LMFDB - Embedded newform 33.2.e.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,2,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, 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:	$0.263506326670$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	33.31
Dual form			33.2.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-2.42705 - 1.76336i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.190983 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-2.42705 - 1.76336i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.61803 q^{10} +(1.69098 + 2.85317i) q^{11} -1.61803 q^{12} +(0.545085 - 1.67760i) q^{13} +(1.50000 - 1.08981i) q^{14} +(2.11803 + 1.53884i) q^{15} +(0.572949 + 1.76336i) q^{16} +(0.500000 + 1.53884i) q^{17} +(0.500000 + 0.363271i) q^{18} +(-4.73607 + 3.44095i) q^{19} +(1.30902 - 4.02874i) q^{20} +3.00000 q^{21} +(-2.00000 + 0.449028i) q^{22} +3.47214 q^{23} +(0.690983 - 2.12663i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(0.881966 + 0.640786i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(-3.61803 - 2.62866i) q^{29} +(-1.30902 + 0.951057i) q^{30} +(0.881966 - 2.71441i) q^{31} -5.61803 q^{32} +(-3.04508 - 1.31433i) q^{33} -1.00000 q^{34} +(-2.42705 + 7.46969i) q^{35} +(1.30902 - 0.951057i) q^{36} +(-0.190983 - 0.138757i) q^{37} +(-1.11803 - 3.44095i) q^{38} +(0.545085 + 1.67760i) q^{39} +(4.73607 + 3.44095i) q^{40} +(9.66312 - 7.02067i) q^{41} +(-0.572949 + 1.76336i) q^{42} +6.23607 q^{43} +(-0.500000 + 5.34307i) q^{44} -2.61803 q^{45} +(-0.663119 + 2.04087i) q^{46} +(-1.30902 + 0.951057i) q^{47} +(-1.50000 - 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-0.354102 - 1.08981i) q^{50} +(-1.30902 - 0.951057i) q^{51} +(2.30902 - 1.67760i) q^{52} +(-2.97214 + 9.14729i) q^{53} -0.618034 q^{54} +(5.73607 - 6.51864i) q^{55} +6.70820 q^{56} +(1.80902 - 5.56758i) q^{57} +(2.23607 - 1.62460i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(1.30902 + 4.02874i) q^{60} +(2.42705 + 7.46969i) q^{61} +(1.42705 + 1.03681i) q^{62} +(-2.42705 + 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} -4.61803 q^{65} +(1.35410 - 1.53884i) q^{66} -9.56231 q^{67} +(-0.809017 + 2.48990i) q^{68} +(-2.80902 + 2.04087i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-1.71885 - 5.29007i) q^{71} +(0.690983 + 2.12663i) q^{72} +(2.61803 + 1.90211i) q^{73} +(0.118034 - 0.0857567i) q^{74} +(0.572949 - 1.76336i) q^{75} -9.47214 q^{76} +(0.927051 - 9.90659i) q^{77} -1.09017 q^{78} +(2.92705 - 9.00854i) q^{79} +(3.92705 - 2.85317i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.28115 + 7.02067i) q^{82} +(0.218847 + 0.673542i) q^{83} +(3.92705 + 2.85317i) q^{84} +(3.42705 - 2.48990i) q^{85} +(-1.19098 + 3.66547i) q^{86} +4.47214 q^{87} +(-6.80902 - 2.93893i) q^{88} +0.527864 q^{89} +(0.500000 - 1.53884i) q^{90} +(-4.28115 + 3.11044i) q^{91} +(4.54508 + 3.30220i) q^{92} +(0.881966 + 2.71441i) q^{93} +(-0.309017 - 0.951057i) q^{94} +(12.3992 + 9.00854i) q^{95} +(4.54508 - 3.30220i) q^{96} +(-4.33688 + 13.3475i) q^{97} -1.23607 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9} + 2 q^{10} + 9 q^{11} - 2 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} + 2 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{20} + 12 q^{21} - 8 q^{22} - 4 q^{23} + 5 q^{24} - 6 q^{25} + 8 q^{26} - q^{27} - 6 q^{28} - 10 q^{29} - 3 q^{30} + 8 q^{31} - 18 q^{32} - q^{33} - 4 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} - 9 q^{39} + 10 q^{40} + 23 q^{41} - 9 q^{42} + 16 q^{43} - 2 q^{44} - 6 q^{45} + 13 q^{46} - 3 q^{47} - 6 q^{48} - 2 q^{49} + 12 q^{50} - 3 q^{51} + 7 q^{52} + 6 q^{53} + 2 q^{54} + 14 q^{55} + 5 q^{57} - 20 q^{59} + 3 q^{60} + 3 q^{61} - q^{62} - 3 q^{63} - 7 q^{64} - 14 q^{65} - 8 q^{66} + 2 q^{67} - q^{68} - 9 q^{69} - 9 q^{70} - 27 q^{71} + 5 q^{72} + 6 q^{73} - 4 q^{74} + 9 q^{75} - 20 q^{76} - 3 q^{77} + 18 q^{78} + 5 q^{79} + 9 q^{80} - q^{81} - 11 q^{82} + 21 q^{83} + 9 q^{84} + 7 q^{85} - 7 q^{86} - 25 q^{88} + 20 q^{89} + 2 q^{90} + 3 q^{91} + 7 q^{92} + 8 q^{93} + q^{94} + 25 q^{95} + 7 q^{96} - 33 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9 + 2 * q^10 + 9 * q^11 - 2 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 + 9 * q^16 + 2 * q^17 + 2 * q^18 - 10 * q^19 + 3 * q^20 + 12 * q^21 - 8 * q^22 - 4 * q^23 + 5 * q^24 - 6 * q^25 + 8 * q^26 - q^27 - 6 * q^28 - 10 * q^29 - 3 * q^30 + 8 * q^31 - 18 * q^32 - q^33 - 4 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 - 9 * q^39 + 10 * q^40 + 23 * q^41 - 9 * q^42 + 16 * q^43 - 2 * q^44 - 6 * q^45 + 13 * q^46 - 3 * q^47 - 6 * q^48 - 2 * q^49 + 12 * q^50 - 3 * q^51 + 7 * q^52 + 6 * q^53 + 2 * q^54 + 14 * q^55 + 5 * q^57 - 20 * q^59 + 3 * q^60 + 3 * q^61 - q^62 - 3 * q^63 - 7 * q^64 - 14 * q^65 - 8 * q^66 + 2 * q^67 - q^68 - 9 * q^69 - 9 * q^70 - 27 * q^71 + 5 * q^72 + 6 * q^73 - 4 * q^74 + 9 * q^75 - 20 * q^76 - 3 * q^77 + 18 * q^78 + 5 * q^79 + 9 * q^80 - q^81 - 11 * q^82 + 21 * q^83 + 9 * q^84 + 7 * q^85 - 7 * q^86 - 25 * q^88 + 20 * q^89 + 2 * q^90 + 3 * q^91 + 7 * q^92 + 8 * q^93 + q^94 + 25 * q^95 + 7 * q^96 - 33 * q^97 + 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	−0.995597	−	0.0937362i	$-0.970119\pi$
$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	0.860552	+	0.509363i	$0.170119\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	−0.809017	−	2.48990i	−0.361803	−	1.11352i	−0.951959	−	0.306227i	$-0.900933\pi$
$5$	−0.809017	−	2.48990i	−0.361803	−	1.11352i	0.590155	−	0.807290i	$-0.299067\pi$
$6$	−0.190983	−	0.587785i	−0.0779685	−	0.239962i
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	0.0255212	−	0.999674i	$-0.491875\pi$
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	−0.942860	+	0.333188i	$0.891875\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.61803			0.511667
$11$	1.69098	+	2.85317i	0.509851	+	0.860263i
$11$	1.69098	+	2.85317i	0.509851	+	0.860263i
$12$	−1.61803			−0.467086
$13$	0.545085	−	1.67760i	0.151179	−	0.465282i	−0.846574	−	0.532270i	$-0.821339\pi$
$13$	0.545085	−	1.67760i	0.151179	−	0.465282i	0.997754	+	0.0669881i	$0.0213390\pi$
$14$	1.50000	−	1.08981i	0.400892	−	0.291265i
$15$	2.11803	+	1.53884i	0.546874	+	0.397327i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	0.500000	+	1.53884i	0.121268	+	0.373224i	0.993203	−	0.116398i	$-0.0371348\pi$
$17$	0.500000	+	1.53884i	0.121268	+	0.373224i	−0.871935	+	0.489622i	$0.837135\pi$
$18$	0.500000	+	0.363271i	0.117851	+	0.0856239i
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.978810	−	0.204772i	$-0.934355\pi$
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.107719	+	0.994181i	$0.534355\pi$
$20$	1.30902	−	4.02874i	0.292705	−	0.900854i
$21$	3.00000			0.654654
$22$	−2.00000	+	0.449028i	−0.426401	+	0.0957331i
$23$	3.47214			0.723990			0.361995	−	0.932180i	$-0.382096\pi$
$23$	3.47214			0.723990			0.361995	+	0.932180i	$0.382096\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$	−1.50000	+	1.08981i	−0.300000	+	0.217963i
$26$	0.881966	+	0.640786i	0.172968	+	0.125668i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.50000	−	4.61653i	−0.283473	−	0.872441i
$29$	−3.61803	−	2.62866i	−0.671852	−	0.488129i	0.198793	−	0.980042i	$-0.436298\pi$
$29$	−3.61803	−	2.62866i	−0.671852	−	0.488129i	−0.870645	+	0.491912i	$0.836298\pi$
$30$	−1.30902	+	0.951057i	−0.238993	+	0.173638i
$31$	0.881966	−	2.71441i	0.158406	−	0.487523i	−0.840084	−	0.542456i	$-0.817495\pi$
$31$	0.881966	−	2.71441i	0.158406	−	0.487523i	0.998490	+	0.0549331i	$0.0174946\pi$
$32$	−5.61803			−0.993137
$33$	−3.04508	−	1.31433i	−0.530081	−	0.228795i
$34$	−1.00000			−0.171499
$35$	−2.42705	+	7.46969i	−0.410246	+	1.26261i
$36$	1.30902	−	0.951057i	0.218169	−	0.158509i
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	0.571976	−	0.820270i	$-0.306177\pi$
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	−0.603373	+	0.797459i	$0.706177\pi$
$38$	−1.11803	−	3.44095i	−0.181369	−	0.558197i
$39$	0.545085	+	1.67760i	0.0872835	+	0.268631i
$40$	4.73607	+	3.44095i	0.748838	+	0.544063i
$41$	9.66312	−	7.02067i	1.50913	−	1.09644i	0.542562	−	0.840015i	$-0.317454\pi$
$41$	9.66312	−	7.02067i	1.50913	−	1.09644i	0.966563	−	0.256428i	$-0.0825458\pi$
$42$	−0.572949	+	1.76336i	−0.0884080	+	0.272092i
$43$	6.23607			0.950991			0.475496	−	0.879718i	$-0.342269\pi$
$43$	6.23607			0.950991			0.475496	+	0.879718i	$0.342269\pi$
$44$	−0.500000	+	5.34307i	−0.0753778	+	0.805498i
$45$	−2.61803			−0.390273
$46$	−0.663119	+	2.04087i	−0.0977716	+	0.300910i
$47$	−1.30902	+	0.951057i	−0.190940	+	0.138726i	−0.679148	−	0.734001i	$-0.737651\pi$
$47$	−1.30902	+	0.951057i	−0.190940	+	0.138726i	0.488208	+	0.872727i	$0.337651\pi$
$48$	−1.50000	−	1.08981i	−0.216506	−	0.157301i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	−0.354102	−	1.08981i	−0.0500776	−	0.154123i
$51$	−1.30902	−	0.951057i	−0.183299	−	0.133175i
$52$	2.30902	−	1.67760i	0.320203	−	0.232641i
$53$	−2.97214	+	9.14729i	−0.408254	+	1.25648i	0.509893	+	0.860238i	$0.329685\pi$
$53$	−2.97214	+	9.14729i	−0.408254	+	1.25648i	−0.918147	+	0.396240i	$0.870315\pi$
$54$	−0.618034			−0.0841038
$55$	5.73607	−	6.51864i	0.773451	−	0.878973i
$56$	6.70820			0.896421
$57$	1.80902	−	5.56758i	0.239610	−	0.737444i
$58$	2.23607	−	1.62460i	0.293610	−	0.213320i
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.108617	−	0.994084i	$-0.534642\pi$
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.978994	+	0.203888i	$0.934642\pi$
$60$	1.30902	+	4.02874i	0.168993	+	0.520108i
