LMFDB - Embedded newform 114.2.i.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	114.85
Dual form			114.2.i.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.20574 - 1.16679i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.43969 - 4.22567i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.20574 - 1.16679i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.43969 - 4.22567i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.592396 + 3.35965i) q^{10} +(1.70574 + 2.95442i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.08125 + 1.74638i) q^{13} +(-4.58512 - 1.66885i) q^{14} +(-3.20574 + 1.16679i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.205737 + 1.16679i) q^{17} -1.00000 q^{18} +(-2.52094 + 3.55596i) q^{19} +3.41147 q^{20} +(-0.847296 - 4.80526i) q^{21} +(2.61334 - 2.19285i) q^{22} +(3.20574 - 1.16679i) q^{23} +(0.939693 + 0.342020i) q^{24} +(5.08512 + 4.26692i) q^{25} +(1.35844 - 2.35289i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.847296 + 4.80526i) q^{28} +(0.655230 - 3.71599i) q^{29} +(1.70574 + 2.95442i) q^{30} +(-3.30793 + 5.72951i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(3.20574 + 1.16679i) q^{33} +(1.11334 - 0.405223i) q^{34} +(-12.7515 + 10.6998i) q^{35} +(0.173648 + 0.984808i) q^{36} +6.75877 q^{37} +(3.93969 + 1.86516i) q^{38} +2.71688 q^{39} +(-0.592396 - 3.35965i) q^{40} +(5.02094 - 4.21307i) q^{41} +(-4.58512 + 1.66885i) q^{42} +(-3.91875 - 1.42631i) q^{43} +(-2.61334 - 2.19285i) q^{44} +(-1.70574 + 2.95442i) q^{45} +(-1.70574 - 2.95442i) q^{46} +(0.496130 - 2.81369i) q^{47} +(0.173648 - 0.984808i) q^{48} +(-8.40420 - 14.5565i) q^{49} +(3.31908 - 5.74881i) q^{50} +(0.907604 + 0.761570i) q^{51} +(-2.55303 - 0.929228i) q^{52} +(-0.592396 + 0.215615i) q^{53} +(-0.766044 + 0.642788i) q^{54} +(-2.02094 - 11.4613i) q^{55} +4.87939 q^{56} +(0.354570 + 4.34445i) q^{57} -3.77332 q^{58} +(2.02094 + 11.4613i) q^{59} +(2.61334 - 2.19285i) q^{60} +(-6.48545 + 2.36051i) q^{61} +(6.21688 + 2.26276i) q^{62} +(-3.73783 - 3.13641i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.63429 - 8.02682i) q^{65} +(0.592396 - 3.35965i) q^{66} +(0.123141 - 0.698367i) q^{67} +(-0.592396 - 1.02606i) q^{68} +(1.70574 - 2.95442i) q^{69} +(12.7515 + 10.6998i) q^{70} +(-7.47818 - 2.72183i) q^{71} +(0.939693 - 0.342020i) q^{72} +(-9.76264 + 8.19183i) q^{73} +(-1.17365 - 6.65609i) q^{74} +6.63816 q^{75} +(1.15270 - 4.20372i) q^{76} +16.6459 q^{77} +(-0.471782 - 2.67561i) q^{78} +(0.228026 - 0.191336i) q^{79} +(-3.20574 + 1.16679i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-5.02094 - 4.21307i) q^{82} +(-7.80200 + 13.5135i) q^{83} +(2.43969 + 4.22567i) q^{84} +(0.701867 - 3.98048i) q^{85} +(-0.724155 + 4.10689i) q^{86} +(-1.88666 - 3.26779i) q^{87} +(-1.70574 + 2.95442i) q^{88} +(5.18866 + 4.35381i) q^{89} +(3.20574 + 1.16679i) q^{90} +(12.4572 - 4.53406i) q^{91} +(-2.61334 + 2.19285i) q^{92} +(1.14883 + 6.51536i) q^{93} -2.85710 q^{94} +(12.2306 - 8.45805i) q^{95} -1.00000 q^{96} +(-1.23736 - 7.01741i) q^{97} +(-12.8760 + 10.8042i) q^{98} +(3.20574 - 1.16679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8	$ 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8} - 3 q^{12} + 15 q^{13} - 6 q^{14} - 9 q^{15} - 9 q^{17} - 6 q^{18} - 12 q^{19} - 3 q^{21} + 9 q^{22} + 9 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{28} - 9 q^{29} - 9 q^{31} + 9 q^{33} - 36 q^{35} + 18 q^{37} + 18 q^{38} + 27 q^{41} - 6 q^{42} - 21 q^{43} - 9 q^{44} + 27 q^{47} - 12 q^{49} + 3 q^{50} + 9 q^{51} - 3 q^{52} - 9 q^{55} + 18 q^{56} + 18 q^{57} - 36 q^{58} + 9 q^{59} + 9 q^{60} - 3 q^{61} + 21 q^{62} - 3 q^{63} - 3 q^{64} - 18 q^{65} - 3 q^{67} + 36 q^{70} + 9 q^{71} - 12 q^{73} - 6 q^{74} + 6 q^{75} + 9 q^{76} + 18 q^{77} + 12 q^{78} - 21 q^{79} - 9 q^{80} - 27 q^{82} - 9 q^{83} + 9 q^{84} + 18 q^{85} - 6 q^{86} - 18 q^{87} + 9 q^{90} + 24 q^{91} - 9 q^{92} + 33 q^{93} - 18 q^{94} + 36 q^{95} - 6 q^{96} - 54 q^{97} - 24 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8 - 3 * q^12 + 15 * q^13 - 6 * q^14 - 9 * q^15 - 9 * q^17 - 6 * q^18 - 12 * q^19 - 3 * q^21 + 9 * q^22 + 9 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^28 - 9 * q^29 - 9 * q^31 + 9 * q^33 - 36 * q^35 + 18 * q^37 + 18 * q^38 + 27 * q^41 - 6 * q^42 - 21 * q^43 - 9 * q^44 + 27 * q^47 - 12 * q^49 + 3 * q^50 + 9 * q^51 - 3 * q^52 - 9 * q^55 + 18 * q^56 + 18 * q^57 - 36 * q^58 + 9 * q^59 + 9 * q^60 - 3 * q^61 + 21 * q^62 - 3 * q^63 - 3 * q^64 - 18 * q^65 - 3 * q^67 + 36 * q^70 + 9 * q^71 - 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 18 * q^77 + 12 * q^78 - 21 * q^79 - 9 * q^80 - 27 * q^82 - 9 * q^83 + 9 * q^84 + 18 * q^85 - 6 * q^86 - 18 * q^87 + 9 * q^90 + 24 * q^91 - 9 * q^92 + 33 * q^93 - 18 * q^94 + 36 * q^95 - 6 * q^96 - 54 * q^97 - 24 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−3.20574	−	1.16679i	−1.43365	−	0.521806i	−0.495674	−	0.868509i	$-0.665079\pi$
$5$	−3.20574	−	1.16679i	−1.43365	−	0.521806i	−0.937975	+	0.346703i	$0.887301\pi$
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.125984	−	0.992032i	$-0.459791\pi$
$7$	2.43969	−	4.22567i	0.922117	−	1.59715i	0.796133	−	0.605121i	$-0.206875\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−0.592396	+	3.35965i	−0.187332	+	1.06241i
$11$	1.70574	+	2.95442i	0.514299	+	0.890792i	0.999862	+	0.0165906i	$0.00528120\pi$
$11$	1.70574	+	2.95442i	0.514299	+	0.890792i	−0.485563	+	0.874202i	$0.661385\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	0.884038	−	0.467415i	$-0.154815\pi$
$13$	2.08125	+	1.74638i	0.577235	+	0.484358i	−0.306803	+	0.951773i	$0.599259\pi$
$14$	−4.58512	−	1.66885i	−1.22543	−	0.446018i
$15$	−3.20574	+	1.16679i	−0.827718	+	0.301265i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.205737	+	1.16679i	0.0498986	+	0.282989i	0.999539	−	0.0303521i	$-0.00966285\pi$
$17$	0.205737	+	1.16679i	0.0498986	+	0.282989i	−0.949641	+	0.313341i	$0.898552\pi$
$18$	−1.00000			−0.235702
$19$	−2.52094	+	3.55596i	−0.578344	+	0.815793i
$19$	−2.52094	+	3.55596i	−0.578344	+	0.815793i
$20$	3.41147			0.762829
$21$	−0.847296	−	4.80526i	−0.184895	−	1.04859i
$22$	2.61334	−	2.19285i	0.557166	−	0.467518i
$23$	3.20574	−	1.16679i	0.668442	−	0.243293i	0.0145653	−	0.999894i	$-0.495364\pi$
$23$	3.20574	−	1.16679i	0.668442	−	0.243293i	0.653877	+	0.756601i	$0.273141\pi$
$24$	0.939693	+	0.342020i	0.191814	+	0.0698146i
$25$	5.08512	+	4.26692i	1.01702	+	0.853385i
$26$	1.35844	−	2.35289i	0.266412	−	0.461439i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−0.847296	+	4.80526i	−0.160124	+	0.908108i
$29$	0.655230	−	3.71599i	0.121673	−	0.690043i	−0.861555	−	0.507664i	$-0.830509\pi$
$29$	0.655230	−	3.71599i	0.121673	−	0.690043i	0.983228	−	0.182379i	$-0.0583797\pi$
$30$	1.70574	+	2.95442i	0.311424	+	0.539401i
$31$	−3.30793	+	5.72951i	−0.594122	+	1.02905i	0.399548	+	0.916712i	$0.369167\pi$
$31$	−3.30793	+	5.72951i	−0.594122	+	1.02905i	−0.993670	+	0.112338i	$0.964166\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	3.20574	+	1.16679i	0.558047	+	0.203113i
$34$	1.11334	−	0.405223i	0.190936	−	0.0694952i
$35$	−12.7515	+	10.6998i	−2.15540	+	1.80859i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	6.75877			1.11114			0.555568	−	0.831471i	$-0.312501\pi$
$37$	6.75877			1.11114			0.555568	+	0.831471i	$0.312501\pi$
$38$	3.93969	+	1.86516i	0.639103	+	0.302569i
$39$	2.71688			0.435049
$40$	−0.592396	−	3.35965i	−0.0936661	−	0.531207i
$41$	5.02094	−	4.21307i	0.784140	−	0.657971i	−0.160148	−	0.987093i	$-0.551197\pi$
$41$	5.02094	−	4.21307i	0.784140	−	0.657971i	0.944288	+	0.329122i	$0.106753\pi$
$42$	−4.58512	+	1.66885i	−0.707500	+	0.257509i
$43$	−3.91875	−	1.42631i	−0.597603	−	0.217510i	0.0254669	−	0.999676i	$-0.491893\pi$
$43$	−3.91875	−	1.42631i	−0.597603	−	0.217510i	−0.623070	+	0.782166i	$0.714115\pi$
$44$	−2.61334	−	2.19285i	−0.393976	−	0.330585i
$45$	−1.70574	+	2.95442i	−0.254276	+	0.440419i
$46$	−1.70574	−	2.95442i	−0.251497	−	0.435606i
$47$	0.496130	−	2.81369i	0.0723679	−	0.410419i	−0.927006	−	0.375046i	$-0.877627\pi$
$47$	0.496130	−	2.81369i	0.0723679	−	0.410419i	0.999374	−	0.0353731i	$-0.0112619\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	−8.40420	−	14.5565i	−1.20060	−	2.07950i
$50$	3.31908	−	5.74881i	0.469388	−	0.813005i
$51$	0.907604	+	0.761570i	0.127090	+	0.106641i
$52$	−2.55303	−	0.929228i	−0.354042	−	0.128861i
$53$	−0.592396	+	0.215615i	−0.0813719	+	0.0296169i	−0.382385	−	0.924003i	$-0.624897\pi$
$53$	−0.592396	+	0.215615i	−0.0813719	+	0.0296169i	0.301013	+	0.953620i	$0.402675\pi$
$54$	−0.766044	+	0.642788i	−0.104245	+	0.0874723i
$55$	−2.02094	−	11.4613i	−0.272504	−	1.54545i
$56$	4.87939			0.652035
$57$	0.354570	+	4.34445i	0.0469640	+	0.575437i
$58$	−3.77332			−0.495461
$59$	2.02094	+	11.4613i	0.263105	+	1.49214i	0.774379	+	0.632722i	$0.218063\pi$
$59$	2.02094	+	11.4613i	0.263105	+	1.49214i	−0.511274	+	0.859418i	$0.670826\pi$
$60$	2.61334	−	2.19285i	0.337381	−	0.283096i
$61$	−6.48545	+	2.36051i	−0.830377	+	0.302233i	−0.722014	−	0.691879i	$-0.756783\pi$
$61$	−6.48545	+	2.36051i	−0.830377	+	0.302233i	−0.108363	+	0.994111i	$0.534561\pi$
$62$	6.21688	+	2.26276i	0.789545	+	0.287371i
$63$	−3.73783	−	3.13641i	−0.470922	−	0.395150i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.63429	−	8.02682i	−0.574812	−	0.995604i
$66$	0.592396	−	3.35965i	0.0729189	−	0.413544i
$67$	0.123141	−	0.698367i	0.0150441	−	0.0853191i	−0.976361	−	0.216145i	$-0.930652\pi$
