LMFDB - Embedded newform 1716.2.z.f.1093.2

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			1093.2
Root			$0.636359 - 1.95851i$ of defining polynomial
Character	$\chi$	$=$	1716.1093
Dual form			1716.2.z.f.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(-0.439009 + 0.318959i) q^{5} +(0.972664 + 2.99355i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.439009 + 0.318959i) q^{5} +(0.972664 + 2.99355i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.15752 - 2.51895i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.167686 - 0.516086i) q^{15} +(0.343251 - 0.249387i) q^{17} +(-1.31416 + 4.04457i) q^{19} -3.14761 q^{21} -2.27123 q^{23} +(-1.45409 + 4.47523i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-0.366751 - 1.12874i) q^{29} +(-6.77479 - 4.92218i) q^{31} +(3.06238 - 1.27352i) q^{33} +(-1.38183 - 1.00396i) q^{35} +(1.78061 + 5.48017i) q^{37} +(0.809017 - 0.587785i) q^{39} +(1.96870 - 6.05904i) q^{41} -6.42624 q^{43} +0.542645 q^{45} +(-2.71992 + 8.37106i) q^{47} +(-2.35215 + 1.70894i) q^{49} +(0.131110 + 0.403516i) q^{51} +(-0.668567 - 0.485742i) q^{53} +(1.75061 + 0.417684i) q^{55} +(-3.44052 - 2.49968i) q^{57} +(-3.32191 - 10.2238i) q^{59} +(-1.19503 + 0.868241i) q^{61} +(0.972664 - 2.99355i) q^{63} +0.542645 q^{65} -0.293181 q^{67} +(0.701847 - 2.16006i) q^{69} +(8.24075 - 5.98725i) q^{71} +(-3.67410 - 11.3077i) q^{73} +(-3.80686 - 2.76585i) q^{75} +(5.44207 - 8.90873i) q^{77} +(-6.94947 - 5.04909i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-9.88188 + 7.17961i) q^{83} +(-0.0711463 + 0.218966i) q^{85} +1.18683 q^{87} +1.06674 q^{89} +(0.972664 - 2.99355i) q^{91} +(6.77479 - 4.92218i) q^{93} +(-0.713123 - 2.19477i) q^{95} +(-0.662664 - 0.481453i) q^{97} +(0.264864 + 3.30603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

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

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
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	−0.439009	+	0.318959i	−0.196331	+	0.142643i	−0.681608	−	0.731718i	$-0.738719\pi$
$5$	−0.439009	+	0.318959i	−0.196331	+	0.142643i	0.485277	+	0.874361i	$0.338719\pi$
$6$		0			0
$7$	0.972664	+	2.99355i	0.367632	+	1.13146i	0.948316	+	0.317327i	$0.102785\pi$
$7$	0.972664	+	2.99355i	0.367632	+	1.13146i	−0.580684	+	0.814129i	$0.697215\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−2.15752	−	2.51895i	−0.650516	−	0.759493i
$11$	−2.15752	−	2.51895i	−0.650516	−	0.759493i
$12$		0			0
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$		0			0
$15$	−0.167686	−	0.516086i	−0.0432965	−	0.133253i
$16$		0			0
$17$	0.343251	−	0.249387i	0.0832506	−	0.0604851i	−0.545381	−	0.838188i	$-0.683615\pi$
$17$	0.343251	−	0.249387i	0.0832506	−	0.0604851i	0.628632	+	0.777703i	$0.283615\pi$
$18$		0			0
$19$	−1.31416	+	4.04457i	−0.301489	+	0.927889i	0.679475	+	0.733699i	$0.262208\pi$
$19$	−1.31416	+	4.04457i	−0.301489	+	0.927889i	−0.980964	+	0.194190i	$0.937792\pi$
$20$		0			0
$21$	−3.14761			−0.686864
$22$		0			0
$23$	−2.27123			−0.473583			−0.236792	−	0.971560i	$-0.576096\pi$
$23$	−2.27123			−0.473583			−0.236792	+	0.971560i	$0.576096\pi$
$24$		0			0
$25$	−1.45409	+	4.47523i	−0.290818	+	0.895046i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	−0.366751	−	1.12874i	−0.0681040	−	0.209602i	0.911213	−	0.411936i	$-0.135147\pi$
$29$	−0.366751	−	1.12874i	−0.0681040	−	0.209602i	−0.979317	+	0.202334i	$0.935147\pi$
$30$		0			0
$31$	−6.77479	−	4.92218i	−1.21679	−	0.884049i	−0.220959	−	0.975283i	$-0.570919\pi$
$31$	−6.77479	−	4.92218i	−1.21679	−	0.884049i	−0.995829	+	0.0912341i	$0.970919\pi$
$32$		0			0
$33$	3.06238	−	1.27352i	0.533091	−	0.221692i
$34$		0			0
$35$	−1.38183	−	1.00396i	−0.233571	−	0.169699i
$36$		0			0
$37$	1.78061	+	5.48017i	0.292731	+	0.900934i	0.983974	+	0.178311i	$0.0570634\pi$
$37$	1.78061	+	5.48017i	0.292731	+	0.900934i	−0.691243	+	0.722622i	$0.742937\pi$
$38$		0			0
$39$	0.809017	−	0.587785i	0.129546	−	0.0941210i
$40$		0			0
$41$	1.96870	−	6.05904i	0.307460	−	0.946263i	−0.671288	−	0.741196i	$-0.734259\pi$
$41$	1.96870	−	6.05904i	0.307460	−	0.946263i	0.978748	−	0.205067i	$-0.0657412\pi$
$42$		0			0
$43$	−6.42624			−0.979992			−0.489996	−	0.871725i	$-0.663002\pi$
$43$	−6.42624			−0.979992			−0.489996	+	0.871725i	$0.663002\pi$
$44$		0			0
$45$	0.542645			0.0808927
$46$		0			0
$47$	−2.71992	+	8.37106i	−0.396741	+	1.22104i	0.530856	+	0.847462i	$0.321871\pi$
$47$	−2.71992	+	8.37106i	−0.396741	+	1.22104i	−0.927597	+	0.373582i	$0.878129\pi$
$48$		0			0
$49$	−2.35215	+	1.70894i	−0.336022	+	0.244134i
$50$		0			0
$51$	0.131110	+	0.403516i	0.0183591	+	0.0565035i
$52$		0			0
$53$	−0.668567	−	0.485742i	−0.0918348	−	0.0667219i	0.540920	−	0.841074i	$-0.318076\pi$
$53$	−0.668567	−	0.485742i	−0.0918348	−	0.0667219i	−0.632755	+	0.774352i	$0.718076\pi$
$54$		0			0
$55$	1.75061	+	0.417684i	0.236052	+	0.0563205i
$56$		0			0
$57$	−3.44052	−	2.49968i	−0.455708	−	0.331091i
$58$		0			0
$59$	−3.32191	−	10.2238i	−0.432475	−	1.33102i	−0.895652	−	0.444756i	$-0.853290\pi$
$59$	−3.32191	−	10.2238i	−0.432475	−	1.33102i	0.463176	−	0.886266i	$-0.346710\pi$
$60$		0			0
$61$	−1.19503	+	0.868241i	−0.153008	+	0.111167i	−0.661655	−	0.749808i	$-0.730146\pi$
$61$	−1.19503	+	0.868241i	−0.153008	+	0.111167i	0.508647	+	0.860975i	$0.330146\pi$
$62$		0			0
$63$	0.972664	−	2.99355i	0.122544	−	0.377152i
$64$		0			0
$65$	0.542645			0.0673068
$66$		0			0
$67$	−0.293181			−0.0358178			−0.0179089	−	0.999840i	$-0.505701\pi$
$67$	−0.293181			−0.0358178			−0.0179089	+	0.999840i	$0.505701\pi$
$68$		0			0
$69$	0.701847	−	2.16006i	0.0844925	−	0.260041i
$70$		0			0
$71$	8.24075	−	5.98725i	0.977997	−	0.710556i	0.0207368	−	0.999785i	$-0.493399\pi$
$71$	8.24075	−	5.98725i	0.977997	−	0.710556i	0.957260	+	0.289229i	$0.0933988\pi$
$72$		0			0
$73$	−3.67410	−	11.3077i	−0.430021	−	1.32347i	−0.898103	−	0.439785i	$-0.855055\pi$
$73$	−3.67410	−	11.3077i	−0.430021	−	1.32347i	0.468082	−	0.883685i	$-0.344945\pi$
$74$		0			0
$75$	−3.80686	−	2.76585i	−0.439578	−	0.319372i
$76$		0			0
$77$	5.44207	−	8.90873i	0.620182	−	1.01524i
$78$		0			0
$79$	−6.94947	−	5.04909i	−0.781877	−	0.568067i	0.123665	−	0.992324i	$-0.460535\pi$
$79$	−6.94947	−	5.04909i	−0.781877	−	0.568067i	−0.905542	+	0.424257i	$0.860535\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−9.88188	+	7.17961i	−1.08468	+	0.788064i	−0.978493	−	0.206282i	$-0.933864\pi$
$83$	−9.88188	+	7.17961i	−1.08468	+	0.788064i	−0.106185	+	0.994346i	$0.533864\pi$
$84$		0			0
