LMFDB - Embedded newform 756.2.ca.a.173.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(173,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 13, 15]))

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

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

chi := DirichletCharacter("756.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ca (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.2
Character	$\chi$	$=$	756.173
Dual form			756.2.ca.a.437.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69481 - 0.357227i) q^{3} +(1.90051 - 1.59472i) q^{5} +(1.42097 - 2.23178i) q^{7} +(2.74478 + 1.21086i) q^{9} +O(q^{10})$	\(q+(-1.69481 - 0.357227i) q^{3} +(1.90051 - 1.59472i) q^{5} +(1.42097 - 2.23178i) q^{7} +(2.74478 + 1.21086i) q^{9} +(0.560840 - 0.668383i) q^{11} +(0.741685 + 0.883906i) q^{13} +(-3.79069 + 2.02384i) q^{15} +(-0.825934 + 1.43056i) q^{17} +(1.68010 - 0.970004i) q^{19} +(-3.20553 + 3.27484i) q^{21} +(1.73474 - 4.76615i) q^{23} +(0.200577 - 1.13753i) q^{25} +(-4.21933 - 3.03270i) q^{27} +(-2.90948 + 3.46738i) q^{29} +(-3.09289 - 3.68597i) q^{31} +(-1.18928 + 0.932437i) q^{33} +(-0.858490 - 6.50758i) q^{35} +5.74721 q^{37} +(-0.941262 - 1.76300i) q^{39} +(1.42301 - 1.19405i) q^{41} +(4.32294 - 1.57342i) q^{43} +(7.14747 - 2.07589i) q^{45} +(-5.30777 - 4.45375i) q^{47} +(-2.96168 - 6.34259i) q^{49} +(1.91084 - 2.12949i) q^{51} +(5.19487 - 2.99926i) q^{53} -2.16465i q^{55} +(-3.19396 + 1.04380i) q^{57} +(-1.89672 - 10.7568i) q^{59} +(3.87453 - 4.61749i) q^{61} +(6.60263 - 4.40514i) q^{63} +(2.81916 + 0.497095i) q^{65} +(10.8849 + 3.96179i) q^{67} +(-4.64265 + 7.45803i) q^{69} +(-14.0958 + 8.13823i) q^{71} -1.69133i q^{73} +(-0.746296 + 1.85625i) q^{75} +(-0.694747 - 2.20143i) q^{77} +(-4.33553 + 1.57801i) q^{79} +(6.06761 + 6.64711i) q^{81} +(-0.417251 - 0.350116i) q^{83} +(0.711644 + 4.03593i) q^{85} +(6.16966 - 4.83722i) q^{87} +(-4.76115 - 8.24656i) q^{89} +(3.02660 - 0.399274i) q^{91} +(3.92515 + 7.35189i) q^{93} +(1.64616 - 4.52279i) q^{95} +(-1.27535 - 3.50400i) q^{97} +(2.34870 - 1.15546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.69481	−	0.357227i	−0.978500	−	0.206245i
$3$	−1.69481	−	0.357227i	−0.978500	−	0.206245i
$4$		0			0
$5$	1.90051	−	1.59472i	0.849935	−	0.713180i	−0.109840	−	0.993949i	$-0.535034\pi$
$5$	1.90051	−	1.59472i	0.849935	−	0.713180i	0.959775	+	0.280769i	$0.0905895\pi$
$6$		0			0
$7$	1.42097	−	2.23178i	0.537076	−	0.843534i
$7$	1.42097	−	2.23178i	0.537076	−	0.843534i
$8$		0			0
$9$	2.74478	+	1.21086i	0.914926	+	0.403622i
$10$		0			0
$11$	0.560840	−	0.668383i	0.169100	−	0.201525i	−0.674839	−	0.737965i	$-0.735787\pi$
$11$	0.560840	−	0.668383i	0.169100	−	0.201525i	0.843938	+	0.536440i	$0.180231\pi$
$12$		0			0
$13$	0.741685	+	0.883906i	0.205706	+	0.245151i	0.859027	−	0.511930i	$-0.171069\pi$
$13$	0.741685	+	0.883906i	0.205706	+	0.245151i	−0.653321	+	0.757081i	$0.726625\pi$
$14$		0			0
$15$	−3.79069	+	2.02384i	−0.978752	+	0.522552i
$16$		0			0
$17$	−0.825934	+	1.43056i	−0.200319	+	0.346962i	−0.948631	−	0.316384i	$-0.897531\pi$
$17$	−0.825934	+	1.43056i	−0.200319	+	0.346962i	0.748313	+	0.663346i	$0.230864\pi$
$18$		0			0
$19$	1.68010	−	0.970004i	0.385441	−	0.222534i	−0.294742	−	0.955577i	$-0.595234\pi$
$19$	1.68010	−	0.970004i	0.385441	−	0.222534i	0.680183	+	0.733043i	$0.261900\pi$
$20$		0			0
$21$	−3.20553	+	3.27484i	−0.699504	+	0.714629i
$22$		0			0
$23$	1.73474	−	4.76615i	0.361717	−	0.993811i	−0.616705	−	0.787195i	$-0.711533\pi$
$23$	1.73474	−	4.76615i	0.361717	−	0.993811i	0.978422	−	0.206616i	$-0.0662451\pi$
$24$		0			0
$25$	0.200577	−	1.13753i	0.0401154	−	0.227506i
$26$		0			0
$27$	−4.21933	−	3.03270i	−0.812010	−	0.583643i
$28$		0			0
$29$	−2.90948	+	3.46738i	−0.540277	+	0.643877i	−0.965250	−	0.261329i	$-0.915839\pi$
$29$	−2.90948	+	3.46738i	−0.540277	+	0.643877i	0.424973	+	0.905206i	$0.360284\pi$
$30$		0			0
$31$	−3.09289	−	3.68597i	−0.555500	−	0.662020i	0.413087	−	0.910691i	$-0.364450\pi$
$31$	−3.09289	−	3.68597i	−0.555500	−	0.662020i	−0.968588	+	0.248672i	$0.920006\pi$
$32$		0			0
$33$	−1.18928	+	0.932437i	−0.207028	+	0.162316i
$34$		0			0
$35$	−0.858490	−	6.50758i	−0.145111	−	1.09998i
$36$		0			0
$37$	5.74721			0.944836			0.472418	−	0.881375i	$-0.343381\pi$
$37$	5.74721			0.944836			0.472418	+	0.881375i	$0.343381\pi$
$38$		0			0
$39$	−0.941262	−	1.76300i	−0.150723	−	0.282307i
$40$		0			0
$41$	1.42301	−	1.19405i	0.222237	−	0.186479i	−0.524871	−	0.851182i	$-0.675886\pi$
$41$	1.42301	−	1.19405i	0.222237	−	0.186479i	0.747108	+	0.664703i	$0.231442\pi$
$42$		0			0
$43$	4.32294	−	1.57342i	0.659243	−	0.239945i	0.00933336	−	0.999956i	$-0.497029\pi$
$43$	4.32294	−	1.57342i	0.659243	−	0.239945i	0.649909	+	0.760012i	$0.274807\pi$
$44$		0			0
$45$	7.14747	−	2.07589i	1.06548	−	0.309455i
$46$		0			0
$47$	−5.30777	−	4.45375i	−0.774218	−	0.649646i	0.167568	−	0.985861i	$-0.446409\pi$
$47$	−5.30777	−	4.45375i	−0.774218	−	0.649646i	−0.941785	+	0.336215i	$0.890853\pi$
$48$		0			0
$49$	−2.96168	−	6.34259i	−0.423098	−	0.906084i
$50$		0			0
$51$	1.91084	−	2.12949i	0.267571	−	0.298188i
$52$		0			0
$53$	5.19487	−	2.99926i	0.713570	−	0.411980i	−0.0988117	−	0.995106i	$-0.531504\pi$
$53$	5.19487	−	2.99926i	0.713570	−	0.411980i	0.812381	+	0.583127i	$0.198171\pi$
$54$		0			0
$55$		−	2.16465i		−	0.291882i
$56$		0			0
$57$	−3.19396	+	1.04380i	−0.423050	+	0.138255i
$58$		0			0
$59$	−1.89672	−	10.7568i	−0.246932	−	1.40042i	−0.815963	−	0.578104i	$-0.803793\pi$
$59$	−1.89672	−	10.7568i	−0.246932	−	1.40042i	0.569031	−	0.822316i	$-0.307318\pi$
$60$		0			0
$61$	3.87453	−	4.61749i	0.496083	−	0.591209i	−0.458671	−	0.888606i	$-0.651674\pi$
$61$	3.87453	−	4.61749i	0.496083	−	0.591209i	0.954754	+	0.297398i	$0.0961187\pi$
$62$		0			0
$63$	6.60263	−	4.40514i	0.831854	−	0.554995i
$64$		0			0
$65$	2.81916	+	0.497095i	0.349674	+	0.0616570i
$66$		0			0
$67$	10.8849	+	3.96179i	1.32980	+	0.484009i	0.906587	−	0.422019i	$-0.138678\pi$
$67$	10.8849	+	3.96179i	1.32980	+	0.484009i	0.423218	+	0.906028i	$0.360901\pi$
$68$		0			0
$69$	−4.64265	+	7.45803i	−0.558909	+	0.897842i
$70$		0			0
$71$	−14.0958	+	8.13823i	−1.67287	+	0.965830i	−0.706846	+	0.707367i	$0.749883\pi$
$71$	−14.0958	+	8.13823i	−1.67287	+	0.965830i	−0.966021	+	0.258463i	$0.916784\pi$
$72$		0			0
$73$		−	1.69133i		−	0.197955i	−0.995090	−	0.0989774i	$-0.968443\pi$
$73$		−	1.69133i		−	0.197955i	0.995090	−	0.0989774i	$-0.0315572\pi$
$74$		0			0
$75$	−0.746296	+	1.85625i	−0.0861749	+	0.214341i
$76$		0			0
$77$	−0.694747	−	2.20143i	−0.0791738	−	0.250876i
$78$		0			0
$79$	−4.33553	+	1.57801i	−0.487786	+	0.177539i	−0.574192	−	0.818721i	$-0.694684\pi$
$79$	−4.33553	+	1.57801i	−0.487786	+	0.177539i	0.0864066	+	0.996260i	$0.472462\pi$
$80$		0			0
