LMFDB - Embedded newform 656.2.u.h.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not 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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			625.1
Root			$-2.23116 - 1.62103i$ of defining polynomial
Character	$\chi$	$=$	656.625
Dual form			656.2.u.h.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75787 q^{3} +(0.675164 + 2.07794i) q^{5} +(1.49390 - 1.08538i) q^{7} +4.60584 q^{9} +O(q^{10})$	\(q-2.75787 q^{3} +(0.675164 + 2.07794i) q^{5} +(1.49390 - 1.08538i) q^{7} +4.60584 q^{9} +(0.329300 - 1.01348i) q^{11} +(-1.76110 - 1.27951i) q^{13} +(-1.86201 - 5.73069i) q^{15} +(0.259109 - 0.797455i) q^{17} +(-3.04606 + 2.21310i) q^{19} +(-4.11999 + 2.99335i) q^{21} +(6.65728 + 4.83680i) q^{23} +(0.183088 - 0.133022i) q^{25} -4.42870 q^{27} +(0.0301361 + 0.0927493i) q^{29} +(-2.85873 + 8.79827i) q^{31} +(-0.908167 + 2.79505i) q^{33} +(3.26399 + 2.37143i) q^{35} +(1.92595 + 5.92745i) q^{37} +(4.85688 + 3.52873i) q^{39} +(5.64403 - 3.02405i) q^{41} +(9.01506 + 6.54983i) q^{43} +(3.10970 + 9.57067i) q^{45} +(-3.40527 - 2.47407i) q^{47} +(-1.10943 + 3.41448i) q^{49} +(-0.714588 + 2.19928i) q^{51} +(3.05281 + 9.39560i) q^{53} +2.32829 q^{55} +(8.40065 - 6.10343i) q^{57} +(-11.1007 - 8.06515i) q^{59} +(-4.15731 + 3.02046i) q^{61} +(6.88068 - 4.99910i) q^{63} +(1.46972 - 4.52334i) q^{65} +(3.11698 + 9.59307i) q^{67} +(-18.3599 - 13.3393i) q^{69} +(-0.0520050 + 0.160055i) q^{71} -4.48379 q^{73} +(-0.504934 + 0.366856i) q^{75} +(-0.608074 - 1.87146i) q^{77} +8.89860 q^{79} -1.60376 q^{81} +10.9844 q^{83} +1.83201 q^{85} +(-0.0831113 - 0.255790i) q^{87} +(-7.41300 + 5.38586i) q^{89} -4.01967 q^{91} +(7.88401 - 24.2645i) q^{93} +(-6.65528 - 4.83534i) q^{95} +(-0.575371 - 1.77081i) q^{97} +(1.51670 - 4.66794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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
$3$	−2.75787			−1.59226			−0.796128	−	0.605128i	$-0.793122\pi$
$3$	−2.75787			−1.59226			−0.796128	+	0.605128i	$0.793122\pi$
$4$		0			0
$5$	0.675164	+	2.07794i	0.301943	+	0.929284i	0.980800	+	0.195014i	$0.0624753\pi$
$5$	0.675164	+	2.07794i	0.301943	+	0.929284i	−0.678858	+	0.734270i	$0.737525\pi$
$6$		0			0
$7$	1.49390	−	1.08538i	0.564642	−	0.410237i	−0.268513	−	0.963276i	$-0.586532\pi$
$7$	1.49390	−	1.08538i	0.564642	−	0.410237i	0.833155	+	0.553040i	$0.186532\pi$
$8$		0			0
$9$	4.60584			1.53528
$10$		0			0
$11$	0.329300	−	1.01348i	0.0992878	−	0.305576i	−0.889060	−	0.457791i	$-0.848641\pi$
$11$	0.329300	−	1.01348i	0.0992878	−	0.305576i	0.988347	+	0.152215i	$0.0486407\pi$
$12$		0			0
$13$	−1.76110	−	1.27951i	−0.488441	−	0.354873i	0.316143	−	0.948711i	$-0.397612\pi$
$13$	−1.76110	−	1.27951i	−0.488441	−	0.354873i	−0.804584	+	0.593838i	$0.797612\pi$
$14$		0			0
$15$	−1.86201	−	5.73069i	−0.480770	−	1.47966i
$16$		0			0
$17$	0.259109	−	0.797455i	0.0628432	−	0.193411i	−0.914706	−	0.404121i	$-0.867577\pi$
$17$	0.259109	−	0.797455i	0.0628432	−	0.193411i	0.977549	+	0.210710i	$0.0675775\pi$
$18$		0			0
$19$	−3.04606	+	2.21310i	−0.698815	+	0.507719i	−0.879546	−	0.475814i	$-0.842154\pi$
$19$	−3.04606	+	2.21310i	−0.698815	+	0.507719i	0.180731	+	0.983533i	$0.442154\pi$
$20$		0			0
$21$	−4.11999	+	2.99335i	−0.899055	+	0.653202i
$22$		0			0
$23$	6.65728	+	4.83680i	1.38814	+	1.00854i	0.996067	+	0.0886086i	$0.0282420\pi$
$23$	6.65728	+	4.83680i	1.38814	+	1.00854i	0.392073	+	0.919934i	$0.371758\pi$
$24$		0			0
$25$	0.183088	−	0.133022i	0.0366177	−	0.0266043i
$26$		0			0
$27$	−4.42870			−0.852303
$28$		0			0
$29$	0.0301361	+	0.0927493i	0.00559613	+	0.0172231i	0.953816	−	0.300393i	$-0.0971178\pi$
$29$	0.0301361	+	0.0927493i	0.00559613	+	0.0172231i	−0.948219	+	0.317616i	$0.897118\pi$
$30$		0			0
$31$	−2.85873	+	8.79827i	−0.513443	+	1.58022i	0.272653	+	0.962112i	$0.412099\pi$
$31$	−2.85873	+	8.79827i	−0.513443	+	1.58022i	−0.786097	+	0.618104i	$0.787901\pi$
$32$		0			0
$33$	−0.908167	+	2.79505i	−0.158092	+	0.486556i
$34$		0			0
$35$	3.26399	+	2.37143i	0.551716	+	0.400845i
$36$		0			0
$37$	1.92595	+	5.92745i	0.316624	+	0.974467i	0.975081	+	0.221849i	$0.0712092\pi$
$37$	1.92595	+	5.92745i	0.316624	+	0.974467i	−0.658457	+	0.752618i	$0.728791\pi$
$38$		0			0
$39$	4.85688	+	3.52873i	0.777723	+	0.565049i
$40$		0			0
$41$	5.64403	−	3.02405i	0.881450	−	0.472277i
$41$	5.64403	−	3.02405i	0.881450	−	0.472277i
$42$		0			0
$43$	9.01506	+	6.54983i	1.37478	+	0.998839i	0.997346	+	0.0728043i	$0.0231948\pi$
$43$	9.01506	+	6.54983i	1.37478	+	0.998839i	0.377438	+	0.926035i	$0.376805\pi$
$44$		0			0
$45$	3.10970	+	9.57067i	0.463567	+	1.42671i
$46$		0			0
$47$	−3.40527	−	2.47407i	−0.496710	−	0.360881i	0.311049	−	0.950394i	$-0.399320\pi$
$47$	−3.40527	−	2.47407i	−0.496710	−	0.360881i	−0.807759	+	0.589513i	$0.799320\pi$
$48$		0			0
$49$	−1.10943	+	3.41448i	−0.158490	+	0.487783i
$50$		0			0
$51$	−0.714588	+	2.19928i	−0.100062	+	0.307960i
$52$		0			0
$53$	3.05281	+	9.39560i	0.419336	+	1.29058i	0.908314	+	0.418288i	$0.137370\pi$
$53$	3.05281	+	9.39560i	0.419336	+	1.29058i	−0.488978	+	0.872296i	$0.662630\pi$
$54$		0			0
$55$	2.32829			0.313946
$56$		0			0
$57$	8.40065	−	6.10343i	1.11269	−	0.808419i
$58$		0			0
$59$	−11.1007	−	8.06515i	−1.44519	−	1.04999i	−0.986925	−	0.161178i	$-0.948471\pi$
$59$	−11.1007	−	8.06515i	−1.44519	−	1.04999i	−0.458266	−	0.888815i	$-0.651529\pi$
$60$		0			0
$61$	−4.15731	+	3.02046i	−0.532289	+	0.386730i	−0.821213	−	0.570622i	$-0.806702\pi$
$61$	−4.15731	+	3.02046i	−0.532289	+	0.386730i	0.288925	+	0.957352i	$0.406702\pi$
$62$		0			0
$63$	6.88068	−	4.99910i	0.866884	−	0.629828i
$64$		0			0
$65$	1.46972	−	4.52334i	0.182297	−	0.561052i
$66$		0			0
$67$	3.11698	+	9.59307i	0.380799	+	1.17198i	0.939482	+	0.342598i	$0.111307\pi$
$67$	3.11698	+	9.59307i	0.380799	+	1.17198i	−0.558683	+	0.829382i	$0.688693\pi$
$68$		0			0
$69$	−18.3599	−	13.3393i	−2.21027	−	1.60586i
$70$		0			0
$71$	−0.0520050	+	0.160055i	−0.00617186	+	0.0189950i	−0.954095	−	0.299504i	$-0.903179\pi$
$71$	−0.0520050	+	0.160055i	−0.00617186	+	0.0189950i	0.947923	+	0.318499i	$0.103179\pi$
$72$		0			0
$73$	−4.48379			−0.524788			−0.262394	−	0.964961i	$-0.584512\pi$
$73$	−4.48379			−0.524788			−0.262394	+	0.964961i	$0.584512\pi$
$74$		0			0
$75$	−0.504934	+	0.366856i	−0.0583047	+	0.0423609i
$76$		0			0
$77$	−0.608074	−	1.87146i	−0.0692965	−	0.213273i
$78$		0			0
$79$	8.89860			1.00117			0.500585	−	0.865687i	$-0.333118\pi$
$79$	8.89860			1.00117			0.500585	+	0.865687i	$0.333118\pi$
