LMFDB - Embedded newform 644.2.i.a.93.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 8 x^{11} + 130 x^{10} - 78 x^{9} + 505 x^{8} - 519 x^{7} + 1508 x^{6} - 955 x^{5} + \cdots + 1 $ x^14 + 13x^12 - 8x^11 + 130x^10 - 78x^9 + 505x^8 - 519x^7 + 1508x^6 - 955x^5 + 1023x^4 + 156x^3 + 107x^2 - 9x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.2
Root			$1.41340 + 2.44808i$ of defining polynomial
Character	$\chi$	$=$	644.93
Dual form			644.2.i.a.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17316 - 2.03197i) q^{3} +(-0.992835 + 1.71964i) q^{5} +(1.00344 + 2.44808i) q^{7} +(-1.25259 + 2.16955i) q^{9} +O(q^{10})$	\(q+(-1.17316 - 2.03197i) q^{3} +(-0.992835 + 1.71964i) q^{5} +(1.00344 + 2.44808i) q^{7} +(-1.25259 + 2.16955i) q^{9} +(-2.17247 - 3.76283i) q^{11} +5.20314 q^{13} +4.65900 q^{15} +(-2.14781 - 3.72012i) q^{17} +(3.32937 - 5.76663i) q^{19} +(3.79722 - 4.91094i) q^{21} +(0.500000 - 0.866025i) q^{23} +(0.528557 + 0.915487i) q^{25} -1.16100 q^{27} +0.865824 q^{29} +(-3.51221 - 6.08333i) q^{31} +(-5.09729 + 8.82877i) q^{33} +(-5.20607 - 0.704980i) q^{35} +(0.537832 - 0.931553i) q^{37} +(-6.10409 - 10.5726i) q^{39} -4.29433 q^{41} +6.80100 q^{43} +(-2.48723 - 4.30801i) q^{45} +(4.18509 - 7.24879i) q^{47} +(-4.98621 + 4.91302i) q^{49} +(-5.03944 + 8.72856i) q^{51} +(-0.387867 - 0.671805i) q^{53} +8.62762 q^{55} -15.6235 q^{57} +(-3.27900 - 5.67939i) q^{59} +(6.03548 - 10.4538i) q^{61} +(-6.56814 - 0.889425i) q^{63} +(-5.16586 + 8.94753i) q^{65} +(0.261374 + 0.452712i) q^{67} -2.34631 q^{69} +2.90210 q^{71} +(-0.498631 - 0.863655i) q^{73} +(1.24016 - 2.14802i) q^{75} +(7.03176 - 9.09417i) q^{77} +(-4.98240 + 8.62978i) q^{79} +(5.11980 + 8.86776i) q^{81} +13.8296 q^{83} +8.52969 q^{85} +(-1.01575 - 1.75932i) q^{87} +(1.66892 - 2.89066i) q^{89} +(5.22105 + 12.7377i) q^{91} +(-8.24075 + 14.2734i) q^{93} +(6.61103 + 11.4506i) q^{95} -13.7740 q^{97} +10.8849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	$ 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) $ 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.17316	−	2.03197i	−0.677322	−	1.17316i	−0.975784	−	0.218735i	$-0.929807\pi$
$3$	−1.17316	−	2.03197i	−0.677322	−	1.17316i	0.298462	−	0.954421i	$-0.403526\pi$
$4$		0			0
$5$	−0.992835	+	1.71964i	−0.444009	+	0.769047i	−0.997983	−	0.0634876i	$-0.979778\pi$
$5$	−0.992835	+	1.71964i	−0.444009	+	0.769047i	0.553973	+	0.832534i	$0.313111\pi$
$6$		0			0
$7$	1.00344	+	2.44808i	0.379266	+	0.925288i
$7$	1.00344	+	2.44808i	0.379266	+	0.925288i
$8$		0			0
$9$	−1.25259	+	2.16955i	−0.417530	+	0.723184i
$10$		0			0
$11$	−2.17247	−	3.76283i	−0.655024	−	1.13454i	−0.981888	−	0.189464i	$-0.939325\pi$
$11$	−2.17247	−	3.76283i	−0.655024	−	1.13454i	0.326863	−	0.945072i	$-0.394008\pi$
$12$		0			0
$13$	5.20314			1.44309			0.721545	−	0.692367i	$-0.243432\pi$
$13$	5.20314			1.44309			0.721545	+	0.692367i	$0.243432\pi$
$14$		0			0
$15$	4.65900			1.20295
$16$		0			0
$17$	−2.14781	−	3.72012i	−0.520921	−	0.902261i	−0.999704	−	0.0243282i	$-0.992255\pi$
$17$	−2.14781	−	3.72012i	−0.520921	−	0.902261i	0.478783	−	0.877933i	$-0.341078\pi$
$18$		0			0
$19$	3.32937	−	5.76663i	0.763809	−	1.32296i	−0.177064	−	0.984199i	$-0.556660\pi$
$19$	3.32937	−	5.76663i	0.763809	−	1.32296i	0.940874	−	0.338757i	$-0.110007\pi$
$20$		0			0
$21$	3.79722	−	4.91094i	0.828622	−	1.07166i
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$		0			0
$25$	0.528557	+	0.915487i	0.105711	+	0.183097i
$26$		0			0
$27$	−1.16100			−0.223434
$28$		0			0
$29$	0.865824			0.160779			0.0803897	−	0.996764i	$-0.474384\pi$
$29$	0.865824			0.160779			0.0803897	+	0.996764i	$0.474384\pi$
$30$		0			0
$31$	−3.51221	−	6.08333i	−0.630812	−	1.09260i	−0.987386	−	0.158331i	$-0.949389\pi$
$31$	−3.51221	−	6.08333i	−0.630812	−	1.09260i	0.356574	−	0.934267i	$-0.383945\pi$
$32$		0			0
$33$	−5.09729	+	8.82877i	−0.887325	+	1.53689i
$34$		0			0
$35$	−5.20607	−	0.704980i	−0.879987	−	0.119163i
$36$		0			0
$37$	0.537832	−	0.931553i	0.0884191	−	0.153146i	−0.818424	−	0.574615i	$-0.805152\pi$
$37$	0.537832	−	0.931553i	0.0884191	−	0.153146i	0.906843	+	0.421469i	$0.138485\pi$
$38$		0			0
$39$	−6.10409	−	10.5726i	−0.977437	−	1.69297i
$40$		0			0
$41$	−4.29433			−0.670662			−0.335331	−	0.942100i	$-0.608848\pi$
$41$	−4.29433			−0.670662			−0.335331	+	0.942100i	$0.608848\pi$
$42$		0			0
$43$	6.80100			1.03714			0.518571	−	0.855034i	$-0.326464\pi$
$43$	6.80100			1.03714			0.518571	+	0.855034i	$0.326464\pi$
$44$		0			0
$45$	−2.48723	−	4.30801i	−0.370775	−	0.642201i
$46$		0			0
$47$	4.18509	−	7.24879i	0.610458	−	1.05734i	−0.380705	−	0.924696i	$-0.624319\pi$
$47$	4.18509	−	7.24879i	0.610458	−	1.05734i	0.991163	−	0.132648i	$-0.0423479\pi$
$48$		0			0
$49$	−4.98621	+	4.91302i	−0.712315	+	0.701860i
$50$		0			0
$51$	−5.03944	+	8.72856i	−0.705662	+	1.22224i
$52$		0			0
$53$	−0.387867	−	0.671805i	−0.0532776	−	0.0922795i	0.838157	−	0.545430i	$-0.183633\pi$
$53$	−0.387867	−	0.671805i	−0.0532776	−	0.0922795i	−0.891434	+	0.453150i	$0.850300\pi$
$54$		0			0
$55$	8.62762			1.16335
$56$		0			0
$57$	−15.6235			−2.06938
$58$		0			0
$59$	−3.27900	−	5.67939i	−0.426889	−	0.739394i	0.569705	−	0.821849i	$-0.307057\pi$
$59$	−3.27900	−	5.67939i	−0.426889	−	0.739394i	−0.996595	+	0.0824549i	$0.973724\pi$
$60$		0			0
$61$	6.03548	−	10.4538i	0.772765	−	1.33847i	−0.163278	−	0.986580i	$-0.552207\pi$
$61$	6.03548	−	10.4538i	0.772765	−	1.33847i	0.936042	−	0.351888i	$-0.114460\pi$
$62$		0			0
$63$	−6.56814	−	0.889425i	−0.827508	−	0.112057i
$64$		0			0
$65$	−5.16586	+	8.94753i	−0.640746	+	1.10980i
$66$		0			0
$67$	0.261374	+	0.452712i	0.0319319	+	0.0553076i	0.881550	−	0.472091i	$-0.156501\pi$
$67$	0.261374	+	0.452712i	0.0319319	+	0.0553076i	−0.849618	+	0.527399i	$0.823167\pi$
$68$		0			0
$69$	−2.34631			−0.282463
$70$		0			0
$71$	2.90210			0.344416			0.172208	−	0.985061i	$-0.444910\pi$
$71$	2.90210			0.344416			0.172208	+	0.985061i	$0.444910\pi$
$72$		0			0
$73$	−0.498631	−	0.863655i	−0.0583604	−	0.101083i	0.835369	−	0.549689i	$-0.185254\pi$
$73$	−0.498631	−	0.863655i	−0.0583604	−	0.101083i	−0.893730	+	0.448606i	$0.851921\pi$
$74$		0			0
$75$	1.24016	−	2.14802i	0.143201	−	0.248032i
$76$		0			0
$77$	7.03176	−	9.09417i	0.801344	−	1.03638i
$78$		0			0
$79$	−4.98240	+	8.62978i	−0.560564	+	0.970926i	0.436883	+	0.899518i	$0.356082\pi$
$79$	−4.98240	+	8.62978i	−0.560564	+	0.970926i	−0.997447	+	0.0714074i	$0.977251\pi$
$80$		0			0