$61$	2.42705	+	7.46969i	0.310752	+	0.956396i	0.977468	+	0.211084i	$0.0676995\pi$
$61$	2.42705	+	7.46969i	0.310752	+	0.956396i	−0.666716	+	0.745312i	$0.732301\pi$
$62$	1.42705	+	1.03681i	0.181236	+	0.131675i
$63$	−2.42705	+	1.76336i	−0.305780	+	0.222162i
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	−4.61803			−0.572797
$66$	1.35410	−	1.53884i	0.166678	−	0.189418i
$67$	−9.56231			−1.16822			−0.584111	−	0.811674i	$-0.698557\pi$
$67$	−9.56231			−1.16822			−0.584111	+	0.811674i	$0.698557\pi$
$68$	−0.809017	+	2.48990i	−0.0981077	+	0.301945i
$69$	−2.80902	+	2.04087i	−0.338166	+	0.245692i
$70$	−3.92705	−	2.85317i	−0.469372	−	0.341019i
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	−0.999753	−	0.0222083i	$-0.992930\pi$
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	0.795764	−	0.605607i	$-0.207070\pi$
$72$	0.690983	+	2.12663i	0.0814331	+	0.250625i
$73$	2.61803	+	1.90211i	0.306418	+	0.222625i	0.730358	−	0.683065i	$-0.239353\pi$
$73$	2.61803	+	1.90211i	0.306418	+	0.222625i	−0.423940	+	0.905690i	$0.639353\pi$
$74$	0.118034	−	0.0857567i	0.0137212	−	0.00996902i
$75$	0.572949	−	1.76336i	0.0661585	−	0.203615i
$76$	−9.47214			−1.08653
$77$	0.927051	−	9.90659i	0.105647	−	1.12896i
$78$	−1.09017			−0.123437
$79$	2.92705	−	9.00854i	0.329319	−	1.01354i	−0.640134	−	0.768263i	$-0.721121\pi$
$79$	2.92705	−	9.00854i	0.329319	−	1.01354i	0.969453	−	0.245276i	$-0.0788787\pi$
$80$	3.92705	−	2.85317i	0.439058	−	0.318994i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	2.28115	+	7.02067i	0.251911	+	0.775303i
$83$	0.218847	+	0.673542i	0.0240216	+	0.0739308i	0.962349	−	0.271818i	$-0.0876249\pi$
$83$	0.218847	+	0.673542i	0.0240216	+	0.0739308i	−0.938327	+	0.345749i	$0.887625\pi$
$84$	3.92705	+	2.85317i	0.428476	+	0.311306i
$85$	3.42705	−	2.48990i	0.371716	−	0.270067i
$86$	−1.19098	+	3.66547i	−0.128427	+	0.395258i
$87$	4.47214			0.479463
$88$	−6.80902	−	2.93893i	−0.725844	−	0.313291i
$89$	0.527864			0.0559535			0.0279767	−	0.999609i	$-0.491094\pi$
$89$	0.527864			0.0559535			0.0279767	+	0.999609i	$0.491094\pi$
$90$	0.500000	−	1.53884i	0.0527046	−	0.162208i
$91$	−4.28115	+	3.11044i	−0.448787	+	0.326063i
$92$	4.54508	+	3.30220i	0.473858	+	0.344278i
$93$	0.881966	+	2.71441i	0.0914556	+	0.281471i
$94$	−0.309017	−	0.951057i	−0.0318727	−	0.0980940i
$95$	12.3992	+	9.00854i	1.27213	+	0.924256i
$96$	4.54508	−	3.30220i	0.463881	−	0.337029i
$97$	−4.33688	+	13.3475i	−0.440344	+	1.35524i	0.447167	+	0.894451i	$0.352433\pi$
$97$	−4.33688	+	13.3475i	−0.440344	+	1.35524i	−0.887510	+	0.460788i	$0.847567\pi$
$98$	−1.23607			−0.124862
$99$	3.23607	−	0.726543i	0.325237	−	0.0730203i
$100$	−3.00000			−0.300000
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	0.809017	−	0.587785i	0.0801046	−	0.0581994i
$103$	4.85410	+	3.52671i	0.478289	+	0.347497i	0.800663	−	0.599115i	$-0.204481\pi$
$103$	4.85410	+	3.52671i	0.478289	+	0.347497i	−0.322374	+	0.946612i	$0.604481\pi$
$104$	1.21885	+	3.75123i	0.119518	+	0.367838i
$105$	−2.42705	−	7.46969i	−0.236856	−	0.728968i
$106$	−4.80902	−	3.49396i	−0.467093	−	0.339363i
$107$	3.42705	−	2.48990i	0.331306	−	0.240708i	−0.409679	−	0.912230i	$-0.634359\pi$
$107$	3.42705	−	2.48990i	0.331306	−	0.240708i	0.740984	+	0.671522i	$0.234359\pi$
$108$	−0.500000	+	1.53884i	−0.0481125	+	0.148075i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	2.73607	+	4.61653i	0.260874	+	0.440168i
$111$	0.236068			0.0224066
$112$	1.71885	−	5.29007i	0.162416	−	0.499864i
$113$	−0.572949	+	0.416272i	−0.0538985	+	0.0391596i	−0.614408	−	0.788988i	$-0.710605\pi$
$113$	−0.572949	+	0.416272i	−0.0538985	+	0.0391596i	0.560510	+	0.828148i	$0.310605\pi$
$114$	2.92705	+	2.12663i	0.274143	+	0.199177i
$115$	−2.80902	−	8.64527i	−0.261942	−	0.806175i
$116$	−2.23607	−	6.88191i	−0.207614	−	0.638969i
$117$	−1.42705	−	1.03681i	−0.131931	−	0.0958534i
$118$	5.16312	−	3.75123i	0.475304	−	0.345328i
$119$	1.50000	−	4.61653i	0.137505	−	0.423196i
$120$	−5.85410			−0.534404
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$	−4.85410			−0.439470
$123$	−3.69098	+	11.3597i	−0.332805	+	1.02427i
$124$	3.73607	−	2.71441i	0.335509	−	0.243761i
$125$	−6.66312	−	4.84104i	−0.595967	−	0.432996i
$126$	−0.572949	−	1.76336i	−0.0510424	−	0.157092i
$127$	−1.14590	−	3.52671i	−0.101682	−	0.312945i	0.887255	−	0.461279i	$-0.152609\pi$
$127$	−1.14590	−	3.52671i	−0.101682	−	0.312945i	−0.988937	+	0.148333i	$0.952609\pi$
$128$	−9.20820	−	6.69015i	−0.813898	−	0.591331i
$129$	−5.04508	+	3.66547i	−0.444195	+	0.322727i
$130$	0.881966	−	2.71441i	0.0773535	−	0.238070i
$131$	−7.14590			−0.624340			−0.312170	−	0.950026i	$-0.601056\pi$
$131$	−7.14590			−0.624340			−0.312170	+	0.950026i	$0.601056\pi$
$132$	−2.73607	−	4.61653i	−0.238144	−	0.401817i
$133$	17.5623			1.52285
$134$	1.82624	−	5.62058i	0.157763	−	0.485544i
$135$	2.11803	−	1.53884i	0.182291	−	0.132442i
$136$	−2.92705	−	2.12663i	−0.250993	−	0.182357i
$137$	2.30902	+	7.10642i	0.197273	+	0.607143i	0.999943	+	0.0107192i	$0.00341210\pi$
$137$	2.30902	+	7.10642i	0.197273	+	0.607143i	−0.802670	+	0.596424i	$0.796588\pi$
$138$	−0.663119	−	2.04087i	−0.0564484	−	0.173730i
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	0.616704	−	0.787195i	$-0.288468\pi$
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	−0.558095	+	0.829777i	$0.688468\pi$
$140$	−10.2812	+	7.46969i	−0.868916	+	0.631304i
$141$	0.500000	−	1.53884i	0.0421076	−	0.129594i
$142$	3.43769			0.288485
$143$	5.70820	−	1.28157i	0.477344	−	0.107170i
$144$	1.85410			0.154508
$145$	−3.61803	+	11.1352i	−0.300461	+	0.924725i
$146$	−1.61803	+	1.17557i	−0.133909	+	0.0972909i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	−0.118034	−	0.363271i	−0.00970233	−	0.0298607i
$149$	4.63525	+	14.2658i	0.379735	+	1.16870i	0.940228	+	0.340545i	$0.110612\pi$
$149$	4.63525	+	14.2658i	0.379735	+	1.16870i	−0.560493	+	0.828159i	$0.689388\pi$
$150$	0.927051	+	0.673542i	0.0756934	+	0.0549945i
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	−0.651673	−	0.758500i	$-0.725932\pi$
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	0.519999	+	0.854167i	$0.325932\pi$
$152$	4.04508	−	12.4495i	0.328100	−	1.00979i
$153$	1.61803			0.130810
$154$	5.64590	+	2.43690i	0.454959	+	0.196371i
$155$	−7.47214			−0.600176
$156$	−0.881966	+	2.71441i	−0.0706138	+	0.217327i
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$	4.73607	+	3.44095i	0.376781	+	0.273748i
$159$	−2.97214	−	9.14729i	−0.235706	−	0.725428i
$160$	4.54508	+	13.9883i	0.359321	+	1.10587i
$161$	−8.42705	−	6.12261i	−0.664145	−	0.482529i
$162$	0.500000	−	0.363271i	0.0392837	−	0.0285413i
$163$	5.64590	−	17.3763i	0.442221	−	1.36102i	−0.443282	−	0.896382i	$-0.646186\pi$
$163$	5.64590	−	17.3763i	0.442221	−	1.36102i	0.885503	−	0.464634i	$-0.153814\pi$
$164$	19.3262			1.50913
$165$	−0.809017	+	8.64527i	−0.0629819	+	0.673033i
$166$	−0.437694			−0.0339717
$167$	3.10081	−	9.54332i	0.239948	−	0.738484i	−0.756478	−	0.654019i	$-0.773082\pi$
$167$	3.10081	−	9.54332i	0.239948	−	0.738484i	0.996426	−	0.0844656i	$-0.0269183\pi$
$168$	−5.42705	+	3.94298i	−0.418706	+	0.304208i
$169$	8.00000	+	5.81234i	0.615385	+	0.447103i
$170$	0.809017	+	2.48990i	0.0620488	+	0.190966i
$171$	1.80902	+	5.56758i	0.138339	+	0.425764i
$172$	8.16312	+	5.93085i	0.622432	+	0.452223i
$173$	−12.4443	+	9.04129i	−0.946120	+	0.687397i	−0.949886	−	0.312596i	$-0.898801\pi$
$173$	−12.4443	+	9.04129i	−0.946120	+	0.687397i	0.00376565	+	0.999993i	$0.498801\pi$
$174$	−0.854102	+	2.62866i	−0.0647493	+	0.199278i
$175$	5.56231			0.420471
$176$	−4.06231	+	4.61653i	−0.306208	+	0.347984i
$177$	10.3262			0.776168
$178$	−0.100813	+	0.310271i	−0.00755626	+	0.0232558i
$179$	1.80902	−	1.31433i	0.135212	−	0.0982375i	−0.518123	−	0.855306i	$-0.673369\pi$
$179$	1.80902	−	1.31433i	0.135212	−	0.0982375i	0.653335	+	0.757069i	$0.273369\pi$
$180$	−3.42705	−	2.48990i	−0.255437	−	0.185586i
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	−0.923930	−	0.382560i	$-0.875042\pi$
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	0.522612	−	0.852571i	$-0.324958\pi$
$182$	−1.01064	−	3.11044i	−0.0749139	−	0.230561i
$183$	−6.35410	−	4.61653i	−0.469709	−	0.341263i
$184$	−6.28115	+	4.56352i	−0.463053	+	0.336428i
$185$	−0.190983	+	0.587785i	−0.0140413	+	0.0432148i
$186$	−1.76393			−0.129338
$187$	−3.54508	+	4.02874i	−0.259242	+	0.294611i
$188$	−2.61803			−0.190940
$189$	0.927051	−	2.85317i	0.0674330	−	0.207538i
$190$	−7.66312	+	5.56758i	−0.555941	+	0.403915i
$191$	6.04508	+	4.39201i	0.437407	+	0.317795i	0.784604	−	0.619998i	$-0.212866\pi$
$191$	6.04508	+	4.39201i	0.437407	+	0.317795i	−0.347197	+	0.937792i	$0.612866\pi$
$192$	−0.0729490	−	0.224514i	−0.00526464	−	0.0162029i
$193$	−5.73607	−	17.6538i	−0.412891	−	1.27075i	−0.914124	−	0.405436i	$-0.867120\pi$
$193$	−5.73607	−	17.6538i	−0.412891	−	1.27075i	0.501232	−	0.865313i	$-0.332880\pi$
$194$	−7.01722	−	5.09831i	−0.503807	−	0.366037i
$195$	3.73607	−	2.71441i	0.267545	−	0.194383i
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$	24.3820			1.73714			0.868572	−	0.495564i	$-0.165039\pi$
$197$	24.3820			1.73714			0.868572	+	0.495564i	$0.165039\pi$
$198$	−0.190983	+	2.04087i	−0.0135726	+	0.145038i
$199$	−16.7082			−1.18441			−0.592207	−	0.805786i	$-0.701743\pi$
$199$	−16.7082			−1.18441			−0.592207	+	0.805786i	$0.701743\pi$
$200$	1.28115	−	3.94298i	0.0905912	−	0.278811i
$201$	7.73607	−	5.62058i	0.545660	−	0.396445i
$202$	−1.50000	−	1.08981i	−0.105540	−	0.0766790i
$203$	4.14590	+	12.7598i	0.290985	+	0.895560i
