LMFDB - Embedded newform 616.2.r.f.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(113,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

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

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

chi := DirichletCharacter("616.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.r (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 21 x^{18} - 58 x^{17} + 225 x^{16} - 348 x^{15} + 1296 x^{14} - 755 x^{13} + \cdots + 10000 $ x^20 - 4x^19 + 21x^18 - 58x^17 + 225x^16 - 348x^15 + 1296x^14 - 755x^13 + 6557x^12 - 5753x^11 + 29289x^10 - 14174x^9 + 85487x^8 + 13430x^7 + 191109x^6 + 166407x^5 + 212971x^4 - 179670x^3 + 72900x^2 - 3000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.1
Root			$2.75053 + 1.99838i$ of defining polynomial
Character	$\chi$	$=$	616.169
Dual form			616.2.r.f.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05061 + 3.23344i) q^{3} +(-0.556182 + 0.404090i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-6.92433 - 5.03082i) q^{9} +(1.80996 - 2.77922i) q^{11} +(-3.70618 - 2.69270i) q^{13} +(-0.722272 - 2.22292i) q^{15} +(-3.81391 + 2.77097i) q^{17} +(0.462816 - 1.42440i) q^{19} +3.39984 q^{21} -2.19201 q^{23} +(-1.39904 + 4.30579i) q^{25} +(15.2900 - 11.1089i) q^{27} +(-2.42815 - 7.47307i) q^{29} +(3.32675 + 2.41702i) q^{31} +(7.08488 + 8.77227i) q^{33} +(0.556182 + 0.404090i) q^{35} +(-0.0655973 - 0.201888i) q^{37} +(12.6004 - 9.15475i) q^{39} +(-0.108464 + 0.333817i) q^{41} -3.09382 q^{43} +5.88409 q^{45} +(-2.50681 + 7.71517i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-4.95284 - 15.2433i) q^{51} +(-10.3297 - 7.50494i) q^{53} +(0.116386 + 2.27714i) q^{55} +(4.11948 + 2.99298i) q^{57} +(2.37226 + 7.30106i) q^{59} +(5.74134 - 4.17132i) q^{61} +(-2.64486 + 8.14003i) q^{63} +3.14940 q^{65} +0.889399 q^{67} +(2.30295 - 7.08774i) q^{69} +(3.95035 - 2.87010i) q^{71} +(-2.83347 - 8.72052i) q^{73} +(-12.4527 - 9.04740i) q^{75} +(-3.20250 - 0.862549i) q^{77} +(-12.6433 - 9.18587i) q^{79} +(11.9214 + 36.6904i) q^{81} +(-9.79813 + 7.11876i) q^{83} +(1.00151 - 3.08232i) q^{85} +26.7148 q^{87} -15.6209 q^{89} +(-1.41563 + 4.35687i) q^{91} +(-11.3104 + 8.21750i) q^{93} +(0.318176 + 0.979246i) q^{95} +(-2.27459 - 1.65258i) q^{97} +(-26.5145 + 10.1386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{3} + 5 q^{7} - 6 q^{9} - 3 q^{11} + 2 q^{13} + 8 q^{15} + 21 q^{19} + 6 q^{21} - 6 q^{23} - 7 q^{25} + 32 q^{27} + 6 q^{29} - 18 q^{31} - 16 q^{33} + 5 q^{37} + 12 q^{39} - 12 q^{41} - 42 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 20 * q - q^3 + 5 * q^7 - 6 * q^9 - 3 * q^11 + 2 * q^13 + 8 * q^15 + 21 * q^19 + 6 * q^21 - 6 * q^23 - 7 * q^25 + 32 * q^27 + 6 * q^29 - 18 * q^31 - 16 * q^33 + 5 * q^37 + 12 * q^39 - 12 * q^41 - 42 * q^43 + 18 * q^45 + 3 * q^47 - 5 * q^49 - q^51 - 38 * q^53 - 15 * q^55 - 3 * q^57 + 36 * q^59 + 23 * q^61 + 11 * q^63 - 30 * q^65 - 2 * q^67 + 43 * q^69 + 48 * q^71 + 6 * q^73 - 67 * q^75 - 17 * q^77 + 43 * q^79 + 16 * q^81 + 5 * q^83 - 16 * q^85 - 16 * q^87 - 46 * q^89 - 2 * q^91 + q^93 + 44 * q^95 + 9 * q^97 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$	$1$

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
$3$	−1.05061	+	3.23344i	−0.606570	+	1.86683i	−0.120952	+	0.992658i	$0.538595\pi$
$3$	−1.05061	+	3.23344i	−0.606570	+	1.86683i	−0.485618	+	0.874171i	$0.661405\pi$
$4$		0			0
$5$	−0.556182	+	0.404090i	−0.248732	+	0.180714i	−0.705165	−	0.709044i	$-0.749127\pi$
$5$	−0.556182	+	0.404090i	−0.248732	+	0.180714i	0.456433	+	0.889758i	$0.349127\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$		0			0
$9$	−6.92433	−	5.03082i	−2.30811	−	1.67694i
$10$		0			0
$11$	1.80996	−	2.77922i	0.545723	−	0.837965i
$11$	1.80996	−	2.77922i	0.545723	−	0.837965i
$12$		0			0
$13$	−3.70618	−	2.69270i	−1.02791	−	0.746820i	−0.0600200	−	0.998197i	$-0.519116\pi$
$13$	−3.70618	−	2.69270i	−1.02791	−	0.746820i	−0.967889	+	0.251378i	$0.919116\pi$
$14$		0			0
$15$	−0.722272	−	2.22292i	−0.186490	−	0.573956i
$16$		0			0
$17$	−3.81391	+	2.77097i	−0.925009	+	0.672058i	−0.944766	−	0.327747i	$-0.893711\pi$
$17$	−3.81391	+	2.77097i	−0.925009	+	0.672058i	0.0197568	+	0.999805i	$0.493711\pi$
$18$		0			0
$19$	0.462816	−	1.42440i	0.106177	−	0.326780i	−0.883828	−	0.467813i	$-0.845042\pi$
$19$	0.462816	−	1.42440i	0.106177	−	0.326780i	0.990005	+	0.141033i	$0.0450422\pi$
$20$		0			0
$21$	3.39984			0.741907
$22$		0			0
$23$	−2.19201			−0.457065			−0.228533	−	0.973536i	$-0.573393\pi$
$23$	−2.19201			−0.457065			−0.228533	+	0.973536i	$0.573393\pi$
$24$		0			0
$25$	−1.39904	+	4.30579i	−0.279807	+	0.861158i
$26$		0			0
$27$	15.2900	−	11.1089i	2.94257	−	2.13790i
$28$		0			0
$29$	−2.42815	−	7.47307i	−0.450895	−	1.38771i	−0.875887	−	0.482516i	$-0.839723\pi$
$29$	−2.42815	−	7.47307i	−0.450895	−	1.38771i	0.424992	−	0.905197i	$-0.360277\pi$
$30$		0			0
$31$	3.32675	+	2.41702i	0.597501	+	0.434110i	0.844991	−	0.534780i	$-0.179606\pi$
$31$	3.32675	+	2.41702i	0.597501	+	0.434110i	−0.247490	+	0.968890i	$0.579606\pi$
$32$		0			0
$33$	7.08488	+	8.77227i	1.23332	+	1.52706i
$34$		0			0
$35$	0.556182	+	0.404090i	0.0940119	+	0.0683037i
$36$		0			0
$37$	−0.0655973	−	0.201888i	−0.0107841	−	0.0331902i	0.945520	−	0.325565i	$-0.105555\pi$
$37$	−0.0655973	−	0.201888i	−0.0107841	−	0.0331902i	−0.956304	+	0.292375i	$0.905555\pi$
$38$		0			0
$39$	12.6004	−	9.15475i	2.01768	−	1.46593i
$40$		0			0
$41$	−0.108464	+	0.333817i	−0.0169392	+	0.0521335i	−0.959169	−	0.282834i	$-0.908725\pi$
$41$	−0.108464	+	0.333817i	−0.0169392	+	0.0521335i	0.942230	+	0.334968i	$0.108725\pi$
$42$		0			0
$43$	−3.09382			−0.471803			−0.235901	−	0.971777i	$-0.575804\pi$
$43$	−3.09382			−0.471803			−0.235901	+	0.971777i	$0.575804\pi$
$44$		0			0
$45$	5.88409			0.877148
$46$		0			0
$47$	−2.50681	+	7.71517i	−0.365656	+	1.12537i	0.583913	+	0.811816i	$0.301521\pi$
$47$	−2.50681	+	7.71517i	−0.365656	+	1.12537i	−0.949569	+	0.313557i	$0.898479\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	−4.95284	−	15.2433i	−0.693536	−	2.13448i
$52$		0			0
$53$	−10.3297	−	7.50494i	−1.41889	−	1.03088i	−0.991954	−	0.126600i	$-0.959594\pi$
$53$	−10.3297	−	7.50494i	−1.41889	−	1.03088i	−0.426934	−	0.904283i	$-0.640406\pi$
$54$		0			0
$55$	0.116386	+	2.27714i	0.0156935	+	0.307049i
$56$		0			0
$57$	4.11948	+	2.99298i	0.545639	+	0.396430i
$58$		0			0
$59$	2.37226	+	7.30106i	0.308842	+	0.950517i	0.978216	+	0.207591i	$0.0665624\pi$
$59$	2.37226	+	7.30106i	0.308842	+	0.950517i	−0.669374	+	0.742926i	$0.733438\pi$
$60$		0			0
$61$	5.74134	−	4.17132i	0.735103	−	0.534083i	−0.156071	−	0.987746i	$-0.549883\pi$
$61$	5.74134	−	4.17132i	0.735103	−	0.534083i	0.891174	+	0.453662i	$0.149883\pi$
$62$		0			0