$81$	5.11980	+	8.86776i	0.568867	+	0.985307i
$82$		0			0
$83$	13.8296			1.51800			0.758999	−	0.651092i	$-0.225689\pi$
$83$	13.8296			1.51800			0.758999	+	0.651092i	$0.225689\pi$
$84$		0			0
$85$	8.52969			0.925175
$86$		0			0
$87$	−1.01575	−	1.75932i	−0.108899	−	0.188619i
$88$		0			0
$89$	1.66892	−	2.89066i	0.176906	−	0.306409i	−0.763914	−	0.645319i	$-0.776725\pi$
$89$	1.66892	−	2.89066i	0.176906	−	0.306409i	0.940819	+	0.338909i	$0.110058\pi$
$90$		0			0
$91$	5.22105	+	12.7377i	0.547315	+	1.33527i
$92$		0			0
$93$	−8.24075	+	14.2734i	−0.854526	+	1.48008i
$94$		0			0
$95$	6.61103	+	11.4506i	0.678277	+	1.17481i
$96$		0			0
$97$	−13.7740			−1.39854			−0.699268	−	0.714860i	$-0.746491\pi$
$97$	−13.7740			−1.39854			−0.699268	+	0.714860i	$0.746491\pi$
$98$		0			0
$99$	10.8849			1.09397
$100$		0			0
$101$	5.67403	+	9.82770i	0.564587	+	0.977893i	0.997088	+	0.0762595i	$0.0242978\pi$
$101$	5.67403	+	9.82770i	0.564587	+	0.977893i	−0.432501	+	0.901633i	$0.642369\pi$
$102$		0			0
$103$	6.18711	−	10.7164i	0.609634	−	1.05592i	−0.381667	−	0.924300i	$-0.624650\pi$
$103$	6.18711	−	10.7164i	0.609634	−	1.05592i	0.991301	−	0.131617i	$-0.0420169\pi$
$104$		0			0
$105$	4.67504	+	11.4056i	0.456237	+	1.11307i
$106$		0			0
$107$	7.06326	−	12.2339i	0.682831	−	1.18270i	−0.291282	−	0.956637i	$-0.594082\pi$
$107$	7.06326	−	12.2339i	0.682831	−	1.18270i	0.974113	−	0.226061i	$-0.0725850\pi$
$108$		0			0
$109$	6.87528	+	11.9083i	0.658533	+	1.14061i	0.980996	+	0.194030i	$0.0621559\pi$
$109$	6.87528	+	11.9083i	0.658533	+	1.14061i	−0.322463	+	0.946582i	$0.604511\pi$
$110$		0			0
$111$	−2.52384			−0.239553
$112$		0			0
$113$	7.88208			0.741483			0.370742	−	0.928736i	$-0.379104\pi$
$113$	7.88208			0.741483			0.370742	+	0.928736i	$0.379104\pi$
$114$		0			0
$115$	0.992835	+	1.71964i	0.0925824	+	0.160357i
$116$		0			0
$117$	−6.51740	+	11.2885i	−0.602534	+	1.04362i
$118$		0			0
$119$	6.95195	−	8.99094i	0.637284	−	0.824199i
$120$		0			0
$121$	−3.93925	+	6.82298i	−0.358114	+	0.620271i
$122$		0			0
$123$	5.03792	+	8.72594i	0.454254	+	0.786791i
$124$		0			0
$125$	−12.0274			−1.07577
$126$		0			0
$127$	−13.7078			−1.21637			−0.608183	−	0.793797i	$-0.708101\pi$
$127$	−13.7078			−1.21637			−0.608183	+	0.793797i	$0.708101\pi$
$128$		0			0
$129$	−7.97863	−	13.8194i	−0.702480	−	1.21673i
$130$		0			0
$131$	−7.22191	+	12.5087i	−0.630981	+	1.09289i	0.356370	+	0.934345i	$0.384014\pi$
$131$	−7.22191	+	12.5087i	−0.630981	+	1.09289i	−0.987351	+	0.158547i	$0.949319\pi$
$132$		0			0
$133$	17.4580	+	2.36408i	1.51380	+	0.204991i
$134$		0			0
$135$	1.15268	−	1.99650i	0.0992069	−	0.171831i
$136$		0			0
$137$	−3.96432	−	6.86641i	−0.338695	−	0.586637i	0.645493	−	0.763766i	$-0.276652\pi$
$137$	−3.96432	−	6.86641i	−0.338695	−	0.586637i	−0.984187	+	0.177130i	$0.943319\pi$
$138$		0			0
$139$	1.90139			0.161274			0.0806371	−	0.996744i	$-0.474305\pi$
$139$	1.90139			0.161274			0.0806371	+	0.996744i	$0.474305\pi$
$140$		0			0
$141$	−19.6391			−1.65391
$142$		0			0
$143$	−11.3037	−	19.5785i	−0.945259	−	1.63724i
$144$		0			0
$145$	−0.859620	+	1.48891i	−0.0713876	+	0.123647i
$146$		0			0
$147$	15.8327	+	4.36806i	1.30586	+	0.360272i
$148$		0			0
$149$	−0.354908	+	0.614718i	−0.0290752	+	0.0503597i	−0.880197	−	0.474609i	$-0.842590\pi$
$149$	−0.354908	+	0.614718i	−0.0290752	+	0.0503597i	0.851122	+	0.524968i	$0.175923\pi$
$150$		0			0
$151$	10.5141	+	18.2110i	0.855628	+	1.48199i	0.876061	+	0.482200i	$0.160162\pi$
$151$	10.5141	+	18.2110i	0.855628	+	1.48199i	−0.0204330	+	0.999791i	$0.506504\pi$
$152$		0			0
$153$	10.7613			0.870001
$154$		0			0
$155$	13.9482			1.12035
$156$		0			0
$157$	−7.86320	−	13.6195i	−0.627552	−	1.08695i	−0.988041	−	0.154189i	$-0.950724\pi$
$157$	−7.86320	−	13.6195i	−0.627552	−	1.08695i	0.360489	−	0.932763i	$-0.382610\pi$
$158$		0			0
$159$	−0.910056	+	1.57626i	−0.0721722	+	0.125006i
$160$		0			0
$161$	2.62182	+	0.355034i	0.206629	+	0.0279806i
$162$		0			0
$163$	−4.68380	+	8.11257i	−0.366863	+	0.635426i	−0.989073	−	0.147425i	$-0.952902\pi$
$163$	−4.68380	+	8.11257i	−0.366863	+	0.635426i	0.622210	+	0.782850i	$0.286235\pi$
$164$		0			0
$165$	−10.1215	−	17.5310i	−0.787961	−	1.36479i
$166$		0			0
$167$	4.37743			0.338736			0.169368	−	0.985553i	$-0.445827\pi$
$167$	4.37743			0.338736			0.169368	+	0.985553i	$0.445827\pi$
$168$		0			0
$169$	14.0726			1.08251
$170$		0			0
$171$	8.34067	+	14.4465i	0.637827	+	1.10475i
$172$		0			0
$173$	−9.60915	+	16.6435i	−0.730570	+	1.26538i	0.226070	+	0.974111i	$0.427412\pi$
$173$	−9.60915	+	16.6435i	−0.730570	+	1.26538i	−0.956640	+	0.291273i	$0.905921\pi$
$174$		0			0
$175$	−1.71081	+	2.21259i	−0.129325	+	0.167256i
$176$		0			0
$177$	−7.69356	+	13.3256i	−0.578283	+	1.00162i
$178$		0			0
$179$	−1.51564	−	2.62516i	−0.113284	−	0.196214i	0.803808	−	0.594888i	$-0.202804\pi$
$179$	−1.51564	−	2.62516i	−0.113284	−	0.196214i	−0.917093	+	0.398674i	$0.869470\pi$
$180$		0			0
$181$	24.2473			1.80229			0.901143	−	0.433522i	$-0.142729\pi$
$181$	24.2473			1.80229			0.901143	+	0.433522i	$0.142729\pi$
$182$		0			0
$183$	−28.3223			−2.09364
$184$		0			0
$185$	1.06796	+	1.84976i	0.0785178	+	0.135997i
$186$		0			0
$187$	−9.33211	+	16.1637i	−0.682432	+	1.18201i
$188$		0			0
$189$	−1.16500	−	2.84222i	−0.0847409	−	0.206741i
$190$		0			0
$191$	−10.6424	+	18.4331i	−0.770056	+	1.33378i	0.167476	+	0.985876i	$0.446438\pi$
$191$	−10.6424	+	18.4331i	−0.770056	+	1.33378i	−0.937532	+	0.347899i	$0.886895\pi$
$192$		0			0
$193$	−0.439287	−	0.760867i	−0.0316206	−	0.0547684i	0.849782	−	0.527134i	$-0.176733\pi$
$193$	−0.439287	−	0.760867i	−0.0316206	−	0.0547684i	−0.881403	+	0.472366i	$0.843400\pi$
$194$		0			0
$195$	24.2414			1.73596
$196$		0			0
$197$	−19.0904			−1.36014			−0.680068	−	0.733149i	$-0.738050\pi$
$197$	−19.0904			−1.36014			−0.680068	+	0.733149i	$0.738050\pi$
$198$		0			0
$199$	−4.19010	−	7.25746i	−0.297028	−	0.514468i	0.678426	−	0.734668i	$-0.262662\pi$
$199$	−4.19010	−	7.25746i	−0.297028	−	0.514468i	−0.975455	+	0.220200i	$0.929329\pi$
$200$		0			0
$201$	0.613264	−	1.06220i	0.0432563	−	0.0749222i
$202$		0			0
$203$	0.868804	+	2.11961i	0.0609781	+	0.148767i
$204$		0			0
$205$	4.26356	−	7.38471i	0.297780	−	0.515771i
$206$		0			0
$207$	1.25259	+	2.16955i	0.0870611	+	0.150794i
$208$		0			0
$209$	−28.9318			−2.00125
$210$		0			0
$211$	−14.6531			−1.00876			−0.504382	−	0.863481i	$-0.668280\pi$
$211$	−14.6531			−1.00876			−0.504382	+	0.863481i	$0.668280\pi$
$212$		0			0
