LMFDB - Embedded newform 882.2.bb.a.151.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (of order $21$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.25
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.a.625.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(1.57737 + 0.715470i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.808957 - 0.750602i) q^{5} +(-1.73159 + 0.0397794i) q^{6} +(-2.34752 - 1.22030i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(1.97620 + 2.25713i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(1.57737 + 0.715470i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.808957 - 0.750602i) q^{5} +(-1.73159 + 0.0397794i) q^{6} +(-2.34752 - 1.22030i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(1.97620 + 2.25713i) q^{9} +(1.05452 + 0.325276i) q^{10} +(2.56422 + 1.74825i) q^{11} +(1.54285 - 0.787150i) q^{12} +(-1.50847 - 1.02846i) q^{13} +(2.64451 + 0.0808975i) q^{14} +(-0.738992 - 1.76276i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(2.09951 - 0.316450i) q^{17} +(-2.75983 - 1.17616i) q^{18} +(3.26316 + 5.65196i) q^{19} +(-1.09122 + 0.164475i) q^{20} +(-2.82983 - 3.60445i) q^{21} +(-3.06882 - 0.462550i) q^{22} +(1.50801 + 3.84234i) q^{23} +(-1.04853 + 1.37862i) q^{24} +(-0.282643 - 3.77161i) q^{25} +(1.80531 + 0.272107i) q^{26} +(1.50230 + 4.97424i) q^{27} +(-2.41773 + 1.07453i) q^{28} +(7.26009 - 1.09428i) q^{29} +(1.43064 + 1.26756i) q^{30} +4.94876 q^{31} +(0.623490 + 0.781831i) q^{32} +(2.79390 + 4.59227i) q^{33} +(-1.75429 + 1.19605i) q^{34} +(0.983088 + 2.74923i) q^{35} +(2.99684 - 0.137764i) q^{36} +(-3.52325 + 8.97710i) q^{37} +(-5.39230 - 3.67641i) q^{38} +(-1.64359 - 2.70152i) q^{39} +(0.911793 - 0.621650i) q^{40} +(7.51605 - 2.31840i) q^{41} +(4.11350 + 2.01968i) q^{42} +(0.128389 + 0.0396028i) q^{43} +(2.96560 - 0.914767i) q^{44} +(0.0955401 - 3.30926i) q^{45} +(-3.02579 - 2.80753i) q^{46} +(8.23940 - 3.96789i) q^{47} +(0.346534 - 1.69703i) q^{48} +(4.02175 + 5.72936i) q^{49} +(1.89109 + 3.27547i) q^{50} +(3.53812 + 1.00298i) q^{51} +(-1.74459 + 0.538136i) q^{52} +(1.34141 + 3.41784i) q^{53} +(-3.51177 - 3.82981i) q^{54} +(-0.762097 - 3.33897i) q^{55} +(1.71208 - 2.01713i) q^{56} +(1.10341 + 11.2499i) q^{57} +(-6.06632 + 4.13595i) q^{58} +(-0.552592 - 2.42106i) q^{59} +(-1.83894 - 0.521298i) q^{60} +(-8.94265 - 11.2137i) q^{61} +(-4.45868 + 2.14719i) q^{62} +(-1.88482 - 7.71022i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(0.448324 + 1.96424i) q^{65} +(-4.50973 - 2.92526i) q^{66} -9.28805 q^{67} +(1.06161 - 1.83877i) q^{68} +(-0.370392 + 7.13973i) q^{69} +(-2.07858 - 2.05042i) q^{70} +(1.45294 - 1.82193i) q^{71} +(-2.64028 + 1.42440i) q^{72} +(6.07431 - 4.14140i) q^{73} +(-0.720677 - 9.61677i) q^{74} +(2.25264 - 6.15145i) q^{75} +(6.45343 + 0.972698i) q^{76} +(-3.88617 - 7.23317i) q^{77} +(2.65297 + 1.72086i) q^{78} -9.19765 q^{79} +(-0.551773 + 0.955699i) q^{80} +(-1.18924 + 8.92108i) q^{81} +(-5.76582 + 5.34989i) q^{82} +(-6.73217 + 4.58992i) q^{83} +(-4.58244 - 0.0348845i) q^{84} +(-1.93594 - 1.31990i) q^{85} +(-0.132858 + 0.0200251i) q^{86} +(12.2348 + 3.46829i) q^{87} +(-2.27501 + 2.11090i) q^{88} +(0.484939 + 6.47106i) q^{89} +(1.34976 + 3.02299i) q^{90} +(2.28614 + 4.25511i) q^{91} +(3.94429 + 1.21665i) q^{92} +(7.80604 + 3.54069i) q^{93} +(-5.70184 + 7.14988i) q^{94} +(1.60262 - 7.02153i) q^{95} +(0.424098 + 1.67933i) q^{96} +(-7.09294 + 12.2853i) q^{97} +(-6.10934 - 3.41700i) q^{98} +(1.12139 + 9.24266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9}+O(q^{10}) $ 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9} + 2 q^{10} + 2 q^{12} - 21 q^{13} - 7 q^{15} - 56 q^{16} + 7 q^{17} + 6 q^{18} - 34 q^{19} + 2 q^{20} + 16 q^{21} - 36 q^{23} + 2 q^{24} + 32 q^{25} + 7 q^{26} + 49 q^{27} - 16 q^{29} - 7 q^{30} + 92 q^{31} - 56 q^{32} + 14 q^{33} + 7 q^{34} + 16 q^{35} - 15 q^{36} - 26 q^{37} + q^{38} + 44 q^{39} + 2 q^{40} + 3 q^{41} - 33 q^{42} - 3 q^{43} + 106 q^{45} - 36 q^{46} + 27 q^{47} + 2 q^{48} - 74 q^{49} - 164 q^{50} - 7 q^{51} + 21 q^{52} - 78 q^{53} - 28 q^{54} - 53 q^{55} - 18 q^{57} + 40 q^{58} - 16 q^{59} - 7 q^{60} - 45 q^{61} - 20 q^{62} - 50 q^{63} - 56 q^{64} - 14 q^{65} + 14 q^{66} + 86 q^{67} - 21 q^{68} - 85 q^{69} - 26 q^{70} + 7 q^{71} + 6 q^{72} + 36 q^{73} + 2 q^{74} - 35 q^{75} + 8 q^{76} - 37 q^{77} - 12 q^{78} - 2 q^{79} - 12 q^{80} + 41 q^{81} + 3 q^{82} + 191 q^{83} - 5 q^{84} + 159 q^{85} - 3 q^{86} + 72 q^{87} + 59 q^{89} + 22 q^{90} - 29 q^{91} + 27 q^{92} + 23 q^{93} + 6 q^{94} + 26 q^{95} + 2 q^{96} - 113 q^{97} - 18 q^{98} - 33 q^{99}+O(q^{100}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9 + 2 * q^10 + 2 * q^12 - 21 * q^13 - 7 * q^15 - 56 * q^16 + 7 * q^17 + 6 * q^18 - 34 * q^19 + 2 * q^20 + 16 * q^21 - 36 * q^23 + 2 * q^24 + 32 * q^25 + 7 * q^26 + 49 * q^27 - 16 * q^29 - 7 * q^30 + 92 * q^31 - 56 * q^32 + 14 * q^33 + 7 * q^34 + 16 * q^35 - 15 * q^36 - 26 * q^37 + q^38 + 44 * q^39 + 2 * q^40 + 3 * q^41 - 33 * q^42 - 3 * q^43 + 106 * q^45 - 36 * q^46 + 27 * q^47 + 2 * q^48 - 74 * q^49 - 164 * q^50 - 7 * q^51 + 21 * q^52 - 78 * q^53 - 28 * q^54 - 53 * q^55 - 18 * q^57 + 40 * q^58 - 16 * q^59 - 7 * q^60 - 45 * q^61 - 20 * q^62 - 50 * q^63 - 56 * q^64 - 14 * q^65 + 14 * q^66 + 86 * q^67 - 21 * q^68 - 85 * q^69 - 26 * q^70 + 7 * q^71 + 6 * q^72 + 36 * q^73 + 2 * q^74 - 35 * q^75 + 8 * q^76 - 37 * q^77 - 12 * q^78 - 2 * q^79 - 12 * q^80 + 41 * q^81 + 3 * q^82 + 191 * q^83 - 5 * q^84 + 159 * q^85 - 3 * q^86 + 72 * q^87 + 59 * q^89 + 22 * q^90 - 29 * q^91 + 27 * q^92 + 23 * q^93 + 6 * q^94 + 26 * q^95 + 2 * q^96 - 113 * q^97 - 18 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$3$	1.57737	+	0.715470i	0.910696	+	0.413077i
$3$	1.57737	+	0.715470i	0.910696	+	0.413077i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−0.808957	−	0.750602i	−0.361776	−	0.335680i	0.478251	−	0.878223i	$-0.341271\pi$
$5$	−0.808957	−	0.750602i	−0.361776	−	0.335680i	−0.840028	+	0.542544i	$0.817461\pi$
$6$	−1.73159	+	0.0397794i	−0.706920	+	0.0162399i
$7$	−2.34752	−	1.22030i	−0.887281	−	0.461229i
$7$	−2.34752	−	1.22030i	−0.887281	−	0.461229i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	1.97620	+	2.25713i	0.658735	+	0.752375i
$10$	1.05452	+	0.325276i	0.333468	+	0.102861i
$11$	2.56422	+	1.74825i	0.773140	+	0.527118i	0.884432	−	0.466670i	$-0.154546\pi$
$11$	2.56422	+	1.74825i	0.773140	+	0.527118i	−0.111291	+	0.993788i	$0.535499\pi$
$12$	1.54285	−	0.787150i	0.445383	−	0.227231i
$13$	−1.50847	−	1.02846i	−0.418374	−	0.285242i	0.335780	−	0.941941i	$-0.391000\pi$
$13$	−1.50847	−	1.02846i	−0.418374	−	0.285242i	−0.754154	+	0.656698i	$0.771953\pi$
$14$	2.64451	+	0.0808975i	0.706776	+	0.0216208i
$15$	−0.738992	−	1.76276i	−0.190807	−	0.455144i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	2.09951	−	0.316450i	0.509206	−	0.0767504i	0.110586	−	0.993867i	$-0.464727\pi$
$17$	2.09951	−	0.316450i	0.509206	−	0.0767504i	0.398620	+	0.917116i	$0.369489\pi$
$18$	−2.75983	−	1.17616i	−0.650498	−	0.277223i
$19$	3.26316	+	5.65196i	0.748621	+	1.29665i	0.948484	+	0.316825i	$0.102617\pi$
$19$	3.26316	+	5.65196i	0.748621	+	1.29665i	−0.199863	+	0.979824i	$0.564050\pi$
$20$	−1.09122	+	0.164475i	−0.244004	+	0.0367777i
$21$	−2.82983	−	3.60445i	−0.617520	−	0.786555i
$22$	−3.06882	−	0.462550i	−0.654274	−	0.0986159i
$23$	1.50801	+	3.84234i	0.314441	+	0.801182i	0.997490	+	0.0708098i	$0.0225583\pi$
$23$	1.50801	+	3.84234i	0.314441	+	0.801182i	−0.683049	+	0.730373i	$0.739346\pi$
$24$	−1.04853	+	1.37862i	−0.214030	+	0.281409i
$25$	−0.282643	−	3.77161i	−0.0565286	−	0.754322i
$26$	1.80531	+	0.272107i	0.354051	+	0.0533646i
$27$	1.50230	+	4.97424i	0.289118	+	0.957293i
$28$	−2.41773	+	1.07453i	−0.456907	+	0.203066i
$29$	7.26009	−	1.09428i	1.34816	−	0.203203i	0.565038	−	0.825065i	$-0.308862\pi$
$29$	7.26009	−	1.09428i	1.34816	−	0.203203i	0.783127	+	0.621862i	$0.213623\pi$
$30$	1.43064	+	1.26756i	0.261199	+	0.231423i
$31$	4.94876			0.888824			0.444412	−	0.895822i	$-0.353413\pi$
$31$	4.94876			0.888824			0.444412	+	0.895822i	$0.353413\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	2.79390	+	4.59227i	0.486355	+	0.799411i
$34$	−1.75429	+	1.19605i	−0.300858	+	0.205122i
$35$	0.983088	+	2.74923i	0.166172	+	0.464704i
$36$	2.99684	−	0.137764i	0.499473	−	0.0229606i
$37$	−3.52325	+	8.97710i	−0.579219	+	1.47583i	0.277850	+	0.960624i	$0.410378\pi$
$37$	−3.52325	+	8.97710i	−0.579219	+	1.47583i	−0.857069	+	0.515201i	$0.827717\pi$
$38$	−5.39230	−	3.67641i	−0.874747	−	0.596392i
$39$	−1.64359	−	2.70152i	−0.263184	−	0.432590i
$40$	0.911793	−	0.621650i	0.144167	−	0.0982915i
$41$	7.51605	−	2.31840i	1.17381	−	0.362072i	0.354297	−	0.935133i	$-0.384720\pi$
$41$	7.51605	−	2.31840i	1.17381	−	0.362072i	0.819513	+	0.573060i	$0.194244\pi$
$42$	4.11350	+	2.01968i	0.634727	+	0.311643i
$43$	0.128389	+	0.0396028i	0.0195792	+	0.00603937i	0.304529	−	0.952503i	$-0.401501\pi$
$43$	0.128389	+	0.0396028i	0.0195792	+	0.00603937i	−0.284950	+	0.958542i	$0.591977\pi$
$44$	2.96560	−	0.914767i	0.447081	−	0.137906i
$45$	0.0955401	−	3.30926i	0.0142423	−	0.493315i
$46$	−3.02579	−	2.80753i	−0.446129	−	0.413947i
$47$	8.23940	−	3.96789i	1.20184	−	0.578776i	0.277640	−	0.960685i	$-0.410448\pi$
$47$	8.23940	−	3.96789i	1.20184	−	0.578776i	0.924200	+	0.381910i	$0.124733\pi$
$48$	0.346534	−	1.69703i	0.0500179	−	0.244945i
$49$	4.02175	+	5.72936i	0.574535	+	0.818480i
$50$	1.89109	+	3.27547i	0.267441	+	0.463221i
$51$	3.53812	+	1.00298i	0.495436	+	0.140445i
$52$	−1.74459	+	0.538136i	−0.241932	+	0.0746260i
$53$	1.34141	+	3.41784i	0.184256	+	0.469477i	0.992919	−	0.118796i	$-0.0379034\pi$
$53$	1.34141	+	3.41784i	0.184256	+	0.469477i	−0.808663	+	0.588273i	$0.799808\pi$
$54$	−3.51177	−	3.82981i	−0.477891	−	0.521172i
$55$	−0.762097	−	3.33897i	−0.102761	−	0.450226i
$56$	1.71208	−	2.01713i	0.228786	−	0.269550i
$57$	1.10341	+	11.2499i	0.146150	+	1.49009i
