LMFDB - Embedded newform 1260.2.q.d.781.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(121,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1260.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			781.2
Character	$\chi$	$=$	1260.781
Dual form			1260.2.q.d.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68198 - 0.413434i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +(2.65814 + 1.39078i) q^{9} +O(q^{10})$	\(q+(-1.68198 - 0.413434i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +(2.65814 + 1.39078i) q^{9} +(-1.44197 - 2.49756i) q^{11} +(0.0827654 + 0.143354i) q^{13} +(1.19904 - 1.24992i) q^{15} +(-0.347478 + 0.601849i) q^{17} +(2.26911 + 3.93021i) q^{19} +(1.09045 - 4.45095i) q^{21} +(-2.15543 + 3.73332i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.89596 - 3.43824i) q^{27} +(3.34476 - 5.79329i) q^{29} -4.57479 q^{31} +(1.39279 + 4.79702i) q^{33} +(-2.29230 - 1.32113i) q^{35} +(0.244258 + 0.423067i) q^{37} +(-0.0799427 - 0.275337i) q^{39} +(-1.99120 - 3.44886i) q^{41} +(-0.488017 + 0.845269i) q^{43} +(-2.53352 + 1.60663i) q^{45} -6.71021 q^{47} +(-6.99999 + 0.0106868i) q^{49} +(0.833277 - 0.868641i) q^{51} +(-0.0191298 + 0.0331338i) q^{53} +2.88394 q^{55} +(-2.19172 - 7.54869i) q^{57} -1.44083 q^{59} -6.57738 q^{61} +(-3.67429 + 7.03560i) q^{63} -0.165531 q^{65} -5.56263 q^{67} +(5.16888 - 5.38825i) q^{69} -8.73689 q^{71} +(-3.12050 + 5.40487i) q^{73} +(0.482948 + 1.66336i) q^{75} +(6.60502 - 3.82013i) q^{77} -9.89693 q^{79} +(5.13146 + 7.39379i) q^{81} +(-4.42924 + 7.67166i) q^{83} +(-0.347478 - 0.601849i) q^{85} +(-8.02098 + 8.36139i) q^{87} +(-1.93095 - 3.34450i) q^{89} +(-0.379111 + 0.219266i) q^{91} +(7.69473 + 1.89138i) q^{93} -4.53822 q^{95} +(-7.94934 + 13.7687i) q^{97} +(-0.359400 - 8.64434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 4 q^{3} - 13 q^{5} - 6 q^{7}+O(q^{10}) $ 26 * q - 4 * q^3 - 13 * q^5 - 6 * q^7	$ 26 q - 4 q^{3} - 13 q^{5} - 6 q^{7} + q^{11} + 7 q^{13} - q^{15} + 8 q^{17} - 9 q^{19} - 8 q^{21} - 3 q^{23} - 13 q^{25} - 7 q^{27} - 7 q^{29} + 2 q^{31} - 7 q^{33} + 3 q^{35} + 10 q^{37} + 16 q^{39} + 13 q^{41} - 8 q^{43} - 3 q^{45} - 12 q^{47} - 28 q^{49} + 17 q^{53} - 2 q^{55} - 16 q^{57} + 16 q^{59} - 20 q^{61} - 16 q^{63} - 14 q^{65} - 48 q^{67} + 54 q^{69} + 4 q^{71} - 17 q^{73} + 5 q^{75} + 19 q^{77} - 38 q^{79} + 12 q^{81} + 9 q^{83} + 8 q^{85} - 28 q^{87} + q^{89} - 2 q^{91} - 40 q^{93} + 18 q^{95} + 9 q^{97} + 33 q^{99}+O(q^{100}) $ 26 * q - 4 * q^3 - 13 * q^5 - 6 * q^7 + q^11 + 7 * q^13 - q^15 + 8 * q^17 - 9 * q^19 - 8 * q^21 - 3 * q^23 - 13 * q^25 - 7 * q^27 - 7 * q^29 + 2 * q^31 - 7 * q^33 + 3 * q^35 + 10 * q^37 + 16 * q^39 + 13 * q^41 - 8 * q^43 - 3 * q^45 - 12 * q^47 - 28 * q^49 + 17 * q^53 - 2 * q^55 - 16 * q^57 + 16 * q^59 - 20 * q^61 - 16 * q^63 - 14 * q^65 - 48 * q^67 + 54 * q^69 + 4 * q^71 - 17 * q^73 + 5 * q^75 + 19 * q^77 - 38 * q^79 + 12 * q^81 + 9 * q^83 + 8 * q^85 - 28 * q^87 + q^89 - 2 * q^91 - 40 * q^93 + 18 * q^95 + 9 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.68198	−	0.413434i	−0.971094	−	0.238696i
$3$	−1.68198	−	0.413434i	−0.971094	−	0.238696i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.00201961	+	2.64575i	0.000763342	+	1.00000i
$7$	0.00201961	+	2.64575i	0.000763342	+	1.00000i
$8$		0			0
$9$	2.65814	+	1.39078i	0.886048	+	0.463593i
$10$		0			0
$11$	−1.44197	−	2.49756i	−0.434770	−	0.753043i	0.562507	−	0.826793i	$-0.309837\pi$
$11$	−1.44197	−	2.49756i	−0.434770	−	0.753043i	−0.997277	+	0.0737491i	$0.976504\pi$
$12$		0			0
$13$	0.0827654	+	0.143354i	0.0229550	+	0.0397592i	0.877275	−	0.479989i	$-0.159359\pi$
$13$	0.0827654	+	0.143354i	0.0229550	+	0.0397592i	−0.854320	+	0.519748i	$0.826026\pi$
$14$		0			0
$15$	1.19904	−	1.24992i	0.309590	−	0.322729i
$16$		0			0
$17$	−0.347478	+	0.601849i	−0.0842757	+	0.145970i	−0.905082	−	0.425236i	$-0.860191\pi$
$17$	−0.347478	+	0.601849i	−0.0842757	+	0.145970i	0.820807	+	0.571206i	$0.193524\pi$
$18$		0			0
$19$	2.26911	+	3.93021i	0.520570	+	0.901653i	0.999714	+	0.0239169i	$0.00761372\pi$
$19$	2.26911	+	3.93021i	0.520570	+	0.901653i	−0.479144	+	0.877736i	$0.659053\pi$
$20$		0			0
$21$	1.09045	−	4.45095i	0.237955	−	0.971276i
$22$		0			0
$23$	−2.15543	+	3.73332i	−0.449439	+	0.778450i	−0.998350	−	0.0574305i	$-0.981709\pi$
$23$	−2.15543	+	3.73332i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−3.89596	−	3.43824i	−0.749778	−	0.661689i
$28$		0			0
$29$	3.34476	−	5.79329i	0.621106	−	1.07579i	−0.368174	−	0.929757i	$-0.620017\pi$
$29$	3.34476	−	5.79329i	0.621106	−	1.07579i	0.989280	−	0.146031i	$-0.0466498\pi$
$30$		0			0
$31$	−4.57479			−0.821657			−0.410829	−	0.911713i	$-0.634761\pi$
$31$	−4.57479			−0.821657			−0.410829	+	0.911713i	$0.634761\pi$
$32$		0			0
$33$	1.39279	+	4.79702i	0.242454	+	0.835054i
$34$		0			0
$35$	−2.29230	−	1.32113i	−0.387469	−	0.223311i
$36$		0			0
$37$	0.244258	+	0.423067i	0.0401557	+	0.0695518i	0.885405	−	0.464821i	$-0.153881\pi$
$37$	0.244258	+	0.423067i	0.0401557	+	0.0695518i	−0.845249	+	0.534373i	$0.820548\pi$
$38$		0			0
$39$	−0.0799427	−	0.275337i	−0.0128011	−	0.0440892i
$40$		0			0
$41$	−1.99120	−	3.44886i	−0.310974	−	0.538622i	0.667600	−	0.744520i	$-0.267322\pi$
$41$	−1.99120	−	3.44886i	−0.310974	−	0.538622i	−0.978573	+	0.205898i	$0.933988\pi$
$42$		0			0
$43$	−0.488017	+	0.845269i	−0.0744218	+	0.128902i	−0.900835	−	0.434162i	$-0.857044\pi$
$43$	−0.488017	+	0.845269i	−0.0744218	+	0.128902i	0.826413	+	0.563065i	$0.190378\pi$
$44$		0			0
$45$	−2.53352	+	1.60663i	−0.377675	+	0.239502i
$46$		0			0
$47$	−6.71021			−0.978785			−0.489392	−	0.872064i	$-0.662781\pi$
$47$	−6.71021			−0.978785			−0.489392	+	0.872064i	$0.662781\pi$
$48$		0			0
$49$	−6.99999	+	0.0106868i	−0.999999	+	0.00152668i
$50$		0			0
$51$	0.833277	−	0.868641i	0.116682	−	0.121634i
$52$		0			0
$53$	−0.0191298	+	0.0331338i	−0.00262768	+	0.00455127i	−0.867336	−	0.497723i	$-0.834170\pi$
$53$	−0.0191298	+	0.0331338i	−0.00262768	+	0.00455127i	0.864709	+	0.502274i	$0.167503\pi$
$54$		0			0
$55$	2.88394			0.388870
$56$		0			0
$57$	−2.19172	−	7.54869i	−0.290301	−	0.999848i
$58$		0			0
$59$	−1.44083			−0.187580			−0.0937898	−	0.995592i	$-0.529898\pi$
$59$	−1.44083			−0.187580			−0.0937898	+	0.995592i	$0.529898\pi$
$60$		0			0
$61$	−6.57738			−0.842147			−0.421074	−	0.907026i	$-0.638347\pi$
$61$	−6.57738			−0.842147			−0.421074	+	0.907026i	$0.638347\pi$
$62$		0			0
$63$	−3.67429	+	7.03560i	−0.462917	+	0.886402i
$64$		0			0
$65$	−0.165531			−0.0205316
$66$		0			0
$67$	−5.56263			−0.679584			−0.339792	−	0.940501i	$-0.610357\pi$
$67$	−5.56263			−0.679584			−0.339792	+	0.940501i	$0.610357\pi$
$68$		0			0
$69$	5.16888	−	5.38825i	0.622260	−	0.648669i
$70$		0			0
$71$	−8.73689			−1.03688			−0.518439	−	0.855115i	$-0.673487\pi$
