LMFDB - Embedded newform 105.2.j.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(8,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("105.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.j (of order $4$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	105.8
Dual form			105.2.j.a.92.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54414 - 1.54414i) q^{2} +(-0.00622252 - 1.73204i) q^{3} +2.76875i q^{4} +(0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +O(q^{10})$	\(q+(-1.54414 - 1.54414i) q^{2} +(-0.00622252 - 1.73204i) q^{3} +2.76875i q^{4} +(0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +(-3.82062 + 3.04083i) q^{10} +3.38507i q^{11} +(4.79558 - 0.0172286i) q^{12} +(-0.206632 - 0.206632i) q^{13} -2.18375 q^{14} +(-3.84976 - 0.423515i) q^{15} +1.87154 q^{16} +(-0.167409 - 0.167409i) q^{17} +(4.66559 + 4.59902i) q^{18} -5.31419i q^{19} +(6.15151 + 0.699108i) q^{20} +(-1.22914 - 1.22034i) q^{21} +(5.22702 - 5.22702i) q^{22} +(5.07773 - 5.07773i) q^{23} +(-2.06341 - 2.04864i) q^{24} +(-4.87249 - 1.12199i) q^{25} +0.638138i q^{26} +(0.0560017 + 5.19585i) q^{27} +(1.95780 + 1.95780i) q^{28} +2.84268 q^{29} +(5.29060 + 6.59854i) q^{30} +9.11776 q^{31} +(-5.26402 - 5.26402i) q^{32} +(5.86307 - 0.0210636i) q^{33} +0.517005i q^{34} +(-1.39248 - 1.74957i) q^{35} +(-0.0596812 - 8.30602i) q^{36} +(-5.27013 + 5.27013i) q^{37} +(-8.20586 + 8.20586i) q^{38} +(-0.356609 + 0.359180i) q^{39} +(-2.33762 - 2.93708i) q^{40} +0.0314968i q^{41} +(0.0135884 + 3.78233i) q^{42} +(-3.76875 - 3.76875i) q^{43} -9.37239 q^{44} +(-0.709590 + 6.67057i) q^{45} -15.6815 q^{46} +(3.56639 + 3.56639i) q^{47} +(-0.0116457 - 3.24158i) q^{48} -1.00000i q^{49} +(5.79130 + 9.25632i) q^{50} +(-0.288917 + 0.291000i) q^{51} +(0.572111 - 0.572111i) q^{52} +(-3.55291 + 3.55291i) q^{53} +(7.93665 - 8.10960i) q^{54} +(7.52082 + 0.854729i) q^{55} -1.67875i q^{56} +(-9.20439 + 0.0330677i) q^{57} +(-4.38949 - 4.38949i) q^{58} +10.3168 q^{59} +(1.17261 - 10.6590i) q^{60} -6.80634 q^{61} +(-14.0791 - 14.0791i) q^{62} +(-2.10602 + 2.13651i) q^{63} +12.5137i q^{64} +(-0.511262 + 0.406913i) q^{65} +(-9.08593 - 9.02088i) q^{66} +(6.34806 - 6.34806i) q^{67} +(0.463512 - 0.463512i) q^{68} +(-8.82642 - 8.76323i) q^{69} +(-0.551396 + 4.85177i) q^{70} +3.95454i q^{71} +(-3.53548 + 3.58665i) q^{72} +(8.61099 + 8.61099i) q^{73} +16.2757 q^{74} +(-1.91302 + 8.44632i) q^{75} +14.7136 q^{76} +(2.39360 + 2.39360i) q^{77} +(1.10528 - 0.00397083i) q^{78} +11.4449i q^{79} +(0.472563 - 4.15812i) q^{80} +(8.99907 - 0.129328i) q^{81} +(0.0486356 - 0.0486356i) q^{82} +(-3.88059 + 3.88059i) q^{83} +(3.37880 - 3.40317i) q^{84} +(-0.414214 + 0.329672i) q^{85} +11.6390i q^{86} +(-0.0176886 - 4.92363i) q^{87} +(4.01825 + 4.01825i) q^{88} -2.00190 q^{89} +(11.3960 - 9.20459i) q^{90} -0.292222 q^{91} +(14.0589 + 14.0589i) q^{92} +(-0.0567354 - 15.7923i) q^{93} -11.0140i q^{94} +(-11.8069 - 1.34183i) q^{95} +(-9.08474 + 9.15025i) q^{96} +(2.26760 - 2.26760i) q^{97} +(-1.54414 + 1.54414i) q^{98} +(-0.0729661 - 10.1549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.54414	−	1.54414i	−1.09187	−	1.09187i	−0.995329	−	0.0965442i	$-0.969221\pi$
$2$	−1.54414	−	1.54414i	−1.09187	−	1.09187i	−0.0965442	−	0.995329i	$-0.530779\pi$
$3$	−0.00622252	−	1.73204i	−0.00359257	−	0.999994i
$3$	−0.00622252	−	1.73204i	−0.00359257	−	0.999994i
$4$			2.76875i			1.38437i
$5$	0.252500	−	2.22177i	0.112921	−	0.993604i
$5$	0.252500	−	2.22177i	0.112921	−	0.993604i
$6$	−2.66491	+	2.68412i	−1.08794	+	1.09579i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	1.18705	−	1.18705i	0.419686	−	0.419686i
$9$	−2.99992	+	0.0215553i	−0.999974	+	0.00718510i
$10$	−3.82062	+	3.04083i	−1.20819	+	0.961593i
$11$			3.38507i			1.02064i	0.859986	+	0.510318i	$0.170472\pi$
$11$			3.38507i			1.02064i	−0.859986	+	0.510318i	$0.829528\pi$
$12$	4.79558	−	0.0172286i	1.38436	−	0.00497346i
$13$	−0.206632	−	0.206632i	−0.0573094	−	0.0573094i	0.677871	−	0.735181i	$-0.262903\pi$
$13$	−0.206632	−	0.206632i	−0.0573094	−	0.0573094i	−0.735181	+	0.677871i	$0.762903\pi$
$14$	−2.18375			−0.583631
$15$	−3.84976	−	0.423515i	−0.994003	−	0.109351i
$16$	1.87154			0.467884
$17$	−0.167409	−	0.167409i	−0.0406026	−	0.0406026i	0.686514	−	0.727117i	$-0.259140\pi$
$17$	−0.167409	−	0.167409i	−0.0406026	−	0.0406026i	−0.727117	+	0.686514i	$0.759140\pi$
$18$	4.66559	+	4.59902i	1.09969	+	1.08400i
$19$		−	5.31419i		−	1.21916i	−0.792725	−	0.609579i	$-0.791338\pi$
$19$		−	5.31419i		−	1.21916i	0.792725	−	0.609579i	$-0.208662\pi$
$20$	6.15151	+	0.699108i	1.37552	+	0.156325i
$21$	−1.22914	−	1.22034i	−0.268220	−	0.266299i
$22$	5.22702	−	5.22702i	1.11440	−	1.11440i
$23$	5.07773	−	5.07773i	1.05878	−	1.05878i	0.0606179	−	0.998161i	$-0.480693\pi$
$23$	5.07773	−	5.07773i	1.05878	−	1.05878i	0.998161	−	0.0606179i	$-0.0193071\pi$
$24$	−2.06341	−	2.04864i	−0.421191	−	0.418176i
$25$	−4.87249	−	1.12199i	−0.974497	−	0.224398i
$26$			0.638138i			0.125149i
$27$	0.0560017	+	5.19585i	0.0107775	+	0.999942i
$28$	1.95780	+	1.95780i	0.369989	+	0.369989i
$29$	2.84268			0.527872			0.263936	−	0.964540i	$-0.414979\pi$
$29$	2.84268			0.527872			0.263936	+	0.964540i	$0.414979\pi$
$30$	5.29060	+	6.59854i	0.965928	+	1.20472i
$31$	9.11776			1.63760			0.818799	−	0.574081i	$-0.194640\pi$
$31$	9.11776			1.63760			0.818799	+	0.574081i	$0.194640\pi$
$32$	−5.26402	−	5.26402i	−0.930557	−	0.930557i
$33$	5.86307	−	0.0210636i	1.02063	−	0.00366671i
$34$			0.517005i			0.0886657i
$35$	−1.39248	−	1.74957i	−0.235372	−	0.295731i
$36$	−0.0596812	−	8.30602i	−0.00994686	−	1.38434i
$37$	−5.27013	+	5.27013i	−0.866404	+	0.866404i	−0.992072	−	0.125668i	$-0.959893\pi$
$37$	−5.27013	+	5.27013i	−0.866404	+	0.866404i	0.125668	+	0.992072i	$0.459893\pi$
$38$	−8.20586	+	8.20586i	−1.33117	+	1.33117i
$39$	−0.356609	+	0.359180i	−0.0571031	+	0.0575149i
$40$	−2.33762	−	2.93708i	−0.369611	−	0.464394i
$41$			0.0314968i			0.00491898i	0.999997	+	0.00245949i	$0.000782881\pi$
$41$			0.0314968i			0.00491898i	−0.999997	+	0.00245949i	$0.999217\pi$
$42$	0.0135884	+	3.78233i	0.00209674	+	0.583627i
$43$	−3.76875	−	3.76875i	−0.574728	−	0.574728i	0.358718	−	0.933446i	$-0.383214\pi$
$43$	−3.76875	−	3.76875i	−0.574728	−	0.574728i	−0.933446	+	0.358718i	$0.883214\pi$
$44$	−9.37239			−1.41294
$45$	−0.709590	+	6.67057i	−0.105779	+	0.994390i
$46$	−15.6815			−2.31210
$47$	3.56639	+	3.56639i	0.520211	+	0.520211i	0.917635	−	0.397424i	$-0.130096\pi$
$47$	3.56639	+	3.56639i	0.520211	+	0.520211i	−0.397424	+	0.917635i	$0.630096\pi$
$48$	−0.0116457	−	3.24158i	−0.00168091	−	0.467881i
$49$		−	1.00000i		−	0.142857i
$50$	5.79130	+	9.25632i	0.819013	+	1.30904i
$51$	−0.288917	+	0.291000i	−0.0404564	+	0.0407482i
$52$	0.572111	−	0.572111i	0.0793376	−	0.0793376i
$53$	−3.55291	+	3.55291i	−0.488030	+	0.488030i	−0.907684	−	0.419654i	$-0.862151\pi$
$53$	−3.55291	+	3.55291i	−0.488030	+	0.488030i	0.419654	+	0.907684i	$0.362151\pi$
$54$	7.93665	−	8.10960i	1.08004	−	1.10358i
$55$	7.52082	+	0.854729i	1.01411	+	0.115252i
$56$		−	1.67875i		−	0.224332i
$57$	−9.20439	+	0.0330677i	−1.21915	+	0.00437992i
$58$	−4.38949	−	4.38949i	−0.576369	−	0.576369i
$59$	10.3168			1.34313			0.671565	−	0.740946i	$-0.265622\pi$
$59$	10.3168			1.34313			0.671565	+	0.740946i	$0.265622\pi$
$60$	1.17261	−	10.6590i	0.151383	−	1.37607i
$61$	−6.80634			−0.871462			−0.435731	−	0.900077i	$-0.643510\pi$
$61$	−6.80634			−0.871462			−0.435731	+	0.900077i	$0.643510\pi$
$62$	−14.0791	−	14.0791i	−1.78805	−	1.78805i
$63$	−2.10602	+	2.13651i	−0.265334	+	0.269175i
$64$			12.5137i			1.56422i
$65$	−0.511262	+	0.406913i	−0.0634143	+	0.0504714i
$66$	−9.08593	−	9.02088i	−1.11840	−	1.11039i
$67$	6.34806	−	6.34806i	0.775539	−	0.775539i	−0.203530	−	0.979069i	$-0.565241\pi$
$67$	6.34806	−	6.34806i	0.775539	−	0.775539i	0.979069	+	0.203530i	$0.0652413\pi$
$68$	0.463512	−	0.463512i	0.0562091	−	0.0562091i
$69$	−8.82642	−	8.76323i	−1.06258	−	1.05497i
$70$	−0.551396	+	4.85177i	−0.0659044	+	0.579898i
$71$			3.95454i			0.469318i	0.972078	+	0.234659i	$0.0753973\pi$
$71$			3.95454i			0.469318i	−0.972078	+	0.234659i	$0.924603\pi$
$72$	−3.53548	+	3.58665i	−0.416660	+	0.422691i
$73$	8.61099	+	8.61099i	1.00784	+	1.00784i	0.999969	+	0.00787086i	$0.00250540\pi$
$73$	8.61099	+	8.61099i	1.00784	+	1.00784i	0.00787086	+	0.999969i	$0.497495\pi$
$74$	16.2757			1.89201
$75$	−1.91302	+	8.44632i	−0.220896	+	0.975297i
$76$	14.7136			1.68777
$77$	2.39360	+	2.39360i	0.272776	+	0.272776i
$78$	1.10528	−	0.00397083i	0.125148	−	0.000449608i
$79$			11.4449i			1.28766i	0.765170	+	0.643828i	$0.222655\pi$
$79$			11.4449i			1.28766i	−0.765170	+	0.643828i	$0.777345\pi$
$80$	0.472563	−	4.15812i	0.0528342	−	0.464892i
$81$	8.99907	−	0.129328i	0.999897	−	0.0143698i