$85$	−0.0711463	+	0.218966i	−0.00771690	+	0.0237502i
$86$		0			0
$87$	1.18683			0.127242
$88$		0			0
$89$	1.06674			0.113074			0.0565371	−	0.998400i	$-0.481994\pi$
$89$	1.06674			0.113074			0.0565371	+	0.998400i	$0.481994\pi$
$90$		0			0
$91$	0.972664	−	2.99355i	0.101963	−	0.313809i
$92$		0			0
$93$	6.77479	−	4.92218i	0.702513	−	0.510406i
$94$		0			0
$95$	−0.713123	−	2.19477i	−0.0731649	−	0.225178i
$96$		0			0
$97$	−0.662664	−	0.481453i	−0.0672833	−	0.0488842i	0.553635	−	0.832759i	$-0.313240\pi$
$97$	−0.662664	−	0.481453i	−0.0672833	−	0.0488842i	−0.620918	+	0.783875i	$0.713240\pi$
$98$		0			0
$99$	0.264864	+	3.30603i	0.0266199	+	0.332269i
$100$		0			0
$101$	0.307980	+	0.223761i	0.0306452	+	0.0222650i	0.603002	−	0.797739i	$-0.293971\pi$
$101$	0.307980	+	0.223761i	0.0306452	+	0.0222650i	−0.572357	+	0.820004i	$0.693971\pi$
$102$		0			0
$103$	2.13767	+	6.57908i	0.210631	+	0.648256i	0.999435	+	0.0336107i	$0.0107006\pi$
$103$	2.13767	+	6.57908i	0.210631	+	0.648256i	−0.788804	+	0.614645i	$0.789299\pi$
$104$		0			0
$105$	1.38183	−	1.00396i	0.134852	−	0.0979760i
$106$		0			0
$107$	−6.03610	+	18.5772i	−0.583532	+	1.79593i	0.0215556	+	0.999768i	$0.493138\pi$
$107$	−6.03610	+	18.5772i	−0.583532	+	1.79593i	−0.605088	+	0.796159i	$0.706862\pi$
$108$		0			0
$109$	−17.0747			−1.63546			−0.817728	−	0.575606i	$-0.804766\pi$
$109$	−17.0747			−1.63546			−0.817728	+	0.575606i	$0.804766\pi$
$110$		0			0
$111$	−5.76219			−0.546923
$112$		0			0
$113$	4.37082	−	13.4520i	0.411172	−	1.26546i	−0.504458	−	0.863436i	$-0.668308\pi$
$113$	4.37082	−	13.4520i	0.411172	−	1.26546i	0.915630	−	0.402021i	$-0.131692\pi$
$114$		0			0
$115$	0.997088	−	0.724427i	0.0929789	−	0.0675532i
$116$		0			0
$117$	0.309017	+	0.951057i	0.0285686	+	0.0879252i
$118$		0			0
$119$	1.08042	+	0.784970i	0.0990419	+	0.0719581i
$120$		0			0
$121$	−1.69024	+	10.8694i	−0.153659	+	0.988124i
$122$		0			0
$123$	5.15413	+	3.74469i	0.464732	+	0.337648i
$124$		0			0
$125$	−1.62749	−	5.00889i	−0.145567	−	0.448009i
$126$		0			0
$127$	−2.77468	+	2.01592i	−0.246213	+	0.178884i	−0.704047	−	0.710154i	$-0.748625\pi$
$127$	−2.77468	+	2.01592i	−0.246213	+	0.178884i	0.457834	+	0.889038i	$0.348625\pi$
$128$		0			0
$129$	1.98582	−	6.11172i	0.174841	−	0.538107i
$130$		0			0
$131$	−11.8799			−1.03795			−0.518976	−	0.854789i	$-0.673687\pi$
$131$	−11.8799			−1.03795			−0.518976	+	0.854789i	$0.673687\pi$
$132$		0			0
$133$	−13.3859			−1.16070
$134$		0			0
$135$	−0.167686	+	0.516086i	−0.0144322	+	0.0444176i
$136$		0			0
$137$	−6.05356	+	4.39817i	−0.517191	+	0.375761i	−0.815545	−	0.578694i	$-0.803562\pi$
$137$	−6.05356	+	4.39817i	−0.517191	+	0.375761i	0.298354	+	0.954455i	$0.403562\pi$
$138$		0			0
$139$	0.804623	+	2.47637i	0.0682472	+	0.210043i	0.979364	−	0.202105i	$-0.0647784\pi$
$139$	0.804623	+	2.47637i	0.0682472	+	0.210043i	−0.911117	+	0.412149i	$0.864778\pi$
$140$		0			0
$141$	−7.12085	−	5.17360i	−0.599684	−	0.435696i
$142$		0			0
$143$	0.264864	+	3.30603i	0.0221491	+	0.276464i
$144$		0			0
$145$	0.521029	+	0.378550i	0.0432691	+	0.0314369i
$146$		0			0
$147$	−0.898442	−	2.76512i	−0.0741022	−	0.228063i
$148$		0			0
$149$	5.55872	−	4.03865i	0.455388	−	0.330859i	−0.336331	−	0.941744i	$-0.609186\pi$
$149$	5.55872	−	4.03865i	0.455388	−	0.330859i	0.791719	+	0.610885i	$0.209186\pi$
$150$		0			0
$151$	3.15017	−	9.69523i	0.256357	−	0.788986i	−0.737202	−	0.675672i	$-0.763853\pi$
$151$	3.15017	−	9.69523i	0.256357	−	0.788986i	0.993559	−	0.113314i	$-0.0361466\pi$
$152$		0			0
$153$	−0.424282			−0.0343011
$154$		0			0
$155$	4.54416			0.364996
$156$		0			0
$157$	−5.60968	+	17.2648i	−0.447701	+	1.37788i	0.431792	+	0.901973i	$0.357881\pi$
$157$	−5.60968	+	17.2648i	−0.447701	+	1.37788i	−0.879494	+	0.475910i	$0.842119\pi$
$158$		0			0
$159$	0.668567	−	0.485742i	0.0530208	−	0.0385219i
$160$		0			0
$161$	−2.20914	−	6.79903i	−0.174105	−	0.535839i
$162$		0			0
$163$	−9.84046	−	7.14951i	−0.770764	−	0.559993i	0.131429	−	0.991326i	$-0.458044\pi$
$163$	−9.84046	−	7.14951i	−0.770764	−	0.559993i	−0.902193	+	0.431333i	$0.858044\pi$
$164$		0			0
$165$	−0.938209	+	1.53586i	−0.0730395	+	0.119566i
$166$		0			0
$167$	15.4249	+	11.2069i	1.19362	+	0.867214i	0.993642	−	0.112587i	$-0.0359138\pi$
$167$	15.4249	+	11.2069i	1.19362	+	0.867214i	0.199975	+	0.979801i	$0.435914\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$		0			0
$171$	3.44052	−	2.49968i	0.263103	−	0.191156i
$172$		0			0
$173$	2.30133	−	7.08277i	0.174967	−	0.538493i	−0.824665	−	0.565621i	$-0.808636\pi$
$173$	2.30133	−	7.08277i	0.174967	−	0.538493i	0.999632	+	0.0271286i	$0.00863637\pi$
$174$		0			0
$175$	−14.8112			−1.11962
$176$		0			0
$177$	10.7499			0.808013
$178$		0			0
$179$	−0.957952	+	2.94827i	−0.0716007	+	0.220364i	−0.980453	−	0.196754i	$-0.936960\pi$
$179$	−0.957952	+	2.94827i	−0.0716007	+	0.220364i	0.908852	+	0.417118i	$0.136960\pi$
$180$		0			0
$181$	6.10326	−	4.43428i	0.453652	−	0.329597i	−0.337384	−	0.941367i	$-0.609542\pi$
$181$	6.10326	−	4.43428i	0.453652	−	0.329597i	0.791036	+	0.611770i	$0.209542\pi$
$182$		0			0
$183$	−0.456461	−	1.40484i	−0.0337426	−	0.103849i
$184$		0			0
$185$	−2.52965	−	1.83790i	−0.185984	−	0.135125i
$186$		0			0
$187$	−1.36876	−	0.326578i	−0.100094	−	0.0238817i
$188$		0			0
$189$	2.54647	+	1.85012i	0.185228	+	0.134576i
$190$		0			0
$191$	−1.68226	−	5.17746i	−0.121724	−	0.374628i	0.871566	−	0.490278i	$-0.163105\pi$
$191$	−1.68226	−	5.17746i	−0.121724	−	0.374628i	−0.993290	+	0.115650i	$0.963105\pi$
$192$		0			0
$193$	3.22454	−	2.34277i	0.232108	−	0.168636i	−0.465652	−	0.884968i	$-0.654180\pi$
$193$	3.22454	−	2.34277i	0.232108	−	0.168636i	0.697760	+	0.716332i	$0.254180\pi$
$194$		0			0
$195$	−0.167686	+	0.516086i	−0.0120083	+	0.0369577i
$196$		0			0
$197$	−7.83786			−0.558424			−0.279212	−	0.960229i	$-0.590073\pi$
$197$	−7.83786			−0.558424			−0.279212	+	0.960229i	$0.590073\pi$
$198$		0			0
$199$	−3.13755			−0.222415			−0.111207	−	0.993797i	$-0.535472\pi$
$199$	−3.13755			−0.222415			−0.111207	+	0.993797i	$0.535472\pi$
$200$		0			0
$201$	0.0905980	−	0.278832i	0.00639029	−	0.0196673i
$202$		0			0
$203$	3.02223	−	2.19578i	0.212119	−	0.154113i
$204$		0			0
$205$	1.06831	+	3.28791i	0.0746137	+	0.229637i
$206$		0			0
$207$	1.83746	+	1.33499i	0.127712	+	0.0927884i
$208$		0			0
$209$	13.0234	−	5.41592i	0.900848	−	0.374627i
$210$		0			0
$211$	12.4072	+	9.01438i	0.854148	+	0.620575i	0.926287	−	0.376819i	$-0.122982\pi$
$211$	12.4072	+	9.01438i	0.854148	+	0.620575i	−0.0721383	+	0.997395i	$0.522982\pi$