$213$	−3.40462	−	5.89697i	−0.233281	−	0.404054i
$214$		0			0
$215$	−6.75227	+	11.6953i	−0.460501	+	0.797611i
$216$		0			0
$217$	11.3682	−	14.7025i	0.771723	−	0.998068i
$218$		0			0
$219$	−1.16994	+	2.02640i	−0.0790576	+	0.136932i
$220$		0			0
$221$	−11.1754	−	19.3563i	−0.751736	−	1.30205i
$222$		0			0
$223$	−10.2471			−0.686197			−0.343098	−	0.939300i	$-0.611476\pi$
$223$	−10.2471			−0.686197			−0.343098	+	0.939300i	$0.611476\pi$
$224$		0			0
$225$	−2.64826			−0.176551
$226$		0			0
$227$	−5.64923	−	9.78475i	−0.374953	−	0.649437i	0.615367	−	0.788240i	$-0.289008\pi$
$227$	−5.64923	−	9.78475i	−0.374953	−	0.649437i	−0.990320	+	0.138804i	$0.955674\pi$
$228$		0			0
$229$	2.42951	−	4.20803i	0.160546	−	0.278075i	−0.774518	−	0.632551i	$-0.782008\pi$
$229$	2.42951	−	4.20803i	0.160546	−	0.278075i	0.935065	+	0.354477i	$0.115341\pi$
$230$		0			0
$231$	−26.7284	−	3.61942i	−1.75860	−	0.238141i
$232$		0			0
$233$	6.66838	−	11.5500i	0.436860	−	0.756664i	−0.560586	−	0.828097i	$-0.689424\pi$
$233$	6.66838	−	11.5500i	0.436860	−	0.756664i	0.997445	+	0.0714330i	$0.0227572\pi$
$234$		0			0
$235$	8.31021	+	14.3937i	0.542098	+	0.938942i
$236$		0			0
$237$	23.3806			1.51873
$238$		0			0
$239$	24.8792			1.60930			0.804651	−	0.593749i	$-0.202353\pi$
$239$	24.8792			1.60930			0.804651	+	0.593749i	$0.202353\pi$
$240$		0			0
$241$	11.6136	+	20.1153i	0.748095	+	1.29574i	0.948735	+	0.316074i	$0.102365\pi$
$241$	11.6136	+	20.1153i	0.748095	+	1.29574i	−0.200640	+	0.979665i	$0.564302\pi$
$242$		0			0
$243$	10.2712	−	17.7902i	0.658895	−	1.14124i
$244$		0			0
$245$	−3.49815	−	13.4523i	−0.223488	−	0.859436i
$246$		0			0
$247$	17.3232	−	30.0046i	1.10225	−	1.90915i
$248$		0			0
$249$	−16.2243	−	28.1013i	−1.02817	−	1.78085i
$250$		0			0
$251$	−20.2281			−1.27679			−0.638393	−	0.769711i	$-0.720400\pi$
$251$	−20.2281			−1.27679			−0.638393	+	0.769711i	$0.720400\pi$
$252$		0			0
$253$	−4.34494			−0.273164
$254$		0			0
$255$	−10.0067	−	17.3320i	−0.626641	−	1.08537i
$256$		0			0
$257$	−10.6173	+	18.3897i	−0.662287	+	1.14712i	0.317726	+	0.948183i	$0.397081\pi$
$257$	−10.6173	+	18.3897i	−0.662287	+	1.14712i	−0.980013	+	0.198933i	$0.936253\pi$
$258$		0			0
$259$	2.82020	+	0.381897i	0.175239	+	0.0237299i
$260$		0			0
$261$	−1.08452	+	1.87845i	−0.0671303	+	0.116273i
$262$		0			0
$263$	8.03443	+	13.9160i	0.495424	+	0.858099i	0.999986	−	0.00527592i	$-0.00167939\pi$
$263$	8.03443	+	13.9160i	0.495424	+	0.858099i	−0.504562	+	0.863375i	$0.668346\pi$
$264$		0			0
$265$	1.54035			0.0946230
$266$		0			0
$267$	−7.83163			−0.479288
$268$		0			0
$269$	6.91958	+	11.9851i	0.421894	+	0.730742i	0.996125	−	0.0879513i	$-0.0280320\pi$
$269$	6.91958	+	11.9851i	0.421894	+	0.730742i	−0.574230	+	0.818694i	$0.694699\pi$
$270$		0			0
$271$	−16.2706	+	28.1815i	−0.988367	+	1.71190i	−0.362473	+	0.931994i	$0.618068\pi$
$271$	−16.2706	+	28.1815i	−0.988367	+	1.71190i	−0.625894	+	0.779908i	$0.715266\pi$
$272$		0			0
$273$	19.7575	−	25.5523i	1.19578	−	1.54650i
$274$		0			0
$275$	2.29655	−	3.97774i	0.138487	−	0.239866i
$276$		0			0
$277$	6.09209	+	10.5518i	0.366038	+	0.633997i	0.988942	−	0.148301i	$-0.0473805\pi$
$277$	6.09209	+	10.5518i	0.366038	+	0.633997i	−0.622904	+	0.782298i	$0.714047\pi$
$278$		0			0
$279$	17.5975			1.05353
$280$		0			0
$281$	−14.7288			−0.878644			−0.439322	−	0.898330i	$-0.644781\pi$
$281$	−14.7288			−0.878644			−0.439322	+	0.898330i	$0.644781\pi$
$282$		0			0
$283$	−2.85042	−	4.93708i	−0.169440	−	0.293479i	0.768783	−	0.639510i	$-0.220863\pi$
$283$	−2.85042	−	4.93708i	−0.169440	−	0.293479i	−0.938223	+	0.346031i	$0.887529\pi$
$284$		0			0
$285$	15.5115	−	26.8668i	0.918824	−	1.59145i
$286$		0			0
$287$	−4.30912	−	10.5129i	−0.254359	−	0.620555i
$288$		0			0
$289$	−0.726192	+	1.25780i	−0.0427172	+	0.0739883i
$290$		0			0
$291$	16.1590	+	27.9883i	0.947259	+	1.64070i
$292$		0			0
$293$	28.0341			1.63777			0.818883	−	0.573960i	$-0.194593\pi$
$293$	28.0341			1.63777			0.818883	+	0.573960i	$0.194593\pi$
$294$		0			0
$295$	13.0220			0.758172
$296$		0			0
$297$	2.52223	+	4.36864i	0.146355	+	0.253494i
$298$		0			0
$299$	2.60157	−	4.50605i	0.150453	−	0.260592i
$300$		0			0
$301$	6.82441	+	16.6494i	0.393353	+	0.959655i
$302$		0			0
$303$	13.3130	−	23.0589i	0.764814	−	1.32470i
$304$		0			0
$305$	11.9845	+	20.7577i	0.686230	+	1.18858i
$306$		0			0
$307$	24.7494			1.41252			0.706262	−	0.707951i	$-0.250380\pi$
$307$	24.7494			1.41252			0.706262	+	0.707951i	$0.250380\pi$
$308$		0			0
$309$	−29.0338			−1.65167
$310$		0			0
$311$	−8.14020	−	14.0992i	−0.461589	−	0.799495i	0.537452	−	0.843295i	$-0.319387\pi$
$311$	−8.14020	−	14.0992i	−0.461589	−	0.799495i	−0.999040	+	0.0437996i	$0.986054\pi$
$312$		0			0
$313$	5.09103	−	8.81792i	0.287762	−	0.498418i	−0.685513	−	0.728060i	$-0.740422\pi$
$313$	5.09103	−	8.81792i	0.287762	−	0.498418i	0.973275	+	0.229642i	$0.0737555\pi$
$314$		0			0
$315$	8.05057	−	10.4118i	0.453598	−	0.586638i
$316$		0			0
$317$	2.02072	−	3.49999i	0.113495	−	0.196579i	−0.803682	−	0.595059i	$-0.797129\pi$
$317$	2.02072	−	3.49999i	0.113495	−	0.196579i	0.917177	+	0.398480i	$0.130462\pi$
$318$		0			0
$319$	−1.88098	−	3.25795i	−0.105314	−	0.182410i
$320$		0			0
$321$	−33.1452			−1.84999
$322$		0			0
$323$	−28.6034			−1.59154
$324$		0			0
$325$	2.75015	+	4.76340i	0.152551	+	0.264226i
$326$		0			0
$327$	16.1316	−	27.9407i	0.892077	−	1.54512i
$328$		0			0
$329$	21.9451	+	2.97170i	1.20987	+	0.163835i
$330$		0			0
$331$	15.5555	−	26.9430i	0.855010	−	1.48092i	−0.0216257	−	0.999766i	$-0.506884\pi$
$331$	15.5555	−	26.9430i	0.855010	−	1.48092i	0.876636	−	0.481155i	$-0.159782\pi$
$332$		0			0
$333$	1.34737	+	2.33371i	0.0738353	+	0.127886i
$334$		0			0
$335$	−1.03800			−0.0567122
$336$		0			0
$337$	−2.88914			−0.157382			−0.0786909	−	0.996899i	$-0.525074\pi$
$337$	−2.88914			−0.157382			−0.0786909	+	0.996899i	$0.525074\pi$
$338$		0			0
$339$	−9.24691	−	16.0161i	−0.502223	−	0.869876i
$340$		0			0
$341$	−15.2604	+	26.4317i	−0.826394	+	1.43136i
$342$		0			0
$343$	−17.0308	−	7.27671i	−0.919579	−	0.392905i
$344$		0			0
$345$	2.32950	−	4.03481i	0.125416	−	0.217227i
$346$		0			0
$347$	3.68801	+	6.38782i	0.197983	+	0.342916i	0.947874	−	0.318645i	$-0.103228\pi$
$347$	3.68801	+	6.38782i	0.197983	+	0.342916i	−0.749892	+	0.661561i	$0.769894\pi$
$348$		0			0
$349$	10.7490			0.575380			0.287690	−	0.957724i	$-0.407113\pi$
$349$	10.7490			0.575380			0.287690	+	0.957724i	$0.407113\pi$
$350$		0			0
$351$	−6.04083			−0.322436
