LMFDB - Embedded newform 336.2.s.c.155.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.8
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.244056 + 1.39300i) q^{2} +(-1.68331 + 0.408017i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(-2.26080 + 2.26080i) q^{5} +(-0.157543 - 2.44442i) q^{6} -1.00000 q^{7} +(1.40619 - 2.45410i) q^{8} +(2.66704 - 1.37363i) q^{9} +O(q^{10})$	\(q+(-0.244056 + 1.39300i) q^{2} +(-1.68331 + 0.408017i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(-2.26080 + 2.26080i) q^{5} +(-0.157543 - 2.44442i) q^{6} -1.00000 q^{7} +(1.40619 - 2.45410i) q^{8} +(2.66704 - 1.37363i) q^{9} +(-2.59752 - 3.70105i) q^{10} +(-1.82069 - 1.82069i) q^{11} +(3.44351 + 0.377119i) q^{12} +(0.915413 - 0.915413i) q^{13} +(0.244056 - 1.39300i) q^{14} +(2.88318 - 4.72806i) q^{15} +(3.07537 + 2.55776i) q^{16} +2.93247i q^{17} +(1.26256 + 4.05043i) q^{18} +(1.79372 + 1.79372i) q^{19} +(5.78948 - 2.71507i) q^{20} +(1.68331 - 0.408017i) q^{21} +(2.98056 - 2.09186i) q^{22} -8.77567i q^{23} +(-1.36574 + 4.70476i) q^{24} -5.22244i q^{25} +(1.05175 + 1.49858i) q^{26} +(-3.92899 + 3.40045i) q^{27} +(1.88087 + 0.679939i) q^{28} +(-1.67539 - 1.67539i) q^{29} +(5.88252 + 5.17017i) q^{30} -8.15507i q^{31} +(-4.31351 + 3.65973i) q^{32} +(3.80765 + 2.32191i) q^{33} +(-4.08491 - 0.715687i) q^{34} +(2.26080 - 2.26080i) q^{35} +(-5.95036 + 0.770204i) q^{36} +(-4.29751 - 4.29751i) q^{37} +(-2.93642 + 2.06088i) q^{38} +(-1.16742 + 1.91442i) q^{39} +(2.36912 + 8.72736i) q^{40} +4.52681 q^{41} +(0.157543 + 2.44442i) q^{42} +(-3.46653 + 3.46653i) q^{43} +(2.18653 + 4.66245i) q^{44} +(-2.92414 + 9.13517i) q^{45} +(12.2245 + 2.14176i) q^{46} -8.60844 q^{47} +(-6.22039 - 3.05069i) q^{48} +1.00000 q^{49} +(7.27483 + 1.27457i) q^{50} +(-1.19649 - 4.93624i) q^{51} +(-2.34420 + 1.09935i) q^{52} +(-6.48541 + 6.48541i) q^{53} +(-3.77791 - 6.30297i) q^{54} +8.23243 q^{55} +(-1.40619 + 2.45410i) q^{56} +(-3.75125 - 2.28752i) q^{57} +(2.74270 - 1.92492i) q^{58} +(-8.08166 - 8.08166i) q^{59} +(-8.63768 + 6.93251i) q^{60} +(2.11377 - 2.11377i) q^{61} +(11.3600 + 1.99030i) q^{62} +(-2.66704 + 1.37363i) q^{63} +(-4.04525 - 6.90188i) q^{64} +4.13913i q^{65} +(-4.16369 + 4.73737i) q^{66} +(-2.17584 - 2.17584i) q^{67} +(1.99390 - 5.51560i) q^{68} +(3.58062 + 14.7721i) q^{69} +(2.59752 + 3.70105i) q^{70} +4.72561i q^{71} +(0.379333 - 8.47680i) q^{72} +8.88001i q^{73} +(7.03525 - 4.93758i) q^{74} +(2.13084 + 8.79096i) q^{75} +(-2.15414 - 4.59338i) q^{76} +(1.82069 + 1.82069i) q^{77} +(-2.38187 - 2.09343i) q^{78} -10.6576i q^{79} +(-12.7354 + 1.17021i) q^{80} +(5.22626 - 7.32709i) q^{81} +(-1.10480 + 6.30583i) q^{82} +(7.45604 - 7.45604i) q^{83} +(-3.44351 - 0.377119i) q^{84} +(-6.62972 - 6.62972i) q^{85} +(-3.98283 - 5.67489i) q^{86} +(3.50379 + 2.13661i) q^{87} +(-7.02840 + 1.90793i) q^{88} -11.6283 q^{89} +(-12.0116 - 6.30281i) q^{90} +(-0.915413 + 0.915413i) q^{91} +(-5.96692 + 16.5059i) q^{92} +(3.32740 + 13.7275i) q^{93} +(2.10095 - 11.9915i) q^{94} -8.11049 q^{95} +(5.76773 - 7.92044i) q^{96} +9.08157 q^{97} +(-0.244056 + 1.39300i) q^{98} +(-7.35683 - 2.35490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.244056	+	1.39300i	−0.172574	+	0.984997i
$2$	−0.244056	+	1.39300i	−0.172574	+	0.984997i
$3$	−1.68331	+	0.408017i	−0.971858	+	0.235568i
$3$	−1.68331	+	0.408017i	−0.971858	+	0.235568i
$4$	−1.88087	−	0.679939i	−0.940436	−	0.339969i
$5$	−2.26080	+	2.26080i	−1.01106	+	1.01106i	−0.0111224	+	0.999938i	$0.503540\pi$
$5$	−2.26080	+	2.26080i	−1.01106	+	1.01106i	−0.999938	+	0.0111224i	$0.996460\pi$
$6$	−0.157543	−	2.44442i	−0.0643168	−	0.997930i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.40619	−	2.45410i	0.497164	−	0.867657i
$9$	2.66704	−	1.37363i	0.889015	−	0.457878i
$10$	−2.59752	−	3.70105i	−0.821409	−	1.17037i
$11$	−1.82069	−	1.82069i	−0.548959	−	0.548959i	0.377181	−	0.926140i	$-0.376894\pi$
$11$	−1.82069	−	1.82069i	−0.548959	−	0.548959i	−0.926140	+	0.377181i	$0.876894\pi$
$12$	3.44351	+	0.377119i	0.994057	+	0.108865i
$13$	0.915413	−	0.915413i	0.253890	−	0.253890i	−0.568674	−	0.822563i	$-0.692543\pi$
$13$	0.915413	−	0.915413i	0.253890	−	0.253890i	0.822563	+	0.568674i	$0.192543\pi$
$14$	0.244056	−	1.39300i	0.0652268	−	0.372294i
$15$	2.88318	−	4.72806i	0.744433	−	1.22078i
$16$	3.07537	+	2.55776i	0.768842	+	0.639439i
$17$			2.93247i			0.711228i	0.934633	+	0.355614i	$0.115728\pi$
$17$			2.93247i			0.711228i	−0.934633	+	0.355614i	$0.884272\pi$
$18$	1.26256	+	4.05043i	0.297588	+	0.954695i
$19$	1.79372	+	1.79372i	0.411508	+	0.411508i	0.882264	−	0.470756i	$-0.156019\pi$
$19$	1.79372	+	1.79372i	0.411508	+	0.411508i	−0.470756	+	0.882264i	$0.656019\pi$
$20$	5.78948	−	2.71507i	1.29457	−	0.607109i
$21$	1.68331	−	0.408017i	0.367328	−	0.0890365i
$22$	2.98056	−	2.09186i	0.635459	−	0.445987i
$23$		−	8.77567i		−	1.82985i	−0.403619	−	0.914927i	$-0.632248\pi$
$23$		−	8.77567i		−	1.82985i	0.403619	−	0.914927i	$-0.367752\pi$
$24$	−1.36574	+	4.70476i	−0.278780	+	0.960355i
$25$		−	5.22244i		−	1.04449i
$26$	1.05175	+	1.49858i	0.206266	+	0.293895i
$27$	−3.92899	+	3.40045i	−0.756134	+	0.654416i
$28$	1.88087	+	0.679939i	0.355452	+	0.128496i
$29$	−1.67539	−	1.67539i	−0.311113	−	0.311113i	0.534228	−	0.845340i	$-0.320602\pi$
$29$	−1.67539	−	1.67539i	−0.311113	−	0.311113i	−0.845340	+	0.534228i	$0.820602\pi$
$30$	5.88252	+	5.17017i	1.07400	+	0.943939i
$31$		−	8.15507i		−	1.46469i	−0.680931	−	0.732347i	$-0.738425\pi$
$31$		−	8.15507i		−	1.46469i	0.680931	−	0.732347i	$-0.261575\pi$
$32$	−4.31351	+	3.65973i	−0.762528	+	0.646956i
$33$	3.80765	+	2.32191i	0.662827	+	0.404192i
$34$	−4.08491	−	0.715687i	−0.700557	−	0.122739i
$35$	2.26080	−	2.26080i	0.382145	−	0.382145i
$36$	−5.95036	+	0.770204i	−0.991727	+	0.128367i
$37$	−4.29751	−	4.29751i	−0.706506	−	0.706506i	0.259293	−	0.965799i	$-0.416511\pi$
$37$	−4.29751	−	4.29751i	−0.706506	−	0.706506i	−0.965799	+	0.259293i	$0.916511\pi$
$38$	−2.93642	+	2.06088i	−0.476349	+	0.334318i
$39$	−1.16742	+	1.91442i	−0.186936	+	0.306553i
$40$	2.36912	+	8.72736i	0.374591	+	1.37992i
$41$	4.52681			0.706969			0.353484	−	0.935440i	$-0.384997\pi$
$41$	4.52681			0.706969			0.353484	+	0.935440i	$0.384997\pi$
$42$	0.157543	+	2.44442i	0.0243095	+	0.377182i
$43$	−3.46653	+	3.46653i	−0.528641	+	0.528641i	−0.920167	−	0.391526i	$-0.871947\pi$
$43$	−3.46653	+	3.46653i	−0.528641	+	0.528641i	0.391526	+	0.920167i	$0.371947\pi$
$44$	2.18653	+	4.66245i	0.329632	+	0.702890i
$45$	−2.92414	+	9.13517i	−0.435905	+	1.36179i
$46$	12.2245	+	2.14176i	1.80240	+	0.315785i
$47$	−8.60844			−1.25567			−0.627835	−	0.778346i	$-0.716059\pi$
$47$	−8.60844			−1.25567			−0.627835	+	0.778346i	$0.716059\pi$
$48$	−6.22039	−	3.05069i	−0.897836	−	0.440329i
$49$	1.00000			0.142857
$50$	7.27483	+	1.27457i	1.02882	+	0.180251i
$51$	−1.19649	−	4.93624i	−0.167543	−	0.691212i
$52$	−2.34420	+	1.09935i	−0.325082	+	0.152452i
$53$	−6.48541	+	6.48541i	−0.890840	+	0.890840i	−0.994602	−	0.103762i	$-0.966912\pi$
$53$	−6.48541	+	6.48541i	−0.890840	+	0.890840i	0.103762	+	0.994602i	$0.466912\pi$
$54$	−3.77791	−	6.30297i	−0.514109	−	0.857725i
$55$	8.23243			1.11006
$56$	−1.40619	+	2.45410i	−0.187910	+	0.327943i
$57$	−3.75125	−	2.28752i	−0.496866	−	0.302989i
$58$	2.74270	−	1.92492i	0.360135	−	0.252755i
$59$	−8.08166	−	8.08166i	−1.05214	−	1.05214i	−0.998564	−	0.0535782i	$-0.982937\pi$
$59$	−8.08166	−	8.08166i	−1.05214	−	1.05214i	−0.0535782	−	0.998564i	$-0.517063\pi$
$60$	−8.63768	+	6.93251i	−1.11512	+	0.894983i
$61$	2.11377	−	2.11377i	0.270641	−	0.270641i	−0.558717	−	0.829358i	$-0.688706\pi$
$61$	2.11377	−	2.11377i	0.270641	−	0.270641i	0.829358	+	0.558717i	$0.188706\pi$
$62$	11.3600	+	1.99030i	1.44272	+	0.252768i
$63$	−2.66704	+	1.37363i	−0.336016	+	0.173062i
$64$	−4.04525	−	6.90188i	−0.505657	−	0.862735i
$65$			4.13913i			0.513396i
$66$	−4.16369	+	4.73737i	−0.512515	+	0.583129i
$67$	−2.17584	−	2.17584i	−0.265821	−	0.265821i	0.561593	−	0.827414i	$-0.310189\pi$
$67$	−2.17584	−	2.17584i	−0.265821	−	0.265821i	−0.827414	+	0.561593i	$0.810189\pi$
$68$	1.99390	−	5.51560i	0.241796	−	0.668864i
$69$	3.58062	+	14.7721i	0.431056	+	1.77836i
$70$	2.59752	+	3.70105i	0.310463	+	0.442360i
$71$			4.72561i			0.560827i	0.959879	+	0.280413i	$0.0904715\pi$
$71$			4.72561i			0.560827i	−0.959879	+	0.280413i	$0.909528\pi$
$72$	0.379333	−	8.47680i	0.0447048	−	0.999000i
$73$			8.88001i			1.03933i	0.854371	+	0.519663i	$0.173942\pi$
$73$			8.88001i			1.03933i	−0.854371	+	0.519663i	$0.826058\pi$
$74$	7.03525	−	4.93758i	0.817831	−	0.573982i
$75$	2.13084	+	8.79096i	0.246048	+	1.01509i
$76$	−2.15414	−	4.59338i	−0.247097	−	0.526897i
$77$	1.82069	+	1.82069i	0.207487	+	0.207487i
$78$	−2.38187	−	2.09343i	−0.269693	−	0.237035i
$79$		−	10.6576i		−	1.19907i	−0.800349	−	0.599535i	$-0.795352\pi$
