	−0.283650	+	0.958928i	$0.591545\pi$
$458$		0			0
$459$	7.35181	+	3.02947i	0.343153	+	0.141403i
$460$		0			0
$461$	1.12640	+	1.55036i	0.0524617	+	0.0722073i	0.834442	−	0.551096i	$-0.185790\pi$
$461$	1.12640	+	1.55036i	0.0524617	+	0.0722073i	−0.781980	+	0.623303i	$0.785790\pi$
$462$		0			0
$463$	−2.40651	+	0.381153i	−0.111840	+	0.0177137i	−0.212103	−	0.977247i	$-0.568031\pi$
$463$	−2.40651	+	0.381153i	−0.111840	+	0.0177137i	0.100264	+	0.994961i	$0.468031\pi$
$464$		0			0
$465$	7.98396	−	38.4265i	0.370247	−	1.78199i
$466$		0			0
$467$	−13.9849	−	7.12568i	−0.647146	−	0.329737i	0.0994231	−	0.995045i	$-0.468300\pi$
$467$	−13.9849	−	7.12568i	−0.647146	−	0.329737i	−0.746569	+	0.665308i	$0.768300\pi$
$468$		0			0
$469$	−10.4429	+	3.39312i	−0.482210	+	0.156680i
$470$		0			0
$471$	−17.9239	+	5.32121i	−0.825891	+	0.245188i
$472$		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
$477$	28.6256	+	16.4805i	1.31068	+	0.754589i
$478$		0			0
$479$	−3.70860	+	11.4139i	−0.169450	+	0.521514i	−0.999337	−	0.0364182i	$-0.988405\pi$
$479$	−3.70860	+	11.4139i	−0.169450	+	0.521514i	0.829886	+	0.557932i	$0.188405\pi$
$480$		0			0
$481$	−4.81400	−	14.8160i	−0.219500	−	0.675550i
$482$		0			0
$483$	12.5514	−	1.66021i	0.571106	−	0.0755421i
$484$		0			0
$485$	−16.3153	−	33.8589i	−0.740838	−	1.53745i
$486$		0			0
$487$	0.279897	+	1.76720i	0.0126833	+	0.0800794i	0.993218	−	0.116266i	$-0.0370926\pi$
$487$	0.279897	+	1.76720i	0.0126833	+	0.0800794i	−0.980535	+	0.196346i	$0.937093\pi$
$488$		0			0
$489$	2.45423	−	6.94399i	0.110984	−	0.314018i
$490$		0			0
$491$	−3.20544	+	4.41191i	−0.144660	+	0.199107i	−0.875198	−	0.483765i	$-0.839269\pi$
$491$	−3.20544	+	4.41191i	−0.144660	+	0.199107i	0.730539	+	0.682871i	$0.239269\pi$
$492$		0			0
$493$	0.117099	−	0.117099i	0.00527387	−	0.00527387i
$494$		0			0
$495$	29.8821	+	12.1962i	1.34310	+	0.548179i
$496$		0			0
$497$	−19.3692	−	38.0141i	−0.868826	−	1.70517i
$498$		0			0
$499$			15.8865i			0.711177i	0.934643	+	0.355588i	$0.115719\pi$
$499$			15.8865i			0.711177i	−0.934643	+	0.355588i	$0.884281\pi$
$500$		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	$-0.748760\pi$
$503$	−12.2021	+	6.21728i	−0.544065	+	0.277215i	0.160282	+	0.987071i	$0.448760\pi$
$504$		0			0
$505$	−38.8015	−	0.861848i	−1.72665	−	0.0383517i
$506$		0			0
$507$	−6.55905	+	35.5104i	−0.291298	+	1.57707i
$508$		0			0
$509$	−14.7649	−	10.7273i	−0.654441	−	0.475479i	0.210340	−	0.977628i	$-0.432543\pi$
$509$	−14.7649	−	10.7273i	−0.654441	−	0.475479i	−0.864781	+	0.502149i	$0.832543\pi$
$510$		0			0
$511$	4.74173	−	3.44507i	0.209762	−	0.152401i
$512$		0			0
$513$	−17.8239	+	7.42116i	−0.786946	+	0.327652i
$514$		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
$519$	−2.48515	+	3.24281i	−0.109086	+	0.142343i
$520$		0			0
$521$	−34.6323	−	11.2527i	−1.51727	−	0.492991i	−0.572272	−	0.820064i	$-0.693938\pi$
$521$	−34.6323	−	11.2527i	−1.51727	−	0.492991i	−0.944999	+	0.327073i	$0.893938\pi$
$522$		0			0
$523$	−3.57185	+	22.5518i	−0.156186	+	0.986120i	0.777722	+	0.628608i	$0.216375\pi$
$523$	−3.57185	+	22.5518i	−0.156186	+	0.986120i	−0.933908	+	0.357512i	$0.883625\pi$
$524$		0			0