$63$	−2.64486	+	8.14003i	−0.333221	+	1.02555i
$64$		0			0
$65$	3.14940			0.390635
$66$		0			0
$67$	0.889399			0.108657			0.0543287	−	0.998523i	$-0.482698\pi$
$67$	0.889399			0.108657			0.0543287	+	0.998523i	$0.482698\pi$
$68$		0			0
$69$	2.30295	−	7.08774i	0.277242	−	0.853263i
$70$		0			0
$71$	3.95035	−	2.87010i	0.468821	−	0.340618i	−0.328161	−	0.944622i	$-0.606429\pi$
$71$	3.95035	−	2.87010i	0.468821	−	0.340618i	0.796981	+	0.604004i	$0.206429\pi$
$72$		0			0
$73$	−2.83347	−	8.72052i	−0.331632	−	1.02066i	−0.968357	−	0.249568i	$-0.919711\pi$
$73$	−2.83347	−	8.72052i	−0.331632	−	1.02066i	0.636725	−	0.771091i	$-0.280289\pi$
$74$		0			0
$75$	−12.4527	−	9.04740i	−1.43791	−	1.04470i
$76$		0			0
$77$	−3.20250	−	0.862549i	−0.364959	−	0.0982966i
$78$		0			0
$79$	−12.6433	−	9.18587i	−1.42248	−	1.03349i	−0.991356	−	0.131198i	$-0.958118\pi$
$79$	−12.6433	−	9.18587i	−1.42248	−	1.03349i	−0.431123	−	0.902293i	$-0.641882\pi$
$80$		0			0
$81$	11.9214	+	36.6904i	1.32460	+	4.07671i
$82$		0			0
$83$	−9.79813	+	7.11876i	−1.07548	+	0.781385i	−0.976890	−	0.213743i	$-0.931435\pi$
$83$	−9.79813	+	7.11876i	−1.07548	+	0.781385i	−0.0985942	+	0.995128i	$0.531435\pi$
$84$		0			0
$85$	1.00151	−	3.08232i	0.108629	−	0.334325i
$86$		0			0
$87$	26.7148			2.86412
$88$		0			0
$89$	−15.6209			−1.65582			−0.827908	−	0.560864i	$-0.810469\pi$
$89$	−15.6209			−1.65582			−0.827908	+	0.560864i	$0.810469\pi$
$90$		0			0
$91$	−1.41563	+	4.35687i	−0.148399	+	0.456725i
$92$		0			0
$93$	−11.3104	+	8.21750i	−1.17284	+	0.852115i
$94$		0			0
$95$	0.318176	+	0.979246i	0.0326442	+	0.100468i
$96$		0			0
$97$	−2.27459	−	1.65258i	−0.230949	−	0.167795i	0.466292	−	0.884631i	$-0.345590\pi$
$97$	−2.27459	−	1.65258i	−0.230949	−	0.167795i	−0.697242	+	0.716836i	$0.745590\pi$
$98$		0			0
$99$	−26.5145	+	10.1386i	−2.66481	+	1.01897i
$100$		0			0
$101$	7.77190	+	5.64662i	0.773333	+	0.561860i	0.902971	−	0.429702i	$-0.141381\pi$
$101$	7.77190	+	5.64662i	0.773333	+	0.561860i	−0.129637	+	0.991561i	$0.541381\pi$
$102$		0			0
$103$	−2.06829	−	6.36555i	−0.203795	−	0.627216i	−0.999761	−	0.0218745i	$-0.993037\pi$
$103$	−2.06829	−	6.36555i	−0.203795	−	0.627216i	0.795966	−	0.605341i	$-0.206963\pi$
$104$		0			0
$105$	−1.89093	+	1.37384i	−0.184536	+	0.134073i
$106$		0			0
$107$	0.863587	−	2.65785i	0.0834861	−	0.256944i	−0.900596	−	0.434657i	$-0.856870\pi$
$107$	0.863587	−	2.65785i	0.0834861	−	0.256944i	0.984082	+	0.177713i	$0.0568698\pi$
$108$		0			0
$109$	9.96649			0.954616			0.477308	−	0.878736i	$-0.341613\pi$
$109$	9.96649			0.954616			0.477308	+	0.878736i	$0.341613\pi$
$110$		0			0
$111$	0.721710			0.0685017
$112$		0			0
$113$	−5.19640	+	15.9929i	−0.488836	+	1.50448i	0.337512	+	0.941321i	$0.390415\pi$
$113$	−5.19640	+	15.9929i	−0.488836	+	1.50448i	−0.826347	+	0.563161i	$0.809585\pi$
$114$		0			0
$115$	1.21916	−	0.885769i	0.113687	−	0.0825983i
$116$		0			0
$117$	12.1163	+	37.2902i	1.12015	+	3.44748i
$118$		0			0
$119$	3.81391	+	2.77097i	0.349620	+	0.254014i
$120$		0			0
$121$	−4.44809	−	10.0605i	−0.404372	−	0.914595i
$122$		0			0
$123$	−0.965425	−	0.701423i	−0.0870495	−	0.0632452i
$124$		0			0
$125$	−2.02402	−	6.22929i	−0.181034	−	0.557165i
$126$		0			0
$127$	−4.56217	+	3.31461i	−0.404827	+	0.294124i	−0.771504	−	0.636224i	$-0.780495\pi$
$127$	−4.56217	+	3.31461i	−0.404827	+	0.294124i	0.366677	+	0.930348i	$0.380495\pi$
$128$		0			0
$129$	3.25039	−	10.0037i	0.286181	−	0.880775i
$130$		0			0
$131$	−11.2444			−0.982430			−0.491215	−	0.871038i	$-0.663447\pi$
$131$	−11.2444			−0.982430			−0.491215	+	0.871038i	$0.663447\pi$
$132$		0			0
$133$	−1.49770			−0.129867
$134$		0			0
$135$	−4.01506	+	12.3571i	−0.345562	+	1.06353i
$136$		0			0
$137$	−15.5886	+	11.3258i	−1.33182	+	0.967625i	−0.332120	+	0.943237i	$0.607764\pi$
$137$	−15.5886	+	11.3258i	−1.33182	+	0.967625i	−0.999703	+	0.0243882i	$0.992236\pi$
$138$		0			0
$139$	0.918385	+	2.82650i	0.0778964	+	0.239741i	0.982420	−	0.186682i	$-0.0597735\pi$
$139$	0.918385	+	2.82650i	0.0778964	+	0.239741i	−0.904524	+	0.426423i	$0.859774\pi$
$140$		0			0
$141$	−22.3129	−	16.2113i	−1.87908	−	1.36523i
$142$		0			0
$143$	−14.1916	+	5.42660i	−1.18676	+	0.453795i
$144$		0			0
$145$	4.37028	+	3.17520i	0.362932	+	0.263686i
$146$		0			0
$147$	−1.05061	−	3.23344i	−0.0866528	−	0.266690i
$148$		0			0
$149$	5.58991	−	4.06131i	0.457944	−	0.332715i	−0.334780	−	0.942296i	$-0.608662\pi$
$149$	5.58991	−	4.06131i	0.457944	−	0.332715i	0.792724	+	0.609581i	$0.208662\pi$
$150$		0			0
$151$	0.819507	−	2.52218i	0.0666906	−	0.205252i	−0.912158	−	0.409839i	$-0.865585\pi$
$151$	0.819507	−	2.52218i	0.0666906	−	0.205252i	0.978849	+	0.204586i	$0.0655849\pi$
$152$		0			0
$153$	40.3490			3.26202
$154$		0			0
$155$	−2.82697			−0.227068
$156$		0			0
$157$	3.53551	−	10.8812i	0.282164	−	0.868412i	−0.705070	−	0.709138i	$-0.749084\pi$
$157$	3.53551	−	10.8812i	0.282164	−	0.868412i	0.987234	−	0.159275i	$-0.0509156\pi$
$158$		0			0
$159$	35.1192	−	25.5156i	2.78514	−	2.02352i
$160$		0			0
$161$	0.677368	+	2.08472i	0.0533841	+	0.164299i
$162$		0			0
$163$	6.66271	+	4.84075i	0.521864	+	0.379156i	0.817306	−	0.576204i	$-0.195467\pi$
$163$	6.66271	+	4.84075i	0.521864	+	0.379156i	−0.295442	+	0.955361i	$0.595467\pi$
$164$		0			0
$165$	−7.48527	−	2.01605i	−0.582727	−	0.156950i
$166$		0			0
$167$	11.4674	+	8.33155i	0.887373	+	0.644714i	0.935192	−	0.354142i	$-0.115227\pi$
$167$	11.4674	+	8.33155i	0.887373	+	0.644714i	−0.0478185	+	0.998856i	$0.515227\pi$
$168$		0			0
$169$	2.46793	+	7.59550i	0.189840	+	0.584269i
$170$		0			0
$171$	−10.3706	+	7.53468i	−0.793059	+	0.576191i
$172$		0			0
$173$	0.0867525	−	0.266997i	0.00659567	−	0.0202994i	−0.947705	−	0.319149i	$-0.896603\pi$
$173$	0.0867525	−	0.266997i	0.00659567	−	0.0202994i	0.954300	+	0.298850i	$0.0966029\pi$
$174$		0			0
$175$	4.52737			0.342237
$176$		0			0
$177$	−26.0999			−1.96179
$178$		0			0
$179$	5.90770	−	18.1820i	0.441562	−	1.35899i	−0.444648	−	0.895705i	$-0.646671\pi$
$179$	5.90770	−	18.1820i	0.441562	−	1.35899i	0.886210	−	0.463283i	$-0.153329\pi$
$180$		0			0
$181$	9.15549	−	6.65185i	0.680522	−	0.494428i	−0.193009	−	0.981197i	$-0.561825\pi$
$181$	9.15549	−	6.65185i	0.680522	−	0.494428i	0.873531	+	0.486769i	$0.161825\pi$
$182$		0			0
$183$	7.45584	+	22.9467i	0.551152	+	1.69627i
$184$		0			0
$185$	0.118065	+	0.0857792i	0.00868030	+	0.00630661i
$186$		0			0
$187$	0.798095	+	15.6150i	0.0583625	+	1.14188i
$188$		0			0
$189$	−15.2900	−	11.1089i	−1.11219	−	0.808050i
$190$		0			0
$191$	4.26518	+	13.1269i	0.308618	+	0.949827i	0.978302	+	0.207182i	$0.0664292\pi$
$191$	4.26518	+	13.1269i	0.308618	+	0.949827i	−0.669685	+	0.742645i	$0.733571\pi$
$192$		0			0
$193$	17.0820	−	12.4108i	1.22959	−	0.893348i	0.232728	−	0.972542i	$-0.425235\pi$