$79$		−	10.6576i		−	1.19907i	0.800349	−	0.599535i	$-0.204648\pi$
$80$	−12.7354	+	1.17021i	−1.42386	+	0.130833i
$81$	5.22626	−	7.32709i	0.580695	−	0.814121i
$82$	−1.10480	+	6.30583i	−0.122004	+	0.696362i
$83$	7.45604	−	7.45604i	0.818407	−	0.818407i	−0.167470	−	0.985877i	$-0.553560\pi$
$83$	7.45604	−	7.45604i	0.818407	−	0.818407i	0.985877	+	0.167470i	$0.0535597\pi$
$84$	−3.44351	−	0.377119i	−0.375718	−	0.0411470i
$85$	−6.62972	−	6.62972i	−0.719094	−	0.719094i
$86$	−3.98283	−	5.67489i	−0.429480	−	0.611939i
$87$	3.50379	+	2.13661i	0.375646	+	0.229069i
$88$	−7.02840	+	1.90793i	−0.749230	+	0.203386i
$89$	−11.6283			−1.23260			−0.616298	−	0.787513i	$-0.711368\pi$
$89$	−11.6283			−1.23260			−0.616298	+	0.787513i	$0.711368\pi$
$90$	−12.0116	−	6.30281i	−1.26613	−	0.664375i
$91$	−0.915413	+	0.915413i	−0.0959613	+	0.0959613i
$92$	−5.96692	+	16.5059i	−0.622094	+	1.72086i
$93$	3.32740	+	13.7275i	0.345036	+	1.42347i
$94$	2.10095	−	11.9915i	0.216696	−	1.23683i
$95$	−8.11049			−0.832119
$96$	5.76773	−	7.92044i	0.588666	−	0.808376i
$97$	9.08157			0.922094			0.461047	−	0.887376i	$-0.347474\pi$
$97$	9.08157			0.922094			0.461047	+	0.887376i	$0.347474\pi$
$98$	−0.244056	+	1.39300i	−0.0246534	+	0.140714i
$99$	−7.35683	−	2.35490i	−0.739389	−	0.236676i
$100$	−3.55094	+	9.82274i	−0.355094	+	0.982274i
$101$	−4.72687	+	4.72687i	−0.470341	+	0.470341i	−0.902025	−	0.431684i	$-0.857920\pi$
$101$	−4.72687	+	4.72687i	−0.470341	+	0.470341i	0.431684	+	0.902025i	$0.357920\pi$
$102$	7.16817	−	0.461991i	0.709755	−	0.0457439i
$103$	−14.7866			−1.45696			−0.728482	−	0.685065i	$-0.759774\pi$
$103$	−14.7866			−1.45696			−0.728482	+	0.685065i	$0.759774\pi$
$104$	−0.959273	−	3.53376i	−0.0940644	−	0.346514i
$105$	−2.88318	+	4.72806i	−0.281369	+	0.461412i
$106$	−7.45135	−	10.6170i	−0.723739	−	1.03121i
$107$	9.12369	+	9.12369i	0.882020	+	0.882020i	0.993740	−	0.111719i	$-0.0356358\pi$
$107$	9.12369	+	9.12369i	0.882020	+	0.882020i	−0.111719	+	0.993740i	$0.535636\pi$
$108$	9.70203	−	3.72434i	0.933578	−	0.358374i
$109$	7.45700	−	7.45700i	0.714251	−	0.714251i	−0.253171	−	0.967422i	$-0.581473\pi$
$109$	7.45700	−	7.45700i	0.714251	−	0.714251i	0.967422	+	0.253171i	$0.0814734\pi$
$110$	−2.00918	+	11.4677i	−0.191568	+	1.09341i
$111$	8.98748	+	5.48057i	0.853054	+	0.520193i
$112$	−3.07537	−	2.55776i	−0.290595	−	0.241685i
$113$		−	18.9798i		−	1.78547i	−0.450580	−	0.892736i	$-0.648783\pi$
$113$		−	18.9798i		−	1.78547i	0.450580	−	0.892736i	$-0.351217\pi$
$114$	4.10202	−	4.66719i	0.384189	−	0.437123i
$115$	19.8400	+	19.8400i	1.85009	+	1.85009i
$116$	2.01204	+	4.29037i	0.186813	+	0.398350i
$117$	1.18400	−	3.69889i	0.109461	−	0.341962i
$118$	13.2301	−	9.28533i	1.21793	−	0.854784i
$119$		−	2.93247i		−	0.268819i
$120$	−7.54887	−	13.7242i	−0.689114	−	1.25284i
$121$		−	4.37017i		−	0.397288i
$122$	2.42860	+	3.46036i	0.219875	+	0.313286i
$123$	−7.62001	+	1.84701i	−0.687073	+	0.166540i
$124$	−5.54495	+	15.3387i	−0.497951	+	1.37745i
$125$	0.502881	+	0.502881i	0.0449791	+	0.0449791i
$126$	−1.26256	−	4.05043i	−0.112478	−	0.360841i
$127$			20.6001i			1.82796i	0.405757	+	0.913981i	$0.367008\pi$
$127$			20.6001i			1.82796i	−0.405757	+	0.913981i	$0.632992\pi$
$128$	10.6016	−	3.95057i	0.937054	−	0.349185i
$129$	4.42083	−	7.24964i	0.389233	−	0.638295i
$130$	−5.76579	−	1.01018i	−0.505693	−	0.0885987i
$131$	8.07416	−	8.07416i	0.705443	−	0.705443i	−0.260131	−	0.965573i	$-0.583766\pi$
$131$	8.07416	−	8.07416i	0.705443	−	0.705443i	0.965573	+	0.260131i	$0.0837656\pi$
$132$	−5.58295	−	6.95619i	−0.485934	−	0.605458i
$133$	−1.79372	−	1.79372i	−0.155535	−	0.155535i
$134$	3.56196	−	2.49990i	0.307706	−	0.215959i
$135$	1.19493	−	16.5704i	0.102843	−	1.42615i
$136$	7.19658	+	4.12361i	0.617101	+	0.353596i
$137$	5.22066			0.446031			0.223016	−	0.974815i	$-0.428410\pi$
$137$	5.22066			0.446031			0.223016	+	0.974815i	$0.428410\pi$
$138$	−21.4514	+	1.38255i	−1.82607	+	0.117690i
$139$	−11.9868	+	11.9868i	−1.01671	+	1.01671i	−0.0168474	+	0.999858i	$0.505363\pi$
$139$	−11.9868	+	11.9868i	−1.01671	+	1.01671i	−0.999858	+	0.0168474i	$0.994637\pi$
$140$	−5.78948	+	2.71507i	−0.489301	+	0.229465i
$141$	14.4907	−	3.51239i	1.22033	−	0.295796i
$142$	−6.58275	−	1.15332i	−0.552412	−	0.0967840i
$143$	−3.33337			−0.278750
$144$	11.7156	+	2.59723i	0.976297	+	0.216435i
$145$	7.57546			0.629107
$146$	−12.3698	−	2.16722i	−1.02373	−	0.179361i
$147$	−1.68331	+	0.408017i	−0.138837	+	0.0336526i
$148$	5.16103	+	11.0051i	0.424234	+	0.904615i
$149$	11.7493	−	11.7493i	0.962540	−	0.962540i	−0.0367834	−	0.999323i	$-0.511711\pi$
$149$	11.7493	−	11.7493i	0.962540	−	0.962540i	0.999323	+	0.0367834i	$0.0117112\pi$
$150$	−12.7658	+	0.822760i	−1.04232	+	0.0671781i
$151$	8.14983			0.663223			0.331612	−	0.943416i	$-0.392408\pi$
$151$	8.14983			0.663223			0.331612	+	0.943416i	$0.392408\pi$
$152$	6.92429	−	1.87966i	0.561634	−	0.152461i
$153$	4.02814	+	7.82102i	0.325656	+	0.632292i
$154$	−2.98056	+	2.09186i	−0.240181	+	0.168567i
$155$	18.4370	+	18.4370i	1.48089	+	1.48089i
$156$	3.49745	−	2.80702i	0.280020	−	0.224741i
$157$	−10.7876	+	10.7876i	−0.860946	+	0.860946i	−0.991448	−	0.130502i	$-0.958341\pi$
$157$	−10.7876	+	10.7876i	−0.860946	+	0.860946i	0.130502	+	0.991448i	$0.458341\pi$
$158$	14.8459	+	2.60105i	1.18108	+	0.206928i
$159$	8.27079	−	13.5631i	0.655916	−	1.07562i
$160$	1.47805	−	18.0259i	0.116850	−	1.42507i
$161$			8.77567i			0.691620i
$162$	8.93110	+	9.06838i	0.701694	+	0.712479i
$163$	−2.26578	−	2.26578i	−0.177469	−	0.177469i	0.612782	−	0.790252i	$-0.290050\pi$
$163$	−2.26578	−	2.26578i	−0.177469	−	0.177469i	−0.790252	+	0.612782i	$0.790050\pi$
$164$	−8.51435	−	3.07795i	−0.664859	−	0.240348i
$165$	−13.8577	+	3.35897i	−1.07882	+	0.261495i
$166$	8.56654	+	12.2059i	0.664893	+	0.947364i
$167$			15.2783i			1.18227i	0.806574	+	0.591133i	$0.201319\pi$
$167$			15.2783i			1.18227i	−0.806574	+	0.591133i	$0.798681\pi$
$168$	1.36574	−	4.70476i	0.105369	−	0.362980i
$169$			11.3240i			0.871080i
$170$	10.8532	−	7.61715i	0.832402	−	0.584208i
$171$	7.24785	+	2.32002i	0.554257	+	0.177416i
$172$	8.87713	−	4.16307i	0.676875	−	0.317431i
$173$	−12.5993	−	12.5993i	−0.957903	−	0.957903i	0.0412456	−	0.999149i	$-0.486867\pi$
$173$	−12.5993	−	12.5993i	−0.957903	−	0.957903i	−0.999149	+	0.0412456i	$0.986867\pi$
$174$	−3.83141	+	4.35931i	−0.290459	+	0.330478i
$175$			5.22244i			0.394779i
$176$	−0.942405	−	10.2562i	−0.0710365	−	0.773088i
$177$	16.9014	+	10.3065i	1.27038	+	0.774681i
$178$	2.83796	−	16.1982i	0.212714	−	1.21410i
$179$	0.354922	−	0.354922i	0.0265281	−	0.0265281i	−0.693718	−	0.720246i	$-0.744029\pi$
$179$	0.354922	−	0.354922i	0.0265281	−	0.0265281i	0.720246	+	0.693718i	$0.244029\pi$
$180$	11.7113	−	15.1939i	0.872909	−	1.13248i
$181$	−3.95505	−	3.95505i	−0.293976	−	0.293976i	0.544672	−	0.838649i	$-0.316654\pi$
$181$	−3.95505	−	3.95505i	−0.293976	−	0.293976i	−0.838649	+	0.544672i	$0.816654\pi$
$182$	−1.05175	−	1.49858i	−0.0779611	−	0.111082i
$183$	−2.69568	+	4.42059i	−0.199270	+	0.326779i
$184$	−21.5364	−	12.3403i	−1.58769	−	0.909737i
$185$	19.4316			1.42864
$186$	−19.9344	+	1.28478i	−1.46166	+	0.0942045i
$187$	5.33911	−	5.33911i	0.390435	−	0.390435i
$188$	16.1914	+	5.85321i	1.18088	+	0.426890i
$189$	3.92899	−	3.40045i	0.285792	−	0.247346i
$190$	1.97942	−	11.2979i	0.143602	−	0.819634i
$191$	−11.1317			−0.805460			−0.402730	−	0.915319i	$-0.631939\pi$
$191$	−11.1317			−0.805460			−0.402730	+	0.915319i	$0.631939\pi$
$192$	9.62549	+	9.96745i	0.694660	+	0.719339i
$193$	−24.2243			−1.74370			−0.871852	−	0.489769i	$-0.837081\pi$
$193$	−24.2243			−1.74370			−0.871852	+	0.489769i	$0.837081\pi$
$194$	−2.21641	+	12.6506i	−0.159129	+	0.908259i
$195$	−1.68883	−	6.96743i	−0.120940	−	0.498948i
$196$	−1.88087	−	0.679939i	−0.134348	−	0.0485671i
$197$	11.9310	−	11.9310i	0.850048	−	0.850048i	−0.140091	−	0.990139i	$-0.544739\pi$
$197$	11.9310	−	11.9310i	0.850048	−	0.850048i	0.990139	+	0.140091i	$0.0447394\pi$
$198$	5.07585	−	9.67330i	0.360725	−	0.687451i
$199$	−5.66656			−0.401692			−0.200846	−	0.979623i	$-0.564369\pi$
$199$	−5.66656			−0.401692			−0.200846	+	0.979623i	$0.564369\pi$
$200$	−12.8164	−	7.34374i	−0.906256	−	0.519281i
$201$	4.55038	+	2.77482i	0.320959	+	0.195721i
$202$	−5.43088	−	7.73813i	−0.382116	−	0.544453i
$203$	1.67539	+	1.67539i	0.117590	+	0.117590i
$204$	−1.10589	+	10.0980i	−0.0774276	+	0.707000i
$205$	−10.2342	+	10.2342i	−0.714788	+	0.714788i
$206$	3.60876	−	20.5976i	0.251434	−	1.43510i
$207$	−12.0546	−	23.4051i	−0.837850	−	1.62677i
$208$	5.15663	−	0.473825i	0.357548	−	0.0328539i
$209$		−	6.53162i		−	0.451802i
$210$	−5.88252	−	5.17017i	−0.405932	−	0.356775i
$211$	11.8208	+	11.8208i	0.813776	+	0.813776i	0.985198	−	0.171422i	$-0.0548362\pi$
$211$	11.8208	+	11.8208i	0.813776	+	0.813776i	−0.171422	+	0.985198i	$0.554836\pi$