$82$	0.0486356	−	0.0486356i	0.00537090	−	0.00537090i
$83$	−3.88059	+	3.88059i	−0.425951	+	0.425951i	−0.887246	−	0.461296i	$-0.847385\pi$
$83$	−3.88059	+	3.88059i	−0.425951	+	0.425951i	0.461296	+	0.887246i	$0.347385\pi$
$84$	3.37880	−	3.40317i	0.368658	−	0.371316i
$85$	−0.414214	+	0.329672i	−0.0449278	+	0.0357580i
$86$			11.6390i			1.25506i
$87$	−0.0176886	−	4.92363i	−0.00189642	−	0.527868i
$88$	4.01825	+	4.01825i	0.428347	+	0.428347i
$89$	−2.00190			−0.212201			−0.106100	−	0.994355i	$-0.533836\pi$
$89$	−2.00190			−0.212201			−0.106100	+	0.994355i	$0.533836\pi$
$90$	11.3960	−	9.20459i	1.20124	−	0.970249i
$91$	−0.292222			−0.0306332
$92$	14.0589	+	14.0589i	1.46574	+	1.46574i
$93$	−0.0567354	−	15.7923i	−0.00588319	−	1.63759i
$94$		−	11.0140i		−	1.13601i
$95$	−11.8069	−	1.34183i	−1.21136	−	0.137669i
$96$	−9.08474	+	9.15025i	−0.927208	+	0.933894i
$97$	2.26760	−	2.26760i	0.230240	−	0.230240i	−0.582553	−	0.812793i	$-0.697946\pi$
$97$	2.26760	−	2.26760i	0.230240	−	0.230240i	0.812793	+	0.582553i	$0.197946\pi$
$98$	−1.54414	+	1.54414i	−0.155982	+	0.155982i
$99$	−0.0729661	−	10.1549i	−0.00733337	−	1.02061i
$100$	3.10651	−	13.4907i	0.310651	−	1.34907i
$101$		−	8.63630i		−	0.859344i	−0.902985	−	0.429672i	$-0.858629\pi$
$101$		−	8.63630i		−	0.859344i	0.902985	−	0.429672i	$-0.141371\pi$
$102$	0.895474	−	0.00321708i	0.0886651	−	0.000318538i
$103$	0.964332	+	0.964332i	0.0950185	+	0.0950185i	0.753018	−	0.658000i	$-0.228597\pi$
$103$	0.964332	+	0.964332i	0.0950185	+	0.0950185i	−0.658000	+	0.753018i	$0.728597\pi$
$104$	−0.490566			−0.0481039
$105$	−3.02166	+	2.42272i	−0.294884	+	0.236433i
$106$	10.9724			1.06573
$107$	2.95847	+	2.95847i	0.286007	+	0.286007i	0.835499	−	0.549492i	$-0.185179\pi$
$107$	2.95847	+	2.95847i	0.286007	+	0.286007i	−0.549492	+	0.835499i	$0.685179\pi$
$108$	−14.3860	+	0.155055i	−1.38429	+	0.0149201i
$109$			2.82182i			0.270281i	0.990826	+	0.135141i	$0.0431486\pi$
$109$			2.82182i			0.270281i	−0.990826	+	0.135141i	$0.956851\pi$
$110$	−10.2934	−	12.9330i	−0.981436	−	1.23312i
$111$	9.16087	+	9.09528i	0.869511	+	0.863286i
$112$	1.32338	−	1.32338i	0.125047	−	0.125047i
$113$	−2.01798	+	2.01798i	−0.189835	+	0.189835i	−0.795625	−	0.605790i	$-0.792857\pi$
$113$	−2.01798	+	2.01798i	−0.189835	+	0.189835i	0.605790	+	0.795625i	$0.292857\pi$
$114$	14.2639	+	14.1618i	1.33594	+	1.32638i
$115$	−9.99939	−	12.5636i	−0.932448	−	1.17157i
$116$			7.87065i			0.730771i
$117$	0.624334	+	0.615426i	0.0577197	+	0.0568961i
$118$	−15.9306	−	15.9306i	−1.46653	−	1.46653i
$119$	−0.236752			−0.0217030
$120$	−5.07260	+	4.06713i	−0.463063	+	0.371276i
$121$	−0.458667			−0.0416970
$122$	10.5099	+	10.5099i	0.951526	+	0.951526i
$123$	0.0545538		0.000195990i	0.00491895		1.76718e-5i
$124$			25.2448i			2.26705i
$125$	−3.72311	+	10.5422i	−0.333005	+	0.942925i
$126$	6.55107	−	0.0470713i	0.583616	−	0.00419345i
$127$	−11.6271	+	11.6271i	−1.03174	+	1.03174i	−0.0322583	+	0.999480i	$0.510270\pi$
$127$	−11.6271	+	11.6271i	−1.03174	+	1.03174i	−0.999480	+	0.0322583i	$0.989730\pi$
$128$	8.79491	−	8.79491i	0.777367	−	0.777367i
$129$	−6.50417	+	6.55107i	−0.572660	+	0.576789i
$130$	1.41779	+	0.161130i	0.124349	+	0.0141320i
$131$		−	12.7013i		−	1.10972i	−0.831943	−	0.554861i	$-0.812772\pi$
$131$		−	12.7013i		−	1.10972i	0.831943	−	0.554861i	$-0.187228\pi$
$132$	0.0583199	+	16.2333i	0.00507609	+	1.41293i
$133$	−3.75770	−	3.75770i	−0.325834	−	0.325834i
$134$	−19.6046			−1.69358
$135$	11.5581	+	1.18753i	0.994763	+	0.102206i
$136$	−0.397446			−0.0340807
$137$	5.19451	+	5.19451i	0.443797	+	0.443797i	0.893286	−	0.449489i	$-0.148394\pi$
$137$	5.19451	+	5.19451i	0.443797	+	0.443797i	−0.449489	+	0.893286i	$0.648394\pi$
$138$	0.0975782	+	27.1609i	0.00830641	+	2.31209i
$139$			12.3138i			1.04444i	0.852810	+	0.522221i	$0.174897\pi$
$139$			12.3138i			1.04444i	−0.852810	+	0.522221i	$0.825103\pi$
$140$	4.84412	−	3.85543i	0.409402	−	0.325843i
$141$	6.15493	−	6.19932i	0.518339	−	0.522077i
$142$	6.10637	−	6.10637i	0.512435	−	0.512435i
$143$	0.699463	−	0.699463i	0.0584920	−	0.0584920i
$144$	−5.61447	+	0.0403416i	−0.467872	+	0.00336180i
$145$	0.717776	−	6.31576i	0.0596080	−	0.524495i
$146$		−	26.5932i		−	2.20087i
$147$	−1.73204	+	0.00622252i	−0.142856	+	0.000513225i
$148$	−14.5917	−	14.5917i	−1.19943	−	1.19943i
$149$	−18.9350			−1.55121			−0.775607	−	0.631216i	$-0.782556\pi$
$149$	−18.9350			−1.55121			−0.775607	+	0.631216i	$0.782556\pi$
$150$	15.9963	−	10.0884i	1.30609	−	0.823710i
$151$	−1.90527			−0.155049			−0.0775243	−	0.996990i	$-0.524702\pi$
$151$	−1.90527			−0.155049			−0.0775243	+	0.996990i	$0.524702\pi$
$152$	−6.30822	−	6.30822i	−0.511665	−	0.511665i
$153$	0.505822	+	0.498604i	0.0408933	+	0.0403098i
$154$		−	7.39212i		−	0.595674i
$155$	2.30223	−	20.2575i	0.184920	−	1.62712i
$156$	−0.994479	−	0.987359i	−0.0796221	−	0.0790520i
$157$	−4.31728	+	4.31728i	−0.344557	+	0.344557i	−0.858077	−	0.513521i	$-0.828341\pi$
$157$	−4.31728	+	4.31728i	−0.344557	+	0.344557i	0.513521	+	0.858077i	$0.328341\pi$
$158$	17.6726	−	17.6726i	1.40596	−	1.40596i
$159$	6.17589	+	6.13167i	0.489780	+	0.486273i
$160$	−13.0246	+	10.3663i	−1.02968	+	0.819525i
$161$		−	7.18099i		−	0.565941i
$162$	−14.0955	−	13.6961i	−1.10745	−	1.07607i
$163$	3.57655	+	3.57655i	0.280137	+	0.280137i	0.833164	−	0.553027i	$-0.186527\pi$
$163$	3.57655	+	3.57655i	0.280137	+	0.280137i	−0.553027	+	0.833164i	$0.686527\pi$
$164$	−0.0872068			−0.00680970
$165$	1.43363	−	13.0317i	0.111608	−	1.01452i
$166$	11.9844			0.930168
$167$	6.39241	+	6.39241i	0.494659	+	0.494659i	0.909771	−	0.415111i	$-0.136257\pi$
$167$	6.39241	+	6.39241i	0.494659	+	0.494659i	−0.415111	+	0.909771i	$0.636257\pi$
$168$	−2.90765	+	0.0104460i	−0.224330	+	0.000805929i
$169$		−	12.9146i		−	0.993431i
$170$	1.14866	+	0.130544i	0.0880986	+	0.0100123i
$171$	0.114549	+	15.9422i	0.00875978	+	1.21913i
$172$	10.4347	−	10.4347i	0.795638	−	0.795638i
$173$	−3.88791	+	3.88791i	−0.295592	+	0.295592i	−0.839285	−	0.543692i	$-0.817026\pi$
$173$	−3.88791	+	3.88791i	−0.295592	+	0.295592i	0.543692	+	0.839285i	$0.317026\pi$
$174$	−7.57546	+	7.63009i	−0.574294	+	0.578436i
$175$	−4.23874	+	2.65200i	−0.320418	+	0.200472i
$176$			6.33528i			0.477540i
$177$	−0.0641964	−	17.8691i	−0.00482529	−	1.34312i
$178$	3.09121	+	3.09121i	0.231696	+	0.231696i
$179$	14.6322			1.09366			0.546832	−	0.837242i	$-0.315834\pi$
$179$	14.6322			1.09366			0.546832	+	0.837242i	$0.315834\pi$
$180$	−18.4691	−	1.96467i	−1.37661	−	0.146438i
$181$	−9.83718			−0.731192			−0.365596	−	0.930774i	$-0.619135\pi$
$181$	−9.83718			−0.731192			−0.365596	+	0.930774i	$0.619135\pi$
$182$	0.451232	+	0.451232i	0.0334475	+	0.0334475i
$183$	0.0423526	+	11.7888i	0.00313079	+	0.871456i
$184$		−	12.0551i		−	0.888710i
$185$	10.3783	+	13.0397i	0.763027	+	0.958698i
$186$	−24.2980	+	24.4732i	−1.78161	+	1.79446i
$187$	0.566689	−	0.566689i	0.0414404	−	0.0414404i
$188$	−9.87442	+	9.87442i	−0.720166	+	0.720166i
$189$	3.71362	+	3.63442i	0.270126	+	0.264365i
$190$	16.1595	+	20.3035i	1.17234	+	1.47297i
$191$		−	6.37886i		−	0.461558i	−0.973006	−	0.230779i	$-0.925873\pi$
$191$		−	6.37886i		−	0.461558i	0.973006	−	0.230779i	$-0.0741275\pi$
$192$	21.6743	−	0.0778669i	1.56421	−	0.00561956i
$193$	7.56336	+	7.56336i	0.544422	+	0.544422i	0.924822	−	0.380400i	$-0.124214\pi$
$193$	7.56336	+	7.56336i	0.544422	+	0.544422i	−0.380400	+	0.924822i	$0.624214\pi$
$194$	−7.00299			−0.502785
$195$	0.707971	+	0.882995i	0.0506989	+	0.0632326i
$196$	2.76875			0.197768
$197$	1.01490	+	1.01490i	0.0723090	+	0.0723090i	0.742336	−	0.670027i	$-0.233718\pi$
$197$	1.01490	+	1.01490i	0.0723090	+	0.0723090i	−0.670027	+	0.742336i	$0.733718\pi$
$198$	−15.5680	+	15.7933i	−1.10637	+	1.12238i
$199$		−	9.40041i		−	0.666378i	−0.942860	−	0.333189i	$-0.891875\pi$
$199$		−	9.40041i		−	0.666378i	0.942860	−	0.333189i	$-0.108125\pi$
$200$	−7.11576	+	4.45204i	−0.503160	+	0.314806i
$201$	−11.0346	−	10.9556i	−0.778320	−	0.772748i
$202$	−13.3357	+	13.3357i	−0.938295	+	0.938295i
$203$	2.01007	−	2.01007i	0.141080	−	0.141080i
$204$	−0.805705	−	0.799937i	−0.0564107	−	0.0560068i
$205$	0.0699786	+	0.00795295i	0.00488752	+	0.000555458i
$206$		−	2.97813i		−	0.207496i
$207$	−15.1233	+	15.3422i	−1.05114	+	1.06636i
$208$	−0.386719	−	0.386719i	−0.0268142	−	0.0268142i
$209$	17.9889			1.24432
$210$	8.40689	+	0.924849i	0.580131	+	0.0638207i
$211$	−8.29157			−0.570815			−0.285407	−	0.958406i	$-0.592129\pi$
$211$	−8.29157			−0.570815			−0.285407	+	0.958406i	$0.592129\pi$
$212$	−9.83710	−	9.83710i	−0.675615	−	0.675615i
$213$	6.84942	−	0.0246072i	0.469315	−	0.00168606i
$214$		−	9.13661i		−	0.624566i
$215$	−9.32488	+	7.42166i	−0.635952	+	0.506153i
$216$	6.23422	+	6.10127i	0.424185	+	0.415139i
$217$	6.44723	−	6.44723i	0.437666	−	0.437666i
$218$	4.35729	−	4.35729i	0.295113	−	0.295113i