$193$	17.0820	−	12.4108i	1.22959	−	0.893348i	0.996859	+	0.0791943i	$0.0252348\pi$
$194$		0			0
$195$	−3.30879	+	10.1834i	−0.236947	+	0.729249i
$196$		0			0
$197$	−11.2684			−0.802843			−0.401422	−	0.915893i	$-0.631484\pi$
$197$	−11.2684			−0.802843			−0.401422	+	0.915893i	$0.631484\pi$
$198$		0			0
$199$	−3.21305			−0.227767			−0.113883	−	0.993494i	$-0.536329\pi$
$199$	−3.21305			−0.227767			−0.113883	+	0.993494i	$0.536329\pi$
$200$		0			0
$201$	−0.934411	+	2.87582i	−0.0659083	+	0.202845i
$202$		0			0
$203$	−6.35697	+	4.61861i	−0.446172	+	0.324163i
$204$		0			0
$205$	−0.0745665	−	0.229492i	−0.00520795	−	0.0160284i
$206$		0			0
$207$	15.1782	+	11.0276i	1.05496	+	0.766471i
$208$		0			0
$209$	−3.12104	−	3.86438i	−0.215887	−	0.267304i
$210$		0			0
$211$	15.4008	+	11.1893i	1.06024	+	0.770306i	0.974132	−	0.225980i	$-0.0725583\pi$
$211$	15.4008	+	11.1893i	1.06024	+	0.770306i	0.0861038	+	0.996286i	$0.472558\pi$
$212$		0			0
$213$	5.13003	+	15.7886i	0.351504	+	1.08182i
$214$		0			0
$215$	1.72072	−	1.25018i	0.117352	−	0.0852615i
$216$		0			0
$217$	1.27070	−	3.91082i	0.0862610	−	0.265484i
$218$		0			0
$219$	31.1742			2.10655
$220$		0			0
$221$	21.5964			1.45273
$222$		0			0
$223$	−5.32283	+	16.3820i	−0.356443	+	1.09702i	0.598724	+	0.800955i	$0.295674\pi$
$223$	−5.32283	+	16.3820i	−0.356443	+	1.09702i	−0.955168	+	0.296065i	$0.904326\pi$
$224$		0			0
$225$	31.3490	−	22.7764i	2.08993	−	1.51843i
$226$		0			0
$227$	−1.61210	−	4.96154i	−0.106999	−	0.329309i	0.883195	−	0.469005i	$-0.155387\pi$
$227$	−1.61210	−	4.96154i	−0.106999	−	0.329309i	−0.990194	+	0.139696i	$0.955387\pi$
$228$		0			0
$229$	−8.74272	−	6.35195i	−0.577735	−	0.419749i	0.260172	−	0.965562i	$-0.416221\pi$
$229$	−8.74272	−	6.35195i	−0.577735	−	0.419749i	−0.837907	+	0.545813i	$0.816221\pi$
$230$		0			0
$231$	6.15358	−	9.44890i	0.404876	−	0.621692i
$232$		0			0
$233$	−1.84254	−	1.33869i	−0.120709	−	0.0877003i	0.525793	−	0.850613i	$-0.323769\pi$
$233$	−1.84254	−	1.33869i	−0.120709	−	0.0877003i	−0.646502	+	0.762912i	$0.723769\pi$
$234$		0			0
$235$	−1.72338	−	5.30401i	−0.112421	−	0.345996i
$236$		0			0
$237$	42.9851	−	31.2305i	2.79218	−	2.02864i
$238$		0			0
$239$	0.0308175	−	0.0948465i	0.00199342	−	0.00613511i	−0.950055	−	0.312083i	$-0.898973\pi$
$239$	0.0308175	−	0.0948465i	0.00199342	−	0.00613511i	0.952048	+	0.305948i	$0.0989733\pi$
$240$		0			0
$241$	−28.3692			−1.82742			−0.913711	−	0.406365i	$-0.866796\pi$
$241$	−28.3692			−1.82742			−0.913711	+	0.406365i	$0.866796\pi$
$242$		0			0
$243$	−74.4626			−4.77678
$244$		0			0
$245$	0.212443	−	0.653831i	0.0135725	−	0.0417717i
$246$		0			0
$247$	−5.55076	+	4.03286i	−0.353186	+	0.256605i
$248$		0			0
$249$	−12.7241	−	39.1607i	−0.806356	−	2.48171i
$250$		0			0
$251$	5.65500	+	4.10860i	0.356940	+	0.259332i	0.751775	−	0.659420i	$-0.229198\pi$
$251$	5.65500	+	4.10860i	0.356940	+	0.259332i	−0.394834	+	0.918752i	$0.629198\pi$
$252$		0			0
$253$	−3.96745	+	6.09207i	−0.249431	+	0.383005i
$254$		0			0
$255$	8.91433	+	6.47664i	0.558237	+	0.405583i
$256$		0			0
$257$	−6.78903	−	20.8945i	−0.423488	−	1.30336i	−0.904434	−	0.426613i	$-0.859707\pi$
$257$	−6.78903	−	20.8945i	−0.423488	−	1.30336i	0.480946	−	0.876750i	$-0.340293\pi$
$258$		0			0
$259$	−0.171736	+	0.124774i	−0.0106712	+	0.00775305i
$260$		0			0
$261$	−20.7824	+	63.9615i	−1.28640	+	3.95912i
$262$		0			0
$263$	13.4087			0.826816			0.413408	−	0.910546i	$-0.364338\pi$
$263$	13.4087			0.826816			0.413408	+	0.910546i	$0.364338\pi$
$264$		0			0
$265$	8.77784			0.539218
$266$		0			0
$267$	16.4115	−	50.5094i	1.00437	−	3.09113i
$268$		0			0
$269$	−25.6050	+	18.6031i	−1.56116	+	1.13425i	−0.626113	+	0.779733i	$0.715355\pi$
$269$	−25.6050	+	18.6031i	−1.56116	+	1.13425i	−0.935049	+	0.354518i	$0.884645\pi$
$270$		0			0
$271$	−6.71934	−	20.6800i	−0.408171	−	1.25622i	−0.918218	−	0.396075i	$-0.870372\pi$
$271$	−6.71934	−	20.6800i	−0.408171	−	1.25622i	0.510047	−	0.860146i	$-0.329628\pi$
$272$		0			0
$273$	−12.6004	−	9.15475i	−0.762613	−	0.554071i
$274$		0			0
$275$	9.43452	+	11.6815i	0.568923	+	0.704422i
$276$		0			0
$277$	−15.6638	−	11.3804i	−0.941147	−	0.683783i	0.00754984	−	0.999971i	$-0.497597\pi$
$277$	−15.6638	−	11.3804i	−0.941147	−	0.683783i	−0.948696	+	0.316189i	$0.897597\pi$
$278$		0			0
$279$	−10.8759	−	33.4725i	−0.651122	−	2.00395i
$280$		0			0
$281$	−17.1956	+	12.4933i	−1.02580	+	0.745290i	−0.967464	−	0.253007i	$-0.918580\pi$
$281$	−17.1956	+	12.4933i	−1.02580	+	0.745290i	−0.0583390	+	0.998297i	$0.518580\pi$
$282$		0			0
$283$	0.807861	−	2.48634i	0.0480224	−	0.147798i	−0.924170	−	0.381982i	$-0.875242\pi$
$283$	0.807861	−	2.48634i	0.0480224	−	0.147798i	0.972192	+	0.234184i	$0.0752418\pi$
$284$		0			0
$285$	−3.50061			−0.207358
$286$		0			0
$287$	0.350996			0.0207186
$288$		0			0
$289$	1.61436	−	4.96847i	0.0949621	−	0.292263i
$290$		0			0
$291$	7.73324	−	5.61853i	0.453331	−	0.329364i
$292$		0			0
$293$	5.75975	+	17.7267i	0.336488	+	1.03560i	0.965984	+	0.258601i	$0.0832614\pi$
$293$	5.75975	+	17.7267i	0.336488	+	1.03560i	−0.629496	+	0.777004i	$0.716739\pi$
$294$		0			0
$295$	−4.26969	−	3.10211i	−0.248591	−	0.180612i
$296$		0			0
$297$	−3.19958	−	62.6009i	−0.185658	−	3.63247i
$298$		0			0
$299$	8.12398	+	5.90241i	0.469822	+	0.341345i
$300$		0			0
$301$	0.956042	+	2.94239i	0.0551053	+	0.169597i
$302$		0			0
$303$	−26.4233	+	19.1976i	−1.51798	+	1.10287i
$304$		0			0
$305$	−1.50764	+	4.64003i	−0.0863271	+	0.265687i
$306$		0			0
$307$	−5.45702			−0.311448			−0.155724	−	0.987801i	$-0.549771\pi$
$307$	−5.45702			−0.311448			−0.155724	+	0.987801i	$0.549771\pi$
$308$		0			0
$309$	22.7556			1.29452
$310$		0			0
$311$	−1.81887	+	5.59792i	−0.103139	+	0.317429i	−0.989289	−	0.145969i	$-0.953370\pi$
$311$	−1.81887	+	5.59792i	−0.103139	+	0.317429i	0.886150	+	0.463398i	$0.153370\pi$
$312$		0			0
$313$	17.2655	−	12.5441i	0.975902	−	0.709034i	0.0191128	−	0.999817i	$-0.493916\pi$
$313$	17.2655	−	12.5441i	0.975902	−	0.709034i	0.956789	+	0.290783i	$0.0939158\pi$
$314$		0			0
$315$	−1.81828	−	5.59610i	−0.102449	−	0.315304i
$316$		0			0
$317$	5.87387	+	4.26762i	0.329910	+	0.239693i	0.740392	−	0.672175i	$-0.234640\pi$
$317$	5.87387	+	4.26762i	0.329910	+	0.239693i	−0.410483	+	0.911868i	$0.634640\pi$
$318$		0			0
$319$	−25.1641	−	6.77761i	−1.40892	−	0.379473i
$320$		0			0
$321$	7.68671	+	5.58472i	0.429030	+	0.311709i
$322$		0			0
$323$	2.18183	+	6.71499i	0.121400	+	0.373632i
$324$		0			0
$325$	16.7793	−	12.1908i	0.930746	−	0.676226i
$326$		0			0
$327$	−10.4709	+	32.2261i	−0.579041	+	1.78211i
$328$		0			0
$329$	8.11221			0.447241
$330$		0			0
$331$	11.8008			0.648629			0.324315	−	0.945949i	$-0.394866\pi$
$331$	11.8008			0.648629			0.324315	+	0.945949i	$0.394866\pi$
$332$		0			0
$333$	−0.561443	+	1.72795i	−0.0307669	+	0.0946908i