$212$	16.6079	−	7.78855i	1.14064	−	0.534920i
$213$	−1.92813	−	7.95465i	−0.132113	−	0.545044i
$214$	−14.9360	+	10.4826i	−1.02100	+	0.716573i
$215$		−	15.6743i		−	1.06898i
$216$	2.82014	+	14.4238i	0.191886	+	0.981417i
$217$			8.15507i			0.553602i
$218$	8.56764	+	12.2075i	0.580274	+	0.826796i
$219$	−3.62319	−	14.9478i	−0.244832	−	1.01008i
$220$	−15.4842	−	5.59755i	−1.04394	−	0.377387i
$221$	2.68442	+	2.68442i	0.180573	+	0.180573i
$222$	−9.82787	+	11.1820i	−0.659603	+	0.750484i
$223$		−	6.81157i		−	0.456136i	−0.973645	−	0.228068i	$-0.926759\pi$
$223$		−	6.81157i		−	0.456136i	0.973645	−	0.228068i	$-0.0732409\pi$
$224$	4.31351	−	3.65973i	0.288208	−	0.244526i
$225$	−7.17372	−	13.9285i	−0.478248	−	0.928565i
$226$	26.4388	+	4.63215i	1.75868	+	0.308126i
$227$	0.205032	−	0.205032i	0.0136084	−	0.0136084i	−0.700270	−	0.713878i	$-0.746937\pi$
$227$	0.205032	−	0.205032i	0.0136084	−	0.0136084i	0.713878	+	0.700270i	$0.246937\pi$
$228$	5.50026	+	6.85315i	0.364263	+	0.453861i
$229$	−13.3965	−	13.3965i	−0.885266	−	0.885266i	0.108798	−	0.994064i	$-0.465300\pi$
$229$	−13.3965	−	13.3965i	−0.885266	−	0.885266i	−0.994064	+	0.108798i	$0.965300\pi$
$230$	−32.4792	+	22.7950i	−2.14161	+	1.50306i
$231$	−3.80765	−	2.32191i	−0.250525	−	0.152770i
$232$	−6.46751	+	1.75567i	−0.424613	+	0.115265i
$233$	−6.01646			−0.394151			−0.197076	−	0.980388i	$-0.563144\pi$
$233$	−6.01646			−0.394151			−0.197076	+	0.980388i	$0.563144\pi$
$234$	4.86357	+	2.55205i	0.317942	+	0.166833i
$235$	19.4620	−	19.4620i	1.26956	−	1.26956i
$236$	9.70553	+	20.6956i	0.631776	+	1.34717i
$237$	4.34846	+	17.9399i	0.282463	+	1.16532i
$238$	4.08491	+	0.715687i	0.264786	+	0.0463911i
$239$	−6.89526			−0.446017			−0.223009	−	0.974816i	$-0.571588\pi$
$239$	−6.89526			−0.446017			−0.223009	+	0.974816i	$0.571588\pi$
$240$	20.9601	−	7.16606i	1.35297	−	0.462567i
$241$	10.9906			0.707966			0.353983	−	0.935252i	$-0.384827\pi$
$241$	10.9906			0.707966			0.353983	+	0.935252i	$0.384827\pi$
$242$	6.08763	+	1.06657i	0.391328	+	0.0685616i
$243$	−5.80782	+	14.4661i	−0.372572	+	0.928003i
$244$	−5.41298	+	2.53850i	−0.346530	+	0.162511i
$245$	−2.26080	+	2.26080i	−0.144437	+	0.144437i
$246$	−0.713169	−	11.0654i	−0.0454700	−	0.705505i
$247$	3.28399			0.208955
$248$	−20.0134	−	11.4676i	−1.27085	−	0.728193i
$249$	−9.50862	+	15.5930i	−0.602584	+	0.988166i
$250$	−0.823243	+	0.577780i	−0.0520664	+	0.0365420i
$251$	−11.8940	−	11.8940i	−0.750744	−	0.750744i	0.223874	−	0.974618i	$-0.428129\pi$
$251$	−11.8940	−	11.8940i	−0.750744	−	0.750744i	−0.974618	+	0.223874i	$0.928129\pi$
$252$	5.95036	−	0.770204i	0.374837	−	0.0485183i
$253$	−15.9778	+	15.9778i	−1.00451	+	1.00451i
$254$	−28.6958	−	5.02758i	−1.80054	−	0.315459i
$255$	13.8649	+	8.45482i	0.868253	+	0.529461i
$256$	2.91575	+	15.7321i	0.182235	+	0.983255i
$257$			14.6730i			0.915275i	0.889139	+	0.457637i	$0.151304\pi$
$257$			14.6730i			0.915275i	−0.889139	+	0.457637i	$0.848696\pi$
$258$	9.01978	+	7.92752i	0.561547	+	0.493546i
$259$	4.29751	+	4.29751i	0.267034	+	0.267034i
$260$	2.81436	−	7.78518i	0.174539	−	0.482816i
$261$	−6.76972	−	2.16697i	−0.419035	−	0.134132i
$262$	9.27672	+	13.2178i	0.573118	+	0.816600i
$263$			20.4151i			1.25885i	0.777061	+	0.629425i	$0.216710\pi$
$263$			20.4151i			1.25885i	−0.777061	+	0.629425i	$0.783290\pi$
$264$	11.0525	−	6.07933i	0.680234	−	0.374157i
$265$		−	29.3245i		−	1.80139i
$266$	2.93642	−	2.06088i	0.180043	−	0.126360i
$267$	19.5740	−	4.74454i	1.19791	−	0.290361i
$268$	2.61304	+	5.57191i	0.159617	+	0.340359i
$269$	−18.6963	−	18.6963i	−1.13993	−	1.13993i	−0.988462	−	0.151469i	$-0.951600\pi$
$269$	−18.6963	−	18.6963i	−1.13993	−	1.13993i	−0.151469	−	0.988462i	$-0.548400\pi$
$270$	22.7909	+	5.70864i	1.38701	+	0.347417i
$271$			5.42038i			0.329265i	0.986355	+	0.164632i	$0.0526438\pi$
$271$			5.42038i			0.329265i	−0.986355	+	0.164632i	$0.947356\pi$
$272$	−7.50054	+	9.01841i	−0.454787	+	0.546821i
$273$	1.16742	−	1.91442i	0.0706553	−	0.115866i
$274$	−1.27414	+	7.27236i	−0.0769733	+	0.439339i
$275$	−9.50844	+	9.50844i	−0.573380	+	0.573380i
$276$	3.30947	−	30.2191i	0.199207	−	1.81898i
$277$	−5.12370	−	5.12370i	−0.307854	−	0.307854i	0.536223	−	0.844076i	$-0.319851\pi$
$277$	−5.12370	−	5.12370i	−0.307854	−	0.307854i	−0.844076	+	0.536223i	$0.819851\pi$
$278$	−13.7721	−	19.6230i	−0.825995	−	1.17691i
$279$	−11.2021	−	21.7499i	−0.670651	−	1.30214i
$280$	−2.36912	−	8.72736i	−0.141582	−	0.521559i
$281$	−5.35336			−0.319355			−0.159677	−	0.987169i	$-0.551045\pi$
$281$	−5.35336			−0.319355			−0.159677	+	0.987169i	$0.551045\pi$
$282$	1.35620	+	21.0426i	0.0807607	+	1.25307i
$283$	−10.6748	+	10.6748i	−0.634552	+	0.634552i	−0.949206	−	0.314654i	$-0.898111\pi$
$283$	−10.6748	+	10.6748i	−0.634552	+	0.634552i	0.314654	+	0.949206i	$0.398111\pi$
$284$	3.21313	−	8.88827i	0.190664	−	0.527422i
$285$	13.6524	−	3.30922i	0.808701	−	0.196021i
$286$	0.813529	−	4.64336i	0.0481050	−	0.274568i
$287$	−4.52681			−0.267209
$288$	−6.47718	+	15.6859i	−0.381672	+	0.924298i
$289$	8.40064			0.494155
$290$	−1.84884	+	10.5526i	−0.108568	+	0.619669i
$291$	−15.2871	+	3.70543i	−0.896144	+	0.217216i
$292$	6.03786	−	16.7022i	0.353339	−	0.977420i
$293$	−0.265538	+	0.265538i	−0.0155129	+	0.0155129i	−0.714821	−	0.699308i	$-0.753492\pi$
$293$	−0.265538	+	0.265538i	−0.0155129	+	0.0155129i	0.699308	+	0.714821i	$0.253492\pi$
$294$	−0.157543	−	2.44442i	−0.00918812	−	0.142561i
$295$	36.5420			2.12756
$296$	−16.5897	+	4.50342i	−0.964254	+	0.261756i
$297$	13.3446	+	0.962313i	0.774334	+	0.0558391i
$298$	13.4992	+	19.2342i	0.781989	+	1.11421i
$299$	−8.03336	−	8.03336i	−0.464581	−	0.464581i
$300$	1.96948	−	17.9835i	0.113708	−	1.03828i
$301$	3.46653	−	3.46653i	0.199808	−	0.199808i
$302$	−1.98902	+	11.3527i	−0.114455	+	0.653273i
$303$	6.02813	−	9.88541i	0.346307	−	0.567902i
$304$	0.928446	+	10.1043i	0.0532500	+	0.579519i
$305$			9.55764i			0.547269i
$306$	−11.8777	+	3.70241i	−0.679005	+	0.211652i
$307$	−7.28530	−	7.28530i	−0.415794	−	0.415794i	0.467957	−	0.883751i	$-0.344990\pi$
$307$	−7.28530	−	7.28530i	−0.415794	−	0.415794i	−0.883751	+	0.467957i	$0.844990\pi$
$308$	−2.18653	−	4.66245i	−0.124589	−	0.265667i
$309$	24.8903	−	6.03317i	1.41596	−	0.343215i
$310$	−30.1823	+	21.1830i	−1.71424	+	1.20311i
$311$			12.0885i			0.685473i	0.939432	+	0.342737i	$0.111354\pi$
$311$			12.0885i			0.685473i	−0.939432	+	0.342737i	$0.888646\pi$
$312$	3.05658	+	5.55701i	0.173045	+	0.314604i
$313$			0.942109i			0.0532511i	0.999645	+	0.0266256i	$0.00847618\pi$
$313$			0.942109i			0.0532511i	−0.999645	+	0.0266256i	$0.991524\pi$
$314$	−12.3943	−	17.6599i	−0.699452	−	0.996605i
$315$	2.92414	−	9.13517i	0.164757	−	0.514708i
$316$	−7.24649	+	20.0455i	−0.407647	+	1.12765i
$317$	3.95890	+	3.95890i	0.222354	+	0.222354i	0.809489	−	0.587135i	$-0.199744\pi$
$317$	3.95890	+	3.95890i	0.222354	+	0.222354i	−0.587135	+	0.809489i	$0.699744\pi$
$318$	16.8748	+	14.8313i	0.946292	+	0.831700i
$319$			6.10074i			0.341576i
$320$	24.7493	+	6.45826i	1.38353	+	0.361027i
$321$	−19.0806	−	11.6354i	−1.06497	−	0.649422i
$322$	−12.2245	−	2.14176i	−0.681243	−	0.119356i
$323$	−5.26003	+	5.26003i	−0.292676	+	0.292676i
$324$	−14.8119	+	10.2278i	−0.822883	+	0.568210i
$325$	−4.78068	−	4.78068i	−0.265185	−	0.265185i
$326$	3.70920	−	2.60324i	0.205433	−	0.144180i
$327$	−9.50984	+	15.5950i	−0.525895	+	0.862405i
$328$	6.36556	−	11.1093i	0.351479	−	0.613406i
$329$	8.60844			0.474599
$330$	−1.29697	−	20.1235i	−0.0713956	−	1.10776i
$331$	−16.3244	+	16.3244i	−0.897271	+	0.897271i	−0.995194	−	0.0979228i	$-0.968780\pi$
$331$	−16.3244	+	16.3244i	−0.897271	+	0.897271i	0.0979228	+	0.995194i	$0.468780\pi$
$332$	−19.0935	+	8.95422i	−1.04789	+	0.491427i
$333$	−17.3649	−	5.55844i	−0.951588	−	0.304601i
$334$	−21.2825	−	3.72876i	−1.16453	−	0.204028i
$335$	9.83827			0.537522
$336$	6.22039	+	3.05069i	0.339350	+	0.166429i
$337$	−18.4456			−1.00480			−0.502398	−	0.864636i	$-0.667549\pi$
$337$	−18.4456			−1.00480			−0.502398	+	0.864636i	$0.667549\pi$
$338$	−15.7743	−	2.76370i	−0.858011	−	0.150326i
$339$	7.74409	+	31.9489i	0.420601	+	1.73523i
$340$	7.96186	+	16.9775i	0.431792	+	0.920732i
$341$	−14.8479	+	14.8479i	−0.804057	+	0.804057i
$342$	−5.00066	+	9.53001i	−0.270405	+	0.515324i
$343$	−1.00000			−0.0539949
$344$	3.63262	+	13.3818i	0.195858	+	0.721500i
$345$	−41.4919	−	25.3018i	−2.23385	−	1.36220i
$346$	20.6256	−	14.4758i	1.10884	−	0.778222i
$347$	−4.16277	−	4.16277i	−0.223469	−	0.223469i	0.586488	−	0.809958i	$-0.300510\pi$
$347$	−4.16277	−	4.16277i	−0.223469	−	0.223469i	−0.809958	+	0.586488i	$0.800510\pi$
$348$	−5.13741	−	6.40106i	−0.275394	−	0.343133i
$349$	−1.74656	+	1.74656i	−0.0934910	+	0.0934910i	−0.752305	−	0.658814i	$-0.771058\pi$
$349$	−1.74656	+	1.74656i	−0.0934910	+	0.0934910i	0.658814	+	0.752305i	$0.271058\pi$