$81$	6.06761	+	6.64711i	0.674179	+	0.738568i
$82$		0			0
$83$	−0.417251	−	0.350116i	−0.0457993	−	0.0384302i	0.619601	−	0.784917i	$-0.287295\pi$
$83$	−0.417251	−	0.350116i	−0.0457993	−	0.0384302i	−0.665400	+	0.746487i	$0.731739\pi$
$84$		0			0
$85$	0.711644	+	4.03593i	0.0771886	+	0.437758i
$86$		0			0
$87$	6.16966	−	4.83722i	0.661457	−	0.518604i
$88$		0			0
$89$	−4.76115	−	8.24656i	−0.504681	−	0.874134i	−0.999985	−	0.00541389i	$-0.998277\pi$
$89$	−4.76115	−	8.24656i	−0.504681	−	0.874134i	0.495304	−	0.868720i	$-0.335057\pi$
$90$		0			0
$91$	3.02660	−	0.399274i	0.317274	−	0.0418553i
$92$		0			0
$93$	3.92515	+	7.35189i	0.407019	+	0.762356i
$94$		0			0
$95$	1.64616	−	4.52279i	0.168892	−	0.464028i
$96$		0			0
$97$	−1.27535	−	3.50400i	−0.129492	−	0.355778i	0.857955	−	0.513725i	$-0.171735\pi$
$97$	−1.27535	−	3.50400i	−0.129492	−	0.355778i	−0.987448	+	0.157947i	$0.949512\pi$
$98$		0			0
$99$	2.34870	−	1.15546i	0.236054	−	0.116128i
$100$		0			0
$101$	−9.91373	+	3.60830i	−0.986453	+	0.359039i	−0.784346	−	0.620324i	$-0.787001\pi$
$101$	−9.91373	+	3.60830i	−0.986453	+	0.359039i	−0.202107	+	0.979363i	$0.564779\pi$
$102$		0			0
$103$	11.0659	+	13.1878i	1.09036	+	1.29944i	0.950999	+	0.309195i	$0.100060\pi$
$103$	11.0659	+	13.1878i	1.09036	+	1.29944i	0.139359	+	0.990242i	$0.455496\pi$
$104$		0			0
$105$	−0.869701	+	11.3358i	−0.0848741	+	1.10626i
$106$		0			0
$107$	−10.5700	−	6.10258i	−1.02184	−	0.589958i	−0.107202	−	0.994237i	$-0.534189\pi$
$107$	−10.5700	−	6.10258i	−1.02184	−	0.589958i	−0.914636	+	0.404279i	$0.867522\pi$
$108$		0			0
$109$	3.72917	+	6.45912i	0.357190	+	0.618672i	0.987490	−	0.157680i	$-0.0504015\pi$
$109$	3.72917	+	6.45912i	0.357190	+	0.618672i	−0.630300	+	0.776352i	$0.717068\pi$
$110$		0			0
$111$	−9.74044	−	2.05306i	−0.924522	−	0.194868i
$112$		0			0
$113$	−1.24798	+	3.42880i	−0.117400	+	0.322555i	−0.984449	−	0.175668i	$-0.943792\pi$
$113$	−1.24798	+	3.42880i	−0.117400	+	0.322555i	0.867049	+	0.498223i	$0.166014\pi$
$114$		0			0
$115$	−4.30378	−	11.8245i	−0.401330	−	1.10264i
$116$		0			0
$117$	0.965471	+	3.32421i	0.0892578	+	0.307323i
$118$		0			0
$119$	2.01907	+	3.87609i	0.185088	+	0.355320i
$120$		0			0
$121$	1.77794	+	10.0832i	0.161630	+	0.916652i
$122$		0			0
$123$	−2.83828	+	1.51535i	−0.255919	+	0.136634i
$124$		0			0
$125$	4.76952	+	8.26105i	0.426599	+	0.738890i
$126$		0			0
$127$	−7.18742	+	12.4490i	−0.637780	+	1.10467i	0.348139	+	0.937443i	$0.386814\pi$
$127$	−7.18742	+	12.4490i	−0.637780	+	1.10467i	−0.985919	+	0.167225i	$0.946520\pi$
$128$		0			0
$129$	−7.88865	+	1.12239i	−0.694557	+	0.0988205i
$130$		0			0
$131$	7.63241	+	2.77797i	0.666847	+	0.242712i	0.653190	−	0.757194i	$-0.273430\pi$
$131$	7.63241	+	2.77797i	0.666847	+	0.242712i	0.0136571	+	0.999907i	$0.495653\pi$
$132$		0			0
$133$	0.222532	−	5.12795i	0.0192960	−	0.444650i
$134$		0			0
$135$	−12.8552	+	0.964969i	−1.10640	+	0.0830513i
$136$		0			0
$137$	−3.10372	−	0.547270i	−0.265169	−	0.0467564i	0.0394828	−	0.999220i	$-0.487429\pi$
$137$	−3.10372	−	0.547270i	−0.265169	−	0.0467564i	−0.304652	+	0.952464i	$0.598540\pi$
$138$		0			0
$139$	−12.5717	+	2.21673i	−1.06632	+	0.188021i	−0.679158	−	0.733992i	$-0.737655\pi$
$139$	−12.5717	+	2.21673i	−1.06632	+	0.188021i	−0.387160	+	0.922013i	$0.626544\pi$
$140$		0			0
$141$	7.40467	+	9.44434i	0.623586	+	0.795357i
$142$		0			0
$143$	1.00675			0.0841891
$144$		0			0
$145$			11.2296i			0.932568i
$146$		0			0
$147$	2.75376	+	11.8075i	0.227126	+	0.973865i
$148$		0			0
$149$	−5.55960	+	0.980308i	−0.455460	+	0.0803099i	−0.396672	−	0.917961i	$-0.629835\pi$
$149$	−5.55960	+	0.980308i	−0.455460	+	0.0803099i	−0.0587885	+	0.998270i	$0.518724\pi$
$150$		0			0
$151$	16.7545	+	14.0587i	1.36346	+	1.14408i	0.974896	+	0.222660i	$0.0714738\pi$
$151$	16.7545	+	14.0587i	1.36346	+	1.14408i	0.388566	+	0.921421i	$0.372971\pi$
$152$		0			0
$153$	−3.99922	+	2.92648i	−0.323318	+	0.236592i
$154$		0			0
$155$	−11.7562	−	2.07293i	−0.944278	−	0.166502i
$156$		0			0
$157$	22.6300	−	3.99028i	1.80607	−	0.318459i	0.833755	−	0.552134i	$-0.186186\pi$
$157$	22.6300	−	3.99028i	1.80607	−	0.318459i	0.972315	+	0.233675i	$0.0750752\pi$
$158$		0			0
$159$	−9.87574	+	3.22743i	−0.783197	+	0.255952i
$160$		0			0
$161$	−8.17199	−	10.6441i	−0.644043	−	0.838873i
$162$		0			0
$163$	−3.61108	+	6.25457i	−0.282841	+	0.489896i	−0.972083	−	0.234635i	$-0.924610\pi$
$163$	−3.61108	+	6.25457i	−0.282841	+	0.489896i	0.689242	+	0.724531i	$0.257944\pi$
$164$		0			0
$165$	−0.773272	+	3.66868i	−0.0601992	+	0.285606i
$166$		0			0
$167$	11.2129	+	4.08117i	0.867681	+	0.315810i	0.737228	−	0.675644i	$-0.236134\pi$
$167$	11.2129	+	4.08117i	0.867681	+	0.315810i	0.130454	+	0.991454i	$0.458357\pi$
$168$		0			0
$169$	2.02623	−	11.4913i	0.155864	−	0.883949i
$170$		0			0
$171$	5.78604	−	0.628076i	0.442469	−	0.0480302i
$172$		0			0
$173$	−1.36420	+	7.73674i	−0.103718	+	0.588214i	0.888007	+	0.459831i	$0.152090\pi$
$173$	−1.36420	+	7.73674i	−0.103718	+	0.588214i	−0.991725	+	0.128383i	$0.959021\pi$
$174$		0			0
$175$	−2.25370	−	2.06404i	−0.170364	−	0.156027i
$176$		0			0
$177$	−0.628045	+	18.9084i	−0.0472068	+	1.42124i
$178$		0			0
$179$	5.43828	+	3.13979i	0.406476	+	0.234679i	0.689274	−	0.724500i	$-0.257929\pi$
$179$	5.43828	+	3.13979i	0.406476	+	0.234679i	−0.282799	+	0.959179i	$0.591263\pi$
$180$		0			0
$181$	11.7793	+	6.80080i	0.875551	+	0.505499i	0.869189	−	0.494480i	$-0.164642\pi$
$181$	11.7793	+	6.80080i	0.875551	+	0.505499i	0.00636187	+	0.999980i	$0.497975\pi$
$182$		0			0
$183$	−8.21609	+	6.44169i	−0.607351	+	0.476183i
$184$		0			0
$185$	10.9226	−	9.16519i	0.803049	−	0.673838i
$186$		0			0
$187$	0.492945	+	1.35436i	0.0360477	+	0.0990404i
$188$		0			0
$189$	−12.7639	+	5.10724i	−0.928434	+	0.371497i
$190$		0			0
$191$	−1.31270	−	3.60660i	−0.0949834	−	0.260965i	0.883098	−	0.469189i	$-0.155454\pi$
$191$	−1.31270	−	3.60660i	−0.0949834	−	0.260965i	−0.978081	+	0.208224i	$0.933232\pi$
$192$		0			0
$193$	2.09261	−	1.75591i	0.150629	−	0.126393i	−0.564359	−	0.825530i	$-0.690877\pi$
$193$	2.09261	−	1.75591i	0.150629	−	0.126393i	0.714988	+	0.699137i	$0.246432\pi$
$194$		0			0
$195$	−4.60038	−	1.84956i	−0.329440	−	0.132450i
$196$		0			0
$197$	−3.32357	−	1.91886i	−0.236795	−	0.136713i	0.376908	−	0.926251i	$-0.376987\pi$
$197$	−3.32357	−	1.91886i	−0.236795	−	0.136713i	−0.613703	+	0.789537i	$0.710321\pi$
$198$		0			0
$199$	−20.5819	−	11.8829i	−1.45901	−	0.842360i	−0.460047	−	0.887894i	$-0.652168\pi$
$199$	−20.5819	−	11.8829i	−1.45901	−	0.842360i	−0.998963	+	0.0455344i	$0.985501\pi$
$200$		0			0
$201$	−17.0326	−	10.6029i	−1.20139	−	0.747869i
$202$		0			0
$203$	3.60415	+	11.4204i	0.252962	+	0.801553i
$204$		0			0
$205$	0.800278	−	4.53860i	0.0558938	−	0.316990i
$206$		0			0
$207$	10.5326	−	10.9815i	0.732068	−	0.763266i