$58$	−6.06632	+	4.13595i	−0.796547	+	0.543077i
$59$	−0.552592	−	2.42106i	−0.0719413	−	0.315196i	0.926135	−	0.377192i	$-0.123110\pi$
$59$	−0.552592	−	2.42106i	−0.0719413	−	0.315196i	−0.998076	+	0.0619965i	$0.980253\pi$
$60$	−1.83894	−	0.521298i	−0.237406	−	0.0672993i
$61$	−8.94265	−	11.2137i	−1.14499	−	1.43577i	−0.882174	−	0.470924i	$-0.843921\pi$
$61$	−8.94265	−	11.2137i	−1.14499	−	1.43577i	−0.262815	−	0.964846i	$-0.584651\pi$
$62$	−4.45868	+	2.14719i	−0.566253	+	0.272693i
$63$	−1.88482	−	7.71022i	−0.237465	−	0.971396i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	0.448324	+	1.96424i	0.0556078	+	0.243634i
$66$	−4.50973	−	2.92526i	−0.555109	−	0.360075i
$67$	−9.28805			−1.13472			−0.567358	−	0.823471i	$-0.692034\pi$
$67$	−9.28805			−1.13472			−0.567358	+	0.823471i	$0.692034\pi$
$68$	1.06161	−	1.83877i	0.128739	−	0.222983i
$69$	−0.370392	+	7.13973i	−0.0445900	+	0.859522i
$70$	−2.07858	−	2.05042i	−0.248437	−	0.245072i
$71$	1.45294	−	1.82193i	0.172432	−	0.216223i	−0.688105	−	0.725611i	$-0.741557\pi$
$71$	1.45294	−	1.82193i	0.172432	−	0.216223i	0.860537	+	0.509389i	$0.170128\pi$
$72$	−2.64028	+	1.42440i	−0.311160	+	0.167867i
$73$	6.07431	−	4.14140i	0.710945	−	0.484714i	−0.153048	−	0.988219i	$-0.548909\pi$
$73$	6.07431	−	4.14140i	0.710945	−	0.484714i	0.863992	+	0.503505i	$0.167956\pi$
$74$	−0.720677	−	9.61677i	−0.0837770	−	1.11793i
$75$	2.25264	−	6.15145i	0.260113	−	0.710309i
$76$	6.45343	+	0.972698i	0.740259	+	0.111576i
$77$	−3.88617	−	7.23317i	−0.442870	−	0.824297i
$78$	2.65297	+	1.72086i	0.300389	+	0.194849i
$79$	−9.19765			−1.03482			−0.517408	−	0.855739i	$-0.673103\pi$
$79$	−9.19765			−1.03482			−0.517408	+	0.855739i	$0.673103\pi$
$80$	−0.551773	+	0.955699i	−0.0616901	+	0.106850i
$81$	−1.18924	+	8.92108i	−0.132137	+	0.991231i
$82$	−5.76582	+	5.34989i	−0.636728	+	0.590797i
$83$	−6.73217	+	4.58992i	−0.738952	+	0.503809i	−0.873335	−	0.487121i	$-0.838047\pi$
$83$	−6.73217	+	4.58992i	−0.738952	+	0.503809i	0.134383	+	0.990929i	$0.457095\pi$
$84$	−4.58244	−	0.0348845i	−0.499986	−	0.00380621i
$85$	−1.93594	−	1.31990i	−0.209982	−	0.143163i
$86$	−0.132858	+	0.0200251i	−0.0143264	+	0.00215936i
$87$	12.2348	+	3.46829i	1.31171	+	0.371840i
$88$	−2.27501	+	2.11090i	−0.242517	+	0.225023i
$89$	0.484939	+	6.47106i	0.0514034	+	0.685931i	0.962072	+	0.272794i	$0.0879478\pi$
$89$	0.484939	+	6.47106i	0.0514034	+	0.685931i	−0.910669	+	0.413137i	$0.864433\pi$
$90$	1.34976	+	3.02299i	0.142277	+	0.318652i
$91$	2.28614	+	4.25511i	0.239653	+	0.446057i
$92$	3.94429	+	1.21665i	0.411220	+	0.126845i
$93$	7.80604	+	3.54069i	0.809449	+	0.367153i
$94$	−5.70184	+	7.14988i	−0.588100	+	0.737454i
$95$	1.60262	−	7.02153i	0.164425	−	0.720394i
$96$	0.424098	+	1.67933i	0.0432843	+	0.171396i
$97$	−7.09294	+	12.2853i	−0.720179	+	1.24739i	0.240749	+	0.970587i	$0.422607\pi$
$97$	−7.09294	+	12.2853i	−0.720179	+	1.24739i	−0.960928	+	0.276799i	$0.910726\pi$
$98$	−6.10934	−	3.41700i	−0.617137	−	0.345170i
$99$	1.12139	+	9.24266i	0.112704	+	0.928923i
$100$	−3.12499	−	2.13058i	−0.312499	−	0.213058i
$101$	−0.204390	+	0.0630460i	−0.0203376	+	0.00627332i	−0.304907	−	0.952382i	$-0.598625\pi$
$101$	−0.204390	+	0.0630460i	−0.0203376	+	0.00627332i	0.284570	+	0.958655i	$0.408149\pi$
$102$	−3.62291	+	0.631480i	−0.358721	+	0.0625259i
$103$	2.20400	+	2.04502i	0.217167	+	0.201501i	0.781253	−	0.624215i	$-0.214581\pi$
$103$	2.20400	+	2.04502i	0.217167	+	0.201501i	−0.564086	+	0.825716i	$0.690771\pi$
$104$	1.33834	−	1.24179i	0.131235	−	0.121768i
$105$	−0.416294	+	5.03992i	−0.0406262	+	0.491846i
$106$	−2.69151	−	2.49736i	−0.261423	−	0.242565i
$107$	−0.224761	−	2.99923i	−0.0217285	−	0.289946i	−0.997474	−	0.0710369i	$-0.977369\pi$
$107$	−0.224761	−	2.99923i	−0.0217285	−	0.289946i	0.975745	−	0.218909i	$-0.0702499\pi$
$108$	4.82569	+	1.92684i	0.464352	+	0.185411i
$109$	1.23760	−	16.5146i	0.118540	−	1.58181i	−0.548089	−	0.836420i	$-0.684645\pi$
$109$	1.23760	−	16.5146i	0.118540	−	1.58181i	0.666629	−	0.745389i	$-0.267736\pi$
$110$	2.13535	+	2.67764i	0.203598	+	0.255303i
$111$	−11.9803	+	11.6394i	−1.13712	+	1.10477i
$112$	−0.667329	+	2.56021i	−0.0630567	+	0.241917i
$113$	0.00718970	+	0.0959399i	0.000676350	+	0.00902526i	0.997532	−	0.0702167i	$-0.0223691\pi$
$113$	0.00718970	+	0.0959399i	0.000676350	+	0.00902526i	−0.996855	+	0.0792420i	$0.974750\pi$
$114$	−5.87530	−	9.65710i	−0.550272	−	0.904470i
$115$	1.66415	−	4.24020i	0.155183	−	0.395400i
$116$	3.67105	−	6.35844i	0.340848	−	0.590366i
$117$	−0.659686	−	5.43724i	−0.0609880	−	0.502673i
$118$	1.54833	+	1.94154i	0.142535	+	0.178733i
$119$	−5.31481	−	1.81915i	−0.487208	−	0.166761i
$120$	1.88301	−	0.328212i	0.171894	−	0.0299615i
$121$	−0.499936	−	1.27382i	−0.0454487	−	0.115801i
$122$	12.9225	+	6.22315i	1.16995	+	0.563417i
$123$	13.5144	+	1.72054i	1.21855	+	0.155136i
$124$	3.08550	−	3.86910i	0.277086	−	0.347455i
$125$	−6.04258	+	7.57716i	−0.540465	+	0.677722i
$126$	5.04350	+	6.12887i	0.449311	+	0.546003i
$127$	11.2908	+	14.1582i	1.00189	+	1.25634i	0.966421	+	0.256965i	$0.0827224\pi$
$127$	11.2908	+	14.1582i	1.00189	+	1.25634i	0.0354731	+	0.999371i	$0.488706\pi$
$128$	1.00000			0.0883883
$129$	0.174183	+	0.154327i	0.0153359	+	0.0135877i
$130$	−1.25618	−	1.57520i	−0.110174	−	0.138154i
$131$	12.6445	+	3.90032i	1.10476	+	0.340773i	0.792897	−	0.609355i	$-0.208572\pi$
$131$	12.6445	+	3.90032i	1.10476	+	0.340773i	0.311860	+	0.950128i	$0.399048\pi$
$132$	5.33235	+	0.678873i	0.464121	+	0.0590883i
$133$	−0.763276	−	17.2501i	−0.0661844	−	1.49578i
$134$	8.36824	−	4.02993i	0.722906	−	0.348133i
$135$	2.51838	−	5.15158i	0.216748	−	0.443377i
$136$	−0.158669	+	2.11729i	−0.0136057	+	0.181556i
$137$	−11.0733	+	10.2745i	−0.946057	+	0.877813i	−0.992640	−	0.121102i	$-0.961357\pi$
$137$	−11.0733	+	10.2745i	−0.946057	+	0.877813i	0.0465830	+	0.998914i	$0.485167\pi$
$138$	−2.76410	−	6.59338i	−0.235296	−	0.561266i
$139$	8.17930	−	2.52298i	0.693759	−	0.213996i	0.0722307	−	0.997388i	$-0.476988\pi$
$139$	8.17930	−	2.52298i	0.693759	−	0.213996i	0.621528	+	0.783392i	$0.286512\pi$
$140$	2.76238	+	0.945505i	0.233463	+	0.0799098i
$141$	15.8355	−	0.363784i	1.33359	−	0.0306362i
$142$	−0.518547	+	2.27190i	−0.0435155	+	0.190654i
$143$	−2.07004	−	5.27437i	−0.173105	−	0.441065i
$144$	1.76079	−	2.42891i	0.146732	−	0.202410i
$145$	−6.69447	−	4.56421i	−0.555945	−	0.379037i
$146$	−3.67588	+	6.36682i	−0.304218	+	0.526921i
$147$	2.24460	+	11.9148i	0.185132	+	0.982714i
$148$	4.82187	+	8.35172i	0.396355	+	0.686507i
$149$	−0.360004	+	4.80391i	−0.0294926	+	0.393552i	0.962850	+	0.270037i	$0.0870358\pi$
$149$	−0.360004	+	4.80391i	−0.0294926	+	0.393552i	−0.992343	+	0.123515i	$0.960583\pi$
$150$	0.639455	+	6.51965i	0.0522113	+	0.532327i
$151$	−12.2141	−	1.84098i	−0.993971	−	0.149817i	−0.368136	−	0.929772i	$-0.620004\pi$
$151$	−12.2141	−	1.84098i	−0.993971	−	0.149817i	−0.625836	+	0.779955i	$0.715242\pi$
$152$	−6.23638	+	1.92367i	−0.505837	+	0.156030i
$153$	4.86333	+	4.11349i	0.393177	+	0.332556i
$154$	6.63968	+	4.83072i	0.535040	+	0.389270i
$155$	−4.00334	−	3.71455i	−0.321556	−	0.298360i
$156$	−3.13689	−	0.399365i	−0.251153	−	0.0319748i
$157$	−3.59559	−	15.7533i	−0.286960	−	1.25725i	−0.888673	−	0.458541i	$-0.848372\pi$
$157$	−3.59559	−	15.7533i	−0.286960	−	1.25725i	0.601714	−	0.798712i	$-0.294485\pi$
$158$	8.28679	−	3.99071i	0.659262	−	0.317484i
$159$	−0.329472	+	6.35095i	−0.0261288	+	0.503663i
$160$	0.0824681	−	1.10046i	0.00651968	−	0.0869991i
$161$	1.14871	−	10.8602i	0.0905313	−	0.855903i
$162$	−2.79925	−	8.55361i	−0.219930	−	0.672035i
$163$	2.88830	−	2.67995i	0.226229	−	0.209910i	−0.558912	−	0.829227i	$-0.688781\pi$
$163$	2.88830	−	2.67995i	0.226229	−	0.209910i	0.785141	+	0.619317i	$0.212590\pi$
$164$	2.87359	−	7.32178i	0.224390	−	0.571735i
$165$	1.18682	−	5.81205i	0.0923939	−	0.452468i
$166$	4.07399	−	7.05635i	0.316203	−	0.547679i
$167$	−2.00635	+	5.11209i	−0.155256	+	0.395585i	−0.987245	−	0.159206i	$-0.949107\pi$
$167$	−2.00635	+	5.11209i	−0.155256	+	0.395585i	0.831990	+	0.554791i	$0.187202\pi$
$168$	4.14377	−	1.95682i	0.319699	−	0.150972i
$169$	−3.53168	−	8.99857i	−0.271668	−	0.692198i
$170$	2.31691	+	0.349217i	0.177699	+	0.0267837i
$171$	−6.30852	+	18.5348i	−0.482424	+	1.41739i
$172$	0.111012	−	0.0756867i	0.00846459	−	0.00577106i
$173$	−4.14903	+	5.20272i	−0.315445	+	0.395556i	−0.914125	−	0.405433i	$-0.867121\pi$
$173$	−4.14903	+	5.20272i	−0.315445	+	0.395556i	0.598680	+	0.800988i	$0.295692\pi$
$174$	−12.5280	+	2.18365i	−0.949745	+	0.165542i
$175$	−3.93898	+	9.19886i	−0.297759	+	0.695368i
$176$	1.13383	−	2.88895i	0.0854656	−	0.217763i
$177$	0.860556	−	4.21428i	0.0646834	−	0.316765i
$178$	−3.24460	−	5.61981i	−0.243193	−	0.421223i
$179$	−3.80040	+	0.572818i	−0.284055	+	0.0428144i	−0.289524	−	0.957171i	$-0.593497\pi$
$179$	−3.80040	+	0.572818i	−0.284055	+	0.0428144i	0.00546928	+	0.999985i	$0.498259\pi$
$180$	−2.52772	−	2.13799i	−0.188405	−	0.159356i
$181$	−14.8178	−	7.13587i	−1.10140	−	0.530405i	−0.207300	−	0.978277i	$-0.566468\pi$
$181$	−14.8178	−	7.13587i	−1.10140	−	0.530405i	−0.894098	+	0.447872i	$0.852182\pi$
$182$	−3.90597	−	2.84180i	−0.289530	−	0.210648i
$183$	−6.08279	−	24.0864i	−0.449653	−	1.78052i
$184$	−4.08156	+	0.615197i	−0.300897	+	0.0453529i
$185$	9.58839	−	4.61752i	0.704952	−	0.339487i
$186$	−8.56925	+	0.196859i	−0.628328	+	0.0144344i
$187$	5.93683	+	2.85903i	0.434144	+	0.209073i
$188$	2.03496	−	8.91576i	0.148415	−	0.650249i
$189$	2.54337	−	13.5104i	0.185003	−	0.982738i
$190$	1.60262	+	7.02153i	0.116266	+	0.509395i
$191$	4.45705	−	19.5276i	0.322501	−	1.41297i	−0.510586	−	0.859827i	$-0.670571\pi$
$191$	4.45705	−	19.5276i	0.322501	−	1.41297i	0.833087	−	0.553143i	$-0.186572\pi$
$192$	−1.11073	−	1.32901i	−0.0801602	−	0.0959132i
$193$	−1.20123	+	5.26294i	−0.0864666	+	0.378835i	−0.999583	−	0.0288632i	$-0.990811\pi$
$193$	−1.20123	+	5.26294i	−0.0864666	+	0.378835i	0.913117	+	0.407698i	$0.133668\pi$
$194$	1.06011	−	14.1462i	0.0761116	−	1.01564i