$350$	−7.27483	−	1.27457i	−0.388856	−	0.0681286i
$351$	−0.483835	+	6.70946i	−0.0258252	+	0.358124i
$352$	14.5168	+	1.19032i	0.773748	+	0.0634442i
$353$			12.3621i			0.657967i	0.944336	+	0.328983i	$0.106706\pi$
$353$			12.3621i			0.657967i	−0.944336	+	0.328983i	$0.893294\pi$
$354$	−18.4817	+	21.0282i	−0.982293	+	1.11763i
$355$	−10.6837	−	10.6837i	−0.567030	−	0.567030i
$356$	21.8713	+	7.90653i	1.15918	+	0.419045i
$357$	1.19649	+	4.93624i	0.0633252	+	0.261254i
$358$	0.407784	+	0.581026i	0.0215521	+	0.0307082i
$359$			16.2343i			0.856814i	0.903586	+	0.428407i	$0.140925\pi$
$359$			16.2343i			0.856814i	−0.903586	+	0.428407i	$0.859075\pi$
$360$	18.3068	+	20.0219i	0.964851	+	1.05525i
$361$		−	12.5651i		−	0.661322i
$362$	6.47462	−	4.54411i	0.340299	−	0.238833i
$363$	1.78310	+	7.35634i	0.0935886	+	0.386108i
$364$	2.34420	−	1.09935i	0.122869	−	0.0576216i
$365$	−20.0759	−	20.0759i	−1.05082	−	1.05082i
$366$	−5.49996	−	4.83394i	−0.287488	−	0.252674i
$367$		−	25.8770i		−	1.35077i	−0.737465	−	0.675385i	$-0.763977\pi$
$367$		−	25.8770i		−	1.35077i	0.737465	−	0.675385i	$-0.236023\pi$
$368$	22.4460	−	26.9884i	1.17008	−	1.40687i
$369$	12.0732	−	6.21818i	0.628506	−	0.323706i
$370$	−4.74241	+	27.0682i	−0.246546	+	1.40721i
$371$	6.48541	−	6.48541i	0.336706	−	0.336706i
$372$	3.07543	−	28.0821i	0.159454	−	1.45599i
$373$	26.0420	+	26.0420i	1.34841	+	1.34841i	0.887394	+	0.461011i	$0.152513\pi$
$373$	26.0420	+	26.0420i	1.34841	+	1.34841i	0.461011	+	0.887394i	$0.347487\pi$
$374$	6.13432	+	8.74041i	0.317198	+	0.451956i
$375$	−1.05169	−	0.641320i	−0.0543089	−	0.0331176i
$376$	−12.1051	+	21.1260i	−0.624274	+	1.08949i
$377$	−3.06735			−0.157977
$378$	3.77791	+	6.30297i	0.194315	+	0.324190i
$379$	5.51674	−	5.51674i	0.283376	−	0.283376i	−0.551078	−	0.834454i	$-0.685783\pi$
$379$	5.51674	−	5.51674i	0.283376	−	0.283376i	0.834454	+	0.551078i	$0.185783\pi$
$380$	15.2548	+	5.51464i	0.782555	+	0.282895i
$381$	−8.40518	−	34.6763i	−0.430610	−	1.77652i
$382$	2.71676	−	15.5064i	0.139001	−	0.793375i
$383$	−10.8580			−0.554818			−0.277409	−	0.960752i	$-0.589476\pi$
$383$	−10.8580			−0.554818			−0.277409	+	0.960752i	$0.589476\pi$
$384$	−16.2338	+	10.9756i	−0.828426	+	0.560098i
$385$	−8.23243			−0.419564
$386$	5.91210	−	33.7444i	0.300918	−	1.71754i
$387$	−4.48365	+	14.0071i	−0.227917	+	0.712023i
$388$	−17.0813	−	6.17491i	−0.867170	−	0.313484i
$389$	18.0972	−	18.0972i	0.917566	−	0.917566i	−0.0792861	−	0.996852i	$-0.525264\pi$
$389$	18.0972	−	18.0972i	0.917566	−	0.917566i	0.996852	+	0.0792861i	$0.0252641\pi$
$390$	10.1178	−	0.652093i	0.512333	−	0.0330200i
$391$	25.7344			1.30144
$392$	1.40619	−	2.45410i	0.0710234	−	0.123951i
$393$	−10.2969	+	16.8857i	−0.519410	+	0.851770i
$394$	13.7080	+	19.5317i	0.690598	+	0.983991i
$395$	24.0946	+	24.0946i	1.21233	+	1.21233i
$396$	12.2361	+	9.43146i	0.614885	+	0.473949i
$397$	12.4866	−	12.4866i	0.626683	−	0.626683i	−0.320549	−	0.947232i	$-0.603867\pi$
$397$	12.4866	−	12.4866i	0.626683	−	0.626683i	0.947232	+	0.320549i	$0.103867\pi$
$398$	1.38296	−	7.89349i	0.0693215	−	0.395665i
$399$	3.75125	+	2.28752i	0.187798	+	0.114519i
$400$	13.3577	−	16.0609i	0.667886	−	0.803045i
$401$		−	3.80237i		−	0.189881i	−0.995483	−	0.0949406i	$-0.969734\pi$
$401$		−	3.80237i		−	0.189881i	0.995483	−	0.0949406i	$-0.0302661\pi$
$402$	−4.97587	+	5.66144i	−0.248174	+	0.282367i
$403$	−7.46526	−	7.46526i	−0.371871	−	0.371871i
$404$	12.1046	−	5.67666i	0.602227	−	0.282424i
$405$	4.74956	+	28.3806i	0.236008	+	1.41024i
$406$	−2.74270	+	1.92492i	−0.136118	+	0.0955324i
$407$			15.6489i			0.775686i
$408$	−13.7966	−	4.00497i	−0.683031	−	0.198276i
$409$		−	8.52624i		−	0.421595i	−0.977530	−	0.210798i	$-0.932394\pi$
$409$		−	8.52624i		−	0.421595i	0.977530	−	0.210798i	$-0.0676061\pi$
$410$	−11.7585	−	16.7539i	−0.580710	−	0.827418i
$411$	−8.78797	+	2.13012i	−0.433479	+	0.105071i
$412$	27.8117	+	10.0540i	1.37018	+	0.495323i
$413$	8.08166	+	8.08166i	0.397672	+	0.397672i
$414$	35.5452	−	11.0798i	1.74695	−	0.544542i
$415$			33.7133i			1.65492i
$416$	−0.598472	+	7.29881i	−0.0293425	+	0.357853i
$417$	15.2866	−	25.0682i	0.748589	−	1.22760i
$418$	9.09852	+	1.59408i	0.445023	+	0.0779692i
$419$	4.56394	−	4.56394i	0.222963	−	0.222963i	−0.586782	−	0.809745i	$-0.699605\pi$
$419$	4.56394	−	4.56394i	0.222963	−	0.222963i	0.809745	+	0.586782i	$0.199605\pi$
$420$	8.63768	−	6.93251i	0.421476	−	0.338272i
$421$	−6.35998	−	6.35998i	−0.309966	−	0.309966i	0.534930	−	0.844896i	$-0.320338\pi$
$421$	−6.35998	−	6.35998i	−0.309966	−	0.309966i	−0.844896	+	0.534930i	$0.820338\pi$
$422$	−19.3512	+	13.5813i	−0.942003	+	0.661130i
$423$	−22.9591	+	11.8249i	−1.11631	+	0.574944i
$424$	6.79615	+	25.0356i	0.330050	+	1.21584i
$425$	15.3146			0.742868
$426$	11.5514	−	0.744489i	0.559665	−	0.0360706i
$427$	−2.11377	+	2.11377i	−0.102293	+	0.102293i
$428$	−10.9569	−	23.3641i	−0.529624	−	1.12934i
$429$	5.61108	−	1.36007i	0.270905	−	0.0656647i
$430$	21.8342	+	3.82541i	1.05294	+	0.184477i
$431$	15.4570			0.744536			0.372268	−	0.928125i	$-0.378580\pi$
$431$	15.4570			0.744536			0.372268	+	0.928125i	$0.378580\pi$
$432$	−20.7806	+	0.408216i	−0.999807	+	0.0196403i
$433$	−6.09769			−0.293036			−0.146518	−	0.989208i	$-0.546807\pi$
$433$	−6.09769			−0.293036			−0.146518	+	0.989208i	$0.546807\pi$
$434$	−11.3600	−	1.99030i	−0.545296	−	0.0955373i
$435$	−12.7518	+	3.09091i	−0.611403	+	0.148198i
$436$	−19.0960	+	8.95536i	−0.914531	+	0.428884i
$437$	15.7411	−	15.7411i	0.753000	−	0.753000i
$438$	21.7064	−	1.39899i	1.03717	−	0.0668462i
$439$	−10.3091			−0.492027			−0.246013	−	0.969266i	$-0.579121\pi$
$439$	−10.3091			−0.492027			−0.246013	+	0.969266i	$0.579121\pi$
$440$	11.5764	−	20.2033i	0.551882	−	0.963152i
$441$	2.66704	−	1.37363i	0.127002	−	0.0654112i
$442$	−4.39453	+	3.08423i	−0.209026	+	0.146702i
$443$	9.98250	+	9.98250i	0.474283	+	0.474283i	0.903297	−	0.429015i	$-0.141139\pi$
$443$	9.98250	+	9.98250i	0.474283	+	0.474283i	−0.429015	+	0.903297i	$0.641139\pi$
$444$	−13.1779	−	16.4192i	−0.625394	−	0.779221i
$445$	26.2892	−	26.2892i	1.24623	−	1.24623i
$446$	9.48849	+	1.66241i	0.449293	+	0.0787173i
$447$	−14.9838	+	24.5716i	−0.708708	+	1.16220i
$448$	4.04525	+	6.90188i	0.191120	+	0.326083i
$449$			11.0455i			0.521268i	0.965438	+	0.260634i	$0.0839315\pi$
$449$			11.0455i			0.521268i	−0.965438	+	0.260634i	$0.916068\pi$
$450$	21.1531	−	6.59362i	0.997166	−	0.310826i
$451$	−8.24192	−	8.24192i	−0.388097	−	0.388097i
$452$	−12.9051	+	35.6987i	−0.607006	+	1.67912i
$453$	−13.7187	+	3.32526i	−0.644559	+	0.156235i
$454$	0.235569	+	0.335648i	0.0110558	+	0.0157527i
$455$		−	4.13913i		−	0.194045i
$456$	−10.8888	+	5.98928i	−0.509914	+	0.280474i
$457$		−	29.4280i		−	1.37659i	−0.725433	−	0.688293i	$-0.758361\pi$
$457$		−	29.4280i		−	1.37659i	0.725433	−	0.688293i	$-0.241639\pi$
$458$	21.9308	−	15.3918i	1.02476	−	0.719210i
$459$	−9.97170	−	11.5216i	−0.465439	−	0.537784i
$460$	−23.8266	−	50.8066i	−1.11092	−	2.36887i
$461$	8.61270	+	8.61270i	0.401134	+	0.401134i	0.878632	−	0.477499i	$-0.158457\pi$
$461$	8.61270	+	8.61270i	0.401134	+	0.401134i	−0.477499	+	0.878632i	$0.658457\pi$
$462$	4.16369	−	4.73737i	0.193712	−	0.220402i
$463$		−	4.16285i		−	0.193464i	−0.995310	−	0.0967321i	$-0.969161\pi$
$463$		−	4.16285i		−	0.193464i	0.995310	−	0.0967321i	$-0.0308390\pi$
$464$	−0.867198	−	9.43769i	−0.0402586	−	0.438134i
$465$	−38.5577	−	23.5125i	−1.78807	−	1.09037i
$466$	1.46835	−	8.38090i	0.0680202	−	0.388238i
$467$	4.41317	−	4.41317i	0.204217	−	0.204217i	−0.597587	−	0.801804i	$-0.703874\pi$
$467$	4.41317	−	4.41317i	0.204217	−	0.204217i	0.801804	+	0.597587i	$0.203874\pi$
$468$	−4.74198	+	6.15209i	−0.219198	+	0.284380i
$469$	2.17584	+	2.17584i	0.100471	+	0.100471i
$470$	22.3606	+	31.8603i	1.03142	+	1.46960i
$471$	13.7573	−	22.5604i	0.633905	−	1.03953i
$472$	−31.1976	+	8.46887i	−1.43598	+	0.389811i
$473$	12.6230			0.580404
$474$	−26.0515	+	1.67903i	−1.19659	+	0.0771203i
$475$	9.36759	−	9.36759i	0.429815	−	0.429815i
$476$	−1.99390	+	5.51560i	−0.0913902	+	0.252807i
$477$	−8.38830	+	26.2055i	−0.384074	+	1.19987i
$478$	1.68283	−	9.60506i	0.0769709	−	0.439325i
$479$	19.6658			0.898553			0.449277	−	0.893393i	$-0.351682\pi$
$479$	19.6658			0.898553			0.449277	+	0.893393i	$0.351682\pi$
$480$	4.86686	+	30.9462i	0.222141	+	1.41249i
$481$	−7.86799			−0.358749
$482$	−2.68232	+	15.3098i	−0.122176	+	0.697344i
$483$	−3.58062	−	14.7721i	−0.162924	−	0.672156i
$484$	−2.97145	+	8.21974i	−0.135066	+	0.373625i
$485$	−20.5316	+	20.5316i	−0.932292	+	0.932292i
$486$	−18.7338	−	11.6208i	−0.849784	−	0.527131i
$487$	−0.727896			−0.0329841			−0.0164921	−	0.999864i	$-0.505250\pi$
$487$	−0.727896			−0.0329841			−0.0164921	+	0.999864i	$0.505250\pi$
$488$	−2.21505	−	8.15979i	−0.100271	−	0.369376i
$489$	4.73847	+	2.88952i	0.214281	+	0.130669i