$71$	−8.73689			−1.03688			−0.518439	+	0.855115i	$0.673487\pi$
$72$		0			0
$73$	−3.12050	+	5.40487i	−0.365227	+	0.632592i	−0.988813	−	0.149163i	$-0.952342\pi$
$73$	−3.12050	+	5.40487i	−0.365227	+	0.632592i	0.623586	+	0.781755i	$0.285675\pi$
$74$		0			0
$75$	0.482948	+	1.66336i	0.0557660	+	0.192068i
$76$		0			0
$77$	6.60502	−	3.82013i	0.752711	−	0.435345i
$78$		0			0
$79$	−9.89693			−1.11349			−0.556746	−	0.830683i	$-0.687950\pi$
$79$	−9.89693			−1.11349			−0.556746	+	0.830683i	$0.687950\pi$
$80$		0			0
$81$	5.13146	+	7.39379i	0.570162	+	0.821532i
$82$		0			0
$83$	−4.42924	+	7.67166i	−0.486172	+	0.842074i	−0.999874	−	0.0158946i	$-0.994940\pi$
$83$	−4.42924	+	7.67166i	−0.486172	+	0.842074i	0.513702	+	0.857969i	$0.328274\pi$
$84$		0			0
$85$	−0.347478	−	0.601849i	−0.0376892	−	0.0652797i
$86$		0			0
$87$	−8.02098	+	8.36139i	−0.859939	+	0.896435i
$88$		0			0
$89$	−1.93095	−	3.34450i	−0.204680	−	0.354516i	0.745351	−	0.666673i	$-0.232282\pi$
$89$	−1.93095	−	3.34450i	−0.204680	−	0.354516i	−0.950031	+	0.312156i	$0.898949\pi$
$90$		0			0
$91$	−0.379111	+	0.219266i	−0.0397417	+	0.0229853i
$92$		0			0
$93$	7.69473	+	1.89138i	0.797907	+	0.196127i
$94$		0			0
$95$	−4.53822			−0.465612
$96$		0			0
$97$	−7.94934	+	13.7687i	−0.807133	+	1.39800i	0.107708	+	0.994183i	$0.465649\pi$
$97$	−7.94934	+	13.7687i	−0.807133	+	1.39800i	−0.914841	+	0.403813i	$0.867685\pi$
$98$		0			0
$99$	−0.359400	−	8.64434i	−0.0361210	−	0.868789i
$100$		0			0
$101$	7.47817	+	12.9526i	0.744106	+	1.28883i	0.950611	+	0.310384i	$0.100458\pi$
$101$	7.47817	+	12.9526i	0.744106	+	1.28883i	−0.206505	+	0.978446i	$0.566209\pi$
$102$		0			0
$103$	−9.89472	+	17.1382i	−0.974955	+	1.68867i	−0.294873	+	0.955536i	$0.595277\pi$
$103$	−9.89472	+	17.1382i	−0.974955	+	1.68867i	−0.680082	+	0.733136i	$0.738056\pi$
$104$		0			0
$105$	3.30941	+	3.16983i	0.322965	+	0.309344i
$106$		0			0
$107$	−6.70336	−	11.6106i	−0.648038	−	1.12244i	−0.983591	−	0.180414i	$-0.942256\pi$
$107$	−6.70336	−	11.6106i	−0.648038	−	1.12244i	0.335552	−	0.942022i	$-0.391077\pi$
$108$		0			0
$109$	−2.49944	+	4.32916i	−0.239403	+	0.414659i	−0.960543	−	0.278131i	$-0.910285\pi$
$109$	−2.49944	+	4.32916i	−0.239403	+	0.414659i	0.721140	+	0.692789i	$0.243618\pi$
$110$		0			0
$111$	−0.235927	−	0.812576i	−0.0223932	−	0.0771263i
$112$		0			0
$113$	−2.49094	−	4.31444i	−0.234328	−	0.405868i	0.724749	−	0.689013i	$-0.241956\pi$
$113$	−2.49094	−	4.31444i	−0.234328	−	0.405868i	−0.959077	+	0.283145i	$0.908622\pi$
$114$		0			0
$115$	−2.15543	−	3.73332i	−0.200995	−	0.348134i
$116$		0			0
$117$	0.0206287	+	0.496164i	0.00190712	+	0.0458703i
$118$		0			0
$119$	−1.59304	−	0.918124i	−0.146034	−	0.0841643i
$120$		0			0
$121$	1.34145	−	2.32347i	0.121950	−	0.211224i
$122$		0			0
$123$	1.92329	+	6.62417i	0.173417	+	0.597281i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	20.5850			1.82663			0.913314	−	0.407257i	$-0.133514\pi$
$127$	20.5850			1.82663			0.913314	+	0.407257i	$0.133514\pi$
$128$		0			0
$129$	1.17030	−	1.21997i	0.103039	−	0.107412i
$130$		0			0
$131$	4.20673	−	7.28627i	0.367544	−	0.636604i	−0.621637	−	0.783305i	$-0.713532\pi$
$131$	4.20673	−	7.28627i	0.367544	−	0.636604i	0.989181	+	0.146701i	$0.0468656\pi$
$132$		0			0
$133$	−10.3938	+	6.01144i	−0.901255	+	0.521258i
$134$		0			0
$135$	4.92558	−	1.65488i	0.423927	−	0.142430i
$136$		0			0
$137$	−5.45388	−	9.44640i	−0.465957	−	0.807060i	0.533288	−	0.845934i	$-0.320956\pi$
$137$	−5.45388	−	9.44640i	−0.465957	−	0.807060i	−0.999244	+	0.0388736i	$0.987623\pi$
$138$		0			0
$139$	−6.94693	−	12.0324i	−0.589231	−	1.02058i	−0.994333	−	0.106307i	$-0.966097\pi$
$139$	−6.94693	−	12.0324i	−0.589231	−	1.02058i	0.405102	−	0.914271i	$-0.367236\pi$
$140$		0			0
$141$	11.2865	+	2.77423i	0.950492	+	0.233632i
$142$		0			0
$143$	0.238690	−	0.413423i	0.0199603	−	0.0345722i
$144$		0			0
$145$	3.34476	+	5.79329i	0.277767	+	0.481107i
$146$		0			0
$147$	11.7783	+	2.87606i	0.971458	+	0.237214i
$148$		0			0
$149$	10.5183	−	18.2182i	0.861692	−	1.49250i	−0.00860180	−	0.999963i	$-0.502738\pi$
$149$	10.5183	−	18.2182i	0.861692	−	1.49250i	0.870294	−	0.492532i	$-0.163929\pi$
$150$		0			0
$151$	−6.07087	−	10.5151i	−0.494041	−	0.855703i	0.505936	−	0.862571i	$-0.331147\pi$
$151$	−6.07087	−	10.5151i	−0.494041	−	0.855703i	−0.999976	+	0.00686769i	$0.997814\pi$
$152$		0			0
$153$	−1.76069	+	1.11654i	−0.142343	+	0.0902666i
$154$		0			0
$155$	2.28740	−	3.96189i	0.183728	−	0.318226i
$156$		0			0
$157$	13.1153			1.04671			0.523356	−	0.852114i	$-0.324680\pi$
$157$	13.1153			1.04671			0.523356	+	0.852114i	$0.324680\pi$
$158$		0			0
$159$	0.0458747	−	0.0478216i	0.00363810	−	0.00379250i
$160$		0			0
$161$	−9.88178	−	5.69519i	−0.778793	−	0.448844i
$162$		0			0
$163$	3.34865	+	5.80003i	0.262287	+	0.454294i	0.966849	−	0.255348i	$-0.0821901\pi$
$163$	3.34865	+	5.80003i	0.262287	+	0.454294i	−0.704563	+	0.709642i	$0.748857\pi$
$164$		0			0
$165$	−4.85074	−	1.19232i	−0.377629	−	0.0928219i
$166$		0			0
$167$	0.0544085	+	0.0942383i	0.00421026	+	0.00729238i	0.868123	−	0.496349i	$-0.165326\pi$
$167$	0.0544085	+	0.0942383i	0.00421026	+	0.00729238i	−0.863913	+	0.503642i	$0.831993\pi$
$168$		0			0
$169$	6.48630	−	11.2346i	0.498946	−	0.864200i
$170$		0			0
$171$	0.565559	+	13.6029i	0.0432494	+	1.04024i
$172$		0			0
$173$	−5.67343			−0.431343			−0.215672	−	0.976466i	$-0.569194\pi$
$173$	−5.67343			−0.431343			−0.215672	+	0.976466i	$0.569194\pi$
$174$		0			0
$175$	2.29028	−	1.32462i	0.173129	−	0.100132i
$176$		0			0
$177$	2.42345	+	0.595687i	0.182158	+	0.0447746i
$178$		0			0
$179$	0.646477	−	1.11973i	0.0483199	−	0.0836926i	−0.840854	−	0.541262i	$-0.817947\pi$
$179$	0.646477	−	1.11973i	0.0483199	−	0.0836926i	0.889174	+	0.457570i	$0.151280\pi$
$180$		0			0
$181$	4.96075			0.368730			0.184365	−	0.982858i	$-0.440977\pi$
$181$	4.96075			0.368730			0.184365	+	0.982858i	$0.440977\pi$
$182$		0			0
$183$	11.0631	+	2.71931i	0.817804	+	0.201017i
$184$		0			0
$185$	−0.488515			−0.0359164
$186$		0			0
$187$	2.00421			0.146562
$188$		0			0
$189$	9.08885	−	10.3147i	0.661117	−	0.750283i
$190$		0			0
$191$	−22.1668			−1.60393			−0.801966	−	0.597370i	$-0.796212\pi$
$191$	−22.1668			−1.60393			−0.801966	+	0.597370i	$0.796212\pi$
$192$		0			0
$193$	−9.41474			−0.677688			−0.338844	−	0.940843i	$-0.610036\pi$
$193$	−9.41474			−0.677688			−0.338844	+	0.940843i	$0.610036\pi$
$194$		0			0
$195$	0.278420	+	0.0684361i	0.0199381	+	0.00490081i
$196$		0			0
$197$	14.4486			1.02942			0.514710	−	0.857364i	$-0.327900\pi$
$197$	14.4486			1.02942			0.514710	+	0.857364i	$0.327900\pi$
$198$		0			0
$199$	6.58651	−	11.4082i	0.466905	−	0.808704i	−0.532380	−	0.846506i	$-0.678702\pi$
$199$	6.58651	−	11.4082i	0.466905	−	0.808704i	0.999285	+	0.0378018i	$0.0120355\pi$
$200$		0			0
$201$	9.35626	+	2.29978i	0.659940	+	0.162214i
$202$		0			0
