LMFDB - Embedded newform 1716.2.z.f.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(157,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("1716.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.z (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:	$13.7023289869$
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} - 6 x^{19} + 41 x^{18} - 146 x^{17} + 650 x^{16} - 1400 x^{15} + 5756 x^{14} - 2122 x^{13} + \cdots + 4096 $ x^20 - 6x^19 + 41x^18 - 146x^17 + 650x^16 - 1400x^15 + 5756x^14 - 2122x^13 + 27469x^12 + 11286x^11 + 72308x^10 + 48512x^9 + 142448x^8 - 37952x^7 + 295552x^6 + 300160x^5 + 272128x^4 + 194048x^3 + 236544x^2 + 49152*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			625.2
Root			$3.54295 - 2.57410i$ of defining polynomial
Character	$\chi$	$=$	1716.625
Dual form			1716.2.z.f.313.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} +(-0.671939 - 2.06802i) q^{5} +(0.699083 + 0.507914i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} +(-0.671939 - 2.06802i) q^{5} +(0.699083 + 0.507914i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-3.10571 - 1.16387i) q^{11} +(0.309017 - 0.951057i) q^{13} +(-1.75916 - 1.27810i) q^{15} +(0.388264 + 1.19495i) q^{17} +(3.38343 - 2.45820i) q^{19} +0.864114 q^{21} -7.56826 q^{23} +(0.219897 - 0.159765i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(2.00359 + 1.45569i) q^{29} +(3.01901 - 9.29157i) q^{31} +(-3.19667 + 0.883898i) q^{33} +(0.580632 - 1.78700i) q^{35} +(-5.70604 - 4.14568i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(-9.50295 + 6.90430i) q^{41} -4.95375 q^{43} -2.17444 q^{45} +(1.87746 - 1.36405i) q^{47} +(-1.93238 - 5.94725i) q^{49} +(1.01649 + 0.738522i) q^{51} +(-0.0120600 + 0.0371167i) q^{53} +(-0.320056 + 7.20470i) q^{55} +(1.29235 - 3.97746i) q^{57} +(0.572210 + 0.415735i) q^{59} +(0.338023 + 1.04033i) q^{61} +(0.699083 - 0.507914i) q^{63} -2.17444 q^{65} +6.33315 q^{67} +(-6.12285 + 4.44851i) q^{69} +(-0.605452 - 1.86339i) q^{71} +(-5.82745 - 4.23389i) q^{73} +(0.0839932 - 0.258505i) q^{75} +(-1.58000 - 2.39107i) q^{77} +(-1.53130 + 4.71286i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.533644 - 1.64239i) q^{83} +(2.21029 - 1.60587i) q^{85} +2.47657 q^{87} -1.30090 q^{89} +(0.699083 - 0.507914i) q^{91} +(-3.01901 - 9.29157i) q^{93} +(-7.35706 - 5.34522i) q^{95} +(-1.39577 + 4.29575i) q^{97} +(-2.06662 + 2.59405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$		0			0
$5$	−0.671939	−	2.06802i	−0.300500	−	0.924845i	−0.981318	−	0.192392i	$-0.938375\pi$
$5$	−0.671939	−	2.06802i	−0.300500	−	0.924845i	0.680818	−	0.732453i	$-0.261625\pi$
$6$		0			0
$7$	0.699083	+	0.507914i	0.264229	+	0.191973i	0.712009	−	0.702170i	$-0.247785\pi$
$7$	0.699083	+	0.507914i	0.264229	+	0.191973i	−0.447781	+	0.894143i	$0.647785\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−3.10571	−	1.16387i	−0.936405	−	0.350920i
$11$	−3.10571	−	1.16387i	−0.936405	−	0.350920i
$12$		0			0
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$		0			0
$15$	−1.75916	−	1.27810i	−0.454213	−	0.330005i
$16$		0			0
$17$	0.388264	+	1.19495i	0.0941679	+	0.289819i	0.987036	−	0.160499i	$-0.0513105\pi$
$17$	0.388264	+	1.19495i	0.0941679	+	0.289819i	−0.892868	+	0.450318i	$0.851310\pi$
$18$		0			0
$19$	3.38343	−	2.45820i	0.776212	−	0.563951i	−0.127628	−	0.991822i	$-0.540736\pi$
$19$	3.38343	−	2.45820i	0.776212	−	0.563951i	0.903840	+	0.427871i	$0.140736\pi$
$20$		0			0
$21$	0.864114			0.188565
$22$		0			0
$23$	−7.56826			−1.57809			−0.789046	−	0.614335i	$-0.789425\pi$
$23$	−7.56826			−1.57809			−0.789046	+	0.614335i	$0.789425\pi$
$24$		0			0
$25$	0.219897	−	0.159765i	0.0439794	−	0.0319529i
$26$		0			0
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$		0			0
$29$	2.00359	+	1.45569i	0.372057	+	0.270315i	0.758063	−	0.652181i	$-0.226146\pi$
$29$	2.00359	+	1.45569i	0.372057	+	0.270315i	−0.386006	+	0.922496i	$0.626146\pi$
$30$		0			0
$31$	3.01901	−	9.29157i	0.542231	−	1.66881i	−0.185254	−	0.982691i	$-0.559311\pi$
$31$	3.01901	−	9.29157i	0.542231	−	1.66881i	0.727485	−	0.686124i	$-0.240689\pi$
$32$		0			0
$33$	−3.19667	+	0.883898i	−0.556470	+	0.153867i
$34$		0			0
$35$	0.580632	−	1.78700i	0.0981447	−	0.302058i
$36$		0			0
$37$	−5.70604	−	4.14568i	−0.938067	−	0.681546i	0.00988726	−	0.999951i	$-0.496853\pi$
$37$	−5.70604	−	4.14568i	−0.938067	−	0.681546i	−0.947955	+	0.318405i	$0.896853\pi$
$38$		0			0
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$		0			0
$41$	−9.50295	+	6.90430i	−1.48411	+	1.07827i	−0.507909	+	0.861411i	$0.669581\pi$
$41$	−9.50295	+	6.90430i	−1.48411	+	1.07827i	−0.976203	+	0.216860i	$0.930419\pi$
$42$		0			0
$43$	−4.95375			−0.755440			−0.377720	−	0.925920i	$-0.623292\pi$
$43$	−4.95375			−0.755440			−0.377720	+	0.925920i	$0.623292\pi$
$44$		0			0
$45$	−2.17444			−0.324146
$46$		0			0
$47$	1.87746	−	1.36405i	0.273855	−	0.198967i	−0.442378	−	0.896829i	$-0.645865\pi$
$47$	1.87746	−	1.36405i	0.273855	−	0.198967i	0.716233	+	0.697861i	$0.245865\pi$
$48$		0			0
$49$	−1.93238	−	5.94725i	−0.276054	−	0.849607i
$50$		0			0
$51$	1.01649	+	0.738522i	0.142337	+	0.103414i
$52$		0			0
$53$	−0.0120600	+	0.0371167i	−0.00165656	+	0.00509838i	−0.951881	−	0.306467i	$-0.900853\pi$
$53$	−0.0120600	+	0.0371167i	−0.00165656	+	0.00509838i	0.950225	+	0.311565i	$0.100853\pi$
$54$		0			0
$55$	−0.320056	+	7.20470i	−0.0431563	+	0.971481i
$56$		0			0
$57$	1.29235	−	3.97746i	0.171177	−	0.526827i
$58$		0			0
$59$	0.572210	+	0.415735i	0.0744954	+	0.0541241i	0.624410	−	0.781097i	$-0.285340\pi$
$59$	0.572210	+	0.415735i	0.0744954	+	0.0541241i	−0.549914	+	0.835221i	$0.685340\pi$
$60$		0			0
$61$	0.338023	+	1.04033i	0.0432794	+	0.133200i	0.970361	−	0.241658i	$-0.0776913\pi$
$61$	0.338023	+	1.04033i	0.0432794	+	0.133200i	−0.927082	+	0.374858i	$0.877691\pi$
$62$		0			0
$63$	0.699083	−	0.507914i	0.0880762	−	0.0639911i
$64$		0			0
$65$	−2.17444			−0.269706
$66$		0			0
$67$	6.33315			0.773718			0.386859	−	0.922139i	$-0.373560\pi$
$67$	6.33315			0.773718			0.386859	+	0.922139i	$0.373560\pi$
$68$		0			0
$69$	−6.12285	+	4.44851i	−0.737105	+	0.535538i
$70$		0			0
$71$	−0.605452	−	1.86339i	−0.0718539	−	0.221144i	0.908680	−	0.417493i	$-0.137091\pi$
$71$	−0.605452	−	1.86339i	−0.0718539	−	0.221144i	−0.980534	+	0.196350i	$0.937091\pi$
$72$		0			0
$73$	−5.82745	−	4.23389i	−0.682052	−	0.495539i	0.191986	−	0.981398i	$-0.438507\pi$
$73$	−5.82745	−	4.23389i	−0.682052	−	0.495539i	−0.874038	+	0.485858i	$0.838507\pi$
$74$		0			0
$75$	0.0839932	−	0.258505i	0.00969870	−	0.0298495i
$76$		0			0