$80$		0			0
$81$	−1.60376			−0.178196
$82$		0			0
$83$	10.9844			1.20570			0.602849	−	0.797855i	$-0.294032\pi$
$83$	10.9844			1.20570			0.602849	+	0.797855i	$0.294032\pi$
$84$		0			0
$85$	1.83201			0.198709
$86$		0			0
$87$	−0.0831113	−	0.255790i	−0.00891047	−	0.0274236i
$88$		0			0
$89$	−7.41300	+	5.38586i	−0.785776	+	0.570900i	−0.906707	−	0.421761i	$-0.861412\pi$
$89$	−7.41300	+	5.38586i	−0.785776	+	0.570900i	0.120931	+	0.992661i	$0.461412\pi$
$90$		0			0
$91$	−4.01967			−0.421376
$92$		0			0
$93$	7.88401	−	24.2645i	0.817533	−	2.51611i
$94$		0			0
$95$	−6.65528	−	4.83534i	−0.682817	−	0.496096i
$96$		0			0
$97$	−0.575371	−	1.77081i	−0.0584201	−	0.179799i	0.917588	−	0.397533i	$-0.130133\pi$
$97$	−0.575371	−	1.77081i	−0.0584201	−	0.179799i	−0.976008	+	0.217734i	$0.930133\pi$
$98$		0			0
$99$	1.51670	−	4.66794i	0.152434	−	0.469145i
$100$		0			0
$101$	11.4527	−	8.32090i	1.13959	−	0.827961i	0.152528	−	0.988299i	$-0.451259\pi$
$101$	11.4527	−	8.32090i	1.13959	−	0.827961i	0.987062	+	0.160338i	$0.0512586\pi$
$102$		0			0
$103$	10.9933	−	7.98713i	1.08321	−	0.786995i	0.104967	−	0.994476i	$-0.466526\pi$
$103$	10.9933	−	7.98713i	1.08321	−	0.786995i	0.978239	+	0.207481i	$0.0665264\pi$
$104$		0			0
$105$	−9.00167	−	6.54010i	−0.878473	−	0.638248i
$106$		0			0
$107$	−7.05104	+	5.12288i	−0.681650	+	0.495248i	−0.873905	−	0.486097i	$-0.838420\pi$
$107$	−7.05104	+	5.12288i	−0.681650	+	0.495248i	0.192255	+	0.981345i	$0.438420\pi$
$108$		0			0
$109$	−13.8045			−1.32224			−0.661118	−	0.750282i	$-0.729918\pi$
$109$	−13.8045			−1.32224			−0.661118	+	0.750282i	$0.729918\pi$
$110$		0			0
$111$	−5.31151	−	16.3471i	−0.504146	−	1.55160i
$112$		0			0
$113$	−2.51136	+	7.72917i	−0.236249	+	0.727099i	0.760704	+	0.649098i	$0.224854\pi$
$113$	−2.51136	+	7.72917i	−0.236249	+	0.727099i	−0.996953	+	0.0780008i	$0.975146\pi$
$114$		0			0
$115$	−5.55583	+	17.0991i	−0.518084	+	1.59450i
$116$		0			0
$117$	−8.11134	−	5.89323i	−0.749894	−	0.544830i
$118$		0			0
$119$	−0.478462	−	1.47255i	−0.0438605	−	0.134989i
$120$		0			0
$121$	7.98048	+	5.79816i	0.725498	+	0.527105i
$122$		0			0
$123$	−15.5655	+	8.33993i	−1.40349	+	0.751986i
$124$		0			0
$125$	9.23804	+	6.71183i	0.826276	+	0.600324i
$126$		0			0
$127$	−3.82943	−	11.7858i	−0.339807	−	1.04582i	−0.964306	−	0.264792i	$-0.914697\pi$
$127$	−3.82943	−	11.7858i	−0.339807	−	1.04582i	0.624499	−	0.781026i	$-0.285303\pi$
$128$		0			0
$129$	−24.8624	−	18.0636i	−2.18901	−	1.59041i
$130$		0			0
$131$	3.06842	−	9.44362i	0.268089	−	0.825093i	−0.722877	−	0.690977i	$-0.757181\pi$
$131$	3.06842	−	9.44362i	0.268089	−	0.825093i	0.990966	−	0.134116i	$-0.0428194\pi$
$132$		0			0
$133$	−2.14847	+	6.61230i	−0.186296	+	0.573359i
$134$		0			0
$135$	−2.99010	−	9.20257i	−0.257347	−	0.792031i
$136$		0			0
$137$	−7.38943			−0.631322			−0.315661	−	0.948872i	$-0.602226\pi$
$137$	−7.38943			−0.631322			−0.315661	+	0.948872i	$0.602226\pi$
$138$		0			0
$139$	2.96490	−	2.15412i	0.251479	−	0.182710i	−0.454903	−	0.890541i	$-0.650326\pi$
$139$	2.96490	−	2.15412i	0.251479	−	0.182710i	0.706382	+	0.707831i	$0.250326\pi$
$140$		0			0
$141$	9.39129	+	6.82317i	0.790889	+	0.574615i
$142$		0			0
$143$	−1.87669	+	1.36350i	−0.156937	+	0.114021i
$144$		0			0
$145$	−0.172381	+	0.125242i	−0.0143155	+	0.0104008i
$146$		0			0
$147$	3.05967	−	9.41669i	0.252357	−	0.776675i
$148$		0			0
$149$	−0.824412	−	2.53728i	−0.0675385	−	0.207862i	0.911591	−	0.411097i	$-0.134854\pi$
$149$	−0.824412	−	2.53728i	−0.0675385	−	0.207862i	−0.979130	+	0.203235i	$0.934854\pi$
$150$		0			0
$151$	5.92990	+	4.30832i	0.482568	+	0.350606i	0.802319	−	0.596895i	$-0.203599\pi$
$151$	5.92990	+	4.30832i	0.482568	+	0.350606i	−0.319751	+	0.947502i	$0.603599\pi$
$152$		0			0
$153$	1.19341	−	3.67295i	0.0964818	−	0.296941i
$154$		0			0
$155$	−20.2124			−1.62350
$156$		0			0
$157$	14.4187	−	10.4758i	1.15074	−	0.836063i	0.162162	−	0.986764i	$-0.448153\pi$
$157$	14.4187	−	10.4758i	1.15074	−	0.836063i	0.988579	+	0.150702i	$0.0481532\pi$
$158$		0			0
$159$	−8.41926	−	25.9118i	−0.667691	−	2.05494i
$160$		0			0
$161$	15.1951			1.19754
$162$		0			0
$163$	−8.58731			−0.672610			−0.336305	−	0.941753i	$-0.609177\pi$
$163$	−8.58731			−0.672610			−0.336305	+	0.941753i	$0.609177\pi$
$164$		0			0
$165$	−6.42111			−0.499883
$166$		0			0
$167$	−0.311563			−0.0241095			−0.0120547	−	0.999927i	$-0.503837\pi$
$167$	−0.311563			−0.0241095			−0.0120547	+	0.999927i	$0.503837\pi$
$168$		0			0
$169$	−2.55291	−	7.85704i	−0.196377	−	0.604387i
$170$		0			0
$171$	−14.0297	+	10.1932i	−1.07288	+	0.779491i
$172$		0			0
$173$	24.6979			1.87775			0.938874	−	0.344260i	$-0.111870\pi$
$173$	24.6979			1.87775			0.938874	+	0.344260i	$0.111870\pi$
$174$		0			0
$175$	0.129137	−	0.397442i	0.00976183	−	0.0300438i
$176$		0			0
$177$	30.6143	+	22.2426i	2.30112	+	1.67186i
$178$		0			0
$179$	−6.21165	−	19.1175i	−0.464280	−	1.42891i	−0.859885	−	0.510487i	$-0.829465\pi$
$179$	−6.21165	−	19.1175i	−0.464280	−	1.42891i	0.395605	−	0.918421i	$-0.370535\pi$
$180$		0			0
$181$	−2.46183	+	7.57673i	−0.182986	+	0.563174i	−0.999908	−	0.0135750i	$-0.995679\pi$
$181$	−2.46183	+	7.57673i	−0.182986	+	0.563174i	0.816922	+	0.576749i	$0.195679\pi$
$182$		0			0
$183$	11.4653	−	8.33003i	0.847540	−	0.615774i
$184$		0			0
$185$	−11.0166	+	8.00401i	−0.809954	+	0.588466i
$186$		0			0
$187$	−0.722882	−	0.525204i	−0.0528624	−	0.0384068i
$188$		0			0
$189$	−6.61604	+	4.80683i	−0.481246	+	0.349646i
$190$		0			0
$191$	−6.20392			−0.448900			−0.224450	−	0.974486i	$-0.572058\pi$
$191$	−6.20392			−0.448900			−0.224450	+	0.974486i	$0.572058\pi$
$192$		0			0
$193$	7.80631	+	24.0253i	0.561910	+	1.72938i	0.676957	+	0.736022i	$0.263298\pi$
$193$	7.80631	+	24.0253i	0.561910	+	1.72938i	−0.115047	+	0.993360i	$0.536702\pi$
$194$		0			0
$195$	−4.05330	+	12.4748i	−0.290263	+	0.893338i
$196$		0			0
$197$	3.55678	−	10.9467i	0.253410	−	0.779917i	−0.740728	−	0.671805i	$-0.765519\pi$
$197$	3.55678	−	10.9467i	0.253410	−	0.779917i	0.994139	−	0.108112i	$-0.0344805\pi$
$198$		0			0
$199$	−0.517367	−	0.375889i	−0.0366752	−	0.0266461i	0.569297	−	0.822132i	$-0.307216\pi$
$199$	−0.517367	−	0.375889i	−0.0366752	−	0.0266461i	−0.605972	+	0.795486i	$0.707216\pi$
$200$		0			0
$201$	−8.59621	−	26.4564i	−0.606330	−	1.86609i
$202$		0			0
$203$	0.145689	+	0.105849i	0.0102254	+	0.00742916i
$204$		0			0
$205$	10.0944	+	9.68625i	0.705027	+	0.676517i
$206$		0			0
$207$	30.6624	+	22.2775i	2.13118	+	1.54840i
$208$		0			0