$67$	0.123141	−	0.698367i	0.0150441	−	0.0853191i	0.991405	+	0.130826i	$0.0417628\pi$
$68$	−0.592396	−	1.02606i	−0.0718386	−	0.124428i
$69$	1.70574	−	2.95442i	0.205347	−	0.355671i
$70$	12.7515	+	10.6998i	1.52410	+	1.27887i
$71$	−7.47818	−	2.72183i	−0.887496	−	0.323022i	−0.142265	−	0.989829i	$-0.545439\pi$
$71$	−7.47818	−	2.72183i	−0.887496	−	0.323022i	−0.745231	+	0.666806i	$0.767661\pi$
$72$	0.939693	−	0.342020i	0.110744	−	0.0403075i
$73$	−9.76264	+	8.19183i	−1.14263	+	0.958781i	−0.999522	−	0.0309259i	$-0.990154\pi$
$73$	−9.76264	+	8.19183i	−1.14263	+	0.958781i	−0.143109	+	0.989707i	$0.545710\pi$
$74$	−1.17365	−	6.65609i	−0.136434	−	0.773755i
$75$	6.63816			0.766508
$76$	1.15270	−	4.20372i	0.132224	−	0.482200i
$77$	16.6459			1.89698
$78$	−0.471782	−	2.67561i	−0.0534187	−	0.302953i
$79$	0.228026	−	0.191336i	0.0256549	−	0.0215270i	−0.629870	−	0.776701i	$-0.716892\pi$
$79$	0.228026	−	0.191336i	0.0256549	−	0.0215270i	0.655525	+	0.755174i	$0.272447\pi$
$80$	−3.20574	+	1.16679i	−0.358412	+	0.130451i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−5.02094	−	4.21307i	−0.554471	−	0.465256i
$83$	−7.80200	+	13.5135i	−0.856381	+	1.48330i	0.0189766	+	0.999820i	$0.493959\pi$
$83$	−7.80200	+	13.5135i	−0.856381	+	1.48330i	−0.875358	+	0.483476i	$0.839374\pi$
$84$	2.43969	+	4.22567i	0.266192	+	0.461059i
$85$	0.701867	−	3.98048i	0.0761281	−	0.431744i
$86$	−0.724155	+	4.10689i	−0.0780877	+	0.442857i
$87$	−1.88666	−	3.26779i	−0.202271	−	0.350344i
$88$	−1.70574	+	2.95442i	−0.181832	+	0.314943i
$89$	5.18866	+	4.35381i	0.549997	+	0.461502i	0.874940	−	0.484231i	$-0.160901\pi$
$89$	5.18866	+	4.35381i	0.549997	+	0.461502i	−0.324943	+	0.945734i	$0.605345\pi$
$90$	3.20574	+	1.16679i	0.337914	+	0.122991i
$91$	12.4572	−	4.53406i	1.30587	−	0.475299i
$92$	−2.61334	+	2.19285i	−0.272460	+	0.228621i
$93$	1.14883	+	6.51536i	0.119128	+	0.675611i
$94$	−2.85710			−0.294687
$95$	12.2306	−	8.45805i	1.25483	−	0.867777i
$96$	−1.00000			−0.102062
$97$	−1.23736	−	7.01741i	−0.125635	−	0.712510i	−0.980929	−	0.194367i	$-0.937735\pi$
$97$	−1.23736	−	7.01741i	−0.125635	−	0.712510i	0.855294	−	0.518143i	$-0.173376\pi$
$98$	−12.8760	+	10.8042i	−1.30067	+	1.09139i
$99$	3.20574	−	1.16679i	0.322189	−	0.117267i
$100$	−6.23783	−	2.27038i	−0.623783	−	0.227038i
$101$	−3.55896	−	2.98632i	−0.354130	−	0.297150i	0.448316	−	0.893875i	$-0.352024\pi$
$101$	−3.55896	−	2.98632i	−0.354130	−	0.297150i	−0.802446	+	0.596725i	$0.796468\pi$
$102$	0.592396	−	1.02606i	0.0586560	−	0.101595i
$103$	6.19119	+	10.7235i	0.610036	+	1.05661i	0.991234	+	0.132120i	$0.0421784\pi$
$103$	6.19119	+	10.7235i	0.610036	+	1.05661i	−0.381198	+	0.924494i	$0.624488\pi$
$104$	−0.471782	+	2.67561i	−0.0462620	+	0.262365i
$105$	−2.89053	+	16.3930i	−0.282087	+	1.59979i
$106$	0.315207	+	0.545955i	0.0306157	+	0.0530279i
$107$	−1.94949	+	3.37662i	−0.188465	+	0.326430i	−0.944739	−	0.327825i	$-0.893684\pi$
$107$	−1.94949	+	3.37662i	−0.188465	+	0.326430i	0.756274	+	0.654255i	$0.227018\pi$
$108$	0.766044	+	0.642788i	0.0737127	+	0.0618523i
$109$	10.8969	+	3.96616i	1.04374	+	0.379889i	0.806295	−	0.591513i	$-0.201469\pi$
$109$	10.8969	+	3.96616i	1.04374	+	0.379889i	0.237441	+	0.971402i	$0.423691\pi$
$110$	−10.9363	+	3.98048i	−1.04273	+	0.379524i
$111$	5.17752	−	4.34445i	0.491428	−	0.412357i
$112$	−0.847296	−	4.80526i	−0.0800620	−	0.454054i
$113$	1.94087			0.182582			0.0912911	−	0.995824i	$-0.470901\pi$
$113$	1.94087			0.182582			0.0912911	+	0.995824i	$0.470901\pi$
$114$	4.21688	−	1.10359i	0.394947	−	0.103361i
$115$	−11.6382			−1.08526
$116$	0.655230	+	3.71599i	0.0608366	+	0.345021i
$117$	2.08125	−	1.74638i	0.192412	−	0.161453i
$118$	10.9363	−	3.98048i	1.00677	−	0.366433i
$119$	5.43242	+	1.97724i	0.497989	+	0.181253i
$120$	−2.61334	−	2.19285i	−0.238564	−	0.200179i
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$	3.45084	+	5.97702i	0.312424	+	0.541134i
$123$	1.13816	−	6.45480i	0.102624	−	0.582010i
$124$	1.14883	−	6.51536i	0.103168	−	0.585096i
$125$	−2.79426	−	4.83981i	−0.249926	−	0.432885i
$126$	−2.43969	+	4.22567i	−0.217345	+	0.376453i
$127$	−4.66044	−	3.91058i	−0.413548	−	0.347008i	0.412155	−	0.911114i	$-0.364776\pi$
$127$	−4.66044	−	3.91058i	−0.413548	−	0.347008i	−0.825702	+	0.564106i	$0.809221\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−3.91875	+	1.42631i	−0.345027	+	0.125579i
$130$	−7.10014	+	5.95772i	−0.622723	+	0.522527i
$131$	−3.23055	−	18.3214i	−0.282255	−	1.60075i	−0.714930	−	0.699196i	$-0.753542\pi$
$131$	−3.23055	−	18.3214i	−0.282255	−	1.60075i	0.432676	−	0.901550i	$-0.357570\pi$
$132$	−3.41147			−0.296931
$133$	8.87598	+	19.3281i	0.769645	+	1.67596i
$134$	−0.709141			−0.0612604
$135$	0.592396	+	3.35965i	0.0509854	+	0.289152i
$136$	−0.907604	+	0.761570i	−0.0778264	+	0.0653041i
$137$	−4.27244	+	1.55504i	−0.365019	+	0.132856i	−0.518017	−	0.855370i	$-0.673330\pi$
$137$	−4.27244	+	1.55504i	−0.365019	+	0.132856i	0.152998	+	0.988227i	$0.451107\pi$
$138$	−3.20574	−	1.16679i	−0.272890	−	0.0993240i
$139$	−2.30928	−	1.93771i	−0.195870	−	0.164355i	0.539578	−	0.841936i	$-0.318584\pi$
$139$	−2.30928	−	1.93771i	−0.195870	−	0.164355i	−0.735448	+	0.677581i	$0.763028\pi$
$140$	8.32295	−	14.4158i	0.703418	−	1.21835i
$141$	−1.42855	−	2.47432i	−0.120305	−	0.208375i
$142$	−1.38191	+	7.83721i	−0.115967	+	0.657684i
$143$	−1.60947	+	9.12776i	−0.134591	+	0.763302i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−6.43629	+	11.1480i	−0.534505	+	0.925789i
$146$	9.76264	+	8.19183i	0.807962	+	0.677961i
$147$	−15.7947	−	5.74881i	−1.30273	−	0.474154i
$148$	−6.35117	+	2.31164i	−0.522063	+	0.190015i
$149$	0.907604	−	0.761570i	0.0743538	−	0.0623902i	−0.604853	−	0.796337i	$-0.706768\pi$
$149$	0.907604	−	0.761570i	0.0743538	−	0.0623902i	0.679207	+	0.733947i	$0.262324\pi$
$150$	−1.15270	−	6.53731i	−0.0941179	−	0.533769i
$151$	−3.63816			−0.296069			−0.148034	−	0.988982i	$-0.547295\pi$
$151$	−3.63816			−0.296069			−0.148034	+	0.988982i	$0.547295\pi$
$152$	−4.34002	−	0.405223i	−0.352022	−	0.0328679i
$153$	1.18479			0.0957848
$154$	−2.89053	−	16.3930i	−0.232926	−	1.32099i
$155$	17.2895	−	14.5076i	1.38873	−	1.16528i
$156$	−2.55303	+	0.929228i	−0.204406	+	0.0743978i
$157$	−5.89306	−	2.14490i	−0.470317	−	0.171181i	0.0959789	−	0.995383i	$-0.469402\pi$
$157$	−5.89306	−	2.14490i	−0.470317	−	0.171181i	−0.566296	+	0.824202i	$0.691624\pi$
$158$	−0.228026	−	0.191336i	−0.0181408	−	0.0152219i
$159$	−0.315207	+	0.545955i	−0.0249976	+	0.0432971i
$160$	1.70574	+	2.95442i	0.134850	+	0.233568i
$161$	2.89053	−	16.3930i	0.227806	−	1.29195i
$162$	−0.173648	+	0.984808i	−0.0136431	+	0.0773738i
$163$	9.64930	+	16.7131i	0.755792	+	1.30907i	0.944980	+	0.327128i	$0.106081\pi$
$163$	9.64930	+	16.7131i	0.755792	+	1.30907i	−0.189188	+	0.981941i	$0.560586\pi$
$164$	−3.27719	+	5.67626i	−0.255905	+	0.443241i
$165$	−8.91534	−	7.48086i	−0.694059	−	0.582384i
$166$	14.6630	+	5.33688i	1.13807	+	0.414223i
$167$	7.25624	−	2.64106i	0.561505	−	0.204371i	−0.0456458	−	0.998958i	$-0.514535\pi$
$167$	7.25624	−	2.64106i	0.561505	−	0.204371i	0.607151	+	0.794587i	$0.292312\pi$
$168$	3.73783	−	3.13641i	0.288380	−	0.241979i
$169$	−0.975652	−	5.53320i	−0.0750501	−	0.425631i
$170$	−4.04189			−0.309999
$171$	3.06418	+	3.10013i	0.234324	+	0.237073i
$172$	4.17024			0.317978
$173$	−2.51707	−	14.2750i	−0.191370	−	1.08531i	−0.917495	−	0.397748i	$-0.869792\pi$
$173$	−2.51707	−	14.2750i	−0.191370	−	1.08531i	0.726125	−	0.687563i	$-0.241319\pi$
$174$	−2.89053	+	2.42544i	−0.219130	+	0.183872i
$175$	30.4368	−	11.0781i	2.30080	−	0.837424i
$176$	3.20574	+	1.16679i	0.241642	+	0.0879503i
$177$	8.91534	+	7.48086i	0.670118	+	0.562296i
$178$	3.38666	−	5.86587i	0.253841	−	0.439665i
$179$	4.91147	+	8.50692i	0.367101	+	0.635837i	0.989111	−	0.147172i	$-0.0470171\pi$
$179$	4.91147	+	8.50692i	0.367101	+	0.635837i	−0.622010	+	0.783009i	$0.713684\pi$
$180$	0.592396	−	3.35965i	0.0441546	−	0.250413i
$181$	3.28446	−	18.6271i	0.244132	−	1.38454i	−0.578367	−	0.815777i	$-0.696310\pi$
$181$	3.28446	−	18.6271i	0.244132	−	1.38454i	0.822499	−	0.568766i	$-0.192579\pi$
$182$	−6.62836	−	11.4806i	−0.491326	−	0.851002i
$183$	−3.45084	+	5.97702i	−0.255093	+	0.441834i
$184$	2.61334	+	2.19285i	0.192658	+	0.161659i
$185$	−21.6668	−	7.88609i	−1.59298	−	0.579797i
$186$	6.21688	−	2.26276i	0.455844	−	0.165914i
$187$	−3.09627	+	2.59808i	−0.226421	+	0.189990i
$188$	0.496130	+	2.81369i	0.0361840	+	0.205209i
$189$	−4.87939			−0.354923
$190$	−10.4534	−	10.5760i	−0.758367	−	0.767265i
$191$	−10.0915			−0.730197			−0.365098	−	0.930969i	$-0.618965\pi$
$191$	−10.0915			−0.730197			−0.365098	+	0.930969i	$0.618965\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	1.93376	−	1.62262i	0.139195	−	0.116799i	−0.570532	−	0.821276i	$-0.693263\pi$
$193$	1.93376	−	1.62262i	0.139195	−	0.116799i	0.709727	+	0.704477i	$0.248818\pi$
$194$	−6.69594	+	2.43712i	−0.480740	+	0.174975i
$195$	−8.70961	−	3.17004i	−0.623708	−	0.227011i
$196$	12.8760	+	10.8042i	0.919713	+	0.771731i
$197$	−7.42855	+	12.8666i	−0.529262	+	0.916709i	0.470155	+	0.882584i	$0.344198\pi$
$197$	−7.42855	+	12.8666i	−0.529262	+	0.916709i	−0.999418	+	0.0341253i	$0.989135\pi$
$198$	−1.70574	−	2.95442i	−0.121221	−	0.209962i
$199$	1.40121	−	7.94664i	0.0993289	−	0.563322i	−0.894006	−	0.448056i	$-0.852117\pi$
$199$	1.40121	−	7.94664i	0.0993289	−	0.563322i	0.993335	−	0.115267i	$-0.0367723\pi$
$200$	−1.15270	+	6.53731i	−0.0815085	+	0.462257i
$201$	−0.354570	−	0.614134i	−0.0250095	−	0.0433177i
$202$	−2.32295	+	4.02346i	−0.163442	+	0.283090i