$77$	−1.58000	−	2.39107i	−0.180058	−	0.272488i
$78$		0			0
$79$	−1.53130	+	4.71286i	−0.172285	+	0.530238i	−0.999499	−	0.0316486i	$-0.989924\pi$
$79$	−1.53130	+	4.71286i	−0.172285	+	0.530238i	0.827214	+	0.561887i	$0.189924\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−0.533644	−	1.64239i	−0.0585750	−	0.180275i	0.917488	−	0.397764i	$-0.130214\pi$
$83$	−0.533644	−	1.64239i	−0.0585750	−	0.180275i	−0.976063	+	0.217488i	$0.930214\pi$
$84$		0			0
$85$	2.21029	−	1.60587i	0.239740	−	0.174181i
$86$		0			0
$87$	2.47657			0.265516
$88$		0			0
$89$	−1.30090			−0.137895			−0.0689474	−	0.997620i	$-0.521964\pi$
$89$	−1.30090			−0.137895			−0.0689474	+	0.997620i	$0.521964\pi$
$90$		0			0
$91$	0.699083	−	0.507914i	0.0732838	−	0.0532438i
$92$		0			0
$93$	−3.01901	−	9.29157i	−0.313057	−	0.963490i
$94$		0			0
$95$	−7.35706	−	5.34522i	−0.754819	−	0.548408i
$96$		0			0
$97$	−1.39577	+	4.29575i	−0.141719	+	0.436167i	−0.996575	−	0.0826996i	$-0.973646\pi$
$97$	−1.39577	+	4.29575i	−0.141719	+	0.436167i	0.854855	+	0.518866i	$0.173646\pi$
$98$		0			0
$99$	−2.06662	+	2.59405i	−0.207703	+	0.260711i
$100$		0			0
$101$	−2.67523	+	8.23351i	−0.266195	+	0.819265i	0.725220	+	0.688517i	$0.241738\pi$
$101$	−2.67523	+	8.23351i	−0.266195	+	0.819265i	−0.991416	+	0.130748i	$0.958262\pi$
$102$		0			0
$103$	−6.67977	−	4.85314i	−0.658177	−	0.478194i	0.207870	−	0.978157i	$-0.433347\pi$
$103$	−6.67977	−	4.85314i	−0.658177	−	0.478194i	−0.866047	+	0.499963i	$0.833347\pi$
$104$		0			0
$105$	−0.580632	−	1.78700i	−0.0566639	−	0.174394i
$106$		0			0
$107$	−3.46309	+	2.51608i	−0.334790	+	0.243239i	−0.742460	−	0.669890i	$-0.766341\pi$
$107$	−3.46309	+	2.51608i	−0.334790	+	0.243239i	0.407671	+	0.913129i	$0.366341\pi$
$108$		0			0
$109$	14.0913			1.34971			0.674853	−	0.737952i	$-0.264207\pi$
$109$	14.0913			1.34971			0.674853	+	0.737952i	$0.264207\pi$
$110$		0			0
$111$	−7.05306			−0.669446
$112$		0			0
$113$	1.09466	−	0.795317i	0.102977	−	0.0748171i	−0.535105	−	0.844785i	$-0.679728\pi$
$113$	1.09466	−	0.795317i	0.102977	−	0.0748171i	0.638082	+	0.769968i	$0.279728\pi$
$114$		0			0
$115$	5.08541	+	15.6513i	0.474217	+	1.45949i
$116$		0			0
$117$	−0.809017	−	0.587785i	−0.0747936	−	0.0543408i
$118$		0			0
$119$	−0.335504	+	1.03258i	−0.0307556	+	0.0946561i
$120$		0			0
$121$	8.29081	+	7.22927i	0.753710	+	0.657207i
$122$		0			0
$123$	−3.62980	+	11.1714i	−0.327288	+	1.00729i
$124$		0			0
$125$	−9.27395	−	6.73792i	−0.829487	−	0.602658i
$126$		0			0
$127$	−5.11840	−	15.7528i	−0.454184	−	1.39784i	−0.872090	−	0.489345i	$-0.837236\pi$
$127$	−5.11840	−	15.7528i	−0.454184	−	1.39784i	0.417906	−	0.908490i	$-0.362764\pi$
$128$		0			0
$129$	−4.00767	+	2.91174i	−0.352856	+	0.256365i
$130$		0			0
$131$	8.20978			0.717292			0.358646	−	0.933474i	$-0.383239\pi$
$131$	8.20978			0.717292			0.358646	+	0.933474i	$0.383239\pi$
$132$		0			0
$133$	3.61385			0.313361
$134$		0			0
$135$	−1.75916	+	1.27810i	−0.151404	+	0.110002i
$136$		0			0
$137$	1.36887	+	4.21294i	0.116950	+	0.359936i	0.992349	−	0.123466i	$-0.0394011\pi$
$137$	1.36887	+	4.21294i	0.116950	+	0.359936i	−0.875399	+	0.483402i	$0.839401\pi$
$138$		0			0
$139$	−3.93677	−	2.86023i	−0.333912	−	0.242602i	0.408176	−	0.912903i	$-0.366165\pi$
$139$	−3.93677	−	2.86023i	−0.333912	−	0.242602i	−0.742089	+	0.670301i	$0.766165\pi$
$140$		0			0
$141$	0.717124	−	2.20708i	0.0603928	−	0.185870i
$142$		0			0
$143$	−2.06662	+	2.59405i	−0.172820	+	0.216925i
$144$		0			0
$145$	1.66410	−	5.12159i	0.138196	−	0.425325i
$146$		0			0
$147$	−5.05903	−	3.67560i	−0.417262	−	0.303158i
$148$		0			0
$149$	−2.98997	−	9.20217i	−0.244948	−	0.753871i	−0.995645	−	0.0932252i	$-0.970282\pi$
$149$	−2.98997	−	9.20217i	−0.244948	−	0.753871i	0.750697	−	0.660646i	$-0.229718\pi$
$150$		0			0
$151$	10.4514	−	7.59342i	0.850526	−	0.617944i	−0.0747647	−	0.997201i	$-0.523821\pi$
$151$	10.4514	−	7.59342i	0.850526	−	0.617944i	0.925291	+	0.379258i	$0.123821\pi$
$152$		0			0
$153$	1.25645			0.101578
$154$		0			0
$155$	−21.2437			−1.70633
$156$		0			0
$157$	−5.38055	+	3.90920i	−0.429415	+	0.311988i	−0.781415	−	0.624012i	$-0.785502\pi$
$157$	−5.38055	+	3.90920i	−0.429415	+	0.311988i	0.352000	+	0.936000i	$0.385502\pi$
$158$		0			0
$159$	0.0120600	+	0.0371167i	0.000956417	+	0.00294355i
$160$		0			0
$161$	−5.29084	−	3.84402i	−0.416977	−	0.302951i
$162$		0			0
$163$	1.16224	−	3.57700i	0.0910334	−	0.280172i	−0.895166	−	0.445732i	$-0.852943\pi$
$163$	1.16224	−	3.57700i	0.0910334	−	0.280172i	0.986200	+	0.165560i	$0.0529433\pi$
$164$		0			0
$165$	3.97588	+	6.01685i	0.309522	+	0.468411i
$166$		0			0
$167$	4.72537	−	14.5432i	0.365660	−	1.12538i	−0.583907	−	0.811820i	$-0.698477\pi$
$167$	4.72537	−	14.5432i	0.365660	−	1.12538i	0.949567	−	0.313565i	$-0.101523\pi$
$168$		0			0
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$		0			0
$171$	−1.29235	−	3.97746i	−0.0988288	−	0.304164i
$172$		0			0
$173$	7.80828	−	5.67304i	0.593652	−	0.431314i	−0.249968	−	0.968254i	$-0.580420\pi$
$173$	7.80828	−	5.67304i	0.593652	−	0.431314i	0.843620	+	0.536941i	$0.180420\pi$
$174$		0			0
$175$	0.234873			0.0177547
$176$		0			0
$177$	0.707290			0.0531632
$178$		0			0
$179$	15.8716	−	11.5314i	1.18630	−	0.861897i	0.193431	−	0.981114i	$-0.438038\pi$
$179$	15.8716	−	11.5314i	1.18630	−	0.861897i	0.992868	+	0.119217i	$0.0380384\pi$
$180$		0			0
$181$	7.79693	+	23.9965i	0.579541	+	1.78364i	0.620166	+	0.784470i	$0.287065\pi$
$181$	7.79693	+	23.9965i	0.579541	+	1.78364i	−0.0406250	+	0.999174i	$0.512935\pi$
$182$		0			0
$183$	0.884955	+	0.642958i	0.0654178	+	0.0475288i
$184$		0			0
$185$	−4.73922	+	14.5858i	−0.348435	+	1.07237i
$186$		0			0
$187$	0.184937	−	4.16306i	0.0135239	−	0.304433i
$188$		0			0
$189$	0.267026	−	0.821821i	0.0194233	−	0.0597787i
$190$		0			0
$191$	−5.58371	−	4.05680i	−0.404023	−	0.293540i	0.367155	−	0.930160i	$-0.380332\pi$
$191$	−5.58371	−	4.05680i	−0.404023	−	0.293540i	−0.771178	+	0.636620i	$0.780332\pi$
$192$		0			0
$193$	0.204992	+	0.630900i	0.0147556	+	0.0454131i	0.958163	−	0.286222i	$-0.0923996\pi$
$193$	0.204992	+	0.630900i	0.0147556	+	0.0454131i	−0.943408	+	0.331635i	$0.892400\pi$
$194$		0			0
$195$	−1.75916	+	1.27810i	−0.125976	+	0.0915269i
$196$		0			0
$197$	22.6850			1.61624			0.808121	−	0.589016i	$-0.200485\pi$
$197$	22.6850			1.61624			0.808121	+	0.589016i	$0.200485\pi$
$198$		0			0
$199$	1.42713			0.101167			0.0505833	−	0.998720i	$-0.483892\pi$
$199$	1.42713			0.101167			0.0505833	+	0.998720i	$0.483892\pi$
$200$		0			0
$201$	5.12363	−	3.72253i	0.361393	−	0.262567i
$202$		0			0