$219$	14.8610	−	14.9682i	1.00421	−	1.01145i
$220$	−2.36653	+	20.8232i	−0.159551	+	1.40390i
$221$			0.0691839i			0.00465382i
$222$	−0.101276	−	28.1901i	−0.00679717	−	1.89199i
$223$	3.86020	+	3.86020i	0.258498	+	0.258498i	0.824443	−	0.565945i	$-0.191489\pi$
$223$	3.86020	+	3.86020i	0.258498	+	0.258498i	−0.565945	+	0.824443i	$0.691489\pi$
$224$	−7.44445			−0.497404
$225$	14.6413	+	3.26086i	0.976085	+	0.217391i
$226$	6.23208			0.414552
$227$	−1.50739	−	1.50739i	−0.100049	−	0.100049i	0.655310	−	0.755360i	$-0.272538\pi$
$227$	−1.50739	−	1.50739i	−0.100049	−	0.100049i	−0.755360	+	0.655310i	$0.772538\pi$
$228$	−0.0915560	−	25.4846i	−0.00606344	−	1.68776i
$229$			6.26009i			0.413678i	0.978375	+	0.206839i	$0.0663177\pi$
$229$			6.26009i			0.413678i	−0.978375	+	0.206839i	$0.933682\pi$
$230$	−3.95957	+	34.8405i	−0.261086	+	2.29732i
$231$	4.13092	−	4.16071i	0.271795	−	0.273755i
$232$	3.37440	−	3.37440i	0.221541	−	0.221541i
$233$	2.67422	−	2.67422i	0.175194	−	0.175194i	−0.614063	−	0.789257i	$-0.710466\pi$
$233$	2.67422	−	2.67422i	0.175194	−	0.175194i	0.789257	+	0.614063i	$0.210466\pi$
$234$	−0.0137553	−	1.91436i	−0.000899209	−	0.125146i
$235$	8.82419	−	7.02317i	0.575627	−	0.458141i
$236$			28.5645i			1.85939i
$237$	19.8231	−	0.0712164i	1.28765	−	0.00462600i
$238$	0.365578	+	0.365578i	0.0236969	+	0.0236969i
$239$	−2.08521			−0.134881			−0.0674406	−	0.997723i	$-0.521483\pi$
$239$	−2.08521			−0.134881			−0.0674406	+	0.997723i	$0.521483\pi$
$240$	−7.20497	−	0.792624i	−0.465079	−	0.0511637i
$241$	−5.43686			−0.350219			−0.175110	−	0.984549i	$-0.556028\pi$
$241$	−5.43686			−0.350219			−0.175110	+	0.984549i	$0.556028\pi$
$242$	0.708247	+	0.708247i	0.0455279	+	0.0455279i
$243$	−0.279999	−	15.5859i	−0.0179619	−	0.999839i
$244$		−	18.8450i		−	1.20643i
$245$	−2.22177	−	0.252500i	−0.141943	−	0.0161316i
$246$	−0.0845414	−	0.0839361i	−0.00539016	−	0.00535157i
$247$	−1.09808	+	1.09808i	−0.0698692	+	0.0698692i
$248$	10.8233	−	10.8233i	0.687278	−	0.687278i
$249$	6.74549	+	6.69720i	0.427478	+	0.424418i
$250$	22.0277	−	10.5297i	1.39315	−	0.665956i
$251$		−	23.3428i		−	1.47339i	−0.676227	−	0.736693i	$-0.736386\pi$
$251$		−	23.3428i		−	1.47339i	0.676227	−	0.736693i	$-0.263614\pi$
$252$	−5.91545	−	5.83104i	−0.372638	−	0.367321i
$253$	17.1884	+	17.1884i	1.08063	+	1.08063i
$254$	35.9078			2.25305
$255$	0.573583	+	0.715383i	0.0359191	+	0.0447990i
$256$	−2.13372			−0.133358
$257$	−10.9273	−	10.9273i	−0.681627	−	0.681627i	0.278740	−	0.960367i	$-0.410083\pi$
$257$	−10.9273	−	10.9273i	−0.681627	−	0.681627i	−0.960367	+	0.278740i	$0.910083\pi$
$258$	20.1591	−	0.0724236i	1.25505	−	0.00450890i
$259$			7.45309i			0.463112i
$260$	−1.12664	−	1.41556i	−0.0698712	−	0.0877890i
$261$	−8.52781	+	0.0612747i	−0.527858	+	0.00379281i
$262$	−19.6127	+	19.6127i	−1.21167	+	1.21167i
$263$	−18.1808	+	18.1808i	−1.12108	+	1.12108i	−0.129497	+	0.991580i	$0.541336\pi$
$263$	−18.1808	+	18.1808i	−1.12108	+	1.12108i	−0.991580	+	0.129497i	$0.958664\pi$
$264$	6.93477	−	6.98477i	0.426805	−	0.429883i
$265$	6.99662	+	8.79084i	0.429799	+	0.540017i
$266$			11.6048i			0.711539i
$267$	0.0124569	+	3.46737i	0.000762347	+	0.212199i
$268$	17.5762	+	17.5762i	1.07364	+	1.07364i
$269$	−28.5125			−1.73844			−0.869219	−	0.494428i	$-0.835378\pi$
$269$	−28.5125			−1.73844			−0.869219	+	0.494428i	$0.835378\pi$
$270$	−16.0136	−	19.6811i	−0.974559	−	1.19775i
$271$	3.12214			0.189656			0.0948282	−	0.995494i	$-0.469770\pi$
$271$	3.12214			0.189656			0.0948282	+	0.995494i	$0.469770\pi$
$272$	−0.313312	−	0.313312i	−0.0189973	−	0.0189973i
$273$	0.00181836	+	0.506139i	0.000110052	+	0.0306330i
$274$		−	16.0421i		−	0.969139i
$275$	3.79802	−	16.4937i	0.229029	−	0.994607i
$276$	24.2631	−	24.4381i	1.46047	−	1.47100i
$277$	12.2472	−	12.2472i	0.735861	−	0.735861i	−0.235913	−	0.971774i	$-0.575808\pi$
$277$	12.2472	−	12.2472i	0.735861	−	0.735861i	0.971774	+	0.235913i	$0.0758081\pi$
$278$	19.0142	−	19.0142i	1.14040	−	1.14040i
$279$	−27.3526	+	0.196536i	−1.63756	+	0.0117663i
$280$	−3.72978	−	0.423883i	−0.222897	−	0.0253319i
$281$			12.7181i			0.758698i	0.925254	+	0.379349i	$0.123852\pi$
$281$			12.7181i			0.758698i	−0.925254	+	0.379349i	$0.876148\pi$
$282$	−19.0767	+	0.0685349i	−1.13600	+	0.00408120i
$283$	−19.8271	−	19.8271i	−1.17860	−	1.17860i	−0.980102	−	0.198495i	$-0.936395\pi$
$283$	−19.8271	−	19.8271i	−1.17860	−	1.17860i	−0.198495	−	0.980102i	$-0.563605\pi$
$284$	−10.9491			−0.649711
$285$	−2.25064	+	20.4583i	−0.133316	+	1.21185i
$286$	−2.16014			−0.127732
$287$	0.0222716	+	0.0222716i	0.00131465	+	0.00131465i
$288$	15.9051	+	15.6782i	0.937219	+	0.923847i
$289$		−	16.9439i		−	0.996703i
$290$	−10.8608	+	8.64408i	−0.637767	+	0.507598i
$291$	−3.94168	−	3.91346i	−0.231066	−	0.229411i
$292$	−23.8416	+	23.8416i	−1.39523	+	1.39523i
$293$	6.72836	−	6.72836i	0.393075	−	0.393075i	−0.482707	−	0.875782i	$-0.660346\pi$
$293$	6.72836	−	6.72836i	0.393075	−	0.393075i	0.875782	+	0.482707i	$0.160346\pi$
$294$	2.68412	+	2.66491i	0.156541	+	0.155420i
$295$	2.60499	−	22.9215i	0.151668	−	1.33454i
$296$			12.5118i			0.727236i
$297$	−17.5883	+	0.189570i	−1.02058	+	0.0109999i
$298$	29.2383	+	29.2383i	1.69373	+	1.69373i
$299$	−2.09844			−0.121356
$300$	−23.3857	−	5.29665i	−1.35018	−	0.305802i
$301$	−5.32981			−0.307205
$302$	2.94201	+	2.94201i	0.169293	+	0.169293i
$303$	−14.9584	+	0.0537396i	−0.859339	+	0.00308726i
$304$		−	9.94571i		−	0.570426i
$305$	−1.71860	+	15.1221i	−0.0984068	+	0.865888i
$306$	−0.0111442	−	1.55098i	−0.000637072	−	0.0886634i
$307$	10.1105	−	10.1105i	0.577034	−	0.577034i	−0.357051	−	0.934085i	$-0.616218\pi$
$307$	10.1105	−	10.1105i	0.577034	−	0.577034i	0.934085	+	0.357051i	$0.116218\pi$
$308$	−6.62728	+	6.62728i	−0.377624	+	0.377624i
$309$	1.66426	−	1.67626i	0.0946765	−	0.0953592i
$310$	−34.8355	+	27.7255i	−1.97852	+	1.57470i
$311$		−	0.394155i		−	0.0223505i	−0.999938	−	0.0111752i	$-0.996443\pi$
$311$		−	0.394155i		−	0.0223505i	0.999938	−	0.0111752i	$-0.00355726\pi$
$312$	0.00305256	+	0.849680i	0.000172817	+	0.0481036i
$313$	−10.3810	−	10.3810i	−0.586767	−	0.586767i	0.349987	−	0.936754i	$-0.386186\pi$
$313$	−10.3810	−	10.3810i	−0.586767	−	0.586767i	−0.936754	+	0.349987i	$0.886186\pi$
$314$	13.3330			0.752424
$315$	4.21505	+	5.21856i	0.237491	+	0.294033i
$316$	−31.6881			−1.78260
$317$	19.8075	+	19.8075i	1.11250	+	1.11250i	0.992812	+	0.119688i	$0.0381896\pi$
$317$	19.8075	+	19.8075i	1.11250	+	1.11250i	0.119688	+	0.992812i	$0.461810\pi$
$318$	−0.0682759	−	19.0046i	−0.00382872	−	1.06573i
$319$			9.62264i			0.538764i
$320$	27.8026	+	3.15971i	1.55421	+	0.176633i
$321$	5.10579	−	5.14260i	0.284977	−	0.287032i
$322$	−11.0885	+	11.0885i	−0.617936	+	0.617936i
$323$	−0.889642	+	0.889642i	−0.0495010	+	0.0495010i
$324$	0.358078	+	24.9161i	0.0198932	+	1.38423i
$325$	0.774972	+	1.23865i	0.0429877	+	0.0687080i
$326$		−	11.0454i		−	0.611748i
$327$	4.88750	−	0.0175588i	0.270279	−	0.000971005i
$328$	0.0373884	+	0.0373884i	0.00206443	+	0.00206443i
$329$	5.04363			0.278065
$330$	−22.3365	+	17.9090i	−1.22958	+	0.985860i
$331$	−24.7348			−1.35955			−0.679774	−	0.733422i	$-0.737922\pi$
$331$	−24.7348			−1.35955			−0.679774	+	0.733422i	$0.737922\pi$
$332$	−10.7444	−	10.7444i	−0.589674	−	0.589674i
$333$	15.6964	−	15.9236i	0.860157	−	0.872607i
$334$		−	19.7416i		−	1.08021i
$335$	−12.5010	−	15.7068i	−0.683004	−	0.858154i
$336$	−2.30038	−	2.28391i	−0.125496	−	0.124597i
$337$	−3.40139	+	3.40139i	−0.185286	+	0.185286i	−0.793655	−	0.608369i	$-0.791824\pi$
$337$	−3.40139	+	3.40139i	−0.185286	+	0.185286i	0.608369	+	0.793655i	$0.291824\pi$
$338$	−19.9420	+	19.9420i	−1.08470	+	1.08470i
$339$	3.50777	+	3.48266i	0.190516	+	0.189152i
$340$	−0.912779	−	1.14685i	−0.0495024	−	0.0621968i
$341$			30.8642i			1.67139i
$342$	24.4401	−	24.7938i	1.32157	−	1.34070i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−8.94740			−0.482411
$345$	−21.6985	+	17.3975i	−1.16821	+	0.936651i
$346$	12.0070			0.645498
$347$	−24.0324	−	24.0324i	−1.29013	−	1.29013i	−0.934706	−	0.355421i	$-0.884337\pi$
$347$	−24.0324	−	24.0324i	−1.29013	−	1.29013i	−0.355421	−	0.934706i	$-0.615663\pi$
$348$	13.6323	−	0.0489753i	0.730766	−	0.00262535i
$349$		−	9.37078i		−	0.501607i	−0.968038	−	0.250803i	$-0.919305\pi$
$349$		−	9.37078i		−	0.501607i	0.968038	−	0.250803i	$-0.0806947\pi$
$350$	10.6403	+	2.45015i	0.568747	+	0.130966i
$351$	1.06206	−	1.08520i	0.0566884	−	0.0579237i
$352$	17.8191	−	17.8191i	0.949759	−	0.949759i
$353$	−14.5888	+	14.5888i	−0.776481	+	0.776481i	−0.979231	−	0.202750i	$-0.935012\pi$
$353$	−14.5888	+	14.5888i	−0.776481	+	0.776481i	0.202750	+	0.979231i	$0.435012\pi$
$354$	−27.4932	+	27.6915i	−1.46125	+	1.47179i
$355$	8.78606	+	0.998522i	0.466316	+	0.0529960i
$356$		−	5.54275i		−	0.293765i