$203$	−14.1040	−	11.8347i	−0.989907	−	0.830631i
$204$	−1.11334	−	0.405223i	−0.0779494	−	0.0283713i
$205$	−21.0116	+	7.64760i	−1.46751	+	0.534132i
$206$	9.48545	−	7.95924i	0.660883	−	0.554546i
$207$	−0.592396	−	3.35965i	−0.0411744	−	0.233512i
$208$	2.71688			0.188382
$209$	−14.8059	−	1.38241i	−1.02414	−	0.0956231i
$210$	16.6459			1.14868
$211$	1.37939	+	7.82288i	0.0949608	+	0.538549i	0.994759	+	0.102244i	$0.0326022\pi$
$211$	1.37939	+	7.82288i	0.0949608	+	0.538549i	−0.899799	+	0.436306i	$0.856287\pi$
$212$	0.482926	−	0.405223i	0.0331675	−	0.0278308i
$213$	−7.47818	+	2.72183i	−0.512396	+	0.186497i
$214$	3.66385	+	1.33353i	0.250455	+	0.0911583i
$215$	10.8983	+	9.14473i	0.743256	+	0.623666i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	16.1407	+	27.9565i	1.09570	+	1.89781i
$218$	2.01367	−	11.4201i	0.136383	−	0.773466i
$219$	−2.21301	+	12.5506i	−0.149541	+	0.848092i
$220$	5.81908	+	10.0789i	0.392322	+	0.679522i
$221$	−1.60947	+	2.78768i	−0.108265	+	0.187520i
$222$	−5.17752	−	4.34445i	−0.347492	−	0.291581i
$223$	−11.2464	−	4.09337i	−0.753118	−	0.274112i	−0.0632006	−	0.998001i	$-0.520131\pi$
$223$	−11.2464	−	4.09337i	−0.753118	−	0.274112i	−0.689917	+	0.723888i	$0.742353\pi$
$224$	−4.58512	+	1.66885i	−0.306356	+	0.111505i
$225$	5.08512	−	4.26692i	0.339008	−	0.284462i
$226$	−0.337029	−	1.91139i	−0.0224189	−	0.127144i
$227$	26.5945			1.76514			0.882570	−	0.470181i	$-0.155811\pi$
$227$	26.5945			1.76514			0.882570	+	0.470181i	$0.155811\pi$
$228$	−1.81908	−	3.96118i	−0.120471	−	0.262336i
$229$	−19.9026			−1.31520			−0.657601	−	0.753367i	$-0.728429\pi$
$229$	−19.9026			−1.31520			−0.657601	+	0.753367i	$0.728429\pi$
$230$	2.02094	+	11.4613i	0.133257	+	0.755739i
$231$	12.7515	−	10.6998i	0.838987	−	0.703994i
$232$	3.54576	−	1.29055i	0.232791	−	0.0847288i
$233$	4.05051	+	1.47426i	0.265358	+	0.0965822i	0.471273	−	0.881988i	$-0.343795\pi$
$233$	4.05051	+	1.47426i	0.265358	+	0.0965822i	−0.205915	+	0.978570i	$0.566017\pi$
$234$	−2.08125	−	1.74638i	−0.136056	−	0.114164i
$235$	−4.87346	+	8.44107i	−0.317909	+	0.550635i
$236$	−5.81908	−	10.0789i	−0.378790	−	0.656083i
$237$	0.0516892	−	0.293144i	0.00335758	−	0.0190418i
$238$	1.00387	−	5.69323i	0.0650713	−	0.369037i
$239$	−0.142903	−	0.247516i	−0.00924366	−	0.0160105i	0.861367	−	0.507984i	$-0.169609\pi$
$239$	−0.142903	−	0.247516i	−0.00924366	−	0.0160105i	−0.870610	+	0.491973i	$0.836276\pi$
$240$	−1.70574	+	2.95442i	−0.110105	+	0.190707i
$241$	7.32816	+	6.14906i	0.472048	+	0.396096i	0.847541	−	0.530730i	$-0.178082\pi$
$241$	7.32816	+	6.14906i	0.472048	+	0.396096i	−0.375493	+	0.926825i	$0.622526\pi$
$242$	0.599670	+	0.218262i	0.0385483	+	0.0140304i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	5.28699	−	4.43631i	0.338465	−	0.284006i
$245$	9.95723	+	56.4703i	0.636144	+	3.60775i
$246$	−6.55438			−0.417892
$247$	−11.4568	+	2.99832i	−0.728977	+	0.190779i
$248$	−6.61587			−0.420108
$249$	2.70961	+	15.3669i	0.171714	+	0.973841i
$250$	−4.28106	+	3.59224i	−0.270758	+	0.227193i
$251$	−27.8974	+	10.1538i	−1.76087	+	0.640903i	−0.999968	−	0.00796619i	$-0.997464\pi$
$251$	−27.8974	+	10.1538i	−1.76087	+	0.640903i	−0.760900	+	0.648870i	$0.775242\pi$
$252$	4.58512	+	1.66885i	0.288836	+	0.105128i
$253$	8.91534	+	7.48086i	0.560503	+	0.470318i
$254$	−3.04189	+	5.26871i	−0.190865	+	0.330588i
$255$	−2.02094	−	3.50038i	−0.126556	−	0.219202i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.74304	−	15.5566i	0.171106	−	0.970391i	−0.771437	−	0.636306i	$-0.780462\pi$
$257$	2.74304	−	15.5566i	0.171106	−	0.970391i	0.942543	−	0.334085i	$-0.108427\pi$
$258$	2.08512	+	3.61154i	0.129814	+	0.224845i
$259$	16.4893	−	28.5603i	1.02460	−	1.77465i
$260$	7.10014	+	5.95772i	0.440332	+	0.369482i
$261$	−3.54576	−	1.29055i	−0.219477	−	0.0798831i
$262$	−17.4820	+	6.36295i	−1.08004	+	0.393104i
$263$	8.32295	−	6.98378i	0.513215	−	0.430638i	−0.349044	−	0.937106i	$-0.613494\pi$
$263$	8.32295	−	6.98378i	0.513215	−	0.430638i	0.862259	+	0.506468i	$0.169049\pi$
$264$	0.592396	+	3.35965i	0.0364595	+	0.206772i
$265$	2.15064			0.132113
$266$	17.4932	−	12.0974i	1.07258	−	0.741741i
$267$	6.77332			0.414520
$268$	0.123141	+	0.698367i	0.00752203	+	0.0426596i
$269$	−13.2476	+	11.1161i	−0.807722	+	0.677759i	−0.950063	−	0.312058i	$-0.898982\pi$
$269$	−13.2476	+	11.1161i	−0.807722	+	0.677759i	0.142341	+	0.989818i	$0.454537\pi$
$270$	3.20574	−	1.16679i	0.195095	−	0.0710088i
$271$	−1.35844	−	0.494432i	−0.0825194	−	0.0300346i	0.300431	−	0.953804i	$-0.402870\pi$
$271$	−1.35844	−	0.494432i	−0.0825194	−	0.0300346i	−0.382950	+	0.923769i	$0.625092\pi$
$272$	0.907604	+	0.761570i	0.0550316	+	0.0461770i
$273$	6.62836	−	11.4806i	0.401166	−	0.694840i
$274$	2.27332	+	3.93750i	0.137336	+	0.237873i
$275$	−3.93242	+	22.3019i	−0.237134	+	1.34485i
$276$	−0.592396	+	3.35965i	−0.0356581	+	0.202227i
$277$	−10.5954	−	18.3518i	−0.636615	−	1.10265i	−0.986170	−	0.165734i	$-0.947001\pi$
$277$	−10.5954	−	18.3518i	−0.636615	−	1.10265i	0.349555	−	0.936916i	$-0.386333\pi$
$278$	−1.50727	+	2.61068i	−0.0904003	+	0.156578i
$279$	5.06805	+	4.25260i	0.303416	+	0.254596i
$280$	−15.6420	−	5.69323i	−0.934790	−	0.340236i
$281$	22.8983	−	8.33429i	1.36600	−	0.497182i	0.448093	−	0.893987i	$-0.352103\pi$
$281$	22.8983	−	8.33429i	1.36600	−	0.497182i	0.917903	+	0.396805i	$0.129881\pi$
$282$	−2.18866	+	1.83651i	−0.130333	+	0.109362i
$283$	−0.716415	−	4.06299i	−0.0425864	−	0.241520i	0.956083	−	0.293098i	$-0.0946861\pi$
$283$	−0.716415	−	4.06299i	−0.0425864	−	0.241520i	−0.998669	+	0.0515779i	$0.983575\pi$
$284$	7.95811			0.472227
$285$	3.93242	−	14.3409i	0.232936	−	0.849481i
$286$	9.26857			0.548062
$287$	−5.55350	−	31.4955i	−0.327813	−	1.85912i
$288$	−0.766044	+	0.642788i	−0.0451396	+	0.0378766i
$289$	14.6557	−	5.33424i	0.862100	−	0.313779i
$290$	12.0963	+	4.40268i	0.710317	+	0.258534i
$291$	−5.45858	−	4.58029i	−0.319987	−	0.268501i
$292$	6.37211	−	11.0368i	0.372900	−	0.645881i
$293$	−1.39053	−	2.40847i	−0.0812356	−	0.140704i	0.822545	−	0.568700i	$-0.192553\pi$
$293$	−1.39053	−	2.40847i	−0.0812356	−	0.140704i	−0.903781	+	0.427995i	$0.859220\pi$
$294$	−2.91875	+	16.5530i	−0.170225	+	0.965393i
$295$	6.89440	−	39.1001i	0.401407	−	2.27649i
$296$	3.37939	+	5.85327i	0.196423	+	0.340214i
$297$	1.70574	−	2.95442i	0.0989769	−	0.171433i
$298$	−0.907604	−	0.761570i	−0.0525761	−	0.0441166i
$299$	8.70961	+	3.17004i	0.503690	+	0.183328i
$300$	−6.23783	+	2.27038i	−0.360141	+	0.131081i
$301$	−15.5876	+	13.0796i	−0.898457	+	0.753895i
$302$	0.631759	+	3.58288i	0.0363537	+	0.206172i
$303$	−4.64590			−0.266900
$304$	0.354570	+	4.34445i	0.0203360	+	0.249172i
$305$	23.5449			1.34818
$306$	−0.205737	−	1.16679i	−0.0117612	−	0.0667011i
$307$	−19.1689	+	16.0846i	−1.09403	+	0.917998i	−0.997009	−	0.0772850i	$-0.975375\pi$
$307$	−19.1689	+	16.0846i	−1.09403	+	0.917998i	−0.0970179	+	0.995283i	$0.530930\pi$
$308$	−15.6420	+	5.69323i	−0.891287	+	0.324402i
$309$	11.6356	+	4.23502i	0.661928	+	0.240922i
$310$	−17.2895	−	14.5076i	−0.981978	−	0.823978i
$311$	−11.9868	+	20.7617i	−0.679709	+	1.17729i	0.295360	+	0.955386i	$0.404561\pi$
$311$	−11.9868	+	20.7617i	−0.679709	+	1.17729i	−0.975068	+	0.221904i	$0.928773\pi$
$312$	1.35844	+	2.35289i	0.0769066	+	0.133206i
$313$	−2.19459	+	12.4462i	−0.124046	+	0.703498i	0.857824	+	0.513943i	$0.171816\pi$
$313$	−2.19459	+	12.4462i	−0.124046	+	0.703498i	−0.981870	+	0.189555i	$0.939295\pi$
$314$	−1.08899	+	6.17598i	−0.0614554	+	0.348531i
$315$	8.32295	+	14.4158i	0.468945	+	0.812237i
$316$	−0.148833	+	0.257787i	−0.00837252	+	0.0145016i
$317$	−10.8268	−	9.08478i	−0.608095	−	0.510252i	0.285941	−	0.958247i	$-0.407694\pi$
$317$	−10.8268	−	9.08478i	−0.608095	−	0.510252i	−0.894036	+	0.447995i	$0.852138\pi$
$318$	0.592396	+	0.215615i	0.0332199	+	0.0120911i
$319$	12.0963	−	4.40268i	0.677261	−	0.246503i
$320$	2.61334	−	2.19285i	0.146090	−	0.122584i
$321$	0.677052	+	3.83975i	0.0377893	+	0.214314i
$322$	−16.6459			−0.927640
$323$	−4.66772	−	2.20983i	−0.259719	−	0.122958i
$324$	1.00000			0.0555556
$325$	3.13176	+	17.7611i	0.173719	+	0.985208i
$326$	14.7836	−	12.4049i	0.818787	−	0.687044i
$327$	10.8969	−	3.96616i	0.602601	−	0.219329i
$328$	6.15910	+	2.24173i	0.340079	+	0.123779i
$329$	−10.6793	−	8.96102i	−0.588770	−	0.494037i
$330$	−5.81908	+	10.0789i	−0.320330	+	0.554827i
$331$	−14.7490	−	25.5460i	−0.810677	−	1.40413i	−0.912391	−	0.409320i	$-0.865766\pi$
$331$	−14.7490	−	25.5460i	−0.810677	−	1.40413i	0.101714	−	0.994814i	$-0.467567\pi$
$332$	2.70961	−	15.3669i	0.148709	−	0.843371i
$333$	1.17365	−	6.65609i	0.0643155	−	0.364751i
$334$	−3.86097	−	6.68739i	−0.211263	−	0.365918i
$335$	−1.20961	+	2.09510i	−0.0660879	+	0.114468i
$336$	−3.73783	−	3.13641i	−0.203915	−	0.171105i
$337$	20.9072	+	7.60960i	1.13889	+	0.414521i	0.841511	−	0.540239i	$-0.181666\pi$
$337$	20.9072	+	7.60960i	1.13889	+	0.414521i	0.297376	+	0.954760i	$0.403889\pi$
$338$	−5.27972	+	1.92166i	−0.287179	+	0.104524i
$339$	1.48680	−	1.24757i	0.0807517	−	0.0677587i
$340$	0.701867	+	3.98048i	0.0380641	+	0.215872i
$341$	−22.5699			−1.22223
$342$	2.52094	−	3.55596i	0.136317	−	0.192284i
$343$	−47.8590			−2.58414
$344$	−0.724155	−	4.10689i	−0.0390438	−	0.221429i
$345$	−8.91534	+	7.48086i	−0.479986	+	0.402756i
$346$	−13.6211	+	4.95767i	−0.732274	+	0.266526i
$347$	13.1792	+	4.79682i	0.707495	+	0.257507i	0.670607	−	0.741812i	$-0.266034\pi$
$347$	13.1792	+	4.79682i	0.707495	+	0.257507i	0.0368873	+	0.999319i	$0.488256\pi$
$348$	2.89053	+	2.42544i	0.154949	+	0.130017i