$212$		0			0
$213$	3.14769	+	9.68758i	0.215676	+	0.663782i
$214$		0			0
$215$	2.82117	−	2.04970i	0.192403	−	0.139789i
$216$		0			0
$217$	8.14519	−	25.0683i	0.552931	−	1.70175i
$218$		0			0
$219$	11.8897			0.803428
$220$		0			0
$221$	−0.424282			−0.0285403
$222$		0			0
$223$	−6.95131	+	21.3939i	−0.465494	+	1.43264i	0.392865	+	0.919596i	$0.371484\pi$
$223$	−6.95131	+	21.3939i	−0.465494	+	1.43264i	−0.858360	+	0.513048i	$0.828516\pi$
$224$		0			0
$225$	3.80686	−	2.76585i	0.253791	−	0.184390i
$226$		0			0
$227$	0.293468	+	0.903201i	0.0194782	+	0.0599476i	0.960323	−	0.278890i	$-0.0899664\pi$
$227$	0.293468	+	0.903201i	0.0194782	+	0.0599476i	−0.940845	+	0.338837i	$0.889966\pi$
$228$		0			0
$229$	0.203032	+	0.147511i	0.0134167	+	0.00974781i	0.594473	−	0.804115i	$-0.297361\pi$
$229$	0.203032	+	0.147511i	0.0134167	+	0.00974781i	−0.581057	+	0.813863i	$0.697361\pi$
$230$		0			0
$231$	6.79101	+	7.92867i	0.446816	+	0.521668i
$232$		0			0
$233$	8.44548	+	6.13600i	0.553282	+	0.401983i	0.828994	−	0.559257i	$-0.188914\pi$
$233$	8.44548	+	6.13600i	0.553282	+	0.401983i	−0.275712	+	0.961240i	$0.588914\pi$
$234$		0			0
$235$	−1.47595	−	4.54251i	−0.0962804	−	0.296321i
$236$		0			0
$237$	6.94947	−	5.04909i	0.451417	−	0.327974i
$238$		0			0
$239$	−1.18927	+	3.66019i	−0.0769273	+	0.236758i	−0.982124	−	0.188235i	$-0.939723\pi$
$239$	−1.18927	+	3.66019i	−0.0769273	+	0.236758i	0.905197	+	0.424993i	$0.139723\pi$
$240$		0			0
$241$	6.69938			0.431545			0.215772	−	0.976444i	$-0.430773\pi$
$241$	6.69938			0.431545			0.215772	+	0.976444i	$0.430773\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.487535	−	1.50048i	0.0311475	−	0.0958620i
$246$		0			0
$247$	3.44052	−	2.49968i	0.218915	−	0.159051i
$248$		0			0
$249$	−3.77454	−	11.6168i	−0.239202	−	0.736188i
$250$		0			0
$251$	5.62380	+	4.08593i	0.354971	+	0.257902i	0.750952	−	0.660357i	$-0.229595\pi$
$251$	5.62380	+	4.08593i	0.354971	+	0.257902i	−0.395980	+	0.918259i	$0.629595\pi$
$252$		0			0
$253$	4.90021	+	5.72111i	0.308073	+	0.359683i
$254$		0			0
$255$	−0.186263	−	0.135328i	−0.0116643	−	0.00847459i
$256$		0			0
$257$	−7.05703	−	21.7193i	−0.440205	−	1.35481i	−0.887657	−	0.460504i	$-0.847669\pi$
$257$	−7.05703	−	21.7193i	−0.440205	−	1.35481i	0.447452	−	0.894308i	$-0.352331\pi$
$258$		0			0
$259$	−14.6732	+	10.6607i	−0.911749	+	0.662425i
$260$		0			0
$261$	−0.366751	+	1.12874i	−0.0227013	+	0.0698675i
$262$		0			0
$263$	8.21555			0.506592			0.253296	−	0.967389i	$-0.418485\pi$
$263$	8.21555			0.506592			0.253296	+	0.967389i	$0.418485\pi$
$264$		0			0
$265$	0.448439			0.0275474
$266$		0			0
$267$	−0.329641	+	1.01453i	−0.0201737	+	0.0620882i
$268$		0			0
$269$	−5.19459	+	3.77409i	−0.316720	+	0.230110i	−0.734774	−	0.678312i	$-0.762712\pi$
$269$	−5.19459	+	3.77409i	−0.316720	+	0.230110i	0.418055	+	0.908422i	$0.362712\pi$
$270$		0			0
$271$	8.11738	+	24.9827i	0.493096	+	1.51759i	0.819904	+	0.572502i	$0.194027\pi$
$271$	8.11738	+	24.9827i	0.493096	+	1.51759i	−0.326808	+	0.945091i	$0.605973\pi$
$272$		0			0
$273$	2.54647	+	1.85012i	0.154119	+	0.111974i
$274$		0			0
$275$	14.4101	−	5.99260i	0.868963	−	0.361367i
$276$		0			0
$277$	−0.0252100	−	0.0183162i	−0.00151472	−	0.00110051i	0.587028	−	0.809567i	$-0.300298\pi$
$277$	−0.0252100	−	0.0183162i	−0.00151472	−	0.00110051i	−0.588542	+	0.808466i	$0.700298\pi$
$278$		0			0
$279$	2.58774	+	7.96425i	0.154924	+	0.476807i
$280$		0			0
$281$	20.0612	−	14.5753i	1.19675	−	0.869489i	0.202789	−	0.979223i	$-0.435000\pi$
$281$	20.0612	−	14.5753i	1.19675	−	0.869489i	0.993961	+	0.109733i	$0.0349996\pi$
$282$		0			0
$283$	−6.61861	+	20.3700i	−0.393435	+	1.21087i	0.536738	+	0.843749i	$0.319656\pi$
$283$	−6.61861	+	20.3700i	−0.393435	+	1.21087i	−0.930173	+	0.367120i	$0.880344\pi$
$284$		0			0
$285$	2.30771			0.136697
$286$		0			0
$287$	20.0529			1.18369
$288$		0			0
$289$	−5.19766	+	15.9968i	−0.305745	+	0.940986i
$290$		0			0
$291$	0.662664	−	0.481453i	0.0388460	−	0.0282233i
$292$		0			0
$293$	6.73506	+	20.7284i	0.393467	+	1.21097i	0.930149	+	0.367182i	$0.119677\pi$
$293$	6.73506	+	20.7284i	0.393467	+	1.21097i	−0.536683	+	0.843784i	$0.680323\pi$
$294$		0			0
$295$	4.71931	+	3.42878i	0.274769	+	0.199631i
$296$		0			0
$297$	−3.22607	−	0.769719i	−0.187196	−	0.0446636i
$298$		0			0
$299$	1.83746	+	1.33499i	0.106263	+	0.0772046i
$300$		0			0
$301$	−6.25057	−	19.2373i	−0.360277	−	1.10882i
$302$		0			0
$303$	−0.307980	+	0.223761i	−0.0176930	+	0.0128547i
$304$		0			0
$305$	0.247696	−	0.762330i	0.0141830	−	0.0436509i
$306$		0			0
$307$	0.570275			0.0325473			0.0162737	−	0.999868i	$-0.494820\pi$
$307$	0.570275			0.0325473			0.0162737	+	0.999868i	$0.494820\pi$
$308$		0			0
$309$	−6.91765			−0.393531
$310$		0			0
$311$	−0.575736	+	1.77193i	−0.0326470	+	0.100477i	−0.966052	−	0.258347i	$-0.916822\pi$
$311$	−0.575736	+	1.77193i	−0.0326470	+	0.100477i	0.933405	+	0.358824i	$0.116822\pi$
$312$		0			0
$313$	16.6433	−	12.0921i	0.940734	−	0.683483i	−0.00786300	−	0.999969i	$-0.502503\pi$
$313$	16.6433	−	12.0921i	0.940734	−	0.683483i	0.948597	+	0.316486i	$0.102503\pi$
$314$		0			0
$315$	0.527811	+	1.62443i	0.0297388	+	0.0915265i
$316$		0			0
$317$	−19.3622	−	14.0675i	−1.08749	−	0.790109i	−0.108517	−	0.994095i	$-0.534610\pi$
$317$	−19.3622	−	14.0675i	−1.08749	−	0.790109i	−0.978974	+	0.203986i	$0.934610\pi$
$318$		0			0
$319$	−2.05198	+	3.35911i	−0.114889	+	0.188074i
$320$		0			0
$321$	−15.8027	−	11.4813i	−0.882022	−	0.640826i
$322$		0			0
$323$	0.557575	+	1.71604i	0.0310243	+	0.0954829i
$324$		0			0
$325$	3.80686	−	2.76585i	0.211167	−	0.153421i
$326$		0			0
$327$	5.27636	−	16.2390i	0.291783	−	0.898016i
$328$		0			0
$329$	−27.7048			−1.52741
$330$		0			0
$331$	−23.4465			−1.28873			−0.644367	−	0.764716i	$-0.722879\pi$
$331$	−23.4465			−1.28873			−0.644367	+	0.764716i	$0.722879\pi$
$332$		0			0
$333$	1.78061	−	5.48017i	0.0975770	−	0.300311i
$334$		0			0
$335$	0.128709	−	0.0935127i	0.00703213	−	0.00510914i
$336$		0			0
$337$	10.5704	+	32.5324i	0.575807	+	1.77215i	0.633415	+	0.773812i	$0.281653\pi$
$337$	10.5704	+	32.5324i	0.575807	+	1.77215i	−0.0576082	+	0.998339i	$0.518347\pi$
$338$		0			0
$339$	11.4430	+	8.31379i	0.621496	+	0.451543i
$340$		0			0
$341$	2.21800	+	27.6851i	0.120112	+	1.49923i
$342$		0			0
$343$	10.4216	+	7.57175i	0.562715	+	0.408836i
$344$		0			0
$345$	0.380854	+	1.17215i	0.0205045	+	0.0631063i
$346$		0			0
$347$	13.7730	−	10.0067i	0.739375	−	0.537187i	−0.153140	−	0.988204i	$-0.548939\pi$
$347$	13.7730	−	10.0067i	0.739375	−	0.537187i	0.892515	+	0.451017i	$0.148939\pi$