$203$	0.661309	+	2.03530i	0.0464148	+	0.142850i
$204$		0			0
$205$	20.6636	+	15.0130i	1.44321	+	1.04855i
$206$		0			0
$207$	−2.33872	+	7.19784i	−0.162552	+	0.500285i
$208$		0			0
$209$	−13.3690	+	3.69659i	−0.924751	+	0.255699i
$210$		0			0
$211$	−1.56389	+	4.81316i	−0.107663	+	0.331352i	−0.990346	−	0.138616i	$-0.955735\pi$
$211$	−1.56389	+	4.81316i	−0.107663	+	0.331352i	0.882683	+	0.469968i	$0.155735\pi$
$212$		0			0
$213$	−1.58509	−	1.15164i	−0.108609	−	0.0789089i
$214$		0			0
$215$	3.32862	+	10.2444i	0.227010	+	0.698665i
$216$		0			0
$217$	6.82985	−	4.96218i	0.463641	−	0.336855i
$218$		0			0
$219$	−7.20313			−0.486742
$220$		0			0
$221$	1.25645			0.0845179
$222$		0			0
$223$	9.15932	−	6.65464i	0.613353	−	0.445627i	−0.237240	−	0.971451i	$-0.576243\pi$
$223$	9.15932	−	6.65464i	0.613353	−	0.445627i	0.850594	+	0.525824i	$0.176243\pi$
$224$		0			0
$225$	−0.0839932	−	0.258505i	−0.00559955	−	0.0172336i
$226$		0			0
$227$	10.1555	+	7.37837i	0.674041	+	0.489719i	0.871375	−	0.490617i	$-0.163228\pi$
$227$	10.1555	+	7.37837i	0.674041	+	0.489719i	−0.197334	+	0.980336i	$0.563228\pi$
$228$		0			0
$229$	−4.39658	+	13.5313i	−0.290534	+	0.894172i	0.694151	+	0.719829i	$0.255780\pi$
$229$	−4.39658	+	13.5313i	−0.290534	+	0.894172i	−0.984685	+	0.174342i	$0.944220\pi$
$230$		0			0
$231$	−2.68368	−	1.00572i	−0.176573	−	0.0661713i
$232$		0			0
$233$	2.62764	−	8.08704i	0.172142	−	0.529799i	−0.827349	−	0.561688i	$-0.810152\pi$
$233$	2.62764	−	8.08704i	0.172142	−	0.529799i	0.999491	+	0.0318885i	$0.0101522\pi$
$234$		0			0
$235$	−4.08242	−	2.96605i	−0.266308	−	0.193484i
$236$		0			0
$237$	1.53130	+	4.71286i	0.0994686	+	0.306133i
$238$		0			0
$239$	24.0781	−	17.4938i	1.55749	−	1.13158i	0.619452	−	0.785034i	$-0.287355\pi$
$239$	24.0781	−	17.4938i	1.55749	−	1.13158i	0.938033	−	0.346545i	$-0.112645\pi$
$240$		0			0
$241$	26.2785			1.69275			0.846373	−	0.532591i	$-0.178782\pi$
$241$	26.2785			1.69275			0.846373	+	0.532591i	$0.178782\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−11.0006	+	7.99238i	−0.702800	+	0.510614i
$246$		0			0
$247$	−1.29235	−	3.97746i	−0.0822306	−	0.253080i
$248$		0			0
$249$	−1.39710	−	1.01505i	−0.0885374	−	0.0643262i
$250$		0			0
$251$	−2.51004	+	7.72512i	−0.158432	+	0.487605i	−0.998492	−	0.0548884i	$-0.982520\pi$
$251$	−2.51004	+	7.72512i	−0.158432	+	0.487605i	0.840060	+	0.542493i	$0.182520\pi$
$252$		0			0
$253$	23.5048	+	8.80847i	1.47773	+	0.553784i
$254$		0			0
$255$	0.844257	−	2.59836i	0.0528694	−	0.162715i
$256$		0			0
$257$	−21.7467	−	15.7999i	−1.35652	−	0.985571i	−0.998658	−	0.0517969i	$-0.983505\pi$
$257$	−21.7467	−	15.7999i	−1.35652	−	0.985571i	−0.357864	−	0.933774i	$-0.616495\pi$
$258$		0			0
$259$	−1.88335	−	5.79635i	−0.117026	−	0.360168i
$260$		0			0
$261$	2.00359	−	1.45569i	0.124019	−	0.0901050i
$262$		0			0
$263$	−4.15202			−0.256024			−0.128012	−	0.991773i	$-0.540860\pi$
$263$	−4.15202			−0.256024			−0.128012	+	0.991773i	$0.540860\pi$
$264$		0			0
$265$	0.0848616			0.00521301
$266$		0			0
$267$	−1.05245	+	0.764648i	−0.0644088	+	0.0467957i
$268$		0			0
$269$	−5.50690	−	16.9485i	−0.335762	−	1.03337i	−0.966346	−	0.257248i	$-0.917184\pi$
$269$	−5.50690	−	16.9485i	−0.335762	−	1.03337i	0.630584	−	0.776121i	$-0.282816\pi$
$270$		0			0
$271$	−16.4689	−	11.9654i	−1.00042	−	0.726845i	−0.0382390	−	0.999269i	$-0.512175\pi$
$271$	−16.4689	−	11.9654i	−1.00042	−	0.726845i	−0.962177	+	0.272424i	$0.912175\pi$
$272$		0			0
$273$	0.267026	−	0.821821i	0.0161611	−	0.0497389i
$274$		0			0
$275$	−0.868881	+	0.240250i	−0.0523955	+	0.0144876i
$276$		0			0
$277$	2.47967	−	7.63165i	0.148989	−	0.458541i	−0.848513	−	0.529174i	$-0.822502\pi$
$277$	2.47967	−	7.63165i	0.148989	−	0.458541i	0.997502	+	0.0706327i	$0.0225018\pi$
$278$		0			0
$279$	−7.90388	−	5.74250i	−0.473193	−	0.343795i
$280$		0			0
$281$	−0.661438	−	2.03570i	−0.0394581	−	0.121440i	0.929387	−	0.369106i	$-0.120336\pi$
$281$	−0.661438	−	2.03570i	−0.0394581	−	0.121440i	−0.968845	+	0.247667i	$0.920336\pi$
$282$		0			0
$283$	−15.2497	+	11.0795i	−0.906499	+	0.658610i	−0.940127	−	0.340824i	$-0.889294\pi$
$283$	−15.2497	+	11.0795i	−0.906499	+	0.658610i	0.0336277	+	0.999434i	$0.489294\pi$
$284$		0			0
$285$	−9.09383			−0.538672
$286$		0			0
$287$	−10.1501			−0.599144
$288$		0			0
$289$	12.4761	−	9.06443i	0.733890	−	0.533202i
$290$		0			0
$291$	1.39577	+	4.29575i	0.0818216	+	0.251821i
$292$		0			0
$293$	23.3947	+	16.9973i	1.36673	+	0.992990i	0.997984	+	0.0634617i	$0.0202141\pi$
$293$	23.3947	+	16.9973i	1.36673	+	0.992990i	0.368750	+	0.929529i	$0.379786\pi$
$294$		0			0
$295$	0.475256	−	1.46269i	0.0276705	−	0.0851610i
$296$		0			0
$297$	−0.147190	+	3.31336i	−0.00854083	+	0.192260i
$298$		0			0
$299$	−2.33872	+	7.19784i	−0.135252	+	0.416262i
$300$		0			0
$301$	−3.46308	−	2.51608i	−0.199609	−	0.145024i
$302$		0			0
$303$	2.67523	+	8.23351i	0.153688	+	0.473003i
$304$		0			0
$305$	1.92428	−	1.39807i	0.110184	−	0.0800534i
$306$		0			0
$307$	10.9585			0.625433			0.312716	−	0.949847i	$-0.398761\pi$
$307$	10.9585			0.625433			0.312716	+	0.949847i	$0.398761\pi$
$308$		0			0
$309$	−8.25665			−0.469704
$310$		0			0
$311$	−18.5481	+	13.4760i	−1.05177	+	0.764155i	−0.972548	−	0.232702i	$-0.925243\pi$
$311$	−18.5481	+	13.4760i	−1.05177	+	0.764155i	−0.0792209	+	0.996857i	$0.525243\pi$
$312$		0			0
$313$	7.09620	+	21.8399i	0.401101	+	1.23446i	0.924107	+	0.382133i	$0.124811\pi$
$313$	7.09620	+	21.8399i	0.401101	+	1.23446i	−0.523006	+	0.852329i	$0.675189\pi$
$314$		0			0
$315$	−1.52011	−	1.10443i	−0.0856488	−	0.0622275i
$316$		0			0
$317$	−5.73706	+	17.6569i	−0.322226	+	0.991709i	0.650452	+	0.759548i	$0.274580\pi$
$317$	−5.73706	+	17.6569i	−0.322226	+	0.991709i	−0.972677	+	0.232161i	$0.925420\pi$
$318$		0			0
$319$	−4.52832	−	6.85286i	−0.253537	−	0.383687i
$320$		0			0
$321$	−1.32278	+	4.07111i	−0.0738306	+	0.227227i
$322$		0			0
$323$	4.25111	+	3.08861i	0.236538	+	0.171855i
$324$		0			0
$325$	−0.0839932	−	0.258505i	−0.00465911	−	0.0143393i
$326$		0			0
$327$	11.4001	−	8.28268i	0.630429	−	0.458033i
$328$		0			0
$329$	2.00532			0.110557
$330$		0			0
$331$	3.51119			0.192993			0.0964963	−	0.995333i	$-0.469236\pi$
$331$	3.51119			0.192993			0.0964963	+	0.995333i	$0.469236\pi$
$332$		0			0
$333$	−5.70604	+	4.14568i	−0.312689	+	0.227182i
$334$		0			0
$335$	−4.25549	−	13.0971i	−0.232502	−	0.715569i
$336$		0			0
$337$	15.2639	+	11.0899i	0.831480	+	0.604106i	0.919978	−	0.391971i	$-0.128207\pi$
$337$	15.2639	+	11.0899i	0.831480	+	0.604106i	−0.0884976	+	0.996076i	$0.528207\pi$
$338$		0			0
$339$	0.418123	−	1.28685i	0.0227093	−	0.0698921i