$209$	1.23986	+	3.81590i	0.0857631	+	0.263952i
$210$		0			0
$211$	15.6636	+	11.3803i	1.07833	+	0.783452i	0.977391	−	0.211441i	$-0.0678155\pi$
$211$	15.6636	+	11.3803i	1.07833	+	0.783452i	0.100938	+	0.994893i	$0.467816\pi$
$212$		0			0
$213$	0.143423	−	0.441411i	0.00982718	−	0.0302450i
$214$		0			0
$215$	−7.52351	+	23.1550i	−0.513099	+	1.57916i
$216$		0			0
$217$	5.27884	+	16.2466i	0.358351	+	1.10289i
$218$		0			0
$219$	12.3657			0.835596
$220$		0			0
$221$	−1.47667	+	1.07286i	−0.0993316	+	0.0721687i
$222$		0			0
$223$	3.87252	+	2.81355i	0.259323	+	0.188409i	0.709849	−	0.704354i	$-0.248763\pi$
$223$	3.87252	+	2.81355i	0.259323	+	0.188409i	−0.450525	+	0.892764i	$0.648763\pi$
$224$		0			0
$225$	0.843276	−	0.612676i	0.0562184	−	0.0408451i
$226$		0			0
$227$	−10.1070	+	7.34317i	−0.670826	+	0.487383i	−0.870301	−	0.492519i	$-0.836076\pi$
$227$	−10.1070	+	7.34317i	−0.670826	+	0.487383i	0.199476	+	0.979903i	$0.436076\pi$
$228$		0			0
$229$	7.60137	−	23.3946i	0.502312	−	1.54596i	−0.302930	−	0.953013i	$-0.597965\pi$
$229$	7.60137	−	23.3946i	0.502312	−	1.54596i	0.805242	−	0.592946i	$-0.202035\pi$
$230$		0			0
$231$	1.67699	+	5.16124i	0.110338	+	0.339585i
$232$		0			0
$233$	−2.45472	−	1.78345i	−0.160814	−	0.116838i	0.504468	−	0.863430i	$-0.331689\pi$
$233$	−2.45472	−	1.78345i	−0.160814	−	0.116838i	−0.665282	+	0.746592i	$0.731689\pi$
$234$		0			0
$235$	2.84187	−	8.74636i	0.185383	−	0.570550i
$236$		0			0
$237$	−24.5412			−1.59412
$238$		0			0
$239$	−2.17362	+	1.57923i	−0.140600	+	0.102152i	−0.655862	−	0.754881i	$-0.727695\pi$
$239$	−2.17362	+	1.57923i	−0.140600	+	0.102152i	0.515262	+	0.857033i	$0.327695\pi$
$240$		0			0
$241$	−1.59588	−	4.91162i	−0.102800	−	0.316385i	0.886408	−	0.462905i	$-0.153193\pi$
$241$	−1.59588	−	4.91162i	−0.102800	−	0.316385i	−0.989208	+	0.146520i	$0.953193\pi$
$242$		0			0
$243$	17.7090			1.13604
$244$		0			0
$245$	−7.84414			−0.501144
$246$		0			0
$247$	8.19611			0.521506
$248$		0			0
$249$	−30.2936			−1.91978
$250$		0			0
$251$	−4.74548	−	14.6051i	−0.299532	−	0.921865i	−0.981661	−	0.190633i	$-0.938946\pi$
$251$	−4.74548	−	14.6051i	−0.299532	−	0.921865i	0.682129	−	0.731232i	$-0.261054\pi$
$252$		0			0
$253$	7.09426	−	5.15428i	0.446012	−	0.324047i
$254$		0			0
$255$	−5.05244			−0.316396
$256$		0			0
$257$	−5.91113	+	18.1926i	−0.368726	+	1.13482i	0.578888	+	0.815407i	$0.303487\pi$
$257$	−5.91113	+	18.1926i	−0.368726	+	1.13482i	−0.947615	+	0.319416i	$0.896513\pi$
$258$		0			0
$259$	9.31074	+	6.76465i	0.578541	+	0.420335i
$260$		0			0
$261$	0.138802	+	0.427188i	0.00859162	+	0.0264423i
$262$		0			0
$263$	3.59460	−	11.0630i	0.221652	−	0.682176i	−0.776962	−	0.629548i	$-0.783240\pi$
$263$	3.59460	−	11.0630i	0.221652	−	0.682176i	0.998614	−	0.0526280i	$-0.0167598\pi$
$264$		0			0
$265$	−17.4624	+	12.6871i	−1.07270	+	0.779365i
$266$		0			0
$267$	20.4441	−	14.8535i	1.25116	−	0.909019i
$268$		0			0
$269$	−4.39540	−	3.19345i	−0.267992	−	0.194708i	0.445671	−	0.895197i	$-0.352965\pi$
$269$	−4.39540	−	3.19345i	−0.267992	−	0.194708i	−0.713663	+	0.700489i	$0.752965\pi$
$270$		0			0
$271$	−15.2629	+	11.0891i	−0.927155	+	0.673618i	−0.945295	−	0.326218i	$-0.894226\pi$
$271$	−15.2629	+	11.0891i	−0.927155	+	0.673618i	0.0181394	+	0.999835i	$0.494226\pi$
$272$		0			0
$273$	11.0857			0.670939
$274$		0			0
$275$	−0.0745239	−	0.229361i	−0.00449396	−	0.0138310i
$276$		0			0
$277$	3.54029	−	10.8959i	0.212716	−	0.654671i	−0.786592	−	0.617473i	$-0.788157\pi$
$277$	3.54029	−	10.8959i	0.212716	−	0.654671i	0.999308	−	0.0371985i	$-0.0118434\pi$
$278$		0			0
$279$	−13.1669	+	40.5234i	−0.788279	+	2.42607i
$280$		0			0
$281$	0.879736	+	0.639166i	0.0524806	+	0.0381294i	0.613716	−	0.789527i	$-0.289674\pi$
$281$	0.879736	+	0.639166i	0.0524806	+	0.0381294i	−0.561236	+	0.827656i	$0.689674\pi$
$282$		0			0
$283$	1.05725	+	3.25390i	0.0628473	+	0.193424i	0.977550	−	0.210703i	$-0.0675753\pi$
$283$	1.05725	+	3.25390i	0.0628473	+	0.193424i	−0.914703	+	0.404127i	$0.867575\pi$
$284$		0			0
$285$	18.3544	+	13.3352i	1.08722	+	0.789912i
$286$		0			0
$287$	5.14939	−	10.6436i	0.303959	−	0.628271i
$288$		0			0
$289$	13.1845	+	9.57909i	0.775558	+	0.563476i
$290$		0			0
$291$	1.58680	+	4.88366i	0.0930198	+	0.286286i
$292$		0			0
$293$	−25.2922	−	18.3759i	−1.47759	−	1.07353i	−0.978325	−	0.207077i	$-0.933605\pi$
$293$	−25.2922	−	18.3759i	−1.47759	−	1.07353i	−0.499261	−	0.866452i	$-0.666395\pi$
$294$		0			0
$295$	9.26410	−	28.5120i	0.539377	−	1.66003i
$296$		0			0
$297$	−1.45837	+	4.48840i	−0.0846232	+	0.260444i
$298$		0			0
$299$	−5.53539	−	17.0362i	−0.320120	−	0.985227i
$300$		0			0
$301$	20.5767			1.18602
$302$		0			0
$303$	−31.5851	+	22.9480i	−1.81452	+	1.31833i
$304$		0			0
$305$	−9.08321	−	6.59934i	−0.520103	−	0.377877i
$306$		0			0
$307$	−23.1714	+	16.8350i	−1.32246	+	0.960824i	−0.322562	+	0.946548i	$0.604544\pi$
$307$	−23.1714	+	16.8350i	−1.32246	+	0.960824i	−0.999898	+	0.0142752i	$0.995456\pi$
$308$		0			0
$309$	−30.3182	+	22.0274i	−1.72474	+	1.25310i
$310$		0			0
$311$	2.91516	−	8.97194i	0.165304	−	0.508752i	−0.833755	−	0.552135i	$-0.813813\pi$
$311$	2.91516	−	8.97194i	0.165304	−	0.508752i	0.999059	+	0.0433825i	$0.0138134\pi$
$312$		0			0
$313$	−5.84353	−	17.9845i	−0.330296	−	1.01655i	−0.968993	−	0.247087i	$-0.920527\pi$
$313$	−5.84353	−	17.9845i	−0.330296	−	1.01655i	0.638698	−	0.769458i	$-0.279473\pi$
$314$		0			0
$315$	15.0334	+	10.9224i	0.847038	+	0.615409i
$316$		0			0
$317$	5.44124	−	16.7464i	0.305611	−	0.940573i	−0.673838	−	0.738879i	$-0.735355\pi$
$317$	5.44124	−	16.7464i	0.305611	−	0.940573i	0.979449	−	0.201694i	$-0.0646446\pi$
$318$		0			0
$319$	0.103924			0.00581860
$320$		0			0
$321$	19.4459	−	14.1282i	1.08536	−	0.788561i
$322$		0			0
$323$	0.975582	+	3.00253i	0.0542829	+	0.167065i
$324$		0			0
$325$	−0.492640			−0.0273267
$326$		0			0
$327$	38.0711			2.10534
$328$		0			0
$329$	−7.77246			−0.428510
$330$		0			0
$331$	−29.0894			−1.59890			−0.799449	−	0.600734i	$-0.794875\pi$
$331$	−29.0894			−1.59890			−0.799449	+	0.600734i	$0.794875\pi$
$332$		0			0
$333$	8.87060	+	27.3009i	0.486106	+	1.49608i
$334$		0			0
$335$	−17.8294	+	12.9538i	−0.974122	+	0.707741i
$336$		0			0
$337$	−9.76929			−0.532167			−0.266084	−	0.963950i	$-0.585730\pi$
$337$	−9.76929			−0.532167			−0.266084	+	0.963950i	$0.585730\pi$
$338$		0			0
$339$	6.92600	−	21.3160i	0.376169	−	1.15773i
$340$		0			0
$341$	7.97551	+	5.79455i	0.431898	+	0.313792i
$342$		0			0
$343$	6.04298	+	18.5984i	0.326290	+	1.00422i
$344$		0			0