$352$		0			0
$353$	11.7093	+	20.2811i	0.623223	+	1.07945i	0.988882	+	0.148705i	$0.0475104\pi$
$353$	11.7093	+	20.2811i	0.623223	+	1.07945i	−0.365659	+	0.930749i	$0.619156\pi$
$354$		0			0
$355$	−2.88131	+	4.99057i	−0.152924	+	0.264872i
$356$		0			0
$357$	−26.4250	−	3.57834i	−1.39856	−	0.189386i
$358$		0			0
$359$	−12.4062	+	21.4882i	−0.654776	+	1.13411i	0.327173	+	0.944964i	$0.393904\pi$
$359$	−12.4062	+	21.4882i	−0.654776	+	1.13411i	−0.981950	+	0.189142i	$0.939429\pi$
$360$		0			0
$361$	−12.6694	−	21.9440i	−0.666809	−	1.15495i
$362$		0			0
$363$	18.4854			0.970233
$364$		0			0
$365$	1.98024			0.103650
$366$		0			0
$367$	−12.5533	−	21.7430i	−0.655277	−	1.13497i	−0.981824	−	0.189792i	$-0.939219\pi$
$367$	−12.5533	−	21.7430i	−0.655277	−	1.13497i	0.326547	−	0.945181i	$-0.394115\pi$
$368$		0			0
$369$	5.37904	−	9.31677i	0.280022	−	0.485012i
$370$		0			0
$371$	1.25543	−	1.62365i	0.0651787	−	0.0842955i
$372$		0			0
$373$	6.32308	−	10.9519i	0.327397	−	0.567068i	−0.654598	−	0.755977i	$-0.727162\pi$
$373$	6.32308	−	10.9519i	0.327397	−	0.567068i	0.981994	+	0.188910i	$0.0604953\pi$
$374$		0			0
$375$	14.1101	+	24.4393i	0.728640	+	1.26204i
$376$		0			0
$377$	4.50500			0.232019
$378$		0			0
$379$	−9.28918			−0.477153			−0.238577	−	0.971124i	$-0.576681\pi$
$379$	−9.28918			−0.477153			−0.238577	+	0.971124i	$0.576681\pi$
$380$		0			0
$381$	16.0813	+	27.8537i	0.823872	+	1.42699i
$382$		0			0
$383$	10.6963	−	18.5264i	0.546553	−	0.946657i	−0.451955	−	0.892041i	$-0.649273\pi$
$383$	10.6963	−	18.5264i	0.546553	−	0.946657i	0.998507	−	0.0546164i	$-0.0173936\pi$
$384$		0			0
$385$	8.65732	+	21.1211i	0.441218	+	1.07643i
$386$		0			0
$387$	−8.51887	+	14.7551i	−0.433038	+	0.750045i
$388$		0			0
$389$	−3.52206	−	6.10039i	−0.178576	−	0.309302i	0.762817	−	0.646614i	$-0.223816\pi$
$389$	−3.52206	−	6.10039i	−0.178576	−	0.309302i	−0.941393	+	0.337312i	$0.890482\pi$
$390$		0			0
$391$	−4.29562			−0.217239
$392$		0			0
$393$	33.8897			1.70951
$394$		0			0
$395$	−9.89341	−	17.1359i	−0.497792	−	0.862200i
$396$		0			0
$397$	4.26894	−	7.39402i	0.214252	−	0.371095i	−0.738789	−	0.673937i	$-0.764602\pi$
$397$	4.26894	−	7.39402i	0.214252	−	0.371095i	0.953041	+	0.302842i	$0.0979353\pi$
$398$		0			0
$399$	−15.6773	−	38.2475i	−0.784845	−	1.91477i
$400$		0			0
$401$	−5.60849	+	9.71419i	−0.280075	+	0.485104i	−0.971403	−	0.237437i	$-0.923693\pi$
$401$	−5.60849	+	9.71419i	−0.280075	+	0.485104i	0.691328	+	0.722541i	$0.257026\pi$
$402$		0			0
$403$	−18.2745	−	31.6524i	−0.910319	−	1.57672i
$404$		0			0
$405$	−20.3325			−1.01033
$406$		0			0
$407$	−4.67370			−0.231667
$408$		0			0
$409$	2.47331	+	4.28390i	0.122297	+	0.211825i	0.920673	−	0.390334i	$-0.127641\pi$
$409$	2.47331	+	4.28390i	0.122297	+	0.211825i	−0.798376	+	0.602159i	$0.794307\pi$
$410$		0			0
$411$	−9.30154	+	16.1107i	−0.458811	+	0.794684i
$412$		0			0
$413$	10.6133	−	13.7262i	0.522248	−	0.675422i
$414$		0			0
$415$	−13.7305	+	23.7820i	−0.674006	+	1.16741i
$416$		0			0
$417$	−2.23063	−	3.86357i	−0.109235	−	0.189200i
$418$		0			0
$419$	−39.2218			−1.91611			−0.958056	−	0.286581i	$-0.907481\pi$
$419$	−39.2218			−1.91611			−0.958056	+	0.286581i	$0.907481\pi$
$420$		0			0
$421$	5.25322			0.256026			0.128013	−	0.991772i	$-0.459140\pi$
$421$	5.25322			0.256026			0.128013	+	0.991772i	$0.459140\pi$
$422$		0			0
$423$	10.4844	+	18.1595i	0.509769	+	0.882947i
$424$		0			0
$425$	2.27048	−	3.93259i	0.110134	−	0.190758i
$426$		0			0
$427$	31.6479	+	4.28560i	1.53155	+	0.207395i
$428$		0			0
$429$	−26.5219	+	45.9373i	−1.28049	+	2.21787i
$430$		0			0
$431$	−9.36939	−	16.2283i	−0.451308	−	0.781688i	0.547160	−	0.837028i	$-0.315709\pi$
$431$	−9.36939	−	16.2283i	−0.451308	−	0.781688i	−0.998468	+	0.0553404i	$0.982376\pi$
$432$		0			0
$433$	2.71183			0.130322			0.0651612	−	0.997875i	$-0.479244\pi$
$433$	2.71183			0.130322			0.0651612	+	0.997875i	$0.479244\pi$
$434$		0			0
$435$	4.03388			0.193410
$436$		0			0
$437$	−3.32937	−	5.76663i	−0.159265	−	0.275856i
$438$		0			0
$439$	−11.5260	+	19.9636i	−0.550106	+	0.952811i	0.448161	+	0.893953i	$0.352079\pi$
$439$	−11.5260	+	19.9636i	−0.550106	+	0.952811i	−0.998266	+	0.0588581i	$0.981254\pi$
$440$		0			0
$441$	−4.41337	−	16.9718i	−0.210160	−	0.808182i
$442$		0			0
$443$	16.8190	−	29.1314i	0.799095	−	1.38407i	−0.121112	−	0.992639i	$-0.538646\pi$
$443$	16.8190	−	29.1314i	0.799095	−	1.38407i	0.920206	−	0.391433i	$-0.128021\pi$
$444$		0			0
$445$	3.31393	+	5.73990i	0.157095	+	0.272097i
$446$		0			0
$447$	1.66545			0.0787730
$448$		0			0
$449$	−3.36497			−0.158803			−0.0794015	−	0.996843i	$-0.525301\pi$
$449$	−3.36497			−0.158803			−0.0794015	+	0.996843i	$0.525301\pi$
$450$		0			0
$451$	9.32931	+	16.1588i	0.439300	+	0.760890i
$452$		0			0
$453$	24.6694	−	42.7287i	1.15907	−	2.00757i
$454$		0			0
$455$	−27.0879	−	3.66811i	−1.26990	−	0.171964i
$456$		0			0
$457$	2.86699	−	4.96578i	0.134112	−	0.232289i	−0.791146	−	0.611628i	$-0.790515\pi$
$457$	2.86699	−	4.96578i	0.134112	−	0.232289i	0.925258	+	0.379338i	$0.123848\pi$
$458$		0			0
$459$	2.49361	+	4.31905i	0.116392	+	0.201596i
$460$		0			0
$461$	26.7865			1.24757			0.623785	−	0.781596i	$-0.285594\pi$
$461$	26.7865			1.24757			0.623785	+	0.781596i	$0.285594\pi$
$462$		0			0
$463$	−14.6705			−0.681794			−0.340897	−	0.940101i	$-0.610731\pi$
$463$	−14.6705			−0.681794			−0.340897	+	0.940101i	$0.610731\pi$
$464$		0			0
$465$	−16.3634	−	28.3423i	−0.758835	−	1.31434i
$466$		0			0
$467$	6.40228	−	11.0891i	0.296262	−	0.513141i	−0.679016	−	0.734124i	$-0.737593\pi$
$467$	6.40228	−	11.0891i	0.296262	−	0.513141i	0.975278	+	0.220983i	$0.0709265\pi$
$468$		0			0
$469$	−0.846003	+	1.09413i	−0.0390648	+	0.0505225i
$470$		0			0
$471$	−18.4495	+	31.9555i	−0.850110	+	1.47243i
$472$		0			0
$473$	−14.7750	−	25.5910i	−0.679354	−	1.17667i
$474$		0			0
$475$	7.03904			0.322973
$476$		0			0
$477$	1.94335			0.0889800
$478$		0			0
$479$	−6.01502	−	10.4183i	−0.274833	−	0.476026i	0.695260	−	0.718759i	$-0.255289\pi$
$479$	−6.01502	−	10.4183i	−0.274833	−	0.476026i	−0.970093	+	0.242733i	$0.921956\pi$
$480$		0			0
$481$	2.79841	−	4.84700i	0.127597	−	0.221004i
$482$		0			0
$483$	−2.35439	−	5.74396i	−0.107128	−	0.261359i
$484$		0			0
$485$	13.6753	−	23.6863i	0.620963	−	1.07554i
$486$		0			0
$487$	12.1068	+	20.9696i	0.548612	+	0.950223i	0.998370	+	0.0570730i	$0.0181768\pi$
$487$	12.1068	+	20.9696i	0.548612	+	0.950223i	−0.449758	+	0.893150i	$0.648490\pi$
$488$		0			0