$525$	−24.0131	+	5.98273i	−1.04802	+	0.261108i
$526$		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
$531$	0.0399649	−	0.780802i	0.00173433	−	0.0338839i
$532$		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
$537$	−5.28560	−	5.56306i	−0.228090	−	0.240064i
$538$		0			0
$539$	4.53708	−	3.29638i	0.195426	−	0.141985i
$540$		0			0
$541$	−14.4743	−	10.5162i	−0.622299	−	0.452126i	0.231425	−	0.972853i	$-0.425661\pi$
$541$	−14.4743	−	10.5162i	−0.622299	−	0.452126i	−0.853724	+	0.520726i	$0.825661\pi$
$542$		0			0
$543$	−13.5054	−	2.49456i	−0.579572	−	0.107052i
$544$		0			0
$545$	30.3700	+	23.1126i	1.30091	+	0.990037i
$546$		0			0
$547$	−13.1268	+	6.68845i	−0.561263	+	0.285978i	−0.711516	−	0.702670i	$-0.751991\pi$
$547$	−13.1268	+	6.68845i	−0.561263	+	0.285978i	0.150253	+	0.988648i	$0.451991\pi$
$548$		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
$555$	3.67204	−	9.69860i	0.155870	−	0.411682i
$556$		0			0
$557$	15.7568	−	15.7568i	0.667638	−	0.667638i	−0.289531	−	0.957169i	$-0.593499\pi$
$557$	15.7568	−	15.7568i	0.667638	−	0.667638i	0.957169	+	0.289531i	$0.0934992\pi$
$558$		0			0
$559$	−9.00083	+	12.3886i	−0.380695	+	0.523981i
$560$		0			0
$561$	12.0235	+	4.24951i	0.507635	+	0.179414i
$562$		0			0
$563$	3.16190	+	19.9634i	0.133258	+	0.841358i	0.960249	+	0.279143i	$0.0900505\pi$
$563$	3.16190	+	19.9634i	0.133258	+	0.841358i	−0.826991	+	0.562215i	$0.809950\pi$
$564$		0			0
$565$	−4.59954	+	0.624136i	−0.193504	+	0.0262576i
$566$		0			0
$567$	23.9873	−	9.27506i	1.00737	−	0.389516i
$568$		0			0
$569$	10.5620	+	32.5066i	0.442783	+	1.36275i	0.884896	+	0.465788i	$0.154229\pi$
$569$	10.5620	+	32.5066i	0.442783	+	1.36275i	−0.442113	+	0.896959i	$0.645771\pi$
$570$		0			0
$571$	−4.84382	+	14.9078i	−0.202708	+	0.623870i	0.797092	+	0.603858i	$0.206371\pi$
$571$	−4.84382	+	14.9078i	−0.202708	+	0.623870i	−0.999800	+	0.0200122i	$0.993629\pi$
$572$		0			0
$573$	6.27142	+	13.1277i	0.261993	+	0.548417i
$574$		0			0
$575$	−12.5313	−	2.55973i	−0.522590	−	0.106748i
$576$		0			0
$577$	−34.5289	−	5.46884i	−1.43746	−	0.227671i	−0.611428	−	0.791300i	$-0.709405\pi$
$577$	−34.5289	−	5.46884i	−1.43746	−	0.227671i	−0.826028	+	0.563629i	$0.809405\pi$
$578$		0			0
$579$	6.79403	+	22.8850i	0.282350	+	0.951067i
$580$		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
$585$	−29.5452	+	25.5005i	−1.22154	+	1.05431i
$586$		0			0
$587$	38.6761	−	6.12569i	1.59633	−	0.252834i	0.706023	−	0.708189i	$-0.250488\pi$
$587$	38.6761	−	6.12569i	1.59633	−	0.252834i	0.890310	+	0.455355i	$0.150488\pi$
$588$		0			0
$589$	22.1319	+	30.4619i	0.911927	+	1.25516i
$590$		0			0
$591$	−26.9144	−	0.688349i	−1.10711	−	0.0283149i
$592$		0			0
$593$	18.8322	+	18.8322i	0.773348	+	0.773348i	0.978690	−	0.205343i	$-0.0658309\pi$
$593$	18.8322	+	18.8322i	0.773348	+	0.773348i	−0.205343	+	0.978690i	$0.565831\pi$
$594$		0			0
$595$	−9.36419	+	2.81431i	−0.383895	+	0.115375i
$596$		0			0
$597$	16.1983	+	8.78214i	0.662950	+	0.359429i
$598$		0			0
$599$	−29.8132			−1.21813			−0.609066	−	0.793119i	$-0.708456\pi$
$599$	−29.8132			−1.21813			−0.609066	+	0.793119i	$0.708456\pi$
$600$		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
