LMFDB - Embedded newform 756.2.bs.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(11,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([9, 13, 12]))

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

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

chi := DirichletCharacter("756.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	756.11
Dual form			756.2.bs.a.275.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35660 + 0.399529i) q^{2} +(0.345844 - 1.69717i) q^{3} +(1.68075 - 1.08401i) q^{4} +(0.871331 - 0.153639i) q^{5} +(0.208897 + 2.44057i) q^{6} +(0.218427 + 2.63672i) q^{7} +(-1.84702 + 2.14208i) q^{8} +(-2.76078 - 1.17391i) q^{9} +O(q^{10})$	\(q+(-1.35660 + 0.399529i) q^{2} +(0.345844 - 1.69717i) q^{3} +(1.68075 - 1.08401i) q^{4} +(0.871331 - 0.153639i) q^{5} +(0.208897 + 2.44057i) q^{6} +(0.218427 + 2.63672i) q^{7} +(-1.84702 + 2.14208i) q^{8} +(-2.76078 - 1.17391i) q^{9} +(-1.12067 + 0.556550i) q^{10} +(0.671349 - 3.80741i) q^{11} +(-1.25847 - 3.22742i) q^{12} +(-3.00415 + 2.52078i) q^{13} +(-1.34977 - 3.48972i) q^{14} +(0.0405923 - 1.53193i) q^{15} +(1.64986 - 3.64389i) q^{16} -4.50995i q^{17} +(4.21431 + 0.489521i) q^{18} -3.64785i q^{19} +(1.29795 - 1.20276i) q^{20} +(4.55051 + 0.541185i) q^{21} +(0.610417 + 5.43338i) q^{22} +(3.05195 - 2.56089i) q^{23} +(2.99669 + 3.87554i) q^{24} +(-3.96285 + 1.44236i) q^{25} +(3.06832 - 4.61995i) q^{26} +(-2.94713 + 4.27953i) q^{27} +(3.22534 + 4.19490i) q^{28} +(5.40259 - 6.43855i) q^{29} +(0.556985 + 2.09445i) q^{30} +(3.43204 - 9.42945i) q^{31} +(-0.782364 + 5.60249i) q^{32} +(-6.22965 - 2.45616i) q^{33} +(1.80186 + 6.11822i) q^{34} +(0.595425 + 2.26390i) q^{35} +(-5.91272 + 1.01965i) q^{36} +(-2.45441 + 4.25116i) q^{37} +(1.45742 + 4.94869i) q^{38} +(3.23923 + 5.97035i) q^{39} +(-1.28026 + 2.15023i) q^{40} +(-0.570454 - 0.679841i) q^{41} +(-6.38946 + 1.08389i) q^{42} +(-0.136201 - 0.374208i) q^{43} +(-2.99889 - 7.12706i) q^{44} +(-2.58592 - 0.598702i) q^{45} +(-3.11714 + 4.69346i) q^{46} +(10.8056 - 3.93290i) q^{47} +(-5.61372 - 4.06031i) q^{48} +(-6.90458 + 1.15186i) q^{49} +(4.79976 - 3.53999i) q^{50} +(-7.65416 - 1.55974i) q^{51} +(-2.31669 + 7.49332i) q^{52} +(-10.5062 - 6.06576i) q^{53} +(2.28829 - 6.98310i) q^{54} -3.42066i q^{55} +(-6.05150 - 4.40220i) q^{56} +(-6.19103 - 1.26159i) q^{57} +(-4.75679 + 10.8931i) q^{58} +(-6.55875 + 5.50344i) q^{59} +(-1.59240 - 2.61880i) q^{60} +(-0.546801 + 0.199019i) q^{61} +(-0.888579 + 14.1632i) q^{62} +(2.49225 - 7.53583i) q^{63} +(-1.17700 - 7.91294i) q^{64} +(-2.23032 + 2.65799i) q^{65} +(9.43248 + 0.843117i) q^{66} +(6.47342 - 1.14144i) q^{67} +(-4.88882 - 7.58011i) q^{68} +(-3.29077 - 6.06535i) q^{69} +(-1.71225 - 2.83332i) q^{70} +(-5.76242 - 9.98080i) q^{71} +(7.61385 - 3.74557i) q^{72} +(1.73780 + 3.00996i) q^{73} +(1.63120 - 6.74774i) q^{74} +(1.07740 + 7.22447i) q^{75} +(-3.95429 - 6.13114i) q^{76} +(10.1857 + 0.938520i) q^{77} +(-6.77969 - 6.80524i) q^{78} +(14.1494 + 2.49492i) q^{79} +(0.877728 - 3.42852i) q^{80} +(6.24386 + 6.48184i) q^{81} +(1.04550 + 0.694362i) q^{82} +(5.16732 + 4.33590i) q^{83} +(8.23493 - 4.02318i) q^{84} +(-0.692905 - 3.92966i) q^{85} +(0.334278 + 0.453237i) q^{86} +(-9.05888 - 11.3959i) q^{87} +(6.91577 + 8.47046i) q^{88} +0.529347i q^{89} +(3.74726 - 0.220947i) q^{90} +(-7.30278 - 7.37049i) q^{91} +(2.35355 - 7.61256i) q^{92} +(-14.8165 - 9.08588i) q^{93} +(-13.0876 + 9.65253i) q^{94} +(-0.560453 - 3.17849i) q^{95} +(9.23781 + 3.26539i) q^{96} +(7.11912 - 2.59115i) q^{97} +(8.90658 - 4.32120i) q^{98} +(-6.32302 + 9.72333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.35660	+	0.399529i	−0.959264	+	0.282510i
$2$	−1.35660	+	0.399529i	−0.959264	+	0.282510i
$3$	0.345844	−	1.69717i	0.199673	−	0.979863i
$3$	0.345844	−	1.69717i	0.199673	−	0.979863i
$4$	1.68075	−	1.08401i	0.840376	−	0.542003i
$5$	0.871331	−	0.153639i	0.389671	−	0.0687095i	0.0246197	−	0.999697i	$-0.492163\pi$
$5$	0.871331	−	0.153639i	0.389671	−	0.0687095i	0.365051	+	0.930987i	$0.381051\pi$
$6$	0.208897	+	2.44057i	0.0852817	+	0.996357i
$7$	0.218427	+	2.63672i	0.0825575	+	0.996586i
$7$	0.218427	+	2.63672i	0.0825575	+	0.996586i
$8$	−1.84702	+	2.14208i	−0.653022	+	0.757339i
$9$	−2.76078	−	1.17391i	−0.920261	−	0.391304i
$10$	−1.12067	+	0.556550i	−0.354386	+	0.175997i
$11$	0.671349	−	3.80741i	0.202419	−	1.14798i	−0.699030	−	0.715093i	$-0.746384\pi$
$11$	0.671349	−	3.80741i	0.202419	−	1.14798i	0.901449	−	0.432885i	$-0.142504\pi$
$12$	−1.25847	−	3.22742i	−0.363288	−	0.931677i
$13$	−3.00415	+	2.52078i	−0.833201	+	0.699139i	−0.956023	−	0.293290i	$-0.905250\pi$
$13$	−3.00415	+	2.52078i	−0.833201	+	0.699139i	0.122823	+	0.992429i	$0.460805\pi$
$14$	−1.34977	−	3.48972i	−0.360740	−	0.932666i
$15$	0.0405923	−	1.53193i	0.0104809	−	0.395544i
$16$	1.64986	−	3.64389i	0.412465	−	0.910974i
$17$		−	4.50995i		−	1.09382i	−0.837190	−	0.546912i	$-0.815803\pi$
$17$		−	4.50995i		−	1.09382i	0.837190	−	0.546912i	$-0.184197\pi$
$18$	4.21431	+	0.489521i	0.993321	+	0.115381i
$19$		−	3.64785i		−	0.836874i	−0.908246	−	0.418437i	$-0.862578\pi$
$19$		−	3.64785i		−	0.836874i	0.908246	−	0.418437i	$-0.137422\pi$
$20$	1.29795	−	1.20276i	0.290230	−	0.268945i
$21$	4.55051	+	0.541185i	0.993002	+	0.118096i
$22$	0.610417	+	5.43338i	0.130141	+	1.15840i
$23$	3.05195	−	2.56089i	0.636376	−	0.533983i	−0.266527	−	0.963827i	$-0.585876\pi$
$23$	3.05195	−	2.56089i	0.636376	−	0.533983i	0.902903	+	0.429845i	$0.141432\pi$
$24$	2.99669	+	3.87554i	0.611697	+	0.791092i
$25$	−3.96285	+	1.44236i	−0.792570	+	0.288472i
$26$	3.06832	−	4.61995i	0.601746	−	0.906046i
$27$	−2.94713	+	4.27953i	−0.567176	+	0.823597i
$28$	3.22534	+	4.19490i	0.609532	+	0.792761i
$29$	5.40259	−	6.43855i	1.00324	−	1.19561i	0.0226045	−	0.999744i	$-0.492804\pi$
$29$	5.40259	−	6.43855i	1.00324	−	1.19561i	0.980631	−	0.195865i	$-0.0627514\pi$
$30$	0.556985	+	2.09445i	0.101691	+	0.382392i
$31$	3.43204	−	9.42945i	0.616413	−	1.69358i	−0.0991870	−	0.995069i	$-0.531624\pi$
$31$	3.43204	−	9.42945i	0.616413	−	1.69358i	0.715600	−	0.698511i	$-0.246154\pi$
$32$	−0.782364	+	5.60249i	−0.138304	+	0.990390i
$33$	−6.22965	−	2.45616i	−1.08444	−	0.427563i
$34$	1.80186	+	6.11822i	0.309016	+	1.04927i
$35$	0.595425	+	2.26390i	0.100645	+	0.382668i
$36$	−5.91272	+	1.01965i	−0.985454	+	0.169942i
$37$	−2.45441	+	4.25116i	−0.403502	+	0.698886i	−0.994146	−	0.108047i	$-0.965540\pi$
$37$	−2.45441	+	4.25116i	−0.403502	+	0.698886i	0.590644	+	0.806932i	$0.298874\pi$
$38$	1.45742	+	4.94869i	0.236425	+	0.802784i
$39$	3.23923	+	5.97035i	0.518692	+	0.956021i
$40$	−1.28026	+	2.15023i	−0.202427	+	0.339982i
$41$	−0.570454	−	0.679841i	−0.0890899	−	0.106173i	0.719658	−	0.694329i	$-0.244299\pi$
$41$	−0.570454	−	0.679841i	−0.0890899	−	0.106173i	−0.808748	+	0.588156i	$0.799854\pi$
$42$	−6.38946	+	1.08389i	−0.985915	+	0.167247i
$43$	−0.136201	−	0.374208i	−0.0207704	−	0.0570663i	0.928874	−	0.370396i	$-0.120778\pi$
$43$	−0.136201	−	0.374208i	−0.0207704	−	0.0570663i	−0.949645	+	0.313329i	$0.898556\pi$
$44$	−2.99889	−	7.12706i	−0.452099	−	1.07445i
$45$	−2.58592	−	0.598702i	−0.385486	−	0.0892492i
$46$	−3.11714	+	4.69346i	−0.459597	+	0.692013i
$47$	10.8056	−	3.93290i	1.57615	−	0.573672i	0.601789	−	0.798655i	$-0.294455\pi$
$47$	10.8056	−	3.93290i	1.57615	−	0.573672i	0.974363	+	0.224983i	$0.0722325\pi$
$48$	−5.61372	−	4.06031i	−0.810271	−	0.586056i
$49$	−6.90458	+	1.15186i	−0.986369	+	0.164551i
$50$	4.79976	−	3.53999i	0.678788	−	0.500630i
$51$	−7.65416	−	1.55974i	−1.07180	−	0.218407i
$52$	−2.31669	+	7.49332i	−0.321267	+	1.03914i
$53$	−10.5062	−	6.06576i	−1.44314	−	0.833196i	−0.445080	−	0.895491i	$-0.646825\pi$
$53$	−10.5062	−	6.06576i	−1.44314	−	0.833196i	−0.998058	+	0.0622950i	$0.980158\pi$
$54$	2.28829	−	6.98310i	0.311397	−	0.950280i
$55$		−	3.42066i		−	0.461242i
$56$	−6.05150	−	4.40220i	−0.808666	−	0.588269i
$57$	−6.19103	−	1.26159i	−0.820022	−	0.167101i
$58$	−4.75679	+	10.8931i	−0.624597	+	1.43033i
$59$	−6.55875	+	5.50344i	−0.853876	+	0.716487i	−0.960640	−	0.277797i	$-0.910396\pi$
$59$	−6.55875	+	5.50344i	−0.853876	+	0.716487i	0.106764	+	0.994284i	$0.465951\pi$
$60$	−1.59240	−	2.61880i	−0.205578	−	0.338086i
$61$	−0.546801	+	0.199019i	−0.0700107	+	0.0254818i	−0.376788	−	0.926299i	$-0.622972\pi$
$61$	−0.546801	+	0.199019i	−0.0700107	+	0.0254818i	0.306777	+	0.951781i	$0.400749\pi$
$62$	−0.888579	+	14.1632i	−0.112850	+	1.79873i
$63$	2.49225	−	7.53583i	0.313994	−	0.949425i
$64$	−1.17700	−	7.91294i	−0.147125	−	0.989118i
$65$	−2.23032	+	2.65799i	−0.276637	+	0.329683i
$66$	9.43248	+	0.843117i	1.16106	+	0.103781i
$67$	6.47342	−	1.14144i	0.790854	−	0.139449i	0.236392	−	0.971658i	$-0.424035\pi$
$67$	6.47342	−	1.14144i	0.790854	−	0.139449i	0.554462	+	0.832209i	$0.312924\pi$
$68$	−4.88882	−	7.58011i	−0.592856	−	0.919224i
$69$	−3.29077	−	6.06535i	−0.396163	−	0.730183i
$70$	−1.71225	−	2.83332i	−0.204653	−	0.338647i
$71$	−5.76242	−	9.98080i	−0.683873	−	1.18450i	−0.973789	−	0.227451i	$-0.926961\pi$
$71$	−5.76242	−	9.98080i	−0.683873	−	1.18450i	0.289916	−	0.957052i	$-0.406373\pi$
$72$	7.61385	−	3.74557i	0.897301	−	0.441420i
$73$	1.73780	+	3.00996i	0.203394	+	0.352289i	0.949620	−	0.313404i	$-0.101469\pi$
$73$	1.73780	+	3.00996i	0.203394	+	0.352289i	−0.746226	+	0.665693i	$0.768136\pi$
$74$	1.63120	−	6.74774i	0.189623	−	0.784409i
$75$	1.07740	+	7.22447i	0.124408	+	0.834210i