$348$		0			0
$349$	−3.97000	+	12.2184i	−0.212509	+	0.654037i	0.786812	+	0.617193i	$0.211730\pi$
$349$	−3.97000	+	12.2184i	−0.212509	+	0.654037i	−0.999321	+	0.0368434i	$0.988270\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	−29.2179			−1.55511			−0.777556	−	0.628814i	$-0.783541\pi$
$353$	−29.2179			−1.55511			−0.777556	+	0.628814i	$0.783541\pi$
$354$		0			0
$355$	−1.70807	+	5.25691i	−0.0906552	+	0.279008i
$356$		0			0
$357$	−1.08042	+	0.784970i	−0.0571818	+	0.0415450i
$358$		0			0
$359$	8.89191	+	27.3665i	0.469297	+	1.44435i	0.853497	+	0.521098i	$0.174477\pi$
$359$	8.89191	+	27.3665i	0.469297	+	1.44435i	−0.384200	+	0.923250i	$0.625523\pi$
$360$		0			0
$361$	0.739769	+	0.537474i	0.0389352	+	0.0282881i
$362$		0			0
$363$	−9.81506	−	4.96634i	−0.515157	−	0.260665i
$364$		0			0
$365$	5.21966	+	3.79231i	0.273210	+	0.198498i
$366$		0			0
$367$	9.48052	+	29.1780i	0.494879	+	1.52308i	0.817145	+	0.576432i	$0.195555\pi$
$367$	9.48052	+	29.1780i	0.494879	+	1.52308i	−0.322266	+	0.946649i	$0.604445\pi$
$368$		0			0
$369$	−5.15413	+	3.74469i	−0.268313	+	0.194941i
$370$		0			0
$371$	0.803804	−	2.47385i	0.0417314	−	0.128436i
$372$		0			0
$373$	−3.81140			−0.197347			−0.0986734	−	0.995120i	$-0.531460\pi$
$373$	−3.81140			−0.197347			−0.0986734	+	0.995120i	$0.531460\pi$
$374$		0			0
$375$	5.26666			0.271969
$376$		0			0
$377$	−0.366751	+	1.12874i	−0.0188886	+	0.0581333i
$378$		0			0
$379$	−15.3287	+	11.1369i	−0.787382	+	0.572067i	−0.907185	−	0.420731i	$-0.861774\pi$
$379$	−15.3287	+	11.1369i	−0.787382	+	0.572067i	0.119803	+	0.992798i	$0.461774\pi$
$380$		0			0
$381$	−1.05983	−	3.26183i	−0.0542969	−	0.167109i
$382$		0			0
$383$	14.6870	+	10.6707i	0.750469	+	0.545247i	0.895972	−	0.444110i	$-0.146480\pi$
$383$	14.6870	+	10.6707i	0.750469	+	0.545247i	−0.145503	+	0.989358i	$0.546480\pi$
$384$		0			0
$385$	0.452397	+	5.64681i	0.0230563	+	0.287788i
$386$		0			0
$387$	5.19894	+	3.77725i	0.264277	+	0.192008i
$388$		0			0
$389$	−3.64608	−	11.2215i	−0.184864	−	0.568952i	0.815082	−	0.579345i	$-0.196692\pi$
$389$	−3.64608	−	11.2215i	−0.184864	−	0.568952i	−0.999946	+	0.0103934i	$0.996692\pi$
$390$		0			0
$391$	−0.779601	+	0.566413i	−0.0394261	+	0.0286447i
$392$		0			0
$393$	3.67109	−	11.2985i	0.185182	−	0.569932i
$394$		0			0
$395$	4.66133			0.234537
$396$		0			0
$397$	36.2281			1.81824			0.909119	−	0.416537i	$-0.136756\pi$
$397$	36.2281			1.81824			0.909119	+	0.416537i	$0.136756\pi$
$398$		0			0
$399$	4.13646	−	12.7307i	0.207082	−	0.637333i
$400$		0			0
$401$	2.10135	−	1.52672i	0.104936	−	0.0762406i	−0.534080	−	0.845434i	$-0.679342\pi$
$401$	2.10135	−	1.52672i	0.104936	−	0.0762406i	0.639016	+	0.769194i	$0.279342\pi$
$402$		0			0
$403$	2.58774	+	7.96425i	0.128905	+	0.396727i
$404$		0			0
$405$	−0.439009	−	0.318959i	−0.0218145	−	0.0158492i
$406$		0			0
$407$	9.96257	−	16.3088i	0.493826	−	0.808399i
$408$		0			0
$409$	17.6030	+	12.7893i	0.870413	+	0.632392i	0.930698	−	0.365789i	$-0.119201\pi$
$409$	17.6030	+	12.7893i	0.870413	+	0.632392i	−0.0602851	+	0.998181i	$0.519201\pi$
$410$		0			0
$411$	−2.31225	−	7.11639i	−0.114055	−	0.351026i
$412$		0			0
$413$	27.3743	−	19.8886i	1.34700	−	0.978654i
$414$		0			0
$415$	2.04824	−	6.30382i	0.100544	−	0.309442i
$416$		0			0
$417$	−2.60381			−0.127509
$418$		0			0
$419$	−4.10269			−0.200430			−0.100215	−	0.994966i	$-0.531953\pi$
$419$	−4.10269			−0.200430			−0.100215	+	0.994966i	$0.531953\pi$
$420$		0			0
$421$	10.0198	−	30.8377i	0.488333	−	1.50294i	−0.338761	−	0.940872i	$-0.610008\pi$
$421$	10.0198	−	30.8377i	0.488333	−	1.50294i	0.827094	−	0.562063i	$-0.189992\pi$
$422$		0			0
$423$	7.12085	−	5.17360i	0.346227	−	0.251549i
$424$		0			0
$425$	0.616944	+	1.89876i	0.0299262	+	0.0921033i
$426$		0			0
$427$	−3.76148	−	2.73288i	−0.182031	−	0.132253i
$428$		0			0
$429$	−3.22607	−	0.769719i	−0.155756	−	0.0371624i
$430$		0			0
$431$	−13.3222	−	9.67917i	−0.641709	−	0.466229i	0.218728	−	0.975786i	$-0.429809\pi$
$431$	−13.3222	−	9.67917i	−0.641709	−	0.466229i	−0.860437	+	0.509557i	$0.829809\pi$
$432$		0			0
$433$	11.1955	+	34.4563i	0.538023	+	1.65587i	0.737024	+	0.675867i	$0.236230\pi$
$433$	11.1955	+	34.4563i	0.538023	+	1.65587i	−0.199000	+	0.979999i	$0.563770\pi$
$434$		0			0
$435$	−0.521029	+	0.378550i	−0.0249814	+	0.0181501i
$436$		0			0
$437$	2.98476	−	9.18614i	0.142780	−	0.439433i
$438$		0			0
$439$	19.5368			0.932441			0.466220	−	0.884669i	$-0.345615\pi$
$439$	19.5368			0.932441			0.466220	+	0.884669i	$0.345615\pi$
$440$		0			0
$441$	2.90742			0.138449
$442$		0			0
$443$	−2.93817	+	9.04276i	−0.139597	+	0.429635i	−0.996277	−	0.0862137i	$-0.972523\pi$
$443$	−2.93817	+	9.04276i	−0.139597	+	0.429635i	0.856680	+	0.515848i	$0.172523\pi$
$444$		0			0
$445$	−0.468308	+	0.340246i	−0.0221999	+	0.0161292i
$446$		0			0
$447$	2.12324	+	6.53467i	0.100426	+	0.309079i
$448$		0			0
$449$	−0.213374	−	0.155026i	−0.0100698	−	0.00731611i	0.582739	−	0.812659i	$-0.301981\pi$
$449$	−0.213374	−	0.155026i	−0.0100698	−	0.00731611i	−0.592809	+	0.805343i	$0.701981\pi$
$450$		0			0
$451$	−19.5099	+	8.11342i	−0.918687	+	0.382046i
$452$		0			0
$453$	8.24725	+	5.99198i	0.387490	+	0.281528i
$454$		0			0
$455$	0.527811	+	1.62443i	0.0247441	+	0.0761547i
$456$		0			0
$457$	−11.9769	+	8.70169i	−0.560253	+	0.407048i	−0.831552	−	0.555447i	$-0.812547\pi$
$457$	−11.9769	+	8.70169i	−0.560253	+	0.407048i	0.271298	+	0.962495i	$0.412547\pi$
$458$		0			0
$459$	0.131110	−	0.403516i	0.00611970	−	0.0188345i
$460$		0			0
$461$	−4.65685			−0.216891			−0.108446	−	0.994102i	$-0.534587\pi$
$461$	−4.65685			−0.216891			−0.108446	+	0.994102i	$0.534587\pi$
$462$		0			0
$463$	−10.7304			−0.498683			−0.249342	−	0.968416i	$-0.580214\pi$
$463$	−10.7304			−0.498683			−0.249342	+	0.968416i	$0.580214\pi$
$464$		0			0
$465$	−1.40422	+	4.32176i	−0.0651193	+	0.200417i
$466$		0			0
$467$	19.0196	−	13.8185i	0.880121	−	0.639446i	−0.0531623	−	0.998586i	$-0.516930\pi$
$467$	19.0196	−	13.8185i	0.880121	−	0.639446i	0.933284	+	0.359140i	$0.116930\pi$
$468$		0			0
$469$	−0.285167	−	0.877653i	−0.0131678	−	0.0405262i
$470$		0			0
$471$	−14.6863	−	10.6703i	−0.676711	−	0.491659i
$472$		0			0
$473$	13.8647	+	16.1874i	0.637500	+	0.744297i
$474$		0			0
$475$	−16.1895	−	11.7624i	−0.742825	−	0.539694i
$476$		0			0
$477$	0.255370	+	0.785948i	0.0116926	+	0.0359861i
$478$		0			0
$479$	−33.9203	+	24.6445i	−1.54986	+	1.12604i	−0.606105	+	0.795385i	$0.707269\pi$
$479$	−33.9203	+	24.6445i	−1.54986	+	1.12604i	−0.943753	+	0.330652i	$0.892731\pi$