$603$	−11.4631	+	1.21896i	−0.466813	+	0.0496399i
$604$		0			0
$605$	25.6429	+	8.96617i	1.04253	+	0.364527i
$606$		0			0
$607$	−16.4938	−	16.4938i	−0.669464	−	0.669464i	0.288128	−	0.957592i	$-0.406967\pi$
$607$	−16.4938	−	16.4938i	−0.669464	−	0.669464i	−0.957592	+	0.288128i	$0.906967\pi$
$608$		0			0
$609$	0.0136942	−	0.535442i	0.000554917	−	0.0216972i
$610$		0			0
$611$	33.8004	+	46.5223i	1.36742	+	1.88209i
$612$		0			0
$613$	34.2415	−	5.42333i	1.38300	−	0.219046i	0.579803	−	0.814756i	$-0.303129\pi$
$613$	34.2415	−	5.42333i	1.38300	−	0.219046i	0.803199	+	0.595710i	$0.203129\pi$
$614$		0			0
$615$	13.5826	−	6.12210i	0.547705	−	0.246867i
$616$		0			0
$617$	24.8462	+	12.6598i	1.00027	+	0.509662i	0.875858	−	0.482568i	$-0.160296\pi$
$617$	24.8462	+	12.6598i	1.00027	+	0.509662i	0.124410	+	0.992231i	$0.460296\pi$
$618$		0			0
$619$	11.8893	−	3.86308i	0.477872	−	0.155270i	−0.0601697	−	0.998188i	$-0.519164\pi$
$619$	11.8893	−	3.86308i	0.477872	−	0.155270i	0.538042	+	0.842918i	$0.319164\pi$
$620$		0			0
$621$	13.2527	+	1.01861i	0.531813	+	0.0408754i
$622$		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
$627$	−27.9397	+	13.3475i	−1.11580	+	0.533047i
$628$		0			0
$629$	1.26620	−	3.89698i	0.0504869	−	0.155383i
$630$		0			0
$631$	5.26220	+	16.1954i	0.209485	+	0.644728i	0.999499	+	0.0316401i	$0.0100730\pi$
$631$	5.26220	+	16.1954i	0.209485	+	0.644728i	−0.790014	+	0.613088i	$0.789927\pi$
$632$		0			0
$633$	2.49155	+	18.8364i	0.0990304	+	0.748681i
$634$		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
$639$	−11.6456	−	43.2506i	−0.460691	−	1.71097i
$640$		0			0
$641$	−2.68121	+	3.69037i	−0.105901	+	0.145761i	−0.858678	−	0.512515i	$-0.828714\pi$
$641$	−2.68121	+	3.69037i	−0.105901	+	0.145761i	0.752777	+	0.658276i	$0.228714\pi$
$642$		0			0
$643$	1.57617	−	1.57617i	0.0621582	−	0.0621582i	−0.675344	−	0.737503i	$-0.736005\pi$
$643$	1.57617	−	1.57617i	0.0621582	−	0.0621582i	0.737503	+	0.675344i	$0.236005\pi$
$644$		0			0
$645$	−9.83432	+	2.68345i	−0.387226	+	0.105661i
$646$		0			0
$647$	10.6313	+	20.8650i	0.417958	+	0.820289i	0.999975	+	0.00711204i	$0.00226385\pi$
$647$	10.6313	+	20.8650i	0.417958	+	0.820289i	−0.582017	+	0.813177i	$0.697736\pi$
$648$		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	$-0.638250\pi$
$653$	1.68056	−	0.856287i	0.0657653	−	0.0335091i	0.486564	+	0.873645i	$0.338250\pi$
$654$		0			0
$655$	3.78042	+	12.5788i	0.147713	+	0.491495i
$656$		0			0
$657$	5.61823	−	2.50961i	0.219188	−	0.0979094i
$658$		0			0
$659$	−39.3347	−	28.5783i	−1.53226	−	1.11325i	−0.954965	−	0.296719i	$-0.904107\pi$
$659$	−39.3347	−	28.5783i	−1.53226	−	1.11325i	−0.577297	−	0.816534i	$-0.695893\pi$
$660$		0			0
$661$	10.8497	−	7.88279i	0.422006	−	0.306605i	−0.356439	−	0.934319i	$-0.616009\pi$
$661$	10.8497	−	7.88279i	0.422006	−	0.306605i	0.778444	+	0.627714i	$0.216009\pi$
$662$		0			0
$663$	−11.1792	+	10.6216i	−0.434164	+	0.412510i
$664$		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
$669$	−24.9094	−	19.0895i	−0.963053	−	0.738044i
$670$		0			0
$671$	24.7123	+	8.02951i	0.954008	+	0.309976i
$672$		0			0
$673$	1.34636	−	8.50057i	0.0518983	−	0.327673i	−0.948056	−	0.318104i	$-0.896954\pi$