$357$	0.00147319	+	0.410063i	7.79696e−5	+	0.0217028i
$358$	−22.5942	−	22.5942i	−1.19414	−	1.19414i
$359$	−27.2654			−1.43901			−0.719506	−	0.694486i	$-0.755632\pi$
$359$	−27.2654			−1.43901			−0.719506	+	0.694486i	$0.755632\pi$
$360$	7.07599	+	8.76064i	0.372938	+	0.461726i
$361$	−9.24062			−0.486349
$362$	15.1900	+	15.1900i	0.798369	+	0.798369i
$363$	0.00285407	+	0.794430i	0.000149800	+	0.0416968i
$364$		−	0.809088i		−	0.0424077i
$365$	21.3059	−	16.9573i	1.11520	−	0.887587i
$366$	18.1382	−	18.2690i	0.948101	−	0.954938i
$367$	15.9239	−	15.9239i	0.831218	−	0.831218i	−0.156465	−	0.987683i	$-0.550010\pi$
$367$	15.9239	−	15.9239i	0.831218	−	0.831218i	0.987683	+	0.156465i	$0.0500099\pi$
$368$	9.50315	−	9.50315i	0.495386	−	0.495386i
$369$	−0.000678924	−	0.0944881i	−3.53434e−5	−	0.00491885i
$370$	4.10960	−	36.1607i	0.213648	−	1.87990i
$371$			5.02457i			0.260863i
$372$	43.7249	−	0.157086i	2.26703	−	0.00814453i
$373$	23.3283	+	23.3283i	1.20790	+	1.20790i	0.971707	+	0.236189i	$0.0758984\pi$
$373$	23.3283	+	23.3283i	1.20790	+	1.20790i	0.236189	+	0.971707i	$0.424102\pi$
$374$	−1.75010			−0.0904954
$375$	18.2827	+	6.38297i	0.944115	+	0.329615i
$376$	8.46698			0.436651
$377$	−0.587387	−	0.587387i	−0.0302520	−	0.0302520i
$378$	−0.122294	−	11.3464i	−0.00629010	−	0.583597i
$379$			37.4477i			1.92356i	0.273828	+	0.961779i	$0.411710\pi$
$379$			37.4477i			1.92356i	−0.273828	+	0.961779i	$0.588290\pi$
$380$	3.71520	−	32.6903i	0.190586	−	1.67698i
$381$	20.2109	+	20.0662i	1.03544	+	1.02802i
$382$	−9.84986	+	9.84986i	−0.503963	+	0.503963i
$383$	4.95443	−	4.95443i	0.253159	−	0.253159i	−0.569105	−	0.822265i	$-0.692710\pi$
$383$	4.95443	−	4.95443i	0.253159	−	0.253159i	0.822265	+	0.569105i	$0.192710\pi$
$384$	−15.2879	−	15.1784i	−0.780155	−	0.774570i
$385$	5.92241	−	4.71364i	0.301834	−	0.240229i
$386$		−	23.3578i		−	1.18888i
$387$	11.3872	+	11.2247i	0.578843	+	0.570584i
$388$	6.27841	+	6.27841i	0.318738	+	0.318738i
$389$	−9.20279			−0.466600			−0.233300	−	0.972405i	$-0.574952\pi$
$389$	−9.20279			−0.466600			−0.233300	+	0.972405i	$0.574952\pi$
$390$	0.270261	−	2.45668i	0.0136852	−	0.124399i
$391$	−1.70011			−0.0859783
$392$	−1.18705	−	1.18705i	−0.0599552	−	0.0599552i
$393$	−21.9992	+	0.0790344i	−1.10971	+	0.00398676i
$394$		−	3.13431i		−	0.157904i
$395$	25.4280	+	2.88985i	1.27942	+	0.145404i
$396$	28.1164	−	0.202025i	1.41290	−	0.0101521i
$397$	21.9242	−	21.9242i	1.10034	−	1.10034i	0.105976	−	0.994369i	$-0.466203\pi$
$397$	21.9242	−	21.9242i	1.10034	−	1.10034i	0.994369	−	0.105976i	$-0.0337966\pi$
$398$	−14.5156	+	14.5156i	−0.727600	+	0.727600i
$399$	−6.48510	+	6.53187i	−0.324661	+	0.327002i
$400$	−9.11904	−	2.09985i	−0.455952	−	0.104993i
$401$			25.7514i			1.28596i	0.765882	+	0.642982i	$0.222303\pi$
$401$			25.7514i			1.28596i	−0.765882	+	0.642982i	$0.777697\pi$
$402$	0.121990	+	33.9560i	0.00608431	+	1.69357i
$403$	−1.88402	−	1.88402i	−0.0938497	−	0.0938497i
$404$	23.9117			1.18965
$405$	1.98493	−	20.0265i	0.0986319	−	0.995124i
$406$	−6.20768			−0.308082
$407$	−17.8397	−	17.8397i	−0.884283	−	0.884283i
$408$	0.00247311	+	0.688392i	0.000122437	+	0.0340805i
$409$			10.9496i			0.541425i	0.962660	+	0.270712i	$0.0872592\pi$
$409$			10.9496i			0.541425i	−0.962660	+	0.270712i	$0.912741\pi$
$410$	−0.0957764	−	0.120337i	−0.00473006	−	0.00594304i
$411$	8.96477	−	9.02942i	0.442200	−	0.445388i
$412$	−2.66999	+	2.66999i	−0.131541	+	0.131541i
$413$	7.29506	−	7.29506i	0.358967	−	0.358967i
$414$	47.0431	−	0.338019i	2.31204	−	0.0166127i
$415$	7.64192	+	9.60162i	0.375127	+	0.471325i
$416$			2.17543i			0.106659i
$417$	21.3280	−	0.0766229i	1.04444	−	0.00375224i
$418$	−27.7774	−	27.7774i	−1.35864	−	1.35864i
$419$	5.86958			0.286748			0.143374	−	0.989669i	$-0.454205\pi$
$419$	5.86958			0.286748			0.143374	+	0.989669i	$0.454205\pi$
$420$	−6.70789	−	8.36621i	−0.327312	−	0.408229i
$421$	26.8842			1.31026			0.655129	−	0.755517i	$-0.272614\pi$
$421$	26.8842			1.31026			0.655129	+	0.755517i	$0.272614\pi$
$422$	12.8034	+	12.8034i	0.623257	+	0.623257i
$423$	−10.7758	−	10.6220i	−0.523936	−	0.516460i
$424$			8.43498i			0.409639i
$425$	0.627865	+	1.00353i	0.0304559	+	0.0486782i
$426$	−10.6145	−	10.5385i	−0.514273	−	0.510591i
$427$	−4.81281	+	4.81281i	−0.232908	+	0.232908i
$428$	−8.19126	+	8.19126i	−0.395940	+	0.395940i
$429$	−1.21585	−	1.20714i	−0.0587018	−	0.0582815i
$430$	25.8590	+	2.93884i	1.24703	+	0.141723i
$431$			4.18118i			0.201400i	0.994917	+	0.100700i	$0.0321083\pi$
$431$			4.18118i			0.201400i	−0.994917	+	0.100700i	$0.967892\pi$
$432$	0.104809	+	9.72423i	0.00504264	+	0.467857i
$433$	−2.20877	−	2.20877i	−0.106146	−	0.106146i	0.652039	−	0.758185i	$-0.273914\pi$
$433$	−2.20877	−	2.20877i	−0.106146	−	0.106146i	−0.758185	+	0.652039i	$0.773914\pi$
$434$	−19.9109			−0.955752
$435$	−10.9436	−	1.20392i	−0.524706	−	0.0577233i
$436$	−7.81290			−0.374170
$437$	−26.9840	−	26.9840i	−1.29082	−	1.29082i
$438$	−46.0604	+	0.165477i	−2.20085	+	0.00790678i
$439$			27.6028i			1.31741i	0.752401	+	0.658706i	$0.228896\pi$
$439$			27.6028i			1.31741i	−0.752401	+	0.658706i	$0.771104\pi$
$440$	9.94222	−	7.91300i	0.473977	−	0.377238i
$441$	0.0215553	+	2.99992i	0.00102644	+	0.142853i
$442$	0.106830	−	0.106830i	0.00508138	−	0.00508138i
$443$	−12.3040	+	12.3040i	−0.584582	+	0.584582i	−0.936159	−	0.351577i	$-0.885646\pi$
$443$	−12.3040	+	12.3040i	−0.584582	+	0.584582i	0.351577	+	0.936159i	$0.385646\pi$
$444$	−25.1825	+	25.3641i	−1.19511	+	1.20373i
$445$	−0.505479	+	4.44775i	−0.0239620	+	0.210843i
$446$		−	11.9214i		−	0.564494i
$447$	0.117823	+	32.7961i	0.00557285	+	1.55120i
$448$	8.84854	+	8.84854i	0.418054	+	0.418054i
$449$	34.1859			1.61333			0.806666	−	0.591008i	$-0.201270\pi$
$449$	34.1859			1.61333			0.806666	+	0.591008i	$0.201270\pi$
$450$	−17.5730	−	27.6434i	−0.828397	−	1.30312i
$451$	−0.106619			−0.00502049
$452$	−5.58726	−	5.58726i	−0.262803	−	0.262803i
$453$	0.0118556	+	3.30000i	0.000557024	+	0.155048i
$454$			4.65526i			0.218482i
$455$	−0.0737860	+	0.649248i	−0.00345914	+	0.0304372i
$456$	−10.8868	+	10.9653i	−0.509823	+	0.513499i
$457$	−9.31021	+	9.31021i	−0.435513	+	0.435513i	−0.890499	−	0.454986i	$-0.849644\pi$
$457$	−9.31021	+	9.31021i	−0.435513	+	0.435513i	0.454986	+	0.890499i	$0.349644\pi$
$458$	9.66646	−	9.66646i	0.451684	−	0.451684i
$459$	0.860455	−	0.879206i	0.0401626	−	0.0410378i
$460$	34.7855	−	27.6858i	1.62188	−	1.29086i
$461$			25.6579i			1.19501i	0.801865	+	0.597505i	$0.203841\pi$
$461$			25.6579i			1.19501i	−0.801865	+	0.597505i	$0.796159\pi$
$462$	−12.8034	+	0.0459976i	−0.595670	+	0.00214000i
$463$	13.2170	+	13.2170i	0.614248	+	0.614248i	0.944050	−	0.329802i	$-0.106982\pi$
$463$	13.2170	+	13.2170i	0.614248	+	0.614248i	−0.329802	+	0.944050i	$0.606982\pi$
$464$	5.32017			0.246983
$465$	−35.1012	−	3.86151i	−1.62778	−	0.179073i
$466$	−8.25874			−0.382579
$467$	19.6659	+	19.6659i	0.910031	+	0.910031i	0.996274	−	0.0862431i	$-0.0274862\pi$
$467$	19.6659	+	19.6659i	0.910031	+	0.910031i	−0.0862431	+	0.996274i	$0.527486\pi$
$468$	−1.70396	+	1.72862i	−0.0787655	+	0.0799056i
$469$		−	8.97752i		−	0.414543i
$470$	−24.4706	−	2.78104i	−1.12874	−	0.128280i
$471$	7.50457	+	7.45084i	0.345792	+	0.343317i
$472$	12.2466	−	12.2466i	0.563693	−	0.563693i
$473$	12.7575	−	12.7575i	0.586588	−	0.586588i
$474$	−30.7196	−	30.4997i	−1.41100	−	1.40090i
$475$	−5.96248	+	25.8933i	−0.273577	+	1.18807i
$476$		−	0.655505i		−	0.0300450i
$477$	10.5819	−	10.7350i	0.484510	−	0.491524i
$478$	3.21986	+	3.21986i	0.147273	+	0.147273i
$479$	26.9725			1.23240			0.616202	−	0.787588i	$-0.288670\pi$
$479$	26.9725			1.23240			0.616202	+	0.787588i	$0.288670\pi$
$480$	18.0358	+	22.4946i	0.823219	+	1.02673i
$481$	2.17795			0.0993062
$482$	8.39528	+	8.39528i	0.382395	+	0.382395i
$483$	−12.4378	+	0.0446838i	−0.565937	+	0.00203319i
$484$		−	1.26993i		−	0.0577242i
$485$	−4.46551	−	5.61064i	−0.202768	−	0.254766i
$486$	−23.6345	+	24.4993i	−1.07208	+	1.11131i
$487$	−28.6505	+	28.6505i	−1.29828	+	1.29828i	−0.368749	+	0.929529i	$0.620214\pi$
$487$	−28.6505	+	28.6505i	−1.29828	+	1.29828i	−0.929529	+	0.368749i	$0.879786\pi$
$488$	−8.07948	+	8.07948i	−0.365741	+	0.365741i
$489$	6.17247	−	6.21698i	0.279129	−	0.281141i
$490$	3.04083	+	3.82062i	0.137370	+	0.172598i
$491$			2.74522i			0.123890i	0.998080	+	0.0619450i	$0.0197303\pi$
$491$			2.74522i			0.123890i	−0.998080	+	0.0619450i	$0.980270\pi$
$492$	0.000542646		0.151046i	2.44644e−5		0.00680966i
$493$	−0.475888	−	0.475888i	−0.0214329	−	0.0214329i
$494$	3.39119			0.152577
$495$	−22.5803	−	2.40201i	−1.01491	−	0.107962i
$496$	17.0642			0.766206
$497$	2.79628	+	2.79628i	0.125430	+	0.125430i
$498$	−0.0745730	−	20.7574i	−0.00334170	−	0.930162i
$499$		−	30.3151i		−	1.35709i	−0.734558	−	0.678546i	$-0.762611\pi$