$349$	17.0560	−	29.5419i	0.912988	−	1.58134i	0.103168	−	0.994664i	$-0.467102\pi$
$349$	17.0560	−	29.5419i	0.912988	−	1.58134i	0.809820	−	0.586678i	$-0.199565\pi$
$350$	−16.1951	−	28.0507i	−0.865662	−	1.49937i
$351$	0.471782	−	2.67561i	0.0251818	−	0.142813i
$352$	0.592396	−	3.35965i	0.0315748	−	0.179070i
$353$	−15.2219	−	26.3652i	−0.810182	−	1.40328i	−0.912737	−	0.408549i	$-0.866035\pi$
$353$	−15.2219	−	26.3652i	−0.810182	−	1.40328i	0.102555	−	0.994727i	$-0.467298\pi$
$354$	5.81908	−	10.0789i	0.309280	−	0.535690i
$355$	20.7973	+	17.4510i	1.10380	+	0.926201i
$356$	−6.36484	−	2.31661i	−0.337336	−	0.122780i
$357$	5.43242	−	1.97724i	0.287514	−	0.104647i
$358$	7.52481	−	6.31407i	0.397699	−	0.333709i
$359$	2.36959	+	13.4386i	0.125062	+	0.709261i	0.981271	+	0.192632i	$0.0617024\pi$
$359$	2.36959	+	13.4386i	0.125062	+	0.709261i	−0.856209	+	0.516629i	$0.827187\pi$
$360$	−3.41147			−0.179800
$361$	−6.28968	−	17.9287i	−0.331036	−	0.943618i
$362$	−18.9145			−0.994122
$363$	0.110815	+	0.628461i	0.00581626	+	0.0329856i
$364$	−10.1552	+	8.52125i	−0.532279	+	0.446635i
$365$	40.8546	−	14.8699i	2.13843	−	0.778324i
$366$	6.48545	+	2.36051i	0.339000	+	0.123386i
$367$	18.2062	+	15.2768i	0.950356	+	0.797443i	0.979357	−	0.202136i	$-0.0647883\pi$
$367$	18.2062	+	15.2768i	0.950356	+	0.797443i	−0.0290014	+	0.999579i	$0.509233\pi$
$368$	1.70574	−	2.95442i	0.0889177	−	0.154010i
$369$	−3.27719	−	5.67626i	−0.170604	−	0.295494i
$370$	−4.00387	+	22.7071i	−0.208151	+	1.18048i
$371$	−0.534148	+	3.02931i	−0.0277316	+	0.157274i
$372$	−3.30793	−	5.72951i	−0.171508	−	0.297061i
$373$	11.6172	−	20.1216i	0.601516	−	1.04186i	−0.391075	−	0.920359i	$-0.627897\pi$
$373$	11.6172	−	20.1216i	0.601516	−	1.04186i	0.992592	−	0.121498i	$-0.0387699\pi$
$374$	3.09627	+	2.59808i	0.160104	+	0.134343i
$375$	−5.25150	−	1.91139i	−0.271186	−	0.0987037i
$376$	2.68479	−	0.977185i	0.138458	−	0.0503944i
$377$	7.85323	−	6.58964i	0.404462	−	0.339384i
$378$	0.847296	+	4.80526i	0.0435802	+	0.247156i
$379$	−4.50030			−0.231165			−0.115583	−	0.993298i	$-0.536873\pi$
$379$	−4.50030			−0.231165			−0.115583	+	0.993298i	$0.536873\pi$
$380$	−8.60014	+	12.1311i	−0.441178	+	0.622310i
$381$	−6.08378			−0.311681
$382$	1.75237	+	9.93821i	0.0896592	+	0.508483i
$383$	3.34002	−	2.80261i	0.170667	−	0.143207i	−0.553453	−	0.832880i	$-0.686690\pi$
$383$	3.34002	−	2.80261i	0.170667	−	0.143207i	0.724121	+	0.689673i	$0.242246\pi$
$384$	0.939693	−	0.342020i	0.0479535	−	0.0174536i
$385$	−53.3624	−	19.4223i	−2.71960	−	0.989853i
$386$	−1.93376	−	1.62262i	−0.0984259	−	0.0825892i
$387$	−2.08512	+	3.61154i	−0.105993	+	0.183585i
$388$	3.56283	+	6.17101i	0.180875	+	0.313286i
$389$	−0.227559	+	1.29055i	−0.0115377	+	0.0654335i	−0.990033	−	0.140836i	$-0.955021\pi$
$389$	−0.227559	+	1.29055i	−0.0115377	+	0.0654335i	0.978495	+	0.206269i	$0.0661322\pi$
$390$	−1.60947	+	9.12776i	−0.0814987	+	0.462202i
$391$	2.02094	+	3.50038i	0.102204	+	0.177022i
$392$	8.40420	−	14.5565i	0.424476	−	0.735214i
$393$	−14.2515	−	11.9584i	−0.718893	−	0.603223i
$394$	13.9611	+	5.08143i	0.703350	+	0.255999i
$395$	−0.954241	+	0.347315i	−0.0480131	+	0.0174753i
$396$	−2.61334	+	2.19285i	−0.131325	+	0.110195i
$397$	−3.30154	−	18.7239i	−0.165699	−	0.939728i	−0.948340	−	0.317255i	$-0.897239\pi$
$397$	−3.30154	−	18.7239i	−0.165699	−	0.939728i	0.782641	−	0.622473i	$-0.213872\pi$
$398$	−8.06923			−0.404474
$399$	19.2233	+	9.10083i	0.962368	+	0.455612i
$400$	6.63816			0.331908
$401$	6.22756	+	35.3182i	0.310989	+	1.76371i	0.593877	+	0.804556i	$0.297597\pi$
$401$	6.22756	+	35.3182i	0.310989	+	1.76371i	−0.282888	+	0.959153i	$0.591292\pi$
$402$	−0.543233	+	0.455827i	−0.0270940	+	0.0227346i
$403$	−16.8905	+	6.14765i	−0.841377	+	0.306236i
$404$	4.36571	+	1.58899i	0.217202	+	0.0790552i
$405$	2.61334	+	2.19285i	0.129858	+	0.108964i
$406$	−9.20574	+	15.9448i	−0.456873	+	0.791327i
$407$	11.5287	+	19.9683i	0.571456	+	0.989790i
$408$	−0.205737	+	1.16679i	−0.0101855	+	0.0577649i
$409$	−5.05468	+	28.6665i	−0.249938	+	1.41747i	0.558801	+	0.829301i	$0.311261\pi$
$409$	−5.05468	+	28.6665i	−0.249938	+	1.41747i	−0.808739	+	0.588167i	$0.799850\pi$
$410$	11.1800	+	19.3644i	0.552143	+	0.956340i
$411$	−2.27332	+	3.93750i	−0.112135	+	0.194223i
$412$	−9.48545	−	7.95924i	−0.467315	−	0.392124i
$413$	53.3624	+	19.4223i	2.62579	+	0.955710i
$414$	−3.20574	+	1.16679i	−0.157553	+	0.0573447i
$415$	40.7786	−	34.2173i	2.00174	−	1.67966i
$416$	−0.471782	−	2.67561i	−0.0231310	−	0.131182i
$417$	−3.01455			−0.147623
$418$	1.20961	+	14.8210i	0.0591638	+	0.724918i
$419$	13.1584			0.642829			0.321415	−	0.946939i	$-0.395842\pi$
$419$	13.1584			0.642829			0.321415	+	0.946939i	$0.395842\pi$
$420$	−2.89053	−	16.3930i	−0.141043	−	0.799897i
$421$	−0.115400	+	0.0968323i	−0.00562426	+	0.00471932i	−0.645595	−	0.763680i	$-0.723391\pi$
$421$	−0.115400	+	0.0968323i	−0.00562426	+	0.00471932i	0.639971	+	0.768399i	$0.278946\pi$
$422$	7.46451	−	2.71686i	0.363367	−	0.132255i
$423$	−2.68479	−	0.977185i	−0.130539	−	0.0475123i
$424$	−0.482926	−	0.405223i	−0.0234530	−	0.0196794i
$425$	−3.93242	+	6.81115i	−0.190750	+	0.330389i
$426$	3.97906	+	6.89193i	0.192786	+	0.333915i
$427$	−5.84776	+	33.1643i	−0.282993	+	1.60493i
$428$	0.677052	−	3.83975i	0.0327265	−	0.185601i
$429$	4.63429	+	8.02682i	0.223745	+	0.387538i
$430$	7.11334	−	12.3207i	0.343036	−	0.594155i
$431$	−23.5915	−	19.7956i	−1.13636	−	0.953522i	−0.137050	−	0.990564i	$-0.543762\pi$
$431$	−23.5915	−	19.7956i	−1.13636	−	0.953522i	−0.999314	+	0.0370420i	$0.988206\pi$
$432$	−0.939693	−	0.342020i	−0.0452110	−	0.0164555i
$433$	27.6587	−	10.0669i	1.32919	−	0.483786i	0.422800	−	0.906223i	$-0.361047\pi$
$433$	27.6587	−	10.0669i	1.32919	−	0.483786i	0.906392	+	0.422437i	$0.138825\pi$
$434$	24.7290	−	20.7501i	1.18703	−	0.996035i
$435$	2.23530	+	12.6770i	0.107174	+	0.607816i
$436$	−11.5963			−0.555360
$437$	−3.93242	+	14.3409i	−0.188113	+	0.686018i
$438$	12.7442			0.608943
$439$	3.43835	+	19.4998i	0.164103	+	0.930677i	0.949984	+	0.312298i	$0.101099\pi$
$439$	3.43835	+	19.4998i	0.164103	+	0.930677i	−0.785881	+	0.618378i	$0.787790\pi$
$440$	8.91534	−	7.48086i	0.425022	−	0.356636i
$441$	−15.7947	+	5.74881i	−0.752130	+	0.273753i
$442$	3.02481	+	1.10094i	0.143876	+	0.0523665i
$443$	−14.2383	−	11.9473i	−0.676482	−	0.567636i	0.238494	−	0.971144i	$-0.423346\pi$
$443$	−14.2383	−	11.9473i	−0.676482	−	0.567636i	−0.914976	+	0.403508i	$0.867791\pi$
$444$	−3.37939	+	5.85327i	−0.160379	+	0.277784i
$445$	−11.5535	−	20.0112i	−0.547688	−	0.948624i
$446$	−2.07826	+	11.7864i	−0.0984084	+	0.558102i
$447$	0.205737	−	1.16679i	0.00973103	−	0.0551874i
$448$	2.43969	+	4.22567i	0.115265	+	0.199644i
$449$	−1.68954	+	2.92637i	−0.0797343	+	0.138104i	−0.903135	−	0.429356i	$-0.858741\pi$
$449$	−1.68954	+	2.92637i	−0.0797343	+	0.138104i	0.823401	+	0.567460i	$0.192074\pi$
$450$	−5.08512	−	4.26692i	−0.239715	−	0.201145i
$451$	21.0116	+	7.64760i	0.989398	+	0.360111i
$452$	−1.82383	+	0.663818i	−0.0857855	+	0.0312234i
$453$	−2.78699	+	2.33856i	−0.130944	+	0.109875i
$454$	−4.61809	−	26.1905i	−0.216738	−	1.22918i
$455$	−45.2249			−2.12018
$456$	−3.58512	+	2.47929i	−0.167889	+	0.116104i
$457$	21.7912			1.01935			0.509674	−	0.860368i	$-0.329766\pi$
$457$	21.7912			1.01935			0.509674	+	0.860368i	$0.329766\pi$
$458$	3.45605	+	19.6002i	0.161491	+	0.915859i
$459$	0.907604	−	0.761570i	0.0423633	−	0.0355470i
$460$	10.9363	−	3.98048i	0.509907	−	0.185591i
$461$	−11.0544	−	4.02346i	−0.514854	−	0.187391i	0.0715092	−	0.997440i	$-0.477218\pi$
$461$	−11.0544	−	4.02346i	−0.514854	−	0.187391i	−0.586363	+	0.810049i	$0.699441\pi$
$462$	−12.7515	−	10.6998i	−0.593253	−	0.497799i
$463$	−8.49660	+	14.7165i	−0.394870	+	0.683935i	−0.993085	−	0.117401i	$-0.962544\pi$
$463$	−8.49660	+	14.7165i	−0.394870	+	0.683935i	0.598214	+	0.801336i	$0.295877\pi$
$464$	−1.88666	−	3.26779i	−0.0875860	−	0.151703i
$465$	3.91921	−	22.2270i	0.181749	−	1.03075i
$466$	0.748503	−	4.24497i	0.0346738	−	0.196645i
$467$	5.85251	+	10.1368i	0.270822	+	0.469077i	0.969073	−	0.246776i	$-0.0793712\pi$
$467$	5.85251	+	10.1368i	0.270822	+	0.469077i	−0.698251	+	0.715853i	$0.746038\pi$
$468$	−1.35844	+	2.35289i	−0.0627939	+	0.108762i
$469$	−2.65064	−	2.22415i	−0.122395	−	0.102702i
$470$	9.15910	+	3.33364i	0.422478	+	0.153769i
$471$	−5.89306	+	2.14490i	−0.271538	+	0.0988316i
$472$	−8.91534	+	7.48086i	−0.410362	+	0.344335i
$473$	−2.47044	−	14.0105i	−0.113591	−	0.644206i
$474$	−0.297667			−0.0136723
$475$	−27.9923	+	7.32580i	−1.28438	+	0.336131i
$476$	−5.78106			−0.264974
$477$	0.109470	+	0.620838i	0.00501231	+	0.0284262i
$478$	−0.218941	+	0.183713i	−0.0100141	+	0.00840284i
$479$	−28.1716	+	10.2536i	−1.28719	+	0.468500i	−0.892805	−	0.450444i	$-0.851266\pi$
$479$	−28.1716	+	10.2536i	−1.28719	+	0.468500i	−0.394388	+	0.918944i	$0.629043\pi$
$480$	3.20574	+	1.16679i	0.146321	+	0.0532566i
$481$	14.0667	+	11.8034i	0.641386	+	0.538187i
$482$	4.78312	−	8.28460i	0.217865	−	0.377353i
$483$	−8.32295	−	14.4158i	−0.378707	−	0.655940i
$484$	0.110815	−	0.628461i	0.00503703	−	0.0285664i
$485$	−4.22122	+	23.9397i	−0.191676	+	1.08705i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−7.25537	+	12.5667i	−0.328772	+	0.569450i	−0.982268	−	0.187480i	$-0.939968\pi$
$487$	−7.25537	+	12.5667i	−0.328772	+	0.569450i	0.653496	+	0.756930i	$0.273301\pi$
$488$	−5.28699	−	4.43631i	−0.239331	−	0.200822i
$489$	18.1348	+	6.60051i	0.820082	+	0.298485i
$490$	53.8833	−	19.6119i	2.43420	−	0.885976i