$203$	15.3344	+	8.83770i	1.07626	+	0.620285i
$204$		0			0
$205$	3.98240			0.278143
$206$		0			0
$207$	−10.9217	+	6.92596i	−0.759109	+	0.481388i
$208$		0			0
$209$	6.54397	−	11.3345i	0.452656	−	0.784023i
$210$		0			0
$211$	5.09767	+	8.82942i	0.350938	+	0.607842i	0.986414	−	0.164278i	$-0.0525294\pi$
$211$	5.09767	+	8.82942i	0.350938	+	0.607842i	−0.635476	+	0.772121i	$0.719196\pi$
$212$		0			0
$213$	14.6953	+	3.61213i	1.00691	+	0.247499i
$214$		0			0
$215$	−0.488017	−	0.845269i	−0.0332825	−	0.0576469i
$216$		0			0
$217$	−0.00923931	−	12.1038i	−0.000627205	−	0.821657i
$218$		0			0
$219$	7.48319	−	7.80078i	0.505667	−	0.527128i
$220$		0			0
$221$	−0.115036			−0.00773819
$222$		0			0
$223$	−11.3620	+	19.6795i	−0.760855	+	1.31784i	0.181555	+	0.983381i	$0.441887\pi$
$223$	−11.3620	+	19.6795i	−0.760855	+	1.31784i	−0.942410	+	0.334459i	$0.891446\pi$
$224$		0			0
$225$	−0.124621	−	2.99741i	−0.00830808	−	0.199827i
$226$		0			0
$227$	−6.19323	−	10.7270i	−0.411059	−	0.711975i	0.583947	−	0.811792i	$-0.301508\pi$
$227$	−6.19323	−	10.7270i	−0.411059	−	0.711975i	−0.995006	+	0.0998167i	$0.968174\pi$
$228$		0			0
$229$	−5.05512	+	8.75572i	−0.334052	+	0.578594i	−0.983302	−	0.181980i	$-0.941749\pi$
$229$	−5.05512	+	8.75572i	−0.334052	+	0.578594i	0.649251	+	0.760575i	$0.275083\pi$
$230$		0			0
$231$	−12.6889	+	3.69467i	−0.834869	+	0.243091i
$232$		0			0
$233$	−11.6322	−	20.1476i	−0.762051	−	1.31991i	−0.941792	−	0.336197i	$-0.890859\pi$
$233$	−11.6322	−	20.1476i	−0.762051	−	1.31991i	0.179741	−	0.983714i	$-0.442474\pi$
$234$		0			0
$235$	3.35510	−	5.81121i	0.218863	−	0.379082i
$236$		0			0
$237$	16.6465	+	4.09173i	1.08131	+	0.265786i
$238$		0			0
$239$	8.25795	+	14.3032i	0.534163	+	0.925197i	0.999203	+	0.0399074i	$0.0127063\pi$
$239$	8.25795	+	14.3032i	0.534163	+	0.925197i	−0.465041	+	0.885289i	$0.653960\pi$
$240$		0			0
$241$	6.37240	+	11.0373i	0.410483	+	0.710977i	0.994943	−	0.100446i	$-0.0320269\pi$
$241$	6.37240	+	11.0373i	0.410483	+	0.710977i	−0.584460	+	0.811423i	$0.698694\pi$
$242$		0			0
$243$	−5.57419	−	14.5578i	−0.357585	−	0.933881i
$244$		0			0
$245$	3.49074	−	6.06751i	0.223015	−	0.387639i
$246$		0			0
$247$	−0.375608	+	0.650571i	−0.0238993	+	0.0413949i
$248$		0			0
$249$	10.6216	−	11.0724i	0.673119	−	0.701686i
$250$		0			0
$251$	−1.88421			−0.118930			−0.0594652	−	0.998230i	$-0.518940\pi$
$251$	−1.88421			−0.118930			−0.0594652	+	0.998230i	$0.518940\pi$
$252$		0			0
$253$	12.4323			0.781609
$254$		0			0
$255$	0.335627	+	1.15596i	0.0210178	+	0.0723890i
$256$		0			0
$257$	7.36431	−	12.7554i	0.459373	−	0.795658i	−0.539555	−	0.841950i	$-0.681407\pi$
$257$	7.36431	−	12.7554i	0.459373	−	0.795658i	0.998928	+	0.0462929i	$0.0147408\pi$
$258$		0			0
$259$	−1.11884	+	0.647099i	−0.0695211	+	0.0402088i
$260$		0			0
$261$	16.9481	−	10.7476i	1.04906	−	0.665259i
$262$		0			0
$263$	14.0652	+	24.3617i	0.867300	+	1.50221i	0.864746	+	0.502210i	$0.167480\pi$
$263$	14.0652	+	24.3617i	0.867300	+	1.50221i	0.00255386	+	0.999997i	$0.499187\pi$
$264$		0			0
$265$	−0.0191298	−	0.0331338i	−0.00117513	−	0.00203539i
$266$		0			0
$267$	1.86509	+	6.42372i	0.114142	+	0.393125i
$268$		0			0
$269$	−8.71758	+	15.0993i	−0.531520	+	0.920620i	0.467803	+	0.883833i	$0.345046\pi$
$269$	−8.71758	+	15.0993i	−0.531520	+	0.920620i	−0.999323	+	0.0367875i	$0.988288\pi$
$270$		0			0
$271$	3.00147	+	5.19869i	0.182326	+	0.315798i	0.942672	−	0.333720i	$-0.108304\pi$
$271$	3.00147	+	5.19869i	0.182326	+	0.315798i	−0.760346	+	0.649518i	$0.774971\pi$
$272$		0			0
$273$	0.728312	−	0.212065i	0.0440794	−	0.0128347i
$274$		0			0
$275$	−1.44197	+	2.49756i	−0.0869540	+	0.150609i
$276$		0			0
$277$	15.3749	+	26.6302i	0.923791	+	1.60005i	0.793494	+	0.608578i	$0.208260\pi$
$277$	15.3749	+	26.6302i	0.923791	+	1.60005i	0.130296	+	0.991475i	$0.458407\pi$
$278$		0			0
$279$	−12.1605	−	6.36253i	−0.728028	−	0.380915i
$280$		0			0
$281$	−1.70731	+	2.95714i	−0.101849	+	0.176408i	−0.912447	−	0.409196i	$-0.865809\pi$
$281$	−1.70731	+	2.95714i	−0.101849	+	0.176408i	0.810597	+	0.585604i	$0.199143\pi$
$282$		0			0
$283$	10.6453			0.632800			0.316400	−	0.948626i	$-0.397526\pi$
$283$	10.6453			0.632800			0.316400	+	0.948626i	$0.397526\pi$
$284$		0			0
$285$	7.63322	+	1.87626i	0.452153	+	0.111140i
$286$		0			0
$287$	9.12081	−	5.27519i	0.538384	−	0.311385i
$288$		0			0
$289$	8.25852	+	14.3042i	0.485795	+	0.841422i
$290$		0			0
$291$	19.0631	−	19.8721i	1.11750	−	1.16493i
$292$		0			0
$293$	−5.81360	−	10.0694i	−0.339634	−	0.588263i	0.644730	−	0.764411i	$-0.276970\pi$
$293$	−5.81360	−	10.0694i	−0.339634	−	0.588263i	−0.984364	+	0.176147i	$0.943637\pi$
$294$		0			0
$295$	0.720413	−	1.24779i	0.0419441	−	0.0726493i
$296$		0			0
$297$	−2.96936	+	14.6882i	−0.172300	+	0.852298i
$298$		0			0
$299$	−0.713580			−0.0412674
$300$		0			0
$301$	−2.23736	−	1.28946i	−0.128959	−	0.0743234i
$302$		0			0
$303$	−7.22313	−	24.8778i	−0.414958	−	1.42919i
$304$		0			0
$305$	3.28869	−	5.69618i	0.188310	−	0.326162i
$306$		0			0
$307$	−12.6798			−0.723674			−0.361837	−	0.932241i	$-0.617850\pi$
$307$	−12.6798			−0.723674			−0.361837	+	0.932241i	$0.617850\pi$
$308$		0			0
$309$	23.7283	−	24.7353i	1.34985	−	1.40714i
$310$		0			0
$311$	19.5976			1.11128			0.555639	−	0.831423i	$-0.312474\pi$
$311$	19.5976			1.11128			0.555639	+	0.831423i	$0.312474\pi$
$312$		0			0
$313$	−4.69075			−0.265137			−0.132568	−	0.991174i	$-0.542322\pi$
$313$	−4.69075			−0.265137			−0.132568	+	0.991174i	$0.542322\pi$
$314$		0			0
$315$	−4.25586	−	6.69983i	−0.239791	−	0.377492i
$316$		0			0
$317$	−26.6638			−1.49759			−0.748794	−	0.662803i	$-0.769367\pi$
$317$	−26.6638			−1.49759			−0.748794	+	0.662803i	$0.769367\pi$
$318$		0			0
$319$	−19.2922			−1.08015
$320$		0			0
$321$	6.47475	+	22.3002i	0.361385	+	1.24467i
$322$		0			0
$323$	−3.15386			−0.175485
$324$		0			0
$325$	0.0827654	−	0.143354i	0.00459100	−	0.00795184i
$326$		0			0
$327$	5.99385	−	6.24823i	0.331461	−	0.345528i
$328$		0			0
$329$	−0.0135520	−	17.7535i	−0.000747147	−	0.978784i
$330$		0			0
$331$	−9.90029			−0.544169			−0.272085	−	0.962273i	$-0.587713\pi$
$331$	−9.90029			−0.544169			−0.272085	+	0.962273i	$0.587713\pi$
$332$		0			0
$333$	0.0608794	+	1.46428i	0.00333617	+	0.0802421i
$334$		0			0
$335$	2.78132	−	4.81738i	0.151960	−	0.263202i
$336$		0			0
$337$	5.76153	+	9.97926i	0.313850	+	0.543605i	0.979192	−	0.202934i	$-0.0650476\pi$
$337$	5.76153	+	9.97926i	0.313850	+	0.543605i	−0.665342	+	0.746539i	$0.731714\pi$
$338$		0			0
$339$	2.40599	+	8.28666i	0.130675	+	0.450069i
$340$		0			0
$341$	6.59671	+	11.4258i	0.357232	+	0.618744i
$342$		0			0
$343$	−0.0424118	−	18.5202i	−0.00229002	−	0.999997i
$344$		0			0
$345$	2.08192	+	7.17051i	0.112087	+	0.386047i
$346$		0			0
$347$	−8.17679			−0.438953			−0.219477	−	0.975618i	$-0.570435\pi$