$334$		0			0
$335$	−0.494668	+	0.359397i	−0.0270266	+	0.0196360i
$336$		0			0
$337$	5.38106	+	16.5612i	0.293125	+	0.902146i	0.983845	+	0.179024i	$0.0572938\pi$
$337$	5.38106	+	16.5612i	0.293125	+	0.902146i	−0.690720	+	0.723123i	$0.742706\pi$
$338$		0			0
$339$	−46.2526	−	33.6045i	−2.51210	−	1.82515i
$340$		0			0
$341$	12.7387	−	4.87103i	0.689840	−	0.263781i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$		0			0
$345$	1.58323	+	4.87267i	0.0852380	+	0.262336i
$346$		0			0
$347$	−8.48193	+	6.16248i	−0.455334	+	0.330819i	−0.791698	−	0.610913i	$-0.790803\pi$
$347$	−8.48193	+	6.16248i	−0.455334	+	0.330819i	0.336364	+	0.941732i	$0.390803\pi$
$348$		0			0
$349$	−4.83339	+	14.8757i	−0.258726	+	0.796276i	0.734347	+	0.678774i	$0.237488\pi$
$349$	−4.83339	+	14.8757i	−0.258726	+	0.796276i	−0.993073	+	0.117501i	$0.962512\pi$
$350$		0			0
$351$	−86.5804			−4.62132
$352$		0			0
$353$	12.3757			0.658692			0.329346	−	0.944209i	$-0.393172\pi$
$353$	12.3757			0.658692			0.329346	+	0.944209i	$0.393172\pi$
$354$		0			0
$355$	−1.03734	+	3.19259i	−0.0550561	+	0.169445i
$356$		0			0
$357$	−12.9667	+	9.42086i	−0.686270	+	0.498605i
$358$		0			0
$359$	−1.70334	−	5.24233i	−0.0898987	−	0.276680i	0.895992	−	0.444070i	$-0.146466\pi$
$359$	−1.70334	−	5.24233i	−0.0898987	−	0.276680i	−0.985891	+	0.167390i	$0.946466\pi$
$360$		0			0
$361$	13.5566	+	9.84945i	0.713505	+	0.518392i
$362$		0			0
$363$	37.2034	−	3.81294i	1.95267	−	0.200128i
$364$		0			0
$365$	5.09980	+	3.70522i	0.266936	+	0.193940i
$366$		0			0
$367$	7.68865	+	23.6632i	0.401344	+	1.23521i	0.923909	+	0.382612i	$0.124975\pi$
$367$	7.68865	+	23.6632i	0.401344	+	1.23521i	−0.522565	+	0.852600i	$0.675025\pi$
$368$		0			0
$369$	2.43041	−	1.76580i	0.126522	−	0.0919237i
$370$		0			0
$371$	−3.94558	+	12.1432i	−0.204844	+	0.630446i
$372$		0			0
$373$	11.2320			0.581573			0.290786	−	0.956788i	$-0.406083\pi$
$373$	11.2320			0.581573			0.290786	+	0.956788i	$0.406083\pi$
$374$		0			0
$375$	22.2685			1.14994
$376$		0			0
$377$	−11.1236	+	34.2348i	−0.572892	+	1.76318i
$378$		0			0
$379$	−3.25121	+	2.36214i	−0.167003	+	0.121335i	−0.668148	−	0.744029i	$-0.732913\pi$
$379$	−3.25121	+	2.36214i	−0.167003	+	0.121335i	0.501144	+	0.865364i	$0.332913\pi$
$380$		0			0
$381$	−5.92455	−	18.2339i	−0.303524	−	0.934150i
$382$		0			0
$383$	−11.0907	−	8.05786i	−0.566708	−	0.411737i	0.267200	−	0.963641i	$-0.413902\pi$
$383$	−11.0907	−	8.05786i	−0.566708	−	0.411737i	−0.833908	+	0.551904i	$0.813902\pi$
$384$		0			0
$385$	2.12972	−	0.814364i	0.108541	−	0.0415038i
$386$		0			0
$387$	21.4226	+	15.5644i	1.08897	+	0.791184i
$388$		0			0
$389$	−9.92146	−	30.5351i	−0.503038	−	1.54819i	−0.804045	−	0.594569i	$-0.797323\pi$
$389$	−9.92146	−	30.5351i	−0.503038	−	1.54819i	0.301007	−	0.953622i	$-0.402677\pi$
$390$		0			0
$391$	8.36012	−	6.07398i	0.422790	−	0.307175i
$392$		0			0
$393$	11.8135	−	36.3582i	0.595912	−	1.83403i
$394$		0			0
$395$	10.7439			0.540583
$396$		0			0
$397$	23.1477			1.16175			0.580875	−	0.813993i	$-0.302711\pi$
$397$	23.1477			1.16175			0.580875	+	0.813993i	$0.302711\pi$
$398$		0			0
$399$	1.57350	−	4.84274i	0.0787736	−	0.242440i
$400$		0			0
$401$	4.51921	−	3.28340i	0.225678	−	0.163965i	−0.469201	−	0.883092i	$-0.655458\pi$
$401$	4.51921	−	3.28340i	0.225678	−	0.163965i	0.694879	+	0.719127i	$0.255458\pi$
$402$		0			0
$403$	−5.82121	−	17.9158i	−0.289975	−	0.892451i
$404$		0			0
$405$	−21.4567	−	15.5892i	−1.06619	−	0.774634i
$406$		0			0
$407$	−0.679819	−	0.183100i	−0.0336974	−	0.00907592i
$408$		0			0
$409$	25.9473	+	18.8518i	1.28301	+	0.932164i	0.999640	−	0.0268460i	$-0.00854639\pi$
$409$	25.9473	+	18.8518i	1.28301	+	0.932164i	0.283374	+	0.959010i	$0.408546\pi$
$410$		0			0
$411$	−20.2437	−	62.3037i	−0.998549	−	3.07322i
$412$		0			0
$413$	6.21065	−	4.51230i	0.305606	−	0.222036i
$414$		0			0
$415$	2.57292	−	7.91865i	0.126300	−	0.388711i
$416$		0			0
$417$	−10.1042			−0.494804
$418$		0			0
$419$	−3.02921			−0.147987			−0.0739934	−	0.997259i	$-0.523574\pi$
$419$	−3.02921			−0.147987			−0.0739934	+	0.997259i	$0.523574\pi$
$420$		0			0
$421$	−0.960654	+	2.95659i	−0.0468194	+	0.144095i	−0.971733	−	0.236081i	$-0.924137\pi$
$421$	−0.960654	+	2.95659i	−0.0468194	+	0.144095i	0.924914	+	0.380177i	$0.124137\pi$
$422$		0			0
$423$	56.1716	−	40.8110i	2.73116	−	1.98430i
$424$		0			0
$425$	−6.59540	−	20.2986i	−0.319924	−	0.984625i
$426$		0			0
$427$	−5.74134	−	4.17132i	−0.277843	−	0.201865i
$428$		0			0
$429$	−2.63675	−	51.5890i	−0.127304	−	2.49074i
$430$		0			0
$431$	17.9314	+	13.0280i	0.863727	+	0.627534i	0.928896	−	0.370340i	$-0.120759\pi$
$431$	17.9314	+	13.0280i	0.863727	+	0.627534i	−0.0651693	+	0.997874i	$0.520759\pi$
$432$		0			0
$433$	0.684143	+	2.10558i	0.0328778	+	0.101188i	0.966149	−	0.257986i	$-0.0830587\pi$
$433$	0.684143	+	2.10558i	0.0328778	+	0.101188i	−0.933271	+	0.359173i	$0.883059\pi$
$434$		0			0
$435$	−14.8583	+	10.7952i	−0.712400	+	0.517589i
$436$		0			0
$437$	−1.01450	+	3.12230i	−0.0485300	+	0.149360i
$438$		0			0
$439$	−9.12789			−0.435651			−0.217825	−	0.975988i	$-0.569896\pi$
$439$	−9.12789			−0.435651			−0.217825	+	0.975988i	$0.569896\pi$
$440$		0			0
$441$	8.55894			0.407568
$442$		0			0
$443$	−3.03131	+	9.32940i	−0.144022	+	0.443253i	−0.996884	−	0.0788829i	$-0.974865\pi$
$443$	−3.03131	+	9.32940i	−0.144022	+	0.443253i	0.852862	+	0.522136i	$0.174865\pi$
$444$		0			0
$445$	8.68808	−	6.31226i	0.411855	−	0.299230i
$446$		0			0
$447$	7.25920	+	22.3415i	0.343348	+	1.05672i
$448$		0			0
$449$	0.832689	+	0.604984i	0.0392970	+	0.0285510i	0.607260	−	0.794503i	$-0.292268\pi$
$449$	0.832689	+	0.604984i	0.0392970	+	0.0285510i	−0.567963	+	0.823054i	$0.692268\pi$
$450$		0			0
$451$	0.731435	+	0.905640i	0.0344419	+	0.0426449i
$452$		0			0
$453$	7.29436	+	5.29966i	0.342719	+	0.249000i
$454$		0			0
$455$	−0.973219	−	2.99526i	−0.0456252	−	0.140420i
$456$		0			0
$457$	25.4777	−	18.5106i	1.19179	−	0.865889i	0.198342	−	0.980133i	$-0.436444\pi$
$457$	25.4777	−	18.5106i	1.19179	−	0.865889i	0.993453	+	0.114244i	$0.0364445\pi$
$458$		0			0
$459$	−27.5325	+	84.7363i	−1.28511	+	3.95515i
$460$		0			0
$461$	−14.9537			−0.696461			−0.348231	−	0.937409i	$-0.613217\pi$
$461$	−14.9537			−0.696461			−0.348231	+	0.937409i	$0.613217\pi$
$462$		0			0
$463$	41.6713			1.93663			0.968315	−	0.249731i	$-0.0803423\pi$
$463$	41.6713			1.93663			0.968315	+	0.249731i	$0.0803423\pi$
$464$		0			0
$465$	2.97004	−	9.14085i	0.137732	−	0.423897i
$466$		0			0
$467$	−14.4022	+	10.4638i	−0.666455	+	0.484208i	−0.868837	−	0.495099i	$-0.835132\pi$
$467$	−14.4022	+	10.4638i	−0.666455	+	0.484208i	0.202382	+	0.979307i	$0.435132\pi$
$468$		0			0
$469$	−0.274839	−	0.845869i	−0.0126909	−	0.0390586i
$470$		0			0
$471$	31.4692	+	22.8637i	1.45003	+	1.05351i