$76$	−3.95429	−	6.13114i	−0.453589	−	0.703289i
$77$	10.1857	+	0.938520i	1.16077	+	0.106954i
$78$	−6.77969	−	6.80524i	−0.767648	−	0.770542i
$79$	14.1494	+	2.49492i	1.59193	+	0.280700i	0.898217	−	0.439552i	$-0.144863\pi$
$79$	14.1494	+	2.49492i	1.59193	+	0.280700i	0.693712	+	0.720253i	$0.255974\pi$
$80$	0.877728	−	3.42852i	0.0981330	−	0.383320i
$81$	6.24386	+	6.48184i	0.693762	+	0.720204i
$82$	1.04550	+	0.694362i	0.115456	+	0.0766794i
$83$	5.16732	+	4.33590i	0.567187	+	0.475927i	0.880711	−	0.473654i	$-0.157065\pi$
$83$	5.16732	+	4.33590i	0.567187	+	0.475927i	−0.313524	+	0.949580i	$0.601510\pi$
$84$	8.23493	−	4.02318i	0.898504	−	0.438965i
$85$	−0.692905	−	3.92966i	−0.0751561	−	0.426231i
$86$	0.334278	+	0.453237i	0.0360461	+	0.0488738i
$87$	−9.05888	−	11.3959i	−0.971214	−	1.22176i
$88$	6.91577	+	8.47046i	0.737224	+	0.902955i
$89$			0.529347i			0.0561107i	0.999606	+	0.0280553i	$0.00893146\pi$
$89$			0.529347i			0.0561107i	−0.999606	+	0.0280553i	$0.991069\pi$
$90$	3.74726	−	0.220947i	0.394996	−	0.0232899i
$91$	−7.30278	−	7.37049i	−0.765539	−	0.772637i
$92$	2.35355	−	7.61256i	0.245375	−	0.793664i
$93$	−14.8165	−	9.08588i	−1.53639	−	0.942162i
$94$	−13.0876	+	9.65253i	−1.34988	+	0.995582i
$95$	−0.560453	−	3.17849i	−0.0575012	−	0.326106i
$96$	9.23781	+	3.26539i	0.942830	+	0.333273i
$97$	7.11912	−	2.59115i	0.722837	−	0.263091i	0.0457073	−	0.998955i	$-0.485446\pi$
$97$	7.11912	−	2.59115i	0.722837	−	0.263091i	0.677130	+	0.735864i	$0.263224\pi$
$98$	8.90658	−	4.32120i	0.899701	−	0.436507i
$99$	−6.32302	+	9.72333i	−0.635487	+	0.977232i
$100$	−5.09704	+	6.72001i	−0.509704	+	0.672001i
$101$	−7.77001	+	9.25994i	−0.773145	+	0.921398i	−0.998602	−	0.0528549i	$-0.983168\pi$
$101$	−7.77001	+	9.25994i	−0.773145	+	0.921398i	0.225457	+	0.974253i	$0.427612\pi$
$102$	11.0068	−	0.942113i	1.08984	−	0.0932831i
$103$	−11.9558	+	2.10813i	−1.17804	+	0.207721i	−0.728186	−	0.685380i	$-0.759636\pi$
$103$	−11.9558	+	2.10813i	−1.17804	+	0.207721i	−0.449857	+	0.893101i	$0.648525\pi$
$104$	0.149028	−	11.0911i	0.0146134	−	1.08757i
$105$	4.04815	−	0.227585i	0.395059	−	0.0222100i
$106$	16.6762	+	4.03130i	1.61974	+	0.391555i
$107$	−3.09640	−	5.36312i	−0.299340	−	0.518473i	0.676645	−	0.736309i	$-0.263433\pi$
$107$	−3.09640	−	5.36312i	−0.299340	−	0.518473i	−0.975985	+	0.217837i	$0.930100\pi$
$108$	−0.314355	+	10.3875i	−0.0302488	+	0.999542i
$109$	2.49658	−	4.32420i	0.239129	−	0.414184i	−0.721336	−	0.692586i	$-0.756471\pi$
$109$	2.49658	−	4.32420i	0.239129	−	0.414184i	0.960465	+	0.278402i	$0.0898048\pi$
$110$	1.36665	+	4.64048i	0.130305	+	0.442453i
$111$	6.36610	+	5.63578i	0.604243	+	0.534925i
$112$	9.96830	+	3.55429i	0.941916	+	0.335849i
$113$	1.51930	−	4.17423i	0.142923	−	0.392678i	−0.847491	−	0.530810i	$-0.821888\pi$
$113$	1.51930	−	4.17423i	0.142923	−	0.392678i	0.990414	+	0.138132i	$0.0441098\pi$
$114$	8.90282	−	0.762024i	0.833826	−	0.0713700i
$115$	2.26581	−	2.70028i	0.211288	−	0.251803i
$116$	2.10098	−	16.6781i	0.195071	−	1.54852i
$117$	11.2530	−	3.43272i	1.04034	−	0.317355i
$118$	6.69884	−	10.0864i	0.616678	−	0.928529i
$119$	11.8915	−	0.985094i	1.09009	−	0.0903034i
$120$	3.20655	+	2.91647i	0.292716	+	0.266236i
$121$	−3.70905	−	1.34998i	−0.337186	−	0.122726i
$122$	0.662278	−	0.488453i	0.0599599	−	0.0442225i
$123$	−1.35109	+	0.733040i	−0.121824	+	0.0660960i
$124$	−4.45318	−	19.5689i	−0.399907	−	1.75734i
$125$	−7.06253	+	4.07755i	−0.631692	+	0.364707i
$126$	−0.370213	+	11.2189i	−0.0329812	+	0.999456i
$127$	10.6895	+	6.17158i	0.948539	+	0.547639i	0.892627	−	0.450797i	$-0.148860\pi$
$127$	10.6895	+	6.17158i	0.948539	+	0.547639i	0.0559121	+	0.998436i	$0.482193\pi$
$128$	4.75818	+	10.2645i	0.420567	+	0.907261i
$129$	−0.682200	+	0.101738i	−0.0600644	+	0.00895756i
$130$	1.96371	−	4.49692i	0.172229	−	0.394406i
$131$	−10.4805	+	8.79422i	−0.915690	+	0.768355i	−0.973193	−	0.229990i	$-0.926131\pi$
$131$	−10.4805	+	8.79422i	−0.915690	+	0.768355i	0.0575032	+	0.998345i	$0.481686\pi$
$132$	−13.1330	+	2.62478i	−1.14308	+	0.228457i
$133$	9.61836	−	0.796788i	0.834018	−	0.0690903i
$134$	−8.32583	+	4.13480i	−0.719242	+	0.357192i
$135$	−1.91042	+	4.18169i	−0.164423	+	0.359902i
$136$	9.66067	+	8.32999i	0.828395	+	0.714291i
$137$	−2.10806	−	5.79184i	−0.180104	−	0.494831i	0.816484	−	0.577367i	$-0.195920\pi$
$137$	−2.10806	−	5.79184i	−0.180104	−	0.494831i	−0.996588	+	0.0825369i	$0.973698\pi$
$138$	6.88757	+	6.91353i	0.586308	+	0.588518i
$139$	−11.1311	+	1.96272i	−0.944128	+	0.166475i	−0.624462	−	0.781055i	$-0.714682\pi$
$139$	−11.1311	+	1.96272i	−0.944128	+	0.166475i	−0.319666	+	0.947530i	$0.603571\pi$
$140$	3.45484	+	3.15960i	0.291987	+	0.267035i
$141$	−2.93777	−	19.6990i	−0.247405	−	1.65896i
$142$	11.8049	+	11.2377i	0.990649	+	0.943051i
$143$	7.58081	+	13.1304i	0.633939	+	1.09802i
$144$	−8.83252	+	8.12321i	−0.736043	+	0.676935i
$145$	3.71823	−	6.44016i	0.308782	−	0.534826i
$146$	−3.56008	−	3.38902i	−0.294634	−	0.280478i
$147$	−0.433002	+	12.1166i	−0.0357134	+	0.999362i
$148$	0.483032	+	9.80573i	0.0397050	+	0.806026i
$149$	−6.24452	+	17.1567i	−0.511571	+	1.40553i	0.368029	+	0.929814i	$0.380033\pi$
$149$	−6.24452	+	17.1567i	−0.511571	+	1.40553i	−0.879600	+	0.475715i	$0.842189\pi$
$150$	−4.34800	−	9.37029i	−0.355013	−	0.765081i
$151$	13.3310	+	2.35061i	1.08486	+	0.191290i	0.687364	−	0.726313i	$-0.258768\pi$
$151$	13.3310	+	2.35061i	1.08486	+	0.191290i	0.397497	+	0.917604i	$0.369879\pi$
$152$	7.81398	+	6.73767i	0.633798	+	0.546497i
$153$	−5.29429	+	12.4510i	−0.428018	+	1.00660i
$154$	−14.1930	+	2.79629i	−1.14370	+	0.225332i
$155$	1.54171	−	8.74347i	0.123833	−	0.702292i
$156$	11.9162	+	6.52334i	0.954063	+	0.522285i
$157$	0.735561	−	0.617209i	0.0587042	−	0.0492587i	−0.612963	−	0.790111i	$-0.710023\pi$
$157$	0.735561	−	0.617209i	0.0587042	−	0.0492587i	0.671668	+	0.740853i	$0.265578\pi$
$158$	−20.1919	+	2.26847i	−1.60638	+	0.180470i
$159$	−13.9281	+	15.7330i	−1.10457	+	1.24771i
$160$	0.179064	+	5.00183i	0.0141562	+	0.395429i
$161$	7.41898	+	7.48777i	0.584697	+	0.590119i
$162$	−11.0601	−	6.29869i	−0.868966	−	0.494872i
$163$	−7.69749	+	4.44415i	−0.602914	+	0.348092i	−0.770187	−	0.637818i	$-0.779837\pi$
$163$	−7.69749	+	4.44415i	−0.602914	+	0.348092i	0.167273	+	0.985911i	$0.446504\pi$
$164$	−1.69574	−	0.524268i	−0.132415	−	0.0409384i
$165$	−5.80545	−	1.18301i	−0.451954	−	0.0920975i
$166$	−8.74233	−	3.81760i	−0.678537	−	0.296303i
$167$	−11.1633	−	4.06311i	−0.863842	−	0.314413i	−0.128171	−	0.991752i	$-0.540911\pi$
$167$	−11.1633	−	4.06311i	−0.863842	−	0.314413i	−0.735671	+	0.677339i	$0.763133\pi$
$168$	−9.56416	+	8.74796i	−0.737891	+	0.674920i
$169$	0.413151	−	2.34309i	0.0317808	−	0.180238i
$170$	2.51001	+	5.05416i	0.192509	+	0.387636i
$171$	−4.28226	+	10.0709i	−0.327472	+	0.770143i
$172$	−0.634564	−	0.481309i	−0.0483851	−	0.0366995i
$173$	8.68438	−	10.3496i	0.660261	−	0.786868i	−0.327162	−	0.944968i	$-0.606092\pi$
$173$	8.68438	−	10.3496i	0.660261	−	0.786868i	0.987423	+	0.158100i	$0.0505368\pi$
$174$	16.8423	+	11.8404i	1.27681	+	0.897617i
$175$	−4.66869	−	10.1339i	−0.352920	−	0.766049i
$176$	−12.7662	−	8.72802i	−0.962286	−	0.657899i
$177$	7.07198	+	13.0346i	0.531563	+	0.979744i
$178$	−0.211490	−	0.718115i	−0.0158518	−	0.0538250i
$179$	14.5852			1.09015			0.545075	−	0.838387i	$-0.316501\pi$
$179$	14.5852			1.09015			0.545075	+	0.838387i	$0.316501\pi$
$180$	−4.99528	+	1.79688i	−0.372326	+	0.133932i
$181$	−10.7745	+	18.6621i	−0.800866	+	1.38714i	0.118181	+	0.992992i	$0.462294\pi$
$181$	−10.7745	+	18.6621i	−0.800866	+	1.38714i	−0.919047	+	0.394148i	$0.871040\pi$
$182$	12.8517	+	7.08117i	0.952632	+	0.524891i
$183$	0.148662	+	0.996844i	0.0109894	+	0.0736889i
$184$	−0.151399	+	11.2675i	−0.0111613	+	0.830655i
$185$	−1.48546	+	4.08126i	−0.109213	+	0.300060i
$186$	23.7301	+	6.40634i	1.73998	+	0.469736i
$187$	−17.1712	−	3.02775i	−1.25569	−	0.221411i
$188$	13.8982	−	18.3235i	1.01363	−	1.33638i
$189$	−11.9277	−	6.83599i	−0.867610	−	0.497245i
$190$	2.03021	+	4.08803i	0.147287	+	0.296577i
$191$	0.838906	−	4.75767i	0.0607011	−	0.344253i	−0.939298	−	0.343102i	$-0.888522\pi$
$191$	0.838906	−	4.75767i	0.0607011	−	0.344253i	0.999999	−	0.00115120i	$-0.000366438\pi$
$192$	−13.8367	−	0.739070i	−0.998577	−	0.0533378i
$193$	1.36609	+	0.497215i	0.0983331	+	0.0357903i	0.390718	−	0.920510i	$-0.372227\pi$
$193$	1.36609	+	0.497215i	0.0983331	+	0.0357903i	−0.292385	+	0.956301i	$0.594449\pi$
$194$	−8.62259	+	6.35946i	−0.619066	+	0.456583i
$195$	3.73972	+	4.70448i	0.267807	+	0.336895i
$196$	−10.3563	+	9.42060i	−0.739733	+	0.672900i
$197$	17.6765	+	10.2055i	1.25940	+	0.727115i	0.972958	−	0.230983i	$-0.0741942\pi$
$197$	17.6765	+	10.2055i	1.25940	+	0.727115i	0.286442	+	0.958098i	$0.407528\pi$
$198$	4.69308	−	15.7170i	0.333523	−	1.11696i
$199$			7.03076i			0.498397i	0.968452	+	0.249199i	$0.0801672\pi$
$199$			7.03076i			0.498397i	−0.968452	+	0.249199i	$0.919833\pi$
$200$	4.22983	−	11.1528i	0.299094	−	0.788623i
$201$	0.301575	−	11.3813i	0.0212714	−	0.802772i
$202$	6.84122	−	15.6664i	0.481346	−	1.10229i
$203$	18.1567	+	12.8388i	1.27435	+	0.901104i
$204$	−14.5555	+	5.67563i	−1.01909	+	0.397373i
$205$	−0.601504	−	0.504722i	−0.0420109	−	0.0352513i
$206$	15.3771	−	7.63661i	1.07137	−	0.532068i
$207$	−11.4320	+	3.48734i	−0.794582	+	0.242387i
$208$	4.22903	+	15.1057i	0.293231	+	1.04739i
$209$	−13.8889	−	2.44898i	−0.960713	−	0.169400i
$210$	−5.40081	+	1.92609i	−0.372691	+	0.132913i