$673$	1.34636	−	8.50057i	0.0518983	−	0.327673i	0.999954	−	0.00956929i	$-0.00304604\pi$
$674$		0			0
$675$	−25.9640	+	0.933907i	−0.999354	+	0.0359461i
$676$		0			0
$677$	−0.116734	+	0.737029i	−0.00448645	+	0.0283263i	−0.989830	−	0.142255i	$-0.954565\pi$
$677$	−0.116734	+	0.737029i	−0.00448645	+	0.0283263i	0.985344	+	0.170582i	$0.0545646\pi$
$678$		0			0
$679$	−45.6802	−	14.8424i	−1.75304	−	0.569599i
$680$		0			0
$681$	3.35192	+	2.56877i	0.128446	+	0.0984355i
$682$		0			0
$683$	−16.4590	+	32.3026i	−0.629785	+	1.23602i	0.326944	+	0.945044i	$0.393981\pi$
$683$	−16.4590	+	32.3026i	−0.629785	+	1.23602i	−0.956729	+	0.290980i	$0.906019\pi$
$684$		0			0
$685$	−2.65665	−	19.5780i	−0.101505	−	0.748038i
$686$		0			0
$687$	18.4115	−	17.4932i	0.702443	−	0.667408i
$688$		0			0
$689$	−51.8234	+	37.6519i	−1.97431	+	1.43442i
$690$		0			0
$691$	−25.1665	−	18.2845i	−0.957378	−	0.695576i	−0.00483787	−	0.999988i	$-0.501540\pi$
$691$	−25.1665	−	18.2845i	−0.957378	−	0.695576i	−0.952540	+	0.304412i	$0.901540\pi$
$692$		0			0
$693$	37.6593	−	16.8221i	1.43056	−	0.639019i
$694$		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
$705$	−1.82827	+	38.2368i	−0.0688566	+	1.44008i
$706$		0			0
$707$	−35.0712	+	35.0712i	−1.31899	+	1.31899i
$708$		0			0
$709$	−27.9112	+	38.4165i	−1.04823	+	1.44276i	−0.157891	+	0.987457i	$0.550469\pi$
$709$	−27.9112	+	38.4165i	−1.04823	+	1.44276i	−0.890336	+	0.455304i	$0.849531\pi$
$710$		0			0
$711$	−6.70150	−	24.8888i	−0.251326	−	0.933404i
$712$		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
$717$	5.24270	+	39.6354i	0.195792	+	1.48021i
$718$		0			0
$719$	−1.22324	−	3.76475i	−0.0456192	−	0.140401i	0.925653	−	0.378375i	$-0.123517\pi$
$719$	−1.22324	−	3.76475i	−0.0456192	−	0.140401i	−0.971272	+	0.237973i	$0.923517\pi$
$720$		0			0
$721$	−4.18452	+	12.8786i	−0.155840	+	0.479626i
$722$		0			0
$723$	−15.4390	+	7.37557i	−0.574181	+	0.274300i
$724$		0			0
$725$	−0.189890	+	0.506676i	−0.00705235	+	0.0188175i
$726$		0			0
$727$	8.95795	+	1.41880i	0.332232	+	0.0526204i	0.320322	−	0.947309i	$-0.396209\pi$
$727$	8.95795	+	1.41880i	0.332232	+	0.0526204i	0.0119099	+	0.999929i	$0.496209\pi$
$728$		0			0
$729$	26.6519	−	4.32131i	0.987109	−	0.160049i
$730$		0			0
$731$	−3.83061	+	1.24464i	−0.141680	+	0.0460347i
$732$		0			0
$733$	20.9011	+	10.6496i	0.772000	+	0.393353i	0.795177	−	0.606378i	$-0.207378\pi$
$733$	20.9011	+	10.6496i	0.772000	+	0.393353i	−0.0231770	+	0.999731i	$0.507378\pi$
$734$		0			0
$735$	−2.23927	+	3.91990i	−0.0825968	+	0.144588i
$736$		0			0
$737$	−18.2602	+	2.89213i	−0.672622	+	0.106533i
$738$		0			0
$739$	6.02439	+	8.29186i	0.221611	+	0.305021i	0.905317	−	0.424736i	$-0.139633\pi$
$739$	6.02439	+	8.29186i	0.221611	+	0.305021i	−0.683706	+	0.729757i	$0.739633\pi$
$740$		0			0
$741$	0.957304	−	37.4306i	0.0351675	−	1.37505i
$742$		0			0
$743$	21.7690	+	21.7690i	0.798626	+	0.798626i	0.982879	−	0.184253i	$-0.0589865\pi$
$743$	21.7690	+	21.7690i	0.798626	+	0.798626i	−0.184253	+	0.982879i	$0.558987\pi$
$744$		0			0
$745$	0.0986303	−	4.44047i	0.00361354	−	0.162686i
$746$		0			0
$747$	20.7943	−	2.21122i	0.760822	−	0.0809043i
$748$		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