$491$	−8.92855	+	7.49194i	−0.402940	+	0.338107i	−0.821629	−	0.570023i	$-0.806934\pi$
$491$	−8.92855	+	7.49194i	−0.402940	+	0.338107i	0.418689	+	0.908130i	$0.362490\pi$
$492$	1.13816	+	6.45480i	0.0513120	+	0.291005i
$493$	4.47060			0.201346
$494$	4.94222	+	10.7621i	0.222361	+	0.484208i
$495$	−11.6382			−0.523096
$496$	1.14883	+	6.51536i	0.0515841	+	0.292548i
$497$	−29.7460	+	24.9599i	−1.33429	+	1.11960i
$498$	14.6630	−	5.33688i	0.657063	−	0.239152i
$499$	1.58512	+	0.576937i	0.0709598	+	0.0258273i	0.377256	−	0.926109i	$-0.376868\pi$
$499$	1.58512	+	0.576937i	0.0709598	+	0.0258273i	−0.306296	+	0.951936i	$0.599090\pi$
$500$	4.28106	+	3.59224i	0.191455	+	0.160650i
$501$	3.86097	−	6.68739i	0.172495	−	0.298771i
$502$	14.8439	+	25.7104i	0.662515	+	1.14751i
$503$	3.00299	−	17.0308i	0.133897	−	0.759367i	−0.841725	−	0.539907i	$-0.818459\pi$
$503$	3.00299	−	17.0308i	0.133897	−	0.759367i	0.975622	−	0.219460i	$-0.0704295\pi$
$504$	0.847296	−	4.80526i	0.0377416	−	0.214043i
$505$	7.92468	+	13.7259i	0.352644	+	0.610797i
$506$	5.81908	−	10.0789i	0.258690	−	0.448063i
$507$	−4.30406	−	3.61154i	−0.191150	−	0.160394i
$508$	5.71688	+	2.08077i	0.253646	+	0.0923194i
$509$	−30.4859	+	11.0960i	−1.35126	+	0.491820i	−0.913342	−	0.407193i	$-0.866508\pi$
$509$	−30.4859	+	11.0960i	−1.35126	+	0.491820i	−0.437922	+	0.899013i	$0.644286\pi$
$510$	−3.09627	+	2.59808i	−0.137105	+	0.115045i
$511$	10.7981	+	61.2393i	0.477681	+	2.70907i
$512$	−1.00000			−0.0441942
$513$	4.34002	+	0.405223i	0.191617	+	0.0178910i
$514$	−15.7965			−0.696756
$515$	−7.33527	−	41.6004i	−0.323231	−	1.83313i
$516$	3.19459	−	2.68058i	0.140634	−	0.118006i
$517$	9.15910	−	3.33364i	0.402817	−	0.146613i
$518$	−30.9898	−	11.2794i	−1.36161	−	0.495587i
$519$	−11.1040	−	9.31737i	−0.487412	−	0.408987i
$520$	4.63429	−	8.02682i	0.203227	−	0.351999i
$521$	−15.5822	−	26.9891i	−0.682668	−	1.18242i	−0.974164	−	0.225843i	$-0.927486\pi$
$521$	−15.5822	−	26.9891i	−0.682668	−	1.18242i	0.291496	−	0.956572i	$-0.405847\pi$
$522$	−0.655230	+	3.71599i	−0.0286786	+	0.162645i
$523$	−2.89306	+	16.4073i	−0.126504	+	0.717443i	0.853898	+	0.520440i	$0.174232\pi$
$523$	−2.89306	+	16.4073i	−0.126504	+	0.717443i	−0.980403	+	0.197003i	$0.936879\pi$
$524$	9.30200	+	16.1115i	0.406360	+	0.703836i
$525$	16.1951	−	28.0507i	0.706810	−	1.22423i
$526$	−8.32295	−	6.98378i	−0.362898	−	0.304507i
$527$	−7.36571	−	2.68090i	−0.320856	−	0.116782i
$528$	3.20574	−	1.16679i	0.139512	−	0.0507781i
$529$	−8.70368	+	7.30325i	−0.378421	+	0.317533i
$530$	−0.373455	−	2.11797i	−0.0162219	−	0.0919988i
$531$	11.6382			0.505053
$532$	−14.9513	−	15.1267i	−0.648221	−	0.655827i
$533$	17.8075			0.771327
$534$	−1.17617	−	6.67042i	−0.0508980	−	0.288657i
$535$	10.1894	−	8.54990i	0.440525	−	0.369645i
$536$	0.666374	−	0.242540i	0.0287830	−	0.0104761i
$537$	9.23055	+	3.35965i	0.398328	+	0.144979i
$538$	13.2476	+	11.1161i	0.571146	+	0.479248i
$539$	28.6707	−	49.6591i	1.23493	−	2.13897i
$540$	−1.70574	−	2.95442i	−0.0734032	−	0.127138i
$541$	6.29385	−	35.6942i	0.270594	−	1.53461i	−0.482025	−	0.876157i	$-0.660099\pi$
$541$	6.29385	−	35.6942i	0.270594	−	1.53461i	0.752619	−	0.658456i	$-0.228790\pi$
$542$	−0.251030	+	1.42366i	−0.0107826	+	0.0611514i
$543$	−9.45723	−	16.3804i	−0.405849	−	0.702951i
$544$	0.592396	−	1.02606i	0.0253988	−	0.0439920i
$545$	−30.3050	−	25.4289i	−1.29812	−	1.08925i
$546$	−12.4572	−	4.53406i	−0.533120	−	0.194040i
$547$	16.1604	−	5.88192i	0.690971	−	0.251493i	0.0274199	−	0.999624i	$-0.491271\pi$
$547$	16.1604	−	5.88192i	0.690971	−	0.251493i	0.663551	+	0.748131i	$0.269049\pi$
$548$	3.48293	−	2.92252i	0.148783	−	0.124844i
$549$	1.19846	+	6.79682i	0.0511492	+	0.290081i
$550$	22.6459			0.965624
$551$	11.5621	+	11.6978i	0.492563	+	0.498342i
$552$	3.41147			0.145202
$553$	−0.252212	−	1.43036i	−0.0107251	−	0.0608253i
$554$	−16.2331	+	13.6212i	−0.689677	+	0.578708i
$555$	−21.6668	+	7.88609i	−0.919706	+	0.334746i
$556$	2.83275	+	1.03104i	0.120135	+	0.0437257i
$557$	−12.6932	−	10.6509i	−0.537830	−	0.451293i	0.332965	−	0.942939i	$-0.391951\pi$
$557$	−12.6932	−	10.6509i	−0.537830	−	0.451293i	−0.870795	+	0.491646i	$0.836395\pi$
$558$	3.30793	−	5.72951i	0.140036	−	0.242549i
$559$	−5.66503	−	9.81212i	−0.239605	−	0.415008i
$560$	−2.89053	+	16.3930i	−0.122147	+	0.692731i
$561$	−0.701867	+	3.98048i	−0.0296328	+	0.168056i
$562$	−12.1839	−	21.1032i	−0.513947	−	0.890183i
$563$	15.3486	−	26.5846i	0.646868	−	1.12041i	−0.336999	−	0.941505i	$-0.609412\pi$
$563$	15.3486	−	26.5846i	0.646868	−	1.12041i	0.983867	−	0.178903i	$-0.0572549\pi$
$564$	2.18866	+	1.83651i	0.0921593	+	0.0773309i
$565$	−6.22193	−	2.26460i	−0.261759	−	0.0952724i
$566$	−3.87686	+	1.41106i	−0.162957	+	0.0593113i
$567$	−3.73783	+	3.13641i	−0.156974	+	0.131717i
$568$	−1.38191	−	7.83721i	−0.0579837	−	0.328842i
$569$	13.4534			0.563994			0.281997	−	0.959415i	$-0.409003\pi$
$569$	13.4534			0.563994			0.281997	+	0.959415i	$0.409003\pi$
$570$	−14.8059	−	1.38241i	−0.620150	−	0.0579027i
$571$	−9.47565			−0.396544			−0.198272	−	0.980147i	$-0.563533\pi$
$571$	−9.47565			−0.396544			−0.198272	+	0.980147i	$0.563533\pi$
$572$	−1.60947	−	9.12776i	−0.0672953	−	0.381651i
$573$	−7.73055	+	6.48670i	−0.322948	+	0.270986i
$574$	−30.0526	+	10.9383i	−1.25437	+	0.456554i
$575$	21.2802	+	7.74535i	0.887445	+	0.323004i
$576$	0.766044	+	0.642788i	0.0319185	+	0.0267828i
$577$	9.38191	−	16.2499i	0.390574	−	0.676494i	−0.601951	−	0.798533i	$-0.705610\pi$
$577$	9.38191	−	16.2499i	0.390574	−	0.676494i	0.992525	+	0.122039i	$0.0389432\pi$
$578$	−7.79813	−	13.5068i	−0.324360	−	0.561807i
$579$	0.438348	−	2.48600i	0.0182171	−	0.103315i
$580$	2.23530	−	12.6770i	0.0928158	−	0.526384i
$581$	38.0690	+	65.9374i	1.57937	+	2.73554i
$582$	−3.56283	+	6.17101i	−0.147684	+	0.255797i
$583$	−1.64749	−	1.38241i	−0.0682320	−	0.0572535i
$584$	−11.9757	−	4.35878i	−0.495556	−	0.180368i
$585$	−8.70961	+	3.17004i	−0.360098	+	0.131065i
$586$	−2.13041	+	1.78763i	−0.0880066	+	0.0738463i
$587$	−3.15611	−	17.8992i	−0.130266	−	0.738778i	−0.978040	−	0.208419i	$-0.933168\pi$
$587$	−3.15611	−	17.8992i	−0.130266	−	0.738778i	0.847773	−	0.530359i	$-0.177943\pi$
$588$	16.8084			0.693167
$589$	−12.0348	−	26.2066i	−0.495884	−	1.07983i
$590$	−39.7033			−1.63456
$591$	2.57991	+	14.6314i	0.106123	+	0.601855i
$592$	5.17752	−	4.34445i	0.212795	−	0.178556i
$593$	30.7221	−	11.1819i	1.26161	−	0.459187i	0.377298	−	0.926092i	$-0.376853\pi$
$593$	30.7221	−	11.1819i	1.26161	−	0.459187i	0.884307	+	0.466905i	$0.154631\pi$
$594$	−3.20574	−	1.16679i	−0.131533	−	0.0478741i
$595$	−15.1079	−	12.6770i	−0.619363	−	0.519707i
$596$	−0.592396	+	1.02606i	−0.0242655	+	0.0420291i
$597$	−4.03462	−	6.98816i	−0.165126	−	0.286006i
$598$	1.60947	−	9.12776i	0.0658161	−	0.373262i
$599$	1.53343	−	8.69653i	0.0626544	−	0.355331i	−0.937322	−	0.348464i	$-0.886703\pi$
$599$	1.53343	−	8.69653i	0.0626544	−	0.355331i	0.999976	−	0.00686632i	$-0.00218563\pi$
$600$	3.31908	+	5.74881i	0.135501	+	0.234694i
$601$	−16.5262	+	28.6241i	−0.674116	+	1.16760i	0.302610	+	0.953114i	$0.402142\pi$
$601$	−16.5262	+	28.6241i	−0.674116	+	1.16760i	−0.976726	+	0.214489i	$0.931191\pi$
$602$	15.5876	+	13.0796i	0.635305	+	0.533084i
$603$	−0.666374	−	0.242540i	−0.0271369	−	0.00987701i
$604$	3.41875	−	1.24432i	0.139107	−	0.0506308i
$605$	1.66772	−	1.39938i	0.0678024	−	0.0568930i
$606$	0.806751	+	4.57531i	0.0327720	+	0.185859i
$607$	5.16250			0.209540			0.104770	−	0.994497i	$-0.466589\pi$
$607$	5.16250			0.209540			0.104770	+	0.994497i	$0.466589\pi$
$608$	4.21688	−	1.10359i	0.171017	−	0.0447565i
$609$	−18.4115			−0.746071
$610$	−4.08853	−	23.1872i	−0.165540	−	0.938822i
$611$	5.94634	−	4.98957i	0.240563	−	0.201856i
$612$	−1.11334	+	0.405223i	−0.0450041	+	0.0163802i
$613$	44.2486	+	16.1052i	1.78718	+	0.650481i	0.999404	+	0.0345227i	$0.0109911\pi$
$613$	44.2486	+	16.1052i	1.78718	+	0.650481i	0.787779	+	0.615959i	$0.211231\pi$
$614$	19.1689	+	16.0846i	0.773594	+	0.649122i
$615$	−11.1800	+	19.3644i	−0.450823	+	0.780848i
$616$	8.32295	+	14.4158i	0.335341	+	0.580828i
$617$	−7.36009	+	41.7411i	−0.296306	+	1.68044i	0.365540	+	0.930796i	$0.380884\pi$
$617$	−7.36009	+	41.7411i	−0.296306	+	1.68044i	−0.661846	+	0.749640i	$0.730227\pi$
$618$	2.15018	−	12.1943i	0.0864928	−	0.490525i
$619$	0.928081	+	1.60748i	0.0373027	+	0.0646102i	0.884074	−	0.467347i	$-0.154790\pi$
$619$	0.928081	+	1.60748i	0.0373027	+	0.0646102i	−0.846771	+	0.531957i	$0.821457\pi$
$620$	−11.2849	+	19.5461i	−0.453214	+	0.784989i
$621$	−2.61334	−	2.19285i	−0.104870	−	0.0879962i
$622$	22.5278	+	8.19945i	0.903283	+	0.328768i
$623$	31.0565	−	11.3036i	1.24425	−	0.452871i
$624$	2.08125	−	1.74638i	0.0833168	−	0.0699111i
$625$	−2.45290	−	13.9111i	−0.0981159	−	0.556443i
$626$	12.6382			0.505122
$627$	−12.2306	+	8.45805i	−0.488441	+	0.337782i
$628$	6.27126			0.250250
$629$	1.39053	+	7.88609i	0.0554440	+	0.314439i
$630$	12.7515	−	10.6998i	0.508032	−	0.426289i
$631$	−23.1618	+	8.43020i	−0.922056	+	0.335601i	−0.759056	−	0.651025i	$-0.774339\pi$
$631$	−23.1618	+	8.43020i	−0.922056	+	0.335601i	−0.163000	+	0.986626i	$0.552117\pi$
$632$	0.279715	+	0.101808i	0.0111265	+	0.00404970i
$633$	6.08512	+	5.10602i	0.241862	+	0.202946i
$634$	−7.06670	+	12.2399i	−0.280655	+	0.486108i
$635$	10.3773	+	17.9741i	0.411812	+	0.713279i
$636$	0.109470	−	0.620838i	0.00434078	−	0.0246178i
$637$	7.92989	−	44.9727i	0.314194	−	1.78188i
$638$	−6.43629	−	11.1480i	−0.254815	−	0.441353i
$639$	−3.97906	+	6.89193i	−0.157409	+	0.272640i
$640$	−2.61334	−	2.19285i	−0.103301	−	0.0866801i