$211$	7.88817	−	21.6726i	0.543044	−	1.49200i	−0.299885	−	0.953975i	$-0.596948\pi$
$211$	7.88817	−	21.6726i	0.543044	−	1.49200i	0.842929	−	0.538026i	$-0.180830\pi$
$212$	−24.2336	+	1.19375i	−1.66437	+	0.0819873i
$213$	−18.9320	+	6.32802i	−1.29720	+	0.433589i
$214$	6.34331	+	6.03853i	0.433620	+	0.412786i
$215$	−0.176169	−	0.305134i	−0.0120146	−	0.0208099i
$216$	−3.72368	−	14.2174i	−0.253364	−	0.967371i
$217$	25.6125	+	6.98968i	1.73869	+	0.474491i
$218$	−1.65923	+	6.86369i	−0.112377	+	0.464868i
$219$	5.70943	−	1.90837i	0.385807	−	0.128956i
$220$	−3.70802	−	5.74928i	−0.249995	−	0.387617i
$221$	11.3686	+	13.5486i	0.764734	+	0.911375i
$222$	−10.8879	−	5.10209i	−0.730751	−	0.342430i
$223$	−11.6953	−	2.06220i	−0.783178	−	0.138095i	−0.232259	−	0.972654i	$-0.574612\pi$
$223$	−11.6953	−	2.06220i	−0.783178	−	0.138095i	−0.550919	+	0.834559i	$0.685723\pi$
$224$	−14.9431	−	0.839141i	−0.998427	−	0.0560675i
$225$	12.6338	+	0.669997i	0.842252	+	0.0446664i
$226$	−0.393356	+	6.26978i	−0.0261657	+	0.417060i
$227$	−1.26479	+	7.17296i	−0.0839468	+	0.476086i	0.913632	+	0.406542i	$0.133266\pi$
$227$	−1.26479	+	7.17296i	−0.0839468	+	0.476086i	−0.997579	+	0.0695441i	$0.977846\pi$
$228$	−11.7732	+	4.59070i	−0.779696	+	0.304027i
$229$	20.4982	+	7.46072i	1.35456	+	0.493018i	0.914367	−	0.404887i	$-0.132689\pi$
$229$	20.4982	+	7.46072i	1.35456	+	0.493018i	0.440189	+	0.897905i	$0.354911\pi$
$230$	−1.99496	+	4.56847i	−0.131544	+	0.301236i
$231$	5.11550	−	16.9623i	0.336575	−	1.11604i
$232$	3.81317	+	23.4649i	0.250347	+	1.54055i
$233$	15.0883	+	8.71125i	0.988469	+	0.570693i	0.904816	−	0.425802i	$-0.140008\pi$
$233$	15.0883	+	8.71125i	0.988469	+	0.570693i	0.0836530	+	0.996495i	$0.473341\pi$
$234$	−13.8944	+	9.15274i	−0.908304	+	0.598333i
$235$	8.81097	−	5.08701i	0.574764	−	0.331840i
$236$	−5.05786	+	16.3596i	−0.329239	+	1.06492i
$237$	9.12777	−	23.1511i	0.592913	−	1.50382i
$238$	−15.7385	+	6.08738i	−1.02017	+	0.394586i
$239$	0.252594	+	1.43253i	0.0163390	+	0.0926629i	0.991887	−	0.127124i	$-0.0405748\pi$
$239$	0.252594	+	1.43253i	0.0163390	+	0.0926629i	−0.975548	+	0.219787i	$0.929464\pi$
$240$	−5.51523	−	2.67539i	−0.356007	−	0.172696i
$241$	24.2683	−	8.83292i	1.56326	−	0.568979i	0.591776	−	0.806102i	$-0.298427\pi$
$241$	24.2683	−	8.83292i	1.56326	−	0.568979i	0.971479	+	0.237124i	$0.0762047\pi$
$242$	5.57107	+	0.349520i	0.358122	+	0.0224680i
$243$	13.1602	−	8.35520i	0.844227	−	0.535986i
$244$	−0.703299	+	0.927238i	−0.0450241	+	0.0593603i
$245$	−5.83920	+	2.06447i	−0.373053	+	0.131894i
$246$	1.54003	−	1.53425i	0.0981887	−	0.0978200i
$247$	9.19543	+	10.9587i	0.585091	+	0.697285i
$248$	13.8596	+	24.7681i	0.880083	+	1.57278i
$249$	9.14585	−	7.27029i	0.579595	−	0.460736i
$250$	7.95196	−	8.35332i	0.502926	−	0.528310i
$251$	0.772989	−	1.33886i	0.0487906	−	0.0845078i	−0.840599	−	0.541658i	$-0.817797\pi$
$251$	0.772989	−	1.33886i	0.0487906	−	0.0845078i	0.889389	+	0.457151i	$0.151130\pi$
$252$	−3.98003	−	15.3675i	−0.250718	−	0.968060i
$253$	−7.70144	−	13.3393i	−0.484185	−	0.838634i
$254$	−16.9671	−	4.10163i	−1.06461	−	0.257359i
$255$	−6.90894	−	0.183069i	−0.432655	−	0.0114643i
$256$	−10.5559	−	12.0238i	−0.659746	−	0.751489i
$257$	0.150030	−	0.412203i	0.00935860	−	0.0257125i	−0.934925	−	0.354844i	$-0.884534\pi$
$257$	0.150030	−	0.412203i	0.00935860	−	0.0257125i	0.944284	+	0.329132i	$0.106756\pi$
$258$	0.884828	−	0.410578i	0.0550870	−	0.0255615i
$259$	−11.7452	−	5.54301i	−0.729812	−	0.344426i
$260$	−0.867334	+	6.88510i	−0.0537898	+	0.426996i
$261$	−22.4737	+	11.4333i	−1.39109	+	0.707703i
$262$	10.7044	−	16.1176i	0.661321	−	0.995747i
$263$	4.85268	+	4.07188i	0.299229	+	0.251083i	0.780023	−	0.625751i	$-0.215207\pi$
$263$	4.85268	+	4.07188i	0.299229	+	0.251083i	−0.480794	+	0.876833i	$0.659652\pi$
$264$	16.7676	−	8.80780i	1.03198	−	0.542083i
$265$	−10.0863	−	3.67112i	−0.619597	−	0.225515i
$266$	−12.7300	+	4.92374i	−0.780525	+	0.301894i
$267$	0.898393	+	0.183071i	0.0549807	+	0.0112038i
$268$	9.64289	−	8.93570i	0.589033	−	0.545835i
$269$	9.98761	+	5.76635i	0.608955	+	0.351581i	0.772556	−	0.634946i	$-0.218978\pi$
$269$	9.98761	+	5.76635i	0.608955	+	0.351581i	−0.163601	+	0.986527i	$0.552311\pi$
$270$	0.920982	−	6.43616i	0.0560492	−	0.391692i
$271$	−1.28848	+	0.743906i	−0.0782698	+	0.0451891i	−0.538624	−	0.842546i	$-0.681056\pi$
$271$	−1.28848	+	0.743906i	−0.0782698	+	0.0451891i	0.460354	+	0.887735i	$0.347722\pi$
$272$	−16.4338	−	7.44078i	−0.996444	−	0.451164i
$273$	−15.0346	+	9.84503i	−0.909936	+	0.595848i
$274$	5.17381	+	7.01501i	0.312561	+	0.423792i
$275$	2.83120	+	16.0565i	0.170728	+	0.968245i
$276$	−12.1059	−	6.62714i	−0.728687	−	0.398907i
$277$	11.5171	+	9.66399i	0.691995	+	0.580653i	0.919484	−	0.393128i	$-0.128607\pi$
$277$	11.5171	+	9.66399i	0.691995	+	0.580653i	−0.227489	+	0.973781i	$0.573051\pi$
$278$	14.3164	−	7.10983i	0.858638	−	0.426419i
$279$	−20.5445	+	22.0038i	−1.22997	+	1.31733i
$280$	−5.94921	−	2.90602i	−0.355533	−	0.173668i
$281$	−6.05985	−	16.6493i	−0.361500	−	0.993214i	−0.978499	−	0.206250i	$-0.933874\pi$
$281$	−6.05985	−	16.6493i	−0.361500	−	0.993214i	0.616999	−	0.786964i	$-0.288348\pi$
$282$	11.8557	+	25.5501i	0.705999	+	1.52149i
$283$	7.83758	−	1.38198i	0.465896	−	0.0821500i	0.0642276	−	0.997935i	$-0.479542\pi$
$283$	7.83758	−	1.38198i	0.465896	−	0.0821500i	0.401668	+	0.915785i	$0.368431\pi$
$284$	−20.5045	−	10.5288i	−1.21672	−	0.624767i
$285$	−5.58827	−	0.148075i	−0.331020	−	0.00877120i
$286$	−15.5301	−	14.7839i	−0.918316	−	0.874193i
$287$	1.66795	−	1.65262i	0.0984558	−	0.0975512i
$288$	8.73677	−	14.5488i	0.514819	−	0.857299i
$289$	−3.33966			−0.196450
$290$	−2.47113	+	10.2223i	−0.145110	+	0.600274i
$291$	−1.93552	−	12.9785i	−0.113462	−	0.760813i
$292$	6.18363	+	3.17521i	0.361870	+	0.185815i
$293$	20.1181	−	3.54737i	1.17531	−	0.207239i	0.448313	−	0.893877i	$-0.352025\pi$
$293$	20.1181	−	3.54737i	1.17531	−	0.207239i	0.727000	+	0.686637i	$0.240914\pi$
$294$	−4.25353	−	16.6105i	−0.248071	−	0.968742i
$295$	−4.86929	+	5.80300i	−0.283501	+	0.337864i
$296$	−4.57296	−	13.1095i	−0.265798	−	0.761975i
$297$	14.3154	+	14.0940i	0.830663	+	0.817817i
$298$	1.61675	−	25.7697i	0.0936558	−	1.49280i
$299$	−2.71307	+	15.3866i	−0.156901	+	0.889830i
$300$	9.64222	+	10.9746i	0.556694	+	0.633621i
$301$	0.956933	−	0.440860i	0.0551567	−	0.0254108i
$302$	−19.0240	+	2.13727i	−1.09471	+	0.122986i
$303$	13.0285	+	16.3895i	0.748467	+	0.941554i
$304$	−13.2924	−	6.01844i	−0.762370	−	0.345181i
$305$	−0.445867	+	0.257422i	−0.0255303	+	0.0147399i
$306$	2.20772	−	19.0063i	0.126207	−	1.08652i
$307$	−3.78251	+	2.18383i	−0.215879	+	0.124638i	−0.604041	−	0.796953i	$-0.706444\pi$
$307$	−3.78251	+	2.18383i	−0.215879	+	0.124638i	0.388161	+	0.921591i	$0.373110\pi$
$308$	18.1370	−	9.46396i	1.03345	−	0.539259i
$309$	−0.556981	+	21.0202i	−0.0316856	+	1.19580i
$310$	1.40178	+	12.4774i	0.0796159	+	0.708668i
$311$	−1.14820	−	6.51179i	−0.0651087	−	0.369250i	−0.999901	−	0.0140554i	$-0.995526\pi$
$311$	−1.14820	−	6.51179i	−0.0651087	−	0.369250i	0.934793	−	0.355194i	$-0.115585\pi$
$312$	−18.7719	−	4.08870i	−1.06275	−	0.231477i
$313$	21.8137	+	18.3039i	1.23299	+	1.03460i	0.998039	+	0.0625888i	$0.0199357\pi$
$313$	21.8137	+	18.3039i	1.23299	+	1.03460i	0.234946	+	0.972009i	$0.424509\pi$
$314$	−0.751273	+	1.13119i	−0.0423968	+	0.0638366i
$315$	1.01378	−	6.94911i	0.0571198	−	0.391538i
$316$	26.4861	−	11.1447i	1.48996	−	0.626937i
$317$	−0.0433369	−	0.119067i	−0.00243404	−	0.00668747i	0.938470	−	0.345362i	$-0.112244\pi$
$317$	−0.0433369	−	0.119067i	−0.00243404	−	0.00668747i	−0.940904	+	0.338674i	$0.890022\pi$
$318$	12.6092	−	26.9082i	0.707087	−	1.50894i
$319$	−20.8872	−	24.8924i	−1.16946	−	1.39371i
$320$	−2.24129	−	6.71396i	−0.125292	−	0.375322i
$321$	−10.1730	+	3.40032i	−0.567802	+	0.189787i
$322$	−13.0562	−	7.19385i	−0.727594	−	0.400897i
$323$	−16.4516			−0.915393
$324$	17.5207	+	4.12598i	0.973374	+	0.229221i
$325$	8.26912	−	14.3225i	0.458688	−	0.794471i
$326$	8.66688	−	9.10432i	0.480014	−	0.504242i
$327$	−6.47549	−	5.73262i	−0.358095	−	0.317015i
$328$	2.50991	+	0.0337251i	0.138587	+	0.00186215i
$329$	12.7302	+	27.6322i	0.701837	+	1.52341i
$330$	8.34835	−	0.714564i	0.459561	−	0.0393355i
$331$	−8.52353	−	23.4182i	−0.468496	−	1.28718i	−0.918947	−	0.394380i	$-0.870959\pi$
$331$	−8.52353	−	23.4182i	−0.468496	−	1.28718i	0.450452	−	0.892801i	$-0.351263\pi$
$332$	13.3851	+	1.68616i	0.734605	+	0.0925401i
$333$	11.7666	−	8.85527i	0.644804	−	0.485266i
$334$	16.7675	+	1.05197i	0.917477	+	0.0575611i
$335$	5.46512	−	1.98914i	0.298591	−	0.108678i
$336$	9.47972	−	15.6887i	0.517161	−	0.855888i
$337$	−17.9207	+	15.0372i	−0.976201	+	0.819129i	−0.983512	−	0.180844i	$-0.942117\pi$
$337$	−17.9207	+	15.0372i	−0.976201	+	0.819129i	0.00731133	+	0.999973i	$0.497673\pi$
$338$	0.375653	+	3.34372i	0.0204328	+	0.181874i
$339$	−6.55894	−	4.02214i	−0.356233	−	0.218452i
$340$	−5.42438	−	5.85367i	−0.294178	−	0.317460i
$341$	−33.5977	−	19.3976i	−1.81942	−	1.05044i
$342$	1.78570	−	15.3732i	0.0965596	−	0.831285i
$343$	−4.54528	−	17.9538i	−0.245422	−	0.969416i
$344$	1.05315	+	0.399420i	0.0567820	+	0.0215353i
$345$	−3.79923	−	4.77934i	−0.204544	−	0.257311i
$346$	−7.64628	+	17.5100i	−0.411067	+	0.941345i
$347$	8.33199	+	3.03260i	0.447285	+	0.162798i	0.555835	−	0.831293i	$-0.312399\pi$
$347$	8.33199	+	3.03260i	0.447285	+	0.162798i	−0.108550	+	0.994091i	$0.534621\pi$