$753$	25.8293	+	14.0038i	0.941273	+	0.510326i
$754$		0			0
$755$	1.06692	−	48.0340i	0.0388291	−	1.74814i
$756$		0			0
$757$	4.50352	+	4.50352i	0.163683	+	0.163683i	0.784196	−	0.620513i	$-0.213076\pi$
$757$	4.50352	+	4.50352i	0.163683	+	0.163683i	−0.620513	+	0.784196i	$0.713076\pi$
$758$		0			0
$759$	21.3100	+	0.545014i	0.773504	+	0.0197827i
$760$		0			0
$761$	−7.27565	−	10.0141i	−0.263742	−	0.363010i	0.656523	−	0.754306i	$-0.272027\pi$
$761$	−7.27565	−	10.0141i	−0.263742	−	0.363010i	−0.920265	+	0.391297i	$0.872027\pi$
$762$		0			0
$763$	48.1714	−	7.62960i	1.74392	−	0.276210i
$764$		0			0
$765$	−10.2294	+	0.858534i	−0.369845	+	0.0310404i
$766$		0			0
$767$	1.35095	+	0.688344i	0.0487800	+	0.0248547i
$768$		0			0
$769$	28.2227	−	9.17010i	1.01774	−	0.330682i	0.247805	−	0.968810i	$-0.420291\pi$
$769$	28.2227	−	9.17010i	1.01774	−	0.330682i	0.769931	+	0.638128i	$0.220291\pi$
$770$		0			0
$771$	−12.2287	−	41.1912i	−0.440407	−	1.48347i
$772$		0			0
$773$	0.378278	+	0.0599133i	0.0136057	+	0.00215493i	0.163234	−	0.986587i	$-0.447808\pi$
$773$	0.378278	+	0.0599133i	0.0136057	+	0.00215493i	−0.149628	+	0.988742i	$0.547808\pi$
$774$		0			0
$775$	13.5022	+	48.8357i	0.485012	+	1.75423i
$776$		0			0
$777$	−5.71278	−	11.9583i	−0.204945	−	0.429002i
$778$		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
$783$	0.130269	−	0.547020i	0.00465545	−	0.0195489i
$784$		0			0
$785$	17.4429	−	16.6848i	0.622563	−	0.595507i
$786$		0			0
$787$	−0.702867	−	4.43773i	−0.0250545	−	0.158188i	0.971989	−	0.235026i	$-0.0755175\pi$
$787$	−0.702867	−	4.43773i	−0.0250545	−	0.158188i	−0.997044	+	0.0768381i	$0.975518\pi$
$788$		0			0
$789$	−26.7140	−	9.44159i	−0.951043	−	0.336129i
$790$		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
$795$	−42.5939	−	2.03660i	−1.51065	−	0.0722306i
$796$		0			0
$797$	−1.40159	−	2.75078i	−0.0496469	−	0.0974376i	0.864850	−	0.502030i	$-0.167413\pi$
$797$	−1.40159	−	2.75078i	−0.0496469	−	0.0974376i	−0.914497	+	0.404593i	$0.867413\pi$
$798$		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
$807$	−13.8045	−	2.54981i	−0.485943	−	0.0897576i
$808$		0			0
$809$	30.0466	+	21.8301i	1.05638	+	0.767506i	0.973415	−	0.229047i	$-0.0735609\pi$
$809$	30.0466	+	21.8301i	1.05638	+	0.767506i	0.0829655	+	0.996552i	$0.473561\pi$
$810$		0			0
$811$	28.0735	−	20.3966i	0.985793	−	0.716221i	0.0267972	−	0.999641i	$-0.491469\pi$
$811$	28.0735	−	20.3966i	0.985793	−	0.716221i	0.958996	+	0.283420i	$0.0914692\pi$
$812$		0			0
$813$	−10.9260	−	11.4996i	−0.383193	−	0.403308i
$814$		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
$819$	−2.54951	+	49.8103i	−0.0890871	+	1.74051i
$820$		0			0
$821$	22.2902	+	7.24251i	0.777932	+	0.252765i	0.670957	−	0.741496i	$-0.265884\pi$
$821$	22.2902	+	7.24251i	0.777932	+	0.252765i	0.106975	+	0.994262i	$0.465884\pi$
$822$		0			0
$823$	−4.56451	+	28.8192i	−0.159109	+	1.00457i	0.770879	+	0.636982i	$0.219817\pi$
$823$	−4.56451	+	28.8192i	−0.159109	+	1.00457i	−0.929988	+	0.367591i	$0.880183\pi$
$824$		0			0
$825$	−41.5092	+	3.62436i	−1.44517	+	0.126184i
$826$		0			0
$827$	5.14586	−	32.4897i	0.178939	−	1.12978i	−0.720733	−	0.693212i	$-0.756195\pi$