$195$	−0.698179	+	3.41909i	−0.0499977	+	0.244846i
$196$	6.98691	+	0.427869i	0.499065	+	0.0305621i
$197$	−20.8417			−1.48491			−0.742453	−	0.669898i	$-0.766338\pi$
$197$	−20.8417			−1.48491			−0.742453	+	0.669898i	$0.766338\pi$
$198$	−5.02058	−	7.84080i	−0.356797	−	0.557221i
$199$	−7.41023	−	6.87568i	−0.525297	−	0.487404i	0.372367	−	0.928086i	$-0.378546\pi$
$199$	−7.41023	−	6.87568i	−0.525297	−	0.487404i	−0.897664	+	0.440681i	$0.854737\pi$
$200$	3.73994	+	0.563705i	0.264454	+	0.0398600i
$201$	−14.6507	−	6.64532i	−1.03338	−	0.468725i
$202$	0.156795	−	0.145484i	0.0110320	−	0.0102362i
$203$	−18.3786	−	6.29062i	−1.28992	−	0.441515i
$204$	2.99014	−	2.14087i	0.209352	−	0.149891i
$205$	−7.82035	−	3.76608i	−0.546197	−	0.263035i
$206$	−2.87304	−	0.886215i	−0.200174	−	0.0617455i
$207$	−5.69251	+	10.9970i	−0.395657	+	0.764344i
$208$	−0.667005	+	1.69950i	−0.0462485	+	0.117839i
$209$	−1.51361	+	20.1977i	−0.104698	+	1.39710i
$210$	−1.81167	−	4.72144i	−0.125017	−	0.325810i
$211$	1.68919	+	22.5407i	0.116289	+	1.55176i	0.684581	+	0.728937i	$0.259985\pi$
$211$	1.68919	+	22.5407i	0.116289	+	1.55176i	−0.568292	+	0.822827i	$0.692396\pi$
$212$	3.50853	+	1.08224i	0.240967	+	0.0743284i
$213$	3.59536	−	1.83432i	0.246350	−	0.125686i
$214$	1.50382	+	2.60469i	0.102799	+	0.178053i
$215$	−0.0741353	−	0.128406i	−0.00505598	−	0.00875722i
$216$	−5.18382	+	0.357763i	−0.352714	+	0.0243427i
$217$	−11.6173	−	6.03897i	−0.788637	−	0.409952i
$218$	6.05037	+	15.4161i	0.409783	+	1.04411i
$219$	12.5445	−	2.18653i	0.847679	−	0.147752i
$220$	−3.08567	−	1.48598i	−0.208036	−	0.100185i
$221$	−3.49250	−	1.68190i	−0.234931	−	0.113137i
$222$	5.74374	−	15.6848i	0.385494	−	1.05270i
$223$	−4.07946	−	10.3943i	−0.273181	−	0.696053i	−0.999958	−	0.00917958i	$-0.997078\pi$
$223$	−4.07946	−	10.3943i	−0.273181	−	0.696053i	0.726777	−	0.686873i	$-0.241017\pi$
$224$	−0.509591	−	2.59621i	−0.0340485	−	0.173467i
$225$	7.95444	−	8.09143i	0.530296	−	0.539429i
$226$	−0.0481044	−	0.0833193i	−0.00319986	−	0.00554232i
$227$	−10.0792	−	17.4577i	−0.668980	−	1.15871i	−0.978190	−	0.207714i	$-0.933398\pi$
$227$	−10.0792	−	17.4577i	−0.668980	−	1.15871i	0.309209	−	0.950994i	$-0.399936\pi$
$228$	9.48352	+	6.15154i	0.628062	+	0.407396i
$229$	3.84346	+	1.18555i	0.253983	+	0.0783435i	0.419132	−	0.907925i	$-0.362334\pi$
$229$	3.84346	+	1.18555i	0.253983	+	0.0783435i	−0.165149	+	0.986269i	$0.552811\pi$
$230$	0.340401	+	4.54233i	0.0224454	+	0.299513i
$231$	−0.954815	−	14.1898i	−0.0628222	−	0.933623i
$232$	−0.548675	+	7.32156i	−0.0360223	+	0.480684i
$233$	8.16359	−	20.8005i	0.534815	−	1.36269i	−0.366862	−	0.930275i	$-0.619568\pi$
$233$	8.16359	−	20.8005i	0.534815	−	1.36269i	0.901677	−	0.432411i	$-0.142337\pi$
$234$	2.95349	+	4.61256i	0.193076	+	0.301532i
$235$	−9.64362	−	2.97466i	−0.629081	−	0.194046i
$236$	−2.23740	−	1.07747i	−0.145642	−	0.0701376i
$237$	−14.5081	−	6.58064i	−0.942403	−	0.427459i
$238$	5.57778	−	0.667012i	0.361554	−	0.0432359i
$239$	16.4604	−	15.2730i	1.06473	−	0.987929i	0.0647843	−	0.997899i	$-0.479364\pi$
$239$	16.4604	−	15.2730i	1.06473	−	0.987929i	0.999950	+	0.00996994i	$0.00317358\pi$
$240$	−1.55413	+	1.11272i	−0.100318	+	0.0718255i
$241$	19.6852	+	2.96707i	1.26804	+	0.191126i	0.748392	−	0.663257i	$-0.230826\pi$
$241$	19.6852	+	2.96707i	1.26804	+	0.191126i	0.519645	+	0.854383i	$0.326064\pi$
$242$	1.00311	+	0.930754i	0.0644826	+	0.0598311i
$243$	−8.25864	+	13.2210i	−0.529792	+	0.848128i
$244$	−14.3429			−0.918210
$245$	1.04705	−	7.65354i	0.0668936	−	0.488966i
$246$	−12.9225	+	4.31350i	−0.823910	+	0.275019i
$247$	0.890420	−	11.8818i	0.0566560	−	0.756022i
$248$	−1.10120	+	4.82469i	−0.0699265	+	0.306368i
$249$	−13.9031	+	2.42334i	−0.881073	+	0.153573i
$250$	2.15657	−	9.44856i	0.136394	−	0.597580i
$251$	0.949449	+	4.15981i	0.0599287	+	0.262565i	0.996013	−	0.0892119i	$-0.0284348\pi$
$251$	0.949449	+	4.15981i	0.0599287	+	0.262565i	−0.936084	+	0.351777i	$0.885578\pi$
$252$	−7.20326	−	3.33363i	−0.453763	−	0.209999i
$253$	−2.85052	+	12.4890i	−0.179211	+	0.785174i
$254$	−16.3156	−	7.85720i	−1.02373	−	0.493004i
$255$	−2.10935	−	3.46708i	−0.132092	−	0.217117i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−3.31857	+	0.500194i	−0.207007	+	0.0312012i	−0.251727	−	0.967798i	$-0.580998\pi$
$257$	−3.31857	+	0.500194i	−0.207007	+	0.0312012i	0.0447202	+	0.999000i	$0.485760\pi$
$258$	−0.223893	−	0.0634687i	−0.0139390	−	0.00395139i
$259$	19.2257	−	16.7745i	1.19462	−	1.04232i
$260$	1.81523	+	0.874168i	0.112576	+	0.0542136i
$261$	16.8174	+	14.2244i	1.04097	+	0.880469i
$262$	−13.0846	+	1.97219i	−0.808370	+	0.121842i
$263$	−11.2347	−	19.4591i	−0.692761	−	1.19990i	−0.970930	−	0.239364i	$-0.923061\pi$
$263$	−11.2347	−	19.4591i	−0.692761	−	1.19990i	0.278169	−	0.960532i	$-0.410272\pi$
$264$	−5.09883	+	1.70197i	−0.313811	+	0.104749i
$265$	1.48030	−	3.77175i	0.0909343	−	0.231697i
$266$	8.17225	+	15.2107i	0.501073	+	0.932626i
$267$	−3.86492	+	10.5542i	−0.236529	+	0.645908i
$268$	−5.79100	+	7.26169i	−0.353742	+	0.443578i
$269$	12.5237	−	8.53850i	0.763582	−	0.520601i	−0.117782	−	0.993039i	$-0.537578\pi$
$269$	12.5237	−	8.53850i	0.763582	−	0.520601i	0.881364	+	0.472438i	$0.156626\pi$
$270$	−0.0337962	+	5.73410i	−0.00205677	+	0.348966i
$271$	16.5734	+	2.49804i	1.00676	+	0.151745i	0.631667	−	0.775240i	$-0.282371\pi$
$271$	16.5734	+	2.49804i	1.00676	+	0.151745i	0.375098	+	0.926985i	$0.377609\pi$
$272$	−0.775701	−	1.97645i	−0.0470338	−	0.119840i
$273$	0.561696	+	8.34756i	0.0339954	+	0.505217i
$274$	5.51876	−	14.0616i	0.333400	−	0.849490i
$275$	5.86897	−	10.1654i	0.353912	−	0.612994i
$276$	5.35113	+	4.74113i	0.322100	+	0.285383i
$277$	2.62205	−	6.68087i	0.157544	−	0.401415i	−0.830207	−	0.557455i	$-0.811778\pi$
$277$	2.62205	−	6.68087i	0.157544	−	0.401415i	0.987751	+	0.156041i	$0.0498730\pi$
$278$	−6.27461	+	5.82199i	−0.376326	+	0.349180i
$279$	9.77977	+	11.1700i	0.585499	+	0.668729i
$280$	−2.89905	+	0.346680i	−0.173252	+	0.0207181i
$281$	−2.15503	+	28.7569i	−0.128558	+	1.71549i	0.444335	+	0.895861i	$0.353440\pi$
$281$	−2.15503	+	28.7569i	−0.128558	+	1.71549i	−0.572894	+	0.819630i	$0.694179\pi$
$282$	−14.1095	+	7.19853i	−0.840206	+	0.428666i
$283$	23.6947	−	11.4108i	1.40851	−	0.678301i	0.433638	−	0.901087i	$-0.357230\pi$
$283$	23.6947	−	11.4108i	1.40851	−	0.678301i	0.974867	+	0.222786i	$0.0715152\pi$
$284$	−0.518547	−	2.27190i	−0.0307701	−	0.134813i
$285$	7.55162	−	9.92894i	0.447319	−	0.588139i
$286$	4.15350	+	3.85389i	0.245602	+	0.227885i
$287$	−20.4733	−	3.72933i	−1.20850	−	0.220136i
$288$	−0.532549	+	2.95235i	−0.0313808	+	0.173969i
$289$	−11.9369	+	3.68206i	−0.702173	+	0.216592i
$290$	8.01185	+	1.20759i	0.470472	+	0.0709122i
$291$	−19.9780	+	14.3038i	−1.17113	+	0.838501i
$292$	0.549398	−	7.33121i	0.0321511	−	0.429027i
$293$	−8.55481	−	14.8174i	−0.499777	−	0.865640i	0.500223	−	0.865897i	$-0.333251\pi$
$293$	−8.55481	−	14.8174i	−0.499777	−	0.865640i	−1.00000		0.000257130i	$0.999918\pi$
$294$	−7.19194	−	9.76094i	−0.419443	−	0.569270i
$295$	−1.37023	+	2.37331i	−0.0797780	+	0.138180i
$296$	−7.96802	−	5.43251i	−0.463132	−	0.315758i
$297$	−4.84401	+	15.3814i	−0.281078	+	0.892521i
$298$	−1.75999	−	4.48438i	−0.101953	−	0.259773i
$299$	1.67690	−	7.34696i	0.0969774	−	0.424886i
$300$	−3.40490	−	5.59656i	−0.196582	−	0.323117i
$301$	−0.253069	−	0.249641i	−0.0145867	−	0.0143891i
$302$	11.8033	−	3.64084i	0.679205	−	0.209507i
$303$	−0.367507	−	0.0467881i	−0.0211127	−	0.00268791i
$304$	4.78413	−	4.43903i	0.274389	−	0.254596i
$305$	−1.18283	+	15.7838i	−0.0677287	+	0.903777i
$306$	−6.16648	−	1.59601i	−0.352514	−	0.0912376i
$307$	20.0247	−	9.64339i	1.14287	−	0.550377i	0.235986	−	0.971756i	$-0.424168\pi$
$307$	20.0247	−	9.64339i	1.14287	−	0.550377i	0.906885	+	0.421379i	$0.138454\pi$
$308$	−8.07811	−	1.47148i	−0.460293	−	0.0838453i
$309$	2.01338	+	4.80265i	0.114537	+	0.273213i
$310$	5.21856	+	1.60971i	0.296395	+	0.0914256i
$311$	−0.418529	−	0.524818i	−0.0237326	−	0.0297597i	0.769824	−	0.638257i	$-0.220344\pi$
$311$	−0.418529	−	0.524818i	−0.0237326	−	0.0297597i	−0.793556	+	0.608497i	$0.791773\pi$
$312$	2.99952	−	1.00123i	0.169815	−	0.0566836i
$313$	−1.68607			−0.0953025			−0.0476512	−	0.998864i	$-0.515174\pi$
$313$	−1.68607			−0.0953025			−0.0476512	+	0.998864i	$0.515174\pi$
$314$	10.0746	+	12.6332i	0.568544	+	0.712932i
$315$	−4.26257	+	7.65198i	−0.240168	+	0.431140i
$316$	−5.73464	+	7.19101i	−0.322599	+	0.404526i
$317$	−12.3865	+	15.5322i	−0.695696	+	0.872375i	−0.996694	−	0.0812498i	$-0.974109\pi$
$317$	−12.3865	+	15.5322i	−0.695696	+	0.872375i	0.300998	+	0.953625i	$0.402680\pi$
$318$	−2.45873	−	5.86496i	−0.137879	−	0.328891i
$319$	20.5295	+	9.88650i	1.14943	+	0.553538i
$320$	0.403171	+	1.02726i	0.0225379	+	0.0574257i
$321$	1.79133	−	4.89171i	0.0999821	−	0.273028i
$322$	3.67711	+	10.2831i	0.204917	+	0.573055i
$323$	8.63960	+	10.8337i	0.480720	+	0.602804i
$324$	6.23331	+	6.49199i	0.346295	+	0.360666i
$325$	−3.45258	+	5.98004i	−0.191515	+	0.331713i
$326$	−1.43948	+	3.66774i	−0.0797256	+	0.203137i
$327$	13.7678	−	25.1642i	0.761363	−	1.39158i
$328$	0.587789	+	7.84350i	0.0324552	+	0.433085i
$329$	−24.1842	−	0.739811i	−1.33332	−	0.0407871i
$330$	1.45247	+	5.75142i	0.0799556	+	0.316605i
$331$	−15.6902	−	19.6748i	−0.862409	−	1.08143i	−0.995908	−	0.0903778i	$-0.971193\pi$
$331$	−15.6902	−	19.6748i	−0.862409	−	1.08143i	0.133498	−	0.991049i	$-0.457379\pi$
$332$	−0.608899	+	8.12519i	−0.0334177	+	0.445928i
$333$	−27.2251	+	9.78815i	−1.49193	+	0.536388i
$334$	−0.410396	−	5.47635i	−0.0224559	−	0.299653i
$335$	7.51363	+	6.97163i	0.410513	+	0.380901i
$336$	−2.88438	+	3.56095i	−0.157356	+	0.194266i
$337$	−7.45542	+	6.91762i	−0.406123	+	0.376827i	−0.856617	−	0.515952i	$-0.827438\pi$
$337$	−7.45542	+	6.91762i	−0.406123	+	0.376827i	0.450495	+	0.892779i	$0.351248\pi$
$338$	7.08627	+	6.57509i	0.385442	+	0.357638i
$339$	−0.0573013	+	0.156477i	−0.00311218	+	0.00849866i