$204$	−0.809017	−	2.48990i	−0.0566425	−	0.174328i
$205$	−25.2984	−	18.3803i	−1.76692	−	1.28374i
$206$	−3.00000	+	2.17963i	−0.209020	+	0.151862i
$207$	1.07295	−	3.30220i	0.0745751	−	0.229519i
$208$	3.27051			0.226769
$209$	−17.8262	−	7.69421i	−1.23307	−	0.532220i
$210$	4.85410			0.334965
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	0.373830	+	0.927497i	$0.378044\pi$
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	−0.847604	+	0.530629i	$0.821956\pi$
$212$	−12.5902	+	9.14729i	−0.864696	+	0.628239i
$213$	4.50000	+	3.26944i	0.308335	+	0.224018i
$214$	0.809017	+	2.48990i	0.0553033	+	0.170206i
$215$	−5.04508	−	15.5272i	−0.344072	−	1.05894i
$216$	−1.80902	−	1.31433i	−0.123088	−	0.0894287i
$217$	−6.92705	+	5.03280i	−0.470239	+	0.341649i
$218$		0			0
$219$	−3.23607			−0.218673
$220$	13.7082	−	3.07768i	0.924207	−	0.207497i
$221$	2.85410			0.191988
$222$	−0.0450850	+	0.138757i	−0.00302591	+	0.00931278i
$223$	−0.572949	+	0.416272i	−0.0383675	+	0.0278756i	−0.606804	−	0.794852i	$-0.707549\pi$
$223$	−0.572949	+	0.416272i	−0.0383675	+	0.0278756i	0.568436	+	0.822727i	$0.307549\pi$
$224$	13.6353	+	9.90659i	0.911044	+	0.661912i
$225$	0.572949	+	1.76336i	0.0381966	+	0.117557i
$226$	−0.135255	−	0.416272i	−0.00899702	−	0.0276900i
$227$	20.1353	+	14.6291i	1.33642	+	0.970969i	0.999567	+	0.0294127i	$0.00936371\pi$
$227$	20.1353	+	14.6291i	1.33642	+	0.970969i	0.336856	+	0.941556i	$0.390636\pi$
$228$	7.66312	−	5.56758i	0.507502	−	0.368722i
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	−0.795541	−	0.605900i	$-0.792813\pi$
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	0.999745	−	0.0225760i	$-0.00718678\pi$
$230$	5.61803			0.370442
$231$	5.07295	+	8.55951i	0.333776	+	0.563174i
$232$	10.0000			0.656532
$233$	7.51722	−	23.1356i	0.492470	−	1.51567i	−0.328394	−	0.944541i	$-0.606507\pi$
$233$	7.51722	−	23.1356i	0.492470	−	1.51567i	0.820863	−	0.571124i	$-0.193493\pi$
$234$	0.881966	−	0.640786i	0.0576559	−	0.0418895i
$235$	3.42705	+	2.48990i	0.223556	+	0.162423i
$236$	−5.16312	−	15.8904i	−0.336090	−	1.03438i
$237$	2.92705	+	9.00854i	0.190132	+	0.585167i
$238$	2.42705	+	1.76336i	0.157322	+	0.114301i
$239$	−2.07295	+	1.50609i	−0.134088	+	0.0974206i	−0.652807	−	0.757524i	$-0.726409\pi$
$239$	−2.07295	+	1.50609i	−0.134088	+	0.0974206i	0.518719	+	0.854945i	$0.326409\pi$
$240$	−1.50000	+	4.61653i	−0.0968246	+	0.297995i
$241$	−23.1246			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$242$	−4.66312	−	4.94704i	−0.299757	−	0.318008i
$243$	1.00000			0.0641500
$244$	−3.92705	+	12.0862i	−0.251404	+	0.773741i
$245$	4.23607	−	3.07768i	0.270632	−	0.196626i
$246$	−5.97214	−	4.33901i	−0.380769	−	0.276645i
$247$	3.19098	+	9.82084i	0.203037	+	0.624885i
$248$	1.97214	+	6.06961i	0.125231	+	0.385421i
$249$	−0.572949	−	0.416272i	−0.0363092	−	0.0263802i
$250$	4.11803	−	2.99193i	0.260447	−	0.189226i
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	−0.997856	−	0.0654431i	$-0.979154\pi$
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	0.845749	+	0.533581i	$0.179154\pi$
$252$	−4.85410			−0.305780
$253$	5.87132	+	9.90659i	0.369127	+	0.622822i
$254$	2.29180			0.143800
$255$	−1.30902	+	4.02874i	−0.0819738	+	0.252289i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	9.44427	+	6.86167i	0.589117	+	0.428019i	0.842000	−	0.539478i	$-0.181378\pi$
$257$	9.44427	+	6.86167i	0.589117	+	0.428019i	−0.252882	+	0.967497i	$0.581378\pi$
$258$	−1.19098	−	3.66547i	−0.0741474	−	0.228202i
$259$	0.218847	+	0.673542i	0.0135985	+	0.0418519i
$260$	−6.04508	−	4.39201i	−0.374900	−	0.272381i
$261$	−3.61803	+	2.62866i	−0.223951	+	0.162710i
$262$	1.36475	−	4.20025i	0.0843142	−	0.259493i
$263$	−16.3262			−1.00672			−0.503359	−	0.864077i	$-0.667903\pi$
$263$	−16.3262			−1.00672			−0.503359	+	0.864077i	$0.667903\pi$
$264$	7.23607	−	1.62460i	0.445349	−	0.0999871i
$265$	25.1803			1.54682
$266$	−3.35410	+	10.3229i	−0.205653	+	0.632935i
$267$	−0.427051	+	0.310271i	−0.0261351	+	0.0189883i
$268$	−12.5172	−	9.09429i	−0.764611	−	0.555522i
$269$	4.79837	+	14.7679i	0.292562	+	0.900413i	0.984029	+	0.178006i	$0.0569645\pi$
$269$	4.79837	+	14.7679i	0.292562	+	0.900413i	−0.691467	+	0.722408i	$0.743035\pi$
$270$	0.500000	+	1.53884i	0.0304290	+	0.0936509i
$271$	22.0623	+	16.0292i	1.34019	+	0.973705i	0.999437	+	0.0335518i	$0.0106819\pi$
$271$	22.0623	+	16.0292i	1.34019	+	0.973705i	0.340753	+	0.940153i	$0.389318\pi$
$272$	−2.42705	+	1.76336i	−0.147162	+	0.106919i
$273$	1.63525	−	5.03280i	0.0989701	−	0.304599i
$274$	−4.61803			−0.278986
$275$	−5.64590	−	2.43690i	−0.340460	−	0.146950i
$276$	−5.61803			−0.338166
$277$	9.44427	−	29.0665i	0.567451	−	1.74644i	−0.0931022	−	0.995657i	$-0.529678\pi$
$277$	9.44427	−	29.0665i	0.567451	−	1.74644i	0.660554	−	0.750779i	$-0.270322\pi$
$278$	−0.427051	+	0.310271i	−0.0256128	+	0.0186088i
$279$	−2.30902	−	1.67760i	−0.138237	−	0.100435i
$280$	−5.42705	−	16.7027i	−0.324328	−	0.998180i
$281$	−0.236068	−	0.726543i	−0.0140826	−	0.0433419i	0.943768	−	0.330608i	$-0.107254\pi$
$281$	−0.236068	−	0.726543i	−0.0140826	−	0.0433419i	−0.957851	+	0.287266i	$0.907254\pi$
$282$	0.809017	+	0.587785i	0.0481763	+	0.0350021i
$283$	−0.145898	+	0.106001i	−0.00867274	+	0.00630111i	−0.592113	−	0.805855i	$-0.701706\pi$
$283$	−0.145898	+	0.106001i	−0.00867274	+	0.00630111i	0.583440	+	0.812156i	$0.301706\pi$
$284$	2.78115	−	8.55951i	0.165031	−	0.507913i
$285$	−15.3262			−0.907848
$286$	−0.336881	+	3.59996i	−0.0199202	+	0.212870i
$287$	−35.8328			−2.11514
$288$	−1.73607	+	5.34307i	−0.102299	+	0.314843i
$289$	11.6353	−	8.45351i	0.684427	−	0.497265i
$290$	−5.85410	−	4.25325i	−0.343765	−	0.249760i
$291$	−4.33688	−	13.3475i	−0.254232	−	0.782447i
$292$	1.61803	+	4.97980i	0.0946883	+	0.291421i
$293$	−0.0450850	−	0.0327561i	−0.00263389	−	0.00191363i	0.586468	−	0.809973i	$-0.300518\pi$
$293$	−0.0450850	−	0.0327561i	−0.00263389	−	0.00191363i	−0.589101	+	0.808059i	$0.700518\pi$
$294$	1.00000	−	0.726543i	0.0583212	−	0.0423728i
$295$	−8.35410	+	25.7113i	−0.486395	+	1.49697i
$296$	0.527864			0.0306815
$297$	−2.19098	+	2.48990i	−0.127134	+	0.144479i
$298$	−9.27051			−0.537026
$299$	1.89261	−	5.82485i	0.109452	−	0.336860i
$300$	2.42705	−	1.76336i	0.140126	−	0.101807i
$301$	−15.1353	−	10.9964i	−0.872382	−	0.633822i
$302$	−0.381966	−	1.17557i	−0.0219797	−	0.0676465i
$303$	−0.927051	−	2.85317i	−0.0532577	−	0.163910i
$304$	−8.78115	−	6.37988i	−0.503634	−	0.365911i
$305$	16.6353	−	12.0862i	0.952532	−	0.692055i
$306$	−0.309017	+	0.951057i	−0.0176653	+	0.0543683i
$307$	0.562306			0.0320925			0.0160462	−	0.999871i	$-0.494892\pi$
$307$	0.562306			0.0320925			0.0160462	+	0.999871i	$0.494892\pi$
$308$	10.6353	−	12.0862i	0.606000	−	0.688676i
$309$	−6.00000			−0.341328
$310$	1.42705	−	4.39201i	0.0810510	−	0.249449i
$311$	−2.04508	+	1.48584i	−0.115966	+	0.0842543i	−0.644257	−	0.764809i	$-0.722833\pi$
$311$	−2.04508	+	1.48584i	−0.115966	+	0.0842543i	0.528291	+	0.849064i	$0.322833\pi$
$312$	−3.19098	−	2.31838i	−0.180654	−	0.131253i
$313$	7.98278	+	24.5685i	0.451213	+	1.38869i	0.875524	+	0.483175i	$0.160517\pi$
$313$	7.98278	+	24.5685i	0.451213	+	1.38869i	−0.424310	+	0.905517i	$0.639483\pi$
$314$	0.708204	+	2.17963i	0.0399663	+	0.123004i
$315$	6.35410	+	4.61653i	0.358013	+	0.260112i
$316$	12.3992	−	9.00854i	0.697509	−	0.506770i
$317$	−5.98278	+	18.4131i	−0.336026	+	1.03418i	0.630188	+	0.776443i	$0.282978\pi$
$317$	−5.98278	+	18.4131i	−0.336026	+	1.03418i	−0.966214	+	0.257740i	$0.917022\pi$
$318$	5.94427			0.333338
$319$	1.38197	−	14.7679i	0.0773752	−	0.826842i
$320$	0.618034			0.0345492
$321$	−1.30902	+	4.02874i	−0.0730622	+	0.224862i
$322$	5.20820	−	3.78398i	0.290242	−	0.210873i
$323$	−7.66312	−	5.56758i	−0.426387	−	0.309789i
$324$	−0.500000	−	1.53884i	−0.0277778	−	0.0854912i
$325$	1.01064	+	3.11044i	0.0560604	+	0.172536i
$326$	9.13525	+	6.63715i	0.505955	+	0.367598i
$327$		0			0
$328$	−8.25329	+	25.4010i	−0.455712	+	1.40254i
$329$	4.85410			0.267615
$330$	−4.92705	−	2.12663i	−0.271225	−	0.117067i
$331$	26.5967			1.46189			0.730945	−	0.682437i	$-0.239080\pi$
$331$	26.5967			1.46189			0.730945	+	0.682437i	$0.239080\pi$
$332$	−0.354102	+	1.08981i	−0.0194339	+	0.0598113i
$333$	−0.190983	+	0.138757i	−0.0104658	+	0.00760385i
$334$	5.01722	+	3.64522i	0.274530	+	0.199458i
$335$	7.73607	+	23.8092i	0.422667	+	1.30083i
$336$	1.71885	+	5.29007i	0.0937708	+	0.288597i
$337$	0.236068	+	0.171513i	0.0128594	+	0.00934293i	0.594196	−	0.804320i	$-0.297470\pi$
$337$	0.236068	+	0.171513i	0.0128594	+	0.00934293i	−0.581337	+	0.813663i	$0.697470\pi$
$338$	−4.94427	+	3.59222i	−0.268933	+	0.195391i
$339$	0.218847	−	0.673542i	0.0118861	−	0.0365818i
$340$	6.85410			0.371716
$341$	9.23607	−	2.07363i	0.500161	−	0.112293i
$342$	−3.61803			−0.195641
$343$	−4.63525	+	14.2658i	−0.250280	+	0.770283i
$344$	−11.2812	+	8.19624i	−0.608239	+	0.441912i
$345$	7.35410	+	5.34307i	0.395932	+	0.287661i
$346$	−2.93769	−	9.04129i	−0.157931	−	0.486063i
$347$	−6.47214	−	19.9192i	−0.347442	−	1.06932i	−0.960263	−	0.279096i	$-0.909965\pi$
$347$	−6.47214	−	19.9192i	−0.347442	−	1.06932i	0.612821	−	0.790222i	$-0.290035\pi$
$348$	5.85410	+	4.25325i	0.313813	+	0.227998i
$349$	8.19098	−	5.95110i	0.438453	−	0.318555i	−0.346567	−	0.938025i	$-0.612653\pi$
$349$	8.19098	−	5.95110i	0.438453	−	0.318555i	0.785020	+	0.619470i	$0.212653\pi$
$350$	−1.06231	+	3.26944i	−0.0567826	+	0.174759i
$351$	1.76393			0.0941517
$352$	−9.50000	−	16.0292i	−0.506352	−	0.854359i