$480$		0			0
$481$	1.78061	−	5.48017i	0.0811890	−	0.249874i
$482$		0			0
$483$	7.14892			0.325287
$484$		0			0
$485$	0.444479			0.0201827
$486$		0			0
$487$	5.54035	−	17.0514i	0.251057	−	0.772674i	−0.743524	−	0.668709i	$-0.766847\pi$
$487$	5.54035	−	17.0514i	0.251057	−	0.772674i	0.994581	−	0.103965i	$-0.0331529\pi$
$488$		0			0
$489$	9.84046	−	7.14951i	0.445001	−	0.323312i
$490$		0			0
$491$	12.2892	+	37.8222i	0.554603	+	1.70689i	0.696988	+	0.717082i	$0.254523\pi$
$491$	12.2892	+	37.8222i	0.554603	+	1.70689i	−0.142385	+	0.989811i	$0.545477\pi$
$492$		0			0
$493$	−0.407381	−	0.295980i	−0.0183475	−	0.0133303i
$494$		0			0
$495$	−1.17076	−	1.36690i	−0.0526220	−	0.0614374i
$496$		0			0
$497$	25.9386	+	18.8455i	1.16351	+	0.845337i
$498$		0			0
$499$	−8.30119	−	25.5484i	−0.371612	−	1.14370i	−0.945736	−	0.324936i	$-0.894657\pi$
$499$	−8.30119	−	25.5484i	−0.371612	−	1.14370i	0.574124	−	0.818768i	$-0.305343\pi$
$500$		0			0
$501$	−15.4249	+	11.2069i	−0.689135	+	0.500686i
$502$		0			0
$503$	6.19481	−	19.0657i	0.276213	−	0.850096i	−0.712683	−	0.701486i	$-0.752520\pi$
$503$	6.19481	−	19.0657i	0.276213	−	0.850096i	0.988896	−	0.148610i	$-0.0474797\pi$
$504$		0			0
$505$	−0.206576			−0.00919253
$506$		0			0
$507$	−1.00000			−0.0444116
$508$		0			0
$509$	11.5602	−	35.5786i	0.512396	−	1.57699i	−0.275574	−	0.961280i	$-0.588868\pi$
$509$	11.5602	−	35.5786i	0.512396	−	1.57699i	0.787970	−	0.615713i	$-0.211132\pi$
$510$		0			0
$511$	30.2766	−	21.9972i	1.33936	−	0.973100i
$512$		0			0
$513$	1.31416	+	4.04457i	0.0580217	+	0.178572i
$514$		0			0
$515$	−3.03691	−	2.20644i	−0.133822	−	0.0972275i
$516$		0			0
$517$	26.9546	−	11.2093i	1.18546	−	0.492986i
$518$		0			0
$519$	6.02496	+	4.37739i	0.264466	+	0.192146i
$520$		0			0
$521$	3.52176	+	10.8389i	0.154291	+	0.474859i	0.998088	−	0.0618028i	$-0.0196850\pi$
$521$	3.52176	+	10.8389i	0.154291	+	0.474859i	−0.843797	+	0.536662i	$0.819685\pi$
$522$		0			0
$523$	−13.0080	+	9.45088i	−0.568801	+	0.413258i	−0.834669	−	0.550751i	$-0.814341\pi$
$523$	−13.0080	+	9.45088i	−0.568801	+	0.413258i	0.265869	+	0.964009i	$0.414341\pi$
$524$		0			0
$525$	4.57690	−	14.0863i	0.199752	−	0.614775i
$526$		0			0
$527$	−3.55298			−0.154770
$528$		0			0
$529$	−17.8415			−0.775719
$530$		0			0
$531$	−3.32191	+	10.2238i	−0.144158	+	0.443674i
$532$		0			0
$533$	−5.15413	+	3.74469i	−0.223250	+	0.162201i
$534$		0			0
$535$	−3.27546	−	10.0808i	−0.141610	−	0.435832i
$536$		0			0
$537$	−2.50795	−	1.82213i	−0.108226	−	0.0786308i
$538$		0			0
$539$	9.37954	+	2.23790i	0.404005	+	0.0963930i
$540$		0			0
$541$	−18.7389	−	13.6146i	−0.805648	−	0.585337i	0.106918	−	0.994268i	$-0.465902\pi$
$541$	−18.7389	−	13.6146i	−0.805648	−	0.585337i	−0.912566	+	0.408930i	$0.865902\pi$
$542$		0			0
$543$	2.33124	+	7.17482i	0.100043	+	0.307901i
$544$		0			0
$545$	7.49592	−	5.44611i	0.321090	−	0.233286i
$546$		0			0
$547$	7.42898	−	22.8640i	0.317640	−	0.977596i	−0.657014	−	0.753878i	$-0.728181\pi$
$547$	7.42898	−	22.8640i	0.317640	−	0.977596i	0.974654	−	0.223717i	$-0.0718192\pi$
$548$		0			0
$549$	1.47714			0.0630428
$550$		0			0
$551$	5.04726			0.215020
$552$		0			0
$553$	8.35520	−	25.7147i	0.355299	−	1.09350i
$554$		0			0
$555$	2.52965	−	1.83790i	0.107378	−	0.0780145i
$556$		0			0
$557$	5.43698	+	16.7333i	0.230372	+	0.709012i	0.997702	+	0.0677595i	$0.0215850\pi$
$557$	5.43698	+	16.7333i	0.230372	+	0.709012i	−0.767330	+	0.641253i	$0.778415\pi$
$558$		0			0
$559$	5.19894	+	3.77725i	0.219892	+	0.159761i
$560$		0			0
$561$	0.733565	−	1.20085i	0.0309711	−	0.0507000i
$562$		0			0
$563$	14.9333	+	10.8497i	0.629362	+	0.457258i	0.856179	−	0.516679i	$-0.172832\pi$
$563$	14.9333	+	10.8497i	0.629362	+	0.457258i	−0.226817	+	0.973937i	$0.572832\pi$
$564$		0			0
$565$	2.37180	+	7.29965i	0.0997824	+	0.307099i
$566$		0			0
$567$	−2.54647	+	1.85012i	−0.106942	+	0.0776976i
$568$		0			0
$569$	−3.81416	+	11.7388i	−0.159898	+	0.492116i	−0.998624	−	0.0524378i	$-0.983301\pi$
$569$	−3.81416	+	11.7388i	−0.159898	+	0.492116i	0.838726	+	0.544554i	$0.183301\pi$
$570$		0			0
$571$	−3.76727			−0.157655			−0.0788277	−	0.996888i	$-0.525118\pi$
$571$	−3.76727			−0.157655			−0.0788277	+	0.996888i	$0.525118\pi$
$572$		0			0
$573$	5.44390			0.227422
$574$		0			0
$575$	3.30257	−	10.1643i	0.137727	−	0.423879i
$576$		0			0
$577$	3.69981	−	2.68807i	0.154025	−	0.111906i	−0.508103	−	0.861296i	$-0.669653\pi$
$577$	3.69981	−	2.68807i	0.154025	−	0.111906i	0.662129	+	0.749390i	$0.269653\pi$
$578$		0			0
$579$	1.23167	+	3.79068i	0.0511863	+	0.157535i
$580$		0			0
$581$	−31.1043	−	22.5986i	−1.29042	−	0.937547i
$582$		0			0
$583$	0.218882	+	2.73209i	0.00906518	+	0.113151i
$584$		0			0
$585$	−0.439009	−	0.318959i	−0.0181508	−	0.0131873i
$586$		0			0
$587$	−11.0025	−	33.8622i	−0.454121	−	1.39764i	−0.872164	−	0.489213i	$-0.837284\pi$
$587$	−11.0025	−	33.8622i	−0.454121	−	1.39764i	0.418043	−	0.908427i	$-0.362716\pi$
$588$		0			0
$589$	28.8113	−	20.9326i	1.18715	−	0.862513i
$590$		0			0
$591$	2.42203	−	7.45424i	0.0996290	−	0.306627i
$592$		0			0
$593$	20.0080			0.821630			0.410815	−	0.911719i	$-0.365244\pi$
$593$	20.0080			0.821630			0.410815	+	0.911719i	$0.365244\pi$
$594$		0			0
$595$	−0.724686			−0.0297092
$596$		0			0
$597$	0.969556	−	2.98399i	0.0396813	−	0.122126i
$598$		0			0
$599$	17.4750	−	12.6963i	0.714007	−	0.518757i	−0.170457	−	0.985365i	$-0.554524\pi$
$599$	17.4750	−	12.6963i	0.714007	−	0.518757i	0.884464	+	0.466608i	$0.154524\pi$
$600$		0			0
$601$	6.76682	+	20.8261i	0.276024	+	0.849516i	0.988947	+	0.148273i	$0.0473713\pi$
$601$	6.76682	+	20.8261i	0.276024	+	0.849516i	−0.712922	+	0.701243i	$0.752629\pi$
$602$		0			0
$603$	0.237189	+	0.172328i	0.00965907	+	0.00701772i
$604$		0			0
$605$	−2.72484	−	5.31086i	−0.110781	−	0.215917i
$606$		0			0
$607$	1.68739	+	1.22596i	0.0684890	+	0.0497602i	0.621503	−	0.783412i	$-0.286522\pi$
$607$	1.68739	+	1.22596i	0.0684890	+	0.0497602i	−0.553014	+	0.833172i	$0.686522\pi$
$608$		0			0
$609$	1.15439	+	3.55284i	0.0467781	+	0.143968i
$610$		0			0
$611$	7.12085	−	5.17360i	0.288079	−	0.209301i
$612$		0			0
$613$	4.98016	−	15.3274i	0.201147	−	0.619067i	−0.798703	−	0.601726i	$-0.794480\pi$
$613$	4.98016	−	15.3274i	0.201147	−	0.619067i	0.999850	−	0.0173408i	$-0.00552002\pi$
$614$		0			0
$615$	−3.45711			−0.139404
$616$		0			0
$617$	−49.0691			−1.97545			−0.987725	−	0.156205i	$-0.950074\pi$
$617$	−49.0691			−1.97545			−0.987725	+	0.156205i	$0.950074\pi$
$618$		0			0