$345$	15.3223	−	47.1570i	0.824922	−	2.53885i
$346$		0			0
$347$	22.0398	−	16.0129i	1.18316	−	0.859615i	0.190634	−	0.981661i	$-0.438946\pi$
$347$	22.0398	−	16.0129i	1.18316	−	0.859615i	0.992524	+	0.122046i	$0.0389455\pi$
$348$		0			0
$349$	−19.2209	+	13.9648i	−1.02887	+	0.747518i	−0.968082	−	0.250633i	$-0.919361\pi$
$349$	−19.2209	+	13.9648i	−1.02887	+	0.747518i	−0.0607877	+	0.998151i	$0.519361\pi$
$350$		0			0
$351$	7.79937	+	5.66657i	0.416300	+	0.302459i
$352$		0			0
$353$	−13.9348	+	10.1242i	−0.741674	+	0.538857i	−0.893235	−	0.449590i	$-0.851570\pi$
$353$	−13.9348	+	10.1242i	−0.741674	+	0.538857i	0.151561	+	0.988448i	$0.451570\pi$
$354$		0			0
$355$	−0.367697			−0.0195153
$356$		0			0
$357$	1.31953	+	4.06111i	0.0698372	+	0.214937i
$358$		0			0
$359$	0.646221	−	1.98886i	0.0341062	−	0.104968i	−0.932554	−	0.361030i	$-0.882425\pi$
$359$	0.646221	−	1.98886i	0.0341062	−	0.104968i	0.966660	+	0.256062i	$0.0824251\pi$
$360$		0			0
$361$	−1.49060	+	4.58761i	−0.0784528	+	0.241453i
$362$		0			0
$363$	−22.0091	−	15.9906i	−1.15518	−	0.839287i
$364$		0			0
$365$	−3.02729	−	9.31705i	−0.158456	−	0.487677i
$366$		0			0
$367$	8.23854	+	5.98565i	0.430048	+	0.312448i	0.781668	−	0.623695i	$-0.214369\pi$
$367$	8.23854	+	5.98565i	0.430048	+	0.312448i	−0.351620	+	0.936143i	$0.614369\pi$
$368$		0			0
$369$	25.9955	−	13.9283i	1.35327	−	0.725077i
$370$		0			0
$371$	14.7584	+	10.7226i	0.766220	+	0.556691i
$372$		0			0
$373$	2.62570	+	8.08108i	0.135954	+	0.418422i	0.995737	−	0.0922365i	$-0.0294016\pi$
$373$	2.62570	+	8.08108i	0.135954	+	0.418422i	−0.859783	+	0.510659i	$0.829402\pi$
$374$		0			0
$375$	−25.4773	−	18.5103i	−1.31564	−	0.955870i
$376$		0			0
$377$	0.0656014	−	0.201900i	0.00337864	−	0.0103984i
$378$		0			0
$379$	−1.78209	+	5.48471i	−0.0915398	+	0.281731i	−0.986336	−	0.164743i	$-0.947320\pi$
$379$	−1.78209	+	5.48471i	−0.0915398	+	0.281731i	0.894797	+	0.446474i	$0.147320\pi$
$380$		0			0
$381$	10.5611	+	32.5036i	0.541059	+	1.66521i
$382$		0			0
$383$	4.09003			0.208991			0.104495	−	0.994525i	$-0.466677\pi$
$383$	4.09003			0.208991			0.104495	+	0.994525i	$0.466677\pi$
$384$		0			0
$385$	3.47824	−	2.52709i	0.177267	−	0.128792i
$386$		0			0
$387$	41.5219	+	30.1675i	2.11068	+	1.53350i
$388$		0			0
$389$	22.2134	−	16.1390i	1.12627	−	0.818280i	0.141118	−	0.989993i	$-0.454930\pi$
$389$	22.2134	−	16.1390i	1.12627	−	0.818280i	0.985147	+	0.171713i	$0.0549303\pi$
$390$		0			0
$391$	5.58209	−	4.05563i	0.282299	−	0.205102i
$392$		0			0
$393$	−8.46229	+	26.0443i	−0.426866	+	1.31376i
$394$		0			0
$395$	6.00802	+	18.4908i	0.302296	+	0.930372i
$396$		0			0
$397$	16.4980	+	11.9865i	0.828013	+	0.601586i	0.918996	−	0.394266i	$-0.129001\pi$
$397$	16.4980	+	11.9865i	0.828013	+	0.601586i	−0.0909838	+	0.995852i	$0.529001\pi$
$398$		0			0
$399$	5.92519	−	18.2359i	0.296630	−	0.912935i
$400$		0			0
$401$	25.3620			1.26652			0.633258	−	0.773940i	$-0.281717\pi$
$401$	25.3620			1.26652			0.633258	+	0.773940i	$0.281717\pi$
$402$		0			0
$403$	16.2920	−	11.8368i	0.811563	−	0.589635i
$404$		0			0
$405$	−1.08280	−	3.33252i	−0.0538048	−	0.165594i
$406$		0			0
$407$	6.64158			0.329211
$408$		0			0
$409$	−4.08136			−0.201810			−0.100905	−	0.994896i	$-0.532174\pi$
$409$	−4.08136			−0.201810			−0.100905	+	0.994896i	$0.532174\pi$
$410$		0			0
$411$	20.3791			1.00523
$412$		0			0
$413$	−25.3372			−1.24676
$414$		0			0
$415$	7.41630	+	22.8250i	0.364052	+	1.12044i
$416$		0			0
$417$	−8.17680	+	5.94079i	−0.400420	+	0.290922i
$418$		0			0
$419$	−37.0062			−1.80787			−0.903936	−	0.427667i	$-0.859335\pi$
$419$	−37.0062			−1.80787			−0.903936	+	0.427667i	$0.859335\pi$
$420$		0			0
$421$	−1.38537	+	4.26373i	−0.0675187	+	0.207801i	−0.979123	−	0.203267i	$-0.934844\pi$
$421$	−1.38537	+	4.26373i	−0.0675187	+	0.207801i	0.911605	+	0.411068i	$0.134844\pi$
$422$		0			0
$423$	−15.6841	−	11.3952i	−0.762589	−	0.554053i
$424$		0			0
$425$	−0.0586389	−	0.180472i	−0.00284440	−	0.00875417i
$426$		0			0
$427$	−2.93225	+	9.02455i	−0.141902	+	0.436729i
$428$		0			0
$429$	5.17567	−	3.76035i	0.249884	−	0.181551i
$430$		0			0
$431$	2.66293	−	1.93474i	0.128269	−	0.0931929i	−0.521801	−	0.853067i	$-0.674740\pi$
$431$	2.66293	−	1.93474i	0.128269	−	0.0931929i	0.650070	+	0.759874i	$0.274740\pi$
$432$		0			0
$433$	−10.5595	−	7.67196i	−0.507459	−	0.368691i	0.304400	−	0.952544i	$-0.401544\pi$
$433$	−10.5595	−	7.67196i	−0.507459	−	0.368691i	−0.811859	+	0.583854i	$0.801544\pi$
$434$		0			0
$435$	0.475404	−	0.345401i	0.0227939	−	0.0165607i
$436$		0			0
$437$	−30.9828			−1.48211
$438$		0			0
$439$	8.86435	+	27.2817i	0.423072	+	1.30208i	0.904828	+	0.425777i	$0.139999\pi$
$439$	8.86435	+	27.2817i	0.423072	+	1.30208i	−0.481756	+	0.876306i	$0.660001\pi$
$440$		0			0
$441$	−5.10986	+	15.7265i	−0.243327	+	0.748883i
$442$		0			0
$443$	3.54637	−	10.9146i	0.168493	−	0.518569i	−0.830784	−	0.556596i	$-0.812107\pi$
$443$	3.54637	−	10.9146i	0.168493	−	0.518569i	0.999277	+	0.0380271i	$0.0121073\pi$
$444$		0			0
$445$	−16.1965	−	11.7674i	−0.767787	−	0.557830i
$446$		0			0
$447$	2.27362	+	6.99749i	0.107539	+	0.330970i
$448$		0			0
$449$	−5.51360	−	4.00586i	−0.260203	−	0.189048i	0.450034	−	0.893012i	$-0.351412\pi$
$449$	−5.51360	−	4.00586i	−0.260203	−	0.189048i	−0.710236	+	0.703963i	$0.751412\pi$
$450$		0			0
$451$	−1.20624	−	6.71595i	−0.0567995	−	0.316242i
$452$		0			0
$453$	−16.3539	−	11.8818i	−0.768372	−	0.558255i
$454$		0			0
$455$	−2.71394	−	8.35265i	−0.127231	−	0.391578i
$456$		0			0
$457$	−11.4818	−	8.34201i	−0.537095	−	0.390223i	0.285910	−	0.958257i	$-0.407704\pi$
$457$	−11.4818	−	8.34201i	−0.537095	−	0.390223i	−0.823005	+	0.568034i	$0.807704\pi$
$458$		0			0
$459$	−1.14751	+	3.53169i	−0.0535614	+	0.164845i
$460$		0			0
$461$	−7.45617	+	22.9477i	−0.347268	+	1.06878i	0.613090	+	0.790013i	$0.289926\pi$
$461$	−7.45617	+	22.9477i	−0.347268	+	1.06878i	−0.960358	+	0.278769i	$0.910074\pi$
$462$		0			0
$463$	−1.44281	−	4.44050i	−0.0670529	−	0.206368i	0.911916	−	0.410377i	$-0.134603\pi$
$463$	−1.44281	−	4.44050i	−0.0670529	−	0.206368i	−0.978969	+	0.204009i	$0.934603\pi$
$464$		0			0
$465$	55.7432			2.58503
$466$		0			0
$467$	11.6618	−	8.47276i	0.539642	−	0.392073i	−0.284310	−	0.958732i	$-0.591765\pi$
$467$	11.6618	−	8.47276i	0.539642	−	0.392073i	0.823952	+	0.566660i	$0.191765\pi$
$468$		0			0
$469$	15.0686	+	10.9480i	0.695804	+	0.505531i
$470$		0			0
$471$	−39.7650	+	28.8910i	−1.83228	+	1.33123i
$472$		0			0
$473$	9.60679	−	6.97974i	0.441721	−	0.320929i
$474$		0			0