$347$	−8.17679			−0.438953			−0.219477	+	0.975618i	$0.570435\pi$
$348$		0			0
$349$	7.11114	−	12.3169i	0.380651	−	0.659306i	−0.610505	−	0.792013i	$-0.709033\pi$
$349$	7.11114	−	12.3169i	0.380651	−	0.659306i	0.991155	+	0.132706i	$0.0423667\pi$
$350$		0			0
$351$	0.170434	−	0.843068i	0.00909709	−	0.0449997i
$352$		0			0
$353$	14.9193	+	25.8409i	0.794072	+	1.37537i	0.923427	+	0.383775i	$0.125376\pi$
$353$	14.9193	+	25.8409i	0.794072	+	1.37537i	−0.129354	+	0.991598i	$0.541290\pi$
$354$		0			0
$355$	4.36844	−	7.56637i	0.231853	−	0.401581i
$356$		0			0
$357$	2.29989	+	2.20289i	0.121723	+	0.116589i
$358$		0			0
$359$	−2.24605	−	3.89027i	−0.118542	−	0.205320i	0.800648	−	0.599135i	$-0.204489\pi$
$359$	−2.24605	−	3.89027i	−0.118542	−	0.205320i	−0.919190	+	0.393814i	$0.871155\pi$
$360$		0			0
$361$	−0.797724	+	1.38170i	−0.0419855	+	0.0727210i
$362$		0			0
$363$	−3.21691	+	3.35343i	−0.168844	+	0.176010i
$364$		0			0
$365$	−3.12050	−	5.40487i	−0.163334	−	0.282904i
$366$		0			0
$367$	4.69690	+	8.13527i	0.245176	+	0.424658i	0.962181	−	0.272410i	$-0.0878208\pi$
$367$	4.69690	+	8.13527i	0.245176	+	0.424658i	−0.717005	+	0.697068i	$0.754487\pi$
$368$		0			0
$369$	−0.496292	−	11.9369i	−0.0258359	−	0.621410i
$370$		0			0
$371$	−0.0877023	−	0.0505458i	−0.00455328	−	0.00262420i
$372$		0			0
$373$	4.37904	−	7.58472i	0.226738	−	0.392722i	−0.730101	−	0.683339i	$-0.760527\pi$
$373$	4.37904	−	7.58472i	0.226738	−	0.392722i	0.956840	+	0.290617i	$0.0938605\pi$
$374$		0			0
$375$	−1.68198	−	0.413434i	−0.0868573	−	0.0213497i
$376$		0			0
$377$	1.10732			0.0570300
$378$		0			0
$379$	22.1660			1.13859			0.569295	−	0.822134i	$-0.307216\pi$
$379$	22.1660			1.13859			0.569295	+	0.822134i	$0.307216\pi$
$380$		0			0
$381$	−34.6237	−	8.51056i	−1.77383	−	0.436009i
$382$		0			0
$383$	−7.57854	+	13.1264i	−0.387245	+	0.670729i	−0.992078	−	0.125624i	$-0.959907\pi$
$383$	−7.57854	+	13.1264i	−0.387245	+	0.670729i	0.604833	+	0.796353i	$0.293240\pi$
$384$		0			0
$385$	0.00582443	+	7.63018i	0.000296841	+	0.388870i
$386$		0			0
$387$	−2.47280	+	1.56812i	−0.125700	+	0.0797122i
$388$		0			0
$389$	10.1815	+	17.6349i	0.516223	+	0.894125i	0.999823	+	0.0188353i	$0.00599581\pi$
$389$	10.1815	+	17.6349i	0.516223	+	0.894125i	−0.483599	+	0.875289i	$0.660671\pi$
$390$		0			0
$391$	−1.49793	−	2.59449i	−0.0757535	−	0.131209i
$392$		0			0
$393$	−10.0880	+	10.5162i	−0.508874	+	0.530471i
$394$		0			0
$395$	4.94847	−	8.57100i	0.248984	−	0.431254i
$396$		0			0
$397$	−3.21832	−	5.57429i	−0.161523	−	0.279766i	0.773892	−	0.633317i	$-0.218307\pi$
$397$	−3.21832	−	5.57429i	−0.161523	−	0.279766i	−0.935415	+	0.353552i	$0.884974\pi$
$398$		0			0
$399$	19.9675	−	5.81400i	0.999626	−	0.291064i
$400$		0			0
$401$	−11.4681	+	19.8633i	−0.572688	+	0.991924i	0.423601	+	0.905849i	$0.360766\pi$
$401$	−11.4681	+	19.8633i	−0.572688	+	0.991924i	−0.996289	+	0.0860754i	$0.972567\pi$
$402$		0			0
$403$	−0.378635	−	0.655814i	−0.0188611	−	0.0326684i
$404$		0			0
$405$	−8.96894	+	0.747082i	−0.445670	+	0.0371228i
$406$		0			0
$407$	0.704424	−	1.22010i	0.0349170	−	0.0604780i
$408$		0			0
$409$	−29.8653			−1.47674			−0.738371	−	0.674394i	$-0.764405\pi$
$409$	−29.8653			−1.47674			−0.738371	+	0.674394i	$0.764405\pi$
$410$		0			0
$411$	5.26788	+	18.1435i	0.259845	+	0.894954i
$412$		0			0
$413$	−0.00290991	−	3.81207i	−0.000143187	−	0.187580i
$414$		0			0
$415$	−4.42924	−	7.67166i	−0.217423	−	0.376587i
$416$		0			0
$417$	6.71001	+	23.1105i	0.328591	+	1.13172i
$418$		0			0
$419$	−2.26868	−	3.92946i	−0.110832	−	0.191967i	0.805274	−	0.592903i	$-0.202018\pi$
$419$	−2.26868	−	3.92946i	−0.110832	−	0.191967i	−0.916106	+	0.400936i	$0.868685\pi$
$420$		0			0
$421$	−14.5625	+	25.2231i	−0.709735	+	1.22930i	0.255221	+	0.966883i	$0.417852\pi$
$421$	−14.5625	+	25.2231i	−0.709735	+	1.22930i	−0.964955	+	0.262414i	$0.915481\pi$
$422$		0			0
$423$	−17.8367	−	9.33243i	−0.867250	−	0.453758i
$424$		0			0
$425$	0.694955			0.0337103
$426$		0			0
$427$	−0.0132838	−	17.4021i	−0.000642846	−	0.842147i
$428$		0			0
$429$	−0.572397	+	0.596689i	−0.0276356	+	0.0288084i
$430$		0			0
$431$	16.6581	−	28.8527i	0.802394	−	1.38979i	−0.115643	−	0.993291i	$-0.536893\pi$
$431$	16.6581	−	28.8527i	0.802394	−	1.38979i	0.918036	−	0.396496i	$-0.129774\pi$
$432$		0			0
$433$	−12.0462			−0.578906			−0.289453	−	0.957192i	$-0.593473\pi$
$433$	−12.0462			−0.578906			−0.289453	+	0.957192i	$0.593473\pi$
$434$		0			0
$435$	−3.23069	−	11.1271i	−0.154900	−	0.533502i
$436$		0			0
$437$	−19.5636			−0.935856
$438$		0			0
$439$	1.84528			0.0880705			0.0440352	−	0.999030i	$-0.485979\pi$
$439$	1.84528			0.0880705			0.0440352	+	0.999030i	$0.485979\pi$
$440$		0			0
$441$	−18.6219	−	9.70704i	−0.886755	−	0.462240i
$442$		0			0
$443$	−9.52596			−0.452592			−0.226296	−	0.974059i	$-0.572662\pi$
$443$	−9.52596			−0.452592			−0.226296	+	0.974059i	$0.572662\pi$
$444$		0			0
$445$	3.86190			0.183071
$446$		0			0
$447$	−25.2237	+	26.2941i	−1.19304	+	1.24367i
$448$		0			0
$449$	11.5363			0.544433			0.272216	−	0.962236i	$-0.412243\pi$
$449$	11.5363			0.544433			0.272216	+	0.962236i	$0.412243\pi$
$450$		0			0
$451$	−5.74250	+	9.94630i	−0.270404	+	0.468353i
$452$		0			0
$453$	5.86383	+	20.1961i	0.275507	+	0.948894i
$454$		0			0
$455$	−0.000334308	−	0.437953i	−1.56726e−5	−	0.0205316i
$456$		0			0
$457$	−11.0284			−0.515886			−0.257943	−	0.966160i	$-0.583045\pi$
$457$	−11.0284			−0.515886			−0.257943	+	0.966160i	$0.583045\pi$
$458$		0			0
$459$	3.42306	−	1.15007i	0.159775	−	0.0536806i
$460$		0			0
$461$	13.0348	−	22.5769i	0.607091	−	1.05151i	−0.384626	−	0.923072i	$-0.625670\pi$
$461$	13.0348	−	22.5769i	0.607091	−	1.05151i	0.991717	−	0.128440i	$-0.0409970\pi$
$462$		0			0
$463$	−5.01294	−	8.68267i	−0.232971	−	0.403518i	0.725710	−	0.688001i	$-0.241511\pi$
$463$	−5.01294	−	8.68267i	−0.232971	−	0.403518i	−0.958681	+	0.284483i	$0.908178\pi$
$464$		0			0
$465$	−5.48535	+	5.71815i	−0.254377	+	0.265173i
$466$		0			0
$467$	2.28156	+	3.95178i	0.105578	+	0.182867i	0.913974	−	0.405772i	$-0.132997\pi$
$467$	2.28156	+	3.95178i	0.105578	+	0.182867i	−0.808396	+	0.588639i	$0.799664\pi$
$468$		0			0
$469$	−0.0112344	−	14.7173i	−0.000518755	−	0.679584i
$470$		0			0
$471$	−22.0597	−	5.42230i	−1.01646	−	0.249846i
$472$		0			0
$473$	2.81482			0.129425
$474$		0			0
$475$	2.26911	−	3.93021i	0.104114	−	0.180331i
$476$		0			0
$477$	−0.0969316	+	0.0614690i	−0.00443819	+	0.00281447i
$478$		0			0
$479$	17.3679	+	30.0820i	0.793558	+	1.37448i	0.923751	+	0.382994i	$0.125107\pi$
$479$	17.3679	+	30.0820i	0.793558	+	1.37448i	−0.130193	+	0.991489i	$0.541560\pi$
$480$		0			0
$481$	−0.0404322	+	0.0700306i	−0.00184355	+	0.00319312i
$482$		0			0
$483$	14.2664	+	13.6647i	0.649144	+	0.621765i
$484$		0			0
$485$	−7.94934	−	13.7687i	−0.360961	−	0.625203i
$486$		0			0