$472$		0			0
$473$	−5.59968	+	8.59838i	−0.257474	+	0.395354i
$474$		0			0
$475$	5.48567	+	3.98558i	0.251700	+	0.182871i
$476$		0			0
$477$	33.7700	+	103.933i	1.54622	+	4.75878i
$478$		0			0
$479$	22.9900	−	16.7032i	1.05044	−	0.763190i	0.0781452	−	0.996942i	$-0.475100\pi$
$479$	22.9900	−	16.7032i	1.05044	−	0.763190i	0.972296	+	0.233752i	$0.0751002\pi$
$480$		0			0
$481$	−0.300507	+	0.924866i	−0.0137019	+	0.0421703i
$482$		0			0
$483$	−7.45249			−0.339100
$484$		0			0
$485$	1.93288			0.0877674
$486$		0			0
$487$	13.4010	−	41.2439i	0.607256	−	1.86894i	0.126786	−	0.991930i	$-0.459534\pi$
$487$	13.4010	−	41.2439i	0.607256	−	1.86894i	0.480470	−	0.877011i	$-0.340466\pi$
$488$		0			0
$489$	−22.6522	+	16.4578i	−1.02437	+	0.744246i
$490$		0			0
$491$	−1.35385	−	4.16673i	−0.0610986	−	0.188042i	0.915848	−	0.401524i	$-0.131519\pi$
$491$	−1.35385	−	4.16673i	−0.0610986	−	0.188042i	−0.976947	+	0.213482i	$0.931519\pi$
$492$		0			0
$493$	29.9684	+	21.7733i	1.34971	+	0.980619i
$494$		0			0
$495$	10.6500	−	16.3532i	0.478680	−	0.735020i
$496$		0			0
$497$	−3.95035	−	2.87010i	−0.177198	−	0.128742i
$498$		0			0
$499$	−2.63267	−	8.10251i	−0.117854	−	0.362718i	0.874677	−	0.484706i	$-0.161073\pi$
$499$	−2.63267	−	8.10251i	−0.117854	−	0.362718i	−0.992532	+	0.121987i	$0.961073\pi$
$500$		0			0
$501$	−38.9873	+	28.3260i	−1.74183	+	1.26551i
$502$		0			0
$503$	−4.88999	+	15.0499i	−0.218034	+	0.671040i	0.780890	+	0.624668i	$0.214766\pi$
$503$	−4.88999	+	15.0499i	−0.218034	+	0.671040i	−0.998924	+	0.0463716i	$0.985234\pi$
$504$		0			0
$505$	−6.60433			−0.293889
$506$		0			0
$507$	−27.1524			−1.20588
$508$		0			0
$509$	−0.0789642	+	0.243027i	−0.00350002	+	0.0107720i	−0.952791	−	0.303626i	$-0.901803\pi$
$509$	−0.0789642	+	0.243027i	−0.00350002	+	0.0107720i	0.949291	+	0.314398i	$0.101803\pi$
$510$		0			0
$511$	−7.41811	+	5.38958i	−0.328158	+	0.238421i
$512$		0			0
$513$	−8.74700	−	26.9205i	−0.386189	−	1.18857i
$514$		0			0
$515$	3.72260	+	2.70463i	0.164037	+	0.119180i
$516$		0			0
$517$	16.9049	+	20.9311i	0.743477	+	0.920549i
$518$		0			0
$519$	0.772175	+	0.561018i	0.0338947	+	0.0246260i
$520$		0			0
$521$	2.26388	+	6.96751i	0.0991824	+	0.305252i	0.988321	−	0.152386i	$-0.0486956\pi$
$521$	2.26388	+	6.96751i	0.0991824	+	0.305252i	−0.889139	+	0.457638i	$0.848696\pi$
$522$		0			0
$523$	8.72460	−	6.33879i	0.381500	−	0.277176i	−0.380463	−	0.924796i	$-0.624235\pi$
$523$	8.72460	−	6.33879i	0.381500	−	0.277176i	0.761964	+	0.647620i	$0.224235\pi$
$524$		0			0
$525$	−4.75650	+	14.6390i	−0.207591	+	0.638899i
$526$		0			0
$527$	−19.3854			−0.844441
$528$		0			0
$529$	−18.1951			−0.791091
$530$		0			0
$531$	20.3040	−	62.4893i	0.881119	−	2.71180i
$532$		0			0
$533$	1.30085	−	0.945126i	0.0563462	−	0.0409379i
$534$		0			0
$535$	0.593698	+	1.82721i	0.0256678	+	0.0789973i
$536$		0			0
$537$	52.5839	+	38.2044i	2.26916	+	1.64864i
$538$		0			0
$539$	0.169294	+	3.31230i	0.00729201	+	0.142671i
$540$		0			0
$541$	6.70061	+	4.86828i	0.288082	+	0.209304i	0.722435	−	0.691439i	$-0.243023\pi$
$541$	6.70061	+	4.86828i	0.288082	+	0.209304i	−0.434353	+	0.900743i	$0.643023\pi$
$542$		0			0
$543$	11.8895	+	36.5923i	0.510229	+	1.57032i
$544$		0			0
$545$	−5.54318	+	4.02736i	−0.237444	+	0.172513i
$546$		0			0
$547$	0.398348	−	1.22599i	0.0170321	−	0.0524195i	−0.942179	−	0.335109i	$-0.891227\pi$
$547$	0.398348	−	1.22599i	0.0170321	−	0.0524195i	0.959211	+	0.282690i	$0.0912267\pi$
$548$		0			0
$549$	−60.7401			−2.59232
$550$		0			0
$551$	−11.7684			−0.501352
$552$		0			0
$553$	−4.82930	+	14.8631i	−0.205363	+	0.632041i
$554$		0			0
$555$	−0.401402	+	0.291636i	−0.0170386	+	0.0123792i
$556$		0			0
$557$	4.07289	+	12.5351i	0.172574	+	0.531127i	0.999514	−	0.0311618i	$-0.00992073\pi$
$557$	4.07289	+	12.5351i	0.172574	+	0.531127i	−0.826941	+	0.562289i	$0.809921\pi$
$558$		0			0
$559$	11.4662	+	8.33071i	0.484970	+	0.352351i
$560$		0			0
$561$	−51.3288	−	13.8247i	−2.16710	−	0.583679i
$562$		0			0
$563$	9.32128	+	6.77231i	0.392845	+	0.285419i	0.766620	−	0.642101i	$-0.221937\pi$
$563$	9.32128	+	6.77231i	0.392845	+	0.285419i	−0.373775	+	0.927519i	$0.621937\pi$
$564$		0			0
$565$	−3.57241	−	10.9948i	−0.150293	−	0.462553i
$566$		0			0
$567$	31.2107	−	22.6759i	1.31073	−	0.952299i
$568$		0			0
$569$	−13.3186	+	40.9905i	−0.558346	+	1.71841i	0.128593	+	0.991697i	$0.458954\pi$
$569$	−13.3186	+	40.9905i	−0.558346	+	1.71841i	−0.686939	+	0.726715i	$0.741046\pi$
$570$		0			0
$571$	−33.9904			−1.42245			−0.711227	−	0.702962i	$-0.751860\pi$
$571$	−33.9904			−1.42245			−0.711227	+	0.702962i	$0.751860\pi$
$572$		0			0
$573$	−46.9260			−1.96036
$574$		0			0
$575$	3.06670	−	9.43832i	0.127890	−	0.393605i
$576$		0			0
$577$	−32.1619	+	23.3670i	−1.33892	+	0.972781i	−0.339435	+	0.940629i	$0.610236\pi$
$577$	−32.1619	+	23.3670i	−1.33892	+	0.972781i	−0.999483	+	0.0321518i	$0.989764\pi$
$578$		0			0
$579$	22.1831	+	68.2725i	0.921897	+	2.83731i
$580$		0			0
$581$	9.79813	+	7.11876i	0.406495	+	0.295336i
$582$		0			0
$583$	−39.5541	+	15.1247i	−1.63816	+	0.626402i
$584$		0			0
$585$	−21.8075	−	15.8441i	−0.901628	−	0.655071i
$586$		0			0
$587$	−11.7049	−	36.0241i	−0.483114	−	1.48687i	−0.834694	−	0.550714i	$-0.814355\pi$
$587$	−11.7049	−	36.0241i	−0.483114	−	1.48687i	0.351580	−	0.936158i	$-0.385645\pi$
$588$		0			0
$589$	4.98248	−	3.61998i	0.205300	−	0.149159i
$590$		0			0
$591$	11.8387	−	36.4359i	0.486980	−	1.49877i
$592$		0			0
$593$	−2.34186			−0.0961686			−0.0480843	−	0.998843i	$-0.515312\pi$
$593$	−2.34186			−0.0961686			−0.0480843	+	0.998843i	$0.515312\pi$
$594$		0			0
$595$	−3.24095			−0.132866
$596$		0			0
$597$	3.37566	−	10.3892i	0.138156	−	0.425202i
$598$		0			0
$599$	14.0649	−	10.2188i	0.574677	−	0.417527i	−0.262124	−	0.965034i	$-0.584423\pi$
$599$	14.0649	−	10.2188i	0.574677	−	0.417527i	0.836801	+	0.547507i	$0.184423\pi$
$600$		0			0
$601$	−4.42219	−	13.6101i	−0.180385	−	0.555168i	0.819453	−	0.573146i	$-0.194277\pi$
$601$	−4.42219	−	13.6101i	−0.180385	−	0.555168i	−0.999838	+	0.0179781i	$0.994277\pi$
$602$		0			0
$603$	−6.15849	−	4.47440i	−0.250793	−	0.182212i
$604$		0			0
$605$	6.53931	+	3.79806i	0.265861	+	0.154413i
$606$		0			0
$607$	19.8396	+	14.4143i	0.805263	+	0.585058i	0.912453	−	0.409181i	$-0.134185\pi$
$607$	19.8396	+	14.4143i	0.805263	+	0.585058i	−0.107190	+	0.994239i	$0.534185\pi$
$608$		0			0
$609$	−8.25532	−	25.4073i	−0.334522	−	1.02955i
$610$		0			0
$611$	30.0653	−	21.8437i	1.21631	−	0.883702i
$612$		0			0
$613$	11.8827	−	36.5713i	0.479939	−	1.47710i	−0.359241	−	0.933245i	$-0.616964\pi$
$613$	11.8827	−	36.5713i	0.479939	−	1.47710i	0.839180	−	0.543854i	$-0.183036\pi$
$614$		0			0
$615$	0.820390			0.0330813
$616$		0			0
$617$	−4.44911			−0.179114			−0.0895572	−	0.995982i	$-0.528545\pi$