$499$		−	30.3151i		−	1.35709i	0.734558	−	0.678546i	$-0.237389\pi$
$500$	−29.1887	−	10.3083i	−1.30536	−	0.461003i
$501$	11.0321	−	11.1117i	0.492879	−	0.496433i
$502$	−36.0446	+	36.0446i	−1.60875	+	1.60875i
$503$	0.331820	−	0.331820i	0.0147951	−	0.0147951i	−0.699671	−	0.714466i	$-0.746670\pi$
$503$	0.331820	−	0.331820i	0.0147951	−	0.0147951i	0.714466	+	0.699671i	$0.246670\pi$
$504$	0.0361859	+	5.03611i	0.00161185	+	0.224326i
$505$	−19.1878	−	2.18067i	−0.853848	−	0.0970384i
$506$		−	53.0827i		−	2.35982i
$507$	−22.3686	+	0.0803614i	−0.993425	+	0.00356898i
$508$	−32.1925	−	32.1925i	−1.42831	−	1.42831i
$509$	−14.6491			−0.649311			−0.324656	−	0.945832i	$-0.605248\pi$
$509$	−14.6491			−0.649311			−0.324656	+	0.945832i	$0.605248\pi$
$510$	0.218960	−	1.99035i	0.00969569	−	0.0881340i
$511$	12.1778			0.538713
$512$	−14.2950	−	14.2950i	−0.631758	−	0.631758i
$513$	27.6117	−	0.297604i	1.21909	−	0.0131395i
$514$			33.7466i			1.48850i
$515$	2.38601	−	1.89903i	0.105140	−	0.0836811i
$516$	−18.1382	−	18.0084i	−0.798492	−	0.792775i
$517$	−12.0725	+	12.0725i	−0.530946	+	0.530946i
$518$	11.5086	−	11.5086i	0.505660	−	0.505660i
$519$	6.75820	+	6.70982i	0.296652	+	0.294528i
$520$	−0.123868	+	1.08992i	−0.00543197	+	0.0477963i
$521$		−	24.6501i		−	1.07994i	−0.841683	−	0.539971i	$-0.818435\pi$
$521$		−	24.6501i		−	1.07994i	0.841683	−	0.539971i	$-0.181565\pi$
$522$	13.2628	+	13.0735i	0.580495	+	0.572212i
$523$	−23.4069	−	23.4069i	−1.02351	−	1.02351i	−0.999717	−	0.0237950i	$-0.992425\pi$
$523$	−23.4069	−	23.4069i	−1.02351	−	1.02351i	−0.0237950	−	0.999717i	$-0.507575\pi$
$524$	35.1668			1.53627
$525$	4.61975	+	7.32516i	0.201622	+	0.319696i
$526$	56.1475			2.44815
$527$	−1.52639	−	1.52639i	−0.0664907	−	0.0664907i
$528$	10.9730	−	0.0394214i	0.477536	−	0.00171560i
$529$		−	28.5666i		−	1.24203i
$530$	2.77053	−	24.3781i	0.120344	−	1.05892i
$531$	−30.9495	+	0.222381i	−1.34310	+	0.00965053i
$532$	10.4041	−	10.4041i	0.451076	−	0.451076i
$533$	0.00650825	−	0.00650825i	0.000281904	−	0.000281904i
$534$	5.33487	−	5.37334i	0.230862	−	0.232527i
$535$	7.32005	−	5.82602i	0.316473	−	0.251881i
$536$		−	15.0710i		−	0.650967i
$537$	−0.0910493	−	25.3436i	−0.00392907	−	1.09366i
$538$	44.0273	+	44.0273i	1.89815	+	1.89815i
$539$	3.38507			0.145805
$540$	−3.28797	+	32.0015i	−0.141492	+	1.37712i
$541$	−27.2143			−1.17003			−0.585017	−	0.811021i	$-0.698912\pi$
$541$	−27.2143			−1.17003			−0.585017	+	0.811021i	$0.698912\pi$
$542$	−4.82102	−	4.82102i	−0.207081	−	0.207081i
$543$	0.0612121	+	17.0384i	0.00262686	+	0.731187i
$544$			1.76249i			0.0755660i
$545$	6.26942	+	0.712509i	0.268552	+	0.0305205i
$546$	0.778743	−	0.784359i	0.0333271	−	0.0335675i
$547$	−3.63475	+	3.63475i	−0.155411	+	0.155411i	−0.780530	−	0.625119i	$-0.785051\pi$
$547$	−3.63475	+	3.63475i	−0.155411	+	0.155411i	0.625119	+	0.780530i	$0.285051\pi$
$548$	−14.3823	+	14.3823i	−0.614380	+	0.614380i
$549$	20.4185	−	0.146713i	0.871440	−	0.00626154i
$550$	−31.3333	+	19.6039i	−1.33605	+	0.835914i
$551$		−	15.1065i		−	0.643559i
$552$	−20.8798	+	0.0750128i	−0.888705	+	0.00319276i
$553$	8.09279	+	8.09279i	0.344141	+	0.344141i
$554$	−37.8227			−1.60693
$555$	22.5207	−	18.0567i	0.955951	−	0.766466i
$556$	−34.0938			−1.44590
$557$	−5.91751	−	5.91751i	−0.250733	−	0.250733i	0.570538	−	0.821271i	$-0.306735\pi$
$557$	−5.91751	−	5.91751i	−0.250733	−	0.250733i	−0.821271	+	0.570538i	$0.806735\pi$
$558$	42.5397	+	41.9328i	1.80085	+	1.77516i
$559$			1.55749i			0.0658747i
$560$	−2.60608	−	3.27439i	−0.110127	−	0.138368i
$561$	−0.985055	−	0.978002i	−0.0415890	−	0.0412913i
$562$	19.6385	−	19.6385i	0.828402	−	0.828402i
$563$	13.8267	−	13.8267i	0.582728	−	0.582728i	−0.352924	−	0.935652i	$-0.614813\pi$
$563$	13.8267	−	13.8267i	0.582728	−	0.582728i	0.935652	+	0.352924i	$0.114813\pi$
$564$	17.1643	+	17.0414i	0.722749	+	0.717574i
$565$	3.97393	+	4.99301i	0.167185	+	0.210058i
$566$			61.2316i			2.57376i
$567$	6.27185	−	6.45475i	0.263393	−	0.271074i
$568$	4.69425	+	4.69425i	0.196966	+	0.196966i
$569$	6.82232			0.286007			0.143003	−	0.989722i	$-0.454324\pi$
$569$	6.82232			0.286007			0.143003	+	0.989722i	$0.454324\pi$
$570$	35.0659	−	28.1153i	1.46875	−	1.17762i
$571$	19.7545			0.826701			0.413351	−	0.910572i	$-0.364358\pi$
$571$	19.7545			0.826701			0.413351	+	0.910572i	$0.364358\pi$
$572$	1.93663	+	1.93663i	0.0809747	+	0.0809747i
$573$	−11.0484	+	0.0396926i	−0.461555	+	0.00165818i
$574$		−	0.0687811i		−	0.00287087i
$575$	−30.4383	+	19.0440i	−1.26937	+	0.794189i
$576$	−0.269737	−	37.5402i	−0.0112390	−	1.56417i
$577$	1.10727	−	1.10727i	0.0460964	−	0.0460964i	−0.683683	−	0.729779i	$-0.739623\pi$
$577$	1.10727	−	1.10727i	0.0460964	−	0.0460964i	0.729779	+	0.683683i	$0.239623\pi$
$578$	−26.1639	+	26.1639i	−1.08827	+	1.08827i
$579$	13.0530	−	13.1471i	0.542463	−	0.546375i
$580$	17.4867	+	1.98734i	0.726097	+	0.0825197i
$581$			5.48799i			0.227680i
$582$	0.0435762	+	12.1295i	0.00180629	+	0.502782i
$583$	−12.0268	−	12.0268i	−0.498100	−	0.498100i
$584$	20.4434			0.845953
$585$	1.52498	−	1.23173i	0.0630500	−	0.0509257i
$586$	−20.7791			−0.858376
$587$	−7.76708	−	7.76708i	−0.320582	−	0.320582i	0.528408	−	0.848990i	$-0.322789\pi$
$587$	−7.76708	−	7.76708i	−0.320582	−	0.320582i	−0.848990	+	0.528408i	$0.822789\pi$
$588$	−0.0172286	−	4.79558i	−0.000710495	−	0.197766i
$589$		−	48.4535i		−	1.99649i
$590$	−39.4165	+	31.3715i	−1.62275	+	1.29154i
$591$	1.75154	−	1.76417i	0.0720487	−	0.0725683i
$592$	−9.86325	+	9.86325i	−0.405377	+	0.405377i
$593$	8.01301	−	8.01301i	0.329055	−	0.329055i	−0.523172	−	0.852227i	$-0.675252\pi$
$593$	8.01301	−	8.01301i	0.329055	−	0.329055i	0.852227	+	0.523172i	$0.175252\pi$
$594$	27.4515	+	26.8661i	1.12635	+	1.10233i
$595$	−0.0597798	+	0.526007i	−0.00245073	+	0.0215642i
$596$		−	52.4261i		−	2.14746i
$597$	−16.2819	+	0.0584943i	−0.666373	+	0.00239401i
$598$	3.24029	+	3.24029i	0.132505	+	0.132505i
$599$	20.3742			0.832467			0.416233	−	0.909258i	$-0.363350\pi$
$599$	20.3742			0.832467			0.416233	+	0.909258i	$0.363350\pi$
$600$	7.75538	+	12.2971i	0.316612	+	0.502026i
$601$	−32.4833			−1.32502			−0.662511	−	0.749052i	$-0.730509\pi$
$601$	−32.4833			−1.32502			−0.662511	+	0.749052i	$0.730509\pi$
$602$	8.22998	+	8.22998i	0.335429	+	0.335429i
$603$	−18.9069	+	19.1805i	−0.769947	+	0.781092i
$604$		−	5.27521i		−	0.214645i
$605$	−0.115814	+	1.01905i	−0.00470849	+	0.0414303i
$606$	23.1809	+	23.0149i	0.941660	+	0.934918i
$607$	−0.0701607	+	0.0701607i	−0.00284774	+	0.00284774i	−0.708529	−	0.705681i	$-0.750641\pi$
$607$	−0.0701607	+	0.0701607i	−0.00284774	+	0.00284774i	0.705681	+	0.708529i	$0.250641\pi$
$608$	−27.9740	+	27.9740i	−1.13450	+	1.13450i
$609$	−3.49404	−	3.46902i	−0.141586	−	0.140572i
$610$	26.0044	−	20.6969i	1.05289	−	0.837992i
$611$		−	1.47386i		−	0.0596260i
$612$	−1.38051	+	1.40049i	−0.0558038	+	0.0566115i
$613$	−26.6840	−	26.6840i	−1.07776	−	1.07776i	−0.996710	−	0.0810445i	$-0.974174\pi$
$613$	−26.6840	−	26.6840i	−1.07776	−	1.07776i	−0.0810445	−	0.996710i	$-0.525826\pi$
$614$	−31.2239			−1.26010
$615$	0.0133394	−	0.121255i	0.000537896	−	0.00488948i
$616$	5.68266			0.228961
$617$	−6.37294	−	6.37294i	−0.256565	−	0.256565i	0.567090	−	0.823656i	$-0.308069\pi$
$617$	−6.37294	−	6.37294i	−0.256565	−	0.256565i	−0.823656	+	0.567090i	$0.808069\pi$
$618$	−5.15824	+	0.0185315i	−0.207495	+	0.000745446i
$619$			17.7676i			0.714139i	0.934078	+	0.357070i	$0.116224\pi$
$619$			17.7676i			0.714139i	−0.934078	+	0.357070i	$0.883776\pi$
$620$	56.0879	+	6.37430i	2.25255	+	0.255998i
$621$	26.6675	+	26.0987i	1.07013	+	1.04731i
$622$	−0.608631	+	0.608631i	−0.0244039	+	0.0244039i
$623$	−1.41556	+	1.41556i	−0.0567130	+	0.0567130i
$624$	−0.667407	+	0.672220i	−0.0267177	+	0.0269103i
$625$	22.4823	+	10.9338i	0.899291	+	0.437351i
$626$			32.0594i			1.28135i
$627$	−0.111936	−	31.1575i	−0.00447030	−	1.24431i
$628$	−11.9535	−	11.9535i	−0.476995	−	0.476995i
$629$	1.76453			0.0703565
$630$	1.54956	−	14.5668i	0.0617361	−	0.580356i
$631$	17.8248			0.709592			0.354796	−	0.934944i	$-0.384550\pi$
$631$	17.8248			0.709592			0.354796	+	0.934944i	$0.384550\pi$
$632$	13.5857	+	13.5857i	0.540412	+	0.540412i
$633$	0.0515944	+	14.3613i	0.00205070	+	0.570811i
$634$		−	61.1712i		−	2.42942i
$635$	22.8968	+	28.7685i	0.908633	+	1.14164i
$636$	−16.9770	+	17.0995i	−0.673183	+	0.678038i
$637$	−0.206632	+	0.206632i	−0.00818705	+	0.00818705i
$638$	14.8587	−	14.8587i	0.588262	−	0.588262i
$639$	−0.0852413	−	11.8633i	−0.00337210	−	0.469306i
$640$	−17.3195	−	21.7609i	−0.684614	−	0.860177i
$641$			14.8270i			0.585630i	0.956169	+	0.292815i	$0.0945920\pi$
$641$			14.8270i			0.585630i	−0.956169	+	0.292815i	$0.905408\pi$
$642$	−15.8250	+	0.0568527i	−0.624562	+	0.00224380i
$643$	−32.7229	−	32.7229i	−1.29047	−	1.29047i	−0.934498	−	0.355968i	$-0.884151\pi$