$340$	−2.23898	+	0.690634i	−0.121426	+	0.0374549i
$341$	12.6897	+	8.65169i	0.687186	+	0.468515i
$342$	−2.35817	−	19.4364i	−0.127515	−	1.05100i
$343$	−2.44962	−	18.3575i	−0.132267	−	0.991214i
$344$	−0.0671791	+	0.116358i	−0.00362206	+	0.00627358i
$345$	5.65873	−	5.49771i	0.304656	−	0.295987i
$346$	1.48077	−	6.48769i	0.0796068	−	0.348780i
$347$	1.33602	−	1.67532i	0.0717213	−	0.0899357i	−0.744677	−	0.667426i	$-0.767396\pi$
$347$	1.33602	−	1.67532i	0.0717213	−	0.0899357i	0.816398	+	0.577490i	$0.195968\pi$
$348$	10.3399	−	7.40310i	0.554276	−	0.396848i
$349$	15.3037	+	4.72057i	0.819189	+	0.252686i	0.675899	−	0.736994i	$-0.263756\pi$
$349$	15.3037	+	4.72057i	0.819189	+	0.252686i	0.143290	+	0.989681i	$0.454232\pi$
$350$	−0.442340	−	9.99694i	−0.0236441	−	0.534359i
$351$	2.84962	−	9.04854i	0.152101	−	0.482975i
$352$	0.231923	+	3.09480i	0.0123616	+	0.164954i
$353$	13.9529	−	12.9464i	0.742638	−	0.689067i	−0.215138	−	0.976584i	$-0.569020\pi$
$353$	13.9529	−	12.9464i	0.742638	−	0.689067i	0.957776	+	0.287516i	$0.0928296\pi$
$354$	1.05317	+	4.17032i	0.0559755	+	0.221650i
$355$	−2.54290	+	0.383281i	−0.134963	+	0.0203424i
$356$	5.36163	+	3.65550i	0.284166	+	0.193741i
$357$	−7.08189	−	6.67207i	−0.374813	−	0.353123i
$358$	3.17551	−	2.16502i	0.167831	−	0.114425i
$359$	−3.15614	+	2.92847i	−0.166575	+	0.154559i	−0.759056	−	0.651026i	$-0.774339\pi$
$359$	−3.15614	+	2.92847i	−0.166575	+	0.154559i	0.592481	+	0.805584i	$0.298149\pi$
$360$	3.20503	+	0.829524i	0.168920	+	0.0437198i
$361$	−11.7964	+	20.4320i	−0.620865	+	1.07537i
$362$	16.4465			0.864409
$363$	0.122793	−	2.36697i	0.00644495	−	0.124234i
$364$	4.75217	+	0.865637i	0.249081	+	0.0453717i
$365$	−8.02240	−	1.20918i	−0.419912	−	0.0632915i
$366$	15.9311	+	19.0619i	0.832732	+	0.996381i
$367$	0.832618	+	11.1105i	0.0434623	+	0.579964i	0.975841	+	0.218481i	$0.0701103\pi$
$367$	0.832618	+	11.1105i	0.0434623	+	0.579964i	−0.932379	+	0.361483i	$0.882271\pi$
$368$	3.41044	−	2.32520i	0.177781	−	0.121209i
$369$	20.0862	+	12.3831i	1.04564	+	0.644636i
$370$	−6.63537	+	8.32049i	−0.344956	+	0.432562i
$371$	1.02181	−	9.66039i	0.0530496	−	0.501542i
$372$	7.63521	−	3.89542i	0.395867	−	0.201968i
$373$	−1.27853	+	2.21447i	−0.0661995	+	0.114661i	−0.897225	−	0.441573i	$-0.854421\pi$
$373$	−1.27853	+	2.21447i	−0.0661995	+	0.114661i	0.831026	+	0.556234i	$0.187754\pi$
$374$	−6.58938			−0.340729
$375$	−14.9526	+	7.62871i	−0.772151	+	0.393945i
$376$	2.03496	+	8.91576i	0.104945	+	0.459795i
$377$	−12.0770	−	5.81600i	−0.621999	−	0.299539i
$378$	3.57045	+	13.2760i	0.183644	+	0.682843i
$379$	−9.07458	+	4.37009i	−0.466130	+	0.224476i	−0.652180	−	0.758064i	$-0.726146\pi$
$379$	−9.07458	+	4.37009i	−0.466130	+	0.224476i	0.186050	+	0.982540i	$0.440431\pi$
$380$	−4.49044	−	5.63083i	−0.230354	−	0.288855i
$381$	7.67999	+	30.4109i	0.393458	+	1.55800i
$382$	4.45705	+	19.5276i	0.228043	+	0.999120i
$383$	−7.08731	+	4.83205i	−0.362145	+	0.246906i	−0.730698	−	0.682700i	$-0.760805\pi$
$383$	−7.08731	+	4.83205i	−0.362145	+	0.246906i	0.368554	+	0.929606i	$0.379853\pi$
$384$	1.57737	+	0.715470i	0.0804949	+	0.0365112i
$385$	−2.28549	+	8.76829i	−0.116479	+	0.446874i
$386$	−1.20123	−	5.26294i	−0.0611411	−	0.267877i
$387$	0.164335	+	0.368054i	0.00835360	+	0.0187092i
$388$	5.18268	+	13.2053i	0.263111	+	0.670396i
$389$	26.3577	−	8.13027i	1.33639	−	0.412221i	0.457483	−	0.889218i	$-0.348751\pi$
$389$	26.3577	−	8.13027i	1.33639	−	0.412221i	0.878905	+	0.476997i	$0.158275\pi$
$390$	−0.854452	−	3.38343i	−0.0432668	−	0.171326i
$391$	4.38198	+	7.58981i	0.221606	+	0.383833i
$392$	−6.48063	+	2.64601i	−0.327321	+	0.133644i
$393$	17.1546	+	15.1990i	0.865333	+	0.766690i
$394$	18.7777	−	9.04286i	0.946006	−	0.455573i
$395$	7.44050	+	6.90377i	0.374372	+	0.347367i
$396$	7.92538	+	4.88597i	0.398265	+	0.245529i
$397$	−37.2762	+	11.4982i	−1.87084	+	0.577078i	−0.875205	+	0.483752i	$0.839274\pi$
$397$	−37.2762	+	11.4982i	−1.87084	+	0.577078i	−0.995636	+	0.0933255i	$0.970250\pi$
$398$	9.65963	+	2.97960i	0.484194	+	0.149354i
$399$	11.1380	−	27.7560i	0.557597	−	1.38954i
$400$	−3.61415	+	1.11482i	−0.180708	+	0.0557409i
$401$	−31.1863	+	21.2624i	−1.55737	+	1.06180i	−0.590330	+	0.807162i	$0.701002\pi$
$401$	−31.1863	+	21.2624i	−1.55737	+	1.06180i	−0.967038	+	0.254633i	$0.918045\pi$
$402$	16.0831	−	0.369473i	0.802153	−	0.0184276i
$403$	−7.46505	−	5.08959i	−0.371861	−	0.253530i
$404$	−0.0781439	+	0.199107i	−0.00388780	+	0.00990596i
$405$	7.65822	−	6.32413i	0.380540	−	0.314248i
$406$	19.2879	−	2.30652i	0.957244	−	0.114471i
$407$	−24.7286	+	16.8597i	−1.22575	+	0.835703i
$408$	−1.76514	+	3.22623i	−0.0873872	+	0.159722i
$409$	−15.7859	−	19.7948i	−0.780561	−	0.978792i	−0.999995	−	0.00316480i	$-0.998993\pi$
$409$	−15.7859	−	19.7948i	−0.780561	−	0.978792i	0.219434	−	0.975627i	$-0.429579\pi$
$410$	8.67994			0.428672
$411$	−24.8179	+	8.28413i	−1.22417	+	0.408626i
$412$	2.97303	−	0.448112i	0.146471	−	0.0220769i
$413$	−1.65720	+	6.35783i	−0.0815452	+	0.312849i
$414$	0.357355	−	12.3778i	0.0175630	−	0.608338i
$415$	8.89124	+	1.34014i	0.436454	+	0.0657848i
$416$	−0.136435	−	1.82060i	−0.00668928	−	0.0892623i
$417$	14.7069	+	1.87237i	0.720201	+	0.0916904i
$418$	−7.39973	−	18.8542i	−0.361933	−	0.922190i
$419$	9.46674	+	1.42688i	0.462480	+	0.0697077i	0.376150	−	0.926559i	$-0.377248\pi$
$419$	9.46674	+	1.42688i	0.462480	+	0.0697077i	0.0863305	+	0.996267i	$0.472486\pi$
$420$	3.68081	+	3.46781i	0.179605	+	0.169212i
$421$	9.03932	−	1.36246i	0.440549	−	0.0664021i	0.0749775	−	0.997185i	$-0.476112\pi$
$421$	9.03932	−	1.36246i	0.440549	−	0.0664021i	0.365572	+	0.930783i	$0.380873\pi$
$422$	−11.3019	−	19.5755i	−0.550170	−	0.952922i
$423$	25.2388	+	10.7560i	1.22715	+	0.522975i
$424$	−3.63064	+	0.547231i	−0.176320	+	0.0265759i
$425$	−1.78694	−	7.82909i	−0.0866792	−	0.379766i
$426$	−2.44342	+	3.21263i	−0.118384	+	0.155652i
$427$	7.30900	+	37.2372i	0.353707	+	1.80203i
$428$	−2.48503	−	1.69426i	−0.120118	−	0.0818952i
$429$	0.508437	−	9.80069i	0.0245476	−	0.473182i
$430$	0.122507	+	0.0835238i	0.00590781	+	0.00402787i
$431$	35.6501	+	10.9966i	1.71721	+	0.529688i	0.987980	−	0.154584i	$-0.0494038\pi$
$431$	35.6501	+	10.9966i	1.71721	+	0.529688i	0.729227	+	0.684272i	$0.239880\pi$
$432$	4.51523	−	2.57151i	0.217239	−	0.123722i
$433$	4.76475	−	20.8757i	0.228979	−	1.00322i	−0.721495	−	0.692420i	$-0.756545\pi$
$433$	4.76475	−	20.8757i	0.228979	−	1.00322i	0.950474	−	0.310804i	$-0.100598\pi$
$434$	13.0871	+	0.400343i	0.628200	+	0.0192171i
$435$	−7.29411	−	11.9892i	−0.349726	−	0.574836i
$436$	−12.1400	−	11.2643i	−0.581400	−	0.539460i
$437$	−16.7959	+	21.0614i	−0.803455	+	1.00750i
$438$	−10.3535	+	7.41285i	−0.494710	+	0.354200i
$439$	13.2998	−	6.40482i	0.634763	−	0.305686i	−0.0886903	−	0.996059i	$-0.528268\pi$
$439$	13.2998	−	6.40482i	0.634763	−	0.305686i	0.723453	+	0.690374i	$0.242554\pi$
$440$	3.42483			0.163273
$441$	−4.98409	+	20.4000i	−0.237338	+	0.971427i
$442$	3.87638			0.184381
$443$	8.81052	−	4.24292i	0.418600	−	0.201587i	−0.212714	−	0.977115i	$-0.568230\pi$
$443$	8.81052	−	4.24292i	0.418600	−	0.201587i	0.631314	+	0.775527i	$0.282516\pi$
$444$	1.63047	+	16.6237i	0.0773786	+	0.788924i
$445$	4.46490	−	5.59880i	0.211656	−	0.265409i
$446$	8.18537	+	7.59492i	0.387589	+	0.359630i
$447$	−4.00492	+	7.31999i	−0.189426	+	0.346223i
$448$	1.58558	+	2.11800i	0.0749116	+	0.100066i
$449$	−1.04015	+	4.55719i	−0.0490876	+	0.215067i	−0.993523	−	0.113630i	$-0.963752\pi$
$449$	−1.04015	+	4.55719i	−0.0490876	+	0.215067i	0.944436	+	0.328697i	$0.106609\pi$
$450$	−3.65596	+	10.7414i	−0.172344	+	0.506356i
$451$	23.3259	+	7.19509i	1.09837	+	0.338804i
$452$	0.0794915	+	0.0541964i	0.00373897	+	0.00254918i
$453$	−17.9490	−	11.6428i	−0.843320	−	0.547025i
$454$	16.6557	+	11.3556i	0.781689	+	0.532946i
$455$	1.34450	−	5.15818i	0.0630312	−	0.241819i
$456$	−11.2134	−	1.42760i	−0.525116	−	0.0668537i
$457$	−0.877222	−	3.84336i	−0.0410347	−	0.179785i	0.950257	−	0.311465i	$-0.100820\pi$
$457$	−0.877222	−	3.84336i	−0.0410347	−	0.179785i	−0.991292	+	0.131681i	$0.957963\pi$
$458$	−3.97723	+	0.599472i	−0.185844	+	0.0280115i
$459$	4.72820	+	9.96806i	0.220693	+	0.465269i
$460$	−2.27754	−	3.94481i	−0.106191	−	0.183928i
$461$	−34.8352	+	5.25057i	−1.62244	+	0.244543i	−0.896444	−	0.443157i	$-0.853858\pi$
$461$	−34.8352	+	5.25057i	−1.62244	+	0.244543i	−0.725994	+	0.687701i	$0.758620\pi$
$462$	7.01700	+	12.3703i	0.326461	+	0.575520i
$463$	6.63184	+	0.999588i	0.308208	+	0.0464548i	0.301325	−	0.953522i	$-0.402571\pi$
$463$	6.63184	+	0.999588i	0.308208	+	0.0464548i	0.00688255	+	0.999976i	$0.497809\pi$
$464$	−2.68237	−	6.83456i	−0.124526	−	0.317287i
$465$	−3.65710	−	8.72350i	−0.169594	−	0.404543i
$466$	1.66985	+	22.2827i	0.0773545	+	1.03222i
$467$	16.2472	+	2.44887i	0.751829	+	0.113320i	0.513767	−	0.857930i	$-0.328250\pi$
$467$	16.2472	+	2.44887i	0.751829	+	0.113320i	0.238062	+	0.971250i	$0.423488\pi$
$468$	−4.66232	−	2.87430i	−0.215516	−	0.132865i
$469$	21.8039	+	11.3342i	1.00681	+	0.523364i
$470$	9.97926	−	1.50413i	0.460309	−	0.0693804i
$471$	5.59945	−	27.4214i	0.258009	−	1.26351i
$472$	2.48333			0.114304
$473$	0.259982	+	0.326007i	0.0119540	+	0.0149898i
$474$	15.9266	−	0.365877i	0.731533	−	0.0168053i
$475$	20.3947	−	13.9049i	0.935772	−	0.637999i
$476$	−4.73600	+	3.02107i	−0.217074	+	0.138470i
$477$	−5.06362	+	9.78208i	−0.231847	+	0.447891i
$478$	−8.20359	+	20.9024i	−0.375224	+	0.956054i
$479$	24.2258	+	16.5169i	1.10691	+	0.754677i	0.971718	−	0.236143i	$-0.0758835\pi$
$479$	24.2258	+	16.5169i	1.10691	+	0.754677i	0.135189	+	0.990820i	$0.456836\pi$
$480$	0.917430	−	1.67683i	0.0418748	−	0.0765366i
$481$	14.5473	−	9.91816i	0.663298	−	0.452229i
$482$	−19.0231	+	5.86786i	−0.866480	+	0.267274i
$483$	9.58210	−	16.3087i	0.436001	−	0.742071i
$484$	−1.30761	−	0.403345i	−0.0594370	−	0.0183339i
$485$	14.9593	−	4.61433i	0.679266	−	0.209526i
$486$	1.70440	−	15.4950i	0.0773130	−	0.702867i
$487$	8.79148	+	8.15730i	0.398380	+	0.369642i	0.853771	−	0.520649i	$-0.174310\pi$