$619$	−10.7671	+	33.1379i	−0.432768	+	1.33192i	0.462589	+	0.886573i	$0.346921\pi$
$619$	−10.7671	+	33.1379i	−0.432768	+	1.33192i	−0.895357	+	0.445350i	$0.853079\pi$
$620$		0			0
$621$	−1.83746	+	1.33499i	−0.0737347	+	0.0535714i
$622$		0			0
$623$	1.03758	+	3.19334i	0.0415697	+	0.127938i
$624$		0			0
$625$	−16.7222	−	12.1494i	−0.668887	−	0.485975i
$626$		0			0
$627$	1.12639	+	14.0596i	0.0449838	+	0.561487i
$628$		0			0
$629$	1.97788	+	1.43701i	0.0788631	+	0.0572974i
$630$		0			0
$631$	−9.96257	−	30.6616i	−0.396603	−	1.22062i	−0.927706	−	0.373312i	$-0.878222\pi$
$631$	−9.96257	−	30.6616i	−0.396603	−	1.22062i	0.531102	−	0.847308i	$-0.321778\pi$
$632$		0			0
$633$	−12.4072	+	9.01438i	−0.493143	+	0.358289i
$634$		0			0
$635$	0.575113	−	1.77001i	0.0228226	−	0.0702409i
$636$		0			0
$637$	2.90742			0.115196
$638$		0			0
$639$	−10.1861			−0.402957
$640$		0			0
$641$	−1.82485	+	5.61632i	−0.0720774	+	0.221831i	−0.980605	−	0.195993i	$-0.937207\pi$
$641$	−1.82485	+	5.61632i	−0.0720774	+	0.221831i	0.908528	+	0.417824i	$0.137207\pi$
$642$		0			0
$643$	−39.5698	+	28.7491i	−1.56048	+	1.13375i	−0.624864	+	0.780734i	$0.714846\pi$
$643$	−39.5698	+	28.7491i	−1.56048	+	1.13375i	−0.935615	+	0.353021i	$0.885154\pi$
$644$		0			0
$645$	1.07759	+	3.31649i	0.0424302	+	0.130587i
$646$		0			0
$647$	22.8181	+	16.5783i	0.897071	+	0.651760i	0.937712	−	0.347414i	$-0.112940\pi$
$647$	22.8181	+	16.5783i	0.897071	+	0.651760i	−0.0406412	+	0.999174i	$0.512940\pi$
$648$		0			0
$649$	−18.5861	+	30.4257i	−0.729570	+	1.19431i
$650$		0			0
$651$	21.3244	+	15.4931i	0.835768	+	0.607221i
$652$		0			0
$653$	−2.29757	−	7.07120i	−0.0899109	−	0.276717i	0.895983	−	0.444088i	$-0.146472\pi$
$653$	−2.29757	−	7.07120i	−0.0899109	−	0.276717i	−0.985894	+	0.167371i	$0.946472\pi$
$654$		0			0
$655$	5.21538	−	3.78920i	0.203782	−	0.148056i
$656$		0			0
$657$	−3.67410	+	11.3077i	−0.143340	+	0.441157i
$658$		0			0
$659$	−49.6193			−1.93290			−0.966448	−	0.256864i	$-0.917311\pi$
$659$	−49.6193			−1.93290			−0.966448	+	0.256864i	$0.917311\pi$
$660$		0			0
$661$	2.32445			0.0904105			0.0452053	−	0.998978i	$-0.485606\pi$
$661$	2.32445			0.0904105			0.0452053	+	0.998978i	$0.485606\pi$
$662$		0			0
$663$	0.131110	−	0.403516i	0.00509190	−	0.0156713i
$664$		0			0
$665$	5.87652	−	4.26954i	0.227881	−	0.165566i
$666$		0			0
$667$	0.832974	+	2.56363i	0.0322529	+	0.0992642i
$668$		0			0
$669$	−18.1988	−	13.2222i	−0.703605	−	0.511199i
$670$		0			0
$671$	4.76535	+	1.13698i	0.183964	+	0.0438927i
$672$		0			0
$673$	11.6663	+	8.47607i	0.449703	+	0.326728i	0.789479	−	0.613778i	$-0.210351\pi$
$673$	11.6663	+	8.47607i	0.449703	+	0.326728i	−0.339775	+	0.940507i	$0.610351\pi$
$674$		0			0
$675$	1.45409	+	4.47523i	0.0559680	+	0.172252i
$676$		0			0
$677$	4.89118	−	3.55365i	0.187984	−	0.136578i	−0.489813	−	0.871827i	$-0.662935\pi$
$677$	4.89118	−	3.55365i	0.187984	−	0.136578i	0.677797	+	0.735249i	$0.262935\pi$
$678$		0			0
$679$	0.796706	−	2.45201i	0.0305748	−	0.0940995i
$680$		0			0
$681$	−0.949682			−0.0363919
$682$		0			0
$683$	−46.4977			−1.77918			−0.889592	−	0.456755i	$-0.849012\pi$
$683$	−46.4977			−1.77918			−0.889592	+	0.456755i	$0.849012\pi$
$684$		0			0
$685$	1.25473	−	3.86167i	0.0479409	−	0.147547i
$686$		0			0
$687$	−0.203032	+	0.147511i	−0.00774614	+	0.00562790i
$688$		0			0
$689$	0.255370	+	0.785948i	0.00972882	+	0.0299422i
$690$		0			0
$691$	−14.9628	−	10.8711i	−0.569210	−	0.413555i	0.265608	−	0.964081i	$-0.414427\pi$
$691$	−14.9628	−	10.8711i	−0.569210	−	0.413555i	−0.834818	+	0.550526i	$0.814427\pi$
$692$		0			0
$693$	−9.63915	+	4.00854i	−0.366161	+	0.152272i
$694$		0			0
$695$	−1.14310	−	0.830509i	−0.0433602	−	0.0315030i
$696$		0			0
$697$	−0.835284	−	2.57074i	−0.0316386	−	0.0973737i
$698$		0			0
$699$	−8.44548	+	6.13600i	−0.319438	+	0.232085i
$700$		0			0
$701$	−8.45639	+	26.0261i	−0.319393	+	0.982992i	0.654515	+	0.756049i	$0.272873\pi$
$701$	−8.45639	+	26.0261i	−0.319393	+	0.982992i	−0.973908	+	0.226943i	$0.927127\pi$
$702$		0			0
$703$	−24.5049			−0.924221
$704$		0			0
$705$	4.77628			0.179885
$706$		0			0
$707$	−0.370278	+	1.13960i	−0.0139257	+	0.0428590i
$708$		0			0
$709$	19.9646	−	14.5051i	0.749786	−	0.544752i	−0.145974	−	0.989288i	$-0.546632\pi$
$709$	19.9646	−	14.5051i	0.749786	−	0.544752i	0.895761	+	0.444537i	$0.146632\pi$
$710$		0			0
$711$	2.65446	+	8.16960i	0.0995501	+	0.306384i
$712$		0			0
$713$	15.3871	+	11.1794i	0.576251	+	0.418671i
$714$		0			0
$715$	−1.17076	−	1.36690i	−0.0437841	−	0.0511190i
$716$		0			0
$717$	−3.11354	−	2.26212i	−0.116277	−	0.0844805i
$718$		0			0
$719$	−11.9135	−	36.6659i	−0.444298	−	1.36741i	−0.883252	−	0.468899i	$-0.844651\pi$
$719$	−11.9135	−	36.6659i	−0.444298	−	1.36741i	0.438954	−	0.898510i	$-0.355349\pi$
$720$		0			0
$721$	−17.6156	+	12.7985i	−0.656038	+	0.476639i
$722$		0			0
$723$	−2.07022	+	6.37149i	−0.0769924	+	0.236958i
$724$		0			0
$725$	5.58468			0.207410
$726$		0			0
$727$	11.6734			0.432943			0.216471	−	0.976289i	$-0.430545\pi$
$727$	11.6734			0.432943			0.216471	+	0.976289i	$0.430545\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−2.20581	+	1.60262i	−0.0815850	+	0.0592749i
$732$		0			0
$733$	−0.925730	−	2.84910i	−0.0341926	−	0.105234i	0.932504	−	0.361161i	$-0.117619\pi$
$733$	−0.925730	−	2.84910i	−0.0341926	−	0.105234i	−0.966696	+	0.255927i	$0.917619\pi$
$734$		0			0
$735$	1.27638	+	0.927346i	0.0470801	+	0.0342057i
$736$		0			0
$737$	0.632543	+	0.738510i	0.0233000	+	0.0272034i
$738$		0			0
$739$	−3.06173	−	2.22448i	−0.112628	−	0.0818288i	0.530046	−	0.847969i	$-0.322175\pi$
$739$	−3.06173	−	2.22448i	−0.112628	−	0.0818288i	−0.642673	+	0.766140i	$0.722175\pi$
$740$		0			0
$741$	1.31416	+	4.04457i	0.0482769	+	0.148581i
$742$		0			0
$743$	9.16621	−	6.65964i	0.336276	−	0.244318i	−0.406813	−	0.913511i	$-0.633360\pi$
$743$	9.16621	−	6.65964i	0.336276	−	0.244318i	0.743089	+	0.669193i	$0.233360\pi$
$744$		0			0
$745$	−1.15217	+	3.54600i	−0.0422121	+	0.129916i
$746$		0			0
$747$	12.2147			0.446912
$748$		0			0
$749$	−61.4829			−2.24654
$750$		0			0
$751$	−3.85274	+	11.8575i	−0.140589	+	0.432687i	−0.996417	−	0.0845719i	$-0.973048\pi$
$751$	−3.85274	+	11.8575i	−0.140589	+	0.432687i	0.855829	+	0.517259i	$0.173048\pi$
$752$		0			0
$753$	−5.62380	+	4.08593i	−0.204943	+	0.148900i
$754$		0			0
$755$	1.70942	+	5.26106i	0.0622123	+	0.191470i
$756$		0			0
$757$	−3.08043	−	2.23806i	−0.111960	−	0.0813438i	0.530396	−	0.847750i	$-0.322043\pi$
$757$	−3.08043	−	2.23806i	−0.111960	−	0.0813438i	−0.642356	+	0.766406i	$0.722043\pi$