$340$		0			0
$341$	−20.1903	+	25.3431i	−1.09337	+	1.37241i
$342$		0			0
$343$	3.53898	−	10.8919i	0.191087	−	0.588105i
$344$		0			0
$345$	13.3138	+	9.67302i	0.716790	+	0.520778i
$346$		0			0
$347$	−2.22292	−	6.84146i	−0.119333	−	0.367269i	0.873493	−	0.486836i	$-0.161849\pi$
$347$	−2.22292	−	6.84146i	−0.119333	−	0.367269i	−0.992826	+	0.119568i	$0.961849\pi$
$348$		0			0
$349$	0.248240	−	0.180357i	0.0132880	−	0.00965429i	−0.581121	−	0.813817i	$-0.697386\pi$
$349$	0.248240	−	0.180357i	0.0132880	−	0.00965429i	0.594409	+	0.804163i	$0.297386\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	14.9026			0.793183			0.396592	−	0.917995i	$-0.370193\pi$
$353$	14.9026			0.793183			0.396592	+	0.917995i	$0.370193\pi$
$354$		0			0
$355$	−3.44669	+	2.50417i	−0.182931	+	0.132907i
$356$		0			0
$357$	0.335504	+	1.03258i	0.0177568	+	0.0546497i
$358$		0			0
$359$	−21.0139	−	15.2675i	−1.10907	−	0.805786i	−0.126552	−	0.991960i	$-0.540391\pi$
$359$	−21.0139	−	15.2675i	−1.10907	−	0.805786i	−0.982517	+	0.186174i	$0.940391\pi$
$360$		0			0
$361$	−0.466504	+	1.43575i	−0.0245528	+	0.0755659i
$362$		0			0
$363$	10.9567	+	0.975386i	0.575076	+	0.0511945i
$364$		0			0
$365$	−4.84006	+	14.8962i	−0.253340	+	0.779702i
$366$		0			0
$367$	25.0935	+	18.2315i	1.30987	+	0.951677i	1.00000		0.000898211i	$0.000285909\pi$
$367$	25.0935	+	18.2315i	1.30987	+	0.951677i	0.309871	+	0.950779i	$0.399714\pi$
$368$		0			0
$369$	3.62980	+	11.1714i	0.188960	+	0.581559i
$370$		0			0
$371$	−0.0272830	+	0.0198223i	−0.00141646	+	0.00102912i
$372$		0			0
$373$	28.8439			1.49348			0.746741	−	0.665115i	$-0.231617\pi$
$373$	28.8439			1.49348			0.746741	+	0.665115i	$0.231617\pi$
$374$		0			0
$375$	−11.4632			−0.591959
$376$		0			0
$377$	2.00359	−	1.45569i	0.103190	−	0.0749719i
$378$		0			0
$379$	−1.18965	−	3.66135i	−0.0611080	−	0.188071i	0.915842	−	0.401538i	$-0.131524\pi$
$379$	−1.18965	−	3.66135i	−0.0611080	−	0.188071i	−0.976950	+	0.213467i	$0.931524\pi$
$380$		0			0
$381$	−13.4001	−	9.73577i	−0.686510	−	0.498778i
$382$		0			0
$383$	8.75714	−	26.9517i	0.447469	−	1.37717i	−0.432284	−	0.901737i	$-0.642292\pi$
$383$	8.75714	−	26.9517i	0.447469	−	1.37717i	0.879753	−	0.475431i	$-0.157708\pi$
$384$		0			0
$385$	−3.88311	+	4.87412i	−0.197902	+	0.248408i
$386$		0			0
$387$	−1.53079	+	4.71130i	−0.0778146	+	0.239489i
$388$		0			0
$389$	5.34138	+	3.88074i	0.270819	+	0.196761i	0.714903	−	0.699224i	$-0.246471\pi$
$389$	5.34138	+	3.88074i	0.270819	+	0.196761i	−0.444084	+	0.895985i	$0.646471\pi$
$390$		0			0
$391$	−2.93848	−	9.04372i	−0.148605	−	0.457361i
$392$		0			0
$393$	6.64185	−	4.82559i	0.335037	−	0.243419i
$394$		0			0
$395$	10.7752			0.542159
$396$		0			0
$397$	−6.90492			−0.346548			−0.173274	−	0.984874i	$-0.555435\pi$
$397$	−6.90492			−0.346548			−0.173274	+	0.984874i	$0.555435\pi$
$398$		0			0
$399$	2.92367	−	2.12417i	0.146367	−	0.106341i
$400$		0			0
$401$	4.61861	+	14.2146i	0.230642	+	0.709844i	0.997670	+	0.0682297i	$0.0217351\pi$
$401$	4.61861	+	14.2146i	0.230642	+	0.709844i	−0.767027	+	0.641614i	$0.778265\pi$
$402$		0			0
$403$	−7.90388	−	5.74250i	−0.393720	−	0.286054i
$404$		0			0
$405$	−0.671939	+	2.06802i	−0.0333889	+	0.102761i
$406$		0			0
$407$	12.8963	+	19.5164i	0.639243	+	0.967390i
$408$		0			0
$409$	−8.65977	+	26.6520i	−0.428198	+	1.31786i	0.471700	+	0.881759i	$0.343641\pi$
$409$	−8.65977	+	26.6520i	−0.428198	+	1.31786i	−0.899898	+	0.436100i	$0.856359\pi$
$410$		0			0
$411$	3.58374	+	2.60374i	0.176773	+	0.128433i
$412$		0			0
$413$	0.188865	+	0.581266i	0.00929343	+	0.0286022i
$414$		0			0
$415$	−3.03790	+	2.20717i	−0.149125	+	0.108346i
$416$		0			0
$417$	−4.86612			−0.238295
$418$		0			0
$419$	12.8564			0.628077			0.314038	−	0.949410i	$-0.398318\pi$
$419$	12.8564			0.628077			0.314038	+	0.949410i	$0.398318\pi$
$420$		0			0
$421$	22.4615	−	16.3193i	1.09471	−	0.795353i	0.114521	−	0.993421i	$-0.463467\pi$
$421$	22.4615	−	16.3193i	1.09471	−	0.795353i	0.980188	+	0.198068i	$0.0634668\pi$
$422$		0			0
$423$	−0.717124	−	2.20708i	−0.0348678	−	0.107312i
$424$		0			0
$425$	0.276290	+	0.200736i	0.0134020	+	0.00973713i
$426$		0			0
$427$	−0.292090	+	0.898961i	−0.0141352	+	0.0435038i
$428$		0			0
$429$	−0.147190	+	3.31336i	−0.00710640	+	0.159970i
$430$		0			0
$431$	6.52139	−	20.0708i	0.314124	−	0.966775i	−0.661989	−	0.749513i	$-0.730288\pi$
$431$	6.52139	−	20.0708i	0.314124	−	0.966775i	0.976113	−	0.217262i	$-0.0697124\pi$
$432$		0			0
$433$	2.40431	+	1.74683i	0.115544	+	0.0839474i	0.644057	−	0.764978i	$-0.277250\pi$
$433$	2.40431	+	1.74683i	0.115544	+	0.0839474i	−0.528513	+	0.848925i	$0.677250\pi$
$434$		0			0
$435$	−1.66410	−	5.12159i	−0.0797877	−	0.245561i
$436$		0			0
$437$	−25.6067	+	18.6043i	−1.22493	+	0.889966i
$438$		0			0
$439$	−8.19906			−0.391320			−0.195660	−	0.980672i	$-0.562685\pi$
$439$	−8.19906			−0.391320			−0.195660	+	0.980672i	$0.562685\pi$
$440$		0			0
$441$	−6.25331			−0.297777
$442$		0			0
$443$	5.25363	−	3.81699i	0.249608	−	0.181351i	−0.455945	−	0.890008i	$-0.650699\pi$
$443$	5.25363	−	3.81699i	0.249608	−	0.181351i	0.705553	+	0.708657i	$0.250699\pi$
$444$		0			0
$445$	0.874124	+	2.69028i	0.0414374	+	0.127531i
$446$		0			0
$447$	−7.82784	−	5.68726i	−0.370244	−	0.268998i
$448$		0			0
$449$	−9.27879	+	28.5572i	−0.437893	+	1.34770i	0.452199	+	0.891917i	$0.350640\pi$
$449$	−9.27879	+	28.5572i	−0.437893	+	1.34770i	−0.890092	+	0.455780i	$0.849360\pi$
$450$		0			0
$451$	37.5491	−	10.3825i	1.76812	−	0.488894i
$452$		0			0
$453$	3.99210	−	12.2864i	0.187565	−	0.577266i
$454$		0			0
$455$	−1.52011	−	1.10443i	−0.0712641	−	0.0517764i
$456$		0			0
$457$	−3.39852	−	10.4596i	−0.158976	−	0.489278i	0.839566	−	0.543258i	$-0.182809\pi$
$457$	−3.39852	−	10.4596i	−0.158976	−	0.489278i	−0.998542	+	0.0539797i	$0.982809\pi$
$458$		0			0
$459$	1.01649	−	0.738522i	0.0474456	−	0.0344713i
$460$		0			0
$461$	17.5812			0.818840			0.409420	−	0.912346i	$-0.365731\pi$
$461$	17.5812			0.818840			0.409420	+	0.912346i	$0.365731\pi$
$462$		0			0
$463$	15.7566			0.732273			0.366136	−	0.930561i	$-0.380680\pi$
$463$	15.7566			0.732273			0.366136	+	0.930561i	$0.380680\pi$
$464$		0			0
$465$	−17.1865	+	12.4867i	−0.797005	+	0.579058i
$466$		0			0
$467$	−2.37317	−	7.30386i	−0.109817	−	0.337982i	0.881014	−	0.473091i	$-0.156862\pi$
$467$	−2.37317	−	7.30386i	−0.109817	−	0.337982i	−0.990831	+	0.135108i	$0.956862\pi$
$468$		0			0
$469$	4.42740	+	3.21669i	0.204438	+	0.148533i
$470$		0			0
$471$	−2.05519	+	6.32522i	−0.0946981	+	0.291451i
$472$		0			0
$473$	15.3849	+	5.76552i	0.707398	+	0.265099i
$474$		0			0