$487$	2.36151	−	4.09026i	0.107010	−	0.185348i	−0.807547	−	0.589803i	$-0.799206\pi$
$487$	2.36151	−	4.09026i	0.107010	−	0.185348i	0.914558	+	0.404455i	$0.132539\pi$
$488$		0			0
$489$	−3.23445	−	11.1400i	−0.146267	−	0.503769i
$490$		0			0
$491$	18.0436	+	31.2523i	0.814294	+	1.41040i	0.909834	+	0.414973i	$0.136209\pi$
$491$	18.0436	+	31.2523i	0.814294	+	1.41040i	−0.0955396	+	0.995426i	$0.530458\pi$
$492$		0			0
$493$	2.32446	+	4.02608i	0.104688	+	0.181326i
$494$		0			0
$495$	7.66592	+	4.01092i	0.344557	+	0.180278i
$496$		0			0
$497$	−0.0176451	−	23.1156i	−0.000791492	−	1.03688i
$498$		0			0
$499$	−2.41475	+	4.18247i	−0.108099	+	0.187233i	−0.915000	−	0.403453i	$-0.867810\pi$
$499$	−2.41475	+	4.18247i	−0.108099	+	0.187233i	0.806901	+	0.590687i	$0.201143\pi$
$500$		0			0
$501$	−0.0525529	−	0.181002i	−0.00234789	−	0.00808656i
$502$		0			0
$503$	−10.3981			−0.463630			−0.231815	−	0.972760i	$-0.574466\pi$
$503$	−10.3981			−0.463630			−0.231815	+	0.972760i	$0.574466\pi$
$504$		0			0
$505$	−14.9563			−0.665549
$506$		0			0
$507$	−15.5546	+	16.2148i	−0.690805	+	0.720123i
$508$		0			0
$509$	1.85088	−	3.20583i	0.0820390	−	0.142096i	−0.822087	−	0.569362i	$-0.807190\pi$
$509$	1.85088	−	3.20583i	0.0820390	−	0.142096i	0.904126	+	0.427267i	$0.140523\pi$
$510$		0			0
$511$	−14.3062	−	8.24515i	−0.632870	−	0.364744i
$512$		0			0
$513$	4.67265	−	23.1137i	0.206302	−	1.02050i
$514$		0			0
$515$	−9.89472	−	17.1382i	−0.436013	−	0.755197i
$516$		0			0
$517$	9.67591	+	16.7592i	0.425546	+	0.737067i
$518$		0			0
$519$	9.54262	+	2.34559i	0.418875	+	0.102960i
$520$		0			0
$521$	−22.1805	+	38.4177i	−0.971744	+	1.68311i	−0.281458	+	0.959574i	$0.590818\pi$
$521$	−22.1805	+	38.4177i	−0.971744	+	1.68311i	−0.690286	+	0.723536i	$0.742515\pi$
$522$		0			0
$523$	7.72373	+	13.3779i	0.337735	+	0.584974i	0.984006	−	0.178133i	$-0.0570059\pi$
$523$	7.72373	+	13.3779i	0.337735	+	0.584974i	−0.646271	+	0.763108i	$0.723673\pi$
$524$		0			0
$525$	−4.39986	+	1.28112i	−0.192025	+	0.0559126i
$526$		0			0
$527$	1.58964	−	2.75333i	0.0692457	−	0.119937i
$528$		0			0
$529$	2.20823	+	3.82477i	0.0960101	+	0.166294i
$530$		0			0
$531$	−3.82992	−	2.00387i	−0.166205	−	0.0869607i
$532$		0			0
$533$	0.329605	−	0.570893i	0.0142768	−	0.0247281i
$534$		0			0
$535$	13.4067			0.579623
$536$		0			0
$537$	−1.55030	+	1.61609i	−0.0669003	+	0.0697396i
$538$		0			0
$539$	10.1205	+	17.4675i	0.435919	+	0.752379i
$540$		0			0
$541$	13.1549	+	22.7850i	0.565573	+	0.979602i	0.996996	+	0.0774520i	$0.0246784\pi$
$541$	13.1549	+	22.7850i	0.565573	+	0.979602i	−0.431423	+	0.902150i	$0.641988\pi$
$542$		0			0
$543$	−8.34391	−	2.05095i	−0.358071	−	0.0880145i
$544$		0			0
$545$	−2.49944	−	4.32916i	−0.107064	−	0.185441i
$546$		0			0
$547$	1.95548	−	3.38700i	0.0836104	−	0.144818i	−0.821188	−	0.570658i	$-0.806688\pi$
$547$	1.95548	−	3.38700i	0.0836104	−	0.144818i	0.904798	+	0.425840i	$0.140022\pi$
$548$		0			0
$549$	−17.4836	−	9.14769i	−0.746183	−	0.390414i
$550$		0			0
$551$	30.3585			1.29332
$552$		0			0
$553$	−0.0199880	−	26.1848i	−0.000849975	−	1.11349i
$554$		0			0
$555$	0.821675	+	0.201969i	0.0348782	+	0.00857311i
$556$		0			0
$557$	2.07374	−	3.59182i	0.0878672	−	0.152190i	−0.818742	−	0.574161i	$-0.805328\pi$
$557$	2.07374	−	3.59182i	0.0878672	−	0.152190i	0.906609	+	0.421971i	$0.138662\pi$
$558$		0			0
$559$	−0.161563			−0.00683341
$560$		0			0
$561$	−3.37105	−	0.828608i	−0.142326	−	0.0349839i
$562$		0			0
$563$	16.4345			0.692630			0.346315	−	0.938118i	$-0.387433\pi$
$563$	16.4345			0.692630			0.346315	+	0.938118i	$0.387433\pi$
$564$		0			0
$565$	4.98188			0.209589
$566$		0			0
$567$	−19.5518	+	13.5915i	−0.821097	+	0.570789i
$568$		0			0
$569$	−1.38319			−0.0579864			−0.0289932	−	0.999580i	$-0.509230\pi$
$569$	−1.38319			−0.0579864			−0.0289932	+	0.999580i	$0.509230\pi$
$570$		0			0
$571$	2.32789			0.0974192			0.0487096	−	0.998813i	$-0.484489\pi$
$571$	2.32789			0.0974192			0.0487096	+	0.998813i	$0.484489\pi$
$572$		0			0
$573$	37.2842	+	9.16451i	1.55757	+	0.382853i
$574$		0			0
$575$	4.31086			0.179775
$576$		0			0
$577$	20.1634	−	34.9241i	0.839414	−	1.45391i	−0.0509707	−	0.998700i	$-0.516232\pi$
$577$	20.1634	−	34.9241i	0.839414	−	1.45391i	0.890385	−	0.455208i	$-0.150435\pi$
$578$		0			0
$579$	15.8354	+	3.89238i	0.658099	+	0.161762i
$580$		0			0
$581$	−20.3062	−	11.7032i	−0.842445	−	0.485529i
$582$		0			0
$583$	0.110338			0.00456974
$584$		0			0
$585$	−0.440005	−	0.230217i	−0.0181920	−	0.00951830i
$586$		0			0
$587$	10.1883	−	17.6466i	0.420516	−	0.728354i	−0.575474	−	0.817820i	$-0.695183\pi$
$587$	10.1883	−	17.6466i	0.420516	−	0.728354i	0.995990	+	0.0894655i	$0.0285159\pi$
$588$		0			0
$589$	−10.3807	−	17.9799i	−0.427730	−	0.740850i
$590$		0			0
$591$	−24.3023	−	5.97354i	−0.999664	−	0.245719i
$592$		0			0
$593$	2.96318	+	5.13239i	0.121683	+	0.210762i	0.920432	−	0.390904i	$-0.127837\pi$
$593$	2.96318	+	5.13239i	0.121683	+	0.210762i	−0.798748	+	0.601665i	$0.794504\pi$
$594$		0			0
$595$	1.59164	−	0.920555i	0.0652509	−	0.0377391i
$596$		0			0
$597$	−15.7949	+	16.4653i	−0.646444	+	0.673879i
$598$		0			0
$599$	−29.4187			−1.20202			−0.601009	−	0.799243i	$-0.705234\pi$
$599$	−29.4187			−1.20202			−0.601009	+	0.799243i	$0.705234\pi$
$600$		0			0
$601$	−12.4991	+	21.6490i	−0.509847	+	0.883082i	0.490087	+	0.871673i	$0.336965\pi$
$601$	−12.4991	+	21.6490i	−0.509847	+	0.883082i	−0.999935	+	0.0114084i	$0.996369\pi$
$602$		0			0
$603$	−14.7863	−	7.73640i	−0.602144	−	0.315051i
$604$		0			0
$605$	1.34145	+	2.32347i	0.0545379	+	0.0944623i
$606$		0			0
$607$	24.3132	−	42.1117i	0.986843	−	1.70926i	0.353398	−	0.935473i	$-0.385026\pi$
$607$	24.3132	−	42.1117i	0.986843	−	1.70926i	0.633444	−	0.773788i	$-0.281641\pi$
$608$		0			0
$609$	−22.1384	−	21.2046i	−0.897092	−	0.859255i
$610$		0			0
$611$	−0.555373	−	0.961934i	−0.0224680	−	0.0389157i
$612$		0			0
$613$	−2.04753	+	3.54643i	−0.0826990	+	0.143239i	−0.904408	−	0.426668i	$-0.859687\pi$
$613$	−2.04753	+	3.54643i	−0.0826990	+	0.143239i	0.821709	+	0.569907i	$0.193021\pi$
$614$		0			0
$615$	−6.69834	−	1.64646i	−0.270103	−	0.0663918i
$616$		0			0
$617$	−7.63565	−	13.2253i	−0.307400	−	0.532432i	0.670393	−	0.742006i	$-0.266125\pi$
$617$	−7.63565	−	13.2253i	−0.307400	−	0.532432i	−0.977793	+	0.209574i	$0.932792\pi$
$618$		0			0
$619$	−20.3552	−	35.2562i	−0.818144	−	1.41707i	−0.907048	−	0.421026i	$-0.861670\pi$
$619$	−20.3552	−	35.2562i	−0.818144	−	1.41707i	0.0889048	−	0.996040i	$-0.471663\pi$
$620$		0			0
$621$	21.2335	−	7.13397i	0.852071	−	0.286276i
$622$		0			0
$623$	8.84482	−	5.11556i	0.354360	−	0.204951i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−15.6929	+	16.3589i	−0.626715	+	0.653313i
$628$		0			0
$629$	−0.339496			−0.0135366
$630$		0			0
$631$	40.9878			1.63170			0.815849	−	0.578265i	$-0.196270\pi$