$758$		0			0
$759$	−6.95535	+	2.89245i	−0.252463	+	0.104989i
$760$		0			0
$761$	−13.3602	−	9.70674i	−0.484306	−	0.351869i	0.318684	−	0.947861i	$-0.396759\pi$
$761$	−13.3602	−	9.70674i	−0.484306	−	0.351869i	−0.802990	+	0.595992i	$0.796759\pi$
$762$		0			0
$763$	−16.6079	−	51.1138i	−0.601246	−	1.85044i
$764$		0			0
$765$	0.186263	−	0.135328i	0.00673437	−	0.00489280i
$766$		0			0
$767$	−3.32191	+	10.2238i	−0.119947	+	0.369159i
$768$		0			0
$769$	−10.4636			−0.377329			−0.188664	−	0.982042i	$-0.560416\pi$
$769$	−10.4636			−0.377329			−0.188664	+	0.982042i	$0.560416\pi$
$770$		0			0
$771$	22.8370			0.822455
$772$		0			0
$773$	7.41746	−	22.8286i	0.266788	−	0.821088i	−0.724489	−	0.689287i	$-0.757924\pi$
$773$	7.41746	−	22.8286i	0.266788	−	0.821088i	0.991276	−	0.131801i	$-0.0420760\pi$
$774$		0			0
$775$	31.8790	−	23.1615i	1.14513	−	0.831985i
$776$		0			0
$777$	−5.60467	−	17.2494i	−0.201066	−	0.618819i
$778$		0			0
$779$	21.9190	+	15.9251i	0.785331	+	0.570577i
$780$		0			0
$781$	−32.8612	−	7.84045i	−1.17586	−	0.280554i
$782$		0			0
$783$	−0.960167	−	0.697602i	−0.0343136	−	0.0249303i
$784$		0			0
$785$	−3.04406	−	9.36867i	−0.108647	−	0.334382i
$786$		0			0
$787$	4.96422	−	3.60672i	0.176955	−	0.128566i	−0.495782	−	0.868447i	$-0.665118\pi$
$787$	4.96422	−	3.60672i	0.176955	−	0.128566i	0.672737	+	0.739881i	$0.265118\pi$
$788$		0			0
$789$	−2.53874	+	7.81345i	−0.0903817	+	0.278166i
$790$		0			0
$791$	44.5206			1.58297
$792$		0			0
$793$	1.47714			0.0524547
$794$		0			0
$795$	−0.138575	+	0.426490i	−0.00491475	+	0.0151261i
$796$		0			0
$797$	−3.42689	+	2.48978i	−0.121387	+	0.0881926i	−0.646822	−	0.762641i	$-0.723902\pi$
$797$	−3.42689	+	2.48978i	−0.121387	+	0.0881926i	0.525436	+	0.850833i	$0.323902\pi$
$798$		0			0
$799$	1.15401	+	3.55169i	0.0408260	+	0.125650i
$800$		0			0
$801$	−0.863011	−	0.627014i	−0.0304930	−	0.0221544i
$802$		0			0
$803$	−20.5567	+	33.6515i	−0.725430	+	1.18754i
$804$		0			0
$805$	3.13844	+	2.28021i	0.110615	+	0.0803668i
$806$		0			0
$807$	−1.98416	−	6.10660i	−0.0698456	−	0.214963i
$808$		0			0
$809$	−26.0207	+	18.9051i	−0.914839	+	0.664669i	−0.942234	−	0.334955i	$-0.891279\pi$
$809$	−26.0207	+	18.9051i	−0.914839	+	0.664669i	0.0273952	+	0.999625i	$0.491279\pi$
$810$		0			0
$811$	7.63882	−	23.5099i	0.268235	−	0.825543i	−0.722695	−	0.691167i	$-0.757097\pi$
$811$	7.63882	−	23.5099i	0.268235	−	0.825543i	0.990930	−	0.134376i	$-0.0429030\pi$
$812$		0			0
$813$	−26.2684			−0.921273
$814$		0			0
$815$	6.60045			0.231204
$816$		0			0
$817$	8.44512	−	25.9914i	0.295457	−	0.909324i
$818$		0			0
$819$	−2.54647	+	1.85012i	−0.0889807	+	0.0646483i
$820$		0			0
$821$	10.1348	+	31.1916i	0.353705	+	1.08859i	0.956756	+	0.290890i	$0.0939515\pi$
$821$	10.1348	+	31.1916i	0.353705	+	1.08859i	−0.603051	+	0.797703i	$0.706048\pi$
$822$		0			0
$823$	9.03299	+	6.56285i	0.314870	+	0.228767i	0.733983	−	0.679167i	$-0.237659\pi$
$823$	9.03299	+	6.56285i	0.314870	+	0.228767i	−0.419113	+	0.907934i	$0.637659\pi$
$824$		0			0
$825$	1.24633	+	15.5567i	0.0433916	+	0.541613i
$826$		0			0
$827$	−4.72021	−	3.42943i	−0.164138	−	0.119253i	0.502684	−	0.864470i	$-0.332346\pi$
$827$	−4.72021	−	3.42943i	−0.164138	−	0.119253i	−0.666822	+	0.745217i	$0.732346\pi$
$828$		0			0
$829$	−0.0488770	−	0.150428i	−0.00169757	−	0.00522458i	0.950204	−	0.311628i	$-0.100874\pi$
$829$	−0.0488770	−	0.150428i	−0.00169757	−	0.00522458i	−0.951902	+	0.306404i	$0.900874\pi$
$830$		0			0
$831$	0.0252100	−	0.0183162i	0.000874526	−	0.000635381i
$832$		0			0
$833$	−0.381192	+	1.17319i	−0.0132075	+	0.0406486i
$834$		0			0
$835$	−10.3462			−0.358045
$836$		0			0
$837$	−8.37411			−0.289451
$838$		0			0
$839$	−6.46396	+	19.8940i	−0.223161	+	0.686818i	0.775312	+	0.631578i	$0.217592\pi$
$839$	−6.46396	+	19.8940i	−0.223161	+	0.686818i	−0.998473	+	0.0552401i	$0.982408\pi$
$840$		0			0
$841$	22.3219	−	16.2178i	0.769722	−	0.559236i
$842$		0			0
$843$	7.66269	+	23.5833i	0.263917	+	0.812253i
$844$		0			0
$845$	−0.439009	−	0.318959i	−0.0151024	−	0.0109725i
$846$		0			0
$847$	−34.1820	+	5.51240i	−1.17451	+	0.189408i
$848$		0			0
$849$	−17.3277	−	12.5893i	−0.594686	−	0.432065i
$850$		0			0
$851$	−4.04418	−	12.4467i	−0.138633	−	0.426667i
$852$		0			0
$853$	19.8876	−	14.4492i	0.680938	−	0.494730i	−0.192731	−	0.981252i	$-0.561734\pi$
$853$	19.8876	−	14.4492i	0.680938	−	0.494730i	0.873669	+	0.486521i	$0.161734\pi$
$854$		0			0
$855$	−0.713123	+	2.19477i	−0.0243883	+	0.0750594i
$856$		0			0
$857$	−44.3261			−1.51415			−0.757076	−	0.653327i	$-0.773373\pi$
$857$	−44.3261			−1.51415			−0.757076	+	0.653327i	$0.773373\pi$
$858$		0			0
$859$	−29.6499			−1.01164			−0.505821	−	0.862638i	$-0.668811\pi$
$859$	−29.6499			−1.01164			−0.505821	+	0.862638i	$0.668811\pi$
$860$		0			0
$861$	−6.19670	+	19.0715i	−0.211183	+	0.649954i
$862$		0			0
$863$	9.36463	−	6.80380i	0.318776	−	0.231604i	−0.416877	−	0.908963i	$-0.636876\pi$
$863$	9.36463	−	6.80380i	0.318776	−	0.231604i	0.735653	+	0.677359i	$0.236876\pi$
$864$		0			0
$865$	1.24880	+	3.84343i	0.0424606	+	0.130680i
$866$		0			0
$867$	−13.6077	−	9.88654i	−0.462140	−	0.335764i
$868$		0			0
$869$	2.27519	+	28.3989i	0.0771806	+	0.963366i
$870$		0			0
$871$	0.237189	+	0.172328i	0.00803683	+	0.00583910i
$872$		0			0
$873$	0.253115	+	0.779008i	0.00856664	+	0.0263654i
$874$		0			0
$875$	13.4114	−	9.74393i	0.453387	−	0.329405i
$876$		0			0
$877$	8.50809	−	26.1852i	0.287298	−	0.884211i	−0.698403	−	0.715705i	$-0.746106\pi$
$877$	8.50809	−	26.1852i	0.287298	−	0.884211i	0.985701	−	0.168506i	$-0.0538944\pi$
$878$		0			0
$879$	−21.7951			−0.735131
$880$		0			0
$881$	1.05880			0.0356720			0.0178360	−	0.999841i	$-0.494322\pi$
$881$	1.05880			0.0356720			0.0178360	+	0.999841i	$0.494322\pi$
$882$		0			0
$883$	−2.25424	+	6.93782i	−0.0758611	+	0.233476i	−0.981795	−	0.189942i	$-0.939170\pi$
$883$	−2.25424	+	6.93782i	−0.0758611	+	0.233476i	0.905934	+	0.423418i	$0.139170\pi$
$884$		0			0
$885$	−4.71931	+	3.42878i	−0.158638	+	0.115257i
$886$		0			0
$887$	−6.62805	−	20.3991i	−0.222548	−	0.684933i	−0.998531	−	0.0541793i	$-0.982746\pi$
$887$	−6.62805	−	20.3991i	−0.222548	−	0.684933i	0.775983	−	0.630754i	$-0.217254\pi$
$888$		0			0
$889$	−8.73359	−	6.34533i	−0.292915	−	0.212815i
$890$		0			0
$891$	1.72896	−	2.83032i	0.0579222	−	0.0948193i
$892$		0			0
$893$	−30.2829	−	22.0018i	−1.01338	−	0.736264i
$894$		0			0
$895$	−0.519828	−	1.59986i	−0.0173759	−	0.0534776i
$896$		0			0
$897$	−1.83746	+	1.33499i	−0.0613510	+	0.0445741i
$898$		0			0