$487$	8.79148	+	8.15730i	0.398380	+	0.369642i	−0.455391	+	0.890292i	$0.650500\pi$
$488$	12.9225	−	6.22315i	0.584974	−	0.281709i
$489$	6.47335	−	2.16079i	0.292735	−	0.0977142i
$490$	2.37738	+	7.34990i	0.107399	+	0.332034i
$491$	−4.52742	−	7.84172i	−0.204320	−	0.353892i	0.745596	−	0.666398i	$-0.232165\pi$
$491$	−4.52742	−	7.84172i	−0.204320	−	0.353892i	−0.949916	+	0.312506i	$0.898832\pi$
$492$	9.77124	−	9.49321i	0.440521	−	0.427987i
$493$	14.8963	−	4.59491i	0.670897	−	0.206944i
$494$	4.35309	+	11.0915i	0.195855	+	0.499030i
$495$	6.03041	−	8.31863i	0.271047	−	0.373895i
$496$	−1.10120	−	4.82469i	−0.0494455	−	0.216635i
$497$	−5.63410	+	2.50400i	−0.252724	+	0.112320i
$498$	11.4748	−	8.21567i	0.514198	−	0.368153i
$499$	−23.7426	+	16.1874i	−1.06286	+	0.724648i	−0.962768	−	0.270330i	$-0.912867\pi$
$499$	−23.7426	+	16.1874i	−1.06286	+	0.724648i	−0.100096	+	0.994978i	$0.531915\pi$
$500$	2.15657	+	9.44856i	0.0964449	+	0.422553i
$501$	−6.82230	+	6.62818i	−0.304798	+	0.296125i
$502$	−2.66030	−	3.33591i	−0.118735	−	0.148889i
$503$	1.57684	−	0.759364i	0.0703076	−	0.0338584i	−0.398400	−	0.917212i	$-0.630434\pi$
$503$	1.57684	−	0.759364i	0.0703076	−	0.0338584i	0.468707	+	0.883354i	$0.344720\pi$
$504$	7.93632	−	0.121881i	0.353512	−	0.00542901i
$505$	0.212665	+	0.102414i	0.00946349	+	0.00455737i
$506$	−2.85052	−	12.4890i	−0.126721	−	0.555202i
$507$	0.867441	−	16.7209i	0.0385244	−	0.742601i
$508$	18.1090			0.803457
$509$	−20.2532	+	35.0796i	−0.897708	+	1.55488i	−0.0672913	+	0.997733i	$0.521436\pi$
$509$	−20.2532	+	35.0796i	−0.897708	+	1.55488i	−0.830417	+	0.557143i	$0.811898\pi$
$510$	3.40477	+	2.20852i	0.150766	+	0.0977951i
$511$	−19.3133	+	2.30956i	−0.854372	+	0.102169i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	−23.2120	+	24.7227i	−1.02483	+	1.09153i
$514$	2.77290	−	1.89053i	0.122307	−	0.0833878i
$515$	−0.247950	−	3.30866i	−0.0109260	−	0.145797i
$516$	0.229259	−	0.0399603i	0.0100926	−	0.00175915i
$517$	28.0645	+	4.23004i	1.23427	+	0.186037i
$518$	−10.0435	+	23.4550i	−0.441287	+	1.03056i
$519$	−10.2670	+	5.23812i	−0.450670	+	0.229928i
$520$	−2.01475			−0.0883527
$521$	4.61113	−	7.98671i	0.202017	−	0.349904i	−0.747161	−	0.664643i	$-0.768584\pi$
$521$	4.61113	−	7.98671i	0.202017	−	0.349904i	0.949178	+	0.314739i	$0.101917\pi$
$522$	−21.3237	−	5.51898i	−0.933311	−	0.241559i
$523$	19.9032	−	18.4675i	0.870307	−	0.807527i	−0.112213	−	0.993684i	$-0.535794\pi$
$523$	19.9032	−	18.4675i	0.870307	−	0.807527i	0.982520	+	0.186157i	$0.0596034\pi$
$524$	10.9331	−	7.45408i	0.477616	−	0.325633i
$525$	−12.7947	+	11.6918i	−0.558408	+	0.510272i
$526$	18.5651	+	12.6575i	0.809476	+	0.551891i
$527$	10.3900	−	1.56604i	0.452594	−	0.0682176i
$528$	3.85543	−	3.74573i	0.167786	−	0.163012i
$529$	4.37073	−	4.05544i	0.190032	−	0.176324i
$530$	0.302794	+	4.04051i	0.0131525	+	0.175508i
$531$	4.37261	−	6.03179i	0.189755	−	0.261757i
$532$	−13.9626	−	10.1585i	−0.605356	−	0.440428i
$533$	−13.7221	−	4.23271i	−0.594370	−	0.183339i
$534$	−1.09713	−	11.1860i	−0.0474775	−	0.484064i
$535$	−2.06940	+	2.59495i	−0.0894681	+	0.112190i
$536$	2.06678	−	9.05517i	0.0892715	−	0.391124i
$537$	−6.40448	−	1.81553i	−0.276374	−	0.0783458i
$538$	−7.57873	+	13.1267i	−0.326742	+	0.565934i
$539$	0.296257	+	21.7223i	0.0127607	+	0.935648i
$540$	−2.45748	−	5.18091i	−0.105753	−	0.222951i
$541$	−6.23766	−	4.25277i	−0.268178	−	0.182841i	0.421763	−	0.906706i	$-0.361411\pi$
$541$	−6.23766	−	4.25277i	−0.268178	−	0.182841i	−0.689941	+	0.723865i	$0.742364\pi$
$542$	−16.0160	+	4.94029i	−0.687947	+	0.212203i
$543$	−18.2677	−	21.8576i	−0.783940	−	0.938000i
$544$	1.55643	+	1.44416i	0.0667315	+	0.0619178i
$545$	−13.3970	+	12.4306i	−0.573866	+	0.532470i
$546$	−4.12794	−	7.27718i	−0.176659	−	0.311434i
$547$	−18.1581	−	16.8482i	−0.776383	−	0.720378i	0.188783	−	0.982019i	$-0.439546\pi$
$547$	−18.1581	−	16.8482i	−0.776383	−	0.720378i	−0.965165	+	0.261641i	$0.915736\pi$
$548$	1.12886	+	15.0635i	0.0482223	+	0.643482i
$549$	7.63829	−	42.3453i	0.325994	−	1.80725i
$550$	−0.877177	+	11.7051i	−0.0374030	+	0.499108i
$551$	29.8757	+	37.4629i	1.27275	+	1.59597i
$552$	−6.87830	−	1.94984i	−0.292760	−	0.0829909i
$553$	21.5917	+	11.2239i	0.918173	+	0.477287i
$554$	0.536337	+	7.15692i	0.0227868	+	0.304069i
$555$	18.4282	−	0.423344i	0.782231	−	0.0179700i
$556$	3.12716	−	7.96789i	0.132621	−	0.337914i
$557$	−23.0869	+	39.9877i	−0.978223	+	1.69433i	−0.309364	+	0.950944i	$0.600116\pi$
$557$	−23.0869	+	39.9877i	−0.978223	+	1.69433i	−0.668859	+	0.743389i	$0.733217\pi$
$558$	−13.6577	−	5.82052i	−0.578178	−	0.246402i
$559$	−0.152941	−	0.191782i	−0.00646872	−	0.00811152i
$560$	2.46154	−	1.57020i	0.104019	−	0.0663531i
$561$	7.31904	+	8.75737i	0.309010	+	0.369737i
$562$	−10.5355	−	26.8441i	−0.444414	−	1.13235i
$563$	−28.4963	−	13.7231i	−1.20097	−	0.578359i	−0.277021	−	0.960864i	$-0.589347\pi$
$563$	−28.4963	−	13.7231i	−1.20097	−	0.578359i	−0.923953	+	0.382505i	$0.875062\pi$
$564$	9.58886	−	12.6075i	0.403764	−	0.530872i
$565$	0.0661965	−	0.0830078i	0.00278491	−	0.00349216i
$566$	−16.3973	+	20.5615i	−0.689228	+	0.864265i
$567$	13.6781	−	19.4912i	0.574428	−	0.818555i
$568$	1.45294	+	1.82193i	0.0609639	+	0.0764463i
$569$	−32.0963			−1.34555			−0.672773	−	0.739849i	$-0.734897\pi$
$569$	−32.0963			−1.34555			−0.672773	+	0.739849i	$0.734897\pi$
$570$	−2.49577	+	12.2222i	−0.104536	+	0.511931i
$571$	−19.6495	−	24.6396i	−0.822304	−	1.03114i	−0.998902	−	0.0468538i	$-0.985081\pi$
$571$	−19.6495	−	24.6396i	−0.822304	−	1.03114i	0.176597	−	0.984283i	$-0.443491\pi$
$572$	−5.41431	−	1.67009i	−0.226384	−	0.0698302i
$573$	21.0019	−	27.6134i	0.877366	−	1.15357i
$574$	20.0639	−	5.52300i	0.837449	−	0.230526i
$575$	14.0656	−	6.77362i	0.586575	−	0.282479i
$576$	−0.801168	−	2.89104i	−0.0333820	−	0.120460i
$577$	0.627465	−	8.37294i	0.0261217	−	0.348570i	−0.968795	−	0.247865i	$-0.920271\pi$
$577$	0.627465	−	8.37294i	0.0261217	−	0.348570i	0.994916	−	0.100705i	$-0.0321099\pi$
$578$	9.15723	−	8.49666i	0.380890	−	0.353415i
$579$	−5.66027	+	7.44217i	−0.235233	+	0.309286i
$580$	−7.74238	+	2.38821i	−0.321485	+	0.0991649i
$581$	21.4050	−	2.55969i	0.888029	−	0.106194i
$582$	11.7934	−	21.5554i	0.488852	−	0.893499i
$583$	−2.53560	+	11.1092i	−0.105014	+	0.460096i
$584$	2.68590	+	6.84357i	0.111143	+	0.283189i
$585$	−3.54755	+	4.89366i	−0.146673	+	0.202328i
$586$	14.1366	+	9.63819i	0.583979	+	0.398150i
$587$	−16.4090	+	28.4213i	−0.677274	+	1.17307i	0.298525	+	0.954402i	$0.403505\pi$
$587$	−16.4090	+	28.4213i	−0.677274	+	1.17307i	−0.975799	+	0.218670i	$0.929828\pi$
$588$	10.7148	+	5.67384i	0.441872	+	0.233985i
$589$	16.1486	+	27.9702i	0.665392	+	1.15249i
$590$	0.204795	−	2.73280i	0.00843129	−	0.112508i
$591$	−32.8751	−	14.9116i	−1.35230	−	0.613381i
$592$	9.53602	+	1.43732i	0.391928	+	0.0590736i
$593$	11.0957	−	3.42258i	0.455648	−	0.140549i	−0.0584316	−	0.998291i	$-0.518610\pi$
$593$	11.0957	−	3.42258i	0.455648	−	0.140549i	0.514079	+	0.857743i	$0.328134\pi$
$594$	−2.30945	−	15.9599i	−0.0947581	−	0.654844i
$595$	2.93399	+	5.46093i	0.120282	+	0.223876i
$596$	3.53139	+	3.27665i	0.144651	+	0.134217i
$597$	−6.76933	−	16.1473i	−0.277050	−	0.660865i
$598$	1.67690	+	7.34696i	0.0685734	+	0.300440i
$599$	−7.78651	+	3.74979i	−0.318148	+	0.153212i	−0.586142	−	0.810209i	$-0.699354\pi$
$599$	−7.78651	+	3.74979i	−0.318148	+	0.153212i	0.267993	+	0.963421i	$0.413639\pi$
$600$	5.49596	+	3.56499i	0.224372	+	0.145540i
$601$	−0.767890	+	10.2468i	−0.0313229	+	0.417975i	0.959397	+	0.282058i	$0.0910171\pi$
$601$	−0.767890	+	10.2468i	−0.0313229	+	0.417975i	−0.990720	+	0.135917i	$0.956602\pi$
$602$	0.336323	+	0.115117i	0.0137075	+	0.00469180i
$603$	−18.3551	−	20.9643i	−0.747476	−	0.853732i
$604$	−9.05472	+	8.40155i	−0.368431	+	0.341854i
$605$	−0.551702	+	1.40571i	−0.0224299	+	0.0571504i
$606$	0.351413	−	0.117301i	0.0142752	−	0.00476501i
$607$	10.6382	−	18.4259i	0.431791	−	0.747885i	−0.565236	−	0.824929i	$-0.691215\pi$
$607$	10.6382	−	18.4259i	0.431791	−	0.747885i	0.997028	+	0.0770444i	$0.0245483\pi$
$608$	−2.38433	+	6.07518i	−0.0966975	+	0.246381i
$609$	−24.4891	−	23.0720i	−0.992349	−	0.934924i
$610$	−5.78263	−	14.7339i	−0.234132	−	0.596559i
$611$	−16.5097	−	2.48843i	−0.667910	−	0.100671i
$612$	6.24829	−	1.23758i	0.252572	−	0.0500264i
$613$	−35.8152	+	24.4184i	−1.44656	+	0.986249i	−0.450962	+	0.892543i	$0.648919\pi$
$613$	−35.8152	+	24.4184i	−1.44656	+	0.986249i	−0.995600	+	0.0937062i	$0.970129\pi$
$614$	−13.8575	+	17.3768i	−0.559244	+	0.701270i
$615$	−9.64108	−	11.5357i	−0.388766	−	0.465166i
$616$	7.91658	−	2.17920i	0.318968	−	0.0878027i
$617$	7.19622	−	18.3357i	0.289709	−	0.738166i	−0.709724	−	0.704480i	$-0.751180\pi$
$617$	7.19622	−	18.3357i	0.289709	−	0.738166i	0.999432	−	0.0336857i	$-0.0107245\pi$
$618$	−3.89779	−	3.45346i	−0.156792	−	0.138919i
$619$	12.7378	+	22.0625i	0.511974	+	0.886766i	0.999904	+	0.0138826i	$0.00441910\pi$
$619$	12.7378	+	22.0625i	0.511974	+	0.886766i	−0.487929	+	0.872883i	$0.662248\pi$
$620$	−5.40019	+	0.813948i	−0.216877	+	0.0326889i
$621$	−16.8472	+	13.2735i	−0.676056	+	0.532649i
$622$	0.604791	+	0.291252i	0.0242499	+	0.0116781i
$623$	6.75821	−	15.7827i	0.270762	−	0.632322i
$624$	−2.26806	+	2.20352i	−0.0907950	+	0.0882115i
$625$	−8.12409	+	1.22451i	−0.324964	+	0.0489804i
$626$	1.51910	−	0.731559i	0.0607154	−	0.0292390i
$627$	−16.8384	+	30.7763i	−0.672460	+	1.22909i
$628$	−14.5583	−	7.01089i	−0.580938	−	0.279765i
$629$	−4.55629	+	19.9624i	−0.181671	+	0.795954i
$630$	0.520368	−	8.74366i	0.0207320	−	0.348356i
$631$	5.76928	+	25.2769i	0.229671	+	1.00626i	0.949909	+	0.312528i	$0.101176\pi$
$631$	5.76928	+	25.2769i	0.229671	+	1.00626i	−0.720237	+	0.693728i	$0.755967\pi$
$632$	2.04667	−	8.96704i	0.0814121	−	0.356690i
$633$	−13.4627	+	36.7636i	−0.535094	+	1.46122i
$634$	4.42070	−	19.3683i	0.175568	−	0.769215i
$635$	1.49341	−	19.9282i	0.0592643	−	0.790828i
$636$	4.75995	+	4.21734i	0.188744	+	0.167229i