$475$	−0.263310	+	0.810384i	−0.0120815	+	0.0371830i
$476$		0			0
$477$	14.0608	+	43.2746i	0.643799	+	1.98141i
$478$		0			0
$479$	−0.728666	−	0.529407i	−0.0332936	−	0.0241892i	0.571014	−	0.820940i	$-0.306550\pi$
$479$	−0.728666	−	0.529407i	−0.0332936	−	0.0241892i	−0.604308	+	0.796751i	$0.706550\pi$
$480$		0			0
$481$	4.19247	−	12.9031i	0.191160	−	0.588331i
$482$		0			0
$483$	−41.9062			−1.90680
$484$		0			0
$485$	3.29117	−	2.39118i	0.149444	−	0.108578i
$486$		0			0
$487$	−12.2765	−	37.7833i	−0.556303	−	1.71212i	−0.692478	−	0.721439i	$-0.743481\pi$
$487$	−12.2765	−	37.7833i	−0.556303	−	1.71212i	0.136175	−	0.990685i	$-0.456519\pi$
$488$		0			0
$489$	23.6827			1.07097
$490$		0			0
$491$	15.1752			0.684848			0.342424	−	0.939545i	$-0.388752\pi$
$491$	15.1752			0.684848			0.342424	+	0.939545i	$0.388752\pi$
$492$		0			0
$493$	0.0817720			0.00368282
$494$		0			0
$495$	10.7237			0.481996
$496$		0			0
$497$	0.0960307	+	0.295552i	0.00430756	+	0.0132573i
$498$		0			0
$499$	−12.9001	+	9.37247i	−0.577488	+	0.419569i	−0.837818	−	0.545950i	$-0.816169\pi$
$499$	−12.9001	+	9.37247i	−0.577488	+	0.419569i	0.260330	+	0.965520i	$0.416169\pi$
$500$		0			0
$501$	0.859249			0.0383884
$502$		0			0
$503$	−4.95763	+	15.2580i	−0.221050	+	0.680322i	0.777619	+	0.628736i	$0.216427\pi$
$503$	−4.95763	+	15.2580i	−0.221050	+	0.680322i	−0.998669	+	0.0515854i	$0.983573\pi$
$504$		0			0
$505$	25.0228	+	18.1802i	1.11350	+	0.809006i
$506$		0			0
$507$	7.04058	+	21.6687i	0.312683	+	0.962340i
$508$		0			0
$509$	5.52063	−	16.9907i	0.244697	−	0.753101i	−0.750989	−	0.660315i	$-0.770423\pi$
$509$	5.52063	−	16.9907i	0.244697	−	0.753101i	0.995686	−	0.0927861i	$-0.0295773\pi$
$510$		0			0
$511$	−6.69834	+	4.86663i	−0.296317	+	0.215287i
$512$		0			0
$513$	13.4901	−	9.80113i	0.595602	−	0.432730i
$514$		0			0
$515$	24.0191	+	17.4509i	1.05841	+	0.768978i
$516$		0			0
$517$	−3.62879	+	2.63647i	−0.159594	+	0.115952i
$518$		0			0
$519$	−68.1137			−2.98986
$520$		0			0
$521$	−1.88370	−	5.79744i	−0.0825265	−	0.253990i	0.901276	−	0.433245i	$-0.142631\pi$
$521$	−1.88370	−	5.79744i	−0.0825265	−	0.253990i	−0.983803	+	0.179254i	$0.942631\pi$
$522$		0			0
$523$	0.625258	−	1.92435i	0.0273406	−	0.0841457i	−0.936455	−	0.350787i	$-0.885914\pi$
$523$	0.625258	−	1.92435i	0.0273406	−	0.0841457i	0.963796	+	0.266642i	$0.0859140\pi$
$524$		0			0
$525$	−0.356143	+	1.09609i	−0.0155433	+	0.0478375i
$526$		0			0
$527$	6.27551	+	4.55942i	0.273365	+	0.198612i
$528$		0			0
$529$	13.8174	+	42.5256i	0.600757	+	1.84894i
$530$		0			0
$531$	−51.1282	−	37.1468i	−2.21877	−	1.61203i
$532$		0			0
$533$	−13.8090	−	1.89597i	−0.598135	−	0.0821235i
$534$		0			0
$535$	−15.4057	−	11.1929i	−0.666045	−	0.483910i
$536$		0			0
$537$	17.1309	+	52.7235i	0.739253	+	2.27519i
$538$		0			0
$539$	3.09518	+	2.24878i	0.133319	+	0.0968617i
$540$		0			0
$541$	2.43163	−	7.48378i	0.104544	−	0.321753i	−0.885079	−	0.465440i	$-0.845896\pi$
$541$	2.43163	−	7.48378i	0.104544	−	0.321753i	0.989623	+	0.143687i	$0.0458960\pi$
$542$		0			0
$543$	6.78940	−	20.8956i	0.291361	−	0.896717i
$544$		0			0
$545$	−9.32033	−	28.6850i	−0.399239	−	1.22873i
$546$		0			0
$547$	34.9595			1.49476			0.747379	−	0.664398i	$-0.231312\pi$
$547$	34.9595			1.49476			0.747379	+	0.664398i	$0.231312\pi$
$548$		0			0
$549$	−19.1479	+	13.9118i	−0.817212	+	0.593739i
$550$		0			0
$551$	−0.297060	−	0.215826i	−0.0126552	−	0.00919451i
$552$		0			0
$553$	13.2936	−	9.65840i	0.565303	−	0.410717i
$554$		0			0
$555$	30.3823	−	22.0740i	1.28966	−	0.936989i
$556$		0			0
$557$	−1.32444	+	4.07620i	−0.0561182	+	0.172714i	−0.975187	−	0.221383i	$-0.928943\pi$
$557$	−1.32444	+	4.07620i	−0.0561182	+	0.172714i	0.919069	+	0.394098i	$0.128943\pi$
$558$		0			0
$559$	−7.49583	−	23.0698i	−0.317040	−	0.975748i
$560$		0			0
$561$	1.99361	+	1.44844i	0.0841704	+	0.0611534i
$562$		0			0
$563$	13.8869	−	42.7394i	0.585262	−	1.80125i	−0.0129543	−	0.999916i	$-0.504124\pi$
$563$	13.8869	−	42.7394i	0.585262	−	1.80125i	0.598216	−	0.801335i	$-0.295876\pi$
$564$		0			0
$565$	−17.7563			−0.747015
$566$		0			0
$567$	−2.39586	+	1.74070i	−0.100617	+	0.0731023i
$568$		0			0
$569$	−12.7075	−	39.1096i	−0.532725	−	1.63956i	−0.748514	−	0.663119i	$-0.769232\pi$
$569$	−12.7075	−	39.1096i	−0.532725	−	1.63956i	0.215789	−	0.976440i	$-0.430768\pi$
$570$		0			0
$571$	−19.2847			−0.807041			−0.403520	−	0.914971i	$-0.632214\pi$
$571$	−19.2847			−0.807041			−0.403520	+	0.914971i	$0.632214\pi$
$572$		0			0
$573$	17.1096			0.714763
$574$		0			0
$575$	1.86227			0.0776620
$576$		0			0
$577$	−44.6284			−1.85791			−0.928953	−	0.370197i	$-0.879290\pi$
$577$	−44.6284			−1.85791			−0.928953	+	0.370197i	$0.879290\pi$
$578$		0			0
$579$	−21.5288	−	66.2588i	−0.894705	−	2.75362i
$580$		0			0
$581$	16.4097	−	11.9223i	0.680788	−	0.494621i
$582$		0			0
$583$	10.5276			0.436007
$584$		0			0
$585$	6.76931	−	20.8338i	0.279877	−	0.861371i
$586$		0			0
$587$	20.8556	+	15.1525i	0.860801	+	0.625409i	0.928103	−	0.372324i	$-0.121439\pi$
$587$	20.8556	+	15.1525i	0.860801	+	0.625409i	−0.0673014	+	0.997733i	$0.521439\pi$
$588$		0			0
$589$	−10.7635	−	33.1268i	−0.443504	−	1.36496i
$590$		0			0
$591$	−9.80914	+	30.1894i	−0.403494	+	1.24183i
$592$		0			0
$593$	19.4641	−	14.1415i	0.799294	−	0.580721i	−0.111413	−	0.993774i	$-0.535538\pi$
$593$	19.4641	−	14.1415i	0.799294	−	0.580721i	0.910707	+	0.413053i	$0.135538\pi$
$594$		0			0
$595$	2.73684	−	1.98843i	0.112200	−	0.0815177i
$596$		0			0
$597$	1.42683	+	1.03665i	0.0583963	+	0.0424274i
$598$		0			0
$599$	−31.3505	+	22.7775i	−1.28095	+	0.930662i	−0.999581	−	0.0289384i	$-0.990787\pi$
$599$	−31.3505	+	22.7775i	−1.28095	+	0.930662i	−0.281366	+	0.959601i	$0.590787\pi$
$600$		0			0
$601$	−7.90249			−0.322349			−0.161175	−	0.986926i	$-0.551528\pi$
$601$	−7.90249			−0.322349			−0.161175	+	0.986926i	$0.551528\pi$
$602$		0			0
$603$	14.3563	+	44.1841i	0.584634	+	1.79932i
$604$		0			0
$605$	−6.66010	+	20.4977i	−0.270772	+	0.833349i
$606$		0			0
$607$	9.95682	−	30.6439i	0.404135	−	1.24380i	−0.517481	−	0.855695i	$-0.673130\pi$
$607$	9.95682	−	30.6439i	0.404135	−	1.24380i	0.921616	−	0.388104i	$-0.126870\pi$
$608$		0			0
$609$	−0.401791	−	0.291918i	−0.0162814	−	0.0118291i
$610$		0			0
$611$	2.83141	+	8.71418i	0.114547	+	0.352538i
$612$		0			0
$613$	3.42625	+	2.48932i	0.138385	+	0.100543i	0.654824	−	0.755781i	$-0.272743\pi$
$613$	3.42625	+	2.48932i	0.138385	+	0.100543i	−0.516439	+	0.856324i	$0.672743\pi$
$614$		0			0
$615$	−27.8392	−	26.7134i	−1.12258	−	1.07719i