$208$		0			0
$209$	0.293931	−	1.66697i	0.0203316	−	0.115306i
$210$		0			0
$211$	26.2398	+	9.55051i	1.80642	+	0.657484i	0.997585	+	0.0694506i	$0.0221246\pi$
$211$	26.2398	+	9.55051i	1.80642	+	0.657484i	0.808837	+	0.588033i	$0.200098\pi$
$212$		0			0
$213$	26.7970	−	8.75737i	1.83610	−	0.600045i
$214$		0			0
$215$	5.70664	−	9.88419i	0.389190	−	0.674096i
$216$		0			0
$217$	−12.6212	+	1.66501i	−0.856782	+	0.113028i
$218$		0			0
$219$	−0.604187	+	2.86648i	−0.0408272	+	0.193699i
$220$		0			0
$221$	−1.87706	+	0.330977i	−0.126265	+	0.0222639i
$222$		0			0
$223$	−7.03311	−	1.24013i	−0.470972	−	0.0830451i	−0.0668753	−	0.997761i	$-0.521303\pi$
$223$	−7.03311	−	1.24013i	−0.470972	−	0.0830451i	−0.404097	+	0.914716i	$0.632414\pi$
$224$		0			0
$225$	1.92793	−	2.87939i	0.128529	−	0.191959i
$226$		0			0
$227$	15.7874	+	13.2472i	1.04784	+	0.879246i	0.992865	−	0.119241i	$-0.0380462\pi$
$227$	15.7874	+	13.2472i	1.04784	+	0.879246i	0.0549796	+	0.998487i	$0.482491\pi$
$228$		0			0
$229$	5.17140	−	0.911857i	0.341736	−	0.0602572i	−0.000146646	−	1.00000i	$-0.500047\pi$
$229$	5.17140	−	0.911857i	0.341736	−	0.0602572i	0.341882	+	0.939743i	$0.388936\pi$
$230$		0			0
$231$	0.391058	+	3.97918i	0.0257297	+	0.261811i
$232$		0			0
$233$		−	15.3906i		−	1.00827i	−0.863624	−	0.504137i	$-0.831811\pi$
$233$		−	15.3906i		−	1.00827i	0.863624	−	0.504137i	$-0.168189\pi$
$234$		0			0
$235$	−17.1900			−1.12135
$236$		0			0
$237$	7.91162	−	1.12565i	0.513915	−	0.0731191i
$238$		0			0
$239$	−7.55229	+	1.33167i	−0.488517	+	0.0861388i	−0.412481	−	0.910966i	$-0.635338\pi$
$239$	−7.55229	+	1.33167i	−0.488517	+	0.0861388i	−0.0760364	+	0.997105i	$0.524227\pi$
$240$		0			0
$241$	−10.3817	−	1.83057i	−0.668742	−	0.117917i	−0.171039	−	0.985264i	$-0.554712\pi$
$241$	−10.3817	−	1.83057i	−0.668742	−	0.117917i	−0.497704	+	0.867347i	$0.665823\pi$
$242$		0			0
$243$	−7.90894	−	13.4331i	−0.507359	−	0.861735i
$244$		0			0
$245$	−15.7434	−	7.33111i	−1.00581	−	0.468368i
$246$		0			0
$247$	2.10350	+	0.765610i	0.133842	+	0.0487146i
$248$		0			0
$249$	0.582092	+	0.742434i	0.0368886	+	0.0470498i
$250$		0			0
$251$	1.84579	−	3.19700i	0.116505	−	0.201793i	−0.801875	−	0.597491i	$-0.796164\pi$
$251$	1.84579	−	3.19700i	0.116505	−	0.201793i	0.918380	+	0.395699i	$0.129498\pi$
$252$		0			0
$253$	−2.21270	−	3.83252i	−0.139112	−	0.240948i
$254$		0			0
$255$	0.235641	−	7.09436i	0.0147564	−	0.444266i
$256$		0			0
$257$	−0.435889	−	2.47205i	−0.0271900	−	0.154202i	0.968190	−	0.250216i	$-0.0805017\pi$
$257$	−0.435889	−	2.47205i	−0.0271900	−	0.154202i	−0.995380	+	0.0960141i	$0.969391\pi$
$258$		0			0
$259$	8.16662	−	12.8265i	0.507449	−	0.797001i
$260$		0			0
$261$	−12.1844	+	5.99421i	−0.754196	+	0.371032i
$262$		0			0
$263$	6.44330	+	17.7028i	0.397311	+	1.09160i	0.963589	+	0.267389i	$0.0861608\pi$
$263$	6.44330	+	17.7028i	0.397311	+	1.09160i	−0.566278	+	0.824215i	$0.691617\pi$
$264$		0			0
$265$	5.08993	−	13.9845i	0.312672	−	0.859060i
$266$		0			0
$267$	5.12337	+	15.6772i	0.313545	+	0.959428i
$268$		0			0
$269$	−4.49619	−	7.78763i	−0.274138	−	0.474820i	0.695779	−	0.718255i	$-0.255059\pi$
$269$	−4.49619	−	7.78763i	−0.274138	−	0.474820i	−0.969917	+	0.243435i	$0.921726\pi$
$270$		0			0
$271$	−23.0777	−	13.3239i	−1.40187	−	0.809369i	−0.407283	−	0.913302i	$-0.633524\pi$
$271$	−23.0777	−	13.3239i	−1.40187	−	0.809369i	−0.994584	+	0.103933i	$0.966857\pi$
$272$		0			0
$273$	−5.27215	−	0.404488i	−0.319085	−	0.0244807i
$274$		0			0
$275$	−0.647813	−	0.772034i	−0.0390646	−	0.0465554i
$276$		0			0
$277$	15.2391	−	5.54660i	0.915632	−	0.333263i	0.159132	−	0.987257i	$-0.449130\pi$
$277$	15.2391	−	5.54660i	0.915632	−	0.333263i	0.756499	+	0.653995i	$0.226908\pi$
$278$		0			0
$279$	−4.02610	−	13.8622i	−0.241036	−	0.829911i
$280$		0			0
$281$	10.2506	+	28.1634i	0.611501	+	1.68009i	0.726881	+	0.686764i	$0.240969\pi$
$281$	10.2506	+	28.1634i	0.611501	+	1.68009i	−0.115380	+	0.993321i	$0.536809\pi$
$282$		0			0
$283$	4.06945	−	11.1807i	0.241904	−	0.664625i	−0.758019	−	0.652232i	$-0.773833\pi$
$283$	4.06945	−	11.1807i	0.241904	−	0.664625i	0.999923	−	0.0123931i	$-0.00394495\pi$
$284$		0			0
$285$	−4.40559	+	7.07722i	−0.260965	+	0.419218i
$286$		0			0
$287$	−0.642795	−	4.87255i	−0.0379430	−	0.287618i
$288$		0			0
$289$	7.13566	+	12.3593i	0.419745	+	0.727020i
$290$		0			0
$291$	0.909760	+	6.39422i	0.0533311	+	0.374836i
$292$		0			0
$293$	4.63962	+	26.3126i	0.271049	+	1.53720i	0.751238	+	0.660032i	$0.229457\pi$
$293$	4.63962	+	26.3126i	0.271049	+	1.53720i	−0.480189	+	0.877165i	$0.659432\pi$
$294$		0			0
$295$	−20.7589	−	17.4188i	−1.20863	−	1.01416i
$296$		0			0
$297$	−4.39337	+	1.11927i	−0.254929	+	0.0649467i
$298$		0			0
$299$	5.49946	−	2.00164i	0.318042	−	0.115758i
$300$		0			0
$301$	2.63124	−	11.8836i	0.151662	−	0.684962i
$302$		0			0
$303$	18.0909	−	2.57395i	1.03929	−	0.147869i
$304$		0			0
$305$		−	14.9544i		−	0.856285i
$306$		0			0
$307$	12.1594	−	7.02025i	0.693975	−	0.400667i	−0.111124	−	0.993807i	$-0.535445\pi$
$307$	12.1594	−	7.02025i	0.693975	−	0.400667i	0.805099	+	0.593140i	$0.202112\pi$
$308$		0			0
$309$	−14.0436	−	26.3040i	−0.798913	−	1.49638i
$310$		0			0
$311$	21.0853	+	7.67443i	1.19564	+	0.435177i	0.861700	−	0.507417i	$-0.169400\pi$
$311$	21.0853	+	7.67443i	1.19564	+	0.435177i	0.333939	+	0.942595i	$0.391622\pi$
$312$		0			0
$313$	−17.9721	−	3.16896i	−1.01584	−	0.179120i	−0.359150	−	0.933280i	$-0.616933\pi$
$313$	−17.9721	−	3.16896i	−1.01584	−	0.179120i	−0.656691	+	0.754159i	$0.728045\pi$
$314$		0			0
$315$	5.52343	−	18.9014i	0.311210	−	1.06497i
$316$		0			0
$317$	−7.11995	+	8.48523i	−0.399896	+	0.476578i	−0.927988	−	0.372609i	$-0.878463\pi$
$317$	−7.11995	+	8.48523i	−0.399896	+	0.476578i	0.528092	+	0.849187i	$0.322908\pi$
$318$		0			0
$319$	0.685787	+	3.88929i	0.0383967	+	0.217759i
$320$		0			0
$321$	15.7341	+	14.1186i	0.878193	+	0.788023i
$322$		0			0
$323$			3.20464i			0.178311i
$324$		0			0
$325$	1.15423	−	0.666397i	0.0640254	−	0.0369651i
$326$		0			0
$327$	−4.01288	−	12.2792i	−0.221913	−	0.679039i
$328$		0			0
$329$	−17.4820	+	5.51713i	−0.963812	+	0.304169i
$330$		0			0
$331$	15.6225	+	13.1088i	0.858690	+	0.720526i	0.961685	−	0.274155i	$-0.0883983\pi$
$331$	15.6225	+	13.1088i	0.858690	+	0.720526i	−0.102996	+	0.994682i	$0.532843\pi$
$332$		0			0
$333$	15.7748	+	6.95910i	0.864455	+	0.381356i
$334$		0			0
$335$	27.0049	−	9.82897i	1.47543	−	0.537014i
$336$		0			0
$337$	3.48238	−	2.92206i	0.189697	−	0.159175i	−0.542993	−	0.839737i	$-0.682709\pi$
$337$	3.48238	−	2.92206i	0.189697	−	0.159175i	0.732690	+	0.680562i	$0.238264\pi$
$338$		0			0
$339$	3.33996	−	5.36537i	0.181402	−	0.291407i
$340$		0			0
$341$	−4.19826			−0.227349
$342$		0			0
$343$	−18.3637	−	2.40280i	−0.991548	−	0.129739i
$344$		0			0