$643$	−32.7229	−	32.7229i	−1.29047	−	1.29047i	−0.355968	−	0.934498i	$-0.615849\pi$
$644$	19.8823			0.783474
$645$	12.9126	+	16.1049i	0.508435	+	0.634129i
$646$	2.74747			0.108098
$647$	27.0564	+	27.0564i	1.06370	+	1.06370i	0.997828	+	0.0658674i	$0.0209814\pi$
$647$	27.0564	+	27.0564i	1.06370	+	1.06370i	0.0658674	+	0.997828i	$0.479019\pi$
$648$	10.5289	−	10.8359i	0.413612	−	0.425674i
$649$			34.9230i			1.37085i
$650$	0.715985	−	3.10932i	0.0280833	−	0.121958i
$651$	−11.2070	−	11.1267i	−0.439236	−	0.436091i
$652$	−9.90255	+	9.90255i	−0.387814	+	0.387814i
$653$	4.04918	−	4.04918i	0.158457	−	0.158457i	−0.623426	−	0.781883i	$-0.714260\pi$
$653$	4.04918	−	4.04918i	0.158457	−	0.158457i	0.781883	+	0.623426i	$0.214260\pi$
$654$	−7.57410	−	7.51988i	−0.296171	−	0.294050i
$655$	−28.2194	−	3.20709i	−1.10262	−	0.125311i
$656$			0.0589475i			0.00230151i
$657$	−26.0179	−	25.6467i	−1.01506	−	1.00057i
$658$	−7.78809	−	7.78809i	−0.303611	−	0.303611i
$659$	−11.5870			−0.451366			−0.225683	−	0.974201i	$-0.572461\pi$
$659$	−11.5870			−0.451366			−0.225683	+	0.974201i	$0.572461\pi$
$660$	36.0814	+	3.96935i	1.40447	+	0.154507i
$661$	−15.1550			−0.589462			−0.294731	−	0.955580i	$-0.595230\pi$
$661$	−15.1550			−0.589462			−0.294731	+	0.955580i	$0.595230\pi$
$662$	38.1940	+	38.1940i	1.48445	+	1.48445i
$663$	0.119829		0.000430499i	0.00465379		1.67192e-5i
$664$			9.21294i			0.357531i
$665$	−9.29755	+	7.39991i	−0.360544	+	0.286956i
$666$	−48.8257	+	0.350827i	−1.89196	+	0.0135943i
$667$	14.4343	−	14.4343i	0.558899	−	0.558899i
$668$	−17.6990	+	17.6990i	−0.684793	+	0.684793i
$669$	6.66199	−	6.71003i	0.257568	−	0.259425i
$670$	−4.95017	+	43.5569i	−0.191242	+	1.68275i
$671$		−	23.0399i		−	0.889445i
$672$	0.0463233	+	12.8941i	0.00178696	+	0.497400i
$673$	−13.7667	−	13.7667i	−0.530666	−	0.530666i	0.390105	−	0.920770i	$-0.372439\pi$
$673$	−13.7667	−	13.7667i	−0.530666	−	0.530666i	−0.920770	+	0.390105i	$0.872439\pi$
$674$	10.5045			0.404617
$675$	5.55683	−	25.3796i	0.213883	−	0.976859i
$676$	35.7573			1.37528
$677$	−16.3594	−	16.3594i	−0.628742	−	0.628742i	0.319009	−	0.947752i	$-0.396650\pi$
$677$	−16.3594	−	16.3594i	−0.628742	−	0.628742i	−0.947752	+	0.319009i	$0.896650\pi$
$678$	−0.0387793	−	10.7942i	−0.00148931	−	0.414549i
$679$		−	3.20687i		−	0.123068i
$680$	−0.100355	+	0.883031i	−0.00384844	+	0.0338627i
$681$	−2.60148	+	2.62024i	−0.0996891	+	0.100408i
$682$	47.6587	−	47.6587i	1.82495	−	1.82495i
$683$	−5.85622	+	5.85622i	−0.224082	+	0.224082i	−0.810215	−	0.586133i	$-0.800650\pi$
$683$	−5.85622	+	5.85622i	−0.224082	+	0.224082i	0.586133	+	0.810215i	$0.300650\pi$
$684$	−44.1398	+	0.317157i	−1.68773	+	0.0121268i
$685$	12.8526	−	10.2294i	0.491072	−	0.390844i
$686$			2.18375i			0.0833758i
$687$	10.8427	−	0.0389535i	0.413676	−	0.00148617i
$688$	−7.05335	−	7.05335i	−0.268906	−	0.268906i
$689$	1.46829			0.0559373
$690$	60.3698	+	6.64133i	2.29824	+	0.252831i
$691$	25.9095			0.985642			0.492821	−	0.870131i	$-0.335966\pi$
$691$	25.9095			0.985642			0.492821	+	0.870131i	$0.335966\pi$
$692$	−10.7646	−	10.7646i	−0.409210	−	0.409210i
$693$	−7.23222	−	7.12903i	−0.274729	−	0.270809i
$694$			74.2189i			2.81731i
$695$	27.3584	+	3.10923i	1.03776	+	0.117940i
$696$	−5.86560	−	5.82361i	−0.222335	−	0.220743i
$697$	0.00527284	−	0.00527284i	0.000199723	−	0.000199723i
$698$	−14.4698	+	14.4698i	−0.547691	+	0.547691i
$699$	−4.64849	−	4.61521i	−0.175822	−	0.174563i
$700$	−7.34272	−	11.7360i	−0.277529	−	0.443579i
$701$			37.9089i			1.43180i	0.698204	+	0.715899i	$0.253983\pi$
$701$			37.9089i			1.43180i	−0.698204	+	0.715899i	$0.746017\pi$
$702$	−3.31567	+	0.0357368i	−0.125142	+	0.00134880i
$703$	28.0065	+	28.0065i	1.05628	+	1.05628i
$704$	−42.3598			−1.59649
$705$	−12.2193	−	15.2402i	−0.460206	−	0.573977i
$706$	45.0542			1.69564
$707$	−6.10679	−	6.10679i	−0.229669	−	0.229669i
$708$	49.4749	−	0.177743i	1.85938	−	0.00668001i
$709$			16.6841i			0.626586i	0.949656	+	0.313293i	$0.101432\pi$
$709$			16.6841i			0.626586i	−0.949656	+	0.313293i	$0.898568\pi$
$710$	−12.0251	−	15.1088i	−0.451293	−	0.567023i
$711$	−0.246699	−	34.3339i	−0.00925194	−	1.28762i
$712$	−2.37636	+	2.37636i	−0.0890578	+	0.0890578i
$713$	46.2975	−	46.2975i	1.73385	−	1.73385i
$714$	0.630921	−	0.635470i	0.0236116	−	0.0237819i
$715$	−1.37743	−	1.73066i	−0.0515129	−	0.0647229i
$716$			40.5129i			1.51404i
$717$	0.0129753	+	3.61167i	0.000484570	+	0.134880i
$718$	42.1016	+	42.1016i	1.57122	+	1.57122i
$719$	−13.0709			−0.487464			−0.243732	−	0.969843i	$-0.578372\pi$
$719$	−13.0709			−0.487464			−0.243732	+	0.969843i	$0.578372\pi$
$720$	−1.32802	+	12.4842i	−0.0494925	+	0.465259i
$721$	1.36377			0.0507895
$722$	14.2688	+	14.2688i	0.531031	+	0.531031i
$723$	0.0338310	+	9.41686i	0.00125819	+	0.350217i
$724$		−	27.2367i		−	1.01224i
$725$	−13.8509	−	3.18946i	−0.514409	−	0.118454i
$726$	1.22231	−	1.23112i	0.0453640	−	0.0456911i
$727$	19.4878	−	19.4878i	0.722761	−	0.722761i	−0.246406	−	0.969167i	$-0.579250\pi$
$727$	19.4878	−	19.4878i	0.722761	−	0.722761i	0.969167	+	0.246406i	$0.0792495\pi$
$728$	−0.346882	+	0.346882i	−0.0128563	+	0.0128563i
$729$	−26.9937	+	0.581953i	−0.999768	+	0.0215538i
$730$	−59.0838	−	6.71478i	−2.18679	−	0.248525i
$731$			1.26184i			0.0466709i
$732$	−32.6403	+	0.117264i	−1.20642	+	0.00433418i
$733$	24.5624	+	24.5624i	0.907232	+	0.907232i	0.996048	−	0.0888162i	$-0.0283084\pi$
$733$	24.5624	+	24.5624i	0.907232	+	0.907232i	−0.0888162	+	0.996048i	$0.528308\pi$
$734$	−49.1774			−1.81517
$735$	−0.423515	+	3.84976i	−0.0156216	+	0.142000i
$736$	−53.4585			−1.97051
$737$	21.4886	+	21.4886i	0.791543	+	0.791543i
$738$	−0.144855	+	0.146951i	−0.00533217	+	0.00540935i
$739$			25.3925i			0.934079i	0.884236	+	0.467040i	$0.154679\pi$
$739$			25.3925i			0.934079i	−0.884236	+	0.467040i	$0.845321\pi$
$740$	−36.1036	+	28.7348i	−1.32720	+	1.05631i
$741$	1.90875	+	1.89509i	0.0701198	+	0.0696178i
$742$	7.75865	−	7.75865i	0.284829	−	0.284829i
$743$	14.4447	−	14.4447i	0.529923	−	0.529923i	−0.390626	−	0.920549i	$-0.627742\pi$
$743$	14.4447	−	14.4447i	0.529923	−	0.529923i	0.920549	+	0.390626i	$0.127742\pi$
$744$	−18.8137	−	18.6790i	−0.689742	−	0.684804i
$745$	−4.78108	+	42.0691i	−0.175165	+	1.54129i
$746$		−	72.0445i		−	2.63774i
$747$	11.5578	−	11.7251i	0.422879	−	0.429000i
$748$	1.56902	+	1.56902i	0.0573690	+	0.0573690i
$749$	4.18391			0.152877
$750$	−18.3749	−	38.0873i	−0.670956	−	1.39075i
$751$	27.4358			1.00115			0.500573	−	0.865694i	$-0.333123\pi$
$751$	27.4358			1.00115			0.500573	+	0.865694i	$0.333123\pi$
$752$	6.67463	+	6.67463i	0.243399	+	0.243399i
$753$	−40.4307	+	0.145251i	−1.47338	+	0.00529325i
$754$			1.81402i			0.0660627i
$755$	−0.481081	+	4.23306i	−0.0175083	+	0.154057i
$756$	−10.0628	+	10.2821i	−0.365980	+	0.373955i
$757$	−11.9760	+	11.9760i	−0.435274	+	0.435274i	−0.890418	−	0.455144i	$-0.849588\pi$
$757$	−11.9760	+	11.9760i	−0.435274	+	0.435274i	0.455144	+	0.890418i	$0.349588\pi$
$758$	57.8245	−	57.8245i	2.10028	−	2.10028i
$759$	29.6641	−	29.8780i	1.07674	−	1.08450i
$760$	−15.6082	+	12.4226i	−0.566170	+	0.450614i
$761$		−	41.1635i		−	1.49217i	−0.665848	−	0.746087i	$-0.731930\pi$
$761$		−	41.1635i		−	1.49217i	0.665848	−	0.746087i	$-0.268070\pi$
$762$	−0.223437	−	62.1937i	−0.00809426	−	2.25304i
$763$	1.99533	+	1.99533i	0.0722357	+	0.0722357i
$764$	17.6614			0.638969
$765$	1.23550	−	0.997919i	0.0446697	−	0.0360799i
$766$	−15.3007			−0.552836
$767$	−2.13178	−	2.13178i	−0.0769740	−	0.0769740i
$768$	0.0132771	+	3.69569i	0.000479097	+	0.133357i
$769$		−	3.96520i		−	0.142989i	−0.997441	−	0.0714944i	$-0.977223\pi$
$769$		−	3.96520i		−	0.142989i	0.997441	−	0.0714944i	$-0.0227768\pi$
$770$	−16.4236	−	1.86651i	−0.591864	−	0.0672644i
$771$	−18.8585	+	18.9945i	−0.679174	+	0.684071i
$772$	−20.9410	+	20.9410i	−0.753684	+	0.753684i
$773$	5.99943	−	5.99943i	0.215785	−	0.215785i	−0.590935	−	0.806719i	$-0.701241\pi$
$773$	5.99943	−	5.99943i	0.215785	−	0.215785i	0.806719	+	0.590935i	$0.201241\pi$
$774$	−0.250881	−	34.9160i	−0.00901774	−	1.25503i
$775$	−44.4262	−	10.2301i	−1.59583	−	0.367474i
$776$		−	5.38352i		−	0.193257i
$777$	12.9090	−	0.0463770i	0.463109	−	0.00166377i
$778$	14.2104	+	14.2104i	0.509468	+	0.509468i
$779$	0.167380			0.00599702
$780$	−2.44479	+	1.96019i	−0.0875374	+	0.0701861i
$781$	−13.3864			−0.479002
$782$	2.62521	+	2.62521i	0.0938774	+	0.0938774i
$783$	0.159195	+	14.7701i	0.00568916	+	0.527841i
$784$		−	1.87154i		−	0.0668406i
$785$	8.50188	+	10.6821i	0.303445	+	0.381261i
$786$	34.0920	+	33.8479i	1.21602	+	1.20731i
$787$	15.8108	−	15.8108i	0.563593	−	0.563593i	−0.366733	−	0.930326i	$-0.619524\pi$
$787$	15.8108	−	15.8108i	0.563593	−	0.563593i	0.930326	+	0.366733i	$0.119524\pi$
$788$	−2.81001	+	2.81001i	−0.100103	+	0.100103i
$789$	31.6030	+	31.3768i	1.12510	+	1.11704i