$616$		0			0
$617$	−8.17771	−	5.94145i	−0.329222	−	0.239194i	0.410878	−	0.911690i	$-0.365222\pi$
$617$	−8.17771	−	5.94145i	−0.329222	−	0.239194i	−0.740100	+	0.672496i	$0.765222\pi$
$618$		0			0
$619$	−2.40525	−	7.40258i	−0.0966750	−	0.297535i	0.891012	−	0.453980i	$-0.149996\pi$
$619$	−2.40525	−	7.40258i	−0.0966750	−	0.297535i	−0.987687	+	0.156446i	$0.949996\pi$
$620$		0			0
$621$	−29.4831	−	21.4207i	−1.18312	−	0.859584i
$622$		0			0
$623$	−5.22857	+	16.0919i	−0.209478	+	0.644708i
$624$		0			0
$625$	−7.35993	+	22.6515i	−0.294397	+	0.906061i
$626$		0			0
$627$	−3.41938	−	10.5238i	−0.136557	−	0.420279i
$628$		0			0
$629$	5.22591			0.208371
$630$		0			0
$631$	16.2992	−	11.8421i	0.648861	−	0.471425i	−0.214022	−	0.976829i	$-0.568656\pi$
$631$	16.2992	−	11.8421i	0.648861	−	0.471425i	0.862883	+	0.505404i	$0.168656\pi$
$632$		0			0
$633$	−43.1982	−	31.3854i	−1.71698	−	1.24746i
$634$		0			0
$635$	21.9046	−	15.9147i	0.869259	−	0.631554i
$636$		0			0
$637$	6.32269	−	4.59370i	0.250514	−	0.182009i
$638$		0			0
$639$	−0.239527	+	0.737188i	−0.00947553	+	0.0291627i
$640$		0			0
$641$	−10.0527	−	30.9390i	−0.397057	−	1.22202i	−0.927348	−	0.374200i	$-0.877917\pi$
$641$	−10.0527	−	30.9390i	−0.397057	−	1.22202i	0.530291	−	0.847816i	$-0.322083\pi$
$642$		0			0
$643$	−0.339502	−	0.246663i	−0.0133887	−	0.00972744i	0.581071	−	0.813853i	$-0.302634\pi$
$643$	−0.339502	−	0.246663i	−0.0133887	−	0.00972744i	−0.594459	+	0.804126i	$0.702634\pi$
$644$		0			0
$645$	20.7489	−	63.8584i	0.816985	−	2.51442i
$646$		0			0
$647$	19.6437			0.772272			0.386136	−	0.922442i	$-0.373810\pi$
$647$	19.6437			0.772272			0.386136	+	0.922442i	$0.373810\pi$
$648$		0			0
$649$	−11.8294	+	8.59453i	−0.464343	+	0.337365i
$650$		0			0
$651$	−14.5583	−	44.8059i	−0.570586	−	1.75608i
$652$		0			0
$653$	−14.4808			−0.566679			−0.283339	−	0.959020i	$-0.591442\pi$
$653$	−14.4808			−0.566679			−0.283339	+	0.959020i	$0.591442\pi$
$654$		0			0
$655$	21.6950			0.847693
$656$		0			0
$657$	−20.6516			−0.805696
$658$		0			0
$659$	16.7546			0.652666			0.326333	−	0.945255i	$-0.394187\pi$
$659$	16.7546			0.652666			0.326333	+	0.945255i	$0.394187\pi$
$660$		0			0
$661$	10.0009	+	30.7797i	0.388991	+	1.19719i	0.933544	+	0.358464i	$0.116699\pi$
$661$	10.0009	+	30.7797i	0.388991	+	1.19719i	−0.544553	+	0.838727i	$0.683301\pi$
$662$		0			0
$663$	4.07246	−	2.95882i	0.158161	−	0.114911i
$664$		0			0
$665$	−15.1905			−0.589064
$666$		0			0
$667$	−0.247985	+	0.763221i	−0.00960203	+	0.0295520i
$668$		0			0
$669$	−10.6799	−	7.75941i	−0.412909	−	0.299996i
$670$		0			0
$671$	1.69218	+	5.20799i	0.0653259	+	0.201052i
$672$		0			0
$673$	13.7027	−	42.1726i	0.528201	−	1.62563i	−0.229698	−	0.973262i	$-0.573774\pi$
$673$	13.7027	−	42.1726i	0.528201	−	1.62563i	0.757899	−	0.652372i	$-0.226226\pi$
$674$		0			0
$675$	−0.810843	+	0.589112i	−0.0312094	+	0.0226749i
$676$		0			0
$677$	3.21155	−	2.33333i	0.123430	−	0.0896770i	−0.524358	−	0.851498i	$-0.675694\pi$
$677$	3.21155	−	2.33333i	0.123430	−	0.0896770i	0.647787	+	0.761821i	$0.275694\pi$
$678$		0			0
$679$	−2.78156	−	2.02092i	−0.106746	−	0.0775558i
$680$		0			0
$681$	27.8738	−	20.2515i	1.06813	−	0.776039i
$682$		0			0
$683$	24.1397			0.923678			0.461839	−	0.886964i	$-0.347190\pi$
$683$	24.1397			0.923678			0.461839	+	0.886964i	$0.347190\pi$
$684$		0			0
$685$	−4.98908	−	15.3548i	−0.190623	−	0.586677i
$686$		0			0
$687$	−20.9636	+	64.5192i	−0.799810	+	2.46156i
$688$		0			0
$689$	6.64548	−	20.4527i	0.253173	−	0.779185i
$690$		0			0
$691$	0.258617	+	0.187896i	0.00983826	+	0.00714792i	0.592694	−	0.805428i	$-0.298065\pi$
$691$	0.258617	+	0.187896i	0.00983826	+	0.00714792i	−0.582855	+	0.812576i	$0.698065\pi$
$692$		0			0
$693$	−2.80069	−	8.61965i	−0.106390	−	0.327433i
$694$		0			0
$695$	6.47794	+	4.70650i	0.245722	+	0.178528i
$696$		0			0
$697$	−0.949124	−	5.28442i	−0.0359506	−	0.200162i
$698$		0			0
$699$	6.76978	+	4.91853i	0.256057	+	0.186036i
$700$		0			0
$701$	−7.23032	−	22.2526i	−0.273085	−	0.840471i	−0.989720	−	0.143021i	$-0.954318\pi$
$701$	−7.23032	−	22.2526i	−0.273085	−	0.840471i	0.716634	−	0.697449i	$-0.245682\pi$
$702$		0			0
$703$	−18.9846	−	13.7931i	−0.716017	−	0.520217i
$704$		0			0
$705$	−7.83749	+	24.1213i	−0.295177	+	0.908461i
$706$		0			0
$707$	8.07791	−	24.8612i	0.303801	−	0.935003i
$708$		0			0
$709$	−9.97426	−	30.6976i	−0.374591	−	1.15287i	−0.943754	−	0.330648i	$-0.892733\pi$
$709$	−9.97426	−	30.6976i	−0.374591	−	1.15287i	0.569163	−	0.822225i	$-0.307267\pi$
$710$		0			0
$711$	40.9855			1.53708
$712$		0			0
$713$	−61.5869	+	44.7455i	−2.30645	+	1.67573i
$714$		0			0
$715$	−4.10035	−	2.97908i	−0.153344	−	0.111411i
$716$		0			0
$717$	5.99456	−	4.35531i	0.223871	−	0.162652i
$718$		0			0
$719$	5.08979	−	3.69795i	0.189817	−	0.137910i	−0.488818	−	0.872386i	$-0.662572\pi$
$719$	5.08979	−	3.69795i	0.189817	−	0.137910i	0.678635	+	0.734476i	$0.262572\pi$
$720$		0			0
$721$	7.75388	−	23.8640i	0.288770	−	0.888741i
$722$		0			0
$723$	4.40123	+	13.5456i	0.163684	+	0.503766i
$724$		0			0
$725$	0.0178552	+	0.0129726i	0.000663126	+	0.000481789i
$726$		0			0
$727$	−15.6303	+	48.1051i	−0.579696	+	1.78412i	0.0399064	+	0.999203i	$0.487294\pi$
$727$	−15.6303	+	48.1051i	−0.579696	+	1.78412i	−0.619602	+	0.784916i	$0.712706\pi$
$728$		0			0
$729$	−44.0279			−1.63066
$730$		0			0
$731$	7.55908	−	5.49199i	0.279583	−	0.203129i
$732$		0			0
$733$	9.20123	+	28.3185i	0.339855	+	1.04597i	0.964281	+	0.264882i	$0.0853332\pi$
$733$	9.20123	+	28.3185i	0.339855	+	1.04597i	−0.624425	+	0.781084i	$0.714667\pi$
$734$		0			0
$735$	21.6331			0.797949
$736$		0			0
$737$	10.7488			0.395938
$738$		0			0
$739$	−28.4634			−1.04704			−0.523522	−	0.852012i	$-0.675382\pi$
$739$	−28.4634			−1.04704			−0.523522	+	0.852012i	$0.675382\pi$
$740$		0			0
$741$	−22.6038			−0.830371
$742$		0			0
$743$	−1.92034	−	5.91021i	−0.0704506	−	0.216825i	0.909632	−	0.415415i	$-0.136364\pi$
$743$	−1.92034	−	5.91021i	−0.0704506	−	0.216825i	−0.980083	+	0.198590i	$0.936364\pi$
$744$		0			0
$745$	4.71571	−	3.42616i	0.172770	−	0.125525i
$746$		0			0
$747$	50.5925			1.85108
$748$		0			0
$749$	−4.97328	+	15.3062i	−0.181720	+	0.559276i
$750$		0			0
$751$	−29.8888	−	21.7155i	−1.09066	−	0.792410i	−0.111148	−	0.993804i	$-0.535453\pi$
$751$	−29.8888	−	21.7155i	−1.09066	−	0.792410i	−0.979510	+	0.201394i	$0.935453\pi$
$752$		0			0
$753$	13.0874	+	40.2789i	0.476932	+	1.46785i
$754$		0			0
$755$	−4.94879	+	15.2308i	−0.180105	+	0.554306i
$756$		0			0