$631$	40.9878			1.63170			0.815849	+	0.578265i	$0.196270\pi$
$632$		0			0
$633$	−4.92382	−	16.9585i	−0.195704	−	0.674040i
$634$		0			0
$635$	−10.2925	+	17.8272i	−0.408446	+	0.707450i
$636$		0			0
$637$	−0.580889	−	1.00259i	−0.0230157	−	0.0397241i
$638$		0			0
$639$	−23.2239	−	12.1511i	−0.918723	−	0.480690i
$640$		0			0
$641$	3.44510	+	5.96709i	0.136073	+	0.235686i	0.926007	−	0.377507i	$-0.123218\pi$
$641$	3.44510	+	5.96709i	0.136073	+	0.235686i	−0.789934	+	0.613192i	$0.789885\pi$
$642$		0			0
$643$	−17.9934	−	31.1654i	−0.709590	−	1.22905i	−0.965010	−	0.262215i	$-0.915547\pi$
$643$	−17.9934	−	31.1654i	−0.709590	−	1.22905i	0.255420	−	0.966830i	$-0.417786\pi$
$644$		0			0
$645$	0.471373	+	1.62349i	0.0185603	+	0.0639250i
$646$		0			0
$647$	−10.4158	+	18.0407i	−0.409488	+	0.709253i	−0.994832	−	0.101531i	$-0.967626\pi$
$647$	−10.4158	+	18.0407i	−0.409488	+	0.709253i	0.585345	+	0.810785i	$0.300959\pi$
$648$		0			0
$649$	2.07763	+	3.59855i	0.0815540	+	0.141256i
$650$		0			0
$651$	−4.98857	+	20.3622i	−0.195517	+	0.798056i
$652$		0			0
$653$	−15.7828	+	27.3366i	−0.617629	+	1.06976i	0.372288	+	0.928117i	$0.378573\pi$
$653$	−15.7828	+	27.3366i	−0.617629	+	1.06976i	−0.989917	+	0.141647i	$0.954760\pi$
$654$		0			0
$655$	4.20673	+	7.28627i	0.164370	+	0.284698i
$656$		0			0
$657$	−15.8117	+	10.0270i	−0.616874	+	0.391190i
$658$		0			0
$659$	−12.5849	+	21.7977i	−0.490238	+	0.849117i	−0.999937	−	0.0112359i	$-0.996423\pi$
$659$	−12.5849	+	21.7977i	−0.490238	+	0.849117i	0.509699	+	0.860353i	$0.329757\pi$
$660$		0			0
$661$	−26.0260			−1.01229			−0.506147	−	0.862447i	$-0.668931\pi$
$661$	−26.0260			−1.01229			−0.506147	+	0.862447i	$0.668931\pi$
$662$		0			0
$663$	0.193490	+	0.0475600i	0.00751451	+	0.00184708i
$664$		0			0
$665$	−0.00916545	−	12.0070i	−0.000355421	−	0.465611i
$666$		0			0
$667$	14.4188	+	24.9741i	0.558298	+	0.967001i
$668$		0			0
$669$	27.2469	−	28.4033i	1.05343	−	1.09813i
$670$		0			0
$671$	9.48437	+	16.4274i	0.366140	+	0.634173i
$672$		0			0
$673$	2.20080	−	3.81189i	0.0848345	−	0.146938i	−0.820486	−	0.571666i	$-0.806297\pi$
$673$	2.20080	−	3.81189i	0.0848345	−	0.146938i	0.905321	+	0.424729i	$0.139631\pi$
$674$		0			0
$675$	−1.02962	+	5.09312i	−0.0396301	+	0.196034i
$676$		0			0
$677$	−47.5279			−1.82665			−0.913323	−	0.407237i	$-0.866492\pi$
$677$	−47.5279			−1.82665			−0.913323	+	0.407237i	$0.866492\pi$
$678$		0			0
$679$	−36.4445	−	21.0042i	−1.39861	−	0.806066i
$680$		0			0
$681$	5.98201	+	20.6031i	0.229231	+	0.789513i
$682$		0			0
$683$	−5.43047	+	9.40586i	−0.207791	+	0.359905i	−0.951018	−	0.309134i	$-0.899961\pi$
$683$	−5.43047	+	9.40586i	−0.207791	+	0.359905i	0.743227	+	0.669039i	$0.233294\pi$
$684$		0			0
$685$	10.9078			0.416764
$686$		0			0
$687$	12.1225	−	12.6370i	0.462504	−	0.482133i
$688$		0			0
$689$	−0.00633314			−0.000241273
$690$		0			0
$691$	51.4216			1.95617			0.978085	−	0.208205i	$-0.0667621\pi$
$691$	51.4216			1.95617			0.978085	+	0.208205i	$0.0667621\pi$
$692$		0			0
$693$	22.8700	−	0.968341i	0.868761	−	0.0367842i
$694$		0			0
$695$	13.8939			0.527024
$696$		0			0
$697$	2.76759			0.104830
$698$		0			0
$699$	11.2355	+	38.6970i	0.424965	+	1.46366i
$700$		0			0
$701$	9.99979			0.377687			0.188843	−	0.982007i	$-0.439526\pi$
$701$	9.99979			0.377687			0.188843	+	0.982007i	$0.439526\pi$
$702$		0			0
$703$	−1.10850	+	1.91997i	−0.0418077	+	0.0724131i
$704$		0			0
$705$	−8.04579	+	8.38725i	−0.303022	+	0.315882i
$706$		0			0
$707$	−34.2542	+	19.8115i	−1.28826	+	0.745090i
$708$		0			0
$709$	−14.2825			−0.536392			−0.268196	−	0.963364i	$-0.586427\pi$
$709$	−14.2825			−0.536392			−0.268196	+	0.963364i	$0.586427\pi$
$710$		0			0
$711$	−26.3075	−	13.7645i	−0.986607	−	0.516207i
$712$		0			0
$713$	9.86065	−	17.0792i	0.369284	−	0.639619i
$714$		0			0
$715$	0.238690	+	0.413423i	0.00892651	+	0.0154612i
$716$		0			0
$717$	−7.97632	−	27.4719i	−0.297881	−	1.02596i
$718$		0			0
$719$	24.0553	+	41.6650i	0.897112	+	1.55384i	0.831169	+	0.556020i	$0.187672\pi$
$719$	24.0553	+	41.6650i	0.897112	+	1.55384i	0.0659425	+	0.997823i	$0.478995\pi$
$720$		0			0
$721$	−45.3633	−	26.1443i	−1.68942	−	0.973666i
$722$		0			0
$723$	−6.15508	−	21.1992i	−0.228910	−	0.788406i
$724$		0			0
$725$	−6.68952			−0.248443
$726$		0			0
$727$	11.4883	−	19.8983i	0.426077	−	0.737988i	−0.570443	−	0.821337i	$-0.693228\pi$
$727$	11.4883	−	19.8983i	0.426077	−	0.737988i	0.996520	+	0.0833496i	$0.0265618\pi$
$728$		0			0
$729$	3.35703	+	26.7905i	0.124335	+	0.992240i
$730$		0			0
$731$	−0.339150	−	0.587424i	−0.0125439	−	0.0217267i
$732$		0			0
$733$	−12.8774	+	22.3043i	−0.475637	+	0.823828i	−0.999611	−	0.0279069i	$-0.991116\pi$
$733$	−12.8774	+	22.3043i	−0.475637	+	0.823828i	0.523973	+	0.851735i	$0.324449\pi$
$734$		0			0
$735$	−8.37989	+	8.76227i	−0.309097	+	0.323201i
$736$		0			0
$737$	8.02114	+	13.8930i	0.295463	+	0.511756i
$738$		0			0
$739$	−23.5796	+	40.8411i	−0.867391	+	1.50237i	−0.00273810	+	0.999996i	$0.500872\pi$
$739$	−23.5796	+	40.8411i	−0.867391	+	1.50237i	−0.864653	+	0.502369i	$0.832462\pi$
$740$		0			0
$741$	0.900735	−	0.938962i	0.0330893	−	0.0344936i
$742$		0			0
$743$	−5.01809	−	8.69159i	−0.184096	−	0.318864i	0.759176	−	0.650886i	$-0.225602\pi$
$743$	−5.01809	−	8.69159i	−0.184096	−	0.318864i	−0.943272	+	0.332022i	$0.892269\pi$
$744$		0			0
$745$	10.5183	+	18.2182i	0.385361	+	0.667464i
$746$		0			0
$747$	−22.4431	+	14.2323i	−0.821151	+	0.520732i
$748$		0			0
$749$	30.7051	−	17.7589i	1.12194	−	0.648895i
$750$		0			0
$751$	11.1888	−	19.3796i	0.408287	−	0.707173i	−0.586411	−	0.810013i	$-0.699460\pi$
$751$	11.1888	−	19.3796i	0.408287	−	0.707173i	0.994698	+	0.102840i	$0.0327931\pi$
$752$		0			0
$753$	3.16922	+	0.778998i	0.115493	+	0.0283883i
$754$		0			0
$755$	12.1417			0.441883
$756$		0			0
$757$	41.3903			1.50436			0.752178	−	0.658960i	$-0.229003\pi$
$757$	41.3903			1.50436			0.752178	+	0.658960i	$0.229003\pi$
$758$		0			0
$759$	−20.9109	−	5.13992i	−0.759016	−	0.186567i
$760$		0			0
$761$	−6.95237	+	12.0419i	−0.252023	+	0.436517i	−0.964083	−	0.265602i	$-0.914429\pi$
$761$	−6.95237	+	12.0419i	−0.252023	+	0.436517i	0.712059	+	0.702119i	$0.247763\pi$
$762$		0			0
$763$	−11.4589	−	6.60416i	−0.414841	−	0.239087i
$764$		0			0
$765$	−0.0866062	−	2.08307i	−0.00313125	−	0.0753134i
$766$		0			0
$767$	−0.119251	−	0.206548i	−0.00430589	−	0.00745802i
$768$		0			0
$769$	−11.8746	−	20.5674i	−0.428208	−	0.741678i	0.568506	−	0.822679i	$-0.307522\pi$
$769$	−11.8746	−	20.5674i	−0.428208	−	0.741678i	−0.996714	+	0.0810010i	$0.974188\pi$
$770$		0			0
$771$	−17.6602	+	18.4097i	−0.636015	+	0.663008i
$772$		0			0
$773$	−11.2082	+	19.4132i	−0.403132	+	0.698244i	−0.994102	−	0.108449i	$-0.965412\pi$
$773$	−11.2082	+	19.4132i	−0.403132	+	0.698244i	0.590970	+	0.806693i	$0.298745\pi$
$774$		0			0
$775$	2.28740	+	3.96189i	0.0821657	+	0.142315i