$348$	−27.5789	−	9.33372i	−1.47839	−	0.500340i
$349$	−16.2555	−	13.6400i	−0.870139	−	0.730134i	0.0939881	−	0.995573i	$-0.470038\pi$
$349$	−16.2555	−	13.6400i	−0.870139	−	0.730134i	−0.964127	+	0.265440i	$0.914483\pi$
$350$	10.3823	+	11.8824i	0.554960	+	0.635140i
$351$	−1.93414	−	20.2854i	−0.103237	−	1.08276i
$352$	20.8057	+	6.74001i	1.10895	+	0.359244i
$353$	−0.706032	−	1.93981i	−0.0375783	−	0.103245i	0.919484	−	0.393126i	$-0.128607\pi$
$353$	−0.706032	−	1.93981i	−0.0375783	−	0.103245i	−0.957063	+	0.289881i	$0.906384\pi$
$354$	−14.8016	−	14.8574i	−0.786697	−	0.789662i
$355$	−6.55442	−	7.81125i	−0.347872	−	0.414578i
$356$	0.573816	+	0.889701i	0.0304122	+	0.0471541i
$357$	2.44072	−	20.5226i	0.129177	−	1.08617i
$358$	−19.7864	+	5.82722i	−1.04574	+	0.307978i
$359$	27.5450			1.45377			0.726886	−	0.686758i	$-0.240967\pi$
$359$	27.5450			1.45377			0.726886	+	0.686758i	$0.240967\pi$
$360$	6.05872	−	4.43342i	0.319322	−	0.233662i
$361$	5.69318			0.299641
$362$	7.16076	−	29.6218i	0.376361	−	1.55689i
$363$	−3.57391	+	5.82801i	−0.187581	+	0.305891i
$364$	−20.2638	−	4.47172i	−1.06211	−	0.234382i
$365$	1.97665	+	2.35568i	0.103462	+	0.123302i
$366$	−0.599944	−	1.29293i	−0.0313596	−	0.0675825i
$367$	23.1316	+	4.07872i	1.20746	+	0.212907i	0.740920	−	0.671593i	$-0.234390\pi$
$367$	23.1316	+	4.07872i	1.20746	+	0.212907i	0.466538	+	0.884501i	$0.345501\pi$
$368$	−4.29633	−	15.3461i	−0.223961	−	0.799971i
$369$	0.776827	+	2.54656i	0.0404400	+	0.132568i
$370$	0.384595	−	6.13013i	0.0199941	−	0.318691i
$371$	13.6989	−	29.0268i	0.711210	−	1.50700i
$372$	−34.7519	+	0.790016i	−1.80180	+	0.0409604i
$373$	−1.63052	−	9.24714i	−0.0844252	−	0.478799i	−0.997479	−	0.0709602i	$-0.977394\pi$
$373$	−1.63052	−	9.24714i	−0.0844252	−	0.478799i	0.913054	−	0.407839i	$-0.133717\pi$
$374$	24.5043	−	2.75295i	1.26708	−	0.142352i
$375$	4.47778	+	13.3965i	0.231231	+	0.691793i
$376$	−11.5335	+	30.4105i	−0.594797	+	1.56830i
$377$			32.9611i			1.69758i
$378$	18.9123	+	4.50829i	0.972744	+	0.231881i
$379$		−	6.14395i		−	0.315593i	−0.987472	−	0.157797i	$-0.949561\pi$
$379$		−	6.14395i		−	0.315593i	0.987472	−	0.157797i	$-0.0504391\pi$
$380$	−4.38748	−	4.73471i	−0.225073	−	0.242886i
$381$	14.1711	−	16.0075i	0.726009	−	0.820089i
$382$	0.762765	+	6.78944i	0.0390265	+	0.347378i
$383$	0.580964	+	3.29481i	0.0296859	+	0.168357i	0.996046	−	0.0888341i	$-0.0283141\pi$
$383$	0.580964	+	3.29481i	0.0296859	+	0.168357i	−0.966361	+	0.257191i	$0.917203\pi$
$384$	19.0662	−	4.52553i	0.972967	−	0.230943i
$385$	9.01932	−	0.747164i	0.459667	−	0.0380790i
$386$	−2.05189	−	0.128732i	−0.104439	−	0.00655231i
$387$	−0.0632672	+	1.19300i	−0.00321605	+	0.0606434i
$388$	9.15666	−	12.0723i	0.464859	−	0.612876i
$389$	−24.5715	−	4.33262i	−1.24583	−	0.219673i	−0.488415	−	0.872611i	$-0.662425\pi$
$389$	−24.5715	−	4.33262i	−1.24583	−	0.219673i	−0.757411	+	0.652939i	$0.773536\pi$
$390$	−6.95290	−	4.88799i	−0.352074	−	0.247513i
$391$	−11.5495	−	13.7641i	−0.584083	−	0.696083i
$392$	10.2856	−	16.9177i	0.519499	−	0.854471i
$393$	11.3007	+	20.8287i	0.570044	+	1.05067i
$394$	−28.0575	−	6.78260i	−1.41351	−	0.341702i
$395$	12.7121			0.639615
$396$	−0.0872703	+	23.1967i	−0.00438550	+	1.16568i
$397$	−28.9874			−1.45484			−0.727419	−	0.686194i	$-0.759280\pi$
$397$	−28.9874			−1.45484			−0.727419	+	0.686194i	$0.759280\pi$
$398$	−2.80899	−	9.53796i	−0.140802	−	0.478095i
$399$	1.97416	−	16.5996i	0.0988318	−	0.831018i
$400$	−1.28234	+	16.8199i	−0.0641170	+	0.840995i
$401$	2.55050	+	3.03957i	0.127366	+	0.151789i	0.825959	−	0.563731i	$-0.190634\pi$
$401$	2.55050	+	3.03957i	0.127366	+	0.151789i	−0.698593	+	0.715520i	$0.746190\pi$
$402$	4.13803	+	15.5604i	0.206386	+	0.776080i
$403$	13.4592	+	36.9789i	0.670451	+	1.84205i
$404$	−3.02163	+	23.9864i	−0.150332	+	1.19337i
$405$	6.43633	+	4.68853i	0.319824	+	0.232975i
$406$	−29.7610	−	10.1630i	−1.47701	−	0.504380i
$407$	14.5381	+	12.1989i	0.720629	+	0.604679i
$408$	17.4785	−	13.5149i	0.865315	−	0.669089i
$409$	−6.63600	−	2.41531i	−0.328129	−	0.119429i	0.172702	−	0.984974i	$-0.444750\pi$
$409$	−6.63600	−	2.41531i	−0.328129	−	0.119429i	−0.500831	+	0.865545i	$0.666972\pi$
$410$	1.01765	+	0.444390i	0.0502584	+	0.0219468i
$411$	−10.5588	+	1.57466i	−0.520828	+	0.0776725i
$412$	−17.8096	+	16.5034i	−0.877414	+	0.813067i
$413$	−15.9436	−	16.0915i	−0.784535	−	0.791810i
$414$	14.1155	−	9.29838i	0.693737	−	0.456991i
$415$	5.16861	+	2.98410i	0.253717	+	0.146484i
$416$	−11.7723	−	18.8029i	−0.577185	−	0.921887i
$417$	−0.518561	+	19.5702i	−0.0253940	+	0.958357i
$418$	19.8201	−	2.22671i	0.969435	−	0.108912i
$419$	−19.1605	+	16.0776i	−0.936052	+	0.785441i	−0.976894	−	0.213725i	$-0.931440\pi$
$419$	−19.1605	+	16.0776i	−0.936052	+	0.785441i	0.0408420	+	0.999166i	$0.486996\pi$
$420$	6.55723	−	4.77073i	0.319960	−	0.232788i
$421$	28.9318	−	10.5303i	1.41005	−	0.513216i	0.478905	−	0.877867i	$-0.341034\pi$
$421$	28.9318	−	10.5303i	1.41005	−	0.513216i	0.931144	+	0.364651i	$0.118812\pi$
$422$	−2.04230	+	32.5527i	−0.0994177	+	1.58464i
$423$	−34.4487	−	1.82689i	−1.67495	−	0.0888263i
$424$	32.3985	−	11.3015i	1.57341	−	0.548849i
$425$	6.50497	+	17.8723i	0.315537	+	0.866932i
$426$	23.1551	−	16.1485i	1.12187	−	0.782398i
$427$	−0.644194	−	1.39829i	−0.0311747	−	0.0676680i
$428$	−11.0179	−	5.65756i	−0.532572	−	0.273469i
$429$	24.9062	−	8.32489i	1.20248	−	0.401930i
$430$	0.360901	+	0.343561i	0.0174042	+	0.0165680i
$431$	10.4073	−	18.0260i	0.501301	−	0.868280i	−0.498697	−	0.866776i	$-0.666188\pi$
$431$	10.4073	−	18.0260i	0.501301	−	0.868280i	0.999999	−	0.00150348i	$-0.000478571\pi$
$432$	10.7318	+	17.7997i	0.516335	+	0.856387i
$433$	−19.2736			−0.926231			−0.463116	−	0.886298i	$-0.653269\pi$
$433$	−19.2736			−0.926231			−0.463116	+	0.886298i	$0.653269\pi$
$434$	−37.5386	+	0.750696i	−1.80191	+	0.0360346i
$435$	−9.64413	−	8.53776i	−0.462401	−	0.409354i
$436$	−0.491332	−	9.97423i	−0.0235305	−	0.477679i
$437$	−9.34175	−	11.1331i	−0.446876	−	0.532567i
$438$	−6.98298	+	4.86999i	−0.333660	+	0.232697i
$439$	4.21541	+	11.5817i	0.201190	+	0.552766i	0.998724	−	0.0505089i	$-0.0160843\pi$
$439$	4.21541	+	11.5817i	0.201190	+	0.552766i	−0.797533	+	0.603275i	$0.793862\pi$
$440$	7.32732	+	6.31804i	0.349316	+	0.301201i
$441$	20.4142	+	4.92534i	0.972107	+	0.234540i
$442$	−20.8357	−	13.8380i	−0.991055	−	0.658204i
$443$	−11.6617	−	9.78531i	−0.554063	−	0.464914i	0.322251	−	0.946654i	$-0.395560\pi$
$443$	−11.6617	−	9.78531i	−0.554063	−	0.464914i	−0.876314	+	0.481740i	$0.840005\pi$
$444$	16.8091	+	2.57146i	0.797723	+	0.122036i
$445$	0.0813284	+	0.461236i	0.00385534	+	0.0218647i
$446$	16.6899	−	1.87504i	0.790288	−	0.0887855i
$447$	26.9582	+	16.5315i	1.27508	+	0.781915i
$448$	20.6071	−	4.83182i	0.973595	−	0.228282i
$449$	−24.2683	+	14.0113i	−1.14529	+	0.661234i	−0.947735	−	0.319058i	$-0.896634\pi$
$449$	−24.2683	+	14.0113i	−1.14529	+	0.661234i	−0.197556	+	0.980292i	$0.563300\pi$
$450$	−17.4067	+	4.13864i	−0.820561	+	0.195098i
$451$	−2.97141	+	1.71554i	−0.139918	+	0.0807817i
$452$	−1.97133	−	8.66277i	−0.0927237	−	0.407463i
$453$	8.59983	−	21.8120i	0.404055	−	1.02482i
$454$	−1.14999	−	10.2362i	−0.0539718	−	0.480408i
$455$	−7.49553	−	5.30014i	−0.351396	−	0.248475i
$456$	14.1374	−	10.9315i	0.662045	−	0.511914i
$457$	2.50409	−	14.2014i	0.117136	−	0.664312i	−0.868534	−	0.495629i	$-0.834937\pi$
$457$	2.50409	−	14.2014i	0.117136	−	0.664312i	0.985670	−	0.168683i	$-0.0539514\pi$
$458$	−30.7887	−	1.93163i	−1.43866	−	0.0902592i
$459$	19.3005	+	13.2914i	0.900870	+	0.620390i
$460$	0.881135	−	6.99466i	0.0410832	−	0.326128i
$461$	12.5727	−	14.9835i	0.585568	−	0.697853i	−0.389180	−	0.921162i	$-0.627241\pi$
$461$	12.5727	−	14.9835i	0.585568	−	0.697853i	0.974748	+	0.223309i	$0.0716859\pi$
$462$	−0.162758	+	25.0550i	−0.00757218	+	1.16566i
$463$	−10.6551	+	1.87878i	−0.495184	+	0.0873144i	−0.415663	−	0.909519i	$-0.636450\pi$
$463$	−10.6551	+	1.87878i	−0.495184	+	0.0873144i	−0.0795216	+	0.996833i	$0.525339\pi$
$464$	−14.5479	−	30.3092i	−0.675369	−	1.40707i
$465$	−14.3060	−	5.64042i	−0.663424	−	0.261568i
$466$	−23.9493	−	5.78950i	−1.10943	−	0.268193i
$467$	−1.28728			−0.0595681			−0.0297841	−	0.999556i	$-0.509482\pi$
$467$	−1.28728			−0.0595681			−0.0297841	+	0.999556i	$0.509482\pi$
$468$	15.1924	−	17.9679i	0.702268	−	0.830565i
$469$	4.42362	+	16.8193i	0.204264	+	0.776642i
$470$	−9.92059	+	10.4213i	−0.457603	+	0.480699i
$471$	−0.793121	−	1.46183i	−0.0365451	−	0.0673577i
$472$	0.325362	−	24.2143i	0.0149760	−	1.11456i
$473$	−1.51620	+	0.267348i	−0.0697151	+	0.0122927i
$474$	−3.13325	+	35.0537i	−0.143915	+	1.61007i
$475$	5.26151	+	14.4559i	0.241415	+	0.663282i
$476$	18.9188	−	14.5461i	0.867141	−	0.666721i
$477$	21.8847	+	29.0796i	1.00203	+	1.33146i
$478$	−0.915010	−	1.84246i	−0.0418516	−	0.0842723i
$479$	3.16736	+	2.65773i	0.144721	+	0.121435i	0.712274	−	0.701902i	$-0.247665\pi$
$479$	3.16736	+	2.65773i	0.144721	+	0.121435i	−0.567553	+	0.823337i	$0.692110\pi$
$480$	8.55089	+	1.42595i	0.390293	+	0.0650853i
$481$	−3.34283	−	18.9581i	−0.152420	−	0.864416i
$482$	−29.3934	+	21.6787i	−1.33883	+	0.987436i
$483$	15.2738	−	10.0017i	0.694984	−	0.455092i
$484$	−7.69739	+	1.75165i	−0.349881	+	0.0796203i
$485$	5.80501	−	3.35152i	0.263592	−	0.152185i
$486$	−14.5150	+	16.5926i	−0.658415	+	0.752655i
$487$	20.1728	+	11.6468i	0.914116	+	0.527765i	0.881753	−	0.471711i	$-0.156363\pi$
$487$	20.1728	+	11.6468i	0.914116	+	0.527765i	0.0323630	+	0.999476i	$0.489697\pi$