$637$	−0.174281	−	12.7787i	−0.00690528	−	0.506312i
$638$	−22.7860			−0.902108
$639$	6.98361	−	0.321034i	0.276267	−	0.0126999i
$640$	−0.808957	−	0.750602i	−0.0319768	−	0.0296702i
$641$	−16.1432	−	2.43319i	−0.637616	−	0.0961052i	−0.177725	−	0.984080i	$-0.556874\pi$
$641$	−16.1432	−	2.43319i	−0.637616	−	0.0961052i	−0.459892	+	0.887975i	$0.652112\pi$
$642$	0.508502	+	5.18450i	0.0200690	+	0.204616i
$643$	18.2137	−	16.8999i	0.718279	−	0.666466i	−0.233811	−	0.972282i	$-0.575120\pi$
$643$	18.2137	−	16.8999i	0.718279	−	0.666466i	0.952091	+	0.305816i	$0.0989293\pi$
$644$	−7.77463	−	7.66932i	−0.306363	−	0.302214i
$645$	−0.0250682	−	0.255586i	−0.000987058	−	0.0100637i
$646$	−12.4846	−	6.01226i	−0.491199	−	0.236549i
$647$	9.56802	+	2.95134i	0.376158	+	0.116029i	0.477068	−	0.878866i	$-0.341699\pi$
$647$	9.56802	+	2.95134i	0.376158	+	0.116029i	−0.100911	+	0.994896i	$0.532176\pi$
$648$	−8.43278	−	3.14455i	−0.331271	−	0.123529i
$649$	2.81567	−	7.17420i	0.110525	−	0.281612i
$650$	0.516023	−	6.88585i	0.0202401	−	0.270085i
$651$	−14.0042	−	17.8376i	−0.548867	−	0.699109i
$652$	−0.294444	−	3.92909i	−0.0115313	−	0.153875i
$653$	−9.72097	−	2.99852i	−0.380411	−	0.117341i	0.0986516	−	0.995122i	$-0.468547\pi$
$653$	−9.72097	−	2.99852i	−0.380411	−	0.117341i	−0.479062	+	0.877781i	$0.659023\pi$
$654$	−1.48607	+	28.6458i	−0.0581101	+	1.12014i
$655$	−7.30129	−	12.6462i	−0.285285	−	0.494128i
$656$	−3.93275	−	6.81172i	−0.153548	−	0.265953i
$657$	21.3517	+	5.52625i	0.833011	+	0.215599i
$658$	22.1102	−	9.82658i	0.861945	−	0.383080i
$659$	−11.4275	−	29.1167i	−0.445151	−	1.13423i	−0.960755	−	0.277400i	$-0.910527\pi$
$659$	−11.4275	−	29.1167i	−0.445151	−	1.13423i	0.515603	−	0.856828i	$-0.327568\pi$
$660$	−3.80407	−	4.55165i	−0.148073	−	0.177173i
$661$	−17.8858	−	8.61332i	−0.695675	−	0.335019i	0.0524068	−	0.998626i	$-0.483311\pi$
$661$	−17.8858	−	8.61332i	−0.695675	−	0.335019i	−0.748082	+	0.663606i	$0.769025\pi$
$662$	22.6729	+	10.9187i	0.881209	+	0.424368i
$663$	−4.30562	−	5.15176i	−0.167216	−	0.200078i
$664$	−2.97679	−	7.58474i	−0.115522	−	0.294345i
$665$	−12.3305	+	14.5275i	−0.478158	+	0.563354i
$666$	20.2820	−	20.6313i	0.785913	−	0.799449i
$667$	15.1529	+	26.2455i	0.586721	+	1.01623i
$668$	2.74585	+	4.75596i	0.106240	+	0.184014i
$669$	1.00198	−	19.3144i	0.0387390	−	0.746737i
$670$	−9.79442	−	3.02118i	−0.378391	−	0.116718i
$671$	−3.32645	−	44.3884i	−0.128416	−	1.71360i
$672$	1.05370	−	4.45979i	0.0406473	−	0.172040i
$673$	−1.27572	+	17.0233i	−0.0491755	+	0.656202i	0.917094	+	0.398670i	$0.130528\pi$
$673$	−1.27572	+	17.0233i	−0.0491755	+	0.656202i	−0.966270	+	0.257531i	$0.917091\pi$
$674$	3.71566	−	9.46735i	0.143122	−	0.364669i
$675$	18.3363	−	7.07203i	0.705764	−	0.272203i
$676$	−9.23733	−	2.84934i	−0.355282	−	0.109590i
$677$	20.2008	+	9.72820i	0.776381	+	0.373885i	0.779735	−	0.626109i	$-0.215354\pi$
$677$	20.2008	+	9.72820i	0.776381	+	0.373885i	−0.00335484	+	0.999994i	$0.501068\pi$
$678$	−0.0162661	−	0.165843i	−0.000624695	−	0.00636916i
$679$	31.6426	−	20.1846i	1.21433	−	0.774615i
$680$	1.71760	−	1.59370i	0.0658668	−	0.0611155i
$681$	−3.40819	−	34.7487i	−0.130602	−	1.33157i
$682$	−15.1869	−	2.28905i	−0.581535	−	0.0876522i
$683$	4.30140	+	3.99111i	0.164588	+	0.152716i	0.758167	−	0.652060i	$-0.226095\pi$
$683$	4.30140	+	3.99111i	0.164588	+	0.152716i	−0.593579	+	0.804776i	$0.702286\pi$
$684$	10.5578	+	16.4885i	0.403687	+	0.630452i
$685$	16.6699			0.636925
$686$	10.1721	+	15.4767i	0.388372	+	0.590904i
$687$	5.21435	+	4.61994i	0.198940	+	0.176262i
$688$	0.0100406	−	0.133983i	0.000382794	−	0.00510804i
$689$	1.49164	−	6.53529i	0.0568268	−	0.248975i
$690$	−2.71297	+	7.40850i	−0.103281	+	0.282037i
$691$	−3.71529	+	16.2777i	−0.141336	+	0.619234i	0.853789	+	0.520619i	$0.174299\pi$
$691$	−3.71529	+	16.2777i	−0.141336	+	0.619234i	−0.995126	+	0.0986158i	$0.968559\pi$
$692$	1.48077	+	6.48769i	0.0562905	+	0.246625i
$693$	8.64632	−	23.0658i	0.328446	−	0.876198i
$694$	−0.476820	+	2.08909i	−0.0180998	+	0.0793006i
$695$	−8.51045	−	4.09842i	−0.322820	−	0.155462i
$696$	−6.10383	+	11.1563i	−0.231365	+	0.422877i
$697$	15.0464	−	7.24595i	0.569922	−	0.274460i
$698$	−15.8363	+	2.38695i	−0.599415	+	0.0903472i
$699$	27.7592	−	26.9693i	1.04995	−	1.02007i
$700$	4.73604	+	8.81501i	0.179006	+	0.333176i
$701$	−10.1873	−	4.90593i	−0.384768	−	0.185295i	0.231493	−	0.972837i	$-0.425639\pi$
$701$	−10.1873	−	4.90593i	−0.384768	−	0.185295i	−0.616261	+	0.787542i	$0.711353\pi$
$702$	1.35860	+	9.38886i	0.0512770	+	0.354360i
$703$	−62.2351	+	9.38044i	−2.34724	+	0.353790i
$704$	−1.55174	−	2.68769i	−0.0584834	−	0.101296i
$705$	−13.0833	−	11.5919i	−0.492745	−	0.436575i
$706$	−6.95390	+	17.7182i	−0.261713	+	0.666835i
$707$	0.556746	+	0.101415i	0.0209386	+	0.00381410i
$708$	−2.75831	−	3.30037i	−0.103664	−	0.124036i
$709$	−23.7903	+	29.8321i	−0.893465	+	1.12037i	0.0986606	+	0.995121i	$0.468544\pi$
$709$	−23.7903	+	29.8321i	−0.893465	+	1.12037i	−0.992125	+	0.125248i	$0.960027\pi$
$710$	2.12478	−	1.44865i	0.0797415	−	0.0543668i
$711$	−18.1764	−	20.7602i	−0.681669	−	0.778570i
$712$	−6.41672	−	0.967166i	−0.240477	−	0.0362461i
$713$	7.46276	+	19.0148i	0.279483	+	0.712110i
$714$	9.27546	+	2.93861i	0.347126	+	0.109975i
$715$	−2.28438	+	5.82051i	−0.0854310	+	0.217675i
$716$	−1.92166	+	3.32842i	−0.0718159	+	0.124389i
$717$	36.8916	−	12.3143i	1.37774	−	0.459886i
$718$	1.57297	−	4.00786i	0.0587027	−	0.149572i
$719$	0.338074	−	0.313686i	0.0126080	−	0.0116985i	−0.673844	−	0.738874i	$-0.735358\pi$
$719$	0.338074	−	0.313686i	0.0126080	−	0.0116985i	0.686452	+	0.727176i	$0.259167\pi$
$720$	−3.24755	+	0.643235i	−0.121029	+	0.0239720i
$721$	−2.67842	−	7.49027i	−0.0997497	−	0.278952i
$722$	1.76310	−	23.5269i	0.0656157	−	0.875581i
$723$	28.9281	+	18.7644i	1.07585	+	0.697854i
$724$	−14.8178	+	7.13587i	−0.550699	+	0.265203i
$725$	−6.17922	−	27.0729i	−0.229490	−	1.00546i
$726$	0.916357	+	2.18584i	0.0340092	+	0.0811243i
$727$	−1.60143	−	1.48591i	−0.0593939	−	0.0551095i	0.649917	−	0.760005i	$-0.274803\pi$
$727$	−1.60143	−	1.48591i	−0.0593939	−	0.0551095i	−0.709311	+	0.704895i	$0.750994\pi$
$728$	−4.65714	+	1.28198i	−0.172605	+	0.0475132i
$729$	−22.4862	+	14.9456i	−0.832821	+	0.553542i
$730$	7.75258	−	2.39135i	0.286936	−	0.0885080i
$731$	0.282086	+	0.0425177i	0.0104333	+	0.00157257i
$732$	−22.6241	−	10.2619i	−0.836210	−	0.379291i
$733$	0.479405	−	6.39722i	0.0177072	−	0.236287i	−0.981327	−	0.192347i	$-0.938390\pi$
$733$	0.479405	−	6.39722i	0.0177072	−	0.236287i	0.999034	−	0.0439395i	$-0.0139909\pi$
$734$	−5.57083	−	9.64897i	−0.205623	−	0.356150i
$735$	7.12747	−	11.3233i	0.262901	−	0.417668i
$736$	−2.06383	+	3.57466i	−0.0760739	+	0.131764i
$737$	−23.8166	−	16.2379i	−0.877294	−	0.598129i
$738$	−23.4698	−	2.44169i	−0.863936	−	0.0898798i
$739$	−3.46192	−	8.82082i	−0.127349	−	0.324479i	0.852952	−	0.521989i	$-0.174810\pi$
$739$	−3.46192	−	8.82082i	−0.127349	−	0.324479i	−0.980301	+	0.197510i	$0.936715\pi$
$740$	2.36814	−	10.3755i	0.0870544	−	0.381410i
$741$	9.90562	−	18.1050i	0.363892	−	0.665103i
$742$	3.27087	+	9.14706i	0.120077	+	0.335799i
$743$	−23.7140	+	7.31481i	−0.869984	+	0.268354i	−0.697436	−	0.716647i	$-0.745676\pi$
$743$	−23.7140	+	7.31481i	−0.869984	+	0.268354i	−0.172547	+	0.985001i	$0.555200\pi$
$744$	−5.18893	+	6.82245i	−0.190235	+	0.250123i
$745$	3.89706	−	3.61594i	0.142777	−	0.132478i
$746$	0.191089	−	2.54990i	0.00699625	−	0.0933585i
$747$	−23.6642	−	6.12475i	−0.865827	−	0.224093i
$748$	5.93683	−	2.85903i	0.217072	−	0.104536i
$749$	−3.13232	+	7.31503i	−0.114452	+	0.267286i
$750$	10.1619	−	13.3609i	0.371060	−	0.487872i
$751$	1.14760	+	0.353987i	0.0418765	+	0.0129172i	0.315623	−	0.948885i	$-0.397787\pi$
$751$	1.14760	+	0.353987i	0.0418765	+	0.0129172i	−0.273746	+	0.961802i	$0.588263\pi$
$752$	−5.70184	−	7.14988i	−0.207925	−	0.260729i
$753$	−1.47859	+	7.24086i	−0.0538826	+	0.263872i
$754$	13.4045			0.488163
$755$	8.49885	+	10.6572i	0.309305	+	0.387856i
$756$	−8.97710	−	10.4121i	−0.326494	−	0.378684i
$757$	−14.8828	+	18.6624i	−0.540924	+	0.678297i	−0.974904	−	0.222626i	$-0.928537\pi$
$757$	−14.8828	+	18.6624i	−0.540924	+	0.678297i	0.433980	+	0.900922i	$0.357109\pi$
$758$	6.27980	−	7.87463i	0.228093	−	0.286019i
$759$	−13.4318	+	17.6603i	−0.487544	+	0.641027i
$760$	6.48887	+	3.12487i	0.235376	+	0.113351i
$761$	7.03762	+	17.9316i	0.255113	+	0.650018i	0.999850	−	0.0173406i	$-0.00551996\pi$
$761$	7.03762	+	17.9316i	0.255113	+	0.650018i	−0.744736	+	0.667359i	$0.767425\pi$
$762$	−20.1142	−	24.0671i	−0.728662	−	0.871858i
$763$	−23.0580	+	37.2581i	−0.834755	+	1.34884i
$764$	−12.4884	−	15.6599i	−0.451814	−	0.566557i
$765$	−0.846629	−	6.97806i	−0.0306099	−	0.252292i
$766$	4.28890	−	7.42859i	0.154964	−	0.268406i
$767$	−1.65639	+	4.22041i	−0.0598088	+	0.152390i
$768$	−1.73159	+	0.0397794i	−0.0624835	+	0.00143542i
$769$	−3.51093	−	46.8500i	−0.126607	−	1.68946i	−0.593257	−	0.805013i	$-0.702158\pi$
$769$	−3.51093	−	46.8500i	−0.126607	−	1.68946i	0.466649	−	0.884442i	$-0.345461\pi$
$770$	−1.74526	−	8.89160i	−0.0628949	−	0.320431i
$771$	−5.59249	−	1.58535i	−0.201409	−	0.0570949i
$772$	3.36578	+	4.22055i	0.121137	+	0.151901i
$773$	3.27082	−	43.6461i	0.117643	−	1.56984i	−0.556252	−	0.831014i	$-0.687761\pi$
$773$	3.27082	−	43.6461i	0.117643	−	1.56984i	0.673895	−	0.738827i	$-0.264620\pi$
$774$	−0.307753	−	0.260303i	−0.0110619	−	0.00935639i
$775$	−1.39873	−	18.6648i	−0.0502440	−	0.670460i
$776$	−10.3990	−	9.64885i	−0.373302	−	0.346374i
$777$	42.3277	−	12.7043i	1.51850	−	0.455764i
$778$	−20.2199	+	18.7613i	−0.724917	+	0.672625i
$779$	37.6296	+	34.9151i	1.34822	+	1.25096i
$780$	2.23785	+	2.67763i	0.0801278	+	0.0958745i
$781$	6.91083	−	2.13171i	0.247289	−	0.0762785i
$782$	−7.24112	−	4.93691i	−0.258942	−	0.176544i
$783$	16.3501	+	34.4695i	0.584304	+	1.23184i
$784$	4.69079	−	5.19582i	0.167528	−	0.185565i
$785$	−8.91580	+	15.4426i	−0.318219	+	0.551171i
$786$	−22.0503	−	6.25078i	−0.786510	−	0.222958i