$641$	−16.5744	−	6.03260i	−0.654651	−	0.238274i	−0.00672584	−	0.999977i	$-0.502141\pi$
$641$	−16.5744	−	6.03260i	−0.654651	−	0.238274i	−0.647925	+	0.761704i	$0.724363\pi$
$642$	3.66385	−	1.33353i	0.144601	−	0.0526303i
$643$	22.8653	−	19.1863i	0.901720	−	0.756633i	−0.0688062	−	0.997630i	$-0.521919\pi$
$643$	22.8653	−	19.1863i	0.901720	−	0.756633i	0.970526	+	0.240997i	$0.0774746\pi$
$644$	2.89053	+	16.3930i	0.113903	+	0.645975i
$645$	14.2267			0.560175
$646$	−1.36571	+	4.98054i	−0.0537333	+	0.195957i
$647$	23.9391			0.941144			0.470572	−	0.882362i	$-0.344048\pi$
$647$	23.9391			0.941144			0.470572	+	0.882362i	$0.344048\pi$
$648$	−0.173648	−	0.984808i	−0.00682154	−	0.0386869i
$649$	−30.4145	+	25.5208i	−1.19387	+	1.00178i
$650$	16.9474	−	6.16836i	0.664733	−	0.241943i
$651$	30.3346	+	11.0409i	1.18891	+	0.432726i
$652$	−14.7836	−	12.4049i	−0.578970	−	0.485813i
$653$	13.2430	−	22.9376i	0.518240	−	0.897618i	−0.481535	−	0.876427i	$-0.659921\pi$
$653$	13.2430	−	22.9376i	0.518240	−	0.897618i	0.999775	−	0.0211916i	$-0.00674602\pi$
$654$	−5.79813	−	10.0427i	−0.226725	−	0.392699i
$655$	−11.0209	+	62.5029i	−0.430624	+	2.44219i
$656$	1.13816	−	6.45480i	0.0444375	−	0.252018i
$657$	6.37211	+	11.0368i	0.248600	+	0.430587i
$658$	−6.97044	+	12.0732i	−0.271736	+	0.470660i
$659$	−4.05509	−	3.40263i	−0.157964	−	0.132548i	0.560380	−	0.828236i	$-0.310655\pi$
$659$	−4.05509	−	3.40263i	−0.157964	−	0.132548i	−0.718344	+	0.695688i	$0.755100\pi$
$660$	10.9363	+	3.98048i	0.425694	+	0.154940i
$661$	−43.3264	+	15.7695i	−1.68520	+	0.613363i	−0.994008	−	0.109306i	$-0.965137\pi$
$661$	−43.3264	+	15.7695i	−1.68520	+	0.613363i	−0.691194	+	0.722669i	$0.742915\pi$
$662$	−22.5967	+	18.9609i	−0.878247	+	0.736937i
$663$	0.558963	+	3.17004i	0.0217083	+	0.123114i
$664$	−15.6040			−0.605553
$665$	−5.90214	−	72.3173i	−0.228875	−	2.80435i
$666$	−6.75877			−0.261897
$667$	−2.23530	−	12.6770i	−0.0865512	−	0.490856i
$668$	−5.91534	+	4.96356i	−0.228872	+	0.192046i
$669$	−11.2464	+	4.09337i	−0.434813	+	0.158259i
$670$	2.27332	+	0.827420i	0.0878260	+	0.0319660i
$671$	−18.0364	−	15.1344i	−0.696289	−	0.584255i
$672$	−2.43969	+	4.22567i	−0.0941132	+	0.163009i
$673$	−1.19072	−	2.06239i	−0.0458990	−	0.0794994i	0.842163	−	0.539223i	$-0.181282\pi$
$673$	−1.19072	−	2.06239i	−0.0458990	−	0.0794994i	−0.888062	+	0.459723i	$0.847949\pi$
$674$	3.86349	−	21.9110i	0.148816	−	0.843979i
$675$	1.15270	−	6.53731i	0.0443676	−	0.251621i
$676$	2.80928	+	4.86581i	0.108049	+	0.187147i
$677$	−7.97431	+	13.8119i	−0.306478	+	0.530835i	−0.977589	−	0.210522i	$-0.932484\pi$
$677$	−7.97431	+	13.8119i	−0.306478	+	0.530835i	0.671112	+	0.741356i	$0.265817\pi$
$678$	−1.48680	−	1.24757i	−0.0571001	−	0.0479126i
$679$	−32.6721	−	11.8917i	−1.25384	−	0.456360i
$680$	3.79813	−	1.38241i	0.145652	−	0.0530129i
$681$	20.3726	−	17.0946i	0.780679	−	0.655067i
$682$	3.91921	+	22.2270i	0.150074	+	0.851115i
$683$	−1.26083			−0.0482443			−0.0241222	−	0.999709i	$-0.507679\pi$
$683$	−1.26083			−0.0482443			−0.0241222	+	0.999709i	$0.507679\pi$
$684$	−3.93969	−	1.86516i	−0.150638	−	0.0713162i
$685$	15.5107			0.592635
$686$	8.31062	+	47.1319i	0.317301	+	1.79950i
$687$	−15.2463	+	12.7931i	−0.581682	+	0.488089i
$688$	−3.91875	+	1.42631i	−0.149401	+	0.0543775i
$689$	−1.60947	−	0.585799i	−0.0613159	−	0.0223172i
$690$	8.91534	+	7.48086i	0.339401	+	0.284792i
$691$	4.05438	−	7.02239i	0.154236	−	0.267144i	−0.778545	−	0.627589i	$-0.784042\pi$
$691$	4.05438	−	7.02239i	0.154236	−	0.267144i	0.932780	+	0.360445i	$0.117375\pi$
$692$	7.24763	+	12.5533i	0.275513	+	0.477203i
$693$	2.89053	−	16.3930i	0.109802	−	0.622719i
$694$	2.43541	−	13.8119i	0.0924470	−	0.524293i
$695$	5.14203	+	8.90625i	0.195048	+	0.337833i
$696$	1.88666	−	3.26779i	0.0715136	−	0.123865i
$697$	5.94878	+	4.99162i	0.225326	+	0.189071i
$698$	−32.0548	−	11.6670i	−1.21329	−	0.441603i
$699$	4.05051	−	1.47426i	0.153204	−	0.0557618i
$700$	−24.8123	+	20.8200i	−0.937816	+	0.786921i
$701$	1.77615	+	10.0730i	0.0670842	+	0.380454i	0.999803	+	0.0198489i	$0.00631853\pi$
$701$	1.77615	+	10.0730i	0.0670842	+	0.380454i	−0.932719	+	0.360605i	$0.882570\pi$
$702$	−2.71688			−0.102542
$703$	−17.0385	+	24.0339i	−0.642619	+	0.906456i
$704$	−3.41147			−0.128575
$705$	1.69253	+	9.59883i	0.0637445	+	0.361513i
$706$	−23.3214	+	19.5689i	−0.877711	+	0.736487i
$707$	−21.3020	+	7.75330i	−0.801144	+	0.291593i
$708$	−10.9363	−	3.98048i	−0.411011	−	0.149596i
$709$	0.156574	+	0.131381i	0.00588026	+	0.00493413i	0.645723	−	0.763572i	$-0.276556\pi$
$709$	0.156574	+	0.131381i	0.00588026	+	0.00493413i	−0.639843	+	0.768506i	$0.721001\pi$
$710$	13.5744	−	23.5116i	0.509440	−	0.882376i
$711$	−0.148833	−	0.257787i	−0.00558168	−	0.00966776i
$712$	−1.17617	+	6.67042i	−0.0440790	+	0.249984i
$713$	−3.91921	+	22.2270i	−0.146776	+	0.832407i
$714$	−2.89053	−	5.00654i	−0.108175	−	0.187365i
$715$	15.8097	−	27.3833i	0.591251	−	1.02408i
$716$	−7.52481	−	6.31407i	−0.281216	−	0.235968i
$717$	−0.268571	−	0.0977517i	−0.0100300	−	0.00365061i
$718$	12.8229	−	4.66717i	0.478548	−	0.174177i
$719$	12.2103	−	10.2457i	0.455368	−	0.382099i	−0.386055	−	0.922476i	$-0.626163\pi$
$719$	12.2103	−	10.2457i	0.455368	−	0.382099i	0.841423	+	0.540376i	$0.181718\pi$
$720$	0.592396	+	3.35965i	0.0220773	+	0.125207i
$721$	60.4184			2.25010
$722$	−16.5642	+	9.30742i	−0.616455	+	0.346386i
$723$	9.56624			0.355772
$724$	3.28446	+	18.6271i	0.122066	+	0.692271i
$725$	19.1878	−	16.1005i	0.712616	−	0.597956i
$726$	0.599670	−	0.218262i	0.0222558	−	0.00810047i
$727$	29.0959	+	10.5900i	1.07911	+	0.392762i	0.819575	−	0.572972i	$-0.194210\pi$
$727$	29.0959	+	10.5900i	1.07911	+	0.392762i	0.259531	+	0.965735i	$0.416432\pi$
$728$	10.1552	+	8.52125i	0.376378	+	0.315819i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−21.7383	−	37.6518i	−0.804570	−	1.39356i
$731$	0.857974	−	4.86581i	0.0317333	−	0.179969i
$732$	1.19846	−	6.79682i	0.0442965	−	0.251218i
$733$	−1.97906	−	3.42782i	−0.0730981	−	0.126610i	0.827160	−	0.561967i	$-0.189955\pi$
$733$	−1.97906	−	3.42782i	−0.0730981	−	0.126610i	−0.900258	+	0.435358i	$0.856622\pi$
$734$	11.8833	−	20.5824i	0.438619	−	0.759710i
$735$	43.9261	+	36.8584i	1.62024	+	1.35954i
$736$	−3.20574	−	1.16679i	−0.118165	−	0.0430086i
$737$	2.27332	−	0.827420i	0.0837388	−	0.0304784i
$738$	−5.02094	+	4.21307i	−0.184824	+	0.155085i
$739$	−4.48070	−	25.4113i	−0.164825	−	0.934771i	−0.949244	−	0.314540i	$-0.898150\pi$
$739$	−4.48070	−	25.4113i	−0.164825	−	0.934771i	0.784419	−	0.620231i	$-0.212961\pi$
$740$	23.0574			0.847606
$741$	−6.84911	+	9.66112i	−0.251608	+	0.354910i
$742$	3.07604			0.112925
$743$	5.54189	+	31.4296i	0.203312	+	1.15304i	0.900074	+	0.435738i	$0.143513\pi$
$743$	5.54189	+	31.4296i	0.203312	+	1.15304i	−0.696761	+	0.717303i	$0.745376\pi$
$744$	−5.06805	+	4.25260i	−0.185804	+	0.155908i
$745$	−3.79813	+	1.38241i	−0.139153	+	0.0506475i
$746$	−21.8332	−	7.94664i	−0.799371	−	0.290947i
$747$	11.9534	+	10.0301i	0.437351	+	0.366981i
$748$	2.02094	−	3.50038i	0.0738931	−	0.127987i
$749$	9.51233	+	16.4758i	0.347573	+	0.602014i
$750$	−0.970437	+	5.50362i	−0.0354354	+	0.200964i
$751$	−0.0882212	+	0.500327i	−0.00321924	+	0.0182572i	−0.986375	−	0.164512i	$-0.947395\pi$
$751$	−0.0882212	+	0.500327i	−0.00321924	+	0.0182572i	0.983156	+	0.182769i	$0.0585061\pi$
$752$	−1.42855	−	2.47432i	−0.0520938	−	0.0902291i
$753$	−14.8439	+	25.7104i	−0.540942	+	0.936938i
$754$	−7.85323	−	6.58964i	−0.285998	−	0.239981i
$755$	11.6630	+	4.24497i	0.424459	+	0.154490i
$756$	4.58512	−	1.66885i	0.166759	−	0.0606954i
$757$	−36.8999	+	30.9627i	−1.34115	+	1.12536i	−0.359822	+	0.933021i	$0.617162\pi$
$757$	−36.8999	+	30.9627i	−1.34115	+	1.12536i	−0.981329	+	0.192338i	$0.938393\pi$
$758$	0.781470	+	4.43193i	0.0283843	+	0.160975i
$759$	11.6382			0.422438
$760$	13.4402	+	6.36295i	0.487526	+	0.230808i
$761$	5.15064			0.186711			0.0933554	−	0.995633i	$-0.470241\pi$
$761$	5.15064			0.186711			0.0933554	+	0.995633i	$0.470241\pi$
$762$	1.05644	+	5.99135i	0.0382707	+	0.217044i
$763$	43.3448	−	36.3706i	1.56919	−	1.31671i
$764$	9.48293	−	3.45150i	0.343080	−	0.124871i
$765$	−3.79813	−	1.38241i	−0.137322	−	0.0499810i
$766$	−3.34002	−	2.80261i	−0.120680	−	0.101262i
$767$	−15.8097	+	27.3833i	−0.570857	+	0.988753i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	3.39874	−	19.2752i	0.122562	−	0.695081i	−0.860165	−	0.510016i	$-0.829639\pi$
$769$	3.39874	−	19.2752i	0.122562	−	0.695081i	0.982726	−	0.185065i	$-0.0592496\pi$
$770$	−9.86097	+	55.9243i	−0.355365	+	2.01537i
$771$	−7.89827	−	13.6802i	−0.284449	−	0.492681i
$772$	−1.26217	+	2.18615i	−0.0454266	+	0.0786812i
$773$	17.1552	+	14.3949i	0.617031	+	0.517750i	0.896869	−	0.442297i	$-0.145836\pi$
$773$	17.1552	+	14.3949i	0.617031	+	0.517750i	−0.279838	+	0.960047i	$0.590281\pi$
$774$	3.91875	+	1.42631i	0.140856	+	0.0512676i
$775$	−41.2686	+	15.0206i	−1.48241	+	0.539554i
$776$	5.45858	−	4.58029i	0.195952	−	0.164423i
$777$	−5.72668	−	32.4776i	−0.205444	−	1.16513i
$778$	1.31046			0.0469823
$779$	2.32399	+	28.4752i	0.0832655	+	1.02023i
$780$	9.26857			0.331868
$781$	−4.71436	−	26.7364i	−0.168693	−	0.956705i
$782$	3.09627	−	2.59808i	0.110722	−	0.0929070i
$783$	−3.54576	+	1.29055i	−0.126715	+	0.0461205i
$784$	−15.7947	−	5.74881i	−0.564097	−	0.205315i
$785$	16.3889	+	13.7520i	0.584946	+	0.490828i
$786$	−9.30200	+	16.1115i	−0.331791	+	0.574680i
$787$	−16.8444	−	29.1753i	−0.600437	−	1.03999i	−0.992755	−	0.120157i	$-0.961660\pi$
$787$	−16.8444	−	29.1753i	−0.600437	−	1.03999i	0.392318	−	0.919830i	$-0.371673\pi$