$490$	−2.59752	−	3.70105i	−0.117344	−	0.167196i
$491$	−2.15522	−	2.15522i	−0.0972636	−	0.0972636i	0.656801	−	0.754064i	$-0.271909\pi$
$491$	−2.15522	−	2.15522i	−0.0972636	−	0.0972636i	−0.754064	+	0.656801i	$0.771909\pi$
$492$	15.5881	+	1.70714i	0.702767	+	0.0769640i
$493$	4.91303	−	4.91303i	0.221272	−	0.221272i
$494$	−0.801479	+	4.57458i	−0.0360602	+	0.205820i
$495$	21.9563	−	11.3084i	0.986861	−	0.508273i
$496$	20.8587	−	25.0798i	0.936583	−	1.12612i
$497$		−	4.72561i		−	0.211973i
$498$	−19.4003	−	17.0510i	−0.869350	−	0.764075i
$499$	−25.4814	−	25.4814i	−1.14070	−	1.14070i	−0.988322	−	0.152381i	$-0.951306\pi$
$499$	−25.4814	−	25.4814i	−1.14070	−	1.14070i	−0.152381	−	0.988322i	$-0.548694\pi$
$500$	−0.603927	−	1.28778i	−0.0270084	−	0.0575915i
$501$	−6.23378	−	25.7180i	−0.278505	−	1.14900i
$502$	19.4711	−	13.6655i	0.869039	−	0.609921i
$503$		−	18.0159i		−	0.803289i	−0.915796	−	0.401645i	$-0.868439\pi$
$503$		−	18.0159i		−	0.803289i	0.915796	−	0.401645i	$-0.131561\pi$
$504$	−0.379333	+	8.47680i	−0.0168968	+	0.377587i
$505$		−	21.3730i		−	0.951086i
$506$	−18.3575	−	26.1565i	−0.816090	−	1.16280i
$507$	−4.62040	−	19.0618i	−0.205199	−	0.846566i
$508$	14.0068	−	38.7461i	0.621451	−	1.71908i
$509$	4.60982	+	4.60982i	0.204327	+	0.204327i	0.801851	−	0.597524i	$-0.203849\pi$
$509$	4.60982	+	4.60982i	0.204327	+	0.204327i	−0.597524	+	0.801851i	$0.703849\pi$
$510$	−15.1613	+	17.2503i	−0.671355	+	0.763855i
$511$		−	8.88001i		−	0.392828i
$512$	−22.6263	+	0.222117i	−0.999952	+	0.00981626i
$513$	−13.1470	−	0.948059i	−0.580453	−	0.0418578i
$514$	−20.4394	−	3.58103i	−0.901543	−	0.157953i
$515$	33.4295	−	33.4295i	1.47308	−	1.47308i
$516$	−13.2443	+	10.6298i	−0.583049	+	0.467949i
$517$	15.6733	+	15.6733i	0.689311	+	0.689311i
$518$	−7.03525	+	4.93758i	−0.309111	+	0.216945i
$519$	26.3491	+	16.0677i	1.15660	+	0.705294i
$520$	10.1579	+	5.82041i	0.445451	+	0.255242i
$521$	−0.205806			−0.00901651			−0.00450825	−	0.999990i	$-0.501435\pi$
$521$	−0.205806			−0.00901651			−0.00450825	+	0.999990i	$0.501435\pi$
$522$	4.67077	−	8.90133i	0.204434	−	0.389601i
$523$	10.4823	−	10.4823i	0.458361	−	0.458361i	−0.439756	−	0.898117i	$-0.644935\pi$
$523$	10.4823	−	10.4823i	0.458361	−	0.458361i	0.898117	+	0.439756i	$0.144935\pi$
$524$	−20.6764	+	9.69654i	−0.903253	+	0.423595i
$525$	−2.13084	−	8.79096i	−0.0929975	−	0.383669i
$526$	−28.4382	−	4.98244i	−1.23996	−	0.217245i
$527$	23.9145			1.04173
$528$	5.77105	+	16.8798i	0.251153	+	0.734598i
$529$	−54.0124			−2.34837
$530$	40.8488	+	7.15682i	1.77436	+	0.310872i
$531$	−32.6554	−	10.4529i	−1.41712	−	0.453617i
$532$	2.15414	+	4.59338i	0.0933939	+	0.199148i
$533$	4.14390	−	4.14390i	0.179492	−	0.179492i
$534$	1.83196	+	28.4244i	0.0792767	+	1.23004i
$535$	−41.2537			−1.78355
$536$	−8.39937	+	2.28009i	−0.362798	+	0.0984848i
$537$	−0.452629	+	0.742257i	−0.0195324	+	0.0320308i
$538$	30.6067	−	21.4809i	1.31955	−	0.926106i
$539$	−1.82069	−	1.82069i	−0.0784227	−	0.0784227i
$540$	−13.5144	+	30.3543i	−0.581566	+	1.30624i
$541$	−20.1726	+	20.1726i	−0.867286	+	0.867286i	−0.992171	−	0.124885i	$-0.960144\pi$
$541$	−20.1726	+	20.1726i	−0.867286	+	0.867286i	0.124885	+	0.992171i	$0.460144\pi$
$542$	−7.55057	−	1.32288i	−0.324325	−	0.0568225i
$543$	8.27129	+	5.04384i	0.354955	+	0.216452i
$544$	−10.7320	−	12.6492i	−0.460133	−	0.542331i
$545$			33.7176i			1.44430i
$546$	2.38187	+	2.09343i	0.101935	+	0.0895907i
$547$	−6.72133	−	6.72133i	−0.287383	−	0.287383i	0.548661	−	0.836045i	$-0.315138\pi$
$547$	−6.72133	−	6.72133i	−0.287383	−	0.287383i	−0.836045	+	0.548661i	$0.815138\pi$
$548$	−9.81940	−	3.54973i	−0.419464	−	0.151637i
$549$	2.73398	−	8.54109i	0.116683	−	0.364525i
$550$	−10.9246	−	15.5658i	−0.465827	−	0.663728i
$551$		−	6.01038i		−	0.256051i
$552$	41.2874	+	11.9852i	1.75731	+	0.510126i
$553$			10.6576i			0.453205i
$554$	8.38777	−	5.88682i	0.356362	−	0.250107i
$555$	−32.7094	+	7.92842i	−1.38844	+	0.336543i
$556$	30.6959	−	14.3953i	1.30180	−	0.610498i
$557$	−5.70500	−	5.70500i	−0.241729	−	0.241729i	0.575836	−	0.817565i	$-0.304677\pi$
$557$	−5.70500	−	5.70500i	−0.241729	−	0.241729i	−0.817565	+	0.575836i	$0.804677\pi$
$558$	33.0315	−	10.2962i	1.39834	−	0.435875i
$559$			6.34661i			0.268433i
$560$	12.7354	−	1.17021i	0.538167	−	0.0494504i
$561$	−6.80892	+	11.1658i	−0.287473	+	0.471421i
$562$	1.30652	−	7.45721i	0.0551123	−	0.314563i
$563$	20.8412	−	20.8412i	0.878353	−	0.878353i	−0.115011	−	0.993364i	$-0.536690\pi$
$563$	20.8412	−	20.8412i	0.878353	−	0.878353i	0.993364	+	0.115011i	$0.0366905\pi$
$564$	−29.6433	−	3.24640i	−1.24821	−	0.136698i
$565$	42.9096	+	42.9096i	1.80522	+	1.80522i
$566$	−12.2647	−	17.4752i	−0.515524	−	0.734539i
$567$	−5.22626	+	7.32709i	−0.219482	+	0.307709i
$568$	11.5971	+	6.64511i	0.486605	+	0.278823i
$569$	7.74936			0.324870			0.162435	−	0.986719i	$-0.448065\pi$
$569$	7.74936			0.324870			0.162435	+	0.986719i	$0.448065\pi$
$570$	1.27775	+	19.8254i	0.0535193	+	0.830396i
$571$	4.96436	−	4.96436i	0.207752	−	0.207752i	−0.595559	−	0.803311i	$-0.703070\pi$
$571$	4.96436	−	4.96436i	0.207752	−	0.207752i	0.803311	+	0.595559i	$0.203070\pi$
$572$	6.26964	+	2.26649i	0.262147	+	0.0947665i
$573$	18.7380	−	4.54191i	0.782792	−	0.189741i
$574$	1.10480	−	6.30583i	0.0461133	−	0.263200i
$575$	−45.8304			−1.91126
$576$	−20.2695	−	12.8509i	−0.844564	−	0.535455i
$577$	42.9528			1.78815			0.894073	−	0.447921i	$-0.147835\pi$
$577$	42.9528			1.78815			0.894073	+	0.447921i	$0.147835\pi$
$578$	−2.05023	+	11.7021i	−0.0852783	+	0.486741i
$579$	40.7770	−	9.88392i	1.69463	−	0.410762i
$580$	−14.2485	−	5.15085i	−0.591636	−	0.213877i
$581$	−7.45604	+	7.45604i	−0.309329	+	0.309329i
$582$	−1.43074	−	22.1992i	−0.0593061	−	0.920184i
$583$	23.6159			0.978069
$584$	21.7925	+	12.4870i	0.901778	+	0.516715i
$585$	5.68565	+	11.0392i	0.235073	+	0.456417i
$586$	−0.305087	−	0.434699i	−0.0126030	−	0.0179573i
$587$	−6.19957	−	6.19957i	−0.255884	−	0.255884i	0.567494	−	0.823378i	$-0.307913\pi$
$587$	−6.19957	−	6.19957i	−0.255884	−	0.255884i	−0.823378	+	0.567494i	$0.807913\pi$
$588$	3.44351	+	0.377119i	0.142008	+	0.0155521i
$589$	14.6279	−	14.6279i	0.602733	−	0.602733i
$590$	−8.91831	+	50.9029i	−0.367161	+	2.09564i
$591$	−15.2155	+	24.9516i	−0.625881	+	1.02637i
$592$	−2.22443	−	24.2084i	−0.0914234	−	0.994959i
$593$			14.7953i			0.607569i	0.952741	+	0.303785i	$0.0982504\pi$
$593$			14.7953i			0.607569i	−0.952741	+	0.303785i	$0.901750\pi$
$594$	−4.59734	+	18.3542i	−0.188631	+	0.753080i
$595$	6.62972	+	6.62972i	0.271792	+	0.271792i
$596$	−30.0877	+	14.1101i	−1.23244	+	0.577973i
$597$	9.53856	−	2.31205i	0.390387	−	0.0946259i
$598$	13.1510	−	9.22984i	0.537785	−	0.377436i
$599$			21.0039i			0.858198i	0.903257	+	0.429099i	$0.141169\pi$
$599$			21.0039i			0.858198i	−0.903257	+	0.429099i	$0.858831\pi$
$600$	24.5703	+	7.13247i	1.00308	+	0.291182i
$601$			39.2853i			1.60248i	0.598343	+	0.801240i	$0.295826\pi$
$601$			39.2853i			1.60248i	−0.598343	+	0.801240i	$0.704174\pi$
$602$	3.98283	+	5.67489i	0.162328	+	0.231291i
$603$	−8.79186	−	2.81425i	−0.358032	−	0.114605i
$604$	−15.3288	−	5.54138i	−0.623720	−	0.225476i
$605$	9.88009	+	9.88009i	0.401683	+	0.401683i
$606$	12.2991	+	10.8098i	0.499618	+	0.439116i
$607$			13.5867i			0.551466i	0.961234	+	0.275733i	$0.0889205\pi$
$607$			13.5867i			0.551466i	−0.961234	+	0.275733i	$0.911079\pi$
$608$	−14.3018	−	1.17269i	−0.580014	−	0.0475588i
$609$	−3.50379	−	2.13661i	−0.141981	−	0.0865799i
$610$	−13.3138	−	2.33260i	−0.539058	−	0.0944444i
$611$	−7.88028	+	7.88028i	−0.318802	+	0.318802i
$612$	−2.25860	−	17.4492i	−0.0912984	−	0.705343i
$613$	7.18766	+	7.18766i	0.290307	+	0.290307i	0.837201	−	0.546895i	$-0.184190\pi$
$613$	7.18766	+	7.18766i	0.290307	+	0.290307i	−0.546895	+	0.837201i	$0.684190\pi$
$614$	11.9264	−	8.37037i	0.481311	−	0.337800i
$615$	13.0516	−	21.4031i	0.526291	−	0.863054i
$616$	7.02840	−	1.90793i	0.283182	−	0.0768725i
$617$	25.4655			1.02520			0.512601	−	0.858627i	$-0.328682\pi$
$617$	25.4655			1.02520			0.512601	+	0.858627i	$0.328682\pi$
$618$	2.32953	+	36.1446i	0.0937073	+	1.45395i
$619$	24.8928	−	24.8928i	1.00052	−	1.00052i	0.000524244	−	1.00000i	$-0.499833\pi$
$619$	24.8928	−	24.8928i	1.00052	−	1.00052i	1.00000		0.000524244i	$-0.000166872\pi$
$620$	−22.1416	−	47.2137i	−0.889228	−	1.89615i
$621$	29.8412	+	34.4795i	1.19749	+	1.38362i
$622$	−16.8392	−	2.95026i	−0.675189	−	0.118295i
$623$	11.6283			0.465878
$624$	−8.48687	+	2.90159i	−0.339747	+	0.116156i
$625$	23.8383			0.953534
$626$	−1.31235	−	0.229928i	−0.0524522	−	0.00918976i
$627$	2.66501	+	10.9947i	0.106430	+	0.439087i
$628$	27.6251	−	12.9552i	1.10236	−	0.516969i
$629$	12.6023	−	12.6023i	0.502487	−	0.502487i
$630$	12.0116	+	6.30281i	0.478553	+	0.251110i
$631$	−0.512718			−0.0204110			−0.0102055	−	0.999948i	$-0.503249\pi$