$489$	21.9793			0.993938
$490$		0			0
$491$	−37.4279			−1.68910			−0.844549	−	0.535478i	$-0.820131\pi$
$491$	−37.4279			−1.68910			−0.844549	+	0.535478i	$0.820131\pi$
$492$		0			0
$493$	−1.85963	−	3.22097i	−0.0837534	−	0.145065i
$494$		0			0
$495$	−10.8069	+	18.7181i	−0.485733	+	0.841314i
$496$		0			0
$497$	2.91209	+	7.10458i	0.130625	+	0.318684i
$498$		0			0
$499$	−14.5989	+	25.2860i	−0.653535	+	1.13196i	0.328724	+	0.944426i	$0.393382\pi$
$499$	−14.5989	+	25.2860i	−0.653535	+	1.13196i	−0.982259	+	0.187530i	$0.939952\pi$
$500$		0			0
$501$	−5.13541	−	8.89479i	−0.229433	−	0.397390i
$502$		0			0
$503$	−1.91541			−0.0854040			−0.0427020	−	0.999088i	$-0.513597\pi$
$503$	−1.91541			−0.0854040			−0.0427020	+	0.999088i	$0.513597\pi$
$504$		0			0
$505$	−22.5335			−1.00273
$506$		0			0
$507$	−16.5094	−	28.5951i	−0.733208	−	1.26995i
$508$		0			0
$509$	−8.48871	+	14.7029i	−0.376255	+	0.651693i	−0.990514	−	0.137411i	$-0.956122\pi$
$509$	−8.48871	+	14.7029i	−0.376255	+	0.651693i	0.614259	+	0.789105i	$0.289455\pi$
$510$		0			0
$511$	1.61395	−	2.08732i	0.0713969	−	0.0923375i
$512$		0			0
$513$	−3.86539	+	6.69505i	−0.170661	+	0.295594i
$514$		0			0
$515$	12.2856	+	21.2792i	0.541366	+	0.937674i
$516$		0			0
$517$	−36.3679			−1.59946
$518$		0			0
$519$	45.0921			1.97932
$520$		0			0
$521$	9.92066	+	17.1831i	0.434632	+	0.752804i	0.997266	−	0.0739019i	$-0.0235452\pi$
$521$	9.92066	+	17.1831i	0.434632	+	0.752804i	−0.562634	+	0.826706i	$0.690212\pi$
$522$		0			0
$523$	−6.31827	+	10.9436i	−0.276279	+	0.478529i	−0.970457	−	0.241274i	$-0.922435\pi$
$523$	−6.31827	+	10.9436i	−0.276279	+	0.478529i	0.694178	+	0.719803i	$0.255768\pi$
$524$		0			0
$525$	6.50295	+	0.880597i	0.283812	+	0.0384324i
$526$		0			0
$527$	−15.0871	+	26.1317i	−0.657206	+	1.13831i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	16.4290			0.712957
$532$		0			0
$533$	−22.3440			−0.967826
$534$		0			0
$535$	14.0253	+	24.2926i	0.606367	+	1.05026i
$536$		0			0
$537$	−3.55616	+	6.15945i	−0.153460	+	0.265800i
$538$		0			0
$539$	29.3192	+	8.08885i	1.26287	+	0.348411i
$540$		0			0
$541$	14.6118	−	25.3084i	0.628211	−	1.08809i	−0.359699	−	0.933068i	$-0.617121\pi$
$541$	14.6118	−	25.3084i	0.628211	−	1.08809i	0.987910	−	0.155025i	$-0.0495460\pi$
$542$		0			0
$543$	−28.4458	−	49.2697i	−1.22073	−	2.11436i
$544$		0			0
$545$	−27.3041			−1.16958
$546$		0			0
$547$	19.8140			0.847187			0.423594	−	0.905852i	$-0.360768\pi$
$547$	19.8140			0.847187			0.423594	+	0.905852i	$0.360768\pi$
$548$		0			0
$549$	15.1200	+	26.1886i	0.645305	+	1.11770i
$550$		0			0
$551$	2.88265	−	4.99289i	0.122805	−	0.212704i
$552$		0			0
$553$	−26.1260	−	3.53785i	−1.11099	−	0.150444i
$554$		0			0
$555$	2.50576	−	4.34011i	0.106364	−	0.184227i
$556$		0			0
$557$	15.5401	+	26.9162i	0.658455	+	1.14048i	0.981016	+	0.193928i	$0.0621229\pi$
$557$	15.5401	+	26.9162i	0.658455	+	1.14048i	−0.322561	+	0.946549i	$0.604544\pi$
$558$		0			0
$559$	35.3865			1.49669
$560$		0			0
$561$	43.7921			1.84890
$562$		0			0
$563$	20.8323	+	36.0826i	0.877978	+	1.52070i	0.853556	+	0.521001i	$0.174441\pi$
$563$	20.8323	+	36.0826i	0.877978	+	1.52070i	0.0244216	+	0.999702i	$0.492226\pi$
$564$		0			0
$565$	−7.82560	+	13.5543i	−0.329226	+	0.570235i
$566$		0			0
$567$	−16.5716	+	21.4320i	−0.695941	+	0.900059i
$568$		0			0
$569$	7.46399	−	12.9280i	0.312907	−	0.541970i	−0.666084	−	0.745877i	$-0.732031\pi$
$569$	7.46399	−	12.9280i	0.312907	−	0.541970i	0.978990	+	0.203907i	$0.0653639\pi$
$570$		0			0
$571$	−14.2471	−	24.6766i	−0.596221	−	1.03268i	−0.993373	−	0.114932i	$-0.963335\pi$
$571$	−14.2471	−	24.6766i	−0.596221	−	1.03268i	0.397153	−	0.917752i	$-0.369998\pi$
$572$		0			0
$573$	49.9407			2.08630
$574$		0			0
$575$	1.05711			0.0440847
$576$		0			0
$577$	9.65060	+	16.7153i	0.401760	+	0.695868i	0.993938	−	0.109938i	$-0.0350654\pi$
$577$	9.65060	+	16.7153i	0.401760	+	0.695868i	−0.592179	+	0.805807i	$0.701732\pi$
$578$		0			0
$579$	−1.03070	+	1.78523i	−0.0428346	+	0.0741917i
$580$		0			0
$581$	13.8772	+	33.8560i	0.575725	+	1.40459i
$582$		0			0
$583$	−1.68526	+	2.91895i	−0.0697962	+	0.120891i
$584$		0			0
$585$	−12.9414	−	22.4152i	−0.535062	−	0.926754i
$586$		0			0
$587$	−38.7294			−1.59853			−0.799266	−	0.600977i	$-0.794778\pi$
$587$	−38.7294			−1.59853			−0.799266	+	0.600977i	$0.794778\pi$
$588$		0			0
$589$	−46.7738			−1.92728
$590$		0			0
$591$	22.3960	+	38.7911i	0.921250	+	1.59565i
$592$		0			0
$593$	2.81545	−	4.87650i	0.115617	−	0.200254i	−0.802409	−	0.596774i	$-0.796449\pi$
$593$	2.81545	−	4.87650i	0.115617	−	0.200254i	0.918026	+	0.396520i	$0.129782\pi$
$594$		0			0
$595$	8.55906	+	20.8814i	0.350887	+	0.856053i
$596$		0			0
$597$	−9.83128	+	17.0283i	−0.402367	+	0.696921i
$598$		0			0
$599$	−0.566841	−	0.981798i	−0.0231605	−	0.0401152i	0.854213	−	0.519923i	$-0.174040\pi$
$599$	−0.566841	−	0.981798i	−0.0231605	−	0.0401152i	−0.877373	+	0.479808i	$0.840706\pi$
$600$		0			0
$601$	27.3775			1.11675			0.558377	−	0.829588i	$-0.311424\pi$
$601$	27.3775			1.11675			0.558377	+	0.829588i	$0.311424\pi$
$602$		0			0
$603$	−1.30958			−0.0533301
$604$		0			0
$605$	−7.82205	−	13.5482i	−0.318012	−	0.550812i
$606$		0			0
$607$	−16.1363	+	27.9489i	−0.654954	+	1.13441i	0.326952	+	0.945041i	$0.393978\pi$
$607$	−16.1363	+	27.9489i	−0.654954	+	1.13441i	−0.981905	+	0.189372i	$0.939355\pi$
$608$		0			0
$609$	3.28773	−	4.25201i	0.133225	−	0.172300i
$610$		0			0
$611$	21.7756	−	37.7164i	0.880946	−	1.52584i
$612$		0			0
$613$	−4.25888	−	7.37660i	−0.172015	−	0.297938i	0.767109	−	0.641516i	$-0.221694\pi$
$613$	−4.25888	−	7.37660i	−0.172015	−	0.297938i	−0.939124	+	0.343578i	$0.888361\pi$
$614$		0			0
$615$	−20.0073			−0.806773
$616$		0			0
$617$	33.6256			1.35372			0.676858	−	0.736114i	$-0.263341\pi$
$617$	33.6256			1.35372			0.676858	+	0.736114i	$0.263341\pi$
$618$		0			0
$619$	19.6025	+	33.9526i	0.787892	+	1.36467i	0.927256	+	0.374428i	$0.122161\pi$
$619$	19.6025	+	33.9526i	0.787892	+	1.36467i	−0.139364	+	0.990241i	$0.544506\pi$
$620$		0			0
$621$	−0.580499	+	1.00545i	−0.0232946	+	0.0403475i
$622$		0			0
$623$	8.75124	+	1.18505i	0.350611	+	0.0474780i
$624$		0			0
$625$	9.29847	−	16.1054i	0.371939	−	0.644217i
$626$		0			0
$627$	33.9415	+	58.7884i	1.35549	+	2.34778i
$628$		0			0
$629$	−4.62065			−0.184237
$630$		0			0
$631$	10.0895			0.401655			0.200827	−	0.979627i	$-0.435637\pi$
$631$	10.0895			0.401655			0.200827	+	0.979627i	$0.435637\pi$
$632$		0			0