$475$	0.351272	−	1.08110i	0.0161175	−	0.0496045i
$476$		0			0
$477$	0.0315734	+	0.0229394i	0.00144565	+	0.00105032i
$478$		0			0
$479$	1.45541	+	4.47930i	0.0664995	+	0.204664i	0.978785	−	0.204891i	$-0.0656839\pi$
$479$	1.45541	+	4.47930i	0.0664995	+	0.204664i	−0.912285	+	0.409555i	$0.865684\pi$
$480$		0			0
$481$	−5.70604	+	4.14568i	−0.260173	+	0.189027i
$482$		0			0
$483$	−6.53984			−0.297573
$484$		0			0
$485$	9.82154			0.445973
$486$		0			0
$487$	−28.5018	+	20.7078i	−1.29154	+	0.938358i	−0.999835	−	0.0181505i	$-0.994222\pi$
$487$	−28.5018	+	20.7078i	−1.29154	+	0.938358i	−0.291704	+	0.956509i	$0.594222\pi$
$488$		0			0
$489$	−1.16224	−	3.57700i	−0.0525581	−	0.161757i
$490$		0			0
$491$	21.4407	+	15.5776i	0.967604	+	0.703005i	0.954904	−	0.296914i	$-0.0959575\pi$
$491$	21.4407	+	15.5776i	0.967604	+	0.703005i	0.0126997	+	0.999919i	$0.495957\pi$
$492$		0			0
$493$	−0.961563	+	2.95939i	−0.0433066	+	0.133284i
$494$		0			0
$495$	6.75317	+	2.53077i	0.303533	+	0.113749i
$496$		0			0
$497$	0.523179	−	1.61018i	0.0234678	−	0.0722265i
$498$		0			0
$499$	−3.88810	−	2.82487i	−0.174055	−	0.126458i	0.497347	−	0.867552i	$-0.334308\pi$
$499$	−3.88810	−	2.82487i	−0.174055	−	0.126458i	−0.671402	+	0.741093i	$0.734308\pi$
$500$		0			0
$501$	−4.72537	−	14.5432i	−0.211114	−	0.649741i
$502$		0			0
$503$	26.3378	−	19.1355i	1.17434	−	0.853210i	0.182821	−	0.983146i	$-0.441477\pi$
$503$	26.3378	−	19.1355i	1.17434	−	0.853210i	0.991522	+	0.129936i	$0.0414772\pi$
$504$		0			0
$505$	18.8246			0.837685
$506$		0			0
$507$	−1.00000			−0.0444116
$508$		0			0
$509$	33.3020	−	24.1953i	1.47609	−	1.07244i	0.497295	−	0.867582i	$-0.334327\pi$
$509$	33.3020	−	24.1953i	1.47609	−	1.07244i	0.978792	−	0.204858i	$-0.0656732\pi$
$510$		0			0
$511$	−1.92342	−	5.91968i	−0.0850872	−	0.261871i
$512$		0			0
$513$	−3.38343	−	2.45820i	−0.149382	−	0.108532i
$514$		0			0
$515$	−5.54796	+	17.0749i	−0.244473	+	0.752409i
$516$		0			0
$517$	−7.41841	+	2.05123i	−0.326261	+	0.0902130i
$518$		0			0
$519$	2.98250	−	9.17918i	0.130917	−	0.402921i
$520$		0			0
$521$	9.25027	+	6.72072i	0.405262	+	0.294440i	0.771681	−	0.636010i	$-0.219416\pi$
$521$	9.25027	+	6.72072i	0.405262	+	0.294440i	−0.366419	+	0.930450i	$0.619416\pi$
$522$		0			0
$523$	−0.578383	−	1.78008i	−0.0252909	−	0.0778375i	0.937614	−	0.347677i	$-0.113029\pi$
$523$	−0.578383	−	1.78008i	−0.0252909	−	0.0778375i	−0.962905	+	0.269839i	$0.913029\pi$
$524$		0			0
$525$	0.190016	−	0.138055i	0.00829299	−	0.00602521i
$526$		0			0
$527$	12.2752			0.534715
$528$		0			0
$529$	34.2786			1.49037
$530$		0			0
$531$	0.572210	−	0.415735i	0.0248318	−	0.0180414i
$532$		0			0
$533$	3.62980	+	11.1714i	0.157224	+	0.483887i
$534$		0			0
$535$	7.53029	+	5.47107i	0.325563	+	0.236535i
$536$		0			0
$537$	6.06241	−	18.6582i	0.261612	−	0.805160i
$538$		0			0
$539$	−0.920424	+	20.7194i	−0.0396455	+	0.892449i
$540$		0			0
$541$	−6.17451	+	19.0032i	−0.265463	+	0.817010i	0.726124	+	0.687564i	$0.241320\pi$
$541$	−6.17451	+	19.0032i	−0.265463	+	0.817010i	−0.991586	+	0.129446i	$0.958680\pi$
$542$		0			0
$543$	20.4126	+	14.8306i	0.875990	+	0.636444i
$544$		0			0
$545$	−9.46852	−	29.1411i	−0.405587	−	1.24827i
$546$		0			0
$547$	−11.4594	+	8.32571i	−0.489967	+	0.355982i	−0.805171	−	0.593042i	$-0.797927\pi$
$547$	−11.4594	+	8.32571i	−0.489967	+	0.355982i	0.315205	+	0.949024i	$0.397927\pi$
$548$		0			0
$549$	1.09386			0.0466850
$550$		0			0
$551$	10.3574			0.441239
$552$		0			0
$553$	−3.46423	+	2.51691i	−0.147314	+	0.107030i
$554$		0			0
$555$	4.73922	+	14.5858i	0.201169	+	0.619134i
$556$		0			0
$557$	0.765629	+	0.556262i	0.0324408	+	0.0235696i	0.603887	−	0.797070i	$-0.293618\pi$
$557$	0.765629	+	0.556262i	0.0324408	+	0.0235696i	−0.571447	+	0.820639i	$0.693618\pi$
$558$		0			0
$559$	−1.53079	+	4.71130i	−0.0647456	+	0.199267i
$560$		0			0
$561$	−2.29737	−	3.47669i	−0.0969951	−	0.146786i
$562$		0			0
$563$	−12.5759	+	38.7047i	−0.530012	+	1.63121i	0.224174	+	0.974549i	$0.428032\pi$
$563$	−12.5759	+	38.7047i	−0.530012	+	1.63121i	−0.754186	+	0.656661i	$0.771968\pi$
$564$		0			0
$565$	−2.38027	−	1.72937i	−0.100139	−	0.0727551i
$566$		0			0
$567$	−0.267026	−	0.821821i	−0.0112140	−	0.0345133i
$568$		0			0
$569$	−29.3164	+	21.2996i	−1.22901	+	0.892925i	−0.996815	−	0.0797456i	$-0.974589\pi$
$569$	−29.3164	+	21.2996i	−1.22901	+	0.892925i	−0.232190	+	0.972670i	$0.574589\pi$
$570$		0			0
$571$	6.59244			0.275885			0.137943	−	0.990440i	$-0.455951\pi$
$571$	6.59244			0.275885			0.137943	+	0.990440i	$0.455951\pi$
$572$		0			0
$573$	−6.90185			−0.288329
$574$		0			0
$575$	−1.66424	+	1.20914i	−0.0694036	+	0.0504246i
$576$		0			0
$577$	11.3398	+	34.9003i	0.472082	+	1.45292i	0.849853	+	0.527020i	$0.176691\pi$
$577$	11.3398	+	34.9003i	0.472082	+	1.45292i	−0.377770	+	0.925899i	$0.623309\pi$
$578$		0			0
$579$	0.536675	+	0.389917i	0.0223035	+	0.0162044i
$580$		0			0
$581$	0.461129	−	1.41921i	0.0191309	−	0.0588787i
$582$		0			0
$583$	0.0806537	−	0.101237i	0.00334034	−	0.00419283i
$584$		0			0
$585$	−0.671939	+	2.06802i	−0.0277813	+	0.0855019i
$586$		0			0
$587$	0.800349	+	0.581487i	0.0330339	+	0.0240006i	0.604180	−	0.796848i	$-0.293501\pi$
$587$	0.800349	+	0.581487i	0.0330339	+	0.0240006i	−0.571146	+	0.820849i	$0.693501\pi$
$588$		0			0
$589$	−12.6260	−	38.8587i	−0.520244	−	1.60114i
$590$		0			0
$591$	18.3526	−	13.3339i	0.754925	−	0.548485i
$592$		0			0
$593$	−6.53611			−0.268406			−0.134203	−	0.990954i	$-0.542847\pi$
$593$	−6.53611			−0.268406			−0.134203	+	0.990954i	$0.542847\pi$
$594$		0			0
$595$	2.36082			0.0967843
$596$		0			0
$597$	1.15457	−	0.838847i	0.0472536	−	0.0343317i
$598$		0			0
$599$	−5.26766	−	16.2122i	−0.215231	−	0.662412i	−0.999137	−	0.0415331i	$-0.986776\pi$
$599$	−5.26766	−	16.2122i	−0.215231	−	0.662412i	0.783906	−	0.620879i	$-0.213224\pi$
$600$		0			0
$601$	−22.8045	−	16.5684i	−0.930214	−	0.675840i	0.0158309	−	0.999875i	$-0.494961\pi$
$601$	−22.8045	−	16.5684i	−0.930214	−	0.675840i	−0.946045	+	0.324034i	$0.894961\pi$
$602$		0			0
$603$	1.95705	−	6.02319i	0.0796973	−	0.245283i
$604$		0			0
$605$	9.37933	−	22.0032i	0.381324	−	0.894556i
$606$		0			0
$607$	11.4185	−	35.1425i	0.463462	−	1.42639i	−0.397444	−	0.917626i	$-0.630103\pi$
$607$	11.4185	−	35.1425i	0.463462	−	1.42639i	0.860906	−	0.508764i	$-0.169897\pi$
$608$		0			0
$609$	1.73133	+	1.25788i	0.0701570	+	0.0509720i
$610$		0			0
$611$	−0.717124	−	2.20708i	−0.0290118	−	0.0892890i
$612$		0			0
$613$	12.9752	−	9.42704i	0.524063	−	0.380754i	−0.294069	−	0.955784i	$-0.595010\pi$
$613$	12.9752	−	9.42704i	0.524063	−	0.380754i	0.818132	+	0.575030i	$0.195010\pi$