$788$	2.57991	−	14.6314i	0.0919054	−	0.521221i
$789$	1.88666	−	10.6998i	0.0671668	−	0.380922i
$790$	0.507741	+	0.879433i	0.0180646	+	0.0312888i
$791$	4.73514	−	8.20150i	0.168362	−	0.291612i
$792$	2.61334	+	2.19285i	0.0928610	+	0.0779196i
$793$	−17.6202	−	6.41323i	−0.625712	−	0.227740i
$794$	−17.8662	+	6.50276i	−0.634047	+	0.230774i
$795$	1.64749	−	1.38241i	0.0584304	−	0.0490289i
$796$	1.40121	+	7.94664i	0.0496645	+	0.281661i
$797$	−47.8631			−1.69540			−0.847699	−	0.530478i	$-0.822012\pi$
$797$	−47.8631			−1.69540			−0.847699	+	0.530478i	$0.822012\pi$
$798$	5.62449	−	20.5116i	0.199105	−	0.726102i
$799$	3.38507			0.119755
$800$	−1.15270	−	6.53731i	−0.0407542	−	0.231129i
$801$	5.18866	−	4.35381i	0.183332	−	0.153834i
$802$	33.7003	−	12.2659i	1.19000	−	0.433124i
$803$	−40.8546	−	14.8699i	−1.44173	−	0.524746i
$804$	0.543233	+	0.455827i	0.0191584	+	0.0160758i
$805$	−28.3935	+	49.1790i	−1.00074	+	1.73333i
$806$	8.98726	+	15.5664i	0.316563	+	0.548303i
$807$	−3.00299	+	17.0308i	−0.105710	+	0.599513i
$808$	0.806751	−	4.57531i	0.0283814	−	0.160959i
$809$	1.83703	+	3.18183i	0.0645865	+	0.111867i	0.896510	−	0.443022i	$-0.146094\pi$
$809$	1.83703	+	3.18183i	0.0645865	+	0.111867i	−0.831924	+	0.554890i	$0.812760\pi$
$810$	1.70574	−	2.95442i	0.0599335	−	0.103808i
$811$	−14.3289	−	12.0234i	−0.503155	−	0.422197i	0.355558	−	0.934654i	$-0.384291\pi$
$811$	−14.3289	−	12.0234i	−0.503155	−	0.422197i	−0.858713	+	0.512457i	$0.828735\pi$
$812$	17.3011	+	6.29710i	0.607151	+	0.220985i
$813$	−1.35844	+	0.494432i	−0.0476426	+	0.0173405i
$814$	17.6630	−	14.8210i	0.619087	−	0.519476i
$815$	−11.4324	−	64.8365i	−0.400460	−	2.27112i
$816$	1.18479			0.0414760
$817$	14.9508	−	10.3393i	0.523064	−	0.361725i
$818$	29.1088			1.01776
$819$	−2.30200	−	13.0553i	−0.0804385	−	0.456190i
$820$	17.1288	−	14.3728i	0.598164	−	0.501920i
$821$	20.9706	−	7.63267i	0.731879	−	0.266382i	0.0509190	−	0.998703i	$-0.483785\pi$
$821$	20.9706	−	7.63267i	0.731879	−	0.266382i	0.680960	+	0.732321i	$0.261563\pi$
$822$	4.27244	+	1.55504i	0.149018	+	0.0542383i
$823$	−20.2264	−	16.9720i	−0.705049	−	0.591606i	0.218156	−	0.975914i	$-0.429996\pi$
$823$	−20.2264	−	16.9720i	−0.705049	−	0.591606i	−0.923205	+	0.384307i	$0.874440\pi$
$824$	−6.19119	+	10.7235i	−0.215680	+	0.373569i
$825$	11.3229	+	19.6119i	0.394214	+	0.682799i
$826$	9.86097	−	55.9243i	0.343107	−	1.94586i
$827$	5.15224	−	29.2198i	0.179161	−	1.01607i	−0.754070	−	0.656794i	$-0.771912\pi$
$827$	5.15224	−	29.2198i	0.179161	−	1.01607i	0.933231	−	0.359277i	$-0.116977\pi$
$828$	1.70574	+	2.95442i	0.0592785	+	0.102673i
$829$	−0.884133	+	1.53136i	−0.0307072	+	0.0531864i	−0.880971	−	0.473171i	$-0.843109\pi$
$829$	−0.884133	+	1.53136i	−0.0307072	+	0.0531864i	0.850263	+	0.526357i	$0.176443\pi$
$830$	−40.7786	−	34.2173i	−1.41545	−	1.18770i
$831$	−19.9128	−	7.24767i	−0.690768	−	0.251419i
$832$	−2.55303	+	0.929228i	−0.0885105	+	0.0322152i
$833$	15.2554	−	12.8008i	0.528567	−	0.443520i
$834$	0.523471	+	2.96875i	0.0181263	+	0.102799i
$835$	−26.3432			−0.911643
$836$	14.3858	−	3.76487i	0.497543	−	0.130211i
$837$	6.61587			0.228678
$838$	−2.28493	−	12.9585i	−0.0789316	−	0.447643i
$839$	20.4643	−	17.1716i	0.706505	−	0.592828i	−0.217111	−	0.976147i	$-0.569663\pi$
$839$	20.4643	−	17.1716i	0.706505	−	0.592828i	0.923616	+	0.383319i	$0.125219\pi$
$840$	−15.6420	+	5.69323i	−0.539701	+	0.196435i
$841$	13.8718	+	5.04892i	0.478338	+	0.174101i
$842$	0.115400	+	0.0968323i	0.00397695	+	0.00333706i
$843$	12.1839	−	21.1032i	0.419636	−	0.726831i
$844$	−3.97178	−	6.87933i	−0.136714	−	0.236796i
$845$	−3.32841	+	18.8764i	−0.114501	+	0.649366i
$846$	−0.496130	+	2.81369i	−0.0170573	+	0.0967367i
$847$	1.55690	+	2.69664i	0.0534958	+	0.0926575i
$848$	−0.315207	+	0.545955i	−0.0108243	+	0.0187482i
$849$	−3.16044	−	2.65193i	−0.108466	−	0.0910139i
$850$	7.39053	+	2.68993i	0.253493	+	0.0922639i
$851$	21.6668	−	7.88609i	0.742730	−	0.270332i
$852$	6.09627	−	5.11538i	0.208855	−	0.175250i
$853$	2.41828	+	13.7148i	0.0828004	+	0.469584i	0.997810	+	0.0661513i	$0.0210720\pi$
$853$	2.41828	+	13.7148i	0.0828004	+	0.469584i	−0.915009	+	0.403433i	$0.867817\pi$
$854$	33.6759			1.15237
$855$	−6.20574	−	13.5135i	−0.212232	−	0.462151i
$856$	−3.89899			−0.133265
$857$	−3.41551	−	19.3703i	−0.116671	−	0.661677i	−0.985909	−	0.167282i	$-0.946501\pi$
$857$	−3.41551	−	19.3703i	−0.116671	−	0.661677i	0.869238	−	0.494395i	$-0.164610\pi$
$858$	7.10014	−	5.95772i	0.242395	−	0.203393i
$859$	40.7806	−	14.8429i	1.39142	−	0.506435i	0.465799	−	0.884891i	$-0.345767\pi$
$859$	40.7806	−	14.8429i	1.39142	−	0.506435i	0.925619	+	0.378456i	$0.123545\pi$
$860$	−13.3687	−	4.86581i	−0.455869	−	0.165923i
$861$	−24.4991	−	20.5572i	−0.834928	−	0.700588i
$862$	−15.3983	+	26.6706i	−0.524467	+	0.908404i
$863$	14.7096	+	25.4778i	0.500721	+	0.867274i	1.00000		0.000832579i	$0.000265018\pi$
$863$	14.7096	+	25.4778i	0.500721	+	0.867274i	−0.499279	+	0.866441i	$0.666402\pi$
$864$	−0.173648	+	0.984808i	−0.00590763	+	0.0335038i
$865$	−8.58693	+	48.6989i	−0.291964	+	1.65581i
$866$	−14.7169	−	25.4904i	−0.500100	−	0.866199i
$867$	7.79813	−	13.5068i	0.264838	−	0.458714i
$868$	−24.7290	−	20.7501i	−0.839356	−	0.704303i
$869$	0.954241	+	0.347315i	0.0323704	+	0.0117819i
$870$	12.0963	−	4.40268i	0.410102	−	0.149265i
$871$	1.47590	−	1.23843i	0.0500090	−	0.0419625i
$872$	2.01367	+	11.4201i	0.0681915	+	0.386733i
$873$	−7.12567			−0.241167
$874$	14.8059	+	1.38241i	0.500816	+	0.0467606i
$875$	−27.2686			−0.921846
$876$	−2.21301	−	12.5506i	−0.0747707	−	0.424046i
$877$	−20.0437	+	16.8187i	−0.676828	+	0.567926i	−0.915077	−	0.403278i	$-0.867871\pi$
$877$	−20.0437	+	16.8187i	−0.676828	+	0.567926i	0.238250	+	0.971204i	$0.423426\pi$
$878$	18.6065	−	6.77222i	0.627940	−	0.228552i
$879$	−2.61334	−	0.951178i	−0.0881458	−	0.0320824i
$880$	−8.91534	−	7.48086i	−0.300536	−	0.252180i
$881$	−11.3143	+	19.5970i	−0.381189	+	0.660240i	−0.991233	−	0.132129i	$-0.957819\pi$
$881$	−11.3143	+	19.5970i	−0.381189	+	0.660240i	0.610043	+	0.792368i	$0.291152\pi$
$882$	8.40420	+	14.5565i	0.282984	+	0.490143i
$883$	−1.43810	+	8.15587i	−0.0483959	+	0.274467i	−0.999397	−	0.0347205i	$-0.988946\pi$
$883$	−1.43810	+	8.15587i	−0.0483959	+	0.274467i	0.951001	+	0.309187i	$0.100057\pi$
$884$	0.558963	−	3.17004i	0.0188000	−	0.106620i
$885$	−19.8516	−	34.3840i	−0.667305	−	1.15581i
$886$	−9.29339	+	16.0966i	−0.312217	+	0.540776i
$887$	30.9152	+	25.9409i	1.03803	+	0.871011i	0.991785	−	0.127919i	$-0.0408299\pi$
$887$	30.9152	+	25.9409i	1.03803	+	0.871011i	0.0462457	+	0.998930i	$0.485274\pi$
$888$	6.35117	+	2.31164i	0.213131	+	0.0775734i
$889$	−27.8949	+	10.1529i	−0.935564	+	0.340517i
$890$	−17.7010	+	14.8529i	−0.593339	+	0.497870i
$891$	−0.592396	−	3.35965i	−0.0198460	−	0.112552i
$892$	11.9682			0.400726
$893$	8.75465	+	8.85737i	0.292963	+	0.296401i
$894$	−1.18479			−0.0396254
$895$	−5.81908	−	33.0016i	−0.194510	−	1.10312i
$896$	3.73783	−	3.13641i	0.124872	−	0.104780i
$897$	8.70961	−	3.17004i	0.290805	−	0.105844i
$898$	3.17530	+	1.15571i	0.105961	+	0.0385667i
$899$	19.1234	+	16.0464i	0.637800	+	0.535178i
$900$	−3.31908	+	5.74881i	−0.110636	+	0.191627i
$901$	−0.373455	−	0.646844i	−0.0124416	−	0.0215495i
$902$	3.88279	−	22.0204i	0.129283	−	0.733199i
$903$	−3.53343	+	20.0391i	−0.117585	+	0.666859i
$904$	0.970437	+	1.68085i	0.0322763	+	0.0559041i
$905$	−32.2631	+	55.8813i	−1.07246	+	1.85756i
$906$	2.78699	+	2.33856i	0.0925915	+	0.0776935i
$907$	18.0903	+	6.58434i	0.600680	+	0.218630i	0.624420	−	0.781089i	$-0.285335\pi$
$907$	18.0903	+	6.58434i	0.600680	+	0.218630i	−0.0237404	+	0.999718i	$0.507558\pi$
$908$	−24.9907	+	9.09586i	−0.829344	+	0.301857i
$909$	−3.55896	+	2.98632i	−0.118043	+	0.0990501i
$910$	7.85323	+	44.5379i	0.260332	+	1.47642i
$911$	−58.7684			−1.94708			−0.973542	−	0.228510i	$-0.926615\pi$
$911$	−58.7684			−1.94708			−0.973542	+	0.228510i	$0.926615\pi$
$912$	3.06418	+	3.10013i	0.101465	+	0.102656i
$913$	−53.2327			−1.76174
$914$	−3.78400	−	21.4601i	−0.125163	−	0.709837i
$915$	18.0364	−	15.1344i	0.596266	−	0.500326i
$916$	18.7023	−	6.80709i	0.617942	−	0.224913i
$917$	−85.3016	−	31.0473i	−2.81691	−	1.02527i
$918$	−0.907604	−	0.761570i	−0.0299554	−	0.0251356i
$919$	26.8714	−	46.5426i	0.886406	−	1.53530i	0.0423114	−	0.999104i	$-0.486528\pi$
$919$	26.8714	−	46.5426i	0.886406	−	1.53530i	0.844094	−	0.536195i	$-0.180139\pi$
$920$	−5.81908	−	10.0789i	−0.191849	−	0.332293i
$921$	−4.34524	+	24.6431i	−0.143180	+	0.812017i
$922$	−2.04277	+	11.5851i	−0.0672749	+	0.381535i
$923$	−10.8106	−	18.7245i	−0.355836	−	0.616326i
$924$	−8.32295	+	14.4158i	−0.273805	+	0.474244i
$925$	34.3692	+	28.8392i	1.13005	+	0.948226i
$926$	15.9684	+	5.81201i	0.524753	+	0.190995i
$927$	11.6356	−	4.23502i	0.382164	−	0.139096i
$928$	−2.89053	+	2.42544i	−0.0948863	+	0.0796190i
$929$	−5.38981	−	30.5672i	−0.176834	−	1.00288i	−0.936006	−	0.351985i	$-0.885507\pi$
$929$	−5.38981	−	30.5672i	−0.176834	−	1.00288i	0.759171	−	0.650891i	$-0.225604\pi$
$930$	−22.5699			−0.740095
$931$	72.9488	+	6.81115i	2.39080	+	0.223226i
$932$	−4.31046			−0.141194
$933$	4.16297	+	23.6094i	0.136290	+	0.772936i
$934$	8.96657	−	7.52384i	0.293395	−	0.246188i
$935$	12.9572	−	4.71605i	0.423747	−	0.154231i
$936$	2.55303	+	0.929228i	0.0834485	+	0.0303728i
$937$	−15.8899	−	13.3332i	−0.519100	−	0.435577i	0.345218	−	0.938523i	$-0.387805\pi$
$937$	−15.8899	−	13.3332i	−0.519100	−	0.435577i	−0.864318	+	0.502946i	$0.832250\pi$