$757$	21.6216	−	15.7090i	0.785851	−	0.570954i	−0.120879	−	0.992667i	$-0.538571\pi$
$757$	21.6216	−	15.7090i	0.785851	−	0.570954i	0.906729	+	0.421713i	$0.138571\pi$
$758$		0			0
$759$	−19.5650	+	14.2148i	−0.710165	+	0.515965i
$760$		0			0
$761$	21.3646	+	15.5223i	0.774464	+	0.562681i	0.903313	−	0.428983i	$-0.141128\pi$
$761$	21.3646	+	15.5223i	0.774464	+	0.562681i	−0.128848	+	0.991664i	$0.541128\pi$
$762$		0			0
$763$	−20.6226	+	14.9832i	−0.746590	+	0.542429i
$764$		0			0
$765$	8.43793			0.305074
$766$		0			0
$767$	9.23001	+	28.4071i	0.333276	+	1.02572i
$768$		0			0
$769$	−8.86098	+	27.2713i	−0.319535	+	0.983428i	0.654312	+	0.756225i	$0.272958\pi$
$769$	−8.86098	+	27.2713i	−0.319535	+	0.983428i	−0.973847	+	0.227204i	$0.927042\pi$
$770$		0			0
$771$	16.3021	−	50.1728i	0.587107	−	1.80693i
$772$		0			0
$773$	5.49168	+	3.98994i	0.197522	+	0.143508i	0.682150	−	0.731212i	$-0.261045\pi$
$773$	5.49168	+	3.98994i	0.197522	+	0.143508i	−0.484628	+	0.874720i	$0.661045\pi$
$774$		0			0
$775$	0.646959	+	1.99113i	0.0232394	+	0.0715237i
$776$		0			0
$777$	−25.6778	−	18.6560i	−0.921186	−	0.669281i
$778$		0			0
$779$	−10.4996	+	21.7022i	−0.376187	+	0.777563i
$780$		0			0
$781$	0.145088	+	0.105412i	0.00519164	+	0.00377195i
$782$		0			0
$783$	−0.133463	−	0.410758i	−0.00476960	−	0.0146793i
$784$		0			0
$785$	31.5032	+	22.8884i	1.12440	+	0.816923i
$786$		0			0
$787$	3.41907	−	10.5228i	0.121877	−	0.375098i	−0.871442	−	0.490498i	$-0.836815\pi$
$787$	3.41907	−	10.5228i	0.121877	−	0.375098i	0.993319	+	0.115400i	$0.0368150\pi$
$788$		0			0
$789$	−9.91342	+	30.5104i	−0.352927	+	1.08620i
$790$		0			0
$791$	4.63739	+	14.2724i	0.164887	+	0.507469i
$792$		0			0
$793$	11.1861			0.397232
$794$		0			0
$795$	48.1589	−	34.9895i	1.70802	−	1.24095i
$796$		0			0
$797$	11.0017	+	7.99321i	0.389701	+	0.283134i	0.765333	−	0.643635i	$-0.222574\pi$
$797$	11.0017	+	7.99321i	0.389701	+	0.283134i	−0.375632	+	0.926769i	$0.622574\pi$
$798$		0			0
$799$	−2.85530	+	2.07450i	−0.101013	+	0.0733904i
$800$		0			0
$801$	−34.1431	+	24.8064i	−1.20639	+	0.876491i
$802$		0			0
$803$	−1.47651	+	4.54424i	−0.0521050	+	0.160363i
$804$		0			0
$805$	10.2592	+	31.5746i	0.361589	+	1.11286i
$806$		0			0
$807$	12.1219	+	8.80711i	0.426713	+	0.310025i
$808$		0			0
$809$	−11.1581	+	34.3412i	−0.392299	+	1.20737i	0.538746	+	0.842468i	$0.318898\pi$
$809$	−11.1581	+	34.3412i	−0.392299	+	1.20737i	−0.931045	+	0.364904i	$0.881102\pi$
$810$		0			0
$811$	−54.9794			−1.93059			−0.965294	−	0.261166i	$-0.915893\pi$
$811$	−54.9794			−1.93059			−0.965294	+	0.261166i	$0.915893\pi$
$812$		0			0
$813$	42.0931	−	30.5824i	1.47627	−	1.07257i
$814$		0			0
$815$	−5.79784	−	17.8439i	−0.203090	−	0.625046i
$816$		0			0
$817$	−41.9559			−1.46785
$818$		0			0
$819$	−18.5140			−0.646931
$820$		0			0
$821$	46.1644			1.61115			0.805574	−	0.592495i	$-0.201857\pi$
$821$	46.1644			1.61115			0.805574	+	0.592495i	$0.201857\pi$
$822$		0			0
$823$	−11.0634			−0.385644			−0.192822	−	0.981234i	$-0.561764\pi$
$823$	−11.0634			−0.385644			−0.192822	+	0.981234i	$0.561764\pi$
$824$		0			0
$825$	0.205527	+	0.632547i	0.00715553	+	0.0220225i
$826$		0			0
$827$	−34.0245	+	24.7202i	−1.18315	+	0.859606i	−0.992523	−	0.122057i	$-0.961051\pi$
$827$	−34.0245	+	24.7202i	−1.18315	+	0.859606i	−0.190623	+	0.981663i	$0.561051\pi$
$828$		0			0
$829$	−9.32571			−0.323895			−0.161948	−	0.986799i	$-0.551778\pi$
$829$	−9.32571			−0.323895			−0.161948	+	0.986799i	$0.551778\pi$
$830$		0			0
$831$	−9.76366	+	30.0495i	−0.338698	+	1.04240i
$832$		0			0
$833$	2.43543	+	1.76944i	0.0843827	+	0.0613076i
$834$		0			0
$835$	−0.210356	−	0.647410i	−0.00727967	−	0.0224045i
$836$		0			0
$837$	12.6605	−	38.9649i	0.437609	−	1.34682i
$838$		0			0
$839$	33.2372	−	24.1483i	1.14748	−	0.833691i	0.159334	−	0.987225i	$-0.449065\pi$
$839$	33.2372	−	24.1483i	1.14748	−	0.833691i	0.988143	+	0.153534i	$0.0490655\pi$
$840$		0			0
$841$	23.4538	−	17.0402i	0.808752	−	0.587592i
$842$		0			0
$843$	−2.42620	−	1.76273i	−0.0835626	−	0.0607118i
$844$		0			0
$845$	14.6028	−	10.6096i	0.502353	−	0.364981i
$846$		0			0
$847$	18.2153			0.625885
$848$		0			0
$849$	−2.91577	−	8.97382i	−0.100069	−	0.307981i
$850$		0			0
$851$	−15.8483	+	48.7762i	−0.543274	+	1.67202i
$852$		0			0
$853$	11.3524	−	34.9392i	0.388700	−	1.19630i	−0.545060	−	0.838397i	$-0.683493\pi$
$853$	11.3524	−	34.9392i	0.388700	−	1.19630i	0.933760	−	0.357899i	$-0.116507\pi$
$854$		0			0
$855$	−30.6531	−	22.2708i	−1.04832	−	0.761646i
$856$		0			0
$857$	5.27568	+	16.2369i	0.180214	+	0.554641i	0.999833	−	0.0182674i	$-0.00581503\pi$
$857$	5.27568	+	16.2369i	0.180214	+	0.554641i	−0.819619	+	0.572909i	$0.805815\pi$
$858$		0			0
$859$	29.8904	+	21.7167i	1.01985	+	0.740964i	0.966252	−	0.257599i	$-0.0829314\pi$
$859$	29.8904	+	21.7167i	1.01985	+	0.740964i	0.0535969	+	0.998563i	$0.482931\pi$
$860$		0			0
$861$	−14.2013	+	29.3536i	−0.483980	+	1.00037i
$862$		0			0
$863$	−7.56608	−	5.49708i	−0.257552	−	0.187123i	0.451515	−	0.892264i	$-0.350884\pi$
$863$	−7.56608	−	5.49708i	−0.257552	−	0.187123i	−0.709067	+	0.705141i	$0.750884\pi$
$864$		0			0
$865$	16.6752	+	51.3209i	0.566973	+	1.74496i
$866$		0			0
$867$	−36.3611	−	26.4179i	−1.23489	−	0.897198i
$868$		0			0
$869$	2.93031	−	9.01857i	0.0994040	−	0.305934i
$870$		0			0
$871$	6.78515	−	20.8826i	0.229906	−	0.707578i
$872$		0			0
$873$	−2.65007	−	8.15607i	−0.0896912	−	0.276041i
$874$		0			0
$875$	21.0856			0.712825
$876$		0			0
$877$	28.1185	−	20.4293i	0.949493	−	0.689847i	−0.00119378	−	0.999999i	$-0.500380\pi$
$877$	28.1185	−	20.4293i	0.949493	−	0.689847i	0.950687	+	0.310152i	$0.100380\pi$
$878$		0			0
$879$	69.7525	+	50.6782i	2.35269	+	1.70933i
$880$		0			0
$881$	−47.2611	+	34.3372i	−1.59227	+	1.15685i	−0.691652	+	0.722231i	$0.743117\pi$
$881$	−47.2611	+	34.3372i	−1.59227	+	1.15685i	−0.900614	+	0.434619i	$0.856883\pi$
$882$		0			0
$883$	−35.5033	+	25.7946i	−1.19478	+	0.868058i	−0.993761	−	0.111529i	$-0.964425\pi$
$883$	−35.5033	+	25.7946i	−1.19478	+	0.868058i	−0.201019	+	0.979587i	$0.564425\pi$
$884$		0			0
$885$	−25.5492	+	78.6323i	−0.858826	+	2.64319i
$886$		0			0
$887$	5.20221	+	16.0108i	0.174673	+	0.537589i	0.999618	−	0.0276238i	$-0.00879405\pi$
$887$	5.20221	+	16.0108i	0.174673	+	0.537589i	−0.824945	+	0.565213i	$0.808794\pi$
$888$		0			0
$889$	−18.5129	−	13.4504i	−0.620902	−	0.451112i
$890$		0			0
$891$	−0.528118	+	1.62538i	−0.0176926	+	0.0544523i
$892$		0			0
$893$	15.8480			0.530334
$894$		0			0