$617$	−4.44911			−0.179114			−0.0895572	+	0.995982i	$0.528545\pi$
$618$		0			0
$619$	−7.92092	+	24.3781i	−0.318369	+	0.979838i	0.655977	+	0.754781i	$0.272257\pi$
$619$	−7.92092	+	24.3781i	−0.318369	+	0.979838i	−0.974346	+	0.225057i	$0.927743\pi$
$620$		0			0
$621$	−33.5159	+	24.3507i	−1.34495	+	0.977160i
$622$		0			0
$623$	4.82713	+	14.8564i	0.193395	+	0.595209i
$624$		0			0
$625$	−14.6707	−	10.6589i	−0.586828	−	0.426355i
$626$		0			0
$627$	15.7742	−	6.03176i	0.629962	−	0.240885i
$628$		0			0
$629$	0.809607	+	0.588214i	0.0322811	+	0.0234536i
$630$		0			0
$631$	−4.63016	−	14.2502i	−0.184324	−	0.567291i	0.815612	−	0.578599i	$-0.196400\pi$
$631$	−4.63016	−	14.2502i	−0.184324	−	0.567291i	−0.999936	+	0.0113084i	$0.996400\pi$
$632$		0			0
$633$	−52.3604	+	38.0420i	−2.08114	+	1.51203i
$634$		0			0
$635$	1.19800	−	3.68705i	0.0475410	−	0.146316i
$636$		0			0
$637$	4.58109			0.181509
$638$		0			0
$639$	−41.7925			−1.65328
$640$		0			0
$641$	8.35393	−	25.7108i	0.329960	−	1.01551i	−0.639191	−	0.769048i	$-0.720731\pi$
$641$	8.35393	−	25.7108i	0.329960	−	1.01551i	0.969151	−	0.246466i	$-0.0792693\pi$
$642$		0			0
$643$	−20.4006	+	14.8219i	−0.804522	+	0.584519i	−0.912237	−	0.409663i	$-0.865646\pi$
$643$	−20.4006	+	14.8219i	−0.804522	+	0.584519i	0.107716	+	0.994182i	$0.465646\pi$
$644$		0			0
$645$	2.23458	+	6.87732i	0.0879863	+	0.270794i
$646$		0			0
$647$	5.54113	+	4.02587i	0.217844	+	0.158273i	0.691356	−	0.722514i	$-0.257014\pi$
$647$	5.54113	+	4.02587i	0.217844	+	0.158273i	−0.473511	+	0.880788i	$0.657014\pi$
$648$		0			0
$649$	24.5849	+	6.62161i	0.965042	+	0.259921i
$650$		0			0
$651$	11.3104	+	8.21750i	0.443290	+	0.322069i
$652$		0			0
$653$	−11.1896	−	34.4382i	−0.437885	−	1.34767i	−0.890102	−	0.455762i	$-0.849367\pi$
$653$	−11.1896	−	34.4382i	−0.437885	−	1.34767i	0.452217	−	0.891908i	$-0.350633\pi$
$654$		0			0
$655$	6.25394	−	4.54376i	0.244362	−	0.177539i
$656$		0			0
$657$	−24.2515	+	74.6384i	−0.946140	+	2.91192i
$658$		0			0
$659$	−26.9081			−1.04819			−0.524096	−	0.851659i	$-0.675597\pi$
$659$	−26.9081			−1.04819			−0.524096	+	0.851659i	$0.675597\pi$
$660$		0			0
$661$	−37.9406			−1.47572			−0.737858	−	0.674956i	$-0.764163\pi$
$661$	−37.9406			−1.47572			−0.737858	+	0.674956i	$0.764163\pi$
$662$		0			0
$663$	−22.6894	+	69.8308i	−0.881183	+	2.71200i
$664$		0			0
$665$	0.832996	−	0.605207i	0.0323022	−	0.0234689i
$666$		0			0
$667$	5.32252	+	16.3810i	0.206089	+	0.634276i
$668$		0			0
$669$	−47.3781	−	34.4222i	−1.83174	−	1.33084i
$670$		0			0
$671$	−1.20143	−	23.5063i	−0.0463805	−	0.907452i
$672$		0			0
$673$	22.3883	+	16.2660i	0.863005	+	0.627010i	0.928701	−	0.370830i	$-0.120927\pi$
$673$	22.3883	+	16.2660i	0.863005	+	0.627010i	−0.0656956	+	0.997840i	$0.520927\pi$
$674$		0			0
$675$	26.4411	+	81.3773i	1.01772	+	3.13221i
$676$		0			0
$677$	4.98739	−	3.62355i	0.191681	−	0.139264i	−0.487806	−	0.872952i	$-0.662203\pi$
$677$	4.98739	−	3.62355i	0.191681	−	0.139264i	0.679487	+	0.733688i	$0.262203\pi$
$678$		0			0
$679$	−0.868815	+	2.67394i	−0.0333421	+	0.102616i
$680$		0			0
$681$	17.7366			0.679667
$682$		0			0
$683$	7.80638			0.298703			0.149351	−	0.988784i	$-0.452281\pi$
$683$	7.80638			0.298703			0.149351	+	0.988784i	$0.452281\pi$
$684$		0			0
$685$	4.09346	−	12.5984i	0.156403	−	0.481359i
$686$		0			0
$687$	29.7239	−	21.5957i	1.13404	−	0.823926i
$688$		0			0
$689$	18.0750	+	55.6293i	0.688605	+	2.11931i
$690$		0			0
$691$	−13.2484	−	9.62555i	−0.503994	−	0.366173i	0.306547	−	0.951856i	$-0.400826\pi$
$691$	−13.2484	−	9.62555i	−0.503994	−	0.366173i	−0.810540	+	0.585683i	$0.800826\pi$
$692$		0			0
$693$	17.8358	+	22.0838i	0.677527	+	0.838893i
$694$		0			0
$695$	−1.65295	−	1.20094i	−0.0626999	−	0.0455542i
$696$		0			0
$697$	−0.511325	−	1.57370i	−0.0193678	−	0.0596080i
$698$		0			0
$699$	6.26436	−	4.55132i	0.236940	−	0.172147i
$700$		0			0
$701$	−0.353613	+	1.08831i	−0.0133558	+	0.0411048i	−0.957512	−	0.288392i	$-0.906879\pi$
$701$	−0.353613	+	1.08831i	−0.0133558	+	0.0411048i	0.944157	+	0.329497i	$0.106879\pi$
$702$		0			0
$703$	−0.317929			−0.0119909
$704$		0			0
$705$	18.9608			0.714106
$706$		0			0
$707$	2.96860	−	9.13642i	0.111646	−	0.343610i
$708$		0			0
$709$	−7.89654	+	5.73718i	−0.296561	+	0.215464i	−0.726109	−	0.687580i	$-0.758673\pi$
$709$	−7.89654	+	5.73718i	−0.296561	+	0.215464i	0.429548	+	0.903044i	$0.358673\pi$
$710$		0			0
$711$	41.3337	+	127.212i	1.55013	+	4.77082i
$712$		0			0
$713$	−7.29226	−	5.29813i	−0.273097	−	0.198417i
$714$		0			0
$715$	5.70029	−	8.75287i	0.213179	−	0.327339i
$716$		0			0
$717$	0.274304	+	0.199293i	0.0102441	+	0.00744274i
$718$		0			0
$719$	−0.397370	−	1.22298i	−0.0148194	−	0.0456094i	0.943373	−	0.331733i	$-0.107633\pi$
$719$	−0.397370	−	1.22298i	−0.0148194	−	0.0456094i	−0.958193	+	0.286123i	$0.907633\pi$
$720$		0			0
$721$	−5.41486	+	3.93412i	−0.201660	+	0.146514i
$722$		0			0
$723$	29.8050	−	91.7302i	1.10846	−	3.41148i
$724$		0			0
$725$	35.5745			1.32120
$726$		0			0
$727$	−46.5455			−1.72628			−0.863138	−	0.504968i	$-0.831504\pi$
$727$	−46.5455			−1.72628			−0.863138	+	0.504968i	$0.831504\pi$
$728$		0			0
$729$	42.4668	−	130.699i	1.57285	−	4.84072i
$730$		0			0
$731$	11.7995	−	8.57286i	0.436421	−	0.317079i
$732$		0			0
$733$	−8.75507	−	26.9453i	−0.323376	−	0.995249i	−0.972168	−	0.234284i	$-0.924726\pi$
$733$	−8.75507	−	26.9453i	−0.323376	−	0.995249i	0.648792	−	0.760966i	$-0.275274\pi$
$734$		0			0
$735$	1.89093	+	1.37384i	0.0697481	+	0.0506749i
$736$		0			0
$737$	1.60978	−	2.47183i	0.0592969	−	0.0910511i
$738$		0			0
$739$	33.5180	+	24.3523i	1.23298	+	0.895812i	0.997110	−	0.0759722i	$-0.0242060\pi$
$739$	33.5180	+	24.3523i	1.23298	+	0.895812i	0.235870	+	0.971785i	$0.424206\pi$
$740$		0			0
$741$	−7.20835	−	22.1850i	−0.264805	−	0.814987i
$742$		0			0
$743$	4.91182	−	3.56865i	0.180197	−	0.130921i	−0.494030	−	0.869445i	$-0.664477\pi$
$743$	4.91182	−	3.56865i	0.180197	−	0.130921i	0.674227	+	0.738524i	$0.264477\pi$
$744$		0			0
$745$	−1.46788	+	4.51765i	−0.0537788	+	0.165514i
$746$		0			0
$747$	103.659			3.79267
$748$		0			0
$749$	−2.79463			−0.102113
$750$		0			0
$751$	−6.71573	+	20.6689i	−0.245060	+	0.754218i	0.750566	+	0.660795i	$0.229781\pi$
$751$	−6.71573	+	20.6689i	−0.245060	+	0.754218i	−0.995627	+	0.0934229i	$0.970219\pi$
$752$		0			0
$753$	−19.2261	+	13.9686i	−0.700639	+	0.509044i
$754$		0			0
$755$	0.563394	+	1.73395i	0.0205040	+	0.0631048i
$756$		0			0
$757$	12.7860	+	9.28954i	0.464713	+	0.337634i	0.795377	−	0.606115i	$-0.207273\pi$
$757$	12.7860	+	9.28954i	0.464713	+	0.337634i	−0.330664	+	0.943749i	$0.607273\pi$
$758$		0			0
$759$	−15.5301	−	19.2289i	−0.563708	−	0.697965i
$760$		0			0
$761$	−14.9993	−	10.8977i	−0.543726	−	0.395040i	0.281741	−	0.959490i	$-0.409088\pi$