$614$		0			0
$615$	25.5416			1.02994
$616$		0			0
$617$	−28.8994			−1.16345			−0.581723	−	0.813387i	$-0.697621\pi$
$617$	−28.8994			−1.16345			−0.581723	+	0.813387i	$0.697621\pi$
$618$		0			0
$619$	16.9009	−	12.2792i	0.679303	−	0.493543i	−0.193823	−	0.981036i	$-0.562089\pi$
$619$	16.9009	−	12.2792i	0.679303	−	0.493543i	0.873126	+	0.487494i	$0.162089\pi$
$620$		0			0
$621$	2.33872	+	7.19784i	0.0938496	+	0.288839i
$622$		0			0
$623$	−0.909435	−	0.660743i	−0.0364357	−	0.0264721i
$624$		0			0
$625$	−7.28263	+	22.4136i	−0.291305	+	0.896545i
$626$		0			0
$627$	−8.64292	+	10.8487i	−0.345165	+	0.433255i
$628$		0			0
$629$	2.73845	−	8.42808i	0.109189	−	0.336049i
$630$		0			0
$631$	−18.0966	−	13.1480i	−0.720416	−	0.523413i	0.166101	−	0.986109i	$-0.446882\pi$
$631$	−18.0966	−	13.1480i	−0.720416	−	0.523413i	−0.886517	+	0.462696i	$0.846882\pi$
$632$		0			0
$633$	1.56389	+	4.81316i	0.0621591	+	0.191306i
$634$		0			0
$635$	−29.1378	+	21.1698i	−1.15630	+	0.840100i
$636$		0			0
$637$	−6.25331			−0.247765
$638$		0			0
$639$	−1.95928			−0.0775080
$640$		0			0
$641$	−12.6765	+	9.21002i	−0.500692	+	0.363774i	−0.809281	−	0.587422i	$-0.800143\pi$
$641$	−12.6765	+	9.21002i	−0.500692	+	0.363774i	0.308590	+	0.951195i	$0.400143\pi$
$642$		0			0
$643$	−11.7429	−	36.1411i	−0.463096	−	1.42526i	−0.861361	−	0.507994i	$-0.830387\pi$
$643$	−11.7429	−	36.1411i	−0.463096	−	1.42526i	0.398264	−	0.917271i	$-0.369613\pi$
$644$		0			0
$645$	8.71444	+	6.33141i	0.343131	+	0.249299i
$646$		0			0
$647$	−4.24738	+	13.0721i	−0.166982	+	0.513918i	−0.999177	−	0.0405656i	$-0.987084\pi$
$647$	−4.24738	+	13.0721i	−0.166982	+	0.513918i	0.832195	+	0.554483i	$0.187084\pi$
$648$		0			0
$649$	−1.29325	−	1.95713i	−0.0507647	−	0.0768240i
$650$		0			0
$651$	2.60877	−	8.02897i	0.102246	−	0.314680i
$652$		0			0
$653$	−29.4264	−	21.3795i	−1.15154	−	0.836646i	−0.162859	−	0.986649i	$-0.552072\pi$
$653$	−29.4264	−	21.3795i	−1.15154	−	0.836646i	−0.988685	+	0.150003i	$0.952072\pi$
$654$		0			0
$655$	−5.51647	−	16.9780i	−0.215546	−	0.663384i
$656$		0			0
$657$	−5.82745	+	4.23389i	−0.227351	+	0.165180i
$658$		0			0
$659$	0.389411			0.0151693			0.00758465	−	0.999971i	$-0.497586\pi$
$659$	0.389411			0.0151693			0.00758465	+	0.999971i	$0.497586\pi$
$660$		0			0
$661$	−28.0796			−1.09217			−0.546086	−	0.837729i	$-0.683883\pi$
$661$	−28.0796			−1.09217			−0.546086	+	0.837729i	$0.683883\pi$
$662$		0			0
$663$	1.01649	−	0.738522i	0.0394771	−	0.0286818i
$664$		0			0
$665$	−2.42829	−	7.47351i	−0.0941650	−	0.289810i
$666$		0			0
$667$	−15.1637	−	11.0171i	−0.587140	−	0.426582i
$668$		0			0
$669$	3.49855	−	10.7674i	0.135262	−	0.416293i
$670$		0			0
$671$	0.161006	−	3.62436i	0.00621556	−	0.139917i
$672$		0			0
$673$	−6.90154	+	21.2407i	−0.266035	+	0.818771i	0.725419	+	0.688308i	$0.241646\pi$
$673$	−6.90154	+	21.2407i	−0.266035	+	0.818771i	−0.991453	+	0.130463i	$0.958354\pi$
$674$		0			0
$675$	−0.219897	−	0.159765i	−0.00846385	−	0.00614934i
$676$		0			0
$677$	−7.67214	−	23.6124i	−0.294864	−	0.907499i	−0.983267	−	0.182170i	$-0.941688\pi$
$677$	−7.67214	−	23.6124i	−0.294864	−	0.907499i	0.688403	−	0.725329i	$-0.258312\pi$
$678$		0			0
$679$	−3.15763	+	2.29415i	−0.121179	+	0.0880414i
$680$		0			0
$681$	12.5528			0.481025
$682$		0			0
$683$	−19.9055			−0.761662			−0.380831	−	0.924645i	$-0.624362\pi$
$683$	−19.9055			−0.761662			−0.380831	+	0.924645i	$0.624362\pi$
$684$		0			0
$685$	7.79263	−	5.66167i	0.297741	−	0.216321i
$686$		0			0
$687$	4.39658	+	13.5313i	0.167740	+	0.516250i
$688$		0			0
$689$	0.0315734	+	0.0229394i	0.00120285	+	0.000873922i
$690$		0			0
$691$	−13.5432	+	41.6816i	−0.515206	+	1.58564i	0.267701	+	0.963502i	$0.413736\pi$
$691$	−13.5432	+	41.6816i	−0.515206	+	1.58564i	−0.782907	+	0.622139i	$0.786264\pi$
$692$		0			0
$693$	−2.76229	+	0.763788i	−0.104931	+	0.0290139i
$694$		0			0
$695$	−3.26973	+	10.0632i	−0.124028	+	0.381719i
$696$		0			0
$697$	−11.9400	−	8.67490i	−0.452259	−	0.328585i
$698$		0			0
$699$	−2.62764	−	8.08704i	−0.0993864	−	0.305880i
$700$		0			0
$701$	25.1485	−	18.2715i	0.949847	−	0.690104i	−0.000923437	−	1.00000i	$-0.500294\pi$
$701$	25.1485	−	18.2715i	0.949847	−	0.690104i	0.950771	+	0.309895i	$0.100294\pi$
$702$		0			0
$703$	−29.4969			−1.11250
$704$		0			0
$705$	−5.04615			−0.190049
$706$		0			0
$707$	−6.05212	+	4.39712i	−0.227613	+	0.165371i
$708$		0			0
$709$	−4.23134	−	13.0227i	−0.158911	−	0.489079i	0.839625	−	0.543167i	$-0.182775\pi$
$709$	−4.23134	−	13.0227i	−0.158911	−	0.489079i	−0.998536	+	0.0540878i	$0.982775\pi$
$710$		0			0
$711$	4.00900	+	2.91271i	0.150349	+	0.109235i
$712$		0			0
$713$	−22.8487	+	70.3210i	−0.855689	+	2.63354i
$714$		0			0
$715$	6.75317	+	2.53077i	0.252554	+	0.0946453i
$716$		0			0
$717$	9.19703	−	28.3056i	0.343469	−	1.05709i
$718$		0			0
$719$	20.4694	+	14.8719i	0.763380	+	0.554628i	0.899945	−	0.436003i	$-0.143606\pi$
$719$	20.4694	+	14.8719i	0.763380	+	0.554628i	−0.136565	+	0.990631i	$0.543606\pi$
$720$		0			0
$721$	−2.20474	−	6.78549i	−0.0821088	−	0.252705i
$722$		0			0
$723$	21.2597	−	15.4461i	0.790658	−	0.574447i
$724$		0			0
$725$	0.673151			0.0250002
$726$		0			0
$727$	−42.4253			−1.57347			−0.786733	−	0.617293i	$-0.788229\pi$
$727$	−42.4253			−1.57347			−0.786733	+	0.617293i	$0.788229\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−1.92336	−	5.91950i	−0.0711382	−	0.218941i
$732$		0			0
$733$	7.55400	+	5.48831i	0.279013	+	0.202715i	0.718487	−	0.695540i	$-0.244835\pi$
$733$	7.55400	+	5.48831i	0.279013	+	0.202715i	−0.439474	+	0.898256i	$0.644835\pi$
$734$		0			0
$735$	−4.20184	+	12.9319i	−0.154987	+	0.477002i
$736$		0			0
$737$	−19.6689	−	7.37096i	−0.724514	−	0.271513i
$738$		0			0
$739$	−5.03638	+	15.5004i	−0.185266	+	0.570191i	−0.999953	−	0.00971077i	$-0.996909\pi$
$739$	−5.03638	+	15.5004i	−0.185266	+	0.570191i	0.814687	+	0.579901i	$0.196909\pi$
$740$		0			0
$741$	−3.38343	−	2.45820i	−0.124293	−	0.0903044i
$742$		0			0
$743$	−0.912872	−	2.80953i	−0.0334900	−	0.103072i	0.932914	−	0.360099i	$-0.117257\pi$
$743$	−0.912872	−	2.80953i	−0.0334900	−	0.103072i	−0.966404	+	0.257027i	$0.917257\pi$
$744$		0			0
$745$	−17.0212	+	12.3666i	−0.623607	+	0.453077i
$746$		0			0
$747$	−1.72691			−0.0631842
$748$		0			0
$749$	−3.69894			−0.135156
$750$		0			0
$751$	22.8558	−	16.6057i	0.834021	−	0.605952i	−0.0866727	−	0.996237i	$-0.527623\pi$
$751$	22.8558	−	16.6057i	0.834021	−	0.605952i	0.920694	+	0.390285i	$0.127623\pi$
$752$		0			0
$753$	2.51004	+	7.72512i	0.0914710	+	0.281519i
$754$		0			0