$345$	3.07006	+	21.5778i	0.165286	+	1.16171i
$346$		0			0
$347$	8.36050	+	9.96366i	0.448815	+	0.534877i	0.942252	−	0.334905i	$-0.108704\pi$
$347$	8.36050	+	9.96366i	0.448815	+	0.534877i	−0.493437	+	0.869782i	$0.664260\pi$
$348$		0			0
$349$	−5.68358	+	6.77342i	−0.304235	+	0.362573i	−0.896402	−	0.443242i	$-0.853828\pi$
$349$	−5.68358	+	6.77342i	−0.304235	+	0.362573i	0.592167	+	0.805815i	$0.298273\pi$
$350$		0			0
$351$	−0.448796	−	5.97880i	−0.0239549	−	0.319125i
$352$		0			0
$353$	−0.683015	+	3.87357i	−0.0363532	+	0.206169i	−0.997574	−	0.0696095i	$-0.977825\pi$
$353$	−0.683015	+	3.87357i	−0.0363532	+	0.206169i	0.961221	+	0.275779i	$0.0889358\pi$
$354$		0			0
$355$	−13.8111	+	37.9457i	−0.733017	+	2.01395i
$356$		0			0
$357$	−2.03730	−	7.29051i	−0.107825	−	0.385855i
$358$		0			0
$359$	−23.8364	+	13.7620i	−1.25804	+	0.726329i	−0.972693	−	0.232096i	$-0.925442\pi$
$359$	−23.8364	+	13.7620i	−1.25804	+	0.726329i	−0.285346	+	0.958425i	$0.592108\pi$
$360$		0			0
$361$	−7.61818	+	13.1951i	−0.400957	+	0.694478i
$362$		0			0
$363$	0.588713	−	17.7242i	0.0308994	−	0.930280i
$364$		0			0
$365$	−2.69719	−	3.21439i	−0.141177	−	0.168249i
$366$		0			0
$367$	−8.34470	+	9.94482i	−0.435590	+	0.519115i	−0.938526	−	0.345208i	$-0.887808\pi$
$367$	−8.34470	+	9.94482i	−0.435590	+	0.519115i	0.502937	+	0.864323i	$0.332253\pi$
$368$		0			0
$369$	5.35168	−	1.55432i	0.278597	−	0.0809147i
$370$		0			0
$371$	0.688070	−	15.8557i	0.0357228	−	0.823185i
$372$		0			0
$373$	9.73062	−	8.16496i	0.503832	−	0.422765i	−0.355120	−	0.934821i	$-0.615560\pi$
$373$	9.73062	−	8.16496i	0.503832	−	0.422765i	0.858953	+	0.512055i	$0.171116\pi$
$374$		0			0
$375$	−5.13237	−	15.7047i	−0.265034	−	0.810988i
$376$		0			0
$377$	−5.22276			−0.268986
$378$		0			0
$379$	−28.2292			−1.45004			−0.725018	−	0.688730i	$-0.758169\pi$
$379$	−28.2292			−1.45004			−0.725018	+	0.688730i	$0.758169\pi$
$380$		0			0
$381$	16.6284	−	18.5311i	0.851900	−	0.949379i
$382$		0			0
$383$	22.0331	−	18.4880i	1.12584	−	0.944692i	0.126956	−	0.991908i	$-0.459479\pi$
$383$	22.0331	−	18.4880i	1.12584	−	0.944692i	0.998885	+	0.0472163i	$0.0150350\pi$
$384$		0			0
$385$	−4.83103	−	3.07591i	−0.246212	−	0.156763i
$386$		0			0
$387$	13.7707	+	0.915804i	0.700005	+	0.0465530i
$388$		0			0
$389$	−13.1452	+	15.6658i	−0.666487	+	0.794288i	−0.988301	−	0.152514i	$-0.951263\pi$
$389$	−13.1452	+	15.6658i	−0.666487	+	0.794288i	0.321814	+	0.946803i	$0.395707\pi$
$390$		0			0
$391$	5.38548	+	6.41817i	0.272356	+	0.324581i
$392$		0			0
$393$	−11.9431	−	7.43464i	−0.602451	−	0.375028i
$394$		0			0
$395$	−5.72326	+	9.91298i	−0.287968	+	0.498776i
$396$		0			0
$397$	0.483326	−	0.279049i	0.0242574	−	0.0140050i	−0.487822	−	0.872943i	$-0.662209\pi$
$397$	0.483326	−	0.279049i	0.0242574	−	0.0140050i	0.512080	+	0.858938i	$0.328875\pi$
$398$		0			0
$399$	−2.20899	+	8.61142i	−0.110588	+	0.431110i
$400$		0			0
$401$	10.2168	−	28.0704i	0.510203	−	1.40177i	−0.370824	−	0.928703i	$-0.620925\pi$
$401$	10.2168	−	28.0704i	0.510203	−	1.40177i	0.881026	−	0.473067i	$-0.156853\pi$
$402$		0			0
$403$	0.964096	−	5.46766i	0.0480250	−	0.272363i
$404$		0			0
$405$	22.1318	+	2.95678i	1.09974	+	0.146923i
$406$		0			0
$407$	3.22327	−	3.84134i	0.159771	−	0.190408i
$408$		0			0
$409$	6.09653	+	7.26556i	0.301454	+	0.359259i	0.895413	−	0.445237i	$-0.146880\pi$
$409$	6.09653	+	7.26556i	0.301454	+	0.359259i	−0.593959	+	0.804495i	$0.702436\pi$
$410$		0			0
$411$	5.06473	+	2.03625i	0.249825	+	0.100441i
$412$		0			0
$413$	−26.7021	−	11.0521i	−1.31392	−	0.543838i
$414$		0			0
$415$	−1.35133			−0.0663341
$416$		0			0
$417$	22.0985	+	0.734007i	1.08217	+	0.0359445i
$418$		0			0
$419$	−11.1641	+	9.36783i	−0.545404	+	0.457648i	−0.873381	−	0.487037i	$-0.838078\pi$
$419$	−11.1641	+	9.36783i	−0.545404	+	0.457648i	0.327977	+	0.944686i	$0.393633\pi$
$420$		0			0
$421$	−16.4485	+	5.98678i	−0.801653	+	0.291778i	−0.710171	−	0.704029i	$-0.751382\pi$
$421$	−16.4485	+	5.98678i	−0.801653	+	0.291778i	−0.0914815	+	0.995807i	$0.529160\pi$
$422$		0			0
$423$	−9.17576	−	18.6515i	−0.446141	−	0.906869i
$424$		0			0
$425$	1.46164	+	1.22646i	0.0709000	+	0.0594921i
$426$		0			0
$427$	−4.79962	−	15.2084i	−0.232270	−	0.735987i
$428$		0			0
$429$	−1.70626	−	0.359640i	−0.0823790	−	0.0173636i
$430$		0			0
$431$	26.8638	−	15.5098i	1.29398	−	0.747082i	0.314626	−	0.949216i	$-0.398121\pi$
$431$	26.8638	−	15.5098i	1.29398	−	0.747082i	0.979358	+	0.202134i	$0.0647877\pi$
$432$		0			0
$433$			17.1170i			0.822593i	0.911502	+	0.411296i	$0.134924\pi$
$433$			17.1170i			0.822593i	−0.911502	+	0.411296i	$0.865076\pi$
$434$		0			0
$435$	4.01152	−	19.0321i	0.192337	−	0.912518i
$436$		0			0
$437$	−1.70866	−	9.69029i	−0.0817363	−	0.463549i
$438$		0			0
$439$	−11.9942	+	14.2941i	−0.572452	+	0.682222i	−0.972132	−	0.234433i	$-0.924677\pi$
$439$	−11.9942	+	14.2941i	−0.572452	+	0.682222i	0.399680	+	0.916655i	$0.369121\pi$
$440$		0			0
$441$	−0.449148	−	20.9952i	−0.0213880	−	0.999771i
$442$		0			0
$443$	29.6314	+	5.22482i	1.40783	+	0.248239i	0.825357	−	0.564611i	$-0.190974\pi$
$443$	29.6314	+	5.22482i	1.40783	+	0.248239i	0.582474	+	0.812850i	$0.302085\pi$
$444$		0			0
$445$	−22.1996	−	8.07999i	−1.05236	−	0.383028i
$446$		0			0
$447$	9.77267	+	0.324601i	0.462232	+	0.0153531i
$448$		0			0
$449$	12.9905	−	7.50006i	0.613059	−	0.353950i	−0.161103	−	0.986938i	$-0.551505\pi$
$449$	12.9905	−	7.50006i	0.613059	−	0.353950i	0.774162	+	0.632988i	$0.218172\pi$
$450$		0			0
$451$		−	1.62079i		−	0.0763198i
$452$		0			0
$453$	−23.3736	−	29.8120i	−1.09819	−	1.40069i
$454$		0			0
$455$	5.11536	−	5.58540i	0.239812	−	0.261847i
$456$		0			0
$457$	39.2134	−	14.2725i	1.83433	−	0.667641i	0.842721	−	0.538351i	$-0.180953\pi$
$457$	39.2134	−	14.2725i	1.83433	−	0.667641i	0.991607	−	0.129289i	$-0.0412696\pi$
$458$		0			0
$459$	7.82335	−	3.53120i	0.365163	−	0.164822i
$460$		0			0
$461$	−18.5581	−	15.5721i	−0.864339	−	0.725267i	0.0985592	−	0.995131i	$-0.468577\pi$
$461$	−18.5581	−	15.5721i	−0.864339	−	0.725267i	−0.962898	+	0.269865i	$0.913021\pi$
$462$		0			0
$463$	−0.385388	−	2.18564i	−0.0179105	−	0.101575i	0.974542	−	0.224205i	$-0.0719785\pi$
$463$	−0.385388	−	2.18564i	−0.0179105	−	0.101575i	−0.992453	+	0.122629i	$0.960867\pi$
$464$		0			0
$465$	19.1840	+	7.71285i	0.889637	+	0.357675i
$466$		0			0
$467$	10.7322	+	18.5887i	0.496626	+	0.860181i	0.999992	−	0.00389157i	$-0.00123873\pi$
$467$	10.7322	+	18.5887i	0.496626	+	0.860181i	−0.503366	+	0.864073i	$0.667905\pi$
$468$		0			0
$469$	24.3090	−	18.6632i	1.12248	−	0.861785i
$470$		0			0
$471$	−39.7790	−	1.32127i	−1.83292	−	0.0608808i
$472$		0			0
$473$	1.37283	−	3.77182i	0.0631228	−	0.173429i
$474$		0			0
$475$	−0.766419	−	2.10572i	−0.0351657	−	0.0966170i
$476$		0			0
$477$	17.8904	−	1.94201i	0.819147	−	0.0889187i