$631$	−0.512718			−0.0204110			−0.0102055	+	0.999948i	$0.503249\pi$
$632$	−26.1548	−	14.9866i	−1.04038	−	0.596133i
$633$	−24.7211	−	15.0749i	−0.982574	−	0.599174i
$634$	−6.48092	+	4.54853i	−0.257390	+	0.180645i
$635$	−46.5727	−	46.5727i	−1.84818	−	1.84818i
$636$	−24.7784	+	19.8868i	−0.982527	+	0.788564i
$637$	0.915413	−	0.915413i	0.0362700	−	0.0362700i
$638$	−8.49831	−	1.48893i	−0.336451	−	0.0589471i
$639$	6.49126	+	12.6034i	0.256790	+	0.498583i
$640$	−15.0365	+	32.8995i	−0.594371	+	1.30047i
$641$			24.2180i			0.956553i	0.878209	+	0.478277i	$0.158738\pi$
$641$			24.2180i			0.956553i	−0.878209	+	0.478277i	$0.841262\pi$
$642$	20.8647	−	23.7395i	0.823465	−	0.936923i
$643$	−1.22963	−	1.22963i	−0.0484917	−	0.0484917i	0.682445	−	0.730937i	$-0.260917\pi$
$643$	−1.22963	−	1.22963i	−0.0484917	−	0.0484917i	−0.730937	+	0.682445i	$0.760917\pi$
$644$	5.96692	−	16.5059i	0.235130	−	0.650424i
$645$	6.39536	+	26.3846i	0.251817	+	1.03889i
$646$	−6.04345	−	8.61094i	−0.237776	−	0.338793i
$647$			32.1398i			1.26355i	0.775153	+	0.631773i	$0.217673\pi$
$647$			32.1398i			1.26355i	−0.775153	+	0.631773i	$0.782327\pi$
$648$	−10.6323	−	23.1291i	−0.417677	−	0.908596i
$649$			29.4284i			1.15517i
$650$	7.82623	−	5.49271i	0.306970	−	0.215442i
$651$	−3.32740	−	13.7275i	−0.130411	−	0.538023i
$652$	2.72105	+	5.80223i	0.106565	+	0.227233i
$653$	4.20090	+	4.20090i	0.164394	+	0.164394i	0.784510	−	0.620116i	$-0.212915\pi$
$653$	4.20090	+	4.20090i	0.164394	+	0.164394i	−0.620116	+	0.784510i	$0.712915\pi$
$654$	−19.4028	−	17.0532i	−0.758710	−	0.666834i
$655$			36.5081i			1.42649i
$656$	13.9216	+	11.5785i	0.543547	+	0.452064i
$657$	12.1979	+	23.6834i	0.475885	+	0.923976i
$658$	−2.10095	+	11.9915i	−0.0819034	+	0.467478i
$659$	−19.3636	+	19.3636i	−0.754299	+	0.754299i	−0.975279	−	0.220979i	$-0.929075\pi$
$659$	−19.3636	+	19.3636i	−0.754299	+	0.754299i	0.220979	+	0.975279i	$0.429075\pi$
$660$	28.3485	+	3.10460i	1.10346	+	0.120847i
$661$	−4.66027	−	4.66027i	−0.181264	−	0.181264i	0.610643	−	0.791906i	$-0.290911\pi$
$661$	−4.66027	−	4.66027i	−0.181264	−	0.181264i	−0.791906	+	0.610643i	$0.790911\pi$
$662$	−18.7558	−	26.7239i	−0.728963	−	1.03865i
$663$	−5.61398	−	3.42341i	−0.218029	−	0.132954i
$664$	−7.81329	−	28.7825i	−0.303214	−	1.11698i
$665$	8.11049			0.314511
$666$	11.9809	−	22.8326i	0.464250	−	0.884745i
$667$	−14.7027	+	14.7027i	−0.569291	+	0.569291i
$668$	10.3883	−	28.7365i	0.401935	−	1.11185i
$669$	2.77923	+	11.4660i	0.107451	+	0.443300i
$670$	−2.40109	+	13.7047i	−0.0927623	+	0.529457i
$671$	−7.69706			−0.297142
$672$	−5.76773	+	7.92044i	−0.222495	+	0.305538i
$673$	−38.8503			−1.49757			−0.748784	−	0.662814i	$-0.769362\pi$
$673$	−38.8503			−1.49757			−0.748784	+	0.662814i	$0.769362\pi$
$674$	4.50177	−	25.6946i	0.173402	−	0.989721i
$675$	17.7586	+	20.5189i	0.683529	+	0.789773i
$676$	7.69966	−	21.2991i	0.296141	−	0.819195i
$677$	3.77109	−	3.77109i	0.144935	−	0.144935i	−0.630916	−	0.775851i	$-0.717321\pi$
$677$	3.77109	−	3.77109i	0.144935	−	0.144935i	0.775851	+	0.630916i	$0.217321\pi$
$678$	−46.3946	+	2.99015i	−1.78178	+	0.114836i
$679$	−9.08157			−0.348519
$680$	−25.5927	+	6.94737i	−0.981434	+	0.266420i
$681$	−0.261475	+	0.428788i	−0.0100197	+	0.0164312i
$682$	−17.0593	−	24.3067i	−0.653234	−	0.930752i
$683$	26.2664	+	26.2664i	1.00506	+	1.00506i	0.999987	+	0.00507032i	$0.00161394\pi$
$683$	26.2664	+	26.2664i	1.00506	+	1.00506i	0.00507032	+	0.999987i	$0.498386\pi$
$684$	−12.0548	−	9.29176i	−0.460928	−	0.355279i
$685$	−11.8029	+	11.8029i	−0.450964	+	0.450964i
$686$	0.244056	−	1.39300i	0.00931812	−	0.0531848i
$687$	28.0164	+	17.0844i	1.06889	+	0.651812i
$688$	−19.5274	+	1.79431i	−0.744475	+	0.0684073i
$689$			11.8737i			0.452350i
$690$	45.3717	−	51.6230i	1.72727	−	1.96525i
$691$	16.9641	+	16.9641i	0.645344	+	0.645344i	0.951864	−	0.306520i	$-0.0991648\pi$
$691$	16.9641	+	16.9641i	0.645344	+	0.645344i	−0.306520	+	0.951864i	$0.599165\pi$
$692$	15.1309	+	32.2643i	0.575189	+	1.22651i
$693$	7.35683	+	2.35490i	0.279463	+	0.0894553i
$694$	6.81467	−	4.78277i	0.258681	−	0.181551i
$695$		−	54.1994i		−	2.05590i
$696$	10.1705	−	5.59418i	0.385510	−	0.212047i
$697$			13.2747i			0.502816i
$698$	−2.00669	−	2.85920i	−0.0759542	−	0.108222i
$699$	10.1275	−	2.45481i	0.383059	−	0.0928496i
$700$	3.55094	−	9.82274i	0.134213	−	0.371265i
$701$	−3.53373	−	3.53373i	−0.133467	−	0.133467i	0.637217	−	0.770684i	$-0.280085\pi$
$701$	−3.53373	−	3.53373i	−0.133467	−	0.133467i	−0.770684	+	0.637217i	$0.780085\pi$
$702$	−9.22816	−	2.31147i	−0.348295	−	0.0872407i
$703$		−	15.4171i		−	0.581466i
$704$	−5.20103	+	19.9313i	−0.196021	+	0.751191i
$705$	−24.8197	+	40.7013i	−0.934762	+	1.53290i
$706$	−17.2203	−	3.01704i	−0.648095	−	0.113548i
$707$	4.72687	−	4.72687i	0.177772	−	0.177772i
$708$	−24.7815	−	30.8770i	−0.931347	−	1.16043i
$709$	36.9985	+	36.9985i	1.38951	+	1.38951i	0.826346	+	0.563162i	$0.190415\pi$
$709$	36.9985	+	36.9985i	1.38951	+	1.38951i	0.563162	+	0.826346i	$0.309585\pi$
$710$	17.4897	−	12.2749i	0.656377	−	0.460668i
$711$	−14.6396	−	28.4242i	−0.549027	−	1.06599i
$712$	−16.3516	+	28.5370i	−0.612802	+	1.06947i
$713$	−71.5662			−2.68018
$714$	−7.16817	+	0.461991i	−0.268262	+	0.0172896i
$715$	7.53607	−	7.53607i	0.281833	−	0.281833i
$716$	−0.908889	+	0.426238i	−0.0339668	+	0.0159293i
$717$	11.6068	−	2.81338i	0.433465	−	0.105068i
$718$	−22.6143	−	3.96209i	−0.843959	−	0.147864i
$719$	1.47388			0.0549663			0.0274831	−	0.999622i	$-0.491251\pi$
$719$	1.47388			0.0549663			0.0274831	+	0.999622i	$0.491251\pi$
$720$	−32.3584	+	20.6147i	−1.20592	+	0.768266i
$721$	14.7866			0.550681
$722$	17.5032	+	3.06660i	0.651400	+	0.114127i
$723$	−18.5005	+	4.48434i	−0.688042	+	0.166774i
$724$	4.74975	+	10.1281i	0.176523	+	0.376409i
$725$	−8.74963	+	8.74963i	−0.324953	+	0.324953i
$726$	−10.6825	+	0.688492i	−0.396466	+	0.0255523i
$727$	−31.5533			−1.17025			−0.585124	−	0.810944i	$-0.698954\pi$
$727$	−31.5533			−1.17025			−0.585124	+	0.810944i	$0.698954\pi$
$728$	0.959273	+	3.53376i	0.0355530	+	0.130970i
$729$	3.87392	−	26.7206i	0.143479	−	0.989653i
$730$	32.8653	−	23.0660i	1.21640	−	0.853711i
$731$	−10.1655	−	10.1655i	−0.375984	−	0.375984i
$732$	8.07595	−	6.48167i	0.298496	−	0.239569i
$733$	4.14193	−	4.14193i	0.152986	−	0.152986i	−0.626464	−	0.779450i	$-0.715499\pi$
$733$	4.14193	−	4.14193i	0.152986	−	0.152986i	0.779450	+	0.626464i	$0.215499\pi$
$734$	36.0466	+	6.31546i	1.33050	+	0.233108i
$735$	2.88318	−	4.72806i	0.106348	−	0.174397i
$736$	32.1166	+	37.8539i	1.18383	+	1.39531i
$737$			7.92305i			0.291849i
$738$	5.71536	+	18.3355i	0.210385	+	0.674939i
$739$	24.0249	+	24.0249i	0.883769	+	0.883769i	0.993915	−	0.110147i	$-0.0351321\pi$
$739$	24.0249	+	24.0249i	0.883769	+	0.883769i	−0.110147	+	0.993915i	$0.535132\pi$
$740$	−36.5484	−	13.2123i	−1.34355	−	0.485694i
$741$	−5.52796	+	1.33992i	−0.203075	+	0.0492233i
$742$	7.45135	+	10.6170i	0.273548	+	0.389761i
$743$		−	14.1448i		−	0.518923i	−0.965753	−	0.259461i	$-0.916455\pi$
$743$		−	14.1448i		−	0.518923i	0.965753	−	0.259461i	$-0.0835450\pi$
$744$	38.3677	+	11.1377i	1.40663	+	0.408327i
$745$			53.1256i			1.94637i
$746$	−42.6322	+	29.9207i	−1.56087	+	1.09548i
$747$	9.64373	−	30.1275i	0.352845	−	1.10231i
$748$	−13.6725	+	6.41192i	−0.499915	+	0.234443i
$749$	−9.12369	−	9.12369i	−0.333372	−	0.333372i
$750$	1.15003	−	1.30848i	0.0419930	−	0.0477788i
$751$			2.98228i			0.108825i	0.998519	+	0.0544125i	$0.0173286\pi$
$751$			2.98228i			0.108825i	−0.998519	+	0.0544125i	$0.982671\pi$
$752$	−26.4741	−	22.0183i	−0.965411	−	0.802925i
$753$	24.8742	+	15.1683i	0.906467	+	0.552764i
$754$	0.748607	−	4.27281i	0.0272626	−	0.155606i
$755$	−18.4251	+	18.4251i	−0.670559	+	0.670559i
$756$	−9.70203	+	3.72434i	−0.352859	+	0.135453i
$757$	−11.2382	−	11.2382i	−0.408459	−	0.408459i	0.472742	−	0.881201i	$-0.343264\pi$
$757$	−11.2382	−	11.2382i	−0.408459	−	0.408459i	−0.881201	+	0.472742i	$0.843264\pi$
$758$	6.33840	+	9.03119i	0.230221	+	0.328028i
$759$	20.3763	−	33.4147i	0.739613	−	1.21288i
$760$	−11.4049	+	19.9040i	−0.413699	+	0.721994i
$761$	46.7489			1.69465			0.847324	−	0.531077i	$-0.178212\pi$
$761$	46.7489			1.69465			0.847324	+	0.531077i	$0.178212\pi$
$762$	50.3552	−	3.24541i	1.82418	−	0.117569i
$763$	−7.45700	+	7.45700i	−0.269961	+	0.269961i
$764$	20.9373	+	7.56886i	0.757484	+	0.273832i
$765$	−26.7886	−	8.57495i	−0.968543	−	0.310028i
$766$	2.64997	−	15.1252i	0.0957472	−	0.546494i
$767$	−14.7961			−0.534256
$768$	−11.3271	−	25.2922i	−0.408730	−	0.912655i
$769$	45.7155			1.64854			0.824272	−	0.566194i	$-0.191585\pi$
$769$	45.7155			1.64854			0.824272	+	0.566194i	$0.191585\pi$
$770$	2.00918	−	11.4677i	0.0724058	−	0.413269i
$771$	−5.98682	−	24.6991i	−0.215610	−	0.889517i
$772$	45.5629	+	16.4711i	1.63984	+	0.592806i