$755$	−22.7260	−	16.5114i	−0.827085	−	0.600913i
$756$		0			0
$757$	−15.1399	+	46.5958i	−0.550269	+	1.69355i	0.157852	+	0.987463i	$0.449543\pi$
$757$	−15.1399	+	46.5958i	−0.550269	+	1.69355i	−0.708121	+	0.706091i	$0.750457\pi$
$758$		0			0
$759$	24.1933	−	6.68957i	0.878160	−	0.242816i
$760$		0			0
$761$	6.77408	−	20.8485i	0.245560	−	0.755756i	−0.749984	−	0.661456i	$-0.769939\pi$
$761$	6.77408	−	20.8485i	0.245560	−	0.755756i	0.995544	−	0.0943001i	$-0.0300613\pi$
$762$		0			0
$763$	9.85102	+	7.15718i	0.356631	+	0.259107i
$764$		0			0
$765$	−0.844257	−	2.59836i	−0.0305242	−	0.0939438i
$766$		0			0
$767$	0.572210	−	0.415735i	0.0206613	−	0.0150113i
$768$		0			0
$769$	25.9247			0.934869			0.467434	−	0.884028i	$-0.345178\pi$
$769$	25.9247			0.934869			0.467434	+	0.884028i	$0.345178\pi$
$770$		0			0
$771$	−26.8804			−0.968074
$772$		0			0
$773$	28.7360	−	20.8779i	1.03356	−	0.750927i	0.0645439	−	0.997915i	$-0.479441\pi$
$773$	28.7360	−	20.8779i	1.03356	−	0.750927i	0.969019	+	0.246988i	$0.0794407\pi$
$774$		0			0
$775$	−0.820591	−	2.52552i	−0.0294765	−	0.0907194i
$776$		0			0
$777$	−4.93067	−	3.58234i	−0.176887	−	0.128516i
$778$		0			0
$779$	−15.1804	+	46.7204i	−0.543894	+	1.67393i
$780$		0			0
$781$	−0.288387	+	6.49181i	−0.0103193	+	0.232295i
$782$		0			0
$783$	0.765302	−	2.35536i	0.0273497	−	0.0841736i
$784$		0			0
$785$	11.6997	+	8.50033i	0.417580	+	0.303390i
$786$		0			0
$787$	−16.8709	−	51.9233i	−0.601383	−	1.85087i	−0.519966	−	0.854187i	$-0.674055\pi$
$787$	−16.8709	−	51.9233i	−0.601383	−	1.85087i	−0.0814174	−	0.996680i	$-0.525945\pi$
$788$		0			0
$789$	−3.35905	+	2.44050i	−0.119585	+	0.0868839i
$790$		0			0
$791$	1.16921			0.0415723
$792$		0			0
$793$	1.09386			0.0388443
$794$		0			0
$795$	0.0686545	−	0.0498804i	0.00243492	−	0.00176908i
$796$		0			0
$797$	−13.0484	−	40.1589i	−0.462199	−	1.42250i	−0.862471	−	0.506106i	$-0.831084\pi$
$797$	−13.0484	−	40.1589i	−0.462199	−	1.42250i	0.400272	−	0.916396i	$-0.368916\pi$
$798$		0			0
$799$	2.35893	+	1.71386i	0.0834529	+	0.0606321i
$800$		0			0
$801$	−0.401999	+	1.23723i	−0.0142039	+	0.0437152i
$802$		0			0
$803$	13.1706	+	19.9316i	0.464782	+	0.703371i
$804$		0			0
$805$	−4.39437	+	13.5245i	−0.154881	+	0.476676i
$806$		0			0
$807$	−14.4173	−	10.4748i	−0.507512	−	0.368729i
$808$		0			0
$809$	−4.89465	−	15.0642i	−0.172087	−	0.529628i	0.827402	−	0.561611i	$-0.189818\pi$
$809$	−4.89465	−	15.0642i	−0.172087	−	0.529628i	−0.999488	+	0.0319821i	$0.989818\pi$
$810$		0			0
$811$	12.1806	−	8.84969i	0.427717	−	0.310755i	−0.353018	−	0.935616i	$-0.614845\pi$
$811$	12.1806	−	8.84969i	0.427717	−	0.310755i	0.780735	+	0.624862i	$0.214845\pi$
$812$		0			0
$813$	−20.3567			−0.713941
$814$		0			0
$815$	−8.17824			−0.286471
$816$		0			0
$817$	−16.7607	+	12.1773i	−0.586381	+	0.426031i
$818$		0			0
$819$	−0.267026	−	0.821821i	−0.00933064	−	0.0287168i
$820$		0			0
$821$	−0.606630	−	0.440742i	−0.0211715	−	0.0153820i	0.577149	−	0.816639i	$-0.304165\pi$
$821$	−0.606630	−	0.440742i	−0.0211715	−	0.0153820i	−0.598321	+	0.801257i	$0.704165\pi$
$822$		0			0
$823$	1.24396	−	3.82850i	0.0433616	−	0.133453i	−0.927032	−	0.374982i	$-0.877649\pi$
$823$	1.24396	−	3.82850i	0.0433616	−	0.133453i	0.970394	+	0.241529i	$0.0776489\pi$
$824$		0			0
$825$	−0.561724	+	0.705082i	−0.0195567	+	0.0245478i
$826$		0			0
$827$	13.3584	−	41.1128i	0.464516	−	1.42963i	−0.395074	−	0.918649i	$-0.629281\pi$
$827$	13.3584	−	41.1128i	0.464516	−	1.42963i	0.859590	−	0.510984i	$-0.170719\pi$
$828$		0			0
$829$	15.0256	+	10.9168i	0.521861	+	0.379154i	0.817305	−	0.576206i	$-0.195467\pi$
$829$	15.0256	+	10.9168i	0.521861	+	0.379154i	−0.295443	+	0.955360i	$0.595467\pi$
$830$		0			0
$831$	−2.47967	−	7.63165i	−0.0860189	−	0.264739i
$832$		0			0
$833$	6.35641	−	4.61821i	0.220237	−	0.160011i
$834$		0			0
$835$	−33.2507			−1.15069
$836$		0			0
$837$	−9.76973			−0.337691
$838$		0			0
$839$	45.1986	−	32.8387i	1.56043	−	1.13372i	0.624775	−	0.780805i	$-0.285191\pi$
$839$	45.1986	−	32.8387i	1.56043	−	1.13372i	0.935656	−	0.352914i	$-0.114809\pi$
$840$		0			0
$841$	−7.06617	−	21.7474i	−0.243661	−	0.749911i
$842$		0			0
$843$	−1.73167	−	1.25813i	−0.0596418	−	0.0433323i
$844$		0			0
$845$	−0.671939	+	2.06802i	−0.0231154	+	0.0711419i
$846$		0			0
$847$	2.12412	+	9.26488i	0.0729857	+	0.318345i
$848$		0			0
$849$	−5.82486	+	17.9271i	−0.199909	+	0.615256i
$850$		0			0
$851$	43.1848	+	31.3756i	1.48036	+	1.07554i
$852$		0			0
$853$	4.21664	+	12.9775i	0.144375	+	0.444341i	0.996930	−	0.0782967i	$-0.0249482\pi$
$853$	4.21664	+	12.9775i	0.144375	+	0.444341i	−0.852555	+	0.522637i	$0.824948\pi$
$854$		0			0
$855$	−7.35706	+	5.34522i	−0.251606	+	0.182803i
$856$		0			0
$857$	−30.5803			−1.04460			−0.522302	−	0.852761i	$-0.674927\pi$
$857$	−30.5803			−1.04460			−0.522302	+	0.852761i	$0.674927\pi$
$858$		0			0
$859$	−39.2668			−1.33977			−0.669884	−	0.742466i	$-0.733656\pi$
$859$	−39.2668			−1.33977			−0.669884	+	0.742466i	$0.733656\pi$
$860$		0			0
$861$	−8.21164	+	5.96610i	−0.279852	+	0.203324i
$862$		0			0
$863$	−9.06284	−	27.8925i	−0.308503	−	0.949473i	−0.978347	−	0.206972i	$-0.933639\pi$
$863$	−9.06284	−	27.8925i	−0.308503	−	0.949473i	0.669844	−	0.742502i	$-0.266361\pi$
$864$		0			0
$865$	−16.9786	−	12.3357i	−0.577291	−	0.419426i
$866$		0			0
$867$	4.76545	−	14.6666i	0.161843	−	0.498103i
$868$		0			0
$869$	10.2409	−	12.8545i	0.347399	−	0.436060i
$870$		0			0
$871$	1.95705	−	6.02319i	0.0663122	−	0.204088i
$872$		0			0
$873$	3.65418	+	2.65492i	0.123675	+	0.0898553i
$874$		0			0
$875$	−3.06098	−	9.42073i	−0.103480	−	0.318479i
$876$		0			0
$877$	−37.1721	+	27.0071i	−1.25521	+	0.911964i	−0.998512	−	0.0545271i	$-0.982635\pi$
$877$	−37.1721	+	27.0071i	−1.25521	+	0.911964i	−0.256699	+	0.966491i	$0.582635\pi$
$878$		0			0
$879$	28.9175			0.975362
$880$		0			0
$881$	−50.4297			−1.69902			−0.849509	−	0.527574i	$-0.823102\pi$
$881$	−50.4297			−1.69902			−0.849509	+	0.527574i	$0.823102\pi$
$882$		0			0
$883$	−25.8742	+	18.7987i	−0.870737	+	0.632628i	−0.930785	−	0.365568i	$-0.880875\pi$
$883$	−25.8742	+	18.7987i	−0.870737	+	0.632628i	0.0600475	+	0.998196i	$0.480875\pi$
$884$		0			0
$885$	−0.475256	−	1.46269i	−0.0159756	−	0.0491677i
$886$		0			0
$887$	−27.8886	−	20.2622i	−0.936407	−	0.680339i	0.0111463	−	0.999938i	$-0.496452\pi$
$887$	−27.8886	−	20.2622i	−0.936407	−	0.680339i	−0.947553	+	0.319599i	$0.896452\pi$
$888$		0			0
$889$	4.42288	−	13.6122i	0.148339	−	0.456539i
$890$		0			0
$891$	1.82846	+	2.76708i	0.0612558	+	0.0927006i
$892$		0			0
$893$	2.99912	−	9.23034i	0.100362	−	0.308882i
$894$		0			0