$776$		0			0
$777$	2.14940	−	0.625846i	0.0771092	−	0.0224521i
$778$		0			0
$779$	9.03651	−	15.6517i	0.323767	−	0.560780i
$780$		0			0
$781$	12.5983	+	21.8209i	0.450803	+	0.780814i
$782$		0			0
$783$	−32.9498	+	11.0704i	−1.17753	+	0.395623i
$784$		0			0
$785$	−6.55764	+	11.3582i	−0.234052	+	0.405390i
$786$		0			0
$787$	28.1346			1.00289			0.501444	−	0.865190i	$-0.332802\pi$
$787$	28.1346			1.00289			0.501444	+	0.865190i	$0.332802\pi$
$788$		0			0
$789$	−13.5855	−	46.7911i	−0.483658	−	1.66581i
$790$		0			0
$791$	11.4099	−	6.59912i	0.405689	−	0.234638i
$792$		0			0
$793$	−0.544379	−	0.942893i	−0.0193315	−	0.0334831i
$794$		0			0
$795$	0.0184774	+	0.0636394i	0.000655325	+	0.00225706i
$796$		0			0
$797$	−0.447494	−	0.775082i	−0.0158510	−	0.0274548i	0.857991	−	0.513665i	$-0.171712\pi$
$797$	−0.447494	−	0.775082i	−0.0158510	−	0.0274548i	−0.873842	+	0.486210i	$0.838379\pi$
$798$		0			0
$799$	2.33165	−	4.03853i	0.0824878	−	0.142873i
$800$		0			0
$801$	−0.481274	−	11.5757i	−0.0170050	−	0.409007i
$802$		0			0
$803$	17.9987			0.635159
$804$		0			0
$805$	9.87307	−	5.71027i	0.347980	−	0.201261i
$806$		0			0
$807$	20.9054	−	21.7926i	0.735905	−	0.767137i
$808$		0			0
$809$	−16.2881	+	28.2118i	−0.572659	+	0.991874i	0.423633	+	0.905834i	$0.360755\pi$
$809$	−16.2881	+	28.2118i	−0.572659	+	0.991874i	−0.996292	+	0.0860398i	$0.972579\pi$
$810$		0			0
$811$	−24.9893			−0.877492			−0.438746	−	0.898611i	$-0.644577\pi$
$811$	−24.9893			−0.877492			−0.438746	+	0.898611i	$0.644577\pi$
$812$		0			0
$813$	−2.89910	−	9.98503i	−0.101676	−	0.350190i
$814$		0			0
$815$	−6.69730			−0.234596
$816$		0			0
$817$	−4.42945			−0.154967
$818$		0			0
$819$	−1.31268	+	0.0555803i	−0.0458689	+	0.00194213i
$820$		0			0
$821$	18.0264			0.629127			0.314564	−	0.949236i	$-0.398142\pi$
$821$	18.0264			0.629127			0.314564	+	0.949236i	$0.398142\pi$
$822$		0			0
$823$	−51.7586			−1.80419			−0.902095	−	0.431537i	$-0.857971\pi$
$823$	−51.7586			−1.80419			−0.902095	+	0.431537i	$0.857971\pi$
$824$		0			0
$825$	3.45795	−	3.60470i	0.120390	−	0.125500i
$826$		0			0
$827$	30.0446			1.04475			0.522376	−	0.852715i	$-0.325046\pi$
$827$	30.0446			1.04475			0.522376	+	0.852715i	$0.325046\pi$
$828$		0			0
$829$	17.9543	−	31.0977i	0.623577	−	1.08007i	−0.365237	−	0.930914i	$-0.619012\pi$
$829$	17.9543	−	31.0977i	0.623577	−	1.08007i	0.988814	−	0.149152i	$-0.0476545\pi$
$830$		0			0
$831$	−14.8506	−	51.1481i	−0.515161	−	1.77431i
$832$		0			0
$833$	2.42591	−	4.21665i	0.0840528	−	0.146098i
$834$		0			0
$835$	−0.108817			−0.00376577
$836$		0			0
$837$	17.8232	+	15.7292i	0.616061	+	0.543682i
$838$		0			0
$839$	−23.9113	+	41.4157i	−0.825511	+	1.42983i	0.0760170	+	0.997107i	$0.475780\pi$
$839$	−23.9113	+	41.4157i	−0.825511	+	1.42983i	−0.901528	+	0.432721i	$0.857554\pi$
$840$		0			0
$841$	−7.87484	−	13.6396i	−0.271546	−	0.470332i
$842$		0			0
$843$	4.09425	−	4.26801i	0.141013	−	0.146998i
$844$		0			0
$845$	6.48630	+	11.2346i	0.223135	+	0.386482i
$846$		0			0
$847$	6.15002	+	3.54446i	0.211317	+	0.121789i
$848$		0			0
$849$	−17.9053	−	4.40115i	−0.614508	−	0.151047i
$850$		0			0
$851$	−2.10592			−0.0721901
$852$		0			0
$853$	−1.82607	+	3.16285i	−0.0625236	+	0.108294i	−0.895593	−	0.444875i	$-0.853248\pi$
$853$	−1.82607	+	3.16285i	−0.0625236	+	0.108294i	0.833069	+	0.553169i	$0.186582\pi$
$854$		0			0
$855$	−12.0632	−	6.31167i	−0.412554	−	0.215854i
$856$		0			0
$857$	−10.5907	−	18.3436i	−0.361770	−	0.626604i	0.626482	−	0.779436i	$-0.284494\pi$
$857$	−10.5907	−	18.3436i	−0.361770	−	0.626604i	−0.988252	+	0.152832i	$0.951161\pi$
$858$		0			0
$859$	19.7367	−	34.1850i	0.673408	−	1.16638i	−0.303523	−	0.952824i	$-0.598163\pi$
$859$	19.7367	−	34.1850i	0.673408	−	1.16638i	0.976931	−	0.213553i	$-0.0685036\pi$
$860$		0			0
$861$	−17.5220	+	5.10193i	−0.597148	+	0.173873i
$862$		0			0
$863$	13.1256	+	22.7342i	0.446800	+	0.773880i	0.998176	−	0.0603773i	$-0.0192304\pi$
$863$	13.1256	+	22.7342i	0.446800	+	0.773880i	−0.551376	+	0.834257i	$0.685897\pi$
$864$		0			0
$865$	2.83672	−	4.91334i	0.0964512	−	0.167058i
$866$		0			0
$867$	−7.97687	−	27.4738i	−0.270909	−	0.933058i
$868$		0			0
$869$	14.2711	+	24.7182i	0.484113	+	0.838508i
$870$		0			0
$871$	−0.460393	−	0.797425i	−0.0155998	−	0.0270197i
$872$		0			0
$873$	−40.2797	+	25.5433i	−1.36326	+	0.864510i
$874$		0			0
$875$	0.00201961	+	2.64575i	6.82754e−5	+	0.0894427i
$876$		0			0
$877$	28.8607	−	49.9883i	0.974558	−	1.68798i	0.293172	−	0.956060i	$-0.405289\pi$
$877$	28.8607	−	49.9883i	0.974558	−	1.68798i	0.681386	−	0.731924i	$-0.261377\pi$
$878$		0			0
$879$	5.61533	+	19.3402i	0.189400	+	0.652329i
$880$		0			0
$881$	−2.06626			−0.0696142			−0.0348071	−	0.999394i	$-0.511082\pi$
$881$	−2.06626			−0.0696142			−0.0348071	+	0.999394i	$0.511082\pi$
$882$		0			0
$883$	15.8908			0.534768			0.267384	−	0.963590i	$-0.413841\pi$
$883$	15.8908			0.534768			0.267384	+	0.963590i	$0.413841\pi$
$884$		0			0
$885$	−1.72760	+	1.80092i	−0.0580728	+	0.0605374i
$886$		0			0
$887$	9.23782	−	16.0004i	0.310176	−	0.537240i	−0.668224	−	0.743960i	$-0.732945\pi$
$887$	9.23782	−	16.0004i	0.310176	−	0.537240i	0.978400	+	0.206720i	$0.0662788\pi$
$888$		0			0
$889$	0.0415738	+	54.4629i	0.00139434	+	1.82663i
$890$		0			0
$891$	11.0670	−	23.4778i	0.370760	−	0.786534i
$892$		0			0
$893$	−15.2262	−	26.3726i	−0.509526	−	0.882524i
$894$		0			0
$895$	0.646477	+	1.11973i	0.0216093	+	0.0374285i
$896$		0			0
$897$	1.20023	+	0.295019i	0.0400746	+	0.00985038i
$898$		0			0
$899$	−15.3016	+	26.5031i	−0.510337	+	0.883929i
$900$		0			0
$901$	−0.0132944	−	0.0230265i	−0.000442899	−	0.000767124i
$902$		0			0
$903$	3.23009	+	3.09386i	0.107491	+	0.102957i
$904$		0			0
$905$	−2.48038	+	4.29614i	−0.0824505	+	0.142808i
$906$		0			0
$907$	27.4315	+	47.5128i	0.910848	+	1.57764i	0.812869	+	0.582447i	$0.197905\pi$
$907$	27.4315	+	47.5128i	0.910848	+	1.57764i	0.0979791	+	0.995188i	$0.468762\pi$
$908$		0			0
$909$	1.86388	+	44.8303i	0.0618210	+	1.48693i
$910$		0			0
$911$	−7.68535	+	13.3114i	−0.254627	+	0.441027i	−0.964794	−	0.263006i	$-0.915286\pi$
$911$	−7.68535	+	13.3114i	−0.254627	+	0.441027i	0.710167	+	0.704033i	$0.248619\pi$
$912$		0			0
$913$	25.5473			0.845491
$914$		0			0
$915$	−7.88652	+	8.22123i	−0.260720	+	0.271785i
$916$		0			0
$917$	19.2861	+	11.1152i	0.636884	+	0.367057i
$918$		0			0
$919$	13.3607	+	23.1413i	0.440728	+	0.763363i	0.997744	−	0.0671392i	$-0.0213872\pi$
$919$	13.3607	+	23.1413i	0.440728	+	0.763363i	−0.557016	+	0.830502i	$0.688054\pi$
$920$		0			0
$921$	21.3272	+	5.24226i	0.702756	+	0.172738i
$922$		0			0
$923$	−0.723112	−	1.25247i	−0.0238015	−	0.0412254i
$924$		0			0
$925$	0.244258	−	0.423067i	0.00803114	−	0.0139104i
$926$		0			0
$927$	−50.1370	+	31.7943i	−1.64671	+	1.04426i
$928$		0			0
$929$	0.956024			0.0313661			0.0156831	−	0.999877i	$-0.495008\pi$