$827$	5.14586	−	32.4897i	0.178939	−	1.12978i	0.899673	−	0.436565i	$-0.143805\pi$
$828$		0			0
$829$	22.5304	+	7.32056i	0.782512	+	0.254254i	0.672912	−	0.739722i	$-0.265043\pi$
$829$	22.5304	+	7.32056i	0.782512	+	0.254254i	0.109600	+	0.993976i	$0.465043\pi$
$830$		0			0
$831$	4.16334	−	5.43264i	0.144425	−	0.188456i
$832$		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
$837$	−20.2394	−	48.6105i	−0.699577	−	1.68022i
$838$		0			0
$839$	35.6364	−	25.8914i	1.23031	−	0.893869i	0.233393	−	0.972383i	$-0.425017\pi$
$839$	35.6364	−	25.8914i	1.23031	−	0.893869i	0.996913	+	0.0785132i	$0.0250173\pi$
$840$		0			0
$841$	23.4520	+	17.0389i	0.808690	+	0.587548i
$842$		0			0
$843$	8.12217	−	43.9730i	0.279742	−	1.51451i
$844$		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	0.999906	−	0.0136947i	$-0.00435930\pi$
$853$	11.7145	+	22.9910i	0.401097	+	0.787197i	−0.598809	+	0.800892i	$0.704359\pi$
$854$		0			0
$855$	16.0892	−	19.0372i	0.550237	−	0.651060i
$856$		0			0
$857$	11.3014	−	11.3014i	0.386047	−	0.386047i	−0.487228	−	0.873275i	$-0.661992\pi$
$857$	11.3014	−	11.3014i	0.386047	−	0.386047i	0.873275	+	0.487228i	$0.161992\pi$
$858$		0			0
$859$	22.0585	−	30.3610i	0.752627	−	1.03590i	−0.245164	−	0.969482i	$-0.578842\pi$
$859$	22.0585	−	30.3610i	0.752627	−	1.03590i	0.997792	−	0.0664210i	$-0.0211580\pi$
$860$		0			0
$861$	6.34455	−	17.9513i	0.216222	−	0.611777i
$862$		0			0
$863$	6.11502	+	38.6087i	0.208158	+	1.31426i	0.841447	+	0.540340i	$0.181704\pi$
$863$	6.11502	+	38.6087i	0.208158	+	1.31426i	−0.633289	+	0.773915i	$0.718296\pi$
$864$		0			0
$865$	0.940582	−	5.18989i	0.0319808	−	0.176461i
$866$		0			0
$867$	25.1696	−	3.32927i	0.854806	−	0.113068i
$868$		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
$873$	−43.7003	−	25.1593i	−1.47903	−	0.851514i
$874$		0			0
$875$	24.0448	−	21.0368i	0.812863	−	0.711175i
$876$		0			0
$877$	41.1085	+	6.51094i	1.38813	+	0.219859i	0.805365	−	0.592779i	$-0.201969\pi$
$877$	41.1085	+	6.51094i	1.38813	+	0.219859i	0.582769	+	0.812638i	$0.301969\pi$
$878$		0			0
$879$	22.1631	−	6.57972i	0.747542	−	0.221928i
$880$		0			0
$881$	−31.4946	+	10.2332i	−1.06108	+	0.344766i	−0.787008	−	0.616943i	$-0.788371\pi$
$881$	−31.4946	+	10.2332i	−1.06108	+	0.344766i	−0.274072	+	0.961709i	$0.588371\pi$
$882$		0			0
$883$	−18.6577	−	9.50655i	−0.627880	−	0.319921i	0.110936	−	0.993828i	$-0.464615\pi$
$883$	−18.6577	−	9.50655i	−0.627880	−	0.319921i	−0.738817	+	0.673907i	$0.764615\pi$
$884$		0			0
$885$	0.414752	+	0.920178i	0.0139417	+	0.0309315i
$886$		0			0
$887$	−20.2617	+	3.20914i	−0.680321	+	0.107752i	−0.487025	−	0.873388i	$-0.661918\pi$
$887$	−20.2617	+	3.20914i	−0.680321	+	0.107752i	−0.193296	+	0.981140i	$0.561918\pi$
$888$		0			0
$889$	2.55468	+	3.51621i	0.0856811	+	0.117930i
$890$		0			0
$891$	42.3334	−	9.10627i	1.41822	−	0.305072i
$892$		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
$897$	−12.2859	+	22.6608i	−0.410215	+	0.756623i
$898$		0			0
$899$	−1.09664			−0.0365748
$900$		0			0
$901$	−16.8487			−0.561311
$902$		0			0
$903$	−6.20901	+	11.4522i	−0.206623	+	0.381106i
$904$		0			0
$905$	16.9800	−	5.10317i	0.564436	−	0.169635i
$906$		0			0