$790$	−34.8021	−	43.7267i	−1.23820	−	1.55573i
$791$			2.85385i			0.101471i
$792$	−12.1411	−	11.9678i	−0.431414	−	0.425258i
$793$	1.40641	+	1.40641i	0.0499429	+	0.0499429i
$794$	−67.7082			−2.40287
$795$	15.1825	−	12.1731i	0.538470	−	0.431736i
$796$	26.0274			0.922515
$797$	−8.46554	−	8.46554i	−0.299865	−	0.299865i	0.541096	−	0.840961i	$-0.318010\pi$
$797$	−8.46554	−	8.46554i	−0.299865	−	0.299865i	−0.840961	+	0.541096i	$0.818010\pi$
$798$	20.1000	−	0.0722114i	0.711534	−	0.00255625i
$799$		−	1.19409i		−	0.0422438i
$800$	19.7427	+	31.5551i	0.698010	+	1.11564i
$801$	6.00554	−	0.0431515i	0.212195	−	0.00152468i
$802$	39.7638	−	39.7638i	1.40411	−	1.40411i
$803$	−29.1488	+	29.1488i	−1.02864	+	1.02864i
$804$	30.3333	−	30.5520i	1.06977	−	1.07749i
$805$	−15.9545	−	1.81320i	−0.562321	−	0.0639069i
$806$			5.81839i			0.204944i
$807$	0.177420	+	49.3848i	0.00624547	+	1.73843i
$808$	−10.2517	−	10.2517i	−0.360655	−	0.360655i
$809$	−25.5350			−0.897764			−0.448882	−	0.893591i	$-0.648178\pi$
$809$	−25.5350			−0.897764			−0.448882	+	0.893591i	$0.648178\pi$
$810$	−33.9887	+	27.8587i	−1.19424	+	0.978855i
$811$	−1.94760			−0.0683895			−0.0341947	−	0.999415i	$-0.510887\pi$
$811$	−1.94760			−0.0683895			−0.0341947	+	0.999415i	$0.510887\pi$
$812$	5.56539	+	5.56539i	0.195307	+	0.195307i
$813$	−0.0194276	−	5.40767i	−0.000681355	−	0.189655i
$814$			55.0942i			1.93105i
$815$	8.84933	−	7.04317i	0.309978	−	0.246712i
$816$	−0.540719	+	0.544618i	−0.0189289	+	0.0190654i
$817$	−20.0278	+	20.0278i	−0.700685	+	0.700685i
$818$	16.9078	−	16.9078i	0.591167	−	0.591167i
$819$	0.876642	−	0.00629893i	0.0306324	−	0.000220102i
$820$	−0.0220197	+	0.193753i	−0.000768962	+	0.00676615i
$821$		−	21.6742i		−	0.756434i	−0.925717	−	0.378217i	$-0.876537\pi$
$821$		−	21.6742i		−	0.756434i	0.925717	−	0.378217i	$-0.123463\pi$
$822$	−27.7856	+	0.0998224i	−0.969133	+	0.00348171i
$823$	8.35207	+	8.35207i	0.291135	+	0.291135i	0.837528	−	0.546394i	$-0.184000\pi$
$823$	8.35207	+	8.35207i	0.291135	+	0.291135i	−0.546394	+	0.837528i	$0.684000\pi$
$824$	2.28943			0.0797559
$825$	−28.5914	−	6.47568i	−0.995423	−	0.225454i
$826$	−22.5292			−0.783892
$827$	14.1747	+	14.1747i	0.492902	+	0.492902i	0.909219	−	0.416318i	$-0.136680\pi$
$827$	14.1747	+	14.1747i	0.492902	+	0.492902i	−0.416318	+	0.909219i	$0.636680\pi$
$828$	−42.4788	−	41.8727i	−1.47624	−	1.45518i
$829$			19.3836i			0.673219i	0.941644	+	0.336610i	$0.109280\pi$
$829$			19.3836i			0.673219i	−0.941644	+	0.336610i	$0.890720\pi$
$830$	3.02605	−	26.6265i	0.105036	−	0.924218i
$831$	−21.2888	−	21.1364i	−0.738500	−	0.733213i
$832$	2.58573	−	2.58573i	0.0896442	−	0.0896442i
$833$	−0.167409	+	0.167409i	−0.00580037	+	0.00580037i
$834$	−33.0517	−	32.8151i	−1.14449	−	1.13629i
$835$	15.8165	−	12.5884i	0.547353	−	0.435638i
$836$			49.8066i			1.72260i
$837$	0.510610	+	47.3745i	0.0176493	+	1.63750i
$838$	−9.06346	−	9.06346i	−0.313092	−	0.313092i
$839$	−26.2528			−0.906346			−0.453173	−	0.891423i	$-0.649708\pi$
$839$	−26.2528			−0.906346			−0.453173	+	0.891423i	$0.649708\pi$
$840$	−0.710974	+	6.46276i	−0.0245309	+	0.222987i
$841$	−20.9192			−0.721352
$842$	−41.5131	−	41.5131i	−1.43063	−	1.43063i
$843$	22.0282	−	0.0791386i	0.758693	−	0.00272568i
$844$		−	22.9572i		−	0.790221i
$845$	−28.6932	−	3.26094i	−0.987077	−	0.112180i
$846$	0.237410	+	33.0412i	0.00816234	+	1.13598i
$847$	−0.324327	+	0.324327i	−0.0111440	+	0.0111440i
$848$	−6.64940	+	6.64940i	−0.228341	+	0.228341i
$849$	−34.2179	+	34.4646i	−1.17435	+	1.18282i
$850$	0.580076	−	2.51910i	0.0198964	−	0.0864045i
$851$			53.5206i			1.83466i
$852$	0.0681311	+	18.9643i	0.00233413	+	0.649707i
$853$	29.8920	+	29.8920i	1.02348	+	1.02348i	0.999718	+	0.0237636i	$0.00756489\pi$
$853$	29.8920	+	29.8920i	1.02348	+	1.02348i	0.0237636	+	0.999718i	$0.492435\pi$
$854$	14.8633			0.508612
$855$	35.4487	+	3.77090i	1.21232	+	0.128962i
$856$	7.02373			0.240066
$857$	−5.92367	−	5.92367i	−0.202349	−	0.202349i	0.598657	−	0.801006i	$-0.295701\pi$
$857$	−5.92367	−	5.92367i	−0.202349	−	0.202349i	−0.801006	+	0.598657i	$0.795701\pi$
$858$	0.0134415	+	3.74145i	0.000458885	+	0.127731i
$859$		−	10.3620i		−	0.353548i	−0.984252	−	0.176774i	$-0.943434\pi$
$859$		−	10.3620i		−	0.353548i	0.984252	−	0.176774i	$-0.0565661\pi$
$860$	−20.5487	−	25.8182i	−0.700705	−	0.880394i
$861$	0.0384368	−	0.0387139i	0.00130992	−	0.00131937i
$862$	6.45633	−	6.45633i	0.219904	−	0.219904i
$863$	13.2818	−	13.2818i	0.452118	−	0.452118i	−0.443939	−	0.896057i	$-0.646419\pi$
$863$	13.2818	−	13.2818i	0.452118	−	0.452118i	0.896057	+	0.443939i	$0.146419\pi$
$864$	27.0563	−	27.6459i	0.920474	−	0.940532i
$865$	7.65632	+	9.61971i	0.260323	+	0.327080i
$866$			6.82129i			0.231797i
$867$	−29.3476	+	0.105434i	−0.996696	+	0.00358073i
$868$	17.8507	+	17.8507i	0.605894	+	0.605894i
$869$	−38.7419			−1.31423
$870$	15.0395	+	18.7575i	0.509886	+	0.635939i
$871$	−2.62342			−0.0888913
$872$	3.34965	+	3.34965i	0.113433	+	0.113433i
$873$	−6.75374	+	6.85150i	−0.228580	+	0.231888i
$874$			83.3342i			2.81882i
$875$	4.82184	+	10.0871i	0.163008	+	0.341007i
$876$	41.4430	+	41.1463i	1.40023	+	1.39020i
$877$	4.84197	−	4.84197i	0.163502	−	0.163502i	−0.620614	−	0.784116i	$-0.713117\pi$
$877$	4.84197	−	4.84197i	0.163502	−	0.163502i	0.784116	+	0.620614i	$0.213117\pi$
$878$	42.6227	−	42.6227i	1.43845	−	1.43845i
$879$	−11.6957	−	11.6119i	−0.394485	−	0.391660i
$880$	14.0755	+	1.59966i	0.474485	+	0.0539245i
$881$			17.0394i			0.574073i	0.957920	+	0.287036i	$0.0926701\pi$
$881$			17.0394i			0.574073i	−0.957920	+	0.287036i	$0.907330\pi$
$882$	4.59902	−	4.66559i	0.154857	−	0.157099i
$883$	12.2389	+	12.2389i	0.411871	+	0.411871i	0.882390	−	0.470519i	$-0.155933\pi$
$883$	12.2389	+	12.2389i	0.411871	+	0.411871i	−0.470519	+	0.882390i	$0.655933\pi$
$884$	−0.191553			−0.00644262
$885$	−39.7171	−	4.36931i	−1.33508	−	0.146873i
$886$	37.9983			1.27658
$887$	41.0767	+	41.0767i	1.37922	+	1.37922i	0.845934	+	0.533287i	$0.179043\pi$
$887$	41.0767	+	41.0767i	1.37922	+	1.37922i	0.533287	+	0.845934i	$0.320957\pi$
$888$	21.6710	−	0.0778552i	0.727231	−	0.00261265i
$889$			16.4432i			0.551487i
$890$	7.64848	−	6.08742i	0.256378	−	0.204051i
$891$	0.437785	+	30.4624i	0.0146664	+	1.02053i
$892$	−10.6879	+	10.6879i	−0.357858	+	0.357858i
$893$	18.9525	−	18.9525i	0.634220	−	0.634220i
$894$	50.4599	−	50.8238i	1.68763	−	1.69980i
$895$	3.69464	−	32.5094i	0.123498	−	1.08667i
$896$		−	12.4379i		−	0.415520i
$897$	0.0130576	+	3.63458i	0.000435980	+	0.121355i
$898$	−52.7879	−	52.7879i	−1.76155	−	1.76155i
$899$	25.9188			0.864441
$900$	−9.02850	+	40.5380i	−0.300950	+	1.35127i
$901$	1.18958			0.0396305
$902$	0.164635	+	0.164635i	0.00548173	+	0.00548173i
$903$	0.0331649	+	9.23144i	0.00110366	+	0.307203i
$904$			4.79089i			0.159343i
$905$	−2.48389	+	21.8559i	−0.0825673	+	0.726515i
$906$	5.07736	−	5.11398i	0.168684	−	0.169901i
$907$	24.8992	−	24.8992i	0.826765	−	0.826765i	−0.160303	−	0.987068i	$-0.551247\pi$
$907$	24.8992	−	24.8992i	0.826765	−	0.826765i	0.987068	+	0.160303i	$0.0512470\pi$
$908$	4.17359	−	4.17359i	0.138505	−	0.138505i
$909$	0.186158	+	25.9082i	0.00617448	+	0.859322i
$910$	1.11647	−	0.888595i	0.0370105	−	0.0294566i
$911$			23.4322i			0.776342i	0.921587	+	0.388171i	$0.126893\pi$
$911$			23.4322i			0.776342i	−0.921587	+	0.388171i	$0.873107\pi$
$912$	−17.2264	+	0.0618874i	−0.570422	+	0.00204930i
$913$	−13.1361	−	13.1361i	−0.434740	−	0.434740i
$914$	28.7526			0.951050
$915$	26.2027	+	2.88259i	0.866236	+	0.0952953i
$916$	−17.3326			−0.572685
$917$	−8.98121	−	8.98121i	−0.296586	−	0.296586i
$918$	−2.68628	+	0.0289532i	−0.0886605	+	0.000955598i
$919$		−	31.9950i		−	1.05542i	−0.849425	−	0.527710i	$-0.823051\pi$
$919$		−	31.9950i		−	1.05542i	0.849425	−	0.527710i	$-0.176949\pi$
$920$	−26.7835	−	3.04390i	−0.883026	−	0.100354i
$921$	−17.5746	−	17.4488i	−0.579103	−	0.574957i
$922$	39.6195	−	39.6195i	1.30480	−	1.30480i
$923$	0.817134	−	0.817134i	0.0268963	−	0.0268963i
$924$	11.5199	+	11.4375i	0.378978	+	0.376265i
$925$	31.5917	−	19.7656i	1.03873	−	0.649889i
$926$		−	40.8180i		−	1.34136i
$927$	−2.91371	−	2.87214i	−0.0956987	−	0.0943333i
$928$	−14.9639	−	14.9639i	−0.491214	−	0.491214i
$929$	49.7858			1.63342			0.816709	−	0.577050i	$-0.195796\pi$
$929$	49.7858			1.63342			0.816709	+	0.577050i	$0.195796\pi$
$930$	48.2384	+	60.1639i	1.58180	+	1.97285i
$931$	−5.31419			−0.174166
$932$	7.40423	+	7.40423i	0.242534	+	0.242534i
$933$	−0.682692	+	0.00245264i	−0.0223503	+	8.02958e-5i
$934$		−	60.7340i		−	1.98728i
$935$	−1.11596	−	1.40214i	−0.0364959	−	0.0458549i
$936$	1.47166	−	0.0105743i	0.0481027	−	0.000345632i
$937$	18.0919	−	18.0919i	0.591035	−	0.591035i	−0.346876	−	0.937911i	$-0.612757\pi$
$937$	18.0919	−	18.0919i	0.591035	−	0.591035i	0.937911	+	0.346876i	$0.112757\pi$