$761$	−14.9993	−	10.8977i	−0.543726	−	0.395040i	−0.825467	+	0.564451i	$0.809088\pi$
$762$		0			0
$763$	−3.07981	−	9.47869i	−0.111497	−	0.343152i
$764$		0			0
$765$	−22.4414	+	16.3046i	−0.811370	+	0.589495i
$766$		0			0
$767$	10.8675	−	33.4468i	0.392404	−	1.20769i
$768$		0			0
$769$	35.3343			1.27419			0.637093	−	0.770787i	$-0.280137\pi$
$769$	35.3343			1.27419			0.637093	+	0.770787i	$0.280137\pi$
$770$		0			0
$771$	74.6938			2.69003
$772$		0			0
$773$	6.57884	−	20.2476i	0.236625	−	0.728256i	−0.760277	−	0.649599i	$-0.774937\pi$
$773$	6.57884	−	20.2476i	0.236625	−	0.728256i	0.996902	−	0.0786567i	$-0.0250631\pi$
$774$		0			0
$775$	−15.0614	+	10.9428i	−0.541022	+	0.393076i
$776$		0			0
$777$	−0.223021	−	0.686387i	−0.00800082	−	0.0246240i
$778$		0			0
$779$	0.425291	+	0.308992i	0.0152376	+	0.0110708i
$780$		0			0
$781$	−0.826647	−	16.1736i	−0.0295797	−	0.578739i
$782$		0			0
$783$	−120.144	−	87.2895i	−4.29358	−	3.11947i
$784$		0			0
$785$	2.43059	+	7.48058i	0.0867514	+	0.266993i
$786$		0			0
$787$	−21.4875	+	15.6116i	−0.765945	+	0.556492i	−0.900728	−	0.434383i	$-0.856966\pi$
$787$	−21.4875	+	15.6116i	−0.765945	+	0.556492i	0.134783	+	0.990875i	$0.456966\pi$
$788$		0			0
$789$	−14.0873	+	43.3563i	−0.501521	+	1.54352i
$790$		0			0
$791$	16.8159			0.597904
$792$		0			0
$793$	−32.5105			−1.15448
$794$		0			0
$795$	−9.22208	+	28.3827i	−0.327074	+	1.00663i
$796$		0			0
$797$	11.8866	−	8.63608i	0.421043	−	0.305906i	−0.357014	−	0.934099i	$-0.616205\pi$
$797$	11.8866	−	8.63608i	0.421043	−	0.305906i	0.778057	+	0.628193i	$0.216205\pi$
$798$		0			0
$799$	−11.8177	−	36.3712i	−0.418081	−	1.28672i
$800$		0			0
$801$	108.164	+	78.5861i	3.82180	+	2.77670i
$802$		0			0
$803$	−29.3647	−	7.90897i	−1.03626	−	0.279101i
$804$		0			0
$805$	−1.21916	−	0.885769i	−0.0429696	−	0.0312192i
$806$		0			0
$807$	−33.2512	−	102.337i	−1.17050	−	3.60243i
$808$		0			0
$809$	12.5236	−	9.09895i	0.440307	−	0.319902i	−0.345450	−	0.938437i	$-0.612274\pi$
$809$	12.5236	−	9.09895i	0.440307	−	0.319902i	0.785757	+	0.618535i	$0.212274\pi$
$810$		0			0
$811$	5.18583	−	15.9604i	0.182099	−	0.560444i	−0.817787	−	0.575521i	$-0.804799\pi$
$811$	5.18583	−	15.9604i	0.182099	−	0.560444i	0.999886	+	0.0150770i	$0.00479933\pi$
$812$		0			0
$813$	73.9270			2.59273
$814$		0			0
$815$	−5.66178			−0.198323
$816$		0			0
$817$	−1.43187	+	4.40684i	−0.0500947	+	0.154176i
$818$		0			0
$819$	31.7210	−	23.0466i	1.10842	−	0.805314i
$820$		0			0
$821$	−4.23855	−	13.0449i	−0.147926	−	0.455270i	0.849449	−	0.527670i	$-0.176934\pi$
$821$	−4.23855	−	13.0449i	−0.147926	−	0.455270i	−0.997376	+	0.0723998i	$0.976934\pi$
$822$		0			0
$823$	−37.2133	−	27.0370i	−1.29717	−	0.942451i	−0.297249	−	0.954800i	$-0.596069\pi$
$823$	−37.2133	−	27.0370i	−1.29717	−	0.942451i	−0.999924	+	0.0123492i	$0.996069\pi$
$824$		0			0
$825$	−47.6835	+	18.2333i	−1.66013	+	0.634801i
$826$		0			0
$827$	1.26848	+	0.921606i	0.0441094	+	0.0320474i	0.609622	−	0.792693i	$-0.291321\pi$
$827$	1.26848	+	0.921606i	0.0441094	+	0.0320474i	−0.565512	+	0.824740i	$0.691321\pi$
$828$		0			0
$829$	−3.45203	−	10.6243i	−0.119894	−	0.368996i	0.873042	−	0.487644i	$-0.162144\pi$
$829$	−3.45203	−	10.6243i	−0.119894	−	0.368996i	−0.992936	+	0.118649i	$0.962144\pi$
$830$		0			0
$831$	53.2545	−	38.6916i	1.84738	−	1.34220i
$832$		0			0
$833$	1.45678	−	4.48352i	0.0504746	−	0.155345i
$834$		0			0
$835$	−9.74465			−0.337228
$836$		0			0
$837$	77.7164			2.68627
$838$		0			0
$839$	−14.0113	+	43.1224i	−0.483724	+	1.48875i	0.350097	+	0.936714i	$0.386149\pi$
$839$	−14.0113	+	43.1224i	−0.483724	+	1.48875i	−0.833821	+	0.552036i	$0.813851\pi$
$840$		0			0
$841$	−26.4893	+	19.2456i	−0.913425	+	0.663642i
$842$		0			0
$843$	−22.3306	−	68.7266i	−0.769108	−	2.36707i
$844$		0			0
$845$	−4.44188	−	3.22721i	−0.152805	−	0.111020i
$846$		0			0
$847$	−8.19361	+	7.33926i	−0.281536	+	0.252180i
$848$		0			0
$849$	7.19070	+	5.22435i	0.246784	+	0.179299i
$850$		0			0
$851$	0.143790	+	0.442540i	0.00492906	+	0.0151701i
$852$		0			0
$853$	14.8508	−	10.7897i	0.508482	−	0.369434i	−0.303766	−	0.952747i	$-0.598244\pi$
$853$	14.8508	−	10.7897i	0.508482	−	0.369434i	0.812247	+	0.583313i	$0.198244\pi$
$854$		0			0
$855$	2.72325	−	8.38130i	0.0931332	−	0.286634i
$856$		0			0
$857$	6.55371			0.223870			0.111935	−	0.993716i	$-0.464295\pi$
$857$	6.55371			0.223870			0.111935	+	0.993716i	$0.464295\pi$
$858$		0			0
$859$	−30.9945			−1.05752			−0.528759	−	0.848772i	$-0.677343\pi$
$859$	−30.9945			−1.05752			−0.528759	+	0.848772i	$0.677343\pi$
$860$		0			0
$861$	−0.368760	+	1.13493i	−0.0125673	+	0.0386782i
$862$		0			0
$863$	−20.1805	+	14.6620i	−0.686952	+	0.499100i	−0.875657	−	0.482934i	$-0.839571\pi$
$863$	−20.1805	+	14.6620i	−0.686952	+	0.499100i	0.188705	+	0.982034i	$0.439571\pi$
$864$		0			0
$865$	0.0596405	+	0.183554i	0.00202784	+	0.00624104i
$866$		0			0
$867$	14.3692	+	10.4399i	0.488004	+	0.354556i
$868$		0			0
$869$	−48.4133	+	18.5123i	−1.64231	+	0.627987i
$870$		0			0
$871$	−3.29627	−	2.39488i	−0.111690	−	0.0811475i
$872$		0			0
$873$	7.43613	+	22.8861i	0.251675	+	0.774576i
$874$		0			0
$875$	−5.29895	+	3.84991i	−0.179137	+	0.130151i
$876$		0			0
$877$	9.86414	−	30.3587i	0.333088	−	1.02514i	−0.634568	−	0.772867i	$-0.718822\pi$
$877$	9.86414	−	30.3587i	0.333088	−	1.02514i	0.967656	−	0.252273i	$-0.0811782\pi$
$878$		0			0
$879$	−63.3695			−2.13740
$880$		0			0
$881$	30.7462			1.03587			0.517933	−	0.855421i	$-0.326702\pi$
$881$	30.7462			1.03587			0.517933	+	0.855421i	$0.326702\pi$
$882$		0			0
$883$	14.1731	−	43.6202i	0.476961	−	1.46794i	−0.366333	−	0.930484i	$-0.619387\pi$
$883$	14.1731	−	43.6202i	0.476961	−	1.46794i	0.843294	−	0.537452i	$-0.180613\pi$
$884$		0			0
$885$	14.5163	−	10.5467i	0.487959	−	0.354523i
$886$		0			0
$887$	−13.5824	−	41.8022i	−0.456051	−	1.40358i	−0.869897	−	0.493234i	$-0.835815\pi$
$887$	−13.5824	−	41.8022i	−0.456051	−	1.40358i	0.413846	−	0.910347i	$-0.364185\pi$
$888$		0			0
$889$	4.56217	+	3.31461i	0.153010	+	0.111168i
$890$		0			0
$891$	123.548	+	33.2759i	4.13901	+	1.11479i
$892$		0			0
$893$	9.82930	+	7.14141i	0.328925	+	0.238978i
$894$		0			0
$895$	4.06142	+	12.4998i	0.135758	+	0.417821i
$896$		0			0
$897$	−27.6203	+	20.0673i	−0.922213	+	0.670027i
$898$		0			0
$899$	9.98474	−	30.7299i	0.333010	−	1.02490i
$900$		0			0
$901$	60.1923			2.00530
$902$		0			0
$903$	−10.5185			−0.350033
$904$		0			0
$905$	−2.40417	+	7.39928i	−0.0799174	+	0.245961i
$906$		0			0
$907$	−10.3097	+	7.49045i	−0.342329	+	0.248716i	−0.745644	−	0.666345i	$-0.767858\pi$
$907$	−10.3097	+	7.49045i	−0.342329	+	0.248716i	0.403315	+	0.915061i	$0.367858\pi$
$908$		0			0
$909$	−25.4081	−	78.1981i	−0.842733	−	2.59367i
$910$		0			0
$911$	−10.1547	−	7.37785i	−0.336441	−	0.244439i	0.406718	−	0.913554i	$-0.366673\pi$