$488$	0.583640	−	1.53888i	0.0264201	−	0.0696620i
$489$	4.88035	+	14.6009i	0.220697	+	0.660277i
$490$	7.09668	−	5.13360i	0.320595	−	0.231912i
$491$	16.9619	+	6.17364i	0.765481	+	0.278612i	0.695105	−	0.718908i	$-0.255358\pi$
$491$	16.9619	+	6.17364i	0.765481	+	0.278612i	0.0703759	+	0.997521i	$0.477580\pi$
$492$	−1.47624	+	2.69665i	−0.0665538	+	0.121575i
$493$	−29.0376	−	24.3654i	−1.30779	−	1.09736i
$494$	−16.8529	−	11.1928i	−0.758247	−	0.503586i
$495$	−4.01556	+	9.44371i	−0.180486	+	0.424463i
$496$	−28.6975	−	28.0633i	−1.28856	−	1.26008i
$497$	25.0579	−	17.3740i	1.12400	−	0.779329i
$498$	−9.50261	+	13.5169i	−0.425822	+	0.605709i
$499$	−1.11555	+	3.06495i	−0.0499389	+	0.137206i	−0.962155	−	0.272504i	$-0.912148\pi$
$499$	−1.11555	+	3.06495i	−0.0499389	+	0.137206i	0.912216	+	0.409710i	$0.134370\pi$
$500$	−7.45027	+	14.5092i	−0.333186	+	0.648871i
$501$	−10.7565	+	17.5408i	−0.480567	+	0.783667i
$502$	−0.513728	+	2.12513i	−0.0229288	+	0.0948492i
$503$	−4.91016	−	8.50464i	−0.218933	−	0.379203i	0.735549	−	0.677472i	$-0.236924\pi$
$503$	−4.91016	−	8.50464i	−0.218933	−	0.379203i	−0.954482	+	0.298268i	$0.903591\pi$
$504$	11.5391	+	19.2575i	0.513992	+	0.857795i
$505$	−5.34756	+	9.26225i	−0.237963	+	0.412165i
$506$	15.7772	+	15.0192i	0.701384	+	0.667684i
$507$	−3.83375	−	1.51153i	−0.170263	−	0.0671295i
$508$	24.6564	−	1.21458i	1.09395	−	0.0538882i
$509$	−15.7995	−	18.8291i	−0.700302	−	0.834587i	0.292259	−	0.956339i	$-0.405593\pi$
$509$	−15.7995	−	18.8291i	−0.700302	−	0.834587i	−0.992561	+	0.121752i	$0.961149\pi$
$510$	9.44585	−	2.51197i	0.418269	−	0.111232i
$511$	−7.55684	+	5.23955i	−0.334295	+	0.231784i
$512$	19.1241	+	12.0942i	0.845174	+	0.534492i
$513$	15.6111	+	10.7507i	0.689247	+	0.474655i
$514$	−0.0388438	+	0.619138i	−0.00171332	+	0.0273090i
$515$	−10.0936	+	3.67377i	−0.444777	+	0.161885i
$516$	−1.03632	+	0.910507i	−0.0456216	+	0.0400828i
$517$	−7.71987	−	43.7815i	−0.339519	−	1.92551i
$518$	18.1482	+	2.82712i	0.797386	+	0.124217i
$519$	−14.5617	−	18.3182i	−0.639187	−	0.804081i
$520$	−1.57417	−	9.68688i	−0.0690319	−	0.424798i
$521$	−11.4316	+	6.60003i	−0.500827	+	0.289153i	−0.729055	−	0.684455i	$-0.760040\pi$
$521$	−11.4316	+	6.60003i	−0.500827	+	0.289153i	0.228228	+	0.973608i	$0.426707\pi$
$522$	25.9200	−	24.4893i	1.13449	−	1.07187i
$523$	−21.6540	−	12.5019i	−0.946864	−	0.546672i	−0.0547584	−	0.998500i	$-0.517439\pi$
$523$	−21.6540	−	12.5019i	−0.946864	−	0.546672i	−0.892105	+	0.451828i	$0.850772\pi$
$524$	−8.08221	+	26.1419i	−0.353073	+	1.14201i
$525$	−18.8136	+	4.41883i	−0.821091	+	0.192854i
$526$	−8.21000	−	3.58514i	−0.357973	−	0.156320i
$527$	−42.5264	−	15.4783i	−1.85248	−	0.674247i
$528$	−19.2280	+	18.6479i	−0.836793	+	0.811544i
$529$	−1.23767	+	7.01915i	−0.0538116	+	0.305181i
$530$	15.1499	+	0.950478i	0.658068	+	0.0412861i
$531$	24.5678	−	7.49442i	1.06615	−	0.325230i
$532$	15.3024	−	11.7656i	0.663441	−	0.510102i
$533$	3.42746	+	0.604353i	0.148460	+	0.0261774i
$534$	−1.29191	+	0.110579i	−0.0559062	+	0.00478521i
$535$	−3.52197	−	4.19733i	−0.152268	−	0.181466i
$536$	−9.51151	+	15.9748i	−0.410835	+	0.690008i
$537$	5.04420	−	24.7536i	0.217673	−	1.06820i
$538$	−15.8531	−	3.83231i	−0.683474	−	0.165223i
$539$	−0.249780	+	27.0619i	−0.0107588	+	1.16564i
$540$	1.32203	+	9.09929i	0.0568910	+	0.391571i
$541$	12.9471	+	22.4251i	0.556640	+	0.964128i	0.997774	+	0.0666872i	$0.0212430\pi$
$541$	12.9471	+	22.4251i	0.556640	+	0.964128i	−0.441134	+	0.897441i	$0.645424\pi$
$542$	1.45075	−	1.52397i	0.0623150	−	0.0654602i
$543$	27.9464	+	24.7404i	1.19930	+	1.06171i
$544$	25.2670	+	3.52842i	1.08331	+	0.151280i
$545$	1.51098	−	4.15139i	0.0647233	−	0.177826i
$546$	16.4626	−	19.3626i	0.704536	−	0.828642i
$547$	26.7858	+	4.72306i	1.14528	+	0.201944i	0.713914	−	0.700234i	$-0.246921\pi$
$547$	26.7858	+	4.72306i	1.14528	+	0.201944i	0.431365	+	0.902177i	$0.358032\pi$
$548$	−9.82152	−	7.44951i	−0.419555	−	0.318227i
$549$	1.74323	+	0.0924472i	0.0743992	+	0.00394555i
$550$	−10.2559	−	20.6512i	−0.437312	−	0.880571i
$551$	−23.4869	−	19.7078i	−1.00057	−	0.839582i
$552$	19.0706	+	4.15376i	0.811699	+	0.176796i
$553$	−3.48779	+	37.8529i	−0.148316	+	1.60967i
$554$	−19.4852	−	8.50880i	−0.827847	−	0.361504i
$555$	6.41286	+	3.93255i	0.272211	+	0.166927i
$556$	−16.5810	+	15.3650i	−0.703193	+	0.651623i
$557$		−	11.3226i		−	0.479753i	−0.970803	−	0.239876i	$-0.922893\pi$
$557$		−	11.3226i		−	0.479753i	0.970803	−	0.239876i	$-0.0771069\pi$
$558$	19.0796	−	38.0585i	0.807703	−	1.61115i
$559$	1.35246	+	0.780846i	0.0572031	+	0.0330263i
$560$	9.23177	+	1.56544i	0.390113	+	0.0661521i
$561$	−11.0772	+	28.0954i	−0.467679	+	1.18619i
$562$	14.8727	+	20.1654i	0.627367	+	0.850627i
$563$	−9.83044	−	3.57799i	−0.414304	−	0.150794i	0.126454	−	0.991972i	$-0.459640\pi$
$563$	−9.83044	−	3.57799i	−0.414304	−	0.150794i	−0.540758	+	0.841178i	$0.681862\pi$
$564$	−26.2916	−	29.9247i	−1.10707	−	1.26006i
$565$	0.682484	−	3.87056i	0.0287123	−	0.162836i
$566$	−10.0804	+	5.00614i	−0.423709	+	0.210424i
$567$	−15.7270	+	17.8791i	−0.660470	+	0.750852i
$568$	32.0230	+	6.09123i	1.34366	+	0.255583i
$569$	−29.6187	−	5.22258i	−1.24168	−	0.218942i	−0.486046	−	0.873933i	$-0.661561\pi$
$569$	−29.6187	−	5.22258i	−1.24168	−	0.218942i	−0.755636	+	0.654991i	$0.772672\pi$
$570$	7.64023	−	2.03180i	0.320014	−	0.0851026i
$571$	−8.72810	+	23.9803i	−0.365260	+	1.00354i	0.611881	+	0.790950i	$0.290413\pi$
$571$	−8.72810	+	23.9803i	−0.365260	+	1.00354i	−0.977141	+	0.212593i	$0.931809\pi$
$572$	26.9749	+	13.8512i	1.12788	+	0.579149i
$573$	−7.78445	−	3.06918i	−0.325200	−	0.128217i
$574$	−1.60247	+	2.90835i	−0.0668859	+	0.121392i
$575$	−8.40070	+	14.5504i	−0.350333	+	0.606795i
$576$	−6.03966	+	23.2276i	−0.251652	+	0.967818i
$577$	−8.87581			−0.369505			−0.184752	−	0.982785i	$-0.559148\pi$
$577$	−8.87581			−0.369505			−0.184752	+	0.982785i	$0.559148\pi$
$578$	4.53059	−	1.33429i	0.188448	−	0.0554992i
$579$	1.31631	−	2.14653i	0.0547041	−	0.0892066i
$580$	−0.731754	−	14.8549i	−0.0303845	−	0.616816i
$581$	−10.3039	+	14.5719i	−0.427476	+	0.604542i
$582$	7.81103	+	16.8334i	0.323777	+	0.697767i
$583$	−30.1482	+	35.9292i	−1.24861	+	1.48803i
$584$	−9.65733	−	1.83696i	−0.399623	−	0.0760141i
$585$	9.27767	−	4.71994i	0.383584	−	0.195145i
$586$	−25.8751	+	12.8502i	−1.06889	+	0.530835i
$587$	−4.65466	+	26.3979i	−0.192118	+	1.08956i	0.724345	+	0.689438i	$0.242142\pi$
$587$	−4.65466	+	26.3979i	−0.192118	+	1.08956i	−0.916463	+	0.400119i	$0.868969\pi$
$588$	12.4067	+	20.8344i	0.511645	+	0.859197i
$589$	−34.3972	−	12.5196i	−1.41731	−	0.515860i
$590$	4.28724	−	9.81780i	0.176503	−	0.404192i
$591$	23.4339	−	26.4706i	0.963940	−	1.08885i
$592$	11.4413	+	15.9574i	0.470236	+	0.655845i
$593$	−21.0170	+	12.1342i	−0.863065	+	0.498291i	−0.865037	−	0.501707i	$-0.832705\pi$
$593$	−21.0170	+	12.1342i	−0.863065	+	0.498291i	0.00197246	+	0.999998i	$0.499372\pi$
$594$	−25.0513	−	13.4006i	−1.02787	−	0.549832i
$595$	10.2101	−	2.68534i	0.418572	−	0.110088i
$596$	8.10246	+	35.6052i	0.331890	+	1.45845i
$597$	11.9324	+	2.43154i	0.488361	+	0.0995165i
$598$	−2.46683	−	21.9575i	−0.100876	−	0.897908i
$599$	9.99307	−	8.38518i	0.408306	−	0.342609i	−0.415388	−	0.909644i	$-0.636354\pi$
$599$	9.99307	−	8.38518i	0.408306	−	0.342609i	0.823694	+	0.567035i	$0.191910\pi$
$600$	−17.4654	−	11.0359i	−0.713021	−	0.450538i
$601$	−0.217260	+	1.23214i	−0.00886224	+	0.0502602i	−0.988918	−	0.148462i	$-0.952568\pi$
$601$	−0.217260	+	1.23214i	−0.00886224	+	0.0502602i	0.980056	+	0.198722i	$0.0636790\pi$
$602$	−1.12204	+	0.980396i	−0.0457311	+	0.0399579i
$603$	−19.2117	−	4.44796i	−0.782359	−	0.181135i
$604$	24.9542	−	10.5001i	1.01537	−	0.427242i
$605$	−3.43922	−	0.606428i	−0.139824	−	0.0246548i
$606$	−24.2226	−	17.0289i	−0.983976	−	0.691750i
$607$	−5.79470	+	15.9208i	−0.235200	+	0.646206i	0.764798	+	0.644270i	$0.222839\pi$
$607$	−5.79470	+	15.9208i	−0.235200	+	0.646206i	−0.999998	+	0.00193632i	$0.999384\pi$
$608$	20.4371	+	2.85395i	0.828832	+	0.115743i
$609$	28.0690	−	26.3749i	1.13741	−	1.06876i
$610$	0.502018	−	0.527356i	0.0203261	−	0.0213520i
$611$	−22.5475	+	39.0534i	−0.912175	+	1.57993i
$612$	4.59858	+	26.6661i	0.185887	+	1.07791i
$613$	−0.686616	−	1.18925i	−0.0277322	−	0.0480335i	0.851826	−	0.523824i	$-0.175495\pi$
$613$	−0.686616	−	1.18925i	−0.0277322	−	0.0480335i	−0.879558	+	0.475791i	$0.842162\pi$
$614$	4.25887	−	4.47382i	0.171874	−	0.180549i
$615$	−1.06463	+	0.846301i	−0.0429299	+	0.0341262i
$616$	−20.8236	+	20.0851i	−0.839009	+	0.809253i
$617$	29.3112	−	5.16836i	1.18002	−	0.208070i	0.450978	−	0.892535i	$-0.351075\pi$
$617$	29.3112	−	5.16836i	1.18002	−	0.208070i	0.729046	+	0.684465i	$0.239964\pi$
$618$	−7.64257	−	28.7386i	−0.307429	−	1.15604i
$619$	−5.27306	−	14.4876i	−0.211942	−	0.582306i	0.787478	−	0.616342i	$-0.211386\pi$
$619$	−5.27306	−	14.4876i	−0.211942	−	0.582306i	−0.999421	+	0.0340359i	$0.989164\pi$
$620$	−6.88675	−	16.3668i	−0.276578	−	0.657308i
$621$	1.96492	+	20.6082i	0.0788496	+	0.826979i
$622$	4.15931	+	8.37518i	0.166773	+	0.335814i
$623$	−1.39574	+	0.115624i	−0.0559191	+	0.00463236i
$624$	27.0996	−	1.95317i	1.08485	−	0.0781895i
$625$	10.6254	−	8.91577i	0.425016	−	0.356631i
$626$	−36.9056	−	16.1159i	−1.47504	−	0.644122i
$627$	−8.95972	+	22.7248i	−0.357817	+	0.907542i
$628$	0.567238	−	1.83473i	0.0226353	−	0.0732137i
$629$	19.1725	+	11.0692i	0.764458	+	0.441360i