$895$	−34.5119	−	25.0743i	−1.15360	−	0.838142i
$896$		0			0
$897$	2.33872	+	7.19784i	0.0780876	+	0.240329i
$898$		0			0
$899$	19.5745	−	14.2217i	0.652846	−	0.474321i
$900$		0			0
$901$	−0.0490353			−0.00163360
$902$		0			0
$903$	−4.28061			−0.142450
$904$		0			0
$905$	44.3861	−	32.2484i	1.47544	−	1.07197i
$906$		0			0
$907$	6.05220	+	18.6268i	0.200960	+	0.618492i	0.999855	+	0.0170212i	$0.00541827\pi$
$907$	6.05220	+	18.6268i	0.200960	+	0.618492i	−0.798895	+	0.601471i	$0.794582\pi$
$908$		0			0
$909$	7.00384	+	5.08859i	0.232303	+	0.168778i
$910$		0			0
$911$	4.99354	−	15.3685i	0.165443	−	0.509182i	−0.833625	−	0.552330i	$-0.813739\pi$
$911$	4.99354	−	15.3685i	0.165443	−	0.509182i	0.999069	+	0.0431483i	$0.0137388\pi$
$912$		0			0
$913$	−0.254183	+	5.72186i	−0.00841224	+	0.189366i
$914$		0			0
$915$	0.735010	−	2.26213i	0.0242987	−	0.0747837i
$916$		0			0
$917$	5.73932	+	4.16986i	0.189529	+	0.137701i
$918$		0			0
$919$	−4.92190	−	15.1480i	−0.162358	−	0.499688i	0.836474	−	0.548007i	$-0.184613\pi$
$919$	−4.92190	−	15.1480i	−0.162358	−	0.499688i	−0.998832	+	0.0483196i	$0.984613\pi$
$920$		0			0
$921$	8.86559	−	6.44123i	0.292131	−	0.212246i
$922$		0			0
$923$	−1.95928			−0.0644906
$924$		0			0
$925$	−1.91708			−0.0630331
$926$		0			0
$927$	−6.67977	+	4.85314i	−0.219392	+	0.159398i
$928$		0			0
$929$	−11.2159	−	34.5189i	−0.367981	−	1.13253i	−0.948093	−	0.317993i	$-0.896991\pi$
$929$	−11.2159	−	34.5189i	−0.367981	−	1.13253i	0.580112	−	0.814537i	$-0.303009\pi$
$930$		0			0
$931$	−21.1576	−	15.3719i	−0.693413	−	0.503794i
$932$		0			0
$933$	−7.08476	+	21.8047i	−0.231945	+	0.713852i
$934$		0			0
$935$	−8.73355	+	2.41487i	−0.285618	+	0.0789748i
$936$		0			0
$937$	6.49558	−	19.9913i	0.212201	−	0.653089i	−0.787139	−	0.616776i	$-0.788439\pi$
$937$	6.49558	−	19.9913i	0.212201	−	0.653089i	0.999340	−	0.0363133i	$-0.0115614\pi$
$938$		0			0
$939$	18.5781	+	13.4978i	0.606273	+	0.440483i
$940$		0			0
$941$	0.434518	+	1.33731i	0.0141649	+	0.0435950i	0.957889	−	0.287138i	$-0.0927039\pi$
$941$	0.434518	+	1.33731i	0.0141649	+	0.0435950i	−0.943724	+	0.330733i	$0.892704\pi$
$942$		0			0
$943$	71.9208	−	52.2535i	2.34206	−	1.70161i
$944$		0			0
$945$	−1.87896			−0.0611227
$946$		0			0
$947$	−37.3688			−1.21432			−0.607162	−	0.794578i	$-0.707692\pi$
$947$	−37.3688			−1.21432			−0.607162	+	0.794578i	$0.707692\pi$
$948$		0			0
$949$	−5.82745	+	4.23389i	−0.189167	+	0.137438i
$950$		0			0
$951$	5.73706	+	17.6569i	0.186037	+	0.572563i
$952$		0			0
$953$	25.8866	+	18.8077i	0.838550	+	0.609242i	0.921965	−	0.387273i	$-0.126583\pi$
$953$	25.8866	+	18.8077i	0.838550	+	0.609242i	−0.0834153	+	0.996515i	$0.526583\pi$
$954$		0			0
$955$	−4.63762	+	14.2731i	−0.150070	+	0.461868i
$956$		0			0
$957$	−7.69150	−	2.88240i	−0.248631	−	0.0931749i
$958$		0			0
$959$	−1.18286	+	3.64046i	−0.0381964	+	0.117557i
$960$		0			0
$961$	−52.1392	−	37.8814i	−1.68191	−	1.22198i
$962$		0			0
$963$	1.32278	+	4.07111i	0.0426261	+	0.131190i
$964$		0			0
$965$	1.16697	−	0.847852i	0.0375660	−	0.0272933i
$966$		0			0
$967$	−38.9624			−1.25295			−0.626473	−	0.779443i	$-0.715502\pi$
$967$	−38.9624			−1.25295			−0.626473	+	0.779443i	$0.715502\pi$
$968$		0			0
$969$	5.25465			0.168804
$970$		0			0
$971$	30.1805	−	21.9274i	0.968540	−	0.703685i	0.0134213	−	0.999910i	$-0.495728\pi$
$971$	30.1805	−	21.9274i	0.968540	−	0.703685i	0.955118	+	0.296225i	$0.0957277\pi$
$972$		0			0
$973$	−1.29938	−	3.99908i	−0.0416562	−	0.128205i
$974$		0			0
$975$	−0.219897	−	0.159765i	−0.00704235	−	0.00511656i
$976$		0			0
$977$	12.9864	−	39.9681i	0.415472	−	1.27869i	−0.496355	−	0.868119i	$-0.665329\pi$
$977$	12.9864	−	39.9681i	0.415472	−	1.27869i	0.911828	−	0.410573i	$-0.134671\pi$
$978$		0			0
$979$	4.04020	+	1.51407i	0.129125	+	0.0483900i
$980$		0			0
$981$	4.35446	−	13.4017i	0.139027	−	0.427882i
$982$		0			0
$983$	−9.05534	−	6.57909i	−0.288820	−	0.209840i	0.433935	−	0.900944i	$-0.357125\pi$
$983$	−9.05534	−	6.57909i	−0.288820	−	0.209840i	−0.722756	+	0.691104i	$0.757125\pi$
$984$		0			0
$985$	−15.2430	−	46.9130i	−0.485681	−	1.49477i
$986$		0			0
$987$	1.62234	−	1.17870i	0.0516395	−	0.0375183i
$988$		0			0
$989$	37.4913			1.19215
$990$		0			0
$991$	−32.8916			−1.04484			−0.522418	−	0.852689i	$-0.674970\pi$
$991$	−32.8916			−1.04484			−0.522418	+	0.852689i	$0.674970\pi$
$992$		0			0
$993$	2.84061	−	2.06383i	0.0901441	−	0.0654936i
$994$		0			0
$995$	−0.958946	−	2.95133i	−0.0304006	−	0.0935635i
$996$		0			0
$997$	−43.9952	−	31.9644i	−1.39334	−	1.01232i	−0.995489	−	0.0948740i	$-0.969755\pi$
$997$	−43.9952	−	31.9644i	−1.39334	−	1.01232i	−0.397854	−	0.917449i	$-0.630245\pi$
$998$		0			0
$999$	−2.17951	+	6.70785i	−0.0689568	+	0.212227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.f.625.2	yes	20
11.5	even	5	inner	1716.2.z.f.313.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.f.313.2	✓	20	11.5	even	5	inner
1716.2.z.f.625.2	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} +(-0.671939 - 2.06802i) q^{5} +(0.699083 + 0.507914i) q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} +(-0.671939 - 2.06802i) q^{5} +(0.699083 + 0.507914i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-3.10571 - 1.16387i) q^{11} +(0.309017 - 0.951057i) q^{13} +(-1.75916 - 1.27810i) q^{15} +(0.388264 + 1.19495i) q^{17} +(3.38343 - 2.45820i) q^{19} +0.864114 q^{21} -7.56826 q^{23} +(0.219897 - 0.159765i) q^{25} +(-0.309017 - 0.951057i) q^{27} +(2.00359 + 1.45569i) q^{29} +(3.01901 - 9.29157i) q^{31} +(-3.19667 + 0.883898i) q^{33} +(0.580632 - 1.78700i) q^{35} +(-5.70604 - 4.14568i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(-9.50295 + 6.90430i) q^{41} -4.95375 q^{43} -2.17444 q^{45} +(1.87746 - 1.36405i) q^{47} +(-1.93238 - 5.94725i) q^{49} +(1.01649 + 0.738522i) q^{51} +(-0.0120600 + 0.0371167i) q^{53} +(-0.320056 + 7.20470i) q^{55} +(1.29235 - 3.97746i) q^{57} +(0.572210 + 0.415735i) q^{59} +(0.338023 + 1.04033i) q^{61} +(0.699083 - 0.507914i) q^{63} -2.17444 q^{65} +6.33315 q^{67} +(-6.12285 + 4.44851i) q^{69} +(-0.605452 - 1.86339i) q^{71} +(-5.82745 - 4.23389i) q^{73} +(0.0839932 - 0.258505i) q^{75} +(-1.58000 - 2.39107i) q^{77} +(-1.53130 + 4.71286i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.533644 - 1.64239i) q^{83} +(2.21029 - 1.60587i) q^{85} +2.47657 q^{87} -1.30090 q^{89} +(0.699083 - 0.507914i) q^{91} +(-3.01901 - 9.29157i) q^{93} +(-7.35706 - 5.34522i) q^{95} +(-1.39577 + 4.29575i) q^{97} +(-2.06662 + 2.59405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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