$911$	−10.1547	−	7.37785i	−0.336441	−	0.244439i	−0.743159	+	0.669115i	$0.766673\pi$
$912$		0			0
$913$	2.05035	+	40.1158i	0.0678566	+	1.32764i
$914$		0			0
$915$	−13.4193	−	9.74972i	−0.443630	−	0.322316i
$916$		0			0
$917$	3.47472	+	10.6941i	0.114745	+	0.353150i
$918$		0			0
$919$	28.3212	−	20.5766i	0.934230	−	0.678758i	−0.0127946	−	0.999918i	$-0.504073\pi$
$919$	28.3212	−	20.5766i	0.934230	−	0.678758i	0.947025	+	0.321160i	$0.104073\pi$
$920$		0			0
$921$	5.73319	−	17.6450i	0.188915	−	0.581421i
$922$		0			0
$923$	−22.3690			−0.736285
$924$		0			0
$925$	0.961059			0.0315994
$926$		0			0
$927$	−17.7024	+	54.4823i	−0.581422	+	1.78943i
$928$		0			0
$929$	−24.3329	+	17.6789i	−0.798336	+	0.580025i	−0.910426	−	0.413673i	$-0.864246\pi$
$929$	−24.3329	+	17.6789i	−0.798336	+	0.580025i	0.112089	+	0.993698i	$0.464246\pi$
$930$		0			0
$931$	0.462816	+	1.42440i	0.0151682	+	0.0466829i
$932$		0			0
$933$	−16.1896	−	11.7625i	−0.530025	−	0.385086i
$934$		0			0
$935$	−6.75376	−	8.36229i	−0.220871	−	0.273476i
$936$		0			0
$937$	2.16391	+	1.57217i	0.0706917	+	0.0513605i	0.622570	−	0.782564i	$-0.286089\pi$
$937$	2.16391	+	1.57217i	0.0706917	+	0.0513605i	−0.551878	+	0.833925i	$0.686089\pi$
$938$		0			0
$939$	22.4214	+	69.0058i	0.731693	+	2.25192i
$940$		0			0
$941$	−14.4251	+	10.4805i	−0.470246	+	0.341654i	−0.797537	−	0.603270i	$-0.793864\pi$
$941$	−14.4251	+	10.4805i	−0.470246	+	0.341654i	0.327291	+	0.944924i	$0.393864\pi$
$942$		0			0
$943$	0.237753	−	0.731730i	0.00774232	−	0.0238284i
$944$		0			0
$945$	12.9930			0.422663
$946$		0			0
$947$	27.4082			0.890647			0.445323	−	0.895370i	$-0.353089\pi$
$947$	27.4082			0.890647			0.445323	+	0.895370i	$0.353089\pi$
$948$		0			0
$949$	−12.9804	+	39.9495i	−0.421361	+	1.29681i
$950$		0			0
$951$	−19.9703	+	14.5092i	−0.647580	+	0.470494i
$952$		0			0
$953$	−12.5821	−	38.7239i	−0.407576	−	1.25439i	−0.918725	−	0.394897i	$-0.870780\pi$
$953$	−12.5821	−	38.7239i	−0.407576	−	1.25439i	0.511150	−	0.859492i	$-0.329220\pi$
$954$		0			0
$955$	−7.67665	−	5.57742i	−0.248411	−	0.180481i
$956$		0			0
$957$	48.3527	−	74.2461i	1.56302	−	2.40004i
$958$		0			0
$959$	15.5886	+	11.3258i	0.503381	+	0.365728i
$960$		0			0
$961$	−4.35429	−	13.4011i	−0.140461	−	0.432294i
$962$		0			0
$963$	−19.3509	+	14.0593i	−0.623574	+	0.453053i
$964$		0			0
$965$	−4.48562	+	13.8053i	−0.144397	+	0.444408i
$966$		0			0
$967$	−59.5033			−1.91350			−0.956749	−	0.290915i	$-0.906040\pi$
$967$	−59.5033			−1.91350			−0.956749	+	0.290915i	$0.906040\pi$
$968$		0			0
$969$	−24.0048			−0.771145
$970$		0			0
$971$	12.9013	−	39.7061i	0.414022	−	1.27423i	−0.499100	−	0.866544i	$-0.666336\pi$
$971$	12.9013	−	39.7061i	0.414022	−	1.27423i	0.913122	−	0.407685i	$-0.133664\pi$
$972$		0			0
$973$	2.40436	−	1.74687i	0.0770804	−	0.0560022i
$974$		0			0
$975$	21.7900	+	67.0626i	0.697837	+	2.14772i
$976$		0			0
$977$	−7.56447	−	5.49591i	−0.242009	−	0.175830i	0.460169	−	0.887831i	$-0.347789\pi$
$977$	−7.56447	−	5.49591i	−0.242009	−	0.175830i	−0.702178	+	0.712002i	$0.747789\pi$
$978$		0			0
$979$	−28.2733	+	43.4140i	−0.903618	+	1.38752i
$980$		0			0
$981$	−69.0112	−	50.1396i	−2.20336	−	1.60083i
$982$		0			0
$983$	−2.16872	−	6.67464i	−0.0691715	−	0.212888i	0.910495	−	0.413519i	$-0.135701\pi$
$983$	−2.16872	−	6.67464i	−0.0691715	−	0.212888i	−0.979667	+	0.200631i	$0.935701\pi$
$984$		0			0
$985$	6.26730	−	4.55346i	0.199693	−	0.145085i
$986$		0			0
$987$	−8.52276	+	26.2304i	−0.271283	+	0.834922i
$988$		0			0
$989$	6.78167			0.215645
$990$		0			0
$991$	−17.8273			−0.566303			−0.283152	−	0.959075i	$-0.591380\pi$
$991$	−17.8273			−0.566303			−0.283152	+	0.959075i	$0.591380\pi$
$992$		0			0
$993$	−12.3980	+	38.1571i	−0.393439	+	1.21088i
$994$		0			0
$995$	1.78704	−	1.29836i	0.0566529	−	0.0411607i
$996$		0			0
$997$	−16.0391	−	49.3632i	−0.507963	−	1.56335i	−0.795731	−	0.605650i	$-0.792913\pi$
$997$	−16.0391	−	49.3632i	−0.507963	−	1.56335i	0.287768	−	0.957700i	$-0.407087\pi$
$998$		0			0
$999$	−3.24573	−	2.35816i	−0.102690	−	0.0746089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.r.f.169.1	yes	20
11.3	even	5	inner	616.2.r.f.113.1	✓	20
11.5	even	5		6776.2.a.bm.1.1		10
11.6	odd	10		6776.2.a.bn.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.r.f.113.1	✓	20	11.3	even	5	inner
616.2.r.f.169.1	yes	20	1.1	even	1	trivial
6776.2.a.bm.1.1		10	11.5	even	5
6776.2.a.bn.1.1		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05061 + 3.23344i) q^{3} +(-0.556182 + 0.404090i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-6.92433 - 5.03082i) q^{9} +(1.80996 - 2.77922i) q^{11} +(-3.70618 - 2.69270i) q^{13} +(-0.722272 - 2.22292i) q^{15} +(-3.81391 + 2.77097i) q^{17} +(0.462816 - 1.42440i) q^{19} +3.39984 q^{21} -2.19201 q^{23} +(-1.39904 + 4.30579i) q^{25} +(15.2900 - 11.1089i) q^{27} +(-2.42815 - 7.47307i) q^{29} +(3.32675 + 2.41702i) q^{31} +(7.08488 + 8.77227i) q^{33} +(0.556182 + 0.404090i) q^{35} +(-0.0655973 - 0.201888i) q^{37} +(12.6004 - 9.15475i) q^{39} +(-0.108464 + 0.333817i) q^{41} -3.09382 q^{43} +5.88409 q^{45} +(-2.50681 + 7.71517i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-4.95284 - 15.2433i) q^{51} +(-10.3297 - 7.50494i) q^{53} +(0.116386 + 2.27714i) q^{55} +(4.11948 + 2.99298i) q^{57} +(2.37226 + 7.30106i) q^{59} +(5.74134 - 4.17132i) q^{61} +(-2.64486 + 8.14003i) q^{63} +3.14940 q^{65} +0.889399 q^{67} +(2.30295 - 7.08774i) q^{69} +(3.95035 - 2.87010i) q^{71} +(-2.83347 - 8.72052i) q^{73} +(-12.4527 - 9.04740i) q^{75} +(-3.20250 - 0.862549i) q^{77} +(-12.6433 - 9.18587i) q^{79} +(11.9214 + 36.6904i) q^{81} +(-9.79813 + 7.11876i) q^{83} +(1.00151 - 3.08232i) q^{85} +26.7148 q^{87} -15.6209 q^{89} +(-1.41563 + 4.35687i) q^{91} +(-11.3104 + 8.21750i) q^{93} +(0.318176 + 0.979246i) q^{95} +(-2.27459 - 1.65258i) q^{97} +(-26.5145 + 10.1386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{3} + 5 q^{7} - 6 q^{9} - 3 q^{11} + 2 q^{13} + 8 q^{15} + 21 q^{19} + 6 q^{21} - 6 q^{23} - 7 q^{25} + 32 q^{27} + 6 q^{29} - 18 q^{31} - 16 q^{33} + 5 q^{37} + 12 q^{39} - 12 q^{41} - 42 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 20 * q - q^3 + 5 * q^7 - 6 * q^9 - 3 * q^11 + 2 * q^13 + 8 * q^15 + 21 * q^19 + 6 * q^21 - 6 * q^23 - 7 * q^25 + 32 * q^27 + 6 * q^29 - 18 * q^31 - 16 * q^33 + 5 * q^37 + 12 * q^39 - 12 * q^41 - 42 * q^43 + 18 * q^45 + 3 * q^47 - 5 * q^49 - q^51 - 38 * q^53 - 15 * q^55 - 3 * q^57 + 36 * q^59 + 23 * q^61 + 11 * q^63 - 30 * q^65 - 2 * q^67 + 43 * q^69 + 48 * q^71 + 6 * q^73 - 67 * q^75 - 17 * q^77 + 43 * q^79 + 16 * q^81 + 5 * q^83 - 16 * q^85 - 16 * q^87 - 46 * q^89 - 2 * q^91 + q^93 + 44 * q^95 + 9 * q^97 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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