$630$	1.40108	+	9.83222i	0.0558203	+	0.391725i
$631$	−16.1481	+	9.32311i	−0.642846	+	0.371147i	−0.785710	−	0.618595i	$-0.787702\pi$
$631$	−16.1481	+	9.32311i	−0.642846	+	0.371147i	0.142864	+	0.989742i	$0.454369\pi$
$632$	−31.4785	+	25.7009i	−1.25215	+	1.02233i
$633$	−34.0540	−	20.8829i	−1.35352	−	0.830021i
$634$	0.106362	+	0.144213i	0.00422416	+	0.00572741i
$635$	10.2623	+	3.73516i	0.407246	+	0.148225i
$636$	−6.35505	+	41.5415i	−0.251994	+	1.64723i
$637$	17.8388	−	20.8653i	0.706799	−	0.826713i
$638$	38.2809	+	25.4241i	1.51556	+	1.00655i
$639$	4.19221	+	34.3194i	0.165841	+	1.35766i
$640$	5.72297	+	8.21273i	0.226220	+	0.324636i
$641$	−8.44175	+	10.0605i	−0.333429	+	0.397365i	−0.906545	−	0.422109i	$-0.861290\pi$
$641$	−8.44175	+	10.0605i	−0.333429	+	0.397365i	0.573116	+	0.819474i	$0.305734\pi$
$642$	12.4422	−	8.67731i	0.491055	−	0.342466i
$643$	13.8931	−	38.1709i	0.547890	−	1.50531i	−0.288664	−	0.957430i	$-0.593211\pi$
$643$	13.8931	−	38.1709i	0.547890	−	1.50531i	0.836554	−	0.547885i	$-0.184567\pi$
$644$	20.5863	+	4.54287i	0.811212	+	0.179014i
$645$	−0.578791	+	0.193460i	−0.0227899	+	0.00761750i
$646$	22.3184	−	6.57291i	0.878104	−	0.258608i
$647$	−15.2593	+	26.4298i	−0.599904	+	1.03906i	0.392931	+	0.919568i	$0.371461\pi$
$647$	−15.2593	+	26.4298i	−0.599904	+	1.03906i	−0.992835	+	0.119496i	$0.961872\pi$
$648$	−25.4172	+	1.40272i	−0.998481	+	0.0551040i
$649$	16.5507	+	28.6666i	0.649670	+	1.12526i
$650$	−5.49565	+	22.7338i	−0.215557	+	0.891692i
$651$	20.7206	−	41.0514i	0.812105	−	1.60893i
$652$	−8.12009	+	15.8136i	−0.318007	+	0.619310i
$653$	−6.73221	+	1.18707i	−0.263452	+	0.0464537i	−0.303814	−	0.952731i	$-0.598260\pi$
$653$	−6.73221	+	1.18707i	−0.263452	+	0.0464537i	0.0403619	+	0.999185i	$0.487149\pi$
$654$	11.0750	+	5.18976i	0.433068	+	0.202936i
$655$	−7.78089	+	9.27290i	−0.304024	+	0.362322i
$656$	−3.41844	+	0.957033i	−0.133467	+	0.0373658i
$657$	−1.26426	−	10.3499i	−0.0493236	−	0.403787i
$658$	−28.3097	−	32.3998i	−1.10363	−	1.26308i
$659$	43.3544	−	15.7797i	1.68885	−	0.614691i	0.694369	−	0.719619i	$-0.255684\pi$
$659$	43.3544	−	15.7797i	1.68885	−	0.614691i	0.994480	+	0.104929i	$0.0334615\pi$
$660$	−11.0399	+	4.30479i	−0.429728	+	0.167564i
$661$	−2.54086	−	14.4099i	−0.0988279	−	0.560481i	−0.993507	−	0.113771i	$-0.963707\pi$
$661$	−2.54086	−	14.4099i	−0.0988279	−	0.560481i	0.894679	−	0.446709i	$-0.147404\pi$
$662$	20.9193	+	28.3638i	0.813053	+	1.10239i
$663$	26.9260	−	14.6088i	1.04572	−	0.567358i
$664$	−18.8320	+	3.06030i	−0.730824	+	0.118763i
$665$	8.25836	−	2.17202i	0.320245	−	0.0842274i
$666$	−12.4246	+	16.7142i	−0.481445	+	0.647661i
$667$		−	33.4856i		−	1.29657i
$668$	−23.1672	+	5.27201i	−0.896365	+	0.203980i
$669$	−7.54468	+	19.1358i	−0.291694	+	0.739833i
$670$	−6.61929	+	4.88195i	−0.255725	+	0.188606i
$671$	0.390654	+	2.21551i	0.0150810	+	0.0855287i
$672$	−6.59214	+	25.0708i	−0.254297	+	0.967126i
$673$	36.2287	+	30.3995i	1.39651	+	1.17181i	0.962622	+	0.270849i	$0.0873043\pi$
$673$	36.2287	+	30.3995i	1.39651	+	1.17181i	0.433891	+	0.900965i	$0.357140\pi$
$674$	18.3034	−	27.5594i	0.705022	−	1.06155i
$675$	5.50641	−	21.2100i	0.211942	−	0.816372i
$676$	−1.84553	−	4.38602i	−0.0709817	−	0.168693i
$677$	−23.1301	−	4.07845i	−0.888960	−	0.156748i	−0.289524	−	0.957171i	$-0.593497\pi$
$677$	−23.1301	−	4.07845i	−0.888960	−	0.156748i	−0.599436	+	0.800423i	$0.704608\pi$
$678$	10.5049	+	2.83596i	0.403437	+	0.108914i
$679$	8.38713	+	18.2051i	0.321869	+	0.698649i
$680$	9.69745	+	5.77392i	0.371880	+	0.221420i
$681$	11.7363	+	4.62728i	0.449737	+	0.177318i
$682$	53.3287	+	12.8917i	2.04206	+	0.493647i
$683$	−0.0833807	−	0.144420i	−0.00319047	−	0.00552606i	0.864426	−	0.502760i	$-0.167682\pi$
$683$	−0.0833807	−	0.144420i	−0.00319047	−	0.00552606i	−0.867616	+	0.497234i	$0.834349\pi$
$684$	3.71954	+	21.5687i	0.142220	+	0.824701i
$685$	−2.72667	−	4.72273i	−0.104181	−	0.180446i
$686$	13.3392	+	22.5403i	0.509294	+	0.860593i
$687$	19.7513	−	32.2086i	0.753558	−	1.22884i
$688$	−1.58829	−	0.121090i	−0.0605529	−	0.00461652i
$689$	46.8526	−	8.26138i	1.78494	−	0.314734i
$690$	7.06354	+	4.96577i	0.268904	+	0.189044i
$691$	−25.0805	+	29.8897i	−0.954106	+	1.13706i	0.0363652	+	0.999339i	$0.488422\pi$
$691$	−25.0805	+	29.8897i	−0.954106	+	1.13706i	−0.990471	+	0.137721i	$0.956022\pi$
$692$	3.37721	−	26.8091i	0.128382	−	1.01913i
$693$	−27.0188	−	14.5482i	−1.02636	−	0.552640i
$694$	−12.5148	−	0.785160i	−0.475056	−	0.0298043i
$695$	−9.39733	+	3.42035i	−0.356461	+	0.129741i
$696$	41.1428	+	1.64359i	1.55951	+	0.0623001i
$697$	−3.06605	+	2.57272i	−0.116135	+	0.0974487i
$698$	27.5019	+	12.0096i	1.04096	+	0.454568i
$699$	20.0027	−	22.5948i	0.756571	−	0.854612i
$700$	−18.8321	−	11.9716i	−0.711787	−	0.452486i
$701$		−	3.05004i		−	0.115199i	−0.998340	−	0.0575993i	$-0.981655\pi$
$701$		−	3.05004i		−	0.115199i	0.998340	−	0.0575993i	$-0.0183446\pi$
$702$	10.7285	+	26.7466i	0.404921	+	1.00948i
$703$	15.5076	+	8.95331i	0.584880	+	0.337680i
$704$	−30.9180	−	0.831024i	−1.16527	−	0.0313204i
$705$	−5.58632	−	16.7130i	−0.210393	−	0.629449i
$706$	1.73281	+	2.34947i	0.0652153	+	0.0884234i
$707$	−26.1130	−	18.4647i	−0.982082	−	0.694437i
$708$	26.0159	+	14.2419i	0.977737	+	0.535245i
$709$	26.1583	−	9.52085i	0.982397	−	0.357563i	0.199625	−	0.979872i	$-0.436028\pi$
$709$	26.1583	−	9.52085i	0.982397	−	0.357563i	0.782772	+	0.622309i	$0.213805\pi$
$710$	12.0126	+	7.97810i	0.450824	+	0.299413i
$711$	−36.1346	−	23.4981i	−1.35515	−	0.881246i
$712$	−1.13390	−	0.977717i	−0.0424948	−	0.0366415i
$713$	−13.6734	−	37.5673i	−0.512072	−	1.40691i
$714$	4.88827	+	28.8161i	0.182939	+	1.07842i
$715$	8.62273	+	10.2762i	0.322472	+	0.384307i
$716$	24.5141	−	15.8105i	0.916136	−	0.590865i
$717$	2.51861	+	0.0667369i	0.0940593	+	0.00249233i
$718$	−37.3677	+	11.0051i	−1.39455	+	0.410705i
$719$	6.51366	−	11.2820i	0.242918	−	0.420747i	−0.718626	−	0.695397i	$-0.755229\pi$
$719$	6.51366	−	11.2820i	0.242918	−	0.420747i	0.961544	+	0.274650i	$0.0885619\pi$
$720$	−6.44800	+	8.43503i	−0.240303	+	0.314355i
$721$	−8.17003	−	31.0637i	−0.304268	−	1.15687i
$722$	−7.72340	+	2.27459i	−0.287435	+	0.0846516i
$723$	−6.59796	−	44.2422i	−0.245381	−	1.64539i
$724$	2.12045	+	43.0460i	0.0788060	+	1.59979i
$725$	−12.1229	+	33.3075i	−0.450235	+	1.23701i
$726$	2.51992	−	9.33419i	0.0935229	−	0.346424i
$727$	15.1981	−	18.1123i	0.563665	−	0.671749i	−0.406653	−	0.913583i	$-0.633304\pi$
$727$	15.1981	−	18.1123i	0.563665	−	0.671749i	0.970318	+	0.241833i	$0.0777487\pi$
$728$	29.2766	−	2.02964i	1.08506	−	0.0752235i
$729$	−9.62883	−	25.2247i	−0.356623	−	0.934248i
$730$	−3.62269	−	2.40599i	−0.134082	−	0.0890498i
$731$	−1.68766	+	0.614259i	−0.0624204	+	0.0227192i
$732$	1.33045	+	1.51430i	0.0491749	+	0.0559701i
$733$	−26.0883	+	21.8907i	−0.963594	+	0.808551i	−0.981534	−	0.191288i	$-0.938734\pi$
$733$	−26.0883	+	21.8907i	−0.963594	+	0.808551i	0.0179399	+	0.999839i	$0.494289\pi$
$734$	−33.0100	+	3.70853i	−1.21842	+	0.136884i
$735$	1.48430	+	10.6241i	0.0547492	+	0.391876i
$736$	11.9596	+	19.1021i	0.440838	+	0.704112i
$737$		−	25.4133i		−	0.936110i
$738$	−2.07127	−	3.14430i	−0.0762445	−	0.115743i
$739$		−	8.19053i		−	0.301293i	−0.988588	−	0.150647i	$-0.951864\pi$
$739$		−	8.19053i		−	0.301293i	0.988588	−	0.150647i	$-0.0481356\pi$
$740$	1.92743	+	8.46983i	0.0708536	+	0.311357i
$741$	21.7790	−	11.8162i	0.800070	−	0.434080i
$742$	−6.98688	+	44.8510i	−0.256496	+	1.64653i
$743$	11.4807	−	9.63344i	0.421185	−	0.353417i	−0.407428	−	0.913237i	$-0.633574\pi$
$743$	11.4807	−	9.63344i	0.421185	−	0.353417i	0.828614	+	0.559821i	$0.189130\pi$
$744$	46.8290	−	14.9562i	1.71683	−	0.548319i
$745$	−2.80510	+	15.9085i	−0.102771	+	0.582844i
$746$	5.90648	+	11.8933i	0.216251	+	0.435444i
$747$	−9.17590	−	18.0365i	−0.335728	−	0.659920i
$748$	−32.1427	+	13.5248i	−1.17525	+	0.494517i
$749$	13.4647	−	9.33579i	0.491990	−	0.341122i
$750$	−11.4269	−	16.3848i	−0.417251	−	0.598288i
$751$	32.3864	−	5.71059i	1.18180	−	0.208382i	0.451981	−	0.892028i	$-0.350717\pi$
$751$	32.3864	−	5.71059i	1.18180	−	0.208382i	0.729815	+	0.683645i	$0.239606\pi$
$752$	3.49657	−	45.8630i	0.127507	−	1.67245i
$753$	−2.00494	−	1.77493i	−0.0730639	−	0.0646820i
$754$	−13.1689	−	44.7152i	−0.479584	−	1.62843i
$755$	11.9768			0.435882
$756$	−27.4577	+	1.44005i	−0.998628	+	0.0523742i
$757$	−18.7986			−0.683245			−0.341623	−	0.939837i	$-0.610976\pi$
$757$	−18.7986			−0.683245			−0.341623	+	0.939837i	$0.610976\pi$
$758$	2.45469	+	8.33491i	0.0891583	+	0.302738i
$759$	−25.3026	+	8.45736i	−0.918424	+	0.306983i
$760$	7.84374	+	4.67021i	0.284522	+	0.169406i
$761$	−26.2472	+	4.62809i	−0.951461	+	0.167768i	−0.627774	−	0.778396i	$-0.716034\pi$
$761$	−26.2472	+	4.62809i	−0.951461	+	0.167768i	−0.323687	+	0.946164i	$0.604923\pi$
$762$	−12.8291	+	27.3776i	−0.464751	+	0.991787i
$763$	11.9470	+	5.63826i	0.432512	+	0.204119i
$764$	−3.74735	−	8.90584i	−0.135574	−	0.322202i
$765$	−2.70012	+	11.6624i	−0.0976229	+	0.421653i
$766$	−2.10451	−	4.23765i	−0.0760391	−	0.153112i
$767$	5.83048	−	33.0663i	0.210527	−	1.19396i
$768$	−24.0572	+	13.7569i	−0.868089	+	0.496408i
$769$	−1.19278	+	1.00086i	−0.0430127	+	0.0360919i	−0.664041	−	0.747697i	$-0.731160\pi$
$769$	−1.19278	+	1.00086i	−0.0430127	+	0.0360919i	0.621028	+	0.783788i	$0.286715\pi$
$770$	−11.9371	+	4.61709i	−0.430185	+	0.166388i
$771$	−0.647693	−	0.397184i	−0.0233261	−	0.0143042i
$772$	2.83504	−	0.645152i	0.102035	−	0.0232195i