$633$	17.1904	+	29.7747i	0.683258	+	1.18344i
$634$		0			0
$635$	13.6095	−	23.5724i	0.540078	−	0.935443i
$636$		0			0
$637$	−25.9439	+	25.5631i	−1.02794	+	1.01285i
$638$		0			0
$639$	−3.63515	+	6.29626i	−0.143804	+	0.249076i
$640$		0			0
$641$	−1.43434	−	2.48435i	−0.0566531	−	0.0981261i	0.836308	−	0.548260i	$-0.184710\pi$
$641$	−1.43434	−	2.48435i	−0.0566531	−	0.0981261i	−0.892961	+	0.450134i	$0.851376\pi$
$642$		0			0
$643$	26.6443			1.05075			0.525374	−	0.850871i	$-0.323925\pi$
$643$	26.6443			1.05075			0.525374	+	0.850871i	$0.323925\pi$
$644$		0			0
$645$	31.6859			1.24763
$646$		0			0
$647$	−4.71877	−	8.17316i	−0.185514	−	0.321320i	0.758236	−	0.651981i	$-0.226062\pi$
$647$	−4.71877	−	8.17316i	−0.185514	−	0.321320i	−0.943750	+	0.330661i	$0.892728\pi$
$648$		0			0
$649$	−14.2471	+	24.6766i	−0.559246	+	0.968642i
$650$		0			0
$651$	−43.2116	−	5.85149i	−1.69359	−	0.229338i
$652$		0			0
$653$	−7.14848	+	12.3815i	−0.279742	+	0.484527i	−0.971320	−	0.237774i	$-0.923582\pi$
$653$	−7.14848	+	12.3815i	−0.279742	+	0.484527i	0.691579	+	0.722301i	$0.256916\pi$
$654$		0			0
$655$	−14.3403	−	24.8382i	−0.560323	−	0.970508i
$656$		0			0
$657$	2.49832			0.0974689
$658$		0			0
$659$	44.9673			1.75168			0.875839	−	0.482603i	$-0.160309\pi$
$659$	44.9673			1.75168			0.875839	+	0.482603i	$0.160309\pi$
$660$		0			0
$661$	−16.6863	−	28.9016i	−0.649023	−	1.12414i	−0.983357	−	0.181686i	$-0.941845\pi$
$661$	−16.6863	−	28.9016i	−0.649023	−	1.12414i	0.334334	−	0.942455i	$-0.391489\pi$
$662$		0			0
$663$	−26.2209	+	45.4159i	−1.01833	+	1.76381i
$664$		0			0
$665$	−21.3983	+	27.6744i	−0.829790	+	1.07317i
$666$		0			0
$667$	0.432912	−	0.749825i	0.0167624	−	0.0290334i
$668$		0			0
$669$	12.0214	+	20.8218i	0.464776	+	0.805016i
$670$		0			0
$671$	−52.4476			−2.02472
$672$		0			0
$673$	15.8329			0.610314			0.305157	−	0.952302i	$-0.401291\pi$
$673$	15.8329			0.610314			0.305157	+	0.952302i	$0.401291\pi$
$674$		0			0
$675$	−0.613653	−	1.06288i	−0.0236195	−	0.0409102i
$676$		0			0
$677$	21.2503	−	36.8066i	0.816715	−	1.41459i	−0.0913744	−	0.995817i	$-0.529126\pi$
$677$	21.2503	−	36.8066i	0.816715	−	1.41459i	0.908090	−	0.418776i	$-0.137541\pi$
$678$		0			0
$679$	−13.8214	−	33.7198i	−0.530417	−	1.29405i
$680$		0			0
$681$	−13.2549	+	22.9581i	−0.507927	+	0.879756i
$682$		0			0
$683$	11.9335	+	20.6694i	0.456623	+	0.790893i	0.998780	−	0.0493836i	$-0.0157257\pi$
$683$	11.9335	+	20.6694i	0.456623	+	0.790893i	−0.542157	+	0.840277i	$0.682392\pi$
$684$		0			0
$685$	15.7437			0.601535
$686$		0			0
$687$	−11.4008			−0.434967
$688$		0			0
$689$	−2.01812	−	3.49549i	−0.0768844	−	0.133168i
$690$		0			0
$691$	2.31148	−	4.00361i	0.0879330	−	0.152304i	−0.818704	−	0.574215i	$-0.805307\pi$
$691$	2.31148	−	4.00361i	0.0879330	−	0.152304i	0.906637	+	0.421911i	$0.138641\pi$
$692$		0			0
$693$	10.9223	+	26.6470i	0.414905	+	1.01224i
$694$		0			0
$695$	−1.88777	+	3.26972i	−0.0716072	+	0.124027i
$696$		0			0
$697$	9.22342	+	15.9754i	0.349362	+	0.605113i
$698$		0			0
$699$	−31.2922			−1.18358
$700$		0			0
$701$	−14.4011			−0.543921			−0.271960	−	0.962308i	$-0.587672\pi$
$701$	−14.4011			−0.543921			−0.271960	+	0.962308i	$0.587672\pi$
$702$		0			0
$703$	−3.58128	−	6.20296i	−0.135071	−	0.233949i
$704$		0			0
$705$	19.4983	−	33.7721i	0.734350	−	1.27193i
$706$		0			0
$707$	−18.3655	+	23.7520i	−0.690704	+	0.893286i
$708$		0			0
$709$	7.38982	−	12.7995i	0.277531	−	0.480697i	−0.693240	−	0.720707i	$-0.743817\pi$
$709$	7.38982	−	12.7995i	0.277531	−	0.480697i	0.970770	+	0.240010i	$0.0771507\pi$
$710$		0			0
$711$	−12.4818	−	21.6192i	−0.468105	−	0.810782i
$712$		0			0
$713$	−7.02443			−0.263067
$714$		0			0
$715$	44.8907			1.67882
$716$		0			0
$717$	−29.1872	−	50.5537i	−1.09002	−	1.88796i
$718$		0			0
$719$	3.20921	−	5.55852i	0.119683	−	0.207298i	−0.799959	−	0.600055i	$-0.795145\pi$
$719$	3.20921	−	5.55852i	0.119683	−	0.207298i	0.919642	+	0.392757i	$0.128479\pi$
$720$		0			0
$721$	32.4430	+	4.39327i	1.20824	+	0.163614i
$722$		0			0
$723$	27.2490	−	47.1967i	1.01340	−	1.75526i
$724$		0			0
$725$	0.457637	+	0.792650i	0.0169962	+	0.0294383i
$726$		0			0
$727$	23.2474			0.862197			0.431098	−	0.902305i	$-0.358126\pi$
$727$	23.2474			0.862197			0.431098	+	0.902305i	$0.358126\pi$
$728$		0			0
$729$	−17.4799			−0.647403
$730$		0			0
$731$	−14.6073	−	25.3005i	−0.540269	−	0.935774i
$732$		0			0
$733$	−10.1339	+	17.5525i	−0.374306	+	0.648317i	−0.990223	−	0.139494i	$-0.955452\pi$
$733$	−10.1339	+	17.5525i	−0.374306	+	0.648317i	0.615917	+	0.787811i	$0.288786\pi$
$734$		0			0
$735$	−23.2307	+	22.8898i	−0.856879	+	0.844302i
$736$		0			0
$737$	1.13565	−	1.96701i	0.0418323	−	0.0724557i
$738$		0			0
$739$	3.44521	+	5.96728i	0.126734	+	0.219510i	0.922409	−	0.386213i	$-0.126217\pi$
$739$	3.44521	+	5.96728i	0.126734	+	0.219510i	−0.795675	+	0.605723i	$0.792884\pi$
$740$		0			0
$741$	−81.2911			−2.98630
$742$		0			0
$743$	11.1270			0.408211			0.204105	−	0.978949i	$-0.434571\pi$
$743$	11.1270			0.408211			0.204105	+	0.978949i	$0.434571\pi$
$744$		0			0
$745$	−0.704729	−	1.22063i	−0.0258193	−	0.0447203i
$746$		0			0
$747$	−17.3229	+	30.0041i	−0.633810	+	1.09779i
$748$		0			0
$749$	37.0372	+	5.01540i	1.35331	+	0.183259i
$750$		0			0
$751$	−9.15977	+	15.8652i	−0.334245	+	0.578929i	−0.983339	−	0.181779i	$-0.941815\pi$
$751$	−9.15977	+	15.8652i	−0.334245	+	0.578929i	0.649095	+	0.760708i	$0.275148\pi$
$752$		0			0
$753$	23.7307	+	41.1028i	0.864795	+	1.49787i
$754$		0			0
$755$	−41.7552			−1.51963
$756$		0			0
$757$	−14.8147			−0.538449			−0.269224	−	0.963077i	$-0.586767\pi$
$757$	−14.8147			−0.538449			−0.269224	+	0.963077i	$0.586767\pi$
$758$		0			0
$759$	5.09729	+	8.82877i	0.185020	+	0.320464i
$760$		0			0
$761$	22.5139	−	38.9953i	0.816130	−	1.41358i	−0.0923836	−	0.995723i	$-0.529449\pi$
$761$	22.5139	−	38.9953i	0.816130	−	1.41358i	0.908514	−	0.417855i	$-0.137218\pi$
$762$		0			0
$763$	−22.2536	+	28.7806i	−0.805636	+	1.04193i
$764$		0			0
$765$	−10.6842	+	18.5056i	−0.386289	+	0.669072i
$766$		0			0
$767$	−17.0611	−	29.5507i	−0.616040	−	1.06701i
$768$		0			0
$769$	1.09825			0.0396037			0.0198019	−	0.999804i	$-0.493696\pi$
$769$	1.09825			0.0396037			0.0198019	+	0.999804i	$0.493696\pi$
$770$		0			0
$771$	49.8229			1.79433
$772$		0			0
$773$	−13.2766	−	22.9957i	−0.477525	−	0.827097i	0.522143	−	0.852858i	$-0.325133\pi$
$773$	−13.2766	−	22.9957i	−0.477525	−	0.827097i	−0.999668	+	0.0257606i	$0.991799\pi$
$774$		0			0