$773$	14.0908	−	14.0908i	0.506812	−	0.506812i	−0.406735	−	0.913546i	$-0.633333\pi$
$773$	14.0908	−	14.0908i	0.506812	−	0.506812i	0.913546	+	0.406735i	$0.133333\pi$
$774$	−18.4176	−	9.66423i	−0.662008	−	0.347374i
$775$	−42.5893			−1.52985
$776$	12.7704	−	22.2871i	0.458431	−	0.800061i
$777$	−8.98748	−	5.48057i	−0.322424	−	0.196614i
$778$	20.7926	+	29.6261i	0.745451	+	1.06215i
$779$	8.11984	+	8.11984i	0.290923	+	0.290923i
$780$	−1.56094	+	14.2531i	−0.0558907	+	0.510345i
$781$	8.60387	−	8.60387i	0.307871	−	0.307871i
$782$	−6.28064	+	35.8479i	−0.224595	+	1.28192i
$783$	12.2797	+	0.885517i	0.438840	+	0.0316458i
$784$	3.07537	+	2.55776i	0.109835	+	0.0913485i
$785$		−	48.7773i		−	1.74094i
$786$	−21.0087	−	18.4646i	−0.749354	−	0.658610i
$787$	−14.7212	−	14.7212i	−0.524752	−	0.524752i	0.394251	−	0.919003i	$-0.371004\pi$
$787$	−14.7212	−	14.7212i	−0.524752	−	0.524752i	−0.919003	+	0.394251i	$0.871004\pi$
$788$	−30.5530	+	14.3283i	−1.08841	+	0.510426i
$789$	−8.32971	−	34.3649i	−0.296546	−	1.22342i
$790$	−39.4441	+	27.6832i	−1.40336	+	0.984925i
$791$			18.9798i			0.674845i
$792$	−16.1243	+	14.7430i	−0.572951	+	0.523869i
$793$		−	3.86995i		−	0.137426i
$794$	14.3463	+	20.4412i	0.509131	+	0.725430i
$795$	11.9649	+	49.3621i	0.424350	+	1.75069i
$796$	10.6581	+	3.85291i	0.377766	+	0.136563i
$797$	−5.16925	−	5.16925i	−0.183104	−	0.183104i	0.609603	−	0.792707i	$-0.291329\pi$
$797$	−5.16925	−	5.16925i	−0.183104	−	0.183104i	−0.792707	+	0.609603i	$0.791329\pi$
$798$	−4.10202	+	4.66719i	−0.145210	+	0.165217i
$799$		−	25.2440i		−	0.893067i
$800$	19.1127	+	22.5270i	0.675737	+	0.796450i
$801$	−31.0132	+	15.9730i	−1.09580	+	0.564379i
$802$	5.29668	+	0.927992i	0.187032	+	0.0327685i
$803$	16.1677	−	16.1677i	0.570547	−	0.570547i
$804$	−6.67197	−	8.31307i	−0.235302	−	0.293179i
$805$	−19.8400	−	19.8400i	−0.699270	−	0.699270i
$806$	12.2210	−	8.57712i	0.430467	−	0.302116i
$807$	39.0999	+	23.8432i	1.37638	+	0.839319i
$808$	4.95335	+	18.2471i	0.174258	+	0.641931i
$809$	−40.7474			−1.43260			−0.716302	−	0.697790i	$-0.754167\pi$
$809$	−40.7474			−1.43260			−0.716302	+	0.697790i	$0.754167\pi$
$810$	−40.6932	−	0.310352i	−1.42981	−	0.0109047i
$811$	−3.79131	+	3.79131i	−0.133131	+	0.133131i	−0.770532	−	0.637401i	$-0.780009\pi$
$811$	−3.79131	+	3.79131i	−0.133131	+	0.133131i	0.637401	+	0.770532i	$0.280009\pi$
$812$	−2.01204	−	4.29037i	−0.0706086	−	0.150562i
$813$	−2.21161	−	9.12417i	−0.0775644	−	0.319999i
$814$	−21.7988	−	3.81921i	−0.764048	−	0.133863i
$815$	10.2449			0.358865
$816$	8.94605	−	18.2411i	0.313174	−	0.638566i
$817$	−12.4360			−0.435080
$818$	11.8770	+	2.08088i	0.415270	+	0.0727564i
$819$	−1.18400	+	3.69889i	−0.0413725	+	0.129250i
$820$	26.2079	−	12.2906i	0.915219	−	0.429207i
$821$	3.18885	−	3.18885i	0.111291	−	0.111291i	−0.649268	−	0.760560i	$-0.724925\pi$
$821$	3.18885	−	3.18885i	0.111291	−	0.111291i	0.760560	+	0.649268i	$0.224925\pi$
$822$	−0.822481	−	12.7615i	−0.0286873	−	0.445108i
$823$	−48.4703			−1.68957			−0.844784	−	0.535107i	$-0.820271\pi$
$823$	−48.4703			−1.68957			−0.844784	+	0.535107i	$0.820271\pi$
$824$	−20.7927	+	36.2878i	−0.724350	+	1.26414i
$825$	12.1260	−	19.8852i	0.422174	−	0.692314i
$826$	−13.2301	+	9.28533i	−0.460334	+	0.323078i
$827$	−13.1317	−	13.1317i	−0.456633	−	0.456633i	0.440916	−	0.897548i	$-0.354654\pi$
$827$	−13.1317	−	13.1317i	−0.456633	−	0.456633i	−0.897548	+	0.440916i	$0.854654\pi$
$828$	6.75906	+	52.2184i	0.234893	+	1.81472i
$829$	22.4142	−	22.4142i	0.778479	−	0.778479i	−0.201093	−	0.979572i	$-0.564449\pi$
$829$	22.4142	−	22.4142i	0.778479	−	0.778479i	0.979572	+	0.201093i	$0.0644494\pi$
$830$	−46.9624	−	8.22793i	−1.63009	−	0.285596i
$831$	10.7153	+	6.53421i	0.371710	+	0.226669i
$832$	−10.0211	−	2.61499i	−0.347421	−	0.0906584i
$833$			2.93247i			0.101604i
$834$	31.1891	+	27.4123i	1.07999	+	0.949209i
$835$	−34.5411	−	34.5411i	−1.19534	−	1.19534i
$836$	−4.44110	+	12.2852i	−0.153599	+	0.424891i
$837$	27.7309	+	32.0412i	0.958520	+	1.10751i
$838$	5.24369	+	7.47141i	0.181140	+	0.258096i
$839$		−	44.4390i		−	1.53420i	−0.641525	−	0.767102i	$-0.721698\pi$
$839$		−	44.4390i		−	1.53420i	0.641525	−	0.767102i	$-0.278302\pi$
$840$	7.54887	+	13.7242i	0.260461	+	0.473529i
$841$		−	23.3861i		−	0.806418i
$842$	10.4116	−	7.30723i	0.358808	−	0.251824i
$843$	9.01135	−	2.18426i	0.310367	−	0.0752299i
$844$	−14.1960	−	30.2708i	−0.488645	−	1.04196i
$845$	−25.6014	−	25.6014i	−0.880715	−	0.880715i
$846$	−10.8686	−	34.8679i	−0.373672	−	1.19878i
$847$			4.37017i			0.150161i
$848$	−36.5331	+	3.35691i	−1.25455	+	0.115277i
$849$	13.6135	−	22.3245i	0.467214	−	0.766175i
$850$	−3.73763	+	21.3332i	−0.128200	+	0.731722i
$851$	−37.7135	+	37.7135i	−1.29280	+	1.29280i
$852$	−1.78211	+	16.2727i	−0.0610542	+	0.557493i
$853$	−28.2563	−	28.2563i	−0.967478	−	0.967478i	0.0320095	−	0.999488i	$-0.489809\pi$
$853$	−28.2563	−	28.2563i	−0.967478	−	0.967478i	−0.999488	+	0.0320095i	$0.989809\pi$
$854$	−2.42860	−	3.46036i	−0.0831049	−	0.118411i
$855$	−21.6310	+	11.1409i	−0.739766	+	0.381009i
$856$	35.2201	−	9.56083i	1.20380	−	0.326783i
$857$	14.0907			0.481328			0.240664	−	0.970609i	$-0.422635\pi$
$857$	14.0907			0.481328			0.240664	+	0.970609i	$0.422635\pi$
$858$	0.525150	+	8.14814i	0.0179283	+	0.278173i
$859$	−11.8054	+	11.8054i	−0.402796	+	0.402796i	−0.879217	−	0.476421i	$-0.841934\pi$
$859$	−11.8054	+	11.8054i	−0.402796	+	0.402796i	0.476421	+	0.879217i	$0.341934\pi$
$860$	−10.6575	+	29.4813i	−0.363419	+	1.00530i
$861$	7.62001	−	1.84701i	0.259689	−	0.0629461i
$862$	−3.77237	+	21.5315i	−0.128488	+	0.733366i
$863$	10.6934			0.364009			0.182004	−	0.983298i	$-0.441741\pi$
$863$	10.6934			0.364009			0.182004	+	0.983298i	$0.441741\pi$
$864$	4.50300	−	29.0469i	0.153195	−	0.988196i
$865$	56.9688			1.93700
$866$	1.48818	−	8.49406i	0.0505704	−	0.288640i
$867$	−14.1409	+	3.42760i	−0.480249	+	0.116407i
$868$	5.54495	−	15.3387i	0.188208	−	0.520628i
$869$	−19.4041	+	19.4041i	−0.658239	+	0.658239i
$870$	−1.19346	−	18.5176i	−0.0404622	−	0.627805i
$871$	−3.98358			−0.134978
$872$	−7.81429	−	28.7862i	−0.264625	−	0.974824i
$873$	24.2210	−	12.4748i	0.819755	−	0.422206i
$874$	18.0856	+	25.7690i	0.611754	+	0.871650i
$875$	−0.502881	−	0.502881i	−0.0170005	−	0.0170005i
$876$	−3.34881	+	30.5784i	−0.113146	+	1.03315i
$877$	0.535576	−	0.535576i	0.0180851	−	0.0180851i	−0.698006	−	0.716092i	$-0.745929\pi$
$877$	0.535576	−	0.535576i	0.0180851	−	0.0180851i	0.716092	+	0.698006i	$0.245929\pi$
$878$	2.51600	−	14.3605i	0.0849110	−	0.484645i
$879$	0.338638	−	0.555326i	0.0114220	−	0.0187307i
$880$	25.3177	+	21.0566i	0.853461	+	0.709817i
$881$			53.6084i			1.80611i	0.429522	+	0.903057i	$0.358682\pi$
$881$			53.6084i			1.80611i	−0.429522	+	0.903057i	$0.641318\pi$
$882$	1.26256	+	4.05043i	0.0425125	+	0.136385i
$883$	−8.11686	−	8.11686i	−0.273154	−	0.273154i	0.557215	−	0.830369i	$-0.311870\pi$
$883$	−8.11686	−	8.11686i	−0.273154	−	0.273154i	−0.830369	+	0.557215i	$0.811870\pi$
$884$	−3.22381	−	6.87429i	−0.108428	−	0.231207i
$885$	−61.5114	+	14.9097i	−2.06768	+	0.501186i
$886$	−16.3419	+	11.4693i	−0.549016	+	0.385318i
$887$		−	19.7832i		−	0.664254i	−0.943235	−	0.332127i	$-0.892234\pi$
$887$		−	19.7832i		−	0.664254i	0.943235	−	0.332127i	$-0.107766\pi$
$888$	26.0880	−	14.3495i	0.875456	−	0.481537i
$889$		−	20.6001i		−	0.690905i
$890$	30.2047	+	43.0369i	1.01247	+	1.44260i
$891$	−22.8558	+	3.82496i	−0.765697	+	0.128141i
$892$	−4.63145	+	12.8117i	−0.155072	+	0.428967i
$893$	−15.4411	−	15.4411i	−0.516718	−	0.516718i
$894$	−30.5712	−	26.8692i	−1.02245	−	0.898639i
$895$			1.60482i			0.0536431i
$896$	−10.6016	+	3.95057i	−0.354173	+	0.131979i
$897$	16.8004	+	10.2449i	0.560948	+	0.342066i
$898$	−15.3863	−	2.69572i	−0.513447	−	0.0899572i
$899$	−13.6629	+	13.6629i	−0.455685	+	0.455685i
$900$	4.02234	+	31.0754i	0.134078	+	1.03585i
$901$	−19.0183	−	19.0183i	−0.633590	−	0.633590i
$902$	13.4924	−	9.46946i	0.449249	−	0.315299i
$903$	−4.42083	+	7.24964i	−0.147116	+	0.241253i
$904$	−46.5785	−	26.6893i	−1.54918	−	0.887672i
$905$	17.8832			0.594456
$906$	−1.28395	−	19.9216i	−0.0426564	−	0.661850i
$907$	24.7075	−	24.7075i	0.820398	−	0.820398i	−0.165767	−	0.986165i	$-0.553010\pi$
$907$	24.7075	−	24.7075i	0.820398	−	0.820398i	0.986165	+	0.165767i	$0.0530100\pi$
$908$	−0.525048	+	0.246230i	−0.0174243	+	0.00817142i
$909$	−6.11378	+	19.0998i	−0.202781	+	0.633499i
$910$	5.76579	+	1.01018i	0.191134	+	0.0334872i
$911$	39.4269			1.30627			0.653135	−	0.757241i	$-0.273453\pi$
$911$	39.4269			1.30627			0.653135	+	0.757241i	$0.273453\pi$
$912$	−5.68556	−	16.6297i	−0.188268	−	0.550666i
$913$	−27.1503			−0.898544
$914$	40.9931	+	7.18210i	1.35593	+	0.237563i
$915$	−3.89968	−	16.0884i	−0.128919	−	0.531868i
$916$	16.0883	+	34.3059i	0.531573	+	1.13350i
$917$	−8.07416	+	8.07416i	−0.266632	+	0.266632i