$353$	−10.4721			−0.557376			−0.278688	−	0.960382i	$-0.589899\pi$
$353$	−10.4721			−0.557376			−0.278688	+	0.960382i	$0.589899\pi$
$354$	−1.97214	+	6.06961i	−0.104818	+	0.322596i
$355$	−11.7812	+	8.55951i	−0.625279	+	0.454292i
$356$	0.690983	+	0.502029i	0.0366220	+	0.0266075i
$357$	1.50000	+	4.61653i	0.0793884	+	0.244332i
$358$	0.427051	+	1.31433i	0.0225703	+	0.0694644i
$359$	10.3262	+	7.50245i	0.544998	+	0.395964i	0.825938	−	0.563761i	$-0.190646\pi$
$359$	10.3262	+	7.50245i	0.544998	+	0.395964i	−0.280940	+	0.959725i	$0.590646\pi$
$360$	4.73607	−	3.44095i	0.249613	−	0.181354i
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	10.7984			0.567550
$363$	−1.39919	−	10.9106i	−0.0734383	−	0.572661i
$364$	−8.56231			−0.448787
$365$	2.61803	−	8.05748i	0.137034	−	0.421748i
$366$	3.92705	−	2.85317i	0.205270	−	0.149138i
$367$	−4.50000	−	3.26944i	−0.234898	−	0.170663i	0.464109	−	0.885778i	$-0.346375\pi$
$367$	−4.50000	−	3.26944i	−0.234898	−	0.170663i	−0.699007	+	0.715115i	$0.746375\pi$
$368$	1.98936	+	6.12261i	0.103702	+	0.319163i
$369$	−3.69098	−	11.3597i	−0.192145	−	0.591361i
$370$	−0.309017	−	0.224514i	−0.0160650	−	0.0116719i
$371$	23.3435	−	16.9600i	1.21193	−	0.880520i
$372$	−1.42705	+	4.39201i	−0.0739891	+	0.227715i
$373$	−4.41641			−0.228673			−0.114336	−	0.993442i	$-0.536474\pi$
$373$	−4.41641			−0.228673			−0.114336	+	0.993442i	$0.536474\pi$
$374$	−1.69098	−	2.85317i	−0.0874386	−	0.147534i
$375$	8.23607			0.425309
$376$	1.11803	−	3.44095i	0.0576582	−	0.177454i
$377$	−6.38197	+	4.63677i	−0.328688	+	0.238806i
$378$	1.50000	+	1.08981i	0.0771517	+	0.0560540i
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	0.962838	−	0.270080i	$-0.0870502\pi$
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	−0.937701	+	0.347443i	$0.887050\pi$
$380$	7.66312	+	23.5847i	0.393110	+	1.20987i
$381$	3.00000	+	2.17963i	0.153695	+	0.111666i
$382$	−3.73607	+	2.71441i	−0.191154	+	0.138881i
$383$	8.30902	−	25.5725i	0.424571	−	1.30669i	−0.478834	−	0.877906i	$-0.658940\pi$
$383$	8.30902	−	25.5725i	0.424571	−	1.30669i	0.903405	−	0.428789i	$-0.141060\pi$
$384$	11.3820			0.580834
$385$	−25.4164	+	5.70634i	−1.29534	+	0.290822i
$386$	11.4721			0.583916
$387$	1.92705	−	5.93085i	0.0979575	−	0.301482i
$388$	−18.3713	+	13.3475i	−0.932663	+	0.677619i
$389$	−19.6353	−	14.2658i	−0.995547	−	0.723307i	−0.0344181	−	0.999408i	$-0.510958\pi$
$389$	−19.6353	−	14.2658i	−0.995547	−	0.723307i	−0.961129	+	0.276100i	$0.910958\pi$
$390$	0.881966	+	2.71441i	0.0446601	+	0.137450i
$391$	1.73607	+	5.34307i	0.0877967	+	0.270211i
$392$	−3.61803	−	2.62866i	−0.182738	−	0.132767i
$393$	5.78115	−	4.20025i	0.291621	−	0.211875i
$394$	−4.65654	+	14.3314i	−0.234593	+	0.722003i
$395$	−24.7984			−1.24774
$396$	4.92705	+	2.12663i	0.247594	+	0.106867i
$397$	−38.7082			−1.94271			−0.971355	−	0.237635i	$-0.923628\pi$
$397$	−38.7082			−1.94271			−0.971355	+	0.237635i	$0.923628\pi$
$398$	3.19098	−	9.82084i	0.159950	−	0.492274i
$399$	−14.2082	+	10.3229i	−0.711300	+	0.516790i
$400$	−2.78115	−	2.02063i	−0.139058	−	0.101031i
$401$	−8.06231	−	24.8132i	−0.402612	−	1.23911i	−0.922873	−	0.385106i	$-0.874165\pi$
$401$	−8.06231	−	24.8132i	−0.402612	−	1.23911i	0.520260	−	0.854008i	$-0.325835\pi$
$402$	1.82624	+	5.62058i	0.0910845	+	0.280329i
$403$	−4.07295	−	2.95917i	−0.202888	−	0.147407i
$404$	−3.92705	+	2.85317i	−0.195378	+	0.141950i
$405$	−0.809017	+	2.48990i	−0.0402004	+	0.123724i
$406$	−8.29180			−0.411515
$407$	0.0729490	−	0.779543i	0.00361595	−	0.0386405i
$408$	3.61803			0.179119
$409$	−3.41641	+	10.5146i	−0.168930	+	0.519915i	−0.999304	−	0.0372920i	$-0.988127\pi$
$409$	−3.41641	+	10.5146i	−0.168930	+	0.519915i	0.830374	+	0.557207i	$0.188127\pi$
$410$	15.6353	−	11.3597i	0.772170	−	0.561014i
$411$	−6.04508	−	4.39201i	−0.298182	−	0.216642i
$412$	3.00000	+	9.23305i	0.147799	+	0.454880i
$413$	9.57295	+	29.4625i	0.471054	+	1.44976i
$414$	1.73607	+	1.26133i	0.0853231	+	0.0619909i
$415$	1.50000	−	1.08981i	0.0736321	−	0.0534969i
$416$	−3.06231	+	9.42481i	−0.150142	+	0.462089i
$417$	−0.854102			−0.0418256
$418$	7.92705	−	9.00854i	0.387725	−	0.440622i
$419$	16.5066			0.806399			0.403200	−	0.915112i	$-0.367898\pi$
$419$	16.5066			0.806399			0.403200	+	0.915112i	$0.367898\pi$
$420$	3.92705	−	12.0862i	0.191620	−	0.589747i
$421$	30.1525	−	21.9071i	1.46954	−	1.06768i	0.488795	−	0.872398i	$-0.337436\pi$
$421$	30.1525	−	21.9071i	1.46954	−	1.06768i	0.980746	−	0.195286i	$-0.0625636\pi$
$422$	−11.1353	−	8.09024i	−0.542056	−	0.393827i
$423$	0.500000	+	1.53884i	0.0243108	+	0.0748210i
$424$	−6.64590	−	20.4540i	−0.322753	−	0.993333i
$425$	−2.42705	−	1.76336i	−0.117729	−	0.0855353i
$426$	−2.78115	+	2.02063i	−0.134747	+	0.0978996i
$427$	7.28115	−	22.4091i	0.352360	−	1.08445i
$428$	6.85410			0.331306
$429$	−3.86475	+	4.39201i	−0.186592	+	0.212048i
$430$	10.0902			0.486591
$431$	−12.2082	+	37.5730i	−0.588048	+	1.80983i	−0.00138127	+	0.999999i	$0.500440\pi$
$431$	−12.2082	+	37.5730i	−0.588048	+	1.80983i	−0.586667	+	0.809828i	$0.699560\pi$
$432$	−1.50000	+	1.08981i	−0.0721688	+	0.0524337i
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	0.698281	−	0.715824i	$-0.253949\pi$
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	−0.465008	+	0.885307i	$0.653949\pi$
$434$	−1.63525	−	5.03280i	−0.0784947	−	0.241582i
$435$	−3.61803	−	11.1352i	−0.173471	−	0.533890i
$436$		0			0
$437$	−16.4443	+	11.9475i	−0.786636	+	0.571525i
$438$	0.618034	−	1.90211i	0.0295308	−	0.0908865i
$439$	3.29180			0.157109			0.0785544	−	0.996910i	$-0.474970\pi$
$439$	3.29180			0.157109			0.0785544	+	0.996910i	$0.474970\pi$
$440$	−1.80902	+	19.3314i	−0.0862415	+	0.921588i
$441$	2.00000			0.0952381
$442$	−0.545085	+	1.67760i	−0.0259270	+	0.0797952i
$443$	33.2705	−	24.1724i	1.58073	−	1.14847i	0.664877	−	0.746953i	$-0.268484\pi$
$443$	33.2705	−	24.1724i	1.58073	−	1.14847i	0.915853	−	0.401514i	$-0.131516\pi$
$444$	0.309017	+	0.224514i	0.0146653	+	0.0106550i
$445$	−0.427051	−	1.31433i	−0.0202442	−	0.0623051i
$446$	−0.135255	−	0.416272i	−0.00640451	−	0.0197110i
$447$	−12.1353	−	8.81678i	−0.573978	−	0.417019i
$448$	0.572949	−	0.416272i	0.0270693	−	0.0196670i
$449$	−7.56231	+	23.2744i	−0.356887	+	1.09839i	0.598020	+	0.801481i	$0.295954\pi$
$449$	−7.56231	+	23.2744i	−0.356887	+	1.09839i	−0.954907	+	0.296905i	$0.904046\pi$
$450$	−1.14590			−0.0540182
$451$	36.3713	+	15.6987i	1.71266	+	0.739222i
$452$	−1.14590			−0.0538985
$453$	0.618034	−	1.90211i	0.0290378	−	0.0893691i
$454$	−12.4443	+	9.04129i	−0.584039	+	0.424329i
$455$	11.2082	+	8.14324i	0.525449	+	0.381761i
$456$	4.04508	+	12.4495i	0.189428	+	0.583001i
$457$	2.53444	+	7.80021i	0.118556	+	0.364878i	0.992672	−	0.120839i	$-0.0385584\pi$
$457$	2.53444	+	7.80021i	0.118556	+	0.364878i	−0.874116	+	0.485717i	$0.838558\pi$
$458$	5.00000	+	3.63271i	0.233635	+	0.169746i
$459$	−1.30902	+	0.951057i	−0.0610997	+	0.0443915i
$460$	4.54508	−	13.9883i	0.211916	−	0.652209i
$461$	−21.0902			−0.982267			−0.491134	−	0.871084i	$-0.663417\pi$
$461$	−21.0902			−0.982267			−0.491134	+	0.871084i	$0.663417\pi$
$462$	−6.00000	+	1.34708i	−0.279145	+	0.0626720i
$463$	−15.7984			−0.734213			−0.367106	−	0.930179i	$-0.619651\pi$
$463$	−15.7984			−0.734213			−0.367106	+	0.930179i	$0.619651\pi$
$464$	2.56231	−	7.88597i	0.118952	−	0.366097i
$465$	6.04508	−	4.39201i	0.280334	−	0.203675i
$466$	12.1631	+	8.83702i	0.563446	+	0.409367i
$467$	−3.01722	−	9.28605i	−0.139620	−	0.429707i	0.856660	−	0.515882i	$-0.172536\pi$
$467$	−3.01722	−	9.28605i	−0.139620	−	0.429707i	−0.996280	+	0.0861747i	$0.972536\pi$
$468$	−0.881966	−	2.71441i	−0.0407689	−	0.125474i
$469$	23.2082	+	16.8617i	1.07166	+	0.778603i
$470$	−2.11803	+	1.53884i	−0.0976976	+	0.0709815i
$471$	−1.14590	+	3.52671i	−0.0528002	+	0.162502i
$472$	23.0902			1.06281
$473$	10.5451	+	17.7926i	0.484864	+	0.818103i
$474$	−5.85410			−0.268888
$475$	3.35410	−	10.3229i	0.153897	−	0.473646i
$476$	6.35410	−	4.61653i	0.291240	−	0.211598i
$477$	7.78115	+	5.65334i	0.356275	+	0.258849i
$478$	−0.489357	−	1.50609i	−0.0223827	−	0.0688868i
$479$	−8.68034	−	26.7153i	−0.396615	−	1.22066i	−0.927697	−	0.373335i	$-0.878214\pi$
$479$	−8.68034	−	26.7153i	−0.396615	−	1.22066i	0.531082	−	0.847320i	$-0.321786\pi$
$480$	−11.8992	−	8.64527i	−0.543121	−	0.394601i
$481$	−0.336881	+	0.244758i	−0.0153605	+	0.0111600i
$482$	4.41641	−	13.5923i	0.201162	−	0.619113i
$483$	10.4164			0.473963
$484$	−16.0902	+	7.60845i	−0.731371	+	0.345839i
$485$	36.7426			1.66840
$486$	−0.190983	+	0.587785i	−0.00866317	+	0.0266625i
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	−0.851736	−	0.523972i	$-0.824450\pi$
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	0.235126	+	0.971965i	$0.424450\pi$
$488$	−14.2082	−	10.3229i	−0.643175	−	0.467294i
$489$	5.64590	+	17.3763i	0.255316	+	0.785783i
$490$	1.00000	+	3.07768i	0.0451754	+	0.139036i
$491$	−20.3992	−	14.8209i	−0.920602	−	0.668857i	0.0230715	−	0.999734i	$-0.492655\pi$
$491$	−20.3992	−	14.8209i	−0.920602	−	0.668857i	−0.943674	+	0.330877i	$0.892655\pi$
$492$	−15.6353	+	11.3597i	−0.704892	+	0.512134i
$493$	2.23607	−	6.88191i	0.100707	−	0.309946i
$494$	−6.38197			−0.287138
$495$	−4.42705	−	7.46969i	−0.198981	−	0.335738i
$496$	5.29180			0.237609
$497$	−5.15654	+	15.8702i	−0.231302	+	0.711876i
$498$	0.354102	−	0.257270i	0.0158677	−	0.0115286i
$499$	14.2082	+	10.3229i	0.636047	+	0.462115i	0.858490	−	0.512831i	$-0.171403\pi$
$499$	14.2082	+	10.3229i	0.636047	+	0.462115i	−0.222443	+	0.974946i	$0.571403\pi$
$500$	−4.11803	−	12.6740i	−0.184164	−	0.566799i