$478$		0			0
$479$	−36.9317	+	13.4421i	−1.68745	+	0.614183i	−0.994301	−	0.106607i	$-0.966001\pi$
$479$	−36.9317	+	13.4421i	−1.68745	+	0.614183i	−0.693153	+	0.720791i	$0.743779\pi$
$480$		0			0
$481$	4.26262	+	5.08000i	0.194359	+	0.231628i
$482$		0			0
$483$	10.0476	+	20.9590i	0.457183	+	0.953668i
$484$		0			0
$485$	−8.01173	−	4.62557i	−0.363794	−	0.210036i
$486$		0			0
$487$	−6.65268	−	11.5228i	−0.301462	−	0.522147i	0.675006	−	0.737813i	$-0.264141\pi$
$487$	−6.65268	−	11.5228i	−0.301462	−	0.522147i	−0.976467	+	0.215666i	$0.930808\pi$
$488$		0			0
$489$	8.35440	−	9.31035i	0.377799	−	0.421029i
$490$		0			0
$491$	6.40724	−	17.6037i	0.289155	−	0.794446i	−0.707031	−	0.707183i	$-0.749966\pi$
$491$	6.40724	−	17.6037i	0.289155	−	0.794446i	0.996185	−	0.0872628i	$-0.0278120\pi$
$492$		0			0
$493$	−2.55726	−	7.02602i	−0.115173	−	0.316436i
$494$		0			0
$495$	2.62110	−	5.94149i	0.117810	−	0.267050i
$496$		0			0
$497$	−1.86702	+	43.0230i	−0.0837473	+	1.92984i
$498$		0			0
$499$	0.108453	+	0.615065i	0.00485500	+	0.0275341i	0.987139	−	0.159864i	$-0.0511056\pi$
$499$	0.108453	+	0.615065i	0.00485500	+	0.0275341i	−0.982284	+	0.187398i	$0.939995\pi$
$500$		0			0
$501$	−17.5459	−	10.9224i	−0.783892	−	0.487975i
$502$		0			0
$503$	4.62878	+	8.01728i	0.206387	+	0.357473i	0.950574	−	0.310499i	$-0.100496\pi$
$503$	4.62878	+	8.01728i	0.206387	+	0.357473i	−0.744187	+	0.667972i	$0.767163\pi$
$504$		0			0
$505$	−13.0869	+	22.6672i	−0.582361	+	1.00868i
$506$		0			0
$507$	−7.53910	+	18.7518i	−0.334823	+	0.832799i
$508$		0			0
$509$	24.9521	+	9.08181i	1.10598	+	0.402544i	0.829518	−	0.558480i	$-0.188615\pi$
$509$	24.9521	+	9.08181i	1.10598	+	0.402544i	0.276463	+	0.961025i	$0.410838\pi$
$510$		0			0
$511$	−3.77467	−	2.40333i	−0.166982	−	0.106317i
$512$		0			0
$513$	−10.0306	−	1.00246i	−0.442862	−	0.0442595i
$514$		0			0
$515$	42.0618	+	7.41664i	1.85347	+	0.326816i
$516$		0			0
$517$	−5.95362	+	1.04978i	−0.261840	+	0.0461694i
$518$		0			0
$519$	5.07583	−	12.6250i	0.222804	−	0.554176i
$520$		0			0
$521$	−5.44781			−0.238673			−0.119336	−	0.992854i	$-0.538077\pi$
$521$	−5.44781			−0.238673			−0.119336	+	0.992854i	$0.538077\pi$
$522$		0			0
$523$			43.4616i			1.90044i	0.311575	+	0.950221i	$0.399143\pi$
$523$			43.4616i			1.90044i	−0.311575	+	0.950221i	$0.600857\pi$
$524$		0			0
$525$	3.08227	+	4.30324i	0.134521	+	0.187809i
$526$		0			0
$527$	7.82753	−	1.38020i	0.340973	−	0.0601227i
$528$		0			0
$529$	−2.08784	−	1.75191i	−0.0907756	−	0.0761698i
$530$		0			0
$531$	7.81900	−	31.8218i	0.339316	−	1.38095i
$532$		0			0
$533$	2.11085	+	0.372200i	0.0914311	+	0.0161218i
$534$		0			0
$535$	−29.8203	+	5.25812i	−1.28924	+	0.227328i
$536$		0			0
$537$	−8.09524	−	7.26405i	−0.349335	−	0.313467i
$538$		0			0
$539$	−5.90031	−	1.57764i	−0.254144	−	0.0679537i
$540$		0			0
$541$	19.8445	−	34.3717i	0.853181	−	1.47775i	−0.0251413	−	0.999684i	$-0.508004\pi$
$541$	19.8445	−	34.3717i	0.853181	−	1.47775i	0.878322	−	0.478069i	$-0.158663\pi$
$542$		0			0
$543$	−17.5343	−	15.7340i	−0.752470	−	0.675209i
$544$		0			0
$545$	17.3878	+	6.32865i	0.744813	+	0.271090i
$546$		0			0
$547$	2.15543	−	12.2240i	0.0921594	−	0.522662i	−0.903421	−	0.428754i	$-0.858953\pi$
$547$	2.15543	−	12.2240i	0.0921594	−	0.522662i	0.995581	−	0.0939084i	$-0.0299361\pi$
$548$		0			0
$549$	16.2259	−	7.98244i	0.692504	−	0.340682i
$550$		0			0
$551$	−1.52483	+	8.64774i	−0.0649599	+	0.368406i
$552$		0			0
$553$	−2.63891	+	11.9183i	−0.112218	+	0.506816i
$554$		0			0
$555$	−21.7859	+	11.6314i	−0.924759	+	0.493726i
$556$		0			0
$557$	−10.6192	−	6.13098i	−0.449949	−	0.259778i	0.257860	−	0.966182i	$-0.416983\pi$
$557$	−10.6192	−	6.13098i	−0.449949	−	0.259778i	−0.707809	+	0.706404i	$0.750316\pi$
$558$		0			0
$559$	4.59702	+	2.65409i	0.194433	+	0.112256i
$560$		0			0
$561$	−0.351638	−	2.47147i	−0.0148461	−	0.104346i
$562$		0			0
$563$	7.53556	−	6.32309i	0.317586	−	0.266486i	−0.470033	−	0.882649i	$-0.655758\pi$
$563$	7.53556	−	6.32309i	0.317586	−	0.266486i	0.787619	+	0.616163i	$0.211314\pi$
$564$		0			0
$565$	3.09617	+	8.50667i	0.130257	+	0.357878i
$566$		0			0
$567$	23.4568	−	4.09623i	0.985093	−	0.172025i
$568$		0			0
$569$	−8.45366	−	23.2262i	−0.354396	−	0.973694i	−0.980940	−	0.194309i	$-0.937754\pi$
$569$	−8.45366	−	23.2262i	−0.354396	−	0.973694i	0.626545	−	0.779386i	$-0.284469\pi$
$570$		0			0
$571$	2.42877	−	2.03798i	0.101641	−	0.0852868i	−0.590551	−	0.807000i	$-0.701090\pi$
$571$	2.42877	−	2.03798i	0.101641	−	0.0852868i	0.692192	+	0.721713i	$0.256645\pi$
$572$		0			0
$573$	0.936399	+	6.58145i	0.0391186	+	0.274944i
$574$		0			0
$575$	−5.07368	−	2.92929i	−0.211587	−	0.122160i
$576$		0			0
$577$	−12.1397	−	7.00885i	−0.505382	−	0.291782i	0.225551	−	0.974231i	$-0.427582\pi$
$577$	−12.1397	−	7.00885i	−0.505382	−	0.291782i	−0.730933	+	0.682449i	$0.760915\pi$
$578$		0			0
$579$	−4.17384	+	2.22840i	−0.173459	+	0.0926091i
$580$		0			0
$581$	−1.37428	+	0.433709i	−0.0570149	+	0.0179933i
$582$		0			0
$583$	0.908836	−	5.15427i	0.0376401	−	0.213468i
$584$		0			0
$585$	7.13607	+	4.77804i	0.295040	+	0.197548i
$586$		0			0
$587$	1.43178	−	8.12004i	0.0590960	−	0.335150i	−0.940898	−	0.338691i	$-0.890016\pi$
$587$	1.43178	−	8.12004i	0.0590960	−	0.335150i	0.999994	+	0.00354081i	$0.00112708\pi$
$588$		0			0
$589$	−8.77177	−	3.19266i	−0.361434	−	0.131551i
$590$		0			0
$591$	4.94736	+	4.43938i	0.203507	+	0.182612i
$592$		0			0
$593$	−4.01055	+	6.94647i	−0.164693	+	0.285258i	−0.936546	−	0.350544i	$-0.885997\pi$
$593$	−4.01055	+	6.94647i	−0.164693	+	0.285258i	0.771853	+	0.635801i	$0.219330\pi$
$594$		0			0
$595$	10.0185	+	4.14671i	0.410720	+	0.169998i
$596$		0			0
$597$	30.6375	+	27.4918i	1.25391	+	1.12516i
$598$		0			0
$599$	−35.2494	+	6.21543i	−1.44025	+	0.253956i	−0.838576	−	0.544784i	$-0.816612\pi$
$599$	−35.2494	+	6.21543i	−1.44025	+	0.253956i	−0.601677	+	0.798740i	$0.705501\pi$
$600$		0			0
$601$	−39.9932	−	7.05187i	−1.63136	−	0.287652i	−0.718375	−	0.695656i	$-0.755114\pi$
$601$	−39.9932	−	7.05187i	−1.63136	−	0.287652i	−0.912980	+	0.408004i	$0.866225\pi$
$602$		0			0
$603$	25.0795	+	24.0544i	1.02132	+	0.979571i
$604$		0			0
$605$	19.4588	+	16.3279i	0.791113	+	0.663823i
$606$		0			0
$607$	−5.10013	+	0.899290i	−0.207008	+	0.0365011i	−0.276190	−	0.961103i	$-0.589072\pi$
$607$	−5.10013	+	0.899290i	−0.207008	+	0.0365011i	0.0691825	+	0.997604i	$0.477961\pi$
$608$		0			0
$609$	−2.02870	−	20.6429i	−0.0822069	−	0.836492i
$610$		0			0
$611$		−	7.99485i		−	0.323437i
$612$		0			0
$613$	−43.0045			−1.73694			−0.868468	−	0.495746i	$-0.834895\pi$
$613$	−43.0045			−1.73694			−0.868468	+	0.495746i	$0.834895\pi$
$614$		0			0
$615$	−2.97763	+	7.40620i	−0.120070	+	0.298647i
$616$		0			0
$617$	24.8905	−	4.38886i	1.00205	−	0.176689i	0.351531	−	0.936176i	$-0.385661\pi$