$938$	−13.8626	+	13.8626i	−0.452628	+	0.452628i
$939$	−17.9157	+	18.0449i	−0.584656	+	0.588872i
$940$	19.4454	+	24.4319i	0.634238	+	0.796882i
$941$		−	61.0502i		−	1.99018i	−0.0989766	−	0.995090i	$-0.531557\pi$
$941$		−	61.0502i		−	1.99018i	0.0989766	−	0.995090i	$-0.468443\pi$
$942$	−0.0829648	−	23.0933i	−0.00270314	−	0.752419i
$943$	0.159932	+	0.159932i	0.00520811	+	0.00520811i
$944$	19.3082			0.628430
$945$	9.01252	−	7.33310i	0.293177	−	0.238546i
$946$	−39.3986			−1.28096
$947$	−28.1297	−	28.1297i	−0.914093	−	0.914093i	0.0824986	−	0.996591i	$-0.473710\pi$
$947$	−28.1297	−	28.1297i	−0.914093	−	0.914093i	−0.996591	+	0.0824986i	$0.973710\pi$
$948$	0.197180	+	54.8851i	0.00640411	+	1.78259i
$949$		−	3.55861i		−	0.115517i
$950$	49.1899	−	30.7761i	1.59593	−	0.998507i
$951$	34.1841	−	34.4306i	1.10850	−	1.11649i
$952$	−0.281037	+	0.281037i	−0.00910845	+	0.00910845i
$953$	16.4406	−	16.4406i	0.532564	−	0.532564i	−0.388771	−	0.921335i	$-0.627100\pi$
$953$	16.4406	−	16.4406i	0.532564	−	0.532564i	0.921335	+	0.388771i	$0.127100\pi$
$954$	−32.9163	+	0.236513i	−1.06571	+	0.00765740i
$955$	−14.1723	−	1.61066i	−0.458606	−	0.0521198i
$956$		−	5.77342i		−	0.186726i
$957$	16.6668	−	0.0598771i	0.538761	−	0.00193555i
$958$	−41.6493	−	41.6493i	−1.34563	−	1.34563i
$959$	7.34614			0.237219
$960$	5.29975	−	48.1748i	0.171049	−	1.55483i
$961$	52.1335			1.68173
$962$	−3.36307	−	3.36307i	−0.108430	−	0.108430i
$963$	−8.93897	−	8.81142i	−0.288054	−	0.283944i
$964$		−	15.0533i		−	0.484834i
$965$	18.7138	−	14.8943i	0.602417	−	0.479463i
$966$	19.2747	+	19.1367i	0.620152	+	0.615712i
$967$	−3.29391	+	3.29391i	−0.105925	+	0.105925i	−0.758083	−	0.652158i	$-0.773864\pi$
$967$	−3.29391	+	3.29391i	−0.105925	+	0.105925i	0.652158	+	0.758083i	$0.273864\pi$
$968$	−0.544462	+	0.544462i	−0.0174997	+	0.0174997i
$969$	1.54643	+	1.53536i	0.0496785	+	0.0493228i
$970$	−1.76825	+	15.5590i	−0.0567752	+	0.499569i
$971$		−	32.3161i		−	1.03707i	−0.855056	−	0.518536i	$-0.826477\pi$
$971$		−	32.3161i		−	1.03707i	0.855056	−	0.518536i	$-0.173523\pi$
$972$	43.1535	−	0.775246i	1.38415	−	0.0248660i
$973$	8.70717	+	8.70717i	0.279139	+	0.279139i
$974$	88.4809			2.83511
$975$	2.14057	−	1.34999i	0.0685531	−	0.0432343i
$976$	−12.7383			−0.407744
$977$	8.42742	+	8.42742i	0.269617	+	0.269617i	0.828946	−	0.559329i	$-0.188941\pi$
$977$	8.42742	+	8.42742i	0.269617	+	0.269617i	−0.559329	+	0.828946i	$0.688941\pi$
$978$	−19.1311	+	0.0687302i	−0.611744	+	0.00219775i
$979$		−	6.77655i		−	0.216580i
$980$	0.699108	−	6.15151i	0.0223322	−	0.196503i
$981$	−0.0608251	−	8.46523i	−0.00194200	−	0.270274i
$982$	4.23900	−	4.23900i	0.135272	−	0.135272i
$983$	−43.2280	+	43.2280i	−1.37876	+	1.37876i	−0.532042	+	0.846718i	$0.678575\pi$
$983$	−43.2280	+	43.2280i	−1.37876	+	1.37876i	−0.846718	+	0.532042i	$0.821425\pi$
$984$	0.0645255	−	0.0649908i	0.00205700	−	0.00207183i
$985$	2.51114	−	1.99862i	0.0800117	−	0.0636812i
$986$			1.46968i			0.0468041i
$987$	−0.0313841	−	8.73578i	−0.000998968	−	0.278063i
$988$	−3.04031	−	3.04031i	−0.0967251	−	0.0967251i
$989$	−38.2733			−1.21702
$990$	31.1582	+	38.5762i	0.990271	+	1.22603i
$991$	−25.2971			−0.803590			−0.401795	−	0.915730i	$-0.631614\pi$
$991$	−25.2971			−0.803590			−0.401795	+	0.915730i	$0.631614\pi$
$992$	−47.9961	−	47.9961i	−1.52388	−	1.52388i
$993$	0.153913	+	42.8417i	0.00488428	+	1.35954i
$994$		−	8.63571i		−	0.273908i
$995$	−20.8855	−	2.37360i	−0.662115	−	0.0752483i
$996$	−18.5428	+	18.6765i	−0.587552	+	0.591789i
$997$	−23.3279	+	23.3279i	−0.738803	+	0.738803i	−0.972346	−	0.233543i	$-0.924968\pi$
$997$	−23.3279	+	23.3279i	−0.738803	+	0.738803i	0.233543	+	0.972346i	$0.424968\pi$
$998$	−46.8108	+	46.8108i	−1.48177	+	1.48177i
$999$	−27.6779	−	27.0877i	−0.875691	−	0.857016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.j.a.8.2	✓	24
3.2	odd	2	inner	105.2.j.a.8.11	yes	24
5.2	odd	4	inner	105.2.j.a.92.11	yes	24
5.3	odd	4		525.2.j.b.407.2		24
5.4	even	2		525.2.j.b.218.11		24
7.2	even	3		735.2.y.j.263.2		48
7.3	odd	6		735.2.y.g.128.11		48
7.4	even	3		735.2.y.j.128.11		48
7.5	odd	6		735.2.y.g.263.2		48
7.6	odd	2		735.2.j.h.638.2		24
15.2	even	4	inner	105.2.j.a.92.2	yes	24
15.8	even	4		525.2.j.b.407.11		24
15.14	odd	2		525.2.j.b.218.2		24
21.2	odd	6		735.2.y.j.263.11		48
21.5	even	6		735.2.y.g.263.11		48
21.11	odd	6		735.2.y.j.128.2		48
21.17	even	6		735.2.y.g.128.2		48
21.20	even	2		735.2.j.h.638.11		24
35.2	odd	12		735.2.y.j.557.2		48
35.12	even	12		735.2.y.g.557.2		48
35.17	even	12		735.2.y.g.422.11		48
35.27	even	4		735.2.j.h.197.11		24
35.32	odd	12		735.2.y.j.422.11		48
105.2	even	12		735.2.y.j.557.11		48
105.17	odd	12		735.2.y.g.422.2		48
105.32	even	12		735.2.y.j.422.2		48
105.47	odd	12		735.2.y.g.557.11		48
105.62	odd	4		735.2.j.h.197.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.2	✓	24	1.1	even	1	trivial
105.2.j.a.8.11	yes	24	3.2	odd	2	inner
105.2.j.a.92.2	yes	24	15.2	even	4	inner
105.2.j.a.92.11	yes	24	5.2	odd	4	inner
525.2.j.b.218.2		24	15.14	odd	2
525.2.j.b.218.11		24	5.4	even	2
525.2.j.b.407.2		24	5.3	odd	4
525.2.j.b.407.11		24	15.8	even	4
735.2.j.h.197.2		24	105.62	odd	4
735.2.j.h.197.11		24	35.27	even	4
735.2.j.h.638.2		24	7.6	odd	2
735.2.j.h.638.11		24	21.20	even	2
735.2.y.g.128.2		48	21.17	even	6
735.2.y.g.128.11		48	7.3	odd	6
735.2.y.g.263.2		48	7.5	odd	6
735.2.y.g.263.11		48	21.5	even	6
735.2.y.g.422.2		48	105.17	odd	12
735.2.y.g.422.11		48	35.17	even	12
735.2.y.g.557.2		48	35.12	even	12
735.2.y.g.557.11		48	105.47	odd	12
735.2.y.j.128.2		48	21.11	odd	6
735.2.y.j.128.11		48	7.4	even	3
735.2.y.j.263.2		48	7.2	even	3
735.2.y.j.263.11		48	21.2	odd	6
735.2.y.j.422.2		48	105.32	even	12
735.2.y.j.422.11		48	35.32	odd	12
735.2.y.j.557.2		48	35.2	odd	12
735.2.y.j.557.11		48	105.2	even	12

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54414 - 1.54414i) q^{2} +(-0.00622252 - 1.73204i) q^{3} +2.76875i q^{4} +(0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +O(q^{10})\)	\(q+(-1.54414 - 1.54414i) q^{2} +(-0.00622252 - 1.73204i) q^{3} +2.76875i q^{4} +(0.252500 - 2.22177i) q^{5} +(-2.66491 + 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.18705 - 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +(-3.82062 + 3.04083i) q^{10} +3.38507i q^{11} +(4.79558 - 0.0172286i) q^{12} +(-0.206632 - 0.206632i) q^{13} -2.18375 q^{14} +(-3.84976 - 0.423515i) q^{15} +1.87154 q^{16} +(-0.167409 - 0.167409i) q^{17} +(4.66559 + 4.59902i) q^{18} -5.31419i q^{19} +(6.15151 + 0.699108i) q^{20} +(-1.22914 - 1.22034i) q^{21} +(5.22702 - 5.22702i) q^{22} +(5.07773 - 5.07773i) q^{23} +(-2.06341 - 2.04864i) q^{24} +(-4.87249 - 1.12199i) q^{25} +0.638138i q^{26} +(0.0560017 + 5.19585i) q^{27} +(1.95780 + 1.95780i) q^{28} +2.84268 q^{29} +(5.29060 + 6.59854i) q^{30} +9.11776 q^{31} +(-5.26402 - 5.26402i) q^{32} +(5.86307 - 0.0210636i) q^{33} +0.517005i q^{34} +(-1.39248 - 1.74957i) q^{35} +(-0.0596812 - 8.30602i) q^{36} +(-5.27013 + 5.27013i) q^{37} +(-8.20586 + 8.20586i) q^{38} +(-0.356609 + 0.359180i) q^{39} +(-2.33762 - 2.93708i) q^{40} +0.0314968i q^{41} +(0.0135884 + 3.78233i) q^{42} +(-3.76875 - 3.76875i) q^{43} -9.37239 q^{44} +(-0.709590 + 6.67057i) q^{45} -15.6815 q^{46} +(3.56639 + 3.56639i) q^{47} +(-0.0116457 - 3.24158i) q^{48} -1.00000i q^{49} +(5.79130 + 9.25632i) q^{50} +(-0.288917 + 0.291000i) q^{51} +(0.572111 - 0.572111i) q^{52} +(-3.55291 + 3.55291i) q^{53} +(7.93665 - 8.10960i) q^{54} +(7.52082 + 0.854729i) q^{55} -1.67875i q^{56} +(-9.20439 + 0.0330677i) q^{57} +(-4.38949 - 4.38949i) q^{58} +10.3168 q^{59} +(1.17261 - 10.6590i) q^{60} -6.80634 q^{61} +(-14.0791 - 14.0791i) q^{62} +(-2.10602 + 2.13651i) q^{63} +12.5137i q^{64} +(-0.511262 + 0.406913i) q^{65} +(-9.08593 - 9.02088i) q^{66} +(6.34806 - 6.34806i) q^{67} +(0.463512 - 0.463512i) q^{68} +(-8.82642 - 8.76323i) q^{69} +(-0.551396 + 4.85177i) q^{70} +3.95454i q^{71} +(-3.53548 + 3.58665i) q^{72} +(8.61099 + 8.61099i) q^{73} +16.2757 q^{74} +(-1.91302 + 8.44632i) q^{75} +14.7136 q^{76} +(2.39360 + 2.39360i) q^{77} +(1.10528 - 0.00397083i) q^{78} +11.4449i q^{79} +(0.472563 - 4.15812i) q^{80} +(8.99907 - 0.129328i) q^{81} +(0.0486356 - 0.0486356i) q^{82} +(-3.88059 + 3.88059i) q^{83} +(3.37880 - 3.40317i) q^{84} +(-0.414214 + 0.329672i) q^{85} +11.6390i q^{86} +(-0.0176886 - 4.92363i) q^{87} +(4.01825 + 4.01825i) q^{88} -2.00190 q^{89} +(11.3960 - 9.20459i) q^{90} -0.292222 q^{91} +(14.0589 + 14.0589i) q^{92} +(-0.0567354 - 15.7923i) q^{93} -11.0140i q^{94} +(-11.8069 - 1.34183i) q^{95} +(-9.08474 + 9.15025i) q^{96} +(2.26760 - 2.26760i) q^{97} +(-1.54414 + 1.54414i) q^{98} +(-0.0729661 - 10.1549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Introduction

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