$907$	18.9719	+	18.9719i	0.629953	+	0.629953i	0.948056	−	0.318103i	$-0.103046\pi$
$907$	18.9719	+	18.9719i	0.629953	+	0.629953i	−0.318103	+	0.948056i	$0.603046\pi$
$908$		0			0
$909$	−43.6354	+	28.4129i	−1.44730	+	0.942397i
$910$		0			0
$911$	−11.4564	−	15.7683i	−0.379567	−	0.522428i	0.575903	−	0.817518i	$-0.304651\pi$
$911$	−11.4564	−	15.7683i	−0.379567	−	0.522428i	−0.955470	+	0.295089i	$0.904651\pi$
$912$		0			0
$913$	33.1243	−	5.24638i	1.09625	−	0.173630i
$914$		0			0
$915$	−20.7917	+	2.28166i	−0.687352	+	0.0754294i
$916$		0			0
$917$	14.9557	+	7.62032i	0.493882	+	0.251645i
$918$		0			0
$919$	39.3312	−	12.7795i	1.29742	−	0.421556i	0.422734	−	0.906254i	$-0.361070\pi$
$919$	39.3312	−	12.7795i	1.29742	−	0.421556i	0.874682	+	0.484698i	$0.161070\pi$
$920$		0			0
$921$	22.1317	−	6.57038i	0.729263	−	0.216502i
$922$		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
$927$	−7.09319	+	12.3204i	−0.232971	+	0.404657i
$928$		0			0
$929$	−6.58580	+	20.2690i	−0.216073	+	0.665004i	0.783003	+	0.622018i	$0.213687\pi$
$929$	−6.58580	+	20.2690i	−0.216073	+	0.665004i	−0.999076	+	0.0429861i	$0.986313\pi$
$930$		0			0
$931$	−1.33837	−	4.11907i	−0.0438632	−	0.134997i
$932$		0			0
$933$	22.7667	−	3.01142i	0.745347	−	0.0985894i
$934$		0			0
$935$	−16.3138	+	2.21370i	−0.533518	+	0.0723959i
$936$		0			0
$937$	−6.55487	−	41.3858i	−0.214138	−	1.35202i	−0.827167	−	0.561955i	$-0.810049\pi$
$937$	−6.55487	−	41.3858i	−0.214138	−	1.35202i	0.613029	−	0.790060i	$-0.289951\pi$
$938$		0			0
$939$	−0.0511267	+	0.144658i	−0.00166846	+	0.00472072i
$940$		0			0
$941$	26.9763	−	37.1297i	0.879402	−	1.21039i	−0.0971843	−	0.995266i	$-0.530984\pi$
$941$	26.9763	−	37.1297i	0.879402	−	1.21039i	0.976586	−	0.215126i	$-0.0690164\pi$
$942$		0			0
$943$	6.95803	−	6.95803i	0.226585	−	0.226585i
$944$		0			0
$945$	−22.0728	+	24.8022i	−0.718028	+	0.806816i
$946$		0			0
$947$	−20.9146	−	41.0473i	−0.679634	−	1.33386i	−0.930663	−	0.365878i	$-0.880769\pi$
$947$	−20.9146	−	41.0473i	−0.679634	−	1.33386i	0.251029	−	0.967980i	$-0.419231\pi$
$948$		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	$-0.592444\pi$
$953$	9.89306	−	5.04077i	0.320468	−	0.163286i	0.606823	+	0.794837i	$0.292444\pi$
$954$		0			0
$955$	−14.9464	−	11.3747i	−0.483654	−	0.368078i
$956$		0			0
$957$	0.163804	−	0.886826i	0.00529503	−	0.0286670i
$958$		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
$963$	−51.5825	−	10.8984i	−1.66222	−	0.351197i
$964$		0			0
$965$	−21.3029	−	22.2708i	−0.685766	−	0.716922i
$966$		0			0
$967$	−11.6265	+	22.8184i	−0.373885	+	0.733790i	−0.998903	−	0.0468200i	$-0.985091\pi$
$967$	−11.6265	+	22.8184i	−0.373885	+	0.733790i	0.625019	+	0.780610i	$0.285091\pi$
$968$		0			0
$969$	5.99056	−	7.81692i	0.192445	−	0.251116i
$970$		0			0
$971$	−32.8712	−	10.6805i	−1.05489	−	0.342753i	−0.270302	−	0.962776i	$-0.587124\pi$
$971$	−32.8712	−	10.6805i	−1.05489	−	0.342753i	−0.784584	+	0.620022i	$0.787124\pi$
$972$		0			0
$973$	2.11076	−	13.3268i	0.0676678	−	0.427238i
$974$		0			0
$975$	18.8826	−	46.7130i	0.604729	−	1.49601i
$976$		0			0
$977$	−2.56693	+	16.2070i	−0.0821234	+	0.518507i	0.911994	+	0.410203i	$0.134542\pi$