$775$	3.71281	−	6.43077i	0.133368	−	0.231000i
$776$		0			0
$777$	−2.53253	−	6.17858i	−0.0908541	−	0.221655i
$778$		0			0
$779$	−14.2974	+	24.7638i	−0.512258	+	0.887257i
$780$		0			0
$781$	−6.30473	−	10.9201i	−0.225601	−	0.390752i
$782$		0			0
$783$	−1.00522			−0.0359236
$784$		0			0
$785$	31.2275			1.11456
$786$		0			0
$787$	−12.1740	−	21.0860i	−0.433956	−	0.751634i	0.563254	−	0.826284i	$-0.309549\pi$
$787$	−12.1740	−	21.0860i	−0.433956	−	0.751634i	−0.997210	+	0.0746501i	$0.976216\pi$
$788$		0			0
$789$	18.8513	−	32.6514i	0.671123	−	1.16242i
$790$		0			0
$791$	7.90921	+	19.2960i	0.281219	+	0.686086i
$792$		0			0
$793$	31.4035	−	54.3924i	1.11517	−	1.93153i
$794$		0			0
$795$	−1.80707	−	3.12994i	−0.0640902	−	0.111008i
$796$		0			0
$797$	4.80359			0.170152			0.0850759	−	0.996374i	$-0.472887\pi$
$797$	4.80359			0.170152			0.0850759	+	0.996374i	$0.472887\pi$
$798$		0			0
$799$	−35.9551			−1.27200
$800$		0			0
$801$	4.18096	+	7.24163i	0.147727	+	0.255870i
$802$		0			0
$803$	−2.16652	+	3.75253i	−0.0764549	+	0.132424i
$804$		0			0
$805$	−3.21357	+	4.15610i	−0.113263	+	0.146483i
$806$		0			0
$807$	16.2355	−	28.1207i	0.571517	−	0.989896i
$808$		0			0
$809$	18.9657	+	32.8496i	0.666799	+	1.15493i	0.978794	+	0.204846i	$0.0656694\pi$
$809$	18.9657	+	32.8496i	0.666799	+	1.15493i	−0.311995	+	0.950084i	$0.600997\pi$
$810$		0			0
$811$	−34.1720			−1.19994			−0.599971	−	0.800022i	$-0.704821\pi$
$811$	−34.1720			−1.19994			−0.599971	+	0.800022i	$0.704821\pi$
$812$		0			0
$813$	76.3517			2.67777
$814$		0			0
$815$	−9.30048	−	16.1089i	−0.325781	−	0.564270i
$816$		0			0
$817$	22.6430	−	39.2189i	0.792179	−	1.37209i
$818$		0			0
$819$	−34.1749	−	4.62780i	−1.19417	−	0.161708i
$820$		0			0
$821$	23.3463	−	40.4369i	0.814791	−	1.41126i	−0.0946876	−	0.995507i	$-0.530185\pi$
$821$	23.3463	−	40.4369i	0.814791	−	1.41126i	0.909478	−	0.415752i	$-0.136481\pi$
$822$		0			0
$823$	20.7851	+	36.0008i	0.724522	+	1.25491i	0.959170	+	0.282829i	$0.0912728\pi$
$823$	20.7851	+	36.0008i	0.724522	+	1.25491i	−0.234648	+	0.972080i	$0.575394\pi$
$824$		0			0
$825$	−10.7768			−0.375201
$826$		0			0
$827$	−1.65425			−0.0575238			−0.0287619	−	0.999586i	$-0.509156\pi$
$827$	−1.65425			−0.0575238			−0.0287619	+	0.999586i	$0.509156\pi$
$828$		0			0
$829$	−3.51911	−	6.09528i	−0.122224	−	0.211698i	0.798421	−	0.602100i	$-0.205669\pi$
$829$	−3.51911	−	6.09528i	−0.122224	−	0.211698i	−0.920644	+	0.390402i	$0.872336\pi$
$830$		0			0
$831$	14.2940	−	24.7579i	0.495852	−	0.858840i
$832$		0			0
$833$	28.9864	+	7.99704i	1.00432	+	0.277081i
$834$		0			0
$835$	−4.34607	+	7.52761i	−0.150402	+	0.260504i
$836$		0			0
$837$	4.07767	+	7.06274i	0.140945	+	0.244124i
$838$		0			0
$839$	44.3675			1.53173			0.765867	−	0.642999i	$-0.222310\pi$
$839$	44.3675			1.53173			0.765867	+	0.642999i	$0.222310\pi$
$840$		0			0
$841$	−28.2503			−0.974150
$842$		0			0
$843$	17.2791	+	29.9283i	0.595125	+	1.03079i
$844$		0			0
$845$	−13.9718	+	24.1999i	−0.480645	+	0.832501i
$846$		0			0
$847$	−20.6560	−	2.79714i	−0.709749	−	0.0961107i
$848$		0			0
$849$	−6.68799	+	11.5839i	−0.229531	+	0.397560i
$850$		0			0
$851$	−0.537832	−	0.931553i	−0.0184366	−	0.0319332i
$852$		0			0
$853$	−33.4439			−1.14510			−0.572548	−	0.819871i	$-0.694045\pi$
$853$	−33.4439			−1.14510			−0.572548	+	0.819871i	$0.694045\pi$
$854$		0			0
$855$	−33.1236			−1.13280
$856$		0			0
$857$	5.14384	+	8.90939i	0.175710	+	0.304339i	0.940407	−	0.340052i	$-0.110445\pi$
$857$	5.14384	+	8.90939i	0.175710	+	0.304339i	−0.764697	+	0.644390i	$0.777111\pi$
$858$		0			0
$859$	−12.4798	+	21.6157i	−0.425806	+	0.737518i	−0.996495	−	0.0836481i	$-0.973343\pi$
$859$	−12.4798	+	21.6157i	−0.425806	+	0.737518i	0.570689	+	0.821166i	$0.306676\pi$
$860$		0			0
$861$	−16.3065	+	21.0892i	−0.555725	+	0.718719i
$862$		0			0
$863$	−9.00694	+	15.6005i	−0.306600	+	0.531046i	−0.977616	−	0.210396i	$-0.932525\pi$
$863$	−9.00694	+	15.6005i	−0.306600	+	0.531046i	0.671016	+	0.741442i	$0.265858\pi$
$864$		0			0
$865$	−19.0806	−	33.0486i	−0.648760	−	1.12369i
$866$		0			0
$867$	3.40774			0.115733
$868$		0			0
$869$	43.2965			1.46873
$870$		0			0
$871$	1.35996	+	2.35552i	0.0460806	+	0.0798139i
$872$		0			0
$873$	17.2532	−	29.8834i	0.583931	−	1.01140i
$874$		0			0
$875$	−12.0688	−	29.4441i	−0.408001	−	0.995393i
$876$		0			0
$877$	6.77780	−	11.7395i	0.228870	−	0.396415i	−0.728603	−	0.684936i	$-0.759830\pi$
$877$	6.77780	−	11.7395i	0.228870	−	0.396415i	0.957473	+	0.288521i	$0.0931636\pi$
$878$		0			0
$879$	−32.8883	−	56.9642i	−1.10930	−	1.92136i
$880$		0			0
$881$	−1.27249			−0.0428713			−0.0214356	−	0.999770i	$-0.506824\pi$
$881$	−1.27249			−0.0428713			−0.0214356	+	0.999770i	$0.506824\pi$
$882$		0			0
$883$	−13.3399			−0.448924			−0.224462	−	0.974483i	$-0.572062\pi$
$883$	−13.3399			−0.448924			−0.224462	+	0.974483i	$0.572062\pi$
$884$		0			0
$885$	−15.2769	−	26.4603i	−0.513526	−	0.889454i
$886$		0			0
$887$	−10.5456	+	18.2656i	−0.354088	+	0.613299i	−0.986961	−	0.160957i	$-0.948542\pi$
$887$	−10.5456	+	18.2656i	−0.354088	+	0.613299i	0.632873	+	0.774255i	$0.281875\pi$
$888$		0			0
$889$	−13.7549	−	33.5577i	−0.461326	−	1.12549i
$890$		0			0
$891$	22.2452	−	38.5299i	0.745244	−	1.29080i
$892$		0			0
$893$	−27.8674	−	48.2678i	−0.932547	−	1.61522i
$894$		0			0
$895$	6.01912			0.201197
$896$		0			0
$897$	−12.2082			−0.407619
$898$		0			0
$899$	−3.04096	−	5.26709i	−0.101422	−	0.175667i
$900$		0			0
$901$	−1.66613	+	2.88582i	−0.0555068	+	0.0961406i
$902$		0			0
$903$	25.8249	−	33.3993i	0.859399	−	1.11146i
$904$		0			0
$905$	−24.0736	+	41.6966i	−0.800232	+	1.38604i
$906$		0			0
$907$	21.9876	+	38.0836i	0.730086	+	1.26455i	0.956846	+	0.290596i	$0.0938534\pi$
$907$	21.9876	+	38.0836i	0.730086	+	1.26455i	−0.226760	+	0.973951i	$0.572813\pi$
$908$		0			0
$909$	−28.4289			−0.942928
$910$		0			0
$911$	−0.648983			−0.0215018			−0.0107509	−	0.999942i	$-0.503422\pi$
$911$	−0.648983			−0.0215018			−0.0107509	+	0.999942i	$0.503422\pi$
$912$		0			0
$913$	−30.0444	−	52.0385i	−0.994326	−	1.72222i
$914$		0			0
$915$	28.1193	−	48.7041i	0.929597	−	1.61011i
$916$		0			0
$917$	−37.8691	−	5.12805i	−1.25055	−	0.169343i
$918$		0			0
$919$	16.7069	−	28.9371i	0.551108	−	0.954548i	−0.447087	−	0.894491i	$-0.647538\pi$
$919$	16.7069	−	28.9371i	0.551108	−	0.954548i	0.998195	−	0.0600569i	$-0.0191282\pi$
$920$		0			0
$921$	−29.0349	−	50.2900i	−0.956733	−	1.65711i
$922$		0			0
$923$	15.1000			0.497024
$924$		0			0
$925$	1.13710			0.0373876