$773$			24.6756i			0.887521i	0.896146	+	0.443760i	$0.146356\pi$
$773$			24.6756i			0.887521i	−0.896146	+	0.443760i	$0.853644\pi$
$774$	−0.390808	−	1.64370i	−0.0140473	−	0.0590816i
$775$			42.3177i			1.52010i
$776$	−7.59875	+	20.0356i	−0.272779	+	0.719237i
$777$	−13.4695	+	18.0166i	−0.483214	+	0.646343i
$778$	35.0649	−	3.93939i	1.25714	−	0.141234i
$779$	−2.47996	+	2.08093i	−0.0888537	+	0.0745571i
$780$	11.3852	+	3.85318i	0.407657	+	0.137966i
$781$	−41.8696	+	15.2393i	−1.49821	+	0.545305i
$782$	21.1673	+	14.0581i	0.756940	+	0.502718i
$783$	11.6319	+	42.0958i	0.415689	+	1.50438i
$784$	−7.19433	+	27.0600i	−0.256940	+	0.966427i
$785$	0.546090	−	0.650805i	0.0194908	−	0.0232282i
$786$	−23.6522	−	23.7414i	−0.843647	−	0.846827i
$787$	−8.23714	+	22.6314i	−0.293622	+	0.806721i	0.701907	+	0.712269i	$0.252332\pi$
$787$	−8.23714	+	22.6314i	−0.293622	+	0.806721i	−0.995529	+	0.0944522i	$0.969890\pi$
$788$	40.7727	−	2.00847i	1.45247	−	0.0715488i
$789$	8.58895	−	6.82759i	0.305775	−	0.243069i
$790$	−17.2453	+	5.07886i	−0.613560	+	0.180698i
$791$	11.3381	+	3.09419i	0.403137	+	0.110017i
$792$	−9.14938	−	31.5036i	−0.325109	−	1.11943i
$793$	1.14099	−	1.97625i	0.0405176	−	0.0701786i
$794$	39.3245	−	11.5813i	1.39557	−	0.411006i
$795$	−9.71881	+	15.8486i	−0.344691	+	0.562091i
$796$	7.62139	+	11.8170i	0.270133	+	0.418841i
$797$	−5.81616	−	6.93143i	−0.206019	−	0.245524i	0.653134	−	0.757242i	$-0.273454\pi$
$797$	−5.81616	−	6.93143i	−0.206019	−	0.245524i	−0.859153	+	0.511718i	$0.829009\pi$
$798$	3.95386	+	23.3078i	0.139965	+	0.825087i
$799$	−17.7372	−	48.7325i	−0.627496	−	1.72403i
$800$	−4.98041	−	23.3303i	−0.176084	−	0.824850i
$801$	0.621407	−	1.46141i	0.0219563	−	0.0516365i
$802$	−4.67441	−	3.10449i	−0.165059	−	0.109623i
$803$	12.6268	−	4.59579i	0.445591	−	0.162182i
$804$	−11.8305	−	19.4560i	−0.417229	−	0.686160i
$805$	7.61480	+	5.38448i	0.268386	+	0.189778i
$806$	−33.0330	−	44.7884i	−1.16354	−	1.57760i
$807$	13.2406	−	14.9564i	0.466093	−	0.526491i
$808$	−5.48411	−	33.7473i	−0.192930	−	1.18723i
$809$	26.0356	+	15.0317i	0.915363	+	0.528485i	0.882153	−	0.470963i	$-0.156094\pi$
$809$	26.0356	+	15.0317i	0.915363	+	0.528485i	0.0332102	+	0.999448i	$0.489427\pi$
$810$	−10.6048	−	3.78897i	−0.372613	−	0.133131i
$811$		−	23.7220i		−	0.832990i	−0.909138	−	0.416495i	$-0.863258\pi$
$811$		−	23.7220i		−	0.832990i	0.909138	−	0.416495i	$-0.136742\pi$
$812$	44.4343	+	1.89676i	1.55934	+	0.0665632i
$813$	0.816922	+	2.44405i	0.0286507	+	0.0857166i
$814$	−24.5963	−	10.7407i	−0.862101	−	0.376462i
$815$	−6.02426	+	5.05496i	−0.211021	+	0.177067i
$816$	−18.3118	+	25.3176i	−0.641042	+	0.886293i
$817$	−1.36506	+	0.496840i	−0.0477573	+	0.0173822i
$818$	9.96741	+	0.625339i	0.348502	+	0.0218645i
$819$	11.5091	+	28.9212i	0.402160	+	1.01059i
$820$	−1.55810	−	0.196278i	−0.0544113	−	0.00685433i
$821$	33.3788	−	39.7793i	1.16493	−	1.38831i	0.258465	−	0.966021i	$-0.416783\pi$
$821$	33.3788	−	39.7793i	1.16493	−	1.38831i	0.906462	−	0.422286i	$-0.138772\pi$
$822$	13.6950	−	6.35475i	0.477668	−	0.221647i
$823$	32.5701	−	5.74298i	1.13532	−	0.200188i	0.425763	−	0.904835i	$-0.360006\pi$
$823$	32.5701	−	5.74298i	1.13532	−	0.200188i	0.709558	+	0.704647i	$0.248895\pi$
$824$	17.5669	−	29.5041i	0.611972	−	1.02782i
$825$	28.2298	+	0.748019i	0.982837	+	0.0260427i
$826$	28.0582	+	15.4598i	0.976271	+	0.537916i
$827$	4.26180	+	7.38166i	0.148197	+	0.256685i	0.930561	−	0.366136i	$-0.119320\pi$
$827$	4.26180	+	7.38166i	0.148197	+	0.256685i	−0.782364	+	0.622822i	$0.785986\pi$
$828$	−15.4341	+	18.2538i	−0.536373	+	0.634362i
$829$	12.5783	+	21.7863i	0.436862	+	0.756668i	0.997446	−	0.0714302i	$-0.0227563\pi$
$829$	12.5783	+	21.7863i	0.436862	+	0.756668i	−0.560583	+	0.828098i	$0.689423\pi$
$830$	−8.20400	−	1.98323i	−0.284765	−	0.0688390i
$831$	20.3846	−	16.2043i	0.707133	−	0.562120i
$832$	23.4827	+	20.8047i	0.814115	+	0.721273i
$833$	5.19483	+	31.1393i	0.179990	+	1.07891i
$834$	−7.11539	−	26.7562i	−0.246386	−	0.926492i
$835$	−10.3512	−	1.82519i	−0.358217	−	0.0631634i
$836$	−25.9985	+	10.9395i	−0.899176	+	0.378350i
$837$	30.2390	+	42.4774i	1.04521	+	1.46823i
$838$	19.5698	−	29.4661i	0.676026	−	1.01789i
$839$	−5.87484	−	4.92958i	−0.202822	−	0.170188i	0.535719	−	0.844396i	$-0.320041\pi$
$839$	−5.87484	−	4.92958i	−0.202822	−	0.170188i	−0.738541	+	0.674208i	$0.764485\pi$
$840$	−6.98952	+	9.09180i	−0.241161	+	0.313697i
$841$	−7.23122	−	41.0103i	−0.249352	−	1.41415i
$842$	−35.0418	+	25.8446i	−1.20762	+	0.890663i
$843$	−30.3525	+	4.52655i	−1.04539	+	0.155903i
$844$	−10.2351	−	44.9771i	−0.352308	−	1.54817i
$845$		−	2.10509i		−	0.0724172i
$846$	47.4631	−	11.2849i	1.63182	−	0.387983i
$847$	2.74937	−	10.0746i	0.0944696	−	0.346167i
$848$	−39.4367	+	28.2758i	−1.35426	+	0.970996i
$849$	0.365126	−	13.7797i	0.0125311	−	0.472917i
$850$	−15.9652	−	21.6467i	−0.547601	−	0.742475i
$851$	3.39602	+	19.2598i	0.116414	+	0.660217i
$852$	−24.9605	+	31.1583i	−0.855131	+	1.06747i
$853$	18.2908	−	6.65732i	0.626266	−	0.227942i	−0.00933929	−	0.999956i	$-0.502973\pi$
$853$	18.2908	−	6.65732i	0.626266	−	0.227942i	0.635605	+	0.772014i	$0.280751\pi$
$854$	1.43257	+	1.63955i	0.0490217	+	0.0561043i
$855$	−2.18398	+	9.43304i	−0.0746904	+	0.322603i
$856$	17.2074	+	3.27309i	0.588135	+	0.111872i
$857$	−22.5786	+	26.9081i	−0.771269	+	0.919163i	−0.998504	−	0.0546772i	$-0.982587\pi$
$857$	−22.5786	+	26.9081i	−0.771269	+	0.919163i	0.227235	+	0.973840i	$0.427031\pi$
$858$	−30.4619	+	21.2444i	−1.03995	+	0.725270i
$859$	−14.7255	+	2.59651i	−0.502429	+	0.0885917i	−0.419118	−	0.907932i	$-0.637661\pi$
$859$	−14.7255	+	2.59651i	−0.502429	+	0.0885917i	−0.0833109	+	0.996524i	$0.526549\pi$
$860$	−0.626863	−	0.321886i	−0.0213759	−	0.0109762i
$861$	−2.22794	−	3.40234i	−0.0759278	−	0.115951i
$862$	−6.91668	+	28.6121i	−0.235583	+	0.974532i
$863$	−21.3409	−	36.9636i	−0.726454	−	1.25826i	−0.958373	−	0.285520i	$-0.907834\pi$
$863$	−21.3409	−	36.9636i	−0.726454	−	1.25826i	0.231918	−	0.972735i	$-0.425500\pi$
$864$	−21.6703	−	19.8594i	−0.737239	−	0.675632i
$865$	5.97686	−	10.3522i	0.203219	−	0.351986i
$866$	26.1467	−	7.70038i	0.888501	−	0.261670i
$867$	−1.15500	+	5.66797i	−0.0392258	+	0.192494i
$868$	50.6251	−	16.0162i	1.71833	−	0.543624i
$869$	18.9983	−	52.1975i	0.644475	−	1.77068i
$870$	16.4944	+	7.72925i	0.559211	+	0.262046i
$871$	−16.5698	+	19.7471i	−0.561446	+	0.669105i
$872$	4.65154	+	13.3348i	0.157521	+	0.451573i
$873$	−22.6961	−	1.20362i	−0.768148	−	0.0407365i
$874$	17.1210	+	11.3709i	0.579128	+	0.384625i
$875$	−12.2940	−	17.7313i	−0.415613	−	0.599426i
$876$	7.52745	−	9.39656i	0.254329	−	0.317480i
$877$	−23.8649	−	8.68611i	−0.805860	−	0.293309i	−0.0939474	−	0.995577i	$-0.529949\pi$
$877$	−23.8649	−	8.68611i	−0.805860	−	0.293309i	−0.711913	+	0.702268i	$0.752171\pi$
$878$	−10.3459	−	14.0277i	−0.349157	−	0.473411i
$879$	0.937235	−	35.3707i	0.0316121	−	1.19303i
$880$	−12.4645	−	5.64361i	−0.420179	−	0.190246i
$881$	−11.5658	+	6.67749i	−0.389660	+	0.224970i	−0.682013	−	0.731340i	$-0.738895\pi$
$881$	−11.5658	+	6.67749i	−0.389660	+	0.224970i	0.292353	+	0.956311i	$0.405562\pi$
$882$	−29.6619	+	1.47435i	−0.998767	+	0.0496440i
$883$	−28.5051	−	16.4574i	−0.959272	−	0.553836i	−0.0633234	−	0.997993i	$-0.520170\pi$
$883$	−28.5051	−	16.4574i	−0.959272	−	0.553836i	−0.895949	+	0.444157i	$0.853503\pi$
$884$	33.7945	+	10.4482i	1.13663	+	0.351409i
$885$	8.16467	+	10.2710i	0.274452	+	0.345255i
$886$	19.7298	+	8.61561i	0.662836	+	0.289447i
$887$	−1.23100	+	1.03293i	−0.0413331	+	0.0346826i	−0.663220	−	0.748424i	$-0.730811\pi$
$887$	−1.23100	+	1.03293i	−0.0413331	+	0.0346826i	0.621887	+	0.783107i	$0.286366\pi$
$888$	−23.8306	+	3.22725i	−0.799704	+	0.108300i
$889$	−13.9379	+	29.5332i	−0.467461	+	0.990512i
$890$	−0.294608	−	0.593222i	−0.00987528	−	0.0198849i
$891$	28.8708	−	19.4214i	0.967209	−	0.650640i
$892$	−21.8924	+	9.21178i	−0.733013	+	0.308433i
$893$	−14.3466	−	39.4170i	−0.480092	−	1.31904i
$894$	−43.1764	−	11.6562i	−1.44404	−	0.389841i
$895$	12.7085	−	2.24086i	0.424800	−	0.0749037i
$896$	−26.0253	+	14.7880i	−0.869443	+	0.494033i
$897$	25.1754	+	9.92591i	0.840582	+	0.331416i
$898$	27.3245	−	28.7037i	0.911832	−	0.957854i
$899$	−42.1701	−	73.0408i	−1.40645	−	2.43605i
$900$	21.9605	−	12.5690i	0.732018	−	0.418967i
$901$	−27.3563	+	47.3824i	−0.911369	+	1.57854i
$902$	3.34561	−	3.51448i	0.111397	−	0.117019i
$903$	−0.417266	−	1.77655i	−0.0138858	−	0.0591198i
$904$	6.13535	+	10.9644i	0.204059	+	0.364669i
$905$	−6.52097	+	17.9162i	−0.216764	+	0.595555i
$906$	−2.95203	+	33.0262i	−0.0980746	+	1.09722i
$907$	22.5570	+	3.97741i	0.748993	+	0.132068i	0.535099	−	0.844789i	$-0.320274\pi$
$907$	22.5570	+	3.97741i	0.748993	+	0.132068i	0.213894	+	0.976857i	$0.431385\pi$
$908$	5.64974	+	13.4270i	0.187493	+	0.445591i
$909$	32.3217	−	16.4434i	1.07204	−	0.545392i
$910$	12.2860	+	4.19552i	0.407278	+	0.139080i
$911$	−2.11632	+	12.0022i	−0.0701168	+	0.397652i	0.929470	+	0.368898i	$0.120265\pi$
$911$	−2.11632	+	12.0022i	−0.0701168	+	0.397652i	−0.999587	+	0.0287538i	$0.990846\pi$
$912$	−14.8114	+	20.4780i	−0.490455	+	0.678095i
$913$	19.9776	−	16.7632i	0.661163	−	0.554782i
$914$	2.27681	+	20.2661i	0.0753102	+	0.670343i
$915$	0.282688	+	0.845741i	0.00934539	+	0.0279593i
$916$	42.5398	−	9.68051i	1.40555	−	0.319853i
$917$	−25.4771	−	25.7134i	−0.841329	−	0.849130i
$918$	−31.4934	−	10.3201i	−1.03944	−	0.340614i