$977$	−2.56693	+	16.2070i	−0.0821234	+	0.518507i	−0.994118	+	0.108304i	$0.965458\pi$
$978$		0			0
$979$	−21.7486	−	7.06653i	−0.695087	−	0.225847i
$980$		0			0
$981$	51.1361	+	2.61737i	1.63265	+	0.0835663i
$982$		0			0
$983$	−17.5734	+	34.4898i	−0.560505	+	1.10005i	0.420721	+	0.907190i	$0.361777\pi$
$983$	−17.5734	+	34.4898i	−0.560505	+	1.10005i	−0.981226	+	0.192863i	$0.938223\pi$
$984$		0			0
$985$	31.3121	−	15.0881i	0.997688	−	0.480746i
$986$		0			0
$987$	33.6960	+	35.4648i	1.07256	+	1.12886i
$988$		0			0
$989$	−5.44694	+	3.95743i	−0.173203	+	0.125839i
$990$		0			0
$991$	5.23172	+	3.80107i	0.166191	+	0.120745i	0.667772	−	0.744366i	$-0.267248\pi$
$991$	5.23172	+	3.80107i	0.166191	+	0.120745i	−0.501581	+	0.865111i	$0.667248\pi$
$992$		0			0
$993$	−8.71946	−	1.61056i	−0.276704	−	0.0511094i
$994$		0			0
$995$	−23.7817	−	0.528232i	−0.753931	−	0.0167461i
$996$		0			0
$997$	1.68687	−	0.859502i	0.0534236	−	0.0272207i	−0.427075	−	0.904216i	$-0.640456\pi$
$997$	1.68687	−	0.859502i	0.0534236	−	0.0272207i	0.480498	+	0.876996i	$0.340456\pi$
$998$		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.77.4	✓	80
3.2	odd	2	inner	300.2.x.a.77.10	yes	80
25.13	odd	20	inner	300.2.x.a.113.10	yes	80
75.38	even	20	inner	300.2.x.a.113.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.77.4	✓	80	1.1	even	1	trivial
300.2.x.a.77.10	yes	80	3.2	odd	2	inner
300.2.x.a.113.4	yes	80	75.38	even	20	inner
300.2.x.a.113.10	yes	80	25.13	odd	20	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.825534 + 1.52266i) q^{3} +(0.0496546 - 2.23552i) q^{5} +(-2.02060 - 2.02060i) q^{7} +(-1.63699 - 2.51402i) q^{9} +O(q^{10})\)	\(q+(-0.825534 + 1.52266i) q^{3} +(0.0496546 - 2.23552i) q^{5} +(-2.02060 - 2.02060i) q^{7} +(-1.63699 - 2.51402i) q^{9} +(-2.82802 - 3.89243i) q^{11} +(5.74634 - 0.910130i) q^{13} +(3.36294 + 1.92110i) q^{15} +(1.36348 + 0.694729i) q^{17} +(-3.53381 + 1.14820i) q^{19} +(4.74475 - 1.40861i) q^{21} +(2.52651 + 0.400161i) q^{23} +(-4.99507 - 0.222007i) q^{25} +(5.17938 - 0.417165i) q^{27} +(0.0334412 - 0.102921i) q^{29} +(-3.13145 - 9.63760i) q^{31} +(8.26147 - 1.09277i) q^{33} +(-4.61741 + 4.41674i) q^{35} +(-0.418876 - 2.64468i) q^{37} +(-3.35798 + 9.50106i) q^{39} +(2.26109 - 3.11213i) q^{41} +(-1.86113 + 1.86113i) q^{43} +(-5.70141 + 3.53468i) q^{45} +(4.48724 + 8.80670i) q^{47} +1.16562i q^{49} +(-2.18344 + 1.50260i) q^{51} +(-9.81020 + 4.99855i) q^{53} +(-8.84201 + 6.12880i) q^{55} +(1.16896 - 6.32867i) q^{57} +(0.210836 + 0.153181i) q^{59} +(-4.36920 + 3.17441i) q^{61} +(-1.77212 + 8.38750i) q^{63} +(-1.74928 - 12.8912i) q^{65} +(1.74449 - 3.42375i) q^{67} +(-2.69503 + 3.51668i) q^{69} +(14.1996 + 4.61373i) q^{71} +(-0.320861 + 2.02584i) q^{73} +(4.46164 - 7.42252i) q^{75} +(-2.15075 + 13.5793i) q^{77} +(8.17124 + 2.65500i) q^{79} +(-3.64056 + 8.23082i) q^{81} +(-3.16454 + 6.21076i) q^{83} +(1.62078 - 3.01359i) q^{85} +(0.129107 + 0.135885i) q^{87} +(3.84520 - 2.79370i) q^{89} +(-13.4500 - 9.77202i) q^{91} +(17.2599 + 3.18805i) q^{93} +(2.39136 + 7.95690i) q^{95} +(14.9764 - 7.63086i) q^{97} +(-5.15621 + 13.4815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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