$895$	35.5311	−	25.8149i	1.18768	−	0.862897i
$896$		0			0
$897$	15.2659	+	46.9835i	0.509713	+	1.56873i
$898$		0			0
$899$	−0.902184			−0.0300895
$900$		0			0
$901$	8.28358			0.275966
$902$		0			0
$903$	−56.7478			−1.88845
$904$		0			0
$905$	−17.4061			−0.578600
$906$		0			0
$907$	−2.16069	−	6.64993i	−0.0717446	−	0.220807i	0.908754	−	0.417331i	$-0.137035\pi$
$907$	−2.16069	−	6.64993i	−0.0717446	−	0.220807i	−0.980499	+	0.196524i	$0.937035\pi$
$908$		0			0
$909$	52.7495	−	38.3247i	1.74959	−	1.27115i
$910$		0			0
$911$	−42.1437			−1.39628			−0.698141	−	0.715960i	$-0.745989\pi$
$911$	−42.1437			−1.39628			−0.698141	+	0.715960i	$0.745989\pi$
$912$		0			0
$913$	3.61718	−	11.1325i	0.119711	−	0.368433i
$914$		0			0
$915$	25.0503	+	18.2001i	0.828137	+	0.601677i
$916$		0			0
$917$	−5.66603	−	17.4383i	−0.187109	−	0.575862i
$918$		0			0
$919$	1.98295	−	6.10288i	0.0654114	−	0.201316i	−0.913009	−	0.407939i	$-0.866248\pi$
$919$	1.98295	−	6.10288i	0.0654114	−	0.201316i	0.978421	+	0.206624i	$0.0662475\pi$
$920$		0			0
$921$	63.9036	−	46.4287i	2.10570	−	1.52988i
$922$		0			0
$923$	0.296378	−	0.215332i	0.00975541	−	0.00708772i
$924$		0			0
$925$	1.14110	+	0.829056i	0.0375190	+	0.0272592i
$926$		0			0
$927$	50.6335	−	36.7874i	1.66302	−	1.20826i
$928$		0			0
$929$	33.5062			1.09930			0.549652	−	0.835394i	$-0.314760\pi$
$929$	33.5062			1.09930			0.549652	+	0.835394i	$0.314760\pi$
$930$		0			0
$931$	−4.17717	−	12.8560i	−0.136901	−	0.421338i
$932$		0			0
$933$	−8.03963	+	24.7434i	−0.263206	+	0.810064i
$934$		0			0
$935$	0.603280	−	1.85671i	0.0197294	−	0.0607208i
$936$		0			0
$937$	29.0852	+	21.1316i	0.950173	+	0.690341i	0.950848	−	0.309659i	$-0.100215\pi$
$937$	29.0852	+	21.1316i	0.950173	+	0.690341i	−0.000675062		1.00000i	$0.500215\pi$
$938$		0			0
$939$	16.1157	+	49.5989i	0.525915	+	1.61860i
$940$		0			0
$941$	−6.38628	−	4.63991i	−0.208187	−	0.151257i	0.478806	−	0.877921i	$-0.341070\pi$
$941$	−6.38628	−	4.63991i	−0.208187	−	0.151257i	−0.686993	+	0.726664i	$0.741070\pi$
$942$		0			0
$943$	52.2007	+	7.16712i	1.69989	+	0.233394i
$944$		0			0
$945$	−14.4552	−	10.5023i	−0.470229	−	0.341641i
$946$		0			0
$947$	−2.46635	−	7.59064i	−0.0801456	−	0.246663i	0.902953	−	0.429739i	$-0.141394\pi$
$947$	−2.46635	−	7.59064i	−0.0801456	−	0.246663i	−0.983099	+	0.183076i	$0.941394\pi$
$948$		0			0
$949$	7.89639	+	5.73706i	0.256328	+	0.186233i
$950$		0			0
$951$	−15.0062	+	46.1844i	−0.486610	+	1.49763i
$952$		0			0
$953$	−15.3331	+	47.1903i	−0.496687	+	1.52864i	0.317625	+	0.948216i	$0.397115\pi$
$953$	−15.3331	+	47.1903i	−0.496687	+	1.52864i	−0.814312	+	0.580428i	$0.802885\pi$
$954$		0			0
$955$	−4.18866	−	12.8914i	−0.135542	−	0.417155i
$956$		0			0
$957$	−0.286608			−0.00926471
$958$		0			0
$959$	−11.0391	+	8.02037i	−0.356471	+	0.258991i
$960$		0			0
$961$	−44.1577	−	32.0824i	−1.42444	−	1.03492i
$962$		0			0
$963$	−32.4760	+	23.5952i	−1.04652	+	0.760344i
$964$		0			0
$965$	−44.6527	+	32.4421i	−1.43742	+	1.04435i
$966$		0			0
$967$	−2.16933	+	6.67652i	−0.0697611	+	0.214702i	−0.979859	−	0.199691i	$-0.936006\pi$
$967$	−2.16933	+	6.67652i	−0.0697611	+	0.214702i	0.910098	+	0.414393i	$0.136006\pi$
$968$		0			0
$969$	−2.69053	−	8.28059i	−0.0864322	−	0.266011i
$970$		0			0
$971$	8.50757	+	6.18111i	0.273021	+	0.198361i	0.715868	−	0.698236i	$-0.246031\pi$
$971$	8.50757	+	6.18111i	0.273021	+	0.198361i	−0.442847	+	0.896597i	$0.646031\pi$
$972$		0			0
$973$	2.09122	−	6.43611i	0.0670414	−	0.206332i
$974$		0			0
$975$	1.35864			0.0435112
$976$		0			0
$977$	−9.02771	+	6.55902i	−0.288822	+	0.209842i	−0.722756	−	0.691103i	$-0.757125\pi$
$977$	−9.02771	+	6.55902i	−0.288822	+	0.209842i	0.433934	+	0.900945i	$0.357125\pi$
$978$		0			0
$979$	3.01737	+	9.28650i	0.0964355	+	0.296798i
$980$		0			0
$981$	−63.5815			−2.03000
$982$		0			0
$983$	24.1526			0.770350			0.385175	−	0.922844i	$-0.374141\pi$
$983$	24.1526			0.770350			0.385175	+	0.922844i	$0.374141\pi$
$984$		0			0
$985$	25.1479			0.801279
$986$		0			0
$987$	21.4354			0.682297
$988$		0			0
$989$	28.3356	+	87.2081i	0.901021	+	2.77306i
$990$		0			0
$991$	−7.96177	+	5.78456i	−0.252914	+	0.183753i	−0.707017	−	0.707196i	$-0.749960\pi$
$991$	−7.96177	+	5.78456i	−0.252914	+	0.183753i	0.454103	+	0.890949i	$0.349960\pi$
$992$		0			0
$993$	80.2247			2.54586
$994$		0			0
$995$	0.431769	−	1.32885i	0.0136880	−	0.0421273i
$996$		0			0
$997$	22.4707	+	16.3259i	0.711654	+	0.517047i	0.883707	−	0.468041i	$-0.155040\pi$
$997$	22.4707	+	16.3259i	0.711654	+	0.517047i	−0.172053	+	0.985088i	$0.555040\pi$
$998$		0			0
$999$	−8.52943	−	26.2509i	−0.269859	−	0.830541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.625.1		20
4.3	odd	2		328.2.m.c.297.5	yes	20
41.37	even	5	inner	656.2.u.h.529.1		20
164.119	odd	10		328.2.m.c.201.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.201.5	✓	20	164.119	odd	10
328.2.m.c.297.5	yes	20	4.3	odd	2
656.2.u.h.529.1		20	41.37	even	5	inner
656.2.u.h.625.1		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q-2.75787 q^{3} +(0.675164 + 2.07794i) q^{5} +(1.49390 - 1.08538i) q^{7} +4.60584 q^{9} +O(q^{10})\)	\(q-2.75787 q^{3} +(0.675164 + 2.07794i) q^{5} +(1.49390 - 1.08538i) q^{7} +4.60584 q^{9} +(0.329300 - 1.01348i) q^{11} +(-1.76110 - 1.27951i) q^{13} +(-1.86201 - 5.73069i) q^{15} +(0.259109 - 0.797455i) q^{17} +(-3.04606 + 2.21310i) q^{19} +(-4.11999 + 2.99335i) q^{21} +(6.65728 + 4.83680i) q^{23} +(0.183088 - 0.133022i) q^{25} -4.42870 q^{27} +(0.0301361 + 0.0927493i) q^{29} +(-2.85873 + 8.79827i) q^{31} +(-0.908167 + 2.79505i) q^{33} +(3.26399 + 2.37143i) q^{35} +(1.92595 + 5.92745i) q^{37} +(4.85688 + 3.52873i) q^{39} +(5.64403 - 3.02405i) q^{41} +(9.01506 + 6.54983i) q^{43} +(3.10970 + 9.57067i) q^{45} +(-3.40527 - 2.47407i) q^{47} +(-1.10943 + 3.41448i) q^{49} +(-0.714588 + 2.19928i) q^{51} +(3.05281 + 9.39560i) q^{53} +2.32829 q^{55} +(8.40065 - 6.10343i) q^{57} +(-11.1007 - 8.06515i) q^{59} +(-4.15731 + 3.02046i) q^{61} +(6.88068 - 4.99910i) q^{63} +(1.46972 - 4.52334i) q^{65} +(3.11698 + 9.59307i) q^{67} +(-18.3599 - 13.3393i) q^{69} +(-0.0520050 + 0.160055i) q^{71} -4.48379 q^{73} +(-0.504934 + 0.366856i) q^{75} +(-0.608074 - 1.87146i) q^{77} +8.89860 q^{79} -1.60376 q^{81} +10.9844 q^{83} +1.83201 q^{85} +(-0.0831113 - 0.255790i) q^{87} +(-7.41300 + 5.38586i) q^{89} -4.01967 q^{91} +(7.88401 - 24.2645i) q^{93} +(-6.65528 - 4.83534i) q^{95} +(-0.575371 - 1.77081i) q^{97} +(1.51670 - 4.66794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more