$918$	18.4832	−	11.0786i	0.610038	−	0.365648i
$919$	−7.10328			−0.234315			−0.117158	−	0.993113i	$-0.537378\pi$
$919$	−7.10328			−0.234315			−0.117158	+	0.993113i	$0.537378\pi$
$920$	76.5884	−	20.7906i	2.52505	−	0.685447i
$921$	15.2359	+	9.29087i	0.502041	+	0.306145i
$922$	−14.0994	+	9.89547i	−0.464340	+	0.325890i
$923$	4.32588	+	4.32588i	0.142388	+	0.142388i
$924$	5.58295	+	6.95619i	0.183666	+	0.228842i
$925$	−22.4435	+	22.4435i	−0.737937	+	0.737937i
$926$	5.79884	+	1.01597i	0.190562	+	0.0333869i
$927$	−39.4365	+	20.3113i	−1.29526	+	0.667112i
$928$	13.3583	+	1.09533i	0.438508	+	0.0359559i
$929$		−	17.0263i		−	0.558615i	−0.960202	−	0.279308i	$-0.909895\pi$
$929$		−	17.0263i		−	0.558615i	0.960202	−	0.279308i	$-0.0901049\pi$
$930$	42.1631	−	47.9723i	1.38258	−	1.57307i
$931$	1.79372	+	1.79372i	0.0587869	+	0.0587869i
$932$	11.3162	+	4.09082i	0.370674	+	0.133999i
$933$	−4.93229	−	20.3486i	−0.161476	−	0.666182i
$934$	5.07046	+	7.22458i	0.165910	+	0.236396i
$935$			24.1413i			0.789506i
$936$	−7.41252	−	8.10701i	−0.242286	−	0.264986i
$937$		−	52.6704i		−	1.72067i	−0.509731	−	0.860334i	$-0.670255\pi$
$937$		−	52.6704i		−	1.72067i	0.509731	−	0.860334i	$-0.329745\pi$
$938$	−3.56196	+	2.49990i	−0.116302	+	0.0816248i
$939$	−0.384396	−	1.58586i	−0.0125443	−	0.0517525i
$940$	−49.8384	+	23.3725i	−1.62555	+	0.762328i
$941$	−11.0340	−	11.0340i	−0.359698	−	0.359698i	0.504004	−	0.863701i	$-0.331860\pi$
$941$	−11.0340	−	11.0340i	−0.359698	−	0.359698i	−0.863701	+	0.504004i	$0.831860\pi$
$942$	28.0690	+	24.6699i	0.914536	+	0.803790i
$943$		−	39.7258i		−	1.29365i
$944$	−4.18313	−	45.5250i	−0.136149	−	1.48171i
$945$	−1.19493	+	16.5704i	−0.0388711	+	0.539035i
$946$	−3.08071	+	17.5837i	−0.100163	+	0.571696i
$947$	1.96456	−	1.96456i	0.0638396	−	0.0638396i	−0.674466	−	0.738306i	$-0.735626\pi$
$947$	1.96456	−	1.96456i	0.0638396	−	0.0638396i	0.738306	+	0.674466i	$0.235626\pi$
$948$	4.01916	−	36.6994i	0.130536	−	1.19194i
$949$	8.12887	+	8.12887i	0.263874	+	0.263874i
$950$	10.7628	+	15.3352i	0.349191	+	0.497541i
$951$	−8.27934	−	5.04874i	−0.268476	−	0.163717i
$952$	−7.19658	−	4.12361i	−0.233242	−	0.133647i
$953$	−32.9580			−1.06761			−0.533807	−	0.845606i	$-0.679239\pi$
$953$	−32.9580			−1.06761			−0.533807	+	0.845606i	$0.679239\pi$
$954$	−34.4569	−	18.0805i	−1.11558	−	0.585377i
$955$	25.1665	−	25.1665i	0.814368	−	0.814368i
$956$	12.9691	+	4.68835i	0.419451	+	0.151632i
$957$	−2.48920	−	10.2694i	−0.0804645	−	0.331963i
$958$	−4.79956	+	27.3944i	−0.155067	+	0.885072i
$959$	−5.22066			−0.168584
$960$	−44.2957	−	0.773111i	−1.42964	−	0.0249521i
$961$	−35.5052			−1.14533
$962$	1.92023	−	10.9601i	0.0619108	−	0.353367i
$963$	36.8659	+	11.8007i	1.18799	+	0.380271i
$964$	−20.6719	−	7.47293i	−0.665797	−	0.240687i
$965$	54.7663	−	54.7663i	1.76299	−	1.76299i
$966$	21.4514	−	1.38255i	0.690188	−	0.0444828i
$967$	−3.67868			−0.118298			−0.0591492	−	0.998249i	$-0.518839\pi$
$967$	−3.67868			−0.118298			−0.0591492	+	0.998249i	$0.518839\pi$
$968$	−10.7249	−	6.14530i	−0.344710	−	0.197517i
$969$	6.70806	−	11.0004i	0.215494	−	0.353384i
$970$	−23.5896	−	33.6113i	−0.757415	−	1.07919i
$971$	19.8765	+	19.8765i	0.637866	+	0.637866i	0.950029	−	0.312162i	$-0.101053\pi$
$971$	19.8765	+	19.8765i	0.637866	+	0.637866i	−0.312162	+	0.950029i	$0.601053\pi$
$972$	20.7599	−	23.2600i	0.665873	−	0.746065i
$973$	11.9868	−	11.9868i	0.384279	−	0.384279i
$974$	0.177648	−	1.01396i	0.00569220	−	0.0324893i
$975$	9.99795	+	6.09676i	0.320191	+	0.195253i
$976$	11.9072	−	1.09411i	0.381139	−	0.0350215i
$977$		−	33.2269i		−	1.06302i	−0.847051	−	0.531511i	$-0.821624\pi$
$977$		−	33.2269i		−	1.06302i	0.847051	−	0.531511i	$-0.178376\pi$
$978$	−5.18155	+	5.89547i	−0.165688	+	0.188516i
$979$	21.1715	+	21.1715i	0.676645	+	0.676645i
$980$	5.78948	−	2.71507i	0.184938	−	0.0867298i
$981$	9.64496	−	30.1313i	0.307940	−	0.962020i
$982$	3.52820	−	2.47621i	0.112589	−	0.0790191i
$983$			17.2861i			0.551341i	0.961252	+	0.275671i	$0.0888999\pi$
$983$			17.2861i			0.551341i	−0.961252	+	0.275671i	$0.911100\pi$
$984$	−6.18243	+	21.2976i	−0.197089	+	0.678941i
$985$			53.9472i			1.71890i
$986$	5.64478	+	8.04289i	0.179766	+	0.256138i
$987$	−14.4907	+	3.51239i	−0.461242	+	0.111801i
$988$	−6.17677	−	2.23291i	−0.196509	−	0.0710384i
$989$	30.4211	+	30.4211i	0.967336	+	0.967336i
$990$	10.3939	+	33.3449i	0.330340	+	1.05977i
$991$			36.1152i			1.14724i	0.819123	+	0.573618i	$0.194461\pi$
$991$			36.1152i			1.14724i	−0.819123	+	0.573618i	$0.805539\pi$
$992$	29.8454	+	35.1770i	0.947592	+	1.11687i
$993$	20.8184	−	34.1396i	0.660651	−	1.08339i
$994$	6.58275	+	1.15332i	0.208792	+	0.0365809i
$995$	12.8110	−	12.8110i	0.406135	−	0.406135i
$996$	28.4868	−	22.8632i	0.902639	−	0.724447i
$997$	0.871700	+	0.871700i	0.0276070	+	0.0276070i	0.720776	−	0.693169i	$-0.243786\pi$
$997$	0.871700	+	0.871700i	0.0276070	+	0.0276070i	−0.693169	+	0.720776i	$0.743786\pi$
$998$	41.7143	−	29.2765i	1.32044	−	0.926733i
$999$	31.4983	+	2.27142i	0.996563	+	0.0718645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.8	✓	40
3.2	odd	2	inner	336.2.s.c.155.13	yes	40
4.3	odd	2		1344.2.s.c.911.19		40
12.11	even	2		1344.2.s.c.911.10		40
16.3	odd	4	inner	336.2.s.c.323.13	yes	40
16.13	even	4		1344.2.s.c.239.10		40
48.29	odd	4		1344.2.s.c.239.19		40
48.35	even	4	inner	336.2.s.c.323.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.8	✓	40	1.1	even	1	trivial
336.2.s.c.155.13	yes	40	3.2	odd	2	inner
336.2.s.c.323.8	yes	40	48.35	even	4	inner
336.2.s.c.323.13	yes	40	16.3	odd	4	inner
1344.2.s.c.239.10		40	16.13	even	4
1344.2.s.c.239.19		40	48.29	odd	4
1344.2.s.c.911.10		40	12.11	even	2
1344.2.s.c.911.19		40	4.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.244056 + 1.39300i) q^{2} +(-1.68331 + 0.408017i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(-2.26080 + 2.26080i) q^{5} +(-0.157543 - 2.44442i) q^{6} -1.00000 q^{7} +(1.40619 - 2.45410i) q^{8} +(2.66704 - 1.37363i) q^{9} +O(q^{10})\)	\(q+(-0.244056 + 1.39300i) q^{2} +(-1.68331 + 0.408017i) q^{3} +(-1.88087 - 0.679939i) q^{4} +(-2.26080 + 2.26080i) q^{5} +(-0.157543 - 2.44442i) q^{6} -1.00000 q^{7} +(1.40619 - 2.45410i) q^{8} +(2.66704 - 1.37363i) q^{9} +(-2.59752 - 3.70105i) q^{10} +(-1.82069 - 1.82069i) q^{11} +(3.44351 + 0.377119i) q^{12} +(0.915413 - 0.915413i) q^{13} +(0.244056 - 1.39300i) q^{14} +(2.88318 - 4.72806i) q^{15} +(3.07537 + 2.55776i) q^{16} +2.93247i q^{17} +(1.26256 + 4.05043i) q^{18} +(1.79372 + 1.79372i) q^{19} +(5.78948 - 2.71507i) q^{20} +(1.68331 - 0.408017i) q^{21} +(2.98056 - 2.09186i) q^{22} -8.77567i q^{23} +(-1.36574 + 4.70476i) q^{24} -5.22244i q^{25} +(1.05175 + 1.49858i) q^{26} +(-3.92899 + 3.40045i) q^{27} +(1.88087 + 0.679939i) q^{28} +(-1.67539 - 1.67539i) q^{29} +(5.88252 + 5.17017i) q^{30} -8.15507i q^{31} +(-4.31351 + 3.65973i) q^{32} +(3.80765 + 2.32191i) q^{33} +(-4.08491 - 0.715687i) q^{34} +(2.26080 - 2.26080i) q^{35} +(-5.95036 + 0.770204i) q^{36} +(-4.29751 - 4.29751i) q^{37} +(-2.93642 + 2.06088i) q^{38} +(-1.16742 + 1.91442i) q^{39} +(2.36912 + 8.72736i) q^{40} +4.52681 q^{41} +(0.157543 + 2.44442i) q^{42} +(-3.46653 + 3.46653i) q^{43} +(2.18653 + 4.66245i) q^{44} +(-2.92414 + 9.13517i) q^{45} +(12.2245 + 2.14176i) q^{46} -8.60844 q^{47} +(-6.22039 - 3.05069i) q^{48} +1.00000 q^{49} +(7.27483 + 1.27457i) q^{50} +(-1.19649 - 4.93624i) q^{51} +(-2.34420 + 1.09935i) q^{52} +(-6.48541 + 6.48541i) q^{53} +(-3.77791 - 6.30297i) q^{54} +8.23243 q^{55} +(-1.40619 + 2.45410i) q^{56} +(-3.75125 - 2.28752i) q^{57} +(2.74270 - 1.92492i) q^{58} +(-8.08166 - 8.08166i) q^{59} +(-8.63768 + 6.93251i) q^{60} +(2.11377 - 2.11377i) q^{61} +(11.3600 + 1.99030i) q^{62} +(-2.66704 + 1.37363i) q^{63} +(-4.04525 - 6.90188i) q^{64} +4.13913i q^{65} +(-4.16369 + 4.73737i) q^{66} +(-2.17584 - 2.17584i) q^{67} +(1.99390 - 5.51560i) q^{68} +(3.58062 + 14.7721i) q^{69} +(2.59752 + 3.70105i) q^{70} +4.72561i q^{71} +(0.379333 - 8.47680i) q^{72} +8.88001i q^{73} +(7.03525 - 4.93758i) q^{74} +(2.13084 + 8.79096i) q^{75} +(-2.15414 - 4.59338i) q^{76} +(1.82069 + 1.82069i) q^{77} +(-2.38187 - 2.09343i) q^{78} -10.6576i q^{79} +(-12.7354 + 1.17021i) q^{80} +(5.22626 - 7.32709i) q^{81} +(-1.10480 + 6.30583i) q^{82} +(7.45604 - 7.45604i) q^{83} +(-3.44351 - 0.377119i) q^{84} +(-6.62972 - 6.62972i) q^{85} +(-3.98283 - 5.67489i) q^{86} +(3.50379 + 2.13661i) q^{87} +(-7.02840 + 1.90793i) q^{88} -11.6283 q^{89} +(-12.0116 - 6.30281i) q^{90} +(-0.915413 + 0.915413i) q^{91} +(-5.96692 + 16.5059i) q^{92} +(3.32740 + 13.7275i) q^{93} +(2.10095 - 11.9915i) q^{94} -8.11049 q^{95} +(5.76773 - 7.92044i) q^{96} +9.08157 q^{97} +(-0.244056 + 1.39300i) q^{98} +(-7.35683 - 2.35490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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