$501$	3.10081	+	9.54332i	0.138534	+	0.426364i
$502$	−3.89919	−	2.83293i	−0.174029	−	0.126440i
$503$	−22.7082	+	16.4985i	−1.01251	+	0.735631i	−0.964734	−	0.263227i	$-0.915213\pi$
$503$	−22.7082	+	16.4985i	−1.01251	+	0.735631i	−0.0477750	+	0.998858i	$0.515213\pi$
$504$	2.07295	−	6.37988i	0.0923365	−	0.284182i
$505$	7.85410			0.349503
$506$	−6.94427	+	1.55909i	−0.308711	+	0.0693098i
$507$	−9.88854			−0.439166
$508$	1.85410	−	5.70634i	0.0822625	−	0.253178i
$509$	−19.1074	+	13.8823i	−0.846920	+	0.615324i	−0.924295	−	0.381679i	$-0.875346\pi$
$509$	−19.1074	+	13.8823i	−0.846920	+	0.615324i	0.0773749	+	0.997002i	$0.475346\pi$
$510$	−2.11803	−	1.53884i	−0.0937881	−	0.0681411i
$511$	−3.00000	−	9.23305i	−0.132712	−	0.408446i
$512$	−5.78115	−	17.7926i	−0.255493	−	0.786327i
$513$	−4.73607	−	3.44095i	−0.209103	−	0.151922i
$514$	−5.83688	+	4.24074i	−0.257454	+	0.187051i
$515$	4.85410	−	14.9394i	0.213897	−	0.658308i
$516$	−10.0902			−0.444195
$517$	−4.92705	−	2.12663i	−0.216691	−	0.0935289i
$518$	−0.437694			−0.0192312
$519$	4.75329	−	14.6291i	0.208646	−	0.642147i
$520$	8.35410	−	6.06961i	0.366352	−	0.266170i
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	0.818758	−	0.574139i	$-0.194663\pi$
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	−0.293028	+	0.956104i	$0.594663\pi$
$522$	−0.854102	−	2.62866i	−0.0373830	−	0.115053i
$523$	−3.70163	−	11.3924i	−0.161861	−	0.498156i	0.836930	−	0.547309i	$-0.184348\pi$
$523$	−3.70163	−	11.3924i	−0.161861	−	0.498156i	−0.998791	+	0.0491529i	$0.984348\pi$
$524$	−9.35410	−	6.79615i	−0.408636	−	0.296891i
$525$	−4.50000	+	3.26944i	−0.196396	+	0.142690i
$526$	3.11803	−	9.59632i	0.135953	−	0.418420i
$527$	4.61803			0.201165
$528$	0.572949	−	6.12261i	0.0249344	−	0.266452i
$529$	−10.9443			−0.475838
$530$	−4.80902	+	14.8006i	−0.208890	+	0.642898i
$531$	−8.35410	+	6.06961i	−0.362537	+	0.263399i
$532$	22.9894	+	16.7027i	0.996715	+	0.724156i
$533$	−6.51064	−	20.0377i	−0.282007	−	0.867929i
$534$	−0.100813	−	0.310271i	−0.00436261	−	0.0134267i
$535$	−8.97214	−	6.51864i	−0.387899	−	0.281825i
$536$	17.2984	−	12.5680i	0.747176	−	0.542855i
$537$	−0.690983	+	2.12663i	−0.0298181	+	0.0917707i
$538$	−9.59675			−0.413745
$539$	−4.38197	+	4.97980i	−0.188745	+	0.214495i
$540$	4.23607			0.182291
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	−0.732926	−	0.680308i	$-0.761846\pi$
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	0.992825	−	0.119577i	$-0.0381540\pi$
$542$	−13.6353	+	9.90659i	−0.585684	+	0.425525i
$543$	14.1353	+	10.2699i	0.606602	+	0.440722i
$544$	−2.80902	−	8.64527i	−0.120436	−	0.370663i
$545$		0			0
$546$	2.64590	+	1.92236i	0.113234	+	0.0822693i
$547$	−17.4894	+	12.7068i	−0.747791	+	0.543302i	−0.895141	−	0.445782i	$-0.852925\pi$
$547$	−17.4894	+	12.7068i	−0.747791	+	0.543302i	0.147350	+	0.989084i	$0.452925\pi$
$548$	−3.73607	+	11.4984i	−0.159597	+	0.491189i
$549$	7.85410			0.335205
$550$	2.51064	−	2.85317i	0.107054	−	0.121660i
$551$	26.1803			1.11532
$552$	2.39919	−	7.38394i	0.102116	−	0.314281i
$553$	−22.9894	+	16.7027i	−0.977607	+	0.710273i
$554$	15.2812	+	11.1024i	0.649234	+	0.471696i
$555$	−0.190983	−	0.587785i	−0.00810678	−	0.0249501i
$556$	0.427051	+	1.31433i	0.0181110	+	0.0557399i
$557$	−12.0623	−	8.76378i	−0.511096	−	0.371333i	0.302143	−	0.953263i	$-0.402298\pi$
$557$	−12.0623	−	8.76378i	−0.511096	−	0.371333i	−0.813239	+	0.581929i	$0.802298\pi$
$558$	1.42705	−	1.03681i	0.0604119	−	0.0438918i
$559$	3.39919	−	10.4616i	0.143770	−	0.442479i
$560$	−14.5623			−0.615370
$561$	0.500000	−	5.34307i	0.0211100	−	0.225585i
$562$	0.472136			0.0199159
$563$	−2.74671	+	8.45351i	−0.115760	+	0.356273i	−0.992105	−	0.125412i	$-0.959975\pi$
$563$	−2.74671	+	8.45351i	−0.115760	+	0.356273i	0.876345	+	0.481684i	$0.159975\pi$
$564$	2.11803	−	1.53884i	0.0891853	−	0.0647969i
$565$	1.50000	+	1.08981i	0.0631055	+	0.0458488i
$566$	−0.0344419	−	0.106001i	−0.00144770	−	0.00445556i
$567$	0.927051	+	2.85317i	0.0389325	+	0.119822i
$568$	10.0623	+	7.31069i	0.422205	+	0.306750i
$569$	19.4721	−	14.1473i	0.816314	−	0.593087i	−0.0993400	−	0.995054i	$-0.531673\pi$
$569$	19.4721	−	14.1473i	0.816314	−	0.593087i	0.915654	+	0.401966i	$0.131673\pi$
$570$	2.92705	−	9.00854i	0.122601	−	0.377326i
$571$	34.6869			1.45160			0.725801	−	0.687905i	$-0.241469\pi$
$571$	34.6869			1.45160			0.725801	+	0.687905i	$0.241469\pi$
$572$	8.69098	+	3.75123i	0.363388	+	0.156847i
$573$	−7.47214			−0.312153
$574$	6.84346	−	21.0620i	0.285640	−	0.879111i
$575$	−5.20820	+	3.78398i	−0.217197	+	0.157803i
$576$	0.190983	+	0.138757i	0.00795763	+	0.00578155i
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	0.996114	−	0.0880726i	$-0.0280707\pi$
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	−0.857641	+	0.514249i	$0.828071\pi$
$578$	2.74671	+	8.45351i	0.114248	+	0.351620i
$579$	15.0172	+	10.9106i	0.624094	+	0.453431i
$580$	−15.3262	+	11.1352i	−0.636387	+	0.462363i
$581$	0.656541	−	2.02063i	0.0272379	−	0.0838297i
$582$	8.67376			0.359539
$583$	−31.1246	+	6.98791i	−1.28905	+	0.289410i
$584$	−7.23607			−0.299431
$585$	−1.42705	+	4.39201i	−0.0590013	+	0.181587i
$586$	0.0278640	−	0.0202444i	0.00115105	−	0.000836289i
$587$	30.9894	+	22.5151i	1.27907	+	0.929297i	0.999524	−	0.0308361i	$-0.00981699\pi$
$587$	30.9894	+	22.5151i	1.27907	+	0.929297i	0.279543	+	0.960133i	$0.409817\pi$
$588$	−1.00000	−	3.07768i	−0.0412393	−	0.126922i
$589$	5.16312	+	15.8904i	0.212743	+	0.654754i
$590$	−13.5172	−	9.82084i	−0.556495	−	0.404317i
$591$	−19.7254	+	14.3314i	−0.811396	+	0.589513i
$592$	0.135255	−	0.416272i	0.00555894	−	0.0171087i
$593$	22.2148			0.912252			0.456126	−	0.889915i	$-0.349237\pi$
$593$	22.2148			0.912252			0.456126	+	0.889915i	$0.349237\pi$
$594$	−1.04508	−	1.76336i	−0.0428804	−	0.0723514i
$595$	−12.7082			−0.520986
$596$	−7.50000	+	23.0826i	−0.307212	+	0.945501i
$597$	13.5172	−	9.82084i	0.553223	−	0.401940i
$598$	3.06231	+	2.22490i	0.125227	+	0.0909827i
$599$	−2.56231	−	7.88597i	−0.104693	−	0.322212i	0.884965	−	0.465657i	$-0.154182\pi$
$599$	−2.56231	−	7.88597i	−0.104693	−	0.322212i	−0.989658	+	0.143445i	$0.954182\pi$
$600$	1.28115	+	3.94298i	0.0523029	+	0.160972i
$601$	−27.3713	−	19.8864i	−1.11650	−	0.811184i	−0.132825	−	0.991140i	$-0.542405\pi$
$601$	−27.3713	−	19.8864i	−1.11650	−	0.811184i	−0.983675	+	0.179955i	$0.942405\pi$
$602$	9.35410	−	6.79615i	0.381245	−	0.276991i
$603$	−2.95492	+	9.09429i	−0.120333	+	0.370348i
$604$	−3.23607			−0.131674
$605$	28.2984	+	5.34307i	1.15049	+	0.217227i
$606$	1.85410			0.0753177
$607$	4.11803	−	12.6740i	0.167146	−	0.514422i	−0.832042	−	0.554712i	$-0.812828\pi$
$607$	4.11803	−	12.6740i	0.167146	−	0.514422i	0.999188	+	0.0402904i	$0.0128283\pi$
$608$	26.6074	−	19.3314i	1.07907	−	0.783992i
$609$	−10.8541	−	7.88597i	−0.439830	−	0.319555i
$610$	3.92705	+	12.0862i	0.159002	+	0.489357i
$611$	0.881966	+	2.71441i	0.0356805	+	0.109813i
$612$	2.11803	+	1.53884i	0.0856164	+	0.0622040i
$613$	−28.0344	+	20.3682i	−1.13230	+	0.822664i	−0.986028	−	0.166580i	$-0.946728\pi$
$613$	−28.0344	+	20.3682i	−1.13230	+	0.822664i	−0.146272	+	0.989244i	$0.546728\pi$
$614$	−0.107391	+	0.330515i	−0.00433394	+	0.0133385i
$615$	31.2705			1.26095
$616$	11.3435	+	19.1396i	0.457041	+	0.771158i
$617$	19.5836			0.788406			0.394203	−	0.919023i	$-0.371021\pi$
$617$	19.5836			0.788406			0.394203	+	0.919023i	$0.371021\pi$
$618$	1.14590	−	3.52671i	0.0460948	−	0.141865i
$619$	7.13525	−	5.18407i	0.286790	−	0.208365i	−0.435084	−	0.900390i	$-0.643281\pi$
$619$	7.13525	−	5.18407i	0.286790	−	0.208365i	0.721874	+	0.692025i	$0.243281\pi$
$620$	−9.78115	−	7.10642i	−0.392821	−	0.285401i
$621$	1.07295	+	3.30220i	0.0430560	+	0.132513i
$622$	−0.482779	−	1.48584i	−0.0193577	−	0.0595768i
$623$	−1.28115	−	0.930812i	−0.0513283	−	0.0372922i
$624$	−2.64590	+	1.92236i	−0.105921	+	0.0769559i
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$	−15.9656			−0.638112
$627$	18.9443	−	4.25325i	0.756561	−	0.169859i
$628$	6.00000			0.239426
$629$	0.118034	−	0.363271i	0.00470632	−	0.0144846i
$630$	−3.92705	+	2.85317i	−0.156457	+	0.113673i
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.974084	−	0.226187i	$-0.927374\pi$
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.516125	−	0.856513i	$-0.672626\pi$
$632$	6.54508	+	20.1437i	0.260350	+	0.801273i
$633$	−6.88197	−	21.1805i	−0.273534	−	0.841850i
$634$	−9.68034	−	7.03318i	−0.384455	−	0.279323i
$635$	−7.85410	+	5.70634i	−0.311681	+	0.226449i
$636$	4.80902	−	14.8006i	0.190690	−	0.586883i
$637$	3.52786			0.139779
$638$	8.41641	+	3.63271i	0.333209	+	0.143820i
$639$	−5.56231			−0.220041
$640$	−9.20820	+	28.3399i	−0.363986	+	1.12023i
$641$	−28.9164	+	21.0090i	−1.14213	+	0.829806i	−0.987415	−	0.158154i	$-0.949446\pi$
$641$	−28.9164	+	21.0090i	−1.14213	+	0.829806i	−0.154715	+	0.987959i	$0.549446\pi$
$642$	−2.11803	−	1.53884i	−0.0835921	−	0.0607332i
$643$	−11.9164	−	36.6749i	−0.469937	−	1.44632i	−0.852666	−	0.522457i	$-0.825015\pi$
$643$	−11.9164	−	36.6749i	−0.469937	−	1.44632i	0.382728	−	0.923861i	$-0.374985\pi$
$644$	−5.20820	−	16.0292i	−0.205232	−	0.631639i
$645$	13.2082	+	9.59632i	0.520073	+	0.377855i
$646$	4.73607	−	3.44095i	0.186338	−	0.135383i
$647$	8.59017	−	26.4378i	0.337714	−	1.03938i	−0.627655	−	0.778492i	$-0.715985\pi$
$647$	8.59017	−	26.4378i	0.337714	−	1.03938i	0.965369	−	0.260887i	$-0.0840149\pi$
$648$	2.23607			0.0878410
$649$	3.19098	−	34.0993i	0.125257	−	1.33851i
$650$	−2.02129			−0.0792814
$651$	2.64590	−	8.14324i	0.103701	−	0.319159i