$899$	−3.07121	+	9.45222i	−0.102431	+	0.315249i
$900$		0			0
$901$	−0.350624			−0.0116810
$902$		0			0
$903$	20.2273			0.673121
$904$		0			0
$905$	−1.26503	+	3.89338i	−0.0420512	+	0.129420i
$906$		0			0
$907$	34.9796	−	25.4141i	1.16148	−	0.843863i	0.171513	−	0.985182i	$-0.445134\pi$
$907$	34.9796	−	25.4141i	1.16148	−	0.843863i	0.989964	+	0.141319i	$0.0451344\pi$
$908$		0			0
$909$	−0.117638	−	0.362053i	−0.00390181	−	0.0120085i
$910$		0			0
$911$	13.2305	+	9.61249i	0.438345	+	0.318476i	0.784977	−	0.619525i	$-0.212675\pi$
$911$	13.2305	+	9.61249i	0.438345	+	0.318476i	−0.346632	+	0.938001i	$0.612675\pi$
$912$		0			0
$913$	39.4054	+	9.40187i	1.30413	+	0.311156i
$914$		0			0
$915$	0.648477	+	0.471146i	0.0214380	+	0.0155756i
$916$		0			0
$917$	−11.5551	−	35.5631i	−0.381585	−	1.17440i
$918$		0			0
$919$	19.7752	−	14.3675i	0.652325	−	0.473942i	−0.211738	−	0.977327i	$-0.567912\pi$
$919$	19.7752	−	14.3675i	0.652325	−	0.473942i	0.864062	+	0.503385i	$0.167912\pi$
$920$		0			0
$921$	−0.176225	+	0.542364i	−0.00580680	+	0.0178715i
$922$		0			0
$923$	−10.1861			−0.335280
$924$		0			0
$925$	−27.1142			−0.891509
$926$		0			0
$927$	2.13767	−	6.57908i	0.0702103	−	0.216085i
$928$		0			0
$929$	−7.65262	+	5.55995i	−0.251074	+	0.182416i	−0.706203	−	0.708010i	$-0.749593\pi$
$929$	−7.65262	+	5.55995i	−0.251074	+	0.182416i	0.455129	+	0.890426i	$0.349593\pi$
$930$		0			0
$931$	−3.82082	−	11.7593i	−0.125222	−	0.385394i
$932$		0			0
$933$	−1.50730	−	1.09512i	−0.0493467	−	0.0358525i
$934$		0			0
$935$	0.705064	−	0.293208i	0.0230580	−	0.00958893i
$936$		0			0
$937$	20.6011	+	14.9676i	0.673008	+	0.488969i	0.871031	−	0.491228i	$-0.163452\pi$
$937$	20.6011	+	14.9676i	0.673008	+	0.488969i	−0.198023	+	0.980197i	$0.563452\pi$
$938$		0			0
$939$	6.35717	+	19.5654i	0.207458	+	0.638491i
$940$		0			0
$941$	−24.0916	+	17.5036i	−0.785365	+	0.570601i	−0.906584	−	0.422025i	$-0.861319\pi$
$941$	−24.0916	+	17.5036i	−0.785365	+	0.570601i	0.121220	+	0.992626i	$0.461319\pi$
$942$		0			0
$943$	−4.47137	+	13.7615i	−0.145608	+	0.448135i
$944$		0			0
$945$	−1.70803			−0.0555623
$946$		0			0
$947$	−48.1273			−1.56393			−0.781963	−	0.623325i	$-0.785782\pi$
$947$	−48.1273			−1.56393			−0.781963	+	0.623325i	$0.785782\pi$
$948$		0			0
$949$	−3.67410	+	11.3077i	−0.119266	+	0.367064i
$950$		0			0
$951$	19.3622	−	14.0675i	0.627863	−	0.456169i
$952$		0			0
$953$	0.424296	+	1.30585i	0.0137443	+	0.0423006i	0.957693	−	0.287790i	$-0.0929206\pi$
$953$	0.424296	+	1.30585i	0.0137443	+	0.0423006i	−0.943949	+	0.330091i	$0.892921\pi$
$954$		0			0
$955$	2.38992	+	1.73638i	0.0773360	+	0.0561879i
$956$		0			0
$957$	−2.56061	−	2.98957i	−0.0827727	−	0.0966391i
$958$		0			0
$959$	−19.0542	−	13.8437i	−0.615293	−	0.447037i
$960$		0			0
$961$	12.0905	+	37.2107i	0.390016	+	1.20035i
$962$		0			0
$963$	15.8027	−	11.4813i	0.509235	−	0.369981i
$964$		0			0
$965$	−0.668357	+	2.05699i	−0.0215152	+	0.0662169i
$966$		0			0
$967$	−14.8966			−0.479042			−0.239521	−	0.970891i	$-0.576990\pi$
$967$	−14.8966			−0.479042			−0.239521	+	0.970891i	$0.576990\pi$
$968$		0			0
$969$	−1.80435			−0.0579641
$970$		0			0
$971$	−14.6497	+	45.0872i	−0.470132	+	1.44692i	0.382280	+	0.924047i	$0.375139\pi$
$971$	−14.6497	+	45.0872i	−0.470132	+	1.44692i	−0.852412	+	0.522871i	$0.824861\pi$
$972$		0			0
$973$	−6.63053	+	4.81736i	−0.212565	+	0.154437i
$974$		0			0
$975$	1.45409	+	4.47523i	0.0465682	+	0.143322i
$976$		0			0
$977$	−24.4406	−	17.7572i	−0.781925	−	0.568102i	0.123631	−	0.992328i	$-0.460546\pi$
$977$	−24.4406	−	17.7572i	−0.781925	−	0.568102i	−0.905556	+	0.424226i	$0.860546\pi$
$978$		0			0
$979$	−2.30151	−	2.68707i	−0.0735565	−	0.0858790i
$980$		0			0
$981$	13.8137	+	10.0362i	0.441037	+	0.320432i
$982$		0			0
$983$	−1.50839	−	4.64233i	−0.0481100	−	0.148067i	0.924116	−	0.382113i	$-0.124803\pi$
$983$	−1.50839	−	4.64233i	−0.0481100	−	0.148067i	−0.972226	+	0.234046i	$0.924803\pi$
$984$		0			0
$985$	3.44089	−	2.49995i	0.109636	−	0.0796551i
$986$		0			0
$987$	8.56124	−	26.3488i	0.272507	−	0.838691i
$988$		0			0
$989$	14.5954			0.464108
$990$		0			0
$991$	41.1929			1.30854			0.654268	−	0.756263i	$-0.272977\pi$
$991$	41.1929			1.30854			0.654268	+	0.756263i	$0.272977\pi$
$992$		0			0
$993$	7.24536	−	22.2989i	0.229924	−	0.707635i
$994$		0			0
$995$	1.37741	−	1.00075i	0.0436669	−	0.0317259i
$996$		0			0
$997$	−12.5669	−	38.6768i	−0.397996	−	1.22491i	−0.926603	−	0.376040i	$-0.877285\pi$
$997$	−12.5669	−	38.6768i	−0.397996	−	1.22491i	0.528607	−	0.848867i	$-0.322715\pi$
$998$		0			0
$999$	4.66171	+	3.38693i	0.147490	+	0.107158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.f.1093.2	yes	20
11.3	even	5	inner	1716.2.z.f.157.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.f.157.2	✓	20	11.3	even	5	inner
1716.2.z.f.1093.2	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.439009 + 0.318959i) q^{5} +(0.972664 + 2.99355i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-0.439009 + 0.318959i) q^{5} +(0.972664 + 2.99355i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.15752 - 2.51895i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(-0.167686 - 0.516086i) q^{15} +(0.343251 - 0.249387i) q^{17} +(-1.31416 + 4.04457i) q^{19} -3.14761 q^{21} -2.27123 q^{23} +(-1.45409 + 4.47523i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-0.366751 - 1.12874i) q^{29} +(-6.77479 - 4.92218i) q^{31} +(3.06238 - 1.27352i) q^{33} +(-1.38183 - 1.00396i) q^{35} +(1.78061 + 5.48017i) q^{37} +(0.809017 - 0.587785i) q^{39} +(1.96870 - 6.05904i) q^{41} -6.42624 q^{43} +0.542645 q^{45} +(-2.71992 + 8.37106i) q^{47} +(-2.35215 + 1.70894i) q^{49} +(0.131110 + 0.403516i) q^{51} +(-0.668567 - 0.485742i) q^{53} +(1.75061 + 0.417684i) q^{55} +(-3.44052 - 2.49968i) q^{57} +(-3.32191 - 10.2238i) q^{59} +(-1.19503 + 0.868241i) q^{61} +(0.972664 - 2.99355i) q^{63} +0.542645 q^{65} -0.293181 q^{67} +(0.701847 - 2.16006i) q^{69} +(8.24075 - 5.98725i) q^{71} +(-3.67410 - 11.3077i) q^{73} +(-3.80686 - 2.76585i) q^{75} +(5.44207 - 8.90873i) q^{77} +(-6.94947 - 5.04909i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-9.88188 + 7.17961i) q^{83} +(-0.0711463 + 0.218966i) q^{85} +1.18683 q^{87} +1.06674 q^{89} +(0.972664 - 2.99355i) q^{91} +(6.77479 - 4.92218i) q^{93} +(-0.713123 - 2.19477i) q^{95} +(-0.662664 - 0.481453i) q^{97} +(0.264864 + 3.30603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) \) 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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