$617$	24.8905	−	4.38886i	1.00205	−	0.176689i	0.650522	+	0.759487i	$0.274550\pi$
$618$		0			0
$619$	−20.7428	−	3.65751i	−0.833723	−	0.147008i	−0.259538	−	0.965733i	$-0.583570\pi$
$619$	−20.7428	−	3.65751i	−0.833723	−	0.147008i	−0.574186	+	0.818725i	$0.694681\pi$
$620$		0			0
$621$	−21.7737	+	14.8490i	−0.873749	+	0.595871i
$622$		0			0
$623$	−25.1700	−	1.09227i	−1.00841	−	0.0437610i
$624$		0			0
$625$	27.6657	+	10.0695i	1.10663	+	0.402779i
$626$		0			0
$627$	−1.09364	+	2.72019i	−0.0436759	+	0.108634i
$628$		0			0
$629$	−4.74682	+	8.22173i	−0.189268	+	0.327822i
$630$		0			0
$631$	−5.23606	−	9.06912i	−0.208444	−	0.361036i	0.742780	−	0.669535i	$-0.233507\pi$
$631$	−5.23606	−	9.06912i	−0.208444	−	0.361036i	−0.951225	+	0.308499i	$0.900173\pi$
$632$		0			0
$633$	−41.0598	−	25.5599i	−1.63198	−	1.01591i
$634$		0			0
$635$	6.19284	+	35.1213i	0.245755	+	1.39375i
$636$		0			0
$637$	3.40961	−	7.32206i	0.135094	−	0.290110i
$638$		0			0
$639$	−48.5442	+	5.26949i	−1.92038	+	0.208458i
$640$		0			0
$641$	8.69747	+	23.8961i	0.343529	+	0.943839i	0.984362	+	0.176158i	$0.0563670\pi$
$641$	8.69747	+	23.8961i	0.343529	+	0.943839i	−0.640833	+	0.767681i	$0.721411\pi$
$642$		0			0
$643$	−10.1011	+	27.7526i	−0.398349	+	1.09446i	0.564739	+	0.825270i	$0.308977\pi$
$643$	−10.1011	+	27.7526i	−0.398349	+	1.09446i	−0.963088	+	0.269186i	$0.913245\pi$
$644$		0			0
$645$	−13.2026	+	14.7133i	−0.519851	+	0.579335i
$646$		0			0
$647$	20.7854	+	36.0013i	0.817157	+	1.41536i	0.907769	+	0.419471i	$0.137785\pi$
$647$	20.7854	+	36.0013i	0.817157	+	1.41536i	−0.0906115	+	0.995886i	$0.528882\pi$
$648$		0			0
$649$	−8.25345	−	4.76513i	−0.323976	−	0.187048i
$650$		0			0
$651$	21.9853	+	1.68675i	0.861673	+	0.0661090i
$652$		0			0
$653$	−9.82666	−	11.7110i	−0.384547	−	0.458285i	0.538697	−	0.842500i	$-0.318917\pi$
$653$	−9.82666	−	11.7110i	−0.384547	−	0.458285i	−0.923244	+	0.384214i	$0.874472\pi$
$654$		0			0
$655$	18.9356	−	6.89198i	0.739874	−	0.269292i
$656$		0			0
$657$	2.04797	−	4.64232i	0.0798988	−	0.181114i
$658$		0			0
$659$	0.375700	+	1.03223i	0.0146352	+	0.0402099i	0.946795	−	0.321837i	$-0.104300\pi$
$659$	0.375700	+	1.03223i	0.0146352	+	0.0402099i	−0.932160	+	0.362047i	$0.882078\pi$
$660$		0			0
$661$	2.44497	−	6.71751i	0.0950984	−	0.261281i	−0.883018	−	0.469339i	$-0.844492\pi$
$661$	2.44497	−	6.71751i	0.0950984	−	0.261281i	0.978116	+	0.208058i	$0.0667144\pi$
$662$		0			0
$663$	3.29951	+	0.109594i	0.128142	+	0.00425627i
$664$		0			0
$665$	−7.75472	−	10.1006i	−0.300715	−	0.391685i
$666$		0			0
$667$	11.4789	+	19.8820i	0.444464	+	0.769834i
$668$		0			0
$669$	11.4768	+	4.61420i	0.443719	+	0.178395i
$670$		0			0
$671$	−0.913258	−	5.17934i	−0.0352559	−	0.199946i
$672$		0			0
$673$	−15.6316	−	13.1164i	−0.602552	−	0.505601i	0.289713	−	0.957114i	$-0.406440\pi$
$673$	−15.6316	−	13.1164i	−0.602552	−	0.505601i	−0.892265	+	0.451512i	$0.850885\pi$
$674$		0			0
$675$	−4.29608	+	4.19132i	−0.165356	+	0.161324i
$676$		0			0
$677$	22.0123	−	8.01183i	0.846002	−	0.307920i	0.117593	−	0.993062i	$-0.462482\pi$
$677$	22.0123	−	8.01183i	0.846002	−	0.307920i	0.728409	+	0.685142i	$0.240260\pi$
$678$		0			0
$679$	−9.63240	−	2.13278i	−0.369658	−	0.0818486i
$680$		0			0
$681$	−22.0244	−	28.0912i	−0.843976	−	1.07646i
$682$		0			0
$683$			38.3733i			1.46831i	0.678980	+	0.734157i	$0.262422\pi$
$683$			38.3733i			1.46831i	−0.678980	+	0.734157i	$0.737578\pi$
$684$		0			0
$685$	−6.77141	+	3.90947i	−0.258722	+	0.149373i
$686$		0			0
$687$	−9.09029	−	0.301936i	−0.346816	−	0.0115196i
$688$		0			0
$689$	6.50402	+	2.36727i	0.247783	+	0.0901858i
$690$		0			0
$691$	19.5868	+	3.45368i	0.745118	+	0.131384i	0.533302	−	0.845925i	$-0.320951\pi$
$691$	19.5868	+	3.45368i	0.745118	+	0.131384i	0.211816	+	0.977310i	$0.432062\pi$
$692$		0			0
$693$	0.758702	−	6.88367i	0.0288207	−	0.261489i
$694$		0			0
$695$	−20.3576	+	24.2613i	−0.772208	+	0.920282i
$696$		0			0
$697$	0.532844	+	3.02191i	0.0201829	+	0.114463i
$698$		0			0
$699$	−5.49794	+	26.0842i	−0.207951	+	0.986596i
$700$		0			0
$701$			51.2062i			1.93403i	0.254720	+	0.967015i	$0.418017\pi$
$701$			51.2062i			1.93403i	−0.254720	+	0.967015i	$0.581983\pi$
$702$		0			0
$703$	9.65587	−	5.57482i	0.364178	−	0.210258i
$704$		0			0
$705$	29.1337	+	6.14071i	1.09724	+	0.231273i
$706$		0			0
$707$	−6.03418	+	27.2526i	−0.226939	+	1.02494i
$708$		0			0
$709$	−13.8018	−	11.5811i	−0.518337	−	0.434936i	0.345715	−	0.938340i	$-0.387636\pi$
$709$	−13.8018	−	11.5811i	−0.518337	−	0.434936i	−0.864051	+	0.503404i	$0.832081\pi$
$710$		0			0
$711$	−13.8108	−	0.918472i	−0.517947	−	0.0344454i
$712$		0			0
$713$	−22.9332	+	8.34701i	−0.858856	+	0.312598i
$714$		0			0
$715$	1.91335	−	1.60549i	0.0715552	−	0.0600420i
$716$		0			0
$717$	13.2754	+	0.440946i	0.495780	+	0.0164674i
$718$		0			0
$719$	37.6051			1.40243			0.701216	−	0.712949i	$-0.252641\pi$
$719$	37.6051			1.40243			0.701216	+	0.712949i	$0.252641\pi$
$720$		0			0
$721$	45.1567	−	5.95715i	1.68172	−	0.221856i
$722$		0			0
$723$	16.9411	+	6.81108i	0.630045	+	0.253307i
$724$		0			0
$725$	3.36067	+	4.00509i	0.124812	+	0.148745i
$726$		0			0
$727$	−20.7271	+	24.7016i	−0.768725	+	0.916131i	−0.998366	−	0.0571448i	$-0.981800\pi$
$727$	−20.7271	+	24.7016i	−0.768725	+	0.916131i	0.229641	+	0.973275i	$0.426245\pi$
$728$		0			0
$729$	8.60550	+	25.5919i	0.318722	+	0.947848i
$730$		0			0
$731$	−1.31959	+	7.48378i	−0.0488069	+	0.276797i
$732$		0			0
$733$	5.51643	−	15.1563i	0.203754	−	0.559809i	−0.795160	−	0.606399i	$-0.792613\pi$
$733$	5.51643	−	15.1563i	0.203754	−	0.559809i	0.998914	+	0.0465901i	$0.0148355\pi$
$734$		0			0
$735$	24.0632	+	18.0488i	0.887584	+	0.665741i
$736$		0			0
$737$	8.75269	−	5.05337i	0.322410	−	0.186143i
$738$		0			0
$739$	3.63270	−	6.29202i	0.133631	−	0.231456i	−0.791443	−	0.611244i	$-0.790670\pi$
$739$	3.63270	−	6.29202i	0.133631	−	0.231456i	0.925074	+	0.379788i	$0.124003\pi$
$740$		0			0
$741$	−3.29153	−	2.04899i	−0.120917	−	0.0752715i
$742$		0			0
$743$	−5.70028	−	6.79333i	−0.209123	−	0.249223i	0.651280	−	0.758838i	$-0.274232\pi$
$743$	−5.70028	−	6.79333i	−0.209123	−	0.249223i	−0.860403	+	0.509615i	$0.829788\pi$
$744$		0			0
$745$	−9.00277	+	10.7291i	−0.329836	+	0.393083i
$746$		0			0
$747$	−0.721320	−	1.46622i	−0.0263917	−	0.0536463i
$748$		0			0
$749$	−28.6392	+	14.9183i	−1.04645	+	0.545102i
$750$		0			0
$751$	−23.9133	+	20.0656i	−0.872608	+	0.732205i	−0.964646	−	0.263551i	$-0.915106\pi$
$751$	−23.9133	+	20.0656i	−0.872608	+	0.732205i	0.0920379	+	0.995756i	$0.470662\pi$
$752$		0			0
$753$	−4.27032	+	4.75895i	−0.155619	+	0.173426i
$754$		0			0
$755$	54.2618			1.97479
$756$		0			0
$757$	−1.50694			−0.0547708			−0.0273854	−	0.999625i	$-0.508718\pi$
$757$	−1.50694			−0.0547708			−0.0273854	+	0.999625i	$0.508718\pi$