$652$	23.9164	−	17.3763i	0.936639	−	0.680508i
$653$	−41.2877	−	29.9973i	−1.61571	−	1.17388i	−0.839323	−	0.543632i	$-0.817049\pi$
$653$	−41.2877	−	29.9973i	−1.61571	−	1.17388i	−0.776390	−	0.630252i	$-0.782951\pi$
$654$		0			0
$655$	5.78115	+	17.7926i	0.225888	+	0.695213i
$656$	17.9164	+	13.0170i	0.699518	+	0.508230i
$657$	2.61803	−	1.90211i	0.102139	−	0.0742085i
$658$	−0.927051	+	2.85317i	−0.0361402	+	0.111228i
$659$	−10.6525			−0.414962			−0.207481	−	0.978239i	$-0.566526\pi$
$659$	−10.6525			−0.414962			−0.207481	+	0.978239i	$0.566526\pi$
$660$	−9.28115	+	10.5474i	−0.361268	+	0.410556i
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$	−5.07953	+	15.6332i	−0.197421	+	0.607601i
$663$	−2.30902	+	1.67760i	−0.0896748	+	0.0651525i
$664$	−1.28115	−	0.930812i	−0.0497184	−	0.0361225i
$665$	−14.2082	−	43.7284i	−0.550971	−	1.69571i
$666$	−0.0450850	−	0.138757i	−0.00174701	−	0.00537674i
$667$	−12.5623	−	9.12705i	−0.486414	−	0.353401i
$668$	13.1353	−	9.54332i	0.508218	−	0.369242i
$669$	0.218847	−	0.673542i	0.00846112	−	0.0260406i
$670$	−15.4721			−0.597741
$671$	−17.2082	+	19.5559i	−0.664315	+	0.754948i
$672$	−16.8541			−0.650161
$673$	3.83688	−	11.8087i	0.147901	−	0.455192i	−0.849472	−	0.527634i	$-0.823079\pi$
$673$	3.83688	−	11.8087i	0.147901	−	0.455192i	0.997373	+	0.0724420i	$0.0230792\pi$
$674$	−0.145898	+	0.106001i	−0.00561978	+	0.00408301i
$675$	−1.50000	−	1.08981i	−0.0577350	−	0.0419470i
$676$	4.94427	+	15.2169i	0.190164	+	0.585266i
$677$	4.18034	+	12.8658i	0.160664	+	0.494471i	0.998691	−	0.0511572i	$-0.0162909\pi$
$677$	4.18034	+	12.8658i	0.160664	+	0.494471i	−0.838027	+	0.545629i	$0.816291\pi$
$678$	0.354102	+	0.257270i	0.0135992	+	0.00988040i
$679$	34.0623	−	24.7477i	1.30719	−	0.949730i
$680$	−2.92705	+	9.00854i	−0.112247	+	0.345462i
$681$	−24.8885			−0.953731
$682$	−0.545085	+	5.82485i	−0.0208724	+	0.223045i
$683$	−3.11146			−0.119057			−0.0595283	−	0.998227i	$-0.518960\pi$
$683$	−3.11146			−0.119057			−0.0595283	+	0.998227i	$0.518960\pi$
$684$	−2.92705	+	9.00854i	−0.111919	+	0.344450i
$685$	15.8262	−	11.4984i	0.604689	−	0.439333i
$686$	−7.50000	−	5.44907i	−0.286351	−	0.208046i
$687$	3.09017	+	9.51057i	0.117897	+	0.362851i
$688$	3.57295	+	10.9964i	0.136217	+	0.419234i
$689$	13.7254	+	9.97210i	0.522897	+	0.379907i
$690$	−4.54508	+	3.30220i	−0.173028	+	0.125713i
$691$	−8.12461	+	25.0050i	−0.309075	+	0.951234i	0.669050	+	0.743217i	$0.266701\pi$
$691$	−8.12461	+	25.0050i	−0.309075	+	0.951234i	−0.978125	+	0.208017i	$0.933299\pi$
$692$	−24.8885			−0.946120
$693$	−9.13525	−	3.94298i	−0.347020	−	0.149782i
$694$	12.9443			0.491358
$695$	0.690983	−	2.12663i	0.0262105	−	0.0806676i
$696$	−8.09017	+	5.87785i	−0.306657	+	0.222799i
$697$	15.6353	+	11.3597i	0.592228	+	0.430278i
$698$	1.93363	+	5.95110i	0.0731889	+	0.225252i
$699$	7.51722	+	23.1356i	0.284327	+	0.875070i
$700$	7.28115	+	5.29007i	0.275202	+	0.199946i
$701$	8.64590	−	6.28161i	0.326551	−	0.237253i	−0.412415	−	0.910996i	$-0.635315\pi$
$701$	8.64590	−	6.28161i	0.326551	−	0.237253i	0.738966	+	0.673743i	$0.235315\pi$
$702$	−0.336881	+	1.03681i	−0.0127148	+	0.0391320i
$703$	1.38197			0.0521218
$704$	−0.763932	+	0.171513i	−0.0287918	+	0.00646416i
$705$	−4.23607			−0.159540
$706$	2.00000	−	6.15537i	0.0752710	−	0.231660i
$707$	7.28115	−	5.29007i	0.273836	−	0.198953i
$708$	13.5172	+	9.82084i	0.508008	+	0.369090i
$709$	15.0623	+	46.3570i	0.565677	+	1.74097i	0.665932	+	0.746012i	$0.268034\pi$
$709$	15.0623	+	46.3570i	0.565677	+	1.74097i	−0.100255	+	0.994962i	$0.531966\pi$
$710$	−2.78115	−	8.55951i	−0.104375	−	0.321233i
$711$	−7.66312	−	5.56758i	−0.287389	−	0.208801i
$712$	−0.954915	+	0.693786i	−0.0357870	+	0.0260007i
$713$	3.06231	−	9.42481i	0.114684	−	0.352962i
$714$	−3.00000			−0.112272
$715$	−7.80902	−	13.1760i	−0.292041	−	0.492756i
$716$	3.61803			0.135212
$717$	0.791796	−	2.43690i	0.0295702	−	0.0910076i
$718$	−6.38197	+	4.63677i	−0.238173	+	0.173043i
$719$	1.28115	+	0.930812i	0.0477789	+	0.0347134i	0.611418	−	0.791307i	$-0.290599\pi$
$719$	1.28115	+	0.930812i	0.0477789	+	0.0347134i	−0.563639	+	0.826021i	$0.690599\pi$
$720$	−1.50000	−	4.61653i	−0.0559017	−	0.172048i
$721$	−5.56231	−	17.1190i	−0.207151	−	0.637546i
$722$	7.63525	+	5.54734i	0.284155	+	0.206451i
$723$	18.7082	−	13.5923i	0.695766	−	0.505503i
$724$	8.73607	−	26.8869i	0.324673	−	0.999242i
$725$	8.29180			0.307950
$726$	6.68034	+	1.26133i	0.247931	+	0.0468122i
$727$	38.8541			1.44102			0.720509	−	0.693445i	$-0.243908\pi$
$727$	38.8541			1.44102			0.720509	+	0.693445i	$0.243908\pi$
$728$	3.65654	−	11.2537i	0.135520	−	0.417089i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	4.23607	+	3.07768i	0.156784	+	0.113910i
$731$	3.11803	+	9.59632i	0.115325	+	0.354933i
$732$	−3.92705	−	12.0862i	−0.145148	−	0.446720i
$733$	30.5066	+	22.1643i	1.12679	+	0.818658i	0.985224	−	0.171271i	$-0.0547875\pi$
$733$	30.5066	+	22.1643i	1.12679	+	0.818658i	0.141562	+	0.989929i	$0.454787\pi$
$734$	2.78115	−	2.02063i	0.102654	−	0.0745827i
$735$	−1.61803	+	4.97980i	−0.0596821	+	0.183683i
$736$	−19.5066			−0.719022
$737$	−16.1697	−	27.2829i	−0.595618	−	1.00498i
$738$	7.38197			0.271734
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	0.702458	+	0.711726i	$0.252086\pi$
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	−0.986642	+	0.162904i	$0.947914\pi$
$740$	−0.809017	+	0.587785i	−0.0297401	+	0.0216074i
$741$	−8.35410	−	6.06961i	−0.306896	−	0.222973i
$742$	5.51064	+	16.9600i	0.202302	+	0.622622i
$743$	10.8713	+	33.4585i	0.398830	+	1.22747i	0.925938	+	0.377675i	$0.123276\pi$
$743$	10.8713	+	33.4585i	0.398830	+	1.22747i	−0.527108	+	0.849798i	$0.676724\pi$
$744$	−5.16312	−	3.75123i	−0.189289	−	0.137527i
$745$	31.7705	−	23.0826i	1.16398	−	0.845682i
$746$	0.843459	−	2.59590i	0.0308812	−	0.0950426i
$747$	0.708204			0.0259118
$748$	−8.47214	+	1.90211i	−0.309772	+	0.0695481i
$749$	−12.7082			−0.464348
$750$	−1.57295	+	4.84104i	−0.0574360	+	0.176770i
$751$	−9.64590	+	7.00816i	−0.351984	+	0.255731i	−0.749701	−	0.661777i	$-0.769803\pi$
$751$	−9.64590	+	7.00816i	−0.351984	+	0.255731i	0.397717	+	0.917508i	$0.369803\pi$
$752$	−2.42705	−	1.76336i	−0.0885054	−	0.0643030i
$753$	−2.40983	−	7.41669i	−0.0878191	−	0.270279i
$754$	−1.50658	−	4.63677i	−0.0548663	−	0.168861i
$755$	4.23607	+	3.07768i	0.154166	+	0.112008i
$756$	3.92705	−	2.85317i	0.142825	−	0.103769i
$757$	0.600813	−	1.84911i	0.0218369	−	0.0672071i	−0.939544	−	0.342428i	$-0.888751\pi$
$757$	0.600813	−	1.84911i	0.0218369	−	0.0672071i	0.961381	+	0.275220i	$0.0887509\pi$
$758$	−0.978714			−0.0355485
$759$	−10.5729	−	4.56352i	−0.383774	−	0.165645i
$760$	−34.2705			−1.24312
$761$	−9.54508	+	29.3768i	−0.346009	+	1.06491i	0.615032	+	0.788502i	$0.289143\pi$
$761$	−9.54508	+	29.3768i	−0.346009	+	1.06491i	−0.961041	+	0.276404i	$0.910857\pi$
$762$	−1.85410	+	1.34708i	−0.0671670	+	0.0487997i
$763$		0			0
$764$	3.73607	+	11.4984i	0.135166	+	0.415999i
$765$	−1.30902	−	4.02874i	−0.0473276	−	0.145659i
$766$	13.4443	+	9.76784i	0.485761	+	0.352926i
$767$	−14.7361	+	10.7064i	−0.532089	+	0.386585i
$768$	−2.02786	+	6.24112i	−0.0731742	+	0.225207i
$769$	12.6869			0.457502			0.228751	−	0.973485i	$-0.426536\pi$
$769$	12.6869			0.457502			0.228751	+	0.973485i	$0.426536\pi$
$770$	1.50000	−	16.0292i	0.0540562	−	0.577652i
$771$	−11.6738			−0.420420
$772$	9.28115	−	28.5645i	0.334036	−	1.02806i
$773$	25.2812	−	18.3678i	0.909300	−	0.660645i	−0.0315378	−	0.999503i	$-0.510040\pi$
$773$	25.2812	−	18.3678i	0.909300	−	0.660645i	0.940838	+	0.338858i	$0.110040\pi$
$774$	3.11803	+	2.26538i	0.112075	+	0.0814276i
$775$	1.63525	+	5.03280i	0.0587401	+	0.180783i
$776$	−9.69756	−	29.8460i	−0.348122	−	1.07141i
$777$	−0.572949	−	0.416272i	−0.0205544	−	0.0149337i
$778$	12.1353	−	8.81678i	0.435070	−	0.316097i
$779$	−21.6074	+	66.5007i	−0.774165	+	2.38264i
$780$	7.47214			0.267545
$781$	12.1869	−	13.8496i	0.436082	−	0.495577i
$782$	−3.47214			−0.124163
$783$	1.38197	−	4.25325i	0.0493874	−	0.151999i
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$	−7.85410	−	5.70634i	−0.280325	−	0.203668i
$786$	1.36475	+	4.20025i	0.0486788	+	0.149818i
$787$	−3.18034	−	9.78808i	−0.113367	−	0.348907i	0.878236	−	0.478227i	$-0.158721\pi$
$787$	−3.18034	−	9.78808i	−0.113367	−	0.348907i	−0.991603	+	0.129320i	$0.958721\pi$
$788$	31.9164	+	23.1886i	1.13697	+	0.826061i
$789$	13.2082	−	9.59632i	0.470225	−	0.341638i
$790$	4.73607	−	14.5761i	0.168502	−	0.518595i
$791$	2.12461			0.0755425
$792$	−4.89919	+	5.56758i	−0.174085	+	0.197835i
$793$	13.8541			0.491974
$794$	7.39261	−	22.7521i	0.262354	−	0.807442i
$795$	−20.3713	+	14.8006i	−0.722496	+	0.524924i
$796$	−21.8713	−	15.8904i	−0.775208	−	0.563222i
$797$	3.32624	+	10.2371i	0.117821	+	0.362617i	0.992525	−	0.122041i	$-0.0389440\pi$
$797$	3.32624	+	10.2371i	0.117821	+	0.362617i	−0.874704	+	0.484658i	$0.838944\pi$
$798$	−3.35410	−	10.3229i	−0.118734	−	0.365425i
$799$	−2.11803	−	1.53884i	−0.0749307	−	0.0544403i
$800$	8.42705	−	6.12261i	0.297941	−	0.216467i
$801$	0.163119	−	0.502029i	0.00576353	−	0.0177383i
$802$	16.1246			0.569380
$803$	−1.00000	+	10.6861i	−0.0352892	+	0.377106i
$804$	15.4721			0.545660
$805$	−8.42705	+	25.9358i	−0.297015	+	0.914117i
$806$	2.51722	−	1.82887i	0.0886653	−	0.0644191i
$807$	−12.5623	−	9.12705i	−0.442214	−	0.321287i
$808$	−2.07295	−	6.37988i	−0.0729261	−	0.224443i
$809$	2.98936	+	9.20029i	0.105100	+	0.323465i	0.989754	−	0.142783i	$-0.0456052\pi$
$809$	2.98936	+	9.20029i	0.105100	+	0.323465i	−0.884654	+	0.466249i	$0.845605\pi$
$810$	−1.30902	−	0.951057i	−0.0459942	−	0.0334167i
$811$	−2.63525	+	1.91462i	−0.0925363	+	0.0672316i	−0.633091	−	0.774077i	$-0.718214\pi$
$811$	−2.63525	+	1.91462i	−0.0925363	+	0.0672316i	0.540555	+	0.841309i	$0.318214\pi$
$812$	−6.70820	+	20.6457i	−0.235412	+	0.724523i
$813$	−27.2705			−0.956419
$814$	0.444272	+	0.191758i	0.0155717	+	0.00672111i
$815$	−47.8328			−1.67551
$816$	0.927051	−	2.85317i	0.0324533	−	0.0998809i
$817$	−29.5344	+	21.4580i	−1.03328	+	0.750721i
$818$	−5.52786	−	4.01623i	−0.193277	−	0.140424i
$819$	1.63525	+	5.03280i	0.0571404	+	0.175860i
$820$	−15.6353	−	48.1204i	−0.546007	−	1.68044i
$821$	−32.6976	−	23.7562i	−1.14115	−	0.829096i	−0.153873	−	0.988091i	$-0.549175\pi$
$821$	−32.6976	−	23.7562i	−1.14115	−	0.829096i	−0.987279	+	0.158995i	$0.949175\pi$
$822$	3.73607	−	2.71441i	0.130310	−	0.0946760i
$823$	−10.9615	+	33.7360i	−0.382094	+	1.17596i	0.556473	+	0.830866i	$0.312154\pi$
$823$	−10.9615	+	33.7360i	−0.382094	+	1.17596i	−0.938567	+	0.345098i	$0.887846\pi$
$824$	−13.4164			−0.467383
$825$	6.00000	−	1.34708i	0.208893	−	0.0468994i
$826$	−19.1459			−0.666171
$827$	16.4164	−	50.5245i	0.570854	−	1.75691i	−0.0790257	−	0.996873i	$-0.525181\pi$
$827$	16.4164	−	50.5245i	0.570854	−	1.75691i	0.649880	−	0.760037i	$-0.274819\pi$
$828$	4.54508	−	3.30220i	0.157953	−	0.114759i
$829$	−14.3090	−	10.3961i	−0.496973	−	0.361072i	0.310887	−	0.950447i	$-0.399374\pi$
$829$	−14.3090	−	10.3961i	−0.496973	−	0.361072i	−0.807859	+	0.589375i	$0.799374\pi$
$830$	0.354102	+	1.08981i	0.0122911	+	0.0378280i
$831$	9.44427	+	29.0665i	0.327618	+	1.00831i
$832$	0.336881	+	0.244758i	0.0116792	+	0.00848547i
$833$	−2.61803	+	1.90211i	−0.0907095	+	0.0659043i
$834$	0.163119	−	0.502029i	0.00564835	−	0.0173838i
$835$	−26.2705			−0.909128
$836$	−16.0172	−	27.0256i	−0.553967	−	0.934700i
$837$	2.85410			0.0986522
$838$	−3.15248	+	9.70232i	−0.108900	+	0.335161i
$839$	29.6976	−	21.5765i	1.02527	−	0.744905i	0.0579164	−	0.998321i	$-0.481554\pi$
$839$	29.6976	−	21.5765i	1.02527	−	0.744905i	0.967357	+	0.253417i	$0.0815543\pi$
$840$	14.2082	+	10.3229i	0.490230	+	0.356173i
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$	7.11803	+	21.9071i	0.245304	+	0.754967i
$843$	0.618034	+	0.449028i	0.0212862	+	0.0154653i
$844$	−29.1525	+	21.1805i	−1.00347	+	0.729063i
$845$	8.00000	−	24.6215i	0.275208	−	0.847004i
$846$	−1.00000			−0.0343807
$847$	29.8328	−	14.1068i	1.02507	−	0.484717i
$848$	−17.8328			−0.612381
$849$	0.0557281	−	0.171513i	0.00191258	−	0.00588633i
$850$	1.50000	−	1.08981i	0.0514496	−	0.0373803i
$851$	−0.663119	−	0.481784i	−0.0227314	−	0.0165153i
$852$	2.78115	+	8.55951i	0.0952807	+	0.293244i
$853$	−3.07295	−	9.45756i	−0.105216	−	0.323821i	0.884565	−	0.466416i	$-0.154455\pi$
$853$	−3.07295	−	9.45756i	−0.105216	−	0.323821i	−0.989781	+	0.142596i	$0.954455\pi$
$854$	11.7812	+	8.55951i	0.403143	+	0.292900i
$855$	12.3992	−	9.00854i	0.424043	−	0.308085i
$856$	−2.92705	+	9.00854i	−0.100045	+	0.307905i
$857$	47.7214			1.63013			0.815065	−	0.579369i	$-0.196701\pi$
$857$	47.7214			1.63013			0.815065	+	0.579369i	$0.196701\pi$
$858$	−1.84346	−	3.11044i	−0.0629346	−	0.106189i
$859$	7.11146			0.242640			0.121320	−	0.992613i	$-0.461287\pi$
$859$	7.11146			0.242640			0.121320	+	0.992613i	$0.461287\pi$
$860$	8.16312	−	25.1235i	0.278360	−	0.856704i
$861$	28.9894	−	21.0620i	0.987955	−	0.717791i
$862$	−19.7533	−	14.3516i	−0.672800	−	0.488818i
$863$	3.67376	+	11.3067i	0.125056	+	0.384884i	0.993911	−	0.110183i	$-0.0351436\pi$
$863$	3.67376	+	11.3067i	0.125056	+	0.384884i	−0.868855	+	0.495067i	$0.835144\pi$
$864$	−1.73607	−	5.34307i	−0.0590622	−	0.181775i
$865$	32.5795	+	23.6704i	1.10774	+	0.804818i
$866$	−3.00000	+	2.17963i	−0.101944	+	0.0740668i
$867$	−4.44427	+	13.6781i	−0.150935	+	0.464531i
$868$	−13.8541			−0.470239
$869$	30.6525	−	6.88191i	1.03981	−	0.233453i
$870$	7.23607			0.245326
$871$	−5.21227	+	16.0417i	−0.176611	+	0.543553i
$872$		0			0
$873$	11.3541	+	8.24924i	0.384278	+	0.279194i
$874$	−3.88197	−	11.9475i	−0.131309	−	0.404129i
$875$	7.63525	+	23.4989i	0.258119	+	0.794408i
$876$	−4.23607	−	3.07768i	−0.143123	−	0.103985i
$877$	−5.19098	+	3.77147i	−0.175287	+	0.127353i	−0.671969	−	0.740579i	$-0.734551\pi$
$877$	−5.19098	+	3.77147i	−0.175287	+	0.127353i	0.496682	+	0.867932i	$0.334551\pi$
$878$	−0.628677	+	1.93487i	−0.0212168	+	0.0652987i
$879$	0.0557281			0.00187966
$880$	14.7812	+	6.37988i	0.498273	+	0.215066i
$881$	13.9098			0.468634			0.234317	−	0.972160i	$-0.424715\pi$
$881$	13.9098			0.468634			0.234317	+	0.972160i	$0.424715\pi$
$882$	−0.381966	+	1.17557i	−0.0128615	+	0.0395835i
$883$	−8.56231	+	6.22088i	−0.288145	+	0.209349i	−0.722462	−	0.691411i	$-0.756990\pi$
$883$	−8.56231	+	6.22088i	−0.288145	+	0.209349i	0.434318	+	0.900760i	$0.356990\pi$
$884$	3.73607	+	2.71441i	0.125658	+	0.0912956i
$885$	−8.35410	−	25.7113i	−0.280820	−	0.864275i
$886$	7.85410	+	24.1724i	0.263864	+	0.812089i
$887$	−2.42705	−	1.76336i	−0.0814924	−	0.0592077i	0.546293	−	0.837594i	$-0.316038\pi$
$887$	−2.42705	−	1.76336i	−0.0814924	−	0.0592077i	−0.627785	+	0.778386i	$0.716038\pi$
$888$	−0.427051	+	0.310271i	−0.0143309	+	0.0104120i
$889$	−3.43769	+	10.5801i	−0.115297	+	0.354846i
$890$	0.854102			0.0286296
$891$	0.309017	−	3.30220i	0.0103525	−	0.110628i
$892$	−1.14590			−0.0383675
$893$	2.92705	−	9.00854i	0.0979500	−	0.301459i
$894$	7.50000	−	5.44907i	0.250838	−	0.182244i
$895$	−4.73607	−	3.44095i	−0.158309	−	0.115018i
$896$	10.5517	+	32.4747i	0.352506	+	1.08490i
$897$	1.89261	+	5.82485i	0.0631924	+	0.194486i
$898$	−12.2361	−	8.89002i	−0.408323	−	0.296664i
$899$	−10.3262	+	7.50245i	−0.344399	+	0.250221i
$900$	−0.927051	+	2.85317i	−0.0309017	+	0.0951057i
$901$	−15.5623			−0.518456
$902$	−16.1738	+	18.3803i	−0.538527	+	0.611999i
$903$	18.7082			0.622570
$904$	0.489357	−	1.50609i	0.0162758	−	0.0500917i
$905$	−37.0066	+	26.8869i	−1.23014	+	0.893749i
$906$	1.00000	+	0.726543i	0.0332228	+	0.0241378i
$907$	−13.2812	−	40.8752i	−0.440993	−	1.35724i	−0.886818	−	0.462118i	$-0.847090\pi$
$907$	−13.2812	−	40.8752i	−0.440993	−	1.35724i	0.445825	−	0.895120i	$-0.352910\pi$
$908$	12.4443	+	38.2995i	0.412978	+	1.27101i
$909$	2.42705	+	1.76336i	0.0805002	+	0.0584868i
$910$	−6.92705	+	5.03280i	−0.229630	+	0.166836i
$911$	5.57953	−	17.1720i	0.184858	−	0.568934i	−0.815088	−	0.579337i	$-0.803311\pi$
$911$	5.57953	−	17.1720i	0.184858	−	0.568934i	0.999946	+	0.0104029i	$0.00331142\pi$
$912$	10.8541			0.359415
$913$	−1.55166	+	1.76336i	−0.0513525	+	0.0583586i
$914$	−5.06888			−0.167664
$915$	−6.35410	+	19.5559i	−0.210060	+	0.646499i
$916$	13.0902	−	9.51057i	0.432511	−	0.314238i
$917$	17.3435	+	12.6008i	0.572731	+	0.416114i
$918$	−0.309017	−	0.951057i	−0.0101991	−	0.0313895i
$919$	14.5106	+	44.6592i	0.478662	+	1.47317i	0.840955	+	0.541106i	$0.181994\pi$
$919$	14.5106	+	44.6592i	0.478662	+	1.47317i	−0.362293	+	0.932064i	$0.618006\pi$
$920$	16.4443	+	11.9475i	0.542152	+	0.393896i
$921$	−0.454915	+	0.330515i	−0.0149900	+	0.0108908i
$922$	4.02786	−	12.3965i	0.132651	−	0.408257i
$923$	−9.81153			−0.322950
$924$	−1.50000	+	16.0292i	−0.0493464	+	0.527322i
$925$	0.437694			0.0143913
$926$	3.01722	−	9.28605i	0.0991520	−	0.305159i
$927$	4.85410	−	3.52671i	0.159430	−	0.115832i
$928$	20.3262	+	14.7679i	0.667241	+	0.484779i
$929$	−10.1631	−	31.2789i	−0.333441	−	1.02623i	−0.967485	−	0.252929i	$-0.918606\pi$
$929$	−10.1631	−	31.2789i	−0.333441	−	1.02623i	0.634044	−	0.773297i	$-0.281394\pi$
$930$	1.42705	+	4.39201i	0.0467948	+	0.144020i
$931$	−9.47214	−	6.88191i	−0.310437	−	0.225545i
$932$	31.8435	−	23.1356i	1.04307	−	0.757833i
$933$	0.781153	−	2.40414i	0.0255738	−	0.0787081i
$934$	6.03444			0.197453
$935$	12.8992	+	5.56758i	0.421849	+	0.182079i
$936$	3.94427			0.128923
$937$	−5.12868	+	15.7844i	−0.167547	+	0.515655i	−0.999215	−	0.0396173i	$-0.987386\pi$
$937$	−5.12868	+	15.7844i	−0.167547	+	0.515655i	0.831668	+	0.555273i	$0.187386\pi$
$938$	−14.3435	+	10.4211i	−0.468331	+	0.340262i
$939$	−20.8992	−	15.1841i	−0.682019	−	0.495516i
$940$	2.11803	+	6.51864i	0.0690827	+	0.212615i
$941$	−13.7918	−	42.4468i	−0.449600	−	1.38373i	−0.877360	−	0.479833i	$-0.840697\pi$
$941$	−13.7918	−	42.4468i	−0.449600	−	1.38373i	0.427760	−	0.903892i	$-0.359303\pi$
$942$	−1.85410	−	1.34708i	−0.0604099	−	0.0438904i
$943$	33.5517	−	24.3767i	1.09259	−	0.793815i
$944$	5.91641	−	18.2088i	0.192563	−	0.592647i
$945$	−7.85410			−0.255494
$946$	−12.4721	+	2.80017i	−0.405504	+	0.0910413i
$947$	18.3262			0.595523			0.297761	−	0.954640i	$-0.403760\pi$
$947$	18.3262			0.595523			0.297761	+	0.954640i	$0.403760\pi$
$948$	−4.73607	+	14.5761i	−0.153820	+	0.473410i
$949$	4.61803	−	3.35520i	0.149908	−	0.108914i
$950$	5.42705	+	3.94298i	0.176077	+	0.127927i
$951$	−5.98278	−	18.4131i	−0.194005	−	0.597086i
$952$	3.35410	+	10.3229i	0.108707	+	0.334566i
$953$	−30.5967	−	22.2298i	−0.991126	−	0.720095i	−0.0309585	−	0.999521i	$-0.509856\pi$
$953$	−30.5967	−	22.2298i	−0.991126	−	0.720095i	−0.960167	+	0.279426i	$0.909856\pi$
$954$	−4.80902	+	3.49396i	−0.155698	+	0.113121i
$955$	6.04508	−	18.6049i	0.195614	−	0.602039i
$956$	−4.14590			−0.134088
$957$	7.56231	+	12.7598i	0.244455	+	0.412465i
$958$	17.3607			0.560898
$959$	6.92705	−	21.3193i	0.223686	−	0.688435i
$960$	−0.500000	+	0.363271i	−0.0161374	+	0.0117245i
$961$	18.4894	+	13.4333i	0.596431	+	0.433332i
$962$	−0.0795268	−	0.244758i	−0.00256405	−	0.00789133i
$963$	−1.30902	−	4.02874i	−0.0421825	−	0.129824i
$964$	−30.2705	−	21.9928i	−0.974947	−	0.708341i
$965$	−39.3156	+	28.5645i	−1.26561	+	0.919522i
$966$	−1.98936	+	6.12261i	−0.0640065	+	0.196992i
$967$	−34.6869			−1.11546			−0.557728	−	0.830024i	$-0.688327\pi$
$967$	−34.6869			−1.11546			−0.557728	+	0.830024i	$0.688327\pi$
$968$	−3.12868	−	24.3970i	−0.100559	−	0.784148i
$969$	9.47214			0.304289
$970$	−7.01722	+	21.5968i	−0.225309	+	0.693431i
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.957885	−	0.287151i	$-0.907292\pi$
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.0229058	+	0.999738i	$0.507292\pi$
$972$	1.30902	+	0.951057i	0.0419867	+	0.0305052i
$973$	−0.791796	−	2.43690i	−0.0253838	−	0.0781234i
$974$	−3.21227	−	9.88635i	−0.102928	−	0.316779i
$975$	−2.64590	−	1.92236i	−0.0847366	−	0.0615647i
$976$	−11.7812	+	8.55951i	−0.377106	+	0.273983i
$977$	−1.43363	+	4.41226i	−0.0458658	+	0.141161i	−0.971367	−	0.237585i	$-0.923644\pi$
$977$	−1.43363	+	4.41226i	−0.0458658	+	0.141161i	0.925501	+	0.378745i	$0.123644\pi$
$978$	−11.2918			−0.361072
$979$	0.892609	+	1.50609i	0.0285279	+	0.0481347i
$980$	8.47214			0.270632
$981$		0			0
$982$	12.6074	−	9.15981i	0.402318	−	0.292301i
$983$	22.0902	+	16.0494i	0.704567	+	0.511898i	0.881416	−	0.472340i	$-0.156591\pi$
$983$	22.0902	+	16.0494i	0.704567	+	0.511898i	−0.176849	+	0.984238i	$0.556591\pi$
$984$	−8.25329	−	25.4010i	−0.263105	−	0.809755i
$985$	−19.7254	−	60.7086i	−0.628504	−	1.93434i
$986$	3.61803	+	2.62866i	0.115222	+	0.0837134i
$987$	−3.92705	+	2.85317i	−0.124999	+	0.0908174i
$988$	−5.16312	+	15.8904i	−0.164261	+	0.505542i
$989$	21.6525			0.688509
$990$	5.23607	−	1.17557i	0.166413	−	0.0373621i
$991$	21.2705			0.675680			0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705			0.675680			0.337840	+	0.941204i	$0.390304\pi$
$992$	−4.95492	+	15.2497i	−0.157319	+	0.484177i
$993$	−21.5172	+	15.6332i	−0.682828	+	0.496104i
$994$	−8.34346	−	6.06188i	−0.264638	−	0.192271i
$995$	13.5172	+	41.6017i	0.428525	+	1.31886i
$996$	−0.354102	−	1.08981i	−0.0112202	−	0.0345321i
$997$	10.5000	+	7.62870i	0.332538	+	0.241603i	0.741507	−	0.670945i	$-0.234111\pi$
$997$	10.5000	+	7.62870i	0.332538	+	0.241603i	−0.408969	+	0.912548i	$0.634111\pi$
$998$	−8.78115	+	6.37988i	−0.277963	+	0.201952i
$999$	0.0729490	−	0.224514i	0.00230800	−	0.00710331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.2.e.a.31.1	yes	4
3.2	odd	2		99.2.f.b.64.1		4
4.3	odd	2		528.2.y.f.97.1		4
5.2	odd	4		825.2.bx.b.724.1		8
5.3	odd	4		825.2.bx.b.724.2		8
5.4	even	2		825.2.n.f.526.1		4
9.2	odd	6		891.2.n.a.757.1		8
9.4	even	3		891.2.n.d.460.1		8
9.5	odd	6		891.2.n.a.460.1		8
9.7	even	3		891.2.n.d.757.1		8
11.2	odd	10		363.2.e.c.124.1		4
11.3	even	5		363.2.e.h.202.1		4
11.4	even	5		363.2.a.h.1.1		2
11.5	even	5	inner	33.2.e.a.16.1	✓	4
11.6	odd	10		363.2.e.j.148.1		4
11.7	odd	10		363.2.a.e.1.2		2
11.8	odd	10		363.2.e.c.202.1		4
11.9	even	5		363.2.e.h.124.1		4
11.10	odd	2		363.2.e.j.130.1		4
33.5	odd	10		99.2.f.b.82.1		4
33.26	odd	10		1089.2.a.m.1.2		2
33.29	even	10		1089.2.a.s.1.1		2
44.7	even	10		5808.2.a.bm.1.1		2
44.15	odd	10		5808.2.a.bl.1.1		2
44.27	odd	10		528.2.y.f.49.1		4
55.4	even	10		9075.2.a.x.1.2		2
55.27	odd	20		825.2.bx.b.49.2		8
55.29	odd	10		9075.2.a.bv.1.1		2
55.38	odd	20		825.2.bx.b.49.1		8
55.49	even	10		825.2.n.f.676.1		4
99.5	odd	30		891.2.n.a.379.1		8
99.16	even	15		891.2.n.d.676.1		8
99.38	odd	30		891.2.n.a.676.1		8
99.49	even	15		891.2.n.d.379.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	11.5	even	5	inner
33.2.e.a.31.1	yes	4	1.1	even	1	trivial
99.2.f.b.64.1		4	3.2	odd	2
99.2.f.b.82.1		4	33.5	odd	10
363.2.a.e.1.2		2	11.7	odd	10
363.2.a.h.1.1		2	11.4	even	5
363.2.e.c.124.1		4	11.2	odd	10
363.2.e.c.202.1		4	11.8	odd	10
363.2.e.h.124.1		4	11.9	even	5
363.2.e.h.202.1		4	11.3	even	5
363.2.e.j.130.1		4	11.10	odd	2
363.2.e.j.148.1		4	11.6	odd	10
528.2.y.f.49.1		4	44.27	odd	10
528.2.y.f.97.1		4	4.3	odd	2
825.2.n.f.526.1		4	5.4	even	2
825.2.n.f.676.1		4	55.49	even	10
825.2.bx.b.49.1		8	55.38	odd	20
825.2.bx.b.49.2		8	55.27	odd	20
825.2.bx.b.724.1		8	5.2	odd	4
825.2.bx.b.724.2		8	5.3	odd	4
891.2.n.a.379.1		8	99.5	odd	30
891.2.n.a.460.1		8	9.5	odd	6
891.2.n.a.676.1		8	99.38	odd	30
891.2.n.a.757.1		8	9.2	odd	6
891.2.n.d.379.1		8	99.49	even	15
891.2.n.d.460.1		8	9.4	even	3
891.2.n.d.676.1		8	99.16	even	15
891.2.n.d.757.1		8	9.7	even	3
1089.2.a.m.1.2		2	33.26	odd	10
1089.2.a.s.1.1		2	33.29	even	10
5808.2.a.bl.1.1		2	44.15	odd	10
5808.2.a.bm.1.1		2	44.7	even	10
9075.2.a.x.1.2		2	55.4	even	10
9075.2.a.bv.1.1		2	55.29	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-2.42705 - 1.76336i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.190983 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(-0.190983 - 0.587785i) q^{6} +(-2.42705 - 1.76336i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.61803 q^{10} +(1.69098 + 2.85317i) q^{11} -1.61803 q^{12} +(0.545085 - 1.67760i) q^{13} +(1.50000 - 1.08981i) q^{14} +(2.11803 + 1.53884i) q^{15} +(0.572949 + 1.76336i) q^{16} +(0.500000 + 1.53884i) q^{17} +(0.500000 + 0.363271i) q^{18} +(-4.73607 + 3.44095i) q^{19} +(1.30902 - 4.02874i) q^{20} +3.00000 q^{21} +(-2.00000 + 0.449028i) q^{22} +3.47214 q^{23} +(0.690983 - 2.12663i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(0.881966 + 0.640786i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(-3.61803 - 2.62866i) q^{29} +(-1.30902 + 0.951057i) q^{30} +(0.881966 - 2.71441i) q^{31} -5.61803 q^{32} +(-3.04508 - 1.31433i) q^{33} -1.00000 q^{34} +(-2.42705 + 7.46969i) q^{35} +(1.30902 - 0.951057i) q^{36} +(-0.190983 - 0.138757i) q^{37} +(-1.11803 - 3.44095i) q^{38} +(0.545085 + 1.67760i) q^{39} +(4.73607 + 3.44095i) q^{40} +(9.66312 - 7.02067i) q^{41} +(-0.572949 + 1.76336i) q^{42} +6.23607 q^{43} +(-0.500000 + 5.34307i) q^{44} -2.61803 q^{45} +(-0.663119 + 2.04087i) q^{46} +(-1.30902 + 0.951057i) q^{47} +(-1.50000 - 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-0.354102 - 1.08981i) q^{50} +(-1.30902 - 0.951057i) q^{51} +(2.30902 - 1.67760i) q^{52} +(-2.97214 + 9.14729i) q^{53} -0.618034 q^{54} +(5.73607 - 6.51864i) q^{55} +6.70820 q^{56} +(1.80902 - 5.56758i) q^{57} +(2.23607 - 1.62460i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(1.30902 + 4.02874i) q^{60} +(2.42705 + 7.46969i) q^{61} +(1.42705 + 1.03681i) q^{62} +(-2.42705 + 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} -4.61803 q^{65} +(1.35410 - 1.53884i) q^{66} -9.56231 q^{67} +(-0.809017 + 2.48990i) q^{68} +(-2.80902 + 2.04087i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-1.71885 - 5.29007i) q^{71} +(0.690983 + 2.12663i) q^{72} +(2.61803 + 1.90211i) q^{73} +(0.118034 - 0.0857567i) q^{74} +(0.572949 - 1.76336i) q^{75} -9.47214 q^{76} +(0.927051 - 9.90659i) q^{77} -1.09017 q^{78} +(2.92705 - 9.00854i) q^{79} +(3.92705 - 2.85317i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.28115 + 7.02067i) q^{82} +(0.218847 + 0.673542i) q^{83} +(3.92705 + 2.85317i) q^{84} +(3.42705 - 2.48990i) q^{85} +(-1.19098 + 3.66547i) q^{86} +4.47214 q^{87} +(-6.80902 - 2.93893i) q^{88} +0.527864 q^{89} +(0.500000 - 1.53884i) q^{90} +(-4.28115 + 3.11044i) q^{91} +(4.54508 + 3.30220i) q^{92} +(0.881966 + 2.71441i) q^{93} +(-0.309017 - 0.951057i) q^{94} +(12.3992 + 9.00854i) q^{95} +(4.54508 - 3.30220i) q^{96} +(-4.33688 + 13.3475i) q^{97} -1.23607 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9} + 2 q^{10} + 9 q^{11} - 2 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} + 2 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{20} + 12 q^{21} - 8 q^{22} - 4 q^{23} + 5 q^{24} - 6 q^{25} + 8 q^{26} - q^{27} - 6 q^{28} - 10 q^{29} - 3 q^{30} + 8 q^{31} - 18 q^{32} - q^{33} - 4 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} - 9 q^{39} + 10 q^{40} + 23 q^{41} - 9 q^{42} + 16 q^{43} - 2 q^{44} - 6 q^{45} + 13 q^{46} - 3 q^{47} - 6 q^{48} - 2 q^{49} + 12 q^{50} - 3 q^{51} + 7 q^{52} + 6 q^{53} + 2 q^{54} + 14 q^{55} + 5 q^{57} - 20 q^{59} + 3 q^{60} + 3 q^{61} - q^{62} - 3 q^{63} - 7 q^{64} - 14 q^{65} - 8 q^{66} + 2 q^{67} - q^{68} - 9 q^{69} - 9 q^{70} - 27 q^{71} + 5 q^{72} + 6 q^{73} - 4 q^{74} + 9 q^{75} - 20 q^{76} - 3 q^{77} + 18 q^{78} + 5 q^{79} + 9 q^{80} - q^{81} - 11 q^{82} + 21 q^{83} + 9 q^{84} + 7 q^{85} - 7 q^{86} - 25 q^{88} + 20 q^{89} + 2 q^{90} + 3 q^{91} + 7 q^{92} + 8 q^{93} + q^{94} + 25 q^{95} + 7 q^{96} - 33 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9 + 2 * q^10 + 9 * q^11 - 2 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 + 9 * q^16 + 2 * q^17 + 2 * q^18 - 10 * q^19 + 3 * q^20 + 12 * q^21 - 8 * q^22 - 4 * q^23 + 5 * q^24 - 6 * q^25 + 8 * q^26 - q^27 - 6 * q^28 - 10 * q^29 - 3 * q^30 + 8 * q^31 - 18 * q^32 - q^33 - 4 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 - 9 * q^39 + 10 * q^40 + 23 * q^41 - 9 * q^42 + 16 * q^43 - 2 * q^44 - 6 * q^45 + 13 * q^46 - 3 * q^47 - 6 * q^48 - 2 * q^49 + 12 * q^50 - 3 * q^51 + 7 * q^52 + 6 * q^53 + 2 * q^54 + 14 * q^55 + 5 * q^57 - 20 * q^59 + 3 * q^60 + 3 * q^61 - q^62 - 3 * q^63 - 7 * q^64 - 14 * q^65 - 8 * q^66 + 2 * q^67 - q^68 - 9 * q^69 - 9 * q^70 - 27 * q^71 + 5 * q^72 + 6 * q^73 - 4 * q^74 + 9 * q^75 - 20 * q^76 - 3 * q^77 + 18 * q^78 + 5 * q^79 + 9 * q^80 - q^81 - 11 * q^82 + 21 * q^83 + 9 * q^84 + 7 * q^85 - 7 * q^86 - 25 * q^88 + 20 * q^89 + 2 * q^90 + 3 * q^91 + 7 * q^92 + 8 * q^93 + q^94 + 25 * q^95 + 7 * q^96 - 33 * q^97 + 4 * q^98 + 4 * q^99

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