$938$	−1.73009	+	2.99660i	−0.0564893	+	0.0978423i
$939$	6.31908	+	10.9450i	0.206215	+	0.357175i
$940$	1.69253	−	9.59883i	0.0552043	−	0.313079i
$941$	−2.58095	+	14.6373i	−0.0841365	+	0.477162i	0.913403	+	0.407056i	$0.133445\pi$
$941$	−2.58095	+	14.6373i	−0.0841365	+	0.477162i	−0.997540	+	0.0701055i	$0.977666\pi$
$942$	3.13563	+	5.43107i	0.102164	+	0.176954i
$943$	11.1800	−	19.3644i	0.364072	−	0.630592i
$944$	8.91534	+	7.48086i	0.290170	+	0.243481i
$945$	15.6420	+	5.69323i	0.508835	+	0.185201i
$946$	−13.3687	+	4.86581i	−0.434654	+	0.158201i
$947$	−19.3043	+	16.1982i	−0.627305	+	0.526371i	−0.900090	−	0.435704i	$-0.856500\pi$
$947$	−19.3043	+	16.1982i	−0.627305	+	0.526371i	0.272785	+	0.962075i	$0.412055\pi$
$948$	0.0516892	+	0.293144i	0.00167879	+	0.00952088i
$949$	−34.6245			−1.12396
$950$	12.0753	+	26.2949i	0.391775	+	0.853120i
$951$	−14.1334			−0.458307
$952$	1.00387	+	5.69323i	0.0325356	+	0.184519i
$953$	−9.48751	+	7.96097i	−0.307331	+	0.257881i	−0.783388	−	0.621533i	$-0.786510\pi$
$953$	−9.48751	+	7.96097i	−0.307331	+	0.257881i	0.476057	+	0.879414i	$0.342066\pi$
$954$	0.592396	−	0.215615i	0.0191795	−	0.00698078i
$955$	32.3508	+	11.7747i	1.04685	+	0.381021i
$956$	0.218941	+	0.183713i	0.00708105	+	0.00594171i
$957$	6.43629	−	11.1480i	0.208056	−	0.360363i
$958$	14.9898	+	25.9631i	0.484298	+	0.838829i
$959$	−3.85235	+	21.8478i	−0.124399	+	0.705501i
$960$	0.592396	−	3.35965i	0.0191195	−	0.108432i
$961$	−6.38485	−	11.0589i	−0.205963	−	0.356738i
$962$	9.18139	−	15.9026i	0.296020	−	0.512721i
$963$	2.98680	+	2.50622i	0.0962482	+	0.0807618i
$964$	−8.98932	−	3.27185i	−0.289527	−	0.105379i
$965$	−8.09240	+	2.94539i	−0.260503	+	0.0948155i
$966$	−12.7515	+	10.6998i	−0.410273	+	0.344260i
$967$	−0.591929	−	3.35700i	−0.0190352	−	0.107954i	0.973810	−	0.227364i	$-0.0730107\pi$
$967$	−0.591929	−	3.35700i	−0.0190352	−	0.107954i	−0.992845	+	0.119410i	$0.961900\pi$
$968$	−0.638156			−0.0205111
$969$	−4.99613	+	1.30753i	−0.160499	+	0.0420038i
$970$	24.3090			0.780516
$971$	−2.41323	−	13.6861i	−0.0774442	−	0.439208i	−0.998733	−	0.0503282i	$-0.983973\pi$
$971$	−2.41323	−	13.6861i	−0.0774442	−	0.439208i	0.921289	−	0.388880i	$-0.127138\pi$
$972$	0.766044	−	0.642788i	0.0245709	−	0.0206174i
$973$	−13.8221	+	5.03082i	−0.443115	+	0.161281i
$974$	13.6356	+	4.96296i	0.436914	+	0.159024i
$975$	13.8157	+	11.5927i	0.442456	+	0.371264i
$976$	−3.45084	+	5.97702i	−0.110459	+	0.191320i
$977$	−6.42009	−	11.1199i	−0.205397	−	0.355758i	0.744862	−	0.667218i	$-0.232515\pi$
$977$	−6.42009	−	11.1199i	−0.205397	−	0.355758i	−0.950259	+	0.311460i	$0.899182\pi$
$978$	3.35117	−	19.0054i	0.107158	−	0.607726i
$979$	−4.01249	+	22.7560i	−0.128240	+	0.727283i
$980$	−28.6707	−	49.6591i	−0.915852	−	1.58630i
$981$	5.79813	−	10.0427i	0.185120	−	0.320638i
$982$	8.92855	+	7.49194i	0.284921	+	0.239077i
$983$	0.814330	+	0.296392i	0.0259731	+	0.00945343i	0.354974	−	0.934876i	$-0.384490\pi$
$983$	0.814330	+	0.296392i	0.0259731	+	0.00945343i	−0.329001	+	0.944330i	$0.606712\pi$
$984$	6.15910	−	2.24173i	0.196345	−	0.0714637i
$985$	38.8267	−	32.5794i	1.23712	−	1.03807i
$986$	−0.776311	−	4.40268i	−0.0247228	−	0.140210i
$987$	−13.9409			−0.443743
$988$	9.74035	−	6.73595i	0.309882	−	0.214299i
$989$	−14.2267			−0.452382
$990$	2.02094	+	11.4613i	0.0642298	+	0.364265i
$991$	−16.0646	+	13.4798i	−0.510310	+	0.428201i	−0.861238	−	0.508201i	$-0.830311\pi$
$991$	−16.0646	+	13.4798i	−0.510310	+	0.428201i	0.350928	+	0.936402i	$0.385866\pi$
$992$	6.21688	−	2.26276i	0.197386	−	0.0718427i
$993$	−27.7190	−	10.0889i	−0.879636	−	0.320161i
$994$	29.7460	+	24.9599i	0.943487	+	0.791680i
$995$	−13.7640	+	23.8399i	−0.436348	+	0.755776i
$996$	−7.80200	−	13.5135i	−0.247216	−	0.428191i
$997$	6.90208	−	39.1437i	0.218591	−	1.23969i	−0.655974	−	0.754784i	$-0.727742\pi$
$997$	6.90208	−	39.1437i	0.218591	−	1.23969i	0.874565	−	0.484909i	$-0.161147\pi$
$998$	0.292919	−	1.66122i	0.00927218	−	0.0525852i
$999$	−3.37939	−	5.85327i	−0.106919	−	0.185189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.a.85.1	yes	6
3.2	odd	2		342.2.u.e.199.1		6
4.3	odd	2		912.2.bo.a.769.1		6
19.6	even	9		2166.2.a.q.1.3		3
19.13	odd	18		2166.2.a.s.1.3		3
19.17	even	9	inner	114.2.i.a.55.1	✓	6
57.17	odd	18		342.2.u.e.55.1		6
57.32	even	18		6498.2.a.bm.1.1		3
57.44	odd	18		6498.2.a.br.1.1		3
76.55	odd	18		912.2.bo.a.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.55.1	✓	6	19.17	even	9	inner
114.2.i.a.85.1	yes	6	1.1	even	1	trivial
342.2.u.e.55.1		6	57.17	odd	18
342.2.u.e.199.1		6	3.2	odd	2
912.2.bo.a.625.1		6	76.55	odd	18
912.2.bo.a.769.1		6	4.3	odd	2
2166.2.a.q.1.3		3	19.6	even	9
2166.2.a.s.1.3		3	19.13	odd	18
6498.2.a.bm.1.1		3	57.32	even	18
6498.2.a.br.1.1		3	57.44	odd	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.20574 - 1.16679i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.43969 - 4.22567i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.20574 - 1.16679i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.43969 - 4.22567i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.592396 + 3.35965i) q^{10} +(1.70574 + 2.95442i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.08125 + 1.74638i) q^{13} +(-4.58512 - 1.66885i) q^{14} +(-3.20574 + 1.16679i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.205737 + 1.16679i) q^{17} -1.00000 q^{18} +(-2.52094 + 3.55596i) q^{19} +3.41147 q^{20} +(-0.847296 - 4.80526i) q^{21} +(2.61334 - 2.19285i) q^{22} +(3.20574 - 1.16679i) q^{23} +(0.939693 + 0.342020i) q^{24} +(5.08512 + 4.26692i) q^{25} +(1.35844 - 2.35289i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.847296 + 4.80526i) q^{28} +(0.655230 - 3.71599i) q^{29} +(1.70574 + 2.95442i) q^{30} +(-3.30793 + 5.72951i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(3.20574 + 1.16679i) q^{33} +(1.11334 - 0.405223i) q^{34} +(-12.7515 + 10.6998i) q^{35} +(0.173648 + 0.984808i) q^{36} +6.75877 q^{37} +(3.93969 + 1.86516i) q^{38} +2.71688 q^{39} +(-0.592396 - 3.35965i) q^{40} +(5.02094 - 4.21307i) q^{41} +(-4.58512 + 1.66885i) q^{42} +(-3.91875 - 1.42631i) q^{43} +(-2.61334 - 2.19285i) q^{44} +(-1.70574 + 2.95442i) q^{45} +(-1.70574 - 2.95442i) q^{46} +(0.496130 - 2.81369i) q^{47} +(0.173648 - 0.984808i) q^{48} +(-8.40420 - 14.5565i) q^{49} +(3.31908 - 5.74881i) q^{50} +(0.907604 + 0.761570i) q^{51} +(-2.55303 - 0.929228i) q^{52} +(-0.592396 + 0.215615i) q^{53} +(-0.766044 + 0.642788i) q^{54} +(-2.02094 - 11.4613i) q^{55} +4.87939 q^{56} +(0.354570 + 4.34445i) q^{57} -3.77332 q^{58} +(2.02094 + 11.4613i) q^{59} +(2.61334 - 2.19285i) q^{60} +(-6.48545 + 2.36051i) q^{61} +(6.21688 + 2.26276i) q^{62} +(-3.73783 - 3.13641i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.63429 - 8.02682i) q^{65} +(0.592396 - 3.35965i) q^{66} +(0.123141 - 0.698367i) q^{67} +(-0.592396 - 1.02606i) q^{68} +(1.70574 - 2.95442i) q^{69} +(12.7515 + 10.6998i) q^{70} +(-7.47818 - 2.72183i) q^{71} +(0.939693 - 0.342020i) q^{72} +(-9.76264 + 8.19183i) q^{73} +(-1.17365 - 6.65609i) q^{74} +6.63816 q^{75} +(1.15270 - 4.20372i) q^{76} +16.6459 q^{77} +(-0.471782 - 2.67561i) q^{78} +(0.228026 - 0.191336i) q^{79} +(-3.20574 + 1.16679i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-5.02094 - 4.21307i) q^{82} +(-7.80200 + 13.5135i) q^{83} +(2.43969 + 4.22567i) q^{84} +(0.701867 - 3.98048i) q^{85} +(-0.724155 + 4.10689i) q^{86} +(-1.88666 - 3.26779i) q^{87} +(-1.70574 + 2.95442i) q^{88} +(5.18866 + 4.35381i) q^{89} +(3.20574 + 1.16679i) q^{90} +(12.4572 - 4.53406i) q^{91} +(-2.61334 + 2.19285i) q^{92} +(1.14883 + 6.51536i) q^{93} -2.85710 q^{94} +(12.2306 - 8.45805i) q^{95} -1.00000 q^{96} +(-1.23736 - 7.01741i) q^{97} +(-12.8760 + 10.8042i) q^{98} +(3.20574 - 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8	\( 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8} - 3 q^{12} + 15 q^{13} - 6 q^{14} - 9 q^{15} - 9 q^{17} - 6 q^{18} - 12 q^{19} - 3 q^{21} + 9 q^{22} + 9 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{28} - 9 q^{29} - 9 q^{31} + 9 q^{33} - 36 q^{35} + 18 q^{37} + 18 q^{38} + 27 q^{41} - 6 q^{42} - 21 q^{43} - 9 q^{44} + 27 q^{47} - 12 q^{49} + 3 q^{50} + 9 q^{51} - 3 q^{52} - 9 q^{55} + 18 q^{56} + 18 q^{57} - 36 q^{58} + 9 q^{59} + 9 q^{60} - 3 q^{61} + 21 q^{62} - 3 q^{63} - 3 q^{64} - 18 q^{65} - 3 q^{67} + 36 q^{70} + 9 q^{71} - 12 q^{73} - 6 q^{74} + 6 q^{75} + 9 q^{76} + 18 q^{77} + 12 q^{78} - 21 q^{79} - 9 q^{80} - 27 q^{82} - 9 q^{83} + 9 q^{84} + 18 q^{85} - 6 q^{86} - 18 q^{87} + 9 q^{90} + 24 q^{91} - 9 q^{92} + 33 q^{93} - 18 q^{94} + 36 q^{95} - 6 q^{96} - 54 q^{97} - 24 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8 - 3 * q^12 + 15 * q^13 - 6 * q^14 - 9 * q^15 - 9 * q^17 - 6 * q^18 - 12 * q^19 - 3 * q^21 + 9 * q^22 + 9 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^28 - 9 * q^29 - 9 * q^31 + 9 * q^33 - 36 * q^35 + 18 * q^37 + 18 * q^38 + 27 * q^41 - 6 * q^42 - 21 * q^43 - 9 * q^44 + 27 * q^47 - 12 * q^49 + 3 * q^50 + 9 * q^51 - 3 * q^52 - 9 * q^55 + 18 * q^56 + 18 * q^57 - 36 * q^58 + 9 * q^59 + 9 * q^60 - 3 * q^61 + 21 * q^62 - 3 * q^63 - 3 * q^64 - 18 * q^65 - 3 * q^67 + 36 * q^70 + 9 * q^71 - 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 18 * q^77 + 12 * q^78 - 21 * q^79 - 9 * q^80 - 27 * q^82 - 9 * q^83 + 9 * q^84 + 18 * q^85 - 6 * q^86 - 18 * q^87 + 9 * q^90 + 24 * q^91 - 9 * q^92 + 33 * q^93 - 18 * q^94 + 36 * q^95 - 6 * q^96 - 54 * q^97 - 24 * q^98 + 9 * q^99

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