$758$		0			0
$759$	2.38104	+	7.28583i	0.0864263	+	0.264459i
$760$		0			0
$761$	29.3741	−	24.6478i	1.06481	−	0.893482i	0.0702379	−	0.997530i	$-0.477624\pi$
$761$	29.3741	−	24.6478i	1.06481	−	0.893482i	0.994572	+	0.104048i	$0.0331797\pi$
$762$		0			0
$763$	19.7144	+	0.855523i	0.713709	+	0.0309720i
$764$		0			0
$765$	−2.93366	+	11.9394i	−0.106067	+	0.431671i
$766$		0			0
$767$	8.10126	−	9.65471i	0.292520	−	0.348611i
$768$		0			0
$769$	−26.9964	−	32.1731i	−0.973516	−	1.16019i	−0.987071	−	0.160283i	$-0.948759\pi$
$769$	−26.9964	−	32.1731i	−0.973516	−	1.16019i	0.0135556	−	0.999908i	$-0.495685\pi$
$770$		0			0
$771$	−0.144332	+	4.34537i	−0.00519800	+	0.156495i
$772$		0			0
$773$	−5.83151	+	10.1005i	−0.209745	+	0.363289i	−0.951634	−	0.307234i	$-0.900597\pi$
$773$	−5.83151	+	10.1005i	−0.209745	+	0.363289i	0.741889	+	0.670522i	$0.233930\pi$
$774$		0			0
$775$	−4.81326	+	2.77894i	−0.172897	+	0.0998223i
$776$		0			0
$777$	−18.4229	+	18.8212i	−0.660916	+	0.675207i
$778$		0			0
$779$	1.23256	−	3.38644i	0.0441612	−	0.121332i
$780$		0			0
$781$	−2.46605	+	13.9857i	−0.0882422	+	0.500446i
$782$		0			0
$783$	22.7916	−	5.80646i	0.814504	−	0.207506i
$784$		0			0
$785$	36.6452	−	43.6721i	1.30792	−	1.55872i
$786$		0			0
$787$	7.29561	+	8.69458i	0.260061	+	0.309928i	0.880237	−	0.474534i	$-0.157383\pi$
$787$	7.29561	+	8.69458i	0.260061	+	0.309928i	−0.620176	+	0.784462i	$0.712939\pi$
$788$		0			0
$789$	−4.59627	−	32.3047i	−0.163631	−	1.15008i
$790$		0			0
$791$	5.87899	+	7.65745i	0.209033	+	0.272268i
$792$		0			0
$793$	6.95511			0.246983
$794$		0			0
$795$	−13.6221	+	21.8828i	−0.483127	+	0.776103i
$796$		0			0
$797$	−35.7540	+	30.0011i	−1.26647	+	1.06270i	−0.271510	+	0.962436i	$0.587523\pi$
$797$	−35.7540	+	30.0011i	−1.26647	+	1.06270i	−0.994961	+	0.100259i	$0.968033\pi$
$798$		0			0
$799$	10.7552	−	3.91458i	0.380492	−	0.138488i
$800$		0			0
$801$	−3.08284	−	28.4001i	−0.108927	−	1.00347i
$802$		0			0
$803$	−1.13045	−	0.948564i	−0.0398929	−	0.0334741i
$804$		0			0
$805$	−32.5053	−	7.19723i	−1.14566	−	0.253669i
$806$		0			0
$807$	4.83825	+	14.8047i	0.170315	+	0.521152i
$808$		0			0
$809$	−22.4852	+	12.9818i	−0.790538	+	0.456417i	−0.840152	−	0.542351i	$-0.817534\pi$
$809$	−22.4852	+	12.9818i	−0.790538	+	0.456417i	0.0496142	+	0.998768i	$0.484201\pi$
$810$		0			0
$811$			44.6800i			1.56893i	0.620175	+	0.784464i	$0.287062\pi$
$811$			44.6800i			1.56893i	−0.620175	+	0.784464i	$0.712938\pi$
$812$		0			0
$813$	34.3526	+	30.8255i	1.20480	+	1.08110i
$814$		0			0
$815$	3.11139	+	17.6455i	0.108987	+	0.618096i
$816$		0			0
$817$	5.73674	−	6.83677i	0.200703	−	0.239188i
$818$		0			0
$819$	8.79080	+	2.56888i	0.307176	+	0.0897640i
$820$		0			0
$821$	−4.69814	−	0.828408i	−0.163966	−	0.0289116i	0.0910624	−	0.995845i	$-0.470974\pi$
$821$	−4.69814	−	0.828408i	−0.163966	−	0.0289116i	−0.255028	+	0.966934i	$0.582085\pi$
$822$		0			0
$823$	7.68200	+	2.79602i	0.267778	+	0.0974631i	0.472419	−	0.881374i	$-0.343381\pi$
$823$	7.68200	+	2.79602i	0.267778	+	0.0974631i	−0.204642	+	0.978837i	$0.565603\pi$
$824$		0			0
$825$	0.822131	+	1.53987i	0.0286229	+	0.0536114i
$826$		0			0
$827$	−3.61886	+	2.08935i	−0.125840	+	0.0726537i	−0.561599	−	0.827410i	$-0.689813\pi$
$827$	−3.61886	+	2.08935i	−0.125840	+	0.0726537i	0.435759	+	0.900064i	$0.356480\pi$
$828$		0			0
$829$		−	29.0348i		−	1.00842i	−0.863581	−	0.504211i	$-0.831783\pi$
$829$		−	29.0348i		−	1.00842i	0.863581	−	0.504211i	$-0.168217\pi$
$830$		0			0
$831$	−27.8089	+	3.95661i	−0.964680	+	0.137253i
$832$		0			0
$833$	11.5196	+	1.00169i	0.399131	+	0.0347066i
$834$		0			0
$835$	27.8186	−	10.1251i	0.962702	−	0.350395i
$836$		0			0
$837$	1.87152	+	24.9321i	0.0646891	+	0.861781i
$838$		0			0
$839$	−33.7093	−	28.2854i	−1.16377	−	0.976522i	−0.163823	−	0.986490i	$-0.552383\pi$
$839$	−33.7093	−	28.2854i	−1.16377	−	0.976522i	−0.999950	+	0.00996767i	$0.996827\pi$
$840$		0			0
$841$	1.47813	+	8.38288i	0.0509699	+	0.289065i
$842$		0			0
$843$	−7.31218	−	51.3934i	−0.251845	−	1.77008i
$844$		0			0
$845$	−14.4746	−	25.0707i	−0.497941	−	0.862459i
$846$		0			0
$847$	25.0298	+	10.3599i	0.860035	+	0.355972i
$848$		0			0
$849$	−10.8910	+	17.4955i	−0.373778	+	0.600444i
$850$		0			0
$851$	9.96990	−	27.3921i	0.341764	−	0.938988i
$852$		0			0
$853$	−3.68163	−	10.1152i	−0.126057	−	0.346337i	0.860571	−	0.509331i	$-0.170107\pi$
$853$	−3.68163	−	10.1152i	−0.126057	−	0.346337i	−0.986627	+	0.162994i	$0.947885\pi$
$854$		0			0
$855$	9.99483	−	10.4208i	0.341816	−	0.356383i
$856$		0			0
$857$	−39.3752	+	14.3314i	−1.34503	+	0.489551i	−0.911393	−	0.411537i	$-0.864992\pi$
$857$	−39.3752	+	14.3314i	−1.34503	+	0.489551i	−0.433637	+	0.901088i	$0.642770\pi$
$858$		0			0
$859$	20.2214	+	24.0989i	0.689945	+	0.822244i	0.991349	−	0.131252i	$-0.0418997\pi$
$859$	20.2214	+	24.0989i	0.689945	+	0.822244i	−0.301404	+	0.953497i	$0.597455\pi$
$860$		0			0
$861$	−0.651189	+	8.48768i	−0.0221925	+	0.289259i
$862$		0			0
$863$	−43.7957	−	25.2854i	−1.49082	−	0.860726i	−0.490877	−	0.871229i	$-0.663324\pi$
$863$	−43.7957	−	25.2854i	−1.49082	−	0.860726i	−0.999945	+	0.0105025i	$0.996657\pi$
$864$		0			0
$865$	9.74526	+	16.8793i	0.331349	+	0.573913i
$866$		0			0
$867$	−7.67853	−	23.4958i	−0.260776	−	0.797959i
$868$		0			0
$869$	−1.37683	+	3.78281i	−0.0467057	+	0.128323i
$870$		0			0
$871$	4.57134	+	12.5596i	0.154894	+	0.425567i
$872$		0			0
$873$	0.742314	−	11.1620i	0.0251235	−	0.377776i
$874$		0			0
$875$	25.2142	+	1.09419i	0.852395	+	0.0369904i
$876$		0			0
$877$	−0.492815	−	2.79489i	−0.0166412	−	0.0943769i	0.975356	−	0.220637i	$-0.0708137\pi$
$877$	−0.492815	−	2.79489i	−0.0166412	−	0.0943769i	−0.991997	+	0.126260i	$0.959703\pi$
$878$		0			0
$879$	1.53628	−	46.2523i	0.0518174	−	1.56005i
$880$		0			0
$881$	−14.4952	−	25.1064i	−0.488355	−	0.845856i	0.511555	−	0.859251i	$-0.329070\pi$
$881$	−14.4952	−	25.1064i	−0.488355	−	0.845856i	−0.999910	+	0.0133942i	$0.995736\pi$
$882$		0			0
$883$	−5.84702	+	10.1273i	−0.196768	+	0.340812i	−0.947479	−	0.319819i	$-0.896378\pi$
$883$	−5.84702	+	10.1273i	−0.196768	+	0.340812i	0.750711	+	0.660631i	$0.229711\pi$
$884$		0			0
$885$	28.9599	+	36.9372i	0.973478	+	1.24163i
$886$		0			0
$887$	−40.0352	−	14.5716i	−1.34425	−	0.489267i	−0.433101	−	0.901346i	$-0.642581\pi$
$887$	−40.0352	−	14.5716i	−1.34425	−	0.489267i	−0.911148	+	0.412079i	$0.864803\pi$
$888$		0			0
$889$	17.5703	+	33.7304i	0.589287	+	1.13128i
$890$		0			0
$891$	7.84578	−	0.327524i	0.262843	−	0.0109725i
$892$		0			0
$893$	−13.2377	−	2.33417i	−0.442983	−	0.0781099i
$894$		0			0
$895$	15.3426	−	2.70531i	0.512846	−	0.0904287i
$896$		0			0
$897$	−10.0356	+	1.42785i	−0.335078	+	0.0476745i
$898$		0			0
$899$	21.7794			0.726383
$900$		0			0
$901$			9.90876i			0.330109i