$919$	16.1528	−	9.32585i	0.532833	−	0.307631i	−0.209336	−	0.977844i	$-0.567130\pi$
$919$	16.1528	−	9.32585i	0.532833	−	0.307631i	0.742169	+	0.670212i	$0.233797\pi$
$920$	1.59922	+	9.84102i	0.0527246	+	0.324449i
$921$	2.39818	+	7.17484i	0.0790228	+	0.236419i
$922$	−11.0698	+	25.3499i	−0.364564	+	0.834854i
$923$	42.4706	+	15.4580i	1.39794	+	0.508807i
$924$	−9.78939	−	34.0547i	−0.322047	−	1.12032i
$925$	3.59475	−	20.3868i	0.118195	−	0.670315i
$926$	13.7041	−	6.80579i	0.450346	−	0.223652i
$927$	35.4822	+	8.21499i	1.16539	+	0.269816i
$928$	31.8451	+	35.3052i	1.04537	+	1.15895i
$929$	34.9446	−	41.6453i	1.14649	−	1.36634i	0.226688	−	0.973967i	$-0.427210\pi$
$929$	34.9446	−	41.6453i	1.14649	−	1.36634i	0.919807	−	0.392372i	$-0.128345\pi$
$930$	21.6611	+	1.93616i	0.710295	+	0.0634893i
$931$	4.20181	+	25.1869i	0.137709	+	0.825467i
$932$	34.8028	−	1.71439i	1.14000	−	0.0561568i
$933$	−11.4487	−	0.303362i	−0.374814	−	0.00993162i
$934$	1.74633	−	0.514305i	0.0571416	−	0.0168286i
$935$	−15.4270			−0.504517
$936$	−13.4314	+	30.4451i	−0.439018	+	0.995129i
$937$	−27.0681	+	46.8833i	−0.884276	+	1.53161i	−0.0377338	+	0.999288i	$0.512014\pi$
$937$	−27.0681	+	46.8833i	−0.884276	+	1.53161i	−0.846542	+	0.532322i	$0.821319\pi$
$938$	−12.7209	−	21.0497i	−0.415352	−	0.687298i
$939$	38.6090	−	30.6914i	1.25996	−	1.00157i
$940$	9.29470	−	18.1012i	0.303160	−	0.590395i
$941$	9.64655	−	26.5037i	0.314468	−	0.863995i	−0.677272	−	0.735733i	$-0.736838\pi$
$941$	9.64655	−	26.5037i	0.314468	−	0.863995i	0.991740	−	0.128262i	$-0.0409399\pi$
$942$	1.66000	+	1.66625i	0.0540856	+	0.0542895i
$943$	−3.48199	−	0.613970i	−0.113389	−	0.0199936i
$944$	9.23295	+	32.9793i	0.300507	+	1.07338i
$945$	−11.4432	−	4.12386i	−0.372248	−	0.134149i
$946$	1.95008	−	0.968453i	0.0634024	−	0.0314871i
$947$	−7.22353	+	40.9667i	−0.234733	+	1.33124i	0.608442	+	0.793599i	$0.291795\pi$
$947$	−7.22353	+	40.9667i	−0.234733	+	1.33124i	−0.843175	+	0.537639i	$0.819316\pi$
$948$	−9.75438	−	48.8058i	−0.316807	−	1.58514i
$949$	−12.8081	−	4.66175i	−0.415767	−	0.151327i
$950$	−12.9133	−	17.5088i	−0.418964	−	0.568060i
$951$	−0.217065	+	0.0323715i	−0.00703881	+	0.00104972i
$952$	−19.8537	+	27.2920i	−0.643462	+	0.884538i
$953$	−10.1945	−	5.88578i	−0.330231	−	0.190659i	0.325712	−	0.945469i	$-0.394396\pi$
$953$	−10.1945	−	5.88578i	−0.330231	−	0.190659i	−0.655944	+	0.754810i	$0.727729\pi$
$954$	−41.3070	−	30.7060i	−1.33736	−	0.994142i
$955$		−	4.27439i		−	0.138316i
$956$	1.97742	+	2.13392i	0.0639545	+	0.0690159i
$957$	−49.4704	+	26.8403i	−1.59915	+	0.867623i
$958$	−5.35870	−	2.34004i	−0.173132	−	0.0756033i
$959$	14.8110	−	6.82345i	0.478272	−	0.220341i
$960$	−12.1699	+	1.48188i	−0.392781	+	0.0478275i
$961$	−53.3883	−	44.7981i	−1.72220	−	1.44510i
$962$	12.1092	+	24.3831i	0.390417	+	0.786143i
$963$	2.25266	+	18.4413i	0.0725908	+	0.594263i
$964$	31.2140	−	41.1529i	1.00533	−	1.32545i
$965$	1.26671	+	0.223354i	0.0407767	+	0.00719004i
$966$	−16.7246	+	19.6707i	−0.538105	+	0.632894i
$967$	−2.67139	+	7.33958i	−0.0859061	+	0.236025i	−0.975206	−	0.221300i	$-0.928970\pi$
$967$	−2.67139	+	7.33958i	−0.0859061	+	0.236025i	0.889300	+	0.457325i	$0.151192\pi$
$968$	9.74248	−	5.45162i	0.313135	−	0.175222i
$969$	−5.68969	+	27.9212i	−0.182779	+	0.896959i
$970$	−6.53607	+	6.86596i	−0.209861	+	0.220453i
$971$	−6.55663	−	11.3564i	−0.210412	−	0.364444i	0.741431	−	0.671029i	$-0.234147\pi$
$971$	−6.55663	−	11.3564i	−0.210412	−	0.364444i	−0.951844	+	0.306584i	$0.900814\pi$
$972$	13.0619	−	28.3088i	0.418962	−	0.908004i
$973$	−7.60646	−	28.9209i	−0.243852	−	0.927162i
$974$	−32.0197	−	7.74044i	−1.02598	−	0.248020i
$975$	−21.4480	−	18.9875i	−0.686885	−	0.608086i
$976$	−0.176939	+	2.32084i	−0.00566369	+	0.0742882i
$977$	−34.3034	−	40.8812i	−1.09746	−	1.30791i	−0.947692	−	0.319185i	$-0.896591\pi$
$977$	−34.3034	−	40.8812i	−1.09746	−	1.30791i	−0.149771	−	0.988721i	$-0.547854\pi$
$978$	−12.4542	−	17.8579i	−0.398242	−	0.571031i
$979$	2.01544	+	0.355377i	0.0644138	+	0.0113579i
$980$	−7.57636	+	9.79959i	−0.242018	+	0.313036i
$981$	−11.9688	+	9.00743i	−0.382133	+	0.287585i
$982$	−25.4772	−	1.59840i	−0.813009	−	0.0510069i
$983$	2.27529	−	12.9038i	0.0725704	−	0.411567i	−0.926783	−	0.375598i	$-0.877437\pi$
$983$	2.27529	−	12.9038i	0.0725704	−	0.411567i	0.999353	−	0.0359687i	$-0.0114517\pi$
$984$	0.925275	−	4.24809i	0.0294967	−	0.135424i
$985$	16.9701	+	6.17660i	0.540711	+	0.196803i
$986$	49.1272	+	21.4529i	1.56453	+	0.683198i
$987$	51.2992	−	12.0489i	1.63287	−	0.383520i
$988$	27.3345	+	8.45093i	0.869627	+	0.268860i
$989$	−1.37398	−	0.793271i	−0.0436902	−	0.0252245i
$990$	1.67449	−	14.4157i	0.0532187	−	0.458161i
$991$	−17.6634	+	10.1980i	−0.561096	+	0.323949i	−0.753585	−	0.657350i	$-0.771677\pi$
$991$	−17.6634	+	10.1980i	−0.561096	+	0.323949i	0.192489	+	0.981299i	$0.438344\pi$
$992$	50.1433	+	26.6052i	1.59205	+	0.844717i
$993$	−42.6925	+	6.36685i	−1.35481	+	0.202046i
$994$	−27.0523	+	33.5810i	−0.858046	+	1.06512i
$995$	1.08020	+	6.12612i	0.0342446	+	0.194211i
$996$	7.49087	−	22.1337i	0.237357	−	0.701334i
$997$	8.78546	−	3.19765i	0.278238	−	0.101271i	−0.199132	−	0.979973i	$-0.563812\pi$
$997$	8.78546	−	3.19765i	0.278238	−	0.101271i	0.477370	+	0.878702i	$0.341590\pi$
$998$	0.288824	−	4.60362i	0.00914256	−	0.145725i
$999$	−10.9595	−	23.0324i	−0.346744	−	0.728714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bs.a.11.13	✓	840
4.3	odd	2	inner	756.2.bs.a.11.29	yes	840
7.2	even	3		756.2.ci.a.443.107	yes	840
27.5	odd	18		756.2.ci.a.599.64	yes	840
28.23	odd	6		756.2.ci.a.443.64	yes	840
108.59	even	18		756.2.ci.a.599.107	yes	840
189.86	odd	18	inner	756.2.bs.a.275.29	yes	840
756.275	even	18	inner	756.2.bs.a.275.13	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.11.13	✓	840	1.1	even	1	trivial
756.2.bs.a.11.29	yes	840	4.3	odd	2	inner
756.2.bs.a.275.13	yes	840	756.275	even	18	inner
756.2.bs.a.275.29	yes	840	189.86	odd	18	inner
756.2.ci.a.443.64	yes	840	28.23	odd	6
756.2.ci.a.443.107	yes	840	7.2	even	3
756.2.ci.a.599.64	yes	840	27.5	odd	18
756.2.ci.a.599.107	yes	840	108.59	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.35660 + 0.399529i) q^{2} +(0.345844 - 1.69717i) q^{3} +(1.68075 - 1.08401i) q^{4} +(0.871331 - 0.153639i) q^{5} +(0.208897 + 2.44057i) q^{6} +(0.218427 + 2.63672i) q^{7} +(-1.84702 + 2.14208i) q^{8} +(-2.76078 - 1.17391i) q^{9} +O(q^{10})\)	\(q+(-1.35660 + 0.399529i) q^{2} +(0.345844 - 1.69717i) q^{3} +(1.68075 - 1.08401i) q^{4} +(0.871331 - 0.153639i) q^{5} +(0.208897 + 2.44057i) q^{6} +(0.218427 + 2.63672i) q^{7} +(-1.84702 + 2.14208i) q^{8} +(-2.76078 - 1.17391i) q^{9} +(-1.12067 + 0.556550i) q^{10} +(0.671349 - 3.80741i) q^{11} +(-1.25847 - 3.22742i) q^{12} +(-3.00415 + 2.52078i) q^{13} +(-1.34977 - 3.48972i) q^{14} +(0.0405923 - 1.53193i) q^{15} +(1.64986 - 3.64389i) q^{16} -4.50995i q^{17} +(4.21431 + 0.489521i) q^{18} -3.64785i q^{19} +(1.29795 - 1.20276i) q^{20} +(4.55051 + 0.541185i) q^{21} +(0.610417 + 5.43338i) q^{22} +(3.05195 - 2.56089i) q^{23} +(2.99669 + 3.87554i) q^{24} +(-3.96285 + 1.44236i) q^{25} +(3.06832 - 4.61995i) q^{26} +(-2.94713 + 4.27953i) q^{27} +(3.22534 + 4.19490i) q^{28} +(5.40259 - 6.43855i) q^{29} +(0.556985 + 2.09445i) q^{30} +(3.43204 - 9.42945i) q^{31} +(-0.782364 + 5.60249i) q^{32} +(-6.22965 - 2.45616i) q^{33} +(1.80186 + 6.11822i) q^{34} +(0.595425 + 2.26390i) q^{35} +(-5.91272 + 1.01965i) q^{36} +(-2.45441 + 4.25116i) q^{37} +(1.45742 + 4.94869i) q^{38} +(3.23923 + 5.97035i) q^{39} +(-1.28026 + 2.15023i) q^{40} +(-0.570454 - 0.679841i) q^{41} +(-6.38946 + 1.08389i) q^{42} +(-0.136201 - 0.374208i) q^{43} +(-2.99889 - 7.12706i) q^{44} +(-2.58592 - 0.598702i) q^{45} +(-3.11714 + 4.69346i) q^{46} +(10.8056 - 3.93290i) q^{47} +(-5.61372 - 4.06031i) q^{48} +(-6.90458 + 1.15186i) q^{49} +(4.79976 - 3.53999i) q^{50} +(-7.65416 - 1.55974i) q^{51} +(-2.31669 + 7.49332i) q^{52} +(-10.5062 - 6.06576i) q^{53} +(2.28829 - 6.98310i) q^{54} -3.42066i q^{55} +(-6.05150 - 4.40220i) q^{56} +(-6.19103 - 1.26159i) q^{57} +(-4.75679 + 10.8931i) q^{58} +(-6.55875 + 5.50344i) q^{59} +(-1.59240 - 2.61880i) q^{60} +(-0.546801 + 0.199019i) q^{61} +(-0.888579 + 14.1632i) q^{62} +(2.49225 - 7.53583i) q^{63} +(-1.17700 - 7.91294i) q^{64} +(-2.23032 + 2.65799i) q^{65} +(9.43248 + 0.843117i) q^{66} +(6.47342 - 1.14144i) q^{67} +(-4.88882 - 7.58011i) q^{68} +(-3.29077 - 6.06535i) q^{69} +(-1.71225 - 2.83332i) q^{70} +(-5.76242 - 9.98080i) q^{71} +(7.61385 - 3.74557i) q^{72} +(1.73780 + 3.00996i) q^{73} +(1.63120 - 6.74774i) q^{74} +(1.07740 + 7.22447i) q^{75} +(-3.95429 - 6.13114i) q^{76} +(10.1857 + 0.938520i) q^{77} +(-6.77969 - 6.80524i) q^{78} +(14.1494 + 2.49492i) q^{79} +(0.877728 - 3.42852i) q^{80} +(6.24386 + 6.48184i) q^{81} +(1.04550 + 0.694362i) q^{82} +(5.16732 + 4.33590i) q^{83} +(8.23493 - 4.02318i) q^{84} +(-0.692905 - 3.92966i) q^{85} +(0.334278 + 0.453237i) q^{86} +(-9.05888 - 11.3959i) q^{87} +(6.91577 + 8.47046i) q^{88} +0.529347i q^{89} +(3.74726 - 0.220947i) q^{90} +(-7.30278 - 7.37049i) q^{91} +(2.35355 - 7.61256i) q^{92} +(-14.8165 - 9.08588i) q^{93} +(-13.0876 + 9.65253i) q^{94} +(-0.560453 - 3.17849i) q^{95} +(9.23781 + 3.26539i) q^{96} +(7.11912 - 2.59115i) q^{97} +(8.90658 - 4.32120i) q^{98} +(-6.32302 + 9.72333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Introduction

L-functions

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