$929$	0.956024			0.0313661			0.0156831	+	0.999877i	$0.495008\pi$
$930$		0			0
$931$	−15.9258	−	27.4872i	−0.521946	−	0.900857i
$932$		0			0
$933$	−32.9629	−	8.10232i	−1.07916	−	0.265258i
$934$		0			0
$935$	−1.00210	+	1.73569i	−0.0327723	+	0.0567633i
$936$		0			0
$937$	−47.2009			−1.54199			−0.770993	−	0.636844i	$-0.780239\pi$
$937$	−47.2009			−1.54199			−0.770993	+	0.636844i	$0.780239\pi$
$938$		0			0
$939$	7.88976	+	1.93931i	0.257473	+	0.0632872i
$940$		0			0
$941$	−38.0114			−1.23914			−0.619568	−	0.784943i	$-0.712692\pi$
$941$	−38.0114			−1.23914			−0.619568	+	0.784943i	$0.712692\pi$
$942$		0			0
$943$	17.1676			0.559054
$944$		0			0
$945$	4.38835	+	13.0285i	0.142753	+	0.423818i
$946$		0			0
$947$	−59.6964			−1.93987			−0.969936	−	0.243359i	$-0.921751\pi$
$947$	−59.6964			−1.93987			−0.969936	+	0.243359i	$0.921751\pi$
$948$		0			0
$949$	−1.03308			−0.0335351
$950$		0			0
$951$	44.8481	+	11.0237i	1.45430	+	0.357469i
$952$		0			0
$953$	−31.6658			−1.02576			−0.512879	−	0.858461i	$-0.671421\pi$
$953$	−31.6658			−1.02576			−0.512879	+	0.858461i	$0.671421\pi$
$954$		0			0
$955$	11.0834	−	19.1970i	0.358650	−	0.621200i
$956$		0			0
$957$	32.4491	+	7.97604i	1.04893	+	0.257829i
$958$		0			0
$959$	24.9818	−	14.4487i	0.806705	−	0.466572i
$960$		0			0
$961$	−10.0713			−0.324879
$962$		0			0
$963$	−1.67076	−	40.1855i	−0.0538396	−	1.29496i
$964$		0			0
$965$	4.70737	−	8.15340i	0.151536	−	0.262467i
$966$		0			0
$967$	16.5585	+	28.6801i	0.532484	+	0.922290i	0.999281	+	0.0379247i	$0.0120747\pi$
$967$	16.5585	+	28.6801i	0.532484	+	0.922290i	−0.466797	+	0.884365i	$0.654592\pi$
$968$		0			0
$969$	5.30474	+	1.30391i	0.170413	+	0.0418877i
$970$		0			0
$971$	−27.2744	−	47.2406i	−0.875276	−	1.51602i	−0.856469	−	0.516199i	$-0.827347\pi$
$971$	−27.2744	−	47.2406i	−0.875276	−	1.51602i	−0.0188069	−	0.999823i	$-0.505987\pi$
$972$		0			0
$973$	31.8208	−	18.4041i	1.02013	−	0.590010i
$974$		0			0
$975$	−0.198477	+	0.206901i	−0.00635637	+	0.00662613i
$976$		0			0
$977$	3.74344			0.119763			0.0598817	−	0.998205i	$-0.480928\pi$
$977$	3.74344			0.119763			0.0598817	+	0.998205i	$0.480928\pi$
$978$		0			0
$979$	−5.56873	+	9.64533i	−0.177978	+	0.308266i
$980$		0			0
$981$	−12.6648	+	8.03136i	−0.404356	+	0.256422i
$982$		0			0
$983$	26.8131	+	46.4417i	0.855205	+	1.48126i	0.876455	+	0.481484i	$0.159902\pi$
$983$	26.8131	+	46.4417i	0.855205	+	1.48126i	−0.0212495	+	0.999774i	$0.506764\pi$
$984$		0			0
$985$	−7.22430	+	12.5129i	−0.230185	+	0.398693i
$986$		0			0
$987$	−7.31713	+	29.8668i	−0.232907	+	0.950670i
$988$		0			0
$989$	−2.10377	−	3.64384i	−0.0668961	−	0.115867i
$990$		0			0
$991$	28.7394	−	49.7781i	0.912938	−	1.58125i	0.103045	−	0.994677i	$-0.467142\pi$
$991$	28.7394	−	49.7781i	0.912938	−	1.58125i	0.809893	−	0.586578i	$-0.199525\pi$
$992$		0			0
$993$	16.6521	+	4.09312i	0.528440	+	0.129891i
$994$		0			0
$995$	6.58651	+	11.4082i	0.208806	+	0.361663i
$996$		0			0
$997$	−0.977818	−	1.69363i	−0.0309678	−	0.0536378i	0.850126	−	0.526579i	$-0.176526\pi$
$997$	−0.977818	−	1.69363i	−0.0309678	−	0.0536378i	−0.881094	+	0.472941i	$0.843192\pi$
$998$		0			0
$999$	0.502986	−	2.48807i	0.0159138	−	0.0787190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.q.d.781.2	yes	26
3.2	odd	2		3780.2.q.d.2881.8		26
7.2	even	3		1260.2.t.d.961.10	yes	26
9.4	even	3		1260.2.t.d.1201.10	yes	26
9.5	odd	6		3780.2.t.d.361.2		26
21.2	odd	6		3780.2.t.d.1801.2		26
63.23	odd	6		3780.2.q.d.3061.8		26
63.58	even	3	inner	1260.2.q.d.121.2	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.q.d.121.2	✓	26	63.58	even	3	inner
1260.2.q.d.781.2	yes	26	1.1	even	1	trivial
1260.2.t.d.961.10	yes	26	7.2	even	3
1260.2.t.d.1201.10	yes	26	9.4	even	3
3780.2.q.d.2881.8		26	3.2	odd	2
3780.2.q.d.3061.8		26	63.23	odd	6
3780.2.t.d.361.2		26	9.5	odd	6
3780.2.t.d.1801.2		26	21.2	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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68198 - 0.413434i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +(2.65814 + 1.39078i) q^{9} +O(q^{10})\)	\(q+(-1.68198 - 0.413434i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +(2.65814 + 1.39078i) q^{9} +(-1.44197 - 2.49756i) q^{11} +(0.0827654 + 0.143354i) q^{13} +(1.19904 - 1.24992i) q^{15} +(-0.347478 + 0.601849i) q^{17} +(2.26911 + 3.93021i) q^{19} +(1.09045 - 4.45095i) q^{21} +(-2.15543 + 3.73332i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.89596 - 3.43824i) q^{27} +(3.34476 - 5.79329i) q^{29} -4.57479 q^{31} +(1.39279 + 4.79702i) q^{33} +(-2.29230 - 1.32113i) q^{35} +(0.244258 + 0.423067i) q^{37} +(-0.0799427 - 0.275337i) q^{39} +(-1.99120 - 3.44886i) q^{41} +(-0.488017 + 0.845269i) q^{43} +(-2.53352 + 1.60663i) q^{45} -6.71021 q^{47} +(-6.99999 + 0.0106868i) q^{49} +(0.833277 - 0.868641i) q^{51} +(-0.0191298 + 0.0331338i) q^{53} +2.88394 q^{55} +(-2.19172 - 7.54869i) q^{57} -1.44083 q^{59} -6.57738 q^{61} +(-3.67429 + 7.03560i) q^{63} -0.165531 q^{65} -5.56263 q^{67} +(5.16888 - 5.38825i) q^{69} -8.73689 q^{71} +(-3.12050 + 5.40487i) q^{73} +(0.482948 + 1.66336i) q^{75} +(6.60502 - 3.82013i) q^{77} -9.89693 q^{79} +(5.13146 + 7.39379i) q^{81} +(-4.42924 + 7.67166i) q^{83} +(-0.347478 - 0.601849i) q^{85} +(-8.02098 + 8.36139i) q^{87} +(-1.93095 - 3.34450i) q^{89} +(-0.379111 + 0.219266i) q^{91} +(7.69473 + 1.89138i) q^{93} -4.53822 q^{95} +(-7.94934 + 13.7687i) q^{97} +(-0.359400 - 8.64434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 4 q^{3} - 13 q^{5} - 6 q^{7}+O(q^{10}) \) 26 * q - 4 * q^3 - 13 * q^5 - 6 * q^7	\( 26 q - 4 q^{3} - 13 q^{5} - 6 q^{7} + q^{11} + 7 q^{13} - q^{15} + 8 q^{17} - 9 q^{19} - 8 q^{21} - 3 q^{23} - 13 q^{25} - 7 q^{27} - 7 q^{29} + 2 q^{31} - 7 q^{33} + 3 q^{35} + 10 q^{37} + 16 q^{39} + 13 q^{41} - 8 q^{43} - 3 q^{45} - 12 q^{47} - 28 q^{49} + 17 q^{53} - 2 q^{55} - 16 q^{57} + 16 q^{59} - 20 q^{61} - 16 q^{63} - 14 q^{65} - 48 q^{67} + 54 q^{69} + 4 q^{71} - 17 q^{73} + 5 q^{75} + 19 q^{77} - 38 q^{79} + 12 q^{81} + 9 q^{83} + 8 q^{85} - 28 q^{87} + q^{89} - 2 q^{91} - 40 q^{93} + 18 q^{95} + 9 q^{97} + 33 q^{99}+O(q^{100}) \) 26 * q - 4 * q^3 - 13 * q^5 - 6 * q^7 + q^11 + 7 * q^13 - q^15 + 8 * q^17 - 9 * q^19 - 8 * q^21 - 3 * q^23 - 13 * q^25 - 7 * q^27 - 7 * q^29 + 2 * q^31 - 7 * q^33 + 3 * q^35 + 10 * q^37 + 16 * q^39 + 13 * q^41 - 8 * q^43 - 3 * q^45 - 12 * q^47 - 28 * q^49 + 17 * q^53 - 2 * q^55 - 16 * q^57 + 16 * q^59 - 20 * q^61 - 16 * q^63 - 14 * q^65 - 48 * q^67 + 54 * q^69 + 4 * q^71 - 17 * q^73 + 5 * q^75 + 19 * q^77 - 38 * q^79 + 12 * q^81 + 9 * q^83 + 8 * q^85 - 28 * q^87 + q^89 - 2 * q^91 - 40 * q^93 + 18 * q^95 + 9 * q^97 + 33 * q^99

Introduction

L-functions

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Database

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