$787$	−5.85939	+	25.6717i	−0.208865	+	0.915096i	0.756459	+	0.654041i	$0.226928\pi$
$787$	−5.85939	+	25.6717i	−0.208865	+	0.915096i	−0.965324	+	0.261055i	$0.915930\pi$
$788$	−12.9946	+	16.2947i	−0.462912	+	0.580474i
$789$	−3.79891	−	38.7322i	−0.135245	−	1.37890i
$790$	−9.69909	−	2.99177i	−0.345078	−	0.106443i
$791$	0.100197	−	0.233995i	0.00356260	−	0.00831990i
$792$	−9.26046	−	0.963414i	−0.329056	−	0.0342334i
$793$	1.95687	+	26.1127i	0.0694906	+	0.927288i
$794$	28.5958	−	26.5331i	1.01483	−	0.941623i
$795$	5.03356	−	4.89034i	0.178522	−	0.173442i
$796$	−9.99583	+	1.50663i	−0.354293	+	0.0534010i
$797$	40.8819	+	27.8728i	1.44811	+	0.987306i	0.995416	+	0.0956420i	$0.0304904\pi$
$797$	40.8819	+	27.8728i	1.44811	+	0.987306i	0.452697	+	0.891664i	$0.350462\pi$
$798$	2.00788	+	29.8399i	0.0710784	+	1.05632i
$799$	16.0431	−	10.9380i	0.567563	−	0.386958i
$800$	2.77254	−	2.57254i	0.0980240	−	0.0909530i
$801$	−13.6477	+	13.8827i	−0.482216	+	0.490521i
$802$	18.8724	−	32.6880i	0.666409	−	1.15425i
$803$	22.8161			0.805161
$804$	−14.3301	+	7.31109i	−0.505383	+	0.257842i
$805$	−9.08095	+	7.92320i	−0.320061	+	0.279256i
$806$	8.93407	+	1.34659i	0.314689	+	0.0474318i
$807$	25.8635	−	4.50807i	0.910440	−	0.158691i
$808$	−0.0159842	−	0.213295i	−0.000562324	−	0.00750369i
$809$	31.5837	−	21.5334i	1.11042	−	0.757074i	0.138031	−	0.990428i	$-0.455923\pi$
$809$	31.5837	−	21.5334i	1.11042	−	0.757074i	0.972392	+	0.233354i	$0.0749701\pi$
$810$	−4.15589	+	9.02062i	−0.146023	+	0.316952i
$811$	13.5106	−	16.9418i	0.474423	−	0.594907i	−0.485825	−	0.874056i	$-0.661481\pi$
$811$	13.5106	−	16.9418i	0.474423	−	0.594907i	0.960248	+	0.279149i	$0.0900522\pi$
$812$	−16.3771	+	10.4468i	−0.574722	+	0.366612i
$813$	24.3552	+	15.7982i	0.854174	+	0.554065i
$814$	14.9646	−	25.9194i	0.524508	−	0.908474i
$815$	−4.34809			−0.152307
$816$	0.190525	−	3.67259i	0.00666972	−	0.128566i
$817$	0.195121	+	0.854881i	0.00682642	+	0.0299085i
$818$	22.8112	+	10.9853i	0.797576	+	0.384092i
$819$	−5.08643	+	13.5691i	−0.177734	+	0.474142i
$820$	−7.82035	+	3.76608i	−0.273099	+	0.131517i
$821$	18.1916	+	22.8115i	0.634890	+	0.796127i	0.990354	−	0.138563i	$-0.0442485\pi$
$821$	18.1916	+	22.8115i	0.634890	+	0.796127i	−0.355464	+	0.934690i	$0.615677\pi$
$822$	18.7658	−	18.2318i	0.654531	−	0.635907i
$823$	−2.54910	−	11.1684i	−0.0888562	−	0.389304i	0.910870	−	0.412693i	$-0.135412\pi$
$823$	−2.54910	−	11.1684i	−0.0888562	−	0.389304i	−0.999726	+	0.0233885i	$0.992555\pi$
$824$	−2.48418	+	1.69369i	−0.0865405	+	0.0590023i
$825$	16.5306	−	11.8355i	0.575520	−	0.412058i
$826$	−1.26548	−	6.44724i	−0.0440317	−	0.224328i
$827$	−6.69772	−	29.3446i	−0.232903	−	1.02041i	−0.947218	−	0.320589i	$-0.896119\pi$
$827$	−6.69772	−	29.3446i	−0.232903	−	1.02041i	0.714316	−	0.699824i	$-0.246738\pi$
$828$	5.04858	+	11.3071i	0.175450	+	0.392949i
$829$	−20.0135	−	50.9937i	−0.695099	−	1.77108i	−0.634502	−	0.772921i	$-0.718795\pi$
$829$	−20.0135	−	50.9937i	−0.695099	−	1.77108i	−0.0605972	−	0.998162i	$-0.519301\pi$
$830$	−8.59219	+	2.65034i	−0.298239	+	0.0919947i
$831$	8.91591	−	8.66222i	0.309290	−	0.300489i
$832$	0.912853	+	1.58111i	0.0316475	+	0.0548150i
$833$	10.2567	+	10.7562i	0.355375	+	0.372679i
$834$	−14.0629	+	4.69414i	−0.486957	+	0.162545i
$835$	5.46019	−	2.62949i	0.188958	−	0.0909972i
$836$	14.8475	+	13.7764i	0.513510	+	0.476468i
$837$	7.43454	+	24.6163i	0.256975	+	0.850866i
$838$	−9.14834	+	2.82189i	−0.316024	+	0.0974805i
$839$	11.6449	+	3.59198i	0.402027	+	0.124009i	0.489174	−	0.872186i	$-0.337298\pi$
$839$	11.6449	+	3.59198i	0.402027	+	0.124009i	−0.0871460	+	0.996196i	$0.527775\pi$
$840$	−4.82093	−	1.52735i	−0.166338	−	0.0526984i
$841$	23.7998	−	7.34128i	0.820684	−	0.253148i
$842$	−7.55300	+	5.14955i	−0.260293	+	0.177465i
$843$	−23.9740	+	43.8184i	−0.825707	+	1.50919i
$844$	18.6762	+	12.7332i	0.642861	+	0.438295i
$845$	−3.89737	+	9.93034i	−0.134074	+	0.341614i
$846$	−27.4062	+	1.25985i	−0.942244	+	0.0433146i
$847$	−0.380823	+	3.60038i	−0.0130852	+	0.123711i
$848$	3.03366	−	2.06832i	0.104176	−	0.0710262i
$849$	45.5395	−	1.04616i	1.56291	−	0.0359043i
$850$	5.00689	+	6.27844i	0.171735	+	0.215349i
$851$	−39.8061			−1.36454
$852$	0.807538	−	3.95464i	0.0276658	−	0.135484i
$853$	−5.54921	+	0.836408i	−0.190001	+	0.0286381i	−0.243353	−	0.969938i	$-0.578247\pi$
$853$	−5.54921	+	0.836408i	−0.190001	+	0.0286381i	0.0533522	+	0.998576i	$0.483009\pi$
$854$	−22.7418	−	30.3783i	−0.778208	−	1.03952i
$855$	19.0156	−	10.2587i	0.650319	−	0.350839i
$856$	2.97404	+	0.448265i	0.101651	+	0.0153214i
$857$	−4.00459	−	53.4375i	−0.136794	−	1.82539i	−0.470148	−	0.882588i	$-0.655799\pi$
$857$	−4.00459	−	53.4375i	−0.136794	−	1.82539i	0.333354	−	0.942802i	$-0.391820\pi$
$858$	3.79428	+	9.05072i	0.129534	+	0.308986i
$859$	15.4002	+	39.2390i	0.525447	+	1.33882i	0.909576	+	0.415538i	$0.136407\pi$
$859$	15.4002	+	39.2390i	0.525447	+	1.33882i	−0.384129	+	0.923280i	$0.625498\pi$
$860$	−0.146615	−	0.0220986i	−0.00499951	−	0.000753555i
$861$	−29.6257	−	20.5306i	−1.00964	−	0.699679i
$862$	−36.8909	+	5.56041i	−1.25651	+	0.189388i
$863$	18.6921	+	32.3757i	0.636288	+	1.10208i	0.986241	+	0.165315i	$0.0528642\pi$
$863$	18.6921	+	32.3757i	0.636288	+	1.10208i	−0.349953	+	0.936767i	$0.613802\pi$
$864$	−2.95235	+	4.27594i	−0.100441	+	0.145470i
$865$	7.26156	−	1.09450i	0.246901	−	0.0372143i
$866$	4.76475	+	20.8757i	0.161913	+	0.709386i
$867$	−21.4634	−	2.73255i	−0.728935	−	0.0928024i
$868$	−11.9647	+	5.31757i	−0.406110	+	0.180490i
$869$	−23.5848	−	16.0798i	−0.800058	−	0.545470i
$870$	11.7737	+	7.63706i	0.399165	+	0.258921i
$871$	14.0107	+	9.55235i	0.474735	+	0.323669i
$872$	15.8251	+	4.88141i	0.535907	+	0.165305i
$873$	−41.7466	+	8.26867i	−1.41291	+	0.279852i
$874$	5.99438	−	26.2631i	0.202763	−	0.888362i
$875$	23.4315	−	10.4138i	0.792129	−	0.352051i
$876$	6.11187	−	11.1710i	0.206501	−	0.377432i
$877$	−21.8563	−	20.2797i	−0.738035	−	0.684796i	0.218688	−	0.975795i	$-0.429822\pi$
$877$	−21.8563	−	20.2797i	−0.738035	−	0.684796i	−0.956724	+	0.290998i	$0.906013\pi$
$878$	−9.20372	+	11.5411i	−0.310610	+	0.389493i
$879$	−2.89273	−	29.4932i	−0.0975693	−	0.994781i
$880$	−3.08567	+	1.48598i	−0.104018	+	0.0500924i
$881$	11.3374			0.381967			0.190984	−	0.981593i	$-0.438832\pi$
$881$	11.3374			0.381967			0.190984	+	0.981593i	$0.438832\pi$
$882$	−4.36070	−	20.5423i	−0.146832	−	0.691694i
$883$	−21.5522			−0.725288			−0.362644	−	0.931928i	$-0.618126\pi$
$883$	−21.5522			−0.725288			−0.362644	+	0.931928i	$0.618126\pi$
$884$	−3.49250	+	1.68190i	−0.117465	+	0.0565684i
$885$	−3.85940	+	2.76324i	−0.129732	+	0.0928851i
$886$	−6.09707	+	7.64548i	−0.204835	+	0.256855i
$887$	−10.6035	−	9.83865i	−0.356032	−	0.330350i	0.481796	−	0.876283i	$-0.339985\pi$
$887$	−10.6035	−	9.83865i	−0.356032	−	0.330350i	−0.837828	+	0.545934i	$0.816175\pi$
$888$	−8.68174	−	14.2700i	−0.291340	−	0.478869i
$889$	−9.22817	−	47.0148i	−0.309503	−	1.57683i
$890$	−1.59350	+	6.98159i	−0.0534143	+	0.234024i
$891$	−18.6458	+	20.7965i	−0.624657	+	0.696709i
$892$	−10.6701	−	3.29128i	−0.357261	−	0.110200i
$893$	49.3128	+	33.6209i	1.65019	+	1.12508i
$894$	0.432283	−	8.33275i	0.0144577	−	0.278689i
$895$	3.50432	+	2.38920i	0.117136	+	0.0798623i
$896$	−2.34752	−	1.22030i	−0.0784253	−	0.0407673i
$897$	7.90162	−	10.3891i	0.263827	−	0.346883i
$898$	−1.04015	−	4.55719i	−0.0347102	−	0.152075i
$899$	35.9285	−	5.41534i	1.19828	−	0.180612i
$900$	−1.36662	−	11.2640i	−0.0455542	−	0.375465i
$901$	3.89787	+	6.75131i	0.129857	+	0.224919i
$902$	−24.1378	+	3.63818i	−0.803700	+	0.121138i
$903$	−0.220573	−	0.574841i	−0.00734022	−	0.0191295i
$904$	−0.0951343	−	0.0143392i	−0.00316412	−	0.000476914i
$905$	6.63075	+	16.8949i	0.220414	+	0.561605i
$906$	21.2231	+	2.70196i	0.705092	+	0.0897668i
$907$	−1.75142	−	23.3710i	−0.0581548	−	0.776022i	−0.947697	−	0.319170i	$-0.896596\pi$
$907$	−1.75142	−	23.3710i	−0.0581548	−	0.776022i	0.889543	−	0.456852i	$-0.151023\pi$
$908$	−19.9333	−	3.00446i	−0.661508	−	0.0997063i
$909$	−0.546220	−	0.336743i	−0.0181170	−	0.0111691i
$910$	1.02670	+	5.23072i	0.0340347	+	0.173397i
$911$	−37.2446	+	5.61371i	−1.23397	+	0.185991i	−0.733455	−	0.679738i	$-0.762093\pi$
$911$	−37.2446	+	5.61371i	−1.23397	+	0.185991i	−0.500513	+	0.865729i	$0.666855\pi$
$912$	10.7223	−	3.57909i	0.355052	−	0.118516i
$913$	−25.2871			−0.836880
$914$	2.45792	+	3.08214i	0.0813009	+	0.101948i
$915$	−13.1586	+	24.0506i	−0.435010	+	0.795089i
$916$	3.32326	−	2.26576i	0.109804	−	0.0748629i
$917$	−24.9238	−	24.5862i	−0.823056	−	0.811907i
$918$	−8.58494	−	6.92943i	−0.283345	−	0.228705i
$919$	−4.64353	+	11.8315i	−0.153176	+	0.390286i	−0.986778	−	0.162080i	$-0.948180\pi$
$919$	−4.64353	+	11.8315i	−0.153176	+	0.390286i	0.833602	+	0.552366i	$0.186275\pi$
$920$	3.76358	+	2.56596i	0.124081	+	0.0845973i
$921$	38.4860	−	0.884127i	1.26816	−	0.0291330i
$922$	29.1073	−	19.8450i	0.958598	−	0.653561i
$923$	−4.06548	+	1.25403i	−0.133817	+	0.0412770i
$924$	−11.6894	−	8.10072i	−0.384553	−	0.266494i
$925$	34.8539	+	10.7510i	1.14599	+	0.353491i
$926$	−6.40878	+	1.97685i	−0.210606	+	0.0649632i
$927$	−0.260299	+	9.01608i	−0.00854934	+	0.296127i
$928$	5.38214	+	4.99389i	0.176677	+	0.163933i
$929$	35.6963	−	17.1904i	1.17116	−	0.563999i	0.255834	−	0.966721i	$-0.417650\pi$
$929$	35.6963	−	17.1904i	1.17116	−	0.563999i	0.915323	+	0.402722i	$0.131936\pi$
$930$	7.07991	+	6.27285i	0.232160	+	0.205695i
$931$	−19.2585	+	41.4266i	−0.631172	+	1.35770i
$932$	−11.1726	−	19.3515i	−0.365970	−	0.633878i
$933$	−0.284683	−	1.12728i	−0.00932011	−	0.0369054i
$934$	−15.7007	+	4.84303i	−0.513743	+	0.158469i
$935$	−2.65665	−	6.76903i	−0.0868817	−	0.221371i
$936$	5.44771	+	0.566754i	0.178064	+	0.0185249i
$937$	1.38456	+	6.06617i	0.0452317	+	0.198173i	0.992495	−	0.122282i	$-0.0390213\pi$
$937$	1.38456	+	6.06617i	0.0452317	+	0.198173i	−0.947264	+	0.320455i	$0.896164\pi$
$938$	−24.5624	−	0.751380i	−0.801990	−	0.0245334i
$939$	−2.65956	−	1.20634i	−0.0867916	−	0.0393673i