$902$		0			0
$903$	−8.70462	+	19.2006i	−0.289672	+	0.638956i
$904$		0			0
$905$	33.2321	−	5.85972i	1.10467	−	0.194784i
$906$		0			0
$907$	−19.9208	−	16.7156i	−0.661461	−	0.555032i	0.249063	−	0.968487i	$-0.419877\pi$
$907$	−19.9208	−	16.7156i	−0.661461	−	0.555032i	−0.910524	+	0.413456i	$0.864322\pi$
$908$		0			0
$909$	−31.5802	−	2.10020i	−1.04745	−	0.0696592i
$910$		0			0
$911$	−24.5635	−	4.33120i	−0.813823	−	0.143499i	−0.248780	−	0.968560i	$-0.580030\pi$
$911$	−24.5635	−	4.33120i	−0.813823	−	0.143499i	−0.565044	+	0.825061i	$0.691141\pi$
$912$		0			0
$913$	−0.468023	+	0.0825250i	−0.0154893	+	0.00273118i
$914$		0			0
$915$	−5.34211	+	25.3449i	−0.176605	+	0.837875i
$916$		0			0
$917$	17.0452	−	13.0864i	0.562884	−	0.432152i
$918$		0			0
$919$	23.8946	−	41.3867i	0.788210	−	1.36522i	−0.138852	−	0.990313i	$-0.544341\pi$
$919$	23.8946	−	41.3867i	0.788210	−	1.36522i	0.927062	−	0.374907i	$-0.122325\pi$
$920$		0			0
$921$	−23.1158	+	7.55433i	−0.761690	+	0.248924i
$922$		0			0
$923$	−17.6481	−	6.42338i	−0.580894	−	0.211428i
$924$		0			0
$925$	1.15276	−	6.53762i	0.0379025	−	0.214956i
$926$		0			0
$927$	14.4048	+	49.5971i	0.473115	+	1.62898i
$928$		0			0
$929$	9.09020	−	51.5531i	0.298240	−	1.69140i	−0.355495	−	0.934678i	$-0.615688\pi$
$929$	9.09020	−	51.5531i	0.298240	−	1.69140i	0.653735	−	0.756724i	$-0.273201\pi$
$930$		0			0
$931$	−11.1283	−	7.78331i	−0.364714	−	0.255088i
$932$		0			0
$933$	−32.9942	−	20.5390i	−1.08018	−	0.672416i
$934$		0			0
$935$	3.09667	+	1.78786i	0.101272	+	0.0584693i
$936$		0			0
$937$	2.54236	+	1.46783i	0.0830554	+	0.0479521i	0.540953	−	0.841053i	$-0.318064\pi$
$937$	2.54236	+	1.46783i	0.0830554	+	0.0479521i	−0.457897	+	0.889005i	$0.651397\pi$
$938$		0			0
$939$	29.3273	+	11.7909i	0.957059	+	0.384782i
$940$		0			0
$941$	−43.5449	+	36.5385i	−1.41952	+	1.19112i	−0.467927	+	0.883767i	$0.654999\pi$
$941$	−43.5449	+	36.5385i	−1.41952	+	1.19112i	−0.951595	+	0.307354i	$0.900556\pi$
$942$		0			0
$943$	−3.22246	−	8.85363i	−0.104938	−	0.288314i
$944$		0			0
$945$	−16.1133	+	30.0611i	−0.524164	+	0.977889i
$946$		0			0
$947$	−9.38872	−	25.7953i	−0.305092	−	0.838235i	−0.993595	−	0.113001i	$-0.963954\pi$
$947$	−9.38872	−	25.7953i	−0.305092	−	0.838235i	0.688503	−	0.725234i	$-0.258268\pi$
$948$		0			0
$949$	1.49497	−	1.25443i	0.0485289	−	0.0407206i
$950$		0			0
$951$	15.0981	−	11.8374i	0.489590	−	0.383855i
$952$		0			0
$953$	24.3650	+	14.0672i	0.789261	+	0.455680i	0.839702	−	0.543047i	$-0.182730\pi$
$953$	24.3650	+	14.0672i	0.789261	+	0.455680i	−0.0504416	+	0.998727i	$0.516063\pi$
$954$		0			0
$955$	−8.24632	−	4.76101i	−0.266845	−	0.154063i
$956$		0			0
$957$	0.227079	−	6.83661i	0.00734042	−	0.220996i
$958$		0			0
$959$	−5.63169	+	6.14917i	−0.181857	+	0.198567i
$960$		0			0
$961$	1.36273	−	7.72841i	0.0439590	−	0.249304i
$962$		0			0
$963$	−21.6228	−	29.5490i	−0.696786	−	0.952204i
$964$		0			0
$965$	1.17685	−	6.67425i	0.0378842	−	0.214852i
$966$		0			0
$967$	26.9954	+	9.82552i	0.868113	+	0.315967i	0.737403	−	0.675453i	$-0.236052\pi$
$967$	26.9954	+	9.82552i	0.868113	+	0.315967i	0.130710	+	0.991421i	$0.458274\pi$
$968$		0			0
$969$	1.14478	−	5.43126i	0.0367757	−	0.174477i
$970$		0			0
$971$	9.63819	−	16.6938i	0.309304	−	0.535731i	−0.668906	−	0.743347i	$-0.733237\pi$
$971$	9.63819	−	16.6938i	0.309304	−	0.535731i	0.978210	+	0.207616i	$0.0665705\pi$
$972$		0			0
$973$	−12.9168	+	31.2072i	−0.414092	+	1.00046i
$974$		0			0
$975$	−2.19426	+	0.717095i	−0.0702727	+	0.0229654i
$976$		0			0
$977$	32.3613	−	5.70617i	1.03533	−	0.182557i	0.369942	−	0.929055i	$-0.379378\pi$
$977$	32.3613	−	5.70617i	1.03533	−	0.182557i	0.665387	+	0.746498i	$0.268266\pi$
$978$		0			0
$979$	−8.18211	−	1.44273i	−0.261501	−	0.0461097i
$980$		0			0
$981$	2.41463	+	22.2444i	0.0770934	+	0.710208i
$982$		0			0
$983$	1.89227	+	1.58780i	0.0603540	+	0.0506430i	0.672466	−	0.740128i	$-0.265235\pi$
$983$	1.89227	+	1.58780i	0.0603540	+	0.0506430i	−0.612112	+	0.790771i	$0.709680\pi$
$984$		0			0
$985$	−9.37653	+	1.65334i	−0.298761	+	0.0526797i
$986$		0			0
$987$	31.5995	−	3.10547i	1.00582	−	0.0988482i
$988$		0			0
$989$		−	23.3333i		−	0.741955i
$990$		0			0
$991$	−14.1349			−0.449010			−0.224505	−	0.974473i	$-0.572076\pi$
$991$	−14.1349			−0.449010			−0.224505	+	0.974473i	$0.572076\pi$
$992$		0			0
$993$	−21.7944	−	27.7978i	−0.691623	−	0.882136i
$994$		0			0
$995$	−58.0661	+	10.2386i	−1.84082	+	0.324586i
$996$		0			0
$997$	22.1004	+	3.89690i	0.699927	+	0.123416i	0.512277	−	0.858820i	$-0.328802\pi$
$997$	22.1004	+	3.89690i	0.699927	+	0.123416i	0.187649	+	0.982236i	$0.439913\pi$
$998$		0			0
$999$	−24.2494	−	17.4296i	−0.767217	−	0.551447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ca.a.173.2	✓	144
7.3	odd	6		756.2.ck.a.605.10	yes	144
27.5	odd	18		756.2.ck.a.5.10	yes	144
189.59	even	18	inner	756.2.ca.a.437.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.2	✓	144	1.1	even	1	trivial
756.2.ca.a.437.2	yes	144	189.59	even	18	inner
756.2.ck.a.5.10	yes	144	27.5	odd	18
756.2.ck.a.605.10	yes	144	7.3	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69481 - 0.357227i) q^{3} +(1.90051 - 1.59472i) q^{5} +(1.42097 - 2.23178i) q^{7} +(2.74478 + 1.21086i) q^{9} +O(q^{10})\)	\(q+(-1.69481 - 0.357227i) q^{3} +(1.90051 - 1.59472i) q^{5} +(1.42097 - 2.23178i) q^{7} +(2.74478 + 1.21086i) q^{9} +(0.560840 - 0.668383i) q^{11} +(0.741685 + 0.883906i) q^{13} +(-3.79069 + 2.02384i) q^{15} +(-0.825934 + 1.43056i) q^{17} +(1.68010 - 0.970004i) q^{19} +(-3.20553 + 3.27484i) q^{21} +(1.73474 - 4.76615i) q^{23} +(0.200577 - 1.13753i) q^{25} +(-4.21933 - 3.03270i) q^{27} +(-2.90948 + 3.46738i) q^{29} +(-3.09289 - 3.68597i) q^{31} +(-1.18928 + 0.932437i) q^{33} +(-0.858490 - 6.50758i) q^{35} +5.74721 q^{37} +(-0.941262 - 1.76300i) q^{39} +(1.42301 - 1.19405i) q^{41} +(4.32294 - 1.57342i) q^{43} +(7.14747 - 2.07589i) q^{45} +(-5.30777 - 4.45375i) q^{47} +(-2.96168 - 6.34259i) q^{49} +(1.91084 - 2.12949i) q^{51} +(5.19487 - 2.99926i) q^{53} -2.16465i q^{55} +(-3.19396 + 1.04380i) q^{57} +(-1.89672 - 10.7568i) q^{59} +(3.87453 - 4.61749i) q^{61} +(6.60263 - 4.40514i) q^{63} +(2.81916 + 0.497095i) q^{65} +(10.8849 + 3.96179i) q^{67} +(-4.64265 + 7.45803i) q^{69} +(-14.0958 + 8.13823i) q^{71} -1.69133i q^{73} +(-0.746296 + 1.85625i) q^{75} +(-0.694747 - 2.20143i) q^{77} +(-4.33553 + 1.57801i) q^{79} +(6.06761 + 6.64711i) q^{81} +(-0.417251 - 0.350116i) q^{83} +(0.711644 + 4.03593i) q^{85} +(6.16966 - 4.83722i) q^{87} +(-4.76115 - 8.24656i) q^{89} +(3.02660 - 0.399274i) q^{91} +(3.92515 + 7.35189i) q^{93} +(1.64616 - 4.52279i) q^{95} +(-1.27535 - 3.50400i) q^{97} +(2.34870 - 1.15546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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