$926$		0			0
$927$	15.4998	+	26.8465i	0.509081	+	0.881755i
$928$		0			0
$929$	−11.8569	+	20.5367i	−0.389011	+	0.673788i	−0.992317	−	0.123723i	$-0.960517\pi$
$929$	−11.8569	+	20.5367i	−0.389011	+	0.673788i	0.603305	+	0.797510i	$0.293850\pi$
$930$		0			0
$931$	11.7307	+	45.1109i	0.384457	+	1.47845i
$932$		0			0
$933$	−19.0995	+	33.0812i	−0.625288	+	1.08303i
$934$		0			0
$935$	−18.5305	−	32.0958i	−0.606012	−	1.04964i
$936$		0			0
$937$	−53.1344			−1.73583			−0.867913	−	0.496716i	$-0.834539\pi$
$937$	−53.1344			−1.73583			−0.867913	+	0.496716i	$0.834539\pi$
$938$		0			0
$939$	−23.8903			−0.779630
$940$		0			0
$941$	15.5970	+	27.0147i	0.508447	+	0.880655i	0.999952	+	0.00978081i	$0.00311338\pi$
$941$	15.5970	+	27.0147i	0.508447	+	0.880655i	−0.491506	+	0.870874i	$0.663553\pi$
$942$		0			0
$943$	−2.14717	+	3.71900i	−0.0699214	+	0.121107i
$944$		0			0
$945$	6.04424	+	0.818481i	0.196619	+	0.0266252i
$946$		0			0
$947$	15.3671	−	26.6166i	0.499364	−	0.864924i	−0.500636	−	0.865658i	$-0.666900\pi$
$947$	15.3671	−	26.6166i	0.499364	−	0.864924i	1.00000		0.000734410i	$0.000233770\pi$
$948$		0			0
$949$	−2.59445	−	4.49371i	−0.0842193	−	0.145872i
$950$		0			0
$951$	−9.48249			−0.307491
$952$		0			0
$953$	27.0904			0.877545			0.438772	−	0.898598i	$-0.355413\pi$
$953$	27.0904			0.877545			0.438772	+	0.898598i	$0.355413\pi$
$954$		0			0
$955$	−21.1323	−	36.6021i	−0.683824	−	1.18442i
$956$		0			0
$957$	−4.41336	+	7.64416i	−0.142664	+	0.247101i
$958$		0			0
$959$	12.8316	−	16.5950i	0.414352	−	0.535881i
$960$		0			0
$961$	−9.17128	+	15.8851i	−0.295848	+	0.512423i
$962$		0			0
$963$	17.6948	+	30.6482i	0.570206	+	0.987625i
$964$		0			0
$965$	1.74456			0.0561593
$966$		0			0
$967$	−5.44203			−0.175004			−0.0875019	−	0.996164i	$-0.527888\pi$
$967$	−5.44203			−0.175004			−0.0875019	+	0.996164i	$0.527888\pi$
$968$		0			0
$969$	33.5563	+	58.1212i	1.07798	+	1.86712i
$970$		0			0
$971$	−7.01720	+	12.1541i	−0.225193	+	0.390045i	−0.956377	−	0.292135i	$-0.905635\pi$
$971$	−7.01720	+	12.1541i	−0.225193	+	0.390045i	0.731185	+	0.682180i	$0.238968\pi$
$972$		0			0
$973$	1.90794	+	4.65477i	0.0611658	+	0.149225i
$974$		0			0
$975$	6.45272	−	11.1764i	0.206652	−	0.357932i
$976$		0			0
$977$	7.27003	+	12.5921i	0.232589	+	0.402856i	0.958569	−	0.284860i	$-0.0919470\pi$
$977$	7.27003	+	12.5921i	0.232589	+	0.402856i	−0.725980	+	0.687716i	$0.758614\pi$
$978$		0			0
$979$	−14.5027			−0.463510
$980$		0			0
$981$	−34.4477			−1.09983
$982$		0			0
$983$	16.6010	+	28.7538i	0.529490	+	0.917104i	0.999408	+	0.0343942i	$0.0109502\pi$
$983$	16.6010	+	28.7538i	0.529490	+	0.917104i	−0.469918	+	0.882710i	$0.655716\pi$
$984$		0			0
$985$	18.9536	−	32.8287i	0.603913	−	1.04601i
$986$		0			0
$987$	−19.7067	−	48.0780i	−0.627270	−	1.53034i
$988$		0			0
$989$	3.40050	−	5.88984i	0.108130	−	0.187286i
$990$		0			0
$991$	−12.4143	−	21.5022i	−0.394353	−	0.683039i	0.598666	−	0.800999i	$-0.295698\pi$
$991$	−12.4143	−	21.5022i	−0.394353	−	0.683039i	−0.993018	+	0.117960i	$0.962364\pi$
$992$		0			0
$993$	−72.9963			−2.31647
$994$		0			0
$995$	16.6403			0.527533
$996$		0			0
$997$	−0.385448	−	0.667616i	−0.0122073	−	0.0211436i	0.859857	−	0.510535i	$-0.170552\pi$
$997$	−0.385448	−	0.667616i	−0.0122073	−	0.0211436i	−0.872065	+	0.489391i	$0.837219\pi$
$998$		0			0
$999$	−0.624422	+	1.08153i	−0.0197558	+	0.0342181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.i.a.93.2	✓	14
7.2	even	3		4508.2.a.m.1.6		7
7.4	even	3	inner	644.2.i.a.277.2	yes	14
7.5	odd	6		4508.2.a.l.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.i.a.93.2	✓	14	1.1	even	1	trivial
644.2.i.a.277.2	yes	14	7.4	even	3	inner
4508.2.a.l.1.2		7	7.5	odd	6
4508.2.a.m.1.6		7	7.2	even	3

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17316 - 2.03197i) q^{3} +(-0.992835 + 1.71964i) q^{5} +(1.00344 + 2.44808i) q^{7} +(-1.25259 + 2.16955i) q^{9} +O(q^{10})\)	\(q+(-1.17316 - 2.03197i) q^{3} +(-0.992835 + 1.71964i) q^{5} +(1.00344 + 2.44808i) q^{7} +(-1.25259 + 2.16955i) q^{9} +(-2.17247 - 3.76283i) q^{11} +5.20314 q^{13} +4.65900 q^{15} +(-2.14781 - 3.72012i) q^{17} +(3.32937 - 5.76663i) q^{19} +(3.79722 - 4.91094i) q^{21} +(0.500000 - 0.866025i) q^{23} +(0.528557 + 0.915487i) q^{25} -1.16100 q^{27} +0.865824 q^{29} +(-3.51221 - 6.08333i) q^{31} +(-5.09729 + 8.82877i) q^{33} +(-5.20607 - 0.704980i) q^{35} +(0.537832 - 0.931553i) q^{37} +(-6.10409 - 10.5726i) q^{39} -4.29433 q^{41} +6.80100 q^{43} +(-2.48723 - 4.30801i) q^{45} +(4.18509 - 7.24879i) q^{47} +(-4.98621 + 4.91302i) q^{49} +(-5.03944 + 8.72856i) q^{51} +(-0.387867 - 0.671805i) q^{53} +8.62762 q^{55} -15.6235 q^{57} +(-3.27900 - 5.67939i) q^{59} +(6.03548 - 10.4538i) q^{61} +(-6.56814 - 0.889425i) q^{63} +(-5.16586 + 8.94753i) q^{65} +(0.261374 + 0.452712i) q^{67} -2.34631 q^{69} +2.90210 q^{71} +(-0.498631 - 0.863655i) q^{73} +(1.24016 - 2.14802i) q^{75} +(7.03176 - 9.09417i) q^{77} +(-4.98240 + 8.62978i) q^{79} +(5.11980 + 8.86776i) q^{81} +13.8296 q^{83} +8.52969 q^{85} +(-1.01575 - 1.75932i) q^{87} +(1.66892 - 2.89066i) q^{89} +(5.22105 + 12.7377i) q^{91} +(-8.24075 + 14.2734i) q^{93} +(6.61103 + 11.4506i) q^{95} -13.7740 q^{97} +10.8849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9	\( 14 q - 3 q^{3} - 2 q^{5} + 6 q^{7} - 12 q^{9} + 12 q^{13} + 2 q^{15} - 4 q^{17} - 11 q^{19} + 7 q^{23} - 3 q^{25} + 48 q^{27} - 2 q^{29} - 24 q^{31} + 13 q^{33} + 5 q^{35} - 11 q^{37} + 16 q^{39} - 18 q^{41} + 10 q^{43} - 38 q^{45} - 8 q^{47} + 20 q^{49} - 23 q^{51} + 20 q^{53} + 50 q^{55} - 8 q^{57} - 13 q^{59} + 2 q^{61} + 26 q^{63} - 21 q^{65} + 4 q^{67} - 6 q^{69} - 16 q^{71} - 11 q^{73} + 10 q^{75} + 70 q^{77} - 28 q^{79} - 3 q^{81} + 42 q^{83} - 46 q^{85} - 59 q^{87} + 9 q^{89} + 14 q^{91} - 31 q^{93} - 12 q^{95} + 2 q^{97} - 44 q^{99}+O(q^{100}) \) 14 * q - 3 * q^3 - 2 * q^5 + 6 * q^7 - 12 * q^9 + 12 * q^13 + 2 * q^15 - 4 * q^17 - 11 * q^19 + 7 * q^23 - 3 * q^25 + 48 * q^27 - 2 * q^29 - 24 * q^31 + 13 * q^33 + 5 * q^35 - 11 * q^37 + 16 * q^39 - 18 * q^41 + 10 * q^43 - 38 * q^45 - 8 * q^47 + 20 * q^49 - 23 * q^51 + 20 * q^53 + 50 * q^55 - 8 * q^57 - 13 * q^59 + 2 * q^61 + 26 * q^63 - 21 * q^65 + 4 * q^67 - 6 * q^69 - 16 * q^71 - 11 * q^73 + 10 * q^75 + 70 * q^77 - 28 * q^79 - 3 * q^81 + 42 * q^83 - 46 * q^85 - 59 * q^87 + 9 * q^89 + 14 * q^91 - 31 * q^93 - 12 * q^95 + 2 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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