$940$	−8.33839	+	5.68501i	−0.271968	+	0.185425i
$941$	−4.28839	−	18.7886i	−0.139797	−	0.612492i	−0.995478	−	0.0949886i	$-0.969719\pi$
$941$	−4.28839	−	18.7886i	−0.139797	−	0.612492i	0.855681	−	0.517504i	$-0.173139\pi$
$942$	6.85277	+	27.1353i	0.223275	+	0.884117i
$943$	20.2423	+	25.3830i	0.659180	+	0.826586i
$944$	−2.23740	+	1.07747i	−0.0728211	+	0.0350688i
$945$	−12.1984	+	9.02028i	−0.396815	+	0.293430i
$946$	−0.375684	−	0.180920i	−0.0122146	−	0.00588222i
$947$	1.61361	+	7.06968i	0.0524352	+	0.229734i	0.994355	−	0.106104i	$-0.0338377\pi$
$947$	1.61361	+	7.06968i	0.0524352	+	0.229734i	−0.941920	+	0.335838i	$0.890981\pi$
$948$	−14.1906	+	7.23993i	−0.460890	+	0.235142i
$949$	−13.4222			−0.435702
$950$	−12.3419	+	21.3768i	−0.400423	+	0.693554i
$951$	−30.6510	+	15.6379i	−0.993926	+	0.507092i
$952$	2.95620	−	4.77676i	0.0958110	−	0.154816i
$953$	31.7460	−	39.8083i	1.02835	−	1.28952i	0.0719696	−	0.997407i	$-0.477072\pi$
$953$	31.7460	−	39.8083i	1.02835	−	1.28952i	0.956385	−	0.292109i	$-0.0943570\pi$
$954$	0.317875	−	11.0104i	0.0102916	−	0.356474i
$955$	−18.2630	+	12.4515i	−0.590978	+	0.402922i
$956$	−1.67804	−	22.3918i	−0.0542715	−	0.724203i
$957$	25.3092	+	30.2829i	0.818130	+	0.978909i
$958$	−28.9931	−	4.37001i	−0.936726	−	0.141189i
$959$	38.5329	−	10.6070i	1.24429	−	0.342517i
$960$	−0.0990257	+	1.90883i	−0.00319604	+	0.0616073i
$961$	−6.50974			−0.209992
$962$	−8.80331	+	15.2478i	−0.283830	+	0.491608i
$963$	6.32546	−	6.43440i	0.203835	−	0.207346i
$964$	14.5933	−	13.5406i	0.470018	−	0.436113i
$965$	4.92212	−	3.35585i	0.158449	−	0.108029i
$966$	−1.55709	+	18.8511i	−0.0500987	+	0.606526i
$967$	−1.56331	−	1.06585i	−0.0502728	−	0.0342754i	0.537923	−	0.842994i	$-0.319209\pi$
$967$	−1.56331	−	1.06585i	−0.0502728	−	0.0342754i	−0.588196	+	0.808719i	$0.700162\pi$
$968$	1.35312	−	0.203951i	0.0434911	−	0.00655522i
$969$	5.87666	+	23.2702i	0.188785	+	0.747546i
$970$	−11.4758	+	10.6480i	−0.368465	+	0.341885i
$971$	3.60024	+	48.0418i	0.115537	+	1.54174i	0.690365	+	0.723461i	$0.257450\pi$
$971$	3.60024	+	48.0418i	0.115537	+	1.54174i	−0.574828	+	0.818274i	$0.694931\pi$
$972$	5.18742	+	14.7000i	0.166387	+	0.471503i
$973$	−22.2799	−	4.05842i	−0.714261	−	0.130107i
$974$	−11.4602	−	3.53499i	−0.367207	−	0.113268i
$975$	−9.72454	+	6.96253i	−0.311435	+	0.222979i
$976$	−8.94265	+	11.2137i	−0.286247	+	0.358943i
$977$	−1.87356	+	8.20860i	−0.0599405	+	0.262616i	−0.996015	−	0.0891852i	$-0.971574\pi$
$977$	−1.87356	+	8.20860i	−0.0599405	+	0.262616i	0.936075	+	0.351802i	$0.114431\pi$
$978$	−4.89476	+	4.75548i	−0.156517	+	0.152064i
$979$	−10.0696	+	17.4410i	−0.321824	+	0.557416i
$980$	−5.33095	−	5.59052i	−0.170291	−	0.178583i
$981$	39.7212	−	29.8428i	1.26820	−	0.952806i
$982$	7.48146	+	5.10077i	0.238743	+	0.162772i
$983$	−28.1415	+	8.68050i	−0.897574	+	0.276865i	−0.709012	−	0.705196i	$-0.750859\pi$
$983$	−28.1415	+	8.68050i	−0.897574	+	0.276865i	−0.188562	+	0.982061i	$0.560383\pi$
$984$	−4.68463	+	12.7927i	−0.149341	+	0.407815i
$985$	16.8600	+	15.6438i	0.537204	+	0.498453i
$986$	−11.4275	+	10.6032i	−0.363925	+	0.337673i
$987$	−37.6182	−	18.4700i	−1.19740	−	0.587908i
$988$	−8.73442	−	8.10435i	−0.277879	−	0.257834i
$989$	0.0414443	+	0.553035i	0.00131785	+	0.0175855i
$990$	−1.82389	+	10.1113i	−0.0579671	+	0.321359i
$991$	0.776749	−	10.3650i	0.0246743	−	0.329255i	−0.971184	−	0.238332i	$-0.923399\pi$
$991$	0.776749	−	10.3650i	0.0246743	−	0.329255i	0.995858	−	0.0909228i	$-0.0289817\pi$
$992$	3.08550	+	3.86910i	0.0979648	+	0.122844i
$993$	−10.6725	−	42.2604i	−0.338680	−	1.34109i
$994$	3.98970	−	4.70057i	0.126546	−	0.149093i
$995$	0.833648	+	11.1243i	0.0264284	+	0.352663i
$996$	−6.77379	+	12.3808i	−0.214636	+	0.392301i
$997$	−9.90575	+	25.2394i	−0.313718	+	0.799341i	0.683849	+	0.729624i	$0.260305\pi$
$997$	−9.90575	+	25.2394i	−0.313718	+	0.799341i	−0.997567	+	0.0697170i	$0.977790\pi$
$998$	14.3679	−	24.8859i	0.454807	−	0.787748i
$999$	−49.9472	−	4.03920i	−1.58026	−	0.127795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.a.151.25	yes	336
9.4	even	3		882.2.y.b.445.18	yes	336
49.37	even	21		882.2.y.b.331.18	✓	336
441.184	even	21	inner	882.2.bb.a.625.25	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.b.331.18	✓	336	49.37	even	21
882.2.y.b.445.18	yes	336	9.4	even	3
882.2.bb.a.151.25	yes	336	1.1	even	1	trivial
882.2.bb.a.625.25	yes	336	441.184	even	21	inner

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(1.57737 + 0.715470i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.808957 - 0.750602i) q^{5} +(-1.73159 + 0.0397794i) q^{6} +(-2.34752 - 1.22030i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(1.97620 + 2.25713i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(1.57737 + 0.715470i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.808957 - 0.750602i) q^{5} +(-1.73159 + 0.0397794i) q^{6} +(-2.34752 - 1.22030i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(1.97620 + 2.25713i) q^{9} +(1.05452 + 0.325276i) q^{10} +(2.56422 + 1.74825i) q^{11} +(1.54285 - 0.787150i) q^{12} +(-1.50847 - 1.02846i) q^{13} +(2.64451 + 0.0808975i) q^{14} +(-0.738992 - 1.76276i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(2.09951 - 0.316450i) q^{17} +(-2.75983 - 1.17616i) q^{18} +(3.26316 + 5.65196i) q^{19} +(-1.09122 + 0.164475i) q^{20} +(-2.82983 - 3.60445i) q^{21} +(-3.06882 - 0.462550i) q^{22} +(1.50801 + 3.84234i) q^{23} +(-1.04853 + 1.37862i) q^{24} +(-0.282643 - 3.77161i) q^{25} +(1.80531 + 0.272107i) q^{26} +(1.50230 + 4.97424i) q^{27} +(-2.41773 + 1.07453i) q^{28} +(7.26009 - 1.09428i) q^{29} +(1.43064 + 1.26756i) q^{30} +4.94876 q^{31} +(0.623490 + 0.781831i) q^{32} +(2.79390 + 4.59227i) q^{33} +(-1.75429 + 1.19605i) q^{34} +(0.983088 + 2.74923i) q^{35} +(2.99684 - 0.137764i) q^{36} +(-3.52325 + 8.97710i) q^{37} +(-5.39230 - 3.67641i) q^{38} +(-1.64359 - 2.70152i) q^{39} +(0.911793 - 0.621650i) q^{40} +(7.51605 - 2.31840i) q^{41} +(4.11350 + 2.01968i) q^{42} +(0.128389 + 0.0396028i) q^{43} +(2.96560 - 0.914767i) q^{44} +(0.0955401 - 3.30926i) q^{45} +(-3.02579 - 2.80753i) q^{46} +(8.23940 - 3.96789i) q^{47} +(0.346534 - 1.69703i) q^{48} +(4.02175 + 5.72936i) q^{49} +(1.89109 + 3.27547i) q^{50} +(3.53812 + 1.00298i) q^{51} +(-1.74459 + 0.538136i) q^{52} +(1.34141 + 3.41784i) q^{53} +(-3.51177 - 3.82981i) q^{54} +(-0.762097 - 3.33897i) q^{55} +(1.71208 - 2.01713i) q^{56} +(1.10341 + 11.2499i) q^{57} +(-6.06632 + 4.13595i) q^{58} +(-0.552592 - 2.42106i) q^{59} +(-1.83894 - 0.521298i) q^{60} +(-8.94265 - 11.2137i) q^{61} +(-4.45868 + 2.14719i) q^{62} +(-1.88482 - 7.71022i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(0.448324 + 1.96424i) q^{65} +(-4.50973 - 2.92526i) q^{66} -9.28805 q^{67} +(1.06161 - 1.83877i) q^{68} +(-0.370392 + 7.13973i) q^{69} +(-2.07858 - 2.05042i) q^{70} +(1.45294 - 1.82193i) q^{71} +(-2.64028 + 1.42440i) q^{72} +(6.07431 - 4.14140i) q^{73} +(-0.720677 - 9.61677i) q^{74} +(2.25264 - 6.15145i) q^{75} +(6.45343 + 0.972698i) q^{76} +(-3.88617 - 7.23317i) q^{77} +(2.65297 + 1.72086i) q^{78} -9.19765 q^{79} +(-0.551773 + 0.955699i) q^{80} +(-1.18924 + 8.92108i) q^{81} +(-5.76582 + 5.34989i) q^{82} +(-6.73217 + 4.58992i) q^{83} +(-4.58244 - 0.0348845i) q^{84} +(-1.93594 - 1.31990i) q^{85} +(-0.132858 + 0.0200251i) q^{86} +(12.2348 + 3.46829i) q^{87} +(-2.27501 + 2.11090i) q^{88} +(0.484939 + 6.47106i) q^{89} +(1.34976 + 3.02299i) q^{90} +(2.28614 + 4.25511i) q^{91} +(3.94429 + 1.21665i) q^{92} +(7.80604 + 3.54069i) q^{93} +(-5.70184 + 7.14988i) q^{94} +(1.60262 - 7.02153i) q^{95} +(0.424098 + 1.67933i) q^{96} +(-7.09294 + 12.2853i) q^{97} +(-6.10934 - 3.41700i) q^{98} +(1.12139 + 9.24266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9}+O(q^{10}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9} + 2 q^{10} + 2 q^{12} - 21 q^{13} - 7 q^{15} - 56 q^{16} + 7 q^{17} + 6 q^{18} - 34 q^{19} + 2 q^{20} + 16 q^{21} - 36 q^{23} + 2 q^{24} + 32 q^{25} + 7 q^{26} + 49 q^{27} - 16 q^{29} - 7 q^{30} + 92 q^{31} - 56 q^{32} + 14 q^{33} + 7 q^{34} + 16 q^{35} - 15 q^{36} - 26 q^{37} + q^{38} + 44 q^{39} + 2 q^{40} + 3 q^{41} - 33 q^{42} - 3 q^{43} + 106 q^{45} - 36 q^{46} + 27 q^{47} + 2 q^{48} - 74 q^{49} - 164 q^{50} - 7 q^{51} + 21 q^{52} - 78 q^{53} - 28 q^{54} - 53 q^{55} - 18 q^{57} + 40 q^{58} - 16 q^{59} - 7 q^{60} - 45 q^{61} - 20 q^{62} - 50 q^{63} - 56 q^{64} - 14 q^{65} + 14 q^{66} + 86 q^{67} - 21 q^{68} - 85 q^{69} - 26 q^{70} + 7 q^{71} + 6 q^{72} + 36 q^{73} + 2 q^{74} - 35 q^{75} + 8 q^{76} - 37 q^{77} - 12 q^{78} - 2 q^{79} - 12 q^{80} + 41 q^{81} + 3 q^{82} + 191 q^{83} - 5 q^{84} + 159 q^{85} - 3 q^{86} + 72 q^{87} + 59 q^{89} + 22 q^{90} - 29 q^{91} + 27 q^{92} + 23 q^{93} + 6 q^{94} + 26 q^{95} + 2 q^{96} - 113 q^{97} - 18 q^{98} - 33 q^{99}+O(q^{100}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9 + 2 * q^10 + 2 * q^12 - 21 * q^13 - 7 * q^15 - 56 * q^16 + 7 * q^17 + 6 * q^18 - 34 * q^19 + 2 * q^20 + 16 * q^21 - 36 * q^23 + 2 * q^24 + 32 * q^25 + 7 * q^26 + 49 * q^27 - 16 * q^29 - 7 * q^30 + 92 * q^31 - 56 * q^32 + 14 * q^33 + 7 * q^34 + 16 * q^35 - 15 * q^36 - 26 * q^37 + q^38 + 44 * q^39 + 2 * q^40 + 3 * q^41 - 33 * q^42 - 3 * q^43 + 106 * q^45 - 36 * q^46 + 27 * q^47 + 2 * q^48 - 74 * q^49 - 164 * q^50 - 7 * q^51 + 21 * q^52 - 78 * q^53 - 28 * q^54 - 53 * q^55 - 18 * q^57 + 40 * q^58 - 16 * q^59 - 7 * q^60 - 45 * q^61 - 20 * q^62 - 50 * q^63 - 56 * q^64 - 14 * q^65 + 14 * q^66 + 86 * q^67 - 21 * q^68 - 85 * q^69 - 26 * q^70 + 7 * q^71 + 6 * q^72 + 36 * q^73 + 2 * q^74 - 35 * q^75 + 8 * q^76 - 37 * q^77 - 12 * q^78 - 2 * q^79 - 12 * q^80 + 41 * q^81 + 3 * q^82 + 191 * q^83 - 5 * q^84 + 159 * q^85 - 3 * q^86 + 72 * q^87 + 59 * q^89 + 22 * q^90 - 29 * q^91 + 27 * q^92 + 23 * q^93 + 6 * q^94 + 26 * q^95 + 2 * q^96 - 113 * q^97 - 18 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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