LMFDB - Embedded newform 361.2.c.d.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(68,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("361.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			68.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	361.68
Dual form			361.2.c.d.292.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.535233i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.618034 - 1.07047i) q^{5} +(0.809017 + 1.40126i) q^{6} +3.00000 q^{7} +2.23607 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.535233i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.618034 - 1.07047i) q^{5} +(0.809017 + 1.40126i) q^{6} +3.00000 q^{7} +2.23607 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-0.381966 - 0.661585i) q^{10} +0.618034 q^{11} -4.23607 q^{12} +(0.500000 + 0.866025i) q^{13} +(0.927051 - 1.60570i) q^{14} +(1.61803 + 2.80252i) q^{15} +(-0.927051 + 1.60570i) q^{16} +(-2.61803 + 4.53457i) q^{17} -2.38197 q^{18} +2.00000 q^{20} +(-3.92705 + 6.80185i) q^{21} +(0.190983 - 0.330792i) q^{22} +(-3.80902 - 6.59741i) q^{23} +(-2.92705 + 5.06980i) q^{24} +(1.73607 + 3.00696i) q^{25} +0.618034 q^{26} +2.23607 q^{27} +(2.42705 + 4.20378i) q^{28} +(0.690983 + 1.19682i) q^{29} +2.00000 q^{30} -2.14590 q^{31} +(2.80902 + 4.86536i) q^{32} +(-0.809017 + 1.40126i) q^{33} +(1.61803 + 2.80252i) q^{34} +(1.85410 - 3.21140i) q^{35} +(3.11803 - 5.40059i) q^{36} +2.14590 q^{37} -2.61803 q^{39} +(1.38197 - 2.39364i) q^{40} +(1.50000 - 2.59808i) q^{41} +(2.42705 + 4.20378i) q^{42} +(3.42705 - 5.93583i) q^{43} +(0.500000 + 0.866025i) q^{44} -4.76393 q^{45} -4.70820 q^{46} +(-1.50000 - 2.59808i) q^{47} +(-2.42705 - 4.20378i) q^{48} +2.00000 q^{49} +2.14590 q^{50} +(-6.85410 - 11.8717i) q^{51} +(-0.809017 + 1.40126i) q^{52} +(-4.66312 - 8.07676i) q^{53} +(0.690983 - 1.19682i) q^{54} +(0.381966 - 0.661585i) q^{55} +6.70820 q^{56} +0.854102 q^{58} +(7.66312 - 13.2729i) q^{59} +(-2.61803 + 4.53457i) q^{60} +(2.88197 + 4.99171i) q^{61} +(-0.663119 + 1.14856i) q^{62} +(-5.78115 - 10.0133i) q^{63} -0.236068 q^{64} +1.23607 q^{65} +(0.500000 + 0.866025i) q^{66} +(3.50000 + 6.06218i) q^{67} -8.47214 q^{68} +19.9443 q^{69} +(-1.14590 - 1.98475i) q^{70} +(-0.736068 + 1.27491i) q^{71} +(-4.30902 - 7.46344i) q^{72} +(-5.35410 + 9.27358i) q^{73} +(0.663119 - 1.14856i) q^{74} -9.09017 q^{75} +1.85410 q^{77} +(-0.809017 + 1.40126i) q^{78} +(6.70820 - 11.6190i) q^{79} +(1.14590 + 1.98475i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-0.927051 - 1.60570i) q^{82} -0.472136 q^{83} -12.7082 q^{84} +(3.23607 + 5.60503i) q^{85} +(-2.11803 - 3.66854i) q^{86} -3.61803 q^{87} +1.38197 q^{88} +(6.11803 + 10.5967i) q^{89} +(-1.47214 + 2.54981i) q^{90} +(1.50000 + 2.59808i) q^{91} +(6.16312 - 10.6748i) q^{92} +(2.80902 - 4.86536i) q^{93} -1.85410 q^{94} -14.7082 q^{96} +(-3.57295 + 6.18853i) q^{97} +(0.618034 - 1.07047i) q^{98} +(-1.19098 - 2.06284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{6} + 12 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^6 + 12 * q^7 - q^9	$ 4 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{6} + 12 q^{7} - q^{9} - 6 q^{10} - 2 q^{11} - 8 q^{12} + 2 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} - 6 q^{17} - 14 q^{18} + 8 q^{20} - 9 q^{21} + 3 q^{22} - 13 q^{23} - 5 q^{24} - 2 q^{25} - 2 q^{26} + 3 q^{28} + 5 q^{29} + 8 q^{30} - 22 q^{31} + 9 q^{32} - q^{33} + 2 q^{34} - 6 q^{35} + 8 q^{36} + 22 q^{37} - 6 q^{39} + 10 q^{40} + 6 q^{41} + 3 q^{42} + 7 q^{43} + 2 q^{44} - 28 q^{45} + 8 q^{46} - 6 q^{47} - 3 q^{48} + 8 q^{49} + 22 q^{50} - 14 q^{51} - q^{52} - 3 q^{53} + 5 q^{54} + 6 q^{55} - 10 q^{58} + 15 q^{59} - 6 q^{60} + 16 q^{61} + 13 q^{62} - 3 q^{63} + 8 q^{64} - 4 q^{65} + 2 q^{66} + 14 q^{67} - 16 q^{68} + 44 q^{69} - 18 q^{70} + 6 q^{71} - 15 q^{72} - 8 q^{73} - 13 q^{74} - 14 q^{75} - 6 q^{77} - q^{78} + 18 q^{80} - 2 q^{81} + 3 q^{82} + 16 q^{83} - 24 q^{84} + 4 q^{85} - 4 q^{86} - 10 q^{87} + 10 q^{88} + 20 q^{89} + 12 q^{90} + 6 q^{91} + 9 q^{92} + 9 q^{93} + 6 q^{94} - 32 q^{96} - 21 q^{97} - 2 q^{98} - 7 q^{99}+O(q^{100}) $ 4 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^6 + 12 * q^7 - q^9 - 6 * q^10 - 2 * q^11 - 8 * q^12 + 2 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 - 6 * q^17 - 14 * q^18 + 8 * q^20 - 9 * q^21 + 3 * q^22 - 13 * q^23 - 5 * q^24 - 2 * q^25 - 2 * q^26 + 3 * q^28 + 5 * q^29 + 8 * q^30 - 22 * q^31 + 9 * q^32 - q^33 + 2 * q^34 - 6 * q^35 + 8 * q^36 + 22 * q^37 - 6 * q^39 + 10 * q^40 + 6 * q^41 + 3 * q^42 + 7 * q^43 + 2 * q^44 - 28 * q^45 + 8 * q^46 - 6 * q^47 - 3 * q^48 + 8 * q^49 + 22 * q^50 - 14 * q^51 - q^52 - 3 * q^53 + 5 * q^54 + 6 * q^55 - 10 * q^58 + 15 * q^59 - 6 * q^60 + 16 * q^61 + 13 * q^62 - 3 * q^63 + 8 * q^64 - 4 * q^65 + 2 * q^66 + 14 * q^67 - 16 * q^68 + 44 * q^69 - 18 * q^70 + 6 * q^71 - 15 * q^72 - 8 * q^73 - 13 * q^74 - 14 * q^75 - 6 * q^77 - q^78 + 18 * q^80 - 2 * q^81 + 3 * q^82 + 16 * q^83 - 24 * q^84 + 4 * q^85 - 4 * q^86 - 10 * q^87 + 10 * q^88 + 20 * q^89 + 12 * q^90 + 6 * q^91 + 9 * q^92 + 9 * q^93 + 6 * q^94 - 32 * q^96 - 21 * q^97 - 2 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.535233i	0.218508	−	0.378467i	−0.735844	−	0.677151i	$-0.763214\pi$
$2$	0.309017	−	0.535233i	0.218508	−	0.378467i	0.954352	+	0.298684i	$0.0965477\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	0.189234	+	0.981932i	$0.439400\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	−0.944995	+	0.327085i	$0.893934\pi$
$4$	0.809017	+	1.40126i	0.404508	+	0.700629i
$5$	0.618034	−	1.07047i	0.276393	−	0.478727i	−0.694092	−	0.719886i	$-0.744194\pi$
$5$	0.618034	−	1.07047i	0.276393	−	0.478727i	0.970486	+	0.241159i	$0.0775275\pi$
$6$	0.809017	+	1.40126i	0.330280	+	0.572061i
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$	2.23607			0.790569
$9$	−1.92705	−	3.33775i	−0.642350	−	1.11258i
$10$	−0.381966	−	0.661585i	−0.120788	−	0.209211i
$11$	0.618034			0.186344			0.0931721	−	0.995650i	$-0.470299\pi$
$11$	0.618034			0.186344			0.0931721	+	0.995650i	$0.470299\pi$
$12$	−4.23607			−1.22285
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$	0.927051	−	1.60570i	0.247765	−	0.429141i
$15$	1.61803	+	2.80252i	0.417775	+	0.723607i
$16$	−0.927051	+	1.60570i	−0.231763	+	0.401425i
$17$	−2.61803	+	4.53457i	−0.634967	+	1.09979i	0.351556	+	0.936167i	$0.385653\pi$
$17$	−2.61803	+	4.53457i	−0.634967	+	1.09979i	−0.986522	+	0.163627i	$0.947681\pi$
$18$	−2.38197			−0.561435
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−3.92705	+	6.80185i	−0.856953	+	1.48429i
$22$	0.190983	−	0.330792i	0.0407177	−	0.0705251i
$23$	−3.80902	−	6.59741i	−0.794235	−	1.37566i	−0.923324	−	0.384022i	$-0.874539\pi$
$23$	−3.80902	−	6.59741i	−0.794235	−	1.37566i	0.129089	−	0.991633i	$-0.458795\pi$
$24$	−2.92705	+	5.06980i	−0.597482	+	1.03487i
$25$	1.73607	+	3.00696i	0.347214	+	0.601392i
$26$	0.618034			0.121206
$27$	2.23607			0.430331
$28$	2.42705	+	4.20378i	0.458670	+	0.794439i
$29$	0.690983	+	1.19682i	0.128312	+	0.222243i	0.923023	−	0.384745i	$-0.125711\pi$
$29$	0.690983	+	1.19682i	0.128312	+	0.222243i	−0.794711	+	0.606989i	$0.792377\pi$
$30$	2.00000			0.365148
$31$	−2.14590			−0.385415			−0.192707	−	0.981256i	$-0.561727\pi$
$31$	−2.14590			−0.385415			−0.192707	+	0.981256i	$0.561727\pi$
$32$	2.80902	+	4.86536i	0.496569	+	0.860082i
$33$	−0.809017	+	1.40126i	−0.140832	+	0.243928i
$34$	1.61803	+	2.80252i	0.277491	+	0.480628i
$35$	1.85410	−	3.21140i	0.313400	−	0.542825i
$36$	3.11803	−	5.40059i	0.519672	−	0.900099i
$37$	2.14590			0.352783			0.176392	−	0.984320i	$-0.443557\pi$
$37$	2.14590			0.352783			0.176392	+	0.984320i	$0.443557\pi$
$38$		0			0
$39$	−2.61803			−0.419221
$40$	1.38197	−	2.39364i	0.218508	−	0.378467i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$	2.42705	+	4.20378i	0.374502	+	0.648657i
$43$	3.42705	−	5.93583i	0.522620	−	0.905205i	−0.477033	−	0.878885i	$-0.658288\pi$
$43$	3.42705	−	5.93583i	0.522620	−	0.905205i	0.999654	−	0.0263198i	$-0.00837881\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	−4.76393			−0.710165
$46$	−4.70820			−0.694187
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$	−2.42705	−	4.20378i	−0.350315	−	0.606763i
$49$	2.00000			0.285714
$50$	2.14590			0.303476
$51$	−6.85410	−	11.8717i	−0.959766	−	1.66236i
$52$	−0.809017	+	1.40126i	−0.112190	+	0.194320i
$53$	−4.66312	−	8.07676i	−0.640529	−	1.10943i	−0.985315	−	0.170747i	$-0.945382\pi$
$53$	−4.66312	−	8.07676i	−0.640529	−	1.10943i	0.344786	−	0.938681i	$-0.387951\pi$
$54$	0.690983	−	1.19682i	0.0940309	−	0.162866i
$55$	0.381966	−	0.661585i	0.0515043	−	0.0892080i
$56$	6.70820			0.896421
$57$		0			0
$58$	0.854102			0.112149
$59$	7.66312	−	13.2729i	0.997653	−	1.72799i	0.439529	−	0.898228i	$-0.355145\pi$
$59$	7.66312	−	13.2729i	0.997653	−	1.72799i	0.558124	−	0.829757i	$-0.311521\pi$
$60$	−2.61803	+	4.53457i	−0.337987	+	0.585410i
$61$	2.88197	+	4.99171i	0.368998	+	0.639123i	0.989409	−	0.145154i	$-0.0463676\pi$
$61$	2.88197	+	4.99171i	0.368998	+	0.639123i	−0.620411	+	0.784277i	$0.713034\pi$
$62$	−0.663119	+	1.14856i	−0.0842162	+	0.145867i
$63$	−5.78115	−	10.0133i	−0.728357	−	1.26155i
$64$	−0.236068			−0.0295085
$65$	1.23607			0.153315
$66$	0.500000	+	0.866025i	0.0615457	+	0.106600i
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−8.47214			−1.02740
$69$	19.9443			2.40101
$70$	−1.14590	−	1.98475i	−0.136961	−	0.237223i
$71$	−0.736068	+	1.27491i	−0.0873552	+	0.151304i	−0.906392	−	0.422437i	$-0.861175\pi$
$71$	−0.736068	+	1.27491i	−0.0873552	+	0.151304i	0.819037	+	0.573740i	$0.194508\pi$
$72$	−4.30902	−	7.46344i	−0.507823	−	0.879574i
$73$	−5.35410	+	9.27358i	−0.626650	+	1.08539i	0.361569	+	0.932345i	$0.382241\pi$
$73$	−5.35410	+	9.27358i	−0.626650	+	1.08539i	−0.988219	+	0.153045i	$0.951092\pi$
$74$	0.663119	−	1.14856i	0.0770860	−	0.133517i
$75$	−9.09017			−1.04964
$76$		0			0
$77$	1.85410			0.211295
$78$	−0.809017	+	1.40126i	−0.0916031	+	0.158661i
$79$	6.70820	−	11.6190i	0.754732	−	1.30723i	−0.190776	−	0.981634i	$-0.561100\pi$
$79$	6.70820	−	11.6190i	0.754732	−	1.30723i	0.945507	−	0.325600i	$-0.105566\pi$
$80$	1.14590	+	1.98475i	0.128115	+	0.221902i
$81$	2.85410	−	4.94345i	0.317122	−	0.549272i
$82$	−0.927051	−	1.60570i	−0.102376	−	0.177320i
$83$	−0.472136			−0.0518237			−0.0259118	−	0.999664i	$-0.508249\pi$
$83$	−0.472136			−0.0518237			−0.0259118	+	0.999664i	$0.508249\pi$
$84$	−12.7082			−1.38658
$85$	3.23607	+	5.60503i	0.351001	+	0.607951i
$86$	−2.11803	−	3.66854i	−0.228393	−	0.395589i
$87$	−3.61803			−0.387894
$88$	1.38197			0.147318
$89$	6.11803	+	10.5967i	0.648510	+	1.12325i	0.983479	+	0.181023i	$0.0579410\pi$
$89$	6.11803	+	10.5967i	0.648510	+	1.12325i	−0.334968	+	0.942229i	$0.608726\pi$
$90$	−1.47214	+	2.54981i	−0.155177	+	0.268774i
$91$	1.50000	+	2.59808i	0.157243	+	0.272352i
$92$	6.16312	−	10.6748i	0.642550	−	1.11293i
$93$	2.80902	−	4.86536i	0.291281	−	0.504514i
$94$	−1.85410			−0.191236
$95$		0			0
$96$	−14.7082			−1.50115
$97$	−3.57295	+	6.18853i	−0.362778	+	0.628350i	−0.988417	−	0.151763i	$-0.951505\pi$
$97$	−3.57295	+	6.18853i	−0.362778	+	0.628350i	0.625639	+	0.780113i	$0.284838\pi$
$98$	0.618034	−	1.07047i	0.0624309	−	0.108133i
$99$	−1.19098	−	2.06284i	−0.119698	−	0.207324i
$100$	−2.80902	+	4.86536i	−0.280902	+	0.486536i
$101$	−6.59017	−	11.4145i	−0.655746	−	1.13579i	−0.981706	−	0.190402i	$-0.939021\pi$
$101$	−6.59017	−	11.4145i	−0.655746	−	1.13579i	0.325960	−	0.945384i	$-0.394313\pi$
$102$	−8.47214			−0.838866
$103$	−1.32624			−0.130678			−0.0653391	−	0.997863i	$-0.520813\pi$
$103$	−1.32624			−0.130678			−0.0653391	+	0.997863i	$0.520813\pi$
$104$	1.11803	+	1.93649i	0.109632	+	0.189889i
$105$	4.85410	+	8.40755i	0.473712	+	0.820493i
$106$	−5.76393			−0.559843
$107$	−10.4164			−1.00699			−0.503496	−	0.863998i	$-0.667953\pi$
$107$	−10.4164			−1.00699			−0.503496	+	0.863998i	$0.667953\pi$
$108$	1.80902	+	3.13331i	0.174073	+	0.301503i
$109$	8.35410	−	14.4697i	0.800178	−	1.38595i	−0.119321	−	0.992856i	$-0.538072\pi$
$109$	8.35410	−	14.4697i	0.800178	−	1.38595i	0.919499	−	0.393093i	$-0.128595\pi$
$110$	−0.236068	−	0.408882i	−0.0225082	−	0.0389853i
$111$	−2.80902	+	4.86536i	−0.266620	+	0.461800i
$112$	−2.78115	+	4.81710i	−0.262794	+	0.455173i
$113$	11.2361			1.05700			0.528500	−	0.848933i	$-0.322755\pi$
$113$	11.2361			1.05700			0.528500	+	0.848933i	$0.322755\pi$
$114$		0			0
$115$	−9.41641			−0.878085
$116$	−1.11803	+	1.93649i	−0.103807	+	0.179799i
$117$	1.92705	−	3.33775i	0.178156	−	0.308575i
$118$	−4.73607	−	8.20311i	−0.435990	−	0.755158i
$119$	−7.85410	+	13.6037i	−0.719984	+	1.24705i
$120$	3.61803	+	6.26662i	0.330280	+	0.572061i
$121$	−10.6180			−0.965276
$122$	3.56231			0.322516
$123$	3.92705	+	6.80185i	0.354090	+	0.613302i
$124$	−1.73607	−	3.00696i	−0.155904	−	0.270033i
$125$	10.4721			0.936656
$126$	−7.14590			−0.636607
$127$	−5.11803	−	8.86469i	−0.454152	−	0.786614i	0.544487	−	0.838769i	$-0.316724\pi$
$127$	−5.11803	−	8.86469i	−0.454152	−	0.786614i	−0.998639	+	0.0521549i	$0.983391\pi$
$128$	−5.69098	+	9.85707i	−0.503017	+	0.871250i
$129$	8.97214	+	15.5402i	0.789953	+	1.36824i
$130$	0.381966	−	0.661585i	0.0335006	−	0.0580248i
$131$	−1.95492	+	3.38601i	−0.170802	+	0.295837i	−0.938700	−	0.344734i	$-0.887969\pi$
$131$	−1.95492	+	3.38601i	−0.170802	+	0.295837i	0.767899	+	0.640571i	$0.221302\pi$
$132$	−2.61803			−0.227871
$133$		0			0
$134$	4.32624			0.373730
$135$	1.38197	−	2.39364i	0.118941	−	0.206011i
$136$	−5.85410	+	10.1396i	−0.501985	+	0.869464i
$137$	0.736068	+	1.27491i	0.0628865	+	0.108923i	0.895755	−	0.444549i	$-0.146636\pi$
$137$	0.736068	+	1.27491i	0.0628865	+	0.108923i	−0.832868	+	0.553472i	$0.813303\pi$
$138$	6.16312	−	10.6748i	0.524640	−	0.908702i
$139$	4.89919	+	8.48564i	0.415544	+	0.719743i	0.995485	−	0.0949153i	$-0.0302580\pi$
$139$	4.89919	+	8.48564i	0.415544	+	0.719743i	−0.579942	+	0.814658i	$0.696925\pi$
$140$	6.00000			0.507093
$141$	7.85410			0.661435
$142$	0.454915	+	0.787936i	0.0381756	+	0.0661221i
$143$	0.309017	+	0.535233i	0.0258413	+	0.0447584i
$144$	7.14590			0.595492
$145$	1.70820			0.141859
$146$	3.30902	+	5.73139i	0.273856	+	0.474333i
$147$	−2.61803	+	4.53457i	−0.215932	+	0.374005i
$148$	1.73607	+	3.00696i	0.142704	+	0.247170i
$149$	6.54508	−	11.3364i	0.536194	−	0.928716i	−0.462910	−	0.886405i	$-0.653195\pi$
$149$	6.54508	−	11.3364i	0.536194	−	0.928716i	0.999105	−	0.0423105i	$-0.0134719\pi$
$150$	−2.80902	+	4.86536i	−0.229355	+	0.397255i
$151$	−9.90983			−0.806451			−0.403225	−	0.915101i	$-0.632111\pi$
$151$	−9.90983			−0.806451			−0.403225	+	0.915101i	$0.632111\pi$
$152$		0			0
$153$	20.1803			1.63148
$154$	0.572949	−	0.992377i	0.0461695	−	0.0799680i
$155$	−1.32624	+	2.29711i	−0.106526	+	0.184508i
$156$	−2.11803	−	3.66854i	−0.169578	−	0.293718i
$157$	5.57295	−	9.65263i	0.444770	−	0.770364i	−0.553266	−	0.833004i	$-0.686619\pi$
$157$	5.57295	−	9.65263i	0.444770	−	0.770364i	0.998036	+	0.0626406i	$0.0199522\pi$
$158$	−4.14590	−	7.18091i	−0.329830	−	0.571282i
$159$	24.4164			1.93635
$160$	6.94427			0.548993
$161$	−11.4271	−	19.7922i	−0.900578	−	1.55985i
$162$	−1.76393	−	3.05522i	−0.138588	−	0.240041i
$163$	6.23607			0.488447			0.244223	−	0.969719i	$-0.421467\pi$
$163$	6.23607			0.488447			0.244223	+	0.969719i	$0.421467\pi$
$164$	4.85410			0.379042
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$	−0.145898	+	0.252703i	−0.0113239	+	0.0196135i
$167$	−7.88197	−	13.6520i	−0.609925	−	1.05642i	−0.991252	−	0.131981i	$-0.957866\pi$
$167$	−7.88197	−	13.6520i	−0.609925	−	1.05642i	0.381327	−	0.924440i	$-0.375467\pi$
$168$	−8.78115	+	15.2094i	−0.677481	+	1.17343i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	4.00000			0.306786
$171$		0			0
$172$	11.0902			0.845618
$173$	−4.23607	+	7.33708i	−0.322062	+	0.557828i	−0.980913	−	0.194445i	$-0.937709\pi$
$173$	−4.23607	+	7.33708i	−0.322062	+	0.557828i	0.658851	+	0.752273i	$0.271043\pi$
$174$	−1.11803	+	1.93649i	−0.0847579	+	0.146805i
$175$	5.20820	+	9.02087i	0.393703	+	0.681914i
$176$	−0.572949	+	0.992377i	−0.0431877	+	0.0748032i
$177$	20.0623	+	34.7489i	1.50798	+	2.61189i
$178$	7.56231			0.566819
$179$	7.76393			0.580304			0.290152	−	0.956981i	$-0.406294\pi$
$179$	7.76393			0.580304			0.290152	+	0.956981i	$0.406294\pi$
$180$	−3.85410	−	6.67550i	−0.287268	−	0.497562i
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	0.552143	−	0.833749i	$-0.313810\pi$
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	−0.998120	+	0.0612954i	$0.980477\pi$
$182$	1.85410			0.137435
$183$	−15.0902			−1.11550
$184$	−8.51722	−	14.7523i	−0.627898	−	1.08755i
$185$	1.32624	−	2.29711i	0.0975070	−	0.168887i
$186$	−1.73607	−	3.00696i	−0.127295	−	0.220481i
$187$	−1.61803	+	2.80252i	−0.118322	+	0.204940i
$188$	2.42705	−	4.20378i	0.177011	−	0.306592i
$189$	6.70820			0.487950
$190$		0			0
$191$	9.76393			0.706493			0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393			0.706493			0.353247	+	0.935530i	$0.385078\pi$
$192$	0.309017	−	0.535233i	0.0223014	−	0.0386271i
$193$	−11.4721	+	19.8703i	−0.825782	+	1.43030i	0.0755374	+	0.997143i	$0.475933\pi$
$193$	−11.4721	+	19.8703i	−0.825782	+	1.43030i	−0.901320	+	0.433154i	$0.857401\pi$
$194$	2.20820	+	3.82472i	0.158540	+	0.274599i
$195$	−1.61803	+	2.80252i	−0.115870	+	0.200692i
$196$	1.61803	+	2.80252i	0.115574	+	0.200180i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$	−1.47214			−0.104620
$199$	−6.70820	−	11.6190i	−0.475532	−	0.823646i	0.524075	−	0.851672i	$-0.324411\pi$
$199$	−6.70820	−	11.6190i	−0.475532	−	0.823646i	−0.999607	+	0.0280265i	$0.991078\pi$
$200$	3.88197	+	6.72376i	0.274496	+	0.475442i
$201$	−18.3262			−1.29263
$202$	−8.14590			−0.573143
$203$	2.07295	+	3.59045i	0.145492	+	0.252000i
$204$	11.0902	−	19.2087i	0.776467	−	1.34488i
$205$	−1.85410	−	3.21140i	−0.129496	−	0.224294i
$206$	−0.409830	+	0.709846i	−0.0285542	+	0.0494573i
$207$	−14.6803	+	25.4271i	−1.02035	+	1.76731i
$208$	−1.85410			−0.128559
$209$		0			0
$210$	6.00000			0.414039
$211$	−1.42705	+	2.47172i	−0.0982422	+	0.170161i	−0.910957	−	0.412501i	$-0.864655\pi$
$211$	−1.42705	+	2.47172i	−0.0982422	+	0.170161i	0.812715	+	0.582662i	$0.197989\pi$
$212$	7.54508	−	13.0685i	0.518199	−	0.897546i
$213$	−1.92705	−	3.33775i	−0.132039	−	0.228699i
$214$	−3.21885	+	5.57521i	−0.220036	+	0.381113i
$215$	−4.23607	−	7.33708i	−0.288897	−	0.500385i
$216$	5.00000			0.340207
$217$	−6.43769			−0.437019
$218$	−5.16312	−	8.94278i	−0.349691	−	0.605682i
$219$	−14.0172	−	24.2785i	−0.947196	−	1.64059i
$220$	1.23607			0.0833357
$221$	−5.23607			−0.352216
$222$	1.73607	+	3.00696i	0.116517	+	0.201814i
$223$	−9.82624	+	17.0195i	−0.658014	+	1.13971i	0.323116	+	0.946359i	$0.395270\pi$
$223$	−9.82624	+	17.0195i	−0.658014	+	1.13971i	−0.981129	+	0.193353i	$0.938064\pi$
$224$	8.42705	+	14.5961i	0.563056	+	0.975242i
$225$	6.69098	−	11.5891i	0.446066	−	0.772608i
$226$	3.47214	−	6.01392i	0.230963	−	0.400040i
$227$	−10.4164			−0.691361			−0.345681	−	0.938352i	$-0.612352\pi$
$227$	−10.4164			−0.691361			−0.345681	+	0.938352i	$0.612352\pi$
$228$		0			0
$229$	−11.3820			−0.752141			−0.376071	−	0.926591i	$-0.622725\pi$
$229$	−11.3820			−0.752141			−0.376071	+	0.926591i	$0.622725\pi$
$230$	−2.90983	+	5.03997i	−0.191869	+	0.332326i
$231$	−2.42705	+	4.20378i	−0.159688	+	0.276588i
$232$	1.54508	+	2.67617i	0.101440	+	0.175699i
$233$	−6.73607	+	11.6672i	−0.441294	+	0.764344i	−0.997786	−	0.0665089i	$-0.978814\pi$
$233$	−6.73607	+	11.6672i	−0.441294	+	0.764344i	0.556491	+	0.830853i	$0.312147\pi$
$234$	−1.19098	−	2.06284i	−0.0778570	−	0.134852i
$235$	−3.70820			−0.241897
$236$	24.7984			1.61424
$237$	17.5623	+	30.4188i	1.14079	+	1.97591i
$238$	4.85410	+	8.40755i	0.314645	+	0.544981i
$239$	15.3262			0.991372			0.495686	−	0.868502i	$-0.334917\pi$
$239$	15.3262			0.991372			0.495686	+	0.868502i	$0.334917\pi$
$240$	−6.00000			−0.387298
$241$	9.59017	+	16.6107i	0.617757	+	1.06999i	0.989894	+	0.141809i	$0.0452919\pi$
$241$	9.59017	+	16.6107i	0.617757	+	1.06999i	−0.372137	+	0.928178i	$0.621375\pi$
$242$	−3.28115	+	5.68312i	−0.210921	+	0.365325i
$243$	10.8262	+	18.7516i	0.694503	+	1.20292i
$244$	−4.66312	+	8.07676i	−0.298526	+	0.517062i
$245$	1.23607	−	2.14093i	0.0789695	−	0.136779i
$246$	4.85410			0.309486
$247$		0			0
$248$	−4.79837			−0.304697
$249$	0.618034	−	1.07047i	0.0391663	−	0.0678380i
$250$	3.23607	−	5.60503i	0.204667	−	0.354493i
$251$	−9.68034	−	16.7668i	−0.611018	−	1.05831i	−0.991069	−	0.133348i	$-0.957427\pi$
$251$	−9.68034	−	16.7668i	−0.611018	−	1.05831i	0.380052	−	0.924965i	$-0.375906\pi$
$252$	9.35410	−	16.2018i	0.589253	−	1.02062i
$253$	−2.35410	−	4.07742i	−0.148001	−	0.256345i
$254$	−6.32624			−0.396943
$255$	−16.9443			−1.06109
$256$	3.28115	+	5.68312i	0.205072	+	0.355195i
$257$	12.1803	+	21.0970i	0.759789	+	1.31599i	0.942958	+	0.332911i	$0.108031\pi$
$257$	12.1803	+	21.0970i	0.759789	+	1.31599i	−0.183169	+	0.983081i	$0.558636\pi$
$258$	11.0902			0.690444
$259$	6.43769			0.400019
$260$	1.00000	+	1.73205i	0.0620174	+	0.107417i
$261$	2.66312	−	4.61266i	0.164843	−	0.285516i
$262$	1.20820	+	2.09267i	0.0746431	+	0.129286i
$263$	−1.47214	+	2.54981i	−0.0907758	+	0.157228i	−0.907838	−	0.419322i	$-0.862268\pi$
$263$	−1.47214	+	2.54981i	−0.0907758	+	0.157228i	0.817062	+	0.576550i	$0.195601\pi$
$264$	−1.80902	+	3.13331i	−0.111337	+	0.192842i
$265$	−11.5279			−0.708151
$266$		0			0
$267$	−32.0344			−1.96048
$268$	−5.66312	+	9.80881i	−0.345930	+	0.599168i
$269$	−7.33688	+	12.7079i	−0.447338	+	0.774811i	−0.998212	−	0.0597769i	$-0.980961\pi$
$269$	−7.33688	+	12.7079i	−0.447338	+	0.774811i	0.550874	+	0.834588i	$0.314294\pi$
$270$	−0.854102	−	1.47935i	−0.0519790	−	0.0900303i
$271$	−3.92705	+	6.80185i	−0.238551	+	0.413183i	−0.960299	−	0.278973i	$-0.910006\pi$
$271$	−3.92705	+	6.80185i	−0.238551	+	0.413183i	0.721747	+	0.692156i	$0.243339\pi$
$272$	−4.85410	−	8.40755i	−0.294323	−	0.509783i
$273$	−7.85410			−0.475352
$274$	0.909830			0.0549648
$275$	1.07295	+	1.85840i	0.0647013	+	0.112066i
$276$	16.1353	+	27.9471i	0.971228	+	1.68222i
$277$	−15.4164			−0.926282			−0.463141	−	0.886285i	$-0.653278\pi$
$277$	−15.4164			−0.926282			−0.463141	+	0.886285i	$0.653278\pi$
$278$	6.05573			0.363198
$279$	4.13525	+	7.16247i	0.247571	+	0.428806i
$280$	4.14590	−	7.18091i	0.247765	−	0.429141i
$281$	−4.25329	−	7.36691i	−0.253730	−	0.439473i	0.710820	−	0.703374i	$-0.248324\pi$
$281$	−4.25329	−	7.36691i	−0.253730	−	0.439473i	−0.964550	+	0.263901i	$0.914991\pi$
$282$	2.42705	−	4.20378i	0.144529	−	0.250331i
$283$	1.51722	−	2.62790i	0.0901894	−	0.156213i	−0.817401	−	0.576069i	$-0.804586\pi$
$283$	1.51722	−	2.62790i	0.0901894	−	0.156213i	0.907591	+	0.419856i	$0.137919\pi$
$284$	−2.38197			−0.141344
$285$		0			0
$286$	0.381966			0.0225861
$287$	4.50000	−	7.79423i	0.265627	−	0.460079i
$288$	10.8262	−	18.7516i	0.637942	−	1.10495i
$289$	−5.20820	−	9.02087i	−0.306365	−	0.530640i
$290$	0.527864	−	0.914287i	0.0309972	−	0.0536888i
$291$	−9.35410	−	16.2018i	−0.548347	−	0.949765i
$292$	−17.3262			−1.01394
$293$	−16.8541			−0.984627			−0.492314	−	0.870418i	$-0.663849\pi$
$293$	−16.8541			−0.984627			−0.492314	+	0.870418i	$0.663849\pi$
$294$	1.61803	+	2.80252i	0.0943657	+	0.163446i
$295$	−9.47214	−	16.4062i	−0.551489	−	0.955207i
$296$	4.79837			0.278900
$297$	1.38197			0.0801898
$298$	−4.04508	−	7.00629i	−0.234325	−	0.405864i
$299$	3.80902	−	6.59741i	0.220281	−	0.381538i
$300$	−7.35410	−	12.7377i	−0.424589	−	0.735410i
$301$	10.2812	−	17.8075i	0.592596	−	1.02641i
$302$	−3.06231	+	5.30407i	−0.176216	+	0.305215i
$303$	34.5066			1.98235
$304$		0			0
$305$	7.12461			0.407954
$306$	6.23607	−	10.8012i	0.356492	−	0.617463i
$307$	0.836881	−	1.44952i	0.0477633	−	0.0827285i	−0.841155	−	0.540794i	$-0.818124\pi$
$307$	0.836881	−	1.44952i	0.0477633	−	0.0827285i	0.888919	+	0.458065i	$0.151457\pi$
$308$	1.50000	+	2.59808i	0.0854704	+	0.148039i
$309$	1.73607	−	3.00696i	0.0987615	−	0.171060i
$310$	0.819660	+	1.41969i	0.0465536	+	0.0806331i
$311$	−18.6525			−1.05768			−0.528842	−	0.848720i	$-0.677374\pi$
$311$	−18.6525			−1.05768			−0.528842	+	0.848720i	$0.677374\pi$
$312$	−5.85410			−0.331423
$313$	−2.16312	−	3.74663i	−0.122267	−	0.211772i	0.798395	−	0.602135i	$-0.205683\pi$
$313$	−2.16312	−	3.74663i	−0.122267	−	0.211772i	−0.920661	+	0.390363i	$0.872350\pi$
$314$	−3.44427	−	5.96565i	−0.194372	−	0.336661i
$315$	−14.2918			−0.805251
$316$	21.7082			1.22118
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	7.54508	−	13.0685i	0.423107	−	0.732843i
$319$	0.427051	+	0.739674i	0.0239103	+	0.0414138i
$320$	−0.145898	+	0.252703i	−0.00815595	+	0.0141265i
$321$	13.6353	−	23.6170i	0.761046	−	1.31817i
$322$	−14.1246			−0.787134
$323$		0			0
$324$	9.23607			0.513115
$325$	−1.73607	+	3.00696i	−0.0962997	+	0.166796i
$326$	1.92705	−	3.33775i	0.106729	−	0.184861i
$327$	21.8713	+	37.8822i	1.20949	+	2.09489i
$328$	3.35410	−	5.80948i	0.185199	−	0.320775i
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$	1.23607			0.0680433
$331$	−6.94427			−0.381692			−0.190846	−	0.981620i	$-0.561123\pi$
$331$	−6.94427			−0.381692			−0.190846	+	0.981620i	$0.561123\pi$
$332$	−0.381966	−	0.661585i	−0.0209631	−	0.0363092i
$333$	−4.13525	−	7.16247i	−0.226611	−	0.392501i
$334$	−9.74265			−0.533094
$335$	8.65248			0.472735
$336$	−7.28115	−	12.6113i	−0.397219	−	0.688004i
$337$	−11.5623	+	20.0265i	−0.629839	+	1.09091i	0.357745	+	0.933819i	$0.383546\pi$
$337$	−11.5623	+	20.0265i	−0.629839	+	1.09091i	−0.987584	+	0.157094i	$0.949788\pi$
$338$	−3.70820	−	6.42280i	−0.201700	−	0.349354i
$339$	−14.7082	+	25.4754i	−0.798840	+	1.38363i
$340$	−5.23607	+	9.06914i	−0.283966	+	0.491843i
$341$	−1.32624			−0.0718198
$342$		0			0
$343$	−15.0000			−0.809924
$344$	7.66312	−	13.2729i	0.413168	−	0.715627i
$345$	12.3262	−	21.3497i	0.663622	−	1.14943i
$346$	2.61803	+	4.53457i	0.140746	+	0.243780i
$347$	−0.708204	+	1.22665i	−0.0380184	+	0.0658498i	−0.884408	−	0.466714i	$-0.845438\pi$
$347$	−0.708204	+	1.22665i	−0.0380184	+	0.0658498i	0.846390	+	0.532563i	$0.178771\pi$
$348$	−2.92705	−	5.06980i	−0.156906	−	0.271770i
$349$	25.9787			1.39061			0.695304	−	0.718715i	$-0.255270\pi$
$349$	25.9787			1.39061			0.695304	+	0.718715i	$0.255270\pi$
$350$	6.43769			0.344109
$351$	1.11803	+	1.93649i	0.0596762	+	0.103362i
$352$	1.73607	+	3.00696i	0.0925327	+	0.160271i
$353$	−31.4508			−1.67396			−0.836980	−	0.547234i	$-0.815681\pi$
$353$	−31.4508			−1.67396			−0.836980	+	0.547234i	$0.815681\pi$
$354$	24.7984			1.31802
$355$	0.909830	+	1.57587i	0.0482888	+	0.0836386i
$356$	−9.89919	+	17.1459i	−0.524656	+	0.908731i
$357$	−20.5623	−	35.6150i	−1.08827	−	1.88494i
$358$	2.39919	−	4.15551i	0.126801	−	0.219626i
$359$	11.0172	−	19.0824i	0.581467	−	1.00713i	−0.413839	−	0.910350i	$-0.635812\pi$
$359$	11.0172	−	19.0824i	0.581467	−	1.00713i	0.995306	−	0.0967798i	$-0.0308543\pi$
$360$	−10.6525			−0.561435
$361$		0			0
$362$	−7.41641			−0.389798
$363$	13.8992	−	24.0741i	0.729518	−	1.26356i
$364$	−2.42705	+	4.20378i	−0.127212	+	0.220338i
$365$	6.61803	+	11.4628i	0.346404	+	0.599989i
$366$	−4.66312	+	8.07676i	−0.243745	+	0.422179i
$367$	−0.972136	−	1.68379i	−0.0507451	−	0.0878931i	0.839537	−	0.543302i	$-0.182826\pi$
$367$	−0.972136	−	1.68379i	−0.0507451	−	0.0878931i	−0.890282	+	0.455409i	$0.849493\pi$
$368$	14.1246			0.736296
$369$	−11.5623			−0.601910
$370$	−0.819660	−	1.41969i	−0.0426121	−	0.0738063i
$371$	−13.9894	−	24.2303i	−0.726291	−	1.25797i
$372$	9.09017			0.471303
$373$	3.47214			0.179780			0.0898902	−	0.995952i	$-0.471348\pi$
$373$	3.47214			0.179780			0.0898902	+	0.995952i	$0.471348\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$	−13.7082	+	23.7433i	−0.707889	+	1.22610i
$376$	−3.35410	−	5.80948i	−0.172975	−	0.299601i
$377$	−0.690983	+	1.19682i	−0.0355874	+	0.0616392i
$378$	2.07295	−	3.59045i	0.106621	−	0.184673i
$379$	25.1246			1.29056			0.645282	−	0.763944i	$-0.276740\pi$
$379$	25.1246			1.29056			0.645282	+	0.763944i	$0.276740\pi$
$380$		0			0
$381$	26.7984			1.37292
$382$	3.01722	−	5.22598i	0.154374	−	0.267384i
$383$	−1.30902	+	2.26728i	−0.0668876	+	0.115853i	−0.897530	−	0.440954i	$-0.854640\pi$
$383$	−1.30902	+	2.26728i	−0.0668876	+	0.115853i	0.830642	+	0.556807i	$0.187974\pi$
$384$	−14.8992	−	25.8061i	−0.760321	−	1.31691i
$385$	1.14590	−	1.98475i	0.0584004	−	0.101152i
$386$	7.09017	+	12.2805i	0.360880	+	0.625063i
$387$	−26.4164			−1.34282
$388$	−11.5623			−0.586987
$389$	12.1353	+	21.0189i	0.615282	+	1.06570i	0.990335	+	0.138696i	$0.0442911\pi$
$389$	12.1353	+	21.0189i	0.615282	+	1.06570i	−0.375053	+	0.927003i	$0.622376\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$	39.8885			2.01725
$392$	4.47214			0.225877
$393$	−5.11803	−	8.86469i	−0.258171	−	0.447165i
$394$	0.927051	−	1.60570i	0.0467042	−	0.0808940i
$395$	−8.29180	−	14.3618i	−0.417206	−	0.722621i
$396$	1.92705	−	3.33775i	0.0968380	−	0.167728i
$397$	1.26393	−	2.18919i	0.0634349	−	0.109873i	−0.832564	−	0.553929i	$-0.813128\pi$
$397$	1.26393	−	2.18919i	0.0634349	−	0.109873i	0.895999	+	0.444057i	$0.146461\pi$
$398$	−8.29180			−0.415630
$399$		0			0
$400$	−6.43769			−0.321885
$401$	0.0557281	−	0.0965239i	0.00278293	−	0.00482017i	−0.864631	−	0.502408i	$-0.832447\pi$
$401$	0.0557281	−	0.0965239i	0.00278293	−	0.00482017i	0.867414	+	0.497588i	$0.165781\pi$
$402$	−5.66312	+	9.80881i	−0.282451	+	0.489219i
$403$	−1.07295	−	1.85840i	−0.0534474	−	0.0925736i
$404$	10.6631	−	18.4691i	0.530510	−	0.918870i
$405$	−3.52786	−	6.11044i	−0.175301	−	0.303630i
$406$	2.56231			0.127165
$407$	1.32624			0.0657392
$408$	−15.3262	−	26.5458i	−0.758762	−	1.31421i
$409$	10.8541	+	18.7999i	0.536701	+	0.929593i	0.999079	+	0.0429102i	$0.0136629\pi$
$409$	10.8541	+	18.7999i	0.536701	+	0.929593i	−0.462378	+	0.886683i	$0.653004\pi$
$410$	−2.29180			−0.113184
$411$	−3.85410			−0.190109
$412$	−1.07295	−	1.85840i	−0.0528604	−	0.0915569i
$413$	22.9894	−	39.8187i	1.13123	−	1.95935i
$414$	9.07295	+	15.7148i	0.445911	+	0.772341i
$415$	−0.291796	+	0.505406i	−0.0143237	+	0.0248094i
$416$	−2.80902	+	4.86536i	−0.137723	+	0.238544i
$417$	−25.6525			−1.25621
$418$		0			0
$419$	8.94427			0.436956			0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427			0.436956			0.218478	+	0.975842i	$0.429891\pi$
$420$	−7.85410	+	13.6037i	−0.383241	+	0.663793i
$421$	9.26393	−	16.0456i	0.451496	−	0.782015i	−0.546983	−	0.837144i	$-0.684224\pi$
$421$	9.26393	−	16.0456i	0.451496	−	0.782015i	0.998479	+	0.0551291i	$0.0175570\pi$
$422$	0.881966	+	1.52761i	0.0429334	+	0.0743629i
$423$	−5.78115	+	10.0133i	−0.281089	+	0.486861i
$424$	−10.4271	−	18.0602i	−0.506382	−	0.877080i
$425$	−18.1803			−0.881876
$426$	−2.38197			−0.115407
$427$	8.64590	+	14.9751i	0.418404	+	0.724698i
$428$	−8.42705	−	14.5961i	−0.407337	−	0.705528i
$429$	−1.61803			−0.0781194
$430$	−5.23607			−0.252506
$431$	1.82624	+	3.16314i	0.0879668	+	0.152363i	0.906652	−	0.421880i	$-0.138630\pi$
$431$	1.82624	+	3.16314i	0.0879668	+	0.152363i	−0.818685	+	0.574243i	$0.805296\pi$
$432$	−2.07295	+	3.59045i	−0.0997348	+	0.172746i
$433$	11.7812	+	20.4056i	0.566166	+	0.980628i	0.996940	+	0.0781686i	$0.0249073\pi$
$433$	11.7812	+	20.4056i	0.566166	+	0.980628i	−0.430774	+	0.902460i	$0.641759\pi$
$434$	−1.98936	+	3.44567i	−0.0954922	+	0.165397i
$435$	−2.23607	+	3.87298i	−0.107211	+	0.185695i
$436$	27.0344			1.29471
$437$		0			0
$438$	−17.3262			−0.827880
$439$	−7.29837	+	12.6412i	−0.348332	+	0.603329i	−0.985953	−	0.167021i	$-0.946585\pi$
$439$	−7.29837	+	12.6412i	−0.348332	+	0.603329i	0.637621	+	0.770350i	$0.279919\pi$
$440$	0.854102	−	1.47935i	0.0407177	−	0.0705251i
$441$	−3.85410	−	6.67550i	−0.183529	−	0.317881i
$442$	−1.61803	+	2.80252i	−0.0769620	+	0.133302i
$443$	17.2082	+	29.8055i	0.817586	+	1.41610i	0.907456	+	0.420148i	$0.138022\pi$
$443$	17.2082	+	29.8055i	0.817586	+	1.41610i	−0.0898693	+	0.995954i	$0.528645\pi$
$444$	−9.09017			−0.431400
$445$	15.1246			0.716975
$446$	6.07295	+	10.5187i	0.287562	+	0.498073i
$447$	17.1353	+	29.6791i	0.810470	+	1.40377i
$448$	−0.708204			−0.0334595
$449$	−32.8885			−1.55211			−0.776053	−	0.630667i	$-0.782781\pi$
$449$	−32.8885			−1.55211			−0.776053	+	0.630667i	$0.782781\pi$
$450$	−4.13525	−	7.16247i	−0.194938	−	0.337642i
$451$	0.927051	−	1.60570i	0.0436531	−	0.0756094i
$452$	9.09017	+	15.7446i	0.427566	+	0.740565i
$453$	12.9721	−	22.4684i	0.609484	−	1.05566i
$454$	−3.21885	+	5.57521i	−0.151068	+	0.261657i
$455$	3.70820			0.173843
$456$		0			0
$457$	6.29180			0.294318			0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180			0.294318			0.147159	+	0.989113i	$0.452987\pi$
$458$	−3.51722	+	6.09201i	−0.164349	+	0.284661i
$459$	−5.85410	+	10.1396i	−0.273246	+	0.473276i
$460$	−7.61803	−	13.1948i	−0.355193	−	0.615212i
$461$	−1.52786	+	2.64634i	−0.0711597	+	0.123252i	−0.899410	−	0.437106i	$-0.856003\pi$
$461$	−1.52786	+	2.64634i	−0.0711597	+	0.123252i	0.828250	+	0.560359i	$0.189337\pi$
$462$	1.50000	+	2.59808i	0.0697863	+	0.120873i
$463$	−5.27051			−0.244941			−0.122471	−	0.992472i	$-0.539082\pi$
$463$	−5.27051			−0.244941			−0.122471	+	0.992472i	$0.539082\pi$
$464$	−2.56231			−0.118952
$465$	−3.47214	−	6.01392i	−0.161016	−	0.278889i
$466$	4.16312	+	7.21073i	0.192853	+	0.334031i
$467$	1.94427			0.0899702			0.0449851	−	0.998988i	$-0.485676\pi$
$467$	1.94427			0.0899702			0.0449851	+	0.998988i	$0.485676\pi$
$468$	6.23607			0.288262
$469$	10.5000	+	18.1865i	0.484845	+	0.839776i
$470$	−1.14590	+	1.98475i	−0.0528563	+	0.0915499i
$471$	14.5902	+	25.2709i	0.672280	+	1.16442i
$472$	17.1353	−	29.6791i	0.788714	−	1.36609i
$473$	2.11803	−	3.66854i	0.0973873	−	0.168680i
$474$	21.7082			0.997091
$475$		0			0
$476$	−25.4164			−1.16496
$477$	−17.9721	+	31.1287i	−0.822888	+	1.42528i
$478$	4.73607	−	8.20311i	0.216623	−	0.375202i
$479$	−5.95492	−	10.3142i	−0.272087	−	0.471269i	0.697309	−	0.716771i	$-0.254381\pi$
$479$	−5.95492	−	10.3142i	−0.272087	−	0.471269i	−0.969396	+	0.245502i	$0.921047\pi$
$480$	−9.09017	+	15.7446i	−0.414908	+	0.718641i
$481$	1.07295	+	1.85840i	0.0489223	+	0.0847358i
$482$	11.8541			0.539940
$483$	59.8328			2.72249
$484$	−8.59017	−	14.8786i	−0.390462	−	0.676300i
$485$	4.41641	+	7.64944i	0.200539	+	0.347343i
$486$	13.3820			0.607018
$487$	−18.1803			−0.823830			−0.411915	−	0.911222i	$-0.635140\pi$
$487$	−18.1803			−0.823830			−0.411915	+	0.911222i	$0.635140\pi$
$488$	6.44427	+	11.1618i	0.291718	+	0.505271i
$489$	−8.16312	+	14.1389i	−0.369149	+	0.639385i
$490$	−0.763932	−	1.32317i	−0.0345109	−	0.0597747i
$491$	−15.1074	+	26.1668i	−0.681787	+	1.18089i	0.292648	+	0.956220i	$0.405464\pi$
$491$	−15.1074	+	26.1668i	−0.681787	+	1.18089i	−0.974435	+	0.224669i	$0.927870\pi$
$492$	−6.35410	+	11.0056i	−0.286465	+	0.496172i
$493$	−7.23607			−0.325896
$494$		0			0
$495$	−2.94427			−0.132335
$496$	1.98936	−	3.44567i	0.0893248	−	0.154715i
$497$	−2.20820	+	3.82472i	−0.0990515	+	0.171562i
$498$	−0.381966	−	0.661585i	−0.0171163	−	0.0296463i
$499$	7.56231	−	13.0983i	0.338535	−	0.586360i	−0.645622	−	0.763657i	$-0.723402\pi$
$499$	7.56231	−	13.0983i	0.338535	−	0.586360i	0.984157	+	0.177297i	$0.0567352\pi$
$500$	8.47214	+	14.6742i	0.378885	+	0.656249i
$501$	41.2705			1.84383
$502$	−11.9656			−0.534049
$503$	8.91641	+	15.4437i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365227\pi$
$503$	8.91641	+	15.4437i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$504$	−12.9271	−	22.3903i	−0.575817	−	0.997344i
$505$	−16.2918			−0.724975
$506$	−2.90983			−0.129358
$507$	15.7082	+	27.2074i	0.697626	+	1.20832i
$508$	8.28115	−	14.3434i	0.367417	−	0.636384i
$509$	13.5172	+	23.4125i	0.599140	+	1.03774i	0.992948	+	0.118549i	$0.0378242\pi$
$509$	13.5172	+	23.4125i	0.599140	+	1.03774i	−0.393808	+	0.919193i	$0.628843\pi$
$510$	−5.23607	+	9.06914i	−0.231857	+	0.401588i
$511$	−16.0623	+	27.8207i	−0.710555	+	1.23072i
$512$	−18.7082			−0.826794
$513$		0			0
$514$	15.0557			0.664080
$515$	−0.819660	+	1.41969i	−0.0361185	+	0.0625591i
$516$	−14.5172	+	25.1446i	−0.639085	+	1.10693i
$517$	−0.927051	−	1.60570i	−0.0407717	−	0.0706186i
$518$	1.98936	−	3.44567i	0.0874073	−	0.151394i
$519$	−11.0902	−	19.2087i	−0.486804	−	0.843170i
$520$	2.76393			0.121206
$521$	−27.2705			−1.19474			−0.597371	−	0.801965i	$-0.703788\pi$
$521$	−27.2705			−1.19474			−0.597371	+	0.801965i	$0.703788\pi$
$522$	−1.64590	−	2.85078i	−0.0720390	−	0.124775i
$523$	−11.2082	−	19.4132i	−0.490101	−	0.848879i	0.509835	−	0.860272i	$-0.329707\pi$
$523$	−11.2082	−	19.4132i	−0.490101	−	0.848879i	−0.999935	+	0.0113934i	$0.996373\pi$
$524$	−6.32624			−0.276363
$525$	−27.2705			−1.19018
$526$	0.909830	+	1.57587i	0.0396705	+	0.0687113i
$527$	5.61803	−	9.73072i	0.244725	−	0.423877i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−17.5172	+	30.3407i	−0.761618	+	1.31916i
$530$	−3.56231	+	6.17009i	−0.154737	+	0.268012i
$531$	−59.0689			−2.56337
$532$		0			0
$533$	3.00000			0.129944
$534$	−9.89919	+	17.1459i	−0.428380	+	0.741975i
$535$	−6.43769	+	11.1504i	−0.278326	+	0.482074i
$536$	7.82624	+	13.5554i	0.338042	+	0.585506i
$537$	−10.1631	+	17.6030i	−0.438571	+	0.759627i
$538$	4.53444	+	7.85388i	0.195494	+	0.338605i
$539$	1.23607			0.0532412
$540$	4.47214			0.192450
$541$	−11.9164	−	20.6398i	−0.512326	−	0.887375i	−0.999898	−	0.0142923i	$-0.995450\pi$
$541$	−11.9164	−	20.6398i	−0.512326	−	0.887375i	0.487571	−	0.873083i	$-0.337883\pi$
$542$	2.42705	+	4.20378i	0.104251	+	0.180568i
$543$	31.4164			1.34821
$544$	−29.4164			−1.26122
$545$	−10.3262	−	17.8856i	−0.442327	−	0.766134i
$546$	−2.42705	+	4.20378i	−0.103868	+	0.179905i
$547$	−18.9615	−	32.8423i	−0.810735	−	1.40423i	−0.912350	−	0.409410i	$-0.865734\pi$
$547$	−18.9615	−	32.8423i	−0.810735	−	1.40423i	0.101615	−	0.994824i	$-0.467599\pi$
$548$	−1.19098	+	2.06284i	−0.0508763	+	0.0881203i
$549$	11.1074	−	19.2386i	0.474052	−	0.821082i
$550$	1.32624			0.0565510
$551$		0			0
$552$	44.5967			1.89816
$553$	20.1246	−	34.8569i	0.855786	−	1.48226i
$554$	−4.76393	+	8.25137i	−0.202400	+	0.350567i
$555$	3.47214	+	6.01392i	0.147384	+	0.255277i
$556$	−7.92705	+	13.7301i	−0.336182	+	0.582284i
$557$	11.5902	+	20.0748i	0.491091	+	0.850595i	0.999947	−	0.0102566i	$-0.00326482\pi$
$557$	11.5902	+	20.0748i	0.491091	+	0.850595i	−0.508856	+	0.860852i	$0.669931\pi$
$558$	5.11146			0.216385
$559$	6.85410			0.289898
$560$	3.43769	+	5.95426i	0.145269	+	0.251613i
$561$	−4.23607	−	7.33708i	−0.178847	−	0.309772i
$562$	−5.25735			−0.221768
$563$	20.8328			0.877999			0.438999	−	0.898487i	$-0.355333\pi$
$563$	20.8328			0.877999			0.438999	+	0.898487i	$0.355333\pi$
$564$	6.35410	+	11.0056i	0.267556	+	0.463421i
$565$	6.94427	−	12.0278i	0.292148	−	0.506015i
$566$	−0.937694	−	1.62413i	−0.0394142	−	0.0682674i
$567$	8.56231	−	14.8303i	0.359583	−	0.622816i
$568$	−1.64590	+	2.85078i	−0.0690603	+	0.119616i
$569$	28.0902			1.17760			0.588801	−	0.808278i	$-0.299600\pi$
$569$	28.0902			1.17760			0.588801	+	0.808278i	$0.299600\pi$
$570$		0			0
$571$	22.3262			0.934324			0.467162	−	0.884172i	$-0.345276\pi$
$571$	22.3262			0.934324			0.467162	+	0.884172i	$0.345276\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	−12.7812	+	22.1376i	−0.533940	+	0.924812i
$574$	−2.78115	−	4.81710i	−0.116083	−	0.201062i
$575$	13.2254	−	22.9071i	0.551538	−	0.955292i
$576$	0.454915	+	0.787936i	0.0189548	+	0.0328307i
$577$	28.1246			1.17084			0.585421	−	0.810729i	$-0.300929\pi$
$577$	28.1246			1.17084			0.585421	+	0.810729i	$0.300929\pi$
$578$	−6.43769			−0.267773
$579$	−30.0344	−	52.0212i	−1.24819	−	2.16193i
$580$	1.38197	+	2.39364i	0.0573830	+	0.0993903i
$581$	−1.41641			−0.0587625
$582$	−11.5623			−0.479273
$583$	−2.88197	−	4.99171i	−0.119359	−	0.206736i
$584$	−11.9721	+	20.7363i	−0.495411	+	0.858076i
$585$	−2.38197	−	4.12569i	−0.0984822	−	0.170576i
$586$	−5.20820	+	9.02087i	−0.215149	+	0.372649i
$587$	−19.0623	+	33.0169i	−0.786786	+	1.36275i	0.141141	+	0.989990i	$0.454923\pi$
$587$	−19.0623	+	33.0169i	−0.786786	+	1.36275i	−0.927927	+	0.372763i	$0.878410\pi$
$588$	−8.47214			−0.349385
$589$		0			0
$590$	−11.7082			−0.482019
$591$	−3.92705	+	6.80185i	−0.161537	+	0.279791i
$592$	−1.98936	+	3.44567i	−0.0817621	+	0.141616i
$593$	6.35410	+	11.0056i	0.260932	+	0.451947i	0.966490	−	0.256705i	$-0.0826369\pi$
$593$	6.35410	+	11.0056i	0.260932	+	0.451947i	−0.705558	+	0.708652i	$0.749304\pi$
$594$	0.427051	−	0.739674i	0.0175221	−	0.0303492i
$595$	9.70820	+	16.8151i	0.397998	+	0.689352i
$596$	21.1803			0.867581
$597$	35.1246			1.43755
$598$	−2.35410	−	4.07742i	−0.0962664	−	0.166738i
$599$	−0.791796	−	1.37143i	−0.0323519	−	0.0560352i	0.849396	−	0.527756i	$-0.176966\pi$
$599$	−0.791796	−	1.37143i	−0.0323519	−	0.0560352i	−0.881748	+	0.471721i	$0.843633\pi$
$600$	−20.3262			−0.829815
$601$	33.7082			1.37499			0.687493	−	0.726191i	$-0.258711\pi$
$601$	33.7082			1.37499			0.687493	+	0.726191i	$0.258711\pi$
$602$	−6.35410	−	11.0056i	−0.258974	−	0.448556i
$603$	13.4894	−	23.3643i	0.549329	−	0.951466i
$604$	−8.01722	−	13.8862i	−0.326216	−	0.565023i
$605$	−6.56231	+	11.3662i	−0.266796	+	0.462104i
$606$	10.6631	−	18.4691i	0.433160	−	0.750254i
$607$	27.2705			1.10688			0.553438	−	0.832890i	$-0.313316\pi$
$607$	27.2705			1.10688			0.553438	+	0.832890i	$0.313316\pi$
$608$		0			0
$609$	−10.8541			−0.439830
$610$	2.20163	−	3.81333i	0.0891412	−	0.154397i
$611$	1.50000	−	2.59808i	0.0606835	−	0.105107i
$612$	16.3262	+	28.2779i	0.659949	+	1.14307i
$613$	1.02786	−	1.78031i	0.0415150	−	0.0719062i	−0.844521	−	0.535522i	$-0.820115\pi$
$613$	1.02786	−	1.78031i	0.0415150	−	0.0719062i	0.886036	+	0.463616i	$0.153448\pi$
$614$	−0.517221	−	0.895853i	−0.0208733	−	0.0361537i
$615$	9.70820			0.391473
$616$	4.14590			0.167043
$617$	−11.6631	−	20.2011i	−0.469539	−	0.813266i	0.529854	−	0.848089i	$-0.322247\pi$
$617$	−11.6631	−	20.2011i	−0.469539	−	0.813266i	−0.999394	+	0.0348226i	$0.988913\pi$
$618$	−1.07295	−	1.85840i	−0.0431603	−	0.0747559i
$619$	−30.1246			−1.21081			−0.605405	−	0.795917i	$-0.706989\pi$
$619$	−30.1246			−1.21081			−0.605405	+	0.795917i	$0.706989\pi$
$620$	−4.29180			−0.172363
$621$	−8.51722	−	14.7523i	−0.341784	−	0.591988i
$622$	−5.76393	+	9.98342i	−0.231113	+	0.400299i
$623$	18.3541	+	31.7902i	0.735342	+	1.27365i
$624$	2.42705	−	4.20378i	0.0971598	−	0.168286i
$625$	−2.20820	+	3.82472i	−0.0883282	+	0.152989i
$626$	−2.67376			−0.106865
$627$		0			0
$628$	18.0344			0.719653
$629$	−5.61803	+	9.73072i	−0.224006	+	0.387989i
$630$	−4.41641	+	7.64944i	−0.175954	+	0.304761i
$631$	7.68034	+	13.3027i	0.305750	+	0.529574i	0.977428	−	0.211269i	$-0.0677597\pi$
$631$	7.68034	+	13.3027i	0.305750	+	0.529574i	−0.671678	+	0.740843i	$0.734426\pi$
$632$	15.0000	−	25.9808i	0.596668	−	1.03346i
$633$	−3.73607	−	6.47106i	−0.148495	−	0.257202i
$634$	−11.1246			−0.441815
$635$	−12.6525			−0.502098
$636$	19.7533	+	34.2137i	0.783269	+	1.35666i
$637$	1.00000	+	1.73205i	0.0396214	+	0.0686264i
$638$	0.527864			0.0208983
$639$	5.67376			0.224451
$640$	7.03444	+	12.1840i	0.278061	+	0.481615i
$641$	0.746711	−	1.29334i	0.0294933	−	0.0510839i	−0.850902	−	0.525324i	$-0.823944\pi$
$641$	0.746711	−	1.29334i	0.0294933	−	0.0510839i	0.880395	+	0.474241i	$0.157277\pi$
$642$	−8.42705	−	14.5961i	−0.332589	−	0.576061i
$643$	18.8541	−	32.6563i	0.743533	−	1.28784i	−0.207344	−	0.978268i	$-0.566482\pi$
$643$	18.8541	−	32.6563i	0.743533	−	1.28784i	0.950877	−	0.309569i	$-0.100185\pi$
$644$	18.4894	−	32.0245i	0.728583	−	1.26194i
$645$	22.1803			0.873350
$646$		0			0
$647$	−1.47214			−0.0578756			−0.0289378	−	0.999581i	$-0.509212\pi$
$647$	−1.47214			−0.0578756			−0.0289378	+	0.999581i	$0.509212\pi$
$648$	6.38197	−	11.0539i	0.250707	−	0.434238i
$649$	4.73607	−	8.20311i	0.185907	−	0.322000i
$650$	1.07295	+	1.85840i	0.0420845	+	0.0728925i
$651$	8.42705	−	14.5961i	0.330282	−	0.572065i
$652$	5.04508	+	8.73834i	0.197581	+	0.342220i
$653$	−3.43769			−0.134527			−0.0672637	−	0.997735i	$-0.521427\pi$
$653$	−3.43769			−0.134527			−0.0672637	+	0.997735i	$0.521427\pi$
$654$	27.0344			1.05713
$655$	2.41641	+	4.18534i	0.0944169	+	0.163535i
$656$	2.78115	+	4.81710i	0.108586	+	0.188076i
$657$	41.2705			1.61012
$658$	−5.56231			−0.216841
$659$	−22.8885	−	39.6441i	−0.891611	−	1.54432i	−0.837944	−	0.545757i	$-0.816242\pi$
$659$	−22.8885	−	39.6441i	−0.891611	−	1.54432i	−0.0536675	−	0.998559i	$-0.517091\pi$
$660$	−1.61803	+	2.80252i	−0.0629819	+	0.109088i
$661$	10.7082	+	18.5472i	0.416501	+	0.721401i	0.995585	−	0.0938673i	$-0.0299230\pi$
$661$	10.7082	+	18.5472i	0.416501	+	0.721401i	−0.579084	+	0.815268i	$0.696590\pi$
$662$	−2.14590	+	3.71680i	−0.0834027	+	0.144458i
$663$	6.85410	−	11.8717i	0.266191	−	0.461057i
$664$	−1.05573			−0.0409702
$665$		0			0
$666$	−5.11146			−0.198065
$667$	5.26393	−	9.11740i	0.203820	−	0.353027i
$668$	12.7533	−	22.0893i	0.493440	−	0.854662i
$669$	−25.7254	−	44.5577i	−0.994602	−	1.72270i
$670$	2.67376	−	4.63109i	0.103296	−	0.178915i
$671$	1.78115	+	3.08505i	0.0687606	+	0.119097i
$672$	−44.1246			−1.70214
$673$	−6.12461			−0.236086			−0.118043	−	0.993008i	$-0.537662\pi$
$673$	−6.12461			−0.236086			−0.118043	+	0.993008i	$0.537662\pi$
$674$	7.14590	+	12.3771i	0.275250	+	0.476746i
$675$	3.88197	+	6.72376i	0.149417	+	0.258798i
$676$	19.4164			0.746785
$677$	11.7426			0.451307			0.225653	−	0.974208i	$-0.427548\pi$
$677$	11.7426			0.451307			0.225653	+	0.974208i	$0.427548\pi$
$678$	9.09017	+	15.7446i	0.349106	+	0.604669i
$679$	−10.7188	+	18.5656i	−0.411352	+	0.712482i
$680$	7.23607	+	12.5332i	0.277491	+	0.480628i
$681$	13.6353	−	23.6170i	0.522504	−	0.905004i
$682$	−0.409830	+	0.709846i	−0.0156932	+	0.0271814i
$683$	−21.6525			−0.828509			−0.414254	−	0.910161i	$-0.635958\pi$
$683$	−21.6525			−0.828509			−0.414254	+	0.910161i	$0.635958\pi$
$684$		0			0
$685$	1.81966			0.0695256
$686$	−4.63525	+	8.02850i	−0.176975	+	0.306529i
$687$	14.8992	−	25.8061i	0.568439	−	0.984566i
$688$	6.35410	+	11.0056i	0.242248	+	0.419586i
$689$	4.66312	−	8.07676i	0.177651	−	0.307700i
$690$	−7.61803	−	13.1948i	−0.290014	−	0.502318i
$691$	−16.8197			−0.639850			−0.319925	−	0.947443i	$-0.603658\pi$
$691$	−16.8197			−0.639850			−0.319925	+	0.947443i	$0.603658\pi$
$692$	−13.7082			−0.521108
$693$	−3.57295	−	6.18853i	−0.135725	−	0.235083i
$694$	0.437694	+	0.758108i	0.0166146	+	0.0287774i
$695$	12.1115			0.459414
$696$	−8.09017			−0.306657
$697$	7.85410	+	13.6037i	0.297495	+	0.515277i
$698$	8.02786	−	13.9047i	0.303859	−	0.526299i
$699$	−17.6353	−	30.5452i	−0.667027	−	1.15532i
$700$	−8.42705	+	14.5961i	−0.318513	+	0.551680i
$701$	−19.3156	+	33.4556i	−0.729540	+	1.26360i	0.227538	+	0.973769i	$0.426932\pi$
$701$	−19.3156	+	33.4556i	−0.729540	+	1.26360i	−0.957078	+	0.289831i	$0.906401\pi$
$702$	1.38197			0.0521589
$703$		0			0
$704$	−0.145898			−0.00549874
$705$	4.85410	−	8.40755i	0.182816	−	0.316647i
$706$	−9.71885	+	16.8335i	−0.365774	+	0.633539i
$707$	−19.7705	−	34.2435i	−0.743547	−	1.28786i
$708$	−32.4615	+	56.2250i	−1.21998	+	2.11306i
$709$	−21.7082	−	37.5997i	−0.815269	−	1.41209i	−0.909135	−	0.416502i	$-0.863256\pi$
$709$	−21.7082	−	37.5997i	−0.815269	−	1.41209i	0.0938661	−	0.995585i	$-0.470077\pi$
$710$	1.12461			0.0422059
$711$	−51.7082			−1.93921
$712$	13.6803	+	23.6950i	0.512692	+	0.888009i
$713$	8.17376	+	14.1574i	0.306110	+	0.530198i
$714$	−25.4164			−0.951185
$715$	0.763932			0.0285694
$716$	6.28115	+	10.8793i	0.234738	+	0.406578i
$717$	−20.0623	+	34.7489i	−0.749241	+	1.29772i
$718$	−6.80902	−	11.7936i	−0.254110	−	0.440132i
$719$	−8.98278	+	15.5586i	−0.335001	+	0.580239i	−0.983485	−	0.180989i	$-0.942070\pi$
$719$	−8.98278	+	15.5586i	−0.335001	+	0.580239i	0.648484	+	0.761228i	$0.275403\pi$
$720$	4.41641	−	7.64944i	0.164590	−	0.285078i
$721$	−3.97871			−0.148175
$722$		0			0
$723$	−50.2148			−1.86751
$724$	9.70820	−	16.8151i	0.360803	−	0.624928i
$725$	−2.39919	+	4.15551i	−0.0891036	+	0.154332i
$726$	−8.59017	−	14.8786i	−0.318811	−	0.552197i
$727$	−21.0344	+	36.4327i	−0.780124	+	1.35121i	0.151745	+	0.988420i	$0.451511\pi$
$727$	−21.0344	+	36.4327i	−0.780124	+	1.35121i	−0.931869	+	0.362795i	$0.881822\pi$
$728$	3.35410	+	5.80948i	0.124311	+	0.215313i
$729$	−39.5623			−1.46527
$730$	8.18034			0.302768
$731$	17.9443	+	31.0804i	0.663693	+	1.14955i
$732$	−12.2082	−	21.1452i	−0.451228	−	0.781550i
$733$	40.9574			1.51280			0.756399	−	0.654111i	$-0.226957\pi$
$733$	40.9574			1.51280			0.756399	+	0.654111i	$0.226957\pi$
$734$	−1.20163			−0.0443528
$735$	3.23607	+	5.60503i	0.119364	+	0.206745i
$736$	21.3992	−	37.0645i	0.788784	−	1.36621i
$737$	2.16312	+	3.74663i	0.0796795	+	0.138009i
$738$	−3.57295	+	6.18853i	−0.131522	+	0.227803i
$739$	12.5000	−	21.6506i	0.459820	−	0.796431i	−0.539131	−	0.842222i	$-0.681247\pi$
$739$	12.5000	−	21.6506i	0.459820	−	0.796431i	0.998951	+	0.0457903i	$0.0145806\pi$
$740$	4.29180			0.157770
$741$		0			0
$742$	−17.2918			−0.634802
$743$	−20.6803	+	35.8194i	−0.758688	+	1.31409i	0.184832	+	0.982770i	$0.440826\pi$
$743$	−20.6803	+	35.8194i	−0.758688	+	1.31409i	−0.943520	+	0.331316i	$0.892507\pi$
$744$	6.28115	−	10.8793i	0.230278	−	0.398854i
$745$	−8.09017	−	14.0126i	−0.296401	−	0.513381i
$746$	1.07295	−	1.85840i	0.0392835	−	0.0680409i
$747$	0.909830	+	1.57587i	0.0332889	+	0.0576581i
$748$	−5.23607			−0.191450
$749$	−31.2492			−1.14182
$750$	8.47214	+	14.6742i	0.309359	+	0.535825i
$751$	11.9271	+	20.6583i	0.435224	+	0.753831i	0.997314	−	0.0732458i	$-0.0233357\pi$
$751$	11.9271	+	20.6583i	0.435224	+	0.753831i	−0.562090	+	0.827076i	$0.690002\pi$
$752$	5.56231			0.202836
$753$	50.6869			1.84713
$754$	0.427051	+	0.739674i	0.0155523	+	0.0269373i
$755$	−6.12461	+	10.6081i	−0.222897	+	0.386070i
$756$	5.42705	+	9.39993i	0.197380	+	0.341872i
$757$	7.87132	−	13.6335i	0.286088	−	0.495519i	−0.686784	−	0.726861i	$-0.740978\pi$
$757$	7.87132	−	13.6335i	0.286088	−	0.495519i	0.972872	+	0.231342i	$0.0743117\pi$
$758$	7.76393	−	13.4475i	0.281999	−	0.488436i
$759$	12.3262			0.447414
$760$		0			0
$761$	−30.8885			−1.11971			−0.559854	−	0.828591i	$-0.689143\pi$
$761$	−30.8885			−1.11971			−0.559854	+	0.828591i	$0.689143\pi$
$762$	8.28115	−	14.3434i	0.299995	−	0.519606i
$763$	25.0623	−	43.4092i	0.907316	−	1.57152i
$764$	7.89919	+	13.6818i	0.285783	+	0.494990i
$765$	12.4721	−	21.6024i	0.450931	−	0.781035i
$766$	0.809017	+	1.40126i	0.0292310	+	0.0506295i
$767$	15.3262			0.553398
$768$	−17.1803			−0.619942
$769$	20.8156	+	36.0537i	0.750630	+	1.30013i	0.947518	+	0.319703i	$0.103583\pi$
$769$	20.8156	+	36.0537i	0.750630	+	1.30013i	−0.196888	+	0.980426i	$0.563084\pi$
$770$	−0.708204	−	1.22665i	−0.0255219	−	0.0442052i
$771$	−63.7771			−2.29688
$772$	−37.1246			−1.33614
$773$	−14.4615	−	25.0480i	−0.520144	−	0.900915i	−0.999726	−	0.0234183i	$-0.992545\pi$
$773$	−14.4615	−	25.0480i	−0.520144	−	0.900915i	0.479582	−	0.877497i	$-0.340788\pi$
$774$	−8.16312	+	14.1389i	−0.293417	+	0.508214i
$775$	−3.72542	−	6.45263i	−0.133821	−	0.231785i
$776$	−7.98936	+	13.8380i	−0.286801	+	0.496754i
$777$	−8.42705	+	14.5961i	−0.302319	+	0.523631i
$778$	15.0000			0.537776
$779$		0			0
$780$	−5.23607			−0.187481
$781$	−0.454915	+	0.787936i	−0.0162781	+	0.0281946i
$782$	12.3262	−	21.3497i	0.440785	−	0.763463i
$783$	1.54508	+	2.67617i	0.0552168	+	0.0956384i
$784$	−1.85410	+	3.21140i	−0.0662179	+	0.114693i
$785$	−6.88854	−	11.9313i	−0.245863	−	0.425847i
$786$	−6.32624			−0.225649
$787$	38.0000			1.35455			0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000			1.35455			0.677277	+	0.735728i	$0.263160\pi$
$788$	2.42705	+	4.20378i	0.0864601	+	0.149753i
$789$	−3.85410	−	6.67550i	−0.137210	−	0.237654i
$790$	−10.2492			−0.364651
$791$	33.7082			1.19853
$792$	−2.66312	−	4.61266i	−0.0946298	−	0.163904i
$793$	−2.88197	+	4.99171i	−0.102342	+	0.177261i
$794$	−0.781153	−	1.35300i	−0.0277221	−	0.0480161i
$795$	15.0902	−	26.1369i	0.535193	−	0.926982i
$796$	10.8541	−	18.7999i	0.384713	−	0.666343i
$797$	−33.7082			−1.19401			−0.597003	−	0.802239i	$-0.703642\pi$
$797$	−33.7082			−1.19401			−0.597003	+	0.802239i	$0.703642\pi$
$798$		0			0
$799$	15.7082			0.555716
$800$	−9.75329	+	16.8932i	−0.344831	+	0.597265i
$801$	23.5795	−	40.8409i	0.833142	−	1.44304i
$802$	−0.0344419	−	0.0596550i	−0.00121618	−	0.00210649i
$803$	−3.30902	+	5.73139i	−0.116773	+	0.202256i
$804$	−14.8262	−	25.6798i	−0.522881	−	0.905657i
$805$	−28.2492			−0.995654
$806$	−1.32624			−0.0467147
$807$	−19.2082	−	33.2696i	−0.676161	−	1.17114i
$808$	−14.7361	−	25.5236i	−0.518413	−	0.897918i
$809$	−0.201626			−0.00708880			−0.00354440	−	0.999994i	$-0.501128\pi$
$809$	−0.201626			−0.00708880			−0.00354440	+	0.999994i	$0.501128\pi$
$810$	−4.36068			−0.153219
$811$	11.9894	+	20.7662i	0.421003	+	0.729199i	0.996038	−	0.0889300i	$-0.0283448\pi$
$811$	11.9894	+	20.7662i	0.421003	+	0.729199i	−0.575035	+	0.818129i	$0.695011\pi$
$812$	−3.35410	+	5.80948i	−0.117706	+	0.203873i
$813$	−10.2812	−	17.8075i	−0.360576	−	0.624536i
$814$	0.409830	−	0.709846i	0.0143645	−	0.0248801i
$815$	3.85410	−	6.67550i	0.135003	−	0.233833i
$816$	25.4164			0.889752
$817$		0			0
$818$	13.4164			0.469094
$819$	5.78115	−	10.0133i	0.202010	−	0.349891i
$820$	3.00000	−	5.19615i	0.104765	−	0.181458i
$821$	26.5238	+	45.9406i	0.925687	+	1.60334i	0.790453	+	0.612523i	$0.209845\pi$
$821$	26.5238	+	45.9406i	0.925687	+	1.60334i	0.135234	+	0.990814i	$0.456821\pi$
$822$	−1.19098	+	2.06284i	−0.0415403	+	0.0719499i
$823$	−11.7984	−	20.4354i	−0.411265	−	0.712333i	0.583763	−	0.811924i	$-0.301580\pi$
$823$	−11.7984	−	20.4354i	−0.411265	−	0.712333i	−0.995028	+	0.0995915i	$0.968246\pi$
$824$	−2.96556			−0.103310
$825$	−5.61803			−0.195595
$826$	−14.2082	−	24.6093i	−0.494367	−	0.856268i
$827$	8.29837	+	14.3732i	0.288563	+	0.499805i	0.973467	−	0.228828i	$-0.0734893\pi$
$827$	8.29837	+	14.3732i	0.288563	+	0.499805i	−0.684904	+	0.728633i	$0.740156\pi$
$828$	−47.5066			−1.65097
$829$	20.3262			0.705959			0.352980	−	0.935631i	$-0.385168\pi$
$829$	20.3262			0.705959			0.352980	+	0.935631i	$0.385168\pi$
$830$	0.180340	+	0.312358i	0.00625969	+	0.0108421i
$831$	20.1803	−	34.9534i	0.700048	−	1.21252i
$832$	−0.118034	−	0.204441i	−0.00409209	−	0.00708771i
$833$	−5.23607	+	9.06914i	−0.181419	+	0.314227i
$834$	−7.92705	+	13.7301i	−0.274491	+	0.475433i
$835$	−19.4853			−0.674316
$836$		0			0
$837$	−4.79837			−0.165856
$838$	2.76393	−	4.78727i	0.0954784	−	0.165374i
$839$	−19.8992	+	34.4664i	−0.686996	+	1.18991i	0.285809	+	0.958287i	$0.407738\pi$
$839$	−19.8992	+	34.4664i	−0.686996	+	1.18991i	−0.972805	+	0.231626i	$0.925596\pi$
$840$	10.8541	+	18.7999i	0.374502	+	0.648657i
$841$	13.5451	−	23.4608i	0.467072	−	0.808992i
$842$	−5.72542	−	9.91673i	−0.197311	−	0.341753i
$843$	22.2705			0.767037
$844$	−4.61803			−0.158959
$845$	−7.41641	−	12.8456i	−0.255132	−	0.441902i
$846$	3.57295	+	6.18853i	0.122841	+	0.212766i
$847$	−31.8541			−1.09452
$848$	17.2918			0.593803
$849$	3.97214	+	6.87994i	0.136323	+	0.236119i
$850$	−5.61803	+	9.73072i	−0.192697	+	0.333761i
$851$	−8.17376	−	14.1574i	−0.280193	−	0.485308i
$852$	3.11803	−	5.40059i	0.106822	−	0.185021i
$853$	−8.64590	+	14.9751i	−0.296030	+	0.512739i	−0.975224	−	0.221220i	$-0.928996\pi$
$853$	−8.64590	+	14.9751i	−0.296030	+	0.512739i	0.679194	+	0.733959i	$0.262329\pi$
$854$	10.6869			0.365699
$855$		0			0
$856$	−23.2918			−0.796097
$857$	4.19098	−	7.25900i	0.143161	−	0.247963i	−0.785524	−	0.618831i	$-0.787607\pi$
$857$	4.19098	−	7.25900i	0.143161	−	0.247963i	0.928685	+	0.370868i	$0.120940\pi$
$858$	−0.500000	+	0.866025i	−0.0170697	+	0.0295656i
$859$	−9.27051	−	16.0570i	−0.316306	−	0.547858i	0.663408	−	0.748257i	$-0.269109\pi$
$859$	−9.27051	−	16.0570i	−0.316306	−	0.547858i	−0.979714	+	0.200400i	$0.935776\pi$
$860$	6.85410	−	11.8717i	0.233723	−	0.404820i
$861$	11.7812	+	20.4056i	0.401501	+	0.695419i
$862$	2.25735			0.0768858
$863$	−44.9443			−1.52992			−0.764960	−	0.644077i	$-0.777241\pi$
$863$	−44.9443			−1.52992			−0.764960	+	0.644077i	$0.777241\pi$
$864$	6.28115	+	10.8793i	0.213689	+	0.370120i
$865$	5.23607	+	9.06914i	0.178032	+	0.308360i
$866$	14.5623			0.494847
$867$	27.2705			0.926155
$868$	−5.20820	−	9.02087i	−0.176778	−	0.306188i
$869$	4.14590	−	7.18091i	0.140640	−	0.243596i
$870$	1.38197	+	2.39364i	0.0468530	+	0.0811518i
$871$	−3.50000	+	6.06218i	−0.118593	+	0.205409i
$872$	18.6803	−	32.3553i	0.632596	−	1.09569i
$873$	27.5410			0.932122
$874$		0			0
$875$	31.4164			1.06207
$876$	22.6803	−	39.2835i	0.766298	−	1.32727i
$877$	−17.0902	+	29.6010i	−0.577094	+	0.999556i	0.418717	+	0.908117i	$0.362480\pi$
$877$	−17.0902	+	29.6010i	−0.577094	+	0.999556i	−0.995811	+	0.0914392i	$0.970853\pi$
$878$	4.51064	+	7.81266i	0.152227	+	0.263665i
$879$	22.0623	−	38.2130i	0.744143	−	1.28889i
$880$	0.708204	+	1.22665i	0.0238735	+	0.0413502i
$881$	−23.4508			−0.790079			−0.395040	−	0.918664i	$-0.629269\pi$
$881$	−23.4508			−0.790079			−0.395040	+	0.918664i	$0.629269\pi$
$882$	−4.76393			−0.160410
$883$	−6.96149	−	12.0577i	−0.234273	−	0.405773i	0.724788	−	0.688972i	$-0.241938\pi$
$883$	−6.96149	−	12.0577i	−0.234273	−	0.405773i	−0.959061	+	0.283199i	$0.908604\pi$
$884$	−4.23607	−	7.33708i	−0.142474	−	0.246773i
$885$	49.5967			1.66718
$886$	21.2705			0.714597
$887$	−29.3262	−	50.7945i	−0.984679	−	1.70551i	−0.643356	−	0.765568i	$-0.722458\pi$
$887$	−29.3262	−	50.7945i	−0.984679	−	1.70551i	−0.341323	−	0.939946i	$-0.610875\pi$
$888$	−6.28115	+	10.8793i	−0.210782	+	0.365085i
$889$	−15.3541	−	26.5941i	−0.514960	−	0.891937i
$890$	4.67376	−	8.09519i	0.156665	−	0.271351i
$891$	1.76393	−	3.05522i	0.0590939	−	0.102354i
$892$	−31.7984			−1.06469
$893$		0			0
$894$	21.1803			0.708377
$895$	4.79837	−	8.31103i	0.160392	−	0.277807i
$896$	−17.0729	+	29.5712i	−0.570367	+	0.987905i
$897$	9.97214	+	17.2722i	0.332960	+	0.576704i
$898$	−10.1631	+	17.6030i	−0.339148	+	0.587421i
$899$	−1.48278	−	2.56825i	−0.0494535	−	0.0856559i
$900$	21.6525			0.721749
$901$	48.8328			1.62686
$902$	−0.572949	−	0.992377i	−0.0190771	−	0.0330425i
$903$	26.9164	+	46.6206i	0.895722	+	1.55144i
$904$	25.1246			0.835632
$905$	−14.8328			−0.493059
$906$	−8.01722	−	13.8862i	−0.266354	−	0.461339i
$907$	8.76393	−	15.1796i	0.291002	−	0.504030i	−0.683045	−	0.730376i	$-0.739345\pi$
$907$	8.76393	−	15.1796i	0.291002	−	0.504030i	0.974047	+	0.226347i	$0.0726782\pi$
$908$	−8.42705	−	14.5961i	−0.279662	−	0.484388i
$909$	−25.3992	+	43.9927i	−0.842438	+	1.45915i
$910$	1.14590	−	1.98475i	0.0379861	−	0.0657939i
$911$	5.61803			0.186134			0.0930669	−	0.995660i	$-0.470333\pi$
$911$	5.61803			0.186134			0.0930669	+	0.995660i	$0.470333\pi$
$912$		0			0
$913$	−0.291796			−0.00965704
$914$	1.94427	−	3.36758i	0.0643108	−	0.111390i
$915$	−9.32624	+	16.1535i	−0.308316	+	0.534019i
$916$	−9.20820	−	15.9491i	−0.304248	−	0.526972i
$917$	−5.86475	+	10.1580i	−0.193671	+	0.335448i
$918$	3.61803	+	6.26662i	0.119413	+	0.206829i
$919$	36.7082			1.21089			0.605446	−	0.795886i	$-0.292995\pi$
$919$	36.7082			1.21089			0.605446	+	0.795886i	$0.292995\pi$
$920$	−21.0557			−0.694187
$921$	2.19098	+	3.79489i	0.0721953	+	0.125046i
$922$	0.944272	+	1.63553i	0.0310979	+	0.0538632i
$923$	−1.47214			−0.0484559
$924$	−7.85410			−0.258381
$925$	3.72542	+	6.45263i	0.122491	+	0.212161i
$926$	−1.62868	+	2.82095i	−0.0535217	+	0.0927022i
$927$	2.55573	+	4.42665i	0.0839411	+	0.145390i
$928$	−3.88197	+	6.72376i	−0.127432	+	0.220718i
$929$	−9.30902	+	16.1237i	−0.305419	+	0.529001i	−0.977355	−	0.211608i	$-0.932130\pi$
$929$	−9.30902	+	16.1237i	−0.305419	+	0.529001i	0.671936	+	0.740610i	$0.265463\pi$
$930$	−4.29180			−0.140734
$931$		0			0
$932$	−21.7984			−0.714029
$933$	24.4164	−	42.2905i	0.799357	−	1.38453i
$934$	0.600813	−	1.04064i	0.0196592	−	0.0340507i
$935$	2.00000	+	3.46410i	0.0654070	+	0.113288i
$936$	4.30902	−	7.46344i	0.140845	−	0.243950i
$937$	−10.2188	−	17.6996i	−0.333835	−	0.578219i	0.649425	−	0.760425i	$-0.275010\pi$
$937$	−10.2188	−	17.6996i	−0.333835	−	0.578219i	−0.983260	+	0.182206i	$0.941676\pi$
$938$	12.9787			0.423770
$939$	11.3262			0.369618
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−24.8435	−	43.0301i	−0.809874	−	1.40274i	−0.912951	−	0.408069i	$-0.866202\pi$
$941$	−24.8435	−	43.0301i	−0.809874	−	1.40274i	0.103078	−	0.994673i	$-0.467131\pi$
$942$	18.0344			0.587594
$943$	−22.8541			−0.744232
$944$	14.2082	+	24.6093i	0.462438	+	0.800966i
$945$	4.14590	−	7.18091i	0.134866	−	0.233595i
$946$	−1.30902	−	2.26728i	−0.0425598	−	0.0737158i
$947$	0.673762	−	1.16699i	0.0218943	−	0.0379221i	−0.854871	−	0.518841i	$-0.826364\pi$
$947$	0.673762	−	1.16699i	0.0218943	−	0.0379221i	0.876765	+	0.480919i	$0.159697\pi$
$948$	−28.4164	+	49.2187i	−0.922922	+	1.59855i
$949$	−10.7082			−0.347603
$950$		0			0
$951$	47.1246			1.52812
$952$	−17.5623	+	30.4188i	−0.569198	+	0.985879i
$953$	−15.3541	+	26.5941i	−0.497368	+	0.861467i	−0.999995	−	0.00303634i	$-0.999034\pi$
$953$	−15.3541	+	26.5941i	−0.497368	+	0.861467i	0.502627	+	0.864503i	$0.332367\pi$
$954$	11.1074	+	19.2386i	0.359615	+	0.622872i
$955$	6.03444	−	10.4520i	0.195270	−	0.338217i
$956$	12.3992	+	21.4760i	0.401018	+	0.694584i
$957$	−2.23607			−0.0722818
$958$	−7.36068			−0.237813
$959$	2.20820	+	3.82472i	0.0713066	+	0.123507i
$960$	−0.381966	−	0.661585i	−0.0123279	−	0.0213525i
$961$	−26.3951			−0.851456
$962$	1.32624			0.0427596
$963$	20.0729	+	34.7674i	0.646842	+	1.12036i
$964$	−15.5172	+	26.8766i	−0.499776	+	0.865637i
$965$	14.1803	+	24.5611i	0.456481	+	0.790649i
$966$	18.4894	−	32.0245i	0.594885	−	1.03037i
$967$	30.2705	−	52.4301i	0.973434	−	1.68604i	0.288425	−	0.957503i	$-0.406868\pi$
$967$	30.2705	−	52.4301i	0.973434	−	1.68604i	0.685009	−	0.728535i	$-0.259798\pi$
$968$	−23.7426			−0.763118
$969$		0			0
$970$	5.45898			0.175277
$971$	7.25329	−	12.5631i	0.232769	−	0.403168i	−0.725853	−	0.687850i	$-0.758555\pi$
$971$	7.25329	−	12.5631i	0.232769	−	0.403168i	0.958622	+	0.284682i	$0.0918880\pi$
$972$	−17.5172	+	30.3407i	−0.561865	+	0.973179i
$973$	14.6976	+	25.4569i	0.471182	+	0.816111i
$974$	−5.61803	+	9.73072i	−0.180013	+	0.311792i
$975$	−4.54508	−	7.87232i	−0.145559	−	0.252116i
$976$	−10.6869			−0.342080
$977$	55.3607			1.77115			0.885573	−	0.464501i	$-0.153766\pi$
$977$	55.3607			1.77115			0.885573	+	0.464501i	$0.153766\pi$
$978$	5.04508	+	8.73834i	0.161324	+	0.279421i
$979$	3.78115	+	6.54915i	0.120846	+	0.209312i
$980$	4.00000			0.127775
$981$	−64.3951			−2.05598
$982$	9.33688	+	16.1720i	0.297952	+	0.516068i
$983$	−15.1910	+	26.3116i	−0.484517	+	0.839208i	−0.999842	−	0.0177868i	$-0.994338\pi$
$983$	−15.1910	+	26.3116i	−0.484517	+	0.839208i	0.515325	+	0.856995i	$0.327671\pi$
$984$	8.78115	+	15.2094i	0.279933	+	0.484858i
$985$	1.85410	−	3.21140i	0.0590766	−	0.102324i
$986$	−2.23607	+	3.87298i	−0.0712109	+	0.123341i
$987$	23.5623			0.749996
$988$		0			0
$989$	−52.2148			−1.66033
$990$	−0.909830	+	1.57587i	−0.0289163	+	0.0500845i
$991$	24.2254	−	41.9597i	0.769546	−	1.33289i	−0.168263	−	0.985742i	$-0.553816\pi$
$991$	24.2254	−	41.9597i	0.769546	−	1.33289i	0.937809	−	0.347151i	$-0.112851\pi$
$992$	−6.02786	−	10.4406i	−0.191385	−	0.331488i
$993$	9.09017	−	15.7446i	0.288468	−	0.499641i
$994$	1.36475	+	2.36381i	0.0432871	+	0.0749754i
$995$	−16.5836			−0.525735
$996$	2.00000			0.0633724
$997$	−13.1459	−	22.7694i	−0.416335	−	0.721113i	0.579233	−	0.815162i	$-0.303352\pi$
$997$	−13.1459	−	22.7694i	−0.416335	−	0.721113i	−0.995568	+	0.0940492i	$0.970019\pi$
$998$	−4.67376	−	8.09519i	−0.147945	−	0.256249i
$999$	4.79837			0.151814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.d.68.2		4
19.2	odd	18		361.2.e.i.234.2		12
19.3	odd	18		361.2.e.i.99.1		12
19.4	even	9		361.2.e.j.62.2		12
19.5	even	9		361.2.e.j.28.1		12
19.6	even	9		361.2.e.j.54.1		12
19.7	even	3	inner	361.2.c.d.292.2		4
19.8	odd	6		361.2.a.c.1.2	✓	2
19.9	even	9		361.2.e.j.245.1		12
19.10	odd	18		361.2.e.i.245.2		12
19.11	even	3		361.2.a.f.1.1	yes	2
19.12	odd	6		361.2.c.g.292.1		4
19.13	odd	18		361.2.e.i.54.2		12
19.14	odd	18		361.2.e.i.28.2		12
19.15	odd	18		361.2.e.i.62.1		12
19.16	even	9		361.2.e.j.99.2		12
19.17	even	9		361.2.e.j.234.1		12
19.18	odd	2		361.2.c.g.68.1		4
57.8	even	6		3249.2.a.o.1.1		2
57.11	odd	6		3249.2.a.i.1.2		2
76.11	odd	6		5776.2.a.s.1.1		2
76.27	even	6		5776.2.a.bg.1.2		2
95.49	even	6		9025.2.a.n.1.2		2
95.84	odd	6		9025.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.2	✓	2	19.8	odd	6
361.2.a.f.1.1	yes	2	19.11	even	3
361.2.c.d.68.2		4	1.1	even	1	trivial
361.2.c.d.292.2		4	19.7	even	3	inner
361.2.c.g.68.1		4	19.18	odd	2
361.2.c.g.292.1		4	19.12	odd	6
361.2.e.i.28.2		12	19.14	odd	18
361.2.e.i.54.2		12	19.13	odd	18
361.2.e.i.62.1		12	19.15	odd	18
361.2.e.i.99.1		12	19.3	odd	18
361.2.e.i.234.2		12	19.2	odd	18
361.2.e.i.245.2		12	19.10	odd	18
361.2.e.j.28.1		12	19.5	even	9
361.2.e.j.54.1		12	19.6	even	9
361.2.e.j.62.2		12	19.4	even	9
361.2.e.j.99.2		12	19.16	even	9
361.2.e.j.234.1		12	19.17	even	9
361.2.e.j.245.1		12	19.9	even	9
3249.2.a.i.1.2		2	57.11	odd	6
3249.2.a.o.1.1		2	57.8	even	6
5776.2.a.s.1.1		2	76.11	odd	6
5776.2.a.bg.1.2		2	76.27	even	6
9025.2.a.n.1.2		2	95.49	even	6
9025.2.a.s.1.1		2	95.84	odd	6

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.535233i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.618034 - 1.07047i) q^{5} +(0.809017 + 1.40126i) q^{6} +3.00000 q^{7} +2.23607 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.535233i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.618034 - 1.07047i) q^{5} +(0.809017 + 1.40126i) q^{6} +3.00000 q^{7} +2.23607 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-0.381966 - 0.661585i) q^{10} +0.618034 q^{11} -4.23607 q^{12} +(0.500000 + 0.866025i) q^{13} +(0.927051 - 1.60570i) q^{14} +(1.61803 + 2.80252i) q^{15} +(-0.927051 + 1.60570i) q^{16} +(-2.61803 + 4.53457i) q^{17} -2.38197 q^{18} +2.00000 q^{20} +(-3.92705 + 6.80185i) q^{21} +(0.190983 - 0.330792i) q^{22} +(-3.80902 - 6.59741i) q^{23} +(-2.92705 + 5.06980i) q^{24} +(1.73607 + 3.00696i) q^{25} +0.618034 q^{26} +2.23607 q^{27} +(2.42705 + 4.20378i) q^{28} +(0.690983 + 1.19682i) q^{29} +2.00000 q^{30} -2.14590 q^{31} +(2.80902 + 4.86536i) q^{32} +(-0.809017 + 1.40126i) q^{33} +(1.61803 + 2.80252i) q^{34} +(1.85410 - 3.21140i) q^{35} +(3.11803 - 5.40059i) q^{36} +2.14590 q^{37} -2.61803 q^{39} +(1.38197 - 2.39364i) q^{40} +(1.50000 - 2.59808i) q^{41} +(2.42705 + 4.20378i) q^{42} +(3.42705 - 5.93583i) q^{43} +(0.500000 + 0.866025i) q^{44} -4.76393 q^{45} -4.70820 q^{46} +(-1.50000 - 2.59808i) q^{47} +(-2.42705 - 4.20378i) q^{48} +2.00000 q^{49} +2.14590 q^{50} +(-6.85410 - 11.8717i) q^{51} +(-0.809017 + 1.40126i) q^{52} +(-4.66312 - 8.07676i) q^{53} +(0.690983 - 1.19682i) q^{54} +(0.381966 - 0.661585i) q^{55} +6.70820 q^{56} +0.854102 q^{58} +(7.66312 - 13.2729i) q^{59} +(-2.61803 + 4.53457i) q^{60} +(2.88197 + 4.99171i) q^{61} +(-0.663119 + 1.14856i) q^{62} +(-5.78115 - 10.0133i) q^{63} -0.236068 q^{64} +1.23607 q^{65} +(0.500000 + 0.866025i) q^{66} +(3.50000 + 6.06218i) q^{67} -8.47214 q^{68} +19.9443 q^{69} +(-1.14590 - 1.98475i) q^{70} +(-0.736068 + 1.27491i) q^{71} +(-4.30902 - 7.46344i) q^{72} +(-5.35410 + 9.27358i) q^{73} +(0.663119 - 1.14856i) q^{74} -9.09017 q^{75} +1.85410 q^{77} +(-0.809017 + 1.40126i) q^{78} +(6.70820 - 11.6190i) q^{79} +(1.14590 + 1.98475i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-0.927051 - 1.60570i) q^{82} -0.472136 q^{83} -12.7082 q^{84} +(3.23607 + 5.60503i) q^{85} +(-2.11803 - 3.66854i) q^{86} -3.61803 q^{87} +1.38197 q^{88} +(6.11803 + 10.5967i) q^{89} +(-1.47214 + 2.54981i) q^{90} +(1.50000 + 2.59808i) q^{91} +(6.16312 - 10.6748i) q^{92} +(2.80902 - 4.86536i) q^{93} -1.85410 q^{94} -14.7082 q^{96} +(-3.57295 + 6.18853i) q^{97} +(0.618034 - 1.07047i) q^{98} +(-1.19098 - 2.06284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{6} + 12 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^6 + 12 * q^7 - q^9	\( 4 q - q^{2} - 3 q^{3} + q^{4} - 2 q^{5} + q^{6} + 12 q^{7} - q^{9} - 6 q^{10} - 2 q^{11} - 8 q^{12} + 2 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} - 6 q^{17} - 14 q^{18} + 8 q^{20} - 9 q^{21} + 3 q^{22} - 13 q^{23} - 5 q^{24} - 2 q^{25} - 2 q^{26} + 3 q^{28} + 5 q^{29} + 8 q^{30} - 22 q^{31} + 9 q^{32} - q^{33} + 2 q^{34} - 6 q^{35} + 8 q^{36} + 22 q^{37} - 6 q^{39} + 10 q^{40} + 6 q^{41} + 3 q^{42} + 7 q^{43} + 2 q^{44} - 28 q^{45} + 8 q^{46} - 6 q^{47} - 3 q^{48} + 8 q^{49} + 22 q^{50} - 14 q^{51} - q^{52} - 3 q^{53} + 5 q^{54} + 6 q^{55} - 10 q^{58} + 15 q^{59} - 6 q^{60} + 16 q^{61} + 13 q^{62} - 3 q^{63} + 8 q^{64} - 4 q^{65} + 2 q^{66} + 14 q^{67} - 16 q^{68} + 44 q^{69} - 18 q^{70} + 6 q^{71} - 15 q^{72} - 8 q^{73} - 13 q^{74} - 14 q^{75} - 6 q^{77} - q^{78} + 18 q^{80} - 2 q^{81} + 3 q^{82} + 16 q^{83} - 24 q^{84} + 4 q^{85} - 4 q^{86} - 10 q^{87} + 10 q^{88} + 20 q^{89} + 12 q^{90} + 6 q^{91} + 9 q^{92} + 9 q^{93} + 6 q^{94} - 32 q^{96} - 21 q^{97} - 2 q^{98} - 7 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 + q^4 - 2 * q^5 + q^6 + 12 * q^7 - q^9 - 6 * q^10 - 2 * q^11 - 8 * q^12 + 2 * q^13 - 3 * q^14 + 2 * q^15 + 3 * q^16 - 6 * q^17 - 14 * q^18 + 8 * q^20 - 9 * q^21 + 3 * q^22 - 13 * q^23 - 5 * q^24 - 2 * q^25 - 2 * q^26 + 3 * q^28 + 5 * q^29 + 8 * q^30 - 22 * q^31 + 9 * q^32 - q^33 + 2 * q^34 - 6 * q^35 + 8 * q^36 + 22 * q^37 - 6 * q^39 + 10 * q^40 + 6 * q^41 + 3 * q^42 + 7 * q^43 + 2 * q^44 - 28 * q^45 + 8 * q^46 - 6 * q^47 - 3 * q^48 + 8 * q^49 + 22 * q^50 - 14 * q^51 - q^52 - 3 * q^53 + 5 * q^54 + 6 * q^55 - 10 * q^58 + 15 * q^59 - 6 * q^60 + 16 * q^61 + 13 * q^62 - 3 * q^63 + 8 * q^64 - 4 * q^65 + 2 * q^66 + 14 * q^67 - 16 * q^68 + 44 * q^69 - 18 * q^70 + 6 * q^71 - 15 * q^72 - 8 * q^73 - 13 * q^74 - 14 * q^75 - 6 * q^77 - q^78 + 18 * q^80 - 2 * q^81 + 3 * q^82 + 16 * q^83 - 24 * q^84 + 4 * q^85 - 4 * q^86 - 10 * q^87 + 10 * q^88 + 20 * q^89 + 12 * q^90 + 6 * q^91 + 9 * q^92 + 9 * q^93 + 6 * q^94 - 32 * q^96 - 21 * q^97 - 2 * q